LMFDB - Embedded newform 8035.2.a.c.1.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8035,2,Mod(1,8035)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8035, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("8035.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8035 = 5 \cdot 1607 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8035.a (trivial)

Newform invariants

comment: select newform

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

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

Self dual:	yes
Analytic conductor:	$64.1597980241$
Analytic rank:	$0$
Dimension:	$127$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.16
Character	$\chi$	$=$	8035.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.17325 q^{2} +2.30276 q^{3} +2.72303 q^{4} -1.00000 q^{5} -5.00447 q^{6} -1.58489 q^{7} -1.57132 q^{8} +2.30268 q^{9} +O(q^{10})$	\(q-2.17325 q^{2} +2.30276 q^{3} +2.72303 q^{4} -1.00000 q^{5} -5.00447 q^{6} -1.58489 q^{7} -1.57132 q^{8} +2.30268 q^{9} +2.17325 q^{10} -0.0320935 q^{11} +6.27046 q^{12} -4.50759 q^{13} +3.44437 q^{14} -2.30276 q^{15} -2.03118 q^{16} -4.91630 q^{17} -5.00431 q^{18} -5.49438 q^{19} -2.72303 q^{20} -3.64962 q^{21} +0.0697472 q^{22} +1.01373 q^{23} -3.61836 q^{24} +1.00000 q^{25} +9.79613 q^{26} -1.60575 q^{27} -4.31570 q^{28} +1.75709 q^{29} +5.00447 q^{30} +2.11976 q^{31} +7.55691 q^{32} -0.0739034 q^{33} +10.6844 q^{34} +1.58489 q^{35} +6.27026 q^{36} +11.3576 q^{37} +11.9407 q^{38} -10.3799 q^{39} +1.57132 q^{40} -1.89293 q^{41} +7.93154 q^{42} +8.57679 q^{43} -0.0873913 q^{44} -2.30268 q^{45} -2.20308 q^{46} -10.1809 q^{47} -4.67732 q^{48} -4.48812 q^{49} -2.17325 q^{50} -11.3210 q^{51} -12.2743 q^{52} -10.8530 q^{53} +3.48971 q^{54} +0.0320935 q^{55} +2.49037 q^{56} -12.6522 q^{57} -3.81859 q^{58} +7.79377 q^{59} -6.27046 q^{60} -8.97932 q^{61} -4.60678 q^{62} -3.64950 q^{63} -12.3607 q^{64} +4.50759 q^{65} +0.160611 q^{66} -3.13831 q^{67} -13.3872 q^{68} +2.33436 q^{69} -3.44437 q^{70} -0.00761166 q^{71} -3.61824 q^{72} +1.79264 q^{73} -24.6830 q^{74} +2.30276 q^{75} -14.9613 q^{76} +0.0508647 q^{77} +22.5581 q^{78} +14.3534 q^{79} +2.03118 q^{80} -10.6057 q^{81} +4.11381 q^{82} +15.7604 q^{83} -9.93800 q^{84} +4.91630 q^{85} -18.6395 q^{86} +4.04614 q^{87} +0.0504290 q^{88} -12.0328 q^{89} +5.00431 q^{90} +7.14404 q^{91} +2.76040 q^{92} +4.88130 q^{93} +22.1257 q^{94} +5.49438 q^{95} +17.4017 q^{96} -12.7330 q^{97} +9.75381 q^{98} -0.0739011 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 127 q + 19 q^{2} + 10 q^{3} + 125 q^{4} - 127 q^{5} + 13 q^{7} + 54 q^{8} + 123 q^{9}+O(q^{10}) $ 127 * q + 19 * q^2 + 10 * q^3 + 125 * q^4 - 127 * q^5 + 13 * q^7 + 54 * q^8 + 123 * q^9	\( 127 q + 19 q^{2} + 10 q^{3} + 125 q^{4} - 127 q^{5} + 13 q^{7} + 54 q^{8} + 123 q^{9} - 19 q^{10} + 30 q^{11} + 35 q^{12} + 30 q^{13} + 39 q^{14} - 10 q^{15} + 121 q^{16} + 63 q^{17} + 53 q^{18} - 35 q^{19} - 125 q^{20} + 33 q^{21} + 49 q^{22} + 61 q^{23} - 5 q^{24} + 127 q^{25} + 10 q^{26} + 40 q^{27} + 32 q^{28} + 134 q^{29} - 25 q^{31} + 122 q^{32} + 48 q^{33} - 21 q^{34} - 13 q^{35} + 133 q^{36} + 60 q^{37} + 33 q^{38} + 26 q^{39} - 54 q^{40} + 9 q^{41} + 45 q^{42} + 48 q^{43} + 85 q^{44} - 123 q^{45} - 11 q^{46} + 57 q^{47} + 71 q^{48} + 70 q^{49} + 19 q^{50} + 45 q^{51} + 68 q^{52} + 182 q^{53} - 29 q^{54} - 30 q^{55} + 96 q^{56} + 74 q^{57} + 47 q^{58} + 19 q^{59} - 35 q^{60} + 16 q^{61} + 43 q^{62} + 73 q^{63} + 110 q^{64} - 30 q^{65} + 8 q^{66} + 40 q^{67} + 129 q^{68} + 2 q^{69} - 39 q^{70} + 48 q^{71} + 151 q^{72} + 30 q^{73} + 117 q^{74} + 10 q^{75} - 98 q^{76} + 134 q^{77} + 54 q^{78} + 23 q^{79} - 121 q^{80} + 111 q^{81} + 4 q^{82} + 92 q^{83} + 48 q^{84} - 63 q^{85} + 42 q^{86} + 69 q^{87} + 121 q^{88} + 12 q^{89} - 53 q^{90} - 30 q^{91} + 175 q^{92} + 82 q^{93} - 23 q^{94} + 35 q^{95} + 6 q^{96} + 67 q^{97} + 122 q^{98} + 73 q^{99}+O(q^{100}) \) 127 * q + 19 * q^2 + 10 * q^3 + 125 * q^4 - 127 * q^5 + 13 * q^7 + 54 * q^8 + 123 * q^9 - 19 * q^10 + 30 * q^11 + 35 * q^12 + 30 * q^13 + 39 * q^14 - 10 * q^15 + 121 * q^16 + 63 * q^17 + 53 * q^18 - 35 * q^19 - 125 * q^20 + 33 * q^21 + 49 * q^22 + 61 * q^23 - 5 * q^24 + 127 * q^25 + 10 * q^26 + 40 * q^27 + 32 * q^28 + 134 * q^29 - 25 * q^31 + 122 * q^32 + 48 * q^33 - 21 * q^34 - 13 * q^35 + 133 * q^36 + 60 * q^37 + 33 * q^38 + 26 * q^39 - 54 * q^40 + 9 * q^41 + 45 * q^42 + 48 * q^43 + 85 * q^44 - 123 * q^45 - 11 * q^46 + 57 * q^47 + 71 * q^48 + 70 * q^49 + 19 * q^50 + 45 * q^51 + 68 * q^52 + 182 * q^53 - 29 * q^54 - 30 * q^55 + 96 * q^56 + 74 * q^57 + 47 * q^58 + 19 * q^59 - 35 * q^60 + 16 * q^61 + 43 * q^62 + 73 * q^63 + 110 * q^64 - 30 * q^65 + 8 * q^66 + 40 * q^67 + 129 * q^68 + 2 * q^69 - 39 * q^70 + 48 * q^71 + 151 * q^72 + 30 * q^73 + 117 * q^74 + 10 * q^75 - 98 * q^76 + 134 * q^77 + 54 * q^78 + 23 * q^79 - 121 * q^80 + 111 * q^81 + 4 * q^82 + 92 * q^83 + 48 * q^84 - 63 * q^85 + 42 * q^86 + 69 * q^87 + 121 * q^88 + 12 * q^89 - 53 * q^90 - 30 * q^91 + 175 * q^92 + 82 * q^93 - 23 * q^94 + 35 * q^95 + 6 * q^96 + 67 * q^97 + 122 * q^98 + 73 * 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 $

$2$	−2.17325	−1.53672	−0.768361	−	0.640017i	$-0.778927\pi$
$2$	−2.17325	−1.53672	−0.768361	+	0.640017i	$0.778927\pi$
$3$	2.30276	1.32950	0.664748	−	0.747068i	$-0.268539\pi$
$3$	2.30276	1.32950	0.664748	+	0.747068i	$0.268539\pi$
$4$	2.72303	1.36151
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	−5.00447	−2.04307
$7$	−1.58489	−0.599033	−0.299516	−	0.954091i	$-0.596825\pi$
$7$	−1.58489	−0.599033	−0.299516	+	0.954091i	$0.596825\pi$
$8$	−1.57132	−0.555544
$9$	2.30268	0.767561
$10$	2.17325	0.687243
$11$	−0.0320935	−0.00967655	−0.00483827	−	0.999988i	$-0.501540\pi$
$11$	−0.0320935	−0.00967655	−0.00483827	+	0.999988i	$0.501540\pi$
$12$	6.27046	1.81013
$13$	−4.50759	−1.25018	−0.625090	−	0.780553i	$-0.714938\pi$
$13$	−4.50759	−1.25018	−0.625090	+	0.780553i	$0.714938\pi$
$14$	3.44437	0.920546
$15$	−2.30276	−0.594569
$16$	−2.03118	−0.507796
$17$	−4.91630	−1.19238	−0.596189	−	0.802844i	$-0.703319\pi$
$17$	−4.91630	−1.19238	−0.596189	+	0.802844i	$0.703319\pi$
$18$	−5.00431	−1.17953
$19$	−5.49438	−1.26050	−0.630248	−	0.776394i	$-0.717047\pi$
$19$	−5.49438	−1.26050	−0.630248	+	0.776394i	$0.717047\pi$
