LMFDB - Embedded newform 4010.2.a.o.1.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4010,2,Mod(1,4010)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4010, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("4010.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4010 = 2 \cdot 5 \cdot 401 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4010.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:	$32.0200112105$
Analytic rank:	$0$
Dimension:	$22$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.14
Character	$\chi$	$=$	4010.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +0.642301 q^{3} +1.00000 q^{4} -1.00000 q^{5} +0.642301 q^{6} +4.88072 q^{7} +1.00000 q^{8} -2.58745 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +0.642301 q^{3} +1.00000 q^{4} -1.00000 q^{5} +0.642301 q^{6} +4.88072 q^{7} +1.00000 q^{8} -2.58745 q^{9} -1.00000 q^{10} -4.59824 q^{11} +0.642301 q^{12} +0.824062 q^{13} +4.88072 q^{14} -0.642301 q^{15} +1.00000 q^{16} +5.12192 q^{17} -2.58745 q^{18} -2.57124 q^{19} -1.00000 q^{20} +3.13489 q^{21} -4.59824 q^{22} +3.63824 q^{23} +0.642301 q^{24} +1.00000 q^{25} +0.824062 q^{26} -3.58882 q^{27} +4.88072 q^{28} +4.06318 q^{29} -0.642301 q^{30} +8.34497 q^{31} +1.00000 q^{32} -2.95345 q^{33} +5.12192 q^{34} -4.88072 q^{35} -2.58745 q^{36} -6.23249 q^{37} -2.57124 q^{38} +0.529296 q^{39} -1.00000 q^{40} -0.0307203 q^{41} +3.13489 q^{42} +2.80087 q^{43} -4.59824 q^{44} +2.58745 q^{45} +3.63824 q^{46} +6.02005 q^{47} +0.642301 q^{48} +16.8214 q^{49} +1.00000 q^{50} +3.28981 q^{51} +0.824062 q^{52} +10.9405 q^{53} -3.58882 q^{54} +4.59824 q^{55} +4.88072 q^{56} -1.65151 q^{57} +4.06318 q^{58} -1.76115 q^{59} -0.642301 q^{60} +11.1367 q^{61} +8.34497 q^{62} -12.6286 q^{63} +1.00000 q^{64} -0.824062 q^{65} -2.95345 q^{66} -3.48614 q^{67} +5.12192 q^{68} +2.33684 q^{69} -4.88072 q^{70} -16.3737 q^{71} -2.58745 q^{72} +5.65216 q^{73} -6.23249 q^{74} +0.642301 q^{75} -2.57124 q^{76} -22.4427 q^{77} +0.529296 q^{78} +1.60419 q^{79} -1.00000 q^{80} +5.45724 q^{81} -0.0307203 q^{82} +9.48422 q^{83} +3.13489 q^{84} -5.12192 q^{85} +2.80087 q^{86} +2.60978 q^{87} -4.59824 q^{88} +9.44602 q^{89} +2.58745 q^{90} +4.02201 q^{91} +3.63824 q^{92} +5.35998 q^{93} +6.02005 q^{94} +2.57124 q^{95} +0.642301 q^{96} -12.1509 q^{97} +16.8214 q^{98} +11.8977 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 22 q + 22 q^{2} + 2 q^{3} + 22 q^{4} - 22 q^{5} + 2 q^{6} + 13 q^{7} + 22 q^{8} + 32 q^{9}+O(q^{10}) $ 22 * q + 22 * q^2 + 2 * q^3 + 22 * q^4 - 22 * q^5 + 2 * q^6 + 13 * q^7 + 22 * q^8 + 32 * q^9	\( 22 q + 22 q^{2} + 2 q^{3} + 22 q^{4} - 22 q^{5} + 2 q^{6} + 13 q^{7} + 22 q^{8} + 32 q^{9} - 22 q^{10} - 3 q^{11} + 2 q^{12} + 6 q^{13} + 13 q^{14} - 2 q^{15} + 22 q^{16} + 17 q^{17} + 32 q^{18} + 13 q^{19} - 22 q^{20} + 16 q^{21} - 3 q^{22} + 19 q^{23} + 2 q^{24} + 22 q^{25} + 6 q^{26} + 14 q^{27} + 13 q^{28} + 14 q^{29} - 2 q^{30} + 13 q^{31} + 22 q^{32} + 12 q^{33} + 17 q^{34} - 13 q^{35} + 32 q^{36} + 35 q^{37} + 13 q^{38} + 30 q^{39} - 22 q^{40} - 5 q^{41} + 16 q^{42} + 19 q^{43} - 3 q^{44} - 32 q^{45} + 19 q^{46} + 29 q^{47} + 2 q^{48} + 61 q^{49} + 22 q^{50} + q^{51} + 6 q^{52} + 29 q^{53} + 14 q^{54} + 3 q^{55} + 13 q^{56} + 33 q^{57} + 14 q^{58} - 4 q^{59} - 2 q^{60} + 20 q^{61} + 13 q^{62} + 50 q^{63} + 22 q^{64} - 6 q^{65} + 12 q^{66} + 48 q^{67} + 17 q^{68} + 19 q^{69} - 13 q^{70} + 2 q^{71} + 32 q^{72} + 16 q^{73} + 35 q^{74} + 2 q^{75} + 13 q^{76} + 53 q^{77} + 30 q^{78} + 29 q^{79} - 22 q^{80} + 54 q^{81} - 5 q^{82} + 13 q^{83} + 16 q^{84} - 17 q^{85} + 19 q^{86} + 56 q^{87} - 3 q^{88} + 20 q^{89} - 32 q^{90} + 42 q^{91} + 19 q^{92} + 50 q^{93} + 29 q^{94} - 13 q^{95} + 2 q^{96} + 36 q^{97} + 61 q^{98} - q^{99}+O(q^{100}) \) 22 * q + 22 * q^2 + 2 * q^3 + 22 * q^4 - 22 * q^5 + 2 * q^6 + 13 * q^7 + 22 * q^8 + 32 * q^9 - 22 * q^10 - 3 * q^11 + 2 * q^12 + 6 * q^13 + 13 * q^14 - 2 * q^15 + 22 * q^16 + 17 * q^17 + 32 * q^18 + 13 * q^19 - 22 * q^20 + 16 * q^21 - 3 * q^22 + 19 * q^23 + 2 * q^24 + 22 * q^25 + 6 * q^26 + 14 * q^27 + 13 * q^28 + 14 * q^29 - 2 * q^30 + 13 * q^31 + 22 * q^32 + 12 * q^33 + 17 * q^34 - 13 * q^35 + 32 * q^36 + 35 * q^37 + 13 * q^38 + 30 * q^39 - 22 * q^40 - 5 * q^41 + 16 * q^42 + 19 * q^43 - 3 * q^44 - 32 * q^45 + 19 * q^46 + 29 * q^47 + 2 * q^48 + 61 * q^49 + 22 * q^50 + q^51 + 6 * q^52 + 29 * q^53 + 14 * q^54 + 3 * q^55 + 13 * q^56 + 33 * q^57 + 14 * q^58 - 4 * q^59 - 2 * q^60 + 20 * q^61 + 13 * q^62 + 50 * q^63 + 22 * q^64 - 6 * q^65 + 12 * q^66 + 48 * q^67 + 17 * q^68 + 19 * q^69 - 13 * q^70 + 2 * q^71 + 32 * q^72 + 16 * q^73 + 35 * q^74 + 2 * q^75 + 13 * q^76 + 53 * q^77 + 30 * q^78 + 29 * q^79 - 22 * q^80 + 54 * q^81 - 5 * q^82 + 13 * q^83 + 16 * q^84 - 17 * q^85 + 19 * q^86 + 56 * q^87 - 3 * q^88 + 20 * q^89 - 32 * q^90 + 42 * q^91 + 19 * q^92 + 50 * q^93 + 29 * q^94 - 13 * q^95 + 2 * q^96 + 36 * q^97 + 61 * q^98 - 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
$3$	0.642301	0.370833	0.185416	−	0.982660i	$-0.440637\pi$
$3$	0.642301	0.370833	0.185416	+	0.982660i	$0.440637\pi$
$4$	1.00000	0.500000
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	0.642301	0.262218
$7$	4.88072	1.84474	0.922368	−	0.386311i	$-0.126251\pi$
$7$	4.88072	1.84474	0.922368	+	0.386311i	$0.126251\pi$
$8$	1.00000	0.353553
$9$	−2.58745	−0.862483
$10$	−1.00000	−0.316228
$11$	−4.59824	−1.38642	−0.693211	−	0.720735i	$-0.743805\pi$
$11$	−4.59824	−1.38642	−0.693211	+	0.720735i	$0.743805\pi$
$12$	0.642301	0.185416
$13$	0.824062	0.228554	0.114277	−	0.993449i	$-0.463545\pi$
$13$	0.824062	0.228554	0.114277	+	0.993449i	$0.463545\pi$
$14$	4.88072	1.30443
$15$	−0.642301	−0.165841
$16$	1.00000	0.250000
$17$	5.12192	1.24225	0.621124	−	0.783713i	$-0.286676\pi$
$17$	5.12192	1.24225	0.621124	+	0.783713i	$0.286676\pi$
$18$	−2.58745	−0.609868
$19$	−2.57124	−0.589884	−0.294942	−	0.955515i	$-0.595300\pi$
$19$	−2.57124	−0.589884	−0.294942	+	0.955515i	$0.595300\pi$
$20$	−1.00000	−0.223607
$21$	3.13489	0.684089
$22$	−4.59824	−0.980348
$23$	3.63824	0.758626	0.379313	−	0.925269i	$-0.376160\pi$
$23$	3.63824	0.758626	0.379313	+	0.925269i	$0.376160\pi$
$24$	0.642301	0.131109
$25$	1.00000	0.200000
$26$	0.824062	0.161612
$27$	−3.58882	−0.690669
$28$	4.88072	0.922368
