LMFDB - Embedded newform 6762.2.a.ct.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6762,2,Mod(1,6762)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6762, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("6762.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6762 = 2 \cdot 3 \cdot 7^{2} \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6762.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$53.9948418468$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	4.4.2624.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 2x^{3} - 3x^{2} + 2x + 1 $ x^4 - 2x^3 - 3x^2 + 2*x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$0.814115$ of defining polynomial
Character	$\chi$	$=$	6762.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +0.585786 q^{5} +1.00000 q^{6} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +0.585786 q^{5} +1.00000 q^{6} +1.00000 q^{8} +1.00000 q^{9} +0.585786 q^{10} -3.93089 q^{11} +1.00000 q^{12} +2.37177 q^{13} +0.585786 q^{15} +1.00000 q^{16} -4.45666 q^{17} +1.00000 q^{18} +1.56821 q^{19} +0.585786 q^{20} -3.93089 q^{22} +1.00000 q^{23} +1.00000 q^{24} -4.65685 q^{25} +2.37177 q^{26} +1.00000 q^{27} +10.6053 q^{29} +0.585786 q^{30} -0.431794 q^{31} +1.00000 q^{32} -3.93089 q^{33} -4.45666 q^{34} +1.00000 q^{36} +4.45666 q^{37} +1.56821 q^{38} +2.37177 q^{39} +0.585786 q^{40} +9.27600 q^{41} +5.71312 q^{43} -3.93089 q^{44} +0.585786 q^{45} +1.00000 q^{46} -7.42999 q^{47} +1.00000 q^{48} -4.65685 q^{50} -4.45666 q^{51} +2.37177 q^{52} +7.40513 q^{53} +1.00000 q^{54} -2.30266 q^{55} +1.56821 q^{57} +10.6053 q^{58} +12.6053 q^{59} +0.585786 q^{60} +15.2760 q^{61} -0.431794 q^{62} +1.00000 q^{64} +1.38935 q^{65} -3.93089 q^{66} -4.11351 q^{67} -4.45666 q^{68} +1.00000 q^{69} -11.5591 q^{71} +1.00000 q^{72} +10.5453 q^{73} +4.45666 q^{74} -4.65685 q^{75} +1.56821 q^{76} +2.37177 q^{78} +3.21598 q^{79} +0.585786 q^{80} +1.00000 q^{81} +9.27600 q^{82} -7.34511 q^{83} -2.61065 q^{85} +5.71312 q^{86} +10.6053 q^{87} -3.93089 q^{88} +16.7465 q^{89} +0.585786 q^{90} +1.00000 q^{92} -0.431794 q^{93} -7.42999 q^{94} +0.918634 q^{95} +1.00000 q^{96} +12.9419 q^{97} -3.93089 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 4 q^{2} + 4 q^{3} + 4 q^{4} + 8 q^{5} + 4 q^{6} + 4 q^{8} + 4 q^{9}+O(q^{10}) $ 4 * q + 4 * q^2 + 4 * q^3 + 4 * q^4 + 8 * q^5 + 4 * q^6 + 4 * q^8 + 4 * q^9	$ 4 q + 4 q^{2} + 4 q^{3} + 4 q^{4} + 8 q^{5} + 4 q^{6} + 4 q^{8} + 4 q^{9} + 8 q^{10} + 4 q^{11} + 4 q^{12} + 12 q^{13} + 8 q^{15} + 4 q^{16} - 4 q^{17} + 4 q^{18} + 4 q^{19} + 8 q^{20} + 4 q^{22} + 4 q^{23} + 4 q^{24} + 4 q^{25} + 12 q^{26} + 4 q^{27} + 8 q^{29} + 8 q^{30} - 4 q^{31} + 4 q^{32} + 4 q^{33} - 4 q^{34} + 4 q^{36} + 4 q^{37} + 4 q^{38} + 12 q^{39} + 8 q^{40} - 8 q^{41} + 4 q^{43} + 4 q^{44} + 8 q^{45} + 4 q^{46} + 12 q^{47} + 4 q^{48} + 4 q^{50} - 4 q^{51} + 12 q^{52} + 4 q^{53} + 4 q^{54} + 8 q^{55} + 4 q^{57} + 8 q^{58} + 16 q^{59} + 8 q^{60} + 16 q^{61} - 4 q^{62} + 4 q^{64} + 16 q^{65} + 4 q^{66} + 20 q^{67} - 4 q^{68} + 4 q^{69} - 24 q^{71} + 4 q^{72} + 8 q^{73} + 4 q^{74} + 4 q^{75} + 4 q^{76} + 12 q^{78} - 32 q^{79} + 8 q^{80} + 4 q^{81} - 8 q^{82} - 4 q^{83} + 4 q^{86} + 8 q^{87} + 4 q^{88} + 20 q^{89} + 8 q^{90} + 4 q^{92} - 4 q^{93} + 12 q^{94} + 4 q^{96} + 4 q^{97} + 4 q^{99}+O(q^{100}) $ 4 * q + 4 * q^2 + 4 * q^3 + 4 * q^4 + 8 * q^5 + 4 * q^6 + 4 * q^8 + 4 * q^9 + 8 * q^10 + 4 * q^11 + 4 * q^12 + 12 * q^13 + 8 * q^15 + 4 * q^16 - 4 * q^17 + 4 * q^18 + 4 * q^19 + 8 * q^20 + 4 * q^22 + 4 * q^23 + 4 * q^24 + 4 * q^25 + 12 * q^26 + 4 * q^27 + 8 * q^29 + 8 * q^30 - 4 * q^31 + 4 * q^32 + 4 * q^33 - 4 * q^34 + 4 * q^36 + 4 * q^37 + 4 * q^38 + 12 * q^39 + 8 * q^40 - 8 * q^41 + 4 * q^43 + 4 * q^44 + 8 * q^45 + 4 * q^46 + 12 * q^47 + 4 * q^48 + 4 * q^50 - 4 * q^51 + 12 * q^52 + 4 * q^53 + 4 * q^54 + 8 * q^55 + 4 * q^57 + 8 * q^58 + 16 * q^59 + 8 * q^60 + 16 * q^61 - 4 * q^62 + 4 * q^64 + 16 * q^65 + 4 * q^66 + 20 * q^67 - 4 * q^68 + 4 * q^69 - 24 * q^71 + 4 * q^72 + 8 * q^73 + 4 * q^74 + 4 * q^75 + 4 * q^76 + 12 * q^78 - 32 * q^79 + 8 * q^80 + 4 * q^81 - 8 * q^82 - 4 * q^83 + 4 * q^86 + 8 * q^87 + 4 * q^88 + 20 * q^89 + 8 * q^90 + 4 * q^92 - 4 * q^93 + 12 * q^94 + 4 * q^96 + 4 * q^97 + 4 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	1.00000	0.500000
$5$	0.585786	0.261972	0.130986	−	0.991384i	$-0.458186\pi$
$5$	0.585786	0.261972	0.130986	+	0.991384i	$0.458186\pi$
$6$	1.00000	0.408248
$7$	0	0
$7$	0	0
$8$	1.00000	0.353553
$9$	1.00000	0.333333
$10$	0.585786	0.185242
$11$	−3.93089	−1.18521	−0.592604	−	0.805494i	$-0.701900\pi$
$11$	−3.93089	−1.18521	−0.592604	+	0.805494i	$0.701900\pi$
$12$	1.00000	0.288675
$13$	2.37177	0.657811	0.328905	−	0.944363i	$-0.393320\pi$
$13$	2.37177	0.657811	0.328905	+	0.944363i	$0.393320\pi$
$14$	0	0
$15$	0.585786	0.151249
$16$	1.00000	0.250000
$17$	−4.45666	−1.08090	−0.540449	−	0.841377i	$-0.681746\pi$
$17$	−4.45666	−1.08090	−0.540449	+	0.841377i	$0.681746\pi$
$18$	1.00000	0.235702
$19$	1.56821	0.359771	0.179886	−	0.983688i	$-0.442427\pi$
$19$	1.56821	0.359771	0.179886	+	0.983688i	$0.442427\pi$
$20$	0.585786	0.130986
$21$	0	0
$22$	−3.93089	−0.838069
$23$	1.00000	0.208514
$23$	1.00000	0.208514
$24$	1.00000	0.204124
$25$	−4.65685	−0.931371
$26$	2.37177	0.465143
$27$	1.00000	0.192450
$28$	0	0
$29$	10.6053	1.96936	0.984680	−	0.174371i	$-0.0557893\pi$
$29$	10.6053	1.96936	0.984680	+	0.174371i	$0.0557893\pi$
$30$	0.585786	0.106949
$31$	−0.431794	−0.0775525	−0.0387762	−	0.999248i	$-0.512346\pi$
$31$	−0.431794	−0.0775525	−0.0387762	+	0.999248i	$0.512346\pi$
$32$	1.00000	0.176777
$33$	−3.93089	−0.684281
$34$	−4.45666	−0.764310
$35$	0	0
$36$	1.00000	0.166667
$37$	4.45666	0.732670	0.366335	−	0.930483i	$-0.380612\pi$
$37$	4.45666	0.732670	0.366335	+	0.930483i	$0.380612\pi$
