LMFDB - Embedded newform 2415.2.a.r.1.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2415,2,Mod(1,2415)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2415, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("2415.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2415 = 3 \cdot 5 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2415.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:	$19.2838720881$
Analytic rank:	$0$
Dimension:	$7$
Coefficient field:	$\mathbb{Q}[x]/(x^{7} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{7} - 2x^{6} - 9x^{5} + 16x^{4} + 20x^{3} - 29x^{2} - 12x + 9 $ x^7 - 2x^6 - 9x^5 + 16x^4 + 20x^3 - 29x^2 - 12x + 9
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.7
Root			$-2.40232$ of defining polynomial
Character	$\chi$	$=$	2415.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.40232 q^{2} +1.00000 q^{3} +3.77112 q^{4} -1.00000 q^{5} +2.40232 q^{6} -1.00000 q^{7} +4.25479 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+2.40232 q^{2} +1.00000 q^{3} +3.77112 q^{4} -1.00000 q^{5} +2.40232 q^{6} -1.00000 q^{7} +4.25479 q^{8} +1.00000 q^{9} -2.40232 q^{10} +2.12689 q^{11} +3.77112 q^{12} +2.58030 q^{13} -2.40232 q^{14} -1.00000 q^{15} +2.67910 q^{16} +2.79674 q^{17} +2.40232 q^{18} +6.41156 q^{19} -3.77112 q^{20} -1.00000 q^{21} +5.10946 q^{22} -1.00000 q^{23} +4.25479 q^{24} +1.00000 q^{25} +6.19870 q^{26} +1.00000 q^{27} -3.77112 q^{28} -5.89901 q^{29} -2.40232 q^{30} -4.23494 q^{31} -2.07353 q^{32} +2.12689 q^{33} +6.71866 q^{34} +1.00000 q^{35} +3.77112 q^{36} +9.81630 q^{37} +15.4026 q^{38} +2.58030 q^{39} -4.25479 q^{40} +11.8343 q^{41} -2.40232 q^{42} +3.96371 q^{43} +8.02076 q^{44} -1.00000 q^{45} -2.40232 q^{46} -8.94014 q^{47} +2.67910 q^{48} +1.00000 q^{49} +2.40232 q^{50} +2.79674 q^{51} +9.73063 q^{52} -7.63284 q^{53} +2.40232 q^{54} -2.12689 q^{55} -4.25479 q^{56} +6.41156 q^{57} -14.1713 q^{58} +0.422750 q^{59} -3.77112 q^{60} -6.69576 q^{61} -10.1737 q^{62} -1.00000 q^{63} -10.3395 q^{64} -2.58030 q^{65} +5.10946 q^{66} -3.05253 q^{67} +10.5469 q^{68} -1.00000 q^{69} +2.40232 q^{70} -11.4898 q^{71} +4.25479 q^{72} -3.17533 q^{73} +23.5819 q^{74} +1.00000 q^{75} +24.1788 q^{76} -2.12689 q^{77} +6.19870 q^{78} -2.35726 q^{79} -2.67910 q^{80} +1.00000 q^{81} +28.4298 q^{82} +14.1911 q^{83} -3.77112 q^{84} -2.79674 q^{85} +9.52208 q^{86} -5.89901 q^{87} +9.04947 q^{88} +8.92411 q^{89} -2.40232 q^{90} -2.58030 q^{91} -3.77112 q^{92} -4.23494 q^{93} -21.4770 q^{94} -6.41156 q^{95} -2.07353 q^{96} +0.838594 q^{97} +2.40232 q^{98} +2.12689 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 7 q - 2 q^{2} + 7 q^{3} + 8 q^{4} - 7 q^{5} - 2 q^{6} - 7 q^{7} - 6 q^{8} + 7 q^{9}+O(q^{10}) $ 7 * q - 2 * q^2 + 7 * q^3 + 8 * q^4 - 7 * q^5 - 2 * q^6 - 7 * q^7 - 6 * q^8 + 7 * q^9	\( 7 q - 2 q^{2} + 7 q^{3} + 8 q^{4} - 7 q^{5} - 2 q^{6} - 7 q^{7} - 6 q^{8} + 7 q^{9} + 2 q^{10} - 2 q^{11} + 8 q^{12} + 6 q^{13} + 2 q^{14} - 7 q^{15} + 10 q^{16} + 14 q^{17} - 2 q^{18} + 6 q^{19} - 8 q^{20} - 7 q^{21} + 28 q^{22} - 7 q^{23} - 6 q^{24} + 7 q^{25} + 5 q^{26} + 7 q^{27} - 8 q^{28} - 4 q^{29} + 2 q^{30} + 4 q^{31} - 19 q^{32} - 2 q^{33} - 7 q^{34} + 7 q^{35} + 8 q^{36} + 18 q^{37} + 22 q^{38} + 6 q^{39} + 6 q^{40} + 10 q^{41} + 2 q^{42} + 26 q^{43} - 29 q^{44} - 7 q^{45} + 2 q^{46} - 4 q^{47} + 10 q^{48} + 7 q^{49} - 2 q^{50} + 14 q^{51} + 18 q^{52} + 2 q^{53} - 2 q^{54} + 2 q^{55} + 6 q^{56} + 6 q^{57} + 12 q^{58} + 6 q^{59} - 8 q^{60} - 4 q^{61} + 4 q^{62} - 7 q^{63} + 38 q^{64} - 6 q^{65} + 28 q^{66} + 22 q^{67} + 52 q^{68} - 7 q^{69} - 2 q^{70} - 8 q^{71} - 6 q^{72} + 24 q^{73} + 17 q^{74} + 7 q^{75} + 15 q^{76} + 2 q^{77} + 5 q^{78} + 2 q^{79} - 10 q^{80} + 7 q^{81} - 10 q^{82} + 26 q^{83} - 8 q^{84} - 14 q^{85} - 22 q^{86} - 4 q^{87} + 79 q^{88} + 22 q^{89} + 2 q^{90} - 6 q^{91} - 8 q^{92} + 4 q^{93} + 14 q^{94} - 6 q^{95} - 19 q^{96} + 44 q^{97} - 2 q^{98} - 2 q^{99}+O(q^{100}) \) 7 * q - 2 * q^2 + 7 * q^3 + 8 * q^4 - 7 * q^5 - 2 * q^6 - 7 * q^7 - 6 * q^8 + 7 * q^9 + 2 * q^10 - 2 * q^11 + 8 * q^12 + 6 * q^13 + 2 * q^14 - 7 * q^15 + 10 * q^16 + 14 * q^17 - 2 * q^18 + 6 * q^19 - 8 * q^20 - 7 * q^21 + 28 * q^22 - 7 * q^23 - 6 * q^24 + 7 * q^25 + 5 * q^26 + 7 * q^27 - 8 * q^28 - 4 * q^29 + 2 * q^30 + 4 * q^31 - 19 * q^32 - 2 * q^33 - 7 * q^34 + 7 * q^35 + 8 * q^36 + 18 * q^37 + 22 * q^38 + 6 * q^39 + 6 * q^40 + 10 * q^41 + 2 * q^42 + 26 * q^43 - 29 * q^44 - 7 * q^45 + 2 * q^46 - 4 * q^47 + 10 * q^48 + 7 * q^49 - 2 * q^50 + 14 * q^51 + 18 * q^52 + 2 * q^53 - 2 * q^54 + 2 * q^55 + 6 * q^56 + 6 * q^57 + 12 * q^58 + 6 * q^59 - 8 * q^60 - 4 * q^61 + 4 * q^62 - 7 * q^63 + 38 * q^64 - 6 * q^65 + 28 * q^66 + 22 * q^67 + 52 * q^68 - 7 * q^69 - 2 * q^70 - 8 * q^71 - 6 * q^72 + 24 * q^73 + 17 * q^74 + 7 * q^75 + 15 * q^76 + 2 * q^77 + 5 * q^78 + 2 * q^79 - 10 * q^80 + 7 * q^81 - 10 * q^82 + 26 * q^83 - 8 * q^84 - 14 * q^85 - 22 * q^86 - 4 * q^87 + 79 * q^88 + 22 * q^89 + 2 * q^90 - 6 * q^91 - 8 * q^92 + 4 * q^93 + 14 * q^94 - 6 * q^95 - 19 * q^96 + 44 * q^97 - 2 * q^98 - 2 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	2.40232	1.69869	0.849347	−	0.527835i	$-0.176996\pi$
$2$	2.40232	1.69869	0.849347	+	0.527835i	$0.176996\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	3.77112	1.88556
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	2.40232	0.980741
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	4.25479	1.50429
$9$	1.00000	0.333333
$10$	−2.40232	−0.759679
$11$	2.12689	0.641282	0.320641	−	0.947201i	$-0.396102\pi$
$11$	2.12689	0.641282	0.320641	+	0.947201i	$0.396102\pi$
$12$	3.77112	1.08863
$13$	2.58030	0.715647	0.357824	−	0.933789i	$-0.383519\pi$
$13$	2.58030	0.715647	0.357824	+	0.933789i	$0.383519\pi$
$14$	−2.40232	−0.642046
$15$	−1.00000	−0.258199
$16$	2.67910	0.669775
$17$	2.79674	0.678310	0.339155	−	0.940730i	$-0.389859\pi$
$17$	2.79674	0.678310	0.339155	+	0.940730i	$0.389859\pi$
$18$	2.40232	0.566231
$19$	6.41156	1.47091	0.735457	−	0.677572i	$-0.236968\pi$
$19$	6.41156	1.47091	0.735457	+	0.677572i	$0.236968\pi$
$20$	−3.77112	−0.843248
$21$	−1.00000	−0.218218
$22$	5.10946	1.08934
$23$	−1.00000	−0.208514
$23$	−1.00000	−0.208514
$24$	4.25479	0.868505
$25$	1.00000	0.200000
