LMFDB - Embedded newform 4009.2.a.c.1.63

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4009,2,Mod(1,4009)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4009, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("4009.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4009 = 19 \cdot 211 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4009.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:	$32.0120261703$
Analytic rank:	$1$
Dimension:	$71$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.63
Character	$\chi$	$=$	4009.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.12402 q^{2} +0.772891 q^{3} +2.51145 q^{4} +2.24829 q^{5} +1.64163 q^{6} -4.92186 q^{7} +1.08632 q^{8} -2.40264 q^{9} +O(q^{10})$	\(q+2.12402 q^{2} +0.772891 q^{3} +2.51145 q^{4} +2.24829 q^{5} +1.64163 q^{6} -4.92186 q^{7} +1.08632 q^{8} -2.40264 q^{9} +4.77541 q^{10} -6.19016 q^{11} +1.94107 q^{12} +4.43111 q^{13} -10.4541 q^{14} +1.73768 q^{15} -2.71553 q^{16} +5.06337 q^{17} -5.10325 q^{18} +1.00000 q^{19} +5.64646 q^{20} -3.80406 q^{21} -13.1480 q^{22} -4.04807 q^{23} +0.839605 q^{24} +0.0548094 q^{25} +9.41175 q^{26} -4.17565 q^{27} -12.3610 q^{28} -9.35778 q^{29} +3.69087 q^{30} -5.58499 q^{31} -7.94047 q^{32} -4.78431 q^{33} +10.7547 q^{34} -11.0658 q^{35} -6.03410 q^{36} +8.06161 q^{37} +2.12402 q^{38} +3.42476 q^{39} +2.44236 q^{40} -1.31485 q^{41} -8.07988 q^{42} -3.33643 q^{43} -15.5462 q^{44} -5.40183 q^{45} -8.59817 q^{46} +8.77839 q^{47} -2.09881 q^{48} +17.2247 q^{49} +0.116416 q^{50} +3.91343 q^{51} +11.1285 q^{52} +0.662194 q^{53} -8.86915 q^{54} -13.9173 q^{55} -5.34670 q^{56} +0.772891 q^{57} -19.8761 q^{58} -10.7853 q^{59} +4.36409 q^{60} +12.2191 q^{61} -11.8626 q^{62} +11.8255 q^{63} -11.4346 q^{64} +9.96242 q^{65} -10.1620 q^{66} -10.5883 q^{67} +12.7164 q^{68} -3.12872 q^{69} -23.5039 q^{70} -14.0106 q^{71} -2.61003 q^{72} -6.74104 q^{73} +17.1230 q^{74} +0.0423617 q^{75} +2.51145 q^{76} +30.4671 q^{77} +7.27425 q^{78} +5.31408 q^{79} -6.10531 q^{80} +3.98060 q^{81} -2.79277 q^{82} -5.37024 q^{83} -9.55369 q^{84} +11.3839 q^{85} -7.08663 q^{86} -7.23254 q^{87} -6.72448 q^{88} -12.4608 q^{89} -11.4736 q^{90} -21.8093 q^{91} -10.1665 q^{92} -4.31659 q^{93} +18.6454 q^{94} +2.24829 q^{95} -6.13712 q^{96} +2.27894 q^{97} +36.5855 q^{98} +14.8727 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 71 q - 15 q^{2} - 8 q^{3} + 69 q^{4} - 18 q^{5} - 9 q^{6} - 19 q^{7} - 39 q^{8} + 63 q^{9}+O(q^{10}) $ 71 * q - 15 * q^2 - 8 * q^3 + 69 * q^4 - 18 * q^5 - 9 * q^6 - 19 * q^7 - 39 * q^8 + 63 * q^9	\( 71 q - 15 q^{2} - 8 q^{3} + 69 q^{4} - 18 q^{5} - 9 q^{6} - 19 q^{7} - 39 q^{8} + 63 q^{9} - 10 q^{10} - 52 q^{11} - 9 q^{12} - 15 q^{13} - 53 q^{14} - 33 q^{15} + 53 q^{16} - 10 q^{17} - 35 q^{18} + 71 q^{19} - 33 q^{20} - 38 q^{21} - 6 q^{22} - 65 q^{23} - 30 q^{24} + 51 q^{25} - 4 q^{26} - 23 q^{27} - 29 q^{28} - 97 q^{29} - 27 q^{30} - 53 q^{31} - 78 q^{32} - 17 q^{33} - 24 q^{34} - 38 q^{35} + 24 q^{36} - 33 q^{37} - 15 q^{38} - 86 q^{39} + 25 q^{40} - 69 q^{41} + 64 q^{42} - 10 q^{43} - 94 q^{44} - 34 q^{45} - 6 q^{46} - 37 q^{47} - q^{48} + 74 q^{49} - 41 q^{50} - 46 q^{51} - 30 q^{52} - 50 q^{53} - 17 q^{54} - 30 q^{55} - 116 q^{56} - 8 q^{57} + 11 q^{58} - 93 q^{59} - 56 q^{60} - 18 q^{61} - q^{62} - 84 q^{63} + 93 q^{64} - 78 q^{65} - 53 q^{66} - 5 q^{67} - 9 q^{68} - 69 q^{69} - 10 q^{70} - 221 q^{71} - 73 q^{72} - 34 q^{73} - 58 q^{74} - 70 q^{75} + 69 q^{76} - 2 q^{77} + 7 q^{78} - 68 q^{79} - 71 q^{80} + 39 q^{81} + 26 q^{82} - 45 q^{83} - 10 q^{84} - 44 q^{85} - 80 q^{86} - 7 q^{87} - 46 q^{88} - 143 q^{89} + 41 q^{90} - 30 q^{91} - 46 q^{92} + 32 q^{93} + 41 q^{94} - 18 q^{95} - 140 q^{96} - 18 q^{97} - 97 q^{98} - 142 q^{99}+O(q^{100}) \) 71 * q - 15 * q^2 - 8 * q^3 + 69 * q^4 - 18 * q^5 - 9 * q^6 - 19 * q^7 - 39 * q^8 + 63 * q^9 - 10 * q^10 - 52 * q^11 - 9 * q^12 - 15 * q^13 - 53 * q^14 - 33 * q^15 + 53 * q^16 - 10 * q^17 - 35 * q^18 + 71 * q^19 - 33 * q^20 - 38 * q^21 - 6 * q^22 - 65 * q^23 - 30 * q^24 + 51 * q^25 - 4 * q^26 - 23 * q^27 - 29 * q^28 - 97 * q^29 - 27 * q^30 - 53 * q^31 - 78 * q^32 - 17 * q^33 - 24 * q^34 - 38 * q^35 + 24 * q^36 - 33 * q^37 - 15 * q^38 - 86 * q^39 + 25 * q^40 - 69 * q^41 + 64 * q^42 - 10 * q^43 - 94 * q^44 - 34 * q^45 - 6 * q^46 - 37 * q^47 - q^48 + 74 * q^49 - 41 * q^50 - 46 * q^51 - 30 * q^52 - 50 * q^53 - 17 * q^54 - 30 * q^55 - 116 * q^56 - 8 * q^57 + 11 * q^58 - 93 * q^59 - 56 * q^60 - 18 * q^61 - q^62 - 84 * q^63 + 93 * q^64 - 78 * q^65 - 53 * q^66 - 5 * q^67 - 9 * q^68 - 69 * q^69 - 10 * q^70 - 221 * q^71 - 73 * q^72 - 34 * q^73 - 58 * q^74 - 70 * q^75 + 69 * q^76 - 2 * q^77 + 7 * q^78 - 68 * q^79 - 71 * q^80 + 39 * q^81 + 26 * q^82 - 45 * q^83 - 10 * q^84 - 44 * q^85 - 80 * q^86 - 7 * q^87 - 46 * q^88 - 143 * q^89 + 41 * q^90 - 30 * q^91 - 46 * q^92 + 32 * q^93 + 41 * q^94 - 18 * q^95 - 140 * q^96 - 18 * q^97 - 97 * q^98 - 142 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	2.12402	1.50191	0.750953	−	0.660355i	$-0.229594\pi$
$2$	2.12402	1.50191	0.750953	+	0.660355i	$0.229594\pi$
$3$	0.772891	0.446229	0.223114	−	0.974792i	$-0.428378\pi$
$3$	0.772891	0.446229	0.223114	+	0.974792i	$0.428378\pi$
$4$	2.51145	1.25572
$5$	2.24829	1.00547	0.502733	−	0.864442i	$-0.332328\pi$
$5$	2.24829	1.00547	0.502733	+	0.864442i	$0.332328\pi$
$6$	1.64163	0.670194
$7$	−4.92186	−1.86029	−0.930144	−	0.367195i	$-0.880318\pi$
$7$	−4.92186	−1.86029	−0.930144	+	0.367195i	$0.880318\pi$
$8$	1.08632	0.384071
$9$	−2.40264	−0.800880
$10$	4.77541	1.51012
$11$	−6.19016	−1.86640	−0.933201	−	0.359354i	$-0.882997\pi$
$11$	−6.19016	−1.86640	−0.933201	+	0.359354i	$0.882997\pi$
$12$	1.94107	0.560339
$13$	4.43111	1.22897	0.614484	−	0.788929i	$-0.289364\pi$
$13$	4.43111	1.22897	0.614484	+	0.788929i	$0.289364\pi$
$14$	−10.4541	−2.79398
$15$	1.73768	0.448668
$16$	−2.71553	−0.678883
$17$	5.06337	1.22805	0.614024	−	0.789287i	$-0.289550\pi$
$17$	5.06337	1.22805	0.614024	+	0.789287i	$0.289550\pi$
$18$	−5.10325	−1.20285
$19$	1.00000	0.229416
$19$	1.00000	0.229416
$20$	5.64646	1.26259
$21$	−3.80406	−0.830114
$22$	−13.1480	−2.80316
$23$	−4.04807	−0.844081	−0.422040	−	0.906577i	$-0.638686\pi$
