LMFDB - Embedded newform 6034.2.a.g.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6034,2,Mod(1,6034)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6034, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("6034.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6034 = 2 \cdot 7 \cdot 431 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6034.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:	$48.1817325796$
Analytic rank:	$1$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{10})^+$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 1 $ x^2 - x - 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$1.61803$ of defining polynomial
Character	$\chi$	$=$	6034.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +2.00000 q^{3} +1.00000 q^{4} -3.61803 q^{5} -2.00000 q^{6} -1.00000 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +2.00000 q^{3} +1.00000 q^{4} -3.61803 q^{5} -2.00000 q^{6} -1.00000 q^{7} -1.00000 q^{8} +1.00000 q^{9} +3.61803 q^{10} -6.09017 q^{11} +2.00000 q^{12} +4.47214 q^{13} +1.00000 q^{14} -7.23607 q^{15} +1.00000 q^{16} -0.618034 q^{17} -1.00000 q^{18} +6.47214 q^{19} -3.61803 q^{20} -2.00000 q^{21} +6.09017 q^{22} +9.23607 q^{23} -2.00000 q^{24} +8.09017 q^{25} -4.47214 q^{26} -4.00000 q^{27} -1.00000 q^{28} +1.23607 q^{29} +7.23607 q^{30} +5.23607 q^{31} -1.00000 q^{32} -12.1803 q^{33} +0.618034 q^{34} +3.61803 q^{35} +1.00000 q^{36} -7.85410 q^{37} -6.47214 q^{38} +8.94427 q^{39} +3.61803 q^{40} -10.9443 q^{41} +2.00000 q^{42} -6.09017 q^{44} -3.61803 q^{45} -9.23607 q^{46} +2.00000 q^{47} +2.00000 q^{48} +1.00000 q^{49} -8.09017 q^{50} -1.23607 q^{51} +4.47214 q^{52} -11.2361 q^{53} +4.00000 q^{54} +22.0344 q^{55} +1.00000 q^{56} +12.9443 q^{57} -1.23607 q^{58} +12.1803 q^{59} -7.23607 q^{60} -7.85410 q^{61} -5.23607 q^{62} -1.00000 q^{63} +1.00000 q^{64} -16.1803 q^{65} +12.1803 q^{66} +4.47214 q^{67} -0.618034 q^{68} +18.4721 q^{69} -3.61803 q^{70} +9.61803 q^{71} -1.00000 q^{72} +4.47214 q^{73} +7.85410 q^{74} +16.1803 q^{75} +6.47214 q^{76} +6.09017 q^{77} -8.94427 q^{78} -7.14590 q^{79} -3.61803 q^{80} -11.0000 q^{81} +10.9443 q^{82} -2.47214 q^{83} -2.00000 q^{84} +2.23607 q^{85} +2.47214 q^{87} +6.09017 q^{88} -13.6180 q^{89} +3.61803 q^{90} -4.47214 q^{91} +9.23607 q^{92} +10.4721 q^{93} -2.00000 q^{94} -23.4164 q^{95} -2.00000 q^{96} -14.1803 q^{97} -1.00000 q^{98} -6.09017 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 2 q^{2} + 4 q^{3} + 2 q^{4} - 5 q^{5} - 4 q^{6} - 2 q^{7} - 2 q^{8} + 2 q^{9}+O(q^{10}) $ 2 * q - 2 * q^2 + 4 * q^3 + 2 * q^4 - 5 * q^5 - 4 * q^6 - 2 * q^7 - 2 * q^8 + 2 * q^9	$ 2 q - 2 q^{2} + 4 q^{3} + 2 q^{4} - 5 q^{5} - 4 q^{6} - 2 q^{7} - 2 q^{8} + 2 q^{9} + 5 q^{10} - q^{11} + 4 q^{12} + 2 q^{14} - 10 q^{15} + 2 q^{16} + q^{17} - 2 q^{18} + 4 q^{19} - 5 q^{20} - 4 q^{21} + q^{22} + 14 q^{23} - 4 q^{24} + 5 q^{25} - 8 q^{27} - 2 q^{28} - 2 q^{29} + 10 q^{30} + 6 q^{31} - 2 q^{32} - 2 q^{33} - q^{34} + 5 q^{35} + 2 q^{36} - 9 q^{37} - 4 q^{38} + 5 q^{40} - 4 q^{41} + 4 q^{42} - q^{44} - 5 q^{45} - 14 q^{46} + 4 q^{47} + 4 q^{48} + 2 q^{49} - 5 q^{50} + 2 q^{51} - 18 q^{53} + 8 q^{54} + 15 q^{55} + 2 q^{56} + 8 q^{57} + 2 q^{58} + 2 q^{59} - 10 q^{60} - 9 q^{61} - 6 q^{62} - 2 q^{63} + 2 q^{64} - 10 q^{65} + 2 q^{66} + q^{68} + 28 q^{69} - 5 q^{70} + 17 q^{71} - 2 q^{72} + 9 q^{74} + 10 q^{75} + 4 q^{76} + q^{77} - 21 q^{79} - 5 q^{80} - 22 q^{81} + 4 q^{82} + 4 q^{83} - 4 q^{84} - 4 q^{87} + q^{88} - 25 q^{89} + 5 q^{90} + 14 q^{92} + 12 q^{93} - 4 q^{94} - 20 q^{95} - 4 q^{96} - 6 q^{97} - 2 q^{98} - q^{99}+O(q^{100}) $ 2 * q - 2 * q^2 + 4 * q^3 + 2 * q^4 - 5 * q^5 - 4 * q^6 - 2 * q^7 - 2 * q^8 + 2 * q^9 + 5 * q^10 - q^11 + 4 * q^12 + 2 * q^14 - 10 * q^15 + 2 * q^16 + q^17 - 2 * q^18 + 4 * q^19 - 5 * q^20 - 4 * q^21 + q^22 + 14 * q^23 - 4 * q^24 + 5 * q^25 - 8 * q^27 - 2 * q^28 - 2 * q^29 + 10 * q^30 + 6 * q^31 - 2 * q^32 - 2 * q^33 - q^34 + 5 * q^35 + 2 * q^36 - 9 * q^37 - 4 * q^38 + 5 * q^40 - 4 * q^41 + 4 * q^42 - q^44 - 5 * q^45 - 14 * q^46 + 4 * q^47 + 4 * q^48 + 2 * q^49 - 5 * q^50 + 2 * q^51 - 18 * q^53 + 8 * q^54 + 15 * q^55 + 2 * q^56 + 8 * q^57 + 2 * q^58 + 2 * q^59 - 10 * q^60 - 9 * q^61 - 6 * q^62 - 2 * q^63 + 2 * q^64 - 10 * q^65 + 2 * q^66 + q^68 + 28 * q^69 - 5 * q^70 + 17 * q^71 - 2 * q^72 + 9 * q^74 + 10 * q^75 + 4 * q^76 + q^77 - 21 * q^79 - 5 * q^80 - 22 * q^81 + 4 * q^82 + 4 * q^83 - 4 * q^84 - 4 * q^87 + q^88 - 25 * q^89 + 5 * q^90 + 14 * q^92 + 12 * q^93 - 4 * q^94 - 20 * q^95 - 4 * q^96 - 6 * q^97 - 2 * q^98 - 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
$3$	2.00000	1.15470	0.577350	−	0.816497i	$-0.304087\pi$
$3$	2.00000	1.15470	0.577350	+	0.816497i	$0.304087\pi$
$4$	1.00000	0.500000
$5$	−3.61803	−1.61803	−0.809017	−	0.587785i	$-0.800000\pi$
$5$	−3.61803	−1.61803	−0.809017	+	0.587785i	$0.800000\pi$
$6$	−2.00000	−0.816497
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	−1.00000	−0.353553
$9$	1.00000	0.333333
$10$	3.61803	1.14412
$11$	−6.09017	−1.83626	−0.918128	−	0.396285i	$-0.870299\pi$
$11$	−6.09017	−1.83626	−0.918128	+	0.396285i	$0.870299\pi$
$12$	2.00000	0.577350
$13$	4.47214	1.24035	0.620174	−	0.784465i	$-0.287062\pi$
$13$	4.47214	1.24035	0.620174	+	0.784465i	$0.287062\pi$
$14$	1.00000	0.267261
$15$	−7.23607	−1.86834
$16$	1.00000	0.250000
$17$	−0.618034	−0.149895	−0.0749476	−	0.997187i	$-0.523879\pi$
$17$	−0.618034	−0.149895	−0.0749476	+	0.997187i	$0.523879\pi$
$18$	−1.00000	−0.235702
$19$	6.47214	1.48481	0.742405	−	0.669951i	$-0.233685\pi$
$19$	6.47214	1.48481	0.742405	+	0.669951i	$0.233685\pi$
$20$	−3.61803	−0.809017
$21$	−2.00000	−0.436436
$22$	6.09017	1.29843
$23$	9.23607	1.92585	0.962927	−	0.269763i	$-0.0869455\pi$
$23$	9.23607	1.92585	0.962927	+	0.269763i	$0.0869455\pi$
$24$	−2.00000	−0.408248
$25$	8.09017	1.61803
$26$	−4.47214	−0.877058
$27$	−4.00000	−0.769800
$28$	−1.00000	−0.188982
$29$	1.23607	0.229532	0.114766	−	0.993393i	$-0.463388\pi$
$29$	1.23607	0.229532	0.114766	+	0.993393i	$0.463388\pi$
$30$	7.23607	1.32112
