LMFDB - Embedded newform 6027.2.a.bk.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6027,2,Mod(1,6027)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6027, 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("6027.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6027 = 3 \cdot 7^{2} \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6027.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:	$48.1258372982$
Analytic rank:	$1$
Dimension:	$14$
Coefficient field:	$\mathbb{Q}[x]/(x^{14} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{14} - 2 x^{13} - 19 x^{12} + 36 x^{11} + 134 x^{10} - 237 x^{9} - 438 x^{8} + 716 x^{7} + 662 x^{6} + \cdots + 16 $ x^14 - 2x^13 - 19x^12 + 36x^11 + 134x^10 - 237x^9 - 438x^8 + 716x^7 + 662x^6 - 1007x^5 - 384x^4 + 579x^3 + 44x^2 - 112*x + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 861)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$1.64093$ of defining polynomial
Character	$\chi$	$=$	6027.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.64093 q^{2} +1.00000 q^{3} +0.692668 q^{4} +0.0817657 q^{5} -1.64093 q^{6} +2.14525 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.64093 q^{2} +1.00000 q^{3} +0.692668 q^{4} +0.0817657 q^{5} -1.64093 q^{6} +2.14525 q^{8} +1.00000 q^{9} -0.134172 q^{10} -4.94328 q^{11} +0.692668 q^{12} +1.23171 q^{13} +0.0817657 q^{15} -4.90555 q^{16} -0.810235 q^{17} -1.64093 q^{18} +6.55953 q^{19} +0.0566365 q^{20} +8.11161 q^{22} -5.53945 q^{23} +2.14525 q^{24} -4.99331 q^{25} -2.02116 q^{26} +1.00000 q^{27} -0.0447280 q^{29} -0.134172 q^{30} +7.20734 q^{31} +3.75919 q^{32} -4.94328 q^{33} +1.32954 q^{34} +0.692668 q^{36} +5.22958 q^{37} -10.7638 q^{38} +1.23171 q^{39} +0.175408 q^{40} -1.00000 q^{41} -8.64881 q^{43} -3.42405 q^{44} +0.0817657 q^{45} +9.08988 q^{46} +10.9081 q^{47} -4.90555 q^{48} +8.19370 q^{50} -0.810235 q^{51} +0.853167 q^{52} -5.99240 q^{53} -1.64093 q^{54} -0.404191 q^{55} +6.55953 q^{57} +0.0733957 q^{58} -4.34053 q^{59} +0.0566365 q^{60} +1.13380 q^{61} -11.8268 q^{62} +3.64251 q^{64} +0.100712 q^{65} +8.11161 q^{66} -2.70626 q^{67} -0.561224 q^{68} -5.53945 q^{69} -5.56029 q^{71} +2.14525 q^{72} -14.5072 q^{73} -8.58140 q^{74} -4.99331 q^{75} +4.54357 q^{76} -2.02116 q^{78} +15.5574 q^{79} -0.401106 q^{80} +1.00000 q^{81} +1.64093 q^{82} +9.02538 q^{83} -0.0662495 q^{85} +14.1921 q^{86} -0.0447280 q^{87} -10.6046 q^{88} +7.38768 q^{89} -0.134172 q^{90} -3.83700 q^{92} +7.20734 q^{93} -17.8995 q^{94} +0.536345 q^{95} +3.75919 q^{96} +5.44556 q^{97} -4.94328 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q - 2 q^{2} + 14 q^{3} + 14 q^{4} - 10 q^{5} - 2 q^{6} - 6 q^{8} + 14 q^{9}+O(q^{10}) $ 14 * q - 2 * q^2 + 14 * q^3 + 14 * q^4 - 10 * q^5 - 2 * q^6 - 6 * q^8 + 14 * q^9	$ 14 q - 2 q^{2} + 14 q^{3} + 14 q^{4} - 10 q^{5} - 2 q^{6} - 6 q^{8} + 14 q^{9} - 3 q^{10} - 16 q^{11} + 14 q^{12} - 21 q^{13} - 10 q^{15} + 22 q^{16} - 12 q^{17} - 2 q^{18} - 2 q^{19} - 40 q^{20} + q^{22} - 7 q^{23} - 6 q^{24} + 22 q^{25} - 2 q^{26} + 14 q^{27} - 16 q^{29} - 3 q^{30} - 8 q^{31} - 19 q^{32} - 16 q^{33} - 33 q^{34} + 14 q^{36} + q^{37} - 32 q^{38} - 21 q^{39} + 13 q^{40} - 14 q^{41} + 14 q^{43} - 36 q^{44} - 10 q^{45} - 12 q^{46} - 12 q^{47} + 22 q^{48} - q^{50} - 12 q^{51} - 60 q^{52} - 20 q^{53} - 2 q^{54} + 11 q^{55} - 2 q^{57} + 21 q^{58} - 25 q^{59} - 40 q^{60} - 26 q^{61} + 33 q^{62} + 42 q^{64} - 8 q^{65} + q^{66} - 22 q^{67} - 15 q^{68} - 7 q^{69} - 36 q^{71} - 6 q^{72} - 31 q^{73} - 65 q^{74} + 22 q^{75} + 2 q^{76} - 2 q^{78} + 12 q^{79} - 112 q^{80} + 14 q^{81} + 2 q^{82} - 20 q^{83} + 40 q^{85} - 9 q^{86} - 16 q^{87} - 54 q^{88} - 39 q^{89} - 3 q^{90} + 63 q^{92} - 8 q^{93} - 14 q^{94} - 55 q^{95} - 19 q^{96} - 18 q^{97} - 16 q^{99}+O(q^{100}) $ 14 * q - 2 * q^2 + 14 * q^3 + 14 * q^4 - 10 * q^5 - 2 * q^6 - 6 * q^8 + 14 * q^9 - 3 * q^10 - 16 * q^11 + 14 * q^12 - 21 * q^13 - 10 * q^15 + 22 * q^16 - 12 * q^17 - 2 * q^18 - 2 * q^19 - 40 * q^20 + q^22 - 7 * q^23 - 6 * q^24 + 22 * q^25 - 2 * q^26 + 14 * q^27 - 16 * q^29 - 3 * q^30 - 8 * q^31 - 19 * q^32 - 16 * q^33 - 33 * q^34 + 14 * q^36 + q^37 - 32 * q^38 - 21 * q^39 + 13 * q^40 - 14 * q^41 + 14 * q^43 - 36 * q^44 - 10 * q^45 - 12 * q^46 - 12 * q^47 + 22 * q^48 - q^50 - 12 * q^51 - 60 * q^52 - 20 * q^53 - 2 * q^54 + 11 * q^55 - 2 * q^57 + 21 * q^58 - 25 * q^59 - 40 * q^60 - 26 * q^61 + 33 * q^62 + 42 * q^64 - 8 * q^65 + q^66 - 22 * q^67 - 15 * q^68 - 7 * q^69 - 36 * q^71 - 6 * q^72 - 31 * q^73 - 65 * q^74 + 22 * q^75 + 2 * q^76 - 2 * q^78 + 12 * q^79 - 112 * q^80 + 14 * q^81 + 2 * q^82 - 20 * q^83 + 40 * q^85 - 9 * q^86 - 16 * q^87 - 54 * q^88 - 39 * q^89 - 3 * q^90 + 63 * q^92 - 8 * q^93 - 14 * q^94 - 55 * q^95 - 19 * q^96 - 18 * q^97 - 16 * 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 $

$2$	−1.64093	−1.16032	−0.580158	−	0.814504i	$-0.697009\pi$
$2$	−1.64093	−1.16032	−0.580158	+	0.814504i	$0.697009\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	0.692668	0.346334
$5$	0.0817657	0.0365667	0.0182834	−	0.999833i	$-0.494180\pi$
$5$	0.0817657	0.0365667	0.0182834	+	0.999833i	$0.494180\pi$
$6$	−1.64093	−0.669909
$7$	0	0
$7$	0	0
$8$	2.14525	0.758459
$9$	1.00000	0.333333
$10$	−0.134172	−0.0424290
$11$	−4.94328	−1.49046	−0.745228	−	0.666810i	$-0.767659\pi$
$11$	−4.94328	−1.49046	−0.745228	+	0.666810i	$0.767659\pi$
$12$	0.692668	0.199956
$13$	1.23171	0.341616	0.170808	−	0.985304i	$-0.445362\pi$
$13$	1.23171	0.341616	0.170808	+	0.985304i	$0.445362\pi$
$14$	0	0
$15$	0.0817657	0.0211118
$16$	−4.90555	−1.22639
$17$	−0.810235	−0.196511	−0.0982555	−	0.995161i	$-0.531326\pi$
$17$	−0.810235	−0.196511	−0.0982555	+	0.995161i	$0.531326\pi$
$18$	−1.64093	−0.386772
$19$	6.55953	1.50486	0.752430	−	0.658673i	$-0.228882\pi$
$19$	6.55953	1.50486	0.752430	+	0.658673i	$0.228882\pi$
$20$	0.0566365	0.0126643
$21$	0	0
$22$	8.11161	1.72940
$23$	−5.53945	−1.15506	−0.577528	−	0.816371i	$-0.695983\pi$
$23$	−5.53945	−1.15506	−0.577528	+	0.816371i	$0.695983\pi$
