LMFDB - Embedded newform 4015.2.a.h.1.26

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4015,2,Mod(1,4015)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4015, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("4015.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4015 = 5 \cdot 11 \cdot 73 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4015.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:	$32.0599364115$
Analytic rank:	$0$
Dimension:	$37$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.26
Character	$\chi$	$=$	4015.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.44464 q^{2} +0.0812853 q^{3} +0.0869915 q^{4} +1.00000 q^{5} +0.117428 q^{6} +1.22786 q^{7} -2.76361 q^{8} -2.99339 q^{9} +O(q^{10})$	\(q+1.44464 q^{2} +0.0812853 q^{3} +0.0869915 q^{4} +1.00000 q^{5} +0.117428 q^{6} +1.22786 q^{7} -2.76361 q^{8} -2.99339 q^{9} +1.44464 q^{10} +1.00000 q^{11} +0.00707113 q^{12} +4.04700 q^{13} +1.77382 q^{14} +0.0812853 q^{15} -4.16642 q^{16} -0.951858 q^{17} -4.32438 q^{18} +6.58356 q^{19} +0.0869915 q^{20} +0.0998069 q^{21} +1.44464 q^{22} +7.77090 q^{23} -0.224641 q^{24} +1.00000 q^{25} +5.84647 q^{26} -0.487174 q^{27} +0.106813 q^{28} -6.21609 q^{29} +0.117428 q^{30} -5.11002 q^{31} -0.491754 q^{32} +0.0812853 q^{33} -1.37509 q^{34} +1.22786 q^{35} -0.260400 q^{36} -4.08507 q^{37} +9.51089 q^{38} +0.328962 q^{39} -2.76361 q^{40} -1.52317 q^{41} +0.144185 q^{42} +8.93425 q^{43} +0.0869915 q^{44} -2.99339 q^{45} +11.2262 q^{46} +7.83137 q^{47} -0.338668 q^{48} -5.49236 q^{49} +1.44464 q^{50} -0.0773720 q^{51} +0.352055 q^{52} -10.1374 q^{53} -0.703793 q^{54} +1.00000 q^{55} -3.39333 q^{56} +0.535146 q^{57} -8.98002 q^{58} +12.5089 q^{59} +0.00707113 q^{60} +4.37595 q^{61} -7.38215 q^{62} -3.67547 q^{63} +7.62242 q^{64} +4.04700 q^{65} +0.117428 q^{66} +15.3385 q^{67} -0.0828036 q^{68} +0.631660 q^{69} +1.77382 q^{70} -4.94122 q^{71} +8.27258 q^{72} +1.00000 q^{73} -5.90146 q^{74} +0.0812853 q^{75} +0.572714 q^{76} +1.22786 q^{77} +0.475232 q^{78} -3.79020 q^{79} -4.16642 q^{80} +8.94058 q^{81} -2.20043 q^{82} +17.4176 q^{83} +0.00868236 q^{84} -0.951858 q^{85} +12.9068 q^{86} -0.505276 q^{87} -2.76361 q^{88} +8.86276 q^{89} -4.32438 q^{90} +4.96915 q^{91} +0.676003 q^{92} -0.415369 q^{93} +11.3135 q^{94} +6.58356 q^{95} -0.0399724 q^{96} +3.39045 q^{97} -7.93449 q^{98} -2.99339 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 37 q + 5 q^{2} + 3 q^{3} + 43 q^{4} + 37 q^{5} + 9 q^{6} + 6 q^{7} + 12 q^{8} + 50 q^{9}+O(q^{10}) $ 37 * q + 5 * q^2 + 3 * q^3 + 43 * q^4 + 37 * q^5 + 9 * q^6 + 6 * q^7 + 12 * q^8 + 50 * q^9	\( 37 q + 5 q^{2} + 3 q^{3} + 43 q^{4} + 37 q^{5} + 9 q^{6} + 6 q^{7} + 12 q^{8} + 50 q^{9} + 5 q^{10} + 37 q^{11} + 6 q^{12} + 11 q^{13} + 11 q^{14} + 3 q^{15} + 43 q^{16} + 38 q^{17} + 11 q^{18} + 34 q^{19} + 43 q^{20} + 39 q^{21} + 5 q^{22} + 4 q^{23} + 25 q^{24} + 37 q^{25} - 9 q^{26} + 3 q^{27} + 14 q^{28} + 58 q^{29} + 9 q^{30} + 8 q^{31} + 14 q^{32} + 3 q^{33} + 8 q^{34} + 6 q^{35} + 20 q^{36} + 2 q^{37} + 15 q^{38} + 14 q^{39} + 12 q^{40} + 62 q^{41} - 13 q^{42} + 30 q^{43} + 43 q^{44} + 50 q^{45} + 31 q^{46} + 5 q^{47} - 25 q^{48} + 59 q^{49} + 5 q^{50} + 23 q^{51} - q^{52} + 18 q^{53} + 13 q^{54} + 37 q^{55} + 22 q^{56} + 5 q^{57} - 40 q^{58} + 15 q^{59} + 6 q^{60} + 57 q^{61} + 20 q^{62} - 29 q^{63} + 10 q^{64} + 11 q^{65} + 9 q^{66} - 14 q^{67} + 53 q^{68} + 24 q^{69} + 11 q^{70} + 8 q^{71} + 15 q^{72} + 37 q^{73} + 7 q^{74} + 3 q^{75} + 59 q^{76} + 6 q^{77} + q^{78} + 42 q^{79} + 43 q^{80} + 61 q^{81} - 22 q^{82} + 44 q^{83} + 66 q^{84} + 38 q^{85} - q^{86} - 26 q^{87} + 12 q^{88} + 69 q^{89} + 11 q^{90} - 10 q^{91} - 21 q^{92} - 26 q^{93} + 29 q^{94} + 34 q^{95} - 9 q^{96} + 37 q^{97} - 15 q^{98} + 50 q^{99}+O(q^{100}) \) 37 * q + 5 * q^2 + 3 * q^3 + 43 * q^4 + 37 * q^5 + 9 * q^6 + 6 * q^7 + 12 * q^8 + 50 * q^9 + 5 * q^10 + 37 * q^11 + 6 * q^12 + 11 * q^13 + 11 * q^14 + 3 * q^15 + 43 * q^16 + 38 * q^17 + 11 * q^18 + 34 * q^19 + 43 * q^20 + 39 * q^21 + 5 * q^22 + 4 * q^23 + 25 * q^24 + 37 * q^25 - 9 * q^26 + 3 * q^27 + 14 * q^28 + 58 * q^29 + 9 * q^30 + 8 * q^31 + 14 * q^32 + 3 * q^33 + 8 * q^34 + 6 * q^35 + 20 * q^36 + 2 * q^37 + 15 * q^38 + 14 * q^39 + 12 * q^40 + 62 * q^41 - 13 * q^42 + 30 * q^43 + 43 * q^44 + 50 * q^45 + 31 * q^46 + 5 * q^47 - 25 * q^48 + 59 * q^49 + 5 * q^50 + 23 * q^51 - q^52 + 18 * q^53 + 13 * q^54 + 37 * q^55 + 22 * q^56 + 5 * q^57 - 40 * q^58 + 15 * q^59 + 6 * q^60 + 57 * q^61 + 20 * q^62 - 29 * q^63 + 10 * q^64 + 11 * q^65 + 9 * q^66 - 14 * q^67 + 53 * q^68 + 24 * q^69 + 11 * q^70 + 8 * q^71 + 15 * q^72 + 37 * q^73 + 7 * q^74 + 3 * q^75 + 59 * q^76 + 6 * q^77 + q^78 + 42 * q^79 + 43 * q^80 + 61 * q^81 - 22 * q^82 + 44 * q^83 + 66 * q^84 + 38 * q^85 - q^86 - 26 * q^87 + 12 * q^88 + 69 * q^89 + 11 * q^90 - 10 * q^91 - 21 * q^92 - 26 * q^93 + 29 * q^94 + 34 * q^95 - 9 * q^96 + 37 * q^97 - 15 * q^98 + 50 * 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 $

$2$	1.44464	1.02152	0.510758	−	0.859724i	$-0.329365\pi$
$2$	1.44464	1.02152	0.510758	+	0.859724i	$0.329365\pi$
$3$	0.0812853	0.0469301	0.0234650	−	0.999725i	$-0.492530\pi$
$3$	0.0812853	0.0469301	0.0234650	+	0.999725i	$0.492530\pi$
$4$	0.0869915	0.0434958
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	0.117428	0.0479398
$7$	1.22786	0.464088	0.232044	−	0.972705i	$-0.425459\pi$
$7$	1.22786	0.464088	0.232044	+	0.972705i	$0.425459\pi$
$8$	−2.76361	−0.977085
$9$	−2.99339	−0.997798
$10$	1.44464	0.456836
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	0.00707113	0.00204126
$13$	4.04700	1.12244	0.561218	−	0.827668i	$-0.310333\pi$
$13$	4.04700	1.12244	0.561218	+	0.827668i	$0.310333\pi$
$14$	1.77382	0.474073
$15$	0.0812853	0.0209878
$16$	−4.16642	−1.04160
$17$	−0.951858	−0.230860	−0.115430	−	0.993316i	$-0.536825\pi$
$17$	−0.951858	−0.230860	−0.115430	+	0.993316i	$0.536825\pi$
$18$	−4.32438	−1.01927
$19$	6.58356	1.51037	0.755186	−	0.655511i	$-0.227547\pi$
$19$	6.58356	1.51037	0.755186	+	0.655511i	$0.227547\pi$
$20$	0.0869915	0.0194519
$21$	0.0998069	0.0217797
$22$	1.44464	0.307999
$23$	7.77090	1.62034	0.810172	−	0.586192i	$-0.199373\pi$
$23$	7.77090	1.62034	0.810172	+	0.586192i	$0.199373\pi$
$24$	−0.224641	−0.0458546
$25$	1.00000	0.200000
$26$	5.84647	1.14659
$27$	−0.487174	−0.0937568