$20$	−2.72303	−0.608887
$21$	−3.64962	−0.796412
$22$	0.0697472	0.0148702
$23$	1.01373	0.211377	0.105688	−	0.994399i	$-0.466295\pi$
$23$	1.01373	0.211377	0.105688	+	0.994399i	$0.466295\pi$
$24$	−3.61836	−0.738594
$25$	1.00000	0.200000
$26$	9.79613	1.92118
$27$	−1.60575	−0.309027
$28$	−4.31570	−0.815591
$29$	1.75709	0.326283	0.163141	−	0.986603i	$-0.447837\pi$
$29$	1.75709	0.326283	0.163141	+	0.986603i	$0.447837\pi$
$30$	5.00447	0.913687
$31$	2.11976	0.380721	0.190361	−	0.981714i	$-0.439034\pi$
$31$	2.11976	0.380721	0.190361	+	0.981714i	$0.439034\pi$
$32$	7.55691	1.33589
$33$	−0.0739034	−0.0128649
$34$	10.6844	1.83235
$35$	1.58489	0.267896
$36$	6.27026	1.04504
$37$	11.3576	1.86718	0.933592	−	0.358339i	$-0.116657\pi$
$37$	11.3576	1.86718	0.933592	+	0.358339i	$0.116657\pi$
$38$	11.9407	1.93703
$39$	−10.3799	−1.66211
$40$	1.57132	0.248447
$41$	−1.89293	−0.295626	−0.147813	−	0.989015i	$-0.547223\pi$
$41$	−1.89293	−0.295626	−0.147813	+	0.989015i	$0.547223\pi$
$42$	7.93154	1.22386
$43$	8.57679	1.30795	0.653974	−	0.756517i	$-0.273100\pi$
$43$	8.57679	1.30795	0.653974	+	0.756517i	$0.273100\pi$
$44$	−0.0873913	−0.0131747
$45$	−2.30268	−0.343264
$46$	−2.20308	−0.324827
$47$	−10.1809	−1.48504	−0.742521	−	0.669823i	$-0.766370\pi$
$47$	−10.1809	−1.48504	−0.742521	+	0.669823i	$0.766370\pi$
$48$	−4.67732	−0.675113
$49$	−4.48812	−0.641160
$50$	−2.17325	−0.307344
$51$	−11.3210	−1.58526
$52$	−12.2743	−1.70214
$53$	−10.8530	−1.49078	−0.745389	−	0.666630i	$-0.767736\pi$
$53$	−10.8530	−1.49078	−0.745389	+	0.666630i	$0.767736\pi$
$54$	3.48971	0.474889
$55$	0.0320935	0.00432748
$56$	2.49037	0.332789
$57$	−12.6522	−1.67583
$58$	−3.81859	−0.501406
$59$	7.79377	1.01466	0.507331	−	0.861751i	$-0.330632\pi$
$59$	7.79377	1.01466	0.507331	+	0.861751i	$0.330632\pi$
$60$	−6.27046	−0.809513
$61$	−8.97932	−1.14968	−0.574842	−	0.818265i	$-0.694936\pi$
$61$	−8.97932	−1.14968	−0.574842	+	0.818265i	$0.694936\pi$
$62$	−4.60678	−0.585062
$63$	−3.64950	−0.459794
$64$	−12.3607	−1.54509
$65$	4.50759	0.559098
$66$	0.160611	0.0197698
$67$	−3.13831	−0.383405	−0.191703	−	0.981453i	$-0.561401\pi$
$67$	−3.13831	−0.383405	−0.191703	+	0.981453i	$0.561401\pi$
$68$	−13.3872	−1.62344
$69$	2.33436	0.281024
$70$	−3.44437	−0.411681
$71$	−0.00761166	−0.000903338 0	−0.000451669	−	1.00000i	$-0.500144\pi$
$71$	−0.00761166	−0.000903338 0	−0.000451669		1.00000i	$0.500144\pi$
$72$	−3.61824	−0.426414
$73$	1.79264	0.209813	0.104906	−	0.994482i	$-0.466546\pi$
$73$	1.79264	0.209813	0.104906	+	0.994482i	$0.466546\pi$
$74$	−24.6830	−2.86934
$75$	2.30276	0.265899
$76$	−14.9613	−1.71618
$77$	0.0508647	0.00579657
$78$	22.5581	2.55420
$79$	14.3534	1.61489	0.807444	−	0.589944i	$-0.200850\pi$
$79$	14.3534	1.61489	0.807444	+	0.589944i	$0.200850\pi$
$80$	2.03118	0.227093
$81$	−10.6057	−1.17841
$82$	4.11381	0.454294
$83$	15.7604	1.72993	0.864966	−	0.501830i	$-0.167340\pi$
$83$	15.7604	1.72993	0.864966	+	0.501830i	$0.167340\pi$
$84$	−9.93800	−1.08432
$85$	4.91630	0.533248
$86$	−18.6395	−2.00995
$87$	4.04614	0.433792
$88$	0.0504290	0.00537575
$89$	−12.0328	−1.27548	−0.637739	−	0.770253i	$-0.720130\pi$
$89$	−12.0328	−1.27548	−0.637739	+	0.770253i	$0.720130\pi$
$90$	5.00431	0.527500
$91$	7.14404	0.748899
$92$	2.76040	0.287792
$93$	4.88130	0.506167
$94$	22.1257	2.28210
$95$	5.49438	0.563711
$96$	17.4017	1.77605
$97$	−12.7330	−1.29284	−0.646418	−	0.762984i	$-0.723734\pi$
$97$	−12.7330	−1.29284	−0.646418	+	0.762984i	$0.723734\pi$
$98$	9.75381	0.985284
$99$	−0.0739011	−0.00742734
$100$	2.72303	0.272303
$101$	−9.08243	−0.903735	−0.451868	−	0.892085i	$-0.649242\pi$
$101$	−9.08243	−0.903735	−0.451868	+	0.892085i	$0.649242\pi$
$102$	24.6035	2.43611
$103$	9.38270	0.924505	0.462253	−	0.886748i	$-0.347041\pi$
$103$	9.38270	0.924505	0.462253	+	0.886748i	$0.347041\pi$
$104$	7.08285	0.694530
$105$	3.64962	0.356166
$106$	23.5864	2.29091
$107$	18.4026	1.77905	0.889524	−	0.456888i	$-0.151036\pi$
$107$	18.4026	1.77905	0.889524	+	0.456888i	$0.151036\pi$
$108$	−4.37251	−0.420745
$109$	0.151960	0.0145551	0.00727754	−	0.999974i	$-0.497683\pi$
$109$	0.151960	0.0145551	0.00727754	+	0.999974i	$0.497683\pi$
$110$	−0.0697472	−0.00665014
$111$	26.1538	2.48241
$112$	3.21921	0.304186
$113$	7.67549	0.722050	0.361025	−	0.932556i	$-0.382427\pi$
$113$	7.67549	0.722050	0.361025	+	0.932556i	$0.382427\pi$
$114$	27.4964	2.57528
$115$	−1.01373	−0.0945305
$116$	4.78459	0.444238
$117$	−10.3795	−0.959589
$118$	−16.9378	−1.55925
$119$	7.79180	0.714273
$120$	3.61836	0.330309
$121$	−10.9990	−0.999906
$122$	19.5143	1.76674
$123$	−4.35895	−0.393033
$124$	5.77217	0.518356
$125$	−1.00000	−0.0894427
$126$	7.93129	0.706575
$127$	−4.83894	−0.429387	−0.214693	−	0.976682i	$-0.568875\pi$
$127$	−4.83894	−0.429387	−0.214693	+	0.976682i	$0.568875\pi$
$128$	11.7491	1.03848
$129$	19.7503	1.73891
$130$	−9.79613	−0.859177
$131$	1.63021	0.142432	0.0712160	−	0.997461i	$-0.477312\pi$
$131$	1.63021	0.142432	0.0712160	+	0.997461i	$0.477312\pi$
$132$	−0.201241	−0.0175158
$133$	8.70799	0.755078
$134$	6.82033	0.589187
$135$	1.60575	0.138201
$136$	7.72506	0.662419
$137$	13.1009	1.11929	0.559643	−	0.828734i	$-0.310938\pi$
$137$	13.1009	1.11929	0.559643	+	0.828734i	$0.310938\pi$
$138$	−5.07316	−0.431856
$139$	7.50552	0.636610	0.318305	−	0.947988i	$-0.396886\pi$
$139$	7.50552	0.636610	0.318305	+	0.947988i	$0.396886\pi$
$140$	4.31570	0.364743
$141$	−23.4442	−1.97436
$142$	0.0165421	0.00138818
$143$	0.144664	0.0120974
$144$	−4.67717	−0.389764
$145$	−1.75709	−0.145918
$146$	−3.89586	−0.322423
$147$	−10.3350	−0.852420
$148$	30.9271	2.54219
$149$	18.8905	1.54757	0.773784	−	0.633450i	$-0.218362\pi$
$149$	18.8905	1.54757	0.773784	+	0.633450i	$0.218362\pi$
$150$	−5.00447	−0.408613
$151$	9.01042	0.733258	0.366629	−	0.930367i	$-0.380512\pi$
$151$	9.01042	0.733258	0.366629	+	0.930367i	$0.380512\pi$
$152$	8.63340	0.700262
$153$	−11.3207	−0.915222
$154$	−0.110542	−0.00890771
$155$	−2.11976	−0.170264
$156$	−28.2647	−2.26298
$157$	−16.3658	−1.30614	−0.653068	−	0.757299i	$-0.726519\pi$
$157$	−16.3658	−1.30614	−0.653068	+	0.757299i	$0.726519\pi$
$158$	−31.1937	−2.48163
$159$	−24.9919	−1.98198
$160$	−7.55691	−0.597426
$161$	−1.60665	−0.126621
$162$	23.0489	1.81089
$163$	9.20630	0.721093	0.360547	−	0.932741i	$-0.382590\pi$
$163$	9.20630	0.721093	0.360547	+	0.932741i	$0.382590\pi$
