LMFDB - Embedded newform 4010.2.a.o.1.17

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			1.17
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)

$f(q)$	$=$	$q+1.00000 q^{2} +1.82747 q^{3} +1.00000 q^{4} -1.00000 q^{5} +1.82747 q^{6} +0.568203 q^{7} +1.00000 q^{8} +0.339635 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +1.82747 q^{3} +1.00000 q^{4} -1.00000 q^{5} +1.82747 q^{6} +0.568203 q^{7} +1.00000 q^{8} +0.339635 q^{9} -1.00000 q^{10} +3.48371 q^{11} +1.82747 q^{12} +1.38044 q^{13} +0.568203 q^{14} -1.82747 q^{15} +1.00000 q^{16} -0.534917 q^{17} +0.339635 q^{18} +5.96908 q^{19} -1.00000 q^{20} +1.03837 q^{21} +3.48371 q^{22} -5.22611 q^{23} +1.82747 q^{24} +1.00000 q^{25} +1.38044 q^{26} -4.86173 q^{27} +0.568203 q^{28} +2.74795 q^{29} -1.82747 q^{30} +9.75235 q^{31} +1.00000 q^{32} +6.36636 q^{33} -0.534917 q^{34} -0.568203 q^{35} +0.339635 q^{36} -1.08092 q^{37} +5.96908 q^{38} +2.52270 q^{39} -1.00000 q^{40} -9.49652 q^{41} +1.03837 q^{42} +4.41643 q^{43} +3.48371 q^{44} -0.339635 q^{45} -5.22611 q^{46} +11.4365 q^{47} +1.82747 q^{48} -6.67715 q^{49} +1.00000 q^{50} -0.977543 q^{51} +1.38044 q^{52} -1.65970 q^{53} -4.86173 q^{54} -3.48371 q^{55} +0.568203 q^{56} +10.9083 q^{57} +2.74795 q^{58} -1.49445 q^{59} -1.82747 q^{60} +4.98538 q^{61} +9.75235 q^{62} +0.192982 q^{63} +1.00000 q^{64} -1.38044 q^{65} +6.36636 q^{66} +3.24215 q^{67} -0.534917 q^{68} -9.55054 q^{69} -0.568203 q^{70} -3.81618 q^{71} +0.339635 q^{72} +9.98503 q^{73} -1.08092 q^{74} +1.82747 q^{75} +5.96908 q^{76} +1.97945 q^{77} +2.52270 q^{78} +4.26913 q^{79} -1.00000 q^{80} -9.90355 q^{81} -9.49652 q^{82} +15.4704 q^{83} +1.03837 q^{84} +0.534917 q^{85} +4.41643 q^{86} +5.02179 q^{87} +3.48371 q^{88} -15.8291 q^{89} -0.339635 q^{90} +0.784369 q^{91} -5.22611 q^{92} +17.8221 q^{93} +11.4365 q^{94} -5.96908 q^{95} +1.82747 q^{96} +13.0123 q^{97} -6.67715 q^{98} +1.18319 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	1.82747	1.05509	0.527544	−	0.849528i	$-0.323113\pi$
$3$	1.82747	1.05509	0.527544	+	0.849528i	$0.323113\pi$
$4$	1.00000	0.500000
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	1.82747	0.746060
$7$	0.568203	0.214761	0.107380	−	0.994218i	$-0.465754\pi$
$7$	0.568203	0.214761	0.107380	+	0.994218i	$0.465754\pi$
$8$	1.00000	0.353553
$9$	0.339635	0.113212
$10$	−1.00000	−0.316228
$11$	3.48371	1.05038	0.525189	−	0.850986i	$-0.323995\pi$
$11$	3.48371	1.05038	0.525189	+	0.850986i	$0.323995\pi$
$12$	1.82747	0.527544
$13$	1.38044	0.382864	0.191432	−	0.981506i	$-0.438687\pi$
$13$	1.38044	0.382864	0.191432	+	0.981506i	$0.438687\pi$
$14$	0.568203	0.151859
$15$	−1.82747	−0.471850
$16$	1.00000	0.250000
$17$	−0.534917	−0.129736	−0.0648682	−	0.997894i	$-0.520663\pi$
$17$	−0.534917	−0.129736	−0.0648682	+	0.997894i	$0.520663\pi$
$18$	0.339635	0.0800528
$19$	5.96908	1.36940	0.684701	−	0.728824i	$-0.259933\pi$
$19$	5.96908	1.36940	0.684701	+	0.728824i	$0.259933\pi$
$20$	−1.00000	−0.223607
$21$	1.03837	0.226591
$22$	3.48371	0.742729
$23$	−5.22611	−1.08972	−0.544859	−	0.838527i	$-0.683417\pi$
$23$	−5.22611	−1.08972	−0.544859	+	0.838527i	$0.683417\pi$
$24$	1.82747	0.373030
$25$	1.00000	0.200000
$26$	1.38044	0.270726
$27$	−4.86173	−0.935640
$28$	0.568203	0.107380
$29$	2.74795	0.510282	0.255141	−	0.966904i	$-0.417878\pi$
$29$	2.74795	0.510282	0.255141	+	0.966904i	$0.417878\pi$
$30$	−1.82747	−0.333648
$31$	9.75235	1.75157	0.875787	−	0.482698i	$-0.160343\pi$
$31$	9.75235	1.75157	0.875787	+	0.482698i	$0.160343\pi$
$32$	1.00000	0.176777
$33$	6.36636	1.10824
$34$	−0.534917	−0.0917375
$35$	−0.568203	−0.0960439
$36$	0.339635	0.0566059
$37$	−1.08092	−0.177702	−0.0888509	−	0.996045i	$-0.528319\pi$
$37$	−1.08092	−0.177702	−0.0888509	+	0.996045i	$0.528319\pi$
$38$	5.96908	0.968313
$39$	2.52270	0.403956
$40$	−1.00000	−0.158114
$41$	−9.49652	−1.48311	−0.741554	−	0.670894i	$-0.765911\pi$
$41$	−9.49652	−1.48311	−0.741554	+	0.670894i	$0.765911\pi$
$42$	1.03837	0.160224
$43$	4.41643	0.673499	0.336749	−	0.941594i	$-0.390672\pi$
$43$	4.41643	0.673499	0.336749	+	0.941594i	$0.390672\pi$
$44$	3.48371	0.525189
$45$	−0.339635	−0.0506298
$46$	−5.22611	−0.770547
$47$	11.4365	1.66818	0.834090	−	0.551629i	$-0.185993\pi$
$47$	11.4365	1.66818	0.834090	+	0.551629i	$0.185993\pi$
$48$	1.82747	0.263772
$49$	−6.67715	−0.953878
$50$	1.00000	0.141421
$51$	−0.977543	−0.136883
$52$	1.38044	0.191432
$53$	−1.65970	−0.227978	−0.113989	−	0.993482i	$-0.536363\pi$
$53$	−1.65970	−0.227978	−0.113989	+	0.993482i	$0.536363\pi$
$54$	−4.86173	−0.661597
$55$	−3.48371	−0.469743
$56$	0.568203	0.0759294
$57$	10.9083	1.44484
$58$	2.74795	0.360824
$59$	−1.49445	−0.194561	−0.0972807	−	0.995257i	$-0.531014\pi$
$59$	−1.49445	−0.194561	−0.0972807	+	0.995257i	$0.531014\pi$
$60$	−1.82747	−0.235925
$61$	4.98538	0.638312	0.319156	−	0.947702i	$-0.396601\pi$
$61$	4.98538	0.638312	0.319156	+	0.947702i	$0.396601\pi$
$62$	9.75235	1.23855
$63$	0.192982	0.0243134
$64$	1.00000	0.125000
$65$	−1.38044	−0.171222
$66$	6.36636	0.783645
$67$	3.24215	0.396092	0.198046	−	0.980193i	$-0.436541\pi$
$67$	3.24215	0.396092	0.198046	+	0.980193i	$0.436541\pi$
$68$	−0.534917	−0.0648682
$69$	−9.55054	−1.14975
$70$	−0.568203	−0.0679133
$71$	−3.81618	−0.452898	−0.226449	−	0.974023i	$-0.572712\pi$
$71$	−3.81618	−0.452898	−0.226449	+	0.974023i	$0.572712\pi$
$72$	0.339635	0.0400264
$73$	9.98503	1.16866	0.584330	−	0.811516i	$-0.301357\pi$
$73$	9.98503	1.16866	0.584330	+	0.811516i	$0.301357\pi$
$74$	−1.08092	−0.125654
$75$	1.82747	0.211018
$76$	5.96908	0.684701
$77$	1.97945	0.225580
$78$	2.52270	0.285640
