LMFDB - Embedded newform 4018.2.a.bs.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4018,2,Mod(1,4018)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4018, 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("4018.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4018 = 2 \cdot 7^{2} \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4018.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:	$32.0838915322$
Analytic rank:	$0$
Dimension:	$10$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 2x^{9} - 17x^{8} + 36x^{7} + 75x^{6} - 174x^{5} - 69x^{4} + 260x^{3} - 104x^{2} - 24x + 14 $ x^10 - 2x^9 - 17x^8 + 36x^7 + 75x^6 - 174x^5 - 69x^4 + 260x^3 - 104x^2 - 24*x + 14
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-3.30199$ of defining polynomial
Character	$\chi$	$=$	4018.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -2.26016 q^{3} +1.00000 q^{4} +0.772879 q^{5} +2.26016 q^{6} -1.00000 q^{8} +2.10833 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -2.26016 q^{3} +1.00000 q^{4} +0.772879 q^{5} +2.26016 q^{6} -1.00000 q^{8} +2.10833 q^{9} -0.772879 q^{10} -1.39324 q^{11} -2.26016 q^{12} -1.97604 q^{13} -1.74683 q^{15} +1.00000 q^{16} +3.97677 q^{17} -2.10833 q^{18} -8.09994 q^{19} +0.772879 q^{20} +1.39324 q^{22} -6.31781 q^{23} +2.26016 q^{24} -4.40266 q^{25} +1.97604 q^{26} +2.01532 q^{27} -2.53459 q^{29} +1.74683 q^{30} +9.61026 q^{31} -1.00000 q^{32} +3.14894 q^{33} -3.97677 q^{34} +2.10833 q^{36} -9.00579 q^{37} +8.09994 q^{38} +4.46618 q^{39} -0.772879 q^{40} +1.00000 q^{41} +10.2182 q^{43} -1.39324 q^{44} +1.62948 q^{45} +6.31781 q^{46} +10.0924 q^{47} -2.26016 q^{48} +4.40266 q^{50} -8.98814 q^{51} -1.97604 q^{52} -13.7300 q^{53} -2.01532 q^{54} -1.07680 q^{55} +18.3072 q^{57} +2.53459 q^{58} -0.000549992 q^{59} -1.74683 q^{60} -7.48024 q^{61} -9.61026 q^{62} +1.00000 q^{64} -1.52724 q^{65} -3.14894 q^{66} +3.47021 q^{67} +3.97677 q^{68} +14.2793 q^{69} +1.50516 q^{71} -2.10833 q^{72} +0.581995 q^{73} +9.00579 q^{74} +9.95072 q^{75} -8.09994 q^{76} -4.46618 q^{78} +15.2384 q^{79} +0.772879 q^{80} -10.8799 q^{81} -1.00000 q^{82} -5.23409 q^{83} +3.07356 q^{85} -10.2182 q^{86} +5.72858 q^{87} +1.39324 q^{88} -14.2874 q^{89} -1.62948 q^{90} -6.31781 q^{92} -21.7208 q^{93} -10.0924 q^{94} -6.26027 q^{95} +2.26016 q^{96} +12.3270 q^{97} -2.93740 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 10 q^{2} + 4 q^{3} + 10 q^{4} + 4 q^{5} - 4 q^{6} - 10 q^{8} + 10 q^{9}+O(q^{10}) $ 10 * q - 10 * q^2 + 4 * q^3 + 10 * q^4 + 4 * q^5 - 4 * q^6 - 10 * q^8 + 10 * q^9	$ 10 q - 10 q^{2} + 4 q^{3} + 10 q^{4} + 4 q^{5} - 4 q^{6} - 10 q^{8} + 10 q^{9} - 4 q^{10} + 4 q^{11} + 4 q^{12} + 4 q^{13} + 4 q^{15} + 10 q^{16} + 20 q^{17} - 10 q^{18} + 4 q^{20} - 4 q^{22} + 4 q^{23} - 4 q^{24} + 6 q^{25} - 4 q^{26} + 16 q^{27} - 4 q^{29} - 4 q^{30} - 4 q^{31} - 10 q^{32} + 36 q^{33} - 20 q^{34} + 10 q^{36} - 16 q^{37} + 20 q^{39} - 4 q^{40} + 10 q^{41} - 8 q^{43} + 4 q^{44} + 4 q^{45} - 4 q^{46} + 24 q^{47} + 4 q^{48} - 6 q^{50} + 20 q^{51} + 4 q^{52} - 4 q^{53} - 16 q^{54} + 20 q^{55} - 4 q^{57} + 4 q^{58} + 4 q^{60} + 4 q^{62} + 10 q^{64} - 12 q^{65} - 36 q^{66} + 8 q^{67} + 20 q^{68} + 4 q^{71} - 10 q^{72} - 24 q^{73} + 16 q^{74} + 48 q^{75} - 20 q^{78} + 24 q^{79} + 4 q^{80} - 18 q^{81} - 10 q^{82} + 48 q^{83} + 8 q^{85} + 8 q^{86} + 4 q^{87} - 4 q^{88} + 20 q^{89} - 4 q^{90} + 4 q^{92} + 4 q^{93} - 24 q^{94} - 4 q^{95} - 4 q^{96} + 4 q^{97} + 32 q^{99}+O(q^{100}) $ 10 * q - 10 * q^2 + 4 * q^3 + 10 * q^4 + 4 * q^5 - 4 * q^6 - 10 * q^8 + 10 * q^9 - 4 * q^10 + 4 * q^11 + 4 * q^12 + 4 * q^13 + 4 * q^15 + 10 * q^16 + 20 * q^17 - 10 * q^18 + 4 * q^20 - 4 * q^22 + 4 * q^23 - 4 * q^24 + 6 * q^25 - 4 * q^26 + 16 * q^27 - 4 * q^29 - 4 * q^30 - 4 * q^31 - 10 * q^32 + 36 * q^33 - 20 * q^34 + 10 * q^36 - 16 * q^37 + 20 * q^39 - 4 * q^40 + 10 * q^41 - 8 * q^43 + 4 * q^44 + 4 * q^45 - 4 * q^46 + 24 * q^47 + 4 * q^48 - 6 * q^50 + 20 * q^51 + 4 * q^52 - 4 * q^53 - 16 * q^54 + 20 * q^55 - 4 * q^57 + 4 * q^58 + 4 * q^60 + 4 * q^62 + 10 * q^64 - 12 * q^65 - 36 * q^66 + 8 * q^67 + 20 * q^68 + 4 * q^71 - 10 * q^72 - 24 * q^73 + 16 * q^74 + 48 * q^75 - 20 * q^78 + 24 * q^79 + 4 * q^80 - 18 * q^81 - 10 * q^82 + 48 * q^83 + 8 * q^85 + 8 * q^86 + 4 * q^87 - 4 * q^88 + 20 * q^89 - 4 * q^90 + 4 * q^92 + 4 * q^93 - 24 * q^94 - 4 * q^95 - 4 * q^96 + 4 * q^97 + 32 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	−2.26016	−1.30491	−0.652453	−	0.757830i	$-0.726260\pi$
$3$	−2.26016	−1.30491	−0.652453	+	0.757830i	$0.726260\pi$
$4$	1.00000	0.500000
$5$	0.772879	0.345642	0.172821	−	0.984953i	$-0.444712\pi$
$5$	0.772879	0.345642	0.172821	+	0.984953i	$0.444712\pi$
$6$	2.26016	0.922707
$7$	0	0
$7$	0	0
$8$	−1.00000	−0.353553
$9$	2.10833	0.702777
$10$	−0.772879	−0.244406
$11$	−1.39324	−0.420077	−0.210038	−	0.977693i	$-0.567359\pi$
$11$	−1.39324	−0.420077	−0.210038	+	0.977693i	$0.567359\pi$
$12$	−2.26016	−0.652453
$13$	−1.97604	−0.548056	−0.274028	−	0.961722i	$-0.588356\pi$
$13$	−1.97604	−0.548056	−0.274028	+	0.961722i	$0.588356\pi$
$14$	0	0
$15$	−1.74683	−0.451030
$16$	1.00000	0.250000
$17$	3.97677	0.964508	0.482254	−	0.876032i	$-0.339818\pi$
$17$	3.97677	0.964508	0.482254	+	0.876032i	$0.339818\pi$
$18$	−2.10833	−0.496938
$19$	−8.09994	−1.85825	−0.929127	−	0.369760i	$-0.879440\pi$
$19$	−8.09994	−1.85825	−0.929127	+	0.369760i	$0.879440\pi$
$20$	0.772879	0.172821
$21$	0	0
$22$	1.39324	0.297039
$23$	−6.31781	−1.31735	−0.658677	−	0.752426i	$-0.728884\pi$
$23$	−6.31781	−1.31735	−0.658677	+	0.752426i	$0.728884\pi$
$24$	2.26016	0.461354
$25$	−4.40266	−0.880532
$26$	1.97604	0.387534
$27$	2.01532	0.387848
$28$	0	0
$29$	−2.53459	−0.470662	−0.235331	−	0.971915i	$-0.575617\pi$
$29$	−2.53459	−0.470662	−0.235331	+	0.971915i	$0.575617\pi$
$30$	1.74683	0.318926
$31$	9.61026	1.72605	0.863027	−	0.505157i	$-0.168566\pi$
