LMFDB - Embedded newform 6017.2.a.e.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6017,2,Mod(1,6017)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6017, 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("6017.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6017 = 11 \cdot 547 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6017.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:	$48.0459868962$
Analytic rank:	$0$
Dimension:	$119$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Character	$\chi$	$=$	6017.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.68163 q^{2} +0.369101 q^{3} +5.19115 q^{4} +2.09046 q^{5} -0.989794 q^{6} +1.10498 q^{7} -8.55750 q^{8} -2.86376 q^{9} +O(q^{10})$	\(q-2.68163 q^{2} +0.369101 q^{3} +5.19115 q^{4} +2.09046 q^{5} -0.989794 q^{6} +1.10498 q^{7} -8.55750 q^{8} -2.86376 q^{9} -5.60585 q^{10} +1.00000 q^{11} +1.91606 q^{12} +5.13703 q^{13} -2.96316 q^{14} +0.771592 q^{15} +12.5658 q^{16} +0.900733 q^{17} +7.67956 q^{18} -4.31013 q^{19} +10.8519 q^{20} +0.407850 q^{21} -2.68163 q^{22} -7.55625 q^{23} -3.15858 q^{24} -0.629976 q^{25} -13.7756 q^{26} -2.16432 q^{27} +5.73613 q^{28} +9.39879 q^{29} -2.06913 q^{30} +9.16747 q^{31} -16.5817 q^{32} +0.369101 q^{33} -2.41543 q^{34} +2.30992 q^{35} -14.8662 q^{36} +7.58160 q^{37} +11.5582 q^{38} +1.89609 q^{39} -17.8891 q^{40} +1.45893 q^{41} -1.09370 q^{42} -6.77290 q^{43} +5.19115 q^{44} -5.98659 q^{45} +20.2631 q^{46} +6.89531 q^{47} +4.63804 q^{48} -5.77901 q^{49} +1.68936 q^{50} +0.332462 q^{51} +26.6671 q^{52} +3.57071 q^{53} +5.80392 q^{54} +2.09046 q^{55} -9.45588 q^{56} -1.59087 q^{57} -25.2041 q^{58} -6.16161 q^{59} +4.00545 q^{60} -4.65836 q^{61} -24.5838 q^{62} -3.16441 q^{63} +19.3346 q^{64} +10.7388 q^{65} -0.989794 q^{66} +2.80548 q^{67} +4.67584 q^{68} -2.78902 q^{69} -6.19436 q^{70} -7.41096 q^{71} +24.5067 q^{72} +1.50888 q^{73} -20.3311 q^{74} -0.232525 q^{75} -22.3745 q^{76} +1.10498 q^{77} -5.08461 q^{78} +16.7592 q^{79} +26.2682 q^{80} +7.79244 q^{81} -3.91232 q^{82} +0.602862 q^{83} +2.11721 q^{84} +1.88295 q^{85} +18.1624 q^{86} +3.46910 q^{87} -8.55750 q^{88} -15.9378 q^{89} +16.0538 q^{90} +5.67633 q^{91} -39.2256 q^{92} +3.38373 q^{93} -18.4907 q^{94} -9.01015 q^{95} -6.12035 q^{96} -3.49976 q^{97} +15.4972 q^{98} -2.86376 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 119 q + 15 q^{2} + 15 q^{3} + 133 q^{4} + 6 q^{5} + 16 q^{6} + 72 q^{7} + 39 q^{8} + 128 q^{9}+O(q^{10}) $ 119 * q + 15 * q^2 + 15 * q^3 + 133 * q^4 + 6 * q^5 + 16 * q^6 + 72 * q^7 + 39 * q^8 + 128 * q^9	\( 119 q + 15 q^{2} + 15 q^{3} + 133 q^{4} + 6 q^{5} + 16 q^{6} + 72 q^{7} + 39 q^{8} + 128 q^{9} + 22 q^{10} + 119 q^{11} + 40 q^{12} + 67 q^{13} + 3 q^{14} + 22 q^{15} + 145 q^{16} + 57 q^{17} + 53 q^{18} + 68 q^{19} + 25 q^{20} + 21 q^{21} + 15 q^{22} + 21 q^{23} + 34 q^{24} + 137 q^{25} + 10 q^{26} + 54 q^{27} + 149 q^{28} + 46 q^{29} + 10 q^{30} + 87 q^{31} + 58 q^{32} + 15 q^{33} + 16 q^{34} + 40 q^{35} + 137 q^{36} + 39 q^{37} + 27 q^{38} + 72 q^{39} + 46 q^{40} + 50 q^{41} - 4 q^{42} + 122 q^{43} + 133 q^{44} + 12 q^{45} + 22 q^{46} + 92 q^{47} + 9 q^{48} + 161 q^{49} + 2 q^{50} - 12 q^{51} + 177 q^{52} + 12 q^{53} + 19 q^{54} + 6 q^{55} - 16 q^{56} + 43 q^{57} + 56 q^{58} + 39 q^{59} + 27 q^{60} + 114 q^{61} + 66 q^{62} + 196 q^{63} + 161 q^{64} + 7 q^{65} + 16 q^{66} + 59 q^{67} + 139 q^{68} - 24 q^{69} + 9 q^{70} + 11 q^{71} + 92 q^{72} + 123 q^{73} + q^{74} + 19 q^{75} + 92 q^{76} + 72 q^{77} - 101 q^{78} + 78 q^{79} - 34 q^{80} + 139 q^{81} + 73 q^{82} + 108 q^{83} - 31 q^{84} + 30 q^{85} - 18 q^{86} + 164 q^{87} + 39 q^{88} + 15 q^{89} - 41 q^{90} + 60 q^{91} - 26 q^{92} - 2 q^{93} + 45 q^{94} + 75 q^{95} + 42 q^{96} + 73 q^{97} + 32 q^{98} + 128 q^{99}+O(q^{100}) \) 119 * q + 15 * q^2 + 15 * q^3 + 133 * q^4 + 6 * q^5 + 16 * q^6 + 72 * q^7 + 39 * q^8 + 128 * q^9 + 22 * q^10 + 119 * q^11 + 40 * q^12 + 67 * q^13 + 3 * q^14 + 22 * q^15 + 145 * q^16 + 57 * q^17 + 53 * q^18 + 68 * q^19 + 25 * q^20 + 21 * q^21 + 15 * q^22 + 21 * q^23 + 34 * q^24 + 137 * q^25 + 10 * q^26 + 54 * q^27 + 149 * q^28 + 46 * q^29 + 10 * q^30 + 87 * q^31 + 58 * q^32 + 15 * q^33 + 16 * q^34 + 40 * q^35 + 137 * q^36 + 39 * q^37 + 27 * q^38 + 72 * q^39 + 46 * q^40 + 50 * q^41 - 4 * q^42 + 122 * q^43 + 133 * q^44 + 12 * q^45 + 22 * q^46 + 92 * q^47 + 9 * q^48 + 161 * q^49 + 2 * q^50 - 12 * q^51 + 177 * q^52 + 12 * q^53 + 19 * q^54 + 6 * q^55 - 16 * q^56 + 43 * q^57 + 56 * q^58 + 39 * q^59 + 27 * q^60 + 114 * q^61 + 66 * q^62 + 196 * q^63 + 161 * q^64 + 7 * q^65 + 16 * q^66 + 59 * q^67 + 139 * q^68 - 24 * q^69 + 9 * q^70 + 11 * q^71 + 92 * q^72 + 123 * q^73 + q^74 + 19 * q^75 + 92 * q^76 + 72 * q^77 - 101 * q^78 + 78 * q^79 - 34 * q^80 + 139 * q^81 + 73 * q^82 + 108 * q^83 - 31 * q^84 + 30 * q^85 - 18 * q^86 + 164 * q^87 + 39 * q^88 + 15 * q^89 - 41 * q^90 + 60 * q^91 - 26 * q^92 - 2 * q^93 + 45 * q^94 + 75 * q^95 + 42 * q^96 + 73 * q^97 + 32 * q^98 + 128 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−2.68163	−1.89620	−0.948100	−	0.317972i	$-0.896998\pi$
$2$	−2.68163	−1.89620	−0.948100	+	0.317972i	$0.896998\pi$
$3$	0.369101	0.213101	0.106550	−	0.994307i	$-0.466019\pi$
$3$	0.369101	0.213101	0.106550	+	0.994307i	$0.466019\pi$
$4$	5.19115	2.59558
$5$	2.09046	0.934882	0.467441	−	0.884024i	$-0.345176\pi$
$5$	2.09046	0.934882	0.467441	+	0.884024i	$0.345176\pi$
$6$	−0.989794	−0.404082
$7$	1.10498	0.417644	0.208822	−	0.977954i	$-0.433037\pi$
$7$	1.10498	0.417644	0.208822	+	0.977954i	$0.433037\pi$
$8$	−8.55750	−3.02553
$9$	−2.86376	−0.954588
$10$	−5.60585	−1.77272
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	1.91606	0.553119
$13$	5.13703	1.42476	0.712378	−	0.701796i	$-0.247618\pi$
$13$	5.13703	1.42476	0.712378	+	0.701796i	$0.247618\pi$
$14$	−2.96316	−0.791937
$15$	0.771592	0.199224
$16$	12.5658	3.14144
$17$	0.900733	0.218460	0.109230	−	0.994017i	$-0.465162\pi$
$17$	0.900733	0.218460	0.109230	+	0.994017i	$0.465162\pi$
$18$	7.67956	1.81009
$19$	−4.31013	−0.988811	−0.494405	−	0.869231i	$-0.664614\pi$
$19$	−4.31013	−0.988811	−0.494405	+	0.869231i	$0.664614\pi$
$20$	10.8519	2.42656
$21$	0.407850	0.0890002
$22$	−2.68163	−0.571726
