LMFDB - Embedded newform 717.2.a.a.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [717,2,Mod(1,717)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(717, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("717.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 717 = 3 \cdot 239 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	717.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:	$5.72527382493$
Analytic rank:	$1$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{10})^+$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 1 $ x^2 - x - 1
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			$-0.618034$ of defining polynomial
Character	$\chi$	$=$	717.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.618034 q^{2} -1.00000 q^{3} -1.61803 q^{4} -1.00000 q^{5} +0.618034 q^{6} +2.23607 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-0.618034 q^{2} -1.00000 q^{3} -1.61803 q^{4} -1.00000 q^{5} +0.618034 q^{6} +2.23607 q^{8} +1.00000 q^{9} +0.618034 q^{10} +4.23607 q^{11} +1.61803 q^{12} -0.763932 q^{13} +1.00000 q^{15} +1.85410 q^{16} -5.00000 q^{17} -0.618034 q^{18} +5.23607 q^{19} +1.61803 q^{20} -2.61803 q^{22} -6.47214 q^{23} -2.23607 q^{24} -4.00000 q^{25} +0.472136 q^{26} -1.00000 q^{27} +7.47214 q^{29} -0.618034 q^{30} -8.70820 q^{31} -5.61803 q^{32} -4.23607 q^{33} +3.09017 q^{34} -1.61803 q^{36} -6.00000 q^{37} -3.23607 q^{38} +0.763932 q^{39} -2.23607 q^{40} -1.70820 q^{41} -10.0000 q^{43} -6.85410 q^{44} -1.00000 q^{45} +4.00000 q^{46} +7.70820 q^{47} -1.85410 q^{48} -7.00000 q^{49} +2.47214 q^{50} +5.00000 q^{51} +1.23607 q^{52} +2.47214 q^{53} +0.618034 q^{54} -4.23607 q^{55} -5.23607 q^{57} -4.61803 q^{58} +3.23607 q^{59} -1.61803 q^{60} -3.94427 q^{61} +5.38197 q^{62} -0.236068 q^{64} +0.763932 q^{65} +2.61803 q^{66} -6.23607 q^{67} +8.09017 q^{68} +6.47214 q^{69} -4.94427 q^{71} +2.23607 q^{72} -2.94427 q^{73} +3.70820 q^{74} +4.00000 q^{75} -8.47214 q^{76} -0.472136 q^{78} +2.94427 q^{79} -1.85410 q^{80} +1.00000 q^{81} +1.05573 q^{82} -4.23607 q^{83} +5.00000 q^{85} +6.18034 q^{86} -7.47214 q^{87} +9.47214 q^{88} +12.9443 q^{89} +0.618034 q^{90} +10.4721 q^{92} +8.70820 q^{93} -4.76393 q^{94} -5.23607 q^{95} +5.61803 q^{96} -8.18034 q^{97} +4.32624 q^{98} +4.23607 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + q^{2} - 2 q^{3} - q^{4} - 2 q^{5} - q^{6} + 2 q^{9}+O(q^{10}) $ 2 * q + q^2 - 2 * q^3 - q^4 - 2 * q^5 - q^6 + 2 * q^9	$ 2 q + q^{2} - 2 q^{3} - q^{4} - 2 q^{5} - q^{6} + 2 q^{9} - q^{10} + 4 q^{11} + q^{12} - 6 q^{13} + 2 q^{15} - 3 q^{16} - 10 q^{17} + q^{18} + 6 q^{19} + q^{20} - 3 q^{22} - 4 q^{23} - 8 q^{25} - 8 q^{26} - 2 q^{27} + 6 q^{29} + q^{30} - 4 q^{31} - 9 q^{32} - 4 q^{33} - 5 q^{34} - q^{36} - 12 q^{37} - 2 q^{38} + 6 q^{39} + 10 q^{41} - 20 q^{43} - 7 q^{44} - 2 q^{45} + 8 q^{46} + 2 q^{47} + 3 q^{48} - 14 q^{49} - 4 q^{50} + 10 q^{51} - 2 q^{52} - 4 q^{53} - q^{54} - 4 q^{55} - 6 q^{57} - 7 q^{58} + 2 q^{59} - q^{60} + 10 q^{61} + 13 q^{62} + 4 q^{64} + 6 q^{65} + 3 q^{66} - 8 q^{67} + 5 q^{68} + 4 q^{69} + 8 q^{71} + 12 q^{73} - 6 q^{74} + 8 q^{75} - 8 q^{76} + 8 q^{78} - 12 q^{79} + 3 q^{80} + 2 q^{81} + 20 q^{82} - 4 q^{83} + 10 q^{85} - 10 q^{86} - 6 q^{87} + 10 q^{88} + 8 q^{89} - q^{90} + 12 q^{92} + 4 q^{93} - 14 q^{94} - 6 q^{95} + 9 q^{96} + 6 q^{97} - 7 q^{98} + 4 q^{99}+O(q^{100}) $ 2 * q + q^2 - 2 * q^3 - q^4 - 2 * q^5 - q^6 + 2 * q^9 - q^10 + 4 * q^11 + q^12 - 6 * q^13 + 2 * q^15 - 3 * q^16 - 10 * q^17 + q^18 + 6 * q^19 + q^20 - 3 * q^22 - 4 * q^23 - 8 * q^25 - 8 * q^26 - 2 * q^27 + 6 * q^29 + q^30 - 4 * q^31 - 9 * q^32 - 4 * q^33 - 5 * q^34 - q^36 - 12 * q^37 - 2 * q^38 + 6 * q^39 + 10 * q^41 - 20 * q^43 - 7 * q^44 - 2 * q^45 + 8 * q^46 + 2 * q^47 + 3 * q^48 - 14 * q^49 - 4 * q^50 + 10 * q^51 - 2 * q^52 - 4 * q^53 - q^54 - 4 * q^55 - 6 * q^57 - 7 * q^58 + 2 * q^59 - q^60 + 10 * q^61 + 13 * q^62 + 4 * q^64 + 6 * q^65 + 3 * q^66 - 8 * q^67 + 5 * q^68 + 4 * q^69 + 8 * q^71 + 12 * q^73 - 6 * q^74 + 8 * q^75 - 8 * q^76 + 8 * q^78 - 12 * q^79 + 3 * q^80 + 2 * q^81 + 20 * q^82 - 4 * q^83 + 10 * q^85 - 10 * q^86 - 6 * q^87 + 10 * q^88 + 8 * q^89 - q^90 + 12 * q^92 + 4 * q^93 - 14 * q^94 - 6 * q^95 + 9 * q^96 + 6 * q^97 - 7 * q^98 + 4 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−0.618034	−0.437016	−0.218508	−	0.975835i	$-0.570119\pi$
$2$	−0.618034	−0.437016	−0.218508	+	0.975835i	$0.570119\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	−1.61803	−0.809017
$5$	−1.00000	−0.447214	−0.223607	−	0.974679i	$-0.571783\pi$
$5$	−1.00000	−0.447214	−0.223607	+	0.974679i	$0.571783\pi$
$6$	0.618034	0.252311
$7$	0	0		−	1.00000i	$-0.5\pi$
$7$	0	0			1.00000i	$0.5\pi$
$8$	2.23607	0.790569
$9$	1.00000	0.333333
$10$	0.618034	0.195440
$11$	4.23607	1.27722	0.638611	−	0.769529i	$-0.279509\pi$
$11$	4.23607	1.27722	0.638611	+	0.769529i	$0.279509\pi$
$12$	1.61803	0.467086
$13$	−0.763932	−0.211877	−0.105938	−	0.994373i	$-0.533785\pi$
$13$	−0.763932	−0.211877	−0.105938	+	0.994373i	$0.533785\pi$
$14$	0	0
$15$	1.00000	0.258199
$16$	1.85410	0.463525
$17$	−5.00000	−1.21268	−0.606339	−	0.795206i	$-0.707363\pi$
$17$	−5.00000	−1.21268	−0.606339	+	0.795206i	$0.707363\pi$
$18$	−0.618034	−0.145672
$19$	5.23607	1.20124	0.600618	−	0.799536i	$-0.294921\pi$
$19$	5.23607	1.20124	0.600618	+	0.799536i	$0.294921\pi$
$20$	1.61803	0.361803
$21$	0	0
$22$	−2.61803	−0.558167
$23$	−6.47214	−1.34953	−0.674767	−	0.738031i	$-0.735756\pi$
$23$	−6.47214	−1.34953	−0.674767	+	0.738031i	$0.735756\pi$
$24$	−2.23607	−0.456435
$25$	−4.00000	−0.800000
$26$	0.472136	0.0925935
$27$	−1.00000	−0.192450
$28$	0	0
$29$	7.47214	1.38754	0.693770	−	0.720196i	$-0.255948\pi$
$29$	7.47214	1.38754	0.693770	+	0.720196i	$0.255948\pi$
$30$	−0.618034	−0.112837
$31$	−8.70820	−1.56404	−0.782020	−	0.623254i	$-0.785810\pi$
