LMFDB - Embedded newform 671.2.a.d.1.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [671,2,Mod(1,671)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(671, 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("671.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 671 = 11 \cdot 61 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	671.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:	$5.35796197563$
Analytic rank:	$0$
Dimension:	$21$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.18
Character	$\chi$	$=$	671.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.16302 q^{2} -0.957308 q^{3} +2.67865 q^{4} +3.42546 q^{5} -2.07068 q^{6} +1.52570 q^{7} +1.46794 q^{8} -2.08356 q^{9} +O(q^{10})$	\(q+2.16302 q^{2} -0.957308 q^{3} +2.67865 q^{4} +3.42546 q^{5} -2.07068 q^{6} +1.52570 q^{7} +1.46794 q^{8} -2.08356 q^{9} +7.40934 q^{10} -1.00000 q^{11} -2.56429 q^{12} +3.58739 q^{13} +3.30011 q^{14} -3.27922 q^{15} -2.18213 q^{16} +5.94398 q^{17} -4.50678 q^{18} -1.65639 q^{19} +9.17561 q^{20} -1.46056 q^{21} -2.16302 q^{22} -3.88910 q^{23} -1.40527 q^{24} +6.73378 q^{25} +7.75960 q^{26} +4.86653 q^{27} +4.08681 q^{28} -9.39965 q^{29} -7.09302 q^{30} -5.87279 q^{31} -7.65586 q^{32} +0.957308 q^{33} +12.8569 q^{34} +5.22621 q^{35} -5.58113 q^{36} +3.29618 q^{37} -3.58280 q^{38} -3.43424 q^{39} +5.02835 q^{40} +11.2659 q^{41} -3.15922 q^{42} +4.96645 q^{43} -2.67865 q^{44} -7.13716 q^{45} -8.41219 q^{46} +0.704770 q^{47} +2.08897 q^{48} -4.67225 q^{49} +14.5653 q^{50} -5.69022 q^{51} +9.60938 q^{52} -5.18291 q^{53} +10.5264 q^{54} -3.42546 q^{55} +2.23962 q^{56} +1.58567 q^{57} -20.3316 q^{58} -2.75436 q^{59} -8.78389 q^{60} +1.00000 q^{61} -12.7030 q^{62} -3.17888 q^{63} -12.1955 q^{64} +12.2885 q^{65} +2.07068 q^{66} +7.28569 q^{67} +15.9219 q^{68} +3.72306 q^{69} +11.3044 q^{70} -13.0352 q^{71} -3.05853 q^{72} +2.44588 q^{73} +7.12970 q^{74} -6.44630 q^{75} -4.43688 q^{76} -1.52570 q^{77} -7.42833 q^{78} -15.0610 q^{79} -7.47480 q^{80} +1.59191 q^{81} +24.3683 q^{82} -10.3614 q^{83} -3.91233 q^{84} +20.3609 q^{85} +10.7425 q^{86} +8.99835 q^{87} -1.46794 q^{88} +0.417315 q^{89} -15.4378 q^{90} +5.47327 q^{91} -10.4175 q^{92} +5.62207 q^{93} +1.52443 q^{94} -5.67389 q^{95} +7.32902 q^{96} -11.7699 q^{97} -10.1062 q^{98} +2.08356 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 21 q + 3 q^{3} + 32 q^{4} + 7 q^{5} + 5 q^{6} + 5 q^{7} - 6 q^{8} + 40 q^{9}+O(q^{10}) $ 21 * q + 3 * q^3 + 32 * q^4 + 7 * q^5 + 5 * q^6 + 5 * q^7 - 6 * q^8 + 40 * q^9	\( 21 q + 3 q^{3} + 32 q^{4} + 7 q^{5} + 5 q^{6} + 5 q^{7} - 6 q^{8} + 40 q^{9} + q^{10} - 21 q^{11} + 6 q^{12} + 20 q^{13} + 17 q^{14} + 18 q^{15} + 50 q^{16} + q^{17} - 5 q^{18} + 15 q^{19} - 2 q^{20} + 16 q^{21} + 11 q^{23} - 16 q^{24} + 48 q^{25} - 5 q^{26} + 12 q^{27} - 16 q^{28} - 9 q^{29} + 16 q^{30} + 22 q^{31} + 3 q^{32} - 3 q^{33} + 33 q^{34} - 39 q^{35} + 57 q^{36} + 21 q^{37} + 11 q^{38} - 28 q^{39} - 16 q^{40} + 7 q^{41} - 55 q^{42} + 16 q^{43} - 32 q^{44} + 44 q^{45} - 3 q^{46} + 5 q^{47} - 71 q^{48} + 80 q^{49} - 33 q^{50} - 19 q^{51} + 60 q^{52} + 9 q^{53} + 13 q^{54} - 7 q^{55} + 44 q^{56} + 39 q^{57} - 27 q^{58} + 13 q^{59} + 70 q^{60} + 21 q^{61} - 23 q^{62} + 24 q^{63} + 66 q^{64} + 25 q^{65} - 5 q^{66} + 38 q^{67} - 74 q^{68} - 17 q^{69} - 33 q^{70} + 12 q^{71} - 75 q^{72} + 20 q^{73} - 12 q^{74} - 10 q^{75} + 59 q^{76} - 5 q^{77} - 14 q^{78} + q^{79} - 38 q^{80} + 89 q^{81} + 7 q^{82} - 19 q^{83} - 14 q^{84} + 38 q^{85} - 3 q^{86} + 4 q^{87} + 6 q^{88} + 37 q^{89} - 174 q^{90} + 24 q^{91} + 31 q^{92} - 15 q^{93} - 64 q^{94} - 43 q^{95} - 38 q^{96} + 68 q^{97} - 2 q^{98} - 40 q^{99}+O(q^{100}) \) 21 * q + 3 * q^3 + 32 * q^4 + 7 * q^5 + 5 * q^6 + 5 * q^7 - 6 * q^8 + 40 * q^9 + q^10 - 21 * q^11 + 6 * q^12 + 20 * q^13 + 17 * q^14 + 18 * q^15 + 50 * q^16 + q^17 - 5 * q^18 + 15 * q^19 - 2 * q^20 + 16 * q^21 + 11 * q^23 - 16 * q^24 + 48 * q^25 - 5 * q^26 + 12 * q^27 - 16 * q^28 - 9 * q^29 + 16 * q^30 + 22 * q^31 + 3 * q^32 - 3 * q^33 + 33 * q^34 - 39 * q^35 + 57 * q^36 + 21 * q^37 + 11 * q^38 - 28 * q^39 - 16 * q^40 + 7 * q^41 - 55 * q^42 + 16 * q^43 - 32 * q^44 + 44 * q^45 - 3 * q^46 + 5 * q^47 - 71 * q^48 + 80 * q^49 - 33 * q^50 - 19 * q^51 + 60 * q^52 + 9 * q^53 + 13 * q^54 - 7 * q^55 + 44 * q^56 + 39 * q^57 - 27 * q^58 + 13 * q^59 + 70 * q^60 + 21 * q^61 - 23 * q^62 + 24 * q^63 + 66 * q^64 + 25 * q^65 - 5 * q^66 + 38 * q^67 - 74 * q^68 - 17 * q^69 - 33 * q^70 + 12 * q^71 - 75 * q^72 + 20 * q^73 - 12 * q^74 - 10 * q^75 + 59 * q^76 - 5 * q^77 - 14 * q^78 + q^79 - 38 * q^80 + 89 * q^81 + 7 * q^82 - 19 * q^83 - 14 * q^84 + 38 * q^85 - 3 * q^86 + 4 * q^87 + 6 * q^88 + 37 * q^89 - 174 * q^90 + 24 * q^91 + 31 * q^92 - 15 * q^93 - 64 * q^94 - 43 * q^95 - 38 * q^96 + 68 * q^97 - 2 * q^98 - 40 * 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 $

$2$	2.16302	1.52949	0.764743	−	0.644336i	$-0.222866\pi$
$2$	2.16302	1.52949	0.764743	+	0.644336i	$0.222866\pi$
$3$	−0.957308	−0.552702	−0.276351	−	0.961057i	$-0.589125\pi$
$3$	−0.957308	−0.552702	−0.276351	+	0.961057i	$0.589125\pi$
$4$	2.67865	1.33933
$5$	3.42546	1.53191	0.765956	−	0.642893i	$-0.222266\pi$
$5$	3.42546	1.53191	0.765956	+	0.642893i	$0.222266\pi$
$6$	−2.07068	−0.845350
$7$	1.52570	0.576659	0.288329	−	0.957531i	$-0.406900\pi$
$7$	1.52570	0.576659	0.288329	+	0.957531i	$0.406900\pi$
$8$	1.46794	0.518994
$9$	−2.08356	−0.694521
$10$	7.40934	2.34304
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	−2.56429	−0.740248
$13$	3.58739	0.994964	0.497482	−	0.867474i	$-0.334258\pi$
$13$	3.58739	0.994964	0.497482	+	0.867474i	$0.334258\pi$
$14$	3.30011	0.881991
$15$	−3.27922	−0.846691
$16$	−2.18213	−0.545533
$17$	5.94398	1.44163	0.720814	−	0.693129i	$-0.243768\pi$
$17$	5.94398	1.44163	0.720814	+	0.693129i	$0.243768\pi$
$18$	−4.50678	−1.06226
$19$	−1.65639	−0.380001	−0.190001	−	0.981784i	$-0.560849\pi$
$19$	−1.65639	−0.380001	−0.190001	+	0.981784i	$0.560849\pi$
$20$	9.17561	2.05173
$21$	−1.46056	−0.318721
$22$	−2.16302	−0.461157
$23$	−3.88910	−0.810933	−0.405467	−	0.914110i	$-0.632891\pi$
$23$	−3.88910	−0.810933	−0.405467	+	0.914110i	$0.632891\pi$
$24$	−1.40527	−0.286849
$25$	6.73378	1.34676
