LMFDB - Embedded newform 6045.2.a.bh.1.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6045,2,Mod(1,6045)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6045, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("6045.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6045 = 3 \cdot 5 \cdot 13 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6045.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:	$48.2695680219$
Analytic rank:	$0$
Dimension:	$17$
Coefficient field:	$\mathbb{Q}[x]/(x^{17} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{17} - 2 x^{16} - 25 x^{15} + 47 x^{14} + 252 x^{13} - 437 x^{12} - 1319 x^{11} + 2056 x^{10} + \cdots + 8 $ x^17 - 2x^16 - 25x^15 + 47x^14 + 252x^13 - 437x^12 - 1319x^11 + 2056x^10 + 3854x^9 - 5201x^8 - 6304x^7 + 6915x^6 + 5469x^5 - 4238x^4 - 2198x^3 + 760x^2 + 306x + 8
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{3} $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.9
Root			$-0.0282840$ of defining polynomial
Character	$\chi$	$=$	6045.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.0282840 q^{2} -1.00000 q^{3} -1.99920 q^{4} +1.00000 q^{5} +0.0282840 q^{6} +2.73754 q^{7} +0.113114 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-0.0282840 q^{2} -1.00000 q^{3} -1.99920 q^{4} +1.00000 q^{5} +0.0282840 q^{6} +2.73754 q^{7} +0.113114 q^{8} +1.00000 q^{9} -0.0282840 q^{10} -0.114878 q^{11} +1.99920 q^{12} +1.00000 q^{13} -0.0774286 q^{14} -1.00000 q^{15} +3.99520 q^{16} +7.00193 q^{17} -0.0282840 q^{18} +0.514736 q^{19} -1.99920 q^{20} -2.73754 q^{21} +0.00324921 q^{22} +7.08082 q^{23} -0.113114 q^{24} +1.00000 q^{25} -0.0282840 q^{26} -1.00000 q^{27} -5.47289 q^{28} +9.04064 q^{29} +0.0282840 q^{30} +1.00000 q^{31} -0.339227 q^{32} +0.114878 q^{33} -0.198043 q^{34} +2.73754 q^{35} -1.99920 q^{36} -4.82413 q^{37} -0.0145588 q^{38} -1.00000 q^{39} +0.113114 q^{40} -4.62893 q^{41} +0.0774286 q^{42} +2.96996 q^{43} +0.229664 q^{44} +1.00000 q^{45} -0.200274 q^{46} -2.53573 q^{47} -3.99520 q^{48} +0.494116 q^{49} -0.0282840 q^{50} -7.00193 q^{51} -1.99920 q^{52} +0.670465 q^{53} +0.0282840 q^{54} -0.114878 q^{55} +0.309653 q^{56} -0.514736 q^{57} -0.255706 q^{58} +11.1319 q^{59} +1.99920 q^{60} +9.34826 q^{61} -0.0282840 q^{62} +2.73754 q^{63} -7.98081 q^{64} +1.00000 q^{65} -0.00324921 q^{66} -9.55962 q^{67} -13.9983 q^{68} -7.08082 q^{69} -0.0774286 q^{70} +3.60128 q^{71} +0.113114 q^{72} +1.23709 q^{73} +0.136446 q^{74} -1.00000 q^{75} -1.02906 q^{76} -0.314483 q^{77} +0.0282840 q^{78} +0.0401830 q^{79} +3.99520 q^{80} +1.00000 q^{81} +0.130925 q^{82} -7.71386 q^{83} +5.47289 q^{84} +7.00193 q^{85} -0.0840025 q^{86} -9.04064 q^{87} -0.0129942 q^{88} -7.55793 q^{89} -0.0282840 q^{90} +2.73754 q^{91} -14.1560 q^{92} -1.00000 q^{93} +0.0717208 q^{94} +0.514736 q^{95} +0.339227 q^{96} +10.8782 q^{97} -0.0139756 q^{98} -0.114878 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 17 q + 2 q^{2} - 17 q^{3} + 20 q^{4} + 17 q^{5} - 2 q^{6} + 18 q^{7} + 9 q^{8} + 17 q^{9}+O(q^{10}) $ 17 * q + 2 * q^2 - 17 * q^3 + 20 * q^4 + 17 * q^5 - 2 * q^6 + 18 * q^7 + 9 * q^8 + 17 * q^9	\( 17 q + 2 q^{2} - 17 q^{3} + 20 q^{4} + 17 q^{5} - 2 q^{6} + 18 q^{7} + 9 q^{8} + 17 q^{9} + 2 q^{10} + 3 q^{11} - 20 q^{12} + 17 q^{13} + q^{14} - 17 q^{15} + 26 q^{16} + 2 q^{18} + 10 q^{19} + 20 q^{20} - 18 q^{21} + 5 q^{22} + 16 q^{23} - 9 q^{24} + 17 q^{25} + 2 q^{26} - 17 q^{27} + 36 q^{28} - 3 q^{29} - 2 q^{30} + 17 q^{31} + 20 q^{32} - 3 q^{33} + q^{34} + 18 q^{35} + 20 q^{36} + 14 q^{37} + 22 q^{38} - 17 q^{39} + 9 q^{40} - 6 q^{41} - q^{42} + 24 q^{43} - 15 q^{44} + 17 q^{45} + 6 q^{46} + 25 q^{47} - 26 q^{48} + 31 q^{49} + 2 q^{50} + 20 q^{52} - 15 q^{53} - 2 q^{54} + 3 q^{55} + 31 q^{56} - 10 q^{57} + 44 q^{58} + 16 q^{59} - 20 q^{60} - 5 q^{61} + 2 q^{62} + 18 q^{63} + 35 q^{64} + 17 q^{65} - 5 q^{66} + 50 q^{67} + 13 q^{68} - 16 q^{69} + q^{70} + 16 q^{71} + 9 q^{72} + 33 q^{73} + 2 q^{74} - 17 q^{75} + 9 q^{77} - 2 q^{78} - 10 q^{79} + 26 q^{80} + 17 q^{81} + 61 q^{82} + 27 q^{83} - 36 q^{84} - 12 q^{86} + 3 q^{87} + 23 q^{88} - 24 q^{89} + 2 q^{90} + 18 q^{91} - 21 q^{92} - 17 q^{93} + 6 q^{94} + 10 q^{95} - 20 q^{96} + 48 q^{97} + 14 q^{98} + 3 q^{99}+O(q^{100}) \) 17 * q + 2 * q^2 - 17 * q^3 + 20 * q^4 + 17 * q^5 - 2 * q^6 + 18 * q^7 + 9 * q^8 + 17 * q^9 + 2 * q^10 + 3 * q^11 - 20 * q^12 + 17 * q^13 + q^14 - 17 * q^15 + 26 * q^16 + 2 * q^18 + 10 * q^19 + 20 * q^20 - 18 * q^21 + 5 * q^22 + 16 * q^23 - 9 * q^24 + 17 * q^25 + 2 * q^26 - 17 * q^27 + 36 * q^28 - 3 * q^29 - 2 * q^30 + 17 * q^31 + 20 * q^32 - 3 * q^33 + q^34 + 18 * q^35 + 20 * q^36 + 14 * q^37 + 22 * q^38 - 17 * q^39 + 9 * q^40 - 6 * q^41 - q^42 + 24 * q^43 - 15 * q^44 + 17 * q^45 + 6 * q^46 + 25 * q^47 - 26 * q^48 + 31 * q^49 + 2 * q^50 + 20 * q^52 - 15 * q^53 - 2 * q^54 + 3 * q^55 + 31 * q^56 - 10 * q^57 + 44 * q^58 + 16 * q^59 - 20 * q^60 - 5 * q^61 + 2 * q^62 + 18 * q^63 + 35 * q^64 + 17 * q^65 - 5 * q^66 + 50 * q^67 + 13 * q^68 - 16 * q^69 + q^70 + 16 * q^71 + 9 * q^72 + 33 * q^73 + 2 * q^74 - 17 * q^75 + 9 * q^77 - 2 * q^78 - 10 * q^79 + 26 * q^80 + 17 * q^81 + 61 * q^82 + 27 * q^83 - 36 * q^84 - 12 * q^86 + 3 * q^87 + 23 * q^88 - 24 * q^89 + 2 * q^90 + 18 * q^91 - 21 * q^92 - 17 * q^93 + 6 * q^94 + 10 * q^95 - 20 * q^96 + 48 * q^97 + 14 * q^98 + 3 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−0.0282840	−0.0199998	−0.00999992	−	0.999950i	$-0.503183\pi$
$2$	−0.0282840	−0.0199998	−0.00999992	+	0.999950i	$0.503183\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	−1.99920	−0.999600
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	0.0282840	0.0115469
$7$	2.73754	1.03469	0.517346	−	0.855776i	$-0.326920\pi$
$7$	2.73754	1.03469	0.517346	+	0.855776i	$0.326920\pi$
$8$	0.113114	0.0399917
$9$	1.00000	0.333333
$10$	−0.0282840	−0.00894420
$11$	−0.114878	−0.0346370	−0.0173185	−	0.999850i	$-0.505513\pi$
$11$	−0.114878	−0.0346370	−0.0173185	+	0.999850i	$0.505513\pi$
$12$	1.99920	0.577119
$13$	1.00000	0.277350
$13$	1.00000	0.277350
$14$	−0.0774286	−0.0206937
$15$	−1.00000	−0.258199
$16$	3.99520	0.998800
$17$	7.00193	1.69822	0.849109	−	0.528218i	$-0.177140\pi$
$17$	7.00193	1.69822	0.849109	+	0.528218i	$0.177140\pi$
$18$	−0.0282840	−0.00666661
$19$	0.514736	0.118089	0.0590443	−	0.998255i	$-0.481195\pi$
$19$	0.514736	0.118089	0.0590443	+	0.998255i	$0.481195\pi$
$20$	−1.99920	−0.447035
$21$	−2.73754	−0.597380