$29$	4.06318	0.754513	0.377256	−	0.926109i	$-0.376868\pi$
$29$	4.06318	0.754513	0.377256	+	0.926109i	$0.376868\pi$
$30$	−0.642301	−0.117268
$31$	8.34497	1.49880	0.749400	−	0.662117i	$-0.230342\pi$
$31$	8.34497	1.49880	0.749400	+	0.662117i	$0.230342\pi$
$32$	1.00000	0.176777
$33$	−2.95345	−0.514130
$34$	5.12192	0.878402
$35$	−4.88072	−0.824991
$36$	−2.58745	−0.431242
$37$	−6.23249	−1.02461	−0.512307	−	0.858802i	$-0.671209\pi$
$37$	−6.23249	−1.02461	−0.512307	+	0.858802i	$0.671209\pi$
$38$	−2.57124	−0.417111
$39$	0.529296	0.0847551
$40$	−1.00000	−0.158114
$41$	−0.0307203	−0.00479770	−0.00239885	−	0.999997i	$-0.500764\pi$
$41$	−0.0307203	−0.00479770	−0.00239885	+	0.999997i	$0.500764\pi$
$42$	3.13489	0.483724
$43$	2.80087	0.427129	0.213564	−	0.976929i	$-0.431493\pi$
$43$	2.80087	0.427129	0.213564	+	0.976929i	$0.431493\pi$
$44$	−4.59824	−0.693211
$45$	2.58745	0.385714
$46$	3.63824	0.536429
$47$	6.02005	0.878114	0.439057	−	0.898459i	$-0.355313\pi$
$47$	6.02005	0.878114	0.439057	+	0.898459i	$0.355313\pi$
$48$	0.642301	0.0927081
$49$	16.8214	2.40305
$50$	1.00000	0.141421
$51$	3.28981	0.460666
$52$	0.824062	0.114277
$53$	10.9405	1.50280	0.751399	−	0.659849i	$-0.229380\pi$
$53$	10.9405	1.50280	0.751399	+	0.659849i	$0.229380\pi$
$54$	−3.58882	−0.488377
$55$	4.59824	0.620027
$56$	4.88072	0.652213
$57$	−1.65151	−0.218748
$58$	4.06318	0.533521
$59$	−1.76115	−0.229282	−0.114641	−	0.993407i	$-0.536572\pi$
$59$	−1.76115	−0.229282	−0.114641	+	0.993407i	$0.536572\pi$
$60$	−0.642301	−0.0829207
$61$	11.1367	1.42591	0.712957	−	0.701208i	$-0.247355\pi$
$61$	11.1367	1.42591	0.712957	+	0.701208i	$0.247355\pi$
$62$	8.34497	1.05981
$63$	−12.6286	−1.59105
$64$	1.00000	0.125000
$65$	−0.824062	−0.102212
$66$	−2.95345	−0.363545
$67$	−3.48614	−0.425900	−0.212950	−	0.977063i	$-0.568307\pi$
$67$	−3.48614	−0.425900	−0.212950	+	0.977063i	$0.568307\pi$
$68$	5.12192	0.621124
$69$	2.33684	0.281323
$70$	−4.88072	−0.583357
$71$	−16.3737	−1.94321	−0.971603	−	0.236616i	$-0.923962\pi$
$71$	−16.3737	−1.94321	−0.971603	+	0.236616i	$0.923962\pi$
$72$	−2.58745	−0.304934
$73$	5.65216	0.661535	0.330768	−	0.943712i	$-0.392692\pi$
$73$	5.65216	0.661535	0.330768	+	0.943712i	$0.392692\pi$
$74$	−6.23249	−0.724512
$75$	0.642301	0.0741665
$76$	−2.57124	−0.294942
$77$	−22.4427	−2.55758
$78$	0.529296	0.0599309
$79$	1.60419	0.180486	0.0902429	−	0.995920i	$-0.471236\pi$
$79$	1.60419	0.180486	0.0902429	+	0.995920i	$0.471236\pi$
$80$	−1.00000	−0.111803
$81$	5.45724	0.606361
$82$	−0.0307203	−0.00339249
$83$	9.48422	1.04103	0.520514	−	0.853853i	$-0.325740\pi$
$83$	9.48422	1.04103	0.520514	+	0.853853i	$0.325740\pi$
$84$	3.13489	0.342044
$85$	−5.12192	−0.555550
$86$	2.80087	0.302026
$87$	2.60978	0.279798
$88$	−4.59824	−0.490174
$89$	9.44602	1.00128	0.500638	−	0.865657i	$-0.333099\pi$
$89$	9.44602	1.00128	0.500638	+	0.865657i	$0.333099\pi$
$90$	2.58745	0.272741
$91$	4.02201	0.421621
$92$	3.63824	0.379313
$93$	5.35998	0.555804
$94$	6.02005	0.620921
$95$	2.57124	0.263804
$96$	0.642301	0.0655546
$97$	−12.1509	−1.23374	−0.616869	−	0.787066i	$-0.711599\pi$
$97$	−12.1509	−1.23374	−0.616869	+	0.787066i	$0.711599\pi$
$98$	16.8214	1.69922
$99$	11.8977	1.19577
$100$	1.00000	0.100000
$101$	−11.5701	−1.15127	−0.575634	−	0.817707i	$-0.695245\pi$
$101$	−11.5701	−1.15127	−0.575634	+	0.817707i	$0.695245\pi$
$102$	3.28981	0.325740
$103$	−3.49555	−0.344427	−0.172213	−	0.985060i	$-0.555092\pi$
$103$	−3.49555	−0.344427	−0.172213	+	0.985060i	$0.555092\pi$
$104$	0.824062	0.0808059
$105$	−3.13489	−0.305934
$106$	10.9405	1.06264
$107$	4.41395	0.426713	0.213356	−	0.976974i	$-0.431560\pi$
$107$	4.41395	0.426713	0.213356	+	0.976974i	$0.431560\pi$
$108$	−3.58882	−0.345335
$109$	9.86926	0.945304	0.472652	−	0.881249i	$-0.343297\pi$
$109$	9.86926	0.945304	0.472652	+	0.881249i	$0.343297\pi$
$110$	4.59824	0.438425
$111$	−4.00313	−0.379961
$112$	4.88072	0.461184
$113$	−6.05902	−0.569984	−0.284992	−	0.958530i	$-0.591991\pi$
$113$	−6.05902	−0.569984	−0.284992	+	0.958530i	$0.591991\pi$
$114$	−1.65151	−0.154678
$115$	−3.63824	−0.339268
$116$	4.06318	0.377256
$117$	−2.13222	−0.197124
$118$	−1.76115	−0.162127
$119$	24.9986	2.29162
$120$	−0.642301	−0.0586338
$121$	10.1438	0.922165
$122$	11.1367	1.00827
$123$	−0.0197317	−0.00177914
$124$	8.34497	0.749400
$125$	−1.00000	−0.0894427
$126$	−12.6286	−1.12505
$127$	5.01094	0.444649	0.222325	−	0.974973i	$-0.428635\pi$
$127$	5.01094	0.444649	0.222325	+	0.974973i	$0.428635\pi$
$128$	1.00000	0.0883883
$129$	1.79900	0.158393
$130$	−0.824062	−0.0722750
$131$	7.12351	0.622384	0.311192	−	0.950347i	$-0.399272\pi$
$131$	7.12351	0.622384	0.311192	+	0.950347i	$0.399272\pi$
$132$	−2.95345	−0.257065
$133$	−12.5495	−1.08818
$134$	−3.48614	−0.301157
$135$	3.58882	0.308877
$136$	5.12192	0.439201
$137$	−0.575018	−0.0491271	−0.0245635	−	0.999698i	$-0.507820\pi$
$137$	−0.575018	−0.0491271	−0.0245635	+	0.999698i	$0.507820\pi$
$138$	2.33684	0.198925
$139$	16.9018	1.43359	0.716795	−	0.697284i	$-0.245608\pi$
$139$	16.9018	1.43359	0.716795	+	0.697284i	$0.245608\pi$
$140$	−4.88072	−0.412496
$141$	3.86668	0.325633
$142$	−16.3737	−1.37405
$143$	−3.78923	−0.316872
$144$	−2.58745	−0.215621
$145$	−4.06318	−0.337428
$146$	5.65216	0.467776
$147$	10.8044	0.891131
$148$	−6.23249	−0.512307
$149$	−10.5086	−0.860902	−0.430451	−	0.902614i	$-0.641645\pi$
$149$	−10.5086	−0.860902	−0.430451	+	0.902614i	$0.641645\pi$
$150$	0.642301	0.0524436
$151$	−9.78471	−0.796269	−0.398134	−	0.917327i	$-0.630342\pi$
$151$	−9.78471	−0.796269	−0.398134	+	0.917327i	$0.630342\pi$
$152$	−2.57124	−0.208555
$153$	−13.2527	−1.07142
$154$	−22.4427	−1.80848
$155$	−8.34497	−0.670284
$156$	0.529296	0.0423776
$157$	−20.1981	−1.61198	−0.805992	−	0.591927i	$-0.798367\pi$
$157$	−20.1981	−1.61198	−0.805992	+	0.591927i	$0.798367\pi$
$158$	1.60419	0.127623
$159$	7.02711	0.557286
$160$	−1.00000	−0.0790569
$161$	17.7572	1.39946
$162$	5.45724	0.428762
$163$	−4.81293	−0.376978	−0.188489	−	0.982075i	$-0.560359\pi$
$163$	−4.81293	−0.376978	−0.188489	+	0.982075i	$0.560359\pi$
$164$	−0.0307203	−0.00239885
$165$	2.95345	0.229926
$166$	9.48422	0.736118
$167$	−22.6923	−1.75599	−0.877993	−	0.478673i	$-0.841118\pi$
$167$	−22.6923	−1.75599	−0.877993	+	0.478673i	$0.841118\pi$
$168$	3.13489	0.241862
$169$	−12.3209	−0.947763
