LMFDB - Embedded newform 6043.2.a.c.1.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6043,2,Mod(1,6043)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6043, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("6043.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6043 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6043.a (trivial)

Newform invariants

comment: select newform

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

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

Self dual:	yes
Analytic conductor:	$48.2535979415$
Analytic rank:	$0$
Dimension:	$259$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.15
Character	$\chi$	$=$	6043.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.51359 q^{2} -1.58136 q^{3} +4.31814 q^{4} -2.14765 q^{5} +3.97489 q^{6} -4.03310 q^{7} -5.82684 q^{8} -0.499302 q^{9} +O(q^{10})$	\(q-2.51359 q^{2} -1.58136 q^{3} +4.31814 q^{4} -2.14765 q^{5} +3.97489 q^{6} -4.03310 q^{7} -5.82684 q^{8} -0.499302 q^{9} +5.39832 q^{10} +1.45330 q^{11} -6.82852 q^{12} +5.99398 q^{13} +10.1376 q^{14} +3.39621 q^{15} +6.01002 q^{16} +3.05722 q^{17} +1.25504 q^{18} -4.62539 q^{19} -9.27386 q^{20} +6.37778 q^{21} -3.65300 q^{22} -6.11521 q^{23} +9.21433 q^{24} -0.387578 q^{25} -15.0664 q^{26} +5.53365 q^{27} -17.4155 q^{28} +5.76067 q^{29} -8.53669 q^{30} -4.60045 q^{31} -3.45305 q^{32} -2.29819 q^{33} -7.68460 q^{34} +8.66171 q^{35} -2.15605 q^{36} +5.02750 q^{37} +11.6263 q^{38} -9.47863 q^{39} +12.5140 q^{40} +5.19115 q^{41} -16.0311 q^{42} +0.992502 q^{43} +6.27555 q^{44} +1.07233 q^{45} +15.3711 q^{46} +0.344740 q^{47} -9.50401 q^{48} +9.26589 q^{49} +0.974212 q^{50} -4.83457 q^{51} +25.8828 q^{52} +6.96823 q^{53} -13.9093 q^{54} -3.12119 q^{55} +23.5002 q^{56} +7.31441 q^{57} -14.4800 q^{58} -8.61780 q^{59} +14.6653 q^{60} +2.73119 q^{61} +11.5636 q^{62} +2.01374 q^{63} -3.34050 q^{64} -12.8730 q^{65} +5.77671 q^{66} +1.71398 q^{67} +13.2015 q^{68} +9.67035 q^{69} -21.7720 q^{70} -2.24222 q^{71} +2.90936 q^{72} -4.81056 q^{73} -12.6371 q^{74} +0.612900 q^{75} -19.9731 q^{76} -5.86131 q^{77} +23.8254 q^{78} -2.06274 q^{79} -12.9075 q^{80} -7.25279 q^{81} -13.0484 q^{82} +0.904838 q^{83} +27.5401 q^{84} -6.56586 q^{85} -2.49474 q^{86} -9.10969 q^{87} -8.46816 q^{88} +2.55235 q^{89} -2.69540 q^{90} -24.1743 q^{91} -26.4063 q^{92} +7.27496 q^{93} -0.866535 q^{94} +9.93375 q^{95} +5.46051 q^{96} +4.08290 q^{97} -23.2906 q^{98} -0.725637 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 259 q + 39 q^{2} + 25 q^{3} + 271 q^{4} + 83 q^{5} + 18 q^{6} + 26 q^{7} + 111 q^{8} + 286 q^{9}+O(q^{10}) $ 259 * q + 39 * q^2 + 25 * q^3 + 271 * q^4 + 83 * q^5 + 18 * q^6 + 26 * q^7 + 111 * q^8 + 286 * q^9	\( 259 q + 39 q^{2} + 25 q^{3} + 271 q^{4} + 83 q^{5} + 18 q^{6} + 26 q^{7} + 111 q^{8} + 286 q^{9} + 36 q^{10} + 35 q^{11} + 58 q^{12} + 109 q^{13} + 31 q^{14} + 30 q^{15} + 287 q^{16} + 124 q^{17} + 97 q^{18} + 42 q^{19} + 149 q^{20} + 99 q^{21} + 22 q^{22} + 63 q^{23} + 53 q^{24} + 308 q^{25} + 86 q^{26} + 82 q^{27} + 52 q^{28} + 131 q^{29} + 6 q^{30} + 29 q^{31} + 251 q^{32} + 147 q^{33} + 24 q^{34} + 79 q^{35} + 315 q^{36} + 108 q^{37} + 124 q^{38} + 48 q^{39} + 87 q^{40} + 190 q^{41} + 28 q^{42} + 36 q^{43} + 70 q^{44} + 211 q^{45} + 19 q^{46} + 186 q^{47} + 103 q^{48} + 297 q^{49} + 161 q^{50} + 20 q^{51} + 173 q^{52} + 213 q^{53} + 56 q^{54} + 35 q^{55} + 99 q^{56} + 80 q^{57} + 32 q^{58} + 135 q^{59} + 23 q^{60} + 83 q^{61} + 172 q^{62} + 85 q^{63} + 297 q^{64} + 177 q^{65} + 41 q^{66} + 30 q^{67} + 271 q^{68} + 168 q^{69} + 24 q^{70} + 63 q^{71} + 241 q^{72} + 152 q^{73} + 32 q^{74} + 36 q^{75} + 92 q^{76} + 396 q^{77} + 21 q^{78} - 2 q^{79} + 242 q^{80} + 343 q^{81} + 40 q^{82} + 236 q^{83} + 92 q^{84} + 124 q^{85} + 55 q^{86} + 113 q^{87} + 7 q^{88} + 214 q^{89} + 100 q^{90} + 2 q^{91} + 176 q^{92} + 228 q^{93} + 51 q^{94} + 96 q^{95} + 48 q^{96} + 135 q^{97} + 261 q^{98} + 26 q^{99}+O(q^{100}) \) 259 * q + 39 * q^2 + 25 * q^3 + 271 * q^4 + 83 * q^5 + 18 * q^6 + 26 * q^7 + 111 * q^8 + 286 * q^9 + 36 * q^10 + 35 * q^11 + 58 * q^12 + 109 * q^13 + 31 * q^14 + 30 * q^15 + 287 * q^16 + 124 * q^17 + 97 * q^18 + 42 * q^19 + 149 * q^20 + 99 * q^21 + 22 * q^22 + 63 * q^23 + 53 * q^24 + 308 * q^25 + 86 * q^26 + 82 * q^27 + 52 * q^28 + 131 * q^29 + 6 * q^30 + 29 * q^31 + 251 * q^32 + 147 * q^33 + 24 * q^34 + 79 * q^35 + 315 * q^36 + 108 * q^37 + 124 * q^38 + 48 * q^39 + 87 * q^40 + 190 * q^41 + 28 * q^42 + 36 * q^43 + 70 * q^44 + 211 * q^45 + 19 * q^46 + 186 * q^47 + 103 * q^48 + 297 * q^49 + 161 * q^50 + 20 * q^51 + 173 * q^52 + 213 * q^53 + 56 * q^54 + 35 * q^55 + 99 * q^56 + 80 * q^57 + 32 * q^58 + 135 * q^59 + 23 * q^60 + 83 * q^61 + 172 * q^62 + 85 * q^63 + 297 * q^64 + 177 * q^65 + 41 * q^66 + 30 * q^67 + 271 * q^68 + 168 * q^69 + 24 * q^70 + 63 * q^71 + 241 * q^72 + 152 * q^73 + 32 * q^74 + 36 * q^75 + 92 * q^76 + 396 * q^77 + 21 * q^78 - 2 * q^79 + 242 * q^80 + 343 * q^81 + 40 * q^82 + 236 * q^83 + 92 * q^84 + 124 * q^85 + 55 * q^86 + 113 * q^87 + 7 * q^88 + 214 * q^89 + 100 * q^90 + 2 * q^91 + 176 * q^92 + 228 * q^93 + 51 * q^94 + 96 * q^95 + 48 * q^96 + 135 * q^97 + 261 * q^98 + 26 * 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 $

$2$	−2.51359	−1.77738	−0.888688	−	0.458512i	$-0.848383\pi$
$2$	−2.51359	−1.77738	−0.888688	+	0.458512i	$0.848383\pi$
$3$	−1.58136	−0.912998	−0.456499	−	0.889724i	$-0.650897\pi$
$3$	−1.58136	−0.912998	−0.456499	+	0.889724i	$0.650897\pi$
$4$	4.31814	2.15907
$5$	−2.14765	−0.960461	−0.480230	−	0.877142i	$-0.659447\pi$
$5$	−2.14765	−0.960461	−0.480230	+	0.877142i	$0.659447\pi$
$6$	3.97489	1.62274
$7$	−4.03310	−1.52437	−0.762184	−	0.647360i	$-0.775873\pi$
$7$	−4.03310	−1.52437	−0.762184	+	0.647360i	$0.775873\pi$
$8$	−5.82684	−2.06010
$9$	−0.499302	−0.166434
$10$	5.39832	1.70710
$11$	1.45330	0.438187	0.219093	−	0.975704i	$-0.429690\pi$
$11$	1.45330	0.438187	0.219093	+	0.975704i	$0.429690\pi$
$12$	−6.82852	−1.97123
$13$	5.99398	1.66243	0.831215	−	0.555951i	$-0.187646\pi$
$13$	5.99398	1.66243	0.831215	+	0.555951i	$0.187646\pi$
$14$	10.1376	2.70938
$15$	3.39621	0.876899
$16$	6.01002	1.50251
$17$	3.05722	0.741485	0.370743	−	0.928736i	$-0.379103\pi$
$17$	3.05722	0.741485	0.370743	+	0.928736i	$0.379103\pi$
