LMFDB - Embedded newform 6010.2.a.i.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6010,2,Mod(1,6010)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6010, 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("6010.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6010 = 2 \cdot 5 \cdot 601 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6010.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:	$47.9900916148$
Analytic rank:	$1$
Dimension:	$29$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Character	$\chi$	$=$	6010.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -3.11389 q^{3} +1.00000 q^{4} -1.00000 q^{5} +3.11389 q^{6} -3.05168 q^{7} -1.00000 q^{8} +6.69634 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -3.11389 q^{3} +1.00000 q^{4} -1.00000 q^{5} +3.11389 q^{6} -3.05168 q^{7} -1.00000 q^{8} +6.69634 q^{9} +1.00000 q^{10} +3.03641 q^{11} -3.11389 q^{12} +1.52509 q^{13} +3.05168 q^{14} +3.11389 q^{15} +1.00000 q^{16} +5.18894 q^{17} -6.69634 q^{18} -4.42160 q^{19} -1.00000 q^{20} +9.50262 q^{21} -3.03641 q^{22} -7.86628 q^{23} +3.11389 q^{24} +1.00000 q^{25} -1.52509 q^{26} -11.5100 q^{27} -3.05168 q^{28} +2.79144 q^{29} -3.11389 q^{30} -5.66023 q^{31} -1.00000 q^{32} -9.45507 q^{33} -5.18894 q^{34} +3.05168 q^{35} +6.69634 q^{36} +5.45907 q^{37} +4.42160 q^{38} -4.74898 q^{39} +1.00000 q^{40} -0.962768 q^{41} -9.50262 q^{42} -11.6132 q^{43} +3.03641 q^{44} -6.69634 q^{45} +7.86628 q^{46} -4.68782 q^{47} -3.11389 q^{48} +2.31276 q^{49} -1.00000 q^{50} -16.1578 q^{51} +1.52509 q^{52} -2.15129 q^{53} +11.5100 q^{54} -3.03641 q^{55} +3.05168 q^{56} +13.7684 q^{57} -2.79144 q^{58} +1.62228 q^{59} +3.11389 q^{60} +11.1800 q^{61} +5.66023 q^{62} -20.4351 q^{63} +1.00000 q^{64} -1.52509 q^{65} +9.45507 q^{66} +1.48887 q^{67} +5.18894 q^{68} +24.4948 q^{69} -3.05168 q^{70} +11.2184 q^{71} -6.69634 q^{72} +3.24060 q^{73} -5.45907 q^{74} -3.11389 q^{75} -4.42160 q^{76} -9.26616 q^{77} +4.74898 q^{78} +7.62195 q^{79} -1.00000 q^{80} +15.7520 q^{81} +0.962768 q^{82} +3.53350 q^{83} +9.50262 q^{84} -5.18894 q^{85} +11.6132 q^{86} -8.69226 q^{87} -3.03641 q^{88} +7.76068 q^{89} +6.69634 q^{90} -4.65410 q^{91} -7.86628 q^{92} +17.6254 q^{93} +4.68782 q^{94} +4.42160 q^{95} +3.11389 q^{96} -3.64962 q^{97} -2.31276 q^{98} +20.3328 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 29 q - 29 q^{2} - 10 q^{3} + 29 q^{4} - 29 q^{5} + 10 q^{6} - 29 q^{8} + 29 q^{9}+O(q^{10}) $ 29 * q - 29 * q^2 - 10 * q^3 + 29 * q^4 - 29 * q^5 + 10 * q^6 - 29 * q^8 + 29 * q^9	\( 29 q - 29 q^{2} - 10 q^{3} + 29 q^{4} - 29 q^{5} + 10 q^{6} - 29 q^{8} + 29 q^{9} + 29 q^{10} - 10 q^{12} - 4 q^{13} + 10 q^{15} + 29 q^{16} - 23 q^{17} - 29 q^{18} + q^{19} - 29 q^{20} + 2 q^{21} - 9 q^{23} + 10 q^{24} + 29 q^{25} + 4 q^{26} - 43 q^{27} - 5 q^{29} - 10 q^{30} + 21 q^{31} - 29 q^{32} - 19 q^{33} + 23 q^{34} + 29 q^{36} - 6 q^{37} - q^{38} + 18 q^{39} + 29 q^{40} - 17 q^{41} - 2 q^{42} - 19 q^{43} - 29 q^{45} + 9 q^{46} - 21 q^{47} - 10 q^{48} + 45 q^{49} - 29 q^{50} + 11 q^{51} - 4 q^{52} - 53 q^{53} + 43 q^{54} - 16 q^{57} + 5 q^{58} - 30 q^{59} + 10 q^{60} + 16 q^{61} - 21 q^{62} - 17 q^{63} + 29 q^{64} + 4 q^{65} + 19 q^{66} - 35 q^{67} - 23 q^{68} + 13 q^{69} + 2 q^{71} - 29 q^{72} - q^{73} + 6 q^{74} - 10 q^{75} + q^{76} - 50 q^{77} - 18 q^{78} + 26 q^{79} - 29 q^{80} + 33 q^{81} + 17 q^{82} - 54 q^{83} + 2 q^{84} + 23 q^{85} + 19 q^{86} - 56 q^{87} - 2 q^{89} + 29 q^{90} + 27 q^{91} - 9 q^{92} - 26 q^{93} + 21 q^{94} - q^{95} + 10 q^{96} + 15 q^{97} - 45 q^{98} + 27 q^{99}+O(q^{100}) \) 29 * q - 29 * q^2 - 10 * q^3 + 29 * q^4 - 29 * q^5 + 10 * q^6 - 29 * q^8 + 29 * q^9 + 29 * q^10 - 10 * q^12 - 4 * q^13 + 10 * q^15 + 29 * q^16 - 23 * q^17 - 29 * q^18 + q^19 - 29 * q^20 + 2 * q^21 - 9 * q^23 + 10 * q^24 + 29 * q^25 + 4 * q^26 - 43 * q^27 - 5 * q^29 - 10 * q^30 + 21 * q^31 - 29 * q^32 - 19 * q^33 + 23 * q^34 + 29 * q^36 - 6 * q^37 - q^38 + 18 * q^39 + 29 * q^40 - 17 * q^41 - 2 * q^42 - 19 * q^43 - 29 * q^45 + 9 * q^46 - 21 * q^47 - 10 * q^48 + 45 * q^49 - 29 * q^50 + 11 * q^51 - 4 * q^52 - 53 * q^53 + 43 * q^54 - 16 * q^57 + 5 * q^58 - 30 * q^59 + 10 * q^60 + 16 * q^61 - 21 * q^62 - 17 * q^63 + 29 * q^64 + 4 * q^65 + 19 * q^66 - 35 * q^67 - 23 * q^68 + 13 * q^69 + 2 * q^71 - 29 * q^72 - q^73 + 6 * q^74 - 10 * q^75 + q^76 - 50 * q^77 - 18 * q^78 + 26 * q^79 - 29 * q^80 + 33 * q^81 + 17 * q^82 - 54 * q^83 + 2 * q^84 + 23 * q^85 + 19 * q^86 - 56 * q^87 - 2 * q^89 + 29 * q^90 + 27 * q^91 - 9 * q^92 - 26 * q^93 + 21 * q^94 - q^95 + 10 * q^96 + 15 * q^97 - 45 * q^98 + 27 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	−3.11389	−1.79781	−0.898904	−	0.438146i	$-0.855635\pi$
$3$	−3.11389	−1.79781	−0.898904	+	0.438146i	$0.855635\pi$
$4$	1.00000	0.500000
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	3.11389	1.27124
$7$	−3.05168	−1.15343	−0.576714	−	0.816946i	$-0.695665\pi$
$7$	−3.05168	−1.15343	−0.576714	+	0.816946i	$0.695665\pi$
$8$	−1.00000	−0.353553
$9$	6.69634	2.23211
$10$	1.00000	0.316228
$11$	3.03641	0.915513	0.457756	−	0.889078i	$-0.348653\pi$
$11$	3.03641	0.915513	0.457756	+	0.889078i	$0.348653\pi$
$12$	−3.11389	−0.898904
$13$	1.52509	0.422985	0.211493	−	0.977380i	$-0.432168\pi$
$13$	1.52509	0.422985	0.211493	+	0.977380i	$0.432168\pi$
$14$	3.05168	0.815596
$15$	3.11389	0.804004
$16$	1.00000	0.250000
$17$	5.18894	1.25850	0.629251	−	0.777202i	$-0.283362\pi$
$17$	5.18894	1.25850	0.629251	+	0.777202i	$0.283362\pi$
$18$	−6.69634	−1.57834
$19$	−4.42160	−1.01439	−0.507193	−	0.861833i	$-0.669317\pi$
$19$	−4.42160	−1.01439	−0.507193	+	0.861833i	$0.669317\pi$
$20$	−1.00000	−0.223607
$21$	9.50262	2.07364
$22$	−3.03641	−0.647365
$23$	−7.86628	−1.64023	−0.820117	−	0.572197i	$-0.806091\pi$
$23$	−7.86628	−1.64023	−0.820117	+	0.572197i	$0.806091\pi$
$24$	3.11389	0.635621
$25$	1.00000	0.200000
$26$	−1.52509	−0.299096
$27$	−11.5100	−2.21510
$28$	−3.05168	−0.576714
$29$	2.79144	0.518358	0.259179	−	0.965829i	$-0.416548\pi$
$29$	2.79144	0.518358	0.259179	+	0.965829i	$0.416548\pi$
$30$	−3.11389	−0.568517
$31$	−5.66023	−1.01661	−0.508304	−	0.861178i	$-0.669727\pi$
