LMFDB - Embedded newform 1205.2.a.d.1.2

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			1.2
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)

$f(q)$	$=$	$q-2.76011 q^{2} +3.30191 q^{3} +5.61819 q^{4} -1.00000 q^{5} -9.11364 q^{6} -4.87082 q^{7} -9.98660 q^{8} +7.90263 q^{9} +O(q^{10})$	\(q-2.76011 q^{2} +3.30191 q^{3} +5.61819 q^{4} -1.00000 q^{5} -9.11364 q^{6} -4.87082 q^{7} -9.98660 q^{8} +7.90263 q^{9} +2.76011 q^{10} +1.41820 q^{11} +18.5508 q^{12} -0.466870 q^{13} +13.4440 q^{14} -3.30191 q^{15} +16.3277 q^{16} -0.431467 q^{17} -21.8121 q^{18} +3.96313 q^{19} -5.61819 q^{20} -16.0830 q^{21} -3.91439 q^{22} -2.67648 q^{23} -32.9749 q^{24} +1.00000 q^{25} +1.28861 q^{26} +16.1881 q^{27} -27.3652 q^{28} +6.57814 q^{29} +9.11364 q^{30} +2.31017 q^{31} -25.0930 q^{32} +4.68278 q^{33} +1.19090 q^{34} +4.87082 q^{35} +44.3985 q^{36} +9.54007 q^{37} -10.9387 q^{38} -1.54156 q^{39} +9.98660 q^{40} -2.14107 q^{41} +44.3909 q^{42} +9.72925 q^{43} +7.96773 q^{44} -7.90263 q^{45} +7.38738 q^{46} -0.849584 q^{47} +53.9127 q^{48} +16.7249 q^{49} -2.76011 q^{50} -1.42467 q^{51} -2.62297 q^{52} +0.687068 q^{53} -44.6808 q^{54} -1.41820 q^{55} +48.6429 q^{56} +13.0859 q^{57} -18.1564 q^{58} -8.86483 q^{59} -18.5508 q^{60} -3.50043 q^{61} -6.37631 q^{62} -38.4923 q^{63} +36.6040 q^{64} +0.466870 q^{65} -12.9250 q^{66} +12.4963 q^{67} -2.42407 q^{68} -8.83752 q^{69} -13.4440 q^{70} +4.14774 q^{71} -78.9204 q^{72} +11.5636 q^{73} -26.3316 q^{74} +3.30191 q^{75} +22.2656 q^{76} -6.90781 q^{77} +4.25488 q^{78} -4.40336 q^{79} -16.3277 q^{80} +29.7437 q^{81} +5.90959 q^{82} +11.8096 q^{83} -90.3576 q^{84} +0.431467 q^{85} -26.8538 q^{86} +21.7205 q^{87} -14.1630 q^{88} -6.36792 q^{89} +21.8121 q^{90} +2.27404 q^{91} -15.0370 q^{92} +7.62798 q^{93} +2.34494 q^{94} -3.96313 q^{95} -82.8550 q^{96} -6.27077 q^{97} -46.1625 q^{98} +11.2075 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.76011	−1.95169	−0.975845	−	0.218463i	$-0.929896\pi$
$2$	−2.76011	−1.95169	−0.975845	+	0.218463i	$0.929896\pi$
$3$	3.30191	1.90636	0.953180	−	0.302402i	$-0.0977886\pi$
$3$	3.30191	1.90636	0.953180	+	0.302402i	$0.0977886\pi$
$4$	5.61819	2.80910
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	−9.11364	−3.72063
$7$	−4.87082	−1.84100	−0.920499	−	0.390746i	$-0.872217\pi$
$7$	−4.87082	−1.84100	−0.920499	+	0.390746i	$0.872217\pi$
$8$	−9.98660	−3.53080
$9$	7.90263	2.63421
$10$	2.76011	0.872823
$11$	1.41820	0.427604	0.213802	−	0.976877i	$-0.431415\pi$
$11$	1.41820	0.427604	0.213802	+	0.976877i	$0.431415\pi$
$12$	18.5508	5.35515
$13$	−0.466870	−0.129486	−0.0647432	−	0.997902i	$-0.520623\pi$
$13$	−0.466870	−0.129486	−0.0647432	+	0.997902i	$0.520623\pi$
$14$	13.4440	3.59306
$15$	−3.30191	−0.852550
$16$	16.3277	4.08193
$17$	−0.431467	−0.104646	−0.0523231	−	0.998630i	$-0.516663\pi$
$17$	−0.431467	−0.104646	−0.0523231	+	0.998630i	$0.516663\pi$
$18$	−21.8121	−5.14117
$19$	3.96313	0.909204	0.454602	−	0.890695i	$-0.349781\pi$
$19$	3.96313	0.909204	0.454602	+	0.890695i	$0.349781\pi$
$20$	−5.61819	−1.25627
$21$	−16.0830	−3.50960
$22$	−3.91439	−0.834550
$23$	−2.67648	−0.558085	−0.279043	−	0.960279i	$-0.590017\pi$
$23$	−2.67648	−0.558085	−0.279043	+	0.960279i	$0.590017\pi$
$24$	−32.9749	−6.73097
$25$	1.00000	0.200000
$26$	1.28861	0.252718
$27$	16.1881	3.11540
$28$	−27.3652	−5.17154
$29$	6.57814	1.22153	0.610765	−	0.791812i	$-0.290862\pi$
$29$	6.57814	1.22153	0.610765	+	0.791812i	$0.290862\pi$
$30$	9.11364	1.66391
$31$	2.31017	0.414918	0.207459	−	0.978244i	$-0.433481\pi$
$31$	2.31017	0.414918	0.207459	+	0.978244i	$0.433481\pi$
$32$	−25.0930	−4.43586
$33$	4.68278	0.815167
$34$	1.19090	0.204237
$35$	4.87082	0.823319
$36$	44.3985	7.39975
$37$	9.54007	1.56838	0.784189	−	0.620522i	$-0.213079\pi$
$37$	9.54007	1.56838	0.784189	+	0.620522i	$0.213079\pi$
$38$	−10.9387	−1.77449
$39$	−1.54156	−0.246848
$40$	9.98660	1.57902
$41$	−2.14107	−0.334380	−0.167190	−	0.985925i	$-0.553469\pi$
$41$	−2.14107	−0.334380	−0.167190	+	0.985925i	$0.553469\pi$
$42$	44.3909	6.84966
$43$	9.72925	1.48370	0.741848	−	0.670568i	$-0.233949\pi$
$43$	9.72925	1.48370	0.741848	+	0.670568i	$0.233949\pi$
$44$	7.96773	1.20118
$45$	−7.90263	−1.17806
$46$	7.38738	1.08921
$47$	−0.849584	−0.123925	−0.0619623	−	0.998078i	$-0.519736\pi$
$47$	−0.849584	−0.123925	−0.0619623	+	0.998078i	$0.519736\pi$
$48$	53.9127	7.78162
$49$	16.7249	2.38927
$50$	−2.76011	−0.390338
$51$	−1.42467	−0.199493
$52$	−2.62297	−0.363740
$53$	0.687068	0.0943760	0.0471880	−	0.998886i	$-0.484974\pi$
$53$	0.687068	0.0943760	0.0471880	+	0.998886i	$0.484974\pi$
$54$	−44.6808	−6.08029
$55$	−1.41820	−0.191230
$56$	48.6429	6.50019
$57$	13.0859	1.73327
$58$	−18.1564	−2.38405
$59$	−8.86483	−1.15410	−0.577051	−	0.816708i	$-0.695797\pi$
$59$	−8.86483	−1.15410	−0.577051	+	0.816708i	$0.695797\pi$
$60$	−18.5508	−2.39490
$61$	−3.50043	−0.448184	−0.224092	−	0.974568i	$-0.571942\pi$
$61$	−3.50043	−0.448184	−0.224092	+	0.974568i	$0.571942\pi$
$62$	−6.37631	−0.809792
$63$	−38.4923	−4.84958
$64$	36.6040	4.57550
$65$	0.466870	0.0579081
$66$	−12.9250	−1.59095
$67$	12.4963	1.52666	0.763332	−	0.646006i	$-0.223562\pi$
$67$	12.4963	1.52666	0.763332	+	0.646006i	$0.223562\pi$
$68$	−2.42407	−0.293961
$69$	−8.83752	−1.06391
$70$	−13.4440	−1.60686
$71$	4.14774	0.492246	0.246123	−	0.969239i	$-0.420843\pi$
$71$	4.14774	0.492246	0.246123	+	0.969239i	$0.420843\pi$
$72$	−78.9204	−9.30086
$73$	11.5636	1.35342	0.676709	−	0.736251i	$-0.263406\pi$
$73$	11.5636	1.35342	0.676709	+	0.736251i	$0.263406\pi$