$26$	7.75960	1.52178
$27$	4.86653	0.936565
$28$	4.08681	0.772334
$29$	−9.39965	−1.74547	−0.872735	−	0.488194i	$-0.837656\pi$
$29$	−9.39965	−1.74547	−0.872735	+	0.488194i	$0.837656\pi$
$30$	−7.09302	−1.29500
$31$	−5.87279	−1.05478	−0.527392	−	0.849622i	$-0.676830\pi$
$31$	−5.87279	−1.05478	−0.527392	+	0.849622i	$0.676830\pi$
$32$	−7.65586	−1.35338
$33$	0.957308	0.166646
$34$	12.8569	2.20495
$35$	5.22621	0.883391
$36$	−5.58113	−0.930189
$37$	3.29618	0.541889	0.270944	−	0.962595i	$-0.412664\pi$
$37$	3.29618	0.541889	0.270944	+	0.962595i	$0.412664\pi$
$38$	−3.58280	−0.581207
$39$	−3.43424	−0.549919
$40$	5.02835	0.795053
$41$	11.2659	1.75943	0.879716	−	0.475500i	$-0.157733\pi$
$41$	11.2659	1.75943	0.879716	+	0.475500i	$0.157733\pi$
$42$	−3.15922	−0.487478
$43$	4.96645	0.757376	0.378688	−	0.925524i	$-0.376375\pi$
$43$	4.96645	0.757376	0.378688	+	0.925524i	$0.376375\pi$
$44$	−2.67865	−0.403822
$45$	−7.13716	−1.06394
$46$	−8.41219	−1.24031
$47$	0.704770	0.102801	0.0514007	−	0.998678i	$-0.483631\pi$
$47$	0.704770	0.102801	0.0514007	+	0.998678i	$0.483631\pi$
$48$	2.08897	0.301517
$49$	−4.67225	−0.667464
$50$	14.5653	2.05984
$51$	−5.69022	−0.796790
$52$	9.60938	1.33258
$53$	−5.18291	−0.711927	−0.355964	−	0.934500i	$-0.615847\pi$
$53$	−5.18291	−0.711927	−0.355964	+	0.934500i	$0.615847\pi$
$54$	10.5264	1.43246
$55$	−3.42546	−0.461889
$56$	2.23962	0.299282
$57$	1.58567	0.210027
$58$	−20.3316	−2.66967
$59$	−2.75436	−0.358587	−0.179294	−	0.983796i	$-0.557381\pi$
$59$	−2.75436	−0.358587	−0.179294	+	0.983796i	$0.557381\pi$
$60$	−8.78389	−1.13399
$61$	1.00000	0.128037
$61$	1.00000	0.128037
$62$	−12.7030	−1.61328
$63$	−3.17888	−0.400501
$64$	−12.1955	−1.52444
$65$	12.2885	1.52420
$66$	2.07068	0.254882
$67$	7.28569	0.890089	0.445045	−	0.895508i	$-0.353188\pi$
$67$	7.28569	0.890089	0.445045	+	0.895508i	$0.353188\pi$
$68$	15.9219	1.93081
$69$	3.72306	0.448204
$70$	11.3044	1.35113
$71$	−13.0352	−1.54700	−0.773498	−	0.633799i	$-0.781495\pi$
$71$	−13.0352	−1.54700	−0.773498	+	0.633799i	$0.781495\pi$
$72$	−3.05853	−0.360452
$73$	2.44588	0.286269	0.143134	−	0.989703i	$-0.454282\pi$
$73$	2.44588	0.286269	0.143134	+	0.989703i	$0.454282\pi$
$74$	7.12970	0.828811
$75$	−6.44630	−0.744354
$76$	−4.43688	−0.508946
$77$	−1.52570	−0.173869
$78$	−7.42833	−0.841093
$79$	−15.0610	−1.69449	−0.847245	−	0.531202i	$-0.821741\pi$
$79$	−15.0610	−1.69449	−0.847245	+	0.531202i	$0.821741\pi$
$80$	−7.47480	−0.835708
$81$	1.59191	0.176879
$82$	24.3683	2.69103
$83$	−10.3614	−1.13731	−0.568656	−	0.822575i	$-0.692537\pi$
$83$	−10.3614	−1.13731	−0.568656	+	0.822575i	$0.692537\pi$
$84$	−3.91233	−0.426871
$85$	20.3609	2.20845
$86$	10.7425	1.15840
$87$	8.99835	0.964725
$88$	−1.46794	−0.156482
$89$	0.417315	0.0442353	0.0221176	−	0.999755i	$-0.492959\pi$
$89$	0.417315	0.0442353	0.0221176	+	0.999755i	$0.492959\pi$
$90$	−15.4378	−1.62729
$91$	5.47327	0.573755
$92$	−10.4175	−1.08610
$93$	5.62207	0.582981
$94$	1.52443	0.157233
$95$	−5.67389	−0.582129
$96$	7.32902	0.748014
$97$	−11.7699	−1.19505	−0.597524	−	0.801851i	$-0.703849\pi$
$97$	−11.7699	−1.19505	−0.597524	+	0.801851i	$0.703849\pi$
$98$	−10.1062	−1.02088
$99$	2.08356	0.209406
$100$	18.0374	1.80374
$101$	−14.0074	−1.39379	−0.696895	−	0.717173i	$-0.745436\pi$
$101$	−14.0074	−1.39379	−0.696895	+	0.717173i	$0.745436\pi$
$102$	−12.3081	−1.21868
$103$	5.51871	0.543775	0.271888	−	0.962329i	$-0.412352\pi$
$103$	5.51871	0.543775	0.271888	+	0.962329i	$0.412352\pi$
$104$	5.26606	0.516380
$105$	−5.00309	−0.488252
$106$	−11.2107	−1.08888
$107$	13.4054	1.29595	0.647976	−	0.761660i	$-0.275615\pi$
$107$	13.4054	1.29595	0.647976	+	0.761660i	$0.275615\pi$
$108$	13.0357	1.25437
$109$	−5.10329	−0.488806	−0.244403	−	0.969674i	$-0.578592\pi$
$109$	−5.10329	−0.488806	−0.244403	+	0.969674i	$0.578592\pi$
$110$	−7.40934	−0.706452
$111$	−3.15546	−0.299503
$112$	−3.32927	−0.314586
$113$	0.905016	0.0851368	0.0425684	−	0.999094i	$-0.486446\pi$
$113$	0.905016	0.0851368	0.0425684	+	0.999094i	$0.486446\pi$
$114$	3.42984	0.321234
$115$	−13.3220	−1.24228
$116$	−25.1784	−2.33775
$117$	−7.47456	−0.691023
$118$	−5.95773	−0.548454
$119$	9.06871	0.831327
$120$	−4.81368	−0.439427
$121$	1.00000	0.0909091
$122$	2.16302	0.195831
$123$	−10.7849	−0.972441
$124$	−15.7312	−1.41270
$125$	5.93899	0.531199
$126$	−6.87598	−0.612561
$127$	2.67303	0.237193	0.118597	−	0.992943i	$-0.462160\pi$
$127$	2.67303	0.237193	0.118597	+	0.992943i	$0.462160\pi$
$128$	−11.0674	−0.978229
$129$	−4.75442	−0.418603
$130$	26.5802	2.33124
$131$	11.8629	1.03647	0.518235	−	0.855238i	$-0.326589\pi$
$131$	11.8629	1.03647	0.518235	+	0.855238i	$0.326589\pi$
$132$	2.56429	0.223193
$133$	−2.52714	−0.219131
$134$	15.7591	1.36138
$135$	16.6701	1.43474
$136$	8.72538	0.748195
$137$	20.2371	1.72897	0.864485	−	0.502658i	$-0.167644\pi$
$137$	20.2371	1.72897	0.864485	+	0.502658i	$0.167644\pi$
$138$	8.05306	0.685522
$139$	−20.2174	−1.71482	−0.857410	−	0.514634i	$-0.827928\pi$
$139$	−20.2174	−1.71482	−0.857410	+	0.514634i	$0.827928\pi$
$140$	13.9992	1.18315
$141$	−0.674682	−0.0568185
$142$	−28.1954	−2.36611
$143$	−3.58739	−0.299993
$144$	4.54660	0.378884
$145$	−32.1981	−2.67391
$146$	5.29049	0.437844
$147$	4.47278	0.368909
$148$	8.82932	0.725766
$149$	−10.2507	−0.839766	−0.419883	−	0.907578i	$-0.637929\pi$
$149$	−10.2507	−0.839766	−0.419883	+	0.907578i	$0.637929\pi$
$150$	−13.9435	−1.13848
$151$	−7.52745	−0.612575	−0.306288	−	0.951939i	$-0.599087\pi$
$151$	−7.52745	−0.612575	−0.306288	+	0.951939i	$0.599087\pi$
$152$	−2.43147	−0.197218
$153$	−12.3847	−1.00124
$154$	−3.30011	−0.265930
$155$	−20.1170	−1.61584
$156$	−9.19913	−0.736520
$157$	2.92328	0.233303	0.116652	−	0.993173i	$-0.462784\pi$
$157$	2.92328	0.233303	0.116652	+	0.993173i	$0.462784\pi$
$158$	−32.5771	−2.59170
$159$	4.96164	0.393484
$160$	−26.2248	−2.07326
$161$	−5.93358	−0.467632
$162$	3.44334	0.270534
$163$	−4.65218	−0.364387	−0.182193	−	0.983263i	$-0.558320\pi$
$163$	−4.65218	−0.364387	−0.182193	+	0.983263i	$0.558320\pi$
$164$	30.1773	2.35645
$165$	3.27922	0.255287
$166$	−22.4119	−1.73950
$167$	9.20733	0.712484	0.356242	−	0.934394i	$-0.384058\pi$
$167$	9.20733	0.712484	0.356242	+	0.934394i	$0.384058\pi$
$168$	−2.14401	−0.165414
$169$	−0.130600	−0.0100461
