LMFDB - Embedded newform 6010.2.a.f.1.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6010,2,Mod(1,6010)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6010, 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("6010.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6010 = 2 \cdot 5 \cdot 601 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6010.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:	$47.9900916148$
Analytic rank:	$1$
Dimension:	$22$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.18
Character	$\chi$	$=$	6010.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +1.73340 q^{3} +1.00000 q^{4} -1.00000 q^{5} +1.73340 q^{6} -0.557678 q^{7} +1.00000 q^{8} +0.00467827 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +1.73340 q^{3} +1.00000 q^{4} -1.00000 q^{5} +1.73340 q^{6} -0.557678 q^{7} +1.00000 q^{8} +0.00467827 q^{9} -1.00000 q^{10} -5.61969 q^{11} +1.73340 q^{12} +2.94035 q^{13} -0.557678 q^{14} -1.73340 q^{15} +1.00000 q^{16} -5.44040 q^{17} +0.00467827 q^{18} +4.55955 q^{19} -1.00000 q^{20} -0.966679 q^{21} -5.61969 q^{22} +5.67869 q^{23} +1.73340 q^{24} +1.00000 q^{25} +2.94035 q^{26} -5.19209 q^{27} -0.557678 q^{28} -6.05637 q^{29} -1.73340 q^{30} -5.26723 q^{31} +1.00000 q^{32} -9.74118 q^{33} -5.44040 q^{34} +0.557678 q^{35} +0.00467827 q^{36} +0.362706 q^{37} +4.55955 q^{38} +5.09680 q^{39} -1.00000 q^{40} -8.03794 q^{41} -0.966679 q^{42} +2.72226 q^{43} -5.61969 q^{44} -0.00467827 q^{45} +5.67869 q^{46} +1.47365 q^{47} +1.73340 q^{48} -6.68900 q^{49} +1.00000 q^{50} -9.43039 q^{51} +2.94035 q^{52} +6.77220 q^{53} -5.19209 q^{54} +5.61969 q^{55} -0.557678 q^{56} +7.90352 q^{57} -6.05637 q^{58} -12.2832 q^{59} -1.73340 q^{60} -2.60608 q^{61} -5.26723 q^{62} -0.00260897 q^{63} +1.00000 q^{64} -2.94035 q^{65} -9.74118 q^{66} -14.1351 q^{67} -5.44040 q^{68} +9.84345 q^{69} +0.557678 q^{70} -4.94805 q^{71} +0.00467827 q^{72} +9.01015 q^{73} +0.362706 q^{74} +1.73340 q^{75} +4.55955 q^{76} +3.13398 q^{77} +5.09680 q^{78} -2.38616 q^{79} -1.00000 q^{80} -9.01401 q^{81} -8.03794 q^{82} +5.52279 q^{83} -0.966679 q^{84} +5.44040 q^{85} +2.72226 q^{86} -10.4981 q^{87} -5.61969 q^{88} -13.6990 q^{89} -0.00467827 q^{90} -1.63977 q^{91} +5.67869 q^{92} -9.13023 q^{93} +1.47365 q^{94} -4.55955 q^{95} +1.73340 q^{96} -7.03462 q^{97} -6.68900 q^{98} -0.0262904 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 22 q + 22 q^{2} - 6 q^{3} + 22 q^{4} - 22 q^{5} - 6 q^{6} - 12 q^{7} + 22 q^{8} + 12 q^{9}+O(q^{10}) $ 22 * q + 22 * q^2 - 6 * q^3 + 22 * q^4 - 22 * q^5 - 6 * q^6 - 12 * q^7 + 22 * q^8 + 12 * q^9	\( 22 q + 22 q^{2} - 6 q^{3} + 22 q^{4} - 22 q^{5} - 6 q^{6} - 12 q^{7} + 22 q^{8} + 12 q^{9} - 22 q^{10} - 4 q^{11} - 6 q^{12} - 20 q^{13} - 12 q^{14} + 6 q^{15} + 22 q^{16} - 23 q^{17} + 12 q^{18} + q^{19} - 22 q^{20} - 8 q^{21} - 4 q^{22} - 17 q^{23} - 6 q^{24} + 22 q^{25} - 20 q^{26} - 21 q^{27} - 12 q^{28} - 13 q^{29} + 6 q^{30} - 13 q^{31} + 22 q^{32} - 21 q^{33} - 23 q^{34} + 12 q^{35} + 12 q^{36} - 16 q^{37} + q^{38} - 4 q^{39} - 22 q^{40} - 31 q^{41} - 8 q^{42} - 9 q^{43} - 4 q^{44} - 12 q^{45} - 17 q^{46} - 41 q^{47} - 6 q^{48} - 6 q^{49} + 22 q^{50} - 7 q^{51} - 20 q^{52} - 15 q^{53} - 21 q^{54} + 4 q^{55} - 12 q^{56} - 26 q^{57} - 13 q^{58} - 32 q^{59} + 6 q^{60} - 22 q^{61} - 13 q^{62} - 55 q^{63} + 22 q^{64} + 20 q^{65} - 21 q^{66} - 19 q^{67} - 23 q^{68} - 37 q^{69} + 12 q^{70} - 36 q^{71} + 12 q^{72} - 47 q^{73} - 16 q^{74} - 6 q^{75} + q^{76} - 26 q^{77} - 4 q^{78} - 10 q^{79} - 22 q^{80} - 18 q^{81} - 31 q^{82} - 48 q^{83} - 8 q^{84} + 23 q^{85} - 9 q^{86} - 50 q^{87} - 4 q^{88} - 42 q^{89} - 12 q^{90} + 25 q^{91} - 17 q^{92} - 48 q^{93} - 41 q^{94} - q^{95} - 6 q^{96} - 67 q^{97} - 6 q^{98} - 3 q^{99}+O(q^{100}) \) 22 * q + 22 * q^2 - 6 * q^3 + 22 * q^4 - 22 * q^5 - 6 * q^6 - 12 * q^7 + 22 * q^8 + 12 * q^9 - 22 * q^10 - 4 * q^11 - 6 * q^12 - 20 * q^13 - 12 * q^14 + 6 * q^15 + 22 * q^16 - 23 * q^17 + 12 * q^18 + q^19 - 22 * q^20 - 8 * q^21 - 4 * q^22 - 17 * q^23 - 6 * q^24 + 22 * q^25 - 20 * q^26 - 21 * q^27 - 12 * q^28 - 13 * q^29 + 6 * q^30 - 13 * q^31 + 22 * q^32 - 21 * q^33 - 23 * q^34 + 12 * q^35 + 12 * q^36 - 16 * q^37 + q^38 - 4 * q^39 - 22 * q^40 - 31 * q^41 - 8 * q^42 - 9 * q^43 - 4 * q^44 - 12 * q^45 - 17 * q^46 - 41 * q^47 - 6 * q^48 - 6 * q^49 + 22 * q^50 - 7 * q^51 - 20 * q^52 - 15 * q^53 - 21 * q^54 + 4 * q^55 - 12 * q^56 - 26 * q^57 - 13 * q^58 - 32 * q^59 + 6 * q^60 - 22 * q^61 - 13 * q^62 - 55 * q^63 + 22 * q^64 + 20 * q^65 - 21 * q^66 - 19 * q^67 - 23 * q^68 - 37 * q^69 + 12 * q^70 - 36 * q^71 + 12 * q^72 - 47 * q^73 - 16 * q^74 - 6 * q^75 + q^76 - 26 * q^77 - 4 * q^78 - 10 * q^79 - 22 * q^80 - 18 * q^81 - 31 * q^82 - 48 * q^83 - 8 * q^84 + 23 * q^85 - 9 * q^86 - 50 * q^87 - 4 * q^88 - 42 * q^89 - 12 * q^90 + 25 * q^91 - 17 * q^92 - 48 * q^93 - 41 * q^94 - q^95 - 6 * q^96 - 67 * q^97 - 6 * q^98 - 3 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	1.73340	1.00078	0.500390	−	0.865800i	$-0.333190\pi$
$3$	1.73340	1.00078	0.500390	+	0.865800i	$0.333190\pi$
$4$	1.00000	0.500000
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	1.73340	0.707658
$7$	−0.557678	−0.210782	−0.105391	−	0.994431i	$-0.533609\pi$
$7$	−0.557678	−0.210782	−0.105391	+	0.994431i	$0.533609\pi$
$8$	1.00000	0.353553
$9$	0.00467827	0.00155942
$10$	−1.00000	−0.316228
$11$	−5.61969	−1.69440	−0.847200	−	0.531273i	$-0.821714\pi$
$11$	−5.61969	−1.69440	−0.847200	+	0.531273i	$0.821714\pi$
$12$	1.73340	0.500390
$13$	2.94035	0.815506	0.407753	−	0.913092i	$-0.366312\pi$
$13$	2.94035	0.815506	0.407753	+	0.913092i	$0.366312\pi$
$14$	−0.557678	−0.149046
$15$	−1.73340	−0.447562
$16$	1.00000	0.250000
$17$	−5.44040	−1.31949	−0.659745	−	0.751490i	$-0.729336\pi$
$17$	−5.44040	−1.31949	−0.659745	+	0.751490i	$0.729336\pi$
$18$	0.00467827	0.00110268
$19$	4.55955	1.04603	0.523016	−	0.852323i	$-0.324807\pi$
$19$	4.55955	1.04603	0.523016	+	0.852323i	$0.324807\pi$
$20$	−1.00000	−0.223607
$21$	−0.966679	−0.210947
$22$	−5.61969	−1.19812
$23$	5.67869	1.18409	0.592045	−	0.805905i	$-0.298321\pi$
$23$	5.67869	1.18409	0.592045	+	0.805905i	$0.298321\pi$
$24$	1.73340	0.353829
$25$	1.00000	0.200000
$26$	2.94035	0.576650
$27$	−5.19209	−0.999219
$28$	−0.557678	−0.105391
