LMFDB - Embedded newform 1205.2.a.d.1.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1205,2,Mod(1,1205)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1205, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("1205.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1205 = 5 \cdot 241 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1205.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:	$9.62197344356$
Analytic rank:	$0$
Dimension:	$25$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.19
Character	$\chi$	$=$	1205.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.54117 q^{2} +2.24256 q^{3} +0.375203 q^{4} -1.00000 q^{5} +3.45617 q^{6} +3.95910 q^{7} -2.50409 q^{8} +2.02910 q^{9} +O(q^{10})$	\(q+1.54117 q^{2} +2.24256 q^{3} +0.375203 q^{4} -1.00000 q^{5} +3.45617 q^{6} +3.95910 q^{7} -2.50409 q^{8} +2.02910 q^{9} -1.54117 q^{10} +1.30396 q^{11} +0.841416 q^{12} +4.16477 q^{13} +6.10164 q^{14} -2.24256 q^{15} -4.60963 q^{16} -5.17819 q^{17} +3.12718 q^{18} +5.17943 q^{19} -0.375203 q^{20} +8.87854 q^{21} +2.00962 q^{22} +2.34425 q^{23} -5.61558 q^{24} +1.00000 q^{25} +6.41861 q^{26} -2.17731 q^{27} +1.48546 q^{28} +5.28000 q^{29} -3.45617 q^{30} +0.379515 q^{31} -2.09604 q^{32} +2.92421 q^{33} -7.98046 q^{34} -3.95910 q^{35} +0.761322 q^{36} -0.812236 q^{37} +7.98238 q^{38} +9.33976 q^{39} +2.50409 q^{40} -7.44673 q^{41} +13.6833 q^{42} -5.18830 q^{43} +0.489249 q^{44} -2.02910 q^{45} +3.61288 q^{46} +4.33873 q^{47} -10.3374 q^{48} +8.67448 q^{49} +1.54117 q^{50} -11.6124 q^{51} +1.56263 q^{52} -8.60945 q^{53} -3.35561 q^{54} -1.30396 q^{55} -9.91394 q^{56} +11.6152 q^{57} +8.13737 q^{58} -0.246688 q^{59} -0.841416 q^{60} -3.55199 q^{61} +0.584897 q^{62} +8.03340 q^{63} +5.98890 q^{64} -4.16477 q^{65} +4.50671 q^{66} -6.57714 q^{67} -1.94287 q^{68} +5.25713 q^{69} -6.10164 q^{70} -9.79306 q^{71} -5.08103 q^{72} +1.04287 q^{73} -1.25179 q^{74} +2.24256 q^{75} +1.94334 q^{76} +5.16251 q^{77} +14.3942 q^{78} +9.26733 q^{79} +4.60963 q^{80} -10.9701 q^{81} -11.4767 q^{82} +2.90789 q^{83} +3.33125 q^{84} +5.17819 q^{85} -7.99605 q^{86} +11.8407 q^{87} -3.26523 q^{88} -17.0836 q^{89} -3.12718 q^{90} +16.4887 q^{91} +0.879568 q^{92} +0.851088 q^{93} +6.68671 q^{94} -5.17943 q^{95} -4.70051 q^{96} +4.07691 q^{97} +13.3688 q^{98} +2.64586 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 25 q - 4 q^{2} + 9 q^{3} + 36 q^{4} - 25 q^{5} + 7 q^{6} + 7 q^{7} - 15 q^{8} + 36 q^{9}+O(q^{10}) $ 25 * q - 4 * q^2 + 9 * q^3 + 36 * q^4 - 25 * q^5 + 7 * q^6 + 7 * q^7 - 15 * q^8 + 36 * q^9	\( 25 q - 4 q^{2} + 9 q^{3} + 36 q^{4} - 25 q^{5} + 7 q^{6} + 7 q^{7} - 15 q^{8} + 36 q^{9} + 4 q^{10} + 10 q^{11} + 22 q^{12} + 10 q^{13} + 13 q^{14} - 9 q^{15} + 54 q^{16} + q^{17} - 13 q^{18} + 50 q^{19} - 36 q^{20} + 9 q^{21} + 11 q^{22} - 31 q^{23} + 22 q^{24} + 25 q^{25} + 8 q^{26} + 42 q^{27} + 14 q^{28} + 4 q^{29} - 7 q^{30} + 34 q^{31} - 44 q^{32} + 28 q^{33} + 33 q^{34} - 7 q^{35} + 83 q^{36} + 14 q^{37} - 10 q^{38} + 23 q^{39} + 15 q^{40} + 11 q^{41} + 23 q^{42} + 49 q^{43} + 20 q^{44} - 36 q^{45} + 27 q^{46} - 28 q^{47} + 30 q^{48} + 66 q^{49} - 4 q^{50} + 49 q^{51} + 39 q^{52} - 16 q^{53} + 5 q^{54} - 10 q^{55} + 51 q^{56} + 10 q^{57} - 8 q^{58} + 30 q^{59} - 22 q^{60} + 35 q^{61} - 18 q^{62} + 73 q^{64} - 10 q^{65} - 13 q^{66} + 37 q^{67} + 11 q^{68} - 4 q^{69} - 13 q^{70} + 12 q^{71} - 90 q^{72} + 36 q^{73} - 12 q^{74} + 9 q^{75} + 57 q^{76} - 31 q^{77} - 9 q^{78} + 16 q^{79} - 54 q^{80} + 65 q^{81} - 11 q^{82} + 43 q^{83} - 62 q^{84} - q^{85} - 9 q^{86} - 22 q^{87} + 20 q^{88} + 38 q^{89} + 13 q^{90} + 86 q^{91} - 119 q^{92} + 10 q^{93} - 18 q^{94} - 50 q^{95} - 34 q^{96} + 17 q^{97} - 32 q^{98} + 26 q^{99}+O(q^{100}) \) 25 * q - 4 * q^2 + 9 * q^3 + 36 * q^4 - 25 * q^5 + 7 * q^6 + 7 * q^7 - 15 * q^8 + 36 * q^9 + 4 * q^10 + 10 * q^11 + 22 * q^12 + 10 * q^13 + 13 * q^14 - 9 * q^15 + 54 * q^16 + q^17 - 13 * q^18 + 50 * q^19 - 36 * q^20 + 9 * q^21 + 11 * q^22 - 31 * q^23 + 22 * q^24 + 25 * q^25 + 8 * q^26 + 42 * q^27 + 14 * q^28 + 4 * q^29 - 7 * q^30 + 34 * q^31 - 44 * q^32 + 28 * q^33 + 33 * q^34 - 7 * q^35 + 83 * q^36 + 14 * q^37 - 10 * q^38 + 23 * q^39 + 15 * q^40 + 11 * q^41 + 23 * q^42 + 49 * q^43 + 20 * q^44 - 36 * q^45 + 27 * q^46 - 28 * q^47 + 30 * q^48 + 66 * q^49 - 4 * q^50 + 49 * q^51 + 39 * q^52 - 16 * q^53 + 5 * q^54 - 10 * q^55 + 51 * q^56 + 10 * q^57 - 8 * q^58 + 30 * q^59 - 22 * q^60 + 35 * q^61 - 18 * q^62 + 73 * q^64 - 10 * q^65 - 13 * q^66 + 37 * q^67 + 11 * q^68 - 4 * q^69 - 13 * q^70 + 12 * q^71 - 90 * q^72 + 36 * q^73 - 12 * q^74 + 9 * q^75 + 57 * q^76 - 31 * q^77 - 9 * q^78 + 16 * q^79 - 54 * q^80 + 65 * q^81 - 11 * q^82 + 43 * q^83 - 62 * q^84 - q^85 - 9 * q^86 - 22 * q^87 + 20 * q^88 + 38 * q^89 + 13 * q^90 + 86 * q^91 - 119 * q^92 + 10 * q^93 - 18 * q^94 - 50 * q^95 - 34 * q^96 + 17 * q^97 - 32 * q^98 + 26 * 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 $

$2$	1.54117	1.08977	0.544886	−	0.838510i	$-0.316573\pi$
$2$	1.54117	1.08977	0.544886	+	0.838510i	$0.316573\pi$
$3$	2.24256	1.29475	0.647373	−	0.762174i	$-0.275868\pi$
$3$	2.24256	1.29475	0.647373	+	0.762174i	$0.275868\pi$
$4$	0.375203	0.187601
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	3.45617	1.41098
$7$	3.95910	1.49640	0.748200	−	0.663473i	$-0.230918\pi$
$7$	3.95910	1.49640	0.748200	+	0.663473i	$0.230918\pi$
$8$	−2.50409	−0.885329
$9$	2.02910	0.676365
$10$	−1.54117	−0.487360
$11$	1.30396	0.393158	0.196579	−	0.980488i	$-0.437017\pi$
$11$	1.30396	0.393158	0.196579	+	0.980488i	$0.437017\pi$
$12$	0.841416	0.242896
$13$	4.16477	1.15510	0.577549	−	0.816356i	$-0.304009\pi$
$13$	4.16477	1.15510	0.577549	+	0.816356i	$0.304009\pi$
$14$	6.10164	1.63073
$15$	−2.24256	−0.579028
$16$	−4.60963	−1.15241
$17$	−5.17819	−1.25589	−0.627947	−	0.778256i	$-0.716105\pi$
$17$	−5.17819	−1.25589	−0.627947	+	0.778256i	$0.716105\pi$
$18$	3.12718	0.737083
$19$	5.17943	1.18824	0.594122	−	0.804375i	$-0.297500\pi$
$19$	5.17943	1.18824	0.594122	+	0.804375i	$0.297500\pi$
$20$	−0.375203	−0.0838978
$21$	8.87854	1.93746
$22$	2.00962	0.428453
$23$	2.34425	0.488810	0.244405	−	0.969673i	$-0.421407\pi$
$23$	2.34425	0.488810	0.244405	+	0.969673i	$0.421407\pi$
$24$	−5.61558	−1.14628
