LMFDB - Embedded newform 4034.2.a.c.1.9

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:	$0$
Dimension:	$49$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.9
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)

$f(q)$	$=$	$q-1.00000 q^{2} -2.38186 q^{3} +1.00000 q^{4} +1.49052 q^{5} +2.38186 q^{6} -1.41584 q^{7} -1.00000 q^{8} +2.67326 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -2.38186 q^{3} +1.00000 q^{4} +1.49052 q^{5} +2.38186 q^{6} -1.41584 q^{7} -1.00000 q^{8} +2.67326 q^{9} -1.49052 q^{10} -1.07167 q^{11} -2.38186 q^{12} +0.488413 q^{13} +1.41584 q^{14} -3.55022 q^{15} +1.00000 q^{16} -7.39470 q^{17} -2.67326 q^{18} +3.62646 q^{19} +1.49052 q^{20} +3.37232 q^{21} +1.07167 q^{22} -2.34046 q^{23} +2.38186 q^{24} -2.77834 q^{25} -0.488413 q^{26} +0.778256 q^{27} -1.41584 q^{28} +8.34523 q^{29} +3.55022 q^{30} -8.27439 q^{31} -1.00000 q^{32} +2.55257 q^{33} +7.39470 q^{34} -2.11034 q^{35} +2.67326 q^{36} -9.34105 q^{37} -3.62646 q^{38} -1.16333 q^{39} -1.49052 q^{40} +0.0389441 q^{41} -3.37232 q^{42} +9.90175 q^{43} -1.07167 q^{44} +3.98455 q^{45} +2.34046 q^{46} +5.58458 q^{47} -2.38186 q^{48} -4.99541 q^{49} +2.77834 q^{50} +17.6131 q^{51} +0.488413 q^{52} -13.0039 q^{53} -0.778256 q^{54} -1.59735 q^{55} +1.41584 q^{56} -8.63773 q^{57} -8.34523 q^{58} +6.50266 q^{59} -3.55022 q^{60} +3.60359 q^{61} +8.27439 q^{62} -3.78489 q^{63} +1.00000 q^{64} +0.727991 q^{65} -2.55257 q^{66} +11.4968 q^{67} -7.39470 q^{68} +5.57464 q^{69} +2.11034 q^{70} -6.86229 q^{71} -2.67326 q^{72} +6.61233 q^{73} +9.34105 q^{74} +6.61762 q^{75} +3.62646 q^{76} +1.51731 q^{77} +1.16333 q^{78} +12.0783 q^{79} +1.49052 q^{80} -9.87347 q^{81} -0.0389441 q^{82} -6.00325 q^{83} +3.37232 q^{84} -11.0220 q^{85} -9.90175 q^{86} -19.8772 q^{87} +1.07167 q^{88} -4.43201 q^{89} -3.98455 q^{90} -0.691513 q^{91} -2.34046 q^{92} +19.7084 q^{93} -5.58458 q^{94} +5.40533 q^{95} +2.38186 q^{96} -8.20825 q^{97} +4.99541 q^{98} -2.86485 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 49 q - 49 q^{2} + 8 q^{3} + 49 q^{4} - 8 q^{5} - 8 q^{6} + 18 q^{7} - 49 q^{8} + 59 q^{9}+O(q^{10}) $ 49 * q - 49 * q^2 + 8 * q^3 + 49 * q^4 - 8 * q^5 - 8 * q^6 + 18 * q^7 - 49 * q^8 + 59 * q^9	\( 49 q - 49 q^{2} + 8 q^{3} + 49 q^{4} - 8 q^{5} - 8 q^{6} + 18 q^{7} - 49 q^{8} + 59 q^{9} + 8 q^{10} + q^{11} + 8 q^{12} + 9 q^{13} - 18 q^{14} + 15 q^{15} + 49 q^{16} - 27 q^{17} - 59 q^{18} + 27 q^{19} - 8 q^{20} + 13 q^{21} - q^{22} + 16 q^{23} - 8 q^{24} + 71 q^{25} - 9 q^{26} + 29 q^{27} + 18 q^{28} - 7 q^{29} - 15 q^{30} + 75 q^{31} - 49 q^{32} - 3 q^{33} + 27 q^{34} - 16 q^{35} + 59 q^{36} + 36 q^{37} - 27 q^{38} + 24 q^{39} + 8 q^{40} - 12 q^{41} - 13 q^{42} + 22 q^{43} + q^{44} + 5 q^{45} - 16 q^{46} + 26 q^{47} + 8 q^{48} + 107 q^{49} - 71 q^{50} + 35 q^{51} + 9 q^{52} - 10 q^{53} - 29 q^{54} + 76 q^{55} - 18 q^{56} - 10 q^{57} + 7 q^{58} + 9 q^{59} + 15 q^{60} + 87 q^{61} - 75 q^{62} + 68 q^{63} + 49 q^{64} - 6 q^{65} + 3 q^{66} + 46 q^{67} - 27 q^{68} + 70 q^{69} + 16 q^{70} + 40 q^{71} - 59 q^{72} + 6 q^{73} - 36 q^{74} + 69 q^{75} + 27 q^{76} - 12 q^{77} - 24 q^{78} + 76 q^{79} - 8 q^{80} + 77 q^{81} + 12 q^{82} - 32 q^{83} + 13 q^{84} + 19 q^{85} - 22 q^{86} + 36 q^{87} - q^{88} + 34 q^{89} - 5 q^{90} + 119 q^{91} + 16 q^{92} - 5 q^{93} - 26 q^{94} - 2 q^{95} - 8 q^{96} + 52 q^{97} - 107 q^{98} + 26 q^{99}+O(q^{100}) \) 49 * q - 49 * q^2 + 8 * q^3 + 49 * q^4 - 8 * q^5 - 8 * q^6 + 18 * q^7 - 49 * q^8 + 59 * q^9 + 8 * q^10 + q^11 + 8 * q^12 + 9 * q^13 - 18 * q^14 + 15 * q^15 + 49 * q^16 - 27 * q^17 - 59 * q^18 + 27 * q^19 - 8 * q^20 + 13 * q^21 - q^22 + 16 * q^23 - 8 * q^24 + 71 * q^25 - 9 * q^26 + 29 * q^27 + 18 * q^28 - 7 * q^29 - 15 * q^30 + 75 * q^31 - 49 * q^32 - 3 * q^33 + 27 * q^34 - 16 * q^35 + 59 * q^36 + 36 * q^37 - 27 * q^38 + 24 * q^39 + 8 * q^40 - 12 * q^41 - 13 * q^42 + 22 * q^43 + q^44 + 5 * q^45 - 16 * q^46 + 26 * q^47 + 8 * q^48 + 107 * q^49 - 71 * q^50 + 35 * q^51 + 9 * q^52 - 10 * q^53 - 29 * q^54 + 76 * q^55 - 18 * q^56 - 10 * q^57 + 7 * q^58 + 9 * q^59 + 15 * q^60 + 87 * q^61 - 75 * q^62 + 68 * q^63 + 49 * q^64 - 6 * q^65 + 3 * q^66 + 46 * q^67 - 27 * q^68 + 70 * q^69 + 16 * q^70 + 40 * q^71 - 59 * q^72 + 6 * q^73 - 36 * q^74 + 69 * q^75 + 27 * q^76 - 12 * q^77 - 24 * q^78 + 76 * q^79 - 8 * q^80 + 77 * q^81 + 12 * q^82 - 32 * q^83 + 13 * q^84 + 19 * q^85 - 22 * q^86 + 36 * q^87 - q^88 + 34 * q^89 - 5 * q^90 + 119 * q^91 + 16 * q^92 - 5 * q^93 - 26 * q^94 - 2 * q^95 - 8 * q^96 + 52 * q^97 - 107 * q^98 + 26 * 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
$3$	−2.38186	−1.37517	−0.687584	−	0.726105i	$-0.741329\pi$
$3$	−2.38186	−1.37517	−0.687584	+	0.726105i	$0.741329\pi$
$4$	1.00000	0.500000
$5$	1.49052	0.666582	0.333291	−	0.942824i	$-0.391841\pi$
$5$	1.49052	0.666582	0.333291	+	0.942824i	$0.391841\pi$
$6$	2.38186	0.972390
$7$	−1.41584	−0.535136	−0.267568	−	0.963539i	$-0.586220\pi$
$7$	−1.41584	−0.535136	−0.267568	+	0.963539i	$0.586220\pi$
$8$	−1.00000	−0.353553
$9$	2.67326	0.891086
$10$	−1.49052	−0.471345
$11$	−1.07167	−0.323120	−0.161560	−	0.986863i	$-0.551653\pi$
$11$	−1.07167	−0.323120	−0.161560	+	0.986863i	$0.551653\pi$
$12$	−2.38186	−0.687584
$13$	0.488413	0.135461	0.0677307	−	0.997704i	$-0.478424\pi$
$13$	0.488413	0.135461	0.0677307	+	0.997704i	$0.478424\pi$
$14$	1.41584	0.378398
$15$	−3.55022	−0.916662
$16$	1.00000	0.250000
$17$	−7.39470	−1.79348	−0.896739	−	0.442559i	$-0.854071\pi$
$17$	−7.39470	−1.79348	−0.896739	+	0.442559i	$0.854071\pi$
$18$	−2.67326	−0.630093
$19$	3.62646	0.831968	0.415984	−	0.909372i	$-0.363437\pi$
$19$	3.62646	0.831968	0.415984	+	0.909372i	$0.363437\pi$
$20$	1.49052	0.333291
$21$	3.37232	0.735901
$22$	1.07167	0.228481
$23$	−2.34046	−0.488019	−0.244010	−	0.969773i	$-0.578463\pi$
$23$	−2.34046	−0.488019	−0.244010	+	0.969773i	$0.578463\pi$
$24$	2.38186	0.486195
$25$	−2.77834	−0.555668
$26$	−0.488413	−0.0957857
$27$	0.778256	0.149775
$28$	−1.41584	−0.267568
$29$	8.34523	1.54967	0.774835	−	0.632163i	$-0.217833\pi$
$29$	8.34523	1.54967	0.774835	+	0.632163i	$0.217833\pi$
$30$	3.55022	0.648178
$31$	−8.27439	−1.48612	−0.743062	−	0.669222i	$-0.766627\pi$
