LMFDB - Embedded newform 6013.2.a.c.1.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6013,2,Mod(1,6013)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6013, 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("6013.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6013 = 7 \cdot 859 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6013.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:	$48.0140467354$
Analytic rank:	$1$
Dimension:	$104$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.19
Character	$\chi$	$=$	6013.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.03131 q^{2} -2.52319 q^{3} +2.12623 q^{4} +0.0590478 q^{5} +5.12539 q^{6} -1.00000 q^{7} -0.256407 q^{8} +3.36649 q^{9} +O(q^{10})$	\(q-2.03131 q^{2} -2.52319 q^{3} +2.12623 q^{4} +0.0590478 q^{5} +5.12539 q^{6} -1.00000 q^{7} -0.256407 q^{8} +3.36649 q^{9} -0.119944 q^{10} -3.81051 q^{11} -5.36488 q^{12} +4.94387 q^{13} +2.03131 q^{14} -0.148989 q^{15} -3.73161 q^{16} -0.804974 q^{17} -6.83839 q^{18} -7.77612 q^{19} +0.125549 q^{20} +2.52319 q^{21} +7.74034 q^{22} +5.99981 q^{23} +0.646965 q^{24} -4.99651 q^{25} -10.0426 q^{26} -0.924718 q^{27} -2.12623 q^{28} +5.60498 q^{29} +0.302643 q^{30} +5.16999 q^{31} +8.09288 q^{32} +9.61464 q^{33} +1.63515 q^{34} -0.0590478 q^{35} +7.15792 q^{36} -6.77671 q^{37} +15.7957 q^{38} -12.4743 q^{39} -0.0151403 q^{40} +1.92936 q^{41} -5.12539 q^{42} +1.48615 q^{43} -8.10201 q^{44} +0.198784 q^{45} -12.1875 q^{46} -0.0617598 q^{47} +9.41556 q^{48} +1.00000 q^{49} +10.1495 q^{50} +2.03110 q^{51} +10.5118 q^{52} +0.213453 q^{53} +1.87839 q^{54} -0.225002 q^{55} +0.256407 q^{56} +19.6206 q^{57} -11.3855 q^{58} -11.4988 q^{59} -0.316784 q^{60} +2.79964 q^{61} -10.5019 q^{62} -3.36649 q^{63} -8.97594 q^{64} +0.291925 q^{65} -19.5303 q^{66} -16.0671 q^{67} -1.71156 q^{68} -15.1387 q^{69} +0.119944 q^{70} +0.691945 q^{71} -0.863193 q^{72} +1.48197 q^{73} +13.7656 q^{74} +12.6072 q^{75} -16.5338 q^{76} +3.81051 q^{77} +25.3393 q^{78} +7.02610 q^{79} -0.220343 q^{80} -7.76622 q^{81} -3.91913 q^{82} -12.1103 q^{83} +5.36488 q^{84} -0.0475319 q^{85} -3.01883 q^{86} -14.1424 q^{87} +0.977044 q^{88} -2.12474 q^{89} -0.403791 q^{90} -4.94387 q^{91} +12.7570 q^{92} -13.0449 q^{93} +0.125453 q^{94} -0.459163 q^{95} -20.4199 q^{96} +14.7929 q^{97} -2.03131 q^{98} -12.8280 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 104 q - 19 q^{2} - 26 q^{3} + 99 q^{4} + 2 q^{5} + 2 q^{6} - 104 q^{7} - 54 q^{8} + 90 q^{9}+O(q^{10}) $ 104 * q - 19 * q^2 - 26 * q^3 + 99 * q^4 + 2 * q^5 + 2 * q^6 - 104 * q^7 - 54 * q^8 + 90 * q^9	\( 104 q - 19 q^{2} - 26 q^{3} + 99 q^{4} + 2 q^{5} + 2 q^{6} - 104 q^{7} - 54 q^{8} + 90 q^{9} + 3 q^{10} - 54 q^{11} - 38 q^{12} + 7 q^{13} + 19 q^{14} - 33 q^{15} + 93 q^{16} - 7 q^{17} - 55 q^{18} - 12 q^{19} - 24 q^{20} + 26 q^{21} - 22 q^{22} - 69 q^{23} + 78 q^{25} - 11 q^{26} - 95 q^{27} - 99 q^{28} - 41 q^{29} - 26 q^{30} - 12 q^{31} - 127 q^{32} - 6 q^{33} - 17 q^{34} - 2 q^{35} + 71 q^{36} - 47 q^{37} - 32 q^{38} - 57 q^{39} + 6 q^{40} + 10 q^{41} - 2 q^{42} - 41 q^{43} - 120 q^{44} + 23 q^{45} - 31 q^{46} - 99 q^{47} - 84 q^{48} + 104 q^{49} - 104 q^{50} - 74 q^{51} + 14 q^{52} - 74 q^{53} + 19 q^{54} - 32 q^{55} + 54 q^{56} - 47 q^{57} - 36 q^{58} - 76 q^{59} - 99 q^{60} + 49 q^{61} - 55 q^{62} - 90 q^{63} + 86 q^{64} - 70 q^{65} + 61 q^{66} - 117 q^{67} - 30 q^{68} + 51 q^{69} - 3 q^{70} - 125 q^{71} - 147 q^{72} - 20 q^{73} - 75 q^{74} - 124 q^{75} + 4 q^{76} + 54 q^{77} - 70 q^{78} - 72 q^{79} - 69 q^{80} + 76 q^{81} - 37 q^{82} - 98 q^{83} + 38 q^{84} - 33 q^{85} - 64 q^{86} - 8 q^{87} - 62 q^{88} - 26 q^{89} + 11 q^{90} - 7 q^{91} - 162 q^{92} - 81 q^{93} + 31 q^{94} - 116 q^{95} + 20 q^{96} - 61 q^{97} - 19 q^{98} - 158 q^{99}+O(q^{100}) \) 104 * q - 19 * q^2 - 26 * q^3 + 99 * q^4 + 2 * q^5 + 2 * q^6 - 104 * q^7 - 54 * q^8 + 90 * q^9 + 3 * q^10 - 54 * q^11 - 38 * q^12 + 7 * q^13 + 19 * q^14 - 33 * q^15 + 93 * q^16 - 7 * q^17 - 55 * q^18 - 12 * q^19 - 24 * q^20 + 26 * q^21 - 22 * q^22 - 69 * q^23 + 78 * q^25 - 11 * q^26 - 95 * q^27 - 99 * q^28 - 41 * q^29 - 26 * q^30 - 12 * q^31 - 127 * q^32 - 6 * q^33 - 17 * q^34 - 2 * q^35 + 71 * q^36 - 47 * q^37 - 32 * q^38 - 57 * q^39 + 6 * q^40 + 10 * q^41 - 2 * q^42 - 41 * q^43 - 120 * q^44 + 23 * q^45 - 31 * q^46 - 99 * q^47 - 84 * q^48 + 104 * q^49 - 104 * q^50 - 74 * q^51 + 14 * q^52 - 74 * q^53 + 19 * q^54 - 32 * q^55 + 54 * q^56 - 47 * q^57 - 36 * q^58 - 76 * q^59 - 99 * q^60 + 49 * q^61 - 55 * q^62 - 90 * q^63 + 86 * q^64 - 70 * q^65 + 61 * q^66 - 117 * q^67 - 30 * q^68 + 51 * q^69 - 3 * q^70 - 125 * q^71 - 147 * q^72 - 20 * q^73 - 75 * q^74 - 124 * q^75 + 4 * q^76 + 54 * q^77 - 70 * q^78 - 72 * q^79 - 69 * q^80 + 76 * q^81 - 37 * q^82 - 98 * q^83 + 38 * q^84 - 33 * q^85 - 64 * q^86 - 8 * q^87 - 62 * q^88 - 26 * q^89 + 11 * q^90 - 7 * q^91 - 162 * q^92 - 81 * q^93 + 31 * q^94 - 116 * q^95 + 20 * q^96 - 61 * q^97 - 19 * q^98 - 158 * 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 $

$2$	−2.03131	−1.43635	−0.718177	−	0.695860i	$-0.755023\pi$
$2$	−2.03131	−1.43635	−0.718177	+	0.695860i	$0.755023\pi$
$3$	−2.52319	−1.45676	−0.728382	−	0.685171i	$-0.759727\pi$
$3$	−2.52319	−1.45676	−0.728382	+	0.685171i	$0.759727\pi$
$4$	2.12623	1.06311
$5$	0.0590478	0.0264070	0.0132035	−	0.999913i	$-0.495797\pi$
$5$	0.0590478	0.0264070	0.0132035	+	0.999913i	$0.495797\pi$
$6$	5.12539	2.09243
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	−0.256407	−0.0906537
$9$	3.36649	1.12216
$10$	−0.119944	−0.0379298
$11$	−3.81051	−1.14891	−0.574456	−	0.818535i	$-0.694786\pi$
$11$	−3.81051	−1.14891	−0.574456	+	0.818535i	$0.694786\pi$
$12$	−5.36488	−1.54871
$13$	4.94387	1.37118	0.685592	−	0.727986i	$-0.259543\pi$
$13$	4.94387	1.37118	0.685592	+	0.727986i	$0.259543\pi$
$14$	2.03131	0.542891
$15$	−0.148989	−0.0384687
$16$	−3.73161	−0.932903
$17$	−0.804974	−0.195235	−0.0976175	−	0.995224i	$-0.531122\pi$
$17$	−0.804974	−0.195235	−0.0976175	+	0.995224i	$0.531122\pi$
$18$	−6.83839	−1.61182
$19$	−7.77612	−1.78396	−0.891982	−	0.452070i	$-0.850686\pi$
$19$	−7.77612	−1.78396	−0.891982	+	0.452070i	$0.850686\pi$
$20$	0.125549	0.0280736
$21$	2.52319	0.550605
$22$	7.74034	1.65025
$23$	5.99981	1.25105	0.625524	−	0.780205i	$-0.284885\pi$