$31$	9.61026	1.72605	0.863027	+	0.505157i	$0.168566\pi$
$32$	−1.00000	−0.176777
$33$	3.14894	0.548160
$34$	−3.97677	−0.682010
$35$	0	0
$36$	2.10833	0.351389
$37$	−9.00579	−1.48054	−0.740271	−	0.672308i	$-0.765303\pi$
$37$	−9.00579	−1.48054	−0.740271	+	0.672308i	$0.765303\pi$
$38$	8.09994	1.31398
$39$	4.46618	0.715161
$40$	−0.772879	−0.122203
$41$	1.00000	0.156174
$41$	1.00000	0.156174
$42$	0	0
$43$	10.2182	1.55826	0.779129	−	0.626864i	$-0.215662\pi$
$43$	10.2182	1.55826	0.779129	+	0.626864i	$0.215662\pi$
$44$	−1.39324	−0.210038
$45$	1.62948	0.242909
$46$	6.31781	0.931510
$47$	10.0924	1.47213	0.736066	−	0.676910i	$-0.236681\pi$
$47$	10.0924	1.47213	0.736066	+	0.676910i	$0.236681\pi$
$48$	−2.26016	−0.326226
$49$	0	0
$50$	4.40266	0.622630
$51$	−8.98814	−1.25859
$52$	−1.97604	−0.274028
$53$	−13.7300	−1.88597	−0.942983	−	0.332841i	$-0.891993\pi$
$53$	−13.7300	−1.88597	−0.942983	+	0.332841i	$0.891993\pi$
$54$	−2.01532	−0.274250
$55$	−1.07680	−0.145196
$56$	0	0
$57$	18.3072	2.42485
$58$	2.53459	0.332808
$59$	−0.000549992 0	−7.16029e−5 0	−3.58015e−5	−	1.00000i	$-0.500011\pi$
$59$	−0.000549992 0	−7.16029e−5 0	−3.58015e−5		1.00000i	$0.500011\pi$
$60$	−1.74683	−0.225515
$61$	−7.48024	−0.957747	−0.478873	−	0.877884i	$-0.658955\pi$
$61$	−7.48024	−0.957747	−0.478873	+	0.877884i	$0.658955\pi$
$62$	−9.61026	−1.22050
$63$	0	0
$64$	1.00000	0.125000
$65$	−1.52724	−0.189431
$66$	−3.14894	−0.387608
$67$	3.47021	0.423953	0.211977	−	0.977275i	$-0.432010\pi$
$67$	3.47021	0.423953	0.211977	+	0.977275i	$0.432010\pi$
$68$	3.97677	0.482254
$69$	14.2793	1.71902
$70$	0	0
$71$	1.50516	0.178630	0.0893151	−	0.996003i	$-0.471532\pi$
$71$	1.50516	0.178630	0.0893151	+	0.996003i	$0.471532\pi$
$72$	−2.10833	−0.248469
$73$	0.581995	0.0681173	0.0340587	−	0.999420i	$-0.489157\pi$
$73$	0.581995	0.0681173	0.0340587	+	0.999420i	$0.489157\pi$
$74$	9.00579	1.04690
$75$	9.95072	1.14901
$76$	−8.09994	−0.929127
$77$	0	0
$78$	−4.46618	−0.505695
$79$	15.2384	1.71445	0.857226	−	0.514940i	$-0.172186\pi$
$79$	15.2384	1.71445	0.857226	+	0.514940i	$0.172186\pi$
$80$	0.772879	0.0864105
$81$	−10.8799	−1.20888
$82$	−1.00000	−0.110432
$83$	−5.23409	−0.574517	−0.287258	−	0.957853i	$-0.592744\pi$
$83$	−5.23409	−0.574517	−0.287258	+	0.957853i	$0.592744\pi$
$84$	0	0
$85$	3.07356	0.333374
$86$	−10.2182	−1.10185
$87$	5.72858	0.614169
$88$	1.39324	0.148520
$89$	−14.2874	−1.51446	−0.757231	−	0.653147i	$-0.773448\pi$
$89$	−14.2874	−1.51446	−0.757231	+	0.653147i	$0.773448\pi$
$90$	−1.62948	−0.171763
$91$	0	0
$92$	−6.31781	−0.658677
$93$	−21.7208	−2.25234
$94$	−10.0924	−1.04095
$95$	−6.26027	−0.642291
$96$	2.26016	0.230677
$97$	12.3270	1.25162	0.625811	−	0.779975i	$-0.284768\pi$
$97$	12.3270	1.25162	0.625811	+	0.779975i	$0.284768\pi$
$98$	0	0
$99$	−2.93740	−0.295220
$100$	−4.40266	−0.440266
$101$	−4.03693	−0.401690	−0.200845	−	0.979623i	$-0.564369\pi$
$101$	−4.03693	−0.401690	−0.200845	+	0.979623i	$0.564369\pi$
$102$	8.98814	0.889958
$103$	0.199567	0.0196639	0.00983195	−	0.999952i	$-0.496870\pi$
$103$	0.199567	0.0196639	0.00983195	+	0.999952i	$0.496870\pi$
$104$	1.97604	0.193767
$105$	0	0
$106$	13.7300	1.33358
$107$	−8.79078	−0.849837	−0.424918	−	0.905232i	$-0.639697\pi$
$107$	−8.79078	−0.849837	−0.424918	+	0.905232i	$0.639697\pi$
$108$	2.01532	0.193924
$109$	−7.30849	−0.700026	−0.350013	−	0.936745i	$-0.613823\pi$
$109$	−7.30849	−0.700026	−0.350013	+	0.936745i	$0.613823\pi$
$110$	1.07680	0.102669
$111$	20.3545	1.93197
$112$	0	0
$113$	13.6804	1.28694	0.643472	−	0.765470i	$-0.277493\pi$
$113$	13.6804	1.28694	0.643472	+	0.765470i	$0.277493\pi$
$114$	−18.3072	−1.71462
$115$	−4.88290	−0.455333
$116$	−2.53459	−0.235331
$117$	−4.16615	−0.385161
$118$	0.000549992 0	5.06309e−5 0
$119$	0	0
$120$	1.74683	0.159463
$121$	−9.05889	−0.823536
$122$	7.48024	0.677229
$123$	−2.26016	−0.203792
$124$	9.61026	0.863027
$125$	−7.26711	−0.649990
$126$	0	0
$127$	0.155608	0.0138079	0.00690397	−	0.999976i	$-0.497802\pi$
$127$	0.155608	0.0138079	0.00690397	+	0.999976i	$0.497802\pi$
$128$	−1.00000	−0.0883883
$129$	−23.0947	−2.03338
$130$	1.52724	0.133948
$131$	14.5223	1.26882	0.634409	−	0.772998i	$-0.281244\pi$
$131$	14.5223	1.26882	0.634409	+	0.772998i	$0.281244\pi$
$132$	3.14894	0.274080
$133$	0	0
$134$	−3.47021	−0.299780
$135$	1.55759	0.134056
$136$	−3.97677	−0.341005
$137$	−0.811743	−0.0693519	−0.0346759	−	0.999399i	$-0.511040\pi$
$137$	−0.811743	−0.0693519	−0.0346759	+	0.999399i	$0.511040\pi$
$138$	−14.2793	−1.21553
$139$	−6.63367	−0.562661	−0.281330	−	0.959611i	$-0.590776\pi$
$139$	−6.63367	−0.562661	−0.281330	+	0.959611i	$0.590776\pi$
$140$	0	0
$141$	−22.8105	−1.92099
$142$	−1.50516	−0.126311
$143$	2.75310	0.230226
$144$	2.10833	0.175694
$145$	−1.95893	−0.162680
$146$	−0.581995	−0.0481662
$147$	0	0
$148$	−9.00579	−0.740271
$149$	9.02621	0.739456	0.369728	−	0.929140i	$-0.379451\pi$
$149$	9.02621	0.739456	0.369728	+	0.929140i	$0.379451\pi$
$150$	−9.95072	−0.812473
$151$	−0.689452	−0.0561068	−0.0280534	−	0.999606i	$-0.508931\pi$
$151$	−0.689452	−0.0561068	−0.0280534	+	0.999606i	$0.508931\pi$
$152$	8.09994	0.656992
$153$	8.38434	0.677834
$154$	0	0
$155$	7.42757	0.596597
$156$	4.46618	0.357580
$157$	22.7408	1.81491	0.907455	−	0.420149i	$-0.138022\pi$
$157$	22.7408	1.81491	0.907455	+	0.420149i	$0.138022\pi$
$158$	−15.2384	−1.21230
$159$	31.0321	2.46101
$160$	−0.772879	−0.0611014
$161$	0	0
$162$	10.8799	0.854808
$163$	−8.24038	−0.645436	−0.322718	−	0.946495i	$-0.604597\pi$
$163$	−8.24038	−0.645436	−0.322718	+	0.946495i	$0.604597\pi$
$164$	1.00000	0.0780869
$165$	2.43375	0.189467
$166$	5.23409	0.406245
$167$	20.1540	1.55956	0.779782	−	0.626051i	$-0.215330\pi$
$167$	20.1540	1.55956	0.779782	+	0.626051i	$0.215330\pi$
$168$	0	0
$169$	−9.09525	−0.699635
$170$	−3.07356	−0.235731
$171$	−17.0774	−1.30594
$172$	10.2182	0.779129
