LMFDB - Embedded newform 4022.2.a.d.1.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4022,2,Mod(1,4022)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4022, 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("4022.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4022 = 2 \cdot 2011 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4022.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:	$32.1158316930$
Analytic rank:	$1$
Dimension:	$37$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Character	$\chi$	$=$	4022.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -2.78933 q^{3} +1.00000 q^{4} +0.171910 q^{5} +2.78933 q^{6} +1.94661 q^{7} -1.00000 q^{8} +4.78038 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -2.78933 q^{3} +1.00000 q^{4} +0.171910 q^{5} +2.78933 q^{6} +1.94661 q^{7} -1.00000 q^{8} +4.78038 q^{9} -0.171910 q^{10} +3.35199 q^{11} -2.78933 q^{12} +2.17653 q^{13} -1.94661 q^{14} -0.479513 q^{15} +1.00000 q^{16} +4.39977 q^{17} -4.78038 q^{18} -5.52826 q^{19} +0.171910 q^{20} -5.42974 q^{21} -3.35199 q^{22} -3.22020 q^{23} +2.78933 q^{24} -4.97045 q^{25} -2.17653 q^{26} -4.96608 q^{27} +1.94661 q^{28} -8.22027 q^{29} +0.479513 q^{30} +6.09156 q^{31} -1.00000 q^{32} -9.34983 q^{33} -4.39977 q^{34} +0.334641 q^{35} +4.78038 q^{36} +2.57700 q^{37} +5.52826 q^{38} -6.07107 q^{39} -0.171910 q^{40} -5.44470 q^{41} +5.42974 q^{42} -8.99492 q^{43} +3.35199 q^{44} +0.821794 q^{45} +3.22020 q^{46} +2.52550 q^{47} -2.78933 q^{48} -3.21072 q^{49} +4.97045 q^{50} -12.2724 q^{51} +2.17653 q^{52} -12.1703 q^{53} +4.96608 q^{54} +0.576240 q^{55} -1.94661 q^{56} +15.4201 q^{57} +8.22027 q^{58} +11.4290 q^{59} -0.479513 q^{60} -0.365270 q^{61} -6.09156 q^{62} +9.30553 q^{63} +1.00000 q^{64} +0.374166 q^{65} +9.34983 q^{66} -6.91964 q^{67} +4.39977 q^{68} +8.98222 q^{69} -0.334641 q^{70} +11.0644 q^{71} -4.78038 q^{72} -5.83857 q^{73} -2.57700 q^{74} +13.8642 q^{75} -5.52826 q^{76} +6.52502 q^{77} +6.07107 q^{78} -0.519633 q^{79} +0.171910 q^{80} -0.489101 q^{81} +5.44470 q^{82} -11.4826 q^{83} -5.42974 q^{84} +0.756363 q^{85} +8.99492 q^{86} +22.9291 q^{87} -3.35199 q^{88} -3.85629 q^{89} -0.821794 q^{90} +4.23685 q^{91} -3.22020 q^{92} -16.9914 q^{93} -2.52550 q^{94} -0.950360 q^{95} +2.78933 q^{96} -7.41097 q^{97} +3.21072 q^{98} +16.0238 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 37 q - 37 q^{2} - 5 q^{3} + 37 q^{4} - 13 q^{5} + 5 q^{6} - 22 q^{7} - 37 q^{8} + 32 q^{9}+O(q^{10}) $ 37 * q - 37 * q^2 - 5 * q^3 + 37 * q^4 - 13 * q^5 + 5 * q^6 - 22 * q^7 - 37 * q^8 + 32 * q^9	\( 37 q - 37 q^{2} - 5 q^{3} + 37 q^{4} - 13 q^{5} + 5 q^{6} - 22 q^{7} - 37 q^{8} + 32 q^{9} + 13 q^{10} + 12 q^{11} - 5 q^{12} - 36 q^{13} + 22 q^{14} - 7 q^{15} + 37 q^{16} + 4 q^{17} - 32 q^{18} - 10 q^{19} - 13 q^{20} - 11 q^{21} - 12 q^{22} - q^{23} + 5 q^{24} + 8 q^{25} + 36 q^{26} - 20 q^{27} - 22 q^{28} - 6 q^{29} + 7 q^{30} - 23 q^{31} - 37 q^{32} - 27 q^{33} - 4 q^{34} + 24 q^{35} + 32 q^{36} - 46 q^{37} + 10 q^{38} + 5 q^{39} + 13 q^{40} + 11 q^{41} + 11 q^{42} - 22 q^{43} + 12 q^{44} - 57 q^{45} + q^{46} - 18 q^{47} - 5 q^{48} - q^{49} - 8 q^{50} + 18 q^{51} - 36 q^{52} - 25 q^{53} + 20 q^{54} - 25 q^{55} + 22 q^{56} - 25 q^{57} + 6 q^{58} + 24 q^{59} - 7 q^{60} - 40 q^{61} + 23 q^{62} - 38 q^{63} + 37 q^{64} + 14 q^{65} + 27 q^{66} - 49 q^{67} + 4 q^{68} - 19 q^{69} - 24 q^{70} + 27 q^{71} - 32 q^{72} - 87 q^{73} + 46 q^{74} - 5 q^{75} - 10 q^{76} - 50 q^{77} - 5 q^{78} + 11 q^{79} - 13 q^{80} + 5 q^{81} - 11 q^{82} - 9 q^{83} - 11 q^{84} - 68 q^{85} + 22 q^{86} - 12 q^{87} - 12 q^{88} - 3 q^{89} + 57 q^{90} - 19 q^{91} - q^{92} - 69 q^{93} + 18 q^{94} + 27 q^{95} + 5 q^{96} - 98 q^{97} + q^{98} + 33 q^{99}+O(q^{100}) \) 37 * q - 37 * q^2 - 5 * q^3 + 37 * q^4 - 13 * q^5 + 5 * q^6 - 22 * q^7 - 37 * q^8 + 32 * q^9 + 13 * q^10 + 12 * q^11 - 5 * q^12 - 36 * q^13 + 22 * q^14 - 7 * q^15 + 37 * q^16 + 4 * q^17 - 32 * q^18 - 10 * q^19 - 13 * q^20 - 11 * q^21 - 12 * q^22 - q^23 + 5 * q^24 + 8 * q^25 + 36 * q^26 - 20 * q^27 - 22 * q^28 - 6 * q^29 + 7 * q^30 - 23 * q^31 - 37 * q^32 - 27 * q^33 - 4 * q^34 + 24 * q^35 + 32 * q^36 - 46 * q^37 + 10 * q^38 + 5 * q^39 + 13 * q^40 + 11 * q^41 + 11 * q^42 - 22 * q^43 + 12 * q^44 - 57 * q^45 + q^46 - 18 * q^47 - 5 * q^48 - q^49 - 8 * q^50 + 18 * q^51 - 36 * q^52 - 25 * q^53 + 20 * q^54 - 25 * q^55 + 22 * q^56 - 25 * q^57 + 6 * q^58 + 24 * q^59 - 7 * q^60 - 40 * q^61 + 23 * q^62 - 38 * q^63 + 37 * q^64 + 14 * q^65 + 27 * q^66 - 49 * q^67 + 4 * q^68 - 19 * q^69 - 24 * q^70 + 27 * q^71 - 32 * q^72 - 87 * q^73 + 46 * q^74 - 5 * q^75 - 10 * q^76 - 50 * q^77 - 5 * q^78 + 11 * q^79 - 13 * q^80 + 5 * q^81 - 11 * q^82 - 9 * q^83 - 11 * q^84 - 68 * q^85 + 22 * q^86 - 12 * q^87 - 12 * q^88 - 3 * q^89 + 57 * q^90 - 19 * q^91 - q^92 - 69 * q^93 + 18 * q^94 + 27 * q^95 + 5 * q^96 - 98 * q^97 + q^98 + 33 * 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
$3$	−2.78933	−1.61042	−0.805211	−	0.592988i	$-0.797948\pi$
$3$	−2.78933	−1.61042	−0.805211	+	0.592988i	$0.797948\pi$
$4$	1.00000	0.500000
$5$	0.171910	0.0768803	0.0384402	−	0.999261i	$-0.487761\pi$
$5$	0.171910	0.0768803	0.0384402	+	0.999261i	$0.487761\pi$
$6$	2.78933	1.13874
$7$	1.94661	0.735749	0.367874	−	0.929875i	$-0.380086\pi$
$7$	1.94661	0.735749	0.367874	+	0.929875i	$0.380086\pi$
$8$	−1.00000	−0.353553
$9$	4.78038	1.59346
$10$	−0.171910	−0.0543626
$11$	3.35199	1.01066	0.505332	−	0.862925i	$-0.331370\pi$
$11$	3.35199	1.01066	0.505332	+	0.862925i	$0.331370\pi$
$12$	−2.78933	−0.805211
$13$	2.17653	0.603661	0.301830	−	0.953362i	$-0.402402\pi$
$13$	2.17653	0.603661	0.301830	+	0.953362i	$0.402402\pi$
$14$	−1.94661	−0.520253
$15$	−0.479513	−0.123810
$16$	1.00000	0.250000
$17$	4.39977	1.06710	0.533551	−	0.845768i	$-0.320857\pi$
$17$	4.39977	1.06710	0.533551	+	0.845768i	$0.320857\pi$
$18$	−4.78038	−1.12675
$19$	−5.52826	−1.26827	−0.634134	−	0.773223i	$-0.718643\pi$
$19$	−5.52826	−1.26827	−0.634134	+	0.773223i	$0.718643\pi$
$20$	0.171910	0.0384402
$21$	−5.42974	−1.18487
$22$	−3.35199	−0.714648
$23$	−3.22020	−0.671459	−0.335730	−	0.941958i	$-0.608983\pi$
$23$	−3.22020	−0.671459	−0.335730	+	0.941958i	$0.608983\pi$
$24$	2.78933	0.569370
$25$	−4.97045	−0.994089
$26$	−2.17653	−0.426852
