LMFDB - Embedded newform 365.2.a.a.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [365,2,Mod(1,365)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(365, 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("365.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 365 = 5 \cdot 73 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	365.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:	$2.91453967378$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{12})^+$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - 3 $ x^2 - 3
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			1.1
Root			$-1.73205$ of defining polynomial
Character	$\chi$	$=$	365.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.73205 q^{2} +2.00000 q^{3} +1.00000 q^{4} +1.00000 q^{5} -3.46410 q^{6} +4.73205 q^{7} +1.73205 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.73205 q^{2} +2.00000 q^{3} +1.00000 q^{4} +1.00000 q^{5} -3.46410 q^{6} +4.73205 q^{7} +1.73205 q^{8} +1.00000 q^{9} -1.73205 q^{10} -1.26795 q^{11} +2.00000 q^{12} -3.46410 q^{13} -8.19615 q^{14} +2.00000 q^{15} -5.00000 q^{16} +3.46410 q^{17} -1.73205 q^{18} +5.46410 q^{19} +1.00000 q^{20} +9.46410 q^{21} +2.19615 q^{22} -8.92820 q^{23} +3.46410 q^{24} +1.00000 q^{25} +6.00000 q^{26} -4.00000 q^{27} +4.73205 q^{28} -0.535898 q^{29} -3.46410 q^{30} +5.26795 q^{31} +5.19615 q^{32} -2.53590 q^{33} -6.00000 q^{34} +4.73205 q^{35} +1.00000 q^{36} +8.00000 q^{37} -9.46410 q^{38} -6.92820 q^{39} +1.73205 q^{40} +1.46410 q^{41} -16.3923 q^{42} -2.19615 q^{43} -1.26795 q^{44} +1.00000 q^{45} +15.4641 q^{46} -3.26795 q^{47} -10.0000 q^{48} +15.3923 q^{49} -1.73205 q^{50} +6.92820 q^{51} -3.46410 q^{52} -0.928203 q^{53} +6.92820 q^{54} -1.26795 q^{55} +8.19615 q^{56} +10.9282 q^{57} +0.928203 q^{58} -1.26795 q^{59} +2.00000 q^{60} -2.53590 q^{61} -9.12436 q^{62} +4.73205 q^{63} +1.00000 q^{64} -3.46410 q^{65} +4.39230 q^{66} -2.00000 q^{67} +3.46410 q^{68} -17.8564 q^{69} -8.19615 q^{70} +8.00000 q^{71} +1.73205 q^{72} -1.00000 q^{73} -13.8564 q^{74} +2.00000 q^{75} +5.46410 q^{76} -6.00000 q^{77} +12.0000 q^{78} -13.4641 q^{79} -5.00000 q^{80} -11.0000 q^{81} -2.53590 q^{82} -7.66025 q^{83} +9.46410 q^{84} +3.46410 q^{85} +3.80385 q^{86} -1.07180 q^{87} -2.19615 q^{88} -15.8564 q^{89} -1.73205 q^{90} -16.3923 q^{91} -8.92820 q^{92} +10.5359 q^{93} +5.66025 q^{94} +5.46410 q^{95} +10.3923 q^{96} -2.92820 q^{97} -26.6603 q^{98} -1.26795 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 4 q^{3} + 2 q^{4} + 2 q^{5} + 6 q^{7} + 2 q^{9}+O(q^{10}) $ 2 * q + 4 * q^3 + 2 * q^4 + 2 * q^5 + 6 * q^7 + 2 * q^9	$ 2 q + 4 q^{3} + 2 q^{4} + 2 q^{5} + 6 q^{7} + 2 q^{9} - 6 q^{11} + 4 q^{12} - 6 q^{14} + 4 q^{15} - 10 q^{16} + 4 q^{19} + 2 q^{20} + 12 q^{21} - 6 q^{22} - 4 q^{23} + 2 q^{25} + 12 q^{26} - 8 q^{27} + 6 q^{28} - 8 q^{29} + 14 q^{31} - 12 q^{33} - 12 q^{34} + 6 q^{35} + 2 q^{36} + 16 q^{37} - 12 q^{38} - 4 q^{41} - 12 q^{42} + 6 q^{43} - 6 q^{44} + 2 q^{45} + 24 q^{46} - 10 q^{47} - 20 q^{48} + 10 q^{49} + 12 q^{53} - 6 q^{55} + 6 q^{56} + 8 q^{57} - 12 q^{58} - 6 q^{59} + 4 q^{60} - 12 q^{61} + 6 q^{62} + 6 q^{63} + 2 q^{64} - 12 q^{66} - 4 q^{67} - 8 q^{69} - 6 q^{70} + 16 q^{71} - 2 q^{73} + 4 q^{75} + 4 q^{76} - 12 q^{77} + 24 q^{78} - 20 q^{79} - 10 q^{80} - 22 q^{81} - 12 q^{82} + 2 q^{83} + 12 q^{84} + 18 q^{86} - 16 q^{87} + 6 q^{88} - 4 q^{89} - 12 q^{91} - 4 q^{92} + 28 q^{93} - 6 q^{94} + 4 q^{95} + 8 q^{97} - 36 q^{98} - 6 q^{99}+O(q^{100}) $ 2 * q + 4 * q^3 + 2 * q^4 + 2 * q^5 + 6 * q^7 + 2 * q^9 - 6 * q^11 + 4 * q^12 - 6 * q^14 + 4 * q^15 - 10 * q^16 + 4 * q^19 + 2 * q^20 + 12 * q^21 - 6 * q^22 - 4 * q^23 + 2 * q^25 + 12 * q^26 - 8 * q^27 + 6 * q^28 - 8 * q^29 + 14 * q^31 - 12 * q^33 - 12 * q^34 + 6 * q^35 + 2 * q^36 + 16 * q^37 - 12 * q^38 - 4 * q^41 - 12 * q^42 + 6 * q^43 - 6 * q^44 + 2 * q^45 + 24 * q^46 - 10 * q^47 - 20 * q^48 + 10 * q^49 + 12 * q^53 - 6 * q^55 + 6 * q^56 + 8 * q^57 - 12 * q^58 - 6 * q^59 + 4 * q^60 - 12 * q^61 + 6 * q^62 + 6 * q^63 + 2 * q^64 - 12 * q^66 - 4 * q^67 - 8 * q^69 - 6 * q^70 + 16 * q^71 - 2 * q^73 + 4 * q^75 + 4 * q^76 - 12 * q^77 + 24 * q^78 - 20 * q^79 - 10 * q^80 - 22 * q^81 - 12 * q^82 + 2 * q^83 + 12 * q^84 + 18 * q^86 - 16 * q^87 + 6 * q^88 - 4 * q^89 - 12 * q^91 - 4 * q^92 + 28 * q^93 - 6 * q^94 + 4 * q^95 + 8 * q^97 - 36 * q^98 - 6 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−1.73205	−1.22474	−0.612372	−	0.790569i	$-0.709785\pi$
$2$	−1.73205	−1.22474	−0.612372	+	0.790569i	$0.709785\pi$
$3$	2.00000	1.15470	0.577350	−	0.816497i	$-0.304087\pi$
$3$	2.00000	1.15470	0.577350	+	0.816497i	$0.304087\pi$
$4$	1.00000	0.500000
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	−3.46410	−1.41421
$7$	4.73205	1.78855	0.894274	−	0.447521i	$-0.147693\pi$
$7$	4.73205	1.78855	0.894274	+	0.447521i	$0.147693\pi$
$8$	1.73205	0.612372
$9$	1.00000	0.333333
$10$	−1.73205	−0.547723
$11$	−1.26795	−0.382301	−0.191151	−	0.981561i	$-0.561222\pi$
$11$	−1.26795	−0.382301	−0.191151	+	0.981561i	$0.561222\pi$
$12$	2.00000	0.577350
$13$	−3.46410	−0.960769	−0.480384	−	0.877058i	$-0.659503\pi$
$13$	−3.46410	−0.960769	−0.480384	+	0.877058i	$0.659503\pi$
$14$	−8.19615	−2.19051
$15$	2.00000	0.516398
$16$	−5.00000	−1.25000
$17$	3.46410	0.840168	0.420084	−	0.907485i	$-0.362001\pi$
$17$	3.46410	0.840168	0.420084	+	0.907485i	$0.362001\pi$
$18$	−1.73205	−0.408248
$19$	5.46410	1.25355	0.626775	−	0.779200i	$-0.284374\pi$
$19$	5.46410	1.25355	0.626775	+	0.779200i	$0.284374\pi$
$20$	1.00000	0.223607
$21$	9.46410	2.06524
$22$	2.19615	0.468221
$23$	−8.92820	−1.86166	−0.930830	−	0.365454i	$-0.880914\pi$
$23$	−8.92820	−1.86166	−0.930830	+	0.365454i	$0.880914\pi$
$24$	3.46410	0.707107
$25$	1.00000	0.200000
$26$	6.00000	1.17670
$27$	−4.00000	−0.769800
$28$	4.73205	0.894274
$29$	−0.535898	−0.0995138	−0.0497569	−	0.998761i	$-0.515845\pi$
$29$	−0.535898	−0.0995138	−0.0497569	+	0.998761i	$0.515845\pi$
$30$	−3.46410	−0.632456
$31$	5.26795	0.946152	0.473076	−	0.881022i	$-0.343144\pi$
$31$	5.26795	0.946152	0.473076	+	0.881022i	$0.343144\pi$