$38$	1.56821	0.254397
$39$	2.37177	0.379787
$40$	0.585786	0.0926210
$41$	9.27600	1.44867	0.724334	−	0.689449i	$-0.242147\pi$
$41$	9.27600	1.44867	0.724334	+	0.689449i	$0.242147\pi$
$42$	0	0
$43$	5.71312	0.871242	0.435621	−	0.900130i	$-0.356529\pi$
$43$	5.71312	0.871242	0.435621	+	0.900130i	$0.356529\pi$
$44$	−3.93089	−0.592604
$45$	0.585786	0.0873239
$46$	1.00000	0.147442
$47$	−7.42999	−1.08378	−0.541888	−	0.840451i	$-0.682290\pi$
$47$	−7.42999	−1.08378	−0.541888	+	0.840451i	$0.682290\pi$
$48$	1.00000	0.144338
$49$	0	0
$50$	−4.65685	−0.658579
$51$	−4.45666	−0.624057
$52$	2.37177	0.328905
$53$	7.40513	1.01717	0.508586	−	0.861011i	$-0.330168\pi$
$53$	7.40513	1.01717	0.508586	+	0.861011i	$0.330168\pi$
$54$	1.00000	0.136083
$55$	−2.30266	−0.310491
$56$	0	0
$57$	1.56821	0.207714
$58$	10.6053	1.39255
$59$	12.6053	1.64107	0.820537	−	0.571593i	$-0.193675\pi$
$59$	12.6053	1.64107	0.820537	+	0.571593i	$0.193675\pi$
$60$	0.585786	0.0756247
$61$	15.2760	1.95589	0.977946	−	0.208859i	$-0.0669751\pi$
$61$	15.2760	1.95589	0.977946	+	0.208859i	$0.0669751\pi$
$62$	−0.431794	−0.0548379
$63$	0	0
$64$	1.00000	0.125000
$65$	1.38935	0.172328
$66$	−3.93089	−0.483860
$67$	−4.11351	−0.502545	−0.251273	−	0.967916i	$-0.580849\pi$
$67$	−4.11351	−0.502545	−0.251273	+	0.967916i	$0.580849\pi$
$68$	−4.45666	−0.540449
$69$	1.00000	0.120386
$70$	0	0
$71$	−11.5591	−1.37182	−0.685908	−	0.727689i	$-0.740595\pi$
$71$	−11.5591	−1.37182	−0.685908	+	0.727689i	$0.740595\pi$
$72$	1.00000	0.117851
$73$	10.5453	1.23423	0.617117	−	0.786871i	$-0.288300\pi$
$73$	10.5453	1.23423	0.617117	+	0.786871i	$0.288300\pi$
$74$	4.45666	0.518076
$75$	−4.65685	−0.537727
$76$	1.56821	0.179886
$77$	0	0
$78$	2.37177	0.268550
$79$	3.21598	0.361826	0.180913	−	0.983499i	$-0.442095\pi$
$79$	3.21598	0.361826	0.180913	+	0.983499i	$0.442095\pi$
$80$	0.585786	0.0654929
$81$	1.00000	0.111111
$82$	9.27600	1.02436
$83$	−7.34511	−0.806230	−0.403115	−	0.915149i	$-0.632073\pi$
$83$	−7.34511	−0.806230	−0.403115	+	0.915149i	$0.632073\pi$
$84$	0	0
$85$	−2.61065	−0.283165
$86$	5.71312	0.616061
$87$	10.6053	1.13701
$88$	−3.93089	−0.419035
$89$	16.7465	1.77512	0.887561	−	0.460689i	$-0.152398\pi$
$89$	16.7465	1.77512	0.887561	+	0.460689i	$0.152398\pi$
$90$	0.585786	0.0617473
$91$	0	0
$92$	1.00000	0.104257
$93$	−0.431794	−0.0447749
$94$	−7.42999	−0.766345
$95$	0.918634	0.0942498
$96$	1.00000	0.102062
$97$	12.9419	1.31405	0.657027	−	0.753867i	$-0.271814\pi$
$97$	12.9419	1.31405	0.657027	+	0.753867i	$0.271814\pi$
$98$	0	0
$99$	−3.93089	−0.395070
$100$	−4.65685	−0.465685
$101$	7.71312	0.767484	0.383742	−	0.923440i	$-0.374635\pi$
$101$	7.71312	0.767484	0.383742	+	0.923440i	$0.374635\pi$
$102$	−4.45666	−0.441275
$103$	−5.77690	−0.569215	−0.284607	−	0.958644i	$-0.591863\pi$
$103$	−5.77690	−0.569215	−0.284607	+	0.958644i	$0.591863\pi$
$104$	2.37177	0.232571
$105$	0	0
$106$	7.40513	0.719250
$107$	13.8957	1.34335	0.671676	−	0.740845i	$-0.265575\pi$
$107$	13.8957	1.34335	0.671676	+	0.740845i	$0.265575\pi$
$108$	1.00000	0.0962250
$109$	−14.9419	−1.43118	−0.715589	−	0.698522i	$-0.753842\pi$
$109$	−14.9419	−1.43118	−0.715589	+	0.698522i	$0.753842\pi$
$110$	−2.30266	−0.219550
$111$	4.45666	0.423007
$112$	0	0
$113$	−16.3027	−1.53363	−0.766813	−	0.641871i	$-0.778159\pi$
$113$	−16.3027	−1.53363	−0.766813	+	0.641871i	$0.778159\pi$
$114$	1.56821	0.146876
$115$	0.585786	0.0546249
$116$	10.6053	0.984680
$117$	2.37177	0.219270
$118$	12.6053	1.16041
$119$	0	0
$120$	0.585786	0.0534747
$121$	4.45192	0.404720
$122$	15.2760	1.38302
$123$	9.27600	0.836389
$124$	−0.431794	−0.0387762
$125$	−5.65685	−0.505964
$126$	0	0
$127$	13.0778	1.16046	0.580232	−	0.814451i	$-0.302962\pi$
$127$	13.0778	1.16046	0.580232	+	0.814451i	$0.302962\pi$
$128$	1.00000	0.0883883
$129$	5.71312	0.503012
$130$	1.38935	0.121854
$131$	−9.96484	−0.870632	−0.435316	−	0.900278i	$-0.643363\pi$
$131$	−9.96484	−0.870632	−0.435316	+	0.900278i	$0.643363\pi$
$132$	−3.93089	−0.342140
$133$	0	0
$134$	−4.11351	−0.355353
$135$	0.585786	0.0504165
$136$	−4.45666	−0.382155
$137$	−18.9133	−1.61587	−0.807937	−	0.589269i	$-0.799416\pi$
$137$	−18.9133	−1.61587	−0.807937	+	0.589269i	$0.799416\pi$
$138$	1.00000	0.0851257
$139$	10.8284	0.918455	0.459228	−	0.888319i	$-0.348126\pi$
$139$	10.8284	0.918455	0.459228	+	0.888319i	$0.348126\pi$
$140$	0	0
$141$	−7.42999	−0.625718
$142$	−11.5591	−0.970020
$143$	−9.32318	−0.779643
$144$	1.00000	0.0833333
$145$	6.21246	0.515916
$146$	10.5453	0.872736
$147$	0	0
$148$	4.45666	0.366335
$149$	−13.1469	−1.07703	−0.538517	−	0.842615i	$-0.681015\pi$
$149$	−13.1469	−1.07703	−0.538517	+	0.842615i	$0.681015\pi$
$150$	−4.65685	−0.380231
$151$	17.3857	1.41483	0.707416	−	0.706797i	$-0.249861\pi$
$151$	17.3857	1.41483	0.707416	+	0.706797i	$0.249861\pi$
$152$	1.56821	0.127198
$153$	−4.45666	−0.360299
$154$	0	0
$155$	−0.252939	−0.0203166
$156$	2.37177	0.189894
$157$	7.00850	0.559339	0.279669	−	0.960096i	$-0.409775\pi$
$157$	7.00850	0.559339	0.279669	+	0.960096i	$0.409775\pi$
$158$	3.21598	0.255849
$159$	7.40513	0.587265
$160$	0.585786	0.0463105
$161$	0	0
$162$	1.00000	0.0785674
$163$	7.95952	0.623438	0.311719	−	0.950174i	$-0.399095\pi$
$163$	7.95952	0.623438	0.311719	+	0.950174i	$0.399095\pi$
$164$	9.27600	0.724334
$165$	−2.30266	−0.179262
$166$	−7.34511	−0.570091
$167$	6.03140	0.466724	0.233362	−	0.972390i	$-0.425027\pi$
$167$	6.03140	0.466724	0.233362	+	0.972390i	$0.425027\pi$
$168$	0	0
$169$	−7.37470	−0.567285
$170$	−2.61065	−0.200228
$171$	1.56821	0.119924
$172$	5.71312	0.435621
$173$	−18.7188	−1.42317	−0.711583	−	0.702602i	$-0.752022\pi$
$173$	−18.7188	−1.42317	−0.711583	+	0.702602i	$0.752022\pi$
$174$	10.6053	0.803988
$175$	0	0
$176$	−3.93089	−0.296302
$177$	12.6053	0.947474
$178$	16.7465	1.25520