$164$	−5.15449	−0.402498
$165$	0.0739034	0.00575337
$166$	−34.2514	−2.65842
$167$	−1.61172	−0.124719	−0.0623595	−	0.998054i	$-0.519863\pi$
$167$	−1.61172	−0.124719	−0.0623595	+	0.998054i	$0.519863\pi$
$168$	5.73470	0.442442
$169$	7.31836	0.562950
$170$	−10.6844	−0.819453
$171$	−12.6518	−0.967507
$172$	23.3548	1.78079
$173$	4.11040	0.312508	0.156254	−	0.987717i	$-0.450058\pi$
$173$	4.11040	0.312508	0.156254	+	0.987717i	$0.450058\pi$
$174$	−8.79329	−0.666617
$175$	−1.58489	−0.119807
$176$	0.0651877	0.00491371
$177$	17.9471	1.34899
$178$	26.1504	1.96005
$179$	−3.71628	−0.277768	−0.138884	−	0.990309i	$-0.544351\pi$
$179$	−3.71628	−0.277768	−0.138884	+	0.990309i	$0.544351\pi$
$180$	−6.27026	−0.467358
$181$	14.7582	1.09697	0.548483	−	0.836162i	$-0.315206\pi$
$181$	14.7582	1.09697	0.548483	+	0.836162i	$0.315206\pi$
$182$	−15.5258	−1.15085
$183$	−20.6772	−1.52850
$184$	−1.59289	−0.117429
$185$	−11.3576	−0.835030
$186$	−10.6083	−0.777838
$187$	0.157781	0.0115381
$188$	−27.7229	−2.02190
$189$	2.54494	0.185117
$190$	−11.9407	−0.866267
$191$	−9.29549	−0.672598	−0.336299	−	0.941755i	$-0.609175\pi$
$191$	−9.29549	−0.672598	−0.336299	+	0.941755i	$0.609175\pi$
$192$	−28.4637	−2.05419
$193$	5.98991	0.431163	0.215581	−	0.976486i	$-0.430835\pi$
$193$	5.98991	0.431163	0.215581	+	0.976486i	$0.430835\pi$
$194$	27.6719	1.98673
$195$	10.3799	0.743318
$196$	−12.2213	−0.872947
$197$	7.25043	0.516572	0.258286	−	0.966069i	$-0.416842\pi$
$197$	7.25043	0.516572	0.258286	+	0.966069i	$0.416842\pi$
$198$	0.160606	0.0114137
$199$	9.33129	0.661478	0.330739	−	0.943722i	$-0.392702\pi$
$199$	9.33129	0.661478	0.330739	+	0.943722i	$0.392702\pi$
$200$	−1.57132	−0.111109
$201$	−7.22675	−0.509736
$202$	19.7384	1.38879
$203$	−2.78479	−0.195454
$204$	−30.8275	−2.15835
$205$	1.89293	0.132208
$206$	−20.3910	−1.42071
$207$	2.33429	0.162244
$208$	9.15574	0.634836
$209$	0.176334	0.0121973
$210$	−7.93154	−0.547328
$211$	2.98332	0.205380	0.102690	−	0.994713i	$-0.467255\pi$
$211$	2.98332	0.205380	0.102690	+	0.994713i	$0.467255\pi$
$212$	−29.5531	−2.02971
$213$	−0.0175278	−0.00120098
$214$	−39.9935	−2.73390
$215$	−8.57679	−0.584932
$216$	2.52315	0.171678
$217$	−3.35960	−0.228064
$218$	−0.330247	−0.0223671
$219$	4.12801	0.278945
$220$	0.0873913	0.00589192
$221$	22.1607	1.49069
$222$	−56.8389	−3.81478
$223$	14.1479	0.947416	0.473708	−	0.880682i	$-0.342915\pi$
$223$	14.1479	0.947416	0.473708	+	0.880682i	$0.342915\pi$
$224$	−11.9769	−0.800239
$225$	2.30268	0.153512
$226$	−16.6808	−1.10959
$227$	13.8270	0.917732	0.458866	−	0.888505i	$-0.348256\pi$
$227$	13.8270	0.917732	0.458866	+	0.888505i	$0.348256\pi$
$228$	−34.4523	−2.28166
$229$	−14.6245	−0.966414	−0.483207	−	0.875506i	$-0.660528\pi$
$229$	−14.6245	−0.966414	−0.483207	+	0.875506i	$0.660528\pi$
$230$	2.20308	0.145267
$231$	0.117129	0.00770652
$232$	−2.76094	−0.181265
$233$	25.4890	1.66984	0.834921	−	0.550370i	$-0.185513\pi$
$233$	25.4890	1.66984	0.834921	+	0.550370i	$0.185513\pi$
$234$	22.5574	1.47462
$235$	10.1809	0.664131
$236$	21.2226	1.38148
$237$	33.0525	2.14699
$238$	−16.9335	−1.09764
$239$	−2.80974	−0.181747	−0.0908735	−	0.995862i	$-0.528966\pi$
$239$	−2.80974	−0.181747	−0.0908735	+	0.995862i	$0.528966\pi$
$240$	4.67732	0.301920
$241$	−6.95070	−0.447734	−0.223867	−	0.974620i	$-0.571868\pi$
$241$	−6.95070	−0.447734	−0.223867	+	0.974620i	$0.571868\pi$
$242$	23.9035	1.53658
$243$	−19.6051	−1.25767
$244$	−24.4509	−1.56531
$245$	4.48812	0.286735
$246$	9.47310	0.603982
$247$	24.7664	1.57585
$248$	−3.33082	−0.211507
$249$	36.2924	2.29994
$250$	2.17325	0.137449
$251$	−12.1437	−0.766505	−0.383252	−	0.923644i	$-0.625196\pi$
$251$	−12.1437	−0.766505	−0.383252	+	0.923644i	$0.625196\pi$
$252$	−9.93768	−0.626015
$253$	−0.0325340	−0.00204540
$254$	10.5162	0.659848
$255$	11.3210	0.708951
$256$	−0.812364	−0.0507727
$257$	21.4424	1.33754	0.668770	−	0.743469i	$-0.266821\pi$
$257$	21.4424	1.33754	0.668770	+	0.743469i	$0.266821\pi$
$258$	−42.9223	−2.67222
$259$	−18.0006	−1.11850
$260$	12.2743	0.761218
$261$	4.04601	0.250442
$262$	−3.54285	−0.218878
$263$	7.89350	0.486734	0.243367	−	0.969934i	$-0.421748\pi$
$263$	7.89350	0.486734	0.243367	+	0.969934i	$0.421748\pi$
$264$	0.116126	0.00714704
$265$	10.8530	0.666696
$266$	−18.9247	−1.16035
$267$	−27.7087	−1.69574
$268$	−8.54569	−0.522011
$269$	18.6692	1.13828	0.569141	−	0.822240i	$-0.307276\pi$
$269$	18.6692	1.13828	0.569141	+	0.822240i	$0.307276\pi$
$270$	−3.48971	−0.212377
$271$	−9.54248	−0.579664	−0.289832	−	0.957077i	$-0.593600\pi$
$271$	−9.54248	−0.579664	−0.289832	+	0.957077i	$0.593600\pi$
$272$	9.98591	0.605485
$273$	16.4510	0.995658
$274$	−28.4716	−1.72003
$275$	−0.0320935	−0.00193531
$276$	6.35653	0.382618
$277$	11.4649	0.688859	0.344430	−	0.938812i	$-0.388072\pi$
$277$	11.4649	0.688859	0.344430	+	0.938812i	$0.388072\pi$
$278$	−16.3114	−0.978292
$279$	4.88114	0.292226
$280$	−2.49037	−0.148828
$281$	15.0453	0.897530	0.448765	−	0.893650i	$-0.351864\pi$
$281$	15.0453	0.897530	0.448765	+	0.893650i	$0.351864\pi$
$282$	50.9502	3.03404
$283$	−30.5767	−1.81760	−0.908798	−	0.417236i	$-0.862999\pi$
$283$	−30.5767	−1.81760	−0.908798	+	0.417236i	$0.862999\pi$
$284$	−0.0207268	−0.00122991
$285$	12.6522	0.749452
$286$	−0.314392	−0.0185904
$287$	3.00008	0.177089
$288$	17.4012	1.02537
$289$	7.17000	0.421764
$290$	3.81859	0.224236
$291$	−29.3209	−1.71882
$292$	4.88140	0.285662
$293$	−22.9454	−1.34048	−0.670241	−	0.742143i	$-0.733809\pi$
$293$	−22.9454	−1.34048	−0.670241	+	0.742143i	$0.733809\pi$
$294$	22.4606	1.30993
$295$	−7.79377	−0.453771
$296$	−17.8464	−1.03730
$297$	0.0515342	0.00299032
$298$	−41.0538	−2.37818
$299$	−4.56946	−0.264259
$300$	6.27046	0.362025
$301$	−13.5933	−0.783504
$302$	−19.5819	−1.12681
$303$	−20.9146	−1.20151
$304$	11.1601	0.640075
$305$	8.97932	0.514154
$306$	24.6027	1.40644
$307$	−6.96275	−0.397385	−0.198693	−	0.980062i	$-0.563670\pi$
$307$	−6.96275	−0.397385	−0.198693	+	0.980062i	$0.563670\pi$
$308$	0.138506	0.00789210
$309$	21.6061	1.22913
$310$	4.60678	0.261648
$311$	19.8463	1.12538	0.562691	−	0.826667i	$-0.309766\pi$
$311$	19.8463	1.12538	0.562691	+	0.826667i	$0.309766\pi$
$312$	16.3101	0.923376
$313$	−23.6987	−1.33953	−0.669765	−	0.742573i	$-0.733605\pi$
$313$	−23.6987	−1.33953	−0.669765	+	0.742573i	$0.733605\pi$
$314$	35.5671	2.00717