$23$	−4.04807	−0.844081	−0.422040	+	0.906577i	$0.638686\pi$
$24$	0.839605	0.171384
$25$	0.0548094	0.0109619
$26$	9.41175	1.84580
$27$	−4.17565	−0.803604
$28$	−12.3610	−2.33601
$29$	−9.35778	−1.73770	−0.868848	−	0.495079i	$-0.835139\pi$
$29$	−9.35778	−1.73770	−0.868848	+	0.495079i	$0.835139\pi$
$30$	3.69087	0.673857
$31$	−5.58499	−1.00309	−0.501547	−	0.865130i	$-0.667236\pi$
$31$	−5.58499	−1.00309	−0.501547	+	0.865130i	$0.667236\pi$
$32$	−7.94047	−1.40369
$33$	−4.78431	−0.832842
$34$	10.7547	1.84441
$35$	−11.0658	−1.87046
$36$	−6.03410	−1.00568
$37$	8.06161	1.32532	0.662660	−	0.748920i	$-0.269427\pi$
$37$	8.06161	1.32532	0.662660	+	0.748920i	$0.269427\pi$
$38$	2.12402	0.344561
$39$	3.42476	0.548401
$40$	2.44236	0.386171
$41$	−1.31485	−0.205346	−0.102673	−	0.994715i	$-0.532739\pi$
$41$	−1.31485	−0.205346	−0.102673	+	0.994715i	$0.532739\pi$
$42$	−8.07988	−1.24675
$43$	−3.33643	−0.508801	−0.254400	−	0.967099i	$-0.581878\pi$
$43$	−3.33643	−0.508801	−0.254400	+	0.967099i	$0.581878\pi$
$44$	−15.5462	−2.34368
$45$	−5.40183	−0.805258
$46$	−8.59817	−1.26773
$47$	8.77839	1.28046	0.640230	−	0.768184i	$-0.278839\pi$
$47$	8.77839	1.28046	0.640230	+	0.768184i	$0.278839\pi$
$48$	−2.09881	−0.302937
$49$	17.2247	2.46067
$50$	0.116416	0.0164637
$51$	3.91343	0.547990
$52$	11.1285	1.54324
$53$	0.662194	0.0909594	0.0454797	−	0.998965i	$-0.485518\pi$
$53$	0.662194	0.0909594	0.0454797	+	0.998965i	$0.485518\pi$
$54$	−8.86915	−1.20694
$55$	−13.9173	−1.87660
$56$	−5.34670	−0.714483
$57$	0.772891	0.102372
$58$	−19.8761	−2.60986
$59$	−10.7853	−1.40412	−0.702061	−	0.712116i	$-0.747737\pi$
$59$	−10.7853	−1.40412	−0.702061	+	0.712116i	$0.747737\pi$
$60$	4.36409	0.563402
$61$	12.2191	1.56450	0.782249	−	0.622966i	$-0.214072\pi$
$61$	12.2191	1.56450	0.782249	+	0.622966i	$0.214072\pi$
$62$	−11.8626	−1.50655
$63$	11.8255	1.48987
$64$	−11.4346	−1.42933
$65$	9.96242	1.23569
$66$	−10.1620	−1.25085
$67$	−10.5883	−1.29357	−0.646786	−	0.762672i	$-0.723887\pi$
$67$	−10.5883	−1.29357	−0.646786	+	0.762672i	$0.723887\pi$
$68$	12.7164	1.54209
$69$	−3.12872	−0.376653
$70$	−23.5039	−2.80925
$71$	−14.0106	−1.66275	−0.831376	−	0.555711i	$-0.812446\pi$
$71$	−14.0106	−1.66275	−0.831376	+	0.555711i	$0.812446\pi$
$72$	−2.61003	−0.307595
$73$	−6.74104	−0.788979	−0.394490	−	0.918900i	$-0.629079\pi$
$73$	−6.74104	−0.788979	−0.394490	+	0.918900i	$0.629079\pi$
$74$	17.1230	1.99051
$75$	0.0423617	0.00489150
$76$	2.51145	0.288083
$77$	30.4671	3.47205
$78$	7.27425	0.823647
$79$	5.31408	0.597880	0.298940	−	0.954272i	$-0.403367\pi$
$79$	5.31408	0.597880	0.298940	+	0.954272i	$0.403367\pi$
$80$	−6.10531	−0.682594
$81$	3.98060	0.442289
$82$	−2.79277	−0.308410
$83$	−5.37024	−0.589461	−0.294730	−	0.955580i	$-0.595230\pi$
$83$	−5.37024	−0.589461	−0.294730	+	0.955580i	$0.595230\pi$
$84$	−9.55369	−1.04239
$85$	11.3839	1.23476
$86$	−7.08663	−0.764171
$87$	−7.23254	−0.775410
$88$	−6.72448	−0.716832
$89$	−12.4608	−1.32085	−0.660423	−	0.750894i	$-0.729623\pi$
$89$	−12.4608	−1.32085	−0.660423	+	0.750894i	$0.729623\pi$
$90$	−11.4736	−1.20942
$91$	−21.8093	−2.28623
$92$	−10.1665	−1.05993
$93$	−4.31659	−0.447609
$94$	18.6454	1.92313
$95$	2.24829	0.230670
$96$	−6.13712	−0.626367
$97$	2.27894	0.231392	0.115696	−	0.993285i	$-0.463090\pi$
$97$	2.27894	0.231392	0.115696	+	0.993285i	$0.463090\pi$
$98$	36.5855	3.69570
$99$	14.8727	1.49476
$100$	0.137651	0.0137651
$101$	9.33528	0.928895	0.464448	−	0.885601i	$-0.346253\pi$
$101$	9.33528	0.928895	0.464448	+	0.885601i	$0.346253\pi$
$102$	8.31219	0.823030
$103$	−2.07693	−0.204646	−0.102323	−	0.994751i	$-0.532628\pi$
$103$	−2.07693	−0.204646	−0.102323	+	0.994751i	$0.532628\pi$
$104$	4.81359	0.472012
$105$	−8.55263	−0.834651
$106$	1.40651	0.136613
$107$	−7.10198	−0.686574	−0.343287	−	0.939230i	$-0.611540\pi$
$107$	−7.10198	−0.686574	−0.343287	+	0.939230i	$0.611540\pi$
$108$	−10.4869	−1.00910
$109$	−3.52723	−0.337848	−0.168924	−	0.985629i	$-0.554029\pi$
$109$	−3.52723	−0.337848	−0.168924	+	0.985629i	$0.554029\pi$
$110$	−29.5605	−2.81848
$111$	6.23074	0.591396
$112$	13.3655	1.26292
$113$	−1.74257	−0.163927	−0.0819635	−	0.996635i	$-0.526119\pi$
$113$	−1.74257	−0.163927	−0.0819635	+	0.996635i	$0.526119\pi$
$114$	1.64163	0.153753
$115$	−9.10124	−0.848695
$116$	−23.5016	−2.18206
$117$	−10.6464	−0.984256
$118$	−22.9081	−2.10886
$119$	−24.9212	−2.28452
$120$	1.88768	0.172320
$121$	27.3180	2.48346
$122$	25.9536	2.34973
$123$	−1.01624	−0.0916312
$124$	−14.0264	−1.25961
$125$	−11.1182	−0.994444
$126$	25.1175	2.23764
$127$	20.8824	1.85301	0.926507	−	0.376276i	$-0.122796\pi$
$127$	20.8824	1.85301	0.926507	+	0.376276i	$0.122796\pi$
$128$	−8.40639	−0.743027
$129$	−2.57870	−0.227042
$130$	21.1603	1.85588
$131$	0.696066	0.0608156	0.0304078	−	0.999538i	$-0.490319\pi$
$131$	0.696066	0.0608156	0.0304078	+	0.999538i	$0.490319\pi$
$132$	−12.0155	−1.04582
$133$	−4.92186	−0.426779
$134$	−22.4898	−1.94282
$135$	−9.38807	−0.807997
$136$	5.50043	0.471658
$137$	−21.0474	−1.79820	−0.899100	−	0.437744i	$-0.855778\pi$
$137$	−21.0474	−1.79820	−0.899100	+	0.437744i	$0.855778\pi$
$138$	−6.64544	−0.565698
$139$	18.2207	1.54546	0.772732	−	0.634733i	$-0.218890\pi$
$139$	18.2207	1.54546	0.772732	+	0.634733i	$0.218890\pi$
$140$	−27.7911	−2.34877
$141$	6.78473	0.571378
$142$	−29.7587	−2.49730
$143$	−27.4293	−2.29375
$144$	6.52445	0.543704
$145$	−21.0390	−1.74719
$146$	−14.3181	−1.18497
$147$	13.3128	1.09802
$148$	20.2463	1.66423
$149$	12.9289	1.05917	0.529587	−	0.848256i	$-0.322347\pi$
$149$	12.9289	1.05917	0.529587	+	0.848256i	$0.322347\pi$
$150$	0.0899769	0.00734658
$151$	18.8845	1.53680	0.768398	−	0.639972i	$-0.221054\pi$
$151$	18.8845	1.53680	0.768398	+	0.639972i	$0.221054\pi$
$152$	1.08632	0.0881120
$153$	−12.1655	−0.983519
$154$	64.7126	5.21469
$155$	−12.5567	−1.00858
$156$	8.60110	0.688639
$157$	−2.28205	−0.182128	−0.0910638	−	0.995845i	$-0.529027\pi$
$157$	−2.28205	−0.182128	−0.0910638	+	0.995845i	$0.529027\pi$
$158$	11.2872	0.897960
$159$	0.511804	0.0405887
$160$	−17.8525	−1.41136
$161$	19.9240	1.57023
$162$	8.45486	0.664276
$163$	10.8278	0.848103	0.424051	−	0.905638i	$-0.360608\pi$
$163$	10.8278	0.848103	0.424051	+	0.905638i	$0.360608\pi$
$164$	−3.30218	−0.257857
$165$	−10.7565	−0.837395
$166$	−11.4065	−0.885315