$26$	6.19870	1.21567
$27$	1.00000	0.192450
$28$	−3.77112	−0.712674
$29$	−5.89901	−1.09542	−0.547710	−	0.836668i	$-0.684500\pi$
$29$	−5.89901	−1.09542	−0.547710	+	0.836668i	$0.684500\pi$
$30$	−2.40232	−0.438601
$31$	−4.23494	−0.760617	−0.380308	−	0.924860i	$-0.624182\pi$
$31$	−4.23494	−0.760617	−0.380308	+	0.924860i	$0.624182\pi$
$32$	−2.07353	−0.366552
$33$	2.12689	0.370244
$34$	6.71866	1.15224
$35$	1.00000	0.169031
$36$	3.77112	0.628520
$37$	9.81630	1.61379	0.806895	−	0.590695i	$-0.201146\pi$
$37$	9.81630	1.61379	0.806895	+	0.590695i	$0.201146\pi$
$38$	15.4026	2.49863
$39$	2.58030	0.413179
$40$	−4.25479	−0.672741
$41$	11.8343	1.84821	0.924105	−	0.382138i	$-0.124812\pi$
$41$	11.8343	1.84821	0.924105	+	0.382138i	$0.124812\pi$
$42$	−2.40232	−0.370685
$43$	3.96371	0.604460	0.302230	−	0.953235i	$-0.402269\pi$
$43$	3.96371	0.604460	0.302230	+	0.953235i	$0.402269\pi$
$44$	8.02076	1.20918
$45$	−1.00000	−0.149071
$46$	−2.40232	−0.354202
$47$	−8.94014	−1.30405	−0.652027	−	0.758196i	$-0.726081\pi$
$47$	−8.94014	−1.30405	−0.652027	+	0.758196i	$0.726081\pi$
$48$	2.67910	0.386695
$49$	1.00000	0.142857
$50$	2.40232	0.339739
$51$	2.79674	0.391623
$52$	9.73063	1.34940
$53$	−7.63284	−1.04845	−0.524225	−	0.851580i	$-0.675645\pi$
$53$	−7.63284	−1.04845	−0.524225	+	0.851580i	$0.675645\pi$
$54$	2.40232	0.326914
$55$	−2.12689	−0.286790
$56$	−4.25479	−0.568570
$57$	6.41156	0.849232
$58$	−14.1713	−1.86078
$59$	0.422750	0.0550373	0.0275187	−	0.999621i	$-0.491239\pi$
$59$	0.422750	0.0550373	0.0275187	+	0.999621i	$0.491239\pi$
$60$	−3.77112	−0.486849
$61$	−6.69576	−0.857304	−0.428652	−	0.903470i	$-0.641011\pi$
$61$	−6.69576	−0.857304	−0.428652	+	0.903470i	$0.641011\pi$
$62$	−10.1737	−1.29205
$63$	−1.00000	−0.125988
$64$	−10.3395	−1.29243
$65$	−2.58030	−0.320047
$66$	5.10946	0.628932
$67$	−3.05253	−0.372926	−0.186463	−	0.982462i	$-0.559703\pi$
$67$	−3.05253	−0.372926	−0.186463	+	0.982462i	$0.559703\pi$
$68$	10.5469	1.27899
$69$	−1.00000	−0.120386
$70$	2.40232	0.287132
$71$	−11.4898	−1.36359	−0.681793	−	0.731545i	$-0.738800\pi$
$71$	−11.4898	−1.36359	−0.681793	+	0.731545i	$0.738800\pi$
$72$	4.25479	0.501431
$73$	−3.17533	−0.371644	−0.185822	−	0.982583i	$-0.559495\pi$
$73$	−3.17533	−0.371644	−0.185822	+	0.982583i	$0.559495\pi$
$74$	23.5819	2.74133
$75$	1.00000	0.115470
$76$	24.1788	2.77349
$77$	−2.12689	−0.242382
$78$	6.19870	0.701865
$79$	−2.35726	−0.265212	−0.132606	−	0.991169i	$-0.542334\pi$
$79$	−2.35726	−0.265212	−0.132606	+	0.991169i	$0.542334\pi$
$80$	−2.67910	−0.299532
$81$	1.00000	0.111111
$82$	28.4298	3.13954
$83$	14.1911	1.55768	0.778838	−	0.627226i	$-0.215810\pi$
$83$	14.1911	1.55768	0.778838	+	0.627226i	$0.215810\pi$
$84$	−3.77112	−0.411463
$85$	−2.79674	−0.303350
$86$	9.52208	1.02679
$87$	−5.89901	−0.632441
$88$	9.04947	0.964677
$89$	8.92411	0.945954	0.472977	−	0.881075i	$-0.343179\pi$
$89$	8.92411	0.945954	0.472977	+	0.881075i	$0.343179\pi$
$90$	−2.40232	−0.253226
$91$	−2.58030	−0.270489
$92$	−3.77112	−0.393166
$93$	−4.23494	−0.439142
$94$	−21.4770	−2.21519
$95$	−6.41156	−0.657812
$96$	−2.07353	−0.211629
$97$	0.838594	0.0851463	0.0425731	−	0.999093i	$-0.486444\pi$
$97$	0.838594	0.0851463	0.0425731	+	0.999093i	$0.486444\pi$
$98$	2.40232	0.242670
$99$	2.12689	0.213761
$100$	3.77112	0.377112
$101$	12.5202	1.24580	0.622902	−	0.782300i	$-0.285953\pi$
$101$	12.5202	1.24580	0.622902	+	0.782300i	$0.285953\pi$
$102$	6.71866	0.665247
$103$	−1.96876	−0.193988	−0.0969938	−	0.995285i	$-0.530923\pi$
$103$	−1.96876	−0.193988	−0.0969938	+	0.995285i	$0.530923\pi$
$104$	10.9786	1.07654
$105$	1.00000	0.0975900
$106$	−18.3365	−1.78100
$107$	1.51658	0.146614	0.0733068	−	0.997309i	$-0.476645\pi$
$107$	1.51658	0.146614	0.0733068	+	0.997309i	$0.476645\pi$
$108$	3.77112	0.362876
$109$	−2.55851	−0.245061	−0.122530	−	0.992465i	$-0.539101\pi$
$109$	−2.55851	−0.245061	−0.122530	+	0.992465i	$0.539101\pi$
$110$	−5.10946	−0.487168
$111$	9.81630	0.931722
$112$	−2.67910	−0.253151
$113$	−15.2421	−1.43386	−0.716928	−	0.697147i	$-0.754452\pi$
$113$	−15.2421	−1.43386	−0.716928	+	0.697147i	$0.754452\pi$
$114$	15.4026	1.44259
$115$	1.00000	0.0932505
$116$	−22.2459	−2.06548
$117$	2.58030	0.238549
$118$	1.01558	0.0934915
$119$	−2.79674	−0.256377
$120$	−4.25479	−0.388407
$121$	−6.47633	−0.588758
$122$	−16.0853	−1.45630
$123$	11.8343	1.06706
$124$	−15.9704	−1.43419
$125$	−1.00000	−0.0894427
$126$	−2.40232	−0.214015
$127$	−2.30473	−0.204511	−0.102256	−	0.994758i	$-0.532606\pi$
$127$	−2.30473	−0.204511	−0.102256	+	0.994758i	$0.532606\pi$
$128$	−20.6916	−1.82890
$129$	3.96371	0.348985
$130$	−6.19870	−0.543662
$131$	−11.2149	−0.979852	−0.489926	−	0.871764i	$-0.662976\pi$
$131$	−11.2149	−0.979852	−0.489926	+	0.871764i	$0.662976\pi$
$132$	8.02076	0.698118
$133$	−6.41156	−0.555953
$134$	−7.33315	−0.633488
$135$	−1.00000	−0.0860663
$136$	11.8995	1.02038
$137$	−8.19366	−0.700032	−0.350016	−	0.936744i	$-0.613824\pi$
$137$	−8.19366	−0.700032	−0.350016	+	0.936744i	$0.613824\pi$
$138$	−2.40232	−0.204499
$139$	−9.46741	−0.803015	−0.401508	−	0.915856i	$-0.631514\pi$
$139$	−9.46741	−0.803015	−0.401508	+	0.915856i	$0.631514\pi$
$140$	3.77112	0.318718
$141$	−8.94014	−0.752896
$142$	−27.6021	−2.31631
$143$	5.48802	0.458932
$144$	2.67910	0.223258
$145$	5.89901	0.489886
$146$	−7.62814	−0.631310
$147$	1.00000	0.0824786
$148$	37.0184	3.04290
$149$	−17.5225	−1.43550	−0.717750	−	0.696300i	$-0.754828\pi$
$149$	−17.5225	−1.43550	−0.717750	+	0.696300i	$0.754828\pi$
$150$	2.40232	0.196148
$151$	10.5644	0.859715	0.429858	−	0.902897i	$-0.358564\pi$
$151$	10.5644	0.859715	0.429858	+	0.902897i	$0.358564\pi$
$152$	27.2798	2.21269
$153$	2.79674	0.226103
$154$	−5.10946	−0.411732
$155$	4.23494	0.340158
$156$	9.73063	0.779074
$157$	11.2756	0.899889	0.449945	−	0.893056i	$-0.351444\pi$
$157$	11.2756	0.899889	0.449945	+	0.893056i	$0.351444\pi$
$158$	−5.66287	−0.450514
$159$	−7.63284	−0.605323
$160$	2.07353	0.163927
$161$	1.00000	0.0788110
$162$	2.40232	0.188744
$163$	3.35169	0.262524	0.131262	−	0.991348i	$-0.458097\pi$
$163$	3.35169	0.262524	0.131262	+	0.991348i	$0.458097\pi$
$164$	44.6286	3.48491
$165$	−2.12689	−0.165578
$166$	34.0915	2.64601
$167$	−16.2114	−1.25447	−0.627236	−	0.778829i	$-0.715814\pi$
$167$	−16.2114	−1.25447	−0.627236	+	0.778829i	$0.715814\pi$