$315$	3.64950	0.205626
$316$	39.0848	2.19869
$317$	−6.87208	−0.385975	−0.192987	−	0.981201i	$-0.561818\pi$
$317$	−6.87208	−0.385975	−0.192987	+	0.981201i	$0.561818\pi$
$318$	54.3136	3.04576
$319$	−0.0563910	−0.00315729
$320$	12.3607	0.690984
$321$	42.3767	2.36524
$322$	3.49165	0.194582
$323$	27.0120	1.50299
$324$	−28.8796	−1.60442
$325$	−4.50759	−0.250036
$326$	−20.0076	−1.10812
$327$	0.349926	0.0193509
$328$	2.97439	0.164233
$329$	16.1357	0.889589
$330$	−0.160611	−0.00884133
$331$	−5.33259	−0.293106	−0.146553	−	0.989203i	$-0.546818\pi$
$331$	−5.33259	−0.293106	−0.146553	+	0.989203i	$0.546818\pi$
$332$	42.9161	2.35532
$333$	26.1530	1.43318
$334$	3.50268	0.191658
$335$	3.13831	0.171464
$336$	7.41304	0.404415
$337$	28.1225	1.53193	0.765965	−	0.642882i	$-0.222261\pi$
$337$	28.1225	1.53193	0.765965	+	0.642882i	$0.222261\pi$
$338$	−15.9046	−0.865098
$339$	17.6748	0.959962
$340$	13.3872	0.726023
$341$	−0.0680306	−0.00368406
$342$	27.4956	1.48679
$343$	18.2074	0.983108
$344$	−13.4769	−0.726623
$345$	−2.33436	−0.125678
$346$	−8.93293	−0.480237
$347$	11.2941	0.606298	0.303149	−	0.952943i	$-0.401962\pi$
$347$	11.2941	0.606298	0.303149	+	0.952943i	$0.401962\pi$
$348$	11.0177	0.590613
$349$	26.3146	1.40859	0.704293	−	0.709909i	$-0.251264\pi$
$349$	26.3146	1.40859	0.704293	+	0.709909i	$0.251264\pi$
$350$	3.44437	0.184109
$351$	7.23808	0.386340
$352$	−0.242527	−0.0129268
$353$	−23.1829	−1.23390	−0.616951	−	0.787001i	$-0.711633\pi$
$353$	−23.1829	−1.23390	−0.616951	+	0.787001i	$0.711633\pi$
$354$	−39.0037	−2.07302
$355$	0.00761166	0.000403985 0
$356$	−32.7657	−1.73658
$357$	17.9426	0.949624
$358$	8.07641	0.426851
$359$	24.5535	1.29589	0.647943	−	0.761689i	$-0.275629\pi$
$359$	24.5535	1.29589	0.647943	+	0.761689i	$0.275629\pi$
$360$	3.61824	0.190698
$361$	11.1882	0.588851
$362$	−32.0732	−1.68573
$363$	−25.3279	−1.32937
$364$	19.4534	1.01964
$365$	−1.79264	−0.0938310
$366$	44.9367	2.34888
$367$	17.9761	0.938344	0.469172	−	0.883107i	$-0.344552\pi$
$367$	17.9761	0.938344	0.469172	+	0.883107i	$0.344552\pi$
$368$	−2.05906	−0.107336
$369$	−4.35881	−0.226911
$370$	24.6830	1.28321
$371$	17.2009	0.893024
$372$	13.2919	0.689153
$373$	2.60429	0.134845	0.0674226	−	0.997725i	$-0.478522\pi$
$373$	2.60429	0.134845	0.0674226	+	0.997725i	$0.478522\pi$
$374$	−0.342898	−0.0177308
$375$	−2.30276	−0.118914
$376$	15.9975	0.825006
$377$	−7.92023	−0.407912
$378$	−5.53081	−0.284474
$379$	−32.2351	−1.65580	−0.827902	−	0.560873i	$-0.810466\pi$
$379$	−32.2351	−1.65580	−0.827902	+	0.560873i	$0.810466\pi$
$380$	14.9613	0.767500
$381$	−11.1429	−0.570868
$382$	20.2014	1.03360
$383$	−5.24543	−0.268029	−0.134015	−	0.990979i	$-0.542787\pi$
$383$	−5.24543	−0.268029	−0.134015	+	0.990979i	$0.542787\pi$
$384$	27.0553	1.38066
$385$	−0.0508647	−0.00259230
$386$	−13.0176	−0.662577
$387$	19.7496	1.00393
$388$	−34.6721	−1.76021
$389$	7.06202	0.358059	0.179029	−	0.983844i	$-0.442704\pi$
$389$	7.06202	0.358059	0.179029	+	0.983844i	$0.442704\pi$
$390$	−22.5581	−1.14227
$391$	−4.98378	−0.252041
$392$	7.05226	0.356193
$393$	3.75397	0.189363
$394$	−15.7570	−0.793827
$395$	−14.3534	−0.722200
$396$	−0.201234	−0.0101124
$397$	0.725278	0.0364007	0.0182003	−	0.999834i	$-0.494206\pi$
$397$	0.725278	0.0364007	0.0182003	+	0.999834i	$0.494206\pi$
$398$	−20.2792	−1.01651
$399$	20.0524	1.00387
$400$	−2.03118	−0.101559
$401$	−33.0187	−1.64887	−0.824437	−	0.565954i	$-0.808508\pi$
$401$	−33.0187	−1.64887	−0.824437	+	0.565954i	$0.808508\pi$
$402$	15.7056	0.783322
$403$	−9.55503	−0.475970
$404$	−24.7317	−1.23045
$405$	10.6057	0.527002
$406$	6.05206	0.300359
$407$	−0.364506	−0.0180679
$408$	17.7889	0.880683
$409$	3.42627	0.169418	0.0847090	−	0.996406i	$-0.473004\pi$
$409$	3.42627	0.169418	0.0847090	+	0.996406i	$0.473004\pi$
$410$	−4.11381	−0.203167
$411$	30.1682	1.48809
$412$	25.5493	1.25873
$413$	−12.3523	−0.607816
$414$	−5.07300	−0.249324
$415$	−15.7604	−0.773649
$416$	−34.0634	−1.67010
$417$	17.2834	0.846370
$418$	−0.383217	−0.0187438
$419$	27.9724	1.36654	0.683271	−	0.730165i	$-0.260557\pi$
$419$	27.9724	1.36654	0.683271	+	0.730165i	$0.260557\pi$
$420$	9.93800	0.484925
$421$	−13.3207	−0.649210	−0.324605	−	0.945850i	$-0.605231\pi$
$421$	−13.3207	−0.649210	−0.324605	+	0.945850i	$0.605231\pi$
$422$	−6.48350	−0.315612
$423$	−23.4434	−1.13986
$424$	17.0535	0.828193
$425$	−4.91630	−0.238476
$426$	0.0380923	0.00184558
$427$	14.2312	0.688698
$428$	50.1108	2.42220
$429$	0.333126	0.0160835
$430$	18.6395	0.898878
$431$	6.65552	0.320585	0.160293	−	0.987070i	$-0.448756\pi$
$431$	6.65552	0.320585	0.160293	+	0.987070i	$0.448756\pi$
$432$	3.26158	0.156923
$433$	−7.30047	−0.350838	−0.175419	−	0.984494i	$-0.556128\pi$
$433$	−7.30047	−0.350838	−0.175419	+	0.984494i	$0.556128\pi$
$434$	7.30125	0.350471
$435$	−4.04614	−0.193998
$436$	0.413790	0.0198169
$437$	−5.56979	−0.266439
$438$	−8.97120	−0.428661
$439$	14.5563	0.694733	0.347367	−	0.937729i	$-0.387076\pi$
$439$	14.5563	0.694733	0.347367	+	0.937729i	$0.387076\pi$
$440$	−0.0504290	−0.00240411
$441$	−10.3347	−0.492129
$442$	−48.1607	−2.29077
$443$	−1.43075	−0.0679771	−0.0339886	−	0.999422i	$-0.510821\pi$
$443$	−1.43075	−0.0679771	−0.0339886	+	0.999422i	$0.510821\pi$
$444$	71.2176	3.37984
$445$	12.0328	0.570411
$446$	−30.7470	−1.45591
$447$	43.5001	2.05749
$448$	19.5904	0.925558
$449$	−1.86295	−0.0879180	−0.0439590	−	0.999033i	$-0.513997\pi$
$449$	−1.86295	−0.0879180	−0.0439590	+	0.999033i	$0.513997\pi$
$450$	−5.00431	−0.235905
$451$	0.0607506	0.00286063
$452$	20.9006	0.983080
$453$	20.7488	0.974863
$454$	−30.0496	−1.41030
$455$	−7.14404	−0.334918
$456$	19.8806	0.930995
$457$	−12.8585	−0.601494	−0.300747	−	0.953704i	$-0.597236\pi$
$457$	−12.8585	−0.601494	−0.300747	+	0.953704i	$0.597236\pi$
$458$	31.7827	1.48511
$459$	7.89436	0.368477
$460$	−2.76040	−0.128704
$461$	−14.1938	−0.661071	−0.330536	−	0.943794i	$-0.607229\pi$
$461$	−14.1938	−0.661071	−0.330536	+	0.943794i	$0.607229\pi$
$462$	−0.254551	−0.0118428
$463$	−10.0380	−0.466506	−0.233253	−	0.972416i	$-0.574937\pi$
$463$	−10.0380	−0.466506	−0.233253	+	0.972416i	$0.574937\pi$
$464$	−3.56897	−0.165685
$465$	−4.88130	−0.226365
$466$	−55.3941	−2.56608
$467$	13.5032	0.624855	0.312428	−	0.949942i	$-0.398858\pi$
$467$	13.5032	0.624855	0.312428	+	0.949942i	$0.398858\pi$
$468$	−28.2638	−1.30649
