LMFDB - Embedded newform 6018.2.a.p.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6018,2,Mod(1,6018)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6018, 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("6018.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6018 = 2 \cdot 3 \cdot 17 \cdot 59 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6018.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:	$48.0539719364$
Analytic rank:	$0$
Dimension:	$5$
Coefficient field:	5.5.1668357.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{5} - x^{4} - 11x^{3} + x^{2} + 17x - 2 $ x^5 - x^4 - 11x^3 + x^2 + 17x - 2
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$3.61712$ of defining polynomial
Character	$\chi$	$=$	6018.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +1.96737 q^{5} -1.00000 q^{6} -3.61712 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +1.96737 q^{5} -1.00000 q^{6} -3.61712 q^{7} -1.00000 q^{8} +1.00000 q^{9} -1.96737 q^{10} +0.322205 q^{11} +1.00000 q^{12} +2.69718 q^{13} +3.61712 q^{14} +1.96737 q^{15} +1.00000 q^{16} -1.00000 q^{17} -1.00000 q^{18} -3.90670 q^{19} +1.96737 q^{20} -3.61712 q^{21} -0.322205 q^{22} -4.79401 q^{23} -1.00000 q^{24} -1.12946 q^{25} -2.69718 q^{26} +1.00000 q^{27} -3.61712 q^{28} -0.708609 q^{29} -1.96737 q^{30} +6.38640 q^{31} -1.00000 q^{32} +0.322205 q^{33} +1.00000 q^{34} -7.11622 q^{35} +1.00000 q^{36} -8.47640 q^{37} +3.90670 q^{38} +2.69718 q^{39} -1.96737 q^{40} +1.55976 q^{41} +3.61712 q^{42} +10.0935 q^{43} +0.322205 q^{44} +1.96737 q^{45} +4.79401 q^{46} +12.0456 q^{47} +1.00000 q^{48} +6.08358 q^{49} +1.12946 q^{50} -1.00000 q^{51} +2.69718 q^{52} -1.01479 q^{53} -1.00000 q^{54} +0.633897 q^{55} +3.61712 q^{56} -3.90670 q^{57} +0.708609 q^{58} -1.00000 q^{59} +1.96737 q^{60} +10.7660 q^{61} -6.38640 q^{62} -3.61712 q^{63} +1.00000 q^{64} +5.30635 q^{65} -0.322205 q^{66} +12.2702 q^{67} -1.00000 q^{68} -4.79401 q^{69} +7.11622 q^{70} +7.07215 q^{71} -1.00000 q^{72} +3.18832 q^{73} +8.47640 q^{74} -1.12946 q^{75} -3.90670 q^{76} -1.16546 q^{77} -2.69718 q^{78} -0.0479121 q^{79} +1.96737 q^{80} +1.00000 q^{81} -1.55976 q^{82} +0.102752 q^{83} -3.61712 q^{84} -1.96737 q^{85} -10.0935 q^{86} -0.708609 q^{87} -0.322205 q^{88} +3.15216 q^{89} -1.96737 q^{90} -9.75603 q^{91} -4.79401 q^{92} +6.38640 q^{93} -12.0456 q^{94} -7.68591 q^{95} -1.00000 q^{96} +2.11803 q^{97} -6.08358 q^{98} +0.322205 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 5 q - 5 q^{2} + 5 q^{3} + 5 q^{4} - q^{5} - 5 q^{6} - q^{7} - 5 q^{8} + 5 q^{9}+O(q^{10}) $ 5 * q - 5 * q^2 + 5 * q^3 + 5 * q^4 - q^5 - 5 * q^6 - q^7 - 5 * q^8 + 5 * q^9	\( 5 q - 5 q^{2} + 5 q^{3} + 5 q^{4} - q^{5} - 5 q^{6} - q^{7} - 5 q^{8} + 5 q^{9} + q^{10} + 6 q^{11} + 5 q^{12} - 2 q^{13} + q^{14} - q^{15} + 5 q^{16} - 5 q^{17} - 5 q^{18} + 4 q^{19} - q^{20} - q^{21} - 6 q^{22} + 12 q^{23} - 5 q^{24} + 4 q^{25} + 2 q^{26} + 5 q^{27} - q^{28} + 19 q^{29} + q^{30} + 5 q^{31} - 5 q^{32} + 6 q^{33} + 5 q^{34} - 4 q^{35} + 5 q^{36} - 11 q^{37} - 4 q^{38} - 2 q^{39} + q^{40} + 6 q^{41} + q^{42} + 2 q^{43} + 6 q^{44} - q^{45} - 12 q^{46} + 22 q^{47} + 5 q^{48} - 12 q^{49} - 4 q^{50} - 5 q^{51} - 2 q^{52} + 15 q^{53} - 5 q^{54} - 36 q^{55} + q^{56} + 4 q^{57} - 19 q^{58} - 5 q^{59} - q^{60} + 16 q^{61} - 5 q^{62} - q^{63} + 5 q^{64} - 2 q^{65} - 6 q^{66} + 25 q^{67} - 5 q^{68} + 12 q^{69} + 4 q^{70} - 5 q^{72} - 10 q^{73} + 11 q^{74} + 4 q^{75} + 4 q^{76} + 6 q^{77} + 2 q^{78} + 10 q^{79} - q^{80} + 5 q^{81} - 6 q^{82} + 19 q^{83} - q^{84} + q^{85} - 2 q^{86} + 19 q^{87} - 6 q^{88} + 23 q^{89} + q^{90} - 17 q^{91} + 12 q^{92} + 5 q^{93} - 22 q^{94} + q^{95} - 5 q^{96} + 8 q^{97} + 12 q^{98} + 6 q^{99}+O(q^{100}) \) 5 * q - 5 * q^2 + 5 * q^3 + 5 * q^4 - q^5 - 5 * q^6 - q^7 - 5 * q^8 + 5 * q^9 + q^10 + 6 * q^11 + 5 * q^12 - 2 * q^13 + q^14 - q^15 + 5 * q^16 - 5 * q^17 - 5 * q^18 + 4 * q^19 - q^20 - q^21 - 6 * q^22 + 12 * q^23 - 5 * q^24 + 4 * q^25 + 2 * q^26 + 5 * q^27 - q^28 + 19 * q^29 + q^30 + 5 * q^31 - 5 * q^32 + 6 * q^33 + 5 * q^34 - 4 * q^35 + 5 * q^36 - 11 * q^37 - 4 * q^38 - 2 * q^39 + q^40 + 6 * q^41 + q^42 + 2 * q^43 + 6 * q^44 - q^45 - 12 * q^46 + 22 * q^47 + 5 * q^48 - 12 * q^49 - 4 * q^50 - 5 * q^51 - 2 * q^52 + 15 * q^53 - 5 * q^54 - 36 * q^55 + q^56 + 4 * q^57 - 19 * q^58 - 5 * q^59 - q^60 + 16 * q^61 - 5 * q^62 - q^63 + 5 * q^64 - 2 * q^65 - 6 * q^66 + 25 * q^67 - 5 * q^68 + 12 * q^69 + 4 * q^70 - 5 * q^72 - 10 * q^73 + 11 * q^74 + 4 * q^75 + 4 * q^76 + 6 * q^77 + 2 * q^78 + 10 * q^79 - q^80 + 5 * q^81 - 6 * q^82 + 19 * q^83 - q^84 + q^85 - 2 * q^86 + 19 * q^87 - 6 * q^88 + 23 * q^89 + q^90 - 17 * q^91 + 12 * q^92 + 5 * q^93 - 22 * q^94 + q^95 - 5 * q^96 + 8 * q^97 + 12 * q^98 + 6 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	1.00000	0.500000
$5$	1.96737	0.879834	0.439917	−	0.898038i	$-0.355008\pi$
$5$	1.96737	0.879834	0.439917	+	0.898038i	$0.355008\pi$
$6$	−1.00000	−0.408248
$7$	−3.61712	−1.36714	−0.683572	−	0.729883i	$-0.739575\pi$
$7$	−3.61712	−1.36714	−0.683572	+	0.729883i	$0.739575\pi$
$8$	−1.00000	−0.353553
$9$	1.00000	0.333333
$10$	−1.96737	−0.622137
$11$	0.322205	0.0971486	0.0485743	−	0.998820i	$-0.484532\pi$
$11$	0.322205	0.0971486	0.0485743	+	0.998820i	$0.484532\pi$
$12$	1.00000	0.288675
$13$	2.69718	0.748063	0.374032	−	0.927416i	$-0.377975\pi$
$13$	2.69718	0.748063	0.374032	+	0.927416i	$0.377975\pi$
$14$	3.61712	0.966717
$15$	1.96737	0.507972
$16$	1.00000	0.250000
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	−1.00000	−0.235702
$19$	−3.90670	−0.896258	−0.448129	−	0.893969i	$-0.647909\pi$
$19$	−3.90670	−0.896258	−0.448129	+	0.893969i	$0.647909\pi$
$20$	1.96737	0.439917
$21$	−3.61712	−0.789321
$22$	−0.322205	−0.0686944
$23$	−4.79401	−0.999620	−0.499810	−	0.866135i	$-0.666597\pi$
$23$	−4.79401	−0.999620	−0.499810	+	0.866135i	$0.666597\pi$
$24$	−1.00000	−0.204124
$25$	−1.12946	−0.225892
$26$	−2.69718	−0.528961
$27$	1.00000	0.192450
$28$	−3.61712	−0.683572
$29$	−0.708609	−0.131585	−0.0657927	−	0.997833i	$-0.520958\pi$
$29$	−0.708609	−0.131585	−0.0657927	+	0.997833i	$0.520958\pi$
$30$	−1.96737	−0.359191
$31$	6.38640	1.14703	0.573516	−	0.819194i	$-0.305579\pi$