$28$	0.106813	0.0201858
$29$	−6.21609	−1.15430	−0.577149	−	0.816639i	$-0.695835\pi$
$29$	−6.21609	−1.15430	−0.577149	+	0.816639i	$0.695835\pi$
$30$	0.117428	0.0214393
$31$	−5.11002	−0.917786	−0.458893	−	0.888492i	$-0.651754\pi$
$31$	−5.11002	−0.917786	−0.458893	+	0.888492i	$0.651754\pi$
$32$	−0.491754	−0.0869307
$33$	0.0812853	0.0141499
$34$	−1.37509	−0.235827
$35$	1.22786	0.207546
$36$	−0.260400	−0.0434000
$37$	−4.08507	−0.671581	−0.335790	−	0.941937i	$-0.609003\pi$
$37$	−4.08507	−0.671581	−0.335790	+	0.941937i	$0.609003\pi$
$38$	9.51089	1.54287
$39$	0.328962	0.0526760
$40$	−2.76361	−0.436966
$41$	−1.52317	−0.237879	−0.118939	−	0.992902i	$-0.537949\pi$
$41$	−1.52317	−0.237879	−0.118939	+	0.992902i	$0.537949\pi$
$42$	0.144185	0.0222483
$43$	8.93425	1.36246	0.681230	−	0.732069i	$-0.261445\pi$
$43$	8.93425	1.36246	0.681230	+	0.732069i	$0.261445\pi$
$44$	0.0869915	0.0131145
$45$	−2.99339	−0.446229
$46$	11.2262	1.65521
$47$	7.83137	1.14232	0.571161	−	0.820838i	$-0.306493\pi$
$47$	7.83137	1.14232	0.571161	+	0.820838i	$0.306493\pi$
$48$	−0.338668	−0.0488825
$49$	−5.49236	−0.784623
$50$	1.44464	0.204303
$51$	−0.0773720	−0.0108343
$52$	0.352055	0.0488213
$53$	−10.1374	−1.39248	−0.696238	−	0.717811i	$-0.745144\pi$
$53$	−10.1374	−1.39248	−0.696238	+	0.717811i	$0.745144\pi$
$54$	−0.703793	−0.0957741
$55$	1.00000	0.134840
$56$	−3.39333	−0.453453
$57$	0.535146	0.0708818
$58$	−8.98002	−1.17913
$59$	12.5089	1.62852	0.814261	−	0.580499i	$-0.197143\pi$
$59$	12.5089	1.62852	0.814261	+	0.580499i	$0.197143\pi$
$60$	0.00707113	0.000912879 0
$61$	4.37595	0.560283	0.280141	−	0.959959i	$-0.409619\pi$
$61$	4.37595	0.560283	0.280141	+	0.959959i	$0.409619\pi$
$62$	−7.38215	−0.937534
$63$	−3.67547	−0.463065
$64$	7.62242	0.952803
$65$	4.04700	0.501969
$66$	0.117428	0.0144544
$67$	15.3385	1.87389	0.936947	−	0.349473i	$-0.113639\pi$
$67$	15.3385	1.87389	0.936947	+	0.349473i	$0.113639\pi$
$68$	−0.0828036	−0.0100414
$69$	0.631660	0.0760429
$70$	1.77382	0.212012
$71$	−4.94122	−0.586415	−0.293207	−	0.956049i	$-0.594723\pi$
$71$	−4.94122	−0.586415	−0.293207	+	0.956049i	$0.594723\pi$
$72$	8.27258	0.974933
$73$	1.00000	0.117041
$73$	1.00000	0.117041
$74$	−5.90146	−0.686031
$75$	0.0812853	0.00938601
$76$	0.572714	0.0656948
$77$	1.22786	0.139928
$78$	0.475232	0.0538094
$79$	−3.79020	−0.426431	−0.213216	−	0.977005i	$-0.568394\pi$
$79$	−3.79020	−0.426431	−0.213216	+	0.977005i	$0.568394\pi$
$80$	−4.16642	−0.465819
$81$	8.94058	0.993398
$82$	−2.20043	−0.242997
$83$	17.4176	1.91183	0.955915	−	0.293644i	$-0.0948680\pi$
$83$	17.4176	1.91183	0.955915	+	0.293644i	$0.0948680\pi$
$84$	0.00868236	0.000947323 0
$85$	−0.951858	−0.103244
$86$	12.9068	1.39178
$87$	−0.505276	−0.0541713
$88$	−2.76361	−0.294602
$89$	8.86276	0.939450	0.469725	−	0.882813i	$-0.344353\pi$
$89$	8.86276	0.939450	0.469725	+	0.882813i	$0.344353\pi$
$90$	−4.32438	−0.455830
$91$	4.96915	0.520909
$92$	0.676003	0.0704781
$93$	−0.415369	−0.0430718
$94$	11.3135	1.16690
$95$	6.58356	0.675459
$96$	−0.0399724	−0.00407966
$97$	3.39045	0.344248	0.172124	−	0.985075i	$-0.444937\pi$
$97$	3.39045	0.344248	0.172124	+	0.985075i	$0.444937\pi$
$98$	−7.93449	−0.801505
$99$	−2.99339	−0.300847
$100$	0.0869915	0.00869915
$101$	−12.2634	−1.22026	−0.610129	−	0.792302i	$-0.708882\pi$
$101$	−12.2634	−1.22026	−0.610129	+	0.792302i	$0.708882\pi$
$102$	−0.111775	−0.0110674
$103$	8.13801	0.801862	0.400931	−	0.916108i	$-0.368687\pi$
$103$	8.13801	0.801862	0.400931	+	0.916108i	$0.368687\pi$
$104$	−11.1844	−1.09672
$105$	0.0998069	0.00974016
$106$	−14.6449	−1.42244
$107$	13.7912	1.33325	0.666625	−	0.745394i	$-0.267738\pi$
$107$	13.7912	1.33325	0.666625	+	0.745394i	$0.267738\pi$
$108$	−0.0423801	−0.00407802
$109$	5.87151	0.562388	0.281194	−	0.959651i	$-0.409270\pi$
$109$	5.87151	0.562388	0.281194	+	0.959651i	$0.409270\pi$
$110$	1.44464	0.137741
$111$	−0.332056	−0.0315173
$112$	−5.11578	−0.483395
$113$	16.6496	1.56626	0.783132	−	0.621856i	$-0.213621\pi$
$113$	16.6496	1.56626	0.783132	+	0.621856i	$0.213621\pi$
$114$	0.773095	0.0724070
$115$	7.77090	0.724640
$116$	−0.540747	−0.0502071
$117$	−12.1143	−1.11996
$118$	18.0709	1.66356
$119$	−1.16875	−0.107139
$120$	−0.224641	−0.0205068
$121$	1.00000	0.0909091
$122$	6.32168	0.572338
$123$	−0.123811	−0.0111637
$124$	−0.444528	−0.0399198
$125$	1.00000	0.0894427
$126$	−5.30974	−0.473029
$127$	−16.2271	−1.43992	−0.719962	−	0.694014i	$-0.755841\pi$
$127$	−16.2271	−1.43992	−0.719962	+	0.694014i	$0.755841\pi$
$128$	11.9952	1.06023
$129$	0.726223	0.0639404
$130$	5.84647	0.512770
$131$	2.54424	0.222291	0.111146	−	0.993804i	$-0.464548\pi$
$131$	2.54424	0.222291	0.111146	+	0.993804i	$0.464548\pi$
$132$	0.00707113	0.000615463 0
$133$	8.08369	0.700945
$134$	22.1586	1.91421
$135$	−0.487174	−0.0419293
$136$	2.63057	0.225569
$137$	−5.03354	−0.430044	−0.215022	−	0.976609i	$-0.568982\pi$
$137$	−5.03354	−0.430044	−0.215022	+	0.976609i	$0.568982\pi$
$138$	0.912522	0.0776791
$139$	1.60146	0.135834	0.0679170	−	0.997691i	$-0.478365\pi$
$139$	1.60146	0.135834	0.0679170	+	0.997691i	$0.478365\pi$
$140$	0.106813	0.00902739
$141$	0.636575	0.0536093
$142$	−7.13829	−0.599032
$143$	4.04700	0.338427
$144$	12.4717	1.03931
$145$	−6.21609	−0.516218
$146$	1.44464	0.119559
$147$	−0.446448	−0.0368224
$148$	−0.355366	−0.0292109
$149$	−0.151848	−0.0124398	−0.00621992	−	0.999981i	$-0.501980\pi$
$149$	−0.151848	−0.0124398	−0.00621992	+	0.999981i	$0.501980\pi$
$150$	0.117428	0.00958797
$151$	16.1694	1.31585	0.657925	−	0.753083i	$-0.271434\pi$
$151$	16.1694	1.31585	0.657925	+	0.753083i	$0.271434\pi$
$152$	−18.1944	−1.47576
$153$	2.84929	0.230351
$154$	1.77382	0.142938
$155$	−5.11002	−0.410446
$156$	0.0286169	0.00229118
$157$	−21.2359	−1.69481	−0.847405	−	0.530947i	$-0.821836\pi$
$157$	−21.2359	−1.69481	−0.847405	+	0.530947i	$0.821836\pi$
$158$	−5.47549	−0.435607
$159$	−0.824019	−0.0653490
$160$	−0.491754	−0.0388766
$161$	9.54158	0.751982
$162$	12.9159	1.01477
$163$	14.8672	1.16449	0.582244	−	0.813014i	$-0.302175\pi$
$163$	14.8672	1.16449	0.582244	+	0.813014i	$0.302175\pi$
$164$	−0.132503	−0.0103467
$165$	0.0812853	0.00632805
$166$	25.1622	1.95297
$167$	−19.6151	−1.51786	−0.758930	−	0.651173i	$-0.774277\pi$
$167$	−19.6151	−1.51786	−0.758930	+	0.651173i	$0.774277\pi$
$168$	−0.275828	−0.0212806
$169$	3.37824	0.259864
$170$	−1.37509	−0.105465
