LMFDB - Embedded newform 105.4.a.g.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [105,4,Mod(1,105)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(105, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("105.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 105 = 3 \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	105.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:	$6.19520055060$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\sqrt{41}) $
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 10 $ x^2 - x - 10
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$3.70156$ of defining polynomial
Character	$\chi$	$=$	105.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+4.70156 q^{2} +3.00000 q^{3} +14.1047 q^{4} -5.00000 q^{5} +14.1047 q^{6} +7.00000 q^{7} +28.7016 q^{8} +9.00000 q^{9} +O(q^{10})$	\(q+4.70156 q^{2} +3.00000 q^{3} +14.1047 q^{4} -5.00000 q^{5} +14.1047 q^{6} +7.00000 q^{7} +28.7016 q^{8} +9.00000 q^{9} -23.5078 q^{10} +24.5969 q^{11} +42.3141 q^{12} -35.0156 q^{13} +32.9109 q^{14} -15.0000 q^{15} +22.1047 q^{16} -18.4187 q^{17} +42.3141 q^{18} -67.4031 q^{19} -70.5234 q^{20} +21.0000 q^{21} +115.644 q^{22} -145.675 q^{23} +86.1047 q^{24} +25.0000 q^{25} -164.628 q^{26} +27.0000 q^{27} +98.7328 q^{28} +214.419 q^{29} -70.5234 q^{30} -88.6594 q^{31} -125.686 q^{32} +73.7906 q^{33} -86.5969 q^{34} -35.0000 q^{35} +126.942 q^{36} +162.125 q^{37} -316.900 q^{38} -105.047 q^{39} -143.508 q^{40} -337.769 q^{41} +98.7328 q^{42} +122.156 q^{43} +346.931 q^{44} -45.0000 q^{45} -684.900 q^{46} +354.219 q^{47} +66.3141 q^{48} +49.0000 q^{49} +117.539 q^{50} -55.2562 q^{51} -493.884 q^{52} +676.691 q^{53} +126.942 q^{54} -122.984 q^{55} +200.911 q^{56} -202.209 q^{57} +1008.10 q^{58} +501.319 q^{59} -211.570 q^{60} -708.931 q^{61} -416.837 q^{62} +63.0000 q^{63} -767.758 q^{64} +175.078 q^{65} +346.931 q^{66} -907.956 q^{67} -259.791 q^{68} -437.025 q^{69} -164.555 q^{70} +430.334 q^{71} +258.314 q^{72} +41.3406 q^{73} +762.241 q^{74} +75.0000 q^{75} -950.700 q^{76} +172.178 q^{77} -493.884 q^{78} +890.388 q^{79} -110.523 q^{80} +81.0000 q^{81} -1588.04 q^{82} -1057.15 q^{83} +296.198 q^{84} +92.0937 q^{85} +574.325 q^{86} +643.256 q^{87} +705.969 q^{88} +1473.72 q^{89} -211.570 q^{90} -245.109 q^{91} -2054.70 q^{92} -265.978 q^{93} +1665.38 q^{94} +337.016 q^{95} -377.058 q^{96} +555.034 q^{97} +230.377 q^{98} +221.372 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 3 q^{2} + 6 q^{3} + 9 q^{4} - 10 q^{5} + 9 q^{6} + 14 q^{7} + 51 q^{8} + 18 q^{9}+O(q^{10}) $ 2 * q + 3 * q^2 + 6 * q^3 + 9 * q^4 - 10 * q^5 + 9 * q^6 + 14 * q^7 + 51 * q^8 + 18 * q^9	\( 2 q + 3 q^{2} + 6 q^{3} + 9 q^{4} - 10 q^{5} + 9 q^{6} + 14 q^{7} + 51 q^{8} + 18 q^{9} - 15 q^{10} + 62 q^{11} + 27 q^{12} - 6 q^{13} + 21 q^{14} - 30 q^{15} + 25 q^{16} + 40 q^{17} + 27 q^{18} - 122 q^{19} - 45 q^{20} + 42 q^{21} + 52 q^{22} + 16 q^{23} + 153 q^{24} + 50 q^{25} - 214 q^{26} + 54 q^{27} + 63 q^{28} + 352 q^{29} - 45 q^{30} + 66 q^{31} - 309 q^{32} + 186 q^{33} - 186 q^{34} - 70 q^{35} + 81 q^{36} - 188 q^{37} - 224 q^{38} - 18 q^{39} - 255 q^{40} + 16 q^{41} + 63 q^{42} - 396 q^{43} + 156 q^{44} - 90 q^{45} - 960 q^{46} - 188 q^{47} + 75 q^{48} + 98 q^{49} + 75 q^{50} + 120 q^{51} - 642 q^{52} + 982 q^{53} + 81 q^{54} - 310 q^{55} + 357 q^{56} - 366 q^{57} + 774 q^{58} + 516 q^{59} - 135 q^{60} - 880 q^{61} - 680 q^{62} + 126 q^{63} - 479 q^{64} + 30 q^{65} + 156 q^{66} - 356 q^{67} - 558 q^{68} + 48 q^{69} - 105 q^{70} + 310 q^{71} + 459 q^{72} + 326 q^{73} + 1358 q^{74} + 150 q^{75} - 672 q^{76} + 434 q^{77} - 642 q^{78} + 1832 q^{79} - 125 q^{80} + 162 q^{81} - 2190 q^{82} - 680 q^{83} + 189 q^{84} - 200 q^{85} + 1456 q^{86} + 1056 q^{87} + 1540 q^{88} + 796 q^{89} - 135 q^{90} - 42 q^{91} - 2880 q^{92} + 198 q^{93} + 2588 q^{94} + 610 q^{95} - 927 q^{96} - 670 q^{97} + 147 q^{98} + 558 q^{99}+O(q^{100}) \) 2 * q + 3 * q^2 + 6 * q^3 + 9 * q^4 - 10 * q^5 + 9 * q^6 + 14 * q^7 + 51 * q^8 + 18 * q^9 - 15 * q^10 + 62 * q^11 + 27 * q^12 - 6 * q^13 + 21 * q^14 - 30 * q^15 + 25 * q^16 + 40 * q^17 + 27 * q^18 - 122 * q^19 - 45 * q^20 + 42 * q^21 + 52 * q^22 + 16 * q^23 + 153 * q^24 + 50 * q^25 - 214 * q^26 + 54 * q^27 + 63 * q^28 + 352 * q^29 - 45 * q^30 + 66 * q^31 - 309 * q^32 + 186 * q^33 - 186 * q^34 - 70 * q^35 + 81 * q^36 - 188 * q^37 - 224 * q^38 - 18 * q^39 - 255 * q^40 + 16 * q^41 + 63 * q^42 - 396 * q^43 + 156 * q^44 - 90 * q^45 - 960 * q^46 - 188 * q^47 + 75 * q^48 + 98 * q^49 + 75 * q^50 + 120 * q^51 - 642 * q^52 + 982 * q^53 + 81 * q^54 - 310 * q^55 + 357 * q^56 - 366 * q^57 + 774 * q^58 + 516 * q^59 - 135 * q^60 - 880 * q^61 - 680 * q^62 + 126 * q^63 - 479 * q^64 + 30 * q^65 + 156 * q^66 - 356 * q^67 - 558 * q^68 + 48 * q^69 - 105 * q^70 + 310 * q^71 + 459 * q^72 + 326 * q^73 + 1358 * q^74 + 150 * q^75 - 672 * q^76 + 434 * q^77 - 642 * q^78 + 1832 * q^79 - 125 * q^80 + 162 * q^81 - 2190 * q^82 - 680 * q^83 + 189 * q^84 - 200 * q^85 + 1456 * q^86 + 1056 * q^87 + 1540 * q^88 + 796 * q^89 - 135 * q^90 - 42 * q^91 - 2880 * q^92 + 198 * q^93 + 2588 * q^94 + 610 * q^95 - 927 * q^96 - 670 * q^97 + 147 * q^98 + 558 * 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 $

$2$	4.70156	1.66225	0.831127	−	0.556083i	$-0.187696\pi$
$2$	4.70156	1.66225	0.831127	+	0.556083i	$0.187696\pi$
$3$	3.00000	0.577350
$3$	3.00000	0.577350
$4$	14.1047	1.76309
$5$	−5.00000	−0.447214
$5$	−5.00000	−0.447214
$6$	14.1047	0.959702
$7$	7.00000	0.377964
$7$	7.00000	0.377964
$8$	28.7016	1.26844
$9$	9.00000	0.333333
$10$	−23.5078	−0.743382
$11$	24.5969	0.674203	0.337102	−	0.941468i	$-0.390553\pi$
$11$	24.5969	0.674203	0.337102	+	0.941468i	$0.390553\pi$
$12$	42.3141	1.01792
$13$	−35.0156	−0.747045	−0.373523	−	0.927621i	$-0.621850\pi$
$13$	−35.0156	−0.747045	−0.373523	+	0.927621i	$0.621850\pi$
$14$	32.9109	0.628273
$15$	−15.0000	−0.258199
$16$	22.1047	0.345386
$17$	−18.4187	−0.262777	−0.131388	−	0.991331i	$-0.541943\pi$
$17$	−18.4187	−0.262777	−0.131388	+	0.991331i	$0.541943\pi$
$18$	42.3141	0.554084
$19$	−67.4031	−0.813860	−0.406930	−	0.913459i	$-0.633401\pi$
$19$	−67.4031	−0.813860	−0.406930	+	0.913459i	$0.633401\pi$
$20$	−70.5234	−0.788476
$21$	21.0000	0.218218
$22$	115.644	1.12070
$23$	−145.675	−1.32067	−0.660333	−	0.750973i	$-0.729585\pi$