$179$	−25.6884	−1.92004	−0.960021	−	0.279928i	$-0.909689\pi$
$179$	−25.6884	−1.92004	−0.960021	+	0.279928i	$0.909689\pi$
$180$	0.585786	0.0436619
$181$	−6.10443	−0.453739	−0.226869	−	0.973925i	$-0.572849\pi$
$181$	−6.10443	−0.453739	−0.226869	+	0.973925i	$0.572849\pi$
$182$	0	0
$183$	15.2760	1.12923
$184$	1.00000	0.0737210
$185$	2.61065	0.191939
$186$	−0.431794	−0.0316607
$187$	17.5186	1.28109
$188$	−7.42999	−0.541888
$189$	0	0
$190$	0.918634	0.0666447
$191$	−12.8156	−0.927303	−0.463651	−	0.886018i	$-0.653461\pi$
$191$	−12.8156	−0.927303	−0.463651	+	0.886018i	$0.653461\pi$
$192$	1.00000	0.0721688
$193$	9.15341	0.658877	0.329438	−	0.944177i	$-0.393141\pi$
$193$	9.15341	0.658877	0.329438	+	0.944177i	$0.393141\pi$
$194$	12.9419	0.929177
$195$	1.38935	0.0994935
$196$	0	0
$197$	19.4209	1.38368	0.691841	−	0.722050i	$-0.256800\pi$
$197$	19.4209	1.38368	0.691841	+	0.722050i	$0.256800\pi$
$198$	−3.93089	−0.279356
$199$	−25.6387	−1.81748	−0.908739	−	0.417364i	$-0.862954\pi$
$199$	−25.6387	−1.81748	−0.908739	+	0.417364i	$0.862954\pi$
$200$	−4.65685	−0.329289
$201$	−4.11351	−0.290145
$202$	7.71312	0.542693
$203$	0	0
$204$	−4.45666	−0.312028
$205$	5.43376	0.379510
$206$	−5.77690	−0.402496
$207$	1.00000	0.0695048
$208$	2.37177	0.164453
$209$	−6.16445	−0.426404
$210$	0	0
$211$	−3.90227	−0.268643	−0.134322	−	0.990938i	$-0.542886\pi$
$211$	−3.90227	−0.268643	−0.134322	+	0.990938i	$0.542886\pi$
$212$	7.40513	0.508586
$213$	−11.5591	−0.792018
$214$	13.8957	0.949893
$215$	3.34667	0.228241
$216$	1.00000	0.0680414
$217$	0	0
$218$	−14.9419	−1.01200
$219$	10.5453	0.712586
$220$	−2.30266	−0.155246
$221$	−10.5702	−0.711026
$222$	4.45666	0.299111
$223$	−4.79703	−0.321233	−0.160616	−	0.987017i	$-0.551348\pi$
$223$	−4.79703	−0.321233	−0.160616	+	0.987017i	$0.551348\pi$
$224$	0	0
$225$	−4.65685	−0.310457
$226$	−16.3027	−1.08444
$227$	26.4006	1.75227	0.876133	−	0.482069i	$-0.160115\pi$
$227$	26.4006	1.75227	0.876133	+	0.482069i	$0.160115\pi$
$228$	1.56821	0.103857
$229$	−2.91077	−0.192349	−0.0961744	−	0.995364i	$-0.530661\pi$
$229$	−2.91077	−0.192349	−0.0961744	+	0.995364i	$0.530661\pi$
$230$	0.585786	0.0386256
$231$	0	0
$232$	10.6053	0.696274
$233$	−6.54808	−0.428979	−0.214489	−	0.976726i	$-0.568809\pi$
$233$	−6.54808	−0.428979	−0.214489	+	0.976726i	$0.568809\pi$
$234$	2.37177	0.155048
$235$	−4.35239	−0.283919
$236$	12.6053	0.820537
$237$	3.21598	0.208900
$238$	0	0
$239$	−28.4724	−1.84173	−0.920864	−	0.389883i	$-0.872515\pi$
$239$	−28.4724	−1.84173	−0.920864	+	0.389883i	$0.872515\pi$
$240$	0.585786	0.0378124
$241$	−21.6673	−1.39571	−0.697857	−	0.716237i	$-0.745863\pi$
$241$	−21.6673	−1.39571	−0.697857	+	0.716237i	$0.745863\pi$
$242$	4.45192	0.286180
$243$	1.00000	0.0641500
$244$	15.2760	0.977946
$245$	0	0
$246$	9.27600	0.591416
$247$	3.71943	0.236661
$248$	−0.431794	−0.0274189
$249$	−7.34511	−0.465477
$250$	−5.65685	−0.357771
$251$	5.08292	0.320831	0.160416	−	0.987050i	$-0.448717\pi$
$251$	5.08292	0.320831	0.160416	+	0.987050i	$0.448717\pi$
$252$	0	0
$253$	−3.93089	−0.247133
$254$	13.0778	0.820572
$255$	−2.61065	−0.163485
$256$	1.00000	0.0625000
$257$	16.8480	1.05095	0.525474	−	0.850810i	$-0.323888\pi$
$257$	16.8480	1.05095	0.525474	+	0.850810i	$0.323888\pi$
$258$	5.71312	0.355683
$259$	0	0
$260$	1.38935	0.0861639
$261$	10.6053	0.656453
$262$	−9.96484	−0.615630
$263$	−31.3137	−1.93089	−0.965443	−	0.260614i	$-0.916075\pi$
$263$	−31.3137	−1.93089	−0.965443	+	0.260614i	$0.916075\pi$
$264$	−3.93089	−0.241930
$265$	4.33782	0.266470
$266$	0	0
$267$	16.7465	1.02487
$268$	−4.11351	−0.251273
$269$	13.6358	0.831387	0.415693	−	0.909505i	$-0.363539\pi$
$269$	13.6358	0.831387	0.415693	+	0.909505i	$0.363539\pi$
$270$	0.585786	0.0356498
$271$	−14.9042	−0.905367	−0.452684	−	0.891671i	$-0.649533\pi$
$271$	−14.9042	−0.905367	−0.452684	+	0.891671i	$0.649533\pi$
$272$	−4.45666	−0.270224
$273$	0	0
$274$	−18.9133	−1.14260
$275$	18.3056	1.10387
$276$	1.00000	0.0601929
$277$	−23.9542	−1.43927	−0.719634	−	0.694353i	$-0.755690\pi$
$277$	−23.9542	−1.43927	−0.719634	+	0.694353i	$0.755690\pi$
$278$	10.8284	0.649446
$279$	−0.431794	−0.0258508
$280$	0	0
$281$	−3.46139	−0.206489	−0.103245	−	0.994656i	$-0.532922\pi$
$281$	−3.46139	−0.206489	−0.103245	+	0.994656i	$0.532922\pi$
$282$	−7.42999	−0.442450
$283$	23.0464	1.36996	0.684982	−	0.728560i	$-0.259810\pi$
$283$	23.0464	1.36996	0.684982	+	0.728560i	$0.259810\pi$
$284$	−11.5591	−0.685908
$285$	0.918634	0.0544152
$286$	−9.32318	−0.551291
$287$	0	0
$288$	1.00000	0.0589256
$289$	2.86179	0.168340
$290$	6.21246	0.364808
$291$	12.9419	0.758670
$292$	10.5453	0.617117
$293$	13.2813	0.775903	0.387952	−	0.921680i	$-0.373183\pi$
$293$	13.2813	0.775903	0.387952	+	0.921680i	$0.373183\pi$
$294$	0	0
$295$	7.38403	0.429915
$296$	4.45666	0.259038
$297$	−3.93089	−0.228094
$298$	−13.1469	−0.761578
$299$	2.37177	0.137163
$300$	−4.65685	−0.268864
$301$	0	0
$302$	17.3857	1.00044
$303$	7.71312	0.443107
$304$	1.56821	0.0899428
$305$	8.94847	0.512388
$306$	−4.45666	−0.254770
$307$	−2.94095	−0.167849	−0.0839244	−	0.996472i	$-0.526745\pi$
$307$	−2.94095	−0.167849	−0.0839244	+	0.996472i	$0.526745\pi$
$308$	0	0
$309$	−5.77690	−0.328636
$310$	−0.252939	−0.0143660
$311$	25.9206	1.46982	0.734911	−	0.678164i	$-0.237224\pi$
$311$	25.9206	1.46982	0.734911	+	0.678164i	$0.237224\pi$
$312$	2.37177	0.134275
$313$	−13.6101	−0.769286	−0.384643	−	0.923065i	$-0.625675\pi$
$313$	−13.6101	−0.769286	−0.384643	+	0.923065i	$0.625675\pi$
$314$	7.00850	0.395512
$315$	0	0
$316$	3.21598	0.180913
$317$	22.3248	1.25388	0.626942	−	0.779066i	$-0.284306\pi$
$317$	22.3248	1.25388	0.626942	+	0.779066i	$0.284306\pi$
$318$	7.40513	0.415259
$319$	−41.6884	−2.33410
$320$	0.585786	0.0327465
$321$	13.8957	0.775584
$322$	0	0
$323$	−6.98896	−0.388876
$324$	1.00000	0.0555556
$325$	−11.0450	−0.612666