$25$	1.00000	0.200000
$26$	6.41861	1.25879
$27$	−2.17731	−0.419024
$28$	1.48546	0.280726
$29$	5.28000	0.980471	0.490235	−	0.871590i	$-0.336911\pi$
$29$	5.28000	0.980471	0.490235	+	0.871590i	$0.336911\pi$
$30$	−3.45617	−0.631008
$31$	0.379515	0.0681630	0.0340815	−	0.999419i	$-0.489149\pi$
$31$	0.379515	0.0681630	0.0340815	+	0.999419i	$0.489149\pi$
$32$	−2.09604	−0.370531
$33$	2.92421	0.509040
$34$	−7.98046	−1.36864
$35$	−3.95910	−0.669210
$36$	0.761322	0.126887
$37$	−0.812236	−0.133531	−0.0667654	−	0.997769i	$-0.521268\pi$
$37$	−0.812236	−0.133531	−0.0667654	+	0.997769i	$0.521268\pi$
$38$	7.98238	1.29491
$39$	9.33976	1.49556
$40$	2.50409	0.395931
$41$	−7.44673	−1.16298	−0.581492	−	0.813552i	$-0.697531\pi$
$41$	−7.44673	−1.16298	−0.581492	+	0.813552i	$0.697531\pi$
$42$	13.6833	2.11138
$43$	−5.18830	−0.791208	−0.395604	−	0.918421i	$-0.629465\pi$
$43$	−5.18830	−0.791208	−0.395604	+	0.918421i	$0.629465\pi$
$44$	0.489249	0.0737570
$45$	−2.02910	−0.302480
$46$	3.61288	0.532691
$47$	4.33873	0.632868	0.316434	−	0.948615i	$-0.397514\pi$
$47$	4.33873	0.632868	0.316434	+	0.948615i	$0.397514\pi$
$48$	−10.3374	−1.49207
$49$	8.67448	1.23921
$50$	1.54117	0.217954
$51$	−11.6124	−1.62606
$52$	1.56263	0.216698
$53$	−8.60945	−1.18260	−0.591299	−	0.806452i	$-0.701385\pi$
$53$	−8.60945	−1.18260	−0.591299	+	0.806452i	$0.701385\pi$
$54$	−3.35561	−0.456641
$55$	−1.30396	−0.175826
$56$	−9.91394	−1.32481
$57$	11.6152	1.53847
$58$	8.13737	1.06849
$59$	−0.246688	−0.0321160	−0.0160580	−	0.999871i	$-0.505112\pi$
$59$	−0.246688	−0.0321160	−0.0160580	+	0.999871i	$0.505112\pi$
$60$	−0.841416	−0.108626
$61$	−3.55199	−0.454786	−0.227393	−	0.973803i	$-0.573020\pi$
$61$	−3.55199	−0.454786	−0.227393	+	0.973803i	$0.573020\pi$
$62$	0.584897	0.0742820
$63$	8.03340	1.01211
$64$	5.98890	0.748613
$65$	−4.16477	−0.516576
$66$	4.50671	0.554737
$67$	−6.57714	−0.803525	−0.401763	−	0.915744i	$-0.631602\pi$
$67$	−6.57714	−0.803525	−0.401763	+	0.915744i	$0.631602\pi$
$68$	−1.94287	−0.235607
$69$	5.25713	0.632884
$70$	−6.10164	−0.729286
$71$	−9.79306	−1.16222	−0.581111	−	0.813824i	$-0.697382\pi$
$71$	−9.79306	−1.16222	−0.581111	+	0.813824i	$0.697382\pi$
$72$	−5.08103	−0.598806
$73$	1.04287	0.122059	0.0610293	−	0.998136i	$-0.480562\pi$
$73$	1.04287	0.122059	0.0610293	+	0.998136i	$0.480562\pi$
$74$	−1.25179	−0.145518
$75$	2.24256	0.258949
$76$	1.94334	0.222916
$77$	5.16251	0.588322
$78$	14.3942	1.62982
$79$	9.26733	1.04266	0.521328	−	0.853356i	$-0.325437\pi$
$79$	9.26733	1.04266	0.521328	+	0.853356i	$0.325437\pi$
$80$	4.60963	0.515372
$81$	−10.9701	−1.21890
$82$	−11.4767	−1.26739
$83$	2.90789	0.319182	0.159591	−	0.987183i	$-0.448982\pi$
$83$	2.90789	0.319182	0.159591	+	0.987183i	$0.448982\pi$
$84$	3.33125	0.363469
$85$	5.17819	0.561653
$86$	−7.99605	−0.862236
$87$	11.8407	1.26946
$88$	−3.26523	−0.348074
$89$	−17.0836	−1.81085	−0.905427	−	0.424502i	$-0.860449\pi$
$89$	−17.0836	−1.81085	−0.905427	+	0.424502i	$0.860449\pi$
$90$	−3.12718	−0.329634
$91$	16.4887	1.72849
$92$	0.879568	0.0917013
$93$	0.851088	0.0882537
$94$	6.68671	0.689681
$95$	−5.17943	−0.531399
$96$	−4.70051	−0.479744
$97$	4.07691	0.413947	0.206974	−	0.978347i	$-0.433639\pi$
$97$	4.07691	0.413947	0.206974	+	0.978347i	$0.433639\pi$
$98$	13.3688	1.35046
$99$	2.64586	0.265919
$100$	0.375203	0.0375203
$101$	7.38047	0.734384	0.367192	−	0.930145i	$-0.380319\pi$
$101$	7.38047	0.734384	0.367192	+	0.930145i	$0.380319\pi$
$102$	−17.8967	−1.77204
$103$	3.39498	0.334517	0.167259	−	0.985913i	$-0.446509\pi$
$103$	3.39498	0.334517	0.167259	+	0.985913i	$0.446509\pi$
$104$	−10.4289	−1.02264
$105$	−8.87854	−0.866457
$106$	−13.2686	−1.28876
$107$	−20.0249	−1.93588	−0.967938	−	0.251190i	$-0.919178\pi$
$107$	−20.0249	−1.93588	−0.967938	+	0.251190i	$0.919178\pi$
$108$	−0.816934	−0.0786095
$109$	5.83434	0.558829	0.279414	−	0.960171i	$-0.409860\pi$
$109$	5.83434	0.558829	0.279414	+	0.960171i	$0.409860\pi$
$110$	−2.00962	−0.191610
$111$	−1.82149	−0.172888
$112$	−18.2500	−1.72446
$113$	12.4416	1.17041	0.585204	−	0.810886i	$-0.301015\pi$
$113$	12.4416	1.17041	0.585204	+	0.810886i	$0.301015\pi$
$114$	17.9010	1.67658
$115$	−2.34425	−0.218602
$116$	1.98107	0.183938
$117$	8.45071	0.781269
$118$	−0.380188	−0.0349991
$119$	−20.5010	−1.87932
$120$	5.61558	0.512630
$121$	−9.29969	−0.845426
$122$	−5.47422	−0.495613
$123$	−16.6998	−1.50577
$124$	0.142395	0.0127875
$125$	−1.00000	−0.0894427
$126$	12.3808	1.10297
$127$	−19.4218	−1.72340	−0.861701	−	0.507416i	$-0.830601\pi$
$127$	−19.4218	−1.72340	−0.861701	+	0.507416i	$0.830601\pi$
$128$	13.4220	1.18635
$129$	−11.6351	−1.02441
$130$	−6.41861	−0.562950
$131$	−13.7603	−1.20225	−0.601123	−	0.799156i	$-0.705280\pi$
$131$	−13.7603	−1.20225	−0.601123	+	0.799156i	$0.705280\pi$
$132$	1.09717	0.0954966
$133$	20.5059	1.77809
$134$	−10.1365	−0.875659
$135$	2.17731	0.187393
$136$	12.9666	1.11188
$137$	22.1634	1.89355	0.946775	−	0.321897i	$-0.104320\pi$
$137$	22.1634	1.89355	0.946775	+	0.321897i	$0.104320\pi$
$138$	8.10213	0.689699
$139$	1.76528	0.149729	0.0748647	−	0.997194i	$-0.476148\pi$
$139$	1.76528	0.149729	0.0748647	+	0.997194i	$0.476148\pi$
$140$	−1.48546	−0.125545
$141$	9.72987	0.819403
$142$	−15.0928	−1.26656
$143$	5.43069	0.454137
$144$	−9.35338	−0.779448
$145$	−5.28000	−0.438480
$146$	1.60724	0.133016
$147$	19.4531	1.60446
$148$	−0.304753	−0.0250505
$149$	11.4010	0.934007	0.467004	−	0.884255i	$-0.345334\pi$
$149$	11.4010	0.934007	0.467004	+	0.884255i	$0.345334\pi$
$150$	3.45617	0.282195
$151$	−4.36715	−0.355394	−0.177697	−	0.984085i	$-0.556865\pi$
$151$	−4.36715	−0.355394	−0.177697	+	0.984085i	$0.556865\pi$
$152$	−12.9698	−1.05199
$153$	−10.5070	−0.849444
$154$	7.95630	0.641137
$155$	−0.379515	−0.0304834
$156$	3.50430	0.280569
$157$	11.6735	0.931647	0.465823	−	0.884878i	$-0.345758\pi$
$157$	11.6735	0.931647	0.465823	+	0.884878i	$0.345758\pi$
$158$	14.2825	1.13626
$159$	−19.3072	−1.53116
$160$	2.09604	0.165707
$161$	9.28112	0.731455
$162$	−16.9067	−1.32832
$163$	1.41520	0.110847	0.0554236	−	0.998463i	$-0.482349\pi$
$163$	1.41520	0.110847	0.0554236	+	0.998463i	$0.482349\pi$
$164$	−2.79403	−0.218177
$165$	−2.92421	−0.227650
$166$	4.48155	0.347836
$167$	−10.9621	−0.848269	−0.424135	−	0.905599i	$-0.639422\pi$
