LMFDB - Embedded newform 2415.2.a.r.1.4

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			1.4
Root			$0.451228$ 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)

$f(q)$	$=$	$q-0.451228 q^{2} +1.00000 q^{3} -1.79639 q^{4} -1.00000 q^{5} -0.451228 q^{6} -1.00000 q^{7} +1.71304 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-0.451228 q^{2} +1.00000 q^{3} -1.79639 q^{4} -1.00000 q^{5} -0.451228 q^{6} -1.00000 q^{7} +1.71304 q^{8} +1.00000 q^{9} +0.451228 q^{10} -0.260456 q^{11} -1.79639 q^{12} -3.87458 q^{13} +0.451228 q^{14} -1.00000 q^{15} +2.81982 q^{16} +2.42741 q^{17} -0.451228 q^{18} +1.68072 q^{19} +1.79639 q^{20} -1.00000 q^{21} +0.117525 q^{22} -1.00000 q^{23} +1.71304 q^{24} +1.00000 q^{25} +1.74832 q^{26} +1.00000 q^{27} +1.79639 q^{28} -0.177100 q^{29} +0.451228 q^{30} -6.56589 q^{31} -4.69846 q^{32} -0.260456 q^{33} -1.09532 q^{34} +1.00000 q^{35} -1.79639 q^{36} -5.24538 q^{37} -0.758388 q^{38} -3.87458 q^{39} -1.71304 q^{40} -5.99886 q^{41} +0.451228 q^{42} +10.3531 q^{43} +0.467881 q^{44} -1.00000 q^{45} +0.451228 q^{46} +11.6589 q^{47} +2.81982 q^{48} +1.00000 q^{49} -0.451228 q^{50} +2.42741 q^{51} +6.96027 q^{52} -0.499822 q^{53} -0.451228 q^{54} +0.260456 q^{55} -1.71304 q^{56} +1.68072 q^{57} +0.0799126 q^{58} +10.0276 q^{59} +1.79639 q^{60} -0.604512 q^{61} +2.96271 q^{62} -1.00000 q^{63} -3.51956 q^{64} +3.87458 q^{65} +0.117525 q^{66} -2.37440 q^{67} -4.36059 q^{68} -1.00000 q^{69} -0.451228 q^{70} +1.89171 q^{71} +1.71304 q^{72} +15.9391 q^{73} +2.36686 q^{74} +1.00000 q^{75} -3.01924 q^{76} +0.260456 q^{77} +1.74832 q^{78} +12.7650 q^{79} -2.81982 q^{80} +1.00000 q^{81} +2.70685 q^{82} +1.77102 q^{83} +1.79639 q^{84} -2.42741 q^{85} -4.67159 q^{86} -0.177100 q^{87} -0.446171 q^{88} +5.18434 q^{89} +0.451228 q^{90} +3.87458 q^{91} +1.79639 q^{92} -6.56589 q^{93} -5.26080 q^{94} -1.68072 q^{95} -4.69846 q^{96} +1.13257 q^{97} -0.451228 q^{98} -0.260456 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−0.451228	−0.319066	−0.159533	−	0.987193i	$-0.550999\pi$
$2$	−0.451228	−0.319066	−0.159533	+	0.987193i	$0.550999\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	−1.79639	−0.898197
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	−0.451228	−0.184213
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	1.71304	0.605650
$9$	1.00000	0.333333
$10$	0.451228	0.142691
$11$	−0.260456	−0.0785304	−0.0392652	−	0.999229i	$-0.512502\pi$
$11$	−0.260456	−0.0785304	−0.0392652	+	0.999229i	$0.512502\pi$
$12$	−1.79639	−0.518574
$13$	−3.87458	−1.07461	−0.537307	−	0.843387i	$-0.680558\pi$
$13$	−3.87458	−1.07461	−0.537307	+	0.843387i	$0.680558\pi$
$14$	0.451228	0.120596
$15$	−1.00000	−0.258199
$16$	2.81982	0.704954
$17$	2.42741	0.588734	0.294367	−	0.955692i	$-0.404891\pi$
$17$	2.42741	0.588734	0.294367	+	0.955692i	$0.404891\pi$
$18$	−0.451228	−0.106355
$19$	1.68072	0.385584	0.192792	−	0.981240i	$-0.438246\pi$
$19$	1.68072	0.385584	0.192792	+	0.981240i	$0.438246\pi$
$20$	1.79639	0.401686
$21$	−1.00000	−0.218218
$22$	0.117525	0.0250564
$23$	−1.00000	−0.208514
$23$	−1.00000	−0.208514
$24$	1.71304	0.349672
$25$	1.00000	0.200000
$26$	1.74832	0.342873
$27$	1.00000	0.192450
$28$	1.79639	0.339486
$29$	−0.177100	−0.0328867	−0.0164434	−	0.999865i	$-0.505234\pi$
$29$	−0.177100	−0.0328867	−0.0164434	+	0.999865i	$0.505234\pi$
$30$	0.451228	0.0823825
$31$	−6.56589	−1.17927	−0.589634	−	0.807670i	$-0.700728\pi$
$31$	−6.56589	−1.17927	−0.589634	+	0.807670i	$0.700728\pi$
$32$	−4.69846	−0.830578
$33$	−0.260456	−0.0453395
$34$	−1.09532	−0.187845
$35$	1.00000	0.169031
$36$	−1.79639	−0.299399
$37$	−5.24538	−0.862334	−0.431167	−	0.902272i	$-0.641898\pi$
$37$	−5.24538	−0.862334	−0.431167	+	0.902272i	$0.641898\pi$
$38$	−0.758388	−0.123027
$39$	−3.87458	−0.620429
$40$	−1.71304	−0.270855
$41$	−5.99886	−0.936865	−0.468433	−	0.883499i	$-0.655181\pi$
$41$	−5.99886	−0.936865	−0.468433	+	0.883499i	$0.655181\pi$
$42$	0.451228	0.0696260
$43$	10.3531	1.57883	0.789414	−	0.613861i	$-0.210385\pi$
$43$	10.3531	1.57883	0.789414	+	0.613861i	$0.210385\pi$
$44$	0.467881	0.0705357
$45$	−1.00000	−0.149071
$46$	0.451228	0.0665299
$47$	11.6589	1.70062	0.850309	−	0.526283i	$-0.176415\pi$
$47$	11.6589	1.70062	0.850309	+	0.526283i	$0.176415\pi$
$48$	2.81982	0.407005
$49$	1.00000	0.142857
$50$	−0.451228	−0.0638132
$51$	2.42741	0.339906
$52$	6.96027	0.965215
$53$	−0.499822	−0.0686558	−0.0343279	−	0.999411i	$-0.510929\pi$
$53$	−0.499822	−0.0686558	−0.0343279	+	0.999411i	$0.510929\pi$
$54$	−0.451228	−0.0614043
$55$	0.260456	0.0351198
$56$	−1.71304	−0.228914
$57$	1.68072	0.222617
$58$	0.0799126	0.0104930
$59$	10.0276	1.30548	0.652741	−	0.757581i	$-0.273619\pi$
$59$	10.0276	1.30548	0.652741	+	0.757581i	$0.273619\pi$
$60$	1.79639	0.231913
$61$	−0.604512	−0.0773998	−0.0386999	−	0.999251i	$-0.512322\pi$
$61$	−0.604512	−0.0773998	−0.0386999	+	0.999251i	$0.512322\pi$
$62$	2.96271	0.376265
$63$	−1.00000	−0.125988
$64$	−3.51956	−0.439945
$65$	3.87458	0.480582
$66$	0.117525	0.0144663
$67$	−2.37440	−0.290079	−0.145040	−	0.989426i	$-0.546331\pi$
$67$	−2.37440	−0.290079	−0.145040	+	0.989426i	$0.546331\pi$
$68$	−4.36059	−0.528799
$69$	−1.00000	−0.120386
$70$	−0.451228	−0.0539320
$71$	1.89171	0.224505	0.112252	−	0.993680i	$-0.464194\pi$
$71$	1.89171	0.224505	0.112252	+	0.993680i	$0.464194\pi$
$72$	1.71304	0.201883
$73$	15.9391	1.86553	0.932763	−	0.360491i	$-0.117391\pi$
$73$	15.9391	1.86553	0.932763	+	0.360491i	$0.117391\pi$
$74$	2.36686	0.275142
$75$	1.00000	0.115470
$76$	−3.01924	−0.346330
$77$	0.260456	0.0296817
$78$	1.74832	0.197958
$79$	12.7650	1.43617	0.718085	−	0.695956i	$-0.245019\pi$
