LMFDB - Embedded newform 4009.2.a.c.1.25

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4009,2,Mod(1,4009)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4009, 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("4009.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4009 = 19 \cdot 211 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4009.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:	$32.0120261703$
Analytic rank:	$1$
Dimension:	$71$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.25
Character	$\chi$	$=$	4009.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.19842 q^{2} +2.70792 q^{3} -0.563786 q^{4} +3.20608 q^{5} -3.24523 q^{6} -3.88119 q^{7} +3.07250 q^{8} +4.33283 q^{9} +O(q^{10})$	\(q-1.19842 q^{2} +2.70792 q^{3} -0.563786 q^{4} +3.20608 q^{5} -3.24523 q^{6} -3.88119 q^{7} +3.07250 q^{8} +4.33283 q^{9} -3.84224 q^{10} -3.11687 q^{11} -1.52669 q^{12} +2.05325 q^{13} +4.65131 q^{14} +8.68181 q^{15} -2.55457 q^{16} -0.497871 q^{17} -5.19256 q^{18} +1.00000 q^{19} -1.80754 q^{20} -10.5100 q^{21} +3.73532 q^{22} -7.71448 q^{23} +8.32008 q^{24} +5.27895 q^{25} -2.46066 q^{26} +3.60921 q^{27} +2.18816 q^{28} -9.87575 q^{29} -10.4045 q^{30} -6.49395 q^{31} -3.08354 q^{32} -8.44023 q^{33} +0.596660 q^{34} -12.4434 q^{35} -2.44279 q^{36} -3.16656 q^{37} -1.19842 q^{38} +5.56004 q^{39} +9.85067 q^{40} +2.47233 q^{41} +12.5954 q^{42} -8.25730 q^{43} +1.75725 q^{44} +13.8914 q^{45} +9.24520 q^{46} -6.05306 q^{47} -6.91758 q^{48} +8.06367 q^{49} -6.32641 q^{50} -1.34820 q^{51} -1.15759 q^{52} -9.46860 q^{53} -4.32535 q^{54} -9.99293 q^{55} -11.9250 q^{56} +2.70792 q^{57} +11.8353 q^{58} +13.5649 q^{59} -4.89468 q^{60} -9.42192 q^{61} +7.78249 q^{62} -16.8166 q^{63} +8.80452 q^{64} +6.58289 q^{65} +10.1150 q^{66} +10.1709 q^{67} +0.280693 q^{68} -20.8902 q^{69} +14.9125 q^{70} +3.40372 q^{71} +13.3126 q^{72} +16.4265 q^{73} +3.79488 q^{74} +14.2950 q^{75} -0.563786 q^{76} +12.0972 q^{77} -6.66328 q^{78} -10.6645 q^{79} -8.19017 q^{80} -3.22505 q^{81} -2.96290 q^{82} -9.32433 q^{83} +5.92537 q^{84} -1.59622 q^{85} +9.89573 q^{86} -26.7428 q^{87} -9.57657 q^{88} +3.86208 q^{89} -16.6478 q^{90} -7.96907 q^{91} +4.34932 q^{92} -17.5851 q^{93} +7.25412 q^{94} +3.20608 q^{95} -8.34997 q^{96} +18.7338 q^{97} -9.66367 q^{98} -13.5049 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 71 q - 15 q^{2} - 8 q^{3} + 69 q^{4} - 18 q^{5} - 9 q^{6} - 19 q^{7} - 39 q^{8} + 63 q^{9}+O(q^{10}) $ 71 * q - 15 * q^2 - 8 * q^3 + 69 * q^4 - 18 * q^5 - 9 * q^6 - 19 * q^7 - 39 * q^8 + 63 * q^9	\( 71 q - 15 q^{2} - 8 q^{3} + 69 q^{4} - 18 q^{5} - 9 q^{6} - 19 q^{7} - 39 q^{8} + 63 q^{9} - 10 q^{10} - 52 q^{11} - 9 q^{12} - 15 q^{13} - 53 q^{14} - 33 q^{15} + 53 q^{16} - 10 q^{17} - 35 q^{18} + 71 q^{19} - 33 q^{20} - 38 q^{21} - 6 q^{22} - 65 q^{23} - 30 q^{24} + 51 q^{25} - 4 q^{26} - 23 q^{27} - 29 q^{28} - 97 q^{29} - 27 q^{30} - 53 q^{31} - 78 q^{32} - 17 q^{33} - 24 q^{34} - 38 q^{35} + 24 q^{36} - 33 q^{37} - 15 q^{38} - 86 q^{39} + 25 q^{40} - 69 q^{41} + 64 q^{42} - 10 q^{43} - 94 q^{44} - 34 q^{45} - 6 q^{46} - 37 q^{47} - q^{48} + 74 q^{49} - 41 q^{50} - 46 q^{51} - 30 q^{52} - 50 q^{53} - 17 q^{54} - 30 q^{55} - 116 q^{56} - 8 q^{57} + 11 q^{58} - 93 q^{59} - 56 q^{60} - 18 q^{61} - q^{62} - 84 q^{63} + 93 q^{64} - 78 q^{65} - 53 q^{66} - 5 q^{67} - 9 q^{68} - 69 q^{69} - 10 q^{70} - 221 q^{71} - 73 q^{72} - 34 q^{73} - 58 q^{74} - 70 q^{75} + 69 q^{76} - 2 q^{77} + 7 q^{78} - 68 q^{79} - 71 q^{80} + 39 q^{81} + 26 q^{82} - 45 q^{83} - 10 q^{84} - 44 q^{85} - 80 q^{86} - 7 q^{87} - 46 q^{88} - 143 q^{89} + 41 q^{90} - 30 q^{91} - 46 q^{92} + 32 q^{93} + 41 q^{94} - 18 q^{95} - 140 q^{96} - 18 q^{97} - 97 q^{98} - 142 q^{99}+O(q^{100}) \) 71 * q - 15 * q^2 - 8 * q^3 + 69 * q^4 - 18 * q^5 - 9 * q^6 - 19 * q^7 - 39 * q^8 + 63 * q^9 - 10 * q^10 - 52 * q^11 - 9 * q^12 - 15 * q^13 - 53 * q^14 - 33 * q^15 + 53 * q^16 - 10 * q^17 - 35 * q^18 + 71 * q^19 - 33 * q^20 - 38 * q^21 - 6 * q^22 - 65 * q^23 - 30 * q^24 + 51 * q^25 - 4 * q^26 - 23 * q^27 - 29 * q^28 - 97 * q^29 - 27 * q^30 - 53 * q^31 - 78 * q^32 - 17 * q^33 - 24 * q^34 - 38 * q^35 + 24 * q^36 - 33 * q^37 - 15 * q^38 - 86 * q^39 + 25 * q^40 - 69 * q^41 + 64 * q^42 - 10 * q^43 - 94 * q^44 - 34 * q^45 - 6 * q^46 - 37 * q^47 - q^48 + 74 * q^49 - 41 * q^50 - 46 * q^51 - 30 * q^52 - 50 * q^53 - 17 * q^54 - 30 * q^55 - 116 * q^56 - 8 * q^57 + 11 * q^58 - 93 * q^59 - 56 * q^60 - 18 * q^61 - q^62 - 84 * q^63 + 93 * q^64 - 78 * q^65 - 53 * q^66 - 5 * q^67 - 9 * q^68 - 69 * q^69 - 10 * q^70 - 221 * q^71 - 73 * q^72 - 34 * q^73 - 58 * q^74 - 70 * q^75 + 69 * q^76 - 2 * q^77 + 7 * q^78 - 68 * q^79 - 71 * q^80 + 39 * q^81 + 26 * q^82 - 45 * q^83 - 10 * q^84 - 44 * q^85 - 80 * q^86 - 7 * q^87 - 46 * q^88 - 143 * q^89 + 41 * q^90 - 30 * q^91 - 46 * q^92 + 32 * q^93 + 41 * q^94 - 18 * q^95 - 140 * q^96 - 18 * q^97 - 97 * q^98 - 142 * 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 $

$2$	−1.19842	−0.847412	−0.423706	−	0.905800i	$-0.639271\pi$
$2$	−1.19842	−0.847412	−0.423706	+	0.905800i	$0.639271\pi$
$3$	2.70792	1.56342	0.781709	−	0.623643i	$-0.214348\pi$
$3$	2.70792	1.56342	0.781709	+	0.623643i	$0.214348\pi$
$4$	−0.563786	−0.281893
$5$	3.20608	1.43380	0.716901	−	0.697175i	$-0.245560\pi$
$5$	3.20608	1.43380	0.716901	+	0.697175i	$0.245560\pi$
$6$	−3.24523	−1.32486
$7$	−3.88119	−1.46695	−0.733477	−	0.679715i	$-0.762104\pi$
$7$	−3.88119	−1.46695	−0.733477	+	0.679715i	$0.762104\pi$
$8$	3.07250	1.08629
$9$	4.33283	1.44428
$10$	−3.84224	−1.21502
$11$	−3.11687	−0.939771	−0.469886	−	0.882727i	$-0.655705\pi$
$11$	−3.11687	−0.939771	−0.469886	+	0.882727i	$0.655705\pi$
$12$	−1.52669	−0.440717
$13$	2.05325	0.569470	0.284735	−	0.958606i	$-0.408094\pi$
$13$	2.05325	0.569470	0.284735	+	0.958606i	$0.408094\pi$
$14$	4.65131	1.24311
$15$	8.68181	2.24163
$16$	−2.55457	−0.638643
$17$	−0.497871	−0.120752	−0.0603758	−	0.998176i	$-0.519230\pi$
$17$	−0.497871	−0.120752	−0.0603758	+	0.998176i	$0.519230\pi$
$18$	−5.19256	−1.22390
$19$	1.00000	0.229416
$19$	1.00000	0.229416
$20$	−1.80754	−0.404179
$21$	−10.5100	−2.29346
$22$	3.73532	0.796374
$23$	−7.71448	−1.60858	−0.804290	−	0.594236i	$-0.797454\pi$