$167$	−10.9621	−0.848269	−0.424135	+	0.905599i	$0.639422\pi$
$168$	−22.2326	−1.71529
$169$	4.34529	0.334253
$170$	7.98046	0.612073
$171$	10.5096	0.803687
$172$	−1.94666	−0.148432
$173$	−20.6516	−1.57011	−0.785057	−	0.619423i	$-0.787367\pi$
$173$	−20.6516	−1.57011	−0.785057	+	0.619423i	$0.787367\pi$
$174$	18.2486	1.38342
$175$	3.95910	0.299280
$176$	−6.01077	−0.453079
$177$	−0.553213	−0.0415820
$178$	−26.3287	−1.97342
$179$	−10.1804	−0.760919	−0.380460	−	0.924798i	$-0.624234\pi$
$179$	−10.1804	−0.760919	−0.380460	+	0.924798i	$0.624234\pi$
$180$	−0.761322	−0.0567456
$181$	−22.6697	−1.68502	−0.842511	−	0.538679i	$-0.818924\pi$
$181$	−22.6697	−1.68502	−0.842511	+	0.538679i	$0.818924\pi$
$182$	25.4119	1.88366
$183$	−7.96558	−0.588832
$184$	−5.87020	−0.432757
$185$	0.812236	0.0597168
$186$	1.31167	0.0961763
$187$	−6.75214	−0.493766
$188$	1.62790	0.118727
$189$	−8.62021	−0.627028
$190$	−7.98238	−0.579103
$191$	−17.0934	−1.23684	−0.618418	−	0.785849i	$-0.712226\pi$
$191$	−17.0934	−1.23684	−0.618418	+	0.785849i	$0.712226\pi$
$192$	13.4305	0.969263
$193$	13.1460	0.946271	0.473136	−	0.880990i	$-0.343122\pi$
$193$	13.1460	0.946271	0.473136	+	0.880990i	$0.343122\pi$
$194$	6.28320	0.451108
$195$	−9.33976	−0.668834
$196$	3.25469	0.232478
$197$	−13.4537	−0.958536	−0.479268	−	0.877669i	$-0.659098\pi$
$197$	−13.4537	−0.958536	−0.479268	+	0.877669i	$0.659098\pi$
$198$	4.07772	0.289791
$199$	1.54857	0.109775	0.0548875	−	0.998493i	$-0.482520\pi$
$199$	1.54857	0.109775	0.0548875	+	0.998493i	$0.482520\pi$
$200$	−2.50409	−0.177066
$201$	−14.7497	−1.04036
$202$	11.3745	0.800310
$203$	20.9040	1.46718
$204$	−4.35701	−0.305052
$205$	7.44673	0.520102
$206$	5.23224	0.364547
$207$	4.75671	0.330614
$208$	−19.1980	−1.33114
$209$	6.75377	0.467168
$210$	−13.6833	−0.944240
$211$	24.6378	1.69614	0.848069	−	0.529886i	$-0.177765\pi$
$211$	24.6378	1.69614	0.848069	+	0.529886i	$0.177765\pi$
$212$	−3.23029	−0.221857
$213$	−21.9616	−1.50478
$214$	−30.8617	−2.10966
$215$	5.18830	0.353839
$216$	5.45219	0.370974
$217$	1.50254	0.101999
$218$	8.99171	0.608995
$219$	2.33870	0.158035
$220$	−0.489249	−0.0329851
$221$	−21.5659	−1.45068
$222$	−2.80723	−0.188409
$223$	16.0388	1.07403	0.537017	−	0.843571i	$-0.319551\pi$
$223$	16.0388	1.07403	0.537017	+	0.843571i	$0.319551\pi$
$224$	−8.29844	−0.554463
$225$	2.02910	0.135273
$226$	19.1746	1.27548
$227$	12.3315	0.818472	0.409236	−	0.912429i	$-0.365795\pi$
$227$	12.3315	0.818472	0.409236	+	0.912429i	$0.365795\pi$
$228$	4.35806	0.288619
$229$	−13.6409	−0.901413	−0.450707	−	0.892672i	$-0.648828\pi$
$229$	−13.6409	−0.901413	−0.450707	+	0.892672i	$0.648828\pi$
$230$	−3.61288	−0.238227
$231$	11.5773	0.761727
$232$	−13.2216	−0.868039
$233$	18.7057	1.22545	0.612726	−	0.790295i	$-0.290073\pi$
$233$	18.7057	1.22545	0.612726	+	0.790295i	$0.290073\pi$
$234$	13.0240	0.851404
$235$	−4.33873	−0.283027
$236$	−0.0925579	−0.00602500
$237$	20.7826	1.34997
$238$	−31.5955	−2.04803
$239$	11.0551	0.715095	0.357547	−	0.933895i	$-0.383613\pi$
$239$	11.0551	0.715095	0.357547	+	0.933895i	$0.383613\pi$
$240$	10.3374	0.667276
$241$	1.00000	0.0644157
$241$	1.00000	0.0644157
$242$	−14.3324	−0.921321
$243$	−18.0691	−1.15913
$244$	−1.33272	−0.0853185
$245$	−8.67448	−0.554192
$246$	−25.7372	−1.64094
$247$	21.5711	1.37254
$248$	−0.950340	−0.0603466
$249$	6.52113	0.413260
$250$	−1.54117	−0.0974721
$251$	−5.08283	−0.320825	−0.160413	−	0.987050i	$-0.551282\pi$
$251$	−5.08283	−0.320825	−0.160413	+	0.987050i	$0.551282\pi$
$252$	3.01415	0.189874
$253$	3.05680	0.192180
$254$	−29.9322	−1.87811
$255$	11.6124	0.727198
$256$	8.70776	0.544235
$257$	15.9317	0.993790	0.496895	−	0.867811i	$-0.334473\pi$
$257$	15.9317	0.993790	0.496895	+	0.867811i	$0.334473\pi$
$258$	−17.9316	−1.11638
$259$	−3.21572	−0.199815
$260$	−1.56263	−0.0969103
$261$	10.7136	0.663157
$262$	−21.2070	−1.31017
$263$	7.36252	0.453992	0.226996	−	0.973896i	$-0.427110\pi$
$263$	7.36252	0.453992	0.226996	+	0.973896i	$0.427110\pi$
$264$	−7.32249	−0.450668
$265$	8.60945	0.528874
$266$	31.6031	1.93771
$267$	−38.3110	−2.34460
$268$	−2.46776	−0.150742
$269$	8.81125	0.537232	0.268616	−	0.963247i	$-0.413434\pi$
$269$	8.81125	0.537232	0.268616	+	0.963247i	$0.413434\pi$
$270$	3.35561	0.204216
$271$	19.5493	1.18753	0.593767	−	0.804637i	$-0.297640\pi$
$271$	19.5493	1.18753	0.593767	+	0.804637i	$0.297640\pi$
$272$	23.8695	1.44730
$273$	36.9771	2.23795
$274$	34.1576	2.06354
$275$	1.30396	0.0786317
$276$	1.97249	0.118730
$277$	15.4524	0.928446	0.464223	−	0.885718i	$-0.346334\pi$
$277$	15.4524	0.928446	0.464223	+	0.885718i	$0.346334\pi$
$278$	2.72060	0.163171
$279$	0.770073	0.0461031
$280$	9.91394	0.592471
$281$	26.5468	1.58365	0.791825	−	0.610748i	$-0.209131\pi$
$281$	26.5468	1.58365	0.791825	+	0.610748i	$0.209131\pi$
$282$	14.9954	0.892962
$283$	−8.39710	−0.499156	−0.249578	−	0.968355i	$-0.580292\pi$
$283$	−8.39710	−0.499156	−0.249578	+	0.968355i	$0.580292\pi$
$284$	−3.67438	−0.218034
$285$	−11.6152	−0.688026
$286$	8.36961	0.494905
$287$	−29.4823	−1.74029
$288$	−4.25307	−0.250615
$289$	9.81361	0.577271
$290$	−8.13737	−0.477843
$291$	9.14272	0.535956
$292$	0.391287	0.0228983
$293$	25.1901	1.47162	0.735810	−	0.677188i	$-0.236802\pi$
$293$	25.1901	1.47162	0.735810	+	0.677188i	$0.236802\pi$
$294$	29.9805	1.74850
$295$	0.246688	0.0143627
$296$	2.03391	0.118219
$297$	−2.83913	−0.164743
$298$	17.5709	1.01785
$299$	9.76325	0.564623
$300$	0.841416	0.0485792
$301$	−20.5410	−1.18396
$302$	−6.73052	−0.387298
$303$	16.5512	0.950840
$304$	−23.8753	−1.36934
$305$	3.55199	0.203387
$306$	−16.1931	−0.925699
$307$	−3.99302	−0.227893	−0.113947	−	0.993487i	$-0.536349\pi$
$307$	−3.99302	−0.227893	−0.113947	+	0.993487i	$0.536349\pi$
$308$	1.93699	0.110370
$309$	7.61346	0.433115
$310$	−0.584897	−0.0332199
$311$	−10.8329	−0.614278	−0.307139	−	0.951665i	$-0.599372\pi$
$311$	−10.8329	−0.614278	−0.307139	+	0.951665i	$0.599372\pi$
$312$	−23.3876	−1.32406
$313$	22.1417	1.25152	0.625762	−	0.780014i	$-0.284788\pi$
$313$	22.1417	1.25152	0.625762	+	0.780014i	$0.284788\pi$
$314$	17.9908	1.01528
$315$	−8.03340	−0.452631
$316$	3.47713	0.195604
$317$	−9.15150	−0.513999	−0.257000	−	0.966412i	$-0.582734\pi$
$317$	−9.15150	−0.513999	−0.257000	+	0.966412i	$0.582734\pi$
$318$	−29.7557	−1.66862
