LMFDB - Embedded newform 4029.2.a.l.1.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4029,2,Mod(1,4029)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4029, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("4029.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4029 = 3 \cdot 17 \cdot 79 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4029.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:	$32.1717269744$
Analytic rank:	$0$
Dimension:	$32$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.7
Character	$\chi$	$=$	4029.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.03180 q^{2} -1.00000 q^{3} +2.12821 q^{4} +1.66964 q^{5} +2.03180 q^{6} -1.52463 q^{7} -0.260503 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.03180 q^{2} -1.00000 q^{3} +2.12821 q^{4} +1.66964 q^{5} +2.03180 q^{6} -1.52463 q^{7} -0.260503 q^{8} +1.00000 q^{9} -3.39237 q^{10} -3.97638 q^{11} -2.12821 q^{12} -5.52996 q^{13} +3.09775 q^{14} -1.66964 q^{15} -3.72714 q^{16} -1.00000 q^{17} -2.03180 q^{18} -3.49865 q^{19} +3.55334 q^{20} +1.52463 q^{21} +8.07920 q^{22} -6.50396 q^{23} +0.260503 q^{24} -2.21231 q^{25} +11.2358 q^{26} -1.00000 q^{27} -3.24474 q^{28} -9.08450 q^{29} +3.39237 q^{30} -3.43398 q^{31} +8.09380 q^{32} +3.97638 q^{33} +2.03180 q^{34} -2.54558 q^{35} +2.12821 q^{36} -0.355776 q^{37} +7.10856 q^{38} +5.52996 q^{39} -0.434945 q^{40} -8.42222 q^{41} -3.09775 q^{42} -6.82010 q^{43} -8.46257 q^{44} +1.66964 q^{45} +13.2147 q^{46} +13.4294 q^{47} +3.72714 q^{48} -4.67550 q^{49} +4.49498 q^{50} +1.00000 q^{51} -11.7689 q^{52} -9.28604 q^{53} +2.03180 q^{54} -6.63911 q^{55} +0.397171 q^{56} +3.49865 q^{57} +18.4579 q^{58} +3.98985 q^{59} -3.55334 q^{60} +11.5255 q^{61} +6.97716 q^{62} -1.52463 q^{63} -8.99072 q^{64} -9.23303 q^{65} -8.07920 q^{66} +13.4563 q^{67} -2.12821 q^{68} +6.50396 q^{69} +5.17211 q^{70} +10.3921 q^{71} -0.260503 q^{72} +16.6564 q^{73} +0.722866 q^{74} +2.21231 q^{75} -7.44587 q^{76} +6.06251 q^{77} -11.2358 q^{78} +1.00000 q^{79} -6.22296 q^{80} +1.00000 q^{81} +17.1123 q^{82} -11.9320 q^{83} +3.24474 q^{84} -1.66964 q^{85} +13.8571 q^{86} +9.08450 q^{87} +1.03586 q^{88} -6.77056 q^{89} -3.39237 q^{90} +8.43116 q^{91} -13.8418 q^{92} +3.43398 q^{93} -27.2859 q^{94} -5.84148 q^{95} -8.09380 q^{96} -4.06995 q^{97} +9.49968 q^{98} -3.97638 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - q^{2} - 32 q^{3} + 41 q^{4} - q^{5} + q^{6} + 4 q^{7} - 3 q^{8} + 32 q^{9}+O(q^{10}) $ 32 * q - q^2 - 32 * q^3 + 41 * q^4 - q^5 + q^6 + 4 * q^7 - 3 * q^8 + 32 * q^9	\( 32 q - q^{2} - 32 q^{3} + 41 q^{4} - q^{5} + q^{6} + 4 q^{7} - 3 q^{8} + 32 q^{9} + 17 q^{10} + 8 q^{11} - 41 q^{12} + 17 q^{13} + q^{14} + q^{15} + 55 q^{16} - 32 q^{17} - q^{18} + 48 q^{19} - 7 q^{20} - 4 q^{21} - 4 q^{22} - 19 q^{23} + 3 q^{24} + 63 q^{25} + 27 q^{26} - 32 q^{27} + 17 q^{28} - 15 q^{29} - 17 q^{30} + 20 q^{31} + 13 q^{32} - 8 q^{33} + q^{34} + 22 q^{35} + 41 q^{36} + 6 q^{37} + 11 q^{38} - 17 q^{39} + 47 q^{40} + q^{41} - q^{42} + 40 q^{43} + 22 q^{44} - q^{45} + 5 q^{46} - 5 q^{47} - 55 q^{48} + 88 q^{49} + 17 q^{50} + 32 q^{51} + 23 q^{52} - 34 q^{53} + q^{54} + 48 q^{55} - 48 q^{57} - 9 q^{58} + 41 q^{59} + 7 q^{60} + 20 q^{61} + 15 q^{62} + 4 q^{63} + 93 q^{64} - 58 q^{65} + 4 q^{66} + 52 q^{67} - 41 q^{68} + 19 q^{69} + 25 q^{70} + q^{71} - 3 q^{72} + 19 q^{73} + 12 q^{74} - 63 q^{75} + 128 q^{76} - 20 q^{77} - 27 q^{78} + 32 q^{79} - 16 q^{80} + 32 q^{81} - 5 q^{82} + 31 q^{83} - 17 q^{84} + q^{85} - 62 q^{86} + 15 q^{87} + 35 q^{88} + 18 q^{89} + 17 q^{90} + 48 q^{91} - 75 q^{92} - 20 q^{93} + 29 q^{94} + 5 q^{95} - 13 q^{96} + 17 q^{97} + 30 q^{98} + 8 q^{99}+O(q^{100}) \) 32 * q - q^2 - 32 * q^3 + 41 * q^4 - q^5 + q^6 + 4 * q^7 - 3 * q^8 + 32 * q^9 + 17 * q^10 + 8 * q^11 - 41 * q^12 + 17 * q^13 + q^14 + q^15 + 55 * q^16 - 32 * q^17 - q^18 + 48 * q^19 - 7 * q^20 - 4 * q^21 - 4 * q^22 - 19 * q^23 + 3 * q^24 + 63 * q^25 + 27 * q^26 - 32 * q^27 + 17 * q^28 - 15 * q^29 - 17 * q^30 + 20 * q^31 + 13 * q^32 - 8 * q^33 + q^34 + 22 * q^35 + 41 * q^36 + 6 * q^37 + 11 * q^38 - 17 * q^39 + 47 * q^40 + q^41 - q^42 + 40 * q^43 + 22 * q^44 - q^45 + 5 * q^46 - 5 * q^47 - 55 * q^48 + 88 * q^49 + 17 * q^50 + 32 * q^51 + 23 * q^52 - 34 * q^53 + q^54 + 48 * q^55 - 48 * q^57 - 9 * q^58 + 41 * q^59 + 7 * q^60 + 20 * q^61 + 15 * q^62 + 4 * q^63 + 93 * q^64 - 58 * q^65 + 4 * q^66 + 52 * q^67 - 41 * q^68 + 19 * q^69 + 25 * q^70 + q^71 - 3 * q^72 + 19 * q^73 + 12 * q^74 - 63 * q^75 + 128 * q^76 - 20 * q^77 - 27 * q^78 + 32 * q^79 - 16 * q^80 + 32 * q^81 - 5 * q^82 + 31 * q^83 - 17 * q^84 + q^85 - 62 * q^86 + 15 * q^87 + 35 * q^88 + 18 * q^89 + 17 * q^90 + 48 * q^91 - 75 * q^92 - 20 * q^93 + 29 * q^94 + 5 * q^95 - 13 * q^96 + 17 * q^97 + 30 * q^98 + 8 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−2.03180	−1.43670	−0.718350	−	0.695682i	$-0.755102\pi$
$2$	−2.03180	−1.43670	−0.718350	+	0.695682i	$0.755102\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	2.12821	1.06411
$5$	1.66964	0.746684	0.373342	−	0.927694i	$-0.378212\pi$
$5$	1.66964	0.746684	0.373342	+	0.927694i	$0.378212\pi$
$6$	2.03180	0.829479
$7$	−1.52463	−0.576257	−0.288128	−	0.957592i	$-0.593033\pi$
$7$	−1.52463	−0.576257	−0.288128	+	0.957592i	$0.593033\pi$
$8$	−0.260503	−0.0921016
$9$	1.00000	0.333333
$10$	−3.39237	−1.07276
$11$	−3.97638	−1.19892	−0.599461	−	0.800404i	$-0.704618\pi$
$11$	−3.97638	−1.19892	−0.599461	+	0.800404i	$0.704618\pi$
$12$	−2.12821	−0.614362
$13$	−5.52996	−1.53374	−0.766868	−	0.641805i	$-0.778186\pi$
$13$	−5.52996	−1.53374	−0.766868	+	0.641805i	$0.778186\pi$
$14$	3.09775	0.827908
$15$	−1.66964	−0.431098
$16$	−3.72714	−0.931784
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	−2.03180	−0.478900
$19$	−3.49865	−0.802645	−0.401323	−	0.915937i	$-0.631449\pi$
$19$	−3.49865	−0.802645	−0.401323	+	0.915937i	$0.631449\pi$
$20$	3.55334	0.794552
$21$	1.52463	0.332702
$22$	8.07920	1.72249
$23$	−6.50396	−1.35617	−0.678085	−	0.734984i	$-0.737190\pi$
$23$	−6.50396	−1.35617	−0.678085	+	0.734984i	$0.737190\pi$
$24$	0.260503	0.0531749
$25$	−2.21231	−0.442462
$26$	11.2358	2.20352
$27$	−1.00000	−0.192450
$28$	−3.24474	−0.613198
