LMFDB - Embedded newform 4010.2.a.o.1.1

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			1.1
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)

$f(q)$	$=$	$q+1.00000 q^{2} -3.30817 q^{3} +1.00000 q^{4} -1.00000 q^{5} -3.30817 q^{6} -2.76226 q^{7} +1.00000 q^{8} +7.94397 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -3.30817 q^{3} +1.00000 q^{4} -1.00000 q^{5} -3.30817 q^{6} -2.76226 q^{7} +1.00000 q^{8} +7.94397 q^{9} -1.00000 q^{10} -3.54494 q^{11} -3.30817 q^{12} -1.81671 q^{13} -2.76226 q^{14} +3.30817 q^{15} +1.00000 q^{16} +7.78402 q^{17} +7.94397 q^{18} -2.92310 q^{19} -1.00000 q^{20} +9.13803 q^{21} -3.54494 q^{22} -0.550681 q^{23} -3.30817 q^{24} +1.00000 q^{25} -1.81671 q^{26} -16.3555 q^{27} -2.76226 q^{28} -10.1730 q^{29} +3.30817 q^{30} -10.0286 q^{31} +1.00000 q^{32} +11.7273 q^{33} +7.78402 q^{34} +2.76226 q^{35} +7.94397 q^{36} +7.71692 q^{37} -2.92310 q^{38} +6.00999 q^{39} -1.00000 q^{40} -8.13968 q^{41} +9.13803 q^{42} -10.5765 q^{43} -3.54494 q^{44} -7.94397 q^{45} -0.550681 q^{46} +3.37747 q^{47} -3.30817 q^{48} +0.630104 q^{49} +1.00000 q^{50} -25.7508 q^{51} -1.81671 q^{52} +1.35304 q^{53} -16.3555 q^{54} +3.54494 q^{55} -2.76226 q^{56} +9.67009 q^{57} -10.1730 q^{58} +4.40247 q^{59} +3.30817 q^{60} +8.84144 q^{61} -10.0286 q^{62} -21.9434 q^{63} +1.00000 q^{64} +1.81671 q^{65} +11.7273 q^{66} +11.7566 q^{67} +7.78402 q^{68} +1.82174 q^{69} +2.76226 q^{70} +3.98572 q^{71} +7.94397 q^{72} -10.1599 q^{73} +7.71692 q^{74} -3.30817 q^{75} -2.92310 q^{76} +9.79206 q^{77} +6.00999 q^{78} +0.773121 q^{79} -1.00000 q^{80} +30.2748 q^{81} -8.13968 q^{82} -15.7131 q^{83} +9.13803 q^{84} -7.78402 q^{85} -10.5765 q^{86} +33.6539 q^{87} -3.54494 q^{88} +12.9946 q^{89} -7.94397 q^{90} +5.01824 q^{91} -0.550681 q^{92} +33.1762 q^{93} +3.37747 q^{94} +2.92310 q^{95} -3.30817 q^{96} -9.04093 q^{97} +0.630104 q^{98} -28.1609 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	−3.30817	−1.90997	−0.954986	−	0.296651i	$-0.904130\pi$
$3$	−3.30817	−1.90997	−0.954986	+	0.296651i	$0.904130\pi$
$4$	1.00000	0.500000
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	−3.30817	−1.35055
$7$	−2.76226	−1.04404	−0.522019	−	0.852934i	$-0.674821\pi$
$7$	−2.76226	−1.04404	−0.522019	+	0.852934i	$0.674821\pi$
$8$	1.00000	0.353553
$9$	7.94397	2.64799
$10$	−1.00000	−0.316228
$11$	−3.54494	−1.06884	−0.534420	−	0.845219i	$-0.679470\pi$
$11$	−3.54494	−1.06884	−0.534420	+	0.845219i	$0.679470\pi$
$12$	−3.30817	−0.954986
$13$	−1.81671	−0.503866	−0.251933	−	0.967745i	$-0.581066\pi$
$13$	−1.81671	−0.503866	−0.251933	+	0.967745i	$0.581066\pi$
$14$	−2.76226	−0.738246
$15$	3.30817	0.854165
$16$	1.00000	0.250000
$17$	7.78402	1.88790	0.943951	−	0.330086i	$-0.107078\pi$
$17$	7.78402	1.88790	0.943951	+	0.330086i	$0.107078\pi$
$18$	7.94397	1.87241
$19$	−2.92310	−0.670604	−0.335302	−	0.942111i	$-0.608838\pi$
$19$	−2.92310	−0.670604	−0.335302	+	0.942111i	$0.608838\pi$
$20$	−1.00000	−0.223607
$21$	9.13803	1.99408
$22$	−3.54494	−0.755784
$23$	−0.550681	−0.114825	−0.0574124	−	0.998351i	$-0.518285\pi$
$23$	−0.550681	−0.114825	−0.0574124	+	0.998351i	$0.518285\pi$
$24$	−3.30817	−0.675277
$25$	1.00000	0.200000
$26$	−1.81671	−0.356287
$27$	−16.3555	−3.14762
$28$	−2.76226	−0.522019
$29$	−10.1730	−1.88908	−0.944538	−	0.328402i	$-0.893490\pi$
$29$	−10.1730	−1.88908	−0.944538	+	0.328402i	$0.893490\pi$
$30$	3.30817	0.603986
$31$	−10.0286	−1.80118	−0.900592	−	0.434665i	$-0.856867\pi$
$31$	−10.0286	−1.80118	−0.900592	+	0.434665i	$0.856867\pi$
$32$	1.00000	0.176777
$33$	11.7273	2.04145
$34$	7.78402	1.33495
$35$	2.76226	0.466908
$36$	7.94397	1.32400
$37$	7.71692	1.26865	0.634327	−	0.773065i	$-0.281277\pi$
$37$	7.71692	1.26865	0.634327	+	0.773065i	$0.281277\pi$
$38$	−2.92310	−0.474189
$39$	6.00999	0.962369
$40$	−1.00000	−0.158114
$41$	−8.13968	−1.27120	−0.635602	−	0.772017i	$-0.719248\pi$
$41$	−8.13968	−1.27120	−0.635602	+	0.772017i	$0.719248\pi$
$42$	9.13803	1.41003
$43$	−10.5765	−1.61291	−0.806453	−	0.591298i	$-0.798616\pi$
$43$	−10.5765	−1.61291	−0.806453	+	0.591298i	$0.798616\pi$
$44$	−3.54494	−0.534420
$45$	−7.94397	−1.18422
$46$	−0.550681	−0.0811934
$47$	3.37747	0.492655	0.246327	−	0.969187i	$-0.420776\pi$
$47$	3.37747	0.492655	0.246327	+	0.969187i	$0.420776\pi$
$48$	−3.30817	−0.477493
$49$	0.630104	0.0900148
$50$	1.00000	0.141421
$51$	−25.7508	−3.60584
$52$	−1.81671	−0.251933
$53$	1.35304	0.185854	0.0929272	−	0.995673i	$-0.470378\pi$
$53$	1.35304	0.185854	0.0929272	+	0.995673i	$0.470378\pi$
$54$	−16.3555	−2.22570
$55$	3.54494	0.478000
$56$	−2.76226	−0.369123
$57$	9.67009	1.28084
$58$	−10.1730	−1.33578
$59$	4.40247	0.573153	0.286576	−	0.958057i	$-0.407483\pi$
$59$	4.40247	0.573153	0.286576	+	0.958057i	$0.407483\pi$
$60$	3.30817	0.427083
$61$	8.84144	1.13203	0.566015	−	0.824395i	$-0.308484\pi$
$61$	8.84144	1.13203	0.566015	+	0.824395i	$0.308484\pi$
$62$	−10.0286	−1.27363
$63$	−21.9434	−2.76460
$64$	1.00000	0.125000
$65$	1.81671	0.225336
$66$	11.7273	1.44353
$67$	11.7566	1.43629	0.718146	−	0.695892i	$-0.244991\pi$
$67$	11.7566	1.43629	0.718146	+	0.695892i	$0.244991\pi$
$68$	7.78402	0.943951
$69$	1.82174	0.219312
$70$	2.76226	0.330154
$71$	3.98572	0.473017	0.236509	−	0.971629i	$-0.423997\pi$
$71$	3.98572	0.473017	0.236509	+	0.971629i	$0.423997\pi$
$72$	7.94397	0.936206
$73$	−10.1599	−1.18913	−0.594563	−	0.804049i	$-0.702675\pi$
$73$	−10.1599	−1.18913	−0.594563	+	0.804049i	$0.702675\pi$
$74$	7.71692	0.897073
$75$	−3.30817	−0.381994
$76$	−2.92310	−0.335302