$27$	−4.96608	−0.955722
$28$	1.94661	0.367874
$29$	−8.22027	−1.52647	−0.763233	−	0.646123i	$-0.776389\pi$
$29$	−8.22027	−1.52647	−0.763233	+	0.646123i	$0.776389\pi$
$30$	0.479513	0.0875467
$31$	6.09156	1.09408	0.547039	−	0.837107i	$-0.315755\pi$
$31$	6.09156	1.09408	0.547039	+	0.837107i	$0.315755\pi$
$32$	−1.00000	−0.176777
$33$	−9.34983	−1.62760
$34$	−4.39977	−0.754554
$35$	0.334641	0.0565646
$36$	4.78038	0.796730
$37$	2.57700	0.423656	0.211828	−	0.977307i	$-0.432058\pi$
$37$	2.57700	0.423656	0.211828	+	0.977307i	$0.432058\pi$
$38$	5.52826	0.896801
$39$	−6.07107	−0.972148
$40$	−0.171910	−0.0271813
$41$	−5.44470	−0.850319	−0.425159	−	0.905119i	$-0.639782\pi$
$41$	−5.44470	−0.850319	−0.425159	+	0.905119i	$0.639782\pi$
$42$	5.42974	0.837827
$43$	−8.99492	−1.37171	−0.685856	−	0.727737i	$-0.740572\pi$
$43$	−8.99492	−1.37171	−0.685856	+	0.727737i	$0.740572\pi$
$44$	3.35199	0.505332
$45$	0.821794	0.122506
$46$	3.22020	0.474793
$47$	2.52550	0.368383	0.184191	−	0.982890i	$-0.441033\pi$
$47$	2.52550	0.368383	0.184191	+	0.982890i	$0.441033\pi$
$48$	−2.78933	−0.402606
$49$	−3.21072	−0.458674
$50$	4.97045	0.702927
$51$	−12.2724	−1.71848
$52$	2.17653	0.301830
$53$	−12.1703	−1.67171	−0.835857	−	0.548947i	$-0.815029\pi$
$53$	−12.1703	−1.67171	−0.835857	+	0.548947i	$0.815029\pi$
$54$	4.96608	0.675797
$55$	0.576240	0.0777002
$56$	−1.94661	−0.260127
$57$	15.4201	2.04245
$58$	8.22027	1.07937
$59$	11.4290	1.48794	0.743968	−	0.668216i	$-0.232942\pi$
$59$	11.4290	1.48794	0.743968	+	0.668216i	$0.232942\pi$
$60$	−0.479513	−0.0619049
$61$	−0.365270	−0.0467680	−0.0233840	−	0.999727i	$-0.507444\pi$
$61$	−0.365270	−0.0467680	−0.0233840	+	0.999727i	$0.507444\pi$
$62$	−6.09156	−0.773630
$63$	9.30553	1.17239
$64$	1.00000	0.125000
$65$	0.374166	0.0464096
$66$	9.34983	1.15088
$67$	−6.91964	−0.845368	−0.422684	−	0.906277i	$-0.638912\pi$
$67$	−6.91964	−0.845368	−0.422684	+	0.906277i	$0.638912\pi$
$68$	4.39977	0.533551
$69$	8.98222	1.08133
$70$	−0.334641	−0.0399972
$71$	11.0644	1.31310	0.656549	−	0.754284i	$-0.272016\pi$
$71$	11.0644	1.31310	0.656549	+	0.754284i	$0.272016\pi$
$72$	−4.78038	−0.563373
$73$	−5.83857	−0.683353	−0.341677	−	0.939818i	$-0.610995\pi$
$73$	−5.83857	−0.683353	−0.341677	+	0.939818i	$0.610995\pi$
$74$	−2.57700	−0.299570
$75$	13.8642	1.60090
$76$	−5.52826	−0.634134
$77$	6.52502	0.743595
$78$	6.07107	0.687413
$79$	−0.519633	−0.0584633	−0.0292317	−	0.999573i	$-0.509306\pi$
$79$	−0.519633	−0.0584633	−0.0292317	+	0.999573i	$0.509306\pi$
$80$	0.171910	0.0192201
$81$	−0.489101	−0.0543446
$82$	5.44470	0.601266
$83$	−11.4826	−1.26038	−0.630189	−	0.776442i	$-0.717023\pi$
$83$	−11.4826	−1.26038	−0.630189	+	0.776442i	$0.717023\pi$
$84$	−5.42974	−0.592433
$85$	0.756363	0.0820391
$86$	8.99492	0.969947
$87$	22.9291	2.45826
$88$	−3.35199	−0.357324
$89$	−3.85629	−0.408766	−0.204383	−	0.978891i	$-0.565519\pi$
$89$	−3.85629	−0.408766	−0.204383	+	0.978891i	$0.565519\pi$
$90$	−0.821794	−0.0866246
$91$	4.23685	0.444143
$92$	−3.22020	−0.335730
$93$	−16.9914	−1.76193
$94$	−2.52550	−0.260486
$95$	−0.950360	−0.0975049
$96$	2.78933	0.284685
$97$	−7.41097	−0.752470	−0.376235	−	0.926524i	$-0.622781\pi$
$97$	−7.41097	−0.752470	−0.376235	+	0.926524i	$0.622781\pi$
$98$	3.21072	0.324331
$99$	16.0238	1.61045
$100$	−4.97045	−0.497045
$101$	10.1336	1.00834	0.504168	−	0.863606i	$-0.331799\pi$
$101$	10.1336	1.00834	0.504168	+	0.863606i	$0.331799\pi$
$102$	12.2724	1.21515
$103$	9.62385	0.948266	0.474133	−	0.880453i	$-0.342762\pi$
$103$	9.62385	0.948266	0.474133	+	0.880453i	$0.342762\pi$
$104$	−2.17653	−0.213426
$105$	−0.933425	−0.0910929
$106$	12.1703	1.18208
$107$	2.95980	0.286134	0.143067	−	0.989713i	$-0.454304\pi$
$107$	2.95980	0.286134	0.143067	+	0.989713i	$0.454304\pi$
$108$	−4.96608	−0.477861
$109$	7.10363	0.680405	0.340202	−	0.940352i	$-0.389504\pi$
$109$	7.10363	0.680405	0.340202	+	0.940352i	$0.389504\pi$
$110$	−0.576240	−0.0549423
$111$	−7.18811	−0.682266
$112$	1.94661	0.183937
$113$	−0.726798	−0.0683714	−0.0341857	−	0.999415i	$-0.510884\pi$
$113$	−0.726798	−0.0683714	−0.0341857	+	0.999415i	$0.510884\pi$
$114$	−15.4201	−1.44423
$115$	−0.553584	−0.0516220
$116$	−8.22027	−0.763233
$117$	10.4046	0.961909
$118$	−11.4290	−1.05213
$119$	8.56463	0.785119
$120$	0.479513	0.0437734
$121$	0.235866	0.0214423
$122$	0.365270	0.0330700
$123$	15.1871	1.36937
$124$	6.09156	0.547039
$125$	−1.71402	−0.153306
$126$	−9.30553	−0.829003
$127$	20.7393	1.84032	0.920159	−	0.391544i	$-0.128059\pi$
$127$	20.7393	1.84032	0.920159	+	0.391544i	$0.128059\pi$
$128$	−1.00000	−0.0883883
$129$	25.0898	2.20904
$130$	−0.374166	−0.0328166
$131$	−3.90102	−0.340834	−0.170417	−	0.985372i	$-0.554511\pi$
$131$	−3.90102	−0.340834	−0.170417	+	0.985372i	$0.554511\pi$
$132$	−9.34983	−0.813798
$133$	−10.7613	−0.933127
$134$	6.91964	0.597766
$135$	−0.853716	−0.0734762
$136$	−4.39977	−0.377277
$137$	−0.907761	−0.0775552	−0.0387776	−	0.999248i	$-0.512346\pi$
$137$	−0.907761	−0.0775552	−0.0387776	+	0.999248i	$0.512346\pi$
$138$	−8.98222	−0.764618
$139$	−14.9978	−1.27210	−0.636050	−	0.771648i	$-0.719433\pi$
$139$	−14.9978	−1.27210	−0.636050	+	0.771648i	$0.719433\pi$
$140$	0.334641	0.0282823
$141$	−7.04447	−0.593252
$142$	−11.0644	−0.928500
$143$	7.29571	0.610098
$144$	4.78038	0.398365
$145$	−1.41314	−0.117355
$146$	5.83857	0.483204
$147$	8.95576	0.738658
$148$	2.57700	0.211828
$149$	6.56511	0.537835	0.268917	−	0.963163i	$-0.413334\pi$
$149$	6.56511	0.537835	0.268917	+	0.963163i	$0.413334\pi$
$150$	−13.8642	−1.13201
$151$	−1.90866	−0.155325	−0.0776624	−	0.996980i	$-0.524746\pi$
$151$	−1.90866	−0.155325	−0.0776624	+	0.996980i	$0.524746\pi$
$152$	5.52826	0.448401
$153$	21.0326	1.70038
$154$	−6.52502	−0.525801
$155$	1.04720	0.0841130
$156$	−6.07107	−0.486074
$157$	−15.1459	−1.20877	−0.604385	−	0.796692i	$-0.706581\pi$
$157$	−15.1459	−1.20877	−0.604385	+	0.796692i	$0.706581\pi$
$158$	0.519633	0.0413398
$159$	33.9469	2.69217
$160$	−0.171910	−0.0135906
$161$	−6.26848	−0.494025
$162$	0.489101	0.0384274
$163$	−20.4278	−1.60003	−0.800016	−	0.599978i	$-0.795176\pi$
$163$	−20.4278	−1.60003	−0.800016	+	0.599978i	$0.795176\pi$
$164$	−5.44470	−0.425159
$165$	−1.60733	−0.125130
$166$	11.4826	0.891222
$167$	−18.2496	−1.41220	−0.706099	−	0.708113i	$-0.749547\pi$