$23$	5.99981	1.25105	0.625524	+	0.780205i	$0.284885\pi$
$24$	0.646965	0.132061
$25$	−4.99651	−0.999303
$26$	−10.0426	−1.96951
$27$	−0.924718	−0.177962
$28$	−2.12623	−0.401819
$29$	5.60498	1.04082	0.520409	−	0.853917i	$-0.325779\pi$
$29$	5.60498	1.04082	0.520409	+	0.853917i	$0.325779\pi$
$30$	0.302643	0.0552547
$31$	5.16999	0.928558	0.464279	−	0.885689i	$-0.346314\pi$
$31$	5.16999	0.928558	0.464279	+	0.885689i	$0.346314\pi$
$32$	8.09288	1.43063
$33$	9.61464	1.67369
$34$	1.63515	0.280427
$35$	−0.0590478	−0.00998090
$36$	7.15792	1.19299
$37$	−6.77671	−1.11408	−0.557042	−	0.830484i	$-0.688064\pi$
$37$	−6.77671	−1.11408	−0.557042	+	0.830484i	$0.688064\pi$
$38$	15.7957	2.56241
$39$	−12.4743	−1.99749
$40$	−0.0151403	−0.00239389
$41$	1.92936	0.301315	0.150658	−	0.988586i	$-0.451861\pi$
$41$	1.92936	0.301315	0.150658	+	0.988586i	$0.451861\pi$
$42$	−5.12539	−0.790864
$43$	1.48615	0.226635	0.113318	−	0.993559i	$-0.463852\pi$
$43$	1.48615	0.226635	0.113318	+	0.993559i	$0.463852\pi$
$44$	−8.10201	−1.22142
$45$	0.198784	0.0296329
$46$	−12.1875	−1.79695
$47$	−0.0617598	−0.00900859	−0.00450430	−	0.999990i	$-0.501434\pi$
$47$	−0.0617598	−0.00900859	−0.00450430	+	0.999990i	$0.501434\pi$
$48$	9.41556	1.35902
$49$	1.00000	0.142857
$50$	10.1495	1.43535
$51$	2.03110	0.284411
$52$	10.5118	1.45772
$53$	0.213453	0.0293200	0.0146600	−	0.999893i	$-0.495333\pi$
$53$	0.213453	0.0293200	0.0146600	+	0.999893i	$0.495333\pi$
$54$	1.87839	0.255617
$55$	−0.225002	−0.0303393
$56$	0.256407	0.0342639
$57$	19.6206	2.59882
$58$	−11.3855	−1.49498
$59$	−11.4988	−1.49701	−0.748505	−	0.663129i	$-0.769228\pi$
$59$	−11.4988	−1.49701	−0.748505	+	0.663129i	$0.769228\pi$
$60$	−0.316784	−0.0408966
$61$	2.79964	0.358458	0.179229	−	0.983807i	$-0.442640\pi$
$61$	2.79964	0.358458	0.179229	+	0.983807i	$0.442640\pi$
$62$	−10.5019	−1.33374
$63$	−3.36649	−0.424138
$64$	−8.97594	−1.12199
$65$	0.291925	0.0362088
$66$	−19.5303	−2.40402
$67$	−16.0671	−1.96291	−0.981456	−	0.191686i	$-0.938605\pi$
$67$	−16.0671	−1.96291	−0.981456	+	0.191686i	$0.938605\pi$
$68$	−1.71156	−0.207557
$69$	−15.1387	−1.82248
$70$	0.119944	0.0143361
$71$	0.691945	0.0821188	0.0410594	−	0.999157i	$-0.486927\pi$
$71$	0.691945	0.0821188	0.0410594	+	0.999157i	$0.486927\pi$
$72$	−0.863193	−0.101728
$73$	1.48197	0.173451	0.0867255	−	0.996232i	$-0.472360\pi$
$73$	1.48197	0.173451	0.0867255	+	0.996232i	$0.472360\pi$
$74$	13.7656	1.60022
$75$	12.6072	1.45575
$76$	−16.5338	−1.89656
$77$	3.81051	0.434248
$78$	25.3393	2.86911
$79$	7.02610	0.790498	0.395249	−	0.918574i	$-0.370658\pi$
$79$	7.02610	0.790498	0.395249	+	0.918574i	$0.370658\pi$
$80$	−0.220343	−0.0246351
$81$	−7.76622	−0.862914
$82$	−3.91913	−0.432795
$83$	−12.1103	−1.32927	−0.664636	−	0.747167i	$-0.731414\pi$
$83$	−12.1103	−1.32927	−0.664636	+	0.747167i	$0.731414\pi$
$84$	5.36488	0.585356
$85$	−0.0475319	−0.00515556
$86$	−3.01883	−0.325529
$87$	−14.1424	−1.51623
$88$	0.977044	0.104153
$89$	−2.12474	−0.225222	−0.112611	−	0.993639i	$-0.535921\pi$
$89$	−2.12474	−0.225222	−0.112611	+	0.993639i	$0.535921\pi$
$90$	−0.403791	−0.0425634
$91$	−4.94387	−0.518259
$92$	12.7570	1.33001
$93$	−13.0449	−1.35269
$94$	0.125453	0.0129395
$95$	−0.459163	−0.0471091
$96$	−20.4199	−2.08410
$97$	14.7929	1.50199	0.750997	−	0.660306i	$-0.229573\pi$
$97$	14.7929	1.50199	0.750997	+	0.660306i	$0.229573\pi$
$98$	−2.03131	−0.205193
$99$	−12.8280	−1.28927
$100$	−10.6237	−1.06237
$101$	−2.47302	−0.246075	−0.123037	−	0.992402i	$-0.539263\pi$
$101$	−2.47302	−0.246075	−0.123037	+	0.992402i	$0.539263\pi$
$102$	−4.12580	−0.408516
$103$	7.37005	0.726192	0.363096	−	0.931752i	$-0.381720\pi$
$103$	7.37005	0.726192	0.363096	+	0.931752i	$0.381720\pi$
$104$	−1.26765	−0.124303
$105$	0.148989	0.0145398
$106$	−0.433589	−0.0421139
$107$	17.7022	1.71134	0.855669	−	0.517524i	$-0.173146\pi$
$107$	17.7022	1.71134	0.855669	+	0.517524i	$0.173146\pi$
$108$	−1.96616	−0.189194
$109$	15.3684	1.47202	0.736012	−	0.676968i	$-0.236707\pi$
$109$	15.3684	1.47202	0.736012	+	0.676968i	$0.236707\pi$
$110$	0.457050	0.0435780
$111$	17.0989	1.62296
$112$	3.73161	0.352604
$113$	−10.4973	−0.987506	−0.493753	−	0.869602i	$-0.664375\pi$
$113$	−10.4973	−0.987506	−0.493753	+	0.869602i	$0.664375\pi$
$114$	−39.8556	−3.73282
$115$	0.354276	0.0330364
$116$	11.9175	1.10651
$117$	16.6435	1.53869
$118$	23.3575	2.15024
$119$	0.804974	0.0737919
$120$	0.0382018	0.00348733
$121$	3.52000	0.320000
$122$	−5.68695	−0.514872
$123$	−4.86814	−0.438945
$124$	10.9926	0.987163
$125$	−0.590272	−0.0527955
$126$	6.83839	0.609212
$127$	2.61801	0.232311	0.116155	−	0.993231i	$-0.462943\pi$
$127$	2.61801	0.232311	0.116155	+	0.993231i	$0.462943\pi$
$128$	2.04717	0.180946
$129$	−3.74983	−0.330154
$130$	−0.592990	−0.0520087
$131$	−13.2406	−1.15684	−0.578418	−	0.815741i	$-0.696330\pi$
$131$	−13.2406	−1.15684	−0.578418	+	0.815741i	$0.696330\pi$
$132$	20.4429	1.77933
$133$	7.77612	0.674275
$134$	32.6374	2.81944
$135$	−0.0546025	−0.00469944
$136$	0.206401	0.0176988
$137$	20.2849	1.73306	0.866530	−	0.499125i	$-0.166345\pi$
$137$	20.2849	1.73306	0.866530	+	0.499125i	$0.166345\pi$
$138$	30.7514	2.61773
$139$	−2.25622	−0.191370	−0.0956852	−	0.995412i	$-0.530504\pi$
$139$	−2.25622	−0.191370	−0.0956852	+	0.995412i	$0.530504\pi$
$140$	−0.125549	−0.0106108
$141$	0.155832	0.0131234
$142$	−1.40556	−0.117952
$143$	−18.8387	−1.57537
$144$	−12.5624	−1.04687
$145$	0.330961	0.0274849
$146$	−3.01033	−0.249137
$147$	−2.52319	−0.208109
$148$	−14.4088	−1.18440
$149$	−6.00759	−0.492161	−0.246081	−	0.969249i	$-0.579143\pi$
$149$	−6.00759	−0.492161	−0.246081	+	0.969249i	$0.579143\pi$
$150$	−25.6091	−2.09097
$151$	22.7954	1.85506	0.927530	−	0.373748i	$-0.121928\pi$
$151$	22.7954	1.85506	0.927530	+	0.373748i	$0.121928\pi$
$152$	1.99386	0.161723
$153$	−2.70994	−0.219085
$154$	−7.74034	−0.623734
$155$	0.305276	0.0245204
$156$	−26.5233	−2.12356
$157$	1.49983	0.119699	0.0598497	−	0.998207i	$-0.480938\pi$
$157$	1.49983	0.119699	0.0598497	+	0.998207i	$0.480938\pi$
$158$	−14.2722	−1.13543
$159$	−0.538582	−0.0427123
$160$	0.477867	0.0377787
$161$	−5.99981	−0.472852
$162$	15.7756	1.23945
$163$	−5.24262	−0.410634	−0.205317	−	0.978696i	$-0.565822\pi$
$163$	−5.24262	−0.410634	−0.205317	+	0.978696i	$0.565822\pi$
$164$	4.10226	0.320332
$165$	0.567723	0.0441972
$166$	24.5997	1.90931
