LMFDB - Embedded newform 2415.2.a.o.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:	$1$
Dimension:	$5$
Coefficient field:	5.5.2508628.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{5} - 10x^{3} - 2x^{2} + 23x + 8 $ x^5 - 10x^3 - 2x^2 + 23*x + 8
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$-1.83189$ 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)

$f(q)$	$=$	$q+1.83189 q^{2} -1.00000 q^{3} +1.35584 q^{4} -1.00000 q^{5} -1.83189 q^{6} -1.00000 q^{7} -1.18004 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.83189 q^{2} -1.00000 q^{3} +1.35584 q^{4} -1.00000 q^{5} -1.83189 q^{6} -1.00000 q^{7} -1.18004 q^{8} +1.00000 q^{9} -1.83189 q^{10} +3.84383 q^{11} -1.35584 q^{12} -1.18773 q^{13} -1.83189 q^{14} +1.00000 q^{15} -4.87338 q^{16} -2.00000 q^{17} +1.83189 q^{18} +5.22153 q^{19} -1.35584 q^{20} +1.00000 q^{21} +7.04149 q^{22} -1.00000 q^{23} +1.18004 q^{24} +1.00000 q^{25} -2.17579 q^{26} -1.00000 q^{27} -1.35584 q^{28} -1.01194 q^{29} +1.83189 q^{30} -8.42888 q^{31} -6.56744 q^{32} -3.84383 q^{33} -3.66379 q^{34} +1.00000 q^{35} +1.35584 q^{36} -1.46412 q^{37} +9.56529 q^{38} +1.18773 q^{39} +1.18004 q^{40} -11.8973 q^{41} +1.83189 q^{42} -9.24115 q^{43} +5.21160 q^{44} -1.00000 q^{45} -1.83189 q^{46} -4.65610 q^{47} +4.87338 q^{48} +1.00000 q^{49} +1.83189 q^{50} +2.00000 q^{51} -1.61037 q^{52} +1.13216 q^{53} -1.83189 q^{54} -3.84383 q^{55} +1.18004 q^{56} -5.22153 q^{57} -1.85376 q^{58} -12.0969 q^{59} +1.35584 q^{60} -0.0668008 q^{61} -15.4408 q^{62} -1.00000 q^{63} -2.28408 q^{64} +1.18773 q^{65} -7.04149 q^{66} -5.31220 q^{67} -2.71167 q^{68} +1.00000 q^{69} +1.83189 q^{70} +13.0949 q^{71} -1.18004 q^{72} -10.4289 q^{73} -2.68212 q^{74} -1.00000 q^{75} +7.07953 q^{76} -3.84383 q^{77} +2.17579 q^{78} -3.15178 q^{79} +4.87338 q^{80} +1.00000 q^{81} -21.7945 q^{82} -15.5414 q^{83} +1.35584 q^{84} +2.00000 q^{85} -16.9288 q^{86} +1.01194 q^{87} -4.53588 q^{88} +14.6524 q^{89} -1.83189 q^{90} +1.18773 q^{91} -1.35584 q^{92} +8.42888 q^{93} -8.52948 q^{94} -5.22153 q^{95} +6.56744 q^{96} +7.09491 q^{97} +1.83189 q^{98} +3.84383 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 5 q - 5 q^{3} + 10 q^{4} - 5 q^{5} - 5 q^{7} - 6 q^{8} + 5 q^{9}+O(q^{10}) $ 5 * q - 5 * q^3 + 10 * q^4 - 5 * q^5 - 5 * q^7 - 6 * q^8 + 5 * q^9	$ 5 q - 5 q^{3} + 10 q^{4} - 5 q^{5} - 5 q^{7} - 6 q^{8} + 5 q^{9} + q^{11} - 10 q^{12} + 5 q^{15} + 8 q^{16} - 10 q^{17} + 3 q^{19} - 10 q^{20} + 5 q^{21} + 12 q^{22} - 5 q^{23} + 6 q^{24} + 5 q^{25} - 14 q^{26} - 5 q^{27} - 10 q^{28} + 4 q^{29} + 2 q^{31} - 12 q^{32} - q^{33} + 5 q^{35} + 10 q^{36} - 4 q^{37} - 24 q^{38} + 6 q^{40} - 9 q^{41} - 8 q^{43} + 2 q^{44} - 5 q^{45} - 11 q^{47} - 8 q^{48} + 5 q^{49} + 10 q^{51} - 22 q^{52} - 19 q^{53} - q^{55} + 6 q^{56} - 3 q^{57} + 8 q^{58} + 5 q^{59} + 10 q^{60} - 17 q^{61} - 24 q^{62} - 5 q^{63} - 8 q^{64} - 12 q^{66} - 2 q^{67} - 20 q^{68} + 5 q^{69} + 10 q^{71} - 6 q^{72} - 8 q^{73} - 34 q^{74} - 5 q^{75} - 8 q^{76} - q^{77} + 14 q^{78} + 24 q^{79} - 8 q^{80} + 5 q^{81} - 8 q^{82} - 24 q^{83} + 10 q^{84} + 10 q^{85} - 10 q^{86} - 4 q^{87} - 26 q^{88} - 4 q^{89} - 10 q^{92} - 2 q^{93} + 2 q^{94} - 3 q^{95} + 12 q^{96} - 20 q^{97} + q^{99}+O(q^{100}) $ 5 * q - 5 * q^3 + 10 * q^4 - 5 * q^5 - 5 * q^7 - 6 * q^8 + 5 * q^9 + q^11 - 10 * q^12 + 5 * q^15 + 8 * q^16 - 10 * q^17 + 3 * q^19 - 10 * q^20 + 5 * q^21 + 12 * q^22 - 5 * q^23 + 6 * q^24 + 5 * q^25 - 14 * q^26 - 5 * q^27 - 10 * q^28 + 4 * q^29 + 2 * q^31 - 12 * q^32 - q^33 + 5 * q^35 + 10 * q^36 - 4 * q^37 - 24 * q^38 + 6 * q^40 - 9 * q^41 - 8 * q^43 + 2 * q^44 - 5 * q^45 - 11 * q^47 - 8 * q^48 + 5 * q^49 + 10 * q^51 - 22 * q^52 - 19 * q^53 - q^55 + 6 * q^56 - 3 * q^57 + 8 * q^58 + 5 * q^59 + 10 * q^60 - 17 * q^61 - 24 * q^62 - 5 * q^63 - 8 * q^64 - 12 * q^66 - 2 * q^67 - 20 * q^68 + 5 * q^69 + 10 * q^71 - 6 * q^72 - 8 * q^73 - 34 * q^74 - 5 * q^75 - 8 * q^76 - q^77 + 14 * q^78 + 24 * q^79 - 8 * q^80 + 5 * q^81 - 8 * q^82 - 24 * q^83 + 10 * q^84 + 10 * q^85 - 10 * q^86 - 4 * q^87 - 26 * q^88 - 4 * q^89 - 10 * q^92 - 2 * q^93 + 2 * q^94 - 3 * q^95 + 12 * q^96 - 20 * q^97 + q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	1.83189	1.29534	0.647672	−	0.761919i	$-0.275743\pi$
$2$	1.83189	1.29534	0.647672	+	0.761919i	$0.275743\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	1.35584	0.677918
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	−1.83189	−0.747868
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	−1.18004	−0.417208
$9$	1.00000	0.333333
$10$	−1.83189	−0.579296
$11$	3.84383	1.15896	0.579479	−	0.814987i	$-0.303256\pi$
$11$	3.84383	1.15896	0.579479	+	0.814987i	$0.303256\pi$
$12$	−1.35584	−0.391396
$13$	−1.18773	−0.329417	−0.164708	−	0.986342i	$-0.552668\pi$
$13$	−1.18773	−0.329417	−0.164708	+	0.986342i	$0.552668\pi$
$14$	−1.83189	−0.489594
$15$	1.00000	0.258199
$16$	−4.87338	−1.21835
$17$	−2.00000	−0.485071	−0.242536	−	0.970143i	$-0.577979\pi$
$17$	−2.00000	−0.485071	−0.242536	+	0.970143i	$0.577979\pi$
$18$	1.83189	0.431782
$19$	5.22153	1.19790	0.598950	−	0.800786i	$-0.295585\pi$
$19$	5.22153	1.19790	0.598950	+	0.800786i	$0.295585\pi$
$20$	−1.35584	−0.303174
$21$	1.00000	0.218218
$22$	7.04149	1.50125
$23$	−1.00000	−0.208514
$23$	−1.00000	−0.208514
$24$	1.18004	0.240875
$25$	1.00000	0.200000
$26$	−2.17579	−0.426708
$27$	−1.00000	−0.192450
$28$	−1.35584	−0.256229
$29$	−1.01194	−0.187912	−0.0939558	−	0.995576i	$-0.529951\pi$
$29$	−1.01194	−0.187912	−0.0939558	+	0.995576i	$0.529951\pi$
$30$	1.83189	0.334457
$31$	−8.42888	−1.51387	−0.756936	−	0.653489i	$-0.773305\pi$
$31$	−8.42888	−1.51387	−0.756936	+	0.653489i	$0.773305\pi$
$32$	−6.56744	−1.16097
$33$	−3.84383	−0.669125
$34$	−3.66379	−0.628334
$35$	1.00000	0.169031
$36$	1.35584	0.225973
$37$	−1.46412	−0.240700	−0.120350	−	0.992731i	$-0.538402\pi$
$37$	−1.46412	−0.240700	−0.120350	+	0.992731i	$0.538402\pi$
$38$	9.56529	1.55169
$39$	1.18773	0.190189
$40$	1.18004	0.186581
$41$	−11.8973	−1.85804	−0.929019	−	0.370031i	$-0.879347\pi$
$41$	−11.8973	−1.85804	−0.929019	+	0.370031i	$0.879347\pi$
