LMFDB - Embedded newform 966.4.a.q.1.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [966,4,Mod(1,966)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(966, 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("966.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 966 = 2 \cdot 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	966.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:	$56.9958450655$
Analytic rank:	$0$
Dimension:	$5$
Coefficient field:	$\mathbb{Q}[x]/(x^{5} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{5} - 570x^{3} - 189x^{2} + 63838x + 254320 $ x^5 - 570x^3 - 189x^2 + 63838*x + 254320
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Root			$-21.0849$ of defining polynomial
Character	$\chi$	$=$	966.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.00000 q^{2} +3.00000 q^{3} +4.00000 q^{4} +19.0849 q^{5} +6.00000 q^{6} -7.00000 q^{7} +8.00000 q^{8} +9.00000 q^{9} +O(q^{10})$	\(q+2.00000 q^{2} +3.00000 q^{3} +4.00000 q^{4} +19.0849 q^{5} +6.00000 q^{6} -7.00000 q^{7} +8.00000 q^{8} +9.00000 q^{9} +38.1698 q^{10} -18.1150 q^{11} +12.0000 q^{12} +48.5288 q^{13} -14.0000 q^{14} +57.2547 q^{15} +16.0000 q^{16} -77.3512 q^{17} +18.0000 q^{18} +87.3969 q^{19} +76.3396 q^{20} -21.0000 q^{21} -36.2299 q^{22} -23.0000 q^{23} +24.0000 q^{24} +239.234 q^{25} +97.0577 q^{26} +27.0000 q^{27} -28.0000 q^{28} -14.6679 q^{29} +114.509 q^{30} +196.525 q^{31} +32.0000 q^{32} -54.3449 q^{33} -154.702 q^{34} -133.594 q^{35} +36.0000 q^{36} -25.2890 q^{37} +174.794 q^{38} +145.587 q^{39} +152.679 q^{40} +208.358 q^{41} -42.0000 q^{42} +198.003 q^{43} -72.4598 q^{44} +171.764 q^{45} -46.0000 q^{46} +220.448 q^{47} +48.0000 q^{48} +49.0000 q^{49} +478.467 q^{50} -232.054 q^{51} +194.115 q^{52} -687.026 q^{53} +54.0000 q^{54} -345.722 q^{55} -56.0000 q^{56} +262.191 q^{57} -29.3359 q^{58} +59.0307 q^{59} +229.019 q^{60} +112.739 q^{61} +393.050 q^{62} -63.0000 q^{63} +64.0000 q^{64} +926.168 q^{65} -108.690 q^{66} -565.798 q^{67} -309.405 q^{68} -69.0000 q^{69} -267.189 q^{70} +130.396 q^{71} +72.0000 q^{72} -59.3013 q^{73} -50.5780 q^{74} +717.701 q^{75} +349.588 q^{76} +126.805 q^{77} +291.173 q^{78} -49.4714 q^{79} +305.359 q^{80} +81.0000 q^{81} +416.717 q^{82} +214.980 q^{83} -84.0000 q^{84} -1476.24 q^{85} +396.005 q^{86} -44.0038 q^{87} -144.920 q^{88} +721.497 q^{89} +343.528 q^{90} -339.702 q^{91} -92.0000 q^{92} +589.574 q^{93} +440.895 q^{94} +1667.96 q^{95} +96.0000 q^{96} -1270.12 q^{97} +98.0000 q^{98} -163.035 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 5 q + 10 q^{2} + 15 q^{3} + 20 q^{4} - 10 q^{5} + 30 q^{6} - 35 q^{7} + 40 q^{8} + 45 q^{9}+O(q^{10}) $ 5 * q + 10 * q^2 + 15 * q^3 + 20 * q^4 - 10 * q^5 + 30 * q^6 - 35 * q^7 + 40 * q^8 + 