$77$	9.79206	1.11591
$78$	6.00999	0.680498
$79$	0.773121	0.0869829	0.0434915	−	0.999054i	$-0.486152\pi$
$79$	0.773121	0.0869829	0.0434915	+	0.999054i	$0.486152\pi$
$80$	−1.00000	−0.111803
$81$	30.2748	3.36387
$82$	−8.13968	−0.898877
$83$	−15.7131	−1.72474	−0.862369	−	0.506281i	$-0.831020\pi$
$83$	−15.7131	−1.72474	−0.862369	+	0.506281i	$0.831020\pi$
$84$	9.13803	0.997041
$85$	−7.78402	−0.844295
$86$	−10.5765	−1.14050
$87$	33.6539	3.60808
$88$	−3.54494	−0.377892
$89$	12.9946	1.37743	0.688714	−	0.725033i	$-0.258175\pi$
$89$	12.9946	1.37743	0.688714	+	0.725033i	$0.258175\pi$
$90$	−7.94397	−0.837368
$91$	5.01824	0.526055
$92$	−0.550681	−0.0574124
$93$	33.1762	3.44021
$94$	3.37747	0.348359
$95$	2.92310	0.299903
$96$	−3.30817	−0.337638
$97$	−9.04093	−0.917968	−0.458984	−	0.888445i	$-0.651786\pi$
$97$	−9.04093	−0.917968	−0.458984	+	0.888445i	$0.651786\pi$
$98$	0.630104	0.0636501
$99$	−28.1609	−2.83028
$100$	1.00000	0.100000
$101$	−7.96420	−0.792468	−0.396234	−	0.918150i	$-0.629683\pi$
$101$	−7.96420	−0.792468	−0.396234	+	0.918150i	$0.629683\pi$
$102$	−25.7508	−2.54971
$103$	5.22893	0.515222	0.257611	−	0.966249i	$-0.417065\pi$
$103$	5.22893	0.515222	0.257611	+	0.966249i	$0.417065\pi$
$104$	−1.81671	−0.178143
$105$	−9.13803	−0.891781
$106$	1.35304	0.131419
$107$	10.2812	0.993917	0.496959	−	0.867774i	$-0.334450\pi$
$107$	10.2812	0.993917	0.496959	+	0.867774i	$0.334450\pi$
$108$	−16.3555	−1.57381
$109$	−2.94698	−0.282270	−0.141135	−	0.989990i	$-0.545075\pi$
$109$	−2.94698	−0.282270	−0.141135	+	0.989990i	$0.545075\pi$
$110$	3.54494	0.337997
$111$	−25.5289	−2.42309
$112$	−2.76226	−0.261009
$113$	9.68359	0.910956	0.455478	−	0.890247i	$-0.349468\pi$
$113$	9.68359	0.910956	0.455478	+	0.890247i	$0.349468\pi$
$114$	9.67009	0.905687
$115$	0.550681	0.0513512
$116$	−10.1730	−0.944538
$117$	−14.4319	−1.33423
$118$	4.40247	0.405280
$119$	−21.5015	−1.97104
$120$	3.30817	0.301993
$121$	1.56660	0.142418
$122$	8.84144	0.800466
$123$	26.9274	2.42796
$124$	−10.0286	−0.900592
$125$	−1.00000	−0.0894427
$126$	−21.9434	−1.95487
$127$	12.5804	1.11633	0.558164	−	0.829731i	$-0.311506\pi$
$127$	12.5804	1.11633	0.558164	+	0.829731i	$0.311506\pi$
$128$	1.00000	0.0883883
$129$	34.9889	3.08060
$130$	1.81671	0.159336
$131$	6.42265	0.561150	0.280575	−	0.959832i	$-0.409475\pi$
$131$	6.42265	0.561150	0.280575	+	0.959832i	$0.409475\pi$
$132$	11.7273	1.02073
$133$	8.07436	0.700136
$134$	11.7566	1.01561
$135$	16.3555	1.40766
$136$	7.78402	0.667474
$137$	17.7410	1.51572	0.757859	−	0.652418i	$-0.226245\pi$
$137$	17.7410	1.51572	0.757859	+	0.652418i	$0.226245\pi$
$138$	1.82174	0.155077
$139$	18.3177	1.55369	0.776844	−	0.629693i	$-0.216819\pi$
$139$	18.3177	1.55369	0.776844	+	0.629693i	$0.216819\pi$
$140$	2.76226	0.233454
$141$	−11.1732	−0.940957
$142$	3.98572	0.334474
$143$	6.44014	0.538552
$144$	7.94397	0.661998
$145$	10.1730	0.844821
$146$	−10.1599	−0.840839
$147$	−2.08449	−0.171926
$148$	7.71692	0.634327
$149$	−0.317429	−0.0260048	−0.0130024	−	0.999915i	$-0.504139\pi$
$149$	−0.317429	−0.0260048	−0.0130024	+	0.999915i	$0.504139\pi$
$150$	−3.30817	−0.270111
$151$	8.20859	0.668006	0.334003	−	0.942572i	$-0.391600\pi$
$151$	8.20859	0.668006	0.334003	+	0.942572i	$0.391600\pi$
$152$	−2.92310	−0.237094
$153$	61.8360	4.99915
$154$	9.79206	0.789067
$155$	10.0286	0.805514
$156$	6.00999	0.481185
$157$	−3.97930	−0.317583	−0.158791	−	0.987312i	$-0.550760\pi$
$157$	−3.97930	−0.317583	−0.158791	+	0.987312i	$0.550760\pi$
$158$	0.773121	0.0615062
$159$	−4.47608	−0.354977
$160$	−1.00000	−0.0790569
$161$	1.52113	0.119881
$162$	30.2748	2.37861
$163$	8.81556	0.690488	0.345244	−	0.938513i	$-0.387796\pi$
$163$	8.81556	0.690488	0.345244	+	0.938513i	$0.387796\pi$
$164$	−8.13968	−0.635602
$165$	−11.7273	−0.912966
$166$	−15.7131	−1.21957
$167$	3.01211	0.233084	0.116542	−	0.993186i	$-0.462819\pi$
$167$	3.01211	0.233084	0.116542	+	0.993186i	$0.462819\pi$
$168$	9.13803	0.705015
$169$	−9.69955	−0.746119
$170$	−7.78402	−0.597007
$171$	−23.2210	−1.77575
$172$	−10.5765	−0.806453
$173$	19.3831	1.47367	0.736833	−	0.676075i	$-0.236320\pi$
$173$	19.3831	1.47367	0.736833	+	0.676075i	$0.236320\pi$
$174$	33.6539	2.55130
$175$	−2.76226	−0.208808
$176$	−3.54494	−0.267210
$177$	−14.5641	−1.09471
$178$	12.9946	0.973989
$179$	−19.1365	−1.43033	−0.715164	−	0.698957i	$-0.753648\pi$
$179$	−19.1365	−1.43033	−0.715164	+	0.698957i	$0.753648\pi$
$180$	−7.94397	−0.592109
$181$	−9.92392	−0.737639	−0.368819	−	0.929501i	$-0.620238\pi$
$181$	−9.92392	−0.737639	−0.368819	+	0.929501i	$0.620238\pi$
$182$	5.01824	0.371977
$183$	−29.2490	−2.16214
$184$	−0.550681	−0.0405967
$185$	−7.71692	−0.567359
$186$	33.1762	2.43260
$187$	−27.5939	−2.01786
$188$	3.37747	0.246327
$189$	45.1782	3.28623
$190$	2.92310	0.212064
$191$	11.7941	0.853393	0.426696	−	0.904395i	$-0.359677\pi$
$191$	11.7941	0.853393	0.426696	+	0.904395i	$0.359677\pi$
$192$	−3.30817	−0.238746
$193$	6.75150	0.485984	0.242992	−	0.970028i	$-0.421871\pi$
$193$	6.75150	0.485984	0.242992	+	0.970028i	$0.421871\pi$
$194$	−9.04093	−0.649101
$195$	−6.00999	−0.430385
$196$	0.630104	0.0450074
$197$	−5.34671	−0.380937	−0.190468	−	0.981693i	$-0.561001\pi$
$197$	−5.34671	−0.380937	−0.190468	+	0.981693i	$0.561001\pi$
$198$	−28.1609	−2.00131
$199$	11.0982	0.786731	0.393366	−	0.919382i	$-0.371311\pi$
$199$	11.0982	0.786731	0.393366	+	0.919382i	$0.371311\pi$
$200$	1.00000	0.0707107
$201$	−38.8927	−2.74328
$202$	−7.96420	−0.560359
$203$	28.1005	1.97227
$204$	−25.7508	−1.80292
$205$	8.13968	0.568500
$206$	5.22893	0.364317
