LMFDB - Embedded newform 4027.2.a.c.1.5

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			1.5
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)

$f(q)$	$=$	$q-2.64301 q^{2} +3.39832 q^{3} +4.98550 q^{4} -0.538898 q^{5} -8.98178 q^{6} -0.766621 q^{7} -7.89070 q^{8} +8.54855 q^{9} +O(q^{10})$	\(q-2.64301 q^{2} +3.39832 q^{3} +4.98550 q^{4} -0.538898 q^{5} -8.98178 q^{6} -0.766621 q^{7} -7.89070 q^{8} +8.54855 q^{9} +1.42431 q^{10} +3.53118 q^{11} +16.9423 q^{12} +5.95840 q^{13} +2.02619 q^{14} -1.83135 q^{15} +10.8842 q^{16} +4.30030 q^{17} -22.5939 q^{18} -3.03480 q^{19} -2.68668 q^{20} -2.60522 q^{21} -9.33293 q^{22} -0.904445 q^{23} -26.8151 q^{24} -4.70959 q^{25} -15.7481 q^{26} +18.8557 q^{27} -3.82199 q^{28} +6.07098 q^{29} +4.84027 q^{30} -4.27899 q^{31} -12.9856 q^{32} +12.0001 q^{33} -11.3657 q^{34} +0.413131 q^{35} +42.6188 q^{36} +2.39736 q^{37} +8.02101 q^{38} +20.2485 q^{39} +4.25228 q^{40} -1.40672 q^{41} +6.88562 q^{42} +1.33175 q^{43} +17.6047 q^{44} -4.60680 q^{45} +2.39046 q^{46} -3.59450 q^{47} +36.9879 q^{48} -6.41229 q^{49} +12.4475 q^{50} +14.6138 q^{51} +29.7056 q^{52} +12.2518 q^{53} -49.8358 q^{54} -1.90295 q^{55} +6.04918 q^{56} -10.3132 q^{57} -16.0457 q^{58} +4.29260 q^{59} -9.13017 q^{60} +7.02427 q^{61} +11.3094 q^{62} -6.55350 q^{63} +12.5527 q^{64} -3.21097 q^{65} -31.7163 q^{66} -13.8068 q^{67} +21.4391 q^{68} -3.07359 q^{69} -1.09191 q^{70} +6.80216 q^{71} -67.4540 q^{72} +3.02047 q^{73} -6.33623 q^{74} -16.0047 q^{75} -15.1300 q^{76} -2.70707 q^{77} -53.5170 q^{78} -6.52080 q^{79} -5.86547 q^{80} +38.4320 q^{81} +3.71797 q^{82} -11.5643 q^{83} -12.9883 q^{84} -2.31742 q^{85} -3.51984 q^{86} +20.6311 q^{87} -27.8635 q^{88} -4.54173 q^{89} +12.1758 q^{90} -4.56783 q^{91} -4.50911 q^{92} -14.5414 q^{93} +9.50028 q^{94} +1.63545 q^{95} -44.1292 q^{96} -9.25650 q^{97} +16.9477 q^{98} +30.1864 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.64301	−1.86889	−0.934445	−	0.356108i	$-0.884104\pi$
$2$	−2.64301	−1.86889	−0.934445	+	0.356108i	$0.884104\pi$
$3$	3.39832	1.96202	0.981009	−	0.193961i	$-0.0621335\pi$
$3$	3.39832	1.96202	0.981009	+	0.193961i	$0.0621335\pi$
$4$	4.98550	2.49275
$5$	−0.538898	−0.241003	−0.120501	−	0.992713i	$-0.538450\pi$
$5$	−0.538898	−0.241003	−0.120501	+	0.992713i	$0.538450\pi$
$6$	−8.98178	−3.66680
$7$	−0.766621	−0.289756	−0.144878	−	0.989450i	$-0.546279\pi$
$7$	−0.766621	−0.289756	−0.144878	+	0.989450i	$0.546279\pi$
$8$	−7.89070	−2.78978
$9$	8.54855	2.84952
$10$	1.42431	0.450407
$11$	3.53118	1.06469	0.532345	−	0.846527i	$-0.321311\pi$
$11$	3.53118	1.06469	0.532345	+	0.846527i	$0.321311\pi$
$12$	16.9423	4.89082
$13$	5.95840	1.65256	0.826281	−	0.563258i	$-0.190452\pi$
$13$	5.95840	1.65256	0.826281	+	0.563258i	$0.190452\pi$
$14$	2.02619	0.541521
$15$	−1.83135	−0.472852
$16$	10.8842	2.72105
$17$	4.30030	1.04298	0.521488	−	0.853259i	$-0.325377\pi$
$17$	4.30030	1.04298	0.521488	+	0.853259i	$0.325377\pi$
$18$	−22.5939	−5.32543
$19$	−3.03480	−0.696232	−0.348116	−	0.937452i	$-0.613178\pi$
$19$	−3.03480	−0.696232	−0.348116	+	0.937452i	$0.613178\pi$
$20$	−2.68668	−0.600759
$21$	−2.60522	−0.568506
$22$	−9.33293	−1.98979
$23$	−0.904445	−0.188590	−0.0942950	−	0.995544i	$-0.530060\pi$
$23$	−0.904445	−0.188590	−0.0942950	+	0.995544i	$0.530060\pi$
$24$	−26.8151	−5.47361
$25$	−4.70959	−0.941918
$26$	−15.7481	−3.08846
$27$	18.8557	3.62879
$28$	−3.82199	−0.722288
$29$	6.07098	1.12735	0.563676	−	0.825996i	$-0.309387\pi$
$29$	6.07098	1.12735	0.563676	+	0.825996i	$0.309387\pi$
$30$	4.84027	0.883707
$31$	−4.27899	−0.768529	−0.384265	−	0.923223i	$-0.625545\pi$
$31$	−4.27899	−0.768529	−0.384265	+	0.923223i	$0.625545\pi$
$32$	−12.9856	−2.29556
$33$	12.0001	2.08894
$34$	−11.3657	−1.94921
$35$	0.413131	0.0698318
$36$	42.6188	7.10313
$37$	2.39736	0.394123	0.197061	−	0.980391i	$-0.436860\pi$
$37$	2.39736	0.394123	0.197061	+	0.980391i	$0.436860\pi$
$38$	8.02101	1.30118
$39$	20.2485	3.24236
$40$	4.25228	0.672345
$41$	−1.40672	−0.219692	−0.109846	−	0.993949i	$-0.535036\pi$
$41$	−1.40672	−0.219692	−0.109846	+	0.993949i	$0.535036\pi$
$42$	6.88562	1.06247
$43$	1.33175	0.203091	0.101545	−	0.994831i	$-0.467621\pi$
$43$	1.33175	0.203091	0.101545	+	0.994831i	$0.467621\pi$
$44$	17.6047	2.65400
$45$	−4.60680	−0.686741
$46$	2.39046	0.352454
$47$	−3.59450	−0.524311	−0.262155	−	0.965026i	$-0.584433\pi$
$47$	−3.59450	−0.524311	−0.262155	+	0.965026i	$0.584433\pi$
$48$	36.9879	5.33875
$49$	−6.41229	−0.916042
$50$	12.4475	1.76034
$51$	14.6138	2.04634
$52$	29.7056	4.11942
$53$	12.2518	1.68292	0.841458	−	0.540322i	$-0.181698\pi$
$53$	12.2518	1.68292	0.841458	+	0.540322i	$0.181698\pi$
$54$	−49.8358	−6.78180
$55$	−1.90295	−0.256593
$56$	6.04918	0.808355
$57$	−10.3132	−1.36602
$58$	−16.0457	−2.10690
$59$	4.29260	0.558849	0.279424	−	0.960168i	$-0.409856\pi$
$59$	4.29260	0.558849	0.279424	+	0.960168i	$0.409856\pi$
$60$	−9.13017	−1.17870
$61$	7.02427	0.899366	0.449683	−	0.893188i	$-0.351537\pi$
$61$	7.02427	0.899366	0.449683	+	0.893188i	$0.351537\pi$
$62$	11.3094	1.43630
$63$	−6.55350	−0.825663
$64$	12.5527	1.56909
$65$	−3.21097	−0.398272
$66$	−31.7163	−3.90400
$67$	−13.8068	−1.68677	−0.843386	−	0.537308i	$-0.819441\pi$
$67$	−13.8068	−1.68677	−0.843386	+	0.537308i	$0.819441\pi$
$68$	21.4391	2.59988
$69$	−3.07359	−0.370017
$70$	−1.09191	−0.130508
$71$	6.80216	0.807268	0.403634	−	0.914921i	$-0.367747\pi$
$71$	6.80216	0.807268	0.403634	+	0.914921i	$0.367747\pi$
$72$	−67.4540	−7.94953
$73$	3.02047	0.353519	0.176760	−	0.984254i	$-0.443438\pi$
