LMFDB - Embedded newform 5290.2.a.bj.1.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [5290,2,Mod(1,5290)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(5290, 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("5290.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 5290 = 2 \cdot 5 \cdot 23^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	5290.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:	$42.2408626693$
Analytic rank:	$0$
Dimension:	$10$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 3x^{9} - 15x^{8} + 35x^{7} + 78x^{6} - 123x^{5} - 185x^{4} + 140x^{3} + 177x^{2} - 15x - 23 $ x^10 - 3x^9 - 15x^8 + 35x^7 + 78x^6 - 123x^5 - 185x^4 + 140x^3 + 177x^2 - 15*x - 23
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 230)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.10
Root			$2.18006$ of defining polynomial
Character	$\chi$	$=$	5290.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +3.38334 q^{3} +1.00000 q^{4} +1.00000 q^{5} -3.38334 q^{6} +3.53778 q^{7} -1.00000 q^{8} +8.44702 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +3.38334 q^{3} +1.00000 q^{4} +1.00000 q^{5} -3.38334 q^{6} +3.53778 q^{7} -1.00000 q^{8} +8.44702 q^{9} -1.00000 q^{10} +3.33417 q^{11} +3.38334 q^{12} -2.43018 q^{13} -3.53778 q^{14} +3.38334 q^{15} +1.00000 q^{16} -4.35358 q^{17} -8.44702 q^{18} +1.78091 q^{19} +1.00000 q^{20} +11.9695 q^{21} -3.33417 q^{22} -3.38334 q^{24} +1.00000 q^{25} +2.43018 q^{26} +18.4291 q^{27} +3.53778 q^{28} -4.44162 q^{29} -3.38334 q^{30} +2.31712 q^{31} -1.00000 q^{32} +11.2806 q^{33} +4.35358 q^{34} +3.53778 q^{35} +8.44702 q^{36} -3.78399 q^{37} -1.78091 q^{38} -8.22212 q^{39} -1.00000 q^{40} +8.33108 q^{41} -11.9695 q^{42} -4.49249 q^{43} +3.33417 q^{44} +8.44702 q^{45} -6.54226 q^{47} +3.38334 q^{48} +5.51592 q^{49} -1.00000 q^{50} -14.7297 q^{51} -2.43018 q^{52} -8.03354 q^{53} -18.4291 q^{54} +3.33417 q^{55} -3.53778 q^{56} +6.02543 q^{57} +4.44162 q^{58} +13.9206 q^{59} +3.38334 q^{60} -10.6374 q^{61} -2.31712 q^{62} +29.8837 q^{63} +1.00000 q^{64} -2.43018 q^{65} -11.2806 q^{66} -3.67337 q^{67} -4.35358 q^{68} -3.53778 q^{70} +9.02535 q^{71} -8.44702 q^{72} +2.44937 q^{73} +3.78399 q^{74} +3.38334 q^{75} +1.78091 q^{76} +11.7956 q^{77} +8.22212 q^{78} -2.29994 q^{79} +1.00000 q^{80} +37.0111 q^{81} -8.33108 q^{82} -1.40697 q^{83} +11.9695 q^{84} -4.35358 q^{85} +4.49249 q^{86} -15.0275 q^{87} -3.33417 q^{88} +16.4072 q^{89} -8.44702 q^{90} -8.59744 q^{91} +7.83961 q^{93} +6.54226 q^{94} +1.78091 q^{95} -3.38334 q^{96} -11.4769 q^{97} -5.51592 q^{98} +28.1638 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 10 q^{2} + 4 q^{3} + 10 q^{4} + 10 q^{5} - 4 q^{6} - 7 q^{7} - 10 q^{8} + 14 q^{9}+O(q^{10}) $ 10 * q - 10 * q^2 + 4 * q^3 + 10 * q^4 + 10 * q^5 - 4 * q^6 - 7 * q^7 - 10 * q^8 + 14 * q^9	\( 10 q - 10 q^{2} + 4 q^{3} + 10 q^{4} + 10 q^{5} - 4 q^{6} - 7 q^{7} - 10 q^{8} + 14 q^{9} - 10 q^{10} + 9 q^{11} + 4 q^{12} - 7 q^{13} + 7 q^{14} + 4 q^{15} + 10 q^{16} - 18 q^{17} - 14 q^{18} + 16 q^{19} + 10 q^{20} + 12 q^{21} - 9 q^{22} - 4 q^{24} + 10 q^{25} + 7 q^{26} + 13 q^{27} - 7 q^{28} + 10 q^{29} - 4 q^{30} - 3 q^{31} - 10 q^{32} + 25 q^{33} + 18 q^{34} - 7 q^{35} + 14 q^{36} - 8 q^{37} - 16 q^{38} + 12 q^{39} - 10 q^{40} + 10 q^{41} - 12 q^{42} - 9 q^{43} + 9 q^{44} + 14 q^{45} + 21 q^{47} + 4 q^{48} + 7 q^{49} - 10 q^{50} - 9 q^{51} - 7 q^{52} - 40 q^{53} - 13 q^{54} + 9 q^{55} + 7 q^{56} + 9 q^{57} - 10 q^{58} + 29 q^{59} + 4 q^{60} + 25 q^{61} + 3 q^{62} + 6 q^{63} + 10 q^{64} - 7 q^{65} - 25 q^{66} - 7 q^{67} - 18 q^{68} + 7 q^{70} + 64 q^{71} - 14 q^{72} - 16 q^{73} + 8 q^{74} + 4 q^{75} + 16 q^{76} + 57 q^{77} - 12 q^{78} + 44 q^{79} + 10 q^{80} + 14 q^{81} - 10 q^{82} - 26 q^{83} + 12 q^{84} - 18 q^{85} + 9 q^{86} + 25 q^{87} - 9 q^{88} + 11 q^{89} - 14 q^{90} + 5 q^{93} - 21 q^{94} + 16 q^{95} - 4 q^{96} - 10 q^{97} - 7 q^{98} + 13 q^{99}+O(q^{100}) \) 10 * q - 10 * q^2 + 4 * q^3 + 10 * q^4 + 10 * q^5 - 4 * q^6 - 7 * q^7 - 10 * q^8 + 14 * q^9 - 10 * q^10 + 9 * q^11 + 4 * q^12 - 7 * q^13 + 7 * q^14 + 4 * q^15 + 10 * q^16 - 18 * q^17 - 14 * q^18 + 16 * q^19 + 10 * q^20 + 12 * q^21 - 9 * q^22 - 4 * q^24 + 10 * q^25 + 7 * q^26 + 13 * q^27 - 7 * q^28 + 10 * q^29 - 4 * q^30 - 3 * q^31 - 10 * q^32 + 25 * q^33 + 18 * q^34 - 7 * q^35 + 14 * q^36 - 8 * q^37 - 16 * q^38 + 12 * q^39 - 10 * q^40 + 10 * q^41 - 12 * q^42 - 9 * q^43 + 9 * q^44 + 14 * q^45 + 21 * q^47 + 4 * q^48 + 7 * q^49 - 10 * q^50 - 9 * q^51 - 7 * q^52 - 40 * q^53 - 13 * q^54 + 9 * q^55 + 7 * q^56 + 9 * q^57 - 10 * q^58 + 29 * q^59 + 4 * q^60 + 25 * q^61 + 3 * q^62 + 6 * q^63 + 10 * q^64 - 7 * q^65 - 25 * q^66 - 7 * q^67 - 18 * q^68 + 7 * q^70 + 64 * q^71 - 14 * q^72 - 16 * q^73 + 8 * q^74 + 4 * q^75 + 16 * q^76 + 57 * q^77 - 12 * q^78 + 44 * q^79 + 10 * q^80 + 14 * q^81 - 10 * q^82 - 26 * q^83 + 12 * q^84 - 18 * q^85 + 9 * q^86 + 25 * q^87 - 9 * q^88 + 11 * q^89 - 14 * q^90 + 5 * q^93 - 21 * q^94 + 16 * q^95 - 4 * q^96 - 10 * q^97 - 7 * q^98 + 13 * 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
$3$	3.38334	1.95337	0.976687	−	0.214667i	$-0.0688665\pi$
$3$	3.38334	1.95337	0.976687	+	0.214667i	$0.0688665\pi$
$4$	1.00000	0.500000
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	−3.38334	−1.38124
$7$	3.53778	1.33716	0.668578	−	0.743642i	$-0.266903\pi$
$7$	3.53778	1.33716	0.668578	+	0.743642i	$0.266903\pi$
$8$	−1.00000	−0.353553
$9$	8.44702	2.81567
$10$	−1.00000	−0.316228
$11$	3.33417	1.00529	0.502645	−	0.864493i	$-0.332360\pi$
$11$	3.33417	1.00529	0.502645	+	0.864493i	$0.332360\pi$
$12$	3.38334	0.976687
$13$	−2.43018	−0.674009	−0.337005	−	0.941503i	$-0.609414\pi$
$13$	−2.43018	−0.674009	−0.337005	+	0.941503i	$0.609414\pi$
$14$	−3.53778	−0.945513
$15$	3.38334	0.873576
$16$	1.00000	0.250000
$17$	−4.35358	−1.05590	−0.527950	−	0.849276i	$-0.677039\pi$
$17$	−4.35358	−1.05590	−0.527950	+	0.849276i	$0.677039\pi$
$18$	−8.44702	−1.99098
$19$	1.78091	0.408568	0.204284	−	0.978912i	$-0.434513\pi$
$19$	1.78091	0.408568	0.204284	+	0.978912i	$0.434513\pi$
$20$	1.00000	0.223607
$21$	11.9695	2.61197
$22$	−3.33417	−0.710847
$23$	0	0