$23$	−7.71448	−1.60858	−0.804290	+	0.594236i	$0.797454\pi$
$24$	8.32008	1.69833
$25$	5.27895	1.05579
$26$	−2.46066	−0.482575
$27$	3.60921	0.694592
$28$	2.18816	0.413524
$29$	−9.87575	−1.83388	−0.916941	−	0.399023i	$-0.869349\pi$
$29$	−9.87575	−1.83388	−0.916941	+	0.399023i	$0.869349\pi$
$30$	−10.4045	−1.89959
$31$	−6.49395	−1.16635	−0.583174	−	0.812347i	$-0.698190\pi$
$31$	−6.49395	−1.16635	−0.583174	+	0.812347i	$0.698190\pi$
$32$	−3.08354	−0.545097
$33$	−8.44023	−1.46926
$34$	0.596660	0.102326
$35$	−12.4434	−2.10332
$36$	−2.44279	−0.407132
$37$	−3.16656	−0.520580	−0.260290	−	0.965531i	$-0.583818\pi$
$37$	−3.16656	−0.520580	−0.260290	+	0.965531i	$0.583818\pi$
$38$	−1.19842	−0.194410
$39$	5.56004	0.890319
$40$	9.85067	1.55753
$41$	2.47233	0.386113	0.193057	−	0.981188i	$-0.438160\pi$
$41$	2.47233	0.386113	0.193057	+	0.981188i	$0.438160\pi$
$42$	12.5954	1.94351
$43$	−8.25730	−1.25923	−0.629613	−	0.776909i	$-0.716787\pi$
$43$	−8.25730	−1.25923	−0.629613	+	0.776909i	$0.716787\pi$
$44$	1.75725	0.264915
$45$	13.8914	2.07081
$46$	9.24520	1.36313
$47$	−6.05306	−0.882929	−0.441465	−	0.897279i	$-0.645541\pi$
$47$	−6.05306	−0.882929	−0.441465	+	0.897279i	$0.645541\pi$
$48$	−6.91758	−0.998467
$49$	8.06367	1.15195
$50$	−6.32641	−0.894689
$51$	−1.34820	−0.188785
$52$	−1.15759	−0.160529
$53$	−9.46860	−1.30061	−0.650306	−	0.759672i	$-0.725359\pi$
$53$	−9.46860	−1.30061	−0.650306	+	0.759672i	$0.725359\pi$
$54$	−4.32535	−0.588606
$55$	−9.99293	−1.34745
$56$	−11.9250	−1.59354
$57$	2.70792	0.358673
$58$	11.8353	1.55405
$59$	13.5649	1.76600	0.883002	−	0.469369i	$-0.155519\pi$
$59$	13.5649	1.76600	0.883002	+	0.469369i	$0.155519\pi$
$60$	−4.89468	−0.631901
$61$	−9.42192	−1.20635	−0.603176	−	0.797608i	$-0.706098\pi$
$61$	−9.42192	−1.20635	−0.603176	+	0.797608i	$0.706098\pi$
$62$	7.78249	0.988378
$63$	−16.8166	−2.11869
$64$	8.80452	1.10057
$65$	6.58289	0.816507
$66$	10.1150	1.24507
$67$	10.1709	1.24257	0.621286	−	0.783584i	$-0.286610\pi$
$67$	10.1709	1.24257	0.621286	+	0.783584i	$0.286610\pi$
$68$	0.280693	0.0340390
$69$	−20.8902	−2.51489
$70$	14.9125	1.78238
$71$	3.40372	0.403947	0.201974	−	0.979391i	$-0.435264\pi$
$71$	3.40372	0.403947	0.201974	+	0.979391i	$0.435264\pi$
$72$	13.3126	1.56891
$73$	16.4265	1.92258	0.961288	−	0.275546i	$-0.0888587\pi$
$73$	16.4265	1.92258	0.961288	+	0.275546i	$0.0888587\pi$
$74$	3.79488	0.441145
$75$	14.2950	1.65064
$76$	−0.563786	−0.0646707
$77$	12.0972	1.37860
$78$	−6.66328	−0.754467
$79$	−10.6645	−1.19985	−0.599923	−	0.800058i	$-0.704802\pi$
$79$	−10.6645	−1.19985	−0.599923	+	0.800058i	$0.704802\pi$
$80$	−8.19017	−0.915689
$81$	−3.22505	−0.358339
$82$	−2.96290	−0.327197
$83$	−9.32433	−1.02348	−0.511739	−	0.859141i	$-0.670999\pi$
$83$	−9.32433	−1.02348	−0.511739	+	0.859141i	$0.670999\pi$
$84$	5.92537	0.646511
$85$	−1.59622	−0.173134
$86$	9.89573	1.06708
$87$	−26.7428	−2.86712
$88$	−9.57657	−1.02087
$89$	3.86208	0.409380	0.204690	−	0.978827i	$-0.434381\pi$
$89$	3.86208	0.409380	0.204690	+	0.978827i	$0.434381\pi$
$90$	−16.6478	−1.75483
$91$	−7.96907	−0.835385
$92$	4.34932	0.453448
$93$	−17.5851	−1.82349
$94$	7.25412	0.748205
$95$	3.20608	0.328937
$96$	−8.34997	−0.852215
$97$	18.7338	1.90213	0.951064	−	0.308995i	$-0.0999927\pi$
$97$	18.7338	1.90213	0.951064	+	0.308995i	$0.0999927\pi$
$98$	−9.66367	−0.976178
$99$	−13.5049	−1.35729
$100$	−2.97620	−0.297620
$101$	5.99882	0.596905	0.298453	−	0.954424i	$-0.403530\pi$
$101$	5.99882	0.596905	0.298453	+	0.954424i	$0.403530\pi$
$102$	1.61571	0.159979
$103$	3.70960	0.365518	0.182759	−	0.983158i	$-0.441497\pi$
$103$	3.70960	0.365518	0.182759	+	0.983158i	$0.441497\pi$
$104$	6.30861	0.618610
$105$	−33.6958	−3.28837
$106$	11.3474	1.10215
$107$	8.13504	0.786444	0.393222	−	0.919444i	$-0.371360\pi$
$107$	8.13504	0.786444	0.393222	+	0.919444i	$0.371360\pi$
$108$	−2.03482	−0.195801
$109$	−13.9567	−1.33681	−0.668406	−	0.743797i	$-0.733023\pi$
$109$	−13.9567	−1.33681	−0.668406	+	0.743797i	$0.733023\pi$
$110$	11.9757	1.14184
$111$	−8.57480	−0.813884
$112$	9.91480	0.936860
$113$	0.449846	0.0423180	0.0211590	−	0.999776i	$-0.493264\pi$
$113$	0.449846	0.0423180	0.0211590	+	0.999776i	$0.493264\pi$
$114$	−3.24523	−0.303944
$115$	−24.7333	−2.30639
$116$	5.56781	0.516958
$117$	8.89640	0.822472
$118$	−16.2565	−1.49653
$119$	1.93234	0.177137
$120$	26.6748	2.43507
$121$	−1.28513	−0.116830
$122$	11.2914	1.02228
$123$	6.69488	0.603657
$124$	3.66120	0.328785
$125$	0.894337	0.0799919
$126$	20.1533	1.79540
$127$	−5.60621	−0.497471	−0.248735	−	0.968571i	$-0.580015\pi$
$127$	−5.60621	−0.497471	−0.248735	+	0.968571i	$0.580015\pi$
$128$	−4.38446	−0.387535
$129$	−22.3601	−1.96870
$130$	−7.88908	−0.691918
$131$	8.74842	0.764353	0.382176	−	0.924089i	$-0.375175\pi$
$131$	8.74842	0.764353	0.382176	+	0.924089i	$0.375175\pi$
$132$	4.75848	0.414173
$133$	−3.88119	−0.336542
$134$	−12.1890	−1.05297
$135$	11.5714	0.995908
$136$	−1.52971	−0.131171
$137$	−8.08914	−0.691102	−0.345551	−	0.938400i	$-0.612308\pi$
$137$	−8.08914	−0.691102	−0.345551	+	0.938400i	$0.612308\pi$
$138$	25.0353	2.13114
$139$	−10.7015	−0.907690	−0.453845	−	0.891081i	$-0.649948\pi$
$139$	−10.7015	−0.907690	−0.453845	+	0.891081i	$0.649948\pi$
$140$	7.01542	0.592911
$141$	−16.3912	−1.38039
$142$	−4.07909	−0.342310
$143$	−6.39972	−0.535171
$144$	−11.0685	−0.922379
$145$	−31.6625	−2.62942
$146$	−19.6859	−1.62921
$147$	21.8358	1.80098
$148$	1.78526	0.146748
$149$	18.7012	1.53206	0.766029	−	0.642806i	$-0.222230\pi$
$149$	18.7012	1.53206	0.766029	+	0.642806i	$0.222230\pi$
$150$	−17.1314	−1.39877
$151$	−7.46205	−0.607253	−0.303626	−	0.952791i	$-0.598197\pi$
$151$	−7.46205	−0.607253	−0.303626	+	0.952791i	$0.598197\pi$
$152$	3.07250	0.249212
$153$	−2.15719	−0.174399
$154$	−14.4975	−1.16824
$155$	−20.8201	−1.67231
$156$	−3.13467	−0.250975
$157$	4.13346	0.329886	0.164943	−	0.986303i	$-0.447256\pi$
$157$	4.13346	0.329886	0.164943	+	0.986303i	$0.447256\pi$
$158$	12.7805	1.01676
$159$	−25.6402	−2.03340
$160$	−9.88606	−0.781562
$161$	29.9414	2.35971
$162$	3.86497	0.303661
$163$	−1.38472	−0.108460	−0.0542300	−	0.998528i	$-0.517270\pi$
$163$	−1.38472	−0.108460	−0.0542300	+	0.998528i	$0.517270\pi$
$164$	−1.39387	−0.108843
$165$	−27.0601	−2.10662
$166$	11.1745	0.867308