$167$	−18.2496	−1.41220	−0.706099	+	0.708113i	$0.749547\pi$
$168$	5.42974	0.418914
$169$	−8.26272	−0.635594
$170$	−0.756363	−0.0580104
$171$	−26.4272	−2.02094
$172$	−8.99492	−0.685856
$173$	−19.3806	−1.47348	−0.736741	−	0.676175i	$-0.763637\pi$
$173$	−19.3806	−1.47348	−0.736741	+	0.676175i	$0.763637\pi$
$174$	−22.9291	−1.73825
$175$	−9.67551	−0.731400
$176$	3.35199	0.252666
$177$	−31.8794	−2.39620
$178$	3.85629	0.289041
$179$	2.35456	0.175988	0.0879939	−	0.996121i	$-0.471954\pi$
$179$	2.35456	0.175988	0.0879939	+	0.996121i	$0.471954\pi$
$180$	0.821794	0.0612529
$181$	20.5218	1.52537	0.762686	−	0.646769i	$-0.223880\pi$
$181$	20.5218	1.52537	0.762686	+	0.646769i	$0.223880\pi$
$182$	−4.23685	−0.314056
$183$	1.01886	0.0753162
$184$	3.22020	0.237397
$185$	0.443011	0.0325708
$186$	16.9914	1.24587
$187$	14.7480	1.07848
$188$	2.52550	0.184191
$189$	−9.66701	−0.703171
$190$	0.950360	0.0689464
$191$	1.47196	0.106507	0.0532537	−	0.998581i	$-0.483041\pi$
$191$	1.47196	0.106507	0.0532537	+	0.998581i	$0.483041\pi$
$192$	−2.78933	−0.201303
$193$	9.63915	0.693841	0.346921	−	0.937895i	$-0.387227\pi$
$193$	9.63915	0.693841	0.346921	+	0.937895i	$0.387227\pi$
$194$	7.41097	0.532077
$195$	−1.04367	−0.0747391
$196$	−3.21072	−0.229337
$197$	12.2603	0.873507	0.436753	−	0.899581i	$-0.356128\pi$
$197$	12.2603	0.873507	0.436753	+	0.899581i	$0.356128\pi$
$198$	−16.0238	−1.13876
$199$	−10.3979	−0.737089	−0.368544	−	0.929610i	$-0.620144\pi$
$199$	−10.3979	−0.737089	−0.368544	+	0.929610i	$0.620144\pi$
$200$	4.97045	0.351464
$201$	19.3012	1.36140
$202$	−10.1336	−0.713001
$203$	−16.0017	−1.12310
$204$	−12.2724	−0.859242
$205$	−0.935996	−0.0653728
$206$	−9.62385	−0.670525
$207$	−15.3938	−1.06994
$208$	2.17653	0.150915
$209$	−18.5307	−1.28179
$210$	0.933425	0.0644124
$211$	−26.4016	−1.81756	−0.908782	−	0.417272i	$-0.862986\pi$
$211$	−26.4016	−1.81756	−0.908782	+	0.417272i	$0.862986\pi$
$212$	−12.1703	−0.835857
$213$	−30.8622	−2.11464
$214$	−2.95980	−0.202328
$215$	−1.54631	−0.105458
$216$	4.96608	0.337899
$217$	11.8579	0.804966
$218$	−7.10363	−0.481119
$219$	16.2857	1.10049
$220$	0.576240	0.0388501
$221$	9.57623	0.644167
$222$	7.18811	0.482435
$223$	16.0183	1.07266	0.536331	−	0.844008i	$-0.319810\pi$
$223$	16.0183	1.07266	0.536331	+	0.844008i	$0.319810\pi$
$224$	−1.94661	−0.130063
$225$	−23.7606	−1.58404
$226$	0.726798	0.0483459
$227$	22.2718	1.47823	0.739116	−	0.673578i	$-0.235243\pi$
$227$	22.2718	1.47823	0.739116	+	0.673578i	$0.235243\pi$
$228$	15.4201	1.02122
$229$	−10.0643	−0.665069	−0.332534	−	0.943091i	$-0.607904\pi$
$229$	−10.0643	−0.665069	−0.332534	+	0.943091i	$0.607904\pi$
$230$	0.553584	0.0365023
$231$	−18.2005	−1.19750
$232$	8.22027	0.539687
$233$	13.5445	0.887332	0.443666	−	0.896192i	$-0.353678\pi$
$233$	13.5445	0.887332	0.443666	+	0.896192i	$0.353678\pi$
$234$	−10.4046	−0.680172
$235$	0.434158	0.0283214
$236$	11.4290	0.743968
$237$	1.44943	0.0941506
$238$	−8.56463	−0.555163
$239$	28.9899	1.87520	0.937601	−	0.347712i	$-0.113041\pi$
$239$	28.9899	1.87520	0.937601	+	0.347712i	$0.113041\pi$
$240$	−0.479513	−0.0309524
$241$	−15.0063	−0.966638	−0.483319	−	0.875444i	$-0.660569\pi$
$241$	−15.0063	−0.966638	−0.483319	+	0.875444i	$0.660569\pi$
$242$	−0.235866	−0.0151620
$243$	16.2625	1.04324
$244$	−0.365270	−0.0233840
$245$	−0.551953	−0.0352630
$246$	−15.1871	−0.968292
$247$	−12.0324	−0.765604
$248$	−6.09156	−0.386815
$249$	32.0288	2.02974
$250$	1.71402	0.108404
$251$	23.0264	1.45341	0.726707	−	0.686947i	$-0.241050\pi$
$251$	23.0264	1.45341	0.726707	+	0.686947i	$0.241050\pi$
$252$	9.30553	0.586193
$253$	−10.7941	−0.678620
$254$	−20.7393	−1.30130
$255$	−2.10975	−0.132118
$256$	1.00000	0.0625000
$257$	−21.3891	−1.33422	−0.667108	−	0.744961i	$-0.732468\pi$
$257$	−21.3891	−1.33422	−0.667108	+	0.744961i	$0.732468\pi$
$258$	−25.0898	−1.56202
$259$	5.01641	0.311705
$260$	0.374166	0.0232048
$261$	−39.2960	−2.43236
$262$	3.90102	0.241006
$263$	−10.1810	−0.627787	−0.313894	−	0.949458i	$-0.601634\pi$
$263$	−10.1810	−0.627787	−0.313894	+	0.949458i	$0.601634\pi$
$264$	9.34983	0.575442
$265$	−2.09219	−0.128522
$266$	10.7613	0.659821
$267$	10.7565	0.658287
$268$	−6.91964	−0.422684
$269$	−5.61648	−0.342443	−0.171221	−	0.985233i	$-0.554771\pi$
$269$	−5.61648	−0.342443	−0.171221	+	0.985233i	$0.554771\pi$
$270$	0.853716	0.0519555
$271$	−12.5674	−0.763416	−0.381708	−	0.924283i	$-0.624664\pi$
$271$	−12.5674	−0.763416	−0.381708	+	0.924283i	$0.624664\pi$
$272$	4.39977	0.266775
$273$	−11.8180	−0.715257
$274$	0.907761	0.0548398
$275$	−16.6609	−1.00469
$276$	8.98222	0.540666
$277$	3.87848	0.233035	0.116518	−	0.993189i	$-0.462827\pi$
$277$	3.87848	0.233035	0.116518	+	0.993189i	$0.462827\pi$
$278$	14.9978	0.899511
$279$	29.1200	1.74337
$280$	−0.334641	−0.0199986
$281$	−20.5551	−1.22621	−0.613106	−	0.790000i	$-0.710080\pi$
$281$	−20.5551	−1.22621	−0.613106	+	0.790000i	$0.710080\pi$
$282$	7.04447	0.419492
$283$	2.00408	0.119130	0.0595651	−	0.998224i	$-0.481029\pi$
$283$	2.00408	0.119130	0.0595651	+	0.998224i	$0.481029\pi$
$284$	11.0644	0.656549
$285$	2.65087	0.157024
$286$	−7.29571	−0.431405
$287$	−10.5987	−0.625621
$288$	−4.78038	−0.281687
$289$	2.35798	0.138705
$290$	1.41314	0.0829827
$291$	20.6717	1.21179
$292$	−5.83857	−0.341677
$293$	−27.4636	−1.60444	−0.802221	−	0.597027i	$-0.796349\pi$
$293$	−27.4636	−1.60444	−0.802221	+	0.597027i	$0.796349\pi$
$294$	−8.95576	−0.522310
$295$	1.96476	0.114393
$296$	−2.57700	−0.149785
$297$	−16.6463	−0.965914
$298$	−6.56511	−0.380307
$299$	−7.00887	−0.405333
$300$	13.8642	0.800452
$301$	−17.5096	−1.00924
$302$	1.90866	0.109831
$303$	−28.2661	−1.62385
$304$	−5.52826	−0.317067
$305$	−0.0627934	−0.00359554
$306$	−21.0326	−1.20235
$307$	−7.00109	−0.399573	−0.199787	−	0.979839i	$-0.564025\pi$
$307$	−7.00109	−0.399573	−0.199787	+	0.979839i	$0.564025\pi$
$308$	6.52502	0.371798
$309$	−26.8441	−1.52711
$310$	−1.04720	−0.0594769
$311$	22.1477	1.25588	0.627940	−	0.778262i	$-0.283898\pi$
$311$	22.1477	1.25588	0.627940	+	0.778262i	$0.283898\pi$
$312$	6.07107	0.343706
$313$	−13.0622	−0.738320	−0.369160	−	0.929366i	$-0.620355\pi$
$313$	−13.0622	−0.738320	−0.369160	+	0.929366i	$0.620355\pi$
$314$	15.1459	0.854730
$315$	1.59971	0.0901335
$316$	−0.519633	−0.0292317
$317$	−0.674755	−0.0378980	−0.0189490	−	0.999820i	$-0.506032\pi$