$31$	−5.66023	−1.01661	−0.508304	+	0.861178i	$0.669727\pi$
$32$	−1.00000	−0.176777
$33$	−9.45507	−1.64592
$34$	−5.18894	−0.889896
$35$	3.05168	0.515828
$36$	6.69634	1.11606
$37$	5.45907	0.897465	0.448733	−	0.893666i	$-0.351876\pi$
$37$	5.45907	0.897465	0.448733	+	0.893666i	$0.351876\pi$
$38$	4.42160	0.717279
$39$	−4.74898	−0.760446
$40$	1.00000	0.158114
$41$	−0.962768	−0.150359	−0.0751796	−	0.997170i	$-0.523953\pi$
$41$	−0.962768	−0.150359	−0.0751796	+	0.997170i	$0.523953\pi$
$42$	−9.50262	−1.46629
$43$	−11.6132	−1.77099	−0.885495	−	0.464649i	$-0.846181\pi$
$43$	−11.6132	−1.77099	−0.885495	+	0.464649i	$0.846181\pi$
$44$	3.03641	0.457756
$45$	−6.69634	−0.998232
$46$	7.86628	1.15982
$47$	−4.68782	−0.683789	−0.341895	−	0.939738i	$-0.611069\pi$
$47$	−4.68782	−0.683789	−0.341895	+	0.939738i	$0.611069\pi$
$48$	−3.11389	−0.449452
$49$	2.31276	0.330395
$50$	−1.00000	−0.141421
$51$	−16.1578	−2.26255
$52$	1.52509	0.211493
$53$	−2.15129	−0.295502	−0.147751	−	0.989025i	$-0.547203\pi$
$53$	−2.15129	−0.295502	−0.147751	+	0.989025i	$0.547203\pi$
$54$	11.5100	1.56632
$55$	−3.03641	−0.409430
$56$	3.05168	0.407798
$57$	13.7684	1.82367
$58$	−2.79144	−0.366535
$59$	1.62228	0.211203	0.105601	−	0.994409i	$-0.466323\pi$
$59$	1.62228	0.211203	0.105601	+	0.994409i	$0.466323\pi$
$60$	3.11389	0.402002
$61$	11.1800	1.43145	0.715727	−	0.698380i	$-0.246096\pi$
$61$	11.1800	1.43145	0.715727	+	0.698380i	$0.246096\pi$
$62$	5.66023	0.718850
$63$	−20.4351	−2.57458
$64$	1.00000	0.125000
$65$	−1.52509	−0.189165
$66$	9.45507	1.16384
$67$	1.48887	0.181895	0.0909474	−	0.995856i	$-0.471010\pi$
$67$	1.48887	0.181895	0.0909474	+	0.995856i	$0.471010\pi$
$68$	5.18894	0.629251
$69$	24.4948	2.94882
$70$	−3.05168	−0.364746
$71$	11.2184	1.33137	0.665687	−	0.746231i	$-0.268139\pi$
$71$	11.2184	1.33137	0.665687	+	0.746231i	$0.268139\pi$
$72$	−6.69634	−0.789171
$73$	3.24060	0.379283	0.189642	−	0.981853i	$-0.439267\pi$
$73$	3.24060	0.379283	0.189642	+	0.981853i	$0.439267\pi$
$74$	−5.45907	−0.634604
$75$	−3.11389	−0.359562
$76$	−4.42160	−0.507193
$77$	−9.26616	−1.05598
$78$	4.74898	0.537717
$79$	7.62195	0.857536	0.428768	−	0.903415i	$-0.358948\pi$
$79$	7.62195	0.857536	0.428768	+	0.903415i	$0.358948\pi$
$80$	−1.00000	−0.111803
$81$	15.7520	1.75022
$82$	0.962768	0.106320
$83$	3.53350	0.387852	0.193926	−	0.981016i	$-0.437878\pi$
$83$	3.53350	0.387852	0.193926	+	0.981016i	$0.437878\pi$
$84$	9.50262	1.03682
$85$	−5.18894	−0.562819
$86$	11.6132	1.25228
$87$	−8.69226	−0.931908
$88$	−3.03641	−0.323683
$89$	7.76068	0.822630	0.411315	−	0.911493i	$-0.365070\pi$
$89$	7.76068	0.822630	0.411315	+	0.911493i	$0.365070\pi$
$90$	6.69634	0.705856
$91$	−4.65410	−0.487883
$92$	−7.86628	−0.820117
$93$	17.6254	1.82766
$94$	4.68782	0.483512
$95$	4.42160	0.453647
$96$	3.11389	0.317811
$97$	−3.64962	−0.370563	−0.185281	−	0.982685i	$-0.559320\pi$
$97$	−3.64962	−0.370563	−0.185281	+	0.982685i	$0.559320\pi$
$98$	−2.31276	−0.233624
$99$	20.3328	2.04353
$100$	1.00000	0.100000
$101$	4.33237	0.431087	0.215544	−	0.976494i	$-0.430848\pi$
$101$	4.33237	0.431087	0.215544	+	0.976494i	$0.430848\pi$
$102$	16.1578	1.59986
$103$	6.52301	0.642731	0.321366	−	0.946955i	$-0.395858\pi$
$103$	6.52301	0.642731	0.321366	+	0.946955i	$0.395858\pi$
$104$	−1.52509	−0.149548
$105$	−9.50262	−0.927360
$106$	2.15129	0.208952
$107$	18.8417	1.82149	0.910747	−	0.412964i	$-0.135506\pi$
$107$	18.8417	1.82149	0.910747	+	0.412964i	$0.135506\pi$
$108$	−11.5100	−1.10755
$109$	−8.10374	−0.776198	−0.388099	−	0.921618i	$-0.626868\pi$
$109$	−8.10374	−0.776198	−0.388099	+	0.921618i	$0.626868\pi$
$110$	3.03641	0.289511
$111$	−16.9990	−1.61347
$112$	−3.05168	−0.288357
$113$	−0.487275	−0.0458390	−0.0229195	−	0.999737i	$-0.507296\pi$
$113$	−0.487275	−0.0458390	−0.0229195	+	0.999737i	$0.507296\pi$
$114$	−13.7684	−1.28953
$115$	7.86628	0.733534
$116$	2.79144	0.259179
$117$	10.2126	0.944151
$118$	−1.62228	−0.149343
$119$	−15.8350	−1.45159
$120$	−3.11389	−0.284258
$121$	−1.78020	−0.161837
$122$	−11.1800	−1.01219
$123$	2.99796	0.270317
$124$	−5.66023	−0.508304
$125$	−1.00000	−0.0894427
$126$	20.4351	1.82050
$127$	11.5898	1.02843	0.514216	−	0.857661i	$-0.328083\pi$
$127$	11.5898	1.02843	0.514216	+	0.857661i	$0.328083\pi$
$128$	−1.00000	−0.0883883
$129$	36.1622	3.18390
$130$	1.52509	0.133760
$131$	−16.6960	−1.45874	−0.729368	−	0.684122i	$-0.760186\pi$
$131$	−16.6960	−1.45874	−0.729368	+	0.684122i	$0.760186\pi$
$132$	−9.45507	−0.822958
$133$	13.4933	1.17002
$134$	−1.48887	−0.128619
$135$	11.5100	0.990625
$136$	−5.18894	−0.444948
$137$	−13.3989	−1.14474	−0.572372	−	0.819994i	$-0.693977\pi$
$137$	−13.3989	−1.14474	−0.572372	+	0.819994i	$0.693977\pi$
$138$	−24.4948	−2.08513
$139$	−15.6086	−1.32391	−0.661953	−	0.749545i	$-0.730272\pi$
$139$	−15.6086	−1.32391	−0.661953	+	0.749545i	$0.730272\pi$
$140$	3.05168	0.257914
$141$	14.5974	1.22932
$142$	−11.2184	−0.941424
$143$	4.63081	0.387248
$144$	6.69634	0.558028
$145$	−2.79144	−0.231817
$146$	−3.24060	−0.268194
$147$	−7.20170	−0.593986
$148$	5.45907	0.448733
$149$	4.49963	0.368624	0.184312	−	0.982868i	$-0.440994\pi$
$149$	4.49963	0.368624	0.184312	+	0.982868i	$0.440994\pi$
$150$	3.11389	0.254248
$151$	21.1160	1.71840	0.859198	−	0.511643i	$-0.170963\pi$
$151$	21.1160	1.71840	0.859198	+	0.511643i	$0.170963\pi$
$152$	4.42160	0.358639
$153$	34.7469	2.80912
$154$	9.26616	0.746689
$155$	5.66023	0.454641
$156$	−4.74898	−0.380223
$157$	−8.86543	−0.707538	−0.353769	−	0.935333i	$-0.615100\pi$
$157$	−8.86543	−0.707538	−0.353769	+	0.935333i	$0.615100\pi$
$158$	−7.62195	−0.606370
$159$	6.69889	0.531257
$160$	1.00000	0.0790569
$161$	24.0054	1.89189
$162$	−15.7520	−1.23759
$163$	6.74943	0.528656	0.264328	−	0.964433i	$-0.414850\pi$
$163$	6.74943	0.528656	0.264328	+	0.964433i	$0.414850\pi$
$164$	−0.962768	−0.0751796
$165$	9.45507	0.736076
$166$	−3.53350	−0.274253
$167$	−3.08800	−0.238957	−0.119478	−	0.992837i	$-0.538122\pi$
$167$	−3.08800	−0.238957	−0.119478	+	0.992837i	$0.538122\pi$
$168$	−9.50262	−0.733143
$169$	−10.6741	−0.821084
$170$	5.18894	0.397973
$171$	−29.6086	−2.26422
$172$	−11.6132	−0.885495
$173$	−2.07300	−0.157607	−0.0788036	−	0.996890i	$-0.525110\pi$
