LMFDB - Embedded newform 4017.2.a.f.1.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4017,2,Mod(1,4017)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4017, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("4017.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4017 = 3 \cdot 13 \cdot 103 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4017.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:	$32.0759064919$
Analytic rank:	$1$
Dimension:	$19$
Coefficient field:	$\mathbb{Q}[x]/(x^{19} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{19} - 4 x^{18} - 16 x^{17} + 77 x^{16} + 88 x^{15} - 594 x^{14} - 154 x^{13} + 2388 x^{12} - 278 x^{11} + \cdots + 4 $ x^19 - 4x^18 - 16x^17 + 77x^16 + 88x^15 - 594x^14 - 154x^13 + 2388x^12 - 278x^11 - 5460x^10 + 1491x^9 + 7285x^8 - 2223x^7 - 5579x^6 + 1430x^5 + 2261x^4 - 352x^3 - 378x^2 + 11x + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.9
Root			$0.725598$ of defining polynomial
Character	$\chi$	$=$	4017.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.725598 q^{2} +1.00000 q^{3} -1.47351 q^{4} -3.68550 q^{5} -0.725598 q^{6} -0.281235 q^{7} +2.52037 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-0.725598 q^{2} +1.00000 q^{3} -1.47351 q^{4} -3.68550 q^{5} -0.725598 q^{6} -0.281235 q^{7} +2.52037 q^{8} +1.00000 q^{9} +2.67419 q^{10} -1.72170 q^{11} -1.47351 q^{12} +1.00000 q^{13} +0.204064 q^{14} -3.68550 q^{15} +1.11824 q^{16} +1.29609 q^{17} -0.725598 q^{18} -6.38831 q^{19} +5.43060 q^{20} -0.281235 q^{21} +1.24926 q^{22} +2.49695 q^{23} +2.52037 q^{24} +8.58288 q^{25} -0.725598 q^{26} +1.00000 q^{27} +0.414402 q^{28} +6.21816 q^{29} +2.67419 q^{30} -0.971398 q^{31} -5.85213 q^{32} -1.72170 q^{33} -0.940441 q^{34} +1.03649 q^{35} -1.47351 q^{36} +3.09327 q^{37} +4.63534 q^{38} +1.00000 q^{39} -9.28882 q^{40} +3.77376 q^{41} +0.204064 q^{42} +9.32426 q^{43} +2.53694 q^{44} -3.68550 q^{45} -1.81178 q^{46} +0.568426 q^{47} +1.11824 q^{48} -6.92091 q^{49} -6.22772 q^{50} +1.29609 q^{51} -1.47351 q^{52} +7.23182 q^{53} -0.725598 q^{54} +6.34532 q^{55} -0.708817 q^{56} -6.38831 q^{57} -4.51189 q^{58} +3.57852 q^{59} +5.43060 q^{60} +3.08194 q^{61} +0.704845 q^{62} -0.281235 q^{63} +2.00982 q^{64} -3.68550 q^{65} +1.24926 q^{66} -11.8815 q^{67} -1.90980 q^{68} +2.49695 q^{69} -0.752077 q^{70} -10.7513 q^{71} +2.52037 q^{72} -3.79188 q^{73} -2.24447 q^{74} +8.58288 q^{75} +9.41321 q^{76} +0.484203 q^{77} -0.725598 q^{78} -14.2833 q^{79} -4.12126 q^{80} +1.00000 q^{81} -2.73824 q^{82} -0.650334 q^{83} +0.414402 q^{84} -4.77674 q^{85} -6.76567 q^{86} +6.21816 q^{87} -4.33932 q^{88} +0.273541 q^{89} +2.67419 q^{90} -0.281235 q^{91} -3.67928 q^{92} -0.971398 q^{93} -0.412449 q^{94} +23.5441 q^{95} -5.85213 q^{96} +5.21056 q^{97} +5.02180 q^{98} -1.72170 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 19 q - 4 q^{2} + 19 q^{3} + 10 q^{4} - 3 q^{5} - 4 q^{6} - 23 q^{7} - 9 q^{8} + 19 q^{9}+O(q^{10}) $ 19 * q - 4 * q^2 + 19 * q^3 + 10 * q^4 - 3 * q^5 - 4 * q^6 - 23 * q^7 - 9 * q^8 + 19 * q^9	\( 19 q - 4 q^{2} + 19 q^{3} + 10 q^{4} - 3 q^{5} - 4 q^{6} - 23 q^{7} - 9 q^{8} + 19 q^{9} - 6 q^{10} - 15 q^{11} + 10 q^{12} + 19 q^{13} - 4 q^{14} - 3 q^{15} - 4 q^{16} - 4 q^{18} - 32 q^{19} - 8 q^{20} - 23 q^{21} - 9 q^{22} - 23 q^{23} - 9 q^{24} - 8 q^{25} - 4 q^{26} + 19 q^{27} - 22 q^{28} + 4 q^{29} - 6 q^{30} - 50 q^{31} - 2 q^{32} - 15 q^{33} - 35 q^{34} - 4 q^{35} + 10 q^{36} - 38 q^{37} + 20 q^{38} + 19 q^{39} - 30 q^{40} - 11 q^{41} - 4 q^{42} - 17 q^{43} - 29 q^{44} - 3 q^{45} - 5 q^{46} - 38 q^{47} - 4 q^{48} - 6 q^{49} - 9 q^{50} + 10 q^{52} - 12 q^{53} - 4 q^{54} - 22 q^{55} + 12 q^{56} - 32 q^{57} - 23 q^{58} - 8 q^{59} - 8 q^{60} - 31 q^{61} + 31 q^{62} - 23 q^{63} + 15 q^{64} - 3 q^{65} - 9 q^{66} - 48 q^{67} + 44 q^{68} - 23 q^{69} + 13 q^{70} - 14 q^{71} - 9 q^{72} - 50 q^{73} - 10 q^{74} - 8 q^{75} - 64 q^{76} + 23 q^{77} - 4 q^{78} - 21 q^{79} + 8 q^{80} + 19 q^{81} - 10 q^{82} - 15 q^{83} - 22 q^{84} - 29 q^{85} + 9 q^{86} + 4 q^{87} + 3 q^{88} - 10 q^{89} - 6 q^{90} - 23 q^{91} - 17 q^{92} - 50 q^{93} - 22 q^{94} - 25 q^{95} - 2 q^{96} - 42 q^{97} - q^{98} - 15 q^{99}+O(q^{100}) \) 19 * q - 4 * q^2 + 19 * q^3 + 10 * q^4 - 3 * q^5 - 4 * q^6 - 23 * q^7 - 9 * q^8 + 19 * q^9 - 6 * q^10 - 15 * q^11 + 10 * q^12 + 19 * q^13 - 4 * q^14 - 3 * q^15 - 4 * q^16 - 4 * q^18 - 32 * q^19 - 8 * q^20 - 23 * q^21 - 9 * q^22 - 23 * q^23 - 9 * q^24 - 8 * q^25 - 4 * q^26 + 19 * q^27 - 22 * q^28 + 4 * q^29 - 6 * q^30 - 50 * q^31 - 2 * q^32 - 15 * q^33 - 35 * q^34 - 4 * q^35 + 10 * q^36 - 38 * q^37 + 20 * q^38 + 19 * q^39 - 30 * q^40 - 11 * q^41 - 4 * q^42 - 17 * q^43 - 29 * q^44 - 3 * q^45 - 5 * q^46 - 38 * q^47 - 4 * q^48 - 6 * q^49 - 9 * q^50 + 10 * q^52 - 12 * q^53 - 4 * q^54 - 22 * q^55 + 12 * q^56 - 32 * q^57 - 23 * q^58 - 8 * q^59 - 8 * q^60 - 31 * q^61 + 31 * q^62 - 23 * q^63 + 15 * q^64 - 3 * q^65 - 9 * q^66 - 48 * q^67 + 44 * q^68 - 23 * q^69 + 13 * q^70 - 14 * q^71 - 9 * q^72 - 50 * q^73 - 10 * q^74 - 8 * q^75 - 64 * q^76 + 23 * q^77 - 4 * q^78 - 21 * q^79 + 8 * q^80 + 19 * q^81 - 10 * q^82 - 15 * q^83 - 22 * q^84 - 29 * q^85 + 9 * q^86 + 4 * q^87 + 3 * q^88 - 10 * q^89 - 6 * q^90 - 23 * q^91 - 17 * q^92 - 50 * q^93 - 22 * q^94 - 25 * q^95 - 2 * q^96 - 42 * q^97 - q^98 - 15 * 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 $

$2$	−0.725598	−0.513075	−0.256538	−	0.966534i	$-0.582582\pi$
$2$	−0.725598	−0.513075	−0.256538	+	0.966534i	$0.582582\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	−1.47351	−0.736754
$5$	−3.68550	−1.64820	−0.824102	−	0.566442i	$-0.808320\pi$
$5$	−3.68550	−1.64820	−0.824102	+	0.566442i	$0.808320\pi$
$6$	−0.725598	−0.296224
$7$	−0.281235	−0.106297	−0.0531485	−	0.998587i	$-0.516926\pi$
$7$	−0.281235	−0.106297	−0.0531485	+	0.998587i	$0.516926\pi$
$8$	2.52037	0.891086
$9$	1.00000	0.333333
$10$	2.67419	0.845653
$11$	−1.72170	−0.519112	−0.259556	−	0.965728i	$-0.583576\pi$
$11$	−1.72170	−0.519112	−0.259556	+	0.965728i	$0.583576\pi$
$12$	−1.47351	−0.425365
$13$	1.00000	0.277350
$13$	1.00000	0.277350
$14$	0.204064	0.0545384
$15$	−3.68550	−0.951591
$16$	1.11824	0.279559
$17$	1.29609	0.314348	0.157174	−	0.987571i	$-0.449762\pi$
$17$	1.29609	0.314348	0.157174	+	0.987571i	$0.449762\pi$
$18$	−0.725598	−0.171025