$317$	−0.674755	−0.0378980	−0.0189490	+	0.999820i	$0.506032\pi$
$318$	−33.9469	−1.90365
$319$	−27.5543	−1.54275
$320$	0.171910	0.00961004
$321$	−8.25586	−0.460797
$322$	6.26848	0.349329
$323$	−24.3231	−1.35337
$324$	−0.489101	−0.0271723
$325$	−10.8183	−0.600093
$326$	20.4278	1.13139
$327$	−19.8144	−1.09574
$328$	5.44470	0.300633
$329$	4.91617	0.271037
$330$	1.60733	0.0884804
$331$	13.8491	0.761217	0.380608	−	0.924736i	$-0.375715\pi$
$331$	13.8491	0.761217	0.380608	+	0.924736i	$0.375715\pi$
$332$	−11.4826	−0.630189
$333$	12.3190	0.675079
$334$	18.2496	0.998574
$335$	−1.18955	−0.0649922
$336$	−5.42974	−0.296217
$337$	−10.6917	−0.582415	−0.291207	−	0.956660i	$-0.594057\pi$
$337$	−10.6917	−0.582415	−0.291207	+	0.956660i	$0.594057\pi$
$338$	8.26272	0.449433
$339$	2.02728	0.110107
$340$	0.756363	0.0410195
$341$	20.4189	1.10574
$342$	26.4272	1.42902
$343$	−19.8763	−1.07322
$344$	8.99492	0.484974
$345$	1.54413	0.0831332
$346$	19.3806	1.04191
$347$	−30.6403	−1.64486	−0.822428	−	0.568869i	$-0.807381\pi$
$347$	−30.6403	−1.64486	−0.822428	+	0.568869i	$0.807381\pi$
$348$	22.9291	1.22913
$349$	−23.2448	−1.24426	−0.622132	−	0.782912i	$-0.713733\pi$
$349$	−23.2448	−1.24426	−0.622132	+	0.782912i	$0.713733\pi$
$350$	9.67551	0.517178
$351$	−10.8088	−0.576932
$352$	−3.35199	−0.178662
$353$	9.64139	0.513159	0.256580	−	0.966523i	$-0.417404\pi$
$353$	9.64139	0.513159	0.256580	+	0.966523i	$0.417404\pi$
$354$	31.8794	1.69437
$355$	1.90207	0.100951
$356$	−3.85629	−0.204383
$357$	−23.8896	−1.26437
$358$	−2.35456	−0.124442
$359$	26.7109	1.40975	0.704874	−	0.709332i	$-0.251003\pi$
$359$	26.7109	1.40975	0.704874	+	0.709332i	$0.251003\pi$
$360$	−0.821794	−0.0433123
$361$	11.5616	0.608506
$362$	−20.5218	−1.07860
$363$	−0.657908	−0.0345312
$364$	4.23685	0.222071
$365$	−1.00371	−0.0525364
$366$	−1.01886	−0.0532566
$367$	−14.2695	−0.744861	−0.372430	−	0.928060i	$-0.621475\pi$
$367$	−14.2695	−0.744861	−0.372430	+	0.928060i	$0.621475\pi$
$368$	−3.22020	−0.167865
$369$	−26.0277	−1.35495
$370$	−0.443011	−0.0230311
$371$	−23.6907	−1.22996
$372$	−16.9914	−0.880963
$373$	24.4395	1.26543	0.632713	−	0.774386i	$-0.281941\pi$
$373$	24.4395	1.26543	0.632713	+	0.774386i	$0.281941\pi$
$374$	−14.7480	−0.762601
$375$	4.78096	0.246888
$376$	−2.52550	−0.130243
$377$	−17.8917	−0.921468
$378$	9.66701	0.497217
$379$	−9.55779	−0.490951	−0.245475	−	0.969403i	$-0.578944\pi$
$379$	−9.55779	−0.490951	−0.245475	+	0.969403i	$0.578944\pi$
$380$	−0.950360	−0.0487525
$381$	−57.8489	−2.96369
$382$	−1.47196	−0.0753122
$383$	13.8094	0.705629	0.352815	−	0.935693i	$-0.385225\pi$
$383$	13.8094	0.705629	0.352815	+	0.935693i	$0.385225\pi$
$384$	2.78933	0.142343
$385$	1.12171	0.0571678
$386$	−9.63915	−0.490620
$387$	−42.9991	−2.18577
$388$	−7.41097	−0.376235
$389$	−35.7092	−1.81053	−0.905263	−	0.424851i	$-0.860326\pi$
$389$	−35.7092	−1.81053	−0.905263	+	0.424851i	$0.860326\pi$
$390$	1.04367	0.0528485
$391$	−14.1682	−0.716515
$392$	3.21072	0.162166
$393$	10.8812	0.548886
$394$	−12.2603	−0.617663
$395$	−0.0893300	−0.00449468
$396$	16.0238	0.805227
$397$	−1.70075	−0.0853583	−0.0426792	−	0.999089i	$-0.513589\pi$
$397$	−1.70075	−0.0853583	−0.0426792	+	0.999089i	$0.513589\pi$
$398$	10.3979	0.521200
$399$	30.0170	1.50273
$400$	−4.97045	−0.248522
$401$	11.3811	0.568345	0.284173	−	0.958773i	$-0.408281\pi$
$401$	11.3811	0.568345	0.284173	+	0.958773i	$0.408281\pi$
$402$	−19.3012	−0.962655
$403$	13.2585	0.660451
$404$	10.1336	0.504168
$405$	−0.0840813	−0.00417803
$406$	16.0017	0.794149
$407$	8.63809	0.428174
$408$	12.2724	0.607576
$409$	6.91144	0.341749	0.170874	−	0.985293i	$-0.445341\pi$
$409$	6.91144	0.341749	0.170874	+	0.985293i	$0.445341\pi$
$410$	0.935996	0.0462255
$411$	2.53205	0.124897
$412$	9.62385	0.474133
$413$	22.2479	1.09475
$414$	15.3938	0.756564
$415$	−1.97397	−0.0968982
$416$	−2.17653	−0.106713
$417$	41.8340	2.04862
$418$	18.5307	0.906365
$419$	18.1818	0.888240	0.444120	−	0.895967i	$-0.353516\pi$
$419$	18.1818	0.888240	0.444120	+	0.895967i	$0.353516\pi$
$420$	−0.933425	−0.0455465
$421$	−17.3654	−0.846340	−0.423170	−	0.906050i	$-0.639083\pi$
$421$	−17.3654	−0.846340	−0.423170	+	0.906050i	$0.639083\pi$
$422$	26.4016	1.28521
$423$	12.0729	0.587003
$424$	12.1703	0.591040
$425$	−21.8688	−1.06079
$426$	30.8622	1.49528
$427$	−0.711037	−0.0344095
$428$	2.95980	0.143067
$429$	−20.3502	−0.982516
$430$	1.54631	0.0745699
$431$	3.77690	0.181927	0.0909634	−	0.995854i	$-0.471005\pi$
$431$	3.77690	0.181927	0.0909634	+	0.995854i	$0.471005\pi$
$432$	−4.96608	−0.238930
$433$	−33.6054	−1.61497	−0.807487	−	0.589885i	$-0.799173\pi$
$433$	−33.6054	−1.61497	−0.807487	+	0.589885i	$0.799173\pi$
$434$	−11.8579	−0.569197
$435$	3.94173	0.188992
$436$	7.10363	0.340202
$437$	17.8021	0.851591
$438$	−16.2857	−0.778162
$439$	10.3223	0.492656	0.246328	−	0.969187i	$-0.420776\pi$
$439$	10.3223	0.492656	0.246328	+	0.969187i	$0.420776\pi$
$440$	−0.576240	−0.0274712
$441$	−15.3484	−0.730878
$442$	−9.57623	−0.455495
$443$	−30.5599	−1.45195	−0.725973	−	0.687723i	$-0.758610\pi$
$443$	−30.5599	−1.45195	−0.725973	+	0.687723i	$0.758610\pi$
$444$	−7.18811	−0.341133
$445$	−0.662934	−0.0314261
$446$	−16.0183	−0.758487
$447$	−18.3123	−0.866141
$448$	1.94661	0.0919686
$449$	32.0642	1.51320	0.756602	−	0.653876i	$-0.226858\pi$
$449$	32.0642	1.51320	0.756602	+	0.653876i	$0.226858\pi$
$450$	23.7606	1.12009
$451$	−18.2506	−0.859387
$452$	−0.726798	−0.0341857
$453$	5.32390	0.250139
$454$	−22.2718	−1.04527
$455$	0.728355	0.0341458
$456$	−15.4201	−0.722115
$457$	−19.7703	−0.924815	−0.462408	−	0.886667i	$-0.653014\pi$
$457$	−19.7703	−0.924815	−0.462408	+	0.886667i	$0.653014\pi$
$458$	10.0643	0.470275
$459$	−21.8496	−1.01985
$460$	−0.553584	−0.0258110
$461$	33.2847	1.55023	0.775113	−	0.631823i	$-0.217693\pi$
$461$	33.2847	1.55023	0.775113	+	0.631823i	$0.217693\pi$
$462$	18.2005	0.846762
$463$	−29.3189	−1.36256	−0.681282	−	0.732021i	$-0.738577\pi$
$463$	−29.3189	−1.36256	−0.681282	+	0.732021i	$0.738577\pi$
$464$	−8.22027	−0.381617
$465$	−2.92099	−0.135457
$466$	−13.5445	−0.627439
$467$	−19.1063	−0.884134	−0.442067	−	0.896982i	$-0.645755\pi$
$467$	−19.1063	−0.884134	−0.442067	+	0.896982i	$0.645755\pi$
$468$	10.4046	0.480955
$469$	−13.4698	−0.621979
$470$	−0.434158	−0.0200262
$471$	42.2468	1.94663
