LMFDB - Embedded newform 1205.2.a.d.1.22

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			1.22
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)

$f(q)$	$=$	$q+2.36481 q^{2} +0.380137 q^{3} +3.59233 q^{4} -1.00000 q^{5} +0.898952 q^{6} +4.83015 q^{7} +3.76557 q^{8} -2.85550 q^{9} +O(q^{10})$	\(q+2.36481 q^{2} +0.380137 q^{3} +3.59233 q^{4} -1.00000 q^{5} +0.898952 q^{6} +4.83015 q^{7} +3.76557 q^{8} -2.85550 q^{9} -2.36481 q^{10} +4.47470 q^{11} +1.36558 q^{12} -5.34811 q^{13} +11.4224 q^{14} -0.380137 q^{15} +1.72020 q^{16} +5.51063 q^{17} -6.75271 q^{18} +3.77908 q^{19} -3.59233 q^{20} +1.83612 q^{21} +10.5818 q^{22} -3.44758 q^{23} +1.43143 q^{24} +1.00000 q^{25} -12.6473 q^{26} -2.22589 q^{27} +17.3515 q^{28} -4.63882 q^{29} -0.898952 q^{30} -0.722543 q^{31} -3.46320 q^{32} +1.70100 q^{33} +13.0316 q^{34} -4.83015 q^{35} -10.2579 q^{36} +1.48789 q^{37} +8.93682 q^{38} -2.03301 q^{39} -3.76557 q^{40} +6.18175 q^{41} +4.34207 q^{42} +0.997748 q^{43} +16.0746 q^{44} +2.85550 q^{45} -8.15287 q^{46} -4.93746 q^{47} +0.653910 q^{48} +16.3303 q^{49} +2.36481 q^{50} +2.09479 q^{51} -19.2122 q^{52} -4.28705 q^{53} -5.26381 q^{54} -4.47470 q^{55} +18.1883 q^{56} +1.43657 q^{57} -10.9699 q^{58} -6.23585 q^{59} -1.36558 q^{60} +0.376249 q^{61} -1.70868 q^{62} -13.7925 q^{63} -11.6302 q^{64} +5.34811 q^{65} +4.02254 q^{66} +6.87362 q^{67} +19.7960 q^{68} -1.31055 q^{69} -11.4224 q^{70} -8.06026 q^{71} -10.7526 q^{72} -6.15739 q^{73} +3.51859 q^{74} +0.380137 q^{75} +13.5757 q^{76} +21.6135 q^{77} -4.80769 q^{78} -14.8153 q^{79} -1.72020 q^{80} +7.72035 q^{81} +14.6187 q^{82} -2.19624 q^{83} +6.59594 q^{84} -5.51063 q^{85} +2.35949 q^{86} -1.76339 q^{87} +16.8498 q^{88} -13.3433 q^{89} +6.75271 q^{90} -25.8322 q^{91} -12.3849 q^{92} -0.274665 q^{93} -11.6762 q^{94} -3.77908 q^{95} -1.31649 q^{96} +7.13909 q^{97} +38.6181 q^{98} -12.7775 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	2.36481	1.67217	0.836087	−	0.548597i	$-0.184838\pi$
$2$	2.36481	1.67217	0.836087	+	0.548597i	$0.184838\pi$
$3$	0.380137	0.219472	0.109736	−	0.993961i	$-0.464999\pi$
$3$	0.380137	0.219472	0.109736	+	0.993961i	$0.464999\pi$
$4$	3.59233	1.79617
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	0.898952	0.366995
$7$	4.83015	1.82562	0.912812	−	0.408380i	$-0.133906\pi$
$7$	4.83015	1.82562	0.912812	+	0.408380i	$0.133906\pi$
$8$	3.76557	1.33133
$9$	−2.85550	−0.951832
$10$	−2.36481	−0.747819
$11$	4.47470	1.34917	0.674587	−	0.738195i	$-0.264322\pi$
$11$	4.47470	1.34917	0.674587	+	0.738195i	$0.264322\pi$
$12$	1.36558	0.394208
$13$	−5.34811	−1.48330	−0.741649	−	0.670788i	$-0.765956\pi$
$13$	−5.34811	−1.48330	−0.741649	+	0.670788i	$0.765956\pi$
$14$	11.4224	3.05276
$15$	−0.380137	−0.0981509
$16$	1.72020	0.430050
$17$	5.51063	1.33652	0.668262	−	0.743926i	$-0.267039\pi$
$17$	5.51063	1.33652	0.668262	+	0.743926i	$0.267039\pi$
$18$	−6.75271	−1.59163
$19$	3.77908	0.866981	0.433490	−	0.901158i	$-0.357282\pi$
$19$	3.77908	0.866981	0.433490	+	0.901158i	$0.357282\pi$
$20$	−3.59233	−0.803270
$21$	1.83612	0.400673
$22$	10.5818	2.25605
$23$	−3.44758	−0.718870	−0.359435	−	0.933170i	$-0.617031\pi$
$23$	−3.44758	−0.718870	−0.359435	+	0.933170i	$0.617031\pi$
$24$	1.43143	0.292190
$25$	1.00000	0.200000
$26$	−12.6473	−2.48033
$27$	−2.22589	−0.428372
$28$	17.3515	3.27913
$29$	−4.63882	−0.861408	−0.430704	−	0.902493i	$-0.641735\pi$
$29$	−4.63882	−0.861408	−0.430704	+	0.902493i	$0.641735\pi$
$30$	−0.898952	−0.164125
$31$	−0.722543	−0.129773	−0.0648863	−	0.997893i	$-0.520668\pi$
$31$	−0.722543	−0.129773	−0.0648863	+	0.997893i	$0.520668\pi$
$32$	−3.46320	−0.612213
$33$	1.70100	0.296106
$34$	13.0316	2.23490
$35$	−4.83015	−0.816444
$36$	−10.2579	−1.70965
$37$	1.48789	0.244608	0.122304	−	0.992493i	$-0.460972\pi$
$37$	1.48789	0.244608	0.122304	+	0.992493i	$0.460972\pi$
$38$	8.93682	1.44974
$39$	−2.03301	−0.325543
$40$	−3.76557	−0.595389
$41$	6.18175	0.965427	0.482714	−	0.875778i	$-0.339651\pi$
$41$	6.18175	0.965427	0.482714	+	0.875778i	$0.339651\pi$
$42$	4.34207	0.669996
$43$	0.997748	0.152155	0.0760776	−	0.997102i	$-0.475760\pi$
$43$	0.997748	0.152155	0.0760776	+	0.997102i	$0.475760\pi$
$44$	16.0746	2.42334
$45$	2.85550	0.425672
$46$	−8.15287	−1.20208
$47$	−4.93746	−0.720203	−0.360101	−	0.932913i	$-0.617258\pi$
$47$	−4.93746	−0.720203	−0.360101	+	0.932913i	$0.617258\pi$
$48$	0.653910	0.0943838
$49$	16.3303	2.33290
$50$	2.36481	0.334435
$51$	2.09479	0.293329
$52$	−19.2122	−2.66425
$53$	−4.28705	−0.588872	−0.294436	−	0.955671i	$-0.595132\pi$
$53$	−4.28705	−0.588872	−0.294436	+	0.955671i	$0.595132\pi$
$54$	−5.26381	−0.716313
$55$	−4.47470	−0.603369
$56$	18.1883	2.43051
$57$	1.43657	0.190278
$58$	−10.9699	−1.44042
$59$	−6.23585	−0.811838	−0.405919	−	0.913909i	$-0.633048\pi$
$59$	−6.23585	−0.811838	−0.405919	+	0.913909i	$0.633048\pi$
$60$	−1.36558	−0.176295
$61$	0.376249	0.0481737	0.0240868	−	0.999710i	$-0.492332\pi$
$61$	0.376249	0.0481737	0.0240868	+	0.999710i	$0.492332\pi$
$62$	−1.70868	−0.217002
$63$	−13.7925	−1.73769
$64$	−11.6302	−1.45378
$65$	5.34811	0.663351
$66$	4.02254	0.495141
$67$	6.87362	0.839746	0.419873	−	0.907583i	$-0.362075\pi$
$67$	6.87362	0.839746	0.419873	+	0.907583i	$0.362075\pi$
$68$	19.7960	2.40062
$69$	−1.31055	−0.157772
$70$	−11.4224	−1.36524
$71$	−8.06026	−0.956577	−0.478288	−	0.878203i	$-0.658743\pi$
$71$	−8.06026	−0.956577	−0.478288	+	0.878203i	$0.658743\pi$
$72$	−10.7526	−1.26720
$73$	−6.15739	−0.720668	−0.360334	−	0.932823i	$-0.617337\pi$
$73$	−6.15739	−0.720668	−0.360334	+	0.932823i	$0.617337\pi$