$22$	0.00324921	0.000692734 0
$23$	7.08082	1.47645	0.738227	−	0.674553i	$-0.235663\pi$
$23$	7.08082	1.47645	0.738227	+	0.674553i	$0.235663\pi$
$24$	−0.113114	−0.0230892
$25$	1.00000	0.200000
$26$	−0.0282840	−0.00554696
$27$	−1.00000	−0.192450
$28$	−5.47289	−1.03428
$29$	9.04064	1.67880	0.839402	−	0.543511i	$-0.182905\pi$
$29$	9.04064	1.67880	0.839402	+	0.543511i	$0.182905\pi$
$30$	0.0282840	0.00516394
$31$	1.00000	0.179605
$31$	1.00000	0.179605
$32$	−0.339227	−0.0599675
$33$	0.114878	0.0199977
$34$	−0.198043	−0.0339641
$35$	2.73754	0.462728
$36$	−1.99920	−0.333200
$37$	−4.82413	−0.793083	−0.396541	−	0.918017i	$-0.629790\pi$
$37$	−4.82413	−0.793083	−0.396541	+	0.918017i	$0.629790\pi$
$38$	−0.0145588	−0.00236175
$39$	−1.00000	−0.160128
$40$	0.113114	0.0178848
$41$	−4.62893	−0.722918	−0.361459	−	0.932388i	$-0.617721\pi$
$41$	−4.62893	−0.722918	−0.361459	+	0.932388i	$0.617721\pi$
$42$	0.0774286	0.0119475
$43$	2.96996	0.452915	0.226457	−	0.974021i	$-0.427286\pi$
$43$	2.96996	0.452915	0.226457	+	0.974021i	$0.427286\pi$
$44$	0.229664	0.0346231
$45$	1.00000	0.149071
$46$	−0.200274	−0.0295288
$47$	−2.53573	−0.369875	−0.184937	−	0.982750i	$-0.559208\pi$
$47$	−2.53573	−0.369875	−0.184937	+	0.982750i	$0.559208\pi$
$48$	−3.99520	−0.576658
$49$	0.494116	0.0705880
$50$	−0.0282840	−0.00399997
$51$	−7.00193	−0.980467
$52$	−1.99920	−0.277239
$53$	0.670465	0.0920955	0.0460477	−	0.998939i	$-0.485337\pi$
$53$	0.670465	0.0920955	0.0460477	+	0.998939i	$0.485337\pi$
$54$	0.0282840	0.00384897
$55$	−0.114878	−0.0154901
$56$	0.309653	0.0413791
$57$	−0.514736	−0.0681784
$58$	−0.255706	−0.0335758
$59$	11.1319	1.44926	0.724628	−	0.689140i	$-0.242012\pi$
$59$	11.1319	1.44926	0.724628	+	0.689140i	$0.242012\pi$
$60$	1.99920	0.258096
$61$	9.34826	1.19692	0.598461	−	0.801152i	$-0.295779\pi$
$61$	9.34826	1.19692	0.598461	+	0.801152i	$0.295779\pi$
$62$	−0.0282840	−0.00359208
$63$	2.73754	0.344897
$64$	−7.98081	−0.997601
$65$	1.00000	0.124035
$66$	−0.00324921	−0.000399950 0
$67$	−9.55962	−1.16789	−0.583947	−	0.811792i	$-0.698492\pi$
$67$	−9.55962	−1.16789	−0.583947	+	0.811792i	$0.698492\pi$
$68$	−13.9983	−1.69754
$69$	−7.08082	−0.852431
$70$	−0.0774286	−0.00925449
$71$	3.60128	0.427394	0.213697	−	0.976900i	$-0.431450\pi$
$71$	3.60128	0.427394	0.213697	+	0.976900i	$0.431450\pi$
$72$	0.113114	0.0133306
$73$	1.23709	0.144790	0.0723950	−	0.997376i	$-0.476936\pi$
$73$	1.23709	0.144790	0.0723950	+	0.997376i	$0.476936\pi$
$74$	0.136446	0.0158615
$75$	−1.00000	−0.115470
$76$	−1.02906	−0.118041
$77$	−0.314483	−0.0358386
$78$	0.0282840	0.00320254
$79$	0.0401830	0.00452094	0.00226047	−	0.999997i	$-0.499280\pi$
$79$	0.0401830	0.00452094	0.00226047	+	0.999997i	$0.499280\pi$
$80$	3.99520	0.446677
$81$	1.00000	0.111111
$82$	0.130925	0.0144582
$83$	−7.71386	−0.846706	−0.423353	−	0.905965i	$-0.639147\pi$
$83$	−7.71386	−0.846706	−0.423353	+	0.905965i	$0.639147\pi$
$84$	5.47289	0.597141
$85$	7.00193	0.759466
$86$	−0.0840025	−0.00905823
$87$	−9.04064	−0.969258
$88$	−0.0129942	−0.00138519
$89$	−7.55793	−0.801139	−0.400569	−	0.916266i	$-0.631188\pi$
$89$	−7.55793	−0.801139	−0.400569	+	0.916266i	$0.631188\pi$
$90$	−0.0282840	−0.00298140
$91$	2.73754	0.286972
$92$	−14.1560	−1.47586
$93$	−1.00000	−0.103695
$94$	0.0717208	0.00739744
$95$	0.514736	0.0528108
$96$	0.339227	0.0346223
$97$	10.8782	1.10452	0.552258	−	0.833674i	$-0.313766\pi$
$97$	10.8782	1.10452	0.552258	+	0.833674i	$0.313766\pi$
$98$	−0.0139756	−0.00141175
$99$	−0.114878	−0.0115457
$100$	−1.99920	−0.199920
$101$	−13.8427	−1.37740	−0.688701	−	0.725046i	$-0.741819\pi$
$101$	−13.8427	−1.37740	−0.688701	+	0.725046i	$0.741819\pi$
$102$	0.198043	0.0196092
$103$	−6.83017	−0.672996	−0.336498	−	0.941684i	$-0.609243\pi$
$103$	−6.83017	−0.672996	−0.336498	+	0.941684i	$0.609243\pi$
$104$	0.113114	0.0110917
$105$	−2.73754	−0.267156
$106$	−0.0189635	−0.00184189
$107$	16.9230	1.63601	0.818004	−	0.575212i	$-0.195081\pi$
$107$	16.9230	1.63601	0.818004	+	0.575212i	$0.195081\pi$
$108$	1.99920	0.192373
$109$	13.2701	1.27105	0.635524	−	0.772081i	$-0.280784\pi$
$109$	13.2701	1.27105	0.635524	+	0.772081i	$0.280784\pi$
$110$	0.00324921	0.000309800 0
$111$	4.82413	0.457887
$112$	10.9370	1.03345
$113$	−16.2944	−1.53285	−0.766424	−	0.642335i	$-0.777966\pi$
$113$	−16.2944	−1.53285	−0.766424	+	0.642335i	$0.777966\pi$
$114$	0.0145588	0.00136356
$115$	7.08082	0.660290
$116$	−18.0740	−1.67813
$117$	1.00000	0.0924500
$118$	−0.314856	−0.0289849
$119$	19.1681	1.75713
$120$	−0.113114	−0.0103258
$121$	−10.9868	−0.998800
$122$	−0.264406	−0.0239382
$123$	4.62893	0.417377
$124$	−1.99920	−0.179533
$125$	1.00000	0.0894427
$126$	−0.0774286	−0.00689789
$127$	−6.35298	−0.563736	−0.281868	−	0.959453i	$-0.590954\pi$
$127$	−6.35298	−0.563736	−0.281868	+	0.959453i	$0.590954\pi$
$128$	0.904184	0.0799194
$129$	−2.96996	−0.261491
$130$	−0.0282840	−0.00248067
$131$	1.43810	0.125648	0.0628239	−	0.998025i	$-0.479989\pi$
$131$	1.43810	0.125648	0.0628239	+	0.998025i	$0.479989\pi$
$132$	−0.229664	−0.0199897
$133$	1.40911	0.122185
$134$	0.270385	0.0233577
$135$	−1.00000	−0.0860663
$136$	0.792013	0.0679146
$137$	−21.0515	−1.79855	−0.899276	−	0.437382i	$-0.855906\pi$
$137$	−21.0515	−1.79855	−0.899276	+	0.437382i	$0.855906\pi$
$138$	0.200274	0.0170485
$139$	−0.507943	−0.0430832	−0.0215416	−	0.999768i	$-0.506857\pi$
$139$	−0.507943	−0.0430832	−0.0215416	+	0.999768i	$0.506857\pi$
$140$	−5.47289	−0.462543
$141$	2.53573	0.213547
$142$	−0.101859	−0.00854780
$143$	−0.114878	−0.00960658
$144$	3.99520	0.332933
$145$	9.04064	0.750784
$146$	−0.0349898	−0.00289578
$147$	−0.494116	−0.0407540
$148$	9.64441	0.792766
$149$	21.8966	1.79384	0.896922	−	0.442190i	$-0.145798\pi$
$149$	21.8966	1.79384	0.896922	+	0.442190i	$0.145798\pi$
$150$	0.0282840	0.00230938
$151$	−14.5125	−1.18101	−0.590507	−	0.807032i	$-0.701072\pi$
$151$	−14.5125	−1.18101	−0.590507	+	0.807032i	$0.701072\pi$
$152$	0.0582236	0.00472256
$153$	7.00193	0.566073
$154$	0.00889484	0.000716767 0
$155$	1.00000	0.0803219
$156$	1.99920	0.160064
$157$	−9.55365	−0.762464	−0.381232	−	0.924479i	$-0.624500\pi$
$157$	−9.55365	−0.762464	−0.381232	+	0.924479i	$0.624500\pi$
$158$	−0.00113654	−9.04180e−5 0
$159$	−0.670465	−0.0531713
$160$	−0.339227	−0.0268183
$161$	19.3840	1.52767
$162$	−0.0282840	−0.00222220
$163$	14.0194	1.09808	0.549042	−	0.835794i	$-0.314993\pi$
$163$	14.0194	1.09808	0.549042	+	0.835794i	$0.314993\pi$
$164$	9.25417	0.722629
$165$	0.114878	0.00894324