$167$	10.2777	0.795309	0.397654	−	0.917535i	$-0.369824\pi$
$167$	10.2777	0.795309	0.397654	+	0.917535i	$0.369824\pi$
$168$	−0.646965	−0.0499144
$169$	11.4419	0.880146
$170$	0.0965522	0.00740522
$171$	−26.1782	−2.00190
$172$	3.15989	0.240939
$173$	−15.8298	−1.20351	−0.601757	−	0.798679i	$-0.705532\pi$
$173$	−15.8298	−1.20351	−0.601757	+	0.798679i	$0.705532\pi$
$174$	28.7277	2.17784
$175$	4.99651	0.377701
$176$	14.2193	1.07182
$177$	29.0135	2.18079
$178$	4.31601	0.323499
$179$	7.30472	0.545981	0.272990	−	0.962017i	$-0.411987\pi$
$179$	7.30472	0.545981	0.272990	+	0.962017i	$0.411987\pi$
$180$	0.422659	0.0315032
$181$	18.7445	1.39327	0.696636	−	0.717425i	$-0.254679\pi$
$181$	18.7445	1.39327	0.696636	+	0.717425i	$0.254679\pi$
$182$	10.0426	0.744403
$183$	−7.06403	−0.522188
$184$	−1.53840	−0.113412
$185$	−0.400150	−0.0294196
$186$	26.4982	1.94294
$187$	3.06736	0.224308
$188$	−0.131315	−0.00957716
$189$	0.924718	0.0672634
$190$	0.932703	0.0676654
$191$	−17.1746	−1.24271	−0.621353	−	0.783530i	$-0.713417\pi$
$191$	−17.1746	−1.24271	−0.621353	+	0.783530i	$0.713417\pi$
$192$	22.6480	1.63448
$193$	7.52330	0.541539	0.270770	−	0.962644i	$-0.412722\pi$
$193$	7.52330	0.541539	0.270770	+	0.962644i	$0.412722\pi$
$194$	−30.0490	−2.15740
$195$	−0.736582	−0.0527477
$196$	2.12623	0.151873
$197$	−10.1283	−0.721615	−0.360807	−	0.932640i	$-0.617499\pi$
$197$	−10.1283	−0.721615	−0.360807	+	0.932640i	$0.617499\pi$
$198$	26.0577	1.85184
$199$	21.0266	1.49053	0.745267	−	0.666766i	$-0.232322\pi$
$199$	21.0266	1.49053	0.745267	+	0.666766i	$0.232322\pi$
$200$	1.28114	0.0905905
$201$	40.5404	2.85950
$202$	5.02347	0.353450
$203$	−5.60498	−0.393392
$204$	4.31859	0.302362
$205$	0.113924	0.00795682
$206$	−14.9709	−1.04307
$207$	20.1983	1.40388
$208$	−18.4486	−1.27918
$209$	29.6310	2.04962
$210$	−0.302643	−0.0208843
$211$	15.6496	1.07736	0.538681	−	0.842510i	$-0.318923\pi$
$211$	15.6496	1.07736	0.538681	+	0.842510i	$0.318923\pi$
$212$	0.453849	0.0311705
$213$	−1.74591	−0.119628
$214$	−35.9587	−2.45809
$215$	0.0877537	0.00598475
$216$	0.237105	0.0161329
$217$	−5.16999	−0.350962
$218$	−31.2180	−2.11435
$219$	−3.73928	−0.252677
$220$	−0.478406	−0.0322541
$221$	−3.97969	−0.267703
$222$	−34.7332	−2.33114
$223$	1.54616	0.103538	0.0517691	−	0.998659i	$-0.483514\pi$
$223$	1.54616	0.103538	0.0517691	+	0.998659i	$0.483514\pi$
$224$	−8.09288	−0.540728
$225$	−16.8207	−1.12138
$226$	21.3234	1.41841
$227$	−9.69819	−0.643691	−0.321846	−	0.946792i	$-0.604303\pi$
$227$	−9.69819	−0.643691	−0.321846	+	0.946792i	$0.604303\pi$
$228$	41.7179	2.76284
$229$	8.55571	0.565378	0.282689	−	0.959212i	$-0.408774\pi$
$229$	8.55571	0.565378	0.282689	+	0.959212i	$0.408774\pi$
$230$	−0.719644	−0.0474519
$231$	−9.61464	−0.632597
$232$	−1.43716	−0.0943541
$233$	−6.54964	−0.429081	−0.214540	−	0.976715i	$-0.568825\pi$
$233$	−6.54964	−0.429081	−0.214540	+	0.976715i	$0.568825\pi$
$234$	−33.8081	−2.21011
$235$	−0.00364678	−0.000237890 0
$236$	−24.4490	−1.59149
$237$	−17.7282	−1.15157
$238$	−1.63515	−0.105991
$239$	−14.4714	−0.936075	−0.468038	−	0.883708i	$-0.655039\pi$
$239$	−14.4714	−0.936075	−0.468038	+	0.883708i	$0.655039\pi$
$240$	0.555968	0.0358876
$241$	16.4638	1.06053	0.530263	−	0.847833i	$-0.322093\pi$
$241$	16.4638	1.06053	0.530263	+	0.847833i	$0.322093\pi$
$242$	−7.15021	−0.459633
$243$	22.3698	1.43502
$244$	5.95268	0.381081
$245$	0.0590478	0.00377242
$246$	9.88871	0.630481
$247$	−38.4442	−2.44614
$248$	−1.32562	−0.0841772
$249$	30.5565	1.93644
$250$	1.19903	0.0758331
$251$	3.13294	0.197749	0.0988746	−	0.995100i	$-0.468476\pi$
$251$	3.13294	0.197749	0.0988746	+	0.995100i	$0.468476\pi$
$252$	−7.15792	−0.450907
$253$	−22.8624	−1.43734
$254$	−5.31799	−0.333680
$255$	0.119932	0.00751044
$256$	13.7934	0.862090
$257$	30.8107	1.92192	0.960960	−	0.276686i	$-0.0892362\pi$
$257$	30.8107	1.92192	0.960960	+	0.276686i	$0.0892362\pi$
$258$	7.61708	0.474219
$259$	6.77671	0.421084
$260$	0.620699	0.0384941
$261$	18.8691	1.16797
$262$	26.8958	1.66163
$263$	−28.6561	−1.76701	−0.883507	−	0.468418i	$-0.844824\pi$
$263$	−28.6561	−1.76701	−0.883507	+	0.468418i	$0.844824\pi$
$264$	−2.46527	−0.151727
$265$	0.0126039	0.000774252 0
$266$	−15.7957	−0.968498
$267$	5.36113	0.328096
$268$	−34.1624	−2.08680
$269$	12.8774	0.785149	0.392574	−	0.919720i	$-0.371585\pi$
$269$	12.8774	0.785149	0.392574	+	0.919720i	$0.371585\pi$
$270$	0.110915	0.00675006
$271$	18.7653	1.13991	0.569956	−	0.821675i	$-0.306960\pi$
$271$	18.7653	1.13991	0.569956	+	0.821675i	$0.306960\pi$
$272$	3.00385	0.182135
$273$	12.4743	0.754981
$274$	−41.2050	−2.48929
$275$	19.0393	1.14811
$276$	−32.1883	−1.93751
$277$	26.3131	1.58100	0.790500	−	0.612462i	$-0.209821\pi$
$277$	26.3131	1.58100	0.790500	+	0.612462i	$0.209821\pi$
$278$	4.58309	0.274876
$279$	17.4047	1.04199
$280$	0.0151403	0.000904805 0
$281$	8.87460	0.529414	0.264707	−	0.964329i	$-0.414725\pi$
$281$	8.87460	0.529414	0.264707	+	0.964329i	$0.414725\pi$
$282$	−0.316543	−0.0188498
$283$	−28.1840	−1.67537	−0.837684	−	0.546156i	$-0.816091\pi$
$283$	−28.1840	−1.67537	−0.837684	+	0.546156i	$0.816091\pi$
$284$	1.47123	0.0873016
$285$	1.15855	0.0686269
$286$	38.2673	2.26279
$287$	−1.92936	−0.113886
$288$	27.2446	1.60540
$289$	−16.3520	−0.961883
$290$	−0.672286	−0.0394780
$291$	−37.3254	−2.18805
$292$	3.15100	0.184398
$293$	−10.0597	−0.587695	−0.293848	−	0.955852i	$-0.594936\pi$
$293$	−10.0597	−0.587695	−0.293848	+	0.955852i	$0.594936\pi$
$294$	5.12539	0.298919
$295$	−0.678976	−0.0395315
$296$	1.73760	0.100996
$297$	3.52365	0.204463
$298$	12.2033	0.706918
$299$	29.6623	1.71542
$300$	26.8057	1.54763
$301$	−1.48615	−0.0856601
$302$	−46.3045	−2.66452
$303$	6.23990	0.358473
$304$	29.0175	1.66427
$305$	0.165313	0.00946578
$306$	5.50473	0.314684
$307$	−19.6110	−1.11926	−0.559629	−	0.828743i	$-0.689056\pi$
$307$	−19.6110	−1.11926	−0.559629	+	0.828743i	$0.689056\pi$
$308$	8.10201	0.461655
$309$	−18.5960	−1.05789
$310$	−0.620112	−0.0352200
$311$	23.7547	1.34701	0.673504	−	0.739184i	$-0.264788\pi$
$311$	23.7547	1.34701	0.673504	+	0.739184i	$0.264788\pi$
$312$	3.19851	0.181080
$313$	−8.67160	−0.490148	−0.245074	−	0.969504i	$-0.578812\pi$
$313$	−8.67160	−0.490148	−0.245074	+	0.969504i	$0.578812\pi$
$314$	−3.04662	−0.171931
$315$	−0.198784	−0.0112002
$316$	14.9391	0.840389