$29$	−9.08450	−1.68695	−0.843474	−	0.537170i	$-0.819494\pi$
$29$	−9.08450	−1.68695	−0.843474	+	0.537170i	$0.819494\pi$
$30$	3.39237	0.619359
$31$	−3.43398	−0.616761	−0.308380	−	0.951263i	$-0.599787\pi$
$31$	−3.43398	−0.616761	−0.308380	+	0.951263i	$0.599787\pi$
$32$	8.09380	1.43080
$33$	3.97638	0.692198
$34$	2.03180	0.348451
$35$	−2.54558	−0.430282
$36$	2.12821	0.354702
$37$	−0.355776	−0.0584892	−0.0292446	−	0.999572i	$-0.509310\pi$
$37$	−0.355776	−0.0584892	−0.0292446	+	0.999572i	$0.509310\pi$
$38$	7.10856	1.15316
$39$	5.52996	0.885503
$40$	−0.434945	−0.0687708
$41$	−8.42222	−1.31533	−0.657665	−	0.753311i	$-0.728456\pi$
$41$	−8.42222	−1.31533	−0.657665	+	0.753311i	$0.728456\pi$
$42$	−3.09775	−0.477993
$43$	−6.82010	−1.04006	−0.520028	−	0.854149i	$-0.674078\pi$
$43$	−6.82010	−1.04006	−0.520028	+	0.854149i	$0.674078\pi$
$44$	−8.46257	−1.27578
$45$	1.66964	0.248895
$46$	13.2147	1.94841
$47$	13.4294	1.95888	0.979440	−	0.201735i	$-0.0646580\pi$
$47$	13.4294	1.95888	0.979440	+	0.201735i	$0.0646580\pi$
$48$	3.72714	0.537966
$49$	−4.67550	−0.667928
$50$	4.49498	0.635686
$51$	1.00000	0.140028
$52$	−11.7689	−1.63206
$53$	−9.28604	−1.27554	−0.637768	−	0.770228i	$-0.720142\pi$
$53$	−9.28604	−1.27554	−0.637768	+	0.770228i	$0.720142\pi$
$54$	2.03180	0.276493
$55$	−6.63911	−0.895217
$56$	0.397171	0.0530742
$57$	3.49865	0.463407
$58$	18.4579	2.42364
$59$	3.98985	0.519434	0.259717	−	0.965685i	$-0.416371\pi$
$59$	3.98985	0.519434	0.259717	+	0.965685i	$0.416371\pi$
$60$	−3.55334	−0.458735
$61$	11.5255	1.47568	0.737841	−	0.674974i	$-0.235845\pi$
$61$	11.5255	1.47568	0.737841	+	0.674974i	$0.235845\pi$
$62$	6.97716	0.886100
$63$	−1.52463	−0.192086
$64$	−8.99072	−1.12384
$65$	−9.23303	−1.14522
$66$	−8.07920	−0.994481
$67$	13.4563	1.64395	0.821974	−	0.569525i	$-0.192873\pi$
$67$	13.4563	1.64395	0.821974	+	0.569525i	$0.192873\pi$
$68$	−2.12821	−0.258084
$69$	6.50396	0.782985
$70$	5.17211	0.618186
$71$	10.3921	1.23332	0.616658	−	0.787231i	$-0.288486\pi$
$71$	10.3921	1.23332	0.616658	+	0.787231i	$0.288486\pi$
$72$	−0.260503	−0.0307005
$73$	16.6564	1.94949	0.974744	−	0.223326i	$-0.0716913\pi$
$73$	16.6564	1.94949	0.974744	+	0.223326i	$0.0716913\pi$
$74$	0.722866	0.0840315
$75$	2.21231	0.255456
$76$	−7.44587	−0.854100
$77$	6.06251	0.690887
$78$	−11.2358	−1.27220
$79$	1.00000	0.112509
$79$	1.00000	0.112509
$80$	−6.22296	−0.695749
$81$	1.00000	0.111111
$82$	17.1123	1.88973
$83$	−11.9320	−1.30971	−0.654853	−	0.755757i	$-0.727269\pi$
$83$	−11.9320	−1.30971	−0.654853	+	0.755757i	$0.727269\pi$
$84$	3.24474	0.354030
$85$	−1.66964	−0.181098
$86$	13.8571	1.49425
$87$	9.08450	0.973960
$88$	1.03586	0.110423
$89$	−6.77056	−0.717678	−0.358839	−	0.933400i	$-0.616827\pi$
$89$	−6.77056	−0.717678	−0.358839	+	0.933400i	$0.616827\pi$
$90$	−3.39237	−0.357587
$91$	8.43116	0.883826
$92$	−13.8418	−1.44311
$93$	3.43398	0.356087
$94$	−27.2859	−2.81432
$95$	−5.84148	−0.599323
$96$	−8.09380	−0.826070
$97$	−4.06995	−0.413241	−0.206620	−	0.978421i	$-0.566247\pi$
$97$	−4.06995	−0.413241	−0.206620	+	0.978421i	$0.566247\pi$
$98$	9.49968	0.959612
$99$	−3.97638	−0.399641
$100$	−4.70827	−0.470827
$101$	13.8713	1.38025	0.690125	−	0.723690i	$-0.257556\pi$
$101$	13.8713	1.38025	0.690125	+	0.723690i	$0.257556\pi$
$102$	−2.03180	−0.201178
$103$	7.47496	0.736530	0.368265	−	0.929721i	$-0.379952\pi$
$103$	7.47496	0.736530	0.368265	+	0.929721i	$0.379952\pi$
$104$	1.44057	0.141260
$105$	2.54558	0.248423
$106$	18.8674	1.83256
$107$	8.76990	0.847818	0.423909	−	0.905705i	$-0.360658\pi$
$107$	8.76990	0.847818	0.423909	+	0.905705i	$0.360658\pi$
$108$	−2.12821	−0.204787
$109$	7.88864	0.755595	0.377797	−	0.925888i	$-0.376682\pi$
$109$	7.88864	0.755595	0.377797	+	0.925888i	$0.376682\pi$
$110$	13.4893	1.28616
$111$	0.355776	0.0337688
$112$	5.68251	0.536947
$113$	−11.9604	−1.12514	−0.562570	−	0.826750i	$-0.690187\pi$
$113$	−11.9604	−1.12514	−0.562570	+	0.826750i	$0.690187\pi$
$114$	−7.10856	−0.665777
$115$	−10.8593	−1.01263
$116$	−19.3337	−1.79509
$117$	−5.52996	−0.511245
$118$	−8.10657	−0.746271
$119$	1.52463	0.139763
$120$	0.434945	0.0397049
$121$	4.81157	0.437415
$122$	−23.4174	−2.12011
$123$	8.42222	0.759406
$124$	−7.30823	−0.656299
$125$	−12.0419	−1.07706
$126$	3.09775	0.275969
$127$	4.45024	0.394895	0.197447	−	0.980314i	$-0.436735\pi$
$127$	4.45024	0.394895	0.197447	+	0.980314i	$0.436735\pi$
$128$	2.07974	0.183825
$129$	6.82010	0.600476
$130$	18.7597	1.64533
$131$	0.358536	0.0313254	0.0156627	−	0.999877i	$-0.495014\pi$
$131$	0.358536	0.0313254	0.0156627	+	0.999877i	$0.495014\pi$
$132$	8.46257	0.736573
$133$	5.33415	0.462530
$134$	−27.3405	−2.36186
$135$	−1.66964	−0.143699
$136$	0.260503	0.0223379
$137$	−21.6014	−1.84554	−0.922768	−	0.385357i	$-0.874078\pi$
$137$	−21.6014	−1.84554	−0.922768	+	0.385357i	$0.874078\pi$
$138$	−13.2147	−1.12491
$139$	1.61548	0.137023	0.0685115	−	0.997650i	$-0.478175\pi$
$139$	1.61548	0.137023	0.0685115	+	0.997650i	$0.478175\pi$
$140$	−5.41754	−0.457866
$141$	−13.4294	−1.13096
$142$	−21.1147	−1.77191
$143$	21.9892	1.83883
$144$	−3.72714	−0.310595
$145$	−15.1678	−1.25962
$146$	−33.8425	−2.80083
$147$	4.67550	0.385629
$148$	−0.757167	−0.0622388
$149$	16.3503	1.33947	0.669734	−	0.742601i	$-0.266408\pi$
$149$	16.3503	1.33947	0.669734	+	0.742601i	$0.266408\pi$
$150$	−4.49498	−0.367013
$151$	20.0928	1.63513	0.817565	−	0.575837i	$-0.195324\pi$
$151$	20.0928	1.63513	0.817565	+	0.575837i	$0.195324\pi$
$152$	0.911408	0.0739249
$153$	−1.00000	−0.0808452
$154$	−12.3178	−0.992597
$155$	−5.73350	−0.460526
$156$	11.7689	0.942269
$157$	−15.5964	−1.24473	−0.622364	−	0.782728i	$-0.713827\pi$
$157$	−15.5964	−1.24473	−0.622364	+	0.782728i	$0.713827\pi$
$158$	−2.03180	−0.161641
$159$	9.28604	0.736431
$160$	13.5137	1.06835
$161$	9.91614	0.781502
$162$	−2.03180	−0.159633
$163$	−15.2348	−1.19328	−0.596641	−	0.802508i	$-0.703498\pi$
$163$	−15.2348	−1.19328	−0.596641	+	0.802508i	$0.703498\pi$
$164$	−17.9243	−1.39965
$165$	6.63911	0.516854
$166$	24.2434	1.88165
$167$	−12.0380	−0.931526	−0.465763	−	0.884910i	$-0.654220\pi$
$167$	−12.0380	−0.931526	−0.465763	+	0.884910i	$0.654220\pi$
$168$	−0.397171	−0.0306424
$169$	17.5805	1.35235
$170$	3.39237	0.260183
$171$	−3.49865	−0.267548