$29$	−6.05637	−1.12464	−0.562320	−	0.826920i	$-0.690091\pi$
$29$	−6.05637	−1.12464	−0.562320	+	0.826920i	$0.690091\pi$
$30$	−1.73340	−0.316474
$31$	−5.26723	−0.946023	−0.473011	−	0.881056i	$-0.656833\pi$
$31$	−5.26723	−0.946023	−0.473011	+	0.881056i	$0.656833\pi$
$32$	1.00000	0.176777
$33$	−9.74118	−1.69572
$34$	−5.44040	−0.933020
$35$	0.557678	0.0942647
$36$	0.00467827	0.000779712 0
$37$	0.362706	0.0596285	0.0298143	−	0.999555i	$-0.490508\pi$
$37$	0.362706	0.0596285	0.0298143	+	0.999555i	$0.490508\pi$
$38$	4.55955	0.739656
$39$	5.09680	0.816142
$40$	−1.00000	−0.158114
$41$	−8.03794	−1.25532	−0.627658	−	0.778489i	$-0.715986\pi$
$41$	−8.03794	−1.25532	−0.627658	+	0.778489i	$0.715986\pi$
$42$	−0.966679	−0.149162
$43$	2.72226	0.415141	0.207570	−	0.978220i	$-0.433444\pi$
$43$	2.72226	0.415141	0.207570	+	0.978220i	$0.433444\pi$
$44$	−5.61969	−0.847200
$45$	−0.00467827	−0.000697396 0
$46$	5.67869	0.837277
$47$	1.47365	0.214954	0.107477	−	0.994208i	$-0.465723\pi$
$47$	1.47365	0.214954	0.107477	+	0.994208i	$0.465723\pi$
$48$	1.73340	0.250195
$49$	−6.68900	−0.955571
$50$	1.00000	0.141421
$51$	−9.43039	−1.32052
$52$	2.94035	0.407753
$53$	6.77220	0.930233	0.465116	−	0.885250i	$-0.346013\pi$
$53$	6.77220	0.930233	0.465116	+	0.885250i	$0.346013\pi$
$54$	−5.19209	−0.706554
$55$	5.61969	0.757759
$56$	−0.557678	−0.0745228
$57$	7.90352	1.04685
$58$	−6.05637	−0.795240
$59$	−12.2832	−1.59914	−0.799571	−	0.600572i	$-0.794940\pi$
$59$	−12.2832	−1.59914	−0.799571	+	0.600572i	$0.794940\pi$
$60$	−1.73340	−0.223781
$61$	−2.60608	−0.333674	−0.166837	−	0.985985i	$-0.553355\pi$
$61$	−2.60608	−0.333674	−0.166837	+	0.985985i	$0.553355\pi$
$62$	−5.26723	−0.668939
$63$	−0.00260897	−0.000328699 0
$64$	1.00000	0.125000
$65$	−2.94035	−0.364706
$66$	−9.74118	−1.19906
$67$	−14.1351	−1.72688	−0.863440	−	0.504451i	$-0.831695\pi$
$67$	−14.1351	−1.72688	−0.863440	+	0.504451i	$0.831695\pi$
$68$	−5.44040	−0.659745
$69$	9.84345	1.18501
$70$	0.557678	0.0666552
$71$	−4.94805	−0.587226	−0.293613	−	0.955924i	$-0.594858\pi$
$71$	−4.94805	−0.587226	−0.293613	+	0.955924i	$0.594858\pi$
$72$	0.00467827	0.000551340 0
$73$	9.01015	1.05456	0.527279	−	0.849692i	$-0.323212\pi$
$73$	9.01015	1.05456	0.527279	+	0.849692i	$0.323212\pi$
$74$	0.362706	0.0421637
$75$	1.73340	0.200156
$76$	4.55955	0.523016
$77$	3.13398	0.357150
$78$	5.09680	0.577100
$79$	−2.38616	−0.268465	−0.134232	−	0.990950i	$-0.542857\pi$
$79$	−2.38616	−0.268465	−0.134232	+	0.990950i	$0.542857\pi$
$80$	−1.00000	−0.111803
$81$	−9.01401	−1.00156
$82$	−8.03794	−0.887642
$83$	5.52279	0.606205	0.303102	−	0.952958i	$-0.401978\pi$
$83$	5.52279	0.606205	0.303102	+	0.952958i	$0.401978\pi$
$84$	−0.966679	−0.105473
$85$	5.44040	0.590094
$86$	2.72226	0.293549
$87$	−10.4981	−1.12552
$88$	−5.61969	−0.599061
$89$	−13.6990	−1.45209	−0.726044	−	0.687648i	$-0.758643\pi$
$89$	−13.6990	−1.45209	−0.726044	+	0.687648i	$0.758643\pi$
$90$	−0.00467827	−0.000493133 0
$91$	−1.63977	−0.171894
$92$	5.67869	0.592045
$93$	−9.13023	−0.946760
$94$	1.47365	0.151995
$95$	−4.55955	−0.467800
$96$	1.73340	0.176914
$97$	−7.03462	−0.714257	−0.357129	−	0.934055i	$-0.616244\pi$
$97$	−7.03462	−0.714257	−0.357129	+	0.934055i	$0.616244\pi$
$98$	−6.68900	−0.675691
$99$	−0.0262904	−0.00264229
$100$	1.00000	0.100000
$101$	−3.36476	−0.334806	−0.167403	−	0.985889i	$-0.553538\pi$
$101$	−3.36476	−0.334806	−0.167403	+	0.985889i	$0.553538\pi$
$102$	−9.43039	−0.933747
$103$	−2.32150	−0.228744	−0.114372	−	0.993438i	$-0.536486\pi$
$103$	−2.32150	−0.228744	−0.114372	+	0.993438i	$0.536486\pi$
$104$	2.94035	0.288325
$105$	0.966679	0.0943382
$106$	6.77220	0.657774
$107$	−3.03095	−0.293013	−0.146506	−	0.989210i	$-0.546803\pi$
$107$	−3.03095	−0.293013	−0.146506	+	0.989210i	$0.546803\pi$
$108$	−5.19209	−0.499609
$109$	18.6491	1.78626	0.893129	−	0.449800i	$-0.148505\pi$
$109$	18.6491	1.78626	0.893129	+	0.449800i	$0.148505\pi$
$110$	5.61969	0.535817
$111$	0.628715	0.0596750
$112$	−0.557678	−0.0526956
$113$	16.6636	1.56758	0.783789	−	0.621027i	$-0.213284\pi$
$113$	16.6636	1.56758	0.783789	+	0.621027i	$0.213284\pi$
$114$	7.90352	0.740233
$115$	−5.67869	−0.529541
$116$	−6.05637	−0.562320
$117$	0.0137558	0.00127172
$118$	−12.2832	−1.13076
$119$	3.03399	0.278125
$120$	−1.73340	−0.158237
$121$	20.5809	1.87099
$122$	−2.60608	−0.235943
$123$	−13.9330	−1.25629
$124$	−5.26723	−0.473011
$125$	−1.00000	−0.0894427
$126$	−0.00260897	−0.000232425 0
$127$	−0.920369	−0.0816695	−0.0408348	−	0.999166i	$-0.513002\pi$
$127$	−0.920369	−0.0816695	−0.0408348	+	0.999166i	$0.513002\pi$
$128$	1.00000	0.0883883
$129$	4.71877	0.415464
$130$	−2.94035	−0.257886
$131$	−6.30250	−0.550652	−0.275326	−	0.961351i	$-0.588786\pi$
$131$	−6.30250	−0.550652	−0.275326	+	0.961351i	$0.588786\pi$
$132$	−9.74118	−0.847861
$133$	−2.54276	−0.220485
$134$	−14.1351	−1.22109
$135$	5.19209	0.446864
$136$	−5.44040	−0.466510
$137$	−21.4006	−1.82837	−0.914187	−	0.405292i	$-0.867170\pi$
$137$	−21.4006	−1.82837	−0.914187	+	0.405292i	$0.867170\pi$
$138$	9.84345	0.837930
$139$	−5.76152	−0.488686	−0.244343	−	0.969689i	$-0.578572\pi$
$139$	−5.76152	−0.488686	−0.244343	+	0.969689i	$0.578572\pi$
$140$	0.557678	0.0471324
$141$	2.55443	0.215122
$142$	−4.94805	−0.415231
$143$	−16.5239	−1.38179
$144$	0.00467827	0.000389856 0
$145$	6.05637	0.502954
$146$	9.01015	0.745686
$147$	−11.5947	−0.956316
$148$	0.362706	0.0298143
$149$	3.98762	0.326679	0.163339	−	0.986570i	$-0.447773\pi$
$149$	3.98762	0.326679	0.163339	+	0.986570i	$0.447773\pi$
$150$	1.73340	0.141532
$151$	−8.09122	−0.658454	−0.329227	−	0.944251i	$-0.606788\pi$
$151$	−8.09122	−0.658454	−0.329227	+	0.944251i	$0.606788\pi$
$152$	4.55955	0.369828
$153$	−0.0254516	−0.00205764
$154$	3.13398	0.252543
$155$	5.26723	0.423074
$156$	5.09680	0.408071
$157$	−18.8504	−1.50442	−0.752212	−	0.658921i	$-0.771013\pi$
$157$	−18.8504	−1.50442	−0.752212	+	0.658921i	$0.771013\pi$
$158$	−2.38616	−0.189833
$159$	11.7389	0.930958
$160$	−1.00000	−0.0790569
$161$	−3.16688	−0.249585
$162$	−9.01401	−0.708208
$163$	5.86359	0.459272	0.229636	−	0.973277i	$-0.426246\pi$
$163$	5.86359	0.459272	0.229636	+	0.973277i	$0.426246\pi$
$164$	−8.03794	−0.627658
$165$	9.74118	0.758350
$166$	5.52279	0.428651
$167$	10.1419	0.784800	0.392400	−	0.919795i	$-0.371645\pi$
$167$	10.1419	0.784800	0.392400	+	0.919795i	$0.371645\pi$
$168$	−0.966679	−0.0745809