$23$	−145.675	−1.32067	−0.660333	+	0.750973i	$0.729585\pi$
$24$	86.1047	0.732335
$25$	25.0000	0.200000
$26$	−164.628	−1.24178
$27$	27.0000	0.192450
$28$	98.7328	0.666384
$29$	214.419	1.37298	0.686492	−	0.727137i	$-0.259149\pi$
$29$	214.419	1.37298	0.686492	+	0.727137i	$0.259149\pi$
$30$	−70.5234	−0.429192
$31$	−88.6594	−0.513667	−0.256834	−	0.966456i	$-0.582679\pi$
$31$	−88.6594	−0.513667	−0.256834	+	0.966456i	$0.582679\pi$
$32$	−125.686	−0.694323
$33$	73.7906	0.389251
$34$	−86.5969	−0.436801
$35$	−35.0000	−0.169031
$36$	126.942	0.587695
$37$	162.125	0.720356	0.360178	−	0.932884i	$-0.382716\pi$
$37$	162.125	0.720356	0.360178	+	0.932884i	$0.382716\pi$
$38$	−316.900	−1.35284
$39$	−105.047	−0.431307
$40$	−143.508	−0.567264
$41$	−337.769	−1.28660	−0.643300	−	0.765614i	$-0.722435\pi$
$41$	−337.769	−1.28660	−0.643300	+	0.765614i	$0.722435\pi$
$42$	98.7328	0.362733
$43$	122.156	0.433224	0.216612	−	0.976258i	$-0.430499\pi$
$43$	122.156	0.433224	0.216612	+	0.976258i	$0.430499\pi$
$44$	346.931	1.18868
$45$	−45.0000	−0.149071
$46$	−684.900	−2.19528
$47$	354.219	1.09932	0.549661	−	0.835388i	$-0.314757\pi$
$47$	354.219	1.09932	0.549661	+	0.835388i	$0.314757\pi$
$48$	66.3141	0.199409
$49$	49.0000	0.142857
$50$	117.539	0.332451
$51$	−55.2562	−0.151714
$52$	−493.884	−1.31710
$53$	676.691	1.75378	0.876892	−	0.480687i	$-0.159613\pi$
$53$	676.691	1.75378	0.876892	+	0.480687i	$0.159613\pi$
$54$	126.942	0.319901
$55$	−122.984	−0.301513
$56$	200.911	0.479426
$57$	−202.209	−0.469882
$58$	1008.10	2.28225
$59$	501.319	1.10621	0.553103	−	0.833113i	$-0.313444\pi$
$59$	501.319	1.10621	0.553103	+	0.833113i	$0.313444\pi$
$60$	−211.570	−0.455227
$61$	−708.931	−1.48802	−0.744011	−	0.668167i	$-0.767079\pi$
$61$	−708.931	−1.48802	−0.744011	+	0.668167i	$0.767079\pi$
$62$	−416.837	−0.853845
$63$	63.0000	0.125988
$64$	−767.758	−1.49953
$65$	175.078	0.334089
$66$	346.931	0.647035
$67$	−907.956	−1.65559	−0.827795	−	0.561031i	$-0.810405\pi$
$67$	−907.956	−1.65559	−0.827795	+	0.561031i	$0.810405\pi$
$68$	−259.791	−0.463298
$69$	−437.025	−0.762487
$70$	−164.555	−0.280972
$71$	430.334	0.719314	0.359657	−	0.933085i	$-0.382894\pi$
$71$	430.334	0.719314	0.359657	+	0.933085i	$0.382894\pi$
$72$	258.314	0.422814
$73$	41.3406	0.0662816	0.0331408	−	0.999451i	$-0.489449\pi$
$73$	41.3406	0.0662816	0.0331408	+	0.999451i	$0.489449\pi$
$74$	762.241	1.19741
$75$	75.0000	0.115470
$76$	−950.700	−1.43490
$77$	172.178	0.254825
$78$	−493.884	−0.716941
$79$	890.388	1.26806	0.634028	−	0.773310i	$-0.281400\pi$
$79$	890.388	1.26806	0.634028	+	0.773310i	$0.281400\pi$
$80$	−110.523	−0.154461
$81$	81.0000	0.111111
$82$	−1588.04	−2.13866
$83$	−1057.15	−1.39804	−0.699020	−	0.715102i	$-0.746380\pi$
$83$	−1057.15	−1.39804	−0.699020	+	0.715102i	$0.746380\pi$
$84$	296.198	0.384737
$85$	92.0937	0.117517
$86$	574.325	0.720129
$87$	643.256	0.792693
$88$	705.969	0.855188
$89$	1473.72	1.75522	0.877610	−	0.479376i	$-0.159137\pi$
$89$	1473.72	1.75522	0.877610	+	0.479376i	$0.159137\pi$
$90$	−211.570	−0.247794
$91$	−245.109	−0.282356
$92$	−2054.70	−2.32845
$93$	−265.978	−0.296566
$94$	1665.38	1.82735
$95$	337.016	0.363969
$96$	−377.058	−0.400868
$97$	555.034	0.580981	0.290491	−	0.956878i	$-0.406181\pi$
$97$	555.034	0.580981	0.290491	+	0.956878i	$0.406181\pi$
$98$	230.377	0.237465
$99$	221.372	0.224734
$100$	352.617	0.352617
$101$	1890.14	1.86214	0.931071	−	0.364838i	$-0.118876\pi$
$101$	1890.14	1.86214	0.931071	+	0.364838i	$0.118876\pi$
$102$	−259.791	−0.252187
$103$	662.700	0.633959	0.316979	−	0.948432i	$-0.397331\pi$
$103$	662.700	0.633959	0.316979	+	0.948432i	$0.397331\pi$
$104$	−1005.00	−0.947583
$105$	−105.000	−0.0975900
$106$	3181.50	2.91523
$107$	1614.53	1.45872	0.729358	−	0.684132i	$-0.239819\pi$
$107$	1614.53	1.45872	0.729358	+	0.684132i	$0.239819\pi$
$108$	380.827	0.339306
$109$	217.206	0.190868	0.0954339	−	0.995436i	$-0.469576\pi$
$109$	217.206	0.190868	0.0954339	+	0.995436i	$0.469576\pi$
$110$	−578.219	−0.501191
$111$	486.375	0.415898
$112$	154.733	0.130544
$113$	−1658.20	−1.38044	−0.690221	−	0.723598i	$-0.742487\pi$
$113$	−1658.20	−1.38044	−0.690221	+	0.723598i	$0.742487\pi$
$114$	−950.700	−0.781063
$115$	728.375	0.590620
$116$	3024.31	2.42069
$117$	−315.141	−0.249015
$118$	2356.98	1.83879
$119$	−128.931	−0.0993202
$120$	−430.523	−0.327510
$121$	−725.994	−0.545450
$122$	−3333.08	−2.47347
$123$	−1013.31	−0.742819
$124$	−1250.51	−0.905640
$125$	−125.000	−0.0894427
$126$	296.198	0.209424
$127$	−1108.81	−0.774734	−0.387367	−	0.921926i	$-0.626615\pi$
$127$	−1108.81	−0.774734	−0.387367	+	0.921926i	$0.626615\pi$
$128$	−2604.17	−1.79827
$129$	366.469	0.250122
$130$	823.141	0.555340
$131$	185.488	0.123711	0.0618554	−	0.998085i	$-0.480298\pi$
$131$	185.488	0.123711	0.0618554	+	0.998085i	$0.480298\pi$
$132$	1040.79	0.686284
$133$	−471.822	−0.307610
$134$	−4268.81	−2.75201
$135$	−135.000	−0.0860663
$136$	−528.647	−0.333317
$137$	−37.9907	−0.0236917	−0.0118458	−	0.999930i	$-0.503771\pi$
$137$	−37.9907	−0.0236917	−0.0118458	+	0.999930i	$0.503771\pi$
$138$	−2054.70	−1.26745
$139$	183.609	0.112040	0.0560199	−	0.998430i	$-0.482159\pi$
$139$	183.609	0.112040	0.0560199	+	0.998430i	$0.482159\pi$
$140$	−493.664	−0.298016
$141$	1062.66	0.634694
$142$	2023.24	1.19568
$143$	−861.275	−0.503660
$144$	198.942	0.115129
$145$	−1072.09	−0.614018
$146$	194.366	0.110177
$147$	147.000	0.0824786
$148$	2286.72	1.27005
$149$	−1383.34	−0.760587	−0.380293	−	0.924866i	$-0.624177\pi$
$149$	−1383.34	−0.760587	−0.380293	+	0.924866i	$0.624177\pi$
$150$	352.617	0.191940
$151$	765.256	0.412422	0.206211	−	0.978508i	$-0.433887\pi$
$151$	765.256	0.412422	0.206211	+	0.978508i	$0.433887\pi$
$152$	−1934.57	−1.03233
$153$	−165.769	−0.0875922
$154$	809.506	0.423584
$155$	443.297	0.229719
$156$	−1481.65	−0.760431
$157$	−2366.76	−1.20311	−0.601554	−	0.798832i	$-0.705452\pi$
$157$	−2366.76	−1.20311	−0.601554	+	0.798832i	$0.705452\pi$
$158$	4186.21	2.10783
$159$	2030.07	1.01255
$160$	628.430	0.310511
$161$	−1019.72	−0.499165
$162$	380.827	0.184695
$163$	−3137.69	−1.50775	−0.753875	−	0.657018i	$-0.771817\pi$
$163$	−3137.69	−1.50775	−0.753875	+	0.657018i	$0.771817\pi$
$164$	−4764.12	−2.26839
$165$	−368.953	−0.174079
$166$	−4970.26	−2.32390
$167$	146.469	0.0678688	0.0339344	−	0.999424i	$-0.489196\pi$
$167$	146.469	0.0678688	0.0339344	+	0.999424i	$0.489196\pi$
