LMFDB - Embedded newform 6034.2.a.n.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

chi = DirichletCharacter(H, H._module([0, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("6034.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6034 = 2 \cdot 7 \cdot 431 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6034.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$48.1817325796$
Analytic rank:	$0$
Dimension:	$24$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	6034.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -2.83864 q^{3} +1.00000 q^{4} +0.330019 q^{5} +2.83864 q^{6} -1.00000 q^{7} -1.00000 q^{8} +5.05788 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -2.83864 q^{3} +1.00000 q^{4} +0.330019 q^{5} +2.83864 q^{6} -1.00000 q^{7} -1.00000 q^{8} +5.05788 q^{9} -0.330019 q^{10} +3.07808 q^{11} -2.83864 q^{12} +2.69265 q^{13} +1.00000 q^{14} -0.936805 q^{15} +1.00000 q^{16} -6.41032 q^{17} -5.05788 q^{18} +3.15184 q^{19} +0.330019 q^{20} +2.83864 q^{21} -3.07808 q^{22} -6.50437 q^{23} +2.83864 q^{24} -4.89109 q^{25} -2.69265 q^{26} -5.84159 q^{27} -1.00000 q^{28} +3.58221 q^{29} +0.936805 q^{30} -0.453720 q^{31} -1.00000 q^{32} -8.73757 q^{33} +6.41032 q^{34} -0.330019 q^{35} +5.05788 q^{36} +0.0743955 q^{37} -3.15184 q^{38} -7.64347 q^{39} -0.330019 q^{40} +9.21562 q^{41} -2.83864 q^{42} +7.47572 q^{43} +3.07808 q^{44} +1.66920 q^{45} +6.50437 q^{46} +10.2092 q^{47} -2.83864 q^{48} +1.00000 q^{49} +4.89109 q^{50} +18.1966 q^{51} +2.69265 q^{52} +3.91618 q^{53} +5.84159 q^{54} +1.01582 q^{55} +1.00000 q^{56} -8.94694 q^{57} -3.58221 q^{58} +7.17457 q^{59} -0.936805 q^{60} -7.56905 q^{61} +0.453720 q^{62} -5.05788 q^{63} +1.00000 q^{64} +0.888626 q^{65} +8.73757 q^{66} +1.60280 q^{67} -6.41032 q^{68} +18.4636 q^{69} +0.330019 q^{70} -5.69325 q^{71} -5.05788 q^{72} -6.01855 q^{73} -0.0743955 q^{74} +13.8840 q^{75} +3.15184 q^{76} -3.07808 q^{77} +7.64347 q^{78} -5.72181 q^{79} +0.330019 q^{80} +1.40852 q^{81} -9.21562 q^{82} +9.56326 q^{83} +2.83864 q^{84} -2.11552 q^{85} -7.47572 q^{86} -10.1686 q^{87} -3.07808 q^{88} -8.49202 q^{89} -1.66920 q^{90} -2.69265 q^{91} -6.50437 q^{92} +1.28795 q^{93} -10.2092 q^{94} +1.04017 q^{95} +2.83864 q^{96} +1.71641 q^{97} -1.00000 q^{98} +15.5686 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 24 q^{2} + 7 q^{3} + 24 q^{4} + 8 q^{5} - 7 q^{6} - 24 q^{7} - 24 q^{8} + 19 q^{9}+O(q^{10}) $ 24 * q - 24 * q^2 + 7 * q^3 + 24 * q^4 + 8 * q^5 - 7 * q^6 - 24 * q^7 - 24 * q^8 + 19 * q^9	\( 24 q - 24 q^{2} + 7 q^{3} + 24 q^{4} + 8 q^{5} - 7 q^{6} - 24 q^{7} - 24 q^{8} + 19 q^{9} - 8 q^{10} + 15 q^{11} + 7 q^{12} - 7 q^{13} + 24 q^{14} + 13 q^{15} + 24 q^{16} - 5 q^{17} - 19 q^{18} + 6 q^{19} + 8 q^{20} - 7 q^{21} - 15 q^{22} + 3 q^{23} - 7 q^{24} + 12 q^{25} + 7 q^{26} + 22 q^{27} - 24 q^{28} + 5 q^{29} - 13 q^{30} + 13 q^{31} - 24 q^{32} - 8 q^{33} + 5 q^{34} - 8 q^{35} + 19 q^{36} + 2 q^{37} - 6 q^{38} + 7 q^{39} - 8 q^{40} + 25 q^{41} + 7 q^{42} - 15 q^{43} + 15 q^{44} + 41 q^{45} - 3 q^{46} + 35 q^{47} + 7 q^{48} + 24 q^{49} - 12 q^{50} + 31 q^{51} - 7 q^{52} + 2 q^{53} - 22 q^{54} + 14 q^{55} + 24 q^{56} - 13 q^{57} - 5 q^{58} + 35 q^{59} + 13 q^{60} - 7 q^{61} - 13 q^{62} - 19 q^{63} + 24 q^{64} - 4 q^{65} + 8 q^{66} + 10 q^{67} - 5 q^{68} + 6 q^{69} + 8 q^{70} + 58 q^{71} - 19 q^{72} + 9 q^{73} - 2 q^{74} + 7 q^{75} + 6 q^{76} - 15 q^{77} - 7 q^{78} + 31 q^{79} + 8 q^{80} + 16 q^{81} - 25 q^{82} - q^{83} - 7 q^{84} - 4 q^{85} + 15 q^{86} + 30 q^{87} - 15 q^{88} + 45 q^{89} - 41 q^{90} + 7 q^{91} + 3 q^{92} + 25 q^{93} - 35 q^{94} - 10 q^{95} - 7 q^{96} - 9 q^{97} - 24 q^{98} + 64 q^{99}+O(q^{100}) \) 24 * q - 24 * q^2 + 7 * q^3 + 24 * q^4 + 8 * q^5 - 7 * q^6 - 24 * q^7 - 24 * q^8 + 19 * q^9 - 8 * q^10 + 15 * q^11 + 7 * q^12 - 7 * q^13 + 24 * q^14 + 13 * q^15 + 24 * q^16 - 5 * q^17 - 19 * q^18 + 6 * q^19 + 8 * q^20 - 7 * q^21 - 15 * q^22 + 3 * q^23 - 7 * q^24 + 12 * q^25 + 7 * q^26 + 22 * q^27 - 24 * q^28 + 5 * q^29 - 13 * q^30 + 13 * q^31 - 24 * q^32 - 8 * q^33 + 5 * q^34 - 8 * q^35 + 19 * q^36 + 2 * q^37 - 6 * q^38 + 7 * q^39 - 8 * q^40 + 25 * q^41 + 7 * q^42 - 15 * q^43 + 15 * q^44 + 41 * q^45 - 3 * q^46 + 35 * q^47 + 7 * q^48 + 24 * q^49 - 12 * q^50 + 31 * q^51 - 7 * q^52 + 2 * q^53 - 22 * q^54 + 14 * q^55 + 24 * q^56 - 13 * q^57 - 5 * q^58 + 35 * q^59 + 13 * q^60 - 7 * q^61 - 13 * q^62 - 19 * q^63 + 24 * q^64 - 4 * q^65 + 8 * q^66 + 10 * q^67 - 5 * q^68 + 6 * q^69 + 8 * q^70 + 58 * q^71 - 19 * q^72 + 9 * q^73 - 2 * q^74 + 7 * q^75 + 6 * q^76 - 15 * q^77 - 7 * q^78 + 31 * q^79 + 8 * q^80 + 16 * q^81 - 25 * q^82 - q^83 - 7 * q^84 - 4 * q^85 + 15 * q^86 + 30 * q^87 - 15 * q^88 + 45 * q^89 - 41 * q^90 + 7 * q^91 + 3 * q^92 + 25 * q^93 - 35 * q^94 - 10 * q^95 - 7 * q^96 - 9 * q^97 - 24 * q^98 + 64 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	−2.83864	−1.63889	−0.819445	−	0.573158i	$-0.805718\pi$
$3$	−2.83864	−1.63889	−0.819445	+	0.573158i	$0.805718\pi$
$4$	1.00000	0.500000
$5$	0.330019	0.147589	0.0737944	−	0.997273i	$-0.476489\pi$
$5$	0.330019	0.147589	0.0737944	+	0.997273i	$0.476489\pi$
$6$	2.83864	1.15887
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	−1.00000	−0.353553
$9$	5.05788	1.68596
$10$	−0.330019	−0.104361
$11$	3.07808	0.928076	0.464038	−	0.885815i	$-0.346400\pi$
$11$	3.07808	0.928076	0.464038	+	0.885815i	$0.346400\pi$
$12$	−2.83864	−0.819445
$13$	2.69265	0.746808	0.373404	−	0.927669i	$-0.378191\pi$
$13$	2.69265	0.746808	0.373404	+	0.927669i	$0.378191\pi$
$14$	1.00000	0.267261
$15$	−0.936805	−0.241882
$16$	1.00000	0.250000
$17$	−6.41032	−1.55473	−0.777365	−	0.629050i	$-0.783444\pi$
$17$	−6.41032	−1.55473	−0.777365	+	0.629050i	$0.783444\pi$
$18$	−5.05788	−1.19215
$19$	3.15184	0.723082	0.361541	−	0.932356i	$-0.382251\pi$
$19$	3.15184	0.723082	0.361541	+	0.932356i	$0.382251\pi$
$20$	0.330019	0.0737944
$21$	2.83864	0.619442
$22$	−3.07808	−0.656249
$23$	−6.50437	−1.35626	−0.678128	−	0.734944i	$-0.737208\pi$
$23$	−6.50437	−1.35626	−0.678128	+	0.734944i	$0.737208\pi$
$24$	2.83864	0.579435
$25$	−4.89109	−0.978218
$26$	−2.69265	−0.528073
$27$	−5.84159	−1.12421
$28$	−1.00000	−0.188982
$29$	3.58221	0.665199	0.332600	−	0.943068i	$-0.392074\pi$
