LMFDB - Embedded newform 6762.2.a.ck.1.4

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:	$1$
Dimension:	$4$
Coefficient field:	4.4.10304.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 2x^{3} - 7x^{2} + 8x + 8 $ x^4 - 2x^3 - 7x^2 + 8*x + 8
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$1.69230$ 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)

$f(q)$	$=$	$q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +3.10651 q^{5} -1.00000 q^{6} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +3.10651 q^{5} -1.00000 q^{6} +1.00000 q^{8} +1.00000 q^{9} +3.10651 q^{10} -5.77786 q^{11} -1.00000 q^{12} -6.91399 q^{13} -3.10651 q^{15} +1.00000 q^{16} -1.17157 q^{17} +1.00000 q^{18} +6.75692 q^{19} +3.10651 q^{20} -5.77786 q^{22} +1.00000 q^{23} -1.00000 q^{24} +4.65041 q^{25} -6.91399 q^{26} -1.00000 q^{27} -3.25714 q^{29} -3.10651 q^{30} -8.79881 q^{31} +1.00000 q^{32} +5.77786 q^{33} -1.17157 q^{34} +1.00000 q^{36} +6.04368 q^{37} +6.75692 q^{38} +6.91399 q^{39} +3.10651 q^{40} -1.94405 q^{41} +8.41960 q^{43} -5.77786 q^{44} +3.10651 q^{45} +1.00000 q^{46} +1.68003 q^{47} -1.00000 q^{48} +4.65041 q^{50} +1.17157 q^{51} -6.91399 q^{52} -9.16246 q^{53} -1.00000 q^{54} -17.9490 q^{55} -6.75692 q^{57} -3.25714 q^{58} +3.26358 q^{59} -3.10651 q^{60} +6.81616 q^{61} -8.79881 q^{62} +1.00000 q^{64} -21.4784 q^{65} +5.77786 q^{66} +0.769189 q^{67} -1.17157 q^{68} -1.00000 q^{69} -0.393270 q^{71} +1.00000 q^{72} -10.4557 q^{73} +6.04368 q^{74} -4.65041 q^{75} +6.75692 q^{76} +6.91399 q^{78} -5.94900 q^{79} +3.10651 q^{80} +1.00000 q^{81} -1.94405 q^{82} -11.1921 q^{83} -3.63950 q^{85} +8.41960 q^{86} +3.25714 q^{87} -5.77786 q^{88} -13.9490 q^{89} +3.10651 q^{90} +1.00000 q^{92} +8.79881 q^{93} +1.68003 q^{94} +20.9904 q^{95} -1.00000 q^{96} -16.1949 q^{97} -5.77786 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 4 q^{2} - 4 q^{3} + 4 q^{4} + 2 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 + 2 * q^5 - 4 * q^6 + 4 * q^8 + 4 * q^9	$ 4 q + 4 q^{2} - 4 q^{3} + 4 q^{4} + 2 q^{5} - 4 q^{6} + 4 q^{8} + 4 q^{9} + 2 q^{10} - 4 q^{11} - 4 q^{12} - 2 q^{13} - 2 q^{15} + 4 q^{16} - 16 q^{17} + 4 q^{18} + 4 q^{19} + 2 q^{20} - 4 q^{22} + 4 q^{23} - 4 q^{24} + 6 q^{25} - 2 q^{26} - 4 q^{27} - 10 q^{29} - 2 q^{30} - 20 q^{31} + 4 q^{32} + 4 q^{33} - 16 q^{34} + 4 q^{36} + 2 q^{37} + 4 q^{38} + 2 q^{39} + 2 q^{40} - 26 q^{41} + 2 q^{43} - 4 q^{44} + 2 q^{45} + 4 q^{46} - 2 q^{47} - 4 q^{48} + 6 q^{50} + 16 q^{51} - 2 q^{52} - 8 q^{53} - 4 q^{54} - 24 q^{55} - 4 q^{57} - 10 q^{58} - 2 q^{60} + 12 q^{61} - 20 q^{62} + 4 q^{64} - 22 q^{65} + 4 q^{66} - 16 q^{67} - 16 q^{68} - 4 q^{69} + 8 q^{71} + 4 q^{72} - 4 q^{73} + 2 q^{74} - 6 q^{75} + 4 q^{76} + 2 q^{78} + 24 q^{79} + 2 q^{80} + 4 q^{81} - 26 q^{82} - 20 q^{83} + 8 q^{85} + 2 q^{86} + 10 q^{87} - 4 q^{88} - 8 q^{89} + 2 q^{90} + 4 q^{92} + 20 q^{93} - 2 q^{94} + 4 q^{95} - 4 q^{96} - 26 q^{97} - 4 q^{99}+O(q^{100}) $ 4 * q + 4 * q^2 - 4 * q^3 + 4 * q^4 + 2 * q^5 - 4 * q^6 + 4 * q^8 + 4 * q^9 + 2 * q^10 - 4 * q^11 - 4 * q^12 - 2 * q^13 - 2 * q^15 + 4 * q^16 - 16 * q^17 + 4 * q^18 + 4 * q^19 + 2 * q^20 - 4 * q^22 + 4 * q^23 - 4 * q^24 + 6 * q^25 - 2 * q^26 - 4 * q^27 - 10 * q^29 - 2 * q^30 - 20 * q^31 + 4 * q^32 + 4 * q^33 - 16 * q^34 + 4 * q^36 + 2 * q^37 + 4 * q^38 + 2 * q^39 + 2 * q^40 - 26 * q^41 + 2 * q^43 - 4 * q^44 + 2 * q^45 + 4 * q^46 - 2 * q^47 - 4 * q^48 + 6 * q^50 + 16 * q^51 - 2 * q^52 - 8 * q^53 - 4 * q^54 - 24 * q^55 - 4 * q^57 - 10 * q^58 - 2 * q^60 + 12 * q^61 - 20 * q^62 + 4 * q^64 - 22 * q^65 + 4 * q^66 - 16 * q^67 - 16 * q^68 - 4 * q^69 + 8 * q^71 + 4 * q^72 - 4 * q^73 + 2 * q^74 - 6 * q^75 + 4 * q^76 + 2 * q^78 + 24 * q^79 + 2 * q^80 + 4 * q^81 - 26 * q^82 - 20 * q^83 + 8 * q^85 + 2 * q^86 + 10 * q^87 - 4 * q^88 - 8 * q^89 + 2 * q^90 + 4 * q^92 + 20 * q^93 - 2 * q^94 + 4 * q^95 - 4 * q^96 - 26 * 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
$5$	3.10651	1.38927	0.694637	−	0.719360i	$-0.255565\pi$
$5$	3.10651	1.38927	0.694637	+	0.719360i	$0.255565\pi$
$6$	−1.00000	−0.408248
$7$	0	0
$7$	0	0
$8$	1.00000	0.353553
$9$	1.00000	0.333333
$10$	3.10651	0.982365
$11$	−5.77786	−1.74209	−0.871046	−	0.491202i	$-0.836558\pi$
$11$	−5.77786	−1.74209	−0.871046	+	0.491202i	$0.836558\pi$
$12$	−1.00000	−0.288675
$13$	−6.91399	−1.91760	−0.958798	−	0.284087i	$-0.908310\pi$
$13$	−6.91399	−1.91760	−0.958798	+	0.284087i	$0.908310\pi$
$14$	0	0
$15$	−3.10651	−0.802098
$16$	1.00000	0.250000
$17$	−1.17157	−0.284148	−0.142074	−	0.989856i	$-0.545377\pi$
$17$	−1.17157	−0.284148	−0.142074	+	0.989856i	$0.545377\pi$
$18$	1.00000	0.235702
$19$	6.75692	1.55014	0.775072	−	0.631873i	$-0.217714\pi$
$19$	6.75692	1.55014	0.775072	+	0.631873i	$0.217714\pi$
$20$	3.10651	0.694637
$21$	0	0
$22$	−5.77786	−1.23184
$23$	1.00000	0.208514
$23$	1.00000	0.208514
$24$	−1.00000	−0.204124
$25$	4.65041	0.930082
$26$	−6.91399	−1.35595
$27$	−1.00000	−0.192450
$28$	0	0
$29$	−3.25714	−0.604836	−0.302418	−	0.953175i	$-0.597794\pi$
$29$	−3.25714	−0.604836	−0.302418	+	0.953175i	$0.597794\pi$
$30$	−3.10651	−0.567169
$31$	−8.79881	−1.58031	−0.790156	−	0.612905i	$-0.790001\pi$
$31$	−8.79881	−1.58031	−0.790156	+	0.612905i	$0.790001\pi$
$32$	1.00000	0.176777
$33$	5.77786	1.00580
$34$	−1.17157	−0.200923
$35$	0	0
$36$	1.00000	0.166667
$37$	6.04368	0.993575	0.496787	−	0.867872i	$-0.334513\pi$
$37$	6.04368	0.993575	0.496787	+	0.867872i	$0.334513\pi$
$38$	6.75692	1.09612
$39$	6.91399	1.10713
$40$	3.10651	0.491182
$41$	−1.94405	−0.303610	−0.151805	−	0.988410i	$-0.548509\pi$
$41$	−1.94405	−0.303610	−0.151805	+	0.988410i	$0.548509\pi$
$42$	0	0
$43$	8.41960	1.28398	0.641988	−	0.766714i	$-0.278110\pi$
$43$	8.41960	1.28398	0.641988	+	0.766714i	$0.278110\pi$
