LMFDB - Embedded newform 6027.2.a.bj.1.5

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:	$0$
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			1.5
Root			$1.21066$ 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)

$f(q)$	$=$	$q-1.21066 q^{2} -1.00000 q^{3} -0.534291 q^{4} +0.826979 q^{5} +1.21066 q^{6} +3.06818 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.21066 q^{2} -1.00000 q^{3} -0.534291 q^{4} +0.826979 q^{5} +1.21066 q^{6} +3.06818 q^{8} +1.00000 q^{9} -1.00119 q^{10} -0.396962 q^{11} +0.534291 q^{12} +3.17185 q^{13} -0.826979 q^{15} -2.64595 q^{16} +0.159142 q^{17} -1.21066 q^{18} +3.91493 q^{19} -0.441847 q^{20} +0.480588 q^{22} +7.13636 q^{23} -3.06818 q^{24} -4.31611 q^{25} -3.84005 q^{26} -1.00000 q^{27} +9.77724 q^{29} +1.00119 q^{30} +6.15497 q^{31} -2.93299 q^{32} +0.396962 q^{33} -0.192668 q^{34} -0.534291 q^{36} +10.0885 q^{37} -4.73967 q^{38} -3.17185 q^{39} +2.53732 q^{40} +1.00000 q^{41} -5.32444 q^{43} +0.212093 q^{44} +0.826979 q^{45} -8.63974 q^{46} -1.31060 q^{47} +2.64595 q^{48} +5.22536 q^{50} -0.159142 q^{51} -1.69469 q^{52} -5.54558 q^{53} +1.21066 q^{54} -0.328280 q^{55} -3.91493 q^{57} -11.8370 q^{58} +1.57839 q^{59} +0.441847 q^{60} -8.56205 q^{61} -7.45161 q^{62} +8.84277 q^{64} +2.62306 q^{65} -0.480588 q^{66} +12.1171 q^{67} -0.0850282 q^{68} -7.13636 q^{69} -1.25998 q^{71} +3.06818 q^{72} +8.34764 q^{73} -12.2138 q^{74} +4.31611 q^{75} -2.09171 q^{76} +3.84005 q^{78} -9.12954 q^{79} -2.18815 q^{80} +1.00000 q^{81} -1.21066 q^{82} +9.77501 q^{83} +0.131607 q^{85} +6.44611 q^{86} -9.77724 q^{87} -1.21795 q^{88} +11.8098 q^{89} -1.00119 q^{90} -3.81289 q^{92} -6.15497 q^{93} +1.58670 q^{94} +3.23757 q^{95} +2.93299 q^{96} +10.4867 q^{97} -0.396962 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−1.21066	−0.856069	−0.428035	−	0.903762i	$-0.640794\pi$
$2$	−1.21066	−0.856069	−0.428035	+	0.903762i	$0.640794\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	−0.534291	−0.267145
$5$	0.826979	0.369836	0.184918	−	0.982754i	$-0.440798\pi$
$5$	0.826979	0.369836	0.184918	+	0.982754i	$0.440798\pi$
$6$	1.21066	0.494252
$7$	0	0
$7$	0	0
$8$	3.06818	1.08476
$9$	1.00000	0.333333
$10$	−1.00119	−0.316606
$11$	−0.396962	−0.119689	−0.0598443	−	0.998208i	$-0.519060\pi$
$11$	−0.396962	−0.119689	−0.0598443	+	0.998208i	$0.519060\pi$
$12$	0.534291	0.154236
$13$	3.17185	0.879714	0.439857	−	0.898068i	$-0.355029\pi$
$13$	3.17185	0.879714	0.439857	+	0.898068i	$0.355029\pi$
$14$	0	0
$15$	−0.826979	−0.213525
$16$	−2.64595	−0.661488
$17$	0.159142	0.0385977	0.0192988	−	0.999814i	$-0.493857\pi$
$17$	0.159142	0.0385977	0.0192988	+	0.999814i	$0.493857\pi$
$18$	−1.21066	−0.285356
$19$	3.91493	0.898147	0.449073	−	0.893495i	$-0.351754\pi$
$19$	3.91493	0.898147	0.449073	+	0.893495i	$0.351754\pi$
$20$	−0.441847	−0.0988001
$21$	0	0
$22$	0.480588	0.102462
$23$	7.13636	1.48803	0.744017	−	0.668161i	$-0.232918\pi$
$23$	7.13636	1.48803	0.744017	+	0.668161i	$0.232918\pi$
$24$	−3.06818	−0.626289
$25$	−4.31611	−0.863221
$26$	−3.84005	−0.753096
$27$	−1.00000	−0.192450
$28$	0	0
$29$	9.77724	1.81559	0.907794	−	0.419416i	$-0.137765\pi$
$29$	9.77724	1.81559	0.907794	+	0.419416i	$0.137765\pi$
$30$	1.00119	0.182792
$31$	6.15497	1.10547	0.552733	−	0.833359i	$-0.313585\pi$
$31$	6.15497	1.10547	0.552733	+	0.833359i	$0.313585\pi$
$32$	−2.93299	−0.518485
$33$	0.396962	0.0691023
$34$	−0.192668	−0.0330423
$35$	0	0
$36$	−0.534291	−0.0890484
$37$	10.0885	1.65854	0.829269	−	0.558850i	$-0.188757\pi$
$37$	10.0885	1.65854	0.829269	+	0.558850i	$0.188757\pi$
$38$	−4.73967	−0.768876
$39$	−3.17185	−0.507903
$40$	2.53732	0.401185
$41$	1.00000	0.156174
$41$	1.00000	0.156174
$42$	0	0
$43$	−5.32444	−0.811969	−0.405985	−	0.913880i	$-0.633071\pi$
$43$	−5.32444	−0.811969	−0.405985	+	0.913880i	$0.633071\pi$
$44$	0.212093	0.0319743
$45$	0.826979	0.123279
$46$	−8.63974	−1.27386
$47$	−1.31060	−0.191171	−0.0955855	−	0.995421i	$-0.530472\pi$
$47$	−1.31060	−0.191171	−0.0955855	+	0.995421i	$0.530472\pi$
$48$	2.64595	0.381910
$49$	0	0
$50$	5.22536	0.738977
$51$	−0.159142	−0.0222844
$52$	−1.69469	−0.235011
$53$	−5.54558	−0.761744	−0.380872	−	0.924628i	$-0.624376\pi$
$53$	−5.54558	−0.761744	−0.380872	+	0.924628i	$0.624376\pi$
$54$	1.21066	0.164751
$55$	−0.328280	−0.0442652
$56$	0	0
$57$	−3.91493	−0.518545
$58$	−11.8370	−1.55427
$59$	1.57839	0.205488	0.102744	−	0.994708i	$-0.467238\pi$
$59$	1.57839	0.205488	0.102744	+	0.994708i	$0.467238\pi$
$60$	0.441847	0.0570422
$61$	−8.56205	−1.09626	−0.548129	−	0.836394i	$-0.684660\pi$
$61$	−8.56205	−1.09626	−0.548129	+	0.836394i	$0.684660\pi$
$62$	−7.45161	−0.946355
$63$	0	0
$64$	8.84277	1.10535
$65$	2.62306	0.325350
$66$	−0.480588	−0.0591564
$67$	12.1171	1.48034	0.740172	−	0.672418i	$-0.234744\pi$
$67$	12.1171	1.48034	0.740172	+	0.672418i	$0.234744\pi$
$68$	−0.0850282	−0.0103112
$69$	−7.13636	−0.859117
$70$	0	0
$71$	−1.25998	−0.149532	−0.0747659	−	0.997201i	$-0.523821\pi$
$71$	−1.25998	−0.149532	−0.0747659	+	0.997201i	$0.523821\pi$
$72$	3.06818	0.361588
$73$	8.34764	0.977017	0.488509	−	0.872559i	$-0.337541\pi$
$73$	8.34764	0.977017	0.488509	+	0.872559i	$0.337541\pi$
$74$	−12.2138	−1.41982
$75$	4.31611	0.498381
$76$	−2.09171	−0.239936
$77$	0	0
$78$	3.84005	0.434800
$79$	−9.12954	−1.02715	−0.513577	−	0.858044i	$-0.671680\pi$