$167$	12.5563	0.971632	0.485816	−	0.874061i	$-0.338523\pi$
$167$	12.5563	0.971632	0.485816	+	0.874061i	$0.338523\pi$
$168$	−32.2918	−2.49137
$169$	−8.78416	−0.675704
$170$	1.91294	0.146716
$171$	4.33283	0.331340
$172$	4.65535	0.354967
$173$	−2.25245	−0.171251	−0.0856253	−	0.996327i	$-0.527289\pi$
$173$	−2.25245	−0.171251	−0.0856253	+	0.996327i	$0.527289\pi$
$174$	32.0491	2.42964
$175$	−20.4886	−1.54879
$176$	7.96227	0.600179
$177$	36.7328	2.76100
$178$	−4.62840	−0.346913
$179$	−0.150229	−0.0112287	−0.00561433	−	0.999984i	$-0.501787\pi$
$179$	−0.150229	−0.0112287	−0.00561433	+	0.999984i	$0.501787\pi$
$180$	−7.83178	−0.583747
$181$	2.87333	0.213573	0.106786	−	0.994282i	$-0.465944\pi$
$181$	2.87333	0.213573	0.106786	+	0.994282i	$0.465944\pi$
$182$	9.55030	0.707916
$183$	−25.5138	−1.88603
$184$	−23.7027	−1.74739
$185$	−10.1523	−0.746409
$186$	21.0744	1.54525
$187$	1.55180	0.113479
$188$	3.41263	0.248892
$189$	−14.0080	−1.01893
$190$	−3.84224	−0.278745
$191$	−0.482914	−0.0349425	−0.0174712	−	0.999847i	$-0.505562\pi$
$191$	−0.482914	−0.0349425	−0.0174712	+	0.999847i	$0.505562\pi$
$192$	23.8420	1.72064
$193$	−1.60638	−0.115630	−0.0578148	−	0.998327i	$-0.518413\pi$
$193$	−1.60638	−0.115630	−0.0578148	+	0.998327i	$0.518413\pi$
$194$	−22.4510	−1.61189
$195$	17.8259	1.27654
$196$	−4.54618	−0.324727
$197$	−17.7811	−1.26685	−0.633427	−	0.773802i	$-0.718352\pi$
$197$	−17.7811	−1.26685	−0.633427	+	0.773802i	$0.718352\pi$
$198$	16.1845	1.15018
$199$	26.3161	1.86550	0.932750	−	0.360524i	$-0.117402\pi$
$199$	26.3161	1.86550	0.932750	+	0.360524i	$0.117402\pi$
$200$	16.2196	1.14690
$201$	27.5420	1.94266
$202$	−7.18912	−0.505825
$203$	38.3297	2.69022
$204$	0.760094	0.0532172
$205$	7.92650	0.553610
$206$	−4.44567	−0.309744
$207$	−33.4256	−2.32324
$208$	−5.24518	−0.363688
$209$	−3.11687	−0.215598
$210$	40.3818	2.78661
$211$	1.00000	0.0688428
$211$	1.00000	0.0688428
$212$	5.33826	0.366633
$213$	9.21701	0.631539
$214$	−9.74921	−0.666442
$215$	−26.4736	−1.80548
$216$	11.0893	0.754530
$217$	25.2043	1.71098
$218$	16.7260	1.13283
$219$	44.4816	3.00579
$220$	5.63387	0.379836
$221$	−1.02226	−0.0687643
$222$	10.2762	0.689695
$223$	−5.63034	−0.377035	−0.188518	−	0.982070i	$-0.560368\pi$
$223$	−5.63034	−0.377035	−0.188518	+	0.982070i	$0.560368\pi$
$224$	11.9678	0.799632
$225$	22.8728	1.52485
$226$	−0.539106	−0.0358608
$227$	0.606143	0.0402311	0.0201156	−	0.999798i	$-0.493597\pi$
$227$	0.606143	0.0402311	0.0201156	+	0.999798i	$0.493597\pi$
$228$	−1.52669	−0.101107
$229$	−9.03693	−0.597177	−0.298589	−	0.954382i	$-0.596516\pi$
$229$	−9.03693	−0.597177	−0.298589	+	0.954382i	$0.596516\pi$
$230$	29.6409	1.95446
$231$	32.7582	2.15533
$232$	−30.3432	−1.99213
$233$	6.94748	0.455144	0.227572	−	0.973761i	$-0.426921\pi$
$233$	6.94748	0.455144	0.227572	+	0.973761i	$0.426921\pi$
$234$	−10.6616	−0.696973
$235$	−19.4066	−1.26595
$236$	−7.64772	−0.497824
$237$	−28.8785	−1.87586
$238$	−2.31575	−0.150108
$239$	−18.1478	−1.17389	−0.586943	−	0.809628i	$-0.699669\pi$
$239$	−18.1478	−1.17389	−0.586943	+	0.809628i	$0.699669\pi$
$240$	−22.1783	−1.43160
$241$	1.41197	0.0909528	0.0454764	−	0.998965i	$-0.485519\pi$
$241$	1.41197	0.0909528	0.0454764	+	0.998965i	$0.485519\pi$
$242$	1.54013	0.0990030
$243$	−19.5608	−1.25483
$244$	5.31194	0.340062
$245$	25.8528	1.65167
$246$	−8.02329	−0.511546
$247$	2.05325	0.130645
$248$	−19.9526	−1.26699
$249$	−25.2495	−1.60012
$250$	−1.07179	−0.0677861
$251$	−2.96795	−0.187335	−0.0936676	−	0.995604i	$-0.529859\pi$
$251$	−2.96795	−0.187335	−0.0936676	+	0.995604i	$0.529859\pi$
$252$	9.48094	0.597243
$253$	24.0450	1.51170
$254$	6.71860	0.421563
$255$	−4.32242	−0.270681
$256$	−12.3546	−0.772164
$257$	26.6436	1.66198	0.830991	−	0.556287i	$-0.187774\pi$
$257$	26.6436	1.66198	0.830991	+	0.556287i	$0.187774\pi$
$258$	26.7968	1.66830
$259$	12.2900	0.763666
$260$	−3.71134	−0.230168
$261$	−42.7900	−2.64863
$262$	−10.4843	−0.647722
$263$	−30.9266	−1.90702	−0.953509	−	0.301364i	$-0.902558\pi$
$263$	−30.9266	−1.90702	−0.953509	+	0.301364i	$0.902558\pi$
$264$	−25.9326	−1.59604
$265$	−30.3571	−1.86482
$266$	4.65131	0.285190
$267$	10.4582	0.640032
$268$	−5.73421	−0.350272
$269$	9.60767	0.585790	0.292895	−	0.956145i	$-0.405381\pi$
$269$	9.60767	0.585790	0.292895	+	0.956145i	$0.405381\pi$
$270$	−13.8674	−0.843945
$271$	26.7403	1.62436	0.812180	−	0.583407i	$-0.198281\pi$
$271$	26.7403	1.62436	0.812180	+	0.583407i	$0.198281\pi$
$272$	1.27185	0.0771172
$273$	−21.5796	−1.30606
$274$	9.69420	0.585648
$275$	−16.4538	−0.992201
$276$	11.7776	0.708928
$277$	−23.0890	−1.38728	−0.693642	−	0.720320i	$-0.743995\pi$
$277$	−23.0890	−1.38728	−0.693642	+	0.720320i	$0.743995\pi$
$278$	12.8249	0.769187
$279$	−28.1372	−1.68453
$280$	−38.2324	−2.28482
$281$	9.39136	0.560241	0.280121	−	0.959965i	$-0.409626\pi$
$281$	9.39136	0.560241	0.280121	+	0.959965i	$0.409626\pi$
$282$	19.6436	1.16976
$283$	−7.15916	−0.425568	−0.212784	−	0.977099i	$-0.568253\pi$
$283$	−7.15916	−0.425568	−0.212784	+	0.977099i	$0.568253\pi$
$284$	−1.91897	−0.113870
$285$	8.68181	0.514266
$286$	7.66956	0.453511
$287$	−9.59560	−0.566410
$288$	−13.3604	−0.787272
$289$	−16.7521	−0.985419
$290$	37.9450	2.22821
$291$	50.7296	2.97382
$292$	−9.26102	−0.541960
$293$	−17.7404	−1.03641	−0.518203	−	0.855258i	$-0.673399\pi$
$293$	−17.7404	−1.03641	−0.518203	+	0.855258i	$0.673399\pi$
$294$	−26.1685	−1.52618
$295$	43.4903	2.53210
$296$	−9.72925	−0.565501
$297$	−11.2494	−0.652758
$298$	−22.4119	−1.29829
$299$	−15.8398	−0.916038
$300$	−8.05931	−0.465304
$301$	32.0482	1.84723
$302$	8.94268	0.514593
$303$	16.2443	0.933213
$304$	−2.55457	−0.146515
$305$	−30.2074	−1.72967
$306$	2.58523	0.147788
$307$	6.14773	0.350869	0.175435	−	0.984491i	$-0.443867\pi$
$307$	6.14773	0.350869	0.175435	+	0.984491i	$0.443867\pi$
$308$	−6.82021	−0.388618
$309$	10.0453	0.571458
$310$	24.9513	1.41714
$311$	−29.3009	−1.66150	−0.830751	−	0.556644i	$-0.812089\pi$
$311$	−29.3009	−1.66150	−0.830751	+	0.556644i	$0.812089\pi$
$312$	17.0832	0.967146
$313$	−24.7706	−1.40012	−0.700060	−	0.714084i	$-0.746843\pi$
$313$	−24.7706	−1.40012	−0.700060	+	0.714084i	$0.746843\pi$
$314$	−4.95363	−0.279549
$315$	−53.9153	−3.03778
$316$	6.01248	0.338228
$317$	26.7135	1.50038	0.750191	−	0.661221i	$-0.229961\pi$