$29$	3.58221	0.665199	0.332600	+	0.943068i	$0.392074\pi$
$30$	0.936805	0.171036
$31$	−0.453720	−0.0814904	−0.0407452	−	0.999170i	$-0.512973\pi$
$31$	−0.453720	−0.0814904	−0.0407452	+	0.999170i	$0.512973\pi$
$32$	−1.00000	−0.176777
$33$	−8.73757	−1.52102
$34$	6.41032	1.09936
$35$	−0.330019	−0.0557833
$36$	5.05788	0.842980
$37$	0.0743955	0.0122305	0.00611527	−	0.999981i	$-0.498053\pi$
$37$	0.0743955	0.0122305	0.00611527	+	0.999981i	$0.498053\pi$
$38$	−3.15184	−0.511296
$39$	−7.64347	−1.22394
$40$	−0.330019	−0.0521805
$41$	9.21562	1.43924	0.719619	−	0.694369i	$-0.244316\pi$
$41$	9.21562	1.43924	0.719619	+	0.694369i	$0.244316\pi$
$42$	−2.83864	−0.438012
$43$	7.47572	1.14004	0.570018	−	0.821632i	$-0.306936\pi$
$43$	7.47572	1.14004	0.570018	+	0.821632i	$0.306936\pi$
$44$	3.07808	0.464038
$45$	1.66920	0.248829
$46$	6.50437	0.959018
$47$	10.2092	1.48916	0.744581	−	0.667532i	$-0.232649\pi$
$47$	10.2092	1.48916	0.744581	+	0.667532i	$0.232649\pi$
$48$	−2.83864	−0.409723
$49$	1.00000	0.142857
$50$	4.89109	0.691704
$51$	18.1966	2.54803
$52$	2.69265	0.373404
$53$	3.91618	0.537929	0.268965	−	0.963150i	$-0.413319\pi$
$53$	3.91618	0.537929	0.268965	+	0.963150i	$0.413319\pi$
$54$	5.84159	0.794939
$55$	1.01582	0.136974
$56$	1.00000	0.133631
$57$	−8.94694	−1.18505
$58$	−3.58221	−0.470367
$59$	7.17457	0.934049	0.467025	−	0.884244i	$-0.345326\pi$
$59$	7.17457	0.934049	0.467025	+	0.884244i	$0.345326\pi$
$60$	−0.936805	−0.120941
$61$	−7.56905	−0.969118	−0.484559	−	0.874759i	$-0.661020\pi$
$61$	−7.56905	−0.969118	−0.484559	+	0.874759i	$0.661020\pi$
$62$	0.453720	0.0576224
$63$	−5.05788	−0.637233
$64$	1.00000	0.125000
$65$	0.888626	0.110220
$66$	8.73757	1.07552
$67$	1.60280	0.195814	0.0979068	−	0.995196i	$-0.468785\pi$
$67$	1.60280	0.195814	0.0979068	+	0.995196i	$0.468785\pi$
$68$	−6.41032	−0.777365
$69$	18.4636	2.22275
$70$	0.330019	0.0394448
$71$	−5.69325	−0.675664	−0.337832	−	0.941206i	$-0.609694\pi$
$71$	−5.69325	−0.675664	−0.337832	+	0.941206i	$0.609694\pi$
$72$	−5.05788	−0.596077
$73$	−6.01855	−0.704417	−0.352209	−	0.935921i	$-0.614569\pi$
$73$	−6.01855	−0.704417	−0.352209	+	0.935921i	$0.614569\pi$
$74$	−0.0743955	−0.00864830
$75$	13.8840	1.60319
$76$	3.15184	0.361541
$77$	−3.07808	−0.350780
$78$	7.64347	0.865453
$79$	−5.72181	−0.643754	−0.321877	−	0.946781i	$-0.604314\pi$
$79$	−5.72181	−0.643754	−0.321877	+	0.946781i	$0.604314\pi$
$80$	0.330019	0.0368972
$81$	1.40852	0.156502
$82$	−9.21562	−1.01769
$83$	9.56326	1.04970	0.524852	−	0.851194i	$-0.324121\pi$
$83$	9.56326	1.04970	0.524852	+	0.851194i	$0.324121\pi$
$84$	2.83864	0.309721
$85$	−2.11552	−0.229461
$86$	−7.47572	−0.806128
$87$	−10.1686	−1.09019
$88$	−3.07808	−0.328125
$89$	−8.49202	−0.900152	−0.450076	−	0.892990i	$-0.648603\pi$
$89$	−8.49202	−0.900152	−0.450076	+	0.892990i	$0.648603\pi$
$90$	−1.66920	−0.175949
$91$	−2.69265	−0.282267
$92$	−6.50437	−0.678128
$93$	1.28795	0.133554
$94$	−10.2092	−1.05300
$95$	1.04017	0.106719
$96$	2.83864	0.289718
$97$	1.71641	0.174275	0.0871374	−	0.996196i	$-0.472228\pi$
$97$	1.71641	0.174275	0.0871374	+	0.996196i	$0.472228\pi$
$98$	−1.00000	−0.101015
$99$	15.5686	1.56470
$100$	−4.89109	−0.489109
$101$	2.22710	0.221605	0.110802	−	0.993842i	$-0.464658\pi$
$101$	2.22710	0.221605	0.110802	+	0.993842i	$0.464658\pi$
$102$	−18.1966	−1.80173
$103$	−10.1067	−0.995844	−0.497922	−	0.867222i	$-0.665903\pi$
$103$	−10.1067	−0.995844	−0.497922	+	0.867222i	$0.665903\pi$
$104$	−2.69265	−0.264036
$105$	0.936805	0.0914228
$106$	−3.91618	−0.380373
$107$	−10.1266	−0.978975	−0.489488	−	0.872010i	$-0.662816\pi$
$107$	−10.1266	−0.978975	−0.489488	+	0.872010i	$0.662816\pi$
$108$	−5.84159	−0.562107
$109$	−11.3383	−1.08601	−0.543004	−	0.839730i	$-0.682713\pi$
$109$	−11.3383	−1.08601	−0.543004	+	0.839730i	$0.682713\pi$
$110$	−1.01582	−0.0968551
$111$	−0.211182	−0.0200445
$112$	−1.00000	−0.0944911
$113$	−9.03856	−0.850276	−0.425138	−	0.905128i	$-0.639775\pi$
$113$	−9.03856	−0.850276	−0.425138	+	0.905128i	$0.639775\pi$
$114$	8.94694	0.837958
$115$	−2.14657	−0.200168
$116$	3.58221	0.332600
$117$	13.6191	1.25909
$118$	−7.17457	−0.660472
$119$	6.41032	0.587633
$120$	0.936805	0.0855182
$121$	−1.52541	−0.138674
$122$	7.56905	0.685270
$123$	−26.1598	−2.35875
$124$	−0.453720	−0.0407452
$125$	−3.26424	−0.291963
$126$	5.05788	0.450592
$127$	−8.78251	−0.779321	−0.389661	−	0.920959i	$-0.627408\pi$
$127$	−8.78251	−0.779321	−0.389661	+	0.920959i	$0.627408\pi$
$128$	−1.00000	−0.0883883
$129$	−21.2209	−1.86839
$130$	−0.888626	−0.0779376
$131$	14.4953	1.26646	0.633231	−	0.773963i	$-0.281728\pi$
$131$	14.4953	1.26646	0.633231	+	0.773963i	$0.281728\pi$
$132$	−8.73757	−0.760508
$133$	−3.15184	−0.273299
$134$	−1.60280	−0.138461
$135$	−1.92783	−0.165921
$136$	6.41032	0.549680
$137$	−6.55574	−0.560094	−0.280047	−	0.959986i	$-0.590350\pi$
$137$	−6.55574	−0.560094	−0.280047	+	0.959986i	$0.590350\pi$
$138$	−18.4636	−1.57172
$139$	12.2483	1.03889	0.519445	−	0.854504i	$-0.326139\pi$
$139$	12.2483	1.03889	0.519445	+	0.854504i	$0.326139\pi$
$140$	−0.330019	−0.0278917
$141$	−28.9802	−2.44057
$142$	5.69325	0.477767
$143$	8.28821	0.693095
$144$	5.05788	0.421490
$145$	1.18220	0.0981760
$146$	6.01855	0.498098
$147$	−2.83864	−0.234127
$148$	0.0743955	0.00611527
$149$	21.1229	1.73046	0.865229	−	0.501377i	$-0.167173\pi$
$149$	21.1229	1.73046	0.865229	+	0.501377i	$0.167173\pi$
$150$	−13.8840	−1.13363
$151$	14.5996	1.18810	0.594051	−	0.804428i	$-0.297528\pi$
$151$	14.5996	1.18810	0.594051	+	0.804428i	$0.297528\pi$
$152$	−3.15184	−0.255648
$153$	−32.4226	−2.62121
$154$	3.07808	0.248039
$155$	−0.149736	−0.0120271
$156$	−7.64347	−0.611968
$157$	17.4928	1.39608	0.698038	−	0.716061i	$-0.254057\pi$
$157$	17.4928	1.39608	0.698038	+	0.716061i	$0.254057\pi$
$158$	5.72181	0.455203
$159$	−11.1166	−0.881607
$160$	−0.330019	−0.0260903
$161$	6.50437	0.512616
$162$	−1.40852	−0.110664
$163$	−11.4612	−0.897708	−0.448854	−	0.893605i	$-0.648168\pi$
$163$	−11.4612	−0.897708	−0.448854	+	0.893605i	$0.648168\pi$
$164$	9.21562	0.719619
$165$	−2.88356	−0.224485
$166$	−9.56326	−0.742253
$167$	−8.42319	−0.651806	−0.325903	−	0.945403i	$-0.605668\pi$
$167$	−8.42319	−0.651806	−0.325903	+	0.945403i	$0.605668\pi$
$168$	−2.83864	−0.219006
$169$	−5.74962	−0.442278