$42$	1.83189	0.282667
$43$	−9.24115	−1.40926	−0.704631	−	0.709574i	$-0.748888\pi$
$43$	−9.24115	−1.40926	−0.704631	+	0.709574i	$0.748888\pi$
$44$	5.21160	0.785678
$45$	−1.00000	−0.149071
$46$	−1.83189	−0.270098
$47$	−4.65610	−0.679162	−0.339581	−	0.940577i	$-0.610285\pi$
$47$	−4.65610	−0.679162	−0.339581	+	0.940577i	$0.610285\pi$
$48$	4.87338	0.703412
$49$	1.00000	0.142857
$50$	1.83189	0.259069
$51$	2.00000	0.280056
$52$	−1.61037	−0.223318
$53$	1.13216	0.155514	0.0777569	−	0.996972i	$-0.475224\pi$
$53$	1.13216	0.155514	0.0777569	+	0.996972i	$0.475224\pi$
$54$	−1.83189	−0.249289
$55$	−3.84383	−0.518302
$56$	1.18004	0.157690
$57$	−5.22153	−0.691608
$58$	−1.85376	−0.243410
$59$	−12.0969	−1.57488	−0.787442	−	0.616389i	$-0.788595\pi$
$59$	−12.0969	−1.57488	−0.787442	+	0.616389i	$0.788595\pi$
$60$	1.35584	0.175038
$61$	−0.0668008	−0.00855296	−0.00427648	−	0.999991i	$-0.501361\pi$
$61$	−0.0668008	−0.00855296	−0.00427648	+	0.999991i	$0.501361\pi$
$62$	−15.4408	−1.96099
$63$	−1.00000	−0.125988
$64$	−2.28408	−0.285510
$65$	1.18773	0.147320
$66$	−7.04149	−0.866747
$67$	−5.31220	−0.648988	−0.324494	−	0.945888i	$-0.605194\pi$
$67$	−5.31220	−0.648988	−0.324494	+	0.945888i	$0.605194\pi$
$68$	−2.71167	−0.328838
$69$	1.00000	0.120386
$70$	1.83189	0.218953
$71$	13.0949	1.55408	0.777040	−	0.629451i	$-0.216720\pi$
$71$	13.0949	1.55408	0.777040	+	0.629451i	$0.216720\pi$
$72$	−1.18004	−0.139069
$73$	−10.4289	−1.22061	−0.610304	−	0.792167i	$-0.708953\pi$
$73$	−10.4289	−1.22061	−0.610304	+	0.792167i	$0.708953\pi$
$74$	−2.68212	−0.311790
$75$	−1.00000	−0.115470
$76$	7.07953	0.812078
$77$	−3.84383	−0.438045
$78$	2.17579	0.246360
$79$	−3.15178	−0.354603	−0.177302	−	0.984157i	$-0.556737\pi$
$79$	−3.15178	−0.354603	−0.177302	+	0.984157i	$0.556737\pi$
$80$	4.87338	0.544861
$81$	1.00000	0.111111
$82$	−21.7945	−2.40680
$83$	−15.5414	−1.70589	−0.852946	−	0.521999i	$-0.825186\pi$
$83$	−15.5414	−1.70589	−0.852946	+	0.521999i	$0.825186\pi$
$84$	1.35584	0.147934
$85$	2.00000	0.216930
$86$	−16.9288	−1.82548
$87$	1.01194	0.108491
$88$	−4.53588	−0.483526
$89$	14.6524	1.55315	0.776576	−	0.630023i	$-0.216955\pi$
$89$	14.6524	1.55315	0.776576	+	0.630023i	$0.216955\pi$
$90$	−1.83189	−0.193099
$91$	1.18773	0.124508
$92$	−1.35584	−0.141356
$93$	8.42888	0.874034
$94$	−8.52948	−0.879749
$95$	−5.22153	−0.535718
$96$	6.56744	0.670286
$97$	7.09491	0.720379	0.360189	−	0.932879i	$-0.382712\pi$
$97$	7.09491	0.720379	0.360189	+	0.932879i	$0.382712\pi$
$98$	1.83189	0.185049
$99$	3.84383	0.386319
$100$	1.35584	0.135584
$101$	8.60892	0.856620	0.428310	−	0.903632i	$-0.359109\pi$
$101$	8.60892	0.856620	0.428310	+	0.903632i	$0.359109\pi$
$102$	3.66379	0.362769
$103$	7.59699	0.748553	0.374277	−	0.927317i	$-0.377891\pi$
$103$	7.59699	0.748553	0.374277	+	0.927317i	$0.377891\pi$
$104$	1.40157	0.137435
$105$	−1.00000	−0.0975900
$106$	2.07399	0.201444
$107$	−6.50561	−0.628921	−0.314461	−	0.949271i	$-0.601824\pi$
$107$	−6.50561	−0.628921	−0.314461	+	0.949271i	$0.601824\pi$
$108$	−1.35584	−0.130465
$109$	0.798095	0.0764436	0.0382218	−	0.999269i	$-0.487831\pi$
$109$	0.798095	0.0764436	0.0382218	+	0.999269i	$0.487831\pi$
$110$	−7.04149	−0.671379
$111$	1.46412	0.138968
$112$	4.87338	0.460491
$113$	13.6547	1.28452	0.642261	−	0.766486i	$-0.277997\pi$
$113$	13.6547	1.28452	0.642261	+	0.766486i	$0.277997\pi$
$114$	−9.56529	−0.895871
$115$	1.00000	0.0932505
$116$	−1.37202	−0.127389
$117$	−1.18773	−0.109806
$118$	−22.1603	−2.04002
$119$	2.00000	0.183340
$120$	−1.18004	−0.107723
$121$	3.77502	0.343184
$122$	−0.122372	−0.0110790
$123$	11.8973	1.07274
$124$	−11.4282	−1.02628
$125$	−1.00000	−0.0894427
$126$	−1.83189	−0.163198
$127$	−4.78625	−0.424711	−0.212356	−	0.977192i	$-0.568114\pi$
$127$	−4.78625	−0.424711	−0.212356	+	0.977192i	$0.568114\pi$
$128$	8.95067	0.791135
$129$	9.24115	0.813638
$130$	2.17579	0.190830
$131$	−17.8318	−1.55797	−0.778984	−	0.627044i	$-0.784265\pi$
$131$	−17.8318	−1.55797	−0.778984	+	0.627044i	$0.784265\pi$
$132$	−5.21160	−0.453612
$133$	−5.22153	−0.452764
$134$	−9.73139	−0.840664
$135$	1.00000	0.0860663
$136$	2.36008	0.202375
$137$	−5.37345	−0.459085	−0.229543	−	0.973299i	$-0.573723\pi$
$137$	−5.37345	−0.459085	−0.229543	+	0.973299i	$0.573723\pi$
$138$	1.83189	0.155941
$139$	19.0055	1.61203	0.806014	−	0.591896i	$-0.201620\pi$
$139$	19.0055	1.61203	0.806014	+	0.591896i	$0.201620\pi$
$140$	1.35584	0.114589
$141$	4.65610	0.392114
$142$	23.9885	2.01307
$143$	−4.56543	−0.381780
$144$	−4.87338	−0.406115
$145$	1.01194	0.0840366
$146$	−19.1046	−1.58111
$147$	−1.00000	−0.0824786
$148$	−1.98511	−0.163175
$149$	2.87754	0.235737	0.117868	−	0.993029i	$-0.462394\pi$
$149$	2.87754	0.235737	0.117868	+	0.993029i	$0.462394\pi$
$150$	−1.83189	−0.149574
$151$	13.1856	1.07303	0.536514	−	0.843892i	$-0.319741\pi$
$151$	13.1856	1.07303	0.536514	+	0.843892i	$0.319741\pi$
$152$	−6.16162	−0.499773
$153$	−2.00000	−0.161690
$154$	−7.04149	−0.567419
$155$	8.42888	0.677024
$156$	1.61037	0.128932
$157$	−12.5337	−1.00030	−0.500150	−	0.865939i	$-0.666722\pi$
$157$	−12.5337	−1.00030	−0.500150	+	0.865939i	$0.666722\pi$
$158$	−5.77373	−0.459333
$159$	−1.13216	−0.0897860
$160$	6.56744	0.519201
$161$	1.00000	0.0788110
$162$	1.83189	0.143927
$163$	13.8495	1.08478	0.542389	−	0.840128i	$-0.317520\pi$
$163$	13.8495	1.08478	0.542389	+	0.840128i	$0.317520\pi$
$164$	−16.1307	−1.25960
$165$	3.84383	0.299242
$166$	−28.4702	−2.20972
$167$	−21.5372	−1.66660	−0.833298	−	0.552824i	$-0.813550\pi$
$167$	−21.5372	−1.66660	−0.833298	+	0.552824i	$0.813550\pi$
$168$	−1.18004	−0.0910422
$169$	−11.5893	−0.891485
$170$	3.66379	0.281000
$171$	5.22153	0.399300
$172$	−12.5295	−0.955364
$173$	−13.4408	−1.02189	−0.510943	−	0.859614i	$-0.670704\pi$
$173$	−13.4408	−1.02189	−0.510943	+	0.859614i	$0.670704\pi$
$174$	1.85376	0.140533
$175$	−1.00000	−0.0755929
$176$	−18.7324	−1.41201
$177$	12.0969	0.909260
$178$	26.8417	2.01187
$179$	12.9162	0.965400	0.482700	−	0.875786i	$-0.339656\pi$
$179$	12.9162	0.965400	0.482700	+	0.875786i	$0.339656\pi$
$180$	−1.35584	−0.101058
