LMFDB - Embedded newform 4021.2.a.c.1.3

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			1.3
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)

$f(q)$	$=$	$q-2.71768 q^{2} -3.37653 q^{3} +5.38576 q^{4} +2.58064 q^{5} +9.17630 q^{6} -1.70858 q^{7} -9.20140 q^{8} +8.40093 q^{9} +O(q^{10})$	\(q-2.71768 q^{2} -3.37653 q^{3} +5.38576 q^{4} +2.58064 q^{5} +9.17630 q^{6} -1.70858 q^{7} -9.20140 q^{8} +8.40093 q^{9} -7.01334 q^{10} +4.51204 q^{11} -18.1852 q^{12} +1.33947 q^{13} +4.64336 q^{14} -8.71359 q^{15} +14.2349 q^{16} -0.525444 q^{17} -22.8310 q^{18} +3.84183 q^{19} +13.8987 q^{20} +5.76906 q^{21} -12.2623 q^{22} +7.36191 q^{23} +31.0688 q^{24} +1.65969 q^{25} -3.64025 q^{26} -18.2364 q^{27} -9.20199 q^{28} -5.08534 q^{29} +23.6807 q^{30} +8.21364 q^{31} -20.2830 q^{32} -15.2350 q^{33} +1.42799 q^{34} -4.40922 q^{35} +45.2454 q^{36} +2.25571 q^{37} -10.4408 q^{38} -4.52276 q^{39} -23.7455 q^{40} -2.79813 q^{41} -15.6784 q^{42} +7.13436 q^{43} +24.3008 q^{44} +21.6798 q^{45} -20.0073 q^{46} +11.2880 q^{47} -48.0645 q^{48} -4.08076 q^{49} -4.51050 q^{50} +1.77417 q^{51} +7.21407 q^{52} +8.47271 q^{53} +49.5606 q^{54} +11.6439 q^{55} +15.7213 q^{56} -12.9720 q^{57} +13.8203 q^{58} +9.95371 q^{59} -46.9293 q^{60} +2.92618 q^{61} -22.3220 q^{62} -14.3536 q^{63} +26.6529 q^{64} +3.45669 q^{65} +41.4038 q^{66} +8.46626 q^{67} -2.82991 q^{68} -24.8577 q^{69} +11.9828 q^{70} -3.44293 q^{71} -77.3003 q^{72} -2.52074 q^{73} -6.13029 q^{74} -5.60399 q^{75} +20.6912 q^{76} -7.70917 q^{77} +12.2914 q^{78} +6.74936 q^{79} +36.7351 q^{80} +36.3728 q^{81} +7.60442 q^{82} +5.19503 q^{83} +31.0708 q^{84} -1.35598 q^{85} -19.3889 q^{86} +17.1708 q^{87} -41.5171 q^{88} +15.1552 q^{89} -58.9185 q^{90} -2.28859 q^{91} +39.6495 q^{92} -27.7336 q^{93} -30.6772 q^{94} +9.91437 q^{95} +68.4861 q^{96} +0.587293 q^{97} +11.0902 q^{98} +37.9053 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.71768	−1.92169	−0.960843	−	0.277092i	$-0.910629\pi$
$2$	−2.71768	−1.92169	−0.960843	+	0.277092i	$0.910629\pi$
$3$	−3.37653	−1.94944	−0.974719	−	0.223434i	$-0.928273\pi$
$3$	−3.37653	−1.94944	−0.974719	+	0.223434i	$0.928273\pi$
$4$	5.38576	2.69288
$5$	2.58064	1.15410	0.577048	−	0.816710i	$-0.304204\pi$
$5$	2.58064	1.15410	0.577048	+	0.816710i	$0.304204\pi$
$6$	9.17630	3.74621
$7$	−1.70858	−0.645782	−0.322891	−	0.946436i	$-0.604655\pi$
$7$	−1.70858	−0.645782	−0.322891	+	0.946436i	$0.604655\pi$
$8$	−9.20140	−3.25319
$9$	8.40093	2.80031
$10$	−7.01334	−2.21781
$11$	4.51204	1.36043	0.680216	−	0.733012i	$-0.261886\pi$
$11$	4.51204	1.36043	0.680216	+	0.733012i	$0.261886\pi$
$12$	−18.1852	−5.24960
$13$	1.33947	0.371502	0.185751	−	0.982597i	$-0.440528\pi$
$13$	1.33947	0.371502	0.185751	+	0.982597i	$0.440528\pi$
$14$	4.64336	1.24099
$15$	−8.71359	−2.24984
$16$	14.2349	3.55872
$17$	−0.525444	−0.127439	−0.0637194	−	0.997968i	$-0.520296\pi$
$17$	−0.525444	−0.127439	−0.0637194	+	0.997968i	$0.520296\pi$
$18$	−22.8310	−5.38132
$19$	3.84183	0.881376	0.440688	−	0.897660i	$-0.354735\pi$
$19$	3.84183	0.881376	0.440688	+	0.897660i	$0.354735\pi$
$20$	13.8987	3.10784
$21$	5.76906	1.25891
$22$	−12.2623	−2.61432
$23$	7.36191	1.53506	0.767532	−	0.641010i	$-0.221484\pi$
$23$	7.36191	1.53506	0.767532	+	0.641010i	$0.221484\pi$
$24$	31.0688	6.34188
$25$	1.65969	0.331938
$26$	−3.64025	−0.713911
$27$	−18.2364	−3.50959
$28$	−9.20199	−1.73901
$29$	−5.08534	−0.944324	−0.472162	−	0.881512i	$-0.656526\pi$
$29$	−5.08534	−0.944324	−0.472162	+	0.881512i	$0.656526\pi$
$30$	23.6807	4.32349
$31$	8.21364	1.47521	0.737607	−	0.675230i	$-0.235956\pi$
$31$	8.21364	1.47521	0.737607	+	0.675230i	$0.235956\pi$
$32$	−20.2830	−3.58557
$33$	−15.2350	−2.65208
$34$	1.42799	0.244897
$35$	−4.40922	−0.745294
$36$	45.2454	7.54090
$37$	2.25571	0.370837	0.185418	−	0.982660i	$-0.440636\pi$
$37$	2.25571	0.370837	0.185418	+	0.982660i	$0.440636\pi$
$38$	−10.4408	−1.69373
$39$	−4.52276	−0.724221
$40$	−23.7455	−3.75449
$41$	−2.79813	−0.436995	−0.218498	−	0.975837i	$-0.570116\pi$
$41$	−2.79813	−0.436995	−0.218498	+	0.975837i	$0.570116\pi$
$42$	−15.6784	−2.41923
$43$	7.13436	1.08798	0.543990	−	0.839092i	$-0.316913\pi$
$43$	7.13436	1.08798	0.543990	+	0.839092i	$0.316913\pi$
$44$	24.3008	3.66348
$45$	21.6798	3.23183
$46$	−20.0073	−2.94991
$47$	11.2880	1.64653	0.823264	−	0.567658i	$-0.192150\pi$
$47$	11.2880	1.64653	0.823264	+	0.567658i	$0.192150\pi$
$48$	−48.0645	−6.93751
$49$	−4.08076	−0.582966
$50$	−4.51050	−0.637882
$51$	1.77417	0.248434
$52$	7.21407	1.00041
$53$	8.47271	1.16382	0.581908	−	0.813254i	$-0.302306\pi$
$53$	8.47271	1.16382	0.581908	+	0.813254i	$0.302306\pi$
$54$	49.5606	6.74434
$55$	11.6439	1.57007
$56$	15.7213	2.10085
$57$	−12.9720	−1.71819
$58$	13.8203	1.81469
$59$	9.95371	1.29586	0.647931	−	0.761699i	$-0.275634\pi$
$59$	9.95371	1.29586	0.647931	+	0.761699i	$0.275634\pi$
$60$	−46.9293	−6.05855
$61$	2.92618	0.374659	0.187329	−	0.982297i	$-0.440017\pi$
$61$	2.92618	0.374659	0.187329	+	0.982297i	$0.440017\pi$
$62$	−22.3220	−2.83490
$63$	−14.3536	−1.80839
$64$	26.6529	3.33161
$65$	3.45669	0.428750
$66$	41.4038	5.09646
$67$	8.46626	1.03432	0.517159	−	0.855889i	$-0.326990\pi$
$67$	8.46626	1.03432	0.517159	+	0.855889i	$0.326990\pi$
$68$	−2.82991	−0.343177
$69$	−24.8577	−2.99251
$70$	11.9828	1.43222
$71$	−3.44293	−0.408601	−0.204301	−	0.978908i	$-0.565492\pi$
$71$	−3.44293	−0.408601	−0.204301	+	0.978908i	$0.565492\pi$
$72$	−77.3003	−9.10993
$73$	−2.52074	−0.295030	−0.147515	−	0.989060i	$-0.547128\pi$