$31$	−8.70820	−1.56404	−0.782020	+	0.623254i	$0.785810\pi$
$32$	−5.61803	−0.993137
$33$	−4.23607	−0.737405
$34$	3.09017	0.529960
$35$	0	0
$36$	−1.61803	−0.269672
$37$	−6.00000	−0.986394	−0.493197	−	0.869918i	$-0.664172\pi$
$37$	−6.00000	−0.986394	−0.493197	+	0.869918i	$0.664172\pi$
$38$	−3.23607	−0.524960
$39$	0.763932	0.122327
$40$	−2.23607	−0.353553
$41$	−1.70820	−0.266777	−0.133388	−	0.991064i	$-0.542586\pi$
$41$	−1.70820	−0.266777	−0.133388	+	0.991064i	$0.542586\pi$
$42$	0	0
$43$	−10.0000	−1.52499	−0.762493	−	0.646997i	$-0.776025\pi$
$43$	−10.0000	−1.52499	−0.762493	+	0.646997i	$0.776025\pi$
$44$	−6.85410	−1.03329
$45$	−1.00000	−0.149071
$46$	4.00000	0.589768
$47$	7.70820	1.12436	0.562179	−	0.827016i	$-0.309963\pi$
$47$	7.70820	1.12436	0.562179	+	0.827016i	$0.309963\pi$
$48$	−1.85410	−0.267617
$49$	−7.00000	−1.00000
$50$	2.47214	0.349613
$51$	5.00000	0.700140
$52$	1.23607	0.171412
$53$	2.47214	0.339574	0.169787	−	0.985481i	$-0.445692\pi$
$53$	2.47214	0.339574	0.169787	+	0.985481i	$0.445692\pi$
$54$	0.618034	0.0841038
$55$	−4.23607	−0.571191
$56$	0	0
$57$	−5.23607	−0.693534
$58$	−4.61803	−0.606378
$59$	3.23607	0.421300	0.210650	−	0.977562i	$-0.432442\pi$
$59$	3.23607	0.421300	0.210650	+	0.977562i	$0.432442\pi$
$60$	−1.61803	−0.208887
$61$	−3.94427	−0.505012	−0.252506	−	0.967595i	$-0.581255\pi$
$61$	−3.94427	−0.505012	−0.252506	+	0.967595i	$0.581255\pi$
$62$	5.38197	0.683510
$63$	0	0
$64$	−0.236068	−0.0295085
$65$	0.763932	0.0947541
$66$	2.61803	0.322258
$67$	−6.23607	−0.761857	−0.380928	−	0.924605i	$-0.624396\pi$
$67$	−6.23607	−0.761857	−0.380928	+	0.924605i	$0.624396\pi$
$68$	8.09017	0.981077
$69$	6.47214	0.779154
$70$	0	0
$71$	−4.94427	−0.586777	−0.293389	−	0.955993i	$-0.594783\pi$
$71$	−4.94427	−0.586777	−0.293389	+	0.955993i	$0.594783\pi$
$72$	2.23607	0.263523
$73$	−2.94427	−0.344601	−0.172300	−	0.985044i	$-0.555120\pi$
$73$	−2.94427	−0.344601	−0.172300	+	0.985044i	$0.555120\pi$
$74$	3.70820	0.431070
$75$	4.00000	0.461880
$76$	−8.47214	−0.971821
$77$	0	0
$78$	−0.472136	−0.0534589
$79$	2.94427	0.331256	0.165628	−	0.986188i	$-0.447035\pi$
$79$	2.94427	0.331256	0.165628	+	0.986188i	$0.447035\pi$
$80$	−1.85410	−0.207295
$81$	1.00000	0.111111
$82$	1.05573	0.116586
$83$	−4.23607	−0.464969	−0.232484	−	0.972600i	$-0.574685\pi$
$83$	−4.23607	−0.464969	−0.232484	+	0.972600i	$0.574685\pi$
$84$	0	0
$85$	5.00000	0.542326
$86$	6.18034	0.666443
$87$	−7.47214	−0.801097
$88$	9.47214	1.00973
$89$	12.9443	1.37209	0.686045	−	0.727559i	$-0.259345\pi$
$89$	12.9443	1.37209	0.686045	+	0.727559i	$0.259345\pi$
$90$	0.618034	0.0651465
$91$	0	0
$92$	10.4721	1.09180
$93$	8.70820	0.902999
$94$	−4.76393	−0.491362
$95$	−5.23607	−0.537209
$96$	5.61803	0.573388
$97$	−8.18034	−0.830588	−0.415294	−	0.909687i	$-0.636321\pi$
$97$	−8.18034	−0.830588	−0.415294	+	0.909687i	$0.636321\pi$
$98$	4.32624	0.437016
$99$	4.23607	0.425741
$100$	6.47214	0.647214
$101$	−13.4164	−1.33498	−0.667491	−	0.744618i	$-0.732632\pi$
$101$	−13.4164	−1.33498	−0.667491	+	0.744618i	$0.732632\pi$
$102$	−3.09017	−0.305972
$103$	5.23607	0.515925	0.257963	−	0.966155i	$-0.416949\pi$
$103$	5.23607	0.515925	0.257963	+	0.966155i	$0.416949\pi$
$104$	−1.70820	−0.167503
$105$	0	0
$106$	−1.52786	−0.148399
$107$	−6.47214	−0.625685	−0.312842	−	0.949805i	$-0.601281\pi$
$107$	−6.47214	−0.625685	−0.312842	+	0.949805i	$0.601281\pi$
$108$	1.61803	0.155695
$109$	−2.00000	−0.191565	−0.0957826	−	0.995402i	$-0.530535\pi$
$109$	−2.00000	−0.191565	−0.0957826	+	0.995402i	$0.530535\pi$
$110$	2.61803	0.249620
$111$	6.00000	0.569495
$112$	0	0
$113$	−14.9443	−1.40584	−0.702919	−	0.711269i	$-0.748121\pi$
$113$	−14.9443	−1.40584	−0.702919	+	0.711269i	$0.748121\pi$
$114$	3.23607	0.303086
$115$	6.47214	0.603530
$116$	−12.0902	−1.12254
$117$	−0.763932	−0.0706255
$118$	−2.00000	−0.184115
$119$	0	0
$120$	2.23607	0.204124
$121$	6.94427	0.631297
$122$	2.43769	0.220698
$123$	1.70820	0.154024
$124$	14.0902	1.26533
$125$	9.00000	0.804984
$126$	0	0
$127$	−13.7639	−1.22135	−0.610676	−	0.791881i	$-0.709102\pi$
$127$	−13.7639	−1.22135	−0.610676	+	0.791881i	$0.709102\pi$
$128$	11.3820	1.00603
$129$	10.0000	0.880451
$130$	−0.472136	−0.0414091
$131$	−11.5279	−1.00719	−0.503597	−	0.863939i	$-0.667990\pi$
$131$	−11.5279	−1.00719	−0.503597	+	0.863939i	$0.667990\pi$
$132$	6.85410	0.596573
$133$	0	0
$134$	3.85410	0.332944
$135$	1.00000	0.0860663
$136$	−11.1803	−0.958706
$137$	18.4721	1.57818	0.789091	−	0.614277i	$-0.210552\pi$
$137$	18.4721	1.57818	0.789091	+	0.614277i	$0.210552\pi$
$138$	−4.00000	−0.340503
$139$	8.94427	0.758643	0.379322	−	0.925265i	$-0.376157\pi$
$139$	8.94427	0.758643	0.379322	+	0.925265i	$0.376157\pi$
$140$	0	0
$141$	−7.70820	−0.649148
$142$	3.05573	0.256431
$143$	−3.23607	−0.270614
$144$	1.85410	0.154508
$145$	−7.47214	−0.620527
$146$	1.81966	0.150596
$147$	7.00000	0.577350
$148$	9.70820	0.798009
$149$	6.00000	0.491539	0.245770	−	0.969328i	$-0.420959\pi$
$149$	6.00000	0.491539	0.245770	+	0.969328i	$0.420959\pi$
$150$	−2.47214	−0.201849
$151$	−16.1803	−1.31674	−0.658369	−	0.752696i	$-0.728753\pi$
$151$	−16.1803	−1.31674	−0.658369	+	0.752696i	$0.728753\pi$
$152$	11.7082	0.949661
$153$	−5.00000	−0.404226
$154$	0	0
$155$	8.70820	0.699460
$156$	−1.23607	−0.0989646
$157$	23.3607	1.86439	0.932193	−	0.361963i	$-0.117893\pi$
$157$	23.3607	1.86439	0.932193	+	0.361963i	$0.117893\pi$
$158$	−1.81966	−0.144764
$159$	−2.47214	−0.196053
$160$	5.61803	0.444145
$161$	0	0
$162$	−0.618034	−0.0485573
$163$	−20.2361	−1.58501	−0.792506	−	0.609865i	$-0.791224\pi$
$163$	−20.2361	−1.58501	−0.792506	+	0.609865i	$0.791224\pi$
$164$	2.76393	0.215827
$165$	4.23607	0.329777
$166$	2.61803	0.203199
$167$	15.4164	1.19296	0.596479	−	0.802629i	$-0.296566\pi$
$167$	15.4164	1.19296	0.596479	+	0.802629i	$0.296566\pi$
$168$	0	0
$169$	−12.4164	−0.955108
$170$	−3.09017	−0.237005
$171$	5.23607	0.400412