$317$	20.8596	1.17159	0.585795	−	0.810460i	$-0.300783\pi$
$317$	20.8596	1.17159	0.585795	+	0.810460i	$0.300783\pi$
$318$	1.09403	0.0613500
$319$	−21.3578	−1.19581
$320$	−0.530009	−0.0296284
$321$	−44.6661	−2.49302
$322$	12.1875	0.679182
$323$	6.25958	0.348292
$324$	−16.5128	−0.917375
$325$	−24.7021	−1.37023
$326$	10.6494	0.589816
$327$	−38.7774	−2.14439
$328$	−0.494702	−0.0273153
$329$	0.0617598	0.00340493
$330$	−1.15322	−0.0634828
$331$	−9.30799	−0.511613	−0.255807	−	0.966728i	$-0.582341\pi$
$331$	−9.30799	−0.511613	−0.255807	+	0.966728i	$0.582341\pi$
$332$	−25.7491	−1.41317
$333$	−22.8137	−1.25018
$334$	−20.8771	−1.14235
$335$	−0.948728	−0.0518346
$336$	−9.41556	−0.513661
$337$	−15.0499	−0.819818	−0.409909	−	0.912126i	$-0.634440\pi$
$337$	−15.0499	−0.819818	−0.409909	+	0.912126i	$0.634440\pi$
$338$	−23.2421	−1.26420
$339$	26.4868	1.43856
$340$	−0.101064	−0.00548095
$341$	−19.7003	−1.06683
$342$	53.1761	2.87544
$343$	−1.00000	−0.0539949
$344$	−0.381059	−0.0205453
$345$	−0.893905	−0.0481262
$346$	32.1552	1.72867
$347$	−29.7642	−1.59783	−0.798914	−	0.601446i	$-0.794592\pi$
$347$	−29.7642	−1.59783	−0.798914	+	0.601446i	$0.794592\pi$
$348$	−30.0700	−1.61192
$349$	10.8619	0.581425	0.290713	−	0.956810i	$-0.406108\pi$
$349$	10.8619	0.581425	0.290713	+	0.956810i	$0.406108\pi$
$350$	−10.1495	−0.542512
$351$	−4.57169	−0.244019
$352$	−30.8380	−1.64367
$353$	−33.8091	−1.79948	−0.899740	−	0.436427i	$-0.856244\pi$
$353$	−33.8091	−1.79948	−0.899740	+	0.436427i	$0.856244\pi$
$354$	−58.9355	−3.13239
$355$	0.0408578	0.00216851
$356$	−4.51769	−0.239437
$357$	−2.03110	−0.107497
$358$	−14.8382	−0.784222
$359$	−19.0498	−1.00541	−0.502704	−	0.864459i	$-0.667661\pi$
$359$	−19.0498	−1.00541	−0.502704	+	0.864459i	$0.667661\pi$
$360$	−0.0509696	−0.00268633
$361$	41.4681	2.18253
$362$	−38.0760	−2.00123
$363$	−8.88162	−0.466164
$364$	−10.5118	−0.550968
$365$	0.0875067	0.00458031
$366$	14.3492	0.750047
$367$	18.6086	0.971363	0.485681	−	0.874136i	$-0.338572\pi$
$367$	18.6086	0.971363	0.485681	+	0.874136i	$0.338572\pi$
$368$	−22.3890	−1.16711
$369$	6.49516	0.338125
$370$	0.812828	0.0422569
$371$	−0.213453	−0.0110819
$372$	−27.7364	−1.43806
$373$	4.17819	0.216339	0.108169	−	0.994132i	$-0.465501\pi$
$373$	4.17819	0.216339	0.108169	+	0.994132i	$0.465501\pi$
$374$	−6.23077	−0.322186
$375$	1.48937	0.0769106
$376$	0.0158357	0.000816662 0
$377$	27.7103	1.42715
$378$	−1.87839	−0.0966140
$379$	7.47790	0.384114	0.192057	−	0.981384i	$-0.438484\pi$
$379$	7.47790	0.384114	0.192057	+	0.981384i	$0.438484\pi$
$380$	−0.976284	−0.0500823
$381$	−6.60573	−0.338422
$382$	34.8869	1.78497
$383$	−8.34037	−0.426173	−0.213086	−	0.977033i	$-0.568352\pi$
$383$	−8.34037	−0.426173	−0.213086	+	0.977033i	$0.568352\pi$
$384$	−5.16541	−0.263596
$385$	0.225002	0.0114672
$386$	−15.2822	−0.777842
$387$	5.00310	0.254322
$388$	31.4531	1.59679
$389$	30.6375	1.55338	0.776692	−	0.629881i	$-0.216896\pi$
$389$	30.6375	1.55338	0.776692	+	0.629881i	$0.216896\pi$
$390$	1.49623	0.0757644
$391$	−4.82970	−0.244248
$392$	−0.256407	−0.0129505
$393$	33.4085	1.68524
$394$	20.5738	1.03649
$395$	0.414875	0.0208746
$396$	−27.2753	−1.37064
$397$	30.1814	1.51476	0.757381	−	0.652973i	$-0.226478\pi$
$397$	30.1814	1.51476	0.757381	+	0.652973i	$0.226478\pi$
$398$	−42.7115	−2.14093
$399$	−19.6206	−0.982260
$400$	18.6450	0.932252
$401$	32.9450	1.64520	0.822598	−	0.568624i	$-0.192524\pi$
$401$	32.9450	1.64520	0.822598	+	0.568624i	$0.192524\pi$
$402$	−82.3503	−4.10726
$403$	25.5598	1.27322
$404$	−5.25820	−0.261605
$405$	−0.458578	−0.0227869
$406$	11.3855	0.565051
$407$	25.8227	1.27998
$408$	−0.520790	−0.0257830
$409$	−9.19800	−0.454812	−0.227406	−	0.973800i	$-0.573024\pi$
$409$	−9.19800	−0.454812	−0.227406	+	0.973800i	$0.573024\pi$
$410$	−0.231416	−0.0114288
$411$	−51.1828	−2.52466
$412$	15.6704	0.772025
$413$	11.4988	0.565817
$414$	−41.0290	−2.01647
$415$	−0.715083	−0.0351021
$416$	40.0102	1.96166
$417$	5.69288	0.278781
$418$	−60.1898	−2.94398
$419$	24.5185	1.19780	0.598902	−	0.800822i	$-0.295604\pi$
$419$	24.5185	1.19780	0.598902	+	0.800822i	$0.295604\pi$
$420$	0.316784	0.0154575
$421$	−20.8720	−1.01724	−0.508620	−	0.860991i	$-0.669844\pi$
$421$	−20.8720	−1.01724	−0.508620	+	0.860991i	$0.669844\pi$
$422$	−31.7892	−1.54747
$423$	−0.207914	−0.0101091
$424$	−0.0547309	−0.00265797
$425$	4.02207	0.195099
$426$	3.54648	0.171828
$427$	−2.79964	−0.135484
$428$	37.6389	1.81935
$429$	47.5336	2.29494
$430$	−0.178255	−0.00859622
$431$	−2.51766	−0.121272	−0.0606358	−	0.998160i	$-0.519313\pi$
$431$	−2.51766	−0.121272	−0.0606358	+	0.998160i	$0.519313\pi$
$432$	3.45069	0.166021
$433$	3.80959	0.183077	0.0915386	−	0.995802i	$-0.470821\pi$
$433$	3.80959	0.183077	0.0915386	+	0.995802i	$0.470821\pi$
$434$	10.5019	0.504106
$435$	−0.835079	−0.0400390
$436$	32.6767	1.56493
$437$	−46.6553	−2.23182
$438$	7.59564	0.362934
$439$	−24.1449	−1.15237	−0.576186	−	0.817318i	$-0.695460\pi$
$439$	−24.1449	−1.15237	−0.576186	+	0.817318i	$0.695460\pi$
$440$	0.0576922	0.00275037
$441$	3.36649	0.160309
$442$	8.08400	0.384517
$443$	7.54442	0.358446	0.179223	−	0.983808i	$-0.442642\pi$
$443$	7.54442	0.358446	0.179223	+	0.983808i	$0.442642\pi$
$444$	36.3562	1.72539
$445$	−0.125461	−0.00594744
$446$	−3.14072	−0.148718
$447$	15.1583	0.716963
$448$	8.97594	0.424073
$449$	−31.1427	−1.46971	−0.734857	−	0.678222i	$-0.762751\pi$
$449$	−31.1427	−1.46971	−0.734857	+	0.678222i	$0.762751\pi$
$450$	34.1681	1.61070
$451$	−7.35184	−0.346185
$452$	−22.3197	−1.04983
$453$	−57.5170	−2.70239
$454$	19.7000	0.924569
$455$	−0.291925	−0.0136856
$456$	−5.03088	−0.235592
$457$	−24.8973	−1.16465	−0.582324	−	0.812957i	$-0.697856\pi$
$457$	−24.8973	−1.16465	−0.582324	+	0.812957i	$0.697856\pi$
$458$	−17.3793	−0.812082
$459$	0.744375	0.0347444
$460$	0.753271	0.0351214
$461$	11.6602	0.543068	0.271534	−	0.962429i	$-0.412469\pi$
$461$	11.6602	0.543068	0.271534	+	0.962429i	$0.412469\pi$
$462$	19.5303	0.908634
$463$	−40.9851	−1.90474	−0.952370	−	0.304946i	$-0.901362\pi$
$463$	−40.9851	−1.90474	−0.952370	+	0.304946i	$0.901362\pi$
$464$	−20.9156	−0.970982
$465$	−0.770271	−0.0357204
$466$	13.3044	0.616312
$467$	−16.8667	−0.780500	−0.390250	−	0.920709i	$-0.627611\pi$
$467$	−16.8667	−0.780500	−0.390250	+	0.920709i	$0.627611\pi$
$468$	35.3879	1.63580
$469$	16.0671	0.741911
$470$	0.00740774	0.000341694 0