$73$	−2.52074	−0.295030	−0.147515	+	0.989060i	$0.547128\pi$
$74$	−6.13029	−0.712632
$75$	−5.60399	−0.647093
$76$	20.6912	2.37344
$77$	−7.70917	−0.878542
$78$	12.2914	1.39173
$79$	6.74936	0.759362	0.379681	−	0.925117i	$-0.376034\pi$
$79$	6.74936	0.759362	0.379681	+	0.925117i	$0.376034\pi$
$80$	36.7351	4.10711
$81$	36.3728	4.04143
$82$	7.60442	0.839768
$83$	5.19503	0.570228	0.285114	−	0.958494i	$-0.407968\pi$
$83$	5.19503	0.570228	0.285114	+	0.958494i	$0.407968\pi$
$84$	31.0708	3.39010
$85$	−1.35598	−0.147077
$86$	−19.3889	−2.09076
$87$	17.1708	1.84090
$88$	−41.5171	−4.42573
$89$	15.1552	1.60644	0.803222	−	0.595680i	$-0.203117\pi$
$89$	15.1552	1.60644	0.803222	+	0.595680i	$0.203117\pi$
$90$	−58.9185	−6.21056
$91$	−2.28859	−0.239910
$92$	39.6495	4.13374
$93$	−27.7336	−2.87584
$94$	−30.6772	−3.16411
$95$	9.91437	1.01719
$96$	68.4861	6.98984
$97$	0.587293	0.0596306	0.0298153	−	0.999555i	$-0.490508\pi$
$97$	0.587293	0.0596306	0.0298153	+	0.999555i	$0.490508\pi$
$98$	11.0902	1.12028
$99$	37.9053	3.80963
$100$	8.93870	0.893870
$101$	8.15074	0.811029	0.405514	−	0.914089i	$-0.367092\pi$
$101$	8.15074	0.811029	0.405514	+	0.914089i	$0.367092\pi$
$102$	−4.82163	−0.477412
$103$	10.0197	0.987274	0.493637	−	0.869668i	$-0.335667\pi$
$103$	10.0197	0.987274	0.493637	+	0.869668i	$0.335667\pi$
$104$	−12.3250	−1.20857
$105$	14.8879	1.45291
$106$	−23.0261	−2.23649
$107$	−6.93013	−0.669961	−0.334980	−	0.942225i	$-0.608730\pi$
$107$	−6.93013	−0.669961	−0.334980	+	0.942225i	$0.608730\pi$
$108$	−98.2168	−9.45091
$109$	−19.7342	−1.89020	−0.945098	−	0.326786i	$-0.894035\pi$
$109$	−19.7342	−1.89020	−0.945098	+	0.326786i	$0.894035\pi$
$110$	−31.6445	−3.01718
$111$	−7.61647	−0.722923
$112$	−24.3214	−2.29816
$113$	−0.944987	−0.0888969	−0.0444485	−	0.999012i	$-0.514153\pi$
$113$	−0.944987	−0.0888969	−0.0444485	+	0.999012i	$0.514153\pi$
$114$	35.2538	3.30182
$115$	18.9984	1.77161
$116$	−27.3884	−2.54295
$117$	11.2528	1.04032
$118$	−27.0510	−2.49024
$119$	0.897761	0.0822977
$120$	80.1772	7.31914
$121$	9.35851	0.850773
$122$	−7.95240	−0.719976
$123$	9.44797	0.851895
$124$	44.2367	3.97257
$125$	−8.62013	−0.771008
$126$	39.0085	3.47516
$127$	−18.2785	−1.62195	−0.810976	−	0.585079i	$-0.801063\pi$
$127$	−18.2785	−1.62195	−0.810976	+	0.585079i	$0.801063\pi$
$128$	−31.8679	−2.81675
$129$	−24.0894	−2.12095
$130$	−9.39416	−0.823923
$131$	15.0890	1.31833	0.659167	−	0.751996i	$-0.270909\pi$
$131$	15.0890	1.31833	0.659167	+	0.751996i	$0.270909\pi$
$132$	−82.0522	−7.14172
$133$	−6.56406	−0.569176
$134$	−23.0085	−1.98763
$135$	−47.0615	−4.05041
$136$	4.83482	0.414582
$137$	11.8650	1.01370	0.506850	−	0.862034i	$-0.330810\pi$
$137$	11.8650	1.01370	0.506850	+	0.862034i	$0.330810\pi$
$138$	67.5551	5.75067
$139$	−13.1620	−1.11639	−0.558194	−	0.829711i	$-0.688505\pi$
$139$	−13.1620	−1.11639	−0.558194	+	0.829711i	$0.688505\pi$
$140$	−23.7470	−2.00699
$141$	−38.1143	−3.20981
$142$	9.35678	0.785203
$143$	6.04375	0.505404
$144$	119.586	9.96553
$145$	−13.1234	−1.08984
$146$	6.85055	0.566956
$147$	13.7788	1.13646
$148$	12.1487	0.998619
$149$	−15.3936	−1.26109	−0.630547	−	0.776151i	$-0.717169\pi$
$149$	−15.3936	−1.26109	−0.630547	+	0.776151i	$0.717169\pi$
$150$	15.2298	1.24351
$151$	−0.924597	−0.0752426	−0.0376213	−	0.999292i	$-0.511978\pi$
$151$	−0.924597	−0.0752426	−0.0376213	+	0.999292i	$0.511978\pi$
$152$	−35.3502	−2.86728
$153$	−4.41421	−0.356868
$154$	20.9510	1.68828
$155$	21.1964	1.70254
$156$	−24.3585	−1.95024
$157$	19.0333	1.51902	0.759512	−	0.650494i	$-0.225438\pi$
$157$	19.0333	1.51902	0.759512	+	0.650494i	$0.225438\pi$
$158$	−18.3426	−1.45926
$159$	−28.6083	−2.26879
$160$	−52.3431	−4.13809
$161$	−12.5784	−0.991317
$162$	−98.8495	−7.76635
$163$	−5.40835	−0.423615	−0.211807	−	0.977311i	$-0.567935\pi$
$163$	−5.40835	−0.423615	−0.211807	+	0.977311i	$0.567935\pi$
$164$	−15.0701	−1.17678
$165$	−39.3161	−3.06075
$166$	−14.1184	−1.09580
$167$	−19.4719	−1.50678	−0.753392	−	0.657572i	$-0.771584\pi$
$167$	−19.4719	−1.50678	−0.753392	+	0.657572i	$0.771584\pi$
$168$	−53.0834	−4.09547
$169$	−11.2058	−0.861986
$170$	3.68511	0.282635
$171$	32.2749	2.46813
$172$	38.4240	2.92980
$173$	−4.38059	−0.333050	−0.166525	−	0.986037i	$-0.553255\pi$
$173$	−4.38059	−0.333050	−0.166525	+	0.986037i	$0.553255\pi$
$174$	−46.6646	−3.53763
$175$	−2.83571	−0.214360
$176$	64.2284	4.84140
$177$	−33.6090	−2.52620
$178$	−41.1868	−3.08708
$179$	−8.61978	−0.644272	−0.322136	−	0.946693i	$-0.604401\pi$
$179$	−8.61978	−0.644272	−0.322136	+	0.946693i	$0.604401\pi$
$180$	116.762	8.70292
$181$	−18.4179	−1.36899	−0.684496	−	0.729016i	$-0.739978\pi$
$181$	−18.4179	−1.36899	−0.684496	+	0.729016i	$0.739978\pi$
$182$	6.21965	0.461031
$183$	−9.88031	−0.730374
$184$	−67.7399	−4.99385
$185$	5.82118	0.427981
$186$	75.3709	5.52646
$187$	−2.37082	−0.173372
$188$	60.7946	4.43390
$189$	31.1583	2.26643
$190$	−26.9440	−1.95473
$191$	−7.03747	−0.509213	−0.254607	−	0.967045i	$-0.581946\pi$
$191$	−7.03747	−0.509213	−0.254607	+	0.967045i	$0.581946\pi$
$192$	−89.9942	−6.49477
$193$	−13.1542	−0.946858	−0.473429	−	0.880832i	$-0.656984\pi$
$193$	−13.1542	−0.946858	−0.473429	+	0.880832i	$0.656984\pi$
$194$	−1.59607	−0.114591
$195$	−11.6716	−0.835821
$196$	−21.9780	−1.56986
$197$	3.40041	0.242269	0.121134	−	0.992636i	$-0.461347\pi$
$197$	3.40041	0.242269	0.121134	+	0.992636i	$0.461347\pi$
$198$	−103.014	−7.32091
$199$	−6.52086	−0.462251	−0.231126	−	0.972924i	$-0.574241\pi$
$199$	−6.52086	−0.462251	−0.231126	+	0.972924i	$0.574241\pi$
$200$	−15.2715	−1.07986
