LMFDB - Embedded newform 805.2.a.f.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [805,2,Mod(1,805)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(805, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("805.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 805 = 5 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	805.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:	$6.42795736271$
Analytic rank:	$1$
Dimension:	$3$
Coefficient field:	$\Q(\zeta_{14})^+$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - x^{2} - 2x + 1 $ x^3 - x^2 - 2*x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-1.24698$ of defining polynomial
Character	$\chi$	$=$	805.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.554958 q^{2} -3.04892 q^{3} -1.69202 q^{4} -1.00000 q^{5} +1.69202 q^{6} -1.00000 q^{7} +2.04892 q^{8} +6.29590 q^{9} +O(q^{10})$	\(q-0.554958 q^{2} -3.04892 q^{3} -1.69202 q^{4} -1.00000 q^{5} +1.69202 q^{6} -1.00000 q^{7} +2.04892 q^{8} +6.29590 q^{9} +0.554958 q^{10} -2.44504 q^{11} +5.15883 q^{12} +5.96077 q^{13} +0.554958 q^{14} +3.04892 q^{15} +2.24698 q^{16} +4.93900 q^{17} -3.49396 q^{18} -3.69202 q^{19} +1.69202 q^{20} +3.04892 q^{21} +1.35690 q^{22} -1.00000 q^{23} -6.24698 q^{24} +1.00000 q^{25} -3.30798 q^{26} -10.0489 q^{27} +1.69202 q^{28} -6.71379 q^{29} -1.69202 q^{30} -2.80194 q^{31} -5.34481 q^{32} +7.45473 q^{33} -2.74094 q^{34} +1.00000 q^{35} -10.6528 q^{36} +1.33513 q^{37} +2.04892 q^{38} -18.1739 q^{39} -2.04892 q^{40} +6.87800 q^{41} -1.69202 q^{42} +0.554958 q^{43} +4.13706 q^{44} -6.29590 q^{45} +0.554958 q^{46} +11.7899 q^{47} -6.85086 q^{48} +1.00000 q^{49} -0.554958 q^{50} -15.0586 q^{51} -10.0858 q^{52} -11.4601 q^{53} +5.57673 q^{54} +2.44504 q^{55} -2.04892 q^{56} +11.2567 q^{57} +3.72587 q^{58} -11.7409 q^{59} -5.15883 q^{60} +4.78986 q^{61} +1.55496 q^{62} -6.29590 q^{63} -1.52781 q^{64} -5.96077 q^{65} -4.13706 q^{66} +11.5646 q^{67} -8.35690 q^{68} +3.04892 q^{69} -0.554958 q^{70} -6.13169 q^{71} +12.8998 q^{72} -10.7899 q^{73} -0.740939 q^{74} -3.04892 q^{75} +6.24698 q^{76} +2.44504 q^{77} +10.0858 q^{78} -10.0707 q^{79} -2.24698 q^{80} +11.7506 q^{81} -3.81700 q^{82} +0.948690 q^{83} -5.15883 q^{84} -4.93900 q^{85} -0.307979 q^{86} +20.4698 q^{87} -5.00969 q^{88} -3.65279 q^{89} +3.49396 q^{90} -5.96077 q^{91} +1.69202 q^{92} +8.54288 q^{93} -6.54288 q^{94} +3.69202 q^{95} +16.2959 q^{96} -11.4155 q^{97} -0.554958 q^{98} -15.3937 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q - 2 q^{2} - 3 q^{5} - 3 q^{7} - 3 q^{8} + 5 q^{9}+O(q^{10}) $ 3 * q - 2 * q^2 - 3 * q^5 - 3 * q^7 - 3 * q^8 + 5 * q^9	$ 3 q - 2 q^{2} - 3 q^{5} - 3 q^{7} - 3 q^{8} + 5 q^{9} + 2 q^{10} - 7 q^{11} + 7 q^{12} + 5 q^{13} + 2 q^{14} + 2 q^{16} + 5 q^{17} - q^{18} - 6 q^{19} - 3 q^{23} - 14 q^{24} + 3 q^{25} - 15 q^{26} - 21 q^{27} - 12 q^{29} - 4 q^{31} + 7 q^{32} + 6 q^{34} + 3 q^{35} - 14 q^{36} + 3 q^{37} - 3 q^{38} - 21 q^{39} + 3 q^{40} + q^{41} + 2 q^{43} + 7 q^{44} - 5 q^{45} + 2 q^{46} + 12 q^{47} - 7 q^{48} + 3 q^{49} - 2 q^{50} - 14 q^{51} + 7 q^{52} - 9 q^{53} + 14 q^{54} + 7 q^{55} + 3 q^{56} + 7 q^{57} + 22 q^{58} - 21 q^{59} - 7 q^{60} - 9 q^{61} + 5 q^{62} - 5 q^{63} - 11 q^{64} - 5 q^{65} - 7 q^{66} + 13 q^{67} - 21 q^{68} - 2 q^{70} - 16 q^{71} + 16 q^{72} - 9 q^{73} + 12 q^{74} + 14 q^{76} + 7 q^{77} - 7 q^{78} - 18 q^{79} - 2 q^{80} - q^{81} + 18 q^{82} - 29 q^{83} - 7 q^{84} - 5 q^{85} - 6 q^{86} + 14 q^{87} + 7 q^{88} + 7 q^{89} + q^{90} - 5 q^{91} + 7 q^{93} - q^{94} + 6 q^{95} + 35 q^{96} + q^{97} - 2 q^{98} - 14 q^{99}+O(q^{100}) $ 3 * q - 2 * q^2 - 3 * q^5 - 3 * q^7 - 3 * q^8 + 5 * q^9 + 2 * q^10 - 7 * q^11 + 7 * q^12 + 5 * q^13 + 2 * q^14 + 2 * q^16 + 5 * q^17 - q^18 - 6 * q^19 - 3 * q^23 - 14 * q^24 + 3 * q^25 - 15 * q^26 - 21 * q^27 - 12 * q^29 - 4 * q^31 + 7 * q^32 + 6 * q^34 + 3 * q^35 - 14 * q^36 + 3 * q^37 - 3 * q^38 - 21 * q^39 + 3 * q^40 + q^41 + 2 * q^43 + 7 * q^44 - 5 * q^45 + 2 * q^46 + 12 * q^47 - 7 * q^48 + 3 * q^49 - 2 * q^50 - 14 * q^51 + 7 * q^52 - 9 * q^53 + 14 * q^54 + 7 * q^55 + 3 * q^56 + 7 * q^57 + 22 * q^58 - 21 * q^59 - 7 * q^60 - 9 * q^61 + 5 * q^62 - 5 * q^63 - 11 * q^64 - 5 * q^65 - 7 * q^66 + 13 * q^67 - 21 * q^68 - 2 * q^70 - 16 * q^71 + 16 * q^72 - 9 * q^73 + 12 * q^74 + 14 * q^76 + 7 * q^77 - 7 * q^78 - 18 * q^79 - 2 * q^80 - q^81 + 18 * q^82 - 29 * q^83 - 7 * q^84 - 5 * q^85 - 6 * q^86 + 14 * q^87 + 7 * q^88 + 7 * q^89 + q^90 - 5 * q^91 + 7 * q^93 - q^94 + 6 * q^95 + 35 * q^96 + q^97 - 2 * q^98 - 14 * 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 $

$2$	−0.554958	−0.392415	−0.196207	−	0.980562i	$-0.562863\pi$
$2$	−0.554958	−0.392415	−0.196207	+	0.980562i	$0.562863\pi$
$3$	−3.04892	−1.76029	−0.880147	−	0.474702i	$-0.842556\pi$
$3$	−3.04892	−1.76029	−0.880147	+	0.474702i	$0.842556\pi$
$4$	−1.69202	−0.846011
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	1.69202	0.690765
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	2.04892	0.724402
$9$	6.29590	2.09863
$10$	0.554958	0.175493
$11$	−2.44504	−0.737208	−0.368604	−	0.929587i	$-0.620164\pi$
$11$	−2.44504	−0.737208	−0.368604	+	0.929587i	$0.620164\pi$
$12$	5.15883	1.48923
$13$	5.96077	1.65322	0.826610	−	0.562775i	$-0.190266\pi$
$13$	5.96077	1.65322	0.826610	+	0.562775i	$0.190266\pi$
$14$	0.554958	0.148319
$15$	3.04892	0.787227
$16$	2.24698	0.561745
$17$	4.93900	1.19788	0.598942	−	0.800793i	$-0.295588\pi$
$17$	4.93900	1.19788	0.598942	+	0.800793i	$0.295588\pi$
$18$	−3.49396	−0.823534
$19$	−3.69202	−0.847008	−0.423504	−	0.905894i	$-0.639200\pi$
$19$	−3.69202	−0.847008	−0.423504	+	0.905894i	$0.639200\pi$
$20$	1.69202	0.378348
$21$	3.04892	0.665328
$22$	1.35690	0.289291
$23$	−1.00000	−0.208514
$23$	−1.00000	−0.208514
$24$	−6.24698	−1.27516
$25$	1.00000	0.200000
$26$	−3.30798	−0.648748
$27$	−10.0489	−1.93392
$28$	1.69202	0.319762
$29$	−6.71379	−1.24672	−0.623360	−	0.781935i	$-0.714233\pi$
$29$	−6.71379	−1.24672	−0.623360	+	0.781935i	$0.714233\pi$
$30$	−1.69202	−0.308919
$31$	−2.80194	−0.503243	−0.251621	−	0.967826i	$-0.580964\pi$
$31$	−2.80194	−0.503243	−0.251621	+	0.967826i	$0.580964\pi$
