LMFDB - Embedded newform 4034.2.a.b.1.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4034,2,Mod(1,4034)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4034, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("4034.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4034 = 2 \cdot 2017 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4034.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:	$32.2116521754$
Analytic rank:	$1$
Dimension:	$35$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.12
Character	$\chi$	$=$	4034.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -1.52925 q^{3} +1.00000 q^{4} +3.51675 q^{5} +1.52925 q^{6} -1.62140 q^{7} -1.00000 q^{8} -0.661396 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -1.52925 q^{3} +1.00000 q^{4} +3.51675 q^{5} +1.52925 q^{6} -1.62140 q^{7} -1.00000 q^{8} -0.661396 q^{9} -3.51675 q^{10} -5.23264 q^{11} -1.52925 q^{12} -0.449585 q^{13} +1.62140 q^{14} -5.37799 q^{15} +1.00000 q^{16} +1.78853 q^{17} +0.661396 q^{18} -1.93746 q^{19} +3.51675 q^{20} +2.47952 q^{21} +5.23264 q^{22} -0.570770 q^{23} +1.52925 q^{24} +7.36753 q^{25} +0.449585 q^{26} +5.59919 q^{27} -1.62140 q^{28} +2.33634 q^{29} +5.37799 q^{30} +7.15712 q^{31} -1.00000 q^{32} +8.00202 q^{33} -1.78853 q^{34} -5.70205 q^{35} -0.661396 q^{36} +0.308958 q^{37} +1.93746 q^{38} +0.687527 q^{39} -3.51675 q^{40} +12.6313 q^{41} -2.47952 q^{42} +8.05384 q^{43} -5.23264 q^{44} -2.32597 q^{45} +0.570770 q^{46} -1.84675 q^{47} -1.52925 q^{48} -4.37107 q^{49} -7.36753 q^{50} -2.73511 q^{51} -0.449585 q^{52} -1.51873 q^{53} -5.59919 q^{54} -18.4019 q^{55} +1.62140 q^{56} +2.96286 q^{57} -2.33634 q^{58} +0.0896840 q^{59} -5.37799 q^{60} -8.72770 q^{61} -7.15712 q^{62} +1.07239 q^{63} +1.00000 q^{64} -1.58108 q^{65} -8.00202 q^{66} -2.67065 q^{67} +1.78853 q^{68} +0.872849 q^{69} +5.70205 q^{70} -6.78228 q^{71} +0.661396 q^{72} -8.78213 q^{73} -0.308958 q^{74} -11.2668 q^{75} -1.93746 q^{76} +8.48420 q^{77} -0.687527 q^{78} -6.71761 q^{79} +3.51675 q^{80} -6.57837 q^{81} -12.6313 q^{82} -4.78396 q^{83} +2.47952 q^{84} +6.28981 q^{85} -8.05384 q^{86} -3.57285 q^{87} +5.23264 q^{88} +2.06724 q^{89} +2.32597 q^{90} +0.728956 q^{91} -0.570770 q^{92} -10.9450 q^{93} +1.84675 q^{94} -6.81355 q^{95} +1.52925 q^{96} +0.506652 q^{97} +4.37107 q^{98} +3.46085 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 35 q - 35 q^{2} - 6 q^{3} + 35 q^{4} + 6 q^{5} + 6 q^{6} - 14 q^{7} - 35 q^{8} + 23 q^{9}+O(q^{10}) $ 35 * q - 35 * q^2 - 6 * q^3 + 35 * q^4 + 6 * q^5 + 6 * q^6 - 14 * q^7 - 35 * q^8 + 23 * q^9	\( 35 q - 35 q^{2} - 6 q^{3} + 35 q^{4} + 6 q^{5} + 6 q^{6} - 14 q^{7} - 35 q^{8} + 23 q^{9} - 6 q^{10} - 9 q^{11} - 6 q^{12} - 7 q^{13} + 14 q^{14} - 19 q^{15} + 35 q^{16} + 17 q^{17} - 23 q^{18} - 25 q^{19} + 6 q^{20} - 15 q^{21} + 9 q^{22} - 12 q^{23} + 6 q^{24} + 7 q^{25} + 7 q^{26} - 27 q^{27} - 14 q^{28} - 13 q^{29} + 19 q^{30} - 69 q^{31} - 35 q^{32} + q^{33} - 17 q^{34} - 4 q^{35} + 23 q^{36} - 22 q^{37} + 25 q^{38} - 38 q^{39} - 6 q^{40} + 15 q^{42} - 32 q^{43} - 9 q^{44} + 9 q^{45} + 12 q^{46} - 18 q^{47} - 6 q^{48} - 19 q^{49} - 7 q^{50} - 21 q^{51} - 7 q^{52} + 20 q^{53} + 27 q^{54} - 54 q^{55} + 14 q^{56} + 28 q^{57} + 13 q^{58} - 21 q^{59} - 19 q^{60} - 67 q^{61} + 69 q^{62} - 28 q^{63} + 35 q^{64} + 22 q^{65} - q^{66} - 18 q^{67} + 17 q^{68} - 42 q^{69} + 4 q^{70} - 36 q^{71} - 23 q^{72} - 18 q^{73} + 22 q^{74} - 49 q^{75} - 25 q^{76} + 20 q^{77} + 38 q^{78} - 92 q^{79} + 6 q^{80} - 25 q^{81} + 42 q^{83} - 15 q^{84} - 29 q^{85} + 32 q^{86} - 40 q^{87} + 9 q^{88} - 8 q^{89} - 9 q^{90} - 89 q^{91} - 12 q^{92} - q^{93} + 18 q^{94} - 62 q^{95} + 6 q^{96} - 40 q^{97} + 19 q^{98} - 64 q^{99}+O(q^{100}) \) 35 * q - 35 * q^2 - 6 * q^3 + 35 * q^4 + 6 * q^5 + 6 * q^6 - 14 * q^7 - 35 * q^8 + 23 * q^9 - 6 * q^10 - 9 * q^11 - 6 * q^12 - 7 * q^13 + 14 * q^14 - 19 * q^15 + 35 * q^16 + 17 * q^17 - 23 * q^18 - 25 * q^19 + 6 * q^20 - 15 * q^21 + 9 * q^22 - 12 * q^23 + 6 * q^24 + 7 * q^25 + 7 * q^26 - 27 * q^27 - 14 * q^28 - 13 * q^29 + 19 * q^30 - 69 * q^31 - 35 * q^32 + q^33 - 17 * q^34 - 4 * q^35 + 23 * q^36 - 22 * q^37 + 25 * q^38 - 38 * q^39 - 6 * q^40 + 15 * q^42 - 32 * q^43 - 9 * q^44 + 9 * q^45 + 12 * q^46 - 18 * q^47 - 6 * q^48 - 19 * q^49 - 7 * q^50 - 21 * q^51 - 7 * q^52 + 20 * q^53 + 27 * q^54 - 54 * q^55 + 14 * q^56 + 28 * q^57 + 13 * q^58 - 21 * q^59 - 19 * q^60 - 67 * q^61 + 69 * q^62 - 28 * q^63 + 35 * q^64 + 22 * q^65 - q^66 - 18 * q^67 + 17 * q^68 - 42 * q^69 + 4 * q^70 - 36 * q^71 - 23 * q^72 - 18 * q^73 + 22 * q^74 - 49 * q^75 - 25 * q^76 + 20 * q^77 + 38 * q^78 - 92 * q^79 + 6 * q^80 - 25 * q^81 + 42 * q^83 - 15 * q^84 - 29 * q^85 + 32 * q^86 - 40 * q^87 + 9 * q^88 - 8 * q^89 - 9 * q^90 - 89 * q^91 - 12 * q^92 - q^93 + 18 * q^94 - 62 * q^95 + 6 * q^96 - 40 * q^97 + 19 * q^98 - 64 * 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 $

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	−1.52925	−0.882913	−0.441456	−	0.897283i	$-0.645538\pi$
$3$	−1.52925	−0.882913	−0.441456	+	0.897283i	$0.645538\pi$
$4$	1.00000	0.500000
$5$	3.51675	1.57274	0.786369	−	0.617757i	$-0.211958\pi$
$5$	3.51675	1.57274	0.786369	+	0.617757i	$0.211958\pi$
$6$	1.52925	0.624313
$7$	−1.62140	−0.612831	−0.306415	−	0.951898i	$-0.599130\pi$
$7$	−1.62140	−0.612831	−0.306415	+	0.951898i	$0.599130\pi$
$8$	−1.00000	−0.353553
$9$	−0.661396	−0.220465
$10$	−3.51675	−1.11209
$11$	−5.23264	−1.57770	−0.788851	−	0.614585i	$-0.789323\pi$
$11$	−5.23264	−1.57770	−0.788851	+	0.614585i	$0.789323\pi$
$12$	−1.52925	−0.441456
$13$	−0.449585	−0.124692	−0.0623462	−	0.998055i	$-0.519858\pi$
$13$	−0.449585	−0.124692	−0.0623462	+	0.998055i	$0.519858\pi$
$14$	1.62140	0.433337
$15$	−5.37799	−1.38859
$16$	1.00000	0.250000
$17$	1.78853	0.433782	0.216891	−	0.976196i	$-0.430408\pi$
$17$	1.78853	0.433782	0.216891	+	0.976196i	$0.430408\pi$
$18$	0.661396	0.155893
$19$	−1.93746	−0.444483	−0.222242	−	0.974992i	$-0.571337\pi$
$19$	−1.93746	−0.444483	−0.222242	+	0.974992i	$0.571337\pi$
$20$	3.51675	0.786369
$21$	2.47952	0.541076
$22$	5.23264	1.11560
$23$	−0.570770	−0.119014	−0.0595068	−	0.998228i	$-0.518953\pi$
$23$	−0.570770	−0.119014	−0.0595068	+	0.998228i	$0.518953\pi$
$24$	1.52925	0.312157
$25$	7.36753	1.47351