$207$	−4.37459	−0.304055
$208$	−1.81671	−0.125966
$209$	10.3622	0.716768
$210$	−9.13803	−0.630584
$211$	−7.52975	−0.518370	−0.259185	−	0.965828i	$-0.583454\pi$
$211$	−7.52975	−0.518370	−0.259185	+	0.965828i	$0.583454\pi$
$212$	1.35304	0.0929272
$213$	−13.1854	−0.903450
$214$	10.2812	0.702806
$215$	10.5765	0.721313
$216$	−16.3555	−1.11285
$217$	27.7016	1.88050
$218$	−2.94698	−0.199595
$219$	33.6106	2.27120
$220$	3.54494	0.239000
$221$	−14.1413	−0.951249
$222$	−25.5289	−1.71338
$223$	−1.58133	−0.105894	−0.0529469	−	0.998597i	$-0.516861\pi$
$223$	−1.58133	−0.105894	−0.0529469	+	0.998597i	$0.516861\pi$
$224$	−2.76226	−0.184562
$225$	7.94397	0.529598
$226$	9.68359	0.644143
$227$	1.88190	0.124906	0.0624529	−	0.998048i	$-0.480108\pi$
$227$	1.88190	0.124906	0.0624529	+	0.998048i	$0.480108\pi$
$228$	9.67009	0.640418
$229$	−23.5549	−1.55655	−0.778275	−	0.627923i	$-0.783905\pi$
$229$	−23.5549	−1.55655	−0.778275	+	0.627923i	$0.783905\pi$
$230$	0.550681	0.0363108
$231$	−32.3938	−2.13135
$232$	−10.1730	−0.667889
$233$	−0.240254	−0.0157396	−0.00786979	−	0.999969i	$-0.502505\pi$
$233$	−0.240254	−0.0157396	−0.00786979	+	0.999969i	$0.502505\pi$
$234$	−14.4319	−0.943445
$235$	−3.37747	−0.220322
$236$	4.40247	0.286576
$237$	−2.55761	−0.166135
$238$	−21.5015	−1.39374
$239$	24.3235	1.57336	0.786678	−	0.617364i	$-0.211799\pi$
$239$	24.3235	1.57336	0.786678	+	0.617364i	$0.211799\pi$
$240$	3.30817	0.213541
$241$	−18.3349	−1.18105	−0.590526	−	0.807018i	$-0.701080\pi$
$241$	−18.3349	−1.18105	−0.590526	+	0.807018i	$0.701080\pi$
$242$	1.56660	0.100705
$243$	−51.0877	−3.27728
$244$	8.84144	0.566015
$245$	−0.630104	−0.0402558
$246$	26.9274	1.71683
$247$	5.31043	0.337894
$248$	−10.0286	−0.636815
$249$	51.9816	3.29420
$250$	−1.00000	−0.0632456
$251$	−4.58736	−0.289552	−0.144776	−	0.989464i	$-0.546246\pi$
$251$	−4.58736	−0.289552	−0.144776	+	0.989464i	$0.546246\pi$
$252$	−21.9434	−1.38230
$253$	1.95213	0.122729
$254$	12.5804	0.789363
$255$	25.7508	1.61258
$256$	1.00000	0.0625000
$257$	12.9111	0.805369	0.402685	−	0.915339i	$-0.368077\pi$
$257$	12.9111	0.805369	0.402685	+	0.915339i	$0.368077\pi$
$258$	34.9889	2.17832
$259$	−21.3162	−1.32452
$260$	1.81671	0.112668
$261$	−80.8140	−5.00226
$262$	6.42265	0.396793
$263$	12.9190	0.796620	0.398310	−	0.917251i	$-0.369597\pi$
$263$	12.9190	0.796620	0.398310	+	0.917251i	$0.369597\pi$
$264$	11.7273	0.721763
$265$	−1.35304	−0.0831166
$266$	8.07436	0.495071
$267$	−42.9884	−2.63085
$268$	11.7566	0.718146
$269$	−8.52334	−0.519677	−0.259838	−	0.965652i	$-0.583669\pi$
$269$	−8.52334	−0.519677	−0.259838	+	0.965652i	$0.583669\pi$
$270$	16.3555	0.995364
$271$	5.89303	0.357976	0.178988	−	0.983851i	$-0.442718\pi$
$271$	5.89303	0.357976	0.178988	+	0.983851i	$0.442718\pi$
$272$	7.78402	0.471975
$273$	−16.6012	−1.00475
$274$	17.7410	1.07178
$275$	−3.54494	−0.213768
$276$	1.82174	0.109656
$277$	23.9230	1.43739	0.718696	−	0.695324i	$-0.244739\pi$
$277$	23.9230	1.43739	0.718696	+	0.695324i	$0.244739\pi$
$278$	18.3177	1.09862
$279$	−79.6667	−4.76952
$280$	2.76226	0.165077
$281$	−12.1945	−0.727465	−0.363733	−	0.931503i	$-0.618498\pi$
$281$	−12.1945	−0.727465	−0.363733	+	0.931503i	$0.618498\pi$
$282$	−11.1732	−0.665357
$283$	−12.4021	−0.737228	−0.368614	−	0.929582i	$-0.620168\pi$
$283$	−12.4021	−0.737228	−0.368614	+	0.929582i	$0.620168\pi$
$284$	3.98572	0.236509
$285$	−9.67009	−0.572807
$286$	6.44014	0.380813
$287$	22.4839	1.32719
$288$	7.94397	0.468103
$289$	43.5909	2.56417
$290$	10.1730	0.597378
$291$	29.9089	1.75329
$292$	−10.1599	−0.594563
$293$	32.4905	1.89811	0.949057	−	0.315103i	$-0.102039\pi$
$293$	32.4905	1.89811	0.949057	+	0.315103i	$0.102039\pi$
$294$	−2.08449	−0.121570
$295$	−4.40247	−0.256322
$296$	7.71692	0.448537
$297$	57.9793	3.36430
$298$	−0.317429	−0.0183881
$299$	1.00043	0.0578563
$300$	−3.30817	−0.190997
$301$	29.2152	1.68393
$302$	8.20859	0.472351
$303$	26.3469	1.51359
$304$	−2.92310	−0.167651
$305$	−8.84144	−0.506259
$306$	61.8360	3.53493
$307$	7.20802	0.411383	0.205692	−	0.978617i	$-0.434056\pi$
$307$	7.20802	0.411383	0.205692	+	0.978617i	$0.434056\pi$
$308$	9.79206	0.557954
$309$	−17.2982	−0.984058
$310$	10.0286	0.569584
$311$	6.23499	0.353554	0.176777	−	0.984251i	$-0.443433\pi$
$311$	6.23499	0.353554	0.176777	+	0.984251i	$0.443433\pi$
$312$	6.00999	0.340249
$313$	14.3509	0.811161	0.405580	−	0.914059i	$-0.367069\pi$
$313$	14.3509	0.811161	0.405580	+	0.914059i	$0.367069\pi$
$314$	−3.97930	−0.224565
$315$	21.9434	1.23637
$316$	0.773121	0.0434915
$317$	−24.2526	−1.36216	−0.681080	−	0.732209i	$-0.738490\pi$
$317$	−24.2526	−1.36216	−0.681080	+	0.732209i	$0.738490\pi$
$318$	−4.47608	−0.251006
$319$	36.0626	2.01912
$320$	−1.00000	−0.0559017
$321$	−34.0118	−1.89835
$322$	1.52113	0.0847690
$323$	−22.7534	−1.26603
$324$	30.2748	1.68193
$325$	−1.81671	−0.100773
$326$	8.81556	0.488249
$327$	9.74912	0.539127
$328$	−8.13968	−0.449439
$329$	−9.32947	−0.514350
$330$	−11.7273	−0.645564
$331$	23.2161	1.27607	0.638035	−	0.770007i	$-0.279748\pi$
$331$	23.2161	1.27607	0.638035	+	0.770007i	$0.279748\pi$
$332$	−15.7131	−0.862369
$333$	61.3030	3.35938
$334$	3.01211	0.164815
$335$	−11.7566	−0.642330
$336$	9.13803	0.498521
$337$	−0.955526	−0.0520508	−0.0260254	−	0.999661i	$-0.508285\pi$
$337$	−0.955526	−0.0520508	−0.0260254	+	0.999661i	$0.508285\pi$
$338$	−9.69955	−0.527586
$339$	−32.0349	−1.73990
$340$	−7.78402	−0.422148
$341$	35.5507	1.92518
$342$	−23.2210	−1.25565
$343$	17.5953	0.950059
$344$	−10.5765	−0.570248
$345$	−1.82174	−0.0980794
$346$	19.3831	1.04204