$79$	12.7650	1.43617	0.718085	+	0.695956i	$0.245019\pi$
$80$	−2.81982	−0.315265
$81$	1.00000	0.111111
$82$	2.70685	0.298922
$83$	1.77102	0.194395	0.0971976	−	0.995265i	$-0.469012\pi$
$83$	1.77102	0.194395	0.0971976	+	0.995265i	$0.469012\pi$
$84$	1.79639	0.196003
$85$	−2.42741	−0.263290
$86$	−4.67159	−0.503751
$87$	−0.177100	−0.0189872
$88$	−0.446171	−0.0475619
$89$	5.18434	0.549539	0.274770	−	0.961510i	$-0.411398\pi$
$89$	5.18434	0.549539	0.274770	+	0.961510i	$0.411398\pi$
$90$	0.451228	0.0475636
$91$	3.87458	0.406166
$92$	1.79639	0.187287
$93$	−6.56589	−0.680851
$94$	−5.26080	−0.542610
$95$	−1.68072	−0.172438
$96$	−4.69846	−0.479534
$97$	1.13257	0.114995	0.0574974	−	0.998346i	$-0.481688\pi$
$97$	1.13257	0.114995	0.0574974	+	0.998346i	$0.481688\pi$
$98$	−0.451228	−0.0455809
$99$	−0.260456	−0.0261768
$100$	−1.79639	−0.179639
$101$	9.01984	0.897508	0.448754	−	0.893655i	$-0.351868\pi$
$101$	9.01984	0.897508	0.448754	+	0.893655i	$0.351868\pi$
$102$	−1.09532	−0.108452
$103$	−2.88861	−0.284623	−0.142312	−	0.989822i	$-0.545453\pi$
$103$	−2.88861	−0.284623	−0.142312	+	0.989822i	$0.545453\pi$
$104$	−6.63730	−0.650841
$105$	1.00000	0.0975900
$106$	0.225533	0.0219057
$107$	−18.5959	−1.79773	−0.898865	−	0.438226i	$-0.855607\pi$
$107$	−18.5959	−1.79773	−0.898865	+	0.438226i	$0.855607\pi$
$108$	−1.79639	−0.172858
$109$	19.8152	1.89795	0.948977	−	0.315345i	$-0.102120\pi$
$109$	19.8152	1.89795	0.948977	+	0.315345i	$0.102120\pi$
$110$	−0.117525	−0.0112056
$111$	−5.24538	−0.497869
$112$	−2.81982	−0.266448
$113$	3.30509	0.310917	0.155458	−	0.987842i	$-0.450315\pi$
$113$	3.30509	0.310917	0.155458	+	0.987842i	$0.450315\pi$
$114$	−0.758388	−0.0710296
$115$	1.00000	0.0932505
$116$	0.318142	0.0295388
$117$	−3.87458	−0.358205
$118$	−4.52473	−0.416535
$119$	−2.42741	−0.222520
$120$	−1.71304	−0.156378
$121$	−10.9322	−0.993833
$122$	0.272773	0.0246957
$123$	−5.99886	−0.540899
$124$	11.7949	1.05921
$125$	−1.00000	−0.0894427
$126$	0.451228	0.0401986
$127$	15.2943	1.35715	0.678575	−	0.734531i	$-0.262598\pi$
$127$	15.2943	1.35715	0.678575	+	0.734531i	$0.262598\pi$
$128$	10.9850	0.970949
$129$	10.3531	0.911536
$130$	−1.74832	−0.153338
$131$	10.8557	0.948468	0.474234	−	0.880399i	$-0.342725\pi$
$131$	10.8557	0.948468	0.474234	+	0.880399i	$0.342725\pi$
$132$	0.467881	0.0407238
$133$	−1.68072	−0.145737
$134$	1.07140	0.0925544
$135$	−1.00000	−0.0860663
$136$	4.15825	0.356567
$137$	−6.37351	−0.544526	−0.272263	−	0.962223i	$-0.587772\pi$
$137$	−6.37351	−0.544526	−0.272263	+	0.962223i	$0.587772\pi$
$138$	0.451228	0.0384111
$139$	16.3451	1.38638	0.693188	−	0.720757i	$-0.256206\pi$
$139$	16.3451	1.38638	0.693188	+	0.720757i	$0.256206\pi$
$140$	−1.79639	−0.151823
$141$	11.6589	0.981853
$142$	−0.853592	−0.0716318
$143$	1.00916	0.0843899
$144$	2.81982	0.234985
$145$	0.177100	0.0147074
$146$	−7.19214	−0.595226
$147$	1.00000	0.0824786
$148$	9.42276	0.774546
$149$	4.83509	0.396106	0.198053	−	0.980191i	$-0.436538\pi$
$149$	4.83509	0.396106	0.198053	+	0.980191i	$0.436538\pi$
$150$	−0.451228	−0.0368426
$151$	−4.66309	−0.379477	−0.189738	−	0.981835i	$-0.560764\pi$
$151$	−4.66309	−0.379477	−0.189738	+	0.981835i	$0.560764\pi$
$152$	2.87914	0.233529
$153$	2.42741	0.196245
$154$	−0.117525	−0.00947042
$155$	6.56589	0.527385
$156$	6.96027	0.557267
$157$	19.2648	1.53750	0.768748	−	0.639552i	$-0.220880\pi$
$157$	19.2648	1.53750	0.768748	+	0.639552i	$0.220880\pi$
$158$	−5.75990	−0.458233
$159$	−0.499822	−0.0396384
$160$	4.69846	0.371446
$161$	1.00000	0.0788110
$162$	−0.451228	−0.0354518
$163$	18.0989	1.41761	0.708806	−	0.705403i	$-0.249234\pi$
$163$	18.0989	1.41761	0.708806	+	0.705403i	$0.249234\pi$
$164$	10.7763	0.841489
$165$	0.260456	0.0202765
$166$	−0.799135	−0.0620249
$167$	−14.2612	−1.10356	−0.551781	−	0.833989i	$-0.686051\pi$
$167$	−14.2612	−1.10356	−0.551781	+	0.833989i	$0.686051\pi$
$168$	−1.71304	−0.132164
$169$	2.01235	0.154796
$170$	1.09532	0.0840069
$171$	1.68072	0.128528
$172$	−18.5982	−1.41810
$173$	8.12489	0.617724	0.308862	−	0.951107i	$-0.400052\pi$
$173$	8.12489	0.617724	0.308862	+	0.951107i	$0.400052\pi$
$174$	0.0799126	0.00605816
$175$	−1.00000	−0.0755929
$176$	−0.734437	−0.0553603
$177$	10.0276	0.753721
$178$	−2.33932	−0.175339
$179$	−2.30163	−0.172032	−0.0860160	−	0.996294i	$-0.527414\pi$
$179$	−2.30163	−0.172032	−0.0860160	+	0.996294i	$0.527414\pi$
$180$	1.79639	0.133895
$181$	−24.3900	−1.81289	−0.906447	−	0.422319i	$-0.861216\pi$
$181$	−24.3900	−1.81289	−0.906447	+	0.422319i	$0.861216\pi$
$182$	−1.74832	−0.129594
$183$	−0.604512	−0.0446868
$184$	−1.71304	−0.126287
$185$	5.24538	0.385648
$186$	2.96271	0.217237
$187$	−0.632233	−0.0462335
$188$	−20.9439	−1.52749
$189$	−1.00000	−0.0727393
$190$	0.758388	0.0550193
$191$	4.88851	0.353720	0.176860	−	0.984236i	$-0.443406\pi$
$191$	4.88851	0.353720	0.176860	+	0.984236i	$0.443406\pi$
$192$	−3.51956	−0.254002
$193$	24.1677	1.73963	0.869814	−	0.493380i	$-0.164239\pi$
$193$	24.1677	1.73963	0.869814	+	0.493380i	$0.164239\pi$
$194$	−0.511046	−0.0366910
$195$	3.87458	0.277464
$196$	−1.79639	−0.128314
$197$	−23.2058	−1.65334	−0.826671	−	0.562685i	$-0.809768\pi$
$197$	−23.2058	−1.65334	−0.826671	+	0.562685i	$0.809768\pi$
$198$	0.117525	0.00835213
$199$	11.8387	0.839223	0.419611	−	0.907704i	$-0.362166\pi$
$199$	11.8387	0.839223	0.419611	+	0.907704i	$0.362166\pi$
$200$	1.71304	0.121130
$201$	−2.37440	−0.167477
$202$	−4.07000	−0.286364
$203$	0.177100	0.0124300
$204$	−4.36059	−0.305302
$205$	5.99886	0.418979
$206$	1.30342	0.0908136
$207$	−1.00000	−0.0695048
$208$	−10.9256	−0.757554
$209$	−0.437754	−0.0302800
$210$	−0.451228	−0.0311377
