LMFDB - Embedded newform 126.9.b.b.71.7

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} - 5134 x^{6} + 15416 x^{5} + 8006273 x^{4} - 16038244 x^{3} - 3602633684 x^{2} + \cdots + 501832517832 $ x^8 - 4x^7 - 5134x^6 + 15416x^5 + 8006273x^4 - 16038244x^3 - 3602633684x^2 + 3610655376*x + 501832517832
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{4}\cdot 3^{4}\cdot 7^{6} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			71.7
Root			$-47.0766 + 1.41421i$ of defining polynomial
Character	$\chi$	$=$	126.71
Dual form			126.9.b.b.71.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+11.3137i q^{2} -128.000 q^{4} +143.014i q^{5} -907.493 q^{7} -1448.15i q^{8} +O(q^{10})$	\(q+11.3137i q^{2} -128.000 q^{4} +143.014i q^{5} -907.493 q^{7} -1448.15i q^{8} -1618.02 q^{10} +18017.5i q^{11} +41411.1 q^{13} -10267.1i q^{14} +16384.0 q^{16} +7650.54i q^{17} -123003. q^{19} -18305.8i q^{20} -203845. q^{22} +270314. i q^{23} +370172. q^{25} +468513. i q^{26} +116159. q^{28} -534877. i q^{29} -891387. q^{31} +185364. i q^{32} -86556.0 q^{34} -129784. i q^{35} -331510. q^{37} -1.39162e6i q^{38} +207107. q^{40} +2.71447e6i q^{41} -6.73292e6 q^{43} -2.30625e6i q^{44} -3.05825e6 q^{46} +7.10133e6i q^{47} +823543. q^{49} +4.18802e6i q^{50} -5.30062e6 q^{52} -1.18859e7i q^{53} -2.57677e6 q^{55} +1.31419e6i q^{56} +6.05144e6 q^{58} -1.18443e7i q^{59} -1.55932e7 q^{61} -1.00849e7i q^{62} -2.09715e6 q^{64} +5.92238e6i q^{65} -1.54658e7 q^{67} -979269. i q^{68} +1.46834e6 q^{70} -1.19193e7i q^{71} +1.47547e7 q^{73} -3.75061e6i q^{74} +1.57443e7 q^{76} -1.63508e7i q^{77} -5.95311e7 q^{79} +2.34315e6i q^{80} -3.07107e7 q^{82} -5.25548e7i q^{83} -1.09414e6 q^{85} -7.61742e7i q^{86} +2.60922e7 q^{88} -6.15650e7i q^{89} -3.75803e7 q^{91} -3.46002e7i q^{92} -8.03424e7 q^{94} -1.75911e7i q^{95} -1.21737e8 q^{97} +9.31733e6i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 1024 q^{4}+O(q^{10}) $ 8 * q - 1024 * q^4	$ 8 q - 1024 q^{4} + 4480 q^{10} + 156632 q^{13} + 131072 q^{16} + 321160 q^{19} + 65216 q^{22} - 2280096 q^{25} - 2427880 q^{31} + 4914560 q^{34} + 2032696 q^{37} - 573440 q^{40} - 14076032 q^{43} + 13935680 q^{46} + 6588344 q^{49} - 20048896 q^{52} + 21354536 q^{55} - 4103168 q^{58} + 46591832 q^{61} - 16777216 q^{64} - 26848632 q^{67} - 39798976 q^{70} + 94257072 q^{73} - 41108480 q^{76} - 244539784 q^{79} + 10967040 q^{82} + 163925624 q^{85} - 8347648 q^{88} - 57547168 q^{91} - 28288512 q^{94} + 109673088 q^{97}+O(q^{100}) $ 8 * q - 1024 * q^4 + 4480 * q^10 + 156632 * q^13 + 131072 * q^16 + 321160 * q^19 + 65216 * q^22 - 2280096 * q^25 - 2427880 * q^31 + 4914560 * q^34 + 2032696 * q^37 - 573440 * q^40 - 14076032 * q^43 + 13935680 * q^46 + 6588344 * q^49 - 20048896 * q^52 + 21354536 * q^55 - 4103168 * q^58 + 46591832 * q^61 - 16777216 * q^64 - 26848632 * q^67 - 39798976 * q^70 + 94257072 * q^73 - 41108480 * q^76 - 244539784 * q^79 + 10967040 * q^82 + 163925624 * q^85 - 8347648 * q^88 - 57547168 * q^91 - 28288512 * q^94 + 109673088 * 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
$5$	143.014i	0.228823i	0.993433	+	0.114411i	$0.0364982\pi$
$5$	143.014i	0.228823i	−0.993433	+	0.114411i	$0.963502\pi$
$6$	0	0
$7$	−907.493	−0.377964
$7$	−907.493	−0.377964
$8$	− 1448.15i	− 0.353553i
$9$	0	0
$10$	−1618.02	−0.161802
$11$	18017.5i	1.23062i	0.788284	+	0.615311i	$0.210970\pi$
$11$	18017.5i	1.23062i	−0.788284	+	0.615311i	$0.789030\pi$
$12$	0	0
$13$	41411.1	1.44992	0.724959	−	0.688792i	$-0.241859\pi$
$13$	41411.1	1.44992	0.724959	+	0.688792i	$0.241859\pi$
$14$	− 10267.1i	− 0.267261i
$15$	0	0
$16$	16384.0	0.250000
$17$	7650.54i	0.0916002i	0.998951	+	0.0458001i	$0.0145837\pi$
$17$	7650.54i	0.0916002i	−0.998951	+	0.0458001i	$0.985416\pi$
$18$	0	0
$19$	−123003.	−0.943844	−0.471922	−	0.881640i	$-0.656440\pi$
$19$	−123003.	−0.943844	−0.471922	+	0.881640i	$0.656440\pi$
$20$	− 18305.8i	− 0.114411i
$21$	0	0
$22$	−203845.	−0.870182
$23$	270314.i	0.965956i	0.875633	+	0.482978i	$0.160445\pi$
$23$	270314.i	0.965956i	−0.875633	+	0.482978i	$0.839555\pi$
$24$	0	0
$25$	370172.	0.947640
$26$	468513.i	1.02525i
$27$	0	0
$28$	116159.	0.188982
$29$	− 534877.i	− 0.756244i	−0.925756	−	0.378122i	$-0.876570\pi$
$29$	− 534877.i	− 0.756244i	0.925756	−	0.378122i	$-0.123430\pi$
$30$	0	0
$31$	−891387.	−0.965205	−0.482602	−	0.875840i	$-0.660308\pi$
$31$	−891387.	−0.965205	−0.482602	+	0.875840i	$0.660308\pi$
$32$	185364.i	0.176777i
$33$	0	0
$34$	−86556.0	−0.0647711
$35$	− 129784.i	− 0.0864869i
$36$	0	0
$37$	−331510.	−0.176885	−0.0884423	−	0.996081i	$-0.528189\pi$
$37$	−331510.	−0.176885	−0.0884423	+	0.996081i	$0.528189\pi$
$38$	− 1.39162e6i	− 0.667399i
$39$	0	0
$40$	207107.	0.0809011
$41$	2.71447e6i	0.960616i	0.877100	+	0.480308i	$0.159475\pi$
$41$	2.71447e6i	0.960616i	−0.877100	+	0.480308i	$0.840525\pi$
$42$	0	0
$43$	−6.73292e6	−1.96938	−0.984690	−	0.174317i	$-0.944228\pi$
$43$	−6.73292e6	−1.96938	−0.984690	+	0.174317i	$0.944228\pi$
$44$	− 2.30625e6i	− 0.615311i
$45$	0	0
$46$	−3.05825e6	−0.683034
$47$	7.10133e6i	1.45529i	0.685956	+	0.727643i	$0.259384\pi$
$47$	7.10133e6i	1.45529i	−0.685956	+	0.727643i	$0.740616\pi$
$48$	0	0
$49$	823543.	0.142857
$50$	4.18802e6i	0.670083i
$51$	0	0
$52$	−5.30062e6	−0.724959
$53$	− 1.18859e7i	− 1.50635i	−0.657818	−	0.753177i	$-0.728520\pi$
$53$	− 1.18859e7i	− 1.50635i	0.657818	−	0.753177i	$-0.271480\pi$
$54$	0	0
$55$	−2.57677e6	−0.281595
$56$	1.31419e6i	0.133631i
$57$	0	0
$58$	6.05144e6	0.534745
$59$	− 1.18443e7i	− 0.977468i	−0.872433	−	0.488734i	$-0.837459\pi$
$59$	− 1.18443e7i	− 0.977468i	0.872433	−	0.488734i	$-0.162541\pi$