$31$	5.23607	0.940426	0.470213	−	0.882553i	$-0.344177\pi$
$31$	5.23607	0.940426	0.470213	+	0.882553i	$0.344177\pi$
$32$	−1.00000	−0.176777
$33$	−12.1803	−2.12033
$34$	0.618034	0.105992
$35$	3.61803	0.611559
$36$	1.00000	0.166667
$37$	−7.85410	−1.29121	−0.645603	−	0.763673i	$-0.723394\pi$
$37$	−7.85410	−1.29121	−0.645603	+	0.763673i	$0.723394\pi$
$38$	−6.47214	−1.04992
$39$	8.94427	1.43223
$40$	3.61803	0.572061
$41$	−10.9443	−1.70921	−0.854604	−	0.519280i	$-0.826200\pi$
$41$	−10.9443	−1.70921	−0.854604	+	0.519280i	$0.826200\pi$
$42$	2.00000	0.308607
$43$	0	0		−	1.00000i	$-0.5\pi$
$43$	0	0			1.00000i	$0.5\pi$
$44$	−6.09017	−0.918128
$45$	−3.61803	−0.539345
$46$	−9.23607	−1.36178
$47$	2.00000	0.291730	0.145865	−	0.989305i	$-0.453403\pi$
$47$	2.00000	0.291730	0.145865	+	0.989305i	$0.453403\pi$
$48$	2.00000	0.288675
$49$	1.00000	0.142857
$50$	−8.09017	−1.14412
$51$	−1.23607	−0.173084
$52$	4.47214	0.620174
$53$	−11.2361	−1.54339	−0.771696	−	0.635991i	$-0.780591\pi$
$53$	−11.2361	−1.54339	−0.771696	+	0.635991i	$0.780591\pi$
$54$	4.00000	0.544331
$55$	22.0344	2.97112
$56$	1.00000	0.133631
$57$	12.9443	1.71451
$58$	−1.23607	−0.162304
$59$	12.1803	1.58575	0.792873	−	0.609387i	$-0.208585\pi$
$59$	12.1803	1.58575	0.792873	+	0.609387i	$0.208585\pi$
$60$	−7.23607	−0.934172
$61$	−7.85410	−1.00561	−0.502807	−	0.864398i	$-0.667699\pi$
$61$	−7.85410	−1.00561	−0.502807	+	0.864398i	$0.667699\pi$
$62$	−5.23607	−0.664981
$63$	−1.00000	−0.125988
$64$	1.00000	0.125000
$65$	−16.1803	−2.00692
$66$	12.1803	1.49930
$67$	4.47214	0.546358	0.273179	−	0.961963i	$-0.411925\pi$
$67$	4.47214	0.546358	0.273179	+	0.961963i	$0.411925\pi$
$68$	−0.618034	−0.0749476
$69$	18.4721	2.22378
$70$	−3.61803	−0.432438
$71$	9.61803	1.14145	0.570725	−	0.821141i	$-0.306662\pi$
$71$	9.61803	1.14145	0.570725	+	0.821141i	$0.306662\pi$
$72$	−1.00000	−0.117851
$73$	4.47214	0.523424	0.261712	−	0.965146i	$-0.415713\pi$
$73$	4.47214	0.523424	0.261712	+	0.965146i	$0.415713\pi$
$74$	7.85410	0.913021
$75$	16.1803	1.86834
$76$	6.47214	0.742405
$77$	6.09017	0.694039
$78$	−8.94427	−1.01274
$79$	−7.14590	−0.803976	−0.401988	−	0.915645i	$-0.631681\pi$
$79$	−7.14590	−0.803976	−0.401988	+	0.915645i	$0.631681\pi$
$80$	−3.61803	−0.404508
$81$	−11.0000	−1.22222
$82$	10.9443	1.20859
$83$	−2.47214	−0.271352	−0.135676	−	0.990753i	$-0.543321\pi$
$83$	−2.47214	−0.271352	−0.135676	+	0.990753i	$0.543321\pi$
$84$	−2.00000	−0.218218
$85$	2.23607	0.242536
$86$	0	0
$87$	2.47214	0.265041
$88$	6.09017	0.649214
$89$	−13.6180	−1.44351	−0.721754	−	0.692149i	$-0.756664\pi$
$89$	−13.6180	−1.44351	−0.721754	+	0.692149i	$0.756664\pi$
$90$	3.61803	0.381374
$91$	−4.47214	−0.468807
$92$	9.23607	0.962927
$93$	10.4721	1.08591
$94$	−2.00000	−0.206284
$95$	−23.4164	−2.40247
$96$	−2.00000	−0.204124
$97$	−14.1803	−1.43980	−0.719898	−	0.694080i	$-0.755811\pi$
$97$	−14.1803	−1.43980	−0.719898	+	0.694080i	$0.755811\pi$
$98$	−1.00000	−0.101015
$99$	−6.09017	−0.612085
$100$	8.09017	0.809017
$101$	−4.47214	−0.444994	−0.222497	−	0.974933i	$-0.571421\pi$
$101$	−4.47214	−0.444994	−0.222497	+	0.974933i	$0.571421\pi$
$102$	1.23607	0.122389
$103$	10.4721	1.03185	0.515925	−	0.856634i	$-0.327448\pi$
$103$	10.4721	1.03185	0.515925	+	0.856634i	$0.327448\pi$
$104$	−4.47214	−0.438529
$105$	7.23607	0.706168
$106$	11.2361	1.09134
$107$	9.23607	0.892884	0.446442	−	0.894812i	$-0.352691\pi$
$107$	9.23607	0.892884	0.446442	+	0.894812i	$0.352691\pi$
$108$	−4.00000	−0.384900
$109$	−2.29180	−0.219514	−0.109757	−	0.993958i	$-0.535007\pi$
$109$	−2.29180	−0.219514	−0.109757	+	0.993958i	$0.535007\pi$
$110$	−22.0344	−2.10090
$111$	−15.7082	−1.49096
$112$	−1.00000	−0.0944911
$113$	4.94427	0.465118	0.232559	−	0.972582i	$-0.425290\pi$
$113$	4.94427	0.465118	0.232559	+	0.972582i	$0.425290\pi$
$114$	−12.9443	−1.21234
$115$	−33.4164	−3.11610
$116$	1.23607	0.114766
$117$	4.47214	0.413449
$118$	−12.1803	−1.12129
$119$	0.618034	0.0566551
$120$	7.23607	0.660560
$121$	26.0902	2.37183
$122$	7.85410	0.711077
$123$	−21.8885	−1.97362
$124$	5.23607	0.470213
$125$	−11.1803	−1.00000
$126$	1.00000	0.0890871
$127$	4.14590	0.367889	0.183944	−	0.982937i	$-0.441113\pi$
$127$	4.14590	0.367889	0.183944	+	0.982937i	$0.441113\pi$
$128$	−1.00000	−0.0883883
$129$	0	0
$130$	16.1803	1.41911
$131$	6.09017	0.532101	0.266050	−	0.963959i	$-0.414281\pi$
$131$	6.09017	0.532101	0.266050	+	0.963959i	$0.414281\pi$
$132$	−12.1803	−1.06016
$133$	−6.47214	−0.561205
$134$	−4.47214	−0.386334
$135$	14.4721	1.24556
$136$	0.618034	0.0529960
$137$	−22.4721	−1.91992	−0.959962	−	0.280130i	$-0.909622\pi$
$137$	−22.4721	−1.91992	−0.959962	+	0.280130i	$0.909622\pi$
$138$	−18.4721	−1.57245
$139$	5.52786	0.468867	0.234434	−	0.972132i	$-0.424676\pi$
$139$	5.52786	0.468867	0.234434	+	0.972132i	$0.424676\pi$
$140$	3.61803	0.305780
$141$	4.00000	0.336861
$142$	−9.61803	−0.807127
$143$	−27.2361	−2.27759
$144$	1.00000	0.0833333
$145$	−4.47214	−0.371391
$146$	−4.47214	−0.370117
$147$	2.00000	0.164957
$148$	−7.85410	−0.645603
$149$	−18.0000	−1.47462	−0.737309	−	0.675556i	$-0.763904\pi$
$149$	−18.0000	−1.47462	−0.737309	+	0.675556i	$0.763904\pi$
$150$	−16.1803	−1.32112
$151$	−4.76393	−0.387683	−0.193842	−	0.981033i	$-0.562095\pi$
$151$	−4.76393	−0.387683	−0.193842	+	0.981033i	$0.562095\pi$
$152$	−6.47214	−0.524960
$153$	−0.618034	−0.0499651
$154$	−6.09017	−0.490760
$155$	−18.9443	−1.52164
$156$	8.94427	0.716115
$157$	−1.05573	−0.0842563	−0.0421281	−	0.999112i	$-0.513414\pi$
$157$	−1.05573	−0.0842563	−0.0421281	+	0.999112i	$0.513414\pi$
$158$	7.14590	0.568497
$159$	−22.4721	−1.78216
$160$	3.61803	0.286031
$161$	−9.23607	−0.727904
$162$	11.0000	0.864242
$163$	−10.7984	−0.845794	−0.422897	−	0.906178i	$-0.638987\pi$
$163$	−10.7984	−0.845794	−0.422897	+	0.906178i	$0.638987\pi$
$164$	−10.9443	−0.854604
$165$	44.0689	3.43076
$166$	2.47214	0.191875
$167$	17.4164	1.34772	0.673861	−	0.738858i	$-0.264635\pi$
$167$	17.4164	1.34772	0.673861	+	0.738858i	$0.264635\pi$
$168$	2.00000	0.154303
$169$	7.00000	0.538462
$170$	−2.23607	−0.171499
$171$	6.47214	0.494937
$172$	0	0
$173$	−0.472136	−0.0358958	−0.0179479	−	0.999839i	$-0.505713\pi$