$79$	−9.12954	−1.02715	−0.513577	+	0.858044i	$0.671680\pi$
$80$	−2.18815	−0.244642
$81$	1.00000	0.111111
$82$	−1.21066	−0.133696
$83$	9.77501	1.07295	0.536473	−	0.843917i	$-0.319756\pi$
$83$	9.77501	1.07295	0.536473	+	0.843917i	$0.319756\pi$
$84$	0	0
$85$	0.131607	0.0142748
$86$	6.44611	0.695102
$87$	−9.77724	−1.04823
$88$	−1.21795	−0.129834
$89$	11.8098	1.25184	0.625919	−	0.779888i	$-0.284724\pi$
$89$	11.8098	1.25184	0.625919	+	0.779888i	$0.284724\pi$
$90$	−1.00119	−0.105535
$91$	0	0
$92$	−3.81289	−0.397521
$93$	−6.15497	−0.638241
$94$	1.58670	0.163656
$95$	3.23757	0.332167
$96$	2.93299	0.299347
$97$	10.4867	1.06476	0.532381	−	0.846505i	$-0.321297\pi$
$97$	10.4867	1.06476	0.532381	+	0.846505i	$0.321297\pi$
$98$	0	0
$99$	−0.396962	−0.0398962
$100$	2.30605	0.230605
$101$	11.1956	1.11401	0.557004	−	0.830510i	$-0.311951\pi$
$101$	11.1956	1.11401	0.557004	+	0.830510i	$0.311951\pi$
$102$	0.192668	0.0190770
$103$	−14.7729	−1.45562	−0.727809	−	0.685780i	$-0.759461\pi$
$103$	−14.7729	−1.45562	−0.727809	+	0.685780i	$0.759461\pi$
$104$	9.73181	0.954282
$105$	0	0
$106$	6.71384	0.652105
$107$	−15.4131	−1.49004	−0.745022	−	0.667039i	$-0.767561\pi$
$107$	−15.4131	−1.49004	−0.745022	+	0.667039i	$0.767561\pi$
$108$	0.534291	0.0514121
$109$	6.49240	0.621859	0.310929	−	0.950433i	$-0.399360\pi$
$109$	6.49240	0.621859	0.310929	+	0.950433i	$0.399360\pi$
$110$	0.397437	0.0378941
$111$	−10.0885	−0.957557
$112$	0	0
$113$	7.90856	0.743975	0.371988	−	0.928238i	$-0.378676\pi$
$113$	7.90856	0.743975	0.371988	+	0.928238i	$0.378676\pi$
$114$	4.73967	0.443911
$115$	5.90162	0.550329
$116$	−5.22389	−0.485026
$117$	3.17185	0.293238
$118$	−1.91090	−0.175912
$119$	0	0
$120$	−2.53732	−0.231624
$121$	−10.8424	−0.985675
$122$	10.3658	0.938473
$123$	−1.00000	−0.0901670
$124$	−3.28854	−0.295320
$125$	−7.70423	−0.689087
$126$	0	0
$127$	14.5557	1.29161	0.645806	−	0.763502i	$-0.276522\pi$
$127$	14.5557	1.29161	0.645806	+	0.763502i	$0.276522\pi$
$128$	−4.83965	−0.427769
$129$	5.32444	0.468791
$130$	−3.17564	−0.278522
$131$	−6.06255	−0.529687	−0.264844	−	0.964291i	$-0.585320\pi$
$131$	−6.06255	−0.529687	−0.264844	+	0.964291i	$0.585320\pi$
$132$	−0.212093	−0.0184604
$133$	0	0
$134$	−14.6698	−1.26728
$135$	−0.826979	−0.0711750
$136$	0.488277	0.0418694
$137$	−20.0820	−1.71572	−0.857861	−	0.513881i	$-0.828207\pi$
$137$	−20.0820	−1.71572	−0.857861	+	0.513881i	$0.828207\pi$
$138$	8.63974	0.735463
$139$	−15.7498	−1.33588	−0.667939	−	0.744216i	$-0.732823\pi$
$139$	−15.7498	−1.33588	−0.667939	+	0.744216i	$0.732823\pi$
$140$	0	0
$141$	1.31060	0.110373
$142$	1.52541	0.128010
$143$	−1.25911	−0.105292
$144$	−2.64595	−0.220496
$145$	8.08558	0.671471
$146$	−10.1062	−0.836394
$147$	0	0
$148$	−5.39019	−0.443071
$149$	−3.75818	−0.307882	−0.153941	−	0.988080i	$-0.549197\pi$
$149$	−3.75818	−0.307882	−0.153941	+	0.988080i	$0.549197\pi$
$150$	−5.22536	−0.426649
$151$	−3.89228	−0.316749	−0.158375	−	0.987379i	$-0.550625\pi$
$151$	−3.89228	−0.316749	−0.158375	+	0.987379i	$0.550625\pi$
$152$	12.0117	0.974278
$153$	0.159142	0.0128659
$154$	0	0
$155$	5.09003	0.408841
$156$	1.69469	0.135684
$157$	1.02175	0.0815444	0.0407722	−	0.999168i	$-0.487018\pi$
$157$	1.02175	0.0815444	0.0407722	+	0.999168i	$0.487018\pi$
$158$	11.0528	0.879315
$159$	5.54558	0.439793
$160$	−2.42552	−0.191754
$161$	0	0
$162$	−1.21066	−0.0951188
$163$	−4.26792	−0.334289	−0.167145	−	0.985932i	$-0.553455\pi$
$163$	−4.26792	−0.334289	−0.167145	+	0.985932i	$0.553455\pi$
$164$	−0.534291	−0.0417211
$165$	0.328280	0.0255565
$166$	−11.8343	−0.918517
$167$	0.771033	0.0596643	0.0298322	−	0.999555i	$-0.490503\pi$
$167$	0.771033	0.0596643	0.0298322	+	0.999555i	$0.490503\pi$
$168$	0	0
$169$	−2.93934	−0.226103
$170$	−0.159332	−0.0122202
$171$	3.91493	0.299382
$172$	2.84480	0.216914
$173$	−23.6355	−1.79697	−0.898487	−	0.439000i	$-0.855333\pi$
$173$	−23.6355	−1.79697	−0.898487	+	0.439000i	$0.855333\pi$
$174$	11.8370	0.897358
$175$	0	0
$176$	1.05034	0.0791726
$177$	−1.57839	−0.118639
$178$	−14.2977	−1.07166
$179$	−15.3604	−1.14809	−0.574043	−	0.818825i	$-0.694626\pi$
$179$	−15.3604	−1.14809	−0.574043	+	0.818825i	$0.694626\pi$
$180$	−0.441847	−0.0329334
$181$	−11.5190	−0.856197	−0.428099	−	0.903732i	$-0.640816\pi$
$181$	−11.5190	−0.856197	−0.428099	+	0.903732i	$0.640816\pi$
$182$	0	0
$183$	8.56205	0.632925
$184$	21.8956	1.61417
$185$	8.34298	0.613388
$186$	7.45161	0.546378
$187$	−0.0631735	−0.00461970
$188$	0.700243	0.0510704
$189$	0	0
$190$	−3.91961	−0.284358
$191$	22.3034	1.61382	0.806908	−	0.590677i	$-0.201139\pi$
$191$	22.3034	1.61382	0.806908	+	0.590677i	$0.201139\pi$
$192$	−8.84277	−0.638172
$193$	−2.09556	−0.150842	−0.0754209	−	0.997152i	$-0.524030\pi$
$193$	−2.09556	−0.150842	−0.0754209	+	0.997152i	$0.524030\pi$
$194$	−12.6959	−0.911511
$195$	−2.62306	−0.187841
$196$	0	0
$197$	−13.2692	−0.945390	−0.472695	−	0.881226i	$-0.656719\pi$
$197$	−13.2692	−0.945390	−0.472695	+	0.881226i	$0.656719\pi$
$198$	0.480588	0.0341539
$199$	16.1873	1.14749	0.573744	−	0.819034i	$-0.305490\pi$
$199$	16.1873	1.14749	0.573744	+	0.819034i	$0.305490\pi$
$200$	−13.2426	−0.936391
$201$	−12.1171	−0.854677
$202$	−13.5542	−0.953668
$203$	0	0
$204$	0.0850282	0.00595317
$205$	0.826979	0.0577587
$206$	17.8850	1.24611
$207$	7.13636	0.496011
$208$	−8.39257	−0.581920
$209$	−1.55408	−0.107498
$210$	0	0