$18$	1.25504	0.295816
$19$	−4.62539	−1.06114	−0.530569	−	0.847642i	$-0.678022\pi$
$19$	−4.62539	−1.06114	−0.530569	+	0.847642i	$0.678022\pi$
$20$	−9.27386	−2.07370
$21$	6.37778	1.39175
$22$	−3.65300	−0.778823
$23$	−6.11521	−1.27511	−0.637555	−	0.770405i	$-0.720054\pi$
$23$	−6.11521	−1.27511	−0.637555	+	0.770405i	$0.720054\pi$
$24$	9.21433	1.88087
$25$	−0.387578	−0.0775156
$26$	−15.0664	−2.95476
$27$	5.53365	1.06495
$28$	−17.4155	−3.29121
$29$	5.76067	1.06973	0.534865	−	0.844937i	$-0.320362\pi$
$29$	5.76067	1.06973	0.534865	+	0.844937i	$0.320362\pi$
$30$	−8.53669	−1.55858
$31$	−4.60045	−0.826265	−0.413133	−	0.910671i	$-0.635565\pi$
$31$	−4.60045	−0.826265	−0.413133	+	0.910671i	$0.635565\pi$
$32$	−3.45305	−0.610418
$33$	−2.29819	−0.400064
$34$	−7.68460	−1.31790
$35$	8.66171	1.46410
$36$	−2.15605	−0.359342
$37$	5.02750	0.826516	0.413258	−	0.910614i	$-0.364391\pi$
$37$	5.02750	0.826516	0.413258	+	0.910614i	$0.364391\pi$
$38$	11.6263	1.88604
$39$	−9.47863	−1.51780
$40$	12.5140	1.97864
$41$	5.19115	0.810721	0.405360	−	0.914157i	$-0.367146\pi$
$41$	5.19115	0.810721	0.405360	+	0.914157i	$0.367146\pi$
$42$	−16.0311	−2.47366
$43$	0.992502	0.151355	0.0756775	−	0.997132i	$-0.475888\pi$
$43$	0.992502	0.151355	0.0756775	+	0.997132i	$0.475888\pi$
$44$	6.27555	0.946075
$45$	1.07233	0.159853
$46$	15.3711	2.26635
$47$	0.344740	0.0502855	0.0251427	−	0.999684i	$-0.491996\pi$
$47$	0.344740	0.0502855	0.0251427	+	0.999684i	$0.491996\pi$
$48$	−9.50401	−1.37178
$49$	9.26589	1.32370
$50$	0.974212	0.137774
$51$	−4.83457	−0.676975
$52$	25.8828	3.58930
$53$	6.96823	0.957160	0.478580	−	0.878044i	$-0.341152\pi$
$53$	6.96823	0.957160	0.478580	+	0.878044i	$0.341152\pi$
$54$	−13.9093	−1.89282
$55$	−3.12119	−0.420861
$56$	23.5002	3.14035
$57$	7.31441	0.968817
$58$	−14.4800	−1.90131
$59$	−8.61780	−1.12194	−0.560971	−	0.827836i	$-0.689572\pi$
$59$	−8.61780	−1.12194	−0.560971	+	0.827836i	$0.689572\pi$
$60$	14.6653	1.89328
$61$	2.73119	0.349693	0.174846	−	0.984596i	$-0.444057\pi$
$61$	2.73119	0.349693	0.174846	+	0.984596i	$0.444057\pi$
$62$	11.5636	1.46858
$63$	2.01374	0.253707
$64$	−3.34050	−0.417562
$65$	−12.8730	−1.59670
$66$	5.77671	0.711064
$67$	1.71398	0.209397	0.104698	−	0.994504i	$-0.466612\pi$
$67$	1.71398	0.209397	0.104698	+	0.994504i	$0.466612\pi$
$68$	13.2015	1.60092
$69$	9.67035	1.16417
$70$	−21.7720	−2.60225
$71$	−2.24222	−0.266103	−0.133051	−	0.991109i	$-0.542477\pi$
$71$	−2.24222	−0.266103	−0.133051	+	0.991109i	$0.542477\pi$
$72$	2.90936	0.342871
$73$	−4.81056	−0.563033	−0.281517	−	0.959556i	$-0.590837\pi$
$73$	−4.81056	−0.563033	−0.281517	+	0.959556i	$0.590837\pi$
$74$	−12.6371	−1.46903
$75$	0.612900	0.0707716
$76$	−19.9731	−2.29107
$77$	−5.86131	−0.667958
$78$	23.8254	2.69770
$79$	−2.06274	−0.232076	−0.116038	−	0.993245i	$-0.537020\pi$
$79$	−2.06274	−0.232076	−0.116038	+	0.993245i	$0.537020\pi$
$80$	−12.9075	−1.44310
$81$	−7.25279	−0.805866
$82$	−13.0484	−1.44096
$83$	0.904838	0.0993189	0.0496594	−	0.998766i	$-0.484186\pi$
$83$	0.904838	0.0993189	0.0496594	+	0.998766i	$0.484186\pi$
$84$	27.5401	3.00487
$85$	−6.56586	−0.712167
$86$	−2.49474	−0.269015
$87$	−9.10969	−0.976662
$88$	−8.46816	−0.902709
$89$	2.55235	0.270548	0.135274	−	0.990808i	$-0.456808\pi$
$89$	2.55235	0.270548	0.135274	+	0.990808i	$0.456808\pi$
$90$	−2.69540	−0.284120
$91$	−24.1743	−2.53416
$92$	−26.4063	−2.75305
$93$	7.27496	0.754379
$94$	−0.866535	−0.0893763
$95$	9.93375	1.01918
$96$	5.46051	0.557311
$97$	4.08290	0.414555	0.207278	−	0.978282i	$-0.433540\pi$
$97$	4.08290	0.414555	0.207278	+	0.978282i	$0.433540\pi$
$98$	−23.2906	−2.35271
$99$	−0.725637	−0.0729292
$100$	−1.67361	−0.167361
$101$	−15.7707	−1.56925	−0.784624	−	0.619972i	$-0.787144\pi$
$101$	−15.7707	−1.56925	−0.784624	+	0.619972i	$0.787144\pi$
$102$	12.1521	1.20324
$103$	−1.48471	−0.146292	−0.0731462	−	0.997321i	$-0.523304\pi$
$103$	−1.48471	−0.146292	−0.0731462	+	0.997321i	$0.523304\pi$
$104$	−34.9260	−3.42477
$105$	−13.6973	−1.33672
$106$	−17.5153	−1.70123
$107$	−13.3562	−1.29119	−0.645595	−	0.763680i	$-0.723391\pi$
$107$	−13.3562	−1.29119	−0.645595	+	0.763680i	$0.723391\pi$
$108$	23.8951	2.29930
$109$	−6.53299	−0.625747	−0.312874	−	0.949795i	$-0.601292\pi$
$109$	−6.53299	−0.625747	−0.312874	+	0.949795i	$0.601292\pi$
$110$	7.84539	0.748029
$111$	−7.95028	−0.754607
$112$	−24.2390	−2.29037
$113$	14.2534	1.34084	0.670422	−	0.741980i	$-0.266113\pi$
$113$	14.2534	1.34084	0.670422	+	0.741980i	$0.266113\pi$
$114$	−18.3854	−1.72195
$115$	13.1334	1.22469
$116$	24.8754	2.30962
$117$	−2.99281	−0.276685
$118$	21.6616	1.99411
$119$	−12.3301	−1.13030
$120$	−19.7892	−1.80650
$121$	−8.88791	−0.807992
$122$	−6.86509	−0.621536
$123$	−8.20907	−0.740187
$124$	−19.8654	−1.78396
$125$	11.5707	1.03491
$126$	−5.06171	−0.450933
$127$	−2.75770	−0.244706	−0.122353	−	0.992487i	$-0.539044\pi$
$127$	−2.75770	−0.244706	−0.122353	+	0.992487i	$0.539044\pi$
$128$	15.3027	1.35258
$129$	−1.56950	−0.138187
$130$	32.3574	2.83794
$131$	5.24117	0.457923	0.228962	−	0.973435i	$-0.426467\pi$
$131$	5.24117	0.457923	0.228962	+	0.973435i	$0.426467\pi$
$132$	−9.92390	−0.863765
$133$	18.6547	1.61756
$134$	−4.30826	−0.372177
$135$	−11.8844	−1.02284
$136$	−17.8140	−1.52753
$137$	6.41681	0.548225	0.274113	−	0.961698i	$-0.411616\pi$
$137$	6.41681	0.548225	0.274113	+	0.961698i	$0.411616\pi$
$138$	−24.3073	−2.06917
$139$	−18.3885	−1.55969	−0.779846	−	0.625972i	$-0.784703\pi$
$139$	−18.3885	−1.55969	−0.779846	+	0.625972i	$0.784703\pi$
$140$	37.4024	3.16108
$141$	−0.545158	−0.0459106
$142$	5.63602	0.472964
$143$	8.71106	0.728455
$144$	−3.00082	−0.250068
$145$	−12.3719	−1.02743
$146$	12.0918	1.00072
$147$	−14.6527	−1.20853
$148$	21.7094	1.78450
$149$	8.03653	0.658378	0.329189	−	0.944264i	$-0.393225\pi$
$149$	8.03653	0.658378	0.329189	+	0.944264i	$0.393225\pi$
$150$	−1.54058	−0.125788
$151$	−7.36833	−0.599626	−0.299813	−	0.953998i	$-0.596924\pi$
$151$	−7.36833	−0.599626	−0.299813	+	0.953998i	$0.596924\pi$
$152$	26.9514	2.18605
$153$	−1.52648	−0.123408
$154$	14.7329	1.18721
$155$	9.88018	0.793595
$156$	−40.9300	−3.27702
$157$	−8.40551	−0.670832	−0.335416	−	0.942070i	$-0.608877\pi$
$157$	−8.40551	−0.670832	−0.335416	+	0.942070i	$0.608877\pi$
$158$	5.18488	0.412487
$159$	−11.0193	−0.873885
$160$	7.41596	0.586283