$173$	−2.07300	−0.157607	−0.0788036	+	0.996890i	$0.525110\pi$
$174$	8.69226	0.658959
$175$	−3.05168	−0.230685
$176$	3.03641	0.228878
$177$	−5.05160	−0.379702
$178$	−7.76068	−0.581687
$179$	15.6292	1.16818	0.584090	−	0.811689i	$-0.301451\pi$
$179$	15.6292	1.16818	0.584090	+	0.811689i	$0.301451\pi$
$180$	−6.69634	−0.499116
$181$	−24.3902	−1.81291	−0.906456	−	0.422301i	$-0.861223\pi$
$181$	−24.3902	−1.81291	−0.906456	+	0.422301i	$0.861223\pi$
$182$	4.65410	0.344985
$183$	−34.8134	−2.57348
$184$	7.86628	0.579910
$185$	−5.45907	−0.401359
$186$	−17.6254	−1.29235
$187$	15.7558	1.15217
$188$	−4.68782	−0.341895
$189$	35.1249	2.55496
$190$	−4.42160	−0.320777
$191$	15.7373	1.13871	0.569357	−	0.822090i	$-0.307192\pi$
$191$	15.7373	1.13871	0.569357	+	0.822090i	$0.307192\pi$
$192$	−3.11389	−0.224726
$193$	0.313268	0.0225495	0.0112747	−	0.999936i	$-0.496411\pi$
$193$	0.313268	0.0225495	0.0112747	+	0.999936i	$0.496411\pi$
$194$	3.64962	0.262028
$195$	4.74898	0.340082
$196$	2.31276	0.165197
$197$	9.69161	0.690499	0.345249	−	0.938511i	$-0.387794\pi$
$197$	9.69161	0.690499	0.345249	+	0.938511i	$0.387794\pi$
$198$	−20.3328	−1.44499
$199$	17.5138	1.24152	0.620761	−	0.784000i	$-0.286824\pi$
$199$	17.5138	1.24152	0.620761	+	0.784000i	$0.286824\pi$
$200$	−1.00000	−0.0707107
$201$	−4.63620	−0.327012
$202$	−4.33237	−0.304825
$203$	−8.51860	−0.597888
$204$	−16.1578	−1.13127
$205$	0.962768	0.0672427
$206$	−6.52301	−0.454480
$207$	−52.6753	−3.66119
$208$	1.52509	0.105746
$209$	−13.4258	−0.928682
$210$	9.50262	0.655743
$211$	14.1183	0.971945	0.485973	−	0.873974i	$-0.338465\pi$
$211$	14.1183	0.971945	0.485973	+	0.873974i	$0.338465\pi$
$212$	−2.15129	−0.147751
$213$	−34.9328	−2.39356
$214$	−18.8417	−1.28799
$215$	11.6132	0.792011
$216$	11.5100	0.783158
$217$	17.2732	1.17258
$218$	8.10374	0.548855
$219$	−10.0909	−0.681879
$220$	−3.03641	−0.204715
$221$	7.91362	0.532328
$222$	16.9990	1.14090
$223$	2.21025	0.148009	0.0740045	−	0.997258i	$-0.476422\pi$
$223$	2.21025	0.148009	0.0740045	+	0.997258i	$0.476422\pi$
$224$	3.05168	0.203899
$225$	6.69634	0.446423
$226$	0.487275	0.0324130
$227$	−4.18462	−0.277743	−0.138871	−	0.990310i	$-0.544347\pi$
$227$	−4.18462	−0.277743	−0.138871	+	0.990310i	$0.544347\pi$
$228$	13.7684	0.911835
$229$	−6.56119	−0.433576	−0.216788	−	0.976219i	$-0.569558\pi$
$229$	−6.56119	−0.433576	−0.216788	+	0.976219i	$0.569558\pi$
$230$	−7.86628	−0.518687
$231$	28.8539	1.89844
$232$	−2.79144	−0.183267
$233$	−13.3894	−0.877166	−0.438583	−	0.898691i	$-0.644519\pi$
$233$	−13.3894	−0.877166	−0.438583	+	0.898691i	$0.644519\pi$
$234$	−10.2126	−0.667615
$235$	4.68782	0.305800
$236$	1.62228	0.105601
$237$	−23.7339	−1.54169
$238$	15.8350	1.02643
$239$	−9.83452	−0.636142	−0.318071	−	0.948067i	$-0.603035\pi$
$239$	−9.83452	−0.636142	−0.318071	+	0.948067i	$0.603035\pi$
$240$	3.11389	0.201001
$241$	10.3124	0.664282	0.332141	−	0.943230i	$-0.392229\pi$
$241$	10.3124	0.664282	0.332141	+	0.943230i	$0.392229\pi$
$242$	1.78020	0.114436
$243$	−14.5199	−0.931452
$244$	11.1800	0.715727
$245$	−2.31276	−0.147757
$246$	−2.99796	−0.191143
$247$	−6.74336	−0.429070
$248$	5.66023	0.359425
$249$	−11.0030	−0.697284
$250$	1.00000	0.0632456
$251$	11.2407	0.709509	0.354754	−	0.934960i	$-0.384565\pi$
$251$	11.2407	0.709509	0.354754	+	0.934960i	$0.384565\pi$
$252$	−20.4351	−1.28729
$253$	−23.8853	−1.50165
$254$	−11.5898	−0.727212
$255$	16.1578	1.01184
$256$	1.00000	0.0625000
$257$	−13.2150	−0.824329	−0.412165	−	0.911109i	$-0.635227\pi$
$257$	−13.2150	−0.824329	−0.412165	+	0.911109i	$0.635227\pi$
$258$	−36.1622	−2.25136
$259$	−16.6593	−1.03516
$260$	−1.52509	−0.0945823
$261$	18.6925	1.15703
$262$	16.6960	1.03148
$263$	−0.522463	−0.0322164	−0.0161082	−	0.999870i	$-0.505128\pi$
$263$	−0.522463	−0.0322164	−0.0161082	+	0.999870i	$0.505128\pi$
$264$	9.45507	0.581919
$265$	2.15129	0.132153
$266$	−13.4933	−0.827329
$267$	−24.1659	−1.47893
$268$	1.48887	0.0909474
$269$	1.18439	0.0722136	0.0361068	−	0.999348i	$-0.488504\pi$
$269$	1.18439	0.0722136	0.0361068	+	0.999348i	$0.488504\pi$
$270$	−11.5100	−0.700477
$271$	−10.0822	−0.612448	−0.306224	−	0.951959i	$-0.599066\pi$
$271$	−10.0822	−0.612448	−0.306224	+	0.951959i	$0.599066\pi$
$272$	5.18894	0.314626
$273$	14.4924	0.877119
$274$	13.3989	0.809457
$275$	3.03641	0.183103
$276$	24.4948	1.47441
$277$	−2.16686	−0.130194	−0.0650971	−	0.997879i	$-0.520736\pi$
$277$	−2.16686	−0.130194	−0.0650971	+	0.997879i	$0.520736\pi$
$278$	15.6086	0.936143
$279$	−37.9028	−2.26918
$280$	−3.05168	−0.182373
$281$	2.77037	0.165267	0.0826333	−	0.996580i	$-0.473667\pi$
$281$	2.77037	0.165267	0.0826333	+	0.996580i	$0.473667\pi$
$282$	−14.5974	−0.869262
$283$	21.4203	1.27330	0.636651	−	0.771152i	$-0.280319\pi$
$283$	21.4203	1.27330	0.636651	+	0.771152i	$0.280319\pi$
$284$	11.2184	0.665687
$285$	−13.7684	−0.815570
$286$	−4.63081	−0.273826
$287$	2.93806	0.173428
$288$	−6.69634	−0.394586
$289$	9.92508	0.583828
$290$	2.79144	0.163919
$291$	11.3645	0.666201
$292$	3.24060	0.189642
$293$	−13.9614	−0.815636	−0.407818	−	0.913063i	$-0.633710\pi$
$293$	−13.9614	−0.815636	−0.407818	+	0.913063i	$0.633710\pi$
$294$	7.20170	0.420012
$295$	−1.62228	−0.0944527
$296$	−5.45907	−0.317302
$297$	−34.9492	−2.02796
$298$	−4.49963	−0.260657
$299$	−11.9968	−0.693794
$300$	−3.11389	−0.179781
$301$	35.4397	2.04271
$302$	−21.1160	−1.21509
$303$	−13.4905	−0.775012
$304$	−4.42160	−0.253596
$305$	−11.1800	−0.640166
$306$	−34.7469	−1.98635
$307$	−25.4003	−1.44967	−0.724837	−	0.688921i	$-0.758085\pi$
$307$	−25.4003	−1.44967	−0.724837	+	0.688921i	$0.758085\pi$
$308$	−9.26616	−0.527989
$309$	−20.3120	−1.15551
$310$	−5.66023	−0.321479
$311$	−34.0918	−1.93317	−0.966584	−	0.256349i	$-0.917481\pi$
$311$	−34.0918	−1.93317	−0.966584	+	0.256349i	$0.917481\pi$
$312$	4.74898	0.268858
$313$	−7.46478	−0.421934	−0.210967	−	0.977493i	$-0.567661\pi$
$313$	−7.46478	−0.421934	−0.210967	+	0.977493i	$0.567661\pi$
$314$	8.86543	0.500305
$315$	20.4351	1.15139
$316$	7.62195	0.428768
$317$	1.76061	0.0988858	0.0494429	−	0.998777i	$-0.484255\pi$
$317$	1.76061	0.0988858	0.0494429	+	0.998777i	$0.484255\pi$
$318$	−6.69889	−0.375655
$319$	8.47597	0.474563
$320$	−1.00000	−0.0559017