$166$	0.218179	0.0169340
$167$	21.9051	1.69506	0.847532	−	0.530744i	$-0.178088\pi$
$167$	21.9051	1.69506	0.847532	+	0.530744i	$0.178088\pi$
$168$	−0.309653	−0.0238902
$169$	1.00000	0.0769231
$170$	−0.198043	−0.0151892
$171$	0.514736	0.0393628
$172$	−5.93755	−0.452734
$173$	−25.1861	−1.91486	−0.957430	−	0.288665i	$-0.906789\pi$
$173$	−25.1861	−1.91486	−0.957430	+	0.288665i	$0.906789\pi$
$174$	0.255706	0.0193850
$175$	2.73754	0.206938
$176$	−0.458960	−0.0345954
$177$	−11.1319	−0.836728
$178$	0.213769	0.0160226
$179$	11.2933	0.844099	0.422049	−	0.906573i	$-0.361311\pi$
$179$	11.2933	0.844099	0.422049	+	0.906573i	$0.361311\pi$
$180$	−1.99920	−0.149012
$181$	1.74274	0.129537	0.0647684	−	0.997900i	$-0.479369\pi$
$181$	1.74274	0.129537	0.0647684	+	0.997900i	$0.479369\pi$
$182$	−0.0774286	−0.00573939
$183$	−9.34826	−0.691043
$184$	0.800937	0.0590458
$185$	−4.82413	−0.354677
$186$	0.0282840	0.00207389
$187$	−0.804368	−0.0588212
$188$	5.06944	0.369727
$189$	−2.73754	−0.199127
$190$	−0.0145588	−0.00105621
$191$	−23.9810	−1.73520	−0.867602	−	0.497259i	$-0.834340\pi$
$191$	−23.9810	−1.73520	−0.867602	+	0.497259i	$0.834340\pi$
$192$	7.98081	0.575965
$193$	7.12566	0.512916	0.256458	−	0.966555i	$-0.417444\pi$
$193$	7.12566	0.512916	0.256458	+	0.966555i	$0.417444\pi$
$194$	−0.307680	−0.0220901
$195$	−1.00000	−0.0716115
$196$	−0.987837	−0.0705598
$197$	−19.2196	−1.36934	−0.684671	−	0.728853i	$-0.740054\pi$
$197$	−19.2196	−1.36934	−0.684671	+	0.728853i	$0.740054\pi$
$198$	0.00324921	0.000230911 0
$199$	24.3608	1.72689	0.863444	−	0.504444i	$-0.168303\pi$
$199$	24.3608	1.72689	0.863444	+	0.504444i	$0.168303\pi$
$200$	0.113114	0.00799833
$201$	9.55962	0.674283
$202$	0.391528	0.0275478
$203$	24.7491	1.73705
$204$	13.9983	0.980074
$205$	−4.62893	−0.323299
$206$	0.193185	0.0134598
$207$	7.08082	0.492151
$208$	3.99520	0.277017
$209$	−0.0591318	−0.00409023
$210$	0.0774286	0.00534308
$211$	−24.1529	−1.66275	−0.831377	−	0.555709i	$-0.812447\pi$
$211$	−24.1529	−1.66275	−0.831377	+	0.555709i	$0.812447\pi$
$212$	−1.34039	−0.0920586
$213$	−3.60128	−0.246756
$214$	−0.478651	−0.0327199
$215$	2.96996	0.202550
$216$	−0.113114	−0.00769640
$217$	2.73754	0.185836
$218$	−0.375333	−0.0254208
$219$	−1.23709	−0.0835946
$220$	0.229664	0.0154839
$221$	7.00193	0.471001
$222$	−0.136446	−0.00915766
$223$	16.3351	1.09388	0.546940	−	0.837172i	$-0.315792\pi$
$223$	16.3351	1.09388	0.546940	+	0.837172i	$0.315792\pi$
$224$	−0.928648	−0.0620479
$225$	1.00000	0.0666667
$226$	0.460871	0.0306567
$227$	−20.1439	−1.33700	−0.668500	−	0.743712i	$-0.733063\pi$
$227$	−20.1439	−1.33700	−0.668500	+	0.743712i	$0.733063\pi$
$228$	1.02906	0.0681512
$229$	0.834261	0.0551295	0.0275648	−	0.999620i	$-0.491225\pi$
$229$	0.834261	0.0551295	0.0275648	+	0.999620i	$0.491225\pi$
$230$	−0.200274	−0.0132057
$231$	0.314483	0.0206914
$232$	1.02262	0.0671382
$233$	28.3149	1.85497	0.927486	−	0.373857i	$-0.121965\pi$
$233$	28.3149	1.85497	0.927486	+	0.373857i	$0.121965\pi$
$234$	−0.0282840	−0.00184899
$235$	−2.53573	−0.165413
$236$	−22.2550	−1.44868
$237$	−0.0401830	−0.00261016
$238$	−0.542150	−0.0351424
$239$	12.6965	0.821270	0.410635	−	0.911800i	$-0.365307\pi$
$239$	12.6965	0.821270	0.410635	+	0.911800i	$0.365307\pi$
$240$	−3.99520	−0.257889
$241$	−21.7114	−1.39856	−0.699278	−	0.714850i	$-0.746495\pi$
$241$	−21.7114	−1.39856	−0.699278	+	0.714850i	$0.746495\pi$
$242$	0.310751	0.0199758
$243$	−1.00000	−0.0641500
$244$	−18.6890	−1.19644
$245$	0.494116	0.0315679
$246$	−0.130925	−0.00834747
$247$	0.514736	0.0327519
$248$	0.113114	0.00718272
$249$	7.71386	0.488846
$250$	−0.0282840	−0.00178884
$251$	−0.768146	−0.0484850	−0.0242425	−	0.999706i	$-0.507717\pi$
$251$	−0.768146	−0.0484850	−0.0242425	+	0.999706i	$0.507717\pi$
$252$	−5.47289	−0.344759
$253$	−0.813430	−0.0511399
$254$	0.179688	0.0112746
$255$	−7.00193	−0.438478
$256$	15.9360	0.996002
$257$	8.12150	0.506605	0.253303	−	0.967387i	$-0.418483\pi$
$257$	8.12150	0.506605	0.253303	+	0.967387i	$0.418483\pi$
$258$	0.0840025	0.00522977
$259$	−13.2063	−0.820597
$260$	−1.99920	−0.123985
$261$	9.04064	0.559601
$262$	−0.0406754	−0.00251293
$263$	−2.31156	−0.142537	−0.0712685	−	0.997457i	$-0.522705\pi$
$263$	−2.31156	−0.142537	−0.0712685	+	0.997457i	$0.522705\pi$
$264$	0.0129942	0.000799741 0
$265$	0.670465	0.0411863
$266$	−0.0398553	−0.00244369
$267$	7.55793	0.462538
$268$	19.1116	1.16743
$269$	−20.7251	−1.26363	−0.631816	−	0.775118i	$-0.717690\pi$
$269$	−20.7251	−1.26363	−0.631816	+	0.775118i	$0.717690\pi$
$270$	0.0282840	0.00172131
$271$	23.7695	1.44390	0.721948	−	0.691947i	$-0.243247\pi$
$271$	23.7695	1.44390	0.721948	+	0.691947i	$0.243247\pi$
$272$	27.9741	1.69618
$273$	−2.73754	−0.165683
$274$	0.595422	0.0359707
$275$	−0.114878	−0.00692740
$276$	14.1560	0.852090
$277$	0.446528	0.0268293	0.0134146	−	0.999910i	$-0.495730\pi$
$277$	0.446528	0.0268293	0.0134146	+	0.999910i	$0.495730\pi$
$278$	0.0143667	0.000861656 0
$279$	1.00000	0.0598684
$280$	0.309653	0.0185053
$281$	14.5904	0.870392	0.435196	−	0.900336i	$-0.356679\pi$
$281$	14.5904	0.870392	0.435196	+	0.900336i	$0.356679\pi$
$282$	−0.0717208	−0.00427091
$283$	15.5371	0.923585	0.461793	−	0.886988i	$-0.347206\pi$
$283$	15.5371	0.923585	0.461793	+	0.886988i	$0.347206\pi$
$284$	−7.19969	−0.427223
$285$	−0.514736	−0.0304903
$286$	0.00324921	0.000192130 0
$287$	−12.6719	−0.747998
$288$	−0.339227	−0.0199892
$289$	32.0271	1.88394
$290$	−0.255706	−0.0150156
$291$	−10.8782	−0.637692
$292$	−2.47318	−0.144732
$293$	2.41848	0.141289	0.0706446	−	0.997502i	$-0.477494\pi$
$293$	2.41848	0.141289	0.0706446	+	0.997502i	$0.477494\pi$
$294$	0.0139756	0.000815074 0
$295$	11.1319	0.648127
$296$	−0.545675	−0.0317167
$297$	0.114878	0.00666589
$298$	−0.619326	−0.0358766
$299$	7.08082	0.409494
$300$	1.99920	0.115424
$301$	8.13039	0.468628
$302$	0.410473	0.0236201
$303$	13.8427	0.795243
$304$	2.05647	0.117947
$305$	9.34826	0.535280
$306$	−0.198043	−0.0113214
$307$	−3.47650	−0.198415	−0.0992073	−	0.995067i	$-0.531631\pi$
$307$	−3.47650	−0.198415	−0.0992073	+	0.995067i	$0.531631\pi$
$308$	0.628714	0.0358243
$309$	6.83017	0.388555
$310$	−0.0282840	−0.00160643
$311$	−4.48570	−0.254361	−0.127180	−	0.991880i	$-0.540593\pi$
$311$	−4.48570	−0.254361	−0.127180	+	0.991880i	$0.540593\pi$
$312$	−0.113114	−0.00640379
$313$	17.0080	0.961348	0.480674	−	0.876899i	$-0.340392\pi$
$313$	17.0080	0.961348	0.480674	+	0.876899i	$0.340392\pi$
$314$	0.270216	0.0152492
$315$	2.73754	0.154243