$211$	9.64598	0.664057	0.332028	−	0.943269i	$-0.392267\pi$
$211$	9.64598	0.664057	0.332028	+	0.943269i	$0.392267\pi$
$212$	2.96295	0.203496
$213$	1.25998	0.0863322
$214$	18.6602	1.27558
$215$	−4.40320	−0.300296
$216$	−3.06818	−0.208763
$217$	0	0
$218$	−7.86012	−0.532354
$219$	−8.34764	−0.564081
$220$	0.175397	0.0118252
$221$	0.504776	0.0339549
$222$	12.2138	0.819736
$223$	−14.1497	−0.947533	−0.473766	−	0.880651i	$-0.657106\pi$
$223$	−14.1497	−0.947533	−0.473766	+	0.880651i	$0.657106\pi$
$224$	0	0
$225$	−4.31611	−0.287740
$226$	−9.57462	−0.636894
$227$	−21.3542	−1.41733	−0.708663	−	0.705548i	$-0.750701\pi$
$227$	−21.3542	−1.41733	−0.708663	+	0.705548i	$0.750701\pi$
$228$	2.09171	0.138527
$229$	27.5147	1.81822	0.909112	−	0.416551i	$-0.136761\pi$
$229$	27.5147	1.81822	0.909112	+	0.416551i	$0.136761\pi$
$230$	−7.14488	−0.471120
$231$	0	0
$232$	29.9983	1.96948
$233$	4.24294	0.277964	0.138982	−	0.990295i	$-0.455617\pi$
$233$	4.24294	0.277964	0.138982	+	0.990295i	$0.455617\pi$
$234$	−3.84005	−0.251032
$235$	−1.08384	−0.0707020
$236$	−0.843317	−0.0548952
$237$	9.12954	0.593027
$238$	0	0
$239$	−19.2763	−1.24688	−0.623441	−	0.781871i	$-0.714266\pi$
$239$	−19.2763	−1.24688	−0.623441	+	0.781871i	$0.714266\pi$
$240$	2.18815	0.141244
$241$	−11.3629	−0.731947	−0.365974	−	0.930625i	$-0.619264\pi$
$241$	−11.3629	−0.731947	−0.365974	+	0.930625i	$0.619264\pi$
$242$	13.1265	0.843806
$243$	−1.00000	−0.0641500
$244$	4.57462	0.292860
$245$	0	0
$246$	1.21066	0.0771892
$247$	12.4176	0.790112
$248$	18.8845	1.19917
$249$	−9.77501	−0.619466
$250$	9.32724	0.589906
$251$	14.5991	0.921485	0.460743	−	0.887534i	$-0.347583\pi$
$251$	14.5991	0.921485	0.460743	+	0.887534i	$0.347583\pi$
$252$	0	0
$253$	−2.83287	−0.178101
$254$	−17.6221	−1.10571
$255$	−0.131607	−0.00824157
$256$	−11.8264	−0.739147
$257$	12.6279	0.787708	0.393854	−	0.919173i	$-0.371142\pi$
$257$	12.6279	0.787708	0.393854	+	0.919173i	$0.371142\pi$
$258$	−6.44611	−0.401317
$259$	0	0
$260$	−1.40148	−0.0869158
$261$	9.77724	0.605196
$262$	7.33971	0.453449
$263$	−13.9102	−0.857740	−0.428870	−	0.903366i	$-0.641088\pi$
$263$	−13.9102	−0.857740	−0.428870	+	0.903366i	$0.641088\pi$
$264$	1.21795	0.0749597
$265$	−4.58608	−0.281721
$266$	0	0
$267$	−11.8098	−0.722749
$268$	−6.47407	−0.395467
$269$	16.8108	1.02497	0.512485	−	0.858696i	$-0.328725\pi$
$269$	16.8108	1.02497	0.512485	+	0.858696i	$0.328725\pi$
$270$	1.00119	0.0609308
$271$	20.3826	1.23815	0.619076	−	0.785331i	$-0.287507\pi$
$271$	20.3826	1.23815	0.619076	+	0.785331i	$0.287507\pi$
$272$	−0.421083	−0.0255319
$273$	0	0
$274$	24.3126	1.46878
$275$	1.71333	0.103318
$276$	3.81289	0.229509
$277$	2.40720	0.144635	0.0723173	−	0.997382i	$-0.476961\pi$
$277$	2.40720	0.144635	0.0723173	+	0.997382i	$0.476961\pi$
$278$	19.0677	1.14360
$279$	6.15497	0.368488
$280$	0	0
$281$	−4.17078	−0.248808	−0.124404	−	0.992232i	$-0.539702\pi$
$281$	−4.17078	−0.248808	−0.124404	+	0.992232i	$0.539702\pi$
$282$	−1.58670	−0.0944866
$283$	25.0304	1.48790	0.743952	−	0.668233i	$-0.232949\pi$
$283$	25.0304	1.48790	0.743952	+	0.668233i	$0.232949\pi$
$284$	0.673194	0.0399467
$285$	−3.23757	−0.191777
$286$	1.52436	0.0901371
$287$	0	0
$288$	−2.93299	−0.172828
$289$	−16.9747	−0.998510
$290$	−9.78892	−0.574825
$291$	−10.4867	−0.614741
$292$	−4.46006	−0.261006
$293$	3.54593	0.207156	0.103578	−	0.994621i	$-0.466971\pi$
$293$	3.54593	0.207156	0.103578	+	0.994621i	$0.466971\pi$
$294$	0	0
$295$	1.30529	0.0759971
$296$	30.9533	1.79912
$297$	0.396962	0.0230341
$298$	4.54990	0.263568
$299$	22.6355	1.30904
$300$	−2.30605	−0.133140
$301$	0	0
$302$	4.71225	0.271159
$303$	−11.1956	−0.643173
$304$	−10.3587	−0.594113
$305$	−7.08064	−0.405436
$306$	−0.192668	−0.0110141
$307$	1.01986	0.0582066	0.0291033	−	0.999576i	$-0.490735\pi$
$307$	1.01986	0.0582066	0.0291033	+	0.999576i	$0.490735\pi$
$308$	0	0
$309$	14.7729	0.840401
$310$	−6.16233	−0.349997
$311$	7.92464	0.449365	0.224683	−	0.974432i	$-0.427865\pi$
$311$	7.92464	0.449365	0.224683	+	0.974432i	$0.427865\pi$
$312$	−9.73181	−0.550955
$313$	22.1862	1.25404	0.627019	−	0.779004i	$-0.284275\pi$
$313$	22.1862	1.25404	0.627019	+	0.779004i	$0.284275\pi$
$314$	−1.23700	−0.0698077
$315$	0	0
$316$	4.87783	0.274399
$317$	−10.0502	−0.564475	−0.282238	−	0.959345i	$-0.591077\pi$
$317$	−10.0502	−0.564475	−0.282238	+	0.959345i	$0.591077\pi$
$318$	−6.71384	−0.376493
$319$	−3.88120	−0.217305
$320$	7.31279	0.408797
$321$	15.4131	0.860278
$322$	0	0
$323$	0.623031	0.0346664
$324$	−0.534291	−0.0296828
$325$	−13.6901	−0.759388
$326$	5.16702	0.286175
$327$	−6.49240	−0.359030
$328$	3.06818	0.169412
$329$	0	0
$330$	−0.397437	−0.0218782
$331$	−17.6949	−0.972600	−0.486300	−	0.873792i	$-0.661654\pi$
$331$	−17.6949	−0.972600	−0.486300	+	0.873792i	$0.661654\pi$
$332$	−5.22270	−0.286633
$333$	10.0885	0.552846
$334$	−0.933462	−0.0510768
$335$	10.0206	0.547485
$336$	0	0
$337$	17.6666	0.962363	0.481182	−	0.876621i	$-0.340208\pi$
$337$	17.6666	0.962363	0.481182	+	0.876621i	$0.340208\pi$
$338$	3.55856	0.193560
$339$	−7.90856	−0.429534
$340$	−0.0703166	−0.00381345
$341$	−2.44329	−0.132312
$342$	−4.73967	−0.256292
$343$	0	0
$344$	−16.3363	−0.880795
$345$	−5.90162	−0.317733
$346$	28.6147	1.53833
$347$	1.78235	0.0956814	0.0478407	−	0.998855i	$-0.484766\pi$
$347$	1.78235	0.0956814	0.0478407	+	0.998855i	$0.484766\pi$