$173$	8.91038	0.677443	0.338722	−	0.940887i	$-0.390005\pi$
$173$	8.91038	0.677443	0.338722	+	0.940887i	$0.390005\pi$
$174$	−5.72858	−0.434283
$175$	0	0
$176$	−1.39324	−0.105019
$177$	0.00124307	9.34350e−5 0
$178$	14.2874	1.07089
$179$	15.5112	1.15936	0.579680	−	0.814844i	$-0.303178\pi$
$179$	15.5112	1.15936	0.579680	+	0.814844i	$0.303178\pi$
$180$	1.62948	0.121455
$181$	−14.2938	−1.06245	−0.531223	−	0.847232i	$-0.678267\pi$
$181$	−14.2938	−1.06245	−0.531223	+	0.847232i	$0.678267\pi$
$182$	0	0
$183$	16.9066	1.24977
$184$	6.31781	0.465755
$185$	−6.96038	−0.511738
$186$	21.7208	1.59264
$187$	−5.54058	−0.405167
$188$	10.0924	0.736066
$189$	0	0
$190$	6.26027	0.454168
$191$	−5.07611	−0.367294	−0.183647	−	0.982992i	$-0.558790\pi$
$191$	−5.07611	−0.367294	−0.183647	+	0.982992i	$0.558790\pi$
$192$	−2.26016	−0.163113
$193$	−2.29028	−0.164858	−0.0824289	−	0.996597i	$-0.526268\pi$
$193$	−2.29028	−0.164858	−0.0824289	+	0.996597i	$0.526268\pi$
$194$	−12.3270	−0.885030
$195$	3.45181	0.247190
$196$	0	0
$197$	−11.4511	−0.815855	−0.407928	−	0.913014i	$-0.633748\pi$
$197$	−11.4511	−0.815855	−0.407928	+	0.913014i	$0.633748\pi$
$198$	2.93740	0.208752
$199$	−13.2032	−0.935953	−0.467976	−	0.883741i	$-0.655017\pi$
$199$	−13.2032	−0.935953	−0.467976	+	0.883741i	$0.655017\pi$
$200$	4.40266	0.311315
$201$	−7.84323	−0.553219
$202$	4.03693	0.284038
$203$	0	0
$204$	−8.98814	−0.629295
$205$	0.772879	0.0539802
$206$	−0.199567	−0.0139045
$207$	−13.3200	−0.925806
$208$	−1.97604	−0.137014
$209$	11.2851	0.780609
$210$	0	0
$211$	−22.7102	−1.56343	−0.781717	−	0.623633i	$-0.785656\pi$
$211$	−22.7102	−1.56343	−0.781717	+	0.623633i	$0.785656\pi$
$212$	−13.7300	−0.942983
$213$	−3.40191	−0.233095
$214$	8.79078	0.600925
$215$	7.89741	0.538599
$216$	−2.01532	−0.137125
$217$	0	0
$218$	7.30849	0.494993
$219$	−1.31540	−0.0888867
$220$	−1.07680	−0.0725981
$221$	−7.85826	−0.528604
$222$	−20.3545	−1.36611
$223$	2.45474	0.164382	0.0821909	−	0.996617i	$-0.473808\pi$
$223$	2.45474	0.164382	0.0821909	+	0.996617i	$0.473808\pi$
$224$	0	0
$225$	−9.28226	−0.618817
$226$	−13.6804	−0.910007
$227$	6.86450	0.455613	0.227807	−	0.973706i	$-0.426845\pi$
$227$	6.86450	0.455613	0.227807	+	0.973706i	$0.426845\pi$
$228$	18.3072	1.21242
$229$	12.0116	0.793748	0.396874	−	0.917873i	$-0.370095\pi$
$229$	12.0116	0.793748	0.396874	+	0.917873i	$0.370095\pi$
$230$	4.88290	0.321969
$231$	0	0
$232$	2.53459	0.166404
$233$	−6.60611	−0.432781	−0.216390	−	0.976307i	$-0.569428\pi$
$233$	−6.60611	−0.432781	−0.216390	+	0.976307i	$0.569428\pi$
$234$	4.16615	0.272350
$235$	7.80022	0.508830
$236$	−0.000549992 0	−3.58015e−5 0
$237$	−34.4412	−2.23720
$238$	0	0
$239$	12.1265	0.784395	0.392198	−	0.919881i	$-0.371715\pi$
$239$	12.1265	0.784395	0.392198	+	0.919881i	$0.371715\pi$
$240$	−1.74683	−0.112757
$241$	3.69318	0.237899	0.118949	−	0.992900i	$-0.462047\pi$
$241$	3.69318	0.237899	0.118949	+	0.992900i	$0.462047\pi$
$242$	9.05889	0.582328
$243$	18.5445	1.18963
$244$	−7.48024	−0.478873
$245$	0	0
$246$	2.26016	0.144103
$247$	16.0058	1.01843
$248$	−9.61026	−0.610252
$249$	11.8299	0.749690
$250$	7.26711	0.459613
$251$	30.8877	1.94961	0.974807	−	0.223049i	$-0.0716009\pi$
$251$	30.8877	1.94961	0.974807	+	0.223049i	$0.0716009\pi$
$252$	0	0
$253$	8.80220	0.553390
$254$	−0.155608	−0.00976369
$255$	−6.94674	−0.435022
$256$	1.00000	0.0625000
$257$	−4.20015	−0.261998	−0.130999	−	0.991382i	$-0.541818\pi$
$257$	−4.20015	−0.261998	−0.130999	+	0.991382i	$0.541818\pi$
$258$	23.0947	1.43782
$259$	0	0
$260$	−1.52724	−0.0947155
$261$	−5.34376	−0.330770
$262$	−14.5223	−0.897190
$263$	30.5241	1.88220	0.941098	−	0.338135i	$-0.109796\pi$
$263$	30.5241	1.88220	0.941098	+	0.338135i	$0.109796\pi$
$264$	−3.14894	−0.193804
$265$	−10.6117	−0.651869
$266$	0	0
$267$	32.2919	1.97623
$268$	3.47021	0.211977
$269$	32.5136	1.98239	0.991196	−	0.132404i	$-0.0422697\pi$
$269$	32.5136	1.98239	0.991196	+	0.132404i	$0.0422697\pi$
$270$	−1.55759	−0.0947922
$271$	−32.3109	−1.96275	−0.981373	−	0.192110i	$-0.938467\pi$
$271$	−32.3109	−1.96275	−0.981373	+	0.192110i	$0.938467\pi$
$272$	3.97677	0.241127
$273$	0	0
$274$	0.811743	0.0490392
$275$	6.13395	0.369891
$276$	14.2793	0.859511
$277$	−4.39472	−0.264053	−0.132027	−	0.991246i	$-0.542148\pi$
$277$	−4.39472	−0.264053	−0.132027	+	0.991246i	$0.542148\pi$
$278$	6.63367	0.397861
$279$	20.2616	1.21303
$280$	0	0
$281$	12.9587	0.773049	0.386524	−	0.922279i	$-0.373676\pi$
$281$	12.9587	0.773049	0.386524	+	0.922279i	$0.373676\pi$
$282$	22.8105	1.35835
$283$	−4.72268	−0.280734	−0.140367	−	0.990100i	$-0.544828\pi$
$283$	−4.72268	−0.280734	−0.140367	+	0.990100i	$0.544828\pi$
$284$	1.50516	0.0893151
$285$	14.1492	0.838128
$286$	−2.75310	−0.162794
$287$	0	0
$288$	−2.10833	−0.124235
$289$	−1.18533	−0.0697251
$290$	1.95893	0.115032
$291$	−27.8611	−1.63325
$292$	0.581995	0.0340587
$293$	6.13087	0.358169	0.179085	−	0.983834i	$-0.442686\pi$
$293$	6.13087	0.358169	0.179085	+	0.983834i	$0.442686\pi$
$294$	0	0
$295$	−0.000425077 0	−2.47490e−5 0
$296$	9.00579	0.523451
$297$	−2.80781	−0.162926
$298$	−9.02621	−0.522874
$299$	12.4843	0.721983
$300$	9.95072	0.574505
$301$	0	0
$302$	0.689452	0.0396735
$303$	9.12412	0.524167
$304$	−8.09994	−0.464564
$305$	−5.78132	−0.331037
$306$	−8.38434	−0.479301
$307$	29.2599	1.66995	0.834975	−	0.550287i	$-0.185482\pi$
$307$	29.2599	1.66995	0.834975	+	0.550287i	$0.185482\pi$
$308$	0	0
$309$	−0.451053	−0.0256595
$310$	−7.42757	−0.421858
$311$	11.1501	0.632264	0.316132	−	0.948715i	$-0.397616\pi$
$311$	11.1501	0.632264	0.316132	+	0.948715i	$0.397616\pi$
$312$	−4.46618	−0.252848
$313$	10.0610	0.568682	0.284341	−	0.958723i	$-0.408225\pi$
$313$	10.0610	0.568682	0.284341	+	0.958723i	$0.408225\pi$
$314$	−22.7408	−1.28334
$315$	0	0
$316$	15.2384	0.857226
$317$	7.92317	0.445010	0.222505	−	0.974932i	$-0.428577\pi$
$317$	7.92317	0.445010	0.222505	+	0.974932i	$0.428577\pi$