$471$	−3.78436	−0.174374
$472$	2.94837	0.135710
$473$	−5.66298	−0.260384
$474$	36.0115	1.65406
$475$	38.8535	1.78272
$476$	1.71156	0.0784492
$477$	0.718586	0.0329018
$478$	29.3959	1.34454
$479$	23.7372	1.08458	0.542291	−	0.840191i	$-0.317557\pi$
$479$	23.7372	1.08458	0.542291	+	0.840191i	$0.317557\pi$
$480$	−1.20575	−0.0550346
$481$	−33.5032	−1.52761
$482$	−33.4431	−1.52329
$483$	15.1387	0.688833
$484$	7.48432	0.340196
$485$	0.873489	0.0396631
$486$	−45.4401	−2.06120
$487$	−1.74868	−0.0792403	−0.0396201	−	0.999215i	$-0.512615\pi$
$487$	−1.74868	−0.0792403	−0.0396201	+	0.999215i	$0.512615\pi$
$488$	−0.717849	−0.0324955
$489$	13.2281	0.598197
$490$	−0.119944	−0.00541854
$491$	−14.6810	−0.662542	−0.331271	−	0.943536i	$-0.607477\pi$
$491$	−14.6810	−0.662542	−0.331271	+	0.943536i	$0.607477\pi$
$492$	−10.3508	−0.466649
$493$	−4.51186	−0.203204
$494$	78.0921	3.51353
$495$	−0.757467	−0.0340456
$496$	−19.2924	−0.866254
$497$	−0.691945	−0.0310380
$498$	−62.0697	−2.78141
$499$	−15.5961	−0.698176	−0.349088	−	0.937090i	$-0.613509\pi$
$499$	−15.5961	−0.698176	−0.349088	+	0.937090i	$0.613509\pi$
$500$	−1.25505	−0.0561276
$501$	−25.9325	−1.15858
$502$	−6.36397	−0.284038
$503$	−38.1278	−1.70003	−0.850016	−	0.526756i	$-0.823408\pi$
$503$	−38.1278	−1.70003	−0.850016	+	0.526756i	$0.823408\pi$
$504$	0.863193	0.0384497
$505$	−0.146026	−0.00649808
$506$	46.4406	2.06454
$507$	−28.8701	−1.28217
$508$	5.56648	0.246973
$509$	−23.0490	−1.02163	−0.510815	−	0.859691i	$-0.670656\pi$
$509$	−23.0490	−1.02163	−0.510815	+	0.859691i	$0.670656\pi$
$510$	−0.243620	−0.0107877
$511$	−1.48197	−0.0655583
$512$	−32.1131	−1.41921
$513$	7.19072	0.317478
$514$	−62.5862	−2.76056
$515$	0.435185	0.0191765
$516$	−7.97300	−0.350992
$517$	0.235336	0.0103501
$518$	−13.7656	−0.604826
$519$	39.9415	1.75324
$520$	−0.0748517	−0.00328246
$521$	5.00503	0.219274	0.109637	−	0.993972i	$-0.465031\pi$
$521$	5.00503	0.219274	0.109637	+	0.993972i	$0.465031\pi$
$522$	−38.3290	−1.67761
$523$	32.1104	1.40409	0.702045	−	0.712133i	$-0.252271\pi$
$523$	32.1104	1.40409	0.702045	+	0.712133i	$0.252271\pi$
$524$	−28.1525	−1.22985
$525$	−12.6072	−0.550221
$526$	58.2096	2.53806
$527$	−4.16171	−0.181287
$528$	−35.8781	−1.56139
$529$	12.9978	0.565120
$530$	−0.0256025	−0.00111210
$531$	−38.7104	−1.67989
$532$	16.5338	0.716831
$533$	9.53851	0.413159
$534$	−10.8901	−0.471262
$535$	1.04528	0.0451912
$536$	4.11973	0.177945
$537$	−18.4312	−0.795365
$538$	−26.1580	−1.12775
$539$	−3.81051	−0.164130
$540$	−0.116097	−0.00499604
$541$	12.7854	0.549689	0.274845	−	0.961489i	$-0.411374\pi$
$541$	12.7854	0.549689	0.274845	+	0.961489i	$0.411374\pi$
$542$	−38.1182	−1.63732
$543$	−47.2961	−2.02967
$544$	−6.51456	−0.279310
$545$	0.907469	0.0388717
$546$	−25.3393	−1.08442
$547$	14.0312	0.599932	0.299966	−	0.953950i	$-0.403025\pi$
$547$	14.0312	0.599932	0.299966	+	0.953950i	$0.403025\pi$
$548$	43.1304	1.84244
$549$	9.42496	0.402248
$550$	−38.6747	−1.64909
$551$	−43.5850	−1.85678
$552$	3.88167	0.165215
$553$	−7.02610	−0.298780
$554$	−53.4501	−2.27088
$555$	1.00965	0.0428574
$556$	−4.79724	−0.203448
$557$	2.81857	0.119427	0.0597134	−	0.998216i	$-0.480981\pi$
$557$	2.81857	0.119427	0.0597134	+	0.998216i	$0.480981\pi$
$558$	−35.3544	−1.49667
$559$	7.34733	0.310759
$560$	0.220343	0.00931121
$561$	−7.73954	−0.326764
$562$	−18.0271	−0.760427
$563$	−32.5929	−1.37363	−0.686813	−	0.726834i	$-0.740991\pi$
$563$	−32.5929	−1.37363	−0.686813	+	0.726834i	$0.740991\pi$
$564$	0.331334	0.0139517
$565$	−0.619844	−0.0260771
$566$	57.2506	2.40642
$567$	7.76622	0.326151
$568$	−0.177420	−0.00744437
$569$	−30.0121	−1.25817	−0.629086	−	0.777336i	$-0.716571\pi$
$569$	−30.0121	−1.25817	−0.629086	+	0.777336i	$0.716571\pi$
$570$	−2.35339	−0.0985725
$571$	−31.2271	−1.30681	−0.653407	−	0.757007i	$-0.726661\pi$
$571$	−31.2271	−1.30681	−0.653407	+	0.757007i	$0.726661\pi$
$572$	−40.0553	−1.67480
$573$	43.3347	1.81033
$574$	3.91913	0.163581
$575$	−29.9781	−1.25018
$576$	−30.2174	−1.25906
$577$	−33.4273	−1.39160	−0.695799	−	0.718236i	$-0.744950\pi$
$577$	−33.4273	−1.39160	−0.695799	+	0.718236i	$0.744950\pi$
$578$	33.2160	1.38161
$579$	−18.9827	−0.788895
$580$	0.703699	0.0292195
$581$	12.1103	0.502418
$582$	75.8195	3.14282
$583$	−0.813364	−0.0336861
$584$	−0.379987	−0.0157240
$585$	0.982761	0.0406322
$586$	20.4344	0.844139
$587$	4.72511	0.195026	0.0975130	−	0.995234i	$-0.468911\pi$
$587$	4.72511	0.195026	0.0975130	+	0.995234i	$0.468911\pi$
$588$	−5.36488	−0.221244
$589$	−40.2025	−1.65651
$590$	1.37921	0.0567812
$591$	25.5557	1.05122
$592$	25.2880	1.03933
$593$	36.5184	1.49963	0.749815	−	0.661647i	$-0.230142\pi$
$593$	36.5184	1.49963	0.749815	+	0.661647i	$0.230142\pi$
$594$	−7.15763	−0.293681
$595$	0.0475319	0.00194862
$596$	−12.7735	−0.523223
$597$	−53.0540	−2.17136
$598$	−60.2534	−2.46395
$599$	−28.5136	−1.16503	−0.582517	−	0.812819i	$-0.697932\pi$
$599$	−28.5136	−1.16503	−0.582517	+	0.812819i	$0.697932\pi$
$600$	−3.23257	−0.131969
$601$	−20.5118	−0.836692	−0.418346	−	0.908288i	$-0.637390\pi$
$601$	−20.5118	−0.836692	−0.418346	+	0.908288i	$0.637390\pi$
$602$	3.01883	0.123038
$603$	−54.0898	−2.20271
$604$	48.4681	1.97214
$605$	0.207848	0.00845022
$606$	−12.6752	−0.514894
$607$	−10.0380	−0.407429	−0.203714	−	0.979030i	$-0.565301\pi$
$607$	−10.0380	−0.407429	−0.203714	+	0.979030i	$0.565301\pi$
$608$	−62.9312	−2.55220
$609$	14.1424	0.573080
$610$	−0.335802	−0.0135962
$611$	−0.305333	−0.0123524
$612$	−5.76194	−0.232913
$613$	11.5200	0.465289	0.232645	−	0.972562i	$-0.425262\pi$
$613$	11.5200	0.465289	0.232645	+	0.972562i	$0.425262\pi$
$614$	39.8360	1.60765
$615$	−0.287453	−0.0115912
$616$	−0.977044	−0.0393662
$617$	−34.0354	−1.37022	−0.685108	−	0.728442i	$-0.740245\pi$
$617$	−34.0354	−1.37022	−0.685108	+	0.728442i	$0.740245\pi$
$618$	37.7743	1.51951
$619$	−46.5809	−1.87224	−0.936121	−	0.351677i	$-0.885611\pi$
$619$	−46.5809	−1.87224	−0.936121	+	0.351677i	$0.885611\pi$
$620$	0.649087	0.0260680
$621$	−5.54814	−0.222639
$622$	−48.2533	−1.93478
$623$	2.12474	0.0851260
$624$	46.5494	1.86347
$625$	24.9477	0.997909
$626$	17.6147	0.704026
$627$	−74.7646	−2.98581
$628$	3.18898	0.127254
$629$	5.45508	0.217508
$630$	0.403791	0.0160874
$631$	−40.1405	−1.59797	−0.798984	−	0.601352i	$-0.794629\pi$
$631$	−40.1405	−1.59797	−0.798984	+	0.601352i	$0.794629\pi$