$347$	27.6587	1.48480	0.742400	−	0.669957i	$-0.233688\pi$
$347$	27.6587	1.48480	0.742400	+	0.669957i	$0.233688\pi$
$348$	33.6539	1.80404
$349$	−11.7225	−0.627490	−0.313745	−	0.949507i	$-0.601584\pi$
$349$	−11.7225	−0.627490	−0.313745	+	0.949507i	$0.601584\pi$
$350$	−2.76226	−0.147649
$351$	29.7133	1.58598
$352$	−3.54494	−0.188946
$353$	5.05585	0.269096	0.134548	−	0.990907i	$-0.457042\pi$
$353$	5.05585	0.269096	0.134548	+	0.990907i	$0.457042\pi$
$354$	−14.5641	−0.774074
$355$	−3.98572	−0.211540
$356$	12.9946	0.688714
$357$	71.1306	3.76463
$358$	−19.1365	−1.01139
$359$	5.58434	0.294730	0.147365	−	0.989082i	$-0.452921\pi$
$359$	5.58434	0.294730	0.147365	+	0.989082i	$0.452921\pi$
$360$	−7.94397	−0.418684
$361$	−10.4555	−0.550290
$362$	−9.92392	−0.521589
$363$	−5.18256	−0.272014
$364$	5.01824	0.263027
$365$	10.1599	0.531793
$366$	−29.2490	−1.52887
$367$	9.90578	0.517078	0.258539	−	0.966001i	$-0.416759\pi$
$367$	9.90578	0.517078	0.258539	+	0.966001i	$0.416759\pi$
$368$	−0.550681	−0.0287062
$369$	−64.6614	−3.36614
$370$	−7.71692	−0.401183
$371$	−3.73745	−0.194039
$372$	33.1762	1.72011
$373$	−2.70589	−0.140105	−0.0700527	−	0.997543i	$-0.522317\pi$
$373$	−2.70589	−0.140105	−0.0700527	+	0.997543i	$0.522317\pi$
$374$	−27.5939	−1.42685
$375$	3.30817	0.170833
$376$	3.37747	0.174180
$377$	18.4814	0.951841
$378$	45.1782	2.32372
$379$	20.2508	1.04021	0.520107	−	0.854101i	$-0.325892\pi$
$379$	20.2508	1.04021	0.520107	+	0.854101i	$0.325892\pi$
$380$	2.92310	0.149952
$381$	−41.6180	−2.13216
$382$	11.7941	0.603440
$383$	−21.6851	−1.10806	−0.554028	−	0.832498i	$-0.686910\pi$
$383$	−21.6851	−1.10806	−0.554028	+	0.832498i	$0.686910\pi$
$384$	−3.30817	−0.168819
$385$	−9.79206	−0.499050
$386$	6.75150	0.343642
$387$	−84.0197	−4.27096
$388$	−9.04093	−0.458984
$389$	−35.2088	−1.78516	−0.892579	−	0.450892i	$-0.851106\pi$
$389$	−35.2088	−1.78516	−0.892579	+	0.450892i	$0.851106\pi$
$390$	−6.00999	−0.304328
$391$	−4.28651	−0.216778
$392$	0.630104	0.0318250
$393$	−21.2472	−1.07178
$394$	−5.34671	−0.269363
$395$	−0.773121	−0.0388999
$396$	−28.1609	−1.41514
$397$	−22.3429	−1.12136	−0.560680	−	0.828033i	$-0.689460\pi$
$397$	−22.3429	−1.12136	−0.560680	+	0.828033i	$0.689460\pi$
$398$	11.0982	0.556303
$399$	−26.7114	−1.33724
$400$	1.00000	0.0500000
$401$	−1.00000	−0.0499376
$401$	−1.00000	−0.0499376
$402$	−38.8927	−1.93979
$403$	18.2190	0.907555
$404$	−7.96420	−0.396234
$405$	−30.2748	−1.50437
$406$	28.1005	1.39460
$407$	−27.3560	−1.35599
$408$	−25.7508	−1.27486
$409$	33.5106	1.65699	0.828495	−	0.559996i	$-0.189197\pi$
$409$	33.5106	1.65699	0.828495	+	0.559996i	$0.189197\pi$
$410$	8.13968	0.401990
$411$	−58.6903	−2.89498
$412$	5.22893	0.257611
$413$	−12.1608	−0.598393
$414$	−4.37459	−0.215000
$415$	15.7131	0.771326
$416$	−1.81671	−0.0890717
$417$	−60.5981	−2.96750
$418$	10.3622	0.506832
$419$	−6.94306	−0.339191	−0.169595	−	0.985514i	$-0.554246\pi$
$419$	−6.94306	−0.339191	−0.169595	+	0.985514i	$0.554246\pi$
$420$	−9.13803	−0.445890
$421$	29.1317	1.41979	0.709896	−	0.704306i	$-0.248742\pi$
$421$	29.1317	1.41979	0.709896	+	0.704306i	$0.248742\pi$
$422$	−7.52975	−0.366543
$423$	26.8305	1.30455
$424$	1.35304	0.0657094
$425$	7.78402	0.377580
$426$	−13.1854	−0.638835
$427$	−24.4224	−1.18188
$428$	10.2812	0.496959
$429$	−21.3051	−1.02862
$430$	10.5765	0.510046
$431$	3.93247	0.189420	0.0947102	−	0.995505i	$-0.469808\pi$
$431$	3.93247	0.189420	0.0947102	+	0.995505i	$0.469808\pi$
$432$	−16.3555	−0.786904
$433$	−18.0698	−0.868381	−0.434190	−	0.900821i	$-0.642966\pi$
$433$	−18.0698	−0.868381	−0.434190	+	0.900821i	$0.642966\pi$
$434$	27.7016	1.32972
$435$	−33.6539	−1.61358
$436$	−2.94698	−0.141135
$437$	1.60969	0.0770020
$438$	33.6106	1.60598
$439$	−5.00221	−0.238743	−0.119371	−	0.992850i	$-0.538088\pi$
$439$	−5.00221	−0.238743	−0.119371	+	0.992850i	$0.538088\pi$
$440$	3.54494	0.168998
$441$	5.00553	0.238358
$442$	−14.1413	−0.672634
$443$	30.1623	1.43305	0.716527	−	0.697559i	$-0.245731\pi$
$443$	30.1623	1.43305	0.716527	+	0.697559i	$0.245731\pi$
$444$	−25.5289	−1.21155
$445$	−12.9946	−0.616005
$446$	−1.58133	−0.0748783
$447$	1.05011	0.0496684
$448$	−2.76226	−0.130505
$449$	4.67245	0.220507	0.110253	−	0.993904i	$-0.464834\pi$
$449$	4.67245	0.220507	0.110253	+	0.993904i	$0.464834\pi$
$450$	7.94397	0.374483
$451$	28.8547	1.35871
$452$	9.68359	0.455478
$453$	−27.1554	−1.27587
$454$	1.88190	0.0883217
$455$	−5.01824	−0.235259
$456$	9.67009	0.452844
$457$	−10.3103	−0.482295	−0.241148	−	0.970488i	$-0.577524\pi$
$457$	−10.3103	−0.482295	−0.241148	+	0.970488i	$0.577524\pi$
$458$	−23.5549	−1.10065
$459$	−127.311	−5.94239
$460$	0.550681	0.0256756
$461$	20.0855	0.935474	0.467737	−	0.883868i	$-0.345069\pi$
$461$	20.0855	0.935474	0.467737	+	0.883868i	$0.345069\pi$
$462$	−32.3938	−1.50709
$463$	34.7972	1.61716	0.808582	−	0.588383i	$-0.200235\pi$
$463$	34.7972	1.61716	0.808582	+	0.588383i	$0.200235\pi$
$464$	−10.1730	−0.472269
$465$	−33.1762	−1.53851
$466$	−0.240254	−0.0111296
$467$	−26.5031	−1.22642	−0.613208	−	0.789922i	$-0.710121\pi$
$467$	−26.5031	−1.22642	−0.613208	+	0.789922i	$0.710121\pi$
$468$	−14.4319	−0.667116
$469$	−32.4747	−1.49954
$470$	−3.37747	−0.155791
$471$	13.1642	0.606575
$472$	4.40247	0.202640
$473$	37.4932	1.72394
$474$	−2.55761	−0.117475
$475$	−2.92310	−0.134121
$476$	−21.5015	−0.985520
$477$	10.7485	0.492141
$478$	24.3235	1.11253
$479$	−29.2063	−1.33447	−0.667235	−	0.744847i	$-0.732522\pi$
$479$	−29.2063	−1.33447	−0.667235	+	0.744847i	$0.732522\pi$
$480$	3.30817	0.150997