$472$	−11.4290	−0.526065
$473$	−30.1509	−1.38634
$474$	−1.44943	−0.0665745
$475$	27.4779	1.26077
$476$	8.56463	0.392559
$477$	−58.1785	−2.66381
$478$	−28.9899	−1.32597
$479$	26.4663	1.20928	0.604639	−	0.796500i	$-0.293317\pi$
$479$	26.4663	1.20928	0.604639	+	0.796500i	$0.293317\pi$
$480$	0.479513	0.0218867
$481$	5.60892	0.255745
$482$	15.0063	0.683516
$483$	17.4849	0.795589
$484$	0.235866	0.0107212
$485$	−1.27402	−0.0578501
$486$	−16.2625	−0.737682
$487$	−7.32515	−0.331934	−0.165967	−	0.986131i	$-0.553075\pi$
$487$	−7.32515	−0.331934	−0.165967	+	0.986131i	$0.553075\pi$
$488$	0.365270	0.0165350
$489$	56.9801	2.57673
$490$	0.551953	0.0249347
$491$	−13.6333	−0.615263	−0.307631	−	0.951506i	$-0.599536\pi$
$491$	−13.6333	−0.615263	−0.307631	+	0.951506i	$0.599536\pi$
$492$	15.1871	0.684686
$493$	−36.1673	−1.62889
$494$	12.0324	0.541364
$495$	2.75465	0.123812
$496$	6.09156	0.273519
$497$	21.5380	0.966110
$498$	−32.0288	−1.43524
$499$	−35.9337	−1.60862	−0.804308	−	0.594213i	$-0.797464\pi$
$499$	−35.9337	−1.60862	−0.804308	+	0.594213i	$0.797464\pi$
$500$	−1.71402	−0.0766531
$501$	50.9042	2.27423
$502$	−23.0264	−1.02772
$503$	−9.10868	−0.406136	−0.203068	−	0.979165i	$-0.565091\pi$
$503$	−9.10868	−0.406136	−0.203068	+	0.979165i	$0.565091\pi$
$504$	−9.30553	−0.414501
$505$	1.74207	0.0775212
$506$	10.7941	0.479857
$507$	23.0475	1.02357
$508$	20.7393	0.920159
$509$	−9.95266	−0.441144	−0.220572	−	0.975371i	$-0.570792\pi$
$509$	−9.95266	−0.441144	−0.220572	+	0.975371i	$0.570792\pi$
$510$	2.10975	0.0934212
$511$	−11.3654	−0.502776
$512$	−1.00000	−0.0441942
$513$	27.4537	1.21211
$514$	21.3891	0.943434
$515$	1.65443	0.0729030
$516$	25.0898	1.10452
$517$	8.46547	0.372311
$518$	−5.01641	−0.220408
$519$	54.0591	2.37293
$520$	−0.374166	−0.0164083
$521$	−28.0042	−1.22688	−0.613442	−	0.789739i	$-0.710216\pi$
$521$	−28.0042	−1.22688	−0.613442	+	0.789739i	$0.710216\pi$
$522$	39.2960	1.71994
$523$	−43.9551	−1.92202	−0.961011	−	0.276511i	$-0.910822\pi$
$523$	−43.9551	−1.92202	−0.961011	+	0.276511i	$0.910822\pi$
$524$	−3.90102	−0.170417
$525$	26.9882	1.17786
$526$	10.1810	0.443913
$527$	26.8015	1.16749
$528$	−9.34983	−0.406899
$529$	−12.6303	−0.549143
$530$	2.09219	0.0908788
$531$	54.6352	2.37097
$532$	−10.7613	−0.466564
$533$	−11.8505	−0.513304
$534$	−10.7565	−0.465479
$535$	0.508818	0.0219981
$536$	6.91964	0.298883
$537$	−6.56764	−0.283415
$538$	5.61648	0.242144
$539$	−10.7623	−0.463565
$540$	−0.853716	−0.0367381
$541$	25.7137	1.10552	0.552760	−	0.833341i	$-0.313575\pi$
$541$	25.7137	1.10552	0.552760	+	0.833341i	$0.313575\pi$
$542$	12.5674	0.539816
$543$	−57.2421	−2.45649
$544$	−4.39977	−0.188639
$545$	1.22118	0.0523097
$546$	11.8180	0.505763
$547$	0.414659	0.0177295	0.00886477	−	0.999961i	$-0.497178\pi$
$547$	0.414659	0.0177295	0.00886477	+	0.999961i	$0.497178\pi$
$548$	−0.907761	−0.0387776
$549$	−1.74613	−0.0745229
$550$	16.6609	0.710424
$551$	45.4438	1.93597
$552$	−8.98222	−0.382309
$553$	−1.01152	−0.0430143
$554$	−3.87848	−0.164781
$555$	−1.23571	−0.0524528
$556$	−14.9978	−0.636050
$557$	7.66741	0.324879	0.162439	−	0.986719i	$-0.448064\pi$
$557$	7.66741	0.324879	0.162439	+	0.986719i	$0.448064\pi$
$558$	−29.1200	−1.23275
$559$	−19.5777	−0.828049
$560$	0.334641	0.0141412
$561$	−41.1371	−1.73681
$562$	20.5551	0.867063
$563$	2.16448	0.0912218	0.0456109	−	0.998959i	$-0.485477\pi$
$563$	2.16448	0.0912218	0.0456109	+	0.998959i	$0.485477\pi$
$564$	−7.04447	−0.296626
$565$	−0.124944	−0.00525642
$566$	−2.00408	−0.0842377
$567$	−0.952089	−0.0399840
$568$	−11.0644	−0.464250
$569$	15.7079	0.658510	0.329255	−	0.944241i	$-0.393202\pi$
$569$	15.7079	0.658510	0.329255	+	0.944241i	$0.393202\pi$
$570$	−2.65087	−0.111033
$571$	35.7734	1.49707	0.748535	−	0.663095i	$-0.230757\pi$
$571$	35.7734	1.49707	0.748535	+	0.663095i	$0.230757\pi$
$572$	7.29571	0.305049
$573$	−4.10579	−0.171522
$574$	10.5987	0.442381
$575$	16.0059	0.667490
$576$	4.78038	0.199183
$577$	−16.3429	−0.680362	−0.340181	−	0.940360i	$-0.610488\pi$
$577$	−16.3429	−0.680362	−0.340181	+	0.940360i	$0.610488\pi$
$578$	−2.35798	−0.0980792
$579$	−26.8868	−1.11738
$580$	−1.41314	−0.0586776
$581$	−22.3521	−0.927321
$582$	−20.6717	−0.856868
$583$	−40.7947	−1.68954
$584$	5.83857	0.241602
$585$	1.78866	0.0739519
$586$	27.4636	1.13451
$587$	18.4064	0.759715	0.379857	−	0.925045i	$-0.375973\pi$
$587$	18.4064	0.759715	0.379857	+	0.925045i	$0.375973\pi$
$588$	8.95576	0.369329
$589$	−33.6757	−1.38758
$590$	−1.96476	−0.0808880
$591$	−34.1979	−1.40672
$592$	2.57700	0.105914
$593$	4.44640	0.182592	0.0912958	−	0.995824i	$-0.470899\pi$
$593$	4.44640	0.182592	0.0912958	+	0.995824i	$0.470899\pi$
$594$	16.6463	0.683004
$595$	1.47234	0.0603602
$596$	6.56511	0.268917
$597$	29.0032	1.18702
$598$	7.00887	0.286614
$599$	−14.4828	−0.591752	−0.295876	−	0.955226i	$-0.595612\pi$
$599$	−14.4828	−0.591752	−0.295876	+	0.955226i	$0.595612\pi$
$600$	−13.8642	−0.566005
$601$	29.9658	1.22233	0.611166	−	0.791503i	$-0.290701\pi$
$601$	29.9658	1.22233	0.611166	+	0.791503i	$0.290701\pi$
$602$	17.5096	0.713638
$603$	−33.0785	−1.34706
$604$	−1.90866	−0.0776624
$605$	0.0405476	0.00164849
$606$	28.2661	1.14823
$607$	0.751827	0.0305157	0.0152578	−	0.999884i	$-0.495143\pi$
$607$	0.751827	0.0305157	0.0152578	+	0.999884i	$0.495143\pi$
$608$	5.52826	0.224200
$609$	44.6339	1.80866
$610$	0.0627934	0.00254243
$611$	5.49683	0.222378
$612$	21.0326	0.850192
$613$	34.2162	1.38198	0.690990	−	0.722864i	$-0.257175\pi$
$613$	34.2162	1.38198	0.690990	+	0.722864i	$0.257175\pi$
$614$	7.00109	0.282541
$615$	2.61080	0.105278
$616$	−6.52502	−0.262901
$617$	40.4120	1.62693	0.813463	−	0.581616i	$-0.197579\pi$
$617$	40.4120	1.62693	0.813463	+	0.581616i	$0.197579\pi$
$618$	26.8441	1.07983
$619$	1.52398	0.0612538	0.0306269	−	0.999531i	$-0.490250\pi$
$619$	1.52398	0.0612538	0.0306269	+	0.999531i	$0.490250\pi$
$620$	1.04720	0.0420565
$621$	15.9918	0.641728
$622$	−22.1477	−0.888041
$623$	−7.50670	−0.300749
$624$	−6.07107	−0.243037
$625$	24.5576	0.982303
$626$	13.0622	0.522071
$627$	51.6882	2.06423
$628$	−15.1459	−0.604385
$629$	11.3382	0.452084
$630$	−1.59971	−0.0637340
$631$	−23.0320	−0.916888	−0.458444	−	0.888723i	$-0.651593\pi$
$631$	−23.0320	−0.916888	−0.458444	+	0.888723i	$0.651593\pi$
$632$	0.519633	0.0206699
$633$	73.6430	2.92705