$73$	3.02047	0.353519	0.176760	+	0.984254i	$0.443438\pi$
$74$	−6.33623	−0.736572
$75$	−16.0047	−1.84806
$76$	−15.1300	−1.73553
$77$	−2.70707	−0.308500
$78$	−53.5170	−6.05961
$79$	−6.52080	−0.733647	−0.366823	−	0.930291i	$-0.619555\pi$
$79$	−6.52080	−0.733647	−0.366823	+	0.930291i	$0.619555\pi$
$80$	−5.86547	−0.655780
$81$	38.4320	4.27023
$82$	3.71797	0.410581
$83$	−11.5643	−1.26935	−0.634673	−	0.772781i	$-0.718865\pi$
$83$	−11.5643	−1.26935	−0.634673	+	0.772781i	$0.718865\pi$
$84$	−12.9883	−1.41714
$85$	−2.31742	−0.251360
$86$	−3.51984	−0.379554
$87$	20.6311	2.21189
$88$	−27.8635	−2.97025
$89$	−4.54173	−0.481423	−0.240711	−	0.970597i	$-0.577381\pi$
$89$	−4.54173	−0.481423	−0.240711	+	0.970597i	$0.577381\pi$
$90$	12.1758	1.28344
$91$	−4.56783	−0.478839
$92$	−4.50911	−0.470107
$93$	−14.5414	−1.50787
$94$	9.50028	0.979879
$95$	1.63545	0.167794
$96$	−44.1292	−4.50392
$97$	−9.25650	−0.939855	−0.469928	−	0.882705i	$-0.655720\pi$
$97$	−9.25650	−0.939855	−0.469928	+	0.882705i	$0.655720\pi$
$98$	16.9477	1.71198
$99$	30.1864	3.03385
$100$	−23.4796	−2.34796
$101$	−7.99738	−0.795769	−0.397885	−	0.917435i	$-0.630256\pi$
$101$	−7.99738	−0.795769	−0.397885	+	0.917435i	$0.630256\pi$
$102$	−38.6244	−3.82438
$103$	−7.39298	−0.728452	−0.364226	−	0.931311i	$-0.618666\pi$
$103$	−7.39298	−0.728452	−0.364226	+	0.931311i	$0.618666\pi$
$104$	−47.0159	−4.61029
$105$	1.40395	0.137011
$106$	−32.3817	−3.14519
$107$	6.93047	0.669994	0.334997	−	0.942219i	$-0.391265\pi$
$107$	6.93047	0.669994	0.334997	+	0.942219i	$0.391265\pi$
$108$	94.0052	9.04565
$109$	3.35598	0.321444	0.160722	−	0.987000i	$-0.448618\pi$
$109$	3.35598	0.321444	0.160722	+	0.987000i	$0.448618\pi$
$110$	5.02950	0.479544
$111$	8.14697	0.773276
$112$	−8.34405	−0.788439
$113$	−0.482270	−0.0453682	−0.0226841	−	0.999743i	$-0.507221\pi$
$113$	−0.482270	−0.0453682	−0.0226841	+	0.999743i	$0.507221\pi$
$114$	27.2579	2.55294
$115$	0.487404	0.0454507
$116$	30.2669	2.81021
$117$	50.9356	4.70900
$118$	−11.3454	−1.04443
$119$	−3.29670	−0.302208
$120$	14.4506	1.31915
$121$	1.46921	0.133565
$122$	−18.5652	−1.68082
$123$	−4.78047	−0.431040
$124$	−21.3329	−1.91575
$125$	5.23248	0.468007
$126$	17.3210	1.54307
$127$	4.95900	0.440040	0.220020	−	0.975495i	$-0.429388\pi$
$127$	4.95900	0.440040	0.220020	+	0.975495i	$0.429388\pi$
$128$	−7.20576	−0.636905
$129$	4.52572	0.398468
$130$	8.48662	0.744326
$131$	19.3864	1.69380	0.846900	−	0.531752i	$-0.178466\pi$
$131$	19.3864	1.69380	0.846900	+	0.531752i	$0.178466\pi$
$132$	59.8262	5.20721
$133$	2.32654	0.201737
$134$	36.4916	3.15239
$135$	−10.1613	−0.874547
$136$	−33.9324	−2.90968
$137$	−19.8528	−1.69614	−0.848069	−	0.529887i	$-0.822234\pi$
$137$	−19.8528	−1.69614	−0.848069	+	0.529887i	$0.822234\pi$
$138$	8.12353	0.691521
$139$	−19.8426	−1.68303	−0.841515	−	0.540233i	$-0.818336\pi$
$139$	−19.8426	−1.68303	−0.841515	+	0.540233i	$0.818336\pi$
$140$	2.05966	0.174073
$141$	−12.2152	−1.02871
$142$	−17.9782	−1.50869
$143$	21.0402	1.75947
$144$	93.0441	7.75367
$145$	−3.27164	−0.271695
$146$	−7.98313	−0.660688
$147$	−21.7910	−1.79729
$148$	11.9520	0.982449
$149$	21.5847	1.76828	0.884142	−	0.467218i	$-0.154744\pi$
$149$	21.5847	1.76828	0.884142	+	0.467218i	$0.154744\pi$
$150$	42.3005	3.45382
$151$	9.37910	0.763261	0.381630	−	0.924315i	$-0.375363\pi$
$151$	9.37910	0.763261	0.381630	+	0.924315i	$0.375363\pi$
$152$	23.9467	1.94234
$153$	36.7613	2.97198
$154$	7.15482	0.576552
$155$	2.30594	0.185218
$156$	100.949	8.08238
$157$	−20.7194	−1.65359	−0.826793	−	0.562506i	$-0.809837\pi$
$157$	−20.7194	−1.65359	−0.826793	+	0.562506i	$0.809837\pi$
$158$	17.2345	1.37110
$159$	41.6355	3.30191
$160$	6.99793	0.553235
$161$	0.693367	0.0546450
$162$	−101.576	−7.98058
$163$	3.39625	0.266015	0.133007	−	0.991115i	$-0.457537\pi$
$163$	3.39625	0.266015	0.133007	+	0.991115i	$0.457537\pi$
$164$	−7.01319	−0.547638
$165$	−6.46681	−0.503440
$166$	30.5645	2.37227
$167$	−23.9428	−1.85275	−0.926376	−	0.376601i	$-0.877093\pi$
$167$	−23.9428	−1.85275	−0.926376	+	0.376601i	$0.877093\pi$
$168$	20.5570	1.58601
$169$	22.5025	1.73096
$170$	6.12497	0.469764
$171$	−25.9432	−1.98392
$172$	6.63946	0.506254
$173$	6.60965	0.502522	0.251261	−	0.967919i	$-0.419155\pi$
$173$	6.60965	0.502522	0.251261	+	0.967919i	$0.419155\pi$
$174$	−54.5282	−4.13377
$175$	3.61047	0.272926
$176$	38.4340	2.89707
$177$	14.5876	1.09647
$178$	12.0038	0.899726
$179$	−18.0160	−1.34658	−0.673291	−	0.739378i	$-0.735120\pi$
$179$	−18.0160	−1.34658	−0.673291	+	0.739378i	$0.735120\pi$
$180$	−22.9672	−1.71187
$181$	−5.48461	−0.407668	−0.203834	−	0.979005i	$-0.565340\pi$
$181$	−5.48461	−0.407668	−0.203834	+	0.979005i	$0.565340\pi$
$182$	12.0728	0.894897
$183$	23.8707	1.76457
$184$	7.13671	0.526125
$185$	−1.29193	−0.0949846
$186$	38.4329	2.81804
$187$	15.1851	1.11045
$188$	−17.9203	−1.30698
$189$	−14.4552	−1.05146
$190$	−4.32251	−0.313588
$191$	−11.7679	−0.851497	−0.425749	−	0.904841i	$-0.639989\pi$
$191$	−11.7679	−0.851497	−0.425749	+	0.904841i	$0.639989\pi$
$192$	42.6582	3.07859
$193$	3.51518	0.253028	0.126514	−	0.991965i	$-0.459621\pi$
$193$	3.51518	0.253028	0.126514	+	0.991965i	$0.459621\pi$
$194$	24.4650	1.75649
$195$	−10.9119	−0.781416
$196$	−31.9685	−2.28346
$197$	−6.32965	−0.450969	−0.225485	−	0.974247i	$-0.572397\pi$
$197$	−6.32965	−0.450969	−0.225485	+	0.974247i	$0.572397\pi$
$198$	−79.7830	−5.66993
$199$	−4.18571	−0.296717	−0.148358	−	0.988934i	$-0.547399\pi$
$199$	−4.18571	−0.296717	−0.148358	+	0.988934i	$0.547399\pi$
$200$	37.1619	2.62775
$201$	−46.9199	−3.30948