$74$	3.51859	0.409028
$75$	0.380137	0.0438944
$76$	13.5757	1.55724
$77$	21.6135	2.46308
$78$	−4.80769	−0.544364
$79$	−14.8153	−1.66685	−0.833426	−	0.552631i	$-0.813624\pi$
$79$	−14.8153	−1.66685	−0.833426	+	0.552631i	$0.813624\pi$
$80$	−1.72020	−0.192324
$81$	7.72035	0.857816
$82$	14.6187	1.61436
$83$	−2.19624	−0.241068	−0.120534	−	0.992709i	$-0.538461\pi$
$83$	−2.19624	−0.241068	−0.120534	+	0.992709i	$0.538461\pi$
$84$	6.59594	0.719676
$85$	−5.51063	−0.597711
$86$	2.35949	0.254430
$87$	−1.76339	−0.189055
$88$	16.8498	1.79620
$89$	−13.3433	−1.41439	−0.707194	−	0.707019i	$-0.750039\pi$
$89$	−13.3433	−1.41439	−0.707194	+	0.707019i	$0.750039\pi$
$90$	6.75271	0.711798
$91$	−25.8322	−2.70795
$92$	−12.3849	−1.29121
$93$	−0.274665	−0.0284815
$94$	−11.6762	−1.20430
$95$	−3.77908	−0.387726
$96$	−1.31649	−0.134364
$97$	7.13909	0.724865	0.362433	−	0.932010i	$-0.381946\pi$
$97$	7.13909	0.724865	0.362433	+	0.932010i	$0.381946\pi$
$98$	38.6181	3.90102
$99$	−12.7775	−1.28419
$100$	3.59233	0.359233
$101$	6.70260	0.666933	0.333467	−	0.942762i	$-0.391782\pi$
$101$	6.70260	0.666933	0.333467	+	0.942762i	$0.391782\pi$
$102$	4.95379	0.490498
$103$	−0.908151	−0.0894828	−0.0447414	−	0.998999i	$-0.514246\pi$
$103$	−0.908151	−0.0894828	−0.0447414	+	0.998999i	$0.514246\pi$
$104$	−20.1387	−1.97476
$105$	−1.83612	−0.179187
$106$	−10.1381	−0.984697
$107$	12.5928	1.21739	0.608696	−	0.793404i	$-0.291693\pi$
$107$	12.5928	1.21739	0.608696	+	0.793404i	$0.291693\pi$
$108$	−7.99614	−0.769429
$109$	−5.26275	−0.504080	−0.252040	−	0.967717i	$-0.581101\pi$
$109$	−5.26275	−0.504080	−0.252040	+	0.967717i	$0.581101\pi$
$110$	−10.5818	−1.00894
$111$	0.565603	0.0536847
$112$	8.30881	0.785109
$113$	6.78203	0.638000	0.319000	−	0.947755i	$-0.396653\pi$
$113$	6.78203	0.638000	0.319000	+	0.947755i	$0.396653\pi$
$114$	3.39721	0.318178
$115$	3.44758	0.321488
$116$	−16.6642	−1.54723
$117$	15.2715	1.41185
$118$	−14.7466	−1.35753
$119$	26.6171	2.43999
$120$	−1.43143	−0.130671
$121$	9.02298	0.820271
$122$	0.889757	0.0805548
$123$	2.34991	0.211884
$124$	−2.59562	−0.233093
$125$	−1.00000	−0.0894427
$126$	−32.6166	−2.90572
$127$	−18.1231	−1.60817	−0.804085	−	0.594515i	$-0.797344\pi$
$127$	−18.1231	−1.60817	−0.804085	+	0.594515i	$0.797344\pi$
$128$	−20.5769	−1.81875
$129$	0.379281	0.0333938
$130$	12.6473	1.10924
$131$	22.3800	1.95535	0.977674	−	0.210126i	$-0.0673875\pi$
$131$	22.3800	1.95535	0.977674	+	0.210126i	$0.0673875\pi$
$132$	6.11056	0.531856
$133$	18.2535	1.58278
$134$	16.2548	1.40420
$135$	2.22589	0.191574
$136$	20.7507	1.77935
$137$	−18.9135	−1.61589	−0.807945	−	0.589258i	$-0.799420\pi$
$137$	−18.9135	−1.61589	−0.807945	+	0.589258i	$0.799420\pi$
$138$	−3.09921	−0.263822
$139$	14.2901	1.21207	0.606037	−	0.795436i	$-0.292758\pi$
$139$	14.2901	1.21207	0.606037	+	0.795436i	$0.292758\pi$
$140$	−17.3515	−1.46647
$141$	−1.87691	−0.158064
$142$	−19.0610	−1.59956
$143$	−23.9312	−2.00123
$144$	−4.91202	−0.409335
$145$	4.63882	0.385233
$146$	−14.5611	−1.20508
$147$	6.20775	0.512007
$148$	5.34502	0.439358
$149$	−12.4924	−1.02341	−0.511707	−	0.859160i	$-0.670987\pi$
$149$	−12.4924	−1.02341	−0.511707	+	0.859160i	$0.670987\pi$
$150$	0.898952	0.0733991
$151$	−22.7962	−1.85513	−0.927563	−	0.373668i	$-0.878100\pi$
$151$	−22.7962	−1.85513	−0.927563	+	0.373668i	$0.878100\pi$
$152$	14.2304	1.15424
$153$	−15.7356	−1.27215
$154$	51.1118	4.11871
$155$	0.722543	0.0580361
$156$	−7.30326	−0.584729
$157$	−20.9876	−1.67499	−0.837494	−	0.546446i	$-0.815980\pi$
$157$	−20.9876	−1.67499	−0.837494	+	0.546446i	$0.815980\pi$
$158$	−35.0354	−2.78727
$159$	−1.62967	−0.129241
$160$	3.46320	0.273790
$161$	−16.6523	−1.31239
$162$	18.2572	1.43442
$163$	17.1140	1.34047	0.670235	−	0.742149i	$-0.266193\pi$
$163$	17.1140	1.34047	0.670235	+	0.742149i	$0.266193\pi$
$164$	22.2069	1.73407
$165$	−1.70100	−0.132423
$166$	−5.19368	−0.403108
$167$	−18.5620	−1.43637	−0.718184	−	0.695853i	$-0.755027\pi$
$167$	−18.5620	−1.43637	−0.718184	+	0.695853i	$0.755027\pi$
$168$	6.91403	0.533429
$169$	15.6023	1.20018
$170$	−13.0316	−0.999478
$171$	−10.7912	−0.825220
$172$	3.58425	0.273296
$173$	14.5482	1.10608	0.553038	−	0.833156i	$-0.313468\pi$
$173$	14.5482	1.10608	0.553038	+	0.833156i	$0.313468\pi$
$174$	−4.17008	−0.316133
$175$	4.83015	0.365125
$176$	7.69738	0.580212
$177$	−2.37047	−0.178176
$178$	−31.5544	−2.36510
$179$	−24.1703	−1.80658	−0.903288	−	0.429035i	$-0.858854\pi$
$179$	−24.1703	−1.80658	−0.903288	+	0.429035i	$0.858854\pi$
$180$	10.2579	0.764579
$181$	3.32022	0.246790	0.123395	−	0.992358i	$-0.460622\pi$
$181$	3.32022	0.246790	0.123395	+	0.992358i	$0.460622\pi$
$182$	−61.0882	−4.52816
$183$	0.143026	0.0105728
$184$	−12.9821	−0.957053
$185$	−1.48789	−0.109392
$186$	−0.649532	−0.0476260
$187$	24.6584	1.80320
$188$	−17.7370	−1.29360
$189$	−10.7514	−0.782047
$190$	−8.93682	−0.648345
$191$	−5.29972	−0.383474	−0.191737	−	0.981446i	$-0.561412\pi$
$191$	−5.29972	−0.383474	−0.191737	+	0.981446i	$0.561412\pi$
$192$	−4.42107	−0.319063
$193$	21.2965	1.53295	0.766477	−	0.642272i	$-0.222008\pi$
$193$	21.2965	1.53295	0.766477	+	0.642272i	$0.222008\pi$
$194$	16.8826	1.21210
$195$	2.03301	0.145587
$196$	58.6640	4.19029
$197$	18.5960	1.32491	0.662454	−	0.749103i	$-0.269515\pi$
$197$	18.5960	1.32491	0.662454	+	0.749103i	$0.269515\pi$
$198$	−30.2164	−2.14738
$199$	9.32717	0.661185	0.330593	−	0.943774i	$-0.392751\pi$
$199$	9.32717	0.661185	0.330593	+	0.943774i	$0.392751\pi$
$200$	3.76557	0.266266
$201$	2.61291	0.184301
$202$	15.8504	1.11523
$203$	−22.4062	−1.57261