$161$	24.6633	1.94374
$162$	18.2305	1.43233
$163$	−5.86048	−0.459028	−0.229514	−	0.973305i	$-0.573714\pi$
$163$	−5.86048	−0.459028	−0.229514	+	0.973305i	$0.573714\pi$
$164$	22.4161	1.75040
$165$	4.93572	0.384246
$166$	−2.27439	−0.176527
$167$	11.3107	0.875246	0.437623	−	0.899159i	$-0.355821\pi$
$167$	11.3107	0.875246	0.437623	+	0.899159i	$0.355821\pi$
$168$	−37.1623	−2.86713
$169$	22.9278	1.76367
$170$	16.5039	1.26579
$171$	2.30947	0.176610
$172$	4.28576	0.326786
$173$	−21.3887	−1.62615	−0.813075	−	0.582160i	$-0.802208\pi$
$173$	−21.3887	−1.62615	−0.813075	+	0.582160i	$0.802208\pi$
$174$	22.8980	1.73590
$175$	1.56314	0.118162
$176$	8.73437	0.658378
$177$	13.6278	1.02433
$178$	−6.41556	−0.480867
$179$	−26.0414	−1.94642	−0.973212	−	0.229908i	$-0.926157\pi$
$179$	−26.0414	−1.94642	−0.973212	+	0.229908i	$0.926157\pi$
$180$	4.63046	0.345134
$181$	−10.6563	−0.792078	−0.396039	−	0.918234i	$-0.629615\pi$
$181$	−10.6563	−0.792078	−0.396039	+	0.918234i	$0.629615\pi$
$182$	60.7643	4.50415
$183$	−4.31899	−0.319269
$184$	35.6324	2.62685
$185$	−10.7973	−0.793836
$186$	−18.2863	−1.34081
$187$	4.44307	0.324909
$188$	1.48863	0.108570
$189$	−22.3178	−1.62338
$190$	−24.9694	−1.81147
$191$	−1.71142	−0.123834	−0.0619169	−	0.998081i	$-0.519721\pi$
$191$	−1.71142	−0.123834	−0.0619169	+	0.998081i	$0.519721\pi$
$192$	5.28253	0.381233
$193$	−11.1641	−0.803610	−0.401805	−	0.915725i	$-0.631617\pi$
$193$	−11.1641	−0.803610	−0.401805	+	0.915725i	$0.631617\pi$
$194$	−10.2627	−0.736821
$195$	20.3568	1.45778
$196$	40.0114	2.85795
$197$	13.9939	0.997021	0.498510	−	0.866884i	$-0.333881\pi$
$197$	13.9939	0.997021	0.498510	+	0.866884i	$0.333881\pi$
$198$	1.82395	0.129623
$199$	5.11843	0.362836	0.181418	−	0.983406i	$-0.441931\pi$
$199$	5.11843	0.362836	0.181418	+	0.983406i	$0.441931\pi$
$200$	2.25836	0.159690
$201$	−2.71043	−0.191179
$202$	39.6412	2.78914
$203$	−23.2334	−1.63066
$204$	−20.8763	−1.46163
$205$	−11.1488	−0.778665
$206$	3.73194	0.260017
$207$	3.05334	0.212222
$208$	36.0239	2.49781
$209$	−6.72209	−0.464977
$210$	34.4293	2.37585
$211$	−24.5075	−1.68717	−0.843584	−	0.536997i	$-0.819559\pi$
$211$	−24.5075	−1.68717	−0.843584	+	0.536997i	$0.819559\pi$
$212$	30.0898	2.06657
$213$	3.54576	0.242951
$214$	33.5720	2.29493
$215$	−2.13155	−0.145371
$216$	−32.2437	−2.19391
$217$	18.5541	1.25953
$218$	16.4213	1.11219
$219$	7.60722	0.514049
$220$	−13.4777	−0.908668
$221$	18.3249	1.23267
$222$	19.9838	1.34122
$223$	−6.71371	−0.449583	−0.224792	−	0.974407i	$-0.572170\pi$
$223$	−6.71371	−0.449583	−0.224792	+	0.974407i	$0.572170\pi$
$224$	13.9265	0.930502
$225$	0.193519	0.0129012
$226$	−35.8271	−2.38319
$227$	17.8903	1.18742	0.593711	−	0.804679i	$-0.297662\pi$
$227$	17.8903	1.18742	0.593711	+	0.804679i	$0.297662\pi$
$228$	31.5846	2.09174
$229$	−7.75326	−0.512350	−0.256175	−	0.966630i	$-0.582462\pi$
$229$	−7.75326	−0.512350	−0.256175	+	0.966630i	$0.582462\pi$
$230$	−33.0119	−2.17674
$231$	9.26884	0.609845
$232$	−33.5665	−2.20375
$233$	−15.4189	−1.01013	−0.505064	−	0.863082i	$-0.668531\pi$
$233$	−15.4189	−1.01013	−0.505064	+	0.863082i	$0.668531\pi$
$234$	7.52269	0.491774
$235$	−0.740383	−0.0482972
$236$	−37.2128	−2.42235
$237$	3.26193	0.211885
$238$	30.9928	2.00896
$239$	22.0561	1.42669	0.713345	−	0.700813i	$-0.247179\pi$
$239$	22.0561	1.42669	0.713345	+	0.700813i	$0.247179\pi$
$240$	20.4113	1.31755
$241$	7.63460	0.491788	0.245894	−	0.969297i	$-0.420919\pi$
$241$	7.63460	0.491788	0.245894	+	0.969297i	$0.420919\pi$
$242$	22.3406	1.43611
$243$	−5.13170	−0.329198
$244$	11.7936	0.755010
$245$	−19.8999	−1.27136
$246$	20.6342	1.31559
$247$	−27.7245	−1.76407
$248$	26.8061	1.70219
$249$	−1.43087	−0.0906779
$250$	−29.0839	−1.83943
$251$	5.29457	0.334190	0.167095	−	0.985941i	$-0.446561\pi$
$251$	5.29457	0.334190	0.167095	+	0.985941i	$0.446561\pi$
$252$	8.69558	0.547770
$253$	−8.88725	−0.558736
$254$	6.93172	0.434935
$255$	10.3830	0.650208
$256$	−31.7838	−1.98649
$257$	16.7436	1.04444	0.522220	−	0.852811i	$-0.325104\pi$
$257$	16.7436	1.04444	0.522220	+	0.852811i	$0.325104\pi$
$258$	3.94508	0.245610
$259$	−20.2764	−1.25991
$260$	−55.5873	−3.44738
$261$	−2.87632	−0.178040
$262$	−13.1742	−0.813902
$263$	−11.3356	−0.698982	−0.349491	−	0.936940i	$-0.613645\pi$
$263$	−11.3356	−0.698982	−0.349491	+	0.936940i	$0.613645\pi$
$264$	13.3912	0.824172
$265$	−14.9654	−0.919314
$266$	−46.8902	−2.87502
$267$	−4.03618	−0.247010
$268$	7.40122	0.452101
$269$	−1.84089	−0.112241	−0.0561205	−	0.998424i	$-0.517873\pi$
$269$	−1.84089	−0.112241	−0.0561205	+	0.998424i	$0.517873\pi$
$270$	29.8725	1.81798
$271$	9.98584	0.606597	0.303298	−	0.952896i	$-0.401912\pi$
$271$	9.98584	0.606597	0.303298	+	0.952896i	$0.401912\pi$
$272$	18.3740	1.11409
$273$	38.2283	2.31368
$274$	−16.1292	−0.974403
$275$	−0.563268	−0.0339663
$276$	41.7579	2.51353
$277$	−16.5129	−0.992161	−0.496081	−	0.868277i	$-0.665228\pi$
$277$	−16.5129	−0.992161	−0.496081	+	0.868277i	$0.665228\pi$
$278$	46.2211	2.77216
$279$	2.29701	0.137519
$280$	−50.4704	−3.01618
$281$	11.7111	0.698623	0.349312	−	0.937007i	$-0.386416\pi$
$281$	11.7111	0.698623	0.349312	+	0.937007i	$0.386416\pi$
$282$	1.37030	0.0816004
$283$	25.7202	1.52891	0.764454	−	0.644679i	$-0.223009\pi$
$283$	25.7202	1.52891	0.764454	+	0.644679i	$0.223009\pi$
$284$	−9.68221	−0.574533
$285$	−15.7088	−0.930510
$286$	−21.8960	−1.29474
$287$	−20.9364	−1.23584
$288$	1.72411	0.101594
$289$	−7.65339	−0.450200
$290$	31.0980	1.82614
$291$	−6.45652	−0.378488
$292$	−20.7726	−1.21563
$293$	4.74029	0.276931	0.138465	−	0.990367i	$-0.455783\pi$
$293$	4.74029	0.276931	0.138465	+	0.990367i	$0.455783\pi$
$294$	36.8309	2.14802
$295$	18.5081	1.07758
$296$	−29.2944	−1.70270
$297$	8.04207	0.466648
$298$	−20.2005	−1.17019
$299$	−36.6544	−2.11978
$300$	2.64659	0.152801
$301$	−4.00286	−0.230721
$302$	18.5210	1.06576
$303$	24.9392	1.43272
$304$	−27.7987	−1.59437
$305$	−5.86565	−0.335866
$306$	3.83694	0.219343
$307$	−15.4333	−0.880825	−0.440412	−	0.897796i	$-0.645168\pi$
$307$	−15.4333	−0.880825	−0.440412	+	0.897796i	$0.645168\pi$
$308$	−25.3099	−1.44217
$309$	2.34785	0.133565
$310$	−24.8347	−1.41052
$311$	−25.4078	−1.44075	−0.720373	−	0.693587i	$-0.756030\pi$
$311$	−25.4078	−1.44075	−0.720373	+	0.693587i	$0.756030\pi$
$312$	55.2305	3.12681
$313$	21.7510	1.22944	0.614720	−	0.788746i	$-0.289269\pi$