$181$	−19.1786	−1.42553	−0.712767	−	0.701401i	$-0.752558\pi$
$181$	−19.1786	−1.42553	−0.712767	+	0.701401i	$0.752558\pi$
$182$	2.17579	0.161281
$183$	0.0668008	0.00493805
$184$	1.18004	0.0869938
$185$	1.46412	0.107644
$186$	15.4408	1.13218
$187$	−7.68766	−0.562177
$188$	−6.31290	−0.460416
$189$	1.00000	0.0727393
$190$	−9.56529	−0.693939
$191$	−13.1961	−0.954838	−0.477419	−	0.878676i	$-0.658428\pi$
$191$	−13.1961	−0.954838	−0.477419	+	0.878676i	$0.658428\pi$
$192$	2.28408	0.164839
$193$	22.9125	1.64928	0.824638	−	0.565660i	$-0.191379\pi$
$193$	22.9125	1.64928	0.824638	+	0.565660i	$0.191379\pi$
$194$	12.9971	0.933139
$195$	−1.18773	−0.0850551
$196$	1.35584	0.0968454
$197$	2.32413	0.165588	0.0827939	−	0.996567i	$-0.473616\pi$
$197$	2.32413	0.165588	0.0827939	+	0.996567i	$0.473616\pi$
$198$	7.04149	0.500417
$199$	16.9484	1.20144	0.600721	−	0.799459i	$-0.294880\pi$
$199$	16.9484	1.20144	0.600721	+	0.799459i	$0.294880\pi$
$200$	−1.18004	−0.0834415
$201$	5.31220	0.374694
$202$	15.7706	1.10962
$203$	1.01194	0.0710239
$204$	2.71167	0.189855
$205$	11.8973	0.830940
$206$	13.9169	0.969635
$207$	−1.00000	−0.0695048
$208$	5.78826	0.401343
$209$	20.0707	1.38832
$210$	−1.83189	−0.126413
$211$	−4.27271	−0.294145	−0.147073	−	0.989126i	$-0.546985\pi$
$211$	−4.27271	−0.294145	−0.147073	+	0.989126i	$0.546985\pi$
$212$	1.53502	0.105426
$213$	−13.0949	−0.897248
$214$	−11.9176	−0.814670
$215$	9.24115	0.630241
$216$	1.18004	0.0802916
$217$	8.42888	0.572190
$218$	1.46203	0.0990208
$219$	10.4289	0.704718
$220$	−5.21160	−0.351366
$221$	2.37546	0.159791
$222$	2.68212	0.180012
$223$	17.8809	1.19740	0.598698	−	0.800975i	$-0.295685\pi$
$223$	17.8809	1.19740	0.598698	+	0.800975i	$0.295685\pi$
$224$	6.56744	0.438805
$225$	1.00000	0.0666667
$226$	25.0139	1.66390
$227$	−3.24908	−0.215649	−0.107825	−	0.994170i	$-0.534388\pi$
$227$	−3.24908	−0.215649	−0.107825	+	0.994170i	$0.534388\pi$
$228$	−7.07953	−0.468854
$229$	−17.2931	−1.14276	−0.571381	−	0.820685i	$-0.693592\pi$
$229$	−17.2931	−1.14276	−0.571381	+	0.820685i	$0.693592\pi$
$230$	1.83189	0.120792
$231$	3.84383	0.252905
$232$	1.19413	0.0783982
$233$	1.76285	0.115488	0.0577442	−	0.998331i	$-0.481609\pi$
$233$	1.76285	0.115488	0.0577442	+	0.998331i	$0.481609\pi$
$234$	−2.17579	−0.142236
$235$	4.65610	0.303730
$236$	−16.4014	−1.06764
$237$	3.15178	0.204730
$238$	3.66379	0.237488
$239$	2.45065	0.158520	0.0792598	−	0.996854i	$-0.474744\pi$
$239$	2.45065	0.158520	0.0792598	+	0.996854i	$0.474744\pi$
$240$	−4.87338	−0.314575
$241$	−8.92126	−0.574669	−0.287335	−	0.957830i	$-0.592769\pi$
$241$	−8.92126	−0.574669	−0.287335	+	0.957830i	$0.592769\pi$
$242$	6.91544	0.444541
$243$	−1.00000	−0.0641500
$244$	−0.0905708	−0.00579820
$245$	−1.00000	−0.0638877
$246$	21.7945	1.38957
$247$	−6.20176	−0.394609
$248$	9.94643	0.631599
$249$	15.5414	0.984897
$250$	−1.83189	−0.115859
$251$	2.02387	0.127746	0.0638728	−	0.997958i	$-0.479655\pi$
$251$	2.02387	0.127746	0.0638728	+	0.997958i	$0.479655\pi$
$252$	−1.35584	−0.0854096
$253$	−3.84383	−0.241659
$254$	−8.76791	−0.550147
$255$	−2.00000	−0.125245
$256$	20.9648	1.31030
$257$	−19.4006	−1.21018	−0.605089	−	0.796158i	$-0.706862\pi$
$257$	−19.4006	−1.21018	−0.605089	+	0.796158i	$0.706862\pi$
$258$	16.9288	1.05394
$259$	1.46412	0.0909762
$260$	1.61037	0.0998706
$261$	−1.01194	−0.0626372
$262$	−32.6659	−2.01810
$263$	13.7384	0.847144	0.423572	−	0.905862i	$-0.360776\pi$
$263$	13.7384	0.847144	0.423572	+	0.905862i	$0.360776\pi$
$264$	4.53588	0.279164
$265$	−1.13216	−0.0695479
$266$	−9.56529	−0.586485
$267$	−14.6524	−0.896713
$268$	−7.20247	−0.439961
$269$	30.1853	1.84043	0.920216	−	0.391410i	$-0.128013\pi$
$269$	30.1853	1.84043	0.920216	+	0.391410i	$0.128013\pi$
$270$	1.83189	0.111486
$271$	19.0567	1.15761	0.578807	−	0.815465i	$-0.303518\pi$
$271$	19.0567	1.15761	0.578807	+	0.815465i	$0.303518\pi$
$272$	9.74676	0.590984
$273$	−1.18773	−0.0718847
$274$	−9.84359	−0.594673
$275$	3.84383	0.231792
$276$	1.35584	0.0816117
$277$	−18.7396	−1.12596	−0.562978	−	0.826472i	$-0.690344\pi$
$277$	−18.7396	−1.12596	−0.562978	+	0.826472i	$0.690344\pi$
$278$	34.8161	2.08813
$279$	−8.42888	−0.504624
$280$	−1.18004	−0.0705209
$281$	−19.8218	−1.18247	−0.591235	−	0.806499i	$-0.701360\pi$
$281$	−19.8218	−1.18247	−0.591235	+	0.806499i	$0.701360\pi$
$282$	8.52948	0.507923
$283$	21.7739	1.29433	0.647163	−	0.762352i	$-0.275955\pi$
$283$	21.7739	1.29433	0.647163	+	0.762352i	$0.275955\pi$
$284$	17.7545	1.05354
$285$	5.22153	0.309297
$286$	−8.36338	−0.494537
$287$	11.8973	0.702273
$288$	−6.56744	−0.386990
$289$	−13.0000	−0.764706
$290$	1.85376	0.108856
$291$	−7.09491	−0.415911
$292$	−14.1398	−0.827472
$293$	15.5694	0.909576	0.454788	−	0.890600i	$-0.349715\pi$
$293$	15.5694	0.909576	0.454788	+	0.890600i	$0.349715\pi$
$294$	−1.83189	−0.106838
$295$	12.0969	0.704310
$296$	1.72773	0.100422
$297$	−3.84383	−0.223042
$298$	5.27134	0.305361
$299$	1.18773	0.0686882
$300$	−1.35584	−0.0782792
$301$	9.24115	0.532651
$302$	24.1546	1.38994
$303$	−8.60892	−0.494570
$304$	−25.4465	−1.45946
$305$	0.0668008	0.00382500
$306$	−3.66379	−0.209445
$307$	1.42249	0.0811860	0.0405930	−	0.999176i	$-0.487075\pi$
$307$	1.42249	0.0811860	0.0405930	+	0.999176i	$0.487075\pi$
$308$	−5.21160	−0.296958
$309$	−7.59699	−0.432177
$310$	15.4408	0.876979
$311$	8.76085	0.496782	0.248391	−	0.968660i	$-0.420098\pi$
$311$	8.76085	0.496782	0.248391	+	0.968660i	$0.420098\pi$
$312$	−1.40157	−0.0793483
$313$	−22.3564	−1.26366	−0.631829	−	0.775108i	$-0.717696\pi$
$313$	−22.3564	−1.26366	−0.631829	+	0.775108i	$0.717696\pi$
$314$	−22.9605	−1.29573
$315$	1.00000	0.0563436
$316$	−4.27330	−0.240392
$317$	−1.33277	−0.0748559	−0.0374279	−	0.999299i	$-0.511916\pi$
$317$	−1.33277	−0.0748559	−0.0374279	+	0.999299i	$0.511916\pi$
$318$	−2.07399	−0.116304
$319$	−3.88971	−0.217782
$320$	2.28408	0.127684
$321$	6.50561	0.363108
$322$	1.83189	0.102087
$323$	−10.4431	−0.581067
$324$	1.35584	0.0753242
$325$	−1.18773	−0.0658834
$326$	25.3708	1.40516
$327$	−0.798095	−0.0441348
$328$	14.0392	0.775188
$329$	4.65610	0.256699
$330$	7.04149	0.387621