$634$	0.674755	0.0267979
$635$	3.56529	0.141484
$636$	33.9469	1.34608
$637$	−6.98822	−0.276883
$638$	27.5543	1.09089
$639$	52.8918	2.09237
$640$	−0.171910	−0.00679532
$641$	9.55171	0.377270	0.188635	−	0.982047i	$-0.439594\pi$
$641$	9.55171	0.377270	0.188635	+	0.982047i	$0.439594\pi$
$642$	8.25586	0.325833
$643$	−25.3522	−0.999793	−0.499896	−	0.866085i	$-0.666629\pi$
$643$	−25.3522	−0.999793	−0.499896	+	0.866085i	$0.666629\pi$
$644$	−6.26848	−0.247013
$645$	4.31318	0.169831
$646$	24.3231	0.956978
$647$	−0.682375	−0.0268269	−0.0134135	−	0.999910i	$-0.504270\pi$
$647$	−0.682375	−0.0268269	−0.0134135	+	0.999910i	$0.504270\pi$
$648$	0.489101	0.0192137
$649$	38.3101	1.50380
$650$	10.8183	0.424330
$651$	−33.0756	−1.29634
$652$	−20.4278	−0.800016
$653$	−34.8109	−1.36226	−0.681129	−	0.732164i	$-0.738511\pi$
$653$	−34.8109	−1.36226	−0.681129	+	0.732164i	$0.738511\pi$
$654$	19.8144	0.774805
$655$	−0.670623	−0.0262034
$656$	−5.44470	−0.212580
$657$	−27.9106	−1.08890
$658$	−4.91617	−0.191652
$659$	41.7338	1.62572	0.812858	−	0.582462i	$-0.197910\pi$
$659$	41.7338	1.62572	0.812858	+	0.582462i	$0.197910\pi$
$660$	−1.60733	−0.0625651
$661$	−17.4363	−0.678195	−0.339097	−	0.940751i	$-0.610122\pi$
$661$	−17.4363	−0.678195	−0.339097	+	0.940751i	$0.610122\pi$
$662$	−13.8491	−0.538262
$663$	−26.7113	−1.03738
$664$	11.4826	0.445611
$665$	−1.84998	−0.0717391
$666$	−12.3190	−0.477353
$667$	26.4710	1.02496
$668$	−18.2496	−0.706099
$669$	−44.6803	−1.72744
$670$	1.18955	0.0459564
$671$	−1.22438	−0.0472667
$672$	5.42974	0.209457
$673$	12.8293	0.494531	0.247266	−	0.968948i	$-0.420468\pi$
$673$	12.8293	0.494531	0.247266	+	0.968948i	$0.420468\pi$
$674$	10.6917	0.411829
$675$	24.6836	0.950073
$676$	−8.26272	−0.317797
$677$	−26.7759	−1.02908	−0.514540	−	0.857466i	$-0.672037\pi$
$677$	−26.7759	−1.02908	−0.514540	+	0.857466i	$0.672037\pi$
$678$	−2.02728	−0.0778573
$679$	−14.4263	−0.553629
$680$	−0.756363	−0.0290052
$681$	−62.1235	−2.38058
$682$	−20.4189	−0.781880
$683$	19.6856	0.753250	0.376625	−	0.926366i	$-0.377085\pi$
$683$	19.6856	0.753250	0.376625	+	0.926366i	$0.377085\pi$
$684$	−26.4272	−1.01047
$685$	−0.156053	−0.00596247
$686$	19.8763	0.758879
$687$	28.0727	1.07104
$688$	−8.99492	−0.342928
$689$	−26.4889	−1.00915
$690$	−1.54413	−0.0587841
$691$	39.5272	1.50369	0.751843	−	0.659343i	$-0.229165\pi$
$691$	39.5272	1.50369	0.751843	+	0.659343i	$0.229165\pi$
$692$	−19.3806	−0.736741
$693$	31.1921	1.18489
$694$	30.6403	1.16309
$695$	−2.57827	−0.0977995
$696$	−22.9291	−0.869125
$697$	−23.9554	−0.907376
$698$	23.2448	0.879827
$699$	−37.7802	−1.42898
$700$	−9.67551	−0.365700
$701$	−2.77305	−0.104737	−0.0523684	−	0.998628i	$-0.516677\pi$
$701$	−2.77305	−0.104737	−0.0523684	+	0.998628i	$0.516677\pi$
$702$	10.8088	0.407952
$703$	−14.2463	−0.537310
$704$	3.35199	0.126333
$705$	−1.21101	−0.0456094
$706$	−9.64139	−0.362859
$707$	19.7262	0.741882
$708$	−31.8794	−1.19810
$709$	19.1527	0.719295	0.359648	−	0.933088i	$-0.382897\pi$
$709$	19.1527	0.719295	0.359648	+	0.933088i	$0.382897\pi$
$710$	−1.90207	−0.0713834
$711$	−2.48404	−0.0931590
$712$	3.85629	0.144521
$713$	−19.6161	−0.734628
$714$	23.8896	0.894046
$715$	1.25420	0.0469045
$716$	2.35456	0.0879939
$717$	−80.8626	−3.01987
$718$	−26.7109	−0.996843
$719$	−13.4887	−0.503043	−0.251521	−	0.967852i	$-0.580931\pi$
$719$	−13.4887	−0.503043	−0.251521	+	0.967852i	$0.580931\pi$
$720$	0.821794	0.0306264
$721$	18.7339	0.697686
$722$	−11.5616	−0.430279
$723$	41.8574	1.55670
$724$	20.5218	0.762686
$725$	40.8584	1.51744
$726$	0.657908	0.0244173
$727$	−16.9076	−0.627070	−0.313535	−	0.949577i	$-0.601513\pi$
$727$	−16.9076	−0.627070	−0.313535	+	0.949577i	$0.601513\pi$
$728$	−4.23685	−0.157028
$729$	−43.8942	−1.62571
$730$	1.00371	0.0371489
$731$	−39.5756	−1.46376
$732$	1.01886	0.0376581
$733$	−3.49888	−0.129234	−0.0646170	−	0.997910i	$-0.520583\pi$
$733$	−3.49888	−0.129234	−0.0646170	+	0.997910i	$0.520583\pi$
$734$	14.2695	0.526696
$735$	1.53958	0.0567883
$736$	3.22020	0.118698
$737$	−23.1946	−0.854384
$738$	26.0277	0.958093
$739$	−11.0588	−0.406803	−0.203402	−	0.979095i	$-0.565200\pi$
$739$	−11.0588	−0.406803	−0.203402	+	0.979095i	$0.565200\pi$
$740$	0.443011	0.0162854
$741$	33.5624	1.23295
$742$	23.6907	0.869715
$743$	45.9328	1.68511	0.842556	−	0.538608i	$-0.181050\pi$
$743$	45.9328	1.68511	0.842556	+	0.538608i	$0.181050\pi$
$744$	16.9914	0.622935
$745$	1.12861	0.0413489
$746$	−24.4395	−0.894792
$747$	−54.8911	−2.00836
$748$	14.7480	0.539241
$749$	5.76157	0.210523
$750$	−4.78096	−0.174576
$751$	50.0221	1.82533	0.912666	−	0.408706i	$-0.134020\pi$
$751$	50.0221	1.82533	0.912666	+	0.408706i	$0.134020\pi$
$752$	2.52550	0.0920956
$753$	−64.2284	−2.34061
$754$	17.8917	0.651576
$755$	−0.328118	−0.0119414
$756$	−9.66701	−0.351586
$757$	−30.1604	−1.09620	−0.548098	−	0.836414i	$-0.684648\pi$
$757$	−30.1604	−1.09620	−0.548098	+	0.836414i	$0.684648\pi$
$758$	9.55779	0.347154
$759$	30.1084	1.09286
$760$	0.950360	0.0344732
$761$	20.7481	0.752118	0.376059	−	0.926596i	$-0.377279\pi$
$761$	20.7481	0.752118	0.376059	+	0.926596i	$0.377279\pi$
$762$	57.8489	2.09565
$763$	13.8280	0.500607
$764$	1.47196	0.0532537
$765$	3.61570	0.130726
$766$	−13.8094	−0.498955
$767$	24.8757	0.898208
$768$	−2.78933	−0.100651
$769$	15.7077	0.566433	0.283217	−	0.959056i	$-0.408598\pi$
$769$	15.7077	0.566433	0.283217	+	0.959056i	$0.408598\pi$
$770$	−1.12171	−0.0404238
$771$	59.6614	2.14865
$772$	9.63915	0.346921
$773$	16.8081	0.604546	0.302273	−	0.953221i	$-0.402255\pi$
$773$	16.8081	0.604546	0.302273	+	0.953221i	$0.402255\pi$
$774$	42.9991	1.54557
$775$	−30.2778	−1.08761
$776$	7.41097	0.266038
$777$	−13.9924	−0.501976
$778$	35.7092	1.28024
$779$	30.0997	1.07843
$780$	−1.04367	−0.0373695
$781$	37.0877	1.32710
$782$	14.1682	0.506652
$783$	40.8225	1.45888
$784$	−3.21072	−0.114668
$785$	−2.60372	−0.0929307
$786$	−10.8812	−0.388121
$787$	46.4566	1.65600	0.827999	−	0.560730i	$-0.189480\pi$
$787$	46.4566	1.65600	0.827999	+	0.560730i	$0.189480\pi$
$788$	12.2603	0.436753
$789$	28.3982	1.01100
$790$	0.0893300	0.00317822
$791$	−1.41479	−0.0503042
$792$	−16.0238	−0.569381
$793$	−0.795020	−0.0282320
$794$	1.70075	0.0603575
$795$	5.83580	0.206975
$796$	−10.3979	−0.368544
$797$	−44.3493	−1.57093	−0.785467	−	0.618903i	$-0.787577\pi$