$19$	−6.38831	−1.46558	−0.732789	−	0.680456i	$-0.761782\pi$
$19$	−6.38831	−1.46558	−0.732789	+	0.680456i	$0.761782\pi$
$20$	5.43060	1.21432
$21$	−0.281235	−0.0613706
$22$	1.24926	0.266344
$23$	2.49695	0.520650	0.260325	−	0.965521i	$-0.416170\pi$
$23$	2.49695	0.520650	0.260325	+	0.965521i	$0.416170\pi$
$24$	2.52037	0.514469
$25$	8.58288	1.71658
$26$	−0.725598	−0.142302
$27$	1.00000	0.192450
$28$	0.414402	0.0783147
$29$	6.21816	1.15468	0.577342	−	0.816502i	$-0.304090\pi$
$29$	6.21816	1.15468	0.577342	+	0.816502i	$0.304090\pi$
$30$	2.67419	0.488238
$31$	−0.971398	−0.174468	−0.0872341	−	0.996188i	$-0.527803\pi$
$31$	−0.971398	−0.174468	−0.0872341	+	0.996188i	$0.527803\pi$
$32$	−5.85213	−1.03452
$33$	−1.72170	−0.299709
$34$	−0.940441	−0.161284
$35$	1.03649	0.175199
$36$	−1.47351	−0.245585
$37$	3.09327	0.508531	0.254266	−	0.967134i	$-0.418166\pi$
$37$	3.09327	0.508531	0.254266	+	0.967134i	$0.418166\pi$
$38$	4.63534	0.751952
$39$	1.00000	0.160128
$40$	−9.28882	−1.46869
$41$	3.77376	0.589363	0.294682	−	0.955596i	$-0.404786\pi$
$41$	3.77376	0.589363	0.294682	+	0.955596i	$0.404786\pi$
$42$	0.204064	0.0314877
$43$	9.32426	1.42194	0.710968	−	0.703224i	$-0.248257\pi$
$43$	9.32426	1.42194	0.710968	+	0.703224i	$0.248257\pi$
$44$	2.53694	0.382458
$45$	−3.68550	−0.549401
$46$	−1.81178	−0.267133
$47$	0.568426	0.0829134	0.0414567	−	0.999140i	$-0.486800\pi$
$47$	0.568426	0.0829134	0.0414567	+	0.999140i	$0.486800\pi$
$48$	1.11824	0.161404
$49$	−6.92091	−0.988701
$50$	−6.22772	−0.880733
$51$	1.29609	0.181489
$52$	−1.47351	−0.204339
$53$	7.23182	0.993367	0.496684	−	0.867932i	$-0.334551\pi$
$53$	7.23182	0.993367	0.496684	+	0.867932i	$0.334551\pi$
$54$	−0.725598	−0.0987414
$55$	6.34532	0.855602
$56$	−0.708817	−0.0947197
$57$	−6.38831	−0.846152
$58$	−4.51189	−0.592440
$59$	3.57852	0.465884	0.232942	−	0.972491i	$-0.425165\pi$
$59$	3.57852	0.465884	0.232942	+	0.972491i	$0.425165\pi$
$60$	5.43060	0.701088
$61$	3.08194	0.394602	0.197301	−	0.980343i	$-0.436782\pi$
$61$	3.08194	0.394602	0.197301	+	0.980343i	$0.436782\pi$
$62$	0.704845	0.0895154
$63$	−0.281235	−0.0354323
$64$	2.00982	0.251228
$65$	−3.68550	−0.457129
$66$	1.24926	0.153774
$67$	−11.8815	−1.45155	−0.725775	−	0.687932i	$-0.758519\pi$
$67$	−11.8815	−1.45155	−0.725775	+	0.687932i	$0.758519\pi$
$68$	−1.90980	−0.231597
$69$	2.49695	0.300598
$70$	−0.752077	−0.0898903
$71$	−10.7513	−1.27594	−0.637971	−	0.770060i	$-0.720226\pi$
$71$	−10.7513	−1.27594	−0.637971	+	0.770060i	$0.720226\pi$
$72$	2.52037	0.297029
$73$	−3.79188	−0.443806	−0.221903	−	0.975069i	$-0.571227\pi$
$73$	−3.79188	−0.443806	−0.221903	+	0.975069i	$0.571227\pi$
$74$	−2.24447	−0.260915
$75$	8.58288	0.991065
$76$	9.41321	1.07977
$77$	0.484203	0.0551800
$78$	−0.725598	−0.0821578
$79$	−14.2833	−1.60700	−0.803498	−	0.595308i	$-0.797030\pi$
$79$	−14.2833	−1.60700	−0.803498	+	0.595308i	$0.797030\pi$
$80$	−4.12126	−0.460771
$81$	1.00000	0.111111
$82$	−2.73824	−0.302388
$83$	−0.650334	−0.0713835	−0.0356917	−	0.999363i	$-0.511363\pi$
$83$	−0.650334	−0.0713835	−0.0356917	+	0.999363i	$0.511363\pi$
$84$	0.414402	0.0452150
$85$	−4.77674	−0.518110
$86$	−6.76567	−0.729561
$87$	6.21816	0.666657
$88$	−4.33932	−0.462573
$89$	0.273541	0.0289953	0.0144976	−	0.999895i	$-0.495385\pi$
$89$	0.273541	0.0289953	0.0144976	+	0.999895i	$0.495385\pi$
$90$	2.67419	0.281884
$91$	−0.281235	−0.0294815
$92$	−3.67928	−0.383591
$93$	−0.971398	−0.100729
$94$	−0.412449	−0.0425408
$95$	23.5441	2.41557
$96$	−5.85213	−0.597281
$97$	5.21056	0.529052	0.264526	−	0.964379i	$-0.414784\pi$
$97$	5.21056	0.529052	0.264526	+	0.964379i	$0.414784\pi$
$98$	5.02180	0.507278
$99$	−1.72170	−0.173037
$100$	−12.6469	−1.26469
$101$	9.68419	0.963613	0.481806	−	0.876278i	$-0.339981\pi$
$101$	9.68419	0.963613	0.481806	+	0.876278i	$0.339981\pi$
$102$	−0.940441	−0.0931176
$103$	−1.00000	−0.0985329
$103$	−1.00000	−0.0985329
$104$	2.52037	0.247143
$105$	1.03649	0.101151
$106$	−5.24740	−0.509672
$107$	−1.68506	−0.162901	−0.0814504	−	0.996677i	$-0.525955\pi$
$107$	−1.68506	−0.162901	−0.0814504	+	0.996677i	$0.525955\pi$
$108$	−1.47351	−0.141788
$109$	−5.44975	−0.521991	−0.260996	−	0.965340i	$-0.584051\pi$
$109$	−5.44975	−0.521991	−0.260996	+	0.965340i	$0.584051\pi$
$110$	−4.60415	−0.438989
$111$	3.09327	0.293601
$112$	−0.314488	−0.0297163
$113$	7.05041	0.663247	0.331623	−	0.943412i	$-0.392404\pi$
$113$	7.05041	0.663247	0.331623	+	0.943412i	$0.392404\pi$
$114$	4.63534	0.434140
$115$	−9.20251	−0.858138
$116$	−9.16251	−0.850717
$117$	1.00000	0.0924500
$118$	−2.59657	−0.239034
$119$	−0.364507	−0.0334143
$120$	−9.28882	−0.847949
$121$	−8.03575	−0.730523
$122$	−2.23625	−0.202461
$123$	3.77376	0.340269
$124$	1.43136	0.128540
$125$	−13.2047	−1.18106
$126$	0.204064	0.0181795
$127$	−7.68097	−0.681576	−0.340788	−	0.940140i	$-0.610694\pi$
$127$	−7.68097	−0.681576	−0.340788	+	0.940140i	$0.610694\pi$
$128$	10.2459	0.905622
$129$	9.32426	0.820956
$130$	2.67419	0.234542
$131$	−16.5563	−1.44653	−0.723265	−	0.690571i	$-0.757359\pi$
$131$	−16.5563	−1.44653	−0.723265	+	0.690571i	$0.757359\pi$
$132$	2.53694	0.220812
$133$	1.79662	0.155786
$134$	8.62116	0.744755
$135$	−3.68550	−0.317197
$136$	3.26663	0.280111
$137$	14.6342	1.25029	0.625143	−	0.780511i	$-0.285041\pi$
$137$	14.6342	1.25029	0.625143	+	0.780511i	$0.285041\pi$
$138$	−1.81178	−0.154229
$139$	4.93012	0.418167	0.209083	−	0.977898i	$-0.432952\pi$
$139$	4.93012	0.418167	0.209083	+	0.977898i	$0.432952\pi$
$140$	−1.52728	−0.129079
$141$	0.568426	0.0478701
$142$	7.80111	0.654655
$143$	−1.72170	−0.143976
$144$	1.11824	0.0931865
$145$	−22.9170	−1.90315
$146$	2.75138	0.227706
$147$	−6.92091	−0.570827
$148$	−4.55796	−0.374662
$149$	9.08802	0.744520	0.372260	−	0.928129i	$-0.378583\pi$
$149$	9.08802	0.744520	0.372260	+	0.928129i	$0.378583\pi$
$150$	−6.22772	−0.508491
$151$	−0.723322	−0.0588631	−0.0294315	−	0.999567i	$-0.509370\pi$
$151$	−0.723322	−0.0588631	−0.0294315	+	0.999567i	$0.509370\pi$
$152$	−16.1009	−1.30596
$153$	1.29609	0.104783
$154$	−0.351337	−0.0283115
$155$	3.58008	0.287559
$156$	−1.47351	−0.117975
$157$	14.7791	1.17950	0.589752	−	0.807584i	$-0.299225\pi$
$157$	14.7791	1.17950	0.589752	+	0.807584i	$0.299225\pi$
$158$	10.3639	0.824510
$159$	7.23182	0.573521
$160$	21.5680	1.70510
$161$	−0.702231	−0.0553436
$162$	−0.725598	−0.0570084
$163$	−12.9862	−1.01715	−0.508577	−	0.861016i	$-0.669828\pi$