$632$	−1.80154	−0.0716616
$633$	−39.4869	−1.56946
$634$	−42.3723	−1.68282
$635$	0.154588	0.00613462
$636$	−1.14515	−0.0454081
$637$	4.94387	0.195883
$638$	43.3844	1.71761
$639$	2.32942	0.0921506
$640$	0.120881	0.00477824
$641$	−45.8779	−1.81207	−0.906035	−	0.423203i	$-0.860906\pi$
$641$	−45.8779	−1.81207	−0.906035	+	0.423203i	$0.860906\pi$
$642$	90.7307	3.58085
$643$	40.7169	1.60572	0.802858	−	0.596170i	$-0.203312\pi$
$643$	40.7169	1.60572	0.802858	+	0.596170i	$0.203312\pi$
$644$	−12.7570	−0.502695
$645$	−0.221419	−0.00871837
$646$	−12.7152	−0.500271
$647$	−49.5217	−1.94690	−0.973449	−	0.228905i	$-0.926486\pi$
$647$	−49.5217	−1.94690	−0.973449	+	0.228905i	$0.926486\pi$
$648$	1.99132	0.0782263
$649$	43.8161	1.71993
$650$	50.1777	1.96813
$651$	13.0449	0.511269
$652$	−11.1470	−0.436550
$653$	−29.2959	−1.14644	−0.573218	−	0.819403i	$-0.694305\pi$
$653$	−29.2959	−1.14644	−0.573218	+	0.819403i	$0.694305\pi$
$654$	78.7689	3.08011
$655$	−0.781827	−0.0305485
$656$	−7.19962	−0.281098
$657$	4.98902	0.194640
$658$	−0.125453	−0.00489068
$659$	43.4148	1.69120	0.845600	−	0.533818i	$-0.179243\pi$
$659$	43.4148	1.69120	0.845600	+	0.533818i	$0.179243\pi$
$660$	1.20711	0.0469867
$661$	−22.1852	−0.862906	−0.431453	−	0.902135i	$-0.641999\pi$
$661$	−22.1852	−0.862906	−0.431453	+	0.902135i	$0.641999\pi$
$662$	18.9074	0.734858
$663$	10.0415	0.389980
$664$	3.10516	0.120504
$665$	0.459163	0.0178056
$666$	46.3417	1.79571
$667$	33.6288	1.30211
$668$	21.8526	0.845504
$669$	−3.90124	−0.150831
$670$	1.92716	0.0744528
$671$	−10.6681	−0.411836
$672$	20.4199	0.787714
$673$	11.1444	0.429585	0.214793	−	0.976660i	$-0.431092\pi$
$673$	11.1444	0.429585	0.214793	+	0.976660i	$0.431092\pi$
$674$	30.5709	1.17755
$675$	4.62037	0.177838
$676$	24.3281	0.935695
$677$	38.3834	1.47520	0.737598	−	0.675241i	$-0.235960\pi$
$677$	38.3834	1.47520	0.737598	+	0.675241i	$0.235960\pi$
$678$	−53.8029	−2.06629
$679$	−14.7929	−0.567700
$680$	0.0121875	0.000467371 0
$681$	24.4704	0.937707
$682$	40.0175	1.53235
$683$	30.4630	1.16563	0.582817	−	0.812603i	$-0.301950\pi$
$683$	30.4630	1.16563	0.582817	+	0.812603i	$0.301950\pi$
$684$	−55.6608	−2.12825
$685$	1.19778	0.0457649
$686$	2.03131	0.0775558
$687$	−21.5877	−0.823622
$688$	−5.54572	−0.211429
$689$	1.05528	0.0402031
$690$	1.81580	0.0691263
$691$	−50.0079	−1.90239	−0.951196	−	0.308588i	$-0.900144\pi$
$691$	−50.0079	−1.90239	−0.951196	+	0.308588i	$0.900144\pi$
$692$	−33.6577	−1.27947
$693$	12.8280	0.487297
$694$	60.4604	2.29505
$695$	−0.133225	−0.00505351
$696$	3.62622	0.137452
$697$	−1.55308	−0.0588273
$698$	−22.0639	−0.835132
$699$	16.5260	0.625070
$700$	10.6237	0.401539
$701$	−30.0555	−1.13518	−0.567591	−	0.823311i	$-0.692124\pi$
$701$	−30.0555	−1.13518	−0.567591	+	0.823311i	$0.692124\pi$
$702$	9.28653	0.350497
$703$	52.6965	1.98749
$704$	34.2029	1.28907
$705$	0.00920151	0.000346549 0
$706$	68.6769	2.58469
$707$	2.47302	0.0930075
$708$	61.6894	2.31843
$709$	6.67386	0.250642	0.125321	−	0.992116i	$-0.460004\pi$
$709$	6.67386	0.250642	0.125321	+	0.992116i	$0.460004\pi$
$710$	−0.0829949	−0.00311474
$711$	23.6533	0.887067
$712$	0.544800	0.0204172
$713$	31.0190	1.16167
$714$	4.12580	0.154404
$715$	−1.11238	−0.0416008
$716$	15.5315	0.580439
$717$	36.5140	1.36364
$718$	38.6960	1.44412
$719$	23.3311	0.870105	0.435053	−	0.900405i	$-0.356730\pi$
$719$	23.3311	0.870105	0.435053	+	0.900405i	$0.356730\pi$
$720$	−0.741783	−0.0276446
$721$	−7.37005	−0.274475
$722$	−84.2346	−3.13489
$723$	−41.5413	−1.54494
$724$	39.8552	1.48121
$725$	−28.0053	−1.04009
$726$	18.0413	0.669577
$727$	35.5288	1.31769	0.658846	−	0.752278i	$-0.271045\pi$
$727$	35.5288	1.31769	0.658846	+	0.752278i	$0.271045\pi$
$728$	1.26765	0.0469821
$729$	−33.1446	−1.22758
$730$	−0.177753	−0.00657895
$731$	−1.19631	−0.0442471
$732$	−15.0197	−0.555145
$733$	−21.2047	−0.783214	−0.391607	−	0.920133i	$-0.628081\pi$
$733$	−21.2047	−0.783214	−0.391607	+	0.920133i	$0.628081\pi$
$734$	−37.7999	−1.39522
$735$	−0.148989	−0.00549553
$736$	48.5558	1.78979
$737$	61.2240	2.25521
$738$	−13.1937	−0.485667
$739$	−8.77496	−0.322792	−0.161396	−	0.986890i	$-0.551600\pi$
$739$	−8.77496	−0.322792	−0.161396	+	0.986890i	$0.551600\pi$
$740$	−0.850809	−0.0312764
$741$	97.0020	3.56346
$742$	0.433589	0.0159176
$743$	−42.6855	−1.56598	−0.782989	−	0.622036i	$-0.786306\pi$
$743$	−42.6855	−1.56598	−0.782989	+	0.622036i	$0.786306\pi$
$744$	3.34480	0.122626
$745$	−0.354735	−0.0129965
$746$	−8.48721	−0.310739
$747$	−40.7690	−1.49166
$748$	6.52191	0.238465
$749$	−17.7022	−0.646825
$750$	−3.02537	−0.110471
$751$	38.4552	1.40325	0.701626	−	0.712546i	$-0.252458\pi$
$751$	38.4552	1.40325	0.701626	+	0.712546i	$0.252458\pi$
$752$	0.230464	0.00840414
$753$	−7.90500	−0.288074
$754$	−56.2883	−2.04990
$755$	1.34602	0.0489865
$756$	1.96616	0.0715086
$757$	27.4956	0.999344	0.499672	−	0.866215i	$-0.333454\pi$
$757$	27.4956	0.999344	0.499672	+	0.866215i	$0.333454\pi$
$758$	−15.1899	−0.551724
$759$	57.6861	2.09387
$760$	0.117733	0.00427062
$761$	30.1050	1.09130	0.545652	−	0.838012i	$-0.316282\pi$
$761$	30.1050	1.09130	0.545652	+	0.838012i	$0.316282\pi$
$762$	13.4183	0.486094
$763$	−15.3684	−0.556373
$764$	−36.5170	−1.32114
$765$	−0.160016	−0.00578538
$766$	16.9419	0.612135
$767$	−56.8484	−2.05268
$768$	−34.8035	−1.25586
$769$	−13.9374	−0.502597	−0.251299	−	0.967910i	$-0.580858\pi$
$769$	−13.9374	−0.502597	−0.251299	+	0.967910i	$0.580858\pi$
$770$	−0.457050	−0.0164709
$771$	−77.7413	−2.79979
$772$	15.9963	0.575718
$773$	−45.1196	−1.62284	−0.811420	−	0.584463i	$-0.801305\pi$
$773$	−45.1196	−1.62284	−0.811420	+	0.584463i	$0.801305\pi$
$774$	−10.1628	−0.365296
$775$	−25.8319	−0.927910
$776$	−3.79302	−0.136161
$777$	−17.0989	−0.613420
$778$	−62.2343	−2.23121
$779$	−15.0029	−0.537536
$780$	−1.56614	−0.0560768
$781$	−2.63666	−0.0943473
$782$	9.81062	0.350827
$783$	−5.18302	−0.185226
$784$	−3.73161	−0.133272
$785$	0.0885616	0.00316090
$786$	−67.8631	−2.42060
$787$	−1.39495	−0.0497246	−0.0248623	−	0.999691i	$-0.507915\pi$
$787$	−1.39495	−0.0497246	−0.0248623	+	0.999691i	$0.507915\pi$
$788$	−21.5352	−0.767158
$789$	72.3049	2.57412
$790$	−0.842741	−0.0299834
$791$	10.4973	0.373242
$792$	3.28921	0.116877
$793$	13.8411	0.491511
$794$	−61.3079	−2.17574
$795$	−0.0318021	−0.00112790
$796$	44.7073	1.58461