$23$	−7.55625	−1.57559	−0.787793	−	0.615940i	$-0.788776\pi$
$23$	−7.55625	−1.57559	−0.787793	+	0.615940i	$0.788776\pi$
$24$	−3.15858	−0.644743
$25$	−0.629976	−0.125995
$26$	−13.7756	−2.70162
$27$	−2.16432	−0.416524
$28$	5.73613	1.08403
$29$	9.39879	1.74531	0.872655	−	0.488337i	$-0.162396\pi$
$29$	9.39879	1.74531	0.872655	+	0.488337i	$0.162396\pi$
$30$	−2.06913	−0.377769
$31$	9.16747	1.64653	0.823264	−	0.567659i	$-0.192151\pi$
$31$	9.16747	1.64653	0.823264	+	0.567659i	$0.192151\pi$
$32$	−16.5817	−2.93127
$33$	0.369101	0.0642523
$34$	−2.41543	−0.414244
$35$	2.30992	0.390448
$36$	−14.8662	−2.47771
$37$	7.58160	1.24641	0.623204	−	0.782059i	$-0.285831\pi$
$37$	7.58160	1.24641	0.623204	+	0.782059i	$0.285831\pi$
$38$	11.5582	1.87498
$39$	1.89609	0.303617
$40$	−17.8891	−2.82852
$41$	1.45893	0.227847	0.113924	−	0.993490i	$-0.463658\pi$
$41$	1.45893	0.227847	0.113924	+	0.993490i	$0.463658\pi$
$42$	−1.09370	−0.168762
$43$	−6.77290	−1.03286	−0.516429	−	0.856330i	$-0.672739\pi$
$43$	−6.77290	−1.03286	−0.516429	+	0.856330i	$0.672739\pi$
$44$	5.19115	0.782596
$45$	−5.98659	−0.892427
$46$	20.2631	2.98763
$47$	6.89531	1.00578	0.502892	−	0.864349i	$-0.332269\pi$
$47$	6.89531	1.00578	0.502892	+	0.864349i	$0.332269\pi$
$48$	4.63804	0.669443
$49$	−5.77901	−0.825574
$50$	1.68936	0.238912
$51$	0.332462	0.0465540
$52$	26.6671	3.69806
$53$	3.57071	0.490474	0.245237	−	0.969463i	$-0.421134\pi$
$53$	3.57071	0.490474	0.245237	+	0.969463i	$0.421134\pi$
$54$	5.80392	0.789813
$55$	2.09046	0.281878
$56$	−9.45588	−1.26360
$57$	−1.59087	−0.210716
$58$	−25.2041	−3.30946
$59$	−6.16161	−0.802174	−0.401087	−	0.916040i	$-0.631367\pi$
$59$	−6.16161	−0.802174	−0.401087	+	0.916040i	$0.631367\pi$
$60$	4.00545	0.517101
$61$	−4.65836	−0.596442	−0.298221	−	0.954497i	$-0.596393\pi$
$61$	−4.65836	−0.596442	−0.298221	+	0.954497i	$0.596393\pi$
$62$	−24.5838	−3.12215
$63$	−3.16441	−0.398678
$64$	19.3346	2.41683
$65$	10.7388	1.33198
$66$	−0.989794	−0.121835
$67$	2.80548	0.342744	0.171372	−	0.985206i	$-0.445180\pi$
$67$	2.80548	0.342744	0.171372	+	0.985206i	$0.445180\pi$
$68$	4.67584	0.567029
$69$	−2.78902	−0.335759
$70$	−6.19436	−0.740368
$71$	−7.41096	−0.879519	−0.439760	−	0.898115i	$-0.644936\pi$
$71$	−7.41096	−0.879519	−0.439760	+	0.898115i	$0.644936\pi$
$72$	24.5067	2.88814
$73$	1.50888	0.176601	0.0883003	−	0.996094i	$-0.471857\pi$
$73$	1.50888	0.176601	0.0883003	+	0.996094i	$0.471857\pi$
$74$	−20.3311	−2.36344
$75$	−0.232525	−0.0268497
$76$	−22.3745	−2.56653
$77$	1.10498	0.125924
$78$	−5.08461	−0.575718
$79$	16.7592	1.88555	0.942776	−	0.333426i	$-0.108205\pi$
$79$	16.7592	1.88555	0.942776	+	0.333426i	$0.108205\pi$
$80$	26.2682	2.93688
$81$	7.79244	0.865826
$82$	−3.91232	−0.432044
$83$	0.602862	0.0661727	0.0330864	−	0.999452i	$-0.489466\pi$
$83$	0.602862	0.0661727	0.0330864	+	0.999452i	$0.489466\pi$
$84$	2.11721	0.231007
$85$	1.88295	0.204234
$86$	18.1624	1.95850
$87$	3.46910	0.371927
$88$	−8.55750	−0.912232
$89$	−15.9378	−1.68940	−0.844700	−	0.535240i	$-0.820221\pi$
$89$	−15.9378	−1.68940	−0.844700	+	0.535240i	$0.820221\pi$
$90$	16.0538	1.69222
$91$	5.67633	0.595041
$92$	−39.2256	−4.08955
$93$	3.38373	0.350876
$94$	−18.4907	−1.90717
$95$	−9.01015	−0.924422
$96$	−6.12035	−0.624655
$97$	−3.49976	−0.355347	−0.177674	−	0.984089i	$-0.556857\pi$
$97$	−3.49976	−0.355347	−0.177674	+	0.984089i	$0.556857\pi$
$98$	15.4972	1.56545
$99$	−2.86376	−0.287819
$100$	−3.27030	−0.327030
$101$	−8.53653	−0.849417	−0.424708	−	0.905330i	$-0.639623\pi$
$101$	−8.53653	−0.849417	−0.424708	+	0.905330i	$0.639623\pi$
$102$	−0.891540	−0.0882756
$103$	17.6052	1.73469	0.867346	−	0.497706i	$-0.165824\pi$
$103$	17.6052	1.73469	0.867346	+	0.497706i	$0.165824\pi$
$104$	−43.9602	−4.31065
$105$	0.852595	0.0832048
$106$	−9.57532	−0.930037
$107$	9.91751	0.958762	0.479381	−	0.877607i	$-0.340861\pi$
$107$	9.91751	0.958762	0.479381	+	0.877607i	$0.340861\pi$
$108$	−11.2353	−1.08112
$109$	6.07821	0.582187	0.291093	−	0.956695i	$-0.405981\pi$
$109$	6.07821	0.582187	0.291093	+	0.956695i	$0.405981\pi$
$110$	−5.60585	−0.534496
$111$	2.79838	0.265611
$112$	13.8849	1.31200
$113$	−10.7904	−1.01508	−0.507540	−	0.861628i	$-0.669445\pi$
$113$	−10.7904	−1.01508	−0.507540	+	0.861628i	$0.669445\pi$
$114$	4.26614	0.399560
$115$	−15.7960	−1.47299
$116$	48.7905	4.53009
$117$	−14.7113	−1.36006
$118$	16.5232	1.52108
$119$	0.995294	0.0912384
$120$	−6.60289	−0.602759
$121$	1.00000	0.0909091
$122$	12.4920	1.13097
$123$	0.538494	0.0485544
$124$	47.5898	4.27369
$125$	−11.7692	−1.05267
$126$	8.48578	0.755973
$127$	13.5910	1.20600	0.603001	−	0.797740i	$-0.293972\pi$
$127$	13.5910	1.20600	0.603001	+	0.797740i	$0.293972\pi$
$128$	−18.6849	−1.65153
$129$	−2.49989	−0.220103
$130$	−28.7974	−2.52570
$131$	13.7819	1.20413	0.602066	−	0.798447i	$-0.294345\pi$
$131$	13.7819	1.20413	0.602066	+	0.798447i	$0.294345\pi$
$132$	1.91606	0.166772
$133$	−4.76261	−0.412971
$134$	−7.52328	−0.649912
$135$	−4.52443	−0.389401
$136$	−7.70802	−0.660957
$137$	−11.6384	−0.994333	−0.497166	−	0.867655i	$-0.665626\pi$
$137$	−11.6384	−0.994333	−0.497166	+	0.867655i	$0.665626\pi$
$138$	7.47913	0.636666
$139$	18.5149	1.57041	0.785206	−	0.619234i	$-0.212557\pi$
$139$	18.5149	1.57041	0.785206	+	0.619234i	$0.212557\pi$
$140$	11.9912	1.01344
$141$	2.54507	0.214333
$142$	19.8735	1.66775
$143$	5.13703	0.429580
$144$	−35.9854	−2.99878
$145$	19.6478	1.63166
$146$	−4.04625	−0.334870
$147$	−2.13304	−0.175930
$148$	39.3573	3.23515
$149$	21.8781	1.79233	0.896164	−	0.443723i	$-0.146343\pi$
$149$	21.8781	1.79233	0.896164	+	0.443723i	$0.146343\pi$
$150$	0.623546	0.0509123
$151$	3.33720	0.271577	0.135789	−	0.990738i	$-0.456643\pi$
$151$	3.33720	0.271577	0.135789	+	0.990738i	$0.456643\pi$
$152$	36.8839	2.99168
$153$	−2.57949	−0.208539
$154$	−2.96316	−0.238778
$155$	19.1642	1.53931
$156$	9.84287	0.788060
$157$	14.2289	1.13559	0.567796	−	0.823170i	$-0.307796\pi$
$157$	14.2289	1.13559	0.567796	+	0.823170i	$0.307796\pi$
$158$	−44.9419	−3.57539
$159$	1.31795	0.104520
$160$	−34.6635	−2.74039
$161$	−8.34952	−0.658034
$162$	−20.8965	−1.64178
$163$	11.7597	0.921089	0.460545	−	0.887637i	$-0.347654\pi$
$163$	11.7597	0.921089	0.460545	+	0.887637i	$0.347654\pi$
$164$	7.57355	0.591395
$165$	0.771592	0.0600683
$166$	−1.61666	−0.125477