$202$	21.1372	1.48721
$203$	−4.65414	−0.326657
$204$	72.8570	5.10101
$205$	0.758077	0.0529464
$206$	19.5397	1.36140
$207$	−7.73170	−0.537390
$208$	64.8523	4.49670
$209$	−10.7164	−0.741271
$210$	−3.71065	−0.256059
$211$	13.0183	0.896215	0.448108	−	0.893980i	$-0.352098\pi$
$211$	13.0183	0.896215	0.448108	+	0.893980i	$0.352098\pi$
$212$	61.0814	4.19509
$213$	23.1159	1.58387
$214$	−18.3173	−1.25214
$215$	−0.717680	−0.0489454
$216$	−148.785	−10.1235
$217$	3.28036	0.222686
$218$	−8.86988	−0.600744
$219$	10.2645	0.693611
$220$	−9.48713	−0.639622
$221$	25.6229	1.72358
$222$	−21.5325	−1.44517
$223$	10.5932	0.709375	0.354688	−	0.934985i	$-0.384587\pi$
$223$	10.5932	0.709375	0.354688	+	0.934985i	$0.384587\pi$
$224$	9.95505	0.665150
$225$	−40.2602	−2.68401
$226$	1.27465	0.0847881
$227$	−14.4668	−0.960194	−0.480097	−	0.877215i	$-0.659399\pi$
$227$	−14.4668	−0.960194	−0.480097	+	0.877215i	$0.659399\pi$
$228$	−51.4165	−3.40514
$229$	6.17814	0.408263	0.204131	−	0.978943i	$-0.434563\pi$
$229$	6.17814	0.408263	0.204131	+	0.978943i	$0.434563\pi$
$230$	−1.28821	−0.0849423
$231$	−9.19950	−0.605282
$232$	−47.9043	−3.14507
$233$	6.81936	0.446751	0.223376	−	0.974732i	$-0.428292\pi$
$233$	6.81936	0.446751	0.223376	+	0.974732i	$0.428292\pi$
$234$	−134.623	−8.80060
$235$	1.93707	0.126360
$236$	21.4007	1.39307
$237$	−22.1597	−1.43943
$238$	8.71321	0.564794
$239$	−24.1310	−1.56091	−0.780453	−	0.625214i	$-0.785012\pi$
$239$	−24.1310	−1.56091	−0.780453	+	0.625214i	$0.785012\pi$
$240$	−19.9327	−1.28665
$241$	24.5130	1.57902	0.789510	−	0.613737i	$-0.210335\pi$
$241$	24.5130	1.57902	0.789510	+	0.613737i	$0.210335\pi$
$242$	−3.88315	−0.249618
$243$	74.0371	4.74948
$244$	35.0195	2.24189
$245$	3.45557	0.220768
$246$	12.6348	0.805567
$247$	−18.0826	−1.15057
$248$	33.7642	2.14403
$249$	−39.2991	−2.49048
$250$	−13.8295	−0.874654
$251$	4.13873	0.261234	0.130617	−	0.991433i	$-0.458304\pi$
$251$	4.13873	0.261234	0.130617	+	0.991433i	$0.458304\pi$
$252$	−32.6724	−2.05817
$253$	−3.19376	−0.200790
$254$	−13.1067	−0.822386
$255$	−7.87534	−0.493173
$256$	−6.06059	−0.378787
$257$	7.37653	0.460135	0.230068	−	0.973175i	$-0.426105\pi$
$257$	7.37653	0.460135	0.230068	+	0.973175i	$0.426105\pi$
$258$	−11.9615	−0.744692
$259$	−1.83786	−0.114199
$260$	−16.0083	−0.992791
$261$	51.8981	3.21241
$262$	−51.2385	−3.16553
$263$	20.5740	1.26865	0.634324	−	0.773067i	$-0.281278\pi$
$263$	20.5740	1.26865	0.634324	+	0.773067i	$0.281278\pi$
$264$	−94.6888	−5.82769
$265$	−6.60248	−0.405587
$266$	−6.14908	−0.377024
$267$	−15.4342	−0.944560
$268$	−68.8339	−4.20470
$269$	−2.28741	−0.139466	−0.0697328	−	0.997566i	$-0.522215\pi$
$269$	−2.28741	−0.139466	−0.0697328	+	0.997566i	$0.522215\pi$
$270$	26.8564	1.63443
$271$	−25.3112	−1.53754	−0.768772	−	0.639522i	$-0.779132\pi$
$271$	−25.3112	−1.53754	−0.768772	+	0.639522i	$0.779132\pi$
$272$	46.8053	2.83799
$273$	−15.5229	−0.939491
$274$	52.4711	3.16989
$275$	−16.6304	−1.00285
$276$	−15.3234	−0.922359
$277$	−13.7706	−0.827394	−0.413697	−	0.910415i	$-0.635763\pi$
$277$	−13.7706	−0.827394	−0.413697	+	0.910415i	$0.635763\pi$
$278$	52.4443	3.14540
$279$	−36.5792	−2.18994
$280$	−3.25989	−0.194816
$281$	26.5276	1.58251	0.791253	−	0.611489i	$-0.209429\pi$
$281$	26.5276	1.58251	0.791253	+	0.611489i	$0.209429\pi$
$282$	32.2850	1.92254
$283$	11.2254	0.667279	0.333639	−	0.942701i	$-0.391723\pi$
$283$	11.2254	0.667279	0.333639	+	0.942701i	$0.391723\pi$
$284$	33.9121	2.01232
$285$	5.55778	0.329214
$286$	−55.6093	−3.28825
$287$	1.07842	0.0636571
$288$	−111.008	−6.54122
$289$	1.49259	0.0877992
$290$	8.64698	0.507768
$291$	−31.4565	−1.84401
$292$	15.0585	0.881234
$293$	21.7378	1.26994	0.634969	−	0.772538i	$-0.281013\pi$
$293$	21.7378	1.26994	0.634969	+	0.772538i	$0.281013\pi$
$294$	57.5938	3.35894
$295$	−2.31327	−0.134684
$296$	−18.9168	−1.09952
$297$	66.5829	3.86353
$298$	−57.0485	−3.30473
$299$	−5.38904	−0.311656
$300$	−79.7912	−4.60675
$301$	−1.02095	−0.0588466
$302$	−24.7891	−1.42645
$303$	−27.1776	−1.56131
$304$	−33.0314	−1.89448
$305$	−3.78537	−0.216750
$306$	−97.1605	−5.55430
$307$	−5.75768	−0.328608	−0.164304	−	0.986410i	$-0.552538\pi$
$307$	−5.75768	−0.328608	−0.164304	+	0.986410i	$0.552538\pi$
$308$	−13.4961	−0.769013
$309$	−25.1237	−1.42924
$310$	−6.09462	−0.346151
$311$	−27.8689	−1.58030	−0.790149	−	0.612914i	$-0.789997\pi$
$311$	−27.8689	−1.58030	−0.790149	+	0.612914i	$0.789997\pi$
$312$	−159.775	−9.04547
$313$	24.4026	1.37932	0.689658	−	0.724135i	$-0.257761\pi$
$313$	24.4026	1.37932	0.689658	+	0.724135i	$0.257761\pi$
$314$	54.7615	3.09037
$315$	3.53167	0.198987
$316$	−32.5094	−1.82880
$317$	32.9600	1.85122	0.925608	−	0.378484i	$-0.123554\pi$
$317$	32.9600	1.85122	0.925608	+	0.378484i	$0.123554\pi$
$318$	−110.043	−6.17091
$319$	21.4377	1.20028
$320$	−6.76465	−0.378155
$321$	23.5519	1.31454
$322$	−1.83258	−0.102125
$323$	−13.0506	−0.726153
$324$	191.603	10.6446
$325$	−28.0616	−1.55658
$326$	−8.97632	−0.497153
$327$	11.4047	0.630680
$328$	11.1000	0.612894
$329$	2.75562	0.151922
$330$	17.0918	0.940875
$331$	−18.7262	−1.02929	−0.514643	−	0.857404i	$-0.672076\pi$
$331$	−18.7262	−1.02929	−0.514643	+	0.857404i	$0.672076\pi$
$332$	−57.6538	−3.16416
$333$	20.4939	1.12306
$334$	63.2811	3.46259
$335$	7.44047	0.406516
$336$	−28.3557	−1.54693
$337$	1.42709	0.0777383	0.0388691	−	0.999244i	$-0.487624\pi$
$337$	1.42709	0.0777383	0.0388691	+	0.999244i	$0.487624\pi$
$338$	−59.4742	−3.23497
$339$	−1.63891	−0.0890132
$340$	−11.5535	−0.626577
$341$	−15.1099	−0.818245
$342$	68.5680	3.70773