$797$	−51.7316	−1.83243	−0.916214	−	0.400689i	$-0.868771\pi$
$797$	−51.7316	−1.83243	−0.916214	+	0.400689i	$0.868771\pi$
$798$	39.8556	1.41087
$799$	0.0497151	0.00175879
$800$	−40.4362	−1.42964
$801$	−7.15292	−0.252736
$802$	−66.9216	−2.36308
$803$	−5.64705	−0.199280
$804$	86.1982	3.03998
$805$	−0.354276	−0.0124866
$806$	−51.9199	−1.82880
$807$	−32.4921	−1.14378
$808$	0.634101	0.0223076
$809$	−52.0231	−1.82903	−0.914517	−	0.404548i	$-0.867429\pi$
$809$	−52.0231	−1.82903	−0.914517	+	0.404548i	$0.867429\pi$
$810$	0.931515	0.0327301
$811$	10.4919	0.368420	0.184210	−	0.982887i	$-0.441027\pi$
$811$	10.4919	0.368420	0.184210	+	0.982887i	$0.441027\pi$
$812$	−11.9175	−0.418221
$813$	−47.3485	−1.66058
$814$	−52.4540	−1.83851
$815$	−0.309565	−0.0108436
$816$	−7.57929	−0.265328
$817$	−11.5565	−0.404309
$818$	18.6840	0.653271
$819$	−16.6435	−0.581571
$820$	0.242229	0.00845901
$821$	−12.4832	−0.435667	−0.217833	−	0.975986i	$-0.569899\pi$
$821$	−12.4832	−0.435667	−0.217833	+	0.975986i	$0.569899\pi$
$822$	103.968	3.62631
$823$	−34.6270	−1.20702	−0.603511	−	0.797355i	$-0.706232\pi$
$823$	−34.6270	−1.20702	−0.603511	+	0.797355i	$0.706232\pi$
$824$	−1.88973	−0.0658320
$825$	−48.0397	−1.67253
$826$	−23.3575	−0.812713
$827$	−6.68795	−0.232563	−0.116281	−	0.993216i	$-0.537097\pi$
$827$	−6.68795	−0.232563	−0.116281	+	0.993216i	$0.537097\pi$
$828$	42.9462	1.49248
$829$	45.8061	1.59091	0.795456	−	0.606011i	$-0.207231\pi$
$829$	45.8061	1.59091	0.795456	+	0.606011i	$0.207231\pi$
$830$	1.45256	0.0504190
$831$	−66.3929	−2.30314
$832$	−44.3759	−1.53846
$833$	−0.804974	−0.0278907
$834$	−11.5640	−0.400429
$835$	0.606873	0.0210017
$836$	63.0023	2.17898
$837$	−4.78079	−0.165248
$838$	−49.8046	−1.72047
$839$	43.4324	1.49945	0.749727	−	0.661747i	$-0.230185\pi$
$839$	43.4324	1.49945	0.749727	+	0.661747i	$0.230185\pi$
$840$	−0.0382018	−0.00131809
$841$	2.41578	0.0833026
$842$	42.3976	1.46112
$843$	−22.3923	−0.771232
$844$	33.2746	1.14536
$845$	0.675619	0.0232420
$846$	0.422337	0.0145203
$847$	−3.52000	−0.120949
$848$	−0.796523	−0.0273527
$849$	71.1137	2.44062
$850$	−8.17007	−0.280231
$851$	−40.6590	−1.39377
$852$	−3.71220	−0.127178
$853$	−38.9867	−1.33488	−0.667440	−	0.744664i	$-0.732610\pi$
$853$	−38.9867	−1.33488	−0.667440	+	0.744664i	$0.732610\pi$
$854$	5.68695	0.194603
$855$	−1.54577	−0.0528641
$856$	−4.53898	−0.155139
$857$	43.8008	1.49621	0.748104	−	0.663582i	$-0.230965\pi$
$857$	43.8008	1.49621	0.748104	+	0.663582i	$0.230965\pi$
$858$	−96.5556	−3.29635
$859$	−1.00000	−0.0341196
$859$	−1.00000	−0.0341196
$860$	0.186584	0.00636247
$861$	4.86814	0.165906
$862$	5.11416	0.174189
$863$	18.0239	0.613540	0.306770	−	0.951784i	$-0.400752\pi$
$863$	18.0239	0.613540	0.306770	+	0.951784i	$0.400752\pi$
$864$	−7.48363	−0.254598
$865$	−0.934712	−0.0317812
$866$	−7.73847	−0.262964
$867$	41.2592	1.40124
$868$	−10.9926	−0.373112
$869$	−26.7730	−0.908213
$870$	1.69630	0.0575101
$871$	−79.4339	−2.69151
$872$	−3.94057	−0.133445
$873$	49.8002	1.68548
$874$	94.7714	3.20569
$875$	0.590272	0.0199548
$876$	−7.95056	−0.268625
$877$	6.51309	0.219931	0.109966	−	0.993935i	$-0.464926\pi$
$877$	6.51309	0.219931	0.109966	+	0.993935i	$0.464926\pi$
$878$	49.0458	1.65522
$879$	25.3826	0.856134
$880$	0.839621	0.0283036
$881$	46.0152	1.55029	0.775146	−	0.631782i	$-0.217676\pi$
$881$	46.0152	1.55029	0.775146	+	0.631782i	$0.217676\pi$
$882$	−6.83839	−0.230260
$883$	−9.29621	−0.312842	−0.156421	−	0.987690i	$-0.549996\pi$
$883$	−9.29621	−0.312842	−0.156421	+	0.987690i	$0.549996\pi$
$884$	−8.46173	−0.284599
$885$	1.71318	0.0575881
$886$	−15.3251	−0.514856
$887$	25.3079	0.849757	0.424879	−	0.905250i	$-0.360317\pi$
$887$	25.3079	0.849757	0.424879	+	0.905250i	$0.360317\pi$
$888$	−4.38429	−0.147127
$889$	−2.61801	−0.0878052
$890$	0.254851	0.00854263
$891$	29.5933	0.991412
$892$	3.28748	0.110073
$893$	0.480252	0.0160710
$894$	−30.7912	−1.02981
$895$	0.431328	0.0144177
$896$	−2.04717	−0.0683913
$897$	−74.8437	−2.49896
$898$	63.2605	2.11103
$899$	28.9777	0.966460
$900$	−35.7646	−1.19215
$901$	−0.171824	−0.00572429
$902$	14.9339	0.497244
$903$	3.74983	0.124787
$904$	2.69160	0.0895211
$905$	1.10682	0.0367921
$906$	116.835	3.88158
$907$	−3.82047	−0.126857	−0.0634283	−	0.997986i	$-0.520203\pi$
$907$	−3.82047	−0.126857	−0.0634283	+	0.997986i	$0.520203\pi$
$908$	−20.6206	−0.684317
$909$	−8.32539	−0.276136
$910$	0.592990	0.0196574
$911$	28.7710	0.953227	0.476613	−	0.879113i	$-0.341864\pi$
$911$	28.7710	0.953227	0.476613	+	0.879113i	$0.341864\pi$
$912$	−73.2166	−2.42444
$913$	46.1462	1.52722
$914$	50.5742	1.67285
$915$	−0.417115	−0.0137894
$916$	18.1914	0.601061
$917$	13.2406	0.437243
$918$	−1.51206	−0.0499053
$919$	−50.4714	−1.66490	−0.832449	−	0.554101i	$-0.813062\pi$
$919$	−50.4714	−1.66490	−0.832449	+	0.554101i	$0.813062\pi$
$920$	−0.0908389	−0.00299487
$921$	49.4822	1.63049
$922$	−23.6854	−0.780037
$923$	3.42089	0.112600
$924$	−20.4429	−0.672523
$925$	33.8599	1.11331
$926$	83.2535	2.73588
$927$	24.8112	0.814906
$928$	45.3604	1.48903
$929$	21.1692	0.694537	0.347269	−	0.937766i	$-0.387109\pi$
$929$	21.1692	0.694537	0.347269	+	0.937766i	$0.387109\pi$
$930$	1.56466	0.0513072
$931$	−7.77612	−0.254852
$932$	−13.9260	−0.456162
$933$	−59.9377	−1.96227
$934$	34.2616	1.12107
$935$	0.181121	0.00592329
$936$	−4.26752	−0.139488
$937$	23.3279	0.762088	0.381044	−	0.924557i	$-0.375565\pi$
$937$	23.3279	0.762088	0.381044	+	0.924557i	$0.375565\pi$
$938$	−32.6374	−1.06565
$939$	21.8801	0.714030
$940$	−0.00775388	−0.000252904 0
$941$	−24.4252	−0.796238	−0.398119	−	0.917334i	$-0.630337\pi$
$941$	−24.4252	−0.796238	−0.398119	+	0.917334i	$0.630337\pi$
$942$	7.68721	0.250463
$943$	11.5758	0.376960
$944$	42.9089	1.39656
$945$	0.0546025	0.00177622
$946$	11.5033	0.374004
$947$	−39.0889	−1.27022	−0.635109	−	0.772423i	$-0.719045\pi$
$947$	−39.0889	−1.27022	−0.635109	+	0.772423i	$0.719045\pi$
$948$	−37.6941	−1.22425
$949$	7.32665	0.237833
$950$	−78.9236	−2.56062
$951$	−52.6326	−1.70673
$952$	−0.206401	−0.00668951
$953$	16.2691	0.527009	0.263505	−	0.964658i	$-0.415122\pi$
$953$	16.2691	0.527009	0.263505	+	0.964658i	$0.415122\pi$
$954$	−1.45967	−0.0472586
$955$	−1.01412	−0.0328161
$956$	−30.7694	−0.995155
$957$	53.8899	1.74201
$958$	−48.2177	−1.55784
$959$	−20.2849	−0.655035
$960$	1.33731	0.0431616