$79$	4.26913	0.480315	0.240157	−	0.970734i	$-0.422801\pi$
$79$	4.26913	0.480315	0.240157	+	0.970734i	$0.422801\pi$
$80$	−1.00000	−0.111803
$81$	−9.90355	−1.10039
$82$	−9.49652	−1.04872
$83$	15.4704	1.69810	0.849050	−	0.528312i	$-0.177175\pi$
$83$	15.4704	1.69810	0.849050	+	0.528312i	$0.177175\pi$
$84$	1.03837	0.113296
$85$	0.534917	0.0580199
$86$	4.41643	0.476236
$87$	5.02179	0.538392
$88$	3.48371	0.371365
$89$	−15.8291	−1.67788	−0.838942	−	0.544220i	$-0.816826\pi$
$89$	−15.8291	−1.67788	−0.838942	+	0.544220i	$0.816826\pi$
$90$	−0.339635	−0.0358007
$91$	0.784369	0.0822242
$92$	−5.22611	−0.544859
$93$	17.8221	1.84806
$94$	11.4365	1.17958
$95$	−5.96908	−0.612415
$96$	1.82747	0.186515
$97$	13.0123	1.32120	0.660598	−	0.750740i	$-0.270303\pi$
$97$	13.0123	1.32120	0.660598	+	0.750740i	$0.270303\pi$
$98$	−6.67715	−0.674494
$99$	1.18319	0.118915
$100$	1.00000	0.100000
$101$	4.44318	0.442113	0.221056	−	0.975261i	$-0.429049\pi$
$101$	4.44318	0.442113	0.221056	+	0.975261i	$0.429049\pi$
$102$	−0.977543	−0.0967912
$103$	−14.8026	−1.45855	−0.729274	−	0.684222i	$-0.760142\pi$
$103$	−14.8026	−1.45855	−0.729274	+	0.684222i	$0.760142\pi$
$104$	1.38044	0.135363
$105$	−1.03837	−0.101335
$106$	−1.65970	−0.161205
$107$	−0.432210	−0.0417833	−0.0208916	−	0.999782i	$-0.506651\pi$
$107$	−0.432210	−0.0417833	−0.0208916	+	0.999782i	$0.506651\pi$
$108$	−4.86173	−0.467820
$109$	−14.7843	−1.41608	−0.708042	−	0.706171i	$-0.750421\pi$
$109$	−14.7843	−1.41608	−0.708042	+	0.706171i	$0.750421\pi$
$110$	−3.48371	−0.332159
$111$	−1.97534	−0.187491
$112$	0.568203	0.0536902
$113$	8.84410	0.831983	0.415991	−	0.909369i	$-0.363435\pi$
$113$	8.84410	0.831983	0.415991	+	0.909369i	$0.363435\pi$
$114$	10.9083	1.02166
$115$	5.22611	0.487337
$116$	2.74795	0.255141
$117$	0.468845	0.0433447
$118$	−1.49445	−0.137576
$119$	−0.303942	−0.0278623
$120$	−1.82747	−0.166824
$121$	1.13623	0.103293
$122$	4.98538	0.451355
$123$	−17.3546	−1.56481
$124$	9.75235	0.875787
$125$	−1.00000	−0.0894427
$126$	0.192982	0.0171922
$127$	−4.26145	−0.378142	−0.189071	−	0.981963i	$-0.560548\pi$
$127$	−4.26145	−0.378142	−0.189071	+	0.981963i	$0.560548\pi$
$128$	1.00000	0.0883883
$129$	8.07087	0.710601
$130$	−1.38044	−0.121072
$131$	−4.24464	−0.370856	−0.185428	−	0.982658i	$-0.559367\pi$
$131$	−4.24464	−0.370856	−0.185428	+	0.982658i	$0.559367\pi$
$132$	6.36636	0.554121
$133$	3.39165	0.294094
$134$	3.24215	0.280079
$135$	4.86173	0.418431
$136$	−0.534917	−0.0458688
$137$	−18.9552	−1.61945	−0.809724	−	0.586811i	$-0.800383\pi$
$137$	−18.9552	−1.61945	−0.809724	+	0.586811i	$0.800383\pi$
$138$	−9.55054	−0.812996
$139$	13.8314	1.17316	0.586581	−	0.809891i	$-0.300474\pi$
$139$	13.8314	1.17316	0.586581	+	0.809891i	$0.300474\pi$
$140$	−0.568203	−0.0480219
$141$	20.8998	1.76008
$142$	−3.81618	−0.320247
$143$	4.80904	0.402152
$144$	0.339635	0.0283029
$145$	−2.74795	−0.228205
$146$	9.98503	0.826367
$147$	−12.2023	−1.00643
$148$	−1.08092	−0.0888509
$149$	0.987255	0.0808791	0.0404395	−	0.999182i	$-0.487124\pi$
$149$	0.987255	0.0808791	0.0404395	+	0.999182i	$0.487124\pi$
$150$	1.82747	0.149212
$151$	21.1989	1.72515	0.862573	−	0.505933i	$-0.168852\pi$
$151$	21.1989	1.72515	0.862573	+	0.505933i	$0.168852\pi$
$152$	5.96908	0.484157
$153$	−0.181677	−0.0146877
$154$	1.97945	0.159509
$155$	−9.75235	−0.783327
$156$	2.52270	0.201978
$157$	5.98459	0.477622	0.238811	−	0.971066i	$-0.423242\pi$
$157$	5.98459	0.477622	0.238811	+	0.971066i	$0.423242\pi$
$158$	4.26913	0.339634
$159$	−3.03305	−0.240537
$160$	−1.00000	−0.0790569
$161$	−2.96949	−0.234029
$162$	−9.90355	−0.778097
$163$	8.85585	0.693644	0.346822	−	0.937931i	$-0.387261\pi$
$163$	8.85585	0.693644	0.346822	+	0.937931i	$0.387261\pi$
$164$	−9.49652	−0.741554
$165$	−6.36636	−0.495621
$166$	15.4704	1.20074
$167$	−2.25867	−0.174781	−0.0873907	−	0.996174i	$-0.527853\pi$
$167$	−2.25867	−0.174781	−0.0873907	+	0.996174i	$0.527853\pi$
$168$	1.03837	0.0801122
$169$	−11.0944	−0.853415
$170$	0.534917	0.0410263
$171$	2.02731	0.155032
$172$	4.41643	0.336749
$173$	12.6390	0.960926	0.480463	−	0.877015i	$-0.340469\pi$
$173$	12.6390	0.960926	0.480463	+	0.877015i	$0.340469\pi$
$174$	5.02179	0.380701
$175$	0.568203	0.0429521
$176$	3.48371	0.262594
$177$	−2.73107	−0.205279
$178$	−15.8291	−1.18644
$179$	−15.9590	−1.19283	−0.596417	−	0.802675i	$-0.703409\pi$
$179$	−15.9590	−1.19283	−0.596417	+	0.802675i	$0.703409\pi$
$180$	−0.339635	−0.0253149
$181$	0.306651	0.0227932	0.0113966	−	0.999935i	$-0.496372\pi$
$181$	0.306651	0.0227932	0.0113966	+	0.999935i	$0.496372\pi$
$182$	0.784369	0.0581413
$183$	9.11062	0.673476
$184$	−5.22611	−0.385274
$185$	1.08092	0.0794707
$186$	17.8221	1.30678
$187$	−1.86350	−0.136272
$188$	11.4365	0.834090
$189$	−2.76245	−0.200939
$190$	−5.96908	−0.433043
$191$	15.2633	1.10441	0.552206	−	0.833708i	$-0.313786\pi$
$191$	15.2633	1.10441	0.552206	+	0.833708i	$0.313786\pi$
$192$	1.82747	0.131886
$193$	1.50207	0.108121	0.0540607	−	0.998538i	$-0.482784\pi$
$193$	1.50207	0.108121	0.0540607	+	0.998538i	$0.482784\pi$
$194$	13.0123	0.934226
$195$	−2.52270	−0.180654
$196$	−6.67715	−0.476939
$197$	−19.6138	−1.39743	−0.698713	−	0.715402i	$-0.746243\pi$
$197$	−19.6138	−1.39743	−0.698713	+	0.715402i	$0.746243\pi$
$198$	1.18319	0.0840857
$199$	−0.119352	−0.00846064	−0.00423032	−	0.999991i	$-0.501347\pi$
$199$	−0.119352	−0.00846064	−0.00423032	+	0.999991i	$0.501347\pi$
$200$	1.00000	0.0707107
$201$	5.92492	0.417912
$202$	4.44318	0.312621
$203$	1.56139	0.109588
$204$	−0.977543	−0.0684417
$205$	9.49652	0.663266
$206$	−14.8026	−1.03135
$207$	−1.77497	−0.123369
$208$	1.38044	0.0957161