$316$	−0.0803338	−0.00451913
$317$	23.2078	1.30348	0.651741	−	0.758441i	$-0.274039\pi$
$317$	23.2078	1.30348	0.651741	+	0.758441i	$0.274039\pi$
$318$	0.0189635	0.00106342
$319$	−1.03857	−0.0581487
$320$	−7.98081	−0.446141
$321$	−16.9230	−0.944550
$322$	−0.548258	−0.0305532
$323$	3.60415	0.200540
$324$	−1.99920	−0.111067
$325$	1.00000	0.0554700
$326$	−0.396526	−0.0219615
$327$	−13.2701	−0.733840
$328$	−0.523595	−0.0289107
$329$	−6.94167	−0.382707
$330$	−0.00324921	−0.000178863 0
$331$	−3.43467	−0.188787	−0.0943933	−	0.995535i	$-0.530091\pi$
$331$	−3.43467	−0.188787	−0.0943933	+	0.995535i	$0.530091\pi$
$332$	15.4215	0.846367
$333$	−4.82413	−0.264361
$334$	−0.619563	−0.0339010
$335$	−9.55962	−0.522298
$336$	−10.9370	−0.596663
$337$	−21.7395	−1.18422	−0.592112	−	0.805856i	$-0.701706\pi$
$337$	−21.7395	−1.18422	−0.592112	+	0.805856i	$0.701706\pi$
$338$	−0.0282840	−0.00153845
$339$	16.2944	0.884990
$340$	−13.9983	−0.759162
$341$	−0.114878	−0.00622099
$342$	−0.0145588	−0.000787250 0
$343$	−17.8101	−0.961655
$344$	0.335943	0.0181128
$345$	−7.08082	−0.381219
$346$	0.712363	0.0382969
$347$	20.5958	1.10564	0.552820	−	0.833301i	$-0.313552\pi$
$347$	20.5958	1.10564	0.552820	+	0.833301i	$0.313552\pi$
$348$	18.0740	0.968870
$349$	6.58195	0.352324	0.176162	−	0.984361i	$-0.443632\pi$
$349$	6.58195	0.352324	0.176162	+	0.984361i	$0.443632\pi$
$350$	−0.0774286	−0.00413874
$351$	−1.00000	−0.0533761
$352$	0.0389698	0.00207709
$353$	10.4351	0.555406	0.277703	−	0.960667i	$-0.410427\pi$
$353$	10.4351	0.555406	0.277703	+	0.960667i	$0.410427\pi$
$354$	0.314856	0.0167344
$355$	3.60128	0.191136
$356$	15.1098	0.800818
$357$	−19.1681	−1.01448
$358$	−0.319419	−0.0168818
$359$	19.6833	1.03884	0.519422	−	0.854518i	$-0.326147\pi$
$359$	19.6833	1.03884	0.519422	+	0.854518i	$0.326147\pi$
$360$	0.113114	0.00596161
$361$	−18.7350	−0.986055
$362$	−0.0492917	−0.00259072
$363$	10.9868	0.576658
$364$	−5.47289	−0.286857
$365$	1.23709	0.0647521
$366$	0.264406	0.0138207
$367$	0.334931	0.0174832	0.00874162	−	0.999962i	$-0.497217\pi$
$367$	0.334931	0.0174832	0.00874162	+	0.999962i	$0.497217\pi$
$368$	28.2893	1.47468
$369$	−4.62893	−0.240973
$370$	0.136446	0.00709349
$371$	1.83542	0.0952905
$372$	1.99920	0.103654
$373$	−1.70064	−0.0880559	−0.0440280	−	0.999030i	$-0.514019\pi$
$373$	−1.70064	−0.0880559	−0.0440280	+	0.999030i	$0.514019\pi$
$374$	0.0227508	0.00117641
$375$	−1.00000	−0.0516398
$376$	−0.286826	−0.0147919
$377$	9.04064	0.465616
$378$	0.0774286	0.00398250
$379$	−15.1157	−0.776439	−0.388220	−	0.921567i	$-0.626910\pi$
$379$	−15.1157	−0.776439	−0.388220	+	0.921567i	$0.626910\pi$
$380$	−1.02906	−0.0527897
$381$	6.35298	0.325473
$382$	0.678279	0.0347038
$383$	−18.2439	−0.932220	−0.466110	−	0.884727i	$-0.654345\pi$
$383$	−18.2439	−0.932220	−0.466110	+	0.884727i	$0.654345\pi$
$384$	−0.904184	−0.0461415
$385$	−0.314483	−0.0160275
$386$	−0.201542	−0.0102582
$387$	2.96996	0.150972
$388$	−21.7477	−1.10407
$389$	14.1032	0.715059	0.357529	−	0.933902i	$-0.383619\pi$
$389$	14.1032	0.715059	0.357529	+	0.933902i	$0.383619\pi$
$390$	0.0282840	0.00143222
$391$	49.5794	2.50734
$392$	0.0558912	0.00282293
$393$	−1.43810	−0.0725428
$394$	0.543608	0.0273866
$395$	0.0401830	0.00202182
$396$	0.229664	0.0115410
$397$	18.3759	0.922262	0.461131	−	0.887332i	$-0.347444\pi$
$397$	18.3759	0.922262	0.461131	+	0.887332i	$0.347444\pi$
$398$	−0.689021	−0.0345375
$399$	−1.40911	−0.0705437
$400$	3.99520	0.199760
$401$	4.55417	0.227424	0.113712	−	0.993514i	$-0.463726\pi$
$401$	4.55417	0.227424	0.113712	+	0.993514i	$0.463726\pi$
$402$	−0.270385	−0.0134856
$403$	1.00000	0.0498135
$404$	27.6744	1.37685
$405$	1.00000	0.0496904
$406$	−0.700004	−0.0347406
$407$	0.554187	0.0274700
$408$	−0.792013	−0.0392105
$409$	−10.2744	−0.508038	−0.254019	−	0.967199i	$-0.581753\pi$
$409$	−10.2744	−0.508038	−0.254019	+	0.967199i	$0.581753\pi$
$410$	0.130925	0.00646592
$411$	21.0515	1.03839
$412$	13.6549	0.672727
$413$	30.4741	1.49953
$414$	−0.200274	−0.00984294
$415$	−7.71386	−0.378658
$416$	−0.339227	−0.0166320
$417$	0.507943	0.0248741
$418$	0.00167249	8.18040e−5 0
$419$	−11.5501	−0.564259	−0.282130	−	0.959376i	$-0.591041\pi$
$419$	−11.5501	−0.564259	−0.282130	+	0.959376i	$0.591041\pi$
$420$	5.47289	0.267050
$421$	−4.09463	−0.199560	−0.0997801	−	0.995010i	$-0.531814\pi$
$421$	−4.09463	−0.199560	−0.0997801	+	0.995010i	$0.531814\pi$
$422$	0.683142	0.0332548
$423$	−2.53573	−0.123292
$424$	0.0758387	0.00368305
$425$	7.00193	0.339644
$426$	0.101859	0.00493508
$427$	25.5912	1.23845
$428$	−33.8325	−1.63535
$429$	0.114878	0.00554636
$430$	−0.0840025	−0.00405096
$431$	19.7588	0.951749	0.475875	−	0.879513i	$-0.342132\pi$
$431$	19.7588	0.951749	0.475875	+	0.879513i	$0.342132\pi$
$432$	−3.99520	−0.192219
$433$	−11.0542	−0.531230	−0.265615	−	0.964079i	$-0.585575\pi$
$433$	−11.0542	−0.531230	−0.265615	+	0.964079i	$0.585575\pi$
$434$	−0.0774286	−0.00371669
$435$	−9.04064	−0.433465
$436$	−26.5297	−1.27054
$437$	3.64475	0.174352
$438$	0.0349898	0.00167188
$439$	10.2471	0.489067	0.244534	−	0.969641i	$-0.421365\pi$
$439$	10.2471	0.489067	0.244534	+	0.969641i	$0.421365\pi$
$440$	−0.0129942	−0.000619477 0
$441$	0.494116	0.0235293
$442$	−0.198043	−0.00941994
$443$	−38.7366	−1.84043	−0.920216	−	0.391411i	$-0.871987\pi$
$443$	−38.7366	−1.84043	−0.920216	+	0.391411i	$0.871987\pi$
$444$	−9.64441	−0.457703
$445$	−7.55793	−0.358280
$446$	−0.462023	−0.0218774
$447$	−21.8966	−1.03568
$448$	−21.8478	−1.03221
$449$	−38.5154	−1.81766	−0.908828	−	0.417171i	$-0.863022\pi$
$449$	−38.5154	−1.81766	−0.908828	+	0.417171i	$0.863022\pi$
$450$	−0.0282840	−0.00133332
$451$	0.531762	0.0250397
$452$	32.5757	1.53223
$453$	14.5125	0.681859
$454$	0.569752	0.0267398
$455$	2.73754	0.128338
$456$	−0.0582236	−0.00272657
$457$	25.7954	1.20666	0.603329	−	0.797492i	$-0.293841\pi$
$457$	25.7954	1.20666	0.603329	+	0.797492i	$0.293841\pi$
$458$	−0.0235963	−0.00110258
$459$	−7.00193	−0.326822
$460$	−14.1560	−0.660026
$461$	37.0036	1.72343	0.861714	−	0.507394i	$-0.169391\pi$
$461$	37.0036	1.72343	0.861714	+	0.507394i	$0.169391\pi$
$462$	−0.00889484	−0.000413826 0
$463$	41.5860	1.93267	0.966333	−	0.257294i	$-0.0828309\pi$
$463$	41.5860	1.93267	0.966333	+	0.257294i	$0.0828309\pi$
$464$	36.1192	1.67679
$465$	−1.00000	−0.0463739
$466$	−0.800861	−0.0370991
$467$	−34.5937	−1.60081	−0.800404	−	0.599462i	$-0.795381\pi$
$467$	−34.5937	−1.60081	−0.800404	+	0.599462i	$0.795381\pi$
$468$	−1.99920	−0.0924131