$24$	2.14525	0.437897
$25$	−4.99331	−0.998663
$26$	−2.02116	−0.396382
$27$	1.00000	0.192450
$28$	0	0
$29$	−0.0447280	−0.00830578	−0.00415289	−	0.999991i	$-0.501322\pi$
$29$	−0.0447280	−0.00830578	−0.00415289	+	0.999991i	$0.501322\pi$
$30$	−0.134172	−0.0244964
$31$	7.20734	1.29448	0.647238	−	0.762288i	$-0.275924\pi$
$31$	7.20734	1.29448	0.647238	+	0.762288i	$0.275924\pi$
$32$	3.75919	0.664537
$33$	−4.94328	−0.860515
$34$	1.32954	0.228015
$35$	0	0
$36$	0.692668	0.115445
$37$	5.22958	0.859737	0.429869	−	0.902891i	$-0.358560\pi$
$37$	5.22958	0.859737	0.429869	+	0.902891i	$0.358560\pi$
$38$	−10.7638	−1.74611
$39$	1.23171	0.197232
$40$	0.175408	0.0277344
$41$	−1.00000	−0.156174
$41$	−1.00000	−0.156174
$42$	0	0
$43$	−8.64881	−1.31893	−0.659466	−	0.751735i	$-0.729217\pi$
$43$	−8.64881	−1.31893	−0.659466	+	0.751735i	$0.729217\pi$
$44$	−3.42405	−0.516195
$45$	0.0817657	0.0121889
$46$	9.08988	1.34023
$47$	10.9081	1.59111	0.795556	−	0.605881i	$-0.207179\pi$
$47$	10.9081	1.59111	0.795556	+	0.605881i	$0.207179\pi$
$48$	−4.90555	−0.708055
$49$	0	0
$50$	8.19370	1.15876
$51$	−0.810235	−0.113456
$52$	0.853167	0.118313
$53$	−5.99240	−0.823120	−0.411560	−	0.911383i	$-0.635016\pi$
$53$	−5.99240	−0.823120	−0.411560	+	0.911383i	$0.635016\pi$
$54$	−1.64093	−0.223303
$55$	−0.404191	−0.0545011
$56$	0	0
$57$	6.55953	0.868831
$58$	0.0733957	0.00963733
$59$	−4.34053	−0.565089	−0.282544	−	0.959254i	$-0.591178\pi$
$59$	−4.34053	−0.565089	−0.282544	+	0.959254i	$0.591178\pi$
$60$	0.0566365	0.00731174
$61$	1.13380	0.145168	0.0725842	−	0.997362i	$-0.476875\pi$
$61$	1.13380	0.145168	0.0725842	+	0.997362i	$0.476875\pi$
$62$	−11.8268	−1.50200
$63$	0	0
$64$	3.64251	0.455314
$65$	0.100712	0.0124918
$66$	8.11161	0.998470
$67$	−2.70626	−0.330622	−0.165311	−	0.986241i	$-0.552863\pi$
$67$	−2.70626	−0.330622	−0.165311	+	0.986241i	$0.552863\pi$
$68$	−0.561224	−0.0680584
$69$	−5.53945	−0.666872
$70$	0	0
$71$	−5.56029	−0.659885	−0.329943	−	0.944001i	$-0.607029\pi$
$71$	−5.56029	−0.659885	−0.329943	+	0.944001i	$0.607029\pi$
$72$	2.14525	0.252820
$73$	−14.5072	−1.69794	−0.848972	−	0.528438i	$-0.822778\pi$
$73$	−14.5072	−1.69794	−0.848972	+	0.528438i	$0.822778\pi$
$74$	−8.58140	−0.997567
$75$	−4.99331	−0.576578
$76$	4.54357	0.521184
$77$	0	0
$78$	−2.02116	−0.228851
$79$	15.5574	1.75034	0.875171	−	0.483813i	$-0.160749\pi$
$79$	15.5574	1.75034	0.875171	+	0.483813i	$0.160749\pi$
$80$	−0.401106	−0.0448450
$81$	1.00000	0.111111
$82$	1.64093	0.181211
$83$	9.02538	0.990664	0.495332	−	0.868704i	$-0.335046\pi$
$83$	9.02538	0.990664	0.495332	+	0.868704i	$0.335046\pi$
$84$	0	0
$85$	−0.0662495	−0.00718577
$86$	14.1921	1.53038
$87$	−0.0447280	−0.00479534
$88$	−10.6046	−1.13045
$89$	7.38768	0.783093	0.391546	−	0.920158i	$-0.371940\pi$
$89$	7.38768	0.783093	0.391546	+	0.920158i	$0.371940\pi$
$90$	−0.134172	−0.0141430
$91$	0	0
$92$	−3.83700	−0.400035
$93$	7.20734	0.747366
$94$	−17.8995	−1.84619
$95$	0.536345	0.0550278
$96$	3.75919	0.383671
$97$	5.44556	0.552912	0.276456	−	0.961027i	$-0.410840\pi$
$97$	5.44556	0.552912	0.276456	+	0.961027i	$0.410840\pi$
$98$	0	0
$99$	−4.94328	−0.496819
$100$	−3.45871	−0.345871
$101$	−3.78486	−0.376607	−0.188304	−	0.982111i	$-0.560299\pi$
$101$	−3.78486	−0.376607	−0.188304	+	0.982111i	$0.560299\pi$
$102$	1.32954	0.131644
$103$	−19.1368	−1.88561	−0.942804	−	0.333349i	$-0.891821\pi$
$103$	−19.1368	−1.88561	−0.942804	+	0.333349i	$0.891821\pi$
$104$	2.64233	0.259102
$105$	0	0
$106$	9.83314	0.955079
$107$	−13.5411	−1.30907	−0.654534	−	0.756032i	$-0.727135\pi$
$107$	−13.5411	−1.30907	−0.654534	+	0.756032i	$0.727135\pi$
$108$	0.692668	0.0666520
$109$	0.705015	0.0675282	0.0337641	−	0.999430i	$-0.489251\pi$
$109$	0.705015	0.0675282	0.0337641	+	0.999430i	$0.489251\pi$
$110$	0.663251	0.0632385
$111$	5.22958	0.496370
$112$	0	0
$113$	−11.6339	−1.09443	−0.547213	−	0.836993i	$-0.684311\pi$
$113$	−11.6339	−1.09443	−0.547213	+	0.836993i	$0.684311\pi$
$114$	−10.7638	−1.00812
$115$	−0.452937	−0.0422366
$116$	−0.0309816	−0.00287657
$117$	1.23171	0.113872
$118$	7.12253	0.655682
$119$	0	0
$120$	0.175408	0.0160125
$121$	13.4360	1.22146
$122$	−1.86049	−0.168441
$123$	−1.00000	−0.0901670
$124$	4.99229	0.448321
$125$	−0.817110	−0.0730846
$126$	0	0
$127$	−2.52451	−0.224014	−0.112007	−	0.993707i	$-0.535728\pi$
$127$	−2.52451	−0.224014	−0.112007	+	0.993707i	$0.535728\pi$
$128$	−13.4955	−1.19284
$129$	−8.64881	−0.761485
$130$	−0.165262	−0.0144944
$131$	−10.8567	−0.948553	−0.474277	−	0.880376i	$-0.657290\pi$
$131$	−10.8567	−0.948553	−0.474277	+	0.880376i	$0.657290\pi$
$132$	−3.42405	−0.298025
$133$	0	0
$134$	4.44080	0.383626
$135$	0.0817657	0.00703727
$136$	−1.73816	−0.149046
$137$	−10.3736	−0.886277	−0.443138	−	0.896453i	$-0.646135\pi$
$137$	−10.3736	−0.886277	−0.443138	+	0.896453i	$0.646135\pi$
$138$	9.08988	0.773782
$139$	−3.46799	−0.294151	−0.147075	−	0.989125i	$-0.546986\pi$
$139$	−3.46799	−0.294151	−0.147075	+	0.989125i	$0.546986\pi$
$140$	0	0
$141$	10.9081	0.918628
$142$	9.12408	0.765676
$143$	−6.08870	−0.509163
$144$	−4.90555	−0.408796
$145$	−0.00365722	−0.000303715 0
$146$	23.8054	1.97015
$147$	0	0
$148$	3.62236	0.297756
$149$	22.9065	1.87657	0.938287	−	0.345857i	$-0.112412\pi$
$149$	22.9065	1.87657	0.938287	+	0.345857i	$0.112412\pi$
$150$	8.19370	0.669013
$151$	−22.3577	−1.81945	−0.909724	−	0.415214i	$-0.863707\pi$
$151$	−22.3577	−1.81945	−0.909724	+	0.415214i	$0.863707\pi$
$152$	14.0718	1.14137
$153$	−0.810235	−0.0655037
$154$	0	0
$155$	0.589313	0.0473348
$156$	0.853167	0.0683081
$157$	12.9470	1.03328	0.516640	−	0.856203i	$-0.327182\pi$
$157$	12.9470	1.03328	0.516640	+	0.856203i	$0.327182\pi$
$158$	−25.5287	−2.03095
$159$	−5.99240	−0.475228
$160$	0.307373	0.0242999
$161$	0	0
$162$	−1.64093	−0.128924
$163$	2.36528	0.185263	0.0926313	−	0.995700i	$-0.470472\pi$
$163$	2.36528	0.185263	0.0926313	+	0.995700i	$0.470472\pi$
$164$	−0.692668	−0.0540883
$165$	−0.404191	−0.0314662
$166$	−14.8101	−1.14948
$167$	14.7792	1.14365	0.571824	−	0.820377i	$-0.306236\pi$