$163$	−12.9862	−1.01715	−0.508577	+	0.861016i	$0.669828\pi$
$164$	−5.56067	−0.434215
$165$	6.34532	0.493982
$166$	0.471881	0.0366251
$167$	−11.2177	−0.868048	−0.434024	−	0.900901i	$-0.642907\pi$
$167$	−11.2177	−0.868048	−0.434024	+	0.900901i	$0.642907\pi$
$168$	−0.708817	−0.0546864
$169$	1.00000	0.0769231
$170$	3.46599	0.265829
$171$	−6.38831	−0.488526
$172$	−13.7394	−1.04762
$173$	−5.06111	−0.384789	−0.192395	−	0.981318i	$-0.561625\pi$
$173$	−5.06111	−0.384789	−0.192395	+	0.981318i	$0.561625\pi$
$174$	−4.51189	−0.342045
$175$	−2.41381	−0.182467
$176$	−1.92527	−0.145123
$177$	3.57852	0.268978
$178$	−0.198481	−0.0148768
$179$	3.63239	0.271498	0.135749	−	0.990743i	$-0.456656\pi$
$179$	3.63239	0.271498	0.135749	+	0.990743i	$0.456656\pi$
$180$	5.43060	0.404773
$181$	−6.53652	−0.485856	−0.242928	−	0.970044i	$-0.578108\pi$
$181$	−6.53652	−0.485856	−0.242928	+	0.970044i	$0.578108\pi$
$182$	0.204064	0.0151262
$183$	3.08194	0.227823
$184$	6.29324	0.463944
$185$	−11.4003	−0.838163
$186$	0.704845	0.0516817
$187$	−2.23148	−0.163182
$188$	−0.837580	−0.0610868
$189$	−0.281235	−0.0204569
$190$	−17.0835	−1.23937
$191$	−21.1632	−1.53132	−0.765659	−	0.643247i	$-0.777587\pi$
$191$	−21.1632	−1.53132	−0.765659	+	0.643247i	$0.777587\pi$
$192$	2.00982	0.145046
$193$	2.04969	0.147540	0.0737700	−	0.997275i	$-0.476497\pi$
$193$	2.04969	0.147540	0.0737700	+	0.997275i	$0.476497\pi$
$194$	−3.78077	−0.271444
$195$	−3.68550	−0.263924
$196$	10.1980	0.728429
$197$	−5.53388	−0.394273	−0.197136	−	0.980376i	$-0.563164\pi$
$197$	−5.53388	−0.394273	−0.197136	+	0.980376i	$0.563164\pi$
$198$	1.24926	0.0887812
$199$	−13.8517	−0.981924	−0.490962	−	0.871181i	$-0.663355\pi$
$199$	−13.8517	−0.981924	−0.490962	+	0.871181i	$0.663355\pi$
$200$	21.6320	1.52962
$201$	−11.8815	−0.838053
$202$	−7.02683	−0.494406
$203$	−1.74877	−0.122739
$204$	−1.90980	−0.133713
$205$	−13.9082	−0.971390
$206$	0.725598	0.0505548
$207$	2.49695	0.173550
$208$	1.11824	0.0775358
$209$	10.9987	0.760799
$210$	−0.752077	−0.0518982
$211$	−25.1800	−1.73346	−0.866732	−	0.498774i	$-0.833784\pi$
$211$	−25.1800	−1.73346	−0.866732	+	0.498774i	$0.833784\pi$
$212$	−10.6561	−0.731867
$213$	−10.7513	−0.736666
$214$	1.22268	0.0835804
$215$	−34.3645	−2.34364
$216$	2.52037	0.171490
$217$	0.273192	0.0185454
$218$	3.95433	0.267821
$219$	−3.79188	−0.256231
$220$	−9.34987	−0.630368
$221$	1.29609	0.0871845
$222$	−2.24447	−0.150639
$223$	−9.62409	−0.644476	−0.322238	−	0.946659i	$-0.604435\pi$
$223$	−9.62409	−0.644476	−0.322238	+	0.946659i	$0.604435\pi$
$224$	1.64583	0.109966
$225$	8.58288	0.572192
$226$	−5.11576	−0.340296
$227$	−14.3514	−0.952534	−0.476267	−	0.879301i	$-0.658011\pi$
$227$	−14.3514	−0.952534	−0.476267	+	0.879301i	$0.658011\pi$
$228$	9.41321	0.623405
$229$	−21.0445	−1.39066	−0.695330	−	0.718691i	$-0.744742\pi$
$229$	−21.0445	−1.39066	−0.695330	+	0.718691i	$0.744742\pi$
$230$	6.67732	0.440290
$231$	0.484203	0.0318582
$232$	15.6721	1.02892
$233$	13.0503	0.854953	0.427476	−	0.904026i	$-0.359403\pi$
$233$	13.0503	0.854953	0.427476	+	0.904026i	$0.359403\pi$
$234$	−0.725598	−0.0474338
$235$	−2.09493	−0.136658
$236$	−5.27298	−0.343242
$237$	−14.2833	−0.927800
$238$	0.264485	0.0171440
$239$	−15.5604	−1.00652	−0.503258	−	0.864136i	$-0.667865\pi$
$239$	−15.5604	−1.00652	−0.503258	+	0.864136i	$0.667865\pi$
$240$	−4.12126	−0.266026
$241$	−13.2899	−0.856080	−0.428040	−	0.903760i	$-0.640796\pi$
$241$	−13.2899	−0.856080	−0.428040	+	0.903760i	$0.640796\pi$
$242$	5.83073	0.374813
$243$	1.00000	0.0641500
$244$	−4.54126	−0.290724
$245$	25.5070	1.62958
$246$	−2.73824	−0.174584
$247$	−6.38831	−0.406478
$248$	−2.44828	−0.155466
$249$	−0.650334	−0.0412133
$250$	9.58129	0.605974
$251$	−7.89965	−0.498621	−0.249311	−	0.968424i	$-0.580204\pi$
$251$	−7.89965	−0.498621	−0.249311	+	0.968424i	$0.580204\pi$
$252$	0.414402	0.0261049
$253$	−4.29900	−0.270276
$254$	5.57330	0.349700
$255$	−4.77674	−0.299131
$256$	−11.4541	−0.715880
$257$	6.60275	0.411869	0.205934	−	0.978566i	$-0.433977\pi$
$257$	6.60275	0.411869	0.205934	+	0.978566i	$0.433977\pi$
$258$	−6.76567	−0.421212
$259$	−0.869938	−0.0540553
$260$	5.43060	0.336792
$261$	6.21816	0.384895
$262$	12.0132	0.742179
$263$	7.27001	0.448288	0.224144	−	0.974556i	$-0.428041\pi$
$263$	7.27001	0.448288	0.224144	+	0.974556i	$0.428041\pi$
$264$	−4.33932	−0.267067
$265$	−26.6528	−1.63727
$266$	−1.30362	−0.0799302
$267$	0.273541	0.0167404
$268$	17.5074	1.06944
$269$	−32.1610	−1.96089	−0.980446	−	0.196789i	$-0.936949\pi$
$269$	−32.1610	−1.96089	−0.980446	+	0.196789i	$0.936949\pi$
$270$	2.67419	0.162746
$271$	29.2718	1.77814	0.889068	−	0.457775i	$-0.151353\pi$
$271$	29.2718	1.77814	0.889068	+	0.457775i	$0.151353\pi$
$272$	1.44934	0.0878790
$273$	−0.281235	−0.0170211
$274$	−10.6186	−0.641491
$275$	−14.7771	−0.891095
$276$	−3.67928	−0.221466
$277$	−14.5030	−0.871399	−0.435699	−	0.900092i	$-0.643499\pi$
$277$	−14.5030	−0.871399	−0.435699	+	0.900092i	$0.643499\pi$
$278$	−3.57728	−0.214551
$279$	−0.971398	−0.0581561
$280$	2.61234	0.156117
$281$	−16.4124	−0.979079	−0.489539	−	0.871981i	$-0.662835\pi$
$281$	−16.4124	−0.979079	−0.489539	+	0.871981i	$0.662835\pi$
$282$	−0.412449	−0.0245610
$283$	−10.7312	−0.637904	−0.318952	−	0.947771i	$-0.603331\pi$
$283$	−10.7312	−0.637904	−0.318952	+	0.947771i	$0.603331\pi$
$284$	15.8421	0.940056
$285$	23.5441	1.39463
$286$	1.24926	0.0738704
$287$	−1.06132	−0.0626475
$288$	−5.85213	−0.344840
$289$	−15.3201	−0.901185
$290$	16.6285	0.976462
$291$	5.21056	0.305449
$292$	5.58736	0.326976
$293$	14.4080	0.841727	0.420863	−	0.907124i	$-0.361727\pi$
$293$	14.4080	0.841727	0.420863	+	0.907124i	$0.361727\pi$
$294$	5.02180	0.292877
$295$	−13.1886	−0.767871
$296$	7.79620	0.453145
$297$	−1.72170	−0.0999031
$298$	−6.59425	−0.381995
$299$	2.49695	0.144402
$300$	−12.6469	−0.730171
$301$	−2.62231	−0.151148
$302$	0.524841	0.0302012
$303$	9.68419	0.556342
$304$	−7.14364	−0.409716
$305$	−11.3585	−0.650384
$306$	−0.940441	−0.0537615
$307$	5.31800	0.303514	0.151757	−	0.988418i	$-0.451507\pi$
$307$	5.31800	0.303514	0.151757	+	0.988418i	$0.451507\pi$
$308$	−0.713476	−0.0406541
$309$	−1.00000	−0.0568880
$310$	−2.59770	−0.147540
$311$	2.68131	0.152043	0.0760215	−	0.997106i	$-0.475778\pi$
$311$	2.68131	0.152043	0.0760215	+	0.997106i	$0.475778\pi$
$312$	2.52037	0.142688