$319$	6.88490	0.385480
$320$	−5.98890	−0.334790
$321$	−44.9070	−2.50647
$322$	14.3038	0.797118
$323$	−26.8201	−1.49231
$324$	−4.11599	−0.228666
$325$	4.16477	0.231020
$326$	2.18107	0.120798
$327$	13.0839	0.723541
$328$	18.6473	1.02962
$329$	17.1775	0.947024
$330$	−4.50671	−0.248086
$331$	0.367537	0.0202017	0.0101008	−	0.999949i	$-0.496785\pi$
$331$	0.367537	0.0202017	0.0101008	+	0.999949i	$0.496785\pi$
$332$	1.09105	0.0598790
$333$	−1.64810	−0.0903156
$334$	−16.8944	−0.924420
$335$	6.57714	0.359347
$336$	−40.9268	−2.23274
$337$	19.9338	1.08586	0.542931	−	0.839777i	$-0.317314\pi$
$337$	19.9338	1.08586	0.542931	+	0.839777i	$0.317314\pi$
$338$	6.69683	0.364260
$339$	27.9011	1.51538
$340$	1.94287	0.105367
$341$	0.494872	0.0267988
$342$	16.1970	0.875834
$343$	6.62944	0.357956
$344$	12.9920	0.700479
$345$	−5.25713	−0.283034
$346$	−31.8277	−1.71107
$347$	−13.7528	−0.738288	−0.369144	−	0.929372i	$-0.620349\pi$
$347$	−13.7528	−0.738288	−0.369144	+	0.929372i	$0.620349\pi$
$348$	4.44267	0.238152
$349$	22.7133	1.21581	0.607906	−	0.794009i	$-0.292010\pi$
$349$	22.7133	1.21581	0.607906	+	0.794009i	$0.292010\pi$
$350$	6.10164	0.326147
$351$	−9.06801	−0.484015
$352$	−2.73315	−0.145678
$353$	−34.9577	−1.86061	−0.930305	−	0.366788i	$-0.880457\pi$
$353$	−34.9577	−1.86061	−0.930305	+	0.366788i	$0.880457\pi$
$354$	−0.852595	−0.0453149
$355$	9.79306	0.519761
$356$	−6.40980	−0.339719
$357$	−45.9747	−2.43324
$358$	−15.6897	−0.829228
$359$	34.3560	1.81324	0.906619	−	0.421950i	$-0.138654\pi$
$359$	34.3560	1.81324	0.906619	+	0.421950i	$0.138654\pi$
$360$	5.08103	0.267794
$361$	7.82651	0.411922
$362$	−34.9378	−1.83629
$363$	−20.8552	−1.09461
$364$	6.18662	0.324267
$365$	−1.04287	−0.0545863
$366$	−12.2763	−0.641693
$367$	−34.9766	−1.82576	−0.912882	−	0.408225i	$-0.866148\pi$
$367$	−34.9766	−1.82576	−0.912882	+	0.408225i	$0.866148\pi$
$368$	−10.8061	−0.563308
$369$	−15.1101	−0.786602
$370$	1.25179	0.0650776
$371$	−34.0857	−1.76964
$372$	0.319330	0.0165565
$373$	−16.1367	−0.835525	−0.417762	−	0.908556i	$-0.637186\pi$
$373$	−16.1367	−0.835525	−0.417762	+	0.908556i	$0.637186\pi$
$374$	−10.4062	−0.538092
$375$	−2.24256	−0.115806
$376$	−10.8645	−0.560296
$377$	21.9900	1.13254
$378$	−13.2852	−0.683317
$379$	−20.0175	−1.02823	−0.514116	−	0.857721i	$-0.671880\pi$
$379$	−20.0175	−1.02823	−0.514116	+	0.857721i	$0.671880\pi$
$380$	−1.94334	−0.0996910
$381$	−43.5546	−2.23137
$382$	−26.3438	−1.34787
$383$	−24.8171	−1.26810	−0.634048	−	0.773294i	$-0.718608\pi$
$383$	−24.8171	−1.26810	−0.634048	+	0.773294i	$0.718608\pi$
$384$	30.0997	1.53602
$385$	−5.16251	−0.263106
$386$	20.2602	1.03122
$387$	−10.5276	−0.535146
$388$	1.52967	0.0776570
$389$	21.9062	1.11069	0.555345	−	0.831620i	$-0.312586\pi$
$389$	21.9062	1.11069	0.555345	+	0.831620i	$0.312586\pi$
$390$	−14.3942	−0.728876
$391$	−12.1390	−0.613893
$392$	−21.7217	−1.09711
$393$	−30.8584	−1.55660
$394$	−20.7344	−1.04458
$395$	−9.26733	−0.466290
$396$	0.992733	0.0498867
$397$	−14.5920	−0.732354	−0.366177	−	0.930545i	$-0.619333\pi$
$397$	−14.5920	−0.732354	−0.366177	+	0.930545i	$0.619333\pi$
$398$	2.38660	0.119630
$399$	45.9858	2.30217
$400$	−4.60963	−0.230481
$401$	16.5366	0.825797	0.412899	−	0.910777i	$-0.364516\pi$
$401$	16.5366	0.825797	0.412899	+	0.910777i	$0.364516\pi$
$402$	−22.7317	−1.13376
$403$	1.58059	0.0787349
$404$	2.76917	0.137771
$405$	10.9701	0.545107
$406$	32.2167	1.59889
$407$	−1.05912	−0.0524988
$408$	29.0785	1.43960
$409$	3.63040	0.179512	0.0897558	−	0.995964i	$-0.471391\pi$
$409$	3.63040	0.179512	0.0897558	+	0.995964i	$0.471391\pi$
$410$	11.4767	0.566792
$411$	49.7029	2.45166
$412$	1.27380	0.0627559
$413$	−0.976662	−0.0480584
$414$	7.33089	0.360293
$415$	−2.90789	−0.142743
$416$	−8.72953	−0.428000
$417$	3.95876	0.193861
$418$	10.4087	0.509106
$419$	−2.97091	−0.145139	−0.0725693	−	0.997363i	$-0.523120\pi$
$419$	−2.97091	−0.145139	−0.0725693	+	0.997363i	$0.523120\pi$
$420$	−3.33125	−0.162548
$421$	−22.1588	−1.07995	−0.539976	−	0.841680i	$-0.681567\pi$
$421$	−22.1588	−1.07995	−0.539976	+	0.841680i	$0.681567\pi$
$422$	37.9710	1.84840
$423$	8.80369	0.428050
$424$	21.5588	1.04699
$425$	−5.17819	−0.251179
$426$	−33.8465	−1.63987
$427$	−14.0627	−0.680542
$428$	−7.51338	−0.363173
$429$	12.1787	0.587992
$430$	7.99605	0.385604
$431$	−1.85703	−0.0894500	−0.0447250	−	0.998999i	$-0.514241\pi$
$431$	−1.85703	−0.0894500	−0.0447250	+	0.998999i	$0.514241\pi$
$432$	10.0366	0.482887
$433$	−15.1668	−0.728872	−0.364436	−	0.931228i	$-0.618738\pi$
$433$	−15.1668	−0.728872	−0.364436	+	0.931228i	$0.618738\pi$
$434$	2.31567	0.111156
$435$	−11.8407	−0.567720
$436$	2.18906	0.104837
$437$	12.1419	0.580825
$438$	3.60433	0.172222
$439$	−9.34416	−0.445972	−0.222986	−	0.974822i	$-0.571580\pi$
$439$	−9.34416	−0.445972	−0.222986	+	0.974822i	$0.571580\pi$
$440$	3.26523	0.155664
$441$	17.6014	0.838160
$442$	−33.2368	−1.58091
$443$	22.3216	1.06053	0.530265	−	0.847832i	$-0.322093\pi$
$443$	22.3216	1.06053	0.530265	+	0.847832i	$0.322093\pi$
$444$	−0.683428	−0.0324341
$445$	17.0836	0.809839
$446$	24.7184	1.17045
$447$	25.5675	1.20930
$448$	23.7107	1.12022
$449$	26.0050	1.22725	0.613626	−	0.789597i	$-0.289710\pi$
$449$	26.0050	1.22725	0.613626	+	0.789597i	$0.289710\pi$
$450$	3.12718	0.147417
$451$	−9.71023	−0.457237
$452$	4.66812	0.219570
$453$	−9.79361	−0.460144
$454$	19.0050	0.891947
$455$	−16.4887	−0.773004
$456$	−29.0855	−1.36205
$457$	−31.5901	−1.47772	−0.738862	−	0.673857i	$-0.764636\pi$
$457$	−31.5901	−1.47772	−0.738862	+	0.673857i	$0.764636\pi$
$458$	−21.0229	−0.982334
$459$	11.2745	0.526251
$460$	−0.879568	−0.0410101
$461$	23.6112	1.09968	0.549842	−	0.835268i	$-0.314688\pi$
$461$	23.6112	1.09968	0.549842	+	0.835268i	$0.314688\pi$
$462$	17.8425	0.830109
$463$	18.8662	0.876786	0.438393	−	0.898783i	$-0.355548\pi$
$463$	18.8662	0.876786	0.438393	+	0.898783i	$0.355548\pi$
$464$	−24.3388	−1.12990
$465$	−0.851088	−0.0394682
$466$	28.8287	1.33546
$467$	34.8572	1.61300	0.806500	−	0.591234i	$-0.201359\pi$
$467$	34.8572	1.61300	0.806500	+	0.591234i	$0.201359\pi$
$468$	3.17073	0.146567
$469$	−26.0396	−1.20240
$470$	−6.68671	−0.308435
$471$	26.1786	1.20625
$472$	0.617728	0.0284332
$473$	−6.76533	−0.311070
$474$	32.0295	1.47116
$475$	5.17943	0.237649