$343$	10.2821	0.555184
$344$	−10.5085	−0.566579
$345$	1.65635	0.0891750
$346$	−17.4694	−0.939159
$347$	−3.87199	−0.207859	−0.103930	−	0.994585i	$-0.533142\pi$
$347$	−3.87199	−0.207859	−0.103930	+	0.994585i	$0.533142\pi$
$348$	102.856	5.51368
$349$	11.7362	0.628224	0.314112	−	0.949386i	$-0.398293\pi$
$349$	11.7362	0.628224	0.314112	+	0.949386i	$0.398293\pi$
$350$	−9.54251	−0.510068
$351$	112.350	5.99679
$352$	−45.8545	−2.44406
$353$	16.8316	0.895855	0.447928	−	0.894070i	$-0.352162\pi$
$353$	16.8316	0.895855	0.447928	+	0.894070i	$0.352162\pi$
$354$	−38.5552	−2.04918
$355$	−3.66567	−0.194554
$356$	−22.6428	−1.20007
$357$	−11.2032	−0.592938
$358$	47.6165	2.51661
$359$	8.79034	0.463937	0.231968	−	0.972723i	$-0.425483\pi$
$359$	8.79034	0.463937	0.231968	+	0.972723i	$0.425483\pi$
$360$	36.3509	1.91586
$361$	−9.78997	−0.515261
$362$	14.4959	0.761887
$363$	4.99285	0.262057
$364$	−22.7729	−1.19362
$365$	−1.62773	−0.0851990
$366$	−63.0905	−3.29779
$367$	35.0997	1.83219	0.916095	−	0.400962i	$-0.131324\pi$
$367$	35.0997	1.83219	0.916095	+	0.400962i	$0.131324\pi$
$368$	−9.84416	−0.513162
$369$	−12.0254	−0.626017
$370$	3.41458	0.177516
$371$	−9.39250	−0.487634
$372$	−72.4959	−3.75874
$373$	−34.4225	−1.78233	−0.891166	−	0.453678i	$-0.850112\pi$
$373$	−34.4225	−1.78233	−0.891166	+	0.453678i	$0.850112\pi$
$374$	−40.1344	−2.07530
$375$	17.7816	0.918239
$376$	28.3631	1.46271
$377$	36.1733	1.86302
$378$	38.2052	1.96506
$379$	−34.7481	−1.78489	−0.892444	−	0.451158i	$-0.851011\pi$
$379$	−34.7481	−1.78489	−0.892444	+	0.451158i	$0.851011\pi$
$380$	8.15353	0.418267
$381$	16.8522	0.863366
$382$	31.1027	1.59135
$383$	14.7302	0.752676	0.376338	−	0.926482i	$-0.377183\pi$
$383$	14.7302	0.752676	0.376338	+	0.926482i	$0.377183\pi$
$384$	−24.4874	−1.24962
$385$	1.45884	0.0743493
$386$	−9.29064	−0.472881
$387$	11.3846	0.578710
$388$	−46.1483	−2.34282
$389$	−5.57475	−0.282651	−0.141326	−	0.989963i	$-0.545136\pi$
$389$	−5.57475	−0.282651	−0.141326	+	0.989963i	$0.545136\pi$
$390$	28.8402	1.46038
$391$	−3.88939	−0.196695
$392$	50.5975	2.55556
$393$	65.8812	3.32327
$394$	16.7293	0.842812
$395$	3.51405	0.176811
$396$	150.494	7.56263
$397$	5.01910	0.251902	0.125951	−	0.992036i	$-0.459802\pi$
$397$	5.01910	0.251902	0.125951	+	0.992036i	$0.459802\pi$
$398$	11.0629	0.554531
$399$	7.90633	0.395812
$400$	−51.2601	−2.56300
$401$	28.4081	1.41863	0.709317	−	0.704890i	$-0.249003\pi$
$401$	28.4081	1.41863	0.709317	+	0.704890i	$0.249003\pi$
$402$	124.010	6.18505
$403$	−25.4959	−1.27004
$404$	−39.8709	−1.98365
$405$	−20.7110	−1.02914
$406$	12.3009	0.610485
$407$	8.46549	0.419619
$408$	−115.313	−5.70884
$409$	1.66558	0.0823578	0.0411789	−	0.999152i	$-0.486889\pi$
$409$	1.66558	0.0823578	0.0411789	+	0.999152i	$0.486889\pi$
$410$	−2.00361	−0.0989510
$411$	−67.4660	−3.32785
$412$	−36.8577	−1.81585
$413$	−3.29080	−0.161930
$414$	20.4349	1.00432
$415$	6.23198	0.305916
$416$	−77.3735	−3.79355
$417$	−67.4315	−3.30214
$418$	28.3236	1.38535
$419$	−25.1116	−1.22678	−0.613390	−	0.789780i	$-0.710195\pi$
$419$	−25.1116	−1.22678	−0.613390	+	0.789780i	$0.710195\pi$
$420$	6.99938	0.341535
$421$	8.09141	0.394351	0.197176	−	0.980368i	$-0.436823\pi$
$421$	8.09141	0.394351	0.197176	+	0.980368i	$0.436823\pi$
$422$	−34.4074	−1.67493
$423$	−30.7277	−1.49403
$424$	−96.6754	−4.69497
$425$	−20.2526	−0.982398
$426$	−61.0955	−2.96009
$427$	−5.38496	−0.260596
$428$	34.5518	1.67013
$429$	71.5011	3.45210
$430$	1.89684	0.0914735
$431$	−12.9219	−0.622428	−0.311214	−	0.950340i	$-0.600736\pi$
$431$	−12.9219	−0.622428	−0.311214	+	0.950340i	$0.600736\pi$
$432$	205.229	9.87410
$433$	−6.57882	−0.316158	−0.158079	−	0.987426i	$-0.550530\pi$
$433$	−6.57882	−0.316158	−0.158079	+	0.987426i	$0.550530\pi$
$434$	−8.67003	−0.416175
$435$	−11.1181	−0.533071
$436$	16.7312	0.801280
$437$	2.74481	0.131302
$438$	−27.1292	−1.29628
$439$	20.9929	1.00194	0.500969	−	0.865465i	$-0.332977\pi$
$439$	20.9929	1.00194	0.500969	+	0.865465i	$0.332977\pi$
$440$	15.0156	0.715839
$441$	−54.8158	−2.61028
$442$	−67.7215	−3.22119
$443$	5.70417	0.271013	0.135507	−	0.990776i	$-0.456734\pi$
$443$	5.70417	0.271013	0.135507	+	0.990776i	$0.456734\pi$
$444$	40.6167	1.92758
$445$	2.44753	0.116024
$446$	−27.9980	−1.32574
$447$	73.3515	3.46941
$448$	−9.62319	−0.454653
$449$	−32.9101	−1.55312	−0.776562	−	0.630041i	$-0.783038\pi$
$449$	−32.9101	−1.55312	−0.776562	+	0.630041i	$0.783038\pi$
$450$	106.408	5.01612
$451$	−4.96737	−0.233904
$452$	−2.40436	−0.113091
$453$	31.8732	1.49753
$454$	38.2359	1.79450
$455$	2.46160	0.115401
$456$	81.3785	3.81090
$457$	37.6707	1.76216	0.881081	−	0.472966i	$-0.156817\pi$
$457$	37.6707	1.76216	0.881081	+	0.472966i	$0.156817\pi$
$458$	−16.3289	−0.762998
$459$	81.0853	3.78474
$460$	2.42995	0.113297
$461$	21.9097	1.02044	0.510218	−	0.860045i	$-0.329565\pi$
$461$	21.9097	1.02044	0.510218	+	0.860045i	$0.329565\pi$
$462$	24.3144	1.13121
$463$	37.9279	1.76266	0.881329	−	0.472502i	$-0.156649\pi$
$463$	37.9279	1.76266	0.881329	+	0.472502i	$0.156649\pi$
$464$	66.0777	3.06758
$465$	7.83631	0.363400
$466$	−18.0236	−0.834929
$467$	−4.06536	−0.188122	−0.0940612	−	0.995566i	$-0.529985\pi$
$467$	−4.06536	−0.188122	−0.0940612	+	0.995566i	$0.529985\pi$
$468$	253.939	11.7384
$469$	10.5846	0.488751
$470$	−5.11969	−0.236154
$471$	−70.4110	−3.24437
$472$	−33.8716	−1.55907
$473$	4.70266	0.216229
$474$	58.5683	2.69013
$475$	14.2927	0.655793
$476$	−16.4357	−0.753329
$477$	104.735	4.79550
$478$	63.7785	2.91716
$479$	23.7766	1.08638	0.543190	−	0.839610i	$-0.317216\pi$
