LMFDB - Embedded newform 6762.2.a.cn.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:	4.4.16448.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 2x^{3} - 7x^{2} + 8x + 14 $ x^4 - 2x^3 - 7x^2 + 8*x + 14
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-1.87996$ 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)

$f(q)$	$=$	$q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -0.879961 q^{5} -1.00000 q^{6} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -0.879961 q^{5} -1.00000 q^{6} +1.00000 q^{8} +1.00000 q^{9} -0.879961 q^{10} -4.07288 q^{11} -1.00000 q^{12} +2.22129 q^{13} +0.879961 q^{15} +1.00000 q^{16} +7.75992 q^{17} +1.00000 q^{18} +0.585786 q^{19} -0.879961 q^{20} -4.07288 q^{22} -1.00000 q^{23} -1.00000 q^{24} -4.22567 q^{25} +2.22129 q^{26} -1.00000 q^{27} +4.60713 q^{29} +0.879961 q^{30} +0.585786 q^{31} +1.00000 q^{32} +4.07288 q^{33} +7.75992 q^{34} +1.00000 q^{36} +3.53863 q^{37} +0.585786 q^{38} -2.22129 q^{39} -0.879961 q^{40} -0.124413 q^{41} -5.85158 q^{43} -4.07288 q^{44} -0.879961 q^{45} -1.00000 q^{46} +0.0515337 q^{47} -1.00000 q^{48} -4.22567 q^{50} -7.75992 q^{51} +2.22129 q^{52} -7.34390 q^{53} -1.00000 q^{54} +3.58397 q^{55} -0.585786 q^{57} +4.60713 q^{58} -4.90131 q^{59} +0.879961 q^{60} +2.14320 q^{61} +0.585786 q^{62} +1.00000 q^{64} -1.95465 q^{65} +4.07288 q^{66} -8.58835 q^{67} +7.75992 q^{68} +1.00000 q^{69} +4.07288 q^{71} +1.00000 q^{72} +4.97162 q^{73} +3.53863 q^{74} +4.22567 q^{75} +0.585786 q^{76} -2.22129 q^{78} -1.92712 q^{79} -0.879961 q^{80} +1.00000 q^{81} -0.124413 q^{82} +6.99819 q^{83} -6.82843 q^{85} -5.85158 q^{86} -4.60713 q^{87} -4.07288 q^{88} +10.4587 q^{89} -0.879961 q^{90} -1.00000 q^{92} -0.585786 q^{93} +0.0515337 q^{94} -0.515469 q^{95} -1.00000 q^{96} +17.5084 q^{97} -4.07288 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 4 q^{2} - 4 q^{3} + 4 q^{4} + 6 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 + 6 * q^5 - 4 * q^6 + 4 * q^8 + 4 * q^9	$ 4 q + 4 q^{2} - 4 q^{3} + 4 q^{4} + 6 q^{5} - 4 q^{6} + 4 q^{8} + 4 q^{9} + 6 q^{10} - 4 q^{12} + 10 q^{13} - 6 q^{15} + 4 q^{16} + 12 q^{17} + 4 q^{18} + 8 q^{19} + 6 q^{20} - 4 q^{23} - 4 q^{24} + 6 q^{25} + 10 q^{26} - 4 q^{27} + 6 q^{29} - 6 q^{30} + 8 q^{31} + 4 q^{32} + 12 q^{34} + 4 q^{36} - 6 q^{37} + 8 q^{38} - 10 q^{39} + 6 q^{40} + 14 q^{41} - 6 q^{43} + 6 q^{45} - 4 q^{46} + 2 q^{47} - 4 q^{48} + 6 q^{50} - 12 q^{51} + 10 q^{52} - 4 q^{53} - 4 q^{54} + 8 q^{55} - 8 q^{57} + 6 q^{58} + 8 q^{59} - 6 q^{60} + 12 q^{61} + 8 q^{62} + 4 q^{64} + 6 q^{65} - 4 q^{67} + 12 q^{68} + 4 q^{69} + 4 q^{72} + 12 q^{73} - 6 q^{74} - 6 q^{75} + 8 q^{76} - 10 q^{78} - 24 q^{79} + 6 q^{80} + 4 q^{81} + 14 q^{82} + 16 q^{83} - 16 q^{85} - 6 q^{86} - 6 q^{87} + 12 q^{89} + 6 q^{90} - 4 q^{92} - 8 q^{93} + 2 q^{94} + 12 q^{95} - 4 q^{96} + 30 q^{97}+O(q^{100}) $ 4 * q + 4 * q^2 - 4 * q^3 + 4 * q^4 + 6 * q^5 - 4 * q^6 + 4 * q^8 + 4 * q^9 + 6 * q^10 - 4 * q^12 + 10 * q^13 - 6 * q^15 + 4 * q^16 + 12 * q^17 + 4 * q^18 + 8 * q^19 + 6 * q^20 - 4 * q^23 - 4 * q^24 + 6 * q^25 + 10 * q^26 - 4 * q^27 + 6 * q^29 - 6 * q^30 + 8 * q^31 + 4 * q^32 + 12 * q^34 + 4 * q^36 - 6 * q^37 + 8 * q^38 - 10 * q^39 + 6 * q^40 + 14 * q^41 - 6 * q^43 + 6 * q^45 - 4 * q^46 + 2 * q^47 - 4 * q^48 + 6 * q^50 - 12 * q^51 + 10 * q^52 - 4 * q^53 - 4 * q^54 + 8 * q^55 - 8 * q^57 + 6 * q^58 + 8 * q^59 - 6 * q^60 + 12 * q^61 + 8 * q^62 + 4 * q^64 + 6 * q^65 - 4 * q^67 + 12 * q^68 + 4 * q^69 + 4 * q^72 + 12 * q^73 - 6 * q^74 - 6 * q^75 + 8 * q^76 - 10 * q^78 - 24 * q^79 + 6 * q^80 + 4 * q^81 + 14 * q^82 + 16 * q^83 - 16 * q^85 - 6 * q^86 - 6 * q^87 + 12 * q^89 + 6 * q^90 - 4 * q^92 - 8 * q^93 + 2 * q^94 + 12 * q^95 - 4 * q^96 + 30 * q^97

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
$5$	−0.879961	−0.393530	−0.196765	−	0.980451i	$-0.563044\pi$
$5$	−0.879961	−0.393530	−0.196765	+	0.980451i	$0.563044\pi$
$6$	−1.00000	−0.408248
$7$	0	0
$7$	0	0
$8$	1.00000	0.353553
$9$	1.00000	0.333333
$10$	−0.879961	−0.278268
$11$	−4.07288	−1.22802	−0.614010	−	0.789298i	$-0.710444\pi$
$11$	−4.07288	−1.22802	−0.614010	+	0.789298i	$0.710444\pi$
$12$	−1.00000	−0.288675
$13$	2.22129	0.616076	0.308038	−	0.951374i	$-0.400328\pi$
$13$	2.22129	0.616076	0.308038	+	0.951374i	$0.400328\pi$
$14$	0	0
$15$	0.879961	0.227205
$16$	1.00000	0.250000
$17$	7.75992	1.88206	0.941029	−	0.338327i	$-0.109861\pi$
$17$	7.75992	1.88206	0.941029	+	0.338327i	$0.109861\pi$
$18$	1.00000	0.235702
$19$	0.585786	0.134389	0.0671943	−	0.997740i	$-0.478595\pi$
$19$	0.585786	0.134389	0.0671943	+	0.997740i	$0.478595\pi$
$20$	−0.879961	−0.196765
$21$	0	0
$22$	−4.07288	−0.868341
$23$	−1.00000	−0.208514
$23$	−1.00000	−0.208514
$24$	−1.00000	−0.204124
$25$	−4.22567	−0.845134
$26$	2.22129	0.435632
$27$	−1.00000	−0.192450
$28$	0	0
$29$	4.60713	0.855523	0.427762	−	0.903892i	$-0.359302\pi$
$29$	4.60713	0.855523	0.427762	+	0.903892i	$0.359302\pi$
$30$	0.879961	0.160658
$31$	0.585786	0.105210	0.0526052	−	0.998615i	$-0.483248\pi$
$31$	0.585786	0.105210	0.0526052	+	0.998615i	$0.483248\pi$
$32$	1.00000	0.176777
$33$	4.07288	0.708997
$34$	7.75992	1.33082
$35$	0	0
$36$	1.00000	0.166667
$37$	3.53863	0.581747	0.290873	−	0.956762i	$-0.406054\pi$
$37$	3.53863	0.581747	0.290873	+	0.956762i	$0.406054\pi$
$38$	0.585786	0.0950271
$39$	−2.22129	−0.355692
$40$	−0.879961	−0.139134
$41$	−0.124413	−0.0194301	−0.00971505	−	0.999953i	$-0.503092\pi$
$41$	−0.124413	−0.0194301	−0.00971505	+	0.999953i	$0.503092\pi$
$42$	0	0
$43$	−5.85158	−0.892358	−0.446179	−	0.894944i	$-0.647216\pi$
$43$	−5.85158	−0.892358	−0.446179	+	0.894944i	$0.647216\pi$
$44$	−4.07288	−0.614010
$45$	−0.879961	−0.131177
$46$	−1.00000	−0.147442
$47$	0.0515337	0.00751696	0.00375848	−	0.999993i	$-0.498804\pi$
