LMFDB - Embedded newform 4027.2.a.c.1.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4027,2,Mod(1,4027)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4027, 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("4027.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4027 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4027.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:	$32.1557568940$
Analytic rank:	$0$
Dimension:	$174$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.18
Character	$\chi$	$=$	4027.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.36345 q^{2} +0.649215 q^{3} +3.58591 q^{4} -0.526324 q^{5} -1.53439 q^{6} +1.65204 q^{7} -3.74822 q^{8} -2.57852 q^{9} +O(q^{10})$	\(q-2.36345 q^{2} +0.649215 q^{3} +3.58591 q^{4} -0.526324 q^{5} -1.53439 q^{6} +1.65204 q^{7} -3.74822 q^{8} -2.57852 q^{9} +1.24394 q^{10} -0.633045 q^{11} +2.32803 q^{12} -4.08101 q^{13} -3.90453 q^{14} -0.341697 q^{15} +1.68692 q^{16} -1.27562 q^{17} +6.09421 q^{18} -0.310985 q^{19} -1.88735 q^{20} +1.07253 q^{21} +1.49617 q^{22} -3.61411 q^{23} -2.43340 q^{24} -4.72298 q^{25} +9.64527 q^{26} -3.62166 q^{27} +5.92408 q^{28} -2.51840 q^{29} +0.807585 q^{30} -1.97607 q^{31} +3.50948 q^{32} -0.410983 q^{33} +3.01487 q^{34} -0.869510 q^{35} -9.24633 q^{36} +4.86204 q^{37} +0.734997 q^{38} -2.64945 q^{39} +1.97278 q^{40} +2.89719 q^{41} -2.53488 q^{42} -10.7661 q^{43} -2.27004 q^{44} +1.35714 q^{45} +8.54177 q^{46} +8.11626 q^{47} +1.09517 q^{48} -4.27075 q^{49} +11.1625 q^{50} -0.828153 q^{51} -14.6341 q^{52} +5.26987 q^{53} +8.55962 q^{54} +0.333187 q^{55} -6.19222 q^{56} -0.201896 q^{57} +5.95212 q^{58} +5.54935 q^{59} -1.22530 q^{60} +4.30300 q^{61} +4.67035 q^{62} -4.25983 q^{63} -11.6683 q^{64} +2.14793 q^{65} +0.971338 q^{66} -3.11613 q^{67} -4.57426 q^{68} -2.34633 q^{69} +2.05504 q^{70} +6.57046 q^{71} +9.66485 q^{72} +0.973762 q^{73} -11.4912 q^{74} -3.06623 q^{75} -1.11516 q^{76} -1.04582 q^{77} +6.26186 q^{78} +4.86469 q^{79} -0.887864 q^{80} +5.38432 q^{81} -6.84738 q^{82} +12.8455 q^{83} +3.84600 q^{84} +0.671389 q^{85} +25.4451 q^{86} -1.63498 q^{87} +2.37279 q^{88} +15.0161 q^{89} -3.20753 q^{90} -6.74200 q^{91} -12.9599 q^{92} -1.28290 q^{93} -19.1824 q^{94} +0.163679 q^{95} +2.27841 q^{96} +11.4793 q^{97} +10.0937 q^{98} +1.63232 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 174 q + 21 q^{2} + 17 q^{3} + 187 q^{4} + 72 q^{5} + 21 q^{6} + 24 q^{7} + 54 q^{8} + 197 q^{9}+O(q^{10}) $ 174 * q + 21 * q^2 + 17 * q^3 + 187 * q^4 + 72 * q^5 + 21 * q^6 + 24 * q^7 + 54 * q^8 + 197 * q^9	\( 174 q + 21 q^{2} + 17 q^{3} + 187 q^{4} + 72 q^{5} + 21 q^{6} + 24 q^{7} + 54 q^{8} + 197 q^{9} + 20 q^{10} + 35 q^{11} + 23 q^{12} + 91 q^{13} + 18 q^{14} + 16 q^{15} + 201 q^{16} + 148 q^{17} + 39 q^{18} + 36 q^{19} + 128 q^{20} + 57 q^{21} + 17 q^{22} + 96 q^{23} + 24 q^{24} + 226 q^{25} + 44 q^{26} + 62 q^{27} + 32 q^{28} + 122 q^{29} + 25 q^{30} + 23 q^{31} + 104 q^{32} + 91 q^{33} + 6 q^{34} + 80 q^{35} + 222 q^{36} + 71 q^{37} + 125 q^{38} + 16 q^{39} + 53 q^{40} + 97 q^{41} + 14 q^{42} + 38 q^{43} + 70 q^{44} + 185 q^{45} - 23 q^{46} + 110 q^{47} + 36 q^{48} + 210 q^{49} + 51 q^{50} + 33 q^{51} + 118 q^{52} + 214 q^{53} + 8 q^{54} + 37 q^{55} + 41 q^{56} + 76 q^{57} + 2 q^{58} + 66 q^{59} - 12 q^{60} + 114 q^{61} + 175 q^{62} + 62 q^{63} + 190 q^{64} + 128 q^{65} + 12 q^{66} - 6 q^{67} + 348 q^{68} + 115 q^{69} - 38 q^{70} + 54 q^{71} + 101 q^{72} + 107 q^{73} + 71 q^{74} - q^{75} + 31 q^{76} + 368 q^{77} - 14 q^{78} - 14 q^{79} + 205 q^{80} + 222 q^{81} + 26 q^{82} + 246 q^{83} + 41 q^{84} + 87 q^{85} + 33 q^{86} + 100 q^{87} - 6 q^{88} + 147 q^{89} + 50 q^{90} - 23 q^{91} + 189 q^{92} + 117 q^{93} + 23 q^{94} + 42 q^{95} + 38 q^{96} + 52 q^{97} + 148 q^{98} + 38 q^{99}+O(q^{100}) \) 174 * q + 21 * q^2 + 17 * q^3 + 187 * q^4 + 72 * q^5 + 21 * q^6 + 24 * q^7 + 54 * q^8 + 197 * q^9 + 20 * q^10 + 35 * q^11 + 23 * q^12 + 91 * q^13 + 18 * q^14 + 16 * q^15 + 201 * q^16 + 148 * q^17 + 39 * q^18 + 36 * q^19 + 128 * q^20 + 57 * q^21 + 17 * q^22 + 96 * q^23 + 24 * q^24 + 226 * q^25 + 44 * q^26 + 62 * q^27 + 32 * q^28 + 122 * q^29 + 25 * q^30 + 23 * q^31 + 104 * q^32 + 91 * q^33 + 6 * q^34 + 80 * q^35 + 222 * q^36 + 71 * q^37 + 125 * q^38 + 16 * q^39 + 53 * q^40 + 97 * q^41 + 14 * q^42 + 38 * q^43 + 70 * q^44 + 185 * q^45 - 23 * q^46 + 110 * q^47 + 36 * q^48 + 210 * q^49 + 51 * q^50 + 33 * q^51 + 118 * q^52 + 214 * q^53 + 8 * q^54 + 37 * q^55 + 41 * q^56 + 76 * q^57 + 2 * q^58 + 66 * q^59 - 12 * q^60 + 114 * q^61 + 175 * q^62 + 62 * q^63 + 190 * q^64 + 128 * q^65 + 12 * q^66 - 6 * q^67 + 348 * q^68 + 115 * q^69 - 38 * q^70 + 54 * q^71 + 101 * q^72 + 107 * q^73 + 71 * q^74 - q^75 + 31 * q^76 + 368 * q^77 - 14 * q^78 - 14 * q^79 + 205 * q^80 + 222 * q^81 + 26 * q^82 + 246 * q^83 + 41 * q^84 + 87 * q^85 + 33 * q^86 + 100 * q^87 - 6 * q^88 + 147 * q^89 + 50 * q^90 - 23 * q^91 + 189 * q^92 + 117 * q^93 + 23 * q^94 + 42 * q^95 + 38 * q^96 + 52 * q^97 + 148 * q^98 + 38 * 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 $

$2$	−2.36345	−1.67121	−0.835607	−	0.549328i	$-0.814884\pi$
$2$	−2.36345	−1.67121	−0.835607	+	0.549328i	$0.814884\pi$
$3$	0.649215	0.374825	0.187412	−	0.982281i	$-0.439990\pi$
$3$	0.649215	0.374825	0.187412	+	0.982281i	$0.439990\pi$
$4$	3.58591	1.79295
$5$	−0.526324	−0.235379	−0.117690	−	0.993050i	$-0.537549\pi$
$5$	−0.526324	−0.235379	−0.117690	+	0.993050i	$0.537549\pi$
$6$	−1.53439	−0.626412
$7$	1.65204	0.624414	0.312207	−	0.950014i	$-0.398932\pi$
$7$	1.65204	0.624414	0.312207	+	0.950014i	$0.398932\pi$
$8$	−3.74822	−1.32519
$9$	−2.57852	−0.859506
$10$	1.24394	0.393369
$11$	−0.633045	−0.190870	−0.0954352	−	0.995436i	$-0.530424\pi$
$11$	−0.633045	−0.190870	−0.0954352	+	0.995436i	$0.530424\pi$
$12$	2.32803	0.672043
$13$	−4.08101	−1.13187	−0.565934	−	0.824450i	$-0.691484\pi$
$13$	−4.08101	−1.13187	−0.565934	+	0.824450i	$0.691484\pi$
$14$	−3.90453	−1.04353
$15$	−0.341697	−0.0882259
$16$	1.68692	0.421729
$17$	−1.27562	−0.309383	−0.154692	−	0.987963i	$-0.549438\pi$
$17$	−1.27562	−0.309383	−0.154692	+	0.987963i	$0.549438\pi$
$18$	6.09421	1.43642
$19$	−0.310985	−0.0713448	−0.0356724	−	0.999364i	$-0.511357\pi$
$19$	−0.310985	−0.0713448	−0.0356724	+	0.999364i	$0.511357\pi$