$32$	−5.34481	−0.944839
$33$	7.45473	1.29770
$34$	−2.74094	−0.470067
$35$	1.00000	0.169031
$36$	−10.6528	−1.77547
$37$	1.33513	0.219493	0.109747	−	0.993960i	$-0.464996\pi$
$37$	1.33513	0.219493	0.109747	+	0.993960i	$0.464996\pi$
$38$	2.04892	0.332378
$39$	−18.1739	−2.91015
$40$	−2.04892	−0.323962
$41$	6.87800	1.07416	0.537082	−	0.843530i	$-0.319527\pi$
$41$	6.87800	1.07416	0.537082	+	0.843530i	$0.319527\pi$
$42$	−1.69202	−0.261085
$43$	0.554958	0.0846303	0.0423152	−	0.999104i	$-0.486527\pi$
$43$	0.554958	0.0846303	0.0423152	+	0.999104i	$0.486527\pi$
$44$	4.13706	0.623686
$45$	−6.29590	−0.938537
$46$	0.554958	0.0818241
$47$	11.7899	1.71973	0.859864	−	0.510524i	$-0.170548\pi$
$47$	11.7899	1.71973	0.859864	+	0.510524i	$0.170548\pi$
$48$	−6.85086	−0.988836
$49$	1.00000	0.142857
$50$	−0.554958	−0.0784829
$51$	−15.0586	−2.10863
$52$	−10.0858	−1.39864
$53$	−11.4601	−1.57417	−0.787083	−	0.616847i	$-0.788410\pi$
$53$	−11.4601	−1.57417	−0.787083	+	0.616847i	$0.788410\pi$
$54$	5.57673	0.758897
$55$	2.44504	0.329689
$56$	−2.04892	−0.273798
$57$	11.2567	1.49098
$58$	3.72587	0.489231
$59$	−11.7409	−1.52854	−0.764270	−	0.644896i	$-0.776901\pi$
$59$	−11.7409	−1.52854	−0.764270	+	0.644896i	$0.776901\pi$
$60$	−5.15883	−0.666003
$61$	4.78986	0.613278	0.306639	−	0.951826i	$-0.400796\pi$
$61$	4.78986	0.613278	0.306639	+	0.951826i	$0.400796\pi$
$62$	1.55496	0.197480
$63$	−6.29590	−0.793208
$64$	−1.52781	−0.190976
$65$	−5.96077	−0.739343
$66$	−4.13706	−0.509237
$67$	11.5646	1.41285	0.706423	−	0.707790i	$-0.250308\pi$
$67$	11.5646	1.41285	0.706423	+	0.707790i	$0.250308\pi$
$68$	−8.35690	−1.01342
$69$	3.04892	0.367047
$70$	−0.554958	−0.0663302
$71$	−6.13169	−0.727697	−0.363849	−	0.931458i	$-0.618537\pi$
$71$	−6.13169	−0.727697	−0.363849	+	0.931458i	$0.618537\pi$
$72$	12.8998	1.52025
$73$	−10.7899	−1.26286	−0.631429	−	0.775434i	$-0.717531\pi$
$73$	−10.7899	−1.26286	−0.631429	+	0.775434i	$0.717531\pi$
$74$	−0.740939	−0.0861324
$75$	−3.04892	−0.352059
$76$	6.24698	0.716578
$77$	2.44504	0.278638
$78$	10.0858	1.14199
$79$	−10.0707	−1.13304	−0.566520	−	0.824048i	$-0.691711\pi$
$79$	−10.0707	−1.13304	−0.566520	+	0.824048i	$0.691711\pi$
$80$	−2.24698	−0.251220
$81$	11.7506	1.30563
$82$	−3.81700	−0.421517
$83$	0.948690	0.104132	0.0520661	−	0.998644i	$-0.483419\pi$
$83$	0.948690	0.104132	0.0520661	+	0.998644i	$0.483419\pi$
$84$	−5.15883	−0.562875
$85$	−4.93900	−0.535710
$86$	−0.307979	−0.0332102
$87$	20.4698	2.19459
$88$	−5.00969	−0.534035
$89$	−3.65279	−0.387195	−0.193598	−	0.981081i	$-0.562016\pi$
$89$	−3.65279	−0.387195	−0.193598	+	0.981081i	$0.562016\pi$
$90$	3.49396	0.368296
$91$	−5.96077	−0.624859
$92$	1.69202	0.176405
$93$	8.54288	0.885855
$94$	−6.54288	−0.674846
$95$	3.69202	0.378793
$96$	16.2959	1.66319
$97$	−11.4155	−1.15907	−0.579534	−	0.814948i	$-0.696766\pi$
$97$	−11.4155	−1.15907	−0.579534	+	0.814948i	$0.696766\pi$
$98$	−0.554958	−0.0560592
$99$	−15.3937	−1.54713
$100$	−1.69202	−0.169202
$101$	12.6799	1.26170	0.630851	−	0.775904i	$-0.282706\pi$
$101$	12.6799	1.26170	0.630851	+	0.775904i	$0.282706\pi$
$102$	8.35690	0.827456
$103$	12.4819	1.22988	0.614938	−	0.788575i	$-0.289181\pi$
$103$	12.4819	1.22988	0.614938	+	0.788575i	$0.289181\pi$
$104$	12.2131	1.19760
$105$	−3.04892	−0.297544
$106$	6.35988	0.617726
$107$	−12.4276	−1.20142	−0.600710	−	0.799467i	$-0.705115\pi$
$107$	−12.4276	−1.20142	−0.600710	+	0.799467i	$0.705115\pi$
$108$	17.0030	1.63611
$109$	−7.18598	−0.688292	−0.344146	−	0.938916i	$-0.611832\pi$
$109$	−7.18598	−0.688292	−0.344146	+	0.938916i	$0.611832\pi$
$110$	−1.35690	−0.129375
$111$	−4.07069	−0.386373
$112$	−2.24698	−0.212320
$113$	−8.10023	−0.762005	−0.381003	−	0.924574i	$-0.624421\pi$
$113$	−8.10023	−0.762005	−0.381003	+	0.924574i	$0.624421\pi$
$114$	−6.24698	−0.585083
$115$	1.00000	0.0932505
$116$	11.3599	1.05474
$117$	37.5284	3.46950
$118$	6.51573	0.599822
$119$	−4.93900	−0.452757
$120$	6.24698	0.570269
$121$	−5.02177	−0.456525
$122$	−2.65817	−0.240659
$123$	−20.9705	−1.89084
$124$	4.74094	0.425749
$125$	−1.00000	−0.0894427
$126$	3.49396	0.311267
$127$	7.24160	0.642588	0.321294	−	0.946979i	$-0.395882\pi$
$127$	7.24160	0.642588	0.321294	+	0.946979i	$0.395882\pi$
$128$	11.5375	1.01978
$129$	−1.69202	−0.148974
$130$	3.30798	0.290129
$131$	11.1099	0.970678	0.485339	−	0.874326i	$-0.338696\pi$
$131$	11.1099	0.970678	0.485339	+	0.874326i	$0.338696\pi$
$132$	−12.6136	−1.09787
$133$	3.69202	0.320139
$134$	−6.41789	−0.554422
$135$	10.0489	0.864873
$136$	10.1196	0.867749
$137$	11.9095	1.01749	0.508747	−	0.860916i	$-0.330109\pi$
$137$	11.9095	1.01749	0.508747	+	0.860916i	$0.330109\pi$
$138$	−1.69202	−0.144034
$139$	7.22952	0.613200	0.306600	−	0.951838i	$-0.400809\pi$
$139$	7.22952	0.613200	0.306600	+	0.951838i	$0.400809\pi$
$140$	−1.69202	−0.143002
$141$	−35.9463	−3.02722
$142$	3.40283	0.285559
$143$	−14.5743	−1.21877
$144$	14.1468	1.17890
$145$	6.71379	0.557550
$146$	5.98792	0.495564
$147$	−3.04892	−0.251470
$148$	−2.25906	−0.185694
$149$	−16.5429	−1.35525	−0.677623	−	0.735410i	$-0.736990\pi$
$149$	−16.5429	−1.35525	−0.677623	+	0.735410i	$0.736990\pi$
$150$	1.69202	0.138153
$151$	17.8116	1.44949	0.724745	−	0.689017i	$-0.241958\pi$
$151$	17.8116	1.44949	0.724745	+	0.689017i	$0.241958\pi$
$152$	−7.56465	−0.613574
$153$	31.0954	2.51392
$154$	−1.35690	−0.109342
$155$	2.80194	0.225057
$156$	30.7506	2.46202
$157$	−16.7409	−1.33607	−0.668036	−	0.744129i	$-0.732865\pi$
$157$	−16.7409	−1.33607	−0.668036	+	0.744129i	$0.732865\pi$
$158$	5.58881	0.444622
$159$	34.9409	2.77100
$160$	5.34481	0.422545
$161$	1.00000	0.0788110
$162$	−6.52111	−0.512346
$163$	−14.5133	−1.13677	−0.568386	−	0.822762i	$-0.692432\pi$
$163$	−14.5133	−1.13677	−0.568386	+	0.822762i	$0.692432\pi$
$164$	−11.6377	−0.908754
$165$	−7.45473	−0.580350
$166$	−0.526483	−0.0408630
$167$	−17.3913	−1.34578	−0.672891	−	0.739742i	$-0.734948\pi$
$167$	−17.3913	−1.34578	−0.672891	+	0.739742i	$0.734948\pi$
$168$	6.24698	0.481965
$169$	22.5308	1.73314
$170$	2.74094	0.210220
$171$	−23.2446	−1.77756
$172$	−0.939001	−0.0715982
$173$	−13.7506	−1.04544	−0.522720	−	0.852504i	$-0.675083\pi$
$173$	−13.7506	−1.04544	−0.522720	+	0.852504i	$0.675083\pi$