$209$	20.7945	1.43839
$210$	−1.03837	−0.0716545
$211$	18.1086	1.24664	0.623322	−	0.781965i	$-0.285782\pi$
$211$	18.1086	1.24664	0.623322	+	0.781965i	$0.285782\pi$
$212$	−1.65970	−0.113989
$213$	−6.97395	−0.477847
$214$	−0.432210	−0.0295452
$215$	−4.41643	−0.301198
$216$	−4.86173	−0.330799
$217$	5.54132	0.376169
$218$	−14.7843	−1.00132
$219$	18.2473	1.23304
$220$	−3.48371	−0.234872
$221$	−0.738419	−0.0496715
$222$	−1.97534	−0.132576
$223$	−20.8994	−1.39953	−0.699763	−	0.714375i	$-0.746711\pi$
$223$	−20.8994	−1.39953	−0.699763	+	0.714375i	$0.746711\pi$
$224$	0.568203	0.0379647
$225$	0.339635	0.0226423
$226$	8.84410	0.588301
$227$	7.81599	0.518766	0.259383	−	0.965775i	$-0.416481\pi$
$227$	7.81599	0.518766	0.259383	+	0.965775i	$0.416481\pi$
$228$	10.9083	0.722420
$229$	−14.8088	−0.978594	−0.489297	−	0.872117i	$-0.662747\pi$
$229$	−14.8088	−0.978594	−0.489297	+	0.872117i	$0.662747\pi$
$230$	5.22611	0.344599
$231$	3.61739	0.238007
$232$	2.74795	0.180412
$233$	−20.9102	−1.36987	−0.684937	−	0.728602i	$-0.740170\pi$
$233$	−20.9102	−1.36987	−0.684937	+	0.728602i	$0.740170\pi$
$234$	0.468845	0.0306494
$235$	−11.4365	−0.746033
$236$	−1.49445	−0.0972807
$237$	7.80169	0.506774
$238$	−0.303942	−0.0197016
$239$	1.75925	0.113797	0.0568984	−	0.998380i	$-0.481879\pi$
$239$	1.75925	0.113797	0.0568984	+	0.998380i	$0.481879\pi$
$240$	−1.82747	−0.117962
$241$	−19.4677	−1.25403	−0.627014	−	0.779008i	$-0.715723\pi$
$241$	−19.4677	−1.25403	−0.627014	+	0.779008i	$0.715723\pi$
$242$	1.13623	0.0730394
$243$	−3.51323	−0.225374
$244$	4.98538	0.319156
$245$	6.67715	0.426587
$246$	−17.3546	−1.10649
$247$	8.23994	0.524295
$248$	9.75235	0.619275
$249$	28.2717	1.79165
$250$	−1.00000	−0.0632456
$251$	−21.1016	−1.33192	−0.665962	−	0.745986i	$-0.731979\pi$
$251$	−21.1016	−1.33192	−0.665962	+	0.745986i	$0.731979\pi$
$252$	0.192982	0.0121567
$253$	−18.2062	−1.14462
$254$	−4.26145	−0.267387
$255$	0.977543	0.0612161
$256$	1.00000	0.0625000
$257$	−20.8650	−1.30152	−0.650761	−	0.759283i	$-0.725550\pi$
$257$	−20.8650	−1.30152	−0.650761	+	0.759283i	$0.725550\pi$
$258$	8.07087	0.502471
$259$	−0.614181	−0.0381634
$260$	−1.38044	−0.0856111
$261$	0.933301	0.0577699
$262$	−4.24464	−0.262235
$263$	0.553402	0.0341243	0.0170621	−	0.999854i	$-0.494569\pi$
$263$	0.553402	0.0341243	0.0170621	+	0.999854i	$0.494569\pi$
$264$	6.36636	0.391823
$265$	1.65970	0.101955
$266$	3.39165	0.207956
$267$	−28.9272	−1.77032
$268$	3.24215	0.198046
$269$	7.20698	0.439417	0.219709	−	0.975566i	$-0.429489\pi$
$269$	7.20698	0.439417	0.219709	+	0.975566i	$0.429489\pi$
$270$	4.86173	0.295875
$271$	−14.6893	−0.892310	−0.446155	−	0.894956i	$-0.647207\pi$
$271$	−14.6893	−0.892310	−0.446155	+	0.894956i	$0.647207\pi$
$272$	−0.534917	−0.0324341
$273$	1.43341	0.0867538
$274$	−18.9552	−1.14512
$275$	3.48371	0.210076
$276$	−9.55054	−0.574875
$277$	6.66485	0.400452	0.200226	−	0.979750i	$-0.435832\pi$
$277$	6.66485	0.400452	0.200226	+	0.979750i	$0.435832\pi$
$278$	13.8314	0.829551
$279$	3.31224	0.198299
$280$	−0.568203	−0.0339566
$281$	−22.0697	−1.31657	−0.658285	−	0.752769i	$-0.728718\pi$
$281$	−22.0697	−1.31657	−0.658285	+	0.752769i	$0.728718\pi$
$282$	20.8998	1.24456
$283$	26.3654	1.56726	0.783631	−	0.621227i	$-0.213366\pi$
$283$	26.3654	1.56726	0.783631	+	0.621227i	$0.213366\pi$
$284$	−3.81618	−0.226449
$285$	−10.9083	−0.646152
$286$	4.80904	0.284364
$287$	−5.39595	−0.318513
$288$	0.339635	0.0200132
$289$	−16.7139	−0.983168
$290$	−2.74795	−0.161365
$291$	23.7795	1.39398
$292$	9.98503	0.584330
$293$	−13.1601	−0.768822	−0.384411	−	0.923162i	$-0.625596\pi$
$293$	−13.1601	−0.768822	−0.384411	+	0.923162i	$0.625596\pi$
$294$	−12.2023	−0.711650
$295$	1.49445	0.0870105
$296$	−1.08092	−0.0628271
$297$	−16.9368	−0.982776
$298$	0.987255	0.0571902
$299$	−7.21431	−0.417214
$300$	1.82747	0.105509
$301$	2.50943	0.144641
$302$	21.1989	1.21986
$303$	8.11976	0.466468
$304$	5.96908	0.342350
$305$	−4.98538	−0.285462
$306$	−0.181677	−0.0103858
$307$	−1.80373	−0.102944	−0.0514722	−	0.998674i	$-0.516391\pi$
$307$	−1.80373	−0.102944	−0.0514722	+	0.998674i	$0.516391\pi$
$308$	1.97945	0.112790
$309$	−27.0513	−1.53890
$310$	−9.75235	−0.553896
$311$	32.1337	1.82213	0.911066	−	0.412260i	$-0.135260\pi$
$311$	32.1337	1.82213	0.911066	+	0.412260i	$0.135260\pi$
$312$	2.52270	0.142820
$313$	−30.6118	−1.73028	−0.865141	−	0.501529i	$-0.832771\pi$
$313$	−30.6118	−1.73028	−0.865141	+	0.501529i	$0.832771\pi$
$314$	5.98459	0.337730
$315$	−0.192982	−0.0108733
$316$	4.26913	0.240157
$317$	27.1057	1.52241	0.761205	−	0.648512i	$-0.224608\pi$
$317$	27.1057	1.52241	0.761205	+	0.648512i	$0.224608\pi$
$318$	−3.03305	−0.170085
$319$	9.57306	0.535988
$320$	−1.00000	−0.0559017
$321$	−0.789849	−0.0440851
$322$	−2.96949	−0.165483
$323$	−3.19296	−0.177661
$324$	−9.90355	−0.550197
$325$	1.38044	0.0765729
$326$	8.85585	0.490480
$327$	−27.0179	−1.49409
$328$	−9.49652	−0.524358
$329$	6.49824	0.358259
$330$	−6.36636	−0.350457
$331$	−2.63733	−0.144961	−0.0724803	−	0.997370i	$-0.523091\pi$
$331$	−2.63733	−0.144961	−0.0724803	+	0.997370i	$0.523091\pi$
$332$	15.4704	0.849050
$333$	−0.367118	−0.0201179
$334$	−2.25867	−0.123589
$335$	−3.24215	−0.177138
$336$	1.03837	0.0566479
$337$	10.7145	0.583655	0.291827	−	0.956471i	$-0.405737\pi$
$337$	10.7145	0.583655	0.291827	+	0.956471i	$0.405737\pi$
$338$	−11.0944	−0.603455
$339$	16.1623	0.877816
$340$	0.534917	0.0290100
$341$	33.9743	1.83981
$342$	2.02731	0.109624
$343$	−7.77140	−0.419616
$344$	4.41643	0.238118
$345$	9.55054	0.514184
$346$	12.6390	0.679477
$347$	−3.38748	−0.181849	−0.0909246	−	0.995858i	$-0.528982\pi$