45 * q^9	\( 5 q + 10 q^{2} + 15 q^{3} + 20 q^{4} - 10 q^{5} + 30 q^{6} - 35 q^{7} + 40 q^{8} + 45 q^{9} - 20 q^{10} + 47 q^{11} + 60 q^{12} + 74 q^{13} - 70 q^{14} - 30 q^{15} + 80 q^{16} - 4 q^{17} + 90 q^{18} + 215 q^{19} - 40 q^{20} - 105 q^{21} + 94 q^{22} - 115 q^{23} + 120 q^{24} + 535 q^{25} + 148 q^{26} + 135 q^{27} - 140 q^{28} + 273 q^{29} - 60 q^{30} + 660 q^{31} + 160 q^{32} + 141 q^{33} - 8 q^{34} + 70 q^{35} + 180 q^{36} - 71 q^{37} + 430 q^{38} + 222 q^{39} - 80 q^{40} + 428 q^{41} - 210 q^{42} + 606 q^{43} + 188 q^{44} - 90 q^{45} - 230 q^{46} + 514 q^{47} + 240 q^{48} + 245 q^{49} + 1070 q^{50} - 12 q^{51} + 296 q^{52} + 376 q^{53} + 270 q^{54} - 395 q^{55} - 280 q^{56} + 645 q^{57} + 546 q^{58} + 1062 q^{59} - 120 q^{60} + 60 q^{61} + 1320 q^{62} - 315 q^{63} + 320 q^{64} + 1755 q^{65} + 282 q^{66} + 671 q^{67} - 16 q^{68} - 345 q^{69} + 140 q^{70} + 1885 q^{71} + 360 q^{72} + 790 q^{73} - 142 q^{74} + 1605 q^{75} + 860 q^{76} - 329 q^{77} + 444 q^{78} + 738 q^{79} - 160 q^{80} + 405 q^{81} + 856 q^{82} + 774 q^{83} - 420 q^{84} + 781 q^{85} + 1212 q^{86} + 819 q^{87} + 376 q^{88} + 131 q^{89} - 180 q^{90} - 518 q^{91} - 460 q^{92} + 1980 q^{93} + 1028 q^{94} + 625 q^{95} + 480 q^{96} - 51 q^{97} + 490 q^{98} + 423 q^{99}+O(q^{100}) \) 5 * q + 10 * q^2 + 15 * q^3 + 20 * q^4 - 10 * q^5 + 30 * q^6 - 35 * q^7 + 40 * q^8 + 45 * q^9 - 20 * q^10 + 47 * q^11 + 60 * q^12 + 74 * q^13 - 70 * q^14 - 30 * q^15 + 80 * q^16 - 4 * q^17 + 90 * q^18 + 215 * q^19 - 40 * q^20 - 105 * q^21 + 94 * q^22 - 115 * q^23 + 120 * q^24 + 535 * q^25 + 148 * q^26 + 135 * q^27 - 140 * q^28 + 273 * q^29 - 60 * q^30 + 660 * q^31 + 160 * q^32 + 141 * q^33 - 8 * q^34 + 70 * q^35 + 180 * q^36 - 71 * q^37 + 430 * q^38 + 222 * q^39 - 80 * q^40 + 428 * q^41 - 210 * q^42 + 606 * q^43 + 188 * q^44 - 90 * q^45 - 230 * q^46 + 514 * q^47 + 240 * q^48 + 245 * q^49 + 1070 * q^50 - 12 * q^51 + 296 * q^52 + 376 * q^53 + 270 * q^54 - 395 * q^55 - 280 * q^56 + 645 * q^57 + 546 * q^58 + 1062 * q^59 - 120 * q^60 + 60 * q^61 + 1320 * q^62 - 315 * q^63 + 320 * q^64 + 1755 * q^65 + 282 * q^66 + 671 * q^67 - 16 * q^68 - 345 * q^69 + 140 * q^70 + 1885 * q^71 + 360 * q^72 + 790 * q^73 - 142 * q^74 + 1605 * q^75 + 860 * q^76 - 329 * q^77 + 444 * q^78 + 738 * q^79 - 160 * q^80 + 405 * q^81 + 856 * q^82 + 774 * q^83 - 420 * q^84 + 781 * q^85 + 1212 * q^86 + 819 * q^87 + 376 * q^88 + 131 * q^89 - 180 * q^90 - 518 * q^91 - 460 * q^92 + 1980 * q^93 + 1028 * q^94 + 625 * q^95 + 480 * q^96 - 51 * q^97 + 490 * q^98 + 423 * 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 $

$2$	2.00000	0.707107
$2$	2.00000	0.707107
$3$	3.00000	0.577350
$3$	3.00000	0.577350
$4$	4.00000	0.500000
$5$	19.0849	1.70701	0.853503	−	0.521088i	$-0.174474\pi$