$26$	0.449585	0.0881708
$27$	5.59919	1.07756
$28$	−1.62140	−0.306415
$29$	2.33634	0.433848	0.216924	−	0.976189i	$-0.430398\pi$
$29$	2.33634	0.433848	0.216924	+	0.976189i	$0.430398\pi$
$30$	5.37799	0.981882
$31$	7.15712	1.28546	0.642728	−	0.766094i	$-0.277803\pi$
$31$	7.15712	1.28546	0.642728	+	0.766094i	$0.277803\pi$
$32$	−1.00000	−0.176777
$33$	8.00202	1.39297
$34$	−1.78853	−0.306730
$35$	−5.70205	−0.963823
$36$	−0.661396	−0.110233
$37$	0.308958	0.0507923	0.0253962	−	0.999677i	$-0.491915\pi$
$37$	0.308958	0.0507923	0.0253962	+	0.999677i	$0.491915\pi$
$38$	1.93746	0.314297
$39$	0.687527	0.110092
$40$	−3.51675	−0.556047
$41$	12.6313	1.97268	0.986341	−	0.164714i	$-0.0526700\pi$
$41$	12.6313	1.97268	0.986341	+	0.164714i	$0.0526700\pi$
$42$	−2.47952	−0.382599
$43$	8.05384	1.22820	0.614099	−	0.789229i	$-0.289519\pi$
$43$	8.05384	1.22820	0.614099	+	0.789229i	$0.289519\pi$
$44$	−5.23264	−0.788851
$45$	−2.32597	−0.346734
$46$	0.570770	0.0841554
$47$	−1.84675	−0.269376	−0.134688	−	0.990888i	$-0.543003\pi$
$47$	−1.84675	−0.269376	−0.134688	+	0.990888i	$0.543003\pi$
$48$	−1.52925	−0.220728
$49$	−4.37107	−0.624438
$50$	−7.36753	−1.04193
$51$	−2.73511	−0.382992
$52$	−0.449585	−0.0623462
$53$	−1.51873	−0.208613	−0.104307	−	0.994545i	$-0.533262\pi$
$53$	−1.51873	−0.208613	−0.104307	+	0.994545i	$0.533262\pi$
$54$	−5.59919	−0.761953
$55$	−18.4019	−2.48131
$56$	1.62140	0.216668
$57$	2.96286	0.392440
$58$	−2.33634	−0.306777
$59$	0.0896840	0.0116759	0.00583793	−	0.999983i	$-0.498142\pi$
$59$	0.0896840	0.0116759	0.00583793	+	0.999983i	$0.498142\pi$
$60$	−5.37799	−0.694295
$61$	−8.72770	−1.11747	−0.558734	−	0.829347i	$-0.688713\pi$
$61$	−8.72770	−1.11747	−0.558734	+	0.829347i	$0.688713\pi$
$62$	−7.15712	−0.908955
$63$	1.07239	0.135108
$64$	1.00000	0.125000
$65$	−1.58108	−0.196108
$66$	−8.00202	−0.984980
$67$	−2.67065	−0.326271	−0.163136	−	0.986604i	$-0.552161\pi$
$67$	−2.67065	−0.326271	−0.163136	+	0.986604i	$0.552161\pi$
$68$	1.78853	0.216891
$69$	0.872849	0.105079
$70$	5.70205	0.681526
$71$	−6.78228	−0.804909	−0.402454	−	0.915440i	$-0.631843\pi$
$71$	−6.78228	−0.804909	−0.402454	+	0.915440i	$0.631843\pi$
$72$	0.661396	0.0779463
$73$	−8.78213	−1.02787	−0.513935	−	0.857829i	$-0.671813\pi$
$73$	−8.78213	−1.02787	−0.513935	+	0.857829i	$0.671813\pi$
$74$	−0.308958	−0.0359156
$75$	−11.2668	−1.30098
$76$	−1.93746	−0.222242
$77$	8.48420	0.966864
$78$	−0.687527	−0.0778471
$79$	−6.71761	−0.755790	−0.377895	−	0.925848i	$-0.623352\pi$
$79$	−6.71761	−0.755790	−0.377895	+	0.925848i	$0.623352\pi$
$80$	3.51675	0.393185
$81$	−6.57837	−0.730930
$82$	−12.6313	−1.39490
$83$	−4.78396	−0.525107	−0.262554	−	0.964917i	$-0.584565\pi$
$83$	−4.78396	−0.525107	−0.262554	+	0.964917i	$0.584565\pi$
$84$	2.47952	0.270538
$85$	6.28981	0.682226
$86$	−8.05384	−0.868467
$87$	−3.57285	−0.383049
$88$	5.23264	0.557802
$89$	2.06724	0.219127	0.109563	−	0.993980i	$-0.465055\pi$
$89$	2.06724	0.219127	0.109563	+	0.993980i	$0.465055\pi$
$90$	2.32597	0.245178
$91$	0.728956	0.0764153
$92$	−0.570770	−0.0595068
$93$	−10.9450	−1.13495
$94$	1.84675	0.190477
$95$	−6.81355	−0.699056
$96$	1.52925	0.156078
$97$	0.506652	0.0514427	0.0257214	−	0.999669i	$-0.491812\pi$
$97$	0.506652	0.0514427	0.0257214	+	0.999669i	$0.491812\pi$
$98$	4.37107	0.441545
$99$	3.46085	0.347829
$100$	7.36753	0.736753
$101$	−16.5981	−1.65157	−0.825784	−	0.563986i	$-0.809267\pi$
$101$	−16.5981	−1.65157	−0.825784	+	0.563986i	$0.809267\pi$
$102$	2.73511	0.270816
$103$	−10.8064	−1.06478	−0.532391	−	0.846498i	$-0.678706\pi$
$103$	−10.8064	−1.06478	−0.532391	+	0.846498i	$0.678706\pi$
$104$	0.449585	0.0440854
$105$	8.71986	0.850971
$106$	1.51873	0.147512
$107$	−12.8942	−1.24653	−0.623263	−	0.782012i	$-0.714193\pi$
$107$	−12.8942	−1.24653	−0.623263	+	0.782012i	$0.714193\pi$
$108$	5.59919	0.538782
$109$	14.1966	1.35979	0.679894	−	0.733311i	$-0.262026\pi$
$109$	14.1966	1.35979	0.679894	+	0.733311i	$0.262026\pi$
$110$	18.4019	1.75455
$111$	−0.472473	−0.0448452
$112$	−1.62140	−0.153208
$113$	8.25831	0.776876	0.388438	−	0.921475i	$-0.373015\pi$
$113$	8.25831	0.776876	0.388438	+	0.921475i	$0.373015\pi$
$114$	−2.96286	−0.277497
$115$	−2.00725	−0.187177
$116$	2.33634	0.216924
$117$	0.297354	0.0274904
$118$	−0.0896840	−0.00825608
$119$	−2.89992	−0.265835
$120$	5.37799	0.490941
$121$	16.3805	1.48914
$122$	8.72770	0.790169
$123$	−19.3165	−1.74171
$124$	7.15712	0.642728
$125$	8.32602	0.744702
$126$	−1.07239	−0.0955358
$127$	−15.8100	−1.40291	−0.701455	−	0.712714i	$-0.747466\pi$
$127$	−15.8100	−1.40291	−0.701455	+	0.712714i	$0.747466\pi$
$128$	−1.00000	−0.0883883
$129$	−12.3163	−1.08439
$130$	1.58108	0.138670
$131$	0.879636	0.0768542	0.0384271	−	0.999261i	$-0.487765\pi$
$131$	0.879636	0.0768542	0.0384271	+	0.999261i	$0.487765\pi$
$132$	8.00202	0.696486
$133$	3.14139	0.272393
$134$	2.67065	0.230709
$135$	19.6909	1.69473
$136$	−1.78853	−0.153365
$137$	−9.99852	−0.854231	−0.427116	−	0.904197i	$-0.640470\pi$
$137$	−9.99852	−0.854231	−0.427116	+	0.904197i	$0.640470\pi$
$138$	−0.872849	−0.0743019
$139$	5.11939	0.434221	0.217111	−	0.976147i	$-0.430337\pi$
$139$	5.11939	0.434221	0.217111	+	0.976147i	$0.430337\pi$
$140$	−5.70205	−0.481911
$141$	2.82414	0.237835
$142$	6.78228	0.569156
$143$	2.35252	0.196727
$144$	−0.661396	−0.0551164
$145$	8.21633	0.682329
$146$	8.78213	0.726814
$147$	6.68445	0.551324
$148$	0.308958	0.0253962
$149$	0.406202	0.0332773	0.0166387	−	0.999862i	$-0.494704\pi$
$149$	0.406202	0.0332773	0.0166387	+	0.999862i	$0.494704\pi$
$150$	11.2668	0.919930
$151$	−21.4088	−1.74223	−0.871113	−	0.491083i	$-0.836601\pi$
$151$	−21.4088	−1.74223	−0.871113	+	0.491083i	$0.836601\pi$
$152$	1.93746	0.157149
$153$	−1.18293	−0.0956340
$154$	−8.48420	−0.683676
$155$	25.1698	2.02169
$156$	0.687527	0.0550462
$157$	−10.1957	−0.813708	−0.406854	−	0.913493i	$-0.633374\pi$
$157$	−10.1957	−0.813708	−0.406854	+	0.913493i	$0.633374\pi$
$158$	6.71761	0.534424
$159$	2.32251	0.184187
$160$	−3.51675	−0.278024
$161$	0.925445	0.0729353
$162$	6.57837	0.516845
$163$	1.76837	0.138509	0.0692546	−	0.997599i	$-0.477938\pi$
$163$	1.76837	0.138509	0.0692546	+	0.997599i	$0.477938\pi$
$164$	12.6313	0.986341
$165$	28.1411	2.19078
$166$	4.78396	0.371307
$167$	−16.8066	−1.30054	−0.650268	−	0.759705i	$-0.725343\pi$