$172$	−14.5146	−1.10673
$173$	−15.1170	−1.14933	−0.574663	−	0.818390i	$-0.694867\pi$
$173$	−15.1170	−1.14933	−0.574663	+	0.818390i	$0.694867\pi$
$174$	−18.4579	−1.39929
$175$	3.37296	0.254972
$176$	14.8205	1.11714
$177$	−3.98985	−0.299895
$178$	13.7564	1.03109
$179$	11.9799	0.895420	0.447710	−	0.894179i	$-0.352240\pi$
$179$	11.9799	0.895420	0.447710	+	0.894179i	$0.352240\pi$
$180$	3.55334	0.264851
$181$	6.20030	0.460864	0.230432	−	0.973088i	$-0.425986\pi$
$181$	6.20030	0.460864	0.230432	+	0.973088i	$0.425986\pi$
$182$	−17.1304	−1.26979
$183$	−11.5255	−0.851986
$184$	1.69430	0.124905
$185$	−0.594017	−0.0436730
$186$	−6.97716	−0.511590
$187$	3.97638	0.290781
$188$	28.5806	2.08446
$189$	1.52463	0.110901
$190$	11.8687	0.861047
$191$	−15.0052	−1.08574	−0.542871	−	0.839816i	$-0.682663\pi$
$191$	−15.0052	−1.08574	−0.542871	+	0.839816i	$0.682663\pi$
$192$	8.99072	0.648849
$193$	−14.1243	−1.01669	−0.508343	−	0.861155i	$-0.669742\pi$
$193$	−14.1243	−1.01669	−0.508343	+	0.861155i	$0.669742\pi$
$194$	8.26933	0.593703
$195$	9.23303	0.661191
$196$	−9.95045	−0.710747
$197$	6.69370	0.476906	0.238453	−	0.971154i	$-0.423360\pi$
$197$	6.69370	0.476906	0.238453	+	0.971154i	$0.423360\pi$
$198$	8.07920	0.574164
$199$	−1.53949	−0.109131	−0.0545657	−	0.998510i	$-0.517377\pi$
$199$	−1.53949	−0.109131	−0.0545657	+	0.998510i	$0.517377\pi$
$200$	0.576313	0.0407515
$201$	−13.4563	−0.949134
$202$	−28.1838	−1.98300
$203$	13.8505	0.972115
$204$	2.12821	0.149005
$205$	−14.0620	−0.982136
$206$	−15.1876	−1.05817
$207$	−6.50396	−0.452056
$208$	20.6109	1.42911
$209$	13.9119	0.962309
$210$	−5.17211	−0.356910
$211$	17.1373	1.17978	0.589891	−	0.807483i	$-0.299171\pi$
$211$	17.1373	1.17978	0.589891	+	0.807483i	$0.299171\pi$
$212$	−19.7627	−1.35731
$213$	−10.3921	−0.712056
$214$	−17.8187	−1.21806
$215$	−11.3871	−0.776593
$216$	0.260503	0.0177250
$217$	5.23555	0.355412
$218$	−16.0281	−1.08556
$219$	−16.6564	−1.12554
$220$	−14.1294	−0.952606
$221$	5.52996	0.371986
$222$	−0.722866	−0.0485156
$223$	−2.95949	−0.198182	−0.0990909	−	0.995078i	$-0.531593\pi$
$223$	−2.95949	−0.198182	−0.0990909	+	0.995078i	$0.531593\pi$
$224$	−12.3401	−0.824505
$225$	−2.21231	−0.147487
$226$	24.3011	1.61649
$227$	−0.639859	−0.0424689	−0.0212345	−	0.999775i	$-0.506760\pi$
$227$	−0.639859	−0.0424689	−0.0212345	+	0.999775i	$0.506760\pi$
$228$	7.44587	0.493115
$229$	14.3383	0.947499	0.473749	−	0.880660i	$-0.342900\pi$
$229$	14.3383	0.947499	0.473749	+	0.880660i	$0.342900\pi$
$230$	22.0638	1.45485
$231$	−6.06251	−0.398884
$232$	2.36654	0.155371
$233$	−22.9544	−1.50379	−0.751895	−	0.659283i	$-0.770860\pi$
$233$	−22.9544	−1.50379	−0.751895	+	0.659283i	$0.770860\pi$
$234$	11.2358	0.734506
$235$	22.4222	1.46267
$236$	8.49124	0.552733
$237$	−1.00000	−0.0649570
$238$	−3.09775	−0.200797
$239$	−2.32206	−0.150202	−0.0751009	−	0.997176i	$-0.523928\pi$
$239$	−2.32206	−0.150202	−0.0751009	+	0.997176i	$0.523928\pi$
$240$	6.22296	0.401691
$241$	13.4898	0.868952	0.434476	−	0.900684i	$-0.356934\pi$
$241$	13.4898	0.868952	0.434476	+	0.900684i	$0.356934\pi$
$242$	−9.77614	−0.628434
$243$	−1.00000	−0.0641500
$244$	24.5286	1.57028
$245$	−7.80638	−0.498732
$246$	−17.1123	−1.09104
$247$	19.3474	1.23105
$248$	0.894560	0.0568046
$249$	11.9320	0.756159
$250$	24.4668	1.54742
$251$	9.74170	0.614891	0.307445	−	0.951566i	$-0.400526\pi$
$251$	9.74170	0.614891	0.307445	+	0.951566i	$0.400526\pi$
$252$	−3.24474	−0.204399
$253$	25.8622	1.62594
$254$	−9.04199	−0.567345
$255$	1.66964	0.104557
$256$	13.7558	0.859739
$257$	−27.3433	−1.70563	−0.852815	−	0.522213i	$-0.825107\pi$
$257$	−27.3433	−1.70563	−0.852815	+	0.522213i	$0.825107\pi$
$258$	−13.8571	−0.862704
$259$	0.542428	0.0337048
$260$	−19.6499	−1.21863
$261$	−9.08450	−0.562316
$262$	−0.728474	−0.0450053
$263$	3.75276	0.231405	0.115702	−	0.993284i	$-0.463088\pi$
$263$	3.75276	0.231405	0.115702	+	0.993284i	$0.463088\pi$
$264$	−1.03586	−0.0637526
$265$	−15.5043	−0.952423
$266$	−10.8379	−0.664516
$267$	6.77056	0.414351
$268$	28.6379	1.74934
$269$	−28.6118	−1.74449	−0.872245	−	0.489069i	$-0.837337\pi$
$269$	−28.6118	−1.74449	−0.872245	+	0.489069i	$0.837337\pi$
$270$	3.39237	0.206453
$271$	−7.75036	−0.470801	−0.235400	−	0.971899i	$-0.575640\pi$
$271$	−7.75036	−0.470801	−0.235400	+	0.971899i	$0.575640\pi$
$272$	3.72714	0.225991
$273$	−8.43116	−0.510277
$274$	43.8898	2.65148
$275$	8.79698	0.530478
$276$	13.8418	0.833179
$277$	20.1967	1.21350	0.606751	−	0.794892i	$-0.292472\pi$
$277$	20.1967	1.21350	0.606751	+	0.794892i	$0.292472\pi$
$278$	−3.28233	−0.196861
$279$	−3.43398	−0.205587
$280$	0.663131	0.0396297
$281$	4.91826	0.293399	0.146700	−	0.989181i	$-0.453135\pi$
$281$	4.91826	0.293399	0.146700	+	0.989181i	$0.453135\pi$
$282$	27.2859	1.62485
$283$	−21.0666	−1.25228	−0.626140	−	0.779711i	$-0.715366\pi$
$283$	−21.0666	−1.25228	−0.626140	+	0.779711i	$0.715366\pi$
$284$	22.1166	1.31238
$285$	5.84148	0.346019
$286$	−44.6777	−2.64185
$287$	12.8408	0.757967
$288$	8.09380	0.476932
$289$	1.00000	0.0588235
$290$	30.8180	1.80969
$291$	4.06995	0.238585
$292$	35.4484	2.07446
$293$	33.2598	1.94306	0.971528	−	0.236924i	$-0.0761393\pi$
$293$	33.2598	1.94306	0.971528	+	0.236924i	$0.0761393\pi$
$294$	−9.49968	−0.554032
$295$	6.66160	0.387853
$296$	0.0926806	0.00538695
$297$	3.97638	0.230733
$298$	−33.2205	−1.92441
$299$	35.9667	2.08001
$300$	4.70827	0.271832
$301$	10.3981	0.599339
$302$	−40.8246	−2.34919
$303$	−13.8713	−0.796888
$304$	13.0399	0.747892
$305$	19.2433	1.10187
$306$	2.03180	0.116150
$307$	6.23375	0.355779	0.177890	−	0.984050i	$-0.443073\pi$
$307$	6.23375	0.355779	0.177890	+	0.984050i	$0.443073\pi$
$308$	12.9023	0.735177
$309$	−7.47496	−0.425236
$310$	11.6493	0.661637
$311$	−0.278986	−0.0158198	−0.00790992	−	0.999969i	$-0.502518\pi$
$311$	−0.278986	−0.0158198	−0.00790992	+	0.999969i	$0.502518\pi$
$312$	−1.44057	−0.0815562
$313$	−9.88410	−0.558683	−0.279341	−	0.960192i	$-0.590116\pi$
$313$	−9.88410	−0.558683	−0.279341	+	0.960192i	$0.590116\pi$
$314$	31.6887	1.78830
$315$	−2.54558	−0.143427
$316$	2.12821	0.119721
$317$	−14.1691	−0.795815	−0.397908	−	0.917426i	$-0.630264\pi$
$317$	−14.1691	−0.795815	−0.397908	+	0.917426i	$0.630264\pi$
$318$	−18.8674	−1.05803
$319$	36.1234	2.02252