$31$	6.38640	1.14703	0.573516	+	0.819194i	$0.305579\pi$
$32$	−1.00000	−0.176777
$33$	0.322205	0.0560888
$34$	1.00000	0.171499
$35$	−7.11622	−1.20286
$36$	1.00000	0.166667
$37$	−8.47640	−1.39351	−0.696755	−	0.717309i	$-0.745374\pi$
$37$	−8.47640	−1.39351	−0.696755	+	0.717309i	$0.745374\pi$
$38$	3.90670	0.633750
$39$	2.69718	0.431894
$40$	−1.96737	−0.311068
$41$	1.55976	0.243594	0.121797	−	0.992555i	$-0.461134\pi$
$41$	1.55976	0.243594	0.121797	+	0.992555i	$0.461134\pi$
$42$	3.61712	0.558134
$43$	10.0935	1.53925	0.769624	−	0.638498i	$-0.220444\pi$
$43$	10.0935	1.53925	0.769624	+	0.638498i	$0.220444\pi$
$44$	0.322205	0.0485743
$45$	1.96737	0.293278
$46$	4.79401	0.706838
$47$	12.0456	1.75703	0.878516	−	0.477712i	$-0.158534\pi$
$47$	12.0456	1.75703	0.878516	+	0.477712i	$0.158534\pi$
$48$	1.00000	0.144338
$49$	6.08358	0.869083
$50$	1.12946	0.159730
$51$	−1.00000	−0.140028
$52$	2.69718	0.374032
$53$	−1.01479	−0.139393	−0.0696963	−	0.997568i	$-0.522203\pi$
$53$	−1.01479	−0.139393	−0.0696963	+	0.997568i	$0.522203\pi$
$54$	−1.00000	−0.136083
$55$	0.633897	0.0854746
$56$	3.61712	0.483358
$57$	−3.90670	−0.517455
$58$	0.708609	0.0930449
$59$	−1.00000	−0.130189
$59$	−1.00000	−0.130189
$60$	1.96737	0.253986
$61$	10.7660	1.37844	0.689221	−	0.724552i	$-0.257953\pi$
$61$	10.7660	1.37844	0.689221	+	0.724552i	$0.257953\pi$
$62$	−6.38640	−0.811074
$63$	−3.61712	−0.455715
$64$	1.00000	0.125000
$65$	5.30635	0.658171
$66$	−0.322205	−0.0396608
$67$	12.2702	1.49905	0.749524	−	0.661977i	$-0.230282\pi$
$67$	12.2702	1.49905	0.749524	+	0.661977i	$0.230282\pi$
$68$	−1.00000	−0.121268
$69$	−4.79401	−0.577131
$70$	7.11622	0.850550
$71$	7.07215	0.839310	0.419655	−	0.907684i	$-0.362151\pi$
$71$	7.07215	0.839310	0.419655	+	0.907684i	$0.362151\pi$
$72$	−1.00000	−0.117851
$73$	3.18832	0.373164	0.186582	−	0.982439i	$-0.440259\pi$
$73$	3.18832	0.373164	0.186582	+	0.982439i	$0.440259\pi$
$74$	8.47640	0.985361
$75$	−1.12946	−0.130419
$76$	−3.90670	−0.448129
$77$	−1.16546	−0.132816
$78$	−2.69718	−0.305396
$79$	−0.0479121	−0.00539053	−0.00269526	−	0.999996i	$-0.500858\pi$
$79$	−0.0479121	−0.00539053	−0.00269526	+	0.999996i	$0.500858\pi$
$80$	1.96737	0.219958
$81$	1.00000	0.111111
$82$	−1.55976	−0.172247
$83$	0.102752	0.0112784	0.00563922	−	0.999984i	$-0.498205\pi$
$83$	0.102752	0.0112784	0.00563922	+	0.999984i	$0.498205\pi$
$84$	−3.61712	−0.394661
$85$	−1.96737	−0.213391
$86$	−10.0935	−1.08841
$87$	−0.708609	−0.0759709
$88$	−0.322205	−0.0343472
$89$	3.15216	0.334128	0.167064	−	0.985946i	$-0.446571\pi$
$89$	3.15216	0.334128	0.167064	+	0.985946i	$0.446571\pi$
$90$	−1.96737	−0.207379
$91$	−9.75603	−1.02271
$92$	−4.79401	−0.499810
$93$	6.38640	0.662239
$94$	−12.0456	−1.24241
$95$	−7.68591	−0.788558
$96$	−1.00000	−0.102062
$97$	2.11803	0.215054	0.107527	−	0.994202i	$-0.465707\pi$
$97$	2.11803	0.215054	0.107527	+	0.994202i	$0.465707\pi$
$98$	−6.08358	−0.614535
$99$	0.322205	0.0323829
$100$	−1.12946	−0.112946
$101$	−3.31580	−0.329934	−0.164967	−	0.986299i	$-0.552752\pi$
$101$	−3.31580	−0.329934	−0.164967	+	0.986299i	$0.552752\pi$
$102$	1.00000	0.0990148
$103$	−5.84405	−0.575831	−0.287916	−	0.957656i	$-0.592962\pi$
$103$	−5.84405	−0.575831	−0.287916	+	0.957656i	$0.592962\pi$
$104$	−2.69718	−0.264480
$105$	−7.11622	−0.694471
$106$	1.01479	0.0985655
$107$	15.5098	1.49939	0.749694	−	0.661785i	$-0.230201\pi$
$107$	15.5098	1.49939	0.749694	+	0.661785i	$0.230201\pi$
$108$	1.00000	0.0962250
$109$	6.44376	0.617201	0.308600	−	0.951192i	$-0.400139\pi$
$109$	6.44376	0.617201	0.308600	+	0.951192i	$0.400139\pi$
$110$	−0.633897	−0.0604397
$111$	−8.47640	−0.804544
$112$	−3.61712	−0.341786
$113$	15.0555	1.41631	0.708153	−	0.706059i	$-0.249529\pi$
$113$	15.0555	1.41631	0.708153	+	0.706059i	$0.249529\pi$
$114$	3.90670	0.365896
$115$	−9.43158	−0.879500
$116$	−0.708609	−0.0657927
$117$	2.69718	0.249354
$118$	1.00000	0.0920575
$119$	3.61712	0.331581
$120$	−1.96737	−0.179595
$121$	−10.8962	−0.990562
$122$	−10.7660	−0.974705
$123$	1.55976	0.140639
$124$	6.38640	0.573516
$125$	−12.0589	−1.07858
$126$	3.61712	0.322239
$127$	19.4634	1.72710	0.863549	−	0.504264i	$-0.168236\pi$
$127$	19.4634	1.72710	0.863549	+	0.504264i	$0.168236\pi$
$128$	−1.00000	−0.0883883
$129$	10.0935	0.888685
$130$	−5.30635	−0.465397
$131$	−6.93292	−0.605732	−0.302866	−	0.953033i	$-0.597943\pi$
$131$	−6.93292	−0.605732	−0.302866	+	0.953033i	$0.597943\pi$
$132$	0.322205	0.0280444
$133$	14.1310	1.22531
$134$	−12.2702	−1.05999
$135$	1.96737	0.169324
$136$	1.00000	0.0857493
$137$	−16.3204	−1.39435	−0.697175	−	0.716901i	$-0.745560\pi$
$137$	−16.3204	−1.39435	−0.697175	+	0.716901i	$0.745560\pi$
$138$	4.79401	0.408093
$139$	1.77264	0.150354	0.0751769	−	0.997170i	$-0.476048\pi$
$139$	1.77264	0.150354	0.0751769	+	0.997170i	$0.476048\pi$
$140$	−7.11622	−0.601430
$141$	12.0456	1.01442
$142$	−7.07215	−0.593482
$143$	0.869046	0.0726733
$144$	1.00000	0.0833333
$145$	−1.39410	−0.115773
$146$	−3.18832	−0.263867
$147$	6.08358	0.501766
$148$	−8.47640	−0.696755
$149$	−1.92331	−0.157564	−0.0787818	−	0.996892i	$-0.525103\pi$
$149$	−1.92331	−0.157564	−0.0787818	+	0.996892i	$0.525103\pi$
$150$	1.12946	0.0922201
$151$	19.1004	1.55437	0.777185	−	0.629273i	$-0.216647\pi$
$151$	19.1004	1.55437	0.777185	+	0.629273i	$0.216647\pi$
$152$	3.90670	0.316875
$153$	−1.00000	−0.0808452
$154$	1.16546	0.0939152
$155$	12.5644	1.00920
$156$	2.69718	0.215947
$157$	−3.76548	−0.300518	−0.150259	−	0.988647i	$-0.548011\pi$
$157$	−3.76548	−0.300518	−0.150259	+	0.988647i	$0.548011\pi$
$158$	0.0479121	0.00381168
$159$	−1.01479	−0.0804784
$160$	−1.96737	−0.155534
$161$	17.3405	1.36662
$162$	−1.00000	−0.0785674
$163$	−4.05277	−0.317437	−0.158719	−	0.987324i	$-0.550736\pi$
$163$	−4.05277	−0.317437	−0.158719	+	0.987324i	$0.550736\pi$
$164$	1.55976	0.121797
$165$	0.633897	0.0493488
$166$	−0.102752	−0.00797507
$167$	8.12354	0.628618	0.314309	−	0.949321i	$-0.398227\pi$
$167$	8.12354	0.628618	0.314309	+	0.949321i	$0.398227\pi$
$168$	3.61712	0.279067
$169$	−5.72522	−0.440401
$170$	1.96737	0.150890
$171$	−3.90670	−0.298753
$172$	10.0935	0.769624
$173$	12.3655	0.940133	0.470067	−	0.882631i	$-0.344230\pi$