$168$	602.733	0.276797
$169$	−970.906	−0.441924
$170$	432.984	0.195343
$171$	−606.628	−0.271287
$172$	1722.98	0.763812
$173$	−1424.12	−0.625860	−0.312930	−	0.949776i	$-0.601311\pi$
$173$	−1424.12	−0.625860	−0.312930	+	0.949776i	$0.601311\pi$
$174$	3024.31	1.31766
$175$	175.000	0.0755929
$176$	543.706	0.232860
$177$	1503.96	0.638668
$178$	6928.81	2.91762
$179$	1244.70	0.519737	0.259869	−	0.965644i	$-0.416321\pi$
$179$	1244.70	0.519737	0.259869	+	0.965644i	$0.416321\pi$
$180$	−634.711	−0.262825
$181$	−3879.09	−1.59299	−0.796493	−	0.604648i	$-0.793314\pi$
$181$	−3879.09	−1.59299	−0.796493	+	0.604648i	$0.793314\pi$
$182$	−1152.40	−0.469348
$183$	−2126.79	−0.859110
$184$	−4181.10	−1.67519
$185$	−810.625	−0.322153
$186$	−1250.51	−0.492968
$187$	−453.044	−0.177165
$188$	4996.14	1.93820
$189$	189.000	0.0727393
$190$	1584.50	0.605009
$191$	1574.90	0.596628	0.298314	−	0.954468i	$-0.403576\pi$
$191$	1574.90	0.596628	0.298314	+	0.954468i	$0.403576\pi$
$192$	−2303.27	−0.865752
$193$	−4775.67	−1.78114	−0.890572	−	0.454843i	$-0.849695\pi$
$193$	−4775.67	−1.78114	−0.890572	+	0.454843i	$0.849695\pi$
$194$	2609.53	0.965738
$195$	525.234	0.192886
$196$	691.130	0.251869
$197$	−2803.58	−1.01394	−0.506971	−	0.861963i	$-0.669235\pi$
$197$	−2803.58	−1.01394	−0.506971	+	0.861963i	$0.669235\pi$
$198$	1040.79	0.373566
$199$	4102.92	1.46155	0.730774	−	0.682620i	$-0.239159\pi$
$199$	4102.92	1.46155	0.730774	+	0.682620i	$0.239159\pi$
$200$	717.539	0.253688
$201$	−2723.87	−0.955855
$202$	8886.63	3.09535
$203$	1500.93	0.518940
$204$	−779.372	−0.267485
$205$	1688.84	0.575385
$206$	3115.72	1.05380
$207$	−1311.07	−0.440222
$208$	−774.009	−0.258019
$209$	−1657.91	−0.548707
$210$	−493.664	−0.162219
$211$	−823.512	−0.268687	−0.134343	−	0.990935i	$-0.542893\pi$
$211$	−823.512	−0.268687	−0.134343	+	0.990935i	$0.542893\pi$
$212$	9544.51	3.09207
$213$	1291.00	0.415296
$214$	7590.82	2.42476
$215$	−610.781	−0.193744
$216$	774.942	0.244112
$217$	−620.616	−0.194148
$218$	1021.21	0.317271
$219$	124.022	0.0382677
$220$	−1734.66	−0.531593
$221$	644.944	0.196306
$222$	2286.72	0.691328
$223$	817.194	0.245396	0.122698	−	0.992444i	$-0.460845\pi$
$223$	817.194	0.245396	0.122698	+	0.992444i	$0.460845\pi$
$224$	−879.802	−0.262430
$225$	225.000	0.0666667
$226$	−7796.12	−2.29465
$227$	3655.85	1.06893	0.534465	−	0.845190i	$-0.320513\pi$
$227$	3655.85	1.06893	0.534465	+	0.845190i	$0.320513\pi$
$228$	−2852.10	−0.828443
$229$	939.393	0.271078	0.135539	−	0.990772i	$-0.456723\pi$
$229$	939.393	0.271078	0.135539	+	0.990772i	$0.456723\pi$
$230$	3424.50	0.981760
$231$	516.534	0.147123
$232$	6154.15	1.74155
$233$	−7.64701	−0.00215010	−0.00107505	−	0.999999i	$-0.500342\pi$
$233$	−7.64701	−0.00215010	−0.00107505	+	0.999999i	$0.500342\pi$
$234$	−1481.65	−0.413926
$235$	−1771.09	−0.491631
$236$	7070.94	1.95034
$237$	2671.16	0.732112
$238$	−606.178	−0.165095
$239$	−889.115	−0.240636	−0.120318	−	0.992735i	$-0.538391\pi$
$239$	−889.115	−0.240636	−0.120318	+	0.992735i	$0.538391\pi$
$240$	−331.570	−0.0891782
$241$	2140.23	0.572051	0.286026	−	0.958222i	$-0.407666\pi$
$241$	2140.23	0.572051	0.286026	+	0.958222i	$0.407666\pi$
$242$	−3413.30	−0.906676
$243$	243.000	0.0641500
$244$	−9999.25	−2.62351
$245$	−245.000	−0.0638877
$246$	−4764.12	−1.23475
$247$	2360.16	0.607990
$248$	−2544.66	−0.651557
$249$	−3171.45	−0.807158
$250$	−587.695	−0.148676
$251$	−6749.81	−1.69739	−0.848693	−	0.528886i	$-0.822610\pi$
$251$	−6749.81	−1.69739	−0.848693	+	0.528886i	$0.822610\pi$
$252$	888.595	0.222128
$253$	−3583.15	−0.890398
$254$	−5213.15	−1.28780
$255$	276.281	0.0678486
$256$	−6101.62	−1.48965
$257$	3068.64	0.744811	0.372405	−	0.928070i	$-0.378533\pi$
$257$	3068.64	0.744811	0.372405	+	0.928070i	$0.378533\pi$
$258$	1722.98	0.415766
$259$	1134.87	0.272269
$260$	2469.42	0.589027
$261$	1929.77	0.457662
$262$	872.081	0.205639
$263$	−4674.12	−1.09589	−0.547944	−	0.836515i	$-0.684589\pi$
$263$	−4674.12	−1.09589	−0.547944	+	0.836515i	$0.684589\pi$
$264$	2117.91	0.493743
$265$	−3383.45	−0.784316
$266$	−2218.30	−0.511326
$267$	4421.17	1.01338
$268$	−12806.4	−2.91895
$269$	2417.38	0.547919	0.273960	−	0.961741i	$-0.411667\pi$
$269$	2417.38	0.547919	0.273960	+	0.961741i	$0.411667\pi$
$270$	−634.711	−0.143064
$271$	7724.30	1.73143	0.865715	−	0.500537i	$-0.166864\pi$
$271$	7724.30	1.73143	0.865715	+	0.500537i	$0.166864\pi$
$272$	−407.141	−0.0907593
$273$	−735.328	−0.163019
$274$	−178.616	−0.0393816
$275$	614.922	0.134841
$276$	−6164.10	−1.34433
$277$	−4576.17	−0.992620	−0.496310	−	0.868145i	$-0.665312\pi$
$277$	−4576.17	−0.992620	−0.496310	+	0.868145i	$0.665312\pi$
$278$	863.250	0.186239
$279$	−797.934	−0.171222
$280$	−1004.55	−0.214406
$281$	−1358.56	−0.288415	−0.144208	−	0.989547i	$-0.546063\pi$
$281$	−1358.56	−0.288415	−0.144208	+	0.989547i	$0.546063\pi$
$282$	4996.14	1.05502
$283$	3885.04	0.816048	0.408024	−	0.912971i	$-0.366218\pi$
$283$	3885.04	0.816048	0.408024	+	0.912971i	$0.366218\pi$
$284$	6069.73	1.26821
$285$	1011.05	0.210138
$286$	−4049.34	−0.837211
$287$	−2364.38	−0.486289
$288$	−1131.17	−0.231441
$289$	−4573.75	−0.930948
$290$	−5040.52	−1.02065
$291$	1665.10	0.335430
$292$	583.097	0.116860
$293$	−4033.91	−0.804312	−0.402156	−	0.915571i	$-0.631739\pi$
$293$	−4033.91	−0.804312	−0.402156	+	0.915571i	$0.631739\pi$
$294$	691.130	0.137100
$295$	−2506.59	−0.494710
$296$	4653.24	0.913730
$297$	664.116	0.129750
$298$	−6503.85	−1.26429
$299$	5100.90	0.986598
$300$	1057.85	0.203584
$301$	855.093	0.163743
$302$	3597.90	0.685549
$303$	5670.43	1.07511
$304$	−1489.92	−0.281096
$305$	3544.66	0.665464
$306$	−779.372	−0.145600
$307$	−4620.36	−0.858950	−0.429475	−	0.903079i	$-0.641301\pi$
$307$	−4620.36	−0.858950	−0.429475	+	0.903079i	$0.641301\pi$
$308$	2428.52	0.449278
$309$	1988.10	0.366016
$310$	2084.19	0.381851
$311$	6675.89	1.21722	0.608609	−	0.793470i	$-0.291728\pi$
$311$	6675.89	1.21722	0.608609	+	0.793470i	$0.291728\pi$
$312$	−3015.01	−0.547087
$313$	2836.78	0.512283	0.256141	−	0.966639i	$-0.417549\pi$
$313$	2836.78	0.512283	0.256141	+	0.966639i	$0.417549\pi$
$314$	−11127.5	−1.99987
$315$	−315.000	−0.0563436
$316$	12558.6	2.23569
$317$	4010.63	0.710597	0.355299	−	0.934753i	$-0.384379\pi$
$317$	4010.63	0.710597	0.355299	+	0.934753i	$0.384379\pi$
$318$	9544.51	1.68311
$319$	5274.03	0.925671
$320$	3838.79	0.670609
$321$	4843.59	0.842190