$331$	−27.1350	−1.49147	−0.745736	−	0.666242i	$-0.767902\pi$
$331$	−27.1350	−1.49147	−0.745736	+	0.666242i	$0.767902\pi$
$332$	−21.0716	−1.15645
$333$	−1.46412	−0.0802335
$334$	−39.4538	−2.15882
$335$	5.31220	0.290236
$336$	−4.87338	−0.265865
$337$	15.1330	0.824345	0.412172	−	0.911106i	$-0.364770\pi$
$337$	15.1330	0.824345	0.412172	+	0.911106i	$0.364770\pi$
$338$	−21.2304	−1.15478
$339$	−13.6547	−0.741619
$340$	2.71167	0.147061
$341$	−32.3992	−1.75451
$342$	9.56529	0.517231
$343$	−1.00000	−0.0539949
$344$	10.9049	0.587955
$345$	−1.00000	−0.0538382
$346$	−24.6221	−1.32369
$347$	−2.90839	−0.156131	−0.0780653	−	0.996948i	$-0.524874\pi$
$347$	−2.90839	−0.156131	−0.0780653	+	0.996948i	$0.524874\pi$
$348$	1.37202	0.0735479
$349$	−11.7715	−0.630113	−0.315056	−	0.949073i	$-0.602023\pi$
$349$	−11.7715	−0.630113	−0.315056	+	0.949073i	$0.602023\pi$
$350$	−1.83189	−0.0979189
$351$	1.18773	0.0633963
$352$	−25.2441	−1.34551
$353$	−24.6189	−1.31033	−0.655165	−	0.755486i	$-0.727401\pi$
$353$	−24.6189	−1.31033	−0.655165	+	0.755486i	$0.727401\pi$
$354$	22.1603	1.17780
$355$	−13.0949	−0.695006
$356$	19.8663	1.05291
$357$	−2.00000	−0.105851
$358$	23.6611	1.25053
$359$	17.2081	0.908211	0.454106	−	0.890948i	$-0.349959\pi$
$359$	17.2081	0.908211	0.454106	+	0.890948i	$0.349959\pi$
$360$	1.18004	0.0621936
$361$	8.26436	0.434966
$362$	−35.1332	−1.84656
$363$	−3.77502	−0.198137
$364$	1.61037	0.0844061
$365$	10.4289	0.545873
$366$	0.122372	0.00639648
$367$	20.3796	1.06380	0.531902	−	0.846806i	$-0.321477\pi$
$367$	20.3796	1.06380	0.531902	+	0.846806i	$0.321477\pi$
$368$	4.87338	0.254043
$369$	−11.8973	−0.619346
$370$	2.68212	0.139437
$371$	−1.13216	−0.0587787
$372$	11.4282	0.592523
$373$	22.2395	1.15152	0.575758	−	0.817620i	$-0.304707\pi$
$373$	22.2395	1.15152	0.575758	+	0.817620i	$0.304707\pi$
$374$	−14.0830	−0.728213
$375$	1.00000	0.0516398
$376$	5.49439	0.283351
$377$	1.20191	0.0619013
$378$	1.83189	0.0942225
$379$	8.28264	0.425451	0.212725	−	0.977112i	$-0.431766\pi$
$379$	8.28264	0.425451	0.212725	+	0.977112i	$0.431766\pi$
$380$	−7.07953	−0.363172
$381$	4.78625	0.245207
$382$	−24.1739	−1.23684
$383$	−29.2445	−1.49432	−0.747161	−	0.664643i	$-0.768584\pi$
$383$	−29.2445	−1.49432	−0.747161	+	0.664643i	$0.768584\pi$
$384$	−8.95067	−0.456762
$385$	3.84383	0.195900
$386$	41.9732	2.13638
$387$	−9.24115	−0.469754
$388$	9.61953	0.488358
$389$	4.97599	0.252293	0.126146	−	0.992012i	$-0.459739\pi$
$389$	4.97599	0.252293	0.126146	+	0.992012i	$0.459739\pi$
$390$	−2.17579	−0.110176
$391$	2.00000	0.101144
$392$	−1.18004	−0.0596011
$393$	17.8318	0.899493
$394$	4.25757	0.214493
$395$	3.15178	0.158583
$396$	5.21160	0.261893
$397$	38.5090	1.93271	0.966355	−	0.257212i	$-0.0828040\pi$
$397$	38.5090	1.93271	0.966355	+	0.257212i	$0.0828040\pi$
$398$	31.0477	1.55628
$399$	5.22153	0.261403
$400$	−4.87338	−0.243669
$401$	−16.1778	−0.807880	−0.403940	−	0.914785i	$-0.632360\pi$
$401$	−16.1778	−0.807880	−0.403940	+	0.914785i	$0.632360\pi$
$402$	9.73139	0.485357
$403$	10.0112	0.498695
$404$	11.6723	0.580718
$405$	−1.00000	−0.0496904
$406$	1.85376	0.0920005
$407$	−5.62784	−0.278962
$408$	−2.36008	−0.116841
$409$	30.4025	1.50331	0.751653	−	0.659559i	$-0.229257\pi$
$409$	30.4025	1.50331	0.751653	+	0.659559i	$0.229257\pi$
$410$	21.7945	1.07635
$411$	5.37345	0.265053
$412$	10.3003	0.507458
$413$	12.0969	0.595250
$414$	−1.83189	−0.0900327
$415$	15.5414	0.762898
$416$	7.80034	0.382443
$417$	−19.0055	−0.930705
$418$	36.7673	1.79835
$419$	−21.3514	−1.04309	−0.521543	−	0.853225i	$-0.674643\pi$
$419$	−21.3514	−1.04309	−0.521543	+	0.853225i	$0.674643\pi$
$420$	−1.35584	−0.0661580
$421$	−29.6917	−1.44708	−0.723541	−	0.690281i	$-0.757487\pi$
$421$	−29.6917	−1.44708	−0.723541	+	0.690281i	$0.757487\pi$
$422$	−7.82715	−0.381020
$423$	−4.65610	−0.226387
$424$	−1.33599	−0.0648816
$425$	−2.00000	−0.0970143
$426$	−23.9885	−1.16225
$427$	0.0668008	0.00323272
$428$	−8.82054	−0.426357
$429$	4.56543	0.220421
$430$	16.9288	0.816380
$431$	33.6230	1.61956	0.809780	−	0.586733i	$-0.199586\pi$
$431$	33.6230	1.61956	0.809780	+	0.586733i	$0.199586\pi$
$432$	4.87338	0.234471
$433$	−0.716766	−0.0344456	−0.0172228	−	0.999852i	$-0.505482\pi$
$433$	−0.716766	−0.0344456	−0.0172228	+	0.999852i	$0.505482\pi$
$434$	15.4408	0.741183
$435$	−1.01194	−0.0485186
$436$	1.08209	0.0518225
$437$	−5.22153	−0.249780
$438$	19.1046	0.912853
$439$	11.0533	0.527544	0.263772	−	0.964585i	$-0.415033\pi$
$439$	11.0533	0.527544	0.263772	+	0.964585i	$0.415033\pi$
$440$	4.53588	0.216239
$441$	1.00000	0.0476190
$442$	4.35159	0.206984
$443$	−21.3240	−1.01313	−0.506567	−	0.862201i	$-0.669086\pi$
$443$	−21.3240	−1.01313	−0.506567	+	0.862201i	$0.669086\pi$
$444$	1.98511	0.0942092
$445$	−14.6524	−0.694591
$446$	32.7560	1.55104
$447$	−2.87754	−0.136103
$448$	2.28408	0.107913
$449$	−13.1074	−0.618577	−0.309289	−	0.950968i	$-0.600091\pi$
$449$	−13.1074	−0.618577	−0.309289	+	0.950968i	$0.600091\pi$
$450$	1.83189	0.0863563
$451$	−45.7310	−2.15339
$452$	18.5135	0.870800
$453$	−13.1856	−0.619513
$454$	−5.95197	−0.279340
$455$	−1.18773	−0.0556816
$456$	6.16162	0.288544
$457$	−39.7126	−1.85768	−0.928838	−	0.370486i	$-0.879191\pi$
$457$	−39.7126	−1.85768	−0.928838	+	0.370486i	$0.879191\pi$
$458$	−31.6792	−1.48027
$459$	2.00000	0.0933520
$460$	1.35584	0.0632162
$461$	28.8697	1.34460	0.672298	−	0.740281i	$-0.265307\pi$
$461$	28.8697	1.34460	0.672298	+	0.740281i	$0.265307\pi$
$462$	7.04149	0.327600
$463$	1.25333	0.0582472	0.0291236	−	0.999576i	$-0.490728\pi$
$463$	1.25333	0.0582472	0.0291236	+	0.999576i	$0.490728\pi$
$464$	4.93155	0.228941
$465$	−8.42888	−0.390880
$466$	3.22936	0.149597
$467$	−18.2166	−0.842963	−0.421481	−	0.906837i	$-0.638490\pi$
$467$	−18.2166	−0.842963	−0.421481	+	0.906837i	$0.638490\pi$
$468$	−1.61037	−0.0744392
$469$	5.31220	0.245295
$470$	8.52948	0.393436
$471$	12.5337	0.577524
$472$	14.2749	0.657054
$473$	−35.5214	−1.63328
$474$	5.77373	0.265196
$475$	5.22153	0.239580
$476$	2.71167	0.124289
$477$	1.13216	0.0518380
$478$	4.48934	0.205337
$479$	28.1853	1.28782	0.643910	−	0.765101i	$-0.277311\pi$