$313$	21.7510	1.22944	0.614720	+	0.788746i	$0.289269\pi$
$314$	21.1280	1.19232
$315$	−4.32481	−0.243675
$316$	−8.90719	−0.501069
$317$	−14.8225	−0.832513	−0.416256	−	0.909247i	$-0.636658\pi$
$317$	−14.8225	−0.832513	−0.416256	+	0.909247i	$0.636658\pi$
$318$	27.6979	1.55322
$319$	8.37199	0.468742
$320$	7.17423	0.401052
$321$	21.1209	1.17886
$322$	−61.9933	−3.45475
$323$	−14.1409	−0.786818
$324$	−31.3185	−1.73992
$325$	−2.32313	−0.128864
$326$	14.7308	0.815866
$327$	10.3310	0.571306
$328$	−30.2480	−1.67017
$329$	−1.39037	−0.0766536
$330$	−12.4064	−0.682949
$331$	−7.91645	−0.435128	−0.217564	−	0.976046i	$-0.569811\pi$
$331$	−7.91645	−0.435128	−0.217564	+	0.976046i	$0.569811\pi$
$332$	3.90721	0.214436
$333$	−2.51024	−0.137560
$334$	−28.4304	−1.55564
$335$	−3.68105	−0.201117
$336$	38.3306	2.09111
$337$	−6.47028	−0.352459	−0.176229	−	0.984349i	$-0.556390\pi$
$337$	−6.47028	−0.352459	−0.176229	+	0.984349i	$0.556390\pi$
$338$	−57.6310	−3.13471
$339$	−22.5397	−1.22419
$340$	−28.3523	−1.53762
$341$	−6.68584	−0.362059
$342$	−5.80506	−0.313902
$343$	−9.13856	−0.493436
$344$	−5.78315	−0.311807
$345$	−20.7686	−1.11814
$346$	53.7623	2.89028
$347$	20.1477	1.08158	0.540792	−	0.841157i	$-0.318125\pi$
$347$	20.1477	1.08158	0.540792	+	0.841157i	$0.318125\pi$
$348$	−39.3369	−2.10868
$349$	−17.3537	−0.928923	−0.464461	−	0.885593i	$-0.653752\pi$
$349$	−17.3537	−0.928923	−0.464461	+	0.885593i	$0.653752\pi$
$350$	−3.92909	−0.210019
$351$	33.1686	1.77041
$352$	−5.01832	−0.267477
$353$	19.6285	1.04472	0.522359	−	0.852726i	$-0.325052\pi$
$353$	19.6285	1.04472	0.522359	+	0.852726i	$0.325052\pi$
$354$	−34.2548	−1.82062
$355$	4.81551	0.255581
$356$	11.0214	0.584132
$357$	19.4983	1.03196
$358$	65.4574	3.45953
$359$	3.16553	0.167070	0.0835350	−	0.996505i	$-0.473379\pi$
$359$	3.16553	0.167070	0.0835350	+	0.996505i	$0.473379\pi$
$360$	−6.24829	−0.329314
$361$	2.39426	0.126013
$362$	26.7856	1.40782
$363$	14.0550	0.737696
$364$	−104.388	−5.47141
$365$	10.3314	0.540771
$366$	10.8562	0.567461
$367$	−10.2259	−0.533787	−0.266893	−	0.963726i	$-0.585997\pi$
$367$	−10.2259	−0.533787	−0.266893	+	0.963726i	$0.585997\pi$
$368$	−36.7526	−1.91586
$369$	−2.59195	−0.134932
$370$	27.1401	1.41095
$371$	−28.1036	−1.45906
$372$	31.4143	1.62875
$373$	−19.6926	−1.01965	−0.509823	−	0.860280i	$-0.670289\pi$
$373$	−19.6926	−1.01965	−0.509823	+	0.860280i	$0.670289\pi$
$374$	−11.1680	−0.577486
$375$	−18.2974	−0.944872
$376$	−2.00875	−0.103593
$377$	34.5293	1.77835
$378$	56.0977	2.88536
$379$	−1.85922	−0.0955015	−0.0477507	−	0.998859i	$-0.515205\pi$
$379$	−1.85922	−0.0955015	−0.0477507	+	0.998859i	$0.515205\pi$
$380$	42.8953	2.20048
$381$	4.36091	0.223416
$382$	4.30180	0.220099
$383$	20.8411	1.06493	0.532465	−	0.846452i	$-0.321266\pi$
$383$	20.8411	1.06493	0.532465	+	0.846452i	$0.321266\pi$
$384$	−24.1991	−1.23491
$385$	12.5881	0.641547
$386$	28.0620	1.42832
$387$	−0.495558	−0.0251907
$388$	17.6305	0.895053
$389$	22.6033	1.14604	0.573018	−	0.819543i	$-0.305773\pi$
$389$	22.6033	1.14604	0.573018	+	0.819543i	$0.305773\pi$
$390$	−51.1687	−2.59103
$391$	−18.6956	−0.945475
$392$	−53.9909	−2.72695
$393$	−8.28818	−0.418083
$394$	−35.1748	−1.77208
$395$	4.43006	0.222900
$396$	−3.13340	−0.157459
$397$	−28.6144	−1.43612	−0.718058	−	0.695983i	$-0.754969\pi$
$397$	−28.6144	−1.43612	−0.718058	+	0.695983i	$0.754969\pi$
$398$	−12.8656	−0.644896
$399$	−29.4997	−1.47683
$400$	−2.32935	−0.116468
$401$	5.05306	0.252338	0.126169	−	0.992009i	$-0.459732\pi$
$401$	5.05306	0.252338	0.126169	+	0.992009i	$0.459732\pi$
$402$	6.81290	0.339797
$403$	−27.5750	−1.37361
$404$	−68.1002	−3.38811
$405$	15.5765	0.774002
$406$	58.3992	2.89830
$407$	7.30647	0.362168
$408$	28.1703	1.39464
$409$	−19.8108	−0.979581	−0.489790	−	0.871840i	$-0.662927\pi$
$409$	−19.8108	−0.979581	−0.489790	+	0.871840i	$0.662927\pi$
$410$	28.0235	1.38398
$411$	−10.1473	−0.500529
$412$	−6.41116	−0.315855
$413$	34.7564	1.71025
$414$	−7.67484	−0.377198
$415$	−1.94328	−0.0953918
$416$	−20.6975	−1.01478
$417$	29.0788	1.42400
$418$	16.8966	0.826439
$419$	−24.9863	−1.22066	−0.610330	−	0.792147i	$-0.708963\pi$
$419$	−24.9863	−1.22066	−0.610330	+	0.792147i	$0.708963\pi$
$420$	−59.1467	−2.88606
$421$	18.5685	0.904976	0.452488	−	0.891771i	$-0.350537\pi$
$421$	18.5685	0.904976	0.452488	+	0.891771i	$0.350537\pi$
$422$	61.6019	2.99873
$423$	−0.172129	−0.00836922
$424$	−40.6028	−1.97184
$425$	−1.18491	−0.0574767
$426$	−8.91257	−0.431816
$427$	−11.0152	−0.533061
$428$	−57.6738	−2.78777
$429$	−13.7753	−0.665078
$430$	5.35785	0.258378
$431$	12.4415	0.599287	0.299644	−	0.954051i	$-0.403132\pi$
$431$	12.4415	0.599287	0.299644	+	0.954051i	$0.403132\pi$
$432$	33.2574	1.60010
$433$	−4.07444	−0.195805	−0.0979025	−	0.995196i	$-0.531213\pi$
$433$	−4.07444	−0.195805	−0.0979025	+	0.995196i	$0.531213\pi$
$434$	−46.6373	−2.23866
$435$	19.5645	0.938045
$436$	−28.2104	−1.35103
$437$	28.2853	1.35307
$438$	−19.1214	−0.913658
$439$	19.4406	0.927847	0.463924	−	0.885875i	$-0.346441\pi$
$439$	19.4406	0.927847	0.463924	+	0.885875i	$0.346441\pi$
$440$	18.1867	0.867016
$441$	−4.62648	−0.220309
$442$	−46.0613	−2.19091
$443$	29.1474	1.38483	0.692416	−	0.721498i	$-0.256546\pi$
$443$	29.1474	1.38483	0.692416	+	0.721498i	$0.256546\pi$
$444$	−34.3304	−1.62925
$445$	−5.48157	−0.259851
$446$	16.8755	0.799079
$447$	−12.7086	−0.601098
$448$	13.4726	0.636518
$449$	35.0399	1.65363	0.826817	−	0.562471i	$-0.190149\pi$
$449$	35.0399	1.65363	0.826817	+	0.562471i	$0.190149\pi$
$450$	−0.486426	−0.0229304
$451$	7.54430	0.355247
$452$	61.5480	2.89497
$453$	11.6520	0.547458
$454$	−44.9689	−2.11049
$455$	51.9181	2.43396
$456$	−42.6199	−1.99586
$457$	−13.0492	−0.610415	−0.305208	−	0.952286i	$-0.598726\pi$
$457$	−13.0492	−0.610415	−0.305208	+	0.952286i	$0.598726\pi$
$458$	19.4885	0.910639
$459$	16.9176	0.789647
$460$	56.7116	2.64419
$461$	1.50240	0.0699738	0.0349869	−	0.999388i	$-0.488861\pi$
$461$	1.50240	0.0699738	0.0349869	+	0.999388i	$0.488861\pi$
$462$	−23.2981	−1.08392
$463$	19.3988	0.901537	0.450769	−	0.892641i	$-0.351150\pi$
$463$	19.3988	0.901537	0.450769	+	0.892641i	$0.351150\pi$
$464$	34.6218	1.60728
$465$	−15.6241	−0.724551
$466$	38.7569	1.79538
$467$	−15.4801	−0.716336	−0.358168	−	0.933657i	$-0.616598\pi$