$204$	7.52519	0.526869
$205$	−6.18175	−0.431752
$206$	−2.14761	−0.149631
$207$	9.84455	0.684243
$208$	−9.19981	−0.637892
$209$	16.9103	1.16971
$210$	−4.34207	−0.299631
$211$	0.847837	0.0583675	0.0291838	−	0.999574i	$-0.490709\pi$
$211$	0.847837	0.0583675	0.0291838	+	0.999574i	$0.490709\pi$
$212$	−15.4005	−1.05771
$213$	−3.06400	−0.209942
$214$	29.7796	2.03569
$215$	−0.997748	−0.0680459
$216$	−8.38174	−0.570305
$217$	−3.48999	−0.236916
$218$	−12.4454	−0.842910
$219$	−2.34065	−0.158166
$220$	−16.0746	−1.08375
$221$	−29.4714	−1.98246
$222$	1.33755	0.0897702
$223$	−8.90822	−0.596539	−0.298269	−	0.954482i	$-0.596409\pi$
$223$	−8.90822	−0.596539	−0.298269	+	0.954482i	$0.596409\pi$
$224$	−16.7278	−1.11767
$225$	−2.85550	−0.190366
$226$	16.0382	1.06685
$227$	−8.63358	−0.573031	−0.286515	−	0.958076i	$-0.592497\pi$
$227$	−8.63358	−0.573031	−0.286515	+	0.958076i	$0.592497\pi$
$228$	5.16063	0.341771
$229$	27.9672	1.84812	0.924062	−	0.382244i	$-0.124848\pi$
$229$	27.9672	1.84812	0.924062	+	0.382244i	$0.124848\pi$
$230$	8.15287	0.537585
$231$	8.21608	0.540578
$232$	−17.4678	−1.14682
$233$	−10.3945	−0.680966	−0.340483	−	0.940251i	$-0.610591\pi$
$233$	−10.3945	−0.680966	−0.340483	+	0.940251i	$0.610591\pi$
$234$	36.1142	2.36086
$235$	4.93746	0.322085
$236$	−22.4012	−1.45820
$237$	−5.63184	−0.365827
$238$	62.9445	4.08009
$239$	5.16421	0.334045	0.167023	−	0.985953i	$-0.446585\pi$
$239$	5.16421	0.334045	0.167023	+	0.985953i	$0.446585\pi$
$240$	−0.653910	−0.0422097
$241$	1.00000	0.0644157
$241$	1.00000	0.0644157
$242$	21.3376	1.37164
$243$	9.61245	0.616639
$244$	1.35161	0.0865280
$245$	−16.3303	−1.04331
$246$	5.55709	0.354307
$247$	−20.2109	−1.28599
$248$	−2.72079	−0.172770
$249$	−0.834870	−0.0529077
$250$	−2.36481	−0.149564
$251$	13.1748	0.831584	0.415792	−	0.909460i	$-0.363504\pi$
$251$	13.1748	0.831584	0.415792	+	0.909460i	$0.363504\pi$
$252$	−49.5472	−3.12118
$253$	−15.4269	−0.969881
$254$	−42.8578	−2.68914
$255$	−2.09479	−0.131181
$256$	−25.4000	−1.58750
$257$	−4.59953	−0.286911	−0.143456	−	0.989657i	$-0.545821\pi$
$257$	−4.59953	−0.286911	−0.143456	+	0.989657i	$0.545821\pi$
$258$	0.896928	0.0558403
$259$	7.18675	0.446563
$260$	19.2122	1.19149
$261$	13.2461	0.819916
$262$	52.9245	3.26968
$263$	21.9954	1.35630	0.678148	−	0.734926i	$-0.262783\pi$
$263$	21.9954	1.35630	0.678148	+	0.734926i	$0.262783\pi$
$264$	6.40523	0.394215
$265$	4.28705	0.263352
$266$	43.1661	2.64669
$267$	−5.07228	−0.310419
$268$	24.6923	1.50832
$269$	12.8637	0.784313	0.392157	−	0.919898i	$-0.371729\pi$
$269$	12.8637	0.784313	0.392157	+	0.919898i	$0.371729\pi$
$270$	5.26381	0.320345
$271$	0.373615	0.0226955	0.0113477	−	0.999936i	$-0.496388\pi$
$271$	0.373615	0.0226955	0.0113477	+	0.999936i	$0.496388\pi$
$272$	9.47937	0.574771
$273$	−9.81975	−0.594318
$274$	−44.7269	−2.70205
$275$	4.47470	0.269835
$276$	−4.70794	−0.283385
$277$	21.7630	1.30761	0.653806	−	0.756662i	$-0.273171\pi$
$277$	21.7630	1.30761	0.653806	+	0.756662i	$0.273171\pi$
$278$	33.7935	2.02680
$279$	2.06322	0.123522
$280$	−18.1883	−1.08696
$281$	8.02405	0.478675	0.239337	−	0.970936i	$-0.423070\pi$
$281$	8.02405	0.478675	0.239337	+	0.970936i	$0.423070\pi$
$282$	−4.43854	−0.264311
$283$	10.4446	0.620866	0.310433	−	0.950595i	$-0.399526\pi$
$283$	10.4446	0.620866	0.310433	+	0.950595i	$0.399526\pi$
$284$	−28.9551	−1.71817
$285$	−1.43657	−0.0850949
$286$	−56.5928	−3.34640
$287$	29.8588	1.76251
$288$	9.88915	0.582724
$289$	13.3670	0.786295
$290$	10.9699	0.644177
$291$	2.71383	0.159088
$292$	−22.1194	−1.29444
$293$	−4.29481	−0.250905	−0.125453	−	0.992100i	$-0.540038\pi$
$293$	−4.29481	−0.250905	−0.125453	+	0.992100i	$0.540038\pi$
$294$	14.6802	0.856165
$295$	6.23585	0.363065
$296$	5.60277	0.325655
$297$	−9.96019	−0.577949
$298$	−29.5421	−1.71133
$299$	18.4380	1.06630
$300$	1.36558	0.0788417
$301$	4.81927	0.277778
$302$	−53.9086	−3.10209
$303$	2.54790	0.146373
$304$	6.50077	0.372845
$305$	−0.376249	−0.0215439
$306$	−37.2117	−2.12725
$307$	7.51149	0.428703	0.214352	−	0.976757i	$-0.431236\pi$
$307$	7.51149	0.428703	0.214352	+	0.976757i	$0.431236\pi$
$308$	77.6429	4.42411
$309$	−0.345221	−0.0196390
$310$	1.70868	0.0970465
$311$	16.7234	0.948299	0.474150	−	0.880444i	$-0.342756\pi$
$311$	16.7234	0.948299	0.474150	+	0.880444i	$0.342756\pi$
$312$	−7.65545	−0.433405
$313$	9.94457	0.562100	0.281050	−	0.959693i	$-0.409317\pi$
$313$	9.94457	0.562100	0.281050	+	0.959693i	$0.409317\pi$
$314$	−49.6316	−2.80087
$315$	13.7925	0.777118
$316$	−53.2215	−2.99394
$317$	−34.7239	−1.95029	−0.975145	−	0.221570i	$-0.928882\pi$
$317$	−34.7239	−1.95029	−0.975145	+	0.221570i	$0.928882\pi$
$318$	−3.85385	−0.216113
$319$	−20.7574	−1.16219
$320$	11.6302	0.650148
$321$	4.78698	0.267183
$322$	−39.3796	−2.19454
$323$	20.8251	1.15874
$324$	27.7341	1.54078
$325$	−5.34811	−0.296660
$326$	40.4713	2.24150
$327$	−2.00056	−0.110631
$328$	23.2778	1.28530
$329$	−23.8487	−1.31482
$330$	−4.02254	−0.221434
$331$	−8.15374	−0.448170	−0.224085	−	0.974570i	$-0.571939\pi$
$331$	−8.15374	−0.448170	−0.224085	+	0.974570i	$0.571939\pi$
$332$	−7.88961	−0.432999
$333$	−4.24868	−0.232826
$334$	−43.8956	−2.40186
$335$	−6.87362	−0.375546
$336$	3.15848	0.172309
$337$	−15.3990	−0.838838	−0.419419	−	0.907793i	$-0.637766\pi$
$337$	−15.3990	−0.838838	−0.419419	+	0.907793i	$0.637766\pi$
$338$	36.8965	2.00690
$339$	2.57810	0.140023
$340$	−19.7960	−1.07359
$341$	−3.23317	−0.175086
$342$	−25.5190	−1.37991
$343$	45.0669	2.43338
$344$	3.75709	0.202569
$345$	1.31055	0.0705577
$346$	34.4037	1.84955