$479$	28.1853	1.28782	0.643910	+	0.765101i	$0.277311\pi$
$480$	−6.56744	−0.299761
$481$	1.73898	0.0792908
$482$	−16.3428	−0.744395
$483$	−1.00000	−0.0455016
$484$	5.11831	0.232650
$485$	−7.09491	−0.322163
$486$	−1.83189	−0.0830964
$487$	19.6133	0.888764	0.444382	−	0.895837i	$-0.353423\pi$
$487$	19.6133	0.888764	0.444382	+	0.895837i	$0.353423\pi$
$488$	0.0788276	0.00356836
$489$	−13.8495	−0.626297
$490$	−1.83189	−0.0827565
$491$	8.33263	0.376046	0.188023	−	0.982165i	$-0.439792\pi$
$491$	8.33263	0.376046	0.188023	+	0.982165i	$0.439792\pi$
$492$	16.1307	0.727229
$493$	2.02387	0.0911505
$494$	−11.3610	−0.511154
$495$	−3.84383	−0.172767
$496$	41.0772	1.84442
$497$	−13.0949	−0.587387
$498$	28.4702	1.27578
$499$	4.72016	0.211304	0.105652	−	0.994403i	$-0.466307\pi$
$499$	4.72016	0.211304	0.105652	+	0.994403i	$0.466307\pi$
$500$	−1.35584	−0.0606348
$501$	21.5372	0.962210
$502$	3.70752	0.165475
$503$	−23.1983	−1.03436	−0.517181	−	0.855876i	$-0.673019\pi$
$503$	−23.1983	−1.03436	−0.517181	+	0.855876i	$0.673019\pi$
$504$	1.18004	0.0525632
$505$	−8.60892	−0.383092
$506$	−7.04149	−0.313032
$507$	11.5893	0.514699
$508$	−6.48937	−0.287919
$509$	−42.9517	−1.90380	−0.951901	−	0.306406i	$-0.900874\pi$
$509$	−42.9517	−1.90380	−0.951901	+	0.306406i	$0.900874\pi$
$510$	−3.66379	−0.162235
$511$	10.4289	0.461347
$512$	20.5040	0.906159
$513$	−5.22153	−0.230536
$514$	−35.5399	−1.56760
$515$	−7.59699	−0.334763
$516$	12.5295	0.551580
$517$	−17.8973	−0.787120
$518$	2.68212	0.117846
$519$	13.4408	0.589986
$520$	−1.40157	−0.0614629
$521$	−24.6635	−1.08053	−0.540264	−	0.841496i	$-0.681675\pi$
$521$	−24.6635	−1.08053	−0.540264	+	0.841496i	$0.681675\pi$
$522$	−1.85376	−0.0811368
$523$	36.0587	1.57674	0.788369	−	0.615203i	$-0.210926\pi$
$523$	36.0587	1.57674	0.788369	+	0.615203i	$0.210926\pi$
$524$	−24.1769	−1.05617
$525$	1.00000	0.0436436
$526$	25.1672	1.09734
$527$	16.8578	0.734336
$528$	18.7324	0.815225
$529$	1.00000	0.0434783
$530$	−2.07399	−0.0900885
$531$	−12.0969	−0.524961
$532$	−7.07953	−0.306937
$533$	14.1307	0.612069
$534$	−26.8417	−1.16155
$535$	6.50561	0.281262
$536$	6.26861	0.270763
$537$	−12.9162	−0.557374
$538$	55.2963	2.38399
$539$	3.84383	0.165565
$540$	1.35584	0.0583459
$541$	41.6871	1.79227	0.896135	−	0.443782i	$-0.146364\pi$
$541$	41.6871	1.79227	0.896135	+	0.443782i	$0.146364\pi$
$542$	34.9099	1.49951
$543$	19.1786	0.823032
$544$	13.1349	0.563153
$545$	−0.798095	−0.0341866
$546$	−2.17579	−0.0931154
$547$	−3.38796	−0.144859	−0.0724293	−	0.997374i	$-0.523075\pi$
$547$	−3.38796	−0.144859	−0.0724293	+	0.997374i	$0.523075\pi$
$548$	−7.28552	−0.311222
$549$	−0.0668008	−0.00285099
$550$	7.04149	0.300250
$551$	−5.28385	−0.225099
$552$	−1.18004	−0.0502259
$553$	3.15178	0.134027
$554$	−34.3290	−1.45850
$555$	−1.46412	−0.0621486
$556$	25.7684	1.09282
$557$	−34.2149	−1.44973	−0.724866	−	0.688890i	$-0.758098\pi$
$557$	−34.2149	−1.44973	−0.724866	+	0.688890i	$0.758098\pi$
$558$	−15.4408	−0.653662
$559$	10.9760	0.464235
$560$	−4.87338	−0.205938
$561$	7.68766	0.324573
$562$	−36.3115	−1.53171
$563$	−8.90438	−0.375275	−0.187637	−	0.982238i	$-0.560083\pi$
$563$	−8.90438	−0.375275	−0.187637	+	0.982238i	$0.560083\pi$
$564$	6.31290	0.265821
$565$	−13.6547	−0.574456
$566$	39.8875	1.67660
$567$	−1.00000	−0.0419961
$568$	−15.4525	−0.648374
$569$	−38.7311	−1.62369	−0.811847	−	0.583870i	$-0.801538\pi$
$569$	−38.7311	−1.62369	−0.811847	+	0.583870i	$0.801538\pi$
$570$	9.56529	0.400646
$571$	33.9658	1.42143	0.710713	−	0.703483i	$-0.248373\pi$
$571$	33.9658	1.42143	0.710713	+	0.703483i	$0.248373\pi$
$572$	−6.18997	−0.258816
$573$	13.1961	0.551276
$574$	21.7945	0.909685
$575$	−1.00000	−0.0417029
$576$	−2.28408	−0.0951701
$577$	−3.71580	−0.154691	−0.0773454	−	0.997004i	$-0.524644\pi$
$577$	−3.71580	−0.154691	−0.0773454	+	0.997004i	$0.524644\pi$
$578$	−23.8146	−0.990558
$579$	−22.9125	−0.952210
$580$	1.37202	0.0569699
$581$	15.5414	0.644767
$582$	−12.9971	−0.538748
$583$	4.35182	0.180234
$584$	12.3065	0.509247
$585$	1.18773	0.0491066
$586$	28.5216	1.17821
$587$	11.4993	0.474628	0.237314	−	0.971433i	$-0.423733\pi$
$587$	11.4993	0.474628	0.237314	+	0.971433i	$0.423733\pi$
$588$	−1.35584	−0.0559137
$589$	−44.0116	−1.81347
$590$	22.1603	0.912324
$591$	−2.32413	−0.0956021
$592$	7.13523	0.293256
$593$	18.9224	0.777050	0.388525	−	0.921438i	$-0.372985\pi$
$593$	18.9224	0.777050	0.388525	+	0.921438i	$0.372985\pi$
$594$	−7.04149	−0.288916
$595$	−2.00000	−0.0819920
$596$	3.90147	0.159810
$597$	−16.9484	−0.693653
$598$	2.17579	0.0889748
$599$	32.1494	1.31359	0.656794	−	0.754070i	$-0.271912\pi$
$599$	32.1494	1.31359	0.656794	+	0.754070i	$0.271912\pi$
$600$	1.18004	0.0481750
$601$	9.62510	0.392616	0.196308	−	0.980542i	$-0.437105\pi$
$601$	9.62510	0.392616	0.196308	+	0.980542i	$0.437105\pi$
$602$	16.9288	0.689967
$603$	−5.31220	−0.216329
$604$	17.8775	0.727424
$605$	−3.77502	−0.153476
$606$	−15.7706	−0.640638
$607$	−12.5485	−0.509328	−0.254664	−	0.967030i	$-0.581965\pi$
$607$	−12.5485	−0.509328	−0.254664	+	0.967030i	$0.581965\pi$
$608$	−34.2920	−1.39073
$609$	−1.01194	−0.0410057
$610$	0.122372	0.00495469
$611$	5.53019	0.223727
$612$	−2.71167	−0.109613
$613$	32.3415	1.30626	0.653130	−	0.757246i	$-0.273456\pi$
$613$	32.3415	1.30626	0.653130	+	0.757246i	$0.273456\pi$
$614$	2.60586	0.105164
$615$	−11.8973	−0.479743
$616$	4.53588	0.182756
$617$	2.90318	0.116877	0.0584387	−	0.998291i	$-0.481388\pi$
$617$	2.90318	0.116877	0.0584387	+	0.998291i	$0.481388\pi$
$618$	−13.9169	−0.559819
$619$	−34.3997	−1.38264	−0.691321	−	0.722548i	$-0.742971\pi$
$619$	−34.3997	−1.38264	−0.691321	+	0.722548i	$0.742971\pi$
$620$	11.4282	0.458967
$621$	1.00000	0.0401286
$622$	16.0489	0.643504
$623$	−14.6524	−0.587037
$624$	−5.78826	−0.231716
$625$	1.00000	0.0400000
$626$	−40.9546	−1.63687
$627$	−20.0707	−0.801545
$628$	−16.9937	−0.678121
$629$	2.92825	0.116757
$630$	1.83189	0.0729844
$631$	−10.6024	−0.422077	−0.211038	−	0.977478i	$-0.567684\pi$
$631$	−10.6024	−0.422077	−0.211038	+	0.977478i	$0.567684\pi$
$632$	3.71923	0.147943
$633$	4.27271	0.169825
$634$	−2.44149	−0.0969641