$479$	23.7766	1.08638	0.543190	+	0.839610i	$0.317216\pi$
$480$	23.7812	1.08546
$481$	14.2844	0.651312
$482$	−64.7881	−2.95102
$483$	2.35628	0.107214
$484$	7.32476	0.332944
$485$	4.98831	0.226508
$486$	−195.681	−8.87625
$487$	−29.0815	−1.31781	−0.658905	−	0.752226i	$-0.728980\pi$
$487$	−29.0815	−1.31781	−0.658905	+	0.752226i	$0.728980\pi$
$488$	−55.4264	−2.50904
$489$	11.5415	0.521926
$490$	−9.13311	−0.412592
$491$	−29.3129	−1.32287	−0.661437	−	0.750001i	$-0.730053\pi$
$491$	−29.3129	−1.32287	−0.661437	+	0.750001i	$0.730053\pi$
$492$	−23.8330	−1.07448
$493$	26.1070	1.17580
$494$	47.7924	2.15028
$495$	−16.2674	−0.731166
$496$	−46.5733	−2.09120
$497$	−5.21468	−0.233910
$498$	103.868	4.65444
$499$	−5.00868	−0.224219	−0.112110	−	0.993696i	$-0.535761\pi$
$499$	−5.00868	−0.224219	−0.112110	+	0.993696i	$0.535761\pi$
$500$	26.0865	1.16662
$501$	−81.3653	−3.63513
$502$	−10.9387	−0.488218
$503$	28.9435	1.29053	0.645264	−	0.763959i	$-0.276747\pi$
$503$	28.9435	1.29053	0.645264	+	0.763959i	$0.276747\pi$
$504$	51.7117	2.30342
$505$	4.30978	0.191783
$506$	8.44113	0.375254
$507$	76.4705	3.39617
$508$	24.7231	1.09691
$509$	19.1032	0.846733	0.423367	−	0.905958i	$-0.360848\pi$
$509$	19.1032	0.846733	0.423367	+	0.905958i	$0.360848\pi$
$510$	20.8146	0.921686
$511$	−2.31556	−0.102434
$512$	30.4297	1.34482
$513$	−57.2234	−2.52648
$514$	−19.4962	−0.859942
$515$	3.98406	0.175559
$516$	22.5630	0.993280
$517$	−12.6928	−0.558229
$518$	4.85749	0.213426
$519$	22.4617	0.985958
$520$	25.3368	1.11109
$521$	−30.4577	−1.33438	−0.667188	−	0.744889i	$-0.732502\pi$
$521$	−30.4577	−1.33438	−0.667188	+	0.744889i	$0.732502\pi$
$522$	−137.167	−6.00364
$523$	12.2475	0.535546	0.267773	−	0.963482i	$-0.413712\pi$
$523$	12.2475	0.535546	0.267773	+	0.963482i	$0.413712\pi$
$524$	96.6510	4.22222
$525$	12.2695	0.535486
$526$	−54.3773	−2.37096
$527$	−18.4009	−0.801558
$528$	130.611	5.68411
$529$	−22.1820	−0.964434
$530$	17.4504	0.757998
$531$	36.6955	1.59245
$532$	11.5990	0.502880
$533$	−8.38178	−0.363055
$534$	40.7928	1.76528
$535$	−3.73482	−0.161470
$536$	108.945	4.70573
$537$	−61.2242	−2.64202
$538$	6.04564	0.260646
$539$	−22.6429	−0.975301
$540$	−50.6592	−2.18003
$541$	−18.1901	−0.782053	−0.391026	−	0.920380i	$-0.627880\pi$
$541$	−18.1901	−0.782053	−0.391026	+	0.920380i	$0.627880\pi$
$542$	66.8977	2.87350
$543$	−18.6385	−0.799853
$544$	−55.8421	−2.39421
$545$	−1.80853	−0.0774689
$546$	41.0273	1.75580
$547$	−15.2069	−0.650202	−0.325101	−	0.945679i	$-0.605398\pi$
$547$	−15.2069	−0.650202	−0.325101	+	0.945679i	$0.605398\pi$
$548$	−98.9760	−4.22804
$549$	60.0474	2.56276
$550$	43.9543	1.87422
$551$	−18.4242	−0.784899
$552$	24.2528	1.03227
$553$	4.99898	0.212578
$554$	36.3958	1.54631
$555$	−4.39039	−0.186362
$556$	−98.9254	−4.19537
$557$	−27.2107	−1.15296	−0.576478	−	0.817113i	$-0.695573\pi$
$557$	−27.2107	−1.15296	−0.576478	+	0.817113i	$0.695573\pi$
$558$	96.6790	4.09275
$559$	7.93512	0.335620
$560$	4.49659	0.190016
$561$	51.6038	2.17872
$562$	−70.1128	−2.95753
$563$	−8.92123	−0.375985	−0.187993	−	0.982170i	$-0.560198\pi$
$563$	−8.92123	−0.375985	−0.187993	+	0.982170i	$0.560198\pi$
$564$	−60.8990	−2.56431
$565$	0.259895	0.0109339
$566$	−29.6688	−1.24707
$567$	−29.4628	−1.23732
$568$	−53.6738	−2.25210
$569$	8.53413	0.357769	0.178885	−	0.983870i	$-0.442751\pi$
$569$	8.53413	0.357769	0.178885	+	0.983870i	$0.442751\pi$
$570$	−14.6893	−0.615265
$571$	−42.9954	−1.79930	−0.899651	−	0.436609i	$-0.856179\pi$
$571$	−42.9954	−1.79930	−0.899651	+	0.436609i	$0.856179\pi$
$572$	104.896	4.38591
$573$	−39.9911	−1.67065
$574$	−2.85027	−0.118968
$575$	4.25957	0.177636
$576$	107.308	4.47115
$577$	−21.7602	−0.905890	−0.452945	−	0.891539i	$-0.649627\pi$
$577$	−21.7602	−0.905890	−0.452945	+	0.891539i	$0.649627\pi$
$578$	−3.94492	−0.164087
$579$	11.9457	0.496445
$580$	−16.3108	−0.677267
$581$	8.86544	0.367800
$582$	83.1398	3.44626
$583$	43.2633	1.79178
$584$	−23.8336	−0.986242
$585$	−27.4491	−1.13488
$586$	−57.4533	−2.37337
$587$	3.16774	0.130746	0.0653732	−	0.997861i	$-0.479176\pi$
$587$	3.16774	0.130746	0.0653732	+	0.997861i	$0.479176\pi$
$588$	−108.639	−4.48019
$589$	12.9859	0.535074
$590$	6.11400	0.251710
$591$	−21.5102	−0.884810
$592$	26.0933	1.07243
$593$	−30.9260	−1.26998	−0.634989	−	0.772521i	$-0.718995\pi$
$593$	−30.9260	−1.26998	−0.634989	+	0.772521i	$0.718995\pi$
$594$	−175.979	−7.22051
$595$	1.77659	0.0728329
$596$	107.610	4.40789
$597$	−14.2243	−0.582164
$598$	14.2433	0.582451
$599$	−12.3337	−0.503943	−0.251972	−	0.967735i	$-0.581079\pi$
$599$	−12.3337	−0.503943	−0.251972	+	0.967735i	$0.581079\pi$
$600$	126.288	5.15569
$601$	25.9101	1.05689	0.528447	−	0.848966i	$-0.322774\pi$
$601$	25.9101	1.05689	0.528447	+	0.848966i	$0.322774\pi$
$602$	2.69838	0.109978
$603$	−118.028	−4.80648
$604$	46.7595	1.90262
$605$	−0.791757	−0.0321895
$606$	71.8307	2.91792
$607$	37.6259	1.52719	0.763595	−	0.645696i	$-0.223433\pi$
$607$	37.6259	1.52719	0.763595	+	0.645696i	$0.223433\pi$
$608$	39.4088	1.59824
$609$	−15.8162	−0.640907
$610$	10.0048	0.405081
$611$	−21.4174	−0.866456
$612$	183.274	7.40839
$613$	20.9962	0.848029	0.424015	−	0.905655i	$-0.360620\pi$
$613$	20.9962	0.848029	0.424015	+	0.905655i	$0.360620\pi$
$614$	15.2176	0.614133
$615$	2.57619	0.103882
$616$	21.3607	0.860648
$617$	15.0335	0.605224	0.302612	−	0.953114i	$-0.402141\pi$
$617$	15.0335	0.605224	0.302612	+	0.953114i	$0.402141\pi$
$618$	66.4021	2.67108
$619$	19.7248	0.792806	0.396403	−	0.918077i	$-0.370258\pi$
$619$	19.7248	0.792806	0.396403	+	0.918077i	$0.370258\pi$