$47$	0.0515337	0.00751696	0.00375848	+	0.999993i	$0.498804\pi$
$48$	−1.00000	−0.144338
$49$	0	0
$50$	−4.22567	−0.597600
$51$	−7.75992	−1.08661
$52$	2.22129	0.308038
$53$	−7.34390	−1.00876	−0.504381	−	0.863481i	$-0.668279\pi$
$53$	−7.34390	−1.00876	−0.504381	+	0.863481i	$0.668279\pi$
$54$	−1.00000	−0.136083
$55$	3.58397	0.483263
$56$	0	0
$57$	−0.585786	−0.0775893
$58$	4.60713	0.604946
$59$	−4.90131	−0.638096	−0.319048	−	0.947739i	$-0.603363\pi$
$59$	−4.90131	−0.638096	−0.319048	+	0.947739i	$0.603363\pi$
$60$	0.879961	0.113602
$61$	2.14320	0.274408	0.137204	−	0.990543i	$-0.456188\pi$
$61$	2.14320	0.274408	0.137204	+	0.990543i	$0.456188\pi$
$62$	0.585786	0.0743950
$63$	0	0
$64$	1.00000	0.125000
$65$	−1.95465	−0.242445
$66$	4.07288	0.501337
$67$	−8.58835	−1.04923	−0.524617	−	0.851338i	$-0.675791\pi$
$67$	−8.58835	−1.04923	−0.524617	+	0.851338i	$0.675791\pi$
$68$	7.75992	0.941029
$69$	1.00000	0.120386
$70$	0	0
$71$	4.07288	0.483362	0.241681	−	0.970356i	$-0.422301\pi$
$71$	4.07288	0.483362	0.241681	+	0.970356i	$0.422301\pi$
$72$	1.00000	0.117851
$73$	4.97162	0.581885	0.290942	−	0.956741i	$-0.406031\pi$
$73$	4.97162	0.581885	0.290942	+	0.956741i	$0.406031\pi$
$74$	3.53863	0.411357
$75$	4.22567	0.487938
$76$	0.585786	0.0671943
$77$	0	0
$78$	−2.22129	−0.251512
$79$	−1.92712	−0.216818	−0.108409	−	0.994106i	$-0.534576\pi$
$79$	−1.92712	−0.216818	−0.108409	+	0.994106i	$0.534576\pi$
$80$	−0.879961	−0.0983826
$81$	1.00000	0.111111
$82$	−0.124413	−0.0137392
$83$	6.99819	0.768151	0.384075	−	0.923302i	$-0.374520\pi$
$83$	6.99819	0.768151	0.384075	+	0.923302i	$0.374520\pi$
$84$	0	0
$85$	−6.82843	−0.740647
$86$	−5.85158	−0.630993
$87$	−4.60713	−0.493936
$88$	−4.07288	−0.434170
$89$	10.4587	1.10862	0.554311	−	0.832310i	$-0.312982\pi$
$89$	10.4587	1.10862	0.554311	+	0.832310i	$0.312982\pi$
$90$	−0.879961	−0.0927560
$91$	0	0
$92$	−1.00000	−0.104257
$93$	−0.585786	−0.0607432
$94$	0.0515337	0.00531530
$95$	−0.515469	−0.0528860
$96$	−1.00000	−0.102062
$97$	17.5084	1.77771	0.888856	−	0.458186i	$-0.151501\pi$
$97$	17.5084	1.77771	0.888856	+	0.458186i	$0.151501\pi$
$98$	0	0
$99$	−4.07288	−0.409340
$100$	−4.22567	−0.422567
$101$	−4.41240	−0.439050	−0.219525	−	0.975607i	$-0.570451\pi$
$101$	−4.41240	−0.439050	−0.219525	+	0.975607i	$0.570451\pi$
$102$	−7.75992	−0.768347
$103$	3.77871	0.372327	0.186163	−	0.982519i	$-0.440395\pi$
$103$	3.77871	0.372327	0.186163	+	0.982519i	$0.440395\pi$
$104$	2.22129	0.217816
$105$	0	0
$106$	−7.34390	−0.713302
$107$	−3.61416	−0.349394	−0.174697	−	0.984622i	$-0.555895\pi$
$107$	−3.61416	−0.349394	−0.174697	+	0.984622i	$0.555895\pi$
$108$	−1.00000	−0.0962250
$109$	6.42381	0.615289	0.307645	−	0.951501i	$-0.400459\pi$
$109$	6.42381	0.615289	0.307645	+	0.951501i	$0.400459\pi$
$110$	3.58397	0.341719
$111$	−3.53863	−0.335872
$112$	0	0
$113$	13.6115	1.28046	0.640231	−	0.768182i	$-0.278838\pi$
$113$	13.6115	1.28046	0.640231	+	0.768182i	$0.278838\pi$
$114$	−0.585786	−0.0548639
$115$	0.879961	0.0820568
$116$	4.60713	0.427762
$117$	2.22129	0.205359
$118$	−4.90131	−0.451202
$119$	0	0
$120$	0.879961	0.0803291
$121$	5.58835	0.508032
$122$	2.14320	0.194036
$123$	0.124413	0.0112180
$124$	0.585786	0.0526052
$125$	8.11823	0.726116
$126$	0	0
$127$	5.92446	0.525711	0.262856	−	0.964835i	$-0.415336\pi$
$127$	5.92446	0.525711	0.262856	+	0.964835i	$0.415336\pi$
$128$	1.00000	0.0883883
$129$	5.85158	0.515203
$130$	−1.95465	−0.171434
$131$	6.76430	0.590999	0.295500	−	0.955343i	$-0.404514\pi$
$131$	6.76430	0.590999	0.295500	+	0.955343i	$0.404514\pi$
$132$	4.07288	0.354499
$133$	0	0
$134$	−8.58835	−0.741920
$135$	0.879961	0.0757350
$136$	7.75992	0.665408
$137$	5.56881	0.475776	0.237888	−	0.971293i	$-0.423545\pi$
$137$	5.56881	0.475776	0.237888	+	0.971293i	$0.423545\pi$
$138$	1.00000	0.0851257
$139$	12.8258	1.08787	0.543934	−	0.839128i	$-0.316934\pi$
$139$	12.8258	1.08787	0.543934	+	0.839128i	$0.316934\pi$
$140$	0	0
$141$	−0.0515337	−0.00433992
$142$	4.07288	0.341788
$143$	−9.04707	−0.756554
$144$	1.00000	0.0833333
$145$	−4.05410	−0.336674
$146$	4.97162	0.411455
$147$	0	0
$148$	3.53863	0.290873
$149$	13.9322	1.14137	0.570687	−	0.821168i	$-0.306677\pi$
$149$	13.9322	1.14137	0.570687	+	0.821168i	$0.306677\pi$
$150$	4.22567	0.345024
$151$	1.15279	0.0938127	0.0469063	−	0.998899i	$-0.485064\pi$
$151$	1.15279	0.0938127	0.0469063	+	0.998899i	$0.485064\pi$
$152$	0.585786	0.0475136
$153$	7.75992	0.627352
$154$	0	0
$155$	−0.515469	−0.0414035
$156$	−2.22129	−0.177846
$157$	15.6970	1.25276	0.626378	−	0.779520i	$-0.284537\pi$
$157$	15.6970	1.25276	0.626378	+	0.779520i	$0.284537\pi$
$158$	−1.92712	−0.153313
$159$	7.34390	0.582409
$160$	−0.879961	−0.0695670
$161$	0	0
$162$	1.00000	0.0785674
$163$	−8.48528	−0.664619	−0.332309	−	0.943170i	$-0.607828\pi$
$163$	−8.48528	−0.664619	−0.332309	+	0.943170i	$0.607828\pi$
$164$	−0.124413	−0.00971505
$165$	−3.58397	−0.279012
$166$	6.99819	0.543165
$167$	19.0409	1.47343	0.736714	−	0.676205i	$-0.236377\pi$
$167$	19.0409	1.47343	0.736714	+	0.676205i	$0.236377\pi$
$168$	0	0
$169$	−8.06585	−0.620450
$170$	−6.82843	−0.523716
$171$	0.585786	0.0447962
$172$	−5.85158	−0.446179
$173$	−12.0087	−0.913008	−0.456504	−	0.889721i	$-0.650899\pi$
$173$	−12.0087	−0.913008	−0.456504	+	0.889721i	$0.650899\pi$
$174$	−4.60713	−0.349266
$175$	0	0
$176$	−4.07288	−0.307005
$177$	4.90131	0.368405
$178$	10.4587	0.783914
$179$	10.6461	0.795725	0.397862	−	0.917445i	$-0.369752\pi$
$179$	10.6461	0.795725	0.397862	+	0.917445i	$0.369752\pi$
$180$	−0.879961	−0.0655884
$181$	−21.5385	−1.60095	−0.800473	−	0.599368i	$-0.795418\pi$
$181$	−21.5385	−1.60095	−0.800473	+	0.599368i	$0.795418\pi$
$182$	0	0
$183$	−2.14320	−0.158430
$184$	−1.00000	−0.0737210