$44$	−5.77786	−0.871046
$45$	3.10651	0.463091
$46$	1.00000	0.147442
$47$	1.68003	0.245057	0.122529	−	0.992465i	$-0.460900\pi$
$47$	1.68003	0.245057	0.122529	+	0.992465i	$0.460900\pi$
$48$	−1.00000	−0.144338
$49$	0	0
$50$	4.65041	0.657667
$51$	1.17157	0.164053
$52$	−6.91399	−0.958798
$53$	−9.16246	−1.25856	−0.629280	−	0.777178i	$-0.716650\pi$
$53$	−9.16246	−1.25856	−0.629280	+	0.777178i	$0.716650\pi$
$54$	−1.00000	−0.136083
$55$	−17.9490	−2.42024
$56$	0	0
$57$	−6.75692	−0.894976
$58$	−3.25714	−0.427683
$59$	3.26358	0.424883	0.212441	−	0.977174i	$-0.431859\pi$
$59$	3.26358	0.424883	0.212441	+	0.977174i	$0.431859\pi$
$60$	−3.10651	−0.401049
$61$	6.81616	0.872720	0.436360	−	0.899772i	$-0.356267\pi$
$61$	6.81616	0.872720	0.436360	+	0.899772i	$0.356267\pi$
$62$	−8.79881	−1.11745
$63$	0	0
$64$	1.00000	0.125000
$65$	−21.4784	−2.66407
$66$	5.77786	0.711206
$67$	0.769189	0.0939714	0.0469857	−	0.998896i	$-0.485038\pi$
$67$	0.769189	0.0939714	0.0469857	+	0.998896i	$0.485038\pi$
$68$	−1.17157	−0.142074
$69$	−1.00000	−0.120386
$70$	0	0
$71$	−0.393270	−0.0466725	−0.0233363	−	0.999728i	$-0.507429\pi$
$71$	−0.393270	−0.0466725	−0.0233363	+	0.999728i	$0.507429\pi$
$72$	1.00000	0.117851
$73$	−10.4557	−1.22374	−0.611871	−	0.790957i	$-0.709583\pi$
$73$	−10.4557	−1.22374	−0.611871	+	0.790957i	$0.709583\pi$
$74$	6.04368	0.702563
$75$	−4.65041	−0.536983
$76$	6.75692	0.775072
$77$	0	0
$78$	6.91399	0.782856
$79$	−5.94900	−0.669315	−0.334657	−	0.942340i	$-0.608621\pi$
$79$	−5.94900	−0.669315	−0.334657	+	0.942340i	$0.608621\pi$
$80$	3.10651	0.347318
$81$	1.00000	0.111111
$82$	−1.94405	−0.214685
$83$	−11.1921	−1.22849	−0.614245	−	0.789115i	$-0.710539\pi$
$83$	−11.1921	−1.22849	−0.614245	+	0.789115i	$0.710539\pi$
$84$	0	0
$85$	−3.63950	−0.394760
$86$	8.41960	0.907909
$87$	3.25714	0.349202
$88$	−5.77786	−0.615922
$89$	−13.9490	−1.47859	−0.739295	−	0.673381i	$-0.764841\pi$
$89$	−13.9490	−1.47859	−0.739295	+	0.673381i	$0.764841\pi$
$90$	3.10651	0.327455
$91$	0	0
$92$	1.00000	0.104257
$93$	8.79881	0.912394
$94$	1.68003	0.173282
$95$	20.9904	2.15357
$96$	−1.00000	−0.102062
$97$	−16.1949	−1.64435	−0.822173	−	0.569238i	$-0.807238\pi$
$97$	−16.1949	−1.64435	−0.822173	+	0.569238i	$0.807238\pi$
$98$	0	0
$99$	−5.77786	−0.580697
$100$	4.65041	0.465041
$101$	−17.6349	−1.75473	−0.877367	−	0.479821i	$-0.840702\pi$
$101$	−17.6349	−1.75473	−0.877367	+	0.479821i	$0.840702\pi$
$102$	1.17157	0.116003
$103$	−15.4702	−1.52432	−0.762160	−	0.647389i	$-0.775861\pi$
$103$	−15.4702	−1.52432	−0.762160	+	0.647389i	$0.775861\pi$
$104$	−6.91399	−0.677973
$105$	0	0
$106$	−9.16246	−0.889937
$107$	−4.00000	−0.386695	−0.193347	−	0.981130i	$-0.561934\pi$
$107$	−4.00000	−0.386695	−0.193347	+	0.981130i	$0.561934\pi$
$108$	−1.00000	−0.0962250
$109$	−18.9840	−1.81834	−0.909169	−	0.416428i	$-0.863282\pi$
$109$	−18.9840	−1.81834	−0.909169	+	0.416428i	$0.863282\pi$
$110$	−17.9490	−1.71137
$111$	−6.04368	−0.573641
$112$	0	0
$113$	17.8215	1.67651	0.838255	−	0.545279i	$-0.183576\pi$
$113$	17.8215	1.67651	0.838255	+	0.545279i	$0.183576\pi$
$114$	−6.75692	−0.632844
$115$	3.10651	0.289684
$116$	−3.25714	−0.302418
$117$	−6.91399	−0.639199
$118$	3.26358	0.300437
$119$	0	0
$120$	−3.10651	−0.283584
$121$	22.3837	2.03488
$122$	6.81616	0.617106
$123$	1.94405	0.175289
$124$	−8.79881	−0.790156
$125$	−1.08601	−0.0971353
$126$	0	0
$127$	−8.83022	−0.783555	−0.391778	−	0.920060i	$-0.628140\pi$
$127$	−8.83022	−0.783555	−0.391778	+	0.920060i	$0.628140\pi$
$128$	1.00000	0.0883883
$129$	−8.41960	−0.741304
$130$	−21.4784	−1.88378
$131$	−15.1798	−1.32627	−0.663133	−	0.748502i	$-0.730774\pi$
$131$	−15.1798	−1.32627	−0.663133	+	0.748502i	$0.730774\pi$
$132$	5.77786	0.502899
$133$	0	0
$134$	0.769189	0.0664478
$135$	−3.10651	−0.267366
$136$	−1.17157	−0.100462
$137$	−0.248465	−0.0212278	−0.0106139	−	0.999944i	$-0.503379\pi$
$137$	−0.248465	−0.0212278	−0.0106139	+	0.999944i	$0.503379\pi$
$138$	−1.00000	−0.0851257
$139$	14.8920	1.26312	0.631561	−	0.775326i	$-0.282414\pi$
$139$	14.8920	1.26312	0.631561	+	0.775326i	$0.282414\pi$
$140$	0	0
$141$	−1.68003	−0.141484
$142$	−0.393270	−0.0330025
$143$	39.9481	3.34063
$144$	1.00000	0.0833333
$145$	−10.1183	−0.840282
$146$	−10.4557	−0.865317
$147$	0	0
$148$	6.04368	0.496787
$149$	−4.76665	−0.390500	−0.195250	−	0.980754i	$-0.562552\pi$
$149$	−4.76665	−0.390500	−0.195250	+	0.980754i	$0.562552\pi$
$150$	−4.65041	−0.379704
$151$	8.05657	0.655634	0.327817	−	0.944741i	$-0.393687\pi$
$151$	8.05657	0.655634	0.327817	+	0.944741i	$0.393687\pi$
$152$	6.75692	0.548059
$153$	−1.17157	−0.0947161
$154$	0	0
$155$	−27.3336	−2.19549
$156$	6.91399	0.553563
$157$	−8.24264	−0.657834	−0.328917	−	0.944359i	$-0.606684\pi$
$157$	−8.24264	−0.657834	−0.328917	+	0.944359i	$0.606684\pi$
$158$	−5.94900	−0.473277
$159$	9.16246	0.726630
$160$	3.10651	0.245591
$161$	0	0
$162$	1.00000	0.0785674
$163$	8.66806	0.678935	0.339468	−	0.940618i	$-0.389753\pi$
$163$	8.66806	0.678935	0.339468	+	0.940618i	$0.389753\pi$
$164$	−1.94405	−0.151805
$165$	17.9490	1.39733
$166$	−11.1921	−0.868674
$167$	3.80748	0.294632	0.147316	−	0.989089i	$-0.452937\pi$
$167$	3.80748	0.294632	0.147316	+	0.989089i	$0.452937\pi$
$168$	0	0
$169$	34.8033	2.67718
$170$	−3.63950	−0.279137
$171$	6.75692	0.516715
$172$	8.41960	0.641988
$173$	14.5553	1.10662	0.553309	−	0.832976i	$-0.313365\pi$
$173$	14.5553	1.10662	0.553309	+	0.832976i	$0.313365\pi$
$174$	3.25714	0.246923
$175$	0	0
$176$	−5.77786	−0.435523
$177$	−3.26358	−0.245306
$178$	−13.9490	−1.04552
$179$	−5.13613	−0.383892	−0.191946	−	0.981405i	$-0.561480\pi$
$179$	−5.13613	−0.383892	−0.191946	+	0.981405i	$0.561480\pi$
$180$	3.10651	0.231546
$181$	−17.0317	−1.26596	−0.632979	−	0.774169i	$-0.718168\pi$
