LMFDB - Embedded newform 4021.2.a.c.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4021,2,Mod(1,4021)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4021, 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("4021.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4021 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4021.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:	$32.1078466528$
Analytic rank:	$0$
Dimension:	$182$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Character	$\chi$	$=$	4021.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.80453 q^{2} +3.34034 q^{3} +5.86536 q^{4} -1.76340 q^{5} -9.36806 q^{6} -4.23059 q^{7} -10.8405 q^{8} +8.15785 q^{9} +O(q^{10})$	\(q-2.80453 q^{2} +3.34034 q^{3} +5.86536 q^{4} -1.76340 q^{5} -9.36806 q^{6} -4.23059 q^{7} -10.8405 q^{8} +8.15785 q^{9} +4.94549 q^{10} +1.60177 q^{11} +19.5923 q^{12} -2.68165 q^{13} +11.8648 q^{14} -5.89034 q^{15} +18.6718 q^{16} +0.843124 q^{17} -22.8789 q^{18} -2.51024 q^{19} -10.3430 q^{20} -14.1316 q^{21} -4.49221 q^{22} -3.93136 q^{23} -36.2110 q^{24} -1.89044 q^{25} +7.52076 q^{26} +17.2290 q^{27} -24.8139 q^{28} +1.77916 q^{29} +16.5196 q^{30} +3.81853 q^{31} -30.6844 q^{32} +5.35046 q^{33} -2.36456 q^{34} +7.46020 q^{35} +47.8488 q^{36} -8.91555 q^{37} +7.04004 q^{38} -8.95762 q^{39} +19.1161 q^{40} +7.40942 q^{41} +39.6324 q^{42} +7.99621 q^{43} +9.39498 q^{44} -14.3855 q^{45} +11.0256 q^{46} +6.20844 q^{47} +62.3700 q^{48} +10.8979 q^{49} +5.30178 q^{50} +2.81632 q^{51} -15.7289 q^{52} +5.61432 q^{53} -48.3191 q^{54} -2.82456 q^{55} +45.8617 q^{56} -8.38505 q^{57} -4.98970 q^{58} +11.7214 q^{59} -34.5490 q^{60} -10.3987 q^{61} -10.7092 q^{62} -34.5125 q^{63} +48.7117 q^{64} +4.72881 q^{65} -15.0055 q^{66} -13.7460 q^{67} +4.94523 q^{68} -13.1321 q^{69} -20.9223 q^{70} +4.85857 q^{71} -88.4353 q^{72} +10.6164 q^{73} +25.0039 q^{74} -6.31470 q^{75} -14.7235 q^{76} -6.77644 q^{77} +25.1219 q^{78} -3.23978 q^{79} -32.9257 q^{80} +33.0770 q^{81} -20.7799 q^{82} +4.16777 q^{83} -82.8869 q^{84} -1.48676 q^{85} -22.4256 q^{86} +5.94299 q^{87} -17.3640 q^{88} +4.97797 q^{89} +40.3446 q^{90} +11.3450 q^{91} -23.0589 q^{92} +12.7552 q^{93} -17.4117 q^{94} +4.42655 q^{95} -102.496 q^{96} +10.4867 q^{97} -30.5633 q^{98} +13.0670 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 182 q + 18 q^{2} + 28 q^{3} + 208 q^{4} + 22 q^{5} + 18 q^{6} + 14 q^{7} + 54 q^{8} + 238 q^{9}+O(q^{10}) $ 182 * q + 18 * q^2 + 28 * q^3 + 208 * q^4 + 22 * q^5 + 18 * q^6 + 14 * q^7 + 54 * q^8 + 238 * q^9	\( 182 q + 18 q^{2} + 28 q^{3} + 208 q^{4} + 22 q^{5} + 18 q^{6} + 14 q^{7} + 54 q^{8} + 238 q^{9} + 7 q^{10} + 138 q^{11} + 47 q^{12} + 5 q^{13} + 72 q^{14} + 41 q^{15} + 256 q^{16} + 29 q^{17} + 35 q^{18} + 48 q^{19} + 56 q^{20} + 22 q^{21} + 19 q^{22} + 91 q^{23} + 46 q^{24} + 230 q^{25} + 88 q^{26} + 103 q^{27} + 15 q^{28} + 75 q^{29} + 18 q^{30} + 43 q^{31} + 116 q^{32} + 15 q^{33} + 13 q^{34} + 185 q^{35} + 364 q^{36} + 15 q^{37} + 53 q^{38} + 80 q^{39} - 13 q^{40} + 68 q^{41} + 32 q^{42} + 82 q^{43} + 259 q^{44} + 37 q^{45} + 13 q^{46} + 121 q^{47} + 53 q^{48} + 244 q^{49} + 93 q^{50} + 144 q^{51} - 16 q^{52} + 101 q^{53} + 47 q^{54} + 49 q^{55} + 199 q^{56} + 3 q^{57} + 4 q^{58} + 254 q^{59} + 24 q^{60} + 8 q^{61} + 37 q^{62} + 19 q^{63} + 326 q^{64} + 65 q^{65} + 41 q^{66} + 91 q^{67} + 50 q^{68} + 50 q^{69} + 5 q^{70} + 212 q^{71} + 77 q^{72} + 5 q^{73} + 101 q^{74} + 127 q^{75} + 22 q^{76} + 87 q^{77} - 20 q^{78} + 86 q^{79} + 71 q^{80} + 358 q^{81} - 20 q^{82} + 139 q^{83} - 30 q^{84} + 25 q^{85} + 82 q^{86} + 36 q^{87} - 8 q^{88} + 100 q^{89} - 87 q^{90} + 74 q^{91} + 171 q^{92} + 50 q^{93} - 13 q^{94} + 217 q^{95} + 42 q^{96} + 20 q^{97} + 47 q^{98} + 389 q^{99}+O(q^{100}) \) 182 * q + 18 * q^2 + 28 * q^3 + 208 * q^4 + 22 * q^5 + 18 * q^6 + 14 * q^7 + 54 * q^8 + 238 * q^9 + 7 * q^10 + 138 * q^11 + 47 * q^12 + 5 * q^13 + 72 * q^14 + 41 * q^15 + 256 * q^16 + 29 * q^17 + 35 * q^18 + 48 * q^19 + 56 * q^20 + 22 * q^21 + 19 * q^22 + 91 * q^23 + 46 * q^24 + 230 * q^25 + 88 * q^26 + 103 * q^27 + 15 * q^28 + 75 * q^29 + 18 * q^30 + 43 * q^31 + 116 * q^32 + 15 * q^33 + 13 * q^34 + 185 * q^35 + 364 * q^36 + 15 * q^37 + 53 * q^38 + 80 * q^39 - 13 * q^40 + 68 * q^41 + 32 * q^42 + 82 * q^43 + 259 * q^44 + 37 * q^45 + 13 * q^46 + 121 * q^47 + 53 * q^48 + 244 * q^49 + 93 * q^50 + 144 * q^51 - 16 * q^52 + 101 * q^53 + 47 * q^54 + 49 * q^55 + 199 * q^56 + 3 * q^57 + 4 * q^58 + 254 * q^59 + 24 * q^60 + 8 * q^61 + 37 * q^62 + 19 * q^63 + 326 * q^64 + 65 * q^65 + 41 * q^66 + 91 * q^67 + 50 * q^68 + 50 * q^69 + 5 * q^70 + 212 * q^71 + 77 * q^72 + 5 * q^73 + 101 * q^74 + 127 * q^75 + 22 * q^76 + 87 * q^77 - 20 * q^78 + 86 * q^79 + 71 * q^80 + 358 * q^81 - 20 * q^82 + 139 * q^83 - 30 * q^84 + 25 * q^85 + 82 * q^86 + 36 * q^87 - 8 * q^88 + 100 * q^89 - 87 * q^90 + 74 * q^91 + 171 * q^92 + 50 * q^93 - 13 * q^94 + 217 * q^95 + 42 * q^96 + 20 * q^97 + 47 * q^98 + 389 * 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 $

$2$	−2.80453	−1.98310	−0.991550	−	0.129729i	$-0.958589\pi$
$2$	−2.80453	−1.98310	−0.991550	+	0.129729i	$0.958589\pi$
$3$	3.34034	1.92854	0.964272	−	0.264913i	$-0.0853433\pi$
$3$	3.34034	1.92854	0.964272	+	0.264913i	$0.0853433\pi$
$4$	5.86536	2.93268
$5$	−1.76340	−0.788614	−0.394307	−	0.918979i	$-0.629015\pi$
$5$	−1.76340	−0.788614	−0.394307	+	0.918979i	$0.629015\pi$
$6$	−9.36806	−3.82450
$7$	−4.23059	−1.59901	−0.799506	−	0.600659i	$-0.794905\pi$
$7$	−4.23059	−1.59901	−0.799506	+	0.600659i	$0.794905\pi$
$8$	−10.8405	−3.83270
$9$	8.15785	2.71928
$10$	4.94549	1.56390
$11$	1.60177	0.482953	0.241476	−	0.970407i	$-0.422368\pi$
$11$	1.60177	0.482953	0.241476	+	0.970407i	$0.422368\pi$
$12$	19.5923	5.65581
$13$	−2.68165	−0.743756	−0.371878	−	0.928282i	$-0.621286\pi$
$13$	−2.68165	−0.743756	−0.371878	+	0.928282i	$0.621286\pi$
$14$	11.8648	3.17100
$15$	−5.89034	−1.52088
$16$	18.6718	4.66794
$17$	0.843124	0.204488	0.102244	−	0.994759i	$-0.467398\pi$
$17$	0.843124	0.204488	0.102244	+	0.994759i	$0.467398\pi$
$18$	−22.8789	−5.39261
$19$	−2.51024	−0.575889	−0.287945	−	0.957647i	$-0.592972\pi$
$19$	−2.51024	−0.575889	−0.287945	+	0.957647i	$0.592972\pi$