$174$	−11.3599	−0.861190
$175$	−1.00000	−0.0755929
$176$	−5.49396	−0.414123
$177$	35.7972	2.69068
$178$	2.02715	0.151941
$179$	−5.73125	−0.428374	−0.214187	−	0.976793i	$-0.568710\pi$
$179$	−5.73125	−0.428374	−0.214187	+	0.976793i	$0.568710\pi$
$180$	10.6528	0.794012
$181$	2.28621	0.169933	0.0849663	−	0.996384i	$-0.472922\pi$
$181$	2.28621	0.169933	0.0849663	+	0.996384i	$0.472922\pi$
$182$	3.30798	0.245204
$183$	−14.6039	−1.07955
$184$	−2.04892	−0.151048
$185$	−1.33513	−0.0981604
$186$	−4.74094	−0.347622
$187$	−12.0761	−0.883089
$188$	−19.9487	−1.45491
$189$	10.0489	0.730951
$190$	−2.04892	−0.148644
$191$	−25.9366	−1.87671	−0.938354	−	0.345677i	$-0.887649\pi$
$191$	−25.9366	−1.87671	−0.938354	+	0.345677i	$0.887649\pi$
$192$	4.65817	0.336174
$193$	3.54527	0.255194	0.127597	−	0.991826i	$-0.459274\pi$
$193$	3.54527	0.255194	0.127597	+	0.991826i	$0.459274\pi$
$194$	6.33513	0.454836
$195$	18.1739	1.30146
$196$	−1.69202	−0.120859
$197$	−8.55794	−0.609728	−0.304864	−	0.952396i	$-0.598611\pi$
$197$	−8.55794	−0.609728	−0.304864	+	0.952396i	$0.598611\pi$
$198$	8.54288	0.607116
$199$	19.8853	1.40963	0.704816	−	0.709390i	$-0.251030\pi$
$199$	19.8853	1.40963	0.704816	+	0.709390i	$0.251030\pi$
$200$	2.04892	0.144880
$201$	−35.2597	−2.48702
$202$	−7.03684	−0.495110
$203$	6.71379	0.471216
$204$	25.4795	1.78392
$205$	−6.87800	−0.480381
$206$	−6.92692	−0.482621
$207$	−6.29590	−0.437595
$208$	13.3937	0.928688
$209$	9.02715	0.624421
$210$	1.69202	0.116761
$211$	−2.80731	−0.193264	−0.0966318	−	0.995320i	$-0.530807\pi$
$211$	−2.80731	−0.193264	−0.0966318	+	0.995320i	$0.530807\pi$
$212$	19.3907	1.33176
$213$	18.6950	1.28096
$214$	6.89679	0.471455
$215$	−0.554958	−0.0378478
$216$	−20.5894	−1.40093
$217$	2.80194	0.190208
$218$	3.98792	0.270096
$219$	32.8974	2.22300
$220$	−4.13706	−0.278921
$221$	29.4403	1.98037
$222$	2.25906	0.151618
$223$	23.9269	1.60227	0.801133	−	0.598487i	$-0.204231\pi$
$223$	23.9269	1.60227	0.801133	+	0.598487i	$0.204231\pi$
$224$	5.34481	0.357115
$225$	6.29590	0.419726
$226$	4.49529	0.299022
$227$	−0.320060	−0.0212431	−0.0106216	−	0.999944i	$-0.503381\pi$
$227$	−0.320060	−0.0212431	−0.0106216	+	0.999944i	$0.503381\pi$
$228$	−19.0465	−1.26139
$229$	−25.1226	−1.66015	−0.830074	−	0.557654i	$-0.811702\pi$
$229$	−25.1226	−1.66015	−0.830074	+	0.557654i	$0.811702\pi$
$230$	−0.554958	−0.0365929
$231$	−7.45473	−0.490485
$232$	−13.7560	−0.903126
$233$	1.08277	0.0709346	0.0354673	−	0.999371i	$-0.488708\pi$
$233$	1.08277	0.0709346	0.0354673	+	0.999371i	$0.488708\pi$
$234$	−20.8267	−1.36148
$235$	−11.7899	−0.769085
$236$	19.8659	1.29316
$237$	30.7047	1.99448
$238$	2.74094	0.177669
$239$	−14.0151	−0.906559	−0.453280	−	0.891368i	$-0.649746\pi$
$239$	−14.0151	−0.906559	−0.453280	+	0.891368i	$0.649746\pi$
$240$	6.85086	0.442221
$241$	−24.4306	−1.57371	−0.786856	−	0.617137i	$-0.788292\pi$
$241$	−24.4306	−1.57371	−0.786856	+	0.617137i	$0.788292\pi$
$242$	2.78687	0.179147
$243$	−5.67994	−0.364368
$244$	−8.10454	−0.518840
$245$	−1.00000	−0.0638877
$246$	11.6377	0.741994
$247$	−22.0073	−1.40029
$248$	−5.74094	−0.364550
$249$	−2.89248	−0.183303
$250$	0.554958	0.0350986
$251$	−26.5972	−1.67880	−0.839399	−	0.543515i	$-0.817093\pi$
$251$	−26.5972	−1.67880	−0.839399	+	0.543515i	$0.817093\pi$
$252$	10.6528	0.671063
$253$	2.44504	0.153718
$254$	−4.01879	−0.252161
$255$	15.0586	0.943006
$256$	−3.34721	−0.209200
$257$	−29.7211	−1.85395	−0.926975	−	0.375122i	$-0.877601\pi$
$257$	−29.7211	−1.85395	−0.926975	+	0.375122i	$0.877601\pi$
$258$	0.939001	0.0584597
$259$	−1.33513	−0.0829607
$260$	10.0858	0.625492
$261$	−42.2693	−2.61641
$262$	−6.16554	−0.380908
$263$	−10.6571	−0.657145	−0.328573	−	0.944479i	$-0.606568\pi$
$263$	−10.6571	−0.657145	−0.328573	+	0.944479i	$0.606568\pi$
$264$	15.2741	0.940058
$265$	11.4601	0.703989
$266$	−2.04892	−0.125627
$267$	11.1371	0.681577
$268$	−19.5676	−1.19528
$269$	−20.1323	−1.22749	−0.613743	−	0.789506i	$-0.710337\pi$
$269$	−20.1323	−1.22749	−0.613743	+	0.789506i	$0.710337\pi$
$270$	−5.57673	−0.339389
$271$	−12.7453	−0.774219	−0.387109	−	0.922034i	$-0.626526\pi$
$271$	−12.7453	−0.774219	−0.387109	+	0.922034i	$0.626526\pi$
$272$	11.0978	0.672905
$273$	18.1739	1.09993
$274$	−6.60925	−0.399280
$275$	−2.44504	−0.147442
$276$	−5.15883	−0.310525
$277$	0.701710	0.0421617	0.0210808	−	0.999778i	$-0.493289\pi$
$277$	0.701710	0.0421617	0.0210808	+	0.999778i	$0.493289\pi$
$278$	−4.01208	−0.240629
$279$	−17.6407	−1.05612
$280$	2.04892	0.122446
$281$	−1.80731	−0.107815	−0.0539077	−	0.998546i	$-0.517168\pi$
$281$	−1.80731	−0.107815	−0.0539077	+	0.998546i	$0.517168\pi$
$282$	19.9487	1.18793
$283$	26.2489	1.56034	0.780168	−	0.625571i	$-0.215134\pi$
$283$	26.2489	1.56034	0.780168	+	0.625571i	$0.215134\pi$
$284$	10.3749	0.615640
$285$	−11.2567	−0.666787
$286$	8.08815	0.478262
$287$	−6.87800	−0.405996
$288$	−33.6504	−1.98287
$289$	7.39373	0.434925
$290$	−3.72587	−0.218791
$291$	34.8049	2.04030
$292$	18.2567	1.06839
$293$	−6.28919	−0.367419	−0.183709	−	0.982981i	$-0.558810\pi$
$293$	−6.28919	−0.367419	−0.183709	+	0.982981i	$0.558810\pi$
$294$	1.69202	0.0986807
$295$	11.7409	0.683584
$296$	2.73556	0.159001
$297$	24.5700	1.42570
$298$	9.18060	0.531818
$299$	−5.96077	−0.344720
$300$	5.15883	0.297845
$301$	−0.554958	−0.0319873
$302$	−9.88471	−0.568801
$303$	−38.6601	−2.22096
$304$	−8.29590	−0.475802
$305$	−4.78986	−0.274266
$306$	−17.2567	−0.986498
$307$	1.08383	0.0618577	0.0309288	−	0.999522i	$-0.490153\pi$
$307$	1.08383	0.0618577	0.0309288	+	0.999522i	$0.490153\pi$
$308$	−4.13706	−0.235731
$309$	−38.0562	−2.16494
$310$	−1.55496	−0.0883157
$311$	−13.8780	−0.786949	−0.393475	−	0.919335i	$-0.628727\pi$
$311$	−13.8780	−0.786949	−0.393475	+	0.919335i	$0.628727\pi$
$312$	−37.2368	−2.10812
$313$	5.14782	0.290972	0.145486	−	0.989360i	$-0.453525\pi$
$313$	5.14782	0.290972	0.145486	+	0.989360i	$0.453525\pi$
$314$	9.29052	0.524294
$315$	6.29590	0.354734
$316$	17.0398	0.958565
$317$	10.5593	0.593068	0.296534	−	0.955022i	$-0.404169\pi$
$317$	10.5593	0.593068	0.296534	+	0.955022i	$0.404169\pi$
$318$	−19.3907	−1.08738
$319$	16.4155	0.919092
$320$	1.52781	0.0854072