$320$	−15.0112	−0.839154
$321$	−8.76990	−0.489488
$322$	−20.1476	−1.12278
$323$	3.49865	0.194670
$324$	2.12821	0.118234
$325$	12.2340	0.678620
$326$	30.9541	1.71439
$327$	−7.88864	−0.436243
$328$	2.19401	0.121144
$329$	−20.4749	−1.12882
$330$	−13.4893	−0.742564
$331$	1.52188	0.0836498	0.0418249	−	0.999125i	$-0.486683\pi$
$331$	1.52188	0.0836498	0.0418249	+	0.999125i	$0.486683\pi$
$332$	−25.3938	−1.39367
$333$	−0.355776	−0.0194964
$334$	24.4587	1.33832
$335$	22.4671	1.22751
$336$	−5.68251	−0.310006
$337$	22.1569	1.20696	0.603481	−	0.797377i	$-0.293780\pi$
$337$	22.1569	1.20696	0.603481	+	0.797377i	$0.293780\pi$
$338$	−35.7201	−1.94292
$339$	11.9604	0.649600
$340$	−3.55334	−0.192707
$341$	13.6548	0.739448
$342$	7.10856	0.384387
$343$	17.8008	0.961155
$344$	1.77665	0.0957908
$345$	10.8593	0.584642
$346$	30.7148	1.65124
$347$	−17.3172	−0.929635	−0.464818	−	0.885406i	$-0.653880\pi$
$347$	−17.3172	−0.929635	−0.464818	+	0.885406i	$0.653880\pi$
$348$	19.3337	1.03640
$349$	−18.0948	−0.968591	−0.484296	−	0.874904i	$-0.660924\pi$
$349$	−18.0948	−0.968591	−0.484296	+	0.874904i	$0.660924\pi$
$350$	−6.85318	−0.366318
$351$	5.52996	0.295168
$352$	−32.1840	−1.71541
$353$	−36.4282	−1.93888	−0.969438	−	0.245336i	$-0.921102\pi$
$353$	−36.4282	−1.93888	−0.969438	+	0.245336i	$0.921102\pi$
$354$	8.10657	0.430860
$355$	17.3511	0.920898
$356$	−14.4092	−0.763685
$357$	−1.52463	−0.0806921
$358$	−24.3408	−1.28645
$359$	34.6754	1.83010	0.915050	−	0.403341i	$-0.132151\pi$
$359$	34.6754	1.83010	0.915050	+	0.403341i	$0.132151\pi$
$360$	−0.434945	−0.0229236
$361$	−6.75945	−0.355761
$362$	−12.5978	−0.662124
$363$	−4.81157	−0.252542
$364$	17.9433	0.940485
$365$	27.8102	1.45565
$366$	23.4174	1.22405
$367$	−20.4626	−1.06814	−0.534069	−	0.845441i	$-0.679338\pi$
$367$	−20.4626	−1.06814	−0.534069	+	0.845441i	$0.679338\pi$
$368$	24.2411	1.26366
$369$	−8.42222	−0.438443
$370$	1.20692	0.0627450
$371$	14.1578	0.735036
$372$	7.30823	0.378914
$373$	18.1350	0.938993	0.469497	−	0.882934i	$-0.344435\pi$
$373$	18.1350	0.938993	0.469497	+	0.882934i	$0.344435\pi$
$374$	−8.07920	−0.417766
$375$	12.0419	0.621843
$376$	−3.49840	−0.180416
$377$	50.2369	2.58733
$378$	−3.09775	−0.159331
$379$	29.4678	1.51366	0.756831	−	0.653611i	$-0.226747\pi$
$379$	29.4678	1.51366	0.756831	+	0.653611i	$0.226747\pi$
$380$	−12.4319	−0.637743
$381$	−4.45024	−0.227993
$382$	30.4877	1.55988
$383$	0.666199	0.0340412	0.0170206	−	0.999855i	$-0.494582\pi$
$383$	0.666199	0.0340412	0.0170206	+	0.999855i	$0.494582\pi$
$384$	−2.07974	−0.106131
$385$	10.1222	0.515875
$386$	28.6977	1.46067
$387$	−6.82010	−0.346685
$388$	−8.66172	−0.439732
$389$	−19.7423	−1.00098	−0.500488	−	0.865744i	$-0.666846\pi$
$389$	−19.7423	−1.00098	−0.500488	+	0.865744i	$0.666846\pi$
$390$	−18.7597	−0.949933
$391$	6.50396	0.328919
$392$	1.21798	0.0615173
$393$	−0.358536	−0.0180858
$394$	−13.6003	−0.685171
$395$	1.66964	0.0840086
$396$	−8.46257	−0.425260
$397$	2.76319	0.138681	0.0693403	−	0.997593i	$-0.477911\pi$
$397$	2.76319	0.138681	0.0693403	+	0.997593i	$0.477911\pi$
$398$	3.12793	0.156789
$399$	−5.33415	−0.267042
$400$	8.24559	0.412279
$401$	−24.3677	−1.21686	−0.608431	−	0.793606i	$-0.708201\pi$
$401$	−24.3677	−1.21686	−0.608431	+	0.793606i	$0.708201\pi$
$402$	27.3405	1.36362
$403$	18.9898	0.945948
$404$	29.5212	1.46873
$405$	1.66964	0.0829649
$406$	−28.1415	−1.39664
$407$	1.41470	0.0701241
$408$	−0.260503	−0.0128968
$409$	13.9418	0.689375	0.344688	−	0.938717i	$-0.387985\pi$
$409$	13.9418	0.689375	0.344688	+	0.938717i	$0.387985\pi$
$410$	28.5713	1.41103
$411$	21.6014	1.06552
$412$	15.9083	0.783746
$413$	−6.08305	−0.299327
$414$	13.2147	0.649469
$415$	−19.9221	−0.977936
$416$	−44.7584	−2.19446
$417$	−1.61548	−0.0791102
$418$	−28.2663	−1.38255
$419$	−14.0530	−0.686533	−0.343266	−	0.939238i	$-0.611533\pi$
$419$	−14.0530	−0.686533	−0.343266	+	0.939238i	$0.611533\pi$
$420$	5.41754	0.264349
$421$	−27.1121	−1.32136	−0.660680	−	0.750667i	$-0.729732\pi$
$421$	−27.1121	−1.32136	−0.660680	+	0.750667i	$0.729732\pi$
$422$	−34.8196	−1.69499
$423$	13.4294	0.652960
$424$	2.41904	0.117479
$425$	2.21231	0.107313
$426$	21.1147	1.02301
$427$	−17.5721	−0.850372
$428$	18.6642	0.902169
$429$	−21.9892	−1.06165
$430$	23.1363	1.11573
$431$	−4.54631	−0.218988	−0.109494	−	0.993987i	$-0.534923\pi$
$431$	−4.54631	−0.218988	−0.109494	+	0.993987i	$0.534923\pi$
$432$	3.72714	0.179322
$433$	−30.0193	−1.44264	−0.721319	−	0.692603i	$-0.756464\pi$
$433$	−30.0193	−1.44264	−0.721319	+	0.692603i	$0.756464\pi$
$434$	−10.6376	−0.510621
$435$	15.1678	0.727241
$436$	16.7887	0.804033
$437$	22.7551	1.08852
$438$	33.8425	1.61706
$439$	−29.5317	−1.40947	−0.704734	−	0.709471i	$-0.748934\pi$
$439$	−29.5317	−1.40947	−0.704734	+	0.709471i	$0.748934\pi$
$440$	1.72950	0.0824509
$441$	−4.67550	−0.222643
$442$	−11.2358	−0.534432
$443$	10.2743	0.488149	0.244074	−	0.969757i	$-0.421516\pi$
$443$	10.2743	0.488149	0.244074	+	0.969757i	$0.421516\pi$
$444$	0.757167	0.0359336
$445$	−11.3044	−0.535879
$446$	6.01309	0.284728
$447$	−16.3503	−0.773342
$448$	13.7075	0.647620
$449$	29.0532	1.37111	0.685553	−	0.728023i	$-0.259561\pi$
$449$	29.0532	1.37111	0.685553	+	0.728023i	$0.259561\pi$
$450$	4.49498	0.211895
$451$	33.4899	1.57698
$452$	−25.4543	−1.19727
$453$	−20.0928	−0.944043
$454$	1.30006	0.0610151
$455$	14.0770	0.659939
$456$	−0.911408	−0.0426806
$457$	−15.9102	−0.744250	−0.372125	−	0.928183i	$-0.621371\pi$
$457$	−15.9102	−0.744250	−0.372125	+	0.928183i	$0.621371\pi$
$458$	−29.1325	−1.36127
$459$	1.00000	0.0466760
$460$	−23.1108	−1.07755
$461$	6.16564	0.287162	0.143581	−	0.989639i	$-0.454138\pi$
$461$	6.16564	0.287162	0.143581	+	0.989639i	$0.454138\pi$
$462$	12.3178	0.573076
$463$	23.8252	1.10725	0.553627	−	0.832765i	$-0.313244\pi$
$463$	23.8252	1.10725	0.553627	+	0.832765i	$0.313244\pi$
$464$	33.8592	1.57187
$465$	5.73350	0.265885
$466$	46.6387	2.16049
$467$	−7.10134	−0.328611	−0.164305	−	0.986410i	$-0.552538\pi$
$467$	−7.10134	−0.328611	−0.164305	+	0.986410i	$0.552538\pi$
$468$	−11.7689	−0.544019
$469$	−20.5159	−0.947336
$470$	−45.5575	−2.10141
$471$	15.5964	0.718644
$472$	−1.03937	−0.0478407
$473$	27.1193	1.24695
$474$	2.03180	0.0933237
$475$	7.74010	0.355140