$211$	−23.0019	−1.58352	−0.791759	−	0.610833i	$-0.790835\pi$
$211$	−23.0019	−1.58352	−0.791759	+	0.610833i	$0.790835\pi$
$212$	0.897876	0.0616664
$213$	1.89171	0.129618
$214$	8.39097	0.573595
$215$	−10.3531	−0.706073
$216$	1.71304	0.116557
$217$	6.56589	0.445722
$218$	−8.94118	−0.605573
$219$	15.9391	1.07706
$220$	−0.467881	−0.0315445
$221$	−9.40520	−0.632662
$222$	2.36686	0.158853
$223$	3.40628	0.228101	0.114051	−	0.993475i	$-0.463617\pi$
$223$	3.40628	0.228101	0.114051	+	0.993475i	$0.463617\pi$
$224$	4.69846	0.313929
$225$	1.00000	0.0666667
$226$	−1.49135	−0.0992030
$227$	−9.05753	−0.601169	−0.300585	−	0.953755i	$-0.597182\pi$
$227$	−9.05753	−0.601169	−0.300585	+	0.953755i	$0.597182\pi$
$228$	−3.01924	−0.199954
$229$	−1.78753	−0.118124	−0.0590618	−	0.998254i	$-0.518811\pi$
$229$	−1.78753	−0.118124	−0.0590618	+	0.998254i	$0.518811\pi$
$230$	−0.451228	−0.0297531
$231$	0.260456	0.0171367
$232$	−0.303380	−0.0199179
$233$	22.9952	1.50647	0.753234	−	0.657752i	$-0.228493\pi$
$233$	22.9952	1.50647	0.753234	+	0.657752i	$0.228493\pi$
$234$	1.74832	0.114291
$235$	−11.6589	−0.760540
$236$	−18.0135	−1.17258
$237$	12.7650	0.829173
$238$	1.09532	0.0709988
$239$	−12.2486	−0.792297	−0.396149	−	0.918186i	$-0.629654\pi$
$239$	−12.2486	−0.792297	−0.396149	+	0.918186i	$0.629654\pi$
$240$	−2.81982	−0.182018
$241$	17.9415	1.15571	0.577857	−	0.816138i	$-0.303889\pi$
$241$	17.9415	1.15571	0.577857	+	0.816138i	$0.303889\pi$
$242$	4.93290	0.317099
$243$	1.00000	0.0641500
$244$	1.08594	0.0695203
$245$	−1.00000	−0.0638877
$246$	2.70685	0.172583
$247$	−6.51209	−0.414354
$248$	−11.2476	−0.714224
$249$	1.77102	0.112234
$250$	0.451228	0.0285382
$251$	−3.47371	−0.219259	−0.109629	−	0.993973i	$-0.534966\pi$
$251$	−3.47371	−0.219259	−0.109629	+	0.993973i	$0.534966\pi$
$252$	1.79639	0.113162
$253$	0.260456	0.0163747
$254$	−6.90122	−0.433021
$255$	−2.42741	−0.152010
$256$	2.08237	0.130148
$257$	21.0688	1.31423	0.657117	−	0.753789i	$-0.271776\pi$
$257$	21.0688	1.31423	0.657117	+	0.753789i	$0.271776\pi$
$258$	−4.67159	−0.290841
$259$	5.24538	0.325932
$260$	−6.96027	−0.431657
$261$	−0.177100	−0.0109622
$262$	−4.89840	−0.302624
$263$	−21.9676	−1.35458	−0.677291	−	0.735715i	$-0.736846\pi$
$263$	−21.9676	−1.35458	−0.677291	+	0.735715i	$0.736846\pi$
$264$	−0.446171	−0.0274599
$265$	0.499822	0.0307038
$266$	0.758388	0.0464998
$267$	5.18434	0.317277
$268$	4.26536	0.260548
$269$	−20.0812	−1.22437	−0.612187	−	0.790713i	$-0.709710\pi$
$269$	−20.0812	−1.22437	−0.612187	+	0.790713i	$0.709710\pi$
$270$	0.451228	0.0274608
$271$	−6.47761	−0.393487	−0.196743	−	0.980455i	$-0.563037\pi$
$271$	−6.47761	−0.393487	−0.196743	+	0.980455i	$0.563037\pi$
$272$	6.84486	0.415030
$273$	3.87458	0.234500
$274$	2.87590	0.173740
$275$	−0.260456	−0.0157061
$276$	1.79639	0.108130
$277$	11.5206	0.692203	0.346102	−	0.938197i	$-0.387505\pi$
$277$	11.5206	0.692203	0.346102	+	0.938197i	$0.387505\pi$
$278$	−7.37538	−0.442346
$279$	−6.56589	−0.393089
$280$	1.71304	0.102374
$281$	−9.22440	−0.550281	−0.275141	−	0.961404i	$-0.588724\pi$
$281$	−9.22440	−0.550281	−0.275141	+	0.961404i	$0.588724\pi$
$282$	−5.26080	−0.313276
$283$	21.9263	1.30338	0.651690	−	0.758485i	$-0.274060\pi$
$283$	21.9263	1.30338	0.651690	+	0.758485i	$0.274060\pi$
$284$	−3.39825	−0.201649
$285$	−1.68072	−0.0995573
$286$	−0.455359	−0.0269260
$287$	5.99886	0.354102
$288$	−4.69846	−0.276859
$289$	−11.1077	−0.653393
$290$	−0.0799126	−0.00469263
$291$	1.13257	0.0663923
$292$	−28.6328	−1.67561
$293$	−22.8924	−1.33739	−0.668693	−	0.743538i	$-0.733146\pi$
$293$	−22.8924	−1.33739	−0.668693	+	0.743538i	$0.733146\pi$
$294$	−0.451228	−0.0263161
$295$	−10.0276	−0.583829
$296$	−8.98553	−0.522273
$297$	−0.260456	−0.0151132
$298$	−2.18173	−0.126384
$299$	3.87458	0.224073
$300$	−1.79639	−0.103715
$301$	−10.3531	−0.596741
$302$	2.10412	0.121078
$303$	9.01984	0.518176
$304$	4.73933	0.271819
$305$	0.604512	0.0346143
$306$	−1.09532	−0.0626150
$307$	−0.397953	−0.0227124	−0.0113562	−	0.999936i	$-0.503615\pi$
$307$	−0.397953	−0.0227124	−0.0113562	+	0.999936i	$0.503615\pi$
$308$	−0.467881	−0.0266600
$309$	−2.88861	−0.164327
$310$	−2.96271	−0.168271
$311$	−5.38425	−0.305313	−0.152657	−	0.988279i	$-0.548783\pi$
$311$	−5.38425	−0.305313	−0.152657	+	0.988279i	$0.548783\pi$
$312$	−6.63730	−0.375763
$313$	3.31953	0.187631	0.0938156	−	0.995590i	$-0.470094\pi$
$313$	3.31953	0.187631	0.0938156	+	0.995590i	$0.470094\pi$
$314$	−8.69280	−0.490563
$315$	1.00000	0.0563436
$316$	−22.9309	−1.28996
$317$	20.1857	1.13374	0.566871	−	0.823806i	$-0.308154\pi$
$317$	20.1857	1.13374	0.566871	+	0.823806i	$0.308154\pi$
$318$	0.225533	0.0126473
$319$	0.0461268	0.00258261
$320$	3.51956	0.196749
$321$	−18.5959	−1.03792
$322$	−0.451228	−0.0251459
$323$	4.07980	0.227006
$324$	−1.79639	−0.0997996
$325$	−3.87458	−0.214923
$326$	−8.16671	−0.452312
$327$	19.8152	1.09578
$328$	−10.2763	−0.567413
$329$	−11.6589	−0.642773
$330$	−0.117525	−0.00646953
$331$	27.5715	1.51547	0.757734	−	0.652564i	$-0.226306\pi$
$331$	27.5715	1.51547	0.757734	+	0.652564i	$0.226306\pi$
$332$	−3.18146	−0.174605
$333$	−5.24538	−0.287445
$334$	6.43503	0.352109
$335$	2.37440	0.129727
$336$	−2.81982	−0.153834
$337$	15.0372	0.819129	0.409564	−	0.912281i	$-0.365681\pi$
$337$	15.0372	0.819129	0.409564	+	0.912281i	$0.365681\pi$
$338$	−0.908030	−0.0493903
$339$	3.30509	0.179508
$340$	4.36059	0.236486
$341$	1.71012	0.0926084
$342$	−0.758388	−0.0410089
$343$	−1.00000	−0.0539949
$344$	17.7352	0.956218
$345$	1.00000	0.0538382
$346$	−3.66618	−0.197095
$347$	29.6270	1.59046	0.795230	−	0.606307i	$-0.207350\pi$
$347$	29.6270	1.59046	0.795230	+	0.606307i	$0.207350\pi$