$167$	0.666060	0.0515413	0.0257706	−	0.999668i	$-0.491796\pi$
$167$	0.666060	0.0515413	0.0257706	+	0.999668i	$0.491796\pi$
$168$	−4.13242	−0.318823
$169$	6.63472	0.510363
$170$	24.1796	1.85449
$171$	−2.40264	−0.183734
$172$	−8.37926	−0.638913
$173$	14.2583	1.08404	0.542021	−	0.840365i	$-0.317659\pi$
$173$	14.2583	1.08404	0.542021	+	0.840365i	$0.317659\pi$
$174$	−15.3620	−1.16459
$175$	−0.269764	−0.0203922
$176$	16.8096	1.26707
$177$	−8.33584	−0.626560
$178$	−26.4670	−1.98379
$179$	9.14645	0.683638	0.341819	−	0.939766i	$-0.388957\pi$
$179$	9.14645	0.683638	0.341819	+	0.939766i	$0.388957\pi$
$180$	−13.5664	−1.01118
$181$	−19.5633	−1.45413	−0.727065	−	0.686568i	$-0.759116\pi$
$181$	−19.5633	−1.45413	−0.727065	+	0.686568i	$0.759116\pi$
$182$	−46.3233	−3.43371
$183$	9.44405	0.698124
$184$	−4.39749	−0.324187
$185$	18.1248	1.33256
$186$	−9.16850	−0.672267
$187$	−31.3431	−2.29203
$188$	22.0464	1.60790
$189$	20.5520	1.49494
$190$	4.77541	0.346444
$191$	16.1047	1.16530	0.582649	−	0.812724i	$-0.302016\pi$
$191$	16.1047	1.16530	0.582649	+	0.812724i	$0.302016\pi$
$192$	−8.83772	−0.637807
$193$	1.18641	0.0854000	0.0427000	−	0.999088i	$-0.486404\pi$
$193$	1.18641	0.0854000	0.0427000	+	0.999088i	$0.486404\pi$
$194$	4.84051	0.347529
$195$	7.69986	0.551398
$196$	43.2589	3.08992
$197$	−16.1901	−1.15350	−0.576748	−	0.816922i	$-0.695679\pi$
$197$	−16.1901	−1.15350	−0.576748	+	0.816922i	$0.695679\pi$
$198$	31.5899	2.24500
$199$	−0.763238	−0.0541045	−0.0270523	−	0.999634i	$-0.508612\pi$
$199$	−0.763238	−0.0541045	−0.0270523	+	0.999634i	$0.508612\pi$
$200$	0.0595404	0.00421014
$201$	−8.18363	−0.577229
$202$	19.8283	1.39511
$203$	46.0577	3.23261
$204$	9.82837	0.688124
$205$	−2.95617	−0.206468
$206$	−4.41144	−0.307360
$207$	9.72605	0.676007
$208$	−12.0328	−0.834326
$209$	−6.19016	−0.428182
$210$	−18.1659	−1.25357
$211$	1.00000	0.0688428
$211$	1.00000	0.0688428
$212$	1.66307	0.114220
$213$	−10.8287	−0.741967
$214$	−15.0847	−1.03117
$215$	−7.50126	−0.511582
$216$	−4.53608	−0.308641
$217$	27.4885	1.86604
$218$	−7.49190	−0.507416
$219$	−5.21009	−0.352065
$220$	−34.9525	−2.35649
$221$	22.4363	1.50923
$222$	13.2342	0.888221
$223$	−13.4300	−0.899336	−0.449668	−	0.893196i	$-0.648458\pi$
$223$	−13.4300	−0.899336	−0.449668	+	0.893196i	$0.648458\pi$
$224$	39.0819	2.61127
$225$	−0.131687	−0.00877915
$226$	−3.70124	−0.246203
$227$	16.2426	1.07806	0.539031	−	0.842286i	$-0.318791\pi$
$227$	16.2426	1.07806	0.539031	+	0.842286i	$0.318791\pi$
$228$	1.94107	0.128551
$229$	11.7965	0.779534	0.389767	−	0.920913i	$-0.372555\pi$
$229$	11.7965	0.779534	0.389767	+	0.920913i	$0.372555\pi$
$230$	−19.3312	−1.27466
$231$	23.5477	1.54933
$232$	−10.1655	−0.667399
$233$	2.79860	0.183342	0.0916712	−	0.995789i	$-0.470779\pi$
$233$	2.79860	0.183342	0.0916712	+	0.995789i	$0.470779\pi$
$234$	−22.6130	−1.47826
$235$	19.7364	1.28746
$236$	−27.0866	−1.76319
$237$	4.10720	0.266791
$238$	−52.9330	−3.43114
$239$	−23.9294	−1.54787	−0.773933	−	0.633267i	$-0.781713\pi$
$239$	−23.9294	−1.54787	−0.773933	+	0.633267i	$0.781713\pi$
$240$	−4.71874	−0.304593
$241$	−12.4472	−0.801796	−0.400898	−	0.916123i	$-0.631302\pi$
$241$	−12.4472	−0.801796	−0.400898	+	0.916123i	$0.631302\pi$
$242$	58.0239	3.72992
$243$	15.6035	1.00097
$244$	30.6877	1.96458
$245$	38.7261	2.47412
$246$	−2.15851	−0.137621
$247$	4.43111	0.281945
$248$	−6.06708	−0.385260
$249$	−4.15061	−0.263034
$250$	−23.6153	−1.49356
$251$	−21.2975	−1.34428	−0.672142	−	0.740422i	$-0.734626\pi$
$251$	−21.2975	−1.34428	−0.672142	+	0.740422i	$0.734626\pi$
$252$	29.6990	1.87086
$253$	25.0582	1.57539
$254$	44.3546	2.78305
$255$	8.79853	0.550985
$256$	5.01395	0.313372
$257$	−17.3960	−1.08513	−0.542565	−	0.840014i	$-0.682547\pi$
$257$	−17.3960	−1.08513	−0.542565	+	0.840014i	$0.682547\pi$
$258$	−5.47719	−0.340995
$259$	−39.6781	−2.46548
$260$	25.0201	1.55168
$261$	22.4834	1.39169
$262$	1.47846	0.0913393
$263$	4.70639	0.290208	0.145104	−	0.989416i	$-0.453648\pi$
$263$	4.70639	0.290208	0.145104	+	0.989416i	$0.453648\pi$
$264$	−5.19729	−0.319871
$265$	1.48881	0.0914566
$266$	−10.4541	−0.640983
$267$	−9.63087	−0.589400
$268$	−26.5920	−1.62437
$269$	−12.7677	−0.778459	−0.389230	−	0.921141i	$-0.627259\pi$
$269$	−12.7677	−0.778459	−0.389230	+	0.921141i	$0.627259\pi$
$270$	−19.9404	−1.21354
$271$	3.62288	0.220075	0.110037	−	0.993927i	$-0.464903\pi$
$271$	3.62288	0.220075	0.110037	+	0.993927i	$0.464903\pi$
$272$	−13.7498	−0.833701
$273$	−16.8562	−1.02018
$274$	−44.7050	−2.70073
$275$	−0.339279	−0.0204593
$276$	−7.85760	−0.472972
$277$	13.7393	0.825514	0.412757	−	0.910841i	$-0.364566\pi$
$277$	13.7393	0.825514	0.412757	+	0.910841i	$0.364566\pi$
$278$	38.7012	2.32114
$279$	13.4187	0.803358
$280$	−12.0209	−0.718389
$281$	−7.24772	−0.432363	−0.216181	−	0.976353i	$-0.569360\pi$
$281$	−7.24772	−0.432363	−0.216181	+	0.976353i	$0.569360\pi$
$282$	14.4109	0.858156
$283$	20.1769	1.19939	0.599697	−	0.800227i	$-0.295288\pi$
$283$	20.1769	1.19939	0.599697	+	0.800227i	$0.295288\pi$
$284$	−35.1868	−2.08795
$285$	1.73768	0.102931
$286$	−58.2602	−3.44500
$287$	6.47153	0.382002
$288$	19.0781	1.12419
$289$	8.63772	0.508101
$290$	−44.6872	−2.62412
$291$	1.76137	0.103254
$292$	−16.9298	−0.990739
$293$	−17.1562	−1.00228	−0.501139	−	0.865367i	$-0.667086\pi$
$293$	−17.1562	−1.00228	−0.501139	+	0.865367i	$0.667086\pi$
$294$	28.2766	1.64913
$295$	−24.2484	−1.41180
$296$	8.75747	0.509018
$297$	25.8479	1.49985
$298$	27.4611	1.59078
$299$	−17.9374	−1.03735
$300$	0.106389	0.00614237
$301$	16.4214	0.946516
$302$	40.1109	2.30812
$303$	7.21515	0.414500
$304$	−2.71553	−0.155747
$305$	27.4721	1.57305
$306$	−25.8396	−1.47715
$307$	−3.94102	−0.224926	−0.112463	−	0.993656i	$-0.535874\pi$
$307$	−3.94102	−0.224926	−0.112463	+	0.993656i	$0.535874\pi$
$308$	76.5164	4.35993
$309$	−1.60524	−0.0913190
$310$	−26.6706	−1.51479
$311$	−5.12299	−0.290498	−0.145249	−	0.989395i	$-0.546398\pi$
$311$	−5.12299	−0.290498	−0.145249	+	0.989395i	$0.546398\pi$
$312$	3.72038	0.210625
$313$	34.6689	1.95960	0.979800	−	0.199981i	$-0.0640881\pi$
$313$	34.6689	1.95960	0.979800	+	0.199981i	$0.0640881\pi$
$314$	−4.84712	−0.273539
$315$	26.5871	1.49801
$316$	13.3460	0.750772
$317$	−17.2317	−0.967828	−0.483914	−	0.875116i	$-0.660785\pi$