$173$	12.3655	0.940133	0.470067	+	0.882631i	$0.344230\pi$
$174$	0.708609	0.0537195
$175$	4.08540	0.308827
$176$	0.322205	0.0242872
$177$	−1.00000	−0.0751646
$178$	−3.15216	−0.236264
$179$	16.6961	1.24793	0.623963	−	0.781454i	$-0.285522\pi$
$179$	16.6961	1.24793	0.623963	+	0.781454i	$0.285522\pi$
$180$	1.96737	0.146639
$181$	−26.2946	−1.95447	−0.977233	−	0.212169i	$-0.931947\pi$
$181$	−26.2946	−1.95447	−0.977233	+	0.212169i	$0.931947\pi$
$182$	9.75603	0.723165
$183$	10.7660	0.795843
$184$	4.79401	0.353419
$185$	−16.6762	−1.22606
$186$	−6.38640	−0.468274
$187$	−0.322205	−0.0235620
$188$	12.0456	0.878516
$189$	−3.61712	−0.263107
$190$	7.68591	0.557595
$191$	5.70129	0.412531	0.206265	−	0.978496i	$-0.433869\pi$
$191$	5.70129	0.412531	0.206265	+	0.978496i	$0.433869\pi$
$192$	1.00000	0.0721688
$193$	6.01143	0.432712	0.216356	−	0.976315i	$-0.430583\pi$
$193$	6.01143	0.432712	0.216356	+	0.976315i	$0.430583\pi$
$194$	−2.11803	−0.152066
$195$	5.30635	0.379995
$196$	6.08358	0.434542
$197$	8.44024	0.601342	0.300671	−	0.953728i	$-0.402789\pi$
$197$	8.44024	0.601342	0.300671	+	0.953728i	$0.402789\pi$
$198$	−0.322205	−0.0228981
$199$	−10.3059	−0.730563	−0.365282	−	0.930897i	$-0.619027\pi$
$199$	−10.3059	−0.730563	−0.365282	+	0.930897i	$0.619027\pi$
$200$	1.12946	0.0798650
$201$	12.2702	0.865476
$202$	3.31580	0.233299
$203$	2.56313	0.179896
$204$	−1.00000	−0.0700140
$205$	3.06863	0.214322
$206$	5.84405	0.407174
$207$	−4.79401	−0.333207
$208$	2.69718	0.187016
$209$	−1.25876	−0.0870702
$210$	7.11622	0.491066
$211$	−8.45060	−0.581763	−0.290882	−	0.956759i	$-0.593949\pi$
$211$	−8.45060	−0.581763	−0.290882	+	0.956759i	$0.593949\pi$
$212$	−1.01479	−0.0696963
$213$	7.07215	0.484576
$214$	−15.5098	−1.06023
$215$	19.8577	1.35428
$216$	−1.00000	−0.0680414
$217$	−23.1004	−1.56816
$218$	−6.44376	−0.436427
$219$	3.18832	0.215446
$220$	0.633897	0.0427373
$221$	−2.69718	−0.181432
$222$	8.47640	0.568898
$223$	23.4257	1.56870	0.784349	−	0.620320i	$-0.212997\pi$
$223$	23.4257	1.56870	0.784349	+	0.620320i	$0.212997\pi$
$224$	3.61712	0.241679
$225$	−1.12946	−0.0752974
$226$	−15.0555	−1.00148
$227$	23.5348	1.56206	0.781030	−	0.624493i	$-0.214694\pi$
$227$	23.5348	1.56206	0.781030	+	0.624493i	$0.214694\pi$
$228$	−3.90670	−0.258727
$229$	−29.8732	−1.97408	−0.987039	−	0.160481i	$-0.948695\pi$
$229$	−29.8732	−1.97408	−0.987039	+	0.160481i	$0.948695\pi$
$230$	9.43158	0.621900
$231$	−1.16546	−0.0766814
$232$	0.708609	0.0465225
$233$	13.5825	0.889820	0.444910	−	0.895575i	$-0.353236\pi$
$233$	13.5825	0.889820	0.444910	+	0.895575i	$0.353236\pi$
$234$	−2.69718	−0.176320
$235$	23.6981	1.54590
$236$	−1.00000	−0.0650945
$237$	−0.0479121	−0.00311222
$238$	−3.61712	−0.234463
$239$	5.64131	0.364906	0.182453	−	0.983215i	$-0.441596\pi$
$239$	5.64131	0.364906	0.182453	+	0.983215i	$0.441596\pi$
$240$	1.96737	0.126993
$241$	22.6870	1.46140	0.730698	−	0.682701i	$-0.239195\pi$
$241$	22.6870	1.46140	0.730698	+	0.682701i	$0.239195\pi$
$242$	10.8962	0.700433
$243$	1.00000	0.0641500
$244$	10.7660	0.689221
$245$	11.9687	0.764649
$246$	−1.55976	−0.0994468
$247$	−10.5371	−0.670458
$248$	−6.38640	−0.405537
$249$	0.102752	0.00651162
$250$	12.0589	0.762672
$251$	−6.93425	−0.437686	−0.218843	−	0.975760i	$-0.570228\pi$
$251$	−6.93425	−0.437686	−0.218843	+	0.975760i	$0.570228\pi$
$252$	−3.61712	−0.227857
$253$	−1.54466	−0.0971117
$254$	−19.4634	−1.22124
$255$	−1.96737	−0.123201
$256$	1.00000	0.0625000
$257$	9.25097	0.577059	0.288530	−	0.957471i	$-0.406834\pi$
$257$	9.25097	0.577059	0.288530	+	0.957471i	$0.406834\pi$
$258$	−10.0935	−0.628395
$259$	30.6602	1.90513
$260$	5.30635	0.329086
$261$	−0.708609	−0.0438618
$262$	6.93292	0.428317
$263$	−1.77066	−0.109184	−0.0545919	−	0.998509i	$-0.517386\pi$
$263$	−1.77066	−0.109184	−0.0545919	+	0.998509i	$0.517386\pi$
$264$	−0.322205	−0.0198304
$265$	−1.99647	−0.122642
$266$	−14.1310	−0.866428
$267$	3.15216	0.192909
$268$	12.2702	0.749524
$269$	1.30106	0.0793269	0.0396634	−	0.999213i	$-0.487371\pi$
$269$	1.30106	0.0793269	0.0396634	+	0.999213i	$0.487371\pi$
$270$	−1.96737	−0.119730
$271$	7.25086	0.440458	0.220229	−	0.975448i	$-0.429319\pi$
$271$	7.25086	0.440458	0.220229	+	0.975448i	$0.429319\pi$
$272$	−1.00000	−0.0606339
$273$	−9.75603	−0.590462
$274$	16.3204	0.985954
$275$	−0.363919	−0.0219451
$276$	−4.79401	−0.288565
$277$	12.3108	0.739683	0.369841	−	0.929095i	$-0.379412\pi$
$277$	12.3108	0.739683	0.369841	+	0.929095i	$0.379412\pi$
$278$	−1.77264	−0.106316
$279$	6.38640	0.382344
$280$	7.11622	0.425275
$281$	−22.8921	−1.36563	−0.682813	−	0.730593i	$-0.739244\pi$
$281$	−22.8921	−1.36563	−0.682813	+	0.730593i	$0.739244\pi$
$282$	−12.0456	−0.717306
$283$	0.128131	0.00761662	0.00380831	−	0.999993i	$-0.498788\pi$
$283$	0.128131	0.00761662	0.00380831	+	0.999993i	$0.498788\pi$
$284$	7.07215	0.419655
$285$	−7.68591	−0.455274
$286$	−0.869046	−0.0513878
$287$	−5.64185	−0.333028
$288$	−1.00000	−0.0589256
$289$	1.00000	0.0588235
$290$	1.39410	0.0818641
$291$	2.11803	0.124161
$292$	3.18832	0.186582
$293$	−21.9385	−1.28166	−0.640830	−	0.767683i	$-0.721410\pi$
$293$	−21.9385	−1.28166	−0.640830	+	0.767683i	$0.721410\pi$
$294$	−6.08358	−0.354802
$295$	−1.96737	−0.114545
$296$	8.47640	0.492681
$297$	0.322205	0.0186963
$298$	1.92331	0.111414
$299$	−12.9303	−0.747779
$300$	−1.12946	−0.0652095
$301$	−36.5095	−2.10437
$302$	−19.1004	−1.09911
$303$	−3.31580	−0.190488
$304$	−3.90670	−0.224064
$305$	21.1806	1.21280
$306$	1.00000	0.0571662
$307$	−12.9495	−0.739066	−0.369533	−	0.929218i	$-0.620482\pi$
$307$	−12.9495	−0.739066	−0.369533	+	0.929218i	$0.620482\pi$
$308$	−1.16546	−0.0664081
$309$	−5.84405	−0.332456
$310$	−12.5644	−0.713611
$311$	26.8328	1.52155	0.760774	−	0.649017i	$-0.224820\pi$
$311$	26.8328	1.52155	0.760774	+	0.649017i	$0.224820\pi$
$312$	−2.69718	−0.152698
$313$	−16.8957	−0.955001	−0.477501	−	0.878631i	$-0.658457\pi$
$313$	−16.8957	−0.955001	−0.477501	+	0.878631i	$0.658457\pi$
$314$	3.76548	0.212499
$315$	−7.11622	−0.400953
$316$	−0.0479121	−0.00269526
$317$	21.1631	1.18864	0.594318	−	0.804230i	$-0.297422\pi$
$317$	21.1631	1.18864	0.594318	+	0.804230i	$0.297422\pi$
$318$	1.01479	0.0569068
$319$	−0.228318	−0.0127833
$320$	1.96737	0.109979
$321$	15.5098	0.865672