$20$	−10.3430	−2.31276
$21$	−14.1316	−3.08376
$22$	−4.49221	−0.957743
$23$	−3.93136	−0.819745	−0.409873	−	0.912143i	$-0.634427\pi$
$23$	−3.93136	−0.819745	−0.409873	+	0.912143i	$0.634427\pi$
$24$	−36.2110	−7.39153
$25$	−1.89044	−0.378087
$26$	7.52076	1.47494
$27$	17.2290	3.31572
$28$	−24.8139	−4.68939
$29$	1.77916	0.330382	0.165191	−	0.986262i	$-0.447176\pi$
$29$	1.77916	0.330382	0.165191	+	0.986262i	$0.447176\pi$
$30$	16.5196	3.01605
$31$	3.81853	0.685829	0.342914	−	0.939367i	$-0.388586\pi$
$31$	3.81853	0.685829	0.342914	+	0.939367i	$0.388586\pi$
$32$	−30.6844	−5.42429
$33$	5.35046	0.931396
$34$	−2.36456	−0.405519
$35$	7.46020	1.26100
$36$	47.8488	7.97480
$37$	−8.91555	−1.46571	−0.732854	−	0.680386i	$-0.761812\pi$
$37$	−8.91555	−1.46571	−0.732854	+	0.680386i	$0.761812\pi$
$38$	7.04004	1.14204
$39$	−8.95762	−1.43437
$40$	19.1161	3.02252
$41$	7.40942	1.15716	0.578579	−	0.815627i	$-0.303608\pi$
$41$	7.40942	1.15716	0.578579	+	0.815627i	$0.303608\pi$
$42$	39.6324	6.11541
$43$	7.99621	1.21941	0.609705	−	0.792628i	$-0.291288\pi$
$43$	7.99621	1.21941	0.609705	+	0.792628i	$0.291288\pi$
$44$	9.39498	1.41635
$45$	−14.3855	−2.14447
$46$	11.0256	1.62564
$47$	6.20844	0.905595	0.452797	−	0.891614i	$-0.350426\pi$
$47$	6.20844	0.905595	0.452797	+	0.891614i	$0.350426\pi$
$48$	62.3700	9.00233
$49$	10.8979	1.55684
$50$	5.30178	0.749785
$51$	2.81632	0.394363
$52$	−15.7289	−2.18120
$53$	5.61432	0.771186	0.385593	−	0.922669i	$-0.373997\pi$
$53$	5.61432	0.771186	0.385593	+	0.922669i	$0.373997\pi$
$54$	−48.3191	−6.57539
$55$	−2.82456	−0.380863
$56$	45.8617	6.12853
$57$	−8.38505	−1.11063
$58$	−4.98970	−0.655179
$59$	11.7214	1.52600	0.762998	−	0.646401i	$-0.223727\pi$
$59$	11.7214	1.52600	0.762998	+	0.646401i	$0.223727\pi$
$60$	−34.5490	−4.46025
$61$	−10.3987	−1.33141	−0.665706	−	0.746214i	$-0.731870\pi$
$61$	−10.3987	−1.33141	−0.665706	+	0.746214i	$0.731870\pi$
$62$	−10.7092	−1.36007
$63$	−34.5125	−4.34817
$64$	48.7117	6.08897
$65$	4.72881	0.586537
$66$	−15.0055	−1.84705
$67$	−13.7460	−1.67935	−0.839674	−	0.543091i	$-0.817254\pi$
$67$	−13.7460	−1.67935	−0.839674	+	0.543091i	$0.817254\pi$
$68$	4.94523	0.599697
$69$	−13.1321	−1.58092
$70$	−20.9223	−2.50069
$71$	4.85857	0.576606	0.288303	−	0.957539i	$-0.406909\pi$
$71$	4.85857	0.576606	0.288303	+	0.957539i	$0.406909\pi$
$72$	−88.4353	−10.4222
$73$	10.6164	1.24256	0.621279	−	0.783589i	$-0.286613\pi$
$73$	10.6164	1.24256	0.621279	+	0.783589i	$0.286613\pi$
$74$	25.0039	2.90664
$75$	−6.31470	−0.729158
$76$	−14.7235	−1.68890
$77$	−6.77644	−0.772247
$78$	25.1219	2.84449
$79$	−3.23978	−0.364504	−0.182252	−	0.983252i	$-0.558339\pi$
$79$	−3.23978	−0.364504	−0.182252	+	0.983252i	$0.558339\pi$
$80$	−32.9257	−3.68121
$81$	33.0770	3.67522
$82$	−20.7799	−2.29476
$83$	4.16777	0.457472	0.228736	−	0.973489i	$-0.426541\pi$
$83$	4.16777	0.457472	0.228736	+	0.973489i	$0.426541\pi$
$84$	−82.8869	−9.04370
$85$	−1.48676	−0.161262
$86$	−22.4256	−2.41821
$87$	5.94299	0.637156
$88$	−17.3640	−1.85101
$89$	4.97797	0.527663	0.263832	−	0.964569i	$-0.415014\pi$
$89$	4.97797	0.527663	0.263832	+	0.964569i	$0.415014\pi$
$90$	40.3446	4.25269
$91$	11.3450	1.18927
$92$	−23.0589	−2.40405
$93$	12.7552	1.32265
$94$	−17.4117	−1.79588
$95$	4.42655	0.454154
$96$	−102.496	−10.4610
$97$	10.4867	1.06476	0.532380	−	0.846506i	$-0.321298\pi$
$97$	10.4867	1.06476	0.532380	+	0.846506i	$0.321298\pi$
$98$	−30.5633	−3.08736
$99$	13.0670	1.31329
$100$	−11.0881	−1.10881
$101$	17.6508	1.75632	0.878160	−	0.478367i	$-0.158771\pi$
$101$	17.6508	1.75632	0.878160	+	0.478367i	$0.158771\pi$
$102$	−7.89844	−0.782062
$103$	16.7984	1.65519	0.827597	−	0.561323i	$-0.189707\pi$
$103$	16.7984	1.65519	0.827597	+	0.561323i	$0.189707\pi$
$104$	29.0705	2.85059
$105$	24.9196	2.43190
$106$	−15.7455	−1.52934
$107$	−8.95391	−0.865607	−0.432804	−	0.901488i	$-0.642476\pi$
$107$	−8.95391	−0.865607	−0.432804	+	0.901488i	$0.642476\pi$
$108$	101.054	9.72394
$109$	−0.599318	−0.0574042	−0.0287021	−	0.999588i	$-0.509137\pi$
$109$	−0.599318	−0.0574042	−0.0287021	+	0.999588i	$0.509137\pi$
$110$	7.92155	0.755290
$111$	−29.7810	−2.82668
$112$	−78.9925	−7.46409
$113$	2.91354	0.274082	0.137041	−	0.990565i	$-0.456241\pi$
$113$	2.91354	0.274082	0.137041	+	0.990565i	$0.456241\pi$
$114$	23.5161	2.20248
$115$	6.93254	0.646463
$116$	10.4354	0.968904
$117$	−21.8765	−2.02248
$118$	−32.8730	−3.02620
$119$	−3.56691	−0.326978
$120$	63.8543	5.82907
$121$	−8.43432	−0.766757
$122$	29.1633	2.64032
$123$	24.7500	2.23163
$124$	22.3971	2.01132
$125$	12.1506	1.08678
$126$	96.7912	8.62284
$127$	−11.8766	−1.05388	−0.526940	−	0.849902i	$-0.676661\pi$
$127$	−11.8766	−1.05388	−0.526940	+	0.849902i	$0.676661\pi$
$128$	−75.2444	−6.65073
$129$	26.7100	2.35169
$130$	−13.2621	−1.16316
$131$	−8.57213	−0.748951	−0.374475	−	0.927237i	$-0.622177\pi$
$131$	−8.57213	−0.748951	−0.374475	+	0.927237i	$0.622177\pi$
$132$	31.3824	2.73149
$133$	10.6198	0.920853
$134$	38.5511	3.33031
$135$	−30.3815	−2.61482
$136$	−9.13990	−0.783740
$137$	3.67115	0.313648	0.156824	−	0.987627i	$-0.449875\pi$
$137$	3.67115	0.313648	0.156824	+	0.987627i	$0.449875\pi$
$138$	36.8292	3.13511
$139$	15.9976	1.35690	0.678449	−	0.734648i	$-0.262653\pi$
$139$	15.9976	1.35690	0.678449	+	0.734648i	$0.262653\pi$
$140$	43.7568	3.69812
$141$	20.7383	1.74648
$142$	−13.6260	−1.14347
$143$	−4.29540	−0.359199
$144$	152.322	12.6935
$145$	−3.13736	−0.260544
$146$	−29.7740	−2.46412
$147$	36.4025	3.00243
$148$	−52.2930	−4.29846
$149$	−9.49930	−0.778213	−0.389107	−	0.921193i	$-0.627216\pi$
$149$	−9.49930	−0.778213	−0.389107	+	0.921193i	$0.627216\pi$
$150$	17.7097	1.44599
$151$	0.741786	0.0603657	0.0301828	−	0.999544i	$-0.490391\pi$
$151$	0.741786	0.0603657	0.0301828	+	0.999544i	$0.490391\pi$
$152$	27.2123	2.20721
$153$	6.87808	0.556060
$154$	19.0047	1.53144
$155$	−6.73359	−0.540855
$156$	−52.5397	−4.20654
$157$	9.66588	0.771421	0.385711	−	0.922620i	$-0.373956\pi$
$157$	9.66588	0.771421	0.385711	+	0.922620i	$0.373956\pi$
$158$	9.08605	0.722847
$159$	18.7537	1.48727
$160$	54.1088	4.27767
$161$	16.6320	1.31078
$162$	−92.7653	−7.28833
$163$	0.700228	0.0548461	0.0274231	−	0.999624i	$-0.491270\pi$
$163$	0.700228	0.0548461	0.0274231	+	0.999624i	$0.491270\pi$