$469$	4.97388	0.229672
$470$	−22.1257	−1.02058
$471$	−37.6865	−1.73650
$472$	−12.2465	−0.563690
$473$	−0.275259	−0.0126564
$474$	−71.8314	−3.29932
$475$	−5.49438	−0.252099
$476$	21.2173	0.972492
$477$	−24.9911	−1.14426
$478$	6.10627	0.279294
$479$	0.160978	0.00735529	0.00367764	−	0.999993i	$-0.498829\pi$
$479$	0.160978	0.00735529	0.00367764	+	0.999993i	$0.498829\pi$
$480$	−17.4017	−0.794276
$481$	−51.1955	−2.33432
$482$	15.1056	0.688042
$483$	−3.69971	−0.168343
$484$	−29.9505	−1.36139
$485$	12.7330	0.578174
$486$	42.6068	1.93268
$487$	24.5329	1.11169	0.555847	−	0.831285i	$-0.312394\pi$
$487$	24.5329	1.11169	0.555847	+	0.831285i	$0.312394\pi$
$488$	14.1093	0.638700
$489$	21.1999	0.958691
$490$	−9.75381	−0.440632
$491$	25.5335	1.15231	0.576154	−	0.817341i	$-0.304553\pi$
$491$	25.5335	1.15231	0.576154	+	0.817341i	$0.304553\pi$
$492$	−11.8695	−0.535120
$493$	−8.63837	−0.389052
$494$	−53.8236	−2.42164
$495$	0.0739011	0.00332161
$496$	−4.30563	−0.193329
$497$	0.0120637	0.000541129 0
$498$	−78.8726	−3.53437
$499$	−42.1303	−1.88601	−0.943005	−	0.332779i	$-0.892014\pi$
$499$	−42.1303	−1.88601	−0.943005	+	0.332779i	$0.892014\pi$
$500$	−2.72303	−0.121777
$501$	−3.71141	−0.165813
$502$	26.3914	1.17790
$503$	38.9087	1.73485	0.867427	−	0.497565i	$-0.165772\pi$
$503$	38.9087	1.73485	0.867427	+	0.497565i	$0.165772\pi$
$504$	5.73452	0.255436
$505$	9.08243	0.404163
$506$	0.0707046	0.00314320
$507$	16.8524	0.748441
$508$	−13.1766	−0.584615
$509$	−0.723169	−0.0320539	−0.0160270	−	0.999872i	$-0.505102\pi$
$509$	−0.723169	−0.0320539	−0.0160270	+	0.999872i	$0.505102\pi$
$510$	−24.6035	−1.08946
$511$	−2.84114	−0.125685
$512$	−21.7327	−0.960460
$513$	8.82261	0.389528
$514$	−46.5997	−2.05543
$515$	−9.38270	−0.413451
$516$	53.7804	2.36755
$517$	0.326742	0.0143701
$518$	39.1199	1.71883
$519$	9.46524	0.415478
$520$	−7.08285	−0.310603
$521$	−28.9529	−1.26845	−0.634224	−	0.773149i	$-0.718680\pi$
$521$	−28.9529	−1.26845	−0.634224	+	0.773149i	$0.718680\pi$
$522$	−8.79301	−0.384859
$523$	−17.7506	−0.776180	−0.388090	−	0.921622i	$-0.626865\pi$
$523$	−17.7506	−0.776180	−0.388090	+	0.921622i	$0.626865\pi$
$524$	4.43910	0.193923
$525$	−3.64962	−0.159282
$526$	−17.1546	−0.747975
$527$	−10.4214	−0.453963
$528$	0.150111	0.00653276
$529$	−21.9724	−0.955320
$530$	−23.5864	−1.02453
$531$	17.9466	0.778815
$532$	23.7121	1.02805
$533$	8.53254	0.369585
$534$	60.2179	2.60588
$535$	−18.4026	−0.795615
$536$	4.93127	0.212999
$537$	−8.55768	−0.369291
$538$	−40.5729	−1.74922
$539$	0.144039	0.00620421
$540$	4.37251	0.188163
$541$	2.04189	0.0877879	0.0438940	−	0.999036i	$-0.486024\pi$
$541$	2.04189	0.0877879	0.0438940	+	0.999036i	$0.486024\pi$
$542$	20.7382	0.890783
$543$	33.9844	1.45841
$544$	−37.1520	−1.59288
$545$	−0.151960	−0.00650923
$546$	−35.7521	−1.53005
$547$	−29.0703	−1.24296	−0.621478	−	0.783432i	$-0.713467\pi$
$547$	−29.0703	−1.24296	−0.621478	+	0.783432i	$0.713467\pi$
$548$	35.6741	1.52392
$549$	−20.6765	−0.882452
$550$	0.0697472	0.00297403
$551$	−9.65410	−0.411278
$552$	−3.66802	−0.156121
$553$	−22.7487	−0.967371
$554$	−24.9161	−1.05858
$555$	−26.1538	−1.11017
$556$	20.4377	0.866752
$557$	−6.40125	−0.271230	−0.135615	−	0.990762i	$-0.543301\pi$
$557$	−6.40125	−0.271230	−0.135615	+	0.990762i	$0.543301\pi$
$558$	−10.6080	−0.449071
$559$	−38.6607	−1.63517
$560$	−3.21921	−0.136036
$561$	0.363331	0.0153399
$562$	−32.6973	−1.37925
$563$	12.4617	0.525199	0.262600	−	0.964905i	$-0.415420\pi$
$563$	12.4617	0.525199	0.262600	+	0.964905i	$0.415420\pi$
$564$	−63.8391	−2.68811
$565$	−7.67549	−0.322910
$566$	66.4509	2.79314
$567$	16.8089	0.705907
$568$	0.0119603	0.000501844 0
$569$	19.2147	0.805523	0.402762	−	0.915305i	$-0.368050\pi$
$569$	19.2147	0.805523	0.402762	+	0.915305i	$0.368050\pi$
$570$	−27.4964	−1.15170
$571$	15.6841	0.656361	0.328180	−	0.944615i	$-0.393565\pi$
$571$	15.6841	0.656361	0.328180	+	0.944615i	$0.393565\pi$
$572$	0.393924	0.0164708
$573$	−21.4052	−0.894217
$574$	−6.51994	−0.272137
$575$	1.01373	0.0422753
$576$	−28.4628	−1.18595
$577$	−5.48834	−0.228483	−0.114241	−	0.993453i	$-0.536444\pi$
$577$	−5.48834	−0.228483	−0.114241	+	0.993453i	$0.536444\pi$
$578$	−15.5822	−0.648135
$579$	13.7933	0.573229
$580$	−4.78459	−0.198669
$581$	−24.9786	−1.03629
$582$	63.7216	2.64135
$583$	0.348311	0.0144256
$584$	−2.81680	−0.116560
$585$	10.3795	0.429141
$586$	49.8661	2.05995
$587$	1.92603	0.0794959	0.0397479	−	0.999210i	$-0.487345\pi$
$587$	1.92603	0.0794959	0.0397479	+	0.999210i	$0.487345\pi$
$588$	−28.1426	−1.16058
$589$	−11.6468	−0.479897
$590$	16.9378	0.697319
$591$	16.6960	0.686780
$592$	−23.0694	−0.948148
$593$	32.0882	1.31770	0.658852	−	0.752272i	$-0.271042\pi$
$593$	32.0882	1.31770	0.658852	+	0.752272i	$0.271042\pi$
$594$	−0.111997	−0.00459529
$595$	−7.79180	−0.319433
$596$	51.4392	2.10703
$597$	21.4877	0.879432
$598$	9.93059	0.406092
$599$	14.6310	0.597804	0.298902	−	0.954284i	$-0.403380\pi$
$599$	14.6310	0.597804	0.298902	+	0.954284i	$0.403380\pi$
$600$	−3.61836	−0.147719
$601$	17.2927	0.705385	0.352692	−	0.935739i	$-0.385266\pi$
$601$	17.2927	0.705385	0.352692	+	0.935739i	$0.385266\pi$
$602$	29.5416	1.20403
$603$	−7.22652	−0.294287
$604$	24.5356	0.998340
$605$	10.9990	0.447172
$606$	45.4527	1.84639
$607$	38.4615	1.56110	0.780552	−	0.625091i	$-0.214938\pi$
$607$	38.4615	1.56110	0.780552	+	0.625091i	$0.214938\pi$
$608$	−41.5205	−1.68388
$609$	−6.41270	−0.259856
$610$	−19.5143	−0.790112
$611$	45.8915	1.85657
$612$	−30.8265	−1.24609
$613$	−9.31639	−0.376286	−0.188143	−	0.982142i	$-0.560247\pi$
$613$	−9.31639	−0.376286	−0.188143	+	0.982142i	$0.560247\pi$
$614$	15.1318	0.610670
$615$	4.35895	0.175770
$616$	−0.0799245	−0.00322025
$617$	33.0464	1.33040	0.665198	−	0.746667i	$-0.268347\pi$
$617$	33.0464	1.33040	0.665198	+	0.746667i	$0.268347\pi$
$618$	−46.9554	−1.88882
$619$	−13.2270	−0.531638	−0.265819	−	0.964023i	$-0.585642\pi$
$619$	−13.2270	−0.531638	−0.265819	+	0.964023i	$0.585642\pi$
$620$	−5.77217	−0.231816
$621$	−1.62779	−0.0653212
$622$	−43.1311	−1.72940
$623$	19.0707	0.764053
$624$	21.0834	0.844013
$625$	1.00000	0.0400000
$626$	51.5033	2.05849
$627$	0.406053	0.0162162
$628$	−44.5646	−1.77832
$629$	−55.8375	−2.22639
$630$	−7.93129	−0.315990
$631$	−15.2643	−0.607663	−0.303831	−	0.952726i	$-0.598266\pi$
$631$	−15.2643	−0.607663	−0.303831	+	0.952726i	$0.598266\pi$