$347$	−3.38748	−0.181849	−0.0909246	+	0.995858i	$0.528982\pi$
$348$	5.02179	0.269196
$349$	−27.2027	−1.45613	−0.728064	−	0.685509i	$-0.759580\pi$
$349$	−27.2027	−1.45613	−0.728064	+	0.685509i	$0.759580\pi$
$350$	0.568203	0.0303717
$351$	−6.71131	−0.358223
$352$	3.48371	0.185682
$353$	−17.3827	−0.925188	−0.462594	−	0.886570i	$-0.653081\pi$
$353$	−17.3827	−0.925188	−0.462594	+	0.886570i	$0.653081\pi$
$354$	−2.73107	−0.145154
$355$	3.81618	0.202542
$356$	−15.8291	−0.838942
$357$	−0.555443	−0.0293972
$358$	−15.9590	−0.843461
$359$	2.11898	0.111835	0.0559176	−	0.998435i	$-0.482192\pi$
$359$	2.11898	0.111835	0.0559176	+	0.998435i	$0.482192\pi$
$360$	−0.339635	−0.0179003
$361$	16.6299	0.875260
$362$	0.306651	0.0161172
$363$	2.07642	0.108984
$364$	0.784369	0.0411121
$365$	−9.98503	−0.522641
$366$	9.11062	0.476219
$367$	5.02288	0.262192	0.131096	−	0.991370i	$-0.458150\pi$
$367$	5.02288	0.262192	0.131096	+	0.991370i	$0.458150\pi$
$368$	−5.22611	−0.272430
$369$	−3.22535	−0.167905
$370$	1.08092	0.0561943
$371$	−0.943049	−0.0489607
$372$	17.8221	0.924032
$373$	0.879927	0.0455609	0.0227804	−	0.999740i	$-0.492748\pi$
$373$	0.879927	0.0455609	0.0227804	+	0.999740i	$0.492748\pi$
$374$	−1.86350	−0.0963591
$375$	−1.82747	−0.0943700
$376$	11.4365	0.589791
$377$	3.79337	0.195369
$378$	−2.76245	−0.142085
$379$	−34.4044	−1.76724	−0.883619	−	0.468207i	$-0.844900\pi$
$379$	−34.4044	−1.76724	−0.883619	+	0.468207i	$0.844900\pi$
$380$	−5.96908	−0.306207
$381$	−7.78765	−0.398973
$382$	15.2633	0.780937
$383$	−3.69011	−0.188556	−0.0942779	−	0.995546i	$-0.530054\pi$
$383$	−3.69011	−0.188556	−0.0942779	+	0.995546i	$0.530054\pi$
$384$	1.82747	0.0932575
$385$	−1.97945	−0.100882
$386$	1.50207	0.0764534
$387$	1.49997	0.0762480
$388$	13.0123	0.660598
$389$	−0.983802	−0.0498808	−0.0249404	−	0.999689i	$-0.507940\pi$
$389$	−0.983802	−0.0498808	−0.0249404	+	0.999689i	$0.507940\pi$
$390$	−2.52270	−0.127742
$391$	2.79553	0.141376
$392$	−6.67715	−0.337247
$393$	−7.75694	−0.391286
$394$	−19.6138	−0.988129
$395$	−4.26913	−0.214803
$396$	1.18319	0.0594575
$397$	−21.8429	−1.09627	−0.548133	−	0.836391i	$-0.684661\pi$
$397$	−21.8429	−1.09627	−0.548133	+	0.836391i	$0.684661\pi$
$398$	−0.119352	−0.00598257
$399$	6.19813	0.310295
$400$	1.00000	0.0500000
$401$	−1.00000	−0.0499376
$401$	−1.00000	−0.0499376
$402$	5.92492	0.295508
$403$	13.4625	0.670615
$404$	4.44318	0.221056
$405$	9.90355	0.492112
$406$	1.56139	0.0774907
$407$	−3.76560	−0.186654
$408$	−0.977543	−0.0483956
$409$	−12.3785	−0.612076	−0.306038	−	0.952019i	$-0.599003\pi$
$409$	−12.3785	−0.612076	−0.306038	+	0.952019i	$0.599003\pi$
$410$	9.49652	0.469000
$411$	−34.6399	−1.70866
$412$	−14.8026	−0.729274
$413$	−0.849154	−0.0417841
$414$	−1.77497	−0.0872350
$415$	−15.4704	−0.759414
$416$	1.38044	0.0676815
$417$	25.2764	1.23779
$418$	20.7945	1.01709
$419$	−27.9664	−1.36625	−0.683125	−	0.730302i	$-0.739380\pi$
$419$	−27.9664	−1.36625	−0.683125	+	0.730302i	$0.739380\pi$
$420$	−1.03837	−0.0506674
$421$	−31.5787	−1.53905	−0.769526	−	0.638616i	$-0.779507\pi$
$421$	−31.5787	−1.53905	−0.769526	+	0.638616i	$0.779507\pi$
$422$	18.1086	0.881511
$423$	3.88423	0.188858
$424$	−1.65970	−0.0806023
$425$	−0.534917	−0.0259473
$426$	−6.97395	−0.337889
$427$	2.83271	0.137084
$428$	−0.432210	−0.0208916
$429$	8.78836	0.424306
$430$	−4.41643	−0.212979
$431$	−4.19263	−0.201952	−0.100976	−	0.994889i	$-0.532197\pi$
$431$	−4.19263	−0.201952	−0.100976	+	0.994889i	$0.532197\pi$
$432$	−4.86173	−0.233910
$433$	8.16858	0.392557	0.196279	−	0.980548i	$-0.437114\pi$
$433$	8.16858	0.392557	0.196279	+	0.980548i	$0.437114\pi$
$434$	5.54132	0.265992
$435$	−5.02179	−0.240776
$436$	−14.7843	−0.708042
$437$	−31.1951	−1.49226
$438$	18.2473	0.871891
$439$	0.494320	0.0235926	0.0117963	−	0.999930i	$-0.496245\pi$
$439$	0.494320	0.0235926	0.0117963	+	0.999930i	$0.496245\pi$
$440$	−3.48371	−0.166079
$441$	−2.26779	−0.107990
$442$	−0.738419	−0.0351230
$443$	29.2202	1.38829	0.694147	−	0.719834i	$-0.255782\pi$
$443$	29.2202	1.38829	0.694147	+	0.719834i	$0.255782\pi$
$444$	−1.97534	−0.0937456
$445$	15.8291	0.750373
$446$	−20.8994	−0.989615
$447$	1.80418	0.0853346
$448$	0.568203	0.0268451
$449$	−21.3335	−1.00679	−0.503396	−	0.864056i	$-0.667916\pi$
$449$	−21.3335	−1.00679	−0.503396	+	0.864056i	$0.667916\pi$
$450$	0.339635	0.0160106
$451$	−33.0831	−1.55782
$452$	8.84410	0.415991
$453$	38.7404	1.82018
$454$	7.81599	0.366823
$455$	−0.784369	−0.0367718
$456$	10.9083	0.510828
$457$	−14.4466	−0.675782	−0.337891	−	0.941185i	$-0.609713\pi$
$457$	−14.4466	−0.675782	−0.337891	+	0.941185i	$0.609713\pi$
$458$	−14.8088	−0.691970
$459$	2.60062	0.121387
$460$	5.22611	0.243669
$461$	25.7905	1.20118	0.600591	−	0.799556i	$-0.294932\pi$
$461$	25.7905	1.20118	0.600591	+	0.799556i	$0.294932\pi$
$462$	3.61739	0.168296
$463$	−6.02721	−0.280108	−0.140054	−	0.990144i	$-0.544728\pi$
$463$	−6.02721	−0.280108	−0.140054	+	0.990144i	$0.544728\pi$
$464$	2.74795	0.127570
$465$	−17.8221	−0.826480
$466$	−20.9102	−0.968648
$467$	38.4498	1.77924	0.889621	−	0.456699i	$-0.150968\pi$
$467$	38.4498	1.77924	0.889621	+	0.456699i	$0.150968\pi$
$468$	0.468845	0.0216724
$469$	1.84220	0.0850649
$470$	−11.4365	−0.527525
$471$	10.9366	0.503934
$472$	−1.49445	−0.0687878
$473$	15.3855	0.707428
$474$	7.80169	0.358344
$475$	5.96908	0.273880
$476$	−0.303942	−0.0139311
$477$	−0.563694	−0.0258098
$478$	1.75925	0.0804664
$479$	2.69596	0.123182	0.0615908	−	0.998101i	$-0.480383\pi$
$479$	2.69596	0.123182	0.0615908	+	0.998101i	$0.480383\pi$
$480$	−1.82747	−0.0834121
$481$	−1.49214	−0.0680357
$482$	−19.4677	−0.886731