$60$	0	0
$61$	−1.55932e7	−1.12620	−0.563102	−	0.826387i	$-0.690392\pi$
$61$	−1.55932e7	−1.12620	−0.563102	+	0.826387i	$0.690392\pi$
$62$	− 1.00849e7i	− 0.682503i
$63$	0	0
$64$	−2.09715e6	−0.125000
$65$	5.92238e6i	0.331774i
$66$	0	0
$67$	−1.54658e7	−0.767489	−0.383745	−	0.923439i	$-0.625366\pi$
$67$	−1.54658e7	−0.767489	−0.383745	+	0.923439i	$0.625366\pi$
$68$	− 979269.i	− 0.0458001i
$69$	0	0
$70$	1.46834e6	0.0611555
$71$	− 1.19193e7i	− 0.469048i	−0.972110	−	0.234524i	$-0.924647\pi$
$71$	− 1.19193e7i	− 0.469048i	0.972110	−	0.234524i	$-0.0753532\pi$
$72$	0	0
$73$	1.47547e7	0.519563	0.259781	−	0.965667i	$-0.416349\pi$
$73$	1.47547e7	0.519563	0.259781	+	0.965667i	$0.416349\pi$
$74$	− 3.75061e6i	− 0.125076i
$75$	0	0
$76$	1.57443e7	0.471922
$77$	− 1.63508e7i	− 0.465132i
$78$	0	0
$79$	−5.95311e7	−1.52839	−0.764197	−	0.644983i	$-0.776865\pi$
$79$	−5.95311e7	−1.52839	−0.764197	+	0.644983i	$0.776865\pi$
$80$	2.34315e6i	0.0572057i
$81$	0	0
$82$	−3.07107e7	−0.679258
$83$	− 5.25548e7i	− 1.10739i	−0.832720	−	0.553694i	$-0.813218\pi$
$83$	− 5.25548e7i	− 1.10739i	0.832720	−	0.553694i	$-0.186782\pi$
$84$	0	0
$85$	−1.09414e6	−0.0209602
$86$	− 7.61742e7i	− 1.39256i
$87$	0	0
$88$	2.60922e7	0.435091
$89$	− 6.15650e7i	− 0.981237i	−0.871374	−	0.490619i	$-0.836771\pi$
$89$	− 6.15650e7i	− 0.981237i	0.871374	−	0.490619i	$-0.163229\pi$
$90$	0	0
$91$	−3.75803e7	−0.548017
$92$	− 3.46002e7i	− 0.482978i
$93$	0	0
$94$	−8.03424e7	−1.02904
$95$	− 1.75911e7i	− 0.215973i
$96$	0	0
$97$	−1.21737e8	−1.37511	−0.687554	−	0.726133i	$-0.741316\pi$
$97$	−1.21737e8	−1.37511	−0.687554	+	0.726133i	$0.741316\pi$
$98$	9.31733e6i	0.101015i
$99$	0	0
$100$	−4.73820e7	−0.473820
$101$	− 7.74818e6i	− 0.0744585i	−0.999307	−	0.0372293i	$-0.988147\pi$
$101$	− 7.74818e6i	− 0.0744585i	0.999307	−	0.0372293i	$-0.0118532\pi$
$102$	0	0
$103$	1.03672e8	0.921112	0.460556	−	0.887631i	$-0.347650\pi$
$103$	1.03672e8	0.921112	0.460556	+	0.887631i	$0.347650\pi$
$104$	− 5.99697e7i	− 0.512623i
$105$	0	0
$106$	1.34473e8	1.06515
$107$	1.20944e8i	0.922679i	0.887224	+	0.461340i	$0.152631\pi$
$107$	1.20944e8i	0.922679i	−0.887224	+	0.461340i	$0.847369\pi$
$108$	0	0
$109$	−1.94717e8	−1.37943	−0.689713	−	0.724082i	$-0.742263\pi$
$109$	−1.94717e8	−1.37943	−0.689713	+	0.724082i	$0.742263\pi$
$110$	− 2.91528e7i	− 0.199117i
$111$	0	0
$112$	−1.48684e7	−0.0944911
$113$	7.89762e7i	0.484376i	0.970229	+	0.242188i	$0.0778651\pi$
$113$	7.89762e7i	0.484376i	−0.970229	+	0.242188i	$0.922135\pi$
$114$	0	0
$115$	−3.86588e7	−0.221033
$116$	6.84642e7i	0.378122i
$117$	0	0
$118$	1.34003e8	0.691175
$119$	− 6.94281e6i	− 0.0346216i
$120$	0	0
$121$	−1.10273e8	−0.514432
$122$	− 1.76417e8i	− 0.796347i
$123$	0	0
$124$	1.14098e8	0.482602
$125$	1.08805e8i	0.445665i
$126$	0	0
$127$	−1.51154e8	−0.581039	−0.290519	−	0.956869i	$-0.593828\pi$
$127$	−1.51154e8	−0.581039	−0.290519	+	0.956869i	$0.593828\pi$
$128$	− 2.37266e7i	− 0.0883883i
$129$	0	0
$130$	−6.70041e7	−0.234600
$131$	3.49424e8i	1.18650i	0.805018	+	0.593250i	$0.202155\pi$
$131$	3.49424e8i	1.18650i	−0.805018	+	0.593250i	$0.797845\pi$
$132$	0	0
$133$	1.11624e8	0.356740
$134$	− 1.74975e8i	− 0.542697i
$135$	0	0
$136$	1.10792e7	0.0323856
$137$	1.48525e8i	0.421616i	0.977527	+	0.210808i	$0.0676096\pi$
$137$	1.48525e8i	0.421616i	−0.977527	+	0.210808i	$0.932390\pi$
$138$	0	0
$139$	2.68872e8	0.720255	0.360127	−	0.932903i	$-0.382733\pi$
$139$	2.68872e8	0.720255	0.360127	+	0.932903i	$0.382733\pi$
$140$	1.66124e7i	0.0432435i
$141$	0	0
$142$	1.34852e8	0.331667
$143$	7.46127e8i	1.78430i
$144$	0	0
$145$	7.64950e7	0.173046
$146$	1.66930e8i	0.367386i
$147$	0	0
$148$	4.24333e7	0.0884423
$149$	7.38366e7i	0.149805i	0.997191	+	0.0749025i	$0.0238646\pi$
$149$	7.38366e7i	0.149805i	−0.997191	+	0.0749025i	$0.976135\pi$
$150$	0	0
$151$	−8.57397e7	−0.164920	−0.0824601	−	0.996594i	$-0.526278\pi$
$151$	−8.57397e7	−0.164920	−0.0824601	+	0.996594i	$0.526278\pi$
$152$	1.78127e8i	0.333699i
$153$	0	0
$154$	1.84988e8	0.328898
$155$	− 1.27481e8i	− 0.220861i
$156$	0	0
$157$	−3.55065e8	−0.584399	−0.292199	−	0.956357i	$-0.594387\pi$
$157$	−3.55065e8	−0.584399	−0.292199	+	0.956357i	$0.594387\pi$
$158$	− 6.73517e8i	− 1.08074i
$159$	0	0
$160$	−2.65097e7	−0.0404506
$161$	− 2.45308e8i	− 0.365097i
$162$	0	0
$163$	3.13927e8	0.444711	0.222356	−	0.974966i	$-0.428625\pi$
$163$	3.13927e8	0.444711	0.222356	+	0.974966i	$0.428625\pi$
$164$	− 3.47452e8i	− 0.480308i
$165$	0	0
$166$	5.94589e8	0.783041
$167$	6.93182e8i	0.891213i	0.895229	+	0.445607i	$0.147012\pi$
$167$	6.93182e8i	0.891213i	−0.895229	+	0.445607i	$0.852988\pi$
$168$	0	0
$169$	8.99149e8	1.10226
$170$	− 1.23787e7i	− 0.0148211i
$171$	0	0
$172$	8.61813e8	0.984690
$173$	1.71015e9i	1.90920i	0.297896	+	0.954598i	$0.403715\pi$
$173$	1.71015e9i	1.90920i	−0.297896	+	0.954598i	$0.596285\pi$
$174$	0	0
$175$	−3.35928e8	−0.358174
$176$	2.95200e8i	0.307656i
$177$	0	0
$178$	6.96529e8	0.693839
$179$	− 1.38437e8i	− 0.134846i	−0.997724	−	0.0674232i	$-0.978522\pi$
$179$	− 1.38437e8i	− 0.134846i	0.997724	−	0.0674232i	$-0.0214778\pi$
$180$	0	0
$181$	3.92454e8	0.365657	0.182829	−	0.983145i	$-0.441475\pi$
$181$	3.92454e8	0.365657	0.182829	+	0.983145i	$0.441475\pi$
$182$	− 4.25172e8i	− 0.387507i
$183$	0	0
$184$	3.91457e8	0.341517
$185$	− 4.74107e7i	− 0.0404752i
$186$	0	0
$187$	−1.37844e8	−0.112725
$188$	− 9.08970e8i	− 0.727643i
$189$	0	0
$190$	1.99021e8	0.152716
$191$	− 3.29361e8i	− 0.247480i	−0.992315	−	0.123740i	$-0.960511\pi$
$191$	− 3.29361e8i	− 0.247480i	0.992315	−	0.123740i	$-0.0394888\pi$
$192$	0	0
$193$	1.26078e9	0.908676	0.454338	−	0.890829i	$-0.349876\pi$