$322$	−17.3405	−0.966350
$323$	3.90670	0.217374
$324$	1.00000	0.0555556
$325$	−3.04636	−0.168982
$326$	4.05277	0.224462
$327$	6.44376	0.356341
$328$	−1.55976	−0.0861235
$329$	−43.5705	−2.40212
$330$	−0.633897	−0.0348949
$331$	−27.4693	−1.50985	−0.754924	−	0.655812i	$-0.772326\pi$
$331$	−27.4693	−1.50985	−0.754924	+	0.655812i	$0.772326\pi$
$332$	0.102752	0.00563922
$333$	−8.47640	−0.464504
$334$	−8.12354	−0.444500
$335$	24.1401	1.31891
$336$	−3.61712	−0.197330
$337$	−12.5651	−0.684465	−0.342232	−	0.939615i	$-0.611183\pi$
$337$	−12.5651	−0.684465	−0.342232	+	0.939615i	$0.611183\pi$
$338$	5.72522	0.311411
$339$	15.0555	0.817705
$340$	−1.96737	−0.106696
$341$	2.05773	0.111433
$342$	3.90670	0.211250
$343$	3.31479	0.178982
$344$	−10.0935	−0.544206
$345$	−9.43158	−0.507779
$346$	−12.3655	−0.664775
$347$	−7.80090	−0.418774	−0.209387	−	0.977833i	$-0.567147\pi$
$347$	−7.80090	−0.418774	−0.209387	+	0.977833i	$0.567147\pi$
$348$	−0.708609	−0.0379854
$349$	−25.2540	−1.35181	−0.675907	−	0.736987i	$-0.736248\pi$
$349$	−25.2540	−1.35181	−0.675907	+	0.736987i	$0.736248\pi$
$350$	−4.08540	−0.218374
$351$	2.69718	0.143965
$352$	−0.322205	−0.0171736
$353$	4.56034	0.242722	0.121361	−	0.992608i	$-0.461274\pi$
$353$	4.56034	0.242722	0.121361	+	0.992608i	$0.461274\pi$
$354$	1.00000	0.0531494
$355$	13.9135	0.738454
$356$	3.15216	0.167064
$357$	3.61712	0.191438
$358$	−16.6961	−0.882417
$359$	14.4272	0.761436	0.380718	−	0.924691i	$-0.375677\pi$
$359$	14.4272	0.761436	0.380718	+	0.924691i	$0.375677\pi$
$360$	−1.96737	−0.103689
$361$	−3.73771	−0.196722
$362$	26.2946	1.38202
$363$	−10.8962	−0.571901
$364$	−9.75603	−0.511355
$365$	6.27259	0.328322
$366$	−10.7660	−0.562746
$367$	−24.9628	−1.30305	−0.651525	−	0.758628i	$-0.725870\pi$
$367$	−24.9628	−1.30305	−0.651525	+	0.758628i	$0.725870\pi$
$368$	−4.79401	−0.249905
$369$	1.55976	0.0811980
$370$	16.6762	0.866954
$371$	3.67063	0.190570
$372$	6.38640	0.331120
$373$	4.05351	0.209883	0.104941	−	0.994478i	$-0.466535\pi$
$373$	4.05351	0.209883	0.104941	+	0.994478i	$0.466535\pi$
$374$	0.322205	0.0166608
$375$	−12.0589	−0.622719
$376$	−12.0456	−0.621205
$377$	−1.91125	−0.0984342
$378$	3.61712	0.186045
$379$	2.67315	0.137310	0.0686552	−	0.997640i	$-0.478129\pi$
$379$	2.67315	0.137310	0.0686552	+	0.997640i	$0.478129\pi$
$380$	−7.68591	−0.394279
$381$	19.4634	0.997141
$382$	−5.70129	−0.291703
$383$	12.6525	0.646512	0.323256	−	0.946312i	$-0.395223\pi$
$383$	12.6525	0.646512	0.323256	+	0.946312i	$0.395223\pi$
$384$	−1.00000	−0.0510310
$385$	−2.29288	−0.116856
$386$	−6.01143	−0.305974
$387$	10.0935	0.513082
$388$	2.11803	0.107527
$389$	19.4285	0.985066	0.492533	−	0.870294i	$-0.336071\pi$
$389$	19.4285	0.985066	0.492533	+	0.870294i	$0.336071\pi$
$390$	−5.30635	−0.268697
$391$	4.79401	0.242443
$392$	−6.08358	−0.307267
$393$	−6.93292	−0.349720
$394$	−8.44024	−0.425213
$395$	−0.0942607	−0.00474277
$396$	0.322205	0.0161914
$397$	−12.0808	−0.606318	−0.303159	−	0.952940i	$-0.598041\pi$
$397$	−12.0808	−0.606318	−0.303159	+	0.952940i	$0.598041\pi$
$398$	10.3059	0.516586
$399$	14.1310	0.707435
$400$	−1.12946	−0.0564731
$401$	−6.06618	−0.302930	−0.151465	−	0.988463i	$-0.548399\pi$
$401$	−6.06618	−0.302930	−0.151465	+	0.988463i	$0.548399\pi$
$402$	−12.2702	−0.611984
$403$	17.2253	0.858052
$404$	−3.31580	−0.164967
$405$	1.96737	0.0977593
$406$	−2.56313	−0.127206
$407$	−2.73114	−0.135378
$408$	1.00000	0.0495074
$409$	29.2302	1.44534	0.722670	−	0.691194i	$-0.242915\pi$
$409$	29.2302	1.44534	0.722670	+	0.691194i	$0.242915\pi$
$410$	−3.06863	−0.151549
$411$	−16.3204	−0.805028
$412$	−5.84405	−0.287916
$413$	3.61712	0.177987
$414$	4.79401	0.235613
$415$	0.202150	0.00992316
$416$	−2.69718	−0.132240
$417$	1.77264	0.0868068
$418$	1.25876	0.0615679
$419$	7.51927	0.367341	0.183670	−	0.982988i	$-0.441202\pi$
$419$	7.51927	0.367341	0.183670	+	0.982988i	$0.441202\pi$
$420$	−7.11622	−0.347236
$421$	−4.10410	−0.200022	−0.100011	−	0.994986i	$-0.531888\pi$
$421$	−4.10410	−0.200022	−0.100011	+	0.994986i	$0.531888\pi$
$422$	8.45060	0.411369
$423$	12.0456	0.585678
$424$	1.01479	0.0492827
$425$	1.12946	0.0547869
$426$	−7.07215	−0.342647
$427$	−38.9418	−1.88453
$428$	15.5098	0.749694
$429$	0.869046	0.0419579
$430$	−19.8577	−0.957622
$431$	−25.4463	−1.22571	−0.612853	−	0.790197i	$-0.709978\pi$
$431$	−25.4463	−1.22571	−0.612853	+	0.790197i	$0.709978\pi$
$432$	1.00000	0.0481125
$433$	26.8467	1.29017	0.645086	−	0.764110i	$-0.276822\pi$
$433$	26.8467	1.29017	0.645086	+	0.764110i	$0.276822\pi$
$434$	23.1004	1.10886
$435$	−1.39410	−0.0668418
$436$	6.44376	0.308600
$437$	18.7287	0.895917
$438$	−3.18832	−0.152344
$439$	−2.80058	−0.133664	−0.0668322	−	0.997764i	$-0.521289\pi$
$439$	−2.80058	−0.133664	−0.0668322	+	0.997764i	$0.521289\pi$
$440$	−0.633897	−0.0302198
$441$	6.08358	0.289694
$442$	2.69718	0.128292
$443$	−11.2291	−0.533509	−0.266755	−	0.963765i	$-0.585951\pi$
$443$	−11.2291	−0.533509	−0.266755	+	0.963765i	$0.585951\pi$
$444$	−8.47640	−0.402272
$445$	6.20145	0.293977
$446$	−23.4257	−1.10924
$447$	−1.92331	−0.0909693
$448$	−3.61712	−0.170893
$449$	−5.64645	−0.266472	−0.133236	−	0.991084i	$-0.542537\pi$
$449$	−5.64645	−0.266472	−0.133236	+	0.991084i	$0.542537\pi$
$450$	1.12946	0.0532433
$451$	0.502564	0.0236648
$452$	15.0555	0.708153
$453$	19.1004	0.897416
$454$	−23.5348	−1.10454
$455$	−19.1937	−0.899815
$456$	3.90670	0.182948
$457$	−25.8898	−1.21108	−0.605538	−	0.795817i	$-0.707042\pi$
$457$	−25.8898	−1.21108	−0.605538	+	0.795817i	$0.707042\pi$
$458$	29.8732	1.39588
$459$	−1.00000	−0.0466760
$460$	−9.43158	−0.439750
$461$	−12.3982	−0.577440	−0.288720	−	0.957414i	$-0.593230\pi$
$461$	−12.3982	−0.577440	−0.288720	+	0.957414i	$0.593230\pi$
$462$	1.16546	0.0542220
$463$	−23.5345	−1.09374	−0.546871	−	0.837217i	$-0.684181\pi$
$463$	−23.5345	−1.09374	−0.546871	+	0.837217i	$0.684181\pi$
$464$	−0.708609	−0.0328964
$465$	12.5644	0.582661
$466$	−13.5825	−0.629198
$467$	13.3905	0.619637	0.309818	−	0.950796i	$-0.399732\pi$
$467$	13.3905	0.619637	0.309818	+	0.950796i	$0.399732\pi$
$468$	2.69718	0.124677
$469$	−44.3830	−2.04942
$470$	−23.6981	−1.09311
$471$	−3.76548	−0.173504
$472$	1.00000	0.0460287
$473$	3.25219	0.149536