$201$	−28.5865	−2.01634
$202$	−22.1511	−1.55854
$203$	8.68870	0.609827
$204$	9.55528	0.669003
$205$	−7.22097	−0.504335
$206$	−27.2304	−1.89723
$207$	61.8469	4.29866
$208$	19.0672	1.32207
$209$	17.3345	1.19905
$210$	−40.4603	−2.79203
$211$	−1.69932	−0.116986	−0.0584931	−	0.998288i	$-0.518630\pi$
$211$	−1.69932	−0.116986	−0.0584931	+	0.998288i	$0.518630\pi$
$212$	45.6320	3.13402
$213$	11.6252	0.796543
$214$	18.8338	1.28746
$215$	18.4112	1.25563
$216$	167.800	11.4174
$217$	−14.0337	−0.952666
$218$	53.6312	3.63237
$219$	8.51134	0.575143
$220$	62.7115	4.22801
$221$	−0.703817	−0.0473438
$222$	20.6991	1.38923
$223$	−7.96621	−0.533457	−0.266728	−	0.963772i	$-0.585943\pi$
$223$	−7.96621	−0.533457	−0.266728	+	0.963772i	$0.585943\pi$
$224$	34.6551	2.31549
$225$	13.9430	0.929530
$226$	2.56817	0.170832
$227$	−21.1207	−1.40183	−0.700914	−	0.713246i	$-0.747224\pi$
$227$	−21.1207	−1.40183	−0.700914	+	0.713246i	$0.747224\pi$
$228$	−69.8643	−4.62687
$229$	−7.59971	−0.502203	−0.251102	−	0.967961i	$-0.580793\pi$
$229$	−7.59971	−0.502203	−0.251102	+	0.967961i	$0.580793\pi$
$230$	−51.6316	−3.40448
$231$	26.0302	1.71266
$232$	46.7922	3.07206
$233$	−7.91124	−0.518282	−0.259141	−	0.965839i	$-0.583439\pi$
$233$	−7.91124	−0.518282	−0.259141	+	0.965839i	$0.583439\pi$
$234$	−30.5815	−1.99917
$235$	29.1303	1.90025
$236$	53.6083	3.48960
$237$	−22.7894	−1.48033
$238$	−2.43982	−0.158150
$239$	24.0030	1.55262	0.776311	−	0.630349i	$-0.217088\pi$
$239$	24.0030	1.55262	0.776311	+	0.630349i	$0.217088\pi$
$240$	−124.037	−8.00656
$241$	22.5481	1.45245	0.726224	−	0.687458i	$-0.241274\pi$
$241$	22.5481	1.45245	0.726224	+	0.687458i	$0.241274\pi$
$242$	−25.4334	−1.63492
$243$	−68.1047	−4.36892
$244$	15.7597	1.00891
$245$	−10.5310	−0.672799
$246$	−25.6765	−1.63708
$247$	5.14602	0.327433
$248$	−75.5770	−4.79914
$249$	−17.5411	−1.11162
$250$	23.4267	1.48163
$251$	12.5374	0.791351	0.395675	−	0.918390i	$-0.370511\pi$
$251$	12.5374	0.791351	0.395675	+	0.918390i	$0.370511\pi$
$252$	−77.3053	−4.86978
$253$	33.2172	2.08835
$254$	49.6750	3.11688
$255$	4.57850	0.286717
$256$	33.3007	2.08129
$257$	14.5816	0.909574	0.454787	−	0.890600i	$-0.349715\pi$
$257$	14.5816	0.909574	0.454787	+	0.890600i	$0.349715\pi$
$258$	65.4671	4.07580
$259$	−3.85406	−0.239480
$260$	18.6169	1.15457
$261$	−42.7216	−2.64440
$262$	−41.0071	−2.53343
$263$	17.8219	1.09894	0.549471	−	0.835513i	$-0.314829\pi$
$263$	17.8219	1.09894	0.549471	+	0.835513i	$0.314829\pi$
$264$	140.183	8.62770
$265$	21.8650	1.34316
$266$	17.8390	1.09378
$267$	−51.1718	−3.13166
$268$	45.5972	2.78529
$269$	−11.9884	−0.730947	−0.365473	−	0.930822i	$-0.619093\pi$
$269$	−11.9884	−0.730947	−0.365473	+	0.930822i	$0.619093\pi$
$270$	127.898	7.78362
$271$	−11.4553	−0.695862	−0.347931	−	0.937520i	$-0.613116\pi$
$271$	−11.4553	−0.695862	−0.347931	+	0.937520i	$0.613116\pi$
$272$	−7.47963	−0.453519
$273$	7.72749	0.467689
$274$	−32.2453	−1.94801
$275$	7.48860	0.451579
$276$	−133.878	−8.05848
$277$	5.60614	0.336840	0.168420	−	0.985715i	$-0.446133\pi$
$277$	5.60614	0.336840	0.168420	+	0.985715i	$0.446133\pi$
$278$	35.7701	2.14535
$279$	69.0022	4.13106
$280$	40.5710	2.42458
$281$	11.8659	0.707861	0.353930	−	0.935272i	$-0.384845\pi$
$281$	11.8659	0.707861	0.353930	+	0.935272i	$0.384845\pi$
$282$	103.582	6.16824
$283$	0.519655	0.0308903	0.0154451	−	0.999881i	$-0.495083\pi$
$283$	0.519655	0.0308903	0.0154451	+	0.999881i	$0.495083\pi$
$284$	−18.5428	−1.10031
$285$	−33.4761	−1.98295
$286$	−16.4249	−0.971227
$287$	4.78083	0.282204
$288$	−170.396	−10.0407
$289$	−16.7239	−0.983759
$290$	35.6652	2.09433
$291$	−1.98301	−0.116246
$292$	−13.5761	−0.794481
$293$	20.8864	1.22019	0.610097	−	0.792326i	$-0.291130\pi$
$293$	20.8864	1.22019	0.610097	+	0.792326i	$0.291130\pi$
$294$	−37.4463	−2.18391
$295$	25.6869	1.49555
$296$	−20.7557	−1.20640
$297$	−82.2833	−4.77456
$298$	41.8349	2.42343
$299$	9.86107	0.570280
$300$	−30.1818	−1.74254
$301$	−12.1896	−0.702598
$302$	2.51275	0.144593
$303$	−27.5212	−1.58105
$304$	54.6880	3.13657
$305$	7.55140	0.432392
$306$	11.9964	0.685789
$307$	−11.0853	−0.632672	−0.316336	−	0.948647i	$-0.602453\pi$
$307$	−11.0853	−0.632672	−0.316336	+	0.948647i	$0.602453\pi$
$308$	−41.5198	−2.36581
$309$	−33.8319	−1.92463
$310$	−57.6050	−3.27175
$311$	−8.56145	−0.485476	−0.242738	−	0.970092i	$-0.578045\pi$
$311$	−8.56145	−0.485476	−0.242738	+	0.970092i	$0.578045\pi$
$312$	41.6157	2.35603
$313$	−23.9279	−1.35248	−0.676241	−	0.736680i	$-0.736392\pi$
$313$	−23.9279	−1.35248	−0.676241	+	0.736680i	$0.736392\pi$
$314$	−51.7264	−2.91909
$315$	−37.0416	−2.08706
$316$	36.3504	2.04487
$317$	33.9725	1.90808	0.954042	−	0.299673i	$-0.0968776\pi$
$317$	33.9725	1.90808	0.954042	+	0.299673i	$0.0968776\pi$
$318$	77.7482	4.35990
$319$	−22.9452	−1.28469
$320$	68.7814	3.84500
$321$	23.3998	1.30605
$322$	34.1840	1.90500
$323$	−2.01866	−0.112321
$324$	195.895	10.8831
$325$	2.22311	0.123316
$326$	14.6981	0.814055
$327$	66.6332	3.68482
$328$	25.7467	1.42163
$329$	−19.2865	−1.06330
$330$	106.848	5.88181
$331$	23.8906	1.31314	0.656572	−	0.754263i	$-0.272006\pi$
$331$	23.8906	1.31314	0.656572	+	0.754263i	$0.272006\pi$
$332$	27.9792	1.53556
$333$	18.9501	1.03846
$334$	52.9184	2.89557
$335$	21.8483	1.19370
$336$	82.1219	4.48012
$337$	5.76586	0.314086	0.157043	−	0.987592i	$-0.449804\pi$
$337$	5.76586	0.314086	0.157043	+	0.987592i	$0.449804\pi$
$338$	30.4538	1.65647
$339$	3.19077	0.173299
$340$	−7.30298	−0.396060
$341$	37.0603	2.00693
$342$	−87.7128	−4.74296
$343$	18.9323	1.02225