$32$	5.19615	0.918559
$33$	−2.53590	−0.441443
$34$	−6.00000	−1.02899
$35$	4.73205	0.799863
$36$	1.00000	0.166667
$37$	8.00000	1.31519	0.657596	−	0.753371i	$-0.271573\pi$
$37$	8.00000	1.31519	0.657596	+	0.753371i	$0.271573\pi$
$38$	−9.46410	−1.53528
$39$	−6.92820	−1.10940
$40$	1.73205	0.273861
$41$	1.46410	0.228654	0.114327	−	0.993443i	$-0.463529\pi$
$41$	1.46410	0.228654	0.114327	+	0.993443i	$0.463529\pi$
$42$	−16.3923	−2.52939
$43$	−2.19615	−0.334910	−0.167455	−	0.985880i	$-0.553555\pi$
$43$	−2.19615	−0.334910	−0.167455	+	0.985880i	$0.553555\pi$
$44$	−1.26795	−0.191151
$45$	1.00000	0.149071
$46$	15.4641	2.28006
$47$	−3.26795	−0.476679	−0.238340	−	0.971182i	$-0.576603\pi$
$47$	−3.26795	−0.476679	−0.238340	+	0.971182i	$0.576603\pi$
$48$	−10.0000	−1.44338
$49$	15.3923	2.19890
$50$	−1.73205	−0.244949
$51$	6.92820	0.970143
$52$	−3.46410	−0.480384
$53$	−0.928203	−0.127499	−0.0637493	−	0.997966i	$-0.520306\pi$
$53$	−0.928203	−0.127499	−0.0637493	+	0.997966i	$0.520306\pi$
$54$	6.92820	0.942809
$55$	−1.26795	−0.170970
$56$	8.19615	1.09526
$57$	10.9282	1.44748
$58$	0.928203	0.121879
$59$	−1.26795	−0.165073	−0.0825365	−	0.996588i	$-0.526302\pi$
$59$	−1.26795	−0.165073	−0.0825365	+	0.996588i	$0.526302\pi$
$60$	2.00000	0.258199
$61$	−2.53590	−0.324689	−0.162344	−	0.986734i	$-0.551906\pi$
$61$	−2.53590	−0.324689	−0.162344	+	0.986734i	$0.551906\pi$
$62$	−9.12436	−1.15879
$63$	4.73205	0.596182
$64$	1.00000	0.125000
$65$	−3.46410	−0.429669
$66$	4.39230	0.540655
$67$	−2.00000	−0.244339	−0.122169	−	0.992509i	$-0.538985\pi$
$67$	−2.00000	−0.244339	−0.122169	+	0.992509i	$0.538985\pi$
$68$	3.46410	0.420084
$69$	−17.8564	−2.14966
$70$	−8.19615	−0.979628
$71$	8.00000	0.949425	0.474713	−	0.880141i	$-0.342552\pi$
$71$	8.00000	0.949425	0.474713	+	0.880141i	$0.342552\pi$
$72$	1.73205	0.204124
$73$	−1.00000	−0.117041
$73$	−1.00000	−0.117041
$74$	−13.8564	−1.61077
$75$	2.00000	0.230940
$76$	5.46410	0.626775
$77$	−6.00000	−0.683763
$78$	12.0000	1.35873
$79$	−13.4641	−1.51483	−0.757415	−	0.652934i	$-0.773538\pi$
$79$	−13.4641	−1.51483	−0.757415	+	0.652934i	$0.773538\pi$
$80$	−5.00000	−0.559017
$81$	−11.0000	−1.22222
$82$	−2.53590	−0.280043
$83$	−7.66025	−0.840822	−0.420411	−	0.907334i	$-0.638114\pi$
$83$	−7.66025	−0.840822	−0.420411	+	0.907334i	$0.638114\pi$
$84$	9.46410	1.03262
$85$	3.46410	0.375735
$86$	3.80385	0.410179
$87$	−1.07180	−0.114909
$88$	−2.19615	−0.234111
$89$	−15.8564	−1.68078	−0.840388	−	0.541985i	$-0.817673\pi$
$89$	−15.8564	−1.68078	−0.840388	+	0.541985i	$0.817673\pi$
$90$	−1.73205	−0.182574
$91$	−16.3923	−1.71838
$92$	−8.92820	−0.930830
$93$	10.5359	1.09252
$94$	5.66025	0.583811
$95$	5.46410	0.560605
$96$	10.3923	1.06066
$97$	−2.92820	−0.297314	−0.148657	−	0.988889i	$-0.547495\pi$
$97$	−2.92820	−0.297314	−0.148657	+	0.988889i	$0.547495\pi$
$98$	−26.6603	−2.69309
$99$	−1.26795	−0.127434
$100$	1.00000	0.100000
$101$	−14.3923	−1.43209	−0.716044	−	0.698055i	$-0.754049\pi$
$101$	−14.3923	−1.43209	−0.716044	+	0.698055i	$0.754049\pi$
$102$	−12.0000	−1.18818
$103$	3.66025	0.360656	0.180328	−	0.983607i	$-0.442284\pi$
$103$	3.66025	0.360656	0.180328	+	0.983607i	$0.442284\pi$
$104$	−6.00000	−0.588348
$105$	9.46410	0.923602
$106$	1.60770	0.156153
$107$	−3.26795	−0.315925	−0.157962	−	0.987445i	$-0.550492\pi$
$107$	−3.26795	−0.315925	−0.157962	+	0.987445i	$0.550492\pi$
$108$	−4.00000	−0.384900
$109$	19.8564	1.90190	0.950949	−	0.309346i	$-0.100110\pi$
$109$	19.8564	1.90190	0.950949	+	0.309346i	$0.100110\pi$
$110$	2.19615	0.209395
$111$	16.0000	1.51865
$112$	−23.6603	−2.23568
$113$	−16.9282	−1.59247	−0.796236	−	0.604987i	$-0.793178\pi$
$113$	−16.9282	−1.59247	−0.796236	+	0.604987i	$0.793178\pi$
$114$	−18.9282	−1.77279
$115$	−8.92820	−0.832559
$116$	−0.535898	−0.0497569
$117$	−3.46410	−0.320256
$118$	2.19615	0.202172
$119$	16.3923	1.50268
$120$	3.46410	0.316228
$121$	−9.39230	−0.853846
$122$	4.39230	0.397661
$123$	2.92820	0.264027
$124$	5.26795	0.473076
$125$	1.00000	0.0894427
$126$	−8.19615	−0.730171
$127$	−12.9282	−1.14719	−0.573596	−	0.819138i	$-0.694452\pi$
$127$	−12.9282	−1.14719	−0.573596	+	0.819138i	$0.694452\pi$
$128$	−12.1244	−1.07165
$129$	−4.39230	−0.386721
$130$	6.00000	0.526235
$131$	16.1962	1.41506	0.707532	−	0.706681i	$-0.249808\pi$
$131$	16.1962	1.41506	0.707532	+	0.706681i	$0.249808\pi$
$132$	−2.53590	−0.220722
$133$	25.8564	2.24203
$134$	3.46410	0.299253
$135$	−4.00000	−0.344265
$136$	6.00000	0.514496
$137$	11.8564	1.01296	0.506481	−	0.862251i	$-0.330946\pi$
$137$	11.8564	1.01296	0.506481	+	0.862251i	$0.330946\pi$
$138$	30.9282	2.63278
$139$	13.2679	1.12537	0.562686	−	0.826670i	$-0.309768\pi$
$139$	13.2679	1.12537	0.562686	+	0.826670i	$0.309768\pi$
$140$	4.73205	0.399931
$141$	−6.53590	−0.550422
$142$	−13.8564	−1.16280
$143$	4.39230	0.367303
$144$	−5.00000	−0.416667
$145$	−0.535898	−0.0445039
$146$	1.73205	0.143346
$147$	30.7846	2.53907
$148$	8.00000	0.657596
$149$	16.3923	1.34291	0.671455	−	0.741045i	$-0.265670\pi$
$149$	16.3923	1.34291	0.671455	+	0.741045i	$0.265670\pi$
$150$	−3.46410	−0.282843
$151$	−19.1244	−1.55632	−0.778159	−	0.628067i	$-0.783846\pi$
$151$	−19.1244	−1.55632	−0.778159	+	0.628067i	$0.783846\pi$
$152$	9.46410	0.767640
$153$	3.46410	0.280056
$154$	10.3923	0.837436
$155$	5.26795	0.423132
$156$	−6.92820	−0.554700
$157$	−7.46410	−0.595700	−0.297850	−	0.954613i	$-0.596270\pi$
$157$	−7.46410	−0.595700	−0.297850	+	0.954613i	$0.596270\pi$
$158$	23.3205	1.85528
$159$	−1.85641	−0.147223
$160$	5.19615	0.410792
$161$	−42.2487	−3.32966
$162$	19.0526	1.49691
$163$	8.73205	0.683947	0.341974	−	0.939710i	$-0.388905\pi$
$163$	8.73205	0.683947	0.341974	+	0.939710i	$0.388905\pi$
$164$	1.46410	0.114327
$165$	−2.53590	−0.197419
$166$	13.2679	1.02979
$167$	−19.6603	−1.52136	−0.760678	−	0.649129i	$-0.775133\pi$
$167$	−19.6603	−1.52136	−0.760678	+	0.649129i	$0.775133\pi$
$168$	16.3923	1.26469
$169$	−1.00000	−0.0769231
$170$	−6.00000	−0.460179
$171$	5.46410	0.417850
$172$	−2.19615	−0.167455
$173$	−10.0000	−0.760286	−0.380143	−	0.924928i	$-0.624125\pi$
$173$	−10.0000	−0.760286	−0.380143	+	0.924928i	$0.624125\pi$
$174$	1.85641	0.140734