$172$	16.1803	1.23374
$173$	6.47214	0.492067	0.246034	−	0.969261i	$-0.420873\pi$
$173$	6.47214	0.492067	0.246034	+	0.969261i	$0.420873\pi$
$174$	4.61803	0.350092
$175$	0	0
$176$	7.85410	0.592025
$177$	−3.23607	−0.243238
$178$	−8.00000	−0.599625
$179$	−19.1246	−1.42944	−0.714720	−	0.699410i	$-0.753446\pi$
$179$	−19.1246	−1.42944	−0.714720	+	0.699410i	$0.753446\pi$
$180$	1.61803	0.120601
$181$	3.23607	0.240535	0.120268	−	0.992742i	$-0.461625\pi$
$181$	3.23607	0.240535	0.120268	+	0.992742i	$0.461625\pi$
$182$	0	0
$183$	3.94427	0.291569
$184$	−14.4721	−1.06690
$185$	6.00000	0.441129
$186$	−5.38197	−0.394625
$187$	−21.1803	−1.54886
$188$	−12.4721	−0.909624
$189$	0	0
$190$	3.23607	0.234769
$191$	−15.2361	−1.10244	−0.551222	−	0.834359i	$-0.685838\pi$
$191$	−15.2361	−1.10244	−0.551222	+	0.834359i	$0.685838\pi$
$192$	0.236068	0.0170367
$193$	−14.5279	−1.04574	−0.522869	−	0.852413i	$-0.675138\pi$
$193$	−14.5279	−1.04574	−0.522869	+	0.852413i	$0.675138\pi$
$194$	5.05573	0.362980
$195$	−0.763932	−0.0547063
$196$	11.3262	0.809017
$197$	25.9443	1.84845	0.924226	−	0.381845i	$-0.124711\pi$
$197$	25.9443	1.84845	0.924226	+	0.381845i	$0.124711\pi$
$198$	−2.61803	−0.186056
$199$	2.00000	0.141776	0.0708881	−	0.997484i	$-0.477417\pi$
$199$	2.00000	0.141776	0.0708881	+	0.997484i	$0.477417\pi$
$200$	−8.94427	−0.632456
$201$	6.23607	0.439858
$202$	8.29180	0.583409
$203$	0	0
$204$	−8.09017	−0.566425
$205$	1.70820	0.119306
$206$	−3.23607	−0.225468
$207$	−6.47214	−0.449845
$208$	−1.41641	−0.0982102
$209$	22.1803	1.53425
$210$	0	0
$211$	−20.2361	−1.39311	−0.696554	−	0.717504i	$-0.745284\pi$
$211$	−20.2361	−1.39311	−0.696554	+	0.717504i	$0.745284\pi$
$212$	−4.00000	−0.274721
$213$	4.94427	0.338776
$214$	4.00000	0.273434
$215$	10.0000	0.681994
$216$	−2.23607	−0.152145
$217$	0	0
$218$	1.23607	0.0837171
$219$	2.94427	0.198955
$220$	6.85410	0.462103
$221$	3.81966	0.256938
$222$	−3.70820	−0.248878
$223$	29.1246	1.95033	0.975164	−	0.221483i	$-0.0710899\pi$
$223$	29.1246	1.95033	0.975164	+	0.221483i	$0.0710899\pi$
$224$	0	0
$225$	−4.00000	−0.266667
$226$	9.23607	0.614374
$227$	−25.7082	−1.70631	−0.853157	−	0.521655i	$-0.825315\pi$
$227$	−25.7082	−1.70631	−0.853157	+	0.521655i	$0.825315\pi$
$228$	8.47214	0.561081
$229$	29.5967	1.95581	0.977904	−	0.209054i	$-0.0670385\pi$
$229$	29.5967	1.95581	0.977904	+	0.209054i	$0.0670385\pi$
$230$	−4.00000	−0.263752
$231$	0	0
$232$	16.7082	1.09695
$233$	14.4721	0.948101	0.474051	−	0.880498i	$-0.342791\pi$
$233$	14.4721	0.948101	0.474051	+	0.880498i	$0.342791\pi$
$234$	0.472136	0.0308645
$235$	−7.70820	−0.502828
$236$	−5.23607	−0.340839
$237$	−2.94427	−0.191251
$238$	0	0
$239$	−1.00000	−0.0646846
$239$	−1.00000	−0.0646846
$240$	1.85410	0.119682
$241$	18.3607	1.18272	0.591358	−	0.806409i	$-0.298592\pi$
$241$	18.3607	1.18272	0.591358	+	0.806409i	$0.298592\pi$
$242$	−4.29180	−0.275887
$243$	−1.00000	−0.0641500
$244$	6.38197	0.408564
$245$	7.00000	0.447214
$246$	−1.05573	−0.0673108
$247$	−4.00000	−0.254514
$248$	−19.4721	−1.23648
$249$	4.23607	0.268450
$250$	−5.56231	−0.351791
$251$	−3.29180	−0.207776	−0.103888	−	0.994589i	$-0.533128\pi$
$251$	−3.29180	−0.207776	−0.103888	+	0.994589i	$0.533128\pi$
$252$	0	0
$253$	−27.4164	−1.72365
$254$	8.50658	0.533750
$255$	−5.00000	−0.313112
$256$	−6.56231	−0.410144
$257$	−11.9443	−0.745063	−0.372532	−	0.928020i	$-0.621510\pi$
$257$	−11.9443	−0.745063	−0.372532	+	0.928020i	$0.621510\pi$
$258$	−6.18034	−0.384771
$259$	0	0
$260$	−1.23607	−0.0766577
$261$	7.47214	0.462514
$262$	7.12461	0.440160
$263$	7.18034	0.442759	0.221379	−	0.975188i	$-0.428944\pi$
$263$	7.18034	0.442759	0.221379	+	0.975188i	$0.428944\pi$
$264$	−9.47214	−0.582970
$265$	−2.47214	−0.151862
$266$	0	0
$267$	−12.9443	−0.792177
$268$	10.0902	0.616355
$269$	−17.4721	−1.06529	−0.532647	−	0.846337i	$-0.678803\pi$
$269$	−17.4721	−1.06529	−0.532647	+	0.846337i	$0.678803\pi$
$270$	−0.618034	−0.0376124
$271$	−4.70820	−0.286003	−0.143002	−	0.989722i	$-0.545675\pi$
$271$	−4.70820	−0.286003	−0.143002	+	0.989722i	$0.545675\pi$
$272$	−9.27051	−0.562107
$273$	0	0
$274$	−11.4164	−0.689690
$275$	−16.9443	−1.02178
$276$	−10.4721	−0.630349
$277$	1.23607	0.0742681	0.0371341	−	0.999310i	$-0.488177\pi$
$277$	1.23607	0.0742681	0.0371341	+	0.999310i	$0.488177\pi$
$278$	−5.52786	−0.331539
$279$	−8.70820	−0.521347
$280$	0	0
$281$	10.0000	0.596550	0.298275	−	0.954480i	$-0.403589\pi$
$281$	10.0000	0.596550	0.298275	+	0.954480i	$0.403589\pi$
$282$	4.76393	0.283688
$283$	14.2361	0.846246	0.423123	−	0.906072i	$-0.360934\pi$
$283$	14.2361	0.846246	0.423123	+	0.906072i	$0.360934\pi$
$284$	8.00000	0.474713
$285$	5.23607	0.310158
$286$	2.00000	0.118262
$287$	0	0
$288$	−5.61803	−0.331046
$289$	8.00000	0.470588
$290$	4.61803	0.271180
$291$	8.18034	0.479540
$292$	4.76393	0.278788
$293$	−10.9443	−0.639371	−0.319686	−	0.947524i	$-0.603577\pi$
$293$	−10.9443	−0.639371	−0.319686	+	0.947524i	$0.603577\pi$
$294$	−4.32624	−0.252311
$295$	−3.23607	−0.188411
$296$	−13.4164	−0.779813
$297$	−4.23607	−0.245802
$298$	−3.70820	−0.214810
$299$	4.94427	0.285935
$300$	−6.47214	−0.373669
$301$	0	0
$302$	10.0000	0.575435
$303$	13.4164	0.770752
$304$	9.70820	0.556804
$305$	3.94427	0.225848
$306$	3.09017	0.176653
$307$	2.34752	0.133980	0.0669901	−	0.997754i	$-0.478660\pi$
$307$	2.34752	0.133980	0.0669901	+	0.997754i	$0.478660\pi$
$308$	0	0
$309$	−5.23607	−0.297870
$310$	−5.38197	−0.305675
$311$	−10.1246	−0.574114	−0.287057	−	0.957913i	$-0.592677\pi$
$311$	−10.1246	−0.574114	−0.287057	+	0.957913i	$0.592677\pi$
$312$	1.70820	0.0967080
$313$	−19.2361	−1.08729	−0.543643	−	0.839316i	$-0.682956\pi$
$313$	−19.2361	−1.08729	−0.543643	+	0.839316i	$0.682956\pi$
$314$	−14.4377	−0.814766
$315$	0	0
$316$	−4.76393	−0.267992
$317$	4.76393	0.267569	0.133785	−	0.991010i	$-0.457287\pi$
$317$	4.76393	0.267569	0.133785	+	0.991010i	$0.457287\pi$