$313$	8.33005	0.470842	0.235421	−	0.971893i	$-0.424353\pi$
$313$	8.33005	0.470842	0.235421	+	0.971893i	$0.424353\pi$
$314$	−10.7237	−0.605175
$315$	1.03649	0.0583997
$316$	21.0465	1.18396
$317$	−25.6234	−1.43916	−0.719578	−	0.694412i	$-0.755665\pi$
$317$	−25.6234	−1.43916	−0.719578	+	0.694412i	$0.755665\pi$
$318$	−5.24740	−0.294259
$319$	−10.7058	−0.599410
$320$	−7.40719	−0.414075
$321$	−1.68506	−0.0940508
$322$	0.509538	0.0283954
$323$	−8.27983	−0.460702
$324$	−1.47351	−0.0818615
$325$	8.58288	0.476092
$326$	9.42274	0.521877
$327$	−5.44975	−0.301372
$328$	9.51129	0.525173
$329$	−0.159861	−0.00881345
$330$	−4.60415	−0.253450
$331$	3.58621	0.197116	0.0985579	−	0.995131i	$-0.468577\pi$
$331$	3.58621	0.197116	0.0985579	+	0.995131i	$0.468577\pi$
$332$	0.958272	0.0525920
$333$	3.09327	0.169510
$334$	8.13951	0.445374
$335$	43.7890	2.39245
$336$	−0.314488	−0.0171567
$337$	−10.8289	−0.589889	−0.294945	−	0.955514i	$-0.595301\pi$
$337$	−10.8289	−0.589889	−0.294945	+	0.955514i	$0.595301\pi$
$338$	−0.725598	−0.0394673
$339$	7.05041	0.382926
$340$	7.03856	0.381719
$341$	1.67246	0.0905686
$342$	4.63534	0.250651
$343$	3.91505	0.211393
$344$	23.5006	1.26707
$345$	−9.20251	−0.495446
$346$	3.67234	0.197426
$347$	8.55392	0.459198	0.229599	−	0.973285i	$-0.426258\pi$
$347$	8.55392	0.459198	0.229599	+	0.973285i	$0.426258\pi$
$348$	−9.16251	−0.491162
$349$	13.7315	0.735031	0.367516	−	0.930017i	$-0.380208\pi$
$349$	13.7315	0.735031	0.367516	+	0.930017i	$0.380208\pi$
$350$	1.75146	0.0936192
$351$	1.00000	0.0533761
$352$	10.0756	0.537032
$353$	24.0058	1.27770	0.638851	−	0.769331i	$-0.279410\pi$
$353$	24.0058	1.27770	0.638851	+	0.769331i	$0.279410\pi$
$354$	−2.59657	−0.138006
$355$	39.6238	2.10301
$356$	−0.403064	−0.0213624
$357$	−0.364507	−0.0192917
$358$	−2.63566	−0.139299
$359$	−19.7400	−1.04184	−0.520918	−	0.853607i	$-0.674410\pi$
$359$	−19.7400	−1.04184	−0.520918	+	0.853607i	$0.674410\pi$
$360$	−9.28882	−0.489564
$361$	21.8105	1.14792
$362$	4.74289	0.249281
$363$	−8.03575	−0.421768
$364$	0.414402	0.0217206
$365$	13.9750	0.731483
$366$	−2.23625	−0.116891
$367$	−12.3316	−0.643706	−0.321853	−	0.946790i	$-0.604306\pi$
$367$	−12.3316	−0.643706	−0.321853	+	0.946790i	$0.604306\pi$
$368$	2.79219	0.145553
$369$	3.77376	0.196454
$370$	8.27200	0.430041
$371$	−2.03384	−0.105592
$372$	1.43136	0.0742127
$373$	12.5243	0.648484	0.324242	−	0.945974i	$-0.394891\pi$
$373$	12.5243	0.648484	0.324242	+	0.945974i	$0.394891\pi$
$374$	1.61916	0.0837246
$375$	−13.2047	−0.681887
$376$	1.43264	0.0738830
$377$	6.21816	0.320252
$378$	0.204064	0.0104959
$379$	17.7571	0.912120	0.456060	−	0.889949i	$-0.349260\pi$
$379$	17.7571	0.912120	0.456060	+	0.889949i	$0.349260\pi$
$380$	−34.6924	−1.77968
$381$	−7.68097	−0.393508
$382$	15.3560	0.785682
$383$	26.4190	1.34995	0.674973	−	0.737842i	$-0.264155\pi$
$383$	26.4190	1.34995	0.674973	+	0.737842i	$0.264155\pi$
$384$	10.2459	0.522861
$385$	−1.78453	−0.0909479
$386$	−1.48725	−0.0756992
$387$	9.32426	0.473979
$388$	−7.67780	−0.389781
$389$	1.22234	0.0619749	0.0309875	−	0.999520i	$-0.490135\pi$
$389$	1.22234	0.0619749	0.0309875	+	0.999520i	$0.490135\pi$
$390$	2.67419	0.135413
$391$	3.23628	0.163666
$392$	−17.4433	−0.881017
$393$	−16.5563	−0.835154
$394$	4.01538	0.202292
$395$	52.6410	2.64866
$396$	2.53694	0.127486
$397$	−18.1490	−0.910872	−0.455436	−	0.890269i	$-0.650517\pi$
$397$	−18.1490	−0.910872	−0.455436	+	0.890269i	$0.650517\pi$
$398$	10.0508	0.503801
$399$	1.79662	0.0899434
$400$	9.59770	0.479885
$401$	24.5647	1.22670	0.613352	−	0.789809i	$-0.289821\pi$
$401$	24.5647	1.22670	0.613352	+	0.789809i	$0.289821\pi$
$402$	8.62116	0.429985
$403$	−0.971398	−0.0483888
$404$	−14.2697	−0.709945
$405$	−3.68550	−0.183134
$406$	1.26890	0.0629746
$407$	−5.32569	−0.263985
$408$	3.26663	0.161722
$409$	18.7606	0.927650	0.463825	−	0.885927i	$-0.346477\pi$
$409$	18.7606	0.927650	0.463825	+	0.885927i	$0.346477\pi$
$410$	10.0918	0.498397
$411$	14.6342	0.721853
$412$	1.47351	0.0725945
$413$	−1.00641	−0.0495220
$414$	−1.81178	−0.0890443
$415$	2.39680	0.117654
$416$	−5.85213	−0.286924
$417$	4.93012	0.241429
$418$	−7.98067	−0.390347
$419$	−13.8829	−0.678223	−0.339111	−	0.940746i	$-0.610126\pi$
$419$	−13.8829	−0.678223	−0.339111	+	0.940746i	$0.610126\pi$
$420$	−1.52728	−0.0745235
$421$	−30.7977	−1.50099	−0.750495	−	0.660876i	$-0.770185\pi$
$421$	−30.7977	−1.50099	−0.750495	+	0.660876i	$0.770185\pi$
$422$	18.2706	0.889398
$423$	0.568426	0.0276378
$424$	18.2269	0.885175
$425$	11.1242	0.539603
$426$	7.80111	0.377965
$427$	−0.866750	−0.0419450
$428$	2.48295	0.120018
$429$	−1.72170	−0.0831244
$430$	24.9348	1.20246
$431$	−15.7715	−0.759687	−0.379844	−	0.925051i	$-0.624022\pi$
$431$	−15.7715	−0.759687	−0.379844	+	0.925051i	$0.624022\pi$
$432$	1.11824	0.0538012
$433$	24.7543	1.18961	0.594807	−	0.803868i	$-0.297228\pi$
$433$	24.7543	1.18961	0.594807	+	0.803868i	$0.297228\pi$
$434$	−0.198227	−0.00951521
$435$	−22.9170	−1.09879
$436$	8.03024	0.384579
$437$	−15.9513	−0.763054
$438$	2.75138	0.131466
$439$	−25.9920	−1.24053	−0.620266	−	0.784392i	$-0.712975\pi$
$439$	−25.9920	−1.24053	−0.620266	+	0.784392i	$0.712975\pi$
$440$	15.9925	0.762415
$441$	−6.92091	−0.329567
$442$	−0.940441	−0.0447322
$443$	−24.6083	−1.16918	−0.584588	−	0.811330i	$-0.698744\pi$
$443$	−24.6083	−1.16918	−0.584588	+	0.811330i	$0.698744\pi$
$444$	−4.55796	−0.216311
$445$	−1.00813	−0.0477901
$446$	6.98322	0.330665
$447$	9.08802	0.429849
$448$	−0.565233	−0.0267048
$449$	−14.2847	−0.674136	−0.337068	−	0.941480i	$-0.609435\pi$
$449$	−14.2847	−0.674136	−0.337068	+	0.941480i	$0.609435\pi$
$450$	−6.22772	−0.293578
$451$	−6.49729	−0.305945
$452$	−10.3888	−0.488649
$453$	−0.723322	−0.0339846
$454$	10.4133	0.488722
$455$	1.03649	0.0485915
$456$	−16.1009	−0.753994
$457$	−20.9008	−0.977698	−0.488849	−	0.872368i	$-0.662583\pi$
$457$	−20.9008	−0.977698	−0.488849	+	0.872368i	$0.662583\pi$
$458$	15.2699	0.713514
$459$	1.29609	0.0604963
$460$	13.5600	0.632236
$461$	17.2488	0.803358	0.401679	−	0.915780i	$-0.368427\pi$
$461$	17.2488	0.803358	0.401679	+	0.915780i	$0.368427\pi$
$462$	−0.351337	−0.0163457
$463$	−35.0234	−1.62768	−0.813839	−	0.581091i	$-0.802626\pi$
$463$	−35.0234	−1.62768	−0.813839	+	0.581091i	$0.802626\pi$
$464$	6.95338	0.322803
$465$	3.58008	0.166022
$466$	−9.46927	−0.438655
$467$	24.2695	1.12306	0.561530	−	0.827457i	$-0.310213\pi$