$170$	44.0409	3.37779
$171$	3.45119	0.263919
$172$	13.3034	1.01437
$173$	−6.01897	−0.457614	−0.228807	−	0.973472i	$-0.573483\pi$
$173$	−6.01897	−0.457614	−0.228807	+	0.973472i	$0.573483\pi$
$174$	19.4636	1.47553
$175$	10.2737	0.776619
$176$	2.18213	0.164484
$177$	2.63677	0.198192
$178$	0.902660	0.0676572
$179$	11.4464	0.855545	0.427773	−	0.903886i	$-0.359298\pi$
$179$	11.4464	0.855545	0.427773	+	0.903886i	$0.359298\pi$
$180$	−19.1180	−1.42497
$181$	19.2696	1.43230	0.716148	−	0.697948i	$-0.245904\pi$
$181$	19.2696	1.43230	0.716148	+	0.697948i	$0.245904\pi$
$182$	11.8388	0.877550
$183$	−0.957308	−0.0707662
$184$	−5.70894	−0.420869
$185$	11.2909	0.830126
$186$	12.1606	0.891661
$187$	−5.94398	−0.434667
$188$	1.88783	0.137684
$189$	7.42485	0.540078
$190$	−12.2727	−0.890357
$191$	−7.11913	−0.515122	−0.257561	−	0.966262i	$-0.582919\pi$
$191$	−7.11913	−0.515122	−0.257561	+	0.966262i	$0.582919\pi$
$192$	11.6749	0.842560
$193$	25.2029	1.81415	0.907073	−	0.420973i	$-0.138311\pi$
$193$	25.2029	1.81415	0.907073	+	0.420973i	$0.138311\pi$
$194$	−25.4584	−1.82781
$195$	−11.7639	−0.842427
$196$	−12.5153	−0.893952
$197$	20.3647	1.45092	0.725461	−	0.688263i	$-0.241626\pi$
$197$	20.3647	1.45092	0.725461	+	0.688263i	$0.241626\pi$
$198$	4.50678	0.320283
$199$	13.8349	0.980729	0.490365	−	0.871517i	$-0.336864\pi$
$199$	13.8349	0.980729	0.490365	+	0.871517i	$0.336864\pi$
$200$	9.88475	0.698957
$201$	−6.97465	−0.491954
$202$	−30.2983	−2.13178
$203$	−14.3410	−1.00654
$204$	−15.2421	−1.06716
$205$	38.5908	2.69530
$206$	11.9371	0.831696
$207$	8.10318	0.563210
$208$	−7.82816	−0.542785
$209$	1.65639	0.114575
$210$	−10.8218	−0.746774
$211$	14.7335	1.01430	0.507149	−	0.861858i	$-0.330699\pi$
$211$	14.7335	1.01430	0.507149	+	0.861858i	$0.330699\pi$
$212$	−13.8832	−0.953503
$213$	12.4787	0.855027
$214$	28.9962	1.98214
$215$	17.0124	1.16023
$216$	7.14376	0.486071
$217$	−8.96009	−0.608251
$218$	−11.0385	−0.747622
$219$	−2.34146	−0.158221
$220$	−9.17561	−0.618620
$221$	21.3234	1.43437
$222$	−6.82532	−0.458086
$223$	25.0230	1.67566	0.837831	−	0.545929i	$-0.183823\pi$
$223$	25.0230	1.67566	0.837831	+	0.545929i	$0.183823\pi$
$224$	−11.6805	−0.780437
$225$	−14.0302	−0.935349
$226$	1.95757	0.130215
$227$	14.9179	0.990136	0.495068	−	0.868854i	$-0.335143\pi$
$227$	14.9179	0.990136	0.495068	+	0.868854i	$0.335143\pi$
$228$	4.24746	0.281295
$229$	13.0514	0.862459	0.431230	−	0.902242i	$-0.358080\pi$
$229$	13.0514	0.862459	0.431230	+	0.902242i	$0.358080\pi$
$230$	−28.8156	−1.90005
$231$	1.46056	0.0960979
$232$	−13.7981	−0.905888
$233$	25.8089	1.69080	0.845399	−	0.534135i	$-0.179363\pi$
$233$	25.8089	1.69080	0.845399	+	0.534135i	$0.179363\pi$
$234$	−16.1676	−1.05691
$235$	2.41416	0.157483
$236$	−7.37797	−0.480265
$237$	14.4180	0.936548
$238$	19.6158	1.27150
$239$	−26.6536	−1.72408	−0.862039	−	0.506841i	$-0.830813\pi$
$239$	−26.6536	−1.72408	−0.862039	+	0.506841i	$0.830813\pi$
$240$	7.15569	0.461898
$241$	7.39439	0.476315	0.238157	−	0.971227i	$-0.423457\pi$
$241$	7.39439	0.476315	0.238157	+	0.971227i	$0.423457\pi$
$242$	2.16302	0.139044
$243$	−16.1236	−1.03433
$244$	2.67865	0.171483
$245$	−16.0046	−1.02250
$246$	−23.3279	−1.48733
$247$	−5.94212	−0.378088
$248$	−8.62088	−0.547426
$249$	9.91906	0.628595
$250$	12.8461	0.812462
$251$	13.6943	0.864374	0.432187	−	0.901784i	$-0.357742\pi$
$251$	13.6943	0.864374	0.432187	+	0.901784i	$0.357742\pi$
$252$	−8.51512	−0.536402
$253$	3.88910	0.244506
$254$	5.78182	0.362784
$255$	−19.4916	−1.22061
$256$	0.452025	0.0282515
$257$	14.3062	0.892395	0.446197	−	0.894935i	$-0.352778\pi$
$257$	14.3062	0.892395	0.446197	+	0.894935i	$0.352778\pi$
$258$	−10.2839	−0.640247
$259$	5.02897	0.312485
$260$	32.9165	2.04140
$261$	19.5847	1.21226
$262$	25.6598	1.58527
$263$	−2.96892	−0.183071	−0.0915356	−	0.995802i	$-0.529178\pi$
$263$	−2.96892	−0.183071	−0.0915356	+	0.995802i	$0.529178\pi$
$264$	1.40527	0.0864881
$265$	−17.7539	−1.09061
$266$	−5.46626	−0.335158
$267$	−0.399499	−0.0244489
$268$	19.5158	1.19212
$269$	24.2725	1.47992	0.739960	−	0.672651i	$-0.234844\pi$
$269$	24.2725	1.47992	0.739960	+	0.672651i	$0.234844\pi$
$270$	36.0578	2.19441
$271$	−14.2938	−0.868289	−0.434144	−	0.900843i	$-0.642949\pi$
$271$	−14.2938	−0.868289	−0.434144	+	0.900843i	$0.642949\pi$
$272$	−12.9705	−0.786455
$273$	−5.23961	−0.317116
$274$	43.7732	2.64444
$275$	−6.73378	−0.406062
$276$	9.97279	0.600291
$277$	−16.6354	−0.999525	−0.499762	−	0.866163i	$-0.666579\pi$
$277$	−16.6354	−0.999525	−0.499762	+	0.866163i	$0.666579\pi$
$278$	−43.7307	−2.62279
$279$	12.2363	0.732569
$280$	7.67174	0.458474
$281$	−19.7970	−1.18099	−0.590496	−	0.807041i	$-0.701068\pi$
$281$	−19.7970	−1.18099	−0.590496	+	0.807041i	$0.701068\pi$
$282$	−1.45935	−0.0869031
$283$	−8.46139	−0.502977	−0.251489	−	0.967860i	$-0.580920\pi$
$283$	−8.46139	−0.502977	−0.251489	+	0.967860i	$0.580920\pi$
$284$	−34.9168	−2.07193
$285$	5.43166	0.321744
$286$	−7.75960	−0.458835
$287$	17.1883	1.01459
$288$	15.9515	0.939949
$289$	18.3309	1.07829
$290$	−69.6451	−4.08970
$291$	11.2674	0.660505
$292$	6.55167	0.383407
$293$	−9.48622	−0.554191	−0.277096	−	0.960842i	$-0.589372\pi$
$293$	−9.48622	−0.554191	−0.277096	+	0.960842i	$0.589372\pi$
$294$	9.67471	0.564241
$295$	−9.43495	−0.549324
$296$	4.83858	0.281237
$297$	−4.86653	−0.282385
$298$	−22.1724	−1.28441
$299$	−13.9517	−0.806849
$300$	−17.2674	−0.996933
$301$	7.57729	0.436748
$302$	−16.2820	−0.936925
$303$	13.4094	0.770351
$304$	3.61445	0.207303
$305$	3.42546	0.196141
$306$	−26.7882	−1.53138
$307$	14.4454	0.824443	0.412221	−	0.911084i	$-0.364753\pi$
$307$	14.4454	0.824443	0.412221	+	0.911084i	$0.364753\pi$
$308$	−4.08681	−0.232867
$309$	−5.28311	−0.300546
$310$	−43.5135	−2.47140
$311$	−15.3587	−0.870911	−0.435455	−	0.900210i	$-0.643413\pi$
$311$	−15.3587	−0.870911	−0.435455	+	0.900210i	$0.643413\pi$
$312$	−5.04124	−0.285404
$313$	−4.36876	−0.246937	−0.123469	−	0.992348i	$-0.539402\pi$
$313$	−4.36876	−0.246937	−0.123469	+	0.992348i	$0.539402\pi$
$314$	6.32312	0.356834
$315$	−10.8891	−0.613533
$316$	−40.3431	−2.26947
$317$	5.20003	0.292063	0.146031	−	0.989280i	$-0.453350\pi$
$317$	5.20003	0.292063	0.146031	+	0.989280i	$0.453350\pi$
$318$	10.7321	0.601828
$319$	9.39965	0.526279