$169$	−4.35434	−0.334949
$170$	5.44040	0.417259
$171$	0.0213308	0.00163121
$172$	2.72226	0.207570
$173$	−2.87627	−0.218679	−0.109340	−	0.994004i	$-0.534874\pi$
$173$	−2.87627	−0.218679	−0.109340	+	0.994004i	$0.534874\pi$
$174$	−10.4981	−0.795860
$175$	−0.557678	−0.0421565
$176$	−5.61969	−0.423600
$177$	−21.2918	−1.60039
$178$	−13.6990	−1.02678
$179$	−23.6402	−1.76695	−0.883474	−	0.468480i	$-0.844802\pi$
$179$	−23.6402	−1.76695	−0.883474	+	0.468480i	$0.844802\pi$
$180$	−0.00467827	−0.000348698 0
$181$	−10.6190	−0.789307	−0.394653	−	0.918830i	$-0.629135\pi$
$181$	−10.6190	−0.789307	−0.394653	+	0.918830i	$0.629135\pi$
$182$	−1.63977	−0.121548
$183$	−4.51737	−0.333934
$184$	5.67869	0.418639
$185$	−0.362706	−0.0266667
$186$	−9.13023	−0.669461
$187$	30.5733	2.23574
$188$	1.47365	0.107477
$189$	2.89551	0.210618
$190$	−4.55955	−0.330784
$191$	−3.92251	−0.283823	−0.141911	−	0.989879i	$-0.545325\pi$
$191$	−3.92251	−0.283823	−0.141911	+	0.989879i	$0.545325\pi$
$192$	1.73340	0.125097
$193$	4.47402	0.322047	0.161024	−	0.986951i	$-0.448520\pi$
$193$	4.47402	0.322047	0.161024	+	0.986951i	$0.448520\pi$
$194$	−7.03462	−0.505056
$195$	−5.09680	−0.364990
$196$	−6.68900	−0.477785
$197$	24.9003	1.77407	0.887036	−	0.461700i	$-0.152760\pi$
$197$	24.9003	1.77407	0.887036	+	0.461700i	$0.152760\pi$
$198$	−0.0262904	−0.00186838
$199$	3.19899	0.226771	0.113385	−	0.993551i	$-0.463831\pi$
$199$	3.19899	0.226771	0.113385	+	0.993551i	$0.463831\pi$
$200$	1.00000	0.0707107
$201$	−24.5018	−1.72823
$202$	−3.36476	−0.236743
$203$	3.37750	0.237054
$204$	−9.43039	−0.660259
$205$	8.03794	0.561394
$206$	−2.32150	−0.161747
$207$	0.0265665	0.00184650
$208$	2.94035	0.203877
$209$	−25.6232	−1.77240
$210$	0.966679	0.0667072
$211$	10.7882	0.742692	0.371346	−	0.928495i	$-0.378896\pi$
$211$	10.7882	0.742692	0.371346	+	0.928495i	$0.378896\pi$
$212$	6.77220	0.465116
$213$	−8.57695	−0.587683
$214$	−3.03095	−0.207191
$215$	−2.72226	−0.185657
$216$	−5.19209	−0.353277
$217$	2.93742	0.199405
$218$	18.6491	1.26308
$219$	15.6182	1.05538
$220$	5.61969	0.378880
$221$	−15.9967	−1.07605
$222$	0.628715	0.0421966
$223$	21.8752	1.46487	0.732435	−	0.680837i	$-0.238384\pi$
$223$	21.8752	1.46487	0.732435	+	0.680837i	$0.238384\pi$
$224$	−0.557678	−0.0372614
$225$	0.00467827	0.000311885 0
$226$	16.6636	1.10845
$227$	−27.8852	−1.85081	−0.925403	−	0.378985i	$-0.876273\pi$
$227$	−27.8852	−1.85081	−0.925403	+	0.378985i	$0.876273\pi$
$228$	7.90352	0.523424
$229$	−20.1720	−1.33300	−0.666502	−	0.745503i	$-0.732209\pi$
$229$	−20.1720	−1.33300	−0.666502	+	0.745503i	$0.732209\pi$
$230$	−5.67869	−0.374442
$231$	5.43244	0.357428
$232$	−6.05637	−0.397620
$233$	−1.53802	−0.100759	−0.0503794	−	0.998730i	$-0.516043\pi$
$233$	−1.53802	−0.100759	−0.0503794	+	0.998730i	$0.516043\pi$
$234$	0.0137558	0.000899242 0
$235$	−1.47365	−0.0961303
$236$	−12.2832	−0.799571
$237$	−4.13618	−0.268674
$238$	3.03399	0.196664
$239$	29.5195	1.90946	0.954730	−	0.297474i	$-0.0961442\pi$
$239$	29.5195	1.90946	0.954730	+	0.297474i	$0.0961442\pi$
$240$	−1.73340	−0.111891
$241$	18.8868	1.21660	0.608302	−	0.793706i	$-0.291851\pi$
$241$	18.8868	1.21660	0.608302	+	0.793706i	$0.291851\pi$
$242$	20.5809	1.32299
$243$	−0.0486180	−0.00311884
$244$	−2.60608	−0.166837
$245$	6.68900	0.427344
$246$	−13.9330	−0.888334
$247$	13.4067	0.853046
$248$	−5.26723	−0.334470
$249$	9.57320	0.606677
$250$	−1.00000	−0.0632456
$251$	−6.87133	−0.433715	−0.216857	−	0.976203i	$-0.569581\pi$
$251$	−6.87133	−0.433715	−0.216857	+	0.976203i	$0.569581\pi$
$252$	−0.00260897	−0.000164350 0
$253$	−31.9125	−2.00632
$254$	−0.920369	−0.0577491
$255$	9.43039	0.590554
$256$	1.00000	0.0625000
$257$	30.6995	1.91498	0.957491	−	0.288464i	$-0.0931446\pi$
$257$	30.6995	1.91498	0.957491	+	0.288464i	$0.0931446\pi$
$258$	4.71877	0.293778
$259$	−0.202273	−0.0125686
$260$	−2.94035	−0.182353
$261$	−0.0283333	−0.00175379
$262$	−6.30250	−0.389370
$263$	11.4830	0.708070	0.354035	−	0.935232i	$-0.384809\pi$
$263$	11.4830	0.708070	0.354035	+	0.935232i	$0.384809\pi$
$264$	−9.74118	−0.599528
$265$	−6.77220	−0.416013
$266$	−2.54276	−0.155907
$267$	−23.7458	−1.45322
$268$	−14.1351	−0.863440
$269$	−9.23907	−0.563316	−0.281658	−	0.959515i	$-0.590884\pi$
$269$	−9.23907	−0.563316	−0.281658	+	0.959515i	$0.590884\pi$
$270$	5.19209	0.315981
$271$	1.69398	0.102902	0.0514511	−	0.998676i	$-0.483615\pi$
$271$	1.69398	0.102902	0.0514511	+	0.998676i	$0.483615\pi$
$272$	−5.44040	−0.329872
$273$	−2.84237	−0.172028
$274$	−21.4006	−1.29286
$275$	−5.61969	−0.338880
$276$	9.84345	0.592506
$277$	16.1685	0.971473	0.485737	−	0.874105i	$-0.338551\pi$
$277$	16.1685	0.971473	0.485737	+	0.874105i	$0.338551\pi$
$278$	−5.76152	−0.345553
$279$	−0.0246415	−0.00147525
$280$	0.557678	0.0333276
$281$	6.54965	0.390720	0.195360	−	0.980732i	$-0.437413\pi$
$281$	6.54965	0.390720	0.195360	+	0.980732i	$0.437413\pi$
$282$	2.55443	0.152114
$283$	33.0143	1.96249	0.981247	−	0.192754i	$-0.0617420\pi$
$283$	33.0143	1.96249	0.981247	+	0.192754i	$0.0617420\pi$
$284$	−4.94805	−0.293613
$285$	−7.90352	−0.468164
$286$	−16.5239	−0.977076
$287$	4.48258	0.264598
$288$	0.00467827	0.000275670 0
$289$	12.5979	0.741053
$290$	6.05637	0.355642
$291$	−12.1938	−0.714814
$292$	9.01015	0.527279
$293$	16.8795	0.986112	0.493056	−	0.869998i	$-0.335880\pi$
$293$	16.8795	0.986112	0.493056	+	0.869998i	$0.335880\pi$
$294$	−11.5947	−0.676217
$295$	12.2832	0.715158
$296$	0.362706	0.0210819
$297$	29.1780	1.69308
$298$	3.98762	0.230997
$299$	16.6973	0.965632
$300$	1.73340	0.100078
$301$	−1.51814	−0.0875044
$302$	−8.09122	−0.465598
$303$	−5.83247	−0.335067
$304$	4.55955	0.261508
$305$	2.60608	0.149223
$306$	−0.0254516	−0.00145497
$307$	33.2452	1.89740	0.948701	−	0.316175i	$-0.102399\pi$
$307$	33.2452	1.89740	0.948701	+	0.316175i	$0.102399\pi$
$308$	3.13398	0.178575
$309$	−4.02409	−0.228922
$310$	5.26723	0.299159
$311$	−12.2209	−0.692983	−0.346492	−	0.938053i	$-0.612627\pi$
$311$	−12.2209	−0.692983	−0.346492	+	0.938053i	$0.612627\pi$
$312$	5.09680	0.288550
$313$	−5.83837	−0.330004	−0.165002	−	0.986293i	$-0.552763\pi$
$313$	−5.83837	−0.330004	−0.165002	+	0.986293i	$0.552763\pi$
$314$	−18.8504	−1.06379
$315$	0.00260897	0.000146999 0
$316$	−2.38616	−0.134232
$317$	22.1842	1.24599	0.622995	−	0.782225i	$-0.285915\pi$
$317$	22.1842	1.24599	0.622995	+	0.782225i	$0.285915\pi$