$481$	−14.0194	−0.639231
$482$	−18.3349	−0.835130
$483$	−5.03214	−0.228970
$484$	1.56660	0.0712089
$485$	9.04093	0.410528
$486$	−51.0877	−2.31738
$487$	31.3856	1.42222	0.711109	−	0.703082i	$-0.248193\pi$
$487$	31.3856	1.42222	0.711109	+	0.703082i	$0.248193\pi$
$488$	8.84144	0.400233
$489$	−29.1633	−1.31881
$490$	−0.630104	−0.0284652
$491$	−5.30866	−0.239576	−0.119788	−	0.992799i	$-0.538222\pi$
$491$	−5.30866	−0.239576	−0.119788	+	0.992799i	$0.538222\pi$
$492$	26.9274	1.21398
$493$	−79.1867	−3.56639
$494$	5.31043	0.238927
$495$	28.1609	1.26574
$496$	−10.0286	−0.450296
$497$	−11.0096	−0.493848
$498$	51.9816	2.32935
$499$	12.0173	0.537969	0.268984	−	0.963145i	$-0.413312\pi$
$499$	12.0173	0.537969	0.268984	+	0.963145i	$0.413312\pi$
$500$	−1.00000	−0.0447214
$501$	−9.96456	−0.445184
$502$	−4.58736	−0.204744
$503$	−24.9063	−1.11052	−0.555259	−	0.831678i	$-0.687381\pi$
$503$	−24.9063	−1.11052	−0.555259	+	0.831678i	$0.687381\pi$
$504$	−21.9434	−0.977435
$505$	7.96420	0.354402
$506$	1.95213	0.0867827
$507$	32.0877	1.42507
$508$	12.5804	0.558164
$509$	31.0863	1.37787	0.688937	−	0.724821i	$-0.258078\pi$
$509$	31.0863	1.37787	0.688937	+	0.724821i	$0.258078\pi$
$510$	25.7508	1.14027
$511$	28.0643	1.24149
$512$	1.00000	0.0441942
$513$	47.8087	2.11081
$514$	12.9111	0.569482
$515$	−5.22893	−0.230414
$516$	34.9889	1.54030
$517$	−11.9729	−0.526569
$518$	−21.3162	−0.936578
$519$	−64.1224	−2.81466
$520$	1.81671	0.0796682
$521$	−34.6620	−1.51857	−0.759284	−	0.650760i	$-0.774451\pi$
$521$	−34.6620	−1.51857	−0.759284	+	0.650760i	$0.774451\pi$
$522$	−80.8140	−3.53713
$523$	−19.2330	−0.841000	−0.420500	−	0.907293i	$-0.638145\pi$
$523$	−19.2330	−0.841000	−0.420500	+	0.907293i	$0.638145\pi$
$524$	6.42265	0.280575
$525$	9.13803	0.398816
$526$	12.9190	0.563295
$527$	−78.0626	−3.40046
$528$	11.7273	0.510363
$529$	−22.6968	−0.986815
$530$	−1.35304	−0.0587723
$531$	34.9731	1.51770
$532$	8.07436	0.350068
$533$	14.7875	0.640516
$534$	−42.9884	−1.86029
$535$	−10.2812	−0.444493
$536$	11.7566	0.507806
$537$	63.3067	2.73188
$538$	−8.52334	−0.367467
$539$	−2.23368	−0.0962114
$540$	16.3555	0.703829
$541$	10.0306	0.431250	0.215625	−	0.976476i	$-0.430821\pi$
$541$	10.0306	0.431250	0.215625	+	0.976476i	$0.430821\pi$
$542$	5.89303	0.253127
$543$	32.8300	1.40887
$544$	7.78402	0.333737
$545$	2.94698	0.126235
$546$	−16.6012	−0.710465
$547$	−22.0561	−0.943049	−0.471524	−	0.881853i	$-0.656296\pi$
$547$	−22.0561	−0.943049	−0.471524	+	0.881853i	$0.656296\pi$
$548$	17.7410	0.757859
$549$	70.2361	2.99761
$550$	−3.54494	−0.151157
$551$	29.7366	1.26682
$552$	1.82174	0.0775386
$553$	−2.13556	−0.0908134
$554$	23.9230	1.01639
$555$	25.5289	1.08364
$556$	18.3177	0.776844
$557$	−35.7581	−1.51512	−0.757561	−	0.652765i	$-0.773609\pi$
$557$	−35.7581	−1.51512	−0.757561	+	0.652765i	$0.773609\pi$
$558$	−79.6667	−3.37256
$559$	19.2145	0.812688
$560$	2.76226	0.116727
$561$	91.2852	3.85406
$562$	−12.1945	−0.514395
$563$	−12.4987	−0.526757	−0.263379	−	0.964693i	$-0.584837\pi$
$563$	−12.4987	−0.526757	−0.263379	+	0.964693i	$0.584837\pi$
$564$	−11.1732	−0.470478
$565$	−9.68359	−0.407392
$566$	−12.4021	−0.521299
$567$	−83.6270	−3.51201
$568$	3.98572	0.167237
$569$	−5.88559	−0.246737	−0.123368	−	0.992361i	$-0.539370\pi$
$569$	−5.88559	−0.246737	−0.123368	+	0.992361i	$0.539370\pi$
$570$	−9.67009	−0.405036
$571$	−35.5844	−1.48916	−0.744581	−	0.667532i	$-0.767351\pi$
$571$	−35.5844	−1.48916	−0.744581	+	0.667532i	$0.767351\pi$
$572$	6.44014	0.269276
$573$	−39.0169	−1.62996
$574$	22.4839	0.938462
$575$	−0.550681	−0.0229650
$576$	7.94397	0.330999
$577$	6.89651	0.287105	0.143553	−	0.989643i	$-0.454147\pi$
$577$	6.89651	0.287105	0.143553	+	0.989643i	$0.454147\pi$
$578$	43.5909	1.81314
$579$	−22.3351	−0.928215
$580$	10.1730	0.422410
$581$	43.4038	1.80069
$582$	29.9089	1.23976
$583$	−4.79645	−0.198648
$584$	−10.1599	−0.420420
$585$	14.4319	0.596687
$586$	32.4905	1.34217
$587$	−25.4476	−1.05034	−0.525168	−	0.850998i	$-0.675998\pi$
$587$	−25.4476	−1.05034	−0.525168	+	0.850998i	$0.675998\pi$
$588$	−2.08449	−0.0859629
$589$	29.3145	1.20788
$590$	−4.40247	−0.181247
$591$	17.6878	0.727579
$592$	7.71692	0.317163
$593$	13.8112	0.567156	0.283578	−	0.958949i	$-0.408478\pi$
$593$	13.8112	0.567156	0.283578	+	0.958949i	$0.408478\pi$
$594$	57.9793	2.37892
$595$	21.5015	0.881476
$596$	−0.317429	−0.0130024
$597$	−36.7148	−1.50263
$598$	1.00043	0.0409106
$599$	−6.64166	−0.271371	−0.135685	−	0.990752i	$-0.543324\pi$
$599$	−6.64166	−0.271371	−0.135685	+	0.990752i	$0.543324\pi$
$600$	−3.30817	−0.135055
$601$	15.6087	0.636690	0.318345	−	0.947975i	$-0.396873\pi$
$601$	15.6087	0.636690	0.318345	+	0.947975i	$0.396873\pi$
$602$	29.2152	1.19072
$603$	93.3938	3.80329
$604$	8.20859	0.334003
$605$	−1.56660	−0.0636912
$606$	26.3469	1.07027
$607$	4.40235	0.178686	0.0893429	−	0.996001i	$-0.471523\pi$
$607$	4.40235	0.178686	0.0893429	+	0.996001i	$0.471523\pi$
$608$	−2.92310	−0.118547
$609$	−92.9611	−3.76697
$610$	−8.84144	−0.357979
$611$	−6.13590	−0.248232
$612$	61.8360	2.49957
$613$	17.2974	0.698635	0.349318	−	0.937004i	$-0.386413\pi$
$613$	17.2974	0.698635	0.349318	+	0.937004i	$0.386413\pi$
$614$	7.20802	0.290892
$615$	−26.9274	−1.08582
$616$	9.79206	0.394533
$617$	13.9182	0.560325	0.280163	−	0.959953i	$-0.409612\pi$
$617$	13.9182	0.560325	0.280163	+	0.959953i	$0.409612\pi$
$618$	−17.2982	−0.695834
$619$	14.2338	0.572106	0.286053	−	0.958214i	$-0.407657\pi$
$619$	14.2338	0.572106	0.286053	+	0.958214i	$0.407657\pi$
$620$	10.0286	0.402757
$621$	9.00666	0.361425