$170$	−5.12192	−0.392833
$171$	6.65296	0.508765
$172$	2.80087	0.213564
$173$	−3.15548	−0.239907	−0.119953	−	0.992780i	$-0.538275\pi$
$173$	−3.15548	−0.239907	−0.119953	+	0.992780i	$0.538275\pi$
$174$	2.60978	0.197847
$175$	4.88072	0.368947
$176$	−4.59824	−0.346605
$177$	−1.13119	−0.0850252
$178$	9.44602	0.708009
$179$	−6.72026	−0.502296	−0.251148	−	0.967949i	$-0.580808\pi$
$179$	−6.72026	−0.502296	−0.251148	+	0.967949i	$0.580808\pi$
$180$	2.58745	0.192857
$181$	3.74246	0.278175	0.139088	−	0.990280i	$-0.455583\pi$
$181$	3.74246	0.278175	0.139088	+	0.990280i	$0.455583\pi$
$182$	4.02201	0.298131
$183$	7.15314	0.528775
$184$	3.63824	0.268215
$185$	6.23249	0.458222
$186$	5.35998	0.393013
$187$	−23.5518	−1.72228
$188$	6.02005	0.439057
$189$	−17.5160	−1.27410
$190$	2.57124	0.186538
$191$	−13.6970	−0.991083	−0.495541	−	0.868584i	$-0.665030\pi$
$191$	−13.6970	−0.991083	−0.495541	+	0.868584i	$0.665030\pi$
$192$	0.642301	0.0463541
$193$	−1.42855	−0.102830	−0.0514148	−	0.998677i	$-0.516373\pi$
$193$	−1.42855	−0.102830	−0.0514148	+	0.998677i	$0.516373\pi$
$194$	−12.1509	−0.872384
$195$	−0.529296	−0.0379036
$196$	16.8214	1.20153
$197$	−12.0054	−0.855346	−0.427673	−	0.903934i	$-0.640666\pi$
$197$	−12.0054	−0.855346	−0.427673	+	0.903934i	$0.640666\pi$
$198$	11.8977	0.845534
$199$	8.91197	0.631753	0.315876	−	0.948800i	$-0.397701\pi$
$199$	8.91197	0.631753	0.315876	+	0.948800i	$0.397701\pi$
$200$	1.00000	0.0707107
$201$	−2.23915	−0.157937
$202$	−11.5701	−0.814070
$203$	19.8312	1.39188
$204$	3.28981	0.230333
$205$	0.0307203	0.00214560
$206$	−3.49555	−0.243546
$207$	−9.41376	−0.654302
$208$	0.824062	0.0571384
$209$	11.8232	0.817828
$210$	−3.13489	−0.216328
$211$	−2.43052	−0.167324	−0.0836618	−	0.996494i	$-0.526662\pi$
$211$	−2.43052	−0.167324	−0.0836618	+	0.996494i	$0.526662\pi$
$212$	10.9405	0.751399
$213$	−10.5169	−0.720604
$214$	4.41395	0.301732
$215$	−2.80087	−0.191018
$216$	−3.58882	−0.244189
$217$	40.7294	2.76489
$218$	9.86926	0.668431
$219$	3.63039	0.245319
$220$	4.59824	0.310013
$221$	4.22078	0.283920
$222$	−4.00313	−0.268673
$223$	19.7097	1.31986	0.659929	−	0.751328i	$-0.270586\pi$
$223$	19.7097	1.31986	0.659929	+	0.751328i	$0.270586\pi$
$224$	4.88072	0.326106
$225$	−2.58745	−0.172497
$226$	−6.05902	−0.403040
$227$	−13.4199	−0.890711	−0.445355	−	0.895354i	$-0.646923\pi$
$227$	−13.4199	−0.890711	−0.445355	+	0.895354i	$0.646923\pi$
$228$	−1.65151	−0.109374
$229$	16.0770	1.06240	0.531199	−	0.847247i	$-0.321742\pi$
$229$	16.0770	1.06240	0.531199	+	0.847247i	$0.321742\pi$
$230$	−3.63824	−0.239898
$231$	−14.4150	−0.948435
$232$	4.06318	0.266761
$233$	2.54947	0.167021	0.0835107	−	0.996507i	$-0.473387\pi$
$233$	2.54947	0.167021	0.0835107	+	0.996507i	$0.473387\pi$
$234$	−2.13222	−0.139387
$235$	−6.02005	−0.392705
$236$	−1.76115	−0.114641
$237$	1.03037	0.0669300
$238$	24.9986	1.62042
$239$	28.8799	1.86809	0.934044	−	0.357159i	$-0.116254\pi$
$239$	28.8799	1.86809	0.934044	+	0.357159i	$0.116254\pi$
$240$	−0.642301	−0.0414603
$241$	30.6512	1.97442	0.987210	−	0.159428i	$-0.0509649\pi$
$241$	30.6512	1.97442	0.987210	+	0.159428i	$0.0509649\pi$
$242$	10.1438	0.652069
$243$	14.2717	0.915528
$244$	11.1367	0.712957
$245$	−16.8214	−1.07468
$246$	−0.0197317	−0.00125804
$247$	−2.11886	−0.134820
$248$	8.34497	0.529906
$249$	6.09172	0.386047
$250$	−1.00000	−0.0632456
$251$	−17.0778	−1.07794	−0.538971	−	0.842324i	$-0.681187\pi$
$251$	−17.0778	−1.07794	−0.538971	+	0.842324i	$0.681187\pi$
$252$	−12.6286	−0.795527
$253$	−16.7295	−1.05178
$254$	5.01094	0.314415
$255$	−3.28981	−0.206016
$256$	1.00000	0.0625000
$257$	−6.95959	−0.434127	−0.217064	−	0.976157i	$-0.569648\pi$
$257$	−6.95959	−0.434127	−0.217064	+	0.976157i	$0.569648\pi$
$258$	1.79900	0.112001
$259$	−30.4190	−1.89014
$260$	−0.824062	−0.0511061
$261$	−10.5133	−0.650755
$262$	7.12351	0.440092
$263$	−9.53649	−0.588045	−0.294023	−	0.955798i	$-0.594994\pi$
$263$	−9.53649	−0.588045	−0.294023	+	0.955798i	$0.594994\pi$
$264$	−2.95345	−0.181773
$265$	−10.9405	−0.672071
$266$	−12.5495	−0.769460
$267$	6.06719	0.371306
$268$	−3.48614	−0.212950
$269$	−13.9069	−0.847920	−0.423960	−	0.905681i	$-0.639360\pi$
$269$	−13.9069	−0.847920	−0.423960	+	0.905681i	$0.639360\pi$
$270$	3.58882	0.218409
$271$	4.37337	0.265663	0.132832	−	0.991139i	$-0.457593\pi$
$271$	4.37337	0.265663	0.132832	+	0.991139i	$0.457593\pi$
$272$	5.12192	0.310562
$273$	2.58334	0.156351
$274$	−0.575018	−0.0347381
$275$	−4.59824	−0.277284
$276$	2.33684	0.140662
$277$	−18.4085	−1.10606	−0.553029	−	0.833162i	$-0.686528\pi$
$277$	−18.4085	−1.10606	−0.553029	+	0.833162i	$0.686528\pi$
$278$	16.9018	1.01370
$279$	−21.5922	−1.29269
$280$	−4.88072	−0.291679
$281$	−5.08630	−0.303423	−0.151711	−	0.988425i	$-0.548478\pi$
$281$	−5.08630	−0.303423	−0.151711	+	0.988425i	$0.548478\pi$
$282$	3.86668	0.230258
$283$	−14.4674	−0.859995	−0.429998	−	0.902830i	$-0.641486\pi$
$283$	−14.4674	−0.859995	−0.429998	+	0.902830i	$0.641486\pi$
$284$	−16.3737	−0.971603
$285$	1.65151	0.0978271
$286$	−3.78923	−0.224062
$287$	−0.149937	−0.00885049
$288$	−2.58745	−0.152467
$289$	9.23404	0.543179
$290$	−4.06318	−0.238598
$291$	−7.80454	−0.457510
$292$	5.65216	0.330768
$293$	−22.7011	−1.32621	−0.663105	−	0.748526i	$-0.730762\pi$
$293$	−22.7011	−1.32621	−0.663105	+	0.748526i	$0.730762\pi$
$294$	10.8044	0.630125
$295$	1.76115	0.102538
$296$	−6.23249	−0.362256
$297$	16.5023	0.957559
$298$	−10.5086	−0.608749
$299$	2.99813	0.173387
$300$	0.642301	0.0370833
$301$	13.6703	0.787940
$302$	−9.78471	−0.563047
$303$	−7.43149	−0.426928
$304$	−2.57124	−0.147471
$305$	−11.1367	−0.637688
$306$	−13.2527	−0.757607
$307$	33.3340	1.90247	0.951237	−	0.308461i	$-0.0998141\pi$
$307$	33.3340	1.90247	0.951237	+	0.308461i	$0.0998141\pi$
$308$	−22.4427	−1.27879
$309$	−2.24519	−0.127725
$310$	−8.34497	−0.473962
$311$	28.7103	1.62801	0.814006	−	0.580857i	$-0.197282\pi$
$311$	28.7103	1.62801	0.814006	+	0.580857i	$0.197282\pi$
$312$	0.529296	0.0299655
$313$	23.1793	1.31017	0.655086	−	0.755555i	$-0.272633\pi$
$313$	23.1793	1.31017	0.655086	+	0.755555i	$0.272633\pi$
$314$	−20.1981	−1.13984
$315$	12.6286	0.711541
$316$	1.60419	0.0902429
$317$	−0.0363307	−0.00204053	−0.00102027	−	0.999999i	$-0.500325\pi$
$317$	−0.0363307	−0.00204053	−0.00102027	+	0.999999i	$0.500325\pi$