$469$	−26.1698	−1.20841
$470$	0.0717208	0.00330823
$471$	9.55365	0.440209
$472$	1.25917	0.0579582
$473$	−0.341183	−0.0156876
$474$	0.00113654	5.22029e−5 0
$475$	0.514736	0.0236177
$476$	−38.3208	−1.75643
$477$	0.670465	0.0306985
$478$	−0.359109	−0.0164253
$479$	−13.1764	−0.602043	−0.301022	−	0.953617i	$-0.597328\pi$
$479$	−13.1764	−0.602043	−0.301022	+	0.953617i	$0.597328\pi$
$480$	0.339227	0.0154835
$481$	−4.82413	−0.219962
$482$	0.614087	0.0279709
$483$	−19.3840	−0.882003
$484$	21.9648	0.998401
$485$	10.8782	0.493954
$486$	0.0282840	0.00128299
$487$	29.8332	1.35187	0.675937	−	0.736960i	$-0.263739\pi$
$487$	29.8332	1.35187	0.675937	+	0.736960i	$0.263739\pi$
$488$	1.05741	0.0478669
$489$	−14.0194	−0.633980
$490$	−0.0139756	−0.000631353 0
$491$	−22.0100	−0.993296	−0.496648	−	0.867952i	$-0.665436\pi$
$491$	−22.0100	−0.993296	−0.496648	+	0.867952i	$0.665436\pi$
$492$	−9.25417	−0.417210
$493$	63.3019	2.85097
$494$	−0.0145588	−0.000655032 0
$495$	−0.114878	−0.00516338
$496$	3.99520	0.179390
$497$	9.85865	0.442221
$498$	−0.218179	−0.00977684
$499$	9.62601	0.430919	0.215460	−	0.976513i	$-0.430875\pi$
$499$	9.62601	0.430919	0.215460	+	0.976513i	$0.430875\pi$
$500$	−1.99920	−0.0894069
$501$	−21.9051	−0.978646
$502$	0.0217263	0.000969692 0
$503$	24.9266	1.11142	0.555710	−	0.831376i	$-0.312446\pi$
$503$	24.9266	1.11142	0.555710	+	0.831376i	$0.312446\pi$
$504$	0.309653	0.0137930
$505$	−13.8427	−0.615993
$506$	0.0230071	0.00102279
$507$	−1.00000	−0.0444116
$508$	12.7009	0.563510
$509$	30.9994	1.37403	0.687013	−	0.726645i	$-0.258922\pi$
$509$	30.9994	1.37403	0.687013	+	0.726645i	$0.258922\pi$
$510$	0.198043	0.00876949
$511$	3.38657	0.149813
$512$	−2.25910	−0.0998393
$513$	−0.514736	−0.0227261
$514$	−0.229709	−0.0101320
$515$	−6.83017	−0.300973
$516$	5.93755	0.261386
$517$	0.291300	0.0128114
$518$	0.373526	0.0164118
$519$	25.1861	1.10555
$520$	0.113114	0.00496036
$521$	−28.5120	−1.24913	−0.624567	−	0.780971i	$-0.714724\pi$
$521$	−28.5120	−1.24913	−0.624567	+	0.780971i	$0.714724\pi$
$522$	−0.255706	−0.0111919
$523$	39.2310	1.71545	0.857727	−	0.514106i	$-0.171876\pi$
$523$	39.2310	1.71545	0.857727	+	0.514106i	$0.171876\pi$
$524$	−2.87506	−0.125597
$525$	−2.73754	−0.119476
$526$	0.0653803	0.00285071
$527$	7.00193	0.305009
$528$	0.458960	0.0199737
$529$	27.1380	1.17991
$530$	−0.0189635	−0.000823720 0
$531$	11.1319	0.483085
$532$	−2.81709	−0.122136
$533$	−4.62893	−0.200501
$534$	−0.213769	−0.00925068
$535$	16.9230	0.731645
$536$	−1.08132	−0.0467060
$537$	−11.2933	−0.487341
$538$	0.586190	0.0252724
$539$	−0.0567630	−0.00244496
$540$	1.99920	0.0860319
$541$	−16.5375	−0.711002	−0.355501	−	0.934676i	$-0.615690\pi$
$541$	−16.5375	−0.711002	−0.355501	+	0.934676i	$0.615690\pi$
$542$	−0.672298	−0.0288777
$543$	−1.74274	−0.0747881
$544$	−2.37525	−0.101838
$545$	13.2701	0.568430
$546$	0.0774286	0.00331364
$547$	1.60900	0.0687958	0.0343979	−	0.999408i	$-0.489049\pi$
$547$	1.60900	0.0687958	0.0343979	+	0.999408i	$0.489049\pi$
$548$	42.0862	1.79783
$549$	9.34826	0.398974
$550$	0.00324921	0.000138547 0
$551$	4.65354	0.198247
$552$	−0.800937	−0.0340901
$553$	0.110002	0.00467778
$554$	−0.0126296	−0.000536581 0
$555$	4.82413	0.204773
$556$	1.01548	0.0430659
$557$	15.1556	0.642162	0.321081	−	0.947052i	$-0.395954\pi$
$557$	15.1556	0.642162	0.321081	+	0.947052i	$0.395954\pi$
$558$	−0.0282840	−0.00119736
$559$	2.96996	0.125616
$560$	10.9370	0.462173
$561$	0.804368	0.0339604
$562$	−0.412676	−0.0174077
$563$	30.1082	1.26891	0.634454	−	0.772960i	$-0.281225\pi$
$563$	30.1082	1.26891	0.634454	+	0.772960i	$0.281225\pi$
$564$	−5.06944	−0.213462
$565$	−16.2944	−0.685510
$566$	−0.439452	−0.0184716
$567$	2.73754	0.114966
$568$	0.407354	0.0170922
$569$	−28.5940	−1.19872	−0.599361	−	0.800479i	$-0.704579\pi$
$569$	−28.5940	−1.19872	−0.599361	+	0.800479i	$0.704579\pi$
$570$	0.0145588	0.000609801 0
$571$	16.1318	0.675094	0.337547	−	0.941309i	$-0.390403\pi$
$571$	16.1318	0.675094	0.337547	+	0.941309i	$0.390403\pi$
$572$	0.229664	0.00960273
$573$	23.9810	1.00182
$574$	0.358412	0.0149598
$575$	7.08082	0.295291
$576$	−7.98081	−0.332534
$577$	−26.8585	−1.11813	−0.559067	−	0.829123i	$-0.688841\pi$
$577$	−26.8585	−1.11813	−0.559067	+	0.829123i	$0.688841\pi$
$578$	−0.905854	−0.0376786
$579$	−7.12566	−0.296132
$580$	−18.0740	−0.750484
$581$	−21.1170	−0.876080
$582$	0.307680	0.0127537
$583$	−0.0770216	−0.00318991
$584$	0.139931	0.00579040
$585$	1.00000	0.0413449
$586$	−0.0684044	−0.00282576
$587$	28.3128	1.16859	0.584297	−	0.811540i	$-0.301370\pi$
$587$	28.3128	1.16859	0.584297	+	0.811540i	$0.301370\pi$
$588$	0.987837	0.0407377
$589$	0.514736	0.0212093
$590$	−0.314856	−0.0129624
$591$	19.2196	0.790589
$592$	−19.2734	−0.792131
$593$	32.2444	1.32412	0.662060	−	0.749451i	$-0.269682\pi$
$593$	32.2444	1.32412	0.662060	+	0.749451i	$0.269682\pi$
$594$	−0.00324921	−0.000133317 0
$595$	19.1681	0.785814
$596$	−43.7758	−1.79313
$597$	−24.3608	−0.997019
$598$	−0.200274	−0.00818982
$599$	−44.4655	−1.81681	−0.908405	−	0.418091i	$-0.862699\pi$
$599$	−44.4655	−1.81681	−0.908405	+	0.418091i	$0.862699\pi$
$600$	−0.113114	−0.00461784
$601$	37.3524	1.52364	0.761818	−	0.647792i	$-0.224307\pi$
$601$	37.3524	1.52364	0.761818	+	0.647792i	$0.224307\pi$
$602$	−0.229960	−0.00937248
$603$	−9.55962	−0.389298
$604$	29.0135	1.18054
$605$	−10.9868	−0.446677
$606$	−0.391528	−0.0159047
$607$	−0.811960	−0.0329564	−0.0164782	−	0.999864i	$-0.505245\pi$
$607$	−0.811960	−0.0329564	−0.0164782	+	0.999864i	$0.505245\pi$
$608$	−0.174613	−0.00708147
$609$	−24.7491	−1.00288
$610$	−0.264406	−0.0107055
$611$	−2.53573	−0.102585
$612$	−13.9983	−0.565846
$613$	35.3576	1.42808	0.714039	−	0.700106i	$-0.246864\pi$
$613$	35.3576	1.42808	0.714039	+	0.700106i	$0.246864\pi$
$614$	0.0983296	0.00396826
$615$	4.62893	0.186657
$616$	−0.0355723	−0.00143325
$617$	−33.6853	−1.35612	−0.678059	−	0.735008i	$-0.737179\pi$
$617$	−33.6853	−1.35612	−0.678059	+	0.735008i	$0.737179\pi$
$618$	−0.193185	−0.00777103
$619$	6.36189	0.255706	0.127853	−	0.991793i	$-0.459191\pi$
$619$	6.36189	0.255706	0.127853	+	0.991793i	$0.459191\pi$
$620$	−1.99920	−0.0802898
$621$	−7.08082	−0.284144
$622$	0.126874	0.00508717
$623$	−20.6901	−0.828932
$624$	−3.99520	−0.159936
$625$	1.00000	0.0400000
$626$	−0.481055	−0.0192268
$627$	0.0591318	0.00236150
$628$	19.0997	0.762159
$629$	−33.7783	−1.34683
$630$	−0.0774286	−0.00308483
$631$	−21.9154	−0.872439	−0.436220	−	0.899840i	$-0.643683\pi$