$171$	−19.7072	−1.50705
$172$	0.777205	0.0592613
$173$	6.00770	0.456757	0.228379	−	0.973572i	$-0.426658\pi$
$173$	6.00770	0.456757	0.228379	+	0.973572i	$0.426658\pi$
$174$	−0.729943	−0.0553369
$175$	1.22786	0.0928175
$176$	−4.16642	−0.314055
$177$	1.01679	0.0764266
$178$	12.8035	0.959664
$179$	8.08492	0.604295	0.302148	−	0.953261i	$-0.402296\pi$
$179$	8.08492	0.604295	0.302148	+	0.953261i	$0.402296\pi$
$180$	−0.260400	−0.0194091
$181$	−7.97341	−0.592659	−0.296330	−	0.955086i	$-0.595763\pi$
$181$	−7.97341	−0.592659	−0.296330	+	0.955086i	$0.595763\pi$
$182$	7.17865	0.532117
$183$	0.355700	0.0262941
$184$	−21.4758	−1.58321
$185$	−4.08507	−0.300340
$186$	−0.600060	−0.0439985
$187$	−0.951858	−0.0696068
$188$	0.681263	0.0496862
$189$	−0.598182	−0.0435114
$190$	9.51089	0.689992
$191$	4.95753	0.358714	0.179357	−	0.983784i	$-0.442598\pi$
$191$	4.95753	0.358714	0.179357	+	0.983784i	$0.442598\pi$
$192$	0.619590	0.0447151
$193$	−13.6383	−0.981704	−0.490852	−	0.871243i	$-0.663314\pi$
$193$	−13.6383	−0.981704	−0.490852	+	0.871243i	$0.663314\pi$
$194$	4.89799	0.351655
$195$	0.328962	0.0235574
$196$	−0.477789	−0.0341278
$197$	12.9966	0.925968	0.462984	−	0.886367i	$-0.346779\pi$
$197$	12.9966	0.925968	0.462984	+	0.886367i	$0.346779\pi$
$198$	−4.32438	−0.307320
$199$	−28.0125	−1.98575	−0.992877	−	0.119147i	$-0.961984\pi$
$199$	−28.0125	−1.98575	−0.992877	+	0.119147i	$0.961984\pi$
$200$	−2.76361	−0.195417
$201$	1.24679	0.0879419
$202$	−17.7163	−1.24651
$203$	−7.63249	−0.535696
$204$	−0.00673071	−0.000471244 0
$205$	−1.52317	−0.106383
$206$	11.7565	0.819115
$207$	−23.2614	−1.61678
$208$	−16.8615	−1.16913
$209$	6.58356	0.455394
$210$	0.144185	0.00994973
$211$	−19.6840	−1.35510	−0.677551	−	0.735476i	$-0.736958\pi$
$211$	−19.6840	−1.35510	−0.677551	+	0.735476i	$0.736958\pi$
$212$	−0.881866	−0.0605668
$213$	−0.401648	−0.0275205
$214$	19.9234	1.36194
$215$	8.93425	0.609311
$216$	1.34636	0.0916083
$217$	−6.27439	−0.425933
$218$	8.48223	0.574489
$219$	0.0812853	0.00549275
$220$	0.0869915	0.00586497
$221$	−3.85217	−0.259125
$222$	−0.479702	−0.0321955
$223$	6.36677	0.426350	0.213175	−	0.977014i	$-0.431620\pi$
$223$	6.36677	0.426350	0.213175	+	0.977014i	$0.431620\pi$
$224$	−0.603806	−0.0403435
$225$	−2.99339	−0.199560
$226$	24.0527	1.59996
$227$	−9.71699	−0.644939	−0.322470	−	0.946580i	$-0.604513\pi$
$227$	−9.71699	−0.644939	−0.322470	+	0.946580i	$0.604513\pi$
$228$	0.0465532	0.00308306
$229$	0.594020	0.0392539	0.0196270	−	0.999807i	$-0.493752\pi$
$229$	0.594020	0.0392539	0.0196270	+	0.999807i	$0.493752\pi$
$230$	11.2262	0.740232
$231$	0.0998069	0.00656681
$232$	17.1789	1.12785
$233$	23.3670	1.53082	0.765412	−	0.643540i	$-0.222535\pi$
$233$	23.3670	1.53082	0.765412	+	0.643540i	$0.222535\pi$
$234$	−17.5008	−1.14406
$235$	7.83137	0.510862
$236$	1.08817	0.0708338
$237$	−0.308088	−0.0200124
$238$	−1.68842	−0.109444
$239$	−2.28003	−0.147483	−0.0737415	−	0.997277i	$-0.523494\pi$
$239$	−2.28003	−0.147483	−0.0737415	+	0.997277i	$0.523494\pi$
$240$	−0.338668	−0.0218609
$241$	−3.18978	−0.205472	−0.102736	−	0.994709i	$-0.532760\pi$
$241$	−3.18978	−0.205472	−0.102736	+	0.994709i	$0.532760\pi$
$242$	1.44464	0.0928651
$243$	2.18826	0.140377
$244$	0.380671	0.0243699
$245$	−5.49236	−0.350894
$246$	−0.178863	−0.0114039
$247$	26.6437	1.69530
$248$	14.1221	0.896755
$249$	1.41579	0.0897223
$250$	1.44464	0.0913672
$251$	−1.20999	−0.0763736	−0.0381868	−	0.999271i	$-0.512158\pi$
$251$	−1.20999	−0.0763736	−0.0381868	+	0.999271i	$0.512158\pi$
$252$	−0.319735	−0.0201414
$253$	7.77090	0.488552
$254$	−23.4424	−1.47091
$255$	−0.0773720	−0.00484523
$256$	2.08390	0.130244
$257$	8.02225	0.500414	0.250207	−	0.968192i	$-0.419501\pi$
$257$	8.02225	0.500414	0.250207	+	0.968192i	$0.419501\pi$
$258$	1.04913	0.0653161
$259$	−5.01589	−0.311672
$260$	0.352055	0.0218335
$261$	18.6072	1.15176
$262$	3.67551	0.227074
$263$	−18.0857	−1.11521	−0.557606	−	0.830106i	$-0.688280\pi$
$263$	−18.0857	−1.11521	−0.557606	+	0.830106i	$0.688280\pi$
$264$	−0.224641	−0.0138257
$265$	−10.1374	−0.622734
$266$	11.6780	0.716027
$267$	0.720412	0.0440885
$268$	1.33432	0.0815064
$269$	−1.39011	−0.0847568	−0.0423784	−	0.999102i	$-0.513494\pi$
$269$	−1.39011	−0.0847568	−0.0423784	+	0.999102i	$0.513494\pi$
$270$	−0.703793	−0.0428315
$271$	−23.4384	−1.42378	−0.711891	−	0.702290i	$-0.752161\pi$
$271$	−23.4384	−1.42378	−0.711891	+	0.702290i	$0.752161\pi$
$272$	3.96584	0.240464
$273$	0.403919	0.0244463
$274$	−7.27166	−0.439297
$275$	1.00000	0.0603023
$276$	0.0549490	0.00330754
$277$	−2.09331	−0.125775	−0.0628875	−	0.998021i	$-0.520031\pi$
$277$	−2.09331	−0.125775	−0.0628875	+	0.998021i	$0.520031\pi$
$278$	2.31354	0.138757
$279$	15.2963	0.915765
$280$	−3.39333	−0.202790
$281$	−19.1565	−1.14278	−0.571391	−	0.820678i	$-0.693596\pi$
$281$	−19.1565	−1.14278	−0.571391	+	0.820678i	$0.693596\pi$
$282$	0.919623	0.0547628
$283$	−3.50372	−0.208275	−0.104137	−	0.994563i	$-0.533208\pi$
$283$	−3.50372	−0.208275	−0.104137	+	0.994563i	$0.533208\pi$
$284$	−0.429844	−0.0255066
$285$	0.535146	0.0316993
$286$	5.84647	0.345709
$287$	−1.87024	−0.110396
$288$	1.47201	0.0867392
$289$	−16.0940	−0.946704
$290$	−8.98002	−0.527325
$291$	0.275594	0.0161556
$292$	0.0869915	0.00509079
$293$	12.9884	0.758792	0.379396	−	0.925234i	$-0.376132\pi$
$293$	12.9884	0.758792	0.379396	+	0.925234i	$0.376132\pi$
$294$	−0.644957	−0.0376147
$295$	12.5089	0.728297
$296$	11.2895	0.656191
$297$	−0.487174	−0.0282687
$298$	−0.219366	−0.0127075
$299$	31.4489	1.81873
$300$	0.00707113	0.000408252 0
$301$	10.9700	0.632301
$302$	23.3591	1.34416
$303$	−0.996836	−0.0572667
$304$	−27.4298	−1.57321
$305$	4.37595	0.250566
$306$	4.11620	0.235307
$307$	5.88821	0.336058	0.168029	−	0.985782i	$-0.446260\pi$
$307$	5.88821	0.336058	0.168029	+	0.985782i	$0.446260\pi$
$308$	0.106813	0.00608626
$309$	0.661500	0.0376314
$310$	−7.38215	−0.419278
$311$	−12.5197	−0.709926	−0.354963	−	0.934880i	$-0.615506\pi$
$311$	−12.5197	−0.709926	−0.354963	+	0.934880i	$0.615506\pi$
$312$	−0.909123	−0.0514689
$313$	26.1771	1.47962	0.739809	−	0.672817i	$-0.234916\pi$
$313$	26.1771	1.47962	0.739809	+	0.672817i	$0.234916\pi$
$314$	−30.6783	−1.73128
$315$	−3.67547	−0.207089
$316$	−0.329716	−0.0185480
$317$	−28.9281	−1.62476	−0.812381	−	0.583127i	$-0.801829\pi$
$317$	−28.9281	−1.62476	−0.812381	+	0.583127i	$0.801829\pi$