$167$	8.43063	0.652382	0.326191	−	0.945304i	$-0.394235\pi$
$167$	8.43063	0.652382	0.326191	+	0.945304i	$0.394235\pi$
$168$	−3.49018	−0.269273
$169$	13.3891	1.02993
$170$	−5.04937	−0.387269
$171$	12.3432	0.943907
$172$	−35.1591	−2.68086
$173$	−10.7745	−0.819171	−0.409585	−	0.912272i	$-0.634327\pi$
$173$	−10.7745	−0.819171	−0.409585	+	0.912272i	$0.634327\pi$
$174$	−9.30286	−0.705248
$175$	−0.696112	−0.0526211
$176$	12.5658	0.947180
$177$	−2.27426	−0.170944
$178$	42.7392	3.20344
$179$	11.8050	0.882346	0.441173	−	0.897422i	$-0.354563\pi$
$179$	11.8050	0.882346	0.441173	+	0.897422i	$0.354563\pi$
$180$	−31.0773	−2.31636
$181$	−9.00279	−0.669172	−0.334586	−	0.942365i	$-0.608597\pi$
$181$	−9.00279	−0.669172	−0.334586	+	0.942365i	$0.608597\pi$
$182$	−15.2218	−1.12832
$183$	−1.71941	−0.127102
$184$	64.6626	4.76699
$185$	15.8490	1.16524
$186$	−9.07391	−0.665332
$187$	0.900733	0.0658681
$188$	35.7946	2.61059
$189$	−2.39154	−0.173959
$190$	24.1619	1.75289
$191$	−5.98064	−0.432744	−0.216372	−	0.976311i	$-0.569422\pi$
$191$	−5.98064	−0.432744	−0.216372	+	0.976311i	$0.569422\pi$
$192$	7.13644	0.515028
$193$	−18.5896	−1.33811	−0.669054	−	0.743214i	$-0.733300\pi$
$193$	−18.5896	−1.33811	−0.669054	+	0.743214i	$0.733300\pi$
$194$	9.38508	0.673809
$195$	3.96369	0.283846
$196$	−29.9997	−2.14284
$197$	−11.5322	−0.821632	−0.410816	−	0.911718i	$-0.634756\pi$
$197$	−11.5322	−0.821632	−0.410816	+	0.911718i	$0.634756\pi$
$198$	7.67956	0.545763
$199$	−11.4773	−0.813605	−0.406803	−	0.913516i	$-0.633356\pi$
$199$	−11.4773	−0.813605	−0.406803	+	0.913516i	$0.633356\pi$
$200$	5.39102	0.381202
$201$	1.03551	0.0730391
$202$	22.8918	1.61066
$203$	10.3855	0.728918
$204$	1.72586	0.120834
$205$	3.04984	0.213010
$206$	−47.2107	−3.28932
$207$	21.6393	1.50404
$208$	64.5507	4.47579
$209$	−4.31013	−0.298138
$210$	−2.28635	−0.157773
$211$	19.4751	1.34072	0.670361	−	0.742035i	$-0.266139\pi$
$211$	19.4751	1.34072	0.670361	+	0.742035i	$0.266139\pi$
$212$	18.5361	1.27306
$213$	−2.73540	−0.187426
$214$	−26.5951	−1.81800
$215$	−14.1585	−0.965600
$216$	18.5212	1.26021
$217$	10.1299	0.687662
$218$	−16.2995	−1.10394
$219$	0.556928	0.0376337
$220$	10.8519	0.731635
$221$	4.62710	0.311252
$222$	−7.50423	−0.503651
$223$	1.61168	0.107926	0.0539630	−	0.998543i	$-0.482815\pi$
$223$	1.61168	0.107926	0.0539630	+	0.998543i	$0.482815\pi$
$224$	−18.3225	−1.22423
$225$	1.80410	0.120273
$226$	28.9360	1.92479
$227$	14.7572	0.979472	0.489736	−	0.871871i	$-0.337093\pi$
$227$	14.7572	0.979472	0.489736	+	0.871871i	$0.337093\pi$
$228$	−8.25847	−0.546930
$229$	8.42188	0.556534	0.278267	−	0.960504i	$-0.410240\pi$
$229$	8.42188	0.556534	0.278267	+	0.960504i	$0.410240\pi$
$230$	42.3592	2.79308
$231$	0.407850	0.0268346
$232$	−80.4301	−5.28049
$233$	10.6895	0.700290	0.350145	−	0.936696i	$-0.386132\pi$
$233$	10.6895	0.700290	0.350145	+	0.936696i	$0.386132\pi$
$234$	39.4502	2.57894
$235$	14.4144	0.940290
$236$	−31.9859	−2.08210
$237$	6.18583	0.401813
$238$	−2.66901	−0.173006
$239$	9.22503	0.596718	0.298359	−	0.954454i	$-0.403561\pi$
$239$	9.22503	0.596718	0.298359	+	0.954454i	$0.403561\pi$
$240$	9.69564	0.625851
$241$	19.0321	1.22596	0.612981	−	0.790098i	$-0.289970\pi$
$241$	19.0321	1.22596	0.612981	+	0.790098i	$0.289970\pi$
$242$	−2.68163	−0.172382
$243$	9.36917	0.601033
$244$	−24.1823	−1.54811
$245$	−12.0808	−0.771814
$246$	−1.44404	−0.0920689
$247$	−22.1413	−1.40881
$248$	−78.4506	−4.98162
$249$	0.222517	0.0141015
$250$	31.5608	1.99608
$251$	5.20180	0.328335	0.164167	−	0.986433i	$-0.447506\pi$
$251$	5.20180	0.328335	0.164167	+	0.986433i	$0.447506\pi$
$252$	−16.4269	−1.03480
$253$	−7.55625	−0.475057
$254$	−36.4459	−2.28682
$255$	0.694998	0.0435225
$256$	11.4367	0.714797
$257$	20.4249	1.27407	0.637034	−	0.770836i	$-0.280161\pi$
$257$	20.4249	1.27407	0.637034	+	0.770836i	$0.280161\pi$
$258$	6.70378	0.417359
$259$	8.37754	0.520555
$260$	55.7466	3.45726
$261$	−26.9159	−1.66605
$262$	−36.9580	−2.28327
$263$	−19.3928	−1.19581	−0.597904	−	0.801568i	$-0.704000\pi$
$263$	−19.3928	−1.19581	−0.597904	+	0.801568i	$0.704000\pi$
$264$	−3.15858	−0.194397
$265$	7.46442	0.458536
$266$	12.7716	0.783075
$267$	−5.88265	−0.360012
$268$	14.5637	0.889619
$269$	−21.4647	−1.30872	−0.654362	−	0.756181i	$-0.727063\pi$
$269$	−21.4647	−1.30872	−0.654362	+	0.756181i	$0.727063\pi$
$270$	12.1329	0.738383
$271$	−8.05910	−0.489556	−0.244778	−	0.969579i	$-0.578715\pi$
$271$	−8.05910	−0.489556	−0.244778	+	0.969579i	$0.578715\pi$
$272$	11.3184	0.686278
$273$	2.09514	0.126804
$274$	31.2098	1.88545
$275$	−0.629976	−0.0379890
$276$	−14.4782	−0.871487
$277$	−31.6092	−1.89921	−0.949606	−	0.313446i	$-0.898516\pi$
$277$	−31.6092	−1.89921	−0.949606	+	0.313446i	$0.898516\pi$
$278$	−49.6501	−2.97782
$279$	−26.2535	−1.57176
$280$	−19.7671	−1.18131
$281$	−3.81756	−0.227737	−0.113868	−	0.993496i	$-0.536324\pi$
$281$	−3.81756	−0.227737	−0.113868	+	0.993496i	$0.536324\pi$
$282$	−6.82493	−0.406419
$283$	4.07480	0.242222	0.121111	−	0.992639i	$-0.461354\pi$
$283$	4.07480	0.242222	0.121111	+	0.992639i	$0.461354\pi$
$284$	−38.4714	−2.28286
$285$	−3.32566	−0.196995
$286$	−13.7756	−0.814570
$287$	1.61210	0.0951590
$288$	47.4862	2.79815
$289$	−16.1887	−0.952275
$290$	−52.6881	−3.09395
$291$	−1.29177	−0.0757247
$292$	7.83280	0.458380
$293$	16.8409	0.983855	0.491927	−	0.870636i	$-0.336293\pi$
$293$	16.8409	0.983855	0.491927	+	0.870636i	$0.336293\pi$
$294$	5.72004	0.333599
$295$	−12.8806	−0.749938
$296$	−64.8796	−3.77105
$297$	−2.16432	−0.125587
$298$	−58.6691	−3.39861
$299$	−38.8167	−2.24483
$300$	−1.20707	−0.0696903
$301$	−7.48393	−0.431367
$302$	−8.94914	−0.514965
$303$	−3.15085	−0.181011
$304$	−54.1600	−3.10629
$305$	−9.73813	−0.557603
$306$	6.91724	0.395432
$307$	14.1447	0.807278	0.403639	−	0.914918i	$-0.367745\pi$
$307$	14.1447	0.807278	0.403639	+	0.914918i	$0.367745\pi$
$308$	5.73613	0.326846
$309$	6.49810	0.369664
$310$	−51.3915	−2.91884
$311$	1.13525	0.0643742	0.0321871	−	0.999482i	$-0.489753\pi$
$311$	1.13525	0.0643742	0.0321871	+	0.999482i	$0.489753\pi$
$312$	−16.2258	−0.918602
$313$	18.1385	1.02525	0.512624	−	0.858613i	$-0.328673\pi$
$313$	18.1385	1.02525	0.512624	+	0.858613i	$0.328673\pi$
$314$	−38.1567	−2.15331
$315$	−6.61507	−0.372717
$316$	86.9993	4.89410