$476$	−7.69201	−0.352563
$477$	−17.4694	−0.799869
$478$	17.0378	0.779290
$479$	0.370966	0.0169499	0.00847494	−	0.999964i	$-0.497302\pi$
$479$	0.370966	0.0169499	0.00847494	+	0.999964i	$0.497302\pi$
$480$	4.70051	0.214548
$481$	−3.38277	−0.154241
$482$	1.54117	0.0701983
$483$	20.8135	0.947047
$484$	−3.48927	−0.158603
$485$	−4.07691	−0.185123
$486$	−27.8476	−1.26319
$487$	−36.4698	−1.65260	−0.826302	−	0.563227i	$-0.809560\pi$
$487$	−36.4698	−1.65260	−0.826302	+	0.563227i	$0.809560\pi$
$488$	8.89451	0.402635
$489$	3.17368	0.143519
$490$	−13.3688	−0.603943
$491$	−1.76693	−0.0797403	−0.0398701	−	0.999205i	$-0.512694\pi$
$491$	−1.76693	−0.0797403	−0.0398701	+	0.999205i	$0.512694\pi$
$492$	−6.26580	−0.282484
$493$	−27.3408	−1.23137
$494$	33.2448	1.49575
$495$	−2.64586	−0.118922
$496$	−1.74942	−0.0785515
$497$	−38.7717	−1.73915
$498$	10.0502	0.450359
$499$	16.4963	0.738474	0.369237	−	0.929335i	$-0.379619\pi$
$499$	16.4963	0.738474	0.369237	+	0.929335i	$0.379619\pi$
$500$	−0.375203	−0.0167796
$501$	−24.5831	−1.09829
$502$	−7.83350	−0.349626
$503$	42.4923	1.89464	0.947319	−	0.320291i	$-0.103781\pi$
$503$	42.4923	1.89464	0.947319	+	0.320291i	$0.103781\pi$
$504$	−20.1163	−0.896053
$505$	−7.38047	−0.328426
$506$	4.71105	0.209432
$507$	9.74460	0.432773
$508$	−7.28709	−0.323313
$509$	14.5392	0.644440	0.322220	−	0.946665i	$-0.395571\pi$
$509$	14.5392	0.644440	0.322220	+	0.946665i	$0.395571\pi$
$510$	17.8967	0.792479
$511$	4.12882	0.182648
$512$	−13.4239	−0.593256
$513$	−11.2773	−0.497903
$514$	24.5534	1.08300
$515$	−3.39498	−0.149601
$516$	−4.36552	−0.192181
$517$	5.65752	0.248817
$518$	−4.95598	−0.217753
$519$	−46.3126	−2.03290
$520$	10.4289	0.457339
$521$	−22.0841	−0.967523	−0.483761	−	0.875200i	$-0.660730\pi$
$521$	−22.0841	−0.967523	−0.483761	+	0.875200i	$0.660730\pi$
$522$	16.5115	0.722689
$523$	1.83879	0.0804049	0.0402024	−	0.999192i	$-0.487200\pi$
$523$	1.83879	0.0804049	0.0402024	+	0.999192i	$0.487200\pi$
$524$	−5.16291	−0.225543
$525$	8.87854	0.387491
$526$	11.3469	0.494748
$527$	−1.96520	−0.0856055
$528$	−13.4795	−0.586621
$529$	−17.5045	−0.761065
$530$	13.2686	0.576352
$531$	−0.500553	−0.0217222
$532$	7.69386	0.333571
$533$	−31.0139	−1.34336
$534$	−59.0437	−2.55507
$535$	20.0249	0.865750
$536$	16.4697	0.711384
$537$	−22.8302	−0.985196
$538$	13.5796	0.585459
$539$	11.3112	0.487207
$540$	0.816934	0.0351552
$541$	18.8092	0.808670	0.404335	−	0.914611i	$-0.367503\pi$
$541$	18.8092	0.808670	0.404335	+	0.914611i	$0.367503\pi$
$542$	30.1288	1.29414
$543$	−50.8382	−2.18167
$544$	10.8537	0.465348
$545$	−5.83434	−0.249916
$546$	56.9879	2.43886
$547$	33.6688	1.43958	0.719788	−	0.694194i	$-0.244239\pi$
$547$	33.6688	1.43958	0.719788	+	0.694194i	$0.244239\pi$
$548$	8.31577	0.355232
$549$	−7.20734	−0.307602
$550$	2.00962	0.0856906
$551$	27.3474	1.16504
$552$	−13.1643	−0.560310
$553$	36.6903	1.56023
$554$	23.8148	1.01179
$555$	1.82149	0.0773180
$556$	0.662339	0.0280894
$557$	10.6377	0.450733	0.225366	−	0.974274i	$-0.427642\pi$
$557$	10.6377	0.450733	0.225366	+	0.974274i	$0.427642\pi$
$558$	1.18681	0.0502418
$559$	−21.6081	−0.913923
$560$	18.2500	0.771203
$561$	−15.1421	−0.639301
$562$	40.9131	1.72582
$563$	−23.0852	−0.972924	−0.486462	−	0.873702i	$-0.661713\pi$
$563$	−23.0852	−0.972924	−0.486462	+	0.873702i	$0.661713\pi$
$564$	3.65067	0.153721
$565$	−12.4416	−0.523422
$566$	−12.9414	−0.543966
$567$	−43.4316	−1.82395
$568$	24.5227	1.02895
$569$	−12.7918	−0.536260	−0.268130	−	0.963383i	$-0.586406\pi$
$569$	−12.7918	−0.536260	−0.268130	+	0.963383i	$0.586406\pi$
$570$	−17.9010	−0.749791
$571$	21.5083	0.900093	0.450047	−	0.893005i	$-0.351407\pi$
$571$	21.5083	0.900093	0.450047	+	0.893005i	$0.351407\pi$
$572$	2.03761	0.0851967
$573$	−38.3331	−1.60139
$574$	−45.4373	−1.89652
$575$	2.34425	0.0977619
$576$	12.1521	0.506336
$577$	32.8878	1.36914	0.684569	−	0.728948i	$-0.259990\pi$
$577$	32.8878	1.36914	0.684569	+	0.728948i	$0.259990\pi$
$578$	15.1244	0.629093
$579$	29.4808	1.22518
$580$	−1.98107	−0.0822594
$581$	11.5126	0.477624
$582$	14.0905	0.584069
$583$	−11.2264	−0.464949
$584$	−2.61144	−0.108062
$585$	−8.45071	−0.349394
$586$	38.8222	1.60373
$587$	3.05853	0.126239	0.0631196	−	0.998006i	$-0.479895\pi$
$587$	3.05853	0.126239	0.0631196	+	0.998006i	$0.479895\pi$
$588$	7.29885	0.300999
$589$	1.96567	0.0809942
$590$	0.380188	0.0156521
$591$	−30.1708	−1.24106
$592$	3.74411	0.153882
$593$	−4.95546	−0.203496	−0.101748	−	0.994810i	$-0.532444\pi$
$593$	−4.95546	−0.203496	−0.101748	+	0.994810i	$0.532444\pi$
$594$	−4.37558	−0.179532
$595$	20.5010	0.840458
$596$	4.27769	0.175221
$597$	3.47276	0.142131
$598$	15.0468	0.615310
$599$	28.9442	1.18263	0.591314	−	0.806442i	$-0.298610\pi$
$599$	28.9442	1.18263	0.591314	+	0.806442i	$0.298610\pi$
$600$	−5.61558	−0.229255
$601$	33.5419	1.36820	0.684100	−	0.729388i	$-0.260195\pi$
$601$	33.5419	1.36820	0.684100	+	0.729388i	$0.260195\pi$
$602$	−31.6572	−1.29025
$603$	−13.3456	−0.543477
$604$	−1.63857	−0.0666723
$605$	9.29969	0.378086
$606$	25.5082	1.03620
$607$	−16.6363	−0.675248	−0.337624	−	0.941281i	$-0.609623\pi$
$607$	−16.6363	−0.675248	−0.337624	+	0.941281i	$0.609623\pi$
$608$	−10.8563	−0.440281
$609$	46.8787	1.89962
$610$	5.47422	0.221645
$611$	18.0698	0.731025
$612$	−3.94227	−0.159357
$613$	11.8840	0.479992	0.239996	−	0.970774i	$-0.422854\pi$
$613$	11.8840	0.479992	0.239996	+	0.970774i	$0.422854\pi$
$614$	−6.15391	−0.248352
$615$	16.6998	0.673400
$616$	−12.9274	−0.520859
$617$	9.11906	0.367120	0.183560	−	0.983009i	$-0.441238\pi$
$617$	9.11906	0.367120	0.183560	+	0.983009i	$0.441238\pi$
$618$	11.7336	0.471996
$619$	43.8371	1.76196	0.880980	−	0.473153i	$-0.156884\pi$
$619$	43.8371	1.76196	0.880980	+	0.473153i	$0.156884\pi$
$620$	−0.142395	−0.00571872
$621$	−5.10417	−0.204823
$622$	−16.6953	−0.669422
$623$	−67.6356	−2.70976
$624$	−43.0528	−1.72349
$625$	1.00000	0.0400000
$626$	34.1241	1.36388
$627$	15.1458	0.604863
$628$	4.37993	0.174778
$629$	4.20591	0.167701
$630$	−12.3808	−0.493264
$631$	6.44876	0.256721	0.128361	−	0.991728i	$-0.459029\pi$
$631$	6.44876	0.256721	0.128361	+	0.991728i	$0.459029\pi$
$632$	−23.2062	−0.923094
$633$	55.2519	2.19607
$634$	−14.1040	−0.560142
$635$	19.4218	0.770729
$636$	−7.24413	−0.287248
$637$	36.1272	1.43141