$321$	37.8907	2.11485
$322$	−0.554958	−0.0309266
$323$	−18.2349	−1.01462
$324$	−19.8823	−1.10457
$325$	5.96077	0.330644
$326$	8.05429	0.446086
$327$	21.9095	1.21160
$328$	14.0925	0.778126
$329$	−11.7899	−0.649996
$330$	4.13706	0.227738
$331$	2.60388	0.143122	0.0715610	−	0.997436i	$-0.477202\pi$
$331$	2.60388	0.143122	0.0715610	+	0.997436i	$0.477202\pi$
$332$	−1.60520	−0.0880970
$333$	8.40581	0.460636
$334$	9.65146	0.528105
$335$	−11.5646	−0.631844
$336$	6.85086	0.373745
$337$	16.1618	0.880390	0.440195	−	0.897902i	$-0.354909\pi$
$337$	16.1618	0.880390	0.440195	+	0.897902i	$0.354909\pi$
$338$	−12.5036	−0.680109
$339$	24.6969	1.34135
$340$	8.35690	0.453216
$341$	6.85086	0.370995
$342$	12.8998	0.697540
$343$	−1.00000	−0.0539949
$344$	1.13706	0.0613063
$345$	−3.04892	−0.164148
$346$	7.63102	0.410246
$347$	−23.3080	−1.25124	−0.625619	−	0.780129i	$-0.715153\pi$
$347$	−23.3080	−1.25124	−0.625619	+	0.780129i	$0.715153\pi$
$348$	−34.6353	−1.85665
$349$	20.8769	1.11752	0.558758	−	0.829330i	$-0.311278\pi$
$349$	20.8769	1.11752	0.558758	+	0.829330i	$0.311278\pi$
$350$	0.554958	0.0296638
$351$	−59.8993	−3.19719
$352$	13.0683	0.696542
$353$	5.40044	0.287436	0.143718	−	0.989619i	$-0.454094\pi$
$353$	5.40044	0.287436	0.143718	+	0.989619i	$0.454094\pi$
$354$	−19.8659	−1.05586
$355$	6.13169	0.325436
$356$	6.18060	0.327571
$357$	15.0586	0.796986
$358$	3.18060	0.168100
$359$	12.4523	0.657209	0.328605	−	0.944468i	$-0.393422\pi$
$359$	12.4523	0.657209	0.328605	+	0.944468i	$0.393422\pi$
$360$	−12.8998	−0.679878
$361$	−5.36898	−0.282578
$362$	−1.26875	−0.0666840
$363$	15.3110	0.803617
$364$	10.0858	0.528637
$365$	10.7899	0.564767
$366$	8.10454	0.423631
$367$	20.3230	1.06085	0.530427	−	0.847731i	$-0.322032\pi$
$367$	20.3230	1.06085	0.530427	+	0.847731i	$0.322032\pi$
$368$	−2.24698	−0.117132
$369$	43.3032	2.25427
$370$	0.740939	0.0385196
$371$	11.4601	0.594979
$372$	−14.4547	−0.749443
$373$	6.29159	0.325766	0.162883	−	0.986645i	$-0.447921\pi$
$373$	6.29159	0.325766	0.162883	+	0.986645i	$0.447921\pi$
$374$	6.70171	0.346537
$375$	3.04892	0.157445
$376$	24.1564	1.24577
$377$	−40.0194	−2.06110
$378$	−5.57673	−0.286836
$379$	−12.2349	−0.628464	−0.314232	−	0.949346i	$-0.601747\pi$
$379$	−12.2349	−0.628464	−0.314232	+	0.949346i	$0.601747\pi$
$380$	−6.24698	−0.320463
$381$	−22.0790	−1.13114
$382$	14.3937	0.736447
$383$	−11.4873	−0.586971	−0.293486	−	0.955963i	$-0.594815\pi$
$383$	−11.4873	−0.586971	−0.293486	+	0.955963i	$0.594815\pi$
$384$	−35.1769	−1.79511
$385$	−2.44504	−0.124611
$386$	−1.96748	−0.100142
$387$	3.49396	0.177608
$388$	19.3153	0.980584
$389$	−6.62671	−0.335988	−0.167994	−	0.985788i	$-0.553729\pi$
$389$	−6.62671	−0.335988	−0.167994	+	0.985788i	$0.553729\pi$
$390$	−10.0858	−0.510712
$391$	−4.93900	−0.249776
$392$	2.04892	0.103486
$393$	−33.8732	−1.70868
$394$	4.74930	0.239266
$395$	10.0707	0.506711
$396$	26.0465	1.30889
$397$	2.99569	0.150349	0.0751746	−	0.997170i	$-0.476049\pi$
$397$	2.99569	0.150349	0.0751746	+	0.997170i	$0.476049\pi$
$398$	−11.0355	−0.553160
$399$	−11.2567	−0.563538
$400$	2.24698	0.112349
$401$	20.0780	1.00265	0.501323	−	0.865260i	$-0.332847\pi$
$401$	20.0780	1.00265	0.501323	+	0.865260i	$0.332847\pi$
$402$	19.5676	0.975945
$403$	−16.7017	−0.831971
$404$	−21.4547	−1.06741
$405$	−11.7506	−0.583893
$406$	−3.72587	−0.184912
$407$	−3.26444	−0.161812
$408$	−30.8538	−1.52749
$409$	22.0043	1.08804	0.544022	−	0.839071i	$-0.316901\pi$
$409$	22.0043	1.08804	0.544022	+	0.839071i	$0.316901\pi$
$410$	3.81700	0.188508
$411$	−36.3110	−1.79109
$412$	−21.1196	−1.04049
$413$	11.7409	0.577734
$414$	3.49396	0.171719
$415$	−0.948690	−0.0465693
$416$	−31.8592	−1.56203
$417$	−22.0422	−1.07941
$418$	−5.00969	−0.245032
$419$	17.9191	0.875408	0.437704	−	0.899119i	$-0.355792\pi$
$419$	17.9191	0.875408	0.437704	+	0.899119i	$0.355792\pi$
$420$	5.15883	0.251725
$421$	17.8049	0.867759	0.433879	−	0.900971i	$-0.357144\pi$
$421$	17.8049	0.867759	0.433879	+	0.900971i	$0.357144\pi$
$422$	1.55794	0.0758394
$423$	74.2277	3.60908
$424$	−23.4808	−1.14033
$425$	4.93900	0.239577
$426$	−10.3749	−0.502668
$427$	−4.78986	−0.231797
$428$	21.0277	1.01641
$429$	44.4359	2.14539
$430$	0.307979	0.0148520
$431$	−9.37435	−0.451547	−0.225773	−	0.974180i	$-0.572491\pi$
$431$	−9.37435	−0.451547	−0.225773	+	0.974180i	$0.572491\pi$
$432$	−22.5797	−1.08637
$433$	−18.2808	−0.878521	−0.439260	−	0.898360i	$-0.644759\pi$
$433$	−18.2808	−0.878521	−0.439260	+	0.898360i	$0.644759\pi$
$434$	−1.55496	−0.0746404
$435$	−20.4698	−0.981452
$436$	12.1588	0.582303
$437$	3.69202	0.176613
$438$	−18.2567	−0.872337
$439$	−3.70602	−0.176879	−0.0884394	−	0.996082i	$-0.528188\pi$
$439$	−3.70602	−0.176879	−0.0884394	+	0.996082i	$0.528188\pi$
$440$	5.00969	0.238828
$441$	6.29590	0.299805
$442$	−16.3381	−0.777125
$443$	1.28382	0.0609959	0.0304980	−	0.999535i	$-0.490291\pi$
$443$	1.28382	0.0609959	0.0304980	+	0.999535i	$0.490291\pi$
$444$	6.88769	0.326875
$445$	3.65279	0.173159
$446$	−13.2784	−0.628752
$447$	50.4379	2.38563
$448$	1.52781	0.0721823
$449$	−20.2814	−0.957140	−0.478570	−	0.878050i	$-0.658845\pi$
$449$	−20.2814	−0.957140	−0.478570	+	0.878050i	$0.658845\pi$
$450$	−3.49396	−0.164707
$451$	−16.8170	−0.791882
$452$	13.7058	0.644665
$453$	−54.3062	−2.55153
$454$	0.177620	0.00833612
$455$	5.96077	0.279445
$456$	23.0640	1.08007
$457$	−16.6165	−0.777289	−0.388645	−	0.921388i	$-0.627057\pi$
$457$	−16.6165	−0.777289	−0.388645	+	0.921388i	$0.627057\pi$
$458$	13.9420	0.651466
$459$	−49.6316	−2.31661
$460$	−1.69202	−0.0788909
$461$	17.9989	0.838294	0.419147	−	0.907918i	$-0.362329\pi$
$461$	17.9989	0.838294	0.419147	+	0.907918i	$0.362329\pi$
$462$	4.13706	0.192474
$463$	−15.6407	−0.726885	−0.363443	−	0.931617i	$-0.618399\pi$
$463$	−15.6407	−0.726885	−0.363443	+	0.931617i	$0.618399\pi$
$464$	−15.0858	−0.700339
$465$	−8.54288	−0.396166
$466$	−0.600892	−0.0278358
$467$	−0.796561	−0.0368604	−0.0184302	−	0.999830i	$-0.505867\pi$
$467$	−0.796561	−0.0368604	−0.0184302	+	0.999830i	$0.505867\pi$
$468$	−63.4989	−2.93524
$469$	−11.5646	−0.534006
$470$	6.54288	0.301800
$471$	51.0417	2.35188
$472$	−24.0562	−1.10728
$473$	−1.35690	−0.0623901