$5$	19.0849	1.70701	0.853503	+	0.521088i	$0.174474\pi$
$6$	6.00000	0.408248
$7$	−7.00000	−0.377964
$7$	−7.00000	−0.377964
$8$	8.00000	0.353553
$9$	9.00000	0.333333
$10$	38.1698	1.20704
$11$	−18.1150	−0.496533	−0.248267	−	0.968692i	$-0.579861\pi$
$11$	−18.1150	−0.496533	−0.248267	+	0.968692i	$0.579861\pi$
$12$	12.0000	0.288675
$13$	48.5288	1.03534	0.517672	−	0.855579i	$-0.326799\pi$
$13$	48.5288	1.03534	0.517672	+	0.855579i	$0.326799\pi$
$14$	−14.0000	−0.267261
$15$	57.2547	0.985540
$16$	16.0000	0.250000
$17$	−77.3512	−1.10355	−0.551777	−	0.833991i	$-0.686050\pi$
$17$	−77.3512	−1.10355	−0.551777	+	0.833991i	$0.686050\pi$
$18$	18.0000	0.235702
$19$	87.3969	1.05528	0.527638	−	0.849470i	$-0.323078\pi$
$19$	87.3969	1.05528	0.527638	+	0.849470i	$0.323078\pi$
$20$	76.3396	0.853503
$21$	−21.0000	−0.218218
$22$	−36.2299	−0.351102
$23$	−23.0000	−0.208514
$23$	−23.0000	−0.208514
$24$	24.0000	0.204124
$25$	239.234	1.91387
$26$	97.0577	0.732099
$27$	27.0000	0.192450
$28$	−28.0000	−0.188982
$29$	−14.6679	−0.0939231	−0.0469615	−	0.998897i	$-0.514954\pi$
$29$	−14.6679	−0.0939231	−0.0469615	+	0.998897i	$0.514954\pi$
$30$	114.509	0.696882
$31$	196.525	1.13861	0.569305	−	0.822127i	$-0.307212\pi$
$31$	196.525	1.13861	0.569305	+	0.822127i	$0.307212\pi$
$32$	32.0000	0.176777
$33$	−54.3449	−0.286674
$34$	−154.702	−0.780331
$35$	−133.594	−0.645188
$36$	36.0000	0.166667
$37$	−25.2890	−0.112364	−0.0561822	−	0.998421i	$-0.517893\pi$
$37$	−25.2890	−0.112364	−0.0561822	+	0.998421i	$0.517893\pi$
$38$	174.794	0.746192
$39$	145.587	0.597756
$40$	152.679	0.603518
$41$	208.358	0.793661	0.396831	−	0.917892i	$-0.370110\pi$
$41$	208.358	0.793661	0.396831	+	0.917892i	$0.370110\pi$
$42$	−42.0000	−0.154303
$43$	198.003	0.702212	0.351106	−	0.936336i	$-0.385806\pi$
$43$	198.003	0.702212	0.351106	+	0.936336i	$0.385806\pi$
$44$	−72.4598	−0.248267
$45$	171.764	0.569002
$46$	−46.0000	−0.147442
$47$	220.448	0.684161	0.342081	−	0.939671i	$-0.388868\pi$
$47$	220.448	0.684161	0.342081	+	0.939671i	$0.388868\pi$
$48$	48.0000	0.144338
$49$	49.0000	0.142857
$50$	478.467	1.35331
$51$	−232.054	−0.637138
$52$	194.115	0.517672
$53$	−687.026	−1.78057	−0.890285	−	0.455403i	$-0.849495\pi$
$53$	−687.026	−1.78057	−0.890285	+	0.455403i	$0.849495\pi$
$54$	54.0000	0.136083
$55$	−345.722	−0.847585
$56$	−56.0000	−0.133631
$57$	262.191	0.609263
$58$	−29.3359	−0.0664136
$59$	59.0307	0.130257	0.0651284	−	0.997877i	$-0.479254\pi$
$59$	59.0307	0.130257	0.0651284	+	0.997877i	$0.479254\pi$
$60$	229.019	0.492770
$61$	112.739	0.236634	0.118317	−	0.992976i	$-0.462250\pi$
$61$	112.739	0.236634	0.118317	+	0.992976i	$0.462250\pi$
$62$	393.050	0.805119
$63$	−63.0000	−0.125988
$64$	64.0000	0.125000
$65$	926.168	1.76734
$66$	−108.690	−0.202709
