LMFDB - Embedded newform 1155.2.a.p.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1155,2,Mod(1,1155)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1155, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("1155.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1155 = 3 \cdot 5 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1155.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:	$9.22272143346$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{8})^+$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - 2 $ x^2 - 2
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-1.41421$ of defining polynomial
Character	$\chi$	$=$	1155.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.41421 q^{2} -1.00000 q^{3} -1.00000 q^{5} +1.41421 q^{6} -1.00000 q^{7} +2.82843 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.41421 q^{2} -1.00000 q^{3} -1.00000 q^{5} +1.41421 q^{6} -1.00000 q^{7} +2.82843 q^{8} +1.00000 q^{9} +1.41421 q^{10} +1.00000 q^{11} +0.585786 q^{13} +1.41421 q^{14} +1.00000 q^{15} -4.00000 q^{16} -1.82843 q^{17} -1.41421 q^{18} -3.82843 q^{19} +1.00000 q^{21} -1.41421 q^{22} -3.82843 q^{23} -2.82843 q^{24} +1.00000 q^{25} -0.828427 q^{26} -1.00000 q^{27} -1.24264 q^{29} -1.41421 q^{30} +0.585786 q^{31} -1.00000 q^{33} +2.58579 q^{34} +1.00000 q^{35} -6.24264 q^{37} +5.41421 q^{38} -0.585786 q^{39} -2.82843 q^{40} +11.0711 q^{41} -1.41421 q^{42} -6.41421 q^{43} -1.00000 q^{45} +5.41421 q^{46} +1.75736 q^{47} +4.00000 q^{48} +1.00000 q^{49} -1.41421 q^{50} +1.82843 q^{51} +8.65685 q^{53} +1.41421 q^{54} -1.00000 q^{55} -2.82843 q^{56} +3.82843 q^{57} +1.75736 q^{58} +14.4142 q^{59} +10.6569 q^{61} -0.828427 q^{62} -1.00000 q^{63} +8.00000 q^{64} -0.585786 q^{65} +1.41421 q^{66} -6.00000 q^{67} +3.82843 q^{69} -1.41421 q^{70} +3.07107 q^{71} +2.82843 q^{72} -8.48528 q^{73} +8.82843 q^{74} -1.00000 q^{75} -1.00000 q^{77} +0.828427 q^{78} -8.24264 q^{79} +4.00000 q^{80} +1.00000 q^{81} -15.6569 q^{82} +17.1421 q^{83} +1.82843 q^{85} +9.07107 q^{86} +1.24264 q^{87} +2.82843 q^{88} -0.0710678 q^{89} +1.41421 q^{90} -0.585786 q^{91} -0.585786 q^{93} -2.48528 q^{94} +3.82843 q^{95} -7.24264 q^{97} -1.41421 q^{98} +1.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 2 q^{3} - 2 q^{5} - 2 q^{7} + 2 q^{9}+O(q^{10}) $ 2 * q - 2 * q^3 - 2 * q^5 - 2 * q^7 + 2 * q^9	$ 2 q - 2 q^{3} - 2 q^{5} - 2 q^{7} + 2 q^{9} + 2 q^{11} + 4 q^{13} + 2 q^{15} - 8 q^{16} + 2 q^{17} - 2 q^{19} + 2 q^{21} - 2 q^{23} + 2 q^{25} + 4 q^{26} - 2 q^{27} + 6 q^{29} + 4 q^{31} - 2 q^{33} + 8 q^{34} + 2 q^{35} - 4 q^{37} + 8 q^{38} - 4 q^{39} + 8 q^{41} - 10 q^{43} - 2 q^{45} + 8 q^{46} + 12 q^{47} + 8 q^{48} + 2 q^{49} - 2 q^{51} + 6 q^{53} - 2 q^{55} + 2 q^{57} + 12 q^{58} + 26 q^{59} + 10 q^{61} + 4 q^{62} - 2 q^{63} + 16 q^{64} - 4 q^{65} - 12 q^{67} + 2 q^{69} - 8 q^{71} + 12 q^{74} - 2 q^{75} - 2 q^{77} - 4 q^{78} - 8 q^{79} + 8 q^{80} + 2 q^{81} - 20 q^{82} + 6 q^{83} - 2 q^{85} + 4 q^{86} - 6 q^{87} + 14 q^{89} - 4 q^{91} - 4 q^{93} + 12 q^{94} + 2 q^{95} - 6 q^{97} + 2 q^{99}+O(q^{100}) $ 2 * q - 2 * q^3 - 2 * q^5 - 2 * q^7 + 2 * q^9 + 2 * q^11 + 4 * q^13 + 2 * q^15 - 8 * q^16 + 2 * q^17 - 2 * q^19 + 2 * q^21 - 2 * q^23 + 2 * q^25 + 4 * q^26 - 2 * q^27 + 6 * q^29 + 4 * q^31 - 2 * q^33 + 8 * q^34 + 2 * q^35 - 4 * q^37 + 8 * q^38 - 4 * q^39 + 8 * q^41 - 10 * q^43 - 2 * q^45 + 8 * q^46 + 12 * q^47 + 8 * q^48 + 2 * q^49 - 2 * q^51 + 6 * q^53 - 2 * q^55 + 2 * q^57 + 12 * q^58 + 26 * q^59 + 10 * q^61 + 4 * q^62 - 2 * q^63 + 16 * q^64 - 4 * q^65 - 12 * q^67 + 2 * q^69 - 8 * q^71 + 12 * q^74 - 2 * q^75 - 2 * q^77 - 4 * q^78 - 8 * q^79 + 8 * q^80 + 2 * q^81 - 20 * q^82 + 6 * q^83 - 2 * q^85 + 4 * q^86 - 6 * q^87 + 14 * q^89 - 4 * q^91 - 4 * q^93 + 12 * q^94 + 2 * q^95 - 6 * q^97 + 2 * 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 $

$2$	−1.41421	−1.00000	−0.500000	−	0.866025i	$-0.666667\pi$
$2$	−1.41421	−1.00000	−0.500000	+	0.866025i	$0.666667\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	0	0
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	1.41421	0.577350
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	2.82843	1.00000
$9$	1.00000	0.333333
$10$	1.41421	0.447214
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	0	0
$13$	0.585786	0.162468	0.0812340	−	0.996695i	$-0.474114\pi$
$13$	0.585786	0.162468	0.0812340	+	0.996695i	$0.474114\pi$
$14$	1.41421	0.377964
$15$	1.00000	0.258199
$16$	−4.00000	−1.00000
$17$	−1.82843	−0.443459	−0.221729	−	0.975108i	$-0.571170\pi$
$17$	−1.82843	−0.443459	−0.221729	+	0.975108i	$0.571170\pi$
$18$	−1.41421	−0.333333
$19$	−3.82843	−0.878301	−0.439151	−	0.898413i	$-0.644721\pi$
$19$	−3.82843	−0.878301	−0.439151	+	0.898413i	$0.644721\pi$
$20$	0	0
$21$	1.00000	0.218218
$22$	−1.41421	−0.301511
$23$	−3.82843	−0.798282	−0.399141	−	0.916890i	$-0.630692\pi$
$23$	−3.82843	−0.798282	−0.399141	+	0.916890i	$0.630692\pi$
$24$	−2.82843	−0.577350
$25$	1.00000	0.200000
$26$	−0.828427	−0.162468
$27$	−1.00000	−0.192450
$28$	0	0
$29$	−1.24264	−0.230753	−0.115376	−	0.993322i	$-0.536807\pi$
$29$	−1.24264	−0.230753	−0.115376	+	0.993322i	$0.536807\pi$
$30$	−1.41421	−0.258199
$31$	0.585786	0.105210	0.0526052	−	0.998615i	$-0.483248\pi$
$31$	0.585786	0.105210	0.0526052	+	0.998615i	$0.483248\pi$
$32$	0	0
$33$	−1.00000	−0.174078
$34$	2.58579	0.443459
$35$	1.00000	0.169031
$36$	0	0
$37$	−6.24264	−1.02628	−0.513142	−	0.858304i	$-0.671519\pi$
$37$	−6.24264	−1.02628	−0.513142	+	0.858304i	$0.671519\pi$
$38$	5.41421	0.878301
$39$	−0.585786	−0.0938009
$40$	−2.82843	−0.447214
$41$	11.0711	1.72901	0.864505	−	0.502624i	$-0.167632\pi$
$41$	11.0711	1.72901	0.864505	+	0.502624i	$0.167632\pi$
$42$	−1.41421	−0.218218