$173$	−0.472136	−0.0358958	−0.0179479	+	0.999839i	$0.505713\pi$
$174$	−2.47214	−0.187412
$175$	−8.09017	−0.611559
$176$	−6.09017	−0.459064
$177$	24.3607	1.83106
$178$	13.6180	1.02071
$179$	−23.7426	−1.77461	−0.887304	−	0.461184i	$-0.847425\pi$
$179$	−23.7426	−1.77461	−0.887304	+	0.461184i	$0.847425\pi$
$180$	−3.61803	−0.269672
$181$	15.1246	1.12420	0.562102	−	0.827068i	$-0.309993\pi$
$181$	15.1246	1.12420	0.562102	+	0.827068i	$0.309993\pi$
$182$	4.47214	0.331497
$183$	−15.7082	−1.16118
$184$	−9.23607	−0.680892
$185$	28.4164	2.08922
$186$	−10.4721	−0.767854
$187$	3.76393	0.275246
$188$	2.00000	0.145865
$189$	4.00000	0.290957
$190$	23.4164	1.69880
$191$	−24.7984	−1.79435	−0.897174	−	0.441678i	$-0.854383\pi$
$191$	−24.7984	−1.79435	−0.897174	+	0.441678i	$0.854383\pi$
$192$	2.00000	0.144338
$193$	−21.4164	−1.54159	−0.770793	−	0.637085i	$-0.780140\pi$
$193$	−21.4164	−1.54159	−0.770793	+	0.637085i	$0.780140\pi$
$194$	14.1803	1.01809
$195$	−32.3607	−2.31740
$196$	1.00000	0.0714286
$197$	20.9443	1.49222	0.746109	−	0.665824i	$-0.231920\pi$
$197$	20.9443	1.49222	0.746109	+	0.665824i	$0.231920\pi$
$198$	6.09017	0.432810
$199$	−19.7082	−1.39708	−0.698539	−	0.715572i	$-0.746166\pi$
$199$	−19.7082	−1.39708	−0.698539	+	0.715572i	$0.746166\pi$
$200$	−8.09017	−0.572061
$201$	8.94427	0.630880
$202$	4.47214	0.314658
$203$	−1.23607	−0.0867550
$204$	−1.23607	−0.0865421
$205$	39.5967	2.76556
$206$	−10.4721	−0.729628
$207$	9.23607	0.641951
$208$	4.47214	0.310087
$209$	−39.4164	−2.72649
$210$	−7.23607	−0.499336
$211$	10.4721	0.720932	0.360466	−	0.932772i	$-0.382618\pi$
$211$	10.4721	0.720932	0.360466	+	0.932772i	$0.382618\pi$
$212$	−11.2361	−0.771696
$213$	19.2361	1.31803
$214$	−9.23607	−0.631365
$215$	0	0
$216$	4.00000	0.272166
$217$	−5.23607	−0.355447
$218$	2.29180	0.155220
$219$	8.94427	0.604398
$220$	22.0344	1.48556
$221$	−2.76393	−0.185922
$222$	15.7082	1.05427
$223$	−21.0902	−1.41230	−0.706151	−	0.708061i	$-0.749570\pi$
$223$	−21.0902	−1.41230	−0.706151	+	0.708061i	$0.749570\pi$
$224$	1.00000	0.0668153
$225$	8.09017	0.539345
$226$	−4.94427	−0.328888
$227$	2.18034	0.144714	0.0723571	−	0.997379i	$-0.476948\pi$
$227$	2.18034	0.144714	0.0723571	+	0.997379i	$0.476948\pi$
$228$	12.9443	0.857255
$229$	−22.6180	−1.49464	−0.747321	−	0.664463i	$-0.768660\pi$
$229$	−22.6180	−1.49464	−0.747321	+	0.664463i	$0.768660\pi$
$230$	33.4164	2.20341
$231$	12.1803	0.801408
$232$	−1.23607	−0.0811518
$233$	−17.2361	−1.12917	−0.564586	−	0.825374i	$-0.690964\pi$
$233$	−17.2361	−1.12917	−0.564586	+	0.825374i	$0.690964\pi$
$234$	−4.47214	−0.292353
$235$	−7.23607	−0.472029
$236$	12.1803	0.792873
$237$	−14.2918	−0.928352
$238$	−0.618034	−0.0400612
$239$	−3.56231	−0.230426	−0.115213	−	0.993341i	$-0.536755\pi$
$239$	−3.56231	−0.230426	−0.115213	+	0.993341i	$0.536755\pi$
$240$	−7.23607	−0.467086
$241$	5.61803	0.361889	0.180945	−	0.983493i	$-0.442084\pi$
$241$	5.61803	0.361889	0.180945	+	0.983493i	$0.442084\pi$
$242$	−26.0902	−1.67714
$243$	−10.0000	−0.641500
$244$	−7.85410	−0.502807
$245$	−3.61803	−0.231148
$246$	21.8885	1.39556
$247$	28.9443	1.84168
$248$	−5.23607	−0.332491
$249$	−4.94427	−0.313331
$250$	11.1803	0.707107
$251$	20.6180	1.30140	0.650699	−	0.759335i	$-0.274476\pi$
$251$	20.6180	1.30140	0.650699	+	0.759335i	$0.274476\pi$
$252$	−1.00000	−0.0629941
$253$	−56.2492	−3.53636
$254$	−4.14590	−0.260137
$255$	4.47214	0.280056
$256$	1.00000	0.0625000
$257$	2.79837	0.174558	0.0872789	−	0.996184i	$-0.472183\pi$
$257$	2.79837	0.174558	0.0872789	+	0.996184i	$0.472183\pi$
$258$	0	0
$259$	7.85410	0.488030
$260$	−16.1803	−1.00346
$261$	1.23607	0.0765107
$262$	−6.09017	−0.376252
$263$	−30.1803	−1.86100	−0.930500	−	0.366293i	$-0.880627\pi$
$263$	−30.1803	−1.86100	−0.930500	+	0.366293i	$0.880627\pi$
$264$	12.1803	0.749648
$265$	40.6525	2.49726
$266$	6.47214	0.396832
$267$	−27.2361	−1.66682
$268$	4.47214	0.273179
$269$	−18.4721	−1.12627	−0.563133	−	0.826366i	$-0.690404\pi$
$269$	−18.4721	−1.12627	−0.563133	+	0.826366i	$0.690404\pi$
$270$	−14.4721	−0.880746
$271$	−24.7639	−1.50430	−0.752151	−	0.658991i	$-0.770984\pi$
$271$	−24.7639	−1.50430	−0.752151	+	0.658991i	$0.770984\pi$
$272$	−0.618034	−0.0374738
$273$	−8.94427	−0.541332
$274$	22.4721	1.35759
$275$	−49.2705	−2.97112
$276$	18.4721	1.11189
$277$	−0.944272	−0.0567358	−0.0283679	−	0.999598i	$-0.509031\pi$
$277$	−0.944272	−0.0567358	−0.0283679	+	0.999598i	$0.509031\pi$
$278$	−5.52786	−0.331539
$279$	5.23607	0.313475
$280$	−3.61803	−0.216219
$281$	−7.81966	−0.466482	−0.233241	−	0.972419i	$-0.574933\pi$
$281$	−7.81966	−0.466482	−0.233241	+	0.972419i	$0.574933\pi$
$282$	−4.00000	−0.238197
$283$	13.2361	0.786803	0.393401	−	0.919367i	$-0.371298\pi$
$283$	13.2361	0.786803	0.393401	+	0.919367i	$0.371298\pi$
$284$	9.61803	0.570725
$285$	−46.8328	−2.77414
$286$	27.2361	1.61050
$287$	10.9443	0.646020
$288$	−1.00000	−0.0589256
$289$	−16.6180	−0.977531
$290$	4.47214	0.262613
$291$	−28.3607	−1.66253
$292$	4.47214	0.261712
$293$	−18.7639	−1.09620	−0.548100	−	0.836413i	$-0.684649\pi$
$293$	−18.7639	−1.09620	−0.548100	+	0.836413i	$0.684649\pi$
$294$	−2.00000	−0.116642
$295$	−44.0689	−2.56579
$296$	7.85410	0.456510
$297$	24.3607	1.41355
$298$	18.0000	1.04271
$299$	41.3050	2.38873
$300$	16.1803	0.934172
$301$	0	0
$302$	4.76393	0.274133
$303$	−8.94427	−0.513835
$304$	6.47214	0.371202
$305$	28.4164	1.62712
$306$	0.618034	0.0353307
$307$	−6.65248	−0.379677	−0.189838	−	0.981815i	$-0.560796\pi$
$307$	−6.65248	−0.379677	−0.189838	+	0.981815i	$0.560796\pi$
$308$	6.09017	0.347020
$309$	20.9443	1.19148
$310$	18.9443	1.07596
$311$	19.7082	1.11755	0.558775	−	0.829319i	$-0.311272\pi$
$311$	19.7082	1.11755	0.558775	+	0.829319i	$0.311272\pi$
$312$	−8.94427	−0.506370
$313$	−12.0902	−0.683377	−0.341688	−	0.939813i	$-0.610999\pi$
$313$	−12.0902	−0.683377	−0.341688	+	0.939813i	$0.610999\pi$
$314$	1.05573	0.0595782
$315$	3.61803	0.203853
$316$	−7.14590	−0.401988
$317$	0.437694	0.0245833	0.0122917	−	0.999924i	$-0.496087\pi$
$317$	0.437694	0.0245833	0.0122917	+	0.999924i	$0.496087\pi$
$318$	22.4721	1.26017