$193$	1.26078e9	0.908676	0.454338	+	0.890829i	$0.349876\pi$
$194$	− 1.37730e9i	− 0.972348i
$195$	0	0
$196$	−1.05414e8	−0.0714286
$197$	1.84705e9i	1.22635i	0.789949	+	0.613173i	$0.210107\pi$
$197$	1.84705e9i	1.22635i	−0.789949	+	0.613173i	$0.789893\pi$
$198$	0	0
$199$	−7.43080e8	−0.473830	−0.236915	−	0.971530i	$-0.576136\pi$
$199$	−7.43080e8	−0.473830	−0.236915	+	0.971530i	$0.576136\pi$
$200$	− 5.36066e8i	− 0.335041i
$201$	0	0
$202$	8.76607e7	0.0526501
$203$	4.85397e8i	0.285833i
$204$	0	0
$205$	−3.88208e8	−0.219811
$206$	1.17291e9i	0.651325i
$207$	0	0
$208$	6.78479e8	0.362479
$209$	− 2.21621e9i	− 1.16152i
$210$	0	0
$211$	3.21838e9	1.62371	0.811854	−	0.583861i	$-0.198459\pi$
$211$	3.21838e9	1.62371	0.811854	+	0.583861i	$0.198459\pi$
$212$	1.52139e9i	0.753177i
$213$	0	0
$214$	−1.36833e9	−0.652433
$215$	− 9.62903e8i	− 0.450639i
$216$	0	0
$217$	8.08927e8	0.364813
$218$	− 2.20298e9i	− 0.975402i
$219$	0	0
$220$	3.29826e8	0.140797
$221$	3.16817e8i	0.132813i
$222$	0	0
$223$	−2.73905e9	−1.10759	−0.553796	−	0.832652i	$-0.686821\pi$
$223$	−2.73905e9	−1.10759	−0.553796	+	0.832652i	$0.686821\pi$
$224$	− 1.68216e8i	− 0.0668153i
$225$	0	0
$226$	−8.93514e8	−0.342505
$227$	3.19898e9i	1.20478i	0.798201	+	0.602391i	$0.205785\pi$
$227$	3.19898e9i	1.20478i	−0.798201	+	0.602391i	$0.794215\pi$
$228$	0	0
$229$	−2.38712e9	−0.868025	−0.434012	−	0.900907i	$-0.642903\pi$
$229$	−2.38712e9	−0.868025	−0.434012	+	0.900907i	$0.642903\pi$
$230$	− 4.37374e8i	− 0.156294i
$231$	0	0
$232$	−7.74584e8	−0.267372
$233$	2.62348e9i	0.890132i	0.895498	+	0.445066i	$0.146820\pi$
$233$	2.62348e9i	0.890132i	−0.895498	+	0.445066i	$0.853180\pi$
$234$	0	0
$235$	−1.01559e9	−0.333003
$236$	1.51608e9i	0.488734i
$237$	0	0
$238$	7.85489e7	0.0244812
$239$	− 3.04827e9i	− 0.934247i	−0.884192	−	0.467124i	$-0.845290\pi$
$239$	− 3.04827e9i	− 0.934247i	0.884192	−	0.467124i	$-0.154710\pi$
$240$	0	0
$241$	−5.78411e9	−1.71462	−0.857311	−	0.514799i	$-0.827867\pi$
$241$	−5.78411e9	−1.71462	−0.857311	+	0.514799i	$0.827867\pi$
$242$	− 1.24760e9i	− 0.363759i
$243$	0	0
$244$	1.99594e9	0.563102
$245$	1.17778e8i	0.0326890i
$246$	0	0
$247$	−5.09368e9	−1.36850
$248$	1.29087e9i	0.341251i
$249$	0	0
$250$	−1.23099e9	−0.315132
$251$	− 3.32768e8i	− 0.0838390i	−0.999121	−	0.0419195i	$-0.986653\pi$
$251$	− 3.32768e8i	− 0.0838390i	0.999121	−	0.0419195i	$-0.0133473\pi$
$252$	0	0
$253$	−4.87040e9	−1.18873
$254$	− 1.71011e9i	− 0.410857i
$255$	0	0
$256$	2.68435e8	0.0625000
$257$	− 5.67052e9i	− 1.29984i	−0.760002	−	0.649921i	$-0.774802\pi$
$257$	− 5.67052e9i	− 1.29984i	0.760002	−	0.649921i	$-0.225198\pi$
$258$	0	0
$259$	3.00843e8	0.0668561
$260$	− 7.58065e8i	− 0.165887i
$261$	0	0
$262$	−3.95328e9	−0.838982
$263$	− 7.45360e9i	− 1.55791i	−0.627079	−	0.778956i	$-0.715750\pi$
$263$	− 7.45360e9i	− 1.55791i	0.627079	−	0.778956i	$-0.284250\pi$
$264$	0	0
$265$	1.69985e9	0.344688
$266$	1.26288e9i	0.252253i
$267$	0	0
$268$	1.97962e9	0.383745
$269$	2.64863e9i	0.505838i	0.967487	+	0.252919i	$0.0813907\pi$
$269$	2.64863e9i	0.505838i	−0.967487	+	0.252919i	$0.918609\pi$
$270$	0	0
$271$	2.74203e9	0.508387	0.254193	−	0.967153i	$-0.418190\pi$
$271$	2.74203e9	0.508387	0.254193	+	0.967153i	$0.418190\pi$
$272$	1.25346e8i	0.0229000i
$273$	0	0
$274$	−1.68037e9	−0.298128
$275$	6.66959e9i	1.16619i
$276$	0	0
$277$	6.07670e8	0.103216	0.0516082	−	0.998667i	$-0.483565\pi$
$277$	6.07670e8	0.103216	0.0516082	+	0.998667i	$0.483565\pi$
$278$	3.04194e9i	0.509297i
$279$	0	0
$280$	−1.87948e8	−0.0305777
$281$	− 5.41340e9i	− 0.868251i	−0.900852	−	0.434125i	$-0.857058\pi$
$281$	− 5.41340e9i	− 0.868251i	0.900852	−	0.434125i	$-0.142942\pi$
$282$	0	0
$283$	−3.40382e9	−0.530665	−0.265333	−	0.964157i	$-0.585482\pi$
$283$	−3.40382e9	−0.530665	−0.265333	+	0.964157i	$0.585482\pi$
$284$	1.52567e9i	0.234524i
$285$	0	0
$286$	−8.44146e9	−1.26169
$287$	− 2.46336e9i	− 0.363079i
$288$	0	0
$289$	6.91723e9	0.991609
$290$	8.65442e8i	0.122362i
$291$	0	0
$292$	−1.88860e9	−0.259781
$293$	− 1.15265e10i	− 1.56397i	−0.623296	−	0.781986i	$-0.714207\pi$
$293$	− 1.15265e10i	− 1.56397i	0.623296	−	0.781986i	$-0.285793\pi$
$294$	0	0
$295$	1.69391e9	0.223667
$296$	4.80078e8i	0.0625381i
$297$	0	0
$298$	−8.35366e8	−0.105928
$299$	1.11940e10i	1.40056i
$300$	0	0
$301$	6.11007e9	0.744355
$302$	− 9.70034e8i	− 0.116616i
$303$	0	0
$304$	−2.01528e9	−0.235961
$305$	− 2.23006e9i	− 0.257701i
$306$	0	0
$307$	−1.10889e10	−1.24834	−0.624171	−	0.781288i	$-0.714563\pi$
$307$	−1.10889e10	−1.24834	−0.624171	+	0.781288i	$0.714563\pi$
$308$	2.09290e9i	0.232566i
$309$	0	0
$310$	1.44228e9	0.156172
$311$	− 5.59669e9i	− 0.598260i	−0.954212	−	0.299130i	$-0.903304\pi$
$311$	− 5.59669e9i	− 0.598260i	0.954212	−	0.299130i	$-0.0966964\pi$
$312$	0	0
$313$	−7.07943e9	−0.737600	−0.368800	−	0.929509i	$-0.620231\pi$
$313$	−7.07943e9	−0.737600	−0.368800	+	0.929509i	$0.620231\pi$
$314$	− 4.01710e9i	− 0.413232i
$315$	0	0
$316$	7.61998e9	0.764197
$317$	− 6.68623e9i	− 0.662131i	−0.943608	−	0.331066i	$-0.892592\pi$
$317$	− 6.68623e9i	− 0.662131i	0.943608	−	0.331066i	$-0.107408\pi$
$318$	0	0
$319$	9.63717e9	0.930651
$320$	− 2.99923e8i	− 0.0286029i
$321$	0	0
$322$	2.77534e9	0.258163
$323$	− 9.41037e8i	− 0.0864563i
$324$	0	0
$325$	1.53292e10	1.37400
$326$	3.55168e9i	0.314458i
$327$	0	0
$328$	3.93097e9	0.339629
$329$	− 6.44441e9i	− 0.550046i
$330$	0	0
$331$	5.56077e9	0.463258	0.231629	−	0.972804i	$-0.425594\pi$
$331$	5.56077e9	0.463258	0.231629	+	0.972804i	$0.425594\pi$
$332$	6.72701e9i	0.553694i
$333$	0	0
$334$	−7.84246e9	−0.630183
$335$	− 2.21183e9i	− 0.175619i
$336$	0	0