$322$	−4794.30	−0.829739
$323$	1241.48	0.213863
$324$	1142.48	0.195898
$325$	−875.391	−0.149409
$326$	−14752.1	−2.50626
$327$	651.619	0.110198
$328$	−9694.49	−1.63198
$329$	2479.53	0.415504
$330$	−1734.66	−0.289363
$331$	11087.5	1.84117	0.920583	−	0.390546i	$-0.127714\pi$
$331$	11087.5	1.84117	0.920583	+	0.390546i	$0.127714\pi$
$332$	−14910.8	−2.46486
$333$	1459.12	0.240119
$334$	688.631	0.112815
$335$	4539.78	0.740402
$336$	464.198	0.0753693
$337$	12118.7	1.95890	0.979450	−	0.201689i	$-0.0646431\pi$
$337$	12118.7	1.95890	0.979450	+	0.201689i	$0.0646431\pi$
$338$	−4564.78	−0.734589
$339$	−4974.59	−0.796999
$340$	1298.95	0.207193
$341$	−2180.74	−0.346316
$342$	−2852.10	−0.450947
$343$	343.000	0.0539949
$344$	3506.07	0.549520
$345$	2185.12	0.340995
$346$	−6695.58	−1.04034
$347$	−6361.22	−0.984116	−0.492058	−	0.870562i	$-0.663755\pi$
$347$	−6361.22	−0.984116	−0.492058	+	0.870562i	$0.663755\pi$
$348$	9072.93	1.39759
$349$	−3115.18	−0.477799	−0.238899	−	0.971044i	$-0.576787\pi$
$349$	−3115.18	−0.477799	−0.238899	+	0.971044i	$0.576787\pi$
$350$	822.773	0.125655
$351$	−945.422	−0.143769
$352$	−3091.48	−0.468115
$353$	−11927.4	−1.79839	−0.899194	−	0.437550i	$-0.855846\pi$
$353$	−11927.4	−1.79839	−0.899194	+	0.437550i	$0.855846\pi$
$354$	7070.94	1.06163
$355$	−2151.67	−0.321687
$356$	20786.4	3.09460
$357$	−386.794	−0.0573426
$358$	5852.02	0.863935
$359$	−6143.95	−0.903245	−0.451623	−	0.892209i	$-0.649155\pi$
$359$	−6143.95	−0.903245	−0.451623	+	0.892209i	$0.649155\pi$
$360$	−1291.57	−0.189088
$361$	−2315.82	−0.337632
$362$	−18237.8	−2.64794
$363$	−2177.98	−0.314916
$364$	−3457.19	−0.497819
$365$	−206.703	−0.0296420
$366$	−9999.25	−1.42806
$367$	−1927.67	−0.274178	−0.137089	−	0.990559i	$-0.543775\pi$
$367$	−1927.67	−0.274178	−0.137089	+	0.990559i	$0.543775\pi$
$368$	−3220.10	−0.456139
$369$	−3039.92	−0.428867
$370$	−3811.20	−0.535500
$371$	4736.83	0.662868
$372$	−3751.54	−0.522871
$373$	10452.0	1.45090	0.725449	−	0.688276i	$-0.241632\pi$
$373$	10452.0	1.45090	0.725449	+	0.688276i	$0.241632\pi$
$374$	−2130.01	−0.294493
$375$	−375.000	−0.0516398
$376$	10166.6	1.39443
$377$	−7508.01	−1.02568
$378$	888.595	0.120911
$379$	7066.43	0.957726	0.478863	−	0.877890i	$-0.341049\pi$
$379$	7066.43	0.957726	0.478863	+	0.877890i	$0.341049\pi$
$380$	4753.50	0.641709
$381$	−3326.44	−0.447293
$382$	7404.51	0.991747
$383$	7168.04	0.956318	0.478159	−	0.878273i	$-0.341304\pi$
$383$	7168.04	0.956318	0.478159	+	0.878273i	$0.341304\pi$
$384$	−7812.52	−1.03823
$385$	−860.891	−0.113961
$386$	−22453.1	−2.96071
$387$	1099.41	0.144408
$388$	7828.58	1.02432
$389$	−7414.06	−0.966344	−0.483172	−	0.875525i	$-0.660515\pi$
$389$	−7414.06	−0.966344	−0.483172	+	0.875525i	$0.660515\pi$
$390$	2469.42	0.320626
$391$	2683.15	0.347040
$392$	1406.38	0.181206
$393$	556.463	0.0714245
$394$	−13181.2	−1.68543
$395$	−4451.94	−0.567092
$396$	3122.38	0.396226
$397$	−8936.01	−1.12969	−0.564843	−	0.825198i	$-0.691063\pi$
$397$	−8936.01	−1.12969	−0.564843	+	0.825198i	$0.691063\pi$
$398$	19290.1	2.42946
$399$	−1415.47	−0.177599
$400$	552.617	0.0690771
$401$	1782.91	0.222031	0.111015	−	0.993819i	$-0.464590\pi$
$401$	1782.91	0.222031	0.111015	+	0.993819i	$0.464590\pi$
$402$	−12806.4	−1.58887
$403$	3104.46	0.383733
$404$	26659.9	3.28312
$405$	−405.000	−0.0496904
$406$	7056.72	0.862609
$407$	3987.77	0.485667
$408$	−1585.94	−0.192441
$409$	−8759.92	−1.05905	−0.529524	−	0.848295i	$-0.677629\pi$
$409$	−8759.92	−1.05905	−0.529524	+	0.848295i	$0.677629\pi$
$410$	7940.20	0.956436
$411$	−113.972	−0.0136784
$412$	9347.17	1.11772
$413$	3509.23	0.418106
$414$	−6164.10	−0.731761
$415$	5285.75	0.625222
$416$	4400.97	0.518691
$417$	550.828	0.0646862
$418$	−7794.75	−0.912090
$419$	−3212.74	−0.374588	−0.187294	−	0.982304i	$-0.559972\pi$
$419$	−3212.74	−0.374588	−0.187294	+	0.982304i	$0.559972\pi$
$420$	−1480.99	−0.172060
$421$	15757.8	1.82420	0.912101	−	0.409965i	$-0.134459\pi$
$421$	15757.8	1.82420	0.912101	+	0.409965i	$0.134459\pi$
$422$	−3871.79	−0.446626
$423$	3187.97	0.366440
$424$	19422.1	2.22457
$425$	−460.469	−0.0525553
$426$	6069.73	0.690327
$427$	−4962.52	−0.562419
$428$	22772.5	2.57184
$429$	−2583.82	−0.290788
$430$	−2871.63	−0.322051
$431$	−405.917	−0.0453650	−0.0226825	−	0.999743i	$-0.507221\pi$
$431$	−405.917	−0.0453650	−0.0226825	+	0.999743i	$0.507221\pi$
$432$	596.827	0.0664695
$433$	−7845.25	−0.870713	−0.435357	−	0.900258i	$-0.643378\pi$
$433$	−7845.25	−0.870713	−0.435357	+	0.900258i	$0.643378\pi$
$434$	−2917.86	−0.322723
$435$	−3216.28	−0.354503
$436$	3063.63	0.336516
$437$	9818.95	1.07484
$438$	583.097	0.0636106
$439$	423.029	0.0459911	0.0229955	−	0.999736i	$-0.492680\pi$
$439$	423.029	0.0459911	0.0229955	+	0.999736i	$0.492680\pi$
$440$	−3529.84	−0.382452
$441$	441.000	0.0476190
$442$	3032.24	0.326310
$443$	−16058.7	−1.72229	−0.861143	−	0.508362i	$-0.830251\pi$
$443$	−16058.7	−1.72229	−0.861143	+	0.508362i	$0.830251\pi$
$444$	6860.17	0.733264
$445$	−7368.62	−0.784958
$446$	3842.09	0.407911
$447$	−4150.01	−0.439125
$448$	−5374.30	−0.566768
$449$	2186.75	0.229842	0.114921	−	0.993375i	$-0.463338\pi$
$449$	2186.75	0.229842	0.114921	+	0.993375i	$0.463338\pi$
$450$	1057.85	0.110817
$451$	−8308.05	−0.867430
$452$	−23388.3	−2.43384
$453$	2295.77	0.238112
$454$	17188.2	1.77683
$455$	1225.55	0.126274
$456$	−5803.72	−0.596018
$457$	−5799.22	−0.593602	−0.296801	−	0.954939i	$-0.595920\pi$
$457$	−5799.22	−0.593602	−0.296801	+	0.954939i	$0.595920\pi$
$458$	4416.62	0.450600
$459$	−497.306	−0.0505714
$460$	10273.5	1.04131
$461$	9873.35	0.997500	0.498750	−	0.866746i	$-0.333793\pi$
$461$	9873.35	0.997500	0.498750	+	0.866746i	$0.333793\pi$
$462$	2428.52	0.244556
$463$	−6181.84	−0.620506	−0.310253	−	0.950654i	$-0.600414\pi$
$463$	−6181.84	−0.620506	−0.310253	+	0.950654i	$0.600414\pi$
$464$	4739.66	0.474209
$465$	1329.89	0.132628
$466$	−35.9529	−0.00357400
$467$	6145.50	0.608950	0.304475	−	0.952520i	$-0.401519\pi$
$467$	6145.50	0.608950	0.304475	+	0.952520i	$0.401519\pi$
$468$	−4444.96	−0.439035
$469$	−6355.69	−0.625754
$470$	−8326.91	−0.817216
$471$	−7100.28	−0.694615
$472$	14388.6	1.40316
$473$	3004.66	0.292081
$474$	12558.6	1.21696
$475$	−1685.08	−0.162772
$476$	−1818.53	−0.175110
$477$	6090.22	0.584595
$478$	−4180.23	−0.399999
$479$	10879.4	1.03777	0.518887	−	0.854843i	$-0.326347\pi$