$321$	−58.6710	−3.27470
$322$	−24.0054	−1.33777
$323$	−22.9434	−1.27661
$324$	15.7520	0.875109
$325$	1.52509	0.0845970
$326$	−6.74943	−0.373816
$327$	25.2342	1.39545
$328$	0.962768	0.0531600
$329$	14.3057	0.788701
$330$	−9.45507	−0.520484
$331$	24.9456	1.37113	0.685567	−	0.728009i	$-0.259554\pi$
$331$	24.9456	1.37113	0.685567	+	0.728009i	$0.259554\pi$
$332$	3.53350	0.193926
$333$	36.5558	2.00324
$334$	3.08800	0.168968
$335$	−1.48887	−0.0813458
$336$	9.50262	0.518410
$337$	30.4486	1.65864	0.829321	−	0.558773i	$-0.188728\pi$
$337$	30.4486	1.65864	0.829321	+	0.558773i	$0.188728\pi$
$338$	10.6741	0.580594
$339$	1.51732	0.0824096
$340$	−5.18894	−0.281410
$341$	−17.1868	−0.930717
$342$	29.6086	1.60105
$343$	14.3040	0.772341
$344$	11.6132	0.626140
$345$	−24.4948	−1.31875
$346$	2.07300	0.111445
$347$	−4.12814	−0.221610	−0.110805	−	0.993842i	$-0.535343\pi$
$347$	−4.12814	−0.221610	−0.110805	+	0.993842i	$0.535343\pi$
$348$	−8.69226	−0.465954
$349$	13.7809	0.737676	0.368838	−	0.929494i	$-0.379756\pi$
$349$	13.7809	0.737676	0.368838	+	0.929494i	$0.379756\pi$
$350$	3.05168	0.163119
$351$	−17.5539	−0.936956
$352$	−3.03641	−0.161841
$353$	−2.84376	−0.151358	−0.0756791	−	0.997132i	$-0.524112\pi$
$353$	−2.84376	−0.151358	−0.0756791	+	0.997132i	$0.524112\pi$
$354$	5.05160	0.268490
$355$	−11.2184	−0.595409
$356$	7.76068	0.411315
$357$	49.3085	2.60968
$358$	−15.6292	−0.826028
$359$	27.7643	1.46534	0.732672	−	0.680582i	$-0.238273\pi$
$359$	27.7643	1.46534	0.732672	+	0.680582i	$0.238273\pi$
$360$	6.69634	0.352928
$361$	0.550570	0.0289774
$362$	24.3902	1.28192
$363$	5.54337	0.290951
$364$	−4.65410	−0.243941
$365$	−3.24060	−0.169621
$366$	34.8134	1.81972
$367$	0.758073	0.0395711	0.0197855	−	0.999804i	$-0.493702\pi$
$367$	0.758073	0.0395711	0.0197855	+	0.999804i	$0.493702\pi$
$368$	−7.86628	−0.410058
$369$	−6.44703	−0.335619
$370$	5.45907	0.283803
$371$	6.56505	0.340841
$372$	17.6254	0.913832
$373$	−34.9450	−1.80939	−0.904693	−	0.426065i	$-0.859900\pi$
$373$	−34.9450	−1.80939	−0.904693	+	0.426065i	$0.859900\pi$
$374$	−15.7558	−0.814711
$375$	3.11389	0.160801
$376$	4.68782	0.241756
$377$	4.25722	0.219258
$378$	−35.1249	−1.80663
$379$	−12.2273	−0.628074	−0.314037	−	0.949411i	$-0.601682\pi$
$379$	−12.2273	−0.628074	−0.314037	+	0.949411i	$0.601682\pi$
$380$	4.42160	0.226823
$381$	−36.0896	−1.84892
$382$	−15.7373	−0.805193
$383$	18.5742	0.949099	0.474549	−	0.880229i	$-0.342611\pi$
$383$	18.5742	0.949099	0.474549	+	0.880229i	$0.342611\pi$
$384$	3.11389	0.158905
$385$	9.26616	0.472247
$386$	−0.313268	−0.0159449
$387$	−77.7657	−3.95305
$388$	−3.64962	−0.185281
$389$	−18.8720	−0.956851	−0.478425	−	0.878128i	$-0.658792\pi$
$389$	−18.8720	−0.956851	−0.478425	+	0.878128i	$0.658792\pi$
$390$	−4.74898	−0.240474
$391$	−40.8176	−2.06424
$392$	−2.31276	−0.116812
$393$	51.9895	2.62253
$394$	−9.69161	−0.488256
$395$	−7.62195	−0.383502
$396$	20.3328	1.02176
$397$	30.9692	1.55430	0.777149	−	0.629317i	$-0.216665\pi$
$397$	30.9692	1.55430	0.777149	+	0.629317i	$0.216665\pi$
$398$	−17.5138	−0.877888
$399$	−42.0168	−2.10347
$400$	1.00000	0.0500000
$401$	−37.6775	−1.88152	−0.940762	−	0.339067i	$-0.889889\pi$
$401$	−37.6775	−1.88152	−0.940762	+	0.339067i	$0.889889\pi$
$402$	4.63620	0.231232
$403$	−8.63238	−0.430010
$404$	4.33237	0.215544
$405$	−15.7520	−0.782721
$406$	8.51860	0.422771
$407$	16.5760	0.821641
$408$	16.1578	0.799931
$409$	21.4446	1.06037	0.530183	−	0.847884i	$-0.322123\pi$
$409$	21.4446	1.06037	0.530183	+	0.847884i	$0.322123\pi$
$410$	−0.962768	−0.0475477
$411$	41.7227	2.05803
$412$	6.52301	0.321366
$413$	−4.95068	−0.243607
$414$	52.6753	2.58885
$415$	−3.53350	−0.173453
$416$	−1.52509	−0.0747739
$417$	48.6036	2.38013
$418$	13.4258	0.656678
$419$	26.0423	1.27225	0.636124	−	0.771587i	$-0.280537\pi$
$419$	26.0423	1.27225	0.636124	+	0.771587i	$0.280537\pi$
$420$	−9.50262	−0.463680
$421$	−21.2029	−1.03337	−0.516683	−	0.856177i	$-0.672834\pi$
$421$	−21.2029	−1.03337	−0.516683	+	0.856177i	$0.672834\pi$
$422$	−14.1183	−0.687269
$423$	−31.3913	−1.52630
$424$	2.15129	0.104476
$425$	5.18894	0.251700
$426$	34.9328	1.69250
$427$	−34.1178	−1.65108
$428$	18.8417	0.910747
$429$	−14.4199	−0.696198
$430$	−11.6132	−0.560036
$431$	−33.5749	−1.61725	−0.808624	−	0.588326i	$-0.799787\pi$
$431$	−33.5749	−1.61725	−0.808624	+	0.588326i	$0.799787\pi$
$432$	−11.5100	−0.553776
$433$	11.8592	0.569915	0.284957	−	0.958540i	$-0.408021\pi$
$433$	11.8592	0.569915	0.284957	+	0.958540i	$0.408021\pi$
$434$	−17.2732	−0.829141
$435$	8.69226	0.416762
$436$	−8.10374	−0.388099
$437$	34.7816	1.66383
$438$	10.0909	0.482161
$439$	−11.3155	−0.540058	−0.270029	−	0.962852i	$-0.587033\pi$
$439$	−11.3155	−0.540058	−0.270029	+	0.962852i	$0.587033\pi$
$440$	3.03641	0.144755
$441$	15.4870	0.737478
$442$	−7.91362	−0.376413
$443$	−2.15593	−0.102431	−0.0512156	−	0.998688i	$-0.516310\pi$
$443$	−2.15593	−0.102431	−0.0512156	+	0.998688i	$0.516310\pi$
$444$	−16.9990	−0.806735
$445$	−7.76068	−0.367891
$446$	−2.21025	−0.104658
$447$	−14.0114	−0.662716
$448$	−3.05168	−0.144178
$449$	−16.4122	−0.774541	−0.387271	−	0.921966i	$-0.626582\pi$
$449$	−16.4122	−0.774541	−0.387271	+	0.921966i	$0.626582\pi$
$450$	−6.69634	−0.315669
$451$	−2.92336	−0.137656
$452$	−0.487275	−0.0229195
$453$	−65.7530	−3.08935
$454$	4.18462	0.196394
$455$	4.65410	0.218188
$456$	−13.7684	−0.644765
$457$	21.5797	1.00946	0.504729	−	0.863278i	$-0.331593\pi$
$457$	21.5797	1.00946	0.504729	+	0.863278i	$0.331593\pi$
$458$	6.56119	0.306584
$459$	−59.7248	−2.78771
$460$	7.86628	0.366767
$461$	−22.9489	−1.06884	−0.534418	−	0.845220i	$-0.679469\pi$
$461$	−22.9489	−1.06884	−0.534418	+	0.845220i	$0.679469\pi$
$462$	−28.8539	−1.34240
$463$	−6.25184	−0.290548	−0.145274	−	0.989391i	$-0.546406\pi$
$463$	−6.25184	−0.290548	−0.145274	+	0.989391i	$0.546406\pi$
$464$	2.79144	0.129590
$465$	−17.6254	−0.817356
$466$	13.3894	0.620250
$467$	−0.257659	−0.0119230	−0.00596152	−	0.999982i	$-0.501898\pi$
$467$	−0.257659	−0.0119230	−0.00596152	+	0.999982i	$0.501898\pi$
$468$	10.2126	0.472075
$469$	−4.54357	−0.209802
$470$	−4.68782	−0.216233
$471$	27.6060	1.27202
$472$	−1.62228	−0.0746714
$473$	−35.2623	−1.62136