$622$	6.23499	0.250000
$623$	−35.8946	−1.43809
$624$	6.00999	0.240592
$625$	1.00000	0.0400000
$626$	14.3509	0.573577
$627$	−34.2799	−1.36901
$628$	−3.97930	−0.158791
$629$	60.0686	2.39509
$630$	21.9434	0.874244
$631$	23.4207	0.932364	0.466182	−	0.884689i	$-0.345629\pi$
$631$	23.4207	0.932364	0.466182	+	0.884689i	$0.345629\pi$
$632$	0.773121	0.0307531
$633$	24.9097	0.990071
$634$	−24.2526	−0.963193
$635$	−12.5804	−0.499237
$636$	−4.47608	−0.177488
$637$	−1.14472	−0.0453554
$638$	36.0626	1.42773
$639$	31.6624	1.25255
$640$	−1.00000	−0.0395285
$641$	−33.9347	−1.34034	−0.670170	−	0.742208i	$-0.733779\pi$
$641$	−33.9347	−1.34034	−0.670170	+	0.742208i	$0.733779\pi$
$642$	−34.0118	−1.34234
$643$	−32.6991	−1.28953	−0.644763	−	0.764382i	$-0.723044\pi$
$643$	−32.6991	−1.28953	−0.644763	+	0.764382i	$0.723044\pi$
$644$	1.52113	0.0599407
$645$	−34.9889	−1.37769
$646$	−22.7534	−0.895222
$647$	−16.9064	−0.664657	−0.332329	−	0.943164i	$-0.607834\pi$
$647$	−16.9064	−0.664657	−0.332329	+	0.943164i	$0.607834\pi$
$648$	30.2748	1.18931
$649$	−15.6065	−0.612609
$650$	−1.81671	−0.0712574
$651$	−91.6414	−3.59171
$652$	8.81556	0.345244
$653$	37.4441	1.46530	0.732650	−	0.680606i	$-0.238283\pi$
$653$	37.4441	1.46530	0.732650	+	0.680606i	$0.238283\pi$
$654$	9.74912	0.381221
$655$	−6.42265	−0.250954
$656$	−8.13968	−0.317801
$657$	−80.7100	−3.14880
$658$	−9.32947	−0.363700
$659$	−35.1890	−1.37077	−0.685385	−	0.728181i	$-0.740366\pi$
$659$	−35.1890	−1.37077	−0.685385	+	0.728181i	$0.740366\pi$
$660$	−11.7273	−0.456483
$661$	43.8275	1.70469	0.852346	−	0.522978i	$-0.175179\pi$
$661$	43.8275	1.70469	0.852346	+	0.522978i	$0.175179\pi$
$662$	23.2161	0.902318
$663$	46.7819	1.81686
$664$	−15.7131	−0.609787
$665$	−8.07436	−0.313110
$666$	61.3030	2.37544
$667$	5.60207	0.216913
$668$	3.01211	0.116542
$669$	5.23131	0.202254
$670$	−11.7566	−0.454196
$671$	−31.3424	−1.20996
$672$	9.13803	0.352507
$673$	−46.6190	−1.79703	−0.898516	−	0.438941i	$-0.855354\pi$
$673$	−46.6190	−1.79703	−0.898516	+	0.438941i	$0.855354\pi$
$674$	−0.955526	−0.0368055
$675$	−16.3555	−0.629523
$676$	−9.69955	−0.373060
$677$	−44.5580	−1.71250	−0.856252	−	0.516559i	$-0.827213\pi$
$677$	−44.5580	−1.71250	−0.856252	+	0.516559i	$0.827213\pi$
$678$	−32.0349	−1.23029
$679$	24.9734	0.958393
$680$	−7.78402	−0.298503
$681$	−6.22563	−0.238567
$682$	35.5507	1.36131
$683$	0.871479	0.0333462	0.0166731	−	0.999861i	$-0.494693\pi$
$683$	0.871479	0.0333462	0.0166731	+	0.999861i	$0.494693\pi$
$684$	−23.2210	−0.887877
$685$	−17.7410	−0.677850
$686$	17.5953	0.671793
$687$	77.9235	2.97297
$688$	−10.5765	−0.403226
$689$	−2.45809	−0.0936456
$690$	−1.82174	−0.0693526
$691$	11.7710	0.447791	0.223895	−	0.974613i	$-0.428123\pi$
$691$	11.7710	0.447791	0.223895	+	0.974613i	$0.428123\pi$
$692$	19.3831	0.736833
$693$	77.7879	2.95492
$694$	27.6587	1.04991
$695$	−18.3177	−0.694830
$696$	33.6539	1.27565
$697$	−63.3594	−2.39991
$698$	−11.7225	−0.443702
$699$	0.794801	0.0300621
$700$	−2.76226	−0.104404
$701$	7.60537	0.287251	0.143625	−	0.989632i	$-0.454124\pi$
$701$	7.60537	0.287251	0.143625	+	0.989632i	$0.454124\pi$
$702$	29.7133	1.12145
$703$	−22.5573	−0.850764
$704$	−3.54494	−0.133605
$705$	11.1732	0.420809
$706$	5.05585	0.190280
$707$	21.9992	0.827366
$708$	−14.5641	−0.547353
$709$	−27.0099	−1.01438	−0.507190	−	0.861834i	$-0.669316\pi$
$709$	−27.0099	−1.01438	−0.507190	+	0.861834i	$0.669316\pi$
$710$	−3.98572	−0.149581
$711$	6.14165	0.230330
$712$	12.9946	0.486994
$713$	5.52254	0.206821
$714$	71.1306	2.66200
$715$	−6.44014	−0.240848
$716$	−19.1365	−0.715164
$717$	−80.4662	−3.00507
$718$	5.58434	0.208406
$719$	1.28875	0.0480624	0.0240312	−	0.999711i	$-0.492350\pi$
$719$	1.28875	0.0480624	0.0240312	+	0.999711i	$0.492350\pi$
$720$	−7.94397	−0.296054
$721$	−14.4437	−0.537911
$722$	−10.4555	−0.389114
$723$	60.6548	2.25578
$724$	−9.92392	−0.368819
$725$	−10.1730	−0.377815
$726$	−5.18256	−0.192343
$727$	−15.8633	−0.588339	−0.294169	−	0.955753i	$-0.595043\pi$
$727$	−15.8633	−0.588339	−0.294169	+	0.955753i	$0.595043\pi$
$728$	5.01824	0.185988
$729$	78.1821	2.89563
$730$	10.1599	0.376035
$731$	−82.3279	−3.04501
$732$	−29.2490	−1.08107
$733$	10.8848	0.402039	0.201019	−	0.979587i	$-0.435575\pi$
$733$	10.8848	0.402039	0.201019	+	0.979587i	$0.435575\pi$
$734$	9.90578	0.365629
$735$	2.08449	0.0768875
$736$	−0.550681	−0.0202984
$737$	−41.6763	−1.53517
$738$	−64.6614	−2.38022
$739$	−12.9525	−0.476465	−0.238233	−	0.971208i	$-0.576568\pi$
$739$	−12.9525	−0.476465	−0.238233	+	0.971208i	$0.576568\pi$
$740$	−7.71692	−0.283680
$741$	−17.5678	−0.645369
$742$	−3.73745	−0.137206
$743$	18.8542	0.691693	0.345847	−	0.938291i	$-0.387592\pi$
$743$	18.8542	0.691693	0.345847	+	0.938291i	$0.387592\pi$
$744$	33.1762	1.21630
$745$	0.317429	0.0116297
$746$	−2.70589	−0.0990695
$747$	−124.825	−4.56709
$748$	−27.5939	−1.00893
$749$	−28.3993	−1.03769
$750$	3.30817	0.120797
$751$	−4.11004	−0.149977	−0.0749887	−	0.997184i	$-0.523892\pi$
$751$	−4.11004	−0.149977	−0.0749887	+	0.997184i	$0.523892\pi$
$752$	3.37747	0.123164
$753$	15.1758	0.553035
$754$	18.4814	0.673053
$755$	−8.20859	−0.298741
$756$	45.1782	1.64312
$757$	12.3295	0.448124	0.224062	−	0.974575i	$-0.428068\pi$
$757$	12.3295	0.448124	0.224062	+	0.974575i	$0.428068\pi$
$758$	20.2508	0.735542
$759$	−6.45797	−0.234410
$760$	2.92310	0.106032
$761$	38.0128	1.37796	0.688982	−	0.724779i	$-0.258058\pi$
$761$	38.0128	1.37796	0.688982	+	0.724779i	$0.258058\pi$
$762$	−41.6180	−1.50766
$763$	8.14035	0.294700
$764$	11.7941	0.426696