$348$	0.318142	0.0170542
$349$	−4.20938	−0.225323	−0.112661	−	0.993633i	$-0.535938\pi$
$349$	−4.20938	−0.225323	−0.112661	+	0.993633i	$0.535938\pi$
$350$	0.451228	0.0241191
$351$	−3.87458	−0.206810
$352$	1.22374	0.0652256
$353$	−32.8482	−1.74833	−0.874167	−	0.485625i	$-0.838592\pi$
$353$	−32.8482	−1.74833	−0.874167	+	0.485625i	$0.838592\pi$
$354$	−4.52473	−0.240487
$355$	−1.89171	−0.100401
$356$	−9.31312	−0.493594
$357$	−2.42741	−0.128472
$358$	1.03856	0.0548896
$359$	−10.7262	−0.566109	−0.283055	−	0.959104i	$-0.591348\pi$
$359$	−10.7262	−0.566109	−0.283055	+	0.959104i	$0.591348\pi$
$360$	−1.71304	−0.0902850
$361$	−16.1752	−0.851325
$362$	11.0054	0.578433
$363$	−10.9322	−0.573790
$364$	−6.96027	−0.364817
$365$	−15.9391	−0.834288
$366$	0.272773	0.0142581
$367$	9.32667	0.486848	0.243424	−	0.969920i	$-0.421729\pi$
$367$	9.32667	0.486848	0.243424	+	0.969920i	$0.421729\pi$
$368$	−2.81982	−0.146993
$369$	−5.99886	−0.312288
$370$	−2.36686	−0.123047
$371$	0.499822	0.0259494
$372$	11.7949	0.611538
$373$	−23.5376	−1.21873	−0.609364	−	0.792890i	$-0.708575\pi$
$373$	−23.5376	−1.21873	−0.609364	+	0.792890i	$0.708575\pi$
$374$	0.285281	0.0147515
$375$	−1.00000	−0.0516398
$376$	19.9721	1.02998
$377$	0.686189	0.0353406
$378$	0.451228	0.0232087
$379$	12.2270	0.628061	0.314030	−	0.949413i	$-0.398321\pi$
$379$	12.2270	0.628061	0.314030	+	0.949413i	$0.398321\pi$
$380$	3.01924	0.154884
$381$	15.2943	0.783551
$382$	−2.20583	−0.112860
$383$	15.2795	0.780747	0.390373	−	0.920657i	$-0.372346\pi$
$383$	15.2795	0.780747	0.390373	+	0.920657i	$0.372346\pi$
$384$	10.9850	0.560578
$385$	−0.260456	−0.0132741
$386$	−10.9051	−0.555056
$387$	10.3531	0.526276
$388$	−2.03454	−0.103288
$389$	28.4883	1.44441	0.722207	−	0.691677i	$-0.243128\pi$
$389$	28.4883	1.44441	0.722207	+	0.691677i	$0.243128\pi$
$390$	−1.74832	−0.0885295
$391$	−2.42741	−0.122759
$392$	1.71304	0.0865215
$393$	10.8557	0.547598
$394$	10.4711	0.527526
$395$	−12.7650	−0.642274
$396$	0.467881	0.0235119
$397$	−18.7157	−0.939316	−0.469658	−	0.882848i	$-0.655623\pi$
$397$	−18.7157	−0.939316	−0.469658	+	0.882848i	$0.655623\pi$
$398$	−5.34195	−0.267768
$399$	−1.68072	−0.0841413
$400$	2.81982	0.140991
$401$	−2.66662	−0.133165	−0.0665823	−	0.997781i	$-0.521210\pi$
$401$	−2.66662	−0.133165	−0.0665823	+	0.997781i	$0.521210\pi$
$402$	1.07140	0.0534363
$403$	25.4400	1.26726
$404$	−16.2032	−0.806139
$405$	−1.00000	−0.0496904
$406$	−0.0799126	−0.00396600
$407$	1.36619	0.0677194
$408$	4.15825	0.205864
$409$	20.7159	1.02434	0.512168	−	0.858885i	$-0.328842\pi$
$409$	20.7159	1.02434	0.512168	+	0.858885i	$0.328842\pi$
$410$	−2.70685	−0.133682
$411$	−6.37351	−0.314382
$412$	5.18908	0.255648
$413$	−10.0276	−0.493426
$414$	0.451228	0.0221766
$415$	−1.77102	−0.0869361
$416$	18.2045	0.892551
$417$	16.3451	0.800424
$418$	0.197527	0.00966134
$419$	15.3289	0.748864	0.374432	−	0.927254i	$-0.377838\pi$
$419$	15.3289	0.748864	0.374432	+	0.927254i	$0.377838\pi$
$420$	−1.79639	−0.0876550
$421$	6.75144	0.329045	0.164522	−	0.986373i	$-0.447392\pi$
$421$	6.75144	0.329045	0.164522	+	0.986373i	$0.447392\pi$
$422$	10.3791	0.505247
$423$	11.6589	0.566873
$424$	−0.856214	−0.0415814
$425$	2.42741	0.117747
$426$	−0.853592	−0.0413567
$427$	0.604512	0.0292544
$428$	33.4055	1.61471
$429$	1.00916	0.0487225
$430$	4.67159	0.225284
$431$	28.6211	1.37863	0.689315	−	0.724462i	$-0.257912\pi$
$431$	28.6211	1.37863	0.689315	+	0.724462i	$0.257912\pi$
$432$	2.81982	0.135668
$433$	39.2704	1.88722	0.943608	−	0.331065i	$-0.107408\pi$
$433$	39.2704	1.88722	0.943608	+	0.331065i	$0.107408\pi$
$434$	−2.96271	−0.142215
$435$	0.177100	0.00849132
$436$	−35.5959	−1.70474
$437$	−1.68072	−0.0803998
$438$	−7.19214	−0.343654
$439$	−38.6728	−1.84575	−0.922877	−	0.385096i	$-0.874168\pi$
$439$	−38.6728	−1.84575	−0.922877	+	0.385096i	$0.874168\pi$
$440$	0.446171	0.0212704
$441$	1.00000	0.0476190
$442$	4.24389	0.201861
$443$	−32.7492	−1.55596	−0.777981	−	0.628288i	$-0.783756\pi$
$443$	−32.7492	−1.55596	−0.777981	+	0.628288i	$0.783756\pi$
$444$	9.42276	0.447184
$445$	−5.18434	−0.245761
$446$	−1.53701	−0.0727793
$447$	4.83509	0.228692
$448$	3.51956	0.166284
$449$	−29.0259	−1.36982	−0.684910	−	0.728628i	$-0.740158\pi$
$449$	−29.0259	−1.36982	−0.684910	+	0.728628i	$0.740158\pi$
$450$	−0.451228	−0.0212711
$451$	1.56244	0.0735724
$452$	−5.93724	−0.279264
$453$	−4.66309	−0.219091
$454$	4.08701	0.191813
$455$	−3.87458	−0.181643
$456$	2.87914	0.134828
$457$	30.4406	1.42395	0.711975	−	0.702205i	$-0.247801\pi$
$457$	30.4406	1.42395	0.711975	+	0.702205i	$0.247801\pi$
$458$	0.806585	0.0376893
$459$	2.42741	0.113302
$460$	−1.79639	−0.0837573
$461$	−40.9625	−1.90782	−0.953908	−	0.300100i	$-0.902980\pi$
$461$	−40.9625	−1.90782	−0.953908	+	0.300100i	$0.902980\pi$
$462$	−0.117525	−0.00546775
$463$	−9.40678	−0.437170	−0.218585	−	0.975818i	$-0.570144\pi$
$463$	−9.40678	−0.437170	−0.218585	+	0.975818i	$0.570144\pi$
$464$	−0.499391	−0.0231836
$465$	6.56589	0.304486
$466$	−10.3761	−0.480663
$467$	−24.6981	−1.14289	−0.571445	−	0.820640i	$-0.693617\pi$
$467$	−24.6981	−1.14289	−0.571445	+	0.820640i	$0.693617\pi$
$468$	6.96027	0.321738
$469$	2.37440	0.109640
$470$	5.26080	0.242663
$471$	19.2648	0.887674
$472$	17.1777	0.790666
$473$	−2.69652	−0.123986
$474$	−5.75990	−0.264561
$475$	1.68072	0.0771168
$476$	4.36059	0.199867
$477$	−0.499822	−0.0228853
$478$	5.52692	0.252795
$479$	−14.5808	−0.666213	−0.333106	−	0.942889i	$-0.608097\pi$
$479$	−14.5808	−0.666213	−0.333106	+	0.942889i	$0.608097\pi$
$480$	4.69846	0.214454
$481$	20.3236	0.926677
$482$	−8.09571	−0.368750
$483$	1.00000	0.0455016
$484$	19.6385	0.892658