$164$	43.4589	3.39357
$165$	−9.43498	−0.734512
$166$	−11.6886	−0.907212
$167$	14.1221	1.09280	0.546401	−	0.837524i	$-0.315998\pi$
$167$	14.1221	1.09280	0.546401	+	0.837524i	$0.315998\pi$
$168$	153.194	11.8191
$169$	−5.80875	−0.446827
$170$	4.16966	0.319798
$171$	−20.4782	−1.56601
$172$	46.9007	3.57614
$173$	3.96827	0.301702	0.150851	−	0.988557i	$-0.451799\pi$
$173$	3.96827	0.301702	0.150851	+	0.988557i	$0.451799\pi$
$174$	−16.6673	−1.26354
$175$	7.99766	0.604566
$176$	29.9079	2.25439
$177$	39.1534	2.94295
$178$	−13.9608	−1.04641
$179$	−8.80581	−0.658177	−0.329089	−	0.944299i	$-0.606742\pi$
$179$	−8.80581	−0.658177	−0.329089	+	0.944299i	$0.606742\pi$
$180$	−84.3763	−6.28904
$181$	−5.62461	−0.418074	−0.209037	−	0.977908i	$-0.567033\pi$
$181$	−5.62461	−0.418074	−0.209037	+	0.977908i	$0.567033\pi$
$182$	−31.8172	−2.35845
$183$	−34.7350	−2.56769
$184$	42.6180	3.14184
$185$	15.7216	1.15588
$186$	−35.7723	−2.62295
$187$	1.35049	0.0987578
$188$	36.4148	2.65582
$189$	−72.8886	−5.30187
$190$	−12.4144	−0.900633
$191$	9.67771	0.700254	0.350127	−	0.936702i	$-0.386138\pi$
$191$	9.67771	0.700254	0.350127	+	0.936702i	$0.386138\pi$
$192$	162.714	11.7428
$193$	−14.8818	−1.07122	−0.535608	−	0.844466i	$-0.679918\pi$
$193$	−14.8818	−1.07122	−0.535608	+	0.844466i	$0.679918\pi$
$194$	−29.4101	−2.11152
$195$	15.7958	1.13116
$196$	63.9199	4.56571
$197$	24.3143	1.73232	0.866161	−	0.499765i	$-0.166580\pi$
$197$	24.3143	1.73232	0.866161	+	0.499765i	$0.166580\pi$
$198$	−36.6468	−2.60438
$199$	−8.11821	−0.575484	−0.287742	−	0.957708i	$-0.592905\pi$
$199$	−8.11821	−0.575484	−0.287742	+	0.957708i	$0.592905\pi$
$200$	20.4933	1.44910
$201$	−45.9164	−3.23870
$202$	−49.5021	−3.48296
$203$	−7.52689	−0.528284
$204$	16.5187	1.15654
$205$	−13.0657	−0.912551
$206$	−47.1115	−3.28241
$207$	−32.0715	−2.22912
$208$	−50.0712	−3.47181
$209$	−4.02084	−0.278127
$210$	−69.8876	−4.82270
$211$	24.0566	1.65613	0.828063	−	0.560635i	$-0.189443\pi$
$211$	24.0566	1.65613	0.828063	+	0.560635i	$0.189443\pi$
$212$	32.9300	2.26164
$213$	16.2293	1.11201
$214$	25.1115	1.71658
$215$	−14.1005	−0.961644
$216$	−186.771	−12.7081
$217$	−16.1546	−1.09665
$218$	1.68080	0.113838
$219$	35.4624	2.39633
$220$	−16.5671	−1.11695
$221$	−2.26096	−0.152089
$222$	83.5215	5.60559
$223$	−0.452946	−0.0303315	−0.0151657	−	0.999885i	$-0.504828\pi$
$223$	−0.452946	−0.0303315	−0.0151657	+	0.999885i	$0.504828\pi$
$224$	129.813	8.67350
$225$	−15.4219	−1.02813
$226$	−8.17108	−0.543532
$227$	−2.54231	−0.168739	−0.0843695	−	0.996435i	$-0.526888\pi$
$227$	−2.54231	−0.168739	−0.0843695	+	0.996435i	$0.526888\pi$
$228$	−49.1814	−3.25712
$229$	27.5895	1.82316	0.911581	−	0.411120i	$-0.134862\pi$
$229$	27.5895	1.82316	0.911581	+	0.411120i	$0.134862\pi$
$230$	−19.4425	−1.28200
$231$	−22.6356	−1.48931
$232$	−19.2870	−1.26625
$233$	−13.0824	−0.857056	−0.428528	−	0.903529i	$-0.640968\pi$
$233$	−13.0824	−0.857056	−0.428528	+	0.903529i	$0.640968\pi$
$234$	61.3532	4.01079
$235$	−10.9479	−0.714165
$236$	68.7503	4.47526
$237$	−10.8220	−0.702962
$238$	10.0035	0.648430
$239$	−22.4143	−1.44986	−0.724929	−	0.688824i	$-0.758127\pi$
$239$	−22.4143	−1.44986	−0.724929	+	0.688824i	$0.758127\pi$
$240$	−109.983	−7.09937
$241$	24.2615	1.56282	0.781411	−	0.624016i	$-0.214500\pi$
$241$	24.2615	1.56282	0.781411	+	0.624016i	$0.214500\pi$
$242$	23.6543	1.52055
$243$	58.8014	3.77211
$244$	−60.9920	−3.90461
$245$	−19.2172	−1.22774
$246$	−69.4119	−4.42554
$247$	6.73159	0.428321
$248$	−41.3949	−2.62858
$249$	13.9217	0.882255
$250$	−34.0766	−2.15519
$251$	−14.1556	−0.893493	−0.446747	−	0.894661i	$-0.647417\pi$
$251$	−14.1556	−0.893493	−0.446747	+	0.894661i	$0.647417\pi$
$252$	−202.428	−12.7518
$253$	−6.29714	−0.395898
$254$	33.3083	2.08995
$255$	−4.96628	−0.311001
$256$	113.601	7.10009
$257$	19.9725	1.24585	0.622926	−	0.782281i	$-0.285944\pi$
$257$	19.9725	1.24585	0.622926	+	0.782281i	$0.285944\pi$
$258$	−74.9089	−4.66363
$259$	37.7180	2.34368
$260$	27.7362	1.72013
$261$	14.5141	0.898401
$262$	24.0408	1.48524
$263$	16.8911	1.04155	0.520774	−	0.853695i	$-0.325644\pi$
$263$	16.8911	1.04155	0.520774	+	0.853695i	$0.325644\pi$
$264$	−58.0017	−3.56976
$265$	−9.90026	−0.608168
$266$	−29.7835	−1.82614
$267$	16.6281	1.01762
$268$	−80.6256	−4.92499
$269$	14.6159	0.891148	0.445574	−	0.895245i	$-0.353000\pi$
$269$	14.6159	0.891148	0.445574	+	0.895245i	$0.353000\pi$
$270$	85.2056	5.18545
$271$	18.1353	1.10164	0.550820	−	0.834624i	$-0.314315\pi$
$271$	18.1353	1.10164	0.550820	+	0.834624i	$0.314315\pi$
$272$	15.7426	0.954536
$273$	37.8960	2.29357
$274$	−10.2958	−0.621994
$275$	−3.02805	−0.182598
$276$	−77.0244	−4.63632
$277$	−3.54739	−0.213142	−0.106571	−	0.994305i	$-0.533987\pi$
$277$	−3.54739	−0.213142	−0.106571	+	0.994305i	$0.533987\pi$
$278$	−44.8656	−2.69086
$279$	31.1510	1.86496
$280$	−80.8724	−4.83305
$281$	12.3981	0.739610	0.369805	−	0.929109i	$-0.379424\pi$
$281$	12.3981	0.739610	0.369805	+	0.929109i	$0.379424\pi$
$282$	−58.1611	−3.46344
$283$	7.82341	0.465053	0.232527	−	0.972590i	$-0.425301\pi$
$283$	7.82341	0.465053	0.232527	+	0.972590i	$0.425301\pi$
$284$	28.4973	1.69100
$285$	14.7862	0.875857
$286$	12.0465	0.712327
$287$	−31.3462	−1.85031
$288$	−250.319	−14.7502
$289$	−16.2891	−0.958185
$290$	8.79881	0.516684
$291$	35.0290	2.05344
$292$	62.2692	3.64403
$293$	−27.5215	−1.60782	−0.803911	−	0.594750i	$-0.797251\pi$
$293$	−27.5215	−1.60782	−0.803911	+	0.594750i	$0.797251\pi$
$294$	−102.092	−5.95412
$295$	−20.6695	−1.20342
$296$	96.6492	5.61762
$297$	27.5969	1.60133
$298$	26.6410	1.54327
$299$	10.5425	0.609691
$300$	−37.0380	−2.13839
$301$	−33.8286	−1.94985
$302$	−2.08036	−0.119711
$303$	58.9596	3.38714
$304$	−46.8707	−2.68822
$305$	18.3370	1.04997
$306$	−19.2898	−1.10272
$307$	−4.90800	−0.280114	−0.140057	−	0.990143i	$-0.544729\pi$
$307$	−4.90800	−0.280114	−0.140057	+	0.990143i	$0.544729\pi$
$308$	−39.7463	−2.26475
$309$	56.1123	3.19211
$310$	18.8845	1.07257
$311$	−24.1535	−1.36962	−0.684808	−	0.728723i	$-0.740114\pi$
$311$	−24.1535	−1.36962	−0.684808	+	0.728723i	$0.740114\pi$
$312$	97.1052	5.49750
$313$	−16.2490	−0.918449	−0.459224	−	0.888320i	$-0.651873\pi$
$313$	−16.2490	−0.918449	−0.459224	+	0.888320i	$0.651873\pi$
$314$	−27.1082	−1.52981