$474$	0.0479121	0.00220067
$475$	4.41246	0.202458
$476$	3.61712	0.165791
$477$	−1.01479	−0.0464642
$478$	−5.64131	−0.258028
$479$	26.8921	1.22873	0.614365	−	0.789022i	$-0.289412\pi$
$479$	26.8921	1.22873	0.614365	+	0.789022i	$0.289412\pi$
$480$	−1.96737	−0.0897977
$481$	−22.8624	−1.04243
$482$	−22.6870	−1.03336
$483$	17.3405	0.789021
$484$	−10.8962	−0.495281
$485$	4.16695	0.189211
$486$	−1.00000	−0.0453609
$487$	−16.0458	−0.727106	−0.363553	−	0.931574i	$-0.618436\pi$
$487$	−16.0458	−0.727106	−0.363553	+	0.931574i	$0.618436\pi$
$488$	−10.7660	−0.487353
$489$	−4.05277	−0.183273
$490$	−11.9687	−0.540689
$491$	33.1658	1.49675	0.748377	−	0.663274i	$-0.230833\pi$
$491$	33.1658	1.49675	0.748377	+	0.663274i	$0.230833\pi$
$492$	1.55976	0.0703195
$493$	0.708609	0.0319141
$494$	10.5371	0.474085
$495$	0.633897	0.0284915
$496$	6.38640	0.286758
$497$	−25.5809	−1.14746
$498$	−0.102752	−0.00460441
$499$	−19.1598	−0.857712	−0.428856	−	0.903373i	$-0.641083\pi$
$499$	−19.1598	−0.857712	−0.428856	+	0.903373i	$0.641083\pi$
$500$	−12.0589	−0.539291
$501$	8.12354	0.362933
$502$	6.93425	0.309491
$503$	5.88667	0.262474	0.131237	−	0.991351i	$-0.458105\pi$
$503$	5.88667	0.262474	0.131237	+	0.991351i	$0.458105\pi$
$504$	3.61712	0.161119
$505$	−6.52339	−0.290287
$506$	1.54466	0.0686683
$507$	−5.72522	−0.254266
$508$	19.4634	0.863549
$509$	−18.1966	−0.806550	−0.403275	−	0.915079i	$-0.632128\pi$
$509$	−18.1966	−0.806550	−0.403275	+	0.915079i	$0.632128\pi$
$510$	1.96737	0.0871165
$511$	−11.5325	−0.510169
$512$	−1.00000	−0.0441942
$513$	−3.90670	−0.172485
$514$	−9.25097	−0.408043
$515$	−11.4974	−0.506636
$516$	10.0935	0.444342
$517$	3.88116	0.170693
$518$	−30.6602	−1.34713
$519$	12.3655	0.542786
$520$	−5.30635	−0.232699
$521$	35.2454	1.54413	0.772064	−	0.635545i	$-0.219225\pi$
$521$	35.2454	1.54413	0.772064	+	0.635545i	$0.219225\pi$
$522$	0.708609	0.0310150
$523$	−13.7504	−0.601265	−0.300632	−	0.953740i	$-0.597198\pi$
$523$	−13.7504	−0.601265	−0.300632	+	0.953740i	$0.597198\pi$
$524$	−6.93292	−0.302866
$525$	4.08540	0.178302
$526$	1.77066	0.0772046
$527$	−6.38640	−0.278196
$528$	0.322205	0.0140222
$529$	−0.0174704	−0.000759583 0
$530$	1.99647	0.0867212
$531$	−1.00000	−0.0433963
$532$	14.1310	0.612657
$533$	4.20696	0.182224
$534$	−3.15216	−0.136407
$535$	30.5135	1.31921
$536$	−12.2702	−0.529994
$537$	16.6961	0.720491
$538$	−1.30106	−0.0560926
$539$	1.96016	0.0844302
$540$	1.96737	0.0846621
$541$	23.7807	1.02241	0.511206	−	0.859459i	$-0.329199\pi$
$541$	23.7807	1.02241	0.511206	+	0.859459i	$0.329199\pi$
$542$	−7.25086	−0.311451
$543$	−26.2946	−1.12841
$544$	1.00000	0.0428746
$545$	12.6773	0.543034
$546$	9.75603	0.417520
$547$	20.1274	0.860584	0.430292	−	0.902690i	$-0.358411\pi$
$547$	20.1274	0.860584	0.430292	+	0.902690i	$0.358411\pi$
$548$	−16.3204	−0.697175
$549$	10.7660	0.459480
$550$	0.363919	0.0155175
$551$	2.76832	0.117934
$552$	4.79401	0.204047
$553$	0.173304	0.00736963
$554$	−12.3108	−0.523035
$555$	−16.6762	−0.707865
$556$	1.77264	0.0751769
$557$	−1.30667	−0.0553654	−0.0276827	−	0.999617i	$-0.508813\pi$
$557$	−1.30667	−0.0553654	−0.0276827	+	0.999617i	$0.508813\pi$
$558$	−6.38640	−0.270358
$559$	27.2240	1.15145
$560$	−7.11622	−0.300715
$561$	−0.322205	−0.0136035
$562$	22.8921	0.965643
$563$	32.0223	1.34958	0.674790	−	0.738010i	$-0.264234\pi$
$563$	32.0223	1.34958	0.674790	+	0.738010i	$0.264234\pi$
$564$	12.0456	0.507212
$565$	29.6198	1.24611
$566$	−0.128131	−0.00538576
$567$	−3.61712	−0.151905
$568$	−7.07215	−0.296741
$569$	−30.1329	−1.26324	−0.631619	−	0.775279i	$-0.717609\pi$
$569$	−30.1329	−1.26324	−0.631619	+	0.775279i	$0.717609\pi$
$570$	7.68591	0.321928
$571$	−27.7915	−1.16304	−0.581519	−	0.813533i	$-0.697541\pi$
$571$	−27.7915	−1.16304	−0.581519	+	0.813533i	$0.697541\pi$
$572$	0.869046	0.0363366
$573$	5.70129	0.238175
$574$	5.64185	0.235486
$575$	5.41465	0.225806
$576$	1.00000	0.0416667
$577$	−18.7594	−0.780964	−0.390482	−	0.920611i	$-0.627692\pi$
$577$	−18.7594	−0.780964	−0.390482	+	0.920611i	$0.627692\pi$
$578$	−1.00000	−0.0415945
$579$	6.01143	0.249826
$580$	−1.39410	−0.0578867
$581$	−0.371665	−0.0154193
$582$	−2.11803	−0.0877953
$583$	−0.326972	−0.0135418
$584$	−3.18832	−0.131933
$585$	5.30635	0.219390
$586$	21.9385	0.906270
$587$	22.0372	0.909572	0.454786	−	0.890601i	$-0.349716\pi$
$587$	22.0372	0.909572	0.454786	+	0.890601i	$0.349716\pi$
$588$	6.08358	0.250883
$589$	−24.9497	−1.02804
$590$	1.96737	0.0809953
$591$	8.44024	0.347185
$592$	−8.47640	−0.348378
$593$	31.9702	1.31286	0.656428	−	0.754388i	$-0.272066\pi$
$593$	31.9702	1.31286	0.656428	+	0.754388i	$0.272066\pi$
$594$	−0.322205	−0.0132203
$595$	7.11622	0.291736
$596$	−1.92331	−0.0787818
$597$	−10.3059	−0.421791
$598$	12.9303	0.528760
$599$	36.8990	1.50765	0.753825	−	0.657075i	$-0.228206\pi$
$599$	36.8990	1.50765	0.753825	+	0.657075i	$0.228206\pi$
$600$	1.12946	0.0461101
$601$	29.8024	1.21567	0.607833	−	0.794065i	$-0.292039\pi$
$601$	29.8024	1.21567	0.607833	+	0.794065i	$0.292039\pi$
$602$	36.5095	1.48802
$603$	12.2702	0.499683
$604$	19.1004	0.777185
$605$	−21.4368	−0.871530
$606$	3.31580	0.134695
$607$	−5.56057	−0.225697	−0.112848	−	0.993612i	$-0.535997\pi$
$607$	−5.56057	−0.225697	−0.112848	+	0.993612i	$0.535997\pi$
$608$	3.90670	0.158438
$609$	2.56313	0.103863
$610$	−21.1806	−0.857579
$611$	32.4892	1.31437
$612$	−1.00000	−0.0404226
$613$	42.5174	1.71726	0.858630	−	0.512596i	$-0.171316\pi$
$613$	42.5174	1.71726	0.858630	+	0.512596i	$0.171316\pi$
$614$	12.9495	0.522599
$615$	3.06863	0.123739
$616$	1.16546	0.0469576
$617$	−9.21261	−0.370886	−0.185443	−	0.982655i	$-0.559372\pi$
$617$	−9.21261	−0.370886	−0.185443	+	0.982655i	$0.559372\pi$
$618$	5.84405	0.235082
$619$	18.2750	0.734534	0.367267	−	0.930116i	$-0.380294\pi$
$619$	18.2750	0.734534	0.367267	+	0.930116i	$0.380294\pi$
$620$	12.5644	0.504599
$621$	−4.79401	−0.192377
$622$	−26.8328	−1.07590
$623$	−11.4017	−0.456801
$624$	2.69718	0.107974
$625$	−18.0770	−0.723080
$626$	16.8957	0.675288
$627$	−1.25876	−0.0502700
$628$	−3.76548	−0.150259
$629$	8.47640	0.337976
$630$	7.11622	0.283517
$631$	18.4487	0.734430	0.367215	−	0.930136i	$-0.380311\pi$
$631$	18.4487	0.734430	0.367215	+	0.930136i	$0.380311\pi$