$318$	1.52786	0.0856784
$319$	31.6525	1.77220
$320$	0.236068	0.0131966
$321$	6.47214	0.361239
$322$	0	0
$323$	−26.1803	−1.45671
$324$	−1.61803	−0.0898908
$325$	3.05573	0.169501
$326$	12.5066	0.692675
$327$	2.00000	0.110600
$328$	−3.81966	−0.210905
$329$	0	0
$330$	−2.61803	−0.144118
$331$	31.5967	1.73671	0.868357	−	0.495939i	$-0.165176\pi$
$331$	31.5967	1.73671	0.868357	+	0.495939i	$0.165176\pi$
$332$	6.85410	0.376168
$333$	−6.00000	−0.328798
$334$	−9.52786	−0.521342
$335$	6.23607	0.340713
$336$	0	0
$337$	−10.5279	−0.573489	−0.286745	−	0.958007i	$-0.592573\pi$
$337$	−10.5279	−0.573489	−0.286745	+	0.958007i	$0.592573\pi$
$338$	7.67376	0.417398
$339$	14.9443	0.811661
$340$	−8.09017	−0.438751
$341$	−36.8885	−1.99763
$342$	−3.23607	−0.174987
$343$	0	0
$344$	−22.3607	−1.20561
$345$	−6.47214	−0.348448
$346$	−4.00000	−0.215041
$347$	−31.6525	−1.69919	−0.849597	−	0.527432i	$-0.823155\pi$
$347$	−31.6525	−1.69919	−0.849597	+	0.527432i	$0.823155\pi$
$348$	12.0902	0.648101
$349$	−31.8328	−1.70397	−0.851986	−	0.523565i	$-0.824602\pi$
$349$	−31.8328	−1.70397	−0.851986	+	0.523565i	$0.824602\pi$
$350$	0	0
$351$	0.763932	0.0407757
$352$	−23.7984	−1.26846
$353$	16.2918	0.867125	0.433562	−	0.901124i	$-0.357256\pi$
$353$	16.2918	0.867125	0.433562	+	0.901124i	$0.357256\pi$
$354$	2.00000	0.106299
$355$	4.94427	0.262415
$356$	−20.9443	−1.11004
$357$	0	0
$358$	11.8197	0.624688
$359$	9.52786	0.502861	0.251431	−	0.967875i	$-0.419099\pi$
$359$	9.52786	0.502861	0.251431	+	0.967875i	$0.419099\pi$
$360$	−2.23607	−0.117851
$361$	8.41641	0.442969
$362$	−2.00000	−0.105118
$363$	−6.94427	−0.364480
$364$	0	0
$365$	2.94427	0.154110
$366$	−2.43769	−0.127420
$367$	−2.70820	−0.141367	−0.0706835	−	0.997499i	$-0.522518\pi$
$367$	−2.70820	−0.141367	−0.0706835	+	0.997499i	$0.522518\pi$
$368$	−12.0000	−0.625543
$369$	−1.70820	−0.0889255
$370$	−3.70820	−0.192780
$371$	0	0
$372$	−14.0902	−0.730541
$373$	−31.8885	−1.65113	−0.825563	−	0.564310i	$-0.809142\pi$
$373$	−31.8885	−1.65113	−0.825563	+	0.564310i	$0.809142\pi$
$374$	13.0902	0.676877
$375$	−9.00000	−0.464758
$376$	17.2361	0.888882
$377$	−5.70820	−0.293987
$378$	0	0
$379$	−18.1803	−0.933861	−0.466931	−	0.884294i	$-0.654640\pi$
$379$	−18.1803	−0.933861	−0.466931	+	0.884294i	$0.654640\pi$
$380$	8.47214	0.434611
$381$	13.7639	0.705148
$382$	9.41641	0.481785
$383$	−15.4164	−0.787742	−0.393871	−	0.919166i	$-0.628864\pi$
$383$	−15.4164	−0.787742	−0.393871	+	0.919166i	$0.628864\pi$
$384$	−11.3820	−0.580834
$385$	0	0
$386$	8.97871	0.457004
$387$	−10.0000	−0.508329
$388$	13.2361	0.671960
$389$	−26.5279	−1.34502	−0.672508	−	0.740090i	$-0.734783\pi$
$389$	−26.5279	−1.34502	−0.672508	+	0.740090i	$0.734783\pi$
$390$	0.472136	0.0239075
$391$	32.3607	1.63655
$392$	−15.6525	−0.790569
$393$	11.5279	0.581504
$394$	−16.0344	−0.807804
$395$	−2.94427	−0.148142
$396$	−6.85410	−0.344432
$397$	20.0000	1.00377	0.501886	−	0.864934i	$-0.332640\pi$
$397$	20.0000	1.00377	0.501886	+	0.864934i	$0.332640\pi$
$398$	−1.23607	−0.0619585
$399$	0	0
$400$	−7.41641	−0.370820
$401$	31.8328	1.58965	0.794827	−	0.606835i	$-0.207561\pi$
$401$	31.8328	1.58965	0.794827	+	0.606835i	$0.207561\pi$
$402$	−3.85410	−0.192225
$403$	6.65248	0.331383
$404$	21.7082	1.08002
$405$	−1.00000	−0.0496904
$406$	0	0
$407$	−25.4164	−1.25984
$408$	11.1803	0.553509
$409$	−3.00000	−0.148340	−0.0741702	−	0.997246i	$-0.523631\pi$
$409$	−3.00000	−0.148340	−0.0741702	+	0.997246i	$0.523631\pi$
$410$	−1.05573	−0.0521387
$411$	−18.4721	−0.911163
$412$	−8.47214	−0.417392
$413$	0	0
$414$	4.00000	0.196589
$415$	4.23607	0.207940
$416$	4.29180	0.210423
$417$	−8.94427	−0.438003
$418$	−13.7082	−0.670490
$419$	10.1246	0.494620	0.247310	−	0.968936i	$-0.420453\pi$
$419$	10.1246	0.494620	0.247310	+	0.968936i	$0.420453\pi$
$420$	0	0
$421$	30.9443	1.50813	0.754066	−	0.656799i	$-0.228090\pi$
$421$	30.9443	1.50813	0.754066	+	0.656799i	$0.228090\pi$
$422$	12.5066	0.608811
$423$	7.70820	0.374786
$424$	5.52786	0.268457
$425$	20.0000	0.970143
$426$	−3.05573	−0.148051
$427$	0	0
$428$	10.4721	0.506190
$429$	3.23607	0.156239
$430$	−6.18034	−0.298042
$431$	−9.18034	−0.442201	−0.221101	−	0.975251i	$-0.570965\pi$
$431$	−9.18034	−0.442201	−0.221101	+	0.975251i	$0.570965\pi$
$432$	−1.85410	−0.0892055
$433$	−3.23607	−0.155516	−0.0777578	−	0.996972i	$-0.524776\pi$
$433$	−3.23607	−0.155516	−0.0777578	+	0.996972i	$0.524776\pi$
$434$	0	0
$435$	7.47214	0.358261
$436$	3.23607	0.154980
$437$	−33.8885	−1.62111
$438$	−1.81966	−0.0869467
$439$	7.41641	0.353966	0.176983	−	0.984214i	$-0.443366\pi$
$439$	7.41641	0.353966	0.176983	+	0.984214i	$0.443366\pi$
$440$	−9.47214	−0.451566
$441$	−7.00000	−0.333333
$442$	−2.36068	−0.112286
$443$	−6.70820	−0.318716	−0.159358	−	0.987221i	$-0.550942\pi$
$443$	−6.70820	−0.318716	−0.159358	+	0.987221i	$0.550942\pi$
$444$	−9.70820	−0.460731
$445$	−12.9443	−0.613617
$446$	−18.0000	−0.852325
$447$	−6.00000	−0.283790
$448$	0	0
$449$	17.1246	0.808160	0.404080	−	0.914724i	$-0.367592\pi$
$449$	17.1246	0.808160	0.404080	+	0.914724i	$0.367592\pi$
$450$	2.47214	0.116538
$451$	−7.23607	−0.340733
$452$	24.1803	1.13735
$453$	16.1803	0.760219
$454$	15.8885	0.745686
$455$	0	0
$456$	−11.7082	−0.548287
$457$	20.4721	0.957646	0.478823	−	0.877911i	$-0.341064\pi$
$457$	20.4721	0.957646	0.478823	+	0.877911i	$0.341064\pi$
$458$	−18.2918	−0.854719
$459$	5.00000	0.233380
$460$	−10.4721	−0.488266
$461$	13.5279	0.630055	0.315028	−	0.949082i	$-0.397986\pi$
$461$	13.5279	0.630055	0.315028	+	0.949082i	$0.397986\pi$
$462$	0	0
$463$	−13.1246	−0.609952	−0.304976	−	0.952360i	$-0.598649\pi$
$463$	−13.1246	−0.609952	−0.304976	+	0.952360i	$0.598649\pi$
$464$	13.8541	0.643161
$465$	−8.70820	−0.403833
$466$	−8.94427	−0.414335
$467$	−11.3475	−0.525101	−0.262550	−	0.964918i	$-0.584564\pi$
$467$	−11.3475	−0.525101	−0.262550	+	0.964918i	$0.584564\pi$