$315$	60.8592	3.42903
$316$	−19.0025	−1.06897
$317$	−12.5638	−0.705652	−0.352826	−	0.935689i	$-0.614779\pi$
$317$	−12.5638	−0.705652	−0.352826	+	0.935689i	$0.614779\pi$
$318$	−52.5953	−2.94940
$319$	2.84981	0.159559
$320$	−85.8980	−4.80185
$321$	−29.9091	−1.66936
$322$	−46.6447	−2.59941
$323$	−2.11645	−0.117762
$324$	194.009	10.7783
$325$	5.06949	0.281205
$326$	−1.96381	−0.108765
$327$	−2.00192	−0.110707
$328$	−80.3219	−4.43504
$329$	−26.2654	−1.44806
$330$	26.4606	1.45661
$331$	−20.5271	−1.12827	−0.564137	−	0.825682i	$-0.690791\pi$
$331$	−20.5271	−1.12827	−0.564137	+	0.825682i	$0.690791\pi$
$332$	24.4455	1.34162
$333$	−72.7318	−3.98568
$334$	−39.6058	−2.16713
$335$	24.2397	1.32436
$336$	−263.862	−14.3948
$337$	−12.5699	−0.684727	−0.342363	−	0.939568i	$-0.611227\pi$
$337$	−12.5699	−0.684727	−0.342363	+	0.939568i	$0.611227\pi$
$338$	16.2908	0.886102
$339$	9.73219	0.528580
$340$	−8.72039	−0.472930
$341$	6.11642	0.331223
$342$	57.4316	3.10554
$343$	−16.4902	−0.890389
$344$	−86.6830	−4.67363
$345$	23.1570	1.24673
$346$	−11.1291	−0.598305
$347$	29.0780	1.56099	0.780493	−	0.625164i	$-0.214968\pi$
$347$	29.0780	1.56099	0.780493	+	0.625164i	$0.214968\pi$
$348$	34.8578	1.86857
$349$	35.6890	1.91039	0.955194	−	0.295979i	$-0.0956459\pi$
$349$	35.6890	1.91039	0.955194	+	0.295979i	$0.0956459\pi$
$350$	−22.4296	−1.19891
$351$	−46.2021	−2.46608
$352$	−49.1495	−2.61968
$353$	5.15510	0.274378	0.137189	−	0.990545i	$-0.456193\pi$
$353$	5.15510	0.274378	0.137189	+	0.990545i	$0.456193\pi$
$354$	−109.807	−5.83616
$355$	−8.56758	−0.454720
$356$	29.1976	1.54747
$357$	−11.9147	−0.630592
$358$	24.6961	1.30523
$359$	33.4617	1.76604	0.883021	−	0.469334i	$-0.155506\pi$
$359$	33.4617	1.76604	0.883021	+	0.469334i	$0.155506\pi$
$360$	155.946	8.21910
$361$	−12.6987	−0.668352
$362$	15.7744	0.829082
$363$	−28.1735	−1.47872
$364$	66.5423	3.48776
$365$	−18.7209	−0.979899
$366$	97.4153	5.09198
$367$	−18.9529	−0.989333	−0.494667	−	0.869083i	$-0.664710\pi$
$367$	−18.9529	−0.989333	−0.494667	+	0.869083i	$0.664710\pi$
$368$	−73.4054	−3.82652
$369$	60.4450	3.14664
$370$	−44.0918	−2.29222
$371$	−23.7519	−1.23314
$372$	74.8138	3.87892
$373$	−1.17017	−0.0605894	−0.0302947	−	0.999541i	$-0.509645\pi$
$373$	−1.17017	−0.0605894	−0.0302947	+	0.999541i	$0.509645\pi$
$374$	−3.78749	−0.195847
$375$	40.5870	2.09590
$376$	−67.3027	−3.47087
$377$	−4.77108	−0.245723
$378$	204.418	10.5141
$379$	18.0055	0.924880	0.462440	−	0.886651i	$-0.346974\pi$
$379$	18.0055	0.924880	0.462440	+	0.886651i	$0.346974\pi$
$380$	25.9633	1.33189
$381$	−39.6720	−2.03246
$382$	−27.1414	−1.38867
$383$	−10.2935	−0.525972	−0.262986	−	0.964800i	$-0.584707\pi$
$383$	−10.2935	−0.525972	−0.262986	+	0.964800i	$0.584707\pi$
$384$	−251.342	−12.8262
$385$	11.9495	0.609005
$386$	41.7364	2.12433
$387$	65.2319	3.31592
$388$	61.5081	3.12260
$389$	3.22662	0.163596	0.0817980	−	0.996649i	$-0.473934\pi$
$389$	3.22662	0.163596	0.0817980	+	0.996649i	$0.473934\pi$
$390$	−44.2998	−2.24321
$391$	−3.31462	−0.167628
$392$	−118.138	−5.96689
$393$	−28.6338	−1.44438
$394$	−68.1901	−3.43537
$395$	5.71301	0.287453
$396$	76.6429	3.85145
$397$	31.3185	1.57183	0.785915	−	0.618335i	$-0.212192\pi$
$397$	31.3185	1.57183	0.785915	+	0.618335i	$0.212192\pi$
$398$	22.7677	1.14124
$399$	35.4737	1.77591
$400$	−35.2978	−1.76489
$401$	−23.3873	−1.16790	−0.583952	−	0.811788i	$-0.698494\pi$
$401$	−23.3873	−1.16790	−0.583952	+	0.811788i	$0.698494\pi$
$402$	128.774	6.42266
$403$	−10.2400	−0.510090
$404$	103.528	5.15073
$405$	−58.3278	−2.89833
$406$	21.1093	1.04764
$407$	−14.2807	−0.707868
$408$	−30.5303	−1.51148
$409$	−12.2548	−0.605959	−0.302979	−	0.952997i	$-0.597981\pi$
$409$	−12.2548	−0.605959	−0.302979	+	0.952997i	$0.597981\pi$
$410$	36.6432	1.80968
$411$	12.2629	0.604883
$412$	98.5286	4.85416
$413$	−49.5884	−2.44008
$414$	89.9452	4.42057
$415$	−7.34942	−0.360769
$416$	82.2849	4.03435
$417$	53.4373	2.61684
$418$	11.2765	0.551554
$419$	−26.6936	−1.30407	−0.652034	−	0.758190i	$-0.726084\pi$
$419$	−26.6936	−1.30407	−0.652034	+	0.758190i	$0.726084\pi$
$420$	146.162	7.13199
$421$	−10.5384	−0.513611	−0.256805	−	0.966463i	$-0.582670\pi$
$421$	−10.5384	−0.513611	−0.256805	+	0.966463i	$0.582670\pi$
$422$	−67.4674	−3.28426
$423$	50.6476	2.46257
$424$	−60.8621	−2.95572
$425$	−1.59387	−0.0773142
$426$	−45.5154	−2.20523
$427$	43.9924	2.12894
$428$	−52.5179	−2.53855
$429$	−14.3481	−0.692731
$430$	39.5451	1.90704
$431$	14.9643	0.720803	0.360402	−	0.932797i	$-0.382640\pi$
$431$	14.9643	0.720803	0.360402	+	0.932797i	$0.382640\pi$
$432$	321.695	15.4776
$433$	28.5058	1.36990	0.684951	−	0.728590i	$-0.259824\pi$
$433$	28.5058	1.36990	0.684951	+	0.728590i	$0.259824\pi$
$434$	45.3061	2.17476
$435$	−10.4798	−0.502470
$436$	−3.51522	−0.168348
$437$	9.86866	0.472082
$438$	−99.4553	−4.75216
$439$	−1.27729	−0.0609618	−0.0304809	−	0.999535i	$-0.509704\pi$
$439$	−1.27729	−0.0609618	−0.0304809	+	0.999535i	$0.509704\pi$
$440$	30.6197	1.45974
$441$	88.9031	4.23348
$442$	6.34093	0.301607
$443$	−5.79590	−0.275371	−0.137686	−	0.990476i	$-0.543966\pi$
$443$	−5.79590	−0.275371	−0.137686	+	0.990476i	$0.543966\pi$
$444$	−174.676	−8.28976
$445$	−8.77812	−0.416123
$446$	1.27030	0.0601504
$447$	−31.7309	−1.50082
$448$	−206.079	−9.73632
$449$	14.2637	0.673144	0.336572	−	0.941658i	$-0.390732\pi$
$449$	14.2637	0.673144	0.336572	+	0.941658i	$0.390732\pi$
$450$	43.2511	2.03888
$451$	11.8682	0.558852
$452$	17.0889	0.803796
$453$	2.47781	0.116418
$454$	7.12997	0.334626
$455$	−20.0056	−0.937879
$456$	90.8983	4.25670
$457$	−8.77875	−0.410653	−0.205326	−	0.978694i	$-0.565826\pi$
$457$	−8.77875	−0.410653	−0.205326	+	0.978694i	$0.565826\pi$
$458$	−77.3753	−3.61551
$459$	14.5262	0.678023
$460$	40.6619	1.89587
$461$	−2.46392	−0.114756	−0.0573782	−	0.998353i	$-0.518274\pi$
$461$	−2.46392	−0.114756	−0.0573782	+	0.998353i	$0.518274\pi$
$462$	63.4821	2.95345
$463$	3.64601	0.169444	0.0847221	−	0.996405i	$-0.473000\pi$
$463$	3.64601	0.169444	0.0847221	+	0.996405i	$0.473000\pi$
$464$	33.2200	1.54220
$465$	−22.4924	−1.04306
$466$	36.6899	1.69963
$467$	15.1545	0.701265	0.350632	−	0.936513i	$-0.385967\pi$
$467$	15.1545	0.701265	0.350632	+	0.936513i	$0.385967\pi$
$468$	−128.314	−5.93130
$469$	58.1539	2.68530