$317$	−10.5286	−0.591343	−0.295672	−	0.955290i	$-0.595543\pi$
$317$	−10.5286	−0.591343	−0.295672	+	0.955290i	$0.595543\pi$
$318$	−3.53426	−0.198192
$319$	9.39879	0.526231
$320$	40.4183	2.25945
$321$	3.66057	0.204313
$322$	22.3903	1.24776
$323$	−3.88227	−0.216015
$324$	40.4517	2.24732
$325$	−3.23621	−0.179512
$326$	−31.5351	−1.74657
$327$	2.24348	0.124064
$328$	−12.4848	−0.689359
$329$	7.61919	0.420060
$330$	−2.06913	−0.113902
$331$	−2.67915	−0.147259	−0.0736297	−	0.997286i	$-0.523458\pi$
$331$	−2.67915	−0.147259	−0.0736297	+	0.997286i	$0.523458\pi$
$332$	3.12955	0.171756
$333$	−21.7119	−1.18981
$334$	−22.6079	−1.23705
$335$	5.86475	0.320426
$336$	5.12495	0.279589
$337$	21.0831	1.14847	0.574236	−	0.818690i	$-0.305299\pi$
$337$	21.0831	1.14847	0.574236	+	0.818690i	$0.305299\pi$
$338$	−35.9047	−1.95296
$339$	−3.98277	−0.216314
$340$	9.77466	0.530106
$341$	9.16747	0.496447
$342$	−33.0999	−1.78984
$343$	−14.1206	−0.762440
$344$	57.9591	3.12494
$345$	−5.83034	−0.313895
$346$	28.8933	1.55331
$347$	0.987385	0.0530056	0.0265028	−	0.999649i	$-0.491563\pi$
$347$	0.987385	0.0530056	0.0265028	+	0.999649i	$0.491563\pi$
$348$	18.0087	0.965365
$349$	−29.8440	−1.59751	−0.798756	−	0.601654i	$-0.794508\pi$
$349$	−29.8440	−1.59751	−0.798756	+	0.601654i	$0.794508\pi$
$350$	1.86672	0.0997802
$351$	−11.1182	−0.593446
$352$	−16.5817	−0.883810
$353$	−18.7377	−0.997306	−0.498653	−	0.866802i	$-0.666172\pi$
$353$	−18.7377	−0.997306	−0.498653	+	0.866802i	$0.666172\pi$
$354$	6.09873	0.324144
$355$	−15.4923	−0.822247
$356$	−82.7354	−4.38497
$357$	0.367364	0.0194430
$358$	−31.6566	−1.67310
$359$	−20.5093	−1.08244	−0.541219	−	0.840882i	$-0.682037\pi$
$359$	−20.5093	−1.08244	−0.541219	+	0.840882i	$0.682037\pi$
$360$	51.2302	2.70007
$361$	−0.422814	−0.0222534
$362$	24.1422	1.26888
$363$	0.369101	0.0193728
$364$	29.4667	1.54447
$365$	3.15424	0.165101
$366$	4.61082	0.241012
$367$	8.50109	0.443753	0.221877	−	0.975075i	$-0.428782\pi$
$367$	8.50109	0.443753	0.221877	+	0.975075i	$0.428782\pi$
$368$	−94.9500	−4.94961
$369$	−4.17804	−0.217500
$370$	−42.5013	−2.20954
$371$	3.94557	0.204844
$372$	17.5654	0.910726
$373$	17.3585	0.898788	0.449394	−	0.893334i	$-0.351640\pi$
$373$	17.3585	0.898788	0.449394	+	0.893334i	$0.351640\pi$
$374$	−2.41543	−0.124899
$375$	−4.34404	−0.224325
$376$	−59.0066	−3.04303
$377$	48.2819	2.48664
$378$	6.41323	0.329861
$379$	−21.1996	−1.08895	−0.544475	−	0.838777i	$-0.683271\pi$
$379$	−21.1996	−1.08895	−0.544475	+	0.838777i	$0.683271\pi$
$380$	−46.7730	−2.39941
$381$	5.01644	0.257000
$382$	16.0379	0.820570
$383$	25.7317	1.31483	0.657413	−	0.753530i	$-0.271651\pi$
$383$	25.7317	1.31483	0.657413	+	0.753530i	$0.271651\pi$
$384$	−6.89662	−0.351942
$385$	2.30992	0.117724
$386$	49.8504	2.53732
$387$	19.3960	0.985953
$388$	−18.1678	−0.922331
$389$	−28.8769	−1.46412	−0.732060	−	0.681241i	$-0.761441\pi$
$389$	−28.8769	−1.46412	−0.732060	+	0.681241i	$0.761441\pi$
$390$	−10.6292	−0.538229
$391$	−6.80616	−0.344202
$392$	49.4539	2.49780
$393$	5.08692	0.256601
$394$	30.9250	1.55798
$395$	35.0344	1.76277
$396$	−14.8662	−0.747056
$397$	31.7060	1.59128	0.795639	−	0.605771i	$-0.207135\pi$
$397$	31.7060	1.59128	0.795639	+	0.605771i	$0.207135\pi$
$398$	30.7779	1.54276
$399$	−1.75789	−0.0880044
$400$	−7.91612	−0.395806
$401$	12.5436	0.626397	0.313199	−	0.949688i	$-0.398599\pi$
$401$	12.5436	0.626397	0.313199	+	0.949688i	$0.398599\pi$
$402$	−2.77685	−0.138497
$403$	47.0936	2.34590
$404$	−44.3145	−2.20473
$405$	16.2898	0.809446
$406$	−27.8501	−1.38218
$407$	7.58160	0.375806
$408$	−2.84504	−0.140851
$409$	6.32297	0.312651	0.156325	−	0.987706i	$-0.450035\pi$
$409$	6.32297	0.312651	0.156325	+	0.987706i	$0.450035\pi$
$410$	−8.17856	−0.403910
$411$	−4.29574	−0.211893
$412$	91.3913	4.50253
$413$	−6.80847	−0.335023
$414$	−58.0287	−2.85195
$415$	1.26026	0.0618637
$416$	−85.1810	−4.17634
$417$	6.83387	0.334656
$418$	11.5582	0.565329
$419$	26.8522	1.31182	0.655909	−	0.754840i	$-0.272286\pi$
$419$	26.8522	1.31182	0.655909	+	0.754840i	$0.272286\pi$
$420$	4.42595	0.215964
$421$	−14.7315	−0.717970	−0.358985	−	0.933343i	$-0.616877\pi$
$421$	−14.7315	−0.717970	−0.358985	+	0.933343i	$0.616877\pi$
$422$	−52.2251	−2.54228
$423$	−19.7465	−0.960109
$424$	−30.5563	−1.48395
$425$	−0.567440	−0.0275249
$426$	7.33533	0.355398
$427$	−5.14741	−0.249101
$428$	51.4833	2.48854
$429$	1.89609	0.0915439
$430$	37.9678	1.83097
$431$	−10.3926	−0.500594	−0.250297	−	0.968169i	$-0.580528\pi$
$431$	−10.3926	−0.500594	−0.250297	+	0.968169i	$0.580528\pi$
$432$	−27.1964	−1.30849
$433$	4.14511	0.199201	0.0996006	−	0.995028i	$-0.468244\pi$
$433$	4.14511	0.199201	0.0996006	+	0.995028i	$0.468244\pi$
$434$	−27.1647	−1.30395
$435$	7.25203	0.347708
$436$	31.5529	1.51111
$437$	32.5684	1.55796
$438$	−1.49348	−0.0713611
$439$	−5.03101	−0.240117	−0.120058	−	0.992767i	$-0.538308\pi$
$439$	−5.03101	−0.240117	−0.120058	+	0.992767i	$0.538308\pi$
$440$	−17.8891	−0.852830
$441$	16.5497	0.788083
$442$	−12.4082	−0.590197
$443$	−11.3097	−0.537342	−0.268671	−	0.963232i	$-0.586584\pi$
$443$	−11.3097	−0.537342	−0.268671	+	0.963232i	$0.586584\pi$
$444$	14.5268	0.689412
$445$	−33.3173	−1.57939
$446$	−4.32193	−0.204649
$447$	8.07525	0.381946
$448$	21.3644	1.00937
$449$	−19.1750	−0.904924	−0.452462	−	0.891784i	$-0.649454\pi$
$449$	−19.1750	−0.904924	−0.452462	+	0.891784i	$0.649454\pi$
$450$	−4.83794	−0.228063
$451$	1.45893	0.0686985
$452$	−56.0148	−2.63472
$453$	1.23176	0.0578733
$454$	−39.5735	−1.85727
$455$	11.8661	0.556293
$456$	13.6139	0.637529
$457$	−17.7688	−0.831191	−0.415595	−	0.909550i	$-0.636427\pi$
$457$	−17.7688	−0.831191	−0.415595	+	0.909550i	$0.636427\pi$
$458$	−22.5844	−1.05530
$459$	−1.94948	−0.0909938
$460$	−81.9996	−3.82325
$461$	−0.130361	−0.00607151	−0.00303576	−	0.999995i	$-0.500966\pi$
$461$	−0.130361	−0.00607151	−0.00303576	+	0.999995i	$0.500966\pi$
$462$	−1.09370	−0.0508838
$463$	−12.9881	−0.603606	−0.301803	−	0.953370i	$-0.597589\pi$
$463$	−12.9881	−0.603606	−0.301803	+	0.953370i	$0.597589\pi$
$464$	118.103	5.48279
$465$	7.07355	0.328028
$466$	−28.6652	−1.32789
$467$	6.57652	0.304325	0.152163	−	0.988355i	$-0.451376\pi$
$467$	6.57652	0.304325	0.152163	+	0.988355i	$0.451376\pi$
$468$	−76.3684	−3.53013
$469$	3.10001	0.143145