$31$	−8.27439	−1.48612	−0.743062	+	0.669222i	$0.766627\pi$
$32$	−1.00000	−0.176777
$33$	2.55257	0.444345
$34$	7.39470	1.26818
$35$	−2.11034	−0.356712
$36$	2.67326	0.445543
$37$	−9.34105	−1.53566	−0.767829	−	0.640655i	$-0.778663\pi$
$37$	−9.34105	−1.53566	−0.767829	+	0.640655i	$0.778663\pi$
$38$	−3.62646	−0.588290
$39$	−1.16333	−0.186282
$40$	−1.49052	−0.235672
$41$	0.0389441	0.00608205	0.00304102	−	0.999995i	$-0.499032\pi$
$41$	0.0389441	0.00608205	0.00304102	+	0.999995i	$0.499032\pi$
$42$	−3.37232	−0.520361
$43$	9.90175	1.51000	0.755001	−	0.655723i	$-0.227636\pi$
$43$	9.90175	1.51000	0.755001	+	0.655723i	$0.227636\pi$
$44$	−1.07167	−0.161560
$45$	3.98455	0.593982
$46$	2.34046	0.345082
$47$	5.58458	0.814595	0.407297	−	0.913296i	$-0.366471\pi$
$47$	5.58458	0.814595	0.407297	+	0.913296i	$0.366471\pi$
$48$	−2.38186	−0.343792
$49$	−4.99541	−0.713630
$50$	2.77834	0.392917
$51$	17.6131	2.46633
$52$	0.488413	0.0677307
$53$	−13.0039	−1.78622	−0.893112	−	0.449834i	$-0.851483\pi$
$53$	−13.0039	−1.78622	−0.893112	+	0.449834i	$0.851483\pi$
$54$	−0.778256	−0.105907
$55$	−1.59735	−0.215386
$56$	1.41584	0.189199
$57$	−8.63773	−1.14410
$58$	−8.34523	−1.09578
$59$	6.50266	0.846575	0.423287	−	0.905996i	$-0.360876\pi$
$59$	6.50266	0.846575	0.423287	+	0.905996i	$0.360876\pi$
$60$	−3.55022	−0.458331
$61$	3.60359	0.461393	0.230696	−	0.973026i	$-0.425900\pi$
$61$	3.60359	0.461393	0.230696	+	0.973026i	$0.425900\pi$
$62$	8.27439	1.05085
$63$	−3.78489	−0.476852
$64$	1.00000	0.125000
$65$	0.727991	0.0902961
$66$	−2.55257	−0.314199
$67$	11.4968	1.40456	0.702280	−	0.711901i	$-0.252166\pi$
$67$	11.4968	1.40456	0.702280	+	0.711901i	$0.252166\pi$
$68$	−7.39470	−0.896739
$69$	5.57464	0.671108
$70$	2.11034	0.252233
$71$	−6.86229	−0.814404	−0.407202	−	0.913338i	$-0.633495\pi$
$71$	−6.86229	−0.814404	−0.407202	+	0.913338i	$0.633495\pi$
$72$	−2.67326	−0.315046
$73$	6.61233	0.773915	0.386958	−	0.922098i	$-0.373526\pi$
$73$	6.61233	0.773915	0.386958	+	0.922098i	$0.373526\pi$
$74$	9.34105	1.08587
$75$	6.61762	0.764137
$76$	3.62646	0.415984
$77$	1.51731	0.172913
$78$	1.16333	0.131721
$79$	12.0783	1.35892	0.679459	−	0.733713i	$-0.262214\pi$
$79$	12.0783	1.35892	0.679459	+	0.733713i	$0.262214\pi$
$80$	1.49052	0.166646
$81$	−9.87347	−1.09705
$82$	−0.0389441	−0.00430066
$83$	−6.00325	−0.658943	−0.329471	−	0.944166i	$-0.606870\pi$
$83$	−6.00325	−0.658943	−0.329471	+	0.944166i	$0.606870\pi$
$84$	3.37232	0.367951
$85$	−11.0220	−1.19550
$86$	−9.90175	−1.06773
$87$	−19.8772	−2.13106
$88$	1.07167	0.114240
$89$	−4.43201	−0.469792	−0.234896	−	0.972021i	$-0.575475\pi$
$89$	−4.43201	−0.469792	−0.234896	+	0.972021i	$0.575475\pi$
$90$	−3.98455	−0.420009
$91$	−0.691513	−0.0724902
$92$	−2.34046	−0.244010
$93$	19.7084	2.04367
$94$	−5.58458	−0.576006
$95$	5.40533	0.554575
$96$	2.38186	0.243098
$97$	−8.20825	−0.833421	−0.416711	−	0.909039i	$-0.636817\pi$
$97$	−8.20825	−0.833421	−0.416711	+	0.909039i	$0.636817\pi$
$98$	4.99541	0.504613
$99$	−2.86485	−0.287928
$100$	−2.77834	−0.277834
$101$	8.38628	0.834466	0.417233	−	0.908800i	$-0.363000\pi$
$101$	8.38628	0.834466	0.417233	+	0.908800i	$0.363000\pi$
$102$	−17.6131	−1.74396
$103$	7.55563	0.744478	0.372239	−	0.928137i	$-0.378590\pi$
$103$	7.55563	0.744478	0.372239	+	0.928137i	$0.378590\pi$
$104$	−0.488413	−0.0478928
$105$	5.02652	0.490538
$106$	13.0039	1.26305
$107$	−2.03090	−0.196334	−0.0981672	−	0.995170i	$-0.531298\pi$
$107$	−2.03090	−0.196334	−0.0981672	+	0.995170i	$0.531298\pi$
$108$	0.778256	0.0748877
$109$	1.47195	0.140987	0.0704934	−	0.997512i	$-0.477543\pi$
$109$	1.47195	0.140987	0.0704934	+	0.997512i	$0.477543\pi$
$110$	1.59735	0.152301
$111$	22.2491	2.11179
$112$	−1.41584	−0.133784
$113$	−9.38170	−0.882556	−0.441278	−	0.897370i	$-0.645475\pi$
$113$	−9.38170	−0.882556	−0.441278	+	0.897370i	$0.645475\pi$
$114$	8.63773	0.808997
$115$	−3.48851	−0.325305
$116$	8.34523	0.774835
$117$	1.30565	0.120708
$118$	−6.50266	−0.598619
$119$	10.4697	0.959754
$120$	3.55022	0.324089
$121$	−9.85153	−0.895593
$122$	−3.60359	−0.326254
$123$	−0.0927594	−0.00836383
$124$	−8.27439	−0.743062
$125$	−11.5938	−1.03698
$126$	3.78489	0.337185
$127$	−9.25126	−0.820917	−0.410458	−	0.911879i	$-0.634631\pi$
$127$	−9.25126	−0.820917	−0.410458	+	0.911879i	$0.634631\pi$
$128$	−1.00000	−0.0883883
$129$	−23.5846	−2.07651
$130$	−0.727991	−0.0638490
$131$	−3.13809	−0.274176	−0.137088	−	0.990559i	$-0.543774\pi$
$131$	−3.13809	−0.274176	−0.137088	+	0.990559i	$0.543774\pi$
$132$	2.55257	0.222172
$133$	−5.13448	−0.445216
$134$	−11.4968	−0.993174
$135$	1.16001	0.0998376
$136$	7.39470	0.634090
$137$	−3.00125	−0.256414	−0.128207	−	0.991747i	$-0.540922\pi$
$137$	−3.00125	−0.256414	−0.128207	+	0.991747i	$0.540922\pi$
$138$	−5.57464	−0.474545
$139$	−0.803271	−0.0681325	−0.0340663	−	0.999420i	$-0.510846\pi$
$139$	−0.803271	−0.0681325	−0.0340663	+	0.999420i	$0.510846\pi$
$140$	−2.11034	−0.178356
$141$	−13.3017	−1.12020
$142$	6.86229	0.575870
$143$	−0.523417	−0.0437703
$144$	2.67326	0.222771
$145$	12.4388	1.03298
$146$	−6.61233	−0.547241
$147$	11.8984	0.981361
$148$	−9.34105	−0.767829
$149$	8.75154	0.716954	0.358477	−	0.933539i	$-0.383296\pi$
$149$	8.75154	0.716954	0.358477	+	0.933539i	$0.383296\pi$
$150$	−6.61762	−0.540327
$151$	4.78960	0.389772	0.194886	−	0.980826i	$-0.437566\pi$
$151$	4.78960	0.389772	0.194886	+	0.980826i	$0.437566\pi$
$152$	−3.62646	−0.294145
$153$	−19.7679	−1.59814
$154$	−1.51731	−0.122268
$155$	−12.3332	−0.990624
$156$	−1.16333	−0.0931411
$157$	−15.6362	−1.24790	−0.623952	−	0.781463i	$-0.714474\pi$
$157$	−15.6362	−1.24790	−0.623952	+	0.781463i	$0.714474\pi$
$158$	−12.0783	−0.960901
$159$	30.9735	2.45636
$160$	−1.49052	−0.117836
$161$	3.31370	0.261156
$162$	9.87347	0.775733
$163$	6.26828	0.490969	0.245485	−	0.969400i	$-0.421053\pi$
$163$	6.26828	0.490969	0.245485	+	0.969400i	$0.421053\pi$
$164$	0.0389441	0.00304102
$165$	3.80466	0.296192
$166$	6.00325	0.465943
$167$	−18.8286	−1.45700	−0.728499	−	0.685046i	$-0.759782\pi$
$167$	−18.8286	−1.45700	−0.728499	+	0.685046i	$0.759782\pi$
$168$	−3.37232	−0.260180
$169$	−12.7615	−0.981650
$170$	11.0220	0.845347
$171$	9.69447	0.741355
$172$	9.90175	0.755001
$173$	4.91097	0.373374	0.186687	−	0.982419i	$-0.440225\pi$