$167$	14.7792	1.14365	0.571824	+	0.820377i	$0.306236\pi$
$168$	0	0
$169$	−11.4829	−0.883299
$170$	0.108711	0.00833776
$171$	6.55953	0.501620
$172$	−5.99075	−0.456790
$173$	−10.5024	−0.798479	−0.399239	−	0.916847i	$-0.630726\pi$
$173$	−10.5024	−0.798479	−0.399239	+	0.916847i	$0.630726\pi$
$174$	0.0733957	0.00556411
$175$	0	0
$176$	24.2495	1.82788
$177$	−4.34053	−0.326254
$178$	−12.1227	−0.908635
$179$	−6.55231	−0.489743	−0.244871	−	0.969556i	$-0.578746\pi$
$179$	−6.55231	−0.489743	−0.244871	+	0.969556i	$0.578746\pi$
$180$	0.0566365	0.00422143
$181$	−2.05872	−0.153023	−0.0765115	−	0.997069i	$-0.524378\pi$
$181$	−2.05872	−0.153023	−0.0765115	+	0.997069i	$0.524378\pi$
$182$	0	0
$183$	1.13380	0.0838130
$184$	−11.8835	−0.876063
$185$	0.427600	0.0314378
$186$	−11.8268	−0.867181
$187$	4.00522	0.292891
$188$	7.55569	0.551056
$189$	0	0
$190$	−0.880107	−0.0638496
$191$	−18.4559	−1.33542	−0.667712	−	0.744419i	$-0.732726\pi$
$191$	−18.4559	−1.33542	−0.667712	+	0.744419i	$0.732726\pi$
$192$	3.64251	0.262875
$193$	22.7365	1.63661	0.818304	−	0.574786i	$-0.194915\pi$
$193$	22.7365	1.63661	0.818304	+	0.574786i	$0.194915\pi$
$194$	−8.93580	−0.641553
$195$	0.100712	0.00721213
$196$	0	0
$197$	1.89397	0.134940	0.0674698	−	0.997721i	$-0.478507\pi$
$197$	1.89397	0.134940	0.0674698	+	0.997721i	$0.478507\pi$
$198$	8.11161	0.576467
$199$	20.6802	1.46598	0.732989	−	0.680241i	$-0.238125\pi$
$199$	20.6802	1.46598	0.732989	+	0.680241i	$0.238125\pi$
$200$	−10.7119	−0.757445
$201$	−2.70626	−0.190885
$202$	6.21070	0.436984
$203$	0	0
$204$	−0.561224	−0.0392935
$205$	−0.0817657	−0.00571077
$206$	31.4023	2.18790
$207$	−5.53945	−0.385019
$208$	−6.04222	−0.418953
$209$	−32.4256	−2.24293
$210$	0	0
$211$	−8.73506	−0.601346	−0.300673	−	0.953727i	$-0.597211\pi$
$211$	−8.73506	−0.601346	−0.300673	+	0.953727i	$0.597211\pi$
$212$	−4.15074	−0.285074
$213$	−5.56029	−0.380985
$214$	22.2201	1.51893
$215$	−0.707176	−0.0482290
$216$	2.14525	0.145966
$217$	0	0
$218$	−1.15688	−0.0783541
$219$	−14.5072	−0.980308
$220$	−0.279970	−0.0188756
$221$	−0.997977	−0.0671312
$222$	−8.58140	−0.575946
$223$	12.8945	0.863483	0.431741	−	0.901997i	$-0.357899\pi$
$223$	12.8945	0.863483	0.431741	+	0.901997i	$0.357899\pi$
$224$	0	0
$225$	−4.99331	−0.332888
$226$	19.0905	1.26988
$227$	−18.9009	−1.25450	−0.627248	−	0.778820i	$-0.715819\pi$
$227$	−18.9009	−1.25450	−0.627248	+	0.778820i	$0.715819\pi$
$228$	4.54357	0.300905
$229$	−1.43656	−0.0949305	−0.0474652	−	0.998873i	$-0.515114\pi$
$229$	−1.43656	−0.0949305	−0.0474652	+	0.998873i	$0.515114\pi$
$230$	0.743241	0.0490078
$231$	0	0
$232$	−0.0959526	−0.00629960
$233$	−14.7809	−0.968331	−0.484166	−	0.874976i	$-0.660877\pi$
$233$	−14.7809	−0.968331	−0.484166	+	0.874976i	$0.660877\pi$
$234$	−2.02116	−0.132127
$235$	0.891909	0.0581817
$236$	−3.00655	−0.195709
$237$	15.5574	1.01056
$238$	0	0
$239$	−1.03844	−0.0671712	−0.0335856	−	0.999436i	$-0.510693\pi$
$239$	−1.03844	−0.0671712	−0.0335856	+	0.999436i	$0.510693\pi$
$240$	−0.401106	−0.0258913
$241$	−24.3864	−1.57087	−0.785433	−	0.618947i	$-0.787559\pi$
$241$	−24.3864	−1.57087	−0.785433	+	0.618947i	$0.787559\pi$
$242$	−22.0477	−1.41728
$243$	1.00000	0.0641500
$244$	0.785347	0.0502767
$245$	0	0
$246$	1.64093	0.104622
$247$	8.07945	0.514083
$248$	15.4615	0.981808
$249$	9.02538	0.571960
$250$	1.34083	0.0848012
$251$	−10.4072	−0.656898	−0.328449	−	0.944522i	$-0.606526\pi$
$251$	−10.4072	−0.656898	−0.328449	+	0.944522i	$0.606526\pi$
$252$	0	0
$253$	27.3831	1.72156
$254$	4.14255	0.259927
$255$	−0.0662495	−0.00414870
$256$	14.8602	0.928764
$257$	18.1220	1.13042	0.565210	−	0.824947i	$-0.308795\pi$
$257$	18.1220	1.13042	0.565210	+	0.824947i	$0.308795\pi$
$258$	14.1921	0.883564
$259$	0	0
$260$	0.0697598	0.00432632
$261$	−0.0447280	−0.00276859
$262$	17.8151	1.10062
$263$	−2.84868	−0.175657	−0.0878284	−	0.996136i	$-0.527993\pi$
$263$	−2.84868	−0.175657	−0.0878284	+	0.996136i	$0.527993\pi$
$264$	−10.6046	−0.652666
$265$	−0.489973	−0.0300988
$266$	0	0
$267$	7.38768	0.452119
$268$	−1.87454	−0.114506
$269$	−7.26180	−0.442760	−0.221380	−	0.975188i	$-0.571056\pi$
$269$	−7.26180	−0.442760	−0.221380	+	0.975188i	$0.571056\pi$
$270$	−0.134172	−0.00816546
$271$	4.19299	0.254706	0.127353	−	0.991857i	$-0.459352\pi$
$271$	4.19299	0.254706	0.127353	+	0.991857i	$0.459352\pi$
$272$	3.97465	0.240998
$273$	0	0
$274$	17.0224	1.02836
$275$	24.6834	1.48846
$276$	−3.83700	−0.230960
$277$	8.00920	0.481226	0.240613	−	0.970621i	$-0.422652\pi$
$277$	8.00920	0.481226	0.240613	+	0.970621i	$0.422652\pi$
$278$	5.69074	0.341308
$279$	7.20734	0.431492
$280$	0	0
$281$	−2.19975	−0.131226	−0.0656131	−	0.997845i	$-0.520900\pi$
$281$	−2.19975	−0.131226	−0.0656131	+	0.997845i	$0.520900\pi$
$282$	−17.8995	−1.06590
$283$	−3.83526	−0.227983	−0.113991	−	0.993482i	$-0.536364\pi$
$283$	−3.83526	−0.227983	−0.113991	+	0.993482i	$0.536364\pi$
$284$	−3.85144	−0.228541
$285$	0.536345	0.0317703
$286$	9.99117	0.590790
$287$	0	0
$288$	3.75919	0.221512
$289$	−16.3435	−0.961383
$290$	0.00600125	0.000352406 0
$291$	5.44556	0.319224
$292$	−10.0487	−0.588055
$293$	−7.82147	−0.456935	−0.228468	−	0.973552i	$-0.573371\pi$
$293$	−7.82147	−0.456935	−0.228468	+	0.973552i	$0.573371\pi$
$294$	0	0
$295$	−0.354907	−0.0206635
$296$	11.2187	0.652076
$297$	−4.94328	−0.286838
$298$	−37.5881	−2.17742
$299$	−6.82301	−0.394585
$300$	−3.45871	−0.199689
$301$	0	0
$302$	36.6876	2.11113
$303$	−3.78486	−0.217434
$304$	−32.1781	−1.84554
$305$	0.0927060	0.00530833
$306$	1.32954	0.0760050
$307$	1.95055	0.111324	0.0556619	−	0.998450i	$-0.482273\pi$
$307$	1.95055	0.111324	0.0556619	+	0.998450i	$0.482273\pi$
$308$	0	0
$309$	−19.1368	−1.08866
$310$	−0.967025	−0.0549233
$311$	25.3798	1.43916	0.719578	−	0.694412i	$-0.244336\pi$
$311$	25.3798	1.43916	0.719578	+	0.694412i	$0.244336\pi$
$312$	2.64233	0.149592
$313$	−16.7300	−0.945636	−0.472818	−	0.881160i	$-0.656763\pi$
$313$	−16.7300	−0.945636	−0.472818	+	0.881160i	$0.656763\pi$
$314$	−21.2451	−1.19893
$315$	0	0
$316$	10.7761	0.606203