$467$	−15.4801	−0.716336	−0.358168	+	0.933657i	$0.616598\pi$
$468$	−12.9233	−0.597382
$469$	−6.91267	−0.319197
$470$	1.86102	0.0858424
$471$	13.2921	0.612469
$472$	50.2146	2.31131
$473$	1.44240	0.0663218
$474$	−8.19917	−0.376600
$475$	1.79270	0.0822547
$476$	−53.2430	−2.44039
$477$	−3.47925	−0.159304
$478$	−55.4400	−2.53577
$479$	20.9538	0.957404	0.478702	−	0.877977i	$-0.341107\pi$
$479$	20.9538	0.957404	0.478702	+	0.877977i	$0.341107\pi$
$480$	−11.7273	−0.535275
$481$	30.1347	1.37402
$482$	−19.1903	−0.874092
$483$	−39.0015	−1.77463
$484$	−38.3792	−1.74451
$485$	−8.76865	−0.398164
$486$	12.8990	0.585110
$487$	28.9381	1.31131	0.655655	−	0.755060i	$-0.272393\pi$
$487$	28.9381	1.31131	0.655655	+	0.755060i	$0.272393\pi$
$488$	−15.9142	−0.720402
$489$	9.26752	0.419092
$490$	50.0203	2.25969
$491$	−15.6624	−0.706835	−0.353418	−	0.935466i	$-0.614981\pi$
$491$	−15.6624	−0.706835	−0.353418	+	0.935466i	$0.614981\pi$
$492$	−35.4479	−1.59811
$493$	17.6117	0.793189
$494$	69.6880	3.13541
$495$	1.55842	0.0700457
$496$	−27.6488	−1.24147
$497$	9.04309	0.405638
$498$	3.59663	0.161169
$499$	39.0294	1.74719	0.873597	−	0.486650i	$-0.161781\pi$
$499$	39.0294	1.74719	0.873597	+	0.486650i	$0.161781\pi$
$500$	49.9637	2.23444
$501$	−17.8862	−0.799098
$502$	−13.3084	−0.593982
$503$	−20.7930	−0.927114	−0.463557	−	0.886067i	$-0.653427\pi$
$503$	−20.7930	−0.927114	−0.463557	+	0.886067i	$0.653427\pi$
$504$	−11.7337	−0.522661
$505$	33.8701	1.50720
$506$	22.3389	0.993085
$507$	−36.2571	−1.61023
$508$	−11.9081	−0.528337
$509$	−5.97723	−0.264936	−0.132468	−	0.991187i	$-0.542290\pi$
$509$	−5.97723	−0.264936	−0.132468	+	0.991187i	$0.542290\pi$
$510$	−26.0986	−1.15566
$511$	19.4015	0.858270
$512$	49.2860	2.17815
$513$	−25.5953	−1.13006
$514$	−42.0867	−1.85636
$515$	3.18864	0.140508
$516$	−6.77732	−0.298355
$517$	0.501011	0.0220344
$518$	50.9666	2.23934
$519$	33.8231	1.48467
$520$	75.0089	3.28936
$521$	−18.0441	−0.790528	−0.395264	−	0.918568i	$-0.629347\pi$
$521$	−18.0441	−0.790528	−0.395264	+	0.918568i	$0.629347\pi$
$522$	7.22988	0.316443
$523$	29.8709	1.30616	0.653081	−	0.757288i	$-0.273476\pi$
$523$	29.8709	1.30616	0.653081	+	0.757288i	$0.273476\pi$
$524$	22.6321	0.988687
$525$	−2.47189	−0.107882
$526$	28.4930	1.24235
$527$	−14.0646	−0.612663
$528$	−13.8122	−0.601098
$529$	14.3958	0.625905
$530$	37.6168	1.63397
$531$	4.30289	0.186729
$532$	80.5534	3.49243
$533$	31.1156	1.34777
$534$	10.1453	0.439030
$535$	28.6845	1.24014
$536$	−9.98712	−0.431378
$537$	41.1808	1.77708
$538$	4.62724	0.199495
$539$	13.4661	0.580027
$540$	−51.3184	−2.20839
$541$	−19.0214	−0.817792	−0.408896	−	0.912581i	$-0.634086\pi$
$541$	−19.0214	−0.817792	−0.408896	+	0.912581i	$0.634086\pi$
$542$	−25.1003	−1.07815
$543$	16.8515	0.723166
$544$	−10.5567	−0.452616
$545$	14.0306	0.601006
$546$	−96.0902	−4.11228
$547$	39.6288	1.69440	0.847202	−	0.531271i	$-0.178285\pi$
$547$	39.6288	1.69440	0.847202	+	0.531271i	$0.178285\pi$
$548$	27.7087	1.18366
$549$	−1.36369	−0.0582008
$550$	1.41582	0.0603710
$551$	−26.6454	−1.13513
$552$	−56.3476	−2.39831
$553$	8.31924	0.353770
$554$	41.5065	1.76344
$555$	17.0745	0.724771
$556$	−79.4040	−3.36748
$557$	−35.6110	−1.50888	−0.754442	−	0.656366i	$-0.772093\pi$
$557$	−35.6110	−1.50888	−0.754442	+	0.656366i	$0.772093\pi$
$558$	−5.77375	−0.244422
$559$	5.94903	0.251617
$560$	52.0570	2.19981
$561$	−7.02608	−0.296642
$562$	−29.4368	−1.24172
$563$	34.4399	1.45147	0.725735	−	0.687974i	$-0.241500\pi$
$563$	34.4399	1.45147	0.725735	+	0.687974i	$0.241500\pi$
$564$	−2.35407	−0.0991240
$565$	−30.6113	−1.28783
$566$	−64.6500	−2.71744
$567$	29.2512	1.22844
$568$	13.0651	0.548198
$569$	−39.4503	−1.65384	−0.826922	−	0.562317i	$-0.809910\pi$
$569$	−39.4503	−1.65384	−0.826922	+	0.562317i	$0.809910\pi$
$570$	39.4855	1.65387
$571$	9.24450	0.386870	0.193435	−	0.981113i	$-0.438037\pi$
$571$	9.24450	0.386870	0.193435	+	0.981113i	$0.438037\pi$
$572$	37.6155	1.57278
$573$	2.70637	0.113060
$574$	52.6256	2.19655
$575$	2.37012	0.0988409
$576$	1.66792	0.0694966
$577$	−0.00412237	−0.000171616 0	−8.58082e−5	−	1.00000i	$-0.500027\pi$
$577$	−0.00412237	−0.000171616 0	−8.58082e−5		1.00000i	$0.500027\pi$
$578$	19.2375	0.800174
$579$	17.6545	0.733694
$580$	−53.4237	−2.21830
$581$	−3.64930	−0.151399
$582$	16.2291	0.672716
$583$	10.1269	0.419415
$584$	28.0304	1.15991
$585$	6.42752	0.265745
$586$	−11.9152	−0.492211
$587$	0.456596	0.0188457	0.00942287	−	0.999956i	$-0.497001\pi$
$587$	0.456596	0.0188457	0.00942287	+	0.999956i	$0.497001\pi$
$588$	−63.2723	−2.60931
$589$	21.2789	0.876781
$590$	−46.5217	−1.91527
$591$	−22.1293	−0.910278
$592$	30.2154	1.24184
$593$	21.9118	0.899808	0.449904	−	0.893077i	$-0.351458\pi$
$593$	21.9118	0.899808	0.449904	+	0.893077i	$0.351458\pi$
$594$	−20.2145	−0.829410
$595$	26.4808	1.08561
$596$	34.7028	1.42148
$597$	−8.09408	−0.331269
$598$	92.1343	3.76765
$599$	16.8150	0.687043	0.343522	−	0.939145i	$-0.388380\pi$
$599$	16.8150	0.687043	0.343522	+	0.939145i	$0.388380\pi$
$600$	−3.57127	−0.145797
$601$	−1.40752	−0.0574141	−0.0287070	−	0.999588i	$-0.509139\pi$
$601$	−1.40752	−0.0574141	−0.0287070	+	0.999588i	$0.509139\pi$
$602$	10.0615	0.410078
$603$	−0.855797	−0.0348507
$604$	−31.8175	−1.29463
$605$	19.0882	0.776045
$606$	−62.6870	−2.54648
$607$	−44.4824	−1.80549	−0.902743	−	0.430181i	$-0.858450\pi$
$607$	−44.4824	−1.80549	−0.902743	+	0.430181i	$0.858450\pi$
$608$	15.9717	0.647738
$609$	36.7403	1.48879
$610$	14.7438	0.596961
$611$	2.06636	0.0835961
$612$	−6.59154	−0.266447
$613$	36.2565	1.46439	0.732194	−	0.681096i	$-0.238497\pi$
$613$	36.2565	1.46439	0.732194	+	0.681096i	$0.238497\pi$
$614$	38.7930	1.56556
$615$	17.6302	0.710920
$616$	34.1529	1.37606
$617$	−31.8405	−1.28185	−0.640924	−	0.767604i	$-0.721449\pi$
$617$	−31.8405	−1.28185	−0.640924	+	0.767604i	$0.721449\pi$
$618$	−5.90154	−0.237395
$619$	19.2328	0.773032	0.386516	−	0.922283i	$-0.373678\pi$
$619$	19.2328	0.773032	0.386516	+	0.922283i	$0.373678\pi$
$620$	42.6639	1.71343
$621$	−33.8395	−1.35793
$622$	63.8649	2.56075
$623$	−10.2939	−0.412415
$624$	−56.9668	−2.28050
$625$	−22.9119	−0.916476
$626$	−54.6731	−2.18518
$627$	10.6300	0.424523
$628$	−36.2961	−1.44837
$629$	15.3702	0.612849
$630$	10.8708	0.433103
$631$	−5.08157	−0.202294	−0.101147	−	0.994871i	$-0.532251\pi$