$318$	7.02711	0.394061
$319$	−18.6835	−1.04607
$320$	−1.00000	−0.0559017
$321$	2.83508	0.158239
$322$	17.7572	0.989571
$323$	−13.1697	−0.732782
$324$	5.45724	0.303180
$325$	0.824062	0.0457107
$326$	−4.81293	−0.266564
$327$	6.33903	0.350549
$328$	−0.0307203	−0.00169624
$329$	29.3821	1.61989
$330$	2.95345	0.162582
$331$	33.9017	1.86341	0.931703	−	0.363222i	$-0.118323\pi$
$331$	33.9017	1.86341	0.931703	+	0.363222i	$0.118323\pi$
$332$	9.48422	0.520514
$333$	16.1262	0.883713
$334$	−22.6923	−1.24167
$335$	3.48614	0.190468
$336$	3.13489	0.171022
$337$	−2.95419	−0.160925	−0.0804626	−	0.996758i	$-0.525640\pi$
$337$	−2.95419	−0.160925	−0.0804626	+	0.996758i	$0.525640\pi$
$338$	−12.3209	−0.670170
$339$	−3.89171	−0.211369
$340$	−5.12192	−0.277775
$341$	−38.3722	−2.07797
$342$	6.65296	0.359751
$343$	47.9354	2.58827
$344$	2.80087	0.151013
$345$	−2.33684	−0.125811
$346$	−3.15548	−0.169640
$347$	−25.2367	−1.35478	−0.677388	−	0.735626i	$-0.736888\pi$
$347$	−25.2367	−1.35478	−0.677388	+	0.735626i	$0.736888\pi$
$348$	2.60978	0.139899
$349$	−4.81064	−0.257508	−0.128754	−	0.991677i	$-0.541098\pi$
$349$	−4.81064	−0.257508	−0.128754	+	0.991677i	$0.541098\pi$
$350$	4.88072	0.260885
$351$	−2.95741	−0.157855
$352$	−4.59824	−0.245087
$353$	7.73257	0.411563	0.205782	−	0.978598i	$-0.434026\pi$
$353$	7.73257	0.411563	0.205782	+	0.978598i	$0.434026\pi$
$354$	−1.13119	−0.0601219
$355$	16.3737	0.869028
$356$	9.44602	0.500638
$357$	16.0566	0.849807
$358$	−6.72026	−0.355177
$359$	−16.4157	−0.866386	−0.433193	−	0.901301i	$-0.642613\pi$
$359$	−16.4157	−0.866386	−0.433193	+	0.901301i	$0.642613\pi$
$360$	2.58745	0.136371
$361$	−12.3887	−0.652037
$362$	3.74246	0.196699
$363$	6.51538	0.341969
$364$	4.02201	0.210811
$365$	−5.65216	−0.295847
$366$	7.15314	0.373901
$367$	14.7669	0.770826	0.385413	−	0.922744i	$-0.374059\pi$
$367$	14.7669	0.770826	0.385413	+	0.922744i	$0.374059\pi$
$368$	3.63824	0.189656
$369$	0.0794871	0.00413794
$370$	6.23249	0.324012
$371$	53.3976	2.77227
$372$	5.35998	0.277902
$373$	16.4860	0.853611	0.426805	−	0.904344i	$-0.359639\pi$
$373$	16.4860	0.853611	0.426805	+	0.904344i	$0.359639\pi$
$374$	−23.5518	−1.21784
$375$	−0.642301	−0.0331683
$376$	6.02005	0.310460
$377$	3.34831	0.172447
$378$	−17.5160	−0.900927
$379$	−21.6323	−1.11117	−0.555587	−	0.831458i	$-0.687507\pi$
$379$	−21.6323	−1.11117	−0.555587	+	0.831458i	$0.687507\pi$
$380$	2.57124	0.131902
$381$	3.21853	0.164890
$382$	−13.6970	−0.700801
$383$	6.07147	0.310237	0.155119	−	0.987896i	$-0.450424\pi$
$383$	6.07147	0.310237	0.155119	+	0.987896i	$0.450424\pi$
$384$	0.642301	0.0327773
$385$	22.4427	1.14379
$386$	−1.42855	−0.0727115
$387$	−7.24711	−0.368391
$388$	−12.1509	−0.616869
$389$	−27.7560	−1.40728	−0.703642	−	0.710554i	$-0.748444\pi$
$389$	−27.7560	−1.40728	−0.703642	+	0.710554i	$0.748444\pi$
$390$	−0.529296	−0.0268019
$391$	18.6348	0.942401
$392$	16.8214	0.849608
$393$	4.57544	0.230800
$394$	−12.0054	−0.604821
$395$	−1.60419	−0.0807157
$396$	11.8977	0.597883
$397$	2.26572	0.113713	0.0568567	−	0.998382i	$-0.481892\pi$
$397$	2.26572	0.113713	0.0568567	+	0.998382i	$0.481892\pi$
$398$	8.91197	0.446717
$399$	−8.06056	−0.403533
$400$	1.00000	0.0500000
$401$	−1.00000	−0.0499376
$401$	−1.00000	−0.0499376
$402$	−2.23915	−0.111679
$403$	6.87677	0.342556
$404$	−11.5701	−0.575634
$405$	−5.45724	−0.271173
$406$	19.8312	0.984206
$407$	28.6585	1.42055
$408$	3.28981	0.162870
$409$	10.0614	0.497507	0.248753	−	0.968567i	$-0.419979\pi$
$409$	10.0614	0.497507	0.248753	+	0.968567i	$0.419979\pi$
$410$	0.0307203	0.00151717
$411$	−0.369334	−0.0182179
$412$	−3.49555	−0.172213
$413$	−8.59566	−0.422965
$414$	−9.41376	−0.462661
$415$	−9.48422	−0.465562
$416$	0.824062	0.0404030
$417$	10.8560	0.531622
$418$	11.8232	0.578292
$419$	−3.11838	−0.152343	−0.0761715	−	0.997095i	$-0.524270\pi$
$419$	−3.11838	−0.152343	−0.0761715	+	0.997095i	$0.524270\pi$
$420$	−3.13489	−0.152967
$421$	−0.814489	−0.0396958	−0.0198479	−	0.999803i	$-0.506318\pi$
$421$	−0.814489	−0.0396958	−0.0198479	+	0.999803i	$0.506318\pi$
$422$	−2.43052	−0.118316
$423$	−15.5766	−0.757359
$424$	10.9405	0.531319
$425$	5.12192	0.248449
$426$	−10.5169	−0.509544
$427$	54.3553	2.63044
$428$	4.41395	0.213356
$429$	−2.43383	−0.117506
$430$	−2.80087	−0.135070
$431$	−12.4162	−0.598066	−0.299033	−	0.954243i	$-0.596664\pi$
$431$	−12.4162	−0.598066	−0.299033	+	0.954243i	$0.596664\pi$
$432$	−3.58882	−0.172667
$433$	−20.6696	−0.993316	−0.496658	−	0.867946i	$-0.665440\pi$
$433$	−20.6696	−0.993316	−0.496658	+	0.867946i	$0.665440\pi$
$434$	40.7294	1.95507
$435$	−2.60978	−0.125129
$436$	9.86926	0.472652
$437$	−9.35480	−0.447501
$438$	3.63039	0.173467
$439$	3.82029	0.182333	0.0911664	−	0.995836i	$-0.470940\pi$
$439$	3.82029	0.182333	0.0911664	+	0.995836i	$0.470940\pi$
$440$	4.59824	0.219213
$441$	−43.5245	−2.07259
$442$	4.22078	0.200762
$443$	23.2282	1.10361	0.551803	−	0.833975i	$-0.313940\pi$
$443$	23.2282	1.10361	0.551803	+	0.833975i	$0.313940\pi$
$444$	−4.00313	−0.189980
$445$	−9.44602	−0.447784
$446$	19.7097	0.933280
$447$	−6.74971	−0.319250
$448$	4.88072	0.230592
$449$	15.5519	0.733937	0.366969	−	0.930233i	$-0.380396\pi$
$449$	15.5519	0.733937	0.366969	+	0.930233i	$0.380396\pi$
$450$	−2.58745	−0.121974
$451$	0.141259	0.00665164
$452$	−6.05902	−0.284992
$453$	−6.28473	−0.295282
$454$	−13.4199	−0.629828
$455$	−4.02201	−0.188555
$456$	−1.65151	−0.0773391
$457$	28.5842	1.33711	0.668556	−	0.743661i	$-0.266912\pi$
$457$	28.5842	1.33711	0.668556	+	0.743661i	$0.266912\pi$
$458$	16.0770	0.751229
$459$	−18.3817	−0.857982
$460$	−3.63824	−0.169634
$461$	−37.0553	−1.72584	−0.862919	−	0.505342i	$-0.831366\pi$
$461$	−37.0553	−1.72584	−0.862919	+	0.505342i	$0.831366\pi$
$462$	−14.4150	−0.670645
$463$	−14.2524	−0.662365	−0.331182	−	0.943567i	$-0.607448\pi$
$463$	−14.2524	−0.662365	−0.331182	+	0.943567i	$0.607448\pi$
$464$	4.06318	0.188628
$465$	−5.35998	−0.248563
$466$	2.54947	0.118102
$467$	−13.5574	−0.627362	−0.313681	−	0.949528i	$-0.601562\pi$
$467$	−13.5574	−0.627362	−0.313681	+	0.949528i	$0.601562\pi$
$468$	−2.13222	−0.0985618
$469$	−17.0149	−0.785673
$470$	−6.02005	−0.277684
$471$	−12.9732	−0.597776
$472$	−1.76115	−0.0810634
$473$	−12.8791	−0.592181
$474$	1.03037	0.0473267
$475$	−2.57124	−0.117977
$476$	24.9986	1.14581