$468$	1.23607	0.0571373
$469$	0	0
$470$	4.76393	0.219744
$471$	−23.3607	−1.07640
$472$	7.23607	0.333067
$473$	−42.3607	−1.94775
$474$	1.81966	0.0835798
$475$	−20.9443	−0.960989
$476$	0	0
$477$	2.47214	0.113191
$478$	0.618034	0.0282682
$479$	34.1246	1.55919	0.779597	−	0.626282i	$-0.215424\pi$
$479$	34.1246	1.55919	0.779597	+	0.626282i	$0.215424\pi$
$480$	−5.61803	−0.256427
$481$	4.58359	0.208994
$482$	−11.3475	−0.516866
$483$	0	0
$484$	−11.2361	−0.510730
$485$	8.18034	0.371450
$486$	0.618034	0.0280346
$487$	27.1803	1.23166	0.615829	−	0.787880i	$-0.288821\pi$
$487$	27.1803	1.23166	0.615829	+	0.787880i	$0.288821\pi$
$488$	−8.81966	−0.399247
$489$	20.2361	0.915107
$490$	−4.32624	−0.195440
$491$	2.00000	0.0902587	0.0451294	−	0.998981i	$-0.485630\pi$
$491$	2.00000	0.0902587	0.0451294	+	0.998981i	$0.485630\pi$
$492$	−2.76393	−0.124608
$493$	−37.3607	−1.68264
$494$	2.47214	0.111227
$495$	−4.23607	−0.190397
$496$	−16.1459	−0.724972
$497$	0	0
$498$	−2.61803	−0.117317
$499$	16.9443	0.758530	0.379265	−	0.925288i	$-0.376177\pi$
$499$	16.9443	0.758530	0.379265	+	0.925288i	$0.376177\pi$
$500$	−14.5623	−0.651246
$501$	−15.4164	−0.688754
$502$	2.03444	0.0908016
$503$	−12.2361	−0.545579	−0.272790	−	0.962074i	$-0.587946\pi$
$503$	−12.2361	−0.545579	−0.272790	+	0.962074i	$0.587946\pi$
$504$	0	0
$505$	13.4164	0.597022
$506$	16.9443	0.753265
$507$	12.4164	0.551432
$508$	22.2705	0.988094
$509$	30.3050	1.34324	0.671622	−	0.740894i	$-0.265598\pi$
$509$	30.3050	1.34324	0.671622	+	0.740894i	$0.265598\pi$
$510$	3.09017	0.136835
$511$	0	0
$512$	−18.7082	−0.826794
$513$	−5.23607	−0.231178
$514$	7.38197	0.325605
$515$	−5.23607	−0.230729
$516$	−16.1803	−0.712300
$517$	32.6525	1.43605
$518$	0	0
$519$	−6.47214	−0.284095
$520$	1.70820	0.0749097
$521$	−26.3607	−1.15488	−0.577441	−	0.816432i	$-0.695949\pi$
$521$	−26.3607	−1.15488	−0.577441	+	0.816432i	$0.695949\pi$
$522$	−4.61803	−0.202126
$523$	−4.23607	−0.185230	−0.0926152	−	0.995702i	$-0.529523\pi$
$523$	−4.23607	−0.185230	−0.0926152	+	0.995702i	$0.529523\pi$
$524$	18.6525	0.814837
$525$	0	0
$526$	−4.43769	−0.193493
$527$	43.5410	1.89668
$528$	−7.85410	−0.341806
$529$	18.8885	0.821241
$530$	1.52786	0.0663662
$531$	3.23607	0.140433
$532$	0	0
$533$	1.30495	0.0565237
$534$	8.00000	0.346194
$535$	6.47214	0.279815
$536$	−13.9443	−0.602301
$537$	19.1246	0.825288
$538$	10.7984	0.465551
$539$	−29.6525	−1.27722
$540$	−1.61803	−0.0696291
$541$	4.47214	0.192272	0.0961361	−	0.995368i	$-0.469352\pi$
$541$	4.47214	0.192272	0.0961361	+	0.995368i	$0.469352\pi$
$542$	2.90983	0.124988
$543$	−3.23607	−0.138873
$544$	28.0902	1.20436
$545$	2.00000	0.0856706
$546$	0	0
$547$	−32.0689	−1.37117	−0.685583	−	0.727994i	$-0.740453\pi$
$547$	−32.0689	−1.37117	−0.685583	+	0.727994i	$0.740453\pi$
$548$	−29.8885	−1.27678
$549$	−3.94427	−0.168337
$550$	10.4721	0.446533
$551$	39.1246	1.66676
$552$	14.4721	0.615975
$553$	0	0
$554$	−0.763932	−0.0324564
$555$	−6.00000	−0.254686
$556$	−14.4721	−0.613755
$557$	−2.76393	−0.117112	−0.0585558	−	0.998284i	$-0.518650\pi$
$557$	−2.76393	−0.117112	−0.0585558	+	0.998284i	$0.518650\pi$
$558$	5.38197	0.227837
$559$	7.63932	0.323109
$560$	0	0
$561$	21.1803	0.894235
$562$	−6.18034	−0.260702
$563$	14.8328	0.625129	0.312564	−	0.949897i	$-0.398812\pi$
$563$	14.8328	0.625129	0.312564	+	0.949897i	$0.398812\pi$
$564$	12.4721	0.525172
$565$	14.9443	0.628710
$566$	−8.79837	−0.369823
$567$	0	0
$568$	−11.0557	−0.463888
$569$	37.9443	1.59071	0.795353	−	0.606146i	$-0.207285\pi$
$569$	37.9443	1.59071	0.795353	+	0.606146i	$0.207285\pi$
$570$	−3.23607	−0.135544
$571$	1.88854	0.0790331	0.0395165	−	0.999219i	$-0.487418\pi$
$571$	1.88854	0.0790331	0.0395165	+	0.999219i	$0.487418\pi$
$572$	5.23607	0.218931
$573$	15.2361	0.636496
$574$	0	0
$575$	25.8885	1.07963
$576$	−0.236068	−0.00983617
$577$	4.11146	0.171162	0.0855811	−	0.996331i	$-0.472725\pi$
$577$	4.11146	0.171162	0.0855811	+	0.996331i	$0.472725\pi$
$578$	−4.94427	−0.205655
$579$	14.5279	0.603757
$580$	12.0902	0.502017
$581$	0	0
$582$	−5.05573	−0.209567
$583$	10.4721	0.433712
$584$	−6.58359	−0.272431
$585$	0.763932	0.0315847
$586$	6.76393	0.279415
$587$	−6.23607	−0.257390	−0.128695	−	0.991684i	$-0.541079\pi$
$587$	−6.23607	−0.257390	−0.128695	+	0.991684i	$0.541079\pi$
$588$	−11.3262	−0.467086
$589$	−45.5967	−1.87878
$590$	2.00000	0.0823387
$591$	−25.9443	−1.06720
$592$	−11.1246	−0.457219
$593$	30.1803	1.23936	0.619679	−	0.784855i	$-0.287263\pi$
$593$	30.1803	1.23936	0.619679	+	0.784855i	$0.287263\pi$
$594$	2.61803	0.107419
$595$	0	0
$596$	−9.70820	−0.397664
$597$	−2.00000	−0.0818546
$598$	−3.05573	−0.124958
$599$	25.8885	1.05778	0.528889	−	0.848691i	$-0.322609\pi$
$599$	25.8885	1.05778	0.528889	+	0.848691i	$0.322609\pi$
$600$	8.94427	0.365148
$601$	41.7771	1.70412	0.852061	−	0.523442i	$-0.175352\pi$
$601$	41.7771	1.70412	0.852061	+	0.523442i	$0.175352\pi$
$602$	0	0
$603$	−6.23607	−0.253952
$604$	26.1803	1.06526
$605$	−6.94427	−0.282325
$606$	−8.29180	−0.336831
$607$	23.5279	0.954967	0.477483	−	0.878641i	$-0.341549\pi$
$607$	23.5279	0.954967	0.477483	+	0.878641i	$0.341549\pi$
$608$	−29.4164	−1.19299
$609$	0	0
$610$	−2.43769	−0.0986993
$611$	−5.88854	−0.238225
$612$	8.09017	0.327026
$613$	−2.00000	−0.0807792	−0.0403896	−	0.999184i	$-0.512860\pi$
$613$	−2.00000	−0.0807792	−0.0403896	+	0.999184i	$0.512860\pi$
$614$	−1.45085	−0.0585515
$615$	−1.70820	−0.0688814
$616$	0	0
$617$	29.7082	1.19601	0.598004	−	0.801493i	$-0.295961\pi$
$617$	29.7082	1.19601	0.598004	+	0.801493i	$0.295961\pi$
$618$	3.23607	0.130174
$619$	−49.3050	−1.98173	−0.990867	−	0.134845i	$-0.956946\pi$
$619$	−49.3050	−1.98173	−0.990867	+	0.134845i	$0.956946\pi$
$620$	−14.0902	−0.565875
$621$	6.47214	0.259718
$622$	6.25735	0.250897
$623$	0	0
$624$	1.41641	0.0567017
$625$	11.0000	0.440000
$626$	11.8885	0.475162
$627$	−22.1803	−0.885797