$467$	24.2695	1.12306	0.561530	+	0.827457i	$0.310213\pi$
$468$	−1.47351	−0.0681129
$469$	3.34149	0.154295
$470$	1.52008	0.0701160
$471$	14.7791	0.680987
$472$	9.01920	0.415142
$473$	−16.0536	−0.738144
$474$	10.3639	0.476031
$475$	−54.8301	−2.51578
$476$	0.537103	0.0246181
$477$	7.23182	0.331122
$478$	11.2906	0.516419
$479$	39.8563	1.82108	0.910540	−	0.413421i	$-0.135666\pi$
$479$	39.8563	1.82108	0.910540	+	0.413421i	$0.135666\pi$
$480$	21.5680	0.984440
$481$	3.09327	0.141041
$482$	9.64315	0.439233
$483$	−0.702231	−0.0319526
$484$	11.8407	0.538215
$485$	−19.2035	−0.871986
$486$	−0.725598	−0.0329138
$487$	22.2241	1.00707	0.503536	−	0.863974i	$-0.332032\pi$
$487$	22.2241	1.00707	0.503536	+	0.863974i	$0.332032\pi$
$488$	7.76763	0.351624
$489$	−12.9862	−0.587255
$490$	−18.5078	−0.836098
$491$	3.88008	0.175106	0.0875528	−	0.996160i	$-0.472095\pi$
$491$	3.88008	0.175106	0.0875528	+	0.996160i	$0.472095\pi$
$492$	−5.56067	−0.250694
$493$	8.05930	0.362973
$494$	4.63534	0.208554
$495$	6.34532	0.285201
$496$	−1.08625	−0.0487742
$497$	3.02364	0.135629
$498$	0.471881	0.0211455
$499$	−20.5660	−0.920660	−0.460330	−	0.887748i	$-0.652269\pi$
$499$	−20.5660	−0.920660	−0.460330	+	0.887748i	$0.652269\pi$
$500$	19.4572	0.870152
$501$	−11.2177	−0.501168
$502$	5.73197	0.255830
$503$	15.7120	0.700562	0.350281	−	0.936645i	$-0.386086\pi$
$503$	15.7120	0.700562	0.350281	+	0.936645i	$0.386086\pi$
$504$	−0.708817	−0.0315732
$505$	−35.6910	−1.58823
$506$	3.11935	0.138672
$507$	1.00000	0.0444116
$508$	11.3180	0.502153
$509$	11.1665	0.494947	0.247474	−	0.968895i	$-0.420400\pi$
$509$	11.1665	0.494947	0.247474	+	0.968895i	$0.420400\pi$
$510$	3.46599	0.153477
$511$	1.06641	0.0471752
$512$	−12.1808	−0.538321
$513$	−6.38831	−0.282051
$514$	−4.79095	−0.211320
$515$	3.68550	0.162402
$516$	−13.7394	−0.604842
$517$	−0.978659	−0.0430414
$518$	0.631226	0.0277345
$519$	−5.06111	−0.222158
$520$	−9.28882	−0.407342
$521$	−23.8905	−1.04666	−0.523331	−	0.852130i	$-0.675311\pi$
$521$	−23.8905	−1.04666	−0.523331	+	0.852130i	$0.675311\pi$
$522$	−4.51189	−0.197480
$523$	−7.55912	−0.330537	−0.165269	−	0.986249i	$-0.552849\pi$
$523$	−7.55912	−0.330537	−0.165269	+	0.986249i	$0.552849\pi$
$524$	24.3958	1.06574
$525$	−2.41381	−0.105347
$526$	−5.27511	−0.230006
$527$	−1.25902	−0.0548438
$528$	−1.92527	−0.0837866
$529$	−16.7652	−0.728923
$530$	19.3393	0.840044
$531$	3.57852	0.155295
$532$	−2.64733	−0.114776
$533$	3.77376	0.163460
$534$	−0.198481	−0.00858910
$535$	6.21028	0.268494
$536$	−29.9457	−1.29346
$537$	3.63239	0.156749
$538$	23.3360	1.00609
$539$	11.9157	0.513246
$540$	5.43060	0.233696
$541$	−21.5305	−0.925670	−0.462835	−	0.886445i	$-0.653168\pi$
$541$	−21.5305	−0.925670	−0.462835	+	0.886445i	$0.653168\pi$
$542$	−21.2396	−0.912318
$543$	−6.53652	−0.280509
$544$	−7.58490	−0.325200
$545$	20.0850	0.860348
$546$	0.204064	0.00873313
$547$	19.9621	0.853516	0.426758	−	0.904366i	$-0.359656\pi$
$547$	19.9621	0.853516	0.426758	+	0.904366i	$0.359656\pi$
$548$	−21.5636	−0.921152
$549$	3.08194	0.131534
$550$	10.7223	0.457199
$551$	−39.7235	−1.69228
$552$	6.29324	0.267858
$553$	4.01697	0.170819
$554$	10.5233	0.447093
$555$	−11.4003	−0.483914
$556$	−7.26456	−0.308086
$557$	28.8503	1.22242	0.611212	−	0.791467i	$-0.290682\pi$
$557$	28.8503	1.22242	0.611212	+	0.791467i	$0.290682\pi$
$558$	0.704845	0.0298385
$559$	9.32426	0.394374
$560$	1.15904	0.0489785
$561$	−2.23148	−0.0942131
$562$	11.9088	0.502341
$563$	10.3622	0.436713	0.218356	−	0.975869i	$-0.429930\pi$
$563$	10.3622	0.436713	0.218356	+	0.975869i	$0.429930\pi$
$564$	−0.837580	−0.0352685
$565$	−25.9842	−1.09317
$566$	7.78655	0.327293
$567$	−0.281235	−0.0118108
$568$	−27.0972	−1.13697
$569$	−38.4762	−1.61301	−0.806504	−	0.591229i	$-0.798643\pi$
$569$	−38.4762	−1.61301	−0.806504	+	0.591229i	$0.798643\pi$
$570$	−17.0835	−0.715551
$571$	44.8074	1.87513	0.937566	−	0.347806i	$-0.113073\pi$
$571$	44.8074	1.87513	0.937566	+	0.347806i	$0.113073\pi$
$572$	2.53694	0.106075
$573$	−21.1632	−0.884107
$574$	0.770089	0.0321429
$575$	21.4310	0.893736
$576$	2.00982	0.0837426
$577$	−21.1736	−0.881467	−0.440733	−	0.897638i	$-0.645282\pi$
$577$	−21.1736	−0.881467	−0.440733	+	0.897638i	$0.645282\pi$
$578$	11.1163	0.462376
$579$	2.04969	0.0851823
$580$	33.7684	1.40216
$581$	0.182897	0.00758784
$582$	−3.78077	−0.156718
$583$	−12.4510	−0.515669
$584$	−9.55694	−0.395469
$585$	−3.68550	−0.152376
$586$	−10.4544	−0.431869
$587$	40.0387	1.65258	0.826288	−	0.563248i	$-0.190449\pi$
$587$	40.0387	1.65258	0.826288	+	0.563248i	$0.190449\pi$
$588$	10.1980	0.420559
$589$	6.20559	0.255697
$590$	9.56964	0.393976
$591$	−5.53388	−0.227634
$592$	3.45902	0.142165
$593$	32.8599	1.34940	0.674698	−	0.738094i	$-0.264274\pi$
$593$	32.8599	1.34940	0.674698	+	0.738094i	$0.264274\pi$
$594$	1.24926	0.0512578
$595$	1.34339	0.0550735
$596$	−13.3913	−0.548528
$597$	−13.8517	−0.566914
$598$	−1.81178	−0.0740894
$599$	−18.5205	−0.756727	−0.378364	−	0.925657i	$-0.623513\pi$
$599$	−18.5205	−0.756727	−0.378364	+	0.925657i	$0.623513\pi$
$600$	21.6320	0.883124
$601$	15.1090	0.616308	0.308154	−	0.951336i	$-0.400289\pi$
$601$	15.1090	0.616308	0.308154	+	0.951336i	$0.400289\pi$
$602$	1.90275	0.0775501
$603$	−11.8815	−0.483850
$604$	1.06582	0.0433676
$605$	29.6157	1.20405
$606$	−7.02683	−0.285445
$607$	−2.31414	−0.0939280	−0.0469640	−	0.998897i	$-0.514955\pi$
$607$	−2.31414	−0.0939280	−0.0469640	+	0.998897i	$0.514955\pi$
$608$	37.3852	1.51617
$609$	−1.74877	−0.0708636
$610$	8.24169	0.333696
$611$	0.568426	0.0229960
$612$	−1.90980	−0.0771991
$613$	−17.6275	−0.711969	−0.355984	−	0.934492i	$-0.615854\pi$
$613$	−17.6275	−0.711969	−0.355984	+	0.934492i	$0.615854\pi$
$614$	−3.85873	−0.155726
$615$	−13.9082	−0.560832
$616$	1.22037	0.0491701
$617$	38.3478	1.54382	0.771912	−	0.635730i	$-0.219301\pi$
$617$	38.3478	1.54382	0.771912	+	0.635730i	$0.219301\pi$
$618$	0.725598	0.0291878
$619$	30.6497	1.23191	0.615957	−	0.787779i	$-0.288769\pi$
$619$	30.6497	1.23191	0.615957	+	0.787779i	$0.288769\pi$
$620$	−5.27528	−0.211860
$621$	2.49695	0.100199
$622$	−1.94555	−0.0780096
$623$	−0.0769293	−0.00308211
$624$	1.11824	0.0447653
$625$	5.75140	0.230056
$626$	−6.04427	−0.241578
$627$	10.9987	0.439247
$628$	−21.7772	−0.869004
$629$	4.00917	0.159856
$630$	−0.752077	−0.0299634
$631$	2.87102	0.114294	0.0571468	−	0.998366i	$-0.481800\pi$