$317$	−17.2317	−0.967828	−0.483914	+	0.875116i	$0.660785\pi$
$318$	1.08708	0.0609604
$319$	57.9261	3.24324
$320$	−25.7084	−1.43714
$321$	−5.48905	−0.306369
$322$	42.3190	2.35834
$323$	5.06337	0.281733
$324$	9.99706	0.555392
$325$	0.242866	0.0134718
$326$	22.9985	1.27377
$327$	−2.72617	−0.150757
$328$	−1.42835	−0.0788674
$329$	−43.2060	−2.38202
$330$	−22.8470	−1.25769
$331$	1.82079	0.100080	0.0500400	−	0.998747i	$-0.484065\pi$
$331$	1.82079	0.100080	0.0500400	+	0.998747i	$0.484065\pi$
$332$	−13.4871	−0.740199
$333$	−19.3691	−1.06142
$334$	1.41472	0.0774102
$335$	−23.8057	−1.30064
$336$	10.3300	0.563550
$337$	−28.4768	−1.55123	−0.775616	−	0.631205i	$-0.782561\pi$
$337$	−28.4768	−1.55123	−0.775616	+	0.631205i	$0.782561\pi$
$338$	14.0923	0.766518
$339$	−1.34681	−0.0731489
$340$	28.5901	1.55052
$341$	34.5720	1.87218
$342$	−5.10325	−0.275952
$343$	−50.3245	−2.71727
$344$	−3.62442	−0.195416
$345$	−7.03426	−0.378712
$346$	30.2850	1.62813
$347$	10.9961	0.590304	0.295152	−	0.955450i	$-0.404630\pi$
$347$	10.9961	0.590304	0.295152	+	0.955450i	$0.404630\pi$
$348$	−18.1641	−0.973700
$349$	17.4284	0.932919	0.466459	−	0.884543i	$-0.345529\pi$
$349$	17.4284	0.932919	0.466459	+	0.884543i	$0.345529\pi$
$350$	−0.572983	−0.0306272
$351$	−18.5028	−0.987604
$352$	49.1528	2.61985
$353$	16.4683	0.876519	0.438259	−	0.898849i	$-0.355595\pi$
$353$	16.4683	0.876519	0.438259	+	0.898849i	$0.355595\pi$
$354$	−17.7055	−0.941034
$355$	−31.4999	−1.67184
$356$	−31.2947	−1.65862
$357$	−19.2614	−1.01942
$358$	19.4272	1.02676
$359$	−21.1469	−1.11609	−0.558046	−	0.829810i	$-0.688449\pi$
$359$	−21.1469	−1.11609	−0.558046	+	0.829810i	$0.688449\pi$
$360$	−5.86811	−0.309276
$361$	1.00000	0.0526316
$362$	−41.5528	−2.18397
$363$	21.1139	1.10819
$364$	−54.7728	−2.87088
$365$	−15.1558	−0.793292
$366$	20.0593	1.04852
$367$	1.93280	0.100892	0.0504458	−	0.998727i	$-0.483936\pi$
$367$	1.93280	0.100892	0.0504458	+	0.998727i	$0.483936\pi$
$368$	10.9927	0.573032
$369$	3.15912	0.164457
$370$	38.4974	2.00139
$371$	−3.25923	−0.169211
$372$	−10.8409	−0.562073
$373$	−3.59742	−0.186268	−0.0931338	−	0.995654i	$-0.529688\pi$
$373$	−3.59742	−0.186268	−0.0931338	+	0.995654i	$0.529688\pi$
$374$	−66.5732	−3.44242
$375$	−8.59317	−0.443750
$376$	9.53612	0.491788
$377$	−41.4653	−2.13557
$378$	43.6527	2.24525
$379$	−6.35006	−0.326181	−0.163090	−	0.986611i	$-0.552146\pi$
$379$	−6.35006	−0.326181	−0.163090	+	0.986611i	$0.552146\pi$
$380$	5.64646	0.289657
$381$	16.1398	0.826868
$382$	34.2067	1.75017
$383$	8.88422	0.453962	0.226981	−	0.973899i	$-0.427114\pi$
$383$	8.88422	0.453962	0.226981	+	0.973899i	$0.427114\pi$
$384$	−6.49722	−0.331560
$385$	68.4988	3.49102
$386$	2.51996	0.128263
$387$	8.01624	0.407488
$388$	5.72344	0.290564
$389$	29.3175	1.48646	0.743229	−	0.669037i	$-0.233293\pi$
$389$	29.3175	1.48646	0.743229	+	0.669037i	$0.233293\pi$
$390$	16.3546	0.828149
$391$	−20.4969	−1.03657
$392$	18.7115	0.945073
$393$	0.537983	0.0271377
$394$	−34.3880	−1.73244
$395$	11.9476	0.601148
$396$	37.3520	1.87701
$397$	−33.4919	−1.68091	−0.840454	−	0.541882i	$-0.817712\pi$
$397$	−33.4919	−1.68091	−0.840454	+	0.541882i	$0.817712\pi$
$398$	−1.62113	−0.0812599
$399$	−3.80406	−0.190441
$400$	−0.148837	−0.00744184
$401$	−18.3970	−0.918702	−0.459351	−	0.888255i	$-0.651918\pi$
$401$	−18.3970	−0.918702	−0.459351	+	0.888255i	$0.651918\pi$
$402$	−17.3822	−0.866943
$403$	−24.7477	−1.23277
$404$	23.4451	1.16643
$405$	8.94954	0.444706
$406$	97.8272	4.85508
$407$	−49.9026	−2.47358
$408$	4.25123	0.210467
$409$	−3.47786	−0.171969	−0.0859845	−	0.996296i	$-0.527404\pi$
$409$	−3.47786	−0.171969	−0.0859845	+	0.996296i	$0.527404\pi$
$410$	−6.27896	−0.310096
$411$	−16.2673	−0.802408
$412$	−5.21610	−0.256979
$413$	53.0836	2.61207
$414$	20.6583	1.01530
$415$	−12.0739	−0.592683
$416$	−35.1851	−1.72509
$417$	14.0826	0.689630
$418$	−13.1480	−0.643089
$419$	−14.6158	−0.714031	−0.357015	−	0.934098i	$-0.616206\pi$
$419$	−14.6158	−0.714031	−0.357015	+	0.934098i	$0.616206\pi$
$420$	−21.4795	−1.04809
$421$	1.64151	0.0800023	0.0400012	−	0.999200i	$-0.487264\pi$
$421$	1.64151	0.0800023	0.0400012	+	0.999200i	$0.487264\pi$
$422$	2.12402	0.103395
$423$	−21.0913	−1.02549
$424$	0.719354	0.0349349
$425$	0.277520	0.0134617
$426$	−23.0002	−1.11437
$427$	−60.1408	−2.91042
$428$	−17.8362	−0.862147
$429$	−21.1998	−1.02354
$430$	−15.9328	−0.768348
$431$	−17.4445	−0.840272	−0.420136	−	0.907461i	$-0.638018\pi$
$431$	−17.4445	−0.840272	−0.420136	+	0.907461i	$0.638018\pi$
$432$	11.3391	0.545554
$433$	16.7519	0.805046	0.402523	−	0.915410i	$-0.368133\pi$
$433$	16.7519	0.805046	0.402523	+	0.915410i	$0.368133\pi$
$434$	58.3861	2.80262
$435$	−16.2609	−0.779648
$436$	−8.85845	−0.424243
$437$	−4.04807	−0.193645
$438$	−11.0663	−0.528769
$439$	39.0319	1.86289	0.931446	−	0.363879i	$-0.118548\pi$
$439$	39.0319	1.86289	0.931446	+	0.363879i	$0.118548\pi$
$440$	−15.1186	−0.720750
$441$	−41.3847	−1.97070
$442$	47.6552	2.26672
$443$	−30.0143	−1.42602	−0.713011	−	0.701153i	$-0.752669\pi$
$443$	−30.0143	−1.42602	−0.713011	+	0.701153i	$0.752669\pi$
$444$	15.6482	0.742629
$445$	−28.0156	−1.32807
$446$	−28.5254	−1.35072
$447$	9.99260	0.472634
$448$	56.2796	2.65896
$449$	−4.46327	−0.210635	−0.105317	−	0.994439i	$-0.533586\pi$
$449$	−4.46327	−0.210635	−0.105317	+	0.994439i	$0.533586\pi$
$450$	−0.279706	−0.0131855
$451$	8.13915	0.383258
$452$	−4.37636	−0.205847
$453$	14.5956	0.685762
$454$	34.4996	1.61915
$455$	−49.0336	−2.29873
$456$	0.839605	0.0393181
$457$	−24.8071	−1.16043	−0.580215	−	0.814464i	$-0.697031\pi$
$457$	−24.8071	−1.16043	−0.580215	+	0.814464i	$0.697031\pi$
$458$	25.0559	1.17079
$459$	−21.1429	−0.986864
$460$	−22.8573	−1.06572
$461$	1.34802	0.0627836	0.0313918	−	0.999507i	$-0.490006\pi$
$461$	1.34802	0.0627836	0.0313918	+	0.999507i	$0.490006\pi$
$462$	50.0157	2.32694
$463$	−15.7110	−0.730150	−0.365075	−	0.930978i	$-0.618957\pi$
$463$	−15.7110	−0.730150	−0.365075	+	0.930978i	$0.618957\pi$
$464$	25.4114	1.17969
$465$	−9.70494	−0.450056
$466$	5.94427	0.275363
$467$	−10.9123	−0.504961	−0.252481	−	0.967602i	$-0.581246\pi$
$467$	−10.9123	−0.504961	−0.252481	+	0.967602i	$0.581246\pi$
$468$	−26.7377	−1.23595
$469$	52.1143	2.40642
$470$	41.9204	1.93364
$471$	−1.76378	−0.0812705
$472$	−11.7162	−0.539283