$20$	−1.88735	−0.422024
$21$	1.07253	0.234046
$22$	1.49617	0.318985
$23$	−3.61411	−0.753593	−0.376797	−	0.926296i	$-0.622974\pi$
$23$	−3.61411	−0.753593	−0.376797	+	0.926296i	$0.622974\pi$
$24$	−2.43340	−0.496716
$25$	−4.72298	−0.944597
$26$	9.64527	1.89159
$27$	−3.62166	−0.696989
$28$	5.92408	1.11955
$29$	−2.51840	−0.467655	−0.233828	−	0.972278i	$-0.575125\pi$
$29$	−2.51840	−0.467655	−0.233828	+	0.972278i	$0.575125\pi$
$30$	0.807585	0.147444
$31$	−1.97607	−0.354913	−0.177456	−	0.984129i	$-0.556787\pi$
$31$	−1.97607	−0.354913	−0.177456	+	0.984129i	$0.556787\pi$
$32$	3.50948	0.620395
$33$	−0.410983	−0.0715429
$34$	3.01487	0.517046
$35$	−0.869510	−0.146974
$36$	−9.24633	−1.54106
$37$	4.86204	0.799314	0.399657	−	0.916665i	$-0.369129\pi$
$37$	4.86204	0.799314	0.399657	+	0.916665i	$0.369129\pi$
$38$	0.734997	0.119232
$39$	−2.64945	−0.424252
$40$	1.97278	0.311923
$41$	2.89719	0.452465	0.226233	−	0.974073i	$-0.427359\pi$
$41$	2.89719	0.452465	0.226233	+	0.974073i	$0.427359\pi$
$42$	−2.53488	−0.391140
$43$	−10.7661	−1.64181	−0.820905	−	0.571064i	$-0.806531\pi$
$43$	−10.7661	−1.64181	−0.820905	+	0.571064i	$0.806531\pi$
$44$	−2.27004	−0.342222
$45$	1.35714	0.202310
$46$	8.54177	1.25942
$47$	8.11626	1.18388	0.591939	−	0.805983i	$-0.298363\pi$
$47$	8.11626	1.18388	0.591939	+	0.805983i	$0.298363\pi$
$48$	1.09517	0.158075
$49$	−4.27075	−0.610107
$50$	11.1625	1.57862
$51$	−0.828153	−0.115965
$52$	−14.6341	−2.02939
$53$	5.26987	0.723873	0.361936	−	0.932203i	$-0.382116\pi$
$53$	5.26987	0.723873	0.361936	+	0.932203i	$0.382116\pi$
$54$	8.55962	1.16482
$55$	0.333187	0.0449269
$56$	−6.19222	−0.827470
$57$	−0.201896	−0.0267418
$58$	5.95212	0.781552
$59$	5.54935	0.722464	0.361232	−	0.932476i	$-0.382356\pi$
$59$	5.54935	0.722464	0.361232	+	0.932476i	$0.382356\pi$
$60$	−1.22530	−0.158185
$61$	4.30300	0.550942	0.275471	−	0.961309i	$-0.411166\pi$
$61$	4.30300	0.550942	0.275471	+	0.961309i	$0.411166\pi$
$62$	4.67035	0.593135
$63$	−4.25983	−0.536688
$64$	−11.6683	−1.45854
$65$	2.14793	0.266418
$66$	0.971338	0.119563
$67$	−3.11613	−0.380695	−0.190348	−	0.981717i	$-0.560962\pi$
$67$	−3.11613	−0.380695	−0.190348	+	0.981717i	$0.560962\pi$
$68$	−4.57426	−0.554710
$69$	−2.34633	−0.282465
$70$	2.05504	0.245625
$71$	6.57046	0.779771	0.389885	−	0.920863i	$-0.372515\pi$
$71$	6.57046	0.779771	0.389885	+	0.920863i	$0.372515\pi$
$72$	9.66485	1.13901
$73$	0.973762	0.113970	0.0569851	−	0.998375i	$-0.481851\pi$
$73$	0.973762	0.113970	0.0569851	+	0.998375i	$0.481851\pi$
$74$	−11.4912	−1.33582
$75$	−3.06623	−0.354058
$76$	−1.11516	−0.127918
$77$	−1.04582	−0.119182
$78$	6.26186	0.709016
$79$	4.86469	0.547320	0.273660	−	0.961826i	$-0.411766\pi$
$79$	4.86469	0.547320	0.273660	+	0.961826i	$0.411766\pi$
$80$	−0.887864	−0.0992663
$81$	5.38432	0.598258
$82$	−6.84738	−0.756166
$83$	12.8455	1.40997	0.704986	−	0.709221i	$-0.250953\pi$
$83$	12.8455	1.40997	0.704986	+	0.709221i	$0.250953\pi$
$84$	3.84600	0.419633
$85$	0.671389	0.0728224
$86$	25.4451	2.74382
$87$	−1.63498	−0.175289
$88$	2.37279	0.252940
$89$	15.0161	1.59170	0.795851	−	0.605492i	$-0.207024\pi$
$89$	15.0161	1.59170	0.795851	+	0.605492i	$0.207024\pi$
$90$	−3.20753	−0.338103
$91$	−6.74200	−0.706754
$92$	−12.9599	−1.35116
$93$	−1.28290	−0.133030
$94$	−19.1824	−1.97851
$95$	0.163679	0.0167931
$96$	2.27841	0.232539
$97$	11.4793	1.16555	0.582774	−	0.812635i	$-0.301967\pi$
$97$	11.4793	1.16555	0.582774	+	0.812635i	$0.301967\pi$
$98$	10.0937	1.01962
$99$	1.63232	0.164054
$100$	−16.9362	−1.69362
$101$	5.98989	0.596016	0.298008	−	0.954563i	$-0.403678\pi$
$101$	5.98989	0.596016	0.298008	+	0.954563i	$0.403678\pi$
$102$	1.95730	0.193801
$103$	−4.94804	−0.487545	−0.243772	−	0.969832i	$-0.578385\pi$
$103$	−4.94804	−0.487545	−0.243772	+	0.969832i	$0.578385\pi$
$104$	15.2965	1.49995
$105$	−0.564499	−0.0550895
$106$	−12.4551	−1.20975
$107$	8.12729	0.785695	0.392847	−	0.919604i	$-0.371490\pi$
$107$	8.12729	0.785695	0.392847	+	0.919604i	$0.371490\pi$
$108$	−12.9869	−1.24967
$109$	−7.64157	−0.731930	−0.365965	−	0.930629i	$-0.619261\pi$
$109$	−7.64157	−0.731930	−0.365965	+	0.930629i	$0.619261\pi$
$110$	−0.787471	−0.0750824
$111$	3.15651	0.299603
$112$	2.78686	0.263334
$113$	7.67191	0.721712	0.360856	−	0.932621i	$-0.382485\pi$
$113$	7.67191	0.721712	0.360856	+	0.932621i	$0.382485\pi$
$114$	0.477172	0.0446912
$115$	1.90219	0.177380
$116$	−9.03075	−0.838484
$117$	10.5230	0.972848
$118$	−13.1156	−1.20739
$119$	−2.10738	−0.193183
$120$	1.28076	0.116916
$121$	−10.5993	−0.963569
$122$	−10.1699	−0.920742
$123$	1.88090	0.169595
$124$	−7.08601	−0.636342
$125$	5.11744	0.457717
$126$	10.0679	0.896920
$127$	14.5359	1.28985	0.644927	−	0.764244i	$-0.276888\pi$
$127$	14.5359	1.28985	0.644927	+	0.764244i	$0.276888\pi$
$128$	20.5586	1.81714
$129$	−6.98950	−0.615391
$130$	−5.07653	−0.445241
$131$	−4.14418	−0.362078	−0.181039	−	0.983476i	$-0.557946\pi$
$131$	−4.14418	−0.362078	−0.181039	+	0.983476i	$0.557946\pi$
$132$	−1.47375	−0.128273
$133$	−0.513760	−0.0445487
$134$	7.36482	0.636223
$135$	1.90617	0.164057
$136$	4.78130	0.409993
$137$	−10.3901	−0.887686	−0.443843	−	0.896105i	$-0.646385\pi$
$137$	−10.3901	−0.887686	−0.443843	+	0.896105i	$0.646385\pi$
$138$	5.54545	0.472060
$139$	14.5831	1.23692	0.618459	−	0.785817i	$-0.287757\pi$
$139$	14.5831	1.23692	0.618459	+	0.785817i	$0.287757\pi$
$140$	−3.11798	−0.263517
$141$	5.26920	0.443747
$142$	−15.5290	−1.30316
$143$	2.58346	0.216040
$144$	−4.34975	−0.362479
$145$	1.32549	0.110076
$146$	−2.30144	−0.190468
$147$	−2.77264	−0.228683
$148$	17.4348	1.43313
$149$	−0.869103	−0.0711997	−0.0355998	−	0.999366i	$-0.511334\pi$
$149$	−0.869103	−0.0711997	−0.0355998	+	0.999366i	$0.511334\pi$
$150$	7.24690	0.591707
$151$	8.95417	0.728680	0.364340	−	0.931266i	$-0.381295\pi$
$151$	8.95417	0.728680	0.364340	+	0.931266i	$0.381295\pi$
$152$	1.16564	0.0945457
$153$	3.28921	0.265917
$154$	2.47174	0.199179
$155$	1.04005	0.0835390
$156$	−9.50069	−0.760664
$157$	−13.5009	−1.07749	−0.538744	−	0.842470i	$-0.681101\pi$
$157$	−13.5009	−1.07749	−0.538744	+	0.842470i	$0.681101\pi$
$158$	−11.4975	−0.914689
$159$	3.42128	0.271325
$160$	−1.84712	−0.146028
$161$	−5.97066	−0.470554
$162$	−12.7256	−0.999817
$163$	17.3353	1.35781	0.678903	−	0.734228i	$-0.262456\pi$
$163$	17.3353	1.35781	0.678903	+	0.734228i	$0.262456\pi$