$317$	−27.1439	−1.52455	−0.762277	−	0.647250i	$-0.775919\pi$
$317$	−27.1439	−1.52455	−0.762277	+	0.647250i	$0.775919\pi$
$318$	9.83314	0.551415
$319$	0.221103	0.0123794
$320$	0.297832	0.0166493
$321$	−13.5411	−0.755791
$322$	0	0
$323$	−5.31476	−0.295721
$324$	0.692668	0.0384815
$325$	−6.15033	−0.341159
$326$	−3.88126	−0.214963
$327$	0.705015	0.0389874
$328$	−2.14525	−0.118451
$329$	0	0
$330$	0.663251	0.0365108
$331$	−1.13038	−0.0621311	−0.0310656	−	0.999517i	$-0.509890\pi$
$331$	−1.13038	−0.0621311	−0.0310656	+	0.999517i	$0.509890\pi$
$332$	6.25159	0.343101
$333$	5.22958	0.286579
$334$	−24.2517	−1.32699
$335$	−0.221279	−0.0120898
$336$	0	0
$337$	27.0417	1.47306	0.736529	−	0.676406i	$-0.236464\pi$
$337$	27.0417	1.47306	0.736529	+	0.676406i	$0.236464\pi$
$338$	18.8427	1.02491
$339$	−11.6339	−0.631867
$340$	−0.0458889	−0.00248867
$341$	−35.6279	−1.92936
$342$	−10.7638	−0.582037
$343$	0	0
$344$	−18.5538	−1.00036
$345$	−0.452937	−0.0243853
$346$	17.2337	0.926488
$347$	−17.4737	−0.938039	−0.469020	−	0.883188i	$-0.655393\pi$
$347$	−17.4737	−0.938039	−0.469020	+	0.883188i	$0.655393\pi$
$348$	−0.0309816	−0.00166079
$349$	22.4220	1.20022	0.600112	−	0.799916i	$-0.295123\pi$
$349$	22.4220	1.20022	0.600112	+	0.799916i	$0.295123\pi$
$350$	0	0
$351$	1.23171	0.0657439
$352$	−18.5827	−0.990463
$353$	−9.96215	−0.530232	−0.265116	−	0.964217i	$-0.585410\pi$
$353$	−9.96215	−0.530232	−0.265116	+	0.964217i	$0.585410\pi$
$354$	7.12253	0.378558
$355$	−0.454641	−0.0241299
$356$	5.11721	0.271212
$357$	0	0
$358$	10.7519	0.568256
$359$	−21.0085	−1.10879	−0.554394	−	0.832254i	$-0.687050\pi$
$359$	−21.0085	−1.10879	−0.554394	+	0.832254i	$0.687050\pi$
$360$	0.175408	0.00924480
$361$	24.0274	1.26460
$362$	3.37822	0.177555
$363$	13.4360	0.705209
$364$	0	0
$365$	−1.18619	−0.0620882
$366$	−1.86049	−0.0972496
$367$	−31.8537	−1.66275	−0.831376	−	0.555711i	$-0.812446\pi$
$367$	−31.8537	−1.66275	−0.831376	+	0.555711i	$0.812446\pi$
$368$	27.1740	1.41655
$369$	−1.00000	−0.0520579
$370$	−0.701664	−0.0364778
$371$	0	0
$372$	4.99229	0.258838
$373$	−22.2169	−1.15035	−0.575175	−	0.818031i	$-0.695066\pi$
$373$	−22.2169	−1.15035	−0.575175	+	0.818031i	$0.695066\pi$
$374$	−6.57231	−0.339846
$375$	−0.817110	−0.0421954
$376$	23.4006	1.20679
$377$	−0.0550920	−0.00283738
$378$	0	0
$379$	28.0974	1.44327	0.721633	−	0.692276i	$-0.243392\pi$
$379$	28.0974	1.44327	0.721633	+	0.692276i	$0.243392\pi$
$380$	0.371509	0.0190580
$381$	−2.52451	−0.129334
$382$	30.2850	1.54952
$383$	7.97911	0.407714	0.203857	−	0.979001i	$-0.434652\pi$
$383$	7.97911	0.407714	0.203857	+	0.979001i	$0.434652\pi$
$384$	−13.4955	−0.688689
$385$	0	0
$386$	−37.3091	−1.89898
$387$	−8.64881	−0.439644
$388$	3.77196	0.191492
$389$	−34.4544	−1.74691	−0.873453	−	0.486908i	$-0.838125\pi$
$389$	−34.4544	−1.74691	−0.873453	+	0.486908i	$0.838125\pi$
$390$	−0.165262	−0.00836835
$391$	4.48826	0.226981
$392$	0	0
$393$	−10.8567	−0.547647
$394$	−3.10788	−0.156573
$395$	1.27206	0.0640043
$396$	−3.42405	−0.172065
$397$	−23.1863	−1.16369	−0.581843	−	0.813301i	$-0.697668\pi$
$397$	−23.1863	−1.16369	−0.581843	+	0.813301i	$0.697668\pi$
$398$	−33.9348	−1.70100
$399$	0	0
$400$	24.4949	1.22475
$401$	−10.7495	−0.536804	−0.268402	−	0.963307i	$-0.586496\pi$
$401$	−10.7495	−0.536804	−0.268402	+	0.963307i	$0.586496\pi$
$402$	4.44080	0.221487
$403$	8.87737	0.442213
$404$	−2.62165	−0.130432
$405$	0.0817657	0.00406297
$406$	0	0
$407$	−25.8513	−1.28140
$408$	−1.73816	−0.0860515
$409$	−15.6989	−0.776261	−0.388130	−	0.921604i	$-0.626879\pi$
$409$	−15.6989	−0.776261	−0.388130	+	0.921604i	$0.626879\pi$
$410$	0.134172	0.00662629
$411$	−10.3736	−0.511692
$412$	−13.2555	−0.653050
$413$	0	0
$414$	9.08988	0.446743
$415$	0.737967	0.0362254
$416$	4.63024	0.227016
$417$	−3.46799	−0.169828
$418$	53.2083	2.60250
$419$	−27.5809	−1.34741	−0.673707	−	0.738999i	$-0.735299\pi$
$419$	−27.5809	−1.34741	−0.673707	+	0.738999i	$0.735299\pi$
$420$	0	0
$421$	24.8712	1.21215	0.606075	−	0.795408i	$-0.292743\pi$
$421$	24.8712	1.21215	0.606075	+	0.795408i	$0.292743\pi$
$422$	14.3337	0.697752
$423$	10.9081	0.530370
$424$	−12.8552	−0.624303
$425$	4.04576	0.196248
$426$	9.12408	0.442063
$427$	0	0
$428$	−9.37949	−0.453375
$429$	−6.08870	−0.293965
$430$	1.16043	0.0559609
$431$	38.0558	1.83308	0.916541	−	0.399942i	$-0.130970\pi$
$431$	38.0558	1.83308	0.916541	+	0.399942i	$0.130970\pi$
$432$	−4.90555	−0.236018
$433$	21.6978	1.04273	0.521365	−	0.853334i	$-0.325423\pi$
$433$	21.6978	1.04273	0.521365	+	0.853334i	$0.325423\pi$
$434$	0	0
$435$	−0.00365722	−0.000175350 0
$436$	0.488341	0.0233873
$437$	−36.3362	−1.73820
$438$	23.8054	1.13747
$439$	−36.9921	−1.76554	−0.882769	−	0.469807i	$-0.844323\pi$
$439$	−36.9921	−1.76554	−0.882769	+	0.469807i	$0.844323\pi$
$440$	−0.867090	−0.0413369
$441$	0	0
$442$	1.63762	0.0778934
$443$	10.9047	0.518100	0.259050	−	0.965864i	$-0.416591\pi$
$443$	10.9047	0.518100	0.259050	+	0.965864i	$0.416591\pi$
$444$	3.62236	0.171910
$445$	0.604059	0.0286352
$446$	−21.1591	−1.00191
$447$	22.9065	1.08344
$448$	0	0
$449$	−28.3090	−1.33599	−0.667993	−	0.744168i	$-0.732846\pi$
$449$	−28.3090	−1.33599	−0.667993	+	0.744168i	$0.732846\pi$
$450$	8.19370	0.386255
$451$	4.94328	0.232770
$452$	−8.05843	−0.379037
$453$	−22.3577	−1.05046
$454$	31.0151	1.45561
$455$	0	0
$456$	14.0718	0.658973
$457$	0.0300373	0.00140509	0.000702543	−	1.00000i	$-0.499776\pi$
$457$	0.0300373	0.00140509	0.000702543		1.00000i	$0.499776\pi$
$458$	2.35730	0.110149
$459$	−0.810235	−0.0378186
$460$	−0.313735	−0.0146280
$461$	−33.9313	−1.58034	−0.790169	−	0.612889i	$-0.790007\pi$
$461$	−33.9313	−1.58034	−0.790169	+	0.612889i	$0.790007\pi$
$462$	0	0
$463$	29.9962	1.39404	0.697020	−	0.717052i	$-0.254509\pi$
$463$	29.9962	1.39404	0.697020	+	0.717052i	$0.254509\pi$
$464$	0.219415	0.0101861
$465$	0.589313	0.0273288
$466$	24.2546	1.12357
$467$	−16.3034	−0.754429	−0.377215	−	0.926126i	$-0.623118\pi$
$467$	−16.3034	−0.754429	−0.377215	+	0.926126i	$0.623118\pi$
$468$	0.853167	0.0394377
$469$	0	0