$344$	−65.6461	−3.53940
$345$	−64.1487	−3.45365
$346$	11.9050	0.640017
$347$	−8.08411	−0.433978	−0.216989	−	0.976174i	$-0.569624\pi$
$347$	−8.08411	−0.433978	−0.216989	+	0.976174i	$0.569624\pi$
$348$	92.4777	4.95732
$349$	−25.2961	−1.35407	−0.677034	−	0.735951i	$-0.736735\pi$
$349$	−25.2961	−1.35407	−0.677034	+	0.735951i	$0.736735\pi$
$350$	7.70655	0.411932
$351$	−24.4271	−1.30382
$352$	−91.5178	−4.87792
$353$	−28.1860	−1.50019	−0.750094	−	0.661332i	$-0.769992\pi$
$353$	−28.1860	−1.50019	−0.750094	+	0.661332i	$0.769992\pi$
$354$	91.3383	4.85457
$355$	−8.88497	−0.471565
$356$	81.6221	4.32596
$357$	−3.03132	−0.160434
$358$	23.4258	1.23809
$359$	−25.2812	−1.33429	−0.667146	−	0.744927i	$-0.732484\pi$
$359$	−25.2812	−1.33429	−0.667146	+	0.744927i	$0.732484\pi$
$360$	−199.484	−10.5137
$361$	−4.24036	−0.223177
$362$	50.0539	2.63078
$363$	−31.5992	−1.65853
$364$	−12.3258	−0.646048
$365$	−6.50512	−0.340493
$366$	26.8515	1.40355
$367$	−34.2374	−1.78718	−0.893588	−	0.448888i	$-0.851820\pi$
$367$	−34.2374	−1.78718	−0.893588	+	0.448888i	$0.851820\pi$
$368$	104.796	5.46287
$369$	−23.5069	−1.22372
$370$	−15.8201	−0.822446
$371$	−14.4763	−0.751572
$372$	−149.366	−7.74429
$373$	−20.0084	−1.03600	−0.517998	−	0.855382i	$-0.673323\pi$
$373$	−20.0084	−1.03600	−0.517998	+	0.855382i	$0.673323\pi$
$374$	6.44313	0.333166
$375$	29.1061	1.50303
$376$	−103.866	−5.35646
$377$	−6.81166	−0.350819
$378$	−84.6781	−4.35537
$379$	−16.6066	−0.853025	−0.426513	−	0.904482i	$-0.640258\pi$
$379$	−16.6066	−0.853025	−0.426513	+	0.904482i	$0.640258\pi$
$380$	53.3964	2.73918
$381$	61.7177	3.16190
$382$	19.1256	0.978549
$383$	29.8053	1.52298	0.761491	−	0.648176i	$-0.224468\pi$
$383$	29.8053	1.52298	0.761491	+	0.648176i	$0.224468\pi$
$384$	107.603	5.49107
$385$	−19.8946	−1.01392
$386$	35.7488	1.81956
$387$	59.9353	3.04668
$388$	3.16302	0.160578
$389$	5.60929	0.284402	0.142201	−	0.989838i	$-0.454582\pi$
$389$	5.60929	0.284402	0.142201	+	0.989838i	$0.454582\pi$
$390$	31.7196	1.60619
$391$	−3.86827	−0.195627
$392$	37.5487	1.89650
$393$	−50.9485	−2.57001
$394$	−9.24120	−0.465565
$395$	17.4177	0.876377
$396$	204.149	10.2589
$397$	−22.7813	−1.14336	−0.571680	−	0.820477i	$-0.693708\pi$
$397$	−22.7813	−1.14336	−0.571680	+	0.820477i	$0.693708\pi$
$398$	17.7216	0.888302
$399$	22.1637	1.10957
$400$	23.6255	1.18128
$401$	23.9610	1.19656	0.598279	−	0.801288i	$-0.295852\pi$
$401$	23.9610	1.19656	0.598279	+	0.801288i	$0.295852\pi$
$402$	77.6889	3.87477
$403$	11.0019	0.548046
$404$	43.8979	2.18400
$405$	93.8651	4.66419
$406$	−23.6131	−1.17190
$407$	10.1779	0.504498
$408$	−16.3249	−0.808202
$409$	35.3619	1.74853	0.874267	−	0.485445i	$-0.161342\pi$
$409$	35.3619	1.74853	0.874267	+	0.485445i	$0.161342\pi$
$410$	19.6243	0.969173
$411$	−40.0626	−1.97614
$412$	53.9639	2.65861
$413$	−17.0067	−0.836845
$414$	−168.080	−8.26067
$415$	13.4065	0.658098
$416$	−27.1685	−1.33205
$417$	44.4419	2.17633
$418$	−47.1095	−2.30420
$419$	−36.2935	−1.77305	−0.886527	−	0.462677i	$-0.846889\pi$
$419$	−36.2935	−1.77305	−0.886527	+	0.462677i	$0.846889\pi$
$420$	80.1824	3.91250
$421$	−17.1151	−0.834139	−0.417069	−	0.908875i	$-0.636943\pi$
$421$	−17.1151	−0.834139	−0.417069	+	0.908875i	$0.636943\pi$
$422$	4.61820	0.224811
$423$	94.8300	4.61079
$424$	−77.9608	−3.78611
$425$	−0.872074	−0.0423018
$426$	−31.5934	−1.53071
$427$	−4.99960	−0.241948
$428$	−37.3240	−1.80412
$429$	−20.4069	−0.985253
$430$	−50.0357	−2.41294
$431$	−15.4259	−0.743040	−0.371520	−	0.928425i	$-0.621163\pi$
$431$	−15.4259	−0.743040	−0.371520	+	0.928425i	$0.621163\pi$
$432$	−259.593	−12.4897
$433$	−30.9500	−1.48736	−0.743682	−	0.668534i	$-0.766922\pi$
$433$	−30.9500	−1.48736	−0.743682	+	0.668534i	$0.766922\pi$
$434$	38.1389	1.83073
$435$	44.3116	2.12458
$436$	−106.284	−5.09007
$437$	28.2832	1.35297
$438$	−23.1311	−1.10525
$439$	16.7168	0.797849	0.398924	−	0.916984i	$-0.369384\pi$
$439$	16.7168	0.797849	0.398924	+	0.916984i	$0.369384\pi$
$440$	−107.141	−5.10772
$441$	−34.2822	−1.63248
$442$	1.91275	0.0909800
$443$	40.8237	1.93959	0.969797	−	0.243915i	$-0.0784319\pi$
$443$	40.8237	1.93959	0.969797	+	0.243915i	$0.0784319\pi$
$444$	−41.0205	−1.94675
$445$	39.1100	1.85399
$446$	21.6496	1.02514
$447$	51.9769	2.45843
$448$	−45.5385	−2.15149
$449$	−1.22619	−0.0578676	−0.0289338	−	0.999581i	$-0.509211\pi$
$449$	−1.22619	−0.0578676	−0.0289338	+	0.999581i	$0.509211\pi$
$450$	−37.8924	−1.78627
$451$	−12.6253	−0.594502
$452$	−5.08947	−0.239389
$453$	3.12193	0.146681
$454$	57.3991	2.69387
$455$	−5.90603	−0.276879
$456$	119.361	5.58958
$457$	22.4570	1.05049	0.525247	−	0.850950i	$-0.323973\pi$
$457$	22.4570	1.05049	0.525247	+	0.850950i	$0.323973\pi$
$458$	20.6536	0.965077
$459$	9.58219	0.447258
$460$	102.321	4.77074
$461$	−18.4686	−0.860168	−0.430084	−	0.902789i	$-0.641516\pi$
$461$	−18.4686	−0.860168	−0.430084	+	0.902789i	$0.641516\pi$
$462$	−70.7417	−3.29120
$463$	−24.9577	−1.15988	−0.579941	−	0.814659i	$-0.696924\pi$
$463$	−24.9577	−1.15988	−0.579941	+	0.814659i	$0.696924\pi$
$464$	−72.3892	−3.36059
$465$	−71.5703	−3.31899
$466$	21.5002	0.995976
$467$	4.61172	0.213405	0.106702	−	0.994291i	$-0.465971\pi$
$467$	4.61172	0.213405	0.106702	+	0.994291i	$0.465971\pi$
$468$	60.6049	2.80146
$469$	−14.4653	−0.667944
$470$	−79.1668	−3.65169
$471$	−64.2665	−2.96124
$472$	−91.5880	−4.21568
$473$	32.1905	1.48012
$474$	61.9342	2.84473
$475$	6.37625	0.292562
$476$	4.83513	0.221618
$477$	71.1787	3.25905
$478$	−65.2323	−2.98365
$479$	9.11387	0.416423	0.208212	−	0.978084i	$-0.433236\pi$