$479$	10879.4	1.03777	0.518887	+	0.854843i	$0.326347\pi$
$480$	1885.29	0.179274
$481$	−5676.91	−0.538139
$482$	10062.4	0.950894
$483$	−3059.17	−0.288193
$484$	−10239.9	−0.961675
$485$	−2775.17	−0.259823
$486$	1142.48	0.106634
$487$	8087.51	0.752526	0.376263	−	0.926513i	$-0.377209\pi$
$487$	8087.51	0.752526	0.376263	+	0.926513i	$0.377209\pi$
$488$	−20347.4	−1.88747
$489$	−9413.08	−0.870499
$490$	−1151.88	−0.106197
$491$	−6959.90	−0.639707	−0.319853	−	0.947467i	$-0.603634\pi$
$491$	−6959.90	−0.639707	−0.319853	+	0.947467i	$0.603634\pi$
$492$	−14292.4	−1.30965
$493$	−3949.32	−0.360788
$494$	11096.4	1.01063
$495$	−1106.86	−0.100504
$496$	−1959.79	−0.177413
$497$	3012.34	0.271875
$498$	−14910.8	−1.34170
$499$	18632.0	1.67151	0.835756	−	0.549101i	$-0.185030\pi$
$499$	18632.0	1.67151	0.835756	+	0.549101i	$0.185030\pi$
$500$	−1763.09	−0.157695
$501$	439.406	0.0391840
$502$	−31734.6	−2.82149
$503$	4627.62	0.410209	0.205105	−	0.978740i	$-0.434247\pi$
$503$	4627.62	0.410209	0.205105	+	0.978740i	$0.434247\pi$
$504$	1808.20	0.159809
$505$	−9450.72	−0.832775
$506$	−16846.4	−1.48007
$507$	−2912.72	−0.255145
$508$	−15639.4	−1.36592
$509$	−11351.8	−0.988528	−0.494264	−	0.869312i	$-0.664562\pi$
$509$	−11351.8	−0.988528	−0.494264	+	0.869312i	$0.664562\pi$
$510$	1298.95	0.112782
$511$	289.384	0.0250521
$512$	−7853.76	−0.677911
$513$	−1819.88	−0.156627
$514$	14427.4	1.23806
$515$	−3313.50	−0.283515
$516$	5168.93	0.440987
$517$	8712.67	0.741166
$518$	5335.68	0.452580
$519$	−4272.36	−0.361340
$520$	5025.02	0.423772
$521$	19096.1	1.60579	0.802893	−	0.596123i	$-0.203293\pi$
$521$	19096.1	1.60579	0.802893	+	0.596123i	$0.203293\pi$
$522$	9072.93	0.760750
$523$	−3145.11	−0.262956	−0.131478	−	0.991319i	$-0.541972\pi$
$523$	−3145.11	−0.262956	−0.131478	+	0.991319i	$0.541972\pi$
$524$	2616.24	0.218113
$525$	525.000	0.0436436
$526$	−21975.7	−1.82164
$527$	1632.99	0.134980
$528$	1631.12	0.134442
$529$	9054.20	0.744160
$530$	−15907.5	−1.30373
$531$	4511.87	0.368735
$532$	−6654.90	−0.542343
$533$	11827.2	0.961148
$534$	20786.4	1.68449
$535$	−8072.66	−0.652358
$536$	−26059.8	−2.10002
$537$	3734.09	0.300071
$538$	11365.5	0.910781
$539$	1205.25	0.0963148
$540$	−1904.13	−0.151742
$541$	8776.12	0.697440	0.348720	−	0.937227i	$-0.386616\pi$
$541$	8776.12	0.697440	0.348720	+	0.937227i	$0.386616\pi$
$542$	36316.3	2.87808
$543$	−11637.3	−0.919710
$544$	2314.98	0.182452
$545$	−1086.03	−0.0853587
$546$	−3457.19	−0.270978
$547$	−13695.1	−1.07049	−0.535247	−	0.844696i	$-0.679781\pi$
$547$	−13695.1	−1.07049	−0.535247	+	0.844696i	$0.679781\pi$
$548$	−535.847	−0.0417705
$549$	−6380.38	−0.496007
$550$	2891.09	0.224139
$551$	−14452.5	−1.11742
$552$	−12543.3	−0.967171
$553$	6232.71	0.479280
$554$	−21515.2	−1.64999
$555$	−2431.87	−0.185995
$556$	2589.75	0.197536
$557$	7850.44	0.597188	0.298594	−	0.954380i	$-0.403482\pi$
$557$	7850.44	0.597188	0.298594	+	0.954380i	$0.403482\pi$
$558$	−3751.54	−0.284615
$559$	−4277.38	−0.323638
$560$	−773.664	−0.0583808
$561$	−1359.13	−0.102286
$562$	−6387.33	−0.479419
$563$	−4948.81	−0.370457	−0.185229	−	0.982695i	$-0.559303\pi$
$563$	−4948.81	−0.370457	−0.185229	+	0.982695i	$0.559303\pi$
$564$	14988.4	1.11902
$565$	8290.98	0.617353
$566$	18265.7	1.35648
$567$	567.000	0.0419961
$568$	12351.3	0.912408
$569$	−8115.76	−0.597945	−0.298972	−	0.954262i	$-0.596644\pi$
$569$	−8115.76	−0.597945	−0.298972	+	0.954262i	$0.596644\pi$
$570$	4753.50	0.349302
$571$	5656.42	0.414560	0.207280	−	0.978282i	$-0.433539\pi$
$571$	5656.42	0.414560	0.207280	+	0.978282i	$0.433539\pi$
$572$	−12148.0	−0.887996
$573$	4724.71	0.344463
$574$	−11116.3	−0.808336
$575$	−3641.87	−0.264133
$576$	−6909.82	−0.499842
$577$	−9536.77	−0.688078	−0.344039	−	0.938955i	$-0.611795\pi$
$577$	−9536.77	−0.688078	−0.344039	+	0.938955i	$0.611795\pi$
$578$	−21503.8	−1.54747
$579$	−14327.0	−1.02834
$580$	−15121.5	−1.08257
$581$	−7400.05	−0.528409
$582$	7828.58	0.557569
$583$	16644.5	1.18241
$584$	1186.54	0.0840743
$585$	1575.70	0.111363
$586$	−18965.7	−1.33697
$587$	−13089.6	−0.920383	−0.460191	−	0.887820i	$-0.652219\pi$
$587$	−13089.6	−0.920383	−0.460191	+	0.887820i	$0.652219\pi$
$588$	2073.39	0.145417
$589$	5975.92	0.418053
$590$	−11784.9	−0.822334
$591$	−8410.73	−0.585400
$592$	3583.72	0.248801
$593$	4281.96	0.296524	0.148262	−	0.988948i	$-0.452632\pi$
$593$	4281.96	0.296524	0.148262	+	0.988948i	$0.452632\pi$
$594$	3122.38	0.215678
$595$	644.656	0.0444173
$596$	−19511.5	−1.34098
$597$	12308.7	0.843825
$598$	23982.2	1.63997
$599$	3699.92	0.252378	0.126189	−	0.992006i	$-0.459725\pi$
$599$	3699.92	0.252378	0.126189	+	0.992006i	$0.459725\pi$
$600$	2152.62	0.146467
$601$	−17286.1	−1.17323	−0.586616	−	0.809865i	$-0.699540\pi$
$601$	−17286.1	−1.17323	−0.586616	+	0.809865i	$0.699540\pi$
$602$	4020.28	0.272183
$603$	−8171.61	−0.551863
$604$	10793.7	0.727135
$605$	3629.97	0.243933
$606$	26659.9	1.78710
$607$	14456.7	0.966689	0.483344	−	0.875430i	$-0.339422\pi$
$607$	14456.7	0.966689	0.483344	+	0.875430i	$0.339422\pi$
$608$	8471.63	0.565082
$609$	4502.79	0.299610
$610$	16665.4	1.10617
$611$	−12403.2	−0.821243
$612$	−2338.12	−0.154433
$613$	17981.9	1.18480	0.592400	−	0.805644i	$-0.298181\pi$
$613$	17981.9	1.18480	0.592400	+	0.805644i	$0.298181\pi$
$614$	−21722.9	−1.42779
$615$	5066.53	0.332199
$616$	4941.78	0.323231
$617$	19614.7	1.27983	0.639916	−	0.768445i	$-0.278969\pi$
$617$	19614.7	1.27983	0.639916	+	0.768445i	$0.278969\pi$
$618$	9347.17	0.608412
$619$	−10462.9	−0.679385	−0.339692	−	0.940537i	$-0.610323\pi$
$619$	−10462.9	−0.679385	−0.339692	+	0.940537i	$0.610323\pi$
$620$	6252.56	0.405014
$621$	−3933.22	−0.254162
$622$	31387.1	2.02332
$623$	10316.1	0.663411
$624$	−2322.03	−0.148967
$625$	625.000	0.0400000
$626$	13337.3	0.851544
$627$	−4973.72	−0.316796
$628$	−33382.4	−2.12118
$629$	−2986.14	−0.189293
$630$	−1480.99	−0.0936574
$631$	24481.9	1.54454	0.772272	−	0.635292i	$-0.219120\pi$
$631$	24481.9	1.54454	0.772272	+	0.635292i	$0.219120\pi$
$632$	25555.5	1.60846
$633$	−2470.54	−0.155126
$634$	18856.2	1.18119
$635$	5544.06	0.346471
$636$	28633.5	1.78521
$637$	−1715.77	−0.106721
$638$	24796.2	1.53870
$639$	3873.01	0.239771
$640$	13020.9	0.804211
$641$	−1109.39	−0.0683595	−0.0341797	−	0.999416i	$-0.510882\pi$
$641$	−1109.39	−0.0683595	−0.0341797	+	0.999416i	$0.510882\pi$
$642$	22772.5	1.39993
$643$	30112.5	1.84684	0.923422	−	0.383787i	$-0.125380\pi$