$470$	−38.6540	−1.78298
$471$	5.25191	0.241995
$472$	52.7280	2.42700
$473$	−6.77290	−0.311418
$474$	−16.5881	−0.761917
$475$	2.71527	0.124585
$476$	5.16672	0.236816
$477$	−10.2257	−0.468201
$478$	−24.7381	−1.13150
$479$	4.49803	0.205520	0.102760	−	0.994706i	$-0.467233\pi$
$479$	4.49803	0.205520	0.102760	+	0.994706i	$0.467233\pi$
$480$	−12.7943	−0.583979
$481$	38.9470	1.77583
$482$	−51.0370	−2.32467
$483$	−3.08182	−0.140228
$484$	5.19115	0.235961
$485$	−7.31612	−0.332208
$486$	−25.1247	−1.13968
$487$	26.9665	1.22197	0.610984	−	0.791643i	$-0.290774\pi$
$487$	26.9665	1.22197	0.610984	+	0.791643i	$0.290774\pi$
$488$	39.8639	1.80456
$489$	4.34051	0.196285
$490$	32.3963	1.46351
$491$	8.55313	0.385997	0.192999	−	0.981199i	$-0.438179\pi$
$491$	8.55313	0.385997	0.192999	+	0.981199i	$0.438179\pi$
$492$	2.79541	0.126027
$493$	8.46580	0.381280
$494$	59.3747	2.67140
$495$	−5.98659	−0.269077
$496$	115.196	5.17247
$497$	−8.18898	−0.367326
$498$	−0.596710	−0.0267392
$499$	−9.24678	−0.413943	−0.206971	−	0.978347i	$-0.566361\pi$
$499$	−9.24678	−0.413943	−0.206971	+	0.978347i	$0.566361\pi$
$500$	−61.0959	−2.73229
$501$	3.11176	0.139023
$502$	−13.9493	−0.622588
$503$	24.2164	1.07976	0.539879	−	0.841743i	$-0.318470\pi$
$503$	24.2164	1.07976	0.539879	+	0.841743i	$0.318470\pi$
$504$	27.0794	1.20621
$505$	−17.8453	−0.794105
$506$	20.2631	0.900803
$507$	4.94194	0.219479
$508$	70.5527	3.13027
$509$	−10.6997	−0.474255	−0.237127	−	0.971479i	$-0.576206\pi$
$509$	−10.6997	−0.474255	−0.237127	+	0.971479i	$0.576206\pi$
$510$	−1.86373	−0.0825273
$511$	1.66728	0.0737561
$512$	6.70064	0.296129
$513$	9.32851	0.411864
$514$	−54.7719	−2.41589
$515$	36.8030	1.62173
$516$	−12.9773	−0.571293
$517$	6.89531	0.303255
$518$	−22.4655	−0.987076
$519$	−3.97689	−0.174566
$520$	−91.8970	−4.02995
$521$	36.7123	1.60840	0.804199	−	0.594361i	$-0.202595\pi$
$521$	36.7123	1.60840	0.804199	+	0.594361i	$0.202595\pi$
$522$	72.1786	3.15917
$523$	13.4636	0.588723	0.294361	−	0.955694i	$-0.404893\pi$
$523$	13.4636	0.588723	0.294361	+	0.955694i	$0.404893\pi$
$524$	71.5440	3.12541
$525$	−0.256936	−0.0112136
$526$	52.0042	2.26749
$527$	8.25745	0.359700
$528$	4.63804	0.201845
$529$	34.0968	1.48247
$530$	−20.0168	−0.869475
$531$	17.6454	0.765745
$532$	−24.7234	−1.07190
$533$	7.49459	0.324627
$534$	15.7751	0.682656
$535$	20.7322	0.896329
$536$	−24.0079	−1.03698
$537$	4.35723	0.188029
$538$	57.5604	2.48160
$539$	−5.77901	−0.248920
$540$	−23.4870	−1.01072
$541$	24.5191	1.05416	0.527080	−	0.849816i	$-0.323287\pi$
$541$	24.5191	1.05416	0.527080	+	0.849816i	$0.323287\pi$
$542$	21.6116	0.928296
$543$	−3.32294	−0.142601
$544$	−14.9357	−0.640364
$545$	12.7063	0.544276
$546$	−5.61840	−0.240445
$547$	−1.00000	−0.0427569
$547$	−1.00000	−0.0427569
$548$	−60.4165	−2.58087
$549$	13.3405	0.569357
$550$	1.68936	0.0720347
$551$	−40.5099	−1.72578
$552$	23.8670	1.01585
$553$	18.5186	0.787490
$554$	84.7642	3.60129
$555$	5.84990	0.248315
$556$	96.1136	4.07613
$557$	7.35244	0.311533	0.155766	−	0.987794i	$-0.450215\pi$
$557$	7.35244	0.311533	0.155766	+	0.987794i	$0.450215\pi$
$558$	70.4022	2.98036
$559$	−34.7926	−1.47157
$560$	29.0259	1.22657
$561$	0.332462	0.0140365
$562$	10.2373	0.431834
$563$	2.49239	0.105042	0.0525209	−	0.998620i	$-0.483274\pi$
$563$	2.49239	0.105042	0.0525209	+	0.998620i	$0.483274\pi$
$564$	13.2118	0.556318
$565$	−22.5570	−0.948979
$566$	−10.9271	−0.459301
$567$	8.61050	0.361607
$568$	63.4193	2.66101
$569$	25.2420	1.05820	0.529100	−	0.848560i	$-0.322530\pi$
$569$	25.2420	1.05820	0.529100	+	0.848560i	$0.322530\pi$
$570$	8.91819	0.373542
$571$	−39.0894	−1.63584	−0.817920	−	0.575332i	$-0.804873\pi$
$571$	−39.0894	−1.63584	−0.817920	+	0.575332i	$0.804873\pi$
$572$	26.6671	1.11501
$573$	−2.20746	−0.0922181
$574$	−4.32305	−0.180441
$575$	4.76025	0.198516
$576$	−55.3698	−2.30708
$577$	17.4830	0.727828	0.363914	−	0.931433i	$-0.381440\pi$
$577$	17.4830	0.727828	0.363914	+	0.931433i	$0.381440\pi$
$578$	43.4121	1.80570
$579$	−6.86144	−0.285152
$580$	101.995	4.23510
$581$	0.666152	0.0276366
$582$	3.46405	0.143589
$583$	3.57071	0.147884
$584$	−12.9122	−0.534311
$585$	−30.7533	−1.27149
$586$	−45.1611	−1.86559
$587$	−41.9099	−1.72981	−0.864903	−	0.501939i	$-0.832620\pi$
$587$	−41.9099	−1.72981	−0.864903	+	0.501939i	$0.832620\pi$
$588$	−11.0729	−0.456641
$589$	−39.5130	−1.62810
$590$	34.5411	1.42203
$591$	−4.25654	−0.175090
$592$	95.2686	3.91552
$593$	11.9898	0.492361	0.246180	−	0.969224i	$-0.420824\pi$
$593$	11.9898	0.492361	0.246180	+	0.969224i	$0.420824\pi$
$594$	5.80392	0.238138
$595$	2.08062	0.0852972
$596$	113.573	4.65212
$597$	−4.23629	−0.173380
$598$	104.092	4.25664
$599$	29.3876	1.20074	0.600372	−	0.799721i	$-0.295019\pi$
$599$	29.3876	1.20074	0.600372	+	0.799721i	$0.295019\pi$
$600$	1.98983	0.0812345
$601$	−14.1249	−0.576168	−0.288084	−	0.957605i	$-0.593018\pi$
$601$	−14.1249	−0.576168	−0.288084	+	0.957605i	$0.593018\pi$
$602$	20.0692	0.817958
$603$	−8.03424	−0.327180
$604$	17.3239	0.704899
$605$	2.09046	0.0849893
$606$	8.44941	0.343234
$607$	25.5010	1.03505	0.517527	−	0.855667i	$-0.326853\pi$
$607$	25.5010	1.03505	0.517527	+	0.855667i	$0.326853\pi$
$608$	71.4694	2.89847
$609$	3.83330	0.155333
$610$	26.1141	1.05733
$611$	35.4214	1.43300
$612$	−13.3905	−0.541279
$613$	28.2303	1.14021	0.570106	−	0.821571i	$-0.306902\pi$
$613$	28.2303	1.14021	0.570106	+	0.821571i	$0.306902\pi$
$614$	−37.9308	−1.53076
$615$	1.12570	0.0453927
$616$	−9.45588	−0.380988
$617$	−40.9148	−1.64717	−0.823584	−	0.567195i	$-0.808029\pi$
$617$	−40.9148	−1.64717	−0.823584	+	0.567195i	$0.808029\pi$
$618$	−17.4255	−0.700957
$619$	4.32499	0.173836	0.0869180	−	0.996215i	$-0.472298\pi$
$619$	4.32499	0.173836	0.0869180	+	0.996215i	$0.472298\pi$
$620$	99.4845	3.99539
$621$	16.3542	0.656270
$622$	−3.04432	−0.122066
$623$	−17.6109	−0.705568
$624$	23.8258	0.953794
$625$	−21.4533	−0.858130
$626$	−48.6408	−1.94408
$627$	−1.59087	−0.0635334
$628$	73.8645	2.94751
$629$	6.82900	0.272290
$630$	17.7392	0.706746
$631$	2.74164	0.109143	0.0545714	−	0.998510i	$-0.482621\pi$
$631$	2.74164	0.109143	0.0545714	+	0.998510i	$0.482621\pi$
$632$	−143.416	−5.70480
$633$	7.18829	0.285709
$634$	28.2337	1.12131
$635$	28.4113	1.12747
$636$	6.84169	0.271291
$637$	−29.6870	−1.17624