$164$	10.3891	0.811250
$165$	0.216310	0.0168397
$166$	−30.3596	−2.35636
$167$	−4.66788	−0.361212	−0.180606	−	0.983556i	$-0.557806\pi$
$167$	−4.66788	−0.361212	−0.180606	+	0.983556i	$0.557806\pi$
$168$	−4.02008	−0.310156
$169$	3.65463	0.281126
$170$	−1.58680	−0.121702
$171$	0.801880	0.0613213
$172$	−38.6061	−2.94369
$173$	−9.99524	−0.759924	−0.379962	−	0.925002i	$-0.624063\pi$
$173$	−9.99524	−0.759924	−0.379962	+	0.925002i	$0.624063\pi$
$174$	3.86421	0.292945
$175$	−7.80257	−0.589819
$176$	−1.06790	−0.0804956
$177$	3.60273	0.270797
$178$	−35.4898	−2.66007
$179$	16.4105	1.22658	0.613291	−	0.789857i	$-0.289845\pi$
$179$	16.4105	1.22658	0.613291	+	0.789857i	$0.289845\pi$
$180$	4.86656	0.362732
$181$	8.86149	0.658670	0.329335	−	0.944213i	$-0.393176\pi$
$181$	8.86149	0.658670	0.329335	+	0.944213i	$0.393176\pi$
$182$	15.9344	1.18114
$183$	2.79357	0.206507
$184$	13.5465	0.998658
$185$	−2.55900	−0.188142
$186$	3.03206	0.222322
$187$	0.807526	0.0590521
$188$	29.1042	2.12264
$189$	−5.98314	−0.435209
$190$	−0.386846	−0.0280648
$191$	−11.6906	−0.845900	−0.422950	−	0.906153i	$-0.639005\pi$
$191$	−11.6906	−0.845900	−0.422950	+	0.906153i	$0.639005\pi$
$192$	−7.57526	−0.546697
$193$	9.31426	0.670455	0.335227	−	0.942137i	$-0.391187\pi$
$193$	9.31426	0.670455	0.335227	+	0.942137i	$0.391187\pi$
$194$	−27.1308	−1.94788
$195$	1.39447	0.0998601
$196$	−15.3145	−1.09389
$197$	−15.1413	−1.07877	−0.539385	−	0.842059i	$-0.681343\pi$
$197$	−15.1413	−1.07877	−0.539385	+	0.842059i	$0.681343\pi$
$198$	−3.85791	−0.274170
$199$	−19.1608	−1.35827	−0.679136	−	0.734012i	$-0.737646\pi$
$199$	−19.1608	−1.35827	−0.679136	+	0.734012i	$0.737646\pi$
$200$	17.7028	1.25177
$201$	−2.02304	−0.142694
$202$	−14.1568	−0.996070
$203$	−4.16051	−0.292010
$204$	−2.96968	−0.207919
$205$	−1.52486	−0.106501
$206$	11.6945	0.814791
$207$	9.31904	0.647718
$208$	−6.88432	−0.477342
$209$	0.196867	0.0136176
$210$	1.33417	0.0920662
$211$	12.8339	0.883522	0.441761	−	0.897133i	$-0.354354\pi$
$211$	12.8339	0.883522	0.441761	+	0.897133i	$0.354354\pi$
$212$	18.8973	1.29787
$213$	4.26565	0.292277
$214$	−19.2085	−1.31306
$215$	5.66644	0.386448
$216$	13.5748	0.923646
$217$	−3.26456	−0.221612
$218$	18.0605	1.22321
$219$	0.632181	0.0427188
$220$	1.19478	0.0805518
$221$	5.20582	0.350181
$222$	−7.46026	−0.500700
$223$	21.8682	1.46441	0.732203	−	0.681087i	$-0.238492\pi$
$223$	21.8682	1.46441	0.732203	+	0.681087i	$0.238492\pi$
$224$	5.79782	0.387383
$225$	12.1783	0.811887
$226$	−18.1322	−1.20614
$227$	3.50310	0.232509	0.116254	−	0.993219i	$-0.462911\pi$
$227$	3.50310	0.232509	0.116254	+	0.993219i	$0.462911\pi$
$228$	−0.723980	−0.0479468
$229$	−17.5497	−1.15972	−0.579860	−	0.814716i	$-0.696893\pi$
$229$	−17.5497	−1.15972	−0.579860	+	0.814716i	$0.696893\pi$
$230$	−4.49573	−0.296440
$231$	−0.678961	−0.0446724
$232$	9.43951	0.619734
$233$	−3.93239	−0.257620	−0.128810	−	0.991669i	$-0.541116\pi$
$233$	−3.93239	−0.257620	−0.128810	+	0.991669i	$0.541116\pi$
$234$	−24.8705	−1.62584
$235$	−4.27178	−0.278660
$236$	19.8995	1.29535
$237$	3.15823	0.205149
$238$	4.98070	0.322851
$239$	−23.6035	−1.52678	−0.763392	−	0.645936i	$-0.776467\pi$
$239$	−23.6035	−1.52678	−0.763392	+	0.645936i	$0.776467\pi$
$240$	−0.576415	−0.0372074
$241$	3.80978	0.245410	0.122705	−	0.992443i	$-0.460843\pi$
$241$	3.80978	0.245410	0.122705	+	0.992443i	$0.460843\pi$
$242$	25.0508	1.61033
$243$	14.3606	0.921231
$244$	15.4301	0.987814
$245$	2.24780	0.143607
$246$	−4.44542	−0.283430
$247$	1.26913	0.0807529
$248$	7.40674	0.470329
$249$	8.33947	0.528492
$250$	−12.0948	−0.764943
$251$	15.0718	0.951322	0.475661	−	0.879629i	$-0.342209\pi$
$251$	15.0718	0.951322	0.475661	+	0.879629i	$0.342209\pi$
$252$	−15.2753	−0.962256
$253$	2.28789	0.143839
$254$	−34.3549	−2.15562
$255$	0.435876	0.0272956
$256$	−25.2526	−1.57829
$257$	−31.1104	−1.94061	−0.970306	−	0.241882i	$-0.922235\pi$
$257$	−31.1104	−1.94061	−0.970306	+	0.241882i	$0.922235\pi$
$258$	16.5193	1.02845
$259$	8.03230	0.499103
$260$	7.70228	0.477675
$261$	6.49375	0.401953
$262$	9.79456	0.605110
$263$	−8.72424	−0.537960	−0.268980	−	0.963146i	$-0.586686\pi$
$263$	−8.72424	−0.537960	−0.268980	+	0.963146i	$0.586686\pi$
$264$	1.54045	0.0948083
$265$	−2.77366	−0.170384
$266$	1.21425	0.0744503
$267$	9.74867	0.596609
$268$	−11.1741	−0.682569
$269$	−31.0441	−1.89279	−0.946396	−	0.323010i	$-0.895305\pi$
$269$	−31.0441	−1.89279	−0.946396	+	0.323010i	$0.895305\pi$
$270$	−4.50513	−0.274174
$271$	8.71066	0.529135	0.264567	−	0.964367i	$-0.414771\pi$
$271$	8.71066	0.529135	0.264567	+	0.964367i	$0.414771\pi$
$272$	−2.15187	−0.130476
$273$	−4.37701	−0.264909
$274$	24.5565	1.48351
$275$	2.98986	0.180296
$276$	−8.41373	−0.506447
$277$	30.9394	1.85897	0.929484	−	0.368861i	$-0.120252\pi$
$277$	30.9394	1.85897	0.929484	+	0.368861i	$0.120252\pi$
$278$	−34.4663	−2.06715
$279$	5.09534	0.305050
$280$	3.25911	0.194769
$281$	32.1693	1.91906	0.959530	−	0.281607i	$-0.0908673\pi$
$281$	32.1693	1.91906	0.959530	+	0.281607i	$0.0908673\pi$
$282$	−12.4535	−0.741595
$283$	−11.3371	−0.673919	−0.336960	−	0.941519i	$-0.609399\pi$
$283$	−11.3371	−0.673919	−0.336960	+	0.941519i	$0.609399\pi$
$284$	23.5611	1.39809
$285$	0.106263	0.00629445
$286$	−6.10589	−0.361049
$287$	4.78629	0.282526
$288$	−9.04927	−0.533234
$289$	−15.3728	−0.904282
$290$	−3.13274	−0.183961
$291$	7.45254	0.436876
$292$	3.49182	0.204343
$293$	5.05427	0.295274	0.147637	−	0.989042i	$-0.452833\pi$
$293$	5.05427	0.295274	0.147637	+	0.989042i	$0.452833\pi$
$294$	6.55300	0.382179
$295$	−2.92076	−0.170053
$296$	−18.2240	−1.05925
$297$	2.29268	0.133035
$298$	2.05408	0.118990
$299$	14.7492	0.852968
$300$	−10.9952	−0.634810
$301$	−17.7860	−1.02517
$302$	−21.1628	−1.21778
$303$	3.88873	0.223402
$304$	−0.524605	−0.0300882
$305$	−2.26477	−0.129680
$306$	−7.77390	−0.444404
$307$	−18.1759	−1.03735	−0.518677	−	0.854970i	$-0.673575\pi$
$307$	−18.1759	−1.03735	−0.518677	+	0.854970i	$0.673575\pi$
$308$	−3.75021	−0.213688
$309$	−3.21234	−0.182744
$310$	−2.45812	−0.139612
$311$	5.07837	0.287968	0.143984	−	0.989580i	$-0.454009\pi$
$311$	5.07837	0.287968	0.143984	+	0.989580i	$0.454009\pi$
$312$	9.93073	0.562217
$313$	−27.1417	−1.53414	−0.767071	−	0.641563i	$-0.778286\pi$
$313$	−27.1417	−1.53414	−0.767071	+	0.641563i	$0.778286\pi$
$314$	31.9087	1.80071
$315$	2.24205	0.126325