$181$	−17.0317	−1.26596	−0.632979	+	0.774169i	$0.718168\pi$
$182$	0	0
$183$	−6.81616	−0.503865
$184$	1.00000	0.0737210
$185$	18.7748	1.38035
$186$	8.79881	0.645160
$187$	6.76919	0.495012
$188$	1.68003	0.122529
$189$	0	0
$190$	20.9904	1.52281
$191$	10.2723	0.743275	0.371637	−	0.928378i	$-0.378797\pi$
$191$	10.2723	0.743275	0.371637	+	0.928378i	$0.378797\pi$
$192$	−1.00000	−0.0721688
$193$	0.604499	0.0435128	0.0217564	−	0.999763i	$-0.493074\pi$
$193$	0.604499	0.0435128	0.0217564	+	0.999763i	$0.493074\pi$
$194$	−16.1949	−1.16273
$195$	21.4784	1.53810
$196$	0	0
$197$	−12.1275	−0.864045	−0.432023	−	0.901863i	$-0.642200\pi$
$197$	−12.1275	−0.864045	−0.432023	+	0.901863i	$0.642200\pi$
$198$	−5.77786	−0.410615
$199$	2.68362	0.190237	0.0951185	−	0.995466i	$-0.469677\pi$
$199$	2.68362	0.190237	0.0951185	+	0.995466i	$0.469677\pi$
$200$	4.65041	0.328834
$201$	−0.769189	−0.0542544
$202$	−17.6349	−1.24078
$203$	0	0
$204$	1.17157	0.0820265
$205$	−6.03922	−0.421797
$206$	−15.4702	−1.07786
$207$	1.00000	0.0695048
$208$	−6.91399	−0.479399
$209$	−39.0406	−2.70049
$210$	0	0
$211$	−0.0372352	−0.00256337	−0.00128169	−	0.999999i	$-0.500408\pi$
$211$	−0.0372352	−0.00256337	−0.00128169	+	0.999999i	$0.500408\pi$
$212$	−9.16246	−0.629280
$213$	0.393270	0.0269464
$214$	−4.00000	−0.273434
$215$	26.1556	1.78380
$216$	−1.00000	−0.0680414
$217$	0	0
$218$	−18.9840	−1.28576
$219$	10.4557	0.706528
$220$	−17.9490	−1.21012
$221$	8.10025	0.544882
$222$	−6.04368	−0.405625
$223$	−0.322641	−0.0216056	−0.0108028	−	0.999942i	$-0.503439\pi$
$223$	−0.322641	−0.0216056	−0.0108028	+	0.999942i	$0.503439\pi$
$224$	0	0
$225$	4.65041	0.310027
$226$	17.8215	1.18547
$227$	−10.8425	−0.719641	−0.359821	−	0.933022i	$-0.617162\pi$
$227$	−10.8425	−0.719641	−0.359821	+	0.933022i	$0.617162\pi$
$228$	−6.75692	−0.447488
$229$	−19.2794	−1.27402	−0.637011	−	0.770855i	$-0.719829\pi$
$229$	−19.2794	−1.27402	−0.637011	+	0.770855i	$0.719829\pi$
$230$	3.10651	0.204837
$231$	0	0
$232$	−3.25714	−0.213842
$233$	−9.35094	−0.612601	−0.306300	−	0.951935i	$-0.599091\pi$
$233$	−9.35094	−0.612601	−0.306300	+	0.951935i	$0.599091\pi$
$234$	−6.91399	−0.451982
$235$	5.21903	0.340452
$236$	3.26358	0.212441
$237$	5.94900	0.386429
$238$	0	0
$239$	14.9577	0.967531	0.483766	−	0.875198i	$-0.339269\pi$
$239$	14.9577	0.967531	0.483766	+	0.875198i	$0.339269\pi$
$240$	−3.10651	−0.200524
$241$	−4.66374	−0.300418	−0.150209	−	0.988654i	$-0.547995\pi$
$241$	−4.66374	−0.300418	−0.150209	+	0.988654i	$0.547995\pi$
$242$	22.3837	1.43888
$243$	−1.00000	−0.0641500
$244$	6.81616	0.436360
$245$	0	0
$246$	1.94405	0.123948
$247$	−46.7173	−2.97255
$248$	−8.79881	−0.558725
$249$	11.1921	0.709269
$250$	−1.08601	−0.0686850
$251$	20.8251	1.31447	0.657236	−	0.753685i	$-0.271726\pi$
$251$	20.8251	1.31447	0.657236	+	0.753685i	$0.271726\pi$
$252$	0	0
$253$	−5.77786	−0.363251
$254$	−8.83022	−0.554057
$255$	3.63950	0.227915
$256$	1.00000	0.0625000
$257$	8.89528	0.554872	0.277436	−	0.960744i	$-0.410515\pi$
$257$	8.89528	0.554872	0.277436	+	0.960744i	$0.410515\pi$
$258$	−8.41960	−0.524181
$259$	0	0
$260$	−21.4784	−1.33203
$261$	−3.25714	−0.201612
$262$	−15.1798	−0.937812
$263$	3.68406	0.227169	0.113584	−	0.993528i	$-0.463767\pi$
$263$	3.68406	0.227169	0.113584	+	0.993528i	$0.463767\pi$
$264$	5.77786	0.355603
$265$	−28.4633	−1.74849
$266$	0	0
$267$	13.9490	0.853665
$268$	0.769189	0.0469857
$269$	2.28137	0.139098	0.0695489	−	0.997579i	$-0.477844\pi$
$269$	2.28137	0.139098	0.0695489	+	0.997579i	$0.477844\pi$
$270$	−3.10651	−0.189056
$271$	−0.869694	−0.0528302	−0.0264151	−	0.999651i	$-0.508409\pi$
$271$	−0.869694	−0.0528302	−0.0264151	+	0.999651i	$0.508409\pi$
$272$	−1.17157	−0.0710370
$273$	0	0
$274$	−0.248465	−0.0150103
$275$	−26.8694	−1.62029
$276$	−1.00000	−0.0601929
$277$	6.66553	0.400493	0.200246	−	0.979746i	$-0.435826\pi$
$277$	6.66553	0.400493	0.200246	+	0.979746i	$0.435826\pi$
$278$	14.8920	0.893162
$279$	−8.79881	−0.526771
$280$	0	0
$281$	14.4187	0.860149	0.430074	−	0.902793i	$-0.358487\pi$
$281$	14.4187	0.860149	0.430074	+	0.902793i	$0.358487\pi$
$282$	−1.68003	−0.100044
$283$	12.4847	0.742136	0.371068	−	0.928606i	$-0.378992\pi$
$283$	12.4847	0.742136	0.371068	+	0.928606i	$0.378992\pi$
$284$	−0.393270	−0.0233363
$285$	−20.9904	−1.24337
$286$	39.9481	2.36218
$287$	0	0
$288$	1.00000	0.0589256
$289$	−15.6274	−0.919260
$290$	−10.1183	−0.594169
$291$	16.1949	0.949364
$292$	−10.4557	−0.611871
$293$	−29.6947	−1.73478	−0.867392	−	0.497626i	$-0.834205\pi$
$293$	−29.6947	−1.73478	−0.867392	+	0.497626i	$0.834205\pi$
$294$	0	0
$295$	10.1384	0.590278
$296$	6.04368	0.351282
$297$	5.77786	0.335266
$298$	−4.76665	−0.276125
$299$	−6.91399	−0.399847
$300$	−4.65041	−0.268492
$301$	0	0
$302$	8.05657	0.463603
$303$	17.6349	1.01310
$304$	6.75692	0.387536
$305$	21.1745	1.21245
$306$	−1.17157	−0.0669744
$307$	25.0934	1.43215	0.716077	−	0.698021i	$-0.245936\pi$
$307$	25.0934	1.43215	0.716077	+	0.698021i	$0.245936\pi$
$308$	0	0
$309$	15.4702	0.880067
$310$	−27.3336	−1.55244
$311$	6.48931	0.367975	0.183988	−	0.982929i	$-0.441099\pi$
$311$	6.48931	0.367975	0.183988	+	0.982929i	$0.441099\pi$
$312$	6.91399	0.391428
$313$	23.5094	1.32883	0.664414	−	0.747364i	$-0.268681\pi$
$313$	23.5094	1.32883	0.664414	+	0.747364i	$0.268681\pi$
$314$	−8.24264	−0.465159
$315$	0	0
$316$	−5.94900	−0.334657
$317$	13.8717	0.779111	0.389555	−	0.921003i	$-0.372629\pi$
$317$	13.8717	0.779111	0.389555	+	0.921003i	$0.372629\pi$
$318$	9.16246	0.513805
$319$	18.8193	1.05368
$320$	3.10651	0.173659
$321$	4.00000	0.223258
$322$	0	0
$323$	−7.91622	−0.440471
$324$	1.00000	0.0555556
$325$	−32.1529	−1.78352
$326$	8.66806	0.480080
$327$	18.9840	1.04982
$328$	−1.94405	−0.107342
$329$	0	0
$330$	17.9490	0.988060
$331$	0.668064	0.0367201	0.0183601	−	0.999831i	$-0.494155\pi$