$632$	−22.5538	−0.897142
$633$	6.86985	0.273052
$634$	14.9348	0.593136
$635$	4.83894	0.192028
$636$	−68.0535	−2.69850
$637$	20.2306	0.801565
$638$	0.122552	0.00485188
$639$	−0.0175272	−0.000693367 0
$640$	−11.7491	−0.464424
$641$	−7.59080	−0.299818	−0.149909	−	0.988700i	$-0.547898\pi$
$641$	−7.59080	−0.299818	−0.149909	+	0.988700i	$0.547898\pi$
$642$	−92.0953	−3.63471
$643$	−45.1267	−1.77962	−0.889812	−	0.456327i	$-0.849165\pi$
$643$	−45.1267	−1.77962	−0.889812	+	0.456327i	$0.849165\pi$
$644$	−4.37494	−0.172397
$645$	−19.7503	−0.777665
$646$	−58.7039	−2.30967
$647$	27.3168	1.07393	0.536967	−	0.843603i	$-0.319570\pi$
$647$	27.3168	1.07393	0.536967	+	0.843603i	$0.319570\pi$
$648$	16.6649	0.654660
$649$	−0.250129	−0.00981843
$650$	9.79613	0.384236
$651$	−7.73633	−0.303211
$652$	25.0690	0.981777
$653$	7.18302	0.281093	0.140547	−	0.990074i	$-0.455114\pi$
$653$	7.18302	0.281093	0.140547	+	0.990074i	$0.455114\pi$
$654$	−0.760477	−0.0297370
$655$	−1.63021	−0.0636975
$656$	3.84488	0.150117
$657$	4.12788	0.161044
$658$	−35.0669	−1.36705
$659$	11.5320	0.449223	0.224612	−	0.974448i	$-0.427889\pi$
$659$	11.5320	0.449223	0.224612	+	0.974448i	$0.427889\pi$
$660$	0.201241	0.00783329
$661$	11.5719	0.450094	0.225047	−	0.974348i	$-0.427746\pi$
$661$	11.5719	0.450094	0.225047	+	0.974348i	$0.427746\pi$
$662$	11.5891	0.450422
$663$	51.0306	1.98186
$664$	−24.7646	−0.961054
$665$	−8.70799	−0.337681
$666$	−56.8371	−2.20239
$667$	1.78121	0.0689686
$668$	−4.38877	−0.169806
$669$	32.5792	1.25959
$670$	−6.82033	−0.263492
$671$	0.288177	0.0111250
$672$	−27.5798	−1.06391
$673$	21.0405	0.811053	0.405527	−	0.914083i	$-0.367088\pi$
$673$	21.0405	0.811053	0.405527	+	0.914083i	$0.367088\pi$
$674$	−61.1173	−2.35415
$675$	−1.60575	−0.0618055
$676$	19.9281	0.766464
$677$	22.2766	0.856160	0.428080	−	0.903741i	$-0.359190\pi$
$677$	22.2766	0.856160	0.428080	+	0.903741i	$0.359190\pi$
$678$	−38.4118	−1.47519
$679$	20.1803	0.774451
$680$	−7.72506	−0.296243
$681$	31.8403	1.22012
$682$	0.147848	0.00566138
$683$	29.2280	1.11838	0.559190	−	0.829039i	$-0.311112\pi$
$683$	29.2280	1.11838	0.559190	+	0.829039i	$0.311112\pi$
$684$	−34.4512	−1.31727
$685$	−13.1009	−0.500560
$686$	−39.5693	−1.51076
$687$	−33.6766	−1.28484
$688$	−17.4210	−0.664171
$689$	48.9210	1.86374
$690$	5.07316	0.193132
$691$	28.7919	1.09529	0.547647	−	0.836710i	$-0.315524\pi$
$691$	28.7919	1.09529	0.547647	+	0.836710i	$0.315524\pi$
$692$	11.1927	0.425483
$693$	0.117125	0.00444922
$694$	−24.5449	−0.931711
$695$	−7.50552	−0.284700
$696$	−6.35777	−0.240991
$697$	9.30620	0.352497
$698$	−57.1882	−2.16461
$699$	58.6950	2.22005
$700$	−4.31570	−0.163118
$701$	−9.94411	−0.375584	−0.187792	−	0.982209i	$-0.560133\pi$
$701$	−9.94411	−0.375584	−0.187792	+	0.982209i	$0.560133\pi$
$702$	−15.7302	−0.593697
$703$	−62.4031	−2.35358
$704$	0.396698	0.0149511
$705$	23.4442	0.882960
$706$	50.3824	1.89617
$707$	14.3947	0.541367
$708$	48.8705	1.83667
$709$	10.8882	0.408916	0.204458	−	0.978875i	$-0.434457\pi$
$709$	10.8882	0.408916	0.204458	+	0.978875i	$0.434457\pi$
$710$	−0.0165421	−0.000620813 0
$711$	33.0514	1.23952
$712$	18.9074	0.708584
$713$	2.14886	0.0804755
$714$	−38.9938	−1.45931
$715$	−0.144664	−0.00541013
$716$	−10.1195	−0.378184
$717$	−6.47014	−0.241632
$718$	−53.3610	−1.99142
$719$	11.6934	0.436089	0.218045	−	0.975939i	$-0.430032\pi$
$719$	11.6934	0.436089	0.218045	+	0.975939i	$0.430032\pi$
$720$	4.67717	0.174308
$721$	−14.8706	−0.553809
$722$	−24.3147	−0.904900
$723$	−16.0057	−0.595260
$724$	40.1868	1.49353
$725$	1.75709	0.0652566
$726$	55.0440	2.04287
$727$	36.3894	1.34961	0.674803	−	0.737998i	$-0.264228\pi$
$727$	36.3894	1.34961	0.674803	+	0.737998i	$0.264228\pi$
$728$	−11.2255	−0.416046
$729$	−13.3286	−0.493651
$730$	3.89586	0.144192
$731$	−42.1661	−1.55957
$732$	−56.3044	−2.08107
$733$	6.21215	0.229451	0.114725	−	0.993397i	$-0.463401\pi$
$733$	6.21215	0.229451	0.114725	+	0.993397i	$0.463401\pi$
$734$	−39.0666	−1.44197
$735$	10.3350	0.381214
$736$	7.66064	0.282375
$737$	0.100719	0.00371004
$738$	9.47279	0.348698
$739$	−18.5017	−0.680597	−0.340298	−	0.940317i	$-0.610528\pi$
$739$	−18.5017	−0.680597	−0.340298	+	0.940317i	$0.610528\pi$
$740$	−30.9271	−1.13690
$741$	57.0309	2.09508
$742$	−37.3818	−1.37233
$743$	10.4621	0.383816	0.191908	−	0.981413i	$-0.438532\pi$
$743$	10.4621	0.383816	0.191908	+	0.981413i	$0.438532\pi$
$744$	−7.67007	−0.281198
$745$	−18.8905	−0.692093
$746$	−5.65978	−0.207219
$747$	36.2913	1.32783
$748$	0.429642	0.0157093
$749$	−29.1662	−1.06571
$750$	5.00447	0.182737
$751$	−49.1875	−1.79488	−0.897439	−	0.441138i	$-0.854575\pi$
$751$	−49.1875	−1.79488	−0.897439	+	0.441138i	$0.854575\pi$
$752$	20.6793	0.754098
$753$	−27.9640	−1.01907
$754$	17.2127	0.626848
$755$	−9.01042	−0.327923
$756$	6.92995	0.252040
$757$	−41.1104	−1.49418	−0.747092	−	0.664721i	$-0.768551\pi$
$757$	−41.1104	−1.49418	−0.747092	+	0.664721i	$0.768551\pi$
$758$	70.0549	2.54451
$759$	−0.0749178	−0.00271935
$760$	−8.63340	−0.313166
$761$	−33.7949	−1.22506	−0.612531	−	0.790446i	$-0.709849\pi$
$761$	−33.7949	−1.22506	−0.612531	+	0.790446i	$0.709849\pi$
$762$	24.2163	0.877265
$763$	−0.240839	−0.00871897
$764$	−25.3119	−0.915751
$765$	11.3207	0.409300
$766$	11.3996	0.411886
$767$	−35.1311	−1.26851
$768$	−1.87067	−0.0675022
$769$	−13.8738	−0.500302	−0.250151	−	0.968207i	$-0.580480\pi$
$769$	−13.8738	−0.500302	−0.250151	+	0.968207i	$0.580480\pi$
$770$	0.110542	0.00398365
$771$	49.3766	1.77825
$772$	16.3107	0.587034
$773$	−40.1887	−1.44549	−0.722743	−	0.691117i	$-0.757119\pi$
$773$	−40.1887	−1.44549	−0.722743	+	0.691117i	$0.757119\pi$
$774$	−42.9209	−1.54276
$775$	2.11976	0.0761442
$776$	20.0075	0.718227
$777$	−41.4510	−1.48705
$778$	−15.3476	−0.550236
$779$	10.4005	0.372635
$780$	28.2647	1.01204
$781$	0.000244285 0	8.74119e−6 0
$782$	10.8310	0.387316
$783$	−2.82145	−0.100830
$784$	9.11619	0.325578
$785$	16.3658	0.584122
$786$	−8.15833	−0.290998
$787$	−48.4120	−1.72570	−0.862851	−	0.505459i	$-0.831323\pi$
$787$	−48.4120	−1.72570	−0.862851	+	0.505459i	$0.831323\pi$
$788$	19.7431	0.703319
$789$	18.1768	0.647111
$790$	31.1937	1.10982
$791$	−12.1648	−0.432531
$792$	0.116122	0.00412621
$793$	40.4751	1.43731
$794$	−1.57621	−0.0559377
$795$	24.9919	0.886370
$796$	25.4093	0.900610