$347$	−25.2989	−1.35811	−0.679057	−	0.734085i	$-0.737611\pi$
$347$	−25.2989	−1.35811	−0.679057	+	0.734085i	$0.737611\pi$
$348$	−6.33468	−0.339574
$349$	20.7431	1.11035	0.555177	−	0.831732i	$-0.312650\pi$
$349$	20.7431	1.11035	0.555177	+	0.831732i	$0.312650\pi$
$350$	11.4224	0.610552
$351$	11.9043	0.635404
$352$	−15.4968	−0.825982
$353$	−23.7995	−1.26672	−0.633359	−	0.773858i	$-0.718325\pi$
$353$	−23.7995	−1.26672	−0.633359	+	0.773858i	$0.718325\pi$
$354$	−5.60572	−0.297941
$355$	8.06026	0.427794
$356$	−47.9336	−2.54048
$357$	10.1182	0.535509
$358$	−57.1583	−3.02091
$359$	11.5770	0.611009	0.305505	−	0.952191i	$-0.401175\pi$
$359$	11.5770	0.611009	0.305505	+	0.952191i	$0.401175\pi$
$360$	10.7526	0.566710
$361$	−4.71854	−0.248344
$362$	7.85170	0.412676
$363$	3.42996	0.180026
$364$	−92.7978	−4.86392
$365$	6.15739	0.322292
$366$	0.338229	0.0176795
$367$	26.3160	1.37369	0.686843	−	0.726806i	$-0.258996\pi$
$367$	26.3160	1.37369	0.686843	+	0.726806i	$0.258996\pi$
$368$	−5.93052	−0.309150
$369$	−17.6520	−0.918924
$370$	−3.51859	−0.182923
$371$	−20.7071	−1.07506
$372$	−0.986689	−0.0511575
$373$	0.882219	0.0456795	0.0228398	−	0.999739i	$-0.492729\pi$
$373$	0.882219	0.0456795	0.0228398	+	0.999739i	$0.492729\pi$
$374$	58.3125	3.01527
$375$	−0.380137	−0.0196302
$376$	−18.5924	−0.958828
$377$	24.8089	1.27773
$378$	−25.4250	−1.30772
$379$	5.62985	0.289186	0.144593	−	0.989491i	$-0.453813\pi$
$379$	5.62985	0.289186	0.144593	+	0.989491i	$0.453813\pi$
$380$	−13.5757	−0.696420
$381$	−6.88927	−0.352948
$382$	−12.5328	−0.641236
$383$	6.24745	0.319230	0.159615	−	0.987179i	$-0.448975\pi$
$383$	6.24745	0.319230	0.159615	+	0.987179i	$0.448975\pi$
$384$	−7.82202	−0.399166
$385$	−21.6135	−1.10153
$386$	50.3622	2.56337
$387$	−2.84907	−0.144826
$388$	25.6460	1.30198
$389$	3.43419	0.174120	0.0870602	−	0.996203i	$-0.472253\pi$
$389$	3.43419	0.174120	0.0870602	+	0.996203i	$0.472253\pi$
$390$	4.80769	0.243447
$391$	−18.9983	−0.960786
$392$	61.4930	3.10587
$393$	8.50745	0.429144
$394$	43.9760	2.21548
$395$	14.8153	0.745439
$396$	−45.9011	−2.30661
$397$	30.2946	1.52044	0.760222	−	0.649663i	$-0.225090\pi$
$397$	30.2946	1.52044	0.760222	+	0.649663i	$0.225090\pi$
$398$	22.0570	1.10562
$399$	6.93883	0.347376
$400$	1.72020	0.0860099
$401$	34.1514	1.70544	0.852719	−	0.522369i	$-0.174952\pi$
$401$	34.1514	1.70544	0.852719	+	0.522369i	$0.174952\pi$
$402$	6.17905	0.308183
$403$	3.86424	0.192492
$404$	24.0780	1.19792
$405$	−7.72035	−0.383627
$406$	−52.9865	−2.62967
$407$	6.65789	0.330019
$408$	7.88809	0.390518
$409$	−9.95127	−0.492059	−0.246029	−	0.969262i	$-0.579126\pi$
$409$	−9.95127	−0.492059	−0.246029	+	0.969262i	$0.579126\pi$
$410$	−14.6187	−0.721965
$411$	−7.18971	−0.354642
$412$	−3.26238	−0.160726
$413$	−30.1201	−1.48211
$414$	23.2805	1.14417
$415$	2.19624	0.107809
$416$	18.5216	0.908094
$417$	5.43221	0.266016
$418$	39.9896	1.95596
$419$	28.1173	1.37362	0.686811	−	0.726836i	$-0.259010\pi$
$419$	28.1173	1.37362	0.686811	+	0.726836i	$0.259010\pi$
$420$	−6.59594	−0.321849
$421$	0.488057	0.0237865	0.0118932	−	0.999929i	$-0.496214\pi$
$421$	0.488057	0.0237865	0.0118932	+	0.999929i	$0.496214\pi$
$422$	2.00497	0.0976006
$423$	14.0989	0.685512
$424$	−16.1432	−0.783983
$425$	5.51063	0.267305
$426$	−7.24578	−0.351059
$427$	1.81734	0.0879471
$428$	45.2375	2.18664
$429$	−9.09713	−0.439214
$430$	−2.35949	−0.113785
$431$	10.4518	0.503445	0.251723	−	0.967799i	$-0.419003\pi$
$431$	10.4518	0.503445	0.251723	+	0.967799i	$0.419003\pi$
$432$	−3.82897	−0.184221
$433$	14.5559	0.699512	0.349756	−	0.936841i	$-0.386264\pi$
$433$	14.5559	0.699512	0.349756	+	0.936841i	$0.386264\pi$
$434$	−8.25317	−0.396165
$435$	1.76339	0.0845479
$436$	−18.9056	−0.905412
$437$	−13.0287	−0.623246
$438$	−5.53519	−0.264482
$439$	6.17828	0.294873	0.147437	−	0.989071i	$-0.452898\pi$
$439$	6.17828	0.294873	0.147437	+	0.989071i	$0.452898\pi$
$440$	−16.8498	−0.803284
$441$	−46.6312	−2.22053
$442$	−69.6944	−3.31502
$443$	−8.80926	−0.418541	−0.209270	−	0.977858i	$-0.567109\pi$
$443$	−8.80926	−0.418541	−0.209270	+	0.977858i	$0.567109\pi$
$444$	2.03184	0.0964267
$445$	13.3433	0.632534
$446$	−21.0663	−0.997517
$447$	−4.74881	−0.224611
$448$	−56.1756	−2.65405
$449$	−16.8616	−0.795747	−0.397873	−	0.917440i	$-0.630252\pi$
$449$	−16.8616	−0.795747	−0.397873	+	0.917440i	$0.630252\pi$
$450$	−6.75271	−0.318326
$451$	27.6615	1.30253
$452$	24.3633	1.14595
$453$	−8.66565	−0.407148
$454$	−20.4168	−0.958207
$455$	25.8322	1.21103
$456$	5.40950	0.253323
$457$	32.5263	1.52152	0.760758	−	0.649035i	$-0.224827\pi$
$457$	32.5263	1.52152	0.760758	+	0.649035i	$0.224827\pi$
$458$	66.1371	3.09038
$459$	−12.2660	−0.572530
$460$	12.3849	0.577447
$461$	5.62215	0.261850	0.130925	−	0.991392i	$-0.458205\pi$
$461$	5.62215	0.261850	0.130925	+	0.991392i	$0.458205\pi$
$462$	19.4295	0.903941
$463$	26.4016	1.22698	0.613492	−	0.789701i	$-0.289764\pi$
$463$	26.4016	1.22698	0.613492	+	0.789701i	$0.289764\pi$
$464$	−7.97970	−0.370448
$465$	0.274665	0.0127373
$466$	−24.5810	−1.13869
$467$	−25.0909	−1.16107	−0.580534	−	0.814236i	$-0.697156\pi$
$467$	−25.0909	−1.16107	−0.580534	+	0.814236i	$0.697156\pi$
$468$	54.8604	2.53592
$469$	33.2006	1.53306
$470$	11.6762	0.538581
$471$	−7.97814	−0.367613
$472$	−23.4815	−1.08082
$473$	4.46463	0.205284
$474$	−13.3182	−0.611727
$475$	3.77908	0.173396
$476$	95.6177	4.38263
$477$	12.2417	0.560507
$478$	12.2124	0.558582
$479$	38.0484	1.73848	0.869238	−	0.494393i	$-0.164610\pi$
$479$	38.0484	1.73848	0.869238	+	0.494393i	$0.164610\pi$
$480$	1.31649	0.0600892
$481$	−7.95742	−0.362827