$185$	−3.11385	−0.228935
$186$	−0.585786	−0.0429519
$187$	−31.6052	−2.31120
$188$	0.0515337	0.00375848
$189$	0	0
$190$	−0.515469	−0.0373961
$191$	25.2194	1.82481	0.912405	−	0.409287i	$-0.134223\pi$
$191$	25.2194	1.82481	0.912405	+	0.409287i	$0.134223\pi$
$192$	−1.00000	−0.0721688
$193$	−7.50844	−0.540469	−0.270235	−	0.962794i	$-0.587101\pi$
$193$	−7.50844	−0.540469	−0.270235	+	0.962794i	$0.587101\pi$
$194$	17.5084	1.25703
$195$	1.95465	0.139976
$196$	0	0
$197$	6.66388	0.474782	0.237391	−	0.971414i	$-0.423708\pi$
$197$	6.66388	0.474782	0.237391	+	0.971414i	$0.423708\pi$
$198$	−4.07288	−0.289447
$199$	−4.80964	−0.340947	−0.170473	−	0.985362i	$-0.554530\pi$
$199$	−4.80964	−0.340947	−0.170473	+	0.985362i	$0.554530\pi$
$200$	−4.22567	−0.298800
$201$	8.58835	0.605775
$202$	−4.41240	−0.310456
$203$	0	0
$204$	−7.75992	−0.543303
$205$	0.109479	0.00764634
$206$	3.77871	0.263275
$207$	−1.00000	−0.0695048
$208$	2.22129	0.154019
$209$	−2.38584	−0.165032
$210$	0	0
$211$	4.79824	0.330324	0.165162	−	0.986266i	$-0.447185\pi$
$211$	4.79824	0.330324	0.165162	+	0.986266i	$0.447185\pi$
$212$	−7.34390	−0.504381
$213$	−4.07288	−0.279069
$214$	−3.61416	−0.247059
$215$	5.14917	0.351170
$216$	−1.00000	−0.0680414
$217$	0	0
$218$	6.42381	0.435075
$219$	−4.97162	−0.335951
$220$	3.58397	0.241632
$221$	17.2371	1.15949
$222$	−3.53863	−0.237497
$223$	−14.5983	−0.977574	−0.488787	−	0.872403i	$-0.662560\pi$
$223$	−14.5983	−0.977574	−0.488787	+	0.872403i	$0.662560\pi$
$224$	0	0
$225$	−4.22567	−0.281711
$226$	13.6115	0.905424
$227$	−9.39543	−0.623597	−0.311798	−	0.950148i	$-0.600931\pi$
$227$	−9.39543	−0.623597	−0.311798	+	0.950148i	$0.600931\pi$
$228$	−0.585786	−0.0387947
$229$	7.14757	0.472325	0.236162	−	0.971714i	$-0.424110\pi$
$229$	7.14757	0.472325	0.236162	+	0.971714i	$0.424110\pi$
$230$	0.879961	0.0580229
$231$	0	0
$232$	4.60713	0.302473
$233$	15.3439	1.00521	0.502606	−	0.864516i	$-0.332375\pi$
$233$	15.3439	1.00521	0.502606	+	0.864516i	$0.332375\pi$
$234$	2.22129	0.145211
$235$	−0.0453476	−0.00295815
$236$	−4.90131	−0.319048
$237$	1.92712	0.125180
$238$	0	0
$239$	17.7687	1.14936	0.574680	−	0.818378i	$-0.305127\pi$
$239$	17.7687	1.14936	0.574680	+	0.818378i	$0.305127\pi$
$240$	0.879961	0.0568012
$241$	5.07629	0.326992	0.163496	−	0.986544i	$-0.447723\pi$
$241$	5.07629	0.326992	0.163496	+	0.986544i	$0.447723\pi$
$242$	5.58835	0.359233
$243$	−1.00000	−0.0641500
$244$	2.14320	0.137204
$245$	0	0
$246$	0.124413	0.00793231
$247$	1.30120	0.0827936
$248$	0.585786	0.0371975
$249$	−6.99819	−0.443492
$250$	8.11823	0.513442
$251$	13.7473	0.867723	0.433862	−	0.900979i	$-0.357151\pi$
$251$	13.7473	0.867723	0.433862	+	0.900979i	$0.357151\pi$
$252$	0	0
$253$	4.07288	0.256060
$254$	5.92446	0.371734
$255$	6.82843	0.427613
$256$	1.00000	0.0625000
$257$	11.0069	0.686594	0.343297	−	0.939227i	$-0.388456\pi$
$257$	11.0069	0.686594	0.343297	+	0.939227i	$0.388456\pi$
$258$	5.85158	0.364304
$259$	0	0
$260$	−1.95465	−0.121222
$261$	4.60713	0.285174
$262$	6.76430	0.417900
$263$	−26.7153	−1.64734	−0.823669	−	0.567071i	$-0.808076\pi$
$263$	−26.7153	−1.64734	−0.823669	+	0.567071i	$0.808076\pi$
$264$	4.07288	0.250668
$265$	6.46234	0.396978
$266$	0	0
$267$	−10.4587	−0.640063
$268$	−8.58835	−0.524617
$269$	17.1693	1.04683	0.523416	−	0.852077i	$-0.324657\pi$
$269$	17.1693	1.04683	0.523416	+	0.852077i	$0.324657\pi$
$270$	0.879961	0.0535527
$271$	−17.5260	−1.06463	−0.532315	−	0.846546i	$-0.678678\pi$
$271$	−17.5260	−1.06463	−0.532315	+	0.846546i	$0.678678\pi$
$272$	7.75992	0.470514
$273$	0	0
$274$	5.56881	0.336424
$275$	17.2106	1.03784
$276$	1.00000	0.0601929
$277$	−5.00075	−0.300466	−0.150233	−	0.988651i	$-0.548002\pi$
$277$	−5.00075	−0.300466	−0.150233	+	0.988651i	$0.548002\pi$
$278$	12.8258	0.769239
$279$	0.585786	0.0350701
$280$	0	0
$281$	4.73676	0.282572	0.141286	−	0.989969i	$-0.454876\pi$
$281$	4.73676	0.282572	0.141286	+	0.989969i	$0.454876\pi$
$282$	−0.0515337	−0.00306879
$283$	−5.12101	−0.304412	−0.152206	−	0.988349i	$-0.548638\pi$
$283$	−5.12101	−0.304412	−0.152206	+	0.988349i	$0.548638\pi$
$284$	4.07288	0.241681
$285$	0.515469	0.0305338
$286$	−9.04707	−0.534964
$287$	0	0
$288$	1.00000	0.0589256
$289$	43.2164	2.54214
$290$	−4.05410	−0.238065
$291$	−17.5084	−1.02636
$292$	4.97162	0.290942
$293$	9.45315	0.552259	0.276129	−	0.961120i	$-0.410948\pi$
$293$	9.45315	0.552259	0.276129	+	0.961120i	$0.410948\pi$
$294$	0	0
$295$	4.31296	0.251110
$296$	3.53863	0.205679
$297$	4.07288	0.236332
$298$	13.9322	0.807073
$299$	−2.22129	−0.128461
$300$	4.22567	0.243969
$301$	0	0
$302$	1.15279	0.0663356
$303$	4.41240	0.253486
$304$	0.585786	0.0335972
$305$	−1.88593	−0.107988
$306$	7.75992	0.443605
$307$	29.8036	1.70098	0.850490	−	0.525991i	$-0.176305\pi$
$307$	29.8036	1.70098	0.850490	+	0.525991i	$0.176305\pi$
$308$	0	0
$309$	−3.77871	−0.214963
$310$	−0.515469	−0.0292767
$311$	−18.5983	−1.05461	−0.527306	−	0.849675i	$-0.676798\pi$
$311$	−18.5983	−1.05461	−0.527306	+	0.849675i	$0.676798\pi$
$312$	−2.22129	−0.125756
$313$	17.1803	0.971089	0.485545	−	0.874212i	$-0.338621\pi$
$313$	17.1803	0.971089	0.485545	+	0.874212i	$0.338621\pi$
$314$	15.6970	0.885832
$315$	0	0
$316$	−1.92712	−0.108409
$317$	2.45775	0.138041	0.0690205	−	0.997615i	$-0.478013\pi$
$317$	2.45775	0.138041	0.0690205	+	0.997615i	$0.478013\pi$
$318$	7.34390	0.411825
$319$	−18.7643	−1.05060
$320$	−0.879961	−0.0491913
$321$	3.61416	0.201723
$322$	0	0
$323$	4.54566	0.252927
$324$	1.00000	0.0555556
$325$	−9.38646	−0.520667
$326$	−8.48528	−0.469956
$327$	−6.42381	−0.355237
$328$	−0.124413	−0.00686958
$329$	0	0
$330$	−3.58397	−0.197291
$331$	19.4595	1.06959	0.534795	−	0.844982i	$-0.320389\pi$
$331$	19.4595	1.06959	0.534795	+	0.844982i	$0.320389\pi$
$332$	6.99819	0.384075
$333$	3.53863	0.193916