$337$	1.92687e10	1.49394	0.746970	−	0.664858i	$-0.231508\pi$
$337$	1.92687e10	1.49394	0.746970	+	0.664858i	$0.231508\pi$
$338$	1.01727e10i	0.779417i
$339$	0	0
$340$	1.40049e8	0.0104801
$341$	− 1.60606e10i	− 1.18780i
$342$	0	0
$343$	−7.47359e8	−0.0539949
$344$	9.75030e9i	0.696281i
$345$	0	0
$346$	−1.93482e10	−1.35001
$347$	− 2.15791e10i	− 1.48839i	−0.667963	−	0.744194i	$-0.732834\pi$
$347$	− 2.15791e10i	− 1.48839i	0.667963	−	0.744194i	$-0.267166\pi$
$348$	0	0
$349$	−3.51874e9	−0.237184	−0.118592	−	0.992943i	$-0.537838\pi$
$349$	−3.51874e9	−0.237184	−0.118592	+	0.992943i	$0.537838\pi$
$350$	− 3.80059e9i	− 0.253267i
$351$	0	0
$352$	−3.33980e9	−0.217545
$353$	2.84617e10i	1.83300i	0.400038	+	0.916499i	$0.368997\pi$
$353$	2.84617e10i	1.83300i	−0.400038	+	0.916499i	$0.631003\pi$
$354$	0	0
$355$	1.70463e9	0.107329
$356$	7.88032e9i	0.490619i
$357$	0	0
$358$	1.56623e9	0.0953509
$359$	1.45922e10i	0.878500i	0.898365	+	0.439250i	$0.144756\pi$
$359$	1.45922e10i	0.878500i	−0.898365	+	0.439250i	$0.855244\pi$
$360$	0	0
$361$	−1.85389e9	−0.109158
$362$	4.44011e9i	0.258559i
$363$	0	0
$364$	4.81027e9	0.274009
$365$	2.11013e9i	0.118888i
$366$	0	0
$367$	−4.22188e9	−0.232724	−0.116362	−	0.993207i	$-0.537123\pi$
$367$	−4.22188e9	−0.232724	−0.116362	+	0.993207i	$0.537123\pi$
$368$	4.42883e9i	0.241489i
$369$	0	0
$370$	5.36391e8	0.0286203
$371$	1.07863e10i	0.569348i
$372$	0	0
$373$	2.79195e10	1.44236	0.721178	−	0.692749i	$-0.243601\pi$
$373$	2.79195e10	1.44236	0.721178	+	0.692749i	$0.243601\pi$
$374$	− 1.55953e9i	− 0.0797088i
$375$	0	0
$376$	1.02838e10	0.514521
$377$	− 2.21498e10i	− 1.09649i
$378$	0	0
$379$	3.75896e10	1.82184	0.910922	−	0.412578i	$-0.135371\pi$
$379$	3.75896e10	1.82184	0.910922	+	0.412578i	$0.135371\pi$
$380$	2.25167e9i	0.107987i
$381$	0	0
$382$	3.72630e9	0.174994
$383$	3.90356e10i	1.81412i	0.421004	+	0.907059i	$0.361678\pi$
$383$	3.90356e10i	1.81412i	−0.421004	+	0.907059i	$0.638322\pi$
$384$	0	0
$385$	2.33840e9	0.106433
$386$	1.42641e10i	0.642531i
$387$	0	0
$388$	1.55824e10	0.687554
$389$	1.77146e10i	0.773630i	0.922157	+	0.386815i	$0.126425\pi$
$389$	1.77146e10i	0.773630i	−0.922157	+	0.386815i	$0.873575\pi$
$390$	0	0
$391$	−2.06805e9	−0.0884817
$392$	− 1.19262e9i	− 0.0505076i
$393$	0	0
$394$	−2.08969e10	−0.867157
$395$	− 8.51380e9i	− 0.349732i
$396$	0	0
$397$	4.03399e10	1.62395	0.811975	−	0.583692i	$-0.198393\pi$
$397$	4.03399e10	1.62395	0.811975	+	0.583692i	$0.198393\pi$
$398$	− 8.40699e9i	− 0.335049i
$399$	0	0
$400$	6.06490e9	0.236910
$401$	2.53088e10i	0.978798i	0.872060	+	0.489399i	$0.162784\pi$
$401$	2.53088e10i	0.978798i	−0.872060	+	0.489399i	$0.837216\pi$
$402$	0	0
$403$	−3.69133e10	−1.39947
$404$	9.91767e8i	0.0372293i
$405$	0	0
$406$	−5.49164e9	−0.202115
$407$	− 5.97300e9i	− 0.217678i
$408$	0	0
$409$	−2.69193e10	−0.961991	−0.480996	−	0.876723i	$-0.659725\pi$
$409$	−2.69193e10	−0.961991	−0.480996	+	0.876723i	$0.659725\pi$
$410$	− 4.39207e9i	− 0.155430i
$411$	0	0
$412$	−1.32700e10	−0.460556
$413$	1.07487e10i	0.369448i
$414$	0	0
$415$	7.51608e9	0.253396
$416$	7.67612e9i	0.256312i
$417$	0	0
$418$	2.50735e10	0.821316
$419$	− 1.55049e10i	− 0.503053i	−0.967850	−	0.251527i	$-0.919067\pi$
$419$	− 1.55049e10i	− 0.503053i	0.967850	−	0.251527i	$-0.0809326\pi$
$420$	0	0
$421$	−3.73552e10	−1.18911	−0.594555	−	0.804055i	$-0.702672\pi$
$421$	−3.73552e10	−1.18911	−0.594555	+	0.804055i	$0.702672\pi$
$422$	3.64118e10i	1.14813i
$423$	0	0
$424$	−1.72126e10	−0.532577
$425$	2.83202e9i	0.0868040i
$426$	0	0
$427$	1.41508e10	0.425665
$428$	− 1.54809e10i	− 0.461340i
$429$	0	0
$430$	1.08940e10	0.318650
$431$	1.56900e10i	0.454689i	0.973814	+	0.227345i	$0.0730044\pi$
$431$	1.56900e10i	0.454689i	−0.973814	+	0.227345i	$0.926996\pi$
$432$	0	0
$433$	−3.74349e10	−1.06494	−0.532470	−	0.846449i	$-0.678736\pi$
$433$	−3.74349e10	−1.06494	−0.532470	+	0.846449i	$0.678736\pi$
$434$	9.15196e9i	0.257962i
$435$	0	0
$436$	2.49238e10	0.689713
$437$	− 3.32494e10i	− 0.911712i
$438$	0	0
$439$	1.56278e10	0.420765	0.210382	−	0.977619i	$-0.432529\pi$
$439$	1.56278e10	0.420765	0.210382	+	0.977619i	$0.432529\pi$
$440$	3.73156e9i	0.0995587i
$441$	0	0
$442$	−3.58438e9	−0.0939128
$443$	− 1.18550e10i	− 0.307813i	−0.988085	−	0.153906i	$-0.950815\pi$
$443$	− 1.18550e10i	− 0.307813i	0.988085	−	0.153906i	$-0.0491854\pi$
$444$	0	0
$445$	8.80468e9	0.224530
$446$	− 3.09888e10i	− 0.783186i
$447$	0	0
$448$	1.90315e9	0.0472456
$449$	2.46327e10i	0.606076i	0.952978	+	0.303038i	$0.0980010\pi$
$449$	2.46327e10i	0.606076i	−0.952978	+	0.303038i	$0.901999\pi$
$450$	0	0
$451$	−4.89081e10	−1.18216
$452$	− 1.01090e10i	− 0.242188i
$453$	0	0
$454$	−3.61924e10	−0.851909
$455$	− 5.37452e9i	− 0.125399i
$456$	0	0
$457$	3.35381e10	0.768906	0.384453	−	0.923145i	$-0.374390\pi$
$457$	3.35381e10	0.768906	0.384453	+	0.923145i	$0.374390\pi$
$458$	− 2.70072e10i	− 0.613786i
$459$	0	0
$460$	4.94832e9	0.110516
$461$	− 7.19782e10i	− 1.59367i	−0.604200	−	0.796833i	$-0.706507\pi$
$461$	− 7.19782e10i	− 1.59367i	0.604200	−	0.796833i	$-0.293493\pi$
$462$	0	0
$463$	5.05950e10	1.10099	0.550495	−	0.834838i	$-0.314439\pi$
$463$	5.05950e10	1.10099	0.550495	+	0.834838i	$0.314439\pi$
$464$	− 8.76342e9i	− 0.189061i
$465$	0	0
$466$	−2.96813e10	−0.629418
$467$	6.94093e10i	1.45932i	0.683811	+	0.729660i	$0.260321\pi$
$467$	6.94093e10i	1.45932i	−0.683811	+	0.729660i	$0.739679\pi$
$468$	0	0
$469$	1.40351e10	0.290084
$470$	− 1.14901e10i	− 0.235468i
$471$	0	0
$472$	−1.71524e10	−0.345587
$473$	− 1.21311e11i	− 2.42356i
$474$	0	0
$475$	−4.55322e10	−0.894425
$476$	8.88680e8i	0.0173108i
$477$	0	0
$478$	3.44872e10	0.660613