$765$	−61.8360	−2.23569
$766$	−21.6851	−0.783514
$767$	−7.99803	−0.288792
$768$	−3.30817	−0.119373
$769$	33.6001	1.21165	0.605826	−	0.795597i	$-0.292843\pi$
$769$	33.6001	1.21165	0.605826	+	0.795597i	$0.292843\pi$
$770$	−9.79206	−0.352881
$771$	−42.7119	−1.53823
$772$	6.75150	0.242992
$773$	16.2052	0.582861	0.291430	−	0.956592i	$-0.405869\pi$
$773$	16.2052	0.582861	0.291430	+	0.956592i	$0.405869\pi$
$774$	−84.0197	−3.02003
$775$	−10.0286	−0.360237
$776$	−9.04093	−0.324551
$777$	70.5174	2.52980
$778$	−35.2088	−1.26230
$779$	23.7931	0.852475
$780$	−6.00999	−0.215192
$781$	−14.1291	−0.505580
$782$	−4.28651	−0.153285
$783$	166.384	5.94609
$784$	0.630104	0.0225037
$785$	3.97930	0.142027
$786$	−21.2472	−0.757863
$787$	38.9775	1.38940	0.694698	−	0.719301i	$-0.255538\pi$
$787$	38.9775	1.38940	0.694698	+	0.719301i	$0.255538\pi$
$788$	−5.34671	−0.190468
$789$	−42.7382	−1.52152
$790$	−0.773121	−0.0275064
$791$	−26.7486	−0.951072
$792$	−28.1609	−1.00065
$793$	−16.0624	−0.570391
$794$	−22.3429	−0.792921
$795$	4.47608	0.158750
$796$	11.0982	0.393366
$797$	25.3825	0.899094	0.449547	−	0.893257i	$-0.351586\pi$
$797$	25.3825	0.899094	0.449547	+	0.893257i	$0.351586\pi$
$798$	−26.7114	−0.945572
$799$	26.2903	0.930084
$800$	1.00000	0.0353553
$801$	103.229	3.64742
$802$	−1.00000	−0.0353112
$803$	36.0162	1.27098
$804$	−38.8927	−1.37164
$805$	−1.52113	−0.0536126
$806$	18.2190	0.641738
$807$	28.1966	0.992568
$808$	−7.96420	−0.280180
$809$	−2.44889	−0.0860984	−0.0430492	−	0.999073i	$-0.513707\pi$
$809$	−2.44889	−0.0860984	−0.0430492	+	0.999073i	$0.513707\pi$
$810$	−30.2748	−1.06375
$811$	5.78728	0.203219	0.101609	−	0.994824i	$-0.467601\pi$
$811$	5.78728	0.203219	0.101609	+	0.994824i	$0.467601\pi$
$812$	28.1005	0.986133
$813$	−19.4951	−0.683724
$814$	−27.3560	−0.958827
$815$	−8.81556	−0.308796
$816$	−25.7508	−0.901460
$817$	30.9162	1.08162
$818$	33.5106	1.17167
$819$	39.8648	1.39299
$820$	8.13968	0.284250
$821$	−44.2874	−1.54564	−0.772820	−	0.634625i	$-0.781155\pi$
$821$	−44.2874	−1.54564	−0.772820	+	0.634625i	$0.781155\pi$
$822$	−58.6903	−2.04706
$823$	−7.70612	−0.268619	−0.134309	−	0.990939i	$-0.542882\pi$
$823$	−7.70612	−0.268619	−0.134309	+	0.990939i	$0.542882\pi$
$824$	5.22893	0.182158
$825$	11.7273	0.408291
$826$	−12.1608	−0.423128
$827$	15.1502	0.526826	0.263413	−	0.964683i	$-0.415152\pi$
$827$	15.1502	0.526826	0.263413	+	0.964683i	$0.415152\pi$
$828$	−4.37459	−0.152028
$829$	20.1866	0.701109	0.350554	−	0.936542i	$-0.385993\pi$
$829$	20.1866	0.701109	0.350554	+	0.936542i	$0.385993\pi$
$830$	15.7131	0.545410
$831$	−79.1412	−2.74538
$832$	−1.81671	−0.0629832
$833$	4.90474	0.169939
$834$	−60.5981	−2.09834
$835$	−3.01211	−0.104238
$836$	10.3622	0.358384
$837$	164.022	5.66944
$838$	−6.94306	−0.239844
$839$	55.6780	1.92222	0.961109	−	0.276170i	$-0.0890653\pi$
$839$	55.6780	1.92222	0.961109	+	0.276170i	$0.0890653\pi$
$840$	−9.13803	−0.315292
$841$	74.4897	2.56861
$842$	29.1317	1.00394
$843$	40.3416	1.38944
$844$	−7.52975	−0.259185
$845$	9.69955	0.333675
$846$	26.8305	0.922453
$847$	−4.32735	−0.148690
$848$	1.35304	0.0464636
$849$	41.0282	1.40809
$850$	7.78402	0.266990
$851$	−4.24956	−0.145673
$852$	−13.1854	−0.451725
$853$	11.6172	0.397765	0.198882	−	0.980023i	$-0.436269\pi$
$853$	11.6172	0.397765	0.198882	+	0.980023i	$0.436269\pi$
$854$	−24.4224	−0.835717
$855$	23.2210	0.794142
$856$	10.2812	0.351403
$857$	−25.1338	−0.858554	−0.429277	−	0.903173i	$-0.641232\pi$
$857$	−25.1338	−0.858554	−0.429277	+	0.903173i	$0.641232\pi$
$858$	−21.3051	−0.727343
$859$	−18.9912	−0.647970	−0.323985	−	0.946062i	$-0.605023\pi$
$859$	−18.9912	−0.647970	−0.323985	+	0.946062i	$0.605023\pi$
$860$	10.5765	0.360657
$861$	−74.3807	−2.53489
$862$	3.93247	0.133940
$863$	−35.3819	−1.20442	−0.602208	−	0.798339i	$-0.705712\pi$
$863$	−35.3819	−1.20442	−0.602208	+	0.798339i	$0.705712\pi$
$864$	−16.3555	−0.556425
$865$	−19.3831	−0.659044
$866$	−18.0698	−0.614038
$867$	−144.206	−4.89750
$868$	27.7016	0.940252
$869$	−2.74067	−0.0929708
$870$	−33.6539	−1.14098
$871$	−21.3583	−0.723699
$872$	−2.94698	−0.0997975
$873$	−71.8209	−2.43077
$874$	1.60969	0.0544487
$875$	2.76226	0.0933816
$876$	33.6106	1.13560
$877$	38.1652	1.28875	0.644374	−	0.764710i	$-0.277118\pi$
$877$	38.1652	1.28875	0.644374	+	0.764710i	$0.277118\pi$
$878$	−5.00221	−0.168817
$879$	−107.484	−3.62535
$880$	3.54494	0.119500
$881$	−54.4176	−1.83337	−0.916687	−	0.399605i	$-0.869147\pi$
$881$	−54.4176	−1.83337	−0.916687	+	0.399605i	$0.869147\pi$
$882$	5.00553	0.168545
$883$	22.9571	0.772569	0.386284	−	0.922380i	$-0.373758\pi$
$883$	22.9571	0.772569	0.386284	+	0.922380i	$0.373758\pi$
$884$	−14.1413	−0.475624
$885$	14.5641	0.489567
$886$	30.1623	1.01332
$887$	13.4075	0.450181	0.225090	−	0.974338i	$-0.427732\pi$
$887$	13.4075	0.450181	0.225090	+	0.974338i	$0.427732\pi$
$888$	−25.5289	−0.856692
$889$	−34.7503	−1.16549
$890$	−12.9946	−0.435581
$891$	−107.322	−3.59544
$892$	−1.58133	−0.0529469
$893$	−9.87267	−0.330376
$894$	1.05011	0.0351208
$895$	19.1365	0.639662
$896$	−2.76226	−0.0922808
$897$	−3.30959	−0.110504
$898$	4.67245	0.155922
$899$	102.021	3.40257
$900$	7.94397	0.264799
$901$	10.5321	0.350875
$902$	28.8547	0.960756
$903$	−96.6487	−3.21627
$904$	9.68359	0.322071
$905$	9.92392	0.329882
$906$	−27.1554	−0.902178
$907$	27.9624	0.928478	0.464239	−	0.885710i	$-0.346328\pi$
$907$	27.9624	0.928478	0.464239	+	0.885710i	$0.346328\pi$
$908$	1.88190	0.0624529
$909$	−63.2674	−2.09845
$910$	−5.01824	−0.166353
$911$	−22.2988	−0.738793	−0.369396	−	0.929272i	$-0.620435\pi$