$23$	0	0
$24$	−3.38334	−0.690622
$25$	1.00000	0.200000
$26$	2.43018	0.476597
$27$	18.4291	3.54669
$28$	3.53778	0.668578
$29$	−4.44162	−0.824788	−0.412394	−	0.911006i	$-0.635307\pi$
$29$	−4.44162	−0.824788	−0.412394	+	0.911006i	$0.635307\pi$
$30$	−3.38334	−0.617711
$31$	2.31712	0.416167	0.208083	−	0.978111i	$-0.433277\pi$
$31$	2.31712	0.416167	0.208083	+	0.978111i	$0.433277\pi$
$32$	−1.00000	−0.176777
$33$	11.2806	1.96371
$34$	4.35358	0.746634
$35$	3.53778	0.597995
$36$	8.44702	1.40784
$37$	−3.78399	−0.622085	−0.311042	−	0.950396i	$-0.600678\pi$
$37$	−3.78399	−0.622085	−0.311042	+	0.950396i	$0.600678\pi$
$38$	−1.78091	−0.288902
$39$	−8.22212	−1.31659
$40$	−1.00000	−0.158114
$41$	8.33108	1.30110	0.650548	−	0.759465i	$-0.274539\pi$
$41$	8.33108	1.30110	0.650548	+	0.759465i	$0.274539\pi$
$42$	−11.9695	−1.84694
$43$	−4.49249	−0.685098	−0.342549	−	0.939500i	$-0.611290\pi$
$43$	−4.49249	−0.685098	−0.342549	+	0.939500i	$0.611290\pi$
$44$	3.33417	0.502645
$45$	8.44702	1.25921
$46$	0	0
$47$	−6.54226	−0.954286	−0.477143	−	0.878826i	$-0.658328\pi$
$47$	−6.54226	−0.954286	−0.477143	+	0.878826i	$0.658328\pi$
$48$	3.38334	0.488344
$49$	5.51592	0.787988
$50$	−1.00000	−0.141421
$51$	−14.7297	−2.06257
$52$	−2.43018	−0.337005
$53$	−8.03354	−1.10349	−0.551746	−	0.834012i	$-0.686038\pi$
$53$	−8.03354	−1.10349	−0.551746	+	0.834012i	$0.686038\pi$
$54$	−18.4291	−2.50789
$55$	3.33417	0.449579
$56$	−3.53778	−0.472756
$57$	6.02543	0.798087
$58$	4.44162	0.583213
$59$	13.9206	1.81230	0.906151	−	0.422953i	$-0.139007\pi$
$59$	13.9206	1.81230	0.906151	+	0.422953i	$0.139007\pi$
$60$	3.38334	0.436788
$61$	−10.6374	−1.36198	−0.680989	−	0.732293i	$-0.738450\pi$
$61$	−10.6374	−1.36198	−0.680989	+	0.732293i	$0.738450\pi$
$62$	−2.31712	−0.294275
$63$	29.8837	3.76500
$64$	1.00000	0.125000
$65$	−2.43018	−0.301426
$66$	−11.2806	−1.38855
$67$	−3.67337	−0.448773	−0.224387	−	0.974500i	$-0.572038\pi$
$67$	−3.67337	−0.448773	−0.224387	+	0.974500i	$0.572038\pi$
$68$	−4.35358	−0.527950
$69$	0	0
$70$	−3.53778	−0.422846
$71$	9.02535	1.07111	0.535556	−	0.844500i	$-0.320102\pi$
$71$	9.02535	1.07111	0.535556	+	0.844500i	$0.320102\pi$
$72$	−8.44702	−0.995491
$73$	2.44937	0.286677	0.143339	−	0.989674i	$-0.454216\pi$
$73$	2.44937	0.286677	0.143339	+	0.989674i	$0.454216\pi$
$74$	3.78399	0.439880
$75$	3.38334	0.390675
$76$	1.78091	0.204284
$77$	11.7956	1.34423
$78$	8.22212	0.930972
$79$	−2.29994	−0.258764	−0.129382	−	0.991595i	$-0.541299\pi$
$79$	−2.29994	−0.258764	−0.129382	+	0.991595i	$0.541299\pi$
$80$	1.00000	0.111803
$81$	37.0111	4.11234
$82$	−8.33108	−0.920014
$83$	−1.40697	−0.154435	−0.0772175	−	0.997014i	$-0.524604\pi$
$83$	−1.40697	−0.154435	−0.0772175	+	0.997014i	$0.524604\pi$
$84$	11.9695	1.30598
$85$	−4.35358	−0.472212
$86$	4.49249	0.484437
$87$	−15.0275	−1.61112
$88$	−3.33417	−0.355424
$89$	16.4072	1.73916	0.869581	−	0.493790i	$-0.164389\pi$
$89$	16.4072	1.73916	0.869581	+	0.493790i	$0.164389\pi$
$90$	−8.44702	−0.890394
$91$	−8.59744	−0.901256
$92$	0	0
$93$	7.83961	0.812930
$94$	6.54226	0.674782
$95$	1.78091	0.182717
$96$	−3.38334	−0.345311
$97$	−11.4769	−1.16530	−0.582649	−	0.812724i	$-0.697984\pi$
$97$	−11.4769	−1.16530	−0.582649	+	0.812724i	$0.697984\pi$
$98$	−5.51592	−0.557192
$99$	28.1638	2.83057
$100$	1.00000	0.100000
$101$	7.61470	0.757691	0.378846	−	0.925460i	$-0.376321\pi$
$101$	7.61470	0.757691	0.378846	+	0.925460i	$0.376321\pi$
$102$	14.7297	1.45846
$103$	−10.2417	−1.00914	−0.504570	−	0.863371i	$-0.668349\pi$
$103$	−10.2417	−1.00914	−0.504570	+	0.863371i	$0.668349\pi$
$104$	2.43018	0.238298
$105$	11.9695	1.16811
$106$	8.03354	0.780287
$107$	−1.59456	−0.154152	−0.0770758	−	0.997025i	$-0.524558\pi$
$107$	−1.59456	−0.154152	−0.0770758	+	0.997025i	$0.524558\pi$
$108$	18.4291	1.77334
$109$	5.94654	0.569575	0.284788	−	0.958591i	$-0.408077\pi$
$109$	5.94654	0.569575	0.284788	+	0.958591i	$0.408077\pi$
$110$	−3.33417	−0.317901
$111$	−12.8025	−1.21516
$112$	3.53778	0.334289
$113$	−7.26518	−0.683450	−0.341725	−	0.939800i	$-0.611011\pi$
$113$	−7.26518	−0.683450	−0.341725	+	0.939800i	$0.611011\pi$
$114$	−6.02543	−0.564333
$115$	0	0
$116$	−4.44162	−0.412394
$117$	−20.5277	−1.89779
$118$	−13.9206	−1.28149
$119$	−15.4020	−1.41190
$120$	−3.38334	−0.308856
$121$	0.116681	0.0106074
$122$	10.6374	0.963064
$123$	28.1869	2.54153
$124$	2.31712	0.208083
$125$	1.00000	0.0894427
$126$	−29.8837	−2.66225
$127$	6.37455	0.565650	0.282825	−	0.959172i	$-0.408728\pi$
$127$	6.37455	0.565650	0.282825	+	0.959172i	$0.408728\pi$
$128$	−1.00000	−0.0883883
$129$	−15.1996	−1.33825
$130$	2.43018	0.213140
$131$	−10.0167	−0.875160	−0.437580	−	0.899179i	$-0.644164\pi$
$131$	−10.0167	−0.875160	−0.437580	+	0.899179i	$0.644164\pi$
$132$	11.2806	0.981854
$133$	6.30047	0.546320
$134$	3.67337	0.317331
$135$	18.4291	1.58613
$136$	4.35358	0.373317
$137$	7.61920	0.650952	0.325476	−	0.945550i	$-0.394475\pi$
$137$	7.61920	0.650952	0.325476	+	0.945550i	$0.394475\pi$
$138$	0	0
$139$	−15.1421	−1.28434	−0.642170	−	0.766563i	$-0.721966\pi$
$139$	−15.1421	−1.28434	−0.642170	+	0.766563i	$0.721966\pi$
$140$	3.53778	0.298997
$141$	−22.1347	−1.86408
$142$	−9.02535	−0.757390
$143$	−8.10262	−0.677575
$144$	8.44702	0.703918
$145$	−4.44162	−0.368856
$146$	−2.44937	−0.202711
$147$	18.6622	1.53924
$148$	−3.78399	−0.311042
$149$	4.48641	0.367541	0.183770	−	0.982969i	$-0.441170\pi$
$149$	4.48641	0.367541	0.183770	+	0.982969i	$0.441170\pi$
$150$	−3.38334	−0.276249
$151$	−9.38108	−0.763422	−0.381711	−	0.924282i	$-0.624665\pi$
$151$	−9.38108	−0.763422	−0.381711	+	0.924282i	$0.624665\pi$
$152$	−1.78091	−0.144451
$153$	−36.7748	−2.97307
$154$	−11.7956	−0.950514
$155$	2.31712	0.186116
$156$	−8.22212	−0.658296
$157$	2.82948	0.225817	0.112909	−	0.993605i	$-0.463983\pi$
$157$	2.82948	0.225817	0.112909	+	0.993605i	$0.463983\pi$
$158$	2.29994	0.182974
$159$	−27.1802	−2.15553
$160$	−1.00000	−0.0790569
$161$	0	0
$162$	−37.0111	−2.90786
$163$	7.11484	0.557277	0.278639	−	0.960396i	$-0.410117\pi$
$163$	7.11484	0.557277	0.278639	+	0.960396i	$0.410117\pi$
$164$	8.33108	0.650548
$165$	11.2806	0.878197
$166$	1.40697	0.109202
$167$	3.99110	0.308841	0.154420	−	0.988005i	$-0.450649\pi$