$320$	−41.7752	−2.33531
$321$	−12.8331	−0.716276
$322$	−12.8345	−0.715236
$323$	−9.84554	−0.547820
$324$	4.26418	0.236899
$325$	24.1567	1.33997
$326$	−10.0628	−0.557324
$327$	4.88542	0.270164
$328$	16.5376	0.913134
$329$	1.07527	0.0592813
$330$	7.09302	0.390458
$331$	5.82973	0.320431	0.160216	−	0.987082i	$-0.448781\pi$
$331$	5.82973	0.320431	0.160216	+	0.987082i	$0.448781\pi$
$332$	−27.7546	−1.52323
$333$	−6.86780	−0.376353
$334$	19.9156	1.08973
$335$	24.9569	1.36354
$336$	3.18713	0.173872
$337$	−23.3465	−1.27176	−0.635882	−	0.771786i	$-0.719363\pi$
$337$	−23.3465	−1.27176	−0.635882	+	0.771786i	$0.719363\pi$
$338$	−0.282490	−0.0153654
$339$	−0.866379	−0.0470553
$340$	54.5397	2.95783
$341$	5.87279	0.318029
$342$	7.46498	0.403660
$343$	−17.8083	−0.961558
$344$	7.29042	0.393073
$345$	12.7532	0.686610
$346$	−13.0192	−0.699914
$347$	−21.7134	−1.16563	−0.582817	−	0.812603i	$-0.698050\pi$
$347$	−21.7134	−1.16563	−0.582817	+	0.812603i	$0.698050\pi$
$348$	24.1035	1.29208
$349$	36.0189	1.92805	0.964023	−	0.265818i	$-0.0856420\pi$
$349$	36.0189	1.92805	0.964023	+	0.265818i	$0.0856420\pi$
$350$	22.2222	1.18783
$351$	17.4582	0.931849
$352$	7.65586	0.408059
$353$	−3.13801	−0.167019	−0.0835097	−	0.996507i	$-0.526613\pi$
$353$	−3.13801	−0.167019	−0.0835097	+	0.996507i	$0.526613\pi$
$354$	5.70339	0.303132
$355$	−44.6516	−2.36986
$356$	1.11784	0.0592455
$357$	−8.68155	−0.459476
$358$	24.7588	1.30854
$359$	4.01251	0.211772	0.105886	−	0.994378i	$-0.466232\pi$
$359$	4.01251	0.211772	0.105886	+	0.994378i	$0.466232\pi$
$360$	−10.4769	−0.552180
$361$	−16.2564	−0.855599
$362$	41.6805	2.19068
$363$	−0.957308	−0.0502456
$364$	14.6610	0.768445
$365$	8.37828	0.438539
$366$	−2.07068	−0.108236
$367$	16.7099	0.872250	0.436125	−	0.899886i	$-0.356350\pi$
$367$	16.7099	0.872250	0.436125	+	0.899886i	$0.356350\pi$
$368$	8.48652	0.442390
$369$	−23.4731	−1.22196
$370$	24.4225	1.26967
$371$	−7.90755	−0.410539
$372$	15.0596	0.780802
$373$	26.5321	1.37378	0.686890	−	0.726761i	$-0.258975\pi$
$373$	26.5321	1.37378	0.686890	+	0.726761i	$0.258975\pi$
$374$	−12.8569	−0.664817
$375$	−5.68544	−0.293595
$376$	1.03456	0.0533532
$377$	−33.7202	−1.73668
$378$	16.0601	0.826042
$379$	5.35976	0.275312	0.137656	−	0.990480i	$-0.456043\pi$
$379$	5.35976	0.275312	0.137656	+	0.990480i	$0.456043\pi$
$380$	−15.1984	−0.779660
$381$	−2.55892	−0.131097
$382$	−15.3988	−0.787871
$383$	−20.8095	−1.06331	−0.531657	−	0.846960i	$-0.678430\pi$
$383$	−20.8095	−1.06331	−0.531657	+	0.846960i	$0.678430\pi$
$384$	10.5949	0.540669
$385$	−5.22621	−0.266352
$386$	54.5144	2.77471
$387$	−10.3479	−0.526013
$388$	−31.5273	−1.60056
$389$	−5.32194	−0.269833	−0.134917	−	0.990857i	$-0.543077\pi$
$389$	−5.32194	−0.269833	−0.134917	+	0.990857i	$0.543077\pi$
$390$	−25.4454	−1.28848
$391$	−23.1167	−1.16906
$392$	−6.85856	−0.346410
$393$	−11.3565	−0.572859
$394$	44.0492	2.21917
$395$	−51.5907	−2.59581
$396$	5.58113	0.280463
$397$	−29.6593	−1.48856	−0.744279	−	0.667869i	$-0.767207\pi$
$397$	−29.6593	−1.48856	−0.744279	+	0.667869i	$0.767207\pi$
$398$	29.9251	1.50001
$399$	2.41925	0.121114
$400$	−14.6940	−0.734699
$401$	−25.5116	−1.27399	−0.636994	−	0.770869i	$-0.719823\pi$
$401$	−25.5116	−1.27399	−0.636994	+	0.770869i	$0.719823\pi$
$402$	−15.0863	−0.752436
$403$	−21.0680	−1.04947
$404$	−37.5210	−1.86674
$405$	5.45304	0.270964
$406$	−31.0199	−1.53949
$407$	−3.29618	−0.163386
$408$	−8.35287	−0.413529
$409$	36.4764	1.80364	0.901822	−	0.432107i	$-0.142230\pi$
$409$	36.4764	1.80364	0.901822	+	0.432107i	$0.142230\pi$
$410$	83.4725	4.12241
$411$	−19.3731	−0.955606
$412$	14.7827	0.728292
$413$	−4.20232	−0.206782
$414$	17.5273	0.861421
$415$	−35.4926	−1.74226
$416$	−27.4646	−1.34656
$417$	19.3543	0.947784
$418$	3.58280	0.175240
$419$	5.85835	0.286199	0.143099	−	0.989708i	$-0.454293\pi$
$419$	5.85835	0.286199	0.143099	+	0.989708i	$0.454293\pi$
$420$	−13.4015	−0.653928
$421$	1.05938	0.0516310	0.0258155	−	0.999667i	$-0.491782\pi$
$421$	1.05938	0.0516310	0.0258155	+	0.999667i	$0.491782\pi$
$422$	31.8689	1.55135
$423$	−1.46843	−0.0713976
$424$	−7.60818	−0.369486
$425$	40.0254	1.94152
$426$	26.9917	1.30775
$427$	1.52570	0.0738336
$428$	35.9085	1.73570
$429$	3.43424	0.165807
$430$	36.7981	1.77456
$431$	−7.71977	−0.371848	−0.185924	−	0.982564i	$-0.559528\pi$
$431$	−7.71977	−0.371848	−0.185924	+	0.982564i	$0.559528\pi$
$432$	−10.6194	−0.510927
$433$	2.29563	0.110321	0.0551605	−	0.998477i	$-0.482433\pi$
$433$	2.29563	0.110321	0.0551605	+	0.998477i	$0.482433\pi$
$434$	−19.3809	−0.930311
$435$	30.8235	1.47787
$436$	−13.6699	−0.654671
$437$	6.44185	0.308156
$438$	−5.06463	−0.241997
$439$	−11.8920	−0.567573	−0.283787	−	0.958887i	$-0.591591\pi$
$439$	−11.8920	−0.567573	−0.283787	+	0.958887i	$0.591591\pi$
$440$	−5.02835	−0.239717
$441$	9.73492	0.463568
$442$	46.1229	2.19384
$443$	−6.93619	−0.329548	−0.164774	−	0.986331i	$-0.552690\pi$
$443$	−6.93619	−0.329548	−0.164774	+	0.986331i	$0.552690\pi$
$444$	−8.45238	−0.401132
$445$	1.42950	0.0677646
$446$	54.1252	2.56290
$447$	9.81303	0.464140
$448$	−18.6066	−0.879081
$449$	24.3086	1.14719	0.573597	−	0.819137i	$-0.305547\pi$
$449$	24.3086	1.14719	0.573597	+	0.819137i	$0.305547\pi$
$450$	−30.3477	−1.43060
$451$	−11.2659	−0.530489
$452$	2.42422	0.114026
$453$	7.20609	0.338571
$454$	32.2677	1.51440
$455$	18.7485	0.878942
$456$	2.32767	0.109003
$457$	19.1536	0.895968	0.447984	−	0.894041i	$-0.352142\pi$
$457$	19.1536	0.895968	0.447984	+	0.894041i	$0.352142\pi$
$458$	28.2304	1.31912
$459$	28.9266	1.35018
$460$	−35.6849	−1.66382
$461$	−21.0634	−0.981019	−0.490509	−	0.871436i	$-0.663189\pi$
$461$	−21.0634	−0.981019	−0.490509	+	0.871436i	$0.663189\pi$
$462$	3.15922	0.146980
$463$	35.7967	1.66361	0.831807	−	0.555064i	$-0.187306\pi$
$463$	35.7967	1.66361	0.831807	+	0.555064i	$0.187306\pi$
$464$	20.5113	0.952211
$465$	19.2582	0.893076
$466$	55.8252	2.58605
$467$	−9.34479	−0.432425	−0.216213	−	0.976346i	$-0.569370\pi$
$467$	−9.34479	−0.432425	−0.216213	+	0.976346i	$0.569370\pi$
$468$	−20.0217	−0.925505
$469$	11.1158	0.513278
$470$	5.22188	0.240867
$471$	−2.79848	−0.128947
$472$	−4.04322	−0.186104
$473$	−4.96645	−0.228357
$474$	31.1864	1.43244
$475$	−11.1537	−0.511769
$476$	24.2919	1.11342
$477$	10.7989	0.494448