$74$	−26.3316	−3.06099
$75$	3.30191	0.381272
$76$	22.2656	2.55404
$77$	−6.90781	−0.787218
$78$	4.25488	0.481771
$79$	−4.40336	−0.495417	−0.247709	−	0.968835i	$-0.579678\pi$
$79$	−4.40336	−0.495417	−0.247709	+	0.968835i	$0.579678\pi$
$80$	−16.3277	−1.82549
$81$	29.7437	3.30486
$82$	5.90959	0.652605
$83$	11.8096	1.29627	0.648135	−	0.761526i	$-0.275549\pi$
$83$	11.8096	1.29627	0.648135	+	0.761526i	$0.275549\pi$
$84$	−90.3576	−9.85882
$85$	0.431467	0.0467992
$86$	−26.8538	−2.89572
$87$	21.7205	2.32868
$88$	−14.1630	−1.50978
$89$	−6.36792	−0.674998	−0.337499	−	0.941326i	$-0.609581\pi$
$89$	−6.36792	−0.674998	−0.337499	+	0.941326i	$0.609581\pi$
$90$	21.8121	2.29920
$91$	2.27404	0.238384
$92$	−15.0370	−1.56772
$93$	7.62798	0.790984
$94$	2.34494	0.241862
$95$	−3.96313	−0.406608
$96$	−82.8550	−8.45635
$97$	−6.27077	−0.636700	−0.318350	−	0.947973i	$-0.603129\pi$
$97$	−6.27077	−0.636700	−0.318350	+	0.947973i	$0.603129\pi$
$98$	−46.1625	−4.66312
$99$	11.2075	1.12640
$100$	5.61819	0.561819
$101$	−13.7018	−1.36338	−0.681689	−	0.731642i	$-0.738754\pi$
$101$	−13.7018	−1.36338	−0.681689	+	0.731642i	$0.738754\pi$
$102$	3.93224	0.389349
$103$	9.88518	0.974016	0.487008	−	0.873397i	$-0.338088\pi$
$103$	9.88518	0.974016	0.487008	+	0.873397i	$0.338088\pi$
$104$	4.66245	0.457190
$105$	16.0830	1.56954
$106$	−1.89638	−0.184193
$107$	−1.79774	−0.173794	−0.0868971	−	0.996217i	$-0.527695\pi$
$107$	−1.79774	−0.173794	−0.0868971	+	0.996217i	$0.527695\pi$
$108$	90.9477	8.75145
$109$	−5.27949	−0.505684	−0.252842	−	0.967508i	$-0.581365\pi$
$109$	−5.27949	−0.505684	−0.252842	+	0.967508i	$0.581365\pi$
$110$	3.91439	0.373222
$111$	31.5005	2.98990
$112$	−79.5293	−7.51481
$113$	−5.66321	−0.532750	−0.266375	−	0.963869i	$-0.585826\pi$
$113$	−5.66321	−0.532750	−0.266375	+	0.963869i	$0.585826\pi$
$114$	−36.1185	−3.38281
$115$	2.67648	0.249583
$116$	36.9573	3.43140
$117$	−3.68950	−0.341095
$118$	24.4679	2.25245
$119$	2.10160	0.192653
$120$	32.9749	3.01018
$121$	−8.98870	−0.817155
$122$	9.66157	0.874717
$123$	−7.06964	−0.637448
$124$	12.9790	1.16555
$125$	−1.00000	−0.0894427
$126$	106.243	9.46487
$127$	−10.5350	−0.934828	−0.467414	−	0.884038i	$-0.654814\pi$
$127$	−10.5350	−0.934828	−0.467414	+	0.884038i	$0.654814\pi$
$128$	−50.8450	−4.49410
$129$	32.1252	2.82846
$130$	−1.28861	−0.113019
$131$	−1.84011	−0.160771	−0.0803854	−	0.996764i	$-0.525615\pi$
$131$	−1.84011	−0.160771	−0.0803854	+	0.996764i	$0.525615\pi$
$132$	26.3088	2.28988
$133$	−19.3037	−1.67384
$134$	−34.4911	−2.97958
$135$	−16.1881	−1.39325
$136$	4.30889	0.369484
$137$	3.20902	0.274166	0.137083	−	0.990560i	$-0.456227\pi$
$137$	3.20902	0.274166	0.137083	+	0.990560i	$0.456227\pi$
$138$	24.3925	2.07643
$139$	7.80458	0.661976	0.330988	−	0.943635i	$-0.392618\pi$
$139$	7.80458	0.661976	0.330988	+	0.943635i	$0.392618\pi$
$140$	27.3652	2.31278
$141$	−2.80525	−0.236245
$142$	−11.4482	−0.960712
$143$	−0.662116	−0.0553689
$144$	129.032	10.7527
$145$	−6.57814	−0.546285
$146$	−31.9168	−2.64145
$147$	55.2242	4.55481
$148$	53.5980	4.40573
$149$	17.4844	1.43238	0.716188	−	0.697907i	$-0.245885\pi$
$149$	17.4844	1.43238	0.716188	+	0.697907i	$0.245885\pi$
$150$	−9.11364	−0.744125
$151$	4.65232	0.378601	0.189300	−	0.981919i	$-0.439378\pi$
$151$	4.65232	0.378601	0.189300	+	0.981919i	$0.439378\pi$
$152$	−39.5782	−3.21021
$153$	−3.40973	−0.275660
$154$	19.0663	1.53641
$155$	−2.31017	−0.185557
$156$	−8.66081	−0.693420
$157$	−12.1048	−0.966068	−0.483034	−	0.875602i	$-0.660465\pi$
$157$	−12.1048	−0.966068	−0.483034	+	0.875602i	$0.660465\pi$
$158$	12.1538	0.966901
$159$	2.26864	0.179915
$160$	25.0930	1.98378
$161$	13.0367	1.02743
$162$	−82.0959	−6.45006
$163$	−20.4247	−1.59979	−0.799894	−	0.600141i	$-0.795111\pi$
$163$	−20.4247	−1.59979	−0.799894	+	0.600141i	$0.795111\pi$
$164$	−12.0290	−0.939304
$165$	−4.68278	−0.364554
$166$	−32.5957	−2.52992
$167$	25.4917	1.97261	0.986304	−	0.164938i	$-0.0527424\pi$
$167$	25.4917	1.97261	0.986304	+	0.164938i	$0.0527424\pi$
$168$	160.615	12.3917
$169$	−12.7820	−0.983233
$170$	−1.19090	−0.0913376
$171$	31.3192	2.39504
$172$	54.6608	4.16785
$173$	−6.46795	−0.491749	−0.245874	−	0.969302i	$-0.579075\pi$
$173$	−6.46795	−0.491749	−0.245874	+	0.969302i	$0.579075\pi$
$174$	−59.9508	−4.54486
$175$	−4.87082	−0.368199
$176$	23.1560	1.74545
$177$	−29.2709	−2.20014
$178$	17.5761	1.31739
$179$	−21.7550	−1.62604	−0.813021	−	0.582234i	$-0.802179\pi$
$179$	−21.7550	−1.62604	−0.813021	+	0.582234i	$0.802179\pi$
$180$	−44.3985	−3.30927
$181$	−15.5318	−1.15447	−0.577236	−	0.816577i	$-0.695869\pi$
$181$	−15.5318	−1.15447	−0.577236	+	0.816577i	$0.695869\pi$
$182$	−6.27660	−0.465252
$183$	−11.5581	−0.854401
$184$	26.7290	1.97049
$185$	−9.54007	−0.701400
$186$	−21.0540	−1.54376
$187$	−0.611908	−0.0447471
$188$	−4.77313	−0.348116
$189$	−78.8492	−5.73544
$190$	10.9387	0.793574
$191$	−3.33416	−0.241251	−0.120626	−	0.992698i	$-0.538490\pi$
$191$	−3.33416	−0.241251	−0.120626	+	0.992698i	$0.538490\pi$
$192$	120.863	8.72256
$193$	−6.26303	−0.450823	−0.225412	−	0.974264i	$-0.572373\pi$
$193$	−6.26303	−0.450823	−0.225412	+	0.974264i	$0.572373\pi$
$194$	17.3080	1.24264
$195$	1.54156	0.110394
$196$	93.9637	6.71169
$197$	8.56802	0.610446	0.305223	−	0.952281i	$-0.401269\pi$
$197$	8.56802	0.610446	0.305223	+	0.952281i	$0.401269\pi$
$198$	−30.9340	−2.19838
$199$	22.3969	1.58767	0.793835	−	0.608133i	$-0.208081\pi$
$199$	22.3969	1.58767	0.793835	+	0.608133i	$0.208081\pi$
$200$	−9.98660	−0.706159
$201$	41.2617	2.91037
$202$	37.8184	2.66089