$316$	17.4443	0.981320
$317$	19.0628	1.07067	0.535337	−	0.844638i	$-0.320185\pi$
$317$	19.0628	1.07067	0.535337	+	0.844638i	$0.320185\pi$
$318$	−8.08604	−0.453442
$319$	1.59426	0.0892615
$320$	6.14132	0.343310
$321$	5.27636	0.294498
$322$	14.1114	0.786396
$323$	0.396698	0.0220729
$324$	19.3077	1.07265
$325$	19.2745	1.06916
$326$	−40.9712	−2.26918
$327$	−4.96103	−0.274345
$328$	−10.8593	−0.599605
$329$	13.4084	0.739230
$330$	−0.511238	−0.0281427
$331$	−9.27026	−0.509540	−0.254770	−	0.967002i	$-0.582000\pi$
$331$	−9.27026	−0.509540	−0.254770	+	0.967002i	$0.582000\pi$
$332$	46.0626	2.52802
$333$	−12.5369	−0.687015
$334$	11.0323	0.603662
$335$	1.64009	0.0896077
$336$	1.80927	0.0987039
$337$	−19.9624	−1.08742	−0.543710	−	0.839273i	$-0.682981\pi$
$337$	−19.9624	−1.08742	−0.543710	+	0.839273i	$0.682981\pi$
$338$	−8.63755	−0.469821
$339$	4.98072	0.270516
$340$	2.40754	0.130567
$341$	1.25094	0.0677423
$342$	−1.89521	−0.102481
$343$	−18.6198	−1.00537
$344$	40.3536	2.17572
$345$	1.23493	0.0664864
$346$	23.6233	1.27000
$347$	23.2231	1.24668	0.623340	−	0.781951i	$-0.285775\pi$
$347$	23.2231	1.24668	0.623340	+	0.781951i	$0.285775\pi$
$348$	−5.86290	−0.314285
$349$	−19.9715	−1.06905	−0.534524	−	0.845153i	$-0.679509\pi$
$349$	−19.9715	−1.06905	−0.534524	+	0.845153i	$0.679509\pi$
$350$	18.4410	0.985714
$351$	14.7800	0.788899
$352$	−2.22166	−0.118415
$353$	6.19470	0.329711	0.164855	−	0.986318i	$-0.447284\pi$
$353$	6.19470	0.329711	0.164855	+	0.986318i	$0.447284\pi$
$354$	−8.51487	−0.452560
$355$	−3.45819	−0.183542
$356$	53.8463	2.85385
$357$	−1.36814	−0.0724099
$358$	−38.7855	−2.04988
$359$	27.9578	1.47556	0.737778	−	0.675044i	$-0.235875\pi$
$359$	27.9578	1.47556	0.737778	+	0.675044i	$0.235875\pi$
$360$	−5.08684	−0.268100
$361$	−18.9033	−0.994910
$362$	−20.9437	−1.10078
$363$	−6.88120	−0.361169
$364$	−24.1762	−1.26718
$365$	−0.512514	−0.0268262
$366$	−6.60247	−0.345117
$367$	7.43665	0.388190	0.194095	−	0.980983i	$-0.437823\pi$
$367$	7.43665	0.388190	0.194095	+	0.980983i	$0.437823\pi$
$368$	−6.09670	−0.317812
$369$	−7.47047	−0.388897
$370$	6.04809	0.314425
$371$	8.70606	0.451996
$372$	−4.60034	−0.238517
$373$	6.51575	0.337373	0.168686	−	0.985670i	$-0.446048\pi$
$373$	6.51575	0.337373	0.168686	+	0.985670i	$0.446048\pi$
$374$	−1.90855	−0.0986887
$375$	3.32232	0.171564
$376$	−30.4215	−1.56887
$377$	10.2776	0.529324
$378$	14.1409	0.727328
$379$	9.91005	0.509045	0.254523	−	0.967067i	$-0.418082\pi$
$379$	9.91005	0.509045	0.254523	+	0.967067i	$0.418082\pi$
$380$	0.586936	0.0301092
$381$	9.43694	0.483469
$382$	27.6301	1.41368
$383$	−0.632507	−0.0323196	−0.0161598	−	0.999869i	$-0.505144\pi$
$383$	−0.632507	−0.0323196	−0.0161598	+	0.999869i	$0.505144\pi$
$384$	13.3469	0.681109
$385$	0.550439	0.0280530
$386$	−22.0138	−1.12047
$387$	27.7605	1.41115
$388$	41.1637	2.08977
$389$	−6.18092	−0.313385	−0.156693	−	0.987647i	$-0.550083\pi$
$389$	−6.18092	−0.313385	−0.156693	+	0.987647i	$0.550083\pi$
$390$	−3.29576	−0.166887
$391$	4.61023	0.233149
$392$	16.0077	0.808511
$393$	−2.69046	−0.135716
$394$	35.7857	1.80286
$395$	−2.56040	−0.128828
$396$	5.85335	0.294142
$397$	15.1784	0.761782	0.380891	−	0.924620i	$-0.375617\pi$
$397$	15.1784	0.761782	0.380891	+	0.924620i	$0.375617\pi$
$398$	45.2856	2.26996
$399$	−0.333541	−0.0166979
$400$	−7.96728	−0.398364
$401$	33.4282	1.66932	0.834662	−	0.550762i	$-0.185663\pi$
$401$	33.4282	1.66932	0.834662	+	0.550762i	$0.185663\pi$
$402$	4.78135	0.238472
$403$	8.06436	0.401715
$404$	21.4792	1.06863
$405$	−2.83390	−0.140817
$406$	9.83316	0.488012
$407$	−3.07789	−0.152565
$408$	3.10410	0.153676
$409$	0.408352	0.0201917	0.0100959	−	0.999949i	$-0.496786\pi$
$409$	0.408352	0.0201917	0.0100959	+	0.999949i	$0.496786\pi$
$410$	3.60394	0.177986
$411$	−6.74541	−0.332726
$412$	−17.7432	−0.874145
$413$	9.16778	0.451117
$414$	−22.0251	−1.08248
$415$	−6.76087	−0.331878
$416$	−14.3222	−0.702205
$417$	9.46754	0.463627
$418$	−0.465287	−0.0227579
$419$	−24.8485	−1.21393	−0.606964	−	0.794729i	$-0.707613\pi$
$419$	−24.8485	−1.21393	−0.606964	+	0.794729i	$0.707613\pi$
$420$	−2.02424	−0.0987728
$421$	−6.48342	−0.315983	−0.157991	−	0.987441i	$-0.550502\pi$
$421$	−6.48342	−0.315983	−0.157991	+	0.987441i	$0.550502\pi$
$422$	−30.3323	−1.47655
$423$	−20.9279	−1.01755
$424$	−19.7526	−0.959272
$425$	6.02474	0.292243
$426$	−10.0817	−0.488458
$427$	7.10874	0.344016
$428$	29.1437	1.40871
$429$	1.67722	0.0809771
$430$	−13.3924	−0.645837
$431$	3.48121	0.167684	0.0838421	−	0.996479i	$-0.473281\pi$
$431$	3.48121	0.167684	0.0838421	+	0.996479i	$0.473281\pi$
$432$	−6.10944	−0.293941
$433$	16.8220	0.808413	0.404206	−	0.914668i	$-0.367548\pi$
$433$	16.8220	0.808413	0.404206	+	0.914668i	$0.367548\pi$
$434$	7.71562	0.370362
$435$	0.860531	0.0412593
$436$	−27.4020	−1.31232
$437$	1.12393	0.0537649
$438$	−1.49413	−0.0713923
$439$	−28.9313	−1.38082	−0.690408	−	0.723420i	$-0.742569\pi$
$439$	−28.9313	−1.38082	−0.690408	+	0.723420i	$0.742569\pi$
$440$	−1.24886	−0.0595369
$441$	11.0122	0.524391
$442$	−12.3037	−0.585228
$443$	14.6616	0.696592	0.348296	−	0.937385i	$-0.386760\pi$
$443$	14.6616	0.696592	0.348296	+	0.937385i	$0.386760\pi$
$444$	11.3189	0.537173
$445$	−7.90332	−0.374653
$446$	−51.6845	−2.44733
$447$	−0.564235	−0.0266874
$448$	−19.2766	−0.910734
$449$	22.4037	1.05730	0.528649	−	0.848841i	$-0.322699\pi$
$449$	22.4037	1.05730	0.528649	+	0.848841i	$0.322699\pi$
$450$	−28.7828	−1.35684
$451$	−1.83405	−0.0863622
$452$	27.5108	1.29400
$453$	5.81318	0.273127
$454$	−8.27941	−0.388572
$455$	3.54848	0.166355
$456$	0.756750	0.0354381
$457$	32.9272	1.54027	0.770135	−	0.637881i	$-0.220189\pi$
$457$	32.9272	1.54027	0.770135	+	0.637881i	$0.220189\pi$
$458$	41.4780	1.93814
$459$	4.61987	0.215637
$460$	6.82108	0.318034
$461$	12.2143	0.568876	0.284438	−	0.958695i	$-0.408193\pi$
$461$	12.2143	0.568876	0.284438	+	0.958695i	$0.408193\pi$
$462$	1.60469	0.0746571
$463$	40.6005	1.88686	0.943432	−	0.331567i	$-0.107577\pi$
$463$	40.6005	1.88686	0.943432	+	0.331567i	$0.107577\pi$
$464$	−4.24833	−0.197224
$465$	0.675218	0.0313125
$466$	9.29402	0.430537
$467$	31.2808	1.44750	0.723751	−	0.690061i	$-0.242416\pi$
$467$	31.2808	1.44750	0.723751	+	0.690061i	$0.242416\pi$
$468$	37.7344	1.74427
$469$	−5.14798	−0.237711
$470$	10.0961	0.465700
$471$	−8.76498	−0.403869