$635$	4.78625	0.189937
$636$	−1.53502	−0.0608675
$637$	−1.18773	−0.0470596
$638$	−7.12553	−0.282102
$639$	13.0949	0.518027
$640$	−8.95067	−0.353806
$641$	−41.6539	−1.64523	−0.822615	−	0.568598i	$-0.807486\pi$
$641$	−41.6539	−1.64523	−0.822615	+	0.568598i	$0.807486\pi$
$642$	11.9176	0.470350
$643$	20.6628	0.814863	0.407432	−	0.913236i	$-0.366424\pi$
$643$	20.6628	0.814863	0.407432	+	0.913236i	$0.366424\pi$
$644$	1.35584	0.0534274
$645$	−9.24115	−0.363870
$646$	−19.1306	−0.752682
$647$	21.2207	0.834272	0.417136	−	0.908844i	$-0.363034\pi$
$647$	21.2207	0.834272	0.417136	+	0.908844i	$0.363034\pi$
$648$	−1.18004	−0.0463564
$649$	−46.4985	−1.82522
$650$	−2.17579	−0.0853417
$651$	−8.42888	−0.330354
$652$	18.7777	0.735390
$653$	−9.36613	−0.366525	−0.183262	−	0.983064i	$-0.558666\pi$
$653$	−9.36613	−0.366525	−0.183262	+	0.983064i	$0.558666\pi$
$654$	−1.46203	−0.0571697
$655$	17.8318	0.696744
$656$	57.9798	2.26373
$657$	−10.4289	−0.406869
$658$	8.52948	0.332514
$659$	6.42832	0.250412	0.125206	−	0.992131i	$-0.460041\pi$
$659$	6.42832	0.250412	0.125206	+	0.992131i	$0.460041\pi$
$660$	5.21160	0.202861
$661$	28.6765	1.11539	0.557694	−	0.830047i	$-0.311686\pi$
$661$	28.6765	1.11539	0.557694	+	0.830047i	$0.311686\pi$
$662$	−49.7084	−1.93197
$663$	−2.37546	−0.0922552
$664$	18.3395	0.711711
$665$	5.22153	0.202482
$666$	−2.68212	−0.103930
$667$	1.01194	0.0391823
$668$	−29.2009	−1.12982
$669$	−17.8809	−0.691317
$670$	9.73139	0.375956
$671$	−0.256771	−0.00991252
$672$	−6.56744	−0.253344
$673$	−20.8494	−0.803684	−0.401842	−	0.915709i	$-0.631630\pi$
$673$	−20.8494	−0.803684	−0.401842	+	0.915709i	$0.631630\pi$
$674$	27.7220	1.06781
$675$	−1.00000	−0.0384900
$676$	−15.7132	−0.604353
$677$	−15.9563	−0.613249	−0.306625	−	0.951831i	$-0.599200\pi$
$677$	−15.9563	−0.613249	−0.306625	+	0.951831i	$0.599200\pi$
$678$	−25.0139	−0.960652
$679$	−7.09491	−0.272278
$680$	−2.36008	−0.0905050
$681$	3.24908	0.124505
$682$	−59.3519	−2.27270
$683$	−8.30215	−0.317673	−0.158837	−	0.987305i	$-0.550774\pi$
$683$	−8.30215	−0.317673	−0.158837	+	0.987305i	$0.550774\pi$
$684$	7.07953	0.270693
$685$	5.37345	0.205309
$686$	−1.83189	−0.0699420
$687$	17.2931	0.659774
$688$	45.0357	1.71697
$689$	−1.34470	−0.0512289
$690$	−1.83189	−0.0697390
$691$	42.9888	1.63537	0.817686	−	0.575664i	$-0.195257\pi$
$691$	42.9888	1.63537	0.817686	+	0.575664i	$0.195257\pi$
$692$	−18.2235	−0.692755
$693$	−3.84383	−0.146015
$694$	−5.32786	−0.202243
$695$	−19.0055	−0.720921
$696$	−1.19413	−0.0452632
$697$	23.7945	0.901281
$698$	−21.5641	−0.816213
$699$	−1.76285	−0.0666772
$700$	−1.35584	−0.0512458
$701$	−3.98004	−0.150324	−0.0751621	−	0.997171i	$-0.523947\pi$
$701$	−3.98004	−0.150324	−0.0751621	+	0.997171i	$0.523947\pi$
$702$	2.17579	0.0821201
$703$	−7.64496	−0.288335
$704$	−8.77962	−0.330894
$705$	−4.65610	−0.175359
$706$	−45.0991	−1.69733
$707$	−8.60892	−0.323772
$708$	16.4014	0.616403
$709$	−10.3248	−0.387757	−0.193879	−	0.981026i	$-0.562107\pi$
$709$	−10.3248	−0.387757	−0.193879	+	0.981026i	$0.562107\pi$
$710$	−23.9885	−0.900272
$711$	−3.15178	−0.118201
$712$	−17.2905	−0.647987
$713$	8.42888	0.315664
$714$	−3.66379	−0.137114
$715$	4.56543	0.170737
$716$	17.5122	0.654462
$717$	−2.45065	−0.0915213
$718$	31.5235	1.17645
$719$	−3.92340	−0.146318	−0.0731591	−	0.997320i	$-0.523308\pi$
$719$	−3.92340	−0.146318	−0.0731591	+	0.997320i	$0.523308\pi$
$720$	4.87338	0.181620
$721$	−7.59699	−0.282927
$722$	15.1394	0.563431
$723$	8.92126	0.331785
$724$	−26.0030	−0.966395
$725$	−1.01194	−0.0375823
$726$	−6.91544	−0.256656
$727$	−1.39177	−0.0516181	−0.0258090	−	0.999667i	$-0.508216\pi$
$727$	−1.39177	−0.0516181	−0.0258090	+	0.999667i	$0.508216\pi$
$728$	−1.40157	−0.0519456
$729$	1.00000	0.0370370
$730$	19.1046	0.707093
$731$	18.4823	0.683593
$732$	0.0905708	0.00334759
$733$	−3.69124	−0.136339	−0.0681696	−	0.997674i	$-0.521716\pi$
$733$	−3.69124	−0.136339	−0.0681696	+	0.997674i	$0.521716\pi$
$734$	37.3332	1.37799
$735$	1.00000	0.0368856
$736$	6.56744	0.242079
$737$	−20.4192	−0.752150
$738$	−21.7945	−0.802267
$739$	26.8622	0.988144	0.494072	−	0.869421i	$-0.335508\pi$
$739$	26.8622	0.988144	0.494072	+	0.869421i	$0.335508\pi$
$740$	1.98511	0.0729741
$741$	6.20176	0.227827
$742$	−2.07399	−0.0761387
$743$	6.52651	0.239434	0.119717	−	0.992808i	$-0.461801\pi$
$743$	6.52651	0.239434	0.119717	+	0.992808i	$0.461801\pi$
$744$	−9.94643	−0.364654
$745$	−2.87754	−0.105425
$746$	40.7404	1.49161
$747$	−15.5414	−0.568631
$748$	−10.4232	−0.381110
$749$	6.50561	0.237710
$750$	1.83189	0.0668913
$751$	−17.2441	−0.629246	−0.314623	−	0.949217i	$-0.601878\pi$
$751$	−17.2441	−0.629246	−0.314623	+	0.949217i	$0.601878\pi$
$752$	22.6909	0.827454
$753$	−2.02387	−0.0737539
$754$	2.20176	0.0801835
$755$	−13.1856	−0.479872
$756$	1.35584	0.0493113
$757$	19.8128	0.720109	0.360055	−	0.932931i	$-0.382758\pi$
$757$	19.8128	0.720109	0.360055	+	0.932931i	$0.382758\pi$
$758$	15.1729	0.551105
$759$	3.84383	0.139522
$760$	6.16162	0.223505
$761$	−36.2842	−1.31530	−0.657650	−	0.753324i	$-0.728449\pi$
$761$	−36.2842	−1.31530	−0.657650	+	0.753324i	$0.728449\pi$
$762$	8.76791	0.317628
$763$	−0.798095	−0.0288930
$764$	−17.8918	−0.647302
$765$	2.00000	0.0723102
$766$	−53.5727	−1.93566
$767$	14.3679	0.518793
$768$	−20.9648	−0.756504
$769$	45.0783	1.62557	0.812783	−	0.582566i	$-0.197951\pi$
$769$	45.0783	1.62557	0.812783	+	0.582566i	$0.197951\pi$
$770$	7.04149	0.253758
$771$	19.4006	0.698696
$772$	31.0656	1.11807
$773$	5.92550	0.213126	0.106563	−	0.994306i	$-0.466015\pi$
$773$	5.92550	0.213126	0.106563	+	0.994306i	$0.466015\pi$
$774$	−16.9288	−0.608494
$775$	−8.42888	−0.302774
$776$	−8.37229	−0.300548
$777$	−1.46412	−0.0525251
$778$	9.11548	0.326806
$779$	−62.1218	−2.22575
$780$	−1.61037	−0.0576603
$781$	50.3346	1.80111
$782$	3.66379	0.131017
$783$	1.01194	0.0361636
$784$	−4.87338	−0.174049
$785$	12.5337	0.447348
$786$	32.6659	1.16515
$787$	3.96137	0.141207	0.0706037	−	0.997504i	$-0.477507\pi$
$787$	3.96137	0.141207	0.0706037	+	0.997504i	$0.477507\pi$
$788$	3.15114	0.112255
$789$	−13.7384	−0.489099