$167$	−16.8066	−1.30054	−0.650268	+	0.759705i	$0.725343\pi$
$168$	−2.47952	−0.191299
$169$	−12.7979	−0.984452
$170$	−6.28981	−0.482407
$171$	1.28143	0.0979932
$172$	8.05384	0.614099
$173$	9.83941	0.748077	0.374038	−	0.927413i	$-0.377973\pi$
$173$	9.83941	0.748077	0.374038	+	0.927413i	$0.377973\pi$
$174$	3.57285	0.270857
$175$	−11.9457	−0.903010
$176$	−5.23264	−0.394425
$177$	−0.137149	−0.0103088
$178$	−2.06724	−0.154946
$179$	−11.1180	−0.830996	−0.415498	−	0.909594i	$-0.636393\pi$
$179$	−11.1180	−0.830996	−0.415498	+	0.909594i	$0.636393\pi$
$180$	−2.32597	−0.173367
$181$	20.0481	1.49016	0.745081	−	0.666974i	$-0.232411\pi$
$181$	20.0481	1.49016	0.745081	+	0.666974i	$0.232411\pi$
$182$	−0.728956	−0.0540338
$183$	13.3468	0.986626
$184$	0.570770	0.0420777
$185$	1.08653	0.0798830
$186$	10.9450	0.802527
$187$	−9.35874	−0.684379
$188$	−1.84675	−0.134688
$189$	−9.07851	−0.660365
$190$	6.81355	0.494307
$191$	−23.7442	−1.71807	−0.859033	−	0.511920i	$-0.828935\pi$
$191$	−23.7442	−1.71807	−0.859033	+	0.511920i	$0.828935\pi$
$192$	−1.52925	−0.110364
$193$	13.5973	0.978757	0.489378	−	0.872072i	$-0.337224\pi$
$193$	13.5973	0.978757	0.489378	+	0.872072i	$0.337224\pi$
$194$	−0.506652	−0.0363755
$195$	2.41786	0.173147
$196$	−4.37107	−0.312219
$197$	−24.1649	−1.72168	−0.860838	−	0.508879i	$-0.830060\pi$
$197$	−24.1649	−1.72168	−0.860838	+	0.508879i	$0.830060\pi$
$198$	−3.46085	−0.245952
$199$	−5.07425	−0.359704	−0.179852	−	0.983694i	$-0.557562\pi$
$199$	−5.07425	−0.359704	−0.179852	+	0.983694i	$0.557562\pi$
$200$	−7.36753	−0.520963
$201$	4.08408	0.288069
$202$	16.5981	1.16784
$203$	−3.78814	−0.265875
$204$	−2.73511	−0.191496
$205$	44.4212	3.10251
$206$	10.8064	0.752915
$207$	0.377505	0.0262384
$208$	−0.449585	−0.0311731
$209$	10.1380	0.701262
$210$	−8.71986	−0.601727
$211$	5.11505	0.352135	0.176067	−	0.984378i	$-0.443662\pi$
$211$	5.11505	0.352135	0.176067	+	0.984378i	$0.443662\pi$
$212$	−1.51873	−0.104307
$213$	10.3718	0.710664
$214$	12.8942	0.881427
$215$	28.3233	1.93163
$216$	−5.59919	−0.380976
$217$	−11.6045	−0.787767
$218$	−14.1966	−0.961515
$219$	13.4301	0.907520
$220$	−18.4019	−1.24066
$221$	−0.804096	−0.0540893
$222$	0.472473	0.0317103
$223$	−14.9667	−1.00225	−0.501123	−	0.865376i	$-0.667080\pi$
$223$	−14.9667	−1.00225	−0.501123	+	0.865376i	$0.667080\pi$
$224$	1.62140	0.108334
$225$	−4.87286	−0.324857
$226$	−8.25831	−0.549334
$227$	25.3845	1.68483	0.842414	−	0.538831i	$-0.181134\pi$
$227$	25.3845	1.68483	0.842414	+	0.538831i	$0.181134\pi$
$228$	2.96286	0.196220
$229$	−15.3735	−1.01591	−0.507956	−	0.861383i	$-0.669599\pi$
$229$	−15.3735	−1.01591	−0.507956	+	0.861383i	$0.669599\pi$
$230$	2.00725	0.132354
$231$	−12.9745	−0.853656
$232$	−2.33634	−0.153388
$233$	5.41878	0.354996	0.177498	−	0.984121i	$-0.443200\pi$
$233$	5.41878	0.354996	0.177498	+	0.984121i	$0.443200\pi$
$234$	−0.297354	−0.0194386
$235$	−6.49455	−0.423658
$236$	0.0896840	0.00583793
$237$	10.2729	0.667297
$238$	2.89992	0.187974
$239$	17.6130	1.13929	0.569646	−	0.821890i	$-0.307080\pi$
$239$	17.6130	1.13929	0.569646	+	0.821890i	$0.307080\pi$
$240$	−5.37799	−0.347148
$241$	8.47734	0.546073	0.273037	−	0.962004i	$-0.411972\pi$
$241$	8.47734	0.546073	0.273037	+	0.962004i	$0.411972\pi$
$242$	−16.3805	−1.05298
$243$	−6.73760	−0.432217
$244$	−8.72770	−0.558734
$245$	−15.3720	−0.982078
$246$	19.3165	1.23157
$247$	0.871051	0.0554237
$248$	−7.15712	−0.454477
$249$	7.31586	0.463624
$250$	−8.32602	−0.526583
$251$	−25.6364	−1.61816	−0.809078	−	0.587702i	$-0.800033\pi$
$251$	−25.6364	−1.61816	−0.809078	+	0.587702i	$0.800033\pi$
$252$	1.07239	0.0675540
$253$	2.98663	0.187768
$254$	15.8100	0.992007
$255$	−9.61869	−0.602346
$256$	1.00000	0.0625000
$257$	25.4043	1.58467	0.792337	−	0.610083i	$-0.208864\pi$
$257$	25.4043	1.58467	0.792337	+	0.610083i	$0.208864\pi$
$258$	12.3163	0.766781
$259$	−0.500943	−0.0311271
$260$	−1.58108	−0.0980542
$261$	−1.54525	−0.0956484
$262$	−0.879636	−0.0543441
$263$	−13.6182	−0.839733	−0.419866	−	0.907586i	$-0.637923\pi$
$263$	−13.6182	−0.839733	−0.419866	+	0.907586i	$0.637923\pi$
$264$	−8.00202	−0.492490
$265$	−5.34099	−0.328094
$266$	−3.14139	−0.192611
$267$	−3.16132	−0.193470
$268$	−2.67065	−0.163136
$269$	−20.1465	−1.22835	−0.614176	−	0.789169i	$-0.710511\pi$
$269$	−20.1465	−1.22835	−0.614176	+	0.789169i	$0.710511\pi$
$270$	−19.6909	−1.19835
$271$	−16.6341	−1.01045	−0.505224	−	0.862988i	$-0.668590\pi$
$271$	−16.6341	−1.01045	−0.505224	+	0.862988i	$0.668590\pi$
$272$	1.78853	0.108446
$273$	−1.11476	−0.0674680
$274$	9.99852	0.604033
$275$	−38.5517	−2.32475
$276$	0.872849	0.0525393
$277$	1.08289	0.0650648	0.0325324	−	0.999471i	$-0.489643\pi$
$277$	1.08289	0.0650648	0.0325324	+	0.999471i	$0.489643\pi$
$278$	−5.11939	−0.307041
$279$	−4.73369	−0.283399
$280$	5.70205	0.340763
$281$	−23.5569	−1.40529	−0.702643	−	0.711543i	$-0.747997\pi$
$281$	−23.5569	−1.40529	−0.702643	+	0.711543i	$0.747997\pi$
$282$	−2.82414	−0.168175
$283$	15.9562	0.948500	0.474250	−	0.880390i	$-0.342719\pi$
$283$	15.9562	0.948500	0.474250	+	0.880390i	$0.342719\pi$
$284$	−6.78228	−0.402454
$285$	10.4196	0.617205
$286$	−2.35252	−0.139107
$287$	−20.4804	−1.20892
$288$	0.661396	0.0389732
$289$	−13.8012	−0.811833
$290$	−8.21633	−0.482479
$291$	−0.774797	−0.0454194
$292$	−8.78213	−0.513935
$293$	16.6877	0.974907	0.487453	−	0.873149i	$-0.337926\pi$
$293$	16.6877	0.974907	0.487453	+	0.873149i	$0.337926\pi$
$294$	−6.68445	−0.389845
$295$	0.315396	0.0183631
$296$	−0.308958	−0.0179578
$297$	−29.2985	−1.70007
$298$	−0.406202	−0.0235306
$299$	0.256609	0.0148401
$300$	−11.2668	−0.650489
$301$	−13.0585	−0.752678
$302$	21.4088	1.23194
$303$	25.3826	1.45819
$304$	−1.93746	−0.111121
$305$	−30.6931	−1.75748
$306$	1.18293	0.0676234
$307$	7.27232	0.415053	0.207527	−	0.978229i	$-0.433459\pi$
$307$	7.27232	0.415053	0.207527	+	0.978229i	$0.433459\pi$
$308$	8.48420	0.483432
$309$	16.5256	0.940110
$310$	−25.1698	−1.42955
$311$	33.7083	1.91142	0.955712	−	0.294302i	$-0.0950872\pi$
$311$	33.7083	1.91142	0.955712	+	0.294302i	$0.0950872\pi$
$312$	−0.687527	−0.0389236
$313$	0.0979706	0.00553763	0.00276881	−	0.999996i	$-0.499119\pi$
$313$	0.0979706	0.00553763	0.00276881	+	0.999996i	$0.499119\pi$
$314$	10.1957	0.575379
$315$	3.77132	0.212490
$316$	−6.71761	−0.377895