$631$	2.87102	0.114294	0.0571468	+	0.998366i	$0.481800\pi$
$632$	−35.9992	−1.43197
$633$	−25.1800	−1.00082
$634$	18.5923	0.738396
$635$	28.3082	1.12338
$636$	−10.6561	−0.422544
$637$	−6.92091	−0.274216
$638$	7.76812	0.307543
$639$	−10.7513	−0.425314
$640$	−37.7614	−1.49265
$641$	21.4818	0.848481	0.424240	−	0.905550i	$-0.360541\pi$
$641$	21.4818	0.848481	0.424240	+	0.905550i	$0.360541\pi$
$642$	1.22268	0.0482552
$643$	33.7618	1.33143	0.665717	−	0.746204i	$-0.268126\pi$
$643$	33.7618	1.33143	0.665717	+	0.746204i	$0.268126\pi$
$644$	1.03474	0.0407746
$645$	−34.3645	−1.35310
$646$	6.00783	0.236375
$647$	−36.7450	−1.44459	−0.722297	−	0.691583i	$-0.756914\pi$
$647$	−36.7450	−1.44459	−0.722297	+	0.691583i	$0.756914\pi$
$648$	2.52037	0.0990095
$649$	−6.16114	−0.241846
$650$	−6.22772	−0.244271
$651$	0.273192	0.0107072
$652$	19.1352	0.749393
$653$	20.7146	0.810623	0.405312	−	0.914179i	$-0.367163\pi$
$653$	20.7146	0.810623	0.405312	+	0.914179i	$0.367163\pi$
$654$	3.95433	0.154626
$655$	61.0181	2.38418
$656$	4.21997	0.164762
$657$	−3.79188	−0.147935
$658$	0.115995	0.00452196
$659$	25.4495	0.991372	0.495686	−	0.868502i	$-0.334917\pi$
$659$	25.4495	0.991372	0.495686	+	0.868502i	$0.334917\pi$
$660$	−9.34987	−0.363943
$661$	−12.9529	−0.503811	−0.251906	−	0.967752i	$-0.581057\pi$
$661$	−12.9529	−0.503811	−0.251906	+	0.967752i	$0.581057\pi$
$662$	−2.60215	−0.101135
$663$	1.29609	0.0503360
$664$	−1.63908	−0.0636088
$665$	−6.62143	−0.256768
$666$	−2.24447	−0.0869716
$667$	15.5265	0.601187
$668$	16.5293	0.639537
$669$	−9.62409	−0.372089
$670$	−31.7733	−1.22751
$671$	−5.30617	−0.204843
$672$	1.64583	0.0634891
$673$	−31.0673	−1.19756	−0.598779	−	0.800914i	$-0.704347\pi$
$673$	−31.0673	−1.19756	−0.598779	+	0.800914i	$0.704347\pi$
$674$	7.85745	0.302658
$675$	8.58288	0.330355
$676$	−1.47351	−0.0566734
$677$	−3.78761	−0.145570	−0.0727848	−	0.997348i	$-0.523189\pi$
$677$	−3.78761	−0.145570	−0.0727848	+	0.997348i	$0.523189\pi$
$678$	−5.11576	−0.196470
$679$	−1.46539	−0.0562367
$680$	−12.0392	−0.461680
$681$	−14.3514	−0.549946
$682$	−1.21353	−0.0464685
$683$	−0.650097	−0.0248753	−0.0124376	−	0.999923i	$-0.503959\pi$
$683$	−0.650097	−0.0248753	−0.0124376	+	0.999923i	$0.503959\pi$
$684$	9.41321	0.359923
$685$	−53.9343	−2.06072
$686$	−2.84075	−0.108461
$687$	−21.0445	−0.802898
$688$	10.4267	0.397516
$689$	7.23182	0.275510
$690$	6.67732	0.254201
$691$	−15.3760	−0.584931	−0.292466	−	0.956276i	$-0.594476\pi$
$691$	−15.3760	−0.584931	−0.292466	+	0.956276i	$0.594476\pi$
$692$	7.45759	0.283495
$693$	0.484203	0.0183933
$694$	−6.20671	−0.235603
$695$	−18.1699	−0.689224
$696$	15.6721	0.594048
$697$	4.89114	0.185265
$698$	−9.96357	−0.377127
$699$	13.0503	0.493607
$700$	3.55676	0.134433
$701$	−42.5435	−1.60685	−0.803424	−	0.595408i	$-0.796991\pi$
$701$	−42.5435	−1.60685	−0.803424	+	0.595408i	$0.796991\pi$
$702$	−0.725598	−0.0273859
$703$	−19.7608	−0.745292
$704$	−3.46031	−0.130415
$705$	−2.09493	−0.0788997
$706$	−17.4186	−0.655557
$707$	−2.72354	−0.102429
$708$	−5.27298	−0.198171
$709$	−30.2954	−1.13777	−0.568884	−	0.822418i	$-0.692625\pi$
$709$	−30.2954	−1.13777	−0.568884	+	0.822418i	$0.692625\pi$
$710$	−28.7510	−1.07900
$711$	−14.2833	−0.535665
$712$	0.689424	0.0258373
$713$	−2.42553	−0.0908370
$714$	0.264485	0.00989812
$715$	6.34532	0.237301
$716$	−5.35236	−0.200027
$717$	−15.5604	−0.581112
$718$	14.3233	0.534540
$719$	1.17775	0.0439228	0.0219614	−	0.999759i	$-0.493009\pi$
$719$	1.17775	0.0439228	0.0219614	+	0.999759i	$0.493009\pi$
$720$	−4.12126	−0.153590
$721$	0.281235	0.0104738
$722$	−15.8256	−0.588969
$723$	−13.2899	−0.494258
$724$	9.63161	0.357956
$725$	53.3697	1.98210
$726$	5.83073	0.216399
$727$	6.46618	0.239817	0.119909	−	0.992785i	$-0.461740\pi$
$727$	6.46618	0.239817	0.119909	+	0.992785i	$0.461740\pi$
$728$	−0.708817	−0.0262705
$729$	1.00000	0.0370370
$730$	−10.1402	−0.375306
$731$	12.0851	0.446983
$732$	−4.54126	−0.167850
$733$	−3.38293	−0.124951	−0.0624757	−	0.998046i	$-0.519900\pi$
$733$	−3.38293	−0.124951	−0.0624757	+	0.998046i	$0.519900\pi$
$734$	8.94780	0.330269
$735$	25.5070	0.940839
$736$	−14.6125	−0.538624
$737$	20.4563	0.753517
$738$	−2.73824	−0.100796
$739$	−39.1822	−1.44134	−0.720669	−	0.693279i	$-0.756165\pi$
$739$	−39.1822	−1.44134	−0.720669	+	0.693279i	$0.756165\pi$
$740$	16.7984	0.617520
$741$	−6.38831	−0.234680
$742$	1.47575	0.0541766
$743$	−0.203423	−0.00746288	−0.00373144	−	0.999993i	$-0.501188\pi$
$743$	−0.203423	−0.00746288	−0.00373144	+	0.999993i	$0.501188\pi$
$744$	−2.44828	−0.0897584
$745$	−33.4939	−1.22712
$746$	−9.08761	−0.332721
$747$	−0.650334	−0.0237945
$748$	3.28810	0.120225
$749$	0.473898	0.0173159
$750$	9.58129	0.349859
$751$	−3.95310	−0.144251	−0.0721254	−	0.997396i	$-0.522978\pi$
$751$	−3.95310	−0.144251	−0.0721254	+	0.997396i	$0.522978\pi$
$752$	0.635635	0.0231792
$753$	−7.89965	−0.287879
$754$	−4.51189	−0.164313
$755$	2.66580	0.0970184
$756$	0.414402	0.0150717
$757$	−21.5184	−0.782100	−0.391050	−	0.920369i	$-0.627888\pi$
$757$	−21.5184	−0.782100	−0.391050	+	0.920369i	$0.627888\pi$
$758$	−12.8845	−0.467986
$759$	−4.29900	−0.156044
$760$	59.3398	2.15248
$761$	−30.9693	−1.12264	−0.561319	−	0.827600i	$-0.689706\pi$
$761$	−30.9693	−1.12264	−0.561319	+	0.827600i	$0.689706\pi$
$762$	5.57330	0.201899
$763$	1.53266	0.0554861
$764$	31.1842	1.12820
$765$	−4.77674	−0.172703
$766$	−19.1696	−0.692625
$767$	3.57852	0.129213
$768$	−11.4541	−0.413314
$769$	11.6305	0.419406	0.209703	−	0.977765i	$-0.432750\pi$
$769$	11.6305	0.419406	0.209703	+	0.977765i	$0.432750\pi$
$770$	1.29485	0.0466632
$771$	6.60275	0.237792
$772$	−3.02024	−0.108701
$773$	−20.0348	−0.720603	−0.360301	−	0.932836i	$-0.617326\pi$
$773$	−20.0348	−0.720603	−0.360301	+	0.932836i	$0.617326\pi$
$774$	−6.76567	−0.243187
$775$	−8.33739	−0.299488
$776$	13.1325	0.471431
$777$	−0.869938	−0.0312089
$778$	−0.886925	−0.0317978
$779$	−24.1080	−0.863757
$780$	5.43060	0.194447
$781$	18.5105	0.662357
$782$	−2.34824	−0.0839728
$783$	6.21816	0.222219
$784$	−7.73922	−0.276401
$785$	−54.4685	−1.94406
$786$	12.0132	0.428497
$787$	−17.5809	−0.626690	−0.313345	−	0.949639i	$-0.601450\pi$
$787$	−17.5809	−0.626690	−0.313345	+	0.949639i	$0.601450\pi$
$788$	8.15422	0.290482
$789$	7.27001	0.258819
$790$	−38.1962	−1.35896
$791$	−1.98282	−0.0705011
$792$	−4.33932	−0.154191