$485$	−1.13257	−0.0514273
$486$	−0.451228	−0.0204681
$487$	−15.2509	−0.691083	−0.345542	−	0.938403i	$-0.612305\pi$
$487$	−15.2509	−0.691083	−0.345542	+	0.938403i	$0.612305\pi$
$488$	−1.03555	−0.0468772
$489$	18.0989	0.818459
$490$	0.451228	0.0203844
$491$	−29.1252	−1.31440	−0.657200	−	0.753716i	$-0.728259\pi$
$491$	−29.1252	−1.31440	−0.657200	+	0.753716i	$0.728259\pi$
$492$	10.7763	0.485834
$493$	−0.429896	−0.0193615
$494$	2.93843	0.132206
$495$	0.260456	0.0117066
$496$	−18.5146	−0.831330
$497$	−1.89171	−0.0848547
$498$	−0.799135	−0.0358101
$499$	17.8485	0.799007	0.399504	−	0.916732i	$-0.369182\pi$
$499$	17.8485	0.799007	0.399504	+	0.916732i	$0.369182\pi$
$500$	1.79639	0.0803372
$501$	−14.2612	−0.637141
$502$	1.56743	0.0699580
$503$	15.8221	0.705472	0.352736	−	0.935723i	$-0.385251\pi$
$503$	15.8221	0.705472	0.352736	+	0.935723i	$0.385251\pi$
$504$	−1.71304	−0.0763048
$505$	−9.01984	−0.401378
$506$	−0.117525	−0.00522462
$507$	2.01235	0.0893717
$508$	−27.4746	−1.21899
$509$	−24.7956	−1.09905	−0.549523	−	0.835478i	$-0.685191\pi$
$509$	−24.7956	−1.09905	−0.549523	+	0.835478i	$0.685191\pi$
$510$	1.09532	0.0485014
$511$	−15.9391	−0.705102
$512$	−22.9097	−1.01247
$513$	1.68072	0.0742057
$514$	−9.50682	−0.419328
$515$	2.88861	0.127287
$516$	−18.5982	−0.818739
$517$	−3.03662	−0.133550
$518$	−2.36686	−0.103994
$519$	8.12489	0.356643
$520$	6.63730	0.291065
$521$	−2.41190	−0.105667	−0.0528337	−	0.998603i	$-0.516825\pi$
$521$	−2.41190	−0.105667	−0.0528337	+	0.998603i	$0.516825\pi$
$522$	0.0799126	0.00349768
$523$	34.6429	1.51483	0.757414	−	0.652935i	$-0.226463\pi$
$523$	34.6429	1.51483	0.757414	+	0.652935i	$0.226463\pi$
$524$	−19.5011	−0.851911
$525$	−1.00000	−0.0436436
$526$	9.91241	0.432202
$527$	−15.9381	−0.694275
$528$	−0.734437	−0.0319623
$529$	1.00000	0.0434783
$530$	−0.225533	−0.00979655
$531$	10.0276	0.435161
$532$	3.01924	0.130901
$533$	23.2431	1.00677
$534$	−2.33932	−0.101232
$535$	18.5959	0.803969
$536$	−4.06744	−0.175687
$537$	−2.30163	−0.0993227
$538$	9.06120	0.390656
$539$	−0.260456	−0.0112186
$540$	1.79639	0.0773045
$541$	−7.04854	−0.303040	−0.151520	−	0.988454i	$-0.548417\pi$
$541$	−7.04854	−0.303040	−0.151520	+	0.988454i	$0.548417\pi$
$542$	2.92288	0.125548
$543$	−24.3900	−1.04668
$544$	−11.4051	−0.488989
$545$	−19.8152	−0.848791
$546$	−1.74832	−0.0748211
$547$	−39.6302	−1.69446	−0.847232	−	0.531223i	$-0.821733\pi$
$547$	−39.6302	−1.69446	−0.847232	+	0.531223i	$0.821733\pi$
$548$	11.4493	0.489091
$549$	−0.604512	−0.0257999
$550$	0.117525	0.00501128
$551$	−0.297657	−0.0126806
$552$	−1.71304	−0.0729117
$553$	−12.7650	−0.542821
$554$	−5.19839	−0.220859
$555$	5.24538	0.222654
$556$	−29.3623	−1.24524
$557$	39.4983	1.67360	0.836799	−	0.547510i	$-0.184424\pi$
$557$	39.4983	1.67360	0.836799	+	0.547510i	$0.184424\pi$
$558$	2.96271	0.125422
$559$	−40.1138	−1.69663
$560$	2.81982	0.119159
$561$	−0.632233	−0.0266929
$562$	4.16230	0.175576
$563$	30.1223	1.26950	0.634751	−	0.772717i	$-0.281103\pi$
$563$	30.1223	1.26950	0.634751	+	0.772717i	$0.281103\pi$
$564$	−20.9439	−0.881897
$565$	−3.30509	−0.139046
$566$	−9.89374	−0.415865
$567$	−1.00000	−0.0419961
$568$	3.24057	0.135971
$569$	−36.5555	−1.53249	−0.766243	−	0.642551i	$-0.777876\pi$
$569$	−36.5555	−1.53249	−0.766243	+	0.642551i	$0.777876\pi$
$570$	0.758388	0.0317654
$571$	−19.5080	−0.816385	−0.408193	−	0.912896i	$-0.633841\pi$
$571$	−19.5080	−0.816385	−0.408193	+	0.912896i	$0.633841\pi$
$572$	−1.81284	−0.0757987
$573$	4.88851	0.204221
$574$	−2.70685	−0.112982
$575$	−1.00000	−0.0417029
$576$	−3.51956	−0.146648
$577$	−13.2929	−0.553391	−0.276695	−	0.960958i	$-0.589239\pi$
$577$	−13.2929	−0.553391	−0.276695	+	0.960958i	$0.589239\pi$
$578$	5.01209	0.208475
$579$	24.1677	1.00437
$580$	−0.318142	−0.0132101
$581$	−1.77102	−0.0734745
$582$	−0.511046	−0.0211835
$583$	0.130181	0.00539156
$584$	27.3042	1.12986
$585$	3.87458	0.160194
$586$	10.3297	0.426715
$587$	5.52641	0.228099	0.114050	−	0.993475i	$-0.463618\pi$
$587$	5.52641	0.228099	0.114050	+	0.993475i	$0.463618\pi$
$588$	−1.79639	−0.0740820
$589$	−11.0354	−0.454707
$590$	4.52473	0.186280
$591$	−23.2058	−0.954558
$592$	−14.7910	−0.607906
$593$	−17.2868	−0.709882	−0.354941	−	0.934889i	$-0.615499\pi$
$593$	−17.2868	−0.709882	−0.354941	+	0.934889i	$0.615499\pi$
$594$	0.117525	0.00482210
$595$	2.42741	0.0995142
$596$	−8.68573	−0.355781
$597$	11.8387	0.484526
$598$	−1.74832	−0.0714940
$599$	2.10733	0.0861032	0.0430516	−	0.999073i	$-0.486292\pi$
$599$	2.10733	0.0861032	0.0430516	+	0.999073i	$0.486292\pi$
$600$	1.71304	0.0699345
$601$	16.8020	0.685368	0.342684	−	0.939451i	$-0.388664\pi$
$601$	16.8020	0.685368	0.342684	+	0.939451i	$0.388664\pi$
$602$	4.67159	0.190400
$603$	−2.37440	−0.0966930
$604$	8.37674	0.340845
$605$	10.9322	0.444456
$606$	−4.07000	−0.165333
$607$	15.6155	0.633812	0.316906	−	0.948457i	$-0.397356\pi$
$607$	15.6155	0.633812	0.316906	+	0.948457i	$0.397356\pi$
$608$	−7.89680	−0.320257
$609$	0.177100	0.00717647
$610$	−0.272773	−0.0110442
$611$	−45.1731	−1.82751
$612$	−4.36059	−0.176266
$613$	−23.1691	−0.935791	−0.467896	−	0.883784i	$-0.654988\pi$
$613$	−23.1691	−0.935791	−0.467896	+	0.883784i	$0.654988\pi$
$614$	0.179568	0.00724676
$615$	5.99886	0.241898
$616$	0.446171	0.0179767
$617$	6.51308	0.262207	0.131103	−	0.991369i	$-0.458148\pi$
$617$	6.51308	0.262207	0.131103	+	0.991369i	$0.458148\pi$
$618$	1.30342	0.0524313
$619$	−20.5011	−0.824010	−0.412005	−	0.911182i	$-0.635171\pi$
$619$	−20.5011	−0.824010	−0.412005	+	0.911182i	$0.635171\pi$
$620$	−11.7949	−0.473695
$621$	−1.00000	−0.0401286
$622$	2.42953	0.0974151
$623$	−5.18434	−0.207706