$479$	9.11387	0.416423	0.208212	+	0.978084i	$0.433236\pi$
$480$	176.738	8.06695
$481$	3.02146	0.137767
$482$	−61.2783	−2.79115
$483$	42.4713	1.93251
$484$	50.4027	2.29103
$485$	1.51559	0.0688195
$486$	185.086	8.39569
$487$	26.1676	1.18577	0.592883	−	0.805288i	$-0.297990\pi$
$487$	26.1676	1.18577	0.592883	+	0.805288i	$0.297990\pi$
$488$	−26.9249	−1.21883
$489$	18.2614	0.825811
$490$	28.6197	1.29291
$491$	22.1243	0.998457	0.499228	−	0.866471i	$-0.333617\pi$
$491$	22.1243	0.998457	0.499228	+	0.866471i	$0.333617\pi$
$492$	50.8845	2.29405
$493$	2.67206	0.120343
$494$	−13.9852	−0.629224
$495$	97.8199	4.39668
$496$	116.920	5.24988
$497$	5.88252	0.263867
$498$	47.6711	2.13619
$499$	−7.36789	−0.329832	−0.164916	−	0.986308i	$-0.552735\pi$
$499$	−7.36789	−0.329832	−0.164916	+	0.986308i	$0.552735\pi$
$500$	−46.4259	−2.07623
$501$	65.7475	2.93738
$502$	−34.0725	−1.52073
$503$	3.54868	0.158228	0.0791138	−	0.996866i	$-0.474791\pi$
$503$	3.54868	0.158228	0.0791138	+	0.996866i	$0.474791\pi$
$504$	132.074	5.88302
$505$	21.0341	0.936006
$506$	−90.2737	−4.01315
$507$	37.8367	1.68039
$508$	−98.4435	−4.36772
$509$	25.1140	1.11316	0.556580	−	0.830794i	$-0.312113\pi$
$509$	25.1140	1.11316	0.556580	+	0.830794i	$0.312113\pi$
$510$	−12.4429	−0.550980
$511$	4.30688	0.190525
$512$	−26.7648	−1.18285
$513$	−70.0610	−3.09327
$514$	−39.6280	−1.74792
$515$	25.8573	1.13941
$516$	−129.740	−5.71146
$517$	50.9321	2.23999
$518$	10.4741	0.460205
$519$	14.7912	0.649260
$520$	−31.8064	−1.39480
$521$	−1.62280	−0.0710962	−0.0355481	−	0.999368i	$-0.511318\pi$
$521$	−1.62280	−0.0710962	−0.0355481	+	0.999368i	$0.511318\pi$
$522$	116.103	5.08171
$523$	12.9870	0.567880	0.283940	−	0.958842i	$-0.408358\pi$
$523$	12.9870	0.567880	0.283940	+	0.958842i	$0.408358\pi$
$524$	81.2659	3.55012
$525$	9.57486	0.417881
$526$	−48.4340	−2.11182
$527$	−4.31581	−0.187999
$528$	−216.869	−9.43801
$529$	31.1977	1.35642
$530$	−59.4220	−2.58113
$531$	83.6204	3.62882
$532$	−35.3525	−1.53272
$533$	−3.74802	−0.162345
$534$	139.068	6.01808
$535$	−17.8842	−0.773199
$536$	−77.9014	−3.36483
$537$	29.1049	1.25597
$538$	32.5806	1.40465
$539$	−18.4126	−0.793085
$540$	−253.462	−10.9073
$541$	41.5402	1.78595	0.892976	−	0.450105i	$-0.148613\pi$
$541$	41.5402	1.78595	0.892976	+	0.450105i	$0.148613\pi$
$542$	31.1319	1.33723
$543$	62.1886	2.66877
$544$	10.6576	0.456940
$545$	−50.9269	−2.18147
$546$	−21.0008	−0.898752
$547$	21.2568	0.908877	0.454439	−	0.890778i	$-0.349840\pi$
$547$	21.2568	0.908877	0.454439	+	0.890778i	$0.349840\pi$
$548$	63.9023	2.72977
$549$	24.5826	1.04916
$550$	−20.3516	−0.867794
$551$	−19.5370	−0.832304
$552$	228.725	9.73520
$553$	−11.5318	−0.490382
$554$	−15.2357	−0.647302
$555$	−19.6554	−0.834323
$556$	−70.8874	−3.00630
$557$	18.4051	0.779850	0.389925	−	0.920847i	$-0.372501\pi$
$557$	18.4051	0.779850	0.389925	+	0.920847i	$0.372501\pi$
$558$	−187.526	−7.93860
$559$	9.55627	0.404187
$560$	−62.7648	−2.65230
$561$	8.00515	0.337977
$562$	−32.2477	−1.36029
$563$	−27.5927	−1.16289	−0.581447	−	0.813584i	$-0.697513\pi$
$563$	−27.5927	−1.16289	−0.581447	+	0.813584i	$0.697513\pi$
$564$	−205.275	−8.64362
$565$	−2.43867	−0.102596
$566$	−1.41225	−0.0593615
$567$	−62.1458	−2.60988
$568$	31.6798	1.32925
$569$	−7.66525	−0.321344	−0.160672	−	0.987008i	$-0.551366\pi$
$569$	−7.66525	−0.321344	−0.160672	+	0.987008i	$0.551366\pi$
$570$	90.9772	3.81062
$571$	−32.4658	−1.35865	−0.679326	−	0.733837i	$-0.737728\pi$
$571$	−32.4658	−1.35865	−0.679326	+	0.733837i	$0.737728\pi$
$572$	32.5502	1.36099
$573$	23.7622	0.992680
$574$	−12.9927	−0.542307
$575$	12.2185	0.509547
$576$	223.909	9.32954
$577$	−16.9187	−0.704336	−0.352168	−	0.935937i	$-0.614555\pi$
$577$	−16.9187	−0.704336	−0.352168	+	0.935937i	$0.614555\pi$
$578$	45.4502	1.89048
$579$	44.4154	1.84584
$580$	−70.6796	−2.93481
$581$	−8.87611	−0.368243
$582$	5.38918	0.223389
$583$	38.2292	1.58329
$584$	23.1943	0.959788
$585$	29.0394	1.20063
$586$	−56.7624	−2.34483
$587$	−35.6260	−1.47044	−0.735221	−	0.677828i	$-0.762922\pi$
$587$	−35.6260	−1.47044	−0.735221	+	0.677828i	$0.762922\pi$
$588$	74.2093	3.06034
$589$	31.5554	1.30022
$590$	−69.8087	−2.87398
$591$	−11.4816	−0.472288
$592$	32.1098	1.31971
$593$	−15.2468	−0.626112	−0.313056	−	0.949735i	$-0.601353\pi$
$593$	−15.2468	−0.626112	−0.313056	+	0.949735i	$0.601353\pi$
$594$	223.619	9.17521
$595$	2.31680	0.0949794
$596$	−82.9063	−3.39598
$597$	22.0178	0.901130
$598$	−26.7992	−1.09590
$599$	−13.4173	−0.548215	−0.274108	−	0.961699i	$-0.588382\pi$
$599$	−13.4173	−0.548215	−0.274108	+	0.961699i	$0.588382\pi$
$600$	51.5646	2.10511
$601$	−42.8632	−1.74843	−0.874213	−	0.485543i	$-0.838622\pi$
$601$	−42.8632	−1.74843	−0.874213	+	0.485543i	$0.838622\pi$
$602$	33.1274	1.35017
$603$	71.1244	2.89641
$604$	−4.97966	−0.202619
$605$	24.1509	0.981874
$606$	74.7937	3.03828
$607$	−23.5155	−0.954464	−0.477232	−	0.878777i	$-0.658360\pi$
$607$	−23.5155	−0.954464	−0.477232	+	0.878777i	$0.658360\pi$
$608$	−77.9239	−3.16023
$609$	−29.3376	−1.18882
$610$	−20.5223	−0.830922
$611$	15.1200	0.611690
$612$	−23.7739	−0.961003
$613$	−35.5564	−1.43611	−0.718054	−	0.695987i	$-0.754967\pi$
$613$	−35.5564	−1.43611	−0.718054	+	0.695987i	$0.754967\pi$
$614$	30.1263	1.21580
$615$	24.3818	0.983169
$616$	70.9352	2.85806
$617$	−8.38507	−0.337570	−0.168785	−	0.985653i	$-0.553984\pi$
$617$	−8.38507	−0.337570	−0.168785	+	0.985653i	$0.553984\pi$
$618$	91.9441	3.69853
$619$	2.57529	0.103510	0.0517548	−	0.998660i	$-0.483519\pi$
$619$	2.57529	0.103510	0.0517548	+	0.998660i	$0.483519\pi$
