LMFDB - Embedded newform 4021.2.a.c.1.8

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			1.8
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)

$f(q)$	$=$	$q-2.58741 q^{2} +0.104608 q^{3} +4.69469 q^{4} -1.37313 q^{5} -0.270664 q^{6} -0.569668 q^{7} -6.97226 q^{8} -2.98906 q^{9} +O(q^{10})$	\(q-2.58741 q^{2} +0.104608 q^{3} +4.69469 q^{4} -1.37313 q^{5} -0.270664 q^{6} -0.569668 q^{7} -6.97226 q^{8} -2.98906 q^{9} +3.55285 q^{10} +4.76169 q^{11} +0.491103 q^{12} -5.01662 q^{13} +1.47396 q^{14} -0.143640 q^{15} +8.65071 q^{16} -7.06927 q^{17} +7.73391 q^{18} -8.50728 q^{19} -6.44641 q^{20} -0.0595920 q^{21} -12.3204 q^{22} -6.68834 q^{23} -0.729355 q^{24} -3.11452 q^{25} +12.9800 q^{26} -0.626504 q^{27} -2.67441 q^{28} -6.93279 q^{29} +0.371657 q^{30} +5.99869 q^{31} -8.43842 q^{32} +0.498112 q^{33} +18.2911 q^{34} +0.782228 q^{35} -14.0327 q^{36} -3.79216 q^{37} +22.0118 q^{38} -0.524779 q^{39} +9.57381 q^{40} +2.31248 q^{41} +0.154189 q^{42} -10.8923 q^{43} +22.3547 q^{44} +4.10436 q^{45} +17.3055 q^{46} +9.96574 q^{47} +0.904935 q^{48} -6.67548 q^{49} +8.05853 q^{50} -0.739503 q^{51} -23.5514 q^{52} -4.45069 q^{53} +1.62102 q^{54} -6.53842 q^{55} +3.97187 q^{56} -0.889931 q^{57} +17.9380 q^{58} -1.41358 q^{59} -0.674347 q^{60} +13.0081 q^{61} -15.5211 q^{62} +1.70277 q^{63} +4.53221 q^{64} +6.88846 q^{65} -1.28882 q^{66} +6.26330 q^{67} -33.1880 q^{68} -0.699655 q^{69} -2.02394 q^{70} +0.941286 q^{71} +20.8405 q^{72} -1.34776 q^{73} +9.81188 q^{74} -0.325804 q^{75} -39.9390 q^{76} -2.71258 q^{77} +1.35782 q^{78} -8.22555 q^{79} -11.8785 q^{80} +8.90163 q^{81} -5.98334 q^{82} +1.46306 q^{83} -0.279766 q^{84} +9.70701 q^{85} +28.1828 q^{86} -0.725226 q^{87} -33.1997 q^{88} +7.94681 q^{89} -10.6197 q^{90} +2.85781 q^{91} -31.3997 q^{92} +0.627512 q^{93} -25.7854 q^{94} +11.6816 q^{95} -0.882727 q^{96} -7.95774 q^{97} +17.2722 q^{98} -14.2330 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.58741	−1.82957	−0.914787	−	0.403936i	$-0.867642\pi$
$2$	−2.58741	−1.82957	−0.914787	+	0.403936i	$0.867642\pi$
$3$	0.104608	0.0603956	0.0301978	−	0.999544i	$-0.490386\pi$
$3$	0.104608	0.0603956	0.0301978	+	0.999544i	$0.490386\pi$
$4$	4.69469	2.34734
$5$	−1.37313	−0.614082	−0.307041	−	0.951696i	$-0.599339\pi$
$5$	−1.37313	−0.614082	−0.307041	+	0.951696i	$0.599339\pi$
$6$	−0.270664	−0.110498
$7$	−0.569668	−0.215314	−0.107657	−	0.994188i	$-0.534335\pi$
$7$	−0.569668	−0.215314	−0.107657	+	0.994188i	$0.534335\pi$
$8$	−6.97226	−2.46507
$9$	−2.98906	−0.996352
$10$	3.55285	1.12351
$11$	4.76169	1.43570	0.717852	−	0.696196i	$-0.245125\pi$
$11$	4.76169	1.43570	0.717852	+	0.696196i	$0.245125\pi$
$12$	0.491103	0.141769
$13$	−5.01662	−1.39136	−0.695680	−	0.718352i	$-0.744897\pi$
$13$	−5.01662	−1.39136	−0.695680	+	0.718352i	$0.744897\pi$
$14$	1.47396	0.393934
$15$	−0.143640	−0.0370878
$16$	8.65071	2.16268
$17$	−7.06927	−1.71455	−0.857275	−	0.514860i	$-0.827844\pi$
$17$	−7.06927	−1.71455	−0.857275	+	0.514860i	$0.827844\pi$
$18$	7.73391	1.82290
$19$	−8.50728	−1.95170	−0.975852	−	0.218433i	$-0.929905\pi$
$19$	−8.50728	−1.95170	−0.975852	+	0.218433i	$0.929905\pi$
$20$	−6.44641	−1.44146
$21$	−0.0595920	−0.0130040
$22$	−12.3204	−2.62673
$23$	−6.68834	−1.39462	−0.697308	−	0.716772i	$-0.745619\pi$
$23$	−6.68834	−1.39462	−0.697308	+	0.716772i	$0.745619\pi$
$24$	−0.729355	−0.148879
$25$	−3.11452	−0.622904
$26$	12.9800	2.54560
$27$	−0.626504	−0.120571
$28$	−2.67441	−0.505417
$29$	−6.93279	−1.28739	−0.643693	−	0.765284i	$-0.722599\pi$
$29$	−6.93279	−1.28739	−0.643693	+	0.765284i	$0.722599\pi$
$30$	0.371657	0.0678549
$31$	5.99869	1.07740	0.538699	−	0.842499i	$-0.318916\pi$
$31$	5.99869	1.07740	0.538699	+	0.842499i	$0.318916\pi$
$32$	−8.43842	−1.49172
$33$	0.498112	0.0867102
$34$	18.2911	3.13690
$35$	0.782228	0.132221
$36$	−14.0327	−2.33878
$37$	−3.79216	−0.623428	−0.311714	−	0.950176i	$-0.600903\pi$
$37$	−3.79216	−0.623428	−0.311714	+	0.950176i	$0.600903\pi$
$38$	22.0118	3.57079
$39$	−0.524779	−0.0840319
$40$	9.57381	1.51375
$41$	2.31248	0.361149	0.180575	−	0.983561i	$-0.442204\pi$
$41$	2.31248	0.361149	0.180575	+	0.983561i	$0.442204\pi$
$42$	0.154189	0.0237918
$43$	−10.8923	−1.66106	−0.830528	−	0.556976i	$-0.811961\pi$
$43$	−10.8923	−1.66106	−0.830528	+	0.556976i	$0.811961\pi$
$44$	22.3547	3.37009
$45$	4.10436	0.611842
$46$	17.3055	2.55155
$47$	9.96574	1.45365	0.726826	−	0.686821i	$-0.240995\pi$
$47$	9.96574	1.45365	0.726826	+	0.686821i	$0.240995\pi$
$48$	0.904935	0.130616
$49$	−6.67548	−0.953640
$50$	8.05853	1.13965
$51$	−0.739503	−0.103551
$52$	−23.5514	−3.26600
$53$	−4.45069	−0.611349	−0.305675	−	0.952136i	$-0.598882\pi$
$53$	−4.45069	−0.611349	−0.305675	+	0.952136i	$0.598882\pi$
$54$	1.62102	0.220593
$55$	−6.53842	−0.881640
$56$	3.97187	0.530764
$57$	−0.889931	−0.117874
$58$	17.9380	2.35537
$59$	−1.41358	−0.184032	−0.0920161	−	0.995758i	$-0.529331\pi$
$59$	−1.41358	−0.184032	−0.0920161	+	0.995758i	$0.529331\pi$
$60$	−0.674347	−0.0870578
$61$	13.0081	1.66552	0.832761	−	0.553633i	$-0.186759\pi$
$61$	13.0081	1.66552	0.832761	+	0.553633i	$0.186759\pi$
$62$	−15.5211	−1.97118
$63$	1.70277	0.214529
$64$	4.53221	0.566526
$65$	6.88846	0.854408
$66$	−1.28882	−0.158643
$67$	6.26330	0.765183	0.382592	−	0.923918i	$-0.375032\pi$
$67$	6.26330	0.765183	0.382592	+	0.923918i	$0.375032\pi$
$68$	−33.1880	−4.02464
$69$	−0.699655	−0.0842286
$70$	−2.02394	−0.241908
$71$	0.941286	0.111710	0.0558551	−	0.998439i	$-0.482212\pi$
$71$	0.941286	0.111710	0.0558551	+	0.998439i	$0.482212\pi$
$72$	20.8405	2.45607
$73$	−1.34776	−0.157743	−0.0788716	−	0.996885i	$-0.525132\pi$
