LMFDB - Embedded newform 8018.2.a.f.1.34

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8018,2,Mod(1,8018)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8018, 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("8018.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8018 = 2 \cdot 19 \cdot 211 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8018.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:	$64.0240523407$
Analytic rank:	$1$
Dimension:	$34$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.34
Character	$\chi$	$=$	8018.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +3.26778 q^{3} +1.00000 q^{4} +0.595639 q^{5} -3.26778 q^{6} -2.99147 q^{7} -1.00000 q^{8} +7.67840 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +3.26778 q^{3} +1.00000 q^{4} +0.595639 q^{5} -3.26778 q^{6} -2.99147 q^{7} -1.00000 q^{8} +7.67840 q^{9} -0.595639 q^{10} +0.495097 q^{11} +3.26778 q^{12} -2.84715 q^{13} +2.99147 q^{14} +1.94642 q^{15} +1.00000 q^{16} -1.90375 q^{17} -7.67840 q^{18} -1.00000 q^{19} +0.595639 q^{20} -9.77549 q^{21} -0.495097 q^{22} -8.88616 q^{23} -3.26778 q^{24} -4.64521 q^{25} +2.84715 q^{26} +15.2880 q^{27} -2.99147 q^{28} -0.0817407 q^{29} -1.94642 q^{30} -4.72927 q^{31} -1.00000 q^{32} +1.61787 q^{33} +1.90375 q^{34} -1.78184 q^{35} +7.67840 q^{36} -1.10528 q^{37} +1.00000 q^{38} -9.30386 q^{39} -0.595639 q^{40} +8.82027 q^{41} +9.77549 q^{42} +4.95602 q^{43} +0.495097 q^{44} +4.57355 q^{45} +8.88616 q^{46} -2.10145 q^{47} +3.26778 q^{48} +1.94892 q^{49} +4.64521 q^{50} -6.22104 q^{51} -2.84715 q^{52} +0.933659 q^{53} -15.2880 q^{54} +0.294899 q^{55} +2.99147 q^{56} -3.26778 q^{57} +0.0817407 q^{58} +10.6946 q^{59} +1.94642 q^{60} +6.78989 q^{61} +4.72927 q^{62} -22.9697 q^{63} +1.00000 q^{64} -1.69587 q^{65} -1.61787 q^{66} -3.28824 q^{67} -1.90375 q^{68} -29.0380 q^{69} +1.78184 q^{70} -13.8027 q^{71} -7.67840 q^{72} +10.0079 q^{73} +1.10528 q^{74} -15.1795 q^{75} -1.00000 q^{76} -1.48107 q^{77} +9.30386 q^{78} -3.99429 q^{79} +0.595639 q^{80} +26.9226 q^{81} -8.82027 q^{82} -10.3525 q^{83} -9.77549 q^{84} -1.13395 q^{85} -4.95602 q^{86} -0.267111 q^{87} -0.495097 q^{88} -11.0506 q^{89} -4.57355 q^{90} +8.51717 q^{91} -8.88616 q^{92} -15.4542 q^{93} +2.10145 q^{94} -0.595639 q^{95} -3.26778 q^{96} -6.88378 q^{97} -1.94892 q^{98} +3.80155 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 34 q - 34 q^{2} - 10 q^{3} + 34 q^{4} + 7 q^{5} + 10 q^{6} - 6 q^{7} - 34 q^{8} + 38 q^{9}+O(q^{10}) $ 34 * q - 34 * q^2 - 10 * q^3 + 34 * q^4 + 7 * q^5 + 10 * q^6 - 6 * q^7 - 34 * q^8 + 38 * q^9	\( 34 q - 34 q^{2} - 10 q^{3} + 34 q^{4} + 7 q^{5} + 10 q^{6} - 6 q^{7} - 34 q^{8} + 38 q^{9} - 7 q^{10} + 4 q^{11} - 10 q^{12} - 5 q^{13} + 6 q^{14} - 17 q^{15} + 34 q^{16} + 8 q^{17} - 38 q^{18} - 34 q^{19} + 7 q^{20} - 4 q^{22} - 24 q^{23} + 10 q^{24} + 5 q^{25} + 5 q^{26} - 31 q^{27} - 6 q^{28} + 24 q^{29} + 17 q^{30} - 28 q^{31} - 34 q^{32} - 16 q^{33} - 8 q^{34} + 2 q^{35} + 38 q^{36} - 36 q^{37} + 34 q^{38} - 9 q^{39} - 7 q^{40} + 9 q^{41} - 24 q^{43} + 4 q^{44} + 22 q^{45} + 24 q^{46} - 29 q^{47} - 10 q^{48} + 22 q^{49} - 5 q^{50} - 21 q^{51} - 5 q^{52} - 9 q^{53} + 31 q^{54} - 28 q^{55} + 6 q^{56} + 10 q^{57} - 24 q^{58} - 28 q^{59} - 17 q^{60} + 23 q^{61} + 28 q^{62} - 27 q^{63} + 34 q^{64} - 6 q^{65} + 16 q^{66} - 51 q^{67} + 8 q^{68} - 17 q^{69} - 2 q^{70} - 31 q^{71} - 38 q^{72} - 26 q^{73} + 36 q^{74} - 109 q^{75} - 34 q^{76} - 28 q^{77} + 9 q^{78} - 36 q^{79} + 7 q^{80} + 6 q^{81} - 9 q^{82} - 10 q^{83} - 32 q^{85} + 24 q^{86} - 8 q^{87} - 4 q^{88} - 34 q^{89} - 22 q^{90} - 41 q^{91} - 24 q^{92} - 33 q^{93} + 29 q^{94} - 7 q^{95} + 10 q^{96} - 56 q^{97} - 22 q^{98} - 28 q^{99}+O(q^{100}) \) 34 * q - 34 * q^2 - 10 * q^3 + 34 * q^4 + 7 * q^5 + 10 * q^6 - 6 * q^7 - 34 * q^8 + 38 * q^9 - 7 * q^10 + 4 * q^11 - 10 * q^12 - 5 * q^13 + 6 * q^14 - 17 * q^15 + 34 * q^16 + 8 * q^17 - 38 * q^18 - 34 * q^19 + 7 * q^20 - 4 * q^22 - 24 * q^23 + 10 * q^24 + 5 * q^25 + 5 * q^26 - 31 * q^27 - 6 * q^28 + 24 * q^29 + 17 * q^30 - 28 * q^31 - 34 * q^32 - 16 * q^33 - 8 * q^34 + 2 * q^35 + 38 * q^36 - 36 * q^37 + 34 * q^38 - 9 * q^39 - 7 * q^40 + 9 * q^41 - 24 * q^43 + 4 * q^44 + 22 * q^45 + 24 * q^46 - 29 * q^47 - 10 * q^48 + 22 * q^49 - 5 * q^50 - 21 * q^51 - 5 * q^52 - 9 * q^53 + 31 * q^54 - 28 * q^55 + 6 * q^56 + 10 * q^57 - 24 * q^58 - 28 * q^59 - 17 * q^60 + 23 * q^61 + 28 * q^62 - 27 * q^63 + 34 * q^64 - 6 * q^65 + 16 * q^66 - 51 * q^67 + 8 * q^68 - 17 * q^69 - 2 * q^70 - 31 * q^71 - 38 * q^72 - 26 * q^73 + 36 * q^74 - 109 * q^75 - 34 * q^76 - 28 * q^77 + 9 * q^78 - 36 * q^79 + 7 * q^80 + 6 * q^81 - 9 * q^82 - 10 * q^83 - 32 * q^85 + 24 * q^86 - 8 * q^87 - 4 * q^88 - 34 * q^89 - 22 * q^90 - 41 * q^91 - 24 * q^92 - 33 * q^93 + 29 * q^94 - 7 * q^95 + 10 * q^96 - 56 * q^97 - 22 * q^98 - 28 * 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
$3$	3.26778	1.88665	0.943327	−	0.331864i	$-0.107678\pi$
$3$	3.26778	1.88665	0.943327	+	0.331864i	$0.107678\pi$
$4$	1.00000	0.500000
$5$	0.595639	0.266378	0.133189	−	0.991091i	$-0.457478\pi$
$5$	0.595639	0.266378	0.133189	+	0.991091i	$0.457478\pi$
$6$	−3.26778	−1.33407
$7$	−2.99147	−1.13067	−0.565336	−	0.824861i	$-0.691253\pi$
$7$	−2.99147	−1.13067	−0.565336	+	0.824861i	$0.691253\pi$
$8$	−1.00000	−0.353553
$9$	7.67840	2.55947
$10$	−0.595639	−0.188358
$11$	0.495097	0.149277	0.0746387	−	0.997211i	$-0.476220\pi$
$11$	0.495097	0.149277	0.0746387	+	0.997211i	$0.476220\pi$
$12$	3.26778	0.943327
$13$	−2.84715	−0.789657	−0.394828	−	0.918755i	$-0.629196\pi$
$13$	−2.84715	−0.789657	−0.394828	+	0.918755i	$0.629196\pi$
$14$	2.99147	0.799505
$15$	1.94642	0.502563
$16$	1.00000	0.250000
$17$	−1.90375	−0.461727	−0.230863	−	0.972986i	$-0.574155\pi$
$17$	−1.90375	−0.461727	−0.230863	+	0.972986i	$0.574155\pi$
$18$	−7.67840	−1.80982
$19$	−1.00000	−0.229416
$19$	−1.00000	−0.229416
$20$	0.595639	0.133189
$21$	−9.77549	−2.13319
$22$	−0.495097	−0.105555
$23$	−8.88616	−1.85289	−0.926446	−	0.376427i	$-0.877153\pi$
$23$	−8.88616	−1.85289	−0.926446	+	0.376427i	$0.877153\pi$
$24$	−3.26778	−0.667033
$25$	−4.64521	−0.929043
$26$	2.84715	0.558372
$27$	15.2880	2.94217
$28$	−2.99147	−0.565336