$620$	114.159	4.58473
$621$	−134.255	−5.38745
$622$	23.2673	0.932932
$623$	−25.8938	−1.03741
$624$	−64.3810	−2.57730
$625$	−30.5439	−1.22176
$626$	65.0282	2.59905
$627$	−58.5303	−2.33748
$628$	102.509	4.09055
$629$	−1.18525	−0.0472590
$630$	100.667	4.01067
$631$	38.8144	1.54518	0.772589	−	0.634907i	$-0.218961\pi$
$631$	38.8144	1.54518	0.772589	+	0.634907i	$0.218961\pi$
$632$	−62.1035	−2.47035
$633$	5.73780	0.228057
$634$	−92.3261	−3.66674
$635$	−47.1701	−1.87189
$636$	−154.078	−6.10958
$637$	−5.46606	−0.216573
$638$	62.3577	2.46877
$639$	−28.9238	−1.14421
$640$	−82.2394	−3.25080
$641$	5.65865	0.223503	0.111752	−	0.993736i	$-0.464354\pi$
$641$	5.65865	0.223503	0.111752	+	0.993736i	$0.464354\pi$
$642$	−63.5930	−2.50981
$643$	−34.8646	−1.37492	−0.687462	−	0.726220i	$-0.741275\pi$
$643$	−34.8646	−1.37492	−0.687462	+	0.726220i	$0.741275\pi$
$644$	−67.7442	−2.66950
$645$	−62.1659	−2.44778
$646$	5.48607	0.215847
$647$	−7.58524	−0.298207	−0.149103	−	0.988822i	$-0.547639\pi$
$647$	−7.58524	−0.298207	−0.149103	+	0.988822i	$0.547639\pi$
$648$	−334.681	−13.1475
$649$	44.9115	1.76293
$650$	−6.04169	−0.236975
$651$	47.3850	1.85716
$652$	−29.1281	−1.14074
$653$	−15.1253	−0.591899	−0.295950	−	0.955204i	$-0.595636\pi$
$653$	−15.1253	−0.591899	−0.295950	+	0.955204i	$0.595636\pi$
$654$	−181.087	−7.08107
$655$	38.9393	1.52148
$656$	−39.8311	−1.55514
$657$	−21.1766	−0.826176
$658$	52.4144	2.04333
$659$	14.5544	0.566957	0.283479	−	0.958979i	$-0.408511\pi$
$659$	14.5544	0.566957	0.283479	+	0.958979i	$0.408511\pi$
$660$	−211.747	−8.24224
$661$	12.7082	0.494291	0.247146	−	0.968978i	$-0.420507\pi$
$661$	12.7082	0.494291	0.247146	+	0.968978i	$0.420507\pi$
$662$	−64.9268	−2.52345
$663$	2.37646	0.0922939
$664$	−47.8015	−1.85506
$665$	−16.9395	−0.656884
$666$	−51.5002	−1.99559
$667$	−37.4378	−1.44960
$668$	−104.871	−4.05759
$669$	26.8981	1.03994
$670$	−59.3767	−2.29392
$671$	13.2030	0.509697
$672$	−117.014	−4.51391
$673$	10.9955	0.423844	0.211922	−	0.977287i	$-0.432028\pi$
$673$	10.9955	0.423844	0.211922	+	0.977287i	$0.432028\pi$
$674$	−15.6697	−0.603576
$675$	−30.2668	−1.16497
$676$	−60.3518	−2.32122
$677$	−48.5848	−1.86727	−0.933633	−	0.358232i	$-0.883380\pi$
$677$	−48.5848	−1.86727	−0.933633	+	0.358232i	$0.883380\pi$
$678$	−8.67149	−0.333026
$679$	−1.00344	−0.0385084
$680$	12.4769	0.478468
$681$	71.3145	2.73278
$682$	−100.718	−3.85669
$683$	22.5989	0.864721	0.432361	−	0.901701i	$-0.357681\pi$
$683$	22.5989	0.864721	0.432361	+	0.901701i	$0.357681\pi$
$684$	173.825	6.64637
$685$	30.6194	1.16991
$686$	−51.4520	−1.96445
$687$	25.6606	0.979014
$688$	101.557	3.87182
$689$	11.3490	0.432361
$690$	174.335	6.63683
$691$	−31.3207	−1.19149	−0.595747	−	0.803172i	$-0.703144\pi$
$691$	−31.3207	−1.19149	−0.595747	+	0.803172i	$0.703144\pi$
$692$	−23.5928	−0.896863
$693$	−64.7642	−2.46019
$694$	21.9700	0.833969
$695$	−33.9664	−1.28842
$696$	−157.995	−5.98879
$697$	1.47026	0.0556901
$698$	68.7466	2.60210
$699$	26.7125	1.01036
$700$	−15.2725	−0.577245
$701$	31.7209	1.19808	0.599041	−	0.800718i	$-0.295549\pi$
$701$	31.7209	1.19808	0.599041	+	0.800718i	$0.295549\pi$
$702$	66.3849	2.50554
$703$	8.66606	0.326847
$704$	120.259	4.53243
$705$	−98.3593	−3.70443
$706$	76.6003	2.88289
$707$	−13.9262	−0.523748
$708$	−181.010	−6.80277
$709$	10.1788	0.382274	0.191137	−	0.981563i	$-0.438782\pi$
$709$	10.1788	0.382274	0.191137	+	0.981563i	$0.438782\pi$
$710$	24.1465	0.906200
$711$	56.7009	2.12645
$712$	−139.449	−5.22606
$713$	60.4681	2.26455
$714$	8.23813	0.308304
$715$	15.5967	0.583284
$716$	−46.4240	−1.73495
$717$	−81.0467	−3.02674
$718$	68.7062	2.56409
$719$	23.5319	0.877591	0.438795	−	0.898587i	$-0.355405\pi$
$719$	23.5319	0.877591	0.438795	+	0.898587i	$0.355405\pi$
$720$	308.609	11.5012
$721$	−17.1195	−0.637563
$722$	11.5239	0.428876
$723$	−76.1341	−2.83146
$724$	−99.1945	−3.68653
$725$	−8.44009	−0.313457
$726$	85.8765	3.18718
$727$	−32.6274	−1.21008	−0.605042	−	0.796193i	$-0.706844\pi$
$727$	−32.6274	−1.21008	−0.605042	+	0.796193i	$0.706844\pi$
$728$	21.0582	0.780470
$729$	120.839	4.47551
$730$	17.6788	0.654322
$731$	−3.74871	−0.138651
$732$	−53.2130	−1.96681
$733$	−20.3716	−0.752442	−0.376221	−	0.926530i	$-0.622777\pi$
$733$	−20.3716	−0.752442	−0.376221	+	0.926530i	$0.622777\pi$
$734$	93.0461	3.43439
$735$	35.5581	1.31158
$736$	−149.322	−5.50407
$737$	38.2001	1.40712
$738$	63.8842	2.35161
$739$	43.9541	1.61688	0.808439	−	0.588579i	$-0.200313\pi$
$739$	43.9541	1.61688	0.808439	+	0.588579i	$0.200313\pi$
$740$	31.3515	1.15250
$741$	−17.3757	−0.638311
$742$	39.3419	1.44429
$743$	39.7971	1.46001	0.730006	−	0.683440i	$-0.239517\pi$
$743$	39.7971	1.46001	0.730006	+	0.683440i	$0.239517\pi$
$744$	255.188	9.35564
$745$	−39.7253	−1.45542
$746$	54.3764	1.99086
$747$	43.6431	1.59682
$748$	−12.7687	−0.466869
$749$	11.8407	0.432649
$750$	−79.1009	−2.88836
$751$	−15.5901	−0.568892	−0.284446	−	0.958692i	$-0.591810\pi$
$751$	−15.5901	−0.568892	−0.284446	+	0.958692i	$0.591810\pi$
$752$	160.684	5.85954
$753$	−42.3327	−1.54269
$754$	18.5119	0.674163
$755$	−2.38605	−0.0868372
$756$	167.811	6.10323
$757$	46.0702	1.67445	0.837225	−	0.546858i	$-0.184176\pi$
$757$	46.0702	1.67445	0.837225	+	0.546858i	$0.184176\pi$
$758$	45.1314	1.63925
$759$	−112.159	−4.07111
$760$	−91.2260	−3.30912
$761$	18.8528	0.683412	0.341706	−	0.939807i	$-0.388995\pi$
$761$	18.8528	0.683412	0.341706	+	0.939807i	$0.388995\pi$
$762$	−167.729	−6.07617
$763$	33.7175	1.22065
$764$	−37.9021	−1.37125
$765$	−11.3915	−0.411860