$961$	−4.27118	−0.137780
$962$	68.0554	2.19420
$963$	59.5943	1.92040
$964$	35.0058	1.12746
$965$	0.444234	0.0143004
$966$	−30.7514	−0.989409
$967$	21.9933	0.707255	0.353628	−	0.935386i	$-0.384948\pi$
$967$	21.9933	0.707255	0.353628	+	0.935386i	$0.384948\pi$
$968$	−0.902554	−0.0290092
$969$	−15.7941	−0.507380
$970$	−1.77433	−0.0569703
$971$	24.2561	0.778415	0.389207	−	0.921150i	$-0.372749\pi$
$971$	24.2561	0.778415	0.389207	+	0.921150i	$0.372749\pi$
$972$	47.5633	1.52559
$973$	2.25622	0.0723312
$974$	3.55211	0.113817
$975$	62.3282	1.99610
$976$	−10.4472	−0.334406
$977$	−7.83903	−0.250793	−0.125396	−	0.992107i	$-0.540020\pi$
$977$	−7.83903	−0.250793	−0.125396	+	0.992107i	$0.540020\pi$
$978$	−26.8705	−0.859222
$979$	8.09635	0.258761
$980$	0.125549	0.00401052
$981$	51.7375	1.65185
$982$	29.8216	0.951645
$983$	−13.7294	−0.437900	−0.218950	−	0.975736i	$-0.570263\pi$
$983$	−13.7294	−0.437900	−0.218950	+	0.975736i	$0.570263\pi$
$984$	1.24823	0.0397920
$985$	−0.598056	−0.0190557
$986$	9.16500	0.291873
$987$	−0.155832	−0.00496018
$988$	−81.7411	−2.60053
$989$	8.91661	0.283532
$990$	1.53865	0.0489016
$991$	0.123777	0.00393192	0.00196596	−	0.999998i	$-0.499374\pi$
$991$	0.123777	0.00393192	0.00196596	+	0.999998i	$0.499374\pi$
$992$	41.8401	1.32843
$993$	23.4858	0.745300
$994$	1.40556	0.0445815
$995$	1.24157	0.0393605
$996$	64.9700	2.05865
$997$	−21.5331	−0.681959	−0.340980	−	0.940071i	$-0.610759\pi$
$997$	−21.5331	−0.681959	−0.340980	+	0.940071i	$0.610759\pi$
$998$	31.6805	1.00283
$999$	6.26655	0.198265

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6013.2.a.c.1.19	✓	104

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6013.2.a.c.1.19	✓	104	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:	\( N \)	\(=\)	\( 6013 = 7 \cdot 859 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6013.a (trivial)

\(f(q)\)	\(=\)	\(q-2.03131 q^{2} -2.52319 q^{3} +2.12623 q^{4} +0.0590478 q^{5} +5.12539 q^{6} -1.00000 q^{7} -0.256407 q^{8} +3.36649 q^{9} +O(q^{10})\)	\(q-2.03131 q^{2} -2.52319 q^{3} +2.12623 q^{4} +0.0590478 q^{5} +5.12539 q^{6} -1.00000 q^{7} -0.256407 q^{8} +3.36649 q^{9} -0.119944 q^{10} -3.81051 q^{11} -5.36488 q^{12} +4.94387 q^{13} +2.03131 q^{14} -0.148989 q^{15} -3.73161 q^{16} -0.804974 q^{17} -6.83839 q^{18} -7.77612 q^{19} +0.125549 q^{20} +2.52319 q^{21} +7.74034 q^{22} +5.99981 q^{23} +0.646965 q^{24} -4.99651 q^{25} -10.0426 q^{26} -0.924718 q^{27} -2.12623 q^{28} +5.60498 q^{29} +0.302643 q^{30} +5.16999 q^{31} +8.09288 q^{32} +9.61464 q^{33} +1.63515 q^{34} -0.0590478 q^{35} +7.15792 q^{36} -6.77671 q^{37} +15.7957 q^{38} -12.4743 q^{39} -0.0151403 q^{40} +1.92936 q^{41} -5.12539 q^{42} +1.48615 q^{43} -8.10201 q^{44} +0.198784 q^{45} -12.1875 q^{46} -0.0617598 q^{47} +9.41556 q^{48} +1.00000 q^{49} +10.1495 q^{50} +2.03110 q^{51} +10.5118 q^{52} +0.213453 q^{53} +1.87839 q^{54} -0.225002 q^{55} +0.256407 q^{56} +19.6206 q^{57} -11.3855 q^{58} -11.4988 q^{59} -0.316784 q^{60} +2.79964 q^{61} -10.5019 q^{62} -3.36649 q^{63} -8.97594 q^{64} +0.291925 q^{65} -19.5303 q^{66} -16.0671 q^{67} -1.71156 q^{68} -15.1387 q^{69} +0.119944 q^{70} +0.691945 q^{71} -0.863193 q^{72} +1.48197 q^{73} +13.7656 q^{74} +12.6072 q^{75} -16.5338 q^{76} +3.81051 q^{77} +25.3393 q^{78} +7.02610 q^{79} -0.220343 q^{80} -7.76622 q^{81} -3.91913 q^{82} -12.1103 q^{83} +5.36488 q^{84} -0.0475319 q^{85} -3.01883 q^{86} -14.1424 q^{87} +0.977044 q^{88} -2.12474 q^{89} -0.403791 q^{90} -4.94387 q^{91} +12.7570 q^{92} -13.0449 q^{93} +0.125453 q^{94} -0.459163 q^{95} -20.4199 q^{96} +14.7929 q^{97} -2.03131 q^{98} -12.8280 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 104 q - 19 q^{2} - 26 q^{3} + 99 q^{4} + 2 q^{5} + 2 q^{6} - 104 q^{7} - 54 q^{8} + 90 q^{9}+O(q^{10}) \) 104 * q - 19 * q^2 - 26 * q^3 + 99 * q^4 + 2 * q^5 + 2 * q^6 - 104 * q^7 - 54 * q^8 + 90 * q^9	\( 104 q - 19 q^{2} - 26 q^{3} + 99 q^{4} + 2 q^{5} + 2 q^{6} - 104 q^{7} - 54 q^{8} + 90 q^{9} + 3 q^{10} - 54 q^{11} - 38 q^{12} + 7 q^{13} + 19 q^{14} - 33 q^{15} + 93 q^{16} - 7 q^{17} - 55 q^{18} - 12 q^{19} - 24 q^{20} + 26 q^{21} - 22 q^{22} - 69 q^{23} + 78 q^{25} - 11 q^{26} - 95 q^{27} - 99 q^{28} - 41 q^{29} - 26 q^{30} - 12 q^{31} - 127 q^{32} - 6 q^{33} - 17 q^{34} - 2 q^{35} + 71 q^{36} - 47 q^{37} - 32 q^{38} - 57 q^{39} + 6 q^{40} + 10 q^{41} - 2 q^{42} - 41 q^{43} - 120 q^{44} + 23 q^{45} - 31 q^{46} - 99 q^{47} - 84 q^{48} + 104 q^{49} - 104 q^{50} - 74 q^{51} + 14 q^{52} - 74 q^{53} + 19 q^{54} - 32 q^{55} + 54 q^{56} - 47 q^{57} - 36 q^{58} - 76 q^{59} - 99 q^{60} + 49 q^{61} - 55 q^{62} - 90 q^{63} + 86 q^{64} - 70 q^{65} + 61 q^{66} - 117 q^{67} - 30 q^{68} + 51 q^{69} - 3 q^{70} - 125 q^{71} - 147 q^{72} - 20 q^{73} - 75 q^{74} - 124 q^{75} + 4 q^{76} + 54 q^{77} - 70 q^{78} - 72 q^{79} - 69 q^{80} + 76 q^{81} - 37 q^{82} - 98 q^{83} + 38 q^{84} - 33 q^{85} - 64 q^{86} - 8 q^{87} - 62 q^{88} - 26 q^{89} + 11 q^{90} - 7 q^{91} - 162 q^{92} - 81 q^{93} + 31 q^{94} - 116 q^{95} + 20 q^{96} - 61 q^{97} - 19 q^{98} - 158 q^{99}+O(q^{100}) \) 104 * q - 19 * q^2 - 26 * q^3 + 99 * q^4 + 2 * q^5 + 2 * q^6 - 104 * q^7 - 54 * q^8 + 90 * q^9 + 3 * q^10 - 54 * q^11 - 38 * q^12 + 7 * q^13 + 19 * q^14 - 33 * q^15 + 93 * q^16 - 7 * q^17 - 55 * q^18 - 12 * q^19 - 24 * q^20 + 26 * q^21 - 22 * q^22 - 69 * q^23 + 78 * q^25 - 11 * q^26 - 95 * q^27 - 99 * q^28 - 41 * q^29 - 26 * q^30 - 12 * q^31 - 127 * q^32 - 6 * q^33 - 17 * q^34 - 2 * q^35 + 71 * q^36 - 47 * q^37 - 32 * q^38 - 57 * q^39 + 6 * q^40 + 10 * q^41 - 2 * q^42 - 41 * q^43 - 120 * q^44 + 23 * q^45 - 31 * q^46 - 99 * q^47 - 84 * q^48 + 104 * q^49 - 104 * q^50 - 74 * q^51 + 14 * q^52 - 74 * q^53 + 19 * q^54 - 32 * q^55 + 54 * q^56 - 47 * q^57 - 36 * q^58 - 76 * q^59 - 99 * q^60 + 49 * q^61 - 55 * q^62 - 90 * q^63 + 86 * q^64 - 70 * q^65 + 61 * q^66 - 117 * q^67 - 30 * q^68 + 51 * q^69 - 3 * q^70 - 125 * q^71 - 147 * q^72 - 20 * q^73 - 75 * q^74 - 124 * q^75 + 4 * q^76 + 54 * q^77 - 70 * q^78 - 72 * q^79 - 69 * q^80 + 76 * q^81 - 37 * q^82 - 98 * q^83 + 38 * q^84 - 33 * q^85 - 64 * q^86 - 8 * q^87 - 62 * q^88 - 26 * q^89 + 11 * q^90 - 7 * q^91 - 162 * q^92 - 81 * q^93 + 31 * q^94 - 116 * q^95 + 20 * q^96 - 61 * q^97 - 19 * q^98 - 158 * q^99

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