$67$	−565.798	−1.03169	−0.515845	−	0.856682i	$-0.672522\pi$
$67$	−565.798	−1.03169	−0.515845	+	0.856682i	$0.672522\pi$
$68$	−309.405	−0.551777
$69$	−69.0000	−0.120386
$70$	−267.189	−0.456217
$71$	130.396	0.217959	0.108980	−	0.994044i	$-0.465242\pi$
$71$	130.396	0.217959	0.108980	+	0.994044i	$0.465242\pi$
$72$	72.0000	0.117851
$73$	−59.3013	−0.0950780	−0.0475390	−	0.998869i	$-0.515138\pi$
$73$	−59.3013	−0.0950780	−0.0475390	+	0.998869i	$0.515138\pi$
$74$	−50.5780	−0.0794537
$75$	717.701	1.10497
$76$	349.588	0.527638
$77$	126.805	0.187672
$78$	291.173	0.422678
$79$	−49.4714	−0.0704553	−0.0352276	−	0.999379i	$-0.511216\pi$
$79$	−49.4714	−0.0704553	−0.0352276	+	0.999379i	$0.511216\pi$
$80$	305.359	0.426752
$81$	81.0000	0.111111
$82$	416.717	0.561203
$83$	214.980	0.284303	0.142151	−	0.989845i	$-0.454598\pi$
$83$	214.980	0.284303	0.142151	+	0.989845i	$0.454598\pi$
$84$	−84.0000	−0.109109
$85$	−1476.24	−1.88377
$86$	396.005	0.496539
$87$	−44.0038	−0.0542265
$88$	−144.920	−0.175551
$89$	721.497	0.859309	0.429655	−	0.902993i	$-0.358635\pi$
$89$	721.497	0.859309	0.429655	+	0.902993i	$0.358635\pi$
$90$	343.528	0.402345
$91$	−339.702	−0.391323
$92$	−92.0000	−0.104257
$93$	589.574	0.657377
$94$	440.895	0.483775
$95$	1667.96	1.80136
$96$	96.0000	0.102062
$97$	−1270.12	−1.32950	−0.664748	−	0.747068i	$-0.731461\pi$
$97$	−1270.12	−1.32950	−0.664748	+	0.747068i	$0.731461\pi$
$98$	98.0000	0.101015
$99$	−163.035	−0.165511
$100$	956.935	0.956935
$101$	−1621.43	−1.59741	−0.798706	−	0.601722i	$-0.794482\pi$
$101$	−1621.43	−1.59741	−0.798706	+	0.601722i	$0.794482\pi$
$102$	−464.107	−0.450524
$103$	1167.83	1.11719	0.558593	−	0.829442i	$-0.311341\pi$
$103$	1167.83	1.11719	0.558593	+	0.829442i	$0.311341\pi$
$104$	388.231	0.366050
$105$	−400.783	−0.372499
$106$	−1374.05	−1.25905
$107$	−1828.29	−1.65185	−0.825923	−	0.563783i	$-0.809345\pi$
$107$	−1828.29	−1.65185	−0.825923	+	0.563783i	$0.809345\pi$
$108$	108.000	0.0962250
$109$	−1160.34	−1.01964	−0.509818	−	0.860282i	$-0.670287\pi$
$109$	−1160.34	−1.01964	−0.509818	+	0.860282i	$0.670287\pi$
$110$	−691.445	−0.599333
$111$	−75.8670	−0.0648736
$112$	−112.000	−0.0944911
$113$	251.820	0.209639	0.104820	−	0.994491i	$-0.466573\pi$
$113$	251.820	0.209639	0.104820	+	0.994491i	$0.466573\pi$
$114$	524.382	0.430814
$115$	−438.953	−0.355935
$116$	−58.6718	−0.0469615
$117$	436.760	0.345115
$118$	118.061	0.0921054
$119$	541.459	0.417104
$120$	458.038	0.348441
$121$	−1002.85	−0.753455
$122$	225.477	0.167326
$123$	625.075	0.458221
$124$	786.099	0.569305
$125$	2180.14	1.55998
$126$	−126.000	−0.0890871
$127$	−1643.36	−1.14823	−0.574114	−	0.818775i	$-0.694653\pi$
$127$	−1643.36	−1.14823	−0.574114	+	0.818775i	$0.694653\pi$
$128$	128.000	0.0883883
$129$	594.008	0.405422
$130$	1852.34	1.24970