$474$	23.7339	1.09014
$475$	−4.42160	−0.202877
$476$	−15.8350	−0.725795
$477$	−14.4058	−0.659595
$478$	9.83452	0.449821
$479$	22.4630	1.02636	0.513181	−	0.858281i	$-0.328467\pi$
$479$	22.4630	1.02636	0.513181	+	0.858281i	$0.328467\pi$
$480$	−3.11389	−0.142129
$481$	8.32559	0.379614
$482$	−10.3124	−0.469719
$483$	−74.7503	−3.40125
$484$	−1.78020	−0.0809184
$485$	3.64962	0.165721
$486$	14.5199	0.658636
$487$	6.66885	0.302195	0.151097	−	0.988519i	$-0.451719\pi$
$487$	6.66885	0.302195	0.151097	+	0.988519i	$0.451719\pi$
$488$	−11.1800	−0.506095
$489$	−21.0170	−0.950422
$490$	2.31276	0.104480
$491$	−16.2477	−0.733250	−0.366625	−	0.930369i	$-0.619487\pi$
$491$	−16.2477	−0.733250	−0.366625	+	0.930369i	$0.619487\pi$
$492$	2.99796	0.135158
$493$	14.4846	0.652355
$494$	6.74336	0.303398
$495$	−20.3328	−0.913894
$496$	−5.66023	−0.254152
$497$	−34.2349	−1.53564
$498$	11.0030	0.493054
$499$	−24.9975	−1.11904	−0.559522	−	0.828816i	$-0.689015\pi$
$499$	−24.9975	−1.11904	−0.559522	+	0.828816i	$0.689015\pi$
$500$	−1.00000	−0.0447214
$501$	9.61571	0.429598
$502$	−11.2407	−0.501698
$503$	−16.5200	−0.736593	−0.368296	−	0.929708i	$-0.620059\pi$
$503$	−16.5200	−0.736593	−0.368296	+	0.929708i	$0.620059\pi$
$504$	20.4351	0.910252
$505$	−4.33237	−0.192788
$506$	23.8853	1.06183
$507$	33.2380	1.47615
$508$	11.5898	0.514216
$509$	−27.2353	−1.20718	−0.603592	−	0.797293i	$-0.706264\pi$
$509$	−27.2353	−1.20718	−0.603592	+	0.797293i	$0.706264\pi$
$510$	−16.1578	−0.715480
$511$	−9.88928	−0.437476
$512$	−1.00000	−0.0441942
$513$	50.8927	2.24697
$514$	13.2150	0.582889
$515$	−6.52301	−0.287438
$516$	36.1622	1.59195
$517$	−14.2342	−0.626018
$518$	16.6593	0.731969
$519$	6.45510	0.283348
$520$	1.52509	0.0668798
$521$	−23.8136	−1.04329	−0.521646	−	0.853162i	$-0.674682\pi$
$521$	−23.8136	−1.04329	−0.521646	+	0.853162i	$0.674682\pi$
$522$	−18.6925	−0.818147
$523$	−16.6433	−0.727762	−0.363881	−	0.931445i	$-0.618548\pi$
$523$	−16.6433	−0.727762	−0.363881	+	0.931445i	$0.618548\pi$
$524$	−16.6960	−0.729368
$525$	9.50262	0.414728
$526$	0.522463	0.0227805
$527$	−29.3706	−1.27940
$528$	−9.45507	−0.411479
$529$	38.8784	1.69036
$530$	−2.15129	−0.0934461
$531$	10.8633	0.471428
$532$	13.4933	0.585010
$533$	−1.46831	−0.0635997
$534$	24.1659	1.04576
$535$	−18.8417	−0.814597
$536$	−1.48887	−0.0643095
$537$	−48.6677	−2.10016
$538$	−1.18439	−0.0510627
$539$	7.02250	0.302480
$540$	11.5100	0.495312
$541$	36.0772	1.55108	0.775539	−	0.631299i	$-0.217478\pi$
$541$	36.0772	1.55108	0.775539	+	0.631299i	$0.217478\pi$
$542$	10.0822	0.433066
$543$	75.9486	3.25927
$544$	−5.18894	−0.222474
$545$	8.10374	0.347126
$546$	−14.4924	−0.620217
$547$	−10.1833	−0.435405	−0.217703	−	0.976015i	$-0.569856\pi$
$547$	−10.1833	−0.435405	−0.217703	+	0.976015i	$0.569856\pi$
$548$	−13.3989	−0.572372
$549$	74.8652	3.19517
$550$	−3.03641	−0.129473
$551$	−12.3427	−0.525815
$552$	−24.4948	−1.04257
$553$	−23.2598	−0.989106
$554$	2.16686	0.0920612
$555$	16.9990	0.721566
$556$	−15.6086	−0.661953
$557$	−7.75670	−0.328662	−0.164331	−	0.986405i	$-0.552546\pi$
$557$	−7.75670	−0.328662	−0.164331	+	0.986405i	$0.552546\pi$
$558$	37.9028	1.60455
$559$	−17.7112	−0.749103
$560$	3.05168	0.128957
$561$	−49.0618	−2.07139
$562$	−2.77037	−0.116861
$563$	−8.81866	−0.371662	−0.185831	−	0.982582i	$-0.559498\pi$
$563$	−8.81866	−0.371662	−0.185831	+	0.982582i	$0.559498\pi$
$564$	14.5974	0.614661
$565$	0.487275	0.0204998
$566$	−21.4203	−0.900361
$567$	−48.0700	−2.01875
$568$	−11.2184	−0.470712
$569$	−5.57474	−0.233705	−0.116853	−	0.993149i	$-0.537281\pi$
$569$	−5.57474	−0.233705	−0.116853	+	0.993149i	$0.537281\pi$
$570$	13.7684	0.576695
$571$	−15.9962	−0.669419	−0.334709	−	0.942321i	$-0.608638\pi$
$571$	−15.9962	−0.669419	−0.334709	+	0.942321i	$0.608638\pi$
$572$	4.63081	0.193624
$573$	−49.0045	−2.04719
$574$	−2.93806	−0.122632
$575$	−7.86628	−0.328047
$576$	6.69634	0.279014
$577$	41.2420	1.71693	0.858463	−	0.512876i	$-0.171420\pi$
$577$	41.2420	1.71693	0.858463	+	0.512876i	$0.171420\pi$
$578$	−9.92508	−0.412829
$579$	−0.975482	−0.0405397
$580$	−2.79144	−0.115908
$581$	−10.7831	−0.447359
$582$	−11.3645	−0.471075
$583$	−6.53220	−0.270536
$584$	−3.24060	−0.134097
$585$	−10.2126	−0.422237
$586$	13.9614	0.576742
$587$	−9.37970	−0.387142	−0.193571	−	0.981086i	$-0.562007\pi$
$587$	−9.37970	−0.387142	−0.193571	+	0.981086i	$0.562007\pi$
$588$	−7.20170	−0.296993
$589$	25.0273	1.03123
$590$	1.62228	0.0667881
$591$	−30.1787	−1.24138
$592$	5.45907	0.224366
$593$	−10.6654	−0.437977	−0.218988	−	0.975727i	$-0.570276\pi$
$593$	−10.6654	−0.437977	−0.218988	+	0.975727i	$0.570276\pi$
$594$	34.9492	1.43398
$595$	15.8350	0.649171
$596$	4.49963	0.184312
$597$	−54.5362	−2.23202
$598$	11.9968	0.490587
$599$	25.8228	1.05509	0.527545	−	0.849527i	$-0.323113\pi$
$599$	25.8228	1.05509	0.527545	+	0.849527i	$0.323113\pi$
$600$	3.11389	0.127124
$601$	−1.00000	−0.0407909
$601$	−1.00000	−0.0407909
$602$	−35.4397	−1.44441
$603$	9.97000	0.406010
$604$	21.1160	0.859198
$605$	1.78020	0.0723756
$606$	13.4905	0.548016
$607$	29.5652	1.20002	0.600008	−	0.799994i	$-0.295164\pi$
$607$	29.5652	1.20002	0.600008	+	0.799994i	$0.295164\pi$
$608$	4.42160	0.179320
$609$	26.5260	1.07489
$610$	11.1800	0.452665
$611$	−7.14937	−0.289233
$612$	34.7469	1.40456
$613$	8.84452	0.357227	0.178613	−	0.983919i	$-0.442839\pi$
$613$	8.84452	0.357227	0.178613	+	0.983919i	$0.442839\pi$
$614$	25.4003	1.02507
$615$	−2.99796	−0.120889
$616$	9.26616	0.373344
$617$	28.1492	1.13325	0.566623	−	0.823977i	$-0.308250\pi$
$617$	28.1492	1.13325	0.566623	+	0.823977i	$0.308250\pi$
$618$	20.3120	0.817067
$619$	−26.3966	−1.06097	−0.530485	−	0.847694i	$-0.677990\pi$
$619$	−26.3966	−1.06097	−0.530485	+	0.847694i	$0.677990\pi$
$620$	5.66023	0.227320
$621$	90.5410	3.63329
$622$	34.0918	1.36696
$623$	−23.6831	−0.948844
$624$	−4.74898	−0.190112
$625$	1.00000	0.0400000
$626$	7.46478	0.298352
$627$	41.8065	1.66959
$628$	−8.86543	−0.353769
$629$	28.3268	1.12946
$630$	−20.4351	−0.814154
$631$	−19.1369	−0.761827	−0.380913	−	0.924611i	$-0.624390\pi$
$631$	−19.1369	−0.761827	−0.380913	+	0.924611i	$0.624390\pi$
$632$	−7.62195	−0.303185
$633$	−43.9630	−1.74737
$634$	−1.76061	−0.0699229