$348$	5.22389	0.280030
$349$	15.5672	0.833292	0.416646	−	0.909069i	$-0.363205\pi$
$349$	15.5672	0.833292	0.416646	+	0.909069i	$0.363205\pi$
$350$	0	0
$351$	−3.17185	−0.169301
$352$	1.16429	0.0620567
$353$	−24.8556	−1.32293	−0.661465	−	0.749976i	$-0.730065\pi$
$353$	−24.8556	−1.32293	−0.661465	+	0.749976i	$0.730065\pi$
$354$	1.91090	0.101563
$355$	−1.04197	−0.0553023
$356$	−6.30987	−0.334423
$357$	0	0
$358$	18.5962	0.982842
$359$	−31.9181	−1.68457	−0.842287	−	0.539030i	$-0.818791\pi$
$359$	−31.9181	−1.68457	−0.842287	+	0.539030i	$0.818791\pi$
$360$	2.53732	0.133728
$361$	−3.67331	−0.193332
$362$	13.9456	0.732964
$363$	10.8424	0.569080
$364$	0	0
$365$	6.90332	0.361336
$366$	−10.3658	−0.541828
$367$	34.5186	1.80186	0.900928	−	0.433969i	$-0.142887\pi$
$367$	34.5186	1.80186	0.900928	+	0.433969i	$0.142887\pi$
$368$	−18.8825	−0.984316
$369$	1.00000	0.0520579
$370$	−10.1005	−0.525102
$371$	0	0
$372$	3.28854	0.170503
$373$	22.5138	1.16572	0.582860	−	0.812573i	$-0.301934\pi$
$373$	22.5138	1.16572	0.582860	+	0.812573i	$0.301934\pi$
$374$	0.0764819	0.00395479
$375$	7.70423	0.397845
$376$	−4.02116	−0.207375
$377$	31.0120	1.59720
$378$	0	0
$379$	15.8824	0.815824	0.407912	−	0.913021i	$-0.366257\pi$
$379$	15.8824	0.815824	0.407912	+	0.913021i	$0.366257\pi$
$380$	−1.72980	−0.0887370
$381$	−14.5557	−0.745712
$382$	−27.0019	−1.38154
$383$	6.79166	0.347038	0.173519	−	0.984831i	$-0.444486\pi$
$383$	6.79166	0.347038	0.173519	+	0.984831i	$0.444486\pi$
$384$	4.83965	0.246972
$385$	0	0
$386$	2.53702	0.129131
$387$	−5.32444	−0.270656
$388$	−5.60294	−0.284446
$389$	19.5990	0.993708	0.496854	−	0.867834i	$-0.334489\pi$
$389$	19.5990	0.993708	0.496854	+	0.867834i	$0.334489\pi$
$390$	3.17564	0.160805
$391$	1.13570	0.0574346
$392$	0	0
$393$	6.06255	0.305815
$394$	16.0645	0.809319
$395$	−7.54994	−0.379879
$396$	0.212093	0.0106581
$397$	22.5654	1.13253	0.566263	−	0.824225i	$-0.308389\pi$
$397$	22.5654	1.13253	0.566263	+	0.824225i	$0.308389\pi$
$398$	−19.5974	−0.982330
$399$	0	0
$400$	11.4202	0.571010
$401$	−29.5304	−1.47468	−0.737340	−	0.675522i	$-0.763918\pi$
$401$	−29.5304	−1.47468	−0.737340	+	0.675522i	$0.763918\pi$
$402$	14.6698	0.731663
$403$	19.5227	0.972493
$404$	−5.98173	−0.297602
$405$	0.826979	0.0410929
$406$	0	0
$407$	−4.00475	−0.198508
$408$	−0.488277	−0.0241733
$409$	9.52324	0.470894	0.235447	−	0.971887i	$-0.424345\pi$
$409$	9.52324	0.470894	0.235447	+	0.971887i	$0.424345\pi$
$410$	−1.00119	−0.0494455
$411$	20.0820	0.990573
$412$	7.89302	0.388861
$413$	0	0
$414$	−8.63974	−0.424620
$415$	8.08373	0.396815
$416$	−9.30302	−0.456118
$417$	15.7498	0.771270
$418$	1.88147	0.0920258
$419$	11.1971	0.547013	0.273506	−	0.961870i	$-0.411817\pi$
$419$	11.1971	0.547013	0.273506	+	0.961870i	$0.411817\pi$
$420$	0	0
$421$	−7.98853	−0.389337	−0.194668	−	0.980869i	$-0.562363\pi$
$421$	−7.98853	−0.389337	−0.194668	+	0.980869i	$0.562363\pi$
$422$	−11.6780	−0.568479
$423$	−1.31060	−0.0637237
$424$	−17.0148	−0.826312
$425$	−0.686875	−0.0333183
$426$	−1.52541	−0.0739063
$427$	0	0
$428$	8.23510	0.398059
$429$	1.25911	0.0607903
$430$	5.33080	0.257074
$431$	5.71725	0.275390	0.137695	−	0.990475i	$-0.456031\pi$
$431$	5.71725	0.275390	0.137695	+	0.990475i	$0.456031\pi$
$432$	2.64595	0.127303
$433$	18.7297	0.900090	0.450045	−	0.893006i	$-0.351408\pi$
$433$	18.7297	0.900090	0.450045	+	0.893006i	$0.351408\pi$
$434$	0	0
$435$	−8.08558	−0.387674
$436$	−3.46883	−0.166127
$437$	27.9384	1.33647
$438$	10.1062	0.482892
$439$	−28.6939	−1.36949	−0.684744	−	0.728784i	$-0.740086\pi$
$439$	−28.6939	−1.36949	−0.684744	+	0.728784i	$0.740086\pi$
$440$	−1.00722	−0.0480173
$441$	0	0
$442$	−0.611115	−0.0290678
$443$	−20.8134	−0.988874	−0.494437	−	0.869214i	$-0.664626\pi$
$443$	−20.8134	−0.988874	−0.494437	+	0.869214i	$0.664626\pi$
$444$	5.39019	0.255807
$445$	9.76647	0.462975
$446$	17.1305	0.811154
$447$	3.75818	0.177756
$448$	0	0
$449$	31.0640	1.46600	0.733001	−	0.680227i	$-0.238119\pi$
$449$	31.0640	1.46600	0.733001	+	0.680227i	$0.238119\pi$
$450$	5.22536	0.246326
$451$	−0.396962	−0.0186922
$452$	−4.22547	−0.198749
$453$	3.89228	0.182875
$454$	25.8527	1.21333
$455$	0	0
$456$	−12.0117	−0.562499
$457$	26.1256	1.22211	0.611053	−	0.791590i	$-0.290746\pi$
$457$	26.1256	1.22211	0.611053	+	0.791590i	$0.290746\pi$
$458$	−33.3111	−1.55653
$459$	−0.159142	−0.00742813
$460$	−3.15318	−0.147018
$461$	17.3348	0.807364	0.403682	−	0.914899i	$-0.367730\pi$
$461$	17.3348	0.807364	0.403682	+	0.914899i	$0.367730\pi$
$462$	0	0
$463$	0.550182	0.0255691	0.0127846	−	0.999918i	$-0.495930\pi$
$463$	0.550182	0.0255691	0.0127846	+	0.999918i	$0.495930\pi$
$464$	−25.8701	−1.20099
$465$	−5.09003	−0.236045
$466$	−5.13678	−0.237957
$467$	17.0821	0.790466	0.395233	−	0.918581i	$-0.370664\pi$
$467$	17.0821	0.790466	0.395233	+	0.918581i	$0.370664\pi$
$468$	−1.69469	−0.0783372
$469$	0	0
$470$	1.31217	0.0605258
$471$	−1.02175	−0.0470797
$472$	4.84277	0.222906
$473$	2.11360	0.0971835
$474$	−11.0528	−0.507673
$475$	−16.8973	−0.775299
$476$	0	0
$477$	−5.54558	−0.253915
$478$	23.3372	1.06742
$479$	10.8316	0.494907	0.247454	−	0.968900i	$-0.420406\pi$
$479$	10.8316	0.494907	0.247454	+	0.968900i	$0.420406\pi$
$480$	2.42552	0.110710
$481$	31.9992	1.45904
$482$	13.7566	0.626597
$483$	0	0
$484$	5.79300	0.263318
$485$	8.67228	0.393788
$486$	1.21066	0.0549169