$632$	0.0479121	0.00190584
$633$	−8.45060	−0.335881
$634$	−21.1631	−0.840493
$635$	38.2917	1.51956
$636$	−1.01479	−0.0402392
$637$	16.4085	0.650129
$638$	0.228318	0.00903919
$639$	7.07215	0.279770
$640$	−1.96737	−0.0777671
$641$	−18.0312	−0.712189	−0.356094	−	0.934450i	$-0.615892\pi$
$641$	−18.0312	−0.712189	−0.356094	+	0.934450i	$0.615892\pi$
$642$	−15.5098	−0.612122
$643$	17.6645	0.696620	0.348310	−	0.937379i	$-0.386756\pi$
$643$	17.6645	0.696620	0.348310	+	0.937379i	$0.386756\pi$
$644$	17.3405	0.683312
$645$	19.8577	0.781895
$646$	−3.90670	−0.153707
$647$	−17.2650	−0.678756	−0.339378	−	0.940650i	$-0.610217\pi$
$647$	−17.2650	−0.678756	−0.339378	+	0.940650i	$0.610217\pi$
$648$	−1.00000	−0.0392837
$649$	−0.322205	−0.0126477
$650$	3.04636	0.119488
$651$	−23.1004	−0.905377
$652$	−4.05277	−0.158719
$653$	33.7022	1.31887	0.659435	−	0.751762i	$-0.270796\pi$
$653$	33.7022	1.31887	0.659435	+	0.751762i	$0.270796\pi$
$654$	−6.44376	−0.251971
$655$	−13.6396	−0.532944
$656$	1.55976	0.0608985
$657$	3.18832	0.124388
$658$	43.5705	1.69855
$659$	−8.24578	−0.321210	−0.160605	−	0.987019i	$-0.551345\pi$
$659$	−8.24578	−0.321210	−0.160605	+	0.987019i	$0.551345\pi$
$660$	0.633897	0.0246744
$661$	34.8127	1.35406	0.677029	−	0.735957i	$-0.263267\pi$
$661$	34.8127	1.35406	0.677029	+	0.735957i	$0.263267\pi$
$662$	27.4693	1.06762
$663$	−2.69718	−0.104750
$664$	−0.102752	−0.00398753
$665$	27.8009	1.07807
$666$	8.47640	0.328454
$667$	3.39708	0.131535
$668$	8.12354	0.314309
$669$	23.4257	0.905688
$670$	−24.1401	−0.932613
$671$	3.46885	0.133914
$672$	3.61712	0.139534
$673$	41.1376	1.58574	0.792870	−	0.609391i	$-0.208586\pi$
$673$	41.1376	1.58574	0.792870	+	0.609391i	$0.208586\pi$
$674$	12.5651	0.483990
$675$	−1.12946	−0.0434730
$676$	−5.72522	−0.220201
$677$	6.78056	0.260598	0.130299	−	0.991475i	$-0.458406\pi$
$677$	6.78056	0.260598	0.130299	+	0.991475i	$0.458406\pi$
$678$	−15.0555	−0.578205
$679$	−7.66118	−0.294009
$680$	1.96737	0.0754451
$681$	23.5348	0.901856
$682$	−2.05773	−0.0787947
$683$	25.8919	0.990726	0.495363	−	0.868686i	$-0.335035\pi$
$683$	25.8919	0.990726	0.495363	+	0.868686i	$0.335035\pi$
$684$	−3.90670	−0.149376
$685$	−32.1083	−1.22680
$686$	−3.31479	−0.126559
$687$	−29.8732	−1.13973
$688$	10.0935	0.384812
$689$	−2.73708	−0.104274
$690$	9.43158	0.359054
$691$	−34.2953	−1.30465	−0.652327	−	0.757937i	$-0.726207\pi$
$691$	−34.2953	−1.30465	−0.652327	+	0.757937i	$0.726207\pi$
$692$	12.3655	0.470067
$693$	−1.16546	−0.0442721
$694$	7.80090	0.296118
$695$	3.48744	0.132286
$696$	0.708609	0.0268598
$697$	−1.55976	−0.0590802
$698$	25.2540	0.955876
$699$	13.5825	0.513738
$700$	4.08540	0.154414
$701$	−0.148640	−0.00561407	−0.00280704	−	0.999996i	$-0.500894\pi$
$701$	−0.148640	−0.00561407	−0.00280704	+	0.999996i	$0.500894\pi$
$702$	−2.69718	−0.101799
$703$	33.1147	1.24895
$704$	0.322205	0.0121436
$705$	23.6981	0.892524
$706$	−4.56034	−0.171631
$707$	11.9936	0.451067
$708$	−1.00000	−0.0375823
$709$	−51.8127	−1.94587	−0.972933	−	0.231089i	$-0.925771\pi$
$709$	−51.8127	−1.94587	−0.972933	+	0.231089i	$0.925771\pi$
$710$	−13.9135	−0.522166
$711$	−0.0479121	−0.00179684
$712$	−3.15216	−0.118132
$713$	−30.6165	−1.14660
$714$	−3.61712	−0.135367
$715$	1.70973	0.0639404
$716$	16.6961	0.623963
$717$	5.64131	0.210679
$718$	−14.4272	−0.538417
$719$	40.7377	1.51926	0.759629	−	0.650356i	$-0.225380\pi$
$719$	40.7377	1.51926	0.759629	+	0.650356i	$0.225380\pi$
$720$	1.96737	0.0733195
$721$	21.1386	0.787244
$722$	3.73771	0.139103
$723$	22.6870	0.843738
$724$	−26.2946	−0.977233
$725$	0.800346	0.0297241
$726$	10.8962	0.404395
$727$	−36.1177	−1.33953	−0.669766	−	0.742572i	$-0.733606\pi$
$727$	−36.1177	−1.33953	−0.669766	+	0.742572i	$0.733606\pi$
$728$	9.75603	0.361583
$729$	1.00000	0.0370370
$730$	−6.27259	−0.232159
$731$	−10.0935	−0.373322
$732$	10.7660	0.397922
$733$	51.8615	1.91555	0.957774	−	0.287521i	$-0.0928312\pi$
$733$	51.8615	1.91555	0.957774	+	0.287521i	$0.0928312\pi$
$734$	24.9628	0.921395
$735$	11.9687	0.441470
$736$	4.79401	0.176710
$737$	3.95354	0.145631
$738$	−1.55976	−0.0574156
$739$	−16.1912	−0.595603	−0.297801	−	0.954628i	$-0.596253\pi$
$739$	−16.1912	−0.595603	−0.297801	+	0.954628i	$0.596253\pi$
$740$	−16.6762	−0.613029
$741$	−10.5371	−0.387089
$742$	−3.67063	−0.134753
$743$	6.64667	0.243843	0.121921	−	0.992540i	$-0.461094\pi$
$743$	6.64667	0.243843	0.121921	+	0.992540i	$0.461094\pi$
$744$	−6.38640	−0.234137
$745$	−3.78386	−0.138630
$746$	−4.05351	−0.148410
$747$	0.102752	0.00375948
$748$	−0.322205	−0.0117810
$749$	−56.1008	−2.04988
$750$	12.0589	0.440329
$751$	−15.5930	−0.568995	−0.284498	−	0.958677i	$-0.591827\pi$
$751$	−15.5930	−0.568995	−0.284498	+	0.958677i	$0.591827\pi$
$752$	12.0456	0.439258
$753$	−6.93425	−0.252698
$754$	1.91125	0.0696035
$755$	37.5775	1.36759
$756$	−3.61712	−0.131554
$757$	13.4225	0.487849	0.243924	−	0.969794i	$-0.421565\pi$
$757$	13.4225	0.487849	0.243924	+	0.969794i	$0.421565\pi$
$758$	−2.67315	−0.0970931
$759$	−1.54466	−0.0560675
$760$	7.68591	0.278797
$761$	−2.63485	−0.0955134	−0.0477567	−	0.998859i	$-0.515207\pi$
$761$	−2.63485	−0.0955134	−0.0477567	+	0.998859i	$0.515207\pi$
$762$	−19.4634	−0.705085
$763$	−23.3079	−0.843802
$764$	5.70129	0.206265
$765$	−1.96737	−0.0711304
$766$	−12.6525	−0.457153
$767$	−2.69718	−0.0973895
$768$	1.00000	0.0360844
$769$	−47.1868	−1.70160	−0.850799	−	0.525491i	$-0.823882\pi$
$769$	−47.1868	−1.70160	−0.850799	+	0.525491i	$0.823882\pi$
$770$	2.29288	0.0826298
$771$	9.25097	0.333165
$772$	6.01143	0.216356
$773$	−28.2857	−1.01737	−0.508683	−	0.860954i	$-0.669867\pi$
$773$	−28.2857	−1.01737	−0.508683	+	0.860954i	$0.669867\pi$
$774$	−10.0935	−0.362804
$775$	−7.21319	−0.259106
$776$	−2.11803	−0.0760329
$777$	30.6602	1.09993
$778$	−19.4285	−0.696547
$779$	−6.09352	−0.218323
$780$	5.30635	0.189998
$781$	2.27869	0.0815378
$782$	−4.79401	−0.171433
$783$	−0.708609	−0.0253236
$784$	6.08358	0.217271
$785$	−7.40809	−0.264406
$786$	6.93292	0.247289
$787$	17.4523	0.622108	0.311054	−	0.950392i	$-0.399318\pi$
$787$	17.4523	0.622108	0.311054	+	0.950392i	$0.399318\pi$
$788$	8.44024	0.300671
$789$	−1.77066	−0.0630373
$790$	0.0942607	0.00335364
$791$	−54.4578	−1.93630
$792$	−0.322205	−0.0114491