$482$	2.36481	0.107714
$483$	−6.33015	−0.288032
$484$	32.4136	1.47334
$485$	−7.13909	−0.324170
$486$	22.7316	1.03113
$487$	−16.5859	−0.751579	−0.375790	−	0.926705i	$-0.622628\pi$
$487$	−16.5859	−0.751579	−0.375790	+	0.926705i	$0.622628\pi$
$488$	1.41679	0.0641351
$489$	6.50565	0.294196
$490$	−38.6181	−1.74459
$491$	16.2926	0.735273	0.367637	−	0.929970i	$-0.380167\pi$
$491$	16.2926	0.735273	0.367637	+	0.929970i	$0.380167\pi$
$492$	8.44166	0.380579
$493$	−25.5628	−1.15129
$494$	−47.7951	−2.15040
$495$	12.7775	0.574306
$496$	−1.24292	−0.0558087
$497$	−38.9322	−1.74635
$498$	−1.97431	−0.0884709
$499$	11.3471	0.507966	0.253983	−	0.967209i	$-0.418259\pi$
$499$	11.3471	0.507966	0.253983	+	0.967209i	$0.418259\pi$
$500$	−3.59233	−0.160654
$501$	−7.05609	−0.315243
$502$	31.1558	1.39055
$503$	−25.7106	−1.14638	−0.573190	−	0.819423i	$-0.694294\pi$
$503$	−25.7106	−1.14638	−0.573190	+	0.819423i	$0.694294\pi$
$504$	−51.9365	−2.31344
$505$	−6.70260	−0.298262
$506$	−36.4817	−1.62181
$507$	5.93100	0.263405
$508$	−65.1044	−2.88854
$509$	40.8846	1.81218	0.906089	−	0.423087i	$-0.139053\pi$
$509$	40.8846	1.81218	0.906089	+	0.423087i	$0.139053\pi$
$510$	−4.95379	−0.219357
$511$	−29.7411	−1.31567
$512$	−18.9124	−0.835820
$513$	−8.41182	−0.371391
$514$	−10.8770	−0.479765
$515$	0.908151	0.0400179
$516$	1.36250	0.0599809
$517$	−22.0937	−0.971679
$518$	16.9953	0.746731
$519$	5.53029	0.242753
$520$	20.1387	0.883140
$521$	−36.8948	−1.61639	−0.808196	−	0.588914i	$-0.799556\pi$
$521$	−36.8948	−1.61639	−0.808196	+	0.588914i	$0.799556\pi$
$522$	31.3246	1.37104
$523$	10.7330	0.469323	0.234662	−	0.972077i	$-0.424602\pi$
$523$	10.7330	0.469323	0.234662	+	0.972077i	$0.424602\pi$
$524$	80.3964	3.51213
$525$	1.83612	0.0801347
$526$	52.0150	2.26796
$527$	−3.98167	−0.173444
$528$	2.92605	0.127340
$529$	−11.1142	−0.483226
$530$	10.1381	0.440370
$531$	17.8064	0.772733
$532$	65.5728	2.84294
$533$	−33.0607	−1.43202
$534$	−11.9950	−0.519074
$535$	−12.5928	−0.544434
$536$	25.8831	1.11798
$537$	−9.18803	−0.396493
$538$	30.4202	1.31151
$539$	73.0734	3.14749
$540$	7.99614	0.344099
$541$	28.1819	1.21164	0.605818	−	0.795604i	$-0.292846\pi$
$541$	28.1819	1.21164	0.605818	+	0.795604i	$0.292846\pi$
$542$	0.883529	0.0379508
$543$	1.26214	0.0541635
$544$	−19.0844	−0.818237
$545$	5.26275	0.225432
$546$	−23.2219	−0.993804
$547$	−18.2871	−0.781901	−0.390950	−	0.920412i	$-0.627854\pi$
$547$	−18.2871	−0.781901	−0.390950	+	0.920412i	$0.627854\pi$
$548$	−67.9436	−2.90241
$549$	−1.07438	−0.0458533
$550$	10.5818	0.451211
$551$	−17.5305	−0.746824
$552$	−4.93497	−0.210046
$553$	−71.5601	−3.04304
$554$	51.4654	2.18656
$555$	−0.565603	−0.0240085
$556$	51.3350	2.17709
$557$	−23.4579	−0.993944	−0.496972	−	0.867767i	$-0.665555\pi$
$557$	−23.4579	−0.993944	−0.496972	+	0.867767i	$0.665555\pi$
$558$	4.87913	0.206550
$559$	−5.33607	−0.225692
$560$	−8.30881	−0.351111
$561$	9.37357	0.395752
$562$	18.9754	0.800427
$563$	−15.8119	−0.666390	−0.333195	−	0.942858i	$-0.608127\pi$
$563$	−15.8119	−0.666390	−0.333195	+	0.942858i	$0.608127\pi$
$564$	−6.74249	−0.283910
$565$	−6.78203	−0.285322
$566$	24.6995	1.03820
$567$	37.2904	1.56605
$568$	−30.3515	−1.27352
$569$	−47.6429	−1.99729	−0.998646	−	0.0520145i	$-0.983436\pi$
$569$	−47.6429	−1.99729	−0.998646	+	0.0520145i	$0.983436\pi$
$570$	−3.39721	−0.142294
$571$	29.5204	1.23539	0.617694	−	0.786418i	$-0.288067\pi$
$571$	29.5204	1.23539	0.617694	+	0.786418i	$0.288067\pi$
$572$	−85.9689	−3.59454
$573$	−2.01462	−0.0841618
$574$	70.6104	2.94722
$575$	−3.44758	−0.143774
$576$	33.2100	1.38375
$577$	3.31394	0.137961	0.0689806	−	0.997618i	$-0.478025\pi$
$577$	3.31394	0.137961	0.0689806	+	0.997618i	$0.478025\pi$
$578$	31.6105	1.31482
$579$	8.09557	0.336440
$580$	16.6642	0.691944
$581$	−10.6081	−0.440100
$582$	6.41770	0.266022
$583$	−19.1833	−0.794491
$584$	−23.1861	−0.959447
$585$	−15.2715	−0.631399
$586$	−10.1564	−0.419558
$587$	−38.0796	−1.57171	−0.785857	−	0.618408i	$-0.787778\pi$
$587$	−38.0796	−1.57171	−0.785857	+	0.618408i	$0.787778\pi$
$588$	22.3003	0.919650
$589$	−2.73055	−0.112510
$590$	14.7466	0.607108
$591$	7.06901	0.290780
$592$	2.55947	0.105194
$593$	33.7674	1.38666	0.693330	−	0.720620i	$-0.256143\pi$
$593$	33.7674	1.38666	0.693330	+	0.720620i	$0.256143\pi$
$594$	−23.5540	−0.966432
$595$	−26.6171	−1.09120
$596$	−44.8768	−1.83822
$597$	3.54560	0.145112
$598$	43.6025	1.78304
$599$	19.0794	0.779565	0.389782	−	0.920907i	$-0.372550\pi$
$599$	19.0794	0.779565	0.389782	+	0.920907i	$0.372550\pi$
$600$	1.43143	0.0584379
$601$	45.9239	1.87328	0.936638	−	0.350299i	$-0.113920\pi$
$601$	45.9239	1.87328	0.936638	+	0.350299i	$0.113920\pi$
$602$	11.3967	0.464494
$603$	−19.6276	−0.799297
$604$	−81.8914	−3.33211
$605$	−9.02298	−0.366836
$606$	6.02531	0.244761
$607$	24.8789	1.00981	0.504903	−	0.863176i	$-0.331528\pi$
$607$	24.8789	1.00981	0.504903	+	0.863176i	$0.331528\pi$
$608$	−13.0877	−0.530777
$609$	−8.51742	−0.345143
$610$	−0.889757	−0.0360252
$611$	26.4061	1.06828
$612$	−56.5274	−2.28499
$613$	38.1001	1.53885	0.769424	−	0.638739i	$-0.220543\pi$
$613$	38.1001	1.53885	0.769424	+	0.638739i	$0.220543\pi$
$614$	17.7633	0.716867
$615$	−2.34991	−0.0947575
$616$	81.3871	3.27918
$617$	1.54528	0.0622105	0.0311053	−	0.999516i	$-0.490097\pi$
$617$	1.54528	0.0622105	0.0311053	+	0.999516i	$0.490097\pi$
$618$	−0.816384	−0.0328398
$619$	−32.7747	−1.31732	−0.658662	−	0.752439i	$-0.728877\pi$
$619$	−32.7747	−1.31732	−0.658662	+	0.752439i	$0.728877\pi$
$620$	2.59562	0.104243
$621$	7.67393	0.307944
$622$	39.5478	1.58572