$478$	−57.6523	−2.63695
$479$	22.2054	1.01459	0.507296	−	0.861772i	$-0.330645\pi$
$479$	22.2054	1.01459	0.507296	+	0.861772i	$0.330645\pi$
$480$	25.1053	1.14589
$481$	11.8247	0.539160
$482$	15.9942	0.728517
$483$	5.68026	0.258461
$484$	2.67865	0.121757
$485$	−40.3172	−1.83071
$486$	−34.8756	−1.58199
$487$	4.44828	0.201571	0.100785	−	0.994908i	$-0.467864\pi$
$487$	4.44828	0.201571	0.100785	+	0.994908i	$0.467864\pi$
$488$	1.46794	0.0664503
$489$	4.45357	0.201397
$490$	−34.6183	−1.56389
$491$	−16.3927	−0.739791	−0.369896	−	0.929073i	$-0.620607\pi$
$491$	−16.3927	−0.739791	−0.369896	+	0.929073i	$0.620607\pi$
$492$	−28.8890	−1.30242
$493$	−55.8713	−2.51632
$494$	−12.8529	−0.578280
$495$	7.13716	0.320791
$496$	12.8152	0.575419
$497$	−19.8878	−0.892089
$498$	21.4551	0.961427
$499$	37.4385	1.67598	0.837989	−	0.545687i	$-0.183731\pi$
$499$	37.4385	1.67598	0.837989	+	0.545687i	$0.183731\pi$
$500$	15.9085	0.711449
$501$	−8.81425	−0.393792
$502$	29.6209	1.32205
$503$	−16.2915	−0.726403	−0.363202	−	0.931711i	$-0.618316\pi$
$503$	−16.2915	−0.726403	−0.363202	+	0.931711i	$0.618316\pi$
$504$	−4.66639	−0.207858
$505$	−47.9819	−2.13516
$506$	8.41219	0.373968
$507$	0.125024	0.00555251
$508$	7.16012	0.317679
$509$	−21.2376	−0.941338	−0.470669	−	0.882310i	$-0.655987\pi$
$509$	−21.2376	−0.941338	−0.470669	+	0.882310i	$0.655987\pi$
$510$	−42.1607	−1.86691
$511$	3.73167	0.165080
$512$	23.1125	1.02144
$513$	−8.06087	−0.355896
$514$	30.9445	1.36490
$515$	18.9041	0.833016
$516$	−12.7354	−0.560646
$517$	−0.704770	−0.0309958
$518$	10.8778	0.477941
$519$	5.76201	0.252924
$520$	18.0387	0.791049
$521$	25.0948	1.09942	0.549711	−	0.835355i	$-0.314738\pi$
$521$	25.0948	1.09942	0.549711	+	0.835355i	$0.314738\pi$
$522$	42.3622	1.85414
$523$	7.35803	0.321744	0.160872	−	0.986975i	$-0.448569\pi$
$523$	7.35803	0.321744	0.160872	+	0.986975i	$0.448569\pi$
$524$	31.7767	1.38817
$525$	−9.83509	−0.429239
$526$	−6.42182	−0.280005
$527$	−34.9077	−1.52061
$528$	−2.08897	−0.0909108
$529$	−7.87492	−0.342388
$530$	−38.4019	−1.66807
$531$	5.73888	0.249046
$532$	−6.76934	−0.293488
$533$	40.4151	1.75057
$534$	−0.864124	−0.0373943
$535$	45.9198	1.98529
$536$	10.6949	0.461950
$537$	−10.9577	−0.472862
$538$	52.5019	2.26352
$539$	4.67225	0.201248
$540$	44.6534	1.92158
$541$	−21.6515	−0.930869	−0.465434	−	0.885082i	$-0.654102\pi$
$541$	−21.6515	−0.930869	−0.465434	+	0.885082i	$0.654102\pi$
$542$	−30.9178	−1.32803
$543$	−18.4469	−0.791633
$544$	−45.5063	−1.95107
$545$	−17.4811	−0.748809
$546$	−11.3334	−0.485024
$547$	21.6436	0.925413	0.462706	−	0.886512i	$-0.346878\pi$
$547$	21.6436	0.925413	0.462706	+	0.886512i	$0.346878\pi$
$548$	54.2081	2.31565
$549$	−2.08356	−0.0889242
$550$	−14.5653	−0.621066
$551$	15.5695	0.663281
$552$	5.46522	0.232615
$553$	−22.9785	−0.977143
$554$	−35.9827	−1.52876
$555$	−10.8089	−0.458813
$556$	−54.1554	−2.29670
$557$	−5.39479	−0.228585	−0.114292	−	0.993447i	$-0.536460\pi$
$557$	−5.39479	−0.228585	−0.114292	+	0.993447i	$0.536460\pi$
$558$	26.4674	1.12045
$559$	17.8166	0.753562
$560$	−11.4043	−0.481919
$561$	5.69022	0.240241
$562$	−42.8213	−1.80631
$563$	−42.3802	−1.78611	−0.893056	−	0.449945i	$-0.851444\pi$
$563$	−42.3802	−1.78611	−0.893056	+	0.449945i	$0.851444\pi$
$564$	−1.80724	−0.0760985
$565$	3.10010	0.130422
$566$	−18.3021	−0.769297
$567$	2.42878	0.101999
$568$	−19.1349	−0.802881
$569$	−14.2313	−0.596609	−0.298304	−	0.954471i	$-0.596421\pi$
$569$	−14.2313	−0.596609	−0.298304	+	0.954471i	$0.596421\pi$
$570$	11.7488	0.492102
$571$	13.9607	0.584237	0.292118	−	0.956382i	$-0.405640\pi$
$571$	13.9607	0.584237	0.292118	+	0.956382i	$0.405640\pi$
$572$	−9.60938	−0.401788
$573$	6.81520	0.284709
$574$	37.1786	1.55180
$575$	−26.1883	−1.09213
$576$	25.4101	1.05875
$577$	4.17275	0.173714	0.0868568	−	0.996221i	$-0.472318\pi$
$577$	4.17275	0.173714	0.0868568	+	0.996221i	$0.472318\pi$
$578$	39.6501	1.64923
$579$	−24.1270	−1.00268
$580$	−86.2475	−3.58123
$581$	−15.8084	−0.655841
$582$	24.3715	1.01023
$583$	5.18291	0.214654
$584$	3.59040	0.148572
$585$	−25.6038	−1.05859
$586$	−20.5189	−0.847627
$587$	−27.1859	−1.12208	−0.561040	−	0.827789i	$-0.689599\pi$
$587$	−27.1859	−1.12208	−0.561040	+	0.827789i	$0.689599\pi$
$588$	11.9810	0.494089
$589$	9.72762	0.400819
$590$	−20.4080	−0.840183
$591$	−19.4953	−0.801928
$592$	−7.19270	−0.295618
$593$	−33.9524	−1.39426	−0.697130	−	0.716945i	$-0.745540\pi$
$593$	−33.9524	−1.39426	−0.697130	+	0.716945i	$0.745540\pi$
$594$	−10.5264	−0.431904
$595$	31.0645	1.27352
$596$	−27.4579	−1.12472
$597$	−13.2442	−0.542051
$598$	−30.1779	−1.23406
$599$	16.5015	0.674234	0.337117	−	0.941463i	$-0.390548\pi$
$599$	16.5015	0.674234	0.337117	+	0.941463i	$0.390548\pi$
$600$	−9.46275	−0.386315
$601$	11.5317	0.470389	0.235195	−	0.971948i	$-0.424427\pi$
$601$	11.5317	0.470389	0.235195	+	0.971948i	$0.424427\pi$
$602$	16.3898	0.667999
$603$	−15.1802	−0.618185
$604$	−20.1634	−0.820437
$605$	3.42546	0.139265
$606$	29.0048	1.17824
$607$	−22.4643	−0.911799	−0.455899	−	0.890031i	$-0.650682\pi$
$607$	−22.4643	−0.911799	−0.455899	+	0.890031i	$0.650682\pi$
$608$	12.6811	0.514285
$609$	13.7288	0.556317
$610$	7.40934	0.299995
$611$	2.52829	0.102284
$612$	−33.1742	−1.34099
$613$	27.6946	1.11858	0.559288	−	0.828973i	$-0.311075\pi$
$613$	27.6946	1.11858	0.559288	+	0.828973i	$0.311075\pi$
$614$	31.2457	1.26097
$615$	−36.9432	−1.48969
$616$	−2.23962	−0.0902370
$617$	1.45117	0.0584219	0.0292109	−	0.999573i	$-0.490701\pi$
$617$	1.45117	0.0584219	0.0292109	+	0.999573i	$0.490701\pi$
$618$	−11.4275	−0.459680
$619$	−5.38440	−0.216417	−0.108209	−	0.994128i	$-0.534511\pi$
$619$	−5.38440	−0.216417	−0.108209	+	0.994128i	$0.534511\pi$
$620$	−53.8864	−2.16413
$621$	−18.9264	−0.759491
$622$	−33.2211	−1.33205
$623$	0.636696	0.0255087
$624$	7.49396	0.299999
$625$	−13.3251	−0.533005
$626$	−9.44972	−0.377687
$627$	−1.58567	−0.0633257
$628$	7.83046	0.312469
$629$	19.5924	0.781202
$630$	−23.5534	−0.938390
$631$	36.7780	1.46411	0.732054	−	0.681247i	$-0.238562\pi$
$631$	36.7780	1.46411	0.732054	+	0.681247i	$0.238562\pi$
$632$	−22.1085	−0.879430
$633$	−14.1045	−0.560604
$634$	11.2478	0.446706
$635$	9.15637	0.363359
$636$	13.2905	0.527003
$637$	−16.7612	−0.664103
$638$	20.3316	0.804936