$167$	3.99110	0.308841	0.154420	+	0.988005i	$0.450649\pi$
$168$	−11.9695	−0.923470
$169$	−7.09425	−0.545711
$170$	4.35358	0.333905
$171$	15.0434	1.15040
$172$	−4.49249	−0.342549
$173$	−25.4031	−1.93136	−0.965681	−	0.259732i	$-0.916366\pi$
$173$	−25.4031	−1.93136	−0.965681	+	0.259732i	$0.916366\pi$
$174$	15.0275	1.13923
$175$	3.53778	0.267431
$176$	3.33417	0.251322
$177$	47.0981	3.54011
$178$	−16.4072	−1.22977
$179$	19.6798	1.47093	0.735467	−	0.677560i	$-0.236963\pi$
$179$	19.6798	1.47093	0.735467	+	0.677560i	$0.236963\pi$
$180$	8.44702	0.629604
$181$	8.50950	0.632506	0.316253	−	0.948675i	$-0.397575\pi$
$181$	8.50950	0.632506	0.316253	+	0.948675i	$0.397575\pi$
$182$	8.59744	0.637284
$183$	−35.9900	−2.66045
$184$	0	0
$185$	−3.78399	−0.278205
$186$	−7.83961	−0.574828
$187$	−14.5156	−1.06148
$188$	−6.54226	−0.477143
$189$	65.1983	4.74248
$190$	−1.78091	−0.129201
$191$	−19.2860	−1.39549	−0.697743	−	0.716348i	$-0.745812\pi$
$191$	−19.2860	−1.39549	−0.697743	+	0.716348i	$0.745812\pi$
$192$	3.38334	0.244172
$193$	−13.9162	−1.00171	−0.500855	−	0.865531i	$-0.666981\pi$
$193$	−13.9162	−1.00171	−0.500855	+	0.865531i	$0.666981\pi$
$194$	11.4769	0.823990
$195$	−8.22212	−0.588798
$196$	5.51592	0.393994
$197$	6.81165	0.485310	0.242655	−	0.970113i	$-0.421982\pi$
$197$	6.81165	0.485310	0.242655	+	0.970113i	$0.421982\pi$
$198$	−28.1638	−2.00151
$199$	−22.0610	−1.56386	−0.781931	−	0.623365i	$-0.785765\pi$
$199$	−22.0610	−1.56386	−0.781931	+	0.623365i	$0.785765\pi$
$200$	−1.00000	−0.0707107
$201$	−12.4283	−0.876622
$202$	−7.61470	−0.535769
$203$	−15.7135	−1.10287
$204$	−14.7297	−1.03128
$205$	8.33108	0.581868
$206$	10.2417	0.713570
$207$	0	0
$208$	−2.43018	−0.168502
$209$	5.93785	0.410730
$210$	−11.9695	−0.825977
$211$	3.01212	0.207363	0.103682	−	0.994611i	$-0.466938\pi$
$211$	3.01212	0.207363	0.103682	+	0.994611i	$0.466938\pi$
$212$	−8.03354	−0.551746
$213$	30.5359	2.09228
$214$	1.59456	0.109002
$215$	−4.49249	−0.306385
$216$	−18.4291	−1.25394
$217$	8.19747	0.556481
$218$	−5.94654	−0.402750
$219$	8.28707	0.559988
$220$	3.33417	0.224790
$221$	10.5800	0.711686
$222$	12.8025	0.859251
$223$	−2.02024	−0.135285	−0.0676426	−	0.997710i	$-0.521548\pi$
$223$	−2.02024	−0.135285	−0.0676426	+	0.997710i	$0.521548\pi$
$224$	−3.53778	−0.236378
$225$	8.44702	0.563135
$226$	7.26518	0.483272
$227$	−12.3916	−0.822456	−0.411228	−	0.911532i	$-0.634900\pi$
$227$	−12.3916	−0.822456	−0.411228	+	0.911532i	$0.634900\pi$
$228$	6.02543	0.399044
$229$	26.1155	1.72576	0.862880	−	0.505409i	$-0.168658\pi$
$229$	26.1155	1.72576	0.862880	+	0.505409i	$0.168658\pi$
$230$	0	0
$231$	39.9085	2.62578
$232$	4.44162	0.291606
$233$	14.1223	0.925184	0.462592	−	0.886571i	$-0.346920\pi$
$233$	14.1223	0.925184	0.462592	+	0.886571i	$0.346920\pi$
$234$	20.5277	1.34194
$235$	−6.54226	−0.426770
$236$	13.9206	0.906151
$237$	−7.78150	−0.505463
$238$	15.4020	0.998366
$239$	4.98764	0.322623	0.161312	−	0.986904i	$-0.448428\pi$
$239$	4.98764	0.322623	0.161312	+	0.986904i	$0.448428\pi$
$240$	3.38334	0.218394
$241$	−1.68484	−0.108530	−0.0542650	−	0.998527i	$-0.517282\pi$
$241$	−1.68484	−0.108530	−0.0542650	+	0.998527i	$0.517282\pi$
$242$	−0.116681	−0.00750054
$243$	69.9338	4.48625
$244$	−10.6374	−0.680989
$245$	5.51592	0.352399
$246$	−28.1869	−1.79713
$247$	−4.32792	−0.275379
$248$	−2.31712	−0.147137
$249$	−4.76026	−0.301669
$250$	−1.00000	−0.0632456
$251$	−23.6506	−1.49282	−0.746408	−	0.665489i	$-0.768223\pi$
$251$	−23.6506	−1.49282	−0.746408	+	0.665489i	$0.768223\pi$
$252$	29.8837	1.88250
$253$	0	0
$254$	−6.37455	−0.399975
$255$	−14.7297	−0.922408
$256$	1.00000	0.0625000
$257$	16.3299	1.01863	0.509317	−	0.860579i	$-0.329898\pi$
$257$	16.3299	1.01863	0.509317	+	0.860579i	$0.329898\pi$
$258$	15.1996	0.946288
$259$	−13.3869	−0.831825
$260$	−2.43018	−0.150713
$261$	−37.5184	−2.32233
$262$	10.0167	0.618832
$263$	1.51751	0.0935736	0.0467868	−	0.998905i	$-0.485102\pi$
$263$	1.51751	0.0935736	0.0467868	+	0.998905i	$0.485102\pi$
$264$	−11.2806	−0.694275
$265$	−8.03354	−0.493497
$266$	−6.30047	−0.386307
$267$	55.5113	3.39723
$268$	−3.67337	−0.224387
$269$	−20.6569	−1.25947	−0.629737	−	0.776808i	$-0.716838\pi$
$269$	−20.6569	−1.25947	−0.629737	+	0.776808i	$0.716838\pi$
$270$	−18.4291	−1.12156
$271$	−11.5571	−0.702044	−0.351022	−	0.936367i	$-0.614166\pi$
$271$	−11.5571	−0.702044	−0.351022	+	0.936367i	$0.614166\pi$
$272$	−4.35358	−0.263975
$273$	−29.0881	−1.76049
$274$	−7.61920	−0.460293
$275$	3.33417	0.201058
$276$	0	0
$277$	1.27581	0.0766562	0.0383281	−	0.999265i	$-0.487797\pi$
$277$	1.27581	0.0766562	0.0383281	+	0.999265i	$0.487797\pi$
$278$	15.1421	0.908165
$279$	19.5728	1.17179
$280$	−3.53778	−0.211423
$281$	5.46716	0.326144	0.163072	−	0.986614i	$-0.447860\pi$
$281$	5.46716	0.326144	0.163072	+	0.986614i	$0.447860\pi$
$282$	22.1347	1.31810
$283$	−0.331807	−0.0197239	−0.00986195	−	0.999951i	$-0.503139\pi$
$283$	−0.331807	−0.0197239	−0.00986195	+	0.999951i	$0.503139\pi$
$284$	9.02535	0.535556
$285$	6.02543	0.356915
$286$	8.10262	0.479118
$287$	29.4736	1.73977
$288$	−8.44702	−0.497745
$289$	1.95369	0.114923
$290$	4.44162	0.260821
$291$	−38.8301	−2.27626
$292$	2.44937	0.143339
$293$	−16.0632	−0.938422	−0.469211	−	0.883086i	$-0.655462\pi$
$293$	−16.0632	−0.938422	−0.469211	+	0.883086i	$0.655462\pi$
$294$	−18.6622	−1.08840
$295$	13.9206	0.810487
$296$	3.78399	0.219940
$297$	61.4459	3.56545
$298$	−4.48641	−0.259891
$299$	0	0
$300$	3.38334	0.195337
$301$	−15.8935	−0.916083
$302$	9.38108	0.539821
$303$	25.7632	1.48006
$304$	1.78091	0.102142
$305$	−10.6374	−0.609095
$306$	36.7748	2.10228
$307$	32.5315	1.85667	0.928334	−	0.371747i	$-0.121241\pi$
$307$	32.5315	1.85667	0.928334	+	0.371747i	$0.121241\pi$
$308$	11.7956	0.672115
$309$	−34.6510	−1.97123
$310$	−2.31712	−0.131604
$311$	−1.98622	−0.112628	−0.0563142	−	0.998413i	$-0.517935\pi$
$311$	−1.98622	−0.112628	−0.0563142	+	0.998413i	$0.517935\pi$
$312$	8.22212	0.465486
$313$	−3.87002	−0.218747	−0.109373	−	0.994001i	$-0.534884\pi$
$313$	−3.87002	−0.218747	−0.109373	+	0.994001i	$0.534884\pi$
$314$	−2.82948	−0.159677
$315$	29.8837	1.68376
$316$	−2.29994	−0.129382
$317$	−2.08907	−0.117334	−0.0586669	−	0.998278i	$-0.518685\pi$