$487$	−20.0891	−0.910326	−0.455163	−	0.890408i	$-0.650419\pi$
$487$	−20.0891	−0.910326	−0.455163	+	0.890408i	$0.650419\pi$
$488$	−26.2699	−1.18918
$489$	4.26792	0.193002
$490$	0	0
$491$	−11.3968	−0.514330	−0.257165	−	0.966368i	$-0.582788\pi$
$491$	−11.3968	−0.514330	−0.257165	+	0.966368i	$0.582788\pi$
$492$	0.534291	0.0240877
$493$	1.55597	0.0700775
$494$	−15.0335	−0.676391
$495$	−0.328280	−0.0147551
$496$	−16.2858	−0.731252
$497$	0	0
$498$	11.8343	0.530306
$499$	5.76670	0.258153	0.129076	−	0.991635i	$-0.458799\pi$
$499$	5.76670	0.258153	0.129076	+	0.991635i	$0.458799\pi$
$500$	4.11630	0.184086
$501$	−0.771033	−0.0344472
$502$	−17.6746	−0.788855
$503$	27.0330	1.20534	0.602671	−	0.797989i	$-0.294103\pi$
$503$	27.0330	1.20534	0.602671	+	0.797989i	$0.294103\pi$
$504$	0	0
$505$	9.25857	0.412001
$506$	3.42965	0.152467
$507$	2.93934	0.130541
$508$	−7.77699	−0.345048
$509$	−23.3862	−1.03657	−0.518287	−	0.855207i	$-0.673430\pi$
$509$	−23.3862	−1.03657	−0.518287	+	0.855207i	$0.673430\pi$
$510$	0.159332	0.00705536
$511$	0	0
$512$	23.9971	1.06053
$513$	−3.91493	−0.172848
$514$	−15.2882	−0.674332
$515$	−12.2169	−0.538340
$516$	−2.84480	−0.125235
$517$	0.520260	0.0228810
$518$	0	0
$519$	23.6355	1.03748
$520$	8.04800	0.352928
$521$	23.7425	1.04018	0.520089	−	0.854112i	$-0.325899\pi$
$521$	23.7425	1.04018	0.520089	+	0.854112i	$0.325899\pi$
$522$	−11.8370	−0.518090
$523$	25.0433	1.09507	0.547534	−	0.836783i	$-0.315567\pi$
$523$	25.0433	1.09507	0.547534	+	0.836783i	$0.315567\pi$
$524$	3.23916	0.141503
$525$	0	0
$526$	16.8406	0.734285
$527$	0.979516	0.0426684
$528$	−1.05034	−0.0457103
$529$	27.9276	1.21424
$530$	5.55220	0.241172
$531$	1.57839	0.0684961
$532$	0	0
$533$	3.17185	0.137388
$534$	14.2977	0.618723
$535$	−12.7464	−0.551073
$536$	37.1775	1.60582
$537$	15.3604	0.662848
$538$	−20.3522	−0.877445
$539$	0	0
$540$	0.441847	0.0190141
$541$	9.63953	0.414436	0.207218	−	0.978295i	$-0.433559\pi$
$541$	9.63953	0.414436	0.207218	+	0.978295i	$0.433559\pi$
$542$	−24.6764	−1.05994
$543$	11.5190	0.494326
$544$	−0.466763	−0.0200123
$545$	5.36908	0.229986
$546$	0	0
$547$	−22.0752	−0.943868	−0.471934	−	0.881634i	$-0.656444\pi$
$547$	−22.0752	−0.943868	−0.471934	+	0.881634i	$0.656444\pi$
$548$	10.7296	0.458347
$549$	−8.56205	−0.365419
$550$	−2.07427	−0.0884472
$551$	38.2772	1.63066
$552$	−21.8956	−0.931939
$553$	0	0
$554$	−2.91431	−0.123817
$555$	−8.34298	−0.354140
$556$	8.41496	0.356874
$557$	−41.1233	−1.74245	−0.871224	−	0.490885i	$-0.836674\pi$
$557$	−41.1233	−1.74245	−0.871224	+	0.490885i	$0.836674\pi$
$558$	−7.45161	−0.315452
$559$	−16.8883	−0.714301
$560$	0	0
$561$	0.0631735	0.00266719
$562$	5.04942	0.212997
$563$	−38.2399	−1.61162	−0.805810	−	0.592174i	$-0.798270\pi$
$563$	−38.2399	−1.61162	−0.805810	+	0.592174i	$0.798270\pi$
$564$	−0.700243	−0.0294855
$565$	6.54022	0.275149
$566$	−30.3035	−1.27375
$567$	0	0
$568$	−3.86583	−0.162207
$569$	34.6025	1.45061	0.725307	−	0.688426i	$-0.241698\pi$
$569$	34.6025	1.45061	0.725307	+	0.688426i	$0.241698\pi$
$570$	3.91961	0.164174
$571$	17.7405	0.742417	0.371208	−	0.928550i	$-0.378944\pi$
$571$	17.7405	0.742417	0.371208	+	0.928550i	$0.378944\pi$
$572$	0.672729	0.0281282
$573$	−22.3034	−0.931737
$574$	0	0
$575$	−30.8013	−1.28450
$576$	8.84277	0.368449
$577$	44.2621	1.84265	0.921327	−	0.388788i	$-0.127106\pi$
$577$	44.2621	1.84265	0.921327	+	0.388788i	$0.127106\pi$
$578$	20.5506	0.854794
$579$	2.09556	0.0870885
$580$	−4.32005	−0.179380
$581$	0	0
$582$	12.6959	0.526261
$583$	2.20139	0.0911721
$584$	25.6120	1.05983
$585$	2.62306	0.108450
$586$	−4.29294	−0.177340
$587$	23.5641	0.972595	0.486298	−	0.873793i	$-0.338347\pi$
$587$	23.5641	0.972595	0.486298	+	0.873793i	$0.338347\pi$
$588$	0	0
$589$	24.0963	0.992870
$590$	−1.58027	−0.0650587
$591$	13.2692	0.545821
$592$	−26.6937	−1.09710
$593$	−29.7934	−1.22347	−0.611734	−	0.791064i	$-0.709528\pi$
$593$	−29.7934	−1.22347	−0.611734	+	0.791064i	$0.709528\pi$
$594$	−0.480588	−0.0197188
$595$	0	0
$596$	2.00796	0.0822493
$597$	−16.1873	−0.662503
$598$	−27.4040	−1.12063
$599$	12.6651	0.517481	0.258741	−	0.965947i	$-0.416692\pi$
$599$	12.6651	0.517481	0.258741	+	0.965947i	$0.416692\pi$
$600$	13.2426	0.540626
$601$	17.6451	0.719757	0.359879	−	0.932999i	$-0.382818\pi$
$601$	17.6451	0.719757	0.359879	+	0.932999i	$0.382818\pi$
$602$	0	0
$603$	12.1171	0.493448
$604$	2.07961	0.0846181
$605$	−8.96646	−0.364538
$606$	13.5542	0.550601
$607$	27.0843	1.09932	0.549658	−	0.835390i	$-0.314758\pi$
$607$	27.0843	1.09932	0.549658	+	0.835390i	$0.314758\pi$
$608$	−11.4825	−0.465675
$609$	0	0
$610$	8.57228	0.347082
$611$	−4.15704	−0.168176
$612$	−0.0850282	−0.00343706
$613$	25.9967	1.05000	0.524998	−	0.851104i	$-0.324066\pi$
$613$	25.9967	1.05000	0.524998	+	0.851104i	$0.324066\pi$
$614$	−1.23471	−0.0498289
$615$	−0.826979	−0.0333470
$616$	0	0
$617$	−2.10539	−0.0847596	−0.0423798	−	0.999102i	$-0.513494\pi$
$617$	−2.10539	−0.0847596	−0.0423798	+	0.999102i	$0.513494\pi$
$618$	−17.8850	−0.719442
$619$	−27.8990	−1.12135	−0.560677	−	0.828034i	$-0.689459\pi$
$619$	−27.8990	−1.12135	−0.560677	+	0.828034i	$0.689459\pi$
$620$	−2.71956	−0.109220
$621$	−7.13636	−0.286372
$622$	−9.59409	−0.384688
$623$	0	0
$624$	8.39257	0.335972
$625$	15.2093	0.608372
$626$	−26.8601	−1.07354
$627$	1.55408	0.0620640
$628$	−0.545911	−0.0217842
$629$	1.60551	0.0640157