$131$	2212.47	1.47560	0.737802	−	0.675017i	$-0.235864\pi$
$131$	2212.47	1.47560	0.737802	+	0.675017i	$0.235864\pi$
$132$	−217.379	−0.143337
$133$	−611.778	−0.398857
$134$	−1131.60	−0.729515
$135$	515.293	0.328513
$136$	−618.810	−0.390166
$137$	−820.854	−0.511900	−0.255950	−	0.966690i	$-0.582388\pi$
$137$	−820.854	−0.511900	−0.255950	+	0.966690i	$0.582388\pi$
$138$	−138.000	−0.0851257
$139$	2337.91	1.42661	0.713305	−	0.700854i	$-0.247197\pi$
$139$	2337.91	1.42661	0.713305	+	0.700854i	$0.247197\pi$
$140$	−534.377	−0.322594
$141$	661.343	0.395001
$142$	260.791	0.154121
$143$	−879.098	−0.514083
$144$	144.000	0.0833333
$145$	−279.936	−0.160327
$146$	−118.603	−0.0672303
$147$	147.000	0.0824786
$148$	−101.156	−0.0561822
$149$	−694.345	−0.381765	−0.190882	−	0.981613i	$-0.561135\pi$
$149$	−694.345	−0.381765	−0.190882	+	0.981613i	$0.561135\pi$
$150$	1435.40	0.781334
$151$	3051.61	1.64461	0.822307	−	0.569043i	$-0.192686\pi$
$151$	3051.61	1.64461	0.822307	+	0.569043i	$0.192686\pi$
$152$	699.175	0.373096
$153$	−696.161	−0.367852
$154$	253.609	0.132704
$155$	3750.66	1.94361
$156$	582.346	0.298878
$157$	−1135.60	−0.577265	−0.288632	−	0.957440i	$-0.593201\pi$
$157$	−1135.60	−0.577265	−0.288632	+	0.957440i	$0.593201\pi$
$158$	−98.9428	−0.0498194
$159$	−2061.08	−1.02801
$160$	610.717	0.301759
$161$	161.000	0.0788110
$162$	162.000	0.0785674
$163$	−2332.93	−1.12104	−0.560518	−	0.828142i	$-0.689398\pi$
$163$	−2332.93	−1.12104	−0.560518	+	0.828142i	$0.689398\pi$
$164$	833.434	0.396831
$165$	−1037.17	−0.489354
$166$	429.960	0.201032
$167$	2113.83	0.979477	0.489739	−	0.871869i	$-0.337092\pi$
$167$	2113.83	0.979477	0.489739	+	0.871869i	$0.337092\pi$
$168$	−168.000	−0.0771517
$169$	158.048	0.0719380
$170$	−2952.48	−1.33203
$171$	786.572	0.351758
$172$	792.010	0.351106
$173$	−1647.40	−0.723987	−0.361994	−	0.932181i	$-0.617904\pi$
$173$	−1647.40	−0.723987	−0.361994	+	0.932181i	$0.617904\pi$
$174$	−88.0077	−0.0383439
$175$	−1674.64	−0.723375
$176$	−289.839	−0.124133
$177$	177.092	0.0752038
$178$	1442.99	0.607623
$179$	−4292.01	−1.79218	−0.896089	−	0.443875i	$-0.853603\pi$
$179$	−4292.01	−1.79218	−0.896089	+	0.443875i	$0.853603\pi$
$180$	687.057	0.284501
$181$	4659.66	1.91354	0.956768	−	0.290853i	$-0.0939390\pi$
$181$	4659.66	1.91354	0.956768	+	0.290853i	$0.0939390\pi$
$182$	−679.404	−0.276707
$183$	338.216	0.136621
$184$	−184.000	−0.0737210
$185$	−482.638	−0.191807
$186$	1179.15	0.464835
$187$	1401.21	0.547952
$188$	881.790	0.342081
$189$	−189.000	−0.0727393
$190$	3335.92	1.27375
$191$	2926.39	1.10862	0.554309	−	0.832311i	$-0.312983\pi$
$191$	2926.39	1.10862	0.554309	+	0.832311i	$0.312983\pi$
$192$	192.000	0.0721688
$193$	2005.18	0.747854	0.373927	−	0.927458i	$-0.378011\pi$
$193$	2005.18	0.747854	0.373927	+	0.927458i	$0.378011\pi$