$173$	4.91097	0.373374	0.186687	+	0.982419i	$0.440225\pi$
$174$	19.8772	1.50688
$175$	3.93368	0.297358
$176$	−1.07167	−0.0807801
$177$	−15.4884	−1.16418
$178$	4.43201	0.332193
$179$	14.2226	1.06305	0.531525	−	0.847042i	$-0.321619\pi$
$179$	14.2226	1.06305	0.531525	+	0.847042i	$0.321619\pi$
$180$	3.98455	0.296991
$181$	13.0700	0.971483	0.485742	−	0.874102i	$-0.338550\pi$
$181$	13.0700	0.971483	0.485742	+	0.874102i	$0.338550\pi$
$182$	0.691513	0.0512583
$183$	−8.58325	−0.634492
$184$	2.34046	0.172541
$185$	−13.9230	−1.02364
$186$	−19.7084	−1.44509
$187$	7.92467	0.579510
$188$	5.58458	0.407297
$189$	−1.10188	−0.0801501
$190$	−5.40533	−0.392144
$191$	16.6827	1.20712	0.603559	−	0.797318i	$-0.293749\pi$
$191$	16.6827	1.20712	0.603559	+	0.797318i	$0.293749\pi$
$192$	−2.38186	−0.171896
$193$	16.1493	1.16245	0.581225	−	0.813743i	$-0.302574\pi$
$193$	16.1493	1.16245	0.581225	+	0.813743i	$0.302574\pi$
$194$	8.20825	0.589318
$195$	−1.73397	−0.124172
$196$	−4.99541	−0.356815
$197$	10.6786	0.760818	0.380409	−	0.924818i	$-0.375783\pi$
$197$	10.6786	0.760818	0.380409	+	0.924818i	$0.375783\pi$
$198$	2.86485	0.203596
$199$	0.127630	0.00904743	0.00452371	−	0.999990i	$-0.498560\pi$
$199$	0.127630	0.00904743	0.00452371	+	0.999990i	$0.498560\pi$
$200$	2.77834	0.196458
$201$	−27.3838	−1.93150
$202$	−8.38628	−0.590056
$203$	−11.8155	−0.829284
$204$	17.6131	1.23317
$205$	0.0580471	0.00405418
$206$	−7.55563	−0.526426
$207$	−6.25665	−0.434867
$208$	0.488413	0.0338653
$209$	−3.88637	−0.268826
$210$	−5.02652	−0.346863
$211$	8.58468	0.590994	0.295497	−	0.955344i	$-0.404515\pi$
$211$	8.58468	0.590994	0.295497	+	0.955344i	$0.404515\pi$
$212$	−13.0039	−0.893112
$213$	16.3450	1.11994
$214$	2.03090	0.138829
$215$	14.7588	1.00654
$216$	−0.778256	−0.0529536
$217$	11.7152	0.795278
$218$	−1.47195	−0.0996927
$219$	−15.7497	−1.06426
$220$	−1.59735	−0.107693
$221$	−3.61167	−0.242947
$222$	−22.2491	−1.49326
$223$	−1.02561	−0.0686797	−0.0343399	−	0.999410i	$-0.510933\pi$
$223$	−1.02561	−0.0686797	−0.0343399	+	0.999410i	$0.510933\pi$
$224$	1.41584	0.0945995
$225$	−7.42722	−0.495148
$226$	9.38170	0.624061
$227$	20.9471	1.39031	0.695155	−	0.718860i	$-0.255336\pi$
$227$	20.9471	1.39031	0.695155	+	0.718860i	$0.255336\pi$
$228$	−8.63773	−0.572048
$229$	26.3855	1.74360	0.871801	−	0.489861i	$-0.162952\pi$
$229$	26.3855	1.74360	0.871801	+	0.489861i	$0.162952\pi$
$230$	3.48851	0.230025
$231$	−3.61401	−0.237785
$232$	−8.34523	−0.547891
$233$	1.58014	0.103519	0.0517593	−	0.998660i	$-0.483517\pi$
$233$	1.58014	0.103519	0.0517593	+	0.998660i	$0.483517\pi$
$234$	−1.30565	−0.0853532
$235$	8.32394	0.542994
$236$	6.50266	0.423287
$237$	−28.7689	−1.86874
$238$	−10.4697	−0.678649
$239$	13.5886	0.878975	0.439488	−	0.898249i	$-0.355160\pi$
$239$	13.5886	0.878975	0.439488	+	0.898249i	$0.355160\pi$
$240$	−3.55022	−0.229165
$241$	−9.34302	−0.601837	−0.300919	−	0.953650i	$-0.597293\pi$
$241$	−9.34302	−0.601837	−0.300919	+	0.953650i	$0.597293\pi$
$242$	9.85153	0.633280
$243$	21.1825	1.35885
$244$	3.60359	0.230696
$245$	−7.44577	−0.475693
$246$	0.0927594	0.00591412
$247$	1.77121	0.112700
$248$	8.27439	0.525424
$249$	14.2989	0.906156
$250$	11.5938	0.733256
$251$	−13.0376	−0.822923	−0.411462	−	0.911427i	$-0.634982\pi$
$251$	−13.0376	−0.822923	−0.411462	+	0.911427i	$0.634982\pi$
$252$	−3.78489	−0.238426
$253$	2.50820	0.157689
$254$	9.25126	0.580476
$255$	26.2528	1.64401
$256$	1.00000	0.0625000
$257$	−8.39355	−0.523575	−0.261788	−	0.965126i	$-0.584312\pi$
$257$	−8.39355	−0.523575	−0.261788	+	0.965126i	$0.584312\pi$
$258$	23.5846	1.46831
$259$	13.2254	0.821785
$260$	0.727991	0.0451481
$261$	22.3089	1.38089
$262$	3.13809	0.193872
$263$	−2.87762	−0.177442	−0.0887208	−	0.996057i	$-0.528278\pi$
$263$	−2.87762	−0.177442	−0.0887208	+	0.996057i	$0.528278\pi$
$264$	−2.55257	−0.157100
$265$	−19.3826	−1.19067
$266$	5.13448	0.314815
$267$	10.5564	0.646042
$268$	11.4968	0.702280
$269$	13.5590	0.826710	0.413355	−	0.910570i	$-0.364357\pi$
$269$	13.5590	0.826710	0.413355	+	0.910570i	$0.364357\pi$
$270$	−1.16001	−0.0705958
$271$	12.8458	0.780328	0.390164	−	0.920745i	$-0.372418\pi$
$271$	12.8458	0.780328	0.390164	+	0.920745i	$0.372418\pi$
$272$	−7.39470	−0.448370
$273$	1.64709	0.0996862
$274$	3.00125	0.181312
$275$	2.97746	0.179548
$276$	5.57464	0.335554
$277$	26.7064	1.60463	0.802315	−	0.596901i	$-0.203602\pi$
$277$	26.7064	1.60463	0.802315	+	0.596901i	$0.203602\pi$
$278$	0.803271	0.0481770
$279$	−22.1196	−1.32426
$280$	2.11034	0.126117
$281$	16.7363	0.998403	0.499202	−	0.866486i	$-0.333627\pi$
$281$	16.7363	0.998403	0.499202	+	0.866486i	$0.333627\pi$
$282$	13.3017	0.792104
$283$	19.8480	1.17984	0.589921	−	0.807461i	$-0.299159\pi$
$283$	19.8480	1.17984	0.589921	+	0.807461i	$0.299159\pi$
$284$	−6.86229	−0.407202
$285$	−12.8747	−0.762633
$286$	0.523417	0.0309503
$287$	−0.0551385	−0.00325472
$288$	−2.67326	−0.157523
$289$	37.6816	2.21657
$290$	−12.4388	−0.730429
$291$	19.5509	1.14609
$292$	6.61233	0.386958
$293$	17.9974	1.05142	0.525711	−	0.850663i	$-0.323799\pi$
$293$	17.9974	1.05142	0.525711	+	0.850663i	$0.323799\pi$
$294$	−11.8984	−0.693927
$295$	9.69237	0.564311
$296$	9.34105	0.542937
$297$	−0.834032	−0.0483955
$298$	−8.75154	−0.506963
$299$	−1.14311	−0.0661078
$300$	6.61762	0.382069
$301$	−14.0192	−0.808056
$302$	−4.78960	−0.275611
$303$	−19.9749	−1.14753
$304$	3.62646	0.207992
$305$	5.37124	0.307556
$306$	19.7679	1.13006
$307$	−24.6367	−1.40609	−0.703044	−	0.711146i	$-0.748176\pi$
$307$	−24.6367	−1.40609	−0.703044	+	0.711146i	$0.748176\pi$
$308$	1.51731	0.0864566
$309$	−17.9965	−1.02378
$310$	12.3332	0.700477
$311$	−14.0560	−0.797043	−0.398521	−	0.917159i	$-0.630477\pi$
$311$	−14.0560	−0.797043	−0.398521	+	0.917159i	$0.630477\pi$
$312$	1.16333	0.0658607
$313$	15.5853	0.880933	0.440467	−	0.897769i	$-0.354813\pi$
$313$	15.5853	0.880933	0.440467	+	0.897769i	$0.354813\pi$
$314$	15.6362	0.882401
$315$	−5.64147	−0.317861
$316$	12.0783	0.679459
$317$	19.3800	1.08849	0.544246	−	0.838926i	$-0.316816\pi$
$317$	19.3800	1.08849	0.544246	+	0.838926i	$0.316816\pi$
$318$	−30.9735	−1.73691
$319$	−8.94333	−0.500730
$320$	1.49052	0.0833228
$321$	4.83732	0.269993
$322$	−3.31370	−0.184665
$323$	−26.8166	−1.49212
$324$	−9.87347	−0.548526