$317$	26.7135	1.50038	0.750191	+	0.661221i	$0.229961\pi$
$318$	30.7278	1.72313
$319$	30.7814	1.72343
$320$	28.2280	1.57799
$321$	22.0290	1.22954
$322$	−35.8824	−1.99965
$323$	−0.497871	−0.0277023
$324$	1.81824	0.101013
$325$	10.8390	0.601240
$326$	1.65948	0.0919103
$327$	−37.7937	−2.09000
$328$	7.59623	0.419432
$329$	23.4931	1.29522
$330$	32.4294	1.78518
$331$	3.80563	0.209177	0.104588	−	0.994516i	$-0.466648\pi$
$331$	3.80563	0.209177	0.104588	+	0.994516i	$0.466648\pi$
$332$	5.25692	0.288511
$333$	−13.7202	−0.751862
$334$	−15.0477	−0.823373
$335$	32.6087	1.78160
$336$	26.8485	1.46470
$337$	31.7293	1.72841	0.864204	−	0.503142i	$-0.167823\pi$
$337$	31.7293	1.72841	0.864204	+	0.503142i	$0.167823\pi$
$338$	10.5271	0.572600
$339$	1.21815	0.0661607
$340$	0.899924	0.0488052
$341$	20.2408	1.09610
$342$	−5.19256	−0.280782
$343$	−4.12829	−0.222907
$344$	−25.3705	−1.36789
$345$	−66.9757	−3.60585
$346$	2.69938	0.145120
$347$	−11.0772	−0.594653	−0.297327	−	0.954776i	$-0.596095\pi$
$347$	−11.0772	−0.594653	−0.297327	+	0.954776i	$0.596095\pi$
$348$	15.0772	0.808222
$349$	−2.42685	−0.129907	−0.0649533	−	0.997888i	$-0.520690\pi$
$349$	−2.42685	−0.129907	−0.0649533	+	0.997888i	$0.520690\pi$
$350$	24.5540	1.31247
$351$	7.41061	0.395549
$352$	9.61098	0.512267
$353$	−0.574125	−0.0305576	−0.0152788	−	0.999883i	$-0.504864\pi$
$353$	−0.574125	−0.0305576	−0.0152788	+	0.999883i	$0.504864\pi$
$354$	−44.0213	−2.33971
$355$	10.9126	0.579181
$356$	−2.17739	−0.115401
$357$	5.23261	0.276939
$358$	0.180038	0.00951530
$359$	23.5884	1.24495	0.622475	−	0.782640i	$-0.286127\pi$
$359$	23.5884	1.24495	0.622475	+	0.782640i	$0.286127\pi$
$360$	42.6813	2.24950
$361$	1.00000	0.0526316
$362$	−3.44346	−0.180984
$363$	−3.48003	−0.182654
$364$	4.49285	0.235489
$365$	52.6647	2.75659
$366$	30.5763	1.59825
$367$	−24.3588	−1.27152	−0.635760	−	0.771886i	$-0.719313\pi$
$367$	−24.3588	−1.27152	−0.635760	+	0.771886i	$0.719313\pi$
$368$	19.7072	1.02731
$369$	10.7122	0.557655
$370$	12.1667	0.632516
$371$	36.7495	1.90794
$372$	9.91424	0.514029
$373$	31.6076	1.63658	0.818291	−	0.574804i	$-0.194922\pi$
$373$	31.6076	1.63658	0.818291	+	0.574804i	$0.194922\pi$
$374$	−1.85971	−0.0961633
$375$	2.42179	0.125061
$376$	−18.5980	−0.959119
$377$	−20.2774	−1.04434
$378$	16.7875	0.863457
$379$	0.659114	0.0338564	0.0169282	−	0.999857i	$-0.494611\pi$
$379$	0.659114	0.0338564	0.0169282	+	0.999857i	$0.494611\pi$
$380$	−1.80754	−0.0927250
$381$	−15.1812	−0.777755
$382$	0.578735	0.0296107
$383$	13.3259	0.680924	0.340462	−	0.940258i	$-0.389417\pi$
$383$	13.3259	0.680924	0.340462	+	0.940258i	$0.389417\pi$
$384$	−11.8728	−0.605880
$385$	38.7845	1.97664
$386$	1.92512	0.0979860
$387$	−35.7775	−1.81867
$388$	−10.5618	−0.536196
$389$	27.1280	1.37544	0.687721	−	0.725975i	$-0.258611\pi$
$389$	27.1280	1.37544	0.687721	+	0.725975i	$0.258611\pi$
$390$	−21.3630	−1.08176
$391$	3.84082	0.194239
$392$	24.7756	1.25136
$393$	23.6900	1.19500
$394$	21.3093	1.07355
$395$	−34.1911	−1.72034
$396$	7.61386	0.382611
$397$	16.8432	0.845336	0.422668	−	0.906285i	$-0.361094\pi$
$397$	16.8432	0.845336	0.422668	+	0.906285i	$0.361094\pi$
$398$	−31.5378	−1.58085
$399$	−10.5100	−0.526156
$400$	−13.4855	−0.674273
$401$	−21.3085	−1.06409	−0.532047	−	0.846715i	$-0.678577\pi$
$401$	−21.3085	−1.06409	−0.532047	+	0.846715i	$0.678577\pi$
$402$	−33.0069	−1.64623
$403$	−13.3337	−0.664200
$404$	−3.38205	−0.168263
$405$	−10.3398	−0.513788
$406$	−45.9352	−2.27972
$407$	9.86976	0.489226
$408$	−4.14233	−0.205076
$409$	−17.9557	−0.887852	−0.443926	−	0.896063i	$-0.646415\pi$
$409$	−17.9557	−0.887852	−0.443926	+	0.896063i	$0.646415\pi$
$410$	−9.49928	−0.469136
$411$	−21.9047	−1.08048
$412$	−2.09142	−0.103037
$413$	−52.6481	−2.59065
$414$	40.0579	1.96874
$415$	−29.8945	−1.46747
$416$	−6.33128	−0.310416
$417$	−28.9788	−1.41910
$418$	3.73532	0.182701
$419$	15.1581	0.740522	0.370261	−	0.928928i	$-0.379268\pi$
$419$	15.1581	0.740522	0.370261	+	0.928928i	$0.379268\pi$
$420$	18.9972	0.926969
$421$	24.6870	1.20317	0.601587	−	0.798808i	$-0.294536\pi$
$421$	24.6870	1.20317	0.601587	+	0.798808i	$0.294536\pi$
$422$	−1.19842	−0.0583382
$423$	−26.2269	−1.27520
$424$	−29.0922	−1.41284
$425$	−2.62824	−0.127488
$426$	−11.0459	−0.535174
$427$	36.5683	1.76966
$428$	−4.58642	−0.221693
$429$	−17.3299	−0.836697
$430$	31.7265	1.52999
$431$	−30.0074	−1.44541	−0.722703	−	0.691159i	$-0.757100\pi$
$431$	−30.0074	−1.44541	−0.722703	+	0.691159i	$0.757100\pi$
$432$	−9.21999	−0.443597
$433$	6.09845	0.293073	0.146537	−	0.989205i	$-0.453187\pi$
$433$	6.09845	0.293073	0.146537	+	0.989205i	$0.453187\pi$
$434$	−30.2054	−1.44990
$435$	−85.7394	−4.11089
$436$	7.86860	0.376838
$437$	−7.71448	−0.369034
$438$	−53.3078	−2.54714
$439$	−1.48619	−0.0709321	−0.0354660	−	0.999371i	$-0.511292\pi$
$439$	−1.48619	−0.0709321	−0.0354660	+	0.999371i	$0.511292\pi$
$440$	−30.7032	−1.46372
$441$	34.9385	1.66374
$442$	1.22509	0.0582717
$443$	4.57291	0.217266	0.108633	−	0.994082i	$-0.465353\pi$
$443$	4.57291	0.217266	0.108633	+	0.994082i	$0.465353\pi$
$444$	4.83435	0.229428
$445$	12.3821	0.586969
$446$	6.74752	0.319504
$447$	50.6413	2.39525
$448$	−34.1721	−1.61448
$449$	1.65254	0.0779883	0.0389941	−	0.999239i	$-0.487585\pi$
$449$	1.65254	0.0779883	0.0389941	+	0.999239i	$0.487585\pi$
$450$	−27.4113	−1.29218
$451$	−7.70594	−0.362858
$452$	−0.253617	−0.0119291
$453$	−20.2066	−0.949390
$454$	−0.726415	−0.0340923
$455$	−25.5495	−1.19778
$456$	8.32008	0.389623
$457$	−32.5166	−1.52106	−0.760532	−	0.649301i	$-0.775062\pi$
$457$	−32.5166	−1.52106	−0.760532	+	0.649301i	$0.775062\pi$
$458$	10.8301	0.506055
$459$	−1.79692	−0.0838731
$460$	13.9443	0.650154
$461$	4.34973	0.202587	0.101294	−	0.994857i	$-0.467702\pi$
$461$	4.34973	0.202587	0.101294	+	0.994857i	$0.467702\pi$
$462$	−39.2581	−1.82645
$463$	−7.18973	−0.334135	−0.167068	−	0.985945i	$-0.553430\pi$
$463$	−7.18973	−0.334135	−0.167068	+	0.985945i	$0.553430\pi$
$464$	25.2283	1.17120
$465$	−56.3793	−2.61453
$466$	−8.32600	−0.385695
$467$	−24.9336	−1.15379	−0.576895	−	0.816818i	$-0.695736\pi$
$467$	−24.9336	−1.15379	−0.576895	+	0.816818i	$0.695736\pi$
$468$	−5.01566	−0.231849
$469$	−39.4752	−1.82280
$470$	23.2573	1.07278
$471$	11.1931	0.515750
$472$	41.6782	1.91840