$334$	19.0409	1.04187
$335$	7.55741	0.412905
$336$	0	0
$337$	26.0213	1.41747	0.708734	−	0.705476i	$-0.249267\pi$
$337$	26.0213	1.41747	0.708734	+	0.705476i	$0.249267\pi$
$338$	−8.06585	−0.438724
$339$	−13.6115	−0.739276
$340$	−6.82843	−0.370323
$341$	−2.38584	−0.129200
$342$	0.585786	0.0316757
$343$	0	0
$344$	−5.85158	−0.315496
$345$	−0.879961	−0.0473755
$346$	−12.0087	−0.645594
$347$	−31.4229	−1.68687	−0.843434	−	0.537233i	$-0.819470\pi$
$347$	−31.4229	−1.68687	−0.843434	+	0.537233i	$0.819470\pi$
$348$	−4.60713	−0.246968
$349$	−13.3688	−0.715614	−0.357807	−	0.933796i	$-0.616475\pi$
$349$	−13.3688	−0.715614	−0.357807	+	0.933796i	$0.616475\pi$
$350$	0	0
$351$	−2.22129	−0.118564
$352$	−4.07288	−0.217085
$353$	−15.8005	−0.840973	−0.420487	−	0.907299i	$-0.638141\pi$
$353$	−15.8005	−0.840973	−0.420487	+	0.907299i	$0.638141\pi$
$354$	4.90131	0.260502
$355$	−3.58397	−0.190218
$356$	10.4587	0.554311
$357$	0	0
$358$	10.6461	0.562662
$359$	26.9642	1.42311	0.711557	−	0.702629i	$-0.247990\pi$
$359$	26.9642	1.42311	0.711557	+	0.702629i	$0.247990\pi$
$360$	−0.879961	−0.0463780
$361$	−18.6569	−0.981940
$362$	−21.5385	−1.13204
$363$	−5.58835	−0.293312
$364$	0	0
$365$	−4.37483	−0.228989
$366$	−2.14320	−0.112027
$367$	5.67201	0.296077	0.148038	−	0.988982i	$-0.452704\pi$
$367$	5.67201	0.296077	0.148038	+	0.988982i	$0.452704\pi$
$368$	−1.00000	−0.0521286
$369$	−0.124413	−0.00647670
$370$	−3.11385	−0.161882
$371$	0	0
$372$	−0.585786	−0.0303716
$373$	7.49704	0.388182	0.194091	−	0.980984i	$-0.437824\pi$
$373$	7.49704	0.388182	0.194091	+	0.980984i	$0.437824\pi$
$374$	−31.6052	−1.63427
$375$	−8.11823	−0.419223
$376$	0.0515337	0.00265765
$377$	10.2338	0.527067
$378$	0	0
$379$	−2.24273	−0.115202	−0.0576008	−	0.998340i	$-0.518345\pi$
$379$	−2.24273	−0.115202	−0.0576008	+	0.998340i	$0.518345\pi$
$380$	−0.515469	−0.0264430
$381$	−5.92446	−0.303520
$382$	25.2194	1.29034
$383$	24.0693	1.22988	0.614941	−	0.788573i	$-0.289180\pi$
$383$	24.0693	1.22988	0.614941	+	0.788573i	$0.289180\pi$
$384$	−1.00000	−0.0510310
$385$	0	0
$386$	−7.50844	−0.382169
$387$	−5.85158	−0.297453
$388$	17.5084	0.888856
$389$	−11.9021	−0.603458	−0.301729	−	0.953394i	$-0.597564\pi$
$389$	−11.9021	−0.603458	−0.301729	+	0.953394i	$0.597564\pi$
$390$	1.95465	0.0989777
$391$	−7.75992	−0.392436
$392$	0	0
$393$	−6.76430	−0.341214
$394$	6.66388	0.335722
$395$	1.69579	0.0853245
$396$	−4.07288	−0.204670
$397$	−12.7305	−0.638925	−0.319462	−	0.947599i	$-0.603502\pi$
$397$	−12.7305	−0.638925	−0.319462	+	0.947599i	$0.603502\pi$
$398$	−4.80964	−0.241086
$399$	0	0
$400$	−4.22567	−0.211283
$401$	−24.8032	−1.23861	−0.619307	−	0.785149i	$-0.712586\pi$
$401$	−24.8032	−1.23861	−0.619307	+	0.785149i	$0.712586\pi$
$402$	8.58835	0.428348
$403$	1.30120	0.0648176
$404$	−4.41240	−0.219525
$405$	−0.879961	−0.0437256
$406$	0	0
$407$	−14.4124	−0.714396
$408$	−7.75992	−0.384173
$409$	−13.1174	−0.648613	−0.324306	−	0.945952i	$-0.605131\pi$
$409$	−13.1174	−0.648613	−0.324306	+	0.945952i	$0.605131\pi$
$410$	0.109479	0.00540678
$411$	−5.56881	−0.274689
$412$	3.77871	0.186163
$413$	0	0
$414$	−1.00000	−0.0491473
$415$	−6.15813	−0.302291
$416$	2.22129	0.108908
$417$	−12.8258	−0.628081
$418$	−2.38584	−0.116695
$419$	31.2417	1.52626	0.763129	−	0.646247i	$-0.223662\pi$
$419$	31.2417	1.52626	0.763129	+	0.646247i	$0.223662\pi$
$420$	0	0
$421$	−38.1129	−1.85751	−0.928755	−	0.370694i	$-0.879120\pi$
$421$	−38.1129	−1.85751	−0.928755	+	0.370694i	$0.879120\pi$
$422$	4.79824	0.233575
$423$	0.0515337	0.00250565
$424$	−7.34390	−0.356651
$425$	−32.7909	−1.59059
$426$	−4.07288	−0.197332
$427$	0	0
$428$	−3.61416	−0.174697
$429$	9.04707	0.436796
$430$	5.14917	0.248315
$431$	29.4031	1.41630	0.708149	−	0.706063i	$-0.249530\pi$
$431$	29.4031	1.41630	0.708149	+	0.706063i	$0.249530\pi$
$432$	−1.00000	−0.0481125
$433$	−14.8309	−0.712727	−0.356364	−	0.934347i	$-0.615984\pi$
$433$	−14.8309	−0.712727	−0.356364	+	0.934347i	$0.615984\pi$
$434$	0	0
$435$	4.05410	0.194379
$436$	6.42381	0.307645
$437$	−0.585786	−0.0280220
$438$	−4.97162	−0.237553
$439$	0.299392	0.0142892	0.00714461	−	0.999974i	$-0.497726\pi$
$439$	0.299392	0.0142892	0.00714461	+	0.999974i	$0.497726\pi$
$440$	3.58397	0.170859
$441$	0	0
$442$	17.2371	0.819884
$443$	10.5202	0.499829	0.249915	−	0.968268i	$-0.419597\pi$
$443$	10.5202	0.499829	0.249915	+	0.968268i	$0.419597\pi$
$444$	−3.53863	−0.167936
$445$	−9.20326	−0.436276
$446$	−14.5983	−0.691249
$447$	−13.9322	−0.658973
$448$	0	0
$449$	−40.9505	−1.93257	−0.966287	−	0.257469i	$-0.917112\pi$
$449$	−40.9505	−1.93257	−0.966287	+	0.257469i	$0.917112\pi$
$450$	−4.22567	−0.199200
$451$	0.506721	0.0238605
$452$	13.6115	0.640231
$453$	−1.15279	−0.0541628
$454$	−9.39543	−0.440949
$455$	0	0
$456$	−0.585786	−0.0274320
$457$	15.1539	0.708869	0.354435	−	0.935081i	$-0.384673\pi$
$457$	15.1539	0.708869	0.354435	+	0.935081i	$0.384673\pi$
$458$	7.14757	0.333984
$459$	−7.75992	−0.362202
$460$	0.879961	0.0410284
$461$	22.0089	1.02506	0.512528	−	0.858671i	$-0.328709\pi$
$461$	22.0089	1.02506	0.512528	+	0.858671i	$0.328709\pi$
$462$	0	0
$463$	−1.83546	−0.0853009	−0.0426505	−	0.999090i	$-0.513580\pi$
$463$	−1.83546	−0.0853009	−0.0426505	+	0.999090i	$0.513580\pi$
$464$	4.60713	0.213881
$465$	0.515469	0.0239043
$466$	15.3439	0.710792
$467$	−22.4586	−1.03926	−0.519631	−	0.854391i	$-0.673930\pi$
$467$	−22.4586	−1.03926	−0.519631	+	0.854391i	$0.673930\pi$
$468$	2.22129	0.102679
$469$	0	0
$470$	−0.0453476	−0.00209173
$471$	−15.6970	−0.723279
$472$	−4.90131	−0.225601
$473$	23.8328	1.09583
$474$	1.92712	0.0885156
$475$	−2.47534	−0.113576
$476$	0	0
$477$	−7.34390	−0.336254
$478$	17.7687	0.812720
$479$	−19.6760	−0.899021	−0.449511	−	0.893275i	$-0.648402\pi$