$638$	10.6108	0.420085
$639$	−19.8711	−0.786087
$640$	−13.4220	−0.530551
$641$	15.4460	0.610078	0.305039	−	0.952340i	$-0.401330\pi$
$641$	15.4460	0.610078	0.305039	+	0.952340i	$0.401330\pi$
$642$	−69.2093	−2.73147
$643$	12.7099	0.501228	0.250614	−	0.968087i	$-0.419367\pi$
$643$	12.7099	0.501228	0.250614	+	0.968087i	$0.419367\pi$
$644$	3.48230	0.137222
$645$	11.6351	0.458131
$646$	−41.3343	−1.62627
$647$	16.2364	0.638320	0.319160	−	0.947701i	$-0.396599\pi$
$647$	16.2364	0.638320	0.319160	+	0.947701i	$0.396599\pi$
$648$	27.4700	1.07912
$649$	−0.321671	−0.0126267
$650$	6.41861	0.251759
$651$	3.36954	0.132063
$652$	0.530988	0.0207951
$653$	−15.0358	−0.588396	−0.294198	−	0.955745i	$-0.595052\pi$
$653$	−15.0358	−0.588396	−0.294198	+	0.955745i	$0.595052\pi$
$654$	20.1645	0.788494
$655$	13.7603	0.537661
$656$	34.3266	1.34023
$657$	2.11608	0.0825562
$658$	26.4734	1.03204
$659$	−15.2407	−0.593694	−0.296847	−	0.954925i	$-0.595935\pi$
$659$	−15.2407	−0.593694	−0.296847	+	0.954925i	$0.595935\pi$
$660$	−1.09717	−0.0427074
$661$	30.3982	1.18235	0.591177	−	0.806542i	$-0.298664\pi$
$661$	30.3982	1.18235	0.591177	+	0.806542i	$0.298664\pi$
$662$	0.566437	0.0220152
$663$	−48.3630	−1.87826
$664$	−7.28161	−0.282581
$665$	−20.5059	−0.795185
$666$	−2.54001	−0.0984233
$667$	12.3776	0.479264
$668$	−4.11299	−0.159136
$669$	35.9679	1.39060
$670$	10.1365	0.391607
$671$	−4.63166	−0.178803
$672$	−18.6098	−0.717888
$673$	−17.2882	−0.666413	−0.333206	−	0.942854i	$-0.608131\pi$
$673$	−17.2882	−0.666413	−0.333206	+	0.942854i	$0.608131\pi$
$674$	30.7213	1.18334
$675$	−2.17731	−0.0838049
$676$	1.63036	0.0627063
$677$	−12.0681	−0.463813	−0.231907	−	0.972738i	$-0.574496\pi$
$677$	−12.0681	−0.463813	−0.231907	+	0.972738i	$0.574496\pi$
$678$	43.0003	1.65142
$679$	16.1409	0.619430
$680$	−12.9666	−0.497248
$681$	27.6542	1.05971
$682$	0.762682	0.0292046
$683$	−47.0346	−1.79973	−0.899864	−	0.436171i	$-0.856334\pi$
$683$	−47.0346	−1.79973	−0.899864	+	0.436171i	$0.856334\pi$
$684$	3.94322	0.150773
$685$	−22.1634	−0.846821
$686$	10.2171	0.390091
$687$	−30.5905	−1.16710
$688$	23.9161	0.911794
$689$	−35.8564	−1.36602
$690$	−8.10213	−0.308443
$691$	36.3967	1.38460	0.692298	−	0.721611i	$-0.256598\pi$
$691$	36.3967	1.38460	0.692298	+	0.721611i	$0.256598\pi$
$692$	−7.74855	−0.294555
$693$	10.4752	0.397921
$694$	−21.1954	−0.804565
$695$	−1.76528	−0.0669610
$696$	−29.6502	−1.12389
$697$	38.5605	1.46058
$698$	35.0050	1.32496
$699$	41.9488	1.58665
$700$	1.48546	0.0561453
$701$	−40.2112	−1.51876	−0.759378	−	0.650649i	$-0.774497\pi$
$701$	−40.2112	−1.51876	−0.759378	+	0.650649i	$0.774497\pi$
$702$	−13.9753	−0.527465
$703$	−4.20692	−0.158667
$704$	7.80928	0.294323
$705$	−9.72987	−0.366448
$706$	−53.8757	−2.02764
$707$	29.2200	1.09893
$708$	−0.207567	−0.00780085
$709$	−14.9828	−0.562690	−0.281345	−	0.959607i	$-0.590781\pi$
$709$	−14.9828	−0.562690	−0.281345	+	0.959607i	$0.590781\pi$
$710$	15.0928	0.566421
$711$	18.8043	0.705217
$712$	42.7788	1.60320
$713$	0.889678	0.0333187
$714$	−70.8548	−2.65168
$715$	−5.43069	−0.203096
$716$	−3.81971	−0.142749
$717$	24.7918	0.925866
$718$	52.9483	1.97601
$719$	35.5027	1.32403	0.662014	−	0.749492i	$-0.269702\pi$
$719$	35.5027	1.32403	0.662014	+	0.749492i	$0.269702\pi$
$720$	9.35338	0.348580
$721$	13.4411	0.500571
$722$	12.0620	0.448901
$723$	2.24256	0.0834019
$724$	−8.50571	−0.316112
$725$	5.28000	0.196094
$726$	−32.1413	−1.19288
$727$	14.8654	0.551328	0.275664	−	0.961254i	$-0.411102\pi$
$727$	14.8654	0.551328	0.275664	+	0.961254i	$0.411102\pi$
$728$	−41.2892	−1.53028
$729$	−7.61099	−0.281889
$730$	−1.60724	−0.0594865
$731$	26.8660	0.993674
$732$	−2.98871	−0.110466
$733$	−5.04295	−0.186266	−0.0931329	−	0.995654i	$-0.529688\pi$
$733$	−5.04295	−0.186266	−0.0931329	+	0.995654i	$0.529688\pi$
$734$	−53.9048	−1.98966
$735$	−19.4531	−0.717538
$736$	−4.91364	−0.181119
$737$	−8.57632	−0.315913
$738$	−23.2873	−0.857216
$739$	1.85037	0.0680668	0.0340334	−	0.999421i	$-0.489165\pi$
$739$	1.85037	0.0680668	0.0340334	+	0.999421i	$0.489165\pi$
$740$	0.304753	0.0112029
$741$	48.3747	1.77709
$742$	−52.5318	−1.92850
$743$	23.2908	0.854458	0.427229	−	0.904143i	$-0.359490\pi$
$743$	23.2908	0.854458	0.427229	+	0.904143i	$0.359490\pi$
$744$	−2.13120	−0.0781335
$745$	−11.4010	−0.417701
$746$	−24.8693	−0.910531
$747$	5.90039	0.215884
$748$	−2.53342	−0.0926311
$749$	−79.2804	−2.89684
$750$	−3.45617	−0.126202
$751$	−45.1536	−1.64768	−0.823839	−	0.566824i	$-0.808172\pi$
$751$	−45.1536	−1.64768	−0.823839	+	0.566824i	$0.808172\pi$
$752$	−19.9999	−0.729322
$753$	−11.3986	−0.415387
$754$	33.8903	1.23421
$755$	4.36715	0.158937
$756$	−3.23432	−0.117631
$757$	−19.3168	−0.702081	−0.351040	−	0.936360i	$-0.614172\pi$
$757$	−19.3168	−0.702081	−0.351040	+	0.936360i	$0.614172\pi$
$758$	−30.8504	−1.12054
$759$	6.85508	0.248824
$760$	12.9698	0.470462
$761$	26.2402	0.951206	0.475603	−	0.879660i	$-0.342230\pi$
$761$	26.2402	0.951206	0.475603	+	0.879660i	$0.342230\pi$
$762$	−67.1249	−2.43168
$763$	23.0987	0.836231
$764$	−6.41349	−0.232032
$765$	10.5070	0.379883
$766$	−38.2474	−1.38193
$767$	−1.02740	−0.0370972
$768$	19.5277	0.704646
$769$	2.20370	0.0794675	0.0397338	−	0.999210i	$-0.487349\pi$
$769$	2.20370	0.0794675	0.0397338	+	0.999210i	$0.487349\pi$
$770$	−7.95630	−0.286725
$771$	35.7278	1.28670
$772$	4.93242	0.177522
$773$	−27.4652	−0.987856	−0.493928	−	0.869503i	$-0.664439\pi$
$773$	−27.4652	−0.987856	−0.493928	+	0.869503i	$0.664439\pi$
$774$	−16.2247	−0.583186
$775$	0.379515	0.0136326
$776$	−10.2089	−0.366479
$777$	−7.21147	−0.258710
$778$	33.7612	1.21040
$779$	−38.5698	−1.38191
$780$	−3.50430	−0.125474
$781$	−12.7697	−0.456937
$782$	−18.7082	−0.669003
$783$	−11.4962	−0.410841
$784$	−39.9861	−1.42808
$785$	−11.6735	−0.416645
$786$	−47.5581	−1.69634
$787$	18.6325	0.664177	0.332089	−	0.943248i	$-0.392247\pi$
$787$	18.6325	0.664177	0.332089	+	0.943248i	$0.392247\pi$
$788$	−5.04786	−0.179823
$789$	16.5109	0.587804
$790$	−14.2825	−0.508150
$791$	49.2575	1.75140
$792$	−6.62546	−0.235426
$793$	−14.7932	−0.525323
$794$	−22.4888	−0.798098
$795$	19.3072	0.684758
$796$	0.581026	0.0205939
$797$	15.6094	0.552915	0.276457	−	0.961026i	$-0.410840\pi$
$797$	15.6094	0.552915	0.276457	+	0.961026i	$0.410840\pi$
$798$	70.8719	2.50884