$203$	−32.0409	−2.24883
$204$	−8.00406	−0.560396
$205$	2.14107	0.149539
$206$	−27.2842	−1.90098
$207$	−21.1513	−1.47011
$208$	−7.62292	−0.528554
$209$	5.62052	0.388779
$210$	−44.3909	−3.06326
$211$	16.8851	1.16242	0.581210	−	0.813754i	$-0.302579\pi$
$211$	16.8851	1.16242	0.581210	+	0.813754i	$0.302579\pi$
$212$	3.86008	0.265111
$213$	13.6955	0.938398
$214$	4.96196	0.339193
$215$	−9.72925	−0.663529
$216$	−161.664	−10.9998
$217$	−11.2524	−0.763864
$218$	14.5720	0.986938
$219$	38.1820	2.58010
$220$	−7.96773	−0.537184
$221$	0.201439	0.0135503
$222$	−86.9448	−5.83535
$223$	−10.6972	−0.716339	−0.358169	−	0.933657i	$-0.616599\pi$
$223$	−10.6972	−0.716339	−0.358169	+	0.933657i	$0.616599\pi$
$224$	122.224	8.16641
$225$	7.90263	0.526842
$226$	15.6311	1.03976
$227$	3.12091	0.207142	0.103571	−	0.994622i	$-0.466973\pi$
$227$	3.12091	0.207142	0.103571	+	0.994622i	$0.466973\pi$
$228$	73.5192	4.86893
$229$	5.92658	0.391639	0.195820	−	0.980640i	$-0.437263\pi$
$229$	5.92658	0.391639	0.195820	+	0.980640i	$0.437263\pi$
$230$	−7.38738	−0.487110
$231$	−22.8090	−1.50072
$232$	−65.6933	−4.31297
$233$	−15.3826	−1.00775	−0.503875	−	0.863777i	$-0.668093\pi$
$233$	−15.3826	−1.00775	−0.503875	+	0.863777i	$0.668093\pi$
$234$	10.1834	0.665711
$235$	0.849584	0.0554207
$236$	−49.8043	−3.24199
$237$	−14.5395	−0.944444
$238$	−5.80064	−0.376000
$239$	22.2336	1.43817	0.719086	−	0.694921i	$-0.244561\pi$
$239$	22.2336	1.43817	0.719086	+	0.694921i	$0.244561\pi$
$240$	−53.9127	−3.48005
$241$	1.00000	0.0644157
$241$	1.00000	0.0644157
$242$	24.8098	1.59483
$243$	49.6470	3.18486
$244$	−19.6661	−1.25899
$245$	−16.7249	−1.06851
$246$	19.5130	1.24410
$247$	−1.85027	−0.117730
$248$	−23.0707	−1.46499
$249$	38.9942	2.47116
$250$	2.76011	0.174565
$251$	−3.63694	−0.229562	−0.114781	−	0.993391i	$-0.536617\pi$
$251$	−3.63694	−0.229562	−0.114781	+	0.993391i	$0.536617\pi$
$252$	−216.257	−13.6229
$253$	−3.79579	−0.238639
$254$	29.0777	1.82450
$255$	1.42467	0.0892162
$256$	67.1295	4.19560
$257$	8.77129	0.547138	0.273569	−	0.961852i	$-0.411796\pi$
$257$	8.77129	0.547138	0.273569	+	0.961852i	$0.411796\pi$
$258$	−88.6689	−5.52028
$259$	−46.4680	−2.88738
$260$	2.62297	0.162669
$261$	51.9846	3.21777
$262$	5.07889	0.313775
$263$	−10.2296	−0.630783	−0.315391	−	0.948962i	$-0.602136\pi$
$263$	−10.2296	−0.630783	−0.315391	+	0.948962i	$0.602136\pi$
$264$	−46.7650	−2.87819
$265$	−0.687068	−0.0422062
$266$	53.2803	3.26682
$267$	−21.0263	−1.28679
$268$	70.2066	4.28855
$269$	13.2698	0.809072	0.404536	−	0.914522i	$-0.367433\pi$
$269$	13.2698	0.809072	0.404536	+	0.914522i	$0.367433\pi$
$270$	44.6808	2.71919
$271$	−5.98510	−0.363569	−0.181785	−	0.983338i	$-0.558187\pi$
$271$	−5.98510	−0.363569	−0.181785	+	0.983338i	$0.558187\pi$
$272$	−7.04487	−0.427158
$273$	7.50869	0.454446
$274$	−8.85725	−0.535086
$275$	1.41820	0.0855208
$276$	−49.6509	−2.98863
$277$	−24.8164	−1.49107	−0.745535	−	0.666466i	$-0.767806\pi$
$277$	−24.8164	−1.49107	−0.745535	+	0.666466i	$0.767806\pi$
$278$	−21.5415	−1.29197
$279$	18.2564	1.09298
$280$	−48.6429	−2.90697
$281$	8.54904	0.509993	0.254996	−	0.966942i	$-0.417926\pi$
$281$	8.54904	0.509993	0.254996	+	0.966942i	$0.417926\pi$
$282$	7.74280	0.461077
$283$	10.4703	0.622392	0.311196	−	0.950346i	$-0.399270\pi$
$283$	10.4703	0.622392	0.311196	+	0.950346i	$0.399270\pi$
$284$	23.3028	1.38277
$285$	−13.0859	−0.775142
$286$	1.82751	0.108063
$287$	10.4288	0.615592
$288$	−198.301	−11.6850
$289$	−16.8138	−0.989049
$290$	18.1564	1.06618
$291$	−20.7055	−1.21378
$292$	64.9666	3.80188
$293$	7.08303	0.413795	0.206898	−	0.978363i	$-0.433663\pi$
$293$	7.08303	0.413795	0.206898	+	0.978363i	$0.433663\pi$
$294$	−152.425	−8.88958
$295$	8.86483	0.516130
$296$	−95.2729	−5.53762
$297$	22.9580	1.33216
$298$	−48.2588	−2.79556
$299$	1.24957	0.0722645
$300$	18.5508	1.07103
$301$	−47.3894	−2.73148
$302$	−12.8409	−0.738911
$303$	−45.2421	−2.59909
$304$	64.7088	3.71130
$305$	3.50043	0.200434
$306$	9.41122	0.538004
$307$	−20.8871	−1.19209	−0.596045	−	0.802951i	$-0.703262\pi$
$307$	−20.8871	−1.19209	−0.596045	+	0.802951i	$0.703262\pi$
$308$	−38.8094	−2.21137
$309$	32.6400	1.85683
$310$	6.37631	0.362150
$311$	2.02138	0.114622	0.0573110	−	0.998356i	$-0.481747\pi$
$311$	2.02138	0.114622	0.0573110	+	0.998356i	$0.481747\pi$
$312$	15.3950	0.871570
$313$	23.3946	1.32234	0.661170	−	0.750236i	$-0.270060\pi$
$313$	23.3946	1.32234	0.661170	+	0.750236i	$0.270060\pi$
$314$	33.4105	1.88547
$315$	38.4923	2.16880
$316$	−24.7389	−1.39167
$317$	26.6040	1.49423	0.747116	−	0.664694i	$-0.231438\pi$
$317$	26.6040	1.49423	0.747116	+	0.664694i	$0.231438\pi$
$318$	−6.26168	−0.351138
$319$	9.32913	0.522331
$320$	−36.6040	−2.04623
$321$	−5.93599	−0.331315
$322$	−35.9826	−2.00523
$323$	−1.70996	−0.0951448
$324$	167.106	9.28367
$325$	−0.466870	−0.0258973
$326$	56.3744	3.12229
$327$	−17.4324	−0.964016
$328$	21.3820	1.18063
$329$	4.13817	0.228145
$330$	12.9250	0.711496
$331$	−17.7268	−0.974352	−0.487176	−	0.873304i	$-0.661973\pi$
$331$	−17.7268	−0.974352	−0.487176	+	0.873304i	$0.661973\pi$
$332$	66.3485	3.64134
$333$	75.3917	4.13144
$334$	−70.3599	−3.84992
$335$	−12.4963	−0.682745
$336$	−262.599	−14.3259
$337$	25.0828	1.36635	0.683173	−	0.730257i	$-0.260600\pi$
$337$	25.0828	1.36635	0.683173	+	0.730257i	$0.260600\pi$
$338$	35.2798	1.91897
$339$	−18.6994	−1.01561
$340$	2.42407	0.131463
$341$	3.27628	0.177421
$342$	−86.4442	−4.67437
$343$	−47.3682	−2.55764
$344$	−97.1621	−5.23863
$345$	8.83752	0.475796
$346$	17.8522	0.959742
$347$	−29.8726	−1.60365	−0.801823	−	0.597562i	$-0.796136\pi$