$317$	−7.04684	−0.395790	−0.197895	−	0.980223i	$-0.563410\pi$
$317$	−7.04684	−0.395790	−0.197895	+	0.980223i	$0.563410\pi$
$318$	−2.32251	−0.130240
$319$	−12.2252	−0.684482
$320$	3.51675	0.196592
$321$	19.7184	1.10057
$322$	−0.925445	−0.0515730
$323$	−3.46520	−0.192809
$324$	−6.57837	−0.365465
$325$	−3.31233	−0.183735
$326$	−1.76837	−0.0979408
$327$	−21.7101	−1.20057
$328$	−12.6313	−0.697449
$329$	2.99431	0.165082
$330$	−28.1411	−1.54912
$331$	−26.6032	−1.46224	−0.731121	−	0.682248i	$-0.761003\pi$
$331$	−26.6032	−1.46224	−0.731121	+	0.682248i	$0.761003\pi$
$332$	−4.78396	−0.262554
$333$	−0.204343	−0.0111979
$334$	16.8066	0.919618
$335$	−9.39199	−0.513139
$336$	2.47952	0.135269
$337$	20.0723	1.09341	0.546704	−	0.837326i	$-0.315882\pi$
$337$	20.0723	1.09341	0.546704	+	0.837326i	$0.315882\pi$
$338$	12.7979	0.696113
$339$	−12.6290	−0.685914
$340$	6.28981	0.341113
$341$	−37.4506	−2.02807
$342$	−1.28143	−0.0692916
$343$	18.4370	0.995506
$344$	−8.05384	−0.434234
$345$	3.06959	0.165261
$346$	−9.83941	−0.528970
$347$	28.1719	1.51235	0.756174	−	0.654370i	$-0.227066\pi$
$347$	28.1719	1.51235	0.756174	+	0.654370i	$0.227066\pi$
$348$	−3.57285	−0.191525
$349$	4.27669	0.228926	0.114463	−	0.993428i	$-0.463485\pi$
$349$	4.27669	0.228926	0.114463	+	0.993428i	$0.463485\pi$
$350$	11.9457	0.638525
$351$	−2.51731	−0.134364
$352$	5.23264	0.278901
$353$	−8.17456	−0.435088	−0.217544	−	0.976051i	$-0.569805\pi$
$353$	−8.17456	−0.435088	−0.217544	+	0.976051i	$0.569805\pi$
$354$	0.137149	0.00728940
$355$	−23.8516	−1.26591
$356$	2.06724	0.109563
$357$	4.43470	0.234709
$358$	11.1180	0.587603
$359$	−22.1043	−1.16662	−0.583309	−	0.812250i	$-0.698242\pi$
$359$	−22.1043	−1.16662	−0.583309	+	0.812250i	$0.698242\pi$
$360$	2.32597	0.122589
$361$	−15.2463	−0.802435
$362$	−20.0481	−1.05370
$363$	−25.0499	−1.31478
$364$	0.728956	0.0382077
$365$	−30.8846	−1.61657
$366$	−13.3468	−0.697650
$367$	25.0467	1.30743	0.653713	−	0.756742i	$-0.273210\pi$
$367$	25.0467	1.30743	0.653713	+	0.756742i	$0.273210\pi$
$368$	−0.570770	−0.0297534
$369$	−8.35432	−0.434908
$370$	−1.08653	−0.0564858
$371$	2.46246	0.127845
$372$	−10.9450	−0.567473
$373$	−2.32979	−0.120632	−0.0603159	−	0.998179i	$-0.519211\pi$
$373$	−2.32979	−0.120632	−0.0603159	+	0.998179i	$0.519211\pi$
$374$	9.35874	0.483929
$375$	−12.7326	−0.657506
$376$	1.84675	0.0952387
$377$	−1.05038	−0.0540975
$378$	9.07851	0.466948
$379$	−16.4170	−0.843287	−0.421644	−	0.906762i	$-0.638547\pi$
$379$	−16.4170	−0.843287	−0.421644	+	0.906762i	$0.638547\pi$
$380$	−6.81355	−0.349528
$381$	24.1774	1.23865
$382$	23.7442	1.21486
$383$	6.32170	0.323024	0.161512	−	0.986871i	$-0.448363\pi$
$383$	6.32170	0.323024	0.161512	+	0.986871i	$0.448363\pi$
$384$	1.52925	0.0780392
$385$	29.8368	1.52062
$386$	−13.5973	−0.692086
$387$	−5.32678	−0.270775
$388$	0.506652	0.0257214
$389$	−12.5399	−0.635796	−0.317898	−	0.948125i	$-0.602977\pi$
$389$	−12.5399	−0.635796	−0.317898	+	0.948125i	$0.602977\pi$
$390$	−2.41786	−0.122433
$391$	−1.02084	−0.0516260
$392$	4.37107	0.220772
$393$	−1.34518	−0.0678555
$394$	24.1649	1.21741
$395$	−23.6242	−1.18866
$396$	3.46085	0.173914
$397$	10.7014	0.537087	0.268543	−	0.963268i	$-0.413458\pi$
$397$	10.7014	0.537087	0.268543	+	0.963268i	$0.413458\pi$
$398$	5.07425	0.254349
$399$	−4.80397	−0.240499
$400$	7.36753	0.368377
$401$	13.6024	0.679272	0.339636	−	0.940557i	$-0.389696\pi$
$401$	13.6024	0.679272	0.339636	+	0.940557i	$0.389696\pi$
$402$	−4.08408	−0.203696
$403$	−3.21773	−0.160287
$404$	−16.5981	−0.825784
$405$	−23.1345	−1.14956
$406$	3.78814	0.188002
$407$	−1.61666	−0.0801351
$408$	2.73511	0.135408
$409$	7.03568	0.347892	0.173946	−	0.984755i	$-0.444348\pi$
$409$	7.03568	0.347892	0.173946	+	0.984755i	$0.444348\pi$
$410$	−44.4212	−2.19381
$411$	15.2902	0.754211
$412$	−10.8064	−0.532391
$413$	−0.145413	−0.00715533
$414$	−0.377505	−0.0185534
$415$	−16.8240	−0.825857
$416$	0.449585	0.0220427
$417$	−7.82883	−0.383379
$418$	−10.1380	−0.495867
$419$	−8.03417	−0.392495	−0.196247	−	0.980554i	$-0.562876\pi$
$419$	−8.03417	−0.392495	−0.196247	+	0.980554i	$0.562876\pi$
$420$	8.71986	0.425486
$421$	−19.6610	−0.958218	−0.479109	−	0.877755i	$-0.659040\pi$
$421$	−19.6610	−0.958218	−0.479109	+	0.877755i	$0.659040\pi$
$422$	−5.11505	−0.248997
$423$	1.22143	0.0593880
$424$	1.51873	0.0737560
$425$	13.1771	0.639181
$426$	−10.3718	−0.502515
$427$	14.1511	0.684819
$428$	−12.8942	−0.623263
$429$	−3.59758	−0.173693
$430$	−28.3233	−1.36587
$431$	−13.7205	−0.660895	−0.330448	−	0.943824i	$-0.607200\pi$
$431$	−13.7205	−0.660895	−0.330448	+	0.943824i	$0.607200\pi$
$432$	5.59919	0.269391
$433$	−22.7536	−1.09347	−0.546734	−	0.837306i	$-0.684129\pi$
$433$	−22.7536	−1.09347	−0.546734	+	0.837306i	$0.684129\pi$
$434$	11.6045	0.557035
$435$	−12.5648	−0.602437
$436$	14.1966	0.679894
$437$	1.10584	0.0528996
$438$	−13.4301	−0.641713
$439$	−20.2854	−0.968171	−0.484086	−	0.875021i	$-0.660848\pi$
$439$	−20.2854	−0.968171	−0.484086	+	0.875021i	$0.660848\pi$
$440$	18.4019	0.877276
$441$	2.89101	0.137667
$442$	0.804096	0.0382469
$443$	11.3472	0.539122	0.269561	−	0.962983i	$-0.413121\pi$
$443$	11.3472	0.539122	0.269561	+	0.962983i	$0.413121\pi$
$444$	−0.472473	−0.0224226
$445$	7.26995	0.344629
$446$	14.9667	0.708695
$447$	−0.621184	−0.0293810
$448$	−1.62140	−0.0766039
$449$	21.6819	1.02323	0.511616	−	0.859214i	$-0.329047\pi$
$449$	21.6819	1.02323	0.511616	+	0.859214i	$0.329047\pi$
$450$	4.87286	0.229709
$451$	−66.0953	−3.11230
$452$	8.25831	0.388438
$453$	32.7394	1.53823
$454$	−25.3845	−1.19135
$455$	2.56355	0.120181
$456$	−2.96286	−0.138748
$457$	5.85669	0.273964	0.136982	−	0.990574i	$-0.456260\pi$
$457$	5.85669	0.273964	0.136982	+	0.990574i	$0.456260\pi$
$458$	15.3735	0.718358
$459$	10.0143	0.467428
$460$	−2.00725	−0.0935887
$461$	−9.26721	−0.431617	−0.215808	−	0.976436i	$-0.569239\pi$
$461$	−9.26721	−0.431617	−0.215808	+	0.976436i	$0.569239\pi$
$462$	12.9745	0.603626
$463$	−33.9117	−1.57601	−0.788006	−	0.615667i	$-0.788887\pi$
$463$	−33.9117	−1.57601	−0.788006	+	0.615667i	$0.788887\pi$
$464$	2.33634	0.108462
$465$	−38.4909	−1.78497
$466$	−5.41878	−0.251020
$467$	−6.61774	−0.306232	−0.153116	−	0.988208i	$-0.548931\pi$
$467$	−6.61774	−0.306232	−0.153116	+	0.988208i	$0.548931\pi$
$468$	0.297354	0.0137452
$469$	4.33018	0.199949
$470$	6.49455	0.299571