$635$	−11.5898	−0.459929
$636$	6.69889	0.265628
$637$	3.52718	0.139752
$638$	−8.47597	−0.335567
$639$	75.1220	2.97178
$640$	1.00000	0.0395285
$641$	−35.8007	−1.41404	−0.707022	−	0.707191i	$-0.749962\pi$
$641$	−35.8007	−1.41404	−0.707022	+	0.707191i	$0.749962\pi$
$642$	58.6710	2.31556
$643$	20.7021	0.816413	0.408206	−	0.912890i	$-0.366154\pi$
$643$	20.7021	0.816413	0.408206	+	0.912890i	$0.366154\pi$
$644$	24.0054	0.945945
$645$	−36.1622	−1.42388
$646$	22.9434	0.902697
$647$	3.76074	0.147850	0.0739249	−	0.997264i	$-0.476447\pi$
$647$	3.76074	0.147850	0.0739249	+	0.997264i	$0.476447\pi$
$648$	−15.7520	−0.618796
$649$	4.92590	0.193359
$650$	−1.52509	−0.0598191
$651$	−53.7870	−2.10808
$652$	6.74943	0.264328
$653$	−49.6598	−1.94334	−0.971670	−	0.236344i	$-0.924051\pi$
$653$	−49.6598	−1.94334	−0.971670	+	0.236344i	$0.924051\pi$
$654$	−25.2342	−0.986736
$655$	16.6960	0.652366
$656$	−0.962768	−0.0375898
$657$	21.7002	0.846604
$658$	−14.3057	−0.557696
$659$	−23.4168	−0.912188	−0.456094	−	0.889932i	$-0.650752\pi$
$659$	−23.4168	−0.912188	−0.456094	+	0.889932i	$0.650752\pi$
$660$	9.45507	0.368038
$661$	−35.1267	−1.36627	−0.683136	−	0.730291i	$-0.739384\pi$
$661$	−35.1267	−1.36627	−0.683136	+	0.730291i	$0.739384\pi$
$662$	−24.9456	−0.969538
$663$	−24.6422	−0.957023
$664$	−3.53350	−0.137126
$665$	−13.4933	−0.523249
$666$	−36.5558	−1.41651
$667$	−21.9583	−0.850228
$668$	−3.08800	−0.119478
$669$	−6.88247	−0.266092
$670$	1.48887	0.0575202
$671$	33.9471	1.31051
$672$	−9.50262	−0.366571
$673$	21.6168	0.833265	0.416632	−	0.909075i	$-0.363210\pi$
$673$	21.6168	0.833265	0.416632	+	0.909075i	$0.363210\pi$
$674$	−30.4486	−1.17284
$675$	−11.5100	−0.443021
$676$	−10.6741	−0.410542
$677$	−14.3735	−0.552417	−0.276209	−	0.961098i	$-0.589078\pi$
$677$	−14.3735	−0.552417	−0.276209	+	0.961098i	$0.589078\pi$
$678$	−1.51732	−0.0582724
$679$	11.1375	0.427417
$680$	5.18894	0.198987
$681$	13.0305	0.499328
$682$	17.1868	0.658116
$683$	23.2485	0.889579	0.444789	−	0.895635i	$-0.353279\pi$
$683$	23.2485	0.889579	0.444789	+	0.895635i	$0.353279\pi$
$684$	−29.6086	−1.13211
$685$	13.3989	0.511945
$686$	−14.3040	−0.546128
$687$	20.4309	0.779486
$688$	−11.6132	−0.442748
$689$	−3.28092	−0.124993
$690$	24.4948	0.932500
$691$	14.8058	0.563239	0.281619	−	0.959526i	$-0.409128\pi$
$691$	14.8058	0.563239	0.281619	+	0.959526i	$0.409128\pi$
$692$	−2.07300	−0.0788036
$693$	−62.0494	−2.35706
$694$	4.12814	0.156702
$695$	15.6086	0.592069
$696$	8.69226	0.329479
$697$	−4.99575	−0.189227
$698$	−13.7809	−0.521616
$699$	41.6930	1.57698
$700$	−3.05168	−0.115343
$701$	1.93740	0.0731746	0.0365873	−	0.999330i	$-0.488351\pi$
$701$	1.93740	0.0731746	0.0365873	+	0.999330i	$0.488351\pi$
$702$	17.5539	0.662528
$703$	−24.1378	−0.910375
$704$	3.03641	0.114439
$705$	−14.5974	−0.549770
$706$	2.84376	0.107026
$707$	−13.2210	−0.497228
$708$	−5.05160	−0.189851
$709$	−24.1375	−0.906504	−0.453252	−	0.891382i	$-0.649736\pi$
$709$	−24.1375	−0.906504	−0.453252	+	0.891382i	$0.649736\pi$
$710$	11.2184	0.421017
$711$	51.0392	1.91412
$712$	−7.76068	−0.290844
$713$	44.5250	1.66747
$714$	−49.3085	−1.84532
$715$	−4.63081	−0.173183
$716$	15.6292	0.584090
$717$	30.6237	1.14366
$718$	−27.7643	−1.03615
$719$	2.00883	0.0749167	0.0374583	−	0.999298i	$-0.488074\pi$
$719$	2.00883	0.0749167	0.0374583	+	0.999298i	$0.488074\pi$
$720$	−6.69634	−0.249558
$721$	−19.9062	−0.741344
$722$	−0.550570	−0.0204901
$723$	−32.1118	−1.19425
$724$	−24.3902	−0.906456
$725$	2.79144	0.103672
$726$	−5.54337	−0.205734
$727$	47.6473	1.76714	0.883570	−	0.468299i	$-0.155133\pi$
$727$	47.6473	1.76714	0.883570	+	0.468299i	$0.155133\pi$
$728$	4.65410	0.172493
$729$	−2.04243	−0.0756457
$730$	3.24060	0.119940
$731$	−60.2600	−2.22880
$732$	−34.8134	−1.28674
$733$	−6.81908	−0.251868	−0.125934	−	0.992039i	$-0.540193\pi$
$733$	−6.81908	−0.251868	−0.125934	+	0.992039i	$0.540193\pi$
$734$	−0.758073	−0.0279810
$735$	7.20170	0.265639
$736$	7.86628	0.289955
$737$	4.52083	0.166527
$738$	6.44703	0.237318
$739$	−6.86791	−0.252640	−0.126320	−	0.991990i	$-0.540317\pi$
$739$	−6.86791	−0.252640	−0.126320	+	0.991990i	$0.540317\pi$
$740$	−5.45907	−0.200679
$741$	20.9981	0.771385
$742$	−6.56505	−0.241011
$743$	−1.44478	−0.0530038	−0.0265019	−	0.999649i	$-0.508437\pi$
$743$	−1.44478	−0.0530038	−0.0265019	+	0.999649i	$0.508437\pi$
$744$	−17.6254	−0.646177
$745$	−4.49963	−0.164854
$746$	34.9450	1.27943
$747$	23.6615	0.865730
$748$	15.7558	0.576087
$749$	−57.4988	−2.10096
$750$	−3.11389	−0.113703
$751$	−5.42653	−0.198017	−0.0990084	−	0.995087i	$-0.531567\pi$
$751$	−5.42653	−0.198017	−0.0990084	+	0.995087i	$0.531567\pi$
$752$	−4.68782	−0.170947
$753$	−35.0025	−1.27556
$754$	−4.25722	−0.155039
$755$	−21.1160	−0.768490
$756$	35.1249	1.27748
$757$	16.8701	0.613155	0.306577	−	0.951846i	$-0.400816\pi$
$757$	16.8701	0.613155	0.306577	+	0.951846i	$0.400816\pi$
$758$	12.2273	0.444115
$759$	74.3762	2.69969
$760$	−4.42160	−0.160388
$761$	−12.2691	−0.444756	−0.222378	−	0.974961i	$-0.571382\pi$
$761$	−12.2691	−0.444756	−0.222378	+	0.974961i	$0.571382\pi$
$762$	36.0896	1.30739
$763$	24.7300	0.895288
$764$	15.7373	0.569357
$765$	−34.7469	−1.25628
$766$	−18.5742	−0.671114
$767$	2.47413	0.0893356
$768$	−3.11389	−0.112363
$769$	−0.894458	−0.0322550	−0.0161275	−	0.999870i	$-0.505134\pi$
$769$	−0.894458	−0.0322550	−0.0161275	+	0.999870i	$0.505134\pi$
$770$	−9.26616	−0.333929
$771$	41.1501	1.48199
$772$	0.313268	0.0112747
$773$	−51.0492	−1.83611	−0.918056	−	0.396451i	$-0.870242\pi$
$773$	−51.0492	−1.83611	−0.918056	+	0.396451i	$0.870242\pi$
$774$	77.7657	2.79523
$775$	−5.66023	−0.203321
$776$	3.64962	0.131014
$777$	51.8754	1.86102
$778$	18.8720	0.676596
$779$	4.25698	0.152522
$780$	4.74898	0.170041
$781$	34.0636	1.21889
$782$	40.8176	1.45964
$783$	−32.1296	−1.14822
$784$	2.31276	0.0825987
$785$	8.86543	0.316421
$786$	−51.9895	−1.85441
$787$	−24.6305	−0.877981	−0.438991	−	0.898492i	$-0.644664\pi$
$787$	−24.6305	−0.877981	−0.438991	+	0.898492i	$0.644664\pi$
$788$	9.69161	0.345249
$789$	1.62689	0.0579189
$790$	7.62195	0.271177
$791$	1.48701	0.0528719
$792$	−20.3328	−0.722496
$793$	17.0506	0.605484
$794$	−30.9692	−1.09905