$175$	4.73205	0.357709
$176$	6.33975	0.477876
$177$	−2.53590	−0.190610
$178$	27.4641	2.05852
$179$	11.8038	0.882261	0.441130	−	0.897443i	$-0.354578\pi$
$179$	11.8038	0.882261	0.441130	+	0.897443i	$0.354578\pi$
$180$	1.00000	0.0745356
$181$	1.46410	0.108826	0.0544129	−	0.998519i	$-0.482671\pi$
$181$	1.46410	0.108826	0.0544129	+	0.998519i	$0.482671\pi$
$182$	28.3923	2.10458
$183$	−5.07180	−0.374918
$184$	−15.4641	−1.14003
$185$	8.00000	0.588172
$186$	−18.2487	−1.33806
$187$	−4.39230	−0.321197
$188$	−3.26795	−0.238340
$189$	−18.9282	−1.37682
$190$	−9.46410	−0.686598
$191$	20.1962	1.46134	0.730671	−	0.682730i	$-0.239207\pi$
$191$	20.1962	1.46134	0.730671	+	0.682730i	$0.239207\pi$
$192$	2.00000	0.144338
$193$	−18.7846	−1.35215	−0.676073	−	0.736835i	$-0.736320\pi$
$193$	−18.7846	−1.35215	−0.676073	+	0.736835i	$0.736320\pi$
$194$	5.07180	0.364134
$195$	−6.92820	−0.496139
$196$	15.3923	1.09945
$197$	−18.3923	−1.31040	−0.655199	−	0.755457i	$-0.727415\pi$
$197$	−18.3923	−1.31040	−0.655199	+	0.755457i	$0.727415\pi$
$198$	2.19615	0.156074
$199$	2.33975	0.165860	0.0829301	−	0.996555i	$-0.473572\pi$
$199$	2.33975	0.165860	0.0829301	+	0.996555i	$0.473572\pi$
$200$	1.73205	0.122474
$201$	−4.00000	−0.282138
$202$	24.9282	1.75394
$203$	−2.53590	−0.177985
$204$	6.92820	0.485071
$205$	1.46410	0.102257
$206$	−6.33975	−0.441711
$207$	−8.92820	−0.620553
$208$	17.3205	1.20096
$209$	−6.92820	−0.479234
$210$	−16.3923	−1.13118
$211$	14.9282	1.02770	0.513850	−	0.857880i	$-0.328219\pi$
$211$	14.9282	1.02770	0.513850	+	0.857880i	$0.328219\pi$
$212$	−0.928203	−0.0637493
$213$	16.0000	1.09630
$214$	5.66025	0.386927
$215$	−2.19615	−0.149776
$216$	−6.92820	−0.471405
$217$	24.9282	1.69224
$218$	−34.3923	−2.32934
$219$	−2.00000	−0.135147
$220$	−1.26795	−0.0854851
$221$	−12.0000	−0.807207
$222$	−27.7128	−1.85996
$223$	4.53590	0.303746	0.151873	−	0.988400i	$-0.451469\pi$
$223$	4.53590	0.303746	0.151873	+	0.988400i	$0.451469\pi$
$224$	24.5885	1.64289
$225$	1.00000	0.0666667
$226$	29.3205	1.95037
$227$	17.3205	1.14960	0.574801	−	0.818293i	$-0.305079\pi$
$227$	17.3205	1.14960	0.574801	+	0.818293i	$0.305079\pi$
$228$	10.9282	0.723738
$229$	3.46410	0.228914	0.114457	−	0.993428i	$-0.463487\pi$
$229$	3.46410	0.228914	0.114457	+	0.993428i	$0.463487\pi$
$230$	15.4641	1.01967
$231$	−12.0000	−0.789542
$232$	−0.928203	−0.0609395
$233$	26.7846	1.75472	0.877359	−	0.479834i	$-0.159303\pi$
$233$	26.7846	1.75472	0.877359	+	0.479834i	$0.159303\pi$
$234$	6.00000	0.392232
$235$	−3.26795	−0.213177
$236$	−1.26795	−0.0825365
$237$	−26.9282	−1.74917
$238$	−28.3923	−1.84040
$239$	−17.2679	−1.11697	−0.558485	−	0.829514i	$-0.688617\pi$
$239$	−17.2679	−1.11697	−0.558485	+	0.829514i	$0.688617\pi$
$240$	−10.0000	−0.645497
$241$	17.3205	1.11571	0.557856	−	0.829938i	$-0.311624\pi$
$241$	17.3205	1.11571	0.557856	+	0.829938i	$0.311624\pi$
$242$	16.2679	1.04574
$243$	−10.0000	−0.641500
$244$	−2.53590	−0.162344
$245$	15.3923	0.983378
$246$	−5.07180	−0.323366
$247$	−18.9282	−1.20437
$248$	9.12436	0.579397
$249$	−15.3205	−0.970898
$250$	−1.73205	−0.109545
$251$	−10.9282	−0.689782	−0.344891	−	0.938643i	$-0.612084\pi$
$251$	−10.9282	−0.689782	−0.344891	+	0.938643i	$0.612084\pi$
$252$	4.73205	0.298091
$253$	11.3205	0.711714
$254$	22.3923	1.40502
$255$	6.92820	0.433861
$256$	19.0000	1.18750
$257$	29.8564	1.86239	0.931196	−	0.364520i	$-0.118767\pi$
$257$	29.8564	1.86239	0.931196	+	0.364520i	$0.118767\pi$
$258$	7.60770	0.473634
$259$	37.8564	2.35228
$260$	−3.46410	−0.214834
$261$	−0.535898	−0.0331713
$262$	−28.0526	−1.73309
$263$	−2.19615	−0.135421	−0.0677103	−	0.997705i	$-0.521569\pi$
$263$	−2.19615	−0.135421	−0.0677103	+	0.997705i	$0.521569\pi$
$264$	−4.39230	−0.270328
$265$	−0.928203	−0.0570191
$266$	−44.7846	−2.74592
$267$	−31.7128	−1.94079
$268$	−2.00000	−0.122169
$269$	−29.7128	−1.81162	−0.905811	−	0.423682i	$-0.860737\pi$
$269$	−29.7128	−1.81162	−0.905811	+	0.423682i	$0.860737\pi$
$270$	6.92820	0.421637
$271$	−7.12436	−0.432774	−0.216387	−	0.976308i	$-0.569427\pi$
$271$	−7.12436	−0.432774	−0.216387	+	0.976308i	$0.569427\pi$
$272$	−17.3205	−1.05021
$273$	−32.7846	−1.98421
$274$	−20.5359	−1.24062
$275$	−1.26795	−0.0764602
$276$	−17.8564	−1.07483
$277$	−4.92820	−0.296107	−0.148054	−	0.988979i	$-0.547301\pi$
$277$	−4.92820	−0.296107	−0.148054	+	0.988979i	$0.547301\pi$
$278$	−22.9808	−1.37829
$279$	5.26795	0.315384
$280$	8.19615	0.489814
$281$	10.3923	0.619953	0.309976	−	0.950744i	$-0.399679\pi$
$281$	10.3923	0.619953	0.309976	+	0.950744i	$0.399679\pi$
$282$	11.3205	0.674126
$283$	−30.3923	−1.80663	−0.903317	−	0.428973i	$-0.858876\pi$
$283$	−30.3923	−1.80663	−0.903317	+	0.428973i	$0.858876\pi$
$284$	8.00000	0.474713
$285$	10.9282	0.647331
$286$	−7.60770	−0.449852
$287$	6.92820	0.408959
$288$	5.19615	0.306186
$289$	−5.00000	−0.294118
$290$	0.928203	0.0545060
$291$	−5.85641	−0.343309
$292$	−1.00000	−0.0585206
$293$	−11.0718	−0.646821	−0.323411	−	0.946259i	$-0.604830\pi$
$293$	−11.0718	−0.646821	−0.323411	+	0.946259i	$0.604830\pi$
$294$	−53.3205	−3.10972
$295$	−1.26795	−0.0738229
$296$	13.8564	0.805387
$297$	5.07180	0.294295
$298$	−28.3923	−1.64472
$299$	30.9282	1.78862
$300$	2.00000	0.115470
$301$	−10.3923	−0.599002
$302$	33.1244	1.90609
$303$	−28.7846	−1.65363
$304$	−27.3205	−1.56694
$305$	−2.53590	−0.145205
$306$	−6.00000	−0.342997
$307$	1.41154	0.0805610	0.0402805	−	0.999188i	$-0.487175\pi$
$307$	1.41154	0.0805610	0.0402805	+	0.999188i	$0.487175\pi$
$308$	−6.00000	−0.341882
$309$	7.32051	0.416449
$310$	−9.12436	−0.518229
$311$	13.4641	0.763479	0.381740	−	0.924270i	$-0.375325\pi$
$311$	13.4641	0.763479	0.381740	+	0.924270i	$0.375325\pi$
$312$	−12.0000	−0.679366
$313$	−13.6077	−0.769152	−0.384576	−	0.923093i	$-0.625652\pi$
$313$	−13.6077	−0.769152	−0.384576	+	0.923093i	$0.625652\pi$
$314$	12.9282	0.729581
$315$	4.73205	0.266621
$316$	−13.4641	−0.757415
$317$	7.85641	0.441260	0.220630	−	0.975358i	$-0.429189\pi$
$317$	7.85641	0.441260	0.220630	+	0.975358i	$0.429189\pi$
$318$	3.21539	0.180310
$319$	0.679492	0.0380442
$320$	1.00000	0.0559017
$321$	−6.53590	−0.364798
$322$	73.1769	4.07799