$43$	−6.41421	−0.978158	−0.489079	−	0.872239i	$-0.662667\pi$
$43$	−6.41421	−0.978158	−0.489079	+	0.872239i	$0.662667\pi$
$44$	0	0
$45$	−1.00000	−0.149071
$46$	5.41421	0.798282
$47$	1.75736	0.256337	0.128169	−	0.991752i	$-0.459090\pi$
$47$	1.75736	0.256337	0.128169	+	0.991752i	$0.459090\pi$
$48$	4.00000	0.577350
$49$	1.00000	0.142857
$50$	−1.41421	−0.200000
$51$	1.82843	0.256031
$52$	0	0
$53$	8.65685	1.18911	0.594555	−	0.804055i	$-0.297328\pi$
$53$	8.65685	1.18911	0.594555	+	0.804055i	$0.297328\pi$
$54$	1.41421	0.192450
$55$	−1.00000	−0.134840
$56$	−2.82843	−0.377964
$57$	3.82843	0.507088
$58$	1.75736	0.230753
$59$	14.4142	1.87657	0.938285	−	0.345862i	$-0.112413\pi$
$59$	14.4142	1.87657	0.938285	+	0.345862i	$0.112413\pi$
$60$	0	0
$61$	10.6569	1.36447	0.682235	−	0.731133i	$-0.261008\pi$
$61$	10.6569	1.36447	0.682235	+	0.731133i	$0.261008\pi$
$62$	−0.828427	−0.105210
$63$	−1.00000	−0.125988
$64$	8.00000	1.00000
$65$	−0.585786	−0.0726579
$66$	1.41421	0.174078
$67$	−6.00000	−0.733017	−0.366508	−	0.930415i	$-0.619447\pi$
$67$	−6.00000	−0.733017	−0.366508	+	0.930415i	$0.619447\pi$
$68$	0	0
$69$	3.82843	0.460888
$70$	−1.41421	−0.169031
$71$	3.07107	0.364469	0.182234	−	0.983255i	$-0.441667\pi$
$71$	3.07107	0.364469	0.182234	+	0.983255i	$0.441667\pi$
$72$	2.82843	0.333333
$73$	−8.48528	−0.993127	−0.496564	−	0.868000i	$-0.665405\pi$
$73$	−8.48528	−0.993127	−0.496564	+	0.868000i	$0.665405\pi$
$74$	8.82843	1.02628
$75$	−1.00000	−0.115470
$76$	0	0
$77$	−1.00000	−0.113961
$78$	0.828427	0.0938009
$79$	−8.24264	−0.927370	−0.463685	−	0.886000i	$-0.653473\pi$
$79$	−8.24264	−0.927370	−0.463685	+	0.886000i	$0.653473\pi$
$80$	4.00000	0.447214
$81$	1.00000	0.111111
$82$	−15.6569	−1.72901
$83$	17.1421	1.88159	0.940797	−	0.338971i	$-0.110079\pi$
$83$	17.1421	1.88159	0.940797	+	0.338971i	$0.110079\pi$
$84$	0	0
$85$	1.82843	0.198321
$86$	9.07107	0.978158
$87$	1.24264	0.133225
$88$	2.82843	0.301511
$89$	−0.0710678	−0.00753317	−0.00376659	−	0.999993i	$-0.501199\pi$
$89$	−0.0710678	−0.00753317	−0.00376659	+	0.999993i	$0.501199\pi$
$90$	1.41421	0.149071
$91$	−0.585786	−0.0614071
$92$	0	0
$93$	−0.585786	−0.0607432
$94$	−2.48528	−0.256337
$95$	3.82843	0.392788
$96$	0	0
$97$	−7.24264	−0.735379	−0.367689	−	0.929949i	$-0.619851\pi$
$97$	−7.24264	−0.735379	−0.367689	+	0.929949i	$0.619851\pi$
$98$	−1.41421	−0.142857
$99$	1.00000	0.100504
$100$	0	0
$101$	0.343146	0.0341443	0.0170721	−	0.999854i	$-0.494566\pi$
$101$	0.343146	0.0341443	0.0170721	+	0.999854i	$0.494566\pi$
$102$	−2.58579	−0.256031
$103$	13.7279	1.35265	0.676326	−	0.736602i	$-0.263571\pi$
$103$	13.7279	1.35265	0.676326	+	0.736602i	$0.263571\pi$
$104$	1.65685	0.162468
$105$	−1.00000	−0.0975900
$106$	−12.2426	−1.18911
$107$	−7.41421	−0.716759	−0.358380	−	0.933576i	$-0.616671\pi$
$107$	−7.41421	−0.716759	−0.358380	+	0.933576i	$0.616671\pi$
$108$	0	0
$109$	17.0711	1.63511	0.817556	−	0.575849i	$-0.195328\pi$
$109$	17.0711	1.63511	0.817556	+	0.575849i	$0.195328\pi$
$110$	1.41421	0.134840
$111$	6.24264	0.592525
$112$	4.00000	0.377964
$113$	8.31371	0.782088	0.391044	−	0.920372i	$-0.372114\pi$
$113$	8.31371	0.782088	0.391044	+	0.920372i	$0.372114\pi$
$114$	−5.41421	−0.507088
$115$	3.82843	0.357003
$116$	0	0
$117$	0.585786	0.0541560
$118$	−20.3848	−1.87657
$119$	1.82843	0.167612
$120$	2.82843	0.258199
$121$	1.00000	0.0909091
$122$	−15.0711	−1.36447
$123$	−11.0711	−0.998245
$124$	0	0
$125$	−1.00000	−0.0894427
$126$	1.41421	0.125988
$127$	13.7279	1.21816	0.609078	−	0.793110i	$-0.291540\pi$
$127$	13.7279	1.21816	0.609078	+	0.793110i	$0.291540\pi$
$128$	−11.3137	−1.00000
$129$	6.41421	0.564740
$130$	0.828427	0.0726579
$131$	1.75736	0.153541	0.0767706	−	0.997049i	$-0.475539\pi$
$131$	1.75736	0.153541	0.0767706	+	0.997049i	$0.475539\pi$
$132$	0	0
$133$	3.82843	0.331967
$134$	8.48528	0.733017
$135$	1.00000	0.0860663
$136$	−5.17157	−0.443459
$137$	2.34315	0.200188	0.100094	−	0.994978i	$-0.468086\pi$
$137$	2.34315	0.200188	0.100094	+	0.994978i	$0.468086\pi$
$138$	−5.41421	−0.460888
$139$	14.0000	1.18746	0.593732	−	0.804663i	$-0.297654\pi$
$139$	14.0000	1.18746	0.593732	+	0.804663i	$0.297654\pi$
$140$	0	0
$141$	−1.75736	−0.147996
$142$	−4.34315	−0.364469
$143$	0.585786	0.0489859
$144$	−4.00000	−0.333333
$145$	1.24264	0.103196
$146$	12.0000	0.993127
$147$	−1.00000	−0.0824786
$148$	0	0
$149$	4.82843	0.395560	0.197780	−	0.980246i	$-0.436627\pi$
$149$	4.82843	0.395560	0.197780	+	0.980246i	$0.436627\pi$
$150$	1.41421	0.115470
$151$	−4.34315	−0.353440	−0.176720	−	0.984261i	$-0.556549\pi$
$151$	−4.34315	−0.353440	−0.176720	+	0.984261i	$0.556549\pi$
$152$	−10.8284	−0.878301
$153$	−1.82843	−0.147820
$154$	1.41421	0.113961
$155$	−0.585786	−0.0470515
$156$	0	0
$157$	9.58579	0.765029	0.382515	−	0.923949i	$-0.375058\pi$
$157$	9.58579	0.765029	0.382515	+	0.923949i	$0.375058\pi$
$158$	11.6569	0.927370
$159$	−8.65685	−0.686533
$160$	0	0
$161$	3.82843	0.301722
$162$	−1.41421	−0.111111
$163$	−14.7279	−1.15358	−0.576790	−	0.816893i	$-0.695695\pi$
$163$	−14.7279	−1.15358	−0.576790	+	0.816893i	$0.695695\pi$
$164$	0	0
$165$	1.00000	0.0778499
$166$	−24.2426	−1.88159
$167$	0.343146	0.0265534	0.0132767	−	0.999912i	$-0.495774\pi$
$167$	0.343146	0.0265534	0.0132767	+	0.999912i	$0.495774\pi$
$168$	2.82843	0.218218
$169$	−12.6569	−0.973604
$170$	−2.58579	−0.198321
$171$	−3.82843	−0.292767
$172$	0	0
$173$	19.3137	1.46839	0.734197	−	0.678936i	$-0.237559\pi$
$173$	19.3137	1.46839	0.734197	+	0.678936i	$0.237559\pi$
$174$	−1.75736	−0.133225
$175$	−1.00000	−0.0755929
$176$	−4.00000	−0.301511
$177$	−14.4142	−1.08344
$178$	0.100505	0.00753317
$179$	7.75736	0.579812	0.289906	−	0.957055i	$-0.406376\pi$
$179$	7.75736	0.579812	0.289906	+	0.957055i	$0.406376\pi$
$180$	0	0
$181$	18.9706	1.41007	0.705035	−	0.709172i	$-0.250931\pi$