$638$	−25.2041	−0.997839
$639$	21.2233	0.839579
$640$	−39.0600	−1.54398
$641$	−50.2916	−1.98640	−0.993199	−	0.116431i	$-0.962855\pi$
$641$	−50.2916	−1.98640	−0.993199	+	0.116431i	$0.962855\pi$
$642$	−9.81629	−0.387418
$643$	−30.3942	−1.19863	−0.599315	−	0.800513i	$-0.704560\pi$
$643$	−30.3942	−1.19863	−0.599315	+	0.800513i	$0.704560\pi$
$644$	−43.3436	−1.70798
$645$	−5.22591	−0.205770
$646$	10.4108	0.409609
$647$	−26.1359	−1.02751	−0.513755	−	0.857937i	$-0.671746\pi$
$647$	−26.1359	−1.02751	−0.513755	+	0.857937i	$0.671746\pi$
$648$	−66.6838	−2.61959
$649$	−6.16161	−0.241864
$650$	8.67832	0.340392
$651$	3.73896	0.146541
$652$	61.0463	2.39076
$653$	44.9209	1.75789	0.878944	−	0.476924i	$-0.158248\pi$
$653$	44.9209	1.75789	0.878944	+	0.476924i	$0.158248\pi$
$654$	−6.01618	−0.235251
$655$	28.8105	1.12572
$656$	18.3326	0.715768
$657$	−4.32106	−0.168581
$658$	−20.4319	−0.796517
$659$	37.0425	1.44297	0.721486	−	0.692429i	$-0.243459\pi$
$659$	37.0425	1.44297	0.721486	+	0.692429i	$0.243459\pi$
$660$	4.00545	0.155912
$661$	−20.6834	−0.804491	−0.402246	−	0.915532i	$-0.631770\pi$
$661$	−20.6834	−0.804491	−0.402246	+	0.915532i	$0.631770\pi$
$662$	7.18450	0.279234
$663$	1.70787	0.0663281
$664$	−5.15899	−0.200208
$665$	−9.95605	−0.386079
$666$	58.2234	2.25611
$667$	−71.0195	−2.74989
$668$	43.7647	1.69331
$669$	0.594873	0.0229991
$670$	−15.7271	−0.607591
$671$	−4.65836	−0.179834
$672$	−6.76287	−0.260883
$673$	14.9959	0.578050	0.289025	−	0.957322i	$-0.406669\pi$
$673$	14.9959	0.578050	0.289025	+	0.957322i	$0.406669\pi$
$674$	−56.5373	−2.17773
$675$	1.36347	0.0524800
$676$	69.5049	2.67327
$677$	−7.02351	−0.269935	−0.134968	−	0.990850i	$-0.543093\pi$
$677$	−7.02351	−0.269935	−0.134968	+	0.990850i	$0.543093\pi$
$678$	10.6803	0.410175
$679$	−3.86718	−0.148409
$680$	−16.1133	−0.617917
$681$	5.44691	0.208726
$682$	−24.5838	−0.941362
$683$	−20.9739	−0.802544	−0.401272	−	0.915959i	$-0.631432\pi$
$683$	−20.9739	−0.802544	−0.401272	+	0.915959i	$0.631432\pi$
$684$	64.0754	2.44998
$685$	−24.3295	−0.929584
$686$	37.8662	1.44574
$687$	3.10853	0.118598
$688$	−85.1066	−3.24466
$689$	18.3428	0.698806
$690$	15.6348	0.595207
$691$	46.1524	1.75572	0.877860	−	0.478917i	$-0.158971\pi$
$691$	46.1524	1.75572	0.877860	+	0.478917i	$0.158971\pi$
$692$	−55.9321	−2.12622
$693$	−3.16441	−0.120206
$694$	−2.64780	−0.100509
$695$	38.7047	1.46815
$696$	−29.6869	−1.12528
$697$	1.31411	0.0497755
$698$	80.0306	3.02920
$699$	3.94549	0.149232
$700$	−3.61362	−0.136582
$701$	19.0573	0.719786	0.359893	−	0.932994i	$-0.382813\pi$
$701$	19.0573	0.719786	0.359893	+	0.932994i	$0.382813\pi$
$702$	29.8149	1.12529
$703$	−32.6777	−1.23246
$704$	19.3346	0.728702
$705$	5.32036	0.200376
$706$	50.2476	1.89109
$707$	−9.43272	−0.354754
$708$	−11.8060	−0.443698
$709$	47.5994	1.78763	0.893816	−	0.448434i	$-0.148018\pi$
$709$	47.5994	1.78763	0.893816	+	0.448434i	$0.148018\pi$
$710$	41.5447	1.55915
$711$	−47.9943	−1.79993
$712$	136.387	5.11133
$713$	−69.2717	−2.59425
$714$	−0.985136	−0.0368678
$715$	10.7388	0.401607
$716$	61.2815	2.29020
$717$	3.40497	0.127161
$718$	54.9983	2.05252
$719$	−32.7974	−1.22314	−0.611568	−	0.791192i	$-0.709461\pi$
$719$	−32.7974	−1.22314	−0.611568	+	0.791192i	$0.709461\pi$
$720$	−75.2260	−2.80351
$721$	19.4534	0.724484
$722$	1.13383	0.0421969
$723$	7.02476	0.261254
$724$	−46.7349	−1.73689
$725$	−5.92101	−0.219901
$726$	−0.989794	−0.0367347
$727$	50.8561	1.88615	0.943075	−	0.332580i	$-0.107919\pi$
$727$	50.8561	1.88615	0.943075	+	0.332580i	$0.107919\pi$
$728$	−48.5752	−1.80032
$729$	−19.9191	−0.737746
$730$	−8.45852	−0.313064
$731$	−6.10057	−0.225638
$732$	−8.92571	−0.329904
$733$	7.61571	0.281293	0.140646	−	0.990060i	$-0.455082\pi$
$733$	7.61571	0.281293	0.140646	+	0.990060i	$0.455082\pi$
$734$	−22.7968	−0.841445
$735$	−4.45904	−0.164474
$736$	125.296	4.61846
$737$	2.80548	0.103341
$738$	11.2040	0.412424
$739$	6.15474	0.226406	0.113203	−	0.993572i	$-0.463889\pi$
$739$	6.15474	0.226406	0.113203	+	0.993572i	$0.463889\pi$
$740$	82.2748	3.02448
$741$	−8.17237	−0.300220
$742$	−10.5806	−0.388424
$743$	−4.61486	−0.169303	−0.0846515	−	0.996411i	$-0.526978\pi$
$743$	−4.61486	−0.169303	−0.0846515	+	0.996411i	$0.526978\pi$
$744$	−28.9562	−1.06159
$745$	45.7354	1.67562
$746$	−46.5491	−1.70428
$747$	−1.72646	−0.0631677
$748$	4.67584	0.170966
$749$	10.9587	0.400421
$750$	11.6491	0.425366
$751$	−37.8461	−1.38102	−0.690512	−	0.723321i	$-0.742615\pi$
$751$	−37.8461	−1.38102	−0.690512	+	0.723321i	$0.742615\pi$
$752$	86.6448	3.15961
$753$	1.91999	0.0699683
$754$	−129.474	−4.71517
$755$	6.97628	0.253893
$756$	−12.4148	−0.451523
$757$	41.4984	1.50829	0.754143	−	0.656710i	$-0.228052\pi$
$757$	41.4984	1.50829	0.754143	+	0.656710i	$0.228052\pi$
$758$	56.8495	2.06487
$759$	−2.78902	−0.101235
$760$	77.1043	2.79687
$761$	−43.1121	−1.56281	−0.781406	−	0.624023i	$-0.785497\pi$
$761$	−43.1121	−1.56281	−0.781406	+	0.624023i	$0.785497\pi$
$762$	−13.4522	−0.487323
$763$	6.71631	0.243147
$764$	−31.0464	−1.12322
$765$	−5.39232	−0.194960
$766$	−69.0028	−2.49317
$767$	−31.6524	−1.14290
$768$	4.22132	0.152324
$769$	−23.4425	−0.845357	−0.422679	−	0.906280i	$-0.638910\pi$
$769$	−23.4425	−0.845357	−0.422679	+	0.906280i	$0.638910\pi$
$770$	−6.19436	−0.223229
$771$	7.53884	0.271505
$772$	−96.5013	−3.47316
$773$	43.5212	1.56535	0.782675	−	0.622431i	$-0.213855\pi$
$773$	43.5212	1.56535	0.782675	+	0.622431i	$0.213855\pi$
$774$	−52.0129	−1.86957
$775$	−5.77529	−0.207454
$776$	29.9492	1.07511
$777$	3.09216	0.110931
$778$	77.4373	2.77626
$779$	−6.28819	−0.225298
$780$	20.5761	0.736744
$781$	−7.41096	−0.265185
$782$	18.2516	0.652677
$783$	−20.3420	−0.726964
$784$	−72.6177	−2.59349
$785$	29.7450	1.06164
$786$	−13.6413	−0.486568
$787$	−16.3497	−0.582806	−0.291403	−	0.956600i	$-0.594122\pi$
$787$	−16.3497	−0.582806	−0.291403	+	0.956600i	$0.594122\pi$
$788$	−59.8652	−2.13261
$789$	−7.15789	−0.254828
$790$	−93.9493	−3.34256
$791$	−11.9232	−0.423942
$792$	24.5067	0.870806
$793$	−23.9302	−0.849785
$794$	−85.0238	−3.01738
$795$	2.75513	0.0977143
$796$	−59.5805	−2.11177
$797$	3.24415	0.114914	0.0574569	−	0.998348i	$-0.481701\pi$
$797$	3.24415	0.114914	0.0574569	+	0.998348i	$0.481701\pi$
$798$	4.71401	0.166874
$799$	6.21083	0.219723