$476$	3.24474	0.148722
$477$	−9.28604	−0.425179
$478$	4.71797	0.215795
$479$	13.0141	0.594628	0.297314	−	0.954780i	$-0.403909\pi$
$479$	13.0141	0.594628	0.297314	+	0.954780i	$0.403909\pi$
$480$	−13.5137	−0.616814
$481$	1.96743	0.0897071
$482$	−27.4085	−1.24842
$483$	−9.91614	−0.451200
$484$	10.2400	0.465456
$485$	−6.79534	−0.308561
$486$	2.03180	0.0921643
$487$	−11.0514	−0.500788	−0.250394	−	0.968144i	$-0.580560\pi$
$487$	−11.0514	−0.500788	−0.250394	+	0.968144i	$0.580560\pi$
$488$	−3.00241	−0.135913
$489$	15.2348	0.688942
$490$	15.8610	0.716528
$491$	11.5027	0.519108	0.259554	−	0.965729i	$-0.416425\pi$
$491$	11.5027	0.519108	0.259554	+	0.965729i	$0.416425\pi$
$492$	17.9243	0.808089
$493$	9.08450	0.409145
$494$	−39.3101	−1.76864
$495$	−6.63911	−0.298406
$496$	12.7989	0.574688
$497$	−15.8441	−0.710707
$498$	−24.2434	−1.08637
$499$	38.3868	1.71843	0.859214	−	0.511616i	$-0.170953\pi$
$499$	38.3868	1.71843	0.859214	+	0.511616i	$0.170953\pi$
$500$	−25.6278	−1.14611
$501$	12.0380	0.537817
$502$	−19.7932	−0.883414
$503$	−3.57974	−0.159613	−0.0798064	−	0.996810i	$-0.525430\pi$
$503$	−3.57974	−0.159613	−0.0798064	+	0.996810i	$0.525430\pi$
$504$	0.397171	0.0176914
$505$	23.1601	1.03061
$506$	−52.5468	−2.33599
$507$	−17.5805	−0.780778
$508$	9.47105	0.420210
$509$	−24.2823	−1.07630	−0.538148	−	0.842851i	$-0.680876\pi$
$509$	−24.2823	−1.07630	−0.538148	+	0.842851i	$0.680876\pi$
$510$	−3.39237	−0.150217
$511$	−25.3949	−1.12341
$512$	−32.1086	−1.41901
$513$	3.49865	0.154469
$514$	55.5562	2.45048
$515$	12.4805	0.549956
$516$	14.5146	0.638971
$517$	−53.4004	−2.34855
$518$	−1.10210	−0.0484237
$519$	15.1170	0.663564
$520$	2.40523	0.105476
$521$	21.4549	0.939956	0.469978	−	0.882678i	$-0.344262\pi$
$521$	21.4549	0.939956	0.469978	+	0.882678i	$0.344262\pi$
$522$	18.4579	0.807880
$523$	−13.0036	−0.568609	−0.284305	−	0.958734i	$-0.591763\pi$
$523$	−13.0036	−0.568609	−0.284305	+	0.958734i	$0.591763\pi$
$524$	0.763041	0.0333336
$525$	−3.37296	−0.147208
$526$	−7.62485	−0.332459
$527$	3.43398	0.149586
$528$	−14.8205	−0.644979
$529$	19.3015	0.839195
$530$	31.5017	1.36835
$531$	3.98985	0.173145
$532$	11.3522	0.492181
$533$	46.5746	2.01737
$534$	−13.7564	−0.595299
$535$	14.6426	0.633053
$536$	−3.50540	−0.151410
$537$	−11.9799	−0.516971
$538$	58.1334	2.50631
$539$	18.5915	0.800794
$540$	−3.55334	−0.152912
$541$	−10.8450	−0.466261	−0.233130	−	0.972445i	$-0.574897\pi$
$541$	−10.8450	−0.466261	−0.233130	+	0.972445i	$0.574897\pi$
$542$	15.7472	0.676399
$543$	−6.20030	−0.266080
$544$	−8.09380	−0.347019
$545$	13.1712	0.564191
$546$	17.1304	0.733115
$547$	24.5778	1.05087	0.525435	−	0.850834i	$-0.323902\pi$
$547$	24.5778	1.05087	0.525435	+	0.850834i	$0.323902\pi$
$548$	−45.9725	−1.96385
$549$	11.5255	0.491894
$550$	−17.8737	−0.762138
$551$	31.7835	1.35402
$552$	−1.69430	−0.0721141
$553$	−1.52463	−0.0648339
$554$	−41.0357	−1.74344
$555$	0.594017	0.0252146
$556$	3.43808	0.145807
$557$	40.0608	1.69743	0.848716	−	0.528850i	$-0.177376\pi$
$557$	40.0608	1.69743	0.848716	+	0.528850i	$0.177376\pi$
$558$	6.97716	0.295367
$559$	37.7149	1.59517
$560$	9.48773	0.400930
$561$	−3.97638	−0.167883
$562$	−9.99293	−0.421526
$563$	−20.7921	−0.876283	−0.438141	−	0.898906i	$-0.644363\pi$
$563$	−20.7921	−0.876283	−0.438141	+	0.898906i	$0.644363\pi$
$564$	−28.5806	−1.20346
$565$	−19.9695	−0.840124
$566$	42.8032	1.79915
$567$	−1.52463	−0.0640285
$568$	−2.70717	−0.113590
$569$	−14.1151	−0.591736	−0.295868	−	0.955229i	$-0.595609\pi$
$569$	−14.1151	−0.591736	−0.295868	+	0.955229i	$0.595609\pi$
$570$	−11.8687	−0.497126
$571$	−11.0469	−0.462298	−0.231149	−	0.972918i	$-0.574248\pi$
$571$	−11.0469	−0.462298	−0.231149	+	0.972918i	$0.574248\pi$
$572$	46.7977	1.95671
$573$	15.0052	0.626853
$574$	−26.0899	−1.08897
$575$	14.3888	0.600054
$576$	−8.99072	−0.374613
$577$	−6.00544	−0.250010	−0.125005	−	0.992156i	$-0.539895\pi$
$577$	−6.00544	−0.250010	−0.125005	+	0.992156i	$0.539895\pi$
$578$	−2.03180	−0.0845118
$579$	14.1243	0.586984
$580$	−32.2803	−1.34037
$581$	18.1919	0.754726
$582$	−8.26933	−0.342775
$583$	36.9248	1.52927
$584$	−4.33905	−0.179551
$585$	−9.23303	−0.381739
$586$	−67.5772	−2.79159
$587$	26.4767	1.09281	0.546405	−	0.837521i	$-0.315996\pi$
$587$	26.4767	1.09281	0.546405	+	0.837521i	$0.315996\pi$
$588$	9.95045	0.410350
$589$	12.0143	0.495040
$590$	−13.5350	−0.557229
$591$	−6.69370	−0.275342
$592$	1.32603	0.0544993
$593$	23.8089	0.977716	0.488858	−	0.872363i	$-0.337414\pi$
$593$	23.8089	0.977716	0.488858	+	0.872363i	$0.337414\pi$
$594$	−8.07920	−0.331494
$595$	2.54558	0.104359
$596$	34.7969	1.42534
$597$	1.53949	0.0630071
$598$	−73.0771	−2.98834
$599$	−36.6656	−1.49811	−0.749057	−	0.662505i	$-0.769493\pi$
$599$	−36.6656	−1.49811	−0.749057	+	0.662505i	$0.769493\pi$
$600$	−0.576313	−0.0235279
$601$	−18.7543	−0.765002	−0.382501	−	0.923955i	$-0.624937\pi$
$601$	−18.7543	−0.765002	−0.382501	+	0.923955i	$0.624937\pi$
$602$	−21.1270	−0.861070
$603$	13.4563	0.547983
$604$	42.7618	1.73995
$605$	8.03357	0.326611
$606$	28.1838	1.14489
$607$	−25.5590	−1.03741	−0.518704	−	0.854954i	$-0.673585\pi$
$607$	−25.5590	−1.03741	−0.518704	+	0.854954i	$0.673585\pi$
$608$	−28.3174	−1.14842
$609$	−13.8505	−0.561251
$610$	−39.0986	−1.58306
$611$	−74.2641	−3.00441
$612$	−2.12821	−0.0860279
$613$	−9.50523	−0.383913	−0.191956	−	0.981403i	$-0.561483\pi$
$613$	−9.50523	−0.383913	−0.191956	+	0.981403i	$0.561483\pi$
$614$	−12.6657	−0.511148
$615$	14.0620	0.567036
$616$	−1.57930	−0.0636318
$617$	−0.345786	−0.0139208	−0.00696040	−	0.999976i	$-0.502216\pi$
$617$	−0.345786	−0.0139208	−0.00696040	+	0.999976i	$0.502216\pi$
$618$	15.1876	0.610936
$619$	−42.3160	−1.70082	−0.850411	−	0.526118i	$-0.823647\pi$
$619$	−42.3160	−1.70082	−0.850411	+	0.526118i	$0.823647\pi$
$620$	−12.2021	−0.490048
$621$	6.50396	0.260995
$622$	0.566844	0.0227284
$623$	10.3226	0.413567
$624$	−20.6109	−0.825097
$625$	−9.04412	−0.361765
$626$	20.0825	0.802659
$627$	−13.9119	−0.555590
$628$	−33.1924	−1.32452
$629$	0.355776	0.0141857
$630$	5.17211	0.206062
$631$	−15.6035	−0.621167	−0.310584	−	0.950546i	$-0.600524\pi$
$631$	−15.6035	−0.621167	−0.310584	+	0.950546i	$0.600524\pi$
$632$	−0.260503	−0.0103622
$633$	−17.1373	−0.681148