$471$	15.5918	0.718433
$472$	−0.0896840	−0.00412804
$473$	−42.1428	−1.93773
$474$	−10.2729	−0.471850
$475$	−14.2743	−0.654949
$476$	−2.89992	−0.132918
$477$	1.00448	0.0459921
$478$	−17.6130	−0.805601
$479$	25.7394	1.17606	0.588031	−	0.808839i	$-0.299903\pi$
$479$	25.7394	1.17606	0.588031	+	0.808839i	$0.299903\pi$
$480$	5.37799	0.245470
$481$	−0.138903	−0.00633341
$482$	−8.47734	−0.386132
$483$	−1.41524	−0.0643955
$484$	16.3805	0.744570
$485$	1.78177	0.0809059
$486$	6.73760	0.305624
$487$	17.5591	0.795681	0.397840	−	0.917455i	$-0.369760\pi$
$487$	17.5591	0.795681	0.397840	+	0.917455i	$0.369760\pi$
$488$	8.72770	0.395085
$489$	−2.70427	−0.122292
$490$	15.3720	0.694434
$491$	23.8652	1.07702	0.538511	−	0.842618i	$-0.318987\pi$
$491$	23.8652	1.07702	0.538511	+	0.842618i	$0.318987\pi$
$492$	−19.3165	−0.870853
$493$	4.17862	0.188195
$494$	−0.871051	−0.0391904
$495$	12.1709	0.547043
$496$	7.15712	0.321364
$497$	10.9968	0.493273
$498$	−7.31586	−0.327832
$499$	−39.7435	−1.77916	−0.889582	−	0.456776i	$-0.849004\pi$
$499$	−39.7435	−1.77916	−0.889582	+	0.456776i	$0.849004\pi$
$500$	8.32602	0.372351
$501$	25.7015	1.14826
$502$	25.6364	1.14421
$503$	30.3279	1.35225	0.676127	−	0.736785i	$-0.263657\pi$
$503$	30.3279	1.35225	0.676127	+	0.736785i	$0.263657\pi$
$504$	−1.07239	−0.0477679
$505$	−58.3712	−2.59749
$506$	−2.98663	−0.132772
$507$	19.5711	0.869185
$508$	−15.8100	−0.701455
$509$	−7.73347	−0.342780	−0.171390	−	0.985203i	$-0.554826\pi$
$509$	−7.73347	−0.342780	−0.171390	+	0.985203i	$0.554826\pi$
$510$	9.61869	0.425923
$511$	14.2393	0.629911
$512$	−1.00000	−0.0441942
$513$	−10.8482	−0.478959
$514$	−25.4043	−1.12053
$515$	−38.0033	−1.67462
$516$	−12.3163	−0.542196
$517$	9.66337	0.424994
$518$	0.500943	0.0220102
$519$	−15.0469	−0.660486
$520$	1.58108	0.0693348
$521$	14.4846	0.634583	0.317292	−	0.948328i	$-0.397227\pi$
$521$	14.4846	0.634583	0.317292	+	0.948328i	$0.397227\pi$
$522$	1.54525	0.0676336
$523$	−16.3954	−0.716922	−0.358461	−	0.933545i	$-0.616698\pi$
$523$	−16.3954	−0.716922	−0.358461	+	0.933545i	$0.616698\pi$
$524$	0.879636	0.0384271
$525$	18.2680	0.797279
$526$	13.6182	0.593781
$527$	12.8007	0.557608
$528$	8.00202	0.348243
$529$	−22.6742	−0.985836
$530$	5.34099	0.231998
$531$	−0.0593167	−0.00257412
$532$	3.14139	0.136197
$533$	−5.67885	−0.245978
$534$	3.16132	0.136804
$535$	−45.3456	−1.96046
$536$	2.67065	0.115354
$537$	17.0021	0.733697
$538$	20.1465	0.868576
$539$	22.8722	0.985177
$540$	19.6909	0.847363
$541$	−26.0133	−1.11840	−0.559200	−	0.829033i	$-0.688891\pi$
$541$	−26.0133	−1.11840	−0.559200	+	0.829033i	$0.688891\pi$
$542$	16.6341	0.714495
$543$	−30.6585	−1.31568
$544$	−1.78853	−0.0766826
$545$	49.9259	2.13859
$546$	1.11476	0.0477071
$547$	17.4907	0.747850	0.373925	−	0.927459i	$-0.378012\pi$
$547$	17.4907	0.747850	0.373925	+	0.927459i	$0.378012\pi$
$548$	−9.99852	−0.427116
$549$	5.77247	0.246363
$550$	38.5517	1.64385
$551$	−4.52656	−0.192838
$552$	−0.872849	−0.0371509
$553$	10.8919	0.463171
$554$	−1.08289	−0.0460078
$555$	−1.66157	−0.0705297
$556$	5.11939	0.217111
$557$	−14.9921	−0.635238	−0.317619	−	0.948218i	$-0.602883\pi$
$557$	−14.9921	−0.635238	−0.317619	+	0.948218i	$0.602883\pi$
$558$	4.73369	0.200393
$559$	−3.62088	−0.153147
$560$	−5.70205	−0.240956
$561$	14.3118	0.604247
$562$	23.5569	0.993687
$563$	41.3920	1.74447	0.872233	−	0.489091i	$-0.162671\pi$
$563$	41.3920	1.74447	0.872233	+	0.489091i	$0.162671\pi$
$564$	2.82414	0.118918
$565$	29.0424	1.22182
$566$	−15.9562	−0.670691
$567$	10.6661	0.447936
$568$	6.78228	0.284578
$569$	−31.8717	−1.33613	−0.668066	−	0.744102i	$-0.732878\pi$
$569$	−31.8717	−1.33613	−0.668066	+	0.744102i	$0.732878\pi$
$570$	−10.4196	−0.436430
$571$	15.8276	0.662364	0.331182	−	0.943567i	$-0.392553\pi$
$571$	15.8276	0.662364	0.331182	+	0.943567i	$0.392553\pi$
$572$	2.35252	0.0983636
$573$	36.3107	1.51690
$574$	20.4804	0.854836
$575$	−4.20516	−0.175367
$576$	−0.661396	−0.0275582
$577$	23.5626	0.980923	0.490461	−	0.871463i	$-0.336828\pi$
$577$	23.5626	0.980923	0.490461	+	0.871463i	$0.336828\pi$
$578$	13.8012	0.574053
$579$	−20.7937	−0.864157
$580$	8.21633	0.341164
$581$	7.75670	0.321802
$582$	0.774797	0.0321164
$583$	7.94696	0.329130
$584$	8.78213	0.363407
$585$	1.04572	0.0432351
$586$	−16.6877	−0.689363
$587$	18.1326	0.748412	0.374206	−	0.927346i	$-0.377915\pi$
$587$	18.1326	0.748412	0.374206	+	0.927346i	$0.377915\pi$
$588$	6.68445	0.275662
$589$	−13.8666	−0.571364
$590$	−0.315396	−0.0129847
$591$	36.9541	1.52009
$592$	0.308958	0.0126981
$593$	−1.54009	−0.0632440	−0.0316220	−	0.999500i	$-0.510067\pi$
$593$	−1.54009	−0.0632440	−0.0316220	+	0.999500i	$0.510067\pi$
$594$	29.2985	1.20213
$595$	−10.1983	−0.418089
$596$	0.406202	0.0166387
$597$	7.75979	0.317587
$598$	−0.256609	−0.0104935
$599$	6.76508	0.276414	0.138207	−	0.990403i	$-0.455866\pi$
$599$	6.76508	0.276414	0.138207	+	0.990403i	$0.455866\pi$
$600$	11.2668	0.459965
$601$	−39.5760	−1.61434	−0.807170	−	0.590319i	$-0.799002\pi$
$601$	−39.5760	−1.61434	−0.807170	+	0.590319i	$0.799002\pi$
$602$	13.0585	0.532224
$603$	1.76636	0.0719315
$604$	−21.4088	−0.871113
$605$	57.6063	2.34203
$606$	−25.3826	−1.03110
$607$	−13.5455	−0.549795	−0.274898	−	0.961473i	$-0.588644\pi$
$607$	−13.5455	−0.549795	−0.274898	+	0.961473i	$0.588644\pi$
$608$	1.93746	0.0785743
$609$	5.79301	0.234745
$610$	30.6931	1.24273
$611$	0.830269	0.0335891
$612$	−1.18293	−0.0478170
$613$	6.00804	0.242663	0.121331	−	0.992612i	$-0.461284\pi$
$613$	6.00804	0.242663	0.121331	+	0.992612i	$0.461284\pi$
$614$	−7.27232	−0.293487
$615$	−67.9312	−2.73925
$616$	−8.48420	−0.341838
$617$	15.9419	0.641796	0.320898	−	0.947114i	$-0.396015\pi$
$617$	15.9419	0.641796	0.320898	+	0.947114i	$0.396015\pi$
$618$	−16.5256	−0.664758
$619$	39.7096	1.59606	0.798032	−	0.602614i	$-0.205874\pi$
$619$	39.7096	1.59606	0.798032	+	0.602614i	$0.205874\pi$
$620$	25.1698	1.01084
$621$	−3.19585	−0.128245
$622$	−33.7083	−1.35158
$623$	−3.35181	−0.134288
$624$	0.687527	0.0275231
$625$	−7.55714	−0.302286
$626$	−0.0979706	−0.00391569
$627$	−15.5036	−0.619153
$628$	−10.1957	−0.406854
$629$	0.552580	0.0220328
$630$	−3.77132	−0.150253
$631$	4.69493	0.186902	0.0934511	−	0.995624i	$-0.470210\pi$
$631$	4.69493	0.186902	0.0934511	+	0.995624i	$0.470210\pi$
$632$	6.71761	0.267212