$318$	−31.0321	−1.74019
$319$	3.53128	0.197714
$320$	0.772879	0.0432052
$321$	19.8686	1.10896
$322$	0	0
$323$	−32.2116	−1.79230
$324$	−10.8799	−0.604441
$325$	8.69984	0.482581
$326$	8.24038	0.456393
$327$	16.5184	0.913468
$328$	−1.00000	−0.0552158
$329$	0	0
$330$	−2.43375	−0.133973
$331$	−7.35260	−0.404136	−0.202068	−	0.979372i	$-0.564766\pi$
$331$	−7.35260	−0.404136	−0.202068	+	0.979372i	$0.564766\pi$
$332$	−5.23409	−0.287258
$333$	−18.9872	−1.04049
$334$	−20.1540	−1.10278
$335$	2.68205	0.146536
$336$	0	0
$337$	28.9055	1.57458	0.787292	−	0.616581i	$-0.211483\pi$
$337$	28.9055	1.57458	0.787292	+	0.616581i	$0.211483\pi$
$338$	9.09525	0.494717
$339$	−30.9199	−1.67934
$340$	3.07356	0.166687
$341$	−13.3894	−0.725075
$342$	17.0774	0.923438
$343$	0	0
$344$	−10.2182	−0.550927
$345$	11.0361	0.594166
$346$	−8.91038	−0.479025
$347$	30.3051	1.62686	0.813431	−	0.581661i	$-0.197597\pi$
$347$	30.3051	1.62686	0.813431	+	0.581661i	$0.197597\pi$
$348$	5.72858	0.307084
$349$	3.39269	0.181607	0.0908033	−	0.995869i	$-0.471057\pi$
$349$	3.39269	0.181607	0.0908033	+	0.995869i	$0.471057\pi$
$350$	0	0
$351$	−3.98235	−0.212562
$352$	1.39324	0.0742598
$353$	−4.03515	−0.214770	−0.107385	−	0.994218i	$-0.534248\pi$
$353$	−4.03515	−0.214770	−0.107385	+	0.994218i	$0.534248\pi$
$354$	−0.00124307	−6.60685e−5 0
$355$	1.16331	0.0617421
$356$	−14.2874	−0.757231
$357$	0	0
$358$	−15.5112	−0.819791
$359$	20.7104	1.09305	0.546526	−	0.837442i	$-0.315950\pi$
$359$	20.7104	1.09305	0.546526	+	0.837442i	$0.315950\pi$
$360$	−1.62948	−0.0858814
$361$	46.6091	2.45311
$362$	14.2938	0.751263
$363$	20.4746	1.07464
$364$	0	0
$365$	0.449811	0.0235442
$366$	−16.9066	−0.883720
$367$	4.80523	0.250831	0.125415	−	0.992104i	$-0.459974\pi$
$367$	4.80523	0.250831	0.125415	+	0.992104i	$0.459974\pi$
$368$	−6.31781	−0.329338
$369$	2.10833	0.109755
$370$	6.96038	0.361853
$371$	0	0
$372$	−21.7208	−1.12617
$373$	4.44046	0.229918	0.114959	−	0.993370i	$-0.463326\pi$
$373$	4.44046	0.229918	0.114959	+	0.993370i	$0.463326\pi$
$374$	5.54058	0.286496
$375$	16.4249	0.848176
$376$	−10.0924	−0.520477
$377$	5.00846	0.257949
$378$	0	0
$379$	13.2860	0.682455	0.341228	−	0.939981i	$-0.389157\pi$
$379$	13.2860	0.682455	0.341228	+	0.939981i	$0.389157\pi$
$380$	−6.26027	−0.321145
$381$	−0.351698	−0.0180180
$382$	5.07611	0.259716
$383$	19.1831	0.980211	0.490105	−	0.871663i	$-0.336958\pi$
$383$	19.1831	0.980211	0.490105	+	0.871663i	$0.336958\pi$
$384$	2.26016	0.115338
$385$	0	0
$386$	2.29028	0.116572
$387$	21.5433	1.09511
$388$	12.3270	0.625811
$389$	5.44777	0.276213	0.138106	−	0.990417i	$-0.455898\pi$
$389$	5.44777	0.276213	0.138106	+	0.990417i	$0.455898\pi$
$390$	−3.45181	−0.174789
$391$	−25.1244	−1.27060
$392$	0	0
$393$	−32.8227	−1.65569
$394$	11.4511	0.576897
$395$	11.7774	0.592586
$396$	−2.93740	−0.147610
$397$	30.7758	1.54459	0.772297	−	0.635262i	$-0.219108\pi$
$397$	30.7758	1.54459	0.772297	+	0.635262i	$0.219108\pi$
$398$	13.2032	0.661818
$399$	0	0
$400$	−4.40266	−0.220133
$401$	33.7550	1.68564	0.842821	−	0.538194i	$-0.180893\pi$
$401$	33.7550	1.68564	0.842821	+	0.538194i	$0.180893\pi$
$402$	7.84323	0.391185
$403$	−18.9903	−0.945974
$404$	−4.03693	−0.200845
$405$	−8.40887	−0.417840
$406$	0	0
$407$	12.5472	0.621941
$408$	8.98814	0.444979
$409$	6.28801	0.310922	0.155461	−	0.987842i	$-0.450314\pi$
$409$	6.28801	0.310922	0.155461	+	0.987842i	$0.450314\pi$
$410$	−0.772879	−0.0381698
$411$	1.83467	0.0904976
$412$	0.199567	0.00983195
$413$	0	0
$414$	13.3200	0.654644
$415$	−4.04532	−0.198577
$416$	1.97604	0.0968835
$417$	14.9932	0.734219
$418$	−11.2851	−0.551974
$419$	−31.6431	−1.54587	−0.772933	−	0.634487i	$-0.781211\pi$
$419$	−31.6431	−1.54587	−0.772933	+	0.634487i	$0.781211\pi$
$420$	0	0
$421$	30.7791	1.50008	0.750041	−	0.661391i	$-0.230034\pi$
$421$	30.7791	1.50008	0.750041	+	0.661391i	$0.230034\pi$
$422$	22.7102	1.10552
$423$	21.2782	1.03458
$424$	13.7300	0.666790
$425$	−17.5083	−0.849280
$426$	3.40191	0.164823
$427$	0	0
$428$	−8.79078	−0.424918
$429$	−6.22244	−0.300422
$430$	−7.89741	−0.380847
$431$	−26.4709	−1.27506	−0.637529	−	0.770427i	$-0.720043\pi$
$431$	−26.4709	−1.27506	−0.637529	+	0.770427i	$0.720043\pi$
$432$	2.01532	0.0969619
$433$	−32.9273	−1.58238	−0.791192	−	0.611567i	$-0.790539\pi$
$433$	−32.9273	−1.58238	−0.791192	+	0.611567i	$0.790539\pi$
$434$	0	0
$435$	4.42750	0.212282
$436$	−7.30849	−0.350013
$437$	51.1739	2.44798
$438$	1.31540	0.0628524
$439$	0.793640	0.0378784	0.0189392	−	0.999821i	$-0.493971\pi$
$439$	0.793640	0.0378784	0.0189392	+	0.999821i	$0.493971\pi$
$440$	1.07680	0.0513346
$441$	0	0
$442$	7.85826	0.373779
$443$	−5.53151	−0.262810	−0.131405	−	0.991329i	$-0.541949\pi$
$443$	−5.53151	−0.262810	−0.131405	+	0.991329i	$0.541949\pi$
$444$	20.3545	0.965984
$445$	−11.0424	−0.523462
$446$	−2.45474	−0.116235
$447$	−20.4007	−0.964920
$448$	0	0
$449$	17.1307	0.808448	0.404224	−	0.914660i	$-0.367542\pi$
$449$	17.1307	0.808448	0.404224	+	0.914660i	$0.367542\pi$
$450$	9.28226	0.437570
$451$	−1.39324	−0.0656050
$452$	13.6804	0.643472
$453$	1.55827	0.0732140
$454$	−6.86450	−0.322167
$455$	0	0
$456$	−18.3072	−0.857312
$457$	23.9352	1.11964	0.559821	−	0.828613i	$-0.310870\pi$
$457$	23.9352	1.11964	0.559821	+	0.828613i	$0.310870\pi$
$458$	−12.0116	−0.561265
$459$	8.01444	0.374082
$460$	−4.88290	−0.227666
$461$	12.8897	0.600333	0.300166	−	0.953887i	$-0.402958\pi$
$461$	12.8897	0.600333	0.300166	+	0.953887i	$0.402958\pi$
$462$	0	0
$463$	16.8067	0.781073	0.390537	−	0.920587i	$-0.372289\pi$
$463$	16.8067	0.781073	0.390537	+	0.920587i	$0.372289\pi$
$464$	−2.53459	−0.117665
$465$	−16.7875	−0.778502
$466$	6.60611	0.306022
$467$	−9.02937	−0.417829	−0.208915	−	0.977934i	$-0.566993\pi$
$467$	−9.02937	−0.417829	−0.208915	+	0.977934i	$0.566993\pi$
$468$	−4.16615	−0.192581
$469$	0	0
$470$	−7.80022	−0.359797
$471$	−51.3978	−2.36829
$472$	0.000549992 0	2.53155e−5 0