$800$	10.4461	0.369325
$801$	45.6420	1.61268
$802$	−33.6373	−1.18777
$803$	1.50888	0.0532471
$804$	5.37548	0.189579
$805$	−17.4543	−0.615184
$806$	−126.288	−4.44830
$807$	−7.92264	−0.278890
$808$	73.0514	2.56994
$809$	3.17473	0.111618	0.0558088	−	0.998441i	$-0.482226\pi$
$809$	3.17473	0.111618	0.0558088	+	0.998441i	$0.482226\pi$
$810$	−43.6832	−1.53487
$811$	−1.36331	−0.0478723	−0.0239361	−	0.999713i	$-0.507620\pi$
$811$	−1.36331	−0.0478723	−0.0239361	+	0.999713i	$0.507620\pi$
$812$	53.9127	1.89196
$813$	−2.97463	−0.104325
$814$	−20.3311	−0.712604
$815$	24.5831	0.861110
$816$	4.17763	0.146246
$817$	29.1920	1.02130
$818$	−16.9559	−0.592849
$819$	−16.2557	−0.568019
$820$	15.8322	0.552884
$821$	−39.8259	−1.38993	−0.694967	−	0.719041i	$-0.744581\pi$
$821$	−39.8259	−1.38993	−0.694967	+	0.719041i	$0.744581\pi$
$822$	11.5196	0.401792
$823$	−5.43391	−0.189414	−0.0947071	−	0.995505i	$-0.530191\pi$
$823$	−5.43391	−0.189414	−0.0947071	+	0.995505i	$0.530191\pi$
$824$	−150.656	−5.24837
$825$	−0.232525	−0.00809548
$826$	18.2578	0.635271
$827$	33.1057	1.15120	0.575599	−	0.817732i	$-0.304769\pi$
$827$	33.1057	1.15120	0.575599	+	0.817732i	$0.304769\pi$
$828$	112.333	3.90384
$829$	−32.7888	−1.13880	−0.569401	−	0.822060i	$-0.692825\pi$
$829$	−32.7888	−1.13880	−0.569401	+	0.822060i	$0.692825\pi$
$830$	−3.37955	−0.117306
$831$	−11.6670	−0.404724
$832$	99.3227	3.44339
$833$	−5.20535	−0.180355
$834$	−18.3259	−0.634575
$835$	17.6239	0.609900
$836$	−22.3745	−0.773839
$837$	−19.8414	−0.685818
$838$	−72.0078	−2.48747
$839$	16.4921	0.569371	0.284686	−	0.958621i	$-0.408111\pi$
$839$	16.4921	0.569371	0.284686	+	0.958621i	$0.408111\pi$
$840$	−7.29608	−0.251739
$841$	59.3372	2.04611
$842$	39.5045	1.36141
$843$	−1.40907	−0.0485308
$844$	101.098	3.47995
$845$	27.9894	0.962865
$846$	52.9529	1.82056
$847$	1.10498	0.0379676
$848$	44.8686	1.54079
$849$	1.50401	0.0516176
$850$	1.52167	0.0521927
$851$	−57.2885	−1.96382
$852$	−14.1999	−0.486479
$853$	−34.4720	−1.18030	−0.590149	−	0.807295i	$-0.700931\pi$
$853$	−34.4720	−1.18030	−0.590149	+	0.807295i	$0.700931\pi$
$854$	13.8035	0.472345
$855$	25.8029	0.882442
$856$	−84.8690	−2.90076
$857$	−36.0448	−1.23127	−0.615633	−	0.788033i	$-0.711100\pi$
$857$	−36.0448	−1.23127	−0.615633	+	0.788033i	$0.711100\pi$
$858$	−5.08461	−0.173586
$859$	56.1059	1.91431	0.957155	−	0.289576i	$-0.0935143\pi$
$859$	56.1059	1.91431	0.957155	+	0.289576i	$0.0935143\pi$
$860$	−73.4988	−2.50629
$861$	0.595027	0.0202785
$862$	27.8691	0.949226
$863$	18.9776	0.646004	0.323002	−	0.946398i	$-0.395308\pi$
$863$	18.9776	0.646004	0.323002	+	0.946398i	$0.395308\pi$
$864$	35.8883	1.22094
$865$	−22.5237	−0.765828
$866$	−11.1157	−0.377725
$867$	−5.97526	−0.202931
$868$	52.5858	1.78488
$869$	16.7592	0.568515
$870$	−19.4473	−0.659324
$871$	14.4119	0.488327
$872$	−52.0143	−1.76143
$873$	10.0225	0.339210
$874$	−87.3364	−2.95420
$875$	−13.0048	−0.439642
$876$	2.89110	0.0976812
$877$	30.7091	1.03697	0.518487	−	0.855086i	$-0.326496\pi$
$877$	30.7091	1.03697	0.518487	+	0.855086i	$0.326496\pi$
$878$	13.4913	0.455310
$879$	6.21599	0.209660
$880$	26.2682	0.885501
$881$	−34.0696	−1.14783	−0.573917	−	0.818913i	$-0.694577\pi$
$881$	−34.0696	−1.14783	−0.573917	+	0.818913i	$0.694577\pi$
$882$	−44.3803	−1.49436
$883$	2.23740	0.0752944	0.0376472	−	0.999291i	$-0.488014\pi$
$883$	2.23740	0.0752944	0.0376472	+	0.999291i	$0.488014\pi$
$884$	24.0200	0.807879
$885$	−4.75425	−0.159812
$886$	30.3286	1.01891
$887$	33.5121	1.12523	0.562613	−	0.826720i	$-0.309796\pi$
$887$	33.5121	1.12523	0.562613	+	0.826720i	$0.309796\pi$
$888$	−23.9471	−0.803613
$889$	15.0178	0.503679
$890$	89.3447	2.99484
$891$	7.79244	0.261056
$892$	8.36648	0.280130
$893$	−29.7196	−0.994530
$894$	−21.6549	−0.724247
$895$	24.6778	0.824889
$896$	−20.6465	−0.689750
$897$	−14.3273	−0.478374
$898$	51.4203	1.71592
$899$	86.1631	2.87370
$900$	9.36537	0.312179
$901$	3.21625	0.107149
$902$	−3.91232	−0.130266
$903$	−2.76233	−0.0919246
$904$	92.3392	3.07115
$905$	−18.8200	−0.625597
$906$	−3.30314	−0.109739
$907$	0.0252276	0.000837670 0	0.000418835	−	1.00000i	$-0.499867\pi$
$907$	0.0252276	0.000837670 0	0.000418835		1.00000i	$0.499867\pi$
$908$	76.6070	2.54229
$909$	24.4466	0.810843
$910$	−31.8206	−1.05484
$911$	6.83916	0.226591	0.113296	−	0.993561i	$-0.463859\pi$
$911$	6.83916	0.226591	0.113296	+	0.993561i	$0.463859\pi$
$912$	−19.9905	−0.661953
$913$	0.602862	0.0199518
$914$	47.6495	1.57610
$915$	−3.59436	−0.118826
$916$	43.7193	1.44453
$917$	15.2288	0.502898
$918$	5.22778	0.172543
$919$	−28.7248	−0.947544	−0.473772	−	0.880647i	$-0.657108\pi$
$919$	−28.7248	−0.947544	−0.473772	+	0.880647i	$0.657108\pi$
$920$	135.175	4.45657
$921$	5.22081	0.172032
$922$	0.349580	0.0115128
$923$	−38.0704	−1.25310
$924$	2.11721	0.0696512
$925$	−4.77623	−0.157041
$926$	34.8292	1.14456
$927$	−50.4171	−1.65592
$928$	−155.848	−5.11597
$929$	−24.6109	−0.807458	−0.403729	−	0.914879i	$-0.632286\pi$
$929$	−24.6109	−0.807458	−0.403729	+	0.914879i	$0.632286\pi$
$930$	−18.9687	−0.622007
$931$	24.9083	0.816336
$932$	55.4906	1.81765
$933$	0.419023	0.0137182
$934$	−17.6358	−0.577062
$935$	1.88295	0.0615789
$936$	125.892	4.11489
$937$	−32.6535	−1.06674	−0.533371	−	0.845881i	$-0.679075\pi$
$937$	−32.6535	−1.06674	−0.533371	+	0.845881i	$0.679075\pi$
$938$	−8.31308	−0.271432
$939$	6.69495	0.218481
$940$	74.8272	2.44059
$941$	−8.42158	−0.274536	−0.137268	−	0.990534i	$-0.543832\pi$
$941$	−8.42158	−0.274536	−0.137268	+	0.990534i	$0.543832\pi$
$942$	−14.0837	−0.458872
$943$	−11.0241	−0.358993
$944$	−77.4253	−2.51998
$945$	−4.99942	−0.162631
$946$	18.1624	0.590511
$947$	24.0927	0.782908	0.391454	−	0.920198i	$-0.371972\pi$
$947$	24.0927	0.782908	0.391454	+	0.920198i	$0.371972\pi$
$948$	32.1116	1.04294
$949$	7.75114	0.251613
$950$	−7.28137	−0.236239
$951$	−3.88611	−0.126016
$952$	−8.51722	−0.276045
$953$	−31.6140	−1.02408	−0.512038	−	0.858963i	$-0.671109\pi$
$953$	−31.6140	−1.02408	−0.512038	+	0.858963i	$0.671109\pi$
$954$	27.4215	0.887802
$955$	−12.5023	−0.404565
$956$	47.8885	1.54883
$957$	3.46910	0.112140
$958$	−12.0621	−0.389708
$959$	−12.8602	−0.415277
$960$	14.9184	0.481491
$961$	53.0426	1.71105
$962$	−104.441	−3.36733
$963$	−28.4014	−0.915222
$964$	98.7983	3.18208