$628$	−37.7984	−1.50832
$629$	30.0000	1.19618
$630$	0	0
$631$	−20.1246	−0.801148	−0.400574	−	0.916264i	$-0.631189\pi$
$631$	−20.1246	−0.801148	−0.400574	+	0.916264i	$0.631189\pi$
$632$	6.58359	0.261881
$633$	20.2361	0.804311
$634$	−2.94427	−0.116932
$635$	13.7639	0.546205
$636$	4.00000	0.158610
$637$	5.34752	0.211877
$638$	−19.5623	−0.774479
$639$	−4.94427	−0.195592
$640$	−11.3820	−0.449912
$641$	11.1115	0.438876	0.219438	−	0.975626i	$-0.429578\pi$
$641$	11.1115	0.438876	0.219438	+	0.975626i	$0.429578\pi$
$642$	−4.00000	−0.157867
$643$	33.1803	1.30850	0.654252	−	0.756276i	$-0.272983\pi$
$643$	33.1803	1.30850	0.654252	+	0.756276i	$0.272983\pi$
$644$	0	0
$645$	−10.0000	−0.393750
$646$	16.1803	0.636607
$647$	−14.8197	−0.582621	−0.291310	−	0.956629i	$-0.594091\pi$
$647$	−14.8197	−0.582621	−0.291310	+	0.956629i	$0.594091\pi$
$648$	2.23607	0.0878410
$649$	13.7082	0.538094
$650$	−1.88854	−0.0740748
$651$	0	0
$652$	32.7426	1.28230
$653$	32.1803	1.25931	0.629657	−	0.776873i	$-0.283195\pi$
$653$	32.1803	1.25931	0.629657	+	0.776873i	$0.283195\pi$
$654$	−1.23607	−0.0483341
$655$	11.5279	0.450431
$656$	−3.16718	−0.123658
$657$	−2.94427	−0.114867
$658$	0	0
$659$	11.7082	0.456087	0.228043	−	0.973651i	$-0.426767\pi$
$659$	11.7082	0.456087	0.228043	+	0.973651i	$0.426767\pi$
$660$	−6.85410	−0.266796
$661$	−18.5279	−0.720650	−0.360325	−	0.932827i	$-0.617334\pi$
$661$	−18.5279	−0.720650	−0.360325	+	0.932827i	$0.617334\pi$
$662$	−19.5279	−0.758972
$663$	−3.81966	−0.148343
$664$	−9.47214	−0.367590
$665$	0	0
$666$	3.70820	0.143690
$667$	−48.3607	−1.87253
$668$	−24.9443	−0.965123
$669$	−29.1246	−1.12602
$670$	−3.85410	−0.148897
$671$	−16.7082	−0.645013
$672$	0	0
$673$	−46.5410	−1.79402	−0.897012	−	0.442006i	$-0.854267\pi$
$673$	−46.5410	−1.79402	−0.897012	+	0.442006i	$0.854267\pi$
$674$	6.50658	0.250624
$675$	4.00000	0.153960
$676$	20.0902	0.772699
$677$	−3.70820	−0.142518	−0.0712589	−	0.997458i	$-0.522702\pi$
$677$	−3.70820	−0.142518	−0.0712589	+	0.997458i	$0.522702\pi$
$678$	−9.23607	−0.354709
$679$	0	0
$680$	11.1803	0.428746
$681$	25.7082	0.985141
$682$	22.7984	0.872995
$683$	18.0689	0.691387	0.345693	−	0.938348i	$-0.387644\pi$
$683$	18.0689	0.691387	0.345693	+	0.938348i	$0.387644\pi$
$684$	−8.47214	−0.323940
$685$	−18.4721	−0.705784
$686$	0	0
$687$	−29.5967	−1.12919
$688$	−18.5410	−0.706870
$689$	−1.88854	−0.0719478
$690$	4.00000	0.152277
$691$	−21.7639	−0.827939	−0.413969	−	0.910291i	$-0.635858\pi$
$691$	−21.7639	−0.827939	−0.413969	+	0.910291i	$0.635858\pi$
$692$	−10.4721	−0.398091
$693$	0	0
$694$	19.5623	0.742575
$695$	−8.94427	−0.339276
$696$	−16.7082	−0.633323
$697$	8.54102	0.323514
$698$	19.6738	0.744663
$699$	−14.4721	−0.547386
$700$	0	0
$701$	0	0		−	1.00000i	$-0.5\pi$
$701$	0	0			1.00000i	$0.5\pi$
$702$	−0.472136	−0.0178196
$703$	−31.4164	−1.18489
$704$	−1.00000	−0.0376889
$705$	7.70820	0.290308
$706$	−10.0689	−0.378947
$707$	0	0
$708$	5.23607	0.196783
$709$	36.6525	1.37651	0.688256	−	0.725468i	$-0.258376\pi$
$709$	36.6525	1.37651	0.688256	+	0.725468i	$0.258376\pi$
$710$	−3.05573	−0.114679
$711$	2.94427	0.110419
$712$	28.9443	1.08473
$713$	56.3607	2.11072
$714$	0	0
$715$	3.23607	0.121022
$716$	30.9443	1.15644
$717$	1.00000	0.0373457
$718$	−5.88854	−0.219759
$719$	33.2918	1.24157	0.620787	−	0.783979i	$-0.286813\pi$
$719$	33.2918	1.24157	0.620787	+	0.783979i	$0.286813\pi$
$720$	−1.85410	−0.0690983
$721$	0	0
$722$	−5.20163	−0.193584
$723$	−18.3607	−0.682841
$724$	−5.23607	−0.194597
$725$	−29.8885	−1.11003
$726$	4.29180	0.159283
$727$	−1.88854	−0.0700422	−0.0350211	−	0.999387i	$-0.511150\pi$
$727$	−1.88854	−0.0700422	−0.0350211	+	0.999387i	$0.511150\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	−1.81966	−0.0673486
$731$	50.0000	1.84932
$732$	−6.38197	−0.235884
$733$	27.9443	1.03215	0.516073	−	0.856545i	$-0.327393\pi$
$733$	27.9443	1.03215	0.516073	+	0.856545i	$0.327393\pi$
$734$	1.67376	0.0617797
$735$	−7.00000	−0.258199
$736$	36.3607	1.34027
$737$	−26.4164	−0.973061
$738$	1.05573	0.0388619
$739$	42.8328	1.57563	0.787815	−	0.615912i	$-0.211212\pi$
$739$	42.8328	1.57563	0.787815	+	0.615912i	$0.211212\pi$
$740$	−9.70820	−0.356881
$741$	4.00000	0.146944
$742$	0	0
$743$	−12.2918	−0.450942	−0.225471	−	0.974250i	$-0.572392\pi$
$743$	−12.2918	−0.450942	−0.225471	+	0.974250i	$0.572392\pi$
$744$	19.4721	0.713883
$745$	−6.00000	−0.219823
$746$	19.7082	0.721569
$747$	−4.23607	−0.154990
$748$	34.2705	1.25305
$749$	0	0
$750$	5.56231	0.203107
$751$	30.4721	1.11194	0.555972	−	0.831201i	$-0.312346\pi$
$751$	30.4721	1.11194	0.555972	+	0.831201i	$0.312346\pi$
$752$	14.2918	0.521168
$753$	3.29180	0.119960
$754$	3.52786	0.128477
$755$	16.1803	0.588863
$756$	0	0
$757$	42.5279	1.54570	0.772851	−	0.634588i	$-0.218830\pi$
$757$	42.5279	1.54570	0.772851	+	0.634588i	$0.218830\pi$
$758$	11.2361	0.408112
$759$	27.4164	0.995153
$760$	−11.7082	−0.424701
$761$	−45.7771	−1.65942	−0.829709	−	0.558196i	$-0.811494\pi$
$761$	−45.7771	−1.65942	−0.829709	+	0.558196i	$0.811494\pi$
$762$	−8.50658	−0.308161
$763$	0	0
$764$	24.6525	0.891895
$765$	5.00000	0.180775
$766$	9.52786	0.344256
$767$	−2.47214	−0.0892637
$768$	6.56231	0.236797
$769$	10.8754	0.392177	0.196088	−	0.980586i	$-0.437176\pi$
$769$	10.8754	0.392177	0.196088	+	0.980586i	$0.437176\pi$
$770$	0	0
$771$	11.9443	0.430162
$772$	23.5066	0.846020
$773$	−5.59675	−0.201301	−0.100651	−	0.994922i	$-0.532092\pi$
$773$	−5.59675	−0.201301	−0.100651	+	0.994922i	$0.532092\pi$
$774$	6.18034	0.222148
$775$	34.8328	1.25123
$776$	−18.2918	−0.656637
$777$	0	0
$778$	16.3951	0.587794
$779$	−8.94427	−0.320462
$780$	1.23607	0.0442583
$781$	−20.9443	−0.749445
$782$	−20.0000	−0.715199
$783$	−7.47214	−0.267032
$784$	−12.9787	−0.463525
$785$	−23.3607	−0.833778
$786$	−7.12461	−0.254126
$787$	0	0		−	1.00000i	$-0.5\pi$
$787$	0	0			1.00000i	$0.5\pi$
$788$	−41.9787	−1.49543