$766$	−81.0012	−2.92669
$767$	13.3327	0.481416
$768$	−112.441	−4.05735
$769$	−14.8675	−0.536135	−0.268068	−	0.963400i	$-0.586385\pi$
$769$	−14.8675	−0.536135	−0.268068	+	0.963400i	$0.586385\pi$
$770$	54.0670	1.94844
$771$	−49.2351	−1.77316
$772$	−70.8452	−2.54977
$773$	−22.7538	−0.818396	−0.409198	−	0.912446i	$-0.634192\pi$
$773$	−22.7538	−0.818396	−0.409198	+	0.912446i	$0.634192\pi$
$774$	−162.885	−5.85477
$775$	13.6321	0.489680
$776$	−5.40392	−0.193989
$777$	13.0133	0.466851
$778$	−15.2442	−0.546532
$779$	−10.7500	−0.385157
$780$	−62.8605	−2.25077
$781$	−15.5347	−0.555874
$782$	10.5127	0.375933
$783$	92.7382	3.31419
$784$	−58.0892	−2.07461
$785$	49.1181	1.75310
$786$	138.461	4.93876
$787$	26.7209	0.952499	0.476249	−	0.879310i	$-0.341996\pi$
$787$	26.7209	0.952499	0.476249	+	0.879310i	$0.341996\pi$
$788$	18.3138	0.652401
$789$	−60.1760	−2.14232
$790$	−47.3355	−1.68412
$791$	1.61458	0.0574080
$792$	−348.782	−12.3934
$793$	3.91953	0.139187
$794$	61.9121	2.19718
$795$	−73.8278	−2.61840
$796$	−35.1198	−1.24479
$797$	2.04580	0.0724658	0.0362329	−	0.999343i	$-0.488464\pi$
$797$	2.04580	0.0724658	0.0362329	+	0.999343i	$0.488464\pi$
$798$	−60.2338	−2.13225
$799$	−5.93122	−0.209832
$800$	−33.6636	−1.19019
$801$	127.317	4.49854
$802$	−65.1184	−2.29941
$803$	−11.3737	−0.401368
$804$	−153.960	−5.42976
$805$	−32.4603	−1.14407
$806$	−29.8997	−1.05317
$807$	40.4792	1.42494
$808$	−74.9982	−2.63843
$809$	12.4845	0.438930	0.219465	−	0.975620i	$-0.429569\pi$
$809$	12.4845	0.438930	0.219465	+	0.975620i	$0.429569\pi$
$810$	−255.095	−8.96312
$811$	−14.9199	−0.523910	−0.261955	−	0.965080i	$-0.584367\pi$
$811$	−14.9199	−0.523910	−0.261955	+	0.965080i	$0.584367\pi$
$812$	46.7952	1.64219
$813$	38.6793	1.35654
$814$	−27.6601	−0.969487
$815$	−13.9570	−0.488892
$816$	25.2552	0.884108
$817$	27.4090	0.958919
$818$	−96.1023	−3.36014
$819$	−19.2263	−0.671821
$820$	−38.8904	−1.35811
$821$	−27.3939	−0.956053	−0.478026	−	0.878345i	$-0.658648\pi$
$821$	−27.3939	−0.956053	−0.478026	+	0.878345i	$0.658648\pi$
$822$	108.877	3.79753
$823$	10.5853	0.368981	0.184491	−	0.982834i	$-0.440936\pi$
$823$	10.5853	0.368981	0.184491	+	0.982834i	$0.440936\pi$
$824$	−92.1956	−3.21178
$825$	−25.2854	−0.880326
$826$	46.2187	1.60815
$827$	32.3385	1.12452	0.562260	−	0.826961i	$-0.309932\pi$
$827$	32.3385	1.12452	0.562260	+	0.826961i	$0.309932\pi$
$828$	333.092	11.5758
$829$	−40.7357	−1.41481	−0.707405	−	0.706808i	$-0.750134\pi$
$829$	−40.7357	−1.41481	−0.707405	+	0.706808i	$0.750134\pi$
$830$	−36.4345	−1.26466
$831$	−18.9293	−0.656650
$832$	35.7008	1.23770
$833$	2.14421	0.0742925
$834$	−120.779	−4.18222
$835$	−50.2500	−1.73897
$836$	93.3594	3.22890
$837$	−149.787	−5.17740
$838$	98.6340	3.40725
$839$	−10.2885	−0.355197	−0.177598	−	0.984103i	$-0.556833\pi$
$839$	−10.2885	−0.355197	−0.177598	+	0.984103i	$0.556833\pi$
$840$	−136.989	−4.72657
$841$	−3.13934	−0.108253
$842$	46.5133	1.60295
$843$	−40.0656	−1.37993
$844$	−9.15214	−0.315030
$845$	−28.9182	−0.994815
$846$	−257.717	−8.86050
$847$	−15.9897	−0.549414
$848$	120.608	4.14170
$849$	−1.75463	−0.0602187
$850$	2.37002	0.0812909
$851$	16.6063	0.569258
$852$	62.6103	2.14499
$853$	19.5819	0.670472	0.335236	−	0.942134i	$-0.391184\pi$
$853$	19.5819	0.670472	0.335236	+	0.942134i	$0.391184\pi$
$854$	13.5873	0.464948
$855$	83.2899	2.84845
$856$	63.7669	2.17951
$857$	−30.8484	−1.05376	−0.526880	−	0.849940i	$-0.676638\pi$
$857$	−30.8484	−1.05376	−0.526880	+	0.849940i	$0.676638\pi$
$858$	55.4593	1.89335
$859$	15.0549	0.513665	0.256833	−	0.966456i	$-0.417321\pi$
$859$	15.0549	0.513665	0.256833	+	0.966456i	$0.417321\pi$
$860$	99.1583	3.38127
$861$	−16.1426	−0.550138
$862$	41.9226	1.42789
$863$	19.7621	0.672711	0.336356	−	0.941735i	$-0.390806\pi$
$863$	19.7621	0.672711	0.336356	+	0.941735i	$0.390806\pi$
$864$	369.889	12.5839
$865$	−11.3047	−0.384371
$866$	84.1121	2.85825
$867$	56.4687	1.91778
$868$	−75.5819	−2.56542
$869$	30.4534	1.03306
$870$	−120.424	−4.08277
$871$	11.3403	0.384252
$872$	181.583	6.14916
$873$	4.93381	0.166984
$874$	−76.8645	−2.59998
$875$	14.7282	0.497903
$876$	45.8401	1.54879
$877$	32.6198	1.10149	0.550747	−	0.834672i	$-0.314343\pi$
$877$	32.6198	1.10149	0.550747	+	0.834672i	$0.314343\pi$
$878$	−45.4308	−1.53322
$879$	−70.5234	−2.37869
$880$	165.750	5.58744
$881$	−47.4587	−1.59892	−0.799462	−	0.600717i	$-0.794882\pi$
$881$	−47.4587	−1.59892	−0.799462	+	0.600717i	$0.794882\pi$
$882$	93.1679	3.13712
$883$	1.90097	0.0639727	0.0319864	−	0.999488i	$-0.489817\pi$
$883$	1.90097	0.0639727	0.0319864	+	0.999488i	$0.489817\pi$
$884$	−3.79059	−0.127491
$885$	−86.7326	−2.91548
$886$	−110.946	−3.72729
$887$	24.1929	0.812317	0.406159	−	0.913803i	$-0.366868\pi$
$887$	24.1929	0.812317	0.406159	+	0.913803i	$0.366868\pi$
$888$	70.0822	2.35180
$889$	31.2302	1.04743
$890$	−106.288	−3.56279
$891$	164.116	5.49808
$892$	−42.9041	−1.43654
$893$	43.3667	1.45121
$894$	−141.256	−4.72432
$895$	−22.2445	−0.743552
$896$	54.4487	1.81900
$897$	−33.2962	−1.11173
$898$	3.33239	0.111203
$899$	−41.7692	−1.39308
$900$	75.0934	2.50311
$901$	−4.45193	−0.148315
$902$	34.3115	1.14245
$903$	41.1586	1.36967
$904$	8.69520	0.289198
$905$	−47.5300	−1.57995
$906$	−8.48438	−0.281875
$907$	15.1808	0.504069	0.252035	−	0.967718i	$-0.418900\pi$
$907$	15.1808	0.504069	0.252035	+	0.967718i	$0.418900\pi$
$908$	−113.751	−3.77495
$909$	68.4738	2.27113
$910$	16.0507	0.532074
$911$	−5.43061	−0.179924	−0.0899621	−	0.995945i	$-0.528675\pi$
$911$	−5.43061	−0.179924	−0.0899621	+	0.995945i	$0.528675\pi$
