LMFDB - Embedded newform 5577.2.a.y.1.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [5577,2,Mod(1,5577)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(5577, 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("5577.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 5577 = 3 \cdot 11 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	5577.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:	$44.5325692073$
Analytic rank:	$0$
Dimension:	$7$
Coefficient field:	$\mathbb{Q}[x]/(x^{7} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{7} - 3x^{6} - 7x^{5} + 21x^{4} + 13x^{3} - 33x^{2} - 7x + 7 $ x^7 - 3x^6 - 7x^5 + 21x^4 + 13x^3 - 33x^2 - 7x + 7
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 429)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.7
Root			$2.73878$ of defining polynomial
Character	$\chi$	$=$	5577.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.73878 q^{2} +1.00000 q^{3} +5.50093 q^{4} -2.84154 q^{5} +2.73878 q^{6} +3.93129 q^{7} +9.58828 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+2.73878 q^{2} +1.00000 q^{3} +5.50093 q^{4} -2.84154 q^{5} +2.73878 q^{6} +3.93129 q^{7} +9.58828 q^{8} +1.00000 q^{9} -7.78236 q^{10} +1.00000 q^{11} +5.50093 q^{12} +10.7670 q^{14} -2.84154 q^{15} +15.2584 q^{16} +3.81818 q^{17} +2.73878 q^{18} -2.94082 q^{19} -15.6311 q^{20} +3.93129 q^{21} +2.73878 q^{22} -1.89484 q^{23} +9.58828 q^{24} +3.07435 q^{25} +1.00000 q^{27} +21.6258 q^{28} -2.09928 q^{29} -7.78236 q^{30} -6.16032 q^{31} +22.6127 q^{32} +1.00000 q^{33} +10.4572 q^{34} -11.1709 q^{35} +5.50093 q^{36} +8.34404 q^{37} -8.05426 q^{38} -27.2455 q^{40} +6.35787 q^{41} +10.7670 q^{42} -11.7275 q^{43} +5.50093 q^{44} -2.84154 q^{45} -5.18956 q^{46} +5.31137 q^{47} +15.2584 q^{48} +8.45506 q^{49} +8.41997 q^{50} +3.81818 q^{51} -2.37985 q^{53} +2.73878 q^{54} -2.84154 q^{55} +37.6943 q^{56} -2.94082 q^{57} -5.74947 q^{58} -5.38624 q^{59} -15.6311 q^{60} -2.34857 q^{61} -16.8718 q^{62} +3.93129 q^{63} +31.4147 q^{64} +2.73878 q^{66} +10.4731 q^{67} +21.0035 q^{68} -1.89484 q^{69} -30.5947 q^{70} +10.0939 q^{71} +9.58828 q^{72} -15.1079 q^{73} +22.8525 q^{74} +3.07435 q^{75} -16.1772 q^{76} +3.93129 q^{77} +1.57120 q^{79} -43.3572 q^{80} +1.00000 q^{81} +17.4128 q^{82} +10.6736 q^{83} +21.6258 q^{84} -10.8495 q^{85} -32.1190 q^{86} -2.09928 q^{87} +9.58828 q^{88} +3.23647 q^{89} -7.78236 q^{90} -10.4234 q^{92} -6.16032 q^{93} +14.5467 q^{94} +8.35645 q^{95} +22.6127 q^{96} -17.7914 q^{97} +23.1566 q^{98} +1.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 7 q + 3 q^{2} + 7 q^{3} + 9 q^{4} + 6 q^{5} + 3 q^{6} + 6 q^{7} + 15 q^{8} + 7 q^{9}+O(q^{10}) $ 7 * q + 3 * q^2 + 7 * q^3 + 9 * q^4 + 6 * q^5 + 3 * q^6 + 6 * q^7 + 15 * q^8 + 7 * q^9	$ 7 q + 3 q^{2} + 7 q^{3} + 9 q^{4} + 6 q^{5} + 3 q^{6} + 6 q^{7} + 15 q^{8} + 7 q^{9} + 7 q^{11} + 9 q^{12} + 8 q^{14} + 6 q^{15} + 17 q^{16} - 2 q^{17} + 3 q^{18} + 8 q^{19} - 2 q^{20} + 6 q^{21} + 3 q^{22} + 4 q^{23} + 15 q^{24} + 13 q^{25} + 7 q^{27} + 12 q^{28} - 12 q^{29} - 10 q^{31} + 33 q^{32} + 7 q^{33} + 28 q^{34} - 4 q^{35} + 9 q^{36} + 6 q^{37} + 16 q^{38} - 10 q^{40} + 2 q^{41} + 8 q^{42} - 16 q^{43} + 9 q^{44} + 6 q^{45} - 26 q^{46} + 18 q^{47} + 17 q^{48} + 23 q^{49} + 39 q^{50} - 2 q^{51} + 10 q^{53} + 3 q^{54} + 6 q^{55} + 16 q^{56} + 8 q^{57} + 10 q^{58} + 2 q^{59} - 2 q^{60} - 10 q^{61} - 36 q^{62} + 6 q^{63} + 29 q^{64} + 3 q^{66} + 8 q^{67} - 10 q^{68} + 4 q^{69} - 20 q^{70} + 36 q^{71} + 15 q^{72} + 20 q^{73} + 13 q^{75} + 10 q^{76} + 6 q^{77} + 6 q^{79} - 20 q^{80} + 7 q^{81} - 10 q^{82} + 30 q^{83} + 12 q^{84} - 40 q^{85} + 6 q^{86} - 12 q^{87} + 15 q^{88} + 34 q^{89} - 12 q^{92} - 10 q^{93} + 32 q^{94} + 18 q^{95} + 33 q^{96} + 16 q^{97} + q^{98} + 7 q^{99}+O(q^{100}) $ 7 * q + 3 * q^2 + 7 * q^3 + 9 * q^4 + 6 * q^5 + 3 * q^6 + 6 * q^7 + 15 * q^8 + 7 * q^9 + 7 * q^11 + 9 * q^12 + 8 * q^14 + 6 * q^15 + 17 * q^16 - 2 * q^17 + 3 * q^18 + 8 * q^19 - 2 * q^20 + 6 * q^21 + 3 * q^22 + 4 * q^23 + 15 * q^24 + 13 * q^25 + 7 * q^27 + 12 * q^28 - 12 * q^29 - 10 * q^31 + 33 * q^32 + 7 * q^33 + 28 * q^34 - 4 * q^35 + 9 * q^36 + 6 * q^37 + 16 * q^38 - 10 * q^40 + 2 * q^41 + 8 * q^42 - 16 * q^43 + 9 * q^44 + 6 * q^45 - 26 * q^46 + 18 * q^47 + 17 * q^48 + 23 * q^49 + 39 * q^50 - 2 * q^51 + 10 * q^53 + 3 * q^54 + 6 * q^55 + 16 * q^56 + 8 * q^57 + 10 * q^58 + 2 * q^59 - 2 * q^60 - 10 * q^61 - 36 * q^62 + 6 * q^63 + 29 * q^64 + 3 * q^66 + 8 * q^67 - 10 * q^68 + 4 * q^69 - 20 * q^70 + 36 * q^71 + 15 * q^72 + 20 * q^73 + 13 * q^75 + 10 * q^76 + 6 * q^77 + 6 * q^79 - 20 * q^80 + 7 * q^81 - 10 * q^82 + 30 * q^83 + 12 * q^84 - 40 * q^85 + 6 * q^86 - 12 * q^87 + 15 * q^88 + 34 * q^89 - 12 * q^92 - 10 * q^93 + 32 * q^94 + 18 * q^95 + 33 * q^96 + 16 * q^97 + q^98 + 7 * 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 $

$2$	2.73878	1.93661	0.968306	−	0.249768i	$-0.0803543\pi$
$2$	2.73878	1.93661	0.968306	+	0.249768i	$0.0803543\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	5.50093	2.75046
$5$	−2.84154	−1.27078	−0.635388	−	0.772193i	$-0.719160\pi$
$5$	−2.84154	−1.27078	−0.635388	+	0.772193i	$0.719160\pi$
$6$	2.73878	1.11810
$7$	3.93129	1.48589	0.742944	−	0.669353i	$-0.233429\pi$
$7$	3.93129	1.48589	0.742944	+	0.669353i	$0.233429\pi$
$8$	9.58828	3.38997
$9$	1.00000	0.333333
$10$	−7.78236	−2.46100
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	5.50093	1.58798
$13$	0	0
$13$	0	0
$14$	10.7670	2.87759
$15$	−2.84154	−0.733682
$16$	15.2584	3.81459
$17$	3.81818	0.926044	0.463022	−	0.886347i	$-0.346765\pi$
$17$	3.81818	0.926044	0.463022	+	0.886347i	$0.346765\pi$
$18$	2.73878	0.645537
$19$	−2.94082	−0.674670	−0.337335	−	0.941385i	$-0.609526\pi$
$19$	−2.94082	−0.674670	−0.337335	+	0.941385i	$0.609526\pi$
$20$	−15.6311	−3.49522
$21$	3.93129	0.857878
$22$	2.73878	0.583910
$23$	−1.89484	−0.395102	−0.197551	−	0.980293i	$-0.563299\pi$
$23$	−1.89484	−0.395102	−0.197551	+	0.980293i	$0.563299\pi$
$24$	9.58828	1.95720
$25$	3.07435	0.614869
$26$	0	0
$27$	1.00000	0.192450