$483$	−5.42665	−0.246921
$484$	1.13623	0.0516467
$485$	−13.0123	−0.590857
$486$	−3.51323	−0.159363
$487$	−39.1366	−1.77345	−0.886723	−	0.462301i	$-0.847024\pi$
$487$	−39.1366	−1.77345	−0.886723	+	0.462301i	$0.847024\pi$
$488$	4.98538	0.225678
$489$	16.1838	0.731856
$490$	6.67715	0.301643
$491$	−19.0376	−0.859153	−0.429576	−	0.903030i	$-0.641337\pi$
$491$	−19.0376	−0.859153	−0.429576	+	0.903030i	$0.641337\pi$
$492$	−17.3546	−0.782405
$493$	−1.46993	−0.0662021
$494$	8.23994	0.370732
$495$	−1.18319	−0.0531804
$496$	9.75235	0.437893
$497$	−2.16837	−0.0972646
$498$	28.2717	1.26689
$499$	16.8672	0.755080	0.377540	−	0.925993i	$-0.376770\pi$
$499$	16.8672	0.755080	0.377540	+	0.925993i	$0.376770\pi$
$500$	−1.00000	−0.0447214
$501$	−4.12765	−0.184410
$502$	−21.1016	−0.941812
$503$	15.3962	0.686482	0.343241	−	0.939247i	$-0.388475\pi$
$503$	15.3962	0.686482	0.343241	+	0.939247i	$0.388475\pi$
$504$	0.192982	0.00859610
$505$	−4.44318	−0.197719
$506$	−18.2062	−0.809366
$507$	−20.2746	−0.900428
$508$	−4.26145	−0.189071
$509$	−18.7898	−0.832842	−0.416421	−	0.909172i	$-0.636716\pi$
$509$	−18.7898	−0.832842	−0.416421	+	0.909172i	$0.636716\pi$
$510$	0.977543	0.0432864
$511$	5.67353	0.250982
$512$	1.00000	0.0441942
$513$	−29.0201	−1.28127
$514$	−20.8650	−0.920315
$515$	14.8026	0.652282
$516$	8.07087	0.355300
$517$	39.8413	1.75222
$518$	−0.614181	−0.0269856
$519$	23.0974	1.01386
$520$	−1.38044	−0.0605362
$521$	−12.0647	−0.528564	−0.264282	−	0.964445i	$-0.585135\pi$
$521$	−12.0647	−0.528564	−0.264282	+	0.964445i	$0.585135\pi$
$522$	0.933301	0.0408495
$523$	18.8957	0.826252	0.413126	−	0.910674i	$-0.364437\pi$
$523$	18.8957	0.826252	0.413126	+	0.910674i	$0.364437\pi$
$524$	−4.24464	−0.185428
$525$	1.03837	0.0453183
$526$	0.553402	0.0241295
$527$	−5.21670	−0.227243
$528$	6.36636	0.277060
$529$	4.31220	0.187487
$530$	1.65970	0.0720929
$531$	−0.507569	−0.0220266
$532$	3.39165	0.147047
$533$	−13.1093	−0.567829
$534$	−28.9272	−1.25180
$535$	0.432210	0.0186861
$536$	3.24215	0.140040
$537$	−29.1646	−1.25854
$538$	7.20698	0.310715
$539$	−23.2612	−1.00193
$540$	4.86173	0.209215
$541$	16.8115	0.722781	0.361390	−	0.932415i	$-0.382302\pi$
$541$	16.8115	0.722781	0.361390	+	0.932415i	$0.382302\pi$
$542$	−14.6893	−0.630959
$543$	0.560394	0.0240488
$544$	−0.534917	−0.0229344
$545$	14.7843	0.633292
$546$	1.43341	0.0613442
$547$	−9.87705	−0.422312	−0.211156	−	0.977452i	$-0.567723\pi$
$547$	−9.87705	−0.422312	−0.211156	+	0.977452i	$0.567723\pi$
$548$	−18.9552	−0.809724
$549$	1.69321	0.0722645
$550$	3.48371	0.148546
$551$	16.4027	0.698780
$552$	−9.55054	−0.406498
$553$	2.42573	0.103153
$554$	6.66485	0.283162
$555$	1.97534	0.0838486
$556$	13.8314	0.586581
$557$	−12.8699	−0.545313	−0.272657	−	0.962111i	$-0.587902\pi$
$557$	−12.8699	−0.545313	−0.272657	+	0.962111i	$0.587902\pi$
$558$	3.31224	0.140218
$559$	6.09660	0.257859
$560$	−0.568203	−0.0240110
$561$	−3.40548	−0.143779
$562$	−22.0697	−0.930956
$563$	9.55686	0.402774	0.201387	−	0.979512i	$-0.435455\pi$
$563$	9.55686	0.402774	0.201387	+	0.979512i	$0.435455\pi$
$564$	20.8998	0.880039
$565$	−8.84410	−0.372074
$566$	26.3654	1.10822
$567$	−5.62723	−0.236322
$568$	−3.81618	−0.160124
$569$	0.0479434	0.00200989	0.00100495	−	0.999999i	$-0.499680\pi$
$569$	0.0479434	0.00200989	0.00100495	+	0.999999i	$0.499680\pi$
$570$	−10.9083	−0.456898
$571$	7.42917	0.310901	0.155451	−	0.987844i	$-0.450317\pi$
$571$	7.42917	0.310901	0.155451	+	0.987844i	$0.450317\pi$
$572$	4.80904	0.201076
$573$	27.8931	1.16525
$574$	−5.39595	−0.225223
$575$	−5.22611	−0.217944
$576$	0.339635	0.0141515
$577$	−8.52061	−0.354718	−0.177359	−	0.984146i	$-0.556755\pi$
$577$	−8.52061	−0.354718	−0.177359	+	0.984146i	$0.556755\pi$
$578$	−16.7139	−0.695205
$579$	2.74498	0.114078
$580$	−2.74795	−0.114102
$581$	8.79035	0.364685
$582$	23.7795	0.985692
$583$	−5.78192	−0.239463
$584$	9.98503	0.413184
$585$	−0.468845	−0.0193844
$586$	−13.1601	−0.543640
$587$	−6.96305	−0.287396	−0.143698	−	0.989622i	$-0.545899\pi$
$587$	−6.96305	−0.287396	−0.143698	+	0.989622i	$0.545899\pi$
$588$	−12.2023	−0.503213
$589$	58.2126	2.39861
$590$	1.49445	0.0615257
$591$	−35.8436	−1.47441
$592$	−1.08092	−0.0444255
$593$	23.9827	0.984853	0.492427	−	0.870354i	$-0.336110\pi$
$593$	23.9827	0.984853	0.492427	+	0.870354i	$0.336110\pi$
$594$	−16.9368	−0.694927
$595$	0.303942	0.0124604
$596$	0.987255	0.0404395
$597$	−0.218112	−0.00892672
$598$	−7.21431	−0.295015
$599$	34.5115	1.41010	0.705051	−	0.709156i	$-0.250924\pi$
$599$	34.5115	1.41010	0.705051	+	0.709156i	$0.250924\pi$
$600$	1.82747	0.0746060
$601$	−29.5871	−1.20688	−0.603441	−	0.797407i	$-0.706204\pi$
$601$	−29.5871	−1.20688	−0.603441	+	0.797407i	$0.706204\pi$
$602$	2.50943	0.102277
$603$	1.10115	0.0448422
$604$	21.1989	0.862573
$605$	−1.13623	−0.0461942
$606$	8.11976	0.329843
$607$	−8.85352	−0.359353	−0.179677	−	0.983726i	$-0.557505\pi$
$607$	−8.85352	−0.359353	−0.179677	+	0.983726i	$0.557505\pi$
$608$	5.96908	0.242078
$609$	2.85340	0.115625
$610$	−4.98538	−0.201852
$611$	15.7873	0.638686
$612$	−0.181677	−0.00734385
$613$	20.2738	0.818853	0.409427	−	0.912343i	$-0.365729\pi$
$613$	20.2738	0.818853	0.409427	+	0.912343i	$0.365729\pi$
$614$	−1.80373	−0.0727927
$615$	17.3546	0.699804
$616$	1.97945	0.0797545
$617$	−31.1476	−1.25395	−0.626977	−	0.779037i	$-0.715708\pi$
$617$	−31.1476	−1.25395	−0.626977	+	0.779037i	$0.715708\pi$
$618$	−27.0513	−1.08816
$619$	8.02425	0.322522	0.161261	−	0.986912i	$-0.448444\pi$
$619$	8.02425	0.322522	0.161261	+	0.986912i	$0.448444\pi$
$620$	−9.75235	−0.391664
$621$	25.4079	1.01958
$622$	32.1337	1.28844