$29$	−0.0817407	−0.0151789	−0.00758943	−	0.999971i	$-0.502416\pi$
$29$	−0.0817407	−0.0151789	−0.00758943	+	0.999971i	$0.502416\pi$
$30$	−1.94642	−0.355366
$31$	−4.72927	−0.849403	−0.424701	−	0.905334i	$-0.639621\pi$
$31$	−4.72927	−0.849403	−0.424701	+	0.905334i	$0.639621\pi$
$32$	−1.00000	−0.176777
$33$	1.61787	0.281635
$34$	1.90375	0.326490
$35$	−1.78184	−0.301186
$36$	7.67840	1.27973
$37$	−1.10528	−0.181706	−0.0908532	−	0.995864i	$-0.528959\pi$
$37$	−1.10528	−0.181706	−0.0908532	+	0.995864i	$0.528959\pi$
$38$	1.00000	0.162221
$39$	−9.30386	−1.48981
$40$	−0.595639	−0.0941788
$41$	8.82027	1.37749	0.688747	−	0.725002i	$-0.258161\pi$
$41$	8.82027	1.37749	0.688747	+	0.725002i	$0.258161\pi$
$42$	9.77549	1.50839
$43$	4.95602	0.755786	0.377893	−	0.925849i	$-0.376649\pi$
$43$	4.95602	0.755786	0.377893	+	0.925849i	$0.376649\pi$
$44$	0.495097	0.0746387
$45$	4.57355	0.681785
$46$	8.88616	1.31019
$47$	−2.10145	−0.306528	−0.153264	−	0.988185i	$-0.548979\pi$
$47$	−2.10145	−0.306528	−0.153264	+	0.988185i	$0.548979\pi$
$48$	3.26778	0.471664
$49$	1.94892	0.278417
$50$	4.64521	0.656932
$51$	−6.22104	−0.871119
$52$	−2.84715	−0.394828
$53$	0.933659	0.128248	0.0641240	−	0.997942i	$-0.479575\pi$
$53$	0.933659	0.128248	0.0641240	+	0.997942i	$0.479575\pi$
$54$	−15.2880	−2.08043
$55$	0.294899	0.0397642
$56$	2.99147	0.399753
$57$	−3.26778	−0.432828
$58$	0.0817407	0.0107331
$59$	10.6946	1.39232	0.696160	−	0.717886i	$-0.254890\pi$
$59$	10.6946	1.39232	0.696160	+	0.717886i	$0.254890\pi$
$60$	1.94642	0.251282
$61$	6.78989	0.869357	0.434678	−	0.900586i	$-0.356862\pi$
$61$	6.78989	0.869357	0.434678	+	0.900586i	$0.356862\pi$
$62$	4.72927	0.600618
$63$	−22.9697	−2.89391
$64$	1.00000	0.125000
$65$	−1.69587	−0.210347
$66$	−1.61787	−0.199146
$67$	−3.28824	−0.401723	−0.200861	−	0.979620i	$-0.564374\pi$
$67$	−3.28824	−0.401723	−0.200861	+	0.979620i	$0.564374\pi$
$68$	−1.90375	−0.230863
$69$	−29.0380	−3.49577
$70$	1.78184	0.212971
$71$	−13.8027	−1.63808	−0.819039	−	0.573738i	$-0.805493\pi$
$71$	−13.8027	−1.63808	−0.819039	+	0.573738i	$0.805493\pi$
$72$	−7.67840	−0.904908
$73$	10.0079	1.17133	0.585667	−	0.810552i	$-0.300833\pi$
$73$	10.0079	1.17133	0.585667	+	0.810552i	$0.300833\pi$
$74$	1.10528	0.128486
$75$	−15.1795	−1.75278
$76$	−1.00000	−0.114708
$77$	−1.48107	−0.168784
$78$	9.30386	1.05345
$79$	−3.99429	−0.449393	−0.224697	−	0.974429i	$-0.572139\pi$
$79$	−3.99429	−0.449393	−0.224697	+	0.974429i	$0.572139\pi$
$80$	0.595639	0.0665945
$81$	26.9226	2.99140
$82$	−8.82027	−0.974036
$83$	−10.3525	−1.13634	−0.568170	−	0.822911i	$-0.692348\pi$
$83$	−10.3525	−1.13634	−0.568170	+	0.822911i	$0.692348\pi$
$84$	−9.77549	−1.06659
$85$	−1.13395	−0.122994
$86$	−4.95602	−0.534421
$87$	−0.267111	−0.0286373
$88$	−0.495097	−0.0527775
$89$	−11.0506	−1.17137	−0.585683	−	0.810540i	$-0.699173\pi$
$89$	−11.0506	−1.17137	−0.585683	+	0.810540i	$0.699173\pi$
$90$	−4.57355	−0.482095
$91$	8.51717	0.892842
$92$	−8.88616	−0.926446
$93$	−15.4542	−1.60253
$94$	2.10145	0.216748
$95$	−0.595639	−0.0611113
$96$	−3.26778	−0.333517
$97$	−6.88378	−0.698942	−0.349471	−	0.936947i	$-0.613639\pi$
$97$	−6.88378	−0.698942	−0.349471	+	0.936947i	$0.613639\pi$
$98$	−1.94892	−0.196871
$99$	3.80155	0.382070
$100$	−4.64521	−0.464521
$101$	−14.4083	−1.43368	−0.716840	−	0.697238i	$-0.754412\pi$
$101$	−14.4083	−1.43368	−0.716840	+	0.697238i	$0.754412\pi$
$102$	6.22104	0.615974
$103$	−18.8307	−1.85545	−0.927723	−	0.373269i	$-0.878237\pi$
$103$	−18.8307	−1.85545	−0.927723	+	0.373269i	$0.878237\pi$
$104$	2.84715	0.279186
$105$	−5.82266	−0.568234
$106$	−0.933659	−0.0906850
$107$	−8.60229	−0.831614	−0.415807	−	0.909453i	$-0.636501\pi$
$107$	−8.60229	−0.831614	−0.415807	+	0.909453i	$0.636501\pi$
$108$	15.2880	1.47109
$109$	15.8524	1.51838	0.759190	−	0.650869i	$-0.225595\pi$
$109$	15.8524	1.51838	0.759190	+	0.650869i	$0.225595\pi$
$110$	−0.294899	−0.0281175
$111$	−3.61180	−0.342817
$112$	−2.99147	−0.282668
$113$	1.67460	0.157533	0.0787664	−	0.996893i	$-0.474902\pi$
$113$	1.67460	0.157533	0.0787664	+	0.996893i	$0.474902\pi$
$114$	3.26778	0.306056
$115$	−5.29294	−0.493570
$116$	−0.0817407	−0.00758943
$117$	−21.8615	−2.02110
$118$	−10.6946	−0.984519
$119$	5.69502	0.522061
$120$	−1.94642	−0.177683
$121$	−10.7549	−0.977716
$122$	−6.78989	−0.614728
$123$	28.8227	2.59886
$124$	−4.72927	−0.424701
$125$	−5.74507	−0.513854
$126$	22.9697	2.04631
$127$	−19.0429	−1.68978	−0.844892	−	0.534937i	$-0.820335\pi$
$127$	−19.0429	−1.68978	−0.844892	+	0.534937i	$0.820335\pi$
$128$	−1.00000	−0.0883883
$129$	16.1952	1.42591
$130$	1.69587	0.148738
$131$	−3.50230	−0.305997	−0.152999	−	0.988226i	$-0.548893\pi$
$131$	−3.50230	−0.305997	−0.152999	+	0.988226i	$0.548893\pi$
$132$	1.61787	0.140817
$133$	2.99147	0.259394
$134$	3.28824	0.284061
$135$	9.10612	0.783730
$136$	1.90375	0.163245
$137$	−8.32344	−0.711119	−0.355560	−	0.934654i	$-0.615710\pi$
$137$	−8.32344	−0.711119	−0.355560	+	0.934654i	$0.615710\pi$
$138$	29.0380	2.47188
$139$	9.07860	0.770036	0.385018	−	0.922909i	$-0.374195\pi$
$139$	9.07860	0.770036	0.385018	+	0.922909i	$0.374195\pi$
$140$	−1.78184	−0.150593
$141$	−6.86708	−0.578313
$142$	13.8027	1.15830
$143$	−1.40962	−0.117878
$144$	7.67840	0.639866
$145$	−0.0486880	−0.00404332
$146$	−10.0079	−0.828258
$147$	6.36865	0.525277
$148$	−1.10528	−0.0908532
$149$	−21.6964	−1.77744	−0.888721	−	0.458449i	$-0.848405\pi$
$149$	−21.6964	−1.77744	−0.888721	+	0.458449i	$0.848405\pi$
$150$	15.1795	1.23940
$151$	−5.30999	−0.432121	−0.216060	−	0.976380i	$-0.569321\pi$
$151$	−5.30999	−0.432121	−0.216060	+	0.976380i	$0.569321\pi$
$152$	1.00000	0.0811107
$153$	−14.6177	−1.18177
$154$	1.48107	0.119348
$155$	−2.81694	−0.226262
$156$	−9.30386	−0.744905
$157$	−10.6815	−0.852476	−0.426238	−	0.904611i	$-0.640161\pi$
$157$	−10.6815	−0.852476	−0.426238	+	0.904611i	$0.640161\pi$
$158$	3.99429	0.317769
$159$	3.05099	0.241960
$160$	−0.595639	−0.0470894
$161$	26.5827	2.09501
$162$	−26.9226	−2.11524
$163$	−3.40812	−0.266944	−0.133472	−	0.991053i	$-0.542613\pi$
$163$	−3.40812	−0.266944	−0.133472	+	0.991053i	$0.542613\pi$
$164$	8.82027	0.688747
$165$	0.963666	0.0750213
$166$	10.3525	0.803513
$167$	0.313528	0.0242616	0.0121308	−	0.999926i	$-0.496139\pi$
$167$	0.313528	0.0242616	0.0121308	+	0.999926i	$0.496139\pi$