$73$	−1.34776	−0.157743	−0.0788716	+	0.996885i	$0.525132\pi$
$74$	9.81188	1.14061
$75$	−0.325804	−0.0376206
$76$	−39.9390	−4.58132
$77$	−2.71258	−0.309128
$78$	1.35782	0.153743
$79$	−8.22555	−0.925447	−0.462724	−	0.886503i	$-0.653128\pi$
$79$	−8.22555	−0.925447	−0.462724	+	0.886503i	$0.653128\pi$
$80$	−11.8785	−1.32806
$81$	8.90163	0.989070
$82$	−5.98334	−0.660750
$83$	1.46306	0.160592	0.0802958	−	0.996771i	$-0.474414\pi$
$83$	1.46306	0.160592	0.0802958	+	0.996771i	$0.474414\pi$
$84$	−0.279766	−0.0305249
$85$	9.70701	1.05287
$86$	28.1828	3.03903
$87$	−0.725226	−0.0777524
$88$	−33.1997	−3.53910
$89$	7.94681	0.842360	0.421180	−	0.906977i	$-0.361616\pi$
$89$	7.94681	0.842360	0.421180	+	0.906977i	$0.361616\pi$
$90$	−10.6197	−1.11941
$91$	2.85781	0.299580
$92$	−31.3997	−3.27364
$93$	0.627512	0.0650700
$94$	−25.7854	−2.65957
$95$	11.6816	1.19851
$96$	−0.882727	−0.0900930
$97$	−7.95774	−0.807986	−0.403993	−	0.914762i	$-0.632378\pi$
$97$	−7.95774	−0.807986	−0.403993	+	0.914762i	$0.632378\pi$
$98$	17.2722	1.74476
$99$	−14.2330	−1.43047
$100$	−14.6217	−1.46217
$101$	1.88706	0.187769	0.0938845	−	0.995583i	$-0.470072\pi$
$101$	1.88706	0.187769	0.0938845	+	0.995583i	$0.470072\pi$
$102$	1.91340	0.189455
$103$	−12.4212	−1.22390	−0.611950	−	0.790897i	$-0.709615\pi$
$103$	−12.4212	−1.22390	−0.611950	+	0.790897i	$0.709615\pi$
$104$	34.9771	3.42979
$105$	0.0818274	0.00798554
$106$	11.5158	1.11851
$107$	4.35806	0.421309	0.210655	−	0.977561i	$-0.432440\pi$
$107$	4.35806	0.421309	0.210655	+	0.977561i	$0.432440\pi$
$108$	−2.94124	−0.283021
$109$	11.3807	1.09007	0.545037	−	0.838412i	$-0.316516\pi$
$109$	11.3807	1.09007	0.545037	+	0.838412i	$0.316516\pi$
$110$	16.9176	1.61303
$111$	−0.396691	−0.0376523
$112$	−4.92804	−0.465656
$113$	18.9605	1.78366	0.891829	−	0.452373i	$-0.149423\pi$
$113$	18.9605	1.78366	0.891829	+	0.452373i	$0.149423\pi$
$114$	2.30262	0.215660
$115$	9.18395	0.856408
$116$	−32.5473	−3.02194
$117$	14.9950	1.38628
$118$	3.65750	0.336700
$119$	4.02714	0.369167
$120$	1.00150	0.0914239
$121$	11.6737	1.06125
$122$	−33.6574	−3.04720
$123$	0.241905	0.0218118
$124$	28.1620	2.52902
$125$	11.1423	0.996596
$126$	−4.40577	−0.392497
$127$	−15.7791	−1.40017	−0.700083	−	0.714062i	$-0.746854\pi$
$127$	−15.7791	−1.40017	−0.700083	+	0.714062i	$0.746854\pi$
$128$	5.15015	0.455213
$129$	−1.13942	−0.100320
$130$	−17.8233	−1.56320
$131$	−7.17756	−0.627106	−0.313553	−	0.949571i	$-0.601519\pi$
$131$	−7.17756	−0.627106	−0.313553	+	0.949571i	$0.601519\pi$
$132$	2.33848	0.203539
$133$	4.84633	0.420230
$134$	−16.2057	−1.39996
$135$	0.860271	0.0740403
$136$	49.2888	4.22648
$137$	4.55009	0.388740	0.194370	−	0.980928i	$-0.437734\pi$
$137$	4.55009	0.388740	0.194370	+	0.980928i	$0.437734\pi$
$138$	1.81029	0.154102
$139$	−9.99955	−0.848150	−0.424075	−	0.905627i	$-0.639401\pi$
$139$	−9.99955	−0.848150	−0.424075	+	0.905627i	$0.639401\pi$
$140$	3.67231	0.310367
$141$	1.04250	0.0877941
$142$	−2.43549	−0.204382
$143$	−23.8876	−1.99758
$144$	−25.8575	−2.15479
$145$	9.51961	0.790560
$146$	3.48720	0.288603
$147$	−0.698310	−0.0575956
$148$	−17.8030	−1.46340
$149$	−0.887822	−0.0727332	−0.0363666	−	0.999339i	$-0.511578\pi$
$149$	−0.887822	−0.0727332	−0.0363666	+	0.999339i	$0.511578\pi$
$150$	0.842988	0.0688297
$151$	13.1028	1.06629	0.533146	−	0.846023i	$-0.321010\pi$
$151$	13.1028	1.06629	0.533146	+	0.846023i	$0.321010\pi$
$152$	59.3149	4.81108
$153$	21.1304	1.70830
$154$	7.01857	0.565572
$155$	−8.23698	−0.661610
$156$	−2.46367	−0.197252
$157$	18.5182	1.47792	0.738958	−	0.673752i	$-0.235318\pi$
$157$	18.5182	1.47792	0.738958	+	0.673752i	$0.235318\pi$
$158$	21.2829	1.69317
$159$	−0.465578	−0.0369228
$160$	11.5870	0.916035
$161$	3.81013	0.300281
$162$	−23.0322	−1.80958
$163$	−12.8832	−1.00909	−0.504544	−	0.863386i	$-0.668339\pi$
$163$	−12.8832	−1.00909	−0.504544	+	0.863386i	$0.668339\pi$
$164$	10.8564	0.847742
$165$	−0.683972	−0.0532471
$166$	−3.78553	−0.293814
$167$	−12.0973	−0.936116	−0.468058	−	0.883698i	$-0.655046\pi$
$167$	−12.0973	−0.936116	−0.468058	+	0.883698i	$0.655046\pi$
$168$	0.415490	0.0320558
$169$	12.1664	0.935881
$170$	−25.1160	−1.92631
$171$	25.4287	1.94458
$172$	−51.1358	−3.89907
$173$	22.8685	1.73866	0.869330	−	0.494232i	$-0.164551\pi$
$173$	22.8685	1.73866	0.869330	+	0.494232i	$0.164551\pi$
$174$	1.87646	0.142254
$175$	1.77424	0.134120
$176$	41.1920	3.10497
$177$	−0.147872	−0.0111147
$178$	−20.5616	−1.54116
$179$	22.8741	1.70969	0.854844	−	0.518885i	$-0.173653\pi$
$179$	22.8741	1.70969	0.854844	+	0.518885i	$0.173653\pi$
$180$	19.2687	1.43620
$181$	−18.5883	−1.38166	−0.690828	−	0.723019i	$-0.742754\pi$
$181$	−18.5883	−1.38166	−0.690828	+	0.723019i	$0.742754\pi$
$182$	−7.39432	−0.548103
$183$	1.36076	0.100590
$184$	46.6328	3.43782
$185$	5.20713	0.382836
$186$	−1.62363	−0.119050
$187$	−33.6617	−2.46159
$188$	46.7860	3.41222
$189$	0.356900	0.0259606
$190$	−30.2251	−2.19276
$191$	−7.84347	−0.567533	−0.283767	−	0.958893i	$-0.591584\pi$
$191$	−7.84347	−0.567533	−0.283767	+	0.958893i	$0.591584\pi$
$192$	0.474106	0.0342157
$193$	−17.4681	−1.25738	−0.628690	−	0.777656i	$-0.716408\pi$
$193$	−17.4681	−1.25738	−0.628690	+	0.777656i	$0.716408\pi$
$194$	20.5899	1.47827
$195$	0.720589	0.0516025
$196$	−31.3393	−2.23852
$197$	−26.0586	−1.85660	−0.928300	−	0.371831i	$-0.878730\pi$
$197$	−26.0586	−1.85660	−0.928300	+	0.371831i	$0.878730\pi$
$198$	36.8265	2.61715
$199$	−24.7049	−1.75128	−0.875642	−	0.482961i	$-0.839561\pi$
$199$	−24.7049	−1.75128	−0.875642	+	0.482961i	$0.839561\pi$
$200$	21.7152	1.53550
$201$	0.655192	0.0462137
$202$	−4.88258	−0.343537