$326$	7.95952	0.440837
$327$	−14.9419	−0.826291
$328$	9.27600	0.512181
$329$	0	0
$330$	−2.30266	−0.126757
$331$	17.6569	0.970508	0.485254	−	0.874373i	$-0.338727\pi$
$331$	17.6569	0.970508	0.485254	+	0.874373i	$0.338727\pi$
$332$	−7.34511	−0.403115
$333$	4.45666	0.244223
$334$	6.03140	0.330023
$335$	−2.40964	−0.131653
$336$	0	0
$337$	−3.25114	−0.177101	−0.0885504	−	0.996072i	$-0.528223\pi$
$337$	−3.25114	−0.177101	−0.0885504	+	0.996072i	$0.528223\pi$
$338$	−7.37470	−0.401131
$339$	−16.3027	−0.885439
$340$	−2.61065	−0.141582
$341$	1.69734	0.0919159
$342$	1.56821	0.0847989
$343$	0	0
$344$	5.71312	0.308031
$345$	0.585786	0.0315377
$346$	−18.7188	−1.00633
$347$	−16.5755	−0.889819	−0.444909	−	0.895576i	$-0.646764\pi$
$347$	−16.5755	−0.889819	−0.444909	+	0.895576i	$0.646764\pi$
$348$	10.6053	0.568505
$349$	24.4882	1.31082	0.655412	−	0.755272i	$-0.272495\pi$
$349$	24.4882	1.31082	0.655412	+	0.755272i	$0.272495\pi$
$350$	0	0
$351$	2.37177	0.126596
$352$	−3.93089	−0.209517
$353$	−20.1765	−1.07388	−0.536942	−	0.843619i	$-0.680421\pi$
$353$	−20.1765	−1.07388	−0.536942	+	0.843619i	$0.680421\pi$
$354$	12.6053	0.669966
$355$	−6.77118	−0.359377
$356$	16.7465	0.887561
$357$	0	0
$358$	−25.6884	−1.35767
$359$	7.95952	0.420087	0.210044	−	0.977692i	$-0.432639\pi$
$359$	7.95952	0.420087	0.210044	+	0.977692i	$0.432639\pi$
$360$	0.585786	0.0308737
$361$	−16.5407	−0.870565
$362$	−6.10443	−0.320842
$363$	4.45192	0.233665
$364$	0	0
$365$	6.17730	0.323334
$366$	15.2760	0.798489
$367$	−17.3986	−0.908199	−0.454100	−	0.890951i	$-0.650039\pi$
$367$	−17.3986	−0.908199	−0.454100	+	0.890951i	$0.650039\pi$
$368$	1.00000	0.0521286
$369$	9.27600	0.482889
$370$	2.61065	0.135721
$371$	0	0
$372$	−0.431794	−0.0223875
$373$	19.7427	1.02224	0.511120	−	0.859509i	$-0.329231\pi$
$373$	19.7427	1.02224	0.511120	+	0.859509i	$0.329231\pi$
$374$	17.5186	0.905867
$375$	−5.65685	−0.292119
$376$	−7.42999	−0.383173
$377$	25.1534	1.29547
$378$	0	0
$379$	−5.03967	−0.258870	−0.129435	−	0.991588i	$-0.541316\pi$
$379$	−5.03967	−0.258870	−0.129435	+	0.991588i	$0.541316\pi$
$380$	0.918634	0.0471249
$381$	13.0778	0.669994
$382$	−12.8156	−0.655702
$383$	−34.6017	−1.76807	−0.884033	−	0.467425i	$-0.845182\pi$
$383$	−34.6017	−1.76807	−0.884033	+	0.467425i	$0.845182\pi$
$384$	1.00000	0.0510310
$385$	0	0
$386$	9.15341	0.465896
$387$	5.71312	0.290414
$388$	12.9419	0.657027
$389$	11.6598	0.591175	0.295587	−	0.955316i	$-0.404485\pi$
$389$	11.6598	0.591175	0.295587	+	0.955316i	$0.404485\pi$
$390$	1.38935	0.0703525
$391$	−4.45666	−0.225383
$392$	0	0
$393$	−9.96484	−0.502660
$394$	19.4209	0.978411
$395$	1.88388	0.0947881
$396$	−3.93089	−0.197535
$397$	8.80372	0.441846	0.220923	−	0.975291i	$-0.429093\pi$
$397$	8.80372	0.441846	0.220923	+	0.975291i	$0.429093\pi$
$398$	−25.6387	−1.28515
$399$	0	0
$400$	−4.65685	−0.232843
$401$	12.9800	0.648192	0.324096	−	0.946024i	$-0.394940\pi$
$401$	12.9800	0.648192	0.324096	+	0.946024i	$0.394940\pi$
$402$	−4.11351	−0.205163
$403$	−1.02412	−0.0510149
$404$	7.71312	0.383742
$405$	0.585786	0.0291080
$406$	0	0
$407$	−17.5186	−0.868367
$408$	−4.45666	−0.220637
$409$	18.9957	0.939274	0.469637	−	0.882859i	$-0.344385\pi$
$409$	18.9957	0.939274	0.469637	+	0.882859i	$0.344385\pi$
$410$	5.43376	0.268354
$411$	−18.9133	−0.932925
$412$	−5.77690	−0.284607
$413$	0	0
$414$	1.00000	0.0491473
$415$	−4.30266	−0.211209
$416$	2.37177	0.116286
$417$	10.8284	0.530270
$418$	−6.16445	−0.301513
$419$	−19.2566	−0.940747	−0.470374	−	0.882467i	$-0.655881\pi$
$419$	−19.2566	−0.940747	−0.470374	+	0.882467i	$0.655881\pi$
$420$	0	0
$421$	11.1078	0.541360	0.270680	−	0.962669i	$-0.412751\pi$
$421$	11.1078	0.541360	0.270680	+	0.962669i	$0.412751\pi$
$422$	−3.90227	−0.189959
$423$	−7.42999	−0.361259
$424$	7.40513	0.359625
$425$	20.7540	1.00672
$426$	−11.5591	−0.560041
$427$	0	0
$428$	13.8957	0.671676
$429$	−9.32318	−0.450127
$430$	3.34667	0.161391
$431$	−14.7656	−0.711235	−0.355618	−	0.934632i	$-0.615729\pi$
$431$	−14.7656	−0.711235	−0.355618	+	0.934632i	$0.615729\pi$
$432$	1.00000	0.0481125
$433$	5.51571	0.265068	0.132534	−	0.991178i	$-0.457689\pi$
$433$	5.51571	0.265068	0.132534	+	0.991178i	$0.457689\pi$
$434$	0	0
$435$	6.21246	0.297865
$436$	−14.9419	−0.715589
$437$	1.56821	0.0750175
$438$	10.5453	0.503874
$439$	4.98912	0.238117	0.119059	−	0.992887i	$-0.462012\pi$
$439$	4.98912	0.238117	0.119059	+	0.992887i	$0.462012\pi$
$440$	−2.30266	−0.109775
$441$	0	0
$442$	−10.5702	−0.502772
$443$	10.7382	0.510188	0.255094	−	0.966916i	$-0.417894\pi$
$443$	10.7382	0.510188	0.255094	+	0.966916i	$0.417894\pi$
$444$	4.45666	0.211504
$445$	9.80986	0.465032
$446$	−4.79703	−0.227146
$447$	−13.1469	−0.621826
$448$	0	0
$449$	−30.0924	−1.42015	−0.710074	−	0.704127i	$-0.751339\pi$
$449$	−30.0924	−1.42015	−0.710074	+	0.704127i	$0.751339\pi$
$450$	−4.65685	−0.219526
$451$	−36.4630	−1.71697
$452$	−16.3027	−0.766813
$453$	17.3857	0.816854
$454$	26.4006	1.23904
$455$	0	0
$456$	1.56821	0.0734380
$457$	−21.8618	−1.02265	−0.511326	−	0.859387i	$-0.670845\pi$
$457$	−21.8618	−1.02265	−0.511326	+	0.859387i	$0.670845\pi$
$458$	−2.91077	−0.136011
$459$	−4.45666	−0.208019
$460$	0.585786	0.0273124
$461$	−20.9238	−0.974517	−0.487259	−	0.873258i	$-0.662003\pi$
$461$	−20.9238	−0.974517	−0.487259	+	0.873258i	$0.662003\pi$
$462$	0	0
$463$	3.73422	0.173544	0.0867718	−	0.996228i	$-0.472345\pi$
$463$	3.73422	0.173544	0.0867718	+	0.996228i	$0.472345\pi$
$464$	10.6053	0.492340
$465$	−0.252939	−0.0117298
$466$	−6.54808	−0.303334
$467$	12.9042	0.597137	0.298568	−	0.954388i	$-0.403491\pi$
$467$	12.9042	0.597137	0.298568	+	0.954388i	$0.403491\pi$
$468$	2.37177	0.109635
$469$	0	0
$470$	−4.35239	−0.200761
$471$	7.00850	0.322934
$472$	12.6053	0.580207
$473$	−22.4576	−1.03260
$474$	3.21598	0.147715
$475$	−7.30291	−0.335080
$476$	0	0