$789$	−7.18034	−0.255627
$790$	1.81966	0.0647406
$791$	0	0
$792$	9.47214	0.336578
$793$	3.01316	0.107000
$794$	−12.3607	−0.438664
$795$	2.47214	0.0876776
$796$	−3.23607	−0.114699
$797$	−37.3607	−1.32338	−0.661692	−	0.749776i	$-0.730161\pi$
$797$	−37.3607	−1.32338	−0.661692	+	0.749776i	$0.730161\pi$
$798$	0	0
$799$	−38.5410	−1.36348
$800$	22.4721	0.794510
$801$	12.9443	0.457363
$802$	−19.6738	−0.694705
$803$	−12.4721	−0.440132
$804$	−10.0902	−0.355853
$805$	0	0
$806$	−4.11146	−0.144820
$807$	17.4721	0.615048
$808$	−30.0000	−1.05540
$809$	−24.6525	−0.866735	−0.433367	−	0.901217i	$-0.642675\pi$
$809$	−24.6525	−0.866735	−0.433367	+	0.901217i	$0.642675\pi$
$810$	0.618034	0.0217155
$811$	−6.00000	−0.210688	−0.105344	−	0.994436i	$-0.533594\pi$
$811$	−6.00000	−0.210688	−0.105344	+	0.994436i	$0.533594\pi$
$812$	0	0
$813$	4.70820	0.165124
$814$	15.7082	0.550572
$815$	20.2361	0.708839
$816$	9.27051	0.324533
$817$	−52.3607	−1.83187
$818$	1.85410	0.0648272
$819$	0	0
$820$	−2.76393	−0.0965207
$821$	−8.00000	−0.279202	−0.139601	−	0.990208i	$-0.544582\pi$
$821$	−8.00000	−0.279202	−0.139601	+	0.990208i	$0.544582\pi$
$822$	11.4164	0.398193
$823$	−50.3607	−1.75546	−0.877731	−	0.479153i	$-0.840944\pi$
$823$	−50.3607	−1.75546	−0.877731	+	0.479153i	$0.840944\pi$
$824$	11.7082	0.407875
$825$	16.9443	0.589924
$826$	0	0
$827$	−34.1246	−1.18663	−0.593315	−	0.804971i	$-0.702181\pi$
$827$	−34.1246	−1.18663	−0.593315	+	0.804971i	$0.702181\pi$
$828$	10.4721	0.363932
$829$	−35.7082	−1.24020	−0.620099	−	0.784524i	$-0.712907\pi$
$829$	−35.7082	−1.24020	−0.620099	+	0.784524i	$0.712907\pi$
$830$	−2.61803	−0.0908733
$831$	−1.23607	−0.0428787
$832$	0.180340	0.00625216
$833$	35.0000	1.21268
$834$	5.52786	0.191414
$835$	−15.4164	−0.533507
$836$	−35.8885	−1.24123
$837$	8.70820	0.301000
$838$	−6.25735	−0.216157
$839$	−22.5967	−0.780126	−0.390063	−	0.920788i	$-0.627547\pi$
$839$	−22.5967	−0.780126	−0.390063	+	0.920788i	$0.627547\pi$
$840$	0	0
$841$	26.8328	0.925270
$842$	−19.1246	−0.659078
$843$	−10.0000	−0.344418
$844$	32.7426	1.12705
$845$	12.4164	0.427137
$846$	−4.76393	−0.163787
$847$	0	0
$848$	4.58359	0.157401
$849$	−14.2361	−0.488581
$850$	−12.3607	−0.423968
$851$	38.8328	1.33117
$852$	−8.00000	−0.274075
$853$	12.4164	0.425130	0.212565	−	0.977147i	$-0.431818\pi$
$853$	12.4164	0.425130	0.212565	+	0.977147i	$0.431818\pi$
$854$	0	0
$855$	−5.23607	−0.179070
$856$	−14.4721	−0.494647
$857$	5.41641	0.185021	0.0925105	−	0.995712i	$-0.470511\pi$
$857$	5.41641	0.185021	0.0925105	+	0.995712i	$0.470511\pi$
$858$	−2.00000	−0.0682789
$859$	23.0689	0.787100	0.393550	−	0.919303i	$-0.371247\pi$
$859$	23.0689	0.787100	0.393550	+	0.919303i	$0.371247\pi$
$860$	−16.1803	−0.551745
$861$	0	0
$862$	5.67376	0.193249
$863$	33.4853	1.13985	0.569926	−	0.821696i	$-0.306972\pi$
$863$	33.4853	1.13985	0.569926	+	0.821696i	$0.306972\pi$
$864$	5.61803	0.191129
$865$	−6.47214	−0.220059
$866$	2.00000	0.0679628
$867$	−8.00000	−0.271694
$868$	0	0
$869$	12.4721	0.423088
$870$	−4.61803	−0.156566
$871$	4.76393	0.161420
$872$	−4.47214	−0.151446
$873$	−8.18034	−0.276863
$874$	20.9443	0.708451
$875$	0	0
$876$	−4.76393	−0.160958
$877$	16.5279	0.558106	0.279053	−	0.960276i	$-0.409979\pi$
$877$	16.5279	0.558106	0.279053	+	0.960276i	$0.409979\pi$
$878$	−4.58359	−0.154689
$879$	10.9443	0.369141
$880$	−7.85410	−0.264762
$881$	−26.2492	−0.884359	−0.442179	−	0.896927i	$-0.645795\pi$
$881$	−26.2492	−0.884359	−0.442179	+	0.896927i	$0.645795\pi$
$882$	4.32624	0.145672
$883$	38.0132	1.27924	0.639622	−	0.768689i	$-0.279091\pi$
$883$	38.0132	1.27924	0.639622	+	0.768689i	$0.279091\pi$
$884$	−6.18034	−0.207867
$885$	3.23607	0.108779
$886$	4.14590	0.139284
$887$	16.3607	0.549338	0.274669	−	0.961539i	$-0.411432\pi$
$887$	16.3607	0.549338	0.274669	+	0.961539i	$0.411432\pi$
$888$	13.4164	0.450225
$889$	0	0
$890$	8.00000	0.268161
$891$	4.23607	0.141914
$892$	−47.1246	−1.57785
$893$	40.3607	1.35062
$894$	3.70820	0.124021
$895$	19.1246	0.639265
$896$	0	0
$897$	−4.94427	−0.165084
$898$	−10.5836	−0.353179
$899$	−65.0689	−2.17017
$900$	6.47214	0.215738
$901$	−12.3607	−0.411794
$902$	4.47214	0.148906
$903$	0	0
$904$	−33.4164	−1.11141
$905$	−3.23607	−0.107571
$906$	−10.0000	−0.332228
$907$	32.0689	1.06483	0.532415	−	0.846484i	$-0.321285\pi$
$907$	32.0689	1.06483	0.532415	+	0.846484i	$0.321285\pi$
$908$	41.5967	1.38044
$909$	−13.4164	−0.444994
$910$	0	0
$911$	−18.1115	−0.600059	−0.300030	−	0.953930i	$-0.596997\pi$
$911$	−18.1115	−0.600059	−0.300030	+	0.953930i	$0.596997\pi$
$912$	−9.70820	−0.321471
$913$	−17.9443	−0.593869
$914$	−12.6525	−0.418507
$915$	−3.94427	−0.130394
$916$	−47.8885	−1.58228
$917$	0	0
$918$	−3.09017	−0.101991
$919$	−52.9574	−1.74690	−0.873452	−	0.486910i	$-0.838124\pi$
$919$	−52.9574	−1.74690	−0.873452	+	0.486910i	$0.838124\pi$
$920$	14.4721	0.477132
$921$	−2.34752	−0.0773536
$922$	−8.36068	−0.275344
$923$	3.77709	0.124324
$924$	0	0
$925$	24.0000	0.789115
$926$	8.11146	0.266559
$927$	5.23607	0.171975
$928$	−41.9787	−1.37802
$929$	−34.6525	−1.13691	−0.568455	−	0.822714i	$-0.692459\pi$
$929$	−34.6525	−1.13691	−0.568455	+	0.822714i	$0.692459\pi$
$930$	5.38197	0.176482
$931$	−36.6525	−1.20124
$932$	−23.4164	−0.767030
$933$	10.1246	0.331465
$934$	7.01316	0.229477
$935$	21.1803	0.692671
$936$	−1.70820	−0.0558344
$937$	0.0557281	0.00182056	0.000910279	−	1.00000i	$-0.499710\pi$
$937$	0.0557281	0.00182056	0.000910279		1.00000i	$0.499710\pi$
$938$	0	0
$939$	19.2361	0.627745
$940$	12.4721	0.406796
$941$	−7.81966	−0.254914	−0.127457	−	0.991844i	$-0.540681\pi$
$941$	−7.81966	−0.254914	−0.127457	+	0.991844i	$0.540681\pi$
$942$	14.4377	0.470405
$943$	11.0557	0.360024
$944$	6.00000	0.195283
$945$	0	0
$946$	26.1803	0.851196
$947$	−35.3050	−1.14726	−0.573628	−	0.819116i	$-0.694465\pi$
$947$	−35.3050	−1.14726	−0.573628	+	0.819116i	$0.694465\pi$
$948$	4.76393	0.154725