$470$	−1.46356	−0.0675092
$471$	12.9470	0.596565
$472$	−9.31151	−0.428597
$473$	42.7535	1.96581
$474$	−25.5287	−1.17257
$475$	−32.7538	−1.50285
$476$	0	0
$477$	−5.99240	−0.274373
$478$	1.70401	0.0779398
$479$	1.76809	0.0807862	0.0403931	−	0.999184i	$-0.487139\pi$
$479$	1.76809	0.0807862	0.0403931	+	0.999184i	$0.487139\pi$
$480$	0.307373	0.0140296
$481$	6.44134	0.293700
$482$	40.0165	1.82270
$483$	0	0
$484$	9.30671	0.423032
$485$	0.445260	0.0202182
$486$	−1.64093	−0.0744343
$487$	12.5458	0.568503	0.284252	−	0.958750i	$-0.408255\pi$
$487$	12.5458	0.568503	0.284252	+	0.958750i	$0.408255\pi$
$488$	2.43228	0.110104
$489$	2.36528	0.106961
$490$	0	0
$491$	−0.480203	−0.0216713	−0.0108356	−	0.999941i	$-0.503449\pi$
$491$	−0.480203	−0.0216713	−0.0108356	+	0.999941i	$0.503449\pi$
$492$	−0.692668	−0.0312279
$493$	0.0362402	0.00163218
$494$	−13.2579	−0.596499
$495$	−0.404191	−0.0181670
$496$	−35.3559	−1.58753
$497$	0	0
$498$	−14.8101	−0.663655
$499$	44.0725	1.97296	0.986479	−	0.163889i	$-0.0524038\pi$
$499$	44.0725	1.97296	0.986479	+	0.163889i	$0.0524038\pi$
$500$	−0.565986	−0.0253117
$501$	14.7792	0.660285
$502$	17.0776	0.762209
$503$	−28.8604	−1.28682	−0.643411	−	0.765521i	$-0.722481\pi$
$503$	−28.8604	−1.28682	−0.643411	+	0.765521i	$0.722481\pi$
$504$	0	0
$505$	−0.309471	−0.0137713
$506$	−44.9339	−1.99755
$507$	−11.4829	−0.509973
$508$	−1.74864	−0.0775836
$509$	29.3896	1.30267	0.651336	−	0.758789i	$-0.274209\pi$
$509$	29.3896	1.30267	0.651336	+	0.758789i	$0.274209\pi$
$510$	0.108711	0.00481381
$511$	0	0
$512$	2.60635	0.115185
$513$	6.55953	0.289610
$514$	−29.7371	−1.31165
$515$	−1.56474	−0.0689505
$516$	−5.99075	−0.263728
$517$	−53.9219	−2.37148
$518$	0	0
$519$	−10.5024	−0.461002
$520$	0.216052	0.00947450
$521$	−4.09206	−0.179277	−0.0896383	−	0.995974i	$-0.528571\pi$
$521$	−4.09206	−0.179277	−0.0896383	+	0.995974i	$0.528571\pi$
$522$	0.0733957	0.00321244
$523$	−7.40617	−0.323849	−0.161925	−	0.986803i	$-0.551770\pi$
$523$	−7.40617	−0.323849	−0.161925	+	0.986803i	$0.551770\pi$
$524$	−7.52008	−0.328516
$525$	0	0
$526$	4.67449	0.203818
$527$	−5.83964	−0.254379
$528$	24.2495	1.05532
$529$	7.68555	0.334154
$530$	0.804014	0.0349241
$531$	−4.34053	−0.188363
$532$	0	0
$533$	−1.23171	−0.0533514
$534$	−12.1227	−0.524601
$535$	−1.10720	−0.0478684
$536$	−5.80560	−0.250764
$537$	−6.55231	−0.282753
$538$	11.9161	0.513742
$539$	0	0
$540$	0.0566365	0.00243725
$541$	−31.6011	−1.35864	−0.679319	−	0.733843i	$-0.737725\pi$
$541$	−31.6011	−1.35864	−0.679319	+	0.733843i	$0.737725\pi$
$542$	−6.88043	−0.295540
$543$	−2.05872	−0.0883479
$544$	−3.04583	−0.130589
$545$	0.0576461	0.00246929
$546$	0	0
$547$	−13.6853	−0.585143	−0.292571	−	0.956244i	$-0.594511\pi$
$547$	−13.6853	−0.585143	−0.292571	+	0.956244i	$0.594511\pi$
$548$	−7.18546	−0.306948
$549$	1.13380	0.0483894
$550$	−40.5038	−1.72709
$551$	−0.293394	−0.0124990
$552$	−11.8835	−0.505795
$553$	0	0
$554$	−13.1426	−0.558374
$555$	0.427600	0.0181506
$556$	−2.40216	−0.101874
$557$	4.80505	0.203597	0.101798	−	0.994805i	$-0.467540\pi$
$557$	4.80505	0.203597	0.101798	+	0.994805i	$0.467540\pi$
$558$	−11.8268	−0.500667
$559$	−10.6528	−0.450567
$560$	0	0
$561$	4.00522	0.169101
$562$	3.60965	0.152264
$563$	8.15180	0.343558	0.171779	−	0.985136i	$-0.445049\pi$
$563$	8.15180	0.343558	0.171779	+	0.985136i	$0.445049\pi$
$564$	7.55569	0.318152
$565$	−0.951255	−0.0400196
$566$	6.29341	0.264532
$567$	0	0
$568$	−11.9282	−0.500496
$569$	−34.3425	−1.43971	−0.719857	−	0.694122i	$-0.755793\pi$
$569$	−34.3425	−1.43971	−0.719857	+	0.694122i	$0.755793\pi$
$570$	−0.880107	−0.0368636
$571$	−8.17313	−0.342035	−0.171017	−	0.985268i	$-0.554705\pi$
$571$	−8.17313	−0.342035	−0.171017	+	0.985268i	$0.554705\pi$
$572$	−4.21745	−0.176340
$573$	−18.4559	−0.771008
$574$	0	0
$575$	27.6602	1.15351
$576$	3.64251	0.151771
$577$	−1.24503	−0.0518312	−0.0259156	−	0.999664i	$-0.508250\pi$
$577$	−1.24503	−0.0518312	−0.0259156	+	0.999664i	$0.508250\pi$
$578$	26.8187	1.11551
$579$	22.7365	0.944896
$580$	−0.00253323	−0.000105187 0
$581$	0	0
$582$	−8.93580	−0.370401
$583$	29.6221	1.22682
$584$	−31.1216	−1.28782
$585$	0.100712	0.00416392
$586$	12.8345	0.530189
$587$	9.16561	0.378305	0.189153	−	0.981948i	$-0.439426\pi$
$587$	9.16561	0.378305	0.189153	+	0.981948i	$0.439426\pi$
$588$	0	0
$589$	47.2768	1.94800
$590$	0.582379	0.0239761
$591$	1.89397	0.0779074
$592$	−25.6539	−1.05437
$593$	19.9726	0.820177	0.410089	−	0.912046i	$-0.365498\pi$
$593$	19.9726	0.820177	0.410089	+	0.912046i	$0.365498\pi$
$594$	8.11161	0.332823
$595$	0	0
$596$	15.8666	0.649921
$597$	20.6802	0.846382
$598$	11.1961	0.457844
$599$	−9.37301	−0.382971	−0.191485	−	0.981495i	$-0.561330\pi$
$599$	−9.37301	−0.382971	−0.191485	+	0.981495i	$0.561330\pi$
$600$	−10.7119	−0.437311
$601$	1.48167	0.0604388	0.0302194	−	0.999543i	$-0.490379\pi$
$601$	1.48167	0.0604388	0.0302194	+	0.999543i	$0.490379\pi$
$602$	0	0
$603$	−2.70626	−0.110207
$604$	−15.4865	−0.630136
$605$	1.09861	0.0446647
$606$	6.21070	0.252293
$607$	−23.5439	−0.955617	−0.477809	−	0.878464i	$-0.658569\pi$
$607$	−23.5439	−0.955617	−0.477809	+	0.878464i	$0.658569\pi$
$608$	24.6585	1.00003
$609$	0	0
$610$	−0.152125	−0.00615934
$611$	13.4357	0.543548
$612$	−0.561224	−0.0226861
$613$	−23.4070	−0.945401	−0.472700	−	0.881223i	$-0.656721\pi$
$613$	−23.4070	−0.945401	−0.472700	+	0.881223i	$0.656721\pi$
$614$	−3.20073	−0.129171
$615$	−0.0817657	−0.00329711
$616$	0	0
$617$	−32.4731	−1.30732	−0.653658	−	0.756790i	$-0.726767\pi$
$617$	−32.4731	−1.30732	−0.653658	+	0.756790i	$0.726767\pi$
$618$	31.4023	1.26318
$619$	9.07557	0.364778	0.182389	−	0.983226i	$-0.441617\pi$
$619$	9.07557	0.364778	0.182389	+	0.983226i	$0.441617\pi$
$620$	0.408198	0.0163936
$621$	−5.53945	−0.222291
$622$	−41.6466	−1.66987
$623$	0	0
$624$	−6.04222	−0.241883
$625$	24.8998	0.995990
$626$	27.4528	1.09724
$627$	−32.4256	−1.29495
$628$	8.96795	0.357860
$629$	−4.23719	−0.168948
$630$	0	0
$631$	−4.18697	−0.166681	−0.0833404	−	0.996521i	$-0.526559\pi$