$194$	−2540.24	−0.940095
$195$	2778.51	1.02037
$196$	196.000	0.0714286
$197$	2818.18	1.01922	0.509611	−	0.860405i	$-0.329789\pi$
$197$	2818.18	1.01922	0.509611	+	0.860405i	$0.329789\pi$
$198$	−326.069	−0.117034
$199$	−1416.09	−0.504442	−0.252221	−	0.967670i	$-0.581161\pi$
$199$	−1416.09	−0.504442	−0.252221	+	0.967670i	$0.581161\pi$
$200$	1913.87	0.676655
$201$	−1697.39	−0.595647
$202$	−3242.86	−1.12954
$203$	102.676	0.0354996
$204$	−928.215	−0.318569
$205$	3976.50	1.35479
$206$	2335.67	0.789970
$207$	−207.000	−0.0695048
$208$	776.461	0.258836
$209$	−1583.19	−0.523979
$210$	−801.566	−0.263397
$211$	3667.94	1.19674	0.598369	−	0.801221i	$-0.295816\pi$
$211$	3667.94	1.19674	0.598369	+	0.801221i	$0.295816\pi$
$212$	−2748.10	−0.890285
$213$	391.187	0.125839
$214$	−3656.58	−1.16803
$215$	3778.86	1.19868
$216$	216.000	0.0680414
$217$	−1375.67	−0.430354
$218$	−2320.68	−0.720992
$219$	−177.904	−0.0548933
$220$	−1382.89	−0.423793
$221$	−3753.77	−1.14256
$222$	−151.734	−0.0458726
$223$	3888.80	1.16777	0.583886	−	0.811835i	$-0.301531\pi$
$223$	3888.80	1.16777	0.583886	+	0.811835i	$0.301531\pi$
$224$	−224.000	−0.0668153
$225$	2153.10	0.637957
$226$	503.640	0.148237
$227$	−2200.18	−0.643308	−0.321654	−	0.946857i	$-0.604239\pi$
$227$	−2200.18	−0.643308	−0.321654	+	0.946857i	$0.604239\pi$
$228$	1048.76	0.304632
$229$	−3208.03	−0.925731	−0.462866	−	0.886428i	$-0.653179\pi$
$229$	−3208.03	−0.925731	−0.462866	+	0.886428i	$0.653179\pi$
$230$	−877.906	−0.251684
$231$	380.414	0.108352
$232$	−117.344	−0.0332068
$233$	−6249.00	−1.75702	−0.878510	−	0.477724i	$-0.841462\pi$
$233$	−6249.00	−1.75702	−0.878510	+	0.477724i	$0.841462\pi$
$234$	873.519	0.244033
$235$	4207.22	1.16787
$236$	236.123	0.0651284
$237$	−148.414	−0.0406774
$238$	1082.92	0.294937
$239$	−2149.24	−0.581685	−0.290843	−	0.956771i	$-0.593936\pi$
$239$	−2149.24	−0.581685	−0.290843	+	0.956771i	$0.593936\pi$
$240$	916.076	0.246385
$241$	−1597.46	−0.426978	−0.213489	−	0.976945i	$-0.568483\pi$
$241$	−1597.46	−0.426978	−0.213489	+	0.976945i	$0.568483\pi$
$242$	−2005.70	−0.532773
$243$	243.000	0.0641500
$244$	450.955	0.118317
$245$	935.161	0.243858
$246$	1250.15	0.324011
$247$	4241.27	1.09257
$248$	1572.20	0.402559
$249$	644.940	0.164142
$250$	4360.28	1.10307
$251$	47.9387	0.0120552	0.00602761	−	0.999982i	$-0.498081\pi$
$251$	47.9387	0.0120552	0.00602761	+	0.999982i	$0.498081\pi$
$252$	−252.000	−0.0629941
$253$	416.644	0.103534
$254$	−3286.73	−0.811920
$255$	−4428.72	−1.08760
$256$	256.000	0.0625000
$257$	−6049.20	−1.46824	−0.734122	−	0.679017i	$-0.762406\pi$
$257$	−6049.20	−1.46824	−0.734122	+	0.679017i	$0.762406\pi$
$258$	1188.02	0.286677
$259$	177.023	0.0424698
$260$	3704.67	0.883670
$261$	−132.012	−0.0313077
$262$	4424.94	1.04341