$633$	−7.82219	−0.310904
$634$	7.04684	0.279866
$635$	−55.5998	−2.20641
$636$	2.32251	0.0920937
$637$	1.96517	0.0778627
$638$	12.2252	0.484002
$639$	4.48578	0.177455
$640$	−3.51675	−0.139012
$641$	5.47313	0.216175	0.108088	−	0.994141i	$-0.465527\pi$
$641$	5.47313	0.216175	0.108088	+	0.994141i	$0.465527\pi$
$642$	−19.7184	−0.778223
$643$	−15.2675	−0.602090	−0.301045	−	0.953610i	$-0.597335\pi$
$643$	−15.2675	−0.602090	−0.301045	+	0.953610i	$0.597335\pi$
$644$	0.925445	0.0364676
$645$	−43.3134	−1.70546
$646$	3.46520	0.136336
$647$	44.7137	1.75788	0.878938	−	0.476935i	$-0.158252\pi$
$647$	44.7137	1.75788	0.878938	+	0.476935i	$0.158252\pi$
$648$	6.57837	0.258423
$649$	−0.469284	−0.0184210
$650$	3.31233	0.129920
$651$	17.7462	0.695529
$652$	1.76837	0.0692546
$653$	−4.22461	−0.165322	−0.0826609	−	0.996578i	$-0.526342\pi$
$653$	−4.22461	−0.165322	−0.0826609	+	0.996578i	$0.526342\pi$
$654$	21.7101	0.848934
$655$	3.09346	0.120872
$656$	12.6313	0.493171
$657$	5.80847	0.226610
$658$	−2.99431	−0.116730
$659$	42.4698	1.65439	0.827193	−	0.561917i	$-0.189936\pi$
$659$	42.4698	1.65439	0.827193	+	0.561917i	$0.189936\pi$
$660$	28.1411	1.09539
$661$	30.5305	1.18750	0.593750	−	0.804650i	$-0.297647\pi$
$661$	30.5305	1.18750	0.593750	+	0.804650i	$0.297647\pi$
$662$	26.6032	1.03396
$663$	1.22966	0.0477561
$664$	4.78396	0.185654
$665$	11.0475	0.428403
$666$	0.204343	0.00791814
$667$	−1.33351	−0.0516338
$668$	−16.8066	−0.650268
$669$	22.8878	0.884895
$670$	9.39199	0.362844
$671$	45.6689	1.76303
$672$	−2.47952	−0.0956496
$673$	−16.1113	−0.621044	−0.310522	−	0.950566i	$-0.600504\pi$
$673$	−16.1113	−0.621044	−0.310522	+	0.950566i	$0.600504\pi$
$674$	−20.0723	−0.773156
$675$	41.2522	1.58780
$676$	−12.7979	−0.492226
$677$	3.91294	0.150387	0.0751933	−	0.997169i	$-0.476043\pi$
$677$	3.91294	0.150387	0.0751933	+	0.997169i	$0.476043\pi$
$678$	12.6290	0.485014
$679$	−0.821484	−0.0315257
$680$	−6.28981	−0.241203
$681$	−38.8192	−1.48756
$682$	37.4506	1.43406
$683$	−24.0915	−0.921836	−0.460918	−	0.887443i	$-0.652480\pi$
$683$	−24.0915	−0.921836	−0.460918	+	0.887443i	$0.652480\pi$
$684$	1.28143	0.0489966
$685$	−35.1623	−1.34348
$686$	−18.4370	−0.703929
$687$	23.5100	0.896962
$688$	8.05384	0.307050
$689$	0.682797	0.0260125
$690$	−3.06959	−0.116857
$691$	−39.6325	−1.50769	−0.753846	−	0.657051i	$-0.771803\pi$
$691$	−39.6325	−1.50769	−0.753846	+	0.657051i	$0.771803\pi$
$692$	9.83941	0.374038
$693$	−5.61142	−0.213160
$694$	−28.1719	−1.06939
$695$	18.0036	0.682916
$696$	3.57285	0.135428
$697$	22.5915	0.855715
$698$	−4.27669	−0.161875
$699$	−8.28666	−0.313430
$700$	−11.9457	−0.451505
$701$	0.722951	0.0273055	0.0136527	−	0.999907i	$-0.495654\pi$
$701$	0.722951	0.0273055	0.0136527	+	0.999907i	$0.495654\pi$
$702$	2.51731	0.0950097
$703$	−0.598592	−0.0225763
$704$	−5.23264	−0.197213
$705$	9.93178	0.374053
$706$	8.17456	0.307653
$707$	26.9121	1.01213
$708$	−0.137149	−0.00515438
$709$	−31.4929	−1.18274	−0.591370	−	0.806401i	$-0.701413\pi$
$709$	−31.4929	−1.18274	−0.591370	+	0.806401i	$0.701413\pi$
$710$	23.8516	0.895134
$711$	4.44300	0.166626
$712$	−2.06724	−0.0774730
$713$	−4.08506	−0.152987
$714$	−4.43470	−0.165964
$715$	8.27321	0.309401
$716$	−11.1180	−0.415498
$717$	−26.9347	−1.00590
$718$	22.1043	0.824924
$719$	14.0424	0.523695	0.261847	−	0.965109i	$-0.415668\pi$
$719$	14.0424	0.523695	0.261847	+	0.965109i	$0.415668\pi$
$720$	−2.32597	−0.0866836
$721$	17.5214	0.652532
$722$	15.2463	0.567407
$723$	−12.9640	−0.482135
$724$	20.0481	0.745081
$725$	17.2131	0.639277
$726$	25.0499	0.929691
$727$	18.2020	0.675075	0.337538	−	0.941312i	$-0.390406\pi$
$727$	18.2020	0.675075	0.337538	+	0.941312i	$0.390406\pi$
$728$	−0.728956	−0.0270169
$729$	30.0386	1.11254
$730$	30.8846	1.14309
$731$	14.4045	0.532771
$732$	13.3468	0.493313
$733$	1.68293	0.0621606	0.0310803	−	0.999517i	$-0.490105\pi$
$733$	1.68293	0.0621606	0.0310803	+	0.999517i	$0.490105\pi$
$734$	−25.0467	−0.924490
$735$	23.5076	0.867089
$736$	0.570770	0.0210388
$737$	13.9745	0.514759
$738$	8.35432	0.307527
$739$	−19.2855	−0.709429	−0.354714	−	0.934975i	$-0.615422\pi$
$739$	−19.2855	−0.709429	−0.354714	+	0.934975i	$0.615422\pi$
$740$	1.08653	0.0399415
$741$	−1.33205	−0.0489342
$742$	−2.46246	−0.0903999
$743$	7.29557	0.267648	0.133824	−	0.991005i	$-0.457274\pi$
$743$	7.29557	0.267648	0.133824	+	0.991005i	$0.457274\pi$
$744$	10.9450	0.401264
$745$	1.42851	0.0523365
$746$	2.32979	0.0852995
$747$	3.16409	0.115768
$748$	−9.35874	−0.342189
$749$	20.9066	0.763910
$750$	12.7326	0.464927
$751$	15.0527	0.549282	0.274641	−	0.961547i	$-0.411441\pi$
$751$	15.0527	0.549282	0.274641	+	0.961547i	$0.411441\pi$
$752$	−1.84675	−0.0673439
$753$	39.2045	1.42869
$754$	1.05038	0.0382527
$755$	−75.2895	−2.74006
$756$	−9.07851	−0.330182
$757$	20.3585	0.739941	0.369970	−	0.929044i	$-0.379368\pi$
$757$	20.3585	0.739941	0.369970	+	0.929044i	$0.379368\pi$
$758$	16.4170	0.596294
$759$	−4.56731	−0.165783
$760$	6.81355	0.247154
$761$	27.6340	1.00173	0.500866	−	0.865525i	$-0.333015\pi$
$761$	27.6340	1.00173	0.500866	+	0.865525i	$0.333015\pi$
$762$	−24.1774	−0.875855
$763$	−23.0183	−0.833320
$764$	−23.7442	−0.859033
$765$	−4.16006	−0.150407
$766$	−6.32170	−0.228412
$767$	−0.0403206	−0.00145589
$768$	−1.52925	−0.0551820
$769$	−23.1376	−0.834363	−0.417182	−	0.908823i	$-0.636982\pi$
$769$	−23.1376	−0.834363	−0.417182	+	0.908823i	$0.636982\pi$
$770$	−29.8368	−1.07524
$771$	−38.8495	−1.39913
$772$	13.5973	0.489378
$773$	24.4812	0.880528	0.440264	−	0.897868i	$-0.354885\pi$
$773$	24.4812	0.880528	0.440264	+	0.897868i	$0.354885\pi$
$774$	5.32678	0.191467
$775$	52.7303	1.89413
$776$	−0.506652	−0.0181877
$777$	0.766067	0.0274825
$778$	12.5399	0.449576
$779$	−24.4727	−0.876824
$780$	2.41786	0.0865733
$781$	35.4892	1.26991
$782$	1.02084	0.0365051
$783$	13.0816	0.467499
$784$	−4.37107	−0.156110
$785$	−35.8559	−1.27975
$786$	1.34518	0.0479811
$787$	−17.6099	−0.627724	−0.313862	−	0.949469i	$-0.601623\pi$
$787$	−17.6099	−0.627724	−0.313862	+	0.949469i	$0.601623\pi$
$788$	−24.1649	−0.860838
$789$	20.8256	0.741411
$790$	23.6242	0.840510
$791$	−13.3900	−0.476094
$792$	−3.46085	−0.122976
$793$	3.92384	0.139340
$794$	−10.7014	−0.379778
$795$	8.16770	0.289679
$796$	−5.07425	−0.179852
$797$	1.76998	0.0626960	0.0313480	−	0.999509i	$-0.490020\pi$