$325$	−1.35698	−0.0752716
$326$	−6.26828	−0.347168
$327$	−3.50597	−0.193880
$328$	−0.0389441	−0.00215033
$329$	−7.90685	−0.435919
$330$	−3.80466	−0.209439
$331$	10.3132	0.566863	0.283432	−	0.958992i	$-0.408527\pi$
$331$	10.3132	0.566863	0.283432	+	0.958992i	$0.408527\pi$
$332$	−6.00325	−0.329471
$333$	−24.9710	−1.36840
$334$	18.8286	1.03025
$335$	17.1363	0.936254
$336$	3.37232	0.183975
$337$	−23.8912	−1.30144	−0.650718	−	0.759320i	$-0.725532\pi$
$337$	−23.8912	−1.30144	−0.650718	+	0.759320i	$0.725532\pi$
$338$	12.7615	0.694132
$339$	22.3459	1.21366
$340$	−11.0220	−0.597750
$341$	8.86741	0.480197
$342$	−9.69447	−0.524217
$343$	16.9835	0.917024
$344$	−9.90175	−0.533866
$345$	8.30913	0.447349
$346$	−4.91097	−0.264015
$347$	−6.57089	−0.352744	−0.176372	−	0.984324i	$-0.556436\pi$
$347$	−6.57089	−0.352744	−0.176372	+	0.984324i	$0.556436\pi$
$348$	−19.8772	−1.06553
$349$	9.81203	0.525226	0.262613	−	0.964901i	$-0.415416\pi$
$349$	9.81203	0.525226	0.262613	+	0.964901i	$0.415416\pi$
$350$	−3.93368	−0.210264
$351$	0.380110	0.0202888
$352$	1.07167	0.0571202
$353$	7.67068	0.408269	0.204135	−	0.978943i	$-0.434562\pi$
$353$	7.67068	0.408269	0.204135	+	0.978943i	$0.434562\pi$
$354$	15.4884	0.823201
$355$	−10.2284	−0.542867
$356$	−4.43201	−0.234896
$357$	−24.9373	−1.31982
$358$	−14.2226	−0.751690
$359$	−29.6755	−1.56621	−0.783106	−	0.621888i	$-0.786366\pi$
$359$	−29.6755	−1.56621	−0.783106	+	0.621888i	$0.786366\pi$
$360$	−3.98455	−0.210004
$361$	−5.84876	−0.307830
$362$	−13.0700	−0.686942
$363$	23.4650	1.23159
$364$	−0.691513	−0.0362451
$365$	9.85584	0.515878
$366$	8.58325	0.448654
$367$	−6.28818	−0.328240	−0.164120	−	0.986440i	$-0.552478\pi$
$367$	−6.28818	−0.328240	−0.164120	+	0.986440i	$0.552478\pi$
$368$	−2.34046	−0.122005
$369$	0.104108	0.00541963
$370$	13.9230	0.723824
$371$	18.4114	0.955872
$372$	19.7084	1.02184
$373$	−3.00475	−0.155580	−0.0777899	−	0.996970i	$-0.524786\pi$
$373$	−3.00475	−0.155580	−0.0777899	+	0.996970i	$0.524786\pi$
$374$	−7.92467	−0.409775
$375$	27.6148	1.42602
$376$	−5.58458	−0.288003
$377$	4.07592	0.209921
$378$	1.10188	0.0566747
$379$	13.6812	0.702755	0.351378	−	0.936234i	$-0.385713\pi$
$379$	13.6812	0.702755	0.351378	+	0.936234i	$0.385713\pi$
$380$	5.40533	0.277287
$381$	22.0352	1.12890
$382$	−16.6827	−0.853561
$383$	−16.7609	−0.856440	−0.428220	−	0.903675i	$-0.640859\pi$
$383$	−16.7609	−0.856440	−0.428220	+	0.903675i	$0.640859\pi$
$384$	2.38186	0.121549
$385$	2.26158	0.115261
$386$	−16.1493	−0.821976
$387$	26.4699	1.34554
$388$	−8.20825	−0.416711
$389$	26.1383	1.32527	0.662633	−	0.748944i	$-0.269439\pi$
$389$	26.1383	1.32527	0.662633	+	0.748944i	$0.269439\pi$
$390$	1.73397	0.0878031
$391$	17.3070	0.875252
$392$	4.99541	0.252306
$393$	7.47448	0.377038
$394$	−10.6786	−0.537980
$395$	18.0030	0.905831
$396$	−2.86485	−0.143964
$397$	25.9053	1.30015	0.650075	−	0.759870i	$-0.274738\pi$
$397$	25.9053	1.30015	0.650075	+	0.759870i	$0.274738\pi$
$398$	−0.127630	−0.00639750
$399$	12.2296	0.612246
$400$	−2.77834	−0.138917
$401$	15.2747	0.762782	0.381391	−	0.924414i	$-0.375445\pi$
$401$	15.2747	0.762782	0.381391	+	0.924414i	$0.375445\pi$
$402$	27.3838	1.36578
$403$	−4.04132	−0.201313
$404$	8.38628	0.417233
$405$	−14.7166	−0.731275
$406$	11.8155	0.586392
$407$	10.0105	0.496203
$408$	−17.6131	−0.871981
$409$	7.13796	0.352949	0.176475	−	0.984305i	$-0.443531\pi$
$409$	7.13796	0.352949	0.176475	+	0.984305i	$0.443531\pi$
$410$	−0.0580471	−0.00286674
$411$	7.14857	0.352613
$412$	7.55563	0.372239
$413$	−9.20670	−0.453032
$414$	6.25665	0.307497
$415$	−8.94798	−0.439239
$416$	−0.488413	−0.0239464
$417$	1.91328	0.0936936
$418$	3.88637	0.190089
$419$	16.7012	0.815909	0.407954	−	0.913002i	$-0.366242\pi$
$419$	16.7012	0.815909	0.407954	+	0.913002i	$0.366242\pi$
$420$	5.02652	0.245269
$421$	−14.2637	−0.695172	−0.347586	−	0.937648i	$-0.612999\pi$
$421$	−14.2637	−0.695172	−0.347586	+	0.937648i	$0.612999\pi$
$422$	−8.58468	−0.417896
$423$	14.9290	0.725874
$424$	13.0039	0.631526
$425$	20.5450	0.996579
$426$	−16.3450	−0.791918
$427$	−5.10209	−0.246908
$428$	−2.03090	−0.0981672
$429$	1.24671	0.0601915
$430$	−14.7588	−0.711732
$431$	−3.14242	−0.151365	−0.0756826	−	0.997132i	$-0.524114\pi$
$431$	−3.14242	−0.151365	−0.0756826	+	0.997132i	$0.524114\pi$
$432$	0.778256	0.0374438
$433$	38.1479	1.83327	0.916635	−	0.399726i	$-0.130895\pi$
$433$	38.1479	1.83327	0.916635	+	0.399726i	$0.130895\pi$
$434$	−11.7152	−0.562347
$435$	−29.6274	−1.42052
$436$	1.47195	0.0704934
$437$	−8.48759	−0.406016
$438$	15.7497	0.752548
$439$	27.6457	1.31946	0.659729	−	0.751504i	$-0.270671\pi$
$439$	27.6457	1.31946	0.659729	+	0.751504i	$0.270671\pi$
$440$	1.59735	0.0761505
$441$	−13.3540	−0.635905
$442$	3.61167	0.171790
$443$	−0.265135	−0.0125969	−0.00629847	−	0.999980i	$-0.502005\pi$
$443$	−0.265135	−0.0125969	−0.00629847	+	0.999980i	$0.502005\pi$
$444$	22.2491	1.05589
$445$	−6.60601	−0.313155
$446$	1.02561	0.0485639
$447$	−20.8449	−0.985932
$448$	−1.41584	−0.0668919
$449$	8.32705	0.392978	0.196489	−	0.980506i	$-0.437046\pi$
$449$	8.32705	0.392978	0.196489	+	0.980506i	$0.437046\pi$
$450$	7.42722	0.350123
$451$	−0.0417352	−0.00196523
$452$	−9.38170	−0.441278
$453$	−11.4082	−0.536002
$454$	−20.9471	−0.983097
$455$	−1.03072	−0.0483207
$456$	8.63773	0.404499
$457$	0.902313	0.0422084	0.0211042	−	0.999777i	$-0.493282\pi$
$457$	0.902313	0.0422084	0.0211042	+	0.999777i	$0.493282\pi$
$458$	−26.3855	−1.23291
$459$	−5.75497	−0.268619
$460$	−3.48851	−0.162652
$461$	−24.9063	−1.16000	−0.580001	−	0.814616i	$-0.696948\pi$
$461$	−24.9063	−1.16000	−0.580001	+	0.814616i	$0.696948\pi$
$462$	3.61401	0.168139
$463$	−12.8193	−0.595762	−0.297881	−	0.954603i	$-0.596280\pi$
$463$	−12.8193	−0.595762	−0.297881	+	0.954603i	$0.596280\pi$
$464$	8.34523	0.387418
$465$	29.3759	1.36227
$466$	−1.58014	−0.0731986
$467$	14.5740	0.674404	0.337202	−	0.941432i	$-0.390519\pi$
$467$	14.5740	0.674404	0.337202	+	0.941432i	$0.390519\pi$
$468$	1.30565	0.0603539
$469$	−16.2776	−0.751630
$470$	−8.32394	−0.383955
$471$	37.2432	1.71608
$472$	−6.50266	−0.299309
$473$	−10.6114	−0.487913
$474$	28.7689	1.32140
$475$	−10.0756	−0.462298
$476$	10.4697	0.479877
$477$	−34.7628	−1.59168
$478$	−13.5886	−0.621529