$474$	−17.0398	−0.782665
$475$	−3.69202	−0.169402
$476$	8.35690	0.383038
$477$	−72.1517	−3.30360
$478$	7.77777	0.355747
$479$	−16.4373	−0.751038	−0.375519	−	0.926815i	$-0.622536\pi$
$479$	−16.4373	−0.751038	−0.375519	+	0.926815i	$0.622536\pi$
$480$	−16.2959	−0.743803
$481$	7.95838	0.362871
$482$	13.5579	0.617547
$483$	−3.04892	−0.138731
$484$	8.49694	0.386225
$485$	11.4155	0.518351
$486$	3.15213	0.142983
$487$	34.9928	1.58568	0.792838	−	0.609432i	$-0.208603\pi$
$487$	34.9928	1.58568	0.792838	+	0.609432i	$0.208603\pi$
$488$	9.81402	0.444260
$489$	44.2500	2.00105
$490$	0.554958	0.0250705
$491$	−11.8834	−0.536289	−0.268145	−	0.963379i	$-0.586411\pi$
$491$	−11.8834	−0.536289	−0.268145	+	0.963379i	$0.586411\pi$
$492$	35.4825	1.59967
$493$	−33.1594	−1.49343
$494$	12.2131	0.549495
$495$	15.3937	0.691897
$496$	−6.29590	−0.282694
$497$	6.13169	0.275044
$498$	1.60520	0.0719309
$499$	4.96615	0.222315	0.111158	−	0.993803i	$-0.464544\pi$
$499$	4.96615	0.222315	0.111158	+	0.993803i	$0.464544\pi$
$500$	1.69202	0.0756695
$501$	53.0248	2.36897
$502$	14.7603	0.658785
$503$	−20.8592	−0.930066	−0.465033	−	0.885293i	$-0.653958\pi$
$503$	−20.8592	−0.930066	−0.465033	+	0.885293i	$0.653958\pi$
$504$	−12.8998	−0.574602
$505$	−12.6799	−0.564250
$506$	−1.35690	−0.0603214
$507$	−68.6945	−3.05083
$508$	−12.2529	−0.543637
$509$	−2.57434	−0.114105	−0.0570527	−	0.998371i	$-0.518170\pi$
$509$	−2.57434	−0.114105	−0.0570527	+	0.998371i	$0.518170\pi$
$510$	−8.35690	−0.370050
$511$	10.7899	0.477315
$512$	−21.2174	−0.937687
$513$	37.1008	1.63804
$514$	16.4940	0.727517
$515$	−12.4819	−0.550017
$516$	2.86294	0.126034
$517$	−28.8267	−1.26780
$518$	0.740939	0.0325550
$519$	41.9245	1.84028
$520$	−12.2131	−0.535581
$521$	18.8237	0.824682	0.412341	−	0.911030i	$-0.364711\pi$
$521$	18.8237	0.824682	0.412341	+	0.911030i	$0.364711\pi$
$522$	23.4577	1.02672
$523$	−44.5797	−1.94933	−0.974667	−	0.223659i	$-0.928200\pi$
$523$	−44.5797	−1.94933	−0.974667	+	0.223659i	$0.928200\pi$
$524$	−18.7982	−0.821204
$525$	3.04892	0.133066
$526$	5.91425	0.257873
$527$	−13.8388	−0.602826
$528$	16.7506	0.728977
$529$	1.00000	0.0434783
$530$	−6.35988	−0.276256
$531$	−73.9197	−3.20784
$532$	−6.24698	−0.270841
$533$	40.9982	1.77583
$534$	−6.18060	−0.267461
$535$	12.4276	0.537291
$536$	23.6950	1.02347
$537$	17.4741	0.754063
$538$	11.1726	0.481684
$539$	−2.44504	−0.105315
$540$	−17.0030	−0.731692
$541$	7.61165	0.327250	0.163625	−	0.986523i	$-0.447681\pi$
$541$	7.61165	0.327250	0.163625	+	0.986523i	$0.447681\pi$
$542$	7.07308	0.303815
$543$	−6.97046	−0.299131
$544$	−26.3980	−1.13181
$545$	7.18598	0.307814
$546$	−10.0858	−0.431630
$547$	−33.4456	−1.43003	−0.715016	−	0.699108i	$-0.753581\pi$
$547$	−33.4456	−1.43003	−0.715016	+	0.699108i	$0.753581\pi$
$548$	−20.1511	−0.860811
$549$	30.1564	1.28705
$550$	1.35690	0.0578582
$551$	24.7875	1.05598
$552$	6.24698	0.265889
$553$	10.0707	0.428249
$554$	−0.389420	−0.0165449
$555$	4.07069	0.172791
$556$	−12.2325	−0.518774
$557$	25.5198	1.08131	0.540654	−	0.841245i	$-0.318177\pi$
$557$	25.5198	1.08131	0.540654	+	0.841245i	$0.318177\pi$
$558$	9.78986	0.414438
$559$	3.30798	0.139913
$560$	2.24698	0.0949522
$561$	36.8189	1.55450
$562$	1.00298	0.0423083
$563$	−7.81269	−0.329266	−0.164633	−	0.986355i	$-0.552644\pi$
$563$	−7.81269	−0.329266	−0.164633	+	0.986355i	$0.552644\pi$
$564$	60.8219	2.56106
$565$	8.10023	0.340779
$566$	−14.5670	−0.612298
$567$	−11.7506	−0.493480
$568$	−12.5633	−0.527145
$569$	−20.6963	−0.867635	−0.433818	−	0.901001i	$-0.642834\pi$
$569$	−20.6963	−0.867635	−0.433818	+	0.901001i	$0.642834\pi$
$570$	6.24698	0.261657
$571$	−21.2416	−0.888933	−0.444467	−	0.895795i	$-0.646607\pi$
$571$	−21.2416	−0.888933	−0.444467	+	0.895795i	$0.646607\pi$
$572$	24.6601	1.03109
$573$	79.0786	3.30355
$574$	3.81700	0.159319
$575$	−1.00000	−0.0417029
$576$	−9.61894	−0.400789
$577$	27.0780	1.12727	0.563636	−	0.826024i	$-0.309402\pi$
$577$	27.0780	1.12727	0.563636	+	0.826024i	$0.309402\pi$
$578$	−4.10321	−0.170671
$579$	−10.8092	−0.449216
$580$	−11.3599	−0.471693
$581$	−0.948690	−0.0393583
$582$	−19.3153	−0.800644
$583$	28.0204	1.16049
$584$	−22.1075	−0.914816
$585$	−37.5284	−1.55161
$586$	3.49024	0.144180
$587$	6.33513	0.261479	0.130739	−	0.991417i	$-0.458265\pi$
$587$	6.33513	0.261479	0.130739	+	0.991417i	$0.458265\pi$
$588$	5.15883	0.212747
$589$	10.3448	0.426251
$590$	−6.51573	−0.268248
$591$	26.0925	1.07330
$592$	3.00000	0.123299
$593$	34.7453	1.42682	0.713408	−	0.700749i	$-0.247151\pi$
$593$	34.7453	1.42682	0.713408	+	0.700749i	$0.247151\pi$
$594$	−13.6353	−0.559465
$595$	4.93900	0.202479
$596$	27.9909	1.14655
$597$	−60.6286	−2.48136
$598$	3.30798	0.135273
$599$	23.7482	0.970327	0.485163	−	0.874424i	$-0.338760\pi$
$599$	23.7482	0.970327	0.485163	+	0.874424i	$0.338760\pi$
$600$	−6.24698	−0.255032
$601$	21.8713	0.892149	0.446074	−	0.894996i	$-0.352822\pi$
$601$	21.8713	0.892149	0.446074	+	0.894996i	$0.352822\pi$
$602$	0.307979	0.0125523
$603$	72.8098	2.96505
$604$	−30.1377	−1.22628
$605$	5.02177	0.204164
$606$	21.4547	0.871539
$607$	−31.7439	−1.28845	−0.644223	−	0.764838i	$-0.722819\pi$
$607$	−31.7439	−1.28845	−0.644223	+	0.764838i	$0.722819\pi$
$608$	19.7332	0.800286
$609$	−20.4698	−0.829478
$610$	2.65817	0.107626
$611$	70.2766	2.84309
$612$	−52.6142	−2.12680
$613$	2.82908	0.114266	0.0571328	−	0.998367i	$-0.481804\pi$
$613$	2.82908	0.114266	0.0571328	+	0.998367i	$0.481804\pi$
$614$	−0.601483	−0.0242739
$615$	20.9705	0.845611
$616$	5.00969	0.201846
$617$	−9.99569	−0.402411	−0.201206	−	0.979549i	$-0.564486\pi$
$617$	−9.99569	−0.402411	−0.201206	+	0.979549i	$0.564486\pi$
$618$	21.1196	0.849555
$619$	23.9396	0.962213	0.481107	−	0.876662i	$-0.340235\pi$
$619$	23.9396	0.962213	0.481107	+	0.876662i	$0.340235\pi$
$620$	−4.74094	−0.190401
$621$	10.0489	0.403249
$622$	7.70171	0.308810
$623$	3.65279	0.146346
$624$	−40.8364	−1.63476
$625$	1.00000	0.0400000
$626$	−2.85682	−0.114182
$627$	−27.5230	−1.09916
$628$	28.3260	1.13033
$629$	6.59419	0.262927
$630$	−3.49396	−0.139203
$631$	−39.8834	−1.58773	−0.793866	−	0.608093i	$-0.791935\pi$
$631$	−39.8834	−1.58773	−0.793866	+	0.608093i	$0.791935\pi$
$632$	−20.6340	−0.820777