$477$	−28.3081	−1.29614
$478$	28.8799	1.32094
$479$	−0.901505	−0.0411908	−0.0205954	−	0.999788i	$-0.506556\pi$
$479$	−0.901505	−0.0411908	−0.0205954	+	0.999788i	$0.506556\pi$
$480$	−0.642301	−0.0293169
$481$	−5.13596	−0.234179
$482$	30.6512	1.39613
$483$	11.4055	0.518967
$484$	10.1438	0.461083
$485$	12.1509	0.551744
$486$	14.2717	0.647376
$487$	−1.04588	−0.0473933	−0.0236966	−	0.999719i	$-0.507544\pi$
$487$	−1.04588	−0.0473933	−0.0236966	+	0.999719i	$0.507544\pi$
$488$	11.1367	0.504137
$489$	−3.09135	−0.139796
$490$	−16.8214	−0.759912
$491$	−20.7061	−0.934453	−0.467226	−	0.884138i	$-0.654747\pi$
$491$	−20.7061	−0.934453	−0.467226	+	0.884138i	$0.654747\pi$
$492$	−0.0197317	−0.000889572 0
$493$	20.8113	0.937292
$494$	−2.11886	−0.0953322
$495$	−11.8977	−0.534763
$496$	8.34497	0.374700
$497$	−79.9156	−3.58470
$498$	6.09172	0.272977
$499$	−18.0198	−0.806676	−0.403338	−	0.915051i	$-0.632150\pi$
$499$	−18.0198	−0.806676	−0.403338	+	0.915051i	$0.632150\pi$
$500$	−1.00000	−0.0447214
$501$	−14.5753	−0.651177
$502$	−17.0778	−0.762220
$503$	−37.5992	−1.67647	−0.838233	−	0.545312i	$-0.816411\pi$
$503$	−37.5992	−1.67647	−0.838233	+	0.545312i	$0.816411\pi$
$504$	−12.6286	−0.562523
$505$	11.5701	0.514863
$506$	−16.7295	−0.743717
$507$	−7.91374	−0.351461
$508$	5.01094	0.222325
$509$	−3.21971	−0.142711	−0.0713556	−	0.997451i	$-0.522733\pi$
$509$	−3.21971	−0.142711	−0.0713556	+	0.997451i	$0.522733\pi$
$510$	−3.28981	−0.145675
$511$	27.5866	1.22036
$512$	1.00000	0.0441942
$513$	9.22774	0.407415
$514$	−6.95959	−0.306974
$515$	3.49555	0.154032
$516$	1.79900	0.0791966
$517$	−27.6816	−1.21744
$518$	−30.4190	−1.33653
$519$	−2.02677	−0.0889653
$520$	−0.824062	−0.0361375
$521$	−41.0239	−1.79729	−0.898646	−	0.438675i	$-0.855448\pi$
$521$	−41.0239	−1.79729	−0.898646	+	0.438675i	$0.855448\pi$
$522$	−10.5133	−0.460153
$523$	14.1609	0.619212	0.309606	−	0.950865i	$-0.399803\pi$
$523$	14.1609	0.619212	0.309606	+	0.950865i	$0.399803\pi$
$524$	7.12351	0.311192
$525$	3.13489	0.136818
$526$	−9.53649	−0.415811
$527$	42.7422	1.86188
$528$	−2.95345	−0.128533
$529$	−9.76321	−0.424487
$530$	−10.9405	−0.475226
$531$	4.55688	0.197752
$532$	−12.5495	−0.544090
$533$	−0.0253154	−0.00109653
$534$	6.06719	0.262553
$535$	−4.41395	−0.190832
$536$	−3.48614	−0.150578
$537$	−4.31643	−0.186268
$538$	−13.9069	−0.599570
$539$	−77.3488	−3.33165
$540$	3.58882	0.154438
$541$	21.1431	0.909014	0.454507	−	0.890743i	$-0.349815\pi$
$541$	21.1431	0.909014	0.454507	+	0.890743i	$0.349815\pi$
$542$	4.37337	0.187852
$543$	2.40379	0.103156
$544$	5.12192	0.219600
$545$	−9.86926	−0.422753
$546$	2.58334	0.110557
$547$	−13.5812	−0.580692	−0.290346	−	0.956922i	$-0.593770\pi$
$547$	−13.5812	−0.580692	−0.290346	+	0.956922i	$0.593770\pi$
$548$	−0.575018	−0.0245635
$549$	−28.8158	−1.22983
$550$	−4.59824	−0.196070
$551$	−10.4474	−0.445075
$552$	2.33684	0.0994627
$553$	7.82961	0.332949
$554$	−18.4085	−0.782102
$555$	4.00313	0.169924
$556$	16.9018	0.716795
$557$	−26.2627	−1.11278	−0.556392	−	0.830920i	$-0.687815\pi$
$557$	−26.2627	−1.11278	−0.556392	+	0.830920i	$0.687815\pi$
$558$	−21.5922	−0.914070
$559$	2.30809	0.0976218
$560$	−4.88072	−0.206248
$561$	−15.1273	−0.638677
$562$	−5.08630	−0.214552
$563$	17.3443	0.730974	0.365487	−	0.930816i	$-0.380902\pi$
$563$	17.3443	0.730974	0.365487	+	0.930816i	$0.380902\pi$
$564$	3.86668	0.162817
$565$	6.05902	0.254905
$566$	−14.4674	−0.608109
$567$	26.6353	1.11858
$568$	−16.3737	−0.687027
$569$	−15.4298	−0.646852	−0.323426	−	0.946253i	$-0.604835\pi$
$569$	−15.4298	−0.646852	−0.323426	+	0.946253i	$0.604835\pi$
$570$	1.65151	0.0691742
$571$	−4.50308	−0.188448	−0.0942240	−	0.995551i	$-0.530037\pi$
$571$	−4.50308	−0.188448	−0.0942240	+	0.995551i	$0.530037\pi$
$572$	−3.78923	−0.158436
$573$	−8.79762	−0.367526
$574$	−0.149937	−0.00625824
$575$	3.63824	0.151725
$576$	−2.58745	−0.107810
$577$	5.78479	0.240824	0.120412	−	0.992724i	$-0.461578\pi$
$577$	5.78479	0.240824	0.120412	+	0.992724i	$0.461578\pi$
$578$	9.23404	0.384085
$579$	−0.917562	−0.0381326
$580$	−4.06318	−0.168714
$581$	46.2898	1.92042
$582$	−7.80454	−0.323509
$583$	−50.3072	−2.08351
$584$	5.65216	0.233888
$585$	2.13222	0.0881564
$586$	−22.7011	−0.937772
$587$	−19.3116	−0.797075	−0.398537	−	0.917152i	$-0.630482\pi$
$587$	−19.3116	−0.797075	−0.398537	+	0.917152i	$0.630482\pi$
$588$	10.8044	0.445565
$589$	−21.4570	−0.884118
$590$	1.76115	0.0725053
$591$	−7.71105	−0.317190
$592$	−6.23249	−0.256154
$593$	−9.35045	−0.383977	−0.191988	−	0.981397i	$-0.561494\pi$
$593$	−9.35045	−0.383977	−0.191988	+	0.981397i	$0.561494\pi$
$594$	16.5023	0.677097
$595$	−24.9986	−1.02484
$596$	−10.5086	−0.430451
$597$	5.72417	0.234275
$598$	2.99813	0.122603
$599$	−41.1026	−1.67941	−0.839703	−	0.543046i	$-0.817271\pi$
$599$	−41.1026	−1.67941	−0.839703	+	0.543046i	$0.817271\pi$
$600$	0.642301	0.0262218
$601$	−3.14460	−0.128271	−0.0641354	−	0.997941i	$-0.520429\pi$
$601$	−3.14460	−0.128271	−0.0641354	+	0.997941i	$0.520429\pi$
$602$	13.6703	0.557158
$603$	9.02021	0.367331
$604$	−9.78471	−0.398134
$605$	−10.1438	−0.412405
$606$	−7.43149	−0.301884
$607$	−45.3589	−1.84106	−0.920531	−	0.390669i	$-0.872244\pi$
$607$	−45.3589	−1.84106	−0.920531	+	0.390669i	$0.872244\pi$
$608$	−2.57124	−0.104278
$609$	12.7376	0.516154
$610$	−11.1367	−0.450914
$611$	4.96089	0.200696
$612$	−13.2527	−0.535709
$613$	44.1464	1.78306	0.891529	−	0.452964i	$-0.149633\pi$
$613$	44.1464	1.78306	0.891529	+	0.452964i	$0.149633\pi$
$614$	33.3340	1.34525
$615$	0.0197317	0.000795657 0
$616$	−22.4427	−0.904242
$617$	38.0582	1.53216	0.766082	−	0.642743i	$-0.222204\pi$
$617$	38.0582	1.53216	0.766082	+	0.642743i	$0.222204\pi$
$618$	−2.24519	−0.0903149
$619$	−4.40913	−0.177218	−0.0886089	−	0.996066i	$-0.528242\pi$
$619$	−4.40913	−0.177218	−0.0886089	+	0.996066i	$0.528242\pi$
$620$	−8.34497	−0.335142
$621$	−13.0570	−0.523959
$622$	28.7103	1.15118
$623$	46.1033	1.84709
$624$	0.529296	0.0211888
$625$	1.00000	0.0400000
$626$	23.1793	0.926431
$627$	7.59405	0.303277
$628$	−20.1981	−0.805992
$629$	−31.9223	−1.27283
$630$	12.6286	0.503136
$631$	37.5021	1.49293	0.746467	−	0.665423i	$-0.231749\pi$
$631$	37.5021	1.49293	0.746467	+	0.665423i	$0.231749\pi$
$632$	1.60419	0.0638114
$633$	−1.56112	−0.0620490
$634$	−0.0363307	−0.00144288