$477$	7.40513	0.339058
$478$	−28.4724	−1.30230
$479$	−35.0298	−1.60055	−0.800275	−	0.599633i	$-0.795313\pi$
$479$	−35.0298	−1.60055	−0.800275	+	0.599633i	$0.795313\pi$
$480$	0.585786	0.0267374
$481$	10.5702	0.481958
$482$	−21.6673	−0.986919
$483$	0	0
$484$	4.45192	0.202360
$485$	7.58121	0.344245
$486$	1.00000	0.0453609
$487$	0.195463	0.00885729	0.00442864	−	0.999990i	$-0.498590\pi$
$487$	0.195463	0.00885729	0.00442864	+	0.999990i	$0.498590\pi$
$488$	15.2760	0.691512
$489$	7.95952	0.359942
$490$	0	0
$491$	18.0519	0.814672	0.407336	−	0.913278i	$-0.366458\pi$
$491$	18.0519	0.814672	0.407336	+	0.913278i	$0.366458\pi$
$492$	9.27600	0.418194
$493$	−47.2643	−2.12868
$494$	3.71943	0.167345
$495$	−2.30266	−0.103497
$496$	−0.431794	−0.0193881
$497$	0	0
$498$	−7.34511	−0.329142
$499$	12.4057	0.555356	0.277678	−	0.960674i	$-0.410435\pi$
$499$	12.4057	0.555356	0.277678	+	0.960674i	$0.410435\pi$
$500$	−5.65685	−0.252982
$501$	6.03140	0.269463
$502$	5.08292	0.226862
$503$	−2.84659	−0.126923	−0.0634617	−	0.997984i	$-0.520214\pi$
$503$	−2.84659	−0.126923	−0.0634617	+	0.997984i	$0.520214\pi$
$504$	0	0
$505$	4.51824	0.201059
$506$	−3.93089	−0.174750
$507$	−7.37470	−0.327522
$508$	13.0778	0.580232
$509$	−7.26692	−0.322100	−0.161050	−	0.986946i	$-0.551488\pi$
$509$	−7.26692	−0.322100	−0.161050	+	0.986946i	$0.551488\pi$
$510$	−2.61065	−0.115601
$511$	0	0
$512$	1.00000	0.0441942
$513$	1.56821	0.0692380
$514$	16.8480	0.743132
$515$	−3.38403	−0.149118
$516$	5.71312	0.251506
$517$	29.2065	1.28450
$518$	0	0
$519$	−18.7188	−0.821666
$520$	1.38935	0.0609271
$521$	−5.08015	−0.222565	−0.111283	−	0.993789i	$-0.535496\pi$
$521$	−5.08015	−0.222565	−0.111283	+	0.993789i	$0.535496\pi$
$522$	10.6053	0.464183
$523$	1.82647	0.0798658	0.0399329	−	0.999202i	$-0.487286\pi$
$523$	1.82647	0.0798658	0.0399329	+	0.999202i	$0.487286\pi$
$524$	−9.96484	−0.435316
$525$	0	0
$526$	−31.3137	−1.36534
$527$	1.92436	0.0838263
$528$	−3.93089	−0.171070
$529$	1.00000	0.0434783
$530$	4.33782	0.188423
$531$	12.6053	0.547025
$532$	0	0
$533$	22.0005	0.952949
$534$	16.7465	0.724691
$535$	8.13993	0.351920
$536$	−4.11351	−0.177677
$537$	−25.6884	−1.10854
$538$	13.6358	0.587879
$539$	0	0
$540$	0.585786	0.0252082
$541$	−24.5445	−1.05525	−0.527625	−	0.849478i	$-0.676917\pi$
$541$	−24.5445	−1.05525	−0.527625	+	0.849478i	$0.676917\pi$
$542$	−14.9042	−0.640191
$543$	−6.10443	−0.261966
$544$	−4.45666	−0.191078
$545$	−8.75278	−0.374928
$546$	0	0
$547$	18.6827	0.798814	0.399407	−	0.916774i	$-0.369216\pi$
$547$	18.6827	0.798814	0.399407	+	0.916774i	$0.369216\pi$
$548$	−18.9133	−0.807937
$549$	15.2760	0.651964
$550$	18.3056	0.780553
$551$	16.6313	0.708519
$552$	1.00000	0.0425628
$553$	0	0
$554$	−23.9542	−1.01772
$555$	2.61065	0.110816
$556$	10.8284	0.459228
$557$	3.05446	0.129422	0.0647108	−	0.997904i	$-0.479388\pi$
$557$	3.05446	0.129422	0.0647108	+	0.997904i	$0.479388\pi$
$558$	−0.431794	−0.0182793
$559$	13.5502	0.573112
$560$	0	0
$561$	17.5186	0.739638
$562$	−3.46139	−0.146010
$563$	32.2626	1.35971	0.679853	−	0.733349i	$-0.262044\pi$
$563$	32.2626	1.35971	0.679853	+	0.733349i	$0.262044\pi$
$564$	−7.42999	−0.312859
$565$	−9.54988	−0.401766
$566$	23.0464	0.968711
$567$	0	0
$568$	−11.5591	−0.485010
$569$	−1.96844	−0.0825214	−0.0412607	−	0.999148i	$-0.513137\pi$
$569$	−1.96844	−0.0825214	−0.0412607	+	0.999148i	$0.513137\pi$
$570$	0.918634	0.0384773
$571$	13.0971	0.548098	0.274049	−	0.961716i	$-0.411637\pi$
$571$	13.0971	0.548098	0.274049	+	0.961716i	$0.411637\pi$
$572$	−9.32318	−0.389822
$573$	−12.8156	−0.535379
$574$	0	0
$575$	−4.65685	−0.194204
$576$	1.00000	0.0416667
$577$	−6.57100	−0.273554	−0.136777	−	0.990602i	$-0.543674\pi$
$577$	−6.57100	−0.273554	−0.136777	+	0.990602i	$0.543674\pi$
$578$	2.86179	0.119035
$579$	9.15341	0.380403
$580$	6.21246	0.257958
$581$	0	0
$582$	12.9419	0.536461
$583$	−29.1088	−1.20556
$584$	10.5453	0.436368
$585$	1.38935	0.0574426
$586$	13.2813	0.548646
$587$	24.0134	0.991139	0.495569	−	0.868568i	$-0.334959\pi$
$587$	24.0134	0.991139	0.495569	+	0.868568i	$0.334959\pi$
$588$	0	0
$589$	−0.677142	−0.0279011
$590$	7.38403	0.303996
$591$	19.4209	0.798869
$592$	4.45666	0.183167
$593$	35.8205	1.47097	0.735485	−	0.677541i	$-0.236954\pi$
$593$	35.8205	1.47097	0.735485	+	0.677541i	$0.236954\pi$
$594$	−3.93089	−0.161287
$595$	0	0
$596$	−13.1469	−0.538517
$597$	−25.6387	−1.04932
$598$	2.37177	0.0969889
$599$	25.5502	1.04395	0.521976	−	0.852960i	$-0.325195\pi$
$599$	25.5502	1.04395	0.521976	+	0.852960i	$0.325195\pi$
$600$	−4.65685	−0.190115
$601$	47.1194	1.92204	0.961020	−	0.276479i	$-0.0891675\pi$
$601$	47.1194	1.92204	0.961020	+	0.276479i	$0.0891675\pi$
$602$	0	0
$603$	−4.11351	−0.167515
$604$	17.3857	0.707416
$605$	2.60788	0.106025
$606$	7.71312	0.313324
$607$	37.8197	1.53506	0.767528	−	0.641015i	$-0.221487\pi$
$607$	37.8197	1.53506	0.767528	+	0.641015i	$0.221487\pi$
$608$	1.56821	0.0635992
$609$	0	0
$610$	8.94847	0.362313
$611$	−17.6222	−0.712919
$612$	−4.45666	−0.180150
$613$	29.4549	1.18967	0.594835	−	0.803848i	$-0.297217\pi$
$613$	29.4549	1.18967	0.594835	+	0.803848i	$0.297217\pi$
$614$	−2.94095	−0.118687
$615$	5.43376	0.219110
$616$	0	0
$617$	−31.8266	−1.28129	−0.640646	−	0.767837i	$-0.721333\pi$
$617$	−31.8266	−1.28129	−0.640646	+	0.767837i	$0.721333\pi$
$618$	−5.77690	−0.232381
$619$	−40.0183	−1.60847	−0.804236	−	0.594310i	$-0.797425\pi$
$619$	−40.0183	−1.60847	−0.804236	+	0.594310i	$0.797425\pi$
$620$	−0.252939	−0.0101583
$621$	1.00000	0.0401286
$622$	25.9206	1.03932
$623$	0	0
$624$	2.37177	0.0949468
$625$	19.9706	0.798823
$626$	−13.6101	−0.543967
$627$	−6.16445	−0.246184
$628$	7.00850	0.279669
$629$	−19.8618	−0.791941
$630$	0	0
$631$	−46.5356	−1.85255	−0.926276	−	0.376847i	$-0.877008\pi$
$631$	−46.5356	−1.85255	−0.926276	+	0.376847i	$0.877008\pi$