$170$	2.11552	0.162253
$171$	15.9416	1.21909
$172$	7.47572	0.570018
$173$	−10.6698	−0.811209	−0.405604	−	0.914049i	$-0.632939\pi$
$173$	−10.6698	−0.811209	−0.405604	+	0.914049i	$0.632939\pi$
$174$	10.1686	0.770880
$175$	4.89109	0.369731
$176$	3.07808	0.232019
$177$	−20.3660	−1.53080
$178$	8.49202	0.636504
$179$	6.89780	0.515566	0.257783	−	0.966203i	$-0.417008\pi$
$179$	6.89780	0.515566	0.257783	+	0.966203i	$0.417008\pi$
$180$	1.66920	0.124414
$181$	12.5011	0.929199	0.464600	−	0.885521i	$-0.346198\pi$
$181$	12.5011	0.929199	0.464600	+	0.885521i	$0.346198\pi$
$182$	2.69265	0.199593
$183$	21.4858	1.58828
$184$	6.50437	0.479509
$185$	0.0245519	0.00180509
$186$	−1.28795	−0.0944368
$187$	−19.7315	−1.44291
$188$	10.2092	0.744581
$189$	5.84159	0.424913
$190$	−1.04017	−0.0754616
$191$	−0.0973263	−0.00704228	−0.00352114	−	0.999994i	$-0.501121\pi$
$191$	−0.0973263	−0.00704228	−0.00352114	+	0.999994i	$0.501121\pi$
$192$	−2.83864	−0.204861
$193$	−11.8903	−0.855884	−0.427942	−	0.903806i	$-0.640761\pi$
$193$	−11.8903	−0.855884	−0.427942	+	0.903806i	$0.640761\pi$
$194$	−1.71641	−0.123231
$195$	−2.52249	−0.180639
$196$	1.00000	0.0714286
$197$	7.03452	0.501189	0.250595	−	0.968092i	$-0.419374\pi$
$197$	7.03452	0.501189	0.250595	+	0.968092i	$0.419374\pi$
$198$	−15.5686	−1.10641
$199$	2.73519	0.193892	0.0969461	−	0.995290i	$-0.469093\pi$
$199$	2.73519	0.193892	0.0969461	+	0.995290i	$0.469093\pi$
$200$	4.89109	0.345852
$201$	−4.54978	−0.320917
$202$	−2.22710	−0.156698
$203$	−3.58221	−0.251422
$204$	18.1966	1.27402
$205$	3.04133	0.212416
$206$	10.1067	0.704168
$207$	−32.8984	−2.28659
$208$	2.69265	0.186702
$209$	9.70162	0.671075
$210$	−0.936805	−0.0646457
$211$	−4.51356	−0.310726	−0.155363	−	0.987857i	$-0.549655\pi$
$211$	−4.51356	−0.310726	−0.155363	+	0.987857i	$0.549655\pi$
$212$	3.91618	0.268965
$213$	16.1611	1.10734
$214$	10.1266	0.692240
$215$	2.46713	0.168257
$216$	5.84159	0.397470
$217$	0.453720	0.0308005
$218$	11.3383	0.767924
$219$	17.0845	1.15446
$220$	1.01582	0.0684869
$221$	−17.2608	−1.16108
$222$	0.211182	0.0141736
$223$	18.3038	1.22571	0.612855	−	0.790195i	$-0.290021\pi$
$223$	18.3038	1.22571	0.612855	+	0.790195i	$0.290021\pi$
$224$	1.00000	0.0668153
$225$	−24.7385	−1.64924
$226$	9.03856	0.601236
$227$	6.09228	0.404359	0.202179	−	0.979349i	$-0.435198\pi$
$227$	6.09228	0.404359	0.202179	+	0.979349i	$0.435198\pi$
$228$	−8.94694	−0.592526
$229$	−22.2252	−1.46869	−0.734343	−	0.678779i	$-0.762510\pi$
$229$	−22.2252	−1.46869	−0.734343	+	0.678779i	$0.762510\pi$
$230$	2.14657	0.141540
$231$	8.73757	0.574890
$232$	−3.58221	−0.235183
$233$	−14.4571	−0.947117	−0.473559	−	0.880762i	$-0.657031\pi$
$233$	−14.4571	−0.947117	−0.473559	+	0.880762i	$0.657031\pi$
$234$	−13.6191	−0.890310
$235$	3.36922	0.219784
$236$	7.17457	0.467025
$237$	16.2422	1.05504
$238$	−6.41032	−0.415519
$239$	25.9559	1.67895	0.839474	−	0.543401i	$-0.182864\pi$
$239$	25.9559	1.67895	0.839474	+	0.543401i	$0.182864\pi$
$240$	−0.936805	−0.0604705
$241$	−3.21440	−0.207058	−0.103529	−	0.994626i	$-0.533013\pi$
$241$	−3.21440	−0.207058	−0.103529	+	0.994626i	$0.533013\pi$
$242$	1.52541	0.0980574
$243$	13.5265	0.867724
$244$	−7.56905	−0.484559
$245$	0.330019	0.0210841
$246$	26.1598	1.66789
$247$	8.48681	0.540003
$248$	0.453720	0.0288112
$249$	−27.1467	−1.72035
$250$	3.26424	0.206449
$251$	2.55475	0.161254	0.0806272	−	0.996744i	$-0.474308\pi$
$251$	2.55475	0.161254	0.0806272	+	0.996744i	$0.474308\pi$
$252$	−5.05788	−0.318617
$253$	−20.0210	−1.25871
$254$	8.78251	0.551063
$255$	6.00521	0.376061
$256$	1.00000	0.0625000
$257$	−0.0593036	−0.00369926	−0.00184963	−	0.999998i	$-0.500589\pi$
$257$	−0.0593036	−0.00369926	−0.00184963	+	0.999998i	$0.500589\pi$
$258$	21.2209	1.32115
$259$	−0.0743955	−0.00462271
$260$	0.888626	0.0551102
$261$	18.1184	1.12150
$262$	−14.4953	−0.895523
$263$	0.204806	0.0126289	0.00631445	−	0.999980i	$-0.497990\pi$
$263$	0.204806	0.0126289	0.00631445	+	0.999980i	$0.497990\pi$
$264$	8.73757	0.537760
$265$	1.29241	0.0793923
$266$	3.15184	0.193252
$267$	24.1058	1.47525
$268$	1.60280	0.0979068
$269$	−15.3989	−0.938887	−0.469444	−	0.882963i	$-0.655545\pi$
$269$	−15.3989	−0.938887	−0.469444	+	0.882963i	$0.655545\pi$
$270$	1.92783	0.117324
$271$	−10.3147	−0.626572	−0.313286	−	0.949659i	$-0.601430\pi$
$271$	−10.3147	−0.626572	−0.313286	+	0.949659i	$0.601430\pi$
$272$	−6.41032	−0.388682
$273$	7.64347	0.462604
$274$	6.55574	0.396047
$275$	−15.0552	−0.907861
$276$	18.4636	1.11138
$277$	−21.6252	−1.29934	−0.649668	−	0.760218i	$-0.725092\pi$
$277$	−21.6252	−1.29934	−0.649668	+	0.760218i	$0.725092\pi$
$278$	−12.2483	−0.734606
$279$	−2.29486	−0.137390
$280$	0.330019	0.0197224
$281$	−11.8424	−0.706461	−0.353230	−	0.935536i	$-0.614917\pi$
$281$	−11.8424	−0.706461	−0.353230	+	0.935536i	$0.614917\pi$
$282$	28.9802	1.72575
$283$	11.4577	0.681088	0.340544	−	0.940229i	$-0.389389\pi$
$283$	11.4577	0.681088	0.340544	+	0.940229i	$0.389389\pi$
$284$	−5.69325	−0.337832
$285$	−2.95266	−0.174900
$286$	−8.28821	−0.490092
$287$	−9.21562	−0.543981
$288$	−5.05788	−0.298039
$289$	24.0922	1.41719
$290$	−1.18220	−0.0694209
$291$	−4.87226	−0.285617
$292$	−6.01855	−0.352209
$293$	14.7623	0.862423	0.431212	−	0.902251i	$-0.358086\pi$
$293$	14.7623	0.862423	0.431212	+	0.902251i	$0.358086\pi$
$294$	2.83864	0.165553
$295$	2.36774	0.137855
$296$	−0.0743955	−0.00432415
$297$	−17.9809	−1.04336
$298$	−21.1229	−1.22362
$299$	−17.5140	−1.01286
$300$	13.8840	0.801595
$301$	−7.47572	−0.430893
$302$	−14.5996	−0.840114
$303$	−6.32194	−0.363186
$304$	3.15184	0.180770
$305$	−2.49793	−0.143031
$306$	32.4226	1.85348
$307$	−17.6752	−1.00878	−0.504389	−	0.863477i	$-0.668282\pi$
$307$	−17.6752	−1.00878	−0.504389	+	0.863477i	$0.668282\pi$
$308$	−3.07808	−0.175390
$309$	28.6893	1.63208
$310$	0.149736	0.00850443
$311$	−4.89400	−0.277513	−0.138757	−	0.990327i	$-0.544311\pi$
$311$	−4.89400	−0.277513	−0.138757	+	0.990327i	$0.544311\pi$
$312$	7.64347	0.432727
$313$	−6.78529	−0.383527	−0.191764	−	0.981441i	$-0.561421\pi$
$313$	−6.78529	−0.383527	−0.191764	+	0.981441i	$0.561421\pi$
$314$	−17.4928	−0.987174
$315$	−1.66920	−0.0940485
$316$	−5.72181	−0.321877
$317$	23.1328	1.29927	0.649633	−	0.760248i	$-0.274922\pi$
$317$	23.1328	1.29927	0.649633	+	0.760248i	$0.274922\pi$