$28$	21.6258	4.08688
$29$	−2.09928	−0.389826	−0.194913	−	0.980821i	$-0.562443\pi$
$29$	−2.09928	−0.389826	−0.194913	+	0.980821i	$0.562443\pi$
$30$	−7.78236	−1.42086
$31$	−6.16032	−1.10643	−0.553213	−	0.833040i	$-0.686598\pi$
$31$	−6.16032	−1.10643	−0.553213	+	0.833040i	$0.686598\pi$
$32$	22.6127	3.99741
$33$	1.00000	0.174078
$34$	10.4572	1.79339
$35$	−11.1709	−1.88823
$36$	5.50093	0.916821
$37$	8.34404	1.37175	0.685876	−	0.727719i	$-0.259419\pi$
$37$	8.34404	1.37175	0.685876	+	0.727719i	$0.259419\pi$
$38$	−8.05426	−1.30657
$39$	0	0
$40$	−27.2455	−4.30789
$41$	6.35787	0.992933	0.496466	−	0.868056i	$-0.334631\pi$
$41$	6.35787	0.992933	0.496466	+	0.868056i	$0.334631\pi$
$42$	10.7670	1.66138
$43$	−11.7275	−1.78842	−0.894212	−	0.447643i	$-0.852264\pi$
$43$	−11.7275	−1.78842	−0.894212	+	0.447643i	$0.852264\pi$
$44$	5.50093	0.829296
$45$	−2.84154	−0.423592
$46$	−5.18956	−0.765159
$47$	5.31137	0.774743	0.387371	−	0.921924i	$-0.373383\pi$
$47$	5.31137	0.774743	0.387371	+	0.921924i	$0.373383\pi$
$48$	15.2584	2.20235
$49$	8.45506	1.20787
$50$	8.41997	1.19076
$51$	3.81818	0.534652
$52$	0	0
$53$	−2.37985	−0.326898	−0.163449	−	0.986552i	$-0.552262\pi$
$53$	−2.37985	−0.326898	−0.163449	+	0.986552i	$0.552262\pi$
$54$	2.73878	0.372701
$55$	−2.84154	−0.383153
$56$	37.6943	5.03712
$57$	−2.94082	−0.389521
$58$	−5.74947	−0.754942
$59$	−5.38624	−0.701229	−0.350615	−	0.936520i	$-0.614027\pi$
$59$	−5.38624	−0.701229	−0.350615	+	0.936520i	$0.614027\pi$
$60$	−15.6311	−2.01797
$61$	−2.34857	−0.300703	−0.150352	−	0.988633i	$-0.548041\pi$
$61$	−2.34857	−0.300703	−0.150352	+	0.988633i	$0.548041\pi$
$62$	−16.8718	−2.14272
$63$	3.93129	0.495296
$64$	31.4147	3.92684
$65$	0	0
$66$	2.73878	0.337121
$67$	10.4731	1.27949	0.639744	−	0.768588i	$-0.279040\pi$
$67$	10.4731	1.27949	0.639744	+	0.768588i	$0.279040\pi$
$68$	21.0035	2.54705
$69$	−1.89484	−0.228112
$70$	−30.5947	−3.65677
$71$	10.0939	1.19793	0.598964	−	0.800776i	$-0.295579\pi$
$71$	10.0939	1.19793	0.598964	+	0.800776i	$0.295579\pi$
$72$	9.58828	1.12999
$73$	−15.1079	−1.76824	−0.884120	−	0.467260i	$-0.845241\pi$
$73$	−15.1079	−1.76824	−0.884120	+	0.467260i	$0.845241\pi$
$74$	22.8525	2.65655
$75$	3.07435	0.354995
$76$	−16.1772	−1.85566
$77$	3.93129	0.448012
$78$	0	0
$79$	1.57120	0.176774	0.0883872	−	0.996086i	$-0.471829\pi$
$79$	1.57120	0.176774	0.0883872	+	0.996086i	$0.471829\pi$
$80$	−43.3572	−4.84748
$81$	1.00000	0.111111
$82$	17.4128	1.92293
$83$	10.6736	1.17157	0.585787	−	0.810465i	$-0.300785\pi$
$83$	10.6736	1.17157	0.585787	+	0.810465i	$0.300785\pi$
$84$	21.6258	2.35956
$85$	−10.8495	−1.17679
$86$	−32.1190	−3.46348
$87$	−2.09928	−0.225066
$88$	9.58828	1.02211
$89$	3.23647	0.343065	0.171533	−	0.985178i	$-0.445128\pi$
$89$	3.23647	0.343065	0.171533	+	0.985178i	$0.445128\pi$
$90$	−7.78236	−0.820333
$91$	0	0
$92$	−10.4234	−1.08671
$93$	−6.16032	−0.638795
$94$	14.5467	1.50038
$95$	8.35645	0.857354
$96$	22.6127	2.30790
$97$	−17.7914	−1.80645	−0.903223	−	0.429172i	$-0.858805\pi$
$97$	−17.7914	−1.80645	−0.903223	+	0.429172i	$0.858805\pi$
$98$	23.1566	2.33917
$99$	1.00000	0.100504
$100$	16.9118	1.69118
$101$	−12.1229	−1.20627	−0.603136	−	0.797638i	$-0.706083\pi$
$101$	−12.1229	−1.20627	−0.603136	+	0.797638i	$0.706083\pi$
$102$	10.4572	1.03541
$103$	−3.40983	−0.335981	−0.167990	−	0.985789i	$-0.553728\pi$
$103$	−3.40983	−0.335981	−0.167990	+	0.985789i	$0.553728\pi$
$104$	0	0
$105$	−11.1709	−1.09017
$106$	−6.51790	−0.633075
$107$	−12.2352	−1.18282	−0.591411	−	0.806370i	$-0.701429\pi$
$107$	−12.2352	−1.18282	−0.591411	+	0.806370i	$0.701429\pi$
$108$	5.50093	0.529327
$109$	−8.72763	−0.835956	−0.417978	−	0.908457i	$-0.637261\pi$
$109$	−8.72763	−0.835956	−0.417978	+	0.908457i	$0.637261\pi$
$110$	−7.78236	−0.742019
$111$	8.34404	0.791981
$112$	59.9850	5.66805
$113$	0.0155525	0.00146305	0.000731527	−	1.00000i	$-0.499767\pi$
$113$	0.0155525	0.00146305	0.000731527		1.00000i	$0.499767\pi$
$114$	−8.05426	−0.754351
$115$	5.38427	0.502086
$116$	−11.5480	−1.07220
$117$	0	0
$118$	−14.7517	−1.35801
$119$	15.0104	1.37600
$120$	−27.2455	−2.48716
$121$	1.00000	0.0909091
$122$	−6.43222	−0.582346
$123$	6.35787	0.573270
$124$	−33.8875	−3.04318
$125$	5.47182	0.489414
$126$	10.7670	0.959196
$127$	−5.91514	−0.524883	−0.262442	−	0.964948i	$-0.584528\pi$
$127$	−5.91514	−0.524883	−0.262442	+	0.964948i	$0.584528\pi$
$128$	40.8125	3.60735
$129$	−11.7275	−1.03255
$130$	0	0
$131$	−1.32191	−0.115496	−0.0577481	−	0.998331i	$-0.518392\pi$
$131$	−1.32191	−0.115496	−0.0577481	+	0.998331i	$0.518392\pi$
$132$	5.50093	0.478794
$133$	−11.5612	−1.00248
$134$	28.6835	2.47787
$135$	−2.84154	−0.244561
$136$	36.6097	3.13926
$137$	4.82127	0.411909	0.205955	−	0.978562i	$-0.433970\pi$
$137$	4.82127	0.411909	0.205955	+	0.978562i	$0.433970\pi$
$138$	−5.18956	−0.441765
$139$	17.1877	1.45784	0.728919	−	0.684600i	$-0.240023\pi$
$139$	17.1877	1.45784	0.728919	+	0.684600i	$0.240023\pi$
$140$	−61.4504	−5.19351
$141$	5.31137	0.447298
$142$	27.6451	2.31992
$143$	0	0
$144$	15.2584	1.27153
$145$	5.96518	0.495382
$146$	−41.3771	−3.42439
$147$	8.45506	0.697361
$148$	45.8999	3.77295
$149$	−5.31754	−0.435629	−0.217815	−	0.975990i	$-0.569893\pi$
$149$	−5.31754	−0.435629	−0.217815	+	0.975990i	$0.569893\pi$
$150$	8.41997	0.687487
$151$	−6.77573	−0.551401	−0.275700	−	0.961244i	$-0.588910\pi$
$151$	−6.77573	−0.551401	−0.275700	+	0.961244i	$0.588910\pi$
$152$	−28.1974	−2.28711
$153$	3.81818	0.308681
$154$	10.7670	0.867626
$155$	17.5048	1.40602
$156$	0	0
$157$	16.2884	1.29995	0.649977	−	0.759954i	$-0.274779\pi$
$157$	16.2884	1.29995	0.649977	+	0.759954i	$0.274779\pi$
$158$	4.30319	0.342343
$159$	−2.37985	−0.188735
$160$	−64.2550	−5.07981
$161$	−7.44918	−0.587077
$162$	2.73878	0.215179
$163$	11.4032	0.893170	0.446585	−	0.894741i	$-0.352640\pi$
$163$	11.4032	0.893170	0.446585	+	0.894741i	$0.352640\pi$
$164$	34.9742	2.73103
$165$	−2.84154	−0.221214
$166$	29.2325	2.26888
$167$	−14.7302	−1.13985	−0.569927	−	0.821695i	$-0.693029\pi$
$167$	−14.7302	−1.13985	−0.569927	+	0.821695i	$0.693029\pi$
$168$	37.6943	2.90818
$169$	0	0