$168$	9.77549	0.754195
$169$	−4.89375	−0.376442
$170$	1.13395	0.0869698
$171$	−7.67840	−0.587182
$172$	4.95602	0.377893
$173$	−0.365104	−0.0277583	−0.0138792	−	0.999904i	$-0.504418\pi$
$173$	−0.365104	−0.0277583	−0.0138792	+	0.999904i	$0.504418\pi$
$174$	0.267111	0.0202496
$175$	13.8960	1.05044
$176$	0.495097	0.0373194
$177$	34.9477	2.62683
$178$	11.0506	0.828280
$179$	−0.0604155	−0.00451566	−0.00225783	−	0.999997i	$-0.500719\pi$
$179$	−0.0604155	−0.00451566	−0.00225783	+	0.999997i	$0.500719\pi$
$180$	4.57355	0.340892
$181$	22.5406	1.67543	0.837715	−	0.546107i	$-0.183891\pi$
$181$	22.5406	1.67543	0.837715	+	0.546107i	$0.183891\pi$
$182$	−8.51717	−0.631335
$183$	22.1879	1.64018
$184$	8.88616	0.655096
$185$	−0.658346	−0.0484025
$186$	15.4542	1.13316
$187$	−0.942541	−0.0689254
$188$	−2.10145	−0.153264
$189$	−45.7336	−3.32663
$190$	0.595639	0.0432122
$191$	2.41398	0.174670	0.0873348	−	0.996179i	$-0.472165\pi$
$191$	2.41398	0.174670	0.0873348	+	0.996179i	$0.472165\pi$
$192$	3.26778	0.235832
$193$	17.3804	1.25107	0.625535	−	0.780196i	$-0.284881\pi$
$193$	17.3804	1.25107	0.625535	+	0.780196i	$0.284881\pi$
$194$	6.88378	0.494227
$195$	−5.54174	−0.396852
$196$	1.94892	0.139209
$197$	1.96372	0.139909	0.0699545	−	0.997550i	$-0.477715\pi$
$197$	1.96372	0.139909	0.0699545	+	0.997550i	$0.477715\pi$
$198$	−3.80155	−0.270165
$199$	6.83514	0.484530	0.242265	−	0.970210i	$-0.422110\pi$
$199$	6.83514	0.484530	0.242265	+	0.970210i	$0.422110\pi$
$200$	4.64521	0.328466
$201$	−10.7453	−0.757912
$202$	14.4083	1.01376
$203$	0.244525	0.0171623
$204$	−6.22104	−0.435560
$205$	5.25370	0.366934
$206$	18.8307	1.31200
$207$	−68.2315	−4.74241
$208$	−2.84715	−0.197414
$209$	−0.495097	−0.0342466
$210$	5.82266	0.401802
$211$	−1.00000	−0.0688428
$211$	−1.00000	−0.0688428
$212$	0.933659	0.0641240
$213$	−45.1042	−3.09049
$214$	8.60229	0.588040
$215$	2.95200	0.201325
$216$	−15.2880	−1.04021
$217$	14.1475	0.960395
$218$	−15.8524	−1.07366
$219$	32.7036	2.20990
$220$	0.294899	0.0198821
$221$	5.42026	0.364606
$222$	3.61180	0.242408
$223$	5.67181	0.379813	0.189906	−	0.981802i	$-0.439182\pi$
$223$	5.67181	0.379813	0.189906	+	0.981802i	$0.439182\pi$
$224$	2.99147	0.199876
$225$	−35.6678	−2.37785
$226$	−1.67460	−0.111393
$227$	21.6723	1.43844	0.719220	−	0.694782i	$-0.244499\pi$
$227$	21.6723	1.43844	0.719220	+	0.694782i	$0.244499\pi$
$228$	−3.26778	−0.216414
$229$	−11.7675	−0.777616	−0.388808	−	0.921319i	$-0.627113\pi$
$229$	−11.7675	−0.777616	−0.388808	+	0.921319i	$0.627113\pi$
$230$	5.29294	0.349006
$231$	−4.83982	−0.318436
$232$	0.0817407	0.00536654
$233$	18.8101	1.23229	0.616147	−	0.787631i	$-0.288693\pi$
$233$	18.8101	1.23229	0.616147	+	0.787631i	$0.288693\pi$
$234$	21.8615	1.42913
$235$	−1.25171	−0.0816523
$236$	10.6946	0.696160
$237$	−13.0525	−0.847850
$238$	−5.69502	−0.369153
$239$	1.98719	0.128541	0.0642703	−	0.997933i	$-0.479528\pi$
$239$	1.98719	0.128541	0.0642703	+	0.997933i	$0.479528\pi$
$240$	1.94642	0.125641
$241$	−16.8906	−1.08802	−0.544010	−	0.839079i	$-0.683095\pi$
$241$	−16.8906	−1.08802	−0.544010	+	0.839079i	$0.683095\pi$
$242$	10.7549	0.691350
$243$	42.1132	2.70156
$244$	6.78989	0.434678
$245$	1.16085	0.0741642
$246$	−28.8227	−1.83767
$247$	2.84715	0.181160
$248$	4.72927	0.300309
$249$	−33.8299	−2.14388
$250$	5.74507	0.363350
$251$	−30.2392	−1.90868	−0.954341	−	0.298719i	$-0.903441\pi$
$251$	−30.2392	−1.90868	−0.954341	+	0.298719i	$0.903441\pi$
$252$	−22.9697	−1.44696
$253$	−4.39951	−0.276595
$254$	19.0429	1.19486
$255$	−3.70549	−0.232047
$256$	1.00000	0.0625000
$257$	8.61342	0.537290	0.268645	−	0.963239i	$-0.413424\pi$
$257$	8.61342	0.537290	0.268645	+	0.963239i	$0.413424\pi$
$258$	−16.1952	−1.00827
$259$	3.30641	0.205450
$260$	−1.69587	−0.105174
$261$	−0.627638	−0.0388498
$262$	3.50230	0.216373
$263$	2.64067	0.162831	0.0814154	−	0.996680i	$-0.474056\pi$
$263$	2.64067	0.162831	0.0814154	+	0.996680i	$0.474056\pi$
$264$	−1.61787	−0.0995730
$265$	0.556124	0.0341624
$266$	−2.99147	−0.183419
$267$	−36.1111	−2.20996
$268$	−3.28824	−0.200861
$269$	9.86437	0.601441	0.300721	−	0.953712i	$-0.402773\pi$
$269$	9.86437	0.601441	0.300721	+	0.953712i	$0.402773\pi$
$270$	−9.10612	−0.554181
$271$	9.89556	0.601113	0.300556	−	0.953764i	$-0.402828\pi$
$271$	9.89556	0.601113	0.300556	+	0.953764i	$0.402828\pi$
$272$	−1.90375	−0.115432
$273$	27.8323	1.68448
$274$	8.32344	0.502837
$275$	−2.29983	−0.138685
$276$	−29.0380	−1.74788
$277$	−15.4663	−0.929278	−0.464639	−	0.885500i	$-0.653816\pi$
$277$	−15.4663	−0.929278	−0.464639	+	0.885500i	$0.653816\pi$
$278$	−9.07860	−0.544498
$279$	−36.3132	−2.17402
$280$	1.78184	0.106485
$281$	12.1275	0.723467	0.361734	−	0.932281i	$-0.382185\pi$
$281$	12.1275	0.723467	0.361734	+	0.932281i	$0.382185\pi$
$282$	6.86708	0.408929
$283$	22.4200	1.33273	0.666364	−	0.745626i	$-0.267850\pi$
$283$	22.4200	1.33273	0.666364	+	0.745626i	$0.267850\pi$
$284$	−13.8027	−0.819039
$285$	−1.94642	−0.115296
$286$	1.40962	0.0833523
$287$	−26.3856	−1.55749
$288$	−7.67840	−0.452454
$289$	−13.3757	−0.786808
$290$	0.0486880	0.00285906
$291$	−22.4947	−1.31866
$292$	10.0079	0.585667
$293$	31.7772	1.85644	0.928221	−	0.372029i	$-0.121338\pi$
$293$	31.7772	1.85644	0.928221	+	0.372029i	$0.121338\pi$
$294$	−6.36865	−0.371427
$295$	6.37013	0.370883
$296$	1.10528	0.0642429
$297$	7.56903	0.439200
$298$	21.6964	1.25684
$299$	25.3002	1.46315
$300$	−15.1795	−0.876391
$301$	−14.8258	−0.854545
$302$	5.30999	0.305556
$303$	−47.0832	−2.70486
$304$	−1.00000	−0.0573539
$305$	4.04433	0.231577
$306$	14.6177	0.835640
$307$	−31.2263	−1.78218	−0.891089	−	0.453828i	$-0.850058\pi$
$307$	−31.2263	−1.78218	−0.891089	+	0.453828i	$0.850058\pi$
$308$	−1.48107	−0.0843918
$309$	−61.5347	−3.50059
$310$	2.81694	0.159991
$311$	3.56826	0.202338	0.101169	−	0.994869i	$-0.467742\pi$
$311$	3.56826	0.202338	0.101169	+	0.994869i	$0.467742\pi$
$312$	9.30386	0.526727
$313$	−9.21005	−0.520583	−0.260291	−	0.965530i	$-0.583819\pi$
$313$	−9.21005	−0.520583	−0.260291	+	0.965530i	$0.583819\pi$
$314$	10.6815	0.602792
$315$	−13.6817	−0.770875
$316$	−3.99429	−0.224697
$317$	−29.0885	−1.63377	−0.816887	−	0.576798i	$-0.804302\pi$
$317$	−29.0885	−1.63377	−0.816887	+	0.576798i	$0.804302\pi$
$318$	−3.05099	−0.171091
$319$	−0.0404696	−0.00226586