$623$	−64.4502	−2.58214
$624$	−3.49718	−0.139999
$625$	1.00000	0.0400000
$626$	23.5170	0.939930
$627$	6.42821	0.256718
$628$	−75.3943	−3.00856
$629$	8.19923	0.326925
$630$	32.6166	1.29948
$631$	11.1404	0.443491	0.221746	−	0.975105i	$-0.428825\pi$
$631$	11.1404	0.443491	0.221746	+	0.975105i	$0.428825\pi$
$632$	−55.7881	−2.21913
$633$	0.322294	0.0128100
$634$	−82.1155	−3.26122
$635$	18.1231	0.719195
$636$	−5.85431	−0.232138
$637$	−87.3364	−3.46039
$638$	−49.0873	−1.94338
$639$	23.0160	0.910500
$640$	20.5769	0.813372
$641$	−33.6826	−1.33038	−0.665191	−	0.746673i	$-0.731650\pi$
$641$	−33.6826	−1.33038	−0.665191	+	0.746673i	$0.731650\pi$
$642$	11.3203	0.446777
$643$	14.2377	0.561479	0.280739	−	0.959784i	$-0.409420\pi$
$643$	14.2377	0.561479	0.280739	+	0.959784i	$0.409420\pi$
$644$	−59.8207	−2.35726
$645$	−0.379281	−0.0149342
$646$	49.2475	1.93762
$647$	−42.3016	−1.66305	−0.831525	−	0.555488i	$-0.812532\pi$
$647$	−42.3016	−1.66305	−0.831525	+	0.555488i	$0.812532\pi$
$648$	29.0715	1.14204
$649$	−27.9036	−1.09531
$650$	−12.6473	−0.496067
$651$	−1.32667	−0.0519964
$652$	61.4791	2.40771
$653$	−13.1509	−0.514634	−0.257317	−	0.966327i	$-0.582838\pi$
$653$	−13.1509	−0.514634	−0.257317	+	0.966327i	$0.582838\pi$
$654$	−4.73096	−0.184995
$655$	−22.3800	−0.874458
$656$	10.6338	0.415181
$657$	17.5824	0.685955
$658$	−56.3976	−2.19861
$659$	−3.25612	−0.126841	−0.0634203	−	0.997987i	$-0.520201\pi$
$659$	−3.25612	−0.126841	−0.0634203	+	0.997987i	$0.520201\pi$
$660$	−6.11056	−0.237853
$661$	−25.9835	−1.01064	−0.505320	−	0.862932i	$-0.668625\pi$
$661$	−25.9835	−1.01064	−0.505320	+	0.862932i	$0.668625\pi$
$662$	−19.2821	−0.749418
$663$	−11.2032	−0.435095
$664$	−8.27008	−0.320941
$665$	−18.2535	−0.707841
$666$	−10.0473	−0.389326
$667$	15.9927	0.619240
$668$	−66.6808	−2.57996
$669$	−3.38634	−0.130924
$670$	−16.2548	−0.627978
$671$	1.68360	0.0649947
$672$	−6.35883	−0.245297
$673$	−20.3160	−0.783123	−0.391562	−	0.920152i	$-0.628065\pi$
$673$	−20.3160	−0.783123	−0.391562	+	0.920152i	$0.628065\pi$
$674$	−36.4158	−1.40268
$675$	−2.22589	−0.0856745
$676$	56.0486	2.15572
$677$	−2.70968	−0.104142	−0.0520708	−	0.998643i	$-0.516582\pi$
$677$	−2.70968	−0.104142	−0.0520708	+	0.998643i	$0.516582\pi$
$678$	6.09672	0.234143
$679$	34.4829	1.32333
$680$	−20.7507	−0.795751
$681$	−3.28194	−0.125764
$682$	−7.64583	−0.292774
$683$	−30.7013	−1.17475	−0.587377	−	0.809313i	$-0.699839\pi$
$683$	−30.7013	−1.17475	−0.587377	+	0.809313i	$0.699839\pi$
$684$	−38.7654	−1.48223
$685$	18.9135	0.722648
$686$	106.575	4.06904
$687$	10.6313	0.405611
$688$	1.71632	0.0654343
$689$	22.9276	0.873473
$690$	3.09921	0.117985
$691$	6.56070	0.249581	0.124790	−	0.992183i	$-0.460174\pi$
$691$	6.56070	0.249581	0.124790	+	0.992183i	$0.460174\pi$
$692$	52.2618	1.98670
$693$	−61.7172	−2.34444
$694$	−59.8271	−2.27100
$695$	−14.2901	−0.542056
$696$	−6.64016	−0.251695
$697$	34.0653	1.29032
$698$	49.0536	1.85671
$699$	−3.95133	−0.149453
$700$	17.3515	0.655825
$701$	−34.9265	−1.31916	−0.659579	−	0.751636i	$-0.729265\pi$
$701$	−34.9265	−1.31916	−0.659579	+	0.751636i	$0.729265\pi$
$702$	28.1514	1.06251
$703$	5.62288	0.212071
$704$	−52.0417	−1.96140
$705$	1.87691	0.0706885
$706$	−56.2813	−2.11817
$707$	32.3745	1.21757
$708$	−8.51553	−0.320033
$709$	27.2548	1.02358	0.511789	−	0.859111i	$-0.328983\pi$
$709$	27.2548	1.02358	0.511789	+	0.859111i	$0.328983\pi$
$710$	19.0610	0.715346
$711$	42.3050	1.58656
$712$	−50.2452	−1.88302
$713$	2.49103	0.0932896
$714$	23.9275	0.895465
$715$	23.9312	0.894977
$716$	−86.8280	−3.24491
$717$	1.96311	0.0733136
$718$	27.3774	1.02171
$719$	12.5596	0.468394	0.234197	−	0.972189i	$-0.424754\pi$
$719$	12.5596	0.468394	0.234197	+	0.972189i	$0.424754\pi$
$720$	4.91202	0.183060
$721$	−4.38650	−0.163362
$722$	−11.1585	−0.415275
$723$	0.380137	0.0141374
$724$	11.9273	0.443276
$725$	−4.63882	−0.172282
$726$	8.11122	0.301036
$727$	−31.2738	−1.15988	−0.579940	−	0.814659i	$-0.696924\pi$
$727$	−31.2738	−1.15988	−0.579940	+	0.814659i	$0.696924\pi$
$728$	−97.2728	−3.60517
$729$	−19.5070	−0.722481
$730$	14.5611	0.538929
$731$	5.49822	0.203359
$732$	0.513797	0.0189905
$733$	34.6464	1.27970	0.639848	−	0.768502i	$-0.278997\pi$
$733$	34.6464	1.27970	0.639848	+	0.768502i	$0.278997\pi$
$734$	62.2324	2.29704
$735$	−6.20775	−0.228976
$736$	11.9396	0.440101
$737$	30.7574	1.13296
$738$	−41.7436	−1.53660
$739$	19.4497	0.715468	0.357734	−	0.933823i	$-0.383549\pi$
$739$	19.4497	0.715468	0.357734	+	0.933823i	$0.383549\pi$
$740$	−5.34502	−0.196487
$741$	−7.68292	−0.282239
$742$	−48.9684	−1.79769
$743$	26.4651	0.970911	0.485456	−	0.874261i	$-0.338654\pi$
$743$	26.4651	0.970911	0.485456	+	0.874261i	$0.338654\pi$
$744$	−1.03427	−0.0379182
$745$	12.4924	0.457685
$746$	2.08628	0.0763842
$747$	6.27134	0.229456
$748$	88.5813	3.23885
$749$	60.8250	2.22250
$750$	−0.898952	−0.0328251
$751$	35.9122	1.31045	0.655227	−	0.755432i	$-0.272573\pi$
$751$	35.9122	1.31045	0.655227	+	0.755432i	$0.272573\pi$
$752$	−8.49341	−0.309723
$753$	5.00821	0.182509
$754$	58.6685	2.13658
$755$	22.7962	0.829637
$756$	−38.6225	−1.40469
$757$	−43.9805	−1.59850	−0.799249	−	0.601000i	$-0.794769\pi$
$757$	−43.9805	−1.59850	−0.799249	+	0.601000i	$0.794769\pi$
$758$	13.3135	0.483569
$759$	−5.86433	−0.212862
$760$	−14.2304	−0.516191
$761$	4.93525	0.178903	0.0894513	−	0.995991i	$-0.471489\pi$
$761$	4.93525	0.178903	0.0894513	+	0.995991i	$0.471489\pi$
$762$	−16.2918	−0.590191
$763$	−25.4199	−0.920261
$764$	−19.0384	−0.688784
$765$	15.7356	0.568921
$766$	14.7741	0.533808
$767$	33.3500	1.20420