$797$	30.7653	1.08976	0.544882	−	0.838513i	$-0.316574\pi$
$797$	30.7653	1.08976	0.544882	+	0.838513i	$0.316574\pi$
$798$	−43.5789	−1.54267
$799$	50.0525	1.77073
$800$	7.55691	0.267177
$801$	−27.7078	−0.979006
$802$	71.7579	2.53386
$803$	−0.0575320	−0.00203026
$804$	−19.6786	−0.694012
$805$	1.60665	0.0566268
$806$	20.7655	0.731433
$807$	42.9906	1.51334
$808$	14.2714	0.502065
$809$	51.8668	1.82354	0.911769	−	0.410703i	$-0.134717\pi$
$809$	51.8668	1.82354	0.911769	+	0.410703i	$0.134717\pi$
$810$	−23.0489	−0.809855
$811$	34.5320	1.21258	0.606291	−	0.795243i	$-0.292656\pi$
$811$	34.5320	1.21258	0.606291	+	0.795243i	$0.292656\pi$
$812$	−7.58306	−0.266113
$813$	−21.9740	−0.770662
$814$	0.792163	0.0277653
$815$	−9.20630	−0.322483
$816$	22.9951	0.804989
$817$	−47.1241	−1.64866
$818$	−7.44614	−0.260348
$819$	16.4504	0.574825
$820$	5.15449	0.180003
$821$	−40.3924	−1.40970	−0.704852	−	0.709355i	$-0.748987\pi$
$821$	−40.3924	−1.40970	−0.704852	+	0.709355i	$0.748987\pi$
$822$	−65.5631	−2.28678
$823$	43.5422	1.51779	0.758893	−	0.651215i	$-0.225740\pi$
$823$	43.5422	1.51779	0.758893	+	0.651215i	$0.225740\pi$
$824$	−14.7432	−0.513604
$825$	−0.0739034	−0.00257299
$826$	26.8446	0.934044
$827$	−32.1552	−1.11815	−0.559073	−	0.829118i	$-0.688843\pi$
$827$	−32.1552	−1.11815	−0.559073	+	0.829118i	$0.688843\pi$
$828$	6.35633	0.220898
$829$	−22.2256	−0.771927	−0.385963	−	0.922514i	$-0.626131\pi$
$829$	−22.2256	−0.771927	−0.385963	+	0.922514i	$0.626131\pi$
$830$	34.2514	1.18888
$831$	26.4009	0.915836
$832$	55.7169	1.93164
$833$	22.0649	0.764505
$834$	−37.5611	−1.30064
$835$	1.61172	0.0557760
$836$	0.480161	0.0166067
$837$	−3.40382	−0.117653
$838$	−60.7911	−2.09999
$839$	−11.8324	−0.408500	−0.204250	−	0.978919i	$-0.565476\pi$
$839$	−11.8324	−0.408500	−0.204250	+	0.978919i	$0.565476\pi$
$840$	−5.73470	−0.197866
$841$	−25.9126	−0.893539
$842$	28.9492	0.997655
$843$	34.6457	1.19326
$844$	8.12365	0.279627
$845$	−7.31836	−0.251759
$846$	50.9485	1.75165
$847$	17.4322	0.598977
$848$	22.0445	0.757011
$849$	−70.4107	−2.41649
$850$	10.6844	0.366470
$851$	11.5135	0.394679
$852$	−0.0477286	−0.00163516
$853$	−18.8934	−0.646896	−0.323448	−	0.946246i	$-0.604842\pi$
$853$	−18.8934	−0.646896	−0.323448	+	0.946246i	$0.604842\pi$
$854$	−30.9281	−1.05834
$855$	12.6518	0.432682
$856$	−28.9163	−0.988340
$857$	9.23795	0.315562	0.157781	−	0.987474i	$-0.449566\pi$
$857$	9.23795	0.315562	0.157781	+	0.987474i	$0.449566\pi$
$858$	−0.723967	−0.0247158
$859$	−8.04722	−0.274568	−0.137284	−	0.990532i	$-0.543837\pi$
$859$	−8.04722	−0.274568	−0.137284	+	0.990532i	$0.543837\pi$
$860$	−23.3548	−0.796393
$861$	6.90846	0.235440
$862$	−14.4641	−0.492650
$863$	−16.4220	−0.559012	−0.279506	−	0.960144i	$-0.590171\pi$
$863$	−16.4220	−0.559012	−0.279506	+	0.960144i	$0.590171\pi$
$864$	−12.1345	−0.412825
$865$	−4.11040	−0.139758
$866$	15.8658	0.539140
$867$	16.5107	0.560734
$868$	−9.14827	−0.310512
$869$	−0.460652	−0.0156265
$870$	8.79329	0.298120
$871$	14.1462	0.479326
$872$	−0.238777	−0.00808600
$873$	−29.3199	−0.992329
$874$	12.1046	0.409443
$875$	1.58489	0.0535791
$876$	11.2407	0.379787
$877$	−24.7659	−0.836284	−0.418142	−	0.908382i	$-0.637319\pi$
$877$	−24.7659	−0.836284	−0.418142	+	0.908382i	$0.637319\pi$
$878$	−31.6345	−1.06761
$879$	−52.8376	−1.78217
$880$	−0.0651877	−0.00219748
$881$	21.3381	0.718898	0.359449	−	0.933165i	$-0.382965\pi$
$881$	21.3381	0.718898	0.359449	+	0.933165i	$0.382965\pi$
$882$	22.4599	0.756265
$883$	4.10249	0.138060	0.0690298	−	0.997615i	$-0.478010\pi$
$883$	4.10249	0.138060	0.0690298	+	0.997615i	$0.478010\pi$
$884$	60.3440	2.02959
$885$	−17.9471	−0.603287
$886$	3.10939	0.104462
$887$	45.3955	1.52423	0.762115	−	0.647441i	$-0.224161\pi$
$887$	45.3955	1.52423	0.762115	+	0.647441i	$0.224161\pi$
$888$	−41.0960	−1.37909
$889$	7.66920	0.257217
$890$	−26.1504	−0.876563
$891$	0.340374	0.0114030
$892$	38.5252	1.28992
$893$	55.9379	1.87189
$894$	−94.5367	−3.16178
$895$	3.71628	0.124221
$896$	−18.6211	−0.622086
$897$	−10.5224	−0.351331
$898$	4.04866	0.135105
$899$	3.72461	0.124223
$900$	6.27026	0.209009
$901$	53.3567	1.77757
$902$	−0.132026	−0.00439600
$903$	−31.3020	−1.04167
$904$	−12.0606	−0.401131
$905$	−14.7582	−0.490578
$906$	−45.0924	−1.49809
$907$	24.8366	0.824685	0.412342	−	0.911029i	$-0.364711\pi$
$907$	24.8366	0.824685	0.412342	+	0.911029i	$0.364711\pi$
$908$	37.6513	1.24950
$909$	−20.9139	−0.693672
$910$	15.5258	0.514675
$911$	0.0719543	0.00238395	0.00119198	−	0.999999i	$-0.499621\pi$
$911$	0.0719543	0.00238395	0.00119198	+	0.999999i	$0.499621\pi$
$912$	25.6989	0.850977
$913$	−0.505807	−0.0167398
$914$	27.9447	0.924329
$915$	20.6772	0.683566
$916$	−39.8229	−1.31579
$917$	−2.58370	−0.0853214
$918$	−17.1564	−0.566247
$919$	−9.59527	−0.316519	−0.158259	−	0.987398i	$-0.550588\pi$
$919$	−9.59527	−0.316519	−0.158259	+	0.987398i	$0.550588\pi$
$920$	1.59289	0.0525159
$921$	−16.0335	−0.528322
$922$	30.8467	1.01588
$923$	0.0343102	0.00112934
$924$	0.318945	0.0104925
$925$	11.3576	0.373437
$926$	21.8152	0.716890
$927$	21.6054	0.709614
$928$	13.2781	0.435876
$929$	−40.6294	−1.33301	−0.666503	−	0.745502i	$-0.732210\pi$
$929$	−40.6294	−1.33301	−0.666503	+	0.745502i	$0.732210\pi$
$930$	10.6083	0.347860
$931$	24.6594	0.808180
$932$	69.4073	2.27351
$933$	45.7012	1.49619
$934$	−29.3459	−0.960229
$935$	−0.157781	−0.00515999
$936$	16.3095	0.533094
$937$	49.1714	1.60636	0.803179	−	0.595737i	$-0.203140\pi$
$937$	49.1714	1.60636	0.803179	+	0.595737i	$0.203140\pi$
$938$	−10.8095	−0.352942
$939$	−54.5723	−1.78090
$940$	27.7229	0.904223
$941$	−14.2722	−0.465261	−0.232630	−	0.972565i	$-0.574733\pi$
$941$	−14.2722	−0.465261	−0.232630	+	0.972565i	$0.574733\pi$
$942$	81.9023	2.66852
$943$	−1.91891	−0.0624883
$944$	−15.8306	−0.515241
$945$	−2.54494	−0.0827871
$946$	0.598207	0.0194494
$947$	−29.8113	−0.968736	−0.484368	−	0.874864i	$-0.660950\pi$
$947$	−29.8113	−0.968736	−0.484368	+	0.874864i	$0.660950\pi$
$948$	90.0027	2.92315
$949$	−8.08048	−0.262303
$950$	11.9407	0.387406
$951$	−15.8247	−0.513152
$952$	−12.2434	−0.396810
$953$	23.2388	0.752779	0.376390	−	0.926461i	$-0.377165\pi$
$953$	23.2388	0.752779	0.376390	+	0.926461i	$0.377165\pi$
$954$	54.3119	1.75841
$955$	9.29549	0.300795
$956$	−7.65099	−0.247451
$957$	−0.129855	−0.00419761
$958$	−0.349847	−0.0113030
$959$	−20.7635	−0.670489