$631$	−21.9154	−0.872439	−0.436220	+	0.899840i	$0.643683\pi$
$632$	0.00454524	0.000180800 0
$633$	24.1529	0.959992
$634$	−0.656412	−0.0260694
$635$	−6.35298	−0.252110
$636$	1.34039	0.0531501
$637$	0.494116	0.0195776
$638$	0.0293749	0.00116297
$639$	3.60128	0.142465
$640$	0.904184	0.0357410
$641$	−18.5951	−0.734462	−0.367231	−	0.930130i	$-0.619694\pi$
$641$	−18.5951	−0.734462	−0.367231	+	0.930130i	$0.619694\pi$
$642$	0.478651	0.0188908
$643$	−3.42988	−0.135261	−0.0676306	−	0.997710i	$-0.521544\pi$
$643$	−3.42988	−0.135261	−0.0676306	+	0.997710i	$0.521544\pi$
$644$	−38.7525	−1.52706
$645$	−2.96996	−0.116942
$646$	−0.101940	−0.00401077
$647$	−8.57463	−0.337104	−0.168552	−	0.985693i	$-0.553909\pi$
$647$	−8.57463	−0.337104	−0.168552	+	0.985693i	$0.553909\pi$
$648$	0.113114	0.00444352
$649$	−1.27882	−0.0501979
$650$	−0.0282840	−0.00110939
$651$	−2.73754	−0.107293
$652$	−28.0276	−1.09765
$653$	11.2776	0.441327	0.220664	−	0.975350i	$-0.429178\pi$
$653$	11.2776	0.441327	0.220664	+	0.975350i	$0.429178\pi$
$654$	0.375333	0.0146767
$655$	1.43810	0.0561914
$656$	−18.4935	−0.722051
$657$	1.23709	0.0482633
$658$	0.196338	0.00765407
$659$	30.5077	1.18841	0.594205	−	0.804314i	$-0.297467\pi$
$659$	30.5077	1.18841	0.594205	+	0.804314i	$0.297467\pi$
$660$	−0.229664	−0.00893966
$661$	46.4700	1.80747	0.903736	−	0.428090i	$-0.140813\pi$
$661$	46.4700	1.80747	0.903736	+	0.428090i	$0.140813\pi$
$662$	0.0971464	0.00377570
$663$	−7.00193	−0.271933
$664$	−0.872542	−0.0338612
$665$	1.40911	0.0546429
$666$	0.136446	0.00528718
$667$	64.0151	2.47868
$668$	−43.7926	−1.69439
$669$	−16.3351	−0.631552
$670$	0.270385	0.0104459
$671$	−1.07391	−0.0414578
$672$	0.928648	0.0358234
$673$	−33.8972	−1.30664	−0.653320	−	0.757082i	$-0.726624\pi$
$673$	−33.8972	−1.30664	−0.653320	+	0.757082i	$0.726624\pi$
$674$	0.614880	0.0236843
$675$	−1.00000	−0.0384900
$676$	−1.99920	−0.0768923
$677$	−34.3264	−1.31927	−0.659635	−	0.751586i	$-0.729289\pi$
$677$	−34.3264	−1.31927	−0.659635	+	0.751586i	$0.729289\pi$
$678$	−0.460871	−0.0176997
$679$	29.7795	1.14283
$680$	0.792013	0.0303723
$681$	20.1439	0.771917
$682$	0.00324921	0.000124419 0
$683$	−22.9130	−0.876741	−0.438371	−	0.898794i	$-0.644444\pi$
$683$	−22.9130	−0.876741	−0.438371	+	0.898794i	$0.644444\pi$
$684$	−1.02906	−0.0393471
$685$	−21.0515	−0.804337
$686$	0.503742	0.0192330
$687$	−0.834261	−0.0318290
$688$	11.8656	0.452372
$689$	0.670465	0.0255427
$690$	0.200274	0.00762431
$691$	32.5309	1.23754	0.618768	−	0.785574i	$-0.287632\pi$
$691$	32.5309	1.23754	0.618768	+	0.785574i	$0.287632\pi$
$692$	50.3520	1.91409
$693$	−0.314483	−0.0119462
$694$	−0.582532	−0.0221126
$695$	−0.507943	−0.0192674
$696$	−1.02262	−0.0387622
$697$	−32.4115	−1.22767
$698$	−0.186164	−0.00704642
$699$	−28.3149	−1.07097
$700$	−5.47289	−0.206856
$701$	−1.06231	−0.0401230	−0.0200615	−	0.999799i	$-0.506386\pi$
$701$	−1.06231	−0.0401230	−0.0200615	+	0.999799i	$0.506386\pi$
$702$	0.0282840	0.00106751
$703$	−2.48316	−0.0936540
$704$	0.916819	0.0345539
$705$	2.53573	0.0955013
$706$	−0.295148	−0.0111080
$707$	−37.8950	−1.42519
$708$	22.2550	0.836394
$709$	−39.6074	−1.48749	−0.743743	−	0.668466i	$-0.766951\pi$
$709$	−39.6074	−1.48749	−0.743743	+	0.668466i	$0.766951\pi$
$710$	−0.101859	−0.00382269
$711$	0.0401830	0.00150698
$712$	−0.854904	−0.0320389
$713$	7.08082	0.265179
$714$	0.542150	0.0202895
$715$	−0.114878	−0.00429619
$716$	−22.5775	−0.843761
$717$	−12.6965	−0.474160
$718$	−0.556722	−0.0207767
$719$	−49.3995	−1.84229	−0.921145	−	0.389220i	$-0.872744\pi$
$719$	−49.3995	−1.84229	−0.921145	+	0.389220i	$0.872744\pi$
$720$	3.99520	0.148892
$721$	−18.6978	−0.696344
$722$	0.529903	0.0197209
$723$	21.7114	0.807457
$724$	−3.48409	−0.129485
$725$	9.04064	0.335761
$726$	−0.310751	−0.0115331
$727$	−25.8777	−0.959751	−0.479875	−	0.877337i	$-0.659318\pi$
$727$	−25.8777	−0.959751	−0.479875	+	0.877337i	$0.659318\pi$
$728$	0.309653	0.0114765
$729$	1.00000	0.0370370
$730$	−0.0349898	−0.00129503
$731$	20.7955	0.769148
$732$	18.6890	0.690767
$733$	−20.3977	−0.753407	−0.376703	−	0.926334i	$-0.622942\pi$
$733$	−20.3977	−0.753407	−0.376703	+	0.926334i	$0.622942\pi$
$734$	−0.00947319	−0.000349662 0
$735$	−0.494116	−0.0182257
$736$	−2.40201	−0.0885392
$737$	1.09819	0.0404523
$738$	0.130925	0.00481941
$739$	37.0174	1.36171	0.680854	−	0.732420i	$-0.261609\pi$
$739$	37.0174	1.36171	0.680854	+	0.732420i	$0.261609\pi$
$740$	9.64441	0.354536
$741$	−0.514736	−0.0189093
$742$	−0.0519132	−0.00190579
$743$	−37.0147	−1.35794	−0.678968	−	0.734168i	$-0.737572\pi$
$743$	−37.0147	−1.35794	−0.678968	+	0.734168i	$0.737572\pi$
$744$	−0.113114	−0.00414694
$745$	21.8966	0.802231
$746$	0.0481010	0.00176110
$747$	−7.71386	−0.282235
$748$	1.60809	0.0587976
$749$	46.3274	1.69277
$750$	0.0282840	0.00103279
$751$	−45.0966	−1.64560	−0.822800	−	0.568331i	$-0.807589\pi$
$751$	−45.0966	−1.64560	−0.822800	+	0.568331i	$0.807589\pi$
$752$	−10.1308	−0.369431
$753$	0.768146	0.0279928
$754$	−0.255706	−0.00931225
$755$	−14.5125	−0.528166
$756$	5.47289	0.199047
$757$	28.3527	1.03050	0.515249	−	0.857041i	$-0.327700\pi$
$757$	28.3527	1.03050	0.515249	+	0.857041i	$0.327700\pi$
$758$	0.427532	0.0155287
$759$	0.813430	0.0295256
$760$	0.0582236	0.00211199
$761$	−29.4629	−1.06803	−0.534015	−	0.845475i	$-0.679317\pi$
$761$	−29.4629	−1.06803	−0.534015	+	0.845475i	$0.679317\pi$
$762$	−0.179688	−0.00650941
$763$	36.3275	1.31514
$764$	47.9428	1.73451
$765$	7.00193	0.253155
$766$	0.516012	0.0186443
$767$	11.1319	0.401951
$768$	−15.9360	−0.575042
$769$	−33.0176	−1.19065	−0.595323	−	0.803486i	$-0.702976\pi$
$769$	−33.0176	−1.19065	−0.595323	+	0.803486i	$0.702976\pi$
$770$	0.00889484	0.000320548 0
$771$	−8.12150	−0.292489
$772$	−14.2456	−0.512711
$773$	13.6510	0.490991	0.245496	−	0.969398i	$-0.421049\pi$
$773$	13.6510	0.490991	0.245496	+	0.969398i	$0.421049\pi$
$774$	−0.0840025	−0.00301941
$775$	1.00000	0.0359211
$776$	1.23047	0.0441714
$777$	13.2063	0.473772
$778$	−0.398895	−0.0143011
$779$	−2.38268	−0.0853683
$780$	1.99920	0.0715828
$781$	−0.413708	−0.0148036
$782$	−1.40231	−0.0501464
$783$	−9.04064	−0.323086
$784$	1.97409	0.0705033
$785$	−9.55365	−0.340984
$786$	0.0406754	0.00145084
$787$	35.0790	1.25043	0.625215	−	0.780453i	$-0.285011\pi$
$787$	35.0790	1.25043	0.625215	+	0.780453i	$0.285011\pi$
$788$	38.4239	1.36879
$789$	2.31156	0.0822937
$790$	−0.00113654	−4.04362e−5 0
$791$	−44.6065	−1.58603
$792$	−0.0129942	−0.000461731 0
$793$	9.34826	0.331966