$318$	11.7389	0.658286
$319$	34.0349	1.90559
$320$	−1.00000	−0.0559017
$321$	−5.25385	−0.293241
$322$	−3.16688	−0.176483
$323$	−24.8057	−1.38023
$324$	−9.01401	−0.500778
$325$	2.94035	0.163101
$326$	5.86359	0.324754
$327$	32.3263	1.78765
$328$	−8.03794	−0.443821
$329$	−0.821822	−0.0453085
$330$	9.74118	0.536234
$331$	4.88594	0.268556	0.134278	−	0.990944i	$-0.457129\pi$
$331$	4.88594	0.268556	0.134278	+	0.990944i	$0.457129\pi$
$332$	5.52279	0.303102
$333$	0.00169684	9.29861e−5 0
$334$	10.1419	0.554937
$335$	14.1351	0.772285
$336$	−0.966679	−0.0527367
$337$	−16.6777	−0.908491	−0.454246	−	0.890877i	$-0.650091\pi$
$337$	−16.6777	−0.908491	−0.454246	+	0.890877i	$0.650091\pi$
$338$	−4.35434	−0.236845
$339$	28.8847	1.56880
$340$	5.44040	0.295047
$341$	29.6002	1.60294
$342$	0.0213308	0.00115344
$343$	7.63405	0.412200
$344$	2.72226	0.146774
$345$	−9.84345	−0.529953
$346$	−2.87627	−0.154629
$347$	−29.9744	−1.60911	−0.804554	−	0.593879i	$-0.797596\pi$
$347$	−29.9744	−1.60911	−0.804554	+	0.593879i	$0.797596\pi$
$348$	−10.4981	−0.562758
$349$	4.71468	0.252371	0.126185	−	0.992007i	$-0.459727\pi$
$349$	4.71468	0.252371	0.126185	+	0.992007i	$0.459727\pi$
$350$	−0.557678	−0.0298091
$351$	−15.2666	−0.814869
$352$	−5.61969	−0.299531
$353$	−29.4951	−1.56987	−0.784934	−	0.619580i	$-0.787303\pi$
$353$	−29.4951	−1.56987	−0.784934	+	0.619580i	$0.787303\pi$
$354$	−21.2918	−1.13165
$355$	4.94805	0.262615
$356$	−13.6990	−0.726044
$357$	5.25912	0.278342
$358$	−23.6402	−1.24942
$359$	−28.1106	−1.48362	−0.741811	−	0.670609i	$-0.766033\pi$
$359$	−28.1106	−1.48362	−0.741811	+	0.670609i	$0.766033\pi$
$360$	−0.00467827	−0.000246567 0
$361$	1.78947	0.0941826
$362$	−10.6190	−0.558124
$363$	35.6750	1.87245
$364$	−1.63977	−0.0859472
$365$	−9.01015	−0.471613
$366$	−4.51737	−0.236127
$367$	7.65218	0.399440	0.199720	−	0.979853i	$-0.435997\pi$
$367$	7.65218	0.399440	0.199720	+	0.979853i	$0.435997\pi$
$368$	5.67869	0.296022
$369$	−0.0376037	−0.00195757
$370$	−0.362706	−0.0188562
$371$	−3.77670	−0.196077
$372$	−9.13023	−0.473380
$373$	−14.1654	−0.733458	−0.366729	−	0.930328i	$-0.619522\pi$
$373$	−14.1654	−0.733458	−0.366729	+	0.930328i	$0.619522\pi$
$374$	30.5733	1.58091
$375$	−1.73340	−0.0895124
$376$	1.47365	0.0759977
$377$	−17.8078	−0.917151
$378$	2.89551	0.148929
$379$	23.9574	1.23061	0.615303	−	0.788290i	$-0.289033\pi$
$379$	23.9574	1.23061	0.615303	+	0.788290i	$0.289033\pi$
$380$	−4.55955	−0.233900
$381$	−1.59537	−0.0817332
$382$	−3.92251	−0.200693
$383$	−26.7018	−1.36440	−0.682199	−	0.731166i	$-0.738976\pi$
$383$	−26.7018	−1.36440	−0.682199	+	0.731166i	$0.738976\pi$
$384$	1.73340	0.0884572
$385$	−3.13398	−0.159722
$386$	4.47402	0.227722
$387$	0.0127355	0.000647380 0
$388$	−7.03462	−0.357129
$389$	−4.55406	−0.230900	−0.115450	−	0.993313i	$-0.536831\pi$
$389$	−4.55406	−0.230900	−0.115450	+	0.993313i	$0.536831\pi$
$390$	−5.09680	−0.258087
$391$	−30.8943	−1.56239
$392$	−6.68900	−0.337845
$393$	−10.9248	−0.551082
$394$	24.9003	1.25446
$395$	2.38616	0.120061
$396$	−0.0262904	−0.00132114
$397$	21.1270	1.06033	0.530167	−	0.847893i	$-0.322129\pi$
$397$	21.1270	1.06033	0.530167	+	0.847893i	$0.322129\pi$
$398$	3.19899	0.160351
$399$	−4.40762	−0.220657
$400$	1.00000	0.0500000
$401$	4.65697	0.232558	0.116279	−	0.993217i	$-0.462903\pi$
$401$	4.65697	0.232558	0.116279	+	0.993217i	$0.462903\pi$
$402$	−24.5018	−1.22204
$403$	−15.4875	−0.771488
$404$	−3.36476	−0.167403
$405$	9.01401	0.447910
$406$	3.37750	0.167623
$407$	−2.03830	−0.101035
$408$	−9.43039	−0.466874
$409$	−37.7382	−1.86603	−0.933016	−	0.359834i	$-0.882833\pi$
$409$	−37.7382	−1.86603	−0.933016	+	0.359834i	$0.882833\pi$
$410$	8.03794	0.396966
$411$	−37.0958	−1.82980
$412$	−2.32150	−0.114372
$413$	6.85009	0.337071
$414$	0.0265665	0.00130567
$415$	−5.52279	−0.271103
$416$	2.94035	0.144163
$417$	−9.98703	−0.489067
$418$	−25.6232	−1.25327
$419$	−0.782439	−0.0382247	−0.0191123	−	0.999817i	$-0.506084\pi$
$419$	−0.782439	−0.0382247	−0.0191123	+	0.999817i	$0.506084\pi$
$420$	0.966679	0.0471691
$421$	−13.3547	−0.650867	−0.325433	−	0.945565i	$-0.605510\pi$
$421$	−13.3547	−0.650867	−0.325433	+	0.945565i	$0.605510\pi$
$422$	10.7882	0.525162
$423$	0.00689414	0.000335204 0
$424$	6.77220	0.328887
$425$	−5.44040	−0.263898
$426$	−8.57695	−0.415555
$427$	1.45335	0.0703326
$428$	−3.03095	−0.146506
$429$	−28.6425	−1.38287
$430$	−2.72226	−0.131279
$431$	6.74017	0.324663	0.162331	−	0.986736i	$-0.448099\pi$
$431$	6.74017	0.324663	0.162331	+	0.986736i	$0.448099\pi$
$432$	−5.19209	−0.249805
$433$	17.9062	0.860519	0.430260	−	0.902705i	$-0.358422\pi$
$433$	17.9062	0.860519	0.430260	+	0.902705i	$0.358422\pi$
$434$	2.93742	0.141001
$435$	10.4981	0.503346
$436$	18.6491	0.893129
$437$	25.8923	1.23859
$438$	15.6182	0.746267
$439$	−11.8138	−0.563840	−0.281920	−	0.959438i	$-0.590971\pi$
$439$	−11.8138	−0.563840	−0.281920	+	0.959438i	$0.590971\pi$
$440$	5.61969	0.267908
$441$	−0.0312929	−0.00149014
$442$	−15.9967	−0.760884
$443$	−15.7423	−0.747941	−0.373971	−	0.927441i	$-0.622004\pi$
$443$	−15.7423	−0.747941	−0.373971	+	0.927441i	$0.622004\pi$
$444$	0.628715	0.0298375
$445$	13.6990	0.649393
$446$	21.8752	1.03582
$447$	6.91215	0.326934
$448$	−0.557678	−0.0263478
$449$	−9.57176	−0.451719	−0.225860	−	0.974160i	$-0.572519\pi$
$449$	−9.57176	−0.451719	−0.225860	+	0.974160i	$0.572519\pi$
$450$	0.00467827	0.000220536 0
$451$	45.1708	2.12701
$452$	16.6636	0.783789
$453$	−14.0253	−0.658968
$454$	−27.8852	−1.30872
$455$	1.63977	0.0768735
$456$	7.90352	0.370116
$457$	38.1141	1.78290	0.891451	−	0.453117i	$-0.149688\pi$
$457$	38.1141	1.78290	0.891451	+	0.453117i	$0.149688\pi$
$458$	−20.1720	−0.942576
$459$	28.2470	1.31846
$460$	−5.67869	−0.264770
$461$	20.1920	0.940435	0.470218	−	0.882551i	$-0.344175\pi$
$461$	20.1920	0.940435	0.470218	+	0.882551i	$0.344175\pi$
$462$	5.43244	0.252740
$463$	−3.04271	−0.141407	−0.0707033	−	0.997497i	$-0.522524\pi$
$463$	−3.04271	−0.141407	−0.0707033	+	0.997497i	$0.522524\pi$
$464$	−6.05637	−0.281160
$465$	9.13023	0.423404
$466$	−1.53802	−0.0712473
$467$	12.8751	0.595787	0.297894	−	0.954599i	$-0.403716\pi$
$467$	12.8751	0.595787	0.297894	+	0.954599i	$0.403716\pi$
$468$	0.0137558	0.000635860 0
$469$	7.88285	0.363996
$470$	−1.47365	−0.0679744
$471$	−32.6753	−1.50560
$472$	−12.2832	−0.565382