$181$	18.9706	1.41007	0.705035	+	0.709172i	$0.250931\pi$
$182$	0.828427	0.0614071
$183$	−10.6569	−0.787777
$184$	−10.8284	−0.798282
$185$	6.24264	0.458968
$186$	0.828427	0.0607432
$187$	−1.82843	−0.133708
$188$	0	0
$189$	1.00000	0.0727393
$190$	−5.41421	−0.392788
$191$	5.65685	0.409316	0.204658	−	0.978834i	$-0.434392\pi$
$191$	5.65685	0.409316	0.204658	+	0.978834i	$0.434392\pi$
$192$	−8.00000	−0.577350
$193$	14.4853	1.04267	0.521337	−	0.853351i	$-0.325434\pi$
$193$	14.4853	1.04267	0.521337	+	0.853351i	$0.325434\pi$
$194$	10.2426	0.735379
$195$	0.585786	0.0419490
$196$	0	0
$197$	−14.8284	−1.05648	−0.528241	−	0.849095i	$-0.677148\pi$
$197$	−14.8284	−1.05648	−0.528241	+	0.849095i	$0.677148\pi$
$198$	−1.41421	−0.100504
$199$	−19.3137	−1.36911	−0.684556	−	0.728960i	$-0.740004\pi$
$199$	−19.3137	−1.36911	−0.684556	+	0.728960i	$0.740004\pi$
$200$	2.82843	0.200000
$201$	6.00000	0.423207
$202$	−0.485281	−0.0341443
$203$	1.24264	0.0872163
$204$	0	0
$205$	−11.0711	−0.773237
$206$	−19.4142	−1.35265
$207$	−3.82843	−0.266094
$208$	−2.34315	−0.162468
$209$	−3.82843	−0.264818
$210$	1.41421	0.0975900
$211$	6.48528	0.446465	0.223233	−	0.974765i	$-0.428339\pi$
$211$	6.48528	0.446465	0.223233	+	0.974765i	$0.428339\pi$
$212$	0	0
$213$	−3.07107	−0.210426
$214$	10.4853	0.716759
$215$	6.41421	0.437446
$216$	−2.82843	−0.192450
$217$	−0.585786	−0.0397658
$218$	−24.1421	−1.63511
$219$	8.48528	0.573382
$220$	0	0
$221$	−1.07107	−0.0720478
$222$	−8.82843	−0.592525
$223$	−1.24264	−0.0832134	−0.0416067	−	0.999134i	$-0.513248\pi$
$223$	−1.24264	−0.0832134	−0.0416067	+	0.999134i	$0.513248\pi$
$224$	0	0
$225$	1.00000	0.0666667
$226$	−11.7574	−0.782088
$227$	−24.6569	−1.63653	−0.818266	−	0.574839i	$-0.805065\pi$
$227$	−24.6569	−1.63653	−0.818266	+	0.574839i	$0.805065\pi$
$228$	0	0
$229$	6.72792	0.444594	0.222297	−	0.974979i	$-0.428645\pi$
$229$	6.72792	0.444594	0.222297	+	0.974979i	$0.428645\pi$
$230$	−5.41421	−0.357003
$231$	1.00000	0.0657952
$232$	−3.51472	−0.230753
$233$	7.75736	0.508202	0.254101	−	0.967178i	$-0.418221\pi$
$233$	7.75736	0.508202	0.254101	+	0.967178i	$0.418221\pi$
$234$	−0.828427	−0.0541560
$235$	−1.75736	−0.114637
$236$	0	0
$237$	8.24264	0.535417
$238$	−2.58579	−0.167612
$239$	14.0711	0.910182	0.455091	−	0.890445i	$-0.349607\pi$
$239$	14.0711	0.910182	0.455091	+	0.890445i	$0.349607\pi$
$240$	−4.00000	−0.258199
$241$	8.48528	0.546585	0.273293	−	0.961931i	$-0.411887\pi$
$241$	8.48528	0.546585	0.273293	+	0.961931i	$0.411887\pi$
$242$	−1.41421	−0.0909091
$243$	−1.00000	−0.0641500
$244$	0	0
$245$	−1.00000	−0.0638877
$246$	15.6569	0.998245
$247$	−2.24264	−0.142696
$248$	1.65685	0.105210
$249$	−17.1421	−1.08634
$250$	1.41421	0.0894427
$251$	6.34315	0.400376	0.200188	−	0.979758i	$-0.435845\pi$
$251$	6.34315	0.400376	0.200188	+	0.979758i	$0.435845\pi$
$252$	0	0
$253$	−3.82843	−0.240691
$254$	−19.4142	−1.21816
$255$	−1.82843	−0.114501
$256$	0	0
$257$	−7.75736	−0.483891	−0.241945	−	0.970290i	$-0.577785\pi$
$257$	−7.75736	−0.483891	−0.241945	+	0.970290i	$0.577785\pi$
$258$	−9.07107	−0.564740
$259$	6.24264	0.387899
$260$	0	0
$261$	−1.24264	−0.0769175
$262$	−2.48528	−0.153541
$263$	−14.1421	−0.872041	−0.436021	−	0.899937i	$-0.643613\pi$
$263$	−14.1421	−0.872041	−0.436021	+	0.899937i	$0.643613\pi$
$264$	−2.82843	−0.174078
$265$	−8.65685	−0.531786
$266$	−5.41421	−0.331967
$267$	0.0710678	0.00434928
$268$	0	0
$269$	−6.55635	−0.399748	−0.199874	−	0.979822i	$-0.564053\pi$
$269$	−6.55635	−0.399748	−0.199874	+	0.979822i	$0.564053\pi$
$270$	−1.41421	−0.0860663
$271$	−7.82843	−0.475543	−0.237772	−	0.971321i	$-0.576417\pi$
$271$	−7.82843	−0.475543	−0.237772	+	0.971321i	$0.576417\pi$
$272$	7.31371	0.443459
$273$	0.585786	0.0354534
$274$	−3.31371	−0.200188
$275$	1.00000	0.0603023
$276$	0	0
$277$	18.8284	1.13129	0.565645	−	0.824649i	$-0.308627\pi$
$277$	18.8284	1.13129	0.565645	+	0.824649i	$0.308627\pi$
$278$	−19.7990	−1.18746
$279$	0.585786	0.0350701
$280$	2.82843	0.169031
$281$	21.1716	1.26299	0.631495	−	0.775380i	$-0.282442\pi$
$281$	21.1716	1.26299	0.631495	+	0.775380i	$0.282442\pi$
$282$	2.48528	0.147996
$283$	15.2132	0.904331	0.452166	−	0.891934i	$-0.350652\pi$
$283$	15.2132	0.904331	0.452166	+	0.891934i	$0.350652\pi$
$284$	0	0
$285$	−3.82843	−0.226776
$286$	−0.828427	−0.0489859
$287$	−11.0711	−0.653504
$288$	0	0
$289$	−13.6569	−0.803344
$290$	−1.75736	−0.103196
$291$	7.24264	0.424571
$292$	0	0
$293$	9.14214	0.534089	0.267045	−	0.963684i	$-0.413953\pi$
$293$	9.14214	0.534089	0.267045	+	0.963684i	$0.413953\pi$
$294$	1.41421	0.0824786
$295$	−14.4142	−0.839228
$296$	−17.6569	−1.02628
$297$	−1.00000	−0.0580259
$298$	−6.82843	−0.395560
$299$	−2.24264	−0.129695
$300$	0	0
$301$	6.41421	0.369709
$302$	6.14214	0.353440
$303$	−0.343146	−0.0197132
$304$	15.3137	0.878301
$305$	−10.6569	−0.610210
$306$	2.58579	0.147820
$307$	−13.5147	−0.771326	−0.385663	−	0.922640i	$-0.626027\pi$
$307$	−13.5147	−0.771326	−0.385663	+	0.922640i	$0.626027\pi$
$308$	0	0
$309$	−13.7279	−0.780954
$310$	0.828427	0.0470515
$311$	−31.1127	−1.76424	−0.882120	−	0.471025i	$-0.843884\pi$
$311$	−31.1127	−1.76424	−0.882120	+	0.471025i	$0.843884\pi$
$312$	−1.65685	−0.0938009
$313$	−6.75736	−0.381949	−0.190974	−	0.981595i	$-0.561165\pi$
$313$	−6.75736	−0.381949	−0.190974	+	0.981595i	$0.561165\pi$
$314$	−13.5563	−0.765029
$315$	1.00000	0.0563436
$316$	0	0
$317$	−22.1421	−1.24363	−0.621813	−	0.783166i	$-0.713604\pi$
$317$	−22.1421	−1.24363	−0.621813	+	0.783166i	$0.713604\pi$
$318$	12.2426	0.686533
$319$	−1.24264	−0.0695745
$320$	−8.00000	−0.447214
$321$	7.41421	0.413821
$322$	−5.41421	−0.301722
$323$	7.00000	0.389490
$324$	0	0
$325$	0.585786	0.0324936
$326$	20.8284	1.15358
$327$	−17.0711	−0.944032
$328$	31.3137	1.72901