$323$	18.9282	1.05319
$324$	−11.0000	−0.611111
$325$	−3.46410	−0.192154
$326$	−15.1244	−0.837661
$327$	39.7128	2.19612
$328$	2.53590	0.140022
$329$	−15.4641	−0.852564
$330$	4.39230	0.241788
$331$	11.5167	0.633013	0.316506	−	0.948590i	$-0.397490\pi$
$331$	11.5167	0.633013	0.316506	+	0.948590i	$0.397490\pi$
$332$	−7.66025	−0.420411
$333$	8.00000	0.438397
$334$	34.0526	1.86327
$335$	−2.00000	−0.109272
$336$	−47.3205	−2.58155
$337$	−20.2487	−1.10302	−0.551509	−	0.834169i	$-0.685948\pi$
$337$	−20.2487	−1.10302	−0.551509	+	0.834169i	$0.685948\pi$
$338$	1.73205	0.0942111
$339$	−33.8564	−1.83883
$340$	3.46410	0.187867
$341$	−6.67949	−0.361715
$342$	−9.46410	−0.511760
$343$	39.7128	2.14429
$344$	−3.80385	−0.205090
$345$	−17.8564	−0.961357
$346$	17.3205	0.931156
$347$	2.39230	0.128426	0.0642128	−	0.997936i	$-0.479546\pi$
$347$	2.39230	0.128426	0.0642128	+	0.997936i	$0.479546\pi$
$348$	−1.07180	−0.0574543
$349$	−27.3205	−1.46243	−0.731217	−	0.682145i	$-0.761047\pi$
$349$	−27.3205	−1.46243	−0.731217	+	0.682145i	$0.761047\pi$
$350$	−8.19615	−0.438103
$351$	13.8564	0.739600
$352$	−6.58846	−0.351166
$353$	−13.0718	−0.695742	−0.347871	−	0.937542i	$-0.613095\pi$
$353$	−13.0718	−0.695742	−0.347871	+	0.937542i	$0.613095\pi$
$354$	4.39230	0.233448
$355$	8.00000	0.424596
$356$	−15.8564	−0.840388
$357$	32.7846	1.73515
$358$	−20.4449	−1.08054
$359$	5.46410	0.288384	0.144192	−	0.989550i	$-0.453942\pi$
$359$	5.46410	0.288384	0.144192	+	0.989550i	$0.453942\pi$
$360$	1.73205	0.0912871
$361$	10.8564	0.571390
$362$	−2.53590	−0.133284
$363$	−18.7846	−0.985936
$364$	−16.3923	−0.859190
$365$	−1.00000	−0.0523424
$366$	8.78461	0.459179
$367$	13.3205	0.695325	0.347662	−	0.937620i	$-0.386976\pi$
$367$	13.3205	0.695325	0.347662	+	0.937620i	$0.386976\pi$
$368$	44.6410	2.32707
$369$	1.46410	0.0762181
$370$	−13.8564	−0.720360
$371$	−4.39230	−0.228037
$372$	10.5359	0.546261
$373$	10.7846	0.558406	0.279203	−	0.960232i	$-0.409930\pi$
$373$	10.7846	0.558406	0.279203	+	0.960232i	$0.409930\pi$
$374$	7.60770	0.393385
$375$	2.00000	0.103280
$376$	−5.66025	−0.291905
$377$	1.85641	0.0956098
$378$	32.7846	1.68626
$379$	37.3731	1.91973	0.959863	−	0.280470i	$-0.0904904\pi$
$379$	37.3731	1.91973	0.959863	+	0.280470i	$0.0904904\pi$
$380$	5.46410	0.280302
$381$	−25.8564	−1.32466
$382$	−34.9808	−1.78977
$383$	29.3205	1.49821	0.749104	−	0.662452i	$-0.230484\pi$
$383$	29.3205	1.49821	0.749104	+	0.662452i	$0.230484\pi$
$384$	−24.2487	−1.23744
$385$	−6.00000	−0.305788
$386$	32.5359	1.65603
$387$	−2.19615	−0.111637
$388$	−2.92820	−0.148657
$389$	0.392305	0.0198906	0.00994532	−	0.999951i	$-0.496834\pi$
$389$	0.392305	0.0198906	0.00994532	+	0.999951i	$0.496834\pi$
$390$	12.0000	0.607644
$391$	−30.9282	−1.56411
$392$	26.6603	1.34655
$393$	32.3923	1.63398
$394$	31.8564	1.60490
$395$	−13.4641	−0.677452
$396$	−1.26795	−0.0637168
$397$	0.928203	0.0465852	0.0232926	−	0.999729i	$-0.492585\pi$
$397$	0.928203	0.0465852	0.0232926	+	0.999729i	$0.492585\pi$
$398$	−4.05256	−0.203136
$399$	51.7128	2.58888
$400$	−5.00000	−0.250000
$401$	18.5359	0.925639	0.462819	−	0.886453i	$-0.346838\pi$
$401$	18.5359	0.925639	0.462819	+	0.886453i	$0.346838\pi$
$402$	6.92820	0.345547
$403$	−18.2487	−0.909033
$404$	−14.3923	−0.716044
$405$	−11.0000	−0.546594
$406$	4.39230	0.217986
$407$	−10.1436	−0.502799
$408$	12.0000	0.594089
$409$	−30.3923	−1.50280	−0.751401	−	0.659845i	$-0.770622\pi$
$409$	−30.3923	−1.50280	−0.751401	+	0.659845i	$0.770622\pi$
$410$	−2.53590	−0.125239
$411$	23.7128	1.16967
$412$	3.66025	0.180328
$413$	−6.00000	−0.295241
$414$	15.4641	0.760019
$415$	−7.66025	−0.376027
$416$	−18.0000	−0.882523
$417$	26.5359	1.29947
$418$	12.0000	0.586939
$419$	−2.53590	−0.123887	−0.0619434	−	0.998080i	$-0.519730\pi$
$419$	−2.53590	−0.123887	−0.0619434	+	0.998080i	$0.519730\pi$
$420$	9.46410	0.461801
$421$	−2.00000	−0.0974740	−0.0487370	−	0.998812i	$-0.515520\pi$
$421$	−2.00000	−0.0974740	−0.0487370	+	0.998812i	$0.515520\pi$
$422$	−25.8564	−1.25867
$423$	−3.26795	−0.158893
$424$	−1.60770	−0.0780766
$425$	3.46410	0.168034
$426$	−27.7128	−1.34269
$427$	−12.0000	−0.580721
$428$	−3.26795	−0.157962
$429$	8.78461	0.424125
$430$	3.80385	0.183438
$431$	15.1244	0.728515	0.364257	−	0.931298i	$-0.381323\pi$
$431$	15.1244	0.728515	0.364257	+	0.931298i	$0.381323\pi$
$432$	20.0000	0.962250
$433$	−19.4641	−0.935385	−0.467693	−	0.883891i	$-0.654915\pi$
$433$	−19.4641	−0.935385	−0.467693	+	0.883891i	$0.654915\pi$
$434$	−43.1769	−2.07256
$435$	−1.07180	−0.0513887
$436$	19.8564	0.950949
$437$	−48.7846	−2.33368
$438$	3.46410	0.165521
$439$	−20.0000	−0.954548	−0.477274	−	0.878755i	$-0.658375\pi$
$439$	−20.0000	−0.954548	−0.477274	+	0.878755i	$0.658375\pi$
$440$	−2.19615	−0.104697
$441$	15.3923	0.732967
$442$	20.7846	0.988623
$443$	27.2679	1.29554	0.647770	−	0.761836i	$-0.275702\pi$
$443$	27.2679	1.29554	0.647770	+	0.761836i	$0.275702\pi$
$444$	16.0000	0.759326
$445$	−15.8564	−0.751666
$446$	−7.85641	−0.372012
$447$	32.7846	1.55066
$448$	4.73205	0.223568
$449$	10.3923	0.490443	0.245222	−	0.969467i	$-0.421139\pi$
$449$	10.3923	0.490443	0.245222	+	0.969467i	$0.421139\pi$
$450$	−1.73205	−0.0816497
$451$	−1.85641	−0.0874148
$452$	−16.9282	−0.796236
$453$	−38.2487	−1.79708
$454$	−30.0000	−1.40797
$455$	−16.3923	−0.768483
$456$	18.9282	0.886394
$457$	8.00000	0.374224	0.187112	−	0.982339i	$-0.440087\pi$
$457$	8.00000	0.374224	0.187112	+	0.982339i	$0.440087\pi$
$458$	−6.00000	−0.280362
$459$	−13.8564	−0.646762
$460$	−8.92820	−0.416280
$461$	−7.07180	−0.329366	−0.164683	−	0.986347i	$-0.552660\pi$
$461$	−7.07180	−0.329366	−0.164683	+	0.986347i	$0.552660\pi$
$462$	20.7846	0.966988
$463$	−25.7128	−1.19498	−0.597488	−	0.801878i	$-0.703834\pi$
$463$	−25.7128	−1.19498	−0.597488	+	0.801878i	$0.703834\pi$
$464$	2.67949	0.124392
$465$	10.5359	0.488591
$466$	−46.3923	−2.14908
$467$	1.41154	0.0653184	0.0326592	−	0.999467i	$-0.489602\pi$
$467$	1.41154	0.0653184	0.0326592	+	0.999467i	$0.489602\pi$
$468$	−3.46410	−0.160128
$469$	−9.46410	−0.437012
$470$	5.66025	0.261088
$471$	−14.9282	−0.687855
$472$	−2.19615	−0.101086
$473$	2.78461	0.128036