$318$	11.1166	0.623390
$319$	11.0263	0.617356
$320$	0.330019	0.0184486
$321$	28.7458	1.60443
$322$	−6.50437	−0.362475
$323$	−20.2043	−1.12420
$324$	1.40852	0.0782511
$325$	−13.1700	−0.730540
$326$	11.4612	0.634775
$327$	32.1853	1.77985
$328$	−9.21562	−0.508847
$329$	−10.2092	−0.562850
$330$	2.88356	0.158735
$331$	10.9640	0.602636	0.301318	−	0.953524i	$-0.402573\pi$
$331$	10.9640	0.602636	0.301318	+	0.953524i	$0.402573\pi$
$332$	9.56326	0.524852
$333$	0.376284	0.0206202
$334$	8.42319	0.460896
$335$	0.528955	0.0288999
$336$	2.83864	0.154861
$337$	19.4040	1.05701	0.528503	−	0.848932i	$-0.322754\pi$
$337$	19.4040	1.05701	0.528503	+	0.848932i	$0.322754\pi$
$338$	5.74962	0.312738
$339$	25.6572	1.39351
$340$	−2.11552	−0.114730
$341$	−1.39659	−0.0756293
$342$	−15.9416	−0.862025
$343$	−1.00000	−0.0539949
$344$	−7.47572	−0.403064
$345$	6.09333	0.328054
$346$	10.6698	0.573611
$347$	23.3104	1.25137	0.625685	−	0.780076i	$-0.284819\pi$
$347$	23.3104	1.25137	0.625685	+	0.780076i	$0.284819\pi$
$348$	−10.1686	−0.545094
$349$	8.83540	0.472948	0.236474	−	0.971638i	$-0.424008\pi$
$349$	8.83540	0.472948	0.236474	+	0.971638i	$0.424008\pi$
$350$	−4.89109	−0.261440
$351$	−15.7294	−0.839571
$352$	−3.07808	−0.164062
$353$	24.5084	1.30445	0.652225	−	0.758025i	$-0.273836\pi$
$353$	24.5084	1.30445	0.652225	+	0.758025i	$0.273836\pi$
$354$	20.3660	1.08244
$355$	−1.87888	−0.0997205
$356$	−8.49202	−0.450076
$357$	−18.1966	−0.963065
$358$	−6.89780	−0.364560
$359$	19.7712	1.04348	0.521742	−	0.853104i	$-0.325283\pi$
$359$	19.7712	1.04348	0.521742	+	0.853104i	$0.325283\pi$
$360$	−1.66920	−0.0879743
$361$	−9.06591	−0.477153
$362$	−12.5011	−0.657043
$363$	4.33010	0.227272
$364$	−2.69265	−0.141133
$365$	−1.98623	−0.103964
$366$	−21.4858	−1.12308
$367$	4.27937	0.223381	0.111691	−	0.993743i	$-0.464373\pi$
$367$	4.27937	0.223381	0.111691	+	0.993743i	$0.464373\pi$
$368$	−6.50437	−0.339064
$369$	46.6115	2.42650
$370$	−0.0245519	−0.00127639
$371$	−3.91618	−0.203318
$372$	1.28795	0.0667769
$373$	17.8953	0.926585	0.463293	−	0.886205i	$-0.346668\pi$
$373$	17.8953	0.926585	0.463293	+	0.886205i	$0.346668\pi$
$374$	19.7315	1.02029
$375$	9.26602	0.478495
$376$	−10.2092	−0.526498
$377$	9.64564	0.496776
$378$	−5.84159	−0.300459
$379$	4.01937	0.206461	0.103231	−	0.994657i	$-0.467082\pi$
$379$	4.01937	0.206461	0.103231	+	0.994657i	$0.467082\pi$
$380$	1.04017	0.0533594
$381$	24.9304	1.27722
$382$	0.0973263	0.00497964
$383$	−10.0772	−0.514921	−0.257461	−	0.966289i	$-0.582886\pi$
$383$	−10.0772	−0.514921	−0.257461	+	0.966289i	$0.582886\pi$
$384$	2.83864	0.144859
$385$	−1.01582	−0.0517712
$386$	11.8903	0.605201
$387$	37.8113	1.92206
$388$	1.71641	0.0871374
$389$	−20.8961	−1.05947	−0.529737	−	0.848162i	$-0.677710\pi$
$389$	−20.8961	−1.05947	−0.529737	+	0.848162i	$0.677710\pi$
$390$	2.52249	0.127731
$391$	41.6951	2.10861
$392$	−1.00000	−0.0505076
$393$	−41.1470	−2.07559
$394$	−7.03452	−0.354394
$395$	−1.88831	−0.0950109
$396$	15.5686	0.782350
$397$	27.2515	1.36771	0.683856	−	0.729617i	$-0.260302\pi$
$397$	27.2515	1.36771	0.683856	+	0.729617i	$0.260302\pi$
$398$	−2.73519	−0.137103
$399$	8.94694	0.447907
$400$	−4.89109	−0.244554
$401$	24.4179	1.21937	0.609686	−	0.792643i	$-0.291296\pi$
$401$	24.4179	1.21937	0.609686	+	0.792643i	$0.291296\pi$
$402$	4.54978	0.226923
$403$	−1.22171	−0.0608577
$404$	2.22710	0.110802
$405$	0.464838	0.0230980
$406$	3.58221	0.177782
$407$	0.228995	0.0113509
$408$	−18.1966	−0.900865
$409$	10.7500	0.531553	0.265776	−	0.964035i	$-0.414372\pi$
$409$	10.7500	0.531553	0.265776	+	0.964035i	$0.414372\pi$
$410$	−3.04133	−0.150200
$411$	18.6094	0.917933
$412$	−10.1067	−0.497922
$413$	−7.17457	−0.353037
$414$	32.8984	1.61687
$415$	3.15605	0.154925
$416$	−2.69265	−0.132018
$417$	−34.7686	−1.70263
$418$	−9.70162	−0.474522
$419$	35.8280	1.75031	0.875155	−	0.483842i	$-0.160759\pi$
$419$	35.8280	1.75031	0.875155	+	0.483842i	$0.160759\pi$
$420$	0.936805	0.0457114
$421$	−7.31605	−0.356563	−0.178281	−	0.983980i	$-0.557054\pi$
$421$	−7.31605	−0.356563	−0.178281	+	0.983980i	$0.557054\pi$
$422$	4.51356	0.219716
$423$	51.6368	2.51067
$424$	−3.91618	−0.190187
$425$	31.3534	1.52086
$426$	−16.1611	−0.783007
$427$	7.56905	0.366292
$428$	−10.1266	−0.489488
$429$	−23.5272	−1.13591
$430$	−2.46713	−0.118975
$431$	1.00000	0.0481683
$431$	1.00000	0.0481683
$432$	−5.84159	−0.281053
$433$	31.8948	1.53277	0.766383	−	0.642384i	$-0.222055\pi$
$433$	31.8948	1.53277	0.766383	+	0.642384i	$0.222055\pi$
$434$	−0.453720	−0.0217792
$435$	−3.35583	−0.160900
$436$	−11.3383	−0.543004
$437$	−20.5007	−0.980683
$438$	−17.0845	−0.816328
$439$	14.7796	0.705392	0.352696	−	0.935738i	$-0.385265\pi$
$439$	14.7796	0.705392	0.352696	+	0.935738i	$0.385265\pi$
$440$	−1.01582	−0.0484275
$441$	5.05788	0.240851
$442$	17.2608	0.821010
$443$	18.3398	0.871350	0.435675	−	0.900104i	$-0.356510\pi$
$443$	18.3398	0.871350	0.435675	+	0.900104i	$0.356510\pi$
$444$	−0.211182	−0.0100223
$445$	−2.80253	−0.132852
$446$	−18.3038	−0.866708
$447$	−59.9604	−2.83603
$448$	−1.00000	−0.0472456
$449$	−26.7154	−1.26078	−0.630388	−	0.776280i	$-0.717104\pi$
$449$	−26.7154	−1.26078	−0.630388	+	0.776280i	$0.717104\pi$
$450$	24.7385	1.16619
$451$	28.3664	1.33572
$452$	−9.03856	−0.425138
$453$	−41.4431	−1.94717
$454$	−6.09228	−0.285925
$455$	−0.888626	−0.0416594
$456$	8.94694	0.418979
$457$	−11.2067	−0.524227	−0.262113	−	0.965037i	$-0.584419\pi$
$457$	−11.2067	−0.524227	−0.262113	+	0.965037i	$0.584419\pi$
$458$	22.2252	1.03852
$459$	37.4464	1.74785
$460$	−2.14657	−0.100084
$461$	14.7644	0.687649	0.343824	−	0.939034i	$-0.388278\pi$
$461$	14.7644	0.687649	0.343824	+	0.939034i	$0.388278\pi$
$462$	−8.73757	−0.406508
$463$	−3.89885	−0.181195	−0.0905974	−	0.995888i	$-0.528878\pi$
$463$	−3.89885	−0.181195	−0.0905974	+	0.995888i	$0.528878\pi$
$464$	3.58221	0.166300
$465$	0.425047	0.0197111
$466$	14.4571	0.669713
$467$	−0.801978	−0.0371111	−0.0185555	−	0.999828i	$-0.505907\pi$
$467$	−0.801978	−0.0371111	−0.0185555	+	0.999828i	$0.505907\pi$
$468$	13.6191	0.629544
$469$	−1.60280	−0.0740106
$470$	−3.36922	−0.155411
$471$	−49.6557	−2.28801
$472$	−7.17457	−0.330236
$473$	23.0109	1.05804
$474$	−16.2422	−0.746028
$475$	−15.4159	−0.707331
$476$	6.41032	0.293816