$318$	−1.19041	−0.0667550
$319$	−6.21609	−0.348034
$320$	7.62242	0.426106
$321$	1.12102	0.0625695
$322$	13.7842	0.768162
$323$	−6.26661	−0.348684
$324$	0.777755	0.0432086
$325$	4.04700	0.224487
$326$	21.4778	1.18954
$327$	0.477267	0.0263929
$328$	4.20944	0.232428
$329$	9.61583	0.530138
$330$	0.117428	0.00646421
$331$	−23.1174	−1.27065	−0.635323	−	0.772247i	$-0.719133\pi$
$331$	−23.1174	−1.27065	−0.635323	+	0.772247i	$0.719133\pi$
$332$	1.51518	0.0831565
$333$	12.2282	0.670101
$334$	−28.3368	−1.55052
$335$	15.3385	0.838030
$336$	−0.415837	−0.0226858
$337$	−36.0136	−1.96179	−0.980893	−	0.194547i	$-0.937676\pi$
$337$	−36.0136	−1.96179	−0.980893	+	0.194547i	$0.937676\pi$
$338$	4.88034	0.265456
$339$	1.35337	0.0735048
$340$	−0.0828036	−0.00449066
$341$	−5.11002	−0.276723
$342$	−28.4698	−1.53947
$343$	−15.3389	−0.828221
$344$	−24.6908	−1.33124
$345$	0.631660	0.0340074
$346$	8.67898	0.466585
$347$	37.1581	1.99475	0.997375	−	0.0724108i	$-0.0230693\pi$
$347$	37.1581	1.99475	0.997375	+	0.0724108i	$0.0230693\pi$
$348$	−0.0439548	−0.00235622
$349$	−30.4055	−1.62757	−0.813784	−	0.581168i	$-0.802596\pi$
$349$	−30.4055	−1.62757	−0.813784	+	0.581168i	$0.802596\pi$
$350$	1.77382	0.0948146
$351$	−1.97160	−0.105236
$352$	−0.491754	−0.0262106
$353$	−6.57822	−0.350123	−0.175062	−	0.984557i	$-0.556012\pi$
$353$	−6.57822	−0.350123	−0.175062	+	0.984557i	$0.556012\pi$
$354$	1.46890	0.0780710
$355$	−4.94122	−0.262253
$356$	0.770985	0.0408621
$357$	−0.0950021	−0.00502804
$358$	11.6798	0.617298
$359$	−24.9088	−1.31464	−0.657319	−	0.753612i	$-0.728310\pi$
$359$	−24.9088	−1.31464	−0.657319	+	0.753612i	$0.728310\pi$
$360$	8.27258	0.436003
$361$	24.3432	1.28122
$362$	−11.5187	−0.605411
$363$	0.0812853	0.00426637
$364$	0.432274	0.0226573
$365$	1.00000	0.0523424
$366$	0.513860	0.0268599
$367$	−15.3434	−0.800918	−0.400459	−	0.916315i	$-0.631149\pi$
$367$	−15.3434	−0.800918	−0.400459	+	0.916315i	$0.631149\pi$
$368$	−32.3768	−1.68776
$369$	4.55943	0.237355
$370$	−5.90146	−0.306802
$371$	−12.4473	−0.646231
$372$	−0.0361336	−0.00187344
$373$	−7.37191	−0.381703	−0.190851	−	0.981619i	$-0.561125\pi$
$373$	−7.37191	−0.381703	−0.190851	+	0.981619i	$0.561125\pi$
$374$	−1.37509	−0.0711045
$375$	0.0812853	0.00419755
$376$	−21.6429	−1.11615
$377$	−25.1565	−1.29563
$378$	−0.864159	−0.0444476
$379$	18.4977	0.950165	0.475083	−	0.879941i	$-0.342418\pi$
$379$	18.4977	0.950165	0.475083	+	0.879941i	$0.342418\pi$
$380$	0.572714	0.0293796
$381$	−1.31903	−0.0675757
$382$	7.16185	0.366432
$383$	13.8519	0.707801	0.353901	−	0.935283i	$-0.384855\pi$
$383$	13.8519	0.707801	0.353901	+	0.935283i	$0.384855\pi$
$384$	0.975031	0.0497569
$385$	1.22786	0.0625776
$386$	−19.7024	−1.00283
$387$	−26.7437	−1.35946
$388$	0.294940	0.0149733
$389$	33.7779	1.71261	0.856305	−	0.516471i	$-0.172755\pi$
$389$	33.7779	1.71261	0.856305	+	0.516471i	$0.172755\pi$
$390$	0.475232	0.0240643
$391$	−7.39680	−0.374072
$392$	15.1788	0.766643
$393$	0.206809	0.0104321
$394$	18.7754	0.945892
$395$	−3.79020	−0.190706
$396$	−0.260400	−0.0130856
$397$	−19.6762	−0.987520	−0.493760	−	0.869598i	$-0.664378\pi$
$397$	−19.6762	−0.987520	−0.493760	+	0.869598i	$0.664378\pi$
$398$	−40.4680	−2.02848
$399$	0.657085	0.0328954
$400$	−4.16642	−0.208321
$401$	19.1104	0.954327	0.477164	−	0.878814i	$-0.341665\pi$
$401$	19.1104	0.954327	0.477164	+	0.878814i	$0.341665\pi$
$402$	1.80117	0.0898341
$403$	−20.6803	−1.03016
$404$	−1.06681	−0.0530760
$405$	8.94058	0.444261
$406$	−11.0262	−0.547222
$407$	−4.08507	−0.202489
$408$	0.213826	0.0105860
$409$	−6.15011	−0.304103	−0.152052	−	0.988373i	$-0.548588\pi$
$409$	−6.15011	−0.304103	−0.152052	+	0.988373i	$0.548588\pi$
$410$	−2.20043	−0.108671
$411$	−0.409152	−0.0201820
$412$	0.707938	0.0348776
$413$	15.3592	0.755777
$414$	−33.6043	−1.65156
$415$	17.4176	0.854996
$416$	−1.99013	−0.0975742
$417$	0.130175	0.00637470
$418$	9.51089	0.465193
$419$	28.8367	1.40877	0.704383	−	0.709820i	$-0.251224\pi$
$419$	28.8367	1.40877	0.704383	+	0.709820i	$0.251224\pi$
$420$	0.00868236	0.000423656 0
$421$	34.4953	1.68120	0.840598	−	0.541659i	$-0.182204\pi$
$421$	34.4953	1.68120	0.840598	+	0.541659i	$0.182204\pi$
$422$	−28.4363	−1.38426
$423$	−23.4424	−1.13981
$424$	28.0158	1.36057
$425$	−0.951858	−0.0461719
$426$	−0.580238	−0.0281126
$427$	5.37306	0.260020
$428$	1.19972	0.0579907
$429$	0.328962	0.0158824
$430$	12.9068	0.622421
$431$	−11.5070	−0.554270	−0.277135	−	0.960831i	$-0.589385\pi$
$431$	−11.5070	−0.554270	−0.277135	+	0.960831i	$0.589385\pi$
$432$	2.02977	0.0976574
$433$	−11.5643	−0.555743	−0.277871	−	0.960618i	$-0.589629\pi$
$433$	−11.5643	−0.555743	−0.277871	+	0.960618i	$0.589629\pi$
$434$	−9.06425	−0.435098
$435$	−0.505276	−0.0242261
$436$	0.510771	0.0244615
$437$	51.1602	2.44732
$438$	0.117428	0.00561093
$439$	−26.9503	−1.28627	−0.643133	−	0.765755i	$-0.722366\pi$
$439$	−26.9503	−1.28627	−0.643133	+	0.765755i	$0.722366\pi$
$440$	−2.76361	−0.131750
$441$	16.4408	0.782895
$442$	−5.56501	−0.264701
$443$	16.7466	0.795654	0.397827	−	0.917460i	$-0.369764\pi$
$443$	16.7466	0.795654	0.397827	+	0.917460i	$0.369764\pi$
$444$	−0.0288860	−0.00137087
$445$	8.86276	0.420135
$446$	9.19770	0.435524
$447$	−0.0123430	−0.000583803 0
$448$	9.35927	0.442184
$449$	−12.0707	−0.569650	−0.284825	−	0.958580i	$-0.591936\pi$
$449$	−12.0707	−0.569650	−0.284825	+	0.958580i	$0.591936\pi$
$450$	−4.32438	−0.203853
$451$	−1.52317	−0.0717231
$452$	1.44838	0.0681258
$453$	1.31434	0.0617529
$454$	−14.0376	−0.658816
$455$	4.96915	0.232958
$456$	−1.47894	−0.0692576
$457$	34.1364	1.59683	0.798416	−	0.602107i	$-0.205672\pi$
$457$	34.1364	1.59683	0.798416	+	0.602107i	$0.205672\pi$
$458$	0.858146	0.0400985
$459$	0.463721	0.0216446
$460$	0.676003	0.0315188
$461$	8.32986	0.387960	0.193980	−	0.981005i	$-0.437860\pi$
$461$	8.32986	0.387960	0.193980	+	0.981005i	$0.437860\pi$
$462$	0.144185	0.00670811
$463$	38.3787	1.78361	0.891806	−	0.452418i	$-0.149439\pi$
$463$	38.3787	1.78361	0.891806	+	0.452418i	$0.149439\pi$
$464$	25.8988	1.20232
$465$	−0.415369	−0.0192623
$466$	33.7570	1.56376
$467$	−41.1033	−1.90203	−0.951016	−	0.309141i	$-0.899958\pi$
$467$	−41.1033	−1.90203	−0.951016	+	0.309141i	$0.899958\pi$
$468$	−1.05384	−0.0487137
$469$	18.8335	0.869651
$470$	11.3135	0.521854
$471$	−1.72617	−0.0795376
$472$	−34.5698	−1.59120
$473$	8.93425	0.410797
$474$	−0.445077	−0.0204430