$620$	11.4963	0.461701
$621$	−17.0540	−0.684352
$622$	73.6577	2.95340
$623$	3.48179	0.139495
$624$	220.389	8.82261
$625$	20.7282	0.829127
$626$	−64.4963	−2.57779
$627$	−36.4178	−1.45439
$628$	−103.296	−4.12198
$629$	10.3093	0.411061
$630$	−9.33423	−0.371885
$631$	3.32990	0.132561	0.0662807	−	0.997801i	$-0.478887\pi$
$631$	3.32990	0.132561	0.0662807	+	0.997801i	$0.478887\pi$
$632$	51.4536	2.04672
$633$	44.2402	1.75839
$634$	−87.1135	−3.45972
$635$	−2.67239	−0.106051
$636$	207.574	8.23084
$637$	−38.2070	−1.51382
$638$	−56.6601	−2.24319
$639$	58.1486	2.30032
$640$	3.88317	0.153496
$641$	−0.774237	−0.0305805	−0.0152903	−	0.999883i	$-0.504867\pi$
$641$	−0.774237	−0.0305805	−0.0152903	+	0.999883i	$0.504867\pi$
$642$	−62.2479	−2.45673
$643$	36.2381	1.42909	0.714546	−	0.699589i	$-0.246633\pi$
$643$	36.2381	1.42909	0.714546	+	0.699589i	$0.246633\pi$
$644$	3.45678	0.136216
$645$	−2.43890	−0.0960317
$646$	34.4928	1.35710
$647$	−30.1243	−1.18431	−0.592153	−	0.805825i	$-0.701722\pi$
$647$	−30.1243	−1.18431	−0.592153	+	0.805825i	$0.701722\pi$
$648$	−303.256	−11.9130
$649$	15.1579	0.595001
$650$	74.1670	2.90907
$651$	11.1477	0.436913
$652$	16.9320	0.663108
$653$	16.2875	0.637379	0.318689	−	0.947859i	$-0.396757\pi$
$653$	16.2875	0.637379	0.318689	+	0.947859i	$0.396757\pi$
$654$	−30.1426	−1.17867
$655$	−10.4473	−0.408210
$656$	−15.3110	−0.597793
$657$	25.8206	1.00736
$658$	−7.28312	−0.283925
$659$	−48.5799	−1.89241	−0.946203	−	0.323574i	$-0.895116\pi$
$659$	−48.5799	−1.89241	−0.946203	+	0.323574i	$0.895116\pi$
$660$	−32.2403	−1.25495
$661$	12.9403	0.503318	0.251659	−	0.967816i	$-0.419024\pi$
$661$	12.9403	0.503318	0.251659	+	0.967816i	$0.419024\pi$
$662$	49.4936	1.92362
$663$	87.0747	3.38170
$664$	91.2504	3.54120
$665$	−1.25377	−0.0486191
$666$	−54.1656	−2.09887
$667$	−5.49087	−0.212607
$668$	−119.367	−4.61844
$669$	35.9991	1.39181
$670$	−19.6652	−0.759734
$671$	24.8040	0.957546
$672$	33.8304	1.30504
$673$	−39.6373	−1.52791	−0.763953	−	0.645272i	$-0.776744\pi$
$673$	−39.6373	−1.52791	−0.763953	+	0.645272i	$0.776744\pi$
$674$	−3.77180	−0.145284
$675$	−88.8027	−3.41802
$676$	112.186	4.31485
$677$	1.73122	0.0665361	0.0332680	−	0.999446i	$-0.489408\pi$
$677$	1.73122	0.0665361	0.0332680	+	0.999446i	$0.489408\pi$
$678$	4.33165	0.166356
$679$	7.09623	0.272328
$680$	18.2861	0.701240
$681$	−49.1627	−1.88392
$682$	39.9355	1.52921
$683$	−15.6405	−0.598467	−0.299233	−	0.954180i	$-0.596731\pi$
$683$	−15.6405	−0.598467	−0.299233	+	0.954180i	$0.596731\pi$
$684$	−129.340	−4.94542
$685$	10.6986	0.408773
$686$	−27.1758	−1.03758
$687$	20.9953	0.801019
$688$	14.4951	0.552619
$689$	73.0012	2.78112
$690$	−4.37776	−0.166658
$691$	−14.9599	−0.569102	−0.284551	−	0.958661i	$-0.591845\pi$
$691$	−14.9599	−0.569102	−0.284551	+	0.958661i	$0.591845\pi$
$692$	32.9524	1.25266
$693$	−23.1416	−0.879075
$694$	10.2337	0.388466
$695$	10.6932	0.405615
$696$	−162.794	−6.17068
$697$	−6.04931	−0.229134
$698$	−31.0188	−1.17408
$699$	23.1744	0.876535
$700$	18.0000	0.680336
$701$	24.9631	0.942842	0.471421	−	0.881908i	$-0.343741\pi$
$701$	24.9631	0.942842	0.471421	+	0.881908i	$0.343741\pi$
$702$	−296.942	−11.2073
$703$	−7.27550	−0.274401
$704$	44.3259	1.67060
$705$	6.58277	0.247921
$706$	−44.4860	−1.67425
$707$	6.13096	0.230579
$708$	72.7265	2.73323
$709$	−48.8325	−1.83394	−0.916971	−	0.398955i	$-0.869373\pi$
$709$	−48.8325	−1.83394	−0.916971	+	0.398955i	$0.869373\pi$
$710$	9.68840	0.363599
$711$	−55.7433	−2.09054
$712$	35.8374	1.34306
$713$	3.87011	0.144937
$714$	29.6102	1.10814
$715$	−11.3385	−0.424036
$716$	−89.8189	−3.35669
$717$	−82.0049	−3.06253
$718$	−23.2330	−0.867046
$719$	37.6124	1.40270	0.701352	−	0.712815i	$-0.252580\pi$
$719$	37.6124	1.40270	0.701352	+	0.712815i	$0.252580\pi$
$720$	−50.1413	−1.86865
$721$	5.66761	0.211073
$722$	25.8750	0.962967
$723$	83.3029	3.09807
$724$	−27.3435	−1.01621
$725$	−28.5918	−1.06187
$726$	−13.1962	−0.489755
$727$	43.6749	1.61981	0.809906	−	0.586560i	$-0.199518\pi$
$727$	43.6749	1.61981	0.809906	+	0.586560i	$0.199518\pi$
$728$	36.0434	1.33586
$729$	136.305	5.04834
$730$	4.30209	0.159228
$731$	5.72695	0.211819
$732$	119.007	4.39864
$733$	−25.4278	−0.939198	−0.469599	−	0.882880i	$-0.655602\pi$
$733$	−25.4278	−0.939198	−0.469599	+	0.882880i	$0.655602\pi$
$734$	−92.7688	−3.42416
$735$	11.7431	0.433152
$736$	11.7448	0.432919
$737$	−48.7543	−1.79589
$738$	31.7832	1.16996
$739$	16.4385	0.604701	0.302351	−	0.953197i	$-0.402229\pi$
$739$	16.4385	0.604701	0.302351	+	0.953197i	$0.402229\pi$
$740$	−6.44092	−0.236773
$741$	−61.4502	−2.25743
$742$	24.8245	0.911335
$743$	−13.1615	−0.482848	−0.241424	−	0.970420i	$-0.577615\pi$
$743$	−13.1615	−0.482848	−0.241424	+	0.970420i	$0.577615\pi$
$744$	114.741	4.20663
$745$	−11.6319	−0.426161
$746$	90.9791	3.33098
$747$	−98.8580	−3.61702
$748$	75.7054	2.76806
$749$	−5.31304	−0.194134
$750$	−46.9970	−1.71609
$751$	−2.19127	−0.0799605	−0.0399802	−	0.999200i	$-0.512729\pi$
$751$	−2.19127	−0.0799605	−0.0399802	+	0.999200i	$0.512729\pi$
$752$	−39.1232	−1.42668
$753$	14.0647	0.512546
$754$	−95.6064	−3.48178
$755$	−5.05438	−0.183948
$756$	−72.0663	−2.62103
$757$	−9.12413	−0.331622	−0.165811	−	0.986158i	$-0.553024\pi$
$757$	−9.12413	−0.331622	−0.165811	+	0.986158i	$0.553024\pi$
$758$	91.8395	3.33576
$759$	−10.8534	−0.393953
$760$	−12.9048	−0.468108
$761$	−22.3110	−0.808773	−0.404387	−	0.914588i	$-0.632515\pi$
$761$	−22.3110	−0.808773	−0.404387	+	0.914588i	$0.632515\pi$
$762$	−44.5406	−1.61354
$763$	−2.57276	−0.0931403
$764$	−58.6690	−2.12257
$765$	−19.8106	−0.716254