$473$	25.7369	1.18339
$474$	34.6087	1.58963
$475$	5.27895	0.242215
$476$	−1.08942	−0.0499336
$477$	−41.0259	−1.87845
$478$	21.7488	0.994765
$479$	−38.9296	−1.77874	−0.889370	−	0.457189i	$-0.848856\pi$
$479$	−38.9296	−1.77874	−0.889370	+	0.457189i	$0.848856\pi$
$480$	−26.7707	−1.22191
$481$	−6.50175	−0.296454
$482$	−1.69213	−0.0770745
$483$	81.0789	3.68922
$484$	0.724537	0.0329335
$485$	60.0620	2.72728
$486$	23.4421	1.06336
$487$	2.36995	0.107393	0.0536963	−	0.998557i	$-0.482900\pi$
$487$	2.36995	0.107393	0.0536963	+	0.998557i	$0.482900\pi$
$488$	−28.9488	−1.31045
$489$	−3.74972	−0.169568
$490$	−30.9825	−1.39965
$491$	−37.5060	−1.69262	−0.846310	−	0.532690i	$-0.821181\pi$
$491$	−37.5060	−1.69262	−0.846310	+	0.532690i	$0.821181\pi$
$492$	−3.77448	−0.170167
$493$	4.91686	0.221444
$494$	−2.46066	−0.110710
$495$	−43.2977	−1.94609
$496$	16.5893	0.744881
$497$	−13.2105	−0.592572
$498$	30.2596	1.35597
$499$	−37.2426	−1.66721	−0.833604	−	0.552363i	$-0.813726\pi$
$499$	−37.2426	−1.66721	−0.833604	+	0.552363i	$0.813726\pi$
$500$	−0.504214	−0.0225492
$501$	34.0013	1.51907
$502$	3.55685	0.158750
$503$	−14.2405	−0.634951	−0.317475	−	0.948267i	$-0.602835\pi$
$503$	−14.2405	−0.634951	−0.317475	+	0.948267i	$0.602835\pi$
$504$	−51.6688	−2.30151
$505$	19.2327	0.855844
$506$	−28.8161	−1.28103
$507$	−23.7868	−1.05641
$508$	3.16070	0.140233
$509$	−8.85841	−0.392642	−0.196321	−	0.980540i	$-0.562899\pi$
$509$	−8.85841	−0.392642	−0.196321	+	0.980540i	$0.562899\pi$
$510$	5.18009	0.229378
$511$	−63.7544	−2.82033
$512$	23.5750	1.04188
$513$	3.60921	0.159350
$514$	−31.9302	−1.40838
$515$	11.8933	0.524081
$516$	12.6063	0.554962
$517$	18.8666	0.829752
$518$	−14.7287	−0.647140
$519$	−6.09946	−0.267736
$520$	20.2259	0.886965
$521$	41.5413	1.81996	0.909979	−	0.414654i	$-0.136097\pi$
$521$	41.5413	1.81996	0.909979	+	0.414654i	$0.136097\pi$
$522$	51.2805	2.24448
$523$	−3.55684	−0.155530	−0.0777650	−	0.996972i	$-0.524778\pi$
$523$	−3.55684	−0.155530	−0.0777650	+	0.996972i	$0.524778\pi$
$524$	−4.93223	−0.215466
$525$	−55.4816	−2.42141
$526$	37.0631	1.61603
$527$	3.23315	0.140838
$528$	21.5612	0.938331
$529$	36.5133	1.58753
$530$	36.3806	1.58027
$531$	58.7746	2.55060
$532$	2.18816	0.0948689
$533$	5.07632	0.219880
$534$	−12.5333	−0.542370
$535$	26.0816	1.12761
$536$	31.2500	1.34980
$537$	−0.406809	−0.0175551
$538$	−11.5140	−0.496405
$539$	−25.1334	−1.08257
$540$	−6.52380	−0.280740
$541$	−13.3182	−0.572595	−0.286298	−	0.958141i	$-0.592425\pi$
$541$	−13.3182	−0.572595	−0.286298	+	0.958141i	$0.592425\pi$
$542$	−32.0462	−1.37650
$543$	7.78074	0.333904
$544$	1.53520	0.0658213
$545$	−44.7464	−1.91672
$546$	25.8615	1.10677
$547$	−11.0967	−0.474462	−0.237231	−	0.971453i	$-0.576240\pi$
$547$	−11.0967	−0.474462	−0.237231	+	0.971453i	$0.576240\pi$
$548$	4.56054	0.194817
$549$	−40.8236	−1.74231
$550$	19.7186	0.840803
$551$	−9.87575	−0.420721
$552$	−64.1851	−2.73190
$553$	41.3909	1.76012
$554$	27.6703	1.17560
$555$	−27.4915	−1.16695
$556$	6.03336	0.255871
$557$	12.6200	0.534727	0.267364	−	0.963596i	$-0.413848\pi$
$557$	12.6200	0.534727	0.267364	+	0.963596i	$0.413848\pi$
$558$	33.7203	1.42749
$559$	−16.9543	−0.717091
$560$	31.7876	1.34327
$561$	4.20215	0.177415
$562$	−11.2548	−0.474755
$563$	−30.0645	−1.26707	−0.633534	−	0.773715i	$-0.718396\pi$
$563$	−30.0645	−1.26707	−0.633534	+	0.773715i	$0.718396\pi$
$564$	9.24113	0.389122
$565$	1.44224	0.0606757
$566$	8.57969	0.360631
$567$	12.5171	0.525667
$568$	10.4579	0.438805
$569$	−7.20108	−0.301885	−0.150943	−	0.988543i	$-0.548231\pi$
$569$	−7.20108	−0.301885	−0.150943	+	0.988543i	$0.548231\pi$
$570$	−10.4045	−0.435795
$571$	−0.245070	−0.0102558	−0.00512792	−	0.999987i	$-0.501632\pi$
$571$	−0.245070	−0.0102558	−0.00512792	+	0.999987i	$0.501632\pi$
$572$	3.60807	0.150861
$573$	−1.30769	−0.0546297
$574$	11.4996	0.479983
$575$	−40.7244	−1.69832
$576$	38.1485	1.58952
$577$	37.5716	1.56413	0.782063	−	0.623200i	$-0.214168\pi$
$577$	37.5716	1.56413	0.782063	+	0.623200i	$0.214168\pi$
$578$	20.0761	0.835056
$579$	−4.34995	−0.180778
$580$	17.8508	0.741216
$581$	36.1895	1.50139
$582$	−60.7954	−2.52005
$583$	29.5124	1.22228
$584$	50.4703	2.08848
$585$	28.5226	1.17926
$586$	21.2605	0.878263
$587$	−11.0268	−0.455124	−0.227562	−	0.973764i	$-0.573075\pi$
$587$	−11.0268	−0.455124	−0.227562	+	0.973764i	$0.573075\pi$
$588$	−12.3107	−0.507685
$589$	−6.49395	−0.267579
$590$	−52.1197	−2.14573
$591$	−48.1499	−1.98062
$592$	8.08922	0.332465
$593$	22.0811	0.906762	0.453381	−	0.891317i	$-0.350218\pi$
$593$	22.0811	0.906762	0.453381	+	0.891317i	$0.350218\pi$
$594$	13.4816	0.553155
$595$	6.19522	0.253979
$596$	−10.5434	−0.431877
$597$	71.2620	2.91656
$598$	18.9827	0.776262
$599$	−27.2864	−1.11489	−0.557447	−	0.830213i	$-0.688219\pi$
$599$	−27.2864	−1.11489	−0.557447	+	0.830213i	$0.688219\pi$
$600$	43.9213	1.79308
$601$	−18.7818	−0.766126	−0.383063	−	0.923722i	$-0.625131\pi$
$601$	−18.7818	−0.766126	−0.383063	+	0.923722i	$0.625131\pi$
$602$	−38.4072	−1.56536
$603$	44.0688	1.79462
$604$	4.20700	0.171180
$605$	−4.12022	−0.167511
$606$	−19.4676	−0.790816
$607$	−34.6242	−1.40535	−0.702676	−	0.711510i	$-0.748012\pi$
$607$	−34.6242	−1.40535	−0.702676	+	0.711510i	$0.748012\pi$
$608$	−3.08354	−0.125054
$609$	103.794	4.20594
$610$	36.2012	1.46574
$611$	−12.4285	−0.502801
$612$	1.21620	0.0491618
$613$	5.50738	0.222441	0.111220	−	0.993796i	$-0.464524\pi$
$613$	5.50738	0.222441	0.111220	+	0.993796i	$0.464524\pi$
$614$	−7.36757	−0.297331
$615$	21.4643	0.865525
$616$	37.1685	1.49756
$617$	−29.5547	−1.18983	−0.594913	−	0.803790i	$-0.702814\pi$
$617$	−29.5547	−1.18983	−0.594913	+	0.803790i	$0.702814\pi$
$618$	−12.0385	−0.484260
$619$	29.2228	1.17457	0.587283	−	0.809382i	$-0.300198\pi$
$619$	29.2228	1.17457	0.587283	+	0.809382i	$0.300198\pi$
$620$	11.7381	0.471413
$621$	−27.8432	−1.11731
$622$	35.1148	1.40798
$623$	−14.9895	−0.600541
$624$	−14.2035	−0.568597
$625$	−23.5274	−0.941097
$626$	29.6857	1.18648
$627$	−8.44023	−0.337070
$628$	−2.33039	−0.0929925
$629$	1.57654	0.0628608
$630$	64.6132	2.57425
$631$	34.8487	1.38730	0.693652	−	0.720310i	$-0.256001\pi$
$631$	34.8487	1.38730	0.693652	+	0.720310i	$0.256001\pi$
$632$	−32.7665	−1.30338
$633$	2.70792	0.107630
$634$	−32.0141	−1.27144