$797$	1.76998	0.0626960	0.0313480	+	0.999509i	$0.490020\pi$
$798$	4.80397	0.170059
$799$	−3.30296	−0.116850
$800$	−7.36753	−0.260482
$801$	−1.36726	−0.0483098
$802$	−13.6024	−0.480318
$803$	45.9537	1.62167
$804$	4.08408	0.144035
$805$	3.25456	0.114708
$806$	3.21773	0.113340
$807$	30.8090	1.08453
$808$	16.5981	0.583918
$809$	0.247233	0.00869227	0.00434613	−	0.999991i	$-0.498617\pi$
$809$	0.247233	0.00869227	0.00434613	+	0.999991i	$0.498617\pi$
$810$	23.1345	0.812862
$811$	42.4040	1.48901	0.744503	−	0.667619i	$-0.232687\pi$
$811$	42.4040	1.48901	0.744503	+	0.667619i	$0.232687\pi$
$812$	−3.78814	−0.132938
$813$	25.4376	0.892137
$814$	1.61666	0.0566641
$815$	6.21891	0.217839
$816$	−2.73511	−0.0957479
$817$	−15.6040	−0.545914
$818$	−7.03568	−0.245997
$819$	−0.482129	−0.0168469
$820$	44.4212	1.55126
$821$	−13.5595	−0.473231	−0.236615	−	0.971603i	$-0.576038\pi$
$821$	−13.5595	−0.473231	−0.236615	+	0.971603i	$0.576038\pi$
$822$	−15.2902	−0.533308
$823$	−26.3922	−0.919975	−0.459988	−	0.887925i	$-0.652146\pi$
$823$	−26.3922	−0.919975	−0.459988	+	0.887925i	$0.652146\pi$
$824$	10.8064	0.376457
$825$	58.9551	2.05255
$826$	0.145413	0.00505958
$827$	27.5248	0.957130	0.478565	−	0.878052i	$-0.341157\pi$
$827$	27.5248	0.957130	0.478565	+	0.878052i	$0.341157\pi$
$828$	0.377505	0.0131192
$829$	5.62533	0.195376	0.0976879	−	0.995217i	$-0.468855\pi$
$829$	5.62533	0.195376	0.0976879	+	0.995217i	$0.468855\pi$
$830$	16.8240	0.583969
$831$	−1.65601	−0.0574465
$832$	−0.449585	−0.0155865
$833$	−7.81779	−0.270870
$834$	7.82883	0.271090
$835$	−59.1047	−2.04540
$836$	10.1380	0.350631
$837$	40.0740	1.38516
$838$	8.03417	0.277536
$839$	−1.53335	−0.0529373	−0.0264686	−	0.999650i	$-0.508426\pi$
$839$	−1.53335	−0.0529373	−0.0264686	+	0.999650i	$0.508426\pi$
$840$	−8.71986	−0.300864
$841$	−23.5415	−0.811776
$842$	19.6610	0.677563
$843$	36.0244	1.24074
$844$	5.11505	0.176067
$845$	−45.0069	−1.54829
$846$	−1.22143	−0.0419937
$847$	−26.5594	−0.912591
$848$	−1.51873	−0.0521534
$849$	−24.4011	−0.837443
$850$	−13.1771	−0.451969
$851$	−0.176344	−0.00604498
$852$	10.3718	0.355332
$853$	45.2373	1.54890	0.774449	−	0.632637i	$-0.218027\pi$
$853$	45.2373	1.54890	0.774449	+	0.632637i	$0.218027\pi$
$854$	−14.1511	−0.484240
$855$	4.50646	0.154118
$856$	12.8942	0.440714
$857$	−33.4653	−1.14315	−0.571577	−	0.820548i	$-0.693668\pi$
$857$	−33.4653	−1.14315	−0.571577	+	0.820548i	$0.693668\pi$
$858$	3.59758	0.122819
$859$	−22.6040	−0.771237	−0.385618	−	0.922658i	$-0.626012\pi$
$859$	−22.6040	−0.771237	−0.385618	+	0.922658i	$0.626012\pi$
$860$	28.3233	0.965817
$861$	31.3197	1.06737
$862$	13.7205	0.467323
$863$	−13.3532	−0.454549	−0.227274	−	0.973831i	$-0.572981\pi$
$863$	−13.3532	−0.454549	−0.227274	+	0.973831i	$0.572981\pi$
$864$	−5.59919	−0.190488
$865$	34.6028	1.17653
$866$	22.7536	0.773199
$867$	21.1054	0.716778
$868$	−11.6045	−0.393884
$869$	35.1508	1.19241
$870$	12.5648	0.425987
$871$	1.20068	0.0406835
$872$	−14.1966	−0.480758
$873$	−0.335098	−0.0113413
$874$	−1.10584	−0.0374057
$875$	−13.4998	−0.456376
$876$	13.4301	0.453760
$877$	−23.3875	−0.789741	−0.394870	−	0.918737i	$-0.629211\pi$
$877$	−23.3875	−0.789741	−0.394870	+	0.918737i	$0.629211\pi$
$878$	20.2854	0.684601
$879$	−25.5197	−0.860757
$880$	−18.4019	−0.620328
$881$	−20.1333	−0.678308	−0.339154	−	0.940731i	$-0.610141\pi$
$881$	−20.1333	−0.678308	−0.339154	+	0.940731i	$0.610141\pi$
$882$	−2.89101	−0.0973453
$883$	39.9800	1.34543	0.672717	−	0.739900i	$-0.265127\pi$
$883$	39.9800	1.34543	0.672717	+	0.739900i	$0.265127\pi$
$884$	−0.804096	−0.0270447
$885$	−0.482320	−0.0162130
$886$	−11.3472	−0.381217
$887$	−41.3801	−1.38941	−0.694705	−	0.719295i	$-0.744465\pi$
$887$	−41.3801	−1.38941	−0.694705	+	0.719295i	$0.744465\pi$
$888$	0.472473	0.0158552
$889$	25.6343	0.859746
$890$	−7.26995	−0.243689
$891$	34.4222	1.15319
$892$	−14.9667	−0.501123
$893$	3.57799	0.119733
$894$	0.621184	0.0207755
$895$	−39.0991	−1.30694
$896$	1.62140	0.0541671
$897$	−0.392420	−0.0131025
$898$	−21.6819	−0.723534
$899$	16.7215	0.557692
$900$	−4.87286	−0.162429
$901$	−2.71629	−0.0904928
$902$	66.0953	2.20073
$903$	19.9697	0.664549
$904$	−8.25831	−0.274667
$905$	70.5041	2.34364
$906$	−32.7394	−1.08769
$907$	−58.5701	−1.94479	−0.972395	−	0.233343i	$-0.925034\pi$
$907$	−58.5701	−1.94479	−0.972395	+	0.233343i	$0.925034\pi$
$908$	25.3845	0.842414
$909$	10.9779	0.364114
$910$	−2.56355	−0.0849810
$911$	1.44062	0.0477298	0.0238649	−	0.999715i	$-0.492403\pi$
$911$	1.44062	0.0477298	0.0238649	+	0.999715i	$0.492403\pi$
$912$	2.96286	0.0981099
$913$	25.0327	0.828463
$914$	−5.85669	−0.193722
$915$	46.9375	1.55171
$916$	−15.3735	−0.507956
$917$	−1.42624	−0.0470986
$918$	−10.0143	−0.330522
$919$	−0.452033	−0.0149112	−0.00745560	−	0.999972i	$-0.502373\pi$
$919$	−0.452033	−0.0149112	−0.00745560	+	0.999972i	$0.502373\pi$
$920$	2.00725	0.0661772
$921$	−11.1212	−0.366456
$922$	9.26721	0.305199
$923$	3.04921	0.100366
$924$	−12.9745	−0.426828
$925$	2.27625	0.0748428
$926$	33.9117	1.11441
$927$	7.14729	0.234748
$928$	−2.33634	−0.0766941
$929$	36.0959	1.18427	0.592133	−	0.805840i	$-0.298286\pi$
$929$	36.0959	1.18427	0.592133	+	0.805840i	$0.298286\pi$
$930$	38.4909	1.26217
$931$	8.46876	0.277552
$932$	5.41878	0.177498
$933$	−51.5485	−1.68762
$934$	6.61774	0.216539
$935$	−32.9123	−1.07635
$936$	−0.297354	−0.00971931
$937$	−30.7958	−1.00605	−0.503027	−	0.864271i	$-0.667780\pi$
$937$	−30.7958	−1.00605	−0.503027	+	0.864271i	$0.667780\pi$
$938$	−4.33018	−0.141385
$939$	−0.149822	−0.00488924
$940$	−6.49455	−0.211829
$941$	46.9850	1.53167	0.765833	−	0.643039i	$-0.222327\pi$
$941$	46.9850	1.53167	0.765833	+	0.643039i	$0.222327\pi$
$942$	−15.5918	−0.508009
$943$	−7.20958	−0.234776
$944$	0.0896840	0.00291897
$945$	−31.9269	−1.03858
$946$	42.1428	1.37018
$947$	−42.4589	−1.37973	−0.689865	−	0.723938i	$-0.742330\pi$
$947$	−42.4589	−1.37973	−0.689865	+	0.723938i	$0.742330\pi$
$948$	10.2729	0.333648
$949$	3.94831	0.128168
$950$	14.2743	0.463119
$951$	10.7764	0.349448
$952$	2.89992	0.0939869
$953$	−4.52854	−0.146694	−0.0733468	−	0.997306i	$-0.523368\pi$
$953$	−4.52854	−0.146694	−0.0733468	+	0.997306i	$0.523368\pi$
$954$	−1.00448	−0.0325213
$955$	−83.5023	−2.70207
$956$	17.6130	0.569646
$957$	18.6954	0.604338
$958$	−25.7394	−0.831601