$170$	−29.7144	−2.27899
$171$	−2.94082	−0.224890
$172$	−64.5121	−4.91900
$173$	0.186647	0.0141905	0.00709527	−	0.999975i	$-0.497741\pi$
$173$	0.186647	0.0141905	0.00709527	+	0.999975i	$0.497741\pi$
$174$	−5.74947	−0.435866
$175$	12.0862	0.913627
$176$	15.2584	1.15014
$177$	−5.38624	−0.404855
$178$	8.86399	0.664384
$179$	10.9555	0.818856	0.409428	−	0.912342i	$-0.365728\pi$
$179$	10.9555	0.818856	0.409428	+	0.912342i	$0.365728\pi$
$180$	−15.6311	−1.16507
$181$	−8.52034	−0.633312	−0.316656	−	0.948540i	$-0.602560\pi$
$181$	−8.52034	−0.633312	−0.316656	+	0.948540i	$0.602560\pi$
$182$	0	0
$183$	−2.34857	−0.173611
$184$	−18.1683	−1.33938
$185$	−23.7099	−1.74319
$186$	−16.8718	−1.23710
$187$	3.81818	0.279213
$188$	29.2175	2.13090
$189$	3.93129	0.285959
$190$	22.8865	1.66036
$191$	−11.8003	−0.853840	−0.426920	−	0.904289i	$-0.640401\pi$
$191$	−11.8003	−0.853840	−0.426920	+	0.904289i	$0.640401\pi$
$192$	31.4147	2.26716
$193$	10.9405	0.787518	0.393759	−	0.919214i	$-0.371174\pi$
$193$	10.9405	0.787518	0.393759	+	0.919214i	$0.371174\pi$
$194$	−48.7268	−3.49838
$195$	0	0
$196$	46.5107	3.32219
$197$	9.43307	0.672079	0.336039	−	0.941848i	$-0.390912\pi$
$197$	9.43307	0.672079	0.336039	+	0.941848i	$0.390912\pi$
$198$	2.73878	0.194637
$199$	−15.3198	−1.08599	−0.542996	−	0.839735i	$-0.682710\pi$
$199$	−15.3198	−1.08599	−0.542996	+	0.839735i	$0.682710\pi$
$200$	29.4777	2.08439
$201$	10.4731	0.738713
$202$	−33.2020	−2.33608
$203$	−8.25288	−0.579238
$204$	21.0035	1.47054
$205$	−18.0661	−1.26179
$206$	−9.33878	−0.650664
$207$	−1.89484	−0.131701
$208$	0	0
$209$	−2.94082	−0.203421
$210$	−30.5947	−2.11124
$211$	2.91243	0.200500	0.100250	−	0.994962i	$-0.468036\pi$
$211$	2.91243	0.200500	0.100250	+	0.994962i	$0.468036\pi$
$212$	−13.0914	−0.899122
$213$	10.0939	0.691625
$214$	−33.5096	−2.29067
$215$	33.3241	2.27269
$216$	9.58828	0.652400
$217$	−24.2180	−1.64403
$218$	−23.9031	−1.61892
$219$	−15.1079	−1.02089
$220$	−15.6311	−1.05385
$221$	0	0
$222$	22.8525	1.53376
$223$	10.8511	0.726641	0.363320	−	0.931664i	$-0.381643\pi$
$223$	10.8511	0.726641	0.363320	+	0.931664i	$0.381643\pi$
$224$	88.8973	5.93970
$225$	3.07435	0.204956
$226$	0.0425948	0.00283337
$227$	0.322636	0.0214141	0.0107070	−	0.999943i	$-0.496592\pi$
$227$	0.322636	0.0214141	0.0107070	+	0.999943i	$0.496592\pi$
$228$	−16.1772	−1.07136
$229$	−5.94060	−0.392566	−0.196283	−	0.980547i	$-0.562887\pi$
$229$	−5.94060	−0.392566	−0.196283	+	0.980547i	$0.562887\pi$
$230$	14.7463	0.972345
$231$	3.93129	0.258660
$232$	−20.1285	−1.32150
$233$	−12.6202	−0.826774	−0.413387	−	0.910555i	$-0.635654\pi$
$233$	−12.6202	−0.826774	−0.413387	+	0.910555i	$0.635654\pi$
$234$	0	0
$235$	−15.0925	−0.984524
$236$	−29.6293	−1.92871
$237$	1.57120	0.102061
$238$	41.1101	2.66477
$239$	20.7706	1.34354	0.671768	−	0.740762i	$-0.265535\pi$
$239$	20.7706	1.34354	0.671768	+	0.740762i	$0.265535\pi$
$240$	−43.3572	−2.79870
$241$	−18.2163	−1.17341	−0.586706	−	0.809800i	$-0.699576\pi$
$241$	−18.2163	−1.17341	−0.586706	+	0.809800i	$0.699576\pi$
$242$	2.73878	0.176056
$243$	1.00000	0.0641500
$244$	−12.9193	−0.827074
$245$	−24.0254	−1.53492
$246$	17.4128	1.11020
$247$	0	0
$248$	−59.0668	−3.75075
$249$	10.6736	0.676409
$250$	14.9861	0.947806
$251$	−22.6662	−1.43068	−0.715340	−	0.698776i	$-0.753728\pi$
$251$	−22.6662	−1.43068	−0.715340	+	0.698776i	$0.753728\pi$
$252$	21.6258	1.36229
$253$	−1.89484	−0.119128
$254$	−16.2003	−1.01650
$255$	−10.8495	−0.679422
$256$	48.9471	3.05920
$257$	17.7333	1.10617	0.553087	−	0.833124i	$-0.313450\pi$
$257$	17.7333	1.10617	0.553087	+	0.833124i	$0.313450\pi$
$258$	−32.1190	−1.99964
$259$	32.8028	2.03827
$260$	0	0
$261$	−2.09928	−0.129942
$262$	−3.62044	−0.223671
$263$	29.5107	1.81971	0.909853	−	0.414930i	$-0.136194\pi$
$263$	29.5107	1.81971	0.909853	+	0.414930i	$0.136194\pi$
$264$	9.58828	0.590118
$265$	6.76245	0.415414
$266$	−31.6637	−1.94142
$267$	3.23647	0.198069
$268$	57.6116	3.51919
$269$	−9.02091	−0.550015	−0.275007	−	0.961442i	$-0.588680\pi$
$269$	−9.02091	−0.550015	−0.275007	+	0.961442i	$0.588680\pi$
$270$	−7.78236	−0.473619
$271$	4.58320	0.278410	0.139205	−	0.990264i	$-0.455545\pi$
$271$	4.58320	0.278410	0.139205	+	0.990264i	$0.455545\pi$
$272$	58.2591	3.53248
$273$	0	0
$274$	13.2044	0.797708
$275$	3.07435	0.185390
$276$	−10.4234	−0.627414
$277$	20.9859	1.26092	0.630461	−	0.776221i	$-0.282866\pi$
$277$	20.9859	1.26092	0.630461	+	0.776221i	$0.282866\pi$
$278$	47.0732	2.82327
$279$	−6.16032	−0.368809
$280$	−107.110	−6.40104
$281$	10.5360	0.628524	0.314262	−	0.949336i	$-0.398243\pi$
$281$	10.5360	0.628524	0.314262	+	0.949336i	$0.398243\pi$
$282$	14.5467	0.866242
$283$	−2.57169	−0.152871	−0.0764355	−	0.997075i	$-0.524354\pi$
$283$	−2.57169	−0.152871	−0.0764355	+	0.997075i	$0.524354\pi$
$284$	55.5260	3.29486
$285$	8.35645	0.494993
$286$	0	0
$287$	24.9947	1.47539
$288$	22.6127	1.33247
$289$	−2.42153	−0.142443
$290$	16.3373	0.959362
$291$	−17.7914	−1.04295
$292$	−83.1072	−4.86348
$293$	5.16162	0.301545	0.150772	−	0.988568i	$-0.451824\pi$
$293$	5.16162	0.301545	0.150772	+	0.988568i	$0.451824\pi$
$294$	23.1566	1.35052
$295$	15.3052	0.891105
$296$	80.0050	4.65019
$297$	1.00000	0.0580259
$298$	−14.5636	−0.843645
$299$	0	0
$300$	16.9118	0.976401
$301$	−46.1042	−2.65740
$302$	−18.5572	−1.06785
$303$	−12.1229	−0.696442
$304$	−44.8720	−2.57359
$305$	6.67355	0.382126
$306$	10.4572	0.597796
$307$	−30.0561	−1.71539	−0.857697	−	0.514156i	$-0.828105\pi$
$307$	−30.0561	−1.71539	−0.857697	+	0.514156i	$0.828105\pi$
$308$	21.6258	1.23224
$309$	−3.40983	−0.193978
$310$	47.9418	2.72291
$311$	−21.7462	−1.23311	−0.616557	−	0.787310i	$-0.711473\pi$
$311$	−21.7462	−1.23311	−0.616557	+	0.787310i	$0.711473\pi$
$312$	0	0
$313$	−24.4361	−1.38121	−0.690606	−	0.723231i	$-0.742656\pi$
$313$	−24.4361	−1.38121	−0.690606	+	0.723231i	$0.742656\pi$
$314$	44.6103	2.51751
$315$	−11.1709	−0.629410
$316$	8.64309	0.486212
$317$	21.1040	1.18532	0.592658	−	0.805454i	$-0.298079\pi$
$317$	21.1040	1.18532	0.592658	+	0.805454i	$0.298079\pi$
$318$	−6.51790	−0.365506