$793$	3.08194	0.109443
$794$	13.1689	0.467346
$795$	−26.6528	−0.945279
$796$	20.4106	0.723436
$797$	28.7282	1.01760	0.508802	−	0.860884i	$-0.330089\pi$
$797$	28.7282	1.01760	0.508802	+	0.860884i	$0.330089\pi$
$798$	−1.30362	−0.0461477
$799$	0.736732	0.0260637
$800$	−50.2281	−1.77583
$801$	0.273541	0.00966508
$802$	−17.8241	−0.629392
$803$	6.52848	0.230385
$804$	17.5074	0.617439
$805$	2.58807	0.0912175
$806$	0.704845	0.0248271
$807$	−32.1610	−1.13212
$808$	24.4077	0.858661
$809$	11.5658	0.406632	0.203316	−	0.979113i	$-0.434828\pi$
$809$	11.5658	0.406632	0.203316	+	0.979113i	$0.434828\pi$
$810$	2.67419	0.0939614
$811$	38.3664	1.34723	0.673613	−	0.739085i	$-0.264742\pi$
$811$	38.3664	1.34723	0.673613	+	0.739085i	$0.264742\pi$
$812$	2.57682	0.0904287
$813$	29.2718	1.02661
$814$	3.86431	0.135444
$815$	47.8605	1.67648
$816$	1.44934	0.0507370
$817$	−59.5662	−2.08396
$818$	−13.6126	−0.475955
$819$	−0.281235	−0.00982716
$820$	20.4938	0.715675
$821$	−16.0898	−0.561537	−0.280768	−	0.959776i	$-0.590589\pi$
$821$	−16.0898	−0.561537	−0.280768	+	0.959776i	$0.590589\pi$
$822$	−10.6186	−0.370365
$823$	−10.3355	−0.360271	−0.180136	−	0.983642i	$-0.557654\pi$
$823$	−10.3355	−0.360271	−0.180136	+	0.983642i	$0.557654\pi$
$824$	−2.52037	−0.0878013
$825$	−14.7771	−0.514474
$826$	0.730247	0.0254085
$827$	−42.3186	−1.47156	−0.735780	−	0.677221i	$-0.763184\pi$
$827$	−42.3186	−1.47156	−0.735780	+	0.677221i	$0.763184\pi$
$828$	−3.67928	−0.127864
$829$	2.57489	0.0894296	0.0447148	−	0.999000i	$-0.485762\pi$
$829$	2.57489	0.0894296	0.0447148	+	0.999000i	$0.485762\pi$
$830$	−1.73912	−0.0603656
$831$	−14.5030	−0.503102
$832$	2.00982	0.0696780
$833$	−8.97012	−0.310796
$834$	−3.57728	−0.123871
$835$	41.3426	1.43072
$836$	−16.2067	−0.560521
$837$	−0.971398	−0.0335764
$838$	10.0734	0.347980
$839$	25.5465	0.881964	0.440982	−	0.897516i	$-0.354630\pi$
$839$	25.5465	0.881964	0.440982	+	0.897516i	$0.354630\pi$
$840$	2.61234	0.0901344
$841$	9.66555	0.333295
$842$	22.3468	0.770121
$843$	−16.4124	−0.565271
$844$	37.1029	1.27714
$845$	−3.68550	−0.126785
$846$	−0.412449	−0.0141803
$847$	2.25994	0.0776524
$848$	8.08690	0.277705
$849$	−10.7312	−0.368294
$850$	−8.07169	−0.276857
$851$	7.72376	0.264767
$852$	15.8421	0.542741
$853$	8.17718	0.279981	0.139991	−	0.990153i	$-0.455293\pi$
$853$	8.17718	0.279981	0.139991	+	0.990153i	$0.455293\pi$
$854$	0.628912	0.0215209
$855$	23.5441	0.805190
$856$	−4.24697	−0.145159
$857$	30.0759	1.02737	0.513686	−	0.857978i	$-0.328280\pi$
$857$	30.0759	1.02737	0.513686	+	0.857978i	$0.328280\pi$
$858$	1.24926	0.0426491
$859$	21.7759	0.742984	0.371492	−	0.928436i	$-0.378846\pi$
$859$	21.7759	0.742984	0.371492	+	0.928436i	$0.378846\pi$
$860$	50.6364	1.72669
$861$	−1.06132	−0.0361696
$862$	11.4438	0.389777
$863$	−36.3682	−1.23799	−0.618993	−	0.785396i	$-0.712459\pi$
$863$	−36.3682	−1.23799	−0.618993	+	0.785396i	$0.712459\pi$
$864$	−5.85213	−0.199094
$865$	18.6527	0.634211
$866$	−17.9617	−0.610362
$867$	−15.3201	−0.520300
$868$	−0.402550	−0.0136634
$869$	24.5915	0.834211
$870$	16.6285	0.563760
$871$	−11.8815	−0.402588
$872$	−13.7354	−0.465139
$873$	5.21056	0.176351
$874$	11.5742	0.391504
$875$	3.71362	0.125543
$876$	5.58736	0.188779
$877$	−7.27382	−0.245620	−0.122810	−	0.992430i	$-0.539191\pi$
$877$	−7.27382	−0.245620	−0.122810	+	0.992430i	$0.539191\pi$
$878$	18.8598	0.636486
$879$	14.4080	0.485971
$880$	7.09557	0.239192
$881$	−20.1227	−0.677951	−0.338976	−	0.940795i	$-0.610080\pi$
$881$	−20.1227	−0.677951	−0.338976	+	0.940795i	$0.610080\pi$
$882$	5.02180	0.169093
$883$	29.9642	1.00837	0.504187	−	0.863594i	$-0.331792\pi$
$883$	29.9642	1.00837	0.504187	+	0.863594i	$0.331792\pi$
$884$	−1.90980	−0.0642335
$885$	−13.1886	−0.443331
$886$	17.8558	0.599876
$887$	−13.9672	−0.468973	−0.234486	−	0.972119i	$-0.575341\pi$
$887$	−13.9672	−0.468973	−0.234486	+	0.972119i	$0.575341\pi$
$888$	7.79620	0.261623
$889$	2.16016	0.0724494
$890$	0.731499	0.0245199
$891$	−1.72170	−0.0576791
$892$	14.1812	0.474820
$893$	−3.63128	−0.121516
$894$	−6.59425	−0.220545
$895$	−13.3872	−0.447484
$896$	−2.88152	−0.0962649
$897$	2.49695	0.0833708
$898$	10.3649	0.345883
$899$	−6.04031	−0.201456
$900$	−12.6469	−0.421564
$901$	9.37310	0.312263
$902$	4.71442	0.156973
$903$	−2.62231	−0.0872651
$904$	17.7696	0.591010
$905$	24.0903	0.800789
$906$	0.524841	0.0174367
$907$	27.2274	0.904070	0.452035	−	0.892000i	$-0.350698\pi$
$907$	27.2274	0.904070	0.452035	+	0.892000i	$0.350698\pi$
$908$	21.1469	0.701783
$909$	9.68419	0.321204
$910$	−0.752077	−0.0249311
$911$	−14.8169	−0.490907	−0.245454	−	0.969408i	$-0.578937\pi$
$911$	−14.8169	−0.490907	−0.245454	+	0.969408i	$0.578937\pi$
$912$	−7.14364	−0.236550
$913$	1.11968	0.0370560
$914$	15.1656	0.501633
$915$	−11.3585	−0.375500
$916$	31.0092	1.02457
$917$	4.65621	0.153762
$918$	−0.940441	−0.0310392
$919$	−0.697098	−0.0229951	−0.0114976	−	0.999934i	$-0.503660\pi$
$919$	−0.697098	−0.0229951	−0.0114976	+	0.999934i	$0.503660\pi$
$920$	−23.1937	−0.764674
$921$	5.31800	0.175234
$922$	−12.5157	−0.412183
$923$	−10.7513	−0.353883
$924$	−0.713476	−0.0234716
$925$	26.5492	0.872932
$926$	25.4129	0.835121
$927$	−1.00000	−0.0328443
$928$	−36.3895	−1.19454
$929$	−39.4874	−1.29554	−0.647770	−	0.761836i	$-0.724298\pi$
$929$	−39.4874	−1.29554	−0.647770	+	0.761836i	$0.724298\pi$
$930$	−2.59770	−0.0851820
$931$	44.2129	1.44902
$932$	−19.2297	−0.629890
$933$	2.68131	0.0877821
$934$	−17.6099	−0.576214
$935$	8.22411	0.268957
$936$	2.52037	0.0823809
$937$	−28.0500	−0.916354	−0.458177	−	0.888861i	$-0.651497\pi$
$937$	−28.0500	−0.916354	−0.458177	+	0.888861i	$0.651497\pi$
$938$	−2.42458	−0.0791652
$939$	8.33005	0.271841
$940$	3.08690	0.100683
$941$	−45.6151	−1.48701	−0.743505	−	0.668731i	$-0.766838\pi$
$941$	−45.6151	−1.48701	−0.743505	+	0.668731i	$0.766838\pi$
$942$	−10.7237	−0.349398
$943$	9.42291	0.306852
$944$	4.00164	0.130242
$945$	1.03649	0.0337171
$946$	11.6484	0.378724
$947$	20.1433	0.654568	0.327284	−	0.944926i	$-0.393867\pi$
$947$	20.1433	0.654568	0.327284	+	0.944926i	$0.393867\pi$
$948$	21.0465	0.683560
$949$	−3.79188	−0.123090
$950$	39.7846	1.29078
$951$	−25.6234	−0.830897
$952$	−0.918692	−0.0297750
$953$	−5.57968	−0.180744	−0.0903718	−	0.995908i	$-0.528806\pi$
$953$	−5.57968	−0.180744	−0.0903718	+	0.995908i	$0.528806\pi$
$954$	−5.24740	−0.169891
$955$	77.9970	2.52392