$203$	3.94939	0.277193
$204$	−3.47174	−0.243070
$205$	−3.17534	−0.221775
$206$	32.1388	2.23922
$207$	19.9918	1.38953
$208$	−43.3973	−3.00906
$209$	−40.5090	−2.80207
$210$	−0.211721	−0.0146101
$211$	−1.35734	−0.0934430	−0.0467215	−	0.998908i	$-0.514877\pi$
$211$	−1.35734	−0.0934430	−0.0467215	+	0.998908i	$0.514877\pi$
$212$	−20.8946	−1.43505
$213$	0.0984662	0.00674679
$214$	−11.2761	−0.770816
$215$	14.9565	1.02002
$216$	4.36815	0.297215
$217$	−3.41726	−0.231979
$218$	−29.4466	−1.99437
$219$	−0.140986	−0.00952698
$220$	−30.6958	−2.06951
$221$	35.4638	2.38555
$222$	1.02640	0.0688876
$223$	26.0389	1.74369	0.871846	−	0.489781i	$-0.162923\pi$
$223$	26.0389	1.74369	0.871846	+	0.489781i	$0.162923\pi$
$224$	4.80710	0.321188
$225$	9.30947	0.620631
$226$	−49.0587	−3.26333
$227$	−14.1426	−0.938675	−0.469337	−	0.883019i	$-0.655507\pi$
$227$	−14.1426	−0.938675	−0.469337	+	0.883019i	$0.655507\pi$
$228$	−4.17795	−0.276691
$229$	−2.44746	−0.161732	−0.0808662	−	0.996725i	$-0.525769\pi$
$229$	−2.44746	−0.161732	−0.0808662	+	0.996725i	$0.525769\pi$
$230$	−23.7626	−1.56686
$231$	−0.283759	−0.0186699
$232$	48.3372	3.17349
$233$	−22.6772	−1.48563	−0.742816	−	0.669496i	$-0.766510\pi$
$233$	−22.6772	−1.48563	−0.742816	+	0.669496i	$0.766510\pi$
$234$	−38.7981	−2.53631
$235$	−13.6842	−0.892662
$236$	−6.63630	−0.431987
$237$	−0.860460	−0.0558929
$238$	−10.4199	−0.675419
$239$	−6.51420	−0.421369	−0.210684	−	0.977554i	$-0.567569\pi$
$239$	−6.51420	−0.421369	−0.210684	+	0.977554i	$0.567569\pi$
$240$	−1.24259	−0.0802090
$241$	−22.8397	−1.47124	−0.735618	−	0.677396i	$-0.763108\pi$
$241$	−22.8397	−1.47124	−0.735618	+	0.677396i	$0.763108\pi$
$242$	−30.2047	−1.94163
$243$	2.81070	0.180306
$244$	61.0691	3.90955
$245$	9.16629	0.585613
$246$	−0.625907	−0.0399063
$247$	42.6778	2.71552
$248$	−41.8244	−2.65585
$249$	0.153048	0.00969902
$250$	−28.8296	−1.82335
$251$	9.05701	0.571673	0.285837	−	0.958278i	$-0.407729\pi$
$251$	9.05701	0.571673	0.285837	+	0.958278i	$0.407729\pi$
$252$	7.99398	0.503573
$253$	−31.8478	−2.00225
$254$	40.8269	2.56171
$255$	1.01543	0.0635889
$256$	−22.3900	−1.39937
$257$	−24.9520	−1.55646	−0.778231	−	0.627978i	$-0.783883\pi$
$257$	−24.9520	−1.55646	−0.778231	+	0.627978i	$0.783883\pi$
$258$	2.94815	0.183544
$259$	2.16028	0.134233
$260$	32.3392	2.00559
$261$	20.7225	1.28269
$262$	18.5713	1.14734
$263$	12.2281	0.754018	0.377009	−	0.926210i	$-0.376953\pi$
$263$	12.2281	0.754018	0.377009	+	0.926210i	$0.376953\pi$
$264$	−3.47296	−0.213746
$265$	6.11137	0.375418
$266$	−12.5394	−0.768842
$267$	0.831301	0.0508748
$268$	29.4042	1.79615
$269$	−31.6467	−1.92953	−0.964766	−	0.263111i	$-0.915251\pi$
$269$	−31.6467	−1.92953	−0.964766	+	0.263111i	$0.915251\pi$
$270$	−2.22587	−0.135462
$271$	−3.27230	−0.198778	−0.0993890	−	0.995049i	$-0.531689\pi$
$271$	−3.27230	−0.198778	−0.0993890	+	0.995049i	$0.531689\pi$
$272$	−61.1542	−3.70802
$273$	0.298950	0.0180933
$274$	−11.7729	−0.711230
$275$	−14.8304	−0.894305
$276$	−3.28466	−0.197713
$277$	−5.00791	−0.300896	−0.150448	−	0.988618i	$-0.548072\pi$
$277$	−5.00791	−0.300896	−0.150448	+	0.988618i	$0.548072\pi$
$278$	25.8729	1.55175
$279$	−17.9304	−1.07347
$280$	−5.45389	−0.325933
$281$	24.5710	1.46578	0.732891	−	0.680346i	$-0.238171\pi$
$281$	24.5710	1.46578	0.732891	+	0.680346i	$0.238171\pi$
$282$	−2.69737	−0.160626
$283$	12.1607	0.722877	0.361439	−	0.932396i	$-0.382286\pi$
$283$	12.1607	0.722877	0.361439	+	0.932396i	$0.382286\pi$
$284$	4.41904	0.262222
$285$	1.22199	0.0723844
$286$	61.8070	3.65472
$287$	−1.31735	−0.0777606
$288$	25.2229	1.48627
$289$	32.9745	1.93968
$290$	−24.6311	−1.44639
$291$	−0.832445	−0.0487988
$292$	−6.32730	−0.370277
$293$	4.43349	0.259007	0.129504	−	0.991579i	$-0.458662\pi$
$293$	4.43349	0.259007	0.129504	+	0.991579i	$0.458662\pi$
$294$	1.80681	0.105375
$295$	1.94102	0.113011
$296$	26.4399	1.53679
$297$	−2.98322	−0.173104
$298$	2.29716	0.133071
$299$	33.5528	1.94041
$300$	−1.52955	−0.0883085
$301$	6.20498	0.357649
$302$	−33.9023	−1.95086
$303$	0.197401	0.0113404
$304$	−73.5940	−4.22091
$305$	−17.8618	−1.02277
$306$	−54.6731	−3.12545
$307$	−18.5629	−1.05944	−0.529720	−	0.848173i	$-0.677703\pi$
$307$	−18.5629	−1.05944	−0.529720	+	0.848173i	$0.677703\pi$
$308$	−12.7347	−0.725629
$309$	−1.29936	−0.0739181
$310$	21.3124	1.21046
$311$	−8.22186	−0.466219	−0.233109	−	0.972451i	$-0.574890\pi$
$311$	−8.22186	−0.466219	−0.233109	+	0.972451i	$0.574890\pi$
$312$	3.65890	0.207144
$313$	18.0405	1.01971	0.509855	−	0.860260i	$-0.329699\pi$
$313$	18.0405	1.01971	0.509855	+	0.860260i	$0.329699\pi$
$314$	−47.9143	−2.70396
$315$	−2.33812	−0.131738
$316$	−38.6164	−2.17234
$317$	9.47562	0.532204	0.266102	−	0.963945i	$-0.414264\pi$
$317$	9.47562	0.532204	0.266102	+	0.963945i	$0.414264\pi$
$318$	1.20464	0.0675530
$319$	−33.0118	−1.84831
$320$	−6.22331	−0.347894
$321$	0.455888	0.0254452
$322$	−9.85838	−0.549386
$323$	60.1402	3.34629
$324$	41.7904	2.32169
$325$	15.6243	0.866683
$326$	33.3340	1.84620
$327$	1.19052	0.0658356
$328$	−16.1232	−0.890257
$329$	−5.67717	−0.312992
$330$	1.76971	0.0974196
$331$	2.47430	0.136000	0.0679999	−	0.997685i	$-0.478338\pi$
$331$	2.47430	0.136000	0.0679999	+	0.997685i	$0.478338\pi$
$332$	6.86860	0.376964
$333$	11.3350	0.621154
$334$	31.3006	1.71269
$335$	−8.60031	−0.469885
$336$	−0.515513	−0.0281235
$337$	−13.9520	−0.760015	−0.380007	−	0.924984i	$-0.624079\pi$
$337$	−13.9520	−0.760015	−0.380007	+	0.924984i	$0.624079\pi$
$338$	−31.4796	−1.71226
$339$	1.98343	0.107725
$340$	45.5714	2.47146
$341$	28.5639	1.54682
$342$	−65.7946	−3.55776
$343$	7.79049	0.420647
$344$	75.9438	4.09461