$319$	−2.09928	−0.117537
$320$	−89.2661	−4.99013
$321$	−12.2352	−0.682903
$322$	−20.4017	−1.13694
$323$	−11.2286	−0.624774
$324$	5.50093	0.305607
$325$	0	0
$326$	31.2310	1.72972
$327$	−8.72763	−0.482639
$328$	60.9611	3.36601
$329$	20.8805	1.15118
$330$	−7.78236	−0.428405
$331$	0.560518	0.0308089	0.0154044	−	0.999881i	$-0.495096\pi$
$331$	0.560518	0.0308089	0.0154044	+	0.999881i	$0.495096\pi$
$332$	58.7144	3.22237
$333$	8.34404	0.457250
$334$	−40.3427	−2.20745
$335$	−29.7596	−1.62594
$336$	59.9850	3.27245
$337$	−7.76850	−0.423177	−0.211589	−	0.977359i	$-0.567864\pi$
$337$	−7.76850	−0.423177	−0.211589	+	0.977359i	$0.567864\pi$
$338$	0	0
$339$	0.0155525	0.000844695 0
$340$	−59.6823	−3.23673
$341$	−6.16032	−0.333600
$342$	−8.05426	−0.435525
$343$	5.72025	0.308864
$344$	−112.446	−6.06270
$345$	5.38427	0.289879
$346$	0.511186	0.0274816
$347$	−10.1357	−0.544110	−0.272055	−	0.962282i	$-0.587703\pi$
$347$	−10.1357	−0.544110	−0.272055	+	0.962282i	$0.587703\pi$
$348$	−11.5480	−0.619037
$349$	−20.0030	−1.07074	−0.535369	−	0.844619i	$-0.679827\pi$
$349$	−20.0030	−1.07074	−0.535369	+	0.844619i	$0.679827\pi$
$350$	33.1013	1.76934
$351$	0	0
$352$	22.6127	1.20526
$353$	−26.7905	−1.42591	−0.712957	−	0.701208i	$-0.752645\pi$
$353$	−26.7905	−1.42591	−0.712957	+	0.701208i	$0.752645\pi$
$354$	−14.7517	−0.784047
$355$	−28.6823	−1.52230
$356$	17.8036	0.943589
$357$	15.0104	0.794433
$358$	30.0049	1.58581
$359$	26.7347	1.41101	0.705503	−	0.708707i	$-0.250721\pi$
$359$	26.7347	1.41101	0.705503	+	0.708707i	$0.250721\pi$
$360$	−27.2455	−1.43596
$361$	−10.3516	−0.544820
$362$	−23.3354	−1.22648
$363$	1.00000	0.0524864
$364$	0	0
$365$	42.9296	2.24704
$366$	−6.43222	−0.336218
$367$	1.89563	0.0989512	0.0494756	−	0.998775i	$-0.484245\pi$
$367$	1.89563	0.0989512	0.0494756	+	0.998775i	$0.484245\pi$
$368$	−28.9122	−1.50715
$369$	6.35787	0.330978
$370$	−64.9363	−3.37588
$371$	−9.35590	−0.485734
$372$	−33.8875	−1.75698
$373$	−36.7517	−1.90293	−0.951464	−	0.307759i	$-0.900421\pi$
$373$	−36.7517	−1.90293	−0.951464	+	0.307759i	$0.900421\pi$
$374$	10.4572	0.540726
$375$	5.47182	0.282564
$376$	50.9269	2.62635
$377$	0	0
$378$	10.7670	0.553792
$379$	−26.1328	−1.34235	−0.671176	−	0.741298i	$-0.734211\pi$
$379$	−26.1328	−1.34235	−0.671176	+	0.741298i	$0.734211\pi$
$380$	45.9682	2.35812
$381$	−5.91514	−0.303042
$382$	−32.3185	−1.65356
$383$	16.9211	0.864629	0.432315	−	0.901723i	$-0.357697\pi$
$383$	16.9211	0.864629	0.432315	+	0.901723i	$0.357697\pi$
$384$	40.8125	2.08270
$385$	−11.1709	−0.569323
$386$	29.9638	1.52512
$387$	−11.7275	−0.596142
$388$	−97.8693	−4.96856
$389$	−5.05607	−0.256353	−0.128177	−	0.991751i	$-0.540912\pi$
$389$	−5.05607	−0.256353	−0.128177	+	0.991751i	$0.540912\pi$
$390$	0	0
$391$	−7.23484	−0.365882
$392$	81.0694	4.09462
$393$	−1.32191	−0.0666818
$394$	25.8351	1.30156
$395$	−4.46464	−0.224640
$396$	5.50093	0.276432
$397$	15.7731	0.791631	0.395815	−	0.918330i	$-0.370462\pi$
$397$	15.7731	0.791631	0.395815	+	0.918330i	$0.370462\pi$
$398$	−41.9576	−2.10314
$399$	−11.5612	−0.578785
$400$	46.9095	2.34547
$401$	8.42218	0.420584	0.210292	−	0.977639i	$-0.432559\pi$
$401$	8.42218	0.420584	0.210292	+	0.977639i	$0.432559\pi$
$402$	28.6835	1.43060
$403$	0	0
$404$	−66.6872	−3.31781
$405$	−2.84154	−0.141197
$406$	−22.6028	−1.12176
$407$	8.34404	0.413599
$408$	36.6097	1.81245
$409$	31.3861	1.55194	0.775971	−	0.630768i	$-0.217260\pi$
$409$	31.3861	1.55194	0.775971	+	0.630768i	$0.217260\pi$
$410$	−49.4792	−2.44361
$411$	4.82127	0.237816
$412$	−18.7572	−0.924102
$413$	−21.1749	−1.04195
$414$	−5.18956	−0.255053
$415$	−30.3293	−1.48881
$416$	0	0
$417$	17.1877	0.841683
$418$	−8.05426	−0.393947
$419$	−6.62928	−0.323861	−0.161931	−	0.986802i	$-0.551772\pi$
$419$	−6.62928	−0.323861	−0.161931	+	0.986802i	$0.551772\pi$
$420$	−61.4504	−2.99847
$421$	−2.61327	−0.127363	−0.0636816	−	0.997970i	$-0.520284\pi$
$421$	−2.61327	−0.127363	−0.0636816	+	0.997970i	$0.520284\pi$
$422$	7.97651	0.388290
$423$	5.31137	0.258248
$424$	−22.8187	−1.10817
$425$	11.7384	0.569396
$426$	27.6451	1.33941
$427$	−9.23291	−0.446812
$428$	−67.3050	−3.25331
$429$	0	0
$430$	91.2675	4.40131
$431$	−24.8745	−1.19816	−0.599081	−	0.800688i	$-0.704467\pi$
$431$	−24.8745	−1.19816	−0.599081	+	0.800688i	$0.704467\pi$
$432$	15.2584	0.734118
$433$	6.55556	0.315040	0.157520	−	0.987516i	$-0.449650\pi$
$433$	6.55556	0.315040	0.157520	+	0.987516i	$0.449650\pi$
$434$	−66.3278	−3.18384
$435$	5.96518	0.286009
$436$	−48.0101	−2.29927
$437$	5.57239	0.266563
$438$	−41.3771	−1.97707
$439$	−38.2180	−1.82405	−0.912023	−	0.410138i	$-0.865480\pi$
$439$	−38.2180	−1.82405	−0.912023	+	0.410138i	$0.865480\pi$
$440$	−27.2455	−1.29888
$441$	8.45506	0.402622
$442$	0	0
$443$	−12.7407	−0.605330	−0.302665	−	0.953097i	$-0.597876\pi$
$443$	−12.7407	−0.605330	−0.302665	+	0.953097i	$0.597876\pi$
$444$	45.8999	2.17831
$445$	−9.19656	−0.435959
$446$	29.7187	1.40722
$447$	−5.31754	−0.251511
$448$	123.500	5.83484
$449$	25.9513	1.22472	0.612358	−	0.790581i	$-0.290221\pi$
$449$	25.9513	1.22472	0.612358	+	0.790581i	$0.290221\pi$
$450$	8.41997	0.396921
$451$	6.35787	0.299381
$452$	0.0855531	0.00402408
$453$	−6.77573	−0.318351
$454$	0.883629	0.0414708
$455$	0	0
$456$	−28.1974	−1.32046
$457$	16.0372	0.750190	0.375095	−	0.926986i	$-0.377610\pi$
$457$	16.0372	0.750190	0.375095	+	0.926986i	$0.377610\pi$
$458$	−16.2700	−0.760247
$459$	3.81818	0.178217
$460$	29.6185	1.38097
$461$	3.48566	0.162343	0.0811716	−	0.996700i	$-0.474134\pi$
$461$	3.48566	0.162343	0.0811716	+	0.996700i	$0.474134\pi$
$462$	10.7670	0.500924
$463$	−27.0784	−1.25844	−0.629220	−	0.777227i	$-0.716626\pi$
$463$	−27.0784	−1.25844	−0.629220	+	0.777227i	$0.716626\pi$
$464$	−32.0315	−1.48703
$465$	17.5048	0.811765
$466$	−34.5639	−1.60114
$467$	−15.6899	−0.726041	−0.363020	−	0.931781i	$-0.618254\pi$
$467$	−15.6899	−0.726041	−0.363020	+	0.931781i	$0.618254\pi$
$468$	0	0
$469$	41.1727	1.90118
$470$	−41.3350	−1.90664
$471$	16.2884	0.750529
$472$	−51.6448	−2.37715
$473$	−11.7275	−0.539230
$474$	4.30319	0.197652
$475$	−9.04109	−0.414834