$473$	−14.2363	−0.654588
$474$	34.4412	1.58194
$475$	35.6613	1.63625
$476$	0	0
$477$	−28.9475	−1.32541
$478$	−12.1265	−0.554651
$479$	−16.9352	−0.773791	−0.386895	−	0.922124i	$-0.626453\pi$
$479$	−16.9352	−0.773791	−0.386895	+	0.922124i	$0.626453\pi$
$480$	1.74683	0.0797316
$481$	17.7958	0.811420
$482$	−3.69318	−0.168220
$483$	0	0
$484$	−9.05889	−0.411768
$485$	9.52731	0.432613
$486$	−18.5445	−0.841194
$487$	−16.1613	−0.732340	−0.366170	−	0.930548i	$-0.619331\pi$
$487$	−16.1613	−0.732340	−0.366170	+	0.930548i	$0.619331\pi$
$488$	7.48024	0.338615
$489$	18.6246	0.842233
$490$	0	0
$491$	37.2140	1.67944	0.839721	−	0.543018i	$-0.182718\pi$
$491$	37.2140	1.67944	0.839721	+	0.543018i	$0.182718\pi$
$492$	−2.26016	−0.101896
$493$	−10.0795	−0.453957
$494$	−16.0058	−0.720137
$495$	−2.27026	−0.102040
$496$	9.61026	0.431514
$497$	0	0
$498$	−11.8299	−0.530111
$499$	−18.1524	−0.812612	−0.406306	−	0.913737i	$-0.633183\pi$
$499$	−18.1524	−0.812612	−0.406306	+	0.913737i	$0.633183\pi$
$500$	−7.26711	−0.324995
$501$	−45.5513	−2.03508
$502$	−30.8877	−1.37859
$503$	−8.27794	−0.369095	−0.184548	−	0.982824i	$-0.559082\pi$
$503$	−8.27794	−0.369095	−0.184548	+	0.982824i	$0.559082\pi$
$504$	0	0
$505$	−3.12006	−0.138841
$506$	−8.80220	−0.391306
$507$	20.5567	0.912957
$508$	0.155608	0.00690397
$509$	14.0158	0.621238	0.310619	−	0.950535i	$-0.399464\pi$
$509$	14.0158	0.621238	0.310619	+	0.950535i	$0.399464\pi$
$510$	6.94674	0.307607
$511$	0	0
$512$	−1.00000	−0.0441942
$513$	−16.3239	−0.720720
$514$	4.20015	0.185261
$515$	0.154241	0.00679666
$516$	−23.0947	−1.01669
$517$	−14.0611	−0.618408
$518$	0	0
$519$	−20.1389	−0.883999
$520$	1.52724	0.0669740
$521$	27.1775	1.19067	0.595333	−	0.803479i	$-0.297020\pi$
$521$	27.1775	1.19067	0.595333	+	0.803479i	$0.297020\pi$
$522$	5.34376	0.233890
$523$	14.7432	0.644675	0.322338	−	0.946625i	$-0.395531\pi$
$523$	14.7432	0.644675	0.322338	+	0.946625i	$0.395531\pi$
$524$	14.5223	0.634409
$525$	0	0
$526$	−30.5241	−1.33091
$527$	38.2178	1.66479
$528$	3.14894	0.137040
$529$	16.9147	0.735420
$530$	10.6117	0.460941
$531$	−0.00115957	−5.03209e−5 0
$532$	0	0
$533$	−1.97604	−0.0855919
$534$	−32.2919	−1.39741
$535$	−6.79421	−0.293739
$536$	−3.47021	−0.149890
$537$	−35.0578	−1.51285
$538$	−32.5136	−1.40176
$539$	0	0
$540$	1.55759	0.0670282
$541$	−45.4433	−1.95376	−0.976880	−	0.213787i	$-0.931420\pi$
$541$	−45.4433	−1.95376	−0.976880	+	0.213787i	$0.931420\pi$
$542$	32.3109	1.38787
$543$	32.3062	1.38639
$544$	−3.97677	−0.170502
$545$	−5.64857	−0.241958
$546$	0	0
$547$	−18.8576	−0.806294	−0.403147	−	0.915135i	$-0.632084\pi$
$547$	−18.8576	−0.806294	−0.403147	+	0.915135i	$0.632084\pi$
$548$	−0.811743	−0.0346759
$549$	−15.7708	−0.673083
$550$	−6.13395	−0.261552
$551$	20.5300	0.874609
$552$	−14.2793	−0.607766
$553$	0	0
$554$	4.39472	0.186714
$555$	15.7316	0.667769
$556$	−6.63367	−0.281330
$557$	−1.21427	−0.0514504	−0.0257252	−	0.999669i	$-0.508189\pi$
$557$	−1.21427	−0.0514504	−0.0257252	+	0.999669i	$0.508189\pi$
$558$	−20.2616	−0.857743
$559$	−20.1916	−0.854012
$560$	0	0
$561$	12.5226	0.528705
$562$	−12.9587	−0.546628
$563$	−9.28139	−0.391164	−0.195582	−	0.980687i	$-0.562660\pi$
$563$	−9.28139	−0.391164	−0.195582	+	0.980687i	$0.562660\pi$
$564$	−22.8105	−0.960496
$565$	10.5733	0.444822
$566$	4.72268	0.198509
$567$	0	0
$568$	−1.50516	−0.0631553
$569$	−14.1111	−0.591568	−0.295784	−	0.955255i	$-0.595581\pi$
$569$	−14.1111	−0.591568	−0.295784	+	0.955255i	$0.595581\pi$
$570$	−14.1492	−0.592646
$571$	−11.3313	−0.474199	−0.237099	−	0.971485i	$-0.576197\pi$
$571$	−11.3313	−0.474199	−0.237099	+	0.971485i	$0.576197\pi$
$572$	2.75310	0.115113
$573$	11.4728	0.479284
$574$	0	0
$575$	27.8151	1.15997
$576$	2.10833	0.0878471
$577$	30.8293	1.28344	0.641721	−	0.766938i	$-0.278221\pi$
$577$	30.8293	1.28344	0.641721	+	0.766938i	$0.278221\pi$
$578$	1.18533	0.0493031
$579$	5.17640	0.215124
$580$	−1.95893	−0.0813402
$581$	0	0
$582$	27.8611	1.15488
$583$	19.1292	0.792250
$584$	−0.581995	−0.0240831
$585$	−3.21993	−0.133128
$586$	−6.13087	−0.253264
$587$	−32.5614	−1.34395	−0.671976	−	0.740573i	$-0.734554\pi$
$587$	−32.5614	−1.34395	−0.671976	+	0.740573i	$0.734554\pi$
$588$	0	0
$589$	−77.8426	−3.20745
$590$	0.000425077 0	1.75002e−5 0
$591$	25.8813	1.06461
$592$	−9.00579	−0.370136
$593$	32.1485	1.32018	0.660091	−	0.751186i	$-0.270518\pi$
$593$	32.1485	1.32018	0.660091	+	0.751186i	$0.270518\pi$
$594$	2.80781	0.115206
$595$	0	0
$596$	9.02621	0.369728
$597$	29.8415	1.22133
$598$	−12.4843	−0.510519
$599$	−34.9613	−1.42848	−0.714240	−	0.699901i	$-0.753228\pi$
$599$	−34.9613	−1.42848	−0.714240	+	0.699901i	$0.753228\pi$
$600$	−9.95072	−0.406236
$601$	8.27457	0.337527	0.168763	−	0.985657i	$-0.446023\pi$
$601$	8.27457	0.337527	0.168763	+	0.985657i	$0.446023\pi$
$602$	0	0
$603$	7.31634	0.297945
$604$	−0.689452	−0.0280534
$605$	−7.00142	−0.284648
$606$	−9.12412	−0.370642
$607$	−47.6053	−1.93224	−0.966119	−	0.258098i	$-0.916904\pi$
$607$	−47.6053	−1.93224	−0.966119	+	0.258098i	$0.916904\pi$
$608$	8.09994	0.328496
$609$	0	0
$610$	5.78132	0.234079
$611$	−19.9431	−0.806810
$612$	8.38434	0.338917
$613$	6.33067	0.255693	0.127847	−	0.991794i	$-0.459193\pi$
$613$	6.33067	0.255693	0.127847	+	0.991794i	$0.459193\pi$
$614$	−29.2599	−1.18083
$615$	−1.74683	−0.0704390
$616$	0	0
$617$	−11.7002	−0.471030	−0.235515	−	0.971871i	$-0.575678\pi$
$617$	−11.7002	−0.471030	−0.235515	+	0.971871i	$0.575678\pi$
$618$	0.451053	0.0181440
$619$	−34.8967	−1.40262	−0.701309	−	0.712857i	$-0.747401\pi$
$619$	−34.8967	−1.40262	−0.701309	+	0.712857i	$0.747401\pi$
$620$	7.42757	0.298298
$621$	−12.7324	−0.510933
$622$	−11.1501	−0.447078
$623$	0	0
$624$	4.46618	0.178790
$625$	16.3967	0.655868
$626$	−10.0610	−0.402119
$627$	−25.5062	−1.01862
$628$	22.7408	0.907455
$629$	−35.8139	−1.42799
$630$	0	0
$631$	−36.9553	−1.47117	−0.735584	−	0.677434i	$-0.763092\pi$