$790$	5.77373	0.205420
$791$	−13.6547	−0.485504
$792$	−4.53588	−0.161175
$793$	0.0793412	0.00281749
$794$	70.5443	2.50353
$795$	1.13216	0.0401535
$796$	22.9793	0.814479
$797$	−10.1927	−0.361044	−0.180522	−	0.983571i	$-0.557779\pi$
$797$	−10.1927	−0.361044	−0.180522	+	0.983571i	$0.557779\pi$
$798$	9.56529	0.338607
$799$	9.31220	0.329442
$800$	−6.56744	−0.232194
$801$	14.6524	0.517718
$802$	−29.6360	−1.04648
$803$	−40.0868	−1.41463
$804$	7.20247	0.254011
$805$	−1.00000	−0.0352454
$806$	18.3395	0.645982
$807$	−30.1853	−1.06257
$808$	−10.1589	−0.357388
$809$	16.1924	0.569295	0.284648	−	0.958632i	$-0.408123\pi$
$809$	16.1924	0.569295	0.284648	+	0.958632i	$0.408123\pi$
$810$	−1.83189	−0.0643662
$811$	−34.3634	−1.20666	−0.603332	−	0.797490i	$-0.706161\pi$
$811$	−34.3634	−1.20666	−0.603332	+	0.797490i	$0.706161\pi$
$812$	1.37202	0.0481484
$813$	−19.0567	−0.668349
$814$	−10.3096	−0.361352
$815$	−13.8495	−0.485127
$816$	−9.74676	−0.341205
$817$	−48.2529	−1.68816
$818$	55.6941	1.94730
$819$	1.18773	0.0415026
$820$	16.1307	0.563309
$821$	−29.6858	−1.03604	−0.518020	−	0.855368i	$-0.673331\pi$
$821$	−29.6858	−1.03604	−0.518020	+	0.855368i	$0.673331\pi$
$822$	9.84359	0.343335
$823$	−13.4193	−0.467767	−0.233883	−	0.972265i	$-0.575143\pi$
$823$	−13.4193	−0.467767	−0.233883	+	0.972265i	$0.575143\pi$
$824$	−8.96476	−0.312302
$825$	−3.84383	−0.133825
$826$	22.1603	0.771054
$827$	−13.0245	−0.452905	−0.226453	−	0.974022i	$-0.572713\pi$
$827$	−13.0245	−0.452905	−0.226453	+	0.974022i	$0.572713\pi$
$828$	−1.35584	−0.0471185
$829$	16.9527	0.588791	0.294395	−	0.955684i	$-0.404882\pi$
$829$	16.9527	0.588791	0.294395	+	0.955684i	$0.404882\pi$
$830$	28.4702	0.988216
$831$	18.7396	0.650071
$832$	2.71287	0.0940519
$833$	−2.00000	−0.0692959
$834$	−34.8161	−1.20558
$835$	21.5372	0.745324
$836$	27.2125	0.941165
$837$	8.42888	0.291345
$838$	−39.1136	−1.35116
$839$	28.2047	0.973735	0.486868	−	0.873476i	$-0.338139\pi$
$839$	28.2047	0.973735	0.486868	+	0.873476i	$0.338139\pi$
$840$	1.18004	0.0407153
$841$	−27.9760	−0.964689
$842$	−54.3920	−1.87447
$843$	19.8218	0.682700
$844$	−5.79309	−0.199406
$845$	11.5893	0.398684
$846$	−8.52948	−0.293250
$847$	−3.77502	−0.129711
$848$	−5.51744	−0.189470
$849$	−21.7739	−0.747279
$850$	−3.66379	−0.125667
$851$	1.46412	0.0501895
$852$	−17.7545	−0.608261
$853$	−38.7182	−1.32569	−0.662843	−	0.748759i	$-0.730650\pi$
$853$	−38.7182	−1.32569	−0.662843	+	0.748759i	$0.730650\pi$
$854$	0.122372	0.00418748
$855$	−5.22153	−0.178573
$856$	7.67689	0.262391
$857$	−12.8046	−0.437396	−0.218698	−	0.975793i	$-0.570181\pi$
$857$	−12.8046	−0.437396	−0.218698	+	0.975793i	$0.570181\pi$
$858$	8.36338	0.285521
$859$	10.6807	0.364421	0.182211	−	0.983260i	$-0.441675\pi$
$859$	10.6807	0.364421	0.182211	+	0.983260i	$0.441675\pi$
$860$	12.5295	0.427252
$861$	−11.8973	−0.405457
$862$	61.5937	2.09789
$863$	−41.8914	−1.42600	−0.713001	−	0.701163i	$-0.752664\pi$
$863$	−41.8914	−1.42600	−0.713001	+	0.701163i	$0.752664\pi$
$864$	6.56744	0.223429
$865$	13.4408	0.457001
$866$	−1.31304	−0.0446189
$867$	13.0000	0.441503
$868$	11.4282	0.387898
$869$	−12.1149	−0.410970
$870$	−1.85376	−0.0628483
$871$	6.30946	0.213788
$872$	−0.941785	−0.0318929
$873$	7.09491	0.240126
$874$	−9.56529	−0.323551
$875$	1.00000	0.0338062
$876$	14.1398	0.477741
$877$	−13.5610	−0.457924	−0.228962	−	0.973435i	$-0.573533\pi$
$877$	−13.5610	−0.457924	−0.228962	+	0.973435i	$0.573533\pi$
$878$	20.2484	0.683352
$879$	−15.5694	−0.525144
$880$	18.7324	0.631471
$881$	−37.5214	−1.26413	−0.632064	−	0.774916i	$-0.717792\pi$
$881$	−37.5214	−1.26413	−0.632064	+	0.774916i	$0.717792\pi$
$882$	1.83189	0.0616831
$883$	51.1740	1.72214	0.861071	−	0.508486i	$-0.169794\pi$
$883$	51.1740	1.72214	0.861071	+	0.508486i	$0.169794\pi$
$884$	3.22073	0.108325
$885$	−12.0969	−0.406633
$886$	−39.0633	−1.31236
$887$	−22.7037	−0.762317	−0.381158	−	0.924510i	$-0.624475\pi$
$887$	−22.7037	−0.762317	−0.381158	+	0.924510i	$0.624475\pi$
$888$	−1.72773	−0.0579787
$889$	4.78625	0.160526
$890$	−26.8417	−0.899735
$891$	3.84383	0.128773
$892$	24.2436	0.811736
$893$	−24.3120	−0.813569
$894$	−5.27134	−0.176300
$895$	−12.9162	−0.431740
$896$	−8.95067	−0.299021
$897$	−1.18773	−0.0396571
$898$	−24.0114	−0.801271
$899$	8.52948	0.284474
$900$	1.35584	0.0451945
$901$	−2.26432	−0.0754353
$902$	−83.7743	−2.78938
$903$	−9.24115	−0.307526
$904$	−16.1131	−0.535912
$905$	19.1786	0.637518
$906$	−24.1546	−0.802482
$907$	0.810022	0.0268963	0.0134482	−	0.999910i	$-0.495719\pi$
$907$	0.810022	0.0268963	0.0134482	+	0.999910i	$0.495719\pi$
$908$	−4.40522	−0.146192
$909$	8.60892	0.285540
$910$	−2.17579	−0.0721269
$911$	−55.4562	−1.83735	−0.918673	−	0.395018i	$-0.870738\pi$
$911$	−55.4562	−1.83735	−0.918673	+	0.395018i	$0.870738\pi$
$912$	25.4465	0.842618
$913$	−59.7385	−1.97706
$914$	−72.7492	−2.40633
$915$	−0.0668008	−0.00220837
$916$	−23.4467	−0.774699
$917$	17.8318	0.588856
$918$	3.66379	0.120923
$919$	1.86049	0.0613718	0.0306859	−	0.999529i	$-0.490231\pi$
$919$	1.86049	0.0613718	0.0306859	+	0.999529i	$0.490231\pi$
$920$	−1.18004	−0.0389048
$921$	−1.42249	−0.0468728
$922$	52.8862	1.74171
$923$	−15.5532	−0.511940
$924$	5.21160	0.171449
$925$	−1.46412	−0.0481401
$926$	2.29597	0.0754501
$927$	7.59699	0.249518
$928$	6.64582	0.218160
$929$	−37.7658	−1.23905	−0.619527	−	0.784975i	$-0.712676\pi$
$929$	−37.7658	−1.23905	−0.619527	+	0.784975i	$0.712676\pi$
$930$	−15.4408	−0.506324
$931$	5.22153	0.171129
$932$	2.39014	0.0782916
$933$	−8.76085	−0.286817
$934$	−33.3708	−1.09193
$935$	7.68766	0.251413
$936$	1.40157	0.0458117
$937$	21.0948	0.689137	0.344569	−	0.938761i	$-0.388025\pi$
$937$	21.0948	0.689137	0.344569	+	0.938761i	$0.388025\pi$
$938$	9.73139	0.317741
$939$	22.3564	0.729573
$940$	6.31290	0.205904
$941$	16.9553	0.552726	0.276363	−	0.961053i	$-0.410871\pi$
$941$	16.9553	0.552726	0.276363	+	0.961053i	$0.410871\pi$
$942$	22.9605	0.748092
$943$	11.8973	0.387428
$944$	58.9529	1.91875
$945$	−1.00000	−0.0325300
$946$	−65.0715	−2.11566
$947$	45.5377	1.47978	0.739888	−	0.672730i	$-0.234879\pi$
$947$	45.5377	1.47978	0.739888	+	0.672730i	$0.234879\pi$