$317$	−2.08907	−0.117334	−0.0586669	+	0.998278i	$0.518685\pi$
$318$	27.1802	1.52419
$319$	−14.8091	−0.829151
$320$	1.00000	0.0559017
$321$	−5.39493	−0.301116
$322$	0	0
$323$	−7.75334	−0.431407
$324$	37.0111	2.05617
$325$	−2.43018	−0.134802
$326$	−7.11484	−0.394055
$327$	20.1192	1.11259
$328$	−8.33108	−0.460007
$329$	−23.1451	−1.27603
$330$	−11.2806	−0.620979
$331$	12.8146	0.704352	0.352176	−	0.935934i	$-0.385442\pi$
$331$	12.8146	0.704352	0.352176	+	0.935934i	$0.385442\pi$
$332$	−1.40697	−0.0772175
$333$	−31.9635	−1.75159
$334$	−3.99110	−0.218384
$335$	−3.67337	−0.200697
$336$	11.9695	0.652992
$337$	11.5172	0.627382	0.313691	−	0.949525i	$-0.398434\pi$
$337$	11.5172	0.627382	0.313691	+	0.949525i	$0.398434\pi$
$338$	7.09425	0.385876
$339$	−24.5806	−1.33503
$340$	−4.35358	−0.236106
$341$	7.72567	0.418368
$342$	−15.0434	−0.813452
$343$	−5.25036	−0.283493
$344$	4.49249	0.242219
$345$	0	0
$346$	25.4031	1.36568
$347$	−4.30390	−0.231045	−0.115523	−	0.993305i	$-0.536854\pi$
$347$	−4.30390	−0.231045	−0.115523	+	0.993305i	$0.536854\pi$
$348$	−15.0275	−0.805560
$349$	−9.62427	−0.515175	−0.257588	−	0.966255i	$-0.582928\pi$
$349$	−9.62427	−0.515175	−0.257588	+	0.966255i	$0.582928\pi$
$350$	−3.53778	−0.189103
$351$	−44.7860	−2.39050
$352$	−3.33417	−0.177712
$353$	−29.0473	−1.54603	−0.773016	−	0.634386i	$-0.781253\pi$
$353$	−29.0473	−1.54603	−0.773016	+	0.634386i	$0.781253\pi$
$354$	−47.0981	−2.50323
$355$	9.02535	0.479016
$356$	16.4072	0.869581
$357$	−52.1104	−2.75798
$358$	−19.6798	−1.04011
$359$	−24.8902	−1.31366	−0.656828	−	0.754040i	$-0.728102\pi$
$359$	−24.8902	−1.31366	−0.656828	+	0.754040i	$0.728102\pi$
$360$	−8.44702	−0.445197
$361$	−15.8284	−0.833072
$362$	−8.50950	−0.447249
$363$	0.394772	0.0207202
$364$	−8.59744	−0.450628
$365$	2.44937	0.128206
$366$	35.9900	1.88123
$367$	32.1217	1.67674	0.838369	−	0.545104i	$-0.183510\pi$
$367$	32.1217	1.67674	0.838369	+	0.545104i	$0.183510\pi$
$368$	0	0
$369$	70.3728	3.66346
$370$	3.78399	0.196720
$371$	−28.4209	−1.47554
$372$	7.83961	0.406465
$373$	20.6793	1.07073	0.535366	−	0.844620i	$-0.320174\pi$
$373$	20.6793	1.07073	0.535366	+	0.844620i	$0.320174\pi$
$374$	14.5156	0.750583
$375$	3.38334	0.174715
$376$	6.54226	0.337391
$377$	10.7939	0.555915
$378$	−65.1983	−3.35344
$379$	−26.0645	−1.33884	−0.669422	−	0.742882i	$-0.733458\pi$
$379$	−26.0645	−1.33884	−0.669422	+	0.742882i	$0.733458\pi$
$380$	1.78091	0.0913587
$381$	21.5673	1.10493
$382$	19.2860	0.986758
$383$	10.9310	0.558547	0.279273	−	0.960212i	$-0.409906\pi$
$383$	10.9310	0.558547	0.279273	+	0.960212i	$0.409906\pi$
$384$	−3.38334	−0.172656
$385$	11.7956	0.601158
$386$	13.9162	0.708315
$387$	−37.9481	−1.92901
$388$	−11.4769	−0.582649
$389$	32.4593	1.64575	0.822876	−	0.568221i	$-0.192368\pi$
$389$	32.4593	1.64575	0.822876	+	0.568221i	$0.192368\pi$
$390$	8.22212	0.416343
$391$	0	0
$392$	−5.51592	−0.278596
$393$	−33.8898	−1.70952
$394$	−6.81165	−0.343166
$395$	−2.29994	−0.115723
$396$	28.1638	1.41528
$397$	13.8549	0.695356	0.347678	−	0.937614i	$-0.386970\pi$
$397$	13.8549	0.695356	0.347678	+	0.937614i	$0.386970\pi$
$398$	22.0610	1.10582
$399$	21.3167	1.06717
$400$	1.00000	0.0500000
$401$	−16.6025	−0.829089	−0.414545	−	0.910029i	$-0.636059\pi$
$401$	−16.6025	−0.829089	−0.414545	+	0.910029i	$0.636059\pi$
$402$	12.4283	0.619865
$403$	−5.63101	−0.280500
$404$	7.61470	0.378846
$405$	37.0111	1.83909
$406$	15.7135	0.779847
$407$	−12.6165	−0.625375
$408$	14.7297	0.729228
$409$	−30.4406	−1.50519	−0.752595	−	0.658483i	$-0.771198\pi$
$409$	−30.4406	−1.50519	−0.752595	+	0.658483i	$0.771198\pi$
$410$	−8.33108	−0.411443
$411$	25.7784	1.27155
$412$	−10.2417	−0.504570
$413$	49.2480	2.42333
$414$	0	0
$415$	−1.40697	−0.0690654
$416$	2.43018	0.119149
$417$	−51.2311	−2.50880
$418$	−5.93785	−0.290430
$419$	19.5903	0.957051	0.478525	−	0.878074i	$-0.341171\pi$
$419$	19.5903	0.957051	0.478525	+	0.878074i	$0.341171\pi$
$420$	11.9695	0.584054
$421$	3.96577	0.193280	0.0966399	−	0.995319i	$-0.469190\pi$
$421$	3.96577	0.193280	0.0966399	+	0.995319i	$0.469190\pi$
$422$	−3.01212	−0.146628
$423$	−55.2626	−2.68696
$424$	8.03354	0.390143
$425$	−4.35358	−0.211180
$426$	−30.5359	−1.47947
$427$	−37.6328	−1.82118
$428$	−1.59456	−0.0770758
$429$	−27.4139	−1.32356
$430$	4.49249	0.216647
$431$	−5.02348	−0.241972	−0.120986	−	0.992654i	$-0.538606\pi$
$431$	−5.02348	−0.241972	−0.120986	+	0.992654i	$0.538606\pi$
$432$	18.4291	0.886672
$433$	3.80524	0.182868	0.0914340	−	0.995811i	$-0.470855\pi$
$433$	3.80524	0.182868	0.0914340	+	0.995811i	$0.470855\pi$
$434$	−8.19747	−0.393491
$435$	−15.0275	−0.720514
$436$	5.94654	0.284788
$437$	0	0
$438$	−8.28707	−0.395971
$439$	−23.5718	−1.12502	−0.562510	−	0.826790i	$-0.690164\pi$
$439$	−23.5718	−1.12502	−0.562510	+	0.826790i	$0.690164\pi$
$440$	−3.33417	−0.158950
$441$	46.5931	2.21872
$442$	−10.5800	−0.503238
$443$	2.78788	0.132456	0.0662281	−	0.997805i	$-0.478903\pi$
$443$	2.78788	0.132456	0.0662281	+	0.997805i	$0.478903\pi$
$444$	−12.8025	−0.607582
$445$	16.4072	0.777777
$446$	2.02024	0.0956611
$447$	15.1791	0.717945
$448$	3.53778	0.167145
$449$	19.5177	0.921095	0.460548	−	0.887635i	$-0.347653\pi$
$449$	19.5177	0.921095	0.460548	+	0.887635i	$0.347653\pi$
$450$	−8.44702	−0.398196
$451$	27.7772	1.30798
$452$	−7.26518	−0.341725
$453$	−31.7394	−1.49125
$454$	12.3916	0.581564
$455$	−8.59744	−0.403054
$456$	−6.02543	−0.282166
$457$	3.19534	0.149472	0.0747358	−	0.997203i	$-0.476189\pi$
$457$	3.19534	0.149472	0.0747358	+	0.997203i	$0.476189\pi$
$458$	−26.1155	−1.22030
$459$	−80.2328	−3.74495
$460$	0	0
$461$	−13.2998	−0.619436	−0.309718	−	0.950829i	$-0.600235\pi$
$461$	−13.2998	−0.619436	−0.309718	+	0.950829i	$0.600235\pi$
$462$	−39.9085	−1.85671
$463$	19.7562	0.918147	0.459073	−	0.888398i	$-0.348182\pi$
$463$	19.7562	0.918147	0.459073	+	0.888398i	$0.348182\pi$
$464$	−4.44162	−0.206197
$465$	7.83961	0.363553
$466$	−14.1223	−0.654204
$467$	−8.14078	−0.376710	−0.188355	−	0.982101i	$-0.560316\pi$
$467$	−8.14078	−0.376710	−0.188355	+	0.982101i	$0.560316\pi$
$468$	−20.5277	−0.948895
$469$	−12.9956	−0.600080
$470$	6.54226	0.301772
$471$	9.57310	0.441105
$472$	−13.9206	−0.640746