$631$	−5.08157	−0.202294	−0.101147	+	0.994871i	$0.532251\pi$
$632$	12.0193	0.478101
$633$	38.7552	1.54038
$634$	37.2576	1.47969
$635$	5.92258	0.235030
$636$	−47.5827	−1.88678
$637$	55.5395	2.20056
$638$	−21.0438	−0.833131
$639$	1.11955	0.0442885
$640$	−32.8650	−1.29910
$641$	3.33988	0.131917	0.0659587	−	0.997822i	$-0.478989\pi$
$641$	3.33988	0.131917	0.0659587	+	0.997822i	$0.478989\pi$
$642$	−53.0893	−2.09527
$643$	16.6651	0.657208	0.328604	−	0.944468i	$-0.393422\pi$
$643$	16.6651	0.657208	0.328604	+	0.944468i	$0.393422\pi$
$644$	106.499	4.19666
$645$	3.37075	0.132723
$646$	35.5443	1.39847
$647$	−11.5043	−0.452280	−0.226140	−	0.974095i	$-0.572611\pi$
$647$	−11.5043	−0.452280	−0.226140	+	0.974095i	$0.572611\pi$
$648$	42.2609	1.66016
$649$	−12.5243	−0.491620
$650$	5.83941	0.229040
$651$	−29.3406	−1.14995
$652$	−25.3063	−0.991073
$653$	−31.3102	−1.22526	−0.612631	−	0.790369i	$-0.709889\pi$
$653$	−31.3102	−1.22526	−0.612631	+	0.790369i	$0.709889\pi$
$654$	−25.9679	−1.01543
$655$	−11.2562	−0.439817
$656$	31.1989	1.21811
$657$	2.40192	0.0937080
$658$	3.49482	0.136242
$659$	−12.8096	−0.498993	−0.249496	−	0.968376i	$-0.580265\pi$
$659$	−12.8096	−0.498993	−0.249496	+	0.968376i	$0.580265\pi$
$660$	21.3131	0.829612
$661$	12.3824	0.481618	0.240809	−	0.970573i	$-0.422587\pi$
$661$	12.3824	0.481618	0.240809	+	0.970573i	$0.422587\pi$
$662$	19.8987	0.773386
$663$	−28.9783	−1.12542
$664$	−5.27235	−0.204607
$665$	−40.0638	−1.55361
$666$	6.30972	0.244497
$667$	−35.2277	−1.36402
$668$	48.8410	1.88971
$669$	10.6168	0.410469
$670$	9.25265	0.357461
$671$	3.96924	0.153231
$672$	−22.0228	−0.849547
$673$	−41.6806	−1.60667	−0.803334	−	0.595529i	$-0.796943\pi$
$673$	−41.6806	−1.60667	−0.803334	+	0.595529i	$0.796943\pi$
$674$	16.2636	0.626452
$675$	−2.14472	−0.0825504
$676$	99.0052	3.80789
$677$	37.0177	1.42271	0.711354	−	0.702834i	$-0.248082\pi$
$677$	37.0177	1.42271	0.711354	+	0.702834i	$0.248082\pi$
$678$	56.6556	2.17585
$679$	−16.4667	−0.631935
$680$	38.2582	1.46714
$681$	−28.2910	−1.08411
$682$	16.8055	0.643514
$683$	12.4848	0.477718	0.238859	−	0.971054i	$-0.423227\pi$
$683$	12.4848	0.477718	0.238859	+	0.971054i	$0.423227\pi$
$684$	9.97260	0.381312
$685$	−13.7811	−0.526549
$686$	22.9706	0.877021
$687$	12.2607	0.467775
$688$	5.96496	0.227412
$689$	41.7674	1.59121
$690$	52.2037	1.98736
$691$	32.4353	1.23390	0.616948	−	0.787004i	$-0.288369\pi$
$691$	32.4353	1.23390	0.616948	+	0.787004i	$0.288369\pi$
$692$	−92.3591	−3.51097
$693$	2.92657	0.111171
$694$	−50.6430	−1.92238
$695$	39.4921	1.49802
$696$	53.0808	2.01202
$697$	15.8705	0.601138
$698$	43.6201	1.65105
$699$	24.3829	0.922246
$700$	6.74985	0.255120
$701$	19.2096	0.725536	0.362768	−	0.931879i	$-0.381832\pi$
$701$	19.2096	0.725536	0.362768	+	0.931879i	$0.381832\pi$
$702$	−83.3723	−3.14668
$703$	−23.2542	−0.877047
$704$	−4.85475	−0.182970
$705$	1.17081	0.0440953
$706$	−49.3379	−1.85686
$707$	63.6050	2.39211
$708$	58.8468	2.21160
$709$	19.0127	0.714037	0.357018	−	0.934097i	$-0.383793\pi$
$709$	19.0127	0.714037	0.357018	+	0.934097i	$0.383793\pi$
$710$	−12.1042	−0.454264
$711$	1.02993	0.0386254
$712$	−14.8721	−0.557357
$713$	28.1327	1.05358
$714$	−49.0107	−1.83418
$715$	−18.7083	−0.699653
$716$	−112.450	−4.20246
$717$	−34.8786	−1.30257
$718$	−7.95683	−0.296946
$719$	3.93276	0.146667	0.0733336	−	0.997307i	$-0.476636\pi$
$719$	3.93276	0.146667	0.0733336	+	0.997307i	$0.476636\pi$
$720$	6.44472	0.240181
$721$	5.98797	0.223004
$722$	−6.01818	−0.223973
$723$	−12.0730	−0.449002
$724$	−46.0154	−1.71015
$725$	−2.23271	−0.0829208
$726$	−35.3285	−1.31116
$727$	40.2268	1.49193	0.745965	−	0.665985i	$-0.231988\pi$
$727$	40.2268	1.49193	0.745965	+	0.665985i	$0.231988\pi$
$728$	140.860	5.22061
$729$	29.8734	1.10642
$730$	−25.9690	−0.961154
$731$	3.03430	0.112228
$732$	−18.6500	−0.689323
$733$	−1.59429	−0.0588864	−0.0294432	−	0.999566i	$-0.509373\pi$
$733$	−1.59429	−0.0588864	−0.0294432	+	0.999566i	$0.509373\pi$
$734$	25.7037	0.948740
$735$	31.4689	1.16075
$736$	21.1161	0.778351
$737$	2.49094	0.0917548
$738$	6.51510	0.239824
$739$	41.4667	1.52538	0.762688	−	0.646766i	$-0.223879\pi$
$739$	41.4667	1.52538	0.762688	+	0.646766i	$0.223879\pi$
$740$	−46.6243	−1.71395
$741$	43.8424	1.61059
$742$	70.6408	2.59331
$743$	32.1161	1.17823	0.589113	−	0.808051i	$-0.299477\pi$
$743$	32.1161	1.17823	0.589113	+	0.808051i	$0.299477\pi$
$744$	−42.3901	−1.55410
$745$	−17.2597	−0.632346
$746$	49.4992	1.81229
$747$	−0.451788	−0.0165300
$748$	19.1858	0.701501
$749$	53.8668	1.96825
$750$	45.9921	1.67939
$751$	21.6998	0.791836	0.395918	−	0.918286i	$-0.370426\pi$
$751$	21.6998	0.791836	0.395918	+	0.918286i	$0.370426\pi$
$752$	2.07190	0.0755542
$753$	−8.37262	−0.305115
$754$	−86.7926	−3.16080
$755$	15.8246	0.575918
$756$	−96.3712	−3.50499
$757$	49.6138	1.80324	0.901621	−	0.432526i	$-0.142378\pi$
$757$	49.6138	1.80324	0.901621	+	0.432526i	$0.142378\pi$
$758$	4.67331	0.169742
$759$	14.0539	0.510125
$760$	−57.8824	−2.09961
$761$	47.2404	1.71246	0.856231	−	0.516593i	$-0.172800\pi$
$761$	47.2404	1.71246	0.856231	+	0.516593i	$0.172800\pi$
$762$	−10.9615	−0.397095
$763$	26.3482	0.953869
$764$	−7.39013	−0.267366
$765$	3.27835	0.118529
$766$	−52.3860	−1.89278
$767$	−51.6549	−1.86515
$768$	50.2616	1.81366
$769$	−33.0061	−1.19023	−0.595114	−	0.803641i	$-0.702893\pi$
$769$	−33.0061	−1.19023	−0.595114	+	0.803641i	$0.702893\pi$
$770$	−31.6412	−1.14027
$771$	−26.4777	−0.953572
$772$	−48.2081	−1.73505
$773$	10.6743	0.383929	0.191965	−	0.981402i	$-0.438514\pi$
$773$	10.6743	0.383929	0.191965	+	0.981402i	$0.438514\pi$
$774$	1.24563	0.0447733
$775$	1.78303	0.0640484
$776$	−23.7904	−0.854025
$777$	32.0643	1.15030
$778$	−56.8155	−2.03694
$779$	−24.0111	−0.860287
$780$	87.9036	3.14745
$781$	−3.25862	−0.116603
$782$	46.9930	1.68047
$783$	31.8776	1.13921
$784$	55.6882	1.98886
$785$	18.0521	0.644308
$786$	20.8331	0.743091
$787$	−16.6240	−0.592583	−0.296291	−	0.955098i	$-0.595750\pi$
$787$	−16.6240	−0.592583	−0.296291	+	0.955098i	$0.595750\pi$
$788$	60.4273	2.15264
$789$	17.9256	0.638169
$790$	−11.1353	−0.396178
$791$	−57.4853	−2.04394
$792$	4.22817	0.150242
$793$	16.3707	0.581340
$794$	71.9249	2.55252
$795$	23.6656	0.839332
$796$	22.1021	0.783387
$797$	−24.9049	−0.882177	−0.441089	−	0.897464i	$-0.645408\pi$
$797$	−24.9049	−0.882177	−0.441089	+	0.897464i	$0.645408\pi$