$347$	−29.8726	−1.60365	−0.801823	+	0.597562i	$0.796136\pi$
$348$	122.030	6.54148
$349$	4.82339	0.258190	0.129095	−	0.991632i	$-0.458793\pi$
$349$	4.82339	0.258190	0.129095	+	0.991632i	$0.458793\pi$
$350$	13.4440	0.718611
$351$	−7.55773	−0.403402
$352$	−35.5870	−1.89679
$353$	−16.1706	−0.860675	−0.430338	−	0.902668i	$-0.641605\pi$
$353$	−16.1706	−0.860675	−0.430338	+	0.902668i	$0.641605\pi$
$354$	80.7908	4.29398
$355$	−4.14774	−0.220139
$356$	−35.7762	−1.89614
$357$	6.93930	0.367267
$358$	60.0460	3.17353
$359$	−19.4214	−1.02502	−0.512512	−	0.858680i	$-0.671285\pi$
$359$	−19.4214	−1.02502	−0.512512	+	0.858680i	$0.671285\pi$
$360$	78.9204	4.15947
$361$	−3.29361	−0.173348
$362$	42.8695	2.25317
$363$	−29.6799	−1.55779
$364$	12.7760	0.669644
$365$	−11.5636	−0.605267
$366$	31.9017	1.66753
$367$	19.0089	0.992256	0.496128	−	0.868249i	$-0.334755\pi$
$367$	19.0089	0.992256	0.496128	+	0.868249i	$0.334755\pi$
$368$	−43.7008	−2.27806
$369$	−16.9201	−0.880826
$370$	26.3316	1.36892
$371$	−3.34658	−0.173746
$372$	42.8554	2.22195
$373$	23.1492	1.19862	0.599311	−	0.800516i	$-0.295441\pi$
$373$	23.1492	1.19862	0.599311	+	0.800516i	$0.295441\pi$
$374$	1.68893	0.0873326
$375$	−3.30191	−0.170510
$376$	8.48445	0.437552
$377$	−3.07114	−0.158172
$378$	217.632	11.1938
$379$	1.90482	0.0978440	0.0489220	−	0.998803i	$-0.484421\pi$
$379$	1.90482	0.0978440	0.0489220	+	0.998803i	$0.484421\pi$
$380$	−22.2656	−1.14220
$381$	−34.7856	−1.78212
$382$	9.20264	0.470848
$383$	4.21428	0.215340	0.107670	−	0.994187i	$-0.465661\pi$
$383$	4.21428	0.215340	0.107670	+	0.994187i	$0.465661\pi$
$384$	−167.886	−8.56738
$385$	6.90781	0.352054
$386$	17.2866	0.879867
$387$	76.8867	3.90837
$388$	−35.2304	−1.78855
$389$	−12.8249	−0.650250	−0.325125	−	0.945671i	$-0.605406\pi$
$389$	−12.8249	−0.650250	−0.325125	+	0.945671i	$0.605406\pi$
$390$	−4.25488	−0.215454
$391$	1.15482	0.0584015
$392$	−167.025	−8.43603
$393$	−6.07587	−0.306487
$394$	−23.6487	−1.19140
$395$	4.40336	0.221557
$396$	62.9661	3.16416
$397$	10.7908	0.541573	0.270786	−	0.962639i	$-0.412716\pi$
$397$	10.7908	0.541573	0.270786	+	0.962639i	$0.412716\pi$
$398$	−61.8177	−3.09864
$399$	−63.7391	−3.19095
$400$	16.3277	0.816385
$401$	−29.8434	−1.49031	−0.745153	−	0.666894i	$-0.767624\pi$
$401$	−29.8434	−1.49031	−0.745153	+	0.666894i	$0.767624\pi$
$402$	−113.887	−5.68015
$403$	−1.07855	−0.0537263
$404$	−76.9792	−3.82986
$405$	−29.7437	−1.47798
$406$	88.4365	4.38903
$407$	13.5297	0.670645
$408$	14.2276	0.704371
$409$	21.7341	1.07468	0.537340	−	0.843366i	$-0.319429\pi$
$409$	21.7341	1.07468	0.537340	+	0.843366i	$0.319429\pi$
$410$	−5.90959	−0.291854
$411$	10.5959	0.522658
$412$	55.5369	2.73611
$413$	43.1790	2.12470
$414$	58.3798	2.86921
$415$	−11.8096	−0.579709
$416$	11.7152	0.574384
$417$	25.7700	1.26196
$418$	−15.5132	−0.758777
$419$	21.4273	1.04679	0.523397	−	0.852089i	$-0.324665\pi$
$419$	21.4273	1.04679	0.523397	+	0.852089i	$0.324665\pi$
$420$	90.3576	4.40900
$421$	−10.3625	−0.505038	−0.252519	−	0.967592i	$-0.581259\pi$
$421$	−10.3625	−0.505038	−0.252519	+	0.967592i	$0.581259\pi$
$422$	−46.6048	−2.26868
$423$	−6.71395	−0.326443
$424$	−6.86147	−0.333222
$425$	−0.431467	−0.0209292
$426$	−37.8010	−1.83146
$427$	17.0500	0.825106
$428$	−10.1001	−0.488205
$429$	−2.18625	−0.105553
$430$	26.8538	1.29500
$431$	22.2602	1.07223	0.536117	−	0.844143i	$-0.319890\pi$
$431$	22.2602	1.07223	0.536117	+	0.844143i	$0.319890\pi$
$432$	264.314	12.7168
$433$	−27.9651	−1.34392	−0.671959	−	0.740589i	$-0.734547\pi$
$433$	−27.9651	−1.34392	−0.671959	+	0.740589i	$0.734547\pi$
$434$	31.0579	1.49083
$435$	−21.7205	−1.04142
$436$	−29.6612	−1.42051
$437$	−10.6073	−0.507414
$438$	−105.386	−5.03556
$439$	−4.39485	−0.209755	−0.104877	−	0.994485i	$-0.533445\pi$
$439$	−4.39485	−0.209755	−0.104877	+	0.994485i	$0.533445\pi$
$440$	14.1630	0.675195
$441$	132.171	6.29384
$442$	−0.555994	−0.0264459
$443$	−0.869919	−0.0413311	−0.0206655	−	0.999786i	$-0.506579\pi$
$443$	−0.869919	−0.0413311	−0.0206655	+	0.999786i	$0.506579\pi$
$444$	176.976	8.39890
$445$	6.36792	0.301868
$446$	29.5255	1.39807
$447$	57.7319	2.73063
$448$	−178.292	−8.42348
$449$	0.875294	0.0413077	0.0206538	−	0.999787i	$-0.493425\pi$
$449$	0.875294	0.0413077	0.0206538	+	0.999787i	$0.493425\pi$
$450$	−21.8121	−1.02823
$451$	−3.03647	−0.142982
$452$	−31.8170	−1.49655
$453$	15.3616	0.721750
$454$	−8.61405	−0.404277
$455$	−2.27404	−0.106609
$456$	−130.684	−6.11983
$457$	−26.4460	−1.23709	−0.618546	−	0.785748i	$-0.712278\pi$
$457$	−26.4460	−1.23709	−0.618546	+	0.785748i	$0.712278\pi$
$458$	−16.3580	−0.764359
$459$	−6.98463	−0.326014
$460$	15.0370	0.701104
$461$	−10.0325	−0.467260	−0.233630	−	0.972326i	$-0.575060\pi$
$461$	−10.0325	−0.467260	−0.233630	+	0.972326i	$0.575060\pi$
$462$	62.9552	2.92894
$463$	5.96049	0.277008	0.138504	−	0.990362i	$-0.455771\pi$
$463$	5.96049	0.277008	0.138504	+	0.990362i	$0.455771\pi$
$464$	107.406	4.98620
$465$	−7.62798	−0.353739
$466$	42.4577	1.96682
$467$	5.11520	0.236703	0.118352	−	0.992972i	$-0.462239\pi$
$467$	5.11520	0.236703	0.118352	+	0.992972i	$0.462239\pi$
$468$	−20.7283	−0.958168
$469$	−60.8672	−2.81059
$470$	−2.34494	−0.108164
$471$	−39.9690	−1.84167
$472$	88.5295	4.07490
$473$	13.7980	0.634435
$474$	40.1307	1.84326
$475$	3.96313	0.181841
$476$	11.8072	0.541182
$477$	5.42964	0.248606
$478$	−61.3671	−2.80687
$479$	−19.6128	−0.896130	−0.448065	−	0.894001i	$-0.647887\pi$
$479$	−19.6128	−0.896130	−0.448065	+	0.894001i	$0.647887\pi$
$480$	82.8550	3.78179
$481$	−4.45398	−0.203084