$473$	−14.9787	−0.688722
$474$	7.78150	0.357416
$475$	1.78091	0.0817137
$476$	−15.4020	−0.705951
$477$	−67.8595	−3.10707
$478$	−4.98764	−0.228129
$479$	5.50415	0.251491	0.125745	−	0.992063i	$-0.459868\pi$
$479$	5.50415	0.251491	0.125745	+	0.992063i	$0.459868\pi$
$480$	−3.38334	−0.154428
$481$	9.19577	0.419291
$482$	1.68484	0.0767423
$483$	0	0
$484$	0.116681	0.00530368
$485$	−11.4769	−0.521137
$486$	−69.9338	−3.17226
$487$	−29.9224	−1.35591	−0.677956	−	0.735103i	$-0.737134\pi$
$487$	−29.9224	−1.35591	−0.677956	+	0.735103i	$0.737134\pi$
$488$	10.6374	0.481532
$489$	24.0720	1.08857
$490$	−5.51592	−0.249184
$491$	29.5996	1.33581	0.667905	−	0.744246i	$-0.267191\pi$
$491$	29.5996	1.33581	0.667905	+	0.744246i	$0.267191\pi$
$492$	28.1869	1.27076
$493$	19.3370	0.870893
$494$	4.32792	0.194722
$495$	28.1638	1.26587
$496$	2.31712	0.104042
$497$	31.9297	1.43224
$498$	4.76026	0.213312
$499$	−20.3461	−0.910816	−0.455408	−	0.890283i	$-0.650507\pi$
$499$	−20.3461	−0.910816	−0.455408	+	0.890283i	$0.650507\pi$
$500$	1.00000	0.0447214
$501$	13.5033	0.603282
$502$	23.6506	1.05558
$503$	6.98370	0.311388	0.155694	−	0.987805i	$-0.450239\pi$
$503$	6.98370	0.311388	0.155694	+	0.987805i	$0.450239\pi$
$504$	−29.8837	−1.33113
$505$	7.61470	0.338850
$506$	0	0
$507$	−24.0023	−1.06598
$508$	6.37455	0.282825
$509$	37.4181	1.65853	0.829264	−	0.558857i	$-0.188760\pi$
$509$	37.4181	1.65853	0.829264	+	0.558857i	$0.188760\pi$
$510$	14.7297	0.652241
$511$	8.66535	0.383332
$512$	−1.00000	−0.0441942
$513$	32.8206	1.44907
$514$	−16.3299	−0.720283
$515$	−10.2417	−0.451301
$516$	−15.1996	−0.669126
$517$	−21.8130	−0.959334
$518$	13.3869	0.588189
$519$	−85.9474	−3.77267
$520$	2.43018	0.106570
$521$	6.13543	0.268798	0.134399	−	0.990927i	$-0.457090\pi$
$521$	6.13543	0.268798	0.134399	+	0.990927i	$0.457090\pi$
$522$	37.5184	1.64214
$523$	−34.1396	−1.49282	−0.746410	−	0.665487i	$-0.768224\pi$
$523$	−34.1396	−1.49282	−0.746410	+	0.665487i	$0.768224\pi$
$524$	−10.0167	−0.437580
$525$	11.9695	0.522394
$526$	−1.51751	−0.0661665
$527$	−10.0878	−0.439430
$528$	11.2806	0.490927
$529$	0	0
$530$	8.03354	0.348955
$531$	117.587	5.10285
$532$	6.30047	0.273160
$533$	−20.2460	−0.876951
$534$	−55.5113	−2.40221
$535$	−1.59456	−0.0689387
$536$	3.67337	0.158665
$537$	66.5834	2.87329
$538$	20.6569	0.890583
$539$	18.3910	0.792157
$540$	18.4291	0.793064
$541$	−5.17218	−0.222370	−0.111185	−	0.993800i	$-0.535465\pi$
$541$	−5.17218	−0.222370	−0.111185	+	0.993800i	$0.535465\pi$
$542$	11.5571	0.496420
$543$	28.7906	1.23552
$544$	4.35358	0.186658
$545$	5.94654	0.254722
$546$	29.0881	1.24486
$547$	−0.525089	−0.0224512	−0.0112256	−	0.999937i	$-0.503573\pi$
$547$	−0.525089	−0.0224512	−0.0112256	+	0.999937i	$0.503573\pi$
$548$	7.61920	0.325476
$549$	−89.8542	−3.83489
$550$	−3.33417	−0.142169
$551$	−7.91011	−0.336982
$552$	0	0
$553$	−8.13670	−0.346008
$554$	−1.27581	−0.0542041
$555$	−12.8025	−0.543438
$556$	−15.1421	−0.642170
$557$	−7.85593	−0.332866	−0.166433	−	0.986053i	$-0.553225\pi$
$557$	−7.85593	−0.332866	−0.166433	+	0.986053i	$0.553225\pi$
$558$	−19.5728	−0.828581
$559$	10.9175	0.461762
$560$	3.53778	0.149499
$561$	−49.1112	−2.07348
$562$	−5.46716	−0.230618
$563$	−9.02179	−0.380223	−0.190112	−	0.981762i	$-0.560885\pi$
$563$	−9.02179	−0.380223	−0.190112	+	0.981762i	$0.560885\pi$
$564$	−22.1347	−0.932039
$565$	−7.26518	−0.305648
$566$	0.331807	0.0139469
$567$	130.937	5.49884
$568$	−9.02535	−0.378695
$569$	36.3897	1.52554	0.762768	−	0.646672i	$-0.223840\pi$
$569$	36.3897	1.52554	0.762768	+	0.646672i	$0.223840\pi$
$570$	−6.02543	−0.252377
$571$	−24.0484	−1.00639	−0.503197	−	0.864172i	$-0.667843\pi$
$571$	−24.0484	−1.00639	−0.503197	+	0.864172i	$0.667843\pi$
$572$	−8.10262	−0.338787
$573$	−65.2512	−2.72591
$574$	−29.4736	−1.23020
$575$	0	0
$576$	8.44702	0.351959
$577$	−10.6131	−0.441831	−0.220915	−	0.975293i	$-0.570904\pi$
$577$	−10.6131	−0.441831	−0.220915	+	0.975293i	$0.570904\pi$
$578$	−1.95369	−0.0812630
$579$	−47.0833	−1.95671
$580$	−4.44162	−0.184428
$581$	−4.97755	−0.206504
$582$	38.8301	1.60956
$583$	−26.7852	−1.10933
$584$	−2.44937	−0.101356
$585$	−20.5277	−0.848717
$586$	16.0632	0.663564
$587$	32.1277	1.32605	0.663027	−	0.748596i	$-0.269272\pi$
$587$	32.1277	1.32605	0.663027	+	0.748596i	$0.269272\pi$
$588$	18.6622	0.769618
$589$	4.12658	0.170033
$590$	−13.9206	−0.573101
$591$	23.0461	0.947992
$592$	−3.78399	−0.155521
$593$	23.3037	0.956969	0.478485	−	0.878096i	$-0.341186\pi$
$593$	23.3037	0.956969	0.478485	+	0.878096i	$0.341186\pi$
$594$	−61.4459	−2.52115
$595$	−15.4020	−0.631422
$596$	4.48641	0.183770
$597$	−74.6399	−3.05481
$598$	0	0
$599$	9.23034	0.377141	0.188571	−	0.982060i	$-0.439615\pi$
$599$	9.23034	0.377141	0.188571	+	0.982060i	$0.439615\pi$
$600$	−3.38334	−0.138124
$601$	39.1513	1.59702	0.798508	−	0.601984i	$-0.205623\pi$
$601$	39.1513	1.59702	0.798508	+	0.601984i	$0.205623\pi$
$602$	15.8935	0.647769
$603$	−31.0290	−1.26360
$604$	−9.38108	−0.381711
$605$	0.116681	0.00474376
$606$	−25.7632	−1.04656
$607$	−0.640097	−0.0259808	−0.0129904	−	0.999916i	$-0.504135\pi$
$607$	−0.640097	−0.0259808	−0.0129904	+	0.999916i	$0.504135\pi$
$608$	−1.78091	−0.0722254
$609$	−53.1641	−2.15432
$610$	10.6374	0.430695
$611$	15.8988	0.643198
$612$	−36.7748	−1.48653
$613$	−4.62122	−0.186649	−0.0933246	−	0.995636i	$-0.529749\pi$
$613$	−4.62122	−0.186649	−0.0933246	+	0.995636i	$0.529749\pi$
$614$	−32.5315	−1.31286
$615$	28.1869	1.13661
$616$	−11.7956	−0.475257
$617$	−24.3299	−0.979485	−0.489742	−	0.871867i	$-0.662909\pi$
$617$	−24.3299	−0.979485	−0.489742	+	0.871867i	$0.662909\pi$
$618$	34.6510	1.39387
$619$	37.1887	1.49474	0.747370	−	0.664408i	$-0.231316\pi$
$619$	37.1887	1.49474	0.747370	+	0.664408i	$0.231316\pi$
$620$	2.31712	0.0930578
$621$	0	0
$622$	1.98622	0.0796404
$623$	58.0452	2.32553
$624$	−8.22212	−0.329148
$625$	1.00000	0.0400000
$626$	3.87002	0.154677
$627$	20.0898	0.802309
$628$	2.82948	0.112909
$629$	16.4739	0.656859
$630$	−29.8837	−1.19060
$631$	36.5510	1.45507	0.727537	−	0.686069i	$-0.240665\pi$
$631$	36.5510	1.45507	0.727537	+	0.686069i	$0.240665\pi$
$632$	2.29994	0.0914868
$633$	10.1910	0.405058
$634$	2.08907	0.0829675