$474$	46.6410	2.14229
$475$	5.46410	0.250710
$476$	16.3923	0.751340
$477$	−0.928203	−0.0424995
$478$	29.9090	1.36800
$479$	28.7846	1.31520	0.657601	−	0.753366i	$-0.271571\pi$
$479$	28.7846	1.31520	0.657601	+	0.753366i	$0.271571\pi$
$480$	10.3923	0.474342
$481$	−27.7128	−1.26360
$482$	−30.0000	−1.36646
$483$	−84.4974	−3.84477
$484$	−9.39230	−0.426923
$485$	−2.92820	−0.132963
$486$	17.3205	0.785674
$487$	−11.8564	−0.537265	−0.268633	−	0.963243i	$-0.586572\pi$
$487$	−11.8564	−0.537265	−0.268633	+	0.963243i	$0.586572\pi$
$488$	−4.39230	−0.198830
$489$	17.4641	0.789754
$490$	−26.6603	−1.20439
$491$	26.0526	1.17574	0.587868	−	0.808957i	$-0.299968\pi$
$491$	26.0526	1.17574	0.587868	+	0.808957i	$0.299968\pi$
$492$	2.92820	0.132014
$493$	−1.85641	−0.0836083
$494$	32.7846	1.47505
$495$	−1.26795	−0.0569901
$496$	−26.3397	−1.18269
$497$	37.8564	1.69809
$498$	26.5359	1.18910
$499$	14.5359	0.650716	0.325358	−	0.945591i	$-0.394515\pi$
$499$	14.5359	0.650716	0.325358	+	0.945591i	$0.394515\pi$
$500$	1.00000	0.0447214
$501$	−39.3205	−1.75671
$502$	18.9282	0.844807
$503$	−16.2487	−0.724494	−0.362247	−	0.932082i	$-0.617990\pi$
$503$	−16.2487	−0.724494	−0.362247	+	0.932082i	$0.617990\pi$
$504$	8.19615	0.365086
$505$	−14.3923	−0.640449
$506$	−19.6077	−0.871668
$507$	−2.00000	−0.0888231
$508$	−12.9282	−0.573596
$509$	26.5359	1.17618	0.588092	−	0.808794i	$-0.299879\pi$
$509$	26.5359	1.17618	0.588092	+	0.808794i	$0.299879\pi$
$510$	−12.0000	−0.531369
$511$	−4.73205	−0.209334
$512$	−8.66025	−0.382733
$513$	−21.8564	−0.964984
$514$	−51.7128	−2.28095
$515$	3.66025	0.161290
$516$	−4.39230	−0.193360
$517$	4.14359	0.182235
$518$	−65.5692	−2.88095
$519$	−20.0000	−0.877903
$520$	−6.00000	−0.263117
$521$	40.6410	1.78052	0.890258	−	0.455457i	$-0.150524\pi$
$521$	40.6410	1.78052	0.890258	+	0.455457i	$0.150524\pi$
$522$	0.928203	0.0406264
$523$	42.7846	1.87084	0.935420	−	0.353538i	$-0.115021\pi$
$523$	42.7846	1.87084	0.935420	+	0.353538i	$0.115021\pi$
$524$	16.1962	0.707532
$525$	9.46410	0.413047
$526$	3.80385	0.165856
$527$	18.2487	0.794926
$528$	12.6795	0.551804
$529$	56.7128	2.46577
$530$	1.60770	0.0698338
$531$	−1.26795	−0.0550243
$532$	25.8564	1.12102
$533$	−5.07180	−0.219684
$534$	54.9282	2.37698
$535$	−3.26795	−0.141286
$536$	−3.46410	−0.149626
$537$	23.6077	1.01875
$538$	51.4641	2.21877
$539$	−19.5167	−0.840642
$540$	−4.00000	−0.172133
$541$	−8.24871	−0.354640	−0.177320	−	0.984153i	$-0.556743\pi$
$541$	−8.24871	−0.354640	−0.177320	+	0.984153i	$0.556743\pi$
$542$	12.3397	0.530037
$543$	2.92820	0.125661
$544$	18.0000	0.771744
$545$	19.8564	0.850555
$546$	56.7846	2.43016
$547$	2.39230	0.102288	0.0511438	−	0.998691i	$-0.483713\pi$
$547$	2.39230	0.102288	0.0511438	+	0.998691i	$0.483713\pi$
$548$	11.8564	0.506481
$549$	−2.53590	−0.108230
$550$	2.19615	0.0936443
$551$	−2.92820	−0.124746
$552$	−30.9282	−1.31639
$553$	−63.7128	−2.70934
$554$	8.53590	0.362656
$555$	16.0000	0.679162
$556$	13.2679	0.562686
$557$	0.928203	0.0393292	0.0196646	−	0.999807i	$-0.493740\pi$
$557$	0.928203	0.0393292	0.0196646	+	0.999807i	$0.493740\pi$
$558$	−9.12436	−0.386265
$559$	7.60770	0.321771
$560$	−23.6603	−0.999828
$561$	−8.78461	−0.370887
$562$	−18.0000	−0.759284
$563$	17.1244	0.721706	0.360853	−	0.932623i	$-0.382486\pi$
$563$	17.1244	0.721706	0.360853	+	0.932623i	$0.382486\pi$
$564$	−6.53590	−0.275211
$565$	−16.9282	−0.712175
$566$	52.6410	2.21267
$567$	−52.0526	−2.18600
$568$	13.8564	0.581402
$569$	32.2487	1.35194	0.675968	−	0.736931i	$-0.263726\pi$
$569$	32.2487	1.35194	0.675968	+	0.736931i	$0.263726\pi$
$570$	−18.9282	−0.792815
$571$	7.41154	0.310163	0.155082	−	0.987902i	$-0.450436\pi$
$571$	7.41154	0.310163	0.155082	+	0.987902i	$0.450436\pi$
$572$	4.39230	0.183651
$573$	40.3923	1.68741
$574$	−12.0000	−0.500870
$575$	−8.92820	−0.372332
$576$	1.00000	0.0416667
$577$	39.1769	1.63096	0.815478	−	0.578788i	$-0.196474\pi$
$577$	39.1769	1.63096	0.815478	+	0.578788i	$0.196474\pi$
$578$	8.66025	0.360219
$579$	−37.5692	−1.56132
$580$	−0.535898	−0.0222520
$581$	−36.2487	−1.50385
$582$	10.1436	0.420465
$583$	1.17691	0.0487428
$584$	−1.73205	−0.0716728
$585$	−3.46410	−0.143223
$586$	19.1769	0.792191
$587$	12.9282	0.533604	0.266802	−	0.963751i	$-0.414033\pi$
$587$	12.9282	0.533604	0.266802	+	0.963751i	$0.414033\pi$
$588$	30.7846	1.26954
$589$	28.7846	1.18605
$590$	2.19615	0.0904142
$591$	−36.7846	−1.51312
$592$	−40.0000	−1.64399
$593$	−14.9282	−0.613028	−0.306514	−	0.951866i	$-0.599163\pi$
$593$	−14.9282	−0.613028	−0.306514	+	0.951866i	$0.599163\pi$
$594$	−8.78461	−0.360437
$595$	16.3923	0.672019
$596$	16.3923	0.671455
$597$	4.67949	0.191519
$598$	−53.5692	−2.19061
$599$	−14.0526	−0.574172	−0.287086	−	0.957905i	$-0.592687\pi$
$599$	−14.0526	−0.574172	−0.287086	+	0.957905i	$0.592687\pi$
$600$	3.46410	0.141421
$601$	−31.1769	−1.27173	−0.635866	−	0.771799i	$-0.719357\pi$
$601$	−31.1769	−1.27173	−0.635866	+	0.771799i	$0.719357\pi$
$602$	18.0000	0.733625
$603$	−2.00000	−0.0814463
$604$	−19.1244	−0.778159
$605$	−9.39230	−0.381851
$606$	49.8564	2.02528
$607$	11.0718	0.449390	0.224695	−	0.974429i	$-0.427861\pi$
$607$	11.0718	0.449390	0.224695	+	0.974429i	$0.427861\pi$
$608$	28.3923	1.15146
$609$	−5.07180	−0.205520
$610$	4.39230	0.177839
$611$	11.3205	0.457979
$612$	3.46410	0.140028
$613$	−22.3923	−0.904417	−0.452208	−	0.891912i	$-0.649364\pi$
$613$	−22.3923	−0.904417	−0.452208	+	0.891912i	$0.649364\pi$
$614$	−2.44486	−0.0986667
$615$	2.92820	0.118077
$616$	−10.3923	−0.418718
$617$	−32.6410	−1.31408	−0.657039	−	0.753857i	$-0.728191\pi$
$617$	−32.6410	−1.31408	−0.657039	+	0.753857i	$0.728191\pi$
$618$	−12.6795	−0.510044
$619$	−31.3205	−1.25888	−0.629439	−	0.777050i	$-0.716715\pi$
$619$	−31.3205	−1.25888	−0.629439	+	0.777050i	$0.716715\pi$
$620$	5.26795	0.211566
$621$	35.7128	1.43311
$622$	−23.3205	−0.935067
$623$	−75.0333	−3.00615
$624$	34.6410	1.38675
$625$	1.00000	0.0400000
$626$	23.5692	0.942015
$627$	−13.8564	−0.553372
$628$	−7.46410	−0.297850
$629$	27.7128	1.10498
$630$	−8.19615	−0.326543
$631$	37.3731	1.48780	0.743899	−	0.668292i	$-0.232974\pi$
$631$	37.3731	1.48780	0.743899	+	0.668292i	$0.232974\pi$