$345$	0.960716	0.0517232
$346$	−59.1702	−3.18101
$347$	−2.94833	−0.158275	−0.0791374	−	0.996864i	$-0.525217\pi$
$347$	−2.94833	−0.158275	−0.0791374	+	0.996864i	$0.525217\pi$
$348$	−3.40471	−0.182512
$349$	2.94400	0.157589	0.0787943	−	0.996891i	$-0.474893\pi$
$349$	2.94400	0.157589	0.0787943	+	0.996891i	$0.474893\pi$
$350$	−4.59069	−0.245383
$351$	3.14293	0.167757
$352$	−40.1811	−2.14166
$353$	4.24341	0.225854	0.112927	−	0.993603i	$-0.463977\pi$
$353$	4.24341	0.225854	0.112927	+	0.993603i	$0.463977\pi$
$354$	0.382605	0.0203352
$355$	−1.29251	−0.0685991
$356$	37.3078	1.97731
$357$	0.421271	0.0222960
$358$	−59.1846	−3.12800
$359$	−4.73805	−0.250065	−0.125032	−	0.992153i	$-0.539904\pi$
$359$	−4.73805	−0.250065	−0.125032	+	0.992153i	$0.539904\pi$
$360$	−28.6167	−1.50823
$361$	53.3738	2.80915
$362$	48.0955	2.52784
$363$	1.22117	0.0640946
$364$	13.4165	0.703216
$365$	1.85064	0.0968672
$366$	−3.52084	−0.184037
$367$	−13.1836	−0.688177	−0.344089	−	0.938937i	$-0.611812\pi$
$367$	−13.1836	−0.688177	−0.344089	+	0.938937i	$0.611812\pi$
$368$	−57.8589	−3.01610
$369$	−6.91215	−0.359832
$370$	−13.4730	−0.700427
$371$	2.53542	0.131632
$372$	2.94597	0.152742
$373$	9.16914	0.474760	0.237380	−	0.971417i	$-0.423711\pi$
$373$	9.16914	0.474760	0.237380	+	0.971417i	$0.423711\pi$
$374$	87.0965	4.50365
$375$	1.16557	0.0601899
$376$	−69.4837	−3.58335
$377$	34.7791	1.79122
$378$	−0.923445	−0.0474969
$379$	−1.42916	−0.0734113	−0.0367056	−	0.999326i	$-0.511686\pi$
$379$	−1.42916	−0.0734113	−0.0367056	+	0.999326i	$0.511686\pi$
$380$	54.8414	2.81330
$381$	−1.65062	−0.0845638
$382$	20.2943	1.03834
$383$	22.5932	1.15446	0.577228	−	0.816583i	$-0.304134\pi$
$383$	22.5932	1.15446	0.577228	+	0.816583i	$0.304134\pi$
$384$	0.538747	0.0274928
$385$	3.72473	0.189830
$386$	45.1971	2.30047
$387$	32.5576	1.65500
$388$	−37.3591	−1.89662
$389$	0.348474	0.0176683	0.00883416	−	0.999961i	$-0.497188\pi$
$389$	0.348474	0.0176683	0.00883416	+	0.999961i	$0.497188\pi$
$390$	−1.86446	−0.0944106
$391$	47.2817	2.39114
$392$	46.5432	2.35078
$393$	−0.750831	−0.0378744
$394$	67.4243	3.39679
$395$	11.2947	0.568300
$396$	−66.8193	−3.35780
$397$	−24.9502	−1.25222	−0.626109	−	0.779736i	$-0.715353\pi$
$397$	−24.9502	−1.25222	−0.626109	+	0.779736i	$0.715353\pi$
$398$	63.9217	3.20411
$399$	0.506965	0.0253800
$400$	−26.9428	−1.34714
$401$	−8.94032	−0.446458	−0.223229	−	0.974766i	$-0.571660\pi$
$401$	−8.94032	−0.446458	−0.223229	+	0.974766i	$0.571660\pi$
$402$	−1.69525	−0.0845514
$403$	−30.0931	−1.49905
$404$	8.85913	0.440758
$405$	−12.2231	−0.607370
$406$	−10.2187	−0.507145
$407$	−18.0571	−0.895058
$408$	5.15601	0.255260
$409$	10.8704	0.537505	0.268753	−	0.963209i	$-0.413389\pi$
$409$	10.8704	0.537505	0.268753	+	0.963209i	$0.413389\pi$
$410$	8.21590	0.405754
$411$	0.475977	0.0234782
$412$	−58.3138	−2.87291
$413$	0.805270	0.0396248
$414$	−51.7270	−2.54225
$415$	−2.00897	−0.0986164
$416$	42.3323	2.07551
$417$	−1.04603	−0.0512245
$418$	104.813	5.12659
$419$	1.06572	0.0520638	0.0260319	−	0.999661i	$-0.491713\pi$
$419$	1.06572	0.0520638	0.0260319	+	0.999661i	$0.491713\pi$
$420$	0.384154	0.0187448
$421$	−17.6579	−0.860594	−0.430297	−	0.902687i	$-0.641591\pi$
$421$	−17.6579	−0.860594	−0.430297	+	0.902687i	$0.641591\pi$
$422$	3.51199	0.170961
$423$	−29.7882	−1.44835
$424$	31.0313	1.50702
$425$	22.0174	1.06800
$426$	−0.254772	−0.0123438
$427$	−7.41032	−0.358611
$428$	20.4597	0.988957
$429$	−2.49884	−0.120645
$430$	−38.6986	−1.86621
$431$	−1.28802	−0.0620420	−0.0310210	−	0.999519i	$-0.509876\pi$
$431$	−1.28802	−0.0620420	−0.0310210	+	0.999519i	$0.509876\pi$
$432$	−5.41971	−0.260756
$433$	0.290131	0.0139428	0.00697140	−	0.999976i	$-0.497781\pi$
$433$	0.290131	0.0139428	0.00697140	+	0.999976i	$0.497781\pi$
$434$	8.84186	0.424423
$435$	0.995829	0.0477463
$436$	53.4289	2.55878
$437$	56.8996	2.72188
$438$	0.364790	0.0174303
$439$	−23.6632	−1.12938	−0.564692	−	0.825302i	$-0.691005\pi$
$439$	−23.6632	−1.12938	−0.564692	+	0.825302i	$0.691005\pi$
$440$	45.5875	2.17330
$441$	19.9534	0.950161
$442$	−91.7594	−4.36455
$443$	1.74771	0.0830364	0.0415182	−	0.999138i	$-0.486781\pi$
$443$	1.74771	0.0830364	0.0415182	+	0.999138i	$0.486781\pi$
$444$	−1.86234	−0.0883828
$445$	−10.9120	−0.517278
$446$	−67.3732	−3.19021
$447$	−0.0928734	−0.00439276
$448$	−2.58186	−0.121981
$449$	33.7394	1.59226	0.796130	−	0.605126i	$-0.206877\pi$
$449$	33.7394	1.59226	0.796130	+	0.605126i	$0.206877\pi$
$450$	−24.0874	−1.13549
$451$	11.0113	0.518504
$452$	89.0138	4.18686
$453$	1.37066	0.0643993
$454$	36.5926	1.71738
$455$	−3.92414	−0.183966
$456$	6.20483	0.290568
$457$	30.9122	1.44601	0.723006	−	0.690841i	$-0.242760\pi$
$457$	30.9122	1.44601	0.723006	+	0.690841i	$0.242760\pi$
$458$	6.33257	0.295902
$459$	4.42893	0.206725
$460$	43.1158	2.01028
$461$	3.92944	0.183012	0.0915061	−	0.995805i	$-0.470832\pi$
$461$	3.92944	0.183012	0.0915061	+	0.995805i	$0.470832\pi$
$462$	0.734200	0.0341581
$463$	−5.70476	−0.265123	−0.132561	−	0.991175i	$-0.542320\pi$
$463$	−5.70476	−0.265123	−0.132561	+	0.991175i	$0.542320\pi$
$464$	−59.9735	−2.78420
$465$	−0.861655	−0.0399583
$466$	58.6752	2.71807
$467$	−26.8212	−1.24114	−0.620569	−	0.784152i	$-0.713098\pi$
$467$	−26.8212	−1.24114	−0.620569	+	0.784152i	$0.713098\pi$
$468$	70.3966	3.25408
$469$	−3.56800	−0.164755
$470$	35.4067	1.63319
$471$	1.93716	0.0892596
$472$	9.85583	0.453651
$473$	−51.8657	−2.38479
$474$	2.22636	0.102260
$475$	26.4961	1.21572
$476$	18.9061	0.866562
$477$	13.3034	0.609119
$478$	16.8549	0.770925
$479$	33.2595	1.51967	0.759833	−	0.650119i	$-0.225281\pi$