$631$	−36.9553	−1.47117	−0.735584	+	0.677434i	$0.763092\pi$
$632$	−15.2384	−0.606150
$633$	51.3287	2.04013
$634$	−7.92317	−0.314669
$635$	0.120266	0.00477260
$636$	31.0321	1.23050
$637$	0	0
$638$	−3.53128	−0.139805
$639$	3.17338	0.125537
$640$	−0.772879	−0.0305507
$641$	−42.5111	−1.67909	−0.839544	−	0.543291i	$-0.817178\pi$
$641$	−42.5111	−1.67909	−0.839544	+	0.543291i	$0.817178\pi$
$642$	−19.8686	−0.784150
$643$	−10.4301	−0.411322	−0.205661	−	0.978623i	$-0.565934\pi$
$643$	−10.4301	−0.411322	−0.205661	+	0.978623i	$0.565934\pi$
$644$	0	0
$645$	−17.8494	−0.702821
$646$	32.2116	1.26735
$647$	12.5732	0.494304	0.247152	−	0.968977i	$-0.420505\pi$
$647$	12.5732	0.494304	0.247152	+	0.968977i	$0.420505\pi$
$648$	10.8799	0.427404
$649$	0.000766270 0	3.00787e−5 0
$650$	−8.69984	−0.341236
$651$	0	0
$652$	−8.24038	−0.322718
$653$	29.3572	1.14884	0.574418	−	0.818562i	$-0.305228\pi$
$653$	29.3572	1.14884	0.574418	+	0.818562i	$0.305228\pi$
$654$	−16.5184	−0.645919
$655$	11.2240	0.438557
$656$	1.00000	0.0390434
$657$	1.22704	0.0478713
$658$	0	0
$659$	−31.8927	−1.24236	−0.621181	−	0.783667i	$-0.713347\pi$
$659$	−31.8927	−1.24236	−0.621181	+	0.783667i	$0.713347\pi$
$660$	2.43375	0.0947336
$661$	−4.30058	−0.167273	−0.0836367	−	0.996496i	$-0.526654\pi$
$661$	−4.30058	−0.167273	−0.0836367	+	0.996496i	$0.526654\pi$
$662$	7.35260	0.285767
$663$	17.7609	0.689778
$664$	5.23409	0.203122
$665$	0	0
$666$	18.9872	0.735738
$667$	16.0130	0.620028
$668$	20.1540	0.779782
$669$	−5.54811	−0.214503
$670$	−2.68205	−0.103617
$671$	10.4217	0.402327
$672$	0	0
$673$	−33.1937	−1.27952	−0.639762	−	0.768573i	$-0.720967\pi$
$673$	−33.1937	−1.27952	−0.639762	+	0.768573i	$0.720967\pi$
$674$	−28.9055	−1.11340
$675$	−8.87275	−0.341512
$676$	−9.09525	−0.349817
$677$	27.7764	1.06753	0.533767	−	0.845632i	$-0.320776\pi$
$677$	27.7764	1.06753	0.533767	+	0.845632i	$0.320776\pi$
$678$	30.9199	1.18747
$679$	0	0
$680$	−3.07356	−0.117866
$681$	−15.5149	−0.594532
$682$	13.3894	0.512706
$683$	39.6291	1.51637	0.758183	−	0.652042i	$-0.226087\pi$
$683$	39.6291	1.51637	0.758183	+	0.652042i	$0.226087\pi$
$684$	−17.0774	−0.652969
$685$	−0.627379	−0.0239709
$686$	0	0
$687$	−27.1481	−1.03577
$688$	10.2182	0.389564
$689$	27.1311	1.03361
$690$	−11.0361	−0.420139
$691$	14.2765	0.543104	0.271552	−	0.962424i	$-0.412463\pi$
$691$	14.2765	0.543104	0.271552	+	0.962424i	$0.412463\pi$
$692$	8.91038	0.338722
$693$	0	0
$694$	−30.3051	−1.15037
$695$	−5.12702	−0.194479
$696$	−5.72858	−0.217141
$697$	3.97677	0.150631
$698$	−3.39269	−0.128415
$699$	14.9309	0.564738
$700$	0	0
$701$	19.3922	0.732434	0.366217	−	0.930529i	$-0.380653\pi$
$701$	19.3922	0.732434	0.366217	+	0.930529i	$0.380653\pi$
$702$	3.98235	0.150304
$703$	72.9464	2.75122
$704$	−1.39324	−0.0525096
$705$	−17.6298	−0.663975
$706$	4.03515	0.151865
$707$	0	0
$708$	0.00124307	4.67175e−5 0
$709$	26.7587	1.00494	0.502472	−	0.864593i	$-0.332424\pi$
$709$	26.7587	1.00494	0.502472	+	0.864593i	$0.332424\pi$
$710$	−1.16331	−0.0436582
$711$	32.1276	1.20488
$712$	14.2874	0.535443
$713$	−60.7158	−2.27382
$714$	0	0
$715$	2.12781	0.0795756
$716$	15.5112	0.579680
$717$	−27.4078	−1.02356
$718$	−20.7104	−0.772905
$719$	21.0025	0.783260	0.391630	−	0.920123i	$-0.371911\pi$
$719$	21.0025	0.783260	0.391630	+	0.920123i	$0.371911\pi$
$720$	1.62948	0.0607273
$721$	0	0
$722$	−46.6091	−1.73461
$723$	−8.34719	−0.310435
$724$	−14.2938	−0.531223
$725$	11.1589	0.414432
$726$	−20.4746	−0.759882
$727$	9.96088	0.369429	0.184714	−	0.982792i	$-0.440864\pi$
$727$	9.96088	0.369429	0.184714	+	0.982792i	$0.440864\pi$
$728$	0	0
$729$	−9.27368	−0.343470
$730$	−0.449811	−0.0166483
$731$	40.6353	1.50295
$732$	16.9066	0.624884
$733$	−12.8550	−0.474809	−0.237404	−	0.971411i	$-0.576297\pi$
$733$	−12.8550	−0.474809	−0.237404	+	0.971411i	$0.576297\pi$
$734$	−4.80523	−0.177364
$735$	0	0
$736$	6.31781	0.232877
$737$	−4.83482	−0.178093
$738$	−2.10833	−0.0776087
$739$	9.88567	0.363650	0.181825	−	0.983331i	$-0.441800\pi$
$739$	9.88567	0.363650	0.181825	+	0.983331i	$0.441800\pi$
$740$	−6.96038	−0.255869
$741$	−36.1758	−1.32895
$742$	0	0
$743$	43.7018	1.60326	0.801632	−	0.597817i	$-0.203965\pi$
$743$	43.7018	1.60326	0.801632	+	0.597817i	$0.203965\pi$
$744$	21.7208	0.796321
$745$	6.97617	0.255587
$746$	−4.44046	−0.162577
$747$	−11.0352	−0.403757
$748$	−5.54058	−0.202584
$749$	0	0
$750$	−16.4249	−0.599751
$751$	15.6062	0.569477	0.284739	−	0.958605i	$-0.408093\pi$
$751$	15.6062	0.569477	0.284739	+	0.958605i	$0.408093\pi$
$752$	10.0924	0.368033
$753$	−69.8112	−2.54406
$754$	−5.00846	−0.182397
$755$	−0.532862	−0.0193928
$756$	0	0
$757$	−14.8199	−0.538637	−0.269319	−	0.963051i	$-0.586798\pi$
$757$	−14.8199	−0.538637	−0.269319	+	0.963051i	$0.586798\pi$
$758$	−13.2860	−0.482569
$759$	−19.8944	−0.722121
$760$	6.26027	0.227084
$761$	−3.92078	−0.142128	−0.0710641	−	0.997472i	$-0.522639\pi$
$761$	−3.92078	−0.142128	−0.0710641	+	0.997472i	$0.522639\pi$
$762$	0.351698	0.0127407
$763$	0	0
$764$	−5.07611	−0.183647
$765$	6.48008	0.234288
$766$	−19.1831	−0.693114
$767$	0.00108681	3.92424e−5 0
$768$	−2.26016	−0.0815566
$769$	−48.3444	−1.74334	−0.871672	−	0.490090i	$-0.836964\pi$
$769$	−48.3444	−1.74334	−0.871672	+	0.490090i	$0.836964\pi$
$770$	0	0
$771$	9.49302	0.341883
$772$	−2.29028	−0.0824289
$773$	−34.6574	−1.24654	−0.623270	−	0.782006i	$-0.714196\pi$
$773$	−34.6574	−1.24654	−0.623270	+	0.782006i	$0.714196\pi$
$774$	−21.5433	−0.774358
$775$	−42.3107	−1.51985
$776$	−12.3270	−0.442515
$777$	0	0
$778$	−5.44777	−0.195312
$779$	−8.09994	−0.290211
$780$	3.45181	0.123595
$781$	−2.09705	−0.0750384
$782$	25.1244	0.898448
$783$	−5.10800	−0.182545
$784$	0	0
$785$	17.5759	0.627309
$786$	32.8227	1.17075
$787$	2.63599	0.0939628	0.0469814	−	0.998896i	$-0.485040\pi$
$787$	2.63599	0.0939628	0.0469814	+	0.998896i	$0.485040\pi$
$788$	−11.4511	−0.407928
$789$	−68.9894	−2.45609