$632$	−23.3205	−0.927640
$633$	29.8564	1.18669
$634$	−13.6077	−0.540431
$635$	−12.9282	−0.513040
$636$	−1.85641	−0.0736113
$637$	−53.3205	−2.11264
$638$	−1.17691	−0.0465945
$639$	8.00000	0.316475
$640$	−12.1244	−0.479257
$641$	−0.679492	−0.0268383	−0.0134192	−	0.999910i	$-0.504272\pi$
$641$	−0.679492	−0.0268383	−0.0134192	+	0.999910i	$0.504272\pi$
$642$	11.3205	0.446785
$643$	38.5885	1.52178	0.760890	−	0.648881i	$-0.224763\pi$
$643$	38.5885	1.52178	0.760890	+	0.648881i	$0.224763\pi$
$644$	−42.2487	−1.66483
$645$	−4.39230	−0.172947
$646$	−32.7846	−1.28989
$647$	1.41154	0.0554935	0.0277467	−	0.999615i	$-0.491167\pi$
$647$	1.41154	0.0554935	0.0277467	+	0.999615i	$0.491167\pi$
$648$	−19.0526	−0.748455
$649$	1.60770	0.0631076
$650$	6.00000	0.235339
$651$	49.8564	1.95403
$652$	8.73205	0.341974
$653$	−16.1436	−0.631748	−0.315874	−	0.948801i	$-0.602298\pi$
$653$	−16.1436	−0.631748	−0.315874	+	0.948801i	$0.602298\pi$
$654$	−68.7846	−2.68969
$655$	16.1962	0.632836
$656$	−7.32051	−0.285818
$657$	−1.00000	−0.0390137
$658$	26.7846	1.04417
$659$	36.0000	1.40236	0.701180	−	0.712984i	$-0.252657\pi$
$659$	36.0000	1.40236	0.701180	+	0.712984i	$0.252657\pi$
$660$	−2.53590	−0.0987097
$661$	41.7128	1.62244	0.811220	−	0.584741i	$-0.198804\pi$
$661$	41.7128	1.62244	0.811220	+	0.584741i	$0.198804\pi$
$662$	−19.9474	−0.775279
$663$	−24.0000	−0.932083
$664$	−13.2679	−0.514896
$665$	25.8564	1.00267
$666$	−13.8564	−0.536925
$667$	4.78461	0.185261
$668$	−19.6603	−0.760678
$669$	9.07180	0.350736
$670$	3.46410	0.133830
$671$	3.21539	0.124129
$672$	49.1769	1.89704
$673$	16.9282	0.652534	0.326267	−	0.945278i	$-0.394209\pi$
$673$	16.9282	0.652534	0.326267	+	0.945278i	$0.394209\pi$
$674$	35.0718	1.35092
$675$	−4.00000	−0.153960
$676$	−1.00000	−0.0384615
$677$	19.4641	0.748066	0.374033	−	0.927415i	$-0.377975\pi$
$677$	19.4641	0.748066	0.374033	+	0.927415i	$0.377975\pi$
$678$	58.6410	2.25209
$679$	−13.8564	−0.531760
$680$	6.00000	0.230089
$681$	34.6410	1.32745
$682$	11.5692	0.443008
$683$	16.7321	0.640234	0.320117	−	0.947378i	$-0.396278\pi$
$683$	16.7321	0.640234	0.320117	+	0.947378i	$0.396278\pi$
$684$	5.46410	0.208925
$685$	11.8564	0.453010
$686$	−68.7846	−2.62621
$687$	6.92820	0.264327
$688$	10.9808	0.418638
$689$	3.21539	0.122497
$690$	30.9282	1.17742
$691$	20.8756	0.794147	0.397073	−	0.917787i	$-0.370026\pi$
$691$	20.8756	0.794147	0.397073	+	0.917787i	$0.370026\pi$
$692$	−10.0000	−0.380143
$693$	−6.00000	−0.227921
$694$	−4.14359	−0.157289
$695$	13.2679	0.503282
$696$	−1.85641	−0.0703669
$697$	5.07180	0.192108
$698$	47.3205	1.79111
$699$	53.5692	2.02617
$700$	4.73205	0.178855
$701$	1.21539	0.0459047	0.0229523	−	0.999737i	$-0.492693\pi$
$701$	1.21539	0.0459047	0.0229523	+	0.999737i	$0.492693\pi$
$702$	−24.0000	−0.905822
$703$	43.7128	1.64866
$704$	−1.26795	−0.0477876
$705$	−6.53590	−0.246156
$706$	22.6410	0.852106
$707$	−68.1051	−2.56136
$708$	−2.53590	−0.0953049
$709$	−19.4641	−0.730990	−0.365495	−	0.930813i	$-0.619100\pi$
$709$	−19.4641	−0.730990	−0.365495	+	0.930813i	$0.619100\pi$
$710$	−13.8564	−0.520022
$711$	−13.4641	−0.504943
$712$	−27.4641	−1.02926
$713$	−47.0333	−1.76141
$714$	−56.7846	−2.12511
$715$	4.39230	0.164263
$716$	11.8038	0.441130
$717$	−34.5359	−1.28977
$718$	−9.46410	−0.353197
$719$	−21.2679	−0.793161	−0.396580	−	0.918000i	$-0.629803\pi$
$719$	−21.2679	−0.793161	−0.396580	+	0.918000i	$0.629803\pi$
$720$	−5.00000	−0.186339
$721$	17.3205	0.645049
$722$	−18.8038	−0.699807
$723$	34.6410	1.28831
$724$	1.46410	0.0544129
$725$	−0.535898	−0.0199028
$726$	32.5359	1.20752
$727$	−21.7128	−0.805284	−0.402642	−	0.915358i	$-0.631908\pi$
$727$	−21.7128	−0.805284	−0.402642	+	0.915358i	$0.631908\pi$
$728$	−28.3923	−1.05229
$729$	13.0000	0.481481
$730$	1.73205	0.0641061
$731$	−7.60770	−0.281381
$732$	−5.07180	−0.187459
$733$	−22.7846	−0.841569	−0.420784	−	0.907161i	$-0.638245\pi$
$733$	−22.7846	−0.841569	−0.420784	+	0.907161i	$0.638245\pi$
$734$	−23.0718	−0.851596
$735$	30.7846	1.13551
$736$	−46.3923	−1.71004
$737$	2.53590	0.0934110
$738$	−2.53590	−0.0933477
$739$	−6.14359	−0.225996	−0.112998	−	0.993595i	$-0.536045\pi$
$739$	−6.14359	−0.225996	−0.112998	+	0.993595i	$0.536045\pi$
$740$	8.00000	0.294086
$741$	−37.8564	−1.39069
$742$	7.60770	0.279287
$743$	33.9090	1.24400	0.622000	−	0.783018i	$-0.286321\pi$
$743$	33.9090	1.24400	0.622000	+	0.783018i	$0.286321\pi$
$744$	18.2487	0.669030
$745$	16.3923	0.600568
$746$	−18.6795	−0.683905
$747$	−7.66025	−0.280274
$748$	−4.39230	−0.160599
$749$	−15.4641	−0.565046
$750$	−3.46410	−0.126491
$751$	43.1244	1.57363	0.786815	−	0.617189i	$-0.211729\pi$
$751$	43.1244	1.57363	0.786815	+	0.617189i	$0.211729\pi$
$752$	16.3397	0.595849
$753$	−21.8564	−0.796492
$754$	−3.21539	−0.117098
$755$	−19.1244	−0.696007
$756$	−18.9282	−0.688412
$757$	−15.0718	−0.547794	−0.273897	−	0.961759i	$-0.588313\pi$
$757$	−15.0718	−0.547794	−0.273897	+	0.961759i	$0.588313\pi$
$758$	−64.7321	−2.35117
$759$	22.6410	0.821817
$760$	9.46410	0.343299
$761$	−18.0000	−0.652499	−0.326250	−	0.945284i	$-0.605785\pi$
$761$	−18.0000	−0.652499	−0.326250	+	0.945284i	$0.605785\pi$
$762$	44.7846	1.62238
$763$	93.9615	3.40164
$764$	20.1962	0.730671
$765$	3.46410	0.125245
$766$	−50.7846	−1.83492
$767$	4.39230	0.158597
$768$	38.0000	1.37121
$769$	51.5692	1.85963	0.929817	−	0.368023i	$-0.119965\pi$
$769$	51.5692	1.85963	0.929817	+	0.368023i	$0.119965\pi$
$770$	10.3923	0.374513
$771$	59.7128	2.15050
$772$	−18.7846	−0.676073
$773$	2.78461	0.100155	0.0500777	−	0.998745i	$-0.484053\pi$
$773$	2.78461	0.100155	0.0500777	+	0.998745i	$0.484053\pi$
$774$	3.80385	0.136726
$775$	5.26795	0.189230
$776$	−5.07180	−0.182067
$777$	75.7128	2.71618
$778$	−0.679492	−0.0243610
$779$	8.00000	0.286630
$780$	−6.92820	−0.248069
$781$	−10.1436	−0.362966
$782$	53.5692	1.91563
$783$	2.14359	0.0766058
$784$	−76.9615	−2.74863
$785$	−7.46410	−0.266405
$786$	−56.1051	−2.00120
$787$	13.3205	0.474825	0.237412	−	0.971409i	$-0.423701\pi$
$787$	13.3205	0.474825	0.237412	+	0.971409i	$0.423701\pi$
$788$	−18.3923	−0.655199
$789$	−4.39230	−0.156370
$790$	23.3205	0.829706