$329$	−1.75736	−0.0968864
$330$	−1.41421	−0.0778499
$331$	−13.1421	−0.722357	−0.361179	−	0.932497i	$-0.617626\pi$
$331$	−13.1421	−0.722357	−0.361179	+	0.932497i	$0.617626\pi$
$332$	0	0
$333$	−6.24264	−0.342095
$334$	−0.485281	−0.0265534
$335$	6.00000	0.327815
$336$	−4.00000	−0.218218
$337$	−1.24264	−0.0676910	−0.0338455	−	0.999427i	$-0.510775\pi$
$337$	−1.24264	−0.0676910	−0.0338455	+	0.999427i	$0.510775\pi$
$338$	17.8995	0.973604
$339$	−8.31371	−0.451539
$340$	0	0
$341$	0.585786	0.0317221
$342$	5.41421	0.292767
$343$	−1.00000	−0.0539949
$344$	−18.1421	−0.978158
$345$	−3.82843	−0.206116
$346$	−27.3137	−1.46839
$347$	19.7990	1.06287	0.531433	−	0.847100i	$-0.321654\pi$
$347$	19.7990	1.06287	0.531433	+	0.847100i	$0.321654\pi$
$348$	0	0
$349$	19.0000	1.01705	0.508523	−	0.861048i	$-0.330192\pi$
$349$	19.0000	1.01705	0.508523	+	0.861048i	$0.330192\pi$
$350$	1.41421	0.0755929
$351$	−0.585786	−0.0312670
$352$	0	0
$353$	−8.14214	−0.433362	−0.216681	−	0.976242i	$-0.569523\pi$
$353$	−8.14214	−0.433362	−0.216681	+	0.976242i	$0.569523\pi$
$354$	20.3848	1.08344
$355$	−3.07107	−0.162995
$356$	0	0
$357$	−1.82843	−0.0967706
$358$	−10.9706	−0.579812
$359$	16.5563	0.873811	0.436905	−	0.899507i	$-0.356074\pi$
$359$	16.5563	0.873811	0.436905	+	0.899507i	$0.356074\pi$
$360$	−2.82843	−0.149071
$361$	−4.34315	−0.228587
$362$	−26.8284	−1.41007
$363$	−1.00000	−0.0524864
$364$	0	0
$365$	8.48528	0.444140
$366$	15.0711	0.787777
$367$	−4.75736	−0.248332	−0.124166	−	0.992261i	$-0.539626\pi$
$367$	−4.75736	−0.248332	−0.124166	+	0.992261i	$0.539626\pi$
$368$	15.3137	0.798282
$369$	11.0711	0.576337
$370$	−8.82843	−0.458968
$371$	−8.65685	−0.449441
$372$	0	0
$373$	3.58579	0.185665	0.0928325	−	0.995682i	$-0.470408\pi$
$373$	3.58579	0.185665	0.0928325	+	0.995682i	$0.470408\pi$
$374$	2.58579	0.133708
$375$	1.00000	0.0516398
$376$	4.97056	0.256337
$377$	−0.727922	−0.0374899
$378$	−1.41421	−0.0727393
$379$	−27.8284	−1.42945	−0.714725	−	0.699405i	$-0.753448\pi$
$379$	−27.8284	−1.42945	−0.714725	+	0.699405i	$0.753448\pi$
$380$	0	0
$381$	−13.7279	−0.703303
$382$	−8.00000	−0.409316
$383$	22.8701	1.16861	0.584303	−	0.811536i	$-0.301368\pi$
$383$	22.8701	1.16861	0.584303	+	0.811536i	$0.301368\pi$
$384$	11.3137	0.577350
$385$	1.00000	0.0509647
$386$	−20.4853	−1.04267
$387$	−6.41421	−0.326053
$388$	0	0
$389$	−23.6985	−1.20156	−0.600780	−	0.799414i	$-0.705143\pi$
$389$	−23.6985	−1.20156	−0.600780	+	0.799414i	$0.705143\pi$
$390$	−0.828427	−0.0419490
$391$	7.00000	0.354005
$392$	2.82843	0.142857
$393$	−1.75736	−0.0886471
$394$	20.9706	1.05648
$395$	8.24264	0.414732
$396$	0	0
$397$	20.4853	1.02813	0.514063	−	0.857752i	$-0.328140\pi$
$397$	20.4853	1.02813	0.514063	+	0.857752i	$0.328140\pi$
$398$	27.3137	1.36911
$399$	−3.82843	−0.191661
$400$	−4.00000	−0.200000
$401$	26.3848	1.31759	0.658796	−	0.752321i	$-0.271066\pi$
$401$	26.3848	1.31759	0.658796	+	0.752321i	$0.271066\pi$
$402$	−8.48528	−0.423207
$403$	0.343146	0.0170933
$404$	0	0
$405$	−1.00000	−0.0496904
$406$	−1.75736	−0.0872163
$407$	−6.24264	−0.309436
$408$	5.17157	0.256031
$409$	36.4853	1.80408	0.902041	−	0.431651i	$-0.142069\pi$
$409$	36.4853	1.80408	0.902041	+	0.431651i	$0.142069\pi$
$410$	15.6569	0.773237
$411$	−2.34315	−0.115579
$412$	0	0
$413$	−14.4142	−0.709277
$414$	5.41421	0.266094
$415$	−17.1421	−0.841474
$416$	0	0
$417$	−14.0000	−0.685583
$418$	5.41421	0.264818
$419$	−6.07107	−0.296591	−0.148296	−	0.988943i	$-0.547379\pi$
$419$	−6.07107	−0.296591	−0.148296	+	0.988943i	$0.547379\pi$
$420$	0	0
$421$	10.6569	0.519383	0.259692	−	0.965692i	$-0.416379\pi$
$421$	10.6569	0.519383	0.259692	+	0.965692i	$0.416379\pi$
$422$	−9.17157	−0.446465
$423$	1.75736	0.0854457
$424$	24.4853	1.18911
$425$	−1.82843	−0.0886917
$426$	4.34315	0.210426
$427$	−10.6569	−0.515721
$428$	0	0
$429$	−0.585786	−0.0282820
$430$	−9.07107	−0.437446
$431$	33.1716	1.59782	0.798909	−	0.601452i	$-0.205411\pi$
$431$	33.1716	1.59782	0.798909	+	0.601452i	$0.205411\pi$
$432$	4.00000	0.192450
$433$	24.1421	1.16020	0.580098	−	0.814546i	$-0.303014\pi$
$433$	24.1421	1.16020	0.580098	+	0.814546i	$0.303014\pi$
$434$	0.828427	0.0397658
$435$	−1.24264	−0.0595801
$436$	0	0
$437$	14.6569	0.701132
$438$	−12.0000	−0.573382
$439$	3.00000	0.143182	0.0715911	−	0.997434i	$-0.477192\pi$
$439$	3.00000	0.143182	0.0715911	+	0.997434i	$0.477192\pi$
$440$	−2.82843	−0.134840
$441$	1.00000	0.0476190
$442$	1.51472	0.0720478
$443$	20.3431	0.966532	0.483266	−	0.875474i	$-0.339450\pi$
$443$	20.3431	0.966532	0.483266	+	0.875474i	$0.339450\pi$
$444$	0	0
$445$	0.0710678	0.00336894
$446$	1.75736	0.0832134
$447$	−4.82843	−0.228377
$448$	−8.00000	−0.377964
$449$	−25.4142	−1.19937	−0.599685	−	0.800236i	$-0.704708\pi$
$449$	−25.4142	−1.19937	−0.599685	+	0.800236i	$0.704708\pi$
$450$	−1.41421	−0.0666667
$451$	11.0711	0.521316
$452$	0	0
$453$	4.34315	0.204059
$454$	34.8701	1.63653
$455$	0.585786	0.0274621
$456$	10.8284	0.507088
$457$	20.4142	0.954937	0.477468	−	0.878649i	$-0.341555\pi$
$457$	20.4142	0.954937	0.477468	+	0.878649i	$0.341555\pi$
$458$	−9.51472	−0.444594
$459$	1.82843	0.0853437
$460$	0	0
$461$	−8.14214	−0.379217	−0.189609	−	0.981860i	$-0.560722\pi$
$461$	−8.14214	−0.379217	−0.189609	+	0.981860i	$0.560722\pi$
$462$	−1.41421	−0.0657952
$463$	−13.5147	−0.628082	−0.314041	−	0.949409i	$-0.601683\pi$
$463$	−13.5147	−0.628082	−0.314041	+	0.949409i	$0.601683\pi$
$464$	4.97056	0.230753
$465$	0.585786	0.0271652
$466$	−10.9706	−0.508202
$467$	−13.4558	−0.622662	−0.311331	−	0.950302i	$-0.600775\pi$
$467$	−13.4558	−0.622662	−0.311331	+	0.950302i	$0.600775\pi$
$468$	0	0
$469$	6.00000	0.277054
$470$	2.48528	0.114637
$471$	−9.58579	−0.441690
$472$	40.7696	1.87657
$473$	−6.41421	−0.294926
$474$	−11.6569	−0.535417
$475$	−3.82843	−0.175660