$632$	3.21598	0.127925
$633$	−3.90227	−0.155101
$634$	22.3248	0.886629
$635$	7.66078	0.304009
$636$	7.40513	0.293633
$637$	0	0
$638$	−41.6884	−1.65046
$639$	−11.5591	−0.457272
$640$	0.585786	0.0231552
$641$	−24.3747	−0.962743	−0.481371	−	0.876517i	$-0.659861\pi$
$641$	−24.3747	−0.962743	−0.481371	+	0.876517i	$0.659861\pi$
$642$	13.8957	0.548421
$643$	−12.0886	−0.476730	−0.238365	−	0.971176i	$-0.576611\pi$
$643$	−12.0886	−0.476730	−0.238365	+	0.971176i	$0.576611\pi$
$644$	0	0
$645$	3.34667	0.131775
$646$	−6.98896	−0.274977
$647$	17.9652	0.706286	0.353143	−	0.935569i	$-0.385113\pi$
$647$	17.9652	0.706286	0.353143	+	0.935569i	$0.385113\pi$
$648$	1.00000	0.0392837
$649$	−49.5502	−1.94502
$650$	−11.0450	−0.433220
$651$	0	0
$652$	7.95952	0.311719
$653$	−2.98363	−0.116759	−0.0583793	−	0.998294i	$-0.518593\pi$
$653$	−2.98363	−0.116759	−0.0583793	+	0.998294i	$0.518593\pi$
$654$	−14.9419	−0.584276
$655$	−5.83727	−0.228081
$656$	9.27600	0.362167
$657$	10.5453	0.411412
$658$	0	0
$659$	−12.5806	−0.490072	−0.245036	−	0.969514i	$-0.578800\pi$
$659$	−12.5806	−0.490072	−0.245036	+	0.969514i	$0.578800\pi$
$660$	−2.30266	−0.0896311
$661$	−38.5194	−1.49823	−0.749115	−	0.662440i	$-0.769521\pi$
$661$	−38.5194	−1.49823	−0.749115	+	0.662440i	$0.769521\pi$
$662$	17.6569	0.686253
$663$	−10.5702	−0.410511
$664$	−7.34511	−0.285045
$665$	0	0
$666$	4.45666	0.172692
$667$	10.6053	0.410640
$668$	6.03140	0.233362
$669$	−4.79703	−0.185464
$670$	−2.40964	−0.0930925
$671$	−60.0483	−2.31814
$672$	0	0
$673$	13.3840	0.515916	0.257958	−	0.966156i	$-0.416950\pi$
$673$	13.3840	0.515916	0.257958	+	0.966156i	$0.416950\pi$
$674$	−3.25114	−0.125229
$675$	−4.65685	−0.179242
$676$	−7.37470	−0.283642
$677$	−4.41601	−0.169721	−0.0848606	−	0.996393i	$-0.527045\pi$
$677$	−4.41601	−0.169721	−0.0848606	+	0.996393i	$0.527045\pi$
$678$	−16.3027	−0.626100
$679$	0	0
$680$	−2.61065	−0.100114
$681$	26.4006	1.01167
$682$	1.69734	0.0649944
$683$	−39.9101	−1.52712	−0.763559	−	0.645738i	$-0.776550\pi$
$683$	−39.9101	−1.52712	−0.763559	+	0.645738i	$0.776550\pi$
$684$	1.56821	0.0599619
$685$	−11.0792	−0.423313
$686$	0	0
$687$	−2.91077	−0.111053
$688$	5.71312	0.217810
$689$	17.5633	0.669107
$690$	0.585786	0.0223005
$691$	31.1937	1.18666	0.593331	−	0.804958i	$-0.297812\pi$
$691$	31.1937	1.18666	0.593331	+	0.804958i	$0.297812\pi$
$692$	−18.7188	−0.711583
$693$	0	0
$694$	−16.5755	−0.629197
$695$	6.34315	0.240609
$696$	10.6053	0.401994
$697$	−41.3399	−1.56586
$698$	24.4882	0.926893
$699$	−6.54808	−0.247671
$700$	0	0
$701$	−14.7761	−0.558085	−0.279043	−	0.960279i	$-0.590017\pi$
$701$	−14.7761	−0.558085	−0.279043	+	0.960279i	$0.590017\pi$
$702$	2.37177	0.0895167
$703$	6.98896	0.263593
$704$	−3.93089	−0.148151
$705$	−4.35239	−0.163920
$706$	−20.1765	−0.759351
$707$	0	0
$708$	12.6053	0.473737
$709$	32.2928	1.21278	0.606390	−	0.795167i	$-0.292617\pi$
$709$	32.2928	1.21278	0.606390	+	0.795167i	$0.292617\pi$
$710$	−6.77118	−0.254118
$711$	3.21598	0.120609
$712$	16.7465	0.627601
$713$	−0.431794	−0.0161708
$714$	0	0
$715$	−5.46139	−0.204244
$716$	−25.6884	−0.960021
$717$	−28.4724	−1.06332
$718$	7.95952	0.297047
$719$	−25.7327	−0.959666	−0.479833	−	0.877360i	$-0.659303\pi$
$719$	−25.7327	−0.959666	−0.479833	+	0.877360i	$0.659303\pi$
$720$	0.585786	0.0218310
$721$	0	0
$722$	−16.5407	−0.615582
$723$	−21.6673	−0.805816
$724$	−6.10443	−0.226869
$725$	−49.3875	−1.83420
$726$	4.45192	0.165226
$727$	−0.623495	−0.0231241	−0.0115621	−	0.999933i	$-0.503680\pi$
$727$	−0.623495	−0.0231241	−0.0115621	+	0.999933i	$0.503680\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	6.17730	0.228632
$731$	−25.4614	−0.941724
$732$	15.2760	0.564617
$733$	32.7449	1.20946	0.604731	−	0.796430i	$-0.293281\pi$
$733$	32.7449	1.20946	0.604731	+	0.796430i	$0.293281\pi$
$734$	−17.3986	−0.642194
$735$	0	0
$736$	1.00000	0.0368605
$737$	16.1698	0.595621
$738$	9.27600	0.341454
$739$	34.8270	1.28113	0.640566	−	0.767903i	$-0.278700\pi$
$739$	34.8270	1.28113	0.640566	+	0.767903i	$0.278700\pi$
$740$	2.61065	0.0959694
$741$	3.71943	0.136636
$742$	0	0
$743$	7.38575	0.270957	0.135478	−	0.990780i	$-0.456743\pi$
$743$	7.38575	0.270957	0.135478	+	0.990780i	$0.456743\pi$
$744$	−0.431794	−0.0158303
$745$	−7.70126	−0.282152
$746$	19.7427	0.722833
$747$	−7.34511	−0.268743
$748$	17.5186	0.640545
$749$	0	0
$750$	−5.65685	−0.206559
$751$	26.9800	0.984515	0.492258	−	0.870450i	$-0.336172\pi$
$751$	26.9800	0.984515	0.492258	+	0.870450i	$0.336172\pi$
$752$	−7.42999	−0.270944
$753$	5.08292	0.185232
$754$	25.1534	0.916033
$755$	10.1843	0.370646
$756$	0	0
$757$	0.577876	0.0210033	0.0105016	−	0.999945i	$-0.496657\pi$
$757$	0.577876	0.0210033	0.0105016	+	0.999945i	$0.496657\pi$
$758$	−5.03967	−0.183049
$759$	−3.93089	−0.142682
$760$	0.918634	0.0333224
$761$	7.36981	0.267155	0.133578	−	0.991038i	$-0.457353\pi$
$761$	7.36981	0.267155	0.133578	+	0.991038i	$0.457353\pi$
$762$	13.0778	0.473757
$763$	0	0
$764$	−12.8156	−0.463651
$765$	−2.61065	−0.0943882
$766$	−34.6017	−1.25021
$767$	29.8969	1.07952
$768$	1.00000	0.0360844
$769$	15.0011	0.540955	0.270477	−	0.962726i	$-0.412818\pi$
$769$	15.0011	0.540955	0.270477	+	0.962726i	$0.412818\pi$
$770$	0	0
$771$	16.8480	0.606765
$772$	9.15341	0.329438
$773$	−15.5013	−0.557543	−0.278772	−	0.960357i	$-0.589927\pi$
$773$	−15.5013	−0.557543	−0.278772	+	0.960357i	$0.589927\pi$
$774$	5.71312	0.205354
$775$	2.01080	0.0722301
$776$	12.9419	0.464588
$777$	0	0
$778$	11.6598	0.418024
$779$	14.5467	0.521189
$780$	1.38935	0.0497467
$781$	45.4377	1.62589
$782$	−4.45666	−0.159370
$783$	10.6053	0.379004
$784$	0	0
$785$	4.10548	0.146531
$786$	−9.96484	−0.355434
$787$	−19.3767	−0.690704	−0.345352	−	0.938473i	$-0.612240\pi$
$787$	−19.3767	−0.690704	−0.345352	+	0.938473i	$0.612240\pi$
$788$	19.4209	0.691841
$789$	−31.3137	−1.11480