$479$	34.6155	1.58162	0.790810	−	0.612061i	$-0.209659\pi$
$479$	34.6155	1.58162	0.790810	+	0.612061i	$0.209659\pi$
$480$	3.55022	0.162044
$481$	−4.56229	−0.208022
$482$	9.34302	0.425563
$483$	−7.89278	−0.359134
$484$	−9.85153	−0.447797
$485$	−12.2346	−0.555544
$486$	−21.1825	−0.960855
$487$	12.8733	0.583345	0.291672	−	0.956518i	$-0.405788\pi$
$487$	12.8733	0.583345	0.291672	+	0.956518i	$0.405788\pi$
$488$	−3.60359	−0.163127
$489$	−14.9302	−0.675165
$490$	7.44577	0.336366
$491$	13.2512	0.598017	0.299009	−	0.954250i	$-0.403344\pi$
$491$	13.2512	0.598017	0.299009	+	0.954250i	$0.403344\pi$
$492$	−0.0927594	−0.00418192
$493$	−61.7105	−2.77930
$494$	−1.77121	−0.0796906
$495$	−4.27012	−0.191928
$496$	−8.27439	−0.371531
$497$	9.71587	0.435816
$498$	−14.2989	−0.640749
$499$	−1.67625	−0.0750391	−0.0375196	−	0.999296i	$-0.511946\pi$
$499$	−1.67625	−0.0750391	−0.0375196	+	0.999296i	$0.511946\pi$
$500$	−11.5938	−0.518490
$501$	44.8470	2.00362
$502$	13.0376	0.581895
$503$	22.7663	1.01510	0.507550	−	0.861623i	$-0.330551\pi$
$503$	22.7663	1.01510	0.507550	+	0.861623i	$0.330551\pi$
$504$	3.78489	0.168593
$505$	12.4999	0.556240
$506$	−2.50820	−0.111503
$507$	30.3960	1.34993
$508$	−9.25126	−0.410458
$509$	−15.4924	−0.686687	−0.343344	−	0.939210i	$-0.611560\pi$
$509$	−15.4924	−0.686687	−0.343344	+	0.939210i	$0.611560\pi$
$510$	−26.2528	−1.16249
$511$	−9.36198	−0.414150
$512$	−1.00000	−0.0441942
$513$	2.82232	0.124608
$514$	8.39355	0.370224
$515$	11.2618	0.496256
$516$	−23.5846	−1.03825
$517$	−5.98482	−0.263212
$518$	−13.2254	−0.581090
$519$	−11.6972	−0.513452
$520$	−0.727991	−0.0319245
$521$	0.776397	0.0340146	0.0170073	−	0.999855i	$-0.494586\pi$
$521$	0.776397	0.0340146	0.0170073	+	0.999855i	$0.494586\pi$
$522$	−22.3089	−0.976436
$523$	26.3271	1.15120	0.575601	−	0.817731i	$-0.304768\pi$
$523$	26.3271	1.15120	0.575601	+	0.817731i	$0.304768\pi$
$524$	−3.13809	−0.137088
$525$	−9.36946	−0.408917
$526$	2.87762	0.125470
$527$	61.1867	2.66533
$528$	2.55257	0.111086
$529$	−17.5223	−0.761837
$530$	19.3826	0.841927
$531$	17.3833	0.754371
$532$	−5.13448	−0.222608
$533$	0.0190208	0.000823883 0
$534$	−10.5564	−0.456821
$535$	−3.02710	−0.130873
$536$	−11.4968	−0.496587
$537$	−33.8763	−1.46187
$538$	−13.5590	−0.584572
$539$	5.35343	0.230588
$540$	1.16001	0.0499188
$541$	−7.47441	−0.321350	−0.160675	−	0.987007i	$-0.551367\pi$
$541$	−7.47441	−0.321350	−0.160675	+	0.987007i	$0.551367\pi$
$542$	−12.8458	−0.551775
$543$	−31.1308	−1.33595
$544$	7.39470	0.317045
$545$	2.19397	0.0939793
$546$	−1.64709	−0.0704888
$547$	34.7114	1.48415	0.742076	−	0.670316i	$-0.233841\pi$
$547$	34.7114	1.48415	0.742076	+	0.670316i	$0.233841\pi$
$548$	−3.00125	−0.128207
$549$	9.63333	0.411141
$550$	−2.97746	−0.126959
$551$	30.2637	1.28928
$552$	−5.57464	−0.237273
$553$	−17.1009	−0.727206
$554$	−26.7064	−1.13464
$555$	33.1627	1.40768
$556$	−0.803271	−0.0340663
$557$	−3.13846	−0.132981	−0.0664904	−	0.997787i	$-0.521180\pi$
$557$	−3.13846	−0.132981	−0.0664904	+	0.997787i	$0.521180\pi$
$558$	22.1196	0.936396
$559$	4.83614	0.204547
$560$	−2.11034	−0.0891779
$561$	−18.8755	−0.796923
$562$	−16.7363	−0.705978
$563$	−9.94694	−0.419213	−0.209607	−	0.977786i	$-0.567218\pi$
$563$	−9.94694	−0.419213	−0.209607	+	0.977786i	$0.567218\pi$
$564$	−13.3017	−0.560102
$565$	−13.9836	−0.588296
$566$	−19.8480	−0.834274
$567$	13.9792	0.587072
$568$	6.86229	0.287935
$569$	20.0390	0.840080	0.420040	−	0.907506i	$-0.362016\pi$
$569$	20.0390	0.840080	0.420040	+	0.907506i	$0.362016\pi$
$570$	12.8747	0.539263
$571$	22.0322	0.922020	0.461010	−	0.887395i	$-0.347487\pi$
$571$	22.0322	0.922020	0.461010	+	0.887395i	$0.347487\pi$
$572$	−0.523417	−0.0218852
$573$	−39.7358	−1.65999
$574$	0.0551385	0.00230143
$575$	6.50259	0.271177
$576$	2.67326	0.111386
$577$	35.7198	1.48703	0.743516	−	0.668718i	$-0.233157\pi$
$577$	35.7198	1.48703	0.743516	+	0.668718i	$0.233157\pi$
$578$	−37.6816	−1.56735
$579$	−38.4653	−1.59856
$580$	12.4388	0.516491
$581$	8.49962	0.352624
$582$	−19.5509	−0.810411
$583$	13.9359	0.577165
$584$	−6.61233	−0.273620
$585$	1.94611	0.0804616
$586$	−17.9974	−0.743467
$587$	4.50528	0.185953	0.0929763	−	0.995668i	$-0.470362\pi$
$587$	4.50528	0.185953	0.0929763	+	0.995668i	$0.470362\pi$
$588$	11.8984	0.490680
$589$	−30.0068	−1.23641
$590$	−9.69237	−0.399028
$591$	−25.4349	−1.04625
$592$	−9.34105	−0.383915
$593$	−25.1947	−1.03462	−0.517312	−	0.855797i	$-0.673067\pi$
$593$	−25.1947	−1.03462	−0.517312	+	0.855797i	$0.673067\pi$
$594$	0.834032	0.0342208
$595$	15.6053	0.639755
$596$	8.75154	0.358477
$597$	−0.303996	−0.0124417
$598$	1.14311	0.0467452
$599$	−5.01587	−0.204943	−0.102471	−	0.994736i	$-0.532675\pi$
$599$	−5.01587	−0.204943	−0.102471	+	0.994736i	$0.532675\pi$
$600$	−6.61762	−0.270163
$601$	19.3727	0.790229	0.395114	−	0.918632i	$-0.370705\pi$
$601$	19.3727	0.790229	0.395114	+	0.918632i	$0.370705\pi$
$602$	14.0192	0.571382
$603$	30.7339	1.25158
$604$	4.78960	0.194886
$605$	−14.6839	−0.596986
$606$	19.9749	0.811426
$607$	−3.54967	−0.144077	−0.0720383	−	0.997402i	$-0.522950\pi$
$607$	−3.54967	−0.144077	−0.0720383	+	0.997402i	$0.522950\pi$
$608$	−3.62646	−0.147073
$609$	28.1428	1.14040
$610$	−5.37124	−0.217475
$611$	2.72758	0.110346
$612$	−19.7679	−0.799072
$613$	25.3457	1.02370	0.511851	−	0.859074i	$-0.328960\pi$
$613$	25.3457	1.02370	0.511851	+	0.859074i	$0.328960\pi$
$614$	24.6367	0.994254
$615$	−0.138260	−0.00557518
$616$	−1.51731	−0.0611340
$617$	−8.58447	−0.345598	−0.172799	−	0.984957i	$-0.555281\pi$
$617$	−8.58447	−0.345598	−0.172799	+	0.984957i	$0.555281\pi$
$618$	17.9965	0.723923
$619$	−12.9522	−0.520595	−0.260297	−	0.965528i	$-0.583821\pi$
$619$	−12.9522	−0.520595	−0.260297	+	0.965528i	$0.583821\pi$
$620$	−12.3332	−0.495312
$621$	−1.82147	−0.0730933
$622$	14.0560	0.563594
$623$	6.27499	0.251402
$624$	−1.16333	−0.0465705
$625$	−3.38911	−0.135564
$626$	−15.5853	−0.622914
$627$	9.25679	0.369680
$628$	−15.6362	−0.623952
$629$	69.0743	2.75417
$630$	5.64147	0.224761
$631$	4.94061	0.196683	0.0983413	−	0.995153i	$-0.468646\pi$
$631$	4.94061	0.196683	0.0983413	+	0.995153i	$0.468646\pi$
$632$	−12.0783	−0.480450
$633$	−20.4475	−0.812715
$634$	−19.3800	−0.769680
$635$	−13.7892	−0.547208
$636$	30.9735	1.22818