$482$	−2.76011	−0.125719
$483$	43.0460	1.95866
$484$	−50.5003	−2.29547
$485$	6.27077	0.284741
$486$	−137.031	−6.21585
$487$	4.14087	0.187641	0.0938203	−	0.995589i	$-0.470092\pi$
$487$	4.14087	0.187641	0.0938203	+	0.995589i	$0.470092\pi$
$488$	34.9574	1.58245
$489$	−67.4407	−3.04977
$490$	46.1625	2.08541
$491$	16.7045	0.753862	0.376931	−	0.926241i	$-0.376979\pi$
$491$	16.7045	0.753862	0.376931	+	0.926241i	$0.376979\pi$
$492$	−39.7186	−1.79065
$493$	−2.83825	−0.127829
$494$	5.10693	0.229772
$495$	−11.2075	−0.503741
$496$	37.7197	1.69367
$497$	−20.2029	−0.906223
$498$	−107.628	−4.82293
$499$	8.39382	0.375759	0.187879	−	0.982192i	$-0.439839\pi$
$499$	8.39382	0.375759	0.187879	+	0.982192i	$0.439839\pi$
$500$	−5.61819	−0.251253
$501$	84.1714	3.76050
$502$	10.0384	0.448034
$503$	−12.6122	−0.562352	−0.281176	−	0.959656i	$-0.590724\pi$
$503$	−12.6122	−0.562352	−0.281176	+	0.959656i	$0.590724\pi$
$504$	384.407	17.1229
$505$	13.7018	0.609721
$506$	10.4768	0.465750
$507$	−42.2052	−1.87440
$508$	−59.1875	−2.62602
$509$	−17.9253	−0.794524	−0.397262	−	0.917705i	$-0.630040\pi$
$509$	−17.9253	−0.794524	−0.397262	+	0.917705i	$0.630040\pi$
$510$	−3.93224	−0.174122
$511$	−56.3242	−2.49164
$512$	−83.5948	−3.69440
$513$	64.1554	2.83253
$514$	−24.2097	−1.06784
$515$	−9.88518	−0.435593
$516$	180.485	7.94542
$517$	−1.20488	−0.0529906
$518$	128.257	5.63527
$519$	−21.3566	−0.937451
$520$	−4.66245	−0.204462
$521$	15.2966	0.670154	0.335077	−	0.942191i	$-0.391238\pi$
$521$	15.2966	0.670154	0.335077	+	0.942191i	$0.391238\pi$
$522$	−143.483	−6.28009
$523$	−9.43212	−0.412438	−0.206219	−	0.978506i	$-0.566116\pi$
$523$	−9.43212	−0.412438	−0.206219	+	0.978506i	$0.566116\pi$
$524$	−10.3381	−0.451621
$525$	−16.0830	−0.701921
$526$	28.2347	1.23109
$527$	−0.996762	−0.0434196
$528$	76.4590	3.32745
$529$	−15.8364	−0.688541
$530$	1.89638	0.0823735
$531$	−70.0555	−3.04015
$532$	−108.452	−4.70198
$533$	0.999603	0.0432976
$534$	58.0349	2.51142
$535$	1.79774	0.0777232
$536$	−124.795	−5.39034
$537$	−71.8330	−3.09982
$538$	−36.6260	−1.57906
$539$	23.7193	1.02166
$540$	−90.9477	−3.91377
$541$	−30.9280	−1.32970	−0.664850	−	0.746977i	$-0.731505\pi$
$541$	−30.9280	−1.32970	−0.664850	+	0.746977i	$0.731505\pi$
$542$	16.5195	0.709574
$543$	−51.2848	−2.20084
$544$	10.8268	0.464196
$545$	5.27949	0.226149
$546$	−20.7248	−0.886939
$547$	−11.0808	−0.473780	−0.236890	−	0.971536i	$-0.576128\pi$
$547$	−11.0808	−0.473780	−0.236890	+	0.971536i	$0.576128\pi$
$548$	18.0289	0.770157
$549$	−27.6626	−1.18061
$550$	−3.91439	−0.166910
$551$	26.0700	1.11062
$552$	88.2568	3.75646
$553$	21.4480	0.912062
$554$	68.4958	2.91011
$555$	−31.5005	−1.33712
$556$	43.8476	1.85955
$557$	−11.3959	−0.482859	−0.241430	−	0.970418i	$-0.577616\pi$
$557$	−11.3959	−0.482859	−0.241430	+	0.970418i	$0.577616\pi$
$558$	−50.3897	−2.13316
$559$	−4.54230	−0.192119
$560$	79.5293	3.36073
$561$	−2.02047	−0.0853042
$562$	−23.5963	−0.995348
$563$	17.7153	0.746611	0.373306	−	0.927708i	$-0.378224\pi$
$563$	17.7153	0.746611	0.373306	+	0.927708i	$0.378224\pi$
$564$	−15.7604	−0.663635
$565$	5.66321	0.238253
$566$	−28.8990	−1.21472
$567$	−144.876	−6.08424
$568$	−41.4218	−1.73802
$569$	7.78742	0.326465	0.163233	−	0.986588i	$-0.447808\pi$
$569$	7.78742	0.326465	0.163233	+	0.986588i	$0.447808\pi$
$570$	36.1185	1.51284
$571$	15.2617	0.638684	0.319342	−	0.947639i	$-0.396538\pi$
$571$	15.2617	0.638684	0.319342	+	0.947639i	$0.396538\pi$
$572$	−3.71989	−0.155537
$573$	−11.0091	−0.459912
$574$	−28.7846	−1.20144
$575$	−2.67648	−0.111617
$576$	289.268	12.0528
$577$	35.5792	1.48118	0.740592	−	0.671955i	$-0.234545\pi$
$577$	35.5792	1.48118	0.740592	+	0.671955i	$0.234545\pi$
$578$	46.4080	1.93032
$579$	−20.6800	−0.859431
$580$	−36.9573	−1.53457
$581$	−57.5223	−2.38643
$582$	57.1495	2.36892
$583$	0.974400	0.0403555
$584$	−115.481	−4.77864
$585$	3.68950	0.152542
$586$	−19.5499	−0.807600
$587$	−8.27871	−0.341699	−0.170850	−	0.985297i	$-0.554651\pi$
$587$	−8.27871	−0.341699	−0.170850	+	0.985297i	$0.554651\pi$
$588$	310.260	12.7949
$589$	9.15550	0.377246
$590$	−24.4679	−1.00733
$591$	28.2909	1.16373
$592$	155.767	6.40200
$593$	0.735816	0.0302163	0.0151082	−	0.999886i	$-0.495191\pi$
$593$	0.735816	0.0302163	0.0151082	+	0.999886i	$0.495191\pi$
$594$	−63.3664	−2.59996
$595$	−2.10160	−0.0861572
$596$	98.2306	4.02368
$597$	73.9525	3.02667
$598$	−3.44895	−0.141038
$599$	−35.0133	−1.43060	−0.715302	−	0.698816i	$-0.753711\pi$
$599$	−35.0133	−1.43060	−0.715302	+	0.698816i	$0.753711\pi$
$600$	−32.9749	−1.34619
$601$	16.4686	0.671769	0.335884	−	0.941903i	$-0.390965\pi$
$601$	16.4686	0.671769	0.335884	+	0.941903i	$0.390965\pi$
$602$	130.800	5.33101
$603$	98.7536	4.02156
$604$	26.1377	1.06353
$605$	8.98870	0.365443
$606$	124.873	5.07262
$607$	−29.7442	−1.20728	−0.603641	−	0.797256i	$-0.706284\pi$
$607$	−29.7442	−1.20728	−0.603641	+	0.797256i	$0.706284\pi$
$608$	−99.4469	−4.03310
$609$	−105.796	−4.28709
$610$	−9.66157	−0.391185
$611$	0.396645	0.0160465
$612$	−19.1565	−0.774356
$613$	−33.0638	−1.33544	−0.667718	−	0.744415i	$-0.732729\pi$
$613$	−33.0638	−1.33544	−0.667718	+	0.744415i	$0.732729\pi$
$614$	57.6506	2.32659
$615$	7.06964	0.285075
$616$	68.9855	2.77950
$617$	27.9340	1.12458	0.562290	−	0.826940i	$-0.309920\pi$
$617$	27.9340	1.12458	0.562290	+	0.826940i	$0.309920\pi$
$618$	−90.0900	−3.62395
$619$	29.9135	1.20233	0.601163	−	0.799127i	$-0.294704\pi$
$619$	29.9135	1.20233	0.601163	+	0.799127i	$0.294704\pi$
$620$	−12.9790	−0.521248
$621$	−43.3271	−1.73866
$622$	−5.57923	−0.223707