$470$	30.7038	1.41626
$471$	32.2873	1.48772
$472$	−127.066	−5.84868
$473$	12.8081	0.588917
$474$	30.3505	1.39404
$475$	4.74545	0.217736
$476$	−20.9212	−0.958922
$477$	45.8008	2.09707
$478$	62.8614	2.87521
$479$	30.5865	1.39753	0.698767	−	0.715349i	$-0.253732\pi$
$479$	30.5865	1.39753	0.698767	+	0.715349i	$0.253732\pi$
$480$	180.742	8.24969
$481$	23.9084	1.09013
$482$	−68.0421	−3.09923
$483$	55.5563	2.52790
$484$	−49.4704	−2.24865
$485$	−18.4921	−0.839684
$486$	−164.910	−7.48048
$487$	−6.68984	−0.303146	−0.151573	−	0.988446i	$-0.548434\pi$
$487$	−6.68984	−0.303146	−0.151573	+	0.988446i	$0.548434\pi$
$488$	112.727	5.10291
$489$	2.33900	0.105773
$490$	53.8952	2.43474
$491$	19.2399	0.868285	0.434143	−	0.900844i	$-0.357051\pi$
$491$	19.2399	0.868285	0.434143	+	0.900844i	$0.357051\pi$
$492$	145.168	6.54466
$493$	1.50005	0.0675589
$494$	−18.8789	−0.849403
$495$	−23.0423	−1.03568
$496$	71.2988	3.20141
$497$	−20.5546	−0.922000
$498$	−39.0439	−1.74960
$499$	8.33994	0.373347	0.186674	−	0.982422i	$-0.440229\pi$
$499$	8.33994	0.373347	0.186674	+	0.982422i	$0.440229\pi$
$500$	71.2675	3.18718
$501$	47.1726	2.10752
$502$	39.6997	1.77189
$503$	12.7762	0.569663	0.284832	−	0.958578i	$-0.408062\pi$
$503$	12.7762	0.569663	0.284832	+	0.958578i	$0.408062\pi$
$504$	374.133	16.6652
$505$	−31.1253	−1.38506
$506$	17.6605	0.785105
$507$	−19.4032	−0.861725
$508$	−69.6608	−3.09070
$509$	13.1448	0.582633	0.291317	−	0.956627i	$-0.405907\pi$
$509$	13.1448	0.582633	0.291317	+	0.956627i	$0.405907\pi$
$510$	13.9281	0.616745
$511$	−44.9137	−1.98686
$512$	−168.109	−7.42946
$513$	−43.2489	−1.90948
$514$	−56.0134	−2.47065
$515$	−29.6222	−1.30531
$516$	156.664	6.89675
$517$	9.94451	0.437359
$518$	−105.781	−4.64776
$519$	13.2554	0.581845
$520$	−51.2627	−2.24802
$521$	−6.46590	−0.283276	−0.141638	−	0.989919i	$-0.545237\pi$
$521$	−6.46590	−0.283276	−0.141638	+	0.989919i	$0.545237\pi$
$522$	−40.7052	−1.78162
$523$	−2.15554	−0.0942553	−0.0471277	−	0.998889i	$-0.515007\pi$
$523$	−2.15554	−0.0942553	−0.0471277	+	0.998889i	$0.515007\pi$
$524$	−50.2787	−2.19643
$525$	26.7149	1.16593
$526$	−47.3714	−2.06549
$527$	3.21950	0.140244
$528$	99.9026	4.34770
$529$	−7.54441	−0.328018
$530$	27.7655	1.20606
$531$	95.6214	4.14962
$532$	62.2890	2.70057
$533$	−19.8695	−0.860643
$534$	−46.6339	−2.01805
$535$	15.7893	0.682630
$536$	149.014	6.43643
$537$	−29.4144	−1.26932
$538$	−40.9907	−1.76724
$539$	17.4559	0.751879
$540$	−178.198	−7.66844
$541$	−35.8289	−1.54040	−0.770202	−	0.637799i	$-0.779845\pi$
$541$	−35.8289	−1.54040	−0.770202	+	0.637799i	$0.779845\pi$
$542$	−50.8609	−2.18466
$543$	−18.7881	−0.806274
$544$	−25.8708	−1.10920
$545$	1.05683	0.0452698
$546$	−106.280	−4.54837
$547$	−26.2263	−1.12136	−0.560679	−	0.828034i	$-0.689460\pi$
$547$	−26.2263	−1.12136	−0.560679	+	0.828034i	$0.689460\pi$
$548$	21.5326	0.919828
$549$	−84.8308	−3.62049
$550$	8.49224	0.362110
$551$	−4.46612	−0.190263
$552$	142.358	6.05917
$553$	13.7062	0.582846
$554$	9.94875	0.422682
$555$	52.5156	2.22916
$556$	93.8316	3.97935
$557$	−28.2834	−1.19841	−0.599204	−	0.800597i	$-0.704516\pi$
$557$	−28.2834	−1.19841	−0.599204	+	0.800597i	$0.704516\pi$
$558$	−87.3639	−3.69841
$559$	−21.4430	−0.906944
$560$	139.295	5.88629
$561$	4.51110	0.190459
$562$	−34.7709	−1.46672
$563$	31.9338	1.34585	0.672924	−	0.739711i	$-0.265038\pi$
$563$	31.9338	1.34585	0.672924	+	0.739711i	$0.265038\pi$
$564$	121.638	5.12187
$565$	−5.13771	−0.216145
$566$	−21.9409	−0.922247
$567$	−139.935	−5.87672
$568$	−52.6694	−2.20996
$569$	21.8671	0.916714	0.458357	−	0.888768i	$-0.348438\pi$
$569$	21.8671	0.916714	0.458357	+	0.888768i	$0.348438\pi$
$570$	−41.4682	−1.73691
$571$	−12.0077	−0.502506	−0.251253	−	0.967922i	$-0.580843\pi$
$571$	−12.0077	−0.502506	−0.251253	+	0.967922i	$0.580843\pi$
$572$	−25.1941	−1.05342
$573$	32.3268	1.35047
$574$	87.9112	3.66934
$575$	7.43199	0.309935
$576$	397.383	16.5576
$577$	8.95437	0.372775	0.186388	−	0.982476i	$-0.440322\pi$
$577$	8.95437	0.372775	0.186388	+	0.982476i	$0.440322\pi$
$578$	45.6833	1.90018
$579$	−49.7103	−2.06589
$580$	−18.4018	−0.764092
$581$	−17.6321	−0.731503
$582$	−98.2397	−4.07217
$583$	8.99286	0.372446
$584$	−115.087	−4.76235
$585$	38.5769	1.59496
$586$	77.1847	3.18847
$587$	12.9716	0.535397	0.267698	−	0.963503i	$-0.413737\pi$
$587$	12.9716	0.535397	0.267698	+	0.963503i	$0.413737\pi$
$588$	213.514	8.80517
$589$	−9.58544	−0.394961
$590$	57.9680	2.38651
$591$	81.2179	3.34086
$592$	−166.469	−6.84184
$593$	−20.5481	−0.843808	−0.421904	−	0.906641i	$-0.638638\pi$
$593$	−20.5481	−0.843808	−0.421904	+	0.906641i	$0.638638\pi$
$594$	−77.3962	−3.17560
$595$	6.28987	0.257860
$596$	−55.7169	−2.28225
$597$	−27.1175	−1.10985
$598$	−29.5668	−1.20908
$599$	17.7747	0.726253	0.363127	−	0.931740i	$-0.381709\pi$
$599$	17.7747	0.726253	0.363127	+	0.931740i	$0.381709\pi$
$600$	68.4545	2.79465
$601$	−32.4542	−1.32384	−0.661918	−	0.749576i	$-0.730257\pi$
$601$	−32.4542	−1.32384	−0.661918	+	0.749576i	$0.730257\pi$
$602$	94.8733	3.86675
$603$	−112.138	−4.56662
$604$	4.35084	0.177033
$605$	14.8730	0.604675
$606$	−165.354	−6.71704
$607$	−39.7489	−1.61336	−0.806679	−	0.590990i	$-0.798737\pi$
$607$	−39.7489	−1.61336	−0.806679	+	0.590990i	$0.798737\pi$
$608$	77.0253	3.12379
$609$	−25.1423	−1.01882
$610$	−51.4265	−2.08220
$611$	−16.6489	−0.673542
$612$	40.3424	1.63075
$613$	20.1877	0.815372	0.407686	−	0.913122i	$-0.366336\pi$
$613$	20.1877	0.815372	0.407686	+	0.913122i	$0.366336\pi$
$614$	13.7646	0.555495
$615$	−43.6440	−1.75989
$616$	73.4601	2.95979
$617$	15.7609	0.634512	0.317256	−	0.948340i	$-0.397239\pi$
$617$	15.7609	0.634512	0.317256	+	0.948340i	$0.397239\pi$
$618$	−157.368	−6.33028
$619$	−47.2958	−1.90098	−0.950489	−	0.310757i	$-0.899417\pi$
$619$	−47.2958	−1.90098	−0.950489	+	0.310757i	$0.899417\pi$
$620$	−39.4949	−1.58615
$621$	−67.7333	−2.71804
$622$	67.7390	2.71609
$623$	−21.0597	−0.843740
$624$	−167.255	−6.69554
$625$	−11.9741	−0.478963
$626$	45.5708	1.82137
$627$	−13.4310	−0.536381
$628$	56.6939	2.26233
$629$	−7.51692	−0.299719
$630$	−170.681	−6.80010
$631$	−12.8211	−0.510400	−0.255200	−	0.966888i	$-0.582141\pi$
$631$	−12.8211	−0.510400	−0.255200	+	0.966888i	$0.582141\pi$
$632$	35.1209	1.39703