$472$	−20.8002	−0.957406
$473$	6.81541	0.313373
$474$	−7.46433	−0.342848
$475$	1.46878	0.0673920
$476$	−7.55687	−0.346369
$477$	−13.5885	−0.622173
$478$	55.7857	2.55158
$479$	20.1463	0.920509	0.460255	−	0.887787i	$-0.347758\pi$
$479$	20.1463	0.920509	0.460255	+	0.887787i	$0.347758\pi$
$480$	−1.19918	−0.0547349
$481$	−19.8420	−0.904718
$482$	−9.00423	−0.410132
$483$	−3.87624	−0.176375
$484$	−38.0079	−1.72763
$485$	−6.04183	−0.274345
$486$	−33.9405	−1.53957
$487$	−6.32709	−0.286708	−0.143354	−	0.989671i	$-0.545789\pi$
$487$	−6.32709	−0.286708	−0.143354	+	0.989671i	$0.545789\pi$
$488$	−16.1286	−0.730106
$489$	11.2543	0.508939
$490$	−5.31256	−0.239997
$491$	−38.6544	−1.74445	−0.872223	−	0.489108i	$-0.837322\pi$
$491$	−38.6544	−1.74445	−0.872223	+	0.489108i	$0.837322\pi$
$492$	6.74474	0.304076
$493$	3.21252	0.144685
$494$	−2.99953	−0.134955
$495$	−0.859128	−0.0386150
$496$	−3.33347	−0.149677
$497$	10.8547	0.486900
$498$	−19.7099	−0.883224
$499$	38.0515	1.70342	0.851709	−	0.524014i	$-0.175566\pi$
$499$	38.0515	1.70342	0.851709	+	0.524014i	$0.175566\pi$
$500$	18.3507	0.820666
$501$	−3.03046	−0.135391
$502$	−35.6214	−1.58986
$503$	25.1828	1.12285	0.561423	−	0.827529i	$-0.310254\pi$
$503$	25.1828	1.12285	0.561423	+	0.827529i	$0.310254\pi$
$504$	15.9668	0.711216
$505$	−3.15262	−0.140290
$506$	−5.40733	−0.240385
$507$	2.37264	0.105373
$508$	52.1244	2.31265
$509$	17.0270	0.754709	0.377355	−	0.926069i	$-0.376834\pi$
$509$	17.0270	0.754709	0.377355	+	0.926069i	$0.376834\pi$
$510$	−1.03017	−0.0456168
$511$	1.60870	0.0711646
$512$	18.5661	0.820512
$513$	1.12628	0.0497265
$514$	73.5279	3.24318
$515$	2.60427	0.114758
$516$	−25.0637	−1.10337
$517$	−5.13796	−0.225967
$518$	−18.9839	−0.834107
$519$	−6.48906	−0.284838
$520$	−8.05091	−0.353056
$521$	21.3881	0.937029	0.468515	−	0.883456i	$-0.344789\pi$
$521$	21.3881	0.937029	0.468515	+	0.883456i	$0.344789\pi$
$522$	−15.3477	−0.671749
$523$	1.55238	0.0678810	0.0339405	−	0.999424i	$-0.489194\pi$
$523$	1.55238	0.0678810	0.0339405	+	0.999424i	$0.489194\pi$
$524$	−14.8606	−0.649190
$525$	−5.06555	−0.221079
$526$	20.6193	0.899045
$527$	2.52072	0.109804
$528$	−0.693294	−0.0301717
$529$	−9.93824	−0.432097
$530$	6.55541	0.284749
$531$	−14.3091	−0.620963
$532$	−1.84230	−0.0798737
$533$	−11.8235	−0.512131
$534$	−23.0405	−0.997061
$535$	−4.27759	−0.184936
$536$	11.6799	0.504496
$537$	10.6540	0.459753
$538$	73.3712	3.16326
$539$	2.70358	0.116451
$540$	6.83533	0.294146
$541$	0.480736	0.0206684	0.0103342	−	0.999947i	$-0.496710\pi$
$541$	0.480736	0.0206684	0.0103342	+	0.999947i	$0.496710\pi$
$542$	−20.5872	−0.884297
$543$	5.75302	0.246886
$544$	−4.47677	−0.191940
$545$	4.02194	0.172281
$546$	10.3449	0.442719
$547$	16.5777	0.708810	0.354405	−	0.935092i	$-0.384683\pi$
$547$	16.5777	0.708810	0.354405	+	0.935092i	$0.384683\pi$
$548$	−37.2579	−1.59158
$549$	−11.0954	−0.473538
$550$	−7.06640	−0.301312
$551$	0.783184	0.0333648
$552$	8.79457	0.374322
$553$	8.03668	0.341754
$554$	−73.1238	−3.10673
$555$	−1.66134	−0.0705202
$556$	52.2935	2.21774
$557$	−25.3169	−1.07271	−0.536356	−	0.843992i	$-0.680200\pi$
$557$	−25.3169	−1.07271	−0.536356	+	0.843992i	$0.680200\pi$
$558$	−12.0426	−0.509803
$559$	43.9364	1.85831
$560$	−1.46679	−0.0619832
$561$	0.524258	0.0221342
$562$	−76.0306	−3.20716
$563$	−24.4573	−1.03075	−0.515376	−	0.856964i	$-0.672348\pi$
$563$	−24.4573	−1.03075	−0.515376	+	0.856964i	$0.672348\pi$
$564$	18.8949	0.795617
$565$	−4.03791	−0.169876
$566$	26.7946	1.12626
$567$	8.89513	0.373560
$568$	−24.6275	−1.03335
$569$	−22.3472	−0.936841	−0.468421	−	0.883506i	$-0.655177\pi$
$569$	−22.3472	−0.936841	−0.468421	+	0.883506i	$0.655177\pi$
$570$	−0.251147	−0.0105194
$571$	25.1290	1.05162	0.525808	−	0.850603i	$-0.323763\pi$
$571$	25.1290	1.05162	0.525808	+	0.850603i	$0.323763\pi$
$572$	9.26406	0.387350
$573$	−7.58970	−0.317064
$574$	−11.3122	−0.472161
$575$	17.0694	0.711842
$576$	30.0870	1.25363
$577$	5.14159	0.214047	0.107024	−	0.994256i	$-0.465868\pi$
$577$	5.14159	0.214047	0.107024	+	0.994256i	$0.465868\pi$
$578$	36.3329	1.51125
$579$	6.04696	0.251303
$580$	4.75310	0.197362
$581$	21.2213	0.880406
$582$	−17.6137	−0.730113
$583$	−3.33607	−0.138166
$584$	−3.64987	−0.151033
$585$	−5.53848	−0.228988
$586$	−11.9455	−0.493465
$587$	27.8853	1.15095	0.575474	−	0.817820i	$-0.304817\pi$
$587$	27.8853	1.15095	0.575474	+	0.817820i	$0.304817\pi$
$588$	−9.94242	−0.410019
$589$	0.614528	0.0253212
$590$	6.90307	0.284195
$591$	−9.82995	−0.404350
$592$	8.20185	0.337094
$593$	−47.1304	−1.93541	−0.967706	−	0.252080i	$-0.918885\pi$
$593$	−47.1304	−1.93541	−0.967706	+	0.252080i	$0.918885\pi$
$594$	−5.41863	−0.222329
$595$	1.10916	0.0454713
$596$	−3.11652	−0.127658
$597$	−12.4395	−0.509114
$598$	−34.8590	−1.42549
$599$	13.1755	0.538337	0.269169	−	0.963093i	$-0.413251\pi$
$599$	13.1755	0.538337	0.269169	+	0.963093i	$0.413251\pi$
$600$	11.4929	0.469196
$601$	−11.7942	−0.481096	−0.240548	−	0.970637i	$-0.577327\pi$
$601$	−11.7942	−0.481096	−0.240548	+	0.970637i	$0.577327\pi$
$602$	42.0364	1.71328
$603$	8.03499	0.327210
$604$	32.1088	1.30649
$605$	5.57864	0.226804
$606$	−9.19082	−0.373352
$607$	28.4747	1.15575	0.577877	−	0.816124i	$-0.303881\pi$
$607$	28.4747	1.15575	0.577877	+	0.816124i	$0.303881\pi$
$608$	−1.09140	−0.0442619
$609$	−2.70107	−0.109453
$610$	5.35267	0.216723
$611$	−33.1225	−1.33999
$612$	11.7948	0.476777
$613$	25.2323	1.01912	0.509562	−	0.860434i	$-0.329808\pi$
$613$	25.2323	1.01912	0.509562	+	0.860434i	$0.329808\pi$
$614$	42.9579	1.73364
$615$	−0.989963	−0.0399192
$616$	3.91995	0.157939
$617$	32.1226	1.29321	0.646603	−	0.762827i	$-0.276189\pi$
$617$	32.1226	1.29321	0.646603	+	0.762827i	$0.276189\pi$
$618$	7.59222	0.305404
$619$	−10.0797	−0.405138	−0.202569	−	0.979268i	$-0.564929\pi$
$619$	−10.0797	−0.405138	−0.202569	+	0.979268i	$0.564929\pi$
$620$	3.72953	0.149782
$621$	13.0891	0.525246
$622$	−12.0025	−0.481256
$623$	24.8072	0.993881
$624$	−4.46941	−0.178920
$625$	20.9215	0.836860
$626$	64.1482	2.56388
$627$	0.127809	0.00510421
$628$	−48.4129	−1.93188
$629$	−6.20211	−0.247295
$630$	−5.29897	−0.211116
$631$	−16.1451	−0.642726	−0.321363	−	0.946956i	$-0.604141\pi$
$631$	−16.1451	−0.642726	−0.321363	+	0.946956i	$0.604141\pi$
$632$	−18.2339	−0.725306
$633$	8.33196	0.331166
$634$	−45.0541	−1.78933
$635$	−7.65059	−0.303605