$635$	−17.9740	−0.713275
$636$	14.4556	0.573202
$637$	16.5567	0.656002
$638$	−36.8891	−1.46045
$639$	14.7478	0.583412
$640$	−14.0569	−0.555649
$641$	−21.4854	−0.848622	−0.424311	−	0.905516i	$-0.639484\pi$
$641$	−21.4854	−0.848622	−0.424311	+	0.905516i	$0.639484\pi$
$642$	−26.4001	−1.04193
$643$	7.50388	0.295924	0.147962	−	0.988993i	$-0.452729\pi$
$643$	7.50388	0.295924	0.147962	+	0.988993i	$0.452729\pi$
$644$	−16.8805	−0.665186
$645$	−71.6883	−2.82272
$646$	0.596660	0.0234753
$647$	27.0920	1.06510	0.532549	−	0.846399i	$-0.321234\pi$
$647$	27.0920	1.06510	0.532549	+	0.846399i	$0.321234\pi$
$648$	−9.90896	−0.389261
$649$	−42.2801	−1.65964
$650$	−12.9897	−0.509498
$651$	68.2512	2.67498
$652$	0.780688	0.0305741
$653$	−27.4736	−1.07513	−0.537563	−	0.843223i	$-0.680655\pi$
$653$	−27.4736	−1.07513	−0.537563	+	0.843223i	$0.680655\pi$
$654$	45.2928	1.77109
$655$	28.0481	1.09593
$656$	−6.31576	−0.246589
$657$	71.1733	2.77673
$658$	−28.1546	−1.09758
$659$	45.9730	1.79085	0.895427	−	0.445208i	$-0.146870\pi$
$659$	45.9730	1.79085	0.895427	+	0.445208i	$0.146870\pi$
$660$	15.2561	0.593842
$661$	12.4933	0.485935	0.242967	−	0.970034i	$-0.421879\pi$
$661$	12.4933	0.485935	0.242967	+	0.970034i	$0.421879\pi$
$662$	−4.56075	−0.177259
$663$	−2.76819	−0.107507
$664$	−28.6490	−1.11180
$665$	−12.4434	−0.482535
$666$	16.4426	0.637137
$667$	76.1863	2.94995
$668$	−7.07904	−0.273896
$669$	−15.2465	−0.589464
$670$	−39.0790	−1.50975
$671$	29.3669	1.13370
$672$	32.4079	1.25016
$673$	25.7553	0.992793	0.496397	−	0.868096i	$-0.334656\pi$
$673$	25.7553	0.992793	0.496397	+	0.868096i	$0.334656\pi$
$674$	−38.0251	−1.46467
$675$	19.0528	0.733344
$676$	4.95238	0.190476
$677$	35.7931	1.37564	0.687821	−	0.725881i	$-0.258568\pi$
$677$	35.7931	1.37564	0.687821	+	0.725881i	$0.258568\pi$
$678$	−1.45986	−0.0560654
$679$	−72.7094	−2.79033
$680$	−4.90437	−0.188074
$681$	1.64139	0.0628981
$682$	−24.2570	−0.928849
$683$	−27.2916	−1.04428	−0.522141	−	0.852859i	$-0.674867\pi$
$683$	−27.2916	−1.04428	−0.522141	+	0.852859i	$0.674867\pi$
$684$	−2.44279	−0.0934024
$685$	−25.9344	−0.990903
$686$	4.94744	0.188894
$687$	−24.4713	−0.933638
$688$	21.0939	0.804197
$689$	−19.4414	−0.740659
$690$	80.2651	3.05564
$691$	−8.10151	−0.308196	−0.154098	−	0.988056i	$-0.549247\pi$
$691$	−8.10151	−0.308196	−0.154098	+	0.988056i	$0.549247\pi$
$692$	1.26990	0.0482743
$693$	52.4150	1.99108
$694$	13.2751	0.503916
$695$	−34.3099	−1.30145
$696$	−82.1670	−3.11453
$697$	−1.23090	−0.0466238
$698$	2.90840	0.110084
$699$	18.8132	0.711581
$700$	11.5512	0.436594
$701$	32.1739	1.21519	0.607595	−	0.794247i	$-0.292134\pi$
$701$	32.1739	1.21519	0.607595	+	0.794247i	$0.292134\pi$
$702$	−8.88104	−0.335193
$703$	−3.16656	−0.119429
$704$	−27.4425	−1.03428
$705$	−52.5515	−1.97920
$706$	0.688044	0.0258949
$707$	−23.2826	−0.875632
$708$	−20.7094	−0.778307
$709$	−34.6541	−1.30146	−0.650730	−	0.759309i	$-0.725537\pi$
$709$	−34.6541	−1.30146	−0.650730	+	0.759309i	$0.725537\pi$
$710$	−13.0779	−0.490805
$711$	−46.2074	−1.73291
$712$	11.8662	0.444705
$713$	50.0975	1.87617
$714$	−6.27087	−0.234682
$715$	−20.5180	−0.767330
$716$	0.0846971	0.00316528
$717$	−49.1429	−1.83527
$718$	−28.2689	−1.05499
$719$	−21.6790	−0.808491	−0.404245	−	0.914651i	$-0.632466\pi$
$719$	−21.6790	−0.808491	−0.404245	+	0.914651i	$0.632466\pi$
$720$	−35.4866	−1.32251
$721$	−14.3977	−0.536198
$722$	−1.19842	−0.0446006
$723$	3.82349	0.142197
$724$	−1.61994	−0.0602047
$725$	−52.1336	−1.93619
$726$	4.17054	0.154783
$727$	13.6687	0.506943	0.253472	−	0.967343i	$-0.418428\pi$
$727$	13.6687	0.506943	0.253472	+	0.967343i	$0.418428\pi$
$728$	−24.4849	−0.907472
$729$	−43.2940	−1.60348
$730$	−63.1145	−2.33597
$731$	4.11107	0.152054
$732$	14.3843	0.531660
$733$	−1.47975	−0.0546558	−0.0273279	−	0.999627i	$-0.508700\pi$
$733$	−1.47975	−0.0546558	−0.0273279	+	0.999627i	$0.508700\pi$
$734$	29.1922	1.07750
$735$	70.0072	2.58226
$736$	23.7879	0.876833
$737$	−31.7013	−1.16773
$738$	−12.8377	−0.472564
$739$	−3.86962	−0.142346	−0.0711731	−	0.997464i	$-0.522674\pi$
$739$	−3.86962	−0.142346	−0.0711731	+	0.997464i	$0.522674\pi$
$740$	5.72370	0.210407
$741$	5.56004	0.204253
$742$	−44.0414	−1.61681
$743$	−53.9234	−1.97826	−0.989129	−	0.147050i	$-0.953022\pi$
$743$	−53.9234	−1.97826	−0.989129	+	0.147050i	$0.953022\pi$
$744$	−54.0302	−1.98084
$745$	59.9574	2.19667
$746$	−37.8793	−1.38686
$747$	−40.4008	−1.47819
$748$	−0.874883	−0.0319889
$749$	−31.5737	−1.15368
$750$	−2.90233	−0.105978
$751$	11.8815	0.433561	0.216780	−	0.976220i	$-0.430444\pi$
$751$	11.8815	0.433561	0.216780	+	0.976220i	$0.430444\pi$
$752$	15.4630	0.563877
$753$	−8.03697	−0.292883
$754$	24.3009	0.884986
$755$	−23.9239	−0.870681
$756$	7.89753	0.287230
$757$	2.17596	0.0790866	0.0395433	−	0.999218i	$-0.487410\pi$
$757$	2.17596	0.0790866	0.0395433	+	0.999218i	$0.487410\pi$
$758$	−0.789896	−0.0286903
$759$	65.1120	2.36342
$760$	9.85067	0.357321
$761$	−3.30780	−0.119907	−0.0599537	−	0.998201i	$-0.519095\pi$
$761$	−3.30780	−0.119907	−0.0599537	+	0.998201i	$0.519095\pi$
$762$	18.1934	0.659079
$763$	54.1687	1.96104
$764$	0.272260	0.00985003
$765$	−6.91614	−0.250053
$766$	−15.9701	−0.577023
$767$	27.8522	1.00569
$768$	−33.4553	−1.20721
$769$	−10.4365	−0.376349	−0.188175	−	0.982136i	$-0.560257\pi$
$769$	−10.4365	−0.376349	−0.188175	+	0.982136i	$0.560257\pi$
$770$	−46.4802	−1.67503
$771$	72.1487	2.59837
$772$	0.905654	0.0325952
$773$	43.7589	1.57390	0.786950	−	0.617017i	$-0.211659\pi$
$773$	43.7589	1.57390	0.786950	+	0.617017i	$0.211659\pi$
$774$	42.8765	1.54117
$775$	−34.2813	−1.23142
$776$	57.5595	2.06626
$777$	33.2805	1.19393
$778$	−32.5107	−1.16557
$779$	2.47233	0.0885805
$780$	−10.0500	−0.359848
$781$	−10.6090	−0.379618
$782$	−4.60292	−0.164600
$783$	−35.6437	−1.27380
$784$	−20.5992	−0.735687
$785$	13.2522	0.472991
$786$	−28.3906	−1.01266
$787$	−22.4221	−0.799261	−0.399630	−	0.916676i	$-0.630862\pi$
$787$	−22.4221	−0.799261	−0.399630	+	0.916676i	$0.630862\pi$
$788$	10.0248	0.357117
$789$	−83.7469	−2.98147
$790$	40.9754	1.45784
$791$	−1.74594	−0.0620785
$792$	−41.4937	−1.47441
$793$	−19.3456	−0.686981
$794$	−20.1853	−0.716348
$795$	−82.2046	−2.91550
$796$	−14.8367	−0.525871
$797$	20.3172	0.719673	0.359836	−	0.933015i	$-0.382832\pi$