$473$	−15.2983	−0.703415
$474$	−4.13618	−0.189981
$475$	4.55955	0.209206
$476$	3.03399	0.139063
$477$	0.0316822	0.00145063
$478$	29.5195	1.35019
$479$	10.5493	0.482011	0.241006	−	0.970524i	$-0.422523\pi$
$479$	10.5493	0.482011	0.241006	+	0.970524i	$0.422523\pi$
$480$	−1.73340	−0.0791186
$481$	1.06648	0.0486274
$482$	18.8868	0.860268
$483$	−5.48947	−0.249780
$484$	20.5809	0.935497
$485$	7.03462	0.319426
$486$	−0.0486180	−0.00220536
$487$	37.8597	1.71558	0.857792	−	0.513996i	$-0.171835\pi$
$487$	37.8597	1.71558	0.857792	+	0.513996i	$0.171835\pi$
$488$	−2.60608	−0.117972
$489$	10.1640	0.459630
$490$	6.68900	0.302178
$491$	−23.0333	−1.03948	−0.519738	−	0.854326i	$-0.673971\pi$
$491$	−23.0333	−1.03948	−0.519738	+	0.854326i	$0.673971\pi$
$492$	−13.9330	−0.628147
$493$	32.9490	1.48395
$494$	13.4067	0.603194
$495$	0.0262904	0.00118167
$496$	−5.26723	−0.236506
$497$	2.75942	0.123777
$498$	9.57320	0.428986
$499$	33.3924	1.49485	0.747424	−	0.664347i	$-0.231290\pi$
$499$	33.3924	1.49485	0.747424	+	0.664347i	$0.231290\pi$
$500$	−1.00000	−0.0447214
$501$	17.5799	0.785412
$502$	−6.87133	−0.306682
$503$	24.9035	1.11039	0.555196	−	0.831720i	$-0.312643\pi$
$503$	24.9035	1.11039	0.555196	+	0.831720i	$0.312643\pi$
$504$	−0.00260897	−0.000116213 0
$505$	3.36476	0.149730
$506$	−31.9125	−1.41868
$507$	−7.54782	−0.335210
$508$	−0.920369	−0.0408348
$509$	−18.9929	−0.841843	−0.420922	−	0.907097i	$-0.638293\pi$
$509$	−18.9929	−0.841843	−0.420922	+	0.907097i	$0.638293\pi$
$510$	9.43039	0.417585
$511$	−5.02476	−0.222282
$512$	1.00000	0.0441942
$513$	−23.6736	−1.04521
$514$	30.6995	1.35410
$515$	2.32150	0.102297
$516$	4.71877	0.207732
$517$	−8.28146	−0.364218
$518$	−0.202273	−0.00888737
$519$	−4.98574	−0.218850
$520$	−2.94035	−0.128943
$521$	−20.0901	−0.880163	−0.440082	−	0.897958i	$-0.645050\pi$
$521$	−20.0901	−0.880163	−0.440082	+	0.897958i	$0.645050\pi$
$522$	−0.0283333	−0.00124012
$523$	18.5832	0.812585	0.406292	−	0.913743i	$-0.366821\pi$
$523$	18.5832	0.812585	0.406292	+	0.913743i	$0.366821\pi$
$524$	−6.30250	−0.275326
$525$	−0.966679	−0.0421893
$526$	11.4830	0.500681
$527$	28.6558	1.24827
$528$	−9.74118	−0.423930
$529$	9.24754	0.402067
$530$	−6.77220	−0.294165
$531$	−0.0574643	−0.00249374
$532$	−2.54276	−0.110243
$533$	−23.6344	−1.02372
$534$	−23.7458	−1.02758
$535$	3.03095	0.131039
$536$	−14.1351	−0.610545
$537$	−40.9779	−1.76833
$538$	−9.23907	−0.398325
$539$	37.5901	1.61912
$540$	5.19209	0.223432
$541$	−18.7741	−0.807162	−0.403581	−	0.914944i	$-0.632235\pi$
$541$	−18.7741	−0.807162	−0.403581	+	0.914944i	$0.632235\pi$
$542$	1.69398	0.0727628
$543$	−18.4071	−0.789922
$544$	−5.44040	−0.233255
$545$	−18.6491	−0.798839
$546$	−2.84237	−0.121642
$547$	−7.22119	−0.308756	−0.154378	−	0.988012i	$-0.549337\pi$
$547$	−7.22119	−0.308756	−0.154378	+	0.988012i	$0.549337\pi$
$548$	−21.4006	−0.914187
$549$	−0.0121919	−0.000520339 0
$550$	−5.61969	−0.239624
$551$	−27.6143	−1.17641
$552$	9.84345	0.418965
$553$	1.33071	0.0565876
$554$	16.1685	0.686935
$555$	−0.628715	−0.0266875
$556$	−5.76152	−0.244343
$557$	−11.8101	−0.500408	−0.250204	−	0.968193i	$-0.580498\pi$
$557$	−11.8101	−0.500408	−0.250204	+	0.968193i	$0.580498\pi$
$558$	−0.0246415	−0.00104316
$559$	8.00440	0.338550
$560$	0.557678	0.0235662
$561$	52.9959	2.23749
$562$	6.54965	0.276280
$563$	5.28742	0.222838	0.111419	−	0.993774i	$-0.464460\pi$
$563$	5.28742	0.222838	0.111419	+	0.993774i	$0.464460\pi$
$564$	2.55443	0.107561
$565$	−16.6636	−0.701042
$566$	33.0143	1.38769
$567$	5.02691	0.211111
$568$	−4.94805	−0.207616
$569$	24.2784	1.01780	0.508901	−	0.860825i	$-0.330052\pi$
$569$	24.2784	1.01780	0.508901	+	0.860825i	$0.330052\pi$
$570$	−7.90352	−0.331042
$571$	−14.5018	−0.606881	−0.303440	−	0.952850i	$-0.598135\pi$
$571$	−14.5018	−0.606881	−0.303440	+	0.952850i	$0.598135\pi$
$572$	−16.5239	−0.690897
$573$	−6.79928	−0.284044
$574$	4.48258	0.187099
$575$	5.67869	0.236818
$576$	0.00467827	0.000194928 0
$577$	−24.3349	−1.01308	−0.506538	−	0.862218i	$-0.669075\pi$
$577$	−24.3349	−1.01308	−0.506538	+	0.862218i	$0.669075\pi$
$578$	12.5979	0.524004
$579$	7.75527	0.322298
$580$	6.05637	0.251477
$581$	−3.07994	−0.127777
$582$	−12.1938	−0.505450
$583$	−38.0577	−1.57619
$584$	9.01015	0.372843
$585$	−0.0137558	−0.000568730 0
$586$	16.8795	0.697286
$587$	−11.2340	−0.463677	−0.231839	−	0.972754i	$-0.574474\pi$
$587$	−11.2340	−0.463677	−0.231839	+	0.972754i	$0.574474\pi$
$588$	−11.5947	−0.478158
$589$	−24.0162	−0.989570
$590$	12.2832	0.505693
$591$	43.1622	1.77546
$592$	0.362706	0.0149071
$593$	31.8961	1.30982	0.654908	−	0.755708i	$-0.272707\pi$
$593$	31.8961	1.30982	0.654908	+	0.755708i	$0.272707\pi$
$594$	29.1780	1.19719
$595$	−3.03399	−0.124381
$596$	3.98762	0.163339
$597$	5.54514	0.226947
$598$	16.6973	0.682805
$599$	−0.171803	−0.00701969	−0.00350984	−	0.999994i	$-0.501117\pi$
$599$	−0.171803	−0.00701969	−0.00350984	+	0.999994i	$0.501117\pi$
$600$	1.73340	0.0707658
$601$	1.00000	0.0407909
$601$	1.00000	0.0407909
$602$	−1.51814	−0.0618749
$603$	−0.0661280	−0.00269294
$604$	−8.09122	−0.329227
$605$	−20.5809	−0.836734
$606$	−5.83247	−0.236928
$607$	−41.3578	−1.67866	−0.839331	−	0.543621i	$-0.817053\pi$
$607$	−41.3578	−1.67866	−0.839331	+	0.543621i	$0.817053\pi$
$608$	4.55955	0.184914
$609$	5.85456	0.237239
$610$	2.60608	0.105517
$611$	4.33305	0.175296
$612$	−0.0254516	−0.00102882
$613$	21.2302	0.857478	0.428739	−	0.903428i	$-0.358958\pi$
$613$	21.2302	0.857478	0.428739	+	0.903428i	$0.358958\pi$
$614$	33.2452	1.34167
$615$	13.9330	0.561832
$616$	3.13398	0.126272
$617$	25.9927	1.04643	0.523214	−	0.852201i	$-0.324733\pi$
$617$	25.9927	1.04643	0.523214	+	0.852201i	$0.324733\pi$
$618$	−4.02409	−0.161873
$619$	−34.9898	−1.40636	−0.703179	−	0.711013i	$-0.748237\pi$
$619$	−34.9898	−1.40636	−0.703179	+	0.711013i	$0.748237\pi$
$620$	5.26723	0.211537
$621$	−29.4843	−1.18316
$622$	−12.2209	−0.490013
$623$	7.63961	0.306075
$624$	5.09680	0.204035
$625$	1.00000	0.0400000
$626$	−5.83837	−0.233348
$627$	−44.4154	−1.77378
$628$	−18.8504	−0.752212
$629$	−1.97326	−0.0786792
$630$	0.00260897	0.000103944 0
$631$	26.9340	1.07222	0.536112	−	0.844147i	$-0.319892\pi$
$631$	26.9340	1.07222	0.536112	+	0.844147i	$0.319892\pi$
$632$	−2.38616	−0.0949165
$633$	18.7003	0.743270
$634$	22.1842	0.881049
$635$	0.920369	0.0365237