$634$	28.7888	1.14335
$635$	7.43028	0.294862
$636$	19.7627	0.783641
$637$	25.8553	1.02443
$638$	−73.3955	−2.90575
$639$	10.3921	0.411105
$640$	3.47241	0.137259
$641$	12.9659	0.512123	0.256062	−	0.966660i	$-0.417575\pi$
$641$	12.9659	0.512123	0.256062	+	0.966660i	$0.417575\pi$
$642$	17.8187	0.703248
$643$	25.0753	0.988875	0.494437	−	0.869213i	$-0.335374\pi$
$643$	25.0753	0.988875	0.494437	+	0.869213i	$0.335374\pi$
$644$	21.1037	0.831601
$645$	11.3871	0.448366
$646$	−7.10856	−0.279682
$647$	6.44283	0.253294	0.126647	−	0.991948i	$-0.459579\pi$
$647$	6.44283	0.253294	0.126647	+	0.991948i	$0.459579\pi$
$648$	−0.260503	−0.0102335
$649$	−15.8651	−0.622761
$650$	−24.8571	−0.974974
$651$	−5.23555	−0.205197
$652$	−32.4229	−1.26978
$653$	17.4342	0.682255	0.341127	−	0.940017i	$-0.389191\pi$
$653$	17.4342	0.682255	0.341127	+	0.940017i	$0.389191\pi$
$654$	16.0281	0.626750
$655$	0.598625	0.0233902
$656$	31.3907	1.22560
$657$	16.6564	0.649829
$658$	41.6009	1.62177
$659$	12.7471	0.496555	0.248278	−	0.968689i	$-0.420136\pi$
$659$	12.7471	0.496555	0.248278	+	0.968689i	$0.420136\pi$
$660$	14.1294	0.549987
$661$	−20.3995	−0.793449	−0.396725	−	0.917938i	$-0.629853\pi$
$661$	−20.3995	−0.793449	−0.396725	+	0.917938i	$0.629853\pi$
$662$	−3.09215	−0.120180
$663$	−5.52996	−0.214766
$664$	3.10831	0.120626
$665$	8.90610	0.345364
$666$	0.722866	0.0280105
$667$	59.0852	2.28779
$668$	−25.6193	−0.991242
$669$	2.95949	0.114420
$670$	−45.6487	−1.76356
$671$	−45.8295	−1.76923
$672$	12.3401	0.476028
$673$	35.3861	1.36404	0.682018	−	0.731336i	$-0.261103\pi$
$673$	35.3861	1.36404	0.682018	+	0.731336i	$0.261103\pi$
$674$	−45.0183	−1.73404
$675$	2.21231	0.0851519
$676$	37.4151	1.43904
$677$	−24.3025	−0.934021	−0.467011	−	0.884252i	$-0.654669\pi$
$677$	−24.3025	−0.934021	−0.467011	+	0.884252i	$0.654669\pi$
$678$	−24.3011	−0.933280
$679$	6.20518	0.238133
$680$	0.434945	0.0166794
$681$	0.639859	0.0245194
$682$	−27.7438	−1.06236
$683$	−38.6470	−1.47879	−0.739393	−	0.673275i	$-0.764887\pi$
$683$	−38.6470	−1.47879	−0.739393	+	0.673275i	$0.764887\pi$
$684$	−7.44587	−0.284700
$685$	−36.0666	−1.37803
$686$	−36.1677	−1.38089
$687$	−14.3383	−0.547039
$688$	25.4194	0.969107
$689$	51.3515	1.95634
$690$	−22.0638	−0.839956
$691$	−38.4848	−1.46403	−0.732015	−	0.681289i	$-0.761420\pi$
$691$	−38.4848	−1.46403	−0.732015	+	0.681289i	$0.761420\pi$
$692$	−32.1722	−1.22301
$693$	6.06251	0.230296
$694$	35.1851	1.33561
$695$	2.69726	0.102313
$696$	−2.36654	−0.0897033
$697$	8.42222	0.319014
$698$	36.7650	1.39158
$699$	22.9544	0.868213
$700$	7.17838	0.271317
$701$	−13.6458	−0.515395	−0.257697	−	0.966226i	$-0.582964\pi$
$701$	−13.6458	−0.515395	−0.257697	+	0.966226i	$0.582964\pi$
$702$	−11.2358	−0.424067
$703$	1.24474	0.0469461
$704$	35.7505	1.34740
$705$	−22.4222	−0.844470
$706$	74.0148	2.78558
$707$	−21.1487	−0.795378
$708$	−8.49124	−0.319121
$709$	−3.32366	−0.124823	−0.0624114	−	0.998051i	$-0.519879\pi$
$709$	−3.32366	−0.124823	−0.0624114	+	0.998051i	$0.519879\pi$
$710$	−35.2539	−1.32305
$711$	1.00000	0.0375029
$712$	1.76375	0.0660993
$713$	22.3344	0.836432
$714$	3.09775	0.115930
$715$	36.7140	1.37303
$716$	25.4958	0.952823
$717$	2.32206	0.0867191
$718$	−70.4536	−2.62930
$719$	−6.02974	−0.224871	−0.112436	−	0.993659i	$-0.535865\pi$
$719$	−6.02974	−0.224871	−0.112436	+	0.993659i	$0.535865\pi$
$720$	−6.22296	−0.231916
$721$	−11.3966	−0.424430
$722$	13.7339	0.511121
$723$	−13.4898	−0.501689
$724$	13.1956	0.490409
$725$	20.0977	0.746411
$726$	9.77614	0.362827
$727$	−26.4670	−0.981605	−0.490802	−	0.871271i	$-0.663296\pi$
$727$	−26.4670	−0.981605	−0.490802	+	0.871271i	$0.663296\pi$
$728$	−2.19634	−0.0814018
$729$	1.00000	0.0370370
$730$	−56.5048	−2.09134
$731$	6.82010	0.252251
$732$	−24.5286	−0.906604
$733$	13.0955	0.483694	0.241847	−	0.970314i	$-0.422247\pi$
$733$	13.0955	0.483694	0.241847	+	0.970314i	$0.422247\pi$
$734$	41.5759	1.53459
$735$	7.80638	0.287943
$736$	−52.6418	−1.94040
$737$	−53.5073	−1.97097
$738$	17.1123	0.629911
$739$	27.8314	1.02380	0.511898	−	0.859047i	$-0.328943\pi$
$739$	27.8314	1.02380	0.511898	+	0.859047i	$0.328943\pi$
$740$	−1.26419	−0.0464727
$741$	−19.3474	−0.710745
$742$	−28.7658	−1.05603
$743$	−36.1775	−1.32722	−0.663612	−	0.748077i	$-0.730977\pi$
$743$	−36.1775	−1.32722	−0.663612	+	0.748077i	$0.730977\pi$
$744$	−0.894560	−0.0327962
$745$	27.2990	1.00016
$746$	−36.8466	−1.34905
$747$	−11.9320	−0.436568
$748$	8.46257	0.309422
$749$	−13.3709	−0.488561
$750$	−24.4668	−0.893402
$751$	−38.4157	−1.40181	−0.700905	−	0.713255i	$-0.747220\pi$
$751$	−38.4157	−1.40181	−0.700905	+	0.713255i	$0.747220\pi$
$752$	−50.0532	−1.82525
$753$	−9.74170	−0.355007
$754$	−102.071	−3.71722
$755$	33.5477	1.22093
$756$	3.24474	0.118010
$757$	24.6869	0.897260	0.448630	−	0.893718i	$-0.351912\pi$
$757$	24.6869	0.897260	0.448630	+	0.893718i	$0.351912\pi$
$758$	−59.8728	−2.17468
$759$	−25.8622	−0.938738
$760$	1.52172	0.0551986
$761$	−7.92913	−0.287431	−0.143715	−	0.989619i	$-0.545905\pi$
$761$	−7.92913	−0.287431	−0.143715	+	0.989619i	$0.545905\pi$
$762$	9.04199	0.327557
$763$	−12.0273	−0.435417
$764$	−31.9344	−1.15534
$765$	−1.66964	−0.0603659
$766$	−1.35358	−0.0489070
$767$	−22.0637	−0.796675
$768$	−13.7558	−0.496370
$769$	−5.52648	−0.199290	−0.0996449	−	0.995023i	$-0.531771\pi$
$769$	−5.52648	−0.199290	−0.0996449	+	0.995023i	$0.531771\pi$
$770$	−20.5663	−0.741157
$771$	27.3433	0.984746
$772$	−30.0594	−1.08186
$773$	41.8960	1.50690	0.753448	−	0.657508i	$-0.228389\pi$
$773$	41.8960	1.50690	0.753448	+	0.657508i	$0.228389\pi$
$774$	13.8571	0.498083
$775$	7.59703	0.272893
$776$	1.06023	0.0380602
$777$	−0.542428	−0.0194595
$778$	40.1125	1.43810
$779$	29.4664	1.05574
$780$	19.6499	0.703578
$781$	−41.3229	−1.47865
$782$	−13.2147	−0.472558
$783$	9.08450	0.324653
$784$	17.4262	0.622365
$785$	−26.0403	−0.929418
$786$	0.728474	0.0259838
$787$	7.39273	0.263522	0.131761	−	0.991281i	$-0.457937\pi$
$787$	7.39273	0.263522	0.131761	+	0.991281i	$0.457937\pi$
$788$	14.2456	0.507479
$789$	−3.75276	−0.133602
$790$	−3.39237	−0.120695
$791$	18.2352	0.648369
$792$	1.03586	0.0368076
$793$	−63.7353	−2.26331
$794$	−5.61425	−0.199242
$795$	15.5043	0.549882
$796$	−3.27636	−0.116127