$168$	−4.25479	−0.328264
$169$	−6.34204	−0.487849
$170$	−6.71866	−0.515298
$171$	6.41156	0.490304
$172$	14.9476	1.13974
$173$	−3.68257	−0.279981	−0.139990	−	0.990153i	$-0.544707\pi$
$173$	−3.68257	−0.279981	−0.139990	+	0.990153i	$0.544707\pi$
$174$	−14.1713	−1.07432
$175$	−1.00000	−0.0755929
$176$	5.69815	0.429515
$177$	0.422750	0.0317758
$178$	21.4385	1.60689
$179$	−15.6204	−1.16753	−0.583763	−	0.811924i	$-0.698420\pi$
$179$	−15.6204	−1.16753	−0.583763	+	0.811924i	$0.698420\pi$
$180$	−3.77112	−0.281083
$181$	−23.1969	−1.72421	−0.862107	−	0.506726i	$-0.830856\pi$
$181$	−23.1969	−1.72421	−0.862107	+	0.506726i	$0.830856\pi$
$182$	−6.19870	−0.459478
$183$	−6.69576	−0.494965
$184$	−4.25479	−0.313667
$185$	−9.81630	−0.721709
$186$	−10.1737	−0.745968
$187$	5.94837	0.434988
$188$	−33.7143	−2.45887
$189$	−1.00000	−0.0727393
$190$	−15.4026	−1.11742
$191$	−0.798049	−0.0577448	−0.0288724	−	0.999583i	$-0.509192\pi$
$191$	−0.798049	−0.0577448	−0.0288724	+	0.999583i	$0.509192\pi$
$192$	−10.3395	−0.746187
$193$	1.76092	0.126754	0.0633769	−	0.997990i	$-0.479813\pi$
$193$	1.76092	0.126754	0.0633769	+	0.997990i	$0.479813\pi$
$194$	2.01457	0.144637
$195$	−2.58030	−0.184779
$196$	3.77112	0.269366
$197$	3.90280	0.278063	0.139032	−	0.990288i	$-0.455601\pi$
$197$	3.90280	0.278063	0.139032	+	0.990288i	$0.455601\pi$
$198$	5.10946	0.363114
$199$	−1.23399	−0.0874753	−0.0437376	−	0.999043i	$-0.513927\pi$
$199$	−1.23399	−0.0874753	−0.0437376	+	0.999043i	$0.513927\pi$
$200$	4.25479	0.300859
$201$	−3.05253	−0.215309
$202$	30.0774	2.11624
$203$	5.89901	0.414030
$204$	10.5469	0.738428
$205$	−11.8343	−0.826545
$206$	−4.72958	−0.329525
$207$	−1.00000	−0.0695048
$208$	6.91289	0.479323
$209$	13.6367	0.943270
$210$	2.40232	0.165776
$211$	3.80866	0.262199	0.131100	−	0.991369i	$-0.458149\pi$
$211$	3.80866	0.262199	0.131100	+	0.991369i	$0.458149\pi$
$212$	−28.7843	−1.97692
$213$	−11.4898	−0.787267
$214$	3.64331	0.249051
$215$	−3.96371	−0.270323
$216$	4.25479	0.289502
$217$	4.23494	0.287486
$218$	−6.14634	−0.416283
$219$	−3.17533	−0.214569
$220$	−8.02076	−0.540760
$221$	7.21645	0.485431
$222$	23.5819	1.58271
$223$	−25.8392	−1.73032	−0.865161	−	0.501494i	$-0.832784\pi$
$223$	−25.8392	−1.73032	−0.865161	+	0.501494i	$0.832784\pi$
$224$	2.07353	0.138543
$225$	1.00000	0.0666667
$226$	−36.6163	−2.43568
$227$	24.5388	1.62870	0.814348	−	0.580376i	$-0.197095\pi$
$227$	24.5388	1.62870	0.814348	+	0.580376i	$0.197095\pi$
$228$	24.1788	1.60128
$229$	21.6752	1.43234	0.716170	−	0.697926i	$-0.245894\pi$
$229$	21.6752	1.43234	0.716170	+	0.697926i	$0.245894\pi$
$230$	2.40232	0.158404
$231$	−2.12689	−0.139939
$232$	−25.0990	−1.64783
$233$	−19.8630	−1.30127	−0.650633	−	0.759392i	$-0.725496\pi$
$233$	−19.8630	−1.30127	−0.650633	+	0.759392i	$0.725496\pi$
$234$	6.19870	0.405222
$235$	8.94014	0.583190
$236$	1.59424	0.103776
$237$	−2.35726	−0.153120
$238$	−6.71866	−0.435506
$239$	−25.8762	−1.67379	−0.836897	−	0.547360i	$-0.815633\pi$
$239$	−25.8762	−1.67379	−0.836897	+	0.547360i	$0.815633\pi$
$240$	−2.67910	−0.172935
$241$	−4.58279	−0.295203	−0.147602	−	0.989047i	$-0.547155\pi$
$241$	−4.58279	−0.295203	−0.147602	+	0.989047i	$0.547155\pi$
$242$	−15.5582	−1.00012
$243$	1.00000	0.0641500
$244$	−25.2505	−1.61650
$245$	−1.00000	−0.0638877
$246$	28.4298	1.81262
$247$	16.5438	1.05266
$248$	−18.0187	−1.14419
$249$	14.1911	0.899324
$250$	−2.40232	−0.151936
$251$	−2.11145	−0.133274	−0.0666369	−	0.997777i	$-0.521227\pi$
$251$	−2.11145	−0.133274	−0.0666369	+	0.997777i	$0.521227\pi$
$252$	−3.77112	−0.237558
$253$	−2.12689	−0.133717
$254$	−5.53668	−0.347402
$255$	−2.79674	−0.175139
$256$	−29.0288	−1.81430
$257$	22.0318	1.37430	0.687152	−	0.726514i	$-0.258861\pi$
$257$	22.0318	1.37430	0.687152	+	0.726514i	$0.258861\pi$
$258$	9.52208	0.592819
$259$	−9.81630	−0.609955
$260$	−9.73063	−0.603468
$261$	−5.89901	−0.365140
$262$	−26.9418	−1.66447
$263$	3.12690	0.192813	0.0964064	−	0.995342i	$-0.469265\pi$
$263$	3.12690	0.192813	0.0964064	+	0.995342i	$0.469265\pi$
$264$	9.04947	0.556956
$265$	7.63284	0.468881
$266$	−15.4026	−0.944394
$267$	8.92411	0.546147
$268$	−11.5115	−0.703175
$269$	−23.3837	−1.42573	−0.712864	−	0.701302i	$-0.752603\pi$
$269$	−23.3837	−1.42573	−0.712864	+	0.701302i	$0.752603\pi$
$270$	−2.40232	−0.146200
$271$	25.1845	1.52985	0.764924	−	0.644121i	$-0.222777\pi$
$271$	25.1845	1.52985	0.764924	+	0.644121i	$0.222777\pi$
$272$	7.49276	0.454315
$273$	−2.58030	−0.156167
$274$	−19.6838	−1.18914
$275$	2.12689	0.128256
$276$	−3.77112	−0.226995
$277$	21.0119	1.26248	0.631241	−	0.775587i	$-0.282546\pi$
$277$	21.0119	1.26248	0.631241	+	0.775587i	$0.282546\pi$
$278$	−22.7437	−1.36408
$279$	−4.23494	−0.253539
$280$	4.25479	0.254272
$281$	32.3091	1.92740	0.963701	−	0.266986i	$-0.0860276\pi$
$281$	32.3091	1.92740	0.963701	+	0.266986i	$0.0860276\pi$
$282$	−21.4770	−1.27894
$283$	14.7384	0.876107	0.438054	−	0.898949i	$-0.355668\pi$
$283$	14.7384	0.876107	0.438054	+	0.898949i	$0.355668\pi$
$284$	−43.3293	−2.57112
$285$	−6.41156	−0.379788
$286$	13.1840	0.779584
$287$	−11.8343	−0.698558
$288$	−2.07353	−0.122184
$289$	−9.17822	−0.539895
$290$	14.1713	0.832167
$291$	0.838594	0.0491592
$292$	−11.9745	−0.700757
$293$	−22.4710	−1.31277	−0.656385	−	0.754426i	$-0.727915\pi$
$293$	−22.4710	−1.31277	−0.656385	+	0.754426i	$0.727915\pi$
$294$	2.40232	0.140106
$295$	−0.422750	−0.0246134
$296$	41.7663	2.42761
$297$	2.12689	0.123415
$298$	−42.0946	−2.43848
$299$	−2.58030	−0.149223
$300$	3.77112	0.217726
$301$	−3.96371	−0.228464
$302$	25.3789	1.46039
$303$	12.5202	0.719266
$304$	17.1772	0.985181
$305$	6.69576	0.383398
$306$	6.71866	0.384080
$307$	14.2415	0.812808	0.406404	−	0.913693i	$-0.366783\pi$
$307$	14.2415	0.812808	0.406404	+	0.913693i	$0.366783\pi$
$308$	−8.02076	−0.457025
$309$	−1.96876	−0.111999
$310$	10.1737	0.577825
$311$	−14.8788	−0.843700	−0.421850	−	0.906666i	$-0.638619\pi$
$311$	−14.8788	−0.843700	−0.421850	+	0.906666i	$0.638619\pi$
$312$	10.9786	0.621543
$313$	6.49839	0.367311	0.183655	−	0.982991i	$-0.441207\pi$
$313$	6.49839	0.367311	0.183655	+	0.982991i	$0.441207\pi$
$314$	27.0875	1.52864
$315$	1.00000	0.0563436
$316$	−8.88949	−0.500073
$317$	33.9283	1.90560	0.952801	−	0.303596i	$-0.0981875\pi$