$479$	− 1.60191e10i	− 0.304297i	−0.988358	−	0.152148i	$-0.951381\pi$
$479$	− 1.60191e10i	− 0.304297i	0.988358	−	0.152148i	$-0.0486192\pi$
$480$	0	0
$481$	−1.37282e10	−0.256468
$482$	− 6.54397e10i	− 1.21242i
$483$	0	0
$484$	1.41150e10	0.257216
$485$	− 1.74102e10i	− 0.314656i
$486$	0	0
$487$	−8.34835e10	−1.48417	−0.742087	−	0.670304i	$-0.766164\pi$
$487$	−8.34835e10	−1.48417	−0.742087	+	0.670304i	$0.766164\pi$
$488$	2.25814e10i	0.398173i
$489$	0	0
$490$	−1.33251e9	−0.0231146
$491$	9.73051e10i	1.67421i	0.547043	+	0.837105i	$0.315753\pi$
$491$	9.73051e10i	1.67421i	−0.547043	+	0.837105i	$0.684247\pi$
$492$	0	0
$493$	4.09210e9	0.0692721
$494$	− 5.76284e10i	− 0.967673i
$495$	0	0
$496$	−1.46045e10	−0.241301
$497$	1.08167e10i	0.177284i
$498$	0	0
$499$	−7.84910e10	−1.26595	−0.632976	−	0.774171i	$-0.718167\pi$
$499$	−7.84910e10	−1.26595	−0.632976	+	0.774171i	$0.718167\pi$
$500$	− 1.39270e10i	− 0.222832i
$501$	0	0
$502$	3.76484e9	0.0592831
$503$	6.93097e10i	1.08273i	0.840786	+	0.541367i	$0.182093\pi$
$503$	6.93097e10i	1.08273i	−0.840786	+	0.541367i	$0.817907\pi$
$504$	0	0
$505$	1.10810e9	0.0170378
$506$	− 5.51022e10i	− 0.840557i
$507$	0	0
$508$	1.93477e10	0.290519
$509$	− 6.96533e10i	− 1.03770i	−0.854866	−	0.518848i	$-0.826361\pi$
$509$	− 6.96533e10i	− 1.03770i	0.854866	−	0.518848i	$-0.173639\pi$
$510$	0	0
$511$	−1.33898e10	−0.196376
$512$	3.03700e9i	0.0441942i
$513$	0	0
$514$	6.41546e10	0.919127
$515$	1.48266e10i	0.210772i
$516$	0	0
$517$	−1.27949e11	−1.79091
$518$	3.40365e9i	0.0472744i
$519$	0	0
$520$	8.57652e9	0.117300
$521$	− 1.03982e11i	− 1.41126i	−0.708578	−	0.705632i	$-0.750663\pi$
$521$	− 1.03982e11i	− 1.41126i	0.708578	−	0.705632i	$-0.249337\pi$
$522$	0	0
$523$	5.60768e9	0.0749508	0.0374754	−	0.999298i	$-0.488068\pi$
$523$	5.60768e9	0.0749508	0.0374754	+	0.999298i	$0.488068\pi$
$524$	− 4.47263e10i	− 0.593250i
$525$	0	0
$526$	8.43278e10	1.10161
$527$	− 6.81959e9i	− 0.0884129i
$528$	0	0
$529$	5.24130e9	0.0669293
$530$	1.92316e10i	0.243731i
$531$	0	0
$532$	−1.42879e10	−0.178370
$533$	1.12409e11i	1.39281i
$534$	0	0
$535$	−1.72968e10	−0.211130
$536$	2.23968e10i	0.271348i
$537$	0	0
$538$	−2.99658e10	−0.357682
$539$	1.48382e10i	0.175803i
$540$	0	0
$541$	1.25762e11	1.46812	0.734058	−	0.679087i	$-0.237624\pi$
$541$	1.25762e11	1.46812	0.734058	+	0.679087i	$0.237624\pi$
$542$	3.10225e10i	0.359484i
$543$	0	0
$544$	−1.41813e9	−0.0161928
$545$	− 2.78474e10i	− 0.315644i
$546$	0	0
$547$	−3.01940e10	−0.337265	−0.168633	−	0.985679i	$-0.553935\pi$
$547$	−3.01940e10	−0.337265	−0.168633	+	0.985679i	$0.553935\pi$
$548$	− 1.90112e10i	− 0.210808i
$549$	0	0
$550$	−7.54578e10	−0.824619
$551$	6.57913e10i	0.713776i
$552$	0	0
$553$	5.40240e10	0.577679
$554$	6.87500e9i	0.0729850i
$555$	0	0
$556$	−3.44156e10	−0.360127
$557$	3.91846e10i	0.407094i	0.979065	+	0.203547i	$0.0652470\pi$
$557$	3.91846e10i	0.407094i	−0.979065	+	0.203547i	$0.934753\pi$
$558$	0	0
$559$	−2.78817e11	−2.85544
$560$	− 2.12639e9i	− 0.0216217i
$561$	0	0
$562$	6.12457e10	0.613946
$563$	− 1.05558e11i	− 1.05065i	−0.850902	−	0.525325i	$-0.823944\pi$
$563$	− 1.05558e11i	− 1.05065i	0.850902	−	0.525325i	$-0.176056\pi$
$564$	0	0
$565$	−1.12947e10	−0.110836
$566$	− 3.85098e10i	− 0.375237i
$567$	0	0
$568$	−1.72610e10	−0.165834
$569$	1.07011e11i	1.02089i	0.859910	+	0.510446i	$0.170520\pi$
$569$	1.07011e11i	1.02089i	−0.859910	+	0.510446i	$0.829480\pi$
$570$	0	0
$571$	−1.62847e11	−1.53192	−0.765961	−	0.642887i	$-0.777736\pi$
$571$	−1.62847e11	−1.53192	−0.765961	+	0.642887i	$0.777736\pi$
$572$	− 9.55042e10i	− 0.892151i
$573$	0	0
$574$	2.78698e10	0.256735
$575$	1.00063e11i	0.915378i
$576$	0	0
$577$	6.94172e10	0.626273	0.313137	−	0.949708i	$-0.398620\pi$
$577$	6.94172e10	0.626273	0.313137	+	0.949708i	$0.398620\pi$
$578$	7.82595e10i	0.701174i
$579$	0	0
$580$	−9.79136e9	−0.0865229
$581$	4.76931e10i	0.418553i
$582$	0	0
$583$	2.14154e11	1.85375
$584$	− 2.13670e10i	− 0.183693i
$585$	0	0
$586$	1.30408e11	1.10589
$587$	− 9.02249e10i	− 0.759931i	−0.925001	−	0.379965i	$-0.875936\pi$
$587$	− 9.02249e10i	− 0.759931i	0.925001	−	0.379965i	$-0.124064\pi$
$588$	0	0
$589$	1.09643e11	0.911003
$590$	1.91644e10i	0.158157i
$591$	0	0
$592$	−5.43146e9	−0.0442211
$593$	1.32665e11i	1.07284i	0.843950	+	0.536422i	$0.180225\pi$
$593$	1.32665e11i	1.07284i	−0.843950	+	0.536422i	$0.819775\pi$
$594$	0	0
$595$	9.92921e8	0.00792222
$596$	− 9.45108e9i	− 0.0749025i
$597$	0	0
$598$	−1.26646e11	−0.990343
$599$	1.92208e10i	0.149301i	0.997210	+	0.0746507i	$0.0237842\pi$
$599$	1.92208e10i	0.149301i	−0.997210	+	0.0746507i	$0.976216\pi$
$600$	0	0
$601$	−1.40320e11	−1.07552	−0.537762	−	0.843097i	$-0.680730\pi$
$601$	−1.40320e11	−1.07552	−0.537762	+	0.843097i	$0.680730\pi$
$602$	6.91276e10i	0.526339i
$603$	0	0
$604$	1.09747e10	0.0824601
$605$	− 1.57706e10i	− 0.117714i
$606$	0	0
$607$	1.24644e11	0.918155	0.459077	−	0.888396i	$-0.348180\pi$
$607$	1.24644e11	0.918155	0.459077	+	0.888396i	$0.348180\pi$
$608$	− 2.28003e10i	− 0.166850i
$609$	0	0
$610$	2.52302e10	0.182222
$611$	2.94074e11i	2.11004i
$612$	0	0
$613$	6.60475e9	0.0467751	0.0233875	−	0.999726i	$-0.492555\pi$
$613$	6.60475e9	0.0467751	0.0233875	+	0.999726i	$0.492555\pi$
$614$	− 1.25456e11i	− 0.882711i
$615$	0	0
$616$	−2.36785e10	−0.164449
$617$	− 1.56086e11i	− 1.07702i	−0.842620	−	0.538509i	$-0.818988\pi$
$617$	− 1.56086e11i	− 1.07702i	0.842620	−	0.538509i	$-0.181012\pi$
$618$	0	0
$619$	6.99194e10	0.476250	0.238125	−	0.971234i	$-0.423467\pi$
$619$	6.99194e10	0.476250	0.238125	+	0.971234i	$0.423467\pi$
$620$	1.63176e10i	0.110430i
$621$	0	0
$622$	6.33193e10	0.423033
