LMFDB - Embedded newform 4029.2.a.e.1.17

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:	$1$
Dimension:	$18$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} - 6 x^{17} - 10 x^{16} + 120 x^{15} - 56 x^{14} - 921 x^{13} + 1181 x^{12} + 3316 x^{11} + \cdots + 138 $ x^18 - 6x^17 - 10x^16 + 120x^15 - 56x^14 - 921x^13 + 1181x^12 + 3316x^11 - 6280x^10 - 5249x^9 + 15005x^8 + 1809x^7 - 16711x^6 + 2434x^5 + 8758x^4 - 1858x^3 - 1942x^2 + 318*x + 138
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.17
Root			$-2.10151$ of defining polynomial
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)

$f(q)$	$=$	$q+2.10151 q^{2} +1.00000 q^{3} +2.41637 q^{4} -0.968130 q^{5} +2.10151 q^{6} -2.79477 q^{7} +0.874998 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+2.10151 q^{2} +1.00000 q^{3} +2.41637 q^{4} -0.968130 q^{5} +2.10151 q^{6} -2.79477 q^{7} +0.874998 q^{8} +1.00000 q^{9} -2.03454 q^{10} +1.65381 q^{11} +2.41637 q^{12} -3.84710 q^{13} -5.87326 q^{14} -0.968130 q^{15} -2.99391 q^{16} +1.00000 q^{17} +2.10151 q^{18} -6.42897 q^{19} -2.33936 q^{20} -2.79477 q^{21} +3.47551 q^{22} +5.76204 q^{23} +0.874998 q^{24} -4.06272 q^{25} -8.08473 q^{26} +1.00000 q^{27} -6.75319 q^{28} -1.39425 q^{29} -2.03454 q^{30} +5.58344 q^{31} -8.04174 q^{32} +1.65381 q^{33} +2.10151 q^{34} +2.70570 q^{35} +2.41637 q^{36} -4.64197 q^{37} -13.5106 q^{38} -3.84710 q^{39} -0.847111 q^{40} -4.80574 q^{41} -5.87326 q^{42} -1.63866 q^{43} +3.99621 q^{44} -0.968130 q^{45} +12.1090 q^{46} -3.46221 q^{47} -2.99391 q^{48} +0.810761 q^{49} -8.53788 q^{50} +1.00000 q^{51} -9.29599 q^{52} -6.66007 q^{53} +2.10151 q^{54} -1.60110 q^{55} -2.44542 q^{56} -6.42897 q^{57} -2.93004 q^{58} +7.59040 q^{59} -2.33936 q^{60} -10.3593 q^{61} +11.7337 q^{62} -2.79477 q^{63} -10.9120 q^{64} +3.72449 q^{65} +3.47551 q^{66} -11.0766 q^{67} +2.41637 q^{68} +5.76204 q^{69} +5.68608 q^{70} +10.9817 q^{71} +0.874998 q^{72} -16.3268 q^{73} -9.75518 q^{74} -4.06272 q^{75} -15.5347 q^{76} -4.62202 q^{77} -8.08473 q^{78} -1.00000 q^{79} +2.89849 q^{80} +1.00000 q^{81} -10.0993 q^{82} +3.58119 q^{83} -6.75319 q^{84} -0.968130 q^{85} -3.44368 q^{86} -1.39425 q^{87} +1.44708 q^{88} +10.3531 q^{89} -2.03454 q^{90} +10.7518 q^{91} +13.9232 q^{92} +5.58344 q^{93} -7.27588 q^{94} +6.22408 q^{95} -8.04174 q^{96} +1.40543 q^{97} +1.70383 q^{98} +1.65381 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q - 6 q^{2} + 18 q^{3} + 20 q^{4} - 5 q^{5} - 6 q^{6} - 13 q^{7} - 12 q^{8} + 18 q^{9}+O(q^{10}) $ 18 * q - 6 * q^2 + 18 * q^3 + 20 * q^4 - 5 * q^5 - 6 * q^6 - 13 * q^7 - 12 * q^8 + 18 * q^9	\( 18 q - 6 q^{2} + 18 q^{3} + 20 q^{4} - 5 q^{5} - 6 q^{6} - 13 q^{7} - 12 q^{8} + 18 q^{9} - 15 q^{10} - 27 q^{11} + 20 q^{12} - 4 q^{13} - 5 q^{14} - 5 q^{15} + 16 q^{16} + 18 q^{17} - 6 q^{18} - 30 q^{19} - 16 q^{20} - 13 q^{21} + 13 q^{22} - 21 q^{23} - 12 q^{24} + 13 q^{25} - 20 q^{26} + 18 q^{27} - 33 q^{28} - 47 q^{29} - 15 q^{30} - 18 q^{31} - 45 q^{32} - 27 q^{33} - 6 q^{34} - 17 q^{35} + 20 q^{36} + q^{37} + 5 q^{38} - 4 q^{39} - 12 q^{40} - 18 q^{41} - 5 q^{42} - 39 q^{43} - 34 q^{44} - 5 q^{45} - 7 q^{46} + 16 q^{48} + 15 q^{49} - 23 q^{50} + 18 q^{51} + 5 q^{52} - 9 q^{53} - 6 q^{54} + q^{55} - 24 q^{56} - 30 q^{57} + 41 q^{58} - 42 q^{59} - 16 q^{60} - 43 q^{61} - 54 q^{62} - 13 q^{63} + 22 q^{64} - 25 q^{65} + 13 q^{66} + 20 q^{68} - 21 q^{69} + 17 q^{70} + 9 q^{71} - 12 q^{72} + 19 q^{73} - 30 q^{74} + 13 q^{75} - 17 q^{76} - 14 q^{77} - 20 q^{78} - 18 q^{79} + 36 q^{80} + 18 q^{81} - 3 q^{82} - 61 q^{83} - 33 q^{84} - 5 q^{85} - 24 q^{86} - 47 q^{87} - 25 q^{88} + 10 q^{89} - 15 q^{90} - 52 q^{91} - 74 q^{92} - 18 q^{93} + 31 q^{94} - 37 q^{95} - 45 q^{96} - 9 q^{97} + 27 q^{98} - 27 q^{99}+O(q^{100}) \) 18 * q - 6 * q^2 + 18 * q^3 + 20 * q^4 - 5 * q^5 - 6 * q^6 - 13 * q^7 - 12 * q^8 + 18 * q^9 - 15 * q^10 - 27 * q^11 + 20 * q^12 - 4 * q^13 - 5 * q^14 - 5 * q^15 + 16 * q^16 + 18 * q^17 - 6 * q^18 - 30 * q^19 - 16 * q^20 - 13 * q^21 + 13 * q^22 - 21 * q^23 - 12 * q^24 + 13 * q^25 - 20 * q^26 + 18 * q^27 - 33 * q^28 - 47 * q^29 - 15 * q^30 - 18 * q^31 - 45 * q^32 - 27 * q^33 - 6 * q^34 - 17 * q^35 + 20 * q^36 + q^37 + 5 * q^38 - 4 * q^39 - 12 * q^40 - 18 * q^41 - 5 * q^42 - 39 * q^43 - 34 * q^44 - 5 * q^45 - 7 * q^46 + 16 * q^48 + 15 * q^49 - 23 * q^50 + 18 * q^51 + 5 * q^52 - 9 * q^53 - 6 * q^54 + q^55 - 24 * q^56 - 30 * q^57 + 41 * q^58 - 42 * q^59 - 16 * q^60 - 43 * q^61 - 54 * q^62 - 13 * q^63 + 22 * q^64 - 25 * q^65 + 13 * q^66 + 20 * q^68 - 21 * q^69 + 17 * q^70 + 9 * q^71 - 12 * q^72 + 19 * q^73 - 30 * q^74 + 13 * q^75 - 17 * q^76 - 14 * q^77 - 20 * q^78 - 18 * q^79 + 36 * q^80 + 18 * q^81 - 3 * q^82 - 61 * q^83 - 33 * q^84 - 5 * q^85 - 24 * q^86 - 47 * q^87 - 25 * q^88 + 10 * q^89 - 15 * q^90 - 52 * q^91 - 74 * q^92 - 18 * q^93 + 31 * q^94 - 37 * q^95 - 45 * q^96 - 9 * q^97 + 27 * q^98 - 27 * 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 $

$2$	2.10151	1.48600	0.742998	−	0.669294i	$-0.233403\pi$
$2$	2.10151	1.48600	0.742998	+	0.669294i	$0.233403\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	2.41637	1.20818
$5$	−0.968130	−0.432961	−0.216480	−	0.976287i	$-0.569458\pi$
$5$	−0.968130	−0.432961	−0.216480	+	0.976287i	$0.569458\pi$
$6$	2.10151	0.857940
$7$	−2.79477	−1.05633	−0.528163	−	0.849143i	$-0.677119\pi$
$7$	−2.79477	−1.05633	−0.528163	+	0.849143i	$0.677119\pi$
$8$	0.874998	0.309358
$9$	1.00000	0.333333
$10$	−2.03454	−0.643378
$11$	1.65381	0.498642	0.249321	−	0.968421i	$-0.419793\pi$
$11$	1.65381	0.498642	0.249321	+	0.968421i	$0.419793\pi$
$12$	2.41637	0.697545
$13$	−3.84710	−1.06699	−0.533496	−	0.845802i	$-0.679122\pi$
$13$	−3.84710	−1.06699	−0.533496	+	0.845802i	$0.679122\pi$
$14$	−5.87326	−1.56969
$15$	−0.968130	−0.249970
$16$	−2.99391	−0.748477
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	2.10151	0.495332
$19$	−6.42897	−1.47491	−0.737454	−	0.675398i	$-0.763972\pi$
$19$	−6.42897	−1.47491	−0.737454	+	0.675398i	$0.763972\pi$
$20$	−2.33936	−0.523096
$21$	−2.79477	−0.609870
$22$	3.47551	0.740980
$23$	5.76204	1.20147	0.600734	−	0.799449i	$-0.294875\pi$
$23$	5.76204	1.20147	0.600734	+	0.799449i	$0.294875\pi$
$24$	0.874998	0.178608