$637$	−2.43982	−0.0966693
$638$	8.94333	0.354070
$639$	−18.3447	−0.725704
$640$	−1.49052	−0.0589181
$641$	−36.6694	−1.44835	−0.724177	−	0.689614i	$-0.757780\pi$
$641$	−36.6694	−1.44835	−0.724177	+	0.689614i	$0.757780\pi$
$642$	−4.83732	−0.190914
$643$	42.0997	1.66025	0.830124	−	0.557578i	$-0.188269\pi$
$643$	42.0997	1.66025	0.830124	+	0.557578i	$0.188269\pi$
$644$	3.31370	0.130578
$645$	−35.1533	−1.38416
$646$	26.8166	1.05509
$647$	−20.1720	−0.793044	−0.396522	−	0.918025i	$-0.629783\pi$
$647$	−20.1720	−0.793044	−0.396522	+	0.918025i	$0.629783\pi$
$648$	9.87347	0.387866
$649$	−6.96870	−0.273546
$650$	1.35698	0.0532251
$651$	−27.9039	−1.09364
$652$	6.26828	0.245485
$653$	−49.0626	−1.91997	−0.959983	−	0.280058i	$-0.909646\pi$
$653$	−49.0626	−1.91997	−0.959983	+	0.280058i	$0.909646\pi$
$654$	3.50597	0.137094
$655$	−4.67739	−0.182761
$656$	0.0389441	0.00152051
$657$	17.6765	0.689625
$658$	7.90685	0.308241
$659$	−14.2824	−0.556363	−0.278182	−	0.960529i	$-0.589732\pi$
$659$	−14.2824	−0.556363	−0.278182	+	0.960529i	$0.589732\pi$
$660$	3.80466	0.148096
$661$	−15.2338	−0.592525	−0.296262	−	0.955107i	$-0.595740\pi$
$661$	−15.2338	−0.592525	−0.296262	+	0.955107i	$0.595740\pi$
$662$	−10.3132	−0.400833
$663$	8.60249	0.334093
$664$	6.00325	0.232971
$665$	−7.65305	−0.296773
$666$	24.9710	0.967607
$667$	−19.5317	−0.756269
$668$	−18.8286	−0.728499
$669$	2.44285	0.0944462
$670$	−17.1363	−0.662032
$671$	−3.86186	−0.149085
$672$	−3.37232	−0.130090
$673$	47.1284	1.81666	0.908332	−	0.418249i	$-0.137356\pi$
$673$	47.1284	1.81666	0.908332	+	0.418249i	$0.137356\pi$
$674$	23.8912	0.920254
$675$	−2.16226	−0.0832254
$676$	−12.7615	−0.490825
$677$	5.97198	0.229522	0.114761	−	0.993393i	$-0.463390\pi$
$677$	5.97198	0.229522	0.114761	+	0.993393i	$0.463390\pi$
$678$	−22.3459	−0.858189
$679$	11.6215	0.445993
$680$	11.0220	0.422673
$681$	−49.8931	−1.91191
$682$	−8.86741	−0.339551
$683$	−29.8353	−1.14162	−0.570809	−	0.821083i	$-0.693370\pi$
$683$	−29.8353	−1.14162	−0.570809	+	0.821083i	$0.693370\pi$
$684$	9.69447	0.370677
$685$	−4.47344	−0.170921
$686$	−16.9835	−0.648434
$687$	−62.8465	−2.39774
$688$	9.90175	0.377501
$689$	−6.35128	−0.241964
$690$	−8.30913	−0.316323
$691$	−28.7531	−1.09382	−0.546910	−	0.837192i	$-0.684196\pi$
$691$	−28.7531	−1.09382	−0.546910	+	0.837192i	$0.684196\pi$
$692$	4.91097	0.186687
$693$	4.05615	0.154080
$694$	6.57089	0.249428
$695$	−1.19729	−0.0454159
$696$	19.8772	0.753442
$697$	−0.287980	−0.0109080
$698$	−9.81203	−0.371391
$699$	−3.76368	−0.142355
$700$	3.93368	0.148679
$701$	−48.2301	−1.82163	−0.910813	−	0.412819i	$-0.864544\pi$
$701$	−48.2301	−1.82163	−0.910813	+	0.412819i	$0.864544\pi$
$702$	−0.380110	−0.0143463
$703$	−33.8750	−1.27762
$704$	−1.07167	−0.0403900
$705$	−19.8265	−0.746708
$706$	−7.67068	−0.288690
$707$	−11.8736	−0.446552
$708$	−15.4884	−0.582091
$709$	−10.6886	−0.401420	−0.200710	−	0.979651i	$-0.564325\pi$
$709$	−10.6886	−0.401420	−0.200710	+	0.979651i	$0.564325\pi$
$710$	10.2284	0.383865
$711$	32.2885	1.21091
$712$	4.43201	0.166096
$713$	19.3659	0.725257
$714$	24.9373	0.933256
$715$	−0.780165	−0.0291765
$716$	14.2226	0.531525
$717$	−32.3662	−1.20874
$718$	29.6755	1.10748
$719$	35.2531	1.31472	0.657360	−	0.753577i	$-0.271673\pi$
$719$	35.2531	1.31472	0.657360	+	0.753577i	$0.271673\pi$
$720$	3.98455	0.148495
$721$	−10.6975	−0.398397
$722$	5.84876	0.217668
$723$	22.2538	0.827627
$724$	13.0700	0.485742
$725$	−23.1859	−0.861103
$726$	−23.4650	−0.870866
$727$	−34.1537	−1.26669	−0.633346	−	0.773869i	$-0.718319\pi$
$727$	−34.1537	−1.26669	−0.633346	+	0.773869i	$0.718319\pi$
$728$	0.691513	0.0256292
$729$	−20.8332	−0.771601
$730$	−9.85584	−0.364781
$731$	−73.2205	−2.70816
$732$	−8.58325	−0.317246
$733$	20.2073	0.746374	0.373187	−	0.927756i	$-0.378265\pi$
$733$	20.2073	0.746374	0.373187	+	0.927756i	$0.378265\pi$
$734$	6.28818	0.232101
$735$	17.7348	0.654157
$736$	2.34046	0.0862704
$737$	−12.3208	−0.453842
$738$	−0.104108	−0.00383225
$739$	−21.2949	−0.783347	−0.391673	−	0.920104i	$-0.628104\pi$
$739$	−21.2949	−0.783347	−0.391673	+	0.920104i	$0.628104\pi$
$740$	−13.9230	−0.511821
$741$	−4.21878	−0.154981
$742$	−18.4114	−0.675904
$743$	−51.6958	−1.89653	−0.948267	−	0.317473i	$-0.897166\pi$
$743$	−51.6958	−1.89653	−0.948267	+	0.317473i	$0.897166\pi$
$744$	−19.7084	−0.722547
$745$	13.0444	0.477909
$746$	3.00475	0.110012
$747$	−16.0482	−0.587174
$748$	7.92467	0.289755
$749$	2.87542	0.105066
$750$	−27.6148	−1.00835
$751$	15.7588	0.575047	0.287524	−	0.957774i	$-0.407168\pi$
$751$	15.7588	0.575047	0.287524	+	0.957774i	$0.407168\pi$
$752$	5.58458	0.203649
$753$	31.0536	1.13166
$754$	−4.07592	−0.148436
$755$	7.13901	0.259815
$756$	−1.10188	−0.0400751
$757$	−37.4669	−1.36176	−0.680878	−	0.732397i	$-0.738402\pi$
$757$	−37.4669	−1.36176	−0.680878	+	0.732397i	$0.738402\pi$
$758$	−13.6812	−0.496923
$759$	−5.97417	−0.216849
$760$	−5.40533	−0.196072
$761$	25.5868	0.927521	0.463761	−	0.885960i	$-0.346500\pi$
$761$	25.5868	0.927521	0.463761	+	0.885960i	$0.346500\pi$
$762$	−22.0352	−0.798252
$763$	−2.08403	−0.0754470
$764$	16.6827	0.603559
$765$	−29.4646	−1.06529
$766$	16.7609	0.605594
$767$	3.17599	0.114678
$768$	−2.38186	−0.0859480
$769$	19.5852	0.706262	0.353131	−	0.935574i	$-0.385117\pi$
$769$	19.5852	0.706262	0.353131	+	0.935574i	$0.385117\pi$
$770$	−2.26158	−0.0815017
$771$	19.9923	0.720004
$772$	16.1493	0.581225
$773$	−46.0439	−1.65609	−0.828043	−	0.560665i	$-0.810546\pi$
$773$	−46.0439	−1.65609	−0.828043	+	0.560665i	$0.810546\pi$
$774$	−26.4699	−0.951442
$775$	22.9891	0.825793
$776$	8.20825	0.294659
$777$	−31.5010	−1.13009
$778$	−26.1383	−0.937105
$779$	0.141229	0.00506007
$780$	−1.73397	−0.0620862
$781$	7.35410	0.263150
$782$	−17.3070	−0.618897
$783$	6.49472	0.232102
$784$	−4.99541	−0.178407
$785$	−23.3061	−0.831830
$786$	−7.47448	−0.266606
$787$	20.3367	0.724926	0.362463	−	0.931998i	$-0.381936\pi$
$787$	20.3367	0.724926	0.362463	+	0.931998i	$0.381936\pi$
$788$	10.6786	0.380409
$789$	6.85409	0.244012
$790$	−18.0030	−0.640519
$791$	13.2829	0.472287
$792$	2.86485	0.101798
$793$	1.76004	0.0625009
$794$	−25.9053	−0.919345
$795$	46.1667	1.63736
$796$	0.127630	0.00452371
$797$	9.48693	0.336044	0.168022	−	0.985783i	$-0.446262\pi$