$635$	6.37455	0.252966
$636$	−27.1802	−1.07777
$637$	−13.4046	−0.531112
$638$	14.8091	0.586298
$639$	76.2373	3.01590
$640$	−1.00000	−0.0395285
$641$	11.1254	0.439425	0.219712	−	0.975565i	$-0.429488\pi$
$641$	11.1254	0.439425	0.219712	+	0.975565i	$0.429488\pi$
$642$	5.39493	0.212921
$643$	−9.80294	−0.386590	−0.193295	−	0.981141i	$-0.561917\pi$
$643$	−9.80294	−0.386590	−0.193295	+	0.981141i	$0.561917\pi$
$644$	0	0
$645$	−15.1996	−0.598485
$646$	7.75334	0.305051
$647$	25.5077	1.00281	0.501406	−	0.865212i	$-0.332816\pi$
$647$	25.5077	1.00281	0.501406	+	0.865212i	$0.332816\pi$
$648$	−37.0111	−1.45393
$649$	46.4135	1.82189
$650$	2.43018	0.0953193
$651$	27.7349	1.08701
$652$	7.11484	0.278639
$653$	42.5074	1.66344	0.831721	−	0.555193i	$-0.187356\pi$
$653$	42.5074	1.66344	0.831721	+	0.555193i	$0.187356\pi$
$654$	−20.1192	−0.786723
$655$	−10.0167	−0.391384
$656$	8.33108	0.325274
$657$	20.6899	0.807189
$658$	23.1451	0.902290
$659$	−33.3969	−1.30096	−0.650479	−	0.759524i	$-0.725432\pi$
$659$	−33.3969	−1.30096	−0.650479	+	0.759524i	$0.725432\pi$
$660$	11.2806	0.439098
$661$	−29.3325	−1.14090	−0.570451	−	0.821332i	$-0.693231\pi$
$661$	−29.3325	−1.14090	−0.570451	+	0.821332i	$0.693231\pi$
$662$	−12.8146	−0.498052
$663$	35.7957	1.39019
$664$	1.40697	0.0546010
$665$	6.30047	0.244322
$666$	31.9635	1.23856
$667$	0	0
$668$	3.99110	0.154420
$669$	−6.83517	−0.264263
$670$	3.67337	0.141915
$671$	−35.4669	−1.36918
$672$	−11.9695	−0.461735
$673$	−38.7584	−1.49403	−0.747014	−	0.664809i	$-0.768513\pi$
$673$	−38.7584	−1.49403	−0.747014	+	0.664809i	$0.768513\pi$
$674$	−11.5172	−0.443626
$675$	18.4291	0.709338
$676$	−7.09425	−0.272856
$677$	−6.17991	−0.237513	−0.118757	−	0.992923i	$-0.537891\pi$
$677$	−6.17991	−0.237513	−0.118757	+	0.992923i	$0.537891\pi$
$678$	24.5806	0.944012
$679$	−40.6026	−1.55819
$680$	4.35358	0.166952
$681$	−41.9249	−1.60656
$682$	−7.72567	−0.295831
$683$	−14.2270	−0.544380	−0.272190	−	0.962244i	$-0.587748\pi$
$683$	−14.2270	−0.544380	−0.272190	+	0.962244i	$0.587748\pi$
$684$	15.0434	0.575198
$685$	7.61920	0.291115
$686$	5.25036	0.200460
$687$	88.3577	3.37106
$688$	−4.49249	−0.171274
$689$	19.5229	0.743764
$690$	0	0
$691$	−18.7466	−0.713153	−0.356576	−	0.934266i	$-0.616056\pi$
$691$	−18.7466	−0.713153	−0.356576	+	0.934266i	$0.616056\pi$
$692$	−25.4031	−0.965681
$693$	99.6374	3.78491
$694$	4.30390	0.163374
$695$	−15.1421	−0.574374
$696$	15.0275	0.569617
$697$	−36.2700	−1.37383
$698$	9.62427	0.364284
$699$	47.7807	1.80723
$700$	3.53778	0.133716
$701$	45.9217	1.73444	0.867219	−	0.497927i	$-0.165905\pi$
$701$	45.9217	1.73444	0.867219	+	0.497927i	$0.165905\pi$
$702$	44.7860	1.69034
$703$	−6.73894	−0.254164
$704$	3.33417	0.125661
$705$	−22.1347	−0.833641
$706$	29.0473	1.09321
$707$	26.9392	1.01315
$708$	47.0981	1.77005
$709$	−2.34170	−0.0879443	−0.0439722	−	0.999033i	$-0.514001\pi$
$709$	−2.34170	−0.0879443	−0.0439722	+	0.999033i	$0.514001\pi$
$710$	−9.02535	−0.338715
$711$	−19.4277	−0.728594
$712$	−16.4072	−0.614887
$713$	0	0
$714$	52.1104	1.95018
$715$	−8.10262	−0.303021
$716$	19.6798	0.735467
$717$	16.8749	0.630204
$718$	24.8902	0.928896
$719$	9.43723	0.351949	0.175975	−	0.984395i	$-0.443692\pi$
$719$	9.43723	0.351949	0.175975	+	0.984395i	$0.443692\pi$
$720$	8.44702	0.314802
$721$	−36.2328	−1.34938
$722$	15.8284	0.589071
$723$	−5.70039	−0.212000
$724$	8.50950	0.316253
$725$	−4.44162	−0.164958
$726$	−0.394772	−0.0146514
$727$	−19.5490	−0.725032	−0.362516	−	0.931977i	$-0.618082\pi$
$727$	−19.5490	−0.725032	−0.362516	+	0.931977i	$0.618082\pi$
$728$	8.59744	0.318642
$729$	125.577	4.65099
$730$	−2.44937	−0.0906553
$731$	19.5584	0.723394
$732$	−35.9900	−1.33023
$733$	−3.35179	−0.123801	−0.0619006	−	0.998082i	$-0.519716\pi$
$733$	−3.35179	−0.123801	−0.0619006	+	0.998082i	$0.519716\pi$
$734$	−32.1217	−1.18563
$735$	18.6622	0.688367
$736$	0	0
$737$	−12.2476	−0.451147
$738$	−70.3728	−2.59046
$739$	−29.4663	−1.08394	−0.541968	−	0.840399i	$-0.682321\pi$
$739$	−29.4663	−1.08394	−0.541968	+	0.840399i	$0.682321\pi$
$740$	−3.78399	−0.139102
$741$	−14.6428	−0.537918
$742$	28.4209	1.04337
$743$	−25.7813	−0.945823	−0.472911	−	0.881110i	$-0.656797\pi$
$743$	−25.7813	−0.945823	−0.472911	+	0.881110i	$0.656797\pi$
$744$	−7.83961	−0.287414
$745$	4.48641	0.164369
$746$	−20.6793	−0.757122
$747$	−11.8847	−0.434838
$748$	−14.5156	−0.530742
$749$	−5.64120	−0.206125
$750$	−3.38334	−0.123542
$751$	3.82448	0.139557	0.0697786	−	0.997563i	$-0.477771\pi$
$751$	3.82448	0.139557	0.0697786	+	0.997563i	$0.477771\pi$
$752$	−6.54226	−0.238572
$753$	−80.0183	−2.91603
$754$	−10.7939	−0.393091
$755$	−9.38108	−0.341413
$756$	65.1983	2.37124
$757$	30.0136	1.09086	0.545432	−	0.838155i	$-0.316366\pi$
$757$	30.0136	1.09086	0.545432	+	0.838155i	$0.316366\pi$
$758$	26.0645	0.946705
$759$	0	0
$760$	−1.78091	−0.0646003
$761$	47.8022	1.73283	0.866415	−	0.499325i	$-0.166419\pi$
$761$	47.8022	1.73283	0.866415	+	0.499325i	$0.166419\pi$
$762$	−21.5673	−0.781301
$763$	21.0376	0.761611
$764$	−19.2860	−0.697743
$765$	−36.7748	−1.32960
$766$	−10.9310	−0.394952
$767$	−33.8294	−1.22151
$768$	3.38334	0.122086
$769$	35.4135	1.27704	0.638521	−	0.769604i	$-0.279546\pi$
$769$	35.4135	1.27704	0.638521	+	0.769604i	$0.279546\pi$
$770$	−11.7956	−0.425083
$771$	55.2498	1.98977
$772$	−13.9162	−0.500855
$773$	−13.9723	−0.502548	−0.251274	−	0.967916i	$-0.580849\pi$
$773$	−13.9723	−0.502548	−0.251274	+	0.967916i	$0.580849\pi$
$774$	37.9481	1.36402
$775$	2.31712	0.0832334
$776$	11.4769	0.411995
$777$	−45.2927	−1.62487
$778$	−32.4593	−1.16372
$779$	14.8369	0.531587
$780$	−8.22212	−0.294399
$781$	30.0920	1.07678
$782$	0	0
$783$	−81.8552	−2.92527
$784$	5.51592	0.196997
$785$	2.82948	0.100988
$786$	33.8898	1.20881
$787$	35.9267	1.28065	0.640324	−	0.768105i	$-0.278800\pi$
$787$	35.9267	1.28065	0.640324	+	0.768105i	$0.278800\pi$
$788$	6.81165	0.242655
$789$	5.13425	0.182784
$790$	2.29994	0.0818283
$791$	−25.7026	−0.913880
$792$	−28.1638	−1.00076
$793$	25.8507	0.917986
$794$	−13.8549	−0.491691
$795$	−27.1802	−0.963984
$796$	−22.0610	−0.781931
$797$	−35.2655	−1.24917	−0.624585	−	0.780957i	$-0.714732\pi$
$797$	−35.2655	−1.24917	−0.624585	+	0.780957i	$0.714732\pi$