$633$	8.55927	0.340200
$634$	−5.85995	−0.232728
$635$	−7.24160	−0.287374
$636$	−59.1208	−2.34429
$637$	5.96077	0.236174
$638$	−9.10992	−0.360665
$639$	−38.6045	−1.52717
$640$	−11.5375	−0.456060
$641$	−9.57779	−0.378300	−0.189150	−	0.981948i	$-0.560573\pi$
$641$	−9.57779	−0.378300	−0.189150	+	0.981948i	$0.560573\pi$
$642$	−21.0277	−0.829899
$643$	5.20882	0.205416	0.102708	−	0.994712i	$-0.467249\pi$
$643$	5.20882	0.205416	0.102708	+	0.994712i	$0.467249\pi$
$644$	−1.69202	−0.0666750
$645$	1.69202	0.0666233
$646$	10.1196	0.398151
$647$	−18.5574	−0.729565	−0.364782	−	0.931093i	$-0.618857\pi$
$647$	−18.5574	−0.729565	−0.364782	+	0.931093i	$0.618857\pi$
$648$	24.0761	0.945797
$649$	28.7071	1.12685
$650$	−3.30798	−0.129750
$651$	−8.54288	−0.334822
$652$	24.5569	0.961722
$653$	−31.9825	−1.25157	−0.625787	−	0.779994i	$-0.715222\pi$
$653$	−31.9825	−1.25157	−0.625787	+	0.779994i	$0.715222\pi$
$654$	−12.1588	−0.475448
$655$	−11.1099	−0.434100
$656$	15.4547	0.603406
$657$	−67.9318	−2.65027
$658$	6.54288	0.255068
$659$	20.1629	0.785434	0.392717	−	0.919659i	$-0.371535\pi$
$659$	20.1629	0.785434	0.392717	+	0.919659i	$0.371535\pi$
$660$	12.6136	0.490982
$661$	−40.1094	−1.56008	−0.780038	−	0.625732i	$-0.784800\pi$
$661$	−40.1094	−1.56008	−0.780038	+	0.625732i	$0.784800\pi$
$662$	−1.44504	−0.0561631
$663$	−89.7609	−3.48602
$664$	1.94379	0.0754336
$665$	−3.69202	−0.143170
$666$	−4.66487	−0.180760
$667$	6.71379	0.259959
$668$	29.4265	1.13855
$669$	−72.9512	−2.82046
$670$	6.41789	0.247945
$671$	−11.7114	−0.452114
$672$	−16.2959	−0.628628
$673$	41.5144	1.60026	0.800131	−	0.599825i	$-0.204763\pi$
$673$	41.5144	1.60026	0.800131	+	0.599825i	$0.204763\pi$
$674$	−8.96913	−0.345478
$675$	−10.0489	−0.386783
$676$	−38.1226	−1.46625
$677$	37.3927	1.43712	0.718558	−	0.695467i	$-0.244802\pi$
$677$	37.3927	1.43712	0.718558	+	0.695467i	$0.244802\pi$
$678$	−13.7058	−0.526367
$679$	11.4155	0.438087
$680$	−10.1196	−0.388069
$681$	0.975837	0.0373941
$682$	−3.80194	−0.145584
$683$	48.1756	1.84339	0.921693	−	0.387920i	$-0.126806\pi$
$683$	48.1756	1.84339	0.921693	+	0.387920i	$0.126806\pi$
$684$	39.3303	1.50383
$685$	−11.9095	−0.455037
$686$	0.554958	0.0211884
$687$	76.5967	2.92235
$688$	1.24698	0.0475407
$689$	−68.3111	−2.60244
$690$	1.69202	0.0644142
$691$	−29.6920	−1.12954	−0.564769	−	0.825249i	$-0.691035\pi$
$691$	−29.6920	−1.12954	−0.564769	+	0.825249i	$0.691035\pi$
$692$	23.2664	0.884454
$693$	15.3937	0.584760
$694$	12.9350	0.491004
$695$	−7.22952	−0.274231
$696$	41.9409	1.58977
$697$	33.9705	1.28672
$698$	−11.5858	−0.438530
$699$	−3.30127	−0.124866
$700$	1.69202	0.0639524
$701$	−14.1280	−0.533606	−0.266803	−	0.963751i	$-0.585967\pi$
$701$	−14.1280	−0.533606	−0.266803	+	0.963751i	$0.585967\pi$
$702$	33.2416	1.25462
$703$	−4.92931	−0.185913
$704$	3.73556	0.140789
$705$	35.9463	1.35382
$706$	−2.99702	−0.112794
$707$	−12.6799	−0.476878
$708$	−60.5695	−2.27634
$709$	16.4437	0.617557	0.308778	−	0.951134i	$-0.400080\pi$
$709$	16.4437	0.617557	0.308778	+	0.951134i	$0.400080\pi$
$710$	−3.40283	−0.127706
$711$	−63.4040	−2.37784
$712$	−7.48427	−0.280485
$713$	2.80194	0.104933
$714$	−8.35690	−0.312749
$715$	14.5743	0.545049
$716$	9.69740	0.362409
$717$	42.7308	1.59581
$718$	−6.91053	−0.257899
$719$	21.9517	0.818659	0.409330	−	0.912387i	$-0.365763\pi$
$719$	21.9517	0.818659	0.409330	+	0.912387i	$0.365763\pi$
$720$	−14.1468	−0.527218
$721$	−12.4819	−0.464849
$722$	2.97956	0.110888
$723$	74.4868	2.77019
$724$	−3.86831	−0.143765
$725$	−6.71379	−0.249344
$726$	−8.49694	−0.315351
$727$	20.8538	0.773426	0.386713	−	0.922200i	$-0.373610\pi$
$727$	20.8538	0.773426	0.386713	+	0.922200i	$0.373610\pi$
$728$	−12.2131	−0.452649
$729$	−17.9342	−0.664230
$730$	−5.98792	−0.221623
$731$	2.74094	0.101377
$732$	24.7101	0.913310
$733$	−49.7053	−1.83591	−0.917953	−	0.396688i	$-0.870159\pi$
$733$	−49.7053	−1.83591	−0.917953	+	0.396688i	$0.870159\pi$
$734$	−11.2784	−0.416295
$735$	3.04892	0.112461
$736$	5.34481	0.197012
$737$	−28.2760	−1.04156
$738$	−24.0315	−0.884610
$739$	−6.82477	−0.251053	−0.125527	−	0.992090i	$-0.540062\pi$
$739$	−6.82477	−0.251053	−0.125527	+	0.992090i	$0.540062\pi$
$740$	2.25906	0.0830447
$741$	67.0984	2.46492
$742$	−6.35988	−0.233479
$743$	9.10023	0.333855	0.166927	−	0.985969i	$-0.446615\pi$
$743$	9.10023	0.333855	0.166927	+	0.985969i	$0.446615\pi$
$744$	17.5036	0.641715
$745$	16.5429	0.606084
$746$	−3.49157	−0.127835
$747$	5.97285	0.218535
$748$	20.4330	0.747103
$749$	12.4276	0.454094
$750$	−1.69202	−0.0617839
$751$	16.6689	0.608258	0.304129	−	0.952631i	$-0.401635\pi$
$751$	16.6689	0.608258	0.304129	+	0.952631i	$0.401635\pi$
$752$	26.4916	0.966048
$753$	81.0926	2.95518
$754$	22.2091	0.808807
$755$	−17.8116	−0.648231
$756$	−17.0030	−0.618393
$757$	21.5198	0.782150	0.391075	−	0.920359i	$-0.372103\pi$
$757$	21.5198	0.782150	0.391075	+	0.920359i	$0.372103\pi$
$758$	6.78986	0.246619
$759$	−7.45473	−0.270590
$760$	7.56465	0.274399
$761$	48.0960	1.74348	0.871740	−	0.489969i	$-0.162992\pi$
$761$	48.0960	1.74348	0.871740	+	0.489969i	$0.162992\pi$
$762$	12.2529	0.443877
$763$	7.18598	0.260150
$764$	43.8853	1.58771
$765$	−31.0954	−1.12426
$766$	6.37495	0.230336
$767$	−69.9851	−2.52701
$768$	10.2054	0.368254
$769$	13.1970	0.475896	0.237948	−	0.971278i	$-0.423525\pi$
$769$	13.1970	0.475896	0.237948	+	0.971278i	$0.423525\pi$
$770$	1.35690	0.0488991
$771$	90.6171	3.26350
$772$	−5.99867	−0.215897
$773$	5.33453	0.191870	0.0959349	−	0.995388i	$-0.469416\pi$
$773$	5.33453	0.191870	0.0959349	+	0.995388i	$0.469416\pi$
$774$	−1.93900	−0.0696960
$775$	−2.80194	−0.100649
$776$	−23.3894	−0.839631
$777$	4.07069	0.146035
$778$	3.67755	0.131846
$779$	−25.3937	−0.909825
$780$	−30.7506	−1.10105
$781$	14.9922	0.536464
$782$	2.74094	0.0980158
$783$	67.4663	2.41105
$784$	2.24698	0.0802493
$785$	16.7409	0.597510
$786$	18.7982	0.670510
$787$	−51.6862	−1.84241	−0.921207	−	0.389074i	$-0.872795\pi$
$787$	−51.6862	−1.84241	−0.921207	+	0.389074i	$0.872795\pi$
$788$	14.4802	0.515837
$789$	32.4926	1.15677
$790$	−5.58881	−0.198841
$791$	8.10023	0.288011
$792$	−31.5405	−1.12074
$793$	28.5512	1.01388
$794$	−1.66248	−0.0589993