$320$	0.595639	0.0332972
$321$	−28.1104	−1.56897
$322$	−26.5827	−1.48140
$323$	1.90375	0.105927
$324$	26.9226	1.49570
$325$	13.2256	0.733625
$326$	3.40812	0.188758
$327$	51.8020	2.86466
$328$	−8.82027	−0.487018
$329$	6.28644	0.346583
$330$	−0.963666	−0.0530481
$331$	−11.4134	−0.627336	−0.313668	−	0.949533i	$-0.601558\pi$
$331$	−11.4134	−0.627336	−0.313668	+	0.949533i	$0.601558\pi$
$332$	−10.3525	−0.568170
$333$	−8.48675	−0.465071
$334$	−0.313528	−0.0171555
$335$	−1.95861	−0.107010
$336$	−9.77549	−0.533296
$337$	−10.7156	−0.583715	−0.291858	−	0.956462i	$-0.594273\pi$
$337$	−10.7156	−0.583715	−0.291858	+	0.956462i	$0.594273\pi$
$338$	4.89375	0.266185
$339$	5.47222	0.297210
$340$	−1.13395	−0.0614969
$341$	−2.34145	−0.126797
$342$	7.67840	0.415200
$343$	15.1102	0.815873
$344$	−4.95602	−0.267211
$345$	−17.2962	−0.931195
$346$	0.365104	0.0196281
$347$	−7.44385	−0.399607	−0.199803	−	0.979836i	$-0.564030\pi$
$347$	−7.44385	−0.399607	−0.199803	+	0.979836i	$0.564030\pi$
$348$	−0.267111	−0.0143186
$349$	27.2479	1.45855	0.729273	−	0.684223i	$-0.239858\pi$
$349$	27.2479	1.45855	0.729273	+	0.684223i	$0.239858\pi$
$350$	−13.8960	−0.742775
$351$	−43.5271	−2.32331
$352$	−0.495097	−0.0263888
$353$	−4.62222	−0.246016	−0.123008	−	0.992406i	$-0.539254\pi$
$353$	−4.62222	−0.246016	−0.123008	+	0.992406i	$0.539254\pi$
$354$	−34.9477	−1.85745
$355$	−8.22142	−0.436348
$356$	−11.0506	−0.585683
$357$	18.6101	0.984949
$358$	0.0604155	0.00319306
$359$	28.0275	1.47923	0.739617	−	0.673028i	$-0.235007\pi$
$359$	28.0275	1.47923	0.739617	+	0.673028i	$0.235007\pi$
$360$	−4.57355	−0.241047
$361$	1.00000	0.0526316
$362$	−22.5406	−1.18471
$363$	−35.1446	−1.84461
$364$	8.51717	0.446421
$365$	5.96108	0.312017
$366$	−22.1879	−1.15978
$367$	12.8611	0.671345	0.335672	−	0.941979i	$-0.391037\pi$
$367$	12.8611	0.671345	0.335672	+	0.941979i	$0.391037\pi$
$368$	−8.88616	−0.463223
$369$	67.7255	3.52565
$370$	0.658346	0.0342258
$371$	−2.79302	−0.145006
$372$	−15.4542	−0.801265
$373$	18.6028	0.963215	0.481608	−	0.876387i	$-0.340053\pi$
$373$	18.6028	0.963215	0.481608	+	0.876387i	$0.340053\pi$
$374$	0.942541	0.0487376
$375$	−18.7736	−0.969466
$376$	2.10145	0.108374
$377$	0.232728	0.0119861
$378$	45.7336	2.35228
$379$	27.9555	1.43598	0.717989	−	0.696055i	$-0.245063\pi$
$379$	27.9555	1.43598	0.717989	+	0.696055i	$0.245063\pi$
$380$	−0.595639	−0.0305556
$381$	−62.2280	−3.18804
$382$	−2.41398	−0.123510
$383$	27.7445	1.41768	0.708839	−	0.705371i	$-0.249219\pi$
$383$	27.7445	1.41768	0.708839	+	0.705371i	$0.249219\pi$
$384$	−3.26778	−0.166758
$385$	−0.882184	−0.0449602
$386$	−17.3804	−0.884640
$387$	38.0543	1.93441
$388$	−6.88378	−0.349471
$389$	14.6916	0.744892	0.372446	−	0.928054i	$-0.378519\pi$
$389$	14.6916	0.744892	0.372446	+	0.928054i	$0.378519\pi$
$390$	5.54174	0.280617
$391$	16.9170	0.855530
$392$	−1.94892	−0.0984354
$393$	−11.4448	−0.577312
$394$	−1.96372	−0.0989306
$395$	−2.37916	−0.119708
$396$	3.80155	0.191035
$397$	−2.97296	−0.149208	−0.0746042	−	0.997213i	$-0.523769\pi$
$397$	−2.97296	−0.149208	−0.0746042	+	0.997213i	$0.523769\pi$
$398$	−6.83514	−0.342614
$399$	9.77549	0.489386
$400$	−4.64521	−0.232261
$401$	37.9993	1.89760	0.948798	−	0.315883i	$-0.102301\pi$
$401$	37.9993	1.89760	0.948798	+	0.315883i	$0.102301\pi$
$402$	10.7453	0.535925
$403$	13.4649	0.670737
$404$	−14.4083	−0.716840
$405$	16.0361	0.796842
$406$	−0.244525	−0.0121356
$407$	−0.547219	−0.0271247
$408$	6.22104	0.307987
$409$	−7.73451	−0.382447	−0.191224	−	0.981547i	$-0.561246\pi$
$409$	−7.73451	−0.382447	−0.191224	+	0.981547i	$0.561246\pi$
$410$	−5.25370	−0.259462
$411$	−27.1992	−1.34164
$412$	−18.8307	−0.927723
$413$	−31.9927	−1.57426
$414$	68.2315	3.35339
$415$	−6.16638	−0.302696
$416$	2.84715	0.139593
$417$	29.6669	1.45279
$418$	0.495097	0.0242160
$419$	−28.8403	−1.40894	−0.704470	−	0.709734i	$-0.748815\pi$
$419$	−28.8403	−1.40894	−0.704470	+	0.709734i	$0.748815\pi$
$420$	−5.82266	−0.284117
$421$	−14.2895	−0.696426	−0.348213	−	0.937415i	$-0.613211\pi$
$421$	−14.2895	−0.696426	−0.348213	+	0.937415i	$0.613211\pi$
$422$	1.00000	0.0486792
$423$	−16.1358	−0.784548
$424$	−0.933659	−0.0453425
$425$	8.84332	0.428964
$426$	45.1042	2.18530
$427$	−20.3118	−0.982956
$428$	−8.60229	−0.415807
$429$	−4.60631	−0.222395
$430$	−2.95200	−0.142358
$431$	18.3478	0.883782	0.441891	−	0.897069i	$-0.354308\pi$
$431$	18.3478	0.883782	0.441891	+	0.897069i	$0.354308\pi$
$432$	15.2880	0.735543
$433$	6.45669	0.310289	0.155144	−	0.987892i	$-0.450416\pi$
$433$	6.45669	0.310289	0.155144	+	0.987892i	$0.450416\pi$
$434$	−14.1475	−0.679102
$435$	−0.159102	−0.00762834
$436$	15.8524	0.759190
$437$	8.88616	0.425083
$438$	−32.7036	−1.56264
$439$	−33.6109	−1.60416	−0.802082	−	0.597215i	$-0.796274\pi$
$439$	−33.6109	−1.60416	−0.802082	+	0.597215i	$0.796274\pi$
$440$	−0.294899	−0.0140588
$441$	14.9646	0.712599
$442$	−5.42026	−0.257815
$443$	−23.1564	−1.10019	−0.550097	−	0.835101i	$-0.685409\pi$
$443$	−23.1564	−1.10019	−0.550097	+	0.835101i	$0.685409\pi$
$444$	−3.61180	−0.171409
$445$	−6.58219	−0.312026
$446$	−5.67181	−0.268568
$447$	−70.8992	−3.35342
$448$	−2.99147	−0.141334
$449$	10.3057	0.486355	0.243178	−	0.969982i	$-0.421810\pi$
$449$	10.3057	0.486355	0.243178	+	0.969982i	$0.421810\pi$
$450$	35.6678	1.68140
$451$	4.36689	0.205629
$452$	1.67460	0.0787664
$453$	−17.3519	−0.815263
$454$	−21.6723	−1.01713
$455$	5.07316	0.237833
$456$	3.26778	0.153028
$457$	−12.5752	−0.588243	−0.294122	−	0.955768i	$-0.595027\pi$
$457$	−12.5752	−0.588243	−0.294122	+	0.955768i	$0.595027\pi$
$458$	11.7675	0.549858
$459$	−29.1045	−1.35848
$460$	−5.29294	−0.246785
$461$	41.3655	1.92658	0.963292	−	0.268458i	$-0.0865139\pi$
$461$	41.3655	1.92658	0.963292	+	0.268458i	$0.0865139\pi$
$462$	4.83982	0.225169
$463$	1.50708	0.0700399	0.0350199	−	0.999387i	$-0.488851\pi$
$463$	1.50708	0.0700399	0.0350199	+	0.999387i	$0.488851\pi$
$464$	−0.0817407	−0.00379472
$465$	−9.20514	−0.426878
$466$	−18.8101	−0.871363
$467$	−35.0388	−1.62140	−0.810702	−	0.585459i	$-0.800914\pi$
$467$	−35.0388	−1.62140	−0.810702	+	0.585459i	$0.800914\pi$
$468$	−21.8615	−1.01055
$469$	9.83670	0.454216
$470$	1.25171	0.0577369
$471$	−34.9048	−1.60833
$472$	−10.6946	−0.492260
$473$	2.45371	0.112822
$474$	13.0525	0.599520