$319$	−7.52786	−0.421479
$320$	−3.61803	−0.202254
$321$	18.4721	1.03101
$322$	9.23607	0.514706
$323$	−4.00000	−0.222566
$324$	−11.0000	−0.611111
$325$	36.1803	2.00692
$326$	10.7984	0.598067
$327$	−4.58359	−0.253473
$328$	10.9443	0.604296
$329$	−2.00000	−0.110264
$330$	−44.0689	−2.42591
$331$	−10.3607	−0.569474	−0.284737	−	0.958606i	$-0.591906\pi$
$331$	−10.3607	−0.569474	−0.284737	+	0.958606i	$0.591906\pi$
$332$	−2.47214	−0.135676
$333$	−7.85410	−0.430402
$334$	−17.4164	−0.952983
$335$	−16.1803	−0.884026
$336$	−2.00000	−0.109109
$337$	−9.85410	−0.536787	−0.268394	−	0.963309i	$-0.586493\pi$
$337$	−9.85410	−0.536787	−0.268394	+	0.963309i	$0.586493\pi$
$338$	−7.00000	−0.380750
$339$	9.88854	0.537072
$340$	2.23607	0.121268
$341$	−31.8885	−1.72686
$342$	−6.47214	−0.349973
$343$	−1.00000	−0.0539949
$344$	0	0
$345$	−66.8328	−3.59816
$346$	0.472136	0.0253822
$347$	−24.5623	−1.31857	−0.659287	−	0.751892i	$-0.729142\pi$
$347$	−24.5623	−1.31857	−0.659287	+	0.751892i	$0.729142\pi$
$348$	2.47214	0.132520
$349$	20.8328	1.11516	0.557578	−	0.830125i	$-0.311731\pi$
$349$	20.8328	1.11516	0.557578	+	0.830125i	$0.311731\pi$
$350$	8.09017	0.432438
$351$	−17.8885	−0.954820
$352$	6.09017	0.324607
$353$	−2.58359	−0.137511	−0.0687554	−	0.997634i	$-0.521903\pi$
$353$	−2.58359	−0.137511	−0.0687554	+	0.997634i	$0.521903\pi$
$354$	−24.3607	−1.29476
$355$	−34.7984	−1.84691
$356$	−13.6180	−0.721754
$357$	1.23607	0.0654197
$358$	23.7426	1.25484
$359$	−14.5623	−0.768569	−0.384285	−	0.923215i	$-0.625552\pi$
$359$	−14.5623	−0.768569	−0.384285	+	0.923215i	$0.625552\pi$
$360$	3.61803	0.190687
$361$	22.8885	1.20466
$362$	−15.1246	−0.794932
$363$	52.1803	2.73876
$364$	−4.47214	−0.234404
$365$	−16.1803	−0.846918
$366$	15.7082	0.821081
$367$	0.472136	0.0246453	0.0123226	−	0.999924i	$-0.496077\pi$
$367$	0.472136	0.0246453	0.0123226	+	0.999924i	$0.496077\pi$
$368$	9.23607	0.481463
$369$	−10.9443	−0.569736
$370$	−28.4164	−1.47730
$371$	11.2361	0.583348
$372$	10.4721	0.542955
$373$	−17.5066	−0.906456	−0.453228	−	0.891395i	$-0.649728\pi$
$373$	−17.5066	−0.906456	−0.453228	+	0.891395i	$0.649728\pi$
$374$	−3.76393	−0.194628
$375$	−22.3607	−1.15470
$376$	−2.00000	−0.103142
$377$	5.52786	0.284699
$378$	−4.00000	−0.205738
$379$	32.7426	1.68188	0.840938	−	0.541131i	$-0.182004\pi$
$379$	32.7426	1.68188	0.840938	+	0.541131i	$0.182004\pi$
$380$	−23.4164	−1.20124
$381$	8.29180	0.424802
$382$	24.7984	1.26880
$383$	−4.94427	−0.252640	−0.126320	−	0.991990i	$-0.540317\pi$
$383$	−4.94427	−0.252640	−0.126320	+	0.991990i	$0.540317\pi$
$384$	−2.00000	−0.102062
$385$	−22.0344	−1.12298
$386$	21.4164	1.09007
$387$	0	0
$388$	−14.1803	−0.719898
$389$	14.1803	0.718972	0.359486	−	0.933151i	$-0.382952\pi$
$389$	14.1803	0.718972	0.359486	+	0.933151i	$0.382952\pi$
$390$	32.3607	1.63865
$391$	−5.70820	−0.288676
$392$	−1.00000	−0.0505076
$393$	12.1803	0.614417
$394$	−20.9443	−1.05516
$395$	25.8541	1.30086
$396$	−6.09017	−0.306043
$397$	4.14590	0.208077	0.104038	−	0.994573i	$-0.466824\pi$
$397$	4.14590	0.208077	0.104038	+	0.994573i	$0.466824\pi$
$398$	19.7082	0.987883
$399$	−12.9443	−0.648024
$400$	8.09017	0.404508
$401$	−13.4164	−0.669983	−0.334992	−	0.942221i	$-0.608734\pi$
$401$	−13.4164	−0.669983	−0.334992	+	0.942221i	$0.608734\pi$
$402$	−8.94427	−0.446100
$403$	23.4164	1.16645
$404$	−4.47214	−0.222497
$405$	39.7984	1.97760
$406$	1.23607	0.0613450
$407$	47.8328	2.37098
$408$	1.23607	0.0611945
$409$	−0.854102	−0.0422326	−0.0211163	−	0.999777i	$-0.506722\pi$
$409$	−0.854102	−0.0422326	−0.0211163	+	0.999777i	$0.506722\pi$
$410$	−39.5967	−1.95554
$411$	−44.9443	−2.21694
$412$	10.4721	0.515925
$413$	−12.1803	−0.599355
$414$	−9.23607	−0.453928
$415$	8.94427	0.439057
$416$	−4.47214	−0.219265
$417$	11.0557	0.541401
$418$	39.4164	1.92792
$419$	24.9787	1.22029	0.610145	−	0.792290i	$-0.291111\pi$
$419$	24.9787	1.22029	0.610145	+	0.792290i	$0.291111\pi$
$420$	7.23607	0.353084
$421$	−16.3820	−0.798408	−0.399204	−	0.916862i	$-0.630714\pi$
$421$	−16.3820	−0.798408	−0.399204	+	0.916862i	$0.630714\pi$
$422$	−10.4721	−0.509776
$423$	2.00000	0.0972433
$424$	11.2361	0.545672
$425$	−5.00000	−0.242536
$426$	−19.2361	−0.931991
$427$	7.85410	0.380087
$428$	9.23607	0.446442
$429$	−54.4721	−2.62994
$430$	0	0
$431$	−1.00000	−0.0481683
$431$	−1.00000	−0.0481683
$432$	−4.00000	−0.192450
$433$	14.1803	0.681464	0.340732	−	0.940161i	$-0.389325\pi$
$433$	14.1803	0.681464	0.340732	+	0.940161i	$0.389325\pi$
$434$	5.23607	0.251339
$435$	−8.94427	−0.428845
$436$	−2.29180	−0.109757
$437$	59.7771	2.85953
$438$	−8.94427	−0.427374
$439$	26.6869	1.27370	0.636849	−	0.770989i	$-0.280238\pi$
$439$	26.6869	1.27370	0.636849	+	0.770989i	$0.280238\pi$
$440$	−22.0344	−1.05045
$441$	1.00000	0.0476190
$442$	2.76393	0.131467
$443$	−7.74265	−0.367864	−0.183932	−	0.982939i	$-0.558883\pi$
$443$	−7.74265	−0.367864	−0.183932	+	0.982939i	$0.558883\pi$
$444$	−15.7082	−0.745478
$445$	49.2705	2.33565
$446$	21.0902	0.998648
$447$	−36.0000	−1.70274
$448$	−1.00000	−0.0472456
$449$	14.5623	0.687238	0.343619	−	0.939109i	$-0.388347\pi$
$449$	14.5623	0.687238	0.343619	+	0.939109i	$0.388347\pi$
$450$	−8.09017	−0.381374
$451$	66.6525	3.13854
$452$	4.94427	0.232559
$453$	−9.52786	−0.447658
$454$	−2.18034	−0.102328
$455$	16.1803	0.758546
$456$	−12.9443	−0.606171
$457$	−14.3607	−0.671764	−0.335882	−	0.941904i	$-0.609034\pi$
$457$	−14.3607	−0.671764	−0.335882	+	0.941904i	$0.609034\pi$
$458$	22.6180	1.05687
$459$	2.47214	0.115389
$460$	−33.4164	−1.55805
$461$	−1.09017	−0.0507743	−0.0253871	−	0.999678i	$-0.508082\pi$
$461$	−1.09017	−0.0507743	−0.0253871	+	0.999678i	$0.508082\pi$
$462$	−12.1803	−0.566681
$463$	−33.5967	−1.56137	−0.780687	−	0.624923i	$-0.785130\pi$
$463$	−33.5967	−1.56137	−0.780687	+	0.624923i	$0.785130\pi$
$464$	1.23607	0.0573830
$465$	−37.8885	−1.75704
$466$	17.2361	0.798445
$467$	12.0000	0.555294	0.277647	−	0.960683i	$-0.410445\pi$
$467$	12.0000	0.555294	0.277647	+	0.960683i	$0.410445\pi$
$468$	4.47214	0.206725
$469$	−4.47214	−0.206504
$470$	7.23607	0.333775
$471$	−2.11146	−0.0972908
$472$	−12.1803	−0.560646