$643$	30112.5	1.84684	0.923422	+	0.383787i	$0.125380\pi$
$644$	−14382.9	−0.880071
$645$	−1832.34	−0.111858
$646$	5836.90	0.355495
$647$	−4260.27	−0.258869	−0.129435	−	0.991588i	$-0.541316\pi$
$647$	−4260.27	−0.258869	−0.129435	+	0.991588i	$0.541316\pi$
$648$	2324.83	0.140938
$649$	12330.9	0.745808
$650$	−4115.70	−0.248356
$651$	−1861.85	−0.112091
$652$	−44256.2	−2.65829
$653$	−10576.8	−0.633844	−0.316922	−	0.948452i	$-0.602649\pi$
$653$	−10576.8	−0.633844	−0.316922	+	0.948452i	$0.602649\pi$
$654$	3063.63	0.183176
$655$	−927.438	−0.0553252
$656$	−7466.27	−0.444373
$657$	372.066	0.0220939
$658$	11657.7	0.690674
$659$	3394.70	0.200666	0.100333	−	0.994954i	$-0.468009\pi$
$659$	3394.70	0.200666	0.100333	+	0.994954i	$0.468009\pi$
$660$	−5203.97	−0.306915
$661$	−33174.4	−1.95210	−0.976048	−	0.217554i	$-0.930192\pi$
$661$	−33174.4	−1.95210	−0.976048	+	0.217554i	$0.930192\pi$
$662$	52128.7	3.06048
$663$	1934.83	0.113337
$664$	−30341.9	−1.77333
$665$	2359.11	0.137567
$666$	6860.17	0.399138
$667$	−31235.4	−1.81326
$668$	2065.89	0.119658
$669$	2451.58	0.141680
$670$	21344.1	1.23074
$671$	−17437.5	−1.00323
$672$	−2639.40	−0.151514
$673$	753.881	0.0431797	0.0215899	−	0.999767i	$-0.493127\pi$
$673$	753.881	0.0431797	0.0215899	+	0.999767i	$0.493127\pi$
$674$	56976.9	3.25619
$675$	675.000	0.0384900
$676$	−13694.3	−0.779149
$677$	15668.8	0.889511	0.444756	−	0.895652i	$-0.353291\pi$
$677$	15668.8	0.889511	0.444756	+	0.895652i	$0.353291\pi$
$678$	−23388.3	−1.32481
$679$	3885.24	0.219590
$680$	2643.23	0.149064
$681$	10967.5	0.617147
$682$	−10252.9	−0.575665
$683$	−11557.4	−0.647485	−0.323742	−	0.946145i	$-0.604941\pi$
$683$	−11557.4	−0.647485	−0.323742	+	0.946145i	$0.604941\pi$
$684$	−8556.30	−0.478302
$685$	189.953	0.0105952
$686$	1612.64	0.0897532
$687$	2818.18	0.156507
$688$	2700.22	0.149630
$689$	−23694.7	−1.31016
$690$	10273.5	0.566819
$691$	−18503.1	−1.01866	−0.509328	−	0.860572i	$-0.670106\pi$
$691$	−18503.1	−1.01866	−0.509328	+	0.860572i	$0.670106\pi$
$692$	−20086.8	−1.10344
$693$	1549.60	0.0849416
$694$	−29907.7	−1.63585
$695$	−918.046	−0.0501057
$696$	18462.5	1.00549
$697$	6221.28	0.338088
$698$	−14646.2	−0.794223
$699$	−22.9410	−0.00124136
$700$	2468.32	0.133277
$701$	22580.4	1.21662	0.608311	−	0.793699i	$-0.291847\pi$
$701$	22580.4	1.21662	0.608311	+	0.793699i	$0.291847\pi$
$702$	−4444.96	−0.238980
$703$	−10927.7	−0.586269
$704$	−18884.4	−1.01099
$705$	−5313.28	−0.283844
$706$	−56077.4	−2.98938
$707$	13231.0	0.703823
$708$	21212.8	1.12603
$709$	−27426.6	−1.45279	−0.726394	−	0.687278i	$-0.758805\pi$
$709$	−27426.6	−1.45279	−0.726394	+	0.687278i	$0.758805\pi$
$710$	−10116.2	−0.534725
$711$	8013.49	0.422685
$712$	42298.2	2.22639
$713$	12915.5	0.678383
$714$	−1818.53	−0.0953178
$715$	4306.37	0.225244
$716$	17556.1	0.916342
$717$	−2667.35	−0.138931
$718$	−28886.1	−1.50142
$719$	19383.0	1.00538	0.502688	−	0.864468i	$-0.332344\pi$
$719$	19383.0	1.00538	0.502688	+	0.864468i	$0.332344\pi$
$720$	−994.711	−0.0514871
$721$	4638.90	0.239614
$722$	−10888.0	−0.561230
$723$	6420.69	0.330274
$724$	−54713.3	−2.80857
$725$	5360.47	0.274597
$726$	−10239.9	−0.523469
$727$	−12317.3	−0.628368	−0.314184	−	0.949362i	$-0.601731\pi$
$727$	−12317.3	−0.628368	−0.314184	+	0.949362i	$0.601731\pi$
$728$	−7035.02	−0.358153
$729$	729.000	0.0370370
$730$	−971.828	−0.0492726
$731$	−2249.96	−0.113841
$732$	−29997.8	−1.51468
$733$	1234.02	0.0621822	0.0310911	−	0.999517i	$-0.490102\pi$
$733$	1234.02	0.0621822	0.0310911	+	0.999517i	$0.490102\pi$
$734$	−9063.05	−0.455754
$735$	−735.000	−0.0368856
$736$	18309.3	0.916970
$737$	−22332.9	−1.11620
$738$	−14292.4	−0.712885
$739$	−15257.3	−0.759473	−0.379736	−	0.925095i	$-0.623985\pi$
$739$	−15257.3	−0.759473	−0.379736	+	0.925095i	$0.623985\pi$
$740$	−11433.6	−0.567984
$741$	7080.49	0.351023
$742$	22270.5	1.10186
$743$	−35565.1	−1.75606	−0.878032	−	0.478602i	$-0.841144\pi$
$743$	−35565.1	−1.75606	−0.878032	+	0.478602i	$0.841144\pi$
$744$	−7633.99	−0.376177
$745$	6916.69	0.340145
$746$	49140.8	2.41176
$747$	−9514.35	−0.466013
$748$	−6390.04	−0.312357
$749$	11301.7	0.551343
$750$	−1763.09	−0.0858384
$751$	14266.7	0.693209	0.346605	−	0.938011i	$-0.387335\pi$
$751$	14266.7	0.693209	0.346605	+	0.938011i	$0.387335\pi$
$752$	7829.89	0.379690
$753$	−20249.4	−0.979986
$754$	−35299.4	−1.70494
$755$	−3826.28	−0.184441
$756$	2665.79	0.128246
$757$	−15927.9	−0.764744	−0.382372	−	0.924009i	$-0.624893\pi$
$757$	−15927.9	−0.764744	−0.382372	+	0.924009i	$0.624893\pi$
$758$	33223.3	1.59198
$759$	−10749.4	−0.514071
$760$	9672.87	0.461674
$761$	−2566.48	−0.122253	−0.0611266	−	0.998130i	$-0.519469\pi$
$761$	−2566.48	−0.122253	−0.0611266	+	0.998130i	$0.519469\pi$
$762$	−15639.4	−0.743514
$763$	1520.44	0.0721413
$764$	22213.5	1.05191
$765$	828.844	0.0391724
$766$	33701.0	1.58964
$767$	−17554.0	−0.826386
$768$	−18304.9	−0.860052
$769$	14433.1	0.676816	0.338408	−	0.940999i	$-0.390112\pi$
$769$	14433.1	0.676816	0.338408	+	0.940999i	$0.390112\pi$
$770$	−4047.53	−0.189432
$771$	9205.91	0.430017
$772$	−67359.4	−3.14031
$773$	−29443.2	−1.36999	−0.684993	−	0.728550i	$-0.740195\pi$
$773$	−29443.2	−1.36999	−0.684993	+	0.728550i	$0.740195\pi$
$774$	5168.93	0.240043
$775$	−2216.48	−0.102733
$776$	15930.4	0.736941
$777$	3404.62	0.157195
$778$	−34857.7	−1.60631
$779$	22766.7	1.04711
$780$	7408.27	0.340075
$781$	10584.9	0.484964
$782$	12615.0	0.576869
$783$	5789.31	0.264231
$784$	1083.13	0.0493408
$785$	11833.8	0.538046
$786$	2616.24	0.118726
$787$	26390.6	1.19533	0.597664	−	0.801747i	$-0.296096\pi$
$787$	26390.6	1.19533	0.597664	+	0.801747i	$0.296096\pi$
$788$	−39543.6	−1.78767
$789$	−14022.4	−0.632711
$790$	−20931.1	−0.942650
$791$	−11607.4	−0.521758
$792$	6353.72	0.285063
$793$	24823.7	1.11162
$794$	−42013.2	−1.87783
$795$	−10150.4	−0.452825
$796$	57870.3	2.57683
$797$	−3738.33	−0.166146	−0.0830730	−	0.996543i	$-0.526473\pi$
$797$	−3738.33	−0.166146	−0.0830730	+	0.996543i	$0.526473\pi$
$798$	−6654.90	−0.295214
$799$	−6524.26	−0.288876
$800$	−3142.15	−0.138865
$801$	13263.5	0.585073
$802$	8382.48	0.369072
$803$	1016.85	0.0446873
$804$	−38419.3	−1.68525
$805$	5098.62	0.223233
$806$	14595.8	0.637861
$807$	7252.14	0.316341
$808$	54250.1	2.36202
$809$	43204.1	1.87760	0.938798	−	0.344468i	$-0.111941\pi$
$809$	43204.1	1.87760	0.938798	+	0.344468i	$0.111941\pi$