$794$	−0.519746	−0.0184451
$795$	−0.670465	−0.0237789
$796$	−48.7020	−1.72620
$797$	−18.5118	−0.655723	−0.327862	−	0.944726i	$-0.606328\pi$
$797$	−18.5118	−0.655723	−0.327862	+	0.944726i	$0.606328\pi$
$798$	0.0398553	0.00141086
$799$	−17.7550	−0.628128
$800$	−0.339227	−0.0119935
$801$	−7.55793	−0.267046
$802$	−0.128810	−0.00454845
$803$	−0.142114	−0.00501509
$804$	−19.1116	−0.674014
$805$	19.3840	0.683197
$806$	−0.0282840	−0.000996263 0
$807$	20.7251	0.729558
$808$	−1.56580	−0.0550846
$809$	3.65834	0.128620	0.0643102	−	0.997930i	$-0.479515\pi$
$809$	3.65834	0.128620	0.0643102	+	0.997930i	$0.479515\pi$
$810$	−0.0282840	−0.000993800 0
$811$	−1.35605	−0.0476173	−0.0238086	−	0.999717i	$-0.507579\pi$
$811$	−1.35605	−0.0476173	−0.0238086	+	0.999717i	$0.507579\pi$
$812$	−49.4784	−1.73635
$813$	−23.7695	−0.833634
$814$	−0.0156746	−0.000549396 0
$815$	14.0194	0.491078
$816$	−27.9741	−0.979290
$817$	1.52875	0.0534841
$818$	0.290603	0.0101607
$819$	2.73754	0.0956573
$820$	9.25417	0.323169
$821$	−35.6822	−1.24532	−0.622659	−	0.782494i	$-0.713947\pi$
$821$	−35.6822	−1.24532	−0.622659	+	0.782494i	$0.713947\pi$
$822$	−0.595422	−0.0207677
$823$	−51.7936	−1.80541	−0.902705	−	0.430259i	$-0.858422\pi$
$823$	−51.7936	−1.80541	−0.902705	+	0.430259i	$0.858422\pi$
$824$	−0.772584	−0.0269143
$825$	0.114878	0.00399954
$826$	−0.861932	−0.0299904
$827$	18.0606	0.628029	0.314014	−	0.949418i	$-0.398326\pi$
$827$	18.0606	0.628029	0.314014	+	0.949418i	$0.398326\pi$
$828$	−14.1560	−0.491954
$829$	−33.0518	−1.14794	−0.573968	−	0.818878i	$-0.694597\pi$
$829$	−33.0518	−1.14794	−0.573968	+	0.818878i	$0.694597\pi$
$830$	0.218179	0.00757310
$831$	−0.446528	−0.0154899
$832$	−7.98081	−0.276685
$833$	3.45977	0.119874
$834$	−0.0143667	−0.000497477 0
$835$	21.9051	0.758056
$836$	0.118216	0.00408860
$837$	−1.00000	−0.0345651
$838$	0.326683	0.0112851
$839$	8.42471	0.290853	0.145427	−	0.989369i	$-0.453545\pi$
$839$	8.42471	0.290853	0.145427	+	0.989369i	$0.453545\pi$
$840$	−0.309653	−0.0106840
$841$	52.7331	1.81838
$842$	0.115813	0.00399117
$843$	−14.5904	−0.502521
$844$	48.2865	1.66209
$845$	1.00000	0.0344010
$846$	0.0717208	0.00246581
$847$	−30.0768	−1.03345
$848$	2.67864	0.0919850
$849$	−15.5371	−0.533232
$850$	−0.198043	−0.00679282
$851$	−34.1588	−1.17095
$852$	7.19969	0.246657
$853$	−47.8331	−1.63777	−0.818886	−	0.573956i	$-0.805408\pi$
$853$	−47.8331	−1.63777	−0.818886	+	0.573956i	$0.805408\pi$
$854$	−0.723823	−0.0247687
$855$	0.514736	0.0176036
$856$	1.91422	0.0654267
$857$	−13.6518	−0.466338	−0.233169	−	0.972436i	$-0.574910\pi$
$857$	−13.6518	−0.466338	−0.233169	+	0.972436i	$0.574910\pi$
$858$	−0.00324921	−0.000110926 0
$859$	38.9800	1.32998	0.664990	−	0.746852i	$-0.268436\pi$
$859$	38.9800	1.32998	0.664990	+	0.746852i	$0.268436\pi$
$860$	−5.93755	−0.202469
$861$	12.6719	0.431857
$862$	−0.558860	−0.0190348
$863$	−5.25799	−0.178984	−0.0894920	−	0.995988i	$-0.528524\pi$
$863$	−5.25799	−0.178984	−0.0894920	+	0.995988i	$0.528524\pi$
$864$	0.339227	0.0115408
$865$	−25.1861	−0.856352
$866$	0.312657	0.0106245
$867$	−32.0271	−1.08770
$868$	−5.47289	−0.185762
$869$	−0.00461614	−0.000156592 0
$870$	0.255706	0.00866924
$871$	−9.55962	−0.323915
$872$	1.50103	0.0508314
$873$	10.8782	0.368172
$874$	−0.103088	−0.00348701
$875$	2.73754	0.0925457
$876$	2.47318	0.0835611
$877$	−28.7366	−0.970366	−0.485183	−	0.874413i	$-0.661247\pi$
$877$	−28.7366	−0.970366	−0.485183	+	0.874413i	$0.661247\pi$
$878$	−0.289829	−0.00978126
$879$	−2.41848	−0.0815734
$880$	−0.458960	−0.0154716
$881$	−34.1147	−1.14935	−0.574676	−	0.818381i	$-0.694872\pi$
$881$	−34.1147	−1.14935	−0.574676	+	0.818381i	$0.694872\pi$
$882$	−0.0139756	−0.000470583 0
$883$	−28.7365	−0.967061	−0.483531	−	0.875327i	$-0.660646\pi$
$883$	−28.7365	−0.967061	−0.483531	+	0.875327i	$0.660646\pi$
$884$	−13.9983	−0.470813
$885$	−11.1319	−0.374196
$886$	1.09563	0.0368083
$887$	−3.83978	−0.128927	−0.0644637	−	0.997920i	$-0.520534\pi$
$887$	−3.83978	−0.128927	−0.0644637	+	0.997920i	$0.520534\pi$
$888$	0.545675	0.0183117
$889$	−17.3915	−0.583293
$890$	0.213769	0.00716555
$891$	−0.114878	−0.00384856
$892$	−32.6572	−1.09344
$893$	−1.30523	−0.0436780
$894$	0.619326	0.0207133
$895$	11.2933	0.377492
$896$	2.47524	0.0826919
$897$	−7.08082	−0.236422
$898$	1.08937	0.0363528
$899$	9.04064	0.301522
$900$	−1.99920	−0.0666400
$901$	4.69455	0.156398
$902$	−0.0150404	−0.000500790 0
$903$	−8.13039	−0.270562
$904$	−1.84312	−0.0613011
$905$	1.74274	0.0579306
$906$	−0.410473	−0.0136371
$907$	2.57473	0.0854926	0.0427463	−	0.999086i	$-0.486389\pi$
$907$	2.57473	0.0854926	0.0427463	+	0.999086i	$0.486389\pi$
$908$	40.2717	1.33646
$909$	−13.8427	−0.459134
$910$	−0.0774286	−0.00256673
$911$	−8.54339	−0.283055	−0.141528	−	0.989934i	$-0.545201\pi$
$911$	−8.54339	−0.283055	−0.141528	+	0.989934i	$0.545201\pi$
$912$	−2.05647	−0.0680966
$913$	0.886152	0.0293273
$914$	−0.729598	−0.0241330
$915$	−9.34826	−0.309044
$916$	−1.66785	−0.0551075
$917$	3.93687	0.130007
$918$	0.198043	0.00653639
$919$	−14.9127	−0.491925	−0.245962	−	0.969279i	$-0.579104\pi$
$919$	−14.9127	−0.491925	−0.245962	+	0.969279i	$0.579104\pi$
$920$	0.800937	0.0264061
$921$	3.47650	0.114555
$922$	−1.04661	−0.0344683
$923$	3.60128	0.118538
$924$	−0.628714	−0.0206832
$925$	−4.82413	−0.158617
$926$	−1.17622	−0.0386530
$927$	−6.83017	−0.224332
$928$	−3.06683	−0.100674
$929$	−45.8823	−1.50535	−0.752674	−	0.658393i	$-0.771236\pi$
$929$	−45.8823	−1.50535	−0.752674	+	0.658393i	$0.771236\pi$
$930$	0.0282840	0.000927470 0
$931$	0.254339	0.00833563
$932$	−56.6072	−1.85423
$933$	4.48570	0.146855
$934$	0.978451	0.0320159
$935$	−0.804368	−0.0263056
$936$	0.113114	0.00369723
$937$	−9.12499	−0.298101	−0.149050	−	0.988830i	$-0.547622\pi$
$937$	−9.12499	−0.298101	−0.149050	+	0.988830i	$0.547622\pi$
$938$	0.740188	0.0241680
$939$	−17.0080	−0.555035
$940$	5.06944	0.165347
$941$	−50.7709	−1.65508	−0.827542	−	0.561404i	$-0.810261\pi$
$941$	−50.7709	−1.65508	−0.827542	+	0.561404i	$0.810261\pi$
$942$	−0.270216	−0.00880411
$943$	−32.7767	−1.06735
$944$	44.4744	1.44752
$945$	−2.73754	−0.0890521
$946$	0.00965004	0.000313750 0
$947$	−32.5331	−1.05718	−0.528592	−	0.848876i	$-0.677280\pi$
$947$	−32.5331	−1.05718	−0.528592	+	0.848876i	$0.677280\pi$
$948$	0.0803338	0.00260912
$949$	1.23709	0.0401575
$950$	−0.0145588	−0.000472350 0
$951$	−23.2078	−0.752566
$952$	2.16817	0.0702707
$953$	−23.8066	−0.771173	−0.385586	−	0.922672i	$-0.626001\pi$