$473$	0	0
$474$	14.2918	0.656444
$475$	52.3607	2.40247
$476$	0.618034	0.0283275
$477$	−11.2361	−0.514464
$478$	3.56231	0.162936
$479$	−25.8885	−1.18288	−0.591439	−	0.806350i	$-0.701440\pi$
$479$	−25.8885	−1.18288	−0.591439	+	0.806350i	$0.701440\pi$
$480$	7.23607	0.330280
$481$	−35.1246	−1.60154
$482$	−5.61803	−0.255894
$483$	−18.4721	−0.840511
$484$	26.0902	1.18592
$485$	51.3050	2.32964
$486$	10.0000	0.453609
$487$	−16.0000	−0.725029	−0.362515	−	0.931978i	$-0.618082\pi$
$487$	−16.0000	−0.725029	−0.362515	+	0.931978i	$0.618082\pi$
$488$	7.85410	0.355538
$489$	−21.5967	−0.976639
$490$	3.61803	0.163446
$491$	5.85410	0.264192	0.132096	−	0.991237i	$-0.457829\pi$
$491$	5.85410	0.264192	0.132096	+	0.991237i	$0.457829\pi$
$492$	−21.8885	−0.986812
$493$	−0.763932	−0.0344058
$494$	−28.9443	−1.30226
$495$	22.0344	0.990375
$496$	5.23607	0.235106
$497$	−9.61803	−0.431428
$498$	4.94427	0.221558
$499$	38.9443	1.74339	0.871693	−	0.490053i	$-0.163023\pi$
$499$	38.9443	1.74339	0.871693	+	0.490053i	$0.163023\pi$
$500$	−11.1803	−0.500000
$501$	34.8328	1.55622
$502$	−20.6180	−0.920228
$503$	22.0344	0.982467	0.491234	−	0.871028i	$-0.336546\pi$
$503$	22.0344	0.982467	0.491234	+	0.871028i	$0.336546\pi$
$504$	1.00000	0.0445435
$505$	16.1803	0.720016
$506$	56.2492	2.50058
$507$	14.0000	0.621762
$508$	4.14590	0.183944
$509$	1.70820	0.0757148	0.0378574	−	0.999283i	$-0.487947\pi$
$509$	1.70820	0.0757148	0.0378574	+	0.999283i	$0.487947\pi$
$510$	−4.47214	−0.198030
$511$	−4.47214	−0.197836
$512$	−1.00000	−0.0441942
$513$	−25.8885	−1.14301
$514$	−2.79837	−0.123431
$515$	−37.8885	−1.66957
$516$	0	0
$517$	−12.1803	−0.535691
$518$	−7.85410	−0.345089
$519$	−0.944272	−0.0414489
$520$	16.1803	0.709555
$521$	−6.58359	−0.288432	−0.144216	−	0.989546i	$-0.546066\pi$
$521$	−6.58359	−0.288432	−0.144216	+	0.989546i	$0.546066\pi$
$522$	−1.23607	−0.0541012
$523$	−32.8328	−1.43568	−0.717839	−	0.696209i	$-0.754869\pi$
$523$	−32.8328	−1.43568	−0.717839	+	0.696209i	$0.754869\pi$
$524$	6.09017	0.266050
$525$	−16.1803	−0.706168
$526$	30.1803	1.31593
$527$	−3.23607	−0.140965
$528$	−12.1803	−0.530081
$529$	62.3050	2.70891
$530$	−40.6525	−1.76583
$531$	12.1803	0.528582
$532$	−6.47214	−0.280603
$533$	−48.9443	−2.12001
$534$	27.2361	1.17862
$535$	−33.4164	−1.44472
$536$	−4.47214	−0.193167
$537$	−47.4853	−2.04914
$538$	18.4721	0.796390
$539$	−6.09017	−0.262322
$540$	14.4721	0.622782
$541$	34.7639	1.49462	0.747309	−	0.664477i	$-0.231345\pi$
$541$	34.7639	1.49462	0.747309	+	0.664477i	$0.231345\pi$
$542$	24.7639	1.06370
$543$	30.2492	1.29812
$544$	0.618034	0.0264980
$545$	8.29180	0.355182
$546$	8.94427	0.382780
$547$	11.3820	0.486658	0.243329	−	0.969944i	$-0.421761\pi$
$547$	11.3820	0.486658	0.243329	+	0.969944i	$0.421761\pi$
$548$	−22.4721	−0.959962
$549$	−7.85410	−0.335205
$550$	49.2705	2.10090
$551$	8.00000	0.340811
$552$	−18.4721	−0.786226
$553$	7.14590	0.303874
$554$	0.944272	0.0401183
$555$	56.8328	2.41242
$556$	5.52786	0.234434
$557$	−27.8885	−1.18168	−0.590838	−	0.806790i	$-0.701203\pi$
$557$	−27.8885	−1.18168	−0.590838	+	0.806790i	$0.701203\pi$
$558$	−5.23607	−0.221660
$559$	0	0
$560$	3.61803	0.152890
$561$	7.52786	0.317827
$562$	7.81966	0.329852
$563$	−14.0000	−0.590030	−0.295015	−	0.955493i	$-0.595325\pi$
$563$	−14.0000	−0.590030	−0.295015	+	0.955493i	$0.595325\pi$
$564$	4.00000	0.168430
$565$	−17.8885	−0.752577
$566$	−13.2361	−0.556353
$567$	11.0000	0.461957
$568$	−9.61803	−0.403564
$569$	28.6738	1.20207	0.601033	−	0.799224i	$-0.294756\pi$
$569$	28.6738	1.20207	0.601033	+	0.799224i	$0.294756\pi$
$570$	46.8328	1.96161
$571$	46.1803	1.93259	0.966294	−	0.257443i	$-0.0828799\pi$
$571$	46.1803	1.93259	0.966294	+	0.257443i	$0.0828799\pi$
$572$	−27.2361	−1.13880
$573$	−49.5967	−2.07193
$574$	−10.9443	−0.456805
$575$	74.7214	3.11610
$576$	1.00000	0.0416667
$577$	−13.9787	−0.581941	−0.290971	−	0.956732i	$-0.593978\pi$
$577$	−13.9787	−0.581941	−0.290971	+	0.956732i	$0.593978\pi$
$578$	16.6180	0.691219
$579$	−42.8328	−1.78007
$580$	−4.47214	−0.185695
$581$	2.47214	0.102561
$582$	28.3607	1.17559
$583$	68.4296	2.83406
$584$	−4.47214	−0.185058
$585$	−16.1803	−0.668975
$586$	18.7639	0.775131
$587$	45.9230	1.89544	0.947722	−	0.319096i	$-0.103379\pi$
$587$	45.9230	1.89544	0.947722	+	0.319096i	$0.103379\pi$
$588$	2.00000	0.0824786
$589$	33.8885	1.39635
$590$	44.0689	1.81429
$591$	41.8885	1.72306
$592$	−7.85410	−0.322802
$593$	15.4164	0.633076	0.316538	−	0.948580i	$-0.397480\pi$
$593$	15.4164	0.633076	0.316538	+	0.948580i	$0.397480\pi$
$594$	−24.3607	−0.999531
$595$	−2.23607	−0.0916698
$596$	−18.0000	−0.737309
$597$	−39.4164	−1.61321
$598$	−41.3050	−1.68909
$599$	24.5066	1.00131	0.500656	−	0.865646i	$-0.333092\pi$
$599$	24.5066	1.00131	0.500656	+	0.865646i	$0.333092\pi$
$600$	−16.1803	−0.660560
$601$	−44.3951	−1.81091	−0.905457	−	0.424437i	$-0.860472\pi$
$601$	−44.3951	−1.81091	−0.905457	+	0.424437i	$0.860472\pi$
$602$	0	0
$603$	4.47214	0.182119
$604$	−4.76393	−0.193842
$605$	−94.3951	−3.83771
$606$	8.94427	0.363336
$607$	7.90983	0.321050	0.160525	−	0.987032i	$-0.448681\pi$
$607$	7.90983	0.321050	0.160525	+	0.987032i	$0.448681\pi$
$608$	−6.47214	−0.262480
$609$	−2.47214	−0.100176
$610$	−28.4164	−1.15055
$611$	8.94427	0.361847
$612$	−0.618034	−0.0249825
$613$	−0.291796	−0.0117855	−0.00589277	−	0.999983i	$-0.501876\pi$
$613$	−0.291796	−0.0117855	−0.00589277	+	0.999983i	$0.501876\pi$
$614$	6.65248	0.268472
$615$	79.1935	3.19339
$616$	−6.09017	−0.245380
$617$	12.6525	0.509369	0.254685	−	0.967024i	$-0.418028\pi$
$617$	12.6525	0.509369	0.254685	+	0.967024i	$0.418028\pi$
$618$	−20.9443	−0.842502
$619$	−2.79837	−0.112476	−0.0562381	−	0.998417i	$-0.517911\pi$
$619$	−2.79837	−0.112476	−0.0562381	+	0.998417i	$0.517911\pi$
$620$	−18.9443	−0.760820
$621$	−36.9443	−1.48252
$622$	−19.7082	−0.790227
$623$	13.6180	0.545595
$624$	8.94427	0.358057
$625$	0	0
$626$	12.0902	0.483220
$627$	−78.8328	−3.14828
$628$	−1.05573	−0.0421281
$629$	4.85410	0.193546
$630$	−3.61803	−0.144146
$631$	−18.2918	−0.728185	−0.364092	−	0.931363i	$-0.618621\pi$