$475$	6.58356	0.302074
$476$	−0.101671	−0.00466010
$477$	30.3451	1.38941
$478$	−3.29383	−0.150656
$479$	36.2952	1.65837	0.829185	−	0.558974i	$-0.188805\pi$
$479$	36.2952	1.65837	0.829185	+	0.558974i	$0.188805\pi$
$480$	−0.0399724	−0.00182448
$481$	−16.5323	−0.753807
$482$	−4.60809	−0.209893
$483$	0.775590	0.0352906
$484$	0.0869915	0.00395416
$485$	3.39045	0.153952
$486$	3.16125	0.143397
$487$	11.0374	0.500155	0.250077	−	0.968226i	$-0.419544\pi$
$487$	11.0374	0.500155	0.250077	+	0.968226i	$0.419544\pi$
$488$	−12.0934	−0.547444
$489$	1.20848	0.0546495
$490$	−7.93449	−0.358444
$491$	−21.7684	−0.982396	−0.491198	−	0.871048i	$-0.663441\pi$
$491$	−21.7684	−0.982396	−0.491198	+	0.871048i	$0.663441\pi$
$492$	−0.0107705	−0.000485572 0
$493$	5.91683	0.266481
$494$	38.4906	1.73177
$495$	−2.99339	−0.134543
$496$	21.2905	0.955970
$497$	−6.06713	−0.272148
$498$	2.04532	0.0916528
$499$	25.4563	1.13958	0.569789	−	0.821791i	$-0.307025\pi$
$499$	25.4563	1.13958	0.569789	+	0.821791i	$0.307025\pi$
$500$	0.0869915	0.00389038
$501$	−1.59442	−0.0712332
$502$	−1.74800	−0.0780169
$503$	−13.1571	−0.586648	−0.293324	−	0.956013i	$-0.594762\pi$
$503$	−13.1571	−0.586648	−0.293324	+	0.956013i	$0.594762\pi$
$504$	10.1576	0.452454
$505$	−12.2634	−0.545716
$506$	11.2262	0.499064
$507$	0.274601	0.0121954
$508$	−1.41162	−0.0626306
$509$	−2.33997	−0.103718	−0.0518588	−	0.998654i	$-0.516515\pi$
$509$	−2.33997	−0.103718	−0.0518588	+	0.998654i	$0.516515\pi$
$510$	−0.111775	−0.00494948
$511$	1.22786	0.0543173
$512$	−20.9799	−0.927188
$513$	−3.20734	−0.141608
$514$	11.5893	0.511181
$515$	8.13801	0.358604
$516$	0.0631753	0.00278114
$517$	7.83137	0.344423
$518$	−7.24617	−0.318378
$519$	0.488338	0.0214356
$520$	−11.1844	−0.490466
$521$	6.22942	0.272916	0.136458	−	0.990646i	$-0.456428\pi$
$521$	6.22942	0.272916	0.136458	+	0.990646i	$0.456428\pi$
$522$	26.8807	1.17654
$523$	27.7343	1.21273	0.606367	−	0.795185i	$-0.292626\pi$
$523$	27.7343	1.21273	0.606367	+	0.795185i	$0.292626\pi$
$524$	0.221327	0.00966873
$525$	0.0998069	0.00435593
$526$	−26.1274	−1.13921
$527$	4.86401	0.211880
$528$	−0.338668	−0.0147386
$529$	37.3869	1.62552
$530$	−14.6449	−0.636133
$531$	−37.4441	−1.62493
$532$	0.703213	0.0304881
$533$	−6.16426	−0.267004
$534$	1.04074	0.0450371
$535$	13.7912	0.596247
$536$	−42.3896	−1.83095
$537$	0.657185	0.0283596
$538$	−2.00822	−0.0865805
$539$	−5.49236	−0.236573
$540$	−0.0423801	−0.00182375
$541$	−30.8347	−1.32569	−0.662844	−	0.748758i	$-0.730651\pi$
$541$	−30.8347	−1.32569	−0.662844	+	0.748758i	$0.730651\pi$
$542$	−33.8601	−1.45442
$543$	−0.648121	−0.0278135
$544$	0.468080	0.0200688
$545$	5.87151	0.251508
$546$	0.583519	0.0249723
$547$	5.97416	0.255437	0.127718	−	0.991810i	$-0.459235\pi$
$547$	5.97416	0.255437	0.127718	+	0.991810i	$0.459235\pi$
$548$	−0.437875	−0.0187051
$549$	−13.0989	−0.559049
$550$	1.44464	0.0615998
$551$	−40.9240	−1.74342
$552$	−1.74566	−0.0743003
$553$	−4.65384	−0.197901
$554$	−3.02409	−0.128481
$555$	−0.332056	−0.0140950
$556$	0.139313	0.00590820
$557$	−3.54818	−0.150341	−0.0751705	−	0.997171i	$-0.523950\pi$
$557$	−3.54818	−0.150341	−0.0751705	+	0.997171i	$0.523950\pi$
$558$	22.0977	0.935469
$559$	36.1570	1.52928
$560$	−5.11578	−0.216181
$561$	−0.0773720	−0.00326665
$562$	−27.6743	−1.16737
$563$	−20.7920	−0.876278	−0.438139	−	0.898907i	$-0.644362\pi$
$563$	−20.7920	−0.876278	−0.438139	+	0.898907i	$0.644362\pi$
$564$	0.0553766	0.00233178
$565$	16.6496	0.700454
$566$	−5.06163	−0.212756
$567$	10.9778	0.461023
$568$	13.6556	0.572977
$569$	−44.9981	−1.88642	−0.943210	−	0.332198i	$-0.892210\pi$
$569$	−44.9981	−1.88642	−0.943210	+	0.332198i	$0.892210\pi$
$570$	0.773095	0.0323814
$571$	22.8576	0.956562	0.478281	−	0.878207i	$-0.341260\pi$
$571$	22.8576	0.956562	0.478281	+	0.878207i	$0.341260\pi$
$572$	0.352055	0.0147202
$573$	0.402974	0.0168345
$574$	−2.70182	−0.112772
$575$	7.77090	0.324069
$576$	−22.8169	−0.950704
$577$	−46.1660	−1.92191	−0.960957	−	0.276696i	$-0.910760\pi$
$577$	−46.1660	−1.92191	−0.960957	+	0.276696i	$0.910760\pi$
$578$	−23.2500	−0.967074
$579$	−1.10859	−0.0460714
$580$	−0.540747	−0.0224533
$581$	21.3864	0.887256
$582$	0.398134	0.0165032
$583$	−10.1374	−0.419847
$584$	−2.76361	−0.114359
$585$	−12.1143	−0.500863
$586$	18.7636	0.775119
$587$	−47.3491	−1.95431	−0.977154	−	0.212533i	$-0.931829\pi$
$587$	−47.3491	−1.95431	−0.977154	+	0.212533i	$0.931829\pi$
$588$	−0.0388372	−0.00160162
$589$	−33.6421	−1.38620
$590$	18.0709	0.743967
$591$	1.05643	0.0434557
$592$	17.0201	0.699521
$593$	−0.873327	−0.0358632	−0.0179316	−	0.999839i	$-0.505708\pi$
$593$	−0.873327	−0.0358632	−0.0179316	+	0.999839i	$0.505708\pi$
$594$	−0.703793	−0.0288770
$595$	−1.16875	−0.0479140
$596$	−0.0132095	−0.000541081 0
$597$	−2.27700	−0.0931915
$598$	45.4324	1.85787
$599$	−19.4084	−0.793006	−0.396503	−	0.918033i	$-0.629776\pi$
$599$	−19.4084	−0.793006	−0.396503	+	0.918033i	$0.629776\pi$
$600$	−0.224641	−0.00917093
$601$	20.6511	0.842378	0.421189	−	0.906973i	$-0.361613\pi$
$601$	20.6511	0.842378	0.421189	+	0.906973i	$0.361613\pi$
$602$	15.8477	0.645906
$603$	−45.9141	−1.86977
$604$	1.40660	0.0572339
$605$	1.00000	0.0406558
$606$	−1.44007	−0.0584989
$607$	32.2021	1.30704	0.653522	−	0.756907i	$-0.273291\pi$
$607$	32.2021	1.30704	0.653522	+	0.756907i	$0.273291\pi$
$608$	−3.23749	−0.131298
$609$	−0.620409	−0.0251402
$610$	6.32168	0.255957
$611$	31.6936	1.28218
$612$	0.247864	0.0100193
$613$	−34.4958	−1.39327	−0.696637	−	0.717424i	$-0.745321\pi$
$613$	−34.4958	−1.39327	−0.696637	+	0.717424i	$0.745321\pi$
$614$	8.50636	0.343289
$615$	−0.123811	−0.00499254
$616$	−3.39333	−0.136721
$617$	−25.4906	−1.02621	−0.513107	−	0.858324i	$-0.671506\pi$
$617$	−25.4906	−1.02621	−0.513107	+	0.858324i	$0.671506\pi$
$618$	0.955632	0.0384411
$619$	−7.81036	−0.313925	−0.156962	−	0.987605i	$-0.550170\pi$
$619$	−7.81036	−0.313925	−0.156962	+	0.987605i	$0.550170\pi$
$620$	−0.444528	−0.0178527
$621$	−3.78578	−0.151918
$622$	−18.0865	−0.725201
$623$	10.8822	0.435987
$624$	−1.37059	−0.0548676
$625$	1.00000	0.0400000
$626$	37.8166	1.51145
$627$	0.535146	0.0213717
$628$	−1.84734	−0.0737171
$629$	3.88840	0.155041
$630$	−5.30974	−0.211545
$631$	−17.5076	−0.696968	−0.348484	−	0.937315i	$-0.613303\pi$
$631$	−17.5076	−0.696968	−0.348484	+	0.937315i	$0.613303\pi$
$632$	10.4747	0.416660
$633$	−1.60002	−0.0635950