$25$	−4.06272	−0.812545
$26$	−8.08473	−1.58555
$27$	1.00000	0.192450
$28$	−6.75319	−1.27623
$29$	−1.39425	−0.258906	−0.129453	−	0.991586i	$-0.541322\pi$
$29$	−1.39425	−0.258906	−0.129453	+	0.991586i	$0.541322\pi$
$30$	−2.03454	−0.371454
$31$	5.58344	1.00282	0.501408	−	0.865211i	$-0.332816\pi$
$31$	5.58344	1.00282	0.501408	+	0.865211i	$0.332816\pi$
$32$	−8.04174	−1.42159
$33$	1.65381	0.287891
$34$	2.10151	0.360407
$35$	2.70570	0.457347
$36$	2.41637	0.402728
$37$	−4.64197	−0.763136	−0.381568	−	0.924341i	$-0.624616\pi$
$37$	−4.64197	−0.763136	−0.381568	+	0.924341i	$0.624616\pi$
$38$	−13.5106	−2.19171
$39$	−3.84710	−0.616028
$40$	−0.847111	−0.133940
$41$	−4.80574	−0.750531	−0.375265	−	0.926917i	$-0.622448\pi$
$41$	−4.80574	−0.750531	−0.375265	+	0.926917i	$0.622448\pi$
$42$	−5.87326	−0.906264
$43$	−1.63866	−0.249894	−0.124947	−	0.992163i	$-0.539876\pi$
$43$	−1.63866	−0.249894	−0.124947	+	0.992163i	$0.539876\pi$
$44$	3.99621	0.602451
$45$	−0.968130	−0.144320
$46$	12.1090	1.78538
$47$	−3.46221	−0.505015	−0.252507	−	0.967595i	$-0.581255\pi$
$47$	−3.46221	−0.505015	−0.252507	+	0.967595i	$0.581255\pi$
$48$	−2.99391	−0.432134
$49$	0.810761	0.115823
$50$	−8.53788	−1.20744
$51$	1.00000	0.140028
$52$	−9.29599	−1.28912
$53$	−6.66007	−0.914830	−0.457415	−	0.889253i	$-0.651225\pi$
$53$	−6.66007	−0.914830	−0.457415	+	0.889253i	$0.651225\pi$
$54$	2.10151	0.285980
$55$	−1.60110	−0.215893
$56$	−2.44542	−0.326783
$57$	−6.42897	−0.851538
$58$	−2.93004	−0.384733
$59$	7.59040	0.988186	0.494093	−	0.869409i	$-0.335500\pi$
$59$	7.59040	0.988186	0.494093	+	0.869409i	$0.335500\pi$
$60$	−2.33936	−0.302009
$61$	−10.3593	−1.32638	−0.663188	−	0.748452i	$-0.730797\pi$
$61$	−10.3593	−1.32638	−0.663188	+	0.748452i	$0.730797\pi$
$62$	11.7337	1.49018
$63$	−2.79477	−0.352108
$64$	−10.9120	−1.36400
$65$	3.72449	0.461966
$66$	3.47551	0.427805
$67$	−11.0766	−1.35322	−0.676609	−	0.736343i	$-0.736551\pi$
$67$	−11.0766	−1.35322	−0.676609	+	0.736343i	$0.736551\pi$
$68$	2.41637	0.293027
$69$	5.76204	0.693668
$70$	5.68608	0.679616
$71$	10.9817	1.30328	0.651642	−	0.758527i	$-0.274080\pi$
$71$	10.9817	1.30328	0.651642	+	0.758527i	$0.274080\pi$
$72$	0.874998	0.103119
$73$	−16.3268	−1.91090	−0.955452	−	0.295146i	$-0.904632\pi$
$73$	−16.3268	−1.91090	−0.955452	+	0.295146i	$0.904632\pi$
$74$	−9.75518	−1.13402
$75$	−4.06272	−0.469123
$76$	−15.5347	−1.78196
$77$	−4.62202	−0.526729
$78$	−8.08473	−0.915415
$79$	−1.00000	−0.112509
$79$	−1.00000	−0.112509
$80$	2.89849	0.324061
$81$	1.00000	0.111111
$82$	−10.0993	−1.11529
$83$	3.58119	0.393087	0.196543	−	0.980495i	$-0.437028\pi$
$83$	3.58119	0.393087	0.196543	+	0.980495i	$0.437028\pi$
$84$	−6.75319	−0.736834
$85$	−0.968130	−0.105008
$86$	−3.44368	−0.371341
$87$	−1.39425	−0.149479
$88$	1.44708	0.154259
$89$	10.3531	1.09743	0.548714	−	0.836010i	$-0.315118\pi$
$89$	10.3531	1.09743	0.548714	+	0.836010i	$0.315118\pi$
$90$	−2.03454	−0.214459
$91$	10.7518	1.12709
$92$	13.9232	1.45159
$93$	5.58344	0.578976
$94$	−7.27588	−0.750449
$95$	6.22408	0.638577
$96$	−8.04174	−0.820757
$97$	1.40543	0.142700	0.0713498	−	0.997451i	$-0.477269\pi$
$97$	1.40543	0.142700	0.0713498	+	0.997451i	$0.477269\pi$
$98$	1.70383	0.172112
$99$	1.65381	0.166214
$100$	−9.81703	−0.981703
$101$	−12.7116	−1.26485	−0.632427	−	0.774620i	$-0.717941\pi$
$101$	−12.7116	−1.26485	−0.632427	+	0.774620i	$0.717941\pi$
$102$	2.10151	0.208081
$103$	11.1350	1.09716	0.548582	−	0.836097i	$-0.315168\pi$
$103$	11.1350	1.09716	0.548582	+	0.836097i	$0.315168\pi$
$104$	−3.36620	−0.330083
$105$	2.70570	0.264050
$106$	−13.9962	−1.35943
$107$	−14.4705	−1.39891	−0.699456	−	0.714676i	$-0.746574\pi$
$107$	−14.4705	−1.39891	−0.699456	+	0.714676i	$0.746574\pi$
$108$	2.41637	0.232515
$109$	−15.5291	−1.48741	−0.743707	−	0.668506i	$-0.766934\pi$
$109$	−15.5291	−1.48741	−0.743707	+	0.668506i	$0.766934\pi$
$110$	−3.36474	−0.320815
$111$	−4.64197	−0.440597
$112$	8.36730	0.790636
$113$	19.2115	1.80727	0.903634	−	0.428305i	$-0.140889\pi$
$113$	19.2115	1.80727	0.903634	+	0.428305i	$0.140889\pi$
$114$	−13.5106	−1.26538
$115$	−5.57840	−0.520189
$116$	−3.36902	−0.312805
$117$	−3.84710	−0.355664
$118$	15.9513	1.46844
$119$	−2.79477	−0.256197
$120$	−0.847111	−0.0773303
$121$	−8.26491	−0.751356
$122$	−21.7703	−1.97099
$123$	−4.80574	−0.433319
$124$	13.4916	1.21158
$125$	8.77389	0.784761
$126$	−5.87326	−0.523232
$127$	13.0626	1.15912	0.579560	−	0.814929i	$-0.303224\pi$
$127$	13.0626	1.15912	0.579560	+	0.814929i	$0.303224\pi$
$128$	−6.84829	−0.605309
$129$	−1.63866	−0.144276
$130$	7.82707	0.686479
$131$	0.865074	0.0755819	0.0377910	−	0.999286i	$-0.487968\pi$
$131$	0.865074	0.0755819	0.0377910	+	0.999286i	$0.487968\pi$
$132$	3.99621	0.347825
$133$	17.9675	1.55798
$134$	−23.2776	−2.01087
$135$	−0.968130	−0.0833233
$136$	0.874998	0.0750304
$137$	7.31125	0.624642	0.312321	−	0.949977i	$-0.398894\pi$
$137$	7.31125	0.624642	0.312321	+	0.949977i	$0.398894\pi$
$138$	12.1090	1.03079
$139$	19.3215	1.63883	0.819416	−	0.573200i	$-0.194298\pi$
$139$	19.3215	1.63883	0.819416	+	0.573200i	$0.194298\pi$
$140$	6.53797	0.552559
$141$	−3.46221	−0.291570
$142$	23.0781	1.93667
$143$	−6.36236	−0.532048
$144$	−2.99391	−0.249492
$145$	1.34981	0.112096
$146$	−34.3110	−2.83959
$147$	0.810761	0.0668705
$148$	−11.2167	−0.922008
$149$	11.7197	0.960117	0.480058	−	0.877237i	$-0.340615\pi$
$149$	11.7197	0.960117	0.480058	+	0.877237i	$0.340615\pi$
$150$	−8.53788	−0.697115
$151$	−2.08714	−0.169849	−0.0849244	−	0.996387i	$-0.527065\pi$
$151$	−2.08714	−0.169849	−0.0849244	+	0.996387i	$0.527065\pi$
$152$	−5.62533	−0.456275
$153$	1.00000	0.0808452
$154$	−9.71325	−0.782716
$155$	−5.40550	−0.434180
$156$	−9.29599	−0.744275
$157$	16.3191	1.30240	0.651202	−	0.758904i	$-0.274265\pi$
$157$	16.3191	1.30240	0.651202	+	0.758904i	$0.274265\pi$
$158$	−2.10151	−0.167188
$159$	−6.66007	−0.528178
$160$	7.78545	0.615494
$161$	−16.1036	−1.26914
$162$	2.10151	0.165111
$163$	−0.836367	−0.0655093	−0.0327547	−	0.999463i	$-0.510428\pi$
$163$	−0.836367	−0.0655093	−0.0327547	+	0.999463i	$0.510428\pi$
$164$	−11.6124	−0.906778
$165$	−1.60110	−0.124646
$166$	7.52593	0.584126
$167$	10.5792	0.818640	0.409320	−	0.912391i	$-0.365766\pi$
$167$	10.5792	0.818640	0.409320	+	0.912391i	$0.365766\pi$