$631$	−18.2918	−0.728185	−0.364092	+	0.931363i	$0.618621\pi$
$632$	7.14590	0.284249
$633$	20.9443	0.832460
$634$	−0.437694	−0.0173831
$635$	−15.0000	−0.595257
$636$	−22.4721	−0.891078
$637$	4.47214	0.177192
$638$	7.52786	0.298031
$639$	9.61803	0.380484
$640$	3.61803	0.143015
$641$	33.5967	1.32699	0.663496	−	0.748180i	$-0.269072\pi$
$641$	33.5967	1.32699	0.663496	+	0.748180i	$0.269072\pi$
$642$	−18.4721	−0.729037
$643$	−7.59675	−0.299586	−0.149793	−	0.988717i	$-0.547861\pi$
$643$	−7.59675	−0.299586	−0.149793	+	0.988717i	$0.547861\pi$
$644$	−9.23607	−0.363952
$645$	0	0
$646$	4.00000	0.157378
$647$	−9.67376	−0.380315	−0.190157	−	0.981754i	$-0.560900\pi$
$647$	−9.67376	−0.380315	−0.190157	+	0.981754i	$0.560900\pi$
$648$	11.0000	0.432121
$649$	−74.1803	−2.91183
$650$	−36.1803	−1.41911
$651$	−10.4721	−0.410435
$652$	−10.7984	−0.422897
$653$	−20.2148	−0.791066	−0.395533	−	0.918452i	$-0.629440\pi$
$653$	−20.2148	−0.791066	−0.395533	+	0.918452i	$0.629440\pi$
$654$	4.58359	0.179233
$655$	−22.0344	−0.860957
$656$	−10.9443	−0.427302
$657$	4.47214	0.174475
$658$	2.00000	0.0779681
$659$	35.9787	1.40153	0.700766	−	0.713391i	$-0.252842\pi$
$659$	35.9787	1.40153	0.700766	+	0.713391i	$0.252842\pi$
$660$	44.0689	1.71538
$661$	−0.965558	−0.0375559	−0.0187779	−	0.999824i	$-0.505978\pi$
$661$	−0.965558	−0.0375559	−0.0187779	+	0.999824i	$0.505978\pi$
$662$	10.3607	0.402679
$663$	−5.52786	−0.214684
$664$	2.47214	0.0959375
$665$	23.4164	0.908049
$666$	7.85410	0.304340
$667$	11.4164	0.442045
$668$	17.4164	0.673861
$669$	−42.1803	−1.63079
$670$	16.1803	0.625101
$671$	47.8328	1.84657
$672$	2.00000	0.0771517
$673$	36.8541	1.42062	0.710311	−	0.703888i	$-0.248554\pi$
$673$	36.8541	1.42062	0.710311	+	0.703888i	$0.248554\pi$
$674$	9.85410	0.379566
$675$	−32.3607	−1.24556
$676$	7.00000	0.269231
$677$	4.21478	0.161987	0.0809936	−	0.996715i	$-0.474191\pi$
$677$	4.21478	0.161987	0.0809936	+	0.996715i	$0.474191\pi$
$678$	−9.88854	−0.379767
$679$	14.1803	0.544191
$680$	−2.23607	−0.0857493
$681$	4.36068	0.167102
$682$	31.8885	1.22108
$683$	−5.70820	−0.218418	−0.109209	−	0.994019i	$-0.534832\pi$
$683$	−5.70820	−0.218418	−0.109209	+	0.994019i	$0.534832\pi$
$684$	6.47214	0.247468
$685$	81.3050	3.10650
$686$	1.00000	0.0381802
$687$	−45.2361	−1.72586
$688$	0	0
$689$	−50.2492	−1.91434
$690$	66.8328	2.54428
$691$	21.1459	0.804428	0.402214	−	0.915546i	$-0.368241\pi$
$691$	21.1459	0.804428	0.402214	+	0.915546i	$0.368241\pi$
$692$	−0.472136	−0.0179479
$693$	6.09017	0.231346
$694$	24.5623	0.932372
$695$	−20.0000	−0.758643
$696$	−2.47214	−0.0937061
$697$	6.76393	0.256202
$698$	−20.8328	−0.788534
$699$	−34.4721	−1.30386
$700$	−8.09017	−0.305780
$701$	12.8328	0.484689	0.242344	−	0.970190i	$-0.422084\pi$
$701$	12.8328	0.484689	0.242344	+	0.970190i	$0.422084\pi$
$702$	17.8885	0.675160
$703$	−50.8328	−1.91720
$704$	−6.09017	−0.229532
$705$	−14.4721	−0.545052
$706$	2.58359	0.0972348
$707$	4.47214	0.168192
$708$	24.3607	0.915530
$709$	5.52786	0.207603	0.103802	−	0.994598i	$-0.466899\pi$
$709$	5.52786	0.207603	0.103802	+	0.994598i	$0.466899\pi$
$710$	34.7984	1.30596
$711$	−7.14590	−0.267992
$712$	13.6180	0.510357
$713$	48.3607	1.81112
$714$	−1.23607	−0.0462587
$715$	98.5410	3.68523
$716$	−23.7426	−0.887304
$717$	−7.12461	−0.266074
$718$	14.5623	0.543460
$719$	−20.2705	−0.755962	−0.377981	−	0.925813i	$-0.623382\pi$
$719$	−20.2705	−0.755962	−0.377981	+	0.925813i	$0.623382\pi$
$720$	−3.61803	−0.134836
$721$	−10.4721	−0.390003
$722$	−22.8885	−0.851823
$723$	11.2361	0.417874
$724$	15.1246	0.562102
$725$	10.0000	0.371391
$726$	−52.1803	−1.93659
$727$	−37.4853	−1.39025	−0.695126	−	0.718888i	$-0.744652\pi$
$727$	−37.4853	−1.39025	−0.695126	+	0.718888i	$0.744652\pi$
$728$	4.47214	0.165748
$729$	13.0000	0.481481
$730$	16.1803	0.598861
$731$	0	0
$732$	−15.7082	−0.580592
$733$	−16.2016	−0.598421	−0.299210	−	0.954187i	$-0.596723\pi$
$733$	−16.2016	−0.598421	−0.299210	+	0.954187i	$0.596723\pi$
$734$	−0.472136	−0.0174269
$735$	−7.23607	−0.266906
$736$	−9.23607	−0.340446
$737$	−27.2361	−1.00325
$738$	10.9443	0.402864
$739$	−39.1246	−1.43922	−0.719611	−	0.694377i	$-0.755680\pi$
$739$	−39.1246	−1.43922	−0.719611	+	0.694377i	$0.755680\pi$
$740$	28.4164	1.04461
$741$	57.8885	2.12659
$742$	−11.2361	−0.412489
$743$	−47.6312	−1.74742	−0.873709	−	0.486448i	$-0.838292\pi$
$743$	−47.6312	−1.74742	−0.873709	+	0.486448i	$0.838292\pi$
$744$	−10.4721	−0.383927
$745$	65.1246	2.38598
$746$	17.5066	0.640961
$747$	−2.47214	−0.0904507
$748$	3.76393	0.137623
$749$	−9.23607	−0.337479
$750$	22.3607	0.816497
$751$	−15.3475	−0.560039	−0.280020	−	0.959994i	$-0.590341\pi$
$751$	−15.3475	−0.560039	−0.280020	+	0.959994i	$0.590341\pi$
$752$	2.00000	0.0729325
$753$	41.2361	1.50273
$754$	−5.52786	−0.201313
$755$	17.2361	0.627285
$756$	4.00000	0.145479
$757$	6.11146	0.222125	0.111062	−	0.993813i	$-0.464575\pi$
$757$	6.11146	0.222125	0.111062	+	0.993813i	$0.464575\pi$
$758$	−32.7426	−1.18927
$759$	−112.498	−4.08343
$760$	23.4164	0.849402
$761$	3.41641	0.123845	0.0619223	−	0.998081i	$-0.480277\pi$
$761$	3.41641	0.123845	0.0619223	+	0.998081i	$0.480277\pi$
$762$	−8.29180	−0.300380
$763$	2.29180	0.0829686
$764$	−24.7984	−0.897174
$765$	2.23607	0.0808452
$766$	4.94427	0.178644
$767$	54.4721	1.96687
$768$	2.00000	0.0721688
$769$	−39.8885	−1.43842	−0.719209	−	0.694794i	$-0.755496\pi$
$769$	−39.8885	−1.43842	−0.719209	+	0.694794i	$0.755496\pi$
$770$	22.0344	0.794066
$771$	5.59675	0.201562
$772$	−21.4164	−0.770793
$773$	−37.6738	−1.35503	−0.677516	−	0.735508i	$-0.736943\pi$
$773$	−37.6738	−1.35503	−0.677516	+	0.735508i	$0.736943\pi$
$774$	0	0
$775$	42.3607	1.52164
$776$	14.1803	0.509045
$777$	15.7082	0.563529
$778$	−14.1803	−0.508390
$779$	−70.8328	−2.53785
$780$	−32.3607	−1.15870
$781$	−58.5755	−2.09599
$782$	5.70820	0.204125
$783$	−4.94427	−0.176694
$784$	1.00000	0.0357143
$785$	3.81966	0.136330
$786$	−12.1803	−0.434458
$787$	−24.7426	−0.881980	−0.440990	−	0.897512i	$-0.645373\pi$
$787$	−24.7426	−0.881980	−0.440990	+	0.897512i	$0.645373\pi$
$788$	20.9443	0.746109
$789$	−60.3607	−2.14890
$790$	−25.8541	−0.919848