$634$	−41.7907	−1.65972
$635$	−16.2271	−0.643953
$636$	−0.0716827	−0.00284240
$637$	−22.2276	−0.880689
$638$	−8.98002	−0.355522
$639$	14.7910	0.585123
$640$	11.9952	0.474151
$641$	−24.0732	−0.950836	−0.475418	−	0.879760i	$-0.657703\pi$
$641$	−24.0732	−0.950836	−0.475418	+	0.879760i	$0.657703\pi$
$642$	1.61948	0.0639157
$643$	1.06264	0.0419066	0.0209533	−	0.999780i	$-0.493330\pi$
$643$	1.06264	0.0419066	0.0209533	+	0.999780i	$0.493330\pi$
$644$	0.830037	0.0327080
$645$	0.726223	0.0285950
$646$	−9.05302	−0.356186
$647$	18.4108	0.723803	0.361902	−	0.932216i	$-0.382128\pi$
$647$	18.4108	0.723803	0.361902	+	0.932216i	$0.382128\pi$
$648$	−24.7083	−0.970634
$649$	12.5089	0.491018
$650$	5.84647	0.229318
$651$	−0.510015	−0.0199891
$652$	1.29332	0.0506503
$653$	10.6930	0.418449	0.209225	−	0.977868i	$-0.432906\pi$
$653$	10.6930	0.418449	0.209225	+	0.977868i	$0.432906\pi$
$654$	0.689480	0.0269608
$655$	2.54424	0.0994116
$656$	6.34614	0.247775
$657$	−2.99339	−0.116783
$658$	13.8914	0.541544
$659$	23.7584	0.925494	0.462747	−	0.886490i	$-0.346864\pi$
$659$	23.7584	0.925494	0.462747	+	0.886490i	$0.346864\pi$
$660$	0.00707113	0.000275243 0
$661$	−16.8969	−0.657215	−0.328607	−	0.944467i	$-0.606579\pi$
$661$	−16.8969	−0.657215	−0.328607	+	0.944467i	$0.606579\pi$
$662$	−33.3963	−1.29799
$663$	−0.313125	−0.0121608
$664$	−48.1355	−1.86802
$665$	8.08369	0.313472
$666$	17.6654	0.684520
$667$	−48.3046	−1.87036
$668$	−1.70634	−0.0660205
$669$	0.517524	0.0200086
$670$	22.1586	0.856062
$671$	4.37595	0.168932
$672$	−0.0490805	−0.00189332
$673$	26.7840	1.03245	0.516224	−	0.856454i	$-0.327337\pi$
$673$	26.7840	1.03245	0.516224	+	0.856454i	$0.327337\pi$
$674$	−52.0268	−2.00400
$675$	−0.487174	−0.0187514
$676$	0.293878	0.0113030
$677$	46.7602	1.79714	0.898571	−	0.438828i	$-0.144606\pi$
$677$	46.7602	1.79714	0.898571	+	0.438828i	$0.144606\pi$
$678$	1.95513	0.0750864
$679$	4.16300	0.159761
$680$	2.63057	0.100878
$681$	−0.789848	−0.0302670
$682$	−7.38215	−0.282677
$683$	−37.3373	−1.42867	−0.714337	−	0.699802i	$-0.753271\pi$
$683$	−37.3373	−1.42867	−0.714337	+	0.699802i	$0.753271\pi$
$684$	−1.71436	−0.0655501
$685$	−5.03354	−0.192321
$686$	−22.1592	−0.846042
$687$	0.0482851	0.00184219
$688$	−37.2238	−1.41914
$689$	−41.0260	−1.56297
$690$	0.912522	0.0347391
$691$	−27.3409	−1.04010	−0.520048	−	0.854137i	$-0.674086\pi$
$691$	−27.3409	−1.04010	−0.520048	+	0.854137i	$0.674086\pi$
$692$	0.522619	0.0198670
$693$	−3.67547	−0.139619
$694$	53.6801	2.03767
$695$	1.60146	0.0607468
$696$	1.39639	0.0529299
$697$	1.44984	0.0549165
$698$	−43.9250	−1.66259
$699$	1.89939	0.0718417
$700$	0.106813	0.00403717
$701$	21.9811	0.830213	0.415107	−	0.909773i	$-0.363744\pi$
$701$	21.9811	0.830213	0.415107	+	0.909773i	$0.363744\pi$
$702$	−2.84825	−0.107500
$703$	−26.8943	−1.01434
$704$	7.62242	0.287281
$705$	0.636575	0.0239748
$706$	−9.50317	−0.357657
$707$	−15.0578	−0.566306
$708$	0.0884521	0.00332423
$709$	−5.55968	−0.208798	−0.104399	−	0.994535i	$-0.533292\pi$
$709$	−5.55968	−0.208798	−0.104399	+	0.994535i	$0.533292\pi$
$710$	−7.13829	−0.267895
$711$	11.3456	0.425492
$712$	−24.4932	−0.917923
$713$	−39.7094	−1.48713
$714$	−0.137244	−0.00513623
$715$	4.04700	0.151349
$716$	0.703320	0.0262843
$717$	−0.185333	−0.00692139
$718$	−35.9844	−1.34292
$719$	26.2943	0.980610	0.490305	−	0.871551i	$-0.336885\pi$
$719$	26.2943	0.980610	0.490305	+	0.871551i	$0.336885\pi$
$720$	12.4717	0.464793
$721$	9.99234	0.372134
$722$	35.1672	1.30879
$723$	−0.259282	−0.00964280
$724$	−0.693620	−0.0257782
$725$	−6.21609	−0.230860
$726$	0.117428	0.00435817
$727$	−23.6379	−0.876682	−0.438341	−	0.898809i	$-0.644434\pi$
$727$	−23.6379	−0.876682	−0.438341	+	0.898809i	$0.644434\pi$
$728$	−13.7328	−0.508972
$729$	−26.6439	−0.986810
$730$	1.44464	0.0534686
$731$	−8.50414	−0.314537
$732$	0.0309429	0.00114368
$733$	−33.7373	−1.24612	−0.623058	−	0.782175i	$-0.714110\pi$
$733$	−33.7373	−1.24612	−0.623058	+	0.782175i	$0.714110\pi$
$734$	−22.1657	−0.818150
$735$	−0.446448	−0.0164675
$736$	−3.82137	−0.140858
$737$	15.3385	0.565000
$738$	6.58675	0.242462
$739$	−2.02925	−0.0746472	−0.0373236	−	0.999303i	$-0.511883\pi$
$739$	−2.02925	−0.0746472	−0.0373236	+	0.999303i	$0.511883\pi$
$740$	−0.355366	−0.0130635
$741$	2.16574	0.0795604
$742$	−17.9819	−0.660135
$743$	−52.0968	−1.91125	−0.955624	−	0.294589i	$-0.904817\pi$
$743$	−52.0968	−1.91125	−0.955624	+	0.294589i	$0.904817\pi$
$744$	1.14792	0.0420848
$745$	−0.151848	−0.00556327
$746$	−10.6498	−0.389916
$747$	−52.1377	−1.90762
$748$	−0.0828036	−0.00302760
$749$	16.9337	0.618744
$750$	0.117428	0.00428787
$751$	−9.85680	−0.359680	−0.179840	−	0.983696i	$-0.557558\pi$
$751$	−9.85680	−0.359680	−0.179840	+	0.983696i	$0.557558\pi$
$752$	−32.6287	−1.18985
$753$	−0.0983540	−0.00358422
$754$	−36.3422	−1.32350
$755$	16.1694	0.588466
$756$	−0.0520368	−0.00189256
$757$	−23.4246	−0.851382	−0.425691	−	0.904869i	$-0.639969\pi$
$757$	−23.4246	−0.851382	−0.425691	+	0.904869i	$0.639969\pi$
$758$	26.7226	0.970610
$759$	0.631660	0.0229278
$760$	−18.1944	−0.659980
$761$	−1.97601	−0.0716304	−0.0358152	−	0.999358i	$-0.511403\pi$
$761$	−1.97601	−0.0716304	−0.0358152	+	0.999358i	$0.511403\pi$
$762$	−1.90552	−0.0690297
$763$	7.20939	0.260997
$764$	0.431263	0.0156025
$765$	2.84929	0.103016
$766$	20.0111	0.723031
$767$	50.6236	1.82791
$768$	0.169391	0.00611236
$769$	−2.62248	−0.0945692	−0.0472846	−	0.998881i	$-0.515057\pi$
$769$	−2.62248	−0.0945692	−0.0472846	+	0.998881i	$0.515057\pi$
$770$	1.77382	0.0639240
$771$	0.652091	0.0234845
$772$	−1.18641	−0.0427000
$773$	33.8528	1.21760	0.608801	−	0.793323i	$-0.291651\pi$
$773$	33.8528	1.21760	0.608801	+	0.793323i	$0.291651\pi$
$774$	−38.6351	−1.38871
$775$	−5.11002	−0.183557
$776$	−9.36989	−0.336359
$777$	−0.407718	−0.0146268
$778$	48.7970	1.74946
$779$	−10.0278	−0.359285
$780$	0.0286169	0.00102465
$781$	−4.94122	−0.176811
$782$	−10.6857	−0.382121
$783$	3.02832	0.108223
$784$	22.8834	0.817266
$785$	−21.2359	−0.757942
$786$	0.298765	0.0106566
$787$	9.79133	0.349023	0.174512	−	0.984655i	$-0.444165\pi$
$787$	9.79133	0.349023	0.174512	+	0.984655i	$0.444165\pi$
$788$	1.13059	0.0402757
$789$	−1.47010	−0.0523370
$790$	−5.47549	−0.194809
$791$	20.4434	0.726883
$792$	8.27258	0.293953
$793$	17.7095	0.628882
$794$	−28.4251	−1.00877
$795$	−0.824019	−0.0292249
$796$	−2.43685	−0.0863719