$168$	−2.44542	−0.188668
$169$	1.80015	0.138473
$170$	−2.03454	−0.156042
$171$	−6.42897	−0.491636
$172$	−3.95961	−0.301917
$173$	−3.28029	−0.249396	−0.124698	−	0.992195i	$-0.539796\pi$
$173$	−3.28029	−0.249396	−0.124698	+	0.992195i	$0.539796\pi$
$174$	−2.93004	−0.222125
$175$	11.3544	0.858312
$176$	−4.95136	−0.373223
$177$	7.59040	0.570530
$178$	21.7572	1.63077
$179$	20.8181	1.55602	0.778009	−	0.628253i	$-0.216230\pi$
$179$	20.8181	1.55602	0.778009	+	0.628253i	$0.216230\pi$
$180$	−2.33936	−0.174365
$181$	−10.4757	−0.778649	−0.389324	−	0.921101i	$-0.627292\pi$
$181$	−10.4757	−0.778649	−0.389324	+	0.921101i	$0.627292\pi$
$182$	22.5950	1.67485
$183$	−10.3593	−0.765784
$184$	5.04177	0.371684
$185$	4.49403	0.330408
$186$	11.7337	0.860356
$187$	1.65381	0.120939
$188$	−8.36595	−0.610150
$189$	−2.79477	−0.203290
$190$	13.0800	0.948923
$191$	11.4398	0.827757	0.413879	−	0.910332i	$-0.364174\pi$
$191$	11.4398	0.827757	0.413879	+	0.910332i	$0.364174\pi$
$192$	−10.9120	−0.787507
$193$	6.88168	0.495354	0.247677	−	0.968843i	$-0.420333\pi$
$193$	6.88168	0.495354	0.247677	+	0.968843i	$0.420333\pi$
$194$	2.95353	0.212051
$195$	3.72449	0.266716
$196$	1.95909	0.139935
$197$	9.17724	0.653851	0.326926	−	0.945050i	$-0.393987\pi$
$197$	9.17724	0.653851	0.326926	+	0.945050i	$0.393987\pi$
$198$	3.47551	0.246993
$199$	−23.6685	−1.67781	−0.838907	−	0.544275i	$-0.816805\pi$
$199$	−23.6685	−1.67781	−0.838907	+	0.544275i	$0.816805\pi$
$200$	−3.55487	−0.251368
$201$	−11.0766	−0.781280
$202$	−26.7137	−1.87957
$203$	3.89661	0.273489
$204$	2.41637	0.169179
$205$	4.65258	0.324950
$206$	23.4003	1.63038
$207$	5.76204	0.400489
$208$	11.5179	0.798620
$209$	−10.6323	−0.735451
$210$	5.68608	0.392377
$211$	−21.7491	−1.49727	−0.748636	−	0.662981i	$-0.769291\pi$
$211$	−21.7491	−1.49727	−0.748636	+	0.662981i	$0.769291\pi$
$212$	−16.0932	−1.10528
$213$	10.9817	0.752452
$214$	−30.4099	−2.07878
$215$	1.58644	0.108194
$216$	0.874998	0.0595360
$217$	−15.6045	−1.05930
$218$	−32.6345	−2.21029
$219$	−16.3268	−1.10326
$220$	−3.86885	−0.260838
$221$	−3.84710	−0.258784
$222$	−9.75518	−0.654725
$223$	14.2541	0.954526	0.477263	−	0.878760i	$-0.341629\pi$
$223$	14.2541	0.954526	0.477263	+	0.878760i	$0.341629\pi$
$224$	22.4748	1.50166
$225$	−4.06272	−0.270848
$226$	40.3733	2.68559
$227$	−24.0993	−1.59953	−0.799764	−	0.600315i	$-0.795042\pi$
$227$	−24.0993	−1.59953	−0.799764	+	0.600315i	$0.795042\pi$
$228$	−15.5347	−1.02881
$229$	11.6509	0.769912	0.384956	−	0.922935i	$-0.374217\pi$
$229$	11.6509	0.769912	0.384956	+	0.922935i	$0.374217\pi$
$230$	−11.7231	−0.772998
$231$	−4.62202	−0.304107
$232$	−1.21997	−0.0800946
$233$	−2.95040	−0.193287	−0.0966434	−	0.995319i	$-0.530811\pi$
$233$	−2.95040	−0.193287	−0.0966434	+	0.995319i	$0.530811\pi$
$234$	−8.08473	−0.528515
$235$	3.35186	0.218652
$236$	18.3412	1.19391
$237$	−1.00000	−0.0649570
$238$	−5.87326	−0.380707
$239$	12.9361	0.836768	0.418384	−	0.908270i	$-0.362597\pi$
$239$	12.9361	0.836768	0.418384	+	0.908270i	$0.362597\pi$
$240$	2.89849	0.187097
$241$	8.90889	0.573872	0.286936	−	0.957950i	$-0.407363\pi$
$241$	8.90889	0.573872	0.286936	+	0.957950i	$0.407363\pi$
$242$	−17.3688	−1.11651
$243$	1.00000	0.0641500
$244$	−25.0319	−1.60251
$245$	−0.784922	−0.0501468
$246$	−10.0993	−0.643910
$247$	24.7329	1.57371
$248$	4.88550	0.310229
$249$	3.58119	0.226949
$250$	18.4385	1.16615
$251$	−14.7523	−0.931156	−0.465578	−	0.885007i	$-0.654154\pi$
$251$	−14.7523	−0.931156	−0.465578	+	0.885007i	$0.654154\pi$
$252$	−6.75319	−0.425411
$253$	9.52932	0.599103
$254$	27.4513	1.72245
$255$	−0.968130	−0.0606266
$256$	7.43225	0.464516
$257$	−3.15337	−0.196702	−0.0983508	−	0.995152i	$-0.531357\pi$
$257$	−3.15337	−0.196702	−0.0983508	+	0.995152i	$0.531357\pi$
$258$	−3.44368	−0.214394
$259$	12.9733	0.806120
$260$	8.99972	0.558139
$261$	−1.39425	−0.0863019
$262$	1.81797	0.112314
$263$	20.0561	1.23671	0.618356	−	0.785898i	$-0.287799\pi$
$263$	20.0561	1.23671	0.618356	+	0.785898i	$0.287799\pi$
$264$	1.44708	0.0890616
$265$	6.44781	0.396086
$266$	37.7590	2.31515
$267$	10.3531	0.633600
$268$	−26.7650	−1.63493
$269$	−23.8964	−1.45699	−0.728494	−	0.685052i	$-0.759779\pi$
$269$	−23.8964	−1.45699	−0.728494	+	0.685052i	$0.759779\pi$
$270$	−2.03454	−0.123818
$271$	−26.0940	−1.58510	−0.792548	−	0.609810i	$-0.791246\pi$
$271$	−26.0940	−1.58510	−0.792548	+	0.609810i	$0.791246\pi$
$272$	−2.99391	−0.181532
$273$	10.7518	0.650726
$274$	15.3647	0.928215
$275$	−6.71897	−0.405169
$276$	13.9232	0.838077
$277$	26.3964	1.58601	0.793004	−	0.609216i	$-0.208516\pi$
$277$	26.3964	1.58601	0.793004	+	0.609216i	$0.208516\pi$
$278$	40.6045	2.43530
$279$	5.58344	0.334272
$280$	2.36748	0.141484
$281$	−16.0419	−0.956978	−0.478489	−	0.878093i	$-0.658815\pi$
$281$	−16.0419	−0.956978	−0.478489	+	0.878093i	$0.658815\pi$
$282$	−7.27588	−0.433272
$283$	−32.9109	−1.95635	−0.978175	−	0.207784i	$-0.933375\pi$
$283$	−32.9109	−1.95635	−0.978175	+	0.207784i	$0.933375\pi$
$284$	26.5357	1.57461
$285$	6.22408	0.368683
$286$	−13.3706	−0.790620
$287$	13.4310	0.792804
$288$	−8.04174	−0.473864
$289$	1.00000	0.0588235
$290$	2.83666	0.166574
$291$	1.40543	0.0823877
$292$	−39.4514	−2.30872
$293$	−27.2883	−1.59420	−0.797100	−	0.603848i	$-0.793633\pi$
$293$	−27.2883	−1.59420	−0.797100	+	0.603848i	$0.793633\pi$
$294$	1.70383	0.0993692
$295$	−7.34850	−0.427846
$296$	−4.06172	−0.236082
$297$	1.65381	0.0959638
$298$	24.6292	1.42673
$299$	−22.1671	−1.28196
$300$	−9.81703	−0.566786
$301$	4.57969	0.263969
$302$	−4.38615	−0.252394
$303$	−12.7116	−0.730263
$304$	19.2478	1.10393
$305$	10.0292	0.574269
$306$	2.10151	0.120136
$307$	−8.12346	−0.463630	−0.231815	−	0.972760i	$-0.574466\pi$
$307$	−8.12346	−0.463630	−0.231815	+	0.972760i	$0.574466\pi$
$308$	−11.1685	−0.636384
$309$	11.1350	0.633447
$310$	−11.3597	−0.645189
$311$	−26.6028	−1.50851	−0.754253	−	0.656584i	$-0.772001\pi$
$311$	−26.6028	−1.50851	−0.754253	+	0.656584i	$0.772001\pi$
$312$	−3.36620	−0.190574
$313$	9.06089	0.512152	0.256076	−	0.966657i	$-0.417570\pi$
$313$	9.06089	0.512152	0.256076	+	0.966657i	$0.417570\pi$
$314$	34.2948	1.93537
$315$	2.70570	0.152449
$316$	−2.41637	−0.135931
$317$	−4.51834	−0.253775	−0.126888	−	0.991917i	$-0.540499\pi$