$623$	5.58698e10i	0.370873i
$624$	0	0
$625$	1.29038e11	0.845662
$626$	− 8.00946e10i	− 0.521562i
$627$	0	0
$628$	4.54483e10	0.292199
$629$	− 2.53623e9i	− 0.0162027i
$630$	0	0
$631$	−1.39781e11	−0.881721	−0.440860	−	0.897576i	$-0.645327\pi$
$631$	−1.39781e11	−0.881721	−0.440860	+	0.897576i	$0.645327\pi$
$632$	8.62102e10i	0.540369i
$633$	0	0
$634$	7.56460e10	0.468198
$635$	− 2.16172e10i	− 0.132955i
$636$	0	0
$637$	3.41038e10	0.207131
$638$	1.09032e11i	0.658069i
$639$	0	0
$640$	3.39324e9	0.0202253
$641$	− 9.79056e10i	− 0.579930i	−0.957037	−	0.289965i	$-0.906356\pi$
$641$	− 9.79056e10i	− 0.579930i	0.957037	−	0.289965i	$-0.0936437\pi$
$642$	0	0
$643$	9.14407e10	0.534928	0.267464	−	0.963568i	$-0.413814\pi$
$643$	9.14407e10	0.534928	0.267464	+	0.963568i	$0.413814\pi$
$644$	3.13994e10i	0.182548i
$645$	0	0
$646$	1.06466e10	0.0611339
$647$	2.63855e11i	1.50573i	0.658172	+	0.752867i	$0.271330\pi$
$647$	2.63855e11i	1.50573i	−0.658172	+	0.752867i	$0.728670\pi$
$648$	0	0
$649$	2.13406e11	1.20289
$650$	1.73430e11i	0.971565i
$651$	0	0
$652$	−4.01826e10	−0.222356
$653$	− 3.13469e11i	− 1.72402i	−0.506892	−	0.862010i	$-0.669206\pi$
$653$	− 3.13469e11i	− 1.72402i	0.506892	−	0.862010i	$-0.330794\pi$
$654$	0	0
$655$	−4.99726e10	−0.271498
$656$	4.44739e10i	0.240154i
$657$	0	0
$658$	7.29101e10	0.388942
$659$	2.88806e11i	1.53131i	0.643249	+	0.765657i	$0.277586\pi$
$659$	2.88806e11i	1.53131i	−0.643249	+	0.765657i	$0.722414\pi$
$660$	0	0
$661$	1.53420e11	0.803667	0.401833	−	0.915713i	$-0.368373\pi$
$661$	1.53420e11	0.803667	0.401833	+	0.915713i	$0.368373\pi$
$662$	6.29130e10i	0.327573i
$663$	0	0
$664$	−7.61074e10	−0.391521
$665$	1.59638e10i	0.0816302i
$666$	0	0
$667$	1.44585e11	0.730498
$668$	− 8.87273e10i	− 0.445607i
$669$	0	0
$670$	2.50240e10	0.124181
$671$	− 2.80952e11i	− 1.38593i
$672$	0	0
$673$	3.48665e11	1.69961	0.849803	−	0.527101i	$-0.176721\pi$
$673$	3.48665e11	1.69961	0.849803	+	0.527101i	$0.176721\pi$
$674$	2.18001e11i	1.05637i
$675$	0	0
$676$	−1.15091e11	−0.551131
$677$	1.29175e11i	0.614929i	0.951560	+	0.307464i	$0.0994805\pi$
$677$	1.29175e11i	0.614929i	−0.951560	+	0.307464i	$0.900520\pi$
$678$	0	0
$679$	1.10476e11	0.519742
$680$	1.58448e9i	0.00741056i
$681$	0	0
$682$	1.81705e11	0.839903
$683$	7.64052e10i	0.351108i	0.984470	+	0.175554i	$0.0561716\pi$
$683$	7.64052e10i	0.351108i	−0.984470	+	0.175554i	$0.943828\pi$
$684$	0	0
$685$	−2.12412e10	−0.0964755
$686$	− 8.45540e9i	− 0.0381802i
$687$	0	0
$688$	−1.10312e11	−0.492345
$689$	− 4.92206e11i	− 2.18409i
$690$	0	0
$691$	−1.58308e11	−0.694369	−0.347184	−	0.937797i	$-0.612862\pi$
$691$	−1.58308e11	−0.694369	−0.347184	+	0.937797i	$0.612862\pi$
$692$	− 2.18900e11i	− 0.954598i
$693$	0	0
$694$	2.44140e11	1.05245
$695$	3.84525e10i	0.164811i
$696$	0	0
$697$	−2.07672e10	−0.0879926
$698$	− 3.98100e10i	− 0.167714i
$699$	0	0
$700$	4.29988e10	0.179087
$701$	− 2.80767e8i	− 0.00116272i	−1.00000		0.000581359i	$-0.999815\pi$
$701$	− 2.80767e8i	− 0.00116272i	1.00000		0.000581359i	$-0.000185052\pi$
$702$	0	0
$703$	4.07766e10	0.166951
$704$	− 3.77855e10i	− 0.153828i
$705$	0	0
$706$	−3.22007e11	−1.29612
$707$	7.03142e9i	0.0281427i
$708$	0	0
$709$	4.18970e11	1.65805	0.829025	−	0.559212i	$-0.188896\pi$
$709$	4.18970e11	1.65805	0.829025	+	0.559212i	$0.188896\pi$
$710$	1.92857e10i	0.0758930i
$711$	0	0
$712$	−8.91557e10	−0.346920
$713$	− 2.40954e11i	− 0.932345i
$714$	0	0
$715$	−1.06707e11	−0.408289
$716$	1.77199e10i	0.0674232i
$717$	0	0
$718$	−1.65091e11	−0.621193
$719$	2.73456e10i	0.102323i	0.998690	+	0.0511613i	$0.0162923\pi$
$719$	2.73456e10i	0.102323i	−0.998690	+	0.0511613i	$0.983708\pi$
$720$	0	0
$721$	−9.40816e10	−0.348148
$722$	− 2.09744e10i	− 0.0771864i
$723$	0	0
$724$	−5.02341e10	−0.182829
$725$	− 1.97996e11i	− 0.716647i
$726$	0	0
$727$	−4.66456e11	−1.66983	−0.834917	−	0.550376i	$-0.814484\pi$
$727$	−4.66456e11	−1.66983	−0.834917	+	0.550376i	$0.814484\pi$
$728$	5.44220e10i	0.193753i
$729$	0	0
$730$	−2.38734e10	−0.0840664
$731$	− 5.15104e10i	− 0.180396i
$732$	0	0
$733$	−4.81476e11	−1.66786	−0.833929	−	0.551872i	$-0.813914\pi$
$733$	−4.81476e11	−1.66786	−0.833929	+	0.551872i	$0.813914\pi$
$734$	− 4.77651e10i	− 0.164561i
$735$	0	0
$736$	−5.01064e10	−0.170758
$737$	− 2.78655e11i	− 0.944490i
$738$	0	0
$739$	1.70560e11	0.571874	0.285937	−	0.958248i	$-0.407695\pi$
$739$	1.70560e11	0.571874	0.285937	+	0.958248i	$0.407695\pi$
$740$	6.06857e9i	0.0202376i
$741$	0	0
$742$	−1.22033e11	−0.402590
$743$	3.72402e11i	1.22196i	0.791646	+	0.610980i	$0.209225\pi$
$743$	3.72402e11i	1.22196i	−0.791646	+	0.610980i	$0.790775\pi$
$744$	0	0
$745$	−1.05597e10	−0.0342788
$746$	3.15873e11i	1.01990i
$747$	0	0
$748$	1.76440e10	0.0563626
$749$	− 1.09756e11i	− 0.348740i
$750$	0	0
$751$	1.81809e11	0.571551	0.285776	−	0.958297i	$-0.407749\pi$
$751$	1.81809e11	0.571551	0.285776	+	0.958297i	$0.407749\pi$
$752$	1.16348e11i	0.363821i
$753$	0	0
$754$	2.50597e11	0.775336
$755$	− 1.22620e10i	− 0.0377375i
$756$	0	0
$757$	1.36535e11	0.415776	0.207888	−	0.978153i	$-0.433341\pi$
$757$	1.36535e11	0.415776	0.207888	+	0.978153i	$0.433341\pi$
$758$	4.25278e11i	1.28824i
$759$	0	0
$760$	−2.54747e10	−0.0763580
$761$	1.91617e11i	0.571342i	0.958328	+	0.285671i	$0.0922164\pi$
$761$	1.91617e11i	0.571342i	−0.958328	+	0.285671i	$0.907784\pi$
$762$	0	0
$763$	1.76705e11	0.521374
$764$	4.21583e10i	0.123740i
$765$	0	0
$766$	−4.41637e11	−1.28277
$767$	− 4.90487e11i	− 1.41725i
$768$	0	0
$769$	−3.47738e11	−0.994367	−0.497183	−	0.867646i	$-0.665632\pi$
$769$	−3.47738e11	−0.994367	−0.497183	+	0.867646i	$0.665632\pi$
$770$	2.64559e10i	0.0752593i