$479$	33.2595	1.51967	0.759833	+	0.650119i	$0.225281\pi$
$480$	1.21210	0.0553245
$481$	19.0238	0.867412
$482$	59.0958	2.69174
$483$	0.398571	0.0181356
$484$	54.8044	2.49111
$485$	10.9270	0.496170
$486$	−7.27242	−0.329884
$487$	−6.72869	−0.304906	−0.152453	−	0.988311i	$-0.548717\pi$
$487$	−6.72869	−0.304906	−0.152453	+	0.988311i	$0.548717\pi$
$488$	−90.6961	−4.10562
$489$	−1.34768	−0.0609444
$490$	−23.7169	−1.07142
$491$	13.8132	0.623381	0.311691	−	0.950184i	$-0.399105\pi$
$491$	13.8132	0.623381	0.311691	+	0.950184i	$0.399105\pi$
$492$	1.13567	0.0511998
$493$	49.0097	2.20729
$494$	−110.425	−4.96825
$495$	19.5437	0.878424
$496$	51.8930	2.33006
$497$	−0.536221	−0.0240528
$498$	−0.395998	−0.0177451
$499$	−21.4283	−0.959263	−0.479632	−	0.877470i	$-0.659230\pi$
$499$	−21.4283	−0.959263	−0.479632	+	0.877470i	$0.659230\pi$
$500$	52.3095	2.33935
$501$	−1.26547	−0.0565372
$502$	−23.4342	−1.04592
$503$	−1.94356	−0.0866592	−0.0433296	−	0.999061i	$-0.513797\pi$
$503$	−1.94356	−0.0866592	−0.0433296	+	0.999061i	$0.513797\pi$
$504$	−11.8722	−0.528828
$505$	−2.59117	−0.115306
$506$	82.4033	3.66327
$507$	1.27271	0.0565230
$508$	−74.0778	−3.28667
$509$	29.1575	1.29238	0.646192	−	0.763175i	$-0.276360\pi$
$509$	29.1575	1.29238	0.646192	+	0.763175i	$0.276360\pi$
$510$	−2.62734	−0.116341
$511$	0.767775	0.0339644
$512$	47.6317	2.10504
$513$	5.32985	0.235319
$514$	64.5610	2.84766
$515$	17.0559	0.751574
$516$	−5.34923	−0.235487
$517$	47.4538	2.08701
$518$	−5.58952	−0.245589
$519$	2.39223	0.105007
$520$	−48.0281	−2.10617
$521$	−34.0634	−1.49234	−0.746172	−	0.665753i	$-0.768111\pi$
$521$	−34.0634	−1.49234	−0.746172	+	0.665753i	$0.768111\pi$
$522$	−53.6176	−2.34678
$523$	−17.7992	−0.778305	−0.389153	−	0.921173i	$-0.627232\pi$
$523$	−17.7992	−0.778305	−0.389153	+	0.921173i	$0.627232\pi$
$524$	−33.6964	−1.47203
$525$	0.185600	0.00810026
$526$	−31.6392	−1.37953
$527$	−42.4064	−1.84725
$528$	4.30902	0.187526
$529$	21.7339	0.944951
$530$	−15.8126	−0.686856
$531$	4.22526	0.183361
$532$	22.7520	0.986424
$533$	−11.6008	−0.502489
$534$	−2.15092	−0.0930793
$535$	−5.98417	−0.258718
$536$	−43.6693	−1.88623
$537$	2.39281	0.103258
$538$	81.8829	3.53022
$539$	−31.7866	−1.36914
$540$	4.03870	0.173798
$541$	−35.8978	−1.54337	−0.771683	−	0.636007i	$-0.780585\pi$
$541$	−35.8978	−1.54337	−0.771683	+	0.636007i	$0.780585\pi$
$542$	8.46678	0.363679
$543$	−1.94449	−0.0834459
$544$	59.6534	2.55762
$545$	−15.6272	−0.669395
$546$	−0.773506	−0.0331030
$547$	10.3406	0.442131	0.221065	−	0.975259i	$-0.429047\pi$
$547$	10.3406	0.442131	0.221065	+	0.975259i	$0.429047\pi$
$548$	21.3613	0.912507
$549$	−38.8821	−1.65945
$550$	38.3722	1.63620
$551$	58.9792	2.51260
$552$	4.87817	0.207629
$553$	4.68584	0.199262
$554$	12.9575	0.550512
$555$	0.544708	0.0231216
$556$	−46.9447	−1.99090
$557$	16.6214	0.704270	0.352135	−	0.935949i	$-0.385456\pi$
$557$	16.6214	0.704270	0.352135	+	0.935949i	$0.385456\pi$
$558$	46.3934	1.96399
$559$	54.6424	2.31113
$560$	6.76683	0.285951
$561$	−3.52129	−0.148669
$562$	−63.5752	−2.68176
$563$	2.81317	0.118561	0.0592805	−	0.998241i	$-0.481119\pi$
$563$	2.81317	0.118561	0.0592805	+	0.998241i	$0.481119\pi$
$564$	4.89420	0.206083
$565$	−26.0353	−1.09531
$566$	−31.4646	−1.32256
$567$	−5.07098	−0.212961
$568$	−6.56289	−0.275373
$569$	−21.2123	−0.889266	−0.444633	−	0.895713i	$-0.646666\pi$
$569$	−21.2123	−0.889266	−0.444633	+	0.895713i	$0.646666\pi$
$570$	−3.16179	−0.132433
$571$	3.75957	0.157333	0.0786666	−	0.996901i	$-0.474934\pi$
$571$	3.75957	0.157333	0.0786666	+	0.996901i	$0.474934\pi$
$572$	−112.145	−4.68901
$573$	−0.820491	−0.0342765
$574$	3.40852	0.142269
$575$	20.8310	0.868711
$576$	−13.5470	−0.564460
$577$	−4.42894	−0.184379	−0.0921896	−	0.995741i	$-0.529387\pi$
$577$	−4.42894	−0.184379	−0.0921896	+	0.995741i	$0.529387\pi$
$578$	−85.3186	−3.54879
$579$	−1.82730	−0.0759401
$580$	44.6916	1.85572
$581$	−0.833458	−0.0345777
$582$	2.15388	0.0892810
$583$	−21.1928	−0.877716
$584$	9.39691	0.388847
$585$	−20.5900	−0.851292
$586$	−11.4712	−0.473873
$587$	−9.42852	−0.389157	−0.194578	−	0.980887i	$-0.562334\pi$
$587$	−9.42852	−0.389157	−0.194578	+	0.980887i	$0.562334\pi$
$588$	−3.27834	−0.135197
$589$	−51.0326	−2.10276
$590$	−5.02222	−0.206762
$591$	−2.72595	−0.112130
$592$	−32.8049	−1.34827
$593$	−31.0909	−1.27675	−0.638375	−	0.769726i	$-0.720393\pi$
$593$	−31.0909	−1.27675	−0.638375	+	0.769726i	$0.720393\pi$
$594$	7.71881	0.316707
$595$	−5.52978	−0.226699
$596$	−4.16805	−0.170730
$597$	−2.58433	−0.105770
$598$	−86.8149	−3.55013
$599$	−17.2888	−0.706402	−0.353201	−	0.935547i	$-0.614907\pi$
$599$	−17.2888	−0.706402	−0.353201	+	0.935547i	$0.614907\pi$
$600$	2.27159	0.0927373
$601$	−33.6100	−1.37098	−0.685490	−	0.728082i	$-0.740412\pi$
$601$	−33.6100	−1.37098	−0.685490	+	0.728082i	$0.740412\pi$
$602$	−16.0548	−0.654346
$603$	−18.7213	−0.762392
$604$	61.5136	2.50295
$605$	−16.0295	−0.651692
$606$	−0.510758	−0.0207481
$607$	11.5231	0.467707	0.233854	−	0.972272i	$-0.424866\pi$
$607$	11.5231	0.467707	0.233854	+	0.972272i	$0.424866\pi$
$608$	71.7880	2.91139
$609$	0.413138	0.0167412
$610$	46.2159	1.87123
$611$	−49.9943	−2.02255
$612$	99.2008	4.00996
$613$	18.6860	0.754722	0.377361	−	0.926066i	$-0.376832\pi$
$613$	18.6860	0.754722	0.377361	+	0.926066i	$0.376832\pi$
$614$	48.0298	1.93832
$615$	−0.332166	−0.0133942
$616$	18.9128	0.762020
$617$	15.6364	0.629497	0.314748	−	0.949175i	$-0.398080\pi$
$617$	15.6364	0.629497	0.314748	+	0.949175i	$0.398080\pi$
$618$	3.36198	0.135239
$619$	35.2310	1.41605	0.708027	−	0.706185i	$-0.249586\pi$
$619$	35.2310	1.41605	0.708027	+	0.706185i	$0.249586\pi$