$623$	31.0170	1.24267
$624$	−25.1702	−1.00761
$625$	1.00000	0.0400000
$626$	−64.5715	−2.58080
$627$	18.5585	0.741154
$628$	−68.0071	−2.71378
$629$	−4.11623	−0.164125
$630$	−106.243	−4.23282
$631$	−19.2101	−0.764740	−0.382370	−	0.924009i	$-0.624892\pi$
$631$	−19.2101	−0.764740	−0.382370	+	0.924009i	$0.624892\pi$
$632$	43.9746	1.74922
$633$	55.7532	2.21599
$634$	−73.4300	−2.91628
$635$	10.5350	0.418068
$636$	12.7456	0.505398
$637$	−7.80835	−0.309378
$638$	−25.7494	−1.01943
$639$	32.7780	1.29668
$640$	50.8450	2.00982
$641$	15.8889	0.627575	0.313787	−	0.949493i	$-0.398402\pi$
$641$	15.8889	0.627575	0.313787	+	0.949493i	$0.398402\pi$
$642$	16.3840	0.646624
$643$	−40.6666	−1.60373	−0.801867	−	0.597503i	$-0.796160\pi$
$643$	−40.6666	−1.60373	−0.801867	+	0.597503i	$0.796160\pi$
$644$	73.2425	2.88616
$645$	−32.1252	−1.26493
$646$	4.71968	0.185693
$647$	−32.7851	−1.28891	−0.644457	−	0.764641i	$-0.722916\pi$
$647$	−32.7851	−1.28891	−0.644457	+	0.764641i	$0.722916\pi$
$648$	−297.039	−11.6688
$649$	−12.5721	−0.493499
$650$	1.28861	0.0505435
$651$	−37.1545	−1.45620
$652$	−114.750	−4.49396
$653$	9.65038	0.377648	0.188824	−	0.982011i	$-0.439532\pi$
$653$	9.65038	0.377648	0.188824	+	0.982011i	$0.439532\pi$
$654$	48.1154	1.88146
$655$	1.84011	0.0718989
$656$	−34.9588	−1.36491
$657$	91.3829	3.56519
$658$	−11.4218	−0.445268
$659$	0.137177	0.00534365	0.00267182	−	0.999996i	$-0.499150\pi$
$659$	0.137177	0.00534365	0.00267182	+	0.999996i	$0.499150\pi$
$660$	−26.3088	−1.02407
$661$	−6.12360	−0.238180	−0.119090	−	0.992883i	$-0.537998\pi$
$661$	−6.12360	−0.238180	−0.119090	+	0.992883i	$0.537998\pi$
$662$	48.9278	1.90163
$663$	0.665135	0.0258317
$664$	−117.937	−4.57686
$665$	19.3037	0.748565
$666$	−208.089	−8.06329
$667$	−17.6063	−0.681718
$668$	143.217	5.54125
$669$	−35.3213	−1.36560
$670$	34.4911	1.33251
$671$	−4.96432	−0.191645
$672$	403.572	15.5681
$673$	−47.4692	−1.82980	−0.914902	−	0.403675i	$-0.867733\pi$
$673$	−47.4692	−1.82980	−0.914902	+	0.403675i	$0.867733\pi$
$674$	−69.2311	−2.66668
$675$	16.1881	0.623079
$676$	−71.8119	−2.76200
$677$	−25.8715	−0.994322	−0.497161	−	0.867658i	$-0.665624\pi$
$677$	−25.8715	−0.994322	−0.497161	+	0.867658i	$0.665624\pi$
$678$	51.6125	1.98216
$679$	30.5438	1.17216
$680$	−4.30889	−0.165238
$681$	10.3050	0.394888
$682$	−9.04290	−0.346270
$683$	−45.7333	−1.74993	−0.874967	−	0.484182i	$-0.839117\pi$
$683$	−45.7333	−1.74993	−0.874967	+	0.484182i	$0.839117\pi$
$684$	175.957	6.72789
$685$	−3.20902	−0.122611
$686$	130.741	4.99173
$687$	19.5691	0.746606
$688$	158.856	6.05634
$689$	−0.320771	−0.0122204
$690$	−24.3925	−0.928607
$691$	−26.5602	−1.01040	−0.505199	−	0.863003i	$-0.668581\pi$
$691$	−26.5602	−1.01040	−0.505199	+	0.863003i	$0.668581\pi$
$692$	−36.3382	−1.38137
$693$	−54.5899	−2.07370
$694$	82.4516	3.12982
$695$	−7.80458	−0.296044
$696$	−216.914	−8.22209
$697$	0.923804	0.0349916
$698$	−13.3131	−0.503907
$699$	−50.7921	−1.92113
$700$	−27.3652	−1.03431
$701$	−0.404642	−0.0152831	−0.00764156	−	0.999971i	$-0.502432\pi$
$701$	−0.404642	−0.0152831	−0.00764156	+	0.999971i	$0.502432\pi$
$702$	20.8601	0.787315
$703$	37.8085	1.42598
$704$	51.9119	1.95650
$705$	2.80525	0.105652
$706$	44.6326	1.67977
$707$	66.7389	2.50997
$708$	−164.450	−6.18039
$709$	−49.2841	−1.85090	−0.925452	−	0.378865i	$-0.876314\pi$
$709$	−49.2841	−1.85090	−0.925452	+	0.378865i	$0.876314\pi$
$710$	11.4482	0.429643
$711$	−34.7982	−1.30503
$712$	63.5939	2.38328
$713$	−6.18313	−0.231560
$714$	−19.1532	−0.716791
$715$	0.662116	0.0247617
$716$	−122.224	−4.56771
$717$	73.4134	2.74168
$718$	53.6052	2.00053
$719$	52.2097	1.94709	0.973546	−	0.228490i	$-0.0733787\pi$
$719$	52.2097	1.94709	0.973546	+	0.228490i	$0.0733787\pi$
$720$	−129.032	−4.80873
$721$	−48.1490	−1.79316
$722$	9.09071	0.338321
$723$	3.30191	0.122799
$724$	−87.2609	−3.24302
$725$	6.57814	0.244306
$726$	81.9198	3.04033
$727$	27.3771	1.01536	0.507680	−	0.861545i	$-0.330503\pi$
$727$	27.3771	1.01536	0.507680	+	0.861545i	$0.330503\pi$
$728$	−22.7099	−0.841686
$729$	74.6989	2.76663
$730$	31.9168	1.18129
$731$	−4.19786	−0.155263
$732$	−64.9358	−2.40010
$733$	46.0785	1.70195	0.850973	−	0.525209i	$-0.176013\pi$
$733$	46.0785	1.70195	0.850973	+	0.525209i	$0.176013\pi$
$734$	−52.4666	−1.93658
$735$	−55.2242	−2.03697
$736$	67.1610	2.47559
$737$	17.7223	0.652808
$738$	46.7014	1.71910
$739$	12.0904	0.444752	0.222376	−	0.974961i	$-0.428619\pi$
$739$	12.0904	0.444752	0.222376	+	0.974961i	$0.428619\pi$
$740$	−53.5980	−1.97030
$741$	−6.10942	−0.224435
$742$	9.23693	0.339098
$743$	15.4093	0.565312	0.282656	−	0.959221i	$-0.408785\pi$
$743$	15.4093	0.565312	0.282656	+	0.959221i	$0.408785\pi$
$744$	−76.1775	−2.79280
$745$	−17.4844	−0.640578
$746$	−63.8944	−2.33934
$747$	93.3267	3.41465
$748$	−3.43782	−0.125699
$749$	8.75648	0.319955
$750$	9.11364	0.332783
$751$	14.2912	0.521494	0.260747	−	0.965407i	$-0.416031\pi$
$751$	14.2912	0.521494	0.260747	+	0.965407i	$0.416031\pi$
$752$	−13.8718	−0.505851
$753$	−12.0089	−0.437628
$754$	8.47667	0.308702
$755$	−4.65232	−0.169315
$756$	−442.990	−16.1114
$757$	−0.301761	−0.0109677	−0.00548385	−	0.999985i	$-0.501746\pi$
$757$	−0.301761	−0.0109677	−0.00548385	+	0.999985i	$0.501746\pi$
$758$	−5.25751	−0.190961
$759$	−12.5334	−0.454933
$760$	39.5782	1.43565
$761$	15.3376	0.555989	0.277995	−	0.960583i	$-0.410330\pi$
$761$	15.3376	0.555989	0.277995	+	0.960583i	$0.410330\pi$
$762$	96.0120	3.47815
$763$	25.7155	0.930963
$764$	−18.7320	−0.677698
$765$	3.40973	0.123279
$766$	−11.6319	−0.420277