$797$	20.3172	0.719673	0.359836	+	0.933015i	$0.382832\pi$
$798$	12.5954	0.445871
$799$	3.01364	0.106615
$800$	−16.2778	−0.575508
$801$	16.7337	0.591258
$802$	25.5365	0.901726
$803$	−51.1992	−1.80678
$804$	−15.5278	−0.547622
$805$	95.9945	3.38336
$806$	15.9794	0.562851
$807$	26.0168	0.915835
$808$	18.4314	0.648413
$809$	−29.6067	−1.04091	−0.520457	−	0.853888i	$-0.674239\pi$
$809$	−29.6067	−1.04091	−0.520457	+	0.853888i	$0.674239\pi$
$810$	12.3914	0.435390
$811$	−47.0105	−1.65076	−0.825382	−	0.564575i	$-0.809040\pi$
$811$	−47.0105	−1.65076	−0.825382	+	0.564575i	$0.809040\pi$
$812$	−21.6098	−0.758354
$813$	72.4107	2.53955
$814$	−11.8281	−0.414576
$815$	−4.43954	−0.155510
$816$	3.44407	0.120566
$817$	−8.25730	−0.288886
$818$	21.5185	0.752377
$819$	−34.5287	−1.20653
$820$	−4.46885	−0.156059
$821$	0.918679	0.0320621	0.0160311	−	0.999871i	$-0.494897\pi$
$821$	0.918679	0.0320621	0.0160311	+	0.999871i	$0.494897\pi$
$822$	26.2511	0.915613
$823$	−6.60553	−0.230254	−0.115127	−	0.993351i	$-0.536728\pi$
$823$	−6.60553	−0.230254	−0.115127	+	0.993351i	$0.536728\pi$
$824$	11.3977	0.397059
$825$	−44.5556	−1.55123
$826$	63.0947	2.19534
$827$	−24.6189	−0.856084	−0.428042	−	0.903759i	$-0.640796\pi$
$827$	−24.6189	−0.856084	−0.428042	+	0.903759i	$0.640796\pi$
$828$	18.8449	0.654904
$829$	29.6043	1.02820	0.514099	−	0.857731i	$-0.328126\pi$
$829$	29.6043	1.02820	0.514099	+	0.857731i	$0.328126\pi$
$830$	35.8263	1.24355
$831$	−62.5232	−2.16890
$832$	18.0779	0.626739
$833$	−4.01467	−0.139100
$834$	34.7289	1.20256
$835$	40.2564	1.39313
$836$	1.75725	0.0607756
$837$	−23.4380	−0.810137
$838$	−18.1658	−0.627527
$839$	32.3234	1.11593	0.557964	−	0.829865i	$-0.311583\pi$
$839$	32.3234	1.11593	0.557964	+	0.829865i	$0.311583\pi$
$840$	−103.530	−3.57213
$841$	68.5305	2.36312
$842$	−29.5855	−1.01958
$843$	25.4310	0.875892
$844$	−0.563786	−0.0194063
$845$	−28.1627	−0.968827
$846$	31.4309	1.08062
$847$	4.98783	0.171384
$848$	24.1882	0.830628
$849$	−19.3864	−0.665341
$850$	3.14974	0.108035
$851$	24.4284	0.837395
$852$	−5.19642	−0.178026
$853$	39.3429	1.34707	0.673537	−	0.739154i	$-0.264774\pi$
$853$	39.3429	1.34707	0.673537	+	0.739154i	$0.264774\pi$
$854$	−43.8242	−1.49963
$855$	13.8914	0.475076
$856$	24.9949	0.854307
$857$	34.7901	1.18841	0.594203	−	0.804315i	$-0.297467\pi$
$857$	34.7901	1.18841	0.594203	+	0.804315i	$0.297467\pi$
$858$	20.7686	0.709027
$859$	37.6416	1.28432	0.642158	−	0.766572i	$-0.278039\pi$
$859$	37.6416	1.28432	0.642158	+	0.766572i	$0.278039\pi$
$860$	14.9254	0.508953
$861$	−25.9841	−0.885537
$862$	35.9615	1.22485
$863$	−17.6272	−0.600038	−0.300019	−	0.953933i	$-0.596993\pi$
$863$	−17.6272	−0.600038	−0.300019	+	0.953933i	$0.596993\pi$
$864$	−11.1291	−0.378620
$865$	−7.22154	−0.245540
$866$	−7.30852	−0.248354
$867$	−45.3634	−1.54062
$868$	−14.2098	−0.482313
$869$	33.2398	1.12758
$870$	102.752	3.48362
$871$	20.8834	0.707607
$872$	−42.8820	−1.45217
$873$	81.1704	2.74720
$874$	9.24520	0.312724
$875$	−3.47109	−0.117344
$876$	−25.0781	−0.847311
$877$	33.7700	1.14033	0.570165	−	0.821530i	$-0.306879\pi$
$877$	33.7700	1.14033	0.570165	+	0.821530i	$0.306879\pi$
$878$	1.78109	0.0601087
$879$	−48.0396	−1.62034
$880$	25.5277	0.860538
$881$	−37.5096	−1.26373	−0.631865	−	0.775079i	$-0.717710\pi$
$881$	−37.5096	−1.26373	−0.631865	+	0.775079i	$0.717710\pi$
$882$	−41.8711	−1.40987
$883$	14.6158	0.491859	0.245930	−	0.969288i	$-0.420907\pi$
$883$	14.6158	0.491859	0.245930	+	0.969288i	$0.420907\pi$
$884$	0.576333	0.0193842
$885$	117.768	3.95873
$886$	−5.48027	−0.184113
$887$	−17.4233	−0.585017	−0.292509	−	0.956263i	$-0.594490\pi$
$887$	−17.4233	−0.585017	−0.292509	+	0.956263i	$0.594490\pi$
$888$	−26.3460	−0.884115
$889$	21.7588	0.729766
$890$	−14.8390	−0.497405
$891$	10.0521	0.336757
$892$	3.17430	0.106284
$893$	−6.05306	−0.202558
$894$	−60.6896	−2.02976
$895$	−0.481647	−0.0160997
$896$	17.0169	0.568496
$897$	−42.8929	−1.43215
$898$	−1.98044	−0.0660882
$899$	64.1327	2.13895
$900$	−12.8954	−0.429846
$901$	4.71415	0.157051
$902$	9.23496	0.307491
$903$	86.7839	2.88799
$904$	1.38215	0.0459697
$905$	9.21212	0.306221
$906$	24.2161	0.804525
$907$	−24.9702	−0.829122	−0.414561	−	0.910021i	$-0.636065\pi$
$907$	−24.9702	−0.829122	−0.414561	+	0.910021i	$0.636065\pi$
$908$	−0.341735	−0.0113409
$909$	25.9919	0.862097
$910$	30.6190	1.01501
$911$	1.12581	0.0372999	0.0186499	−	0.999826i	$-0.494063\pi$
$911$	1.12581	0.0372999	0.0186499	+	0.999826i	$0.494063\pi$
$912$	−6.91758	−0.229064
$913$	29.0627	0.961835
$914$	38.9686	1.28897
$915$	−81.7993	−2.70420
$916$	5.09489	0.168340
$917$	−33.9543	−1.12127
$918$	2.15347	0.0710751
$919$	12.6766	0.418163	0.209082	−	0.977898i	$-0.432953\pi$
$919$	12.6766	0.418163	0.209082	+	0.977898i	$0.432953\pi$
$920$	−75.9928	−2.50541
$921$	16.6476	0.548555
$922$	−5.21281	−0.171675
$923$	6.98870	0.230036
$924$	−18.4686	−0.607572
$925$	−16.7161	−0.549623
$926$	8.61633	0.283150
$927$	16.0731	0.527910
$928$	30.4522	0.999644
$929$	−48.2673	−1.58360	−0.791799	−	0.610782i	$-0.790855\pi$
$929$	−48.2673	−1.58360	−0.791799	+	0.610782i	$0.790855\pi$
$930$	67.5661	2.21558
$931$	8.06367	0.264276
$932$	−3.91689	−0.128302
$933$	−79.3445	−2.59762
$934$	29.8810	0.977736
$935$	4.97519	0.162706
$936$	27.3342	0.893445
$937$	26.3755	0.861649	0.430824	−	0.902436i	$-0.358223\pi$
$937$	26.3755	0.861649	0.430824	+	0.902436i	$0.358223\pi$
$938$	47.3079	1.54466
$939$	−67.0769	−2.18897
$940$	10.9412	0.356861
$941$	−0.0196174	−0.000639508 0	−0.000319754	−	1.00000i	$-0.500102\pi$
$941$	−0.0196174	−0.000639508 0	−0.000319754		1.00000i	$0.500102\pi$
$942$	−13.4140	−0.437053
$943$	−19.0728	−0.621095
$944$	−34.6526	−1.12785
$945$	−44.9109	−1.46095
$946$	−30.8437	−1.00281
$947$	−28.9671	−0.941303	−0.470651	−	0.882319i	$-0.655981\pi$
$947$	−28.9671	−0.941303	−0.470651	+	0.882319i	$0.655981\pi$
$948$	16.2813	0.528792
$949$	33.7277	1.09485
$950$	−6.32641	−0.205256
$951$	72.3382	2.34573
$952$	5.93709	0.192422
$953$	−8.56168	−0.277340	−0.138670	−	0.990339i	$-0.544283\pi$
$953$	−8.56168	−0.277340	−0.138670	+	0.990339i	$0.544283\pi$
$954$	49.1663	1.59182
$955$	−1.54826	−0.0501006
$956$	10.2315	0.330910
$957$	83.3537	2.69444
$958$	46.6541	1.50732
$959$	31.3955	1.01381
$960$	76.4392	2.46706
$961$	11.1714	0.360369