$635$	−5.01094	−0.198853
$636$	7.02711	0.278643
$637$	13.8619	0.549227
$638$	−18.6835	−0.739685
$639$	42.3662	1.67598
$640$	−1.00000	−0.0395285
$641$	−21.3148	−0.841882	−0.420941	−	0.907088i	$-0.638300\pi$
$641$	−21.3148	−0.841882	−0.420941	+	0.907088i	$0.638300\pi$
$642$	2.83508	0.111892
$643$	−27.4416	−1.08219	−0.541096	−	0.840961i	$-0.681991\pi$
$643$	−27.4416	−1.08219	−0.541096	+	0.840961i	$0.681991\pi$
$644$	17.7572	0.699732
$645$	−1.79900	−0.0708356
$646$	−13.1697	−0.518155
$647$	−10.1988	−0.400958	−0.200479	−	0.979698i	$-0.564250\pi$
$647$	−10.1988	−0.400958	−0.200479	+	0.979698i	$0.564250\pi$
$648$	5.45724	0.214381
$649$	8.09818	0.317881
$650$	0.824062	0.0323224
$651$	26.1605	1.02531
$652$	−4.81293	−0.188489
$653$	−23.6991	−0.927419	−0.463709	−	0.885987i	$-0.653482\pi$
$653$	−23.6991	−0.927419	−0.463709	+	0.885987i	$0.653482\pi$
$654$	6.33903	0.247876
$655$	−7.12351	−0.278339
$656$	−0.0307203	−0.00119942
$657$	−14.6247	−0.570563
$658$	29.3821	1.14544
$659$	42.0606	1.63845	0.819224	−	0.573473i	$-0.194404\pi$
$659$	42.0606	1.63845	0.819224	+	0.573473i	$0.194404\pi$
$660$	2.95345	0.114963
$661$	−6.33865	−0.246545	−0.123272	−	0.992373i	$-0.539339\pi$
$661$	−6.33865	−0.246545	−0.123272	+	0.992373i	$0.539339\pi$
$662$	33.9017	1.31763
$663$	2.71101	0.105287
$664$	9.48422	0.368059
$665$	12.5495	0.486649
$666$	16.1262	0.624879
$667$	14.7828	0.572393
$668$	−22.6923	−0.877993
$669$	12.6595	0.489446
$670$	3.48614	0.134681
$671$	−51.2094	−1.97692
$672$	3.13489	0.120931
$673$	46.9203	1.80864	0.904322	−	0.426851i	$-0.140377\pi$
$673$	46.9203	1.80864	0.904322	+	0.426851i	$0.140377\pi$
$674$	−2.95419	−0.113791
$675$	−3.58882	−0.138134
$676$	−12.3209	−0.473882
$677$	−29.4060	−1.13017	−0.565083	−	0.825034i	$-0.691156\pi$
$677$	−29.4060	−1.13017	−0.565083	+	0.825034i	$0.691156\pi$
$678$	−3.89171	−0.149460
$679$	−59.3051	−2.27592
$680$	−5.12192	−0.196417
$681$	−8.61962	−0.330304
$682$	−38.3722	−1.46935
$683$	−29.4360	−1.12634	−0.563170	−	0.826341i	$-0.690418\pi$
$683$	−29.4360	−1.12634	−0.563170	+	0.826341i	$0.690418\pi$
$684$	6.65296	0.254382
$685$	0.575018	0.0219703
$686$	47.9354	1.83018
$687$	10.3263	0.393972
$688$	2.80087	0.106782
$689$	9.01567	0.343470
$690$	−2.33684	−0.0889622
$691$	−51.8037	−1.97071	−0.985353	−	0.170527i	$-0.945453\pi$
$691$	−51.8037	−1.97071	−0.985353	+	0.170527i	$0.945453\pi$
$692$	−3.15548	−0.119953
$693$	58.0694	2.20587
$694$	−25.2367	−0.957971
$695$	−16.9018	−0.641121
$696$	2.60978	0.0989235
$697$	−0.157347	−0.00595993
$698$	−4.81064	−0.182085
$699$	1.63753	0.0619369
$700$	4.88072	0.184474
$701$	−10.0208	−0.378481	−0.189240	−	0.981931i	$-0.560603\pi$
$701$	−10.0208	−0.378481	−0.189240	+	0.981931i	$0.560603\pi$
$702$	−2.95741	−0.111620
$703$	16.0252	0.604404
$704$	−4.59824	−0.173303
$705$	−3.86668	−0.145628
$706$	7.73257	0.291019
$707$	−56.4704	−2.12379
$708$	−1.13119	−0.0425126
$709$	−36.9426	−1.38741	−0.693705	−	0.720259i	$-0.744023\pi$
$709$	−36.9426	−1.38741	−0.693705	+	0.720259i	$0.744023\pi$
$710$	16.3737	0.614496
$711$	−4.15077	−0.155666
$712$	9.44602	0.354005
$713$	30.3610	1.13703
$714$	16.0566	0.600904
$715$	3.78923	0.141709
$716$	−6.72026	−0.251148
$717$	18.5496	0.692748
$718$	−16.4157	−0.612627
$719$	21.8218	0.813816	0.406908	−	0.913469i	$-0.366607\pi$
$719$	21.8218	0.813816	0.406908	+	0.913469i	$0.366607\pi$
$720$	2.58745	0.0964286
$721$	−17.0608	−0.635376
$722$	−12.3887	−0.461060
$723$	19.6873	0.732179
$724$	3.74246	0.139088
$725$	4.06318	0.150903
$726$	6.51538	0.241809
$727$	31.6287	1.17304	0.586521	−	0.809934i	$-0.300497\pi$
$727$	31.6287	1.17304	0.586521	+	0.809934i	$0.300497\pi$
$728$	4.02201	0.149066
$729$	−7.20503	−0.266853
$730$	−5.65216	−0.209196
$731$	14.3458	0.530600
$732$	7.15314	0.264388
$733$	18.2414	0.673763	0.336882	−	0.941547i	$-0.390628\pi$
$733$	18.2414	0.673763	0.336882	+	0.941547i	$0.390628\pi$
$734$	14.7669	0.545056
$735$	−10.8044	−0.398526
$736$	3.63824	0.134107
$737$	16.0301	0.590477
$738$	0.0794871	0.00292596
$739$	−44.7927	−1.64773	−0.823863	−	0.566789i	$-0.808186\pi$
$739$	−44.7927	−1.64773	−0.823863	+	0.566789i	$0.808186\pi$
$740$	6.23249	0.229111
$741$	−1.36095	−0.0499957
$742$	53.3976	1.96029
$743$	−33.6056	−1.23287	−0.616435	−	0.787406i	$-0.711424\pi$
$743$	−33.6056	−1.23287	−0.616435	+	0.787406i	$0.711424\pi$
$744$	5.35998	0.196506
$745$	10.5086	0.385007
$746$	16.4860	0.603594
$747$	−24.5399	−0.897869
$748$	−23.5518	−0.861139
$749$	21.5432	0.787173
$750$	−0.642301	−0.0234535
$751$	−18.8406	−0.687504	−0.343752	−	0.939060i	$-0.611698\pi$
$751$	−18.8406	−0.687504	−0.343752	+	0.939060i	$0.611698\pi$
$752$	6.02005	0.219529
$753$	−10.9691	−0.399736
$754$	3.34831	0.121938
$755$	9.78471	0.356102
$756$	−17.5160	−0.637052
$757$	−13.6798	−0.497202	−0.248601	−	0.968606i	$-0.579971\pi$
$757$	−13.6798	−0.497202	−0.248601	+	0.968606i	$0.579971\pi$
$758$	−21.6323	−0.785719
$759$	−10.7454	−0.390032
$760$	2.57124	0.0932688
$761$	41.1091	1.49020	0.745102	−	0.666951i	$-0.232401\pi$
$761$	41.1091	1.49020	0.745102	+	0.666951i	$0.232401\pi$
$762$	3.21853	0.116595
$763$	48.1690	1.74384
$764$	−13.6970	−0.495541
$765$	13.2527	0.479153
$766$	6.07147	0.219371
$767$	−1.45129	−0.0524032
$768$	0.642301	0.0231770
$769$	38.3946	1.38454	0.692272	−	0.721636i	$-0.256610\pi$
$769$	38.3946	1.38454	0.692272	+	0.721636i	$0.256610\pi$
$770$	22.4427	0.808779
$771$	−4.47015	−0.160988
$772$	−1.42855	−0.0514148
$773$	−16.8759	−0.606982	−0.303491	−	0.952834i	$-0.598152\pi$
$773$	−16.8759	−0.606982	−0.303491	+	0.952834i	$0.598152\pi$
$774$	−7.24711	−0.260492
$775$	8.34497	0.299760
$776$	−12.1509	−0.436192
$777$	−19.5381	−0.700927
$778$	−27.7560	−0.995100
$779$	0.0789893	0.00283009
$780$	−0.529296	−0.0189518
$781$	75.2904	2.69410
$782$	18.6348	0.666378
$783$	−14.5820	−0.521119
$784$	16.8214	0.600764
$785$	20.1981	0.720901
$786$	4.57544	0.163200
$787$	−39.5699	−1.41051	−0.705257	−	0.708952i	$-0.749168\pi$
$787$	−39.5699	−1.41051	−0.705257	+	0.708952i	$0.749168\pi$
$788$	−12.0054	−0.427673
$789$	−6.12530	−0.218066
$790$	−1.60419	−0.0570746
$791$	−29.5723	−1.05147
$792$	11.8977	0.422767
$793$	9.17737	0.325898
$794$	2.26572	0.0804075
$795$	−7.02711	−0.249226
$796$	8.91197	0.315876
$797$	39.1354	1.38625	0.693123	−	0.720819i	$-0.256234\pi$
$797$	39.1354	1.38625	0.693123	+	0.720819i	$0.256234\pi$