$473$	20.6530	0.949627
$474$	8.72376	0.400696
$475$	0.0548094	0.00251483
$476$	−62.5882	−2.86873
$477$	−1.59101	−0.0728476
$478$	−50.8265	−2.32475
$479$	34.1142	1.55872	0.779360	−	0.626577i	$-0.215545\pi$
$479$	34.1142	1.55872	0.779360	+	0.626577i	$0.215545\pi$
$480$	−13.7980	−0.629791
$481$	35.7219	1.62878
$482$	−26.4381	−1.20422
$483$	15.3991	0.700683
$484$	68.6077	3.11853
$485$	5.12373	0.232657
$486$	33.1421	1.50336
$487$	−31.8828	−1.44475	−0.722375	−	0.691502i	$-0.756949\pi$
$487$	−31.8828	−1.44475	−0.722375	+	0.691502i	$0.756949\pi$
$488$	13.2739	0.600879
$489$	8.36874	0.378448
$490$	82.2549	3.71590
$491$	17.0287	0.768495	0.384247	−	0.923230i	$-0.374461\pi$
$491$	17.0287	0.768495	0.384247	+	0.923230i	$0.374461\pi$
$492$	−2.55223	−0.115063
$493$	−47.3819	−2.13397
$494$	9.41175	0.423454
$495$	33.4382	1.50293
$496$	15.1662	0.680984
$497$	68.9581	3.09320
$498$	−8.81597	−0.395053
$499$	5.08178	0.227492	0.113746	−	0.993510i	$-0.463715\pi$
$499$	5.08178	0.227492	0.113746	+	0.993510i	$0.463715\pi$
$500$	−27.9228	−1.24875
$501$	0.514792	0.0229992
$502$	−45.2362	−2.01899
$503$	−8.37566	−0.373452	−0.186726	−	0.982412i	$-0.559788\pi$
$503$	−8.37566	−0.373452	−0.186726	+	0.982412i	$0.559788\pi$
$504$	12.8462	0.572215
$505$	20.9884	0.933973
$506$	53.2240	2.36609
$507$	5.12791	0.227739
$508$	52.4450	2.32687
$509$	−6.08632	−0.269771	−0.134886	−	0.990861i	$-0.543067\pi$
$509$	−6.08632	−0.269771	−0.134886	+	0.990861i	$0.543067\pi$
$510$	18.6882	0.827528
$511$	33.1785	1.46773
$512$	27.4625	1.21368
$513$	−4.17565	−0.184359
$514$	−36.9493	−1.62976
$515$	−4.66955	−0.205765
$516$	−6.47625	−0.285101
$517$	−54.3396	−2.38985
$518$	−84.2769	−3.70292
$519$	11.0201	0.483731
$520$	10.8224	0.474592
$521$	−4.68253	−0.205145	−0.102573	−	0.994726i	$-0.532707\pi$
$521$	−4.68253	−0.205145	−0.102573	+	0.994726i	$0.532707\pi$
$522$	47.7551	2.09018
$523$	−26.6334	−1.16460	−0.582298	−	0.812975i	$-0.697846\pi$
$523$	−26.6334	−1.16460	−0.582298	+	0.812975i	$0.697846\pi$
$524$	1.74813	0.0763675
$525$	−0.208498	−0.00909961
$526$	9.99644	0.435865
$527$	−28.2789	−1.23185
$528$	12.9920	0.565403
$529$	−6.61313	−0.287528
$530$	3.16225	0.137359
$531$	25.9131	1.12453
$532$	−12.3610	−0.535916
$533$	−5.82626	−0.252363
$534$	−20.4561	−0.885223
$535$	−15.9673	−0.690327
$536$	−11.5023	−0.496824
$537$	7.06921	0.305059
$538$	−27.1188	−1.16917
$539$	−106.624	−4.59260
$540$	−23.5776	−1.01462
$541$	−43.6455	−1.87647	−0.938233	−	0.346004i	$-0.887538\pi$
$541$	−43.6455	−1.87647	−0.938233	+	0.346004i	$0.887538\pi$
$542$	7.69507	0.330531
$543$	−15.1203	−0.648875
$544$	−40.2056	−1.72380
$545$	−7.93025	−0.339694
$546$	−35.8028	−1.53222
$547$	0.0780287	0.00333627	0.00166813	−	0.999999i	$-0.499469\pi$
$547$	0.0780287	0.00333627	0.00166813	+	0.999999i	$0.499469\pi$
$548$	−52.8594	−2.25804
$549$	−29.3581	−1.25298
$550$	−0.720633	−0.0307279
$551$	−9.35778	−0.398655
$552$	−3.39878	−0.144662
$553$	−26.1551	−1.11223
$554$	29.1825	1.23985
$555$	14.0085	0.594628
$556$	45.7604	1.94067
$557$	−17.6143	−0.746343	−0.373172	−	0.927762i	$-0.621730\pi$
$557$	−17.6143	−0.746343	−0.373172	+	0.927762i	$0.621730\pi$
$558$	28.5016	1.20657
$559$	−14.7841	−0.625300
$560$	30.0495	1.26982
$561$	−24.2248	−1.02277
$562$	−15.3943	−0.649368
$563$	−13.7769	−0.580628	−0.290314	−	0.956931i	$-0.593760\pi$
$563$	−13.7769	−0.580628	−0.290314	+	0.956931i	$0.593760\pi$
$564$	17.0395	0.717492
$565$	−3.91780	−0.164823
$566$	42.8562	1.80138
$567$	−19.5919	−0.822784
$568$	−15.2200	−0.638615
$569$	−6.52933	−0.273724	−0.136862	−	0.990590i	$-0.543702\pi$
$569$	−6.52933	−0.273724	−0.136862	+	0.990590i	$0.543702\pi$
$570$	3.69087	0.154593
$571$	−16.7526	−0.701075	−0.350538	−	0.936549i	$-0.614001\pi$
$571$	−16.7526	−0.701075	−0.350538	+	0.936549i	$0.614001\pi$
$572$	−68.8871	−2.88031
$573$	12.4472	0.519990
$574$	13.7456	0.573731
$575$	−0.221872	−0.00925271
$576$	27.4733	1.14472
$577$	−13.8483	−0.576511	−0.288256	−	0.957554i	$-0.593075\pi$
$577$	−13.8483	−0.576511	−0.288256	+	0.957554i	$0.593075\pi$
$578$	18.3467	0.763120
$579$	0.916968	0.0381079
$580$	−52.8383	−2.19399
$581$	26.4316	1.09657
$582$	3.74119	0.155077
$583$	−4.09909	−0.169767
$584$	−7.32292	−0.303024
$585$	−23.9361	−0.989636
$586$	−36.4401	−1.50533
$587$	30.4524	1.25690	0.628452	−	0.777848i	$-0.283689\pi$
$587$	30.4524	1.25690	0.628452	+	0.777848i	$0.283689\pi$
$588$	33.4344	1.37881
$589$	−5.58499	−0.230126
$590$	−51.5040	−2.12039
$591$	−12.5132	−0.514723
$592$	−21.8916	−0.899738
$593$	−28.6493	−1.17648	−0.588242	−	0.808685i	$-0.700180\pi$
$593$	−28.6493	−1.17648	−0.588242	+	0.808685i	$0.700180\pi$
$594$	54.9014	2.25263
$595$	−56.0301	−2.29701
$596$	32.4701	1.33003
$597$	−0.589900	−0.0241430
$598$	−38.0994	−1.55800
$599$	3.89517	0.159152	0.0795762	−	0.996829i	$-0.474643\pi$
$599$	3.89517	0.159152	0.0795762	+	0.996829i	$0.474643\pi$
$600$	0.0460182	0.00187869
$601$	−47.3149	−1.93002	−0.965008	−	0.262222i	$-0.915545\pi$
$601$	−47.3149	−1.93002	−0.965008	+	0.262222i	$0.915545\pi$
$602$	34.8794	1.42158
$603$	25.4400	1.03600
$604$	47.4273	1.92979
$605$	61.4189	2.49703
$606$	15.3251	0.622540
$607$	−21.5682	−0.875425	−0.437713	−	0.899115i	$-0.644211\pi$
$607$	−21.5682	−0.875425	−0.437713	+	0.899115i	$0.644211\pi$
$608$	−7.94047	−0.322029
$609$	35.5975	1.44249
$610$	58.3513	2.36257
$611$	38.8980	1.57364
$612$	−30.5529	−1.23503
$613$	−36.3024	−1.46624	−0.733120	−	0.680099i	$-0.761937\pi$
$613$	−36.3024	−1.46624	−0.733120	+	0.680099i	$0.761937\pi$
$614$	−8.37078	−0.337817
$615$	−2.28480	−0.0921320
$616$	33.0969	1.33351
$617$	−15.0748	−0.606889	−0.303444	−	0.952849i	$-0.598137\pi$
$617$	−15.0748	−0.606889	−0.303444	+	0.952849i	$0.598137\pi$
$618$	−3.40956	−0.137153
$619$	2.23676	0.0899029	0.0449515	−	0.998989i	$-0.485687\pi$
$619$	2.23676	0.0899029	0.0449515	+	0.998989i	$0.485687\pi$
$620$	−31.5354	−1.26649
$621$	16.9033	0.678307
$622$	−10.8813	−0.436301
$623$	61.3305	2.45715
$624$	−9.30006	−0.372300
$625$	−25.2710	−1.01084
$626$	73.6372	2.94313
$627$	−4.78431	−0.191067
$628$	−5.73125	−0.228702
$629$	40.8189	1.62756
$630$	56.4713	2.24987
$631$	−5.61146	−0.223389	−0.111694	−	0.993743i	$-0.535628\pi$
$631$	−5.61146	−0.223389	−0.111694	+	0.993743i	$0.535628\pi$
$632$	5.77278	0.229629
$633$	0.772891	0.0307196