$791$	−80.1051	−2.84821
$792$	−2.19615	−0.0780369
$793$	8.78461	0.311951
$794$	−1.60770	−0.0570550
$795$	−1.85641	−0.0658400
$796$	2.33975	0.0829301
$797$	−29.5692	−1.04740	−0.523698	−	0.851904i	$-0.675448\pi$
$797$	−29.5692	−1.04740	−0.523698	+	0.851904i	$0.675448\pi$
$798$	−89.5692	−3.17072
$799$	−11.3205	−0.400491
$800$	5.19615	0.183712
$801$	−15.8564	−0.560259
$802$	−32.1051	−1.13367
$803$	1.26795	0.0447450
$804$	−4.00000	−0.141069
$805$	−42.2487	−1.48907
$806$	31.6077	1.11333
$807$	−59.4256	−2.09188
$808$	−24.9282	−0.876971
$809$	30.5359	1.07359	0.536793	−	0.843714i	$-0.319636\pi$
$809$	30.5359	1.07359	0.536793	+	0.843714i	$0.319636\pi$
$810$	19.0526	0.669439
$811$	−23.7128	−0.832669	−0.416335	−	0.909211i	$-0.636686\pi$
$811$	−23.7128	−0.832669	−0.416335	+	0.909211i	$0.636686\pi$
$812$	−2.53590	−0.0889926
$813$	−14.2487	−0.499724
$814$	17.5692	0.615801
$815$	8.73205	0.305870
$816$	−34.6410	−1.21268
$817$	−12.0000	−0.419827
$818$	52.6410	1.84055
$819$	−16.3923	−0.572793
$820$	1.46410	0.0511286
$821$	−30.0000	−1.04701	−0.523504	−	0.852023i	$-0.675375\pi$
$821$	−30.0000	−1.04701	−0.523504	+	0.852023i	$0.675375\pi$
$822$	−41.0718	−1.43254
$823$	38.5885	1.34511	0.672555	−	0.740048i	$-0.265197\pi$
$823$	38.5885	1.34511	0.672555	+	0.740048i	$0.265197\pi$
$824$	6.33975	0.220856
$825$	−2.53590	−0.0882886
$826$	10.3923	0.361595
$827$	−22.0000	−0.765015	−0.382507	−	0.923952i	$-0.624939\pi$
$827$	−22.0000	−0.765015	−0.382507	+	0.923952i	$0.624939\pi$
$828$	−8.92820	−0.310277
$829$	13.7128	0.476266	0.238133	−	0.971233i	$-0.423465\pi$
$829$	13.7128	0.476266	0.238133	+	0.971233i	$0.423465\pi$
$830$	13.2679	0.460537
$831$	−9.85641	−0.341915
$832$	−3.46410	−0.120096
$833$	53.3205	1.84745
$834$	−45.9615	−1.59152
$835$	−19.6603	−0.680371
$836$	−6.92820	−0.239617
$837$	−21.0718	−0.728348
$838$	4.39230	0.151730
$839$	−16.7846	−0.579469	−0.289735	−	0.957107i	$-0.593567\pi$
$839$	−16.7846	−0.579469	−0.289735	+	0.957107i	$0.593567\pi$
$840$	16.3923	0.565588
$841$	−28.7128	−0.990097
$842$	3.46410	0.119381
$843$	20.7846	0.715860
$844$	14.9282	0.513850
$845$	−1.00000	−0.0344010
$846$	5.66025	0.194604
$847$	−44.4449	−1.52714
$848$	4.64102	0.159373
$849$	−60.7846	−2.08612
$850$	−6.00000	−0.205798
$851$	−71.4256	−2.44844
$852$	16.0000	0.548151
$853$	24.1436	0.826661	0.413330	−	0.910581i	$-0.364365\pi$
$853$	24.1436	0.826661	0.413330	+	0.910581i	$0.364365\pi$
$854$	20.7846	0.711235
$855$	5.46410	0.186868
$856$	−5.66025	−0.193464
$857$	−26.7846	−0.914945	−0.457472	−	0.889224i	$-0.651245\pi$
$857$	−26.7846	−0.914945	−0.457472	+	0.889224i	$0.651245\pi$
$858$	−15.2154	−0.519445
$859$	−8.58846	−0.293034	−0.146517	−	0.989208i	$-0.546806\pi$
$859$	−8.58846	−0.293034	−0.146517	+	0.989208i	$0.546806\pi$
$860$	−2.19615	−0.0748882
$861$	13.8564	0.472225
$862$	−26.1962	−0.892244
$863$	−15.6603	−0.533081	−0.266541	−	0.963824i	$-0.585881\pi$
$863$	−15.6603	−0.533081	−0.266541	+	0.963824i	$0.585881\pi$
$864$	−20.7846	−0.707107
$865$	−10.0000	−0.340010
$866$	33.7128	1.14561
$867$	−10.0000	−0.339618
$868$	24.9282	0.846118
$869$	17.0718	0.579121
$870$	1.85641	0.0629381
$871$	6.92820	0.234753
$872$	34.3923	1.16467
$873$	−2.92820	−0.0991047
$874$	84.4974	2.85817
$875$	4.73205	0.159973
$876$	−2.00000	−0.0675737
$877$	56.7846	1.91748	0.958740	−	0.284284i	$-0.0917560\pi$
$877$	56.7846	1.91748	0.958740	+	0.284284i	$0.0917560\pi$
$878$	34.6410	1.16908
$879$	−22.1436	−0.746885
$880$	6.33975	0.213713
$881$	29.6077	0.997509	0.498754	−	0.866743i	$-0.333791\pi$
$881$	29.6077	0.997509	0.498754	+	0.866743i	$0.333791\pi$
$882$	−26.6603	−0.897697
$883$	−56.8372	−1.91272	−0.956362	−	0.292186i	$-0.905617\pi$
$883$	−56.8372	−1.91272	−0.956362	+	0.292186i	$0.905617\pi$
$884$	−12.0000	−0.403604
$885$	−2.53590	−0.0852433
$886$	−47.2295	−1.58671
$887$	−24.7321	−0.830421	−0.415210	−	0.909725i	$-0.636292\pi$
$887$	−24.7321	−0.830421	−0.415210	+	0.909725i	$0.636292\pi$
$888$	27.7128	0.929981
$889$	−61.1769	−2.05181
$890$	27.4641	0.920599
$891$	13.9474	0.467257
$892$	4.53590	0.151873
$893$	−17.8564	−0.597542
$894$	−56.7846	−1.89916
$895$	11.8038	0.394559
$896$	−57.3731	−1.91670
$897$	61.8564	2.06533
$898$	−18.0000	−0.600668
$899$	−2.82309	−0.0941552
$900$	1.00000	0.0333333
$901$	−3.21539	−0.107120
$902$	3.21539	0.107061
$903$	−20.7846	−0.691669
$904$	−29.3205	−0.975186
$905$	1.46410	0.0486684
$906$	66.2487	2.20097
$907$	50.5885	1.67976	0.839881	−	0.542770i	$-0.182625\pi$
$907$	50.5885	1.67976	0.839881	+	0.542770i	$0.182625\pi$
$908$	17.3205	0.574801
$909$	−14.3923	−0.477363
$910$	28.3923	0.941196
$911$	−2.24871	−0.0745031	−0.0372516	−	0.999306i	$-0.511860\pi$
$911$	−2.24871	−0.0745031	−0.0372516	+	0.999306i	$0.511860\pi$
$912$	−54.6410	−1.80934
$913$	9.71281	0.321447
$914$	−13.8564	−0.458329
$915$	−5.07180	−0.167668
$916$	3.46410	0.114457
$917$	76.6410	2.53091
$918$	24.0000	0.792118
$919$	−30.7321	−1.01376	−0.506878	−	0.862018i	$-0.669201\pi$
$919$	−30.7321	−1.01376	−0.506878	+	0.862018i	$0.669201\pi$
$920$	−15.4641	−0.509836
$921$	2.82309	0.0930238
$922$	12.2487	0.403390
$923$	−27.7128	−0.912178
$924$	−12.0000	−0.394771
$925$	8.00000	0.263038
$926$	44.5359	1.46354
$927$	3.66025	0.120219
$928$	−2.78461	−0.0914093
$929$	−48.2487	−1.58299	−0.791494	−	0.611176i	$-0.790697\pi$
$929$	−48.2487	−1.58299	−0.791494	+	0.611176i	$0.790697\pi$
$930$	−18.2487	−0.598399
$931$	84.1051	2.75643
$932$	26.7846	0.877359
$933$	26.9282	0.881590
$934$	−2.44486	−0.0799984
$935$	−4.39230	−0.143644
$936$	−6.00000	−0.196116
$937$	16.0000	0.522697	0.261349	−	0.965244i	$-0.415833\pi$
$937$	16.0000	0.522697	0.261349	+	0.965244i	$0.415833\pi$
$938$	16.3923	0.535228
$939$	−27.2154	−0.888141
$940$	−3.26795	−0.106589
$941$	23.6077	0.769589	0.384794	−	0.923002i	$-0.374272\pi$
$941$	23.6077	0.769589	0.384794	+	0.923002i	$0.374272\pi$
$942$	25.8564	0.842447
$943$	−13.0718	−0.425676
$944$	6.33975	0.206341
$945$	−18.9282	−0.615734
$946$	−4.82309	−0.156812
$947$	−4.53590	−0.147397	−0.0736984	−	0.997281i	$-0.523480\pi$
$947$	−4.53590	−0.147397	−0.0736984	+	0.997281i	$0.523480\pi$
$948$	−26.9282	−0.874587
$949$	3.46410	0.112449