$798$	−21.3167	−0.754602
$799$	28.4823	1.00763
$800$	−1.00000	−0.0353553
$801$	138.592	4.89691
$802$	16.6025	0.586255
$803$	8.16662	0.288194
$804$	−12.4283	−0.438311
$805$	0	0
$806$	5.63101	0.198344
$807$	−69.8895	−2.46023
$808$	−7.61470	−0.267884
$809$	−5.97462	−0.210056	−0.105028	−	0.994469i	$-0.533493\pi$
$809$	−5.97462	−0.210056	−0.105028	+	0.994469i	$0.533493\pi$
$810$	−37.0111	−1.30044
$811$	32.6426	1.14624	0.573118	−	0.819473i	$-0.305734\pi$
$811$	32.6426	1.14624	0.573118	+	0.819473i	$0.305734\pi$
$812$	−15.7135	−0.551435
$813$	−39.1016	−1.37135
$814$	12.6165	0.442207
$815$	7.11484	0.249222
$816$	−14.7297	−0.515642
$817$	−8.00071	−0.279909
$818$	30.4406	1.06433
$819$	−72.6227	−2.53764
$820$	8.33108	0.290934
$821$	6.16756	0.215249	0.107625	−	0.994192i	$-0.465676\pi$
$821$	6.16756	0.215249	0.107625	+	0.994192i	$0.465676\pi$
$822$	−25.7784	−0.899124
$823$	33.4121	1.16467	0.582335	−	0.812949i	$-0.302139\pi$
$823$	33.4121	1.16467	0.582335	+	0.812949i	$0.302139\pi$
$824$	10.2417	0.356785
$825$	11.2806	0.392741
$826$	−49.2480	−1.71356
$827$	41.1796	1.43196	0.715978	−	0.698123i	$-0.245981\pi$
$827$	41.1796	1.43196	0.715978	+	0.698123i	$0.245981\pi$
$828$	0	0
$829$	1.03538	0.0359601	0.0179800	−	0.999838i	$-0.494276\pi$
$829$	1.03538	0.0359601	0.0179800	+	0.999838i	$0.494276\pi$
$830$	1.40697	0.0488366
$831$	4.31652	0.149738
$832$	−2.43018	−0.0842512
$833$	−24.0140	−0.832036
$834$	51.2311	1.77399
$835$	3.99110	0.138118
$836$	5.93785	0.205365
$837$	42.7025	1.47602
$838$	−19.5903	−0.676737
$839$	−9.25745	−0.319603	−0.159801	−	0.987149i	$-0.551085\pi$
$839$	−9.25745	−0.319603	−0.159801	+	0.987149i	$0.551085\pi$
$840$	−11.9695	−0.412988
$841$	−9.27203	−0.319725
$842$	−3.96577	−0.136669
$843$	18.4973	0.637081
$844$	3.01212	0.103682
$845$	−7.09425	−0.244050
$846$	55.2626	1.89997
$847$	0.412792	0.0141837
$848$	−8.03354	−0.275873
$849$	−1.12262	−0.0385282
$850$	4.35358	0.149327
$851$	0	0
$852$	30.5359	1.04614
$853$	23.2154	0.794879	0.397440	−	0.917628i	$-0.369899\pi$
$853$	23.2154	0.794879	0.397440	+	0.917628i	$0.369899\pi$
$854$	37.6328	1.28777
$855$	15.0434	0.514472
$856$	1.59456	0.0545008
$857$	12.2121	0.417156	0.208578	−	0.978006i	$-0.433117\pi$
$857$	12.2121	0.417156	0.208578	+	0.978006i	$0.433117\pi$
$858$	27.4139	0.935896
$859$	−43.1156	−1.47109	−0.735543	−	0.677478i	$-0.763073\pi$
$859$	−43.1156	−1.47109	−0.735543	+	0.677478i	$0.763073\pi$
$860$	−4.49249	−0.153193
$861$	99.7192	3.39842
$862$	5.02348	0.171100
$863$	5.15794	0.175578	0.0877892	−	0.996139i	$-0.472020\pi$
$863$	5.15794	0.175578	0.0877892	+	0.996139i	$0.472020\pi$
$864$	−18.4291	−0.626972
$865$	−25.4031	−0.863731
$866$	−3.80524	−0.129307
$867$	6.61002	0.224488
$868$	8.19747	0.278240
$869$	−7.66840	−0.260133
$870$	15.0275	0.509481
$871$	8.92693	0.302477
$872$	−5.94654	−0.201375
$873$	−96.9452	−3.28110
$874$	0	0
$875$	3.53778	0.119599
$876$	8.28707	0.279994
$877$	53.3279	1.80075	0.900377	−	0.435111i	$-0.143291\pi$
$877$	53.3279	1.80075	0.900377	+	0.435111i	$0.143291\pi$
$878$	23.5718	0.795509
$879$	−54.3473	−1.83309
$880$	3.33417	0.112395
$881$	36.8218	1.24056	0.620279	−	0.784382i	$-0.287020\pi$
$881$	36.8218	1.24056	0.620279	+	0.784382i	$0.287020\pi$
$882$	−46.5931	−1.56887
$883$	17.7223	0.596402	0.298201	−	0.954503i	$-0.403613\pi$
$883$	17.7223	0.596402	0.298201	+	0.954503i	$0.403613\pi$
$884$	10.5800	0.355843
$885$	47.0981	1.58318
$886$	−2.78788	−0.0936607
$887$	−20.4874	−0.687899	−0.343949	−	0.938988i	$-0.611765\pi$
$887$	−20.4874	−0.687899	−0.343949	+	0.938988i	$0.611765\pi$
$888$	12.8025	0.429625
$889$	22.5518	0.756362
$890$	−16.4072	−0.549971
$891$	123.401	4.13409
$892$	−2.02024	−0.0676426
$893$	−11.6512	−0.389891
$894$	−15.1791	−0.507664
$895$	19.6798	0.657822
$896$	−3.53778	−0.118189
$897$	0	0
$898$	−19.5177	−0.651313
$899$	−10.2918	−0.343249
$900$	8.44702	0.281567
$901$	34.9747	1.16518
$902$	−27.7772	−0.924880
$903$	−53.7730	−1.78945
$904$	7.26518	0.241636
$905$	8.50950	0.282865
$906$	31.7394	1.05447
$907$	27.8969	0.926300	0.463150	−	0.886280i	$-0.346719\pi$
$907$	27.8969	0.926300	0.463150	+	0.886280i	$0.346719\pi$
$908$	−12.3916	−0.411228
$909$	64.3215	2.13341
$910$	8.59744	0.285002
$911$	−25.4869	−0.844417	−0.422209	−	0.906499i	$-0.638745\pi$
$911$	−25.4869	−0.844417	−0.422209	+	0.906499i	$0.638745\pi$
$912$	6.02543	0.199522
$913$	−4.69107	−0.155252
$914$	−3.19534	−0.105692
$915$	−35.9900	−1.18979
$916$	26.1155	0.862880
$917$	−35.4368	−1.17023
$918$	80.2328	2.64808
$919$	−45.4554	−1.49944	−0.749718	−	0.661758i	$-0.769811\pi$
$919$	−45.4554	−1.49944	−0.749718	+	0.661758i	$0.769811\pi$
$920$	0	0
$921$	110.065	3.62677
$922$	13.2998	0.438007
$923$	−21.9332	−0.721939
$924$	39.9085	1.31289
$925$	−3.78399	−0.124417
$926$	−19.7562	−0.649228
$927$	−86.5114	−2.84141
$928$	4.44162	0.145803
$929$	22.5441	0.739649	0.369824	−	0.929102i	$-0.379418\pi$
$929$	22.5441	0.739649	0.369824	+	0.929102i	$0.379418\pi$
$930$	−7.83961	−0.257071
$931$	9.82335	0.321947
$932$	14.1223	0.462592
$933$	−6.72008	−0.220006
$934$	8.14078	0.266374
$935$	−14.5156	−0.474710
$936$	20.5277	0.670970
$937$	−19.6387	−0.641567	−0.320783	−	0.947153i	$-0.603946\pi$
$937$	−19.6387	−0.641567	−0.320783	+	0.947153i	$0.603946\pi$
$938$	12.9956	0.424321
$939$	−13.0936	−0.427294
$940$	−6.54226	−0.213385
$941$	−5.64058	−0.183878	−0.0919388	−	0.995765i	$-0.529306\pi$
$941$	−5.64058	−0.183878	−0.0919388	+	0.995765i	$0.529306\pi$
$942$	−9.57310	−0.311909
$943$	0	0
$944$	13.9206	0.453076
$945$	65.1983	2.12090
$946$	14.9787	0.487000
$947$	0.967129	0.0314275	0.0157137	−	0.999877i	$-0.494998\pi$
$947$	0.967129	0.0314275	0.0157137	+	0.999877i	$0.494998\pi$
$948$	−7.78150	−0.252731
$949$	−5.95240	−0.193223
$950$	−1.78091	−0.0577803
$951$	−7.06804	−0.229197
$952$	15.4020	0.499183
$953$	−32.6466	−1.05753	−0.528764	−	0.848769i	$-0.677344\pi$
$953$	−32.6466	−1.05753	−0.528764	+	0.848769i	$0.677344\pi$
$954$	67.8595	2.19703
$955$	−19.2860	−0.624081
$956$	4.98764	0.161312
$957$	−50.1043	−1.61964
$958$	−5.50415	−0.177831
$959$	26.9551	0.870425
$960$	3.38334	0.109197
$961$	−25.6310	−0.826805
$962$	−9.19577	−0.296483
$963$	−13.4692	−0.434040
$964$	−1.68484	−0.0542650