$631$	−4.18697	−0.166681	−0.0833404	+	0.996521i	$0.526559\pi$
$632$	33.3744	1.32756
$633$	−8.73506	−0.347187
$634$	44.5414	1.76897
$635$	−0.206418	−0.00819145
$636$	−4.15074	−0.164588
$637$	0	0
$638$	−0.362816	−0.0143640
$639$	−5.56029	−0.219962
$640$	−1.10347	−0.0436184
$641$	−28.6487	−1.13156	−0.565778	−	0.824558i	$-0.691424\pi$
$641$	−28.6487	−1.13156	−0.565778	+	0.824558i	$0.691424\pi$
$642$	22.2201	0.876957
$643$	−26.3904	−1.04073	−0.520367	−	0.853943i	$-0.674205\pi$
$643$	−26.3904	−1.04073	−0.520367	+	0.853943i	$0.674205\pi$
$644$	0	0
$645$	−0.707176	−0.0278450
$646$	8.72118	0.343130
$647$	16.5423	0.650344	0.325172	−	0.945655i	$-0.394578\pi$
$647$	16.5423	0.650344	0.325172	+	0.945655i	$0.394578\pi$
$648$	2.14525	0.0842733
$649$	21.4565	0.842240
$650$	10.0923	0.395852
$651$	0	0
$652$	1.63835	0.0641627
$653$	37.0887	1.45139	0.725697	−	0.688015i	$-0.241518\pi$
$653$	37.0887	1.45139	0.725697	+	0.688015i	$0.241518\pi$
$654$	−1.15688	−0.0452377
$655$	−0.887705	−0.0346855
$656$	4.90555	0.191529
$657$	−14.5072	−0.565981
$658$	0	0
$659$	−4.20478	−0.163795	−0.0818975	−	0.996641i	$-0.526098\pi$
$659$	−4.20478	−0.163795	−0.0818975	+	0.996641i	$0.526098\pi$
$660$	−0.279970	−0.0108978
$661$	11.6207	0.451994	0.225997	−	0.974128i	$-0.427436\pi$
$661$	11.6207	0.451994	0.225997	+	0.974128i	$0.427436\pi$
$662$	1.85488	0.0720918
$663$	−0.997977	−0.0387582
$664$	19.3617	0.751379
$665$	0	0
$666$	−8.58140	−0.332522
$667$	0.247769	0.00959364
$668$	10.2371	0.396084
$669$	12.8945	0.498532
$670$	0.363105	0.0140280
$671$	−5.60470	−0.216367
$672$	0	0
$673$	−33.7947	−1.30269	−0.651346	−	0.758781i	$-0.725795\pi$
$673$	−33.7947	−1.30269	−0.651346	+	0.758781i	$0.725795\pi$
$674$	−44.3737	−1.70921
$675$	−4.99331	−0.192193
$676$	−7.95382	−0.305916
$677$	22.3305	0.858229	0.429115	−	0.903250i	$-0.358826\pi$
$677$	22.3305	0.858229	0.429115	+	0.903250i	$0.358826\pi$
$678$	19.0905	0.733166
$679$	0	0
$680$	−0.142122	−0.00545011
$681$	−18.9009	−0.724283
$682$	58.4631	2.23867
$683$	1.70074	0.0650769	0.0325385	−	0.999470i	$-0.489641\pi$
$683$	1.70074	0.0650769	0.0325385	+	0.999470i	$0.489641\pi$
$684$	4.54357	0.173728
$685$	−0.848205	−0.0324082
$686$	0	0
$687$	−1.43656	−0.0548081
$688$	42.4271	1.61752
$689$	−7.38091	−0.281190
$690$	0.743241	0.0282947
$691$	18.1625	0.690934	0.345467	−	0.938431i	$-0.387721\pi$
$691$	18.1625	0.690934	0.345467	+	0.938431i	$0.387721\pi$
$692$	−7.27464	−0.276540
$693$	0	0
$694$	28.6733	1.08842
$695$	−0.283562	−0.0107561
$696$	−0.0959526	−0.00363707
$697$	0.810235	0.0306899
$698$	−36.7931	−1.39264
$699$	−14.7809	−0.559066
$700$	0	0
$701$	−16.2740	−0.614662	−0.307331	−	0.951603i	$-0.599436\pi$
$701$	−16.2740	−0.614662	−0.307331	+	0.951603i	$0.599436\pi$
$702$	−2.02116	−0.0762838
$703$	34.3036	1.29378
$704$	−18.0060	−0.678625
$705$	0.891909	0.0335912
$706$	16.3472	0.615236
$707$	0	0
$708$	−3.00655	−0.112993
$709$	−29.3971	−1.10403	−0.552016	−	0.833833i	$-0.686141\pi$
$709$	−29.3971	−1.10403	−0.552016	+	0.833833i	$0.686141\pi$
$710$	0.746037	0.0279983
$711$	15.5574	0.583447
$712$	15.8484	0.593944
$713$	−39.9247	−1.49519
$714$	0	0
$715$	−0.497847	−0.0186184
$716$	−4.53857	−0.169614
$717$	−1.03844	−0.0387813
$718$	34.4736	1.28655
$719$	−21.6187	−0.806240	−0.403120	−	0.915147i	$-0.632074\pi$
$719$	−21.6187	−0.806240	−0.403120	+	0.915147i	$0.632074\pi$
$720$	−0.401106	−0.0149483
$721$	0	0
$722$	−39.4274	−1.46734
$723$	−24.3864	−0.906939
$724$	−1.42601	−0.0529971
$725$	0.223341	0.00829467
$726$	−22.0477	−0.818266
$727$	−30.5668	−1.13366	−0.566830	−	0.823834i	$-0.691831\pi$
$727$	−30.5668	−1.13366	−0.566830	+	0.823834i	$0.691831\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	1.94647	0.0720420
$731$	7.00757	0.259184
$732$	0.785347	0.0290273
$733$	−6.44019	−0.237874	−0.118937	−	0.992902i	$-0.537949\pi$
$733$	−6.44019	−0.237874	−0.118937	+	0.992902i	$0.537949\pi$
$734$	52.2699	1.92932
$735$	0	0
$736$	−20.8239	−0.767577
$737$	13.3778	0.492778
$738$	1.64093	0.0604037
$739$	−17.7546	−0.653114	−0.326557	−	0.945178i	$-0.605889\pi$
$739$	−17.7546	−0.653114	−0.326557	+	0.945178i	$0.605889\pi$
$740$	0.296185	0.0108880
$741$	8.07945	0.296806
$742$	0	0
$743$	−13.7838	−0.505678	−0.252839	−	0.967508i	$-0.581364\pi$
$743$	−13.7838	−0.505678	−0.252839	+	0.967508i	$0.581364\pi$
$744$	15.4615	0.566847
$745$	1.87297	0.0686202
$746$	36.4565	1.33477
$747$	9.02538	0.330221
$748$	2.77429	0.101438
$749$	0	0
$750$	1.34083	0.0489600
$751$	−31.6129	−1.15357	−0.576785	−	0.816896i	$-0.695693\pi$
$751$	−31.6129	−1.15357	−0.576785	+	0.816896i	$0.695693\pi$
$752$	−53.5102	−1.95132
$753$	−10.4072	−0.379260
$754$	0.0904024	0.00329226
$755$	−1.82810	−0.0665313
$756$	0	0
$757$	25.1875	0.915454	0.457727	−	0.889093i	$-0.348664\pi$
$757$	25.1875	0.915454	0.457727	+	0.889093i	$0.348664\pi$
$758$	−46.1060	−1.67464
$759$	27.3831	0.993943
$760$	1.15059	0.0417363
$761$	−24.5389	−0.889534	−0.444767	−	0.895646i	$-0.646714\pi$
$761$	−24.5389	−0.889534	−0.444767	+	0.895646i	$0.646714\pi$
$762$	4.14255	0.150069
$763$	0	0
$764$	−12.7838	−0.462503
$765$	−0.0662495	−0.00239526
$766$	−13.0932	−0.473077
$767$	−5.34629	−0.193043
$768$	14.8602	0.536222
$769$	27.2252	0.981766	0.490883	−	0.871226i	$-0.336674\pi$
$769$	27.2252	0.981766	0.490883	+	0.871226i	$0.336674\pi$
$770$	0	0
$771$	18.1220	0.652649
$772$	15.7488	0.566813
$773$	−39.2782	−1.41274	−0.706369	−	0.707844i	$-0.749668\pi$
$773$	−39.2782	−1.41274	−0.706369	+	0.707844i	$0.749668\pi$
$774$	14.1921	0.510126
$775$	−35.9885	−1.29275
$776$	11.6821	0.419362
$777$	0	0
$778$	56.5374	2.02696
$779$	−6.55953	−0.235019
$780$	0.0697598	0.00249780
$781$	27.4861	0.983530
$782$	−7.36495	−0.263370
$783$	−0.0447280	−0.00159845
$784$	0	0
$785$	1.05862	0.0377837
$786$	17.8151	0.635444
$787$	−54.3409	−1.93704	−0.968522	−	0.248927i	$-0.919922\pi$
$787$	−54.3409	−1.93704	−0.968522	+	0.248927i	$0.919922\pi$
$788$	1.31189	0.0467341
$789$	−2.84868	−0.101416
$790$	−2.08737	−0.0742652
$791$	0	0
$792$	−10.6046	−0.376817
$793$	1.39652	0.0495918