$795$	−6.69889	−0.237585
$796$	17.5138	0.620761
$797$	21.8848	0.775199	0.387599	−	0.921828i	$-0.373304\pi$
$797$	21.8848	0.775199	0.387599	+	0.921828i	$0.373304\pi$
$798$	42.0168	1.48738
$799$	−24.3248	−0.860551
$800$	−1.00000	−0.0353553
$801$	51.9682	1.83620
$802$	37.6775	1.33044
$803$	9.83979	0.347239
$804$	−4.63620	−0.163506
$805$	−24.0054	−0.846079
$806$	8.63238	0.304063
$807$	−3.68807	−0.129826
$808$	−4.33237	−0.152412
$809$	−31.0885	−1.09301	−0.546507	−	0.837455i	$-0.684043\pi$
$809$	−31.0885	−1.09301	−0.546507	+	0.837455i	$0.684043\pi$
$810$	15.7520	0.553468
$811$	−26.6461	−0.935670	−0.467835	−	0.883816i	$-0.654966\pi$
$811$	−26.6461	−0.935670	−0.467835	+	0.883816i	$0.654966\pi$
$812$	−8.51860	−0.298944
$813$	31.3948	1.10106
$814$	−16.5760	−0.580988
$815$	−6.74943	−0.236422
$816$	−16.1578	−0.565636
$817$	51.3488	1.79647
$818$	−21.4446	−0.749791
$819$	−31.1655	−1.08901
$820$	0.962768	0.0336213
$821$	−20.9152	−0.729946	−0.364973	−	0.931018i	$-0.618922\pi$
$821$	−20.9152	−0.729946	−0.364973	+	0.931018i	$0.618922\pi$
$822$	−41.7227	−1.45525
$823$	−42.0449	−1.46559	−0.732796	−	0.680448i	$-0.761785\pi$
$823$	−42.0449	−1.46559	−0.732796	+	0.680448i	$0.761785\pi$
$824$	−6.52301	−0.227240
$825$	−9.45507	−0.329183
$826$	4.95068	0.172256
$827$	−39.1409	−1.36106	−0.680530	−	0.732720i	$-0.738251\pi$
$827$	−39.1409	−1.36106	−0.680530	+	0.732720i	$0.738251\pi$
$828$	−52.6753	−1.83059
$829$	−24.1727	−0.839553	−0.419777	−	0.907627i	$-0.637892\pi$
$829$	−24.1727	−0.839553	−0.419777	+	0.907627i	$0.637892\pi$
$830$	3.53350	0.122650
$831$	6.74739	0.234064
$832$	1.52509	0.0528731
$833$	12.0008	0.415802
$834$	−48.6036	−1.68300
$835$	3.08800	0.106865
$836$	−13.4258	−0.464341
$837$	65.1493	2.25189
$838$	−26.0423	−0.899616
$839$	−28.5400	−0.985311	−0.492655	−	0.870225i	$-0.663974\pi$
$839$	−28.5400	−0.985311	−0.492655	+	0.870225i	$0.663974\pi$
$840$	9.50262	0.327871
$841$	−21.2078	−0.731305
$842$	21.2029	0.730701
$843$	−8.62665	−0.297118
$844$	14.1183	0.485973
$845$	10.6741	0.367200
$846$	31.3913	1.07925
$847$	5.43262	0.186667
$848$	−2.15129	−0.0738756
$849$	−66.7005	−2.28915
$850$	−5.18894	−0.177979
$851$	−42.9426	−1.47205
$852$	−34.9328	−1.19678
$853$	−50.5926	−1.73226	−0.866129	−	0.499821i	$-0.833399\pi$
$853$	−50.5926	−1.73226	−0.866129	+	0.499821i	$0.833399\pi$
$854$	34.1178	1.16749
$855$	29.6086	1.01259
$856$	−18.8417	−0.643996
$857$	−26.4827	−0.904633	−0.452317	−	0.891857i	$-0.649402\pi$
$857$	−26.4827	−0.904633	−0.452317	+	0.891857i	$0.649402\pi$
$858$	14.4199	0.492286
$859$	−9.85294	−0.336178	−0.168089	−	0.985772i	$-0.553760\pi$
$859$	−9.85294	−0.336178	−0.168089	+	0.985772i	$0.553760\pi$
$860$	11.6132	0.396005
$861$	−9.14882	−0.311791
$862$	33.5749	1.14357
$863$	−35.6758	−1.21442	−0.607210	−	0.794542i	$-0.707711\pi$
$863$	−35.6758	−1.21442	−0.607210	+	0.794542i	$0.707711\pi$
$864$	11.5100	0.391579
$865$	2.07300	0.0704841
$866$	−11.8592	−0.402991
$867$	−30.9057	−1.04961
$868$	17.2732	0.586291
$869$	23.1434	0.785085
$870$	−8.69226	−0.294695
$871$	2.27067	0.0769388
$872$	8.10374	0.274427
$873$	−24.4391	−0.827139
$874$	−34.7816	−1.17650
$875$	3.05168	0.103166
$876$	−10.0909	−0.340939
$877$	33.9943	1.14790	0.573952	−	0.818889i	$-0.305409\pi$
$877$	33.9943	1.14790	0.573952	+	0.818889i	$0.305409\pi$
$878$	11.3155	0.381879
$879$	43.4744	1.46636
$880$	−3.03641	−0.102357
$881$	−49.2209	−1.65829	−0.829146	−	0.559032i	$-0.811173\pi$
$881$	−49.2209	−1.65829	−0.829146	+	0.559032i	$0.811173\pi$
$882$	−15.4870	−0.521476
$883$	−43.1438	−1.45190	−0.725952	−	0.687745i	$-0.758601\pi$
$883$	−43.1438	−1.45190	−0.725952	+	0.687745i	$0.758601\pi$
$884$	7.91362	0.266164
$885$	5.05160	0.169808
$886$	2.15593	0.0724299
$887$	−0.532101	−0.0178662	−0.00893310	−	0.999960i	$-0.502844\pi$
$887$	−0.532101	−0.0178662	−0.00893310	+	0.999960i	$0.502844\pi$
$888$	16.9990	0.570448
$889$	−35.3685	−1.18622
$890$	7.76068	0.260139
$891$	47.8294	1.60235
$892$	2.21025	0.0740045
$893$	20.7277	0.693626
$894$	14.0114	0.468611
$895$	−15.6292	−0.522426
$896$	3.05168	0.101950
$897$	37.3568	1.24731
$898$	16.4122	0.547683
$899$	−15.8002	−0.526967
$900$	6.69634	0.223211
$901$	−11.1629	−0.371891
$902$	2.92336	0.0973373
$903$	−110.355	−3.67240
$904$	0.487275	0.0162065
$905$	24.3902	0.810759
$906$	65.7530	2.18450
$907$	40.3906	1.34115	0.670574	−	0.741843i	$-0.266048\pi$
$907$	40.3906	1.34115	0.670574	+	0.741843i	$0.266048\pi$
$908$	−4.18462	−0.138871
$909$	29.0110	0.962235
$910$	−4.65410	−0.154282
$911$	10.5820	0.350598	0.175299	−	0.984515i	$-0.443911\pi$
$911$	10.5820	0.350598	0.175299	+	0.984515i	$0.443911\pi$
$912$	13.7684	0.455917
$913$	10.7292	0.355084
$914$	−21.5797	−0.713794
$915$	34.8134	1.15089
$916$	−6.56119	−0.216788
$917$	50.9508	1.68254
$918$	59.7248	1.97121
$919$	−29.0266	−0.957498	−0.478749	−	0.877952i	$-0.658910\pi$
$919$	−29.0266	−0.957498	−0.478749	+	0.877952i	$0.658910\pi$
$920$	−7.86628	−0.259344
$921$	79.0940	2.60623
$922$	22.9489	0.755781
$923$	17.1091	0.563151
$924$	28.8539	0.949222
$925$	5.45907	0.179493
$926$	6.25184	0.205448
$927$	43.6803	1.43465
$928$	−2.79144	−0.0916336
$929$	37.3335	1.22487	0.612435	−	0.790521i	$-0.290190\pi$
$929$	37.3335	1.22487	0.612435	+	0.790521i	$0.290190\pi$
$930$	17.6254	0.577958
$931$	−10.2261	−0.335147
$932$	−13.3894	−0.438583
$933$	106.158	3.47547
$934$	0.257659	0.00843086
$935$	−15.7558	−0.515268
$936$	−10.2126	−0.333808
$937$	−1.06504	−0.0347934	−0.0173967	−	0.999849i	$-0.505538\pi$
$937$	−1.06504	−0.0347934	−0.0173967	+	0.999849i	$0.505538\pi$
$938$	4.54357	0.148353
$939$	23.2445	0.758556
$940$	4.68782	0.152900
$941$	−54.9883	−1.79257	−0.896284	−	0.443480i	$-0.853744\pi$
$941$	−54.9883	−1.79257	−0.896284	+	0.443480i	$0.853744\pi$
$942$	−27.6060	−0.899453
$943$	7.57341	0.246624
$944$	1.62228	0.0528007
$945$	−35.1249	−1.14261
$946$	35.2623	1.14648
$947$	−29.2251	−0.949689	−0.474845	−	0.880070i	$-0.657496\pi$
$947$	−29.2251	−0.949689	−0.474845	+	0.880070i	$0.657496\pi$
$948$	−23.7339	−0.770843
$949$	4.94222	0.160431
$950$	4.42160	0.143456
$951$	−5.48236	−0.177778
$952$	15.8350	0.513215
$953$	25.5187	0.826630	0.413315	−	0.910588i	$-0.364371\pi$