$790$	−11.7774	−0.419022
$791$	0	0
$792$	2.93740	0.104376
$793$	14.7813	0.524899
$794$	−30.7758	−1.09219
$795$	23.9841	0.850627
$796$	−13.2032	−0.467976
$797$	10.1409	0.359209	0.179604	−	0.983739i	$-0.442518\pi$
$797$	10.1409	0.359209	0.179604	+	0.983739i	$0.442518\pi$
$798$	0	0
$799$	40.1352	1.41988
$800$	4.40266	0.155657
$801$	−30.1226	−1.06433
$802$	−33.7550	−1.19193
$803$	−0.810857	−0.0286145
$804$	−7.84323	−0.276609
$805$	0	0
$806$	18.9903	0.668905
$807$	−73.4861	−2.58683
$808$	4.03693	0.142019
$809$	−19.7227	−0.693412	−0.346706	−	0.937974i	$-0.612700\pi$
$809$	−19.7227	−0.693412	−0.346706	+	0.937974i	$0.612700\pi$
$810$	8.40887	0.295458
$811$	−16.9646	−0.595706	−0.297853	−	0.954612i	$-0.596271\pi$
$811$	−16.9646	−0.595706	−0.297853	+	0.954612i	$0.596271\pi$
$812$	0	0
$813$	73.0278	2.56120
$814$	−12.5472	−0.439779
$815$	−6.36882	−0.223090
$816$	−8.98814	−0.314648
$817$	−82.7667	−2.89564
$818$	−6.28801	−0.219855
$819$	0	0
$820$	0.772879	0.0269901
$821$	22.3240	0.779113	0.389557	−	0.921002i	$-0.372628\pi$
$821$	22.3240	0.779113	0.389557	+	0.921002i	$0.372628\pi$
$822$	−1.83467	−0.0639915
$823$	−0.300506	−0.0104750	−0.00523749	−	0.999986i	$-0.501667\pi$
$823$	−0.300506	−0.0104750	−0.00523749	+	0.999986i	$0.501667\pi$
$824$	−0.199567	−0.00695223
$825$	−13.8637	−0.482672
$826$	0	0
$827$	30.5943	1.06387	0.531934	−	0.846786i	$-0.321465\pi$
$827$	30.5943	1.06387	0.531934	+	0.846786i	$0.321465\pi$
$828$	−13.3200	−0.462903
$829$	26.2533	0.911816	0.455908	−	0.890027i	$-0.349315\pi$
$829$	26.2533	0.911816	0.455908	+	0.890027i	$0.349315\pi$
$830$	4.04532	0.140415
$831$	9.93278	0.344564
$832$	−1.97604	−0.0685070
$833$	0	0
$834$	−14.9932	−0.519171
$835$	15.5766	0.539051
$836$	11.2851	0.390305
$837$	19.3677	0.669446
$838$	31.6431	1.09309
$839$	−25.2016	−0.870055	−0.435027	−	0.900417i	$-0.643261\pi$
$839$	−25.2016	−0.870055	−0.435027	+	0.900417i	$0.643261\pi$
$840$	0	0
$841$	−22.5759	−0.778478
$842$	−30.7791	−1.06072
$843$	−29.2887	−1.00875
$844$	−22.7102	−0.781717
$845$	−7.02953	−0.241823
$846$	−21.2782	−0.731559
$847$	0	0
$848$	−13.7300	−0.471491
$849$	10.6740	0.366331
$850$	17.5083	0.600531
$851$	56.8968	1.95040
$852$	−3.40191	−0.116548
$853$	−48.7872	−1.67044	−0.835221	−	0.549915i	$-0.814660\pi$
$853$	−48.7872	−1.67044	−0.835221	+	0.549915i	$0.814660\pi$
$854$	0	0
$855$	−13.1987	−0.451387
$856$	8.79078	0.300463
$857$	−2.58723	−0.0883781	−0.0441890	−	0.999023i	$-0.514070\pi$
$857$	−2.58723	−0.0883781	−0.0441890	+	0.999023i	$0.514070\pi$
$858$	6.22244	0.212431
$859$	25.0604	0.855051	0.427525	−	0.904003i	$-0.359385\pi$
$859$	25.0604	0.855051	0.427525	+	0.904003i	$0.359385\pi$
$860$	7.89741	0.269300
$861$	0	0
$862$	26.4709	0.901601
$863$	39.3760	1.34037	0.670187	−	0.742192i	$-0.266214\pi$
$863$	39.3760	1.34037	0.670187	+	0.742192i	$0.266214\pi$
$864$	−2.01532	−0.0685624
$865$	6.88664	0.234153
$866$	32.9273	1.11891
$867$	2.67903	0.0909846
$868$	0	0
$869$	−21.2307	−0.720201
$870$	−4.42750	−0.150106
$871$	−6.85728	−0.232350
$872$	7.30849	0.247497
$873$	25.9895	0.879611
$874$	−51.1739	−1.73098
$875$	0	0
$876$	−1.31540	−0.0444433
$877$	2.37551	0.0802154	0.0401077	−	0.999195i	$-0.487230\pi$
$877$	2.37551	0.0802154	0.0401077	+	0.999195i	$0.487230\pi$
$878$	−0.793640	−0.0267841
$879$	−13.8568	−0.467377
$880$	−1.07680	−0.0362990
$881$	−5.64173	−0.190075	−0.0950373	−	0.995474i	$-0.530297\pi$
$881$	−5.64173	−0.190075	−0.0950373	+	0.995474i	$0.530297\pi$
$882$	0	0
$883$	−15.0384	−0.506084	−0.253042	−	0.967455i	$-0.581431\pi$
$883$	−15.0384	−0.506084	−0.253042	+	0.967455i	$0.581431\pi$
$884$	−7.85826	−0.264302
$885$	0.000960744 0	3.22951e−5 0
$886$	5.53151	0.185835
$887$	16.9123	0.567860	0.283930	−	0.958845i	$-0.408362\pi$
$887$	16.9123	0.567860	0.283930	+	0.958845i	$0.408362\pi$
$888$	−20.3545	−0.683054
$889$	0	0
$890$	11.0424	0.370143
$891$	15.1583	0.507823
$892$	2.45474	0.0821909
$893$	−81.7481	−2.73560
$894$	20.4007	0.682301
$895$	11.9883	0.400723
$896$	0	0
$897$	−28.2164	−0.942120
$898$	−17.1307	−0.571659
$899$	−24.3581	−0.812387
$900$	−9.28226	−0.309409
$901$	−54.6012	−1.81903
$902$	1.39324	0.0463897
$903$	0	0
$904$	−13.6804	−0.455003
$905$	−11.0473	−0.367226
$906$	−1.55827	−0.0517701
$907$	33.9431	1.12706	0.563531	−	0.826095i	$-0.309442\pi$
$907$	33.9431	1.12706	0.563531	+	0.826095i	$0.309442\pi$
$908$	6.86450	0.227807
$909$	−8.51119	−0.282298
$910$	0	0
$911$	−32.0028	−1.06030	−0.530150	−	0.847904i	$-0.677864\pi$
$911$	−32.0028	−1.06030	−0.530150	+	0.847904i	$0.677864\pi$
$912$	18.3072	0.606211
$913$	7.29233	0.241341
$914$	−23.9352	−0.791707
$915$	13.0667	0.431972
$916$	12.0116	0.396874
$917$	0	0
$918$	−8.01444	−0.264516
$919$	12.2189	0.403065	0.201532	−	0.979482i	$-0.435408\pi$
$919$	12.2189	0.403065	0.201532	+	0.979482i	$0.435408\pi$
$920$	4.88290	0.160984
$921$	−66.1321	−2.17913
$922$	−12.8897	−0.424499
$923$	−2.97427	−0.0978993
$924$	0	0
$925$	39.6494	1.30366
$926$	−16.8067	−0.552302
$927$	0.420753	0.0138193
$928$	2.53459	0.0832020
$929$	−32.9335	−1.08051	−0.540257	−	0.841500i	$-0.681673\pi$
$929$	−32.9335	−1.08051	−0.540257	+	0.841500i	$0.681673\pi$
$930$	16.7875	0.550484
$931$	0	0
$932$	−6.60611	−0.216390
$933$	−25.2010	−0.825044
$934$	9.02937	0.295450
$935$	−4.28219	−0.140043
$936$	4.16615	0.136175
$937$	−5.49977	−0.179670	−0.0898348	−	0.995957i	$-0.528634\pi$
$937$	−5.49977	−0.179670	−0.0898348	+	0.995957i	$0.528634\pi$
$938$	0	0
$939$	−22.7395	−0.742076
$940$	7.80022	0.254415
$941$	−20.5021	−0.668349	−0.334175	−	0.942511i	$-0.608458\pi$
$941$	−20.5021	−0.668349	−0.334175	+	0.942511i	$0.608458\pi$
$942$	51.3978	1.67463
$943$	−6.31781	−0.205736
$944$	−0.000549992 0	−1.79007e−5 0
$945$	0	0
$946$	14.2363	0.462864
$947$	2.50743	0.0814805	0.0407403	−	0.999170i	$-0.487028\pi$
$947$	2.50743	0.0814805	0.0407403	+	0.999170i	$0.487028\pi$
$948$	−34.4412	−1.11860