$794$	38.0472	1.35024
$795$	−0.489973	−0.0173775
$796$	14.3245	0.507718
$797$	−45.0852	−1.59700	−0.798500	−	0.601995i	$-0.794373\pi$
$797$	−45.0852	−1.59700	−0.798500	+	0.601995i	$0.794373\pi$
$798$	0	0
$799$	−8.83814	−0.312671
$800$	−18.7708	−0.663648
$801$	7.38768	0.261031
$802$	17.6392	0.622862
$803$	71.7134	2.53071
$804$	−1.87454	−0.0661099
$805$	0	0
$806$	−14.5672	−0.513107
$807$	−7.26180	−0.255628
$808$	−8.11945	−0.285641
$809$	44.8906	1.57827	0.789135	−	0.614220i	$-0.210529\pi$
$809$	44.8906	1.57827	0.789135	+	0.614220i	$0.210529\pi$
$810$	−0.134172	−0.00471433
$811$	43.9625	1.54373	0.771865	−	0.635786i	$-0.219324\pi$
$811$	43.9625	1.54373	0.771865	+	0.635786i	$0.219324\pi$
$812$	0	0
$813$	4.19299	0.147055
$814$	42.4203	1.48683
$815$	0.193398	0.00677445
$816$	3.97465	0.139141
$817$	−56.7321	−1.98481
$818$	25.7609	0.900708
$819$	0	0
$820$	−0.0566365	−0.00197783
$821$	−9.16765	−0.319953	−0.159977	−	0.987121i	$-0.551142\pi$
$821$	−9.16765	−0.319953	−0.159977	+	0.987121i	$0.551142\pi$
$822$	17.0224	0.593725
$823$	−8.42471	−0.293667	−0.146834	−	0.989161i	$-0.546908\pi$
$823$	−8.42471	−0.293667	−0.146834	+	0.989161i	$0.546908\pi$
$824$	−41.0532	−1.43016
$825$	24.6834	0.859364
$826$	0	0
$827$	48.2599	1.67816	0.839080	−	0.544008i	$-0.183094\pi$
$827$	48.2599	1.67816	0.839080	+	0.544008i	$0.183094\pi$
$828$	−3.83700	−0.133345
$829$	0.597727	0.0207599	0.0103800	−	0.999946i	$-0.496696\pi$
$829$	0.597727	0.0207599	0.0103800	+	0.999946i	$0.496696\pi$
$830$	−1.21096	−0.0420329
$831$	8.00920	0.277836
$832$	4.48652	0.155542
$833$	0	0
$834$	5.69074	0.197054
$835$	1.20843	0.0418195
$836$	−22.4602	−0.776801
$837$	7.20734	0.249122
$838$	45.2584	1.56343
$839$	12.7920	0.441630	0.220815	−	0.975316i	$-0.429128\pi$
$839$	12.7920	0.441630	0.220815	+	0.975316i	$0.429128\pi$
$840$	0	0
$841$	−28.9980	−0.999931
$842$	−40.8121	−1.40648
$843$	−2.19975	−0.0757635
$844$	−6.05049	−0.208267
$845$	−0.938906	−0.0322994
$846$	−17.8995	−0.615397
$847$	0	0
$848$	29.3960	1.00946
$849$	−3.83526	−0.131626
$850$	−6.63883	−0.227710
$851$	−28.9690	−0.993045
$852$	−3.85144	−0.131948
$853$	−14.5985	−0.499841	−0.249921	−	0.968266i	$-0.580405\pi$
$853$	−14.5985	−0.499841	−0.249921	+	0.968266i	$0.580405\pi$
$854$	0	0
$855$	0.536345	0.0183426
$856$	−29.0490	−0.992875
$857$	−7.40299	−0.252881	−0.126441	−	0.991974i	$-0.540355\pi$
$857$	−7.40299	−0.252881	−0.126441	+	0.991974i	$0.540355\pi$
$858$	9.99117	0.341093
$859$	−43.1440	−1.47206	−0.736028	−	0.676951i	$-0.763301\pi$
$859$	−43.1440	−1.47206	−0.736028	+	0.676951i	$0.763301\pi$
$860$	−0.489838	−0.0167033
$861$	0	0
$862$	−62.4470	−2.12695
$863$	27.0789	0.921776	0.460888	−	0.887458i	$-0.347531\pi$
$863$	27.0789	0.921776	0.460888	+	0.887458i	$0.347531\pi$
$864$	3.75919	0.127890
$865$	−0.858732	−0.0291978
$866$	−35.6047	−1.20990
$867$	−16.3435	−0.555055
$868$	0	0
$869$	−76.9045	−2.60881
$870$	0.00600125	0.000203462 0
$871$	−3.33333	−0.112946
$872$	1.51243	0.0512174
$873$	5.44556	0.184304
$874$	59.6253	2.01686
$875$	0	0
$876$	−10.0487	−0.339514
$877$	33.0013	1.11438	0.557188	−	0.830387i	$-0.311880\pi$
$877$	33.0013	1.11438	0.557188	+	0.830387i	$0.311880\pi$
$878$	60.7017	2.04858
$879$	−7.82147	−0.263812
$880$	1.98278	0.0668394
$881$	−22.3933	−0.754451	−0.377225	−	0.926122i	$-0.623122\pi$
$881$	−22.3933	−0.754451	−0.377225	+	0.926122i	$0.623122\pi$
$882$	0	0
$883$	12.8447	0.432257	0.216129	−	0.976365i	$-0.430657\pi$
$883$	12.8447	0.432257	0.216129	+	0.976365i	$0.430657\pi$
$884$	−0.691266	−0.0232498
$885$	−0.354907	−0.0119301
$886$	−17.8940	−0.601160
$887$	−26.8473	−0.901445	−0.450722	−	0.892664i	$-0.648834\pi$
$887$	−26.8473	−0.901445	−0.450722	+	0.892664i	$0.648834\pi$
$888$	11.2187	0.376476
$889$	0	0
$890$	−0.991222	−0.0332258
$891$	−4.94328	−0.165606
$892$	8.93164	0.299053
$893$	71.5520	2.39440
$894$	−37.5881	−1.25713
$895$	−0.535754	−0.0179083
$896$	0	0
$897$	−6.82301	−0.227814
$898$	46.4533	1.55017
$899$	−0.322370	−0.0107516
$900$	−3.45871	−0.115290
$901$	4.85526	0.161752
$902$	−8.11161	−0.270087
$903$	0	0
$904$	−24.9576	−0.830078
$905$	−0.168332	−0.00559556
$906$	36.6876	1.21886
$907$	−32.9319	−1.09349	−0.546743	−	0.837300i	$-0.684133\pi$
$907$	−32.9319	−1.09349	−0.546743	+	0.837300i	$0.684133\pi$
$908$	−13.0920	−0.434474
$909$	−3.78486	−0.125536
$910$	0	0
$911$	−1.75669	−0.0582018	−0.0291009	−	0.999576i	$-0.509264\pi$
$911$	−1.75669	−0.0582018	−0.0291009	+	0.999576i	$0.509264\pi$
$912$	−32.1781	−1.06552
$913$	−44.6150	−1.47654
$914$	−0.0492893	−0.00163034
$915$	0.0927060	0.00306477
$916$	−0.995058	−0.0328776
$917$	0	0
$918$	1.32954	0.0438815
$919$	−31.1103	−1.02623	−0.513117	−	0.858319i	$-0.671509\pi$
$919$	−31.1103	−1.02623	−0.513117	+	0.858319i	$0.671509\pi$
$920$	−0.971663	−0.0320348
$921$	1.95055	0.0642728
$922$	55.6790	1.83369
$923$	−6.84868	−0.225427
$924$	0	0
$925$	−26.1129	−0.858588
$926$	−49.2217	−1.61753
$927$	−19.1368	−0.628536
$928$	−0.168141	−0.00551950
$929$	−14.9878	−0.491734	−0.245867	−	0.969304i	$-0.579073\pi$
$929$	−14.9878	−0.491734	−0.245867	+	0.969304i	$0.579073\pi$
$930$	−0.967025	−0.0317100
$931$	0	0
$932$	−10.2383	−0.335366
$933$	25.3798	0.830897
$934$	26.7527	0.875376
$935$	0.327490	0.0107101
$936$	2.64233	0.0863672
$937$	−46.7766	−1.52812	−0.764062	−	0.645143i	$-0.776798\pi$
$937$	−46.7766	−1.52812	−0.764062	+	0.645143i	$0.776798\pi$
$938$	0	0
$939$	−16.7300	−0.545963
$940$	0.617797	0.0201503
$941$	−1.19448	−0.0389391	−0.0194695	−	0.999810i	$-0.506198\pi$
$941$	−1.19448	−0.0389391	−0.0194695	+	0.999810i	$0.506198\pi$
$942$	−21.2451	−0.692204
$943$	5.53945	0.180389
$944$	21.2927	0.693018
$945$	0	0
$946$	−70.1557	−2.28096
$947$	0.760030	0.0246977	0.0123488	−	0.999924i	$-0.496069\pi$
$947$	0.760030	0.0246977	0.0123488	+	0.999924i	$0.496069\pi$
$948$	10.7761	0.349991
$949$	−17.8687	−0.580044
$950$	53.7468	1.74378
$951$	−27.1439	−0.880202
$952$	0	0
$953$	−45.9749	−1.48927	−0.744637	−	0.667470i	$-0.767377\pi$
$953$	−45.9749	−1.48927	−0.744637	+	0.667470i	$0.767377\pi$
$954$	9.83314	0.318360