$793$	29.0378	1.03116
$794$	12.0808	0.428732
$795$	−1.99647	−0.0708076
$796$	−10.3059	−0.365282
$797$	−29.7203	−1.05275	−0.526373	−	0.850254i	$-0.676448\pi$
$797$	−29.7203	−1.05275	−0.526373	+	0.850254i	$0.676448\pi$
$798$	−14.1310	−0.500232
$799$	−12.0456	−0.426143
$800$	1.12946	0.0399325
$801$	3.15216	0.111376
$802$	6.06618	0.214204
$803$	1.02729	0.0362524
$804$	12.2702	0.432738
$805$	34.1152	1.20240
$806$	−17.2253	−0.606735
$807$	1.30106	0.0457994
$808$	3.31580	0.116649
$809$	−19.9190	−0.700314	−0.350157	−	0.936691i	$-0.613872\pi$
$809$	−19.9190	−0.700314	−0.350157	+	0.936691i	$0.613872\pi$
$810$	−1.96737	−0.0691263
$811$	35.6195	1.25077	0.625385	−	0.780316i	$-0.284942\pi$
$811$	35.6195	1.25077	0.625385	+	0.780316i	$0.284942\pi$
$812$	2.56313	0.0899481
$813$	7.25086	0.254299
$814$	2.73114	0.0957265
$815$	−7.97329	−0.279292
$816$	−1.00000	−0.0350070
$817$	−39.4323	−1.37956
$818$	−29.2302	−1.02201
$819$	−9.75603	−0.340903
$820$	3.06863	0.107161
$821$	35.0511	1.22329	0.611646	−	0.791131i	$-0.290508\pi$
$821$	35.0511	1.22329	0.611646	+	0.791131i	$0.290508\pi$
$822$	16.3204	0.569241
$823$	5.80101	0.202210	0.101105	−	0.994876i	$-0.467762\pi$
$823$	5.80101	0.202210	0.101105	+	0.994876i	$0.467762\pi$
$824$	5.84405	0.203587
$825$	−0.363919	−0.0126700
$826$	−3.61712	−0.125856
$827$	−44.0917	−1.53322	−0.766608	−	0.642115i	$-0.778057\pi$
$827$	−44.0917	−1.53322	−0.766608	+	0.642115i	$0.778057\pi$
$828$	−4.79401	−0.166603
$829$	7.17727	0.249277	0.124638	−	0.992202i	$-0.460223\pi$
$829$	7.17727	0.249277	0.124638	+	0.992202i	$0.460223\pi$
$830$	−0.202150	−0.00701674
$831$	12.3108	0.427056
$832$	2.69718	0.0935079
$833$	−6.08358	−0.210784
$834$	−1.77264	−0.0613817
$835$	15.9820	0.553080
$836$	−1.25876	−0.0435351
$837$	6.38640	0.220746
$838$	−7.51927	−0.259749
$839$	−7.56212	−0.261073	−0.130537	−	0.991443i	$-0.541670\pi$
$839$	−7.56212	−0.261073	−0.130537	+	0.991443i	$0.541670\pi$
$840$	7.11622	0.245533
$841$	−28.4979	−0.982685
$842$	4.10410	0.141437
$843$	−22.8921	−0.788445
$844$	−8.45060	−0.290882
$845$	−11.2636	−0.387480
$846$	−12.0456	−0.414137
$847$	39.4128	1.35424
$848$	−1.01479	−0.0348482
$849$	0.128131	0.00439746
$850$	−1.12946	−0.0387402
$851$	40.6359	1.39298
$852$	7.07215	0.242288
$853$	−4.18783	−0.143388	−0.0716942	−	0.997427i	$-0.522841\pi$
$853$	−4.18783	−0.143388	−0.0716942	+	0.997427i	$0.522841\pi$
$854$	38.9418	1.33256
$855$	−7.68591	−0.262853
$856$	−15.5098	−0.530113
$857$	26.8730	0.917965	0.458982	−	0.888445i	$-0.348214\pi$
$857$	26.8730	0.917965	0.458982	+	0.888445i	$0.348214\pi$
$858$	−0.869046	−0.0296687
$859$	18.3419	0.625816	0.312908	−	0.949783i	$-0.398697\pi$
$859$	18.3419	0.625816	0.312908	+	0.949783i	$0.398697\pi$
$860$	19.8577	0.677141
$861$	−5.64185	−0.192274
$862$	25.4463	0.866705
$863$	−48.6135	−1.65482	−0.827411	−	0.561597i	$-0.810187\pi$
$863$	−48.6135	−1.65482	−0.827411	+	0.561597i	$0.810187\pi$
$864$	−1.00000	−0.0340207
$865$	24.3275	0.827161
$866$	−26.8467	−0.912289
$867$	1.00000	0.0339618
$868$	−23.1004	−0.784079
$869$	−0.0154375	−0.000523682 0
$870$	1.39410	0.0472643
$871$	33.0951	1.12138
$872$	−6.44376	−0.218213
$873$	2.11803	0.0716845
$874$	−18.7287	−0.633509
$875$	43.6186	1.47458
$876$	3.18832	0.107723
$877$	−0.851478	−0.0287524	−0.0143762	−	0.999897i	$-0.504576\pi$
$877$	−0.851478	−0.0287524	−0.0143762	+	0.999897i	$0.504576\pi$
$878$	2.80058	0.0945151
$879$	−21.9385	−0.739967
$880$	0.633897	0.0213687
$881$	36.3285	1.22394	0.611969	−	0.790881i	$-0.290378\pi$
$881$	36.3285	1.22394	0.611969	+	0.790881i	$0.290378\pi$
$882$	−6.08358	−0.204845
$883$	−56.4060	−1.89821	−0.949107	−	0.314955i	$-0.898011\pi$
$883$	−56.4060	−1.89821	−0.949107	+	0.314955i	$0.898011\pi$
$884$	−2.69718	−0.0907160
$885$	−1.96737	−0.0661324
$886$	11.2291	0.377248
$887$	31.0751	1.04340	0.521701	−	0.853129i	$-0.325298\pi$
$887$	31.0751	1.04340	0.521701	+	0.853129i	$0.325298\pi$
$888$	8.47640	0.284449
$889$	−70.4016	−2.36119
$890$	−6.20145	−0.207873
$891$	0.322205	0.0107943
$892$	23.4257	0.784349
$893$	−47.0585	−1.57475
$894$	1.92331	0.0643250
$895$	32.8474	1.09797
$896$	3.61712	0.120840
$897$	−12.9303	−0.431730
$898$	5.64645	0.188424
$899$	−4.52546	−0.150933
$900$	−1.12946	−0.0376487
$901$	1.01479	0.0338077
$902$	−0.502564	−0.0167336
$903$	−36.5095	−1.21496
$904$	−15.0555	−0.500740
$905$	−51.7313	−1.71961
$906$	−19.1004	−0.634569
$907$	−55.9171	−1.85670	−0.928349	−	0.371711i	$-0.878771\pi$
$907$	−55.9171	−1.85670	−0.928349	+	0.371711i	$0.878771\pi$
$908$	23.5348	0.781030
$909$	−3.31580	−0.109978
$910$	19.1937	0.636265
$911$	−41.9901	−1.39119	−0.695597	−	0.718433i	$-0.744860\pi$
$911$	−41.9901	−1.39119	−0.695597	+	0.718433i	$0.744860\pi$
$912$	−3.90670	−0.129364
$913$	0.0331071	0.00109569
$914$	25.8898	0.856359
$915$	21.1806	0.700210
$916$	−29.8732	−0.987039
$917$	25.0772	0.828123
$918$	1.00000	0.0330049
$919$	−38.2639	−1.26221	−0.631106	−	0.775697i	$-0.717399\pi$
$919$	−38.2639	−1.26221	−0.631106	+	0.775697i	$0.717399\pi$
$920$	9.43158	0.310950
$921$	−12.9495	−0.426700
$922$	12.3982	0.408312
$923$	19.0749	0.627857
$924$	−1.16546	−0.0383407
$925$	9.57376	0.314783
$926$	23.5345	0.773392
$927$	−5.84405	−0.191944
$928$	0.708609	0.0232612
$929$	0.719669	0.0236116	0.0118058	−	0.999930i	$-0.496242\pi$
$929$	0.719669	0.0236116	0.0118058	+	0.999930i	$0.496242\pi$
$930$	−12.5644	−0.412003
$931$	−23.7667	−0.778923
$932$	13.5825	0.444910
$933$	26.8328	0.878466
$934$	−13.3905	−0.438149
$935$	−0.633897	−0.0207306
$936$	−2.69718	−0.0881601
$937$	−52.1853	−1.70482	−0.852410	−	0.522874i	$-0.824860\pi$
$937$	−52.1853	−1.70482	−0.852410	+	0.522874i	$0.824860\pi$
$938$	44.3830	1.44916
$939$	−16.8957	−0.551370
$940$	23.6981	0.772948
$941$	6.51151	0.212269	0.106135	−	0.994352i	$-0.466153\pi$
$941$	6.51151	0.212269	0.106135	+	0.994352i	$0.466153\pi$
$942$	3.76548	0.122686
$943$	−7.47752	−0.243501
$944$	−1.00000	−0.0325472
$945$	−7.11622	−0.231490
$946$	−3.25219	−0.105738
$947$	50.1578	1.62991	0.814955	−	0.579524i	$-0.196762\pi$
$947$	50.1578	1.62991	0.814955	+	0.579524i	$0.196762\pi$
$948$	−0.0479121	−0.00155611
$949$	8.59946	0.279150
$950$	−4.41246	−0.143159
$951$	21.1631	0.686259
$952$	−3.61712	−0.117232