$948$	4.27330	0.138790
$949$	12.3867	0.402089
$950$	9.56529	0.310339
$951$	1.33277	0.0432181
$952$	−2.36008	−0.0764907
$953$	−10.5987	−0.343324	−0.171662	−	0.985156i	$-0.554914\pi$
$953$	−10.5987	−0.343324	−0.171662	+	0.985156i	$0.554914\pi$
$954$	2.07399	0.0671480
$955$	13.1961	0.427017
$956$	3.32268	0.107463
$957$	3.88971	0.125736
$958$	51.6325	1.66817
$959$	5.37345	0.173518
$960$	−2.28408	−0.0737184
$961$	40.0460	1.29181
$962$	3.18563	0.102709
$963$	−6.50561	−0.209640
$964$	−12.0958	−0.389578
$965$	−22.9125	−0.737579
$966$	−1.83189	−0.0589402
$967$	21.4807	0.690774	0.345387	−	0.938460i	$-0.387748\pi$
$967$	21.4807	0.690774	0.345387	+	0.938460i	$0.387748\pi$
$968$	−4.45468	−0.143179
$969$	10.4431	0.335479
$970$	−12.9971	−0.417312
$971$	−7.81016	−0.250640	−0.125320	−	0.992116i	$-0.539996\pi$
$971$	−7.81016	−0.250640	−0.125320	+	0.992116i	$0.539996\pi$
$972$	−1.35584	−0.0434884
$973$	−19.0055	−0.609290
$974$	35.9295	1.15126
$975$	1.18773	0.0380378
$976$	0.325546	0.0104205
$977$	17.0250	0.544678	0.272339	−	0.962201i	$-0.412203\pi$
$977$	17.0250	0.544678	0.272339	+	0.962201i	$0.412203\pi$
$978$	−25.3708	−0.811270
$979$	56.3214	1.80004
$980$	−1.35584	−0.0433106
$981$	0.798095	0.0254812
$982$	15.2645	0.487109
$983$	−58.5933	−1.86884	−0.934418	−	0.356178i	$-0.884080\pi$
$983$	−58.5933	−1.86884	−0.934418	+	0.356178i	$0.884080\pi$
$984$	−14.0392	−0.447555
$985$	−2.32413	−0.0740531
$986$	3.70752	0.118071
$987$	−4.65610	−0.148205
$988$	−8.40857	−0.267512
$989$	9.24115	0.293852
$990$	−7.04149	−0.223793
$991$	36.1812	1.14933	0.574667	−	0.818387i	$-0.305131\pi$
$991$	36.1812	1.14933	0.574667	+	0.818387i	$0.305131\pi$
$992$	55.3561	1.75756
$993$	27.1350	0.861102
$994$	−23.9885	−0.760869
$995$	−16.9484	−0.537301
$996$	21.0716	0.667679
$997$	27.8400	0.881702	0.440851	−	0.897580i	$-0.354677\pi$
$997$	27.8400	0.881702	0.440851	+	0.897580i	$0.354677\pi$
$998$	8.64684	0.273711
$999$	1.46412	0.0463228

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2415.2.a.o.1.4	✓	5
3.2	odd	2		7245.2.a.bg.1.2		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2415.2.a.o.1.4	✓	5	1.1	even	1	trivial
7245.2.a.bg.1.2		5	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)

\(f(q)\)	\(=\)	\(q+1.83189 q^{2} -1.00000 q^{3} +1.35584 q^{4} -1.00000 q^{5} -1.83189 q^{6} -1.00000 q^{7} -1.18004 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.83189 q^{2} -1.00000 q^{3} +1.35584 q^{4} -1.00000 q^{5} -1.83189 q^{6} -1.00000 q^{7} -1.18004 q^{8} +1.00000 q^{9} -1.83189 q^{10} +3.84383 q^{11} -1.35584 q^{12} -1.18773 q^{13} -1.83189 q^{14} +1.00000 q^{15} -4.87338 q^{16} -2.00000 q^{17} +1.83189 q^{18} +5.22153 q^{19} -1.35584 q^{20} +1.00000 q^{21} +7.04149 q^{22} -1.00000 q^{23} +1.18004 q^{24} +1.00000 q^{25} -2.17579 q^{26} -1.00000 q^{27} -1.35584 q^{28} -1.01194 q^{29} +1.83189 q^{30} -8.42888 q^{31} -6.56744 q^{32} -3.84383 q^{33} -3.66379 q^{34} +1.00000 q^{35} +1.35584 q^{36} -1.46412 q^{37} +9.56529 q^{38} +1.18773 q^{39} +1.18004 q^{40} -11.8973 q^{41} +1.83189 q^{42} -9.24115 q^{43} +5.21160 q^{44} -1.00000 q^{45} -1.83189 q^{46} -4.65610 q^{47} +4.87338 q^{48} +1.00000 q^{49} +1.83189 q^{50} +2.00000 q^{51} -1.61037 q^{52} +1.13216 q^{53} -1.83189 q^{54} -3.84383 q^{55} +1.18004 q^{56} -5.22153 q^{57} -1.85376 q^{58} -12.0969 q^{59} +1.35584 q^{60} -0.0668008 q^{61} -15.4408 q^{62} -1.00000 q^{63} -2.28408 q^{64} +1.18773 q^{65} -7.04149 q^{66} -5.31220 q^{67} -2.71167 q^{68} +1.00000 q^{69} +1.83189 q^{70} +13.0949 q^{71} -1.18004 q^{72} -10.4289 q^{73} -2.68212 q^{74} -1.00000 q^{75} +7.07953 q^{76} -3.84383 q^{77} +2.17579 q^{78} -3.15178 q^{79} +4.87338 q^{80} +1.00000 q^{81} -21.7945 q^{82} -15.5414 q^{83} +1.35584 q^{84} +2.00000 q^{85} -16.9288 q^{86} +1.01194 q^{87} -4.53588 q^{88} +14.6524 q^{89} -1.83189 q^{90} +1.18773 q^{91} -1.35584 q^{92} +8.42888 q^{93} -8.52948 q^{94} -5.22153 q^{95} +6.56744 q^{96} +7.09491 q^{97} +1.83189 q^{98} +3.84383 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q - 5 q^{3} + 10 q^{4} - 5 q^{5} - 5 q^{7} - 6 q^{8} + 5 q^{9}+O(q^{10}) \) 5 * q - 5 * q^3 + 10 * q^4 - 5 * q^5 - 5 * q^7 - 6 * q^8 + 5 * q^9	\( 5 q - 5 q^{3} + 10 q^{4} - 5 q^{5} - 5 q^{7} - 6 q^{8} + 5 q^{9} + q^{11} - 10 q^{12} + 5 q^{15} + 8 q^{16} - 10 q^{17} + 3 q^{19} - 10 q^{20} + 5 q^{21} + 12 q^{22} - 5 q^{23} + 6 q^{24} + 5 q^{25} - 14 q^{26} - 5 q^{27} - 10 q^{28} + 4 q^{29} + 2 q^{31} - 12 q^{32} - q^{33} + 5 q^{35} + 10 q^{36} - 4 q^{37} - 24 q^{38} + 6 q^{40} - 9 q^{41} - 8 q^{43} + 2 q^{44} - 5 q^{45} - 11 q^{47} - 8 q^{48} + 5 q^{49} + 10 q^{51} - 22 q^{52} - 19 q^{53} - q^{55} + 6 q^{56} - 3 q^{57} + 8 q^{58} + 5 q^{59} + 10 q^{60} - 17 q^{61} - 24 q^{62} - 5 q^{63} - 8 q^{64} - 12 q^{66} - 2 q^{67} - 20 q^{68} + 5 q^{69} + 10 q^{71} - 6 q^{72} - 8 q^{73} - 34 q^{74} - 5 q^{75} - 8 q^{76} - q^{77} + 14 q^{78} + 24 q^{79} - 8 q^{80} + 5 q^{81} - 8 q^{82} - 24 q^{83} + 10 q^{84} + 10 q^{85} - 10 q^{86} - 4 q^{87} - 26 q^{88} - 4 q^{89} - 10 q^{92} - 2 q^{93} + 2 q^{94} - 3 q^{95} + 12 q^{96} - 20 q^{97} + q^{99}+O(q^{100}) \) 5 * q - 5 * q^3 + 10 * q^4 - 5 * q^5 - 5 * q^7 - 6 * q^8 + 5 * q^9 + q^11 - 10 * q^12 + 5 * q^15 + 8 * q^16 - 10 * q^17 + 3 * q^19 - 10 * q^20 + 5 * q^21 + 12 * q^22 - 5 * q^23 + 6 * q^24 + 5 * q^25 - 14 * q^26 - 5 * q^27 - 10 * q^28 + 4 * q^29 + 2 * q^31 - 12 * q^32 - q^33 + 5 * q^35 + 10 * q^36 - 4 * q^37 - 24 * q^38 + 6 * q^40 - 9 * q^41 - 8 * q^43 + 2 * q^44 - 5 * q^45 - 11 * q^47 - 8 * q^48 + 5 * q^49 + 10 * q^51 - 22 * q^52 - 19 * q^53 - q^55 + 6 * q^56 - 3 * q^57 + 8 * q^58 + 5 * q^59 + 10 * q^60 - 17 * q^61 - 24 * q^62 - 5 * q^63 - 8 * q^64 - 12 * q^66 - 2 * q^67 - 20 * q^68 + 5 * q^69 + 10 * q^71 - 6 * q^72 - 8 * q^73 - 34 * q^74 - 5 * q^75 - 8 * q^76 - q^77 + 14 * q^78 + 24 * q^79 - 8 * q^80 + 5 * q^81 - 8 * q^82 - 24 * q^83 + 10 * q^84 + 10 * q^85 - 10 * q^86 - 4 * q^87 - 26 * q^88 - 4 * q^89 - 10 * q^92 - 2 * q^93 + 2 * q^94 - 3 * q^95 + 12 * q^96 - 20 * q^97 + q^99

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