$476$	0	0
$477$	8.65685	0.396370
$478$	−19.8995	−0.910182
$479$	−25.5563	−1.16770	−0.583850	−	0.811862i	$-0.698454\pi$
$479$	−25.5563	−1.16770	−0.583850	+	0.811862i	$0.698454\pi$
$480$	0	0
$481$	−3.65685	−0.166738
$482$	−12.0000	−0.546585
$483$	−3.82843	−0.174199
$484$	0	0
$485$	7.24264	0.328871
$486$	1.41421	0.0641500
$487$	−11.1716	−0.506232	−0.253116	−	0.967436i	$-0.581455\pi$
$487$	−11.1716	−0.506232	−0.253116	+	0.967436i	$0.581455\pi$
$488$	30.1421	1.36447
$489$	14.7279	0.666020
$490$	1.41421	0.0638877
$491$	−34.5563	−1.55951	−0.779753	−	0.626087i	$-0.784655\pi$
$491$	−34.5563	−1.55951	−0.779753	+	0.626087i	$0.784655\pi$
$492$	0	0
$493$	2.27208	0.102329
$494$	3.17157	0.142696
$495$	−1.00000	−0.0449467
$496$	−2.34315	−0.105210
$497$	−3.07107	−0.137756
$498$	24.2426	1.08634
$499$	−31.9706	−1.43120	−0.715599	−	0.698511i	$-0.753846\pi$
$499$	−31.9706	−1.43120	−0.715599	+	0.698511i	$0.753846\pi$
$500$	0	0
$501$	−0.343146	−0.0153306
$502$	−8.97056	−0.400376
$503$	28.4558	1.26878	0.634392	−	0.773012i	$-0.281251\pi$
$503$	28.4558	1.26878	0.634392	+	0.773012i	$0.281251\pi$
$504$	−2.82843	−0.125988
$505$	−0.343146	−0.0152698
$506$	5.41421	0.240691
$507$	12.6569	0.562111
$508$	0	0
$509$	19.5858	0.868125	0.434062	−	0.900883i	$-0.357080\pi$
$509$	19.5858	0.868125	0.434062	+	0.900883i	$0.357080\pi$
$510$	2.58579	0.114501
$511$	8.48528	0.375367
$512$	22.6274	1.00000
$513$	3.82843	0.169029
$514$	10.9706	0.483891
$515$	−13.7279	−0.604925
$516$	0	0
$517$	1.75736	0.0772886
$518$	−8.82843	−0.387899
$519$	−19.3137	−0.847778
$520$	−1.65685	−0.0726579
$521$	17.3848	0.761641	0.380820	−	0.924649i	$-0.375642\pi$
$521$	17.3848	0.761641	0.380820	+	0.924649i	$0.375642\pi$
$522$	1.75736	0.0769175
$523$	9.45584	0.413475	0.206738	−	0.978396i	$-0.433715\pi$
$523$	9.45584	0.413475	0.206738	+	0.978396i	$0.433715\pi$
$524$	0	0
$525$	1.00000	0.0436436
$526$	20.0000	0.872041
$527$	−1.07107	−0.0466564
$528$	4.00000	0.174078
$529$	−8.34315	−0.362745
$530$	12.2426	0.531786
$531$	14.4142	0.625524
$532$	0	0
$533$	6.48528	0.280909
$534$	−0.100505	−0.00434928
$535$	7.41421	0.320544
$536$	−16.9706	−0.733017
$537$	−7.75736	−0.334755
$538$	9.27208	0.399748
$539$	1.00000	0.0430730
$540$	0	0
$541$	0.100505	0.00432105	0.00216053	−	0.999998i	$-0.499312\pi$
$541$	0.100505	0.00432105	0.00216053	+	0.999998i	$0.499312\pi$
$542$	11.0711	0.475543
$543$	−18.9706	−0.814105
$544$	0	0
$545$	−17.0711	−0.731244
$546$	−0.828427	−0.0354534
$547$	36.6985	1.56911	0.784557	−	0.620057i	$-0.212890\pi$
$547$	36.6985	1.56911	0.784557	+	0.620057i	$0.212890\pi$
$548$	0	0
$549$	10.6569	0.454823
$550$	−1.41421	−0.0603023
$551$	4.75736	0.202670
$552$	10.8284	0.460888
$553$	8.24264	0.350513
$554$	−26.6274	−1.13129
$555$	−6.24264	−0.264985
$556$	0	0
$557$	42.7696	1.81220	0.906102	−	0.423059i	$-0.139044\pi$
$557$	42.7696	1.81220	0.906102	+	0.423059i	$0.139044\pi$
$558$	−0.828427	−0.0350701
$559$	−3.75736	−0.158919
$560$	−4.00000	−0.169031
$561$	1.82843	0.0771963
$562$	−29.9411	−1.26299
$563$	−9.51472	−0.400998	−0.200499	−	0.979694i	$-0.564256\pi$
$563$	−9.51472	−0.400998	−0.200499	+	0.979694i	$0.564256\pi$
$564$	0	0
$565$	−8.31371	−0.349760
$566$	−21.5147	−0.904331
$567$	−1.00000	−0.0419961
$568$	8.68629	0.364469
$569$	26.6985	1.11926	0.559629	−	0.828743i	$-0.310944\pi$
$569$	26.6985	1.11926	0.559629	+	0.828743i	$0.310944\pi$
$570$	5.41421	0.226776
$571$	1.89949	0.0794914	0.0397457	−	0.999210i	$-0.487345\pi$
$571$	1.89949	0.0794914	0.0397457	+	0.999210i	$0.487345\pi$
$572$	0	0
$573$	−5.65685	−0.236318
$574$	15.6569	0.653504
$575$	−3.82843	−0.159656
$576$	8.00000	0.333333
$577$	22.9706	0.956277	0.478139	−	0.878284i	$-0.341312\pi$
$577$	22.9706	0.956277	0.478139	+	0.878284i	$0.341312\pi$
$578$	19.3137	0.803344
$579$	−14.4853	−0.601988
$580$	0	0
$581$	−17.1421	−0.711176
$582$	−10.2426	−0.424571
$583$	8.65685	0.358530
$584$	−24.0000	−0.993127
$585$	−0.585786	−0.0242193
$586$	−12.9289	−0.534089
$587$	−0.928932	−0.0383411	−0.0191706	−	0.999816i	$-0.506103\pi$
$587$	−0.928932	−0.0383411	−0.0191706	+	0.999816i	$0.506103\pi$
$588$	0	0
$589$	−2.24264	−0.0924064
$590$	20.3848	0.839228
$591$	14.8284	0.609960
$592$	24.9706	1.02628
$593$	−32.4853	−1.33401	−0.667005	−	0.745053i	$-0.732424\pi$
$593$	−32.4853	−1.33401	−0.667005	+	0.745053i	$0.732424\pi$
$594$	1.41421	0.0580259
$595$	−1.82843	−0.0749582
$596$	0	0
$597$	19.3137	0.790457
$598$	3.17157	0.129695
$599$	28.1421	1.14986	0.574928	−	0.818204i	$-0.305030\pi$
$599$	28.1421	1.14986	0.574928	+	0.818204i	$0.305030\pi$
$600$	−2.82843	−0.115470
$601$	4.85786	0.198156	0.0990782	−	0.995080i	$-0.468411\pi$
$601$	4.85786	0.198156	0.0990782	+	0.995080i	$0.468411\pi$
$602$	−9.07107	−0.369709
$603$	−6.00000	−0.244339
$604$	0	0
$605$	−1.00000	−0.0406558
$606$	0.485281	0.0197132
$607$	16.8284	0.683045	0.341522	−	0.939874i	$-0.389057\pi$
$607$	16.8284	0.683045	0.341522	+	0.939874i	$0.389057\pi$
$608$	0	0
$609$	−1.24264	−0.0503543
$610$	15.0711	0.610210
$611$	1.02944	0.0416466
$612$	0	0
$613$	−2.97056	−0.119980	−0.0599899	−	0.998199i	$-0.519107\pi$
$613$	−2.97056	−0.119980	−0.0599899	+	0.998199i	$0.519107\pi$
$614$	19.1127	0.771326
$615$	11.0711	0.446429
$616$	−2.82843	−0.113961
$617$	42.4264	1.70802	0.854011	−	0.520254i	$-0.174163\pi$
$617$	42.4264	1.70802	0.854011	+	0.520254i	$0.174163\pi$
$618$	19.4142	0.780954
$619$	39.9411	1.60537	0.802685	−	0.596404i	$-0.203404\pi$
$619$	39.9411	1.60537	0.802685	+	0.596404i	$0.203404\pi$
$620$	0	0
$621$	3.82843	0.153629
$622$	44.0000	1.76424
$623$	0.0710678	0.00284727
$624$	2.34315	0.0938009
$625$	1.00000	0.0400000
$626$	9.55635	0.381949
$627$	3.82843	0.152893
$628$	0	0
$629$	11.4142	0.455114
$630$	−1.41421	−0.0563436
$631$	−12.5147	−0.498203	−0.249102	−	0.968477i	$-0.580135\pi$