$317$	−4.51834	−0.253775	−0.126888	+	0.991917i	$0.540499\pi$
$318$	−13.9962	−0.784869
$319$	−2.30582	−0.129101
$320$	10.5643	0.590560
$321$	−14.4705	−0.807662
$322$	−33.8419	−1.88594
$323$	−6.42897	−0.357718
$324$	2.41637	0.134243
$325$	15.6297	0.866979
$326$	−1.75764	−0.0973466
$327$	−15.5291	−0.858759
$328$	−4.20501	−0.232183
$329$	9.67608	0.533460
$330$	−3.36474	−0.185223
$331$	−17.2968	−0.950718	−0.475359	−	0.879792i	$-0.657682\pi$
$331$	−17.2968	−0.950718	−0.475359	+	0.879792i	$0.657682\pi$
$332$	8.65347	0.474921
$333$	−4.64197	−0.254379
$334$	22.2323	1.21650
$335$	10.7235	0.585890
$336$	8.36730	0.456474
$337$	12.5411	0.683158	0.341579	−	0.939853i	$-0.389038\pi$
$337$	12.5411	0.683158	0.341579	+	0.939853i	$0.389038\pi$
$338$	3.78303	0.205770
$339$	19.2115	1.04343
$340$	−2.33936	−0.126869
$341$	9.23395	0.500046
$342$	−13.5106	−0.730568
$343$	17.2975	0.933978
$344$	−1.43383	−0.0773067
$345$	−5.57840	−0.300331
$346$	−6.89358	−0.370601
$347$	−12.7345	−0.683626	−0.341813	−	0.939768i	$-0.611041\pi$
$347$	−12.7345	−0.683626	−0.341813	+	0.939768i	$0.611041\pi$
$348$	−3.36902	−0.180598
$349$	−6.59080	−0.352798	−0.176399	−	0.984319i	$-0.556445\pi$
$349$	−6.59080	−0.352798	−0.176399	+	0.984319i	$0.556445\pi$
$350$	23.8614	1.27545
$351$	−3.84710	−0.205343
$352$	−13.2995	−0.708866
$353$	15.6572	0.833348	0.416674	−	0.909056i	$-0.363196\pi$
$353$	15.6572	0.833348	0.416674	+	0.909056i	$0.363196\pi$
$354$	15.9513	0.847805
$355$	−10.6317	−0.564271
$356$	25.0169	1.32589
$357$	−2.79477	−0.147915
$358$	43.7496	2.31224
$359$	29.8670	1.57632	0.788160	−	0.615471i	$-0.211034\pi$
$359$	29.8670	1.57632	0.788160	+	0.615471i	$0.211034\pi$
$360$	−0.847111	−0.0446467
$361$	22.3317	1.17535
$362$	−22.0147	−1.15707
$363$	−8.26491	−0.433795
$364$	25.9802	1.36173
$365$	15.8064	0.827347
$366$	−21.7703	−1.13795
$367$	9.83346	0.513302	0.256651	−	0.966504i	$-0.417381\pi$
$367$	9.83346	0.513302	0.256651	+	0.966504i	$0.417381\pi$
$368$	−17.2510	−0.899272
$369$	−4.80574	−0.250177
$370$	9.44428	0.490985
$371$	18.6134	0.966358
$372$	13.4916	0.699509
$373$	−18.0779	−0.936036	−0.468018	−	0.883719i	$-0.655032\pi$
$373$	−18.0779	−0.936036	−0.468018	+	0.883719i	$0.655032\pi$
$374$	3.47551	0.179714
$375$	8.77389	0.453082
$376$	−3.02942	−0.156230
$377$	5.36381	0.276250
$378$	−5.87326	−0.302088
$379$	10.9356	0.561726	0.280863	−	0.959748i	$-0.409379\pi$
$379$	10.9356	0.561726	0.280863	+	0.959748i	$0.409379\pi$
$380$	15.0396	0.771518
$381$	13.0626	0.669219
$382$	24.0410	1.23004
$383$	−17.9946	−0.919479	−0.459740	−	0.888054i	$-0.652057\pi$
$383$	−17.9946	−0.919479	−0.459740	+	0.888054i	$0.652057\pi$
$384$	−6.84829	−0.349475
$385$	4.47472	0.228053
$386$	14.4619	0.736094
$387$	−1.63866	−0.0832979
$388$	3.39603	0.172407
$389$	−13.3188	−0.675291	−0.337645	−	0.941273i	$-0.609630\pi$
$389$	−13.3188	−0.675291	−0.337645	+	0.941273i	$0.609630\pi$
$390$	7.82707	0.396339
$391$	5.76204	0.291399
$392$	0.709414	0.0358308
$393$	0.865074	0.0436372
$394$	19.2861	0.971620
$395$	0.968130	0.0487119
$396$	3.99621	0.200817
$397$	22.7372	1.14115	0.570573	−	0.821247i	$-0.306721\pi$
$397$	22.7372	1.14115	0.570573	+	0.821247i	$0.306721\pi$
$398$	−49.7397	−2.49322
$399$	17.9675	0.899501
$400$	12.1634	0.608172
$401$	6.42738	0.320968	0.160484	−	0.987038i	$-0.448695\pi$
$401$	6.42738	0.320968	0.160484	+	0.987038i	$0.448695\pi$
$402$	−23.2776	−1.16098
$403$	−21.4800	−1.07000
$404$	−30.7159	−1.52817
$405$	−0.968130	−0.0481068
$406$	8.18879	0.406403
$407$	−7.67694	−0.380532
$408$	0.874998	0.0433188
$409$	−4.72261	−0.233518	−0.116759	−	0.993160i	$-0.537251\pi$
$409$	−4.72261	−0.233518	−0.116759	+	0.993160i	$0.537251\pi$
$410$	9.77747	0.482875
$411$	7.31125	0.360637
$412$	26.9062	1.32557
$413$	−21.2135	−1.04385
$414$	12.1090	0.595125
$415$	−3.46706	−0.170191
$416$	30.9373	1.51683
$417$	19.3215	0.946180
$418$	−22.3439	−1.09288
$419$	27.3786	1.33753	0.668766	−	0.743473i	$-0.266823\pi$
$419$	27.3786	1.33753	0.668766	+	0.743473i	$0.266823\pi$
$420$	6.53797	0.319020
$421$	27.1931	1.32531	0.662655	−	0.748924i	$-0.269429\pi$
$421$	27.1931	1.32531	0.662655	+	0.748924i	$0.269429\pi$
$422$	−45.7061	−2.22494
$423$	−3.46221	−0.168338
$424$	−5.82754	−0.283010
$425$	−4.06272	−0.197071
$426$	23.0781	1.11814
$427$	28.9520	1.40109
$428$	−34.9659	−1.69014
$429$	−6.36236	−0.307178
$430$	3.33392	0.160776
$431$	33.6181	1.61933	0.809664	−	0.586894i	$-0.199649\pi$
$431$	33.6181	1.61933	0.809664	+	0.586894i	$0.199649\pi$
$432$	−2.99391	−0.144045
$433$	12.4511	0.598360	0.299180	−	0.954197i	$-0.403287\pi$
$433$	12.4511	0.598360	0.299180	+	0.954197i	$0.403287\pi$
$434$	−32.7930	−1.57411
$435$	1.34981	0.0647187
$436$	−37.5239	−1.79707
$437$	−37.0440	−1.77205
$438$	−34.3110	−1.63944
$439$	6.67733	0.318692	0.159346	−	0.987223i	$-0.449062\pi$
$439$	6.67733	0.318692	0.159346	+	0.987223i	$0.449062\pi$
$440$	−1.40096	−0.0667882
$441$	0.810761	0.0386077
$442$	−8.08473	−0.384551
$443$	37.0928	1.76233	0.881166	−	0.472807i	$-0.156759\pi$
$443$	37.0928	1.76233	0.881166	+	0.472807i	$0.156759\pi$
$444$	−11.2167	−0.532321
$445$	−10.0232	−0.475143
$446$	29.9552	1.41842
$447$	11.7197	0.554324
$448$	30.4966	1.44083
$449$	−14.5414	−0.686253	−0.343126	−	0.939289i	$-0.611486\pi$
$449$	−14.5414	−0.686253	−0.343126	+	0.939289i	$0.611486\pi$
$450$	−8.53788	−0.402479
$451$	−7.94778	−0.374246
$452$	46.4221	2.18351
$453$	−2.08714	−0.0980622
$454$	−50.6451	−2.37689
$455$	−10.4091	−0.487986
$456$	−5.62533	−0.263430
$457$	−19.7321	−0.923028	−0.461514	−	0.887133i	$-0.652694\pi$
$457$	−19.7321	−0.923028	−0.461514	+	0.887133i	$0.652694\pi$
$458$	24.4845	1.14409
$459$	1.00000	0.0466760
$460$	−13.4795	−0.628483
$461$	16.1101	0.750324	0.375162	−	0.926959i	$-0.377587\pi$
$461$	16.1101	0.750324	0.375162	+	0.926959i	$0.377587\pi$
$462$	−9.71325	−0.451901
$463$	−20.3828	−0.947271	−0.473636	−	0.880721i	$-0.657059\pi$
$463$	−20.3828	−0.947271	−0.473636	+	0.880721i	$0.657059\pi$
$464$	4.17426	0.193785
$465$	−5.40550	−0.250674
$466$	−6.20030	−0.287223
$467$	10.5043	0.486080	0.243040	−	0.970016i	$-0.421855\pi$
$467$	10.5043	0.486080	0.243040	+	0.970016i	$0.421855\pi$
$468$	−9.29599	−0.429707
$469$	30.9565	1.42944
$470$	7.04399	0.324915
$471$	16.3191	0.751944
$472$	6.64158	0.305704