$636$	12.2684	0.486474
$637$	17.4290	0.690561
$638$	−3.76796	−0.149175
$639$	−16.9421	−0.670218
$640$	−10.8205	−0.427717
$641$	11.1707	0.441217	0.220608	−	0.975362i	$-0.429196\pi$
$641$	11.1707	0.441217	0.220608	+	0.975362i	$0.429196\pi$
$642$	−12.4704	−0.492169
$643$	−41.0142	−1.61744	−0.808722	−	0.588191i	$-0.799840\pi$
$643$	−41.0142	−1.61744	−0.808722	+	0.588191i	$0.799840\pi$
$644$	−21.4102	−0.843682
$645$	3.67874	0.144850
$646$	−0.937578	−0.0368885
$647$	−2.94961	−0.115961	−0.0579806	−	0.998318i	$-0.518466\pi$
$647$	−2.94961	−0.115961	−0.0579806	+	0.998318i	$0.518466\pi$
$648$	−20.1816	−0.792808
$649$	−3.51299	−0.137897
$650$	−45.5545	−1.78679
$651$	−2.11940	−0.0830658
$652$	62.1628	2.43448
$653$	18.7782	0.734847	0.367424	−	0.930054i	$-0.380240\pi$
$653$	18.7782	0.734847	0.367424	+	0.930054i	$0.380240\pi$
$654$	11.7252	0.458490
$655$	2.18118	0.0852256
$656$	4.88732	0.190818
$657$	−2.51086	−0.0979581
$658$	−31.6901	−1.23541
$659$	33.6369	1.31031	0.655153	−	0.755496i	$-0.272604\pi$
$659$	33.6369	1.31031	0.655153	+	0.755496i	$0.272604\pi$
$660$	0.775667	0.0301928
$661$	−13.3413	−0.518915	−0.259457	−	0.965755i	$-0.583544\pi$
$661$	−13.3413	−0.518915	−0.259457	+	0.965755i	$0.583544\pi$
$662$	21.9098	0.851549
$663$	3.37970	0.131257
$664$	−48.1476	−1.86849
$665$	0.270404	0.0104858
$666$	29.6303	1.14815
$667$	9.10177	0.352422
$668$	−16.7386	−0.647636
$669$	14.1972	0.548895
$670$	−3.87628	−0.149754
$671$	−2.72399	−0.105159
$672$	3.76403	0.145201
$673$	−0.197926	−0.00762950	−0.00381475	−	0.999993i	$-0.501214\pi$
$673$	−0.197926	−0.00762950	−0.00381475	+	0.999993i	$0.501214\pi$
$674$	47.1801	1.81731
$675$	17.1050	0.658373
$676$	13.1052	0.504045
$677$	10.9735	0.421745	0.210872	−	0.977514i	$-0.432370\pi$
$677$	10.9735	0.421745	0.210872	+	0.977514i	$0.432370\pi$
$678$	−11.7717	−0.452089
$679$	18.9643	0.727784
$680$	−2.51651	−0.0965039
$681$	2.27427	0.0871501
$682$	−2.95654	−0.113212
$683$	30.6641	1.17333	0.586664	−	0.809830i	$-0.300441\pi$
$683$	30.6641	1.17333	0.586664	+	0.809830i	$0.300441\pi$
$684$	2.87547	0.109946
$685$	5.46855	0.208943
$686$	44.0069	1.68019
$687$	−11.3936	−0.434691
$688$	−18.1615	−0.692400
$689$	−21.5064	−0.819328
$690$	−2.91870	−0.111113
$691$	18.6644	0.710026	0.355013	−	0.934861i	$-0.384476\pi$
$691$	18.6644	0.710026	0.355013	+	0.934861i	$0.384476\pi$
$692$	−35.8420	−1.36251
$693$	2.69666	0.102438
$694$	−54.8866	−2.08347
$695$	−7.67540	−0.291145
$696$	6.12828	0.232292
$697$	−3.69572	−0.139985
$698$	47.2016	1.78661
$699$	−2.55297	−0.0965622
$700$	−27.9793	−1.05752
$701$	−14.2851	−0.539541	−0.269770	−	0.962925i	$-0.586948\pi$
$701$	−14.2851	−0.539541	−0.269770	+	0.962925i	$0.586948\pi$
$702$	−34.9319	−1.31842
$703$	−1.51202	−0.0570269
$704$	7.38659	0.278392
$705$	−2.77330	−0.104449
$706$	−14.6409	−0.551017
$707$	9.89556	0.372161
$708$	12.9190	0.485527
$709$	16.7757	0.630024	0.315012	−	0.949088i	$-0.397992\pi$
$709$	16.7757	0.630024	0.315012	+	0.949088i	$0.397992\pi$
$710$	8.17327	0.306737
$711$	−12.5437	−0.470425
$712$	−56.2836	−2.10932
$713$	7.14173	0.267460
$714$	3.23354	0.121012
$715$	−1.35974	−0.0508513
$716$	58.8467	2.19920
$717$	−15.3238	−0.572276
$718$	−66.0769	−2.46597
$719$	−17.9755	−0.670373	−0.335187	−	0.942152i	$-0.608799\pi$
$719$	−17.9755	−0.670373	−0.335187	+	0.942152i	$0.608799\pi$
$720$	2.28938	0.0853200
$721$	−8.17437	−0.304430
$722$	44.6770	1.66271
$723$	2.47337	0.0919855
$724$	31.7765	1.18096
$725$	11.8944	0.441746
$726$	16.2634	0.603591
$727$	12.5687	0.466146	0.233073	−	0.972459i	$-0.425122\pi$
$727$	12.5687	0.466146	0.233073	+	0.972459i	$0.425122\pi$
$728$	25.2705	0.936587
$729$	−6.82987	−0.252958
$730$	1.21130	0.0448323
$731$	13.7334	0.507949
$732$	10.0175	0.370257
$733$	−15.9789	−0.590194	−0.295097	−	0.955467i	$-0.595352\pi$
$733$	−15.9789	−0.590194	−0.295097	+	0.955467i	$0.595352\pi$
$734$	−17.5762	−0.648748
$735$	1.45930	0.0538273
$736$	−12.6837	−0.467526
$737$	1.97265	0.0726635
$738$	17.6561	0.649930
$739$	−39.0078	−1.43493	−0.717463	−	0.696596i	$-0.754697\pi$
$739$	−39.0078	−1.43493	−0.717463	+	0.696596i	$0.754697\pi$
$740$	−9.17635	−0.337329
$741$	0.823939	0.0302682
$742$	−20.5764	−0.755382
$743$	26.5753	0.974952	0.487476	−	0.873136i	$-0.337918\pi$
$743$	26.5753	0.974952	0.487476	+	0.873136i	$0.337918\pi$
$744$	4.80857	0.176291
$745$	0.457429	0.0167589
$746$	−15.3997	−0.563821
$747$	−33.1223	−1.21188
$748$	2.89571	0.105878
$749$	13.4266	0.490599
$750$	−7.85214	−0.286720
$751$	−23.4259	−0.854822	−0.427411	−	0.904057i	$-0.640574\pi$
$751$	−23.4259	−0.854822	−0.427411	+	0.904057i	$0.640574\pi$
$752$	13.6915	0.499276
$753$	9.78483	0.356579
$754$	−24.2907	−0.884614
$755$	−4.71279	−0.171516
$756$	−21.4550	−0.780310
$757$	40.0411	1.45532	0.727659	−	0.685939i	$-0.240608\pi$
$757$	40.0411	1.45532	0.727659	+	0.685939i	$0.240608\pi$
$758$	−23.4219	−0.850723
$759$	1.48534	0.0539143
$760$	−0.613503	−0.0222541
$761$	−16.7667	−0.607792	−0.303896	−	0.952705i	$-0.598287\pi$
$761$	−16.7667	−0.607792	−0.303896	+	0.952705i	$0.598287\pi$
$762$	−22.3038	−0.807980
$763$	−12.6242	−0.457027
$764$	−41.9213	−1.51666
$765$	−1.73119	−0.0625913
$766$	1.49490	0.0540129
$767$	−22.6470	−0.817734
$768$	−16.3944	−0.591580
$769$	30.6719	1.10606	0.553028	−	0.833163i	$-0.313472\pi$
$769$	30.6719	1.10606	0.553028	+	0.833163i	$0.313472\pi$
$770$	−1.30094	−0.0468825
$771$	−20.1973	−0.727389
$772$	33.4001	1.20209
$773$	−16.3817	−0.589210	−0.294605	−	0.955619i	$-0.595188\pi$
$773$	−16.3817	−0.589210	−0.294605	+	0.955619i	$0.595188\pi$
$774$	−65.6107	−2.35833
$775$	9.33295	0.335249
$776$	−43.0269	−1.54458
$777$	5.21469	0.187076
$778$	14.6083	0.523733
$779$	−0.900982	−0.0322810
$780$	5.00044	0.179044
$781$	−4.15940	−0.148835
$782$	−10.8961	−0.389642
$783$	9.12079	0.325951
$784$	−7.20441	−0.257300
$785$	7.10583	0.253618
$786$	6.35878	0.226810
$787$	−30.2666	−1.07889	−0.539444	−	0.842022i	$-0.681365\pi$
$787$	−30.2666	−1.07889	−0.539444	+	0.842022i	$0.681365\pi$
$788$	−54.2952	−1.93419
$789$	−5.66391	−0.201640
$790$	6.05139	0.215299
$791$	12.6743	0.450647
$792$	−6.11829	−0.217404
$793$	−17.5606	−0.623594
$794$	−35.8734	−1.27310
$795$	−1.80070	−0.0638643
$796$	−68.7088	−2.43532
$797$	31.5290	1.11681	0.558406	−	0.829567i	$-0.311413\pi$
$797$	31.5290	1.11681	0.558406	+	0.829567i	$0.311413\pi$