$479$	−19.6760	−0.899021	−0.449511	+	0.893275i	$0.648402\pi$
$480$	0.879961	0.0401645
$481$	7.86033	0.358400
$482$	5.07629	0.231218
$483$	0	0
$484$	5.58835	0.254016
$485$	−15.4067	−0.699584
$486$	−1.00000	−0.0453609
$487$	−6.01154	−0.272409	−0.136204	−	0.990681i	$-0.543490\pi$
$487$	−6.01154	−0.272409	−0.136204	+	0.990681i	$0.543490\pi$
$488$	2.14320	0.0970180
$489$	8.48528	0.383718
$490$	0	0
$491$	26.2401	1.18420	0.592099	−	0.805865i	$-0.298299\pi$
$491$	26.2401	1.18420	0.592099	+	0.805865i	$0.298299\pi$
$492$	0.124413	0.00560899
$493$	35.7510	1.61014
$494$	1.30120	0.0585440
$495$	3.58397	0.161088
$496$	0.585786	0.0263026
$497$	0	0
$498$	−6.99819	−0.313596
$499$	−6.49934	−0.290950	−0.145475	−	0.989362i	$-0.546471\pi$
$499$	−6.49934	−0.290950	−0.145475	+	0.989362i	$0.546471\pi$
$500$	8.11823	0.363058
$501$	−19.0409	−0.850684
$502$	13.7473	0.613573
$503$	−34.4071	−1.53414	−0.767068	−	0.641566i	$-0.778285\pi$
$503$	−34.4071	−1.53414	−0.767068	+	0.641566i	$0.778285\pi$
$504$	0	0
$505$	3.88274	0.172780
$506$	4.07288	0.181062
$507$	8.06585	0.358217
$508$	5.92446	0.262856
$509$	−7.76368	−0.344119	−0.172059	−	0.985087i	$-0.555042\pi$
$509$	−7.76368	−0.344119	−0.172059	+	0.985087i	$0.555042\pi$
$510$	6.82843	0.302368
$511$	0	0
$512$	1.00000	0.0441942
$513$	−0.585786	−0.0258631
$514$	11.0069	0.485495
$515$	−3.32511	−0.146522
$516$	5.85158	0.257602
$517$	−0.209891	−0.00923098
$518$	0	0
$519$	12.0087	0.527126
$520$	−1.95465	−0.0857172
$521$	31.7347	1.39032	0.695162	−	0.718853i	$-0.255333\pi$
$521$	31.7347	1.39032	0.695162	+	0.718853i	$0.255333\pi$
$522$	4.60713	0.201649
$523$	0.0771298	0.00337265	0.00168632	−	0.999999i	$-0.499463\pi$
$523$	0.0771298	0.00337265	0.00168632	+	0.999999i	$0.499463\pi$
$524$	6.76430	0.295500
$525$	0	0
$526$	−26.7153	−1.16484
$527$	4.54566	0.198012
$528$	4.07288	0.177249
$529$	1.00000	0.0434783
$530$	6.46234	0.280706
$531$	−4.90131	−0.212699
$532$	0	0
$533$	−0.276359	−0.0119704
$534$	−10.4587	−0.452593
$535$	3.18032	0.137497
$536$	−8.58835	−0.370960
$537$	−10.6461	−0.459412
$538$	17.1693	0.740222
$539$	0	0
$540$	0.879961	0.0378675
$541$	10.9550	0.470992	0.235496	−	0.971875i	$-0.424328\pi$
$541$	10.9550	0.470992	0.235496	+	0.971875i	$0.424328\pi$
$542$	−17.5260	−0.752807
$543$	21.5385	0.924307
$544$	7.75992	0.332704
$545$	−5.65270	−0.242135
$546$	0	0
$547$	−34.9490	−1.49431	−0.747155	−	0.664649i	$-0.768581\pi$
$547$	−34.9490	−1.49431	−0.747155	+	0.664649i	$0.768581\pi$
$548$	5.56881	0.237888
$549$	2.14320	0.0914694
$550$	17.2106	0.733864
$551$	2.69880	0.114973
$552$	1.00000	0.0425628
$553$	0	0
$554$	−5.00075	−0.212462
$555$	3.11385	0.132176
$556$	12.8258	0.543934
$557$	9.65685	0.409174	0.204587	−	0.978848i	$-0.434415\pi$
$557$	9.65685	0.409174	0.204587	+	0.978848i	$0.434415\pi$
$558$	0.585786	0.0247983
$559$	−12.9981	−0.549761
$560$	0	0
$561$	31.6052	1.33437
$562$	4.73676	0.199808
$563$	−23.7010	−0.998878	−0.499439	−	0.866349i	$-0.666461\pi$
$563$	−23.7010	−0.998878	−0.499439	+	0.866349i	$0.666461\pi$
$564$	−0.0515337	−0.00216996
$565$	−11.9776	−0.503901
$566$	−5.12101	−0.215252
$567$	0	0
$568$	4.07288	0.170894
$569$	20.8825	0.875441	0.437720	−	0.899111i	$-0.355786\pi$
$569$	20.8825	0.875441	0.437720	+	0.899111i	$0.355786\pi$
$570$	0.515469	0.0215906
$571$	0.686292	0.0287204	0.0143602	−	0.999897i	$-0.495429\pi$
$571$	0.686292	0.0287204	0.0143602	+	0.999897i	$0.495429\pi$
$572$	−9.04707	−0.378277
$573$	−25.2194	−1.05356
$574$	0	0
$575$	4.22567	0.176223
$576$	1.00000	0.0416667
$577$	29.9707	1.24770	0.623848	−	0.781546i	$-0.285568\pi$
$577$	29.9707	1.24770	0.623848	+	0.781546i	$0.285568\pi$
$578$	43.2164	1.79756
$579$	7.50844	0.312040
$580$	−4.05410	−0.168337
$581$	0	0
$582$	−17.5084	−0.725748
$583$	29.9108	1.23878
$584$	4.97162	0.205727
$585$	−1.95465	−0.0808149
$586$	9.45315	0.390506
$587$	24.2577	1.00122	0.500611	−	0.865672i	$-0.333109\pi$
$587$	24.2577	1.00122	0.500611	+	0.865672i	$0.333109\pi$
$588$	0	0
$589$	0.343146	0.0141391
$590$	4.31296	0.177562
$591$	−6.66388	−0.274116
$592$	3.53863	0.145437
$593$	20.7179	0.850782	0.425391	−	0.905010i	$-0.360137\pi$
$593$	20.7179	0.850782	0.425391	+	0.905010i	$0.360137\pi$
$594$	4.07288	0.167112
$595$	0	0
$596$	13.9322	0.570687
$597$	4.80964	0.196846
$598$	−2.22129	−0.0908355
$599$	29.9322	1.22300	0.611499	−	0.791245i	$-0.290567\pi$
$599$	29.9322	1.22300	0.611499	+	0.791245i	$0.290567\pi$
$600$	4.22567	0.172512
$601$	23.2985	0.950364	0.475182	−	0.879888i	$-0.342382\pi$
$601$	23.2985	0.950364	0.475182	+	0.879888i	$0.342382\pi$
$602$	0	0
$603$	−8.58835	−0.349745
$604$	1.15279	0.0469063
$605$	−4.91753	−0.199926
$606$	4.41240	0.179242
$607$	−21.6809	−0.879999	−0.439999	−	0.897998i	$-0.645021\pi$
$607$	−21.6809	−0.879999	−0.439999	+	0.897998i	$0.645021\pi$
$608$	0.585786	0.0237568
$609$	0	0
$610$	−1.88593	−0.0763590
$611$	0.114472	0.00463102
$612$	7.75992	0.313676
$613$	−30.9746	−1.25105	−0.625526	−	0.780203i	$-0.715116\pi$
$613$	−30.9746	−1.25105	−0.625526	+	0.780203i	$0.715116\pi$
$614$	29.8036	1.20277
$615$	−0.109479	−0.00441462
$616$	0	0
$617$	−12.6274	−0.508361	−0.254180	−	0.967157i	$-0.581806\pi$
$617$	−12.6274	−0.508361	−0.254180	+	0.967157i	$0.581806\pi$
$618$	−3.77871	−0.152002
$619$	35.4672	1.42555	0.712773	−	0.701395i	$-0.247439\pi$
$619$	35.4672	1.42555	0.712773	+	0.701395i	$0.247439\pi$
$620$	−0.515469	−0.0207017
$621$	1.00000	0.0401286
$622$	−18.5983	−0.745724
$623$	0	0
$624$	−2.22129	−0.0889230
$625$	13.9846	0.559385
$626$	17.1803	0.686664
$627$	2.38584	0.0952812
$628$	15.6970	0.626378
$629$	27.4595	1.09488
$630$	0	0
$631$	−16.3025	−0.648993	−0.324497	−	0.945887i	$-0.605195\pi$
$631$	−16.3025	−0.648993	−0.324497	+	0.945887i	$0.605195\pi$
$632$	−1.92712	−0.0766567
$633$	−4.79824	−0.190713
$634$	2.45775	0.0976097