$633$	80.3572	3.19391
$634$	35.2354	1.39938
$635$	20.9432	0.831105
$636$	109.997	4.36168
$637$	−29.2243	−1.15791
$638$	−7.99236	−0.316421
$639$	39.6355	1.56796
$640$	132.686	5.24486
$641$	−16.7217	−0.660467	−0.330233	−	0.943899i	$-0.607127\pi$
$641$	−16.7217	−0.660467	−0.330233	+	0.943899i	$0.607127\pi$
$642$	83.8808	3.31051
$643$	−37.3492	−1.47291	−0.736454	−	0.676488i	$-0.763501\pi$
$643$	−37.3492	−1.47291	−0.736454	+	0.676488i	$0.763501\pi$
$644$	97.5525	3.84411
$645$	−47.1003	−1.85457
$646$	5.93562	0.233534
$647$	41.0825	1.61512	0.807560	−	0.589785i	$-0.200788\pi$
$647$	41.0825	1.61512	0.807560	+	0.589785i	$0.200788\pi$
$648$	−358.572	−14.0860
$649$	18.7750	0.736984
$650$	−14.2175	−0.557657
$651$	−53.9619	−2.11494
$652$	4.10709	0.160846
$653$	−37.7668	−1.47793	−0.738964	−	0.673745i	$-0.764685\pi$
$653$	−37.7668	−1.47793	−0.738964	+	0.673745i	$0.764685\pi$
$654$	5.61445	0.219542
$655$	15.1161	0.590633
$656$	138.347	5.40154
$657$	86.6072	3.37887
$658$	73.6619	2.87164
$659$	38.6005	1.50366	0.751830	−	0.659356i	$-0.229171\pi$
$659$	38.6005	1.50366	0.751830	+	0.659356i	$0.229171\pi$
$660$	−55.3396	−2.15409
$661$	38.4640	1.49608	0.748038	−	0.663656i	$-0.230996\pi$
$661$	38.4640	1.49608	0.748038	+	0.663656i	$0.230996\pi$
$662$	57.5689	2.23748
$663$	−7.55238	−0.293310
$664$	−45.1807	−1.75335
$665$	−18.7269	−0.726198
$666$	203.978	7.90399
$667$	−6.99451	−0.270829
$668$	82.8313	3.20484
$669$	−1.51299	−0.0584956
$670$	−67.9809	−2.62633
$671$	−16.6563	−0.643009
$672$	433.620	16.7272
$673$	1.11564	0.0430046	0.0215023	−	0.999769i	$-0.493155\pi$
$673$	1.11564	0.0430046	0.0215023	+	0.999769i	$0.493155\pi$
$674$	35.2526	1.35788
$675$	−32.5703	−1.25363
$676$	−34.0704	−1.31040
$677$	−19.1096	−0.734443	−0.367221	−	0.930134i	$-0.619691\pi$
$677$	−19.1096	−0.734443	−0.367221	+	0.930134i	$0.619691\pi$
$678$	−27.2942	−1.04823
$679$	−44.3647	−1.70256
$680$	16.1172	0.618068
$681$	−8.49217	−0.325421
$682$	−17.1537	−0.656848
$683$	29.8233	1.14116	0.570579	−	0.821243i	$-0.306719\pi$
$683$	29.8233	1.14116	0.570579	+	0.821243i	$0.306719\pi$
$684$	−120.112	−4.59260
$685$	−6.47369	−0.247347
$686$	46.2473	1.76573
$687$	92.1581	3.51605
$688$	149.303	5.69214
$689$	−15.0556	−0.573574
$690$	−64.9445	−2.47239
$691$	−20.9449	−0.796782	−0.398391	−	0.917216i	$-0.630431\pi$
$691$	−20.9449	−0.796782	−0.398391	+	0.917216i	$0.630431\pi$
$692$	23.2753	0.884796
$693$	−55.2812	−2.09996
$694$	−81.5499	−3.09559
$695$	−28.2101	−1.07007
$696$	−64.4251	−2.44203
$697$	6.24706	0.236624
$698$	−100.091	−3.78849
$699$	−43.6996	−1.65287
$700$	46.9092	1.77300
$701$	−31.7489	−1.19914	−0.599569	−	0.800323i	$-0.704662\pi$
$701$	−31.7489	−1.19914	−0.599569	+	0.800323i	$0.704662\pi$
$702$	129.575	4.89049
$703$	22.3802	0.844085
$704$	78.0251	2.94068
$705$	−36.5698	−1.37730
$706$	−14.4576	−0.544120
$707$	−74.6732	−2.80838
$708$	229.649	8.63074
$709$	3.59393	0.134973	0.0674864	−	0.997720i	$-0.478502\pi$
$709$	3.59393	0.134973	0.0674864	+	0.997720i	$0.478502\pi$
$710$	24.0280	0.901755
$711$	−26.4296	−0.991189
$712$	−53.9637	−2.02237
$713$	−15.0120	−0.562205
$714$	33.4150	1.25053
$715$	7.57448	0.283269
$716$	−51.6493	−1.93023
$717$	−74.8712	−2.79612
$718$	−93.8442	−3.50224
$719$	38.3630	1.43070	0.715348	−	0.698768i	$-0.246268\pi$
$719$	38.3630	1.43070	0.715348	+	0.698768i	$0.246268\pi$
$720$	−268.603	−10.0102
$721$	−71.0670	−2.64667
$722$	35.6138	1.32541
$723$	81.0417	3.01397
$724$	−32.9904	−1.22608
$725$	−3.36339	−0.124913
$726$	79.0133	2.93246
$727$	8.89388	0.329856	0.164928	−	0.986306i	$-0.447261\pi$
$727$	8.89388	0.329856	0.164928	+	0.986306i	$0.447261\pi$
$728$	−122.985	−4.55813
$729$	97.1856	3.59947
$730$	52.5034	1.94324
$731$	6.74179	0.249354
$732$	−203.734	−7.53021
$733$	24.4089	0.901564	0.450782	−	0.892634i	$-0.351145\pi$
$733$	24.4089	0.901564	0.450782	+	0.892634i	$0.351145\pi$
$734$	53.1539	1.96195
$735$	−64.1920	−2.36776
$736$	120.632	4.44654
$737$	−22.0180	−0.811045
$738$	−169.519	−6.24010
$739$	−19.6607	−0.723232	−0.361616	−	0.932327i	$-0.617775\pi$
$739$	−19.6607	−0.723232	−0.361616	+	0.932327i	$0.617775\pi$
$740$	92.2132	3.38982
$741$	22.4858	0.826036
$742$	66.6127	2.44543
$743$	10.7641	0.394896	0.197448	−	0.980313i	$-0.436735\pi$
$743$	10.7641	0.394896	0.197448	+	0.980313i	$0.436735\pi$
$744$	−138.273	−5.06933
$745$	16.7510	0.613710
$746$	3.28179	0.120155
$747$	34.0000	1.24400
$748$	7.92113	0.289625
$749$	37.8803	1.38412
$750$	−113.827	−4.15638
$751$	−33.0098	−1.20455	−0.602273	−	0.798290i	$-0.705738\pi$
$751$	−33.0098	−1.20455	−0.602273	+	0.798290i	$0.705738\pi$
$752$	115.923	4.22726
$753$	−47.2845	−1.72314
$754$	13.3806	0.487294
$755$	−1.30806	−0.0476052
$756$	−427.518	−15.5487
$757$	13.9067	0.505446	0.252723	−	0.967539i	$-0.418674\pi$
$757$	13.9067	0.505446	0.252723	+	0.967539i	$0.418674\pi$
$758$	−50.4969	−1.83413
$759$	−21.0346	−0.763507
$760$	−47.9861	−1.74064
$761$	−39.6958	−1.43897	−0.719485	−	0.694508i	$-0.755622\pi$
$761$	−39.6958	−1.43897	−0.719485	+	0.694508i	$0.755622\pi$
$762$	111.261	4.03056
$763$	2.53547	0.0917900
$764$	56.7633	2.05362
$765$	−12.1288	−0.438517
$766$	28.8683	1.04306
$767$	−31.4327	−1.13497
$768$	379.467	13.6928
$769$	−16.8786	−0.608658	−0.304329	−	0.952567i	$-0.598432\pi$
$769$	−16.8786	−0.608658	−0.304329	+	0.952567i	$0.598432\pi$
$770$	−33.5128	−1.20772
$771$	66.7149	2.40268
$772$	−87.2873	−3.14154
$773$	6.94680	0.249859	0.124929	−	0.992166i	$-0.460130\pi$
$773$	6.94680	0.249859	0.124929	+	0.992166i	$0.460130\pi$
$774$	−182.944	−6.57580
$775$	−7.21870	−0.259303
$776$	−113.681	−4.08090
$777$	125.991	4.51990
$778$	−9.04914	−0.324427
$779$	−18.5994	−0.666394
$780$	92.6483	3.31734
$781$	7.78233	0.278474
$782$	9.29595	0.332422
$783$	30.6531	1.09545
$784$	203.482	7.26723
$785$	−17.0448	−0.608354
$786$	80.3042	2.86436
$787$	−0.940300	−0.0335181	−0.0167590	−	0.999860i	$-0.505335\pi$
$787$	−0.940300	−0.0335181	−0.0167590	+	0.999860i	$0.505335\pi$
$788$	142.612	5.08035
$789$	56.4218	2.00867
$790$	−16.0223	−0.570048
$791$	−12.3260	−0.438261
$792$	−141.653	−5.03343
$793$	27.8856	0.990246
$794$	−87.8335	−3.11709
$795$	−33.0702	−1.17288
$796$	−47.6162	−1.68771
$797$	−10.6989	−0.378973	−0.189487	−	0.981883i	$-0.560682\pi$