$953$	−23.8066	−0.771173	−0.385586	+	0.922672i	$0.626001\pi$
$954$	−0.0189635	−0.000613965 0
$955$	−23.9810	−0.776007
$956$	−25.3829	−0.820941
$957$	1.03857	0.0335722
$958$	0.372681	0.0120408
$959$	−57.6293	−1.86095
$960$	7.98081	0.257579
$961$	1.00000	0.0322581
$962$	0.136446	0.00439920
$963$	16.9230	0.545336
$964$	43.4055	1.39800
$965$	7.12566	0.229383
$966$	0.548258	0.0176399
$967$	−8.80312	−0.283089	−0.141545	−	0.989932i	$-0.545207\pi$
$967$	−8.80312	−0.283089	−0.141545	+	0.989932i	$0.545207\pi$
$968$	−1.24276	−0.0399437
$969$	−3.60415	−0.115782
$970$	−0.307680	−0.00987900
$971$	−23.9976	−0.770119	−0.385060	−	0.922892i	$-0.625819\pi$
$971$	−23.9976	−0.770119	−0.385060	+	0.922892i	$0.625819\pi$
$972$	1.99920	0.0641244
$973$	−1.39051	−0.0445778
$974$	−0.843805	−0.0270372
$975$	−1.00000	−0.0320256
$976$	37.3482	1.19549
$977$	25.2496	0.807805	0.403902	−	0.914802i	$-0.367654\pi$
$977$	25.2496	0.807805	0.403902	+	0.914802i	$0.367654\pi$
$978$	0.396526	0.0126795
$979$	0.868239	0.0277490
$980$	−0.987837	−0.0315553
$981$	13.2701	0.423683
$982$	0.622531	0.0198658
$983$	19.8776	0.633996	0.316998	−	0.948426i	$-0.397325\pi$
$983$	19.8776	0.633996	0.316998	+	0.948426i	$0.397325\pi$
$984$	0.523595	0.0166916
$985$	−19.2196	−0.612388
$986$	−1.79043	−0.0570190
$987$	6.94167	0.220956
$988$	−1.02906	−0.0327388
$989$	21.0298	0.668708
$990$	0.00324921	0.000103267 0
$991$	54.1494	1.72011	0.860056	−	0.510200i	$-0.170428\pi$
$991$	54.1494	1.72011	0.860056	+	0.510200i	$0.170428\pi$
$992$	−0.339227	−0.0107705
$993$	3.43467	0.108996
$994$	−0.278842	−0.00884435
$995$	24.3608	0.772288
$996$	−15.4215	−0.488650
$997$	29.2273	0.925638	0.462819	−	0.886453i	$-0.346838\pi$
$997$	29.2273	0.925638	0.462819	+	0.886453i	$0.346838\pi$
$998$	−0.272262	−0.00861832
$999$	4.82413	0.152629

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6045.2.a.bh.1.9	✓	17

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6045.2.a.bh.1.9	✓	17	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:	\( N \)	\(=\)	\( 6045 = 3 \cdot 5 \cdot 13 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6045.a (trivial)

\(f(q)\)	\(=\)	\(q-0.0282840 q^{2} -1.00000 q^{3} -1.99920 q^{4} +1.00000 q^{5} +0.0282840 q^{6} +2.73754 q^{7} +0.113114 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-0.0282840 q^{2} -1.00000 q^{3} -1.99920 q^{4} +1.00000 q^{5} +0.0282840 q^{6} +2.73754 q^{7} +0.113114 q^{8} +1.00000 q^{9} -0.0282840 q^{10} -0.114878 q^{11} +1.99920 q^{12} +1.00000 q^{13} -0.0774286 q^{14} -1.00000 q^{15} +3.99520 q^{16} +7.00193 q^{17} -0.0282840 q^{18} +0.514736 q^{19} -1.99920 q^{20} -2.73754 q^{21} +0.00324921 q^{22} +7.08082 q^{23} -0.113114 q^{24} +1.00000 q^{25} -0.0282840 q^{26} -1.00000 q^{27} -5.47289 q^{28} +9.04064 q^{29} +0.0282840 q^{30} +1.00000 q^{31} -0.339227 q^{32} +0.114878 q^{33} -0.198043 q^{34} +2.73754 q^{35} -1.99920 q^{36} -4.82413 q^{37} -0.0145588 q^{38} -1.00000 q^{39} +0.113114 q^{40} -4.62893 q^{41} +0.0774286 q^{42} +2.96996 q^{43} +0.229664 q^{44} +1.00000 q^{45} -0.200274 q^{46} -2.53573 q^{47} -3.99520 q^{48} +0.494116 q^{49} -0.0282840 q^{50} -7.00193 q^{51} -1.99920 q^{52} +0.670465 q^{53} +0.0282840 q^{54} -0.114878 q^{55} +0.309653 q^{56} -0.514736 q^{57} -0.255706 q^{58} +11.1319 q^{59} +1.99920 q^{60} +9.34826 q^{61} -0.0282840 q^{62} +2.73754 q^{63} -7.98081 q^{64} +1.00000 q^{65} -0.00324921 q^{66} -9.55962 q^{67} -13.9983 q^{68} -7.08082 q^{69} -0.0774286 q^{70} +3.60128 q^{71} +0.113114 q^{72} +1.23709 q^{73} +0.136446 q^{74} -1.00000 q^{75} -1.02906 q^{76} -0.314483 q^{77} +0.0282840 q^{78} +0.0401830 q^{79} +3.99520 q^{80} +1.00000 q^{81} +0.130925 q^{82} -7.71386 q^{83} +5.47289 q^{84} +7.00193 q^{85} -0.0840025 q^{86} -9.04064 q^{87} -0.0129942 q^{88} -7.55793 q^{89} -0.0282840 q^{90} +2.73754 q^{91} -14.1560 q^{92} -1.00000 q^{93} +0.0717208 q^{94} +0.514736 q^{95} +0.339227 q^{96} +10.8782 q^{97} -0.0139756 q^{98} -0.114878 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 17 q + 2 q^{2} - 17 q^{3} + 20 q^{4} + 17 q^{5} - 2 q^{6} + 18 q^{7} + 9 q^{8} + 17 q^{9}+O(q^{10}) \) 17 * q + 2 * q^2 - 17 * q^3 + 20 * q^4 + 17 * q^5 - 2 * q^6 + 18 * q^7 + 9 * q^8 + 17 * q^9	\( 17 q + 2 q^{2} - 17 q^{3} + 20 q^{4} + 17 q^{5} - 2 q^{6} + 18 q^{7} + 9 q^{8} + 17 q^{9} + 2 q^{10} + 3 q^{11} - 20 q^{12} + 17 q^{13} + q^{14} - 17 q^{15} + 26 q^{16} + 2 q^{18} + 10 q^{19} + 20 q^{20} - 18 q^{21} + 5 q^{22} + 16 q^{23} - 9 q^{24} + 17 q^{25} + 2 q^{26} - 17 q^{27} + 36 q^{28} - 3 q^{29} - 2 q^{30} + 17 q^{31} + 20 q^{32} - 3 q^{33} + q^{34} + 18 q^{35} + 20 q^{36} + 14 q^{37} + 22 q^{38} - 17 q^{39} + 9 q^{40} - 6 q^{41} - q^{42} + 24 q^{43} - 15 q^{44} + 17 q^{45} + 6 q^{46} + 25 q^{47} - 26 q^{48} + 31 q^{49} + 2 q^{50} + 20 q^{52} - 15 q^{53} - 2 q^{54} + 3 q^{55} + 31 q^{56} - 10 q^{57} + 44 q^{58} + 16 q^{59} - 20 q^{60} - 5 q^{61} + 2 q^{62} + 18 q^{63} + 35 q^{64} + 17 q^{65} - 5 q^{66} + 50 q^{67} + 13 q^{68} - 16 q^{69} + q^{70} + 16 q^{71} + 9 q^{72} + 33 q^{73} + 2 q^{74} - 17 q^{75} + 9 q^{77} - 2 q^{78} - 10 q^{79} + 26 q^{80} + 17 q^{81} + 61 q^{82} + 27 q^{83} - 36 q^{84} - 12 q^{86} + 3 q^{87} + 23 q^{88} - 24 q^{89} + 2 q^{90} + 18 q^{91} - 21 q^{92} - 17 q^{93} + 6 q^{94} + 10 q^{95} - 20 q^{96} + 48 q^{97} + 14 q^{98} + 3 q^{99}+O(q^{100}) \) 17 * q + 2 * q^2 - 17 * q^3 + 20 * q^4 + 17 * q^5 - 2 * q^6 + 18 * q^7 + 9 * q^8 + 17 * q^9 + 2 * q^10 + 3 * q^11 - 20 * q^12 + 17 * q^13 + q^14 - 17 * q^15 + 26 * q^16 + 2 * q^18 + 10 * q^19 + 20 * q^20 - 18 * q^21 + 5 * q^22 + 16 * q^23 - 9 * q^24 + 17 * q^25 + 2 * q^26 - 17 * q^27 + 36 * q^28 - 3 * q^29 - 2 * q^30 + 17 * q^31 + 20 * q^32 - 3 * q^33 + q^34 + 18 * q^35 + 20 * q^36 + 14 * q^37 + 22 * q^38 - 17 * q^39 + 9 * q^40 - 6 * q^41 - q^42 + 24 * q^43 - 15 * q^44 + 17 * q^45 + 6 * q^46 + 25 * q^47 - 26 * q^48 + 31 * q^49 + 2 * q^50 + 20 * q^52 - 15 * q^53 - 2 * q^54 + 3 * q^55 + 31 * q^56 - 10 * q^57 + 44 * q^58 + 16 * q^59 - 20 * q^60 - 5 * q^61 + 2 * q^62 + 18 * q^63 + 35 * q^64 + 17 * q^65 - 5 * q^66 + 50 * q^67 + 13 * q^68 - 16 * q^69 + q^70 + 16 * q^71 + 9 * q^72 + 33 * q^73 + 2 * q^74 - 17 * q^75 + 9 * q^77 - 2 * q^78 - 10 * q^79 + 26 * q^80 + 17 * q^81 + 61 * q^82 + 27 * q^83 - 36 * q^84 - 12 * q^86 + 3 * q^87 + 23 * q^88 - 24 * q^89 + 2 * q^90 + 18 * q^91 - 21 * q^92 - 17 * q^93 + 6 * q^94 + 10 * q^95 - 20 * q^96 + 48 * q^97 + 14 * q^98 + 3 * q^99

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