$624$	−10.9256	−0.437374
$625$	1.00000	0.0400000
$626$	−1.49787	−0.0598668
$627$	−0.437754	−0.0174822
$628$	−34.6071	−1.38097
$629$	−12.7327	−0.507685
$630$	−0.451228	−0.0179773
$631$	−3.86595	−0.153901	−0.0769505	−	0.997035i	$-0.524518\pi$
$631$	−3.86595	−0.153901	−0.0769505	+	0.997035i	$0.524518\pi$
$632$	21.8668	0.869817
$633$	−23.0019	−0.914245
$634$	−9.10836	−0.361739
$635$	−15.2943	−0.606936
$636$	0.897876	0.0356031
$637$	−3.87458	−0.153516
$638$	−0.0208137	−0.000824023 0
$639$	1.89171	0.0748349
$640$	−10.9850	−0.434222
$641$	−15.0993	−0.596386	−0.298193	−	0.954506i	$-0.596384\pi$
$641$	−15.0993	−0.596386	−0.298193	+	0.954506i	$0.596384\pi$
$642$	8.39097	0.331165
$643$	10.4350	0.411516	0.205758	−	0.978603i	$-0.434034\pi$
$643$	10.4350	0.411516	0.205758	+	0.978603i	$0.434034\pi$
$644$	−1.79639	−0.0707878
$645$	−10.3531	−0.407652
$646$	−1.84092	−0.0724300
$647$	38.4616	1.51208	0.756042	−	0.654524i	$-0.227131\pi$
$647$	38.4616	1.51208	0.756042	+	0.654524i	$0.227131\pi$
$648$	1.71304	0.0672945
$649$	−2.61175	−0.102520
$650$	1.74832	0.0685746
$651$	6.56589	0.257337
$652$	−32.5127	−1.27329
$653$	11.8979	0.465601	0.232800	−	0.972525i	$-0.425211\pi$
$653$	11.8979	0.465601	0.232800	+	0.972525i	$0.425211\pi$
$654$	−8.94118	−0.349628
$655$	−10.8557	−0.424168
$656$	−16.9157	−0.660447
$657$	15.9391	0.621842
$658$	5.26080	0.205087
$659$	−31.0431	−1.20927	−0.604633	−	0.796504i	$-0.706680\pi$
$659$	−31.0431	−1.20927	−0.604633	+	0.796504i	$0.706680\pi$
$660$	−0.467881	−0.0182122
$661$	40.9761	1.59378	0.796892	−	0.604121i	$-0.206476\pi$
$661$	40.9761	1.59378	0.796892	+	0.604121i	$0.206476\pi$
$662$	−12.4410	−0.483535
$663$	−9.40520	−0.365268
$664$	3.03383	0.117736
$665$	1.68072	0.0651756
$666$	2.36686	0.0917139
$667$	0.177100	0.00685736
$668$	25.6186	0.991215
$669$	3.40628	0.131694
$670$	−1.07140	−0.0413916
$671$	0.157449	0.00607824
$672$	4.69846	0.181247
$673$	38.2740	1.47536	0.737678	−	0.675153i	$-0.235922\pi$
$673$	38.2740	1.47536	0.737678	+	0.675153i	$0.235922\pi$
$674$	−6.78520	−0.261356
$675$	1.00000	0.0384900
$676$	−3.61498	−0.139038
$677$	27.9070	1.07255	0.536277	−	0.844042i	$-0.319830\pi$
$677$	27.9070	1.07255	0.536277	+	0.844042i	$0.319830\pi$
$678$	−1.49135	−0.0572749
$679$	−1.13257	−0.0434640
$680$	−4.15825	−0.159462
$681$	−9.05753	−0.347085
$682$	−0.771655	−0.0295482
$683$	−38.7239	−1.48173	−0.740865	−	0.671654i	$-0.765584\pi$
$683$	−38.7239	−1.48173	−0.740865	+	0.671654i	$0.765584\pi$
$684$	−3.01924	−0.115443
$685$	6.37351	0.243519
$686$	0.451228	0.0172280
$687$	−1.78753	−0.0681987
$688$	29.1937	1.11300
$689$	1.93660	0.0737785
$690$	−0.451228	−0.0171779
$691$	−3.68449	−0.140165	−0.0700823	−	0.997541i	$-0.522326\pi$
$691$	−3.68449	−0.140165	−0.0700823	+	0.997541i	$0.522326\pi$
$692$	−14.5955	−0.554838
$693$	0.260456	0.00989390
$694$	−13.3685	−0.507462
$695$	−16.3451	−0.620006
$696$	−0.303380	−0.0114996
$697$	−14.5617	−0.551564
$698$	1.89939	0.0718930
$699$	22.9952	0.869760
$700$	1.79639	0.0678973
$701$	18.9303	0.714988	0.357494	−	0.933915i	$-0.383631\pi$
$701$	18.9303	0.714988	0.357494	+	0.933915i	$0.383631\pi$
$702$	1.74832	0.0659860
$703$	−8.81601	−0.332502
$704$	0.916689	0.0345490
$705$	−11.6589	−0.439098
$706$	14.8220	0.557834
$707$	−9.01984	−0.339226
$708$	−18.0135	−0.676989
$709$	5.18881	0.194870	0.0974349	−	0.995242i	$-0.468936\pi$
$709$	5.18881	0.194870	0.0974349	+	0.995242i	$0.468936\pi$
$710$	0.853592	0.0320347
$711$	12.7650	0.478723
$712$	8.88098	0.332829
$713$	6.56589	0.245894
$714$	1.09532	0.0409912
$715$	−1.00916	−0.0377403
$716$	4.13464	0.154519
$717$	−12.2486	−0.457433
$718$	4.83998	0.180626
$719$	17.5526	0.654601	0.327300	−	0.944920i	$-0.393861\pi$
$719$	17.5526	0.654601	0.327300	+	0.944920i	$0.393861\pi$
$720$	−2.81982	−0.105088
$721$	2.88861	0.107577
$722$	7.29869	0.271629
$723$	17.9415	0.667252
$724$	43.8140	1.62834
$725$	−0.177100	−0.00657735
$726$	4.93290	0.183077
$727$	26.5786	0.985745	0.492873	−	0.870102i	$-0.335947\pi$
$727$	26.5786	0.985745	0.492873	+	0.870102i	$0.335947\pi$
$728$	6.63730	0.245995
$729$	1.00000	0.0370370
$730$	7.19214	0.266193
$731$	25.1311	0.929509
$732$	1.08594	0.0401376
$733$	17.9479	0.662922	0.331461	−	0.943469i	$-0.392458\pi$
$733$	17.9479	0.662922	0.331461	+	0.943469i	$0.392458\pi$
$734$	−4.20845	−0.155337
$735$	−1.00000	−0.0368856
$736$	4.69846	0.173187
$737$	0.618426	0.0227800
$738$	2.70685	0.0996407
$739$	−4.67546	−0.171990	−0.0859948	−	0.996296i	$-0.527407\pi$
$739$	−4.67546	−0.171990	−0.0859948	+	0.996296i	$0.527407\pi$
$740$	−9.42276	−0.346387
$741$	−6.51209	−0.239227
$742$	−0.225533	−0.00827959
$743$	−18.1992	−0.667664	−0.333832	−	0.942633i	$-0.608342\pi$
$743$	−18.1992	−0.667664	−0.333832	+	0.942633i	$0.608342\pi$
$744$	−11.2476	−0.412358
$745$	−4.83509	−0.177144
$746$	10.6208	0.388855
$747$	1.77102	0.0647984
$748$	1.13574	0.0415268
$749$	18.5959	0.679478
$750$	0.451228	0.0164765
$751$	−30.1708	−1.10095	−0.550473	−	0.834853i	$-0.685553\pi$
$751$	−30.1708	−1.10095	−0.550473	+	0.834853i	$0.685553\pi$
$752$	32.8758	1.19886
$753$	−3.47371	−0.126589
$754$	−0.309628	−0.0112760
$755$	4.66309	0.169707
$756$	1.79639	0.0653342
$757$	11.6088	0.421930	0.210965	−	0.977494i	$-0.432339\pi$
$757$	11.6088	0.421930	0.210965	+	0.977494i	$0.432339\pi$
$758$	−5.51718	−0.200393
$759$	0.260456	0.00945394
$760$	−2.87914	−0.104437
$761$	36.9458	1.33929	0.669643	−	0.742683i	$-0.266447\pi$
$761$	36.9458	1.33929	0.669643	+	0.742683i	$0.266447\pi$
$762$	−6.90122	−0.250005
$763$	−19.8152	−0.717359
$764$	−8.78169	−0.317711
$765$	−2.42741	−0.0877633
$766$	−6.89454	−0.249110
$767$	−38.8527	−1.40289
$768$	2.08237	0.0751409