$476$	82.5709	3.78463
$477$	−2.37985	−0.108966
$478$	56.8860	2.60191
$479$	33.0061	1.50809	0.754043	−	0.656825i	$-0.228101\pi$
$479$	33.0061	1.50809	0.754043	+	0.656825i	$0.228101\pi$
$480$	−64.2550	−2.93283
$481$	0	0
$482$	−49.8904	−2.27244
$483$	−7.44918	−0.338949
$484$	5.50093	0.250042
$485$	50.5550	2.29559
$486$	2.73878	0.124234
$487$	18.6684	0.845945	0.422973	−	0.906142i	$-0.360987\pi$
$487$	18.6684	0.845945	0.422973	+	0.906142i	$0.360987\pi$
$488$	−22.5187	−1.01938
$489$	11.4032	0.515672
$490$	−65.8003	−2.97255
$491$	−6.78238	−0.306084	−0.153042	−	0.988220i	$-0.548907\pi$
$491$	−6.78238	−0.306084	−0.153042	+	0.988220i	$0.548907\pi$
$492$	34.9742	1.57676
$493$	−8.01542	−0.360996
$494$	0	0
$495$	−2.84154	−0.127718
$496$	−93.9963	−4.22056
$497$	39.6822	1.77999
$498$	29.2325	1.30994
$499$	−0.212900	−0.00953070	−0.00476535	−	0.999989i	$-0.501517\pi$
$499$	−0.212900	−0.00953070	−0.00476535	+	0.999989i	$0.501517\pi$
$500$	30.1001	1.34612
$501$	−14.7302	−0.658095
$502$	−62.0779	−2.77067
$503$	−10.5282	−0.469430	−0.234715	−	0.972064i	$-0.575416\pi$
$503$	−10.5282	−0.469430	−0.234715	+	0.972064i	$0.575416\pi$
$504$	37.6943	1.67904
$505$	34.4477	1.53290
$506$	−5.18956	−0.230704
$507$	0	0
$508$	−32.5387	−1.44367
$509$	−26.1335	−1.15835	−0.579175	−	0.815204i	$-0.696625\pi$
$509$	−26.1335	−1.15835	−0.579175	+	0.815204i	$0.696625\pi$
$510$	−29.7144	−1.31578
$511$	−59.3934	−2.62741
$512$	52.4306	2.31713
$513$	−2.94082	−0.129840
$514$	48.5677	2.14223
$515$	9.68917	0.426956
$516$	−64.5121	−2.83999
$517$	5.31137	0.233594
$518$	89.8398	3.94734
$519$	0.186647	0.00819291
$520$	0	0
$521$	44.5983	1.95389	0.976944	−	0.213495i	$-0.0684847\pi$
$521$	44.5983	1.95389	0.976944	+	0.213495i	$0.0684847\pi$
$522$	−5.74947	−0.251647
$523$	−35.9788	−1.57324	−0.786622	−	0.617435i	$-0.788172\pi$
$523$	−35.9788	−1.57324	−0.786622	+	0.617435i	$0.788172\pi$
$524$	−7.27176	−0.317668
$525$	12.0862	0.527483
$526$	80.8233	3.52406
$527$	−23.5212	−1.02460
$528$	15.2584	0.664035
$529$	−19.4096	−0.843895
$530$	18.5209	0.804495
$531$	−5.38624	−0.233743
$532$	−63.5974	−2.75730
$533$	0	0
$534$	8.86399	0.383583
$535$	34.7668	1.50310
$536$	100.419	4.33743
$537$	10.9555	0.472767
$538$	−24.7063	−1.06516
$539$	8.45506	0.364185
$540$	−15.6311	−0.672656
$541$	19.2806	0.828937	0.414469	−	0.910064i	$-0.363967\pi$
$541$	19.2806	0.828937	0.414469	+	0.910064i	$0.363967\pi$
$542$	12.5524	0.539172
$543$	−8.52034	−0.365643
$544$	86.3395	3.70177
$545$	24.7999	1.06231
$546$	0	0
$547$	−18.3680	−0.785359	−0.392679	−	0.919675i	$-0.628452\pi$
$547$	−18.3680	−0.785359	−0.392679	+	0.919675i	$0.628452\pi$
$548$	26.5215	1.13294
$549$	−2.34857	−0.100234
$550$	8.41997	0.359029
$551$	6.17360	0.263004
$552$	−18.1683	−0.773293
$553$	6.17686	0.262667
$554$	57.4759	2.44192
$555$	−23.7099	−1.00643
$556$	94.5481	4.00973
$557$	−20.9920	−0.889459	−0.444730	−	0.895665i	$-0.646700\pi$
$557$	−20.9920	−0.889459	−0.444730	+	0.895665i	$0.646700\pi$
$558$	−16.8718	−0.714239
$559$	0	0
$560$	−170.450	−7.20282
$561$	3.81818	0.161204
$562$	28.8558	1.21721
$563$	3.18924	0.134411	0.0672053	−	0.997739i	$-0.478592\pi$
$563$	3.18924	0.134411	0.0672053	+	0.997739i	$0.478592\pi$
$564$	29.2175	1.23028
$565$	−0.0441930	−0.00185921
$566$	−7.04329	−0.296052
$567$	3.93129	0.165099
$568$	96.7834	4.06094
$569$	19.0570	0.798909	0.399455	−	0.916753i	$-0.369200\pi$
$569$	19.0570	0.798909	0.399455	+	0.916753i	$0.369200\pi$
$570$	22.8865	0.958610
$571$	13.1418	0.549967	0.274984	−	0.961449i	$-0.411328\pi$
$571$	13.1418	0.549967	0.274984	+	0.961449i	$0.411328\pi$
$572$	0	0
$573$	−11.8003	−0.492965
$574$	68.4549	2.85725
$575$	−5.82540	−0.242936
$576$	31.4147	1.30895
$577$	6.38825	0.265946	0.132973	−	0.991120i	$-0.457548\pi$
$577$	6.38825	0.265946	0.132973	+	0.991120i	$0.457548\pi$
$578$	−6.63205	−0.275857
$579$	10.9405	0.454674
$580$	32.8140	1.36253
$581$	41.9608	1.74083
$582$	−48.7268	−2.01979
$583$	−2.37985	−0.0985635
$584$	−144.858	−5.99428
$585$	0	0
$586$	14.1365	0.583975
$587$	−8.66483	−0.357636	−0.178818	−	0.983882i	$-0.557227\pi$
$587$	−8.66483	−0.357636	−0.178818	+	0.983882i	$0.557227\pi$
$588$	46.5107	1.91807
$589$	18.1164	0.746472
$590$	41.9177	1.72572
$591$	9.43307	0.388025
$592$	127.316	5.23267
$593$	5.41552	0.222389	0.111194	−	0.993799i	$-0.464532\pi$
$593$	5.41552	0.222389	0.111194	+	0.993799i	$0.464532\pi$
$594$	2.73878	0.112374
$595$	−42.6525	−1.74858
$596$	−29.2514	−1.19818
$597$	−15.3198	−0.626997
$598$	0	0
$599$	17.1821	0.702041	0.351021	−	0.936368i	$-0.385835\pi$
$599$	17.1821	0.702041	0.351021	+	0.936368i	$0.385835\pi$
$600$	29.4777	1.20342
$601$	4.44618	0.181364	0.0906818	−	0.995880i	$-0.471095\pi$
$601$	4.44618	0.181364	0.0906818	+	0.995880i	$0.471095\pi$
$602$	−126.269	−5.14635
$603$	10.4731	0.426496
$604$	−37.2728	−1.51661
$605$	−2.84154	−0.115525
$606$	−33.2020	−1.34874
$607$	12.1499	0.493148	0.246574	−	0.969124i	$-0.420695\pi$
$607$	12.1499	0.493148	0.246574	+	0.969124i	$0.420695\pi$
$608$	−66.5000	−2.69693
$609$	−8.25288	−0.334423
$610$	18.2774	0.740031
$611$	0	0
$612$	21.0035	0.849017
$613$	−30.6073	−1.23622	−0.618108	−	0.786093i	$-0.712101\pi$
$613$	−30.6073	−1.23622	−0.618108	+	0.786093i	$0.712101\pi$
$614$	−82.3172	−3.32205
$615$	−18.0661	−0.728497
$616$	37.6943	1.51875
$617$	15.3414	0.617622	0.308811	−	0.951123i	$-0.400069\pi$
$617$	15.3414	0.617622	0.308811	+	0.951123i	$0.400069\pi$
$618$	−9.33878	−0.375661
$619$	−10.0391	−0.403505	−0.201752	−	0.979437i	$-0.564664\pi$
$619$	−10.0391	−0.403505	−0.201752	+	0.979437i	$0.564664\pi$
$620$	96.2926	3.86720
$621$	−1.89484	−0.0760374
$622$	−59.5581	−2.38806
$623$	12.7235	0.509757
$624$	0	0
$625$	−30.9201	−1.23681
$626$	−66.9253	−2.67487
$627$	−2.94082	−0.117445
$628$	89.6012	3.57548
$629$	31.8590	1.27030
$630$	−30.5947	−1.21892
$631$	20.8523	0.830119	0.415059	−	0.909794i	$-0.363761\pi$
$631$	20.8523	0.830119	0.415059	+	0.909794i	$0.363761\pi$
$632$	15.0652	0.599260
$633$	2.91243	0.115759
$634$	57.7991	2.29550
$635$	16.8081	0.667009
$636$	−13.0914	−0.519108
$637$	0	0
$638$	−5.74947	−0.227624