$965$	−38.8608	−1.25097
$966$	8.26430	0.265900
$967$	20.4609	0.657979	0.328989	−	0.944334i	$-0.393292\pi$
$967$	20.4609	0.657979	0.328989	+	0.944334i	$0.393292\pi$
$968$	−8.55750	−0.275048
$969$	−1.43295	−0.0460331
$970$	19.6191	0.629932
$971$	29.1117	0.934240	0.467120	−	0.884194i	$-0.345292\pi$
$971$	29.1117	0.934240	0.467120	+	0.884194i	$0.345292\pi$
$972$	48.6368	1.56003
$973$	20.4586	0.655873
$974$	−72.3142	−2.31710
$975$	−1.19449	−0.0382542
$976$	−58.5359	−1.87369
$977$	20.5133	0.656279	0.328139	−	0.944629i	$-0.393578\pi$
$977$	20.5133	0.656279	0.328139	+	0.944629i	$0.393578\pi$
$978$	−11.6397	−0.372195
$979$	−15.9378	−0.509373
$980$	−62.7133	−2.00330
$981$	−17.4066	−0.555749
$982$	−22.9363	−0.731928
$983$	−13.3956	−0.427252	−0.213626	−	0.976916i	$-0.568527\pi$
$983$	−13.3956	−0.427252	−0.213626	+	0.976916i	$0.568527\pi$
$984$	−4.60816	−0.146903
$985$	−24.1075	−0.768129
$986$	−22.7022	−0.722984
$987$	2.81225	0.0895150
$988$	−114.939	−3.65669
$989$	51.1777	1.62736
$990$	16.0538	0.510224
$991$	−53.0738	−1.68594	−0.842972	−	0.537957i	$-0.819196\pi$
$991$	−53.0738	−1.68594	−0.842972	+	0.537957i	$0.819196\pi$
$992$	−152.013	−4.82641
$993$	−0.988879	−0.0313811
$994$	21.9598	0.696524
$995$	−23.9929	−0.760625
$996$	1.15512	0.0366014
$997$	−1.68567	−0.0533856	−0.0266928	−	0.999644i	$-0.508498\pi$
$997$	−1.68567	−0.0533856	−0.0266928	+	0.999644i	$0.508498\pi$
$998$	24.7965	0.784918
$999$	−16.4090	−0.519159

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6017.2.a.e.1.3	✓	119

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6017.2.a.e.1.3	✓	119	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:	\( N \)	\(=\)	\( 6017 = 11 \cdot 547 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6017.a (trivial)

\(f(q)\)	\(=\)	\(q-2.68163 q^{2} +0.369101 q^{3} +5.19115 q^{4} +2.09046 q^{5} -0.989794 q^{6} +1.10498 q^{7} -8.55750 q^{8} -2.86376 q^{9} +O(q^{10})\)	\(q-2.68163 q^{2} +0.369101 q^{3} +5.19115 q^{4} +2.09046 q^{5} -0.989794 q^{6} +1.10498 q^{7} -8.55750 q^{8} -2.86376 q^{9} -5.60585 q^{10} +1.00000 q^{11} +1.91606 q^{12} +5.13703 q^{13} -2.96316 q^{14} +0.771592 q^{15} +12.5658 q^{16} +0.900733 q^{17} +7.67956 q^{18} -4.31013 q^{19} +10.8519 q^{20} +0.407850 q^{21} -2.68163 q^{22} -7.55625 q^{23} -3.15858 q^{24} -0.629976 q^{25} -13.7756 q^{26} -2.16432 q^{27} +5.73613 q^{28} +9.39879 q^{29} -2.06913 q^{30} +9.16747 q^{31} -16.5817 q^{32} +0.369101 q^{33} -2.41543 q^{34} +2.30992 q^{35} -14.8662 q^{36} +7.58160 q^{37} +11.5582 q^{38} +1.89609 q^{39} -17.8891 q^{40} +1.45893 q^{41} -1.09370 q^{42} -6.77290 q^{43} +5.19115 q^{44} -5.98659 q^{45} +20.2631 q^{46} +6.89531 q^{47} +4.63804 q^{48} -5.77901 q^{49} +1.68936 q^{50} +0.332462 q^{51} +26.6671 q^{52} +3.57071 q^{53} +5.80392 q^{54} +2.09046 q^{55} -9.45588 q^{56} -1.59087 q^{57} -25.2041 q^{58} -6.16161 q^{59} +4.00545 q^{60} -4.65836 q^{61} -24.5838 q^{62} -3.16441 q^{63} +19.3346 q^{64} +10.7388 q^{65} -0.989794 q^{66} +2.80548 q^{67} +4.67584 q^{68} -2.78902 q^{69} -6.19436 q^{70} -7.41096 q^{71} +24.5067 q^{72} +1.50888 q^{73} -20.3311 q^{74} -0.232525 q^{75} -22.3745 q^{76} +1.10498 q^{77} -5.08461 q^{78} +16.7592 q^{79} +26.2682 q^{80} +7.79244 q^{81} -3.91232 q^{82} +0.602862 q^{83} +2.11721 q^{84} +1.88295 q^{85} +18.1624 q^{86} +3.46910 q^{87} -8.55750 q^{88} -15.9378 q^{89} +16.0538 q^{90} +5.67633 q^{91} -39.2256 q^{92} +3.38373 q^{93} -18.4907 q^{94} -9.01015 q^{95} -6.12035 q^{96} -3.49976 q^{97} +15.4972 q^{98} -2.86376 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 119 q + 15 q^{2} + 15 q^{3} + 133 q^{4} + 6 q^{5} + 16 q^{6} + 72 q^{7} + 39 q^{8} + 128 q^{9}+O(q^{10}) \) 119 * q + 15 * q^2 + 15 * q^3 + 133 * q^4 + 6 * q^5 + 16 * q^6 + 72 * q^7 + 39 * q^8 + 128 * q^9	\( 119 q + 15 q^{2} + 15 q^{3} + 133 q^{4} + 6 q^{5} + 16 q^{6} + 72 q^{7} + 39 q^{8} + 128 q^{9} + 22 q^{10} + 119 q^{11} + 40 q^{12} + 67 q^{13} + 3 q^{14} + 22 q^{15} + 145 q^{16} + 57 q^{17} + 53 q^{18} + 68 q^{19} + 25 q^{20} + 21 q^{21} + 15 q^{22} + 21 q^{23} + 34 q^{24} + 137 q^{25} + 10 q^{26} + 54 q^{27} + 149 q^{28} + 46 q^{29} + 10 q^{30} + 87 q^{31} + 58 q^{32} + 15 q^{33} + 16 q^{34} + 40 q^{35} + 137 q^{36} + 39 q^{37} + 27 q^{38} + 72 q^{39} + 46 q^{40} + 50 q^{41} - 4 q^{42} + 122 q^{43} + 133 q^{44} + 12 q^{45} + 22 q^{46} + 92 q^{47} + 9 q^{48} + 161 q^{49} + 2 q^{50} - 12 q^{51} + 177 q^{52} + 12 q^{53} + 19 q^{54} + 6 q^{55} - 16 q^{56} + 43 q^{57} + 56 q^{58} + 39 q^{59} + 27 q^{60} + 114 q^{61} + 66 q^{62} + 196 q^{63} + 161 q^{64} + 7 q^{65} + 16 q^{66} + 59 q^{67} + 139 q^{68} - 24 q^{69} + 9 q^{70} + 11 q^{71} + 92 q^{72} + 123 q^{73} + q^{74} + 19 q^{75} + 92 q^{76} + 72 q^{77} - 101 q^{78} + 78 q^{79} - 34 q^{80} + 139 q^{81} + 73 q^{82} + 108 q^{83} - 31 q^{84} + 30 q^{85} - 18 q^{86} + 164 q^{87} + 39 q^{88} + 15 q^{89} - 41 q^{90} + 60 q^{91} - 26 q^{92} - 2 q^{93} + 45 q^{94} + 75 q^{95} + 42 q^{96} + 73 q^{97} + 32 q^{98} + 128 q^{99}+O(q^{100}) \) 119 * q + 15 * q^2 + 15 * q^3 + 133 * q^4 + 6 * q^5 + 16 * q^6 + 72 * q^7 + 39 * q^8 + 128 * q^9 + 22 * q^10 + 119 * q^11 + 40 * q^12 + 67 * q^13 + 3 * q^14 + 22 * q^15 + 145 * q^16 + 57 * q^17 + 53 * q^18 + 68 * q^19 + 25 * q^20 + 21 * q^21 + 15 * q^22 + 21 * q^23 + 34 * q^24 + 137 * q^25 + 10 * q^26 + 54 * q^27 + 149 * q^28 + 46 * q^29 + 10 * q^30 + 87 * q^31 + 58 * q^32 + 15 * q^33 + 16 * q^34 + 40 * q^35 + 137 * q^36 + 39 * q^37 + 27 * q^38 + 72 * q^39 + 46 * q^40 + 50 * q^41 - 4 * q^42 + 122 * q^43 + 133 * q^44 + 12 * q^45 + 22 * q^46 + 92 * q^47 + 9 * q^48 + 161 * q^49 + 2 * q^50 - 12 * q^51 + 177 * q^52 + 12 * q^53 + 19 * q^54 + 6 * q^55 - 16 * q^56 + 43 * q^57 + 56 * q^58 + 39 * q^59 + 27 * q^60 + 114 * q^61 + 66 * q^62 + 196 * q^63 + 161 * q^64 + 7 * q^65 + 16 * q^66 + 59 * q^67 + 139 * q^68 - 24 * q^69 + 9 * q^70 + 11 * q^71 + 92 * q^72 + 123 * q^73 + q^74 + 19 * q^75 + 92 * q^76 + 72 * q^77 - 101 * q^78 + 78 * q^79 - 34 * q^80 + 139 * q^81 + 73 * q^82 + 108 * q^83 - 31 * q^84 + 30 * q^85 - 18 * q^86 + 164 * q^87 + 39 * q^88 + 15 * q^89 - 41 * q^90 + 60 * q^91 - 26 * q^92 - 2 * q^93 + 45 * q^94 + 75 * q^95 + 42 * q^96 + 73 * q^97 + 32 * q^98 + 128 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more