$798$	74.1502	2.62489
$799$	1.05395	0.0372860
$800$	1.33833	0.0473170
$801$	−1.27439	−0.0450285
$802$	−12.7013	−0.448499
$803$	−6.99119	−0.246714
$804$	−11.7040	−0.412768
$805$	−52.9682	−1.86688
$806$	69.3122	2.44142
$807$	2.91111	0.102476
$808$	91.8936	3.23281
$809$	−41.1673	−1.44736	−0.723682	−	0.690133i	$-0.757552\pi$
$809$	−41.1673	−1.44736	−0.723682	+	0.690133i	$0.757552\pi$
$810$	−39.1529	−1.37569
$811$	−33.5450	−1.17792	−0.588962	−	0.808160i	$-0.700463\pi$
$811$	−33.5450	−1.17792	−0.588962	+	0.808160i	$0.700463\pi$
$812$	−100.325	−3.52071
$813$	−15.7912	−0.553822
$814$	−18.3655	−0.643710
$815$	12.5863	0.440878
$816$	−29.0559	−1.01716
$817$	−4.59071	−0.160609
$818$	49.7962	1.74108
$819$	12.0703	0.421770
$820$	−48.1420	−1.68119
$821$	26.9611	0.940948	0.470474	−	0.882414i	$-0.344083\pi$
$821$	26.9611	0.940948	0.470474	+	0.882414i	$0.344083\pi$
$822$	25.5061	0.889628
$823$	−8.37615	−0.291974	−0.145987	−	0.989286i	$-0.546636\pi$
$823$	−8.37615	−0.291974	−0.145987	+	0.989286i	$0.546636\pi$
$824$	8.65115	0.301377
$825$	0.890729	0.0310112
$826$	−87.3634	−3.03976
$827$	−47.9002	−1.66565	−0.832826	−	0.553534i	$-0.813279\pi$
$827$	−47.9002	−1.66565	−0.832826	+	0.553534i	$0.813279\pi$
$828$	13.1847	0.458201
$829$	−23.3482	−0.810918	−0.405459	−	0.914113i	$-0.632888\pi$
$829$	−23.3482	−0.810918	−0.405459	+	0.914113i	$0.632888\pi$
$830$	4.88461	0.169547
$831$	26.1128	0.905841
$832$	−20.0229	−0.694168
$833$	28.3279	0.981503
$834$	−73.0922	−2.53098
$835$	−24.2914	−0.840639
$836$	−29.0269	−1.00392
$837$	−25.4573	−0.879933
$838$	62.8053	2.16957
$839$	41.6674	1.43852	0.719260	−	0.694741i	$-0.244481\pi$
$839$	41.6674	1.43852	0.719260	+	0.694741i	$0.244481\pi$
$840$	79.8118	2.75377
$841$	4.18535	0.144322
$842$	−46.6737	−1.60848
$843$	−18.5194	−0.637842
$844$	−105.827	−3.64271
$845$	−49.2409	−1.69394
$846$	0.432663	0.0148753
$847$	35.8458	1.23168
$848$	41.8792	1.43814
$849$	−40.6729	−1.39589
$850$	2.97838	0.102158
$851$	−30.7442	−1.05390
$852$	15.3111	0.524548
$853$	21.2591	0.727898	0.363949	−	0.931419i	$-0.381428\pi$
$853$	21.2591	0.727898	0.363949	+	0.931419i	$0.381428\pi$
$854$	27.6876	0.947449
$855$	−4.95994	−0.169626
$856$	77.8244	2.65998
$857$	−28.8200	−0.984471	−0.492235	−	0.870462i	$-0.663820\pi$
$857$	−28.8200	−0.984471	−0.492235	+	0.870462i	$0.663820\pi$
$858$	34.6255	1.18209
$859$	37.3713	1.27509	0.637545	−	0.770413i	$-0.279950\pi$
$859$	37.3713	1.27509	0.637545	+	0.770413i	$0.279950\pi$
$860$	−9.20433	−0.313865
$861$	33.1080	1.12832
$862$	−31.2729	−1.06516
$863$	3.24018	0.110297	0.0551486	−	0.998478i	$-0.482437\pi$
$863$	3.24018	0.110297	0.0551486	+	0.998478i	$0.482437\pi$
$864$	−19.1080	−0.650067
$865$	45.9354	1.56185
$866$	10.2415	0.348019
$867$	12.1028	0.411031
$868$	80.1190	2.71942
$869$	−2.99778	−0.101693
$870$	−49.1771	−1.66726
$871$	10.2736	0.348107
$872$	38.0667	1.28910
$873$	−2.03860	−0.0689961
$874$	−71.0975	−2.40491
$875$	−46.6656	−1.57759
$876$	32.8490	1.10987
$877$	−24.2544	−0.819013	−0.409507	−	0.912307i	$-0.634299\pi$
$877$	−24.2544	−0.819013	−0.409507	+	0.912307i	$0.634299\pi$
$878$	−48.8656	−1.64913
$879$	−7.49611	−0.252837
$880$	−18.7584	−0.632346
$881$	−4.21297	−0.141939	−0.0709693	−	0.997478i	$-0.522609\pi$
$881$	−4.21297	−0.141939	−0.0709693	+	0.997478i	$0.522609\pi$
$882$	11.6291	0.391571
$883$	5.51587	0.185624	0.0928120	−	0.995684i	$-0.470414\pi$
$883$	5.51587	0.185624	0.0928120	+	0.995684i	$0.470414\pi$
$884$	79.1295	2.66141
$885$	−29.2679	−0.983829
$886$	−73.2645	−2.46137
$887$	−29.8451	−1.00210	−0.501051	−	0.865418i	$-0.667053\pi$
$887$	−29.8451	−1.00210	−0.501051	+	0.865418i	$0.667053\pi$
$888$	46.3250	1.55457
$889$	11.1221	0.373022
$890$	13.7784	0.461853
$891$	−10.5405	−0.353120
$892$	−28.9907	−0.970681
$893$	−1.59456	−0.0533598
$894$	31.9443	1.06838
$895$	55.9279	1.86946
$896$	−61.7175	−2.06184
$897$	57.9639	1.93536
$898$	−88.0759	−2.93913
$899$	−26.5017	−0.883881
$900$	0.835640	0.0278547
$901$	21.3034	0.709720
$902$	−18.9633	−0.631408
$903$	6.32996	0.210648
$904$	−83.0522	−2.76227
$905$	22.8861	0.760759
$906$	−29.2883	−0.973039
$907$	−54.4889	−1.80927	−0.904637	−	0.426183i	$-0.859858\pi$
$907$	−54.4889	−1.80927	−0.904637	+	0.426183i	$0.859858\pi$
$908$	77.2528	2.56372
$909$	7.87437	0.261176
$910$	−130.501	−4.32606
$911$	44.4358	1.47222	0.736112	−	0.676859i	$-0.236659\pi$
$911$	44.4358	1.47222	0.736112	+	0.676859i	$0.236659\pi$
$912$	43.9598	1.45565
$913$	1.31500	0.0435202
$914$	32.8003	1.08494
$915$	9.27570	0.306645
$916$	−33.4796	−1.10620
$917$	−21.1382	−0.698044
$918$	−42.5239	−1.40350
$919$	26.8154	0.884557	0.442279	−	0.896878i	$-0.354170\pi$
$919$	26.8154	0.884557	0.442279	+	0.896878i	$0.354170\pi$
$920$	−76.5260	−2.52299
$921$	24.4056	0.804192
$922$	−3.77642	−0.124370
$923$	−13.4398	−0.442377
$924$	40.0241	1.31670
$925$	−1.94855	−0.0640679
$926$	−48.7605	−1.60237
$927$	0.741317	0.0243481
$928$	−19.8919	−0.652983
$929$	−46.3915	−1.52206	−0.761028	−	0.648719i	$-0.775305\pi$
$929$	−46.3915	−1.52206	−0.761028	+	0.648719i	$0.775305\pi$
$930$	39.2726	1.28780
$931$	−42.8584	−1.40463
$932$	−66.5811	−2.18094
$933$	40.1789	1.31540
$934$	38.9107	1.27320
$935$	−9.54217	−0.312062
$936$	17.4386	0.569999
$937$	−31.9396	−1.04342	−0.521710	−	0.853123i	$-0.674706\pi$
$937$	−31.9396	−1.04342	−0.521710	+	0.853123i	$0.674706\pi$
$938$	17.3756	0.567334
$939$	−34.3961	−1.12248
$940$	−3.19707	−0.104277
$941$	−1.73551	−0.0565761	−0.0282880	−	0.999600i	$-0.509006\pi$
$941$	−1.73551	−0.0565761	−0.0282880	+	0.999600i	$0.509006\pi$
$942$	−33.4110	−1.08859
$943$	−31.7450	−1.03376
$944$	−51.7932	−1.68572
$945$	47.9309	1.55919
$946$	−3.62561	−0.117879
$947$	−25.4388	−0.826650	−0.413325	−	0.910584i	$-0.635633\pi$
$947$	−25.4388	−0.826650	−0.413325	+	0.910584i	$0.635633\pi$
$948$	14.0855	0.457475
$949$	−28.8344	−0.936004
$950$	−4.50611	−0.146198
$951$	23.4397	0.760083
$952$	71.8454	2.32852
$953$	23.3547	0.756533	0.378266	−	0.925697i	$-0.376520\pi$
$953$	23.3547	0.756533	0.378266	+	0.925697i	$0.376520\pi$
$954$	8.74542	0.283143
$955$	3.67554	0.118938
$956$	95.2413	3.08032
$957$	−13.2391	−0.427960
$958$	−52.6693	−1.70167
$959$	−25.8796	−0.835697
$960$	−11.3450	−0.366160
$961$	−9.83587	−0.317286
$962$	−75.7463	−2.44216
$963$	6.66877	0.214898