$639$	10.0939	0.399310
$640$	−115.970	−4.58413
$641$	29.3934	1.16097	0.580484	−	0.814272i	$-0.302863\pi$
$641$	29.3934	1.16097	0.580484	+	0.814272i	$0.302863\pi$
$642$	−33.5096	−1.32252
$643$	−7.23812	−0.285444	−0.142722	−	0.989763i	$-0.545585\pi$
$643$	−7.23812	−0.285444	−0.142722	+	0.989763i	$0.545585\pi$
$644$	−40.9774	−1.61474
$645$	33.3241	1.31214
$646$	−30.7526	−1.20994
$647$	−25.4069	−0.998848	−0.499424	−	0.866358i	$-0.666455\pi$
$647$	−25.4069	−0.998848	−0.499424	+	0.866358i	$0.666455\pi$
$648$	9.58828	0.376663
$649$	−5.38624	−0.211429
$650$	0	0
$651$	−24.2180	−0.949178
$652$	62.7284	2.45663
$653$	−10.1486	−0.397146	−0.198573	−	0.980086i	$-0.563631\pi$
$653$	−10.1486	−0.397146	−0.198573	+	0.980086i	$0.563631\pi$
$654$	−23.9031	−0.934685
$655$	3.75627	0.146770
$656$	97.0107	3.78763
$657$	−15.1079	−0.589413
$658$	57.1873	2.22939
$659$	−18.8648	−0.734869	−0.367434	−	0.930049i	$-0.619764\pi$
$659$	−18.8648	−0.734869	−0.367434	+	0.930049i	$0.619764\pi$
$660$	−15.6311	−0.608440
$661$	−7.39059	−0.287461	−0.143730	−	0.989617i	$-0.545910\pi$
$661$	−7.39059	−0.287461	−0.143730	+	0.989617i	$0.545910\pi$
$662$	1.53514	0.0596648
$663$	0	0
$664$	102.341	3.97160
$665$	32.8516	1.27393
$666$	22.8525	0.885516
$667$	3.97780	0.154021
$668$	−81.0296	−3.13513
$669$	10.8511	0.419526
$670$	−81.5052	−3.14882
$671$	−2.34857	−0.0906655
$672$	88.8973	3.42929
$673$	−13.8241	−0.532879	−0.266439	−	0.963852i	$-0.585847\pi$
$673$	−13.8241	−0.532879	−0.266439	+	0.963852i	$0.585847\pi$
$674$	−21.2762	−0.819530
$675$	3.07435	0.118332
$676$	0	0
$677$	−28.1714	−1.08272	−0.541358	−	0.840792i	$-0.682090\pi$
$677$	−28.1714	−1.08272	−0.541358	+	0.840792i	$0.682090\pi$
$678$	0.0425948	0.00163585
$679$	−69.9433	−2.68418
$680$	−104.028	−3.98929
$681$	0.322636	0.0123634
$682$	−16.8718	−0.646053
$683$	−20.1458	−0.770856	−0.385428	−	0.922738i	$-0.625946\pi$
$683$	−20.1458	−0.770856	−0.385428	+	0.922738i	$0.625946\pi$
$684$	−16.1772	−0.618552
$685$	−13.6998	−0.523444
$686$	15.6665	0.598150
$687$	−5.94060	−0.226648
$688$	−178.942	−6.82211
$689$	0	0
$690$	14.7463	0.561384
$691$	−4.60090	−0.175026	−0.0875132	−	0.996163i	$-0.527892\pi$
$691$	−4.60090	−0.175026	−0.0875132	+	0.996163i	$0.527892\pi$
$692$	1.02673	0.0390306
$693$	3.93129	0.149337
$694$	−27.7593	−1.05373
$695$	−48.8394	−1.85258
$696$	−20.1285	−0.762968
$697$	24.2755	0.919499
$698$	−54.7839	−2.07360
$699$	−12.6202	−0.477338
$700$	66.4851	2.51290
$701$	−2.14477	−0.0810067	−0.0405033	−	0.999179i	$-0.512896\pi$
$701$	−2.14477	−0.0810067	−0.0405033	+	0.999179i	$0.512896\pi$
$702$	0	0
$703$	−24.5383	−0.925479
$704$	31.4147	1.18399
$705$	−15.0925	−0.568415
$706$	−73.3733	−2.76144
$707$	−47.6586	−1.79239
$708$	−29.6293	−1.11354
$709$	−18.0751	−0.678826	−0.339413	−	0.940637i	$-0.610228\pi$
$709$	−18.0751	−0.678826	−0.339413	+	0.940637i	$0.610228\pi$
$710$	−78.5546	−2.94810
$711$	1.57120	0.0589248
$712$	31.0322	1.16298
$713$	11.6728	0.437151
$714$	41.1101	1.53851
$715$	0	0
$716$	60.2657	2.25223
$717$	20.7706	0.775691
$718$	73.2206	2.73257
$719$	−5.67258	−0.211552	−0.105776	−	0.994390i	$-0.533733\pi$
$719$	−5.67258	−0.211552	−0.105776	+	0.994390i	$0.533733\pi$
$720$	−43.3572	−1.61583
$721$	−13.4050	−0.499230
$722$	−28.3507	−1.05511
$723$	−18.2163	−0.677470
$724$	−46.8698	−1.74190
$725$	−6.45391	−0.239692
$726$	2.73878	0.101646
$727$	20.7279	0.768756	0.384378	−	0.923176i	$-0.374416\pi$
$727$	20.7279	0.768756	0.384378	+	0.923176i	$0.374416\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	117.575	4.35163
$731$	−44.7776	−1.65616
$732$	−12.9193	−0.477511
$733$	13.8875	0.512945	0.256473	−	0.966552i	$-0.417440\pi$
$733$	13.8875	0.512945	0.256473	+	0.966552i	$0.417440\pi$
$734$	5.19172	0.191630
$735$	−24.0254	−0.886189
$736$	−42.8476	−1.57938
$737$	10.4731	0.385780
$738$	17.4128	0.640975
$739$	−2.10062	−0.0772725	−0.0386362	−	0.999253i	$-0.512301\pi$
$739$	−2.10062	−0.0772725	−0.0386362	+	0.999253i	$0.512301\pi$
$740$	−130.427	−4.79457
$741$	0	0
$742$	−25.6238	−0.940678
$743$	39.5255	1.45005	0.725025	−	0.688722i	$-0.241828\pi$
$743$	39.5255	1.45005	0.725025	+	0.688722i	$0.241828\pi$
$744$	−59.0668	−2.16550
$745$	15.1100	0.553587
$746$	−100.655	−3.68523
$747$	10.6736	0.390525
$748$	21.0035	0.767964
$749$	−48.1002	−1.75754
$750$	14.9861	0.547216
$751$	−7.96076	−0.290492	−0.145246	−	0.989396i	$-0.546397\pi$
$751$	−7.96076	−0.290492	−0.145246	+	0.989396i	$0.546397\pi$
$752$	81.0427	2.95532
$753$	−22.6662	−0.826004
$754$	0	0
$755$	19.2535	0.700707
$756$	21.6258	0.786521
$757$	−21.7720	−0.791316	−0.395658	−	0.918398i	$-0.629484\pi$
$757$	−21.7720	−0.791316	−0.395658	+	0.918398i	$0.629484\pi$
$758$	−71.5721	−2.59962
$759$	−1.89484	−0.0687784
$760$	80.1240	2.90640
$761$	−25.3978	−0.920668	−0.460334	−	0.887746i	$-0.652270\pi$
$761$	−25.3978	−0.920668	−0.460334	+	0.887746i	$0.652270\pi$
$762$	−16.2003	−0.586874
$763$	−34.3109	−1.24214
$764$	−64.9126	−2.34846
$765$	−10.8495	−0.392264
$766$	46.3433	1.67445
$767$	0	0
$768$	48.9471	1.76623
$769$	−17.5471	−0.632763	−0.316382	−	0.948632i	$-0.602468\pi$
$769$	−17.5471	−0.632763	−0.316382	+	0.948632i	$0.602468\pi$
$770$	−30.5947	−1.10256
$771$	17.7333	0.638649
$772$	60.1832	2.16604
$773$	16.9181	0.608503	0.304251	−	0.952592i	$-0.401594\pi$
$773$	16.9181	0.608503	0.304251	+	0.952592i	$0.401594\pi$
$774$	−32.1190	−1.15449
$775$	−18.9389	−0.680307
$776$	−170.589	−6.12379
$777$	32.8028	1.17680
$778$	−13.8475	−0.496456
$779$	−18.6974	−0.669902
$780$	0	0
$781$	10.0939	0.361189
$782$	−19.8147	−0.708570
$783$	−2.09928	−0.0750221
$784$	129.010	4.60751
$785$	−46.2841	−1.65195
$786$	−3.62044	−0.129137
$787$	27.1659	0.968361	0.484181	−	0.874968i	$-0.339118\pi$
$787$	27.1659	0.968361	0.484181	+	0.874968i	$0.339118\pi$
$788$	51.8907	1.84853
$789$	29.5107	1.05061
$790$	−12.2277	−0.435041
$791$	0.0611413	0.00217394
$792$	9.58828	0.340705
$793$	0	0
$794$	43.1992	1.53308
$795$	6.76245	0.239839
$796$	−84.2731	−2.98698
$797$	12.3253	0.436583	0.218292	−	0.975884i	$-0.429952\pi$
$797$	12.3253	0.436583	0.218292	+	0.975884i	$0.429952\pi$