$797$	−30.8992	−1.09451	−0.547253	−	0.836967i	$-0.684326\pi$
$797$	−30.8992	−1.09451	−0.547253	+	0.836967i	$0.684326\pi$
$798$	10.8379	0.383659
$799$	−13.4294	−0.475098
$800$	−17.9060	−0.633073
$801$	−6.77056	−0.239226
$802$	49.5102	1.74827
$803$	−66.2322	−2.33728
$804$	−28.6379	−1.00998
$805$	16.5564	0.583535
$806$	−38.5834	−1.35904
$807$	28.6118	1.00718
$808$	−3.61352	−0.127123
$809$	−36.1205	−1.26993	−0.634964	−	0.772542i	$-0.718985\pi$
$809$	−36.1205	−1.26993	−0.634964	+	0.772542i	$0.718985\pi$
$810$	−3.39237	−0.119196
$811$	45.1838	1.58662	0.793308	−	0.608820i	$-0.208357\pi$
$811$	45.1838	1.58662	0.793308	+	0.608820i	$0.208357\pi$
$812$	29.4768	1.03443
$813$	7.75036	0.271817
$814$	−2.87439	−0.100747
$815$	−25.4366	−0.891005
$816$	−3.72714	−0.130476
$817$	23.8611	0.834796
$818$	−28.3269	−0.990426
$819$	8.43116	0.294609
$820$	−29.9270	−1.04510
$821$	27.9903	0.976870	0.488435	−	0.872600i	$-0.337568\pi$
$821$	27.9903	0.976870	0.488435	+	0.872600i	$0.337568\pi$
$822$	−43.8898	−1.53083
$823$	−20.6349	−0.719289	−0.359644	−	0.933089i	$-0.617102\pi$
$823$	−20.6349	−0.719289	−0.359644	+	0.933089i	$0.617102\pi$
$824$	−1.94725	−0.0678356
$825$	−8.79698	−0.306272
$826$	12.3595	0.430043
$827$	28.8514	1.00326	0.501631	−	0.865082i	$-0.332733\pi$
$827$	28.8514	1.00326	0.501631	+	0.865082i	$0.332733\pi$
$828$	−13.8418	−0.481036
$829$	20.9851	0.728842	0.364421	−	0.931234i	$-0.381267\pi$
$829$	20.9851	0.728842	0.364421	+	0.931234i	$0.381267\pi$
$830$	40.4777	1.40500
$831$	−20.1967	−0.700616
$832$	49.7183	1.72367
$833$	4.67550	0.161996
$834$	3.28233	0.113658
$835$	−20.0990	−0.695556
$836$	29.6076	1.02400
$837$	3.43398	0.118696
$838$	28.5528	0.986342
$839$	26.0788	0.900341	0.450170	−	0.892943i	$-0.351363\pi$
$839$	26.0788	0.900341	0.450170	+	0.892943i	$0.351363\pi$
$840$	−0.663131	−0.0228802
$841$	53.5281	1.84580
$842$	55.0863	1.89840
$843$	−4.91826	−0.169394
$844$	36.4719	1.25541
$845$	29.3531	1.00978
$846$	−27.2859	−0.938108
$847$	−7.33587	−0.252063
$848$	34.6103	1.18852
$849$	21.0666	0.723004
$850$	−4.49498	−0.154176
$851$	2.31395	0.0793213
$852$	−22.1166	−0.757703
$853$	−26.8755	−0.920200	−0.460100	−	0.887867i	$-0.652186\pi$
$853$	−26.8755	−0.920200	−0.460100	+	0.887867i	$0.652186\pi$
$854$	35.7029	1.22173
$855$	−5.84148	−0.199774
$856$	−2.28458	−0.0780854
$857$	11.0895	0.378810	0.189405	−	0.981899i	$-0.439344\pi$
$857$	11.0895	0.378810	0.189405	+	0.981899i	$0.439344\pi$
$858$	44.6777	1.52527
$859$	57.7197	1.96937	0.984685	−	0.174344i	$-0.0557806\pi$
$859$	57.7197	1.96937	0.984685	+	0.174344i	$0.0557806\pi$
$860$	−24.2342	−0.826378
$861$	−12.8408	−0.437613
$862$	9.23720	0.314620
$863$	−49.6681	−1.69072	−0.845361	−	0.534196i	$-0.820614\pi$
$863$	−49.6681	−1.69072	−0.845361	+	0.534196i	$0.820614\pi$
$864$	−8.09380	−0.275357
$865$	−25.2399	−0.858184
$866$	60.9933	2.07264
$867$	−1.00000	−0.0339618
$868$	11.1424	0.378197
$869$	−3.97638	−0.134889
$870$	−30.8180	−1.04483
$871$	−74.4128	−2.52138
$872$	−2.05501	−0.0695915
$873$	−4.06995	−0.137747
$874$	−46.2338	−1.56388
$875$	18.3595	0.620665
$876$	−35.4484	−1.19769
$877$	26.0893	0.880974	0.440487	−	0.897759i	$-0.354806\pi$
$877$	26.0893	0.880974	0.440487	+	0.897759i	$0.354806\pi$
$878$	60.0024	2.02498
$879$	−33.2598	−1.12182
$880$	24.7448	0.834149
$881$	27.5958	0.929727	0.464863	−	0.885382i	$-0.346103\pi$
$881$	27.5958	0.929727	0.464863	+	0.885382i	$0.346103\pi$
$882$	9.49968	0.319871
$883$	18.8199	0.633340	0.316670	−	0.948536i	$-0.397435\pi$
$883$	18.8199	0.633340	0.316670	+	0.948536i	$0.397435\pi$
$884$	11.7689	0.395832
$885$	−6.66160	−0.223927
$886$	−20.8754	−0.701323
$887$	7.77121	0.260932	0.130466	−	0.991453i	$-0.458353\pi$
$887$	7.77121	0.260932	0.130466	+	0.991453i	$0.458353\pi$
$888$	−0.0926806	−0.00311016
$889$	−6.78497	−0.227561
$890$	22.9682	0.769897
$891$	−3.97638	−0.133214
$892$	−6.29842	−0.210887
$893$	−46.9848	−1.57229
$894$	33.2205	1.11106
$895$	20.0021	0.668596
$896$	−3.17084	−0.105930
$897$	−35.9667	−1.20089
$898$	−59.0303	−1.96987
$899$	31.1960	1.04044
$900$	−4.70827	−0.156942
$901$	9.28604	0.309363
$902$	−68.0448	−2.26564
$903$	−10.3981	−0.346029
$904$	3.11572	0.103627
$905$	10.3522	0.344120
$906$	40.8246	1.35631
$907$	−9.27973	−0.308128	−0.154064	−	0.988061i	$-0.549236\pi$
$907$	−9.27973	−0.308128	−0.154064	+	0.988061i	$0.549236\pi$
$908$	−1.36176	−0.0451914
$909$	13.8713	0.460083
$910$	−28.6016	−0.948134
$911$	−32.3933	−1.07324	−0.536619	−	0.843825i	$-0.680299\pi$
$911$	−32.3933	−1.07324	−0.536619	+	0.843825i	$0.680299\pi$
$912$	−13.0399	−0.431796
$913$	47.4460	1.57023
$914$	32.3264	1.06926
$915$	−19.2433	−0.636165
$916$	30.5149	1.00824
$917$	−0.546636	−0.0180515
$918$	−2.03180	−0.0670594
$919$	0.939396	0.0309878	0.0154939	−	0.999880i	$-0.495068\pi$
$919$	0.939396	0.0309878	0.0154939	+	0.999880i	$0.495068\pi$
$920$	2.82886	0.0932649
$921$	−6.23375	−0.205409
$922$	−12.5273	−0.412566
$923$	−57.4680	−1.89158
$924$	−12.9023	−0.424455
$925$	0.787088	0.0258793
$926$	−48.4081	−1.59079
$927$	7.47496	0.245510
$928$	−73.5281	−2.41368
$929$	−38.0401	−1.24806	−0.624028	−	0.781402i	$-0.714505\pi$
$929$	−38.0401	−1.24806	−0.624028	+	0.781402i	$0.714505\pi$
$930$	−11.6493	−0.381996
$931$	16.3579	0.536109
$932$	−48.8517	−1.60019
$933$	0.278986	0.00913359
$934$	14.4285	0.472115
$935$	6.63911	0.217122
$936$	1.44057	0.0470865
$937$	−42.2179	−1.37920	−0.689599	−	0.724192i	$-0.742213\pi$
$937$	−42.2179	−1.37920	−0.689599	+	0.724192i	$0.742213\pi$
$938$	41.6842	1.36104
$939$	9.88410	0.322556
$940$	47.7193	1.55643
$941$	−14.5206	−0.473359	−0.236680	−	0.971588i	$-0.576059\pi$
$941$	−14.5206	−0.473359	−0.236680	+	0.971588i	$0.576059\pi$
$942$	−31.6887	−1.03248
$943$	54.7778	1.78381
$944$	−14.8707	−0.484000
$945$	2.54558	0.0828078
$946$	−55.1010	−1.79149
$947$	−21.2506	−0.690551	−0.345276	−	0.938501i	$-0.612215\pi$
$947$	−21.2506	−0.690551	−0.345276	+	0.938501i	$0.612215\pi$
$948$	−2.12821	−0.0691211
$949$	−92.1095	−2.99000
$950$	−15.7263	−0.510230
$951$	14.1691	0.459464
$952$	−0.397171	−0.0128724
$953$	22.6889	0.734967	0.367484	−	0.930030i	$-0.380219\pi$
$953$	22.6889	0.734967	0.367484	+	0.930030i	$0.380219\pi$
$954$	18.8674	0.610854
$955$	−25.0533	−0.810706
$956$	−4.94185	−0.159831
$957$	−36.1234	−1.16770