$477$	19.8076	0.906927
$478$	−25.9559	−1.18719
$479$	9.83182	0.449227	0.224614	−	0.974448i	$-0.427888\pi$
$479$	9.83182	0.449227	0.224614	+	0.974448i	$0.427888\pi$
$480$	0.936805	0.0427591
$481$	0.200321	0.00913386
$482$	3.21440	0.146412
$483$	−18.4636	−0.840122
$484$	−1.52541	−0.0693370
$485$	0.566447	0.0257210
$486$	−13.5265	−0.613573
$487$	−1.12362	−0.0509163	−0.0254582	−	0.999676i	$-0.508104\pi$
$487$	−1.12362	−0.0509163	−0.0254582	+	0.999676i	$0.508104\pi$
$488$	7.56905	0.342635
$489$	32.5341	1.47124
$490$	−0.330019	−0.0149087
$491$	3.87935	0.175073	0.0875363	−	0.996161i	$-0.472101\pi$
$491$	3.87935	0.175073	0.0875363	+	0.996161i	$0.472101\pi$
$492$	−26.1598	−1.17938
$493$	−22.9631	−1.03421
$494$	−8.48681	−0.381840
$495$	5.13792	0.230932
$496$	−0.453720	−0.0203726
$497$	5.69325	0.255377
$498$	27.1467	1.21647
$499$	−30.7306	−1.37569	−0.687846	−	0.725857i	$-0.741443\pi$
$499$	−30.7306	−1.37569	−0.687846	+	0.725857i	$0.741443\pi$
$500$	−3.26424	−0.145981
$501$	23.9104	1.06824
$502$	−2.55475	−0.114024
$503$	−15.1130	−0.673857	−0.336929	−	0.941530i	$-0.609388\pi$
$503$	−15.1130	−0.673857	−0.336929	+	0.941530i	$0.609388\pi$
$504$	5.05788	0.225296
$505$	0.734985	0.0327064
$506$	20.0210	0.890042
$507$	16.3211	0.724846
$508$	−8.78251	−0.389661
$509$	12.6963	0.562756	0.281378	−	0.959597i	$-0.409209\pi$
$509$	12.6963	0.562756	0.281378	+	0.959597i	$0.409209\pi$
$510$	−6.00521	−0.265915
$511$	6.01855	0.266245
$512$	−1.00000	−0.0441942
$513$	−18.4117	−0.812898
$514$	0.0593036	0.00261577
$515$	−3.33540	−0.146975
$516$	−21.2209	−0.934197
$517$	31.4247	1.38206
$518$	0.0743955	0.00326875
$519$	30.2877	1.32948
$520$	−0.888626	−0.0389688
$521$	−19.9584	−0.874394	−0.437197	−	0.899366i	$-0.644029\pi$
$521$	−19.9584	−0.874394	−0.437197	+	0.899366i	$0.644029\pi$
$522$	−18.1184	−0.793020
$523$	10.8536	0.474597	0.237298	−	0.971437i	$-0.423738\pi$
$523$	10.8536	0.474597	0.237298	+	0.971437i	$0.423738\pi$
$524$	14.4953	0.633231
$525$	−13.8840	−0.605949
$526$	−0.204806	−0.00892998
$527$	2.90849	0.126696
$528$	−8.73757	−0.380254
$529$	19.3069	0.839429
$530$	−1.29241	−0.0561389
$531$	36.2881	1.57477
$532$	−3.15184	−0.136650
$533$	24.8145	1.07483
$534$	−24.1058	−1.04316
$535$	−3.34197	−0.144486
$536$	−1.60280	−0.0692305
$537$	−19.5804	−0.844955
$538$	15.3989	0.663893
$539$	3.07808	0.132582
$540$	−1.92783	−0.0829607
$541$	32.1501	1.38224	0.691120	−	0.722740i	$-0.257118\pi$
$541$	32.1501	1.38224	0.691120	+	0.722740i	$0.257118\pi$
$542$	10.3147	0.443053
$543$	−35.4861	−1.52285
$544$	6.41032	0.274840
$545$	−3.74184	−0.160283
$546$	−7.64347	−0.327111
$547$	−37.6713	−1.61071	−0.805353	−	0.592795i	$-0.798024\pi$
$547$	−37.6713	−1.61071	−0.805353	+	0.592795i	$0.798024\pi$
$548$	−6.55574	−0.280047
$549$	−38.2834	−1.63389
$550$	15.0552	0.641954
$551$	11.2905	0.480993
$552$	−18.4636	−0.785862
$553$	5.72181	0.243316
$554$	21.6252	0.918769
$555$	−0.0696940	−0.00295835
$556$	12.2483	0.519445
$557$	−37.3679	−1.58333	−0.791663	−	0.610957i	$-0.790785\pi$
$557$	−37.3679	−1.58333	−0.791663	+	0.610957i	$0.790785\pi$
$558$	2.29486	0.0971491
$559$	20.1295	0.851388
$560$	−0.330019	−0.0139458
$561$	56.0106	2.36477
$562$	11.8424	0.499543
$563$	18.5627	0.782325	0.391162	−	0.920322i	$-0.372073\pi$
$563$	18.5627	0.782325	0.391162	+	0.920322i	$0.372073\pi$
$564$	−28.9802	−1.22029
$565$	−2.98290	−0.125491
$566$	−11.4577	−0.481602
$567$	−1.40852	−0.0591523
$568$	5.69325	0.238883
$569$	−16.0103	−0.671188	−0.335594	−	0.942007i	$-0.608937\pi$
$569$	−16.0103	−0.671188	−0.335594	+	0.942007i	$0.608937\pi$
$570$	2.95266	0.123673
$571$	11.3038	0.473051	0.236526	−	0.971625i	$-0.423991\pi$
$571$	11.3038	0.473051	0.236526	+	0.971625i	$0.423991\pi$
$572$	8.28821	0.346547
$573$	0.276274	0.0115415
$574$	9.21562	0.384653
$575$	31.8135	1.32671
$576$	5.05788	0.210745
$577$	−11.5786	−0.482025	−0.241012	−	0.970522i	$-0.577479\pi$
$577$	−11.5786	−0.482025	−0.241012	+	0.970522i	$0.577479\pi$
$578$	−24.0922	−1.00210
$579$	33.7523	1.40270
$580$	1.18220	0.0490880
$581$	−9.56326	−0.396751
$582$	4.87226	0.201962
$583$	12.0543	0.499239
$584$	6.01855	0.249049
$585$	4.49456	0.185827
$586$	−14.7623	−0.609825
$587$	0.201402	0.00831275	0.00415638	−	0.999991i	$-0.498677\pi$
$587$	0.201402	0.00831275	0.00415638	+	0.999991i	$0.498677\pi$
$588$	−2.83864	−0.117064
$589$	−1.43005	−0.0589242
$590$	−2.36774	−0.0974784
$591$	−19.9685	−0.821394
$592$	0.0743955	0.00305764
$593$	29.3912	1.20695	0.603475	−	0.797382i	$-0.293782\pi$
$593$	29.3912	1.20695	0.603475	+	0.797382i	$0.293782\pi$
$594$	17.9809	0.737764
$595$	2.11552	0.0867280
$596$	21.1229	0.865229
$597$	−7.76421	−0.317768
$598$	17.5140	0.716202
$599$	4.45914	0.182195	0.0910977	−	0.995842i	$-0.470962\pi$
$599$	4.45914	0.182195	0.0910977	+	0.995842i	$0.470962\pi$
$600$	−13.8840	−0.566814
$601$	18.8668	0.769592	0.384796	−	0.923002i	$-0.374272\pi$
$601$	18.8668	0.769592	0.384796	+	0.923002i	$0.374272\pi$
$602$	7.47572	0.304688
$603$	8.10679	0.330134
$604$	14.5996	0.594051
$605$	−0.503415	−0.0204667
$606$	6.32194	0.256811
$607$	5.78788	0.234923	0.117461	−	0.993077i	$-0.462524\pi$
$607$	5.78788	0.234923	0.117461	+	0.993077i	$0.462524\pi$
$608$	−3.15184	−0.127824
$609$	10.1686	0.412052
$610$	2.49793	0.101138
$611$	27.4898	1.11212
$612$	−32.4226	−1.31061
$613$	26.7243	1.07939	0.539693	−	0.841862i	$-0.318540\pi$
$613$	26.7243	1.07939	0.539693	+	0.841862i	$0.318540\pi$
$614$	17.6752	0.713313
$615$	−8.63324	−0.348126
$616$	3.07808	0.124019
$617$	16.9714	0.683241	0.341620	−	0.939838i	$-0.389024\pi$
$617$	16.9714	0.683241	0.341620	+	0.939838i	$0.389024\pi$
$618$	−28.6893	−1.15405
$619$	−19.8861	−0.799290	−0.399645	−	0.916670i	$-0.630867\pi$
$619$	−19.8861	−0.799290	−0.399645	+	0.916670i	$0.630867\pi$
$620$	−0.149736	−0.00601354
$621$	37.9959	1.52472
$622$	4.89400	0.196232
$623$	8.49202	0.340226
$624$	−7.64347	−0.305984
$625$	23.3782	0.935127
$626$	6.78529	0.271195
$627$	−27.5394	−1.09982
$628$	17.4928	0.698038
$629$	−0.476899	−0.0190152
$630$	1.66920	0.0665023
$631$	17.1759	0.683763	0.341881	−	0.939743i	$-0.388936\pi$
$631$	17.1759	0.683763	0.341881	+	0.939743i	$0.388936\pi$
$632$	5.72181	0.227601
$633$	12.8124	0.509246
$634$	−23.1328	−0.918720
$635$	−2.89839	−0.115019
$636$	−11.1166	−0.440803