$475$	4.64521	0.213137
$476$	5.69502	0.261031
$477$	7.16901	0.328246
$478$	−1.98719	−0.0908919
$479$	−14.0967	−0.644096	−0.322048	−	0.946723i	$-0.604371\pi$
$479$	−14.0967	−0.644096	−0.322048	+	0.946723i	$0.604371\pi$
$480$	−1.94642	−0.0888414
$481$	3.14689	0.143486
$482$	16.8906	0.769346
$483$	86.8665	3.95256
$484$	−10.7549	−0.488858
$485$	−4.10025	−0.186183
$486$	−42.1132	−1.91029
$487$	−17.0378	−0.772057	−0.386029	−	0.922487i	$-0.626153\pi$
$487$	−17.0378	−0.772057	−0.386029	+	0.922487i	$0.626153\pi$
$488$	−6.78989	−0.307364
$489$	−11.1370	−0.503631
$490$	−1.16085	−0.0524420
$491$	0.328562	0.0148278	0.00741391	−	0.999973i	$-0.497640\pi$
$491$	0.328562	0.0148278	0.00741391	+	0.999973i	$0.497640\pi$
$492$	28.8227	1.29943
$493$	0.155614	0.00700849
$494$	−2.84715	−0.128099
$495$	2.26435	0.101775
$496$	−4.72927	−0.212351
$497$	41.2904	1.85213
$498$	33.8299	1.51595
$499$	1.49375	0.0668694	0.0334347	−	0.999441i	$-0.489355\pi$
$499$	1.49375	0.0668694	0.0334347	+	0.999441i	$0.489355\pi$
$500$	−5.74507	−0.256927
$501$	1.02454	0.0457732
$502$	30.2392	1.34964
$503$	19.7560	0.880877	0.440438	−	0.897783i	$-0.354823\pi$
$503$	19.7560	0.880877	0.440438	+	0.897783i	$0.354823\pi$
$504$	22.9697	1.02315
$505$	−8.58215	−0.381901
$506$	4.39951	0.195582
$507$	−15.9917	−0.710216
$508$	−19.0429	−0.844892
$509$	−9.61557	−0.426203	−0.213101	−	0.977030i	$-0.568356\pi$
$509$	−9.61557	−0.426203	−0.213101	+	0.977030i	$0.568356\pi$
$510$	3.70549	0.164082
$511$	−29.9383	−1.32439
$512$	−1.00000	−0.0441942
$513$	−15.2880	−0.674981
$514$	−8.61342	−0.379922
$515$	−11.2163	−0.494250
$516$	16.1952	0.712953
$517$	−1.04042	−0.0457577
$518$	−3.30641	−0.145275
$519$	−1.19308	−0.0523704
$520$	1.69587	0.0743689
$521$	−32.5266	−1.42502	−0.712508	−	0.701664i	$-0.752441\pi$
$521$	−32.5266	−1.42502	−0.712508	+	0.701664i	$0.752441\pi$
$522$	0.627638	0.0274709
$523$	1.88304	0.0823395	0.0411697	−	0.999152i	$-0.486892\pi$
$523$	1.88304	0.0823395	0.0411697	+	0.999152i	$0.486892\pi$
$524$	−3.50230	−0.152999
$525$	45.4092	1.98182
$526$	−2.64067	−0.115139
$527$	9.00335	0.392192
$528$	1.61787	0.0704087
$529$	55.9638	2.43321
$530$	−0.556124	−0.0241565
$531$	82.1175	3.56360
$532$	2.99147	0.129697
$533$	−25.1126	−1.08775
$534$	36.1111	1.56268
$535$	−5.12386	−0.221524
$536$	3.28824	0.142030
$537$	−0.197425	−0.00851950
$538$	−9.86437	−0.425283
$539$	0.964905	0.0415614
$540$	9.10612	0.391865
$541$	−0.671178	−0.0288562	−0.0144281	−	0.999896i	$-0.504593\pi$
$541$	−0.671178	−0.0288562	−0.0144281	+	0.999896i	$0.504593\pi$
$542$	−9.89556	−0.425051
$543$	73.6578	3.16096
$544$	1.90375	0.0816226
$545$	9.44228	0.404463
$546$	−27.8323	−1.19111
$547$	9.52062	0.407073	0.203536	−	0.979067i	$-0.434757\pi$
$547$	9.52062	0.407073	0.203536	+	0.979067i	$0.434757\pi$
$548$	−8.32344	−0.355560
$549$	52.1355	2.22509
$550$	2.29983	0.0980652
$551$	0.0817407	0.00348227
$552$	29.0380	1.23594
$553$	11.9488	0.508116
$554$	15.4663	0.657099
$555$	−2.15133	−0.0913189
$556$	9.07860	0.385018
$557$	8.07247	0.342041	0.171021	−	0.985267i	$-0.445293\pi$
$557$	8.07247	0.342041	0.171021	+	0.985267i	$0.445293\pi$
$558$	36.3132	1.53726
$559$	−14.1105	−0.596811
$560$	−1.78184	−0.0752965
$561$	−3.08002	−0.130038
$562$	−12.1275	−0.511569
$563$	−30.9043	−1.30246	−0.651230	−	0.758880i	$-0.725747\pi$
$563$	−30.9043	−1.30246	−0.651230	+	0.758880i	$0.725747\pi$
$564$	−6.86708	−0.289156
$565$	0.997455	0.0419633
$566$	−22.4200	−0.942381
$567$	−80.5382	−3.38229
$568$	13.8027	0.579148
$569$	30.3513	1.27239	0.636196	−	0.771527i	$-0.280507\pi$
$569$	30.3513	1.27239	0.636196	+	0.771527i	$0.280507\pi$
$570$	1.94642	0.0815265
$571$	−45.8428	−1.91846	−0.959231	−	0.282624i	$-0.908795\pi$
$571$	−45.8428	−1.91846	−0.959231	+	0.282624i	$0.908795\pi$
$572$	−1.40962	−0.0589390
$573$	7.88836	0.329541
$574$	26.3856	1.10131
$575$	41.2781	1.72142
$576$	7.67840	0.319933
$577$	23.9754	0.998107	0.499053	−	0.866571i	$-0.333681\pi$
$577$	23.9754	0.998107	0.499053	+	0.866571i	$0.333681\pi$
$578$	13.3757	0.556357
$579$	56.7954	2.36034
$580$	−0.0486880	−0.00202166
$581$	30.9694	1.28483
$582$	22.4947	0.932435
$583$	0.462252	0.0191445
$584$	−10.0079	−0.414129
$585$	−13.0216	−0.538376
$586$	−31.7772	−1.31270
$587$	8.49237	0.350517	0.175259	−	0.984522i	$-0.443924\pi$
$587$	8.49237	0.350517	0.175259	+	0.984522i	$0.443924\pi$
$588$	6.36865	0.262639
$589$	4.72927	0.194866
$590$	−6.37013	−0.262254
$591$	6.41699	0.263960
$592$	−1.10528	−0.0454266
$593$	−38.2367	−1.57019	−0.785097	−	0.619372i	$-0.787387\pi$
$593$	−38.2367	−1.57019	−0.785097	+	0.619372i	$0.787387\pi$
$594$	−7.56903	−0.310561
$595$	3.39217	0.139066
$596$	−21.6964	−0.888721
$597$	22.3357	0.914141
$598$	−25.3002	−1.03460
$599$	18.7729	0.767038	0.383519	−	0.923533i	$-0.374712\pi$
$599$	18.7729	0.767038	0.383519	+	0.923533i	$0.374712\pi$
$600$	15.1795	0.619702
$601$	39.4013	1.60721	0.803607	−	0.595160i	$-0.202912\pi$
$601$	39.4013	1.60721	0.803607	+	0.595160i	$0.202912\pi$
$602$	14.8258	0.604255
$603$	−25.2484	−1.02820
$604$	−5.30999	−0.216060
$605$	−6.40603	−0.260442
$606$	47.0832	1.91262
$607$	−38.0332	−1.54372	−0.771860	−	0.635793i	$-0.780673\pi$
$607$	−38.0332	−1.54372	−0.771860	+	0.635793i	$0.780673\pi$
$608$	1.00000	0.0405554
$609$	0.799055	0.0323793
$610$	−4.04433	−0.163750
$611$	5.98314	0.242052
$612$	−14.6177	−0.590887
$613$	−10.1886	−0.411514	−0.205757	−	0.978603i	$-0.565966\pi$
$613$	−10.1886	−0.411514	−0.205757	+	0.978603i	$0.565966\pi$
$614$	31.2263	1.26019
$615$	17.1679	0.692278
$616$	1.48107	0.0596740
$617$	7.87871	0.317185	0.158593	−	0.987344i	$-0.449304\pi$
$617$	7.87871	0.317185	0.158593	+	0.987344i	$0.449304\pi$
$618$	61.5347	2.47529
$619$	−11.3787	−0.457348	−0.228674	−	0.973503i	$-0.573439\pi$
$619$	−11.3787	−0.457348	−0.228674	+	0.973503i	$0.573439\pi$
$620$	−2.81694	−0.113131
$621$	−135.851	−5.45153
$622$	−3.56826	−0.143074
$623$	33.0577	1.32443
$624$	−9.30386	−0.372452
$625$	19.8041	0.792163
$626$	9.21005	0.368108
$627$	−1.61787	−0.0646115
$628$	−10.6815	−0.426238
$629$	2.10417	0.0838987
$630$	13.6817	0.545091
$631$	8.36517	0.333012	0.166506	−	0.986040i	$-0.446751\pi$
$631$	8.36517	0.333012	0.166506	+	0.986040i	$0.446751\pi$
$632$	3.99429	0.158884
$633$	−3.26778	−0.129883
$634$	29.0885	1.15525