$634$	−36.6004	−1.45359
$635$	46.9497	1.86314
$636$	1.28537	0.0509681
$637$	76.3245	3.02409
$638$	123.036	4.87104
$639$	33.6624	1.33166
$640$	−18.9000	−0.747088
$641$	17.9698	0.709764	0.354882	−	0.934911i	$-0.384521\pi$
$641$	17.9698	0.709764	0.354882	+	0.934911i	$0.384521\pi$
$642$	−11.6588	−0.460138
$643$	1.38033	0.0544348	0.0272174	−	0.999630i	$-0.491335\pi$
$643$	1.38033	0.0544348	0.0272174	+	0.999630i	$0.491335\pi$
$644$	50.0381	1.97178
$645$	−5.79766	−0.228283
$646$	10.7547	0.423137
$647$	−9.86753	−0.387933	−0.193966	−	0.981008i	$-0.562135\pi$
$647$	−9.86753	−0.387933	−0.193966	+	0.981008i	$0.562135\pi$
$648$	4.32420	0.169870
$649$	66.7625	2.62066
$650$	0.515852	0.0202334
$651$	21.2456	0.832682
$652$	27.1936	1.06498
$653$	15.6403	0.612050	0.306025	−	0.952023i	$-0.401001\pi$
$653$	15.6403	0.612050	0.306025	+	0.952023i	$0.401001\pi$
$654$	−5.79042	−0.226423
$655$	1.56496	0.0611480
$656$	3.57053	0.139406
$657$	16.1963	0.631878
$658$	−91.7702	−3.57758
$659$	18.5533	0.722734	0.361367	−	0.932424i	$-0.382310\pi$
$659$	18.5533	0.722734	0.361367	+	0.932424i	$0.382310\pi$
$660$	−27.0144	−1.05154
$661$	8.22920	0.320079	0.160039	−	0.987111i	$-0.448838\pi$
$661$	8.22920	0.320079	0.160039	+	0.987111i	$0.448838\pi$
$662$	3.86740	0.150311
$663$	17.3408	0.673462
$664$	−5.83379	−0.226395
$665$	−11.0658	−0.429112
$666$	−41.1404	−1.59416
$667$	37.8809	1.46676
$668$	1.67277	0.0647215
$669$	−10.3799	−0.401310
$670$	−50.5636	−1.95344
$671$	−75.6383	−2.91998
$672$	30.2060	1.16522
$673$	−41.3746	−1.59487	−0.797437	−	0.603403i	$-0.793811\pi$
$673$	−41.3746	−1.59487	−0.797437	+	0.603403i	$0.793811\pi$
$674$	−60.4852	−2.32980
$675$	−0.228865	−0.00880901
$676$	16.6627	0.640875
$677$	−19.7034	−0.757264	−0.378632	−	0.925547i	$-0.623605\pi$
$677$	−19.7034	−0.757264	−0.378632	+	0.925547i	$0.623605\pi$
$678$	−2.86065	−0.109863
$679$	−11.2166	−0.430455
$680$	12.3666	0.474236
$681$	12.5538	0.481062
$682$	73.4314	2.81183
$683$	−0.401024	−0.0153448	−0.00767238	−	0.999971i	$-0.502442\pi$
$683$	−0.401024	−0.0153448	−0.00767238	+	0.999971i	$0.502442\pi$
$684$	−6.03410	−0.230720
$685$	−47.3206	−1.80803
$686$	−106.890	−4.08108
$687$	9.11740	0.347851
$688$	9.06019	0.345416
$689$	2.93426	0.111786
$690$	−14.9409	−0.568790
$691$	−14.0148	−0.533147	−0.266574	−	0.963815i	$-0.585892\pi$
$691$	−14.0148	−0.533147	−0.266574	+	0.963815i	$0.585892\pi$
$692$	35.8091	1.36126
$693$	−73.2014	−2.78069
$694$	23.3560	0.886581
$695$	40.9655	1.55391
$696$	−7.85684	−0.297813
$697$	−6.65759	−0.252174
$698$	37.0181	1.40116
$699$	2.16301	0.0818126
$700$	−0.677498	−0.0256070
$701$	27.9370	1.05517	0.527584	−	0.849503i	$-0.323098\pi$
$701$	27.9370	1.05517	0.527584	+	0.849503i	$0.323098\pi$
$702$	−39.3002	−1.48329
$703$	8.06161	0.304049
$704$	70.7821	2.66770
$705$	15.2541	0.574501
$706$	34.9789	1.31645
$707$	−45.9469	−1.72801
$708$	−20.9350	−0.786785
$709$	7.82035	0.293699	0.146850	−	0.989159i	$-0.453087\pi$
$709$	7.82035	0.293699	0.146850	+	0.989159i	$0.453087\pi$
$710$	−66.9062	−2.51095
$711$	−12.7678	−0.478830
$712$	−13.5364	−0.507299
$713$	22.6084	0.846692
$714$	−40.9114	−1.53107
$715$	−61.6689	−2.30629
$716$	22.9708	0.858460
$717$	−18.4948	−0.690702
$718$	−44.9164	−1.67627
$719$	−10.3945	−0.387648	−0.193824	−	0.981036i	$-0.562089\pi$
$719$	−10.3945	−0.387648	−0.193824	+	0.981036i	$0.562089\pi$
$720$	14.6689	0.546676
$721$	10.2224	0.380701
$722$	2.12402	0.0790477
$723$	−9.62034	−0.357784
$724$	−49.1322	−1.82598
$725$	−0.512894	−0.0190484
$726$	44.8462	1.66440
$727$	−14.4079	−0.534359	−0.267180	−	0.963647i	$-0.586092\pi$
$727$	−14.4079	−0.534359	−0.267180	+	0.963647i	$0.586092\pi$
$728$	−23.6918	−0.878077
$729$	0.118019	0.00437106
$730$	−32.1912	−1.19145
$731$	−16.8936	−0.624832
$732$	23.7182	0.876650
$733$	13.9162	0.514005	0.257003	−	0.966411i	$-0.417265\pi$
$733$	13.9162	0.514005	0.257003	+	0.966411i	$0.417265\pi$
$734$	4.10531	0.151530
$735$	29.9311	1.10402
$736$	32.1436	1.18483
$737$	65.5435	2.41432
$738$	6.71003	0.246999
$739$	14.7917	0.544122	0.272061	−	0.962280i	$-0.412295\pi$
$739$	14.7917	0.544122	0.272061	+	0.962280i	$0.412295\pi$
$740$	45.5195	1.67333
$741$	3.42476	0.125812
$742$	−6.92265	−0.254139
$743$	−7.10363	−0.260607	−0.130303	−	0.991474i	$-0.541595\pi$
$743$	−7.10363	−0.260607	−0.130303	+	0.991474i	$0.541595\pi$
$744$	−4.68919	−0.171914
$745$	29.0678	1.06496
$746$	−7.64099	−0.279756
$747$	12.9028	0.472087
$748$	−78.7164	−2.87816
$749$	34.9549	1.27723
$750$	−18.2520	−0.666470
$751$	28.2222	1.02984	0.514921	−	0.857238i	$-0.327821\pi$
$751$	28.2222	1.02984	0.514921	+	0.857238i	$0.327821\pi$
$752$	−23.8380	−0.869283
$753$	−16.4606	−0.599858
$754$	−88.0730	−3.20743
$755$	42.4578	1.54520
$756$	51.6151	1.87722
$757$	23.3313	0.847991	0.423995	−	0.905664i	$-0.360627\pi$
$757$	23.3313	0.847991	0.423995	+	0.905664i	$0.360627\pi$
$758$	−13.4876	−0.489893
$759$	19.3672	0.702986
$760$	2.44236	0.0885936
$761$	17.8307	0.646364	0.323182	−	0.946337i	$-0.395247\pi$
$761$	17.8307	0.646364	0.323182	+	0.946337i	$0.395247\pi$
$762$	34.2813	1.24188
$763$	17.3605	0.628494
$764$	40.4462	1.46329
$765$	−27.3515	−0.988895
$766$	18.8702	0.681809
$767$	−47.7907	−1.72562
$768$	3.87523	0.139835
$769$	−46.1244	−1.66329	−0.831643	−	0.555310i	$-0.812600\pi$
$769$	−46.1244	−1.66329	−0.831643	+	0.555310i	$0.812600\pi$
$770$	145.493	5.24319
$771$	−13.4452	−0.484216
$772$	2.97961	0.107239
$773$	−44.2755	−1.59248	−0.796239	−	0.604982i	$-0.793180\pi$
$773$	−44.2755	−1.59248	−0.796239	+	0.604982i	$0.793180\pi$
$774$	17.0266	0.612009
$775$	−0.306110	−0.0109958
$776$	2.47566	0.0888709
$777$	−30.6668	−1.10017
$778$	62.2709	2.23252
$779$	−1.31485	−0.0471095
$780$	19.3378	0.692403
$781$	86.7277	3.10336
$782$	−43.5357	−1.55683
$783$	39.0748	1.39642
$784$	−46.7742	−1.67051
$785$	−5.13072	−0.183123
$786$	1.14268	0.0407582
$787$	16.4878	0.587726	0.293863	−	0.955848i	$-0.405059\pi$
$787$	16.4878	0.587726	0.293863	+	0.955848i	$0.405059\pi$
$788$	−40.6605	−1.44847
$789$	3.63752	0.129499
$790$	25.3769	0.902868
$791$	8.57667	0.304951
$792$	16.1565	0.574096
$793$	54.1443	1.92272
$794$	−71.1373	−2.52457
$795$	1.15068	0.0408106
$796$	−1.91683	−0.0679403
$797$	−15.2648	−0.540706	−0.270353	−	0.962761i	$-0.587140\pi$