$769$	−46.1212	−1.66317	−0.831587	−	0.555394i	$-0.812567\pi$
$769$	−46.1212	−1.66317	−0.831587	+	0.555394i	$0.812567\pi$
$770$	0.117525	0.00423530
$771$	21.0688	0.758773
$772$	−43.4147	−1.56253
$773$	2.83756	0.102060	0.0510300	−	0.998697i	$-0.483750\pi$
$773$	2.83756	0.102060	0.0510300	+	0.998697i	$0.483750\pi$
$774$	−4.67159	−0.167917
$775$	−6.56589	−0.235854
$776$	1.94013	0.0696467
$777$	5.24538	0.188177
$778$	−12.8547	−0.460864
$779$	−10.0824	−0.361240
$780$	−6.96027	−0.249218
$781$	−0.492706	−0.0176304
$782$	1.09532	0.0391684
$783$	−0.177100	−0.00632905
$784$	2.81982	0.100708
$785$	−19.2648	−0.687589
$786$	−4.89840	−0.174720
$787$	−36.2954	−1.29379	−0.646895	−	0.762579i	$-0.723933\pi$
$787$	−36.2954	−1.29379	−0.646895	+	0.762579i	$0.723933\pi$
$788$	41.6867	1.48503
$789$	−21.9676	−0.782069
$790$	5.75990	0.204928
$791$	−3.30509	−0.117515
$792$	−0.446171	−0.0158540
$793$	2.34223	0.0831750
$794$	8.44506	0.299704
$795$	0.499822	0.0177268
$796$	−21.2670	−0.753787
$797$	8.45933	0.299645	0.149822	−	0.988713i	$-0.452130\pi$
$797$	8.45933	0.299645	0.149822	+	0.988713i	$0.452130\pi$
$798$	0.758388	0.0268467
$799$	28.3008	1.00121
$800$	−4.69846	−0.166116
$801$	5.18434	0.183180
$802$	1.20325	0.0424883
$803$	−4.15142	−0.146500
$804$	4.26536	0.150428
$805$	−1.00000	−0.0352454
$806$	−11.4793	−0.404339
$807$	−20.0812	−0.706892
$808$	15.4513	0.543576
$809$	−3.97454	−0.139737	−0.0698687	−	0.997556i	$-0.522258\pi$
$809$	−3.97454	−0.139737	−0.0698687	+	0.997556i	$0.522258\pi$
$810$	0.451228	0.0158545
$811$	−18.1155	−0.636120	−0.318060	−	0.948071i	$-0.603031\pi$
$811$	−18.1155	−0.636120	−0.318060	+	0.948071i	$0.603031\pi$
$812$	−0.318142	−0.0111646
$813$	−6.47761	−0.227180
$814$	−0.616462	−0.0216070
$815$	−18.0989	−0.633976
$816$	6.84486	0.239618
$817$	17.4006	0.608771
$818$	−9.34760	−0.326831
$819$	3.87458	0.135389
$820$	−10.7763	−0.376325
$821$	−9.42679	−0.328997	−0.164499	−	0.986377i	$-0.552601\pi$
$821$	−9.42679	−0.328997	−0.164499	+	0.986377i	$0.552601\pi$
$822$	2.87590	0.100309
$823$	−5.70597	−0.198898	−0.0994488	−	0.995043i	$-0.531708\pi$
$823$	−5.70597	−0.198898	−0.0994488	+	0.995043i	$0.531708\pi$
$824$	−4.94830	−0.172382
$825$	−0.260456	−0.00906790
$826$	4.52473	0.157436
$827$	−49.0508	−1.70566	−0.852832	−	0.522185i	$-0.825117\pi$
$827$	−49.0508	−1.70566	−0.852832	+	0.522185i	$0.825117\pi$
$828$	1.79639	0.0624290
$829$	3.18239	0.110529	0.0552645	−	0.998472i	$-0.482400\pi$
$829$	3.18239	0.110529	0.0552645	+	0.998472i	$0.482400\pi$
$830$	0.799135	0.0277384
$831$	11.5206	0.399644
$832$	13.6368	0.472771
$833$	2.42741	0.0841048
$834$	−7.37538	−0.255388
$835$	14.2612	0.493528
$836$	0.786378	0.0271974
$837$	−6.56589	−0.226950
$838$	−6.91681	−0.238937
$839$	−5.42800	−0.187395	−0.0936976	−	0.995601i	$-0.529869\pi$
$839$	−5.42800	−0.187395	−0.0936976	+	0.995601i	$0.529869\pi$
$840$	1.71304	0.0591054
$841$	−28.9686	−0.998918
$842$	−3.04644	−0.104987
$843$	−9.22440	−0.317705
$844$	41.3205	1.42231
$845$	−2.01235	−0.0692271
$846$	−5.26080	−0.180870
$847$	10.9322	0.375634
$848$	−1.40941	−0.0483992
$849$	21.9263	0.752507
$850$	−1.09532	−0.0375690
$851$	5.24538	0.179809
$852$	−3.39825	−0.116422
$853$	−20.2660	−0.693894	−0.346947	−	0.937885i	$-0.612782\pi$
$853$	−20.2660	−0.693894	−0.346947	+	0.937885i	$0.612782\pi$
$854$	−0.272773	−0.00933409
$855$	−1.68072	−0.0574795
$856$	−31.8554	−1.08880
$857$	41.3069	1.41102	0.705509	−	0.708701i	$-0.250718\pi$
$857$	41.3069	1.41102	0.705509	+	0.708701i	$0.250718\pi$
$858$	−0.455359	−0.0155457
$859$	−6.68005	−0.227920	−0.113960	−	0.993485i	$-0.536354\pi$
$859$	−6.68005	−0.227920	−0.113960	+	0.993485i	$0.536354\pi$
$860$	18.5982	0.634193
$861$	5.99886	0.204441
$862$	−12.9146	−0.439874
$863$	11.8741	0.404201	0.202100	−	0.979365i	$-0.435223\pi$
$863$	11.8741	0.404201	0.202100	+	0.979365i	$0.435223\pi$
$864$	−4.69846	−0.159845
$865$	−8.12489	−0.276255
$866$	−17.7199	−0.602147
$867$	−11.1077	−0.377236
$868$	−11.7949	−0.400346
$869$	−3.32470	−0.112783
$870$	−0.0799126	−0.00270929
$871$	9.19980	0.311723
$872$	33.9442	1.14950
$873$	1.13257	0.0383316
$874$	0.758388	0.0256529
$875$	1.00000	0.0338062
$876$	−28.6328	−0.967413
$877$	−28.3028	−0.955717	−0.477859	−	0.878437i	$-0.658587\pi$
$877$	−28.3028	−0.955717	−0.477859	+	0.878437i	$0.658587\pi$
$878$	17.4503	0.588917
$879$	−22.8924	−0.772141
$880$	0.734437	0.0247579
$881$	24.7376	0.833432	0.416716	−	0.909037i	$-0.363181\pi$
$881$	24.7376	0.833432	0.416716	+	0.909037i	$0.363181\pi$
$882$	−0.451228	−0.0151936
$883$	10.2275	0.344182	0.172091	−	0.985081i	$-0.444948\pi$
$883$	10.2275	0.344182	0.172091	+	0.985081i	$0.444948\pi$
$884$	16.8954	0.568255
$885$	−10.0276	−0.337074
$886$	14.7774	0.496455
$887$	8.84203	0.296886	0.148443	−	0.988921i	$-0.452574\pi$
$887$	8.84203	0.296886	0.148443	+	0.988921i	$0.452574\pi$
$888$	−8.98553	−0.301535
$889$	−15.2943	−0.512955
$890$	2.33932	0.0784142
$891$	−0.260456	−0.00872560
$892$	−6.11901	−0.204880
$893$	19.5953	0.655731
$894$	−2.18173	−0.0729679
$895$	2.30163	0.0769351
$896$	−10.9850	−0.366984
$897$	3.87458	0.129368
$898$	13.0973	0.437063
$899$	1.16282	0.0387823
$900$	−1.79639	−0.0598798
$901$	−1.21327	−0.0404200
$902$	−0.705016	−0.0234745
$903$	−10.3531	−0.344528
$904$	5.66174	0.188307
$905$	24.3900	0.810751
$906$	2.10412	0.0699046
$907$	7.44217	0.247113	0.123557	−	0.992338i	$-0.460570\pi$
$907$	7.44217	0.247113	0.123557	+	0.992338i	$0.460570\pi$
$908$	16.2709	0.539968
$909$	9.01984	0.299169
$910$	1.74832	0.0579561
$911$	−38.1886	−1.26525	−0.632623	−	0.774460i	$-0.718022\pi$
$911$	−38.1886	−1.26525	−0.632623	+	0.774460i	$0.718022\pi$
$912$	4.73933	0.156935