$956$	22.9283	0.741554
$957$	−10.7058	−0.346070
$958$	−28.9197	−0.934352
$959$	−4.11566	−0.132902
$960$	−7.40719	−0.239066
$961$	−30.0564	−0.969561
$962$	−2.24447	−0.0723648
$963$	−1.68506	−0.0543003
$964$	19.5828	0.630720
$965$	−7.55413	−0.243176
$966$	0.509538	0.0163941
$967$	34.8971	1.12221	0.561107	−	0.827743i	$-0.310376\pi$
$967$	34.8971	1.12221	0.561107	+	0.827743i	$0.310376\pi$
$968$	−20.2531	−0.650958
$969$	−8.27983	−0.265986
$970$	13.9340	0.447395
$971$	25.9765	0.833624	0.416812	−	0.908993i	$-0.363147\pi$
$971$	25.9765	0.833624	0.416812	+	0.908993i	$0.363147\pi$
$972$	−1.47351	−0.0472628
$973$	−1.38652	−0.0444499
$974$	−16.1258	−0.516704
$975$	8.58288	0.274872
$976$	3.44634	0.110315
$977$	−38.5508	−1.23335	−0.616675	−	0.787218i	$-0.711521\pi$
$977$	−38.5508	−1.23335	−0.616675	+	0.787218i	$0.711521\pi$
$978$	9.42274	0.301306
$979$	−0.470955	−0.0150518
$980$	−37.5847	−1.20060
$981$	−5.44975	−0.173997
$982$	−2.81538	−0.0898424
$983$	−16.5440	−0.527672	−0.263836	−	0.964568i	$-0.584988\pi$
$983$	−16.5440	−0.527672	−0.263836	+	0.964568i	$0.584988\pi$
$984$	9.51129	0.303209
$985$	20.3951	0.649842
$986$	−5.84782	−0.186232
$987$	−0.159861	−0.00508845
$988$	9.41321	0.299474
$989$	23.2822	0.740332
$990$	−4.60415	−0.146330
$991$	−58.6674	−1.86363	−0.931815	−	0.362934i	$-0.881775\pi$
$991$	−58.6674	−1.86363	−0.931815	+	0.362934i	$0.881775\pi$
$992$	5.68475	0.180491
$993$	3.58621	0.113805
$994$	−2.19395	−0.0695878
$995$	51.0505	1.61841
$996$	0.958272	0.0303640
$997$	−14.2120	−0.450098	−0.225049	−	0.974347i	$-0.572254\pi$
$997$	−14.2120	−0.450098	−0.225049	+	0.974347i	$0.572254\pi$
$998$	14.9226	0.472368
$999$	3.09327	0.0978669

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4017.2.a.f.1.9	✓	19

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4017.2.a.f.1.9	✓	19	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 4017 = 3 \cdot 13 \cdot 103 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4017.a (trivial)

\(f(q)\)	\(=\)	\(q-0.725598 q^{2} +1.00000 q^{3} -1.47351 q^{4} -3.68550 q^{5} -0.725598 q^{6} -0.281235 q^{7} +2.52037 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-0.725598 q^{2} +1.00000 q^{3} -1.47351 q^{4} -3.68550 q^{5} -0.725598 q^{6} -0.281235 q^{7} +2.52037 q^{8} +1.00000 q^{9} +2.67419 q^{10} -1.72170 q^{11} -1.47351 q^{12} +1.00000 q^{13} +0.204064 q^{14} -3.68550 q^{15} +1.11824 q^{16} +1.29609 q^{17} -0.725598 q^{18} -6.38831 q^{19} +5.43060 q^{20} -0.281235 q^{21} +1.24926 q^{22} +2.49695 q^{23} +2.52037 q^{24} +8.58288 q^{25} -0.725598 q^{26} +1.00000 q^{27} +0.414402 q^{28} +6.21816 q^{29} +2.67419 q^{30} -0.971398 q^{31} -5.85213 q^{32} -1.72170 q^{33} -0.940441 q^{34} +1.03649 q^{35} -1.47351 q^{36} +3.09327 q^{37} +4.63534 q^{38} +1.00000 q^{39} -9.28882 q^{40} +3.77376 q^{41} +0.204064 q^{42} +9.32426 q^{43} +2.53694 q^{44} -3.68550 q^{45} -1.81178 q^{46} +0.568426 q^{47} +1.11824 q^{48} -6.92091 q^{49} -6.22772 q^{50} +1.29609 q^{51} -1.47351 q^{52} +7.23182 q^{53} -0.725598 q^{54} +6.34532 q^{55} -0.708817 q^{56} -6.38831 q^{57} -4.51189 q^{58} +3.57852 q^{59} +5.43060 q^{60} +3.08194 q^{61} +0.704845 q^{62} -0.281235 q^{63} +2.00982 q^{64} -3.68550 q^{65} +1.24926 q^{66} -11.8815 q^{67} -1.90980 q^{68} +2.49695 q^{69} -0.752077 q^{70} -10.7513 q^{71} +2.52037 q^{72} -3.79188 q^{73} -2.24447 q^{74} +8.58288 q^{75} +9.41321 q^{76} +0.484203 q^{77} -0.725598 q^{78} -14.2833 q^{79} -4.12126 q^{80} +1.00000 q^{81} -2.73824 q^{82} -0.650334 q^{83} +0.414402 q^{84} -4.77674 q^{85} -6.76567 q^{86} +6.21816 q^{87} -4.33932 q^{88} +0.273541 q^{89} +2.67419 q^{90} -0.281235 q^{91} -3.67928 q^{92} -0.971398 q^{93} -0.412449 q^{94} +23.5441 q^{95} -5.85213 q^{96} +5.21056 q^{97} +5.02180 q^{98} -1.72170 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 19 q - 4 q^{2} + 19 q^{3} + 10 q^{4} - 3 q^{5} - 4 q^{6} - 23 q^{7} - 9 q^{8} + 19 q^{9}+O(q^{10}) \) 19 * q - 4 * q^2 + 19 * q^3 + 10 * q^4 - 3 * q^5 - 4 * q^6 - 23 * q^7 - 9 * q^8 + 19 * q^9	\( 19 q - 4 q^{2} + 19 q^{3} + 10 q^{4} - 3 q^{5} - 4 q^{6} - 23 q^{7} - 9 q^{8} + 19 q^{9} - 6 q^{10} - 15 q^{11} + 10 q^{12} + 19 q^{13} - 4 q^{14} - 3 q^{15} - 4 q^{16} - 4 q^{18} - 32 q^{19} - 8 q^{20} - 23 q^{21} - 9 q^{22} - 23 q^{23} - 9 q^{24} - 8 q^{25} - 4 q^{26} + 19 q^{27} - 22 q^{28} + 4 q^{29} - 6 q^{30} - 50 q^{31} - 2 q^{32} - 15 q^{33} - 35 q^{34} - 4 q^{35} + 10 q^{36} - 38 q^{37} + 20 q^{38} + 19 q^{39} - 30 q^{40} - 11 q^{41} - 4 q^{42} - 17 q^{43} - 29 q^{44} - 3 q^{45} - 5 q^{46} - 38 q^{47} - 4 q^{48} - 6 q^{49} - 9 q^{50} + 10 q^{52} - 12 q^{53} - 4 q^{54} - 22 q^{55} + 12 q^{56} - 32 q^{57} - 23 q^{58} - 8 q^{59} - 8 q^{60} - 31 q^{61} + 31 q^{62} - 23 q^{63} + 15 q^{64} - 3 q^{65} - 9 q^{66} - 48 q^{67} + 44 q^{68} - 23 q^{69} + 13 q^{70} - 14 q^{71} - 9 q^{72} - 50 q^{73} - 10 q^{74} - 8 q^{75} - 64 q^{76} + 23 q^{77} - 4 q^{78} - 21 q^{79} + 8 q^{80} + 19 q^{81} - 10 q^{82} - 15 q^{83} - 22 q^{84} - 29 q^{85} + 9 q^{86} + 4 q^{87} + 3 q^{88} - 10 q^{89} - 6 q^{90} - 23 q^{91} - 17 q^{92} - 50 q^{93} - 22 q^{94} - 25 q^{95} - 2 q^{96} - 42 q^{97} - q^{98} - 15 q^{99}+O(q^{100}) \) 19 * q - 4 * q^2 + 19 * q^3 + 10 * q^4 - 3 * q^5 - 4 * q^6 - 23 * q^7 - 9 * q^8 + 19 * q^9 - 6 * q^10 - 15 * q^11 + 10 * q^12 + 19 * q^13 - 4 * q^14 - 3 * q^15 - 4 * q^16 - 4 * q^18 - 32 * q^19 - 8 * q^20 - 23 * q^21 - 9 * q^22 - 23 * q^23 - 9 * q^24 - 8 * q^25 - 4 * q^26 + 19 * q^27 - 22 * q^28 + 4 * q^29 - 6 * q^30 - 50 * q^31 - 2 * q^32 - 15 * q^33 - 35 * q^34 - 4 * q^35 + 10 * q^36 - 38 * q^37 + 20 * q^38 + 19 * q^39 - 30 * q^40 - 11 * q^41 - 4 * q^42 - 17 * q^43 - 29 * q^44 - 3 * q^45 - 5 * q^46 - 38 * q^47 - 4 * q^48 - 6 * q^49 - 9 * q^50 + 10 * q^52 - 12 * q^53 - 4 * q^54 - 22 * q^55 + 12 * q^56 - 32 * q^57 - 23 * q^58 - 8 * q^59 - 8 * q^60 - 31 * q^61 + 31 * q^62 - 23 * q^63 + 15 * q^64 - 3 * q^65 - 9 * q^66 - 48 * q^67 + 44 * q^68 - 23 * q^69 + 13 * q^70 - 14 * q^71 - 9 * q^72 - 50 * q^73 - 10 * q^74 - 8 * q^75 - 64 * q^76 + 23 * q^77 - 4 * q^78 - 21 * q^79 + 8 * q^80 + 19 * q^81 - 10 * q^82 - 15 * q^83 - 22 * q^84 - 29 * q^85 + 9 * q^86 + 4 * q^87 + 3 * q^88 - 10 * q^89 - 6 * q^90 - 23 * q^91 - 17 * q^92 - 50 * q^93 - 22 * q^94 - 25 * q^95 - 2 * q^96 - 42 * q^97 - q^98 - 15 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more