$797$	−44.3493	−1.57093	−0.785467	+	0.618903i	$0.787577\pi$
$798$	−30.0170	−1.06259
$799$	11.1116	0.393101
$800$	4.97045	0.175732
$801$	−18.4346	−0.651353
$802$	−11.3811	−0.401881
$803$	−19.5709	−0.690641
$804$	19.3012	0.680700
$805$	−1.07761	−0.0379808
$806$	−13.2585	−0.467010
$807$	15.6662	0.551477
$808$	−10.1336	−0.356500
$809$	23.6773	0.832450	0.416225	−	0.909262i	$-0.363353\pi$
$809$	23.6773	0.832450	0.416225	+	0.909262i	$0.363353\pi$
$810$	0.0840813	0.00295431
$811$	1.61668	0.0567694	0.0283847	−	0.999597i	$-0.490964\pi$
$811$	1.61668	0.0567694	0.0283847	+	0.999597i	$0.490964\pi$
$812$	−16.0017	−0.561548
$813$	35.0547	1.22942
$814$	−8.63809	−0.302765
$815$	−3.51174	−0.123011
$816$	−12.2724	−0.429621
$817$	49.7262	1.73970
$818$	−6.91144	−0.241653
$819$	20.2538	0.707724
$820$	−0.935996	−0.0326864
$821$	45.8814	1.60127	0.800637	−	0.599150i	$-0.204495\pi$
$821$	45.8814	1.60127	0.800637	+	0.599150i	$0.204495\pi$
$822$	−2.53205	−0.0883153
$823$	30.4841	1.06261	0.531305	−	0.847181i	$-0.321702\pi$
$823$	30.4841	1.06261	0.531305	+	0.847181i	$0.321702\pi$
$824$	−9.62385	−0.335263
$825$	46.4728	1.61798
$826$	−22.2479	−0.774103
$827$	−23.3113	−0.810613	−0.405306	−	0.914181i	$-0.632835\pi$
$827$	−23.3113	−0.810613	−0.405306	+	0.914181i	$0.632835\pi$
$828$	−15.3938	−0.534972
$829$	−19.2261	−0.667752	−0.333876	−	0.942617i	$-0.608357\pi$
$829$	−19.2261	−0.667752	−0.333876	+	0.942617i	$0.608357\pi$
$830$	1.97397	0.0685174
$831$	−10.8184	−0.375285
$832$	2.17653	0.0754576
$833$	−14.1264	−0.489451
$834$	−41.8340	−1.44859
$835$	−3.13728	−0.108570
$836$	−18.5307	−0.640897
$837$	−30.2512	−1.04563
$838$	−18.1818	−0.628081
$839$	−46.4050	−1.60208	−0.801040	−	0.598611i	$-0.795719\pi$
$839$	−46.4050	−1.60208	−0.801040	+	0.598611i	$0.795719\pi$
$840$	0.933425	0.0322062
$841$	38.5729	1.33010
$842$	17.3654	0.598453
$843$	57.3350	1.97472
$844$	−26.4016	−0.908782
$845$	−1.42044	−0.0488647
$846$	−12.0729	−0.415074
$847$	0.459138	0.0157762
$848$	−12.1703	−0.417929
$849$	−5.59004	−0.191850
$850$	21.8688	0.750095
$851$	−8.29847	−0.284468
$852$	−30.8622	−1.05732
$853$	−48.1463	−1.64850	−0.824248	−	0.566229i	$-0.808402\pi$
$853$	−48.1463	−1.64850	−0.824248	+	0.566229i	$0.808402\pi$
$854$	0.711037	0.0243312
$855$	−4.54308	−0.155370
$856$	−2.95980	−0.101164
$857$	−16.5866	−0.566588	−0.283294	−	0.959033i	$-0.591427\pi$
$857$	−16.5866	−0.566588	−0.283294	+	0.959033i	$0.591427\pi$
$858$	20.3502	0.694744
$859$	17.6789	0.603198	0.301599	−	0.953435i	$-0.402480\pi$
$859$	17.6789	0.603198	0.301599	+	0.953435i	$0.402480\pi$
$860$	−1.54631	−0.0527288
$861$	29.5633	1.00751
$862$	−3.77690	−0.128642
$863$	18.0235	0.613528	0.306764	−	0.951786i	$-0.400754\pi$
$863$	18.0235	0.613528	0.306764	+	0.951786i	$0.400754\pi$
$864$	4.96608	0.168949
$865$	−3.33172	−0.113282
$866$	33.6054	1.14196
$867$	−6.57721	−0.223374
$868$	11.8579	0.402483
$869$	−1.74181	−0.0590868
$870$	−3.94173	−0.133637
$871$	−15.0608	−0.510316
$872$	−7.10363	−0.240559
$873$	−35.4273	−1.19903
$874$	−17.8021	−0.602166
$875$	−3.33652	−0.112795
$876$	16.2857	0.550244
$877$	0.193439	0.00653196	0.00326598	−	0.999995i	$-0.498960\pi$
$877$	0.193439	0.00653196	0.00326598	+	0.999995i	$0.498960\pi$
$878$	−10.3223	−0.348360
$879$	76.6052	2.58383
$880$	0.576240	0.0194251
$881$	−28.7602	−0.968956	−0.484478	−	0.874803i	$-0.660990\pi$
$881$	−28.7602	−0.968956	−0.484478	+	0.874803i	$0.660990\pi$
$882$	15.3484	0.516809
$883$	−28.6629	−0.964584	−0.482292	−	0.876011i	$-0.660196\pi$
$883$	−28.6629	−0.964584	−0.482292	+	0.876011i	$0.660196\pi$
$884$	9.57623	0.322083
$885$	−5.48038	−0.184221
$886$	30.5599	1.02668
$887$	26.7213	0.897215	0.448607	−	0.893729i	$-0.351920\pi$
$887$	26.7213	0.897215	0.448607	+	0.893729i	$0.351920\pi$
$888$	7.18811	0.241217
$889$	40.3714	1.35401
$890$	0.662934	0.0222216
$891$	−1.63947	−0.0549242
$892$	16.0183	0.536331
$893$	−13.9616	−0.467208
$894$	18.3123	0.612454
$895$	0.404771	0.0135300
$896$	−1.94661	−0.0650316
$897$	19.5501	0.652758
$898$	−32.0642	−1.07000
$899$	−50.0743	−1.67007
$900$	−23.7606	−0.792021
$901$	−53.5464	−1.78389
$902$	18.2506	0.607678
$903$	48.8401	1.62530
$904$	0.726798	0.0241730
$905$	3.52789	0.117271
$906$	−5.32390	−0.176875
$907$	20.7990	0.690618	0.345309	−	0.938489i	$-0.387774\pi$
$907$	20.7990	0.690618	0.345309	+	0.938489i	$0.387774\pi$
$908$	22.2718	0.739116
$909$	48.4427	1.60674
$910$	−0.728355	−0.0241447
$911$	38.3991	1.27222	0.636110	−	0.771598i	$-0.280542\pi$
$911$	38.3991	1.27222	0.636110	+	0.771598i	$0.280542\pi$
$912$	15.4201	0.510612
$913$	−38.4896	−1.27382
$914$	19.7703	0.653943
$915$	0.175152	0.00579034
$916$	−10.0643	−0.332534
$917$	−7.59376	−0.250768
$918$	21.8496	0.721144
$919$	−33.0509	−1.09025	−0.545125	−	0.838355i	$-0.683518\pi$
$919$	−33.0509	−1.09025	−0.545125	+	0.838355i	$0.683518\pi$
$920$	0.553584	0.0182511
$921$	19.5284	0.643481
$922$	−33.2847	−1.09617
$923$	24.0819	0.792665
$924$	−18.2005	−0.598751
$925$	−12.8088	−0.421152
$926$	29.3189	0.963478
$927$	46.0057	1.51102
$928$	8.22027	0.269844
$929$	38.8825	1.27569	0.637847	−	0.770163i	$-0.279825\pi$
$929$	38.8825	1.27569	0.637847	+	0.770163i	$0.279825\pi$
$930$	2.92099	0.0957829
$931$	17.7497	0.581721
$932$	13.5445	0.443666
$933$	−61.7773	−2.02250
$934$	19.1063	0.625177
$935$	2.53532	0.0829140
$936$	−10.4046	−0.340086
$937$	−53.8941	−1.76064	−0.880322	−	0.474376i	$-0.842674\pi$
$937$	−53.8941	−1.76064	−0.880322	+	0.474376i	$0.842674\pi$
$938$	13.4698	0.439805
$939$	36.4349	1.18901
$940$	0.434158	0.0141607
$941$	−9.61953	−0.313588	−0.156794	−	0.987631i	$-0.550116\pi$
$941$	−9.61953	−0.313588	−0.156794	+	0.987631i	$0.550116\pi$
$942$	−42.2468	−1.37648
$943$	17.5330	0.570954
$944$	11.4290	0.371984
$945$	−1.66185	−0.0540600
$946$	30.1509	0.980291
$947$	4.29774	0.139658	0.0698289	−	0.997559i	$-0.477755\pi$
$947$	4.29774	0.139658	0.0698289	+	0.997559i	$0.477755\pi$
$948$	1.44943	0.0470753
$949$	−12.7078	−0.412513
$950$	−27.4779	−0.891501
$951$	1.88212	0.0610318
$952$	−8.56463	−0.277581
$953$	0.180889	0.00585957	0.00292978	−	0.999996i	$-0.499067\pi$
$953$	0.180889	0.00585957	0.00292978	+	0.999996i	$0.499067\pi$
$954$	58.1785	1.88360
$955$	0.253045	0.00818833
$956$	28.9899	0.937601
$957$	76.8582	2.48447
$958$	−26.4663	−0.855089
$959$	−1.76706	−0.0570612