$913$	−0.461273	−0.0152659
$914$	−13.7356	−0.454334
$915$	0.604512	0.0199846
$916$	3.21112	0.106098
$917$	−10.8557	−0.358487
$918$	−1.09532	−0.0361508
$919$	49.3125	1.62667	0.813334	−	0.581797i	$-0.197650\pi$
$919$	49.3125	1.62667	0.813334	+	0.581797i	$0.197650\pi$
$920$	1.71304	0.0564772
$921$	−0.397953	−0.0131130
$922$	18.4834	0.608719
$923$	−7.32957	−0.241256
$924$	−0.467881	−0.0153922
$925$	−5.24538	−0.172467
$926$	4.24460	0.139486
$927$	−2.88861	−0.0948744
$928$	0.832099	0.0273150
$929$	36.5431	1.19894	0.599469	−	0.800398i	$-0.295378\pi$
$929$	36.5431	1.19894	0.599469	+	0.800398i	$0.295378\pi$
$930$	−2.96271	−0.0971511
$931$	1.68072	0.0550834
$932$	−41.3085	−1.35311
$933$	−5.38425	−0.176273
$934$	11.1445	0.364658
$935$	0.632233	0.0206762
$936$	−6.63730	−0.216947
$937$	44.8264	1.46441	0.732207	−	0.681082i	$-0.238490\pi$
$937$	44.8264	1.46441	0.732207	+	0.681082i	$0.238490\pi$
$938$	−1.07140	−0.0349823
$939$	3.31953	0.108329
$940$	20.9439	0.683114
$941$	−45.6965	−1.48966	−0.744832	−	0.667252i	$-0.767471\pi$
$941$	−45.6965	−1.48966	−0.744832	+	0.667252i	$0.767471\pi$
$942$	−8.69280	−0.283227
$943$	5.99886	0.195350
$944$	28.2760	0.920305
$945$	1.00000	0.0325300
$946$	1.21674	0.0395597
$947$	36.1798	1.17569	0.587843	−	0.808975i	$-0.299977\pi$
$947$	36.1798	1.17569	0.587843	+	0.808975i	$0.299977\pi$
$948$	−22.9309	−0.744760
$949$	−61.7571	−2.00472
$950$	−0.758388	−0.0246054
$951$	20.1857	0.654567
$952$	−4.15825	−0.134770
$953$	23.9608	0.776168	0.388084	−	0.921624i	$-0.373137\pi$
$953$	23.9608	0.776168	0.388084	+	0.921624i	$0.373137\pi$
$954$	0.225533	0.00730191
$955$	−4.88851	−0.158189
$956$	22.0033	0.711639
$957$	0.0461268	0.00149107
$958$	6.57925	0.212566
$959$	6.37351	0.205811
$960$	3.51956	0.113593
$961$	12.1109	0.390674
$962$	−9.17058	−0.295671
$963$	−18.5959	−0.599243
$964$	−32.2300	−1.03806
$965$	−24.1677	−0.777985
$966$	−0.451228	−0.0145180
$967$	−11.7400	−0.377535	−0.188767	−	0.982022i	$-0.560449\pi$
$967$	−11.7400	−0.377535	−0.188767	+	0.982022i	$0.560449\pi$
$968$	−18.7272	−0.601915
$969$	4.07980	0.131062
$970$	0.511046	0.0164087
$971$	27.8385	0.893380	0.446690	−	0.894689i	$-0.352603\pi$
$971$	27.8385	0.893380	0.446690	+	0.894689i	$0.352603\pi$
$972$	−1.79639	−0.0576193
$973$	−16.3451	−0.524001
$974$	6.88162	0.220501
$975$	−3.87458	−0.124086
$976$	−1.70461	−0.0545633
$977$	14.0756	0.450319	0.225159	−	0.974322i	$-0.427710\pi$
$977$	14.0756	0.450319	0.225159	+	0.974322i	$0.427710\pi$
$978$	−8.16671	−0.261143
$979$	−1.35029	−0.0431555
$980$	1.79639	0.0573837
$981$	19.8152	0.632651
$982$	13.1421	0.419381
$983$	24.9915	0.797104	0.398552	−	0.917146i	$-0.369513\pi$
$983$	24.9915	0.797104	0.398552	+	0.917146i	$0.369513\pi$
$984$	−10.2763	−0.327596
$985$	23.2058	0.739397
$986$	0.193981	0.00617761
$987$	−11.6589	−0.371105
$988$	11.6983	0.372172
$989$	−10.3531	−0.329208
$990$	−0.117525	−0.00373519
$991$	−8.59745	−0.273107	−0.136553	−	0.990633i	$-0.543603\pi$
$991$	−8.59745	−0.273107	−0.136553	+	0.990633i	$0.543603\pi$
$992$	30.8495	0.979474
$993$	27.5715	0.874956
$994$	0.853592	0.0270743
$995$	−11.8387	−0.375312
$996$	−3.18146	−0.100808
$997$	44.5192	1.40994	0.704968	−	0.709239i	$-0.250961\pi$
$997$	44.5192	1.40994	0.704968	+	0.709239i	$0.250961\pi$
$998$	−8.05373	−0.254936
$999$	−5.24538	−0.165956

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2415.2.a.r.1.4	✓	7
3.2	odd	2		7245.2.a.bn.1.4		7

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2415.2.a.r.1.4	✓	7	1.1	even	1	trivial
7245.2.a.bn.1.4		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)

\(f(q)\)	\(=\)	\(q-0.451228 q^{2} +1.00000 q^{3} -1.79639 q^{4} -1.00000 q^{5} -0.451228 q^{6} -1.00000 q^{7} +1.71304 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-0.451228 q^{2} +1.00000 q^{3} -1.79639 q^{4} -1.00000 q^{5} -0.451228 q^{6} -1.00000 q^{7} +1.71304 q^{8} +1.00000 q^{9} +0.451228 q^{10} -0.260456 q^{11} -1.79639 q^{12} -3.87458 q^{13} +0.451228 q^{14} -1.00000 q^{15} +2.81982 q^{16} +2.42741 q^{17} -0.451228 q^{18} +1.68072 q^{19} +1.79639 q^{20} -1.00000 q^{21} +0.117525 q^{22} -1.00000 q^{23} +1.71304 q^{24} +1.00000 q^{25} +1.74832 q^{26} +1.00000 q^{27} +1.79639 q^{28} -0.177100 q^{29} +0.451228 q^{30} -6.56589 q^{31} -4.69846 q^{32} -0.260456 q^{33} -1.09532 q^{34} +1.00000 q^{35} -1.79639 q^{36} -5.24538 q^{37} -0.758388 q^{38} -3.87458 q^{39} -1.71304 q^{40} -5.99886 q^{41} +0.451228 q^{42} +10.3531 q^{43} +0.467881 q^{44} -1.00000 q^{45} +0.451228 q^{46} +11.6589 q^{47} +2.81982 q^{48} +1.00000 q^{49} -0.451228 q^{50} +2.42741 q^{51} +6.96027 q^{52} -0.499822 q^{53} -0.451228 q^{54} +0.260456 q^{55} -1.71304 q^{56} +1.68072 q^{57} +0.0799126 q^{58} +10.0276 q^{59} +1.79639 q^{60} -0.604512 q^{61} +2.96271 q^{62} -1.00000 q^{63} -3.51956 q^{64} +3.87458 q^{65} +0.117525 q^{66} -2.37440 q^{67} -4.36059 q^{68} -1.00000 q^{69} -0.451228 q^{70} +1.89171 q^{71} +1.71304 q^{72} +15.9391 q^{73} +2.36686 q^{74} +1.00000 q^{75} -3.01924 q^{76} +0.260456 q^{77} +1.74832 q^{78} +12.7650 q^{79} -2.81982 q^{80} +1.00000 q^{81} +2.70685 q^{82} +1.77102 q^{83} +1.79639 q^{84} -2.42741 q^{85} -4.67159 q^{86} -0.177100 q^{87} -0.446171 q^{88} +5.18434 q^{89} +0.451228 q^{90} +3.87458 q^{91} +1.79639 q^{92} -6.56589 q^{93} -5.26080 q^{94} -1.68072 q^{95} -4.69846 q^{96} +1.13257 q^{97} -0.451228 q^{98} -0.260456 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 7 q - 2 q^{2} + 7 q^{3} + 8 q^{4} - 7 q^{5} - 2 q^{6} - 7 q^{7} - 6 q^{8} + 7 q^{9}+O(q^{10}) \) 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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