$631$	−12.5147	−0.498203	−0.249102	+	0.968477i	$0.580135\pi$
$632$	−23.3137	−0.927370
$633$	−6.48528	−0.257767
$634$	31.3137	1.24363
$635$	−13.7279	−0.544776
$636$	0	0
$637$	0.585786	0.0232097
$638$	1.75736	0.0695745
$639$	3.07107	0.121490
$640$	11.3137	0.447214
$641$	−45.5980	−1.80101	−0.900506	−	0.434844i	$-0.856804\pi$
$641$	−45.5980	−1.80101	−0.900506	+	0.434844i	$0.856804\pi$
$642$	−10.4853	−0.413821
$643$	−28.5563	−1.12615	−0.563076	−	0.826405i	$-0.690382\pi$
$643$	−28.5563	−1.12615	−0.563076	+	0.826405i	$0.690382\pi$
$644$	0	0
$645$	−6.41421	−0.252559
$646$	−9.89949	−0.389490
$647$	−32.4853	−1.27713	−0.638564	−	0.769569i	$-0.720471\pi$
$647$	−32.4853	−1.27713	−0.638564	+	0.769569i	$0.720471\pi$
$648$	2.82843	0.111111
$649$	14.4142	0.565807
$650$	−0.828427	−0.0324936
$651$	0.585786	0.0229588
$652$	0	0
$653$	14.6569	0.573567	0.286784	−	0.957995i	$-0.407414\pi$
$653$	14.6569	0.573567	0.286784	+	0.957995i	$0.407414\pi$
$654$	24.1421	0.944032
$655$	−1.75736	−0.0686657
$656$	−44.2843	−1.72901
$657$	−8.48528	−0.331042
$658$	2.48528	0.0968864
$659$	−35.0416	−1.36503	−0.682514	−	0.730872i	$-0.739113\pi$
$659$	−35.0416	−1.36503	−0.682514	+	0.730872i	$0.739113\pi$
$660$	0	0
$661$	−5.55635	−0.216117	−0.108058	−	0.994145i	$-0.534463\pi$
$661$	−5.55635	−0.216117	−0.108058	+	0.994145i	$0.534463\pi$
$662$	18.5858	0.722357
$663$	1.07107	0.0415968
$664$	48.4853	1.88159
$665$	−3.82843	−0.148460
$666$	8.82843	0.342095
$667$	4.75736	0.184206
$668$	0	0
$669$	1.24264	0.0480433
$670$	−8.48528	−0.327815
$671$	10.6569	0.411403
$672$	0	0
$673$	−5.04163	−0.194341	−0.0971703	−	0.995268i	$-0.530979\pi$
$673$	−5.04163	−0.194341	−0.0971703	+	0.995268i	$0.530979\pi$
$674$	1.75736	0.0676910
$675$	−1.00000	−0.0384900
$676$	0	0
$677$	−37.1421	−1.42749	−0.713744	−	0.700407i	$-0.753002\pi$
$677$	−37.1421	−1.42749	−0.713744	+	0.700407i	$0.753002\pi$
$678$	11.7574	0.451539
$679$	7.24264	0.277947
$680$	5.17157	0.198321
$681$	24.6569	0.944853
$682$	−0.828427	−0.0317221
$683$	−16.6863	−0.638483	−0.319242	−	0.947673i	$-0.603428\pi$
$683$	−16.6863	−0.638483	−0.319242	+	0.947673i	$0.603428\pi$
$684$	0	0
$685$	−2.34315	−0.0895270
$686$	1.41421	0.0539949
$687$	−6.72792	−0.256686
$688$	25.6569	0.978158
$689$	5.07107	0.193192
$690$	5.41421	0.206116
$691$	2.97056	0.113006	0.0565028	−	0.998402i	$-0.482005\pi$
$691$	2.97056	0.113006	0.0565028	+	0.998402i	$0.482005\pi$
$692$	0	0
$693$	−1.00000	−0.0379869
$694$	−28.0000	−1.06287
$695$	−14.0000	−0.531050
$696$	3.51472	0.133225
$697$	−20.2426	−0.766745
$698$	−26.8701	−1.01705
$699$	−7.75736	−0.293410
$700$	0	0
$701$	−7.04163	−0.265959	−0.132979	−	0.991119i	$-0.542454\pi$
$701$	−7.04163	−0.265959	−0.132979	+	0.991119i	$0.542454\pi$
$702$	0.828427	0.0312670
$703$	23.8995	0.901387
$704$	8.00000	0.301511
$705$	1.75736	0.0661860
$706$	11.5147	0.433362
$707$	−0.343146	−0.0129053
$708$	0	0
$709$	−18.6569	−0.700673	−0.350336	−	0.936624i	$-0.613933\pi$
$709$	−18.6569	−0.700673	−0.350336	+	0.936624i	$0.613933\pi$
$710$	4.34315	0.162995
$711$	−8.24264	−0.309123
$712$	−0.201010	−0.00753317
$713$	−2.24264	−0.0839876
$714$	2.58579	0.0967706
$715$	−0.585786	−0.0219072
$716$	0	0
$717$	−14.0711	−0.525494
$718$	−23.4142	−0.873811
$719$	38.0122	1.41762	0.708808	−	0.705402i	$-0.249233\pi$
$719$	38.0122	1.41762	0.708808	+	0.705402i	$0.249233\pi$
$720$	4.00000	0.149071
$721$	−13.7279	−0.511255
$722$	6.14214	0.228587
$723$	−8.48528	−0.315571
$724$	0	0
$725$	−1.24264	−0.0461505
$726$	1.41421	0.0524864
$727$	1.44365	0.0535420	0.0267710	−	0.999642i	$-0.491478\pi$
$727$	1.44365	0.0535420	0.0267710	+	0.999642i	$0.491478\pi$
$728$	−1.65685	−0.0614071
$729$	1.00000	0.0370370
$730$	−12.0000	−0.444140
$731$	11.7279	0.433773
$732$	0	0
$733$	−29.7990	−1.10065	−0.550325	−	0.834950i	$-0.685496\pi$
$733$	−29.7990	−1.10065	−0.550325	+	0.834950i	$0.685496\pi$
$734$	6.72792	0.248332
$735$	1.00000	0.0368856
$736$	0	0
$737$	−6.00000	−0.221013
$738$	−15.6569	−0.576337
$739$	−36.4264	−1.33997	−0.669984	−	0.742376i	$-0.733699\pi$
$739$	−36.4264	−1.33997	−0.669984	+	0.742376i	$0.733699\pi$
$740$	0	0
$741$	2.24264	0.0823855
$742$	12.2426	0.449441
$743$	−20.1421	−0.738943	−0.369472	−	0.929242i	$-0.620461\pi$
$743$	−20.1421	−0.738943	−0.369472	+	0.929242i	$0.620461\pi$
$744$	−1.65685	−0.0607432
$745$	−4.82843	−0.176900
$746$	−5.07107	−0.185665
$747$	17.1421	0.627198
$748$	0	0
$749$	7.41421	0.270909
$750$	−1.41421	−0.0516398
$751$	−15.4853	−0.565066	−0.282533	−	0.959258i	$-0.591175\pi$
$751$	−15.4853	−0.565066	−0.282533	+	0.959258i	$0.591175\pi$
$752$	−7.02944	−0.256337
$753$	−6.34315	−0.231157
$754$	1.02944	0.0374899
$755$	4.34315	0.158063
$756$	0	0
$757$	45.1127	1.63965	0.819824	−	0.572615i	$-0.194071\pi$
$757$	45.1127	1.63965	0.819824	+	0.572615i	$0.194071\pi$
$758$	39.3553	1.42945
$759$	3.82843	0.138963
$760$	10.8284	0.392788
$761$	18.2843	0.662804	0.331402	−	0.943490i	$-0.392478\pi$
$761$	18.2843	0.662804	0.331402	+	0.943490i	$0.392478\pi$
$762$	19.4142	0.703303
$763$	−17.0711	−0.618014
$764$	0	0
$765$	1.82843	0.0661069
$766$	−32.3431	−1.16861
$767$	8.44365	0.304883
$768$	0	0
$769$	−37.9706	−1.36925	−0.684627	−	0.728894i	$-0.740035\pi$
$769$	−37.9706	−1.36925	−0.684627	+	0.728894i	$0.740035\pi$
$770$	−1.41421	−0.0509647
$771$	7.75736	0.279374
$772$	0	0
$773$	48.1421	1.73155	0.865776	−	0.500432i	$-0.166825\pi$
$773$	48.1421	1.73155	0.865776	+	0.500432i	$0.166825\pi$
$774$	9.07107	0.326053
$775$	0.585786	0.0210421
$776$	−20.4853	−0.735379
$777$	−6.24264	−0.223953
$778$	33.5147	1.20156
$779$	−42.3848	−1.51859
$780$	0	0
$781$	3.07107	0.109891
$782$	−9.89949	−0.354005
$783$	1.24264	0.0444084
$784$	−4.00000	−0.142857
$785$	−9.58579	−0.342131
$786$	2.48528	0.0886471