$953$	25.5187	0.826630	0.413315	+	0.910588i	$0.364371\pi$
$954$	14.4058	0.466404
$955$	−15.7373	−0.509249
$956$	−9.83452	−0.318071
$957$	−26.3933	−0.853174
$958$	−22.4630	−0.725747
$959$	40.8892	1.32038
$960$	3.11389	0.100501
$961$	1.03819	0.0334901
$962$	−8.32559	−0.268428
$963$	126.170	4.06578
$964$	10.3124	0.332141
$965$	−0.313268	−0.0100844
$966$	74.7503	2.40505
$967$	41.5054	1.33472	0.667361	−	0.744734i	$-0.267424\pi$
$967$	41.5054	1.33472	0.667361	+	0.744734i	$0.267424\pi$
$968$	1.78020	0.0572179
$969$	71.4434	2.29509
$970$	−3.64962	−0.117182
$971$	−16.7560	−0.537726	−0.268863	−	0.963178i	$-0.586648\pi$
$971$	−16.7560	−0.537726	−0.268863	+	0.963178i	$0.586648\pi$
$972$	−14.5199	−0.465726
$973$	47.6325	1.52703
$974$	−6.66885	−0.213684
$975$	−4.74898	−0.152089
$976$	11.1800	0.357863
$977$	13.7858	0.441047	0.220524	−	0.975382i	$-0.429223\pi$
$977$	13.7858	0.441047	0.220524	+	0.975382i	$0.429223\pi$
$978$	21.0170	0.672050
$979$	23.5646	0.753128
$980$	−2.31276	−0.0738785
$981$	−54.2654	−1.73256
$982$	16.2477	0.518486
$983$	33.3158	1.06261	0.531304	−	0.847181i	$-0.321702\pi$
$983$	33.3158	1.06261	0.531304	+	0.847181i	$0.321702\pi$
$984$	−2.99796	−0.0955715
$985$	−9.69161	−0.308800
$986$	−14.4846	−0.461285
$987$	−44.5466	−1.41793
$988$	−6.74336	−0.214535
$989$	91.3524	2.90484
$990$	20.3328	0.646220
$991$	−37.7936	−1.20055	−0.600276	−	0.799793i	$-0.704943\pi$
$991$	−37.7936	−1.20055	−0.600276	+	0.799793i	$0.704943\pi$
$992$	5.66023	0.179712
$993$	−77.6780	−2.46504
$994$	34.2349	1.08586
$995$	−17.5138	−0.555225
$996$	−11.0030	−0.348642
$997$	−29.1884	−0.924404	−0.462202	−	0.886775i	$-0.652941\pi$
$997$	−29.1884	−0.924404	−0.462202	+	0.886775i	$0.652941\pi$
$998$	24.9975	0.791284
$999$	−62.8340	−1.98798

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6010.2.a.i.1.4	✓	29

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6010.2.a.i.1.4	✓	29	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:	\( N \)	\(=\)	\( 6010 = 2 \cdot 5 \cdot 601 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6010.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -3.11389 q^{3} +1.00000 q^{4} -1.00000 q^{5} +3.11389 q^{6} -3.05168 q^{7} -1.00000 q^{8} +6.69634 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -3.11389 q^{3} +1.00000 q^{4} -1.00000 q^{5} +3.11389 q^{6} -3.05168 q^{7} -1.00000 q^{8} +6.69634 q^{9} +1.00000 q^{10} +3.03641 q^{11} -3.11389 q^{12} +1.52509 q^{13} +3.05168 q^{14} +3.11389 q^{15} +1.00000 q^{16} +5.18894 q^{17} -6.69634 q^{18} -4.42160 q^{19} -1.00000 q^{20} +9.50262 q^{21} -3.03641 q^{22} -7.86628 q^{23} +3.11389 q^{24} +1.00000 q^{25} -1.52509 q^{26} -11.5100 q^{27} -3.05168 q^{28} +2.79144 q^{29} -3.11389 q^{30} -5.66023 q^{31} -1.00000 q^{32} -9.45507 q^{33} -5.18894 q^{34} +3.05168 q^{35} +6.69634 q^{36} +5.45907 q^{37} +4.42160 q^{38} -4.74898 q^{39} +1.00000 q^{40} -0.962768 q^{41} -9.50262 q^{42} -11.6132 q^{43} +3.03641 q^{44} -6.69634 q^{45} +7.86628 q^{46} -4.68782 q^{47} -3.11389 q^{48} +2.31276 q^{49} -1.00000 q^{50} -16.1578 q^{51} +1.52509 q^{52} -2.15129 q^{53} +11.5100 q^{54} -3.03641 q^{55} +3.05168 q^{56} +13.7684 q^{57} -2.79144 q^{58} +1.62228 q^{59} +3.11389 q^{60} +11.1800 q^{61} +5.66023 q^{62} -20.4351 q^{63} +1.00000 q^{64} -1.52509 q^{65} +9.45507 q^{66} +1.48887 q^{67} +5.18894 q^{68} +24.4948 q^{69} -3.05168 q^{70} +11.2184 q^{71} -6.69634 q^{72} +3.24060 q^{73} -5.45907 q^{74} -3.11389 q^{75} -4.42160 q^{76} -9.26616 q^{77} +4.74898 q^{78} +7.62195 q^{79} -1.00000 q^{80} +15.7520 q^{81} +0.962768 q^{82} +3.53350 q^{83} +9.50262 q^{84} -5.18894 q^{85} +11.6132 q^{86} -8.69226 q^{87} -3.03641 q^{88} +7.76068 q^{89} +6.69634 q^{90} -4.65410 q^{91} -7.86628 q^{92} +17.6254 q^{93} +4.68782 q^{94} +4.42160 q^{95} +3.11389 q^{96} -3.64962 q^{97} -2.31276 q^{98} +20.3328 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 29 q - 29 q^{2} - 10 q^{3} + 29 q^{4} - 29 q^{5} + 10 q^{6} - 29 q^{8} + 29 q^{9}+O(q^{10}) \) 29 * q - 29 * q^2 - 10 * q^3 + 29 * q^4 - 29 * q^5 + 10 * q^6 - 29 * q^8 + 29 * q^9	\( 29 q - 29 q^{2} - 10 q^{3} + 29 q^{4} - 29 q^{5} + 10 q^{6} - 29 q^{8} + 29 q^{9} + 29 q^{10} - 10 q^{12} - 4 q^{13} + 10 q^{15} + 29 q^{16} - 23 q^{17} - 29 q^{18} + q^{19} - 29 q^{20} + 2 q^{21} - 9 q^{23} + 10 q^{24} + 29 q^{25} + 4 q^{26} - 43 q^{27} - 5 q^{29} - 10 q^{30} + 21 q^{31} - 29 q^{32} - 19 q^{33} + 23 q^{34} + 29 q^{36} - 6 q^{37} - q^{38} + 18 q^{39} + 29 q^{40} - 17 q^{41} - 2 q^{42} - 19 q^{43} - 29 q^{45} + 9 q^{46} - 21 q^{47} - 10 q^{48} + 45 q^{49} - 29 q^{50} + 11 q^{51} - 4 q^{52} - 53 q^{53} + 43 q^{54} - 16 q^{57} + 5 q^{58} - 30 q^{59} + 10 q^{60} + 16 q^{61} - 21 q^{62} - 17 q^{63} + 29 q^{64} + 4 q^{65} + 19 q^{66} - 35 q^{67} - 23 q^{68} + 13 q^{69} + 2 q^{71} - 29 q^{72} - q^{73} + 6 q^{74} - 10 q^{75} + q^{76} - 50 q^{77} - 18 q^{78} + 26 q^{79} - 29 q^{80} + 33 q^{81} + 17 q^{82} - 54 q^{83} + 2 q^{84} + 23 q^{85} + 19 q^{86} - 56 q^{87} - 2 q^{89} + 29 q^{90} + 27 q^{91} - 9 q^{92} - 26 q^{93} + 21 q^{94} - q^{95} + 10 q^{96} + 15 q^{97} - 45 q^{98} + 27 q^{99}+O(q^{100}) \) 29 * q - 29 * q^2 - 10 * q^3 + 29 * q^4 - 29 * q^5 + 10 * q^6 - 29 * q^8 + 29 * q^9 + 29 * q^10 - 10 * q^12 - 4 * q^13 + 10 * q^15 + 29 * q^16 - 23 * q^17 - 29 * q^18 + q^19 - 29 * q^20 + 2 * q^21 - 9 * q^23 + 10 * q^24 + 29 * q^25 + 4 * q^26 - 43 * q^27 - 5 * q^29 - 10 * q^30 + 21 * q^31 - 29 * q^32 - 19 * q^33 + 23 * q^34 + 29 * q^36 - 6 * q^37 - q^38 + 18 * q^39 + 29 * q^40 - 17 * q^41 - 2 * q^42 - 19 * q^43 - 29 * q^45 + 9 * q^46 - 21 * q^47 - 10 * q^48 + 45 * q^49 - 29 * q^50 + 11 * q^51 - 4 * q^52 - 53 * q^53 + 43 * q^54 - 16 * q^57 + 5 * q^58 - 30 * q^59 + 10 * q^60 + 16 * q^61 - 21 * q^62 - 17 * q^63 + 29 * q^64 + 4 * q^65 + 19 * q^66 - 35 * q^67 - 23 * q^68 + 13 * q^69 + 2 * q^71 - 29 * q^72 - q^73 + 6 * q^74 - 10 * q^75 + q^76 - 50 * q^77 - 18 * q^78 + 26 * q^79 - 29 * q^80 + 33 * q^81 + 17 * q^82 - 54 * q^83 + 2 * q^84 + 23 * q^85 + 19 * q^86 - 56 * q^87 - 2 * q^89 + 29 * q^90 + 27 * q^91 - 9 * q^92 - 26 * q^93 + 21 * q^94 - q^95 + 10 * q^96 + 15 * q^97 - 45 * q^98 + 27 * q^99

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