$620$	−38.6700	−1.55303
$621$	4.19027	0.168150
$622$	21.2733	0.852982
$623$	−4.52704	−0.181372
$624$	−4.53971	−0.181734
$625$	0.272808	0.0109123
$626$	−46.6782	−1.86564
$627$	−4.23758	−0.169233
$628$	86.9373	3.46918
$629$	26.8078	1.06890
$630$	6.04968	0.241025
$631$	−7.03709	−0.280142	−0.140071	−	0.990141i	$-0.544733\pi$
$631$	−7.03709	−0.280142	−0.140071	+	0.990141i	$0.544733\pi$
$632$	57.3507	2.28129
$633$	−0.141989	−0.00564354
$634$	−24.5173	−0.973707
$635$	21.6667	0.859816
$636$	−2.18574	−0.0866704
$637$	33.4883	1.32686
$638$	85.4150	3.38161
$639$	−2.81356	−0.111303
$640$	−7.07181	−0.279538
$641$	−26.7135	−1.05512	−0.527560	−	0.849518i	$-0.676893\pi$
$641$	−26.7135	−1.05512	−0.527560	+	0.849518i	$0.676893\pi$
$642$	−1.17957	−0.0465539
$643$	5.04810	0.199078	0.0995388	−	0.995034i	$-0.468263\pi$
$643$	5.04810	0.199078	0.0995388	+	0.995034i	$0.468263\pi$
$644$	17.8874	0.704862
$645$	1.56457	0.0616050
$646$	−155.607	−6.12229
$647$	1.15190	0.0452861	0.0226430	−	0.999744i	$-0.492792\pi$
$647$	1.15190	0.0452861	0.0226430	+	0.999744i	$0.492792\pi$
$648$	−62.0645	−2.43812
$649$	−6.73102	−0.264216
$650$	−40.4266	−1.58566
$651$	−0.357474	−0.0140105
$652$	−60.4825	−2.36868
$653$	4.09008	0.160057	0.0800285	−	0.996793i	$-0.474499\pi$
$653$	4.09008	0.160057	0.0800285	+	0.996793i	$0.474499\pi$
$654$	−3.08035	−0.120451
$655$	9.85571	0.385094
$656$	20.0046	0.781050
$657$	4.02852	0.157168
$658$	14.6892	0.572643
$659$	−0.571948	−0.0222799	−0.0111400	−	0.999938i	$-0.503546\pi$
$659$	−0.571948	−0.0222799	−0.0111400	+	0.999938i	$0.503546\pi$
$660$	−3.21103	−0.124989
$661$	21.8060	0.848157	0.424078	−	0.905625i	$-0.360598\pi$
$661$	21.8060	0.848157	0.424078	+	0.905625i	$0.360598\pi$
$662$	−6.40203	−0.248822
$663$	3.70980	0.144077
$664$	−10.2008	−0.395869
$665$	−6.65463	−0.258056
$666$	−29.3283	−1.13645
$667$	46.3688	1.79541
$668$	−56.7930	−2.19739
$669$	2.72388	0.105311
$670$	22.2525	0.859690
$671$	61.9407	2.39120
$672$	0.502862	0.0193983
$673$	9.23239	0.355883	0.177941	−	0.984041i	$-0.443056\pi$
$673$	9.23239	0.355883	0.177941	+	0.984041i	$0.443056\pi$
$674$	36.0996	1.39050
$675$	1.95126	0.0751040
$676$	57.1177	2.19683
$677$	40.6641	1.56285	0.781425	−	0.623999i	$-0.214493\pi$
$677$	40.6641	1.56285	0.781425	+	0.623999i	$0.214493\pi$
$678$	−5.13194	−0.197091
$679$	4.53327	0.173971
$680$	−67.6798	−2.59540
$681$	−1.47943	−0.0566918
$682$	−73.9066	−2.83003
$683$	−14.2865	−0.546659	−0.273329	−	0.961921i	$-0.588125\pi$
$683$	−14.2865	−0.546659	−0.273329	+	0.961921i	$0.588125\pi$
$684$	119.380	4.56461
$685$	−6.24786	−0.238718
$686$	−20.1572	−0.769605
$687$	−0.256024	−0.00976792
$688$	−94.2259	−3.59233
$689$	22.3274	0.850606
$690$	−2.48577	−0.0946315
$691$	−1.32278	−0.0503207	−0.0251604	−	0.999683i	$-0.508010\pi$
$691$	−1.32278	−0.0503207	−0.0251604	+	0.999683i	$0.508010\pi$
$692$	107.360	4.08123
$693$	8.10807	0.308000
$694$	7.62854	0.289575
$695$	13.7307	0.520834
$696$	5.05646	0.191665
$697$	−16.3476	−0.619208
$698$	−7.61733	−0.288320
$699$	−2.37222	−0.0897256
$700$	8.32951	0.314826
$701$	−26.3196	−0.994077	−0.497038	−	0.867729i	$-0.665579\pi$
$701$	−26.3196	−0.994077	−0.497038	+	0.867729i	$0.665579\pi$
$702$	−8.13205	−0.306925
$703$	32.2610	1.21675
$704$	21.5810	0.813364
$705$	−1.43148	−0.0539128
$706$	−10.9794	−0.413217
$707$	−1.07500	−0.0404294
$708$	−0.694212	−0.0260901
$709$	37.1821	1.39640	0.698201	−	0.715902i	$-0.253984\pi$
$709$	37.1821	1.39640	0.698201	+	0.715902i	$0.253984\pi$
$710$	3.34424	0.125507
$711$	24.5866	0.922071
$712$	−55.4072	−2.07647
$713$	−40.1213	−1.50255
$714$	−1.09000	−0.0407923
$715$	32.8007	1.22668
$716$	107.387	4.01322
$717$	−0.681439	−0.0254488
$718$	12.2593	0.457512
$719$	33.2040	1.23830	0.619150	−	0.785273i	$-0.287477\pi$
$719$	33.2040	1.23830	0.619150	+	0.785273i	$0.287477\pi$
$720$	35.5056	1.32322
$721$	7.07598	0.263523
$722$	−138.100	−5.13955
$723$	−2.38922	−0.0888562
$724$	−87.2662	−3.24322
$725$	21.5923	0.801917
$726$	−3.15966	−0.117266
$727$	16.2173	0.601465	0.300732	−	0.953709i	$-0.402769\pi$
$727$	16.2173	0.601465	0.300732	+	0.953709i	$0.402769\pi$
$728$	−19.9254	−0.738483
$729$	−26.4109	−0.978181
$730$	−4.78838	−0.177226
$731$	77.0004	2.84796
$732$	6.38833	0.236119
$733$	−3.65145	−0.134869	−0.0674347	−	0.997724i	$-0.521481\pi$
$733$	−3.65145	−0.134869	−0.0674347	+	0.997724i	$0.521481\pi$
$734$	34.1113	1.25907
$735$	0.958869	0.0353684
$736$	56.4390	2.08037
$737$	29.8239	1.09858
$738$	17.8846	0.658340
$739$	−39.7669	−1.46285	−0.731425	−	0.681922i	$-0.761144\pi$
$739$	−39.7669	−1.46285	−0.731425	+	0.681922i	$0.761144\pi$
$740$	24.4458	0.898647
$741$	4.46444	0.164005
$742$	−6.56016	−0.240831
$743$	5.55588	0.203826	0.101913	−	0.994793i	$-0.467504\pi$
$743$	5.55588	0.203826	0.101913	+	0.994793i	$0.467504\pi$
$744$	−4.37518	−0.160402
$745$	1.21909	0.0446641
$746$	−23.7243	−0.868609
$747$	−4.37317	−0.160006
$748$	−158.031	−5.77819
$749$	−2.48265	−0.0907139
$750$	−3.01581	−0.110122
$751$	16.7296	0.610473	0.305237	−	0.952277i	$-0.401264\pi$
$751$	16.7296	0.610473	0.305237	+	0.952277i	$0.401264\pi$
$752$	86.2107	3.14378
$753$	0.947437	0.0345265
$754$	−89.9879	−3.27716
$755$	−17.9918	−0.654790
$756$	1.67553	0.0609385
$757$	0.137760	0.00500698	0.00250349	−	0.999997i	$-0.499203\pi$
$757$	0.137760	0.00500698	0.00250349	+	0.999997i	$0.499203\pi$
$758$	3.69783	0.134311
$759$	−3.33154	−0.120927
$760$	−81.4471	−2.95440
$761$	−12.7959	−0.463851	−0.231926	−	0.972733i	$-0.574503\pi$
$761$	−12.7959	−0.463851	−0.231926	+	0.972733i	$0.574503\pi$
$762$	4.27083	0.154716
$763$	−6.48323	−0.234709
$764$	−36.8226	−1.33220