$639$	27.1597	1.07442
$640$	−37.9109	−1.49856
$641$	8.54776	0.337616	0.168808	−	0.985649i	$-0.446008\pi$
$641$	8.54776	0.337616	0.168808	+	0.985649i	$0.446008\pi$
$642$	−27.7583	−1.09553
$643$	−14.3390	−0.565475	−0.282737	−	0.959197i	$-0.591242\pi$
$643$	−14.3390	−0.565475	−0.282737	+	0.959197i	$0.591242\pi$
$644$	−15.8940	−0.626311
$645$	−16.2861	−0.641263
$646$	−21.2961	−0.837883
$647$	23.0276	0.905308	0.452654	−	0.891686i	$-0.350477\pi$
$647$	23.0276	0.905308	0.452654	+	0.891686i	$0.350477\pi$
$648$	2.33683	0.0917992
$649$	2.75436	0.108118
$650$	52.2514	2.04947
$651$	8.57757	0.336181
$652$	−12.4616	−0.488033
$653$	−21.8911	−0.856666	−0.428333	−	0.903621i	$-0.640899\pi$
$653$	−21.8911	−0.856666	−0.428333	+	0.903621i	$0.640899\pi$
$654$	10.5673	0.413212
$655$	40.6361	1.58778
$656$	−24.5836	−0.959827
$657$	−5.09615	−0.198820
$658$	2.32582	0.0906699
$659$	−40.5421	−1.57930	−0.789648	−	0.613560i	$-0.789737\pi$
$659$	−40.5421	−1.57930	−0.789648	+	0.613560i	$0.789737\pi$
$660$	8.78389	0.341912
$661$	−32.1044	−1.24872	−0.624358	−	0.781138i	$-0.714639\pi$
$661$	−32.1044	−1.24872	−0.624358	+	0.781138i	$0.714639\pi$
$662$	12.6098	0.490095
$663$	−20.4131	−0.792778
$664$	−15.2099	−0.590258
$665$	−8.65663	−0.335690
$666$	−14.8552	−0.575626
$667$	36.5561	1.41546
$668$	24.6632	0.954249
$669$	−23.9547	−0.926142
$670$	53.9821	2.08551
$671$	−1.00000	−0.0386046
$672$	11.1818	0.431349
$673$	23.8166	0.918061	0.459030	−	0.888421i	$-0.348197\pi$
$673$	23.8166	0.918061	0.459030	+	0.888421i	$0.348197\pi$
$674$	−50.4989	−1.94514
$675$	32.7702	1.26132
$676$	−0.349831	−0.0134550
$677$	−6.82508	−0.262309	−0.131155	−	0.991362i	$-0.541868\pi$
$677$	−6.82508	−0.262309	−0.131155	+	0.991362i	$0.541868\pi$
$678$	−1.87400	−0.0719703
$679$	−17.9572	−0.689135
$680$	29.8884	1.14617
$681$	−14.2810	−0.547250
$682$	12.7030	0.486421
$683$	22.7708	0.871301	0.435651	−	0.900116i	$-0.356518\pi$
$683$	22.7708	0.871301	0.435651	+	0.900116i	$0.356518\pi$
$684$	9.24452	0.353473
$685$	69.3213	2.64863
$686$	−38.5197	−1.47069
$687$	−12.4942	−0.476683
$688$	−10.8374	−0.413173
$689$	−18.5931	−0.708342
$690$	27.5854	1.05016
$691$	25.6291	0.974978	0.487489	−	0.873129i	$-0.337913\pi$
$691$	25.6291	0.974978	0.487489	+	0.873129i	$0.337913\pi$
$692$	−16.1227	−0.612894
$693$	3.17888	0.120756
$694$	−46.9664	−1.78282
$695$	−69.2540	−2.62695
$696$	13.2090	0.500686
$697$	66.9641	2.53644
$698$	77.9095	2.94892
$699$	−24.7071	−0.934508
$700$	27.5197	1.04015
$701$	−39.5842	−1.49507	−0.747537	−	0.664220i	$-0.768764\pi$
$701$	−39.5842	−1.49507	−0.747537	+	0.664220i	$0.768764\pi$
$702$	37.7624	1.42525
$703$	−5.45975	−0.205919
$704$	12.1955	0.459636
$705$	−2.31110	−0.0870410
$706$	−6.78757	−0.255454
$707$	−21.3711	−0.803742
$708$	7.06299	0.265443
$709$	−47.7140	−1.79194	−0.895969	−	0.444117i	$-0.853518\pi$
$709$	−47.7140	−1.79194	−0.895969	+	0.444117i	$0.853518\pi$
$710$	−96.5823	−3.62467
$711$	31.3804	1.17686
$712$	0.612591	0.0229578
$713$	22.8399	0.855359
$714$	−18.7783	−0.702762
$715$	−12.2885	−0.459563
$716$	30.6610	1.14585
$717$	25.5157	0.952902
$718$	8.67914	0.323903
$719$	6.77246	0.252570	0.126285	−	0.991994i	$-0.459695\pi$
$719$	6.77246	0.252570	0.126285	+	0.991994i	$0.459695\pi$
$720$	15.5742	0.580416
$721$	8.41988	0.313573
$722$	−35.1629	−1.30863
$723$	−7.07871	−0.263260
$724$	51.6165	1.91831
$725$	−63.2951	−2.35072
$726$	−2.07068	−0.0768500
$727$	−10.5969	−0.393017	−0.196509	−	0.980502i	$-0.562960\pi$
$727$	−10.5969	−0.393017	−0.196509	+	0.980502i	$0.562960\pi$
$728$	8.03441	0.297775
$729$	10.6595	0.394795
$730$	18.1224	0.670739
$731$	29.5205	1.09185
$732$	−2.56429	−0.0947790
$733$	−13.7993	−0.509690	−0.254845	−	0.966982i	$-0.582025\pi$
$733$	−13.7993	−0.509690	−0.254845	+	0.966982i	$0.582025\pi$
$734$	36.1439	1.33409
$735$	15.3213	0.565136
$736$	29.7744	1.09750
$737$	−7.28569	−0.268372
$738$	−50.7728	−1.86897
$739$	19.6135	0.721493	0.360746	−	0.932664i	$-0.382522\pi$
$739$	19.6135	0.721493	0.360746	+	0.932664i	$0.382522\pi$
$740$	30.2445	1.11181
$741$	5.68843	0.208970
$742$	−17.1042	−0.627914
$743$	−42.1891	−1.54777	−0.773884	−	0.633327i	$-0.781689\pi$
$743$	−42.1891	−1.54777	−0.773884	+	0.633327i	$0.781689\pi$
$744$	8.25283	0.302564
$745$	−35.1132	−1.28645
$746$	57.3895	2.10118
$747$	21.5886	0.789887
$748$	−15.9219	−0.582161
$749$	20.4526	0.747323
$750$	−12.2977	−0.449049
$751$	37.1798	1.35671	0.678355	−	0.734734i	$-0.262693\pi$
$751$	37.1798	1.35671	0.678355	+	0.734734i	$0.262693\pi$
$752$	−1.53790	−0.0560815
$753$	−13.1096	−0.477741
$754$	−72.9375	−2.65623
$755$	−25.7850	−0.938411
$756$	19.8886	0.723341
$757$	−1.57018	−0.0570691	−0.0285345	−	0.999593i	$-0.509084\pi$
$757$	−1.57018	−0.0570691	−0.0285345	+	0.999593i	$0.509084\pi$
$758$	11.5933	0.421086
$759$	−3.72306	−0.135139
$760$	−8.32890	−0.302121
$761$	20.3178	0.736519	0.368259	−	0.929723i	$-0.379954\pi$
$761$	20.3178	0.736519	0.368259	+	0.929723i	$0.379954\pi$
$762$	−5.53498	−0.200511
$763$	−7.78607	−0.281875
$764$	−19.0697	−0.689916
$765$	−42.4231	−1.53381
$766$	−45.0112	−1.62632
$767$	−9.88098	−0.356781
$768$	−0.432727	−0.0156147
$769$	15.8861	0.572868	0.286434	−	0.958100i	$-0.407530\pi$
$769$	15.8861	0.572868	0.286434	+	0.958100i	$0.407530\pi$
$770$	−11.3044	−0.407382
$771$	−13.6954	−0.493228
$772$	67.5098	2.42973
$773$	53.2900	1.91671	0.958354	−	0.285582i	$-0.0921868\pi$
$773$	53.2900	1.91671	0.958354	+	0.285582i	$0.0921868\pi$
$774$	−22.3827	−0.804529
$775$	−39.5461	−1.42054
$776$	−17.2774	−0.620222
$777$	−4.81427	−0.172711
$778$	−11.5115	−0.412706
$779$	−18.6606	−0.668586
$780$	−31.5113	−1.12828
$781$	13.0352	0.466437
$782$	−50.0019	−1.78806
$783$	−45.7437	−1.63475
$784$	10.1955	0.364124
$785$	10.0136	0.357400
$786$	−24.5643	−0.876180
$787$	30.4125	1.08409	0.542044	−	0.840350i	$-0.317651\pi$
$787$	30.4125	1.08409	0.542044	+	0.840350i	$0.317651\pi$
$788$	54.5499	1.94326
$789$	2.84217	0.101184
$790$	−111.592	−3.97026
$791$	1.38078	0.0490949
$792$	3.05853	0.108680
$793$	3.58739	0.127392
$794$	−64.1537	−2.27673
$795$	16.9959	0.602783
$796$	37.0588	1.31352
$797$	−17.0007	−0.602194	−0.301097	−	0.953594i	$-0.597353\pi$
$797$	−17.0007	−0.602194	−0.301097	+	0.953594i	$0.597353\pi$
$798$	5.23289	0.185242