$473$	−2.71004	−0.124608
$474$	−2.10151	−0.0965258
$475$	26.1191	1.19843
$476$	−6.75319	−0.309532
$477$	−6.66007	−0.304943
$478$	27.1854	1.24343
$479$	−26.5571	−1.21342	−0.606712	−	0.794922i	$-0.707512\pi$
$479$	−26.5571	−1.21342	−0.606712	+	0.794922i	$0.707512\pi$
$480$	7.78545	0.355356
$481$	17.8581	0.814260
$482$	18.7222	0.852771
$483$	−16.1036	−0.732739
$484$	−19.9710	−0.907775
$485$	−1.36064	−0.0617833
$486$	2.10151	0.0953267
$487$	−15.3673	−0.696360	−0.348180	−	0.937428i	$-0.613200\pi$
$487$	−15.3673	−0.696360	−0.348180	+	0.937428i	$0.613200\pi$
$488$	−9.06439	−0.410326
$489$	−0.836367	−0.0378218
$490$	−1.64953	−0.0745180
$491$	−29.2700	−1.32094	−0.660468	−	0.750854i	$-0.729642\pi$
$491$	−29.2700	−1.32094	−0.660468	+	0.750854i	$0.729642\pi$
$492$	−11.6124	−0.523528
$493$	−1.39425	−0.0627938
$494$	51.9765	2.33853
$495$	−1.60110	−0.0719642
$496$	−16.7163	−0.750585
$497$	−30.6913	−1.37669
$498$	7.52593	0.337245
$499$	−18.9174	−0.846859	−0.423429	−	0.905929i	$-0.639174\pi$
$499$	−18.9174	−0.846859	−0.423429	+	0.905929i	$0.639174\pi$
$500$	21.2009	0.948134
$501$	10.5792	0.472642
$502$	−31.0022	−1.38369
$503$	−29.5461	−1.31740	−0.658698	−	0.752407i	$-0.728893\pi$
$503$	−29.5461	−1.31740	−0.658698	+	0.752407i	$0.728893\pi$
$504$	−2.44542	−0.108928
$505$	12.3065	0.547632
$506$	20.0260	0.890264
$507$	1.80015	0.0799473
$508$	31.5641	1.40043
$509$	−2.95755	−0.131091	−0.0655455	−	0.997850i	$-0.520879\pi$
$509$	−2.95755	−0.131091	−0.0655455	+	0.997850i	$0.520879\pi$
$510$	−2.03454	−0.0900909
$511$	45.6296	2.01854
$512$	29.3156	1.29558
$513$	−6.42897	−0.283846
$514$	−6.62685	−0.292298
$515$	−10.7801	−0.475029
$516$	−3.95961	−0.174312
$517$	−5.72583	−0.251822
$518$	27.2635	1.19789
$519$	−3.28029	−0.143989
$520$	3.25892	0.142913
$521$	−44.1789	−1.93551	−0.967756	−	0.251891i	$-0.918948\pi$
$521$	−44.1789	−1.93551	−0.967756	+	0.251891i	$0.918948\pi$
$522$	−2.93004	−0.128244
$523$	−31.9170	−1.39563	−0.697816	−	0.716277i	$-0.745845\pi$
$523$	−31.9170	−1.39563	−0.697816	+	0.716277i	$0.745845\pi$
$524$	2.09034	0.0913167
$525$	11.3544	0.495547
$526$	42.1482	1.83775
$527$	5.58344	0.243219
$528$	−4.95136	−0.215480
$529$	10.2011	0.443526
$530$	13.5502	0.588582
$531$	7.59040	0.329395
$532$	43.4161	1.88233
$533$	18.4881	0.800810
$534$	21.7572	0.941527
$535$	14.0093	0.605674
$536$	−9.69196	−0.418629
$537$	20.8181	0.898368
$538$	−50.2186	−2.16508
$539$	1.34084	0.0577543
$540$	−2.33936	−0.100670
$541$	−30.1128	−1.29465	−0.647325	−	0.762214i	$-0.724112\pi$
$541$	−30.1128	−1.29465	−0.647325	+	0.762214i	$0.724112\pi$
$542$	−54.8369	−2.35544
$543$	−10.4757	−0.449553
$544$	−8.04174	−0.344787
$545$	15.0341	0.643992
$546$	22.5950	0.966976
$547$	−19.4378	−0.831101	−0.415551	−	0.909570i	$-0.636411\pi$
$547$	−19.4378	−0.831101	−0.415551	+	0.909570i	$0.636411\pi$
$548$	17.6666	0.754681
$549$	−10.3593	−0.442126
$550$	−14.1200	−0.602080
$551$	8.96359	0.381862
$552$	5.04177	0.214592
$553$	2.79477	0.118846
$554$	55.4725	2.35680
$555$	4.49403	0.190761
$556$	46.6879	1.98001
$557$	30.0061	1.27140	0.635699	−	0.771937i	$-0.280712\pi$
$557$	30.0061	1.27140	0.635699	+	0.771937i	$0.280712\pi$
$558$	11.7337	0.496727
$559$	6.30409	0.266635
$560$	−8.10063	−0.342314
$561$	1.65381	0.0698239
$562$	−33.7123	−1.42207
$563$	−8.70383	−0.366823	−0.183411	−	0.983036i	$-0.558714\pi$
$563$	−8.70383	−0.366823	−0.183411	+	0.983036i	$0.558714\pi$
$564$	−8.36595	−0.352270
$565$	−18.5993	−0.782476
$566$	−69.1627	−2.90713
$567$	−2.79477	−0.117369
$568$	9.60893	0.403182
$569$	−2.57970	−0.108147	−0.0540734	−	0.998537i	$-0.517220\pi$
$569$	−2.57970	−0.108147	−0.0540734	+	0.998537i	$0.517220\pi$
$570$	13.0800	0.547861
$571$	−1.20284	−0.0503372	−0.0251686	−	0.999683i	$-0.508012\pi$
$571$	−1.20284	−0.0503372	−0.0251686	+	0.999683i	$0.508012\pi$
$572$	−15.3738	−0.642811
$573$	11.4398	0.477906
$574$	28.2254	1.17810
$575$	−23.4096	−0.976247
$576$	−10.9120	−0.454668
$577$	18.9230	0.787775	0.393887	−	0.919159i	$-0.371130\pi$
$577$	18.9230	0.787775	0.393887	+	0.919159i	$0.371130\pi$
$578$	2.10151	0.0874115
$579$	6.88168	0.285993
$580$	3.26165	0.135432
$581$	−10.0086	−0.415228
$582$	2.95353	0.122428
$583$	−11.0145	−0.456173
$584$	−14.2859	−0.591154
$585$	3.72449	0.153989
$586$	−57.3468	−2.36897
$587$	0.934893	0.0385872	0.0192936	−	0.999814i	$-0.493858\pi$
$587$	0.934893	0.0385872	0.0192936	+	0.999814i	$0.493858\pi$
$588$	1.95909	0.0807917
$589$	−35.8958	−1.47906
$590$	−15.4430	−0.635777
$591$	9.17724	0.377501
$592$	13.8977	0.571190
$593$	7.55816	0.310376	0.155188	−	0.987885i	$-0.450402\pi$
$593$	7.55816	0.310376	0.155188	+	0.987885i	$0.450402\pi$
$594$	3.47551	0.142602
$595$	2.70570	0.110923
$596$	28.3191	1.16000
$597$	−23.6685	−0.968686
$598$	−46.5845	−1.90498
$599$	−1.65005	−0.0674191	−0.0337096	−	0.999432i	$-0.510732\pi$
$599$	−1.65005	−0.0674191	−0.0337096	+	0.999432i	$0.510732\pi$
$600$	−3.55487	−0.145127
$601$	−40.3669	−1.64660	−0.823300	−	0.567606i	$-0.807870\pi$
$601$	−40.3669	−1.64660	−0.823300	+	0.567606i	$0.807870\pi$
$602$	9.62429	0.392257
$603$	−11.0766	−0.451072
$604$	−5.04328	−0.205208
$605$	8.00151	0.325308
$606$	−26.7137	−1.08517
$607$	−32.1219	−1.30379	−0.651893	−	0.758311i	$-0.726025\pi$
$607$	−32.1219	−1.30379	−0.651893	+	0.758311i	$0.726025\pi$
$608$	51.7001	2.09672
$609$	3.89661	0.157899
$610$	21.0765	0.853361
$611$	13.3194	0.538847
$612$	2.41637	0.0976758
$613$	22.5484	0.910722	0.455361	−	0.890307i	$-0.349510\pi$
$613$	22.5484	0.910722	0.455361	+	0.890307i	$0.349510\pi$
$614$	−17.0716	−0.688953
$615$	4.65258	0.187610
$616$	−4.04426	−0.162948
$617$	12.8977	0.519241	0.259621	−	0.965711i	$-0.416403\pi$
$617$	12.8977	0.519241	0.259621	+	0.965711i	$0.416403\pi$
$618$	23.4003	0.941300
$619$	−36.4606	−1.46548	−0.732738	−	0.680510i	$-0.761758\pi$
$619$	−36.4606	−1.46548	−0.732738	+	0.680510i	$0.761758\pi$
$620$	−13.0617	−0.524569
$621$	5.76204	0.231223
$622$	−55.9062	−2.24163
$623$	−28.9346	−1.15924
$624$	11.5179	0.461083
$625$	11.8194	0.472774
$626$	19.0416	0.761055
$627$	−10.6323	−0.424613
$628$	39.4329	1.57354
$629$	−4.64197	−0.185088
$630$	5.68608	0.226539
$631$	−24.0158	−0.956054	−0.478027	−	0.878345i	$-0.658648\pi$
$631$	−24.0158	−0.956054	−0.478027	+	0.878345i	$0.658648\pi$