$765$	−29.0148	−1.04903
$766$	−58.4577	−2.11216
$767$	7.09138	0.256055
$768$	−2.34217	−0.0845159
$769$	36.4775	1.31541	0.657707	−	0.753274i	$-0.271527\pi$
$769$	36.4775	1.31541	0.657707	+	0.753274i	$0.271527\pi$
$770$	−9.63740	−0.347308
$771$	−2.61018	−0.0940034
$772$	−82.0071	−2.95150
$773$	−43.1050	−1.55038	−0.775190	−	0.631729i	$-0.782346\pi$
$773$	−43.1050	−1.55038	−0.775190	+	0.631729i	$0.782346\pi$
$774$	−84.2399	−3.02794
$775$	−18.6830	−0.671114
$776$	55.4834	1.99174
$777$	0.225982	0.00810708
$778$	−0.901644	−0.0323255
$779$	−19.6730	−0.704857
$780$	3.38294	0.121129
$781$	4.48211	0.160383
$782$	−122.337	−4.37476
$783$	4.34342	0.155221
$784$	−57.7476	−2.06242
$785$	−25.4279	−0.907561
$786$	1.94271	0.0692941
$787$	7.89744	0.281513	0.140757	−	0.990044i	$-0.455046\pi$
$787$	7.89744	0.281513	0.140757	+	0.990044i	$0.455046\pi$
$788$	−122.337	−4.35808
$789$	1.27916	0.0455394
$790$	−29.2241	−1.03975
$791$	−10.8012	−0.384047
$792$	99.2359	3.52620
$793$	−65.2569	−2.31734
$794$	64.5565	2.29102
$795$	0.639299	0.0226736
$796$	−115.982	−4.11087
$797$	14.6216	0.517922	0.258961	−	0.965888i	$-0.416620\pi$
$797$	14.6216	0.517922	0.258961	+	0.965888i	$0.416620\pi$
$798$	−1.31173	−0.0464346
$799$	−70.4505	−2.49236
$800$	26.2816	0.929195
$801$	−23.7535	−0.839287
$802$	23.1323	0.816828
$803$	−6.41761	−0.226472
$804$	3.07592	0.108479
$805$	−5.23181	−0.184397
$806$	77.8633	2.74262
$807$	−3.31050	−0.116535
$808$	−13.1570	−0.462863
$809$	55.5689	1.95370	0.976849	−	0.213932i	$-0.0686270\pi$
$809$	55.5689	1.95370	0.976849	+	0.213932i	$0.0686270\pi$
$810$	31.6261	1.11123
$811$	10.1610	0.356802	0.178401	−	0.983958i	$-0.442908\pi$
$811$	10.1610	0.356802	0.178401	+	0.983958i	$0.442908\pi$
$812$	18.5411	0.650667
$813$	−0.342309	−0.0120053
$814$	46.7211	1.63758
$815$	17.6903	0.619662
$816$	−6.39723	−0.223948
$817$	92.6636	3.24189
$818$	−28.1261	−0.983406
$819$	−8.54215	−0.298487
$820$	−14.9072	−0.520583
$821$	−17.9479	−0.626385	−0.313193	−	0.949690i	$-0.601399\pi$
$821$	−17.9479	−0.626385	−0.313193	+	0.949690i	$0.601399\pi$
$822$	−1.23155	−0.0429551
$823$	−43.8336	−1.52794	−0.763972	−	0.645249i	$-0.776754\pi$
$823$	−43.8336	−1.52794	−0.763972	+	0.645249i	$0.776754\pi$
$824$	86.6040	3.01699
$825$	−1.55138	−0.0540121
$826$	−2.08356	−0.0724965
$827$	5.11950	0.178023	0.0890113	−	0.996031i	$-0.471629\pi$
$827$	5.11950	0.178023	0.0890113	+	0.996031i	$0.471629\pi$
$828$	93.8554	3.26170
$829$	18.4359	0.640305	0.320152	−	0.947366i	$-0.396266\pi$
$829$	18.4359	0.640305	0.320152	+	0.947366i	$0.396266\pi$
$830$	5.19802	0.180426
$831$	−0.523868	−0.0181728
$832$	−22.7364	−0.788242
$833$	47.1907	1.63506
$834$	2.70652	0.0937191
$835$	16.6111	0.574852
$836$	−190.177	−6.57742
$837$	−3.75821	−0.129903
$838$	−2.75745	−0.0952546
$839$	−52.7019	−1.81947	−0.909736	−	0.415186i	$-0.863716\pi$
$839$	−52.7019	−1.81947	−0.909736	+	0.415186i	$0.863716\pi$
$840$	−0.570522	−0.0196849
$841$	19.0635	0.657363
$842$	45.6882	1.57452
$843$	2.57033	0.0885267
$844$	−6.37227	−0.219343
$845$	−16.7061	−0.574707
$846$	77.0742	2.64986
$847$	−6.65014	−0.228502
$848$	−38.5016	−1.32215
$849$	1.27211	0.0436586
$850$	−56.9679	−1.95398
$851$	25.3633	0.869442
$852$	0.462268	0.0158370
$853$	−57.9555	−1.98436	−0.992179	−	0.124819i	$-0.960165\pi$
$853$	−57.9555	−1.98436	−0.992179	+	0.124819i	$0.960165\pi$
$854$	19.1735	0.656105
$855$	−34.9169	−1.19413
$856$	−30.3855	−1.03855
$857$	−22.4633	−0.767333	−0.383666	−	0.923472i	$-0.625339\pi$
$857$	−22.4633	−0.767333	−0.383666	+	0.923472i	$0.625339\pi$
$858$	6.46551	0.220729
$859$	−15.7244	−0.536510	−0.268255	−	0.963348i	$-0.586447\pi$
$859$	−15.7244	−0.536510	−0.268255	+	0.963348i	$0.586447\pi$
$860$	70.2161	2.39435
$861$	−0.137805	−0.00469640
$862$	3.33265	0.113510
$863$	36.2024	1.23235	0.616173	−	0.787611i	$-0.288682\pi$
$863$	36.2024	1.23235	0.616173	+	0.787611i	$0.288682\pi$
$864$	5.28670	0.179857
$865$	−31.4014	−1.06768
$866$	−0.750687	−0.0255094
$867$	3.44941	0.117148
$868$	−16.0430	−0.544535
$869$	−39.1676	−1.32867
$870$	−2.57662	−0.0873555
$871$	−31.4206	−1.06464
$872$	−79.3492	−2.68710
$873$	23.7862	0.805039
$874$	−147.222	−4.97987
$875$	−6.34740	−0.214581
$876$	−0.661887	−0.0223631
$877$	−9.50345	−0.320909	−0.160454	−	0.987043i	$-0.551296\pi$
$877$	−9.50345	−0.320909	−0.160454	+	0.987043i	$0.551296\pi$
$878$	61.2264	2.06629
$879$	0.463779	0.0156429
$880$	−56.5619	−1.90670
$881$	8.61682	0.290308	0.145154	−	0.989409i	$-0.453632\pi$
$881$	8.61682	0.290308	0.145154	+	0.989409i	$0.453632\pi$
$882$	−51.6276	−1.73839
$883$	−4.16461	−0.140150	−0.0700751	−	0.997542i	$-0.522324\pi$
$883$	−4.16461	−0.140150	−0.0700751	+	0.997542i	$0.522324\pi$
$884$	166.491	5.59971
$885$	0.203047	0.00682535
$886$	−4.52205	−0.151921
$887$	−41.6956	−1.40000	−0.700000	−	0.714143i	$-0.746817\pi$
$887$	−41.6956	−1.40000	−0.700000	+	0.714143i	$0.746817\pi$
$888$	2.76583	0.0928153
$889$	8.98883	0.301476
$890$	28.2338	0.946399
$891$	42.3868	1.42001
$892$	122.244	4.09304
$893$	−84.7813	−2.83710
$894$	0.240302	0.00803689
$895$	−31.4090	−1.04989
$896$	−2.93387	−0.0980139
$897$	3.50990	0.117192
$898$	−87.2975	−2.91316
$899$	−41.5877	−1.38703
$900$	43.7051	1.45684
$901$	31.4631	1.04819
$902$	−28.4908	−0.948641
$903$	0.649092	0.0216004
$904$	−132.198	−4.39683
$905$	25.5241	0.848450
$906$	−3.54646	−0.117823
$907$	−2.09847	−0.0696786	−0.0348393	−	0.999393i	$-0.511092\pi$
$907$	−2.09847	−0.0696786	−0.0348393	+	0.999393i	$0.511092\pi$
$908$	−66.3949	−2.20339
$909$	−5.64052	−0.187084
$910$	10.1534	0.336580
$911$	−20.4126	−0.676301	−0.338150	−	0.941092i	$-0.609801\pi$