$317$	33.9283	1.90560	0.952801	+	0.303596i	$0.0981875\pi$
$318$	−18.3365	−1.02826
$319$	−12.5466	−0.702473
$320$	10.3395	0.577994
$321$	1.51658	0.0846474
$322$	2.40232	0.133876
$323$	17.9315	0.997735
$324$	3.77112	0.209507
$325$	2.58030	0.143129
$326$	8.05181	0.445949
$327$	−2.55851	−0.141486
$328$	50.3525	2.78025
$329$	8.94014	0.492886
$330$	−5.10946	−0.281267
$331$	−9.32250	−0.512411	−0.256205	−	0.966622i	$-0.582472\pi$
$331$	−9.32250	−0.512411	−0.256205	+	0.966622i	$0.582472\pi$
$332$	53.5163	2.93709
$333$	9.81630	0.537930
$334$	−38.9448	−2.13096
$335$	3.05253	0.166778
$336$	−2.67910	−0.146157
$337$	1.20074	0.0654087	0.0327044	−	0.999465i	$-0.489588\pi$
$337$	1.20074	0.0654087	0.0327044	+	0.999465i	$0.489588\pi$
$338$	−15.2356	−0.828706
$339$	−15.2421	−0.827837
$340$	−10.5469	−0.571984
$341$	−9.00725	−0.487770
$342$	15.4026	0.832877
$343$	−1.00000	−0.0539949
$344$	16.8647	0.909285
$345$	1.00000	0.0538382
$346$	−8.84670	−0.475602
$347$	2.65954	0.142772	0.0713859	−	0.997449i	$-0.477258\pi$
$347$	2.65954	0.142772	0.0713859	+	0.997449i	$0.477258\pi$
$348$	−22.2459	−1.19250
$349$	−2.12584	−0.113794	−0.0568969	−	0.998380i	$-0.518121\pi$
$349$	−2.12584	−0.113794	−0.0568969	+	0.998380i	$0.518121\pi$
$350$	−2.40232	−0.128409
$351$	2.58030	0.137726
$352$	−4.41017	−0.235063
$353$	−9.58637	−0.510231	−0.255115	−	0.966911i	$-0.582113\pi$
$353$	−9.58637	−0.510231	−0.255115	+	0.966911i	$0.582113\pi$
$354$	1.01558	0.0539774
$355$	11.4898	0.609814
$356$	33.6539	1.78365
$357$	−2.79674	−0.148019
$358$	−37.5252	−1.98327
$359$	23.5121	1.24092	0.620459	−	0.784239i	$-0.286946\pi$
$359$	23.5121	1.24092	0.620459	+	0.784239i	$0.286946\pi$
$360$	−4.25479	−0.224247
$361$	22.1081	1.16359
$362$	−55.7263	−2.92891
$363$	−6.47633	−0.339919
$364$	−9.73063	−0.510024
$365$	3.17533	0.166204
$366$	−16.0853	−0.840793
$367$	16.8222	0.878110	0.439055	−	0.898460i	$-0.355313\pi$
$367$	16.8222	0.878110	0.439055	+	0.898460i	$0.355313\pi$
$368$	−2.67910	−0.139658
$369$	11.8343	0.616070
$370$	−23.5819	−1.22596
$371$	7.63284	0.396277
$372$	−15.9704	−0.828029
$373$	−12.8904	−0.667437	−0.333719	−	0.942673i	$-0.608304\pi$
$373$	−12.8904	−0.667437	−0.333719	+	0.942673i	$0.608304\pi$
$374$	14.2899	0.738911
$375$	−1.00000	−0.0516398
$376$	−38.0384	−1.96168
$377$	−15.2212	−0.783934
$378$	−2.40232	−0.123562
$379$	−0.188039	−0.00965892	−0.00482946	−	0.999988i	$-0.501537\pi$
$379$	−0.188039	−0.00965892	−0.00482946	+	0.999988i	$0.501537\pi$
$380$	−24.1788	−1.24034
$381$	−2.30473	−0.118075
$382$	−1.91716	−0.0980907
$383$	−20.8450	−1.06513	−0.532566	−	0.846389i	$-0.678772\pi$
$383$	−20.8450	−1.06513	−0.532566	+	0.846389i	$0.678772\pi$
$384$	−20.6916	−1.05591
$385$	2.12689	0.108396
$386$	4.23029	0.215316
$387$	3.96371	0.201487
$388$	3.16244	0.160548
$389$	12.5135	0.634458	0.317229	−	0.948349i	$-0.397248\pi$
$389$	12.5135	0.634458	0.317229	+	0.948349i	$0.397248\pi$
$390$	−6.19870	−0.313883
$391$	−2.79674	−0.141437
$392$	4.25479	0.214899
$393$	−11.2149	−0.565718
$394$	9.37577	0.472344
$395$	2.35726	0.118606
$396$	8.02076	0.403058
$397$	9.36008	0.469769	0.234885	−	0.972023i	$-0.424529\pi$
$397$	9.36008	0.469769	0.234885	+	0.972023i	$0.424529\pi$
$398$	−2.96444	−0.148594
$399$	−6.41156	−0.320980
$400$	2.67910	0.133955
$401$	−4.27500	−0.213483	−0.106742	−	0.994287i	$-0.534042\pi$
$401$	−4.27500	−0.213483	−0.106742	+	0.994287i	$0.534042\pi$
$402$	−7.33315	−0.365744
$403$	−10.9274	−0.544333
$404$	47.2151	2.34904
$405$	−1.00000	−0.0496904
$406$	14.1713	0.703309
$407$	20.8782	1.03489
$408$	11.8995	0.589115
$409$	−18.8417	−0.931664	−0.465832	−	0.884873i	$-0.654245\pi$
$409$	−18.8417	−0.931664	−0.465832	+	0.884873i	$0.654245\pi$
$410$	−28.4298	−1.40405
$411$	−8.19366	−0.404163
$412$	−7.42442	−0.365775
$413$	−0.422750	−0.0208022
$414$	−2.40232	−0.118067
$415$	−14.1911	−0.696613
$416$	−5.35033	−0.262322
$417$	−9.46741	−0.463621
$418$	32.7596	1.60233
$419$	3.92346	0.191674	0.0958368	−	0.995397i	$-0.469447\pi$
$419$	3.92346	0.191674	0.0958368	+	0.995397i	$0.469447\pi$
$420$	3.77112	0.184012
$421$	12.4403	0.606301	0.303151	−	0.952943i	$-0.401961\pi$
$421$	12.4403	0.606301	0.303151	+	0.952943i	$0.401961\pi$
$422$	9.14961	0.445396
$423$	−8.94014	−0.434684
$424$	−32.4761	−1.57718
$425$	2.79674	0.135662
$426$	−27.6021	−1.33732
$427$	6.69576	0.324030
$428$	5.71921	0.276449
$429$	5.48802	0.264964
$430$	−9.52208	−0.459195
$431$	−12.1439	−0.584950	−0.292475	−	0.956273i	$-0.594479\pi$
$431$	−12.1439	−0.584950	−0.292475	+	0.956273i	$0.594479\pi$
$432$	2.67910	0.128898
$433$	−14.3473	−0.689489	−0.344745	−	0.938697i	$-0.612034\pi$
$433$	−14.3473	−0.689489	−0.344745	+	0.938697i	$0.612034\pi$
$434$	10.1737	0.488351
$435$	5.89901	0.282836
$436$	−9.64844	−0.462076
$437$	−6.41156	−0.306707
$438$	−7.62814	−0.364487
$439$	28.5155	1.36097	0.680484	−	0.732763i	$-0.261769\pi$
$439$	28.5155	1.36097	0.680484	+	0.732763i	$0.261769\pi$
$440$	−9.04947	−0.431416
$441$	1.00000	0.0476190
$442$	17.3362	0.824598
$443$	−39.1559	−1.86035	−0.930176	−	0.367113i	$-0.880346\pi$
$443$	−39.1559	−1.86035	−0.930176	+	0.367113i	$0.880346\pi$
$444$	37.0184	1.75682
$445$	−8.92411	−0.423043
$446$	−62.0740	−2.93929
$447$	−17.5225	−0.828787
$448$	10.3395	0.488494
$449$	41.0371	1.93666	0.968330	−	0.249674i	$-0.0803236\pi$
$449$	41.0371	1.93666	0.968330	+	0.249674i	$0.0803236\pi$
$450$	2.40232	0.113246
$451$	25.1703	1.18522
$452$	−57.4798	−2.70362
$453$	10.5644	0.496357
$454$	58.9499	2.76666
$455$	2.58030	0.120966
$456$	27.2798	1.27749
$457$	26.4214	1.23594	0.617971	−	0.786201i	$-0.287955\pi$
$457$	26.4214	1.23594	0.617971	+	0.786201i	$0.287955\pi$
$458$	52.0707	2.43311
$459$	2.79674	0.130541
$460$	3.77112	0.175829
$461$	31.5078	1.46746	0.733732	−	0.679438i	$-0.237777\pi$
$461$	31.5078	1.46746	0.733732	+	0.679438i	$0.237777\pi$
$462$	−5.10946	−0.237714
$463$	−1.90784	−0.0886649	−0.0443325	−	0.999017i	$-0.514116\pi$
$463$	−1.90784	−0.0886649	−0.0443325	+	0.999017i	$0.514116\pi$
$464$	−15.8040	−0.733685
$465$	4.23494	0.196390
$466$	−47.7171	−2.21045
$467$	14.7135	0.680859	0.340429	−	0.940270i	$-0.389428\pi$
$467$	14.7135	0.680859	0.340429	+	0.940270i	$0.389428\pi$
$468$	9.73063	0.449799
$469$	3.05253	0.140953
$470$	21.4770	0.990662
$471$	11.2756	0.519551
$472$	1.79871	0.0827923