$960$	−0.479513	−0.0154762
$961$	6.10716	0.197005
$962$	−5.60892	−0.180839
$963$	14.1490	0.455944
$964$	−15.0063	−0.483319
$965$	1.65706	0.0533427
$966$	−17.4849	−0.562567
$967$	−41.5427	−1.33592	−0.667961	−	0.744196i	$-0.732833\pi$
$967$	−41.5427	−1.33592	−0.667961	+	0.744196i	$0.732833\pi$
$968$	−0.235866	−0.00758101
$969$	67.8451	2.17950
$970$	1.27402	0.0409062
$971$	−24.3942	−0.782847	−0.391424	−	0.920211i	$-0.628017\pi$
$971$	−24.3942	−0.782847	−0.391424	+	0.920211i	$0.628017\pi$
$972$	16.2625	0.521620
$973$	−29.1949	−0.935946
$974$	7.32515	0.234713
$975$	30.1759	0.966403
$976$	−0.365270	−0.0116920
$977$	−39.5721	−1.26602	−0.633012	−	0.774142i	$-0.718182\pi$
$977$	−39.5721	−1.26602	−0.633012	+	0.774142i	$0.718182\pi$
$978$	−56.9801	−1.82202
$979$	−12.9263	−0.413126
$980$	−0.551953	−0.0176315
$981$	33.9581	1.08420
$982$	13.6333	0.435057
$983$	−4.90739	−0.156521	−0.0782606	−	0.996933i	$-0.524937\pi$
$983$	−4.90739	−0.156521	−0.0782606	+	0.996933i	$0.524937\pi$
$984$	−15.1871	−0.484146
$985$	2.10766	0.0671555
$986$	36.1673	1.15180
$987$	−13.7128	−0.436484
$988$	−12.0324	−0.382802
$989$	28.9655	0.921049
$990$	−2.75465	−0.0875484
$991$	26.2638	0.834297	0.417148	−	0.908838i	$-0.363030\pi$
$991$	26.2638	0.834297	0.417148	+	0.908838i	$0.363030\pi$
$992$	−6.09156	−0.193407
$993$	−38.6298	−1.22588
$994$	−21.5380	−0.683143
$995$	−1.78750	−0.0566676
$996$	32.0288	1.01487
$997$	−41.5634	−1.31633	−0.658163	−	0.752875i	$-0.728666\pi$
$997$	−41.5634	−1.31633	−0.658163	+	0.752875i	$0.728666\pi$
$998$	35.9337	1.13746
$999$	−12.7976	−0.404898

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4022.2.a.d.1.5	✓	37

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4022.2.a.d.1.5	✓	37	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 4022 = 2 \cdot 2011 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4022.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -2.78933 q^{3} +1.00000 q^{4} +0.171910 q^{5} +2.78933 q^{6} +1.94661 q^{7} -1.00000 q^{8} +4.78038 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -2.78933 q^{3} +1.00000 q^{4} +0.171910 q^{5} +2.78933 q^{6} +1.94661 q^{7} -1.00000 q^{8} +4.78038 q^{9} -0.171910 q^{10} +3.35199 q^{11} -2.78933 q^{12} +2.17653 q^{13} -1.94661 q^{14} -0.479513 q^{15} +1.00000 q^{16} +4.39977 q^{17} -4.78038 q^{18} -5.52826 q^{19} +0.171910 q^{20} -5.42974 q^{21} -3.35199 q^{22} -3.22020 q^{23} +2.78933 q^{24} -4.97045 q^{25} -2.17653 q^{26} -4.96608 q^{27} +1.94661 q^{28} -8.22027 q^{29} +0.479513 q^{30} +6.09156 q^{31} -1.00000 q^{32} -9.34983 q^{33} -4.39977 q^{34} +0.334641 q^{35} +4.78038 q^{36} +2.57700 q^{37} +5.52826 q^{38} -6.07107 q^{39} -0.171910 q^{40} -5.44470 q^{41} +5.42974 q^{42} -8.99492 q^{43} +3.35199 q^{44} +0.821794 q^{45} +3.22020 q^{46} +2.52550 q^{47} -2.78933 q^{48} -3.21072 q^{49} +4.97045 q^{50} -12.2724 q^{51} +2.17653 q^{52} -12.1703 q^{53} +4.96608 q^{54} +0.576240 q^{55} -1.94661 q^{56} +15.4201 q^{57} +8.22027 q^{58} +11.4290 q^{59} -0.479513 q^{60} -0.365270 q^{61} -6.09156 q^{62} +9.30553 q^{63} +1.00000 q^{64} +0.374166 q^{65} +9.34983 q^{66} -6.91964 q^{67} +4.39977 q^{68} +8.98222 q^{69} -0.334641 q^{70} +11.0644 q^{71} -4.78038 q^{72} -5.83857 q^{73} -2.57700 q^{74} +13.8642 q^{75} -5.52826 q^{76} +6.52502 q^{77} +6.07107 q^{78} -0.519633 q^{79} +0.171910 q^{80} -0.489101 q^{81} +5.44470 q^{82} -11.4826 q^{83} -5.42974 q^{84} +0.756363 q^{85} +8.99492 q^{86} +22.9291 q^{87} -3.35199 q^{88} -3.85629 q^{89} -0.821794 q^{90} +4.23685 q^{91} -3.22020 q^{92} -16.9914 q^{93} -2.52550 q^{94} -0.950360 q^{95} +2.78933 q^{96} -7.41097 q^{97} +3.21072 q^{98} +16.0238 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 37 q - 37 q^{2} - 5 q^{3} + 37 q^{4} - 13 q^{5} + 5 q^{6} - 22 q^{7} - 37 q^{8} + 32 q^{9}+O(q^{10}) \) 37 * q - 37 * q^2 - 5 * q^3 + 37 * q^4 - 13 * q^5 + 5 * q^6 - 22 * q^7 - 37 * q^8 + 32 * q^9	\( 37 q - 37 q^{2} - 5 q^{3} + 37 q^{4} - 13 q^{5} + 5 q^{6} - 22 q^{7} - 37 q^{8} + 32 q^{9} + 13 q^{10} + 12 q^{11} - 5 q^{12} - 36 q^{13} + 22 q^{14} - 7 q^{15} + 37 q^{16} + 4 q^{17} - 32 q^{18} - 10 q^{19} - 13 q^{20} - 11 q^{21} - 12 q^{22} - q^{23} + 5 q^{24} + 8 q^{25} + 36 q^{26} - 20 q^{27} - 22 q^{28} - 6 q^{29} + 7 q^{30} - 23 q^{31} - 37 q^{32} - 27 q^{33} - 4 q^{34} + 24 q^{35} + 32 q^{36} - 46 q^{37} + 10 q^{38} + 5 q^{39} + 13 q^{40} + 11 q^{41} + 11 q^{42} - 22 q^{43} + 12 q^{44} - 57 q^{45} + q^{46} - 18 q^{47} - 5 q^{48} - q^{49} - 8 q^{50} + 18 q^{51} - 36 q^{52} - 25 q^{53} + 20 q^{54} - 25 q^{55} + 22 q^{56} - 25 q^{57} + 6 q^{58} + 24 q^{59} - 7 q^{60} - 40 q^{61} + 23 q^{62} - 38 q^{63} + 37 q^{64} + 14 q^{65} + 27 q^{66} - 49 q^{67} + 4 q^{68} - 19 q^{69} - 24 q^{70} + 27 q^{71} - 32 q^{72} - 87 q^{73} + 46 q^{74} - 5 q^{75} - 10 q^{76} - 50 q^{77} - 5 q^{78} + 11 q^{79} - 13 q^{80} + 5 q^{81} - 11 q^{82} - 9 q^{83} - 11 q^{84} - 68 q^{85} + 22 q^{86} - 12 q^{87} - 12 q^{88} - 3 q^{89} + 57 q^{90} - 19 q^{91} - q^{92} - 69 q^{93} + 18 q^{94} + 27 q^{95} + 5 q^{96} - 98 q^{97} + q^{98} + 33 q^{99}+O(q^{100}) \) 37 * q - 37 * q^2 - 5 * q^3 + 37 * q^4 - 13 * q^5 + 5 * q^6 - 22 * q^7 - 37 * q^8 + 32 * q^9 + 13 * q^10 + 12 * q^11 - 5 * q^12 - 36 * q^13 + 22 * q^14 - 7 * q^15 + 37 * q^16 + 4 * q^17 - 32 * q^18 - 10 * q^19 - 13 * q^20 - 11 * q^21 - 12 * q^22 - q^23 + 5 * q^24 + 8 * q^25 + 36 * q^26 - 20 * q^27 - 22 * q^28 - 6 * q^29 + 7 * q^30 - 23 * q^31 - 37 * q^32 - 27 * q^33 - 4 * q^34 + 24 * q^35 + 32 * q^36 - 46 * q^37 + 10 * q^38 + 5 * q^39 + 13 * q^40 + 11 * q^41 + 11 * q^42 - 22 * q^43 + 12 * q^44 - 57 * q^45 + q^46 - 18 * q^47 - 5 * q^48 - q^49 - 8 * q^50 + 18 * q^51 - 36 * q^52 - 25 * q^53 + 20 * q^54 - 25 * q^55 + 22 * q^56 - 25 * q^57 + 6 * q^58 + 24 * q^59 - 7 * q^60 - 40 * q^61 + 23 * q^62 - 38 * q^63 + 37 * q^64 + 14 * q^65 + 27 * q^66 - 49 * q^67 + 4 * q^68 - 19 * q^69 - 24 * q^70 + 27 * q^71 - 32 * q^72 - 87 * q^73 + 46 * q^74 - 5 * q^75 - 10 * q^76 - 50 * q^77 - 5 * q^78 + 11 * q^79 - 13 * q^80 + 5 * q^81 - 11 * q^82 - 9 * q^83 - 11 * q^84 - 68 * q^85 + 22 * q^86 - 12 * q^87 - 12 * q^88 - 3 * q^89 + 57 * q^90 - 19 * q^91 - q^92 - 69 * q^93 + 18 * q^94 + 27 * q^95 + 5 * q^96 - 98 * q^97 + q^98 + 33 * q^99

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