$630$	0	0
$631$	−21.9270	−0.872900	−0.436450	−	0.899728i	$-0.643764\pi$
$631$	−21.9270	−0.872900	−0.436450	+	0.899728i	$0.643764\pi$
$632$	−28.0110	−1.11422
$633$	−9.64598	−0.383393
$634$	12.1674	0.483230
$635$	12.0373	0.477685
$636$	−2.96295	−0.117489
$637$	0	0
$638$	4.69883	0.186028
$639$	−1.25998	−0.0498439
$640$	−4.00229	−0.158205
$641$	34.8883	1.37801	0.689003	−	0.724758i	$-0.258048\pi$
$641$	34.8883	1.37801	0.689003	+	0.724758i	$0.258048\pi$
$642$	−18.6602	−0.736457
$643$	−38.0533	−1.50067	−0.750337	−	0.661055i	$-0.770109\pi$
$643$	−38.0533	−1.50067	−0.750337	+	0.661055i	$0.770109\pi$
$644$	0	0
$645$	4.40320	0.173376
$646$	−0.754282	−0.0296768
$647$	−0.560042	−0.0220175	−0.0110088	−	0.999939i	$-0.503504\pi$
$647$	−0.560042	−0.0220175	−0.0110088	+	0.999939i	$0.503504\pi$
$648$	3.06818	0.120529
$649$	−0.626560	−0.0245946
$650$	16.5741	0.650088
$651$	0	0
$652$	2.28031	0.0893038
$653$	−25.1642	−0.984751	−0.492375	−	0.870383i	$-0.663871\pi$
$653$	−25.1642	−0.984751	−0.492375	+	0.870383i	$0.663871\pi$
$654$	7.86012	0.307355
$655$	−5.01360	−0.195898
$656$	−2.64595	−0.103307
$657$	8.34764	0.325672
$658$	0	0
$659$	−45.6924	−1.77992	−0.889962	−	0.456035i	$-0.849269\pi$
$659$	−45.6924	−1.77992	−0.889962	+	0.456035i	$0.849269\pi$
$660$	−0.175397	−0.00682731
$661$	13.5821	0.528283	0.264141	−	0.964484i	$-0.414911\pi$
$661$	13.5821	0.528283	0.264141	+	0.964484i	$0.414911\pi$
$662$	21.4226	0.832613
$663$	−0.504776	−0.0196039
$664$	29.9915	1.16389
$665$	0	0
$666$	−12.2138	−0.473275
$667$	69.7739	2.70166
$668$	−0.411956	−0.0159390
$669$	14.1497	0.547058
$670$	−12.1316	−0.468685
$671$	3.39881	0.131210
$672$	0	0
$673$	11.3582	0.437825	0.218913	−	0.975744i	$-0.429749\pi$
$673$	11.3582	0.437825	0.218913	+	0.975744i	$0.429749\pi$
$674$	−21.3884	−0.823850
$675$	4.31611	0.166127
$676$	1.57046	0.0604024
$677$	0.333596	0.0128211	0.00641056	−	0.999979i	$-0.497959\pi$
$677$	0.333596	0.0128211	0.00641056	+	0.999979i	$0.497959\pi$
$678$	9.57462	0.367711
$679$	0	0
$680$	0.403795	0.0154848
$681$	21.3542	0.818293
$682$	2.95801	0.113268
$683$	−42.6711	−1.63277	−0.816383	−	0.577511i	$-0.804024\pi$
$683$	−42.6711	−1.63277	−0.816383	+	0.577511i	$0.804024\pi$
$684$	−2.09171	−0.0799786
$685$	−16.6074	−0.634537
$686$	0	0
$687$	−27.5147	−1.04975
$688$	14.0882	0.537108
$689$	−17.5898	−0.670117
$690$	7.14488	0.272001
$691$	45.1639	1.71812	0.859058	−	0.511879i	$-0.171050\pi$
$691$	45.1639	1.71812	0.859058	+	0.511879i	$0.171050\pi$
$692$	12.6282	0.480053
$693$	0	0
$694$	−2.15782	−0.0819099
$695$	−13.0247	−0.494057
$696$	−29.9983	−1.13708
$697$	0.159142	0.00602794
$698$	−18.8466	−0.713356
$699$	−4.24294	−0.160483
$700$	0	0
$701$	−40.4169	−1.52653	−0.763263	−	0.646088i	$-0.776404\pi$
$701$	−40.4169	−1.52653	−0.763263	+	0.646088i	$0.776404\pi$
$702$	3.84005	0.144933
$703$	39.4958	1.48961
$704$	−3.51025	−0.132298
$705$	1.08384	0.0408198
$706$	30.0918	1.13252
$707$	0	0
$708$	0.843317	0.0316938
$709$	−18.6305	−0.699682	−0.349841	−	0.936809i	$-0.613764\pi$
$709$	−18.6305	−0.699682	−0.349841	+	0.936809i	$0.613764\pi$
$710$	1.26148	0.0473426
$711$	−9.12954	−0.342385
$712$	36.2346	1.35795
$713$	43.9241	1.64497
$714$	0	0
$715$	−1.04126	−0.0389407
$716$	8.20689	0.306706
$717$	19.2763	0.719887
$718$	38.6421	1.44211
$719$	−34.1061	−1.27194	−0.635971	−	0.771713i	$-0.719400\pi$
$719$	−34.1061	−1.27194	−0.635971	+	0.771713i	$0.719400\pi$
$720$	−2.18815	−0.0815475
$721$	0	0
$722$	4.44715	0.165506
$723$	11.3629	0.422590
$724$	6.15447	0.228729
$725$	−42.1996	−1.56725
$726$	−13.1265	−0.487172
$727$	−10.7831	−0.399923	−0.199961	−	0.979804i	$-0.564082\pi$
$727$	−10.7831	−0.399923	−0.199961	+	0.979804i	$0.564082\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	−8.35761	−0.309329
$731$	−0.847343	−0.0313401
$732$	−4.57462	−0.169083
$733$	−34.2830	−1.26627	−0.633136	−	0.774041i	$-0.718233\pi$
$733$	−34.2830	−1.26627	−0.633136	+	0.774041i	$0.718233\pi$
$734$	−41.7904	−1.54251
$735$	0	0
$736$	−20.9309	−0.771522
$737$	−4.81005	−0.177180
$738$	−1.21066	−0.0445652
$739$	29.1016	1.07052	0.535261	−	0.844687i	$-0.320213\pi$
$739$	29.1016	1.07052	0.535261	+	0.844687i	$0.320213\pi$
$740$	−4.45757	−0.163864
$741$	−12.4176	−0.456172
$742$	0	0
$743$	−29.1285	−1.06862	−0.534311	−	0.845288i	$-0.679429\pi$
$743$	−29.1285	−1.06862	−0.534311	+	0.845288i	$0.679429\pi$
$744$	−18.8845	−0.692341
$745$	−3.10794	−0.113866
$746$	−27.2567	−0.997937
$747$	9.77501	0.357649
$748$	0.0337530	0.00123413
$749$	0	0
$750$	−9.32724	−0.340583
$751$	33.0634	1.20650	0.603250	−	0.797552i	$-0.293872\pi$
$751$	33.0634	1.20650	0.603250	+	0.797552i	$0.293872\pi$
$752$	3.46779	0.126457
$753$	−14.5991	−0.532020
$754$	−37.5451	−1.36731
$755$	−3.21884	−0.117145
$756$	0	0
$757$	3.40606	0.123795	0.0618977	−	0.998083i	$-0.480285\pi$
$757$	3.40606	0.123795	0.0618977	+	0.998083i	$0.480285\pi$
$758$	−19.2283	−0.698402
$759$	2.83287	0.102827
$760$	9.93343	0.360323
$761$	3.37754	0.122436	0.0612178	−	0.998124i	$-0.480502\pi$
$761$	3.37754	0.122436	0.0612178	+	0.998124i	$0.480502\pi$
$762$	17.6221	0.638381
$763$	0	0
$764$	−11.9165	−0.431124
$765$	0.131607	0.00475827
$766$	−8.22242	−0.297088
$767$	5.00641	0.180771
$768$	11.8264	0.426747
$769$	−1.44772	−0.0522063	−0.0261031	−	0.999659i	$-0.508310\pi$
$769$	−1.44772	−0.0522063	−0.0261031	+	0.999659i	$0.508310\pi$
$770$	0	0