$771$	0	0
$772$	−1.61379e11	−0.454338
$773$	− 1.08396e11i	− 0.303596i	−0.988412	−	0.151798i	$-0.951494\pi$
$773$	− 1.08396e11i	− 0.303596i	0.988412	−	0.151798i	$-0.0485064\pi$
$774$	0	0
$775$	−3.29966e11	−0.914667
$776$	1.76295e11i	0.486174i
$777$	0	0
$778$	−2.00418e11	−0.547039
$779$	− 3.33887e11i	− 0.906672i
$780$	0	0
$781$	2.14757e11	0.577221
$782$	− 2.33973e10i	− 0.0625660i
$783$	0	0
$784$	1.34929e10	0.0357143
$785$	− 5.07794e10i	− 0.133724i
$786$	0	0
$787$	−1.50639e11	−0.392681	−0.196340	−	0.980536i	$-0.562906\pi$
$787$	−1.50639e11	−0.392681	−0.196340	+	0.980536i	$0.562906\pi$
$788$	− 2.36422e11i	− 0.613173i
$789$	0	0
$790$	9.63226e10	0.247298
$791$	− 7.16703e10i	− 0.183077i
$792$	0	0
$793$	−6.45734e11	−1.63290
$794$	4.56394e11i	1.14831i
$795$	0	0
$796$	9.51142e10	0.236915
$797$	− 5.48993e11i	− 1.36061i	−0.732930	−	0.680304i	$-0.761848\pi$
$797$	− 5.48993e11i	− 1.36061i	0.732930	−	0.680304i	$-0.238152\pi$
$798$	0	0
$799$	−5.43290e10	−0.133304
$800$	6.86165e10i	0.167521i
$801$	0	0
$802$	−2.86336e11	−0.692115
$803$	2.65843e11i	0.639386i
$804$	0	0
$805$	3.50826e10	0.0835425
$806$	− 4.17626e11i	− 0.989573i
$807$	0	0
$808$	−1.12206e10	−0.0263251
$809$	− 1.25085e11i	− 0.292018i	−0.989283	−	0.146009i	$-0.953357\pi$
$809$	− 1.25085e11i	− 0.292018i	0.989283	−	0.146009i	$-0.0466429\pi$
$810$	0	0
$811$	−1.25353e11	−0.289770	−0.144885	−	0.989449i	$-0.546281\pi$
$811$	−1.25353e11	−0.289770	−0.144885	+	0.989449i	$0.546281\pi$
$812$	− 6.21308e10i	− 0.142917i
$813$	0	0
$814$	6.75768e10	0.153922
$815$	4.48960e10i	0.101760i
$816$	0	0
$817$	8.28167e11	1.85879
$818$	− 3.04558e11i	− 0.680230i
$819$	0	0
$820$	4.96907e10	0.109905
$821$	7.24317e11i	1.59425i	0.603815	+	0.797125i	$0.293647\pi$
$821$	7.24317e11i	1.59425i	−0.603815	+	0.797125i	$0.706353\pi$
$822$	0	0
$823$	−4.87592e11	−1.06281	−0.531407	−	0.847117i	$-0.678336\pi$
$823$	−4.87592e11	−1.06281	−0.531407	+	0.847117i	$0.678336\pi$
$824$	− 1.50133e11i	− 0.325662i
$825$	0	0
$826$	−1.21607e11	−0.261239
$827$	− 2.94810e10i	− 0.0630261i	−0.999503	−	0.0315131i	$-0.989967\pi$
$827$	− 2.94810e10i	− 0.0630261i	0.999503	−	0.0315131i	$-0.0100326\pi$
$828$	0	0
$829$	−6.47683e11	−1.37134	−0.685669	−	0.727914i	$-0.740490\pi$
$829$	−6.47683e11	−1.37134	−0.685669	+	0.727914i	$0.740490\pi$
$830$	8.50348e10i	0.179178i
$831$	0	0
$832$	−8.68454e10	−0.181240
$833$	6.30055e9i	0.0130857i
$834$	0	0
$835$	−9.91350e10	−0.203930
$836$	2.83675e11i	0.580758i
$837$	0	0
$838$	1.75418e11	0.355712
$839$	8.00043e11i	1.61460i	0.590139	+	0.807301i	$0.299073\pi$
$839$	8.00043e11i	1.61460i	−0.590139	+	0.807301i	$0.700927\pi$
$840$	0	0
$841$	2.14153e11	0.428096
$842$	− 4.22625e11i	− 0.840828i
$843$	0	0
$844$	−4.11953e11	−0.811854
$845$	1.28591e11i	0.252223i
$846$	0	0
$847$	1.00072e11	0.194437
$848$	− 1.94738e11i	− 0.376589i
$849$	0	0
$850$	−3.20406e10	−0.0613797
$851$	− 8.96118e10i	− 0.170863i
$852$	0	0
$853$	7.72052e11	1.45831	0.729156	−	0.684348i	$-0.239913\pi$
$853$	7.72052e11	1.45831	0.729156	+	0.684348i	$0.239913\pi$
$854$	1.60098e11i	0.300991i
$855$	0	0
$856$	1.75146e11	0.326216
$857$	− 5.01334e11i	− 0.929403i	−0.885467	−	0.464701i	$-0.846162\pi$
$857$	− 5.01334e11i	− 0.929403i	0.885467	−	0.464701i	$-0.153838\pi$
$858$	0	0
$859$	−2.54197e11	−0.466872	−0.233436	−	0.972372i	$-0.574997\pi$
$859$	−2.54197e11	−0.466872	−0.233436	+	0.972372i	$0.574997\pi$
$860$	1.23252e11i	0.225319i
$861$	0	0
$862$	−1.77512e11	−0.321514
$863$	− 2.68734e11i	− 0.484485i	−0.970216	−	0.242242i	$-0.922117\pi$
$863$	− 2.68734e11i	− 0.484485i	0.970216	−	0.242242i	$-0.0778829\pi$
$864$	0	0
$865$	−2.44576e11	−0.436868
$866$	− 4.23528e11i	− 0.753027i
$867$	0	0
$868$	−1.03543e11	−0.182407
$869$	− 1.07260e12i	− 1.88088i
$870$	0	0
$871$	−6.40455e11	−1.11280
$872$	2.81981e11i	0.487701i
$873$	0	0
$874$	3.76174e11	0.644678
$875$	− 9.87396e10i	− 0.168445i
$876$	0	0
$877$	1.81112e10	0.0306161	0.0153080	−	0.999883i	$-0.495127\pi$
$877$	1.81112e10	0.0306161	0.0153080	+	0.999883i	$0.495127\pi$
$878$	1.76808e11i	0.297525i
$879$	0	0
$880$	−4.22178e10	−0.0703987
$881$	6.23747e11i	1.03539i	0.855564	+	0.517696i	$0.173210\pi$
$881$	6.23747e11i	1.03539i	−0.855564	+	0.517696i	$0.826790\pi$
$882$	0	0
$883$	1.35657e11	0.223150	0.111575	−	0.993756i	$-0.464410\pi$
$883$	1.35657e11	0.223150	0.111575	+	0.993756i	$0.464410\pi$
$884$	− 4.05526e10i	− 0.0664064i
$885$	0	0
$886$	1.34124e11	0.217656
$887$	− 2.88388e11i	− 0.465889i	−0.972490	−	0.232944i	$-0.925164\pi$
$887$	− 2.88388e11i	− 0.465889i	0.972490	−	0.232944i	$-0.0748360\pi$
$888$	0	0
$889$	1.37171e11	0.219612
$890$	9.96136e10i	0.158766i
$891$	0	0
$892$	3.50598e11	0.553796
$893$	− 8.73483e11i	− 1.37356i
$894$	0	0
$895$	1.97984e10	0.0308560
$896$	2.15317e10i	0.0334077i
$897$	0	0
$898$	−2.78688e11	−0.428561
$899$	4.76782e11i	0.729930i
$900$	0	0
$901$	9.09332e10	0.137982
$902$	− 5.53332e11i	− 0.835911i
$903$	0	0
$904$	1.14370e11	0.171253
$905$	5.61265e10i	0.0836708i
$906$	0	0
$907$	1.20662e12	1.78296	0.891481	−	0.453058i	$-0.149667\pi$
$907$	1.20662e12	1.78296	0.891481	+	0.453058i	$0.149667\pi$
$908$	− 4.09470e11i	− 0.602391i
$909$	0	0
$910$	6.08057e10	0.0886704
$911$	2.92953e11i	0.425329i	0.977125	+	0.212664i	$0.0682141\pi$
$911$	2.92953e11i	0.425329i	−0.977125	+	0.212664i	$0.931786\pi$
$912$	0	0
$913$	9.46908e11	1.36278
$914$	3.79440e11i	0.543699i
$915$	0	0
$916$	3.05551e11	0.434012
$917$	− 3.17100e11i	− 0.448455i
$918$	0	0
$919$	−1.61412e11	−0.226294	−0.113147	−	0.993578i	$-0.536093\pi$
$919$	−1.61412e11	−0.226294	−0.113147	+	0.993578i	$0.536093\pi$
$920$	5.59839e10i	0.0781469i
$921$	0	0