$787$	53.9411	1.92279	0.961397	−	0.275166i	$-0.0887328\pi$
$787$	53.9411	1.92279	0.961397	+	0.275166i	$0.0887328\pi$
$788$	0	0
$789$	14.1421	0.503473
$790$	−11.6569	−0.414732
$791$	−8.31371	−0.295601
$792$	2.82843	0.100504
$793$	6.24264	0.221683
$794$	−28.9706	−1.02813
$795$	8.65685	0.307027
$796$	0	0
$797$	−1.79899	−0.0637235	−0.0318617	−	0.999492i	$-0.510144\pi$
$797$	−1.79899	−0.0637235	−0.0318617	+	0.999492i	$0.510144\pi$
$798$	5.41421	0.191661
$799$	−3.21320	−0.113675
$800$	0	0
$801$	−0.0710678	−0.00251106
$802$	−37.3137	−1.31759
$803$	−8.48528	−0.299439
$804$	0	0
$805$	−3.82843	−0.134934
$806$	−0.485281	−0.0170933
$807$	6.55635	0.230794
$808$	0.970563	0.0341443
$809$	4.14214	0.145630	0.0728149	−	0.997345i	$-0.476802\pi$
$809$	4.14214	0.145630	0.0728149	+	0.997345i	$0.476802\pi$
$810$	1.41421	0.0496904
$811$	−21.9411	−0.770457	−0.385229	−	0.922821i	$-0.625877\pi$
$811$	−21.9411	−0.770457	−0.385229	+	0.922821i	$0.625877\pi$
$812$	0	0
$813$	7.82843	0.274555
$814$	8.82843	0.309436
$815$	14.7279	0.515897
$816$	−7.31371	−0.256031
$817$	24.5563	0.859118
$818$	−51.5980	−1.80408
$819$	−0.585786	−0.0204690
$820$	0	0
$821$	−4.07107	−0.142081	−0.0710406	−	0.997473i	$-0.522632\pi$
$821$	−4.07107	−0.142081	−0.0710406	+	0.997473i	$0.522632\pi$
$822$	3.31371	0.115579
$823$	−39.2132	−1.36689	−0.683443	−	0.730004i	$-0.739518\pi$
$823$	−39.2132	−1.36689	−0.683443	+	0.730004i	$0.739518\pi$
$824$	38.8284	1.35265
$825$	−1.00000	−0.0348155
$826$	20.3848	0.709277
$827$	10.1421	0.352677	0.176338	−	0.984330i	$-0.443575\pi$
$827$	10.1421	0.352677	0.176338	+	0.984330i	$0.443575\pi$
$828$	0	0
$829$	2.48528	0.0863174	0.0431587	−	0.999068i	$-0.486258\pi$
$829$	2.48528	0.0863174	0.0431587	+	0.999068i	$0.486258\pi$
$830$	24.2426	0.841474
$831$	−18.8284	−0.653151
$832$	4.68629	0.162468
$833$	−1.82843	−0.0633512
$834$	19.7990	0.685583
$835$	−0.343146	−0.0118750
$836$	0	0
$837$	−0.585786	−0.0202477
$838$	8.58579	0.296591
$839$	−31.5858	−1.09046	−0.545231	−	0.838286i	$-0.683558\pi$
$839$	−31.5858	−1.09046	−0.545231	+	0.838286i	$0.683558\pi$
$840$	−2.82843	−0.0975900
$841$	−27.4558	−0.946753
$842$	−15.0711	−0.519383
$843$	−21.1716	−0.729188
$844$	0	0
$845$	12.6569	0.435409
$846$	−2.48528	−0.0854457
$847$	−1.00000	−0.0343604
$848$	−34.6274	−1.18911
$849$	−15.2132	−0.522116
$850$	2.58579	0.0886917
$851$	23.8995	0.819264
$852$	0	0
$853$	12.9289	0.442678	0.221339	−	0.975197i	$-0.428957\pi$
$853$	12.9289	0.442678	0.221339	+	0.975197i	$0.428957\pi$
$854$	15.0711	0.515721
$855$	3.82843	0.130929
$856$	−20.9706	−0.716759
$857$	−20.6274	−0.704619	−0.352310	−	0.935884i	$-0.614604\pi$
$857$	−20.6274	−0.704619	−0.352310	+	0.935884i	$0.614604\pi$
$858$	0.828427	0.0282820
$859$	39.0122	1.33108	0.665539	−	0.746363i	$-0.268202\pi$
$859$	39.0122	1.33108	0.665539	+	0.746363i	$0.268202\pi$
$860$	0	0
$861$	11.0711	0.377301
$862$	−46.9117	−1.59782
$863$	−15.6863	−0.533968	−0.266984	−	0.963701i	$-0.586027\pi$
$863$	−15.6863	−0.533968	−0.266984	+	0.963701i	$0.586027\pi$
$864$	0	0
$865$	−19.3137	−0.656686
$866$	−34.1421	−1.16020
$867$	13.6569	0.463811
$868$	0	0
$869$	−8.24264	−0.279612
$870$	1.75736	0.0595801
$871$	−3.51472	−0.119092
$872$	48.2843	1.63511
$873$	−7.24264	−0.245126
$874$	−20.7279	−0.701132
$875$	1.00000	0.0338062
$876$	0	0
$877$	23.5858	0.796435	0.398218	−	0.917291i	$-0.369629\pi$
$877$	23.5858	0.796435	0.398218	+	0.917291i	$0.369629\pi$
$878$	−4.24264	−0.143182
$879$	−9.14214	−0.308357
$880$	4.00000	0.134840
$881$	−9.92893	−0.334514	−0.167257	−	0.985913i	$-0.553491\pi$
$881$	−9.92893	−0.334514	−0.167257	+	0.985913i	$0.553491\pi$
$882$	−1.41421	−0.0476190
$883$	−23.5147	−0.791333	−0.395667	−	0.918394i	$-0.629486\pi$
$883$	−23.5147	−0.791333	−0.395667	+	0.918394i	$0.629486\pi$
$884$	0	0
$885$	14.4142	0.484528
$886$	−28.7696	−0.966532
$887$	−0.656854	−0.0220550	−0.0110275	−	0.999939i	$-0.503510\pi$
$887$	−0.656854	−0.0220550	−0.0110275	+	0.999939i	$0.503510\pi$
$888$	17.6569	0.592525
$889$	−13.7279	−0.460420
$890$	−0.100505	−0.00336894
$891$	1.00000	0.0335013
$892$	0	0
$893$	−6.72792	−0.225141
$894$	6.82843	0.228377
$895$	−7.75736	−0.259300
$896$	11.3137	0.377964
$897$	2.24264	0.0748796
$898$	35.9411	1.19937
$899$	−0.727922	−0.0242776
$900$	0	0
$901$	−15.8284	−0.527321
$902$	−15.6569	−0.521316
$903$	−6.41421	−0.213452
$904$	23.5147	0.782088
$905$	−18.9706	−0.630603
$906$	−6.14214	−0.204059
$907$	−15.6985	−0.521260	−0.260630	−	0.965439i	$-0.583930\pi$
$907$	−15.6985	−0.521260	−0.260630	+	0.965439i	$0.583930\pi$
$908$	0	0
$909$	0.343146	0.0113814
$910$	−0.828427	−0.0274621
$911$	−34.1421	−1.13118	−0.565590	−	0.824687i	$-0.691351\pi$
$911$	−34.1421	−1.13118	−0.565590	+	0.824687i	$0.691351\pi$
$912$	−15.3137	−0.507088
$913$	17.1421	0.567322
$914$	−28.8701	−0.954937
$915$	10.6569	0.352305
$916$	0	0
$917$	−1.75736	−0.0580331
$918$	−2.58579	−0.0853437
$919$	−21.3137	−0.703074	−0.351537	−	0.936174i	$-0.614341\pi$
$919$	−21.3137	−0.703074	−0.351537	+	0.936174i	$0.614341\pi$
$920$	10.8284	0.357003
$921$	13.5147	0.445325
$922$	11.5147	0.379217
$923$	1.79899	0.0592145
$924$	0	0
$925$	−6.24264	−0.205257
$926$	19.1127	0.628082
$927$	13.7279	0.450884
$928$	0	0
$929$	−19.7990	−0.649584	−0.324792	−	0.945786i	$-0.605294\pi$
$929$	−19.7990	−0.649584	−0.324792	+	0.945786i	$0.605294\pi$
$930$	−0.828427	−0.0271652
$931$	−3.82843	−0.125472
$932$	0	0
$933$	31.1127	1.01858
$934$	19.0294	0.622662
$935$	1.82843	0.0597960
$936$	1.65685	0.0541560
$937$	−48.5269	−1.58531	−0.792653	−	0.609674i	$-0.791301\pi$
$937$	−48.5269	−1.58531	−0.792653	+	0.609674i	$0.791301\pi$
$938$	−8.48528	−0.277054
$939$	6.75736	0.220518
$940$	0	0
$941$	37.3553	1.21775	0.608875	−	0.793266i	$-0.291621\pi$
$941$	37.3553	1.21775	0.608875	+	0.793266i	$0.291621\pi$