$635$	−5.21330	−0.206883
$636$	7.34390	0.291204
$637$	0	0
$638$	−18.7643	−0.742886
$639$	4.07288	0.161121
$640$	−0.879961	−0.0347835
$641$	−13.8228	−0.545966	−0.272983	−	0.962019i	$-0.588010\pi$
$641$	−13.8228	−0.545966	−0.272983	+	0.962019i	$0.588010\pi$
$642$	3.61416	0.142640
$643$	−26.9502	−1.06281	−0.531406	−	0.847117i	$-0.678336\pi$
$643$	−26.9502	−1.06281	−0.531406	+	0.847117i	$0.678336\pi$
$644$	0	0
$645$	−5.14917	−0.202748
$646$	4.54566	0.178846
$647$	25.4495	1.00052	0.500262	−	0.865874i	$-0.333237\pi$
$647$	25.4495	1.00052	0.500262	+	0.865874i	$0.333237\pi$
$648$	1.00000	0.0392837
$649$	19.9624	0.783594
$650$	−9.38646	−0.368167
$651$	0	0
$652$	−8.48528	−0.332309
$653$	−29.2277	−1.14377	−0.571885	−	0.820334i	$-0.693788\pi$
$653$	−29.2277	−1.14377	−0.571885	+	0.820334i	$0.693788\pi$
$654$	−6.42381	−0.251191
$655$	−5.95232	−0.232576
$656$	−0.124413	−0.00485753
$657$	4.97162	0.193962
$658$	0	0
$659$	17.6958	0.689330	0.344665	−	0.938726i	$-0.387992\pi$
$659$	17.6958	0.689330	0.344665	+	0.938726i	$0.387992\pi$
$660$	−3.58397	−0.139506
$661$	−4.52334	−0.175938	−0.0879688	−	0.996123i	$-0.528038\pi$
$661$	−4.52334	−0.175938	−0.0879688	+	0.996123i	$0.528038\pi$
$662$	19.4595	0.756314
$663$	−17.2371	−0.669432
$664$	6.99819	0.271582
$665$	0	0
$666$	3.53863	0.137119
$667$	−4.60713	−0.178389
$668$	19.0409	0.736714
$669$	14.5983	0.564403
$670$	7.55741	0.291968
$671$	−8.72898	−0.336979
$672$	0	0
$673$	−40.9679	−1.57920	−0.789598	−	0.613624i	$-0.789711\pi$
$673$	−40.9679	−1.57920	−0.789598	+	0.613624i	$0.789711\pi$
$674$	26.0213	1.00230
$675$	4.22567	0.162646
$676$	−8.06585	−0.310225
$677$	8.96787	0.344663	0.172332	−	0.985039i	$-0.444870\pi$
$677$	8.96787	0.344663	0.172332	+	0.985039i	$0.444870\pi$
$678$	−13.6115	−0.522747
$679$	0	0
$680$	−6.82843	−0.261858
$681$	9.39543	0.360034
$682$	−2.38584	−0.0913584
$683$	41.3579	1.58252	0.791258	−	0.611482i	$-0.209426\pi$
$683$	41.3579	1.58252	0.791258	+	0.611482i	$0.209426\pi$
$684$	0.585786	0.0223981
$685$	−4.90034	−0.187232
$686$	0	0
$687$	−7.14757	−0.272697
$688$	−5.85158	−0.223090
$689$	−16.3130	−0.621474
$690$	−0.879961	−0.0334995
$691$	−29.6028	−1.12614	−0.563071	−	0.826409i	$-0.690380\pi$
$691$	−29.6028	−1.12614	−0.563071	+	0.826409i	$0.690380\pi$
$692$	−12.0087	−0.456504
$693$	0	0
$694$	−31.4229	−1.19280
$695$	−11.2862	−0.428109
$696$	−4.60713	−0.174633
$697$	−0.965438	−0.0365686
$698$	−13.3688	−0.506016
$699$	−15.3439	−0.580359
$700$	0	0
$701$	31.4306	1.18712	0.593560	−	0.804790i	$-0.297722\pi$
$701$	31.4306	1.18712	0.593560	+	0.804790i	$0.297722\pi$
$702$	−2.22129	−0.0838374
$703$	2.07288	0.0781801
$704$	−4.07288	−0.153502
$705$	0.0453476	0.00170789
$706$	−15.8005	−0.594658
$707$	0	0
$708$	4.90131	0.184202
$709$	46.0250	1.72851	0.864253	−	0.503058i	$-0.167792\pi$
$709$	46.0250	1.72851	0.864253	+	0.503058i	$0.167792\pi$
$710$	−3.58397	−0.134504
$711$	−1.92712	−0.0722727
$712$	10.4587	0.391957
$713$	−0.585786	−0.0219379
$714$	0	0
$715$	7.96106	0.297727
$716$	10.6461	0.397862
$717$	−17.7687	−0.663583
$718$	26.9642	1.00629
$719$	−18.3195	−0.683204	−0.341602	−	0.939845i	$-0.610969\pi$
$719$	−18.3195	−0.683204	−0.341602	+	0.939845i	$0.610969\pi$
$720$	−0.879961	−0.0327942
$721$	0	0
$722$	−18.6569	−0.694336
$723$	−5.07629	−0.188789
$724$	−21.5385	−0.800473
$725$	−19.4682	−0.723031
$726$	−5.58835	−0.207403
$727$	−3.36365	−0.124751	−0.0623754	−	0.998053i	$-0.519868\pi$
$727$	−3.36365	−0.124751	−0.0623754	+	0.998053i	$0.519868\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	−4.37483	−0.161920
$731$	−45.4078	−1.67947
$732$	−2.14320	−0.0792148
$733$	18.5909	0.686671	0.343335	−	0.939213i	$-0.388443\pi$
$733$	18.5909	0.686671	0.343335	+	0.939213i	$0.388443\pi$
$734$	5.67201	0.209358
$735$	0	0
$736$	−1.00000	−0.0368605
$737$	34.9793	1.28848
$738$	−0.124413	−0.00457972
$739$	13.9802	0.514272	0.257136	−	0.966375i	$-0.417221\pi$
$739$	13.9802	0.514272	0.257136	+	0.966375i	$0.417221\pi$
$740$	−3.11385	−0.114468
$741$	−1.30120	−0.0478009
$742$	0	0
$743$	29.7015	1.08964	0.544821	−	0.838552i	$-0.316598\pi$
$743$	29.7015	1.08964	0.544821	+	0.838552i	$0.316598\pi$
$744$	−0.585786	−0.0214760
$745$	−12.2598	−0.449165
$746$	7.49704	0.274486
$747$	6.99819	0.256050
$748$	−31.6052	−1.15560
$749$	0	0
$750$	−8.11823	−0.296436
$751$	−24.8409	−0.906458	−0.453229	−	0.891394i	$-0.649728\pi$
$751$	−24.8409	−0.906458	−0.453229	+	0.891394i	$0.649728\pi$
$752$	0.0515337	0.00187924
$753$	−13.7473	−0.500980
$754$	10.2338	0.372693
$755$	−1.01441	−0.0369181
$756$	0	0
$757$	−22.9866	−0.835461	−0.417730	−	0.908571i	$-0.637174\pi$
$757$	−22.9866	−0.835461	−0.417730	+	0.908571i	$0.637174\pi$
$758$	−2.24273	−0.0814598
$759$	−4.07288	−0.147836
$760$	−0.515469	−0.0186980
$761$	−41.1614	−1.49210	−0.746051	−	0.665889i	$-0.768052\pi$
$761$	−41.1614	−1.49210	−0.746051	+	0.665889i	$0.768052\pi$
$762$	−5.92446	−0.214621
$763$	0	0
$764$	25.2194	0.912405
$765$	−6.82843	−0.246882
$766$	24.0693	0.869658
$767$	−10.8872	−0.393116
$768$	−1.00000	−0.0360844
$769$	24.8876	0.897472	0.448736	−	0.893664i	$-0.351874\pi$
$769$	24.8876	0.897472	0.448736	+	0.893664i	$0.351874\pi$
$770$	0	0
$771$	−11.0069	−0.396405
$772$	−7.50844	−0.270235
$773$	−43.6051	−1.56837	−0.784184	−	0.620529i	$-0.786918\pi$
$773$	−43.6051	−1.56837	−0.784184	+	0.620529i	$0.786918\pi$
$774$	−5.85158	−0.210331
$775$	−2.47534	−0.0889168
$776$	17.5084	0.628516
$777$	0	0
$778$	−11.9021	−0.426709
$779$	−0.0728797	−0.00261119
$780$	1.95465	0.0699878
$781$	−16.5883	−0.593578
$782$	−7.75992	−0.277494
$783$	−4.60713	−0.164645
$784$	0	0
$785$	−13.8127	−0.492998
$786$	−6.76430	−0.241274
$787$	34.6048	1.23353	0.616764	−	0.787148i	$-0.288443\pi$
$787$	34.6048	1.23353	0.616764	+	0.787148i	$0.288443\pi$