$636$	11.7389	0.465479
$637$	−19.6680	−0.779274
$638$	34.0349	1.34746
$639$	−0.0231483	−0.000915733 0
$640$	−1.00000	−0.0395285
$641$	35.8218	1.41487	0.707437	−	0.706776i	$-0.249851\pi$
$641$	35.8218	1.41487	0.707437	+	0.706776i	$0.249851\pi$
$642$	−5.25385	−0.207353
$643$	20.0545	0.790873	0.395437	−	0.918493i	$-0.370593\pi$
$643$	20.0545	0.790873	0.395437	+	0.918493i	$0.370593\pi$
$644$	−3.16688	−0.124793
$645$	−4.71877	−0.185801
$646$	−24.8057	−0.975969
$647$	−14.1889	−0.557824	−0.278912	−	0.960317i	$-0.589974\pi$
$647$	−14.1889	−0.557824	−0.278912	+	0.960317i	$0.589974\pi$
$648$	−9.01401	−0.354104
$649$	69.0280	2.70959
$650$	2.94035	0.115330
$651$	5.09172	0.199560
$652$	5.86359	0.229636
$653$	8.09487	0.316777	0.158388	−	0.987377i	$-0.449370\pi$
$653$	8.09487	0.316777	0.158388	+	0.987377i	$0.449370\pi$
$654$	32.3263	1.26406
$655$	6.30250	0.246259
$656$	−8.03794	−0.313829
$657$	0.0421519	0.00164450
$658$	−0.821822	−0.0320380
$659$	−27.2953	−1.06328	−0.531638	−	0.846972i	$-0.678423\pi$
$659$	−27.2953	−1.06328	−0.531638	+	0.846972i	$0.678423\pi$
$660$	9.74118	0.379175
$661$	23.0419	0.896228	0.448114	−	0.893976i	$-0.352096\pi$
$661$	23.0419	0.896228	0.448114	+	0.893976i	$0.352096\pi$
$662$	4.88594	0.189897
$663$	−27.7286	−1.07689
$664$	5.52279	0.214326
$665$	2.54276	0.0986039
$666$	0.00169684	6.57511e−5 0
$667$	−34.3923	−1.33167
$668$	10.1419	0.392400
$669$	37.9185	1.46601
$670$	14.1351	0.546088
$671$	14.6453	0.565377
$672$	−0.966679	−0.0372905
$673$	−14.4932	−0.558672	−0.279336	−	0.960193i	$-0.590114\pi$
$673$	−14.4932	−0.558672	−0.279336	+	0.960193i	$0.590114\pi$
$674$	−16.6777	−0.642400
$675$	−5.19209	−0.199844
$676$	−4.35434	−0.167475
$677$	4.54999	0.174870	0.0874351	−	0.996170i	$-0.472133\pi$
$677$	4.54999	0.174870	0.0874351	+	0.996170i	$0.472133\pi$
$678$	28.8847	1.10931
$679$	3.92305	0.150553
$680$	5.44040	0.208630
$681$	−48.3362	−1.85225
$682$	29.6002	1.13345
$683$	−27.6741	−1.05892	−0.529460	−	0.848335i	$-0.677605\pi$
$683$	−27.6741	−1.05892	−0.529460	+	0.848335i	$0.677605\pi$
$684$	0.0213308	0.000815603 0
$685$	21.4006	0.817674
$686$	7.63405	0.291469
$687$	−34.9662	−1.33404
$688$	2.72226	0.103785
$689$	19.9126	0.758611
$690$	−9.84345	−0.374734
$691$	−27.4093	−1.04270	−0.521349	−	0.853343i	$-0.674571\pi$
$691$	−27.4093	−1.04270	−0.521349	+	0.853343i	$0.674571\pi$
$692$	−2.87627	−0.109340
$693$	0.0146616	0.000556948 0
$694$	−29.9744	−1.13781
$695$	5.76152	0.218547
$696$	−10.4981	−0.397930
$697$	43.7296	1.65638
$698$	4.71468	0.178453
$699$	−2.66600	−0.100837
$700$	−0.557678	−0.0210782
$701$	−36.2531	−1.36926	−0.684631	−	0.728890i	$-0.740037\pi$
$701$	−36.2531	−1.36926	−0.684631	+	0.728890i	$0.740037\pi$
$702$	−15.2666	−0.576200
$703$	1.65378	0.0623733
$704$	−5.61969	−0.211800
$705$	−2.55443	−0.0962053
$706$	−29.4951	−1.11006
$707$	1.87645	0.0705712
$708$	−21.2918	−0.800194
$709$	−28.5698	−1.07296	−0.536481	−	0.843912i	$-0.680247\pi$
$709$	−28.5698	−1.07296	−0.536481	+	0.843912i	$0.680247\pi$
$710$	4.94805	0.185697
$711$	−0.0111631	−0.000418650 0
$712$	−13.6990	−0.513391
$713$	−29.9110	−1.12018
$714$	5.25912	0.196818
$715$	16.5239	0.617957
$716$	−23.6402	−0.883474
$717$	51.1692	1.91095
$718$	−28.1106	−1.04908
$719$	45.9958	1.71535	0.857676	−	0.514190i	$-0.171907\pi$
$719$	45.9958	1.71535	0.857676	+	0.514190i	$0.171907\pi$
$720$	−0.00467827	−0.000174349 0
$721$	1.29465	0.0482152
$722$	1.78947	0.0665972
$723$	32.7383	1.21755
$724$	−10.6190	−0.394653
$725$	−6.05637	−0.224928
$726$	35.6750	1.32402
$727$	−44.9244	−1.66616	−0.833078	−	0.553156i	$-0.813423\pi$
$727$	−44.9244	−1.66616	−0.833078	+	0.553156i	$0.813423\pi$
$728$	−1.63977	−0.0607738
$729$	26.9578	0.998436
$730$	−9.01015	−0.333481
$731$	−14.8102	−0.547774
$732$	−4.51737	−0.166967
$733$	−32.6804	−1.20708	−0.603539	−	0.797334i	$-0.706243\pi$
$733$	−32.6804	−1.20708	−0.603539	+	0.797334i	$0.706243\pi$
$734$	7.65218	0.282447
$735$	11.5947	0.427677
$736$	5.67869	0.209319
$737$	79.4351	2.92603
$738$	−0.0376037	−0.00138421
$739$	−5.43358	−0.199878	−0.0999388	−	0.994994i	$-0.531865\pi$
$739$	−5.43358	−0.199878	−0.0999388	+	0.994994i	$0.531865\pi$
$740$	−0.362706	−0.0133333
$741$	23.2391	0.853710
$742$	−3.77670	−0.138647
$743$	−8.87430	−0.325566	−0.162783	−	0.986662i	$-0.552047\pi$
$743$	−8.87430	−0.325566	−0.162783	+	0.986662i	$0.552047\pi$
$744$	−9.13023	−0.334730
$745$	−3.98762	−0.146095
$746$	−14.1654	−0.518633
$747$	0.0258371	0.000945330 0
$748$	30.5733	1.11787
$749$	1.69029	0.0617619
$750$	−1.73340	−0.0632948
$751$	36.5684	1.33440	0.667201	−	0.744878i	$-0.267492\pi$
$751$	36.5684	1.33440	0.667201	+	0.744878i	$0.267492\pi$
$752$	1.47365	0.0537385
$753$	−11.9108	−0.434053
$754$	−17.8078	−0.648523
$755$	8.09122	0.294470
$756$	2.89551	0.105309
$757$	49.0119	1.78137	0.890683	−	0.454624i	$-0.150226\pi$
$757$	49.0119	1.78137	0.890683	+	0.454624i	$0.150226\pi$
$758$	23.9574	0.870170
$759$	−55.3172	−2.00789
$760$	−4.55955	−0.165392
$761$	−14.9955	−0.543588	−0.271794	−	0.962356i	$-0.587617\pi$
$761$	−14.9955	−0.543588	−0.271794	+	0.962356i	$0.587617\pi$
$762$	−1.59537	−0.0577941
$763$	−10.4002	−0.376512
$764$	−3.92251	−0.141911
$765$	0.0254516	0.000920206 0
$766$	−26.7018	−0.964775
$767$	−36.1170	−1.30411
$768$	1.73340	0.0625487
$769$	−0.621260	−0.0224032	−0.0112016	−	0.999937i	$-0.503566\pi$
$769$	−0.621260	−0.0224032	−0.0112016	+	0.999937i	$0.503566\pi$
$770$	−3.13398	−0.112941
$771$	53.2145	1.91647
$772$	4.47402	0.161024
$773$	−1.45717	−0.0524109	−0.0262055	−	0.999657i	$-0.508342\pi$
$773$	−1.45717	−0.0524109	−0.0262055	+	0.999657i	$0.508342\pi$
$774$	0.0127355	0.000457767 0
$775$	−5.26723	−0.189205
$776$	−7.03462	−0.252528
$777$	−0.350620	−0.0125784
$778$	−4.55406	−0.163271
$779$	−36.6494	−1.31310
$780$	−5.09680	−0.182495
$781$	27.8065	0.994995
$782$	−30.8943	−1.10478
$783$	31.4452	1.12376
$784$	−6.68900	−0.238893
$785$	18.8504	0.672799
$786$	−10.9248	−0.389674
$787$	2.77762	0.0990114	0.0495057	−	0.998774i	$-0.484235\pi$
$787$	2.77762	0.0990114	0.0495057	+	0.998774i	$0.484235\pi$
$788$	24.9003	0.887036
$789$	19.9046	0.708622
$790$	2.38616	0.0848959
$791$	−9.29291	−0.330418
$792$	−0.0262904	−0.000934190 0
$793$	−7.66278	−0.272113
$794$	21.1270	0.749770
$795$	−11.7389	−0.416337
$796$	3.19899	0.113385
$797$	−27.0557	−0.958364	−0.479182	−	0.877716i	$-0.659067\pi$