$623$	−8.99417	−0.360344
$624$	2.52270	0.100989
$625$	1.00000	0.0400000
$626$	−30.6118	−1.22349
$627$	38.0013	1.51763
$628$	5.98459	0.238811
$629$	0.578202	0.0230544
$630$	−0.192982	−0.00768858
$631$	−13.7742	−0.548342	−0.274171	−	0.961681i	$-0.588403\pi$
$631$	−13.7742	−0.548342	−0.274171	+	0.961681i	$0.588403\pi$
$632$	4.26913	0.169817
$633$	33.0928	1.31532
$634$	27.1057	1.07651
$635$	4.26145	0.169110
$636$	−3.03305	−0.120268
$637$	−9.21738	−0.365206
$638$	9.57306	0.379001
$639$	−1.29611	−0.0512733
$640$	−1.00000	−0.0395285
$641$	−5.87919	−0.232214	−0.116107	−	0.993237i	$-0.537042\pi$
$641$	−5.87919	−0.232214	−0.116107	+	0.993237i	$0.537042\pi$
$642$	−0.789849	−0.0311728
$643$	−13.2102	−0.520958	−0.260479	−	0.965479i	$-0.583881\pi$
$643$	−13.2102	−0.520958	−0.260479	+	0.965479i	$0.583881\pi$
$644$	−2.96949	−0.117014
$645$	−8.07087	−0.317790
$646$	−3.19296	−0.125626
$647$	−25.7937	−1.01406	−0.507028	−	0.861929i	$-0.669256\pi$
$647$	−25.7937	−1.01406	−0.507028	+	0.861929i	$0.669256\pi$
$648$	−9.90355	−0.389048
$649$	−5.20624	−0.204363
$650$	1.38044	0.0541452
$651$	10.1266	0.396892
$652$	8.85585	0.346822
$653$	4.57893	0.179188	0.0895938	−	0.995978i	$-0.471443\pi$
$653$	4.57893	0.179188	0.0895938	+	0.995978i	$0.471443\pi$
$654$	−27.0179	−1.05648
$655$	4.24464	0.165852
$656$	−9.49652	−0.370777
$657$	3.39127	0.132306
$658$	6.49824	0.253328
$659$	−45.8882	−1.78755	−0.893774	−	0.448517i	$-0.851952\pi$
$659$	−45.8882	−1.78755	−0.893774	+	0.448517i	$0.851952\pi$
$660$	−6.36636	−0.247810
$661$	48.8225	1.89897	0.949487	−	0.313807i	$-0.101604\pi$
$661$	48.8225	1.89897	0.949487	+	0.313807i	$0.101604\pi$
$662$	−2.63733	−0.102503
$663$	−1.34944	−0.0524078
$664$	15.4704	0.600369
$665$	−3.39165	−0.131523
$666$	−0.367118	−0.0142255
$667$	−14.3611	−0.556063
$668$	−2.25867	−0.0873907
$669$	−38.1929	−1.47662
$670$	−3.24215	−0.125255
$671$	17.3676	0.670469
$672$	1.03837	0.0400561
$673$	22.8840	0.882115	0.441058	−	0.897479i	$-0.354603\pi$
$673$	22.8840	0.882115	0.441058	+	0.897479i	$0.354603\pi$
$674$	10.7145	0.412706
$675$	−4.86173	−0.187128
$676$	−11.0944	−0.426707
$677$	−24.4069	−0.938033	−0.469017	−	0.883189i	$-0.655392\pi$
$677$	−24.4069	−0.938033	−0.469017	+	0.883189i	$0.655392\pi$
$678$	16.1623	0.620709
$679$	7.39361	0.283741
$680$	0.534917	0.0205131
$681$	14.2835	0.547344
$682$	33.9743	1.30094
$683$	−35.5217	−1.35920	−0.679600	−	0.733583i	$-0.737847\pi$
$683$	−35.5217	−1.35920	−0.679600	+	0.733583i	$0.737847\pi$
$684$	2.02731	0.0775162
$685$	18.9552	0.724239
$686$	−7.77140	−0.296713
$687$	−27.0626	−1.03250
$688$	4.41643	0.168375
$689$	−2.29112	−0.0872846
$690$	9.55054	0.363583
$691$	33.7237	1.28291	0.641455	−	0.767161i	$-0.278331\pi$
$691$	33.7237	1.28291	0.641455	+	0.767161i	$0.278331\pi$
$692$	12.6390	0.480463
$693$	0.672293	0.0255383
$694$	−3.38748	−0.128587
$695$	−13.8314	−0.524654
$696$	5.02179	0.190350
$697$	5.07985	0.192413
$698$	−27.2027	−1.02964
$699$	−38.2128	−1.44534
$700$	0.568203	0.0214761
$701$	14.6282	0.552501	0.276250	−	0.961086i	$-0.410908\pi$
$701$	14.6282	0.552501	0.276250	+	0.961086i	$0.410908\pi$
$702$	−6.71131	−0.253302
$703$	−6.45209	−0.243345
$704$	3.48371	0.131297
$705$	−20.8998	−0.787130
$706$	−17.3827	−0.654207
$707$	2.52463	0.0949485
$708$	−2.73107	−0.102640
$709$	49.9485	1.87586	0.937928	−	0.346831i	$-0.112742\pi$
$709$	49.9485	1.87586	0.937928	+	0.346831i	$0.112742\pi$
$710$	3.81618	0.143219
$711$	1.44995	0.0543772
$712$	−15.8291	−0.593222
$713$	−50.9668	−1.90872
$714$	−0.555443	−0.0207869
$715$	−4.80904	−0.179848
$716$	−15.9590	−0.596417
$717$	3.21498	0.120066
$718$	2.11898	0.0790795
$719$	−18.2270	−0.679754	−0.339877	−	0.940470i	$-0.610385\pi$
$719$	−18.2270	−0.679754	−0.339877	+	0.940470i	$0.610385\pi$
$720$	−0.339635	−0.0126575
$721$	−8.41091	−0.313239
$722$	16.6299	0.618902
$723$	−35.5766	−1.32311
$724$	0.306651	0.0113966
$725$	2.74795	0.102056
$726$	2.07642	0.0770631
$727$	28.6329	1.06194	0.530968	−	0.847392i	$-0.321828\pi$
$727$	28.6329	1.06194	0.530968	+	0.847392i	$0.321828\pi$
$728$	0.784369	0.0290706
$729$	23.2903	0.862605
$730$	−9.98503	−0.369563
$731$	−2.36242	−0.0873774
$732$	9.11062	0.336738
$733$	18.4551	0.681655	0.340827	−	0.940126i	$-0.389293\pi$
$733$	18.4551	0.681655	0.340827	+	0.940126i	$0.389293\pi$
$734$	5.02288	0.185398
$735$	12.2023	0.450087
$736$	−5.22611	−0.192637
$737$	11.2947	0.416046
$738$	−3.22535	−0.118727
$739$	38.0415	1.39938	0.699690	−	0.714447i	$-0.253322\pi$
$739$	38.0415	1.39938	0.699690	+	0.714447i	$0.253322\pi$
$740$	1.08092	0.0397354
$741$	15.0582	0.553178
$742$	−0.943049	−0.0346204
$743$	−1.20783	−0.0443110	−0.0221555	−	0.999755i	$-0.507053\pi$
$743$	−1.20783	−0.0443110	−0.0221555	+	0.999755i	$0.507053\pi$
$744$	17.8221	0.653390
$745$	−0.987255	−0.0361702
$746$	0.879927	0.0322164
$747$	5.25430	0.192245
$748$	−1.86350	−0.0681362
$749$	−0.245583	−0.00897341
$750$	−1.82747	−0.0667297
$751$	8.05005	0.293750	0.146875	−	0.989155i	$-0.453078\pi$
$751$	8.05005	0.293750	0.146875	+	0.989155i	$0.453078\pi$
$752$	11.4365	0.417045
$753$	−38.5625	−1.40530
$754$	3.79337	0.138146
$755$	−21.1989	−0.771509
$756$	−2.76245	−0.100469
$757$	46.1471	1.67724	0.838622	−	0.544713i	$-0.183362\pi$
$757$	46.1471	1.67724	0.838622	+	0.544713i	$0.183362\pi$
$758$	−34.4044	−1.24963
$759$	−33.2713	−1.20767
$760$	−5.96908	−0.216521
$761$	−37.7475	−1.36835	−0.684174	−	0.729319i	$-0.739837\pi$
$761$	−37.7475	−1.36835	−0.684174	+	0.729319i	$0.739837\pi$
$762$	−7.78765	−0.282117
$763$	−8.40051	−0.304119
$764$	15.2633	0.552206
$765$	0.181677	0.00656854
$766$	−3.69011	−0.133329
$767$	−2.06300	−0.0744906