$637$	2.69265	0.106687
$638$	−11.0263	−0.436536
$639$	−28.7958	−1.13914
$640$	−0.330019	−0.0130451
$641$	1.29706	0.0512309	0.0256154	−	0.999672i	$-0.491845\pi$
$641$	1.29706	0.0512309	0.0256154	+	0.999672i	$0.491845\pi$
$642$	−28.7458	−1.13451
$643$	−2.09592	−0.0826550	−0.0413275	−	0.999146i	$-0.513159\pi$
$643$	−2.09592	−0.0826550	−0.0413275	+	0.999146i	$0.513159\pi$
$644$	6.50437	0.256308
$645$	−7.00329	−0.275754
$646$	20.2043	0.794927
$647$	16.5203	0.649481	0.324741	−	0.945803i	$-0.394723\pi$
$647$	16.5203	0.649481	0.324741	+	0.945803i	$0.394723\pi$
$648$	−1.40852	−0.0553319
$649$	22.0839	0.866869
$650$	13.1700	0.516570
$651$	−1.28795	−0.0504786
$652$	−11.4612	−0.448854
$653$	4.95189	0.193783	0.0968913	−	0.995295i	$-0.469110\pi$
$653$	4.95189	0.193783	0.0968913	+	0.995295i	$0.469110\pi$
$654$	−32.1853	−1.25854
$655$	4.78373	0.186916
$656$	9.21562	0.359810
$657$	−30.4411	−1.18762
$658$	10.2092	0.397995
$659$	22.4752	0.875511	0.437755	−	0.899094i	$-0.355774\pi$
$659$	22.4752	0.875511	0.437755	+	0.899094i	$0.355774\pi$
$660$	−2.88356	−0.112242
$661$	−14.7057	−0.571986	−0.285993	−	0.958232i	$-0.592323\pi$
$661$	−14.7057	−0.571986	−0.285993	+	0.958232i	$0.592323\pi$
$662$	−10.9640	−0.426128
$663$	48.9971	1.90289
$664$	−9.56326	−0.371126
$665$	−1.04017	−0.0403359
$666$	−0.376284	−0.0145807
$667$	−23.3000	−0.902180
$668$	−8.42319	−0.325903
$669$	−51.9578	−2.00881
$670$	−0.528955	−0.0204353
$671$	−23.2982	−0.899416
$672$	−2.83864	−0.109503
$673$	7.64237	0.294592	0.147296	−	0.989092i	$-0.452943\pi$
$673$	7.64237	0.294592	0.147296	+	0.989092i	$0.452943\pi$
$674$	−19.4040	−0.747415
$675$	28.5717	1.09973
$676$	−5.74962	−0.221139
$677$	44.5369	1.71169	0.855846	−	0.517230i	$-0.173037\pi$
$677$	44.5369	1.71169	0.855846	+	0.517230i	$0.173037\pi$
$678$	−25.6572	−0.985360
$679$	−1.71641	−0.0658697
$680$	2.11552	0.0811267
$681$	−17.2938	−0.662699
$682$	1.39659	0.0534780
$683$	−28.5032	−1.09064	−0.545322	−	0.838227i	$-0.683593\pi$
$683$	−28.5032	−1.09064	−0.545322	+	0.838227i	$0.683593\pi$
$684$	15.9416	0.609543
$685$	−2.16352	−0.0826637
$686$	1.00000	0.0381802
$687$	63.0895	2.40701
$688$	7.47572	0.285009
$689$	10.5449	0.401729
$690$	−6.09333	−0.231969
$691$	40.7632	1.55071	0.775353	−	0.631528i	$-0.217572\pi$
$691$	40.7632	1.55071	0.775353	+	0.631528i	$0.217572\pi$
$692$	−10.6698	−0.405604
$693$	−15.5686	−0.591401
$694$	−23.3104	−0.884852
$695$	4.04218	0.153329
$696$	10.1686	0.385440
$697$	−59.0750	−2.23763
$698$	−8.83540	−0.334425
$699$	41.0386	1.55222
$700$	4.89109	0.184866
$701$	10.9502	0.413585	0.206793	−	0.978385i	$-0.433697\pi$
$701$	10.9502	0.413585	0.206793	+	0.978385i	$0.433697\pi$
$702$	15.7294	0.593667
$703$	0.234483	0.00884368
$704$	3.07808	0.116010
$705$	−9.56401	−0.360201
$706$	−24.5084	−0.922386
$707$	−2.22710	−0.0837588
$708$	−20.3660	−0.765402
$709$	10.5735	0.397097	0.198548	−	0.980091i	$-0.436377\pi$
$709$	10.5735	0.397097	0.198548	+	0.980091i	$0.436377\pi$
$710$	1.87888	0.0705130
$711$	−28.9402	−1.08534
$712$	8.49202	0.318252
$713$	2.95116	0.110522
$714$	18.1966	0.680990
$715$	2.73526	0.102293
$716$	6.89780	0.257783
$717$	−73.6795	−2.75161
$718$	−19.7712	−0.737854
$719$	23.6357	0.881463	0.440732	−	0.897639i	$-0.354719\pi$
$719$	23.6357	0.881463	0.440732	+	0.897639i	$0.354719\pi$
$720$	1.66920	0.0622072
$721$	10.1067	0.376394
$722$	9.06591	0.337398
$723$	9.12453	0.339345
$724$	12.5011	0.464600
$725$	−17.5209	−0.650710
$726$	−4.33010	−0.160705
$727$	19.5599	0.725437	0.362718	−	0.931899i	$-0.381849\pi$
$727$	19.5599	0.725437	0.362718	+	0.931899i	$0.381849\pi$
$728$	2.69265	0.0997964
$729$	−42.6224	−1.57861
$730$	1.98623	0.0735138
$731$	−47.9217	−1.77245
$732$	21.4858	0.794139
$733$	−21.4507	−0.792300	−0.396150	−	0.918186i	$-0.629654\pi$
$733$	−21.4507	−0.792300	−0.396150	+	0.918186i	$0.629654\pi$
$734$	−4.27937	−0.157955
$735$	−0.936805	−0.0345546
$736$	6.50437	0.239754
$737$	4.93356	0.181730
$738$	−46.6115	−1.71579
$739$	45.7656	1.68351	0.841757	−	0.539856i	$-0.181521\pi$
$739$	45.7656	1.68351	0.841757	+	0.539856i	$0.181521\pi$
$740$	0.0245519	0.000902546 0
$741$	−24.0910	−0.885005
$742$	3.91618	0.143768
$743$	26.4781	0.971389	0.485694	−	0.874129i	$-0.338567\pi$
$743$	26.4781	0.971389	0.485694	+	0.874129i	$0.338567\pi$
$744$	−1.28795	−0.0472184
$745$	6.97096	0.255396
$746$	−17.8953	−0.655195
$747$	48.3698	1.76976
$748$	−19.7315	−0.721454
$749$	10.1266	0.370018
$750$	−9.26602	−0.338347
$751$	−3.24857	−0.118542	−0.0592710	−	0.998242i	$-0.518878\pi$
$751$	−3.24857	−0.118542	−0.0592710	+	0.998242i	$0.518878\pi$
$752$	10.2092	0.372291
$753$	−7.25202	−0.264278
$754$	−9.64564	−0.351274
$755$	4.81815	0.175350
$756$	5.84159	0.212456
$757$	−9.47097	−0.344228	−0.172114	−	0.985077i	$-0.555060\pi$
$757$	−9.47097	−0.344228	−0.172114	+	0.985077i	$0.555060\pi$
$758$	−4.01937	−0.145990
$759$	56.8324	2.06289
$760$	−1.04017	−0.0377308
$761$	−7.54176	−0.273388	−0.136694	−	0.990613i	$-0.543648\pi$
$761$	−7.54176	−0.273388	−0.136694	+	0.990613i	$0.543648\pi$
$762$	−24.9304	−0.903132
$763$	11.3383	0.410473
$764$	−0.0973263	−0.00352114
$765$	−10.7001	−0.386862
$766$	10.0772	0.364104
$767$	19.3186	0.697555
$768$	−2.83864	−0.102431
$769$	20.1783	0.727647	0.363824	−	0.931468i	$-0.381471\pi$
$769$	20.1783	0.727647	0.363824	+	0.931468i	$0.381471\pi$
$770$	1.01582	0.0366078
$771$	0.168342	0.00606267
$772$	−11.8903	−0.427942
$773$	−36.9712	−1.32976	−0.664881	−	0.746950i	$-0.731518\pi$
$773$	−36.9712	−1.32976	−0.664881	+	0.746950i	$0.731518\pi$
$774$	−37.8113	−1.35910
$775$	2.21918	0.0797154
$776$	−1.71641	−0.0616154
$777$	0.211182	0.00757612
$778$	20.8961	0.749162
$779$	29.0462	1.04069
$780$	−2.52249	−0.0903196
$781$	−17.5243	−0.627068
$782$	−41.6951	−1.49101
$783$	−20.9258	−0.747826
$784$	1.00000	0.0357143
$785$	5.77294	0.206045
$786$	41.1470	1.46766
$787$	21.8352	0.778339	0.389170	−	0.921166i	$-0.372762\pi$
$787$	21.8352	0.778339	0.389170	+	0.921166i	$0.372762\pi$
$788$	7.03452	0.250595
$789$	−0.581372	−0.0206974
$790$	1.88831	0.0671829
$791$	9.03856	0.321374
$792$	−15.5686	−0.553205
$793$	−20.3808	−0.723745
$794$	−27.2515	−0.967119
$795$	−3.66870	−0.130115
$796$	2.73519	0.0969461
$797$	27.6137	0.978128	0.489064	−	0.872248i	$-0.337338\pi$