$473$	8.43038	0.387629
$474$	−5.66287	−0.260104
$475$	6.41156	0.294183
$476$	−10.5469	−0.483414
$477$	−7.63284	−0.349484
$478$	−62.1629	−2.84326
$479$	−25.2654	−1.15441	−0.577203	−	0.816601i	$-0.695856\pi$
$479$	−25.2654	−1.15441	−0.577203	+	0.816601i	$0.695856\pi$
$480$	2.07353	0.0946432
$481$	25.3290	1.15490
$482$	−11.0093	−0.501460
$483$	1.00000	0.0455016
$484$	−24.4230	−1.11014
$485$	−0.838594	−0.0380786
$486$	2.40232	0.108971
$487$	24.3353	1.10274	0.551369	−	0.834262i	$-0.314106\pi$
$487$	24.3353	1.10274	0.551369	+	0.834262i	$0.314106\pi$
$488$	−28.4890	−1.28964
$489$	3.35169	0.151569
$490$	−2.40232	−0.108526
$491$	42.6066	1.92281	0.961405	−	0.275135i	$-0.0887227\pi$
$491$	42.6066	1.92281	0.961405	+	0.275135i	$0.0887227\pi$
$492$	44.6286	2.01201
$493$	−16.4980	−0.743034
$494$	39.7434	1.78814
$495$	−2.12689	−0.0955967
$496$	−11.3458	−0.509442
$497$	11.4898	0.515387
$498$	34.0915	1.52768
$499$	−14.1695	−0.634312	−0.317156	−	0.948373i	$-0.602728\pi$
$499$	−14.1695	−0.634312	−0.317156	+	0.948373i	$0.602728\pi$
$500$	−3.77112	−0.168650
$501$	−16.2114	−0.724270
$502$	−5.07238	−0.226391
$503$	30.8837	1.37704	0.688519	−	0.725218i	$-0.258261\pi$
$503$	30.8837	1.37704	0.688519	+	0.725218i	$0.258261\pi$
$504$	−4.25479	−0.189523
$505$	−12.5202	−0.557141
$506$	−5.10946	−0.227143
$507$	−6.34204	−0.281660
$508$	−8.69139	−0.385618
$509$	30.7130	1.36133	0.680664	−	0.732596i	$-0.261691\pi$
$509$	30.7130	1.36133	0.680664	+	0.732596i	$0.261691\pi$
$510$	−6.71866	−0.297507
$511$	3.17533	0.140468
$512$	−28.3532	−1.25305
$513$	6.41156	0.283077
$514$	52.9272	2.33452
$515$	1.96876	0.0867539
$516$	14.9476	0.658032
$517$	−19.0147	−0.836266
$518$	−23.5819	−1.03613
$519$	−3.68257	−0.161647
$520$	−10.9786	−0.481445
$521$	−23.0644	−1.01047	−0.505236	−	0.862981i	$-0.668594\pi$
$521$	−23.0644	−1.01047	−0.505236	+	0.862981i	$0.668594\pi$
$522$	−14.1713	−0.620261
$523$	34.9175	1.52683	0.763417	−	0.645906i	$-0.223520\pi$
$523$	34.9175	1.52683	0.763417	+	0.645906i	$0.223520\pi$
$524$	−42.2928	−1.84757
$525$	−1.00000	−0.0436436
$526$	7.51180	0.327530
$527$	−11.8440	−0.515934
$528$	5.69815	0.247980
$529$	1.00000	0.0434783
$530$	18.3365	0.796486
$531$	0.422750	0.0183458
$532$	−24.1788	−1.04828
$533$	30.5361	1.32267
$534$	21.4385	0.927736
$535$	−1.51658	−0.0655676
$536$	−12.9879	−0.560991
$537$	−15.6204	−0.674072
$538$	−56.1750	−2.42188
$539$	2.12689	0.0916117
$540$	−3.77112	−0.162283
$541$	44.5495	1.91533	0.957665	−	0.287884i	$-0.0929518\pi$
$541$	44.5495	1.91533	0.957665	+	0.287884i	$0.0929518\pi$
$542$	60.5010	2.59874
$543$	−23.1969	−0.995476
$544$	−5.79913	−0.248636
$545$	2.55851	0.109594
$546$	−6.19870	−0.265280
$547$	−24.9810	−1.06811	−0.534054	−	0.845450i	$-0.679332\pi$
$547$	−24.9810	−1.06811	−0.534054	+	0.845450i	$0.679332\pi$
$548$	−30.8993	−1.31995
$549$	−6.69576	−0.285768
$550$	5.10946	0.217868
$551$	−37.8219	−1.61127
$552$	−4.25479	−0.181096
$553$	2.35726	0.100241
$554$	50.4772	2.14457
$555$	−9.81630	−0.416679
$556$	−35.7027	−1.51413
$557$	−33.6788	−1.42702	−0.713508	−	0.700647i	$-0.752895\pi$
$557$	−33.6788	−1.42702	−0.713508	+	0.700647i	$0.752895\pi$
$558$	−10.1737	−0.430685
$559$	10.2276	0.432580
$560$	2.67910	0.113213
$561$	5.94837	0.251140
$562$	77.6167	3.27406
$563$	−8.22387	−0.346595	−0.173297	−	0.984870i	$-0.555442\pi$
$563$	−8.22387	−0.346595	−0.173297	+	0.984870i	$0.555442\pi$
$564$	−33.7143	−1.41963
$565$	15.2421	0.641240
$566$	35.4063	1.48824
$567$	−1.00000	−0.0419961
$568$	−48.8866	−2.05123
$569$	−23.4864	−0.984602	−0.492301	−	0.870425i	$-0.663844\pi$
$569$	−23.4864	−0.984602	−0.492301	+	0.870425i	$0.663844\pi$
$570$	−15.4026	−0.645144
$571$	−31.7678	−1.32944	−0.664721	−	0.747092i	$-0.731449\pi$
$571$	−31.7678	−1.32944	−0.664721	+	0.747092i	$0.731449\pi$
$572$	20.6960	0.865343
$573$	−0.798049	−0.0333390
$574$	−28.4298	−1.18664
$575$	−1.00000	−0.0417029
$576$	−10.3395	−0.430811
$577$	−19.8884	−0.827964	−0.413982	−	0.910285i	$-0.635862\pi$
$577$	−19.8884	−0.827964	−0.413982	+	0.910285i	$0.635862\pi$
$578$	−22.0490	−0.917117
$579$	1.76092	0.0731814
$580$	22.2459	0.923710
$581$	−14.1911	−0.588746
$582$	2.01457	0.0835064
$583$	−16.2342	−0.672352
$584$	−13.5103	−0.559062
$585$	−2.58030	−0.106682
$586$	−53.9824	−2.22999
$587$	−12.7073	−0.524486	−0.262243	−	0.965002i	$-0.584462\pi$
$587$	−12.7073	−0.524486	−0.262243	+	0.965002i	$0.584462\pi$
$588$	3.77112	0.155518
$589$	−27.1526	−1.11880
$590$	−1.01558	−0.0418107
$591$	3.90280	0.160540
$592$	26.2989	1.08088
$593$	9.75444	0.400567	0.200283	−	0.979738i	$-0.435814\pi$
$593$	9.75444	0.400567	0.200283	+	0.979738i	$0.435814\pi$
$594$	5.10946	0.209644
$595$	2.79674	0.114655
$596$	−66.0795	−2.70672
$597$	−1.23399	−0.0505039
$598$	−6.19870	−0.253484
$599$	−23.5640	−0.962800	−0.481400	−	0.876501i	$-0.659872\pi$
$599$	−23.5640	−0.962800	−0.481400	+	0.876501i	$0.659872\pi$
$600$	4.25479	0.173701
$601$	17.1062	0.697778	0.348889	−	0.937164i	$-0.386559\pi$
$601$	17.1062	0.697778	0.348889	+	0.937164i	$0.386559\pi$
$602$	−9.52208	−0.388091
$603$	−3.05253	−0.124309
$604$	39.8395	1.62104
$605$	6.47633	0.263300
$606$	30.0774	1.22181
$607$	38.9145	1.57949	0.789746	−	0.613434i	$-0.210212\pi$
$607$	38.9145	1.57949	0.789746	+	0.613434i	$0.210212\pi$
$608$	−13.2946	−0.539166
$609$	5.89901	0.239040
$610$	16.0853	0.651276
$611$	−23.0683	−0.933242
$612$	10.5469	0.426331
$613$	31.5159	1.27291	0.636457	−	0.771312i	$-0.280399\pi$
$613$	31.5159	1.27291	0.636457	+	0.771312i	$0.280399\pi$
$614$	34.2127	1.38071
$615$	−11.8343	−0.477206
$616$	−9.04947	−0.364613
$617$	−39.8605	−1.60472	−0.802362	−	0.596837i	$-0.796424\pi$
$617$	−39.8605	−1.60472	−0.802362	+	0.596837i	$0.796424\pi$
$618$	−4.72958	−0.190252
$619$	−21.2659	−0.854748	−0.427374	−	0.904075i	$-0.640561\pi$
$619$	−21.2659	−0.854748	−0.427374	+	0.904075i	$0.640561\pi$
$620$	15.9704	0.641389
$621$	−1.00000	−0.0401286
$622$	−35.7436	−1.43319
$623$	−8.92411	−0.357537
$624$	6.91289	0.276737
$625$	1.00000	0.0400000
$626$	15.6112	0.623948
$627$	13.6367	0.544597
$628$	42.5216	1.69679
$629$	27.4537	1.09465
$630$	2.40232	0.0957105
$631$	22.0002	0.875813	0.437907	−	0.899020i	$-0.355720\pi$
$631$	22.0002	0.875813	0.437907	+	0.899020i	$0.355720\pi$
$632$	−10.0296	−0.398957
$633$	3.80866	0.151381