$797$	−10.6989	−0.378973	−0.189487	+	0.981883i	$0.560682\pi$
$798$	−99.4869	−3.52180
$799$	5.23449	0.185183
$800$	58.0070	2.05086
$801$	40.6095	1.43487
$802$	65.5902	2.31607
$803$	17.0051	0.600097
$804$	−269.317	−9.49807
$805$	−29.3287	−1.03370
$806$	28.7183	1.01156
$807$	48.8221	1.71862
$808$	−191.344	−6.73145
$809$	13.0954	0.460411	0.230206	−	0.973142i	$-0.426060\pi$
$809$	13.0954	0.460411	0.230206	+	0.973142i	$0.426060\pi$
$810$	163.582	5.74768
$811$	48.5700	1.70552	0.852762	−	0.522299i	$-0.174925\pi$
$811$	48.5700	1.70552	0.852762	+	0.522299i	$0.174925\pi$
$812$	−44.1479	−1.54929
$813$	60.5780	2.12456
$814$	40.0506	1.40377
$815$	−1.23478	−0.0432524
$816$	52.5856	1.84087
$817$	−20.0724	−0.702245
$818$	34.3688	1.20168
$819$	92.5505	3.23398
$820$	−76.6353	−2.67622
$821$	22.1991	0.774753	0.387376	−	0.921922i	$-0.373381\pi$
$821$	22.1991	0.774753	0.387376	+	0.921922i	$0.373381\pi$
$822$	−34.3916	−1.19954
$823$	21.5157	0.749989	0.374995	−	0.927027i	$-0.377645\pi$
$823$	21.5157	0.749989	0.374995	+	0.927027i	$0.377645\pi$
$824$	−182.103	−6.34386
$825$	−10.1147	−0.352149
$826$	139.072	4.83893
$827$	−30.0723	−1.04571	−0.522857	−	0.852420i	$-0.675134\pi$
$827$	−30.0723	−1.04571	−0.522857	+	0.852420i	$0.675134\pi$
$828$	−188.111	−6.53730
$829$	44.2895	1.53824	0.769119	−	0.639106i	$-0.220696\pi$
$829$	44.2895	1.53824	0.769119	+	0.639106i	$0.220696\pi$
$830$	20.6116	0.715440
$831$	−11.8495	−0.411054
$832$	−130.628	−4.52871
$833$	9.18825	0.318354
$834$	−149.866	−5.18945
$835$	−24.9029	−0.861799
$836$	−23.5837	−0.815658
$837$	65.7894	2.27401
$838$	74.8629	2.58610
$839$	−20.8555	−0.720013	−0.360006	−	0.932950i	$-0.617225\pi$
$839$	−20.8555	−0.720013	−0.360006	+	0.932950i	$0.617225\pi$
$840$	−270.141	−9.32075
$841$	−25.8346	−0.890848
$842$	29.5553	1.01854
$843$	41.4139	1.42637
$844$	141.101	4.85689
$845$	10.2431	0.352374
$846$	−142.042	−4.88352
$847$	35.6821	1.22605
$848$	104.829	3.59985
$849$	26.1328	0.896876
$850$	4.47006	0.153322
$851$	35.0503	1.20151
$852$	95.1906	3.26118
$853$	33.3683	1.14251	0.571254	−	0.820773i	$-0.306457\pi$
$853$	33.3683	1.14251	0.571254	+	0.820773i	$0.306457\pi$
$854$	−123.378	−4.22191
$855$	36.1111	1.23497
$856$	97.0650	3.31761
$857$	34.2620	1.17037	0.585183	−	0.810901i	$-0.301023\pi$
$857$	34.2620	1.17037	0.585183	+	0.810901i	$0.301023\pi$
$858$	40.2395	1.37375
$859$	13.6874	0.467007	0.233504	−	0.972356i	$-0.424981\pi$
$859$	13.6874	0.467007	0.233504	+	0.972356i	$0.424981\pi$
$860$	−82.7044	−2.82020
$861$	−104.707	−3.56840
$862$	−41.9677	−1.42942
$863$	−30.4211	−1.03555	−0.517773	−	0.855518i	$-0.673239\pi$
$863$	−30.4211	−1.03555	−0.517773	+	0.855518i	$0.673239\pi$
$864$	−528.661	−17.9854
$865$	−6.99763	−0.237926
$866$	−79.9452	−2.71665
$867$	−54.4112	−1.84790
$868$	−94.7528	−3.21612
$869$	−5.18939	−0.176038
$870$	29.3910	0.996448
$871$	36.8621	1.24902
$872$	6.49691	0.220013
$873$	85.5486	2.89538
$874$	−27.6769	−0.936186
$875$	−51.4040	−1.73777
$876$	208.000	7.02767
$877$	6.38553	0.215624	0.107812	−	0.994171i	$-0.465616\pi$
$877$	6.38553	0.215624	0.107812	+	0.994171i	$0.465616\pi$
$878$	3.58220	0.120893
$879$	−91.9310	−3.10075
$880$	−52.7395	−1.77785
$881$	−30.0971	−1.01400	−0.506998	−	0.861947i	$-0.669245\pi$
$881$	−30.0971	−1.01400	−0.506998	+	0.861947i	$0.669245\pi$
$882$	−249.331	−8.39542
$883$	−27.0732	−0.911086	−0.455543	−	0.890214i	$-0.650555\pi$
$883$	−27.0732	−0.911086	−0.455543	+	0.890214i	$0.650555\pi$
$884$	−13.2614	−0.446028
$885$	−69.0429	−2.32085
$886$	16.2547	0.546089
$887$	−30.0920	−1.01039	−0.505196	−	0.863005i	$-0.668580\pi$
$887$	−30.0920	−1.01039	−0.505196	+	0.863005i	$0.668580\pi$
$888$	322.841	10.8338
$889$	50.2451	1.68517
$890$	24.6185	0.825213
$891$	52.9818	1.77496
$892$	−2.65669	−0.0889526
$893$	−15.5847	−0.521522
$894$	88.9900	2.97627
$895$	15.5281	0.519048
$896$	318.328	10.6346
$897$	35.2156	1.17582
$898$	−40.0028	−1.33491
$899$	6.79378	0.226585
$900$	−90.4551	−3.01517
$901$	4.73357	0.157698
$902$	−33.2847	−1.10826
$903$	−112.999	−3.76037
$904$	−31.5842	−1.05048
$905$	9.91841	0.329699
$906$	−6.94909	−0.230868
$907$	−5.81886	−0.193212	−0.0966061	−	0.995323i	$-0.530799\pi$
$907$	−5.81886	−0.193212	−0.0966061	+	0.995323i	$0.530799\pi$
$908$	−14.9116	−0.494858
$909$	143.993	4.77593
$910$	56.1063	1.85991
$911$	−41.0042	−1.35853	−0.679265	−	0.733893i	$-0.737701\pi$
$911$	−41.0042	−1.35853	−0.679265	+	0.733893i	$0.737701\pi$
$912$	−156.564	−5.18435
$913$	6.67581	0.220937
$914$	24.6202	0.814365
$915$	61.2516	2.02492
$916$	161.822	5.34676
$917$	36.2651	1.19758
$918$	−40.7390	−1.34459
$919$	12.5543	0.414129	0.207065	−	0.978327i	$-0.433609\pi$
$919$	12.5543	0.414129	0.207065	+	0.978327i	$0.433609\pi$
$920$	−75.1523	−2.47770
$921$	−16.3944	−0.540213
$922$	6.91014	0.227573
$923$	−13.0290	−0.428855
$924$	−132.766	−4.36768
$925$	16.8543	0.554166
$926$	−10.2253	−0.336025
$927$	137.039	4.50094
$928$	−54.5925	−1.79209
$929$	−48.4040	−1.58808	−0.794041	−	0.607864i	$-0.792027\pi$
$929$	−48.4040	−1.58808	−0.794041	+	0.607864i	$0.792027\pi$
$930$	63.0806	2.06850
$931$	−27.3563	−0.896565
$932$	−76.7330	−2.51347
$933$	−80.6807	−2.64137
$934$	−42.5011	−1.39068
$935$	−2.38145	−0.0778818
$936$	237.153	7.75158
$937$	26.4820	0.865129	0.432564	−	0.901603i	$-0.357609\pi$
$937$	26.4820	0.865129	0.432564	+	0.901603i	$0.357609\pi$
$938$	−163.094	−5.32521
$939$	−54.2772	−1.77127
$940$	−64.2137	−2.09442
$941$	8.86726	0.289064	0.144532	−	0.989500i	$-0.453832\pi$
$941$	8.86726	0.289064	0.144532	+	0.989500i	$0.453832\pi$
$942$	−90.5506	−2.95030
$943$	−29.1291	−0.948574
$944$	218.859	7.12326
$945$	128.531	4.18113
$946$	−35.9207	−1.16788
$947$	33.6862	1.09465	0.547327	−	0.836919i	$-0.315645\pi$
$947$	33.6862	1.09465	0.547327	+	0.836919i	$0.315645\pi$
$948$	−63.4747	−2.06156
$949$	−28.4695	−0.924160
$950$	−13.3087	−0.431793
$951$	−41.9672	−1.36088
$952$	38.6671	1.25321
$953$	9.11596	0.295295	0.147647	−	0.989040i	$-0.452830\pi$
$953$	9.11596	0.295295	0.147647	+	0.989040i	$0.452830\pi$
$954$	−128.449	−4.15871
$955$	−17.0656	−0.552231
$956$	−131.468	−4.25197
$957$	9.51932	0.307716
$958$	−85.7807	−2.77145
$959$	−15.5311	−0.501526
$960$	−286.928	−9.26057
$961$	−16.4188	−0.529639
$962$	−67.0517	−2.16183
$963$	−73.0447	−2.35383
$964$	142.303	4.58326