$767$	4.13872	0.149441
$768$	221.656	7.99832
$769$	−11.3995	−0.411077	−0.205539	−	0.978649i	$-0.565895\pi$
$769$	−11.3995	−0.411077	−0.205539	+	0.978649i	$0.565895\pi$
$770$	−19.0663	−0.687101
$771$	28.9621	1.04304
$772$	−35.1869	−1.26641
$773$	0.690516	0.0248361	0.0124181	−	0.999923i	$-0.496047\pi$
$773$	0.690516	0.0248361	0.0124181	+	0.999923i	$0.496047\pi$
$774$	−212.216	−7.62793
$775$	2.31017	0.0829837
$776$	62.6236	2.24806
$777$	−153.433	−5.50439
$778$	35.3982	1.26909
$779$	−8.48535	−0.304019
$780$	8.66081	0.310107
$781$	5.88233	0.210486
$782$	−3.18741	−0.113982
$783$	106.487	3.80555
$784$	273.079	9.75283
$785$	12.1048	0.432039
$786$	16.7701	0.598168
$787$	17.2636	0.615379	0.307690	−	0.951487i	$-0.400444\pi$
$787$	17.2636	0.615379	0.307690	+	0.951487i	$0.400444\pi$
$788$	48.1368	1.71480
$789$	−33.7772	−1.20250
$790$	−12.1538	−0.432411
$791$	27.5845	0.980792
$792$	−111.925	−3.97709
$793$	1.63425	0.0580338
$794$	−29.7837	−1.05698
$795$	−2.26864	−0.0804603
$796$	125.830	4.45992
$797$	6.87794	0.243629	0.121814	−	0.992553i	$-0.461129\pi$
$797$	6.87794	0.243629	0.121814	+	0.992553i	$0.461129\pi$
$798$	175.927	6.22774
$799$	0.366568	0.0129682
$800$	−25.0930	−0.887172
$801$	−50.3233	−1.77809
$802$	82.3709	2.90862
$803$	16.3995	0.578727
$804$	231.816	8.17552
$805$	−13.0367	−0.459482
$806$	2.97691	0.104857
$807$	43.8156	1.54238
$808$	136.834	4.81381
$809$	47.1897	1.65910	0.829551	−	0.558431i	$-0.188596\pi$
$809$	47.1897	1.65910	0.829551	+	0.558431i	$0.188596\pi$
$810$	82.0959	2.88456
$811$	−15.8238	−0.555648	−0.277824	−	0.960632i	$-0.589613\pi$
$811$	−15.8238	−0.555648	−0.277824	+	0.960632i	$0.589613\pi$
$812$	−180.012	−6.31719
$813$	−19.7623	−0.693094
$814$	−37.3436	−1.30889
$815$	20.4247	0.715447
$816$	−23.2616	−0.814317
$817$	38.5583	1.34898
$818$	−59.9884	−2.09744
$819$	17.9709	0.627954
$820$	12.0290	0.420070
$821$	−18.7126	−0.653074	−0.326537	−	0.945184i	$-0.605882\pi$
$821$	−18.7126	−0.653074	−0.326537	+	0.945184i	$0.605882\pi$
$822$	−29.2459	−1.02007
$823$	−21.6915	−0.756117	−0.378058	−	0.925782i	$-0.623408\pi$
$823$	−21.6915	−0.756117	−0.378058	+	0.925782i	$0.623408\pi$
$824$	−98.7194	−3.43905
$825$	4.68278	0.163033
$826$	−119.179	−4.14676
$827$	−3.72591	−0.129562	−0.0647812	−	0.997899i	$-0.520635\pi$
$827$	−3.72591	−0.129562	−0.0647812	+	0.997899i	$0.520635\pi$
$828$	−118.832	−4.12969
$829$	−31.1895	−1.08326	−0.541628	−	0.840618i	$-0.682192\pi$
$829$	−31.1895	−1.08326	−0.541628	+	0.840618i	$0.682192\pi$
$830$	32.5957	1.13141
$831$	−81.9415	−2.84252
$832$	−17.0893	−0.592465
$833$	−7.21625	−0.250028
$834$	−71.1281	−2.46296
$835$	−25.4917	−0.882177
$836$	31.5771	1.09212
$837$	37.3972	1.29264
$838$	−59.1417	−2.04302
$839$	40.3346	1.39251	0.696253	−	0.717796i	$-0.254849\pi$
$839$	40.3346	1.39251	0.696253	+	0.717796i	$0.254849\pi$
$840$	−160.615	−5.54174
$841$	14.2719	0.492136
$842$	28.6016	0.985677
$843$	28.2282	0.972230
$844$	94.8639	3.26535
$845$	12.7820	0.439715
$846$	18.5312	0.637117
$847$	43.7824	1.50438
$848$	11.2182	0.385236
$849$	34.5719	1.18650
$850$	1.19090	0.0408474
$851$	−25.5339	−0.875289
$852$	76.9438	2.63605
$853$	−6.49969	−0.222545	−0.111273	−	0.993790i	$-0.535493\pi$
$853$	−6.49969	−0.222545	−0.111273	+	0.993790i	$0.535493\pi$
$854$	−47.0598	−1.61035
$855$	−31.3192	−1.07109
$856$	17.9533	0.613632
$857$	−44.1937	−1.50963	−0.754814	−	0.655939i	$-0.772273\pi$
$857$	−44.1937	−1.50963	−0.754814	+	0.655939i	$0.772273\pi$
$858$	6.03428	0.206007
$859$	23.8873	0.815023	0.407512	−	0.913200i	$-0.366397\pi$
$859$	23.8873	0.815023	0.407512	+	0.913200i	$0.366397\pi$
$860$	−54.6608	−1.86392
$861$	34.4350	1.17354
$862$	−61.4405	−2.09267
$863$	−3.98064	−0.135502	−0.0677512	−	0.997702i	$-0.521582\pi$
$863$	−3.98064	−0.135502	−0.0677512	+	0.997702i	$0.521582\pi$
$864$	−406.208	−13.8195
$865$	6.46795	0.219917
$866$	77.1867	2.62291
$867$	−55.5178	−1.88548
$868$	−63.2182	−2.14577
$869$	−6.24486	−0.211842
$870$	59.9508	2.03252
$871$	−5.83414	−0.197682
$872$	52.7242	1.78547
$873$	−49.5556	−1.67720
$874$	29.2772	0.990314
$875$	4.87082	0.164664
$876$	214.514	7.24776
$877$	−33.6884	−1.13758	−0.568788	−	0.822484i	$-0.692588\pi$
$877$	−33.6884	−1.13758	−0.568788	+	0.822484i	$0.692588\pi$
$878$	12.1303	0.409376
$879$	23.3876	0.788843
$880$	−23.1560	−0.780588
$881$	7.78872	0.262409	0.131204	−	0.991355i	$-0.458116\pi$
$881$	7.78872	0.262409	0.131204	+	0.991355i	$0.458116\pi$
$882$	−364.805	−12.2836
$883$	49.9405	1.68063	0.840316	−	0.542097i	$-0.182369\pi$
$883$	49.9405	1.68063	0.840316	+	0.542097i	$0.182369\pi$
$884$	1.13172	0.0380640
$885$	29.2709	0.983931
$886$	2.40107	0.0806655
$887$	−33.5013	−1.12486	−0.562432	−	0.826843i	$-0.690134\pi$
$887$	−33.5013	−1.12486	−0.562432	+	0.826843i	$0.690134\pi$
$888$	−314.583	−10.5567
$889$	51.3140	1.72102
$890$	−17.5761	−0.589154
$891$	42.1826	1.41317
$892$	−60.0990	−2.01226
$893$	−3.36701	−0.112673
$894$	−159.346	−5.32934
$895$	21.7550	0.727188
$896$	247.657	8.27363
$897$	4.12597	0.137762
$898$	−2.41590	−0.0806198
$899$	15.1966	0.506835
$900$	44.3985	1.47995
$901$	−0.296447	−0.00987609
$902$	8.38099	0.279057
$903$	−156.476	−5.20719
$904$	56.5562	1.88103
$905$	15.5318	0.516296
$906$	−42.3996	−1.40863
$907$	40.2677	1.33707	0.668533	−	0.743682i	$-0.266922\pi$
$907$	40.2677	1.33707	0.668533	+	0.743682i	$0.266922\pi$
$908$	17.5339	0.581882
$909$	−108.280	−3.59143
$910$	6.27660	0.208067
$911$	43.3440	1.43605	0.718026	−	0.696016i	$-0.245046\pi$
$911$	43.3440	1.43605	0.718026	+	0.696016i	$0.245046\pi$
$912$	213.663	7.07508