$797$	−15.2648	−0.540706	−0.270353	+	0.962761i	$0.587140\pi$
$798$	−8.07988	−0.286025
$799$	44.4482	1.57247
$800$	−0.435212	−0.0153871
$801$	29.9389	1.05784
$802$	−39.0755	−1.37980
$803$	41.7281	1.47255
$804$	−20.5527	−0.724839
$805$	44.7950	1.57882
$806$	−52.5645	−1.85151
$807$	−9.86802	−0.347371
$808$	10.1411	0.356762
$809$	−37.8888	−1.33210	−0.666050	−	0.745907i	$-0.732016\pi$
$809$	−37.8888	−1.33210	−0.666050	+	0.745907i	$0.732016\pi$
$810$	19.0090	0.667907
$811$	−0.956591	−0.0335904	−0.0167952	−	0.999859i	$-0.505346\pi$
$811$	−0.956591	−0.0335904	−0.0167952	+	0.999859i	$0.505346\pi$
$812$	115.671	4.05927
$813$	2.80009	0.0982036
$814$	−105.994	−3.71509
$815$	24.3441	0.852738
$816$	−10.6271	−0.372021
$817$	−3.33643	−0.116727
$818$	−7.38703	−0.258281
$819$	52.3999	1.83100
$820$	−7.42427	−0.259267
$821$	−4.13005	−0.144140	−0.0720699	−	0.997400i	$-0.522960\pi$
$821$	−4.13005	−0.144140	−0.0720699	+	0.997400i	$0.522960\pi$
$822$	−34.5521	−1.20514
$823$	25.3925	0.885126	0.442563	−	0.896737i	$-0.354069\pi$
$823$	25.3925	0.885126	0.442563	+	0.896737i	$0.354069\pi$
$824$	−2.25621	−0.0785988
$825$	−0.262225	−0.00912951
$826$	112.750	3.92309
$827$	38.6562	1.34421	0.672105	−	0.740456i	$-0.265391\pi$
$827$	38.6562	1.34421	0.672105	+	0.740456i	$0.265391\pi$
$828$	24.4265	0.848878
$829$	−21.5026	−0.746817	−0.373409	−	0.927667i	$-0.621811\pi$
$829$	−21.5026	−0.746817	−0.373409	+	0.927667i	$0.621811\pi$
$830$	−25.6451	−0.890154
$831$	10.6190	0.368368
$832$	−50.6681	−1.75660
$833$	87.2150	3.02182
$834$	29.9118	1.03576
$835$	1.49750	0.0518230
$836$	−15.5462	−0.537678
$837$	23.3210	0.806091
$838$	−31.0443	−1.07241
$839$	26.3176	0.908584	0.454292	−	0.890853i	$-0.349892\pi$
$839$	26.3176	0.908584	0.454292	+	0.890853i	$0.349892\pi$
$840$	−9.29087	−0.320566
$841$	58.5680	2.01959
$842$	3.48659	0.120156
$843$	−5.60169	−0.192933
$844$	2.51145	0.0864475
$845$	14.9168	0.513153
$846$	−44.7983	−1.54020
$847$	−134.456	−4.61995
$848$	−1.79821	−0.0617508
$849$	15.5946	0.535204
$850$	0.589458	0.0202182
$851$	−32.6339	−1.11868
$852$	−27.1956	−0.931705
$853$	−35.4385	−1.21339	−0.606696	−	0.794934i	$-0.707505\pi$
$853$	−35.4385	−1.21339	−0.606696	+	0.794934i	$0.707505\pi$
$854$	−127.740	−4.37117
$855$	−5.40183	−0.184739
$856$	−7.71501	−0.263694
$857$	−21.3616	−0.729698	−0.364849	−	0.931067i	$-0.618879\pi$
$857$	−21.3616	−0.729698	−0.364849	+	0.931067i	$0.618879\pi$
$858$	−45.0288	−1.53726
$859$	38.1499	1.30166	0.650828	−	0.759225i	$-0.274422\pi$
$859$	38.1499	1.30166	0.650828	+	0.759225i	$0.274422\pi$
$860$	−18.8390	−0.642405
$861$	5.00178	0.170460
$862$	−37.0524	−1.26201
$863$	37.0063	1.25971	0.629855	−	0.776712i	$-0.283114\pi$
$863$	37.0063	1.25971	0.629855	+	0.776712i	$0.283114\pi$
$864$	33.1566	1.12801
$865$	32.0569	1.08997
$866$	35.5814	1.20910
$867$	6.67601	0.226729
$868$	69.0360	2.34323
$869$	−32.8950	−1.11589
$870$	−34.5383	−1.17096
$871$	−46.9181	−1.58976
$872$	−3.83170	−0.129758
$873$	−5.47548	−0.185317
$874$	−8.59817	−0.290837
$875$	54.7223	1.84995
$876$	−13.0849	−0.442096
$877$	−11.2550	−0.380053	−0.190027	−	0.981779i	$-0.560857\pi$
$877$	−11.2550	−0.380053	−0.190027	+	0.981779i	$0.560857\pi$
$878$	82.9044	2.79789
$879$	−13.2599	−0.447245
$880$	37.7928	1.27400
$881$	28.6750	0.966085	0.483043	−	0.875597i	$-0.339532\pi$
$881$	28.6750	0.966085	0.483043	+	0.875597i	$0.339532\pi$
$882$	−87.9019	−2.95981
$883$	10.2646	0.345431	0.172716	−	0.984972i	$-0.444746\pi$
$883$	10.2646	0.345431	0.172716	+	0.984972i	$0.444746\pi$
$884$	56.3476	1.89518
$885$	−18.7414	−0.629985
$886$	−63.7509	−2.14175
$887$	−5.71113	−0.191761	−0.0958805	−	0.995393i	$-0.530567\pi$
$887$	−5.71113	−0.191761	−0.0958805	+	0.995393i	$0.530567\pi$
$888$	6.76857	0.227138
$889$	−102.780	−3.44714
$890$	−59.5056	−1.99463
$891$	−24.6405	−0.825489
$892$	−33.7286	−1.12932
$893$	8.77839	0.293758
$894$	21.2244	0.709851
$895$	20.5639	0.687375
$896$	41.3751	1.38224
$897$	−13.8637	−0.462895
$898$	−9.48006	−0.316354
$899$	52.2631	1.74307
$900$	−0.330725	−0.0110242
$901$	3.35294	0.111702
$902$	17.2877	0.575617
$903$	12.6920	0.422363
$904$	−1.89298	−0.0629596
$905$	−43.9840	−1.46208
$906$	31.0014	1.02995
$907$	42.8815	1.42386	0.711928	−	0.702252i	$-0.247822\pi$
$907$	42.8815	1.42386	0.711928	+	0.702252i	$0.247822\pi$
$908$	40.7925	1.35375
$909$	−22.4293	−0.743934
$910$	−104.148	−3.45248
$911$	45.1310	1.49526	0.747629	−	0.664117i	$-0.231192\pi$
$911$	45.1310	1.49526	0.747629	+	0.664117i	$0.231192\pi$
$912$	−2.09881	−0.0694986
$913$	33.2426	1.10017
$914$	−52.6908	−1.74286
$915$	21.2330	0.701940
$916$	29.6263	0.978879
$917$	−3.42594	−0.113135
$918$	−44.9078	−1.48218
$919$	13.7865	0.454774	0.227387	−	0.973805i	$-0.426982\pi$
$919$	13.7865	0.454774	0.227387	+	0.973805i	$0.426982\pi$
$920$	−9.88684	−0.325959
$921$	−3.04597	−0.100368
$922$	2.86322	0.0942951
$923$	−62.0824	−2.04347
$924$	59.1388	1.94552
$925$	0.441852	0.0145280
$926$	−33.3703	−1.09662
$927$	4.99012	0.163897
$928$	74.3052	2.43919
$929$	22.4151	0.735417	0.367709	−	0.929941i	$-0.380142\pi$
$929$	22.4151	0.735417	0.367709	+	0.929941i	$0.380142\pi$
$930$	−20.6135	−0.675942
$931$	17.2247	0.564517
$932$	7.02853	0.230227
$933$	−3.95951	−0.129629
$934$	−23.1779	−0.758404
$935$	−70.4683	−2.30456
$936$	−11.5653	−0.378025
$937$	−11.7817	−0.384892	−0.192446	−	0.981308i	$-0.561642\pi$
$937$	−11.7817	−0.384892	−0.192446	+	0.981308i	$0.561642\pi$
$938$	110.692	3.61421
$939$	26.7952	0.874429
$940$	49.5668	1.61669
$941$	−4.66073	−0.151935	−0.0759677	−	0.997110i	$-0.524205\pi$
$941$	−4.66073	−0.151935	−0.0759677	+	0.997110i	$0.524205\pi$
$942$	−3.74629	−0.122061
$943$	5.32262	0.173328
$944$	29.2878	0.953236
$945$	46.2068	1.50311
$946$	43.8674	1.42625
$947$	−37.0083	−1.20261	−0.601305	−	0.799020i	$-0.705352\pi$
$947$	−37.0083	−1.20261	−0.601305	+	0.799020i	$0.705352\pi$
$948$	10.3150	0.335016
$949$	−29.8703	−0.969631
$950$	0.116416	0.00377704
$951$	−13.3182	−0.431873
$952$	−27.0723	−0.877420
$953$	33.8964	1.09801	0.549006	−	0.835819i	$-0.315006\pi$
$953$	33.8964	1.09801	0.549006	+	0.835819i	$0.315006\pi$
$954$	−3.37934	−0.109410
$955$	36.2081	1.17167
$956$	−60.0975	−1.94369
$957$	44.7706	1.44723
$958$	72.4592	2.34105
$959$	103.592	3.34517
$960$	−19.8698	−0.641294
$961$	0.192128	0.00619767