$768$	−9.65546	−0.348411
$769$	8.10784	0.292376	0.146188	−	0.989257i	$-0.453300\pi$
$769$	8.10784	0.292376	0.146188	+	0.989257i	$0.453300\pi$
$770$	−51.1118	−1.84194
$771$	−1.74845	−0.0629689
$772$	76.5041	2.75344
$773$	−50.8999	−1.83074	−0.915372	−	0.402610i	$-0.868103\pi$
$773$	−50.8999	−1.83074	−0.915372	+	0.402610i	$0.868103\pi$
$774$	−6.73751	−0.242175
$775$	−0.722543	−0.0259545
$776$	26.8828	0.965035
$777$	2.73195	0.0980081
$778$	8.12122	0.291160
$779$	23.3613	0.837007
$780$	7.30326	0.261499
$781$	−36.0673	−1.29059
$782$	−44.9275	−1.60660
$783$	10.3255	0.369004
$784$	28.0914	1.00326
$785$	20.9876	0.749078
$786$	20.1185	0.717604
$787$	−19.5351	−0.696351	−0.348176	−	0.937429i	$-0.613199\pi$
$787$	−19.5351	−0.696351	−0.348176	+	0.937429i	$0.613199\pi$
$788$	66.8030	2.37976
$789$	8.36126	0.297669
$790$	35.0354	1.24650
$791$	32.7582	1.16475
$792$	−48.1146	−1.70968
$793$	−2.01222	−0.0714560
$794$	71.6411	2.54245
$795$	1.62967	0.0577983
$796$	33.5063	1.18760
$797$	49.0755	1.73834	0.869171	−	0.494511i	$-0.164653\pi$
$797$	49.0755	1.73834	0.869171	+	0.494511i	$0.164653\pi$
$798$	16.4090	0.580873
$799$	−27.2085	−0.962568
$800$	−3.46320	−0.122443
$801$	38.1018	1.34626
$802$	80.7616	2.85179
$803$	−27.5525	−0.972306
$804$	9.38646	0.331035
$805$	16.6523	0.586917
$806$	9.13820	0.321880
$807$	4.88996	0.172135
$808$	25.2391	0.887908
$809$	27.6132	0.970827	0.485414	−	0.874285i	$-0.338669\pi$
$809$	27.6132	0.970827	0.485414	+	0.874285i	$0.338669\pi$
$810$	−18.2572	−0.641491
$811$	25.7395	0.903838	0.451919	−	0.892059i	$-0.350740\pi$
$811$	25.7395	0.903838	0.451919	+	0.892059i	$0.350740\pi$
$812$	−80.4906	−2.82467
$813$	0.142025	0.00498102
$814$	15.7447	0.551850
$815$	−17.1140	−0.599476
$816$	3.60346	0.126146
$817$	3.77057	0.131916
$818$	−23.5329	−0.822808
$819$	73.7636	2.57751
$820$	−22.2069	−0.775499
$821$	17.8762	0.623885	0.311942	−	0.950101i	$-0.399020\pi$
$821$	17.8762	0.623885	0.311942	+	0.950101i	$0.399020\pi$
$822$	−17.0023	−0.593024
$823$	−45.3750	−1.58167	−0.790836	−	0.612028i	$-0.790354\pi$
$823$	−45.3750	−1.58167	−0.790836	+	0.612028i	$0.790354\pi$
$824$	−3.41971	−0.119131
$825$	1.70100	0.0592212
$826$	−71.2283	−2.47835
$827$	−54.9576	−1.91106	−0.955531	−	0.294890i	$-0.904717\pi$
$827$	−54.9576	−1.91106	−0.955531	+	0.294890i	$0.904717\pi$
$828$	35.3649	1.22902
$829$	46.2236	1.60541	0.802705	−	0.596376i	$-0.203393\pi$
$829$	46.2236	1.60541	0.802705	+	0.596376i	$0.203393\pi$
$830$	5.19368	0.180275
$831$	8.27292	0.286984
$832$	62.1996	2.15638
$833$	89.9903	3.11798
$834$	12.8461	0.444826
$835$	18.5620	0.642364
$836$	60.7474	2.10099
$837$	1.60830	0.0555910
$838$	66.4922	2.29694
$839$	−43.3571	−1.49685	−0.748426	−	0.663218i	$-0.769190\pi$
$839$	−43.3571	−1.49685	−0.748426	+	0.663218i	$0.769190\pi$
$840$	−6.91403	−0.238557
$841$	−7.48130	−0.257976
$842$	1.15416	0.0397751
$843$	3.05023	0.105056
$844$	3.04571	0.104838
$845$	−15.6023	−0.536735
$846$	33.3413	1.14630
$847$	43.5823	1.49751
$848$	−7.37458	−0.253244
$849$	3.97037	0.136263
$850$	13.0316	0.446980
$851$	−5.12963	−0.175842
$852$	−11.0069	−0.377091
$853$	−23.9859	−0.821260	−0.410630	−	0.911802i	$-0.634691\pi$
$853$	−23.9859	−0.821260	−0.410630	+	0.911802i	$0.634691\pi$
$854$	4.29766	0.147063
$855$	10.7912	0.369050
$856$	47.4191	1.62075
$857$	9.85502	0.336641	0.168320	−	0.985732i	$-0.446166\pi$
$857$	9.85502	0.336641	0.168320	+	0.985732i	$0.446166\pi$
$858$	−21.5130	−0.734442
$859$	2.72713	0.0930486	0.0465243	−	0.998917i	$-0.485186\pi$
$859$	2.72713	0.0930486	0.0465243	+	0.998917i	$0.485186\pi$
$860$	−3.58425	−0.122222
$861$	11.3504	0.386821
$862$	24.7165	0.841848
$863$	−27.5736	−0.938617	−0.469308	−	0.883034i	$-0.655497\pi$
$863$	−27.5736	−0.938617	−0.469308	+	0.883034i	$0.655497\pi$
$864$	7.70869	0.262255
$865$	−14.5482	−0.494652
$866$	34.4220	1.16971
$867$	5.08129	0.172570
$868$	−12.5372	−0.425541
$869$	−66.2941	−2.24887
$870$	4.17008	0.141379
$871$	−36.7609	−1.24559
$872$	−19.8173	−0.671097
$873$	−20.3857	−0.689950
$874$	−30.8104	−1.04218
$875$	−4.83015	−0.163289
$876$	−8.40839	−0.284093
$877$	38.0501	1.28486	0.642430	−	0.766344i	$-0.277926\pi$
$877$	38.0501	1.28486	0.642430	+	0.766344i	$0.277926\pi$
$878$	14.6105	0.493080
$879$	−1.63261	−0.0550667
$880$	−7.69738	−0.259479
$881$	6.58466	0.221843	0.110921	−	0.993829i	$-0.464620\pi$
$881$	6.58466	0.221843	0.110921	+	0.993829i	$0.464620\pi$
$882$	−110.274	−3.71312
$883$	−28.3998	−0.955730	−0.477865	−	0.878433i	$-0.658589\pi$
$883$	−28.3998	−0.955730	−0.477865	+	0.878433i	$0.658589\pi$
$884$	−105.871	−3.56084
$885$	2.37047	0.0796826
$886$	−20.8322	−0.699873
$887$	−22.6432	−0.760286	−0.380143	−	0.924928i	$-0.624125\pi$
$887$	−22.6432	−0.760286	−0.380143	+	0.924928i	$0.624125\pi$
$888$	2.12982	0.0714721
$889$	−87.5375	−2.93591
$890$	31.5544	1.05771
$891$	34.5463	1.15734
$892$	−32.0013	−1.07148
$893$	−18.6591	−0.624402
$894$	−11.2300	−0.375588
$895$	24.1703	0.807925
$896$	−99.3892	−3.32036
$897$	7.00897	0.234023
$898$	−39.8744	−1.33063
$899$	3.35175	0.111787
$900$	−10.2579	−0.341930
$901$	−23.6244	−0.787041
$902$	65.4142	2.17806
$903$	1.83198	0.0609645
$904$	25.5382	0.849388
$905$	−3.32022	−0.110368
$906$	−20.4926	−0.680822
$907$	−24.7934	−0.823253	−0.411626	−	0.911353i	$-0.635039\pi$
$907$	−24.7934	−0.823253	−0.411626	+	0.911353i	$0.635039\pi$
$908$	−31.0147	−1.02926
$909$	−19.1392	−0.634808
$910$	61.0882	2.02505
$911$	50.1183	1.66049	0.830247	−	0.557396i	$-0.188200\pi$
$911$	50.1183	1.66049	0.830247	+	0.557396i	$0.188200\pi$
$912$	2.47118	0.0818290
$913$	−9.82750	−0.325243