$911$	−20.4126	−0.676301	−0.338150	+	0.941092i	$0.609801\pi$
$912$	−7.69854	−0.254924
$913$	6.96664	0.230562
$914$	−79.9826	−2.64559
$915$	−1.86850	−0.0617705
$916$	−11.4900	−0.379642
$917$	4.08883	0.135025
$918$	−11.4594	−0.378218
$919$	−30.5916	−1.00912	−0.504562	−	0.863376i	$-0.668346\pi$
$919$	−30.5916	−1.00912	−0.504562	+	0.863376i	$0.668346\pi$
$920$	−64.0329	−2.11110
$921$	−1.94183	−0.0639854
$922$	−10.1671	−0.334834
$923$	−4.72207	−0.155429
$924$	−1.33216	−0.0438248
$925$	11.8108	0.388335
$926$	14.7606	0.485062
$927$	37.1277	1.21944
$928$	58.5017	1.92041
$929$	6.54421	0.214708	0.107354	−	0.994221i	$-0.465762\pi$
$929$	6.54421	0.214708	0.107354	+	0.994221i	$0.465762\pi$
$930$	2.22945	0.0731067
$931$	56.7902	1.86122
$932$	−106.462	−3.48729
$933$	−0.860073	−0.0281575
$934$	69.3975	2.27076
$935$	46.2218	1.51161
$936$	−104.549	−3.41728
$937$	24.5735	0.802780	0.401390	−	0.915907i	$-0.368527\pi$
$937$	24.5735	0.802780	0.401390	+	0.915907i	$0.368527\pi$
$938$	9.23188	0.301432
$939$	1.88718	0.0615859
$940$	−64.2432	−2.09538
$941$	−12.9398	−0.421824	−0.210912	−	0.977505i	$-0.567643\pi$
$941$	−12.9398	−0.421824	−0.210912	+	0.977505i	$0.567643\pi$
$942$	−5.01222	−0.163307
$943$	−15.4667	−0.503664
$944$	−12.2285	−0.398002
$945$	−0.490069	−0.0159419
$946$	134.198	4.36314
$947$	11.1382	0.361941	0.180971	−	0.983488i	$-0.442076\pi$
$947$	11.1382	0.361941	0.180971	+	0.983488i	$0.442076\pi$
$948$	−4.03959	−0.131200
$949$	6.76118	0.219477
$950$	−68.5562	−2.22426
$951$	0.991228	0.0321428
$952$	−28.0782	−0.910021
$953$	−16.8947	−0.547273	−0.273636	−	0.961833i	$-0.588227\pi$
$953$	−16.8947	−0.547273	−0.273636	+	0.961833i	$0.588227\pi$
$954$	−34.4212	−1.11443
$955$	10.7701	0.348512
$956$	−30.5821	−0.989097
$957$	−3.45330	−0.111629
$958$	−86.0560	−2.78034
$959$	−2.59204	−0.0837014
$960$	−0.651009	−0.0210112
$961$	4.98432	0.160784
$962$	−49.2224	−1.58700
$963$	−13.0265	−0.419772
$964$	−107.225	−3.45350
$965$	23.9859	0.772134
$966$	−1.03127	−0.0331805
$967$	1.11241	0.0357727	0.0178864	−	0.999840i	$-0.494306\pi$
$967$	1.11241	0.0357727	0.0178864	+	0.999840i	$0.494306\pi$
$968$	−81.3921	−2.61604
$969$	6.29116	0.202101
$970$	−28.2726	−0.907780
$971$	11.2308	0.360413	0.180207	−	0.983629i	$-0.442323\pi$
$971$	11.2308	0.360413	0.180207	+	0.983629i	$0.442323\pi$
$972$	13.1953	0.423241
$973$	5.69642	0.182619
$974$	17.4099	0.557849
$975$	1.63443	0.0523438
$976$	112.530	3.60199
$977$	−17.5756	−0.562294	−0.281147	−	0.959665i	$-0.590715\pi$
$977$	−17.5756	−0.562294	−0.281147	+	0.959665i	$0.590715\pi$
$978$	3.48701	0.111502
$979$	37.8403	1.20938
$980$	43.0329	1.37463
$981$	−34.0176	−1.08610
$982$	−35.7404	−1.14052
$983$	−24.5992	−0.784594	−0.392297	−	0.919839i	$-0.628319\pi$
$983$	−24.5992	−0.784594	−0.392297	+	0.919839i	$0.628319\pi$
$984$	−1.68662	−0.0537676
$985$	35.7819	1.14010
$986$	−126.808	−4.03840
$987$	−0.593878	−0.0189033
$988$	200.359	6.37426
$989$	72.8512	2.31653
$990$	−50.5675	−1.60714
$991$	4.90322	0.155756	0.0778779	−	0.996963i	$-0.475186\pi$
$991$	4.90322	0.155756	0.0778779	+	0.996963i	$0.475186\pi$
$992$	−50.6195	−1.60717
$993$	0.258832	0.00821378
$994$	1.38742	0.0440064
$995$	33.9230	1.07543
$996$	0.718512	0.0227669
$997$	−40.2044	−1.27329	−0.636643	−	0.771159i	$-0.719677\pi$
$997$	−40.2044	−1.27329	−0.636643	+	0.771159i	$0.719677\pi$
$998$	55.4438	1.75504
$999$	2.37581	0.0751672

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4021.2.a.c.1.8	✓	182

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4021.2.a.c.1.8	✓	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)

\(f(q)\)	\(=\)	\(q-2.58741 q^{2} +0.104608 q^{3} +4.69469 q^{4} -1.37313 q^{5} -0.270664 q^{6} -0.569668 q^{7} -6.97226 q^{8} -2.98906 q^{9} +O(q^{10})\)	\(q-2.58741 q^{2} +0.104608 q^{3} +4.69469 q^{4} -1.37313 q^{5} -0.270664 q^{6} -0.569668 q^{7} -6.97226 q^{8} -2.98906 q^{9} +3.55285 q^{10} +4.76169 q^{11} +0.491103 q^{12} -5.01662 q^{13} +1.47396 q^{14} -0.143640 q^{15} +8.65071 q^{16} -7.06927 q^{17} +7.73391 q^{18} -8.50728 q^{19} -6.44641 q^{20} -0.0595920 q^{21} -12.3204 q^{22} -6.68834 q^{23} -0.729355 q^{24} -3.11452 q^{25} +12.9800 q^{26} -0.626504 q^{27} -2.67441 q^{28} -6.93279 q^{29} +0.371657 q^{30} +5.99869 q^{31} -8.43842 q^{32} +0.498112 q^{33} +18.2911 q^{34} +0.782228 q^{35} -14.0327 q^{36} -3.79216 q^{37} +22.0118 q^{38} -0.524779 q^{39} +9.57381 q^{40} +2.31248 q^{41} +0.154189 q^{42} -10.8923 q^{43} +22.3547 q^{44} +4.10436 q^{45} +17.3055 q^{46} +9.96574 q^{47} +0.904935 q^{48} -6.67548 q^{49} +8.05853 q^{50} -0.739503 q^{51} -23.5514 q^{52} -4.45069 q^{53} +1.62102 q^{54} -6.53842 q^{55} +3.97187 q^{56} -0.889931 q^{57} +17.9380 q^{58} -1.41358 q^{59} -0.674347 q^{60} +13.0081 q^{61} -15.5211 q^{62} +1.70277 q^{63} +4.53221 q^{64} +6.88846 q^{65} -1.28882 q^{66} +6.26330 q^{67} -33.1880 q^{68} -0.699655 q^{69} -2.02394 q^{70} +0.941286 q^{71} +20.8405 q^{72} -1.34776 q^{73} +9.81188 q^{74} -0.325804 q^{75} -39.9390 q^{76} -2.71258 q^{77} +1.35782 q^{78} -8.22555 q^{79} -11.8785 q^{80} +8.90163 q^{81} -5.98334 q^{82} +1.46306 q^{83} -0.279766 q^{84} +9.70701 q^{85} +28.1828 q^{86} -0.725226 q^{87} -33.1997 q^{88} +7.94681 q^{89} -10.6197 q^{90} +2.85781 q^{91} -31.3997 q^{92} +0.627512 q^{93} -25.7854 q^{94} +11.6816 q^{95} -0.882727 q^{96} -7.95774 q^{97} +17.2722 q^{98} -14.2330 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 182 q + 18 q^{2} + 28 q^{3} + 208 q^{4} + 22 q^{5} + 18 q^{6} + 14 q^{7} + 54 q^{8} + 238 q^{9}+O(q^{10}) \) 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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