$962$	75.8738	2.44627
$963$	17.0635	0.549864
$964$	−31.2605	−1.00683
$965$	2.66740	0.0858667
$966$	32.7079	1.05236
$967$	38.9051	1.25110	0.625552	−	0.780182i	$-0.284874\pi$
$967$	38.9051	1.25110	0.625552	+	0.780182i	$0.284874\pi$
$968$	29.6761	0.953825
$969$	3.91343	0.125718
$970$	10.8829	0.349428
$971$	−6.98999	−0.224319	−0.112160	−	0.993690i	$-0.535777\pi$
$971$	−6.98999	−0.224319	−0.112160	+	0.993690i	$0.535777\pi$
$972$	39.1874	1.25694
$973$	−89.6799	−2.87501
$974$	−67.7197	−2.16988
$975$	0.187709	0.00601150
$976$	−33.1814	−1.06211
$977$	60.2266	1.92682	0.963409	−	0.268035i	$-0.0863744\pi$
$977$	60.2266	1.92682	0.963409	+	0.268035i	$0.0863744\pi$
$978$	17.7753	0.568393
$979$	77.1346	2.46523
$980$	97.2585	3.10681
$981$	8.47467	0.270575
$982$	36.1692	1.15421
$983$	−4.92607	−0.157117	−0.0785587	−	0.996909i	$-0.525032\pi$
$983$	−4.92607	−0.157117	−0.0785587	+	0.996909i	$0.525032\pi$
$984$	−1.10396	−0.0351929
$985$	−36.4000	−1.15980
$986$	−100.640	−3.20503
$987$	−33.3935	−1.06293
$988$	11.1285	0.354044
$989$	13.5061	0.429469
$990$	71.0232	2.25727
$991$	−43.2309	−1.37327	−0.686637	−	0.727001i	$-0.740914\pi$
$991$	−43.2309	−1.37327	−0.686637	+	0.727001i	$0.740914\pi$
$992$	44.3475	1.40803
$993$	1.40727	0.0446585
$994$	146.468	4.64569
$995$	−1.71598	−0.0544003
$996$	−10.4240	−0.330298
$997$	−25.9673	−0.822393	−0.411196	−	0.911547i	$-0.634889\pi$
$997$	−25.9673	−0.822393	−0.411196	+	0.911547i	$0.634889\pi$
$998$	10.7938	0.341671
$999$	−33.6625	−1.06503

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4009.2.a.c.1.63	✓	71

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4009.2.a.c.1.63	✓	71	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:	\( N \)	\(=\)	\( 4009 = 19 \cdot 211 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4009.a (trivial)

\(f(q)\)	\(=\)	\(q+2.12402 q^{2} +0.772891 q^{3} +2.51145 q^{4} +2.24829 q^{5} +1.64163 q^{6} -4.92186 q^{7} +1.08632 q^{8} -2.40264 q^{9} +O(q^{10})\)	\(q+2.12402 q^{2} +0.772891 q^{3} +2.51145 q^{4} +2.24829 q^{5} +1.64163 q^{6} -4.92186 q^{7} +1.08632 q^{8} -2.40264 q^{9} +4.77541 q^{10} -6.19016 q^{11} +1.94107 q^{12} +4.43111 q^{13} -10.4541 q^{14} +1.73768 q^{15} -2.71553 q^{16} +5.06337 q^{17} -5.10325 q^{18} +1.00000 q^{19} +5.64646 q^{20} -3.80406 q^{21} -13.1480 q^{22} -4.04807 q^{23} +0.839605 q^{24} +0.0548094 q^{25} +9.41175 q^{26} -4.17565 q^{27} -12.3610 q^{28} -9.35778 q^{29} +3.69087 q^{30} -5.58499 q^{31} -7.94047 q^{32} -4.78431 q^{33} +10.7547 q^{34} -11.0658 q^{35} -6.03410 q^{36} +8.06161 q^{37} +2.12402 q^{38} +3.42476 q^{39} +2.44236 q^{40} -1.31485 q^{41} -8.07988 q^{42} -3.33643 q^{43} -15.5462 q^{44} -5.40183 q^{45} -8.59817 q^{46} +8.77839 q^{47} -2.09881 q^{48} +17.2247 q^{49} +0.116416 q^{50} +3.91343 q^{51} +11.1285 q^{52} +0.662194 q^{53} -8.86915 q^{54} -13.9173 q^{55} -5.34670 q^{56} +0.772891 q^{57} -19.8761 q^{58} -10.7853 q^{59} +4.36409 q^{60} +12.2191 q^{61} -11.8626 q^{62} +11.8255 q^{63} -11.4346 q^{64} +9.96242 q^{65} -10.1620 q^{66} -10.5883 q^{67} +12.7164 q^{68} -3.12872 q^{69} -23.5039 q^{70} -14.0106 q^{71} -2.61003 q^{72} -6.74104 q^{73} +17.1230 q^{74} +0.0423617 q^{75} +2.51145 q^{76} +30.4671 q^{77} +7.27425 q^{78} +5.31408 q^{79} -6.10531 q^{80} +3.98060 q^{81} -2.79277 q^{82} -5.37024 q^{83} -9.55369 q^{84} +11.3839 q^{85} -7.08663 q^{86} -7.23254 q^{87} -6.72448 q^{88} -12.4608 q^{89} -11.4736 q^{90} -21.8093 q^{91} -10.1665 q^{92} -4.31659 q^{93} +18.6454 q^{94} +2.24829 q^{95} -6.13712 q^{96} +2.27894 q^{97} +36.5855 q^{98} +14.8727 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 71 q - 15 q^{2} - 8 q^{3} + 69 q^{4} - 18 q^{5} - 9 q^{6} - 19 q^{7} - 39 q^{8} + 63 q^{9}+O(q^{10}) \) 71 * q - 15 * q^2 - 8 * q^3 + 69 * q^4 - 18 * q^5 - 9 * q^6 - 19 * q^7 - 39 * q^8 + 63 * q^9	\( 71 q - 15 q^{2} - 8 q^{3} + 69 q^{4} - 18 q^{5} - 9 q^{6} - 19 q^{7} - 39 q^{8} + 63 q^{9} - 10 q^{10} - 52 q^{11} - 9 q^{12} - 15 q^{13} - 53 q^{14} - 33 q^{15} + 53 q^{16} - 10 q^{17} - 35 q^{18} + 71 q^{19} - 33 q^{20} - 38 q^{21} - 6 q^{22} - 65 q^{23} - 30 q^{24} + 51 q^{25} - 4 q^{26} - 23 q^{27} - 29 q^{28} - 97 q^{29} - 27 q^{30} - 53 q^{31} - 78 q^{32} - 17 q^{33} - 24 q^{34} - 38 q^{35} + 24 q^{36} - 33 q^{37} - 15 q^{38} - 86 q^{39} + 25 q^{40} - 69 q^{41} + 64 q^{42} - 10 q^{43} - 94 q^{44} - 34 q^{45} - 6 q^{46} - 37 q^{47} - q^{48} + 74 q^{49} - 41 q^{50} - 46 q^{51} - 30 q^{52} - 50 q^{53} - 17 q^{54} - 30 q^{55} - 116 q^{56} - 8 q^{57} + 11 q^{58} - 93 q^{59} - 56 q^{60} - 18 q^{61} - q^{62} - 84 q^{63} + 93 q^{64} - 78 q^{65} - 53 q^{66} - 5 q^{67} - 9 q^{68} - 69 q^{69} - 10 q^{70} - 221 q^{71} - 73 q^{72} - 34 q^{73} - 58 q^{74} - 70 q^{75} + 69 q^{76} - 2 q^{77} + 7 q^{78} - 68 q^{79} - 71 q^{80} + 39 q^{81} + 26 q^{82} - 45 q^{83} - 10 q^{84} - 44 q^{85} - 80 q^{86} - 7 q^{87} - 46 q^{88} - 143 q^{89} + 41 q^{90} - 30 q^{91} - 46 q^{92} + 32 q^{93} + 41 q^{94} - 18 q^{95} - 140 q^{96} - 18 q^{97} - 97 q^{98} - 142 q^{99}+O(q^{100}) \) 71 * q - 15 * q^2 - 8 * q^3 + 69 * q^4 - 18 * q^5 - 9 * q^6 - 19 * q^7 - 39 * q^8 + 63 * q^9 - 10 * q^10 - 52 * q^11 - 9 * q^12 - 15 * q^13 - 53 * q^14 - 33 * q^15 + 53 * q^16 - 10 * q^17 - 35 * q^18 + 71 * q^19 - 33 * q^20 - 38 * q^21 - 6 * q^22 - 65 * q^23 - 30 * q^24 + 51 * q^25 - 4 * q^26 - 23 * q^27 - 29 * q^28 - 97 * q^29 - 27 * q^30 - 53 * q^31 - 78 * q^32 - 17 * q^33 - 24 * q^34 - 38 * q^35 + 24 * q^36 - 33 * q^37 - 15 * q^38 - 86 * q^39 + 25 * q^40 - 69 * q^41 + 64 * q^42 - 10 * q^43 - 94 * q^44 - 34 * q^45 - 6 * q^46 - 37 * q^47 - q^48 + 74 * q^49 - 41 * q^50 - 46 * q^51 - 30 * q^52 - 50 * q^53 - 17 * q^54 - 30 * q^55 - 116 * q^56 - 8 * q^57 + 11 * q^58 - 93 * q^59 - 56 * q^60 - 18 * q^61 - q^62 - 84 * q^63 + 93 * q^64 - 78 * q^65 - 53 * q^66 - 5 * q^67 - 9 * q^68 - 69 * q^69 - 10 * q^70 - 221 * q^71 - 73 * q^72 - 34 * q^73 - 58 * q^74 - 70 * q^75 + 69 * q^76 - 2 * q^77 + 7 * q^78 - 68 * q^79 - 71 * q^80 + 39 * q^81 + 26 * q^82 - 45 * q^83 - 10 * q^84 - 44 * q^85 - 80 * q^86 - 7 * q^87 - 46 * q^88 - 143 * q^89 + 41 * q^90 - 30 * q^91 - 46 * q^92 + 32 * q^93 + 41 * q^94 - 18 * q^95 - 140 * q^96 - 18 * q^97 - 97 * q^98 - 142 * q^99

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