$331$	0.668064	0.0367201	0.0183601	+	0.999831i	$0.494155\pi$
$332$	−11.1921	−0.614245
$333$	6.04368	0.331192
$334$	3.80748	0.208336
$335$	2.38949	0.130552
$336$	0	0
$337$	28.1330	1.53250	0.766252	−	0.642541i	$-0.222120\pi$
$337$	28.1330	1.53250	0.766252	+	0.642541i	$0.222120\pi$
$338$	34.8033	1.89305
$339$	−17.8215	−0.967933
$340$	−3.63950	−0.197380
$341$	50.8383	2.75305
$342$	6.75692	0.365372
$343$	0	0
$344$	8.41960	0.453954
$345$	−3.10651	−0.167249
$346$	14.5553	0.782497
$347$	5.32015	0.285601	0.142800	−	0.989752i	$-0.454389\pi$
$347$	5.32015	0.285601	0.142800	+	0.989752i	$0.454389\pi$
$348$	3.25714	0.174601
$349$	34.4006	1.84142	0.920712	−	0.390243i	$-0.127609\pi$
$349$	34.4006	1.84142	0.920712	+	0.390243i	$0.127609\pi$
$350$	0	0
$351$	6.91399	0.369042
$352$	−5.77786	−0.307961
$353$	13.8666	0.738044	0.369022	−	0.929421i	$-0.379693\pi$
$353$	13.8666	0.738044	0.369022	+	0.929421i	$0.379693\pi$
$354$	−3.26358	−0.173458
$355$	−1.22170	−0.0648409
$356$	−13.9490	−0.739295
$357$	0	0
$358$	−5.13613	−0.271453
$359$	−25.6123	−1.35177	−0.675883	−	0.737009i	$-0.736237\pi$
$359$	−25.6123	−1.35177	−0.675883	+	0.737009i	$0.736237\pi$
$360$	3.10651	0.163727
$361$	26.6560	1.40295
$362$	−17.0317	−0.895167
$363$	−22.3837	−1.17484
$364$	0	0
$365$	−32.4806	−1.70011
$366$	−6.81616	−0.356286
$367$	−23.0388	−1.20261	−0.601307	−	0.799018i	$-0.705353\pi$
$367$	−23.0388	−1.20261	−0.601307	+	0.799018i	$0.705353\pi$
$368$	1.00000	0.0521286
$369$	−1.94405	−0.101203
$370$	18.7748	0.976053
$371$	0	0
$372$	8.79881	0.456197
$373$	−29.1115	−1.50733	−0.753667	−	0.657256i	$-0.771717\pi$
$373$	−29.1115	−1.50733	−0.753667	+	0.657256i	$0.771717\pi$
$374$	6.76919	0.350026
$375$	1.08601	0.0560811
$376$	1.68003	0.0866409
$377$	22.5198	1.15983
$378$	0	0
$379$	5.22349	0.268313	0.134156	−	0.990960i	$-0.457168\pi$
$379$	5.22349	0.268313	0.134156	+	0.990960i	$0.457168\pi$
$380$	20.9904	1.07679
$381$	8.83022	0.452386
$382$	10.2723	0.525575
$383$	−16.2084	−0.828209	−0.414104	−	0.910229i	$-0.635905\pi$
$383$	−16.2084	−0.828209	−0.414104	+	0.910229i	$0.635905\pi$
$384$	−1.00000	−0.0510310
$385$	0	0
$386$	0.604499	0.0307682
$387$	8.41960	0.427992
$388$	−16.1949	−0.822173
$389$	8.08290	0.409819	0.204910	−	0.978781i	$-0.434310\pi$
$389$	8.08290	0.409819	0.204910	+	0.978781i	$0.434310\pi$
$390$	21.4784	1.08760
$391$	−1.17157	−0.0592490
$392$	0	0
$393$	15.1798	0.765720
$394$	−12.1275	−0.610972
$395$	−18.4806	−0.929861
$396$	−5.77786	−0.290349
$397$	−29.2964	−1.47034	−0.735171	−	0.677882i	$-0.762898\pi$
$397$	−29.2964	−1.47034	−0.735171	+	0.677882i	$0.762898\pi$
$398$	2.68362	0.134518
$399$	0	0
$400$	4.65041	0.232520
$401$	−14.7994	−0.739048	−0.369524	−	0.929221i	$-0.620479\pi$
$401$	−14.7994	−0.739048	−0.369524	+	0.929221i	$0.620479\pi$
$402$	−0.769189	−0.0383637
$403$	60.8349	3.03040
$404$	−17.6349	−0.877367
$405$	3.10651	0.154364
$406$	0	0
$407$	−34.9196	−1.73090
$408$	1.17157	0.0580015
$409$	−16.4548	−0.813637	−0.406818	−	0.913509i	$-0.633362\pi$
$409$	−16.4548	−0.813637	−0.406818	+	0.913509i	$0.633362\pi$
$410$	−6.03922	−0.298256
$411$	0.248465	0.0122559
$412$	−15.4702	−0.762160
$413$	0	0
$414$	1.00000	0.0491473
$415$	−34.7683	−1.70671
$416$	−6.91399	−0.338986
$417$	−14.8920	−0.729264
$418$	−39.0406	−1.90954
$419$	7.87837	0.384884	0.192442	−	0.981308i	$-0.438359\pi$
$419$	7.87837	0.384884	0.192442	+	0.981308i	$0.438359\pi$
$420$	0	0
$421$	−1.80166	−0.0878075	−0.0439037	−	0.999036i	$-0.513979\pi$
$421$	−1.80166	−0.0878075	−0.0439037	+	0.999036i	$0.513979\pi$
$422$	−0.0372352	−0.00181258
$423$	1.68003	0.0816858
$424$	−9.16246	−0.444968
$425$	−5.44829	−0.264281
$426$	0.393270	0.0190540
$427$	0	0
$428$	−4.00000	−0.193347
$429$	−39.9481	−1.92871
$430$	26.1556	1.26133
$431$	16.2977	0.785033	0.392517	−	0.919745i	$-0.371605\pi$
$431$	16.2977	0.785033	0.392517	+	0.919745i	$0.371605\pi$
$432$	−1.00000	−0.0481125
$433$	7.83443	0.376499	0.188249	−	0.982121i	$-0.439719\pi$
$433$	7.83443	0.376499	0.188249	+	0.982121i	$0.439719\pi$
$434$	0	0
$435$	10.1183	0.485137
$436$	−18.9840	−0.909169
$437$	6.75692	0.323227
$438$	10.4557	0.499591
$439$	31.0412	1.48152	0.740758	−	0.671772i	$-0.234467\pi$
$439$	31.0412	1.48152	0.740758	+	0.671772i	$0.234467\pi$
$440$	−17.9490	−0.855685
$441$	0	0
$442$	8.10025	0.385290
$443$	29.5658	1.40471	0.702356	−	0.711826i	$-0.252132\pi$
$443$	29.5658	1.40471	0.702356	+	0.711826i	$0.252132\pi$
$444$	−6.04368	−0.286820
$445$	−43.3327	−2.05417
$446$	−0.322641	−0.0152775
$447$	4.76665	0.225455
$448$	0	0
$449$	7.05880	0.333125	0.166563	−	0.986031i	$-0.446733\pi$
$449$	7.05880	0.333125	0.166563	+	0.986031i	$0.446733\pi$
$450$	4.65041	0.219222
$451$	11.2325	0.528916
$452$	17.8215	0.838255
$453$	−8.05657	−0.378531
$454$	−10.8425	−0.508863
$455$	0	0
$456$	−6.75692	−0.316422
$457$	−21.9291	−1.02580	−0.512900	−	0.858448i	$-0.671429\pi$
$457$	−21.9291	−1.02580	−0.512900	+	0.858448i	$0.671429\pi$
$458$	−19.2794	−0.900869
$459$	1.17157	0.0546843
$460$	3.10651	0.144842
$461$	−9.92088	−0.462061	−0.231031	−	0.972946i	$-0.574210\pi$
$461$	−9.92088	−0.462061	−0.231031	+	0.972946i	$0.574210\pi$
$462$	0	0
$463$	−9.77054	−0.454076	−0.227038	−	0.973886i	$-0.572904\pi$
$463$	−9.77054	−0.454076	−0.227038	+	0.973886i	$0.572904\pi$
$464$	−3.25714	−0.151209
$465$	27.3336	1.26757
$466$	−9.35094	−0.433174
$467$	−35.6518	−1.64977	−0.824885	−	0.565301i	$-0.808760\pi$
$467$	−35.6518	−1.64977	−0.824885	+	0.565301i	$0.808760\pi$
$468$	−6.91399	−0.319599
$469$	0	0
$470$	5.21903	0.240736
$471$	8.24264	0.379801
$472$	3.26358	0.150219
$473$	−48.6473	−2.23681
$474$	5.94900	0.273247
$475$	31.4225	1.44176
$476$	0	0
$477$	−9.16246	−0.419520
$478$	14.9577	0.684148
$479$	−18.8811	−0.862699	−0.431349	−	0.902185i	$-0.641962\pi$