$960$	28.4637	0.918661
$961$	−26.5066	−0.855052
$962$	111.261	3.58719
$963$	42.3754	1.36553
$964$	−18.9269	−0.609595
$965$	−5.98991	−0.192822
$966$	8.04041	0.258696
$967$	−38.0731	−1.22435	−0.612174	−	0.790723i	$-0.709705\pi$
$967$	−38.0731	−1.22435	−0.612174	+	0.790723i	$0.709705\pi$
$968$	17.2829	0.555492
$969$	62.2020	1.99822
$970$	−27.6719	−0.888492
$971$	−56.6681	−1.81856	−0.909282	−	0.416180i	$-0.863369\pi$
$971$	−56.6681	−1.81856	−0.909282	+	0.416180i	$0.863369\pi$
$972$	−53.3851	−1.71233
$973$	−11.8954	−0.381350
$974$	−53.3163	−1.70836
$975$	−10.3799	−0.332422
$976$	18.2386	0.583805
$977$	54.1879	1.73362	0.866812	−	0.498634i	$-0.166165\pi$
$977$	54.1879	1.73362	0.866812	+	0.498634i	$0.166165\pi$
$978$	−46.0726	−1.47324
$979$	0.386175	0.0123422
$980$	12.2213	0.390394
$981$	0.349915	0.0111719
$982$	−55.4906	−1.77078
$983$	2.94435	0.0939101	0.0469550	−	0.998897i	$-0.485048\pi$
$983$	2.94435	0.0939101	0.0469550	+	0.998897i	$0.485048\pi$
$984$	6.84929	0.218347
$985$	−7.25043	−0.231018
$986$	18.7733	0.597865
$987$	37.1565	1.18270
$988$	67.4395	2.14554
$989$	8.69452	0.276470
$990$	−0.160606	−0.00510438
$991$	56.6491	1.79952	0.899759	−	0.436387i	$-0.143742\pi$
$991$	56.6491	1.79952	0.899759	+	0.436387i	$0.143742\pi$
$992$	16.0189	0.508600
$993$	−12.2796	−0.389683
$994$	−0.0262174	−0.000831565 0
$995$	−9.33129	−0.295822
$996$	98.8252	3.13140
$997$	27.0328	0.856138	0.428069	−	0.903746i	$-0.359194\pi$
$997$	27.0328	0.856138	0.428069	+	0.903746i	$0.359194\pi$
$998$	91.5597	2.89827
$999$	−18.2376	−0.577011

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8035.2.a.c.1.16	✓	127

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8035.2.a.c.1.16	✓	127	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:	\( N \)	\(=\)	\( 8035 = 5 \cdot 1607 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8035.a (trivial)

\(f(q)\)	\(=\)	\(q-2.17325 q^{2} +2.30276 q^{3} +2.72303 q^{4} -1.00000 q^{5} -5.00447 q^{6} -1.58489 q^{7} -1.57132 q^{8} +2.30268 q^{9} +O(q^{10})\)	\(q-2.17325 q^{2} +2.30276 q^{3} +2.72303 q^{4} -1.00000 q^{5} -5.00447 q^{6} -1.58489 q^{7} -1.57132 q^{8} +2.30268 q^{9} +2.17325 q^{10} -0.0320935 q^{11} +6.27046 q^{12} -4.50759 q^{13} +3.44437 q^{14} -2.30276 q^{15} -2.03118 q^{16} -4.91630 q^{17} -5.00431 q^{18} -5.49438 q^{19} -2.72303 q^{20} -3.64962 q^{21} +0.0697472 q^{22} +1.01373 q^{23} -3.61836 q^{24} +1.00000 q^{25} +9.79613 q^{26} -1.60575 q^{27} -4.31570 q^{28} +1.75709 q^{29} +5.00447 q^{30} +2.11976 q^{31} +7.55691 q^{32} -0.0739034 q^{33} +10.6844 q^{34} +1.58489 q^{35} +6.27026 q^{36} +11.3576 q^{37} +11.9407 q^{38} -10.3799 q^{39} +1.57132 q^{40} -1.89293 q^{41} +7.93154 q^{42} +8.57679 q^{43} -0.0873913 q^{44} -2.30268 q^{45} -2.20308 q^{46} -10.1809 q^{47} -4.67732 q^{48} -4.48812 q^{49} -2.17325 q^{50} -11.3210 q^{51} -12.2743 q^{52} -10.8530 q^{53} +3.48971 q^{54} +0.0320935 q^{55} +2.49037 q^{56} -12.6522 q^{57} -3.81859 q^{58} +7.79377 q^{59} -6.27046 q^{60} -8.97932 q^{61} -4.60678 q^{62} -3.64950 q^{63} -12.3607 q^{64} +4.50759 q^{65} +0.160611 q^{66} -3.13831 q^{67} -13.3872 q^{68} +2.33436 q^{69} -3.44437 q^{70} -0.00761166 q^{71} -3.61824 q^{72} +1.79264 q^{73} -24.6830 q^{74} +2.30276 q^{75} -14.9613 q^{76} +0.0508647 q^{77} +22.5581 q^{78} +14.3534 q^{79} +2.03118 q^{80} -10.6057 q^{81} +4.11381 q^{82} +15.7604 q^{83} -9.93800 q^{84} +4.91630 q^{85} -18.6395 q^{86} +4.04614 q^{87} +0.0504290 q^{88} -12.0328 q^{89} +5.00431 q^{90} +7.14404 q^{91} +2.76040 q^{92} +4.88130 q^{93} +22.1257 q^{94} +5.49438 q^{95} +17.4017 q^{96} -12.7330 q^{97} +9.75381 q^{98} -0.0739011 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 127 q + 19 q^{2} + 10 q^{3} + 125 q^{4} - 127 q^{5} + 13 q^{7} + 54 q^{8} + 123 q^{9}+O(q^{10}) \) 127 * q + 19 * q^2 + 10 * q^3 + 125 * q^4 - 127 * q^5 + 13 * q^7 + 54 * q^8 + 123 * q^9	\( 127 q + 19 q^{2} + 10 q^{3} + 125 q^{4} - 127 q^{5} + 13 q^{7} + 54 q^{8} + 123 q^{9} - 19 q^{10} + 30 q^{11} + 35 q^{12} + 30 q^{13} + 39 q^{14} - 10 q^{15} + 121 q^{16} + 63 q^{17} + 53 q^{18} - 35 q^{19} - 125 q^{20} + 33 q^{21} + 49 q^{22} + 61 q^{23} - 5 q^{24} + 127 q^{25} + 10 q^{26} + 40 q^{27} + 32 q^{28} + 134 q^{29} - 25 q^{31} + 122 q^{32} + 48 q^{33} - 21 q^{34} - 13 q^{35} + 133 q^{36} + 60 q^{37} + 33 q^{38} + 26 q^{39} - 54 q^{40} + 9 q^{41} + 45 q^{42} + 48 q^{43} + 85 q^{44} - 123 q^{45} - 11 q^{46} + 57 q^{47} + 71 q^{48} + 70 q^{49} + 19 q^{50} + 45 q^{51} + 68 q^{52} + 182 q^{53} - 29 q^{54} - 30 q^{55} + 96 q^{56} + 74 q^{57} + 47 q^{58} + 19 q^{59} - 35 q^{60} + 16 q^{61} + 43 q^{62} + 73 q^{63} + 110 q^{64} - 30 q^{65} + 8 q^{66} + 40 q^{67} + 129 q^{68} + 2 q^{69} - 39 q^{70} + 48 q^{71} + 151 q^{72} + 30 q^{73} + 117 q^{74} + 10 q^{75} - 98 q^{76} + 134 q^{77} + 54 q^{78} + 23 q^{79} - 121 q^{80} + 111 q^{81} + 4 q^{82} + 92 q^{83} + 48 q^{84} - 63 q^{85} + 42 q^{86} + 69 q^{87} + 121 q^{88} + 12 q^{89} - 53 q^{90} - 30 q^{91} + 175 q^{92} + 82 q^{93} - 23 q^{94} + 35 q^{95} + 6 q^{96} + 67 q^{97} + 122 q^{98} + 73 q^{99}+O(q^{100}) \) 127 * q + 19 * q^2 + 10 * q^3 + 125 * q^4 - 127 * q^5 + 13 * q^7 + 54 * q^8 + 123 * q^9 - 19 * q^10 + 30 * q^11 + 35 * q^12 + 30 * q^13 + 39 * q^14 - 10 * q^15 + 121 * q^16 + 63 * q^17 + 53 * q^18 - 35 * q^19 - 125 * q^20 + 33 * q^21 + 49 * q^22 + 61 * q^23 - 5 * q^24 + 127 * q^25 + 10 * q^26 + 40 * q^27 + 32 * q^28 + 134 * q^29 - 25 * q^31 + 122 * q^32 + 48 * q^33 - 21 * q^34 - 13 * q^35 + 133 * q^36 + 60 * q^37 + 33 * q^38 + 26 * q^39 - 54 * q^40 + 9 * q^41 + 45 * q^42 + 48 * q^43 + 85 * q^44 - 123 * q^45 - 11 * q^46 + 57 * q^47 + 71 * q^48 + 70 * q^49 + 19 * q^50 + 45 * q^51 + 68 * q^52 + 182 * q^53 - 29 * q^54 - 30 * q^55 + 96 * q^56 + 74 * q^57 + 47 * q^58 + 19 * q^59 - 35 * q^60 + 16 * q^61 + 43 * q^62 + 73 * q^63 + 110 * q^64 - 30 * q^65 + 8 * q^66 + 40 * q^67 + 129 * q^68 + 2 * q^69 - 39 * q^70 + 48 * q^71 + 151 * q^72 + 30 * q^73 + 117 * q^74 + 10 * q^75 - 98 * q^76 + 134 * q^77 + 54 * q^78 + 23 * q^79 - 121 * q^80 + 111 * q^81 + 4 * q^82 + 92 * q^83 + 48 * q^84 - 63 * q^85 + 42 * q^86 + 69 * q^87 + 121 * q^88 + 12 * q^89 - 53 * q^90 - 30 * q^91 + 175 * q^92 + 82 * q^93 - 23 * q^94 + 35 * q^95 + 6 * q^96 + 67 * q^97 + 122 * q^98 + 73 * q^99

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