$799$	−22.4667	−0.794816
$800$	−2.09604	−0.0741063
$801$	−34.6642	−1.22480
$802$	25.4857	0.899930
$803$	1.35986	0.0479884
$804$	−5.53411	−0.195173
$805$	−9.28112	−0.327116
$806$	2.43596	0.0858031
$807$	19.7598	0.695578
$808$	−18.4813	−0.650171
$809$	−45.6024	−1.60329	−0.801647	−	0.597798i	$-0.796043\pi$
$809$	−45.6024	−1.60329	−0.801647	+	0.597798i	$0.796043\pi$
$810$	16.9067	0.594041
$811$	39.4708	1.38601	0.693004	−	0.720934i	$-0.256287\pi$
$811$	39.4708	1.38601	0.693004	+	0.720934i	$0.256287\pi$
$812$	7.84325	0.275244
$813$	43.8405	1.53755
$814$	−1.63229	−0.0572116
$815$	−1.41520	−0.0495724
$816$	53.5289	1.87389
$817$	−26.8724	−0.940148
$818$	5.59505	0.195626
$819$	33.4572	1.16909
$820$	2.79403	0.0975718
$821$	10.2820	0.358845	0.179423	−	0.983772i	$-0.442577\pi$
$821$	10.2820	0.358845	0.179423	+	0.983772i	$0.442577\pi$
$822$	76.6006	2.67175
$823$	−3.48096	−0.121339	−0.0606693	−	0.998158i	$-0.519324\pi$
$823$	−3.48096	−0.121339	−0.0606693	+	0.998158i	$0.519324\pi$
$824$	−8.50133	−0.296158
$825$	2.92421	0.101808
$826$	−1.50520	−0.0523726
$827$	−8.03988	−0.279574	−0.139787	−	0.990182i	$-0.544642\pi$
$827$	−8.03988	−0.279574	−0.139787	+	0.990182i	$0.544642\pi$
$828$	1.78473	0.0620236
$829$	3.91565	0.135996	0.0679980	−	0.997685i	$-0.478339\pi$
$829$	3.91565	0.135996	0.0679980	+	0.997685i	$0.478339\pi$
$830$	−4.48155	−0.155557
$831$	34.6530	1.20210
$832$	24.9424	0.864722
$833$	−44.9181	−1.55632
$834$	6.10112	0.211265
$835$	10.9621	0.379358
$836$	2.53403	0.0876413
$837$	−0.826324	−0.0285619
$838$	−4.57868	−0.158168
$839$	−25.3679	−0.875796	−0.437898	−	0.899025i	$-0.644277\pi$
$839$	−25.3679	−0.875796	−0.437898	+	0.899025i	$0.644277\pi$
$840$	22.2326	0.767099
$841$	−1.12163	−0.0386768
$842$	−34.1504	−1.17690
$843$	59.5330	2.05042
$844$	9.24417	0.318197
$845$	−4.34529	−0.149483
$846$	13.5680	0.466477
$847$	−36.8184	−1.26510
$848$	39.6864	1.36284
$849$	−18.8310	−0.646280
$850$	−7.98046	−0.273728
$851$	−1.90408	−0.0652711
$852$	−8.24003	−0.282299
$853$	22.7447	0.778763	0.389381	−	0.921077i	$-0.372689\pi$
$853$	22.7447	0.778763	0.389381	+	0.921077i	$0.372689\pi$
$854$	−21.6730	−0.741635
$855$	−10.5096	−0.359420
$856$	50.1440	1.71389
$857$	−45.6730	−1.56016	−0.780081	−	0.625679i	$-0.784822\pi$
$857$	−45.6730	−1.56016	−0.780081	+	0.625679i	$0.784822\pi$
$858$	18.7694	0.640776
$859$	−14.2182	−0.485117	−0.242559	−	0.970137i	$-0.577987\pi$
$859$	−14.2182	−0.485117	−0.242559	+	0.970137i	$0.577987\pi$
$860$	1.94666	0.0663806
$861$	−66.1161	−2.25323
$862$	−2.86200	−0.0974800
$863$	−47.6592	−1.62234	−0.811169	−	0.584811i	$-0.801169\pi$
$863$	−47.6592	−1.62234	−0.811169	+	0.584811i	$0.801169\pi$
$864$	4.56374	0.155262
$865$	20.6516	0.702177
$866$	−23.3747	−0.794304
$867$	22.0077	0.747419
$868$	0.563757	0.0191351
$869$	12.0842	0.409929
$870$	−18.2486	−0.618685
$871$	−27.3923	−0.928151
$872$	−14.6097	−0.494747
$873$	8.27243	0.279979
$874$	18.7127	0.632966
$875$	−3.95910	−0.133842
$876$	0.877487	0.0296475
$877$	16.8547	0.569143	0.284571	−	0.958655i	$-0.408149\pi$
$877$	16.8547	0.569143	0.284571	+	0.958655i	$0.408149\pi$
$878$	−14.4009	−0.486008
$879$	56.4903	1.90537
$880$	6.01077	0.202623
$881$	−11.3922	−0.383811	−0.191906	−	0.981413i	$-0.561467\pi$
$881$	−11.3922	−0.383811	−0.191906	+	0.981413i	$0.561467\pi$
$882$	27.1267	0.913403
$883$	−12.0068	−0.404062	−0.202031	−	0.979379i	$-0.564754\pi$
$883$	−12.0068	−0.404062	−0.202031	+	0.979379i	$0.564754\pi$
$884$	−8.09160	−0.272150
$885$	0.553213	0.0185961
$886$	34.4013	1.15573
$887$	−6.48807	−0.217848	−0.108924	−	0.994050i	$-0.534741\pi$
$887$	−6.48807	−0.217848	−0.108924	+	0.994050i	$0.534741\pi$
$888$	4.56118	0.153063
$889$	−76.8927	−2.57890
$890$	26.3287	0.882539
$891$	−14.3045	−0.479219
$892$	6.01778	0.201490
$893$	22.4721	0.752001
$894$	39.4038	1.31786
$895$	10.1804	0.340293
$896$	53.1390	1.77525
$897$	21.8947	0.731043
$898$	40.0781	1.33742
$899$	2.00384	0.0668318
$900$	0.761322	0.0253774
$901$	44.5813	1.48522
$902$	−14.9651	−0.498284
$903$	−46.0645	−1.53293
$904$	−31.1549	−1.03620
$905$	22.6697	0.753565
$906$	−15.0936	−0.501452
$907$	25.2417	0.838135	0.419068	−	0.907955i	$-0.362357\pi$
$907$	25.2417	0.838135	0.419068	+	0.907955i	$0.362357\pi$
$908$	4.62682	0.153546
$909$	14.9757	0.496712
$910$	−25.4119	−0.842397
$911$	−10.9345	−0.362276	−0.181138	−	0.983458i	$-0.557978\pi$
$911$	−10.9345	−0.362276	−0.181138	+	0.983458i	$0.557978\pi$
$912$	−53.5418	−1.77295
$913$	3.79177	0.125489
$914$	−48.6857	−1.61038
$915$	7.96558	0.263334
$916$	−5.11808	−0.169106
$917$	−54.4786	−1.79904
$918$	17.3760	0.573493
$919$	53.0515	1.75001	0.875003	−	0.484117i	$-0.160859\pi$
$919$	53.0515	1.75001	0.875003	+	0.484117i	$0.160859\pi$
$920$	5.87020	0.193535
$921$	−8.95460	−0.295064
$922$	36.3889	1.19840
$923$	−40.7858	−1.34248
$924$	4.34382	0.142901
$925$	−0.812236	−0.0267062
$926$	29.0760	0.955496
$927$	6.88874	0.226256
$928$	−11.0671	−0.363295
$929$	26.0239	0.853817	0.426908	−	0.904295i	$-0.359603\pi$
$929$	26.0239	0.853817	0.426908	+	0.904295i	$0.359603\pi$
$930$	−1.31167	−0.0430114
$931$	44.9289	1.47248
$932$	7.01843	0.229896
$933$	−24.2935	−0.795333
$934$	53.7209	1.75780
$935$	6.75214	0.220819
$936$	−21.1613	−0.691680
$937$	28.1945	0.921074	0.460537	−	0.887640i	$-0.347657\pi$
$937$	28.1945	0.921074	0.460537	+	0.887640i	$0.347657\pi$
$938$	−40.1314	−1.31034
$939$	49.6543	1.62041
$940$	−1.62790	−0.0530963
$941$	−29.2585	−0.953800	−0.476900	−	0.878958i	$-0.658240\pi$
$941$	−29.2585	−0.953800	−0.476900	+	0.878958i	$0.658240\pi$
$942$	40.3456	1.31453
$943$	−17.4570	−0.568478
$944$	1.13714	0.0370107
$945$	8.62021	0.280415
$946$	−10.4265	−0.338995
$947$	42.0500	1.36644	0.683221	−	0.730211i	$-0.260578\pi$
$947$	42.0500	1.36644	0.683221	+	0.730211i	$0.260578\pi$
$948$	7.79768	0.253257
$949$	4.34331	0.140990
$950$	7.98238	0.258983
$951$	−20.5228	−0.665498
$952$	51.3362	1.66382
$953$	−30.1297	−0.975998	−0.487999	−	0.872844i	$-0.662273\pi$
$953$	−30.1297	−0.975998	−0.487999	+	0.872844i	$0.662273\pi$
$954$	−26.9233	−0.871674
$955$	17.0934	0.553130
$956$	4.14790	0.134153
$957$	15.4398	0.499099
$958$	0.571722	0.0184715
$959$	87.7473	2.83351
$960$	−13.4305	−0.433468
$961$	−30.8560	−0.995354
$962$	−5.21343	−0.168088
$963$	−40.6324	−1.30936