$953$	30.9124	1.00135	0.500676	−	0.865635i	$-0.333085\pi$
$953$	30.9124	1.00135	0.500676	+	0.865635i	$0.333085\pi$
$954$	1.01479	0.0328552
$955$	11.2165	0.362958
$956$	5.64131	0.182453
$957$	−0.228318	−0.00738046
$958$	−26.8921	−0.868843
$959$	59.0331	1.90628
$960$	1.96737	0.0634965
$961$	9.78615	0.315682
$962$	22.8624	0.737112
$963$	15.5098	0.499796
$964$	22.6870	0.730698
$965$	11.8267	0.380715
$966$	−17.3405	−0.557922
$967$	−41.9689	−1.34963	−0.674815	−	0.737987i	$-0.735776\pi$
$967$	−41.9689	−1.34963	−0.674815	+	0.737987i	$0.735776\pi$
$968$	10.8962	0.350217
$969$	3.90670	0.125501
$970$	−4.16695	−0.133793
$971$	−6.27634	−0.201417	−0.100709	−	0.994916i	$-0.532111\pi$
$971$	−6.27634	−0.201417	−0.100709	+	0.994916i	$0.532111\pi$
$972$	1.00000	0.0320750
$973$	−6.41187	−0.205555
$974$	16.0458	0.514141
$975$	−3.04636	−0.0975616
$976$	10.7660	0.344610
$977$	−45.0880	−1.44249	−0.721247	−	0.692678i	$-0.756431\pi$
$977$	−45.0880	−1.44249	−0.721247	+	0.692678i	$0.756431\pi$
$978$	4.05277	0.129593
$979$	1.01564	0.0324601
$980$	11.9687	0.382325
$981$	6.44376	0.205734
$982$	−33.1658	−1.05836
$983$	9.23375	0.294511	0.147255	−	0.989098i	$-0.452956\pi$
$983$	9.23375	0.294511	0.147255	+	0.989098i	$0.452956\pi$
$984$	−1.55976	−0.0497234
$985$	16.6051	0.529081
$986$	−0.708609	−0.0225667
$987$	−43.5705	−1.38686
$988$	−10.5371	−0.335229
$989$	−48.3884	−1.53866
$990$	−0.633897	−0.0201466
$991$	18.0309	0.572771	0.286386	−	0.958114i	$-0.407546\pi$
$991$	18.0309	0.572771	0.286386	+	0.958114i	$0.407546\pi$
$992$	−6.38640	−0.202769
$993$	−27.4693	−0.871712
$994$	25.5809	0.811376
$995$	−20.2754	−0.642774
$996$	0.102752	0.00325581
$997$	−31.7402	−1.00522	−0.502611	−	0.864513i	$-0.667627\pi$
$997$	−31.7402	−1.00522	−0.502611	+	0.864513i	$0.667627\pi$
$998$	19.1598	0.606494
$999$	−8.47640	−0.268181

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6018.2.a.p.1.4	✓	5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6018.2.a.p.1.4	✓	5	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:	\( N \)	\(=\)	\( 6018 = 2 \cdot 3 \cdot 17 \cdot 59 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6018.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +1.96737 q^{5} -1.00000 q^{6} -3.61712 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +1.96737 q^{5} -1.00000 q^{6} -3.61712 q^{7} -1.00000 q^{8} +1.00000 q^{9} -1.96737 q^{10} +0.322205 q^{11} +1.00000 q^{12} +2.69718 q^{13} +3.61712 q^{14} +1.96737 q^{15} +1.00000 q^{16} -1.00000 q^{17} -1.00000 q^{18} -3.90670 q^{19} +1.96737 q^{20} -3.61712 q^{21} -0.322205 q^{22} -4.79401 q^{23} -1.00000 q^{24} -1.12946 q^{25} -2.69718 q^{26} +1.00000 q^{27} -3.61712 q^{28} -0.708609 q^{29} -1.96737 q^{30} +6.38640 q^{31} -1.00000 q^{32} +0.322205 q^{33} +1.00000 q^{34} -7.11622 q^{35} +1.00000 q^{36} -8.47640 q^{37} +3.90670 q^{38} +2.69718 q^{39} -1.96737 q^{40} +1.55976 q^{41} +3.61712 q^{42} +10.0935 q^{43} +0.322205 q^{44} +1.96737 q^{45} +4.79401 q^{46} +12.0456 q^{47} +1.00000 q^{48} +6.08358 q^{49} +1.12946 q^{50} -1.00000 q^{51} +2.69718 q^{52} -1.01479 q^{53} -1.00000 q^{54} +0.633897 q^{55} +3.61712 q^{56} -3.90670 q^{57} +0.708609 q^{58} -1.00000 q^{59} +1.96737 q^{60} +10.7660 q^{61} -6.38640 q^{62} -3.61712 q^{63} +1.00000 q^{64} +5.30635 q^{65} -0.322205 q^{66} +12.2702 q^{67} -1.00000 q^{68} -4.79401 q^{69} +7.11622 q^{70} +7.07215 q^{71} -1.00000 q^{72} +3.18832 q^{73} +8.47640 q^{74} -1.12946 q^{75} -3.90670 q^{76} -1.16546 q^{77} -2.69718 q^{78} -0.0479121 q^{79} +1.96737 q^{80} +1.00000 q^{81} -1.55976 q^{82} +0.102752 q^{83} -3.61712 q^{84} -1.96737 q^{85} -10.0935 q^{86} -0.708609 q^{87} -0.322205 q^{88} +3.15216 q^{89} -1.96737 q^{90} -9.75603 q^{91} -4.79401 q^{92} +6.38640 q^{93} -12.0456 q^{94} -7.68591 q^{95} -1.00000 q^{96} +2.11803 q^{97} -6.08358 q^{98} +0.322205 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q - 5 q^{2} + 5 q^{3} + 5 q^{4} - q^{5} - 5 q^{6} - q^{7} - 5 q^{8} + 5 q^{9}+O(q^{10}) \) 5 * q - 5 * q^2 + 5 * q^3 + 5 * q^4 - q^5 - 5 * q^6 - q^7 - 5 * q^8 + 5 * q^9	\( 5 q - 5 q^{2} + 5 q^{3} + 5 q^{4} - q^{5} - 5 q^{6} - q^{7} - 5 q^{8} + 5 q^{9} + q^{10} + 6 q^{11} + 5 q^{12} - 2 q^{13} + q^{14} - q^{15} + 5 q^{16} - 5 q^{17} - 5 q^{18} + 4 q^{19} - q^{20} - q^{21} - 6 q^{22} + 12 q^{23} - 5 q^{24} + 4 q^{25} + 2 q^{26} + 5 q^{27} - q^{28} + 19 q^{29} + q^{30} + 5 q^{31} - 5 q^{32} + 6 q^{33} + 5 q^{34} - 4 q^{35} + 5 q^{36} - 11 q^{37} - 4 q^{38} - 2 q^{39} + q^{40} + 6 q^{41} + q^{42} + 2 q^{43} + 6 q^{44} - q^{45} - 12 q^{46} + 22 q^{47} + 5 q^{48} - 12 q^{49} - 4 q^{50} - 5 q^{51} - 2 q^{52} + 15 q^{53} - 5 q^{54} - 36 q^{55} + q^{56} + 4 q^{57} - 19 q^{58} - 5 q^{59} - q^{60} + 16 q^{61} - 5 q^{62} - q^{63} + 5 q^{64} - 2 q^{65} - 6 q^{66} + 25 q^{67} - 5 q^{68} + 12 q^{69} + 4 q^{70} - 5 q^{72} - 10 q^{73} + 11 q^{74} + 4 q^{75} + 4 q^{76} + 6 q^{77} + 2 q^{78} + 10 q^{79} - q^{80} + 5 q^{81} - 6 q^{82} + 19 q^{83} - q^{84} + q^{85} - 2 q^{86} + 19 q^{87} - 6 q^{88} + 23 q^{89} + q^{90} - 17 q^{91} + 12 q^{92} + 5 q^{93} - 22 q^{94} + q^{95} - 5 q^{96} + 8 q^{97} + 12 q^{98} + 6 q^{99}+O(q^{100}) \) 5 * q - 5 * q^2 + 5 * q^3 + 5 * q^4 - q^5 - 5 * q^6 - q^7 - 5 * q^8 + 5 * q^9 + q^10 + 6 * q^11 + 5 * q^12 - 2 * q^13 + q^14 - q^15 + 5 * q^16 - 5 * q^17 - 5 * q^18 + 4 * q^19 - q^20 - q^21 - 6 * q^22 + 12 * q^23 - 5 * q^24 + 4 * q^25 + 2 * q^26 + 5 * q^27 - q^28 + 19 * q^29 + q^30 + 5 * q^31 - 5 * q^32 + 6 * q^33 + 5 * q^34 - 4 * q^35 + 5 * q^36 - 11 * q^37 - 4 * q^38 - 2 * q^39 + q^40 + 6 * q^41 + q^42 + 2 * q^43 + 6 * q^44 - q^45 - 12 * q^46 + 22 * q^47 + 5 * q^48 - 12 * q^49 - 4 * q^50 - 5 * q^51 - 2 * q^52 + 15 * q^53 - 5 * q^54 - 36 * q^55 + q^56 + 4 * q^57 - 19 * q^58 - 5 * q^59 - q^60 + 16 * q^61 - 5 * q^62 - q^63 + 5 * q^64 - 2 * q^65 - 6 * q^66 + 25 * q^67 - 5 * q^68 + 12 * q^69 + 4 * q^70 - 5 * q^72 - 10 * q^73 + 11 * q^74 + 4 * q^75 + 4 * q^76 + 6 * q^77 + 2 * q^78 + 10 * q^79 - q^80 + 5 * q^81 - 6 * q^82 + 19 * q^83 - q^84 + q^85 - 2 * q^86 + 19 * q^87 - 6 * q^88 + 23 * q^89 + q^90 - 17 * q^91 + 12 * q^92 + 5 * q^93 - 22 * q^94 + q^95 - 5 * q^96 + 8 * q^97 + 12 * q^98 + 6 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more