$632$	−0.874998	−0.0348055
$633$	−21.7491	−0.864450
$634$	−9.49536	−0.377109
$635$	−12.6463	−0.501854
$636$	−16.0932	−0.638135
$637$	−3.11908	−0.123582
$638$	−4.84572	−0.191844
$639$	10.9817	0.434428
$640$	6.63003	0.262075
$641$	6.12531	0.241935	0.120968	−	0.992656i	$-0.461400\pi$
$641$	6.12531	0.241935	0.120968	+	0.992656i	$0.461400\pi$
$642$	−30.4099	−1.20018
$643$	−25.3181	−0.998446	−0.499223	−	0.866473i	$-0.666381\pi$
$643$	−25.3181	−0.998446	−0.499223	+	0.866473i	$0.666381\pi$
$644$	−38.9122	−1.53335
$645$	1.58644	0.0624660
$646$	−13.5106	−0.531567
$647$	36.4230	1.43193	0.715967	−	0.698134i	$-0.245986\pi$
$647$	36.4230	1.43193	0.715967	+	0.698134i	$0.245986\pi$
$648$	0.874998	0.0343731
$649$	12.5531	0.492752
$650$	32.8460	1.28833
$651$	−15.6045	−0.611587
$652$	−2.02097	−0.0791472
$653$	−13.8417	−0.541667	−0.270833	−	0.962626i	$-0.587299\pi$
$653$	−13.8417	−0.541667	−0.270833	+	0.962626i	$0.587299\pi$
$654$	−32.6345	−1.27611
$655$	−0.837504	−0.0327240
$656$	14.3880	0.561755
$657$	−16.3268	−0.636968
$658$	20.3344	0.792719
$659$	−39.7542	−1.54860	−0.774302	−	0.632816i	$-0.781899\pi$
$659$	−39.7542	−1.54860	−0.774302	+	0.632816i	$0.781899\pi$
$660$	−3.86885	−0.150595
$661$	32.3007	1.25635	0.628176	−	0.778071i	$-0.283802\pi$
$661$	32.3007	1.25635	0.628176	+	0.778071i	$0.283802\pi$
$662$	−36.3495	−1.41276
$663$	−3.84710	−0.149409
$664$	3.13354	0.121605
$665$	−17.3949	−0.674545
$666$	−9.75518	−0.378006
$667$	−8.03372	−0.311067
$668$	25.5631	0.989067
$669$	14.2541	0.551096
$670$	22.5357	0.870630
$671$	−17.1324	−0.661388
$672$	22.4748	0.866986
$673$	30.4610	1.17418	0.587092	−	0.809520i	$-0.300273\pi$
$673$	30.4610	1.17418	0.587092	+	0.809520i	$0.300273\pi$
$674$	26.3553	1.01517
$675$	−4.06272	−0.156374
$676$	4.34981	0.167300
$677$	−31.2168	−1.19976	−0.599880	−	0.800090i	$-0.704785\pi$
$677$	−31.2168	−1.19976	−0.599880	+	0.800090i	$0.704785\pi$
$678$	40.3733	1.55053
$679$	−3.92785	−0.150737
$680$	−0.847111	−0.0324852
$681$	−24.0993	−0.923488
$682$	19.4053	0.743067
$683$	1.90274	0.0728063	0.0364031	−	0.999337i	$-0.488410\pi$
$683$	1.90274	0.0728063	0.0364031	+	0.999337i	$0.488410\pi$
$684$	−15.5347	−0.593986
$685$	−7.07824	−0.270445
$686$	36.3510	1.38789
$687$	11.6509	0.444509
$688$	4.90601	0.187040
$689$	25.6219	0.976117
$690$	−11.7231	−0.446291
$691$	42.6970	1.62427	0.812136	−	0.583469i	$-0.198305\pi$
$691$	42.6970	1.62427	0.812136	+	0.583469i	$0.198305\pi$
$692$	−7.92638	−0.301316
$693$	−4.62202	−0.175576
$694$	−26.7618	−1.01586
$695$	−18.7058	−0.709550
$696$	−1.21997	−0.0462427
$697$	−4.80574	−0.182030
$698$	−13.8507	−0.524256
$699$	−2.95040	−0.111594
$700$	27.4364	1.03700
$701$	−41.2154	−1.55668	−0.778342	−	0.627841i	$-0.783939\pi$
$701$	−41.2154	−1.55668	−0.778342	+	0.627841i	$0.783939\pi$
$702$	−8.08473	−0.305138
$703$	29.8431	1.12555
$704$	−18.0464	−0.680149
$705$	3.35186	0.126239
$706$	32.9038	1.23835
$707$	35.5261	1.33610
$708$	18.3412	0.689304
$709$	22.7659	0.854990	0.427495	−	0.904018i	$-0.359396\pi$
$709$	22.7659	0.854990	0.427495	+	0.904018i	$0.359396\pi$
$710$	−22.3426	−0.838504
$711$	−1.00000	−0.0375029
$712$	9.05895	0.339499
$713$	32.1720	1.20485
$714$	−5.87326	−0.219801
$715$	6.15959	0.230356
$716$	50.3042	1.87995
$717$	12.9361	0.483108
$718$	62.7659	2.34240
$719$	12.9044	0.481253	0.240627	−	0.970618i	$-0.422647\pi$
$719$	12.9044	0.481253	0.240627	+	0.970618i	$0.422647\pi$
$720$	2.89849	0.108020
$721$	−31.1198	−1.15896
$722$	46.9303	1.74657
$723$	8.90889	0.331325
$724$	−25.3130	−0.940750
$725$	5.66445	0.210372
$726$	−17.3688	−0.644618
$727$	27.8475	1.03281	0.516404	−	0.856345i	$-0.327270\pi$
$727$	27.8475	1.03281	0.516404	+	0.856345i	$0.327270\pi$
$728$	9.40777	0.348675
$729$	1.00000	0.0370370
$730$	33.2175	1.22943
$731$	−1.63866	−0.0606081
$732$	−25.0319	−0.925207
$733$	12.9071	0.476736	0.238368	−	0.971175i	$-0.423388\pi$
$733$	12.9071	0.476736	0.238368	+	0.971175i	$0.423388\pi$
$734$	20.6652	0.762765
$735$	−0.784922	−0.0289523
$736$	−46.3368	−1.70800
$737$	−18.3185	−0.674771
$738$	−10.0993	−0.371762
$739$	49.8658	1.83434	0.917171	−	0.398493i	$-0.130467\pi$
$739$	49.8658	1.83434	0.917171	+	0.398493i	$0.130467\pi$
$740$	10.8592	0.399193
$741$	24.7329	0.908585
$742$	39.1163	1.43600
$743$	−30.1969	−1.10782	−0.553908	−	0.832578i	$-0.686864\pi$
$743$	−30.1969	−1.10782	−0.553908	+	0.832578i	$0.686864\pi$
$744$	4.88550	0.179111
$745$	−11.3462	−0.415693
$746$	−37.9909	−1.39095
$747$	3.58119	0.131029
$748$	3.99621	0.146116
$749$	40.4417	1.47771
$750$	18.4385	0.673278
$751$	−25.5540	−0.932478	−0.466239	−	0.884659i	$-0.654391\pi$
$751$	−25.5540	−0.932478	−0.466239	+	0.884659i	$0.654391\pi$
$752$	10.3655	0.377992
$753$	−14.7523	−0.537603
$754$	11.2721	0.410507
$755$	2.02062	0.0735379
$756$	−6.75319	−0.245611
$757$	−44.4463	−1.61543	−0.807713	−	0.589575i	$-0.799295\pi$
$757$	−44.4463	−1.61543	−0.807713	+	0.589575i	$0.799295\pi$
$758$	22.9814	0.834722
$759$	9.52932	0.345892
$760$	5.44605	0.197549
$761$	−10.3241	−0.374248	−0.187124	−	0.982336i	$-0.559917\pi$
$761$	−10.3241	−0.374248	−0.187124	+	0.982336i	$0.559917\pi$
$762$	27.4513	0.994456
$763$	43.4002	1.57119
$764$	27.6428	1.00008
$765$	−0.968130	−0.0350028
$766$	−37.8158	−1.36634
$767$	−29.2010	−1.05439
$768$	7.43225	0.268188
$769$	−4.76696	−0.171901	−0.0859506	−	0.996299i	$-0.527393\pi$
$769$	−4.76696	−0.171901	−0.0859506	+	0.996299i	$0.527393\pi$
$770$	9.40369	0.338885
$771$	−3.15337	−0.113566
$772$	16.6286	0.598478
$773$	1.74902	0.0629080	0.0314540	−	0.999505i	$-0.489986\pi$
$773$	1.74902	0.0629080	0.0314540	+	0.999505i	$0.489986\pi$
$774$	−3.44368	−0.123780
$775$	−22.6840	−0.814833
$776$	1.22975	0.0441453
$777$	12.9733	0.465413
$778$	−27.9897	−1.00348
$779$	30.8960	1.10696
$780$	8.99972	0.322242
$781$	18.1616	0.649873
$782$	12.1090	0.433017
$783$	−1.39425	−0.0498264
$784$	−2.42735	−0.0866909
$785$	−15.7990	−0.563890
$786$	1.81797	0.0648447
$787$	−2.49569	−0.0889619	−0.0444809	−	0.999010i	$-0.514163\pi$
$787$	−2.49569	−0.0889619	−0.0444809	+	0.999010i	$0.514163\pi$
$788$	22.1756	0.789972
$789$	20.0561	0.714016
$790$	2.03454	0.0723857
$791$	−53.6919	−1.90906
$792$	1.44708	0.0514197
$793$	39.8534	1.41523
$794$	47.7825	1.69574
$795$	6.44781	0.228680
$796$	−57.1917	−2.02711