$634$	81.5064	3.23703
$635$	2.30473	0.0914602
$636$	−28.7843	−1.14137
$637$	2.58030	0.102235
$638$	−30.1408	−1.19329
$639$	−11.4898	−0.454529
$640$	20.6916	0.817908
$641$	−16.5431	−0.653414	−0.326707	−	0.945126i	$-0.605939\pi$
$641$	−16.5431	−0.653414	−0.326707	+	0.945126i	$0.605939\pi$
$642$	3.64331	0.143790
$643$	0.483333	0.0190608	0.00953039	−	0.999955i	$-0.496966\pi$
$643$	0.483333	0.0190608	0.00953039	+	0.999955i	$0.496966\pi$
$644$	3.77112	0.148603
$645$	−3.96371	−0.156071
$646$	43.0771	1.69485
$647$	0.867540	0.0341065	0.0170533	−	0.999855i	$-0.494572\pi$
$647$	0.867540	0.0341065	0.0170533	+	0.999855i	$0.494572\pi$
$648$	4.25479	0.167144
$649$	0.899143	0.0352944
$650$	6.19870	0.243133
$651$	4.23494	0.165980
$652$	12.6396	0.495005
$653$	−42.1470	−1.64934	−0.824669	−	0.565615i	$-0.808639\pi$
$653$	−42.1470	−1.64934	−0.824669	+	0.565615i	$0.808639\pi$
$654$	−6.14634	−0.240341
$655$	11.2149	0.438203
$656$	31.7053	1.23789
$657$	−3.17533	−0.123881
$658$	21.4770	0.837262
$659$	16.4456	0.640629	0.320315	−	0.947311i	$-0.396211\pi$
$659$	16.4456	0.640629	0.320315	+	0.947311i	$0.396211\pi$
$660$	−8.02076	−0.312208
$661$	−2.69903	−0.104980	−0.0524900	−	0.998621i	$-0.516716\pi$
$661$	−2.69903	−0.104980	−0.0524900	+	0.998621i	$0.516716\pi$
$662$	−22.3956	−0.870429
$663$	7.21645	0.280264
$664$	60.3801	2.34320
$665$	6.41156	0.248630
$666$	23.5819	0.913778
$667$	5.89901	0.228411
$668$	−61.1350	−2.36538
$669$	−25.8392	−0.999002
$670$	7.33315	0.283304
$671$	−14.2411	−0.549773
$672$	2.07353	0.0799881
$673$	−25.2831	−0.974593	−0.487296	−	0.873237i	$-0.662017\pi$
$673$	−25.2831	−0.974593	−0.487296	+	0.873237i	$0.662017\pi$
$674$	2.88457	0.111109
$675$	1.00000	0.0384900
$676$	−23.9166	−0.919868
$677$	48.8704	1.87824	0.939122	−	0.343585i	$-0.111641\pi$
$677$	48.8704	1.87824	0.939122	+	0.343585i	$0.111641\pi$
$678$	−36.6163	−1.40624
$679$	−0.838594	−0.0321823
$680$	−11.8995	−0.456327
$681$	24.5388	0.940329
$682$	−21.6382	−0.828571
$683$	−43.0442	−1.64704	−0.823520	−	0.567287i	$-0.807993\pi$
$683$	−43.0442	−1.64704	−0.823520	+	0.567287i	$0.807993\pi$
$684$	24.1788	0.924498
$685$	8.19366	0.313064
$686$	−2.40232	−0.0917208
$687$	21.6752	0.826962
$688$	10.6192	0.404852
$689$	−19.6950	−0.750321
$690$	2.40232	0.0914546
$691$	−17.8228	−0.678009	−0.339005	−	0.940785i	$-0.610090\pi$
$691$	−17.8228	−0.678009	−0.339005	+	0.940785i	$0.610090\pi$
$692$	−13.8874	−0.527920
$693$	−2.12689	−0.0807939
$694$	6.38906	0.242525
$695$	9.46741	0.359119
$696$	−25.0990	−0.951377
$697$	33.0976	1.25366
$698$	−5.10694	−0.193301
$699$	−19.8630	−0.751286
$700$	−3.77112	−0.142535
$701$	6.38974	0.241337	0.120669	−	0.992693i	$-0.461496\pi$
$701$	6.38974	0.241337	0.120669	+	0.992693i	$0.461496\pi$
$702$	6.19870	0.233955
$703$	62.9378	2.37375
$704$	−21.9909	−0.828814
$705$	8.94014	0.336705
$706$	−23.0295	−0.866726
$707$	−12.5202	−0.470870
$708$	1.59424	0.0599152
$709$	22.6736	0.851523	0.425762	−	0.904835i	$-0.360006\pi$
$709$	22.6736	0.851523	0.425762	+	0.904835i	$0.360006\pi$
$710$	27.6021	1.03589
$711$	−2.35726	−0.0884040
$712$	37.9702	1.42299
$713$	4.23494	0.158600
$714$	−6.71866	−0.251440
$715$	−5.48802	−0.205240
$716$	−58.9065	−2.20144
$717$	−25.8762	−0.966366
$718$	56.4834	2.10794
$719$	−15.4768	−0.577189	−0.288594	−	0.957451i	$-0.593188\pi$
$719$	−15.4768	−0.577189	−0.288594	+	0.957451i	$0.593188\pi$
$720$	−2.67910	−0.0998442
$721$	1.96876	0.0733204
$722$	53.1107	1.97658
$723$	−4.58279	−0.170436
$724$	−87.4784	−3.25111
$725$	−5.89901	−0.219084
$726$	−15.5582	−0.577419
$727$	34.4968	1.27942	0.639708	−	0.768618i	$-0.279055\pi$
$727$	34.4968	1.27942	0.639708	+	0.768618i	$0.279055\pi$
$728$	−10.9786	−0.406895
$729$	1.00000	0.0370370
$730$	7.62814	0.282330
$731$	11.0855	0.410011
$732$	−25.2505	−0.933285
$733$	35.6423	1.31648	0.658240	−	0.752808i	$-0.271301\pi$
$733$	35.6423	1.31648	0.658240	+	0.752808i	$0.271301\pi$
$734$	40.4122	1.49164
$735$	−1.00000	−0.0368856
$736$	2.07353	0.0764313
$737$	−6.49241	−0.239151
$738$	28.4298	1.04651
$739$	−5.34068	−0.196460	−0.0982301	−	0.995164i	$-0.531318\pi$
$739$	−5.34068	−0.196460	−0.0982301	+	0.995164i	$0.531318\pi$
$740$	−37.0184	−1.36082
$741$	16.5438	0.607751
$742$	18.3365	0.673153
$743$	9.58851	0.351768	0.175884	−	0.984411i	$-0.443722\pi$
$743$	9.58851	0.351768	0.175884	+	0.984411i	$0.443722\pi$
$744$	−18.0187	−0.660599
$745$	17.5225	0.641976
$746$	−30.9667	−1.13377
$747$	14.1911	0.519225
$748$	22.4320	0.820196
$749$	−1.51658	−0.0554147
$750$	−2.40232	−0.0877202
$751$	7.92942	0.289349	0.144674	−	0.989479i	$-0.453787\pi$
$751$	7.92942	0.289349	0.144674	+	0.989479i	$0.453787\pi$
$752$	−23.9515	−0.873422
$753$	−2.11145	−0.0769456
$754$	−36.5662	−1.33166
$755$	−10.5644	−0.384476
$756$	−3.77112	−0.137154
$757$	18.0254	0.655144	0.327572	−	0.944826i	$-0.393770\pi$
$757$	18.0254	0.655144	0.327572	+	0.944826i	$0.393770\pi$
$758$	−0.451729	−0.0164075
$759$	−2.12689	−0.0772013
$760$	−27.2798	−0.989543
$761$	−18.1228	−0.656949	−0.328475	−	0.944513i	$-0.606535\pi$
$761$	−18.1228	−0.656949	−0.328475	+	0.944513i	$0.606535\pi$
$762$	−5.53668	−0.200573
$763$	2.55851	0.0926242
$764$	−3.00954	−0.108881
$765$	−2.79674	−0.101117
$766$	−50.0763	−1.80933
$767$	1.09082	0.0393873
$768$	−29.0288	−1.04749
$769$	−11.9841	−0.432159	−0.216080	−	0.976376i	$-0.569327\pi$
$769$	−11.9841	−0.432159	−0.216080	+	0.976376i	$0.569327\pi$
$770$	5.10946	0.184132
$771$	22.0318	0.793454
$772$	6.64064	0.239002
$773$	15.4031	0.554010	0.277005	−	0.960868i	$-0.410658\pi$
$773$	15.4031	0.554010	0.277005	+	0.960868i	$0.410658\pi$
$774$	9.52208	0.342264
$775$	−4.23494	−0.152123
$776$	3.56804	0.128085
$777$	−9.81630	−0.352158
$778$	30.0613	1.07775
$779$	75.8765	2.71856
$780$	−9.73063	−0.348412
$781$	−24.4375	−0.874443
$782$	−6.71866	−0.240259
$783$	−5.89901	−0.210814
$784$	2.67910	0.0956821
$785$	−11.2756	−0.402443
$786$	−26.9418	−0.960981
$787$	−6.20932	−0.221338	−0.110669	−	0.993857i	$-0.535299\pi$
$787$	−6.20932	−0.221338	−0.110669	+	0.993857i	$0.535299\pi$
$788$	14.7179	0.524305
$789$	3.12690	0.111321
$790$	5.66287	0.201476
$791$	15.2421	0.541947
$792$	9.04947	0.321559
$793$	−17.2771	−0.613527
$794$	22.4859	0.797994
$795$	7.63284	0.270709
$796$	−4.65353	−0.164940
$797$	−28.1821	−0.998263	−0.499131	−	0.866526i	$-0.666347\pi$