$635$	−11.3427	−0.450121
$636$	3.05099	0.120980
$637$	−5.54887	−0.219854
$638$	0.0404696	0.00160221
$639$	−105.982	−4.19260
$640$	−0.595639	−0.0235447
$641$	46.8610	1.85090	0.925450	−	0.378871i	$-0.123688\pi$
$641$	46.8610	1.85090	0.925450	+	0.378871i	$0.123688\pi$
$642$	28.1104	1.10943
$643$	13.5912	0.535985	0.267992	−	0.963421i	$-0.413640\pi$
$643$	13.5912	0.535985	0.267992	+	0.963421i	$0.413640\pi$
$644$	26.5827	1.04751
$645$	9.64648	0.379830
$646$	−1.90375	−0.0749020
$647$	29.5982	1.16363	0.581813	−	0.813323i	$-0.302344\pi$
$647$	29.5982	1.16363	0.581813	+	0.813323i	$0.302344\pi$
$648$	−26.9226	−1.05762
$649$	5.29488	0.207842
$650$	−13.2256	−0.518751
$651$	46.2309	1.81193
$652$	−3.40812	−0.133472
$653$	24.0933	0.942845	0.471423	−	0.881907i	$-0.343741\pi$
$653$	24.0933	0.942845	0.471423	+	0.881907i	$0.343741\pi$
$654$	−51.8020	−2.02562
$655$	−2.08611	−0.0815110
$656$	8.82027	0.344374
$657$	76.8444	2.99799
$658$	−6.28644	−0.245071
$659$	20.5042	0.798729	0.399365	−	0.916792i	$-0.369231\pi$
$659$	20.5042	0.798729	0.399365	+	0.916792i	$0.369231\pi$
$660$	0.963666	0.0375107
$661$	−43.2392	−1.68181	−0.840905	−	0.541183i	$-0.817977\pi$
$661$	−43.2392	−1.68181	−0.840905	+	0.541183i	$0.817977\pi$
$662$	11.4134	0.443593
$663$	17.7122	0.687885
$664$	10.3525	0.401757
$665$	1.78184	0.0690968
$666$	8.48675	0.328855
$667$	0.726361	0.0281248
$668$	0.313528	0.0121308
$669$	18.5342	0.716575
$670$	1.95861	0.0756676
$671$	3.36166	0.129775
$672$	9.77549	0.377098
$673$	−22.0677	−0.850649	−0.425325	−	0.905041i	$-0.639840\pi$
$673$	−22.0677	−0.850649	−0.425325	+	0.905041i	$0.639840\pi$
$674$	10.7156	0.412749
$675$	−71.0159	−2.73340
$676$	−4.89375	−0.188221
$677$	−2.07471	−0.0797375	−0.0398688	−	0.999205i	$-0.512694\pi$
$677$	−2.07471	−0.0797375	−0.0398688	+	0.999205i	$0.512694\pi$
$678$	−5.47222	−0.210159
$679$	20.5927	0.790274
$680$	1.13395	0.0434849
$681$	70.8203	2.71384
$682$	2.34145	0.0896588
$683$	−42.4940	−1.62599	−0.812994	−	0.582272i	$-0.802164\pi$
$683$	−42.4940	−1.62599	−0.812994	+	0.582272i	$0.802164\pi$
$684$	−7.67840	−0.293591
$685$	−4.95777	−0.189427
$686$	−15.1102	−0.576909
$687$	−38.4535	−1.46709
$688$	4.95602	0.188946
$689$	−2.65827	−0.101272
$690$	17.2962	0.658455
$691$	16.9513	0.644858	0.322429	−	0.946594i	$-0.395501\pi$
$691$	16.9513	0.644858	0.322429	+	0.946594i	$0.395501\pi$
$692$	−0.365104	−0.0138792
$693$	−11.3722	−0.431996
$694$	7.44385	0.282565
$695$	5.40757	0.205121
$696$	0.267111	0.0101248
$697$	−16.7916	−0.636026
$698$	−27.2479	−1.03135
$699$	61.4675	2.32491
$700$	13.8960	0.525221
$701$	47.9954	1.81276	0.906380	−	0.422464i	$-0.138835\pi$
$701$	47.9954	1.81276	0.906380	+	0.422464i	$0.138835\pi$
$702$	43.5271	1.64283
$703$	1.10528	0.0416863
$704$	0.495097	0.0186597
$705$	−4.09030	−0.154050
$706$	4.62222	0.173959
$707$	43.1021	1.62102
$708$	34.9477	1.31341
$709$	45.8860	1.72329	0.861643	−	0.507514i	$-0.169436\pi$
$709$	45.8860	1.72329	0.861643	+	0.507514i	$0.169436\pi$
$710$	8.22142	0.308544
$711$	−30.6698	−1.15021
$712$	11.0506	0.414140
$713$	42.0251	1.57385
$714$	−18.6101	−0.696464
$715$	−0.839622	−0.0314001
$716$	−0.0604155	−0.00225783
$717$	6.49370	0.242512
$718$	−28.0275	−1.04598
$719$	10.0234	0.373810	0.186905	−	0.982378i	$-0.440154\pi$
$719$	10.0234	0.373810	0.186905	+	0.982378i	$0.440154\pi$
$720$	4.57355	0.170446
$721$	56.3316	2.09790
$722$	−1.00000	−0.0372161
$723$	−55.1948	−2.05272
$724$	22.5406	0.837715
$725$	0.379703	0.0141018
$726$	35.1446	1.30434
$727$	11.7520	0.435859	0.217930	−	0.975965i	$-0.430070\pi$
$727$	11.7520	0.435859	0.217930	+	0.975965i	$0.430070\pi$
$728$	−8.51717	−0.315667
$729$	56.8489	2.10551
$730$	−5.96108	−0.220630
$731$	−9.43501	−0.348967
$732$	22.1879	0.820088
$733$	−33.3254	−1.23090	−0.615451	−	0.788175i	$-0.711026\pi$
$733$	−33.3254	−1.23090	−0.615451	+	0.788175i	$0.711026\pi$
$734$	−12.8611	−0.474712
$735$	3.79342	0.139922
$736$	8.88616	0.327548
$737$	−1.62800	−0.0599681
$738$	−67.7255	−2.49301
$739$	49.0404	1.80398	0.901989	−	0.431758i	$-0.142107\pi$
$739$	49.0404	1.80398	0.901989	+	0.431758i	$0.142107\pi$
$740$	−0.658346	−0.0242013
$741$	9.30386	0.341786
$742$	2.79302	0.102535
$743$	20.6653	0.758137	0.379068	−	0.925369i	$-0.376245\pi$
$743$	20.6653	0.758137	0.379068	+	0.925369i	$0.376245\pi$
$744$	15.4542	0.566580
$745$	−12.9232	−0.473471
$746$	−18.6028	−0.681096
$747$	−79.4909	−2.90842
$748$	−0.942541	−0.0344627
$749$	25.7335	0.940282
$750$	18.7736	0.685516
$751$	−15.4919	−0.565309	−0.282655	−	0.959222i	$-0.591215\pi$
$751$	−15.4919	−0.565309	−0.282655	+	0.959222i	$0.591215\pi$
$752$	−2.10145	−0.0766321
$753$	−98.8151	−3.60102
$754$	−0.232728	−0.00847545
$755$	−3.16284	−0.115107
$756$	−45.7336	−1.66331
$757$	11.3261	0.411652	0.205826	−	0.978589i	$-0.434012\pi$
$757$	11.3261	0.411652	0.205826	+	0.978589i	$0.434012\pi$
$758$	−27.9555	−1.01539
$759$	−14.3766	−0.521839
$760$	0.595639	0.0216061
$761$	−43.3859	−1.57274	−0.786370	−	0.617756i	$-0.788042\pi$
$761$	−43.3859	−1.57274	−0.786370	+	0.617756i	$0.788042\pi$
$762$	62.2280	2.25428
$763$	−47.4219	−1.71679
$764$	2.41398	0.0873348
$765$	−8.70690	−0.314798
$766$	−27.7445	−1.00245
$767$	−30.4492	−1.09946
$768$	3.26778	0.117916
$769$	−6.40277	−0.230890	−0.115445	−	0.993314i	$-0.536829\pi$
$769$	−6.40277	−0.230890	−0.115445	+	0.993314i	$0.536829\pi$
$770$	0.882184	0.0317917
$771$	28.1468	1.01368
$772$	17.3804	0.625535
$773$	−21.1472	−0.760611	−0.380305	−	0.924861i	$-0.624181\pi$
$773$	−21.1472	−0.760611	−0.380305	+	0.924861i	$0.624181\pi$
$774$	−38.0543	−1.36783
$775$	21.9685	0.789131
$776$	6.88378	0.247113
$777$	10.8046	0.387613
$778$	−14.6916	−0.526718
$779$	−8.82027	−0.316019
$780$	−5.54174	−0.198426
$781$	−6.83367	−0.244528
$782$	−16.9170	−0.604951
$783$	−1.24965	−0.0446588
$784$	1.94892	0.0696043
$785$	−6.36232	−0.227081
$786$	11.4448	0.408221
$787$	42.7108	1.52247	0.761237	−	0.648474i	$-0.224592\pi$
$787$	42.7108	1.52247	0.761237	+	0.648474i	$0.224592\pi$
$788$	1.96372	0.0699545
$789$	8.62914	0.307205
$790$	2.37916	0.0846466
$791$	−5.00951	−0.178118
$792$	−3.80155	−0.135082
$793$	−19.3318	−0.686493
$794$	2.97296	0.105506
$795$	1.81729	0.0644527
$796$	6.83514	0.242265
$797$	−30.7253	−1.08834	−0.544172	−	0.838973i	$-0.683156\pi$