$798$	0.788308	0.0279058
$799$	−10.3533	−0.366272
$800$	−16.5752	−0.586023
$801$	−38.7193	−1.36808
$802$	−79.0059	−2.78980
$803$	−0.616435	−0.0217535
$804$	−7.25442	−0.255844
$805$	3.14250	0.110759
$806$	−19.0597	−0.671351
$807$	−20.1543	−0.709465
$808$	−22.4514	−0.789838
$809$	10.0219	0.352352	0.176176	−	0.984359i	$-0.443627\pi$
$809$	10.0219	0.352352	0.176176	+	0.984359i	$0.443627\pi$
$810$	6.69778	0.235336
$811$	−28.8994	−1.01479	−0.507397	−	0.861712i	$-0.669392\pi$
$811$	−28.8994	−1.01479	−0.507397	+	0.861712i	$0.669392\pi$
$812$	−14.9192	−0.523561
$813$	5.65509	0.198333
$814$	7.27445	0.254969
$815$	−9.12398	−0.319599
$816$	−1.39702	−0.0489057
$817$	3.34808	0.117135
$818$	−0.965121	−0.0337447
$819$	17.3844	0.607460
$820$	−5.46801	−0.190951
$821$	−48.9801	−1.70942	−0.854709	−	0.519107i	$-0.826265\pi$
$821$	−48.9801	−1.70942	−0.854709	+	0.519107i	$0.826265\pi$
$822$	15.9424	0.556057
$823$	−2.10161	−0.0732576	−0.0366288	−	0.999329i	$-0.511662\pi$
$823$	−2.10161	−0.0732576	−0.0366288	+	0.999329i	$0.511662\pi$
$824$	18.5463	0.646092
$825$	1.94106	0.0675792
$826$	−21.6676	−0.753912
$827$	8.59211	0.298777	0.149388	−	0.988779i	$-0.452269\pi$
$827$	8.59211	0.298777	0.149388	+	0.988779i	$0.452269\pi$
$828$	33.4172	1.16133
$829$	6.46277	0.224461	0.112231	−	0.993682i	$-0.464200\pi$
$829$	6.46277	0.224461	0.112231	+	0.993682i	$0.464200\pi$
$830$	15.9790	0.554639
$831$	20.0863	0.696787
$832$	47.6186	1.65088
$833$	5.44786	0.188757
$834$	−22.3761	−0.774820
$835$	2.45682	0.0850217
$836$	0.705948	0.0244157
$837$	7.15666	0.247370
$838$	58.7282	2.02873
$839$	−28.6908	−0.990515	−0.495257	−	0.868746i	$-0.664926\pi$
$839$	−28.6908	−0.990515	−0.495257	+	0.868746i	$0.664926\pi$
$840$	2.11586	0.0730043
$841$	−22.6577	−0.781298
$842$	15.3233	0.528074
$843$	20.8848	0.719311
$844$	46.0212	1.58411
$845$	−1.92352	−0.0661711
$846$	49.4622	1.70054
$847$	−17.5104	−0.601665
$848$	8.88984	0.305278
$849$	−7.36020	−0.252601
$850$	−14.2392	−0.488400
$851$	−17.5719	−0.602358
$852$	15.2962	0.524040
$853$	23.8723	0.817371	0.408686	−	0.912675i	$-0.365987\pi$
$853$	23.8723	0.817371	0.408686	+	0.912675i	$0.365987\pi$
$854$	−16.8012	−0.574924
$855$	−0.422048	−0.0144337
$856$	−30.4629	−1.04120
$857$	−37.1228	−1.26809	−0.634045	−	0.773296i	$-0.718607\pi$
$857$	−37.1228	−1.26809	−0.634045	+	0.773296i	$0.718607\pi$
$858$	−3.96404	−0.135330
$859$	−20.2360	−0.690442	−0.345221	−	0.938521i	$-0.612196\pi$
$859$	−20.2360	−0.690442	−0.345221	+	0.938521i	$0.612196\pi$
$860$	20.3193	0.692883
$861$	3.10733	0.105898
$862$	−8.22769	−0.280236
$863$	−31.4426	−1.07032	−0.535159	−	0.844751i	$-0.679748\pi$
$863$	−31.4426	−1.07032	−0.535159	+	0.844751i	$0.679748\pi$
$864$	−12.7102	−0.432408
$865$	5.26073	0.178870
$866$	−39.7579	−1.35103
$867$	−9.98025	−0.338947
$868$	−11.7064	−0.397341
$869$	−3.07957	−0.104467
$870$	−2.03382	−0.0689531
$871$	12.7169	0.430897
$872$	28.6423	0.969950
$873$	−29.5996	−1.00180
$874$	−2.65636	−0.0898527
$875$	8.45423	0.285805
$876$	2.26694	0.0765929
$877$	−42.6242	−1.43932	−0.719659	−	0.694328i	$-0.755702\pi$
$877$	−42.6242	−1.43932	−0.719659	+	0.694328i	$0.755702\pi$
$878$	68.3778	2.30764
$879$	3.28131	0.110676
$880$	0.562059	0.0189470
$881$	−26.2582	−0.884661	−0.442330	−	0.896852i	$-0.645848\pi$
$881$	−26.2582	−0.884661	−0.442330	+	0.896852i	$0.645848\pi$
$882$	−26.0269	−0.876370
$883$	−30.4910	−1.02610	−0.513052	−	0.858357i	$-0.671485\pi$
$883$	−30.4910	−1.02610	−0.513052	+	0.858357i	$0.671485\pi$
$884$	18.6676	0.627859
$885$	−1.89620	−0.0637401
$886$	−34.6519	−1.16415
$887$	−19.5268	−0.655644	−0.327822	−	0.944739i	$-0.606315\pi$
$887$	−19.5268	−0.655644	−0.327822	+	0.944739i	$0.606315\pi$
$888$	−11.8313	−0.397032
$889$	24.0140	0.805402
$890$	18.6791	0.626126
$891$	−3.40852	−0.114190
$892$	78.4175	2.62561
$893$	−2.52403	−0.0844635
$894$	1.33354	0.0446003
$895$	−8.63726	−0.288712
$896$	33.9637	1.13465
$897$	9.57541	0.319713
$898$	−52.9502	−1.76697
$899$	4.97654	0.165977
$900$	43.6703	1.45568
$901$	−6.72236	−0.223954
$902$	4.33470	0.144330
$903$	−11.5470	−0.384259
$904$	−28.7560	−0.956410
$905$	−4.66401	−0.155037
$906$	−13.7392	−0.456454
$907$	24.1460	0.801756	0.400878	−	0.916131i	$-0.368705\pi$
$907$	24.1460	0.801756	0.400878	+	0.916131i	$0.368705\pi$
$908$	12.5618	0.416878
$909$	−15.4450	−0.512280
$910$	−8.38665	−0.278015
$911$	−28.5199	−0.944907	−0.472453	−	0.881356i	$-0.656631\pi$
$911$	−28.5199	−0.944907	−0.472453	+	0.881356i	$0.656631\pi$
$912$	−0.340582	−0.0112778
$913$	−8.13176	−0.269122
$914$	−77.8219	−2.57412
$915$	−1.47032	−0.0486074
$916$	−62.9317	−2.07932
$917$	−6.84636	−0.226087
$918$	−10.9188	−0.360375
$919$	−38.8303	−1.28089	−0.640446	−	0.768003i	$-0.721251\pi$
$919$	−38.8303	−1.28089	−0.640446	+	0.768003i	$0.721251\pi$
$920$	−7.12982	−0.235063
$921$	−11.8001	−0.388826
$922$	−28.8679	−0.950712
$923$	−26.8141	−0.882598
$924$	−2.43469	−0.0800955
$925$	−22.9633	−0.755029
$926$	−95.9572	−3.15335
$927$	12.7586	0.419048
$928$	−8.83829	−0.290131
$929$	−13.3814	−0.439029	−0.219514	−	0.975609i	$-0.570447\pi$
$929$	−13.3814	−0.439029	−0.219514	+	0.975609i	$0.570447\pi$
$930$	−1.59585	−0.0523299
$931$	1.32814	0.0435280
$932$	−14.1012	−0.461900
$933$	3.29696	0.107938
$934$	−73.9307	−2.41909
$935$	−0.425020	−0.0138996
$936$	−39.4423	−1.28921
$937$	33.2360	1.08577	0.542887	−	0.839806i	$-0.317331\pi$
$937$	33.2360	1.08577	0.542887	+	0.839806i	$0.317331\pi$
$938$	12.1670	0.397267
$939$	−17.6208	−0.575034
$940$	−15.3182	−0.499625
$941$	16.6981	0.544344	0.272172	−	0.962249i	$-0.412258\pi$
$941$	16.6981	0.544344	0.272172	+	0.962249i	$0.412258\pi$
$942$	20.7156	0.674951
$943$	−10.4708	−0.340975
$944$	9.36130	0.304684
$945$	3.14907	0.102439
$946$	−16.1079	−0.523713
$947$	−41.6671	−1.35400	−0.676999	−	0.735984i	$-0.736720\pi$
$947$	−41.6671	−1.35400	−0.676999	+	0.735984i	$0.736720\pi$
$948$	11.3251	0.367823
$949$	−3.97393	−0.128999
$950$	−3.47138	−0.112626
$951$	12.3759	0.401315
$952$	7.89892	0.256006
$953$	−0.601559	−0.0194864	−0.00974321	−	0.999953i	$-0.503101\pi$
$953$	−0.601559	−0.0194864	−0.00974321	+	0.999953i	$0.503101\pi$
$954$	32.1157	1.03978
$955$	6.15302	0.199107
$956$	−84.6400	−2.73745
$957$	1.03502	0.0334574
$958$	−47.6149	−1.53837
$959$	−17.1649	−0.554283
$960$	3.98704	0.128681
$961$	−27.0951	−0.874037