$959$	16.2116	0.523499
$960$	−5.37799	−0.173574
$961$	20.2243	0.652397
$962$	0.138903	0.00447840
$963$	8.52815	0.274816
$964$	8.47734	0.273037
$965$	47.8184	1.53933
$966$	1.41524	0.0455345
$967$	−6.14998	−0.197770	−0.0988850	−	0.995099i	$-0.531528\pi$
$967$	−6.14998	−0.197770	−0.0988850	+	0.995099i	$0.531528\pi$
$968$	−16.3805	−0.526491
$969$	5.29916	0.170233
$970$	−1.78177	−0.0572091
$971$	−7.62147	−0.244585	−0.122292	−	0.992494i	$-0.539025\pi$
$971$	−7.62147	−0.244585	−0.122292	+	0.992494i	$0.539025\pi$
$972$	−6.73760	−0.216109
$973$	−8.30057	−0.266104
$974$	−17.5591	−0.562631
$975$	5.06538	0.162222
$976$	−8.72770	−0.279367
$977$	−31.8413	−1.01869	−0.509347	−	0.860561i	$-0.670113\pi$
$977$	−31.8413	−1.01869	−0.509347	+	0.860561i	$0.670113\pi$
$978$	2.70427	0.0864732
$979$	−10.8171	−0.345716
$980$	−15.3720	−0.491039
$981$	−9.38958	−0.299786
$982$	−23.8652	−0.761570
$983$	−0.0954871	−0.00304557	−0.00152278	−	0.999999i	$-0.500485\pi$
$983$	−0.0954871	−0.00304557	−0.00152278	+	0.999999i	$0.500485\pi$
$984$	19.3165	0.615786
$985$	−84.9818	−2.70775
$986$	−4.17862	−0.133074
$987$	−4.57905	−0.145753
$988$	0.871051	0.0277118
$989$	−4.59688	−0.146172
$990$	−12.1709	−0.386818
$991$	47.8478	1.51993	0.759967	−	0.649961i	$-0.225215\pi$
$991$	47.8478	1.51993	0.759967	+	0.649961i	$0.225215\pi$
$992$	−7.15712	−0.227239
$993$	40.6829	1.29103
$994$	−10.9968	−0.348797
$995$	−17.8449	−0.565720
$996$	7.31586	0.231812
$997$	−42.4150	−1.34330	−0.671649	−	0.740870i	$-0.734413\pi$
$997$	−42.4150	−1.34330	−0.671649	+	0.740870i	$0.734413\pi$
$998$	39.7435	1.25806
$999$	1.72991	0.0547320

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4034.2.a.b.1.12	✓	35

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4034.2.a.b.1.12	✓	35	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:	\( N \)	\(=\)	\( 4034 = 2 \cdot 2017 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4034.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -1.52925 q^{3} +1.00000 q^{4} +3.51675 q^{5} +1.52925 q^{6} -1.62140 q^{7} -1.00000 q^{8} -0.661396 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -1.52925 q^{3} +1.00000 q^{4} +3.51675 q^{5} +1.52925 q^{6} -1.62140 q^{7} -1.00000 q^{8} -0.661396 q^{9} -3.51675 q^{10} -5.23264 q^{11} -1.52925 q^{12} -0.449585 q^{13} +1.62140 q^{14} -5.37799 q^{15} +1.00000 q^{16} +1.78853 q^{17} +0.661396 q^{18} -1.93746 q^{19} +3.51675 q^{20} +2.47952 q^{21} +5.23264 q^{22} -0.570770 q^{23} +1.52925 q^{24} +7.36753 q^{25} +0.449585 q^{26} +5.59919 q^{27} -1.62140 q^{28} +2.33634 q^{29} +5.37799 q^{30} +7.15712 q^{31} -1.00000 q^{32} +8.00202 q^{33} -1.78853 q^{34} -5.70205 q^{35} -0.661396 q^{36} +0.308958 q^{37} +1.93746 q^{38} +0.687527 q^{39} -3.51675 q^{40} +12.6313 q^{41} -2.47952 q^{42} +8.05384 q^{43} -5.23264 q^{44} -2.32597 q^{45} +0.570770 q^{46} -1.84675 q^{47} -1.52925 q^{48} -4.37107 q^{49} -7.36753 q^{50} -2.73511 q^{51} -0.449585 q^{52} -1.51873 q^{53} -5.59919 q^{54} -18.4019 q^{55} +1.62140 q^{56} +2.96286 q^{57} -2.33634 q^{58} +0.0896840 q^{59} -5.37799 q^{60} -8.72770 q^{61} -7.15712 q^{62} +1.07239 q^{63} +1.00000 q^{64} -1.58108 q^{65} -8.00202 q^{66} -2.67065 q^{67} +1.78853 q^{68} +0.872849 q^{69} +5.70205 q^{70} -6.78228 q^{71} +0.661396 q^{72} -8.78213 q^{73} -0.308958 q^{74} -11.2668 q^{75} -1.93746 q^{76} +8.48420 q^{77} -0.687527 q^{78} -6.71761 q^{79} +3.51675 q^{80} -6.57837 q^{81} -12.6313 q^{82} -4.78396 q^{83} +2.47952 q^{84} +6.28981 q^{85} -8.05384 q^{86} -3.57285 q^{87} +5.23264 q^{88} +2.06724 q^{89} +2.32597 q^{90} +0.728956 q^{91} -0.570770 q^{92} -10.9450 q^{93} +1.84675 q^{94} -6.81355 q^{95} +1.52925 q^{96} +0.506652 q^{97} +4.37107 q^{98} +3.46085 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 35 q - 35 q^{2} - 6 q^{3} + 35 q^{4} + 6 q^{5} + 6 q^{6} - 14 q^{7} - 35 q^{8} + 23 q^{9}+O(q^{10}) \) 35 * q - 35 * q^2 - 6 * q^3 + 35 * q^4 + 6 * q^5 + 6 * q^6 - 14 * q^7 - 35 * q^8 + 23 * q^9	\( 35 q - 35 q^{2} - 6 q^{3} + 35 q^{4} + 6 q^{5} + 6 q^{6} - 14 q^{7} - 35 q^{8} + 23 q^{9} - 6 q^{10} - 9 q^{11} - 6 q^{12} - 7 q^{13} + 14 q^{14} - 19 q^{15} + 35 q^{16} + 17 q^{17} - 23 q^{18} - 25 q^{19} + 6 q^{20} - 15 q^{21} + 9 q^{22} - 12 q^{23} + 6 q^{24} + 7 q^{25} + 7 q^{26} - 27 q^{27} - 14 q^{28} - 13 q^{29} + 19 q^{30} - 69 q^{31} - 35 q^{32} + q^{33} - 17 q^{34} - 4 q^{35} + 23 q^{36} - 22 q^{37} + 25 q^{38} - 38 q^{39} - 6 q^{40} + 15 q^{42} - 32 q^{43} - 9 q^{44} + 9 q^{45} + 12 q^{46} - 18 q^{47} - 6 q^{48} - 19 q^{49} - 7 q^{50} - 21 q^{51} - 7 q^{52} + 20 q^{53} + 27 q^{54} - 54 q^{55} + 14 q^{56} + 28 q^{57} + 13 q^{58} - 21 q^{59} - 19 q^{60} - 67 q^{61} + 69 q^{62} - 28 q^{63} + 35 q^{64} + 22 q^{65} - q^{66} - 18 q^{67} + 17 q^{68} - 42 q^{69} + 4 q^{70} - 36 q^{71} - 23 q^{72} - 18 q^{73} + 22 q^{74} - 49 q^{75} - 25 q^{76} + 20 q^{77} + 38 q^{78} - 92 q^{79} + 6 q^{80} - 25 q^{81} + 42 q^{83} - 15 q^{84} - 29 q^{85} + 32 q^{86} - 40 q^{87} + 9 q^{88} - 8 q^{89} - 9 q^{90} - 89 q^{91} - 12 q^{92} - q^{93} + 18 q^{94} - 62 q^{95} + 6 q^{96} - 40 q^{97} + 19 q^{98} - 64 q^{99}+O(q^{100}) \) 35 * q - 35 * q^2 - 6 * q^3 + 35 * q^4 + 6 * q^5 + 6 * q^6 - 14 * q^7 - 35 * q^8 + 23 * q^9 - 6 * q^10 - 9 * q^11 - 6 * q^12 - 7 * q^13 + 14 * q^14 - 19 * q^15 + 35 * q^16 + 17 * q^17 - 23 * q^18 - 25 * q^19 + 6 * q^20 - 15 * q^21 + 9 * q^22 - 12 * q^23 + 6 * q^24 + 7 * q^25 + 7 * q^26 - 27 * q^27 - 14 * q^28 - 13 * q^29 + 19 * q^30 - 69 * q^31 - 35 * q^32 + q^33 - 17 * q^34 - 4 * q^35 + 23 * q^36 - 22 * q^37 + 25 * q^38 - 38 * q^39 - 6 * q^40 + 15 * q^42 - 32 * q^43 - 9 * q^44 + 9 * q^45 + 12 * q^46 - 18 * q^47 - 6 * q^48 - 19 * q^49 - 7 * q^50 - 21 * q^51 - 7 * q^52 + 20 * q^53 + 27 * q^54 - 54 * q^55 + 14 * q^56 + 28 * q^57 + 13 * q^58 - 21 * q^59 - 19 * q^60 - 67 * q^61 + 69 * q^62 - 28 * q^63 + 35 * q^64 + 22 * q^65 - q^66 - 18 * q^67 + 17 * q^68 - 42 * q^69 + 4 * q^70 - 36 * q^71 - 23 * q^72 - 18 * q^73 + 22 * q^74 - 49 * q^75 - 25 * q^76 + 20 * q^77 + 38 * q^78 - 92 * q^79 + 6 * q^80 - 25 * q^81 + 42 * q^83 - 15 * q^84 - 29 * q^85 + 32 * q^86 - 40 * q^87 + 9 * q^88 - 8 * q^89 - 9 * q^90 - 89 * q^91 - 12 * q^92 - q^93 + 18 * q^94 - 62 * q^95 + 6 * q^96 - 40 * q^97 + 19 * q^98 - 64 * q^99

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