$949$	2.24922	0.0730129
$950$	12.9443	0.419968
$951$	−4.76393	−0.154481
$952$	0	0
$953$	−34.3607	−1.11305	−0.556526	−	0.830830i	$-0.687866\pi$
$953$	−34.3607	−1.11305	−0.556526	+	0.830830i	$0.687866\pi$
$954$	−1.52786	−0.0494664
$955$	15.2361	0.493028
$956$	1.61803	0.0523310
$957$	−31.6525	−1.02318
$958$	−21.0902	−0.681392
$959$	0	0
$960$	−0.236068	−0.00761906
$961$	44.8328	1.44622
$962$	−2.83282	−0.0913336
$963$	−6.47214	−0.208562
$964$	−29.7082	−0.956837
$965$	14.5279	0.467668
$966$	0	0
$967$	−44.9443	−1.44531	−0.722655	−	0.691209i	$-0.757079\pi$
$967$	−44.9443	−1.44531	−0.722655	+	0.691209i	$0.757079\pi$
$968$	15.5279	0.499084
$969$	26.1803	0.841034
$970$	−5.05573	−0.162330
$971$	−51.4296	−1.65045	−0.825227	−	0.564802i	$-0.808953\pi$
$971$	−51.4296	−1.65045	−0.825227	+	0.564802i	$0.808953\pi$
$972$	1.61803	0.0518985
$973$	0	0
$974$	−16.7984	−0.538255
$975$	−3.05573	−0.0978616
$976$	−7.31308	−0.234086
$977$	18.8328	0.602515	0.301258	−	0.953543i	$-0.402594\pi$
$977$	18.8328	0.602515	0.301258	+	0.953543i	$0.402594\pi$
$978$	−12.5066	−0.399916
$979$	54.8328	1.75246
$980$	−11.3262	−0.361803
$981$	−2.00000	−0.0638551
$982$	−1.23607	−0.0394445
$983$	−11.5410	−0.368101	−0.184051	−	0.982917i	$-0.558921\pi$
$983$	−11.5410	−0.368101	−0.184051	+	0.982917i	$0.558921\pi$
$984$	3.81966	0.121766
$985$	−25.9443	−0.826653
$986$	23.0902	0.735341
$987$	0	0
$988$	6.47214	0.205906
$989$	64.7214	2.05802
$990$	2.61803	0.0832066
$991$	33.1246	1.05224	0.526119	−	0.850411i	$-0.323647\pi$
$991$	33.1246	1.05224	0.526119	+	0.850411i	$0.323647\pi$
$992$	48.9230	1.55331
$993$	−31.5967	−1.00269
$994$	0	0
$995$	−2.00000	−0.0634043
$996$	−6.85410	−0.217181
$997$	−45.8885	−1.45330	−0.726652	−	0.687005i	$-0.758925\pi$
$997$	−45.8885	−1.45330	−0.726652	+	0.687005i	$0.758925\pi$
$998$	−10.4721	−0.331490
$999$	6.00000	0.189832

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	717.2.a.a.1.1	✓	2
3.2	odd	2		2151.2.a.c.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
717.2.a.a.1.1	✓	2	1.1	even	1	trivial
2151.2.a.c.1.2		2	3.2	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:	\( N \)	\(=\)	\( 717 = 3 \cdot 239 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	717.a (trivial)

\(f(q)\)	\(=\)	\(q-0.618034 q^{2} -1.00000 q^{3} -1.61803 q^{4} -1.00000 q^{5} +0.618034 q^{6} +2.23607 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-0.618034 q^{2} -1.00000 q^{3} -1.61803 q^{4} -1.00000 q^{5} +0.618034 q^{6} +2.23607 q^{8} +1.00000 q^{9} +0.618034 q^{10} +4.23607 q^{11} +1.61803 q^{12} -0.763932 q^{13} +1.00000 q^{15} +1.85410 q^{16} -5.00000 q^{17} -0.618034 q^{18} +5.23607 q^{19} +1.61803 q^{20} -2.61803 q^{22} -6.47214 q^{23} -2.23607 q^{24} -4.00000 q^{25} +0.472136 q^{26} -1.00000 q^{27} +7.47214 q^{29} -0.618034 q^{30} -8.70820 q^{31} -5.61803 q^{32} -4.23607 q^{33} +3.09017 q^{34} -1.61803 q^{36} -6.00000 q^{37} -3.23607 q^{38} +0.763932 q^{39} -2.23607 q^{40} -1.70820 q^{41} -10.0000 q^{43} -6.85410 q^{44} -1.00000 q^{45} +4.00000 q^{46} +7.70820 q^{47} -1.85410 q^{48} -7.00000 q^{49} +2.47214 q^{50} +5.00000 q^{51} +1.23607 q^{52} +2.47214 q^{53} +0.618034 q^{54} -4.23607 q^{55} -5.23607 q^{57} -4.61803 q^{58} +3.23607 q^{59} -1.61803 q^{60} -3.94427 q^{61} +5.38197 q^{62} -0.236068 q^{64} +0.763932 q^{65} +2.61803 q^{66} -6.23607 q^{67} +8.09017 q^{68} +6.47214 q^{69} -4.94427 q^{71} +2.23607 q^{72} -2.94427 q^{73} +3.70820 q^{74} +4.00000 q^{75} -8.47214 q^{76} -0.472136 q^{78} +2.94427 q^{79} -1.85410 q^{80} +1.00000 q^{81} +1.05573 q^{82} -4.23607 q^{83} +5.00000 q^{85} +6.18034 q^{86} -7.47214 q^{87} +9.47214 q^{88} +12.9443 q^{89} +0.618034 q^{90} +10.4721 q^{92} +8.70820 q^{93} -4.76393 q^{94} -5.23607 q^{95} +5.61803 q^{96} -8.18034 q^{97} +4.32624 q^{98} +4.23607 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + q^{2} - 2 q^{3} - q^{4} - 2 q^{5} - q^{6} + 2 q^{9}+O(q^{10}) \) 2 * q + q^2 - 2 * q^3 - q^4 - 2 * q^5 - q^6 + 2 * q^9	\( 2 q + q^{2} - 2 q^{3} - q^{4} - 2 q^{5} - q^{6} + 2 q^{9} - q^{10} + 4 q^{11} + q^{12} - 6 q^{13} + 2 q^{15} - 3 q^{16} - 10 q^{17} + q^{18} + 6 q^{19} + q^{20} - 3 q^{22} - 4 q^{23} - 8 q^{25} - 8 q^{26} - 2 q^{27} + 6 q^{29} + q^{30} - 4 q^{31} - 9 q^{32} - 4 q^{33} - 5 q^{34} - q^{36} - 12 q^{37} - 2 q^{38} + 6 q^{39} + 10 q^{41} - 20 q^{43} - 7 q^{44} - 2 q^{45} + 8 q^{46} + 2 q^{47} + 3 q^{48} - 14 q^{49} - 4 q^{50} + 10 q^{51} - 2 q^{52} - 4 q^{53} - q^{54} - 4 q^{55} - 6 q^{57} - 7 q^{58} + 2 q^{59} - q^{60} + 10 q^{61} + 13 q^{62} + 4 q^{64} + 6 q^{65} + 3 q^{66} - 8 q^{67} + 5 q^{68} + 4 q^{69} + 8 q^{71} + 12 q^{73} - 6 q^{74} + 8 q^{75} - 8 q^{76} + 8 q^{78} - 12 q^{79} + 3 q^{80} + 2 q^{81} + 20 q^{82} - 4 q^{83} + 10 q^{85} - 10 q^{86} - 6 q^{87} + 10 q^{88} + 8 q^{89} - q^{90} + 12 q^{92} + 4 q^{93} - 14 q^{94} - 6 q^{95} + 9 q^{96} + 6 q^{97} - 7 q^{98} + 4 q^{99}+O(q^{100}) \) 2 * q + q^2 - 2 * q^3 - q^4 - 2 * q^5 - q^6 + 2 * q^9 - q^10 + 4 * q^11 + q^12 - 6 * q^13 + 2 * q^15 - 3 * q^16 - 10 * q^17 + q^18 + 6 * q^19 + q^20 - 3 * q^22 - 4 * q^23 - 8 * q^25 - 8 * q^26 - 2 * q^27 + 6 * q^29 + q^30 - 4 * q^31 - 9 * q^32 - 4 * q^33 - 5 * q^34 - q^36 - 12 * q^37 - 2 * q^38 + 6 * q^39 + 10 * q^41 - 20 * q^43 - 7 * q^44 - 2 * q^45 + 8 * q^46 + 2 * q^47 + 3 * q^48 - 14 * q^49 - 4 * q^50 + 10 * q^51 - 2 * q^52 - 4 * q^53 - q^54 - 4 * q^55 - 6 * q^57 - 7 * q^58 + 2 * q^59 - q^60 + 10 * q^61 + 13 * q^62 + 4 * q^64 + 6 * q^65 + 3 * q^66 - 8 * q^67 + 5 * q^68 + 4 * q^69 + 8 * q^71 + 12 * q^73 - 6 * q^74 + 8 * q^75 - 8 * q^76 + 8 * q^78 - 12 * q^79 + 3 * q^80 + 2 * q^81 + 20 * q^82 - 4 * q^83 + 10 * q^85 - 10 * q^86 - 6 * q^87 + 10 * q^88 + 8 * q^89 - q^90 + 12 * q^92 + 4 * q^93 - 14 * q^94 - 6 * q^95 + 9 * q^96 + 6 * q^97 - 7 * q^98 + 4 * q^99

Introduction

L-functions

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