$791$	−4.94427	−0.175798
$792$	6.09017	0.216405
$793$	−35.1246	−1.24731
$794$	−4.14590	−0.147132
$795$	81.3050	2.88359
$796$	−19.7082	−0.698539
$797$	0.965558	0.0342018	0.0171009	−	0.999854i	$-0.494556\pi$
$797$	0.965558	0.0342018	0.0171009	+	0.999854i	$0.494556\pi$
$798$	12.9443	0.458222
$799$	−1.23607	−0.0437289
$800$	−8.09017	−0.286031
$801$	−13.6180	−0.481170
$802$	13.4164	0.473750
$803$	−27.2361	−0.961140
$804$	8.94427	0.315440
$805$	33.4164	1.17777
$806$	−23.4164	−0.824808
$807$	−36.9443	−1.30050
$808$	4.47214	0.157329
$809$	25.8885	0.910193	0.455096	−	0.890442i	$-0.349605\pi$
$809$	25.8885	0.910193	0.455096	+	0.890442i	$0.349605\pi$
$810$	−39.7984	−1.39837
$811$	−29.2361	−1.02662	−0.513309	−	0.858204i	$-0.671580\pi$
$811$	−29.2361	−1.02662	−0.513309	+	0.858204i	$0.671580\pi$
$812$	−1.23607	−0.0433775
$813$	−49.5279	−1.73702
$814$	−47.8328	−1.67654
$815$	39.0689	1.36852
$816$	−1.23607	−0.0432710
$817$	0	0
$818$	0.854102	0.0298630
$819$	−4.47214	−0.156269
$820$	39.5967	1.38278
$821$	3.27051	0.114142	0.0570708	−	0.998370i	$-0.481824\pi$
$821$	3.27051	0.114142	0.0570708	+	0.998370i	$0.481824\pi$
$822$	44.9443	1.56761
$823$	4.83282	0.168461	0.0842307	−	0.996446i	$-0.473157\pi$
$823$	4.83282	0.168461	0.0842307	+	0.996446i	$0.473157\pi$
$824$	−10.4721	−0.364814
$825$	−98.5410	−3.43076
$826$	12.1803	0.423808
$827$	31.6738	1.10140	0.550702	−	0.834702i	$-0.314360\pi$
$827$	31.6738	1.10140	0.550702	+	0.834702i	$0.314360\pi$
$828$	9.23607	0.320976
$829$	14.0000	0.486240	0.243120	−	0.969996i	$-0.421829\pi$
$829$	14.0000	0.486240	0.243120	+	0.969996i	$0.421829\pi$
$830$	−8.94427	−0.310460
$831$	−1.88854	−0.0655129
$832$	4.47214	0.155043
$833$	−0.618034	−0.0214136
$834$	−11.0557	−0.382829
$835$	−63.0132	−2.18066
$836$	−39.4164	−1.36324
$837$	−20.9443	−0.723940
$838$	−24.9787	−0.862875
$839$	20.0000	0.690477	0.345238	−	0.938515i	$-0.387798\pi$
$839$	20.0000	0.690477	0.345238	+	0.938515i	$0.387798\pi$
$840$	−7.23607	−0.249668
$841$	−27.4721	−0.947315
$842$	16.3820	0.564560
$843$	−15.6393	−0.538647
$844$	10.4721	0.360466
$845$	−25.3262	−0.871249
$846$	−2.00000	−0.0687614
$847$	−26.0902	−0.896469
$848$	−11.2361	−0.385848
$849$	26.4721	0.908521
$850$	5.00000	0.171499
$851$	−72.5410	−2.48667
$852$	19.2361	0.659017
$853$	−26.4721	−0.906389	−0.453194	−	0.891412i	$-0.649716\pi$
$853$	−26.4721	−0.906389	−0.453194	+	0.891412i	$0.649716\pi$
$854$	−7.85410	−0.268762
$855$	−23.4164	−0.800824
$856$	−9.23607	−0.315682
$857$	−5.27051	−0.180037	−0.0900186	−	0.995940i	$-0.528693\pi$
$857$	−5.27051	−0.180037	−0.0900186	+	0.995940i	$0.528693\pi$
$858$	54.4721	1.85965
$859$	−17.7295	−0.604922	−0.302461	−	0.953162i	$-0.597808\pi$
$859$	−17.7295	−0.604922	−0.302461	+	0.953162i	$0.597808\pi$
$860$	0	0
$861$	21.8885	0.745960
$862$	1.00000	0.0340601
$863$	52.4296	1.78472	0.892362	−	0.451321i	$-0.149047\pi$
$863$	52.4296	1.78472	0.892362	+	0.451321i	$0.149047\pi$
$864$	4.00000	0.136083
$865$	1.70820	0.0580807
$866$	−14.1803	−0.481868
$867$	−33.2361	−1.12876
$868$	−5.23607	−0.177724
$869$	43.5197	1.47631
$870$	8.94427	0.303239
$871$	20.0000	0.677674
$872$	2.29180	0.0776100
$873$	−14.1803	−0.479932
$874$	−59.7771	−2.02199
$875$	11.1803	0.377964
$876$	8.94427	0.302199
$877$	−37.3050	−1.25970	−0.629849	−	0.776717i	$-0.716883\pi$
$877$	−37.3050	−1.25970	−0.629849	+	0.776717i	$0.716883\pi$
$878$	−26.6869	−0.900640
$879$	−37.5279	−1.26578
$880$	22.0344	0.742781
$881$	−4.29180	−0.144594	−0.0722971	−	0.997383i	$-0.523033\pi$
$881$	−4.29180	−0.144594	−0.0722971	+	0.997383i	$0.523033\pi$
$882$	−1.00000	−0.0336718
$883$	42.8328	1.44144	0.720720	−	0.693227i	$-0.243812\pi$
$883$	42.8328	1.44144	0.720720	+	0.693227i	$0.243812\pi$
$884$	−2.76393	−0.0929611
$885$	−88.1378	−2.96272
$886$	7.74265	0.260119
$887$	−36.0000	−1.20876	−0.604381	−	0.796696i	$-0.706579\pi$
$887$	−36.0000	−1.20876	−0.604381	+	0.796696i	$0.706579\pi$
$888$	15.7082	0.527133
$889$	−4.14590	−0.139049
$890$	−49.2705	−1.65155
$891$	66.9919	2.24431
$892$	−21.0902	−0.706151
$893$	12.9443	0.433164
$894$	36.0000	1.20402
$895$	85.9017	2.87138
$896$	1.00000	0.0334077
$897$	82.6099	2.75826
$898$	−14.5623	−0.485950
$899$	6.47214	0.215858
$900$	8.09017	0.269672
$901$	6.94427	0.231347
$902$	−66.6525	−2.21928
$903$	0	0
$904$	−4.94427	−0.164444
$905$	−54.7214	−1.81900
$906$	9.52786	0.316542
$907$	13.8541	0.460018	0.230009	−	0.973189i	$-0.426124\pi$
$907$	13.8541	0.460018	0.230009	+	0.973189i	$0.426124\pi$
$908$	2.18034	0.0723571
$909$	−4.47214	−0.148331
$910$	−16.1803	−0.536373
$911$	−36.1803	−1.19871	−0.599354	−	0.800484i	$-0.704576\pi$
$911$	−36.1803	−1.19871	−0.599354	+	0.800484i	$0.704576\pi$
$912$	12.9443	0.428628
$913$	15.0557	0.498272
$914$	14.3607	0.475009
$915$	56.8328	1.87883
$916$	−22.6180	−0.747321
$917$	−6.09017	−0.201115
$918$	−2.47214	−0.0815926
$919$	−29.0132	−0.957056	−0.478528	−	0.878072i	$-0.658829\pi$
$919$	−29.0132	−0.957056	−0.478528	+	0.878072i	$0.658829\pi$
$920$	33.4164	1.10171
$921$	−13.3050	−0.438413
$922$	1.09017	0.0359028
$923$	43.0132	1.41580
$924$	12.1803	0.400704
$925$	−63.5410	−2.08922
$926$	33.5967	1.10406
$927$	10.4721	0.343950
$928$	−1.23607	−0.0405759
$929$	18.3607	0.602394	0.301197	−	0.953562i	$-0.402614\pi$
$929$	18.3607	0.602394	0.301197	+	0.953562i	$0.402614\pi$
$930$	37.8885	1.24241
$931$	6.47214	0.212116
$932$	−17.2361	−0.564586
$933$	39.4164	1.29044
$934$	−12.0000	−0.392652
$935$	−13.6180	−0.445357
$936$	−4.47214	−0.146176
$937$	28.0689	0.916970	0.458485	−	0.888702i	$-0.348392\pi$
$937$	28.0689	0.916970	0.458485	+	0.888702i	$0.348392\pi$
$938$	4.47214	0.146020
$939$	−24.1803	−0.789096
$940$	−7.23607	−0.236015
$941$	−11.7082	−0.381677	−0.190838	−	0.981621i	$-0.561121\pi$
$941$	−11.7082	−0.381677	−0.190838	+	0.981621i	$0.561121\pi$
$942$	2.11146	0.0687950
$943$	−101.082	−3.29168
$944$	12.1803	0.396436
$945$	−14.4721	−0.470779
$946$	0	0
$947$	11.8197	0.384087	0.192044	−	0.981386i	$-0.438488\pi$
$947$	11.8197	0.384087	0.192044	+	0.981386i	$0.438488\pi$
$948$	−14.2918	−0.464176
$949$	20.0000	0.649227
$950$	−52.3607	−1.69880