$965$	26.2425	0.844777
$966$	−155.809	−5.01308
$967$	38.5659	1.24020	0.620098	−	0.784524i	$-0.287093\pi$
$967$	38.5659	1.24020	0.620098	+	0.784524i	$0.287093\pi$
$968$	91.4324	2.93875
$969$	−7.06964	−0.227110
$970$	51.8616	1.66518
$971$	48.2629	1.54883	0.774415	−	0.632677i	$-0.218044\pi$
$971$	48.2629	1.54883	0.774415	+	0.632677i	$0.218044\pi$
$972$	344.892	11.0624
$973$	−67.6791	−2.16969
$974$	18.7618	0.601168
$975$	16.9338	0.542316
$976$	−194.161	−6.21496
$977$	3.12235	0.0998930	0.0499465	−	0.998752i	$-0.484095\pi$
$977$	3.12235	0.0998930	0.0499465	+	0.998752i	$0.484095\pi$
$978$	−6.55978	−0.209759
$979$	7.97357	0.254836
$980$	−112.716	−3.60058
$981$	−4.88915	−0.156098
$982$	−53.9589	−1.72190
$983$	15.3822	0.490617	0.245309	−	0.969445i	$-0.421111\pi$
$983$	15.3822	0.490617	0.245309	+	0.969445i	$0.421111\pi$
$984$	−268.302	−8.55316
$985$	−42.8757	−1.36613
$986$	−4.20693	−0.133976
$987$	−87.7351	−2.79264
$988$	39.4832	1.25613
$989$	−31.4360	−0.999605
$990$	64.6228	2.05385
$991$	−10.9424	−0.347597	−0.173798	−	0.984781i	$-0.555604\pi$
$991$	−10.9424	−0.347597	−0.173798	+	0.984781i	$0.555604\pi$
$992$	−117.170	−3.72014
$993$	−68.5675	−2.17592
$994$	57.6459	1.82842
$995$	14.3156	0.453835
$996$	81.6561	2.58737
$997$	−29.0517	−0.920078	−0.460039	−	0.887899i	$-0.652165\pi$
$997$	−29.0517	−0.920078	−0.460039	+	0.887899i	$0.652165\pi$
$998$	−23.3896	−0.740384
$999$	−153.606	−4.85987

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4021.2.a.c.1.2	✓	182

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4021.2.a.c.1.2	✓	182	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:	\( N \)	\(=\)	\( 4021 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4021.a (trivial)

\(f(q)\)	\(=\)	\(q-2.80453 q^{2} +3.34034 q^{3} +5.86536 q^{4} -1.76340 q^{5} -9.36806 q^{6} -4.23059 q^{7} -10.8405 q^{8} +8.15785 q^{9} +O(q^{10})\)	\(q-2.80453 q^{2} +3.34034 q^{3} +5.86536 q^{4} -1.76340 q^{5} -9.36806 q^{6} -4.23059 q^{7} -10.8405 q^{8} +8.15785 q^{9} +4.94549 q^{10} +1.60177 q^{11} +19.5923 q^{12} -2.68165 q^{13} +11.8648 q^{14} -5.89034 q^{15} +18.6718 q^{16} +0.843124 q^{17} -22.8789 q^{18} -2.51024 q^{19} -10.3430 q^{20} -14.1316 q^{21} -4.49221 q^{22} -3.93136 q^{23} -36.2110 q^{24} -1.89044 q^{25} +7.52076 q^{26} +17.2290 q^{27} -24.8139 q^{28} +1.77916 q^{29} +16.5196 q^{30} +3.81853 q^{31} -30.6844 q^{32} +5.35046 q^{33} -2.36456 q^{34} +7.46020 q^{35} +47.8488 q^{36} -8.91555 q^{37} +7.04004 q^{38} -8.95762 q^{39} +19.1161 q^{40} +7.40942 q^{41} +39.6324 q^{42} +7.99621 q^{43} +9.39498 q^{44} -14.3855 q^{45} +11.0256 q^{46} +6.20844 q^{47} +62.3700 q^{48} +10.8979 q^{49} +5.30178 q^{50} +2.81632 q^{51} -15.7289 q^{52} +5.61432 q^{53} -48.3191 q^{54} -2.82456 q^{55} +45.8617 q^{56} -8.38505 q^{57} -4.98970 q^{58} +11.7214 q^{59} -34.5490 q^{60} -10.3987 q^{61} -10.7092 q^{62} -34.5125 q^{63} +48.7117 q^{64} +4.72881 q^{65} -15.0055 q^{66} -13.7460 q^{67} +4.94523 q^{68} -13.1321 q^{69} -20.9223 q^{70} +4.85857 q^{71} -88.4353 q^{72} +10.6164 q^{73} +25.0039 q^{74} -6.31470 q^{75} -14.7235 q^{76} -6.77644 q^{77} +25.1219 q^{78} -3.23978 q^{79} -32.9257 q^{80} +33.0770 q^{81} -20.7799 q^{82} +4.16777 q^{83} -82.8869 q^{84} -1.48676 q^{85} -22.4256 q^{86} +5.94299 q^{87} -17.3640 q^{88} +4.97797 q^{89} +40.3446 q^{90} +11.3450 q^{91} -23.0589 q^{92} +12.7552 q^{93} -17.4117 q^{94} +4.42655 q^{95} -102.496 q^{96} +10.4867 q^{97} -30.5633 q^{98} +13.0670 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 182 q + 18 q^{2} + 28 q^{3} + 208 q^{4} + 22 q^{5} + 18 q^{6} + 14 q^{7} + 54 q^{8} + 238 q^{9}+O(q^{10}) \) 182 * q + 18 * q^2 + 28 * q^3 + 208 * q^4 + 22 * q^5 + 18 * q^6 + 14 * q^7 + 54 * q^8 + 238 * q^9	\( 182 q + 18 q^{2} + 28 q^{3} + 208 q^{4} + 22 q^{5} + 18 q^{6} + 14 q^{7} + 54 q^{8} + 238 q^{9} + 7 q^{10} + 138 q^{11} + 47 q^{12} + 5 q^{13} + 72 q^{14} + 41 q^{15} + 256 q^{16} + 29 q^{17} + 35 q^{18} + 48 q^{19} + 56 q^{20} + 22 q^{21} + 19 q^{22} + 91 q^{23} + 46 q^{24} + 230 q^{25} + 88 q^{26} + 103 q^{27} + 15 q^{28} + 75 q^{29} + 18 q^{30} + 43 q^{31} + 116 q^{32} + 15 q^{33} + 13 q^{34} + 185 q^{35} + 364 q^{36} + 15 q^{37} + 53 q^{38} + 80 q^{39} - 13 q^{40} + 68 q^{41} + 32 q^{42} + 82 q^{43} + 259 q^{44} + 37 q^{45} + 13 q^{46} + 121 q^{47} + 53 q^{48} + 244 q^{49} + 93 q^{50} + 144 q^{51} - 16 q^{52} + 101 q^{53} + 47 q^{54} + 49 q^{55} + 199 q^{56} + 3 q^{57} + 4 q^{58} + 254 q^{59} + 24 q^{60} + 8 q^{61} + 37 q^{62} + 19 q^{63} + 326 q^{64} + 65 q^{65} + 41 q^{66} + 91 q^{67} + 50 q^{68} + 50 q^{69} + 5 q^{70} + 212 q^{71} + 77 q^{72} + 5 q^{73} + 101 q^{74} + 127 q^{75} + 22 q^{76} + 87 q^{77} - 20 q^{78} + 86 q^{79} + 71 q^{80} + 358 q^{81} - 20 q^{82} + 139 q^{83} - 30 q^{84} + 25 q^{85} + 82 q^{86} + 36 q^{87} - 8 q^{88} + 100 q^{89} - 87 q^{90} + 74 q^{91} + 171 q^{92} + 50 q^{93} - 13 q^{94} + 217 q^{95} + 42 q^{96} + 20 q^{97} + 47 q^{98} + 389 q^{99}+O(q^{100}) \) 182 * q + 18 * q^2 + 28 * q^3 + 208 * q^4 + 22 * q^5 + 18 * q^6 + 14 * q^7 + 54 * q^8 + 238 * q^9 + 7 * q^10 + 138 * q^11 + 47 * q^12 + 5 * q^13 + 72 * q^14 + 41 * q^15 + 256 * q^16 + 29 * q^17 + 35 * q^18 + 48 * q^19 + 56 * q^20 + 22 * q^21 + 19 * q^22 + 91 * q^23 + 46 * q^24 + 230 * q^25 + 88 * q^26 + 103 * q^27 + 15 * q^28 + 75 * q^29 + 18 * q^30 + 43 * q^31 + 116 * q^32 + 15 * q^33 + 13 * q^34 + 185 * q^35 + 364 * q^36 + 15 * q^37 + 53 * q^38 + 80 * q^39 - 13 * q^40 + 68 * q^41 + 32 * q^42 + 82 * q^43 + 259 * q^44 + 37 * q^45 + 13 * q^46 + 121 * q^47 + 53 * q^48 + 244 * q^49 + 93 * q^50 + 144 * q^51 - 16 * q^52 + 101 * q^53 + 47 * q^54 + 49 * q^55 + 199 * q^56 + 3 * q^57 + 4 * q^58 + 254 * q^59 + 24 * q^60 + 8 * q^61 + 37 * q^62 + 19 * q^63 + 326 * q^64 + 65 * q^65 + 41 * q^66 + 91 * q^67 + 50 * q^68 + 50 * q^69 + 5 * q^70 + 212 * q^71 + 77 * q^72 + 5 * q^73 + 101 * q^74 + 127 * q^75 + 22 * q^76 + 87 * q^77 - 20 * q^78 + 86 * q^79 + 71 * q^80 + 358 * q^81 - 20 * q^82 + 139 * q^83 - 30 * q^84 + 25 * q^85 + 82 * q^86 + 36 * q^87 - 8 * q^88 + 100 * q^89 - 87 * q^90 + 74 * q^91 + 171 * q^92 + 50 * q^93 - 13 * q^94 + 217 * q^95 + 42 * q^96 + 20 * q^97 + 47 * q^98 + 389 * q^99

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