$942$	13.5563	0.441690
$943$	−42.3848	−1.38024
$944$	−57.6569	−1.87657
$945$	−1.00000	−0.0325300
$946$	9.07107	0.294926
$947$	50.3137	1.63498	0.817488	−	0.575946i	$-0.195366\pi$
$947$	50.3137	1.63498	0.817488	+	0.575946i	$0.195366\pi$
$948$	0	0
$949$	−4.97056	−0.161351
$950$	5.41421	0.175660
$951$	22.1421	0.718008
$952$	5.17157	0.167612
$953$	−36.3431	−1.17727	−0.588635	−	0.808399i	$-0.700334\pi$
$953$	−36.3431	−1.17727	−0.588635	+	0.808399i	$0.700334\pi$
$954$	−12.2426	−0.396370
$955$	−5.65685	−0.183052
$956$	0	0
$957$	1.24264	0.0401689
$958$	36.1421	1.16770
$959$	−2.34315	−0.0756641
$960$	8.00000	0.258199
$961$	−30.6569	−0.988931
$962$	5.17157	0.166738
$963$	−7.41421	−0.238920
$964$	0	0
$965$	−14.4853	−0.466298
$966$	5.41421	0.174199
$967$	44.2132	1.42180	0.710900	−	0.703293i	$-0.248288\pi$
$967$	44.2132	1.42180	0.710900	+	0.703293i	$0.248288\pi$
$968$	2.82843	0.0909091
$969$	−7.00000	−0.224872
$970$	−10.2426	−0.328871
$971$	42.5563	1.36570	0.682849	−	0.730559i	$-0.260741\pi$
$971$	42.5563	1.36570	0.682849	+	0.730559i	$0.260741\pi$
$972$	0	0
$973$	−14.0000	−0.448819
$974$	15.7990	0.506232
$975$	−0.585786	−0.0187602
$976$	−42.6274	−1.36447
$977$	−39.6274	−1.26779	−0.633897	−	0.773418i	$-0.718546\pi$
$977$	−39.6274	−1.26779	−0.633897	+	0.773418i	$0.718546\pi$
$978$	−20.8284	−0.666020
$979$	−0.0710678	−0.00227134
$980$	0	0
$981$	17.0711	0.545037
$982$	48.8701	1.55951
$983$	−35.1716	−1.12180	−0.560899	−	0.827884i	$-0.689545\pi$
$983$	−35.1716	−1.12180	−0.560899	+	0.827884i	$0.689545\pi$
$984$	−31.3137	−0.998245
$985$	14.8284	0.472473
$986$	−3.21320	−0.102329
$987$	1.75736	0.0559374
$988$	0	0
$989$	24.5563	0.780846
$990$	1.41421	0.0449467
$991$	−12.0294	−0.382128	−0.191064	−	0.981578i	$-0.561194\pi$
$991$	−12.0294	−0.382128	−0.191064	+	0.981578i	$0.561194\pi$
$992$	0	0
$993$	13.1421	0.417053
$994$	4.34315	0.137756
$995$	19.3137	0.612286
$996$	0	0
$997$	27.9411	0.884904	0.442452	−	0.896792i	$-0.354109\pi$
$997$	27.9411	0.884904	0.442452	+	0.896792i	$0.354109\pi$
$998$	45.2132	1.43120
$999$	6.24264	0.197508

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1155.2.a.p.1.1	✓	2
3.2	odd	2		3465.2.a.w.1.2		2
5.4	even	2		5775.2.a.bi.1.2		2
7.6	odd	2		8085.2.a.bf.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1155.2.a.p.1.1	✓	2	1.1	even	1	trivial
3465.2.a.w.1.2		2	3.2	odd	2
5775.2.a.bi.1.2		2	5.4	even	2
8085.2.a.bf.1.1		2	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:	\( N \)	\(=\)	\( 1155 = 3 \cdot 5 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1155.a (trivial)

\(f(q)\)	\(=\)	\(q-1.41421 q^{2} -1.00000 q^{3} -1.00000 q^{5} +1.41421 q^{6} -1.00000 q^{7} +2.82843 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.41421 q^{2} -1.00000 q^{3} -1.00000 q^{5} +1.41421 q^{6} -1.00000 q^{7} +2.82843 q^{8} +1.00000 q^{9} +1.41421 q^{10} +1.00000 q^{11} +0.585786 q^{13} +1.41421 q^{14} +1.00000 q^{15} -4.00000 q^{16} -1.82843 q^{17} -1.41421 q^{18} -3.82843 q^{19} +1.00000 q^{21} -1.41421 q^{22} -3.82843 q^{23} -2.82843 q^{24} +1.00000 q^{25} -0.828427 q^{26} -1.00000 q^{27} -1.24264 q^{29} -1.41421 q^{30} +0.585786 q^{31} -1.00000 q^{33} +2.58579 q^{34} +1.00000 q^{35} -6.24264 q^{37} +5.41421 q^{38} -0.585786 q^{39} -2.82843 q^{40} +11.0711 q^{41} -1.41421 q^{42} -6.41421 q^{43} -1.00000 q^{45} +5.41421 q^{46} +1.75736 q^{47} +4.00000 q^{48} +1.00000 q^{49} -1.41421 q^{50} +1.82843 q^{51} +8.65685 q^{53} +1.41421 q^{54} -1.00000 q^{55} -2.82843 q^{56} +3.82843 q^{57} +1.75736 q^{58} +14.4142 q^{59} +10.6569 q^{61} -0.828427 q^{62} -1.00000 q^{63} +8.00000 q^{64} -0.585786 q^{65} +1.41421 q^{66} -6.00000 q^{67} +3.82843 q^{69} -1.41421 q^{70} +3.07107 q^{71} +2.82843 q^{72} -8.48528 q^{73} +8.82843 q^{74} -1.00000 q^{75} -1.00000 q^{77} +0.828427 q^{78} -8.24264 q^{79} +4.00000 q^{80} +1.00000 q^{81} -15.6569 q^{82} +17.1421 q^{83} +1.82843 q^{85} +9.07107 q^{86} +1.24264 q^{87} +2.82843 q^{88} -0.0710678 q^{89} +1.41421 q^{90} -0.585786 q^{91} -0.585786 q^{93} -2.48528 q^{94} +3.82843 q^{95} -7.24264 q^{97} -1.41421 q^{98} +1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 2 q^{3} - 2 q^{5} - 2 q^{7} + 2 q^{9}+O(q^{10}) \) 2 * q - 2 * q^3 - 2 * q^5 - 2 * q^7 + 2 * q^9	\( 2 q - 2 q^{3} - 2 q^{5} - 2 q^{7} + 2 q^{9} + 2 q^{11} + 4 q^{13} + 2 q^{15} - 8 q^{16} + 2 q^{17} - 2 q^{19} + 2 q^{21} - 2 q^{23} + 2 q^{25} + 4 q^{26} - 2 q^{27} + 6 q^{29} + 4 q^{31} - 2 q^{33} + 8 q^{34} + 2 q^{35} - 4 q^{37} + 8 q^{38} - 4 q^{39} + 8 q^{41} - 10 q^{43} - 2 q^{45} + 8 q^{46} + 12 q^{47} + 8 q^{48} + 2 q^{49} - 2 q^{51} + 6 q^{53} - 2 q^{55} + 2 q^{57} + 12 q^{58} + 26 q^{59} + 10 q^{61} + 4 q^{62} - 2 q^{63} + 16 q^{64} - 4 q^{65} - 12 q^{67} + 2 q^{69} - 8 q^{71} + 12 q^{74} - 2 q^{75} - 2 q^{77} - 4 q^{78} - 8 q^{79} + 8 q^{80} + 2 q^{81} - 20 q^{82} + 6 q^{83} - 2 q^{85} + 4 q^{86} - 6 q^{87} + 14 q^{89} - 4 q^{91} - 4 q^{93} + 12 q^{94} + 2 q^{95} - 6 q^{97} + 2 q^{99}+O(q^{100}) \) 2 * q - 2 * q^3 - 2 * q^5 - 2 * q^7 + 2 * q^9 + 2 * q^11 + 4 * q^13 + 2 * q^15 - 8 * q^16 + 2 * q^17 - 2 * q^19 + 2 * q^21 - 2 * q^23 + 2 * q^25 + 4 * q^26 - 2 * q^27 + 6 * q^29 + 4 * q^31 - 2 * q^33 + 8 * q^34 + 2 * q^35 - 4 * q^37 + 8 * q^38 - 4 * q^39 + 8 * q^41 - 10 * q^43 - 2 * q^45 + 8 * q^46 + 12 * q^47 + 8 * q^48 + 2 * q^49 - 2 * q^51 + 6 * q^53 - 2 * q^55 + 2 * q^57 + 12 * q^58 + 26 * q^59 + 10 * q^61 + 4 * q^62 - 2 * q^63 + 16 * q^64 - 4 * q^65 - 12 * q^67 + 2 * q^69 - 8 * q^71 + 12 * q^74 - 2 * q^75 - 2 * q^77 - 4 * q^78 - 8 * q^79 + 8 * q^80 + 2 * q^81 - 20 * q^82 + 6 * q^83 - 2 * q^85 + 4 * q^86 - 6 * q^87 + 14 * q^89 - 4 * q^91 - 4 * q^93 + 12 * q^94 + 2 * q^95 - 6 * q^97 + 2 * q^99

Introduction

L-functions

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