$766$	−38.9320	−1.40667
$767$	25.5770	0.923532
$768$	−20.5958	−0.743187
$769$	−21.9569	−0.791786	−0.395893	−	0.918297i	$-0.629565\pi$
$769$	−21.9569	−0.791786	−0.395893	+	0.918297i	$0.629565\pi$
$770$	−3.85572	−0.138951
$771$	25.0678	0.902794
$772$	17.5249	0.630735
$773$	37.9323	1.36433	0.682165	−	0.731198i	$-0.261039\pi$
$773$	37.9323	1.36433	0.682165	+	0.731198i	$0.261039\pi$
$774$	−30.0895	−1.08155
$775$	20.1523	0.723891
$776$	73.0402	2.62199
$777$	−6.24564	−0.224061
$778$	14.7341	0.528244
$779$	4.26911	0.152957
$780$	−54.4012	−1.94787
$781$	24.0196	0.859490
$782$	10.2797	0.367601
$783$	114.473	4.09092
$784$	−69.7926	−2.49259
$785$	11.1656	0.398519
$786$	−174.125	−6.21082
$787$	2.92294	0.104191	0.0520957	−	0.998642i	$-0.483410\pi$
$787$	2.92294	0.104191	0.0520957	+	0.998642i	$0.483410\pi$
$788$	−31.5565	−1.12415
$789$	69.9170	2.48911
$790$	−9.28765	−0.330440
$791$	0.369719	0.0131457
$792$	−238.192	−8.46379
$793$	41.8534	1.48626
$794$	−13.2655	−0.470776
$795$	−22.4373	−0.795770
$796$	−20.8678	−0.739640
$797$	18.6167	0.659438	0.329719	−	0.944079i	$-0.393046\pi$
$797$	18.6167	0.659438	0.329719	+	0.944079i	$0.393046\pi$
$798$	−20.8965	−0.739728
$799$	−15.4574	−0.546844
$800$	61.1569	2.16222
$801$	−38.8252	−1.37182
$802$	−75.0829	−2.65127
$803$	10.6658	0.376388
$804$	−233.919	−8.24970
$805$	−0.373654	−0.0131696
$806$	67.3859	2.37357
$807$	−7.77333	−0.273634
$808$	63.1049	2.22002
$809$	−29.7620	−1.04638	−0.523189	−	0.852217i	$-0.675258\pi$
$809$	−29.7620	−1.04638	−0.523189	+	0.852217i	$0.675258\pi$
$810$	54.7393	1.92334
$811$	−37.3455	−1.31138	−0.655690	−	0.755030i	$-0.727622\pi$
$811$	−37.3455	−1.31138	−0.655690	+	0.755030i	$0.727622\pi$
$812$	−23.2032	−0.814273
$813$	−86.0154	−3.01669
$814$	−22.3744	−0.784221
$815$	−1.83023	−0.0641103
$816$	159.059	5.56819
$817$	−4.04161	−0.141398
$818$	−4.40215	−0.153918
$819$	−39.0483	−1.36446
$820$	3.77939	0.131982
$821$	5.14191	0.179454	0.0897269	−	0.995966i	$-0.471401\pi$
$821$	5.14191	0.179454	0.0897269	+	0.995966i	$0.471401\pi$
$822$	178.313	6.21939
$823$	19.3509	0.674528	0.337264	−	0.941410i	$-0.390498\pi$
$823$	19.3509	0.674528	0.337264	+	0.941410i	$0.390498\pi$
$824$	58.3358	2.03222
$825$	−56.5153	−1.96761
$826$	8.69761	0.302628
$827$	28.5534	0.992900	0.496450	−	0.868065i	$-0.334637\pi$
$827$	28.5534	0.992900	0.496450	+	0.868065i	$0.334637\pi$
$828$	−38.5464	−1.33958
$829$	−34.2301	−1.18886	−0.594431	−	0.804147i	$-0.702623\pi$
$829$	−34.2301	−1.18886	−0.594431	+	0.804147i	$0.702623\pi$
$830$	−16.4712	−0.571723
$831$	−46.7968	−1.62336
$832$	74.7942	2.59302
$833$	−27.5748	−0.955410
$834$	178.222	6.17133
$835$	12.9027	0.446518
$836$	−53.4267	−1.84780
$837$	−80.6834	−2.78883
$838$	66.3701	2.29272
$839$	−5.87969	−0.202989	−0.101495	−	0.994836i	$-0.532362\pi$
$839$	−5.87969	−0.202989	−0.101495	+	0.994836i	$0.532362\pi$
$840$	−11.0781	−0.382232
$841$	7.85681	0.270924
$842$	−21.3857	−0.736999
$843$	90.1493	3.10491
$844$	64.9026	2.23404
$845$	−12.1265	−0.417166
$846$	81.2136	2.79218
$847$	−1.12633	−0.0387012
$848$	133.351	4.57930
$849$	38.1473	1.30921
$850$	53.5279	1.83599
$851$	−2.16828	−0.0743276
$852$	115.244	3.94820
$853$	20.0162	0.685343	0.342671	−	0.939455i	$-0.388668\pi$
$853$	20.0162	0.685343	0.342671	+	0.939455i	$0.388668\pi$
$854$	14.2325	0.487026
$855$	13.9807	0.478131
$856$	−54.6862	−1.86914
$857$	17.1083	0.584408	0.292204	−	0.956356i	$-0.405611\pi$
$857$	17.1083	0.584408	0.292204	+	0.956356i	$0.405611\pi$
$858$	−188.978	−6.45160
$859$	−47.4499	−1.61897	−0.809485	−	0.587141i	$-0.800253\pi$
$859$	−47.4499	−1.61897	−0.809485	+	0.587141i	$0.800253\pi$
$860$	−3.57799	−0.122009
$861$	3.66481	0.124896
$862$	34.1528	1.16325
$863$	24.6280	0.838348	0.419174	−	0.907906i	$-0.362320\pi$
$863$	24.6280	0.838348	0.419174	+	0.907906i	$0.362320\pi$
$864$	−244.853	−8.33008
$865$	−3.56193	−0.121109
$866$	17.3879	0.590864
$867$	5.07228	0.172264
$868$	16.3542	0.555099
$869$	−23.0261	−0.781106
$870$	29.3852	0.996250
$871$	−82.2665	−2.78749
$872$	−26.4810	−0.896760
$873$	−79.1296	−2.67813
$874$	−7.25457	−0.245389
$875$	−4.01133	−0.135608
$876$	51.1737	1.72900
$877$	36.1108	1.21938	0.609688	−	0.792641i	$-0.291295\pi$
$877$	36.1108	1.21938	0.609688	+	0.792641i	$0.291295\pi$
$878$	−55.4845	−1.87251
$879$	73.8720	2.49164
$880$	−20.7120	−0.698202
$881$	−54.6533	−1.84132	−0.920659	−	0.390369i	$-0.872348\pi$
$881$	−54.6533	−1.84132	−0.920659	+	0.390369i	$0.872348\pi$
$882$	144.879	4.87832
$883$	4.44337	0.149531	0.0747657	−	0.997201i	$-0.476179\pi$
$883$	4.44337	0.149531	0.0747657	+	0.997201i	$0.476179\pi$
$884$	127.743	4.29646
$885$	−7.86123	−0.264252
$886$	−15.0762	−0.506494
$887$	−2.56509	−0.0861274	−0.0430637	−	0.999072i	$-0.513712\pi$
$887$	−2.56509	−0.0861274	−0.0430637	+	0.999072i	$0.513712\pi$
$888$	−64.2853	−2.15727
$889$	−3.80167	−0.127504
$890$	−6.46885	−0.216836
$891$	135.710	4.54647
$892$	52.8125	1.76829
$893$	10.9086	0.365042
$894$	−193.869	−6.48394
$895$	9.70881	0.324530
$896$	5.52409	0.184547
$897$	−18.3137	−0.611476
$898$	86.9817	2.90262
$899$	−25.9777	−0.866404
$900$	−200.717	−6.69056
$901$	52.6865	1.75524
$902$	13.1288	0.437141
$903$	−3.46951	−0.115458
$904$	3.80545	0.126567
$905$	2.95565	0.0982491
$906$	−84.2410	−2.79872
$907$	28.7252	0.953803	0.476902	−	0.878957i	$-0.341760\pi$
$907$	28.7252	0.953803	0.476902	+	0.878957i	$0.341760\pi$
$908$	−72.1241	−2.39352
$909$	−68.3660	−2.26756
$910$	−6.50602	−0.215673
$911$	40.6836	1.34791	0.673953	−	0.738774i	$-0.264595\pi$
$911$	40.6836	1.34791	0.673953	+	0.738774i	$0.264595\pi$