$797$	−44.5167	−1.57686	−0.788431	−	0.615123i	$-0.789106\pi$
$797$	−44.5167	−1.57686	−0.788431	+	0.615123i	$0.789106\pi$
$798$	37.7590	1.33665
$799$	−3.46221	−0.122484
$800$	32.6714	1.15511
$801$	10.3531	0.365809
$802$	13.5072	0.476957
$803$	−27.0014	−0.952858
$804$	−26.7650	−0.943929
$805$	15.5904	0.549488
$806$	−45.1406	−1.59001
$807$	−23.8964	−0.841192
$808$	−11.1226	−0.391293
$809$	4.49316	0.157971	0.0789856	−	0.996876i	$-0.474832\pi$
$809$	4.49316	0.157971	0.0789856	+	0.996876i	$0.474832\pi$
$810$	−2.03454	−0.0714864
$811$	−38.5206	−1.35264	−0.676321	−	0.736607i	$-0.736427\pi$
$811$	−38.5206	−1.35264	−0.676321	+	0.736607i	$0.736427\pi$
$812$	9.41564	0.330424
$813$	−26.0940	−0.915155
$814$	−16.1332	−0.565469
$815$	0.809712	0.0283630
$816$	−2.99391	−0.104808
$817$	10.5349	0.368570
$818$	−9.92464	−0.347007
$819$	10.7518	0.375697
$820$	11.2423	0.392599
$821$	15.9344	0.556115	0.278058	−	0.960564i	$-0.410309\pi$
$821$	15.9344	0.556115	0.278058	+	0.960564i	$0.410309\pi$
$822$	15.3647	0.535905
$823$	5.53450	0.192921	0.0964603	−	0.995337i	$-0.469248\pi$
$823$	5.53450	0.192921	0.0964603	+	0.995337i	$0.469248\pi$
$824$	9.74309	0.339417
$825$	−6.71897	−0.233925
$826$	−44.5804	−1.55115
$827$	−9.51469	−0.330858	−0.165429	−	0.986222i	$-0.552901\pi$
$827$	−9.51469	−0.330858	−0.165429	+	0.986222i	$0.552901\pi$
$828$	13.9232	0.483864
$829$	−55.1485	−1.91539	−0.957693	−	0.287792i	$-0.907079\pi$
$829$	−55.1485	−1.91539	−0.957693	+	0.287792i	$0.907079\pi$
$830$	−7.28608	−0.252903
$831$	26.3964	0.915682
$832$	41.9796	1.45538
$833$	0.810761	0.0280912
$834$	40.6045	1.40602
$835$	−10.2420	−0.354439
$836$	−25.6915	−0.888559
$837$	5.58344	0.192992
$838$	57.5366	1.98757
$839$	−46.3301	−1.59949	−0.799746	−	0.600339i	$-0.795032\pi$
$839$	−46.3301	−1.59949	−0.799746	+	0.600339i	$0.795032\pi$
$840$	2.36748	0.0816860
$841$	−27.0561	−0.932968
$842$	57.1467	1.96941
$843$	−16.0419	−0.552512
$844$	−52.5538	−1.80898
$845$	−1.74277	−0.0599533
$846$	−7.27588	−0.250150
$847$	23.0986	0.793676
$848$	19.9396	0.684730
$849$	−32.9109	−1.12950
$850$	−8.53788	−0.292847
$851$	−26.7472	−0.916883
$852$	26.5357	0.909099
$853$	25.8564	0.885305	0.442652	−	0.896693i	$-0.354038\pi$
$853$	25.8564	0.885305	0.442652	+	0.896693i	$0.354038\pi$
$854$	60.8431	2.08201
$855$	6.22408	0.212859
$856$	−12.6616	−0.432765
$857$	−30.4281	−1.03940	−0.519702	−	0.854348i	$-0.673957\pi$
$857$	−30.4281	−1.03940	−0.519702	+	0.854348i	$0.673957\pi$
$858$	−13.3706	−0.456465
$859$	−6.71740	−0.229195	−0.114597	−	0.993412i	$-0.536558\pi$
$859$	−6.71740	−0.229195	−0.114597	+	0.993412i	$0.536558\pi$
$860$	3.83342	0.130718
$861$	13.4310	0.457726
$862$	70.6490	2.40631
$863$	38.6835	1.31680	0.658401	−	0.752667i	$-0.271233\pi$
$863$	38.6835	1.31680	0.658401	+	0.752667i	$0.271233\pi$
$864$	−8.04174	−0.273586
$865$	3.17575	0.107979
$866$	26.1661	0.889161
$867$	1.00000	0.0339618
$868$	−37.7061	−1.27983
$869$	−1.65381	−0.0561017
$870$	2.83666	0.0961716
$871$	42.6126	1.44387
$872$	−13.5879	−0.460144
$873$	1.40543	0.0475665
$874$	−77.8485	−2.63326
$875$	−24.5210	−0.828963
$876$	−39.4514	−1.33294
$877$	−1.55658	−0.0525620	−0.0262810	−	0.999655i	$-0.508366\pi$
$877$	−1.55658	−0.0525620	−0.0262810	+	0.999655i	$0.508366\pi$
$878$	14.0325	0.473574
$879$	−27.2883	−0.920411
$880$	4.79356	0.161591
$881$	50.1715	1.69032	0.845160	−	0.534513i	$-0.179505\pi$
$881$	50.1715	1.69032	0.845160	+	0.534513i	$0.179505\pi$
$882$	1.70383	0.0573708
$883$	−40.8890	−1.37602	−0.688012	−	0.725700i	$-0.741516\pi$
$883$	−40.8890	−1.37602	−0.688012	+	0.725700i	$0.741516\pi$
$884$	−9.29599	−0.312658
$885$	−7.34850	−0.247017
$886$	77.9511	2.61882
$887$	25.4174	0.853433	0.426716	−	0.904386i	$-0.359670\pi$
$887$	25.4174	0.853433	0.426716	+	0.904386i	$0.359670\pi$
$888$	−4.06172	−0.136302
$889$	−36.5071	−1.22441
$890$	−21.0638	−0.706061
$891$	1.65381	0.0554047
$892$	34.4431	1.15324
$893$	22.2584	0.744850
$894$	24.6292	0.823722
$895$	−20.1546	−0.673695
$896$	19.1394	0.639403
$897$	−22.1671	−0.740138
$898$	−30.5590	−1.01977
$899$	−7.78471	−0.259635
$900$	−9.81703	−0.327234
$901$	−6.66007	−0.221879
$902$	−16.7024	−0.556128
$903$	4.57969	0.152403
$904$	16.8100	0.559094
$905$	10.1418	0.337125
$906$	−4.38615	−0.145720
$907$	−37.5557	−1.24702	−0.623508	−	0.781817i	$-0.714293\pi$
$907$	−37.5557	−1.24702	−0.623508	+	0.781817i	$0.714293\pi$
$908$	−58.2328	−1.93252
$909$	−12.7116	−0.421618
$910$	−21.8749	−0.725145
$911$	15.4376	0.511471	0.255735	−	0.966747i	$-0.417682\pi$
$911$	15.4376	0.511471	0.255735	+	0.966747i	$0.417682\pi$
$912$	19.2478	0.637357
$913$	5.92261	0.196010
$914$	−41.4673	−1.37162
$915$	10.0292	0.331554
$916$	28.1528	0.930194
$917$	−2.41769	−0.0798391
$918$	2.10151	0.0693603
$919$	17.2868	0.570238	0.285119	−	0.958492i	$-0.407967\pi$
$919$	17.2868	0.570238	0.285119	+	0.958492i	$0.407967\pi$
$920$	−4.88109	−0.160925
$921$	−8.12346	−0.267677
$922$	33.8557	1.11498
$923$	−42.2475	−1.39059
$924$	−11.1685	−0.367417
$925$	18.8591	0.620082
$926$	−42.8349	−1.40764
$927$	11.1350	0.365721
$928$	11.2122	0.368058
$929$	−46.4787	−1.52492	−0.762458	−	0.647038i	$-0.776008\pi$
$929$	−46.4787	−1.52492	−0.762458	+	0.647038i	$0.776008\pi$
$930$	−11.3597	−0.372500
$931$	−5.21236	−0.170828
$932$	−7.12923	−0.233526
$933$	−26.6028	−0.870936
$934$	22.0749	0.722313
$935$	−1.60110	−0.0523617
$936$	−3.36620	−0.110028
$937$	−13.6512	−0.445964	−0.222982	−	0.974823i	$-0.571579\pi$
$937$	−13.6512	−0.445964	−0.222982	+	0.974823i	$0.571579\pi$
$938$	65.0555	2.12414
$939$	9.06089	0.295691
$940$	8.09933	0.264171
$941$	43.2653	1.41041	0.705204	−	0.709004i	$-0.250855\pi$
$941$	43.2653	1.41041	0.705204	+	0.709004i	$0.250855\pi$
$942$	34.2948	1.11738
$943$	−27.6909	−0.901738
$944$	−22.7250	−0.739635
$945$	2.70570	0.0880166
$946$	−5.69518	−0.185166
$947$	50.7743	1.64994	0.824972	−	0.565174i	$-0.191191\pi$
$947$	50.7743	1.64994	0.824972	+	0.565174i	$0.191191\pi$
$948$	−2.41637	−0.0784799
$949$	62.8107	2.03892
$950$	54.8898	1.78086
$951$	−4.51834	−0.146517
$952$	−2.44542	−0.0792565
$953$	−57.6746	−1.86826	−0.934132	−	0.356928i	$-0.883824\pi$
$953$	−57.6746	−1.86826	−0.934132	+	0.356928i	$0.883824\pi$
$954$	−13.9962	−0.453145
$955$	−11.0752	−0.358387
$956$	31.2584	1.01097