$790$	1.88388	0.0670253
$791$	0	0
$792$	−3.93089	−0.139678
$793$	36.2312	1.28661
$794$	8.80372	0.312432
$795$	4.33782	0.153847
$796$	−25.6387	−0.908739
$797$	−50.6436	−1.79389	−0.896944	−	0.442144i	$-0.854218\pi$
$797$	−50.6436	−1.79389	−0.896944	+	0.442144i	$0.854218\pi$
$798$	0	0
$799$	33.1129	1.17145
$800$	−4.65685	−0.164645
$801$	16.7465	0.591708
$802$	12.9800	0.458341
$803$	−41.4525	−1.46283
$804$	−4.11351	−0.145072
$805$	0	0
$806$	−1.02412	−0.0360730
$807$	13.6358	0.480001
$808$	7.71312	0.271346
$809$	−14.7530	−0.518688	−0.259344	−	0.965785i	$-0.583506\pi$
$809$	−14.7530	−0.518688	−0.259344	+	0.965785i	$0.583506\pi$
$810$	0.585786	0.0205824
$811$	1.24699	0.0437877	0.0218939	−	0.999760i	$-0.493030\pi$
$811$	1.24699	0.0437877	0.0218939	+	0.999760i	$0.493030\pi$
$812$	0	0
$813$	−14.9042	−0.522714
$814$	−17.5186	−0.614028
$815$	4.66258	0.163323
$816$	−4.45666	−0.156014
$817$	8.95934	0.313448
$818$	18.9957	0.664167
$819$	0	0
$820$	5.43376	0.189755
$821$	28.9652	1.01089	0.505447	−	0.862858i	$-0.331328\pi$
$821$	28.9652	1.01089	0.505447	+	0.862858i	$0.331328\pi$
$822$	−18.9133	−0.659678
$823$	30.3820	1.05905	0.529525	−	0.848294i	$-0.322370\pi$
$823$	30.3820	1.05905	0.529525	+	0.848294i	$0.322370\pi$
$824$	−5.77690	−0.201248
$825$	18.3056	0.637319
$826$	0	0
$827$	30.6286	1.06506	0.532531	−	0.846411i	$-0.321241\pi$
$827$	30.6286	1.06506	0.532531	+	0.846411i	$0.321241\pi$
$828$	1.00000	0.0347524
$829$	−5.36487	−0.186330	−0.0931649	−	0.995651i	$-0.529698\pi$
$829$	−5.36487	−0.186330	−0.0931649	+	0.995651i	$0.529698\pi$
$830$	−4.30266	−0.149348
$831$	−23.9542	−0.830962
$832$	2.37177	0.0822264
$833$	0	0
$834$	10.8284	0.374958
$835$	3.53311	0.122268
$836$	−6.16445	−0.213202
$837$	−0.431794	−0.0149250
$838$	−19.2566	−0.665209
$839$	−14.2306	−0.491296	−0.245648	−	0.969359i	$-0.579001\pi$
$839$	−14.2306	−0.491296	−0.245648	+	0.969359i	$0.579001\pi$
$840$	0	0
$841$	83.4730	2.87838
$842$	11.1078	0.382800
$843$	−3.46139	−0.119217
$844$	−3.90227	−0.134322
$845$	−4.32000	−0.148613
$846$	−7.42999	−0.255448
$847$	0	0
$848$	7.40513	0.254293
$849$	23.0464	0.790949
$850$	20.7540	0.711856
$851$	4.45666	0.152772
$852$	−11.5591	−0.396009
$853$	6.59879	0.225938	0.112969	−	0.993598i	$-0.463964\pi$
$853$	6.59879	0.225938	0.112969	+	0.993598i	$0.463964\pi$
$854$	0	0
$855$	0.918634	0.0314166
$856$	13.8957	0.474946
$857$	13.2280	0.451860	0.225930	−	0.974144i	$-0.427458\pi$
$857$	13.2280	0.451860	0.225930	+	0.974144i	$0.427458\pi$
$858$	−9.32318	−0.318288
$859$	−38.3692	−1.30914	−0.654569	−	0.756002i	$-0.727150\pi$
$859$	−38.3692	−1.30914	−0.654569	+	0.756002i	$0.727150\pi$
$860$	3.34667	0.114120
$861$	0	0
$862$	−14.7656	−0.502919
$863$	−55.3143	−1.88292	−0.941460	−	0.337126i	$-0.890545\pi$
$863$	−55.3143	−1.88292	−0.941460	+	0.337126i	$0.890545\pi$
$864$	1.00000	0.0340207
$865$	−10.9652	−0.372829
$866$	5.51571	0.187431
$867$	2.86179	0.0971914
$868$	0	0
$869$	−12.6417	−0.428839
$870$	6.21246	0.210622
$871$	−9.75630	−0.330580
$872$	−14.9419	−0.505998
$873$	12.9419	0.438018
$874$	1.56821	0.0530454
$875$	0	0
$876$	10.5453	0.356293
$877$	−29.0099	−0.979594	−0.489797	−	0.871837i	$-0.662929\pi$
$877$	−29.0099	−0.979594	−0.489797	+	0.871837i	$0.662929\pi$
$878$	4.98912	0.168374
$879$	13.2813	0.447968
$880$	−2.30266	−0.0776228
$881$	−56.4179	−1.90077	−0.950384	−	0.311081i	$-0.899309\pi$
$881$	−56.4179	−1.90077	−0.950384	+	0.311081i	$0.899309\pi$
$882$	0	0
$883$	21.9690	0.739315	0.369658	−	0.929168i	$-0.379475\pi$
$883$	21.9690	0.739315	0.369658	+	0.929168i	$0.379475\pi$
$884$	−10.5702	−0.355513
$885$	7.38403	0.248211
$886$	10.7382	0.360758
$887$	−12.7844	−0.429258	−0.214629	−	0.976696i	$-0.568854\pi$
$887$	−12.7844	−0.429258	−0.214629	+	0.976696i	$0.568854\pi$
$888$	4.45666	0.149556
$889$	0	0
$890$	9.80986	0.328827
$891$	−3.93089	−0.131690
$892$	−4.79703	−0.160616
$893$	−11.6518	−0.389911
$894$	−13.1469	−0.439697
$895$	−15.0479	−0.502997
$896$	0	0
$897$	2.37177	0.0791911
$898$	−30.0924	−1.00420
$899$	−4.57932	−0.152729
$900$	−4.65685	−0.155228
$901$	−33.0021	−1.09946
$902$	−36.4630	−1.21408
$903$	0	0
$904$	−16.3027	−0.542219
$905$	−3.57589	−0.118867
$906$	17.3857	0.577603
$907$	27.8349	0.924242	0.462121	−	0.886817i	$-0.347089\pi$
$907$	27.8349	0.924242	0.462121	+	0.886817i	$0.347089\pi$
$908$	26.4006	0.876133
$909$	7.71312	0.255828
$910$	0	0
$911$	48.2181	1.59754	0.798768	−	0.601639i	$-0.205485\pi$
$911$	48.2181	1.59754	0.798768	+	0.601639i	$0.205485\pi$
$912$	1.56821	0.0519285
$913$	28.8728	0.955551
$914$	−21.8618	−0.723124
$915$	8.94847	0.295827
$916$	−2.91077	−0.0961744
$917$	0	0
$918$	−4.45666	−0.147092
$919$	−30.0941	−0.992714	−0.496357	−	0.868119i	$-0.665329\pi$
$919$	−30.0941	−0.992714	−0.496357	+	0.868119i	$0.665329\pi$
$920$	0.585786	0.0193128
$921$	−2.94095	−0.0969076
$922$	−20.9238	−0.689088
$923$	−27.4156	−0.902395
$924$	0	0
$925$	−20.7540	−0.682387
$926$	3.73422	0.122714
$927$	−5.77690	−0.189738
$928$	10.6053	0.348137
$929$	7.98438	0.261959	0.130980	−	0.991385i	$-0.458188\pi$
$929$	7.98438	0.261959	0.130980	+	0.991385i	$0.458188\pi$
$930$	−0.252939	−0.00829420
$931$	0	0
$932$	−6.54808	−0.214489
$933$	25.9206	0.848602
$934$	12.9042	0.422239
$935$	10.2622	0.335609
$936$	2.37177	0.0775238
$937$	−17.4146	−0.568910	−0.284455	−	0.958689i	$-0.591813\pi$
$937$	−17.4146	−0.568910	−0.284455	+	0.958689i	$0.591813\pi$
$938$	0	0
$939$	−13.6101	−0.444148
$940$	−4.35239	−0.141959
$941$	36.8310	1.20066	0.600328	−	0.799754i	$-0.295037\pi$
$941$	36.8310	1.20066	0.600328	+	0.799754i	$0.295037\pi$
$942$	7.00850	0.228349
$943$	9.27600	0.302068
$944$	12.6053	0.410268
$945$	0	0
$946$	−22.4576	−0.730161
$947$	−9.61637	−0.312490	−0.156245	−	0.987718i	$-0.549939\pi$
$947$	−9.61637	−0.312490	−0.156245	+	0.987718i	$0.549939\pi$
$948$	3.21598	0.104450