$964$	32.9672	1.06180
$965$	23.9766	0.771836
$966$	98.0337	3.15418
$967$	20.1870	0.649170	0.324585	−	0.945857i	$-0.394775\pi$
$967$	20.1870	0.649170	0.324585	+	0.945857i	$0.394775\pi$
$968$	51.7885	1.66454
$969$	22.3618	0.718364
$970$	22.0408	0.707687
$971$	55.1655	1.77035	0.885173	−	0.465263i	$-0.154040\pi$
$971$	55.1655	1.77035	0.885173	+	0.465263i	$0.154040\pi$
$972$	−22.1594	−0.710762
$973$	74.1626	2.37754
$974$	−72.7385	−2.33069
$975$	3.67371	0.117653
$976$	16.4145	0.525415
$977$	−36.9354	−1.18167	−0.590835	−	0.806793i	$-0.701201\pi$
$977$	−36.9354	−1.18167	−0.590835	+	0.806793i	$0.701201\pi$
$978$	−23.2948	−0.744884
$979$	3.70933	0.118551
$980$	−85.9306	−2.74495
$981$	3.26194	0.104146
$982$	39.3689	1.25631
$983$	−25.3534	−0.808648	−0.404324	−	0.914616i	$-0.632493\pi$
$983$	−25.3534	−0.808648	−0.404324	+	0.914616i	$0.632493\pi$
$984$	47.8329	1.52486
$985$	−30.0540	−0.957599
$986$	−44.2685	−1.40980
$987$	2.19868	0.0699846
$988$	−119.718	−3.80874
$989$	−6.06936	−0.192994
$990$	−3.91722	−0.124498
$991$	1.09472	0.0347750	0.0173875	−	0.999849i	$-0.494465\pi$
$991$	1.09472	0.0347750	0.0173875	+	0.999849i	$0.494465\pi$
$992$	15.8856	0.504367
$993$	12.5188	0.397271
$994$	−22.7306	−0.720972
$995$	−10.9926	−0.348490
$996$	−6.17871	−0.195780
$997$	32.6848	1.03514	0.517569	−	0.855641i	$-0.326837\pi$
$997$	32.6848	1.03514	0.517569	+	0.855641i	$0.326837\pi$
$998$	−98.1038	−3.10542
$999$	27.8204	0.880200

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6043.2.a.c.1.15	✓	259

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6043.2.a.c.1.15	✓	259	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:	\( N \)	\(=\)	\( 6043 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6043.a (trivial)

\(f(q)\)	\(=\)	\(q-2.51359 q^{2} -1.58136 q^{3} +4.31814 q^{4} -2.14765 q^{5} +3.97489 q^{6} -4.03310 q^{7} -5.82684 q^{8} -0.499302 q^{9} +O(q^{10})\)	\(q-2.51359 q^{2} -1.58136 q^{3} +4.31814 q^{4} -2.14765 q^{5} +3.97489 q^{6} -4.03310 q^{7} -5.82684 q^{8} -0.499302 q^{9} +5.39832 q^{10} +1.45330 q^{11} -6.82852 q^{12} +5.99398 q^{13} +10.1376 q^{14} +3.39621 q^{15} +6.01002 q^{16} +3.05722 q^{17} +1.25504 q^{18} -4.62539 q^{19} -9.27386 q^{20} +6.37778 q^{21} -3.65300 q^{22} -6.11521 q^{23} +9.21433 q^{24} -0.387578 q^{25} -15.0664 q^{26} +5.53365 q^{27} -17.4155 q^{28} +5.76067 q^{29} -8.53669 q^{30} -4.60045 q^{31} -3.45305 q^{32} -2.29819 q^{33} -7.68460 q^{34} +8.66171 q^{35} -2.15605 q^{36} +5.02750 q^{37} +11.6263 q^{38} -9.47863 q^{39} +12.5140 q^{40} +5.19115 q^{41} -16.0311 q^{42} +0.992502 q^{43} +6.27555 q^{44} +1.07233 q^{45} +15.3711 q^{46} +0.344740 q^{47} -9.50401 q^{48} +9.26589 q^{49} +0.974212 q^{50} -4.83457 q^{51} +25.8828 q^{52} +6.96823 q^{53} -13.9093 q^{54} -3.12119 q^{55} +23.5002 q^{56} +7.31441 q^{57} -14.4800 q^{58} -8.61780 q^{59} +14.6653 q^{60} +2.73119 q^{61} +11.5636 q^{62} +2.01374 q^{63} -3.34050 q^{64} -12.8730 q^{65} +5.77671 q^{66} +1.71398 q^{67} +13.2015 q^{68} +9.67035 q^{69} -21.7720 q^{70} -2.24222 q^{71} +2.90936 q^{72} -4.81056 q^{73} -12.6371 q^{74} +0.612900 q^{75} -19.9731 q^{76} -5.86131 q^{77} +23.8254 q^{78} -2.06274 q^{79} -12.9075 q^{80} -7.25279 q^{81} -13.0484 q^{82} +0.904838 q^{83} +27.5401 q^{84} -6.56586 q^{85} -2.49474 q^{86} -9.10969 q^{87} -8.46816 q^{88} +2.55235 q^{89} -2.69540 q^{90} -24.1743 q^{91} -26.4063 q^{92} +7.27496 q^{93} -0.866535 q^{94} +9.93375 q^{95} +5.46051 q^{96} +4.08290 q^{97} -23.2906 q^{98} -0.725637 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 259 q + 39 q^{2} + 25 q^{3} + 271 q^{4} + 83 q^{5} + 18 q^{6} + 26 q^{7} + 111 q^{8} + 286 q^{9}+O(q^{10}) \) 259 * q + 39 * q^2 + 25 * q^3 + 271 * q^4 + 83 * q^5 + 18 * q^6 + 26 * q^7 + 111 * q^8 + 286 * q^9	\( 259 q + 39 q^{2} + 25 q^{3} + 271 q^{4} + 83 q^{5} + 18 q^{6} + 26 q^{7} + 111 q^{8} + 286 q^{9} + 36 q^{10} + 35 q^{11} + 58 q^{12} + 109 q^{13} + 31 q^{14} + 30 q^{15} + 287 q^{16} + 124 q^{17} + 97 q^{18} + 42 q^{19} + 149 q^{20} + 99 q^{21} + 22 q^{22} + 63 q^{23} + 53 q^{24} + 308 q^{25} + 86 q^{26} + 82 q^{27} + 52 q^{28} + 131 q^{29} + 6 q^{30} + 29 q^{31} + 251 q^{32} + 147 q^{33} + 24 q^{34} + 79 q^{35} + 315 q^{36} + 108 q^{37} + 124 q^{38} + 48 q^{39} + 87 q^{40} + 190 q^{41} + 28 q^{42} + 36 q^{43} + 70 q^{44} + 211 q^{45} + 19 q^{46} + 186 q^{47} + 103 q^{48} + 297 q^{49} + 161 q^{50} + 20 q^{51} + 173 q^{52} + 213 q^{53} + 56 q^{54} + 35 q^{55} + 99 q^{56} + 80 q^{57} + 32 q^{58} + 135 q^{59} + 23 q^{60} + 83 q^{61} + 172 q^{62} + 85 q^{63} + 297 q^{64} + 177 q^{65} + 41 q^{66} + 30 q^{67} + 271 q^{68} + 168 q^{69} + 24 q^{70} + 63 q^{71} + 241 q^{72} + 152 q^{73} + 32 q^{74} + 36 q^{75} + 92 q^{76} + 396 q^{77} + 21 q^{78} - 2 q^{79} + 242 q^{80} + 343 q^{81} + 40 q^{82} + 236 q^{83} + 92 q^{84} + 124 q^{85} + 55 q^{86} + 113 q^{87} + 7 q^{88} + 214 q^{89} + 100 q^{90} + 2 q^{91} + 176 q^{92} + 228 q^{93} + 51 q^{94} + 96 q^{95} + 48 q^{96} + 135 q^{97} + 261 q^{98} + 26 q^{99}+O(q^{100}) \) 259 * q + 39 * q^2 + 25 * q^3 + 271 * q^4 + 83 * q^5 + 18 * q^6 + 26 * q^7 + 111 * q^8 + 286 * q^9 + 36 * q^10 + 35 * q^11 + 58 * q^12 + 109 * q^13 + 31 * q^14 + 30 * q^15 + 287 * q^16 + 124 * q^17 + 97 * q^18 + 42 * q^19 + 149 * q^20 + 99 * q^21 + 22 * q^22 + 63 * q^23 + 53 * q^24 + 308 * q^25 + 86 * q^26 + 82 * q^27 + 52 * q^28 + 131 * q^29 + 6 * q^30 + 29 * q^31 + 251 * q^32 + 147 * q^33 + 24 * q^34 + 79 * q^35 + 315 * q^36 + 108 * q^37 + 124 * q^38 + 48 * q^39 + 87 * q^40 + 190 * q^41 + 28 * q^42 + 36 * q^43 + 70 * q^44 + 211 * q^45 + 19 * q^46 + 186 * q^47 + 103 * q^48 + 297 * q^49 + 161 * q^50 + 20 * q^51 + 173 * q^52 + 213 * q^53 + 56 * q^54 + 35 * q^55 + 99 * q^56 + 80 * q^57 + 32 * q^58 + 135 * q^59 + 23 * q^60 + 83 * q^61 + 172 * q^62 + 85 * q^63 + 297 * q^64 + 177 * q^65 + 41 * q^66 + 30 * q^67 + 271 * q^68 + 168 * q^69 + 24 * q^70 + 63 * q^71 + 241 * q^72 + 152 * q^73 + 32 * q^74 + 36 * q^75 + 92 * q^76 + 396 * q^77 + 21 * q^78 - 2 * q^79 + 242 * q^80 + 343 * q^81 + 40 * q^82 + 236 * q^83 + 92 * q^84 + 124 * q^85 + 55 * q^86 + 113 * q^87 + 7 * q^88 + 214 * q^89 + 100 * q^90 + 2 * q^91 + 176 * q^92 + 228 * q^93 + 51 * q^94 + 96 * q^95 + 48 * q^96 + 135 * q^97 + 261 * q^98 + 26 * q^99

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