$771$	−12.6279	−0.454783
$772$	1.11964	0.0402967
$773$	−5.01065	−0.180220	−0.0901102	−	0.995932i	$-0.528722\pi$
$773$	−5.01065	−0.180220	−0.0901102	+	0.995932i	$0.528722\pi$
$774$	6.44611	0.231701
$775$	−26.5655	−0.954261
$776$	32.1750	1.15502
$777$	0	0
$778$	−23.7278	−0.850683
$779$	3.91493	0.140267
$780$	1.40148	0.0501809
$781$	0.500163	0.0178973
$782$	−1.37495	−0.0491680
$783$	−9.77724	−0.349410
$784$	0	0
$785$	0.844965	0.0301581
$786$	−7.33971	−0.261799
$787$	−49.3694	−1.75983	−0.879915	−	0.475132i	$-0.842400\pi$
$787$	−49.3694	−1.75983	−0.879915	+	0.475132i	$0.842400\pi$
$788$	7.08960	0.252556
$789$	13.9102	0.495217
$790$	9.14045	0.325203
$791$	0	0
$792$	−1.21795	−0.0432780
$793$	−27.1576	−0.964394
$794$	−27.3191	−0.969520
$795$	4.58608	0.162651
$796$	−8.64873	−0.306546
$797$	−12.2118	−0.432565	−0.216283	−	0.976331i	$-0.569393\pi$
$797$	−12.2118	−0.432565	−0.216283	+	0.976331i	$0.569393\pi$
$798$	0	0
$799$	−0.208572	−0.00737876
$800$	12.6591	0.447567
$801$	11.8098	0.417279
$802$	35.7515	1.26243
$803$	−3.31370	−0.116938
$804$	6.47407	0.228323
$805$	0	0
$806$	−23.6354	−0.832522
$807$	−16.8108	−0.591767
$808$	34.3502	1.20844
$809$	0.715187	0.0251446	0.0125723	−	0.999921i	$-0.495998\pi$
$809$	0.715187	0.0251446	0.0125723	+	0.999921i	$0.495998\pi$
$810$	−1.00119	−0.0351784
$811$	36.3424	1.27616	0.638078	−	0.769972i	$-0.279730\pi$
$811$	36.3424	1.27616	0.638078	+	0.769972i	$0.279730\pi$
$812$	0	0
$813$	−20.3826	−0.714848
$814$	4.84841	0.169937
$815$	−3.52948	−0.123632
$816$	0.421083	0.0147408
$817$	−20.8448	−0.729268
$818$	−11.5294	−0.403118
$819$	0	0
$820$	−0.441847	−0.0154300
$821$	−28.7101	−1.00199	−0.500995	−	0.865450i	$-0.667033\pi$
$821$	−28.7101	−1.00199	−0.500995	+	0.865450i	$0.667033\pi$
$822$	−24.3126	−0.847999
$823$	49.9050	1.73958	0.869790	−	0.493422i	$-0.164254\pi$
$823$	49.9050	1.73958	0.869790	+	0.493422i	$0.164254\pi$
$824$	−45.3259	−1.57900
$825$	−1.71333	−0.0596506
$826$	0	0
$827$	−19.8378	−0.689829	−0.344914	−	0.938634i	$-0.612092\pi$
$827$	−19.8378	−0.689829	−0.344914	+	0.938634i	$0.612092\pi$
$828$	−3.81289	−0.132507
$829$	−16.3642	−0.568352	−0.284176	−	0.958772i	$-0.591720\pi$
$829$	−16.3642	−0.568352	−0.284176	+	0.958772i	$0.591720\pi$
$830$	−9.78669	−0.339701
$831$	−2.40720	−0.0835048
$832$	28.0480	0.972389
$833$	0	0
$834$	−19.0677	−0.660261
$835$	0.637628	0.0220660
$836$	0.830331	0.0287176
$837$	−6.15497	−0.212747
$838$	−13.5559	−0.468281
$839$	−9.07123	−0.313174	−0.156587	−	0.987664i	$-0.550049\pi$
$839$	−9.07123	−0.313174	−0.156587	+	0.987664i	$0.550049\pi$
$840$	0	0
$841$	66.5944	2.29636
$842$	9.67143	0.333299
$843$	4.17078	0.143649
$844$	−5.15376	−0.177400
$845$	−2.43078	−0.0836212
$846$	1.58670	0.0545519
$847$	0	0
$848$	14.6733	0.503884
$849$	−25.0304	−0.859042
$850$	0.831575	0.0285228
$851$	71.9951	2.46796
$852$	−0.673194	−0.0230632
$853$	24.6232	0.843083	0.421542	−	0.906809i	$-0.361489\pi$
$853$	24.6232	0.843083	0.421542	+	0.906809i	$0.361489\pi$
$854$	0	0
$855$	3.23757	0.110722
$856$	−47.2902	−1.61635
$857$	43.2834	1.47853	0.739266	−	0.673413i	$-0.235173\pi$
$857$	43.2834	1.47853	0.739266	+	0.673413i	$0.235173\pi$
$858$	−1.52436	−0.0520407
$859$	7.88554	0.269051	0.134526	−	0.990910i	$-0.457049\pi$
$859$	7.88554	0.269051	0.134526	+	0.990910i	$0.457049\pi$
$860$	2.35259	0.0802226
$861$	0	0
$862$	−6.92167	−0.235753
$863$	9.60001	0.326788	0.163394	−	0.986561i	$-0.447756\pi$
$863$	9.60001	0.326788	0.163394	+	0.986561i	$0.447756\pi$
$864$	2.93299	0.0997824
$865$	−19.5461	−0.664586
$866$	−22.6753	−0.770539
$867$	16.9747	0.576490
$868$	0	0
$869$	3.62409	0.122939
$870$	9.78892	0.331876
$871$	38.4338	1.30228
$872$	19.9198	0.674570
$873$	10.4867	0.354921
$874$	−33.8240	−1.14411
$875$	0	0
$876$	4.46006	0.150692
$877$	42.5859	1.43802	0.719012	−	0.694998i	$-0.244595\pi$
$877$	42.5859	1.43802	0.719012	+	0.694998i	$0.244595\pi$
$878$	34.7388	1.17238
$879$	−3.54593	−0.119601
$880$	0.868613	0.0292809
$881$	−21.6986	−0.731043	−0.365521	−	0.930803i	$-0.619109\pi$
$881$	−21.6986	−0.731043	−0.365521	+	0.930803i	$0.619109\pi$
$882$	0	0
$883$	44.7964	1.50752	0.753759	−	0.657151i	$-0.228239\pi$
$883$	44.7964	1.50752	0.753759	+	0.657151i	$0.228239\pi$
$884$	−0.269697	−0.00907090
$885$	−1.30529	−0.0438769
$886$	25.1980	0.846544
$887$	−14.8695	−0.499269	−0.249635	−	0.968340i	$-0.580311\pi$
$887$	−14.8695	−0.499269	−0.249635	+	0.968340i	$0.580311\pi$
$888$	−30.9533	−1.03872
$889$	0	0
$890$	−11.8239	−0.396339
$891$	−0.396962	−0.0132987
$892$	7.56004	0.253129
$893$	−5.13092	−0.171700
$894$	−4.54990	−0.152171
$895$	−12.7027	−0.424604
$896$	0	0
$897$	−22.6355	−0.755777
$898$	−37.6081	−1.25500
$899$	60.1786	2.00707
$900$	2.30605	0.0768685
$901$	−0.882536	−0.0294015
$902$	0.480588	0.0160018
$903$	0	0
$904$	24.2649	0.807038
$905$	−9.52594	−0.316653
$906$	−4.71225	−0.156554
$907$	39.2897	1.30459	0.652297	−	0.757963i	$-0.273805\pi$
$907$	39.2897	1.30459	0.652297	+	0.757963i	$0.273805\pi$
$908$	11.4093	0.378632
$909$	11.1956	0.371336
$910$	0	0
$911$	−20.6834	−0.685270	−0.342635	−	0.939469i	$-0.611319\pi$
$911$	−20.6834	−0.685270	−0.342635	+	0.939469i	$0.611319\pi$
$912$	10.3587	0.343012
$913$	−3.88031	−0.128420
$914$	−31.6294	−1.04621
$915$	7.08064	0.234079
$916$	−14.7009	−0.485730
$917$	0	0
$918$	0.192668	0.00635899
$919$	−41.7508	−1.37723	−0.688616	−	0.725127i	$-0.741781\pi$