$797$	27.6137	0.978128	0.489064	+	0.872248i	$0.337338\pi$
$798$	−8.94694	−0.316718
$799$	−65.4441	−2.31525
$800$	4.89109	0.172926
$801$	−42.9516	−1.51762
$802$	−24.4179	−0.862226
$803$	−18.5256	−0.653753
$804$	−4.54978	−0.160458
$805$	2.14657	0.0756565
$806$	1.22171	0.0430329
$807$	43.7119	1.53873
$808$	−2.22710	−0.0783492
$809$	−38.1032	−1.33964	−0.669819	−	0.742525i	$-0.733628\pi$
$809$	−38.1032	−1.33964	−0.669819	+	0.742525i	$0.733628\pi$
$810$	−0.464838	−0.0163327
$811$	−22.5350	−0.791310	−0.395655	−	0.918399i	$-0.629482\pi$
$811$	−22.5350	−0.791310	−0.395655	+	0.918399i	$0.629482\pi$
$812$	−3.58221	−0.125711
$813$	29.2797	1.02688
$814$	−0.228995	−0.00802628
$815$	−3.78240	−0.132492
$816$	18.1966	0.637008
$817$	23.5623	0.824339
$818$	−10.7500	−0.375865
$819$	−13.6191	−0.475891
$820$	3.04133	0.106208
$821$	−49.7278	−1.73551	−0.867756	−	0.496991i	$-0.834438\pi$
$821$	−49.7278	−1.73551	−0.867756	+	0.496991i	$0.834438\pi$
$822$	−18.6094	−0.649077
$823$	−5.11618	−0.178339	−0.0891693	−	0.996016i	$-0.528421\pi$
$823$	−5.11618	−0.178339	−0.0891693	+	0.996016i	$0.528421\pi$
$824$	10.1067	0.352084
$825$	42.7362	1.48788
$826$	7.17457	0.249635
$827$	44.5796	1.55018	0.775092	−	0.631848i	$-0.217703\pi$
$827$	44.5796	1.55018	0.775092	+	0.631848i	$0.217703\pi$
$828$	−32.8984	−1.14330
$829$	28.9940	1.00700	0.503502	−	0.863994i	$-0.332045\pi$
$829$	28.9940	1.00700	0.503502	+	0.863994i	$0.332045\pi$
$830$	−3.15605	−0.109548
$831$	61.3863	2.12947
$832$	2.69265	0.0933509
$833$	−6.41032	−0.222104
$834$	34.7686	1.20394
$835$	−2.77981	−0.0961993
$836$	9.70162	0.335537
$837$	2.65044	0.0916127
$838$	−35.8280	−1.23766
$839$	24.8167	0.856769	0.428384	−	0.903597i	$-0.359083\pi$
$839$	24.8167	0.856769	0.428384	+	0.903597i	$0.359083\pi$
$840$	−0.936805	−0.0323228
$841$	−16.1678	−0.557510
$842$	7.31605	0.252128
$843$	33.6164	1.15781
$844$	−4.51356	−0.155363
$845$	−1.89748	−0.0652754
$846$	−51.6368	−1.77531
$847$	1.52541	0.0524139
$848$	3.91618	0.134482
$849$	−32.5242	−1.11623
$850$	−31.3534	−1.07541
$851$	−0.483896	−0.0165877
$852$	16.1611	0.553669
$853$	−37.0082	−1.26714	−0.633568	−	0.773687i	$-0.718410\pi$
$853$	−37.0082	−1.26714	−0.633568	+	0.773687i	$0.718410\pi$
$854$	−7.56905	−0.259008
$855$	5.26104	0.179924
$856$	10.1266	0.346120
$857$	27.0014	0.922349	0.461174	−	0.887309i	$-0.347428\pi$
$857$	27.0014	0.922349	0.461174	+	0.887309i	$0.347428\pi$
$858$	23.5272	0.803207
$859$	−6.55694	−0.223720	−0.111860	−	0.993724i	$-0.535681\pi$
$859$	−6.55694	−0.223720	−0.111860	+	0.993724i	$0.535681\pi$
$860$	2.46713	0.0841283
$861$	26.1598	0.891525
$862$	−1.00000	−0.0340601
$863$	32.8848	1.11941	0.559706	−	0.828691i	$-0.310914\pi$
$863$	32.8848	1.11941	0.559706	+	0.828691i	$0.310914\pi$
$864$	5.84159	0.198735
$865$	−3.52123	−0.119725
$866$	−31.8948	−1.08383
$867$	−68.3890	−2.32261
$868$	0.453720	0.0154002
$869$	−17.6122	−0.597453
$870$	3.35583	0.113773
$871$	4.31579	0.146235
$872$	11.3383	0.383962
$873$	8.68139	0.293820
$874$	20.5007	0.693448
$875$	3.26424	0.110352
$876$	17.0845	0.577231
$877$	30.6105	1.03364	0.516822	−	0.856093i	$-0.327115\pi$
$877$	30.6105	1.03364	0.516822	+	0.856093i	$0.327115\pi$
$878$	−14.7796	−0.498787
$879$	−41.9049	−1.41342
$880$	1.01582	0.0342434
$881$	4.74842	0.159978	0.0799892	−	0.996796i	$-0.474511\pi$
$881$	4.74842	0.159978	0.0799892	+	0.996796i	$0.474511\pi$
$882$	−5.05788	−0.170308
$883$	−25.0104	−0.841666	−0.420833	−	0.907138i	$-0.638262\pi$
$883$	−25.0104	−0.841666	−0.420833	+	0.907138i	$0.638262\pi$
$884$	−17.2608	−0.580542
$885$	−6.72117	−0.225930
$886$	−18.3398	−0.616138
$887$	−5.84207	−0.196158	−0.0980788	−	0.995179i	$-0.531270\pi$
$887$	−5.84207	−0.196158	−0.0980788	+	0.995179i	$0.531270\pi$
$888$	0.211182	0.00708681
$889$	8.78251	0.294556
$890$	2.80253	0.0939409
$891$	4.33554	0.145246
$892$	18.3038	0.612855
$893$	32.1777	1.07679
$894$	59.9604	2.00538
$895$	2.27640	0.0760918
$896$	1.00000	0.0334077
$897$	49.7160	1.65997
$898$	26.7154	0.891504
$899$	−1.62532	−0.0542074
$900$	−24.7385	−0.824618
$901$	−25.1040	−0.836334
$902$	−28.3664	−0.944499
$903$	21.2209	0.706187
$904$	9.03856	0.300618
$905$	4.12560	0.137139
$906$	41.4431	1.37685
$907$	−6.29419	−0.208995	−0.104498	−	0.994525i	$-0.533323\pi$
$907$	−6.29419	−0.208995	−0.104498	+	0.994525i	$0.533323\pi$
$908$	6.09228	0.202179
$909$	11.2644	0.373617
$910$	0.888626	0.0294577
$911$	60.0376	1.98913	0.994567	−	0.104094i	$-0.0331944\pi$
$911$	60.0376	1.98913	0.994567	+	0.104094i	$0.0331944\pi$
$912$	−8.94694	−0.296263
$913$	29.4365	0.974205
$914$	11.2067	0.370684
$915$	7.09072	0.234412
$916$	−22.2252	−0.734343
$917$	−14.4953	−0.478677
$918$	−37.4464	−1.23592
$919$	47.7603	1.57547	0.787733	−	0.616017i	$-0.211255\pi$
$919$	47.7603	1.57547	0.787733	+	0.616017i	$0.211255\pi$
$920$	2.14657	0.0707702
$921$	50.1736	1.65327
$922$	−14.7644	−0.486241
$923$	−15.3299	−0.504591
$924$	8.73757	0.287445
$925$	−0.363875	−0.0119641
$926$	3.89885	0.128124
$927$	−51.1185	−1.67895
$928$	−3.58221	−0.117592
$929$	32.5774	1.06883	0.534416	−	0.845222i	$-0.320532\pi$
$929$	32.5774	1.06883	0.534416	+	0.845222i	$0.320532\pi$
$930$	−0.425047	−0.0139378
$931$	3.15184	0.103297
$932$	−14.4571	−0.473559
$933$	13.8923	0.454814
$934$	0.801978	0.0262415
$935$	−6.51176	−0.212957
$936$	−13.6191	−0.445155
$937$	−18.1623	−0.593338	−0.296669	−	0.954980i	$-0.595876\pi$
$937$	−18.1623	−0.593338	−0.296669	+	0.954980i	$0.595876\pi$
$938$	1.60280	0.0523334
$939$	19.2610	0.628559
$940$	3.36922	0.109892
$941$	1.41149	0.0460133	0.0230067	−	0.999735i	$-0.492676\pi$
$941$	1.41149	0.0460133	0.0230067	+	0.999735i	$0.492676\pi$
$942$	49.6557	1.61787
$943$	−59.9418	−1.95197
$944$	7.17457	0.233512
$945$	1.92783	0.0627124
$946$	−23.0109	−0.748148
$947$	4.00449	0.130128	0.0650642	−	0.997881i	$-0.479275\pi$
$947$	4.00449	0.130128	0.0650642	+	0.997881i	$0.479275\pi$
$948$	16.2422	0.527521
$949$	−16.2059	−0.526064
$950$	15.4159	0.500159
$951$	−65.6657	−2.12936
$952$	−6.41032	−0.207760
$953$	17.7370	0.574558	0.287279	−	0.957847i	$-0.407249\pi$
$953$	17.7370	0.574558	0.287279	+	0.957847i	$0.407249\pi$
$954$	−19.8076	−0.641294
$955$	−0.0321195	−0.00103936
$956$	25.9559	0.839474
$957$	−31.2998	−1.01178
$958$	−9.83182	−0.317652
$959$	6.55574	0.211696
$960$	−0.936805	−0.0302352