$949$	−1.15005	−0.0373321
$950$	−35.6613	−1.15700
$951$	−17.9077	−0.580696
$952$	0	0
$953$	41.7937	1.35383	0.676915	−	0.736061i	$-0.263316\pi$
$953$	41.7937	1.35383	0.676915	+	0.736061i	$0.263316\pi$
$954$	28.9475	0.937209
$955$	−3.92322	−0.126952
$956$	12.1265	0.392198
$957$	−7.98127	−0.257998
$958$	16.9352	0.547153
$959$	0	0
$960$	−1.74683	−0.0563787
$961$	61.3572	1.97926
$962$	−17.7958	−0.573761
$963$	−18.5339	−0.597246
$964$	3.69318	0.118949
$965$	−1.77011	−0.0569817
$966$	0	0
$967$	10.3048	0.331379	0.165689	−	0.986178i	$-0.447015\pi$
$967$	10.3048	0.331379	0.165689	+	0.986178i	$0.447015\pi$
$968$	9.05889	0.291164
$969$	72.8034	2.33878
$970$	−9.52731	−0.305903
$971$	41.6025	1.33509	0.667543	−	0.744571i	$-0.267346\pi$
$971$	41.6025	1.33509	0.667543	+	0.744571i	$0.267346\pi$
$972$	18.5445	0.594814
$973$	0	0
$974$	16.1613	0.517843
$975$	−19.6631	−0.629722
$976$	−7.48024	−0.239437
$977$	−1.92980	−0.0617399	−0.0308699	−	0.999523i	$-0.509828\pi$
$977$	−1.92980	−0.0617399	−0.0308699	+	0.999523i	$0.509828\pi$
$978$	−18.6246	−0.595549
$979$	19.9058	0.636191
$980$	0	0
$981$	−15.4087	−0.491962
$982$	−37.2140	−1.18755
$983$	−24.7329	−0.788858	−0.394429	−	0.918926i	$-0.629058\pi$
$983$	−24.7329	−0.788858	−0.394429	+	0.918926i	$0.629058\pi$
$984$	2.26016	0.0720513
$985$	−8.85029	−0.281994
$986$	10.0795	0.320996
$987$	0	0
$988$	16.0058	0.509214
$989$	−64.5565	−2.05278
$990$	2.27026	0.0721535
$991$	10.3527	0.328864	0.164432	−	0.986388i	$-0.447421\pi$
$991$	10.3527	0.328864	0.164432	+	0.986388i	$0.447421\pi$
$992$	−9.61026	−0.305126
$993$	16.6181	0.527359
$994$	0	0
$995$	−10.2045	−0.323504
$996$	11.8299	0.374845
$997$	−40.7892	−1.29181	−0.645903	−	0.763420i	$-0.723519\pi$
$997$	−40.7892	−1.29181	−0.645903	+	0.763420i	$0.723519\pi$
$998$	18.1524	0.574604
$999$	−18.1495	−0.574225

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4018.2.a.bs.1.1	yes	10
7.6	odd	2		4018.2.a.br.1.10	✓	10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4018.2.a.br.1.10	✓	10	7.6	odd	2
4018.2.a.bs.1.1	yes	10	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:	\( N \)	\(=\)	\( 4018 = 2 \cdot 7^{2} \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4018.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -2.26016 q^{3} +1.00000 q^{4} +0.772879 q^{5} +2.26016 q^{6} -1.00000 q^{8} +2.10833 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -2.26016 q^{3} +1.00000 q^{4} +0.772879 q^{5} +2.26016 q^{6} -1.00000 q^{8} +2.10833 q^{9} -0.772879 q^{10} -1.39324 q^{11} -2.26016 q^{12} -1.97604 q^{13} -1.74683 q^{15} +1.00000 q^{16} +3.97677 q^{17} -2.10833 q^{18} -8.09994 q^{19} +0.772879 q^{20} +1.39324 q^{22} -6.31781 q^{23} +2.26016 q^{24} -4.40266 q^{25} +1.97604 q^{26} +2.01532 q^{27} -2.53459 q^{29} +1.74683 q^{30} +9.61026 q^{31} -1.00000 q^{32} +3.14894 q^{33} -3.97677 q^{34} +2.10833 q^{36} -9.00579 q^{37} +8.09994 q^{38} +4.46618 q^{39} -0.772879 q^{40} +1.00000 q^{41} +10.2182 q^{43} -1.39324 q^{44} +1.62948 q^{45} +6.31781 q^{46} +10.0924 q^{47} -2.26016 q^{48} +4.40266 q^{50} -8.98814 q^{51} -1.97604 q^{52} -13.7300 q^{53} -2.01532 q^{54} -1.07680 q^{55} +18.3072 q^{57} +2.53459 q^{58} -0.000549992 q^{59} -1.74683 q^{60} -7.48024 q^{61} -9.61026 q^{62} +1.00000 q^{64} -1.52724 q^{65} -3.14894 q^{66} +3.47021 q^{67} +3.97677 q^{68} +14.2793 q^{69} +1.50516 q^{71} -2.10833 q^{72} +0.581995 q^{73} +9.00579 q^{74} +9.95072 q^{75} -8.09994 q^{76} -4.46618 q^{78} +15.2384 q^{79} +0.772879 q^{80} -10.8799 q^{81} -1.00000 q^{82} -5.23409 q^{83} +3.07356 q^{85} -10.2182 q^{86} +5.72858 q^{87} +1.39324 q^{88} -14.2874 q^{89} -1.62948 q^{90} -6.31781 q^{92} -21.7208 q^{93} -10.0924 q^{94} -6.26027 q^{95} +2.26016 q^{96} +12.3270 q^{97} -2.93740 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 10 q^{2} + 4 q^{3} + 10 q^{4} + 4 q^{5} - 4 q^{6} - 10 q^{8} + 10 q^{9}+O(q^{10}) \) 10 * q - 10 * q^2 + 4 * q^3 + 10 * q^4 + 4 * q^5 - 4 * q^6 - 10 * q^8 + 10 * q^9	\( 10 q - 10 q^{2} + 4 q^{3} + 10 q^{4} + 4 q^{5} - 4 q^{6} - 10 q^{8} + 10 q^{9} - 4 q^{10} + 4 q^{11} + 4 q^{12} + 4 q^{13} + 4 q^{15} + 10 q^{16} + 20 q^{17} - 10 q^{18} + 4 q^{20} - 4 q^{22} + 4 q^{23} - 4 q^{24} + 6 q^{25} - 4 q^{26} + 16 q^{27} - 4 q^{29} - 4 q^{30} - 4 q^{31} - 10 q^{32} + 36 q^{33} - 20 q^{34} + 10 q^{36} - 16 q^{37} + 20 q^{39} - 4 q^{40} + 10 q^{41} - 8 q^{43} + 4 q^{44} + 4 q^{45} - 4 q^{46} + 24 q^{47} + 4 q^{48} - 6 q^{50} + 20 q^{51} + 4 q^{52} - 4 q^{53} - 16 q^{54} + 20 q^{55} - 4 q^{57} + 4 q^{58} + 4 q^{60} + 4 q^{62} + 10 q^{64} - 12 q^{65} - 36 q^{66} + 8 q^{67} + 20 q^{68} + 4 q^{71} - 10 q^{72} - 24 q^{73} + 16 q^{74} + 48 q^{75} - 20 q^{78} + 24 q^{79} + 4 q^{80} - 18 q^{81} - 10 q^{82} + 48 q^{83} + 8 q^{85} + 8 q^{86} + 4 q^{87} - 4 q^{88} + 20 q^{89} - 4 q^{90} + 4 q^{92} + 4 q^{93} - 24 q^{94} - 4 q^{95} - 4 q^{96} + 4 q^{97} + 32 q^{99}+O(q^{100}) \) 10 * q - 10 * q^2 + 4 * q^3 + 10 * q^4 + 4 * q^5 - 4 * q^6 - 10 * q^8 + 10 * q^9 - 4 * q^10 + 4 * q^11 + 4 * q^12 + 4 * q^13 + 4 * q^15 + 10 * q^16 + 20 * q^17 - 10 * q^18 + 4 * q^20 - 4 * q^22 + 4 * q^23 - 4 * q^24 + 6 * q^25 - 4 * q^26 + 16 * q^27 - 4 * q^29 - 4 * q^30 - 4 * q^31 - 10 * q^32 + 36 * q^33 - 20 * q^34 + 10 * q^36 - 16 * q^37 + 20 * q^39 - 4 * q^40 + 10 * q^41 - 8 * q^43 + 4 * q^44 + 4 * q^45 - 4 * q^46 + 24 * q^47 + 4 * q^48 - 6 * q^50 + 20 * q^51 + 4 * q^52 - 4 * q^53 - 16 * q^54 + 20 * q^55 - 4 * q^57 + 4 * q^58 + 4 * q^60 + 4 * q^62 + 10 * q^64 - 12 * q^65 - 36 * q^66 + 8 * q^67 + 20 * q^68 + 4 * q^71 - 10 * q^72 - 24 * q^73 + 16 * q^74 + 48 * q^75 - 20 * q^78 + 24 * q^79 + 4 * q^80 - 18 * q^81 - 10 * q^82 + 48 * q^83 + 8 * q^85 + 8 * q^86 + 4 * q^87 - 4 * q^88 + 20 * q^89 - 4 * q^90 + 4 * q^92 + 4 * q^93 - 24 * q^94 - 4 * q^95 - 4 * q^96 + 4 * q^97 + 32 * q^99

Introduction

L-functions

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