$951$	0.875388	0.0283864
$952$	−0.618034	−0.0200306
$953$	42.7984	1.38638	0.693188	−	0.720757i	$-0.256206\pi$
$953$	42.7984	1.38638	0.693188	+	0.720757i	$0.256206\pi$
$954$	11.2361	0.363781
$955$	89.7214	2.90332
$956$	−3.56231	−0.115213
$957$	−15.0557	−0.486683
$958$	25.8885	0.836421
$959$	22.4721	0.725663
$960$	−7.23607	−0.233543
$961$	−3.58359	−0.115600
$962$	35.1246	1.13246
$963$	9.23607	0.297628
$964$	5.61803	0.180945
$965$	77.4853	2.49434
$966$	18.4721	0.594331
$967$	−8.67376	−0.278929	−0.139465	−	0.990227i	$-0.544538\pi$
$967$	−8.67376	−0.278929	−0.139465	+	0.990227i	$0.544538\pi$
$968$	−26.0902	−0.838570
$969$	−8.00000	−0.256997
$970$	−51.3050	−1.64730
$971$	50.5410	1.62194	0.810969	−	0.585089i	$-0.198940\pi$
$971$	50.5410	1.62194	0.810969	+	0.585089i	$0.198940\pi$
$972$	−10.0000	−0.320750
$973$	−5.52786	−0.177215
$974$	16.0000	0.512673
$975$	72.3607	2.31740
$976$	−7.85410	−0.251404
$977$	34.5066	1.10396	0.551982	−	0.833856i	$-0.313872\pi$
$977$	34.5066	1.10396	0.551982	+	0.833856i	$0.313872\pi$
$978$	21.5967	0.690588
$979$	82.9361	2.65065
$980$	−3.61803	−0.115574
$981$	−2.29180	−0.0731714
$982$	−5.85410	−0.186812
$983$	2.83282	0.0903528	0.0451764	−	0.998979i	$-0.485615\pi$
$983$	2.83282	0.0903528	0.0451764	+	0.998979i	$0.485615\pi$
$984$	21.8885	0.697781
$985$	−75.7771	−2.41446
$986$	0.763932	0.0243286
$987$	−4.00000	−0.127321
$988$	28.9443	0.920840
$989$	0	0
$990$	−22.0344	−0.700301
$991$	14.3820	0.456858	0.228429	−	0.973561i	$-0.426641\pi$
$991$	14.3820	0.456858	0.228429	+	0.973561i	$0.426641\pi$
$992$	−5.23607	−0.166245
$993$	−20.7214	−0.657572
$994$	9.61803	0.305066
$995$	71.3050	2.26052
$996$	−4.94427	−0.156665
$997$	−53.0902	−1.68138	−0.840691	−	0.541515i	$-0.817851\pi$
$997$	−53.0902	−1.68138	−0.840691	+	0.541515i	$0.817851\pi$
$998$	−38.9443	−1.23276
$999$	31.4164	0.993971

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6034.2.a.g.1.1	✓	2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6034.2.a.g.1.1	✓	2	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:	\( N \)	\(=\)	\( 6034 = 2 \cdot 7 \cdot 431 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6034.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +2.00000 q^{3} +1.00000 q^{4} -3.61803 q^{5} -2.00000 q^{6} -1.00000 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +2.00000 q^{3} +1.00000 q^{4} -3.61803 q^{5} -2.00000 q^{6} -1.00000 q^{7} -1.00000 q^{8} +1.00000 q^{9} +3.61803 q^{10} -6.09017 q^{11} +2.00000 q^{12} +4.47214 q^{13} +1.00000 q^{14} -7.23607 q^{15} +1.00000 q^{16} -0.618034 q^{17} -1.00000 q^{18} +6.47214 q^{19} -3.61803 q^{20} -2.00000 q^{21} +6.09017 q^{22} +9.23607 q^{23} -2.00000 q^{24} +8.09017 q^{25} -4.47214 q^{26} -4.00000 q^{27} -1.00000 q^{28} +1.23607 q^{29} +7.23607 q^{30} +5.23607 q^{31} -1.00000 q^{32} -12.1803 q^{33} +0.618034 q^{34} +3.61803 q^{35} +1.00000 q^{36} -7.85410 q^{37} -6.47214 q^{38} +8.94427 q^{39} +3.61803 q^{40} -10.9443 q^{41} +2.00000 q^{42} -6.09017 q^{44} -3.61803 q^{45} -9.23607 q^{46} +2.00000 q^{47} +2.00000 q^{48} +1.00000 q^{49} -8.09017 q^{50} -1.23607 q^{51} +4.47214 q^{52} -11.2361 q^{53} +4.00000 q^{54} +22.0344 q^{55} +1.00000 q^{56} +12.9443 q^{57} -1.23607 q^{58} +12.1803 q^{59} -7.23607 q^{60} -7.85410 q^{61} -5.23607 q^{62} -1.00000 q^{63} +1.00000 q^{64} -16.1803 q^{65} +12.1803 q^{66} +4.47214 q^{67} -0.618034 q^{68} +18.4721 q^{69} -3.61803 q^{70} +9.61803 q^{71} -1.00000 q^{72} +4.47214 q^{73} +7.85410 q^{74} +16.1803 q^{75} +6.47214 q^{76} +6.09017 q^{77} -8.94427 q^{78} -7.14590 q^{79} -3.61803 q^{80} -11.0000 q^{81} +10.9443 q^{82} -2.47214 q^{83} -2.00000 q^{84} +2.23607 q^{85} +2.47214 q^{87} +6.09017 q^{88} -13.6180 q^{89} +3.61803 q^{90} -4.47214 q^{91} +9.23607 q^{92} +10.4721 q^{93} -2.00000 q^{94} -23.4164 q^{95} -2.00000 q^{96} -14.1803 q^{97} -1.00000 q^{98} -6.09017 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 2 q^{2} + 4 q^{3} + 2 q^{4} - 5 q^{5} - 4 q^{6} - 2 q^{7} - 2 q^{8} + 2 q^{9}+O(q^{10}) \) 2 * q - 2 * q^2 + 4 * q^3 + 2 * q^4 - 5 * q^5 - 4 * q^6 - 2 * q^7 - 2 * q^8 + 2 * q^9	\( 2 q - 2 q^{2} + 4 q^{3} + 2 q^{4} - 5 q^{5} - 4 q^{6} - 2 q^{7} - 2 q^{8} + 2 q^{9} + 5 q^{10} - q^{11} + 4 q^{12} + 2 q^{14} - 10 q^{15} + 2 q^{16} + q^{17} - 2 q^{18} + 4 q^{19} - 5 q^{20} - 4 q^{21} + q^{22} + 14 q^{23} - 4 q^{24} + 5 q^{25} - 8 q^{27} - 2 q^{28} - 2 q^{29} + 10 q^{30} + 6 q^{31} - 2 q^{32} - 2 q^{33} - q^{34} + 5 q^{35} + 2 q^{36} - 9 q^{37} - 4 q^{38} + 5 q^{40} - 4 q^{41} + 4 q^{42} - q^{44} - 5 q^{45} - 14 q^{46} + 4 q^{47} + 4 q^{48} + 2 q^{49} - 5 q^{50} + 2 q^{51} - 18 q^{53} + 8 q^{54} + 15 q^{55} + 2 q^{56} + 8 q^{57} + 2 q^{58} + 2 q^{59} - 10 q^{60} - 9 q^{61} - 6 q^{62} - 2 q^{63} + 2 q^{64} - 10 q^{65} + 2 q^{66} + q^{68} + 28 q^{69} - 5 q^{70} + 17 q^{71} - 2 q^{72} + 9 q^{74} + 10 q^{75} + 4 q^{76} + q^{77} - 21 q^{79} - 5 q^{80} - 22 q^{81} + 4 q^{82} + 4 q^{83} - 4 q^{84} - 4 q^{87} + q^{88} - 25 q^{89} + 5 q^{90} + 14 q^{92} + 12 q^{93} - 4 q^{94} - 20 q^{95} - 4 q^{96} - 6 q^{97} - 2 q^{98} - q^{99}+O(q^{100}) \) 2 * q - 2 * q^2 + 4 * q^3 + 2 * q^4 - 5 * q^5 - 4 * q^6 - 2 * q^7 - 2 * q^8 + 2 * q^9 + 5 * q^10 - q^11 + 4 * q^12 + 2 * q^14 - 10 * q^15 + 2 * q^16 + q^17 - 2 * q^18 + 4 * q^19 - 5 * q^20 - 4 * q^21 + q^22 + 14 * q^23 - 4 * q^24 + 5 * q^25 - 8 * q^27 - 2 * q^28 - 2 * q^29 + 10 * q^30 + 6 * q^31 - 2 * q^32 - 2 * q^33 - q^34 + 5 * q^35 + 2 * q^36 - 9 * q^37 - 4 * q^38 + 5 * q^40 - 4 * q^41 + 4 * q^42 - q^44 - 5 * q^45 - 14 * q^46 + 4 * q^47 + 4 * q^48 + 2 * q^49 - 5 * q^50 + 2 * q^51 - 18 * q^53 + 8 * q^54 + 15 * q^55 + 2 * q^56 + 8 * q^57 + 2 * q^58 + 2 * q^59 - 10 * q^60 - 9 * q^61 - 6 * q^62 - 2 * q^63 + 2 * q^64 - 10 * q^65 + 2 * q^66 + q^68 + 28 * q^69 - 5 * q^70 + 17 * q^71 - 2 * q^72 + 9 * q^74 + 10 * q^75 + 4 * q^76 + q^77 - 21 * q^79 - 5 * q^80 - 22 * q^81 + 4 * q^82 + 4 * q^83 - 4 * q^84 - 4 * q^87 + q^88 - 25 * q^89 + 5 * q^90 + 14 * q^92 + 12 * q^93 - 4 * q^94 - 20 * q^95 - 4 * q^96 - 6 * q^97 - 2 * q^98 - q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more