$798$	−31.6637	−1.12088
$799$	20.2797	0.717446
$800$	69.5194	2.45788
$801$	3.23647	0.114355
$802$	23.0665	0.814507
$803$	−15.1079	−0.533144
$804$	57.6116	2.03180
$805$	21.1671	0.746043
$806$	0	0
$807$	−9.02091	−0.317551
$808$	−116.238	−4.08923
$809$	51.6306	1.81523	0.907617	−	0.419798i	$-0.137899\pi$
$809$	51.6306	1.81523	0.907617	+	0.419798i	$0.137899\pi$
$810$	−7.78236	−0.273444
$811$	22.5443	0.791637	0.395818	−	0.918329i	$-0.370461\pi$
$811$	22.5443	0.791637	0.395818	+	0.918329i	$0.370461\pi$
$812$	−45.3985	−1.59317
$813$	4.58320	0.160740
$814$	22.8525	0.800980
$815$	−32.4027	−1.13502
$816$	58.2591	2.03948
$817$	34.4884	1.20660
$818$	85.9597	3.00551
$819$	0	0
$820$	−99.3806	−3.47052
$821$	−18.1907	−0.634861	−0.317430	−	0.948282i	$-0.602820\pi$
$821$	−18.1907	−0.634861	−0.317430	+	0.948282i	$0.602820\pi$
$822$	13.2044	0.460557
$823$	44.4631	1.54989	0.774944	−	0.632030i	$-0.217778\pi$
$823$	44.4631	1.54989	0.774944	+	0.632030i	$0.217778\pi$
$824$	−32.6944	−1.13896
$825$	3.07435	0.107035
$826$	−57.9934	−2.01785
$827$	−6.33341	−0.220234	−0.110117	−	0.993919i	$-0.535123\pi$
$827$	−6.33341	−0.220234	−0.110117	+	0.993919i	$0.535123\pi$
$828$	−10.4234	−0.362238
$829$	7.54455	0.262033	0.131017	−	0.991380i	$-0.458176\pi$
$829$	7.54455	0.262033	0.131017	+	0.991380i	$0.458176\pi$
$830$	−83.0654	−2.88324
$831$	20.9859	0.727994
$832$	0	0
$833$	32.2829	1.11854
$834$	47.0732	1.63001
$835$	41.8563	1.44850
$836$	−16.1772	−0.559501
$837$	−6.16032	−0.212932
$838$	−18.1561	−0.627194
$839$	30.1703	1.04159	0.520797	−	0.853681i	$-0.325635\pi$
$839$	30.1703	1.04159	0.520797	+	0.853681i	$0.325635\pi$
$840$	−107.110	−3.69564
$841$	−24.5930	−0.848035
$842$	−7.15719	−0.246653
$843$	10.5360	0.362878
$844$	16.0211	0.551468
$845$	0	0
$846$	14.5467	0.500125
$847$	3.93129	0.135081
$848$	−36.3127	−1.24698
$849$	−2.57169	−0.0882601
$850$	32.1489	1.10270
$851$	−15.8106	−0.541981
$852$	55.5260	1.90229
$853$	−14.6801	−0.502637	−0.251319	−	0.967904i	$-0.580864\pi$
$853$	−14.6801	−0.502637	−0.251319	+	0.967904i	$0.580864\pi$
$854$	−25.2869	−0.865301
$855$	8.35645	0.285785
$856$	−117.315	−4.00973
$857$	−21.1257	−0.721641	−0.360821	−	0.932635i	$-0.617503\pi$
$857$	−21.1257	−0.721641	−0.360821	+	0.932635i	$0.617503\pi$
$858$	0	0
$859$	29.4462	1.00469	0.502346	−	0.864667i	$-0.332470\pi$
$859$	29.4462	1.00469	0.502346	+	0.864667i	$0.332470\pi$
$860$	183.314	6.25094
$861$	24.9947	0.851816
$862$	−68.1258	−2.32038
$863$	33.8929	1.15373	0.576865	−	0.816840i	$-0.304276\pi$
$863$	33.8929	1.15373	0.576865	+	0.816840i	$0.304276\pi$
$864$	22.6127	0.769301
$865$	−0.530366	−0.0180330
$866$	17.9543	0.610111
$867$	−2.42153	−0.0822396
$868$	−133.221	−4.52183
$869$	1.57120	0.0532995
$870$	16.3373	0.553888
$871$	0	0
$872$	−83.6830	−2.83386
$873$	−17.7914	−0.602148
$874$	15.2616	0.516230
$875$	21.5113	0.727215
$876$	−83.1072	−2.80793
$877$	−6.62356	−0.223662	−0.111831	−	0.993727i	$-0.535671\pi$
$877$	−6.62356	−0.223662	−0.111831	+	0.993727i	$0.535671\pi$
$878$	−104.671	−3.53247
$879$	5.16162	0.174097
$880$	−43.3572	−1.46157
$881$	18.7993	0.633366	0.316683	−	0.948531i	$-0.397431\pi$
$881$	18.7993	0.633366	0.316683	+	0.948531i	$0.397431\pi$
$882$	23.1566	0.779722
$883$	−35.0323	−1.17893	−0.589465	−	0.807794i	$-0.700661\pi$
$883$	−35.0323	−1.17893	−0.589465	+	0.807794i	$0.700661\pi$
$884$	0	0
$885$	15.3052	0.514479
$886$	−34.8941	−1.17229
$887$	12.8619	0.431860	0.215930	−	0.976409i	$-0.430722\pi$
$887$	12.8619	0.431860	0.215930	+	0.976409i	$0.430722\pi$
$888$	80.0050	2.68479
$889$	−23.2541	−0.779918
$890$	−25.1874	−0.844283
$891$	1.00000	0.0335013
$892$	59.6909	1.99860
$893$	−15.6198	−0.522696
$894$	−14.5636	−0.487079
$895$	−31.1306	−1.04058
$896$	160.446	5.36012
$897$	0	0
$898$	71.0749	2.37180
$899$	12.9322	0.431314
$900$	16.9118	0.563725
$901$	−9.08670	−0.302722
$902$	17.4128	0.579784
$903$	−46.1042	−1.53425
$904$	0.149121	0.00495971
$905$	24.2109	0.804797
$906$	−18.5572	−0.616523
$907$	47.0378	1.56187	0.780933	−	0.624615i	$-0.214744\pi$
$907$	47.0378	1.56187	0.780933	+	0.624615i	$0.214744\pi$
$908$	1.77480	0.0588987
$909$	−12.1229	−0.402091
$910$	0	0
$911$	40.3206	1.33588	0.667940	−	0.744215i	$-0.267176\pi$
$911$	40.3206	1.33588	0.667940	+	0.744215i	$0.267176\pi$
$912$	−44.8720	−1.48586
$913$	10.6736	0.353243
$914$	43.9225	1.45283
$915$	6.67355	0.220621
$916$	−32.6788	−1.07974
$917$	−5.19683	−0.171614
$918$	10.4572	0.345137
$919$	−1.80179	−0.0594356	−0.0297178	−	0.999558i	$-0.509461\pi$
$919$	−1.80179	−0.0594356	−0.0297178	+	0.999558i	$0.509461\pi$
$920$	51.6259	1.70205
$921$	−30.0561	−0.990383
$922$	9.54646	0.314396
$923$	0	0
$924$	21.6258	0.711435
$925$	25.6525	0.843448
$926$	−74.1619	−2.43711
$927$	−3.40983	−0.111994
$928$	−47.4705	−1.55829
$929$	26.3015	0.862924	0.431462	−	0.902131i	$-0.357998\pi$
$929$	26.3015	0.862924	0.431462	+	0.902131i	$0.357998\pi$
$930$	47.9418	1.57207
$931$	−24.8648	−0.814910
$932$	−69.4226	−2.27401
$933$	−21.7462	−0.711939
$934$	−42.9711	−1.40606
$935$	−10.8495	−0.354817
$936$	0	0
$937$	8.45280	0.276141	0.138070	−	0.990422i	$-0.455910\pi$
$937$	8.45280	0.276141	0.138070	+	0.990422i	$0.455910\pi$
$938$	112.763	3.68184
$939$	−24.4361	−0.797443
$940$	−83.0226	−2.70790
$941$	−8.34188	−0.271937	−0.135969	−	0.990713i	$-0.543415\pi$
$941$	−8.34188	−0.271937	−0.135969	+	0.990713i	$0.543415\pi$
$942$	44.6103	1.45348
$943$	−12.0472	−0.392310
$944$	−82.1852	−2.67490
$945$	−11.1709	−0.363390
$946$	−32.1190	−1.04428
$947$	−21.8593	−0.710330	−0.355165	−	0.934804i	$-0.615575\pi$
$947$	−21.8593	−0.710330	−0.355165	+	0.934804i	$0.615575\pi$
$948$	8.64309	0.280714
$949$	0	0
$950$	−24.7616	−0.803372
$951$	21.1040	0.684343
$952$	143.924	4.66459
$953$	57.6509	1.86750	0.933748	−	0.357932i	$-0.116518\pi$
$953$	57.6509	1.86750	0.933748	+	0.357932i	$0.116518\pi$
$954$	−6.51790	−0.211025
$955$	33.5310	1.08504
$956$	114.257	3.69535
$957$	−2.09928	−0.0678600
$958$	90.3964	2.92058
$959$	18.9538	0.612051
$960$	−89.2661	−2.88105
$961$	6.94950	0.224177
$962$	0	0
$963$	−12.2352	−0.394274
$964$	−100.206	−3.22743