$799$	4.18914	0.148201
$800$	−51.5529	−1.82267
$801$	−0.869501	−0.0307223
$802$	−55.1821	−1.94855
$803$	−2.44588	−0.0863133
$804$	−18.6827	−0.658887
$805$	−20.3252	−0.716371
$806$	−45.5705	−1.60515
$807$	−23.2363	−0.817955
$808$	−20.5620	−0.723368
$809$	−35.1744	−1.23667	−0.618333	−	0.785916i	$-0.712192\pi$
$809$	−35.1744	−1.23667	−0.618333	+	0.785916i	$0.712192\pi$
$810$	11.7950	0.414435
$811$	1.02516	0.0359982	0.0179991	−	0.999838i	$-0.494270\pi$
$811$	1.02516	0.0359982	0.0179991	+	0.999838i	$0.494270\pi$
$812$	−38.4145	−1.34809
$813$	13.6836	0.479905
$814$	−7.12970	−0.249896
$815$	−15.9359	−0.558209
$816$	12.4168	0.434675
$817$	−8.22636	−0.287804
$818$	78.8993	2.75865
$819$	−11.4039	−0.398485
$820$	103.371	3.60988
$821$	−8.69425	−0.303431	−0.151716	−	0.988424i	$-0.548480\pi$
$821$	−8.69425	−0.303431	−0.151716	+	0.988424i	$0.548480\pi$
$822$	−41.9044	−1.46158
$823$	−9.37576	−0.326819	−0.163409	−	0.986558i	$-0.552249\pi$
$823$	−9.37576	−0.326819	−0.163409	+	0.986558i	$0.552249\pi$
$824$	8.10111	0.282216
$825$	6.44630	0.224431
$826$	−9.08969	−0.316271
$827$	0.250732	0.00871880	0.00435940	−	0.999990i	$-0.498612\pi$
$827$	0.250732	0.00871880	0.00435940	+	0.999990i	$0.498612\pi$
$828$	21.7056	0.754321
$829$	21.2866	0.739316	0.369658	−	0.929168i	$-0.379475\pi$
$829$	21.2866	0.739316	0.369658	+	0.929168i	$0.379475\pi$
$830$	−76.7712	−2.66477
$831$	15.9252	0.552439
$832$	−43.7501	−1.51676
$833$	−27.7718	−0.962235
$834$	41.8637	1.44962
$835$	31.5393	1.09146
$836$	4.43688	0.153453
$837$	−28.5801	−0.987874
$838$	12.6717	0.437737
$839$	−21.3671	−0.737674	−0.368837	−	0.929494i	$-0.620244\pi$
$839$	−21.3671	−0.737674	−0.368837	+	0.929494i	$0.620244\pi$
$840$	−7.34422	−0.253400
$841$	59.3533	2.04667
$842$	2.29146	0.0789688
$843$	18.9518	0.652736
$844$	39.4660	1.35847
$845$	−0.447364	−0.0153898
$846$	−3.17625	−0.109202
$847$	1.52570	0.0524235
$848$	11.3098	0.388380
$849$	8.10016	0.277997
$850$	86.5758	2.96953
$851$	−12.8192	−0.439436
$852$	33.4261	1.14516
$853$	−8.32954	−0.285198	−0.142599	−	0.989781i	$-0.545546\pi$
$853$	−8.32954	−0.285198	−0.142599	+	0.989781i	$0.545546\pi$
$854$	3.30011	0.112927
$855$	11.8219	0.404300
$856$	19.6783	0.672591
$857$	16.3095	0.557123	0.278562	−	0.960418i	$-0.410142\pi$
$857$	16.3095	0.557123	0.278562	+	0.960418i	$0.410142\pi$
$858$	7.42833	0.253599
$859$	−22.0010	−0.750665	−0.375332	−	0.926890i	$-0.622471\pi$
$859$	−22.0010	−0.750665	−0.375332	+	0.926890i	$0.622471\pi$
$860$	45.5702	1.55393
$861$	−16.4545	−0.560767
$862$	−16.6980	−0.568737
$863$	−11.0086	−0.374736	−0.187368	−	0.982290i	$-0.559996\pi$
$863$	−11.0086	−0.374736	−0.187368	+	0.982290i	$0.559996\pi$
$864$	−37.2575	−1.26753
$865$	−20.6178	−0.701025
$866$	4.96550	0.168734
$867$	−17.5483	−0.595972
$868$	−24.0010	−0.814646
$869$	15.0610	0.510908
$870$	66.6718	2.26039
$871$	26.1367	0.885607
$872$	−7.49130	−0.253687
$873$	24.5232	0.829985
$874$	13.9339	0.471320
$875$	9.06109	0.306321
$876$	−6.27196	−0.211910
$877$	−44.9955	−1.51939	−0.759694	−	0.650280i	$-0.774651\pi$
$877$	−44.9955	−1.51939	−0.759694	+	0.650280i	$0.774651\pi$
$878$	−25.7226	−0.868095
$879$	9.08124	0.306303
$880$	7.47480	0.251975
$881$	30.3369	1.02208	0.511038	−	0.859558i	$-0.329261\pi$
$881$	30.3369	1.02208	0.511038	+	0.859558i	$0.329261\pi$
$882$	21.0568	0.709020
$883$	49.0282	1.64993	0.824964	−	0.565185i	$-0.191195\pi$
$883$	49.0282	1.64993	0.824964	+	0.565185i	$0.191195\pi$
$884$	57.1180	1.92108
$885$	9.03215	0.303613
$886$	−15.0031	−0.504039
$887$	−29.5968	−0.993765	−0.496882	−	0.867818i	$-0.665522\pi$
$887$	−29.5968	−0.993765	−0.496882	+	0.867818i	$0.665522\pi$
$888$	−4.63201	−0.155440
$889$	4.07824	0.136780
$890$	3.09203	0.103645
$891$	−1.59191	−0.0533311
$892$	67.0278	2.24426
$893$	−1.16737	−0.0390646
$894$	21.2258	0.709896
$895$	39.2093	1.31062
$896$	−16.8855	−0.564105
$897$	13.3561	0.445947
$898$	52.5800	1.75462
$899$	55.2021	1.84109
$900$	−37.5821	−1.25274
$901$	−30.8071	−1.02633
$902$	−24.3683	−0.811375
$903$	−7.25380	−0.241391
$904$	1.32851	0.0441854
$905$	66.0072	2.19415
$906$	15.5869	0.517840
$907$	−50.4919	−1.67656	−0.838278	−	0.545243i	$-0.816438\pi$
$907$	−50.4919	−1.67656	−0.838278	+	0.545243i	$0.816438\pi$
$908$	39.9599	1.32611
$909$	29.1853	0.968016
$910$	40.5533	1.34433
$911$	4.74832	0.157319	0.0786594	−	0.996902i	$-0.474936\pi$
$911$	4.74832	0.157319	0.0786594	+	0.996902i	$0.474936\pi$
$912$	−3.46014	−0.114577
$913$	10.3614	0.342913
$914$	41.4296	1.37037
$915$	−3.27922	−0.108408
$916$	34.9601	1.15511
$917$	18.0993	0.597690
$918$	62.5687	2.06508
$919$	−1.12645	−0.0371581	−0.0185791	−	0.999827i	$-0.505914\pi$
$919$	−1.12645	−0.0371581	−0.0185791	+	0.999827i	$0.505914\pi$
$920$	−19.5558	−0.644734
$921$	−13.8287	−0.455671
$922$	−45.5605	−1.50045
$923$	−46.7625	−1.53921
$924$	3.91233	0.128706
$925$	22.1958	0.729792
$926$	77.4290	2.54447
$927$	−11.4986	−0.377663
$928$	71.9624	2.36228
$929$	−33.0322	−1.08375	−0.541876	−	0.840458i	$-0.682286\pi$
$929$	−33.0322	−1.08375	−0.541876	+	0.840458i	$0.682286\pi$
$930$	41.6558	1.36595
$931$	7.73906	0.253637
$932$	69.1331	2.26453
$933$	14.7030	0.481354
$934$	−20.2130	−0.661388
$935$	−20.3609	−0.665872
$936$	−10.9722	−0.358637
$937$	−3.78011	−0.123491	−0.0617454	−	0.998092i	$-0.519667\pi$
$937$	−3.78011	−0.123491	−0.0617454	+	0.998092i	$0.519667\pi$
$938$	24.0436	0.785051
$939$	4.18225	0.136483
$940$	6.46670	0.210920
$941$	−37.2259	−1.21353	−0.606764	−	0.794882i	$-0.707533\pi$
$941$	−37.2259	−1.21353	−0.606764	+	0.794882i	$0.707533\pi$
$942$	−6.05317	−0.197223
$943$	−43.8140	−1.42678
$944$	6.01037	0.195621
$945$	25.4335	0.827353
$946$	−10.7425	−0.349269
$947$	4.77277	0.155094	0.0775472	−	0.996989i	$-0.475291\pi$
$947$	4.77277	0.155094	0.0775472	+	0.996989i	$0.475291\pi$
$948$	38.6207	1.25434
$949$	8.77435	0.284827
$950$	−24.1258	−0.782743
$951$	−4.97803	−0.161424
$952$	13.3123	0.431453
$953$	42.2165	1.36753	0.683764	−	0.729703i	$-0.260342\pi$
$953$	42.2165	1.36753	0.683764	+	0.729703i	$0.260342\pi$
$954$	23.3583	0.756251
$955$	−24.3863	−0.789122
$956$	−71.3957	−2.30910
$957$	−8.99835	−0.290875
$958$	48.0308	1.55180
$959$	30.8756	0.997026
$960$	39.9918	1.29073
$961$	3.48966	0.112570
$962$	25.5771	0.824638
$963$	−27.9311	−0.900066