$795$	−34.9409	−1.23923
$796$	−33.6464	−1.19256
$797$	3.37867	0.119678	0.0598392	−	0.998208i	$-0.480941\pi$
$797$	3.37867	0.119678	0.0598392	+	0.998208i	$0.480941\pi$
$798$	6.24698	0.221141
$799$	58.2301	2.06003
$800$	−5.34481	−0.188968
$801$	−22.9976	−0.812580
$802$	−11.1424	−0.393453
$803$	26.3817	0.930988
$804$	59.6601	2.10405
$805$	−1.00000	−0.0352454
$806$	9.26875	0.326478
$807$	61.3817	2.16074
$808$	25.9801	0.913978
$809$	42.2529	1.48553	0.742767	−	0.669550i	$-0.233513\pi$
$809$	42.2529	1.48553	0.742767	+	0.669550i	$0.233513\pi$
$810$	6.52111	0.229128
$811$	19.9202	0.699493	0.349747	−	0.936844i	$-0.386268\pi$
$811$	19.9202	0.699493	0.349747	+	0.936844i	$0.386268\pi$
$812$	−11.3599	−0.398654
$813$	38.8592	1.36285
$814$	1.81163	0.0634975
$815$	14.5133	0.508380
$816$	−33.8364	−1.18451
$817$	−2.04892	−0.0716825
$818$	−12.2115	−0.426964
$819$	−37.5284	−1.31135
$820$	11.6377	0.406407
$821$	−14.8933	−0.519781	−0.259890	−	0.965638i	$-0.583686\pi$
$821$	−14.8933	−0.519781	−0.259890	+	0.965638i	$0.583686\pi$
$822$	20.1511	0.702849
$823$	9.46117	0.329796	0.164898	−	0.986311i	$-0.447271\pi$
$823$	9.46117	0.329796	0.164898	+	0.986311i	$0.447271\pi$
$824$	25.5743	0.890924
$825$	7.45473	0.259540
$826$	−6.51573	−0.226711
$827$	36.1081	1.25560	0.627801	−	0.778374i	$-0.283955\pi$
$827$	36.1081	1.25560	0.627801	+	0.778374i	$0.283955\pi$
$828$	10.6528	0.370210
$829$	−5.85145	−0.203229	−0.101615	−	0.994824i	$-0.532401\pi$
$829$	−5.85145	−0.203229	−0.101615	+	0.994824i	$0.532401\pi$
$830$	0.526483	0.0182745
$831$	−2.13946	−0.0742169
$832$	−9.10693	−0.315726
$833$	4.93900	0.171126
$834$	12.2325	0.423577
$835$	17.3913	0.601852
$836$	−15.2741	−0.528267
$837$	28.1564	0.973229
$838$	−9.94438	−0.343523
$839$	−5.63043	−0.194384	−0.0971920	−	0.995266i	$-0.530986\pi$
$839$	−5.63043	−0.194384	−0.0971920	+	0.995266i	$0.530986\pi$
$840$	−6.24698	−0.215541
$841$	16.0750	0.554310
$842$	−9.88099	−0.340521
$843$	5.51035	0.189787
$844$	4.75004	0.163503
$845$	−22.5308	−0.775083
$846$	−41.1933	−1.41625
$847$	5.02177	0.172550
$848$	−25.7506	−0.884280
$849$	−80.0307	−2.74665
$850$	−2.74094	−0.0940134
$851$	−1.33513	−0.0457675
$852$	−31.6324	−1.08371
$853$	47.0331	1.61038	0.805192	−	0.593015i	$-0.202062\pi$
$853$	47.0331	1.61038	0.805192	+	0.593015i	$0.202062\pi$
$854$	2.65817	0.0909607
$855$	23.2446	0.794948
$856$	−25.4631	−0.870311
$857$	−10.5593	−0.360698	−0.180349	−	0.983603i	$-0.557723\pi$
$857$	−10.5593	−0.360698	−0.180349	+	0.983603i	$0.557723\pi$
$858$	−24.6601	−0.841882
$859$	11.3139	0.386027	0.193013	−	0.981196i	$-0.438174\pi$
$859$	11.3139	0.386027	0.193013	+	0.981196i	$0.438174\pi$
$860$	0.939001	0.0320197
$861$	20.9705	0.714671
$862$	5.20237	0.177194
$863$	−43.3702	−1.47634	−0.738169	−	0.674616i	$-0.764309\pi$
$863$	−43.3702	−1.47634	−0.738169	+	0.674616i	$0.764309\pi$
$864$	53.7096	1.82724
$865$	13.7506	0.467535
$866$	10.1451	0.344744
$867$	−22.5429	−0.765596
$868$	−4.74094	−0.160918
$869$	24.6233	0.835287
$870$	11.3599	0.385136
$871$	68.9342	2.33575
$872$	−14.7235	−0.498600
$873$	−71.8708	−2.43246
$874$	−2.04892	−0.0693057
$875$	1.00000	0.0338062
$876$	−55.6631	−1.88068
$877$	−46.9657	−1.58592	−0.792959	−	0.609275i	$-0.791461\pi$
$877$	−46.9657	−1.58592	−0.792959	+	0.609275i	$0.791461\pi$
$878$	2.05669	0.0694098
$879$	19.1752	0.646764
$880$	5.49396	0.185201
$881$	−3.22654	−0.108705	−0.0543524	−	0.998522i	$-0.517309\pi$
$881$	−3.22654	−0.108705	−0.0543524	+	0.998522i	$0.517309\pi$
$882$	−3.49396	−0.117648
$883$	−43.2006	−1.45382	−0.726908	−	0.686735i	$-0.759043\pi$
$883$	−43.2006	−1.45382	−0.726908	+	0.686735i	$0.759043\pi$
$884$	−49.8135	−1.67541
$885$	−35.7972	−1.20331
$886$	−0.712464	−0.0239357
$887$	5.05084	0.169590	0.0847952	−	0.996398i	$-0.472976\pi$
$887$	5.05084	0.169590	0.0847952	+	0.996398i	$0.472976\pi$
$888$	−8.34050	−0.279889
$889$	−7.24160	−0.242876
$890$	−2.02715	−0.0679501
$891$	−28.7308	−0.962517
$892$	−40.4849	−1.35553
$893$	−43.5284	−1.45662
$894$	−27.9909	−0.936156
$895$	5.73125	0.191575
$896$	−11.5375	−0.385441
$897$	18.1739	0.606809
$898$	11.2553	0.375596
$899$	18.8116	0.627403
$900$	−10.6528	−0.355093
$901$	−56.6015	−1.88567
$902$	9.33273	0.310746
$903$	1.69202	0.0563069
$904$	−16.5967	−0.551998
$905$	−2.28621	−0.0759961
$906$	30.1377	1.00126
$907$	20.6722	0.686408	0.343204	−	0.939261i	$-0.388488\pi$
$907$	20.6722	0.686408	0.343204	+	0.939261i	$0.388488\pi$
$908$	0.541549	0.0179719
$909$	79.8316	2.64785
$910$	−3.30798	−0.109658
$911$	−13.1841	−0.436807	−0.218404	−	0.975859i	$-0.570085\pi$
$911$	−13.1841	−0.436807	−0.218404	+	0.975859i	$0.570085\pi$
$912$	25.2935	0.837552
$913$	−2.31959	−0.0767671
$914$	9.22149	0.305020
$915$	14.6039	0.482789
$916$	42.5080	1.40450
$917$	−11.1099	−0.366882
$918$	27.5435	0.909070
$919$	−35.2034	−1.16125	−0.580627	−	0.814170i	$-0.697193\pi$
$919$	−35.2034	−1.16125	−0.580627	+	0.814170i	$0.697193\pi$
$920$	2.04892	0.0675508
$921$	−3.30452	−0.108888
$922$	−9.98866	−0.328959
$923$	−36.5496	−1.20304
$924$	12.6136	0.414956
$925$	1.33513	0.0438987
$926$	8.67994	0.285241
$927$	78.5846	2.58106
$928$	35.8840	1.17795
$929$	−0.924527	−0.0303327	−0.0151664	−	0.999885i	$-0.504828\pi$
$929$	−0.924527	−0.0303327	−0.0151664	+	0.999885i	$0.504828\pi$
$930$	4.74094	0.155462
$931$	−3.69202	−0.121001
$932$	−1.83207	−0.0600114
$933$	42.3129	1.38526
$934$	0.442058	0.0144646
$935$	12.0761	0.394930
$936$	76.8926	2.51331
$937$	−33.2247	−1.08540	−0.542702	−	0.839925i	$-0.682599\pi$
$937$	−33.2247	−1.08540	−0.542702	+	0.839925i	$0.682599\pi$
$938$	6.41789	0.209552
$939$	−15.6953	−0.512196
$940$	19.9487	0.650655
$941$	−39.4446	−1.28586	−0.642928	−	0.765927i	$-0.722281\pi$
$941$	−39.4446	−1.28586	−0.642928	+	0.765927i	$0.722281\pi$
$942$	−28.3260	−0.922912
$943$	−6.87800	−0.223979
$944$	−26.3817	−0.858650
$945$	−10.0489	−0.326891
$946$	0.753020	0.0244828
$947$	−27.2362	−0.885058	−0.442529	−	0.896754i	$-0.645919\pi$
$947$	−27.2362	−0.885058	−0.442529	+	0.896754i	$0.645919\pi$
$948$	−51.9530	−1.68736
$949$	−64.3159	−2.08778
$950$	2.04892	0.0664757
$951$	−32.1943	−1.04397
$952$	−10.1196	−0.327978
$953$	9.02044	0.292201	0.146100	−	0.989270i	$-0.453328\pi$