$965$	−31.0880	−1.00076
$966$	−20.4017	−0.656413
$967$	41.2637	1.32695	0.663476	−	0.748197i	$-0.269080\pi$
$967$	41.2637	1.32695	0.663476	+	0.748197i	$0.269080\pi$
$968$	9.58828	0.308179
$969$	−11.2286	−0.360713
$970$	138.459	4.44566
$971$	10.2876	0.330146	0.165073	−	0.986281i	$-0.447214\pi$
$971$	10.2876	0.330146	0.165073	+	0.986281i	$0.447214\pi$
$972$	5.50093	0.176442
$973$	67.5697	2.16618
$974$	51.1286	1.63827
$975$	0	0
$976$	−35.8353	−1.14706
$977$	−54.0502	−1.72922	−0.864609	−	0.502445i	$-0.832434\pi$
$977$	−54.0502	−1.72922	−0.864609	+	0.502445i	$0.832434\pi$
$978$	31.2310	0.998657
$979$	3.23647	0.103438
$980$	−132.162	−4.22176
$981$	−8.72763	−0.278652
$982$	−18.5755	−0.592766
$983$	−33.3316	−1.06311	−0.531557	−	0.847022i	$-0.678393\pi$
$983$	−33.3316	−1.06311	−0.531557	+	0.847022i	$0.678393\pi$
$984$	60.9611	1.94337
$985$	−26.8045	−0.854061
$986$	−21.9525	−0.699109
$987$	20.8805	0.664635
$988$	0	0
$989$	22.2217	0.706610
$990$	−7.78236	−0.247340
$991$	15.1783	0.482155	0.241077	−	0.970506i	$-0.422499\pi$
$991$	15.1783	0.482155	0.241077	+	0.970506i	$0.422499\pi$
$992$	−139.302	−4.42283
$993$	0.560518	0.0177875
$994$	108.681	3.44715
$995$	43.5318	1.38005
$996$	58.7144	1.86044
$997$	−23.6131	−0.747834	−0.373917	−	0.927462i	$-0.621986\pi$
$997$	−23.6131	−0.747834	−0.373917	+	0.927462i	$0.621986\pi$
$998$	−0.583086	−0.0184573
$999$	8.34404	0.263994

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5577.2.a.y.1.7		7
13.5	odd	4		429.2.b.b.298.1	✓	14
13.8	odd	4		429.2.b.b.298.14	yes	14
13.12	even	2		5577.2.a.x.1.1		7
39.5	even	4		1287.2.b.c.298.14		14
39.8	even	4		1287.2.b.c.298.1		14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
429.2.b.b.298.1	✓	14	13.5	odd	4
429.2.b.b.298.14	yes	14	13.8	odd	4
1287.2.b.c.298.1		14	39.8	even	4
1287.2.b.c.298.14		14	39.5	even	4
5577.2.a.x.1.1		7	13.12	even	2
5577.2.a.y.1.7		7	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:	\( N \)	\(=\)	\( 5577 = 3 \cdot 11 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	5577.a (trivial)

\(f(q)\)	\(=\)	\(q+2.73878 q^{2} +1.00000 q^{3} +5.50093 q^{4} -2.84154 q^{5} +2.73878 q^{6} +3.93129 q^{7} +9.58828 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+2.73878 q^{2} +1.00000 q^{3} +5.50093 q^{4} -2.84154 q^{5} +2.73878 q^{6} +3.93129 q^{7} +9.58828 q^{8} +1.00000 q^{9} -7.78236 q^{10} +1.00000 q^{11} +5.50093 q^{12} +10.7670 q^{14} -2.84154 q^{15} +15.2584 q^{16} +3.81818 q^{17} +2.73878 q^{18} -2.94082 q^{19} -15.6311 q^{20} +3.93129 q^{21} +2.73878 q^{22} -1.89484 q^{23} +9.58828 q^{24} +3.07435 q^{25} +1.00000 q^{27} +21.6258 q^{28} -2.09928 q^{29} -7.78236 q^{30} -6.16032 q^{31} +22.6127 q^{32} +1.00000 q^{33} +10.4572 q^{34} -11.1709 q^{35} +5.50093 q^{36} +8.34404 q^{37} -8.05426 q^{38} -27.2455 q^{40} +6.35787 q^{41} +10.7670 q^{42} -11.7275 q^{43} +5.50093 q^{44} -2.84154 q^{45} -5.18956 q^{46} +5.31137 q^{47} +15.2584 q^{48} +8.45506 q^{49} +8.41997 q^{50} +3.81818 q^{51} -2.37985 q^{53} +2.73878 q^{54} -2.84154 q^{55} +37.6943 q^{56} -2.94082 q^{57} -5.74947 q^{58} -5.38624 q^{59} -15.6311 q^{60} -2.34857 q^{61} -16.8718 q^{62} +3.93129 q^{63} +31.4147 q^{64} +2.73878 q^{66} +10.4731 q^{67} +21.0035 q^{68} -1.89484 q^{69} -30.5947 q^{70} +10.0939 q^{71} +9.58828 q^{72} -15.1079 q^{73} +22.8525 q^{74} +3.07435 q^{75} -16.1772 q^{76} +3.93129 q^{77} +1.57120 q^{79} -43.3572 q^{80} +1.00000 q^{81} +17.4128 q^{82} +10.6736 q^{83} +21.6258 q^{84} -10.8495 q^{85} -32.1190 q^{86} -2.09928 q^{87} +9.58828 q^{88} +3.23647 q^{89} -7.78236 q^{90} -10.4234 q^{92} -6.16032 q^{93} +14.5467 q^{94} +8.35645 q^{95} +22.6127 q^{96} -17.7914 q^{97} +23.1566 q^{98} +1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 7 q + 3 q^{2} + 7 q^{3} + 9 q^{4} + 6 q^{5} + 3 q^{6} + 6 q^{7} + 15 q^{8} + 7 q^{9}+O(q^{10}) \) 7 * q + 3 * q^2 + 7 * q^3 + 9 * q^4 + 6 * q^5 + 3 * q^6 + 6 * q^7 + 15 * q^8 + 7 * q^9	\( 7 q + 3 q^{2} + 7 q^{3} + 9 q^{4} + 6 q^{5} + 3 q^{6} + 6 q^{7} + 15 q^{8} + 7 q^{9} + 7 q^{11} + 9 q^{12} + 8 q^{14} + 6 q^{15} + 17 q^{16} - 2 q^{17} + 3 q^{18} + 8 q^{19} - 2 q^{20} + 6 q^{21} + 3 q^{22} + 4 q^{23} + 15 q^{24} + 13 q^{25} + 7 q^{27} + 12 q^{28} - 12 q^{29} - 10 q^{31} + 33 q^{32} + 7 q^{33} + 28 q^{34} - 4 q^{35} + 9 q^{36} + 6 q^{37} + 16 q^{38} - 10 q^{40} + 2 q^{41} + 8 q^{42} - 16 q^{43} + 9 q^{44} + 6 q^{45} - 26 q^{46} + 18 q^{47} + 17 q^{48} + 23 q^{49} + 39 q^{50} - 2 q^{51} + 10 q^{53} + 3 q^{54} + 6 q^{55} + 16 q^{56} + 8 q^{57} + 10 q^{58} + 2 q^{59} - 2 q^{60} - 10 q^{61} - 36 q^{62} + 6 q^{63} + 29 q^{64} + 3 q^{66} + 8 q^{67} - 10 q^{68} + 4 q^{69} - 20 q^{70} + 36 q^{71} + 15 q^{72} + 20 q^{73} + 13 q^{75} + 10 q^{76} + 6 q^{77} + 6 q^{79} - 20 q^{80} + 7 q^{81} - 10 q^{82} + 30 q^{83} + 12 q^{84} - 40 q^{85} + 6 q^{86} - 12 q^{87} + 15 q^{88} + 34 q^{89} - 12 q^{92} - 10 q^{93} + 32 q^{94} + 18 q^{95} + 33 q^{96} + 16 q^{97} + q^{98} + 7 q^{99}+O(q^{100}) \) 7 * q + 3 * q^2 + 7 * q^3 + 9 * q^4 + 6 * q^5 + 3 * q^6 + 6 * q^7 + 15 * q^8 + 7 * q^9 + 7 * q^11 + 9 * q^12 + 8 * q^14 + 6 * q^15 + 17 * q^16 - 2 * q^17 + 3 * q^18 + 8 * q^19 - 2 * q^20 + 6 * q^21 + 3 * q^22 + 4 * q^23 + 15 * q^24 + 13 * q^25 + 7 * q^27 + 12 * q^28 - 12 * q^29 - 10 * q^31 + 33 * q^32 + 7 * q^33 + 28 * q^34 - 4 * q^35 + 9 * q^36 + 6 * q^37 + 16 * q^38 - 10 * q^40 + 2 * q^41 + 8 * q^42 - 16 * q^43 + 9 * q^44 + 6 * q^45 - 26 * q^46 + 18 * q^47 + 17 * q^48 + 23 * q^49 + 39 * q^50 - 2 * q^51 + 10 * q^53 + 3 * q^54 + 6 * q^55 + 16 * q^56 + 8 * q^57 + 10 * q^58 + 2 * q^59 - 2 * q^60 - 10 * q^61 - 36 * q^62 + 6 * q^63 + 29 * q^64 + 3 * q^66 + 8 * q^67 - 10 * q^68 + 4 * q^69 - 20 * q^70 + 36 * q^71 + 15 * q^72 + 20 * q^73 + 13 * q^75 + 10 * q^76 + 6 * q^77 + 6 * q^79 - 20 * q^80 + 7 * q^81 - 10 * q^82 + 30 * q^83 + 12 * q^84 - 40 * q^85 + 6 * q^86 - 12 * q^87 + 15 * q^88 + 34 * q^89 - 12 * q^92 - 10 * q^93 + 32 * q^94 + 18 * q^95 + 33 * q^96 + 16 * q^97 + q^98 + 7 * q^99

Introduction

L-functions

Modular forms

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