$949$	25.0110	0.811893
$950$	−7.30291	−0.236938
$951$	22.3248	0.723930
$952$	0	0
$953$	−34.5964	−1.12069	−0.560344	−	0.828260i	$-0.689331\pi$
$953$	−34.5964	−1.12069	−0.560344	+	0.828260i	$0.689331\pi$
$954$	7.40513	0.239750
$955$	−7.50719	−0.242927
$956$	−28.4724	−0.920864
$957$	−41.6884	−1.34759
$958$	−35.0298	−1.13176
$959$	0	0
$960$	0.585786	0.0189062
$961$	−30.8136	−0.993986
$962$	10.5702	0.340796
$963$	13.8957	0.447784
$964$	−21.6673	−0.697857
$965$	5.36194	0.172607
$966$	0	0
$967$	−29.1146	−0.936264	−0.468132	−	0.883659i	$-0.655073\pi$
$967$	−29.1146	−0.936264	−0.468132	+	0.883659i	$0.655073\pi$
$968$	4.45192	0.143090
$969$	−6.98896	−0.224518
$970$	7.58121	0.243418
$971$	−20.7601	−0.666225	−0.333112	−	0.942887i	$-0.608099\pi$
$971$	−20.7601	−0.666225	−0.333112	+	0.942887i	$0.608099\pi$
$972$	1.00000	0.0320750
$973$	0	0
$974$	0.195463	0.00626305
$975$	−11.0450	−0.353723
$976$	15.2760	0.488973
$977$	47.8582	1.53112	0.765559	−	0.643365i	$-0.222462\pi$
$977$	47.8582	1.53112	0.765559	+	0.643365i	$0.222462\pi$
$978$	7.95952	0.254517
$979$	−65.8286	−2.10389
$980$	0	0
$981$	−14.9419	−0.477059
$982$	18.0519	0.576060
$983$	47.2959	1.50850	0.754252	−	0.656585i	$-0.228000\pi$
$983$	47.2959	1.50850	0.754252	+	0.656585i	$0.228000\pi$
$984$	9.27600	0.295708
$985$	11.3765	0.362486
$986$	−47.2643	−1.50520
$987$	0	0
$988$	3.71943	0.118331
$989$	5.71312	0.181666
$990$	−2.30266	−0.0731835
$991$	−19.3530	−0.614769	−0.307384	−	0.951585i	$-0.599454\pi$
$991$	−19.3530	−0.614769	−0.307384	+	0.951585i	$0.599454\pi$
$992$	−0.431794	−0.0137095
$993$	17.6569	0.560323
$994$	0	0
$995$	−15.0188	−0.476128
$996$	−7.34511	−0.232739
$997$	−32.4957	−1.02915	−0.514575	−	0.857445i	$-0.672050\pi$
$997$	−32.4957	−1.02915	−0.514575	+	0.857445i	$0.672050\pi$
$998$	12.4057	0.392696
$999$	4.45666	0.141002

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6762.2.a.ct.1.1	yes	4
7.6	odd	2		6762.2.a.ci.1.3	✓	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6762.2.a.ci.1.3	✓	4	7.6	odd	2
6762.2.a.ct.1.1	yes	4	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:	\( N \)	\(=\)	\( 6762 = 2 \cdot 3 \cdot 7^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6762.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +0.585786 q^{5} +1.00000 q^{6} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +0.585786 q^{5} +1.00000 q^{6} +1.00000 q^{8} +1.00000 q^{9} +0.585786 q^{10} -3.93089 q^{11} +1.00000 q^{12} +2.37177 q^{13} +0.585786 q^{15} +1.00000 q^{16} -4.45666 q^{17} +1.00000 q^{18} +1.56821 q^{19} +0.585786 q^{20} -3.93089 q^{22} +1.00000 q^{23} +1.00000 q^{24} -4.65685 q^{25} +2.37177 q^{26} +1.00000 q^{27} +10.6053 q^{29} +0.585786 q^{30} -0.431794 q^{31} +1.00000 q^{32} -3.93089 q^{33} -4.45666 q^{34} +1.00000 q^{36} +4.45666 q^{37} +1.56821 q^{38} +2.37177 q^{39} +0.585786 q^{40} +9.27600 q^{41} +5.71312 q^{43} -3.93089 q^{44} +0.585786 q^{45} +1.00000 q^{46} -7.42999 q^{47} +1.00000 q^{48} -4.65685 q^{50} -4.45666 q^{51} +2.37177 q^{52} +7.40513 q^{53} +1.00000 q^{54} -2.30266 q^{55} +1.56821 q^{57} +10.6053 q^{58} +12.6053 q^{59} +0.585786 q^{60} +15.2760 q^{61} -0.431794 q^{62} +1.00000 q^{64} +1.38935 q^{65} -3.93089 q^{66} -4.11351 q^{67} -4.45666 q^{68} +1.00000 q^{69} -11.5591 q^{71} +1.00000 q^{72} +10.5453 q^{73} +4.45666 q^{74} -4.65685 q^{75} +1.56821 q^{76} +2.37177 q^{78} +3.21598 q^{79} +0.585786 q^{80} +1.00000 q^{81} +9.27600 q^{82} -7.34511 q^{83} -2.61065 q^{85} +5.71312 q^{86} +10.6053 q^{87} -3.93089 q^{88} +16.7465 q^{89} +0.585786 q^{90} +1.00000 q^{92} -0.431794 q^{93} -7.42999 q^{94} +0.918634 q^{95} +1.00000 q^{96} +12.9419 q^{97} -3.93089 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 4 q^{2} + 4 q^{3} + 4 q^{4} + 8 q^{5} + 4 q^{6} + 4 q^{8} + 4 q^{9}+O(q^{10}) \) 4 * q + 4 * q^2 + 4 * q^3 + 4 * q^4 + 8 * q^5 + 4 * q^6 + 4 * q^8 + 4 * q^9	\( 4 q + 4 q^{2} + 4 q^{3} + 4 q^{4} + 8 q^{5} + 4 q^{6} + 4 q^{8} + 4 q^{9} + 8 q^{10} + 4 q^{11} + 4 q^{12} + 12 q^{13} + 8 q^{15} + 4 q^{16} - 4 q^{17} + 4 q^{18} + 4 q^{19} + 8 q^{20} + 4 q^{22} + 4 q^{23} + 4 q^{24} + 4 q^{25} + 12 q^{26} + 4 q^{27} + 8 q^{29} + 8 q^{30} - 4 q^{31} + 4 q^{32} + 4 q^{33} - 4 q^{34} + 4 q^{36} + 4 q^{37} + 4 q^{38} + 12 q^{39} + 8 q^{40} - 8 q^{41} + 4 q^{43} + 4 q^{44} + 8 q^{45} + 4 q^{46} + 12 q^{47} + 4 q^{48} + 4 q^{50} - 4 q^{51} + 12 q^{52} + 4 q^{53} + 4 q^{54} + 8 q^{55} + 4 q^{57} + 8 q^{58} + 16 q^{59} + 8 q^{60} + 16 q^{61} - 4 q^{62} + 4 q^{64} + 16 q^{65} + 4 q^{66} + 20 q^{67} - 4 q^{68} + 4 q^{69} - 24 q^{71} + 4 q^{72} + 8 q^{73} + 4 q^{74} + 4 q^{75} + 4 q^{76} + 12 q^{78} - 32 q^{79} + 8 q^{80} + 4 q^{81} - 8 q^{82} - 4 q^{83} + 4 q^{86} + 8 q^{87} + 4 q^{88} + 20 q^{89} + 8 q^{90} + 4 q^{92} - 4 q^{93} + 12 q^{94} + 4 q^{96} + 4 q^{97} + 4 q^{99}+O(q^{100}) \) 4 * q + 4 * q^2 + 4 * q^3 + 4 * q^4 + 8 * q^5 + 4 * q^6 + 4 * q^8 + 4 * q^9 + 8 * q^10 + 4 * q^11 + 4 * q^12 + 12 * q^13 + 8 * q^15 + 4 * q^16 - 4 * q^17 + 4 * q^18 + 4 * q^19 + 8 * q^20 + 4 * q^22 + 4 * q^23 + 4 * q^24 + 4 * q^25 + 12 * q^26 + 4 * q^27 + 8 * q^29 + 8 * q^30 - 4 * q^31 + 4 * q^32 + 4 * q^33 - 4 * q^34 + 4 * q^36 + 4 * q^37 + 4 * q^38 + 12 * q^39 + 8 * q^40 - 8 * q^41 + 4 * q^43 + 4 * q^44 + 8 * q^45 + 4 * q^46 + 12 * q^47 + 4 * q^48 + 4 * q^50 - 4 * q^51 + 12 * q^52 + 4 * q^53 + 4 * q^54 + 8 * q^55 + 4 * q^57 + 8 * q^58 + 16 * q^59 + 8 * q^60 + 16 * q^61 - 4 * q^62 + 4 * q^64 + 16 * q^65 + 4 * q^66 + 20 * q^67 - 4 * q^68 + 4 * q^69 - 24 * q^71 + 4 * q^72 + 8 * q^73 + 4 * q^74 + 4 * q^75 + 4 * q^76 + 12 * q^78 - 32 * q^79 + 8 * q^80 + 4 * q^81 - 8 * q^82 - 4 * q^83 + 4 * q^86 + 8 * q^87 + 4 * q^88 + 20 * q^89 + 8 * q^90 + 4 * q^92 - 4 * q^93 + 12 * q^94 + 4 * q^96 + 4 * q^97 + 4 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more