$912$	−184.655	−6.11455
$913$	23.4402	0.775756
$914$	−61.0309	−2.01872
$915$	−25.4975	−0.842922
$916$	−40.9302	−1.35237
$917$	−25.7808	−0.851356
$918$	−26.0413	−0.859490
$919$	55.9000	1.84397	0.921985	−	0.387226i	$-0.126567\pi$
$919$	55.9000	1.84397	0.921985	+	0.387226i	$0.126567\pi$
$920$	−174.812	−5.76338
$921$	37.4298	1.23335
$922$	50.1916	1.65297
$923$	−4.61171	−0.151796
$924$	140.193	4.61200
$925$	3.74379	0.123095
$926$	67.8269	2.22893
$927$	84.1751	2.76467
$928$	103.146	3.38593
$929$	19.4053	0.636667	0.318333	−	0.947979i	$-0.396877\pi$
$929$	19.4053	0.636667	0.318333	+	0.947979i	$0.396877\pi$
$930$	194.505	6.37807
$931$	−15.6776	−0.513812
$932$	−42.6080	−1.39567
$933$	28.9080	0.946405
$934$	−12.5332	−0.410097
$935$	−6.11823	−0.200088
$936$	−103.542	−3.38436
$937$	19.8333	0.647926	0.323963	−	0.946070i	$-0.394985\pi$
$937$	19.8333	0.647926	0.323963	+	0.946070i	$0.394985\pi$
$938$	39.3119	1.28358
$939$	80.7931	2.63658
$940$	156.889	5.11715
$941$	2.11658	0.0689986	0.0344993	−	0.999405i	$-0.489016\pi$
$941$	2.11658	0.0689986	0.0344993	+	0.999405i	$0.489016\pi$
$942$	174.655	5.69058
$943$	−20.5996	−0.670816
$944$	141.690	4.61162
$945$	80.4082	2.61568
$946$	−87.4834	−2.84433
$947$	−57.9495	−1.88310	−0.941552	−	0.336867i	$-0.890633\pi$
$947$	−57.9495	−1.88310	−0.941552	+	0.336867i	$0.890633\pi$
$948$	−122.738	−3.98635
$949$	−3.37646	−0.109604
$950$	−17.3286	−0.562213
$951$	−114.709	−3.71969
$952$	−8.26066	−0.267730
$953$	18.2619	0.591562	0.295781	−	0.955256i	$-0.404420\pi$
$953$	18.2619	0.591562	0.295781	+	0.955256i	$0.404420\pi$
$954$	−193.441	−6.26287
$955$	−18.1612	−0.587681
$956$	129.274	4.18103
$957$	77.4752	2.50442
$958$	−24.7685	−0.800235
$959$	−20.2724	−0.654629
$960$	−232.242	−7.49559
$961$	36.4639	1.17626
$962$	−8.21135	−0.264745
$963$	−58.2195	−1.87610
$964$	121.438	3.91127
$965$	−33.9461	−1.09276
$966$	−115.423	−3.71368
$967$	−39.4752	−1.26944	−0.634718	−	0.772744i	$-0.718884\pi$
$967$	−39.4752	−1.26944	−0.634718	+	0.772744i	$0.718884\pi$
$968$	−86.1113	−2.76772
$969$	6.81607	0.218964
$970$	−4.11889	−0.132249
$971$	18.0947	0.580687	0.290343	−	0.956922i	$-0.406230\pi$
$971$	18.0947	0.580687	0.290343	+	0.956922i	$0.406230\pi$
$972$	−366.795	−11.7650
$973$	22.4883	0.720943
$974$	−71.1150	−2.27867
$975$	−7.50639	−0.240397
$976$	41.6538	1.33331
$977$	−0.796872	−0.0254942	−0.0127471	−	0.999919i	$-0.504058\pi$
$977$	−0.796872	−0.0254942	−0.0127471	+	0.999919i	$0.504058\pi$
$978$	−49.6287	−1.58695
$979$	68.3807	2.18546
$980$	−56.7173	−1.81177
$981$	−165.786	−5.29314
$982$	−60.1267	−1.91872
$983$	8.73152	0.278492	0.139246	−	0.990258i	$-0.455532\pi$
$983$	8.73152	0.278492	0.139246	+	0.990258i	$0.455532\pi$
$984$	−86.9346	−2.77137
$985$	8.77522	0.279602
$986$	−7.26179	−0.231262
$987$	65.1213	2.07283
$988$	27.7152	0.881739
$989$	52.5225	1.67012
$990$	−265.843	−8.44904
$991$	−58.5704	−1.86055	−0.930276	−	0.366862i	$-0.880432\pi$
$991$	−58.5704	−1.86055	−0.930276	+	0.366862i	$0.880432\pi$
$992$	−166.597	−5.28948
$993$	−80.6672	−2.55989
$994$	−15.9868	−0.507070
$995$	−16.8280	−0.533482
$996$	−94.4724	−2.99347
$997$	49.3472	1.56284	0.781420	−	0.624005i	$-0.214496\pi$
$997$	49.3472	1.56284	0.781420	+	0.624005i	$0.214496\pi$
$998$	20.0235	0.633834
$999$	−41.1360	−1.30149

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4021.2.a.c.1.3	✓	182

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4021.2.a.c.1.3	✓	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)

\(f(q)\)	\(=\)	\(q-2.71768 q^{2} -3.37653 q^{3} +5.38576 q^{4} +2.58064 q^{5} +9.17630 q^{6} -1.70858 q^{7} -9.20140 q^{8} +8.40093 q^{9} +O(q^{10})\)	\(q-2.71768 q^{2} -3.37653 q^{3} +5.38576 q^{4} +2.58064 q^{5} +9.17630 q^{6} -1.70858 q^{7} -9.20140 q^{8} +8.40093 q^{9} -7.01334 q^{10} +4.51204 q^{11} -18.1852 q^{12} +1.33947 q^{13} +4.64336 q^{14} -8.71359 q^{15} +14.2349 q^{16} -0.525444 q^{17} -22.8310 q^{18} +3.84183 q^{19} +13.8987 q^{20} +5.76906 q^{21} -12.2623 q^{22} +7.36191 q^{23} +31.0688 q^{24} +1.65969 q^{25} -3.64025 q^{26} -18.2364 q^{27} -9.20199 q^{28} -5.08534 q^{29} +23.6807 q^{30} +8.21364 q^{31} -20.2830 q^{32} -15.2350 q^{33} +1.42799 q^{34} -4.40922 q^{35} +45.2454 q^{36} +2.25571 q^{37} -10.4408 q^{38} -4.52276 q^{39} -23.7455 q^{40} -2.79813 q^{41} -15.6784 q^{42} +7.13436 q^{43} +24.3008 q^{44} +21.6798 q^{45} -20.0073 q^{46} +11.2880 q^{47} -48.0645 q^{48} -4.08076 q^{49} -4.51050 q^{50} +1.77417 q^{51} +7.21407 q^{52} +8.47271 q^{53} +49.5606 q^{54} +11.6439 q^{55} +15.7213 q^{56} -12.9720 q^{57} +13.8203 q^{58} +9.95371 q^{59} -46.9293 q^{60} +2.92618 q^{61} -22.3220 q^{62} -14.3536 q^{63} +26.6529 q^{64} +3.45669 q^{65} +41.4038 q^{66} +8.46626 q^{67} -2.82991 q^{68} -24.8577 q^{69} +11.9828 q^{70} -3.44293 q^{71} -77.3003 q^{72} -2.52074 q^{73} -6.13029 q^{74} -5.60399 q^{75} +20.6912 q^{76} -7.70917 q^{77} +12.2914 q^{78} +6.74936 q^{79} +36.7351 q^{80} +36.3728 q^{81} +7.60442 q^{82} +5.19503 q^{83} +31.0708 q^{84} -1.35598 q^{85} -19.3889 q^{86} +17.1708 q^{87} -41.5171 q^{88} +15.1552 q^{89} -58.9185 q^{90} -2.28859 q^{91} +39.6495 q^{92} -27.7336 q^{93} -30.6772 q^{94} +9.91437 q^{95} +68.4861 q^{96} +0.587293 q^{97} +11.0902 q^{98} +37.9053 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 182 q + 18 q^{2} + 28 q^{3} + 208 q^{4} + 22 q^{5} + 18 q^{6} + 14 q^{7} + 54 q^{8} + 238 q^{9}+O(q^{10}) \) 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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