$798$	−8.06056	−0.285341
$799$	30.8342	1.09084
$800$	1.00000	0.0353553
$801$	−24.4411	−0.863584
$802$	−1.00000	−0.0353112
$803$	−25.9900	−0.917167
$804$	−2.23915	−0.0789687
$805$	−17.7572	−0.625860
$806$	6.87677	0.242224
$807$	−8.93242	−0.314436
$808$	−11.5701	−0.407035
$809$	−21.5254	−0.756793	−0.378396	−	0.925644i	$-0.623524\pi$
$809$	−21.5254	−0.756793	−0.378396	+	0.925644i	$0.623524\pi$
$810$	−5.45724	−0.191748
$811$	−33.0943	−1.16210	−0.581049	−	0.813868i	$-0.697358\pi$
$811$	−33.0943	−1.16210	−0.581049	+	0.813868i	$0.697358\pi$
$812$	19.8312	0.695939
$813$	2.80902	0.0985167
$814$	28.6585	1.00448
$815$	4.81293	0.168590
$816$	3.28981	0.115166
$817$	−7.20172	−0.251956
$818$	10.0614	0.351790
$819$	−10.4068	−0.363641
$820$	0.0307203	0.00107280
$821$	8.20462	0.286343	0.143172	−	0.989698i	$-0.454270\pi$
$821$	8.20462	0.286343	0.143172	+	0.989698i	$0.454270\pi$
$822$	−0.369334	−0.0128820
$823$	−36.1077	−1.25863	−0.629317	−	0.777149i	$-0.716665\pi$
$823$	−36.1077	−1.25863	−0.629317	+	0.777149i	$0.716665\pi$
$824$	−3.49555	−0.121773
$825$	−2.95345	−0.102826
$826$	−8.59566	−0.299081
$827$	37.9921	1.32112	0.660558	−	0.750775i	$-0.270320\pi$
$827$	37.9921	1.32112	0.660558	+	0.750775i	$0.270320\pi$
$828$	−9.41376	−0.327151
$829$	43.2857	1.50338	0.751688	−	0.659519i	$-0.229240\pi$
$829$	43.2857	1.50338	0.751688	+	0.659519i	$0.229240\pi$
$830$	−9.48422	−0.329202
$831$	−11.8238	−0.410163
$832$	0.824062	0.0285692
$833$	86.1577	2.98519
$834$	10.8560	0.375914
$835$	22.6923	0.785301
$836$	11.8232	0.408914
$837$	−29.9486	−1.03518
$838$	−3.11838	−0.107723
$839$	2.25336	0.0777947	0.0388974	−	0.999243i	$-0.487615\pi$
$839$	2.25336	0.0777947	0.0388974	+	0.999243i	$0.487615\pi$
$840$	−3.13489	−0.108164
$841$	−12.4906	−0.430710
$842$	−0.814489	−0.0280691
$843$	−3.26693	−0.112519
$844$	−2.43052	−0.0836618
$845$	12.3209	0.423853
$846$	−15.5766	−0.535534
$847$	49.5091	1.70115
$848$	10.9405	0.375699
$849$	−9.29240	−0.318914
$850$	5.12192	0.175680
$851$	−22.6753	−0.777299
$852$	−10.5169	−0.360302
$853$	49.4075	1.69168	0.845840	−	0.533437i	$-0.179100\pi$
$853$	49.4075	1.69168	0.845840	+	0.533437i	$0.179100\pi$
$854$	54.3553	1.86000
$855$	−6.65296	−0.227527
$856$	4.41395	0.150866
$857$	−21.9390	−0.749421	−0.374711	−	0.927142i	$-0.622258\pi$
$857$	−21.9390	−0.749421	−0.374711	+	0.927142i	$0.622258\pi$
$858$	−2.43383	−0.0830895
$859$	−53.6462	−1.83038	−0.915192	−	0.403018i	$-0.867961\pi$
$859$	−53.6462	−1.83038	−0.915192	+	0.403018i	$0.867961\pi$
$860$	−2.80087	−0.0955089
$861$	−0.0963046	−0.00328205
$862$	−12.4162	−0.422896
$863$	41.8883	1.42589	0.712947	−	0.701218i	$-0.247360\pi$
$863$	41.8883	1.42589	0.712947	+	0.701218i	$0.247360\pi$
$864$	−3.58882	−0.122094
$865$	3.15548	0.107290
$866$	−20.6696	−0.702381
$867$	5.93103	0.201428
$868$	40.7294	1.38245
$869$	−7.37647	−0.250229
$870$	−2.60978	−0.0884799
$871$	−2.87279	−0.0973409
$872$	9.86926	0.334215
$873$	31.4399	1.06408
$874$	−9.35480	−0.316431
$875$	−4.88072	−0.164998
$876$	3.63039	0.122659
$877$	18.0921	0.610927	0.305463	−	0.952204i	$-0.401189\pi$
$877$	18.0921	0.610927	0.305463	+	0.952204i	$0.401189\pi$
$878$	3.82029	0.128929
$879$	−14.5809	−0.491802
$880$	4.59824	0.155007
$881$	28.9409	0.975044	0.487522	−	0.873111i	$-0.337901\pi$
$881$	28.9409	0.975044	0.487522	+	0.873111i	$0.337901\pi$
$882$	−43.5245	−1.46555
$883$	−10.5152	−0.353865	−0.176932	−	0.984223i	$-0.556617\pi$
$883$	−10.5152	−0.353865	−0.176932	+	0.984223i	$0.556617\pi$
$884$	4.22078	0.141960
$885$	1.13119	0.0380244
$886$	23.2282	0.780367
$887$	19.1660	0.643531	0.321766	−	0.946819i	$-0.395724\pi$
$887$	19.1660	0.643531	0.321766	+	0.946819i	$0.395724\pi$
$888$	−4.00313	−0.134336
$889$	24.4570	0.820261
$890$	−9.44602	−0.316631
$891$	−25.0937	−0.840671
$892$	19.7097	0.659929
$893$	−15.4790	−0.517986
$894$	−6.74971	−0.225744
$895$	6.72026	0.224634
$896$	4.88072	0.163053
$897$	1.92570	0.0642974
$898$	15.5519	0.518972
$899$	33.9071	1.13086
$900$	−2.58745	−0.0862483
$901$	56.0365	1.86685
$902$	0.141259	0.00470342
$903$	8.78041	0.292194
$904$	−6.05902	−0.201520
$905$	−3.74246	−0.124404
$906$	−6.28473	−0.208796
$907$	−8.48988	−0.281902	−0.140951	−	0.990017i	$-0.545016\pi$
$907$	−8.48988	−0.281902	−0.140951	+	0.990017i	$0.545016\pi$
$908$	−13.4199	−0.445355
$909$	29.9371	0.992950
$910$	−4.02201	−0.133328
$911$	1.30397	0.0432024	0.0216012	−	0.999767i	$-0.493124\pi$
$911$	1.30397	0.0432024	0.0216012	+	0.999767i	$0.493124\pi$
$912$	−1.65151	−0.0546870
$913$	−43.6107	−1.44330
$914$	28.5842	0.945482
$915$	−7.15314	−0.236476
$916$	16.0770	0.531199
$917$	34.7678	1.14814
$918$	−18.3817	−0.606685
$919$	−44.3172	−1.46189	−0.730944	−	0.682437i	$-0.760920\pi$
$919$	−44.3172	−1.46189	−0.730944	+	0.682437i	$0.760920\pi$
$920$	−3.63824	−0.119949
$921$	21.4105	0.705499
$922$	−37.0553	−1.22035
$923$	−13.4930	−0.444127
$924$	−14.4150	−0.474218
$925$	−6.23249	−0.204923
$926$	−14.2524	−0.468362
$927$	9.04455	0.297062
$928$	4.06318	0.133380
$929$	−2.08875	−0.0685297	−0.0342648	−	0.999413i	$-0.510909\pi$
$929$	−2.08875	−0.0685297	−0.0342648	+	0.999413i	$0.510909\pi$
$930$	−5.35998	−0.175761
$931$	−43.2519	−1.41752
$932$	2.54947	0.0835107
$933$	18.4406	0.603720
$934$	−13.5574	−0.443612
$935$	23.5518	0.770227
$936$	−2.13222	−0.0696937
$937$	−42.9407	−1.40281	−0.701406	−	0.712762i	$-0.747444\pi$
$937$	−42.9407	−1.40281	−0.701406	+	0.712762i	$0.747444\pi$
$938$	−17.0149	−0.555555
$939$	14.8881	0.485854
$940$	−6.02005	−0.196352
$941$	39.1287	1.27556	0.637780	−	0.770219i	$-0.279853\pi$
$941$	39.1287	1.27556	0.637780	+	0.770219i	$0.279853\pi$
$942$	−12.9732	−0.422691
$943$	−0.111768	−0.00363966
$944$	−1.76115	−0.0573205
$945$	17.5160	0.569796
$946$	−12.8791	−0.418735
$947$	31.0339	1.00847	0.504233	−	0.863568i	$-0.331775\pi$
$947$	31.0339	1.00847	0.504233	+	0.863568i	$0.331775\pi$
$948$	1.03037	0.0334650
$949$	4.65773	0.151196
$950$	−2.57124	−0.0834222
$951$	−0.0233352	−0.000756696 0
$952$	24.9986	0.810210
$953$	10.2435	0.331818	0.165909	−	0.986141i	$-0.446944\pi$
$953$	10.2435	0.331818	0.165909	+	0.986141i	$0.446944\pi$
$954$	−28.3081	−0.916508
$955$	13.6970	0.443226
$956$	28.8799	0.934044
$957$	−12.0004	−0.387918
$958$	−0.901505	−0.0291263
$959$	−2.80650	−0.0906266
$960$	−0.642301	−0.0207302