$479$	−18.8811	−0.862699	−0.431349	+	0.902185i	$0.641962\pi$
$480$	−3.10651	−0.141792
$481$	−41.7860	−1.90528
$482$	−4.66374	−0.212427
$483$	0	0
$484$	22.3837	1.01744
$485$	−50.3097	−2.28445
$486$	−1.00000	−0.0453609
$487$	−9.95990	−0.451326	−0.225663	−	0.974205i	$-0.572455\pi$
$487$	−9.95990	−0.451326	−0.225663	+	0.974205i	$0.572455\pi$
$488$	6.81616	0.308553
$489$	−8.66806	−0.391983
$490$	0	0
$491$	21.6604	0.977522	0.488761	−	0.872418i	$-0.337449\pi$
$491$	21.6604	0.977522	0.488761	+	0.872418i	$0.337449\pi$
$492$	1.94405	0.0876446
$493$	3.81598	0.171863
$494$	−46.7173	−2.10191
$495$	−17.9490	−0.806747
$496$	−8.79881	−0.395078
$497$	0	0
$498$	11.1921	0.501529
$499$	−40.6974	−1.82187	−0.910933	−	0.412553i	$-0.864637\pi$
$499$	−40.6974	−1.82187	−0.910933	+	0.412553i	$0.864637\pi$
$500$	−1.08601	−0.0485677
$501$	−3.80748	−0.170106
$502$	20.8251	0.929471
$503$	32.3613	1.44292	0.721459	−	0.692457i	$-0.243472\pi$
$503$	32.3613	1.44292	0.721459	+	0.692457i	$0.243472\pi$
$504$	0	0
$505$	−54.7829	−2.43781
$506$	−5.77786	−0.256857
$507$	−34.8033	−1.54567
$508$	−8.83022	−0.391778
$509$	−2.57605	−0.114182	−0.0570908	−	0.998369i	$-0.518182\pi$
$509$	−2.57605	−0.114182	−0.0570908	+	0.998369i	$0.518182\pi$
$510$	3.63950	0.161160
$511$	0	0
$512$	1.00000	0.0441942
$513$	−6.75692	−0.298325
$514$	8.89528	0.392354
$515$	−48.0582	−2.11770
$516$	−8.41960	−0.370652
$517$	−9.70698	−0.426912
$518$	0	0
$519$	−14.5553	−0.638906
$520$	−21.4784	−0.941890
$521$	26.9403	1.18028	0.590139	−	0.807302i	$-0.299073\pi$
$521$	26.9403	1.18028	0.590139	+	0.807302i	$0.299073\pi$
$522$	−3.25714	−0.142561
$523$	33.2094	1.45215	0.726073	−	0.687617i	$-0.241343\pi$
$523$	33.2094	1.45215	0.726073	+	0.687617i	$0.241343\pi$
$524$	−15.1798	−0.663133
$525$	0	0
$526$	3.68406	0.160633
$527$	10.3084	0.449043
$528$	5.77786	0.251449
$529$	1.00000	0.0434783
$530$	−28.4633	−1.23637
$531$	3.26358	0.141628
$532$	0	0
$533$	13.4412	0.582201
$534$	13.9490	0.603632
$535$	−12.4260	−0.537225
$536$	0.769189	0.0332239
$537$	5.13613	0.221640
$538$	2.28137	0.0983570
$539$	0	0
$540$	−3.10651	−0.133683
$541$	43.6075	1.87483	0.937417	−	0.348210i	$-0.113210\pi$
$541$	43.6075	1.87483	0.937417	+	0.348210i	$0.113210\pi$
$542$	−0.869694	−0.0373566
$543$	17.0317	0.730901
$544$	−1.17157	−0.0502308
$545$	−58.9740	−2.52617
$546$	0	0
$547$	−32.7554	−1.40052	−0.700260	−	0.713888i	$-0.746933\pi$
$547$	−32.7554	−1.40052	−0.700260	+	0.713888i	$0.746933\pi$
$548$	−0.248465	−0.0106139
$549$	6.81616	0.290907
$550$	−26.8694	−1.14572
$551$	−22.0082	−0.937582
$552$	−1.00000	−0.0425628
$553$	0	0
$554$	6.66553	0.283191
$555$	−18.7748	−0.796944
$556$	14.8920	0.631561
$557$	−11.5255	−0.488351	−0.244175	−	0.969731i	$-0.578517\pi$
$557$	−11.5255	−0.488351	−0.244175	+	0.969731i	$0.578517\pi$
$558$	−8.79881	−0.372483
$559$	−58.2131	−2.46215
$560$	0	0
$561$	−6.76919	−0.285795
$562$	14.4187	0.608217
$563$	36.6834	1.54602	0.773010	−	0.634394i	$-0.218750\pi$
$563$	36.6834	1.54602	0.773010	+	0.634394i	$0.218750\pi$
$564$	−1.68003	−0.0707420
$565$	55.3628	2.32913
$566$	12.4847	0.524769
$567$	0	0
$568$	−0.393270	−0.0165012
$569$	−20.7350	−0.869256	−0.434628	−	0.900610i	$-0.643120\pi$
$569$	−20.7350	−0.869256	−0.434628	+	0.900610i	$0.643120\pi$
$570$	−20.9904	−0.879193
$571$	13.9871	0.585342	0.292671	−	0.956213i	$-0.405456\pi$
$571$	13.9871	0.585342	0.292671	+	0.956213i	$0.405456\pi$
$572$	39.9481	1.67031
$573$	−10.2723	−0.429130
$574$	0	0
$575$	4.65041	0.193935
$576$	1.00000	0.0416667
$577$	−37.2322	−1.55000	−0.774999	−	0.631963i	$-0.782249\pi$
$577$	−37.2322	−1.55000	−0.774999	+	0.631963i	$0.782249\pi$
$578$	−15.6274	−0.650015
$579$	−0.604499	−0.0251221
$580$	−10.1183	−0.420141
$581$	0	0
$582$	16.1949	0.671301
$583$	52.9394	2.19253
$584$	−10.4557	−0.432658
$585$	−21.4784	−0.888022
$586$	−29.6947	−1.22668
$587$	−30.6054	−1.26322	−0.631610	−	0.775286i	$-0.717606\pi$
$587$	−30.6054	−1.26322	−0.631610	+	0.775286i	$0.717606\pi$
$588$	0	0
$589$	−59.4528	−2.44971
$590$	10.1384	0.417390
$591$	12.1275	0.498857
$592$	6.04368	0.248394
$593$	20.7578	0.852422	0.426211	−	0.904624i	$-0.359848\pi$
$593$	20.7578	0.852422	0.426211	+	0.904624i	$0.359848\pi$
$594$	5.77786	0.237069
$595$	0	0
$596$	−4.76665	−0.195250
$597$	−2.68362	−0.109833
$598$	−6.91399	−0.282734
$599$	−47.1963	−1.92839	−0.964194	−	0.265198i	$-0.914563\pi$
$599$	−47.1963	−1.92839	−0.964194	+	0.265198i	$0.914563\pi$
$600$	−4.65041	−0.189852
$601$	8.55932	0.349142	0.174571	−	0.984645i	$-0.444146\pi$
$601$	8.55932	0.349142	0.174571	+	0.984645i	$0.444146\pi$
$602$	0	0
$603$	0.769189	0.0313238
$604$	8.05657	0.327817
$605$	69.5353	2.82701
$606$	17.6349	0.716367
$607$	22.5701	0.916092	0.458046	−	0.888929i	$-0.348550\pi$
$607$	22.5701	0.916092	0.458046	+	0.888929i	$0.348550\pi$
$608$	6.75692	0.274029
$609$	0	0
$610$	21.1745	0.857329
$611$	−11.6157	−0.469921
$612$	−1.17157	−0.0473580
$613$	2.39971	0.0969235	0.0484618	−	0.998825i	$-0.484568\pi$
$613$	2.39971	0.0969235	0.0484618	+	0.998825i	$0.484568\pi$
$614$	25.0934	1.01269
$615$	6.03922	0.243525
$616$	0	0
$617$	16.7692	0.675102	0.337551	−	0.941307i	$-0.390401\pi$
$617$	16.7692	0.675102	0.337551	+	0.941307i	$0.390401\pi$
$618$	15.4702	0.622301
$619$	14.3255	0.575792	0.287896	−	0.957662i	$-0.407044\pi$
$619$	14.3255	0.575792	0.287896	+	0.957662i	$0.407044\pi$
$620$	−27.3336	−1.09774
$621$	−1.00000	−0.0401286
$622$	6.48931	0.260198
$623$	0	0
$624$	6.91399	0.276781
$625$	−26.6257	−1.06503
$626$	23.5094	0.939624
$627$	39.0406	1.55913
$628$	−8.24264	−0.328917
$629$	−7.08061	−0.282322
$630$	0	0
$631$	40.0061	1.59262	0.796309	−	0.604890i	$-0.206783\pi$
$631$	40.0061	1.59262	0.796309	+	0.604890i	$0.206783\pi$
$632$	−5.94900	−0.236638
$633$	0.0372352	0.00147996
$634$	13.8717	0.550914