$797$	9.48693	0.336044	0.168022	+	0.985783i	$0.446262\pi$
$798$	−12.2296	−0.432923
$799$	−41.2963	−1.46096
$800$	2.77834	0.0982292
$801$	−11.8479	−0.418625
$802$	−15.2747	−0.539368
$803$	−7.08623	−0.250068
$804$	−27.3838	−0.965752
$805$	4.93915	0.174082
$806$	4.04132	0.142349
$807$	−32.2958	−1.13686
$808$	−8.38628	−0.295028
$809$	−30.4691	−1.07124	−0.535618	−	0.844460i	$-0.679921\pi$
$809$	−30.4691	−1.07124	−0.535618	+	0.844460i	$0.679921\pi$
$810$	14.7166	0.517090
$811$	−18.6564	−0.655114	−0.327557	−	0.944831i	$-0.606225\pi$
$811$	−18.6564	−0.655114	−0.327557	+	0.944831i	$0.606225\pi$
$812$	−11.8155	−0.414642
$813$	−30.5969	−1.07308
$814$	−10.0105	−0.350868
$815$	9.34301	0.327271
$816$	17.6131	0.616583
$817$	35.9083	1.25627
$818$	−7.13796	−0.249573
$819$	−1.84859	−0.0645950
$820$	0.0580471	0.00202709
$821$	37.1257	1.29570	0.647848	−	0.761770i	$-0.275669\pi$
$821$	37.1257	1.29570	0.647848	+	0.761770i	$0.275669\pi$
$822$	−7.14857	−0.249335
$823$	38.8831	1.35538	0.677691	−	0.735347i	$-0.262981\pi$
$823$	38.8831	1.35538	0.677691	+	0.735347i	$0.262981\pi$
$824$	−7.55563	−0.263213
$825$	−7.09190	−0.246908
$826$	9.20670	0.320342
$827$	−1.97172	−0.0685634	−0.0342817	−	0.999412i	$-0.510914\pi$
$827$	−1.97172	−0.0685634	−0.0342817	+	0.999412i	$0.510914\pi$
$828$	−6.25665	−0.217433
$829$	−16.3651	−0.568384	−0.284192	−	0.958767i	$-0.591725\pi$
$829$	−16.3651	−0.568384	−0.284192	+	0.958767i	$0.591725\pi$
$830$	8.94798	0.310589
$831$	−63.6108	−2.20663
$832$	0.488413	0.0169327
$833$	36.9396	1.27988
$834$	−1.91328	−0.0662514
$835$	−28.0644	−0.971209
$836$	−3.88637	−0.134413
$837$	−6.43959	−0.222585
$838$	−16.7012	−0.576935
$839$	−23.5412	−0.812732	−0.406366	−	0.913710i	$-0.633204\pi$
$839$	−23.5412	−0.812732	−0.406366	+	0.913710i	$0.633204\pi$
$840$	−5.02652	−0.173432
$841$	40.6429	1.40148
$842$	14.2637	0.491561
$843$	−39.8635	−1.37297
$844$	8.58468	0.295497
$845$	−19.0212	−0.654350
$846$	−14.9290	−0.513270
$847$	13.9481	0.479264
$848$	−13.0039	−0.446556
$849$	−47.2752	−1.62248
$850$	−20.5450	−0.704688
$851$	21.8623	0.749431
$852$	16.3450	0.559971
$853$	22.9780	0.786751	0.393376	−	0.919378i	$-0.371307\pi$
$853$	22.9780	0.786751	0.393376	+	0.919378i	$0.371307\pi$
$854$	5.10209	0.174590
$855$	14.4498	0.494174
$856$	2.03090	0.0694147
$857$	−31.6932	−1.08262	−0.541310	−	0.840823i	$-0.682071\pi$
$857$	−31.6932	−1.08262	−0.541310	+	0.840823i	$0.682071\pi$
$858$	−1.24671	−0.0425618
$859$	27.2301	0.929079	0.464539	−	0.885553i	$-0.346220\pi$
$859$	27.2301	0.929079	0.464539	+	0.885553i	$0.346220\pi$
$860$	14.7588	0.503270
$861$	0.131332	0.00447579
$862$	3.14242	0.107031
$863$	−42.9947	−1.46356	−0.731779	−	0.681542i	$-0.761310\pi$
$863$	−42.9947	−1.46356	−0.731779	+	0.681542i	$0.761310\pi$
$864$	−0.778256	−0.0264768
$865$	7.31991	0.248884
$866$	−38.1479	−1.29632
$867$	−89.7523	−3.04815
$868$	11.7152	0.397639
$869$	−12.9440	−0.439094
$870$	29.6274	1.00446
$871$	5.61519	0.190264
$872$	−1.47195	−0.0498464
$873$	−21.9428	−0.742650
$874$	8.48759	0.287097
$875$	16.4149	0.554925
$876$	−15.7497	−0.532132
$877$	−21.2205	−0.716567	−0.358283	−	0.933613i	$-0.616638\pi$
$877$	−21.2205	−0.716567	−0.358283	+	0.933613i	$0.616638\pi$
$878$	−27.6457	−0.932997
$879$	−42.8674	−1.44588
$880$	−1.59735	−0.0538466
$881$	27.5856	0.929383	0.464692	−	0.885473i	$-0.346165\pi$
$881$	27.5856	0.929383	0.464692	+	0.885473i	$0.346165\pi$
$882$	13.3540	0.449653
$883$	−32.5853	−1.09658	−0.548292	−	0.836287i	$-0.684722\pi$
$883$	−32.5853	−1.09658	−0.548292	+	0.836287i	$0.684722\pi$
$884$	−3.61167	−0.121474
$885$	−23.0859	−0.776023
$886$	0.265135	0.00890738
$887$	35.5398	1.19331	0.596655	−	0.802498i	$-0.296496\pi$
$887$	35.5398	1.19331	0.596655	+	0.802498i	$0.296496\pi$
$888$	−22.2491	−0.746630
$889$	13.0983	0.439302
$890$	6.60601	0.221434
$891$	10.5811	0.354480
$892$	−1.02561	−0.0343399
$893$	20.2523	0.677717
$894$	20.8449	0.697159
$895$	21.1992	0.708610
$896$	1.41584	0.0472997
$897$	2.72273	0.0909092
$898$	−8.32705	−0.277877
$899$	−69.0517	−2.30300
$900$	−7.42722	−0.247574
$901$	96.1600	3.20356
$902$	0.0417352	0.00138963
$903$	33.3919	1.11121
$904$	9.38170	0.312031
$905$	19.4811	0.647573
$906$	11.4082	0.379011
$907$	29.3849	0.975709	0.487855	−	0.872925i	$-0.337780\pi$
$907$	29.3849	0.975709	0.487855	+	0.872925i	$0.337780\pi$
$908$	20.9471	0.695155
$909$	22.4187	0.743581
$910$	1.03072	0.0341679
$911$	36.1472	1.19761	0.598805	−	0.800895i	$-0.295642\pi$
$911$	36.1472	1.19761	0.598805	+	0.800895i	$0.295642\pi$
$912$	−8.63773	−0.286024
$913$	6.43350	0.212918
$914$	−0.902313	−0.0298459
$915$	−12.7935	−0.422941
$916$	26.3855	0.871801
$917$	4.44301	0.146721
$918$	5.75497	0.189942
$919$	−29.3142	−0.966986	−0.483493	−	0.875348i	$-0.660632\pi$
$919$	−29.3142	−0.966986	−0.483493	+	0.875348i	$0.660632\pi$
$920$	3.48851	0.115013
$921$	58.6811	1.93361
$922$	24.9063	0.820246
$923$	−3.35163	−0.110320
$924$	−3.61401	−0.118892
$925$	25.9526	0.853317
$926$	12.8193	0.421268
$927$	20.1981	0.663394
$928$	−8.34523	−0.273946
$929$	−37.2444	−1.22195	−0.610975	−	0.791650i	$-0.709222\pi$
$929$	−37.2444	−1.22195	−0.610975	+	0.791650i	$0.709222\pi$
$930$	−29.3759	−0.963273
$931$	−18.1157	−0.593717
$932$	1.58014	0.0517593
$933$	33.4794	1.09607
$934$	−14.5740	−0.476876
$935$	11.8119	0.386291
$936$	−1.30565	−0.0426766
$937$	8.42166	0.275124	0.137562	−	0.990493i	$-0.456073\pi$
$937$	8.42166	0.275124	0.137562	+	0.990493i	$0.456073\pi$
$938$	16.2776	0.531483
$939$	−37.1220	−1.21143
$940$	8.32394	0.271497
$941$	8.63385	0.281456	0.140728	−	0.990048i	$-0.455056\pi$
$941$	8.63385	0.281456	0.140728	+	0.990048i	$0.455056\pi$
$942$	−37.2432	−1.21345
$943$	−0.0911470	−0.00296816
$944$	6.50266	0.211644
$945$	−1.64238	−0.0534266
$946$	10.6114	0.345006
$947$	13.1365	0.426878	0.213439	−	0.976956i	$-0.431534\pi$
$947$	13.1365	0.426878	0.213439	+	0.976956i	$0.431534\pi$
$948$	−28.7689	−0.934371
$949$	3.22955	0.104836
$950$	10.0756	0.326894
$951$	−46.1606	−1.49686
$952$	−10.4697	−0.339324
$953$	−19.7904	−0.641075	−0.320538	−	0.947236i	$-0.603864\pi$
$953$	−19.7904	−0.641075	−0.320538	+	0.947236i	$0.603864\pi$
$954$	34.7628	1.12549
$955$	24.8659	0.804643
$956$	13.5886	0.439488
$957$	21.3017	0.688588