$768$	1.82747	0.0659430
$769$	−45.7899	−1.65123	−0.825613	−	0.564236i	$-0.809171\pi$
$769$	−45.7899	−1.65123	−0.825613	+	0.564236i	$0.809171\pi$
$770$	−1.97945	−0.0713346
$771$	−38.1301	−1.37322
$772$	1.50207	0.0540607
$773$	41.4975	1.49256	0.746280	−	0.665632i	$-0.231838\pi$
$773$	41.4975	1.49256	0.746280	+	0.665632i	$0.231838\pi$
$774$	1.49997	0.0539155
$775$	9.75235	0.350315
$776$	13.0123	0.467113
$777$	−1.12240	−0.0402657
$778$	−0.983802	−0.0352710
$779$	−56.6855	−2.03097
$780$	−2.52270	−0.0903272
$781$	−13.2945	−0.475714
$782$	2.79553	0.0999681
$783$	−13.3598	−0.477440
$784$	−6.67715	−0.238469
$785$	−5.98459	−0.213599
$786$	−7.75694	−0.276681
$787$	−4.45817	−0.158917	−0.0794583	−	0.996838i	$-0.525319\pi$
$787$	−4.45817	−0.158917	−0.0794583	+	0.996838i	$0.525319\pi$
$788$	−19.6138	−0.698713
$789$	1.01132	0.0360041
$790$	−4.26913	−0.151889
$791$	5.02525	0.178677
$792$	1.18319	0.0420428
$793$	6.88200	0.244387
$794$	−21.8429	−0.775177
$795$	3.03305	0.107571
$796$	−0.119352	−0.00423032
$797$	−4.28833	−0.151900	−0.0759502	−	0.997112i	$-0.524199\pi$
$797$	−4.28833	−0.151900	−0.0759502	+	0.997112i	$0.524199\pi$
$798$	6.19813	0.219411
$799$	−6.11756	−0.216424
$800$	1.00000	0.0353553
$801$	−5.37613	−0.189956
$802$	−1.00000	−0.0353112
$803$	34.7850	1.22753
$804$	5.92492	0.208956
$805$	2.96949	0.104661
$806$	13.4625	0.474196
$807$	13.1705	0.463624
$808$	4.44318	0.156311
$809$	−23.8128	−0.837214	−0.418607	−	0.908168i	$-0.637482\pi$
$809$	−23.8128	−0.837214	−0.418607	+	0.908168i	$0.637482\pi$
$810$	9.90355	0.347975
$811$	28.0656	0.985516	0.492758	−	0.870166i	$-0.335989\pi$
$811$	28.0656	0.985516	0.492758	+	0.870166i	$0.335989\pi$
$812$	1.56139	0.0547942
$813$	−26.8442	−0.941467
$814$	−3.76560	−0.131984
$815$	−8.85585	−0.310207
$816$	−0.977543	−0.0342209
$817$	26.3620	0.922290
$818$	−12.3785	−0.432803
$819$	0.266399	0.00930874
$820$	9.49652	0.331633
$821$	46.8785	1.63607	0.818035	−	0.575168i	$-0.195063\pi$
$821$	46.8785	1.63607	0.818035	+	0.575168i	$0.195063\pi$
$822$	−34.6399	−1.20821
$823$	−45.6564	−1.59148	−0.795741	−	0.605637i	$-0.792918\pi$
$823$	−45.6564	−1.59148	−0.795741	+	0.605637i	$0.792918\pi$
$824$	−14.8026	−0.515674
$825$	6.36636	0.221648
$826$	−0.849154	−0.0295458
$827$	−20.3628	−0.708082	−0.354041	−	0.935230i	$-0.615193\pi$
$827$	−20.3628	−0.708082	−0.354041	+	0.935230i	$0.615193\pi$
$828$	−1.77497	−0.0616845
$829$	−16.8236	−0.584307	−0.292154	−	0.956371i	$-0.594372\pi$
$829$	−16.8236	−0.584307	−0.292154	+	0.956371i	$0.594372\pi$
$830$	−15.4704	−0.536987
$831$	12.1798	0.422512
$832$	1.38044	0.0478580
$833$	3.57172	0.123753
$834$	25.2764	0.875249
$835$	2.25867	0.0781646
$836$	20.7945	0.719194
$837$	−47.4133	−1.63884
$838$	−27.9664	−0.966084
$839$	−49.3226	−1.70281	−0.851403	−	0.524512i	$-0.824248\pi$
$839$	−49.3226	−1.70281	−0.851403	+	0.524512i	$0.824248\pi$
$840$	−1.03837	−0.0358273
$841$	−21.4488	−0.739613
$842$	−31.5787	−1.08827
$843$	−40.3317	−1.38910
$844$	18.1086	0.623322
$845$	11.0944	0.381659
$846$	3.88423	0.133542
$847$	0.645608	0.0221834
$848$	−1.65970	−0.0569945
$849$	48.1819	1.65360
$850$	−0.534917	−0.0183475
$851$	5.64900	0.193645
$852$	−6.97395	−0.238924
$853$	11.2232	0.384275	0.192138	−	0.981368i	$-0.438458\pi$
$853$	11.2232	0.384275	0.192138	+	0.981368i	$0.438458\pi$
$854$	2.83271	0.0969333
$855$	−2.02731	−0.0693326
$856$	−0.432210	−0.0147726
$857$	47.9924	1.63939	0.819694	−	0.572802i	$-0.194144\pi$
$857$	47.9924	1.63939	0.819694	+	0.572802i	$0.194144\pi$
$858$	8.78836	0.300030
$859$	3.59863	0.122784	0.0613919	−	0.998114i	$-0.480446\pi$
$859$	3.59863	0.122784	0.0613919	+	0.998114i	$0.480446\pi$
$860$	−4.41643	−0.150599
$861$	−9.86093	−0.336060
$862$	−4.19263	−0.142802
$863$	35.4751	1.20759	0.603793	−	0.797141i	$-0.293655\pi$
$863$	35.4751	1.20759	0.603793	+	0.797141i	$0.293655\pi$
$864$	−4.86173	−0.165399
$865$	−12.6390	−0.429739
$866$	8.16858	0.277580
$867$	−30.5440	−1.03733
$868$	5.54132	0.188085
$869$	14.8724	0.504512
$870$	−5.02179	−0.170255
$871$	4.47558	0.151649
$872$	−14.7843	−0.500661
$873$	4.41942	0.149575
$874$	−31.1951	−1.05519
$875$	−0.568203	−0.0192088
$876$	18.2473	0.616520
$877$	15.1194	0.510547	0.255274	−	0.966869i	$-0.417834\pi$
$877$	15.1194	0.510547	0.255274	+	0.966869i	$0.417834\pi$
$878$	0.494320	0.0166825
$879$	−24.0497	−0.811176
$880$	−3.48371	−0.117436
$881$	−21.5543	−0.726182	−0.363091	−	0.931754i	$-0.618279\pi$
$881$	−21.5543	−0.726182	−0.363091	+	0.931754i	$0.618279\pi$
$882$	−2.26779	−0.0763606
$883$	56.1282	1.88886	0.944432	−	0.328708i	$-0.106613\pi$
$883$	56.1282	1.88886	0.944432	+	0.328708i	$0.106613\pi$
$884$	−0.738419	−0.0248357
$885$	2.73107	0.0918038
$886$	29.2202	0.981672
$887$	44.4397	1.49214	0.746070	−	0.665867i	$-0.231938\pi$
$887$	44.4397	1.49214	0.746070	+	0.665867i	$0.231938\pi$
$888$	−1.97534	−0.0662882
$889$	−2.42137	−0.0812101
$890$	15.8291	0.530594
$891$	−34.5011	−1.15583
$892$	−20.8994	−0.699763
$893$	68.2652	2.28441
$894$	1.80418	0.0603407
$895$	15.9590	0.533451
$896$	0.568203	0.0189823
$897$	−13.1839	−0.440198
$898$	−21.3335	−0.711909
$899$	26.7990	0.893796
$900$	0.339635	0.0113212
$901$	0.887804	0.0295770
$902$	−33.0831	−1.10155
$903$	4.58590	0.152609
$904$	8.84410	0.294150
$905$	−0.306651	−0.0101934
$906$	38.7404	1.28706
$907$	−2.19669	−0.0729398	−0.0364699	−	0.999335i	$-0.511611\pi$
$907$	−2.19669	−0.0729398	−0.0364699	+	0.999335i	$0.511611\pi$
$908$	7.81599	0.259383
$909$	1.50906	0.0500524
$910$	−0.784369	−0.0260016
$911$	32.1784	1.06612	0.533059	−	0.846078i	$-0.321042\pi$
$911$	32.1784	1.06612	0.533059	+	0.846078i	$0.321042\pi$