$797$	−27.0557	−0.958364	−0.479182	+	0.877716i	$0.659067\pi$
$798$	−4.40762	−0.156028
$799$	−8.01724	−0.283630
$800$	1.00000	0.0353553
$801$	−0.0640875	−0.00226442
$802$	4.65697	0.164443
$803$	−50.6343	−1.78684
$804$	−24.5018	−0.864113
$805$	3.16688	0.111618
$806$	−15.4875	−0.545524
$807$	−16.0150	−0.563755
$808$	−3.36476	−0.118372
$809$	−53.5218	−1.88173	−0.940863	−	0.338787i	$-0.889983\pi$
$809$	−53.5218	−1.88173	−0.940863	+	0.338787i	$0.889983\pi$
$810$	9.01401	0.316720
$811$	−10.5657	−0.371012	−0.185506	−	0.982643i	$-0.559392\pi$
$811$	−10.5657	−0.371012	−0.185506	+	0.982643i	$0.559392\pi$
$812$	3.37750	0.118527
$813$	2.93635	0.102982
$814$	−2.03830	−0.0714422
$815$	−5.86359	−0.205393
$816$	−9.43039	−0.330130
$817$	12.4123	0.434250
$818$	−37.7382	−1.31948
$819$	−0.00767128	−0.000268056 0
$820$	8.03794	0.280697
$821$	−39.5014	−1.37861	−0.689305	−	0.724471i	$-0.742084\pi$
$821$	−39.5014	−1.37861	−0.689305	+	0.724471i	$0.742084\pi$
$822$	−37.0958	−1.29386
$823$	0.561830	0.0195842	0.00979209	−	0.999952i	$-0.496883\pi$
$823$	0.561830	0.0195842	0.00979209	+	0.999952i	$0.496883\pi$
$824$	−2.32150	−0.0808733
$825$	−9.74118	−0.339144
$826$	6.85009	0.238345
$827$	28.0323	0.974779	0.487389	−	0.873185i	$-0.337949\pi$
$827$	28.0323	0.974779	0.487389	+	0.873185i	$0.337949\pi$
$828$	0.0265665	0.000923248 0
$829$	−3.41173	−0.118494	−0.0592471	−	0.998243i	$-0.518870\pi$
$829$	−3.41173	−0.118494	−0.0592471	+	0.998243i	$0.518870\pi$
$830$	−5.52279	−0.191699
$831$	28.0266	0.972231
$832$	2.94035	0.101938
$833$	36.3908	1.26087
$834$	−9.98703	−0.345823
$835$	−10.1419	−0.350973
$836$	−25.6232	−0.886199
$837$	27.3480	0.945284
$838$	−0.782439	−0.0270289
$839$	21.4297	0.739837	0.369918	−	0.929064i	$-0.379386\pi$
$839$	21.4297	0.739837	0.369918	+	0.929064i	$0.379386\pi$
$840$	0.966679	0.0333536
$841$	7.67960	0.264814
$842$	−13.3547	−0.460232
$843$	11.3532	0.391024
$844$	10.7882	0.371346
$845$	4.35434	0.149794
$846$	0.00689414	0.000237025 0
$847$	−11.4775	−0.394373
$848$	6.77220	0.232558
$849$	57.2269	1.96402
$850$	−5.44040	−0.186604
$851$	2.05970	0.0706055
$852$	−8.57695	−0.293842
$853$	4.54272	0.155540	0.0777698	−	0.996971i	$-0.475220\pi$
$853$	4.54272	0.155540	0.0777698	+	0.996971i	$0.475220\pi$
$854$	1.45335	0.0497326
$855$	−0.0213308	−0.000729498 0
$856$	−3.03095	−0.103596
$857$	−20.8264	−0.711417	−0.355709	−	0.934597i	$-0.615760\pi$
$857$	−20.8264	−0.711417	−0.355709	+	0.934597i	$0.615760\pi$
$858$	−28.6425	−0.977838
$859$	−2.64930	−0.0903928	−0.0451964	−	0.998978i	$-0.514391\pi$
$859$	−2.64930	−0.0903928	−0.0451964	+	0.998978i	$0.514391\pi$
$860$	−2.72226	−0.0928283
$861$	7.77011	0.264805
$862$	6.74017	0.229571
$863$	48.5367	1.65221	0.826104	−	0.563518i	$-0.190552\pi$
$863$	48.5367	1.65221	0.826104	+	0.563518i	$0.190552\pi$
$864$	−5.19209	−0.176639
$865$	2.87627	0.0977963
$866$	17.9062	0.608479
$867$	21.8372	0.741631
$868$	2.93742	0.0997025
$869$	13.4095	0.454886
$870$	10.4981	0.355919
$871$	−41.5622	−1.40828
$872$	18.6491	0.631538
$873$	−0.0329099	−0.00111383
$874$	25.8923	0.875819
$875$	0.557678	0.0188529
$876$	15.6182	0.527690
$877$	−39.1231	−1.32109	−0.660547	−	0.750785i	$-0.729676\pi$
$877$	−39.1231	−1.32109	−0.660547	+	0.750785i	$0.729676\pi$
$878$	−11.8138	−0.398695
$879$	29.2590	0.986881
$880$	5.61969	0.189440
$881$	27.0542	0.911479	0.455740	−	0.890113i	$-0.349375\pi$
$881$	27.0542	0.911479	0.455740	+	0.890113i	$0.349375\pi$
$882$	−0.0312929	−0.00105369
$883$	−30.3921	−1.02278	−0.511388	−	0.859350i	$-0.670869\pi$
$883$	−30.3921	−1.02278	−0.511388	+	0.859350i	$0.670869\pi$
$884$	−15.9967	−0.538026
$885$	21.2918	0.715715
$886$	−15.7423	−0.528874
$887$	−52.4060	−1.75962	−0.879810	−	0.475326i	$-0.842330\pi$
$887$	−52.4060	−1.75962	−0.879810	+	0.475326i	$0.842330\pi$
$888$	0.628715	0.0210983
$889$	0.513269	0.0172145
$890$	13.6990	0.459191
$891$	50.6560	1.69704
$892$	21.8752	0.732435
$893$	6.71918	0.224849
$894$	6.91215	0.231177
$895$	23.6402	0.790203
$896$	−0.557678	−0.0186307
$897$	28.9432	0.966385
$898$	−9.57176	−0.319414
$899$	31.9003	1.06393
$900$	0.00467827	0.000155942 0
$901$	−36.8434	−1.22743
$902$	45.1708	1.50402
$903$	−2.63155	−0.0875726
$904$	16.6636	0.554223
$905$	10.6190	0.352989
$906$	−14.0253	−0.465960
$907$	−5.64898	−0.187571	−0.0937856	−	0.995592i	$-0.529897\pi$
$907$	−5.64898	−0.187571	−0.0937856	+	0.995592i	$0.529897\pi$
$908$	−27.8852	−0.925403
$909$	−0.0157412	−0.000522104 0
$910$	1.63977	0.0543578
$911$	32.6446	1.08156	0.540781	−	0.841163i	$-0.318129\pi$
$911$	32.6446	1.08156	0.540781	+	0.841163i	$0.318129\pi$
$912$	7.90352	0.261712
$913$	−31.0364	−1.02715
$914$	38.1141	1.26070
$915$	4.51737	0.149340
$916$	−20.1720	−0.666502
$917$	3.51477	0.116068
$918$	28.2470	0.932291
$919$	−44.5703	−1.47024	−0.735120	−	0.677937i	$-0.762874\pi$
$919$	−44.5703	−1.47024	−0.735120	+	0.677937i	$0.762874\pi$
$920$	−5.67869	−0.187221
$921$	57.6272	1.89888
$922$	20.1920	0.664988
$923$	−14.5490	−0.478886
$924$	5.43244	0.178714
$925$	0.362706	0.0119257
$926$	−3.04271	−0.0999896
$927$	−0.0108606	−0.000356709 0
$928$	−6.05637	−0.198810
$929$	7.23715	0.237443	0.118722	−	0.992928i	$-0.462120\pi$
$929$	7.23715	0.237443	0.118722	+	0.992928i	$0.462120\pi$
$930$	9.13023	0.299392
$931$	−30.4988	−0.999557
$932$	−1.53802	−0.0503794
$933$	−21.1837	−0.693523
$934$	12.8751	0.421285
$935$	−30.5733	−0.999855
$936$	0.0137558	0.000449621 0
$937$	33.4962	1.09427	0.547137	−	0.837043i	$-0.315718\pi$
$937$	33.4962	1.09427	0.547137	+	0.837043i	$0.315718\pi$
$938$	7.88285	0.257384
$939$	−10.1202	−0.330262
$940$	−1.47365	−0.0480652
$941$	−38.6569	−1.26018	−0.630089	−	0.776523i	$-0.716982\pi$
$941$	−38.6569	−1.26018	−0.630089	+	0.776523i	$0.716982\pi$
$942$	−32.6753	−1.06462
$943$	−45.6450	−1.48641
$944$	−12.2832	−0.399785
$945$	−2.89551	−0.0941911
$946$	−15.2983	−0.497389
$947$	36.6370	1.19054	0.595271	−	0.803525i	$-0.297045\pi$
$947$	36.6370	1.19054	0.595271	+	0.803525i	$0.297045\pi$
$948$	−4.13618	−0.134337
$949$	26.4930	0.859999
$950$	4.55955	0.147931
$951$	38.4542	1.24696
$952$	3.03399	0.0983321
$953$	35.7285	1.15736	0.578680	−	0.815555i	$-0.303568\pi$
$953$	35.7285	1.15736	0.578680	+	0.815555i	$0.303568\pi$
$954$	0.0316822	0.00102575
$955$	3.92251	0.126929
$956$	29.5195	0.954730
$957$	58.9962	1.90708
$958$	10.5493	0.340833
$959$	11.9346	0.385389