$810$	−1904.13	−0.0825980
$811$	−30192.4	−1.30727	−0.653637	−	0.756809i	$-0.726758\pi$
$811$	−30192.4	−1.30727	−0.653637	+	0.756809i	$0.726758\pi$
$812$	21170.2	0.914935
$813$	23172.9	0.999642
$814$	18748.7	0.807301
$815$	15688.5	0.674286
$816$	−1221.42	−0.0523999
$817$	−8233.71	−0.352584
$818$	−41185.3	−1.76041
$819$	−2205.98	−0.0941188
$820$	23820.6	1.01445
$821$	−40274.7	−1.71206	−0.856028	−	0.516929i	$-0.827075\pi$
$821$	−40274.7	−1.71206	−0.856028	+	0.516929i	$0.827075\pi$
$822$	−535.847	−0.0227370
$823$	25184.2	1.06667	0.533334	−	0.845905i	$-0.320939\pi$
$823$	25184.2	1.06667	0.533334	+	0.845905i	$0.320939\pi$
$824$	19020.5	0.804140
$825$	1844.77	0.0778503
$826$	16498.9	0.694999
$827$	−38941.7	−1.63741	−0.818703	−	0.574218i	$-0.805306\pi$
$827$	−38941.7	−1.63741	−0.818703	+	0.574218i	$0.805306\pi$
$828$	−18492.3	−0.776150
$829$	−8327.05	−0.348867	−0.174433	−	0.984669i	$-0.555809\pi$
$829$	−8327.05	−0.348867	−0.174433	+	0.984669i	$0.555809\pi$
$830$	24851.3	1.03928
$831$	−13728.5	−0.573089
$832$	26883.5	1.12021
$833$	−902.519	−0.0375395
$834$	2589.75	0.107525
$835$	−732.343	−0.0303518
$836$	−23384.2	−0.967418
$837$	−2393.80	−0.0988553
$838$	−15104.9	−0.622660
$839$	8784.41	0.361468	0.180734	−	0.983532i	$-0.442153\pi$
$839$	8784.41	0.361468	0.180734	+	0.983532i	$0.442153\pi$
$840$	−3013.66	−0.123787
$841$	21586.4	0.885087
$842$	74086.4	3.03229
$843$	−4075.67	−0.166517
$844$	−11615.4	−0.473718
$845$	4854.53	0.197634
$846$	14988.4	0.609117
$847$	−5081.96	−0.206161
$848$	14958.0	0.605732
$849$	11655.1	0.471145
$850$	−2164.92	−0.0873602
$851$	−23617.6	−0.951350
$852$	18209.2	0.732203
$853$	−9076.15	−0.364316	−0.182158	−	0.983269i	$-0.558308\pi$
$853$	−9076.15	−0.364316	−0.182158	+	0.983269i	$0.558308\pi$
$854$	−23331.6	−0.934884
$855$	3033.14	0.121323
$856$	46339.6	1.85030
$857$	36396.7	1.45074	0.725372	−	0.688357i	$-0.241668\pi$
$857$	36396.7	1.45074	0.725372	+	0.688357i	$0.241668\pi$
$858$	−12148.0	−0.483364
$859$	8915.27	0.354115	0.177058	−	0.984200i	$-0.443342\pi$
$859$	8915.27	0.354115	0.177058	+	0.984200i	$0.443342\pi$
$860$	−8614.88	−0.341587
$861$	−7093.14	−0.280759
$862$	−1908.44	−0.0754081
$863$	−6148.26	−0.242514	−0.121257	−	0.992621i	$-0.538692\pi$
$863$	−6148.26	−0.242514	−0.121257	+	0.992621i	$0.538692\pi$
$864$	−3393.52	−0.133623
$865$	7120.59	0.279893
$866$	−36884.9	−1.44735
$867$	−13721.2	−0.537483
$868$	−8753.59	−0.342300
$869$	21900.8	0.854928
$870$	−15121.5	−0.589274
$871$	31792.6	1.23680
$872$	6234.16	0.242105
$873$	4995.31	0.193660
$874$	46164.4	1.78665
$875$	−875.000	−0.0338062
$876$	1749.29	0.0674692
$877$	−14287.0	−0.550101	−0.275050	−	0.961430i	$-0.588694\pi$
$877$	−14287.0	−0.550101	−0.275050	+	0.961430i	$0.588694\pi$
$878$	1988.90	0.0764488
$879$	−12101.7	−0.464370
$880$	−2718.53	−0.104138
$881$	−13315.9	−0.509221	−0.254610	−	0.967044i	$-0.581947\pi$
$881$	−13315.9	−0.509221	−0.254610	+	0.967044i	$0.581947\pi$
$882$	2073.39	0.0791549
$883$	−5271.78	−0.200917	−0.100458	−	0.994941i	$-0.532031\pi$
$883$	−5271.78	−0.200917	−0.100458	+	0.994941i	$0.532031\pi$
$884$	9096.73	0.346104
$885$	−7519.78	−0.285621
$886$	−75501.1	−2.86288
$887$	2606.07	0.0986507	0.0493253	−	0.998783i	$-0.484293\pi$
$887$	2606.07	0.0986507	0.0493253	+	0.998783i	$0.484293\pi$
$888$	13959.7	0.527542
$889$	−7761.69	−0.292822
$890$	−34644.0	−1.30480
$891$	1992.35	0.0749115
$892$	11526.3	0.432654
$893$	−23875.4	−0.894694
$894$	−19511.5	−0.729937
$895$	−6223.48	−0.232434
$896$	−18229.2	−0.679682
$897$	15302.7	0.569612
$898$	10281.1	0.382056
$899$	−19010.2	−0.705258
$900$	3173.55	0.117539
$901$	−12463.8	−0.460854
$902$	−39060.8	−1.44189
$903$	2565.28	0.0945373
$904$	−47592.8	−1.75101
$905$	19395.4	0.712405
$906$	10793.7	0.395802
$907$	18610.6	0.681317	0.340659	−	0.940187i	$-0.389350\pi$
$907$	18610.6	0.681317	0.340659	+	0.940187i	$0.389350\pi$
$908$	51564.6	1.88462
$909$	17011.3	0.620714
$910$	5761.98	0.209899
$911$	41091.7	1.49443	0.747216	−	0.664581i	$-0.231390\pi$
$911$	41091.7	1.49443	0.747216	+	0.664581i	$0.231390\pi$
$912$	−4469.77	−0.162291
$913$	−26002.6	−0.942563
$914$	−27265.4	−0.986716
$915$	10634.0	0.384206
$916$	13249.8	0.477934
$917$	1298.41	0.0467583
$918$	−2338.12	−0.0840624
$919$	38891.3	1.39598	0.697990	−	0.716107i	$-0.254078\pi$
$919$	38891.3	1.39598	0.697990	+	0.716107i	$0.254078\pi$
$920$	20905.5	0.749167
$921$	−13861.1	−0.495915
$922$	46420.2	1.65810
$923$	−15068.4	−0.537360
$924$	7285.56	0.259391
$925$	4053.12	0.144071
$926$	−29064.3	−1.03144
$927$	5964.30	0.211320
$928$	−26949.4	−0.953295
$929$	18699.4	0.660396	0.330198	−	0.943912i	$-0.392885\pi$
$929$	18699.4	0.660396	0.330198	+	0.943912i	$0.392885\pi$
$930$	6252.56	0.220462
$931$	−3302.75	−0.116266
$932$	−107.859	−0.00379080
$933$	20027.7	0.702761
$934$	28893.4	1.01223
$935$	2265.22	0.0792305
$936$	−9045.03	−0.315861
$937$	21509.6	0.749933	0.374967	−	0.927038i	$-0.377654\pi$
$937$	21509.6	0.749933	0.374967	+	0.927038i	$0.377654\pi$
$938$	−29881.7	−1.04016
$939$	8510.35	0.295767
$940$	−24980.7	−0.866788
$941$	−11241.7	−0.389448	−0.194724	−	0.980858i	$-0.562381\pi$
$941$	−11241.7	−0.389448	−0.194724	+	0.980858i	$0.562381\pi$
$942$	−33382.4	−1.15463
$943$	49204.5	1.69917
$944$	11081.5	0.382068
$945$	−945.000	−0.0325300
$946$	14126.6	0.485513
$947$	−36556.3	−1.25441	−0.627203	−	0.778856i	$-0.715800\pi$
$947$	−36556.3	−1.25441	−0.627203	+	0.778856i	$0.715800\pi$
$948$	37675.9	1.29078
$949$	−1447.57	−0.0495153
$950$	−7922.50	−0.270568
$951$	12031.9	0.410263
$952$	−3700.53	−0.125982
$953$	−36633.4	−1.24520	−0.622598	−	0.782542i	$-0.713923\pi$
$953$	−36633.4	−1.24520	−0.622598	+	0.782542i	$0.713923\pi$
$954$	28633.5	0.971745
$955$	−7874.52	−0.266820
$956$	−12540.7	−0.424263
$957$	15822.1	0.534436
$958$	51150.3	1.72504
$959$	−265.935	−0.00895462
$960$	11516.4	0.387176
$961$	−21930.5	−0.736146
$962$	−26690.3	−0.894523
$963$	14530.8	0.486239
$964$	30187.3	1.00858
$965$	23878.4	0.796551
$966$	−14382.9	−0.479050
$967$	−35515.8	−1.18109	−0.590544	−	0.807006i	$-0.701087\pi$
$967$	−35515.8	−1.18109	−0.590544	+	0.807006i	$0.701087\pi$
$968$	−20837.2	−0.691871
$969$	3724.44	0.123474
$970$	−13047.6	−0.431891
$971$	−39661.0	−1.31080	−0.655398	−	0.755283i	$-0.727499\pi$
$971$	−39661.0	−1.31080	−0.655398	+	0.755283i	$0.727499\pi$
$972$	3427.44	0.113102
$973$	1285.26	0.0423471