$635$	−27.4312	−1.08857
$636$	9.16246	0.363315
$637$	0	0
$638$	18.8193	0.745064
$639$	−0.393270	−0.0155575
$640$	3.10651	0.122796
$641$	41.6487	1.64502	0.822511	−	0.568748i	$-0.192572\pi$
$641$	41.6487	1.64502	0.822511	+	0.568748i	$0.192572\pi$
$642$	4.00000	0.157867
$643$	43.1493	1.70164	0.850821	−	0.525455i	$-0.176105\pi$
$643$	43.1493	1.70164	0.850821	+	0.525455i	$0.176105\pi$
$644$	0	0
$645$	−26.1556	−1.02987
$646$	−7.91622	−0.311460
$647$	−14.7595	−0.580254	−0.290127	−	0.956988i	$-0.593698\pi$
$647$	−14.7595	−0.580254	−0.290127	+	0.956988i	$0.593698\pi$
$648$	1.00000	0.0392837
$649$	−18.8565	−0.740184
$650$	−32.1529	−1.26114
$651$	0	0
$652$	8.66806	0.339468
$653$	−4.57173	−0.178905	−0.0894527	−	0.995991i	$-0.528512\pi$
$653$	−4.57173	−0.178905	−0.0894527	+	0.995991i	$0.528512\pi$
$654$	18.9840	0.742333
$655$	−47.1562	−1.84255
$656$	−1.94405	−0.0759025
$657$	−10.4557	−0.407914
$658$	0	0
$659$	26.6602	1.03853	0.519267	−	0.854612i	$-0.326205\pi$
$659$	26.6602	1.03853	0.519267	+	0.854612i	$0.326205\pi$
$660$	17.9490	0.698664
$661$	−42.8481	−1.66660	−0.833298	−	0.552824i	$-0.813550\pi$
$661$	−42.8481	−1.66660	−0.833298	+	0.552824i	$0.813550\pi$
$662$	0.668064	0.0259650
$663$	−8.10025	−0.314588
$664$	−11.1921	−0.434337
$665$	0	0
$666$	6.04368	0.234188
$667$	−3.25714	−0.126117
$668$	3.80748	0.147316
$669$	0.322641	0.0124740
$670$	2.38949	0.0923142
$671$	−39.3828	−1.52036
$672$	0	0
$673$	−43.3764	−1.67204	−0.836019	−	0.548701i	$-0.815122\pi$
$673$	−43.3764	−1.67204	−0.836019	+	0.548701i	$0.815122\pi$
$674$	28.1330	1.08364
$675$	−4.65041	−0.178994
$676$	34.8033	1.33859
$677$	7.57835	0.291260	0.145630	−	0.989339i	$-0.453479\pi$
$677$	7.57835	0.291260	0.145630	+	0.989339i	$0.453479\pi$
$678$	−17.8215	−0.684432
$679$	0	0
$680$	−3.63950	−0.139569
$681$	10.8425	0.415485
$682$	50.8383	1.94670
$683$	−2.85655	−0.109303	−0.0546514	−	0.998505i	$-0.517405\pi$
$683$	−2.85655	−0.109303	−0.0546514	+	0.998505i	$0.517405\pi$
$684$	6.75692	0.258357
$685$	−0.771859	−0.0294912
$686$	0	0
$687$	19.2794	0.735556
$688$	8.41960	0.320994
$689$	63.3492	2.41341
$690$	−3.10651	−0.118263
$691$	19.7225	0.750281	0.375140	−	0.926968i	$-0.377595\pi$
$691$	19.7225	0.750281	0.375140	+	0.926968i	$0.377595\pi$
$692$	14.5553	0.553309
$693$	0	0
$694$	5.32015	0.201950
$695$	46.2621	1.75482
$696$	3.25714	0.123462
$697$	2.27760	0.0862702
$698$	34.4006	1.30208
$699$	9.35094	0.353685
$700$	0	0
$701$	−0.835614	−0.0315607	−0.0157804	−	0.999875i	$-0.505023\pi$
$701$	−0.835614	−0.0315607	−0.0157804	+	0.999875i	$0.505023\pi$
$702$	6.91399	0.260952
$703$	40.8367	1.54018
$704$	−5.77786	−0.217761
$705$	−5.21903	−0.196560
$706$	13.8666	0.521876
$707$	0	0
$708$	−3.26358	−0.122653
$709$	7.82887	0.294019	0.147010	−	0.989135i	$-0.453035\pi$
$709$	7.82887	0.294019	0.147010	+	0.989135i	$0.453035\pi$
$710$	−1.22170	−0.0458495
$711$	−5.94900	−0.223105
$712$	−13.9490	−0.522761
$713$	−8.79881	−0.329518
$714$	0	0
$715$	124.099	4.64105
$716$	−5.13613	−0.191946
$717$	−14.9577	−0.558605
$718$	−25.6123	−0.955842
$719$	−48.7487	−1.81802	−0.909010	−	0.416774i	$-0.863161\pi$
$719$	−48.7487	−1.81802	−0.909010	+	0.416774i	$0.863161\pi$
$720$	3.10651	0.115773
$721$	0	0
$722$	26.6560	0.992033
$723$	4.66374	0.173446
$724$	−17.0317	−0.632979
$725$	−15.1470	−0.562547
$726$	−22.3837	−0.830738
$727$	20.8587	0.773605	0.386803	−	0.922163i	$-0.373579\pi$
$727$	20.8587	0.773605	0.386803	+	0.922163i	$0.373579\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	−32.4806	−1.20216
$731$	−9.86417	−0.364840
$732$	−6.81616	−0.251932
$733$	11.6981	0.432080	0.216040	−	0.976385i	$-0.430686\pi$
$733$	11.6981	0.432080	0.216040	+	0.976385i	$0.430686\pi$
$734$	−23.0388	−0.850377
$735$	0	0
$736$	1.00000	0.0368605
$737$	−4.44427	−0.163707
$738$	−1.94405	−0.0715615
$739$	32.2084	1.18480	0.592402	−	0.805643i	$-0.298180\pi$
$739$	32.2084	1.18480	0.592402	+	0.805643i	$0.298180\pi$
$740$	18.7748	0.690174
$741$	46.7173	1.71620
$742$	0	0
$743$	−28.9706	−1.06283	−0.531413	−	0.847113i	$-0.678339\pi$
$743$	−28.9706	−1.06283	−0.531413	+	0.847113i	$0.678339\pi$
$744$	8.79881	0.322580
$745$	−14.8077	−0.542511
$746$	−29.1115	−1.06585
$747$	−11.1921	−0.409497
$748$	6.76919	0.247506
$749$	0	0
$750$	1.08601	0.0396553
$751$	48.0666	1.75398	0.876988	−	0.480513i	$-0.159550\pi$
$751$	48.0666	1.75398	0.876988	+	0.480513i	$0.159550\pi$
$752$	1.68003	0.0612643
$753$	−20.8251	−0.758910
$754$	22.5198	0.820124
$755$	25.0278	0.910856
$756$	0	0
$757$	7.34395	0.266920	0.133460	−	0.991054i	$-0.457391\pi$
$757$	7.34395	0.266920	0.133460	+	0.991054i	$0.457391\pi$
$758$	5.22349	0.189726
$759$	5.77786	0.209723
$760$	20.9904	0.761404
$761$	4.75526	0.172378	0.0861891	−	0.996279i	$-0.472531\pi$
$761$	4.75526	0.172378	0.0861891	+	0.996279i	$0.472531\pi$
$762$	8.83022	0.319885
$763$	0	0
$764$	10.2723	0.371637
$765$	−3.63950	−0.131587
$766$	−16.2084	−0.585632
$767$	−22.5644	−0.814753
$768$	−1.00000	−0.0360844
$769$	−1.52475	−0.0549838	−0.0274919	−	0.999622i	$-0.508752\pi$
$769$	−1.52475	−0.0549838	−0.0274919	+	0.999622i	$0.508752\pi$
$770$	0	0
$771$	−8.89528	−0.320356
$772$	0.604499	0.0217564
$773$	−45.9021	−1.65098	−0.825491	−	0.564415i	$-0.809102\pi$
$773$	−45.9021	−1.65098	−0.825491	+	0.564415i	$0.809102\pi$
$774$	8.41960	0.302636
$775$	−40.9181	−1.46982
$776$	−16.1949	−0.581364
$777$	0	0
$778$	8.08290	0.289786
$779$	−13.1358	−0.470639
$780$	21.4784	0.769050
$781$	2.27226	0.0813078
$782$	−1.17157	−0.0418954
$783$	3.25714	0.116401
$784$	0	0
$785$	−25.6059	−0.913912
$786$	15.1798	0.541446
$787$	14.7751	0.526677	0.263339	−	0.964703i	$-0.415176\pi$
$787$	14.7751	0.526677	0.263339	+	0.964703i	$0.415176\pi$
$788$	−12.1275	−0.432023
$789$	−3.68406	−0.131156
$790$	−18.4806	−0.657511
$791$	0	0
$792$	−5.77786	−0.205307