$797$	21.4830	0.760967	0.380483	−	0.924788i	$-0.375758\pi$
$797$	21.4830	0.760967	0.380483	+	0.924788i	$0.375758\pi$
$798$	0.949252	0.0336032
$799$	−7.45435	−0.263716
$800$	−0.491754	−0.0173861
$801$	−26.5297	−0.937381
$802$	27.6077	0.974861
$803$	1.00000	0.0352892
$804$	0.108460	0.00382510
$805$	9.54158	0.336297
$806$	−29.8756	−1.05232
$807$	−0.112996	−0.00397764
$808$	33.8914	1.19229
$809$	−34.0412	−1.19682	−0.598412	−	0.801189i	$-0.704201\pi$
$809$	−34.0412	−1.19682	−0.598412	+	0.801189i	$0.704201\pi$
$810$	12.9159	0.453820
$811$	38.3385	1.34625	0.673124	−	0.739530i	$-0.264952\pi$
$811$	38.3385	1.34625	0.673124	+	0.739530i	$0.264952\pi$
$812$	−0.663962	−0.0233005
$813$	−1.90520	−0.0668182
$814$	−5.90146	−0.206846
$815$	14.8672	0.520775
$816$	0.322364	0.0112850
$817$	58.8192	2.05782
$818$	−8.88470	−0.310646
$819$	−14.8746	−0.519762
$820$	−0.132503	−0.00462719
$821$	32.8376	1.14604	0.573020	−	0.819542i	$-0.305772\pi$
$821$	32.8376	1.14604	0.573020	+	0.819542i	$0.305772\pi$
$822$	−0.591079	−0.0206162
$823$	31.2654	1.08984	0.544922	−	0.838486i	$-0.316559\pi$
$823$	31.2654	1.08984	0.544922	+	0.838486i	$0.316559\pi$
$824$	−22.4903	−0.783487
$825$	0.0812853	0.00282999
$826$	22.1885	0.772038
$827$	56.4142	1.96171	0.980856	−	0.194733i	$-0.0623840\pi$
$827$	56.4142	1.96171	0.980856	+	0.194733i	$0.0623840\pi$
$828$	−2.02354	−0.0703229
$829$	−44.0925	−1.53140	−0.765698	−	0.643200i	$-0.777606\pi$
$829$	−44.0925	−1.53140	−0.765698	+	0.643200i	$0.777606\pi$
$830$	25.1622	0.873393
$831$	−0.170155	−0.00590263
$832$	30.8480	1.06946
$833$	5.22795	0.181138
$834$	0.188056	0.00651186
$835$	−19.6151	−0.678807
$836$	0.572714	0.0198077
$837$	2.48947	0.0860487
$838$	41.6588	1.43908
$839$	−29.9604	−1.03435	−0.517175	−	0.855880i	$-0.673016\pi$
$839$	−29.9604	−1.03435	−0.517175	+	0.855880i	$0.673016\pi$
$840$	−0.275828	−0.00951696
$841$	9.63973	0.332405
$842$	49.8333	1.71737
$843$	−1.55714	−0.0536308
$844$	−1.71234	−0.0589412
$845$	3.37824	0.116215
$846$	−33.8658	−1.16433
$847$	1.22786	0.0421898
$848$	42.2365	1.45041
$849$	−0.284801	−0.00977435
$850$	−1.37509	−0.0471654
$851$	−31.7446	−1.08819
$852$	−0.0349400	−0.00119702
$853$	14.2546	0.488068	0.244034	−	0.969767i	$-0.421529\pi$
$853$	14.2546	0.488068	0.244034	+	0.969767i	$0.421529\pi$
$854$	7.76214	0.265615
$855$	−19.7072	−0.673971
$856$	−38.1136	−1.30270
$857$	−9.92955	−0.339187	−0.169593	−	0.985514i	$-0.554245\pi$
$857$	−9.92955	−0.339187	−0.169593	+	0.985514i	$0.554245\pi$
$858$	0.475232	0.0162242
$859$	−26.4558	−0.902659	−0.451329	−	0.892357i	$-0.649050\pi$
$859$	−26.4558	−0.902659	−0.451329	+	0.892357i	$0.649050\pi$
$860$	0.777205	0.0265025
$861$	−0.152023	−0.00518091
$862$	−16.6234	−0.566196
$863$	−33.1124	−1.12716	−0.563580	−	0.826061i	$-0.690576\pi$
$863$	−33.1124	−1.12716	−0.563580	+	0.826061i	$0.690576\pi$
$864$	0.239570	0.00815034
$865$	6.00770	0.204268
$866$	−16.7062	−0.567700
$867$	−1.30820	−0.0444289
$868$	−0.545819	−0.0185263
$869$	−3.79020	−0.128574
$870$	−0.729943	−0.0247474
$871$	62.0749	2.10333
$872$	−16.2266	−0.549501
$873$	−10.1489	−0.343490
$874$	73.9081	2.49998
$875$	1.22786	0.0415093
$876$	0.00707113	0.000238911 0
$877$	−13.8967	−0.469257	−0.234628	−	0.972085i	$-0.575387\pi$
$877$	−13.8967	−0.469257	−0.234628	+	0.972085i	$0.575387\pi$
$878$	−38.9335	−1.31394
$879$	1.05577	0.0356102
$880$	−4.16642	−0.140450
$881$	−38.9021	−1.31065	−0.655323	−	0.755349i	$-0.727467\pi$
$881$	−38.9021	−1.31065	−0.655323	+	0.755349i	$0.727467\pi$
$882$	23.7511	0.799740
$883$	−5.76391	−0.193971	−0.0969856	−	0.995286i	$-0.530920\pi$
$883$	−5.76391	−0.193971	−0.0969856	+	0.995286i	$0.530920\pi$
$884$	−0.335107	−0.0112709
$885$	1.01679	0.0341790
$886$	24.1928	0.812774
$887$	−41.5589	−1.39541	−0.697705	−	0.716385i	$-0.745795\pi$
$887$	−41.5589	−1.39541	−0.697705	+	0.716385i	$0.745795\pi$
$888$	0.917673	0.0307951
$889$	−19.9246	−0.668251
$890$	12.8035	0.429175
$891$	8.94058	0.299521
$892$	0.553855	0.0185444
$893$	51.5583	1.72533
$894$	−0.0178312	−0.000596364 0
$895$	8.08492	0.270249
$896$	14.7284	0.492042
$897$	2.55633	0.0853533
$898$	−17.4378	−0.581907
$899$	31.7643	1.05940
$900$	−0.260400	−0.00867999
$901$	9.64934	0.321466
$902$	−2.20043	−0.0732663
$903$	0.891701	0.0296739
$904$	−46.0131	−1.53037
$905$	−7.97341	−0.265045
$906$	1.89875	0.0630816
$907$	45.7501	1.51911	0.759553	−	0.650446i	$-0.225418\pi$
$907$	45.7501	1.51911	0.759553	+	0.650446i	$0.225418\pi$
$908$	−0.845296	−0.0280521
$909$	36.7093	1.21757
$910$	7.17865	0.237970
$911$	−24.3987	−0.808366	−0.404183	−	0.914678i	$-0.632444\pi$
$911$	−24.3987	−0.808366	−0.404183	+	0.914678i	$0.632444\pi$
$912$	−2.22964	−0.0738308
$913$	17.4176	0.576438
$914$	49.3148	1.63119
$915$	0.355700	0.0117591
$916$	0.0516747	0.00170738
$917$	3.12397	0.103163
$918$	0.669911	0.0221104
$919$	23.1037	0.762121	0.381061	−	0.924550i	$-0.375559\pi$
$919$	23.1037	0.762121	0.381061	+	0.924550i	$0.375559\pi$
$920$	−21.4758	−0.708035
$921$	0.478625	0.0157712
$922$	12.0337	0.396308
$923$	−19.9971	−0.658214
$924$	0.00868236	0.000285629 0
$925$	−4.08507	−0.134316
$926$	55.4436	1.82199
$927$	−24.3603	−0.800096
$928$	3.05679	0.100344
$929$	59.3955	1.94870	0.974351	−	0.225032i	$-0.0722486\pi$
$929$	59.3955	1.94870	0.974351	+	0.225032i	$0.0722486\pi$
$930$	−0.600060	−0.0196767
$931$	−36.1593	−1.18507
$932$	2.03273	0.0665844
$933$	−1.01766	−0.0333169
$934$	−59.3795	−1.94296
$935$	−0.951858	−0.0311291
$936$	33.4792	1.09430
$937$	−44.6211	−1.45771	−0.728853	−	0.684670i	$-0.759946\pi$
$937$	−44.6211	−1.45771	−0.728853	+	0.684670i	$0.759946\pi$
$938$	27.2077	0.888362
$939$	2.12781	0.0694385
$940$	0.681263	0.0222203
$941$	34.8353	1.13560	0.567800	−	0.823167i	$-0.307795\pi$
$941$	34.8353	1.13560	0.567800	+	0.823167i	$0.307795\pi$
$942$	−2.49369	−0.0812489
$943$	−11.8364	−0.385445
$944$	−52.1173	−1.69627
$945$	−0.598182	−0.0194589
$946$	12.9068	0.419636
$947$	43.4204	1.41097	0.705486	−	0.708724i	$-0.250729\pi$
$947$	43.4204	1.41097	0.705486	+	0.708724i	$0.250729\pi$
$948$	−0.0268010	−0.000870457 0
$949$	4.04700	0.131371
$950$	9.51089	0.308574
$951$	−2.35142	−0.0762502
$952$	3.22997	0.104684
$953$	−14.8196	−0.480053	−0.240026	−	0.970766i	$-0.577156\pi$
$953$	−14.8196	−0.480053	−0.240026	+	0.970766i	$0.577156\pi$
$954$	43.8379	1.41930
$955$	4.95753	0.160422
$956$	−0.198344	−0.00641489
$957$	−0.505276	−0.0163333