$953$	9.02044	0.292201	0.146100	+	0.989270i	$0.453328\pi$
$954$	40.0411	1.29638
$955$	25.9366	0.839289
$956$	23.7138	0.766959
$957$	−50.0495	−1.61787
$958$	9.12200	0.294718
$959$	−11.9095	−0.384577
$960$	−4.65817	−0.150342
$961$	−23.1491	−0.746747
$962$	−4.41657	−0.142396
$963$	−78.2428	−2.52134
$964$	41.3370	1.33138
$965$	−3.54527	−0.114126
$966$	1.69202	0.0544399
$967$	7.97525	0.256467	0.128233	−	0.991744i	$-0.459069\pi$
$967$	7.97525	0.256467	0.128233	+	0.991744i	$0.459069\pi$
$968$	−10.2892	−0.330707
$969$	55.5967	1.78602
$970$	−6.33513	−0.203409
$971$	−28.1062	−0.901971	−0.450985	−	0.892531i	$-0.648927\pi$
$971$	−28.1062	−0.901971	−0.450985	+	0.892531i	$0.648927\pi$
$972$	9.61058	0.308260
$973$	−7.22952	−0.231768
$974$	−19.4196	−0.622243
$975$	−18.1739	−0.582031
$976$	10.7627	0.344506
$977$	48.7547	1.55980	0.779900	−	0.625904i	$-0.215270\pi$
$977$	48.7547	1.55980	0.779900	+	0.625904i	$0.215270\pi$
$978$	−24.5569	−0.785242
$979$	8.93123	0.285443
$980$	1.69202	0.0540496
$981$	−45.2422	−1.44447
$982$	6.59478	0.210448
$983$	3.62266	0.115545	0.0577725	−	0.998330i	$-0.481600\pi$
$983$	3.62266	0.115545	0.0577725	+	0.998330i	$0.481600\pi$
$984$	−42.9667	−1.36973
$985$	8.55794	0.272679
$986$	18.4021	0.586042
$987$	35.9463	1.14418
$988$	37.2368	1.18466
$989$	−0.554958	−0.0176466
$990$	−8.54288	−0.271510
$991$	−2.00538	−0.0637029	−0.0318514	−	0.999493i	$-0.510140\pi$
$991$	−2.00538	−0.0637029	−0.0318514	+	0.999493i	$0.510140\pi$
$992$	14.9758	0.475483
$993$	−7.93900	−0.251937
$994$	−3.40283	−0.107931
$995$	−19.8853	−0.630406
$996$	4.89413	0.155077
$997$	−5.31634	−0.168370	−0.0841851	−	0.996450i	$-0.526829\pi$
$997$	−5.31634	−0.168370	−0.0841851	+	0.996450i	$0.526829\pi$
$998$	−2.75600	−0.0872398
$999$	−13.4166	−0.424481

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	805.2.a.f.1.2	✓	3
3.2	odd	2		7245.2.a.ba.1.2		3
5.4	even	2		4025.2.a.k.1.2		3
7.6	odd	2		5635.2.a.r.1.2		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
805.2.a.f.1.2	✓	3	1.1	even	1	trivial
4025.2.a.k.1.2		3	5.4	even	2
5635.2.a.r.1.2		3	7.6	odd	2
7245.2.a.ba.1.2		3	3.2	odd	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:	\( N \)	\(=\)	\( 805 = 5 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	805.a (trivial)

\(f(q)\)	\(=\)	\(q-0.554958 q^{2} -3.04892 q^{3} -1.69202 q^{4} -1.00000 q^{5} +1.69202 q^{6} -1.00000 q^{7} +2.04892 q^{8} +6.29590 q^{9} +O(q^{10})\)	\(q-0.554958 q^{2} -3.04892 q^{3} -1.69202 q^{4} -1.00000 q^{5} +1.69202 q^{6} -1.00000 q^{7} +2.04892 q^{8} +6.29590 q^{9} +0.554958 q^{10} -2.44504 q^{11} +5.15883 q^{12} +5.96077 q^{13} +0.554958 q^{14} +3.04892 q^{15} +2.24698 q^{16} +4.93900 q^{17} -3.49396 q^{18} -3.69202 q^{19} +1.69202 q^{20} +3.04892 q^{21} +1.35690 q^{22} -1.00000 q^{23} -6.24698 q^{24} +1.00000 q^{25} -3.30798 q^{26} -10.0489 q^{27} +1.69202 q^{28} -6.71379 q^{29} -1.69202 q^{30} -2.80194 q^{31} -5.34481 q^{32} +7.45473 q^{33} -2.74094 q^{34} +1.00000 q^{35} -10.6528 q^{36} +1.33513 q^{37} +2.04892 q^{38} -18.1739 q^{39} -2.04892 q^{40} +6.87800 q^{41} -1.69202 q^{42} +0.554958 q^{43} +4.13706 q^{44} -6.29590 q^{45} +0.554958 q^{46} +11.7899 q^{47} -6.85086 q^{48} +1.00000 q^{49} -0.554958 q^{50} -15.0586 q^{51} -10.0858 q^{52} -11.4601 q^{53} +5.57673 q^{54} +2.44504 q^{55} -2.04892 q^{56} +11.2567 q^{57} +3.72587 q^{58} -11.7409 q^{59} -5.15883 q^{60} +4.78986 q^{61} +1.55496 q^{62} -6.29590 q^{63} -1.52781 q^{64} -5.96077 q^{65} -4.13706 q^{66} +11.5646 q^{67} -8.35690 q^{68} +3.04892 q^{69} -0.554958 q^{70} -6.13169 q^{71} +12.8998 q^{72} -10.7899 q^{73} -0.740939 q^{74} -3.04892 q^{75} +6.24698 q^{76} +2.44504 q^{77} +10.0858 q^{78} -10.0707 q^{79} -2.24698 q^{80} +11.7506 q^{81} -3.81700 q^{82} +0.948690 q^{83} -5.15883 q^{84} -4.93900 q^{85} -0.307979 q^{86} +20.4698 q^{87} -5.00969 q^{88} -3.65279 q^{89} +3.49396 q^{90} -5.96077 q^{91} +1.69202 q^{92} +8.54288 q^{93} -6.54288 q^{94} +3.69202 q^{95} +16.2959 q^{96} -11.4155 q^{97} -0.554958 q^{98} -15.3937 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q - 2 q^{2} - 3 q^{5} - 3 q^{7} - 3 q^{8} + 5 q^{9}+O(q^{10}) \) 3 * q - 2 * q^2 - 3 * q^5 - 3 * q^7 - 3 * q^8 + 5 * q^9	\( 3 q - 2 q^{2} - 3 q^{5} - 3 q^{7} - 3 q^{8} + 5 q^{9} + 2 q^{10} - 7 q^{11} + 7 q^{12} + 5 q^{13} + 2 q^{14} + 2 q^{16} + 5 q^{17} - q^{18} - 6 q^{19} - 3 q^{23} - 14 q^{24} + 3 q^{25} - 15 q^{26} - 21 q^{27} - 12 q^{29} - 4 q^{31} + 7 q^{32} + 6 q^{34} + 3 q^{35} - 14 q^{36} + 3 q^{37} - 3 q^{38} - 21 q^{39} + 3 q^{40} + q^{41} + 2 q^{43} + 7 q^{44} - 5 q^{45} + 2 q^{46} + 12 q^{47} - 7 q^{48} + 3 q^{49} - 2 q^{50} - 14 q^{51} + 7 q^{52} - 9 q^{53} + 14 q^{54} + 7 q^{55} + 3 q^{56} + 7 q^{57} + 22 q^{58} - 21 q^{59} - 7 q^{60} - 9 q^{61} + 5 q^{62} - 5 q^{63} - 11 q^{64} - 5 q^{65} - 7 q^{66} + 13 q^{67} - 21 q^{68} - 2 q^{70} - 16 q^{71} + 16 q^{72} - 9 q^{73} + 12 q^{74} + 14 q^{76} + 7 q^{77} - 7 q^{78} - 18 q^{79} - 2 q^{80} - q^{81} + 18 q^{82} - 29 q^{83} - 7 q^{84} - 5 q^{85} - 6 q^{86} + 14 q^{87} + 7 q^{88} + 7 q^{89} + q^{90} - 5 q^{91} + 7 q^{93} - q^{94} + 6 q^{95} + 35 q^{96} + q^{97} - 2 q^{98} - 14 q^{99}+O(q^{100}) \) 3 * q - 2 * q^2 - 3 * q^5 - 3 * q^7 - 3 * q^8 + 5 * q^9 + 2 * q^10 - 7 * q^11 + 7 * q^12 + 5 * q^13 + 2 * q^14 + 2 * q^16 + 5 * q^17 - q^18 - 6 * q^19 - 3 * q^23 - 14 * q^24 + 3 * q^25 - 15 * q^26 - 21 * q^27 - 12 * q^29 - 4 * q^31 + 7 * q^32 + 6 * q^34 + 3 * q^35 - 14 * q^36 + 3 * q^37 - 3 * q^38 - 21 * q^39 + 3 * q^40 + q^41 + 2 * q^43 + 7 * q^44 - 5 * q^45 + 2 * q^46 + 12 * q^47 - 7 * q^48 + 3 * q^49 - 2 * q^50 - 14 * q^51 + 7 * q^52 - 9 * q^53 + 14 * q^54 + 7 * q^55 + 3 * q^56 + 7 * q^57 + 22 * q^58 - 21 * q^59 - 7 * q^60 - 9 * q^61 + 5 * q^62 - 5 * q^63 - 11 * q^64 - 5 * q^65 - 7 * q^66 + 13 * q^67 - 21 * q^68 - 2 * q^70 - 16 * q^71 + 16 * q^72 - 9 * q^73 + 12 * q^74 + 14 * q^76 + 7 * q^77 - 7 * q^78 - 18 * q^79 - 2 * q^80 - q^81 + 18 * q^82 - 29 * q^83 - 7 * q^84 - 5 * q^85 - 6 * q^86 + 14 * q^87 + 7 * q^88 + 7 * q^89 + q^90 - 5 * q^91 + 7 * q^93 - q^94 + 6 * q^95 + 35 * q^96 + q^97 - 2 * q^98 - 14 * q^99

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