$950$	−9.46410	−0.307056
$951$	15.7128	0.509523
$952$	28.3923	0.920200
$953$	17.0718	0.553010	0.276505	−	0.961013i	$-0.410824\pi$
$953$	17.0718	0.553010	0.276505	+	0.961013i	$0.410824\pi$
$954$	1.60770	0.0520511
$955$	20.1962	0.653532
$956$	−17.2679	−0.558485
$957$	1.35898	0.0439297
$958$	−49.8564	−1.61079
$959$	56.1051	1.81173
$960$	2.00000	0.0645497
$961$	−3.24871	−0.104797
$962$	48.0000	1.54758
$963$	−3.26795	−0.105308
$964$	17.3205	0.557856
$965$	−18.7846	−0.604698
$966$	146.354	4.70886
$967$	−52.5359	−1.68944	−0.844720	−	0.535208i	$-0.820233\pi$
$967$	−52.5359	−1.68944	−0.844720	+	0.535208i	$0.820233\pi$
$968$	−16.2679	−0.522872
$969$	37.8564	1.21612
$970$	5.07180	0.162846
$971$	12.5885	0.403983	0.201991	−	0.979387i	$-0.435259\pi$
$971$	12.5885	0.403983	0.201991	+	0.979387i	$0.435259\pi$
$972$	−10.0000	−0.320750
$973$	62.7846	2.01278
$974$	20.5359	0.658013
$975$	−6.92820	−0.221880
$976$	12.6795	0.405861
$977$	−24.9282	−0.797524	−0.398762	−	0.917054i	$-0.630560\pi$
$977$	−24.9282	−0.797524	−0.398762	+	0.917054i	$0.630560\pi$
$978$	−30.2487	−0.967247
$979$	20.1051	0.642562
$980$	15.3923	0.491689
$981$	19.8564	0.633966
$982$	−45.1244	−1.43998
$983$	−15.2679	−0.486972	−0.243486	−	0.969904i	$-0.578291\pi$
$983$	−15.2679	−0.486972	−0.243486	+	0.969904i	$0.578291\pi$
$984$	5.07180	0.161683
$985$	−18.3923	−0.586028
$986$	3.21539	0.102399
$987$	−30.9282	−0.984456
$988$	−18.9282	−0.602186
$989$	19.6077	0.623488
$990$	2.19615	0.0697983
$991$	8.98076	0.285283	0.142642	−	0.989774i	$-0.454440\pi$
$991$	8.98076	0.285283	0.142642	+	0.989774i	$0.454440\pi$
$992$	27.3731	0.869096
$993$	23.0333	0.730940
$994$	−65.5692	−2.07973
$995$	2.33975	0.0741749
$996$	−15.3205	−0.485449
$997$	1.07180	0.0339441	0.0169721	−	0.999856i	$-0.494597\pi$
$997$	1.07180	0.0339441	0.0169721	+	0.999856i	$0.494597\pi$
$998$	−25.1769	−0.796961
$999$	−32.0000	−1.01244

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	365.2.a.a.1.1	✓	2
3.2	odd	2		3285.2.a.c.1.2		2
4.3	odd	2		5840.2.a.n.1.1		2
5.4	even	2		1825.2.a.c.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
365.2.a.a.1.1	✓	2	1.1	even	1	trivial
1825.2.a.c.1.2		2	5.4	even	2
3285.2.a.c.1.2		2	3.2	odd	2
5840.2.a.n.1.1		2	4.3	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:	\( N \)	\(=\)	\( 365 = 5 \cdot 73 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	365.a (trivial)

\(f(q)\)	\(=\)	\(q-1.73205 q^{2} +2.00000 q^{3} +1.00000 q^{4} +1.00000 q^{5} -3.46410 q^{6} +4.73205 q^{7} +1.73205 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.73205 q^{2} +2.00000 q^{3} +1.00000 q^{4} +1.00000 q^{5} -3.46410 q^{6} +4.73205 q^{7} +1.73205 q^{8} +1.00000 q^{9} -1.73205 q^{10} -1.26795 q^{11} +2.00000 q^{12} -3.46410 q^{13} -8.19615 q^{14} +2.00000 q^{15} -5.00000 q^{16} +3.46410 q^{17} -1.73205 q^{18} +5.46410 q^{19} +1.00000 q^{20} +9.46410 q^{21} +2.19615 q^{22} -8.92820 q^{23} +3.46410 q^{24} +1.00000 q^{25} +6.00000 q^{26} -4.00000 q^{27} +4.73205 q^{28} -0.535898 q^{29} -3.46410 q^{30} +5.26795 q^{31} +5.19615 q^{32} -2.53590 q^{33} -6.00000 q^{34} +4.73205 q^{35} +1.00000 q^{36} +8.00000 q^{37} -9.46410 q^{38} -6.92820 q^{39} +1.73205 q^{40} +1.46410 q^{41} -16.3923 q^{42} -2.19615 q^{43} -1.26795 q^{44} +1.00000 q^{45} +15.4641 q^{46} -3.26795 q^{47} -10.0000 q^{48} +15.3923 q^{49} -1.73205 q^{50} +6.92820 q^{51} -3.46410 q^{52} -0.928203 q^{53} +6.92820 q^{54} -1.26795 q^{55} +8.19615 q^{56} +10.9282 q^{57} +0.928203 q^{58} -1.26795 q^{59} +2.00000 q^{60} -2.53590 q^{61} -9.12436 q^{62} +4.73205 q^{63} +1.00000 q^{64} -3.46410 q^{65} +4.39230 q^{66} -2.00000 q^{67} +3.46410 q^{68} -17.8564 q^{69} -8.19615 q^{70} +8.00000 q^{71} +1.73205 q^{72} -1.00000 q^{73} -13.8564 q^{74} +2.00000 q^{75} +5.46410 q^{76} -6.00000 q^{77} +12.0000 q^{78} -13.4641 q^{79} -5.00000 q^{80} -11.0000 q^{81} -2.53590 q^{82} -7.66025 q^{83} +9.46410 q^{84} +3.46410 q^{85} +3.80385 q^{86} -1.07180 q^{87} -2.19615 q^{88} -15.8564 q^{89} -1.73205 q^{90} -16.3923 q^{91} -8.92820 q^{92} +10.5359 q^{93} +5.66025 q^{94} +5.46410 q^{95} +10.3923 q^{96} -2.92820 q^{97} -26.6603 q^{98} -1.26795 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 4 q^{3} + 2 q^{4} + 2 q^{5} + 6 q^{7} + 2 q^{9}+O(q^{10}) \) 2 * q + 4 * q^3 + 2 * q^4 + 2 * q^5 + 6 * q^7 + 2 * q^9	\( 2 q + 4 q^{3} + 2 q^{4} + 2 q^{5} + 6 q^{7} + 2 q^{9} - 6 q^{11} + 4 q^{12} - 6 q^{14} + 4 q^{15} - 10 q^{16} + 4 q^{19} + 2 q^{20} + 12 q^{21} - 6 q^{22} - 4 q^{23} + 2 q^{25} + 12 q^{26} - 8 q^{27} + 6 q^{28} - 8 q^{29} + 14 q^{31} - 12 q^{33} - 12 q^{34} + 6 q^{35} + 2 q^{36} + 16 q^{37} - 12 q^{38} - 4 q^{41} - 12 q^{42} + 6 q^{43} - 6 q^{44} + 2 q^{45} + 24 q^{46} - 10 q^{47} - 20 q^{48} + 10 q^{49} + 12 q^{53} - 6 q^{55} + 6 q^{56} + 8 q^{57} - 12 q^{58} - 6 q^{59} + 4 q^{60} - 12 q^{61} + 6 q^{62} + 6 q^{63} + 2 q^{64} - 12 q^{66} - 4 q^{67} - 8 q^{69} - 6 q^{70} + 16 q^{71} - 2 q^{73} + 4 q^{75} + 4 q^{76} - 12 q^{77} + 24 q^{78} - 20 q^{79} - 10 q^{80} - 22 q^{81} - 12 q^{82} + 2 q^{83} + 12 q^{84} + 18 q^{86} - 16 q^{87} + 6 q^{88} - 4 q^{89} - 12 q^{91} - 4 q^{92} + 28 q^{93} - 6 q^{94} + 4 q^{95} + 8 q^{97} - 36 q^{98} - 6 q^{99}+O(q^{100}) \) 2 * q + 4 * q^3 + 2 * q^4 + 2 * q^5 + 6 * q^7 + 2 * q^9 - 6 * q^11 + 4 * q^12 - 6 * q^14 + 4 * q^15 - 10 * q^16 + 4 * q^19 + 2 * q^20 + 12 * q^21 - 6 * q^22 - 4 * q^23 + 2 * q^25 + 12 * q^26 - 8 * q^27 + 6 * q^28 - 8 * q^29 + 14 * q^31 - 12 * q^33 - 12 * q^34 + 6 * q^35 + 2 * q^36 + 16 * q^37 - 12 * q^38 - 4 * q^41 - 12 * q^42 + 6 * q^43 - 6 * q^44 + 2 * q^45 + 24 * q^46 - 10 * q^47 - 20 * q^48 + 10 * q^49 + 12 * q^53 - 6 * q^55 + 6 * q^56 + 8 * q^57 - 12 * q^58 - 6 * q^59 + 4 * q^60 - 12 * q^61 + 6 * q^62 + 6 * q^63 + 2 * q^64 - 12 * q^66 - 4 * q^67 - 8 * q^69 - 6 * q^70 + 16 * q^71 - 2 * q^73 + 4 * q^75 + 4 * q^76 - 12 * q^77 + 24 * q^78 - 20 * q^79 - 10 * q^80 - 22 * q^81 - 12 * q^82 + 2 * q^83 + 12 * q^84 + 18 * q^86 - 16 * q^87 + 6 * q^88 - 4 * q^89 - 12 * q^91 - 4 * q^92 + 28 * q^93 - 6 * q^94 + 4 * q^95 + 8 * q^97 - 36 * q^98 - 6 * q^99

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