$955$	−1.50906	−0.0488321
$956$	−0.719295	−0.0232636
$957$	0.221103	0.00714725
$958$	−2.90132	−0.0937376
$959$	0	0
$960$	0.297832	0.00961250
$961$	20.9458	0.675670
$962$	−10.5698	−0.340784
$963$	−13.5411	−0.436356
$964$	−16.8917	−0.544044
$965$	1.85906	0.0598454
$966$	0	0
$967$	20.1637	0.648421	0.324211	−	0.945985i	$-0.394901\pi$
$967$	20.1637	0.648421	0.324211	+	0.945985i	$0.394901\pi$
$968$	28.8236	0.926427
$969$	−5.31476	−0.170735
$970$	−0.730642	−0.0234595
$971$	−35.0294	−1.12415	−0.562074	−	0.827087i	$-0.689996\pi$
$971$	−35.0294	−1.12415	−0.562074	+	0.827087i	$0.689996\pi$
$972$	0.692668	0.0222173
$973$	0	0
$974$	−20.5868	−0.659644
$975$	−6.15033	−0.196968
$976$	−5.56191	−0.178033
$977$	−58.3885	−1.86801	−0.934006	−	0.357257i	$-0.883712\pi$
$977$	−58.3885	−1.86801	−0.934006	+	0.357257i	$0.883712\pi$
$978$	−3.88126	−0.124109
$979$	−36.5194	−1.16717
$980$	0	0
$981$	0.705015	0.0225094
$982$	0.787983	0.0251455
$983$	36.7120	1.17093	0.585465	−	0.810698i	$-0.300912\pi$
$983$	36.7120	1.17093	0.585465	+	0.810698i	$0.300912\pi$
$984$	−2.14525	−0.0683880
$985$	0.154862	0.00493430
$986$	−0.0594678	−0.00189384
$987$	0	0
$988$	5.59638	0.178044
$989$	47.9097	1.52344
$990$	0.663251	0.0210795
$991$	25.4394	0.808108	0.404054	−	0.914735i	$-0.367601\pi$
$991$	25.4394	0.808108	0.404054	+	0.914735i	$0.367601\pi$
$992$	27.0938	0.860228
$993$	−1.13038	−0.0358714
$994$	0	0
$995$	1.69093	0.0536060
$996$	6.25159	0.198089
$997$	−23.9681	−0.759076	−0.379538	−	0.925176i	$-0.623917\pi$
$997$	−23.9681	−0.759076	−0.379538	+	0.925176i	$0.623917\pi$
$998$	−72.3202	−2.28925
$999$	5.22958	0.165457

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6027.2.a.bk.1.4		14
7.3	odd	6		861.2.i.g.247.11	✓	28
7.5	odd	6		861.2.i.g.739.11	yes	28
7.6	odd	2		6027.2.a.bj.1.4		14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
861.2.i.g.247.11	✓	28	7.3	odd	6
861.2.i.g.739.11	yes	28	7.5	odd	6
6027.2.a.bj.1.4		14	7.6	odd	2
6027.2.a.bk.1.4		14	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:	\( N \)	\(=\)	\( 6027 = 3 \cdot 7^{2} \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6027.a (trivial)

\(f(q)\)	\(=\)	\(q-1.64093 q^{2} +1.00000 q^{3} +0.692668 q^{4} +0.0817657 q^{5} -1.64093 q^{6} +2.14525 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.64093 q^{2} +1.00000 q^{3} +0.692668 q^{4} +0.0817657 q^{5} -1.64093 q^{6} +2.14525 q^{8} +1.00000 q^{9} -0.134172 q^{10} -4.94328 q^{11} +0.692668 q^{12} +1.23171 q^{13} +0.0817657 q^{15} -4.90555 q^{16} -0.810235 q^{17} -1.64093 q^{18} +6.55953 q^{19} +0.0566365 q^{20} +8.11161 q^{22} -5.53945 q^{23} +2.14525 q^{24} -4.99331 q^{25} -2.02116 q^{26} +1.00000 q^{27} -0.0447280 q^{29} -0.134172 q^{30} +7.20734 q^{31} +3.75919 q^{32} -4.94328 q^{33} +1.32954 q^{34} +0.692668 q^{36} +5.22958 q^{37} -10.7638 q^{38} +1.23171 q^{39} +0.175408 q^{40} -1.00000 q^{41} -8.64881 q^{43} -3.42405 q^{44} +0.0817657 q^{45} +9.08988 q^{46} +10.9081 q^{47} -4.90555 q^{48} +8.19370 q^{50} -0.810235 q^{51} +0.853167 q^{52} -5.99240 q^{53} -1.64093 q^{54} -0.404191 q^{55} +6.55953 q^{57} +0.0733957 q^{58} -4.34053 q^{59} +0.0566365 q^{60} +1.13380 q^{61} -11.8268 q^{62} +3.64251 q^{64} +0.100712 q^{65} +8.11161 q^{66} -2.70626 q^{67} -0.561224 q^{68} -5.53945 q^{69} -5.56029 q^{71} +2.14525 q^{72} -14.5072 q^{73} -8.58140 q^{74} -4.99331 q^{75} +4.54357 q^{76} -2.02116 q^{78} +15.5574 q^{79} -0.401106 q^{80} +1.00000 q^{81} +1.64093 q^{82} +9.02538 q^{83} -0.0662495 q^{85} +14.1921 q^{86} -0.0447280 q^{87} -10.6046 q^{88} +7.38768 q^{89} -0.134172 q^{90} -3.83700 q^{92} +7.20734 q^{93} -17.8995 q^{94} +0.536345 q^{95} +3.75919 q^{96} +5.44556 q^{97} -4.94328 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q - 2 q^{2} + 14 q^{3} + 14 q^{4} - 10 q^{5} - 2 q^{6} - 6 q^{8} + 14 q^{9}+O(q^{10}) \) 14 * q - 2 * q^2 + 14 * q^3 + 14 * q^4 - 10 * q^5 - 2 * q^6 - 6 * q^8 + 14 * q^9	\( 14 q - 2 q^{2} + 14 q^{3} + 14 q^{4} - 10 q^{5} - 2 q^{6} - 6 q^{8} + 14 q^{9} - 3 q^{10} - 16 q^{11} + 14 q^{12} - 21 q^{13} - 10 q^{15} + 22 q^{16} - 12 q^{17} - 2 q^{18} - 2 q^{19} - 40 q^{20} + q^{22} - 7 q^{23} - 6 q^{24} + 22 q^{25} - 2 q^{26} + 14 q^{27} - 16 q^{29} - 3 q^{30} - 8 q^{31} - 19 q^{32} - 16 q^{33} - 33 q^{34} + 14 q^{36} + q^{37} - 32 q^{38} - 21 q^{39} + 13 q^{40} - 14 q^{41} + 14 q^{43} - 36 q^{44} - 10 q^{45} - 12 q^{46} - 12 q^{47} + 22 q^{48} - q^{50} - 12 q^{51} - 60 q^{52} - 20 q^{53} - 2 q^{54} + 11 q^{55} - 2 q^{57} + 21 q^{58} - 25 q^{59} - 40 q^{60} - 26 q^{61} + 33 q^{62} + 42 q^{64} - 8 q^{65} + q^{66} - 22 q^{67} - 15 q^{68} - 7 q^{69} - 36 q^{71} - 6 q^{72} - 31 q^{73} - 65 q^{74} + 22 q^{75} + 2 q^{76} - 2 q^{78} + 12 q^{79} - 112 q^{80} + 14 q^{81} + 2 q^{82} - 20 q^{83} + 40 q^{85} - 9 q^{86} - 16 q^{87} - 54 q^{88} - 39 q^{89} - 3 q^{90} + 63 q^{92} - 8 q^{93} - 14 q^{94} - 55 q^{95} - 19 q^{96} - 18 q^{97} - 16 q^{99}+O(q^{100}) \) 14 * q - 2 * q^2 + 14 * q^3 + 14 * q^4 - 10 * q^5 - 2 * q^6 - 6 * q^8 + 14 * q^9 - 3 * q^10 - 16 * q^11 + 14 * q^12 - 21 * q^13 - 10 * q^15 + 22 * q^16 - 12 * q^17 - 2 * q^18 - 2 * q^19 - 40 * q^20 + q^22 - 7 * q^23 - 6 * q^24 + 22 * q^25 - 2 * q^26 + 14 * q^27 - 16 * q^29 - 3 * q^30 - 8 * q^31 - 19 * q^32 - 16 * q^33 - 33 * q^34 + 14 * q^36 + q^37 - 32 * q^38 - 21 * q^39 + 13 * q^40 - 14 * q^41 + 14 * q^43 - 36 * q^44 - 10 * q^45 - 12 * q^46 - 12 * q^47 + 22 * q^48 - q^50 - 12 * q^51 - 60 * q^52 - 20 * q^53 - 2 * q^54 + 11 * q^55 - 2 * q^57 + 21 * q^58 - 25 * q^59 - 40 * q^60 - 26 * q^61 + 33 * q^62 + 42 * q^64 - 8 * q^65 + q^66 - 22 * q^67 - 15 * q^68 - 7 * q^69 - 36 * q^71 - 6 * q^72 - 31 * q^73 - 65 * q^74 + 22 * q^75 + 2 * q^76 - 2 * q^78 + 12 * q^79 - 112 * q^80 + 14 * q^81 + 2 * q^82 - 20 * q^83 + 40 * q^85 - 9 * q^86 - 16 * q^87 - 54 * q^88 - 39 * q^89 - 3 * q^90 + 63 * q^92 - 8 * q^93 - 14 * q^94 - 55 * q^95 - 19 * q^96 - 18 * q^97 - 16 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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