$919$	−41.7508	−1.37723	−0.688616	+	0.725127i	$0.741781\pi$
$920$	18.1072	0.596977
$921$	−1.01986	−0.0336056
$922$	−20.9867	−0.691160
$923$	−3.99646	−0.131545
$924$	0	0
$925$	−43.5430	−1.43168
$926$	−0.666086	−0.0218889
$927$	−14.7729	−0.485206
$928$	−28.6766	−0.941354
$929$	−5.14643	−0.168849	−0.0844245	−	0.996430i	$-0.526905\pi$
$929$	−5.14643	−0.168849	−0.0844245	+	0.996430i	$0.526905\pi$
$930$	6.16233	0.202071
$931$	0	0
$932$	−2.26697	−0.0742569
$933$	−7.92464	−0.259441
$934$	−20.6807	−0.676694
$935$	−0.0522432	−0.00170853
$936$	9.73181	0.318094
$937$	2.92520	0.0955623	0.0477811	−	0.998858i	$-0.484785\pi$
$937$	2.92520	0.0955623	0.0477811	+	0.998858i	$0.484785\pi$
$938$	0	0
$939$	−22.1862	−0.724019
$940$	0.579086	0.0188877
$941$	33.3784	1.08811	0.544053	−	0.839051i	$-0.316889\pi$
$941$	33.3784	1.08811	0.544053	+	0.839051i	$0.316889\pi$
$942$	1.23700	0.0403035
$943$	7.13636	0.232392
$944$	−4.17633	−0.135928
$945$	0	0
$946$	−2.55886	−0.0831958
$947$	25.3265	0.823002	0.411501	−	0.911409i	$-0.365005\pi$
$947$	25.3265	0.823002	0.411501	+	0.911409i	$0.365005\pi$
$948$	−4.87783	−0.158425
$949$	26.4775	0.859496
$950$	20.4569	0.663710
$951$	10.0502	0.325900
$952$	0	0
$953$	43.0540	1.39466	0.697328	−	0.716752i	$-0.254372\pi$
$953$	43.0540	1.39466	0.697328	+	0.716752i	$0.254372\pi$
$954$	6.71384	0.217368
$955$	18.4444	0.596848
$956$	10.2992	0.333099
$957$	3.88120	0.125461
$958$	−13.1134	−0.423675
$959$	0	0
$960$	−7.31279	−0.236019
$961$	6.88367	0.222054
$962$	−38.7403	−1.24904
$963$	−15.4131	−0.496682
$964$	6.07108	0.195536
$965$	−1.73299	−0.0557868
$966$	0	0
$967$	−26.3902	−0.848653	−0.424327	−	0.905509i	$-0.639489\pi$
$967$	−26.3902	−0.848653	−0.424327	+	0.905509i	$0.639489\pi$
$968$	−33.2665	−1.06922
$969$	−0.623031	−0.0200146
$970$	−10.4992	−0.337110
$971$	7.15683	0.229673	0.114837	−	0.993384i	$-0.463366\pi$
$971$	7.15683	0.229673	0.114837	+	0.993384i	$0.463366\pi$
$972$	0.534291	0.0171374
$973$	0	0
$974$	24.3212	0.779302
$975$	13.6901	0.438433
$976$	22.6548	0.725162
$977$	9.93668	0.317903	0.158951	−	0.987286i	$-0.449189\pi$
$977$	9.93668	0.317903	0.158951	+	0.987286i	$0.449189\pi$
$978$	−5.16702	−0.165223
$979$	−4.68805	−0.149831
$980$	0	0
$981$	6.49240	0.207286
$982$	13.7977	0.440302
$983$	−26.8718	−0.857076	−0.428538	−	0.903524i	$-0.640971\pi$
$983$	−26.8718	−0.857076	−0.428538	+	0.903524i	$0.640971\pi$
$984$	−3.06818	−0.0978099
$985$	−10.9733	−0.349639
$986$	−1.88376	−0.0599912
$987$	0	0
$988$	−6.63460	−0.211075
$989$	−37.9971	−1.20824
$990$	0.397437	0.0126314
$991$	−49.3369	−1.56724	−0.783620	−	0.621241i	$-0.786629\pi$
$991$	−49.3369	−1.56724	−0.783620	+	0.621241i	$0.786629\pi$
$992$	−18.0525	−0.573167
$993$	17.6949	0.561531
$994$	0	0
$995$	13.3866	0.424383
$996$	5.22270	0.165487
$997$	13.6316	0.431718	0.215859	−	0.976425i	$-0.430745\pi$
$997$	13.6316	0.431718	0.215859	+	0.976425i	$0.430745\pi$
$998$	−6.98154	−0.220997
$999$	−10.0885	−0.319186

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6027.2.a.bj.1.5		14
7.2	even	3		861.2.i.g.739.10	yes	28
7.4	even	3		861.2.i.g.247.10	✓	28
7.6	odd	2		6027.2.a.bk.1.5		14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
861.2.i.g.247.10	✓	28	7.4	even	3
861.2.i.g.739.10	yes	28	7.2	even	3
6027.2.a.bj.1.5		14	1.1	even	1	trivial
6027.2.a.bk.1.5		14	7.6	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 6027 = 3 \cdot 7^{2} \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6027.a (trivial)

\(f(q)\)	\(=\)	\(q-1.21066 q^{2} -1.00000 q^{3} -0.534291 q^{4} +0.826979 q^{5} +1.21066 q^{6} +3.06818 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.21066 q^{2} -1.00000 q^{3} -0.534291 q^{4} +0.826979 q^{5} +1.21066 q^{6} +3.06818 q^{8} +1.00000 q^{9} -1.00119 q^{10} -0.396962 q^{11} +0.534291 q^{12} +3.17185 q^{13} -0.826979 q^{15} -2.64595 q^{16} +0.159142 q^{17} -1.21066 q^{18} +3.91493 q^{19} -0.441847 q^{20} +0.480588 q^{22} +7.13636 q^{23} -3.06818 q^{24} -4.31611 q^{25} -3.84005 q^{26} -1.00000 q^{27} +9.77724 q^{29} +1.00119 q^{30} +6.15497 q^{31} -2.93299 q^{32} +0.396962 q^{33} -0.192668 q^{34} -0.534291 q^{36} +10.0885 q^{37} -4.73967 q^{38} -3.17185 q^{39} +2.53732 q^{40} +1.00000 q^{41} -5.32444 q^{43} +0.212093 q^{44} +0.826979 q^{45} -8.63974 q^{46} -1.31060 q^{47} +2.64595 q^{48} +5.22536 q^{50} -0.159142 q^{51} -1.69469 q^{52} -5.54558 q^{53} +1.21066 q^{54} -0.328280 q^{55} -3.91493 q^{57} -11.8370 q^{58} +1.57839 q^{59} +0.441847 q^{60} -8.56205 q^{61} -7.45161 q^{62} +8.84277 q^{64} +2.62306 q^{65} -0.480588 q^{66} +12.1171 q^{67} -0.0850282 q^{68} -7.13636 q^{69} -1.25998 q^{71} +3.06818 q^{72} +8.34764 q^{73} -12.2138 q^{74} +4.31611 q^{75} -2.09171 q^{76} +3.84005 q^{78} -9.12954 q^{79} -2.18815 q^{80} +1.00000 q^{81} -1.21066 q^{82} +9.77501 q^{83} +0.131607 q^{85} +6.44611 q^{86} -9.77724 q^{87} -1.21795 q^{88} +11.8098 q^{89} -1.00119 q^{90} -3.81289 q^{92} -6.15497 q^{93} +1.58670 q^{94} +3.23757 q^{95} +2.93299 q^{96} +10.4867 q^{97} -0.396962 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q - 2 q^{2} - 14 q^{3} + 14 q^{4} + 10 q^{5} + 2 q^{6} - 6 q^{8} + 14 q^{9}+O(q^{10}) \) 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

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Database

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