$961$	−30.7941	−0.993359
$962$	−0.200321	−0.00645862
$963$	−51.2191	−1.65051
$964$	−3.21440	−0.103529
$965$	−3.92403	−0.126319
$966$	18.4636	0.594056
$967$	29.2920	0.941969	0.470984	−	0.882142i	$-0.343899\pi$
$967$	29.2920	0.941969	0.470984	+	0.882142i	$0.343899\pi$
$968$	1.52541	0.0490287
$969$	57.3527	1.84243
$970$	−0.566447	−0.0181875
$971$	9.47562	0.304087	0.152044	−	0.988374i	$-0.451415\pi$
$971$	9.47562	0.304087	0.152044	+	0.988374i	$0.451415\pi$
$972$	13.5265	0.433862
$973$	−12.2483	−0.392663
$974$	1.12362	0.0360033
$975$	37.3849	1.19728
$976$	−7.56905	−0.242279
$977$	−22.5524	−0.721517	−0.360758	−	0.932659i	$-0.617482\pi$
$977$	−22.5524	−0.721517	−0.360758	+	0.932659i	$0.617482\pi$
$978$	−32.5341	−1.04033
$979$	−26.1391	−0.835410
$980$	0.330019	0.0105421
$981$	−57.3476	−1.83097
$982$	−3.87935	−0.123795
$983$	−17.3279	−0.552673	−0.276337	−	0.961061i	$-0.589120\pi$
$983$	−17.3279	−0.552673	−0.276337	+	0.961061i	$0.589120\pi$
$984$	26.1598	0.833945
$985$	2.32152	0.0739699
$986$	22.9631	0.731293
$987$	28.9802	0.922450
$988$	8.48681	0.270001
$989$	−48.6249	−1.54618
$990$	−5.13792	−0.163294
$991$	−34.0054	−1.08022	−0.540109	−	0.841595i	$-0.681617\pi$
$991$	−34.0054	−1.08022	−0.540109	+	0.841595i	$0.681617\pi$
$992$	0.453720	0.0144056
$993$	−31.1229	−0.987654
$994$	−5.69325	−0.180579
$995$	0.902663	0.0286163
$996$	−27.1467	−0.860175
$997$	−23.0964	−0.731469	−0.365735	−	0.930719i	$-0.619182\pi$
$997$	−23.0964	−0.731469	−0.365735	+	0.930719i	$0.619182\pi$
$998$	30.7306	0.972761
$999$	−0.434588	−0.0137497

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6034.2.a.n.1.1	✓	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6034.2.a.n.1.1	✓	24	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 6034 = 2 \cdot 7 \cdot 431 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6034.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -2.83864 q^{3} +1.00000 q^{4} +0.330019 q^{5} +2.83864 q^{6} -1.00000 q^{7} -1.00000 q^{8} +5.05788 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -2.83864 q^{3} +1.00000 q^{4} +0.330019 q^{5} +2.83864 q^{6} -1.00000 q^{7} -1.00000 q^{8} +5.05788 q^{9} -0.330019 q^{10} +3.07808 q^{11} -2.83864 q^{12} +2.69265 q^{13} +1.00000 q^{14} -0.936805 q^{15} +1.00000 q^{16} -6.41032 q^{17} -5.05788 q^{18} +3.15184 q^{19} +0.330019 q^{20} +2.83864 q^{21} -3.07808 q^{22} -6.50437 q^{23} +2.83864 q^{24} -4.89109 q^{25} -2.69265 q^{26} -5.84159 q^{27} -1.00000 q^{28} +3.58221 q^{29} +0.936805 q^{30} -0.453720 q^{31} -1.00000 q^{32} -8.73757 q^{33} +6.41032 q^{34} -0.330019 q^{35} +5.05788 q^{36} +0.0743955 q^{37} -3.15184 q^{38} -7.64347 q^{39} -0.330019 q^{40} +9.21562 q^{41} -2.83864 q^{42} +7.47572 q^{43} +3.07808 q^{44} +1.66920 q^{45} +6.50437 q^{46} +10.2092 q^{47} -2.83864 q^{48} +1.00000 q^{49} +4.89109 q^{50} +18.1966 q^{51} +2.69265 q^{52} +3.91618 q^{53} +5.84159 q^{54} +1.01582 q^{55} +1.00000 q^{56} -8.94694 q^{57} -3.58221 q^{58} +7.17457 q^{59} -0.936805 q^{60} -7.56905 q^{61} +0.453720 q^{62} -5.05788 q^{63} +1.00000 q^{64} +0.888626 q^{65} +8.73757 q^{66} +1.60280 q^{67} -6.41032 q^{68} +18.4636 q^{69} +0.330019 q^{70} -5.69325 q^{71} -5.05788 q^{72} -6.01855 q^{73} -0.0743955 q^{74} +13.8840 q^{75} +3.15184 q^{76} -3.07808 q^{77} +7.64347 q^{78} -5.72181 q^{79} +0.330019 q^{80} +1.40852 q^{81} -9.21562 q^{82} +9.56326 q^{83} +2.83864 q^{84} -2.11552 q^{85} -7.47572 q^{86} -10.1686 q^{87} -3.07808 q^{88} -8.49202 q^{89} -1.66920 q^{90} -2.69265 q^{91} -6.50437 q^{92} +1.28795 q^{93} -10.2092 q^{94} +1.04017 q^{95} +2.83864 q^{96} +1.71641 q^{97} -1.00000 q^{98} +15.5686 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 24 q^{2} + 7 q^{3} + 24 q^{4} + 8 q^{5} - 7 q^{6} - 24 q^{7} - 24 q^{8} + 19 q^{9}+O(q^{10}) \) 24 * q - 24 * q^2 + 7 * q^3 + 24 * q^4 + 8 * q^5 - 7 * q^6 - 24 * q^7 - 24 * q^8 + 19 * q^9	\( 24 q - 24 q^{2} + 7 q^{3} + 24 q^{4} + 8 q^{5} - 7 q^{6} - 24 q^{7} - 24 q^{8} + 19 q^{9} - 8 q^{10} + 15 q^{11} + 7 q^{12} - 7 q^{13} + 24 q^{14} + 13 q^{15} + 24 q^{16} - 5 q^{17} - 19 q^{18} + 6 q^{19} + 8 q^{20} - 7 q^{21} - 15 q^{22} + 3 q^{23} - 7 q^{24} + 12 q^{25} + 7 q^{26} + 22 q^{27} - 24 q^{28} + 5 q^{29} - 13 q^{30} + 13 q^{31} - 24 q^{32} - 8 q^{33} + 5 q^{34} - 8 q^{35} + 19 q^{36} + 2 q^{37} - 6 q^{38} + 7 q^{39} - 8 q^{40} + 25 q^{41} + 7 q^{42} - 15 q^{43} + 15 q^{44} + 41 q^{45} - 3 q^{46} + 35 q^{47} + 7 q^{48} + 24 q^{49} - 12 q^{50} + 31 q^{51} - 7 q^{52} + 2 q^{53} - 22 q^{54} + 14 q^{55} + 24 q^{56} - 13 q^{57} - 5 q^{58} + 35 q^{59} + 13 q^{60} - 7 q^{61} - 13 q^{62} - 19 q^{63} + 24 q^{64} - 4 q^{65} + 8 q^{66} + 10 q^{67} - 5 q^{68} + 6 q^{69} + 8 q^{70} + 58 q^{71} - 19 q^{72} + 9 q^{73} - 2 q^{74} + 7 q^{75} + 6 q^{76} - 15 q^{77} - 7 q^{78} + 31 q^{79} + 8 q^{80} + 16 q^{81} - 25 q^{82} - q^{83} - 7 q^{84} - 4 q^{85} + 15 q^{86} + 30 q^{87} - 15 q^{88} + 45 q^{89} - 41 q^{90} + 7 q^{91} + 3 q^{92} + 25 q^{93} - 35 q^{94} - 10 q^{95} - 7 q^{96} - 9 q^{97} - 24 q^{98} + 64 q^{99}+O(q^{100}) \) 24 * q - 24 * q^2 + 7 * q^3 + 24 * q^4 + 8 * q^5 - 7 * q^6 - 24 * q^7 - 24 * q^8 + 19 * q^9 - 8 * q^10 + 15 * q^11 + 7 * q^12 - 7 * q^13 + 24 * q^14 + 13 * q^15 + 24 * q^16 - 5 * q^17 - 19 * q^18 + 6 * q^19 + 8 * q^20 - 7 * q^21 - 15 * q^22 + 3 * q^23 - 7 * q^24 + 12 * q^25 + 7 * q^26 + 22 * q^27 - 24 * q^28 + 5 * q^29 - 13 * q^30 + 13 * q^31 - 24 * q^32 - 8 * q^33 + 5 * q^34 - 8 * q^35 + 19 * q^36 + 2 * q^37 - 6 * q^38 + 7 * q^39 - 8 * q^40 + 25 * q^41 + 7 * q^42 - 15 * q^43 + 15 * q^44 + 41 * q^45 - 3 * q^46 + 35 * q^47 + 7 * q^48 + 24 * q^49 - 12 * q^50 + 31 * q^51 - 7 * q^52 + 2 * q^53 - 22 * q^54 + 14 * q^55 + 24 * q^56 - 13 * q^57 - 5 * q^58 + 35 * q^59 + 13 * q^60 - 7 * q^61 - 13 * q^62 - 19 * q^63 + 24 * q^64 - 4 * q^65 + 8 * q^66 + 10 * q^67 - 5 * q^68 + 6 * q^69 + 8 * q^70 + 58 * q^71 - 19 * q^72 + 9 * q^73 - 2 * q^74 + 7 * q^75 + 6 * q^76 - 15 * q^77 - 7 * q^78 + 31 * q^79 + 8 * q^80 + 16 * q^81 - 25 * q^82 - q^83 - 7 * q^84 - 4 * q^85 + 15 * q^86 + 30 * q^87 - 15 * q^88 + 45 * q^89 - 41 * q^90 + 7 * q^91 + 3 * q^92 + 25 * q^93 - 35 * q^94 - 10 * q^95 - 7 * q^96 - 9 * q^97 - 24 * q^98 + 64 * q^99

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