$962$	46.8957	1.51198
$963$	−20.9564	−0.675310
$964$	13.6615	0.440008
$965$	−4.90231	−0.157811
$966$	9.16132	0.294761
$967$	42.4904	1.36640	0.683199	−	0.730232i	$-0.260588\pi$
$967$	42.4904	1.36640	0.683199	+	0.730232i	$0.260588\pi$
$968$	39.7283	1.27692
$969$	0.257543	0.00827346
$970$	14.2796	0.458490
$971$	−53.6985	−1.72327	−0.861633	−	0.507531i	$-0.830558\pi$
$971$	−53.6985	−1.72327	−0.861633	+	0.507531i	$0.830558\pi$
$972$	51.4957	1.65172
$973$	24.0918	0.772349
$974$	14.9538	0.479150
$975$	12.5133	0.400747
$976$	7.25880	0.232349
$977$	52.4695	1.67865	0.839324	−	0.543632i	$-0.182951\pi$
$977$	52.4695	1.67865	0.839324	+	0.543632i	$0.182951\pi$
$978$	−26.5991	−0.850546
$979$	−9.50587	−0.303809
$980$	8.06039	0.257480
$981$	19.7039	0.629099
$982$	91.3577	2.91534
$983$	21.0306	0.670772	0.335386	−	0.942081i	$-0.391133\pi$
$983$	21.0306	0.670772	0.335386	+	0.942081i	$0.391133\pi$
$984$	−7.05003	−0.224747
$985$	7.96921	0.253920
$986$	−7.59265	−0.241799
$987$	8.70495	0.277082
$988$	4.55099	0.144786
$989$	38.9097	1.23726
$990$	2.03051	0.0645338
$991$	−13.7116	−0.435563	−0.217782	−	0.975998i	$-0.569882\pi$
$991$	−13.7116	−0.435563	−0.217782	+	0.975998i	$0.569882\pi$
$992$	−6.93499	−0.220186
$993$	−6.01840	−0.190988
$994$	−25.6546	−0.813713
$995$	10.0848	0.319709
$996$	29.9046	0.947562
$997$	23.1884	0.734385	0.367192	−	0.930145i	$-0.380319\pi$
$997$	23.1884	0.734385	0.367192	+	0.930145i	$0.380319\pi$
$998$	−89.9329	−2.84678
$999$	−17.6086	−0.557113

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4027.2.a.c.1.18	✓	174

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4027.2.a.c.1.18	✓	174	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:	\( N \)	\(=\)	\( 4027 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4027.a (trivial)

\(f(q)\)	\(=\)	\(q-2.36345 q^{2} +0.649215 q^{3} +3.58591 q^{4} -0.526324 q^{5} -1.53439 q^{6} +1.65204 q^{7} -3.74822 q^{8} -2.57852 q^{9} +O(q^{10})\)	\(q-2.36345 q^{2} +0.649215 q^{3} +3.58591 q^{4} -0.526324 q^{5} -1.53439 q^{6} +1.65204 q^{7} -3.74822 q^{8} -2.57852 q^{9} +1.24394 q^{10} -0.633045 q^{11} +2.32803 q^{12} -4.08101 q^{13} -3.90453 q^{14} -0.341697 q^{15} +1.68692 q^{16} -1.27562 q^{17} +6.09421 q^{18} -0.310985 q^{19} -1.88735 q^{20} +1.07253 q^{21} +1.49617 q^{22} -3.61411 q^{23} -2.43340 q^{24} -4.72298 q^{25} +9.64527 q^{26} -3.62166 q^{27} +5.92408 q^{28} -2.51840 q^{29} +0.807585 q^{30} -1.97607 q^{31} +3.50948 q^{32} -0.410983 q^{33} +3.01487 q^{34} -0.869510 q^{35} -9.24633 q^{36} +4.86204 q^{37} +0.734997 q^{38} -2.64945 q^{39} +1.97278 q^{40} +2.89719 q^{41} -2.53488 q^{42} -10.7661 q^{43} -2.27004 q^{44} +1.35714 q^{45} +8.54177 q^{46} +8.11626 q^{47} +1.09517 q^{48} -4.27075 q^{49} +11.1625 q^{50} -0.828153 q^{51} -14.6341 q^{52} +5.26987 q^{53} +8.55962 q^{54} +0.333187 q^{55} -6.19222 q^{56} -0.201896 q^{57} +5.95212 q^{58} +5.54935 q^{59} -1.22530 q^{60} +4.30300 q^{61} +4.67035 q^{62} -4.25983 q^{63} -11.6683 q^{64} +2.14793 q^{65} +0.971338 q^{66} -3.11613 q^{67} -4.57426 q^{68} -2.34633 q^{69} +2.05504 q^{70} +6.57046 q^{71} +9.66485 q^{72} +0.973762 q^{73} -11.4912 q^{74} -3.06623 q^{75} -1.11516 q^{76} -1.04582 q^{77} +6.26186 q^{78} +4.86469 q^{79} -0.887864 q^{80} +5.38432 q^{81} -6.84738 q^{82} +12.8455 q^{83} +3.84600 q^{84} +0.671389 q^{85} +25.4451 q^{86} -1.63498 q^{87} +2.37279 q^{88} +15.0161 q^{89} -3.20753 q^{90} -6.74200 q^{91} -12.9599 q^{92} -1.28290 q^{93} -19.1824 q^{94} +0.163679 q^{95} +2.27841 q^{96} +11.4793 q^{97} +10.0937 q^{98} +1.63232 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 174 q + 21 q^{2} + 17 q^{3} + 187 q^{4} + 72 q^{5} + 21 q^{6} + 24 q^{7} + 54 q^{8} + 197 q^{9}+O(q^{10}) \) 174 * q + 21 * q^2 + 17 * q^3 + 187 * q^4 + 72 * q^5 + 21 * q^6 + 24 * q^7 + 54 * q^8 + 197 * q^9	\( 174 q + 21 q^{2} + 17 q^{3} + 187 q^{4} + 72 q^{5} + 21 q^{6} + 24 q^{7} + 54 q^{8} + 197 q^{9} + 20 q^{10} + 35 q^{11} + 23 q^{12} + 91 q^{13} + 18 q^{14} + 16 q^{15} + 201 q^{16} + 148 q^{17} + 39 q^{18} + 36 q^{19} + 128 q^{20} + 57 q^{21} + 17 q^{22} + 96 q^{23} + 24 q^{24} + 226 q^{25} + 44 q^{26} + 62 q^{27} + 32 q^{28} + 122 q^{29} + 25 q^{30} + 23 q^{31} + 104 q^{32} + 91 q^{33} + 6 q^{34} + 80 q^{35} + 222 q^{36} + 71 q^{37} + 125 q^{38} + 16 q^{39} + 53 q^{40} + 97 q^{41} + 14 q^{42} + 38 q^{43} + 70 q^{44} + 185 q^{45} - 23 q^{46} + 110 q^{47} + 36 q^{48} + 210 q^{49} + 51 q^{50} + 33 q^{51} + 118 q^{52} + 214 q^{53} + 8 q^{54} + 37 q^{55} + 41 q^{56} + 76 q^{57} + 2 q^{58} + 66 q^{59} - 12 q^{60} + 114 q^{61} + 175 q^{62} + 62 q^{63} + 190 q^{64} + 128 q^{65} + 12 q^{66} - 6 q^{67} + 348 q^{68} + 115 q^{69} - 38 q^{70} + 54 q^{71} + 101 q^{72} + 107 q^{73} + 71 q^{74} - q^{75} + 31 q^{76} + 368 q^{77} - 14 q^{78} - 14 q^{79} + 205 q^{80} + 222 q^{81} + 26 q^{82} + 246 q^{83} + 41 q^{84} + 87 q^{85} + 33 q^{86} + 100 q^{87} - 6 q^{88} + 147 q^{89} + 50 q^{90} - 23 q^{91} + 189 q^{92} + 117 q^{93} + 23 q^{94} + 42 q^{95} + 38 q^{96} + 52 q^{97} + 148 q^{98} + 38 q^{99}+O(q^{100}) \) 174 * q + 21 * q^2 + 17 * q^3 + 187 * q^4 + 72 * q^5 + 21 * q^6 + 24 * q^7 + 54 * q^8 + 197 * q^9 + 20 * q^10 + 35 * q^11 + 23 * q^12 + 91 * q^13 + 18 * q^14 + 16 * q^15 + 201 * q^16 + 148 * q^17 + 39 * q^18 + 36 * q^19 + 128 * q^20 + 57 * q^21 + 17 * q^22 + 96 * q^23 + 24 * q^24 + 226 * q^25 + 44 * q^26 + 62 * q^27 + 32 * q^28 + 122 * q^29 + 25 * q^30 + 23 * q^31 + 104 * q^32 + 91 * q^33 + 6 * q^34 + 80 * q^35 + 222 * q^36 + 71 * q^37 + 125 * q^38 + 16 * q^39 + 53 * q^40 + 97 * q^41 + 14 * q^42 + 38 * q^43 + 70 * q^44 + 185 * q^45 - 23 * q^46 + 110 * q^47 + 36 * q^48 + 210 * q^49 + 51 * q^50 + 33 * q^51 + 118 * q^52 + 214 * q^53 + 8 * q^54 + 37 * q^55 + 41 * q^56 + 76 * q^57 + 2 * q^58 + 66 * q^59 - 12 * q^60 + 114 * q^61 + 175 * q^62 + 62 * q^63 + 190 * q^64 + 128 * q^65 + 12 * q^66 - 6 * q^67 + 348 * q^68 + 115 * q^69 - 38 * q^70 + 54 * q^71 + 101 * q^72 + 107 * q^73 + 71 * q^74 - q^75 + 31 * q^76 + 368 * q^77 - 14 * q^78 - 14 * q^79 + 205 * q^80 + 222 * q^81 + 26 * q^82 + 246 * q^83 + 41 * q^84 + 87 * q^85 + 33 * q^86 + 100 * q^87 - 6 * q^88 + 147 * q^89 + 50 * q^90 - 23 * q^91 + 189 * q^92 + 117 * q^93 + 23 * q^94 + 42 * q^95 + 38 * q^96 + 52 * q^97 + 148 * q^98 + 38 * q^99

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