$913$	16.7484	0.554290
$914$	72.9938	2.41442
$915$	11.5581	0.382100
$916$	33.2967	1.10015
$917$	8.96283	0.295979
$918$	19.2783	0.636279
$919$	−8.86966	−0.292583	−0.146292	−	0.989242i	$-0.546734\pi$
$919$	−8.86966	−0.292583	−0.146292	+	0.989242i	$0.546734\pi$
$920$	−26.7290	−0.881228
$921$	−68.9674	−2.27255
$922$	27.6908	0.911947
$923$	−1.93645	−0.0637392
$924$	−128.145	−4.21567
$925$	9.54007	0.313676
$926$	−16.4516	−0.540633
$927$	78.1190	2.56576
$928$	−165.065	−5.41854
$929$	−12.8321	−0.421009	−0.210504	−	0.977593i	$-0.567511\pi$
$929$	−12.8321	−0.421009	−0.210504	+	0.977593i	$0.567511\pi$
$930$	21.0540	0.690389
$931$	66.2829	2.17233
$932$	−86.4226	−2.83087
$933$	6.67443	0.218511
$934$	−14.1185	−0.461971
$935$	0.611908	0.0200115
$936$	36.8456	1.20434
$937$	52.9973	1.73135	0.865674	−	0.500609i	$-0.166890\pi$
$937$	52.9973	1.73135	0.865674	+	0.500609i	$0.166890\pi$
$938$	168.000	5.48539
$939$	77.2469	2.52086
$940$	4.77313	0.155682
$941$	25.0940	0.818041	0.409020	−	0.912525i	$-0.365871\pi$
$941$	25.0940	0.818041	0.409020	+	0.912525i	$0.365871\pi$
$942$	110.319	3.59438
$943$	5.73055	0.186612
$944$	−144.742	−4.71096
$945$	78.8492	2.56497
$946$	−38.0841	−1.23822
$947$	−55.9791	−1.81908	−0.909539	−	0.415619i	$-0.863565\pi$
$947$	−55.9791	−1.81908	−0.909539	+	0.415619i	$0.863565\pi$
$948$	−81.6859	−2.65303
$949$	−5.39870	−0.175249
$950$	−10.9387	−0.354897
$951$	87.8442	2.84854
$952$	−20.9878	−0.680220
$953$	16.4960	0.534357	0.267178	−	0.963647i	$-0.413909\pi$
$953$	16.4960	0.534357	0.267178	+	0.963647i	$0.413909\pi$
$954$	−14.9864	−0.485203
$955$	3.33416	0.107891
$956$	124.913	4.03996
$957$	30.8040	0.995751
$958$	54.1333	1.74897
$959$	−15.6306	−0.504738
$960$	−120.863	−3.90085
$961$	−25.6631	−0.827843
$962$	12.2934	0.396357
$963$	−14.2069	−0.457811
$964$	5.61819	0.180950
$965$	6.26303	0.201614
$966$	−118.811	−3.82270
$967$	35.4558	1.14018	0.570091	−	0.821581i	$-0.306908\pi$
$967$	35.4558	1.14018	0.570091	+	0.821581i	$0.306908\pi$
$968$	89.7666	2.88521
$969$	−5.64614	−0.181380
$970$	−17.3080	−0.555726
$971$	−15.3750	−0.493409	−0.246704	−	0.969091i	$-0.579348\pi$
$971$	−15.3750	−0.493409	−0.246704	+	0.969091i	$0.579348\pi$
$972$	278.926	8.94657
$973$	−38.0147	−1.21870
$974$	−11.4292	−0.366216
$975$	−1.54156	−0.0493696
$976$	−57.1540	−1.82946
$977$	−31.9931	−1.02355	−0.511775	−	0.859120i	$-0.671012\pi$
$977$	−31.9931	−1.02355	−0.511775	+	0.859120i	$0.671012\pi$
$978$	186.143	5.95221
$979$	−9.03100	−0.288632
$980$	−93.9637	−3.00156
$981$	−41.7219	−1.33208
$982$	−46.1061	−1.47131
$983$	30.1757	0.962456	0.481228	−	0.876595i	$-0.340191\pi$
$983$	30.1757	0.962456	0.481228	+	0.876595i	$0.340191\pi$
$984$	70.6017	2.25070
$985$	−8.56802	−0.273000
$986$	7.83389	0.249482
$987$	13.6639	0.434926
$988$	−10.3952	−0.330714
$989$	−26.0402	−0.828030
$990$	30.9340	0.983147
$991$	−33.8931	−1.07665	−0.538325	−	0.842737i	$-0.680943\pi$
$991$	−33.8931	−1.07665	−0.538325	+	0.842737i	$0.680943\pi$
$992$	−57.9691	−1.84052
$993$	−58.5323	−1.85747
$994$	55.7621	1.76867
$995$	−22.3969	−0.710028
$996$	219.077	6.94172
$997$	−32.1252	−1.01742	−0.508708	−	0.860939i	$-0.669877\pi$
$997$	−32.1252	−1.01742	−0.508708	+	0.860939i	$0.669877\pi$
$998$	−23.1678	−0.733365
$999$	154.435	4.88612

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1205.2.a.d.1.2	✓	25
5.4	even	2		6025.2.a.k.1.24		25

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1205.2.a.d.1.2	✓	25	1.1	even	1	trivial
6025.2.a.k.1.24		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)

\(f(q)\)	\(=\)	\(q-2.76011 q^{2} +3.30191 q^{3} +5.61819 q^{4} -1.00000 q^{5} -9.11364 q^{6} -4.87082 q^{7} -9.98660 q^{8} +7.90263 q^{9} +O(q^{10})\)	\(q-2.76011 q^{2} +3.30191 q^{3} +5.61819 q^{4} -1.00000 q^{5} -9.11364 q^{6} -4.87082 q^{7} -9.98660 q^{8} +7.90263 q^{9} +2.76011 q^{10} +1.41820 q^{11} +18.5508 q^{12} -0.466870 q^{13} +13.4440 q^{14} -3.30191 q^{15} +16.3277 q^{16} -0.431467 q^{17} -21.8121 q^{18} +3.96313 q^{19} -5.61819 q^{20} -16.0830 q^{21} -3.91439 q^{22} -2.67648 q^{23} -32.9749 q^{24} +1.00000 q^{25} +1.28861 q^{26} +16.1881 q^{27} -27.3652 q^{28} +6.57814 q^{29} +9.11364 q^{30} +2.31017 q^{31} -25.0930 q^{32} +4.68278 q^{33} +1.19090 q^{34} +4.87082 q^{35} +44.3985 q^{36} +9.54007 q^{37} -10.9387 q^{38} -1.54156 q^{39} +9.98660 q^{40} -2.14107 q^{41} +44.3909 q^{42} +9.72925 q^{43} +7.96773 q^{44} -7.90263 q^{45} +7.38738 q^{46} -0.849584 q^{47} +53.9127 q^{48} +16.7249 q^{49} -2.76011 q^{50} -1.42467 q^{51} -2.62297 q^{52} +0.687068 q^{53} -44.6808 q^{54} -1.41820 q^{55} +48.6429 q^{56} +13.0859 q^{57} -18.1564 q^{58} -8.86483 q^{59} -18.5508 q^{60} -3.50043 q^{61} -6.37631 q^{62} -38.4923 q^{63} +36.6040 q^{64} +0.466870 q^{65} -12.9250 q^{66} +12.4963 q^{67} -2.42407 q^{68} -8.83752 q^{69} -13.4440 q^{70} +4.14774 q^{71} -78.9204 q^{72} +11.5636 q^{73} -26.3316 q^{74} +3.30191 q^{75} +22.2656 q^{76} -6.90781 q^{77} +4.25488 q^{78} -4.40336 q^{79} -16.3277 q^{80} +29.7437 q^{81} +5.90959 q^{82} +11.8096 q^{83} -90.3576 q^{84} +0.431467 q^{85} -26.8538 q^{86} +21.7205 q^{87} -14.1630 q^{88} -6.36792 q^{89} +21.8121 q^{90} +2.27404 q^{91} -15.0370 q^{92} +7.62798 q^{93} +2.34494 q^{94} -3.96313 q^{95} -82.8550 q^{96} -6.27077 q^{97} -46.1625 q^{98} +11.2075 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 25 q - 4 q^{2} + 9 q^{3} + 36 q^{4} - 25 q^{5} + 7 q^{6} + 7 q^{7} - 15 q^{8} + 36 q^{9}+O(q^{10}) \) 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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