$962$	7.79184	0.251219
$963$	35.2478	1.13584
$964$	−0.796047	−0.0256389
$965$	−5.15018	−0.165790
$966$	−97.1668	−3.12629
$967$	−49.1568	−1.58078	−0.790388	−	0.612607i	$-0.790121\pi$
$967$	−49.1568	−1.58078	−0.790388	+	0.612607i	$0.790121\pi$
$968$	−3.94855	−0.126911
$969$	−1.34820	−0.0433103
$970$	−71.9796	−2.31113
$971$	33.6636	1.08032	0.540158	−	0.841564i	$-0.318364\pi$
$971$	33.6636	1.08032	0.540158	+	0.841564i	$0.318364\pi$
$972$	11.0281	0.353727
$973$	41.5346	1.33154
$974$	−2.84020	−0.0910057
$975$	29.3512	0.939990
$976$	24.0690	0.770429
$977$	−24.0354	−0.768962	−0.384481	−	0.923133i	$-0.625620\pi$
$977$	−24.0354	−0.768962	−0.384481	+	0.923133i	$0.625620\pi$
$978$	4.49375	0.143694
$979$	−12.0376	−0.384723
$980$	−14.5754	−0.465595
$981$	−60.4721	−1.93073
$982$	44.9480	1.43435
$983$	−13.3894	−0.427055	−0.213528	−	0.976937i	$-0.568495\pi$
$983$	−13.3894	−0.427055	−0.213528	+	0.976937i	$0.568495\pi$
$984$	20.5700	0.655747
$985$	−57.0078	−1.81642
$986$	−5.89247	−0.187654
$987$	63.6174	2.02497
$988$	−1.15759	−0.0368280
$989$	63.7008	2.02557
$990$	51.8889	1.64914
$991$	33.2348	1.05574	0.527870	−	0.849325i	$-0.322991\pi$
$991$	33.2348	1.05574	0.527870	+	0.849325i	$0.322991\pi$
$992$	20.0243	0.635773
$993$	10.3054	0.327030
$994$	15.8318	0.502153
$995$	84.3716	2.67476
$996$	14.2353	0.451064
$997$	−10.2442	−0.324436	−0.162218	−	0.986755i	$-0.551865\pi$
$997$	−10.2442	−0.324436	−0.162218	+	0.986755i	$0.551865\pi$
$998$	44.6323	1.41281
$999$	−11.4288	−0.361591

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4009.2.a.c.1.25	✓	71

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4009.2.a.c.1.25	✓	71	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:	\( N \)	\(=\)	\( 4009 = 19 \cdot 211 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4009.a (trivial)

\(f(q)\)	\(=\)	\(q-1.19842 q^{2} +2.70792 q^{3} -0.563786 q^{4} +3.20608 q^{5} -3.24523 q^{6} -3.88119 q^{7} +3.07250 q^{8} +4.33283 q^{9} +O(q^{10})\)	\(q-1.19842 q^{2} +2.70792 q^{3} -0.563786 q^{4} +3.20608 q^{5} -3.24523 q^{6} -3.88119 q^{7} +3.07250 q^{8} +4.33283 q^{9} -3.84224 q^{10} -3.11687 q^{11} -1.52669 q^{12} +2.05325 q^{13} +4.65131 q^{14} +8.68181 q^{15} -2.55457 q^{16} -0.497871 q^{17} -5.19256 q^{18} +1.00000 q^{19} -1.80754 q^{20} -10.5100 q^{21} +3.73532 q^{22} -7.71448 q^{23} +8.32008 q^{24} +5.27895 q^{25} -2.46066 q^{26} +3.60921 q^{27} +2.18816 q^{28} -9.87575 q^{29} -10.4045 q^{30} -6.49395 q^{31} -3.08354 q^{32} -8.44023 q^{33} +0.596660 q^{34} -12.4434 q^{35} -2.44279 q^{36} -3.16656 q^{37} -1.19842 q^{38} +5.56004 q^{39} +9.85067 q^{40} +2.47233 q^{41} +12.5954 q^{42} -8.25730 q^{43} +1.75725 q^{44} +13.8914 q^{45} +9.24520 q^{46} -6.05306 q^{47} -6.91758 q^{48} +8.06367 q^{49} -6.32641 q^{50} -1.34820 q^{51} -1.15759 q^{52} -9.46860 q^{53} -4.32535 q^{54} -9.99293 q^{55} -11.9250 q^{56} +2.70792 q^{57} +11.8353 q^{58} +13.5649 q^{59} -4.89468 q^{60} -9.42192 q^{61} +7.78249 q^{62} -16.8166 q^{63} +8.80452 q^{64} +6.58289 q^{65} +10.1150 q^{66} +10.1709 q^{67} +0.280693 q^{68} -20.8902 q^{69} +14.9125 q^{70} +3.40372 q^{71} +13.3126 q^{72} +16.4265 q^{73} +3.79488 q^{74} +14.2950 q^{75} -0.563786 q^{76} +12.0972 q^{77} -6.66328 q^{78} -10.6645 q^{79} -8.19017 q^{80} -3.22505 q^{81} -2.96290 q^{82} -9.32433 q^{83} +5.92537 q^{84} -1.59622 q^{85} +9.89573 q^{86} -26.7428 q^{87} -9.57657 q^{88} +3.86208 q^{89} -16.6478 q^{90} -7.96907 q^{91} +4.34932 q^{92} -17.5851 q^{93} +7.25412 q^{94} +3.20608 q^{95} -8.34997 q^{96} +18.7338 q^{97} -9.66367 q^{98} -13.5049 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 71 q - 15 q^{2} - 8 q^{3} + 69 q^{4} - 18 q^{5} - 9 q^{6} - 19 q^{7} - 39 q^{8} + 63 q^{9}+O(q^{10}) \) 71 * q - 15 * q^2 - 8 * q^3 + 69 * q^4 - 18 * q^5 - 9 * q^6 - 19 * q^7 - 39 * q^8 + 63 * q^9	\( 71 q - 15 q^{2} - 8 q^{3} + 69 q^{4} - 18 q^{5} - 9 q^{6} - 19 q^{7} - 39 q^{8} + 63 q^{9} - 10 q^{10} - 52 q^{11} - 9 q^{12} - 15 q^{13} - 53 q^{14} - 33 q^{15} + 53 q^{16} - 10 q^{17} - 35 q^{18} + 71 q^{19} - 33 q^{20} - 38 q^{21} - 6 q^{22} - 65 q^{23} - 30 q^{24} + 51 q^{25} - 4 q^{26} - 23 q^{27} - 29 q^{28} - 97 q^{29} - 27 q^{30} - 53 q^{31} - 78 q^{32} - 17 q^{33} - 24 q^{34} - 38 q^{35} + 24 q^{36} - 33 q^{37} - 15 q^{38} - 86 q^{39} + 25 q^{40} - 69 q^{41} + 64 q^{42} - 10 q^{43} - 94 q^{44} - 34 q^{45} - 6 q^{46} - 37 q^{47} - q^{48} + 74 q^{49} - 41 q^{50} - 46 q^{51} - 30 q^{52} - 50 q^{53} - 17 q^{54} - 30 q^{55} - 116 q^{56} - 8 q^{57} + 11 q^{58} - 93 q^{59} - 56 q^{60} - 18 q^{61} - q^{62} - 84 q^{63} + 93 q^{64} - 78 q^{65} - 53 q^{66} - 5 q^{67} - 9 q^{68} - 69 q^{69} - 10 q^{70} - 221 q^{71} - 73 q^{72} - 34 q^{73} - 58 q^{74} - 70 q^{75} + 69 q^{76} - 2 q^{77} + 7 q^{78} - 68 q^{79} - 71 q^{80} + 39 q^{81} + 26 q^{82} - 45 q^{83} - 10 q^{84} - 44 q^{85} - 80 q^{86} - 7 q^{87} - 46 q^{88} - 143 q^{89} + 41 q^{90} - 30 q^{91} - 46 q^{92} + 32 q^{93} + 41 q^{94} - 18 q^{95} - 140 q^{96} - 18 q^{97} - 97 q^{98} - 142 q^{99}+O(q^{100}) \) 71 * q - 15 * q^2 - 8 * q^3 + 69 * q^4 - 18 * q^5 - 9 * q^6 - 19 * q^7 - 39 * q^8 + 63 * q^9 - 10 * q^10 - 52 * q^11 - 9 * q^12 - 15 * q^13 - 53 * q^14 - 33 * q^15 + 53 * q^16 - 10 * q^17 - 35 * q^18 + 71 * q^19 - 33 * q^20 - 38 * q^21 - 6 * q^22 - 65 * q^23 - 30 * q^24 + 51 * q^25 - 4 * q^26 - 23 * q^27 - 29 * q^28 - 97 * q^29 - 27 * q^30 - 53 * q^31 - 78 * q^32 - 17 * q^33 - 24 * q^34 - 38 * q^35 + 24 * q^36 - 33 * q^37 - 15 * q^38 - 86 * q^39 + 25 * q^40 - 69 * q^41 + 64 * q^42 - 10 * q^43 - 94 * q^44 - 34 * q^45 - 6 * q^46 - 37 * q^47 - q^48 + 74 * q^49 - 41 * q^50 - 46 * q^51 - 30 * q^52 - 50 * q^53 - 17 * q^54 - 30 * q^55 - 116 * q^56 - 8 * q^57 + 11 * q^58 - 93 * q^59 - 56 * q^60 - 18 * q^61 - q^62 - 84 * q^63 + 93 * q^64 - 78 * q^65 - 53 * q^66 - 5 * q^67 - 9 * q^68 - 69 * q^69 - 10 * q^70 - 221 * q^71 - 73 * q^72 - 34 * q^73 - 58 * q^74 - 70 * q^75 + 69 * q^76 - 2 * q^77 + 7 * q^78 - 68 * q^79 - 71 * q^80 + 39 * q^81 + 26 * q^82 - 45 * q^83 - 10 * q^84 - 44 * q^85 - 80 * q^86 - 7 * q^87 - 46 * q^88 - 143 * q^89 + 41 * q^90 - 30 * q^91 - 46 * q^92 + 32 * q^93 + 41 * q^94 - 18 * q^95 - 140 * q^96 - 18 * q^97 - 97 * q^98 - 142 * q^99

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