$911$	−22.2988	−0.738793	−0.369396	+	0.929272i	$0.620435\pi$
$912$	9.67009	0.320209
$913$	55.7020	1.84347
$914$	−10.3103	−0.341034
$915$	29.2490	0.966941
$916$	−23.5549	−0.778275
$917$	−17.7411	−0.585862
$918$	−127.311	−4.20191
$919$	19.0708	0.629086	0.314543	−	0.949243i	$-0.398149\pi$
$919$	19.0708	0.629086	0.314543	+	0.949243i	$0.398149\pi$
$920$	0.550681	0.0181554
$921$	−23.8453	−0.785730
$922$	20.0855	0.661480
$923$	−7.24090	−0.238337
$924$	−32.3938	−1.06568
$925$	7.71692	0.253731
$926$	34.7972	1.14351
$927$	41.5385	1.36430
$928$	−10.1730	−0.333945
$929$	−27.3162	−0.896214	−0.448107	−	0.893980i	$-0.647902\pi$
$929$	−27.3162	−0.896214	−0.448107	+	0.893980i	$0.647902\pi$
$930$	−33.1762	−1.08789
$931$	−1.84185	−0.0603643
$932$	−0.240254	−0.00786979
$933$	−20.6264	−0.675277
$934$	−26.5031	−0.867207
$935$	27.5939	0.902416
$936$	−14.4319	−0.471722
$937$	−34.5167	−1.12761	−0.563806	−	0.825907i	$-0.690664\pi$
$937$	−34.5167	−1.12761	−0.563806	+	0.825907i	$0.690664\pi$
$938$	−32.4747	−1.06034
$939$	−47.4752	−1.54929
$940$	−3.37747	−0.110161
$941$	49.7472	1.62171	0.810856	−	0.585245i	$-0.199002\pi$
$941$	49.7472	1.62171	0.810856	+	0.585245i	$0.199002\pi$
$942$	13.1642	0.428913
$943$	4.48236	0.145966
$944$	4.40247	0.143288
$945$	−45.1782	−1.46965
$946$	37.4932	1.21901
$947$	−16.6430	−0.540824	−0.270412	−	0.962745i	$-0.587160\pi$
$947$	−16.6430	−0.540824	−0.270412	+	0.962745i	$0.587160\pi$
$948$	−2.55761	−0.0830674
$949$	18.4576	0.599160
$950$	−2.92310	−0.0948378
$951$	80.2316	2.60169
$952$	−21.5015	−0.696868
$953$	53.5879	1.73588	0.867942	−	0.496666i	$-0.165443\pi$
$953$	53.5879	1.73588	0.867942	+	0.496666i	$0.165443\pi$
$954$	10.7485	0.347996
$955$	−11.7941	−0.381649
$956$	24.3235	0.786678
$957$	−119.301	−3.85646
$958$	−29.2063	−0.943613
$959$	−49.0054	−1.58247
$960$	3.30817	0.106771
$961$	69.5722	2.24426
$962$	−14.0194	−0.452004
$963$	81.6733	2.63188
$964$	−18.3349	−0.590526
$965$	−6.75150	−0.217338
$966$	−5.03214	−0.161906
$967$	−28.7426	−0.924299	−0.462149	−	0.886802i	$-0.652922\pi$
$967$	−28.7426	−0.924299	−0.462149	+	0.886802i	$0.652922\pi$
$968$	1.56660	0.0503523
$969$	75.2722	2.41809
$970$	9.04093	0.290287
$971$	12.7378	0.408776	0.204388	−	0.978890i	$-0.434480\pi$
$971$	12.7378	0.408776	0.204388	+	0.978890i	$0.434480\pi$
$972$	−51.0877	−1.63864
$973$	−50.5983	−1.62211
$974$	31.3856	1.00566
$975$	6.00999	0.192474
$976$	8.84144	0.283007
$977$	42.0272	1.34457	0.672285	−	0.740293i	$-0.265313\pi$
$977$	42.0272	1.34457	0.672285	+	0.740293i	$0.265313\pi$
$978$	−29.1633	−0.932541
$979$	−46.0652	−1.47225
$980$	−0.630104	−0.0201279
$981$	−23.4108	−0.747448
$982$	−5.30866	−0.169406
$983$	25.4313	0.811131	0.405566	−	0.914066i	$-0.367075\pi$
$983$	25.4313	0.811131	0.405566	+	0.914066i	$0.367075\pi$
$984$	26.9274	0.858415
$985$	5.34671	0.170360
$986$	−79.1867	−2.52182
$987$	30.8634	0.982394
$988$	5.31043	0.168947
$989$	5.82429	0.185202
$990$	28.1609	0.895013
$991$	6.82556	0.216821	0.108410	−	0.994106i	$-0.465424\pi$
$991$	6.82556	0.216821	0.108410	+	0.994106i	$0.465424\pi$
$992$	−10.0286	−0.318407
$993$	−76.8026	−2.43726
$994$	−11.0096	−0.349203
$995$	−11.0982	−0.351837
$996$	51.9816	1.64710
$997$	4.77295	0.151161	0.0755804	−	0.997140i	$-0.475919\pi$
$997$	4.77295	0.151161	0.0755804	+	0.997140i	$0.475919\pi$
$998$	12.0173	0.380402
$999$	−126.214	−3.99324

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4010.2.a.o.1.1	✓	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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -3.30817 q^{3} +1.00000 q^{4} -1.00000 q^{5} -3.30817 q^{6} -2.76226 q^{7} +1.00000 q^{8} +7.94397 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -3.30817 q^{3} +1.00000 q^{4} -1.00000 q^{5} -3.30817 q^{6} -2.76226 q^{7} +1.00000 q^{8} +7.94397 q^{9} -1.00000 q^{10} -3.54494 q^{11} -3.30817 q^{12} -1.81671 q^{13} -2.76226 q^{14} +3.30817 q^{15} +1.00000 q^{16} +7.78402 q^{17} +7.94397 q^{18} -2.92310 q^{19} -1.00000 q^{20} +9.13803 q^{21} -3.54494 q^{22} -0.550681 q^{23} -3.30817 q^{24} +1.00000 q^{25} -1.81671 q^{26} -16.3555 q^{27} -2.76226 q^{28} -10.1730 q^{29} +3.30817 q^{30} -10.0286 q^{31} +1.00000 q^{32} +11.7273 q^{33} +7.78402 q^{34} +2.76226 q^{35} +7.94397 q^{36} +7.71692 q^{37} -2.92310 q^{38} +6.00999 q^{39} -1.00000 q^{40} -8.13968 q^{41} +9.13803 q^{42} -10.5765 q^{43} -3.54494 q^{44} -7.94397 q^{45} -0.550681 q^{46} +3.37747 q^{47} -3.30817 q^{48} +0.630104 q^{49} +1.00000 q^{50} -25.7508 q^{51} -1.81671 q^{52} +1.35304 q^{53} -16.3555 q^{54} +3.54494 q^{55} -2.76226 q^{56} +9.67009 q^{57} -10.1730 q^{58} +4.40247 q^{59} +3.30817 q^{60} +8.84144 q^{61} -10.0286 q^{62} -21.9434 q^{63} +1.00000 q^{64} +1.81671 q^{65} +11.7273 q^{66} +11.7566 q^{67} +7.78402 q^{68} +1.82174 q^{69} +2.76226 q^{70} +3.98572 q^{71} +7.94397 q^{72} -10.1599 q^{73} +7.71692 q^{74} -3.30817 q^{75} -2.92310 q^{76} +9.79206 q^{77} +6.00999 q^{78} +0.773121 q^{79} -1.00000 q^{80} +30.2748 q^{81} -8.13968 q^{82} -15.7131 q^{83} +9.13803 q^{84} -7.78402 q^{85} -10.5765 q^{86} +33.6539 q^{87} -3.54494 q^{88} +12.9946 q^{89} -7.94397 q^{90} +5.01824 q^{91} -0.550681 q^{92} +33.1762 q^{93} +3.37747 q^{94} +2.92310 q^{95} -3.30817 q^{96} -9.04093 q^{97} +0.630104 q^{98} -28.1609 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q + 22 q^{2} + 2 q^{3} + 22 q^{4} - 22 q^{5} + 2 q^{6} + 13 q^{7} + 22 q^{8} + 32 q^{9}+O(q^{10}) \) 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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