$797$	−30.7253	−1.08834	−0.544172	+	0.838973i	$0.683156\pi$
$798$	−9.77549	−0.346048
$799$	4.00064	0.141532
$800$	4.64521	0.164233
$801$	−84.8512	−2.99807
$802$	−37.9993	−1.34180
$803$	4.95487	0.174854
$804$	−10.7453	−0.378956
$805$	15.8337	0.558065
$806$	−13.4649	−0.474282
$807$	32.2346	1.13471
$808$	14.4083	0.506882
$809$	−9.04409	−0.317973	−0.158987	−	0.987281i	$-0.550823\pi$
$809$	−9.04409	−0.317973	−0.158987	+	0.987281i	$0.550823\pi$
$810$	−16.0361	−0.563452
$811$	26.4572	0.929039	0.464520	−	0.885563i	$-0.346227\pi$
$811$	26.4572	0.929039	0.464520	+	0.885563i	$0.346227\pi$
$812$	0.244525	0.00858116
$813$	32.3365	1.13409
$814$	0.547219	0.0191800
$815$	−2.03001	−0.0711080
$816$	−6.22104	−0.217780
$817$	−4.95602	−0.173389
$818$	7.73451	0.270431
$819$	65.3982	2.28520
$820$	5.25370	0.183467
$821$	−26.8504	−0.937085	−0.468543	−	0.883441i	$-0.655221\pi$
$821$	−26.8504	−0.937085	−0.468543	+	0.883441i	$0.655221\pi$
$822$	27.1992	0.948680
$823$	1.78159	0.0621025	0.0310512	−	0.999518i	$-0.490114\pi$
$823$	1.78159	0.0621025	0.0310512	+	0.999518i	$0.490114\pi$
$824$	18.8307	0.655999
$825$	−7.51535	−0.261651
$826$	31.9927	1.11317
$827$	9.31898	0.324053	0.162026	−	0.986786i	$-0.448197\pi$
$827$	9.31898	0.324053	0.162026	+	0.986786i	$0.448197\pi$
$828$	−68.2315	−2.37121
$829$	9.01445	0.313085	0.156542	−	0.987671i	$-0.449965\pi$
$829$	9.01445	0.313085	0.156542	+	0.987671i	$0.449965\pi$
$830$	6.16638	0.214038
$831$	−50.5404	−1.75323
$832$	−2.84715	−0.0987071
$833$	−3.71026	−0.128553
$834$	−29.6669	−1.02728
$835$	0.186750	0.00646274
$836$	−0.495097	−0.0171233
$837$	−72.3010	−2.49909
$838$	28.8403	0.996270
$839$	−32.4366	−1.11984	−0.559918	−	0.828548i	$-0.689167\pi$
$839$	−32.4366	−1.11984	−0.559918	+	0.828548i	$0.689167\pi$
$840$	5.82266	0.200901
$841$	−28.9933	−0.999770
$842$	14.2895	0.492447
$843$	39.6301	1.36493
$844$	−1.00000	−0.0344214
$845$	−2.91491	−0.100276
$846$	16.1358	0.554759
$847$	32.1729	1.10548
$848$	0.933659	0.0320620
$849$	73.2635	2.51440
$850$	−8.84332	−0.303323
$851$	9.82166	0.336682
$852$	−45.1042	−1.54524
$853$	−4.75390	−0.162771	−0.0813853	−	0.996683i	$-0.525934\pi$
$853$	−4.75390	−0.162771	−0.0813853	+	0.996683i	$0.525934\pi$
$854$	20.3118	0.695055
$855$	−4.57355	−0.156412
$856$	8.60229	0.294020
$857$	−54.9257	−1.87623	−0.938113	−	0.346328i	$-0.887428\pi$
$857$	−54.9257	−1.87623	−0.938113	+	0.346328i	$0.887428\pi$
$858$	4.60631	0.157257
$859$	−38.8642	−1.32603	−0.663015	−	0.748606i	$-0.730723\pi$
$859$	−38.8642	−1.32603	−0.663015	+	0.748606i	$0.730723\pi$
$860$	2.95200	0.100662
$861$	−86.2224	−2.93845
$862$	−18.3478	−0.624928
$863$	22.0537	0.750717	0.375359	−	0.926880i	$-0.377520\pi$
$863$	22.0537	0.750717	0.375359	+	0.926880i	$0.377520\pi$
$864$	−15.2880	−0.520107
$865$	−0.217470	−0.00739420
$866$	−6.45669	−0.219407
$867$	−43.7090	−1.48444
$868$	14.1475	0.480197
$869$	−1.97756	−0.0670843
$870$	0.159102	0.00539405
$871$	9.36212	0.317223
$872$	−15.8524	−0.536828
$873$	−52.8564	−1.78892
$874$	−8.88616	−0.300579
$875$	17.1862	0.581000
$876$	32.7036	1.10495
$877$	30.4868	1.02947	0.514733	−	0.857351i	$-0.327891\pi$
$877$	30.4868	1.02947	0.514733	+	0.857351i	$0.327891\pi$
$878$	33.6109	1.13431
$879$	103.841	3.50247
$880$	0.294899	0.00994105
$881$	−32.1836	−1.08429	−0.542147	−	0.840283i	$-0.682389\pi$
$881$	−32.1836	−1.08429	−0.542147	+	0.840283i	$0.682389\pi$
$882$	−14.9646	−0.503884
$883$	−16.1616	−0.543880	−0.271940	−	0.962314i	$-0.587665\pi$
$883$	−16.1616	−0.543880	−0.271940	+	0.962314i	$0.587665\pi$
$884$	5.42026	0.182303
$885$	20.8162	0.699729
$886$	23.1564	0.777955
$887$	−14.1693	−0.475757	−0.237879	−	0.971295i	$-0.576452\pi$
$887$	−14.1693	−0.475757	−0.237879	+	0.971295i	$0.576452\pi$
$888$	3.61180	0.121204
$889$	56.9663	1.91059
$890$	6.58219	0.220636
$891$	13.3293	0.446548
$892$	5.67181	0.189906
$893$	2.10145	0.0703224
$894$	70.8992	2.37122
$895$	−0.0359858	−0.00120287
$896$	2.99147	0.0999382
$897$	82.6756	2.76046
$898$	−10.3057	−0.343905
$899$	0.386574	0.0128930
$900$	−35.6678	−1.18893
$901$	−1.77745	−0.0592155
$902$	−4.36689	−0.145402
$903$	−48.4475	−1.61223
$904$	−1.67460	−0.0556963
$905$	13.4261	0.446298
$906$	17.3519	0.576478
$907$	31.5563	1.04781	0.523904	−	0.851777i	$-0.324475\pi$
$907$	31.5563	1.04781	0.523904	+	0.851777i	$0.324475\pi$
$908$	21.6723	0.719220
$909$	−110.633	−3.66945
$910$	−5.07316	−0.168174
$911$	12.4511	0.412525	0.206262	−	0.978497i	$-0.433870\pi$
$911$	12.4511	0.412525	0.206262	+	0.978497i	$0.433870\pi$
$912$	−3.26778	−0.108207
$913$	−5.12552	−0.169630
$914$	12.5752	0.415951
$915$	13.2160	0.436907
$916$	−11.7675	−0.388808
$917$	10.4770	0.345983
$918$	29.1045	0.960590
$919$	−9.82004	−0.323933	−0.161967	−	0.986796i	$-0.551784\pi$
$919$	−9.82004	−0.323933	−0.161967	+	0.986796i	$0.551784\pi$
$920$	5.29294	0.174503
$921$	−102.041	−3.36235
$922$	−41.3655	−1.36230
$923$	39.2983	1.29352
$924$	−4.83982	−0.159218
$925$	5.13425	0.168813
$926$	−1.50708	−0.0495257
$927$	−144.590	−4.74895
$928$	0.0817407	0.00268327
$929$	13.3004	0.436373	0.218187	−	0.975907i	$-0.429986\pi$
$929$	13.3004	0.436373	0.218187	+	0.975907i	$0.429986\pi$
$930$	9.20514	0.301849
$931$	−1.94892	−0.0638733
$932$	18.8101	0.616147
$933$	11.6603	0.381741
$934$	35.0388	1.14651
$935$	−0.561414	−0.0183602
$936$	21.8615	0.714567
$937$	18.6557	0.609456	0.304728	−	0.952439i	$-0.401434\pi$
$937$	18.6557	0.609456	0.304728	+	0.952439i	$0.401434\pi$
$938$	−9.83670	−0.321180
$939$	−30.0964	−0.982160
$940$	−1.25171	−0.0408262
$941$	−10.2926	−0.335528	−0.167764	−	0.985827i	$-0.553655\pi$
$941$	−10.2926	−0.335528	−0.167764	+	0.985827i	$0.553655\pi$
$942$	34.9048	1.13726
$943$	−78.3783	−2.55235
$944$	10.6946	0.348080
$945$	−27.2407	−0.886140
$946$	−2.45371	−0.0797770
$947$	−28.6077	−0.929627	−0.464813	−	0.885409i	$-0.653879\pi$
$947$	−28.6077	−0.929627	−0.464813	+	0.885409i	$0.653879\pi$
$948$	−13.0525	−0.423925
$949$	−28.4939	−0.924952
$950$	−4.64521	−0.150711
$951$	−95.0549	−3.08237
$952$	−5.69502	−0.184577
$953$	−1.65219	−0.0535197	−0.0267598	−	0.999642i	$-0.508519\pi$
$953$	−1.65219	−0.0535197	−0.0267598	+	0.999642i	$0.508519\pi$
$954$	−7.16901	−0.232105
$955$	1.43786	0.0465281
$956$	1.98719	0.0642703
$957$	−0.132246	−0.00427490
$958$	14.0967	0.455445
$959$	24.8994	0.804042