$965$	−13.9162	−0.447978
$966$	0	0
$967$	−40.2297	−1.29370	−0.646851	−	0.762617i	$-0.723914\pi$
$967$	−40.2297	−1.29370	−0.646851	+	0.762617i	$0.723914\pi$
$968$	−0.116681	−0.00375027
$969$	−26.2322	−0.842700
$970$	11.4769	0.368499
$971$	1.15777	0.0371546	0.0185773	−	0.999827i	$-0.494086\pi$
$971$	1.15777	0.0371546	0.0185773	+	0.999827i	$0.494086\pi$
$972$	69.9338	2.24313
$973$	−53.5696	−1.71736
$974$	29.9224	0.958774
$975$	−8.22212	−0.263319
$976$	−10.6374	−0.340495
$977$	55.3644	1.77126	0.885632	−	0.464388i	$-0.153726\pi$
$977$	55.3644	1.77126	0.885632	+	0.464388i	$0.153726\pi$
$978$	−24.0720	−0.769736
$979$	54.7044	1.74836
$980$	5.51592	0.176200
$981$	50.2305	1.60374
$982$	−29.5996	−0.944561
$983$	−1.28674	−0.0410405	−0.0205203	−	0.999789i	$-0.506532\pi$
$983$	−1.28674	−0.0410405	−0.0205203	+	0.999789i	$0.506532\pi$
$984$	−28.1869	−0.898566
$985$	6.81165	0.217037
$986$	−19.3370	−0.615814
$987$	−78.3078	−2.49257
$988$	−4.32792	−0.137689
$989$	0	0
$990$	−28.1638	−0.895104
$991$	−10.8991	−0.346222	−0.173111	−	0.984902i	$-0.555382\pi$
$991$	−10.8991	−0.346222	−0.173111	+	0.984902i	$0.555382\pi$
$992$	−2.31712	−0.0735686
$993$	43.3561	1.37586
$994$	−31.9297	−1.01275
$995$	−22.0610	−0.699381
$996$	−4.76026	−0.150835
$997$	−6.87495	−0.217732	−0.108866	−	0.994056i	$-0.534722\pi$
$997$	−6.87495	−0.217732	−0.108866	+	0.994056i	$0.534722\pi$
$998$	20.3461	0.644044
$999$	−69.7357	−2.20634

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5290.2.a.bj.1.10		10
23.13	even	11		230.2.g.b.31.2	✓	20
23.16	even	11		230.2.g.b.141.2	yes	20
23.22	odd	2		5290.2.a.bi.1.10		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
230.2.g.b.31.2	✓	20	23.13	even	11
230.2.g.b.141.2	yes	20	23.16	even	11
5290.2.a.bi.1.10		10	23.22	odd	2
5290.2.a.bj.1.10		10	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:	\( N \)	\(=\)	\( 5290 = 2 \cdot 5 \cdot 23^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	5290.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +3.38334 q^{3} +1.00000 q^{4} +1.00000 q^{5} -3.38334 q^{6} +3.53778 q^{7} -1.00000 q^{8} +8.44702 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +3.38334 q^{3} +1.00000 q^{4} +1.00000 q^{5} -3.38334 q^{6} +3.53778 q^{7} -1.00000 q^{8} +8.44702 q^{9} -1.00000 q^{10} +3.33417 q^{11} +3.38334 q^{12} -2.43018 q^{13} -3.53778 q^{14} +3.38334 q^{15} +1.00000 q^{16} -4.35358 q^{17} -8.44702 q^{18} +1.78091 q^{19} +1.00000 q^{20} +11.9695 q^{21} -3.33417 q^{22} -3.38334 q^{24} +1.00000 q^{25} +2.43018 q^{26} +18.4291 q^{27} +3.53778 q^{28} -4.44162 q^{29} -3.38334 q^{30} +2.31712 q^{31} -1.00000 q^{32} +11.2806 q^{33} +4.35358 q^{34} +3.53778 q^{35} +8.44702 q^{36} -3.78399 q^{37} -1.78091 q^{38} -8.22212 q^{39} -1.00000 q^{40} +8.33108 q^{41} -11.9695 q^{42} -4.49249 q^{43} +3.33417 q^{44} +8.44702 q^{45} -6.54226 q^{47} +3.38334 q^{48} +5.51592 q^{49} -1.00000 q^{50} -14.7297 q^{51} -2.43018 q^{52} -8.03354 q^{53} -18.4291 q^{54} +3.33417 q^{55} -3.53778 q^{56} +6.02543 q^{57} +4.44162 q^{58} +13.9206 q^{59} +3.38334 q^{60} -10.6374 q^{61} -2.31712 q^{62} +29.8837 q^{63} +1.00000 q^{64} -2.43018 q^{65} -11.2806 q^{66} -3.67337 q^{67} -4.35358 q^{68} -3.53778 q^{70} +9.02535 q^{71} -8.44702 q^{72} +2.44937 q^{73} +3.78399 q^{74} +3.38334 q^{75} +1.78091 q^{76} +11.7956 q^{77} +8.22212 q^{78} -2.29994 q^{79} +1.00000 q^{80} +37.0111 q^{81} -8.33108 q^{82} -1.40697 q^{83} +11.9695 q^{84} -4.35358 q^{85} +4.49249 q^{86} -15.0275 q^{87} -3.33417 q^{88} +16.4072 q^{89} -8.44702 q^{90} -8.59744 q^{91} +7.83961 q^{93} +6.54226 q^{94} +1.78091 q^{95} -3.38334 q^{96} -11.4769 q^{97} -5.51592 q^{98} +28.1638 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 10 q^{2} + 4 q^{3} + 10 q^{4} + 10 q^{5} - 4 q^{6} - 7 q^{7} - 10 q^{8} + 14 q^{9}+O(q^{10}) \) 10 * q - 10 * q^2 + 4 * q^3 + 10 * q^4 + 10 * q^5 - 4 * q^6 - 7 * q^7 - 10 * q^8 + 14 * q^9	\( 10 q - 10 q^{2} + 4 q^{3} + 10 q^{4} + 10 q^{5} - 4 q^{6} - 7 q^{7} - 10 q^{8} + 14 q^{9} - 10 q^{10} + 9 q^{11} + 4 q^{12} - 7 q^{13} + 7 q^{14} + 4 q^{15} + 10 q^{16} - 18 q^{17} - 14 q^{18} + 16 q^{19} + 10 q^{20} + 12 q^{21} - 9 q^{22} - 4 q^{24} + 10 q^{25} + 7 q^{26} + 13 q^{27} - 7 q^{28} + 10 q^{29} - 4 q^{30} - 3 q^{31} - 10 q^{32} + 25 q^{33} + 18 q^{34} - 7 q^{35} + 14 q^{36} - 8 q^{37} - 16 q^{38} + 12 q^{39} - 10 q^{40} + 10 q^{41} - 12 q^{42} - 9 q^{43} + 9 q^{44} + 14 q^{45} + 21 q^{47} + 4 q^{48} + 7 q^{49} - 10 q^{50} - 9 q^{51} - 7 q^{52} - 40 q^{53} - 13 q^{54} + 9 q^{55} + 7 q^{56} + 9 q^{57} - 10 q^{58} + 29 q^{59} + 4 q^{60} + 25 q^{61} + 3 q^{62} + 6 q^{63} + 10 q^{64} - 7 q^{65} - 25 q^{66} - 7 q^{67} - 18 q^{68} + 7 q^{70} + 64 q^{71} - 14 q^{72} - 16 q^{73} + 8 q^{74} + 4 q^{75} + 16 q^{76} + 57 q^{77} - 12 q^{78} + 44 q^{79} + 10 q^{80} + 14 q^{81} - 10 q^{82} - 26 q^{83} + 12 q^{84} - 18 q^{85} + 9 q^{86} + 25 q^{87} - 9 q^{88} + 11 q^{89} - 14 q^{90} + 5 q^{93} - 21 q^{94} + 16 q^{95} - 4 q^{96} - 10 q^{97} - 7 q^{98} + 13 q^{99}+O(q^{100}) \) 10 * q - 10 * q^2 + 4 * q^3 + 10 * q^4 + 10 * q^5 - 4 * q^6 - 7 * q^7 - 10 * q^8 + 14 * q^9 - 10 * q^10 + 9 * q^11 + 4 * q^12 - 7 * q^13 + 7 * q^14 + 4 * q^15 + 10 * q^16 - 18 * q^17 - 14 * q^18 + 16 * q^19 + 10 * q^20 + 12 * q^21 - 9 * q^22 - 4 * q^24 + 10 * q^25 + 7 * q^26 + 13 * q^27 - 7 * q^28 + 10 * q^29 - 4 * q^30 - 3 * q^31 - 10 * q^32 + 25 * q^33 + 18 * q^34 - 7 * q^35 + 14 * q^36 - 8 * q^37 - 16 * q^38 + 12 * q^39 - 10 * q^40 + 10 * q^41 - 12 * q^42 - 9 * q^43 + 9 * q^44 + 14 * q^45 + 21 * q^47 + 4 * q^48 + 7 * q^49 - 10 * q^50 - 9 * q^51 - 7 * q^52 - 40 * q^53 - 13 * q^54 + 9 * q^55 + 7 * q^56 + 9 * q^57 - 10 * q^58 + 29 * q^59 + 4 * q^60 + 25 * q^61 + 3 * q^62 + 6 * q^63 + 10 * q^64 - 7 * q^65 - 25 * q^66 - 7 * q^67 - 18 * q^68 + 7 * q^70 + 64 * q^71 - 14 * q^72 - 16 * q^73 + 8 * q^74 + 4 * q^75 + 16 * q^76 + 57 * q^77 - 12 * q^78 + 44 * q^79 + 10 * q^80 + 14 * q^81 - 10 * q^82 - 26 * q^83 + 12 * q^84 - 18 * q^85 + 9 * q^86 + 25 * q^87 - 9 * q^88 + 11 * q^89 - 14 * q^90 + 5 * q^93 - 21 * q^94 + 16 * q^95 - 4 * q^96 - 10 * q^97 - 7 * q^98 + 13 * q^99

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