$912$	−112.251	−3.71700
$913$	−40.8356	−1.35146
$914$	−99.5640	−3.29329
$915$	−12.8639	−0.425267
$916$	30.8011	1.01770
$917$	−14.8621	−0.490788
$918$	−214.309	−7.07326
$919$	−0.463363	−0.0152849	−0.00764247	−	0.999971i	$-0.502433\pi$
$919$	−0.463363	−0.0152849	−0.00764247	+	0.999971i	$0.502433\pi$
$920$	−3.84596	−0.126797
$921$	−19.5664	−0.644736
$922$	−57.9075	−1.90708
$923$	40.5299	1.33406
$924$	−45.8641	−1.50882
$925$	−11.2906	−0.371231
$926$	−100.244	−3.29422
$927$	−63.1992	−2.07574
$928$	−78.8355	−2.58790
$929$	−18.7449	−0.615001	−0.307500	−	0.951548i	$-0.599493\pi$
$929$	−18.7449	−0.615001	−0.307500	+	0.951548i	$0.599493\pi$
$930$	−20.7114	−0.679155
$931$	19.4600	0.637777
$932$	33.9979	1.11364
$933$	−94.7072	−3.10057
$934$	10.7448	0.351580
$935$	−8.18324	−0.267620
$936$	−401.918	−13.1371
$937$	−30.8652	−1.00832	−0.504161	−	0.863609i	$-0.668198\pi$
$937$	−30.8652	−1.00832	−0.504161	+	0.863609i	$0.668198\pi$
$938$	−27.9752	−0.913422
$939$	82.9277	2.70624
$940$	9.65724	0.314985
$941$	9.02895	0.294335	0.147168	−	0.989112i	$-0.452984\pi$
$941$	9.02895	0.294335	0.147168	+	0.989112i	$0.452984\pi$
$942$	186.097	6.06336
$943$	1.27230	0.0414318
$944$	46.7215	1.52065
$945$	7.78988	0.253405
$946$	−12.4292	−0.404107
$947$	34.9491	1.13569	0.567846	−	0.823135i	$-0.307777\pi$
$947$	34.9491	1.13569	0.567846	+	0.823135i	$0.307777\pi$
$948$	−110.477	−3.58813
$949$	17.9971	0.584212
$950$	−37.7757	−1.22560
$951$	112.008	3.63212
$952$	26.0133	0.843095
$953$	−4.88111	−0.158115	−0.0790574	−	0.996870i	$-0.525191\pi$
$953$	−4.88111	−0.158115	−0.0790574	+	0.996870i	$0.525191\pi$
$954$	−276.816	−8.96226
$955$	6.34172	0.205213
$956$	−120.305	−3.89095
$957$	72.8521	2.35497
$958$	−62.8417	−2.03032
$959$	15.2196	0.491465
$960$	−22.9884	−0.741948
$961$	−12.6903	−0.409363
$962$	−37.7538	−1.21723
$963$	59.2454	1.90916
$964$	122.209	3.93610
$965$	−1.89432	−0.0609804
$966$	−6.22767	−0.200372
$967$	−7.59910	−0.244370	−0.122185	−	0.992507i	$-0.538990\pi$
$967$	−7.59910	−0.244370	−0.122185	+	0.992507i	$0.538990\pi$
$968$	−11.5931	−0.372617
$969$	−44.3500	−1.42473
$970$	−13.1842	−0.423318
$971$	28.6258	0.918647	0.459323	−	0.888269i	$-0.348092\pi$
$971$	28.6258	0.918647	0.459323	+	0.888269i	$0.348092\pi$
$972$	369.112	11.8393
$973$	15.2118	0.487667
$974$	76.8628	2.46284
$975$	−95.3621	−3.05403
$976$	76.4535	2.44722
$977$	48.9492	1.56602	0.783012	−	0.622007i	$-0.213682\pi$
$977$	48.9492	1.56602	0.783012	+	0.622007i	$0.213682\pi$
$978$	−30.5044	−0.975423
$979$	−16.0377	−0.512566
$980$	17.2278	0.550320
$981$	28.6887	0.915961
$982$	77.4743	2.47231
$983$	−45.0087	−1.43555	−0.717777	−	0.696273i	$-0.754840\pi$
$983$	−45.0087	−1.43555	−0.717777	+	0.696273i	$0.754840\pi$
$984$	37.7212	1.20251
$985$	3.41104	0.108685
$986$	−69.0012	−2.19744
$987$	9.36445	0.298074
$988$	−90.1506	−2.86807
$989$	−1.20450	−0.0383009
$990$	42.9949	1.36647
$991$	56.2460	1.78671	0.893356	−	0.449350i	$-0.148344\pi$
$991$	56.2460	1.78671	0.893356	+	0.449350i	$0.148344\pi$
$992$	55.5653	1.76420
$993$	−63.6376	−2.01948
$994$	13.7824	0.437152
$995$	2.25567	0.0715095
$996$	−195.926	−6.20815
$997$	−1.58315	−0.0501389	−0.0250694	−	0.999686i	$-0.507981\pi$
$997$	−1.58315	−0.0501389	−0.0250694	+	0.999686i	$0.507981\pi$
$998$	13.2380	0.419041
$999$	45.2039	1.43019

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4027.2.a.c.1.5	✓	174

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4027.2.a.c.1.5	✓	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)

\(f(q)\)	\(=\)	\(q-2.64301 q^{2} +3.39832 q^{3} +4.98550 q^{4} -0.538898 q^{5} -8.98178 q^{6} -0.766621 q^{7} -7.89070 q^{8} +8.54855 q^{9} +O(q^{10})\)	\(q-2.64301 q^{2} +3.39832 q^{3} +4.98550 q^{4} -0.538898 q^{5} -8.98178 q^{6} -0.766621 q^{7} -7.89070 q^{8} +8.54855 q^{9} +1.42431 q^{10} +3.53118 q^{11} +16.9423 q^{12} +5.95840 q^{13} +2.02619 q^{14} -1.83135 q^{15} +10.8842 q^{16} +4.30030 q^{17} -22.5939 q^{18} -3.03480 q^{19} -2.68668 q^{20} -2.60522 q^{21} -9.33293 q^{22} -0.904445 q^{23} -26.8151 q^{24} -4.70959 q^{25} -15.7481 q^{26} +18.8557 q^{27} -3.82199 q^{28} +6.07098 q^{29} +4.84027 q^{30} -4.27899 q^{31} -12.9856 q^{32} +12.0001 q^{33} -11.3657 q^{34} +0.413131 q^{35} +42.6188 q^{36} +2.39736 q^{37} +8.02101 q^{38} +20.2485 q^{39} +4.25228 q^{40} -1.40672 q^{41} +6.88562 q^{42} +1.33175 q^{43} +17.6047 q^{44} -4.60680 q^{45} +2.39046 q^{46} -3.59450 q^{47} +36.9879 q^{48} -6.41229 q^{49} +12.4475 q^{50} +14.6138 q^{51} +29.7056 q^{52} +12.2518 q^{53} -49.8358 q^{54} -1.90295 q^{55} +6.04918 q^{56} -10.3132 q^{57} -16.0457 q^{58} +4.29260 q^{59} -9.13017 q^{60} +7.02427 q^{61} +11.3094 q^{62} -6.55350 q^{63} +12.5527 q^{64} -3.21097 q^{65} -31.7163 q^{66} -13.8068 q^{67} +21.4391 q^{68} -3.07359 q^{69} -1.09191 q^{70} +6.80216 q^{71} -67.4540 q^{72} +3.02047 q^{73} -6.33623 q^{74} -16.0047 q^{75} -15.1300 q^{76} -2.70707 q^{77} -53.5170 q^{78} -6.52080 q^{79} -5.86547 q^{80} +38.4320 q^{81} +3.71797 q^{82} -11.5643 q^{83} -12.9883 q^{84} -2.31742 q^{85} -3.51984 q^{86} +20.6311 q^{87} -27.8635 q^{88} -4.54173 q^{89} +12.1758 q^{90} -4.56783 q^{91} -4.50911 q^{92} -14.5414 q^{93} +9.50028 q^{94} +1.63545 q^{95} -44.1292 q^{96} -9.25650 q^{97} +16.9477 q^{98} +30.1864 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 174 q + 21 q^{2} + 17 q^{3} + 187 q^{4} + 72 q^{5} + 21 q^{6} + 24 q^{7} + 54 q^{8} + 197 q^{9}+O(q^{10}) \) 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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