$914$	76.9186	2.54424
$915$	−0.143026	−0.00472829
$916$	100.467	3.31954
$917$	108.099	3.56973
$918$	−29.0069	−0.957370
$919$	−1.41609	−0.0467125	−0.0233562	−	0.999727i	$-0.507435\pi$
$919$	−1.41609	−0.0467125	−0.0233562	+	0.999727i	$0.507435\pi$
$920$	12.9821	0.428007
$921$	2.85539	0.0940884
$922$	13.2953	0.437858
$923$	43.1071	1.41889
$924$	29.5149	0.970969
$925$	1.48789	0.0489217
$926$	62.4347	2.05173
$927$	2.59322	0.0851726
$928$	16.0652	0.527365
$929$	31.0043	1.01722	0.508609	−	0.860998i	$-0.330160\pi$
$929$	31.0043	1.01722	0.508609	+	0.860998i	$0.330160\pi$
$930$	0.649532	0.0212990
$931$	61.7136	2.02258
$932$	−37.3405	−1.22313
$933$	6.35719	0.208125
$934$	−59.3352	−1.94151
$935$	−24.6584	−0.806417
$936$	57.5059	1.87964
$937$	6.20080	0.202571	0.101286	−	0.994857i	$-0.467704\pi$
$937$	6.20080	0.202571	0.101286	+	0.994857i	$0.467704\pi$
$938$	78.5131	2.56354
$939$	3.78029	0.123365
$940$	17.7370	0.578518
$941$	2.20890	0.0720082	0.0360041	−	0.999352i	$-0.488537\pi$
$941$	2.20890	0.0720082	0.0360041	+	0.999352i	$0.488537\pi$
$942$	−18.8668	−0.614713
$943$	−21.3121	−0.694016
$944$	−10.7269	−0.349131
$945$	10.7514	0.349742
$946$	10.5580	0.343270
$947$	−14.5471	−0.472717	−0.236358	−	0.971666i	$-0.575954\pi$
$947$	−14.5471	−0.472717	−0.236358	+	0.971666i	$0.575954\pi$
$948$	−20.2314	−0.657087
$949$	32.9304	1.06897
$950$	8.93682	0.289949
$951$	−13.1998	−0.428034
$952$	100.229	3.24843
$953$	14.9524	0.484355	0.242178	−	0.970232i	$-0.422138\pi$
$953$	14.9524	0.484355	0.242178	+	0.970232i	$0.422138\pi$
$954$	28.9492	0.937266
$955$	5.29972	0.171495
$956$	18.5516	0.600001
$957$	−7.89064	−0.255068
$958$	89.9773	2.90704
$959$	−91.3550	−2.95001
$960$	4.42107	0.142689
$961$	−30.4779	−0.983159
$962$	−18.8178	−0.606711
$963$	−35.9587	−1.15875
$964$	3.59233	0.115701
$965$	−21.2965	−0.685558
$966$	−14.9696	−0.481640
$967$	−13.0430	−0.419434	−0.209717	−	0.977762i	$-0.567254\pi$
$967$	−13.0430	−0.419434	−0.209717	+	0.977762i	$0.567254\pi$
$968$	33.9767	1.09205
$969$	7.91639	0.254311
$970$	−16.8826	−0.542068
$971$	−42.5741	−1.36627	−0.683134	−	0.730293i	$-0.739383\pi$
$971$	−42.5741	−1.36627	−0.683134	+	0.730293i	$0.739383\pi$
$972$	34.5311	1.10759
$973$	69.0235	2.21279
$974$	−39.2226	−1.25677
$975$	−2.03301	−0.0651085
$976$	0.647222	0.0207171
$977$	−7.78726	−0.249136	−0.124568	−	0.992211i	$-0.539755\pi$
$977$	−7.78726	−0.249136	−0.124568	+	0.992211i	$0.539755\pi$
$978$	15.3846	0.491946
$979$	−59.7074	−1.90826
$980$	−58.6640	−1.87395
$981$	15.0278	0.479800
$982$	38.5288	1.22950
$983$	−20.0317	−0.638912	−0.319456	−	0.947601i	$-0.603500\pi$
$983$	−20.0317	−0.638912	−0.319456	+	0.947601i	$0.603500\pi$
$984$	8.84875	0.282088
$985$	−18.5960	−0.592517
$986$	−60.4513	−1.92516
$987$	−9.06575	−0.288566
$988$	−72.6045	−2.30986
$989$	−3.43982	−0.109380
$990$	30.2164	0.960340
$991$	57.6129	1.83013	0.915067	−	0.403302i	$-0.132138\pi$
$991$	57.6129	1.83013	0.915067	+	0.403302i	$0.132138\pi$
$992$	2.50231	0.0794485
$993$	−3.09953	−0.0983607
$994$	−92.0674	−2.92020
$995$	−9.32717	−0.295691
$996$	−2.99913	−0.0950311
$997$	5.07108	0.160603	0.0803013	−	0.996771i	$-0.474412\pi$
$997$	5.07108	0.160603	0.0803013	+	0.996771i	$0.474412\pi$
$998$	26.8338	0.849408
$999$	−3.31189	−0.104783

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1205.2.a.d.1.22	✓	25
5.4	even	2		6025.2.a.k.1.4		25

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1205.2.a.d.1.22	✓	25	1.1	even	1	trivial
6025.2.a.k.1.4		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)

\(f(q)\)	\(=\)	\(q+2.36481 q^{2} +0.380137 q^{3} +3.59233 q^{4} -1.00000 q^{5} +0.898952 q^{6} +4.83015 q^{7} +3.76557 q^{8} -2.85550 q^{9} +O(q^{10})\)	\(q+2.36481 q^{2} +0.380137 q^{3} +3.59233 q^{4} -1.00000 q^{5} +0.898952 q^{6} +4.83015 q^{7} +3.76557 q^{8} -2.85550 q^{9} -2.36481 q^{10} +4.47470 q^{11} +1.36558 q^{12} -5.34811 q^{13} +11.4224 q^{14} -0.380137 q^{15} +1.72020 q^{16} +5.51063 q^{17} -6.75271 q^{18} +3.77908 q^{19} -3.59233 q^{20} +1.83612 q^{21} +10.5818 q^{22} -3.44758 q^{23} +1.43143 q^{24} +1.00000 q^{25} -12.6473 q^{26} -2.22589 q^{27} +17.3515 q^{28} -4.63882 q^{29} -0.898952 q^{30} -0.722543 q^{31} -3.46320 q^{32} +1.70100 q^{33} +13.0316 q^{34} -4.83015 q^{35} -10.2579 q^{36} +1.48789 q^{37} +8.93682 q^{38} -2.03301 q^{39} -3.76557 q^{40} +6.18175 q^{41} +4.34207 q^{42} +0.997748 q^{43} +16.0746 q^{44} +2.85550 q^{45} -8.15287 q^{46} -4.93746 q^{47} +0.653910 q^{48} +16.3303 q^{49} +2.36481 q^{50} +2.09479 q^{51} -19.2122 q^{52} -4.28705 q^{53} -5.26381 q^{54} -4.47470 q^{55} +18.1883 q^{56} +1.43657 q^{57} -10.9699 q^{58} -6.23585 q^{59} -1.36558 q^{60} +0.376249 q^{61} -1.70868 q^{62} -13.7925 q^{63} -11.6302 q^{64} +5.34811 q^{65} +4.02254 q^{66} +6.87362 q^{67} +19.7960 q^{68} -1.31055 q^{69} -11.4224 q^{70} -8.06026 q^{71} -10.7526 q^{72} -6.15739 q^{73} +3.51859 q^{74} +0.380137 q^{75} +13.5757 q^{76} +21.6135 q^{77} -4.80769 q^{78} -14.8153 q^{79} -1.72020 q^{80} +7.72035 q^{81} +14.6187 q^{82} -2.19624 q^{83} +6.59594 q^{84} -5.51063 q^{85} +2.35949 q^{86} -1.76339 q^{87} +16.8498 q^{88} -13.3433 q^{89} +6.75271 q^{90} -25.8322 q^{91} -12.3849 q^{92} -0.274665 q^{93} -11.6762 q^{94} -3.77908 q^{95} -1.31649 q^{96} +7.13909 q^{97} +38.6181 q^{98} -12.7775 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 25 q - 4 q^{2} + 9 q^{3} + 36 q^{4} - 25 q^{5} + 7 q^{6} + 7 q^{7} - 15 q^{8} + 36 q^{9}+O(q^{10}) \) 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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