$964$	0.375203	0.0120845
$965$	−13.1460	−0.423185
$966$	32.0771	1.03206
$967$	−31.4411	−1.01108	−0.505539	−	0.862803i	$-0.668707\pi$
$967$	−31.4411	−1.01108	−0.505539	+	0.862803i	$0.668707\pi$
$968$	23.2872	0.748480
$969$	−60.1457	−1.93216
$970$	−6.28320	−0.201741
$971$	36.4772	1.17061	0.585304	−	0.810814i	$-0.300975\pi$
$971$	36.4772	1.17061	0.585304	+	0.810814i	$0.300975\pi$
$972$	−6.77958	−0.217455
$973$	6.98893	0.224055
$974$	−56.2061	−1.80096
$975$	9.33976	0.299112
$976$	16.3734	0.524099
$977$	−23.3751	−0.747835	−0.373917	−	0.927462i	$-0.621986\pi$
$977$	−23.3751	−0.747835	−0.373917	+	0.927462i	$0.621986\pi$
$978$	4.89118	0.156403
$979$	−22.2763	−0.711953
$980$	−3.25469	−0.103967
$981$	11.8384	0.377972
$982$	−2.72313	−0.0868987
$983$	−12.7710	−0.407332	−0.203666	−	0.979040i	$-0.565286\pi$
$983$	−12.7710	−0.407332	−0.203666	+	0.979040i	$0.565286\pi$
$984$	41.8177	1.33310
$985$	13.4537	0.428670
$986$	−42.1368	−1.34191
$987$	38.5215	1.22615
$988$	8.09354	0.257490
$989$	−12.1627	−0.386750
$990$	−4.07772	−0.129598
$991$	−13.3868	−0.425246	−0.212623	−	0.977134i	$-0.568201\pi$
$991$	−13.3868	−0.425246	−0.212623	+	0.977134i	$0.568201\pi$
$992$	−0.795480	−0.0252565
$993$	0.824226	0.0261560
$994$	−59.7537	−1.89527
$995$	−1.54857	−0.0490929
$996$	2.44674	0.0775281
$997$	−7.71179	−0.244235	−0.122117	−	0.992516i	$-0.538968\pi$
$997$	−7.71179	−0.244235	−0.122117	+	0.992516i	$0.538968\pi$
$998$	25.4235	0.804767
$999$	1.76849	0.0559527

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1205.2.a.d.1.19	✓	25
5.4	even	2		6025.2.a.k.1.7		25

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1205.2.a.d.1.19	✓	25	1.1	even	1	trivial
6025.2.a.k.1.7		25	5.4	even	2

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:	\( N \)	\(=\)	\( 1205 = 5 \cdot 241 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1205.a (trivial)

\(f(q)\)	\(=\)	\(q+1.54117 q^{2} +2.24256 q^{3} +0.375203 q^{4} -1.00000 q^{5} +3.45617 q^{6} +3.95910 q^{7} -2.50409 q^{8} +2.02910 q^{9} +O(q^{10})\)	\(q+1.54117 q^{2} +2.24256 q^{3} +0.375203 q^{4} -1.00000 q^{5} +3.45617 q^{6} +3.95910 q^{7} -2.50409 q^{8} +2.02910 q^{9} -1.54117 q^{10} +1.30396 q^{11} +0.841416 q^{12} +4.16477 q^{13} +6.10164 q^{14} -2.24256 q^{15} -4.60963 q^{16} -5.17819 q^{17} +3.12718 q^{18} +5.17943 q^{19} -0.375203 q^{20} +8.87854 q^{21} +2.00962 q^{22} +2.34425 q^{23} -5.61558 q^{24} +1.00000 q^{25} +6.41861 q^{26} -2.17731 q^{27} +1.48546 q^{28} +5.28000 q^{29} -3.45617 q^{30} +0.379515 q^{31} -2.09604 q^{32} +2.92421 q^{33} -7.98046 q^{34} -3.95910 q^{35} +0.761322 q^{36} -0.812236 q^{37} +7.98238 q^{38} +9.33976 q^{39} +2.50409 q^{40} -7.44673 q^{41} +13.6833 q^{42} -5.18830 q^{43} +0.489249 q^{44} -2.02910 q^{45} +3.61288 q^{46} +4.33873 q^{47} -10.3374 q^{48} +8.67448 q^{49} +1.54117 q^{50} -11.6124 q^{51} +1.56263 q^{52} -8.60945 q^{53} -3.35561 q^{54} -1.30396 q^{55} -9.91394 q^{56} +11.6152 q^{57} +8.13737 q^{58} -0.246688 q^{59} -0.841416 q^{60} -3.55199 q^{61} +0.584897 q^{62} +8.03340 q^{63} +5.98890 q^{64} -4.16477 q^{65} +4.50671 q^{66} -6.57714 q^{67} -1.94287 q^{68} +5.25713 q^{69} -6.10164 q^{70} -9.79306 q^{71} -5.08103 q^{72} +1.04287 q^{73} -1.25179 q^{74} +2.24256 q^{75} +1.94334 q^{76} +5.16251 q^{77} +14.3942 q^{78} +9.26733 q^{79} +4.60963 q^{80} -10.9701 q^{81} -11.4767 q^{82} +2.90789 q^{83} +3.33125 q^{84} +5.17819 q^{85} -7.99605 q^{86} +11.8407 q^{87} -3.26523 q^{88} -17.0836 q^{89} -3.12718 q^{90} +16.4887 q^{91} +0.879568 q^{92} +0.851088 q^{93} +6.68671 q^{94} -5.17943 q^{95} -4.70051 q^{96} +4.07691 q^{97} +13.3688 q^{98} +2.64586 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 25 q - 4 q^{2} + 9 q^{3} + 36 q^{4} - 25 q^{5} + 7 q^{6} + 7 q^{7} - 15 q^{8} + 36 q^{9}+O(q^{10}) \) 25 * q - 4 * q^2 + 9 * q^3 + 36 * q^4 - 25 * q^5 + 7 * q^6 + 7 * q^7 - 15 * q^8 + 36 * q^9	\( 25 q - 4 q^{2} + 9 q^{3} + 36 q^{4} - 25 q^{5} + 7 q^{6} + 7 q^{7} - 15 q^{8} + 36 q^{9} + 4 q^{10} + 10 q^{11} + 22 q^{12} + 10 q^{13} + 13 q^{14} - 9 q^{15} + 54 q^{16} + q^{17} - 13 q^{18} + 50 q^{19} - 36 q^{20} + 9 q^{21} + 11 q^{22} - 31 q^{23} + 22 q^{24} + 25 q^{25} + 8 q^{26} + 42 q^{27} + 14 q^{28} + 4 q^{29} - 7 q^{30} + 34 q^{31} - 44 q^{32} + 28 q^{33} + 33 q^{34} - 7 q^{35} + 83 q^{36} + 14 q^{37} - 10 q^{38} + 23 q^{39} + 15 q^{40} + 11 q^{41} + 23 q^{42} + 49 q^{43} + 20 q^{44} - 36 q^{45} + 27 q^{46} - 28 q^{47} + 30 q^{48} + 66 q^{49} - 4 q^{50} + 49 q^{51} + 39 q^{52} - 16 q^{53} + 5 q^{54} - 10 q^{55} + 51 q^{56} + 10 q^{57} - 8 q^{58} + 30 q^{59} - 22 q^{60} + 35 q^{61} - 18 q^{62} + 73 q^{64} - 10 q^{65} - 13 q^{66} + 37 q^{67} + 11 q^{68} - 4 q^{69} - 13 q^{70} + 12 q^{71} - 90 q^{72} + 36 q^{73} - 12 q^{74} + 9 q^{75} + 57 q^{76} - 31 q^{77} - 9 q^{78} + 16 q^{79} - 54 q^{80} + 65 q^{81} - 11 q^{82} + 43 q^{83} - 62 q^{84} - q^{85} - 9 q^{86} - 22 q^{87} + 20 q^{88} + 38 q^{89} + 13 q^{90} + 86 q^{91} - 119 q^{92} + 10 q^{93} - 18 q^{94} - 50 q^{95} - 34 q^{96} + 17 q^{97} - 32 q^{98} + 26 q^{99}+O(q^{100}) \) 25 * q - 4 * q^2 + 9 * q^3 + 36 * q^4 - 25 * q^5 + 7 * q^6 + 7 * q^7 - 15 * q^8 + 36 * q^9 + 4 * q^10 + 10 * q^11 + 22 * q^12 + 10 * q^13 + 13 * q^14 - 9 * q^15 + 54 * q^16 + q^17 - 13 * q^18 + 50 * q^19 - 36 * q^20 + 9 * q^21 + 11 * q^22 - 31 * q^23 + 22 * q^24 + 25 * q^25 + 8 * q^26 + 42 * q^27 + 14 * q^28 + 4 * q^29 - 7 * q^30 + 34 * q^31 - 44 * q^32 + 28 * q^33 + 33 * q^34 - 7 * q^35 + 83 * q^36 + 14 * q^37 - 10 * q^38 + 23 * q^39 + 15 * q^40 + 11 * q^41 + 23 * q^42 + 49 * q^43 + 20 * q^44 - 36 * q^45 + 27 * q^46 - 28 * q^47 + 30 * q^48 + 66 * q^49 - 4 * q^50 + 49 * q^51 + 39 * q^52 - 16 * q^53 + 5 * q^54 - 10 * q^55 + 51 * q^56 + 10 * q^57 - 8 * q^58 + 30 * q^59 - 22 * q^60 + 35 * q^61 - 18 * q^62 + 73 * q^64 - 10 * q^65 - 13 * q^66 + 37 * q^67 + 11 * q^68 - 4 * q^69 - 13 * q^70 + 12 * q^71 - 90 * q^72 + 36 * q^73 - 12 * q^74 + 9 * q^75 + 57 * q^76 - 31 * q^77 - 9 * q^78 + 16 * q^79 - 54 * q^80 + 65 * q^81 - 11 * q^82 + 43 * q^83 - 62 * q^84 - q^85 - 9 * q^86 - 22 * q^87 + 20 * q^88 + 38 * q^89 + 13 * q^90 + 86 * q^91 - 119 * q^92 + 10 * q^93 - 18 * q^94 - 50 * q^95 - 34 * q^96 + 17 * q^97 - 32 * q^98 + 26 * q^99

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