$788$	6.66388	0.237391
$789$	26.7153	0.951091
$790$	1.69579	0.0603335
$791$	0	0
$792$	−4.07288	−0.144723
$793$	4.76067	0.169056
$794$	−12.7305	−0.451788
$795$	−6.46234	−0.229196
$796$	−4.80964	−0.170473
$797$	38.5951	1.36711	0.683554	−	0.729900i	$-0.260433\pi$
$797$	38.5951	1.36711	0.683554	+	0.729900i	$0.260433\pi$
$798$	0	0
$799$	0.399898	0.0141474
$800$	−4.22567	−0.149400
$801$	10.4587	0.369541
$802$	−24.8032	−0.875833
$803$	−20.2488	−0.714566
$804$	8.58835	0.302888
$805$	0	0
$806$	1.30120	0.0458330
$807$	−17.1693	−0.604389
$808$	−4.41240	−0.155228
$809$	−1.95505	−0.0687360	−0.0343680	−	0.999409i	$-0.510942\pi$
$809$	−1.95505	−0.0687360	−0.0343680	+	0.999409i	$0.510942\pi$
$810$	−0.879961	−0.0309187
$811$	−5.50694	−0.193375	−0.0966874	−	0.995315i	$-0.530825\pi$
$811$	−5.50694	−0.193375	−0.0966874	+	0.995315i	$0.530825\pi$
$812$	0	0
$813$	17.5260	0.614665
$814$	−14.4124	−0.505154
$815$	7.46672	0.261548
$816$	−7.75992	−0.271652
$817$	−3.42778	−0.119923
$818$	−13.1174	−0.458639
$819$	0	0
$820$	0.109479	0.00382317
$821$	−51.6392	−1.80222	−0.901110	−	0.433591i	$-0.857246\pi$
$821$	−51.6392	−1.80222	−0.901110	+	0.433591i	$0.857246\pi$
$822$	−5.56881	−0.194235
$823$	−29.3892	−1.02444	−0.512222	−	0.858853i	$-0.671178\pi$
$823$	−29.3892	−1.02444	−0.512222	+	0.858853i	$0.671178\pi$
$824$	3.77871	0.131637
$825$	−17.2106	−0.599198
$826$	0	0
$827$	−19.1112	−0.664561	−0.332281	−	0.943181i	$-0.607818\pi$
$827$	−19.1112	−0.664561	−0.332281	+	0.943181i	$0.607818\pi$
$828$	−1.00000	−0.0347524
$829$	−5.30858	−0.184375	−0.0921874	−	0.995742i	$-0.529386\pi$
$829$	−5.30858	−0.184375	−0.0921874	+	0.995742i	$0.529386\pi$
$830$	−6.15813	−0.213752
$831$	5.00075	0.173474
$832$	2.22129	0.0770095
$833$	0	0
$834$	−12.8258	−0.444120
$835$	−16.7552	−0.579839
$836$	−2.38584	−0.0825159
$837$	−0.585786	−0.0202477
$838$	31.2417	1.07923
$839$	−52.6220	−1.81671	−0.908356	−	0.418197i	$-0.862662\pi$
$839$	−52.6220	−1.81671	−0.908356	+	0.418197i	$0.862662\pi$
$840$	0	0
$841$	−7.77433	−0.268080
$842$	−38.1129	−1.31346
$843$	−4.73676	−0.163143
$844$	4.79824	0.165162
$845$	7.09763	0.244166
$846$	0.0515337	0.00177177
$847$	0	0
$848$	−7.34390	−0.252190
$849$	5.12101	0.175753
$850$	−32.7909	−1.12472
$851$	−3.53863	−0.121303
$852$	−4.07288	−0.139535
$853$	−25.6808	−0.879293	−0.439646	−	0.898171i	$-0.644896\pi$
$853$	−25.6808	−0.879293	−0.439646	+	0.898171i	$0.644896\pi$
$854$	0	0
$855$	−0.515469	−0.0176287
$856$	−3.61416	−0.123530
$857$	−51.9661	−1.77513	−0.887564	−	0.460684i	$-0.847604\pi$
$857$	−51.9661	−1.77513	−0.887564	+	0.460684i	$0.847604\pi$
$858$	9.04707	0.308862
$859$	−14.5806	−0.497483	−0.248741	−	0.968570i	$-0.580017\pi$
$859$	−14.5806	−0.497483	−0.248741	+	0.968570i	$0.580017\pi$
$860$	5.14917	0.175585
$861$	0	0
$862$	29.4031	1.00147
$863$	−28.1046	−0.956691	−0.478345	−	0.878172i	$-0.658763\pi$
$863$	−28.1046	−0.956691	−0.478345	+	0.878172i	$0.658763\pi$
$864$	−1.00000	−0.0340207
$865$	10.5672	0.359297
$866$	−14.8309	−0.503974
$867$	−43.2164	−1.46771
$868$	0	0
$869$	7.84893	0.266257
$870$	4.05410	0.137447
$871$	−19.0773	−0.646408
$872$	6.42381	0.217538
$873$	17.5084	0.592571
$874$	−0.585786	−0.0198145
$875$	0	0
$876$	−4.97162	−0.167976
$877$	−0.645101	−0.0217835	−0.0108917	−	0.999941i	$-0.503467\pi$
$877$	−0.645101	−0.0217835	−0.0108917	+	0.999941i	$0.503467\pi$
$878$	0.299392	0.0101040
$879$	−9.45315	−0.318847
$880$	3.58397	0.120816
$881$	11.0581	0.372556	0.186278	−	0.982497i	$-0.440358\pi$
$881$	11.0581	0.372556	0.186278	+	0.982497i	$0.440358\pi$
$882$	0	0
$883$	9.56047	0.321735	0.160868	−	0.986976i	$-0.448571\pi$
$883$	9.56047	0.321735	0.160868	+	0.986976i	$0.448571\pi$
$884$	17.2371	0.579746
$885$	−4.31296	−0.144978
$886$	10.5202	0.353433
$887$	54.7189	1.83728	0.918640	−	0.395096i	$-0.129289\pi$
$887$	54.7189	1.83728	0.918640	+	0.395096i	$0.129289\pi$
$888$	−3.53863	−0.118749
$889$	0	0
$890$	−9.20326	−0.308494
$891$	−4.07288	−0.136447
$892$	−14.5983	−0.488787
$893$	0.0301877	0.00101019
$894$	−13.9322	−0.465964
$895$	−9.36812	−0.313142
$896$	0	0
$897$	2.22129	0.0741669
$898$	−40.9505	−1.36654
$899$	2.69880	0.0900099
$900$	−4.22567	−0.140856
$901$	−56.9881	−1.89855
$902$	0.506721	0.0168720
$903$	0	0
$904$	13.6115	0.452712
$905$	18.9531	0.630021
$906$	−1.15279	−0.0382989
$907$	−2.58738	−0.0859126	−0.0429563	−	0.999077i	$-0.513678\pi$
$907$	−2.58738	−0.0859126	−0.0429563	+	0.999077i	$0.513678\pi$
$908$	−9.39543	−0.311798
$909$	−4.41240	−0.146350
$910$	0	0
$911$	42.6050	1.41157	0.705783	−	0.708428i	$-0.250595\pi$
$911$	42.6050	1.41157	0.705783	+	0.708428i	$0.250595\pi$
$912$	−0.585786	−0.0193973
$913$	−28.5028	−0.943304
$914$	15.1539	0.501246
$915$	1.88593	0.0623469
$916$	7.14757	0.236162
$917$	0	0
$918$	−7.75992	−0.256116
$919$	−5.53823	−0.182689	−0.0913446	−	0.995819i	$-0.529116\pi$
$919$	−5.53823	−0.182689	−0.0913446	+	0.995819i	$0.529116\pi$
$920$	0.879961	0.0290114
$921$	−29.8036	−0.982061
$922$	22.0089	0.724824
$923$	9.04707	0.297788
$924$	0	0
$925$	−14.9531	−0.491654
$926$	−1.83546	−0.0603169
$927$	3.77871	0.124109
$928$	4.60713	0.151237
$929$	−13.9855	−0.458848	−0.229424	−	0.973327i	$-0.573684\pi$
$929$	−13.9855	−0.458848	−0.229424	+	0.973327i	$0.573684\pi$
$930$	0.515469	0.0169029
$931$	0	0
$932$	15.3439	0.502606
$933$	18.5983	0.608881
$934$	−22.4586	−0.734869
$935$	27.8114	0.909529
$936$	2.22129	0.0726053
$937$	−24.5733	−0.802775	−0.401388	−	0.915908i	$-0.631472\pi$
$937$	−24.5733	−0.802775	−0.401388	+	0.915908i	$0.631472\pi$
$938$	0	0
$939$	−17.1803	−0.560659
$940$	−0.0453476	−0.00147908
$941$	3.20030	0.104327	0.0521634	−	0.998639i	$-0.483388\pi$
$941$	3.20030	0.104327	0.0521634	+	0.998639i	$0.483388\pi$
$942$	−15.6970	−0.511435
$943$	0.124413	0.00405146
$944$	−4.90131	−0.159524