$960$	−1.73340	−0.0559453
$961$	−3.25626	−0.105041
$962$	1.06648	0.0343848
$963$	−0.0141796	−0.000456931 0
$964$	18.8868	0.608302
$965$	−4.47402	−0.144024
$966$	−5.48947	−0.176621
$967$	−53.8849	−1.73282	−0.866410	−	0.499333i	$-0.833578\pi$
$967$	−53.8849	−1.73282	−0.866410	+	0.499333i	$0.833578\pi$
$968$	20.5809	0.661496
$969$	−42.9983	−1.38130
$970$	7.03462	0.225868
$971$	50.2683	1.61319	0.806593	−	0.591107i	$-0.201309\pi$
$971$	50.2683	1.61319	0.806593	+	0.591107i	$0.201309\pi$
$972$	−0.0486180	−0.00155942
$973$	3.21307	0.103006
$974$	37.8597	1.21310
$975$	5.09680	0.163228
$976$	−2.60608	−0.0834185
$977$	14.8054	0.473667	0.236834	−	0.971550i	$-0.423890\pi$
$977$	14.8054	0.473667	0.236834	+	0.971550i	$0.423890\pi$
$978$	10.1640	0.325008
$979$	76.9840	2.46042
$980$	6.68900	0.213672
$981$	0.0872455	0.00278553
$982$	−23.0333	−0.735021
$983$	−22.9944	−0.733407	−0.366703	−	0.930338i	$-0.619514\pi$
$983$	−22.9944	−0.733407	−0.366703	+	0.930338i	$0.619514\pi$
$984$	−13.9330	−0.444167
$985$	−24.9003	−0.793389
$986$	32.9490	1.04931
$987$	−1.42455	−0.0453438
$988$	13.4067	0.426523
$989$	15.4589	0.491564
$990$	0.0262904	0.000835565 0
$991$	−58.6384	−1.86271	−0.931355	−	0.364112i	$-0.881373\pi$
$991$	−58.6384	−1.86271	−0.931355	+	0.364112i	$0.881373\pi$
$992$	−5.26723	−0.167235
$993$	8.46929	0.268765
$994$	2.75942	0.0875234
$995$	−3.19899	−0.101415
$996$	9.57320	0.303339
$997$	6.70679	0.212406	0.106203	−	0.994344i	$-0.466131\pi$
$997$	6.70679	0.212406	0.106203	+	0.994344i	$0.466131\pi$
$998$	33.3924	1.05702
$999$	−1.88320	−0.0595819

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6010.2.a.f.1.18	✓	22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6010.2.a.f.1.18	✓	22	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:	\( N \)	\(=\)	\( 6010 = 2 \cdot 5 \cdot 601 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6010.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +1.73340 q^{3} +1.00000 q^{4} -1.00000 q^{5} +1.73340 q^{6} -0.557678 q^{7} +1.00000 q^{8} +0.00467827 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +1.73340 q^{3} +1.00000 q^{4} -1.00000 q^{5} +1.73340 q^{6} -0.557678 q^{7} +1.00000 q^{8} +0.00467827 q^{9} -1.00000 q^{10} -5.61969 q^{11} +1.73340 q^{12} +2.94035 q^{13} -0.557678 q^{14} -1.73340 q^{15} +1.00000 q^{16} -5.44040 q^{17} +0.00467827 q^{18} +4.55955 q^{19} -1.00000 q^{20} -0.966679 q^{21} -5.61969 q^{22} +5.67869 q^{23} +1.73340 q^{24} +1.00000 q^{25} +2.94035 q^{26} -5.19209 q^{27} -0.557678 q^{28} -6.05637 q^{29} -1.73340 q^{30} -5.26723 q^{31} +1.00000 q^{32} -9.74118 q^{33} -5.44040 q^{34} +0.557678 q^{35} +0.00467827 q^{36} +0.362706 q^{37} +4.55955 q^{38} +5.09680 q^{39} -1.00000 q^{40} -8.03794 q^{41} -0.966679 q^{42} +2.72226 q^{43} -5.61969 q^{44} -0.00467827 q^{45} +5.67869 q^{46} +1.47365 q^{47} +1.73340 q^{48} -6.68900 q^{49} +1.00000 q^{50} -9.43039 q^{51} +2.94035 q^{52} +6.77220 q^{53} -5.19209 q^{54} +5.61969 q^{55} -0.557678 q^{56} +7.90352 q^{57} -6.05637 q^{58} -12.2832 q^{59} -1.73340 q^{60} -2.60608 q^{61} -5.26723 q^{62} -0.00260897 q^{63} +1.00000 q^{64} -2.94035 q^{65} -9.74118 q^{66} -14.1351 q^{67} -5.44040 q^{68} +9.84345 q^{69} +0.557678 q^{70} -4.94805 q^{71} +0.00467827 q^{72} +9.01015 q^{73} +0.362706 q^{74} +1.73340 q^{75} +4.55955 q^{76} +3.13398 q^{77} +5.09680 q^{78} -2.38616 q^{79} -1.00000 q^{80} -9.01401 q^{81} -8.03794 q^{82} +5.52279 q^{83} -0.966679 q^{84} +5.44040 q^{85} +2.72226 q^{86} -10.4981 q^{87} -5.61969 q^{88} -13.6990 q^{89} -0.00467827 q^{90} -1.63977 q^{91} +5.67869 q^{92} -9.13023 q^{93} +1.47365 q^{94} -4.55955 q^{95} +1.73340 q^{96} -7.03462 q^{97} -6.68900 q^{98} -0.0262904 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q + 22 q^{2} - 6 q^{3} + 22 q^{4} - 22 q^{5} - 6 q^{6} - 12 q^{7} + 22 q^{8} + 12 q^{9}+O(q^{10}) \) 22 * q + 22 * q^2 - 6 * q^3 + 22 * q^4 - 22 * q^5 - 6 * q^6 - 12 * q^7 + 22 * q^8 + 12 * q^9	\( 22 q + 22 q^{2} - 6 q^{3} + 22 q^{4} - 22 q^{5} - 6 q^{6} - 12 q^{7} + 22 q^{8} + 12 q^{9} - 22 q^{10} - 4 q^{11} - 6 q^{12} - 20 q^{13} - 12 q^{14} + 6 q^{15} + 22 q^{16} - 23 q^{17} + 12 q^{18} + q^{19} - 22 q^{20} - 8 q^{21} - 4 q^{22} - 17 q^{23} - 6 q^{24} + 22 q^{25} - 20 q^{26} - 21 q^{27} - 12 q^{28} - 13 q^{29} + 6 q^{30} - 13 q^{31} + 22 q^{32} - 21 q^{33} - 23 q^{34} + 12 q^{35} + 12 q^{36} - 16 q^{37} + q^{38} - 4 q^{39} - 22 q^{40} - 31 q^{41} - 8 q^{42} - 9 q^{43} - 4 q^{44} - 12 q^{45} - 17 q^{46} - 41 q^{47} - 6 q^{48} - 6 q^{49} + 22 q^{50} - 7 q^{51} - 20 q^{52} - 15 q^{53} - 21 q^{54} + 4 q^{55} - 12 q^{56} - 26 q^{57} - 13 q^{58} - 32 q^{59} + 6 q^{60} - 22 q^{61} - 13 q^{62} - 55 q^{63} + 22 q^{64} + 20 q^{65} - 21 q^{66} - 19 q^{67} - 23 q^{68} - 37 q^{69} + 12 q^{70} - 36 q^{71} + 12 q^{72} - 47 q^{73} - 16 q^{74} - 6 q^{75} + q^{76} - 26 q^{77} - 4 q^{78} - 10 q^{79} - 22 q^{80} - 18 q^{81} - 31 q^{82} - 48 q^{83} - 8 q^{84} + 23 q^{85} - 9 q^{86} - 50 q^{87} - 4 q^{88} - 42 q^{89} - 12 q^{90} + 25 q^{91} - 17 q^{92} - 48 q^{93} - 41 q^{94} - q^{95} - 6 q^{96} - 67 q^{97} - 6 q^{98} - 3 q^{99}+O(q^{100}) \) 22 * q + 22 * q^2 - 6 * q^3 + 22 * q^4 - 22 * q^5 - 6 * q^6 - 12 * q^7 + 22 * q^8 + 12 * q^9 - 22 * q^10 - 4 * q^11 - 6 * q^12 - 20 * q^13 - 12 * q^14 + 6 * q^15 + 22 * q^16 - 23 * q^17 + 12 * q^18 + q^19 - 22 * q^20 - 8 * q^21 - 4 * q^22 - 17 * q^23 - 6 * q^24 + 22 * q^25 - 20 * q^26 - 21 * q^27 - 12 * q^28 - 13 * q^29 + 6 * q^30 - 13 * q^31 + 22 * q^32 - 21 * q^33 - 23 * q^34 + 12 * q^35 + 12 * q^36 - 16 * q^37 + q^38 - 4 * q^39 - 22 * q^40 - 31 * q^41 - 8 * q^42 - 9 * q^43 - 4 * q^44 - 12 * q^45 - 17 * q^46 - 41 * q^47 - 6 * q^48 - 6 * q^49 + 22 * q^50 - 7 * q^51 - 20 * q^52 - 15 * q^53 - 21 * q^54 + 4 * q^55 - 12 * q^56 - 26 * q^57 - 13 * q^58 - 32 * q^59 + 6 * q^60 - 22 * q^61 - 13 * q^62 - 55 * q^63 + 22 * q^64 + 20 * q^65 - 21 * q^66 - 19 * q^67 - 23 * q^68 - 37 * q^69 + 12 * q^70 - 36 * q^71 + 12 * q^72 - 47 * q^73 - 16 * q^74 - 6 * q^75 + q^76 - 26 * q^77 - 4 * q^78 - 10 * q^79 - 22 * q^80 - 18 * q^81 - 31 * q^82 - 48 * q^83 - 8 * q^84 + 23 * q^85 - 9 * q^86 - 50 * q^87 - 4 * q^88 - 42 * q^89 - 12 * q^90 + 25 * q^91 - 17 * q^92 - 48 * q^93 - 41 * q^94 - q^95 - 6 * q^96 - 67 * q^97 - 6 * q^98 - 3 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more