$793$	−47.1269	−1.67352
$794$	−29.2964	−1.03969
$795$	28.4633	1.00949
$796$	2.68362	0.0951185
$797$	9.20106	0.325918	0.162959	−	0.986633i	$-0.447896\pi$
$797$	9.20106	0.325918	0.162959	+	0.986633i	$0.447896\pi$
$798$	0	0
$799$	−1.96828	−0.0696326
$800$	4.65041	0.164417
$801$	−13.9490	−0.492864
$802$	−14.7994	−0.522586
$803$	60.4114	2.13187
$804$	−0.769189	−0.0271272
$805$	0	0
$806$	60.8349	2.14282
$807$	−2.28137	−0.0803081
$808$	−17.6349	−0.620392
$809$	−17.0171	−0.598289	−0.299145	−	0.954208i	$-0.596701\pi$
$809$	−17.0171	−0.598289	−0.299145	+	0.954208i	$0.596701\pi$
$810$	3.10651	0.109152
$811$	36.1112	1.26803	0.634017	−	0.773319i	$-0.281405\pi$
$811$	36.1112	1.26803	0.634017	+	0.773319i	$0.281405\pi$
$812$	0	0
$813$	0.869694	0.0305015
$814$	−34.9196	−1.22393
$815$	26.9274	0.943227
$816$	1.17157	0.0410133
$817$	56.8906	1.99035
$818$	−16.4548	−0.575328
$819$	0	0
$820$	−6.03922	−0.210899
$821$	−13.2479	−0.462355	−0.231177	−	0.972912i	$-0.574258\pi$
$821$	−13.2479	−0.462355	−0.231177	+	0.972912i	$0.574258\pi$
$822$	0.248465	0.00866621
$823$	−4.65550	−0.162281	−0.0811403	−	0.996703i	$-0.525856\pi$
$823$	−4.65550	−0.162281	−0.0811403	+	0.996703i	$0.525856\pi$
$824$	−15.4702	−0.538929
$825$	26.8694	0.935474
$826$	0	0
$827$	3.30082	0.114781	0.0573904	−	0.998352i	$-0.481722\pi$
$827$	3.30082	0.114781	0.0573904	+	0.998352i	$0.481722\pi$
$828$	1.00000	0.0347524
$829$	−32.6577	−1.13425	−0.567124	−	0.823633i	$-0.691944\pi$
$829$	−32.6577	−1.13425	−0.567124	+	0.823633i	$0.691944\pi$
$830$	−34.7683	−1.20683
$831$	−6.66553	−0.231225
$832$	−6.91399	−0.239700
$833$	0	0
$834$	−14.8920	−0.515667
$835$	11.8280	0.409324
$836$	−39.0406	−1.35025
$837$	8.79881	0.304131
$838$	7.87837	0.272154
$839$	14.6879	0.507084	0.253542	−	0.967324i	$-0.418404\pi$
$839$	14.6879	0.507084	0.253542	+	0.967324i	$0.418404\pi$
$840$	0	0
$841$	−18.3910	−0.634174
$842$	−1.80166	−0.0620893
$843$	−14.4187	−0.496607
$844$	−0.0372352	−0.00128169
$845$	108.117	3.71933
$846$	1.68003	0.0577606
$847$	0	0
$848$	−9.16246	−0.314640
$849$	−12.4847	−0.428472
$850$	−5.44829	−0.186875
$851$	6.04368	0.207175
$852$	0.393270	0.0134732
$853$	26.2095	0.897395	0.448698	−	0.893684i	$-0.351888\pi$
$853$	26.2095	0.897395	0.448698	+	0.893684i	$0.351888\pi$
$854$	0	0
$855$	20.9904	0.717858
$856$	−4.00000	−0.136717
$857$	14.0096	0.478559	0.239279	−	0.970951i	$-0.423089\pi$
$857$	14.0096	0.478559	0.239279	+	0.970951i	$0.423089\pi$
$858$	−39.9481	−1.36381
$859$	47.6950	1.62733	0.813666	−	0.581332i	$-0.197468\pi$
$859$	47.6950	1.62733	0.813666	+	0.581332i	$0.197468\pi$
$860$	26.1556	0.891898
$861$	0	0
$862$	16.2977	0.555102
$863$	−2.61541	−0.0890294	−0.0445147	−	0.999009i	$-0.514174\pi$
$863$	−2.61541	−0.0890294	−0.0445147	+	0.999009i	$0.514174\pi$
$864$	−1.00000	−0.0340207
$865$	45.2162	1.53740
$866$	7.83443	0.266225
$867$	15.6274	0.530735
$868$	0	0
$869$	34.3725	1.16601
$870$	10.1183	0.343044
$871$	−5.31817	−0.180199
$872$	−18.9840	−0.642879
$873$	−16.1949	−0.548115
$874$	6.75692	0.228556
$875$	0	0
$876$	10.4557	0.353264
$877$	34.2765	1.15743	0.578717	−	0.815529i	$-0.303554\pi$
$877$	34.2765	1.15743	0.578717	+	0.815529i	$0.303554\pi$
$878$	31.0412	1.04759
$879$	29.6947	1.00158
$880$	−17.9490	−0.605061
$881$	−34.7791	−1.17174	−0.585869	−	0.810406i	$-0.699247\pi$
$881$	−34.7791	−1.17174	−0.585869	+	0.810406i	$0.699247\pi$
$882$	0	0
$883$	−16.0899	−0.541468	−0.270734	−	0.962654i	$-0.587266\pi$
$883$	−16.0899	−0.541468	−0.270734	+	0.962654i	$0.587266\pi$
$884$	8.10025	0.272441
$885$	−10.1384	−0.340797
$886$	29.5658	0.993281
$887$	−16.1845	−0.543421	−0.271710	−	0.962379i	$-0.587589\pi$
$887$	−16.1845	−0.543421	−0.271710	+	0.962379i	$0.587589\pi$
$888$	−6.04368	−0.202813
$889$	0	0
$890$	−43.3327	−1.45252
$891$	−5.77786	−0.193566
$892$	−0.322641	−0.0108028
$893$	11.3518	0.379874
$894$	4.76665	0.159421
$895$	−15.9554	−0.533332
$896$	0	0
$897$	6.91399	0.230852
$898$	7.05880	0.235555
$899$	28.6590	0.955829
$900$	4.65041	0.155014
$901$	10.7345	0.357618
$902$	11.2325	0.374000
$903$	0	0
$904$	17.8215	0.592736
$905$	−52.9092	−1.75876
$906$	−8.05657	−0.267662
$907$	−17.4784	−0.580361	−0.290180	−	0.956972i	$-0.593715\pi$
$907$	−17.4784	−0.580361	−0.290180	+	0.956972i	$0.593715\pi$
$908$	−10.8425	−0.359821
$909$	−17.6349	−0.584911
$910$	0	0
$911$	−52.2795	−1.73210	−0.866048	−	0.499960i	$-0.833348\pi$
$911$	−52.2795	−1.73210	−0.866048	+	0.499960i	$0.833348\pi$
$912$	−6.75692	−0.223744
$913$	64.6663	2.14014
$914$	−21.9291	−0.725351
$915$	−21.1745	−0.700006
$916$	−19.2794	−0.637011
$917$	0	0
$918$	1.17157	0.0386677
$919$	58.6092	1.93334	0.966669	−	0.256028i	$-0.0824139\pi$
$919$	58.6092	1.93334	0.966669	+	0.256028i	$0.0824139\pi$
$920$	3.10651	0.102419
$921$	−25.0934	−0.826854
$922$	−9.92088	−0.326727
$923$	2.71907	0.0894991
$924$	0	0
$925$	28.1056	0.924106
$926$	−9.77054	−0.321080
$927$	−15.4702	−0.508107
$928$	−3.25714	−0.106921
$929$	−28.2163	−0.925747	−0.462874	−	0.886424i	$-0.653182\pi$
$929$	−28.2163	−0.925747	−0.462874	+	0.886424i	$0.653182\pi$
$930$	27.3336	0.896304
$931$	0	0
$932$	−9.35094	−0.306300
$933$	−6.48931	−0.212451
$934$	−35.6518	−1.16656
$935$	21.0286	0.687707
$936$	−6.91399	−0.225991
$937$	7.15979	0.233900	0.116950	−	0.993138i	$-0.462688\pi$
$937$	7.15979	0.233900	0.116950	+	0.993138i	$0.462688\pi$
$938$	0	0
$939$	−23.5094	−0.767200
$940$	5.21903	0.170226
$941$	32.1105	1.04677	0.523387	−	0.852095i	$-0.324668\pi$
$941$	32.1105	1.04677	0.523387	+	0.852095i	$0.324668\pi$
$942$	8.24264	0.268560
$943$	−1.94405	−0.0633070
$944$	3.26358	0.106221
$945$	0	0
$946$	−48.6473	−1.58166
$947$	27.3028	0.887222	0.443611	−	0.896219i	$-0.353697\pi$
$947$	27.3028	0.887222	0.443611	+	0.896219i	$0.353697\pi$
$948$	5.94900	0.193214