$945$	0	0
$946$	23.8328	0.774871
$947$	−2.21392	−0.0719426	−0.0359713	−	0.999353i	$-0.511452\pi$
$947$	−2.21392	−0.0719426	−0.0359713	+	0.999353i	$0.511452\pi$
$948$	1.92712	0.0625900
$949$	11.0434	0.358485
$950$	−2.47534	−0.0803106
$951$	−2.45775	−0.0796980
$952$	0	0
$953$	37.1750	1.20422	0.602108	−	0.798414i	$-0.294328\pi$
$953$	37.1750	1.20422	0.602108	+	0.798414i	$0.294328\pi$
$954$	−7.34390	−0.237767
$955$	−22.1921	−0.718119
$956$	17.7687	0.574680
$957$	18.7643	0.606564
$958$	−19.6760	−0.635704
$959$	0	0
$960$	0.879961	0.0284006
$961$	−30.6569	−0.988931
$962$	7.86033	0.253427
$963$	−3.61416	−0.116465
$964$	5.07629	0.163496
$965$	6.60713	0.212691
$966$	0	0
$967$	39.5449	1.27168	0.635838	−	0.771822i	$-0.280654\pi$
$967$	39.5449	1.27168	0.635838	+	0.771822i	$0.280654\pi$
$968$	5.58835	0.179616
$969$	−4.54566	−0.146028
$970$	−15.4067	−0.494681
$971$	32.6674	1.04835	0.524174	−	0.851611i	$-0.324374\pi$
$971$	32.6674	1.04835	0.524174	+	0.851611i	$0.324374\pi$
$972$	−1.00000	−0.0320750
$973$	0	0
$974$	−6.01154	−0.192622
$975$	9.38646	0.300607
$976$	2.14320	0.0686021
$977$	−42.7155	−1.36659	−0.683294	−	0.730143i	$-0.739453\pi$
$977$	−42.7155	−1.36659	−0.683294	+	0.730143i	$0.739453\pi$
$978$	8.48528	0.271329
$979$	−42.5971	−1.36141
$980$	0	0
$981$	6.42381	0.205096
$982$	26.2401	0.837355
$983$	−13.7812	−0.439551	−0.219776	−	0.975550i	$-0.570533\pi$
$983$	−13.7812	−0.439551	−0.219776	+	0.975550i	$0.570533\pi$
$984$	0.124413	0.00396615
$985$	−5.86396	−0.186841
$986$	35.7510	1.13854
$987$	0	0
$988$	1.30120	0.0413968
$989$	5.85158	0.186070
$990$	3.58397	0.113906
$991$	51.1765	1.62568	0.812838	−	0.582490i	$-0.197922\pi$
$991$	51.1765	1.62568	0.812838	+	0.582490i	$0.197922\pi$
$992$	0.585786	0.0185987
$993$	−19.4595	−0.617528
$994$	0	0
$995$	4.23230	0.134173
$996$	−6.99819	−0.221746
$997$	41.3363	1.30913	0.654567	−	0.756004i	$-0.272851\pi$
$997$	41.3363	1.30913	0.654567	+	0.756004i	$0.272851\pi$
$998$	−6.49934	−0.205733
$999$	−3.53863	−0.111957

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6762.2.a.cn.1.1	✓	4	1.1	even	1	trivial
6762.2.a.co.1.4	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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -0.879961 q^{5} -1.00000 q^{6} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -0.879961 q^{5} -1.00000 q^{6} +1.00000 q^{8} +1.00000 q^{9} -0.879961 q^{10} -4.07288 q^{11} -1.00000 q^{12} +2.22129 q^{13} +0.879961 q^{15} +1.00000 q^{16} +7.75992 q^{17} +1.00000 q^{18} +0.585786 q^{19} -0.879961 q^{20} -4.07288 q^{22} -1.00000 q^{23} -1.00000 q^{24} -4.22567 q^{25} +2.22129 q^{26} -1.00000 q^{27} +4.60713 q^{29} +0.879961 q^{30} +0.585786 q^{31} +1.00000 q^{32} +4.07288 q^{33} +7.75992 q^{34} +1.00000 q^{36} +3.53863 q^{37} +0.585786 q^{38} -2.22129 q^{39} -0.879961 q^{40} -0.124413 q^{41} -5.85158 q^{43} -4.07288 q^{44} -0.879961 q^{45} -1.00000 q^{46} +0.0515337 q^{47} -1.00000 q^{48} -4.22567 q^{50} -7.75992 q^{51} +2.22129 q^{52} -7.34390 q^{53} -1.00000 q^{54} +3.58397 q^{55} -0.585786 q^{57} +4.60713 q^{58} -4.90131 q^{59} +0.879961 q^{60} +2.14320 q^{61} +0.585786 q^{62} +1.00000 q^{64} -1.95465 q^{65} +4.07288 q^{66} -8.58835 q^{67} +7.75992 q^{68} +1.00000 q^{69} +4.07288 q^{71} +1.00000 q^{72} +4.97162 q^{73} +3.53863 q^{74} +4.22567 q^{75} +0.585786 q^{76} -2.22129 q^{78} -1.92712 q^{79} -0.879961 q^{80} +1.00000 q^{81} -0.124413 q^{82} +6.99819 q^{83} -6.82843 q^{85} -5.85158 q^{86} -4.60713 q^{87} -4.07288 q^{88} +10.4587 q^{89} -0.879961 q^{90} -1.00000 q^{92} -0.585786 q^{93} +0.0515337 q^{94} -0.515469 q^{95} -1.00000 q^{96} +17.5084 q^{97} -4.07288 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 4 q^{2} - 4 q^{3} + 4 q^{4} + 6 q^{5} - 4 q^{6} + 4 q^{8} + 4 q^{9}+O(q^{10}) \) 4 * q + 4 * q^2 - 4 * q^3 + 4 * q^4 + 6 * q^5 - 4 * q^6 + 4 * q^8 + 4 * q^9	\( 4 q + 4 q^{2} - 4 q^{3} + 4 q^{4} + 6 q^{5} - 4 q^{6} + 4 q^{8} + 4 q^{9} + 6 q^{10} - 4 q^{12} + 10 q^{13} - 6 q^{15} + 4 q^{16} + 12 q^{17} + 4 q^{18} + 8 q^{19} + 6 q^{20} - 4 q^{23} - 4 q^{24} + 6 q^{25} + 10 q^{26} - 4 q^{27} + 6 q^{29} - 6 q^{30} + 8 q^{31} + 4 q^{32} + 12 q^{34} + 4 q^{36} - 6 q^{37} + 8 q^{38} - 10 q^{39} + 6 q^{40} + 14 q^{41} - 6 q^{43} + 6 q^{45} - 4 q^{46} + 2 q^{47} - 4 q^{48} + 6 q^{50} - 12 q^{51} + 10 q^{52} - 4 q^{53} - 4 q^{54} + 8 q^{55} - 8 q^{57} + 6 q^{58} + 8 q^{59} - 6 q^{60} + 12 q^{61} + 8 q^{62} + 4 q^{64} + 6 q^{65} - 4 q^{67} + 12 q^{68} + 4 q^{69} + 4 q^{72} + 12 q^{73} - 6 q^{74} - 6 q^{75} + 8 q^{76} - 10 q^{78} - 24 q^{79} + 6 q^{80} + 4 q^{81} + 14 q^{82} + 16 q^{83} - 16 q^{85} - 6 q^{86} - 6 q^{87} + 12 q^{89} + 6 q^{90} - 4 q^{92} - 8 q^{93} + 2 q^{94} + 12 q^{95} - 4 q^{96} + 30 q^{97}+O(q^{100}) \) 4 * q + 4 * q^2 - 4 * q^3 + 4 * q^4 + 6 * q^5 - 4 * q^6 + 4 * q^8 + 4 * q^9 + 6 * q^10 - 4 * q^12 + 10 * q^13 - 6 * q^15 + 4 * q^16 + 12 * q^17 + 4 * q^18 + 8 * q^19 + 6 * q^20 - 4 * q^23 - 4 * q^24 + 6 * q^25 + 10 * q^26 - 4 * q^27 + 6 * q^29 - 6 * q^30 + 8 * q^31 + 4 * q^32 + 12 * q^34 + 4 * q^36 - 6 * q^37 + 8 * q^38 - 10 * q^39 + 6 * q^40 + 14 * q^41 - 6 * q^43 + 6 * q^45 - 4 * q^46 + 2 * q^47 - 4 * q^48 + 6 * q^50 - 12 * q^51 + 10 * q^52 - 4 * q^53 - 4 * q^54 + 8 * q^55 - 8 * q^57 + 6 * q^58 + 8 * q^59 - 6 * q^60 + 12 * q^61 + 8 * q^62 + 4 * q^64 + 6 * q^65 - 4 * q^67 + 12 * q^68 + 4 * q^69 + 4 * q^72 + 12 * q^73 - 6 * q^74 - 6 * q^75 + 8 * q^76 - 10 * q^78 - 24 * q^79 + 6 * q^80 + 4 * q^81 + 14 * q^82 + 16 * q^83 - 16 * q^85 - 6 * q^86 - 6 * q^87 + 12 * q^89 + 6 * q^90 - 4 * q^92 - 8 * q^93 + 2 * q^94 + 12 * q^95 - 4 * q^96 + 30 * q^97

Introduction

L-functions

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Database

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