$958$	−26.4420	−0.854302
$959$	32.9342	1.06350
$960$	15.0112	0.484486
$961$	−19.2078	−0.619606
$962$	−3.99742	−0.128882
$963$	8.76990	0.282606
$964$	28.7091	0.924657
$965$	−23.5824	−0.759144
$966$	20.1476	0.648239
$967$	−38.2444	−1.22986	−0.614928	−	0.788583i	$-0.710815\pi$
$967$	−38.2444	−1.22986	−0.614928	+	0.788583i	$0.710815\pi$
$968$	−1.25343	−0.0402866
$969$	−3.49865	−0.112393
$970$	13.8068	0.443309
$971$	−12.9786	−0.416502	−0.208251	−	0.978075i	$-0.566777\pi$
$971$	−12.9786	−0.416502	−0.208251	+	0.978075i	$0.566777\pi$
$972$	−2.12821	−0.0682625
$973$	−2.46301	−0.0789604
$974$	22.4543	0.719483
$975$	−12.2340	−0.391802
$976$	−42.9569	−1.37502
$977$	17.0495	0.545462	0.272731	−	0.962090i	$-0.412073\pi$
$977$	17.0495	0.545462	0.272731	+	0.962090i	$0.412073\pi$
$978$	−30.9541	−0.989803
$979$	26.9223	0.860440
$980$	−16.6136	−0.530703
$981$	7.88864	0.251865
$982$	−23.3711	−0.745802
$983$	−41.9697	−1.33863	−0.669313	−	0.742981i	$-0.733411\pi$
$983$	−41.9697	−1.33863	−0.669313	+	0.742981i	$0.733411\pi$
$984$	−2.19401	−0.0699425
$985$	11.1760	0.356098
$986$	−18.4579	−0.587819
$987$	20.4749	0.651723
$988$	41.1754	1.30996
$989$	44.3577	1.41049
$990$	13.4893	0.428719
$991$	26.6719	0.847261	0.423631	−	0.905835i	$-0.360755\pi$
$991$	26.6719	0.847261	0.423631	+	0.905835i	$0.360755\pi$
$992$	−27.7939	−0.882458
$993$	−1.52188	−0.0482953
$994$	32.1921	1.02107
$995$	−2.57039	−0.0814868
$996$	25.3938	0.804633
$997$	−22.6392	−0.716992	−0.358496	−	0.933531i	$-0.616710\pi$
$997$	−22.6392	−0.716992	−0.358496	+	0.933531i	$0.616710\pi$
$998$	−77.9943	−2.46887
$999$	0.355776	0.0112563

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4029.2.a.l.1.7	✓	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4029.2.a.l.1.7	✓	32	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:	\( N \)	\(=\)	\( 4029 = 3 \cdot 17 \cdot 79 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4029.a (trivial)

\(f(q)\)	\(=\)	\(q-2.03180 q^{2} -1.00000 q^{3} +2.12821 q^{4} +1.66964 q^{5} +2.03180 q^{6} -1.52463 q^{7} -0.260503 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.03180 q^{2} -1.00000 q^{3} +2.12821 q^{4} +1.66964 q^{5} +2.03180 q^{6} -1.52463 q^{7} -0.260503 q^{8} +1.00000 q^{9} -3.39237 q^{10} -3.97638 q^{11} -2.12821 q^{12} -5.52996 q^{13} +3.09775 q^{14} -1.66964 q^{15} -3.72714 q^{16} -1.00000 q^{17} -2.03180 q^{18} -3.49865 q^{19} +3.55334 q^{20} +1.52463 q^{21} +8.07920 q^{22} -6.50396 q^{23} +0.260503 q^{24} -2.21231 q^{25} +11.2358 q^{26} -1.00000 q^{27} -3.24474 q^{28} -9.08450 q^{29} +3.39237 q^{30} -3.43398 q^{31} +8.09380 q^{32} +3.97638 q^{33} +2.03180 q^{34} -2.54558 q^{35} +2.12821 q^{36} -0.355776 q^{37} +7.10856 q^{38} +5.52996 q^{39} -0.434945 q^{40} -8.42222 q^{41} -3.09775 q^{42} -6.82010 q^{43} -8.46257 q^{44} +1.66964 q^{45} +13.2147 q^{46} +13.4294 q^{47} +3.72714 q^{48} -4.67550 q^{49} +4.49498 q^{50} +1.00000 q^{51} -11.7689 q^{52} -9.28604 q^{53} +2.03180 q^{54} -6.63911 q^{55} +0.397171 q^{56} +3.49865 q^{57} +18.4579 q^{58} +3.98985 q^{59} -3.55334 q^{60} +11.5255 q^{61} +6.97716 q^{62} -1.52463 q^{63} -8.99072 q^{64} -9.23303 q^{65} -8.07920 q^{66} +13.4563 q^{67} -2.12821 q^{68} +6.50396 q^{69} +5.17211 q^{70} +10.3921 q^{71} -0.260503 q^{72} +16.6564 q^{73} +0.722866 q^{74} +2.21231 q^{75} -7.44587 q^{76} +6.06251 q^{77} -11.2358 q^{78} +1.00000 q^{79} -6.22296 q^{80} +1.00000 q^{81} +17.1123 q^{82} -11.9320 q^{83} +3.24474 q^{84} -1.66964 q^{85} +13.8571 q^{86} +9.08450 q^{87} +1.03586 q^{88} -6.77056 q^{89} -3.39237 q^{90} +8.43116 q^{91} -13.8418 q^{92} +3.43398 q^{93} -27.2859 q^{94} -5.84148 q^{95} -8.09380 q^{96} -4.06995 q^{97} +9.49968 q^{98} -3.97638 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - q^{2} - 32 q^{3} + 41 q^{4} - q^{5} + q^{6} + 4 q^{7} - 3 q^{8} + 32 q^{9}+O(q^{10}) \) 32 * q - q^2 - 32 * q^3 + 41 * q^4 - q^5 + q^6 + 4 * q^7 - 3 * q^8 + 32 * q^9	\( 32 q - q^{2} - 32 q^{3} + 41 q^{4} - q^{5} + q^{6} + 4 q^{7} - 3 q^{8} + 32 q^{9} + 17 q^{10} + 8 q^{11} - 41 q^{12} + 17 q^{13} + q^{14} + q^{15} + 55 q^{16} - 32 q^{17} - q^{18} + 48 q^{19} - 7 q^{20} - 4 q^{21} - 4 q^{22} - 19 q^{23} + 3 q^{24} + 63 q^{25} + 27 q^{26} - 32 q^{27} + 17 q^{28} - 15 q^{29} - 17 q^{30} + 20 q^{31} + 13 q^{32} - 8 q^{33} + q^{34} + 22 q^{35} + 41 q^{36} + 6 q^{37} + 11 q^{38} - 17 q^{39} + 47 q^{40} + q^{41} - q^{42} + 40 q^{43} + 22 q^{44} - q^{45} + 5 q^{46} - 5 q^{47} - 55 q^{48} + 88 q^{49} + 17 q^{50} + 32 q^{51} + 23 q^{52} - 34 q^{53} + q^{54} + 48 q^{55} - 48 q^{57} - 9 q^{58} + 41 q^{59} + 7 q^{60} + 20 q^{61} + 15 q^{62} + 4 q^{63} + 93 q^{64} - 58 q^{65} + 4 q^{66} + 52 q^{67} - 41 q^{68} + 19 q^{69} + 25 q^{70} + q^{71} - 3 q^{72} + 19 q^{73} + 12 q^{74} - 63 q^{75} + 128 q^{76} - 20 q^{77} - 27 q^{78} + 32 q^{79} - 16 q^{80} + 32 q^{81} - 5 q^{82} + 31 q^{83} - 17 q^{84} + q^{85} - 62 q^{86} + 15 q^{87} + 35 q^{88} + 18 q^{89} + 17 q^{90} + 48 q^{91} - 75 q^{92} - 20 q^{93} + 29 q^{94} + 5 q^{95} - 13 q^{96} + 17 q^{97} + 30 q^{98} + 8 q^{99}+O(q^{100}) \) 32 * q - q^2 - 32 * q^3 + 41 * q^4 - q^5 + q^6 + 4 * q^7 - 3 * q^8 + 32 * q^9 + 17 * q^10 + 8 * q^11 - 41 * q^12 + 17 * q^13 + q^14 + q^15 + 55 * q^16 - 32 * q^17 - q^18 + 48 * q^19 - 7 * q^20 - 4 * q^21 - 4 * q^22 - 19 * q^23 + 3 * q^24 + 63 * q^25 + 27 * q^26 - 32 * q^27 + 17 * q^28 - 15 * q^29 - 17 * q^30 + 20 * q^31 + 13 * q^32 - 8 * q^33 + q^34 + 22 * q^35 + 41 * q^36 + 6 * q^37 + 11 * q^38 - 17 * q^39 + 47 * q^40 + q^41 - q^42 + 40 * q^43 + 22 * q^44 - q^45 + 5 * q^46 - 5 * q^47 - 55 * q^48 + 88 * q^49 + 17 * q^50 + 32 * q^51 + 23 * q^52 - 34 * q^53 + q^54 + 48 * q^55 - 48 * q^57 - 9 * q^58 + 41 * q^59 + 7 * q^60 + 20 * q^61 + 15 * q^62 + 4 * q^63 + 93 * q^64 - 58 * q^65 + 4 * q^66 + 52 * q^67 - 41 * q^68 + 19 * q^69 + 25 * q^70 + q^71 - 3 * q^72 + 19 * q^73 + 12 * q^74 - 63 * q^75 + 128 * q^76 - 20 * q^77 - 27 * q^78 + 32 * q^79 - 16 * q^80 + 32 * q^81 - 5 * q^82 + 31 * q^83 - 17 * q^84 + q^85 - 62 * q^86 + 15 * q^87 + 35 * q^88 + 18 * q^89 + 17 * q^90 + 48 * q^91 - 75 * q^92 - 20 * q^93 + 29 * q^94 + 5 * q^95 - 13 * q^96 + 17 * q^97 + 30 * q^98 + 8 * q^99

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