$960$	1.94642	0.0628204
$961$	−8.63397	−0.278515
$962$	−3.14689	−0.101460
$963$	−66.0518	−2.12849
$964$	−16.8906	−0.544010
$965$	10.3525	0.333257
$966$	−86.8665	−2.79488
$967$	−4.93976	−0.158852	−0.0794259	−	0.996841i	$-0.525309\pi$
$967$	−4.93976	−0.158852	−0.0794259	+	0.996841i	$0.525309\pi$
$968$	10.7549	0.345675
$969$	6.22104	0.199848
$970$	4.10025	0.131651
$971$	54.2923	1.74232	0.871161	−	0.490997i	$-0.163367\pi$
$971$	54.2923	1.74232	0.871161	+	0.490997i	$0.163367\pi$
$972$	42.1132	1.35078
$973$	−27.1584	−0.870658
$974$	17.0378	0.545927
$975$	43.2184	1.38410
$976$	6.78989	0.217339
$977$	26.1764	0.837458	0.418729	−	0.908111i	$-0.362476\pi$
$977$	26.1764	0.837458	0.418729	+	0.908111i	$0.362476\pi$
$978$	11.1370	0.356121
$979$	−5.47114	−0.174858
$980$	1.16085	0.0370821
$981$	121.721	3.88624
$982$	−0.328562	−0.0104848
$983$	−10.0687	−0.321141	−0.160570	−	0.987024i	$-0.551333\pi$
$983$	−10.0687	−0.321141	−0.160570	+	0.987024i	$0.551333\pi$
$984$	−28.8227	−0.918834
$985$	1.16967	0.0372686
$986$	−0.155614	−0.00495575
$987$	20.5427	0.653882
$988$	2.84715	0.0905799
$989$	−44.0400	−1.40039
$990$	−2.26435	−0.0719659
$991$	−52.6995	−1.67406	−0.837028	−	0.547160i	$-0.815709\pi$
$991$	−52.6995	−1.67406	−0.837028	+	0.547160i	$0.815709\pi$
$992$	4.72927	0.150155
$993$	−37.2964	−1.18357
$994$	−41.2904	−1.30965
$995$	4.07128	0.129068
$996$	−33.8299	−1.07194
$997$	−26.1407	−0.827885	−0.413943	−	0.910303i	$-0.635849\pi$
$997$	−26.1407	−0.827885	−0.413943	+	0.910303i	$0.635849\pi$
$998$	−1.49375	−0.0472838
$999$	−16.8974	−0.534611

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8018.2.a.f.1.34	✓	34

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8018.2.a.f.1.34	✓	34	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:	\( N \)	\(=\)	\( 8018 = 2 \cdot 19 \cdot 211 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8018.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +3.26778 q^{3} +1.00000 q^{4} +0.595639 q^{5} -3.26778 q^{6} -2.99147 q^{7} -1.00000 q^{8} +7.67840 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +3.26778 q^{3} +1.00000 q^{4} +0.595639 q^{5} -3.26778 q^{6} -2.99147 q^{7} -1.00000 q^{8} +7.67840 q^{9} -0.595639 q^{10} +0.495097 q^{11} +3.26778 q^{12} -2.84715 q^{13} +2.99147 q^{14} +1.94642 q^{15} +1.00000 q^{16} -1.90375 q^{17} -7.67840 q^{18} -1.00000 q^{19} +0.595639 q^{20} -9.77549 q^{21} -0.495097 q^{22} -8.88616 q^{23} -3.26778 q^{24} -4.64521 q^{25} +2.84715 q^{26} +15.2880 q^{27} -2.99147 q^{28} -0.0817407 q^{29} -1.94642 q^{30} -4.72927 q^{31} -1.00000 q^{32} +1.61787 q^{33} +1.90375 q^{34} -1.78184 q^{35} +7.67840 q^{36} -1.10528 q^{37} +1.00000 q^{38} -9.30386 q^{39} -0.595639 q^{40} +8.82027 q^{41} +9.77549 q^{42} +4.95602 q^{43} +0.495097 q^{44} +4.57355 q^{45} +8.88616 q^{46} -2.10145 q^{47} +3.26778 q^{48} +1.94892 q^{49} +4.64521 q^{50} -6.22104 q^{51} -2.84715 q^{52} +0.933659 q^{53} -15.2880 q^{54} +0.294899 q^{55} +2.99147 q^{56} -3.26778 q^{57} +0.0817407 q^{58} +10.6946 q^{59} +1.94642 q^{60} +6.78989 q^{61} +4.72927 q^{62} -22.9697 q^{63} +1.00000 q^{64} -1.69587 q^{65} -1.61787 q^{66} -3.28824 q^{67} -1.90375 q^{68} -29.0380 q^{69} +1.78184 q^{70} -13.8027 q^{71} -7.67840 q^{72} +10.0079 q^{73} +1.10528 q^{74} -15.1795 q^{75} -1.00000 q^{76} -1.48107 q^{77} +9.30386 q^{78} -3.99429 q^{79} +0.595639 q^{80} +26.9226 q^{81} -8.82027 q^{82} -10.3525 q^{83} -9.77549 q^{84} -1.13395 q^{85} -4.95602 q^{86} -0.267111 q^{87} -0.495097 q^{88} -11.0506 q^{89} -4.57355 q^{90} +8.51717 q^{91} -8.88616 q^{92} -15.4542 q^{93} +2.10145 q^{94} -0.595639 q^{95} -3.26778 q^{96} -6.88378 q^{97} -1.94892 q^{98} +3.80155 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 34 q - 34 q^{2} - 10 q^{3} + 34 q^{4} + 7 q^{5} + 10 q^{6} - 6 q^{7} - 34 q^{8} + 38 q^{9}+O(q^{10}) \) 34 * q - 34 * q^2 - 10 * q^3 + 34 * q^4 + 7 * q^5 + 10 * q^6 - 6 * q^7 - 34 * q^8 + 38 * q^9	\( 34 q - 34 q^{2} - 10 q^{3} + 34 q^{4} + 7 q^{5} + 10 q^{6} - 6 q^{7} - 34 q^{8} + 38 q^{9} - 7 q^{10} + 4 q^{11} - 10 q^{12} - 5 q^{13} + 6 q^{14} - 17 q^{15} + 34 q^{16} + 8 q^{17} - 38 q^{18} - 34 q^{19} + 7 q^{20} - 4 q^{22} - 24 q^{23} + 10 q^{24} + 5 q^{25} + 5 q^{26} - 31 q^{27} - 6 q^{28} + 24 q^{29} + 17 q^{30} - 28 q^{31} - 34 q^{32} - 16 q^{33} - 8 q^{34} + 2 q^{35} + 38 q^{36} - 36 q^{37} + 34 q^{38} - 9 q^{39} - 7 q^{40} + 9 q^{41} - 24 q^{43} + 4 q^{44} + 22 q^{45} + 24 q^{46} - 29 q^{47} - 10 q^{48} + 22 q^{49} - 5 q^{50} - 21 q^{51} - 5 q^{52} - 9 q^{53} + 31 q^{54} - 28 q^{55} + 6 q^{56} + 10 q^{57} - 24 q^{58} - 28 q^{59} - 17 q^{60} + 23 q^{61} + 28 q^{62} - 27 q^{63} + 34 q^{64} - 6 q^{65} + 16 q^{66} - 51 q^{67} + 8 q^{68} - 17 q^{69} - 2 q^{70} - 31 q^{71} - 38 q^{72} - 26 q^{73} + 36 q^{74} - 109 q^{75} - 34 q^{76} - 28 q^{77} + 9 q^{78} - 36 q^{79} + 7 q^{80} + 6 q^{81} - 9 q^{82} - 10 q^{83} - 32 q^{85} + 24 q^{86} - 8 q^{87} - 4 q^{88} - 34 q^{89} - 22 q^{90} - 41 q^{91} - 24 q^{92} - 33 q^{93} + 29 q^{94} - 7 q^{95} + 10 q^{96} - 56 q^{97} - 22 q^{98} - 28 q^{99}+O(q^{100}) \) 34 * q - 34 * q^2 - 10 * q^3 + 34 * q^4 + 7 * q^5 + 10 * q^6 - 6 * q^7 - 34 * q^8 + 38 * q^9 - 7 * q^10 + 4 * q^11 - 10 * q^12 - 5 * q^13 + 6 * q^14 - 17 * q^15 + 34 * q^16 + 8 * q^17 - 38 * q^18 - 34 * q^19 + 7 * q^20 - 4 * q^22 - 24 * q^23 + 10 * q^24 + 5 * q^25 + 5 * q^26 - 31 * q^27 - 6 * q^28 + 24 * q^29 + 17 * q^30 - 28 * q^31 - 34 * q^32 - 16 * q^33 - 8 * q^34 + 2 * q^35 + 38 * q^36 - 36 * q^37 + 34 * q^38 - 9 * q^39 - 7 * q^40 + 9 * q^41 - 24 * q^43 + 4 * q^44 + 22 * q^45 + 24 * q^46 - 29 * q^47 - 10 * q^48 + 22 * q^49 - 5 * q^50 - 21 * q^51 - 5 * q^52 - 9 * q^53 + 31 * q^54 - 28 * q^55 + 6 * q^56 + 10 * q^57 - 24 * q^58 - 28 * q^59 - 17 * q^60 + 23 * q^61 + 28 * q^62 - 27 * q^63 + 34 * q^64 - 6 * q^65 + 16 * q^66 - 51 * q^67 + 8 * q^68 - 17 * q^69 - 2 * q^70 - 31 * q^71 - 38 * q^72 - 26 * q^73 + 36 * q^74 - 109 * q^75 - 34 * q^76 - 28 * q^77 + 9 * q^78 - 36 * q^79 + 7 * q^80 + 6 * q^81 - 9 * q^82 - 10 * q^83 - 32 * q^85 + 24 * q^86 - 8 * q^87 - 4 * q^88 - 34 * q^89 - 22 * q^90 - 41 * q^91 - 24 * q^92 - 33 * q^93 + 29 * q^94 - 7 * q^95 + 10 * q^96 - 56 * q^97 - 22 * q^98 - 28 * q^99

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