$922$	8.14340e11	1.12689
$923$	− 4.93591e11i	− 0.680081i
$924$	0	0
$925$	−1.22716e11	−0.167623
$926$	5.72417e11i	0.778518i
$927$	0	0
$928$	9.91468e10	0.133686
$929$	9.94131e11i	1.33469i	0.744748	+	0.667346i	$0.232570\pi$
$929$	9.94131e11i	1.33469i	−0.744748	+	0.667346i	$0.767430\pi$
$930$	0	0
$931$	−1.01298e11	−0.134835
$932$	− 3.35806e11i	− 0.445066i
$933$	0	0
$934$	−7.85277e11	−1.03189
$935$	− 1.97137e10i	− 0.0257941i
$936$	0	0
$937$	−3.30191e11	−0.428359	−0.214179	−	0.976794i	$-0.568708\pi$
$937$	−3.30191e11	−0.428359	−0.214179	+	0.976794i	$0.568708\pi$
$938$	1.58789e11i	0.205120i
$939$	0	0
$940$	1.29996e11	0.166501
$941$	9.14497e11i	1.16634i	0.812352	+	0.583168i	$0.198187\pi$
$941$	9.14497e11i	1.16634i	−0.812352	+	0.583168i	$0.801813\pi$
$942$	0	0
$943$	−7.33760e11	−0.927913
$944$	− 1.94058e11i	− 0.244367i
$945$	0	0
$946$	1.37247e12	1.71372
$947$	3.79565e11i	0.471939i	0.971760	+	0.235970i	$0.0758266\pi$
$947$	3.79565e11i	0.471939i	−0.971760	+	0.235970i	$0.924173\pi$
$948$	0	0
$949$	6.11007e11	0.753323
$950$	− 5.15138e11i	− 0.632454i
$951$	0	0
$952$	−1.00543e10	−0.0122406
$953$	1.64228e12i	1.99103i	0.0946255	+	0.995513i	$0.469835\pi$
$953$	1.64228e12i	1.99103i	−0.0946255	+	0.995513i	$0.530165\pi$
$954$	0	0
$955$	4.71034e10	0.0566290
$956$	3.90179e11i	0.467124i
$957$	0	0
$958$	1.81236e11	0.215170
$959$	− 1.34785e11i	− 0.159356i
$960$	0	0
$961$	−5.83205e10	−0.0683798
$962$	− 1.55317e11i	− 0.181350i
$963$	0	0
$964$	7.40366e11	0.857311
$965$	1.80309e11i	0.207926i
$966$	0	0
$967$	−1.29196e11	−0.147755	−0.0738777	−	0.997267i	$-0.523537\pi$
$967$	−1.29196e11	−0.147755	−0.0738777	+	0.997267i	$0.523537\pi$
$968$	1.59693e11i	0.181879i
$969$	0	0
$970$	1.96974e11	0.222496
$971$	1.66125e12i	1.86878i	0.356257	+	0.934388i	$0.384053\pi$
$971$	1.66125e12i	1.86878i	−0.356257	+	0.934388i	$0.615947\pi$
$972$	0	0
$973$	−2.43999e11	−0.272231
$974$	− 9.44508e11i	− 1.04947i
$975$	0	0
$976$	−2.55480e11	−0.281551
$977$	− 5.59214e11i	− 0.613762i	−0.951748	−	0.306881i	$-0.900715\pi$
$977$	− 5.59214e11i	− 0.613762i	0.951748	−	0.306881i	$-0.0992853\pi$
$978$	0	0
$979$	1.10925e12	1.20753
$980$	− 1.50756e10i	− 0.0163445i
$981$	0	0
$982$	−1.10088e12	−1.18384
$983$	1.33975e12i	1.43486i	0.696630	+	0.717430i	$0.254682\pi$
$983$	1.33975e12i	1.43486i	−0.696630	+	0.717430i	$0.745318\pi$
$984$	0	0
$985$	−2.64154e11	−0.280616
$986$	4.62968e10i	0.0489827i
$987$	0	0
$988$	6.51991e11	0.684248
$989$	− 1.82000e12i	− 1.90233i
$990$	0	0
$991$	1.81295e12	1.87971	0.939854	−	0.341576i	$-0.110961\pi$
$991$	1.81295e12	1.87971	0.939854	+	0.341576i	$0.110961\pi$
$992$	− 1.65231e11i	− 0.170626i
$993$	0	0
$994$	−1.22377e11	−0.125358
$995$	− 1.06271e11i	− 0.108423i
$996$	0	0
$997$	2.24018e11	0.226726	0.113363	−	0.993554i	$-0.463838\pi$
$997$	2.24018e11	0.226726	0.113363	+	0.993554i	$0.463838\pi$
$998$	− 8.88024e11i	− 0.895164i
$999$	0	0

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
126.9.b.b.71.2	✓	8	3.2	odd	2	inner
126.9.b.b.71.7	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)

\(f(q)\)	\(=\)	\(q+11.3137i q^{2} -128.000 q^{4} +143.014i q^{5} -907.493 q^{7} -1448.15i q^{8} +O(q^{10})\)	\(q+11.3137i q^{2} -128.000 q^{4} +143.014i q^{5} -907.493 q^{7} -1448.15i q^{8} -1618.02 q^{10} +18017.5i q^{11} +41411.1 q^{13} -10267.1i q^{14} +16384.0 q^{16} +7650.54i q^{17} -123003. q^{19} -18305.8i q^{20} -203845. q^{22} +270314. i q^{23} +370172. q^{25} +468513. i q^{26} +116159. q^{28} -534877. i q^{29} -891387. q^{31} +185364. i q^{32} -86556.0 q^{34} -129784. i q^{35} -331510. q^{37} -1.39162e6i q^{38} +207107. q^{40} +2.71447e6i q^{41} -6.73292e6 q^{43} -2.30625e6i q^{44} -3.05825e6 q^{46} +7.10133e6i q^{47} +823543. q^{49} +4.18802e6i q^{50} -5.30062e6 q^{52} -1.18859e7i q^{53} -2.57677e6 q^{55} +1.31419e6i q^{56} +6.05144e6 q^{58} -1.18443e7i q^{59} -1.55932e7 q^{61} -1.00849e7i q^{62} -2.09715e6 q^{64} +5.92238e6i q^{65} -1.54658e7 q^{67} -979269. i q^{68} +1.46834e6 q^{70} -1.19193e7i q^{71} +1.47547e7 q^{73} -3.75061e6i q^{74} +1.57443e7 q^{76} -1.63508e7i q^{77} -5.95311e7 q^{79} +2.34315e6i q^{80} -3.07107e7 q^{82} -5.25548e7i q^{83} -1.09414e6 q^{85} -7.61742e7i q^{86} +2.60922e7 q^{88} -6.15650e7i q^{89} -3.75803e7 q^{91} -3.46002e7i q^{92} -8.03424e7 q^{94} -1.75911e7i q^{95} -1.21737e8 q^{97} +9.31733e6i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 1024 q^{4}+O(q^{10}) \) 8 * q - 1024 * q^4	\( 8 q - 1024 q^{4} + 4480 q^{10} + 156632 q^{13} + 131072 q^{16} + 321160 q^{19} + 65216 q^{22} - 2280096 q^{25} - 2427880 q^{31} + 4914560 q^{34} + 2032696 q^{37} - 573440 q^{40} - 14076032 q^{43} + 13935680 q^{46} + 6588344 q^{49} - 20048896 q^{52} + 21354536 q^{55} - 4103168 q^{58} + 46591832 q^{61} - 16777216 q^{64} - 26848632 q^{67} - 39798976 q^{70} + 94257072 q^{73} - 41108480 q^{76} - 244539784 q^{79} + 10967040 q^{82} + 163925624 q^{85} - 8347648 q^{88} - 57547168 q^{91} - 28288512 q^{94} + 109673088 q^{97}+O(q^{100}) \) 8 * q - 1024 * q^4 + 4480 * q^10 + 156632 * q^13 + 131072 * q^16 + 321160 * q^19 + 65216 * q^22 - 2280096 * q^25 - 2427880 * q^31 + 4914560 * q^34 + 2032696 * q^37 - 573440 * q^40 - 14076032 * q^43 + 13935680 * q^46 + 6588344 * q^49 - 20048896 * q^52 + 21354536 * q^55 - 4103168 * q^58 + 46591832 * q^61 - 16777216 * q^64 - 26848632 * q^67 - 39798976 * q^70 + 94257072 * q^73 - 41108480 * q^76 - 244539784 * q^79 + 10967040 * q^82 + 163925624 * q^85 - 8347648 * q^88 - 57547168 * q^91 - 28288512 * q^94 + 109673088 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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