$958$	−34.6155	−1.11837
$959$	4.24928	0.137216
$960$	−3.55022	−0.114583
$961$	37.4656	1.20857
$962$	4.56229	0.147094
$963$	−5.42912	−0.174951
$964$	−9.34302	−0.300919
$965$	24.0708	0.774868
$966$	7.89278	0.253946
$967$	38.9197	1.25157	0.625787	−	0.779994i	$-0.284778\pi$
$967$	38.9197	1.25157	0.625787	+	0.779994i	$0.284778\pi$
$968$	9.85153	0.316640
$969$	63.8734	2.05191
$970$	12.2346	0.392829
$971$	19.5507	0.627413	0.313707	−	0.949520i	$-0.398429\pi$
$971$	19.5507	0.627413	0.313707	+	0.949520i	$0.398429\pi$
$972$	21.1825	0.679427
$973$	1.13730	0.0364601
$974$	−12.8733	−0.412487
$975$	3.23213	0.103511
$976$	3.60359	0.115348
$977$	−31.9602	−1.02250	−0.511248	−	0.859433i	$-0.670817\pi$
$977$	−31.9602	−1.02250	−0.511248	+	0.859433i	$0.670817\pi$
$978$	14.9302	0.477414
$979$	4.74964	0.151799
$980$	−7.44577	−0.237846
$981$	3.93489	0.125631
$982$	−13.2512	−0.422862
$983$	−50.8957	−1.62332	−0.811660	−	0.584130i	$-0.801436\pi$
$983$	−50.8957	−1.62332	−0.811660	+	0.584130i	$0.801436\pi$
$984$	0.0927594	0.00295706
$985$	15.9167	0.507148
$986$	61.7105	1.96526
$987$	18.8330	0.599461
$988$	1.77121	0.0563498
$989$	−23.1746	−0.736910
$990$	4.27012	0.135713
$991$	−9.13380	−0.290145	−0.145072	−	0.989421i	$-0.546342\pi$
$991$	−9.13380	−0.290145	−0.145072	+	0.989421i	$0.546342\pi$
$992$	8.27439	0.262712
$993$	−24.5645	−0.779532
$994$	−9.71587	−0.308169
$995$	0.190235	0.00603085
$996$	14.2989	0.453078
$997$	−53.4679	−1.69335	−0.846673	−	0.532114i	$-0.821398\pi$
$997$	−53.4679	−1.69335	−0.846673	+	0.532114i	$0.821398\pi$
$998$	1.67625	0.0530607
$999$	−7.26972	−0.230004

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4034.2.a.c.1.9	✓	49

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4034.2.a.c.1.9	✓	49	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)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -2.38186 q^{3} +1.00000 q^{4} +1.49052 q^{5} +2.38186 q^{6} -1.41584 q^{7} -1.00000 q^{8} +2.67326 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -2.38186 q^{3} +1.00000 q^{4} +1.49052 q^{5} +2.38186 q^{6} -1.41584 q^{7} -1.00000 q^{8} +2.67326 q^{9} -1.49052 q^{10} -1.07167 q^{11} -2.38186 q^{12} +0.488413 q^{13} +1.41584 q^{14} -3.55022 q^{15} +1.00000 q^{16} -7.39470 q^{17} -2.67326 q^{18} +3.62646 q^{19} +1.49052 q^{20} +3.37232 q^{21} +1.07167 q^{22} -2.34046 q^{23} +2.38186 q^{24} -2.77834 q^{25} -0.488413 q^{26} +0.778256 q^{27} -1.41584 q^{28} +8.34523 q^{29} +3.55022 q^{30} -8.27439 q^{31} -1.00000 q^{32} +2.55257 q^{33} +7.39470 q^{34} -2.11034 q^{35} +2.67326 q^{36} -9.34105 q^{37} -3.62646 q^{38} -1.16333 q^{39} -1.49052 q^{40} +0.0389441 q^{41} -3.37232 q^{42} +9.90175 q^{43} -1.07167 q^{44} +3.98455 q^{45} +2.34046 q^{46} +5.58458 q^{47} -2.38186 q^{48} -4.99541 q^{49} +2.77834 q^{50} +17.6131 q^{51} +0.488413 q^{52} -13.0039 q^{53} -0.778256 q^{54} -1.59735 q^{55} +1.41584 q^{56} -8.63773 q^{57} -8.34523 q^{58} +6.50266 q^{59} -3.55022 q^{60} +3.60359 q^{61} +8.27439 q^{62} -3.78489 q^{63} +1.00000 q^{64} +0.727991 q^{65} -2.55257 q^{66} +11.4968 q^{67} -7.39470 q^{68} +5.57464 q^{69} +2.11034 q^{70} -6.86229 q^{71} -2.67326 q^{72} +6.61233 q^{73} +9.34105 q^{74} +6.61762 q^{75} +3.62646 q^{76} +1.51731 q^{77} +1.16333 q^{78} +12.0783 q^{79} +1.49052 q^{80} -9.87347 q^{81} -0.0389441 q^{82} -6.00325 q^{83} +3.37232 q^{84} -11.0220 q^{85} -9.90175 q^{86} -19.8772 q^{87} +1.07167 q^{88} -4.43201 q^{89} -3.98455 q^{90} -0.691513 q^{91} -2.34046 q^{92} +19.7084 q^{93} -5.58458 q^{94} +5.40533 q^{95} +2.38186 q^{96} -8.20825 q^{97} +4.99541 q^{98} -2.86485 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 49 q - 49 q^{2} + 8 q^{3} + 49 q^{4} - 8 q^{5} - 8 q^{6} + 18 q^{7} - 49 q^{8} + 59 q^{9}+O(q^{10}) \) 49 * q - 49 * q^2 + 8 * q^3 + 49 * q^4 - 8 * q^5 - 8 * q^6 + 18 * q^7 - 49 * q^8 + 59 * q^9	\( 49 q - 49 q^{2} + 8 q^{3} + 49 q^{4} - 8 q^{5} - 8 q^{6} + 18 q^{7} - 49 q^{8} + 59 q^{9} + 8 q^{10} + q^{11} + 8 q^{12} + 9 q^{13} - 18 q^{14} + 15 q^{15} + 49 q^{16} - 27 q^{17} - 59 q^{18} + 27 q^{19} - 8 q^{20} + 13 q^{21} - q^{22} + 16 q^{23} - 8 q^{24} + 71 q^{25} - 9 q^{26} + 29 q^{27} + 18 q^{28} - 7 q^{29} - 15 q^{30} + 75 q^{31} - 49 q^{32} - 3 q^{33} + 27 q^{34} - 16 q^{35} + 59 q^{36} + 36 q^{37} - 27 q^{38} + 24 q^{39} + 8 q^{40} - 12 q^{41} - 13 q^{42} + 22 q^{43} + q^{44} + 5 q^{45} - 16 q^{46} + 26 q^{47} + 8 q^{48} + 107 q^{49} - 71 q^{50} + 35 q^{51} + 9 q^{52} - 10 q^{53} - 29 q^{54} + 76 q^{55} - 18 q^{56} - 10 q^{57} + 7 q^{58} + 9 q^{59} + 15 q^{60} + 87 q^{61} - 75 q^{62} + 68 q^{63} + 49 q^{64} - 6 q^{65} + 3 q^{66} + 46 q^{67} - 27 q^{68} + 70 q^{69} + 16 q^{70} + 40 q^{71} - 59 q^{72} + 6 q^{73} - 36 q^{74} + 69 q^{75} + 27 q^{76} - 12 q^{77} - 24 q^{78} + 76 q^{79} - 8 q^{80} + 77 q^{81} + 12 q^{82} - 32 q^{83} + 13 q^{84} + 19 q^{85} - 22 q^{86} + 36 q^{87} - q^{88} + 34 q^{89} - 5 q^{90} + 119 q^{91} + 16 q^{92} - 5 q^{93} - 26 q^{94} - 2 q^{95} - 8 q^{96} + 52 q^{97} - 107 q^{98} + 26 q^{99}+O(q^{100}) \) 49 * q - 49 * q^2 + 8 * q^3 + 49 * q^4 - 8 * q^5 - 8 * q^6 + 18 * q^7 - 49 * q^8 + 59 * q^9 + 8 * q^10 + q^11 + 8 * q^12 + 9 * q^13 - 18 * q^14 + 15 * q^15 + 49 * q^16 - 27 * q^17 - 59 * q^18 + 27 * q^19 - 8 * q^20 + 13 * q^21 - q^22 + 16 * q^23 - 8 * q^24 + 71 * q^25 - 9 * q^26 + 29 * q^27 + 18 * q^28 - 7 * q^29 - 15 * q^30 + 75 * q^31 - 49 * q^32 - 3 * q^33 + 27 * q^34 - 16 * q^35 + 59 * q^36 + 36 * q^37 - 27 * q^38 + 24 * q^39 + 8 * q^40 - 12 * q^41 - 13 * q^42 + 22 * q^43 + q^44 + 5 * q^45 - 16 * q^46 + 26 * q^47 + 8 * q^48 + 107 * q^49 - 71 * q^50 + 35 * q^51 + 9 * q^52 - 10 * q^53 - 29 * q^54 + 76 * q^55 - 18 * q^56 - 10 * q^57 + 7 * q^58 + 9 * q^59 + 15 * q^60 + 87 * q^61 - 75 * q^62 + 68 * q^63 + 49 * q^64 - 6 * q^65 + 3 * q^66 + 46 * q^67 - 27 * q^68 + 70 * q^69 + 16 * q^70 + 40 * q^71 - 59 * q^72 + 6 * q^73 - 36 * q^74 + 69 * q^75 + 27 * q^76 - 12 * q^77 - 24 * q^78 + 76 * q^79 - 8 * q^80 + 77 * q^81 + 12 * q^82 - 32 * q^83 + 13 * q^84 + 19 * q^85 - 22 * q^86 + 36 * q^87 - q^88 + 34 * q^89 - 5 * q^90 + 119 * q^91 + 16 * q^92 - 5 * q^93 - 26 * q^94 - 2 * q^95 - 8 * q^96 + 52 * q^97 - 107 * q^98 + 26 * q^99

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