$949$	72.2904	2.34665
$950$	31.4225	1.01948
$951$	−13.8717	−0.449820
$952$	0	0
$953$	−50.1529	−1.62461	−0.812306	−	0.583231i	$-0.801788\pi$
$953$	−50.1529	−1.62461	−0.812306	+	0.583231i	$0.801788\pi$
$954$	−9.16246	−0.296646
$955$	31.9109	1.03261
$956$	14.9577	0.483766
$957$	−18.8193	−0.608342
$958$	−18.8811	−0.610020
$959$	0	0
$960$	−3.10651	−0.100262
$961$	46.4190	1.49739
$962$	−41.7860	−1.34723
$963$	−4.00000	−0.128898
$964$	−4.66374	−0.150209
$965$	1.87788	0.0604512
$966$	0	0
$967$	4.03977	0.129910	0.0649551	−	0.997888i	$-0.479310\pi$
$967$	4.03977	0.129910	0.0649551	+	0.997888i	$0.479310\pi$
$968$	22.3837	0.719440
$969$	7.91622	0.254306
$970$	−50.3097	−1.61535
$971$	24.7059	0.792851	0.396425	−	0.918067i	$-0.370251\pi$
$971$	24.7059	0.792851	0.396425	+	0.918067i	$0.370251\pi$
$972$	−1.00000	−0.0320750
$973$	0	0
$974$	−9.95990	−0.319136
$975$	32.1529	1.02972
$976$	6.81616	0.218180
$977$	11.5475	0.369438	0.184719	−	0.982791i	$-0.440862\pi$
$977$	11.5475	0.369438	0.184719	+	0.982791i	$0.440862\pi$
$978$	−8.66806	−0.277174
$979$	80.5954	2.57584
$980$	0	0
$981$	−18.9840	−0.606113
$982$	21.6604	0.691212
$983$	11.3509	0.362039	0.181019	−	0.983480i	$-0.442060\pi$
$983$	11.3509	0.362039	0.181019	+	0.983480i	$0.442060\pi$
$984$	1.94405	0.0619741
$985$	−37.6741	−1.20040
$986$	3.81598	0.121525
$987$	0	0
$988$	−46.7173	−1.48628
$989$	8.41960	0.267728
$990$	−17.9490	−0.570457
$991$	3.56950	0.113389	0.0566944	−	0.998392i	$-0.481944\pi$
$991$	3.56950	0.113389	0.0566944	+	0.998392i	$0.481944\pi$
$992$	−8.79881	−0.279362
$993$	−0.668064	−0.0212004
$994$	0	0
$995$	8.33670	0.264291
$996$	11.1921	0.354635
$997$	48.6187	1.53977	0.769885	−	0.638182i	$-0.220313\pi$
$997$	48.6187	1.53977	0.769885	+	0.638182i	$0.220313\pi$
$998$	−40.6974	−1.28825
$999$	−6.04368	−0.191214

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6762.2.a.ck.1.4	✓	4
7.6	odd	2		6762.2.a.cq.1.1	yes	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6762.2.a.ck.1.4	✓	4	1.1	even	1	trivial
6762.2.a.cq.1.1	yes	4	7.6	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +3.10651 q^{5} -1.00000 q^{6} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +3.10651 q^{5} -1.00000 q^{6} +1.00000 q^{8} +1.00000 q^{9} +3.10651 q^{10} -5.77786 q^{11} -1.00000 q^{12} -6.91399 q^{13} -3.10651 q^{15} +1.00000 q^{16} -1.17157 q^{17} +1.00000 q^{18} +6.75692 q^{19} +3.10651 q^{20} -5.77786 q^{22} +1.00000 q^{23} -1.00000 q^{24} +4.65041 q^{25} -6.91399 q^{26} -1.00000 q^{27} -3.25714 q^{29} -3.10651 q^{30} -8.79881 q^{31} +1.00000 q^{32} +5.77786 q^{33} -1.17157 q^{34} +1.00000 q^{36} +6.04368 q^{37} +6.75692 q^{38} +6.91399 q^{39} +3.10651 q^{40} -1.94405 q^{41} +8.41960 q^{43} -5.77786 q^{44} +3.10651 q^{45} +1.00000 q^{46} +1.68003 q^{47} -1.00000 q^{48} +4.65041 q^{50} +1.17157 q^{51} -6.91399 q^{52} -9.16246 q^{53} -1.00000 q^{54} -17.9490 q^{55} -6.75692 q^{57} -3.25714 q^{58} +3.26358 q^{59} -3.10651 q^{60} +6.81616 q^{61} -8.79881 q^{62} +1.00000 q^{64} -21.4784 q^{65} +5.77786 q^{66} +0.769189 q^{67} -1.17157 q^{68} -1.00000 q^{69} -0.393270 q^{71} +1.00000 q^{72} -10.4557 q^{73} +6.04368 q^{74} -4.65041 q^{75} +6.75692 q^{76} +6.91399 q^{78} -5.94900 q^{79} +3.10651 q^{80} +1.00000 q^{81} -1.94405 q^{82} -11.1921 q^{83} -3.63950 q^{85} +8.41960 q^{86} +3.25714 q^{87} -5.77786 q^{88} -13.9490 q^{89} +3.10651 q^{90} +1.00000 q^{92} +8.79881 q^{93} +1.68003 q^{94} +20.9904 q^{95} -1.00000 q^{96} -16.1949 q^{97} -5.77786 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 4 q^{2} - 4 q^{3} + 4 q^{4} + 2 q^{5} - 4 q^{6} + 4 q^{8} + 4 q^{9}+O(q^{10}) \) 4 * q + 4 * q^2 - 4 * q^3 + 4 * q^4 + 2 * q^5 - 4 * q^6 + 4 * q^8 + 4 * q^9	\( 4 q + 4 q^{2} - 4 q^{3} + 4 q^{4} + 2 q^{5} - 4 q^{6} + 4 q^{8} + 4 q^{9} + 2 q^{10} - 4 q^{11} - 4 q^{12} - 2 q^{13} - 2 q^{15} + 4 q^{16} - 16 q^{17} + 4 q^{18} + 4 q^{19} + 2 q^{20} - 4 q^{22} + 4 q^{23} - 4 q^{24} + 6 q^{25} - 2 q^{26} - 4 q^{27} - 10 q^{29} - 2 q^{30} - 20 q^{31} + 4 q^{32} + 4 q^{33} - 16 q^{34} + 4 q^{36} + 2 q^{37} + 4 q^{38} + 2 q^{39} + 2 q^{40} - 26 q^{41} + 2 q^{43} - 4 q^{44} + 2 q^{45} + 4 q^{46} - 2 q^{47} - 4 q^{48} + 6 q^{50} + 16 q^{51} - 2 q^{52} - 8 q^{53} - 4 q^{54} - 24 q^{55} - 4 q^{57} - 10 q^{58} - 2 q^{60} + 12 q^{61} - 20 q^{62} + 4 q^{64} - 22 q^{65} + 4 q^{66} - 16 q^{67} - 16 q^{68} - 4 q^{69} + 8 q^{71} + 4 q^{72} - 4 q^{73} + 2 q^{74} - 6 q^{75} + 4 q^{76} + 2 q^{78} + 24 q^{79} + 2 q^{80} + 4 q^{81} - 26 q^{82} - 20 q^{83} + 8 q^{85} + 2 q^{86} + 10 q^{87} - 4 q^{88} - 8 q^{89} + 2 q^{90} + 4 q^{92} + 20 q^{93} - 2 q^{94} + 4 q^{95} - 4 q^{96} - 26 q^{97} - 4 q^{99}+O(q^{100}) \) 4 * q + 4 * q^2 - 4 * q^3 + 4 * q^4 + 2 * q^5 - 4 * q^6 + 4 * q^8 + 4 * q^9 + 2 * q^10 - 4 * q^11 - 4 * q^12 - 2 * q^13 - 2 * q^15 + 4 * q^16 - 16 * q^17 + 4 * q^18 + 4 * q^19 + 2 * q^20 - 4 * q^22 + 4 * q^23 - 4 * q^24 + 6 * q^25 - 2 * q^26 - 4 * q^27 - 10 * q^29 - 2 * q^30 - 20 * q^31 + 4 * q^32 + 4 * q^33 - 16 * q^34 + 4 * q^36 + 2 * q^37 + 4 * q^38 + 2 * q^39 + 2 * q^40 - 26 * q^41 + 2 * q^43 - 4 * q^44 + 2 * q^45 + 4 * q^46 - 2 * q^47 - 4 * q^48 + 6 * q^50 + 16 * q^51 - 2 * q^52 - 8 * q^53 - 4 * q^54 - 24 * q^55 - 4 * q^57 - 10 * q^58 - 2 * q^60 + 12 * q^61 - 20 * q^62 + 4 * q^64 - 22 * q^65 + 4 * q^66 - 16 * q^67 - 16 * q^68 - 4 * q^69 + 8 * q^71 + 4 * q^72 - 4 * q^73 + 2 * q^74 - 6 * q^75 + 4 * q^76 + 2 * q^78 + 24 * q^79 + 2 * q^80 + 4 * q^81 - 26 * q^82 - 20 * q^83 + 8 * q^85 + 2 * q^86 + 10 * q^87 - 4 * q^88 - 8 * q^89 + 2 * q^90 + 4 * q^92 + 20 * q^93 - 2 * q^94 + 4 * q^95 - 4 * q^96 - 26 * q^97 - 4 * q^99

Introduction

L-functions

Modular forms

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Database

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