$974$	38023.9	1.25089
$975$	−2626.17	−0.0862613
$976$	−15670.7	−0.513942
$977$	50325.3	1.64795	0.823977	−	0.566624i	$-0.191751\pi$
$977$	50325.3	1.64795	0.823977	+	0.566624i	$0.191751\pi$
$978$	−44256.2	−1.44699
$979$	36249.0	1.18337
$980$	−3455.65	−0.112639
$981$	1954.86	0.0636226
$982$	−32722.4	−1.06335
$983$	51189.0	1.66091	0.830456	−	0.557084i	$-0.188080\pi$
$983$	51189.0	1.66091	0.830456	+	0.557084i	$0.188080\pi$
$984$	−29083.5	−0.942223
$985$	14017.9	0.453449
$986$	−18568.0	−0.599721
$987$	7438.59	0.239892
$988$	33289.3	1.07194
$989$	−17795.1	−0.572145
$990$	−5203.97	−0.167064
$991$	−55137.3	−1.76740	−0.883700	−	0.468054i	$-0.844955\pi$
$991$	−55137.3	−1.76740	−0.883700	+	0.468054i	$0.844955\pi$
$992$	11143.2	0.356651
$993$	33262.6	1.06300
$994$	14162.7	0.451925
$995$	−20514.6	−0.653624
$996$	−44732.3	−1.42309
$997$	41606.5	1.32166	0.660828	−	0.750537i	$-0.270205\pi$
$997$	41606.5	1.32166	0.660828	+	0.750537i	$0.270205\pi$
$998$	87599.6	2.77848
$999$	4377.37	0.138633

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	105.4.a.g.1.2	✓	2
3.2	odd	2		315.4.a.g.1.1		2
4.3	odd	2		1680.4.a.y.1.2		2
5.2	odd	4		525.4.d.j.274.4		4
5.3	odd	4		525.4.d.j.274.1		4
5.4	even	2		525.4.a.i.1.1		2
7.6	odd	2		735.4.a.q.1.2		2
15.14	odd	2		1575.4.a.y.1.2		2
21.20	even	2		2205.4.a.v.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.4.a.g.1.2	✓	2	1.1	even	1	trivial
315.4.a.g.1.1		2	3.2	odd	2
525.4.a.i.1.1		2	5.4	even	2
525.4.d.j.274.1		4	5.3	odd	4
525.4.d.j.274.4		4	5.2	odd	4
735.4.a.q.1.2		2	7.6	odd	2
1575.4.a.y.1.2		2	15.14	odd	2
1680.4.a.y.1.2		2	4.3	odd	2
2205.4.a.v.1.1		2	21.20	even	2

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:	\( N \)	\(=\)	\( 105 = 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	105.a (trivial)

\(f(q)\)	\(=\)	\(q+4.70156 q^{2} +3.00000 q^{3} +14.1047 q^{4} -5.00000 q^{5} +14.1047 q^{6} +7.00000 q^{7} +28.7016 q^{8} +9.00000 q^{9} +O(q^{10})\)	\(q+4.70156 q^{2} +3.00000 q^{3} +14.1047 q^{4} -5.00000 q^{5} +14.1047 q^{6} +7.00000 q^{7} +28.7016 q^{8} +9.00000 q^{9} -23.5078 q^{10} +24.5969 q^{11} +42.3141 q^{12} -35.0156 q^{13} +32.9109 q^{14} -15.0000 q^{15} +22.1047 q^{16} -18.4187 q^{17} +42.3141 q^{18} -67.4031 q^{19} -70.5234 q^{20} +21.0000 q^{21} +115.644 q^{22} -145.675 q^{23} +86.1047 q^{24} +25.0000 q^{25} -164.628 q^{26} +27.0000 q^{27} +98.7328 q^{28} +214.419 q^{29} -70.5234 q^{30} -88.6594 q^{31} -125.686 q^{32} +73.7906 q^{33} -86.5969 q^{34} -35.0000 q^{35} +126.942 q^{36} +162.125 q^{37} -316.900 q^{38} -105.047 q^{39} -143.508 q^{40} -337.769 q^{41} +98.7328 q^{42} +122.156 q^{43} +346.931 q^{44} -45.0000 q^{45} -684.900 q^{46} +354.219 q^{47} +66.3141 q^{48} +49.0000 q^{49} +117.539 q^{50} -55.2562 q^{51} -493.884 q^{52} +676.691 q^{53} +126.942 q^{54} -122.984 q^{55} +200.911 q^{56} -202.209 q^{57} +1008.10 q^{58} +501.319 q^{59} -211.570 q^{60} -708.931 q^{61} -416.837 q^{62} +63.0000 q^{63} -767.758 q^{64} +175.078 q^{65} +346.931 q^{66} -907.956 q^{67} -259.791 q^{68} -437.025 q^{69} -164.555 q^{70} +430.334 q^{71} +258.314 q^{72} +41.3406 q^{73} +762.241 q^{74} +75.0000 q^{75} -950.700 q^{76} +172.178 q^{77} -493.884 q^{78} +890.388 q^{79} -110.523 q^{80} +81.0000 q^{81} -1588.04 q^{82} -1057.15 q^{83} +296.198 q^{84} +92.0937 q^{85} +574.325 q^{86} +643.256 q^{87} +705.969 q^{88} +1473.72 q^{89} -211.570 q^{90} -245.109 q^{91} -2054.70 q^{92} -265.978 q^{93} +1665.38 q^{94} +337.016 q^{95} -377.058 q^{96} +555.034 q^{97} +230.377 q^{98} +221.372 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 3 q^{2} + 6 q^{3} + 9 q^{4} - 10 q^{5} + 9 q^{6} + 14 q^{7} + 51 q^{8} + 18 q^{9}+O(q^{10}) \) 2 * q + 3 * q^2 + 6 * q^3 + 9 * q^4 - 10 * q^5 + 9 * q^6 + 14 * q^7 + 51 * q^8 + 18 * q^9	\( 2 q + 3 q^{2} + 6 q^{3} + 9 q^{4} - 10 q^{5} + 9 q^{6} + 14 q^{7} + 51 q^{8} + 18 q^{9} - 15 q^{10} + 62 q^{11} + 27 q^{12} - 6 q^{13} + 21 q^{14} - 30 q^{15} + 25 q^{16} + 40 q^{17} + 27 q^{18} - 122 q^{19} - 45 q^{20} + 42 q^{21} + 52 q^{22} + 16 q^{23} + 153 q^{24} + 50 q^{25} - 214 q^{26} + 54 q^{27} + 63 q^{28} + 352 q^{29} - 45 q^{30} + 66 q^{31} - 309 q^{32} + 186 q^{33} - 186 q^{34} - 70 q^{35} + 81 q^{36} - 188 q^{37} - 224 q^{38} - 18 q^{39} - 255 q^{40} + 16 q^{41} + 63 q^{42} - 396 q^{43} + 156 q^{44} - 90 q^{45} - 960 q^{46} - 188 q^{47} + 75 q^{48} + 98 q^{49} + 75 q^{50} + 120 q^{51} - 642 q^{52} + 982 q^{53} + 81 q^{54} - 310 q^{55} + 357 q^{56} - 366 q^{57} + 774 q^{58} + 516 q^{59} - 135 q^{60} - 880 q^{61} - 680 q^{62} + 126 q^{63} - 479 q^{64} + 30 q^{65} + 156 q^{66} - 356 q^{67} - 558 q^{68} + 48 q^{69} - 105 q^{70} + 310 q^{71} + 459 q^{72} + 326 q^{73} + 1358 q^{74} + 150 q^{75} - 672 q^{76} + 434 q^{77} - 642 q^{78} + 1832 q^{79} - 125 q^{80} + 162 q^{81} - 2190 q^{82} - 680 q^{83} + 189 q^{84} - 200 q^{85} + 1456 q^{86} + 1056 q^{87} + 1540 q^{88} + 796 q^{89} - 135 q^{90} - 42 q^{91} - 2880 q^{92} + 198 q^{93} + 2588 q^{94} + 610 q^{95} - 927 q^{96} - 670 q^{97} + 147 q^{98} + 558 q^{99}+O(q^{100}) \) 2 * q + 3 * q^2 + 6 * q^3 + 9 * q^4 - 10 * q^5 + 9 * q^6 + 14 * q^7 + 51 * q^8 + 18 * q^9 - 15 * q^10 + 62 * q^11 + 27 * q^12 - 6 * q^13 + 21 * q^14 - 30 * q^15 + 25 * q^16 + 40 * q^17 + 27 * q^18 - 122 * q^19 - 45 * q^20 + 42 * q^21 + 52 * q^22 + 16 * q^23 + 153 * q^24 + 50 * q^25 - 214 * q^26 + 54 * q^27 + 63 * q^28 + 352 * q^29 - 45 * q^30 + 66 * q^31 - 309 * q^32 + 186 * q^33 - 186 * q^34 - 70 * q^35 + 81 * q^36 - 188 * q^37 - 224 * q^38 - 18 * q^39 - 255 * q^40 + 16 * q^41 + 63 * q^42 - 396 * q^43 + 156 * q^44 - 90 * q^45 - 960 * q^46 - 188 * q^47 + 75 * q^48 + 98 * q^49 + 75 * q^50 + 120 * q^51 - 642 * q^52 + 982 * q^53 + 81 * q^54 - 310 * q^55 + 357 * q^56 - 366 * q^57 + 774 * q^58 + 516 * q^59 - 135 * q^60 - 880 * q^61 - 680 * q^62 + 126 * q^63 - 479 * q^64 + 30 * q^65 + 156 * q^66 - 356 * q^67 - 558 * q^68 + 48 * q^69 - 105 * q^70 + 310 * q^71 + 459 * q^72 + 326 * q^73 + 1358 * q^74 + 150 * q^75 - 672 * q^76 + 434 * q^77 - 642 * q^78 + 1832 * q^79 - 125 * q^80 + 162 * q^81 - 2190 * q^82 - 680 * q^83 + 189 * q^84 - 200 * q^85 + 1456 * q^86 + 1056 * q^87 + 1540 * q^88 + 796 * q^89 - 135 * q^90 - 42 * q^91 - 2880 * q^92 + 198 * q^93 + 2588 * q^94 + 610 * q^95 - 927 * q^96 - 670 * q^97 + 147 * q^98 + 558 * q^99

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