$964$	19.8070	0.637941
$965$	86.3316	2.77911
$966$	12.2865	0.395312
$967$	13.6122	0.437740	0.218870	−	0.975754i	$-0.429763\pi$
$967$	13.6122	0.437740	0.218870	+	0.975754i	$0.429763\pi$
$968$	1.46794	0.0471812
$969$	9.42521	0.302781
$970$	−87.2068	−2.80004
$971$	−57.5696	−1.84750	−0.923748	−	0.383001i	$-0.874891\pi$
$971$	−57.5696	−1.84750	−0.923748	+	0.383001i	$0.874891\pi$
$972$	−43.1894	−1.38530
$973$	−30.8457	−0.988866
$974$	9.62172	0.308300
$975$	−23.1254	−0.740606
$976$	−2.18213	−0.0698483
$977$	−0.417882	−0.0133692	−0.00668462	−	0.999978i	$-0.502128\pi$
$977$	−0.417882	−0.0133692	−0.00668462	+	0.999978i	$0.502128\pi$
$978$	9.63315	0.308034
$979$	−0.417315	−0.0133374
$980$	−42.8708	−1.36946
$981$	10.6330	0.339486
$982$	−35.4577	−1.13150
$983$	40.5086	1.29202	0.646012	−	0.763328i	$-0.276436\pi$
$983$	40.5086	1.29202	0.646012	+	0.763328i	$0.276436\pi$
$984$	−15.8315	−0.504691
$985$	69.7584	2.22269
$986$	−120.851	−3.84867
$987$	−1.02936	−0.0327649
$988$	−15.9169	−0.506383
$989$	−19.3150	−0.614181
$990$	15.4378	0.490646
$991$	38.3965	1.21971	0.609853	−	0.792514i	$-0.291228\pi$
$991$	38.3965	1.21971	0.609853	+	0.792514i	$0.291228\pi$
$992$	44.9613	1.42752
$993$	−5.58085	−0.177103
$994$	−43.0176	−1.36444
$995$	47.3909	1.50239
$996$	26.5697	0.841893
$997$	−8.37560	−0.265258	−0.132629	−	0.991166i	$-0.542342\pi$
$997$	−8.37560	−0.265258	−0.132629	+	0.991166i	$0.542342\pi$
$998$	80.9802	2.56338
$999$	16.0410	0.507514

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	671.2.a.d.1.18	✓	21
3.2	odd	2		6039.2.a.l.1.4		21
11.10	odd	2		7381.2.a.j.1.4		21

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
671.2.a.d.1.18	✓	21	1.1	even	1	trivial
6039.2.a.l.1.4		21	3.2	odd	2
7381.2.a.j.1.4		21	11.10	odd	2

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:	\( N \)	\(=\)	\( 671 = 11 \cdot 61 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	671.a (trivial)

\(f(q)\)	\(=\)	\(q+2.16302 q^{2} -0.957308 q^{3} +2.67865 q^{4} +3.42546 q^{5} -2.07068 q^{6} +1.52570 q^{7} +1.46794 q^{8} -2.08356 q^{9} +O(q^{10})\)	\(q+2.16302 q^{2} -0.957308 q^{3} +2.67865 q^{4} +3.42546 q^{5} -2.07068 q^{6} +1.52570 q^{7} +1.46794 q^{8} -2.08356 q^{9} +7.40934 q^{10} -1.00000 q^{11} -2.56429 q^{12} +3.58739 q^{13} +3.30011 q^{14} -3.27922 q^{15} -2.18213 q^{16} +5.94398 q^{17} -4.50678 q^{18} -1.65639 q^{19} +9.17561 q^{20} -1.46056 q^{21} -2.16302 q^{22} -3.88910 q^{23} -1.40527 q^{24} +6.73378 q^{25} +7.75960 q^{26} +4.86653 q^{27} +4.08681 q^{28} -9.39965 q^{29} -7.09302 q^{30} -5.87279 q^{31} -7.65586 q^{32} +0.957308 q^{33} +12.8569 q^{34} +5.22621 q^{35} -5.58113 q^{36} +3.29618 q^{37} -3.58280 q^{38} -3.43424 q^{39} +5.02835 q^{40} +11.2659 q^{41} -3.15922 q^{42} +4.96645 q^{43} -2.67865 q^{44} -7.13716 q^{45} -8.41219 q^{46} +0.704770 q^{47} +2.08897 q^{48} -4.67225 q^{49} +14.5653 q^{50} -5.69022 q^{51} +9.60938 q^{52} -5.18291 q^{53} +10.5264 q^{54} -3.42546 q^{55} +2.23962 q^{56} +1.58567 q^{57} -20.3316 q^{58} -2.75436 q^{59} -8.78389 q^{60} +1.00000 q^{61} -12.7030 q^{62} -3.17888 q^{63} -12.1955 q^{64} +12.2885 q^{65} +2.07068 q^{66} +7.28569 q^{67} +15.9219 q^{68} +3.72306 q^{69} +11.3044 q^{70} -13.0352 q^{71} -3.05853 q^{72} +2.44588 q^{73} +7.12970 q^{74} -6.44630 q^{75} -4.43688 q^{76} -1.52570 q^{77} -7.42833 q^{78} -15.0610 q^{79} -7.47480 q^{80} +1.59191 q^{81} +24.3683 q^{82} -10.3614 q^{83} -3.91233 q^{84} +20.3609 q^{85} +10.7425 q^{86} +8.99835 q^{87} -1.46794 q^{88} +0.417315 q^{89} -15.4378 q^{90} +5.47327 q^{91} -10.4175 q^{92} +5.62207 q^{93} +1.52443 q^{94} -5.67389 q^{95} +7.32902 q^{96} -11.7699 q^{97} -10.1062 q^{98} +2.08356 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 21 q + 3 q^{3} + 32 q^{4} + 7 q^{5} + 5 q^{6} + 5 q^{7} - 6 q^{8} + 40 q^{9}+O(q^{10}) \) 21 * q + 3 * q^3 + 32 * q^4 + 7 * q^5 + 5 * q^6 + 5 * q^7 - 6 * q^8 + 40 * q^9	\( 21 q + 3 q^{3} + 32 q^{4} + 7 q^{5} + 5 q^{6} + 5 q^{7} - 6 q^{8} + 40 q^{9} + q^{10} - 21 q^{11} + 6 q^{12} + 20 q^{13} + 17 q^{14} + 18 q^{15} + 50 q^{16} + q^{17} - 5 q^{18} + 15 q^{19} - 2 q^{20} + 16 q^{21} + 11 q^{23} - 16 q^{24} + 48 q^{25} - 5 q^{26} + 12 q^{27} - 16 q^{28} - 9 q^{29} + 16 q^{30} + 22 q^{31} + 3 q^{32} - 3 q^{33} + 33 q^{34} - 39 q^{35} + 57 q^{36} + 21 q^{37} + 11 q^{38} - 28 q^{39} - 16 q^{40} + 7 q^{41} - 55 q^{42} + 16 q^{43} - 32 q^{44} + 44 q^{45} - 3 q^{46} + 5 q^{47} - 71 q^{48} + 80 q^{49} - 33 q^{50} - 19 q^{51} + 60 q^{52} + 9 q^{53} + 13 q^{54} - 7 q^{55} + 44 q^{56} + 39 q^{57} - 27 q^{58} + 13 q^{59} + 70 q^{60} + 21 q^{61} - 23 q^{62} + 24 q^{63} + 66 q^{64} + 25 q^{65} - 5 q^{66} + 38 q^{67} - 74 q^{68} - 17 q^{69} - 33 q^{70} + 12 q^{71} - 75 q^{72} + 20 q^{73} - 12 q^{74} - 10 q^{75} + 59 q^{76} - 5 q^{77} - 14 q^{78} + q^{79} - 38 q^{80} + 89 q^{81} + 7 q^{82} - 19 q^{83} - 14 q^{84} + 38 q^{85} - 3 q^{86} + 4 q^{87} + 6 q^{88} + 37 q^{89} - 174 q^{90} + 24 q^{91} + 31 q^{92} - 15 q^{93} - 64 q^{94} - 43 q^{95} - 38 q^{96} + 68 q^{97} - 2 q^{98} - 40 q^{99}+O(q^{100}) \) 21 * q + 3 * q^3 + 32 * q^4 + 7 * q^5 + 5 * q^6 + 5 * q^7 - 6 * q^8 + 40 * q^9 + q^10 - 21 * q^11 + 6 * q^12 + 20 * q^13 + 17 * q^14 + 18 * q^15 + 50 * q^16 + q^17 - 5 * q^18 + 15 * q^19 - 2 * q^20 + 16 * q^21 + 11 * q^23 - 16 * q^24 + 48 * q^25 - 5 * q^26 + 12 * q^27 - 16 * q^28 - 9 * q^29 + 16 * q^30 + 22 * q^31 + 3 * q^32 - 3 * q^33 + 33 * q^34 - 39 * q^35 + 57 * q^36 + 21 * q^37 + 11 * q^38 - 28 * q^39 - 16 * q^40 + 7 * q^41 - 55 * q^42 + 16 * q^43 - 32 * q^44 + 44 * q^45 - 3 * q^46 + 5 * q^47 - 71 * q^48 + 80 * q^49 - 33 * q^50 - 19 * q^51 + 60 * q^52 + 9 * q^53 + 13 * q^54 - 7 * q^55 + 44 * q^56 + 39 * q^57 - 27 * q^58 + 13 * q^59 + 70 * q^60 + 21 * q^61 - 23 * q^62 + 24 * q^63 + 66 * q^64 + 25 * q^65 - 5 * q^66 + 38 * q^67 - 74 * q^68 - 17 * q^69 - 33 * q^70 + 12 * q^71 - 75 * q^72 + 20 * q^73 - 12 * q^74 - 10 * q^75 + 59 * q^76 - 5 * q^77 - 14 * q^78 + q^79 - 38 * q^80 + 89 * q^81 + 7 * q^82 - 19 * q^83 - 14 * q^84 + 38 * q^85 - 3 * q^86 + 4 * q^87 + 6 * q^88 + 37 * q^89 - 174 * q^90 + 24 * q^91 + 31 * q^92 - 15 * q^93 - 64 * q^94 - 43 * q^95 - 38 * q^96 + 68 * q^97 - 2 * q^98 - 40 * q^99

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