$797$	−28.1821	−0.998263	−0.499131	+	0.866526i	$0.666347\pi$
$798$	−15.4026	−0.545246
$799$	−25.0033	−0.884553
$800$	−2.07353	−0.0733103
$801$	8.92411	0.315318
$802$	−10.2699	−0.362643
$803$	−6.75358	−0.238329
$804$	−11.5115	−0.405978
$805$	−1.00000	−0.0352454
$806$	−26.2511	−0.924656
$807$	−23.3837	−0.823145
$808$	53.2707	1.87406
$809$	0.465992	0.0163834	0.00819171	−	0.999966i	$-0.497392\pi$
$809$	0.465992	0.0163834	0.00819171	+	0.999966i	$0.497392\pi$
$810$	−2.40232	−0.0844088
$811$	11.5440	0.405365	0.202683	−	0.979245i	$-0.435034\pi$
$811$	11.5440	0.405365	0.202683	+	0.979245i	$0.435034\pi$
$812$	22.2459	0.780677
$813$	25.1845	0.883258
$814$	50.1560	1.75797
$815$	−3.35169	−0.117404
$816$	7.49276	0.262299
$817$	25.4136	0.889108
$818$	−45.2638	−1.58261
$819$	−2.58030	−0.0901631
$820$	−44.6286	−1.55850
$821$	14.0218	0.489363	0.244682	−	0.969603i	$-0.421317\pi$
$821$	14.0218	0.489363	0.244682	+	0.969603i	$0.421317\pi$
$822$	−19.6838	−0.686550
$823$	23.8610	0.831743	0.415871	−	0.909423i	$-0.363477\pi$
$823$	23.8610	0.831743	0.415871	+	0.909423i	$0.363477\pi$
$824$	−8.37665	−0.291814
$825$	2.12689	0.0740489
$826$	−1.01558	−0.0353365
$827$	3.03606	0.105574	0.0527872	−	0.998606i	$-0.483190\pi$
$827$	3.03606	0.105574	0.0527872	+	0.998606i	$0.483190\pi$
$828$	−3.77112	−0.131055
$829$	−25.4787	−0.884913	−0.442456	−	0.896790i	$-0.645893\pi$
$829$	−25.4787	−0.884913	−0.442456	+	0.896790i	$0.645893\pi$
$830$	−34.0915	−1.18333
$831$	21.0119	0.728894
$832$	−26.6790	−0.924927
$833$	2.79674	0.0969014
$834$	−22.7437	−0.787550
$835$	16.2114	0.561017
$836$	51.4256	1.77859
$837$	−4.23494	−0.146381
$838$	9.42539	0.325595
$839$	−53.6528	−1.85230	−0.926150	−	0.377156i	$-0.876902\pi$
$839$	−53.6528	−1.85230	−0.926150	+	0.377156i	$0.876902\pi$
$840$	4.25479	0.146804
$841$	5.79836	0.199944
$842$	29.8854	1.02992
$843$	32.3091	1.11279
$844$	14.3629	0.494392
$845$	6.34204	0.218173
$846$	−21.4770	−0.738396
$847$	6.47633	0.222529
$848$	−20.4491	−0.702226
$849$	14.7384	0.505821
$850$	6.71866	0.230448
$851$	−9.81630	−0.336498
$852$	−43.3293	−1.48444
$853$	−16.5568	−0.566894	−0.283447	−	0.958988i	$-0.591478\pi$
$853$	−16.5568	−0.566894	−0.283447	+	0.958988i	$0.591478\pi$
$854$	16.0853	0.550428
$855$	−6.41156	−0.219271
$856$	6.45273	0.220550
$857$	−12.2401	−0.418112	−0.209056	−	0.977904i	$-0.567039\pi$
$857$	−12.2401	−0.418112	−0.209056	+	0.977904i	$0.567039\pi$
$858$	13.1840	0.450093
$859$	35.1459	1.19916	0.599582	−	0.800313i	$-0.295334\pi$
$859$	35.1459	1.19916	0.599582	+	0.800313i	$0.295334\pi$
$860$	−14.9476	−0.509709
$861$	−11.8343	−0.403313
$862$	−29.1734	−0.993651
$863$	−18.3530	−0.624744	−0.312372	−	0.949960i	$-0.601124\pi$
$863$	−18.3530	−0.624744	−0.312372	+	0.949960i	$0.601124\pi$
$864$	−2.07353	−0.0705429
$865$	3.68257	0.125211
$866$	−34.4668	−1.17123
$867$	−9.17822	−0.311709
$868$	15.9704	0.542072
$869$	−5.01363	−0.170076
$870$	14.1713	0.480452
$871$	−7.87646	−0.266884
$872$	−10.8859	−0.368643
$873$	0.838594	0.0283821
$874$	−15.4026	−0.521001
$875$	1.00000	0.0338062
$876$	−11.9745	−0.404582
$877$	30.5854	1.03279	0.516397	−	0.856349i	$-0.327273\pi$
$877$	30.5854	1.03279	0.516397	+	0.856349i	$0.327273\pi$
$878$	68.5031	2.31187
$879$	−22.4710	−0.757928
$880$	−5.69815	−0.192085
$881$	−43.8227	−1.47642	−0.738212	−	0.674569i	$-0.764330\pi$
$881$	−43.8227	−1.47642	−0.738212	+	0.674569i	$0.764330\pi$
$882$	2.40232	0.0808902
$883$	11.3080	0.380545	0.190273	−	0.981731i	$-0.439063\pi$
$883$	11.3080	0.380545	0.190273	+	0.981731i	$0.439063\pi$
$884$	27.2141	0.915309
$885$	−0.422750	−0.0142106
$886$	−94.0648	−3.16017
$887$	−33.0297	−1.10903	−0.554514	−	0.832175i	$-0.687096\pi$
$887$	−33.0297	−1.10903	−0.554514	+	0.832175i	$0.687096\pi$
$888$	41.7663	1.40158
$889$	2.30473	0.0772980
$890$	−21.4385	−0.718621
$891$	2.12689	0.0712535
$892$	−97.4428	−3.26263
$893$	−57.3203	−1.91815
$894$	−42.0946	−1.40785
$895$	15.6204	0.522134
$896$	20.6916	0.691258
$897$	−2.58030	−0.0861538
$898$	98.5840	3.28979
$899$	24.9819	0.833194
$900$	3.77112	0.125704
$901$	−21.3471	−0.711175
$902$	60.4670	2.01333
$903$	−3.96371	−0.131904
$904$	−64.8519	−2.15694
$905$	23.1969	0.771092
$906$	25.3789	0.843158
$907$	−7.46742	−0.247952	−0.123976	−	0.992285i	$-0.539565\pi$
$907$	−7.46742	−0.247952	−0.123976	+	0.992285i	$0.539565\pi$
$908$	92.5387	3.07100
$909$	12.5202	0.415268
$910$	6.19870	0.205485
$911$	−29.5341	−0.978509	−0.489255	−	0.872141i	$-0.662731\pi$
$911$	−29.5341	−0.978509	−0.489255	+	0.872141i	$0.662731\pi$
$912$	17.1772	0.568795
$913$	30.1829	0.998909
$914$	63.4726	2.09949
$915$	6.69576	0.221355
$916$	81.7399	2.70076
$917$	11.2149	0.370349
$918$	6.71866	0.221749
$919$	26.9246	0.888162	0.444081	−	0.895987i	$-0.353530\pi$
$919$	26.9246	0.888162	0.444081	+	0.895987i	$0.353530\pi$
$920$	4.25479	0.140276
$921$	14.2415	0.469275
$922$	75.6917	2.49277
$923$	−29.6471	−0.975847
$924$	−8.02076	−0.263864
$925$	9.81630	0.322758
$926$	−4.58324	−0.150614
$927$	−1.96876	−0.0646625
$928$	12.2318	0.401528
$929$	7.04851	0.231254	0.115627	−	0.993293i	$-0.463112\pi$
$929$	7.04851	0.231254	0.115627	+	0.993293i	$0.463112\pi$
$930$	10.1737	0.333607
$931$	6.41156	0.210130
$932$	−74.9056	−2.45361
$933$	−14.8788	−0.487110
$934$	35.3464	1.15657
$935$	−5.94837	−0.194533
$936$	10.9786	0.358848
$937$	10.0260	0.327535	0.163767	−	0.986499i	$-0.447635\pi$
$937$	10.0260	0.327535	0.163767	+	0.986499i	$0.447635\pi$
$938$	7.33315	0.239436
$939$	6.49839	0.212067
$940$	33.7143	1.09964
$941$	−28.5886	−0.931962	−0.465981	−	0.884795i	$-0.654299\pi$
$941$	−28.5886	−0.931962	−0.465981	+	0.884795i	$0.654299\pi$
$942$	27.0875	0.882559
$943$	−11.8343	−0.385378
$944$	1.13259	0.0368626
$945$	1.00000	0.0325300
$946$	20.2524	0.658463
$947$	32.7024	1.06268	0.531342	−	0.847157i	$-0.321688\pi$
$947$	32.7024	1.06268	0.531342	+	0.847157i	$0.321688\pi$
$948$	−8.88949	−0.288717
$949$	−8.19331	−0.265966
$950$	15.4026	0.499726
$951$	33.9283	1.10020
$952$	−11.8995	−0.385667
$953$	7.55296	0.244664	0.122332	−	0.992489i	$-0.460963\pi$
$953$	7.55296	0.244664	0.122332	+	0.992489i	$0.460963\pi$
$954$	−18.3365	−0.593666
$955$	0.798049	0.0258243
$956$	−97.5824	−3.15604
$957$	−12.5466	−0.405573
$958$	−60.6954	−1.96098
$959$	8.19366	0.264587