$961$	38.6385	1.24640
$962$	−5.13596	−0.165590
$963$	−11.4209	−0.368033
$964$	30.6512	0.987210
$965$	1.42855	0.0459868
$966$	11.4055	0.366965
$967$	22.1245	0.711476	0.355738	−	0.934586i	$-0.384229\pi$
$967$	22.1245	0.711476	0.355738	+	0.934586i	$0.384229\pi$
$968$	10.1438	0.326035
$969$	−8.45891	−0.271739
$970$	12.1509	0.390142
$971$	−59.7081	−1.91612	−0.958062	−	0.286562i	$-0.907488\pi$
$971$	−59.7081	−1.91612	−0.958062	+	0.286562i	$0.907488\pi$
$972$	14.2717	0.457764
$973$	82.4928	2.64460
$974$	−1.04588	−0.0335121
$975$	0.529296	0.0169510
$976$	11.1367	0.356479
$977$	−48.9408	−1.56575	−0.782877	−	0.622176i	$-0.786249\pi$
$977$	−48.9408	−1.56575	−0.782877	+	0.622176i	$0.786249\pi$
$978$	−3.09135	−0.0988505
$979$	−43.4351	−1.38819
$980$	−16.8214	−0.537339
$981$	−25.5362	−0.815308
$982$	−20.7061	−0.660758
$983$	46.8278	1.49357	0.746787	−	0.665064i	$-0.231596\pi$
$983$	46.8278	1.49357	0.746787	+	0.665064i	$0.231596\pi$
$984$	−0.0197317	−0.000629022 0
$985$	12.0054	0.382522
$986$	20.8113	0.662765
$987$	18.8722	0.600708
$988$	−2.11886	−0.0674100
$989$	10.1902	0.324031
$990$	−11.8977	−0.378134
$991$	−42.7024	−1.35649	−0.678243	−	0.734837i	$-0.737258\pi$
$991$	−42.7024	−1.35649	−0.678243	+	0.734837i	$0.737258\pi$
$992$	8.34497	0.264953
$993$	21.7751	0.691011
$994$	−79.9156	−2.53477
$995$	−8.91197	−0.282529
$996$	6.09172	0.193024
$997$	−53.5361	−1.69551	−0.847753	−	0.530392i	$-0.822045\pi$
$997$	−53.5361	−1.69551	−0.847753	+	0.530392i	$0.822045\pi$
$998$	−18.0198	−0.570406
$999$	22.3673	0.707670

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4010.2.a.o.1.14	✓	22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4010.2.a.o.1.14	✓	22	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:	\( N \)	\(=\)	\( 4010 = 2 \cdot 5 \cdot 401 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4010.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +0.642301 q^{3} +1.00000 q^{4} -1.00000 q^{5} +0.642301 q^{6} +4.88072 q^{7} +1.00000 q^{8} -2.58745 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +0.642301 q^{3} +1.00000 q^{4} -1.00000 q^{5} +0.642301 q^{6} +4.88072 q^{7} +1.00000 q^{8} -2.58745 q^{9} -1.00000 q^{10} -4.59824 q^{11} +0.642301 q^{12} +0.824062 q^{13} +4.88072 q^{14} -0.642301 q^{15} +1.00000 q^{16} +5.12192 q^{17} -2.58745 q^{18} -2.57124 q^{19} -1.00000 q^{20} +3.13489 q^{21} -4.59824 q^{22} +3.63824 q^{23} +0.642301 q^{24} +1.00000 q^{25} +0.824062 q^{26} -3.58882 q^{27} +4.88072 q^{28} +4.06318 q^{29} -0.642301 q^{30} +8.34497 q^{31} +1.00000 q^{32} -2.95345 q^{33} +5.12192 q^{34} -4.88072 q^{35} -2.58745 q^{36} -6.23249 q^{37} -2.57124 q^{38} +0.529296 q^{39} -1.00000 q^{40} -0.0307203 q^{41} +3.13489 q^{42} +2.80087 q^{43} -4.59824 q^{44} +2.58745 q^{45} +3.63824 q^{46} +6.02005 q^{47} +0.642301 q^{48} +16.8214 q^{49} +1.00000 q^{50} +3.28981 q^{51} +0.824062 q^{52} +10.9405 q^{53} -3.58882 q^{54} +4.59824 q^{55} +4.88072 q^{56} -1.65151 q^{57} +4.06318 q^{58} -1.76115 q^{59} -0.642301 q^{60} +11.1367 q^{61} +8.34497 q^{62} -12.6286 q^{63} +1.00000 q^{64} -0.824062 q^{65} -2.95345 q^{66} -3.48614 q^{67} +5.12192 q^{68} +2.33684 q^{69} -4.88072 q^{70} -16.3737 q^{71} -2.58745 q^{72} +5.65216 q^{73} -6.23249 q^{74} +0.642301 q^{75} -2.57124 q^{76} -22.4427 q^{77} +0.529296 q^{78} +1.60419 q^{79} -1.00000 q^{80} +5.45724 q^{81} -0.0307203 q^{82} +9.48422 q^{83} +3.13489 q^{84} -5.12192 q^{85} +2.80087 q^{86} +2.60978 q^{87} -4.59824 q^{88} +9.44602 q^{89} +2.58745 q^{90} +4.02201 q^{91} +3.63824 q^{92} +5.35998 q^{93} +6.02005 q^{94} +2.57124 q^{95} +0.642301 q^{96} -12.1509 q^{97} +16.8214 q^{98} +11.8977 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q + 22 q^{2} + 2 q^{3} + 22 q^{4} - 22 q^{5} + 2 q^{6} + 13 q^{7} + 22 q^{8} + 32 q^{9}+O(q^{10}) \) 22 * q + 22 * q^2 + 2 * q^3 + 22 * q^4 - 22 * q^5 + 2 * q^6 + 13 * q^7 + 22 * q^8 + 32 * q^9	\( 22 q + 22 q^{2} + 2 q^{3} + 22 q^{4} - 22 q^{5} + 2 q^{6} + 13 q^{7} + 22 q^{8} + 32 q^{9} - 22 q^{10} - 3 q^{11} + 2 q^{12} + 6 q^{13} + 13 q^{14} - 2 q^{15} + 22 q^{16} + 17 q^{17} + 32 q^{18} + 13 q^{19} - 22 q^{20} + 16 q^{21} - 3 q^{22} + 19 q^{23} + 2 q^{24} + 22 q^{25} + 6 q^{26} + 14 q^{27} + 13 q^{28} + 14 q^{29} - 2 q^{30} + 13 q^{31} + 22 q^{32} + 12 q^{33} + 17 q^{34} - 13 q^{35} + 32 q^{36} + 35 q^{37} + 13 q^{38} + 30 q^{39} - 22 q^{40} - 5 q^{41} + 16 q^{42} + 19 q^{43} - 3 q^{44} - 32 q^{45} + 19 q^{46} + 29 q^{47} + 2 q^{48} + 61 q^{49} + 22 q^{50} + q^{51} + 6 q^{52} + 29 q^{53} + 14 q^{54} + 3 q^{55} + 13 q^{56} + 33 q^{57} + 14 q^{58} - 4 q^{59} - 2 q^{60} + 20 q^{61} + 13 q^{62} + 50 q^{63} + 22 q^{64} - 6 q^{65} + 12 q^{66} + 48 q^{67} + 17 q^{68} + 19 q^{69} - 13 q^{70} + 2 q^{71} + 32 q^{72} + 16 q^{73} + 35 q^{74} + 2 q^{75} + 13 q^{76} + 53 q^{77} + 30 q^{78} + 29 q^{79} - 22 q^{80} + 54 q^{81} - 5 q^{82} + 13 q^{83} + 16 q^{84} - 17 q^{85} + 19 q^{86} + 56 q^{87} - 3 q^{88} + 20 q^{89} - 32 q^{90} + 42 q^{91} + 19 q^{92} + 50 q^{93} + 29 q^{94} - 13 q^{95} + 2 q^{96} + 36 q^{97} + 61 q^{98} - q^{99}+O(q^{100}) \) 22 * q + 22 * q^2 + 2 * q^3 + 22 * q^4 - 22 * q^5 + 2 * q^6 + 13 * q^7 + 22 * q^8 + 32 * q^9 - 22 * q^10 - 3 * q^11 + 2 * q^12 + 6 * q^13 + 13 * q^14 - 2 * q^15 + 22 * q^16 + 17 * q^17 + 32 * q^18 + 13 * q^19 - 22 * q^20 + 16 * q^21 - 3 * q^22 + 19 * q^23 + 2 * q^24 + 22 * q^25 + 6 * q^26 + 14 * q^27 + 13 * q^28 + 14 * q^29 - 2 * q^30 + 13 * q^31 + 22 * q^32 + 12 * q^33 + 17 * q^34 - 13 * q^35 + 32 * q^36 + 35 * q^37 + 13 * q^38 + 30 * q^39 - 22 * q^40 - 5 * q^41 + 16 * q^42 + 19 * q^43 - 3 * q^44 - 32 * q^45 + 19 * q^46 + 29 * q^47 + 2 * q^48 + 61 * q^49 + 22 * q^50 + q^51 + 6 * q^52 + 29 * q^53 + 14 * q^54 + 3 * q^55 + 13 * q^56 + 33 * q^57 + 14 * q^58 - 4 * q^59 - 2 * q^60 + 20 * q^61 + 13 * q^62 + 50 * q^63 + 22 * q^64 - 6 * q^65 + 12 * q^66 + 48 * q^67 + 17 * q^68 + 19 * q^69 - 13 * q^70 + 2 * q^71 + 32 * q^72 + 16 * q^73 + 35 * q^74 + 2 * q^75 + 13 * q^76 + 53 * q^77 + 30 * q^78 + 29 * q^79 - 22 * q^80 + 54 * q^81 - 5 * q^82 + 13 * q^83 + 16 * q^84 - 17 * q^85 + 19 * q^86 + 56 * q^87 - 3 * q^88 + 20 * q^89 - 32 * q^90 + 42 * q^91 + 19 * q^92 + 50 * q^93 + 29 * q^94 - 13 * q^95 + 2 * q^96 + 36 * q^97 + 61 * q^98 - q^99

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