$957$	−2.30582	−0.0745367
$958$	−55.8101	−1.80314
$959$	−20.4333	−0.659825
$960$	10.5643	0.340960
$961$	0.174823	0.00563946
$962$	37.5291	1.20999
$963$	−14.4705	−0.466304
$964$	21.5271	0.693342
$965$	−6.66236	−0.214469
$966$	−33.8419	−1.08885
$967$	33.6605	1.08245	0.541225	−	0.840878i	$-0.317961\pi$
$967$	33.6605	1.08245	0.541225	+	0.840878i	$0.317961\pi$
$968$	−7.23178	−0.232438
$969$	−6.42897	−0.206528
$970$	−2.85940	−0.0918098
$971$	−27.9296	−0.896305	−0.448152	−	0.893957i	$-0.647918\pi$
$971$	−27.9296	−0.896305	−0.448152	+	0.893957i	$0.647918\pi$
$972$	2.41637	0.0775049
$973$	−53.9993	−1.73114
$974$	−32.2946	−1.03479
$975$	15.6297	0.500551
$976$	31.0149	0.992763
$977$	−22.5400	−0.721118	−0.360559	−	0.932736i	$-0.617414\pi$
$977$	−22.5400	−0.721118	−0.360559	+	0.932736i	$0.617414\pi$
$978$	−1.75764	−0.0562031
$979$	17.1221	0.547224
$980$	−1.89666	−0.0605865
$981$	−15.5291	−0.495805
$982$	−61.5113	−1.96290
$983$	−49.6509	−1.58362	−0.791808	−	0.610770i	$-0.790860\pi$
$983$	−49.6509	−1.58362	−0.791808	+	0.610770i	$0.790860\pi$
$984$	−4.20501	−0.134051
$985$	−8.88476	−0.283092
$986$	−2.93004	−0.0933114
$987$	9.67608	0.307993
$988$	59.7636	1.90133
$989$	−9.44204	−0.300239
$990$	−3.36474	−0.106938
$991$	−1.60035	−0.0508368	−0.0254184	−	0.999677i	$-0.508092\pi$
$991$	−1.60035	−0.0508368	−0.0254184	+	0.999677i	$0.508092\pi$
$992$	−44.9006	−1.42560
$993$	−17.2968	−0.548897
$994$	−64.4982	−2.04576
$995$	22.9142	0.726428
$996$	8.65347	0.274196
$997$	37.8432	1.19851	0.599253	−	0.800560i	$-0.295464\pi$
$997$	37.8432	1.19851	0.599253	+	0.800560i	$0.295464\pi$
$998$	−39.7552	−1.25843
$999$	−4.64197	−0.146866

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4029.2.a.e.1.17	✓	18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4029.2.a.e.1.17	✓	18	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)

\(f(q)\)	\(=\)	\(q+2.10151 q^{2} +1.00000 q^{3} +2.41637 q^{4} -0.968130 q^{5} +2.10151 q^{6} -2.79477 q^{7} +0.874998 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+2.10151 q^{2} +1.00000 q^{3} +2.41637 q^{4} -0.968130 q^{5} +2.10151 q^{6} -2.79477 q^{7} +0.874998 q^{8} +1.00000 q^{9} -2.03454 q^{10} +1.65381 q^{11} +2.41637 q^{12} -3.84710 q^{13} -5.87326 q^{14} -0.968130 q^{15} -2.99391 q^{16} +1.00000 q^{17} +2.10151 q^{18} -6.42897 q^{19} -2.33936 q^{20} -2.79477 q^{21} +3.47551 q^{22} +5.76204 q^{23} +0.874998 q^{24} -4.06272 q^{25} -8.08473 q^{26} +1.00000 q^{27} -6.75319 q^{28} -1.39425 q^{29} -2.03454 q^{30} +5.58344 q^{31} -8.04174 q^{32} +1.65381 q^{33} +2.10151 q^{34} +2.70570 q^{35} +2.41637 q^{36} -4.64197 q^{37} -13.5106 q^{38} -3.84710 q^{39} -0.847111 q^{40} -4.80574 q^{41} -5.87326 q^{42} -1.63866 q^{43} +3.99621 q^{44} -0.968130 q^{45} +12.1090 q^{46} -3.46221 q^{47} -2.99391 q^{48} +0.810761 q^{49} -8.53788 q^{50} +1.00000 q^{51} -9.29599 q^{52} -6.66007 q^{53} +2.10151 q^{54} -1.60110 q^{55} -2.44542 q^{56} -6.42897 q^{57} -2.93004 q^{58} +7.59040 q^{59} -2.33936 q^{60} -10.3593 q^{61} +11.7337 q^{62} -2.79477 q^{63} -10.9120 q^{64} +3.72449 q^{65} +3.47551 q^{66} -11.0766 q^{67} +2.41637 q^{68} +5.76204 q^{69} +5.68608 q^{70} +10.9817 q^{71} +0.874998 q^{72} -16.3268 q^{73} -9.75518 q^{74} -4.06272 q^{75} -15.5347 q^{76} -4.62202 q^{77} -8.08473 q^{78} -1.00000 q^{79} +2.89849 q^{80} +1.00000 q^{81} -10.0993 q^{82} +3.58119 q^{83} -6.75319 q^{84} -0.968130 q^{85} -3.44368 q^{86} -1.39425 q^{87} +1.44708 q^{88} +10.3531 q^{89} -2.03454 q^{90} +10.7518 q^{91} +13.9232 q^{92} +5.58344 q^{93} -7.27588 q^{94} +6.22408 q^{95} -8.04174 q^{96} +1.40543 q^{97} +1.70383 q^{98} +1.65381 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q - 6 q^{2} + 18 q^{3} + 20 q^{4} - 5 q^{5} - 6 q^{6} - 13 q^{7} - 12 q^{8} + 18 q^{9}+O(q^{10}) \) 18 * q - 6 * q^2 + 18 * q^3 + 20 * q^4 - 5 * q^5 - 6 * q^6 - 13 * q^7 - 12 * q^8 + 18 * q^9	\( 18 q - 6 q^{2} + 18 q^{3} + 20 q^{4} - 5 q^{5} - 6 q^{6} - 13 q^{7} - 12 q^{8} + 18 q^{9} - 15 q^{10} - 27 q^{11} + 20 q^{12} - 4 q^{13} - 5 q^{14} - 5 q^{15} + 16 q^{16} + 18 q^{17} - 6 q^{18} - 30 q^{19} - 16 q^{20} - 13 q^{21} + 13 q^{22} - 21 q^{23} - 12 q^{24} + 13 q^{25} - 20 q^{26} + 18 q^{27} - 33 q^{28} - 47 q^{29} - 15 q^{30} - 18 q^{31} - 45 q^{32} - 27 q^{33} - 6 q^{34} - 17 q^{35} + 20 q^{36} + q^{37} + 5 q^{38} - 4 q^{39} - 12 q^{40} - 18 q^{41} - 5 q^{42} - 39 q^{43} - 34 q^{44} - 5 q^{45} - 7 q^{46} + 16 q^{48} + 15 q^{49} - 23 q^{50} + 18 q^{51} + 5 q^{52} - 9 q^{53} - 6 q^{54} + q^{55} - 24 q^{56} - 30 q^{57} + 41 q^{58} - 42 q^{59} - 16 q^{60} - 43 q^{61} - 54 q^{62} - 13 q^{63} + 22 q^{64} - 25 q^{65} + 13 q^{66} + 20 q^{68} - 21 q^{69} + 17 q^{70} + 9 q^{71} - 12 q^{72} + 19 q^{73} - 30 q^{74} + 13 q^{75} - 17 q^{76} - 14 q^{77} - 20 q^{78} - 18 q^{79} + 36 q^{80} + 18 q^{81} - 3 q^{82} - 61 q^{83} - 33 q^{84} - 5 q^{85} - 24 q^{86} - 47 q^{87} - 25 q^{88} + 10 q^{89} - 15 q^{90} - 52 q^{91} - 74 q^{92} - 18 q^{93} + 31 q^{94} - 37 q^{95} - 45 q^{96} - 9 q^{97} + 27 q^{98} - 27 q^{99}+O(q^{100}) \) 18 * q - 6 * q^2 + 18 * q^3 + 20 * q^4 - 5 * q^5 - 6 * q^6 - 13 * q^7 - 12 * q^8 + 18 * q^9 - 15 * q^10 - 27 * q^11 + 20 * q^12 - 4 * q^13 - 5 * q^14 - 5 * q^15 + 16 * q^16 + 18 * q^17 - 6 * q^18 - 30 * q^19 - 16 * q^20 - 13 * q^21 + 13 * q^22 - 21 * q^23 - 12 * q^24 + 13 * q^25 - 20 * q^26 + 18 * q^27 - 33 * q^28 - 47 * q^29 - 15 * q^30 - 18 * q^31 - 45 * q^32 - 27 * q^33 - 6 * q^34 - 17 * q^35 + 20 * q^36 + q^37 + 5 * q^38 - 4 * q^39 - 12 * q^40 - 18 * q^41 - 5 * q^42 - 39 * q^43 - 34 * q^44 - 5 * q^45 - 7 * q^46 + 16 * q^48 + 15 * q^49 - 23 * q^50 + 18 * q^51 + 5 * q^52 - 9 * q^53 - 6 * q^54 + q^55 - 24 * q^56 - 30 * q^57 + 41 * q^58 - 42 * q^59 - 16 * q^60 - 43 * q^61 - 54 * q^62 - 13 * q^63 + 22 * q^64 - 25 * q^65 + 13 * q^66 + 20 * q^68 - 21 * q^69 + 17 * q^70 + 9 * q^71 - 12 * q^72 + 19 * q^73 - 30 * q^74 + 13 * q^75 - 17 * q^76 - 14 * q^77 - 20 * q^78 - 18 * q^79 + 36 * q^80 + 18 * q^81 - 3 * q^82 - 61 * q^83 - 33 * q^84 - 5 * q^85 - 24 * q^86 - 47 * q^87 - 25 * q^88 + 10 * q^89 - 15 * q^90 - 52 * q^91 - 74 * q^92 - 18 * q^93 + 31 * q^94 - 37 * q^95 - 45 * q^96 - 9 * q^97 + 27 * q^98 - 27 * q^99

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