$960$	10.3395	0.333705
$961$	−13.0653	−0.421462
$962$	60.8483	1.96183
$963$	1.51658	0.0488712
$964$	−17.2822	−0.556624
$965$	−1.76092	−0.0566860
$966$	2.40232	0.0772932
$967$	−19.2082	−0.617694	−0.308847	−	0.951112i	$-0.599943\pi$
$967$	−19.2082	−0.617694	−0.308847	+	0.951112i	$0.599943\pi$
$968$	−27.5554	−0.885664
$969$	17.9315	0.576043
$970$	−2.01457	−0.0646838
$971$	−6.15823	−0.197627	−0.0988135	−	0.995106i	$-0.531505\pi$
$971$	−6.15823	−0.197627	−0.0988135	+	0.995106i	$0.531505\pi$
$972$	3.77112	0.120959
$973$	9.46741	0.303511
$974$	58.4611	1.87321
$975$	2.58030	0.0826358
$976$	−17.9386	−0.574201
$977$	8.00603	0.256136	0.128068	−	0.991765i	$-0.459122\pi$
$977$	8.00603	0.256136	0.128068	+	0.991765i	$0.459122\pi$
$978$	8.05181	0.257468
$979$	18.9806	0.606623
$980$	−3.77112	−0.120464
$981$	−2.55851	−0.0816869
$982$	102.355	3.26627
$983$	−15.3447	−0.489420	−0.244710	−	0.969596i	$-0.578693\pi$
$983$	−15.3447	−0.489420	−0.244710	+	0.969596i	$0.578693\pi$
$984$	50.3525	1.60518
$985$	−3.90280	−0.124354
$986$	−39.6335	−1.26219
$987$	8.94014	0.284568
$988$	62.3885	1.98484
$989$	−3.96371	−0.126039
$990$	−5.10946	−0.162389
$991$	−21.6048	−0.686298	−0.343149	−	0.939281i	$-0.611494\pi$
$991$	−21.6048	−0.686298	−0.343149	+	0.939281i	$0.611494\pi$
$992$	8.78126	0.278805
$993$	−9.32250	−0.295840
$994$	27.6021	0.875485
$995$	1.23399	0.0391201
$996$	53.5163	1.69573
$997$	−15.6058	−0.494239	−0.247120	−	0.968985i	$-0.579484\pi$
$997$	−15.6058	−0.494239	−0.247120	+	0.968985i	$0.579484\pi$
$998$	−34.0395	−1.07750
$999$	9.81630	0.310574

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2415.2.a.r.1.7	✓	7
3.2	odd	2		7245.2.a.bn.1.1		7

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2415.2.a.r.1.7	✓	7	1.1	even	1	trivial
7245.2.a.bn.1.1		7	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:	\( N \)	\(=\)	\( 2415 = 3 \cdot 5 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2415.a (trivial)

\(f(q)\)	\(=\)	\(q+2.40232 q^{2} +1.00000 q^{3} +3.77112 q^{4} -1.00000 q^{5} +2.40232 q^{6} -1.00000 q^{7} +4.25479 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+2.40232 q^{2} +1.00000 q^{3} +3.77112 q^{4} -1.00000 q^{5} +2.40232 q^{6} -1.00000 q^{7} +4.25479 q^{8} +1.00000 q^{9} -2.40232 q^{10} +2.12689 q^{11} +3.77112 q^{12} +2.58030 q^{13} -2.40232 q^{14} -1.00000 q^{15} +2.67910 q^{16} +2.79674 q^{17} +2.40232 q^{18} +6.41156 q^{19} -3.77112 q^{20} -1.00000 q^{21} +5.10946 q^{22} -1.00000 q^{23} +4.25479 q^{24} +1.00000 q^{25} +6.19870 q^{26} +1.00000 q^{27} -3.77112 q^{28} -5.89901 q^{29} -2.40232 q^{30} -4.23494 q^{31} -2.07353 q^{32} +2.12689 q^{33} +6.71866 q^{34} +1.00000 q^{35} +3.77112 q^{36} +9.81630 q^{37} +15.4026 q^{38} +2.58030 q^{39} -4.25479 q^{40} +11.8343 q^{41} -2.40232 q^{42} +3.96371 q^{43} +8.02076 q^{44} -1.00000 q^{45} -2.40232 q^{46} -8.94014 q^{47} +2.67910 q^{48} +1.00000 q^{49} +2.40232 q^{50} +2.79674 q^{51} +9.73063 q^{52} -7.63284 q^{53} +2.40232 q^{54} -2.12689 q^{55} -4.25479 q^{56} +6.41156 q^{57} -14.1713 q^{58} +0.422750 q^{59} -3.77112 q^{60} -6.69576 q^{61} -10.1737 q^{62} -1.00000 q^{63} -10.3395 q^{64} -2.58030 q^{65} +5.10946 q^{66} -3.05253 q^{67} +10.5469 q^{68} -1.00000 q^{69} +2.40232 q^{70} -11.4898 q^{71} +4.25479 q^{72} -3.17533 q^{73} +23.5819 q^{74} +1.00000 q^{75} +24.1788 q^{76} -2.12689 q^{77} +6.19870 q^{78} -2.35726 q^{79} -2.67910 q^{80} +1.00000 q^{81} +28.4298 q^{82} +14.1911 q^{83} -3.77112 q^{84} -2.79674 q^{85} +9.52208 q^{86} -5.89901 q^{87} +9.04947 q^{88} +8.92411 q^{89} -2.40232 q^{90} -2.58030 q^{91} -3.77112 q^{92} -4.23494 q^{93} -21.4770 q^{94} -6.41156 q^{95} -2.07353 q^{96} +0.838594 q^{97} +2.40232 q^{98} +2.12689 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 7 q - 2 q^{2} + 7 q^{3} + 8 q^{4} - 7 q^{5} - 2 q^{6} - 7 q^{7} - 6 q^{8} + 7 q^{9}+O(q^{10}) \) 7 * q - 2 * q^2 + 7 * q^3 + 8 * q^4 - 7 * q^5 - 2 * q^6 - 7 * q^7 - 6 * q^8 + 7 * q^9	\( 7 q - 2 q^{2} + 7 q^{3} + 8 q^{4} - 7 q^{5} - 2 q^{6} - 7 q^{7} - 6 q^{8} + 7 q^{9} + 2 q^{10} - 2 q^{11} + 8 q^{12} + 6 q^{13} + 2 q^{14} - 7 q^{15} + 10 q^{16} + 14 q^{17} - 2 q^{18} + 6 q^{19} - 8 q^{20} - 7 q^{21} + 28 q^{22} - 7 q^{23} - 6 q^{24} + 7 q^{25} + 5 q^{26} + 7 q^{27} - 8 q^{28} - 4 q^{29} + 2 q^{30} + 4 q^{31} - 19 q^{32} - 2 q^{33} - 7 q^{34} + 7 q^{35} + 8 q^{36} + 18 q^{37} + 22 q^{38} + 6 q^{39} + 6 q^{40} + 10 q^{41} + 2 q^{42} + 26 q^{43} - 29 q^{44} - 7 q^{45} + 2 q^{46} - 4 q^{47} + 10 q^{48} + 7 q^{49} - 2 q^{50} + 14 q^{51} + 18 q^{52} + 2 q^{53} - 2 q^{54} + 2 q^{55} + 6 q^{56} + 6 q^{57} + 12 q^{58} + 6 q^{59} - 8 q^{60} - 4 q^{61} + 4 q^{62} - 7 q^{63} + 38 q^{64} - 6 q^{65} + 28 q^{66} + 22 q^{67} + 52 q^{68} - 7 q^{69} - 2 q^{70} - 8 q^{71} - 6 q^{72} + 24 q^{73} + 17 q^{74} + 7 q^{75} + 15 q^{76} + 2 q^{77} + 5 q^{78} + 2 q^{79} - 10 q^{80} + 7 q^{81} - 10 q^{82} + 26 q^{83} - 8 q^{84} - 14 q^{85} - 22 q^{86} - 4 q^{87} + 79 q^{88} + 22 q^{89} + 2 q^{90} - 6 q^{91} - 8 q^{92} + 4 q^{93} + 14 q^{94} - 6 q^{95} - 19 q^{96} + 44 q^{97} - 2 q^{98} - 2 q^{99}+O(q^{100}) \) 7 * q - 2 * q^2 + 7 * q^3 + 8 * q^4 - 7 * q^5 - 2 * q^6 - 7 * q^7 - 6 * q^8 + 7 * q^9 + 2 * q^10 - 2 * q^11 + 8 * q^12 + 6 * q^13 + 2 * q^14 - 7 * q^15 + 10 * q^16 + 14 * q^17 - 2 * q^18 + 6 * q^19 - 8 * q^20 - 7 * q^21 + 28 * q^22 - 7 * q^23 - 6 * q^24 + 7 * q^25 + 5 * q^26 + 7 * q^27 - 8 * q^28 - 4 * q^29 + 2 * q^30 + 4 * q^31 - 19 * q^32 - 2 * q^33 - 7 * q^34 + 7 * q^35 + 8 * q^36 + 18 * q^37 + 22 * q^38 + 6 * q^39 + 6 * q^40 + 10 * q^41 + 2 * q^42 + 26 * q^43 - 29 * q^44 - 7 * q^45 + 2 * q^46 - 4 * q^47 + 10 * q^48 + 7 * q^49 - 2 * q^50 + 14 * q^51 + 18 * q^52 + 2 * q^53 - 2 * q^54 + 2 * q^55 + 6 * q^56 + 6 * q^57 + 12 * q^58 + 6 * q^59 - 8 * q^60 - 4 * q^61 + 4 * q^62 - 7 * q^63 + 38 * q^64 - 6 * q^65 + 28 * q^66 + 22 * q^67 + 52 * q^68 - 7 * q^69 - 2 * q^70 - 8 * q^71 - 6 * q^72 + 24 * q^73 + 17 * q^74 + 7 * q^75 + 15 * q^76 + 2 * q^77 + 5 * q^78 + 2 * q^79 - 10 * q^80 + 7 * q^81 - 10 * q^82 + 26 * q^83 - 8 * q^84 - 14 * q^85 - 22 * q^86 - 4 * q^87 + 79 * q^88 + 22 * q^89 + 2 * q^90 - 6 * q^91 - 8 * q^92 + 4 * q^93 + 14 * q^94 - 6 * q^95 - 19 * q^96 + 44 * q^97 - 2 * q^98 - 2 * q^99

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