$958$	52.4336	1.69405
$959$	−6.18048	−0.199578
$960$	0.619590	0.0199972
$961$	−4.88773	−0.157669
$962$	−23.8832	−0.770026
$963$	−41.2826	−1.33031
$964$	−0.277484	−0.00893715
$965$	−13.6383	−0.439031
$966$	1.12045	0.0360499
$967$	22.1032	0.710791	0.355396	−	0.934716i	$-0.384346\pi$
$967$	22.1032	0.710791	0.355396	+	0.934716i	$0.384346\pi$
$968$	−2.76361	−0.0888259
$969$	−0.509383	−0.0163637
$970$	4.89799	0.157265
$971$	32.0946	1.02996	0.514982	−	0.857201i	$-0.327799\pi$
$971$	32.0946	1.02996	0.514982	+	0.857201i	$0.327799\pi$
$972$	0.190360	0.00610580
$973$	1.96637	0.0630389
$974$	15.9452	0.510916
$975$	0.328962	0.0105352
$976$	−18.2320	−0.583593
$977$	4.87261	0.155888	0.0779442	−	0.996958i	$-0.475164\pi$
$977$	4.87261	0.155888	0.0779442	+	0.996958i	$0.475164\pi$
$978$	1.74583	0.0558253
$979$	8.86276	0.283255
$980$	−0.477789	−0.0152624
$981$	−17.5757	−0.561150
$982$	−31.4476	−1.00353
$983$	16.5953	0.529309	0.264654	−	0.964343i	$-0.414742\pi$
$983$	16.5953	0.529309	0.264654	+	0.964343i	$0.414742\pi$
$984$	0.342165	0.0109078
$985$	12.9966	0.414105
$986$	8.54771	0.272215
$987$	0.781625	0.0248794
$988$	2.31777	0.0737382
$989$	69.4272	2.20766
$990$	−4.32438	−0.137438
$991$	51.8327	1.64652	0.823260	−	0.567664i	$-0.192153\pi$
$991$	51.8327	1.64652	0.823260	+	0.567664i	$0.192153\pi$
$992$	2.51287	0.0797838
$993$	−1.87910	−0.0596315
$994$	−8.76483	−0.278003
$995$	−28.0125	−0.888056
$996$	0.123162	0.00390254
$997$	15.9301	0.504511	0.252255	−	0.967661i	$-0.418828\pi$
$997$	15.9301	0.504511	0.252255	+	0.967661i	$0.418828\pi$
$998$	36.7752	1.16410
$999$	1.99014	0.0629652

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4015.2.a.h.1.26	✓	37

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4015.2.a.h.1.26	✓	37	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 4015 = 5 \cdot 11 \cdot 73 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4015.a (trivial)

\(f(q)\)	\(=\)	\(q+1.44464 q^{2} +0.0812853 q^{3} +0.0869915 q^{4} +1.00000 q^{5} +0.117428 q^{6} +1.22786 q^{7} -2.76361 q^{8} -2.99339 q^{9} +O(q^{10})\)	\(q+1.44464 q^{2} +0.0812853 q^{3} +0.0869915 q^{4} +1.00000 q^{5} +0.117428 q^{6} +1.22786 q^{7} -2.76361 q^{8} -2.99339 q^{9} +1.44464 q^{10} +1.00000 q^{11} +0.00707113 q^{12} +4.04700 q^{13} +1.77382 q^{14} +0.0812853 q^{15} -4.16642 q^{16} -0.951858 q^{17} -4.32438 q^{18} +6.58356 q^{19} +0.0869915 q^{20} +0.0998069 q^{21} +1.44464 q^{22} +7.77090 q^{23} -0.224641 q^{24} +1.00000 q^{25} +5.84647 q^{26} -0.487174 q^{27} +0.106813 q^{28} -6.21609 q^{29} +0.117428 q^{30} -5.11002 q^{31} -0.491754 q^{32} +0.0812853 q^{33} -1.37509 q^{34} +1.22786 q^{35} -0.260400 q^{36} -4.08507 q^{37} +9.51089 q^{38} +0.328962 q^{39} -2.76361 q^{40} -1.52317 q^{41} +0.144185 q^{42} +8.93425 q^{43} +0.0869915 q^{44} -2.99339 q^{45} +11.2262 q^{46} +7.83137 q^{47} -0.338668 q^{48} -5.49236 q^{49} +1.44464 q^{50} -0.0773720 q^{51} +0.352055 q^{52} -10.1374 q^{53} -0.703793 q^{54} +1.00000 q^{55} -3.39333 q^{56} +0.535146 q^{57} -8.98002 q^{58} +12.5089 q^{59} +0.00707113 q^{60} +4.37595 q^{61} -7.38215 q^{62} -3.67547 q^{63} +7.62242 q^{64} +4.04700 q^{65} +0.117428 q^{66} +15.3385 q^{67} -0.0828036 q^{68} +0.631660 q^{69} +1.77382 q^{70} -4.94122 q^{71} +8.27258 q^{72} +1.00000 q^{73} -5.90146 q^{74} +0.0812853 q^{75} +0.572714 q^{76} +1.22786 q^{77} +0.475232 q^{78} -3.79020 q^{79} -4.16642 q^{80} +8.94058 q^{81} -2.20043 q^{82} +17.4176 q^{83} +0.00868236 q^{84} -0.951858 q^{85} +12.9068 q^{86} -0.505276 q^{87} -2.76361 q^{88} +8.86276 q^{89} -4.32438 q^{90} +4.96915 q^{91} +0.676003 q^{92} -0.415369 q^{93} +11.3135 q^{94} +6.58356 q^{95} -0.0399724 q^{96} +3.39045 q^{97} -7.93449 q^{98} -2.99339 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 37 q + 5 q^{2} + 3 q^{3} + 43 q^{4} + 37 q^{5} + 9 q^{6} + 6 q^{7} + 12 q^{8} + 50 q^{9}+O(q^{10}) \) 37 * q + 5 * q^2 + 3 * q^3 + 43 * q^4 + 37 * q^5 + 9 * q^6 + 6 * q^7 + 12 * q^8 + 50 * q^9	\( 37 q + 5 q^{2} + 3 q^{3} + 43 q^{4} + 37 q^{5} + 9 q^{6} + 6 q^{7} + 12 q^{8} + 50 q^{9} + 5 q^{10} + 37 q^{11} + 6 q^{12} + 11 q^{13} + 11 q^{14} + 3 q^{15} + 43 q^{16} + 38 q^{17} + 11 q^{18} + 34 q^{19} + 43 q^{20} + 39 q^{21} + 5 q^{22} + 4 q^{23} + 25 q^{24} + 37 q^{25} - 9 q^{26} + 3 q^{27} + 14 q^{28} + 58 q^{29} + 9 q^{30} + 8 q^{31} + 14 q^{32} + 3 q^{33} + 8 q^{34} + 6 q^{35} + 20 q^{36} + 2 q^{37} + 15 q^{38} + 14 q^{39} + 12 q^{40} + 62 q^{41} - 13 q^{42} + 30 q^{43} + 43 q^{44} + 50 q^{45} + 31 q^{46} + 5 q^{47} - 25 q^{48} + 59 q^{49} + 5 q^{50} + 23 q^{51} - q^{52} + 18 q^{53} + 13 q^{54} + 37 q^{55} + 22 q^{56} + 5 q^{57} - 40 q^{58} + 15 q^{59} + 6 q^{60} + 57 q^{61} + 20 q^{62} - 29 q^{63} + 10 q^{64} + 11 q^{65} + 9 q^{66} - 14 q^{67} + 53 q^{68} + 24 q^{69} + 11 q^{70} + 8 q^{71} + 15 q^{72} + 37 q^{73} + 7 q^{74} + 3 q^{75} + 59 q^{76} + 6 q^{77} + q^{78} + 42 q^{79} + 43 q^{80} + 61 q^{81} - 22 q^{82} + 44 q^{83} + 66 q^{84} + 38 q^{85} - q^{86} - 26 q^{87} + 12 q^{88} + 69 q^{89} + 11 q^{90} - 10 q^{91} - 21 q^{92} - 26 q^{93} + 29 q^{94} + 34 q^{95} - 9 q^{96} + 37 q^{97} - 15 q^{98} + 50 q^{99}+O(q^{100}) \) 37 * q + 5 * q^2 + 3 * q^3 + 43 * q^4 + 37 * q^5 + 9 * q^6 + 6 * q^7 + 12 * q^8 + 50 * q^9 + 5 * q^10 + 37 * q^11 + 6 * q^12 + 11 * q^13 + 11 * q^14 + 3 * q^15 + 43 * q^16 + 38 * q^17 + 11 * q^18 + 34 * q^19 + 43 * q^20 + 39 * q^21 + 5 * q^22 + 4 * q^23 + 25 * q^24 + 37 * q^25 - 9 * q^26 + 3 * q^27 + 14 * q^28 + 58 * q^29 + 9 * q^30 + 8 * q^31 + 14 * q^32 + 3 * q^33 + 8 * q^34 + 6 * q^35 + 20 * q^36 + 2 * q^37 + 15 * q^38 + 14 * q^39 + 12 * q^40 + 62 * q^41 - 13 * q^42 + 30 * q^43 + 43 * q^44 + 50 * q^45 + 31 * q^46 + 5 * q^47 - 25 * q^48 + 59 * q^49 + 5 * q^50 + 23 * q^51 - q^52 + 18 * q^53 + 13 * q^54 + 37 * q^55 + 22 * q^56 + 5 * q^57 - 40 * q^58 + 15 * q^59 + 6 * q^60 + 57 * q^61 + 20 * q^62 - 29 * q^63 + 10 * q^64 + 11 * q^65 + 9 * q^66 - 14 * q^67 + 53 * q^68 + 24 * q^69 + 11 * q^70 + 8 * q^71 + 15 * q^72 + 37 * q^73 + 7 * q^74 + 3 * q^75 + 59 * q^76 + 6 * q^77 + q^78 + 42 * q^79 + 43 * q^80 + 61 * q^81 - 22 * q^82 + 44 * q^83 + 66 * q^84 + 38 * q^85 - q^86 - 26 * q^87 + 12 * q^88 + 69 * q^89 + 11 * q^90 - 10 * q^91 - 21 * q^92 - 26 * q^93 + 29 * q^94 + 34 * q^95 - 9 * q^96 + 37 * q^97 - 15 * q^98 + 50 * q^99

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