$912$	10.9083	0.361210
$913$	53.8945	1.78365
$914$	−14.4466	−0.477850
$915$	−9.11062	−0.301188
$916$	−14.8088	−0.489297
$917$	−2.41182	−0.0796453
$918$	2.60062	0.0858333
$919$	12.4922	0.412078	0.206039	−	0.978544i	$-0.433943\pi$
$919$	12.4922	0.412078	0.206039	+	0.978544i	$0.433943\pi$
$920$	5.22611	0.172300
$921$	−3.29626	−0.108615
$922$	25.7905	0.849365
$923$	−5.26800	−0.173398
$924$	3.61739	0.119003
$925$	−1.08092	−0.0355404
$926$	−6.02721	−0.198067
$927$	−5.02750	−0.165125
$928$	2.74795	0.0902059
$929$	−46.1489	−1.51410	−0.757048	−	0.653359i	$-0.773359\pi$
$929$	−46.1489	−1.51410	−0.757048	+	0.653359i	$0.773359\pi$
$930$	−17.8221	−0.584409
$931$	−39.8564	−1.30624
$932$	−20.9102	−0.684937
$933$	58.7232	1.92251
$934$	38.4498	1.25811
$935$	1.86350	0.0609428
$936$	0.468845	0.0153247
$937$	−32.5511	−1.06340	−0.531699	−	0.846933i	$-0.678446\pi$
$937$	−32.5511	−1.06340	−0.531699	+	0.846933i	$0.678446\pi$
$938$	1.84220	0.0601500
$939$	−55.9421	−1.82560
$940$	−11.4365	−0.373016
$941$	36.7453	1.19786	0.598932	−	0.800800i	$-0.295592\pi$
$941$	36.7453	1.19786	0.598932	+	0.800800i	$0.295592\pi$
$942$	10.9366	0.356335
$943$	49.6298	1.61617
$944$	−1.49445	−0.0486403
$945$	2.76245	0.0898625
$946$	15.3855	0.500227
$947$	3.92562	0.127566	0.0637828	−	0.997964i	$-0.479684\pi$
$947$	3.92562	0.127566	0.0637828	+	0.997964i	$0.479684\pi$
$948$	7.80169	0.253387
$949$	13.7837	0.447438
$950$	5.96908	0.193663
$951$	49.5348	1.60628
$952$	−0.303942	−0.00985081
$953$	57.4022	1.85944	0.929720	−	0.368268i	$-0.120049\pi$
$953$	57.4022	1.85944	0.929720	+	0.368268i	$0.120049\pi$
$954$	−0.563694	−0.0182503
$955$	−15.2633	−0.493908
$956$	1.75925	0.0568984
$957$	17.4944	0.565515
$958$	2.69596	0.0871026
$959$	−10.7704	−0.347794
$960$	−1.82747	−0.0589812
$961$	64.1083	2.06801
$962$	−1.49214	−0.0481085
$963$	−0.146794	−0.00473036
$964$	−19.4677	−0.627014
$965$	−1.50207	−0.0483534
$966$	−5.42665	−0.174600
$967$	33.9728	1.09249	0.546247	−	0.837624i	$-0.316056\pi$
$967$	33.9728	1.09249	0.546247	+	0.837624i	$0.316056\pi$
$968$	1.13623	0.0365197
$969$	−5.83504	−0.187448
$970$	−13.0123	−0.417799
$971$	30.8263	0.989262	0.494631	−	0.869103i	$-0.335303\pi$
$971$	30.8263	0.989262	0.494631	+	0.869103i	$0.335303\pi$
$972$	−3.51323	−0.112687
$973$	7.85903	0.251949
$974$	−39.1366	−1.25402
$975$	2.52270	0.0807911
$976$	4.98538	0.159578
$977$	−36.7285	−1.17505	−0.587524	−	0.809206i	$-0.699897\pi$
$977$	−36.7285	−1.17505	−0.587524	+	0.809206i	$0.699897\pi$
$978$	16.1838	0.517500
$979$	−55.1441	−1.76241
$980$	6.67715	0.213294
$981$	−5.02128	−0.160317
$982$	−19.0376	−0.607513
$983$	−5.70768	−0.182047	−0.0910234	−	0.995849i	$-0.529014\pi$
$983$	−5.70768	−0.182047	−0.0910234	+	0.995849i	$0.529014\pi$
$984$	−17.3546	−0.553244
$985$	19.6138	0.624948
$986$	−1.46993	−0.0468120
$987$	11.8753	0.377995
$988$	8.23994	0.262147
$989$	−23.0807	−0.733924
$990$	−1.18319	−0.0376043
$991$	−4.00438	−0.127203	−0.0636016	−	0.997975i	$-0.520259\pi$
$991$	−4.00438	−0.127203	−0.0636016	+	0.997975i	$0.520259\pi$
$992$	9.75235	0.309637
$993$	−4.81963	−0.152946
$994$	−2.16837	−0.0687765
$995$	0.119352	0.00378371
$996$	28.2717	0.895823
$997$	−1.70310	−0.0539377	−0.0269688	−	0.999636i	$-0.508585\pi$
$997$	−1.70310	−0.0539377	−0.0269688	+	0.999636i	$0.508585\pi$
$998$	16.8672	0.533922
$999$	5.25513	0.166265

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4010.2.a.o.1.17	✓	22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4010.2.a.o.1.17	✓	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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +1.82747 q^{3} +1.00000 q^{4} -1.00000 q^{5} +1.82747 q^{6} +0.568203 q^{7} +1.00000 q^{8} +0.339635 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +1.82747 q^{3} +1.00000 q^{4} -1.00000 q^{5} +1.82747 q^{6} +0.568203 q^{7} +1.00000 q^{8} +0.339635 q^{9} -1.00000 q^{10} +3.48371 q^{11} +1.82747 q^{12} +1.38044 q^{13} +0.568203 q^{14} -1.82747 q^{15} +1.00000 q^{16} -0.534917 q^{17} +0.339635 q^{18} +5.96908 q^{19} -1.00000 q^{20} +1.03837 q^{21} +3.48371 q^{22} -5.22611 q^{23} +1.82747 q^{24} +1.00000 q^{25} +1.38044 q^{26} -4.86173 q^{27} +0.568203 q^{28} +2.74795 q^{29} -1.82747 q^{30} +9.75235 q^{31} +1.00000 q^{32} +6.36636 q^{33} -0.534917 q^{34} -0.568203 q^{35} +0.339635 q^{36} -1.08092 q^{37} +5.96908 q^{38} +2.52270 q^{39} -1.00000 q^{40} -9.49652 q^{41} +1.03837 q^{42} +4.41643 q^{43} +3.48371 q^{44} -0.339635 q^{45} -5.22611 q^{46} +11.4365 q^{47} +1.82747 q^{48} -6.67715 q^{49} +1.00000 q^{50} -0.977543 q^{51} +1.38044 q^{52} -1.65970 q^{53} -4.86173 q^{54} -3.48371 q^{55} +0.568203 q^{56} +10.9083 q^{57} +2.74795 q^{58} -1.49445 q^{59} -1.82747 q^{60} +4.98538 q^{61} +9.75235 q^{62} +0.192982 q^{63} +1.00000 q^{64} -1.38044 q^{65} +6.36636 q^{66} +3.24215 q^{67} -0.534917 q^{68} -9.55054 q^{69} -0.568203 q^{70} -3.81618 q^{71} +0.339635 q^{72} +9.98503 q^{73} -1.08092 q^{74} +1.82747 q^{75} +5.96908 q^{76} +1.97945 q^{77} +2.52270 q^{78} +4.26913 q^{79} -1.00000 q^{80} -9.90355 q^{81} -9.49652 q^{82} +15.4704 q^{83} +1.03837 q^{84} +0.534917 q^{85} +4.41643 q^{86} +5.02179 q^{87} +3.48371 q^{88} -15.8291 q^{89} -0.339635 q^{90} +0.784369 q^{91} -5.22611 q^{92} +17.8221 q^{93} +11.4365 q^{94} -5.96908 q^{95} +1.82747 q^{96} +13.0123 q^{97} -6.67715 q^{98} +1.18319 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q + 22 q^{2} + 2 q^{3} + 22 q^{4} - 22 q^{5} + 2 q^{6} + 13 q^{7} + 22 q^{8} + 32 q^{9}+O(q^{10}) \) 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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