$263$	947.202	0.222080	0.111040	−	0.993816i	$-0.464582\pi$
$263$	947.202	0.222080	0.111040	+	0.993816i	$0.464582\pi$
$264$	−434.759	−0.101354
$265$	−13111.8	−3.03945
$266$	−1223.56	−0.282034
$267$	2164.49	0.496122
$268$	−2263.19	−0.515845
$269$	−2618.51	−0.593507	−0.296754	−	0.954954i	$-0.595904\pi$
$269$	−2618.51	−0.593507	−0.296754	+	0.954954i	$0.595904\pi$
$270$	1030.59	0.232294
$271$	253.834	0.0568978	0.0284489	−	0.999595i	$-0.490943\pi$
$271$	253.834	0.0568978	0.0284489	+	0.999595i	$0.490943\pi$
$272$	−1237.62	−0.275889
$273$	−1019.11	−0.225931
$274$	−1641.71	−0.361968
$275$	−4333.71	−0.950300
$276$	−276.000	−0.0601929
$277$	−7769.58	−1.68530	−0.842651	−	0.538460i	$-0.819006\pi$
$277$	−7769.58	−1.68530	−0.842651	+	0.538460i	$0.819006\pi$
$278$	4675.82	1.00877
$279$	1768.72	0.379537
$280$	−1068.75	−0.228108
$281$	3011.60	0.639348	0.319674	−	0.947528i	$-0.396427\pi$
$281$	3011.60	0.639348	0.319674	+	0.947528i	$0.396427\pi$
$282$	1322.69	0.279308
$283$	−8482.67	−1.78178	−0.890888	−	0.454224i	$-0.849917\pi$
$283$	−8482.67	−1.78178	−0.890888	+	0.454224i	$0.849917\pi$
$284$	521.583	0.108980
$285$	5003.89	1.04002
$286$	−1758.20	−0.363511
$287$	−1458.51	−0.299976
$288$	288.000	0.0589256
$289$	1070.21	0.217833
$290$	−559.873	−0.113368
$291$	−3810.36	−0.767585
$292$	−237.205	−0.0475390
$293$	−117.306	−0.0233894	−0.0116947	−	0.999932i	$-0.503723\pi$
$293$	−117.306	−0.0233894	−0.0116947	+	0.999932i	$0.503723\pi$
$294$	294.000	0.0583212
$295$	1126.60	0.222349
$296$	−202.312	−0.0397268
$297$	−489.104	−0.0955579
$298$	−1388.69	−0.269948
$299$	−1116.16	−0.215884
$300$	2870.80	0.552487
$301$	−1386.02	−0.265411
$302$	6103.23	1.16292
$303$	−4864.30	−0.922266
$304$	1398.35	0.263819
$305$	2151.61	0.403937
$306$	−1392.32	−0.260110
$307$	3261.26	0.606286	0.303143	−	0.952945i	$-0.401964\pi$
$307$	3261.26	0.606286	0.303143	+	0.952945i	$0.401964\pi$
$308$	507.219	0.0938360
$309$	3503.50	0.645008
$310$	7501.32	1.37434
$311$	1474.60	0.268864	0.134432	−	0.990923i	$-0.457079\pi$
$311$	1474.60	0.268864	0.134432	+	0.990923i	$0.457079\pi$
$312$	1164.69	0.211339
$313$	5703.29	1.02993	0.514966	−	0.857211i	$-0.327804\pi$
$313$	5703.29	1.02993	0.514966	+	0.857211i	$0.327804\pi$
$314$	−2271.19	−0.408188
$315$	−1202.35	−0.215063
$316$	−197.886	−0.0352276
$317$	−3186.01	−0.564492	−0.282246	−	0.959342i	$-0.591079\pi$
$317$	−3186.01	−0.564492	−0.282246	+	0.959342i	$0.591079\pi$
$318$	−4122.15	−0.726915
$319$	265.709	0.0466359
$320$	1221.43	0.213376
$321$	−5484.87	−0.953694
$322$	322.000	0.0557278
$323$	−6760.26	−1.16455
$324$	324.000	0.0555556
$325$	11609.7	1.98151
$326$	−4665.85	−0.792692
$327$	−3481.02	−0.588687
$328$	1666.87	0.280602
$329$	−1543.13	−0.258589
$330$	−2074.33	−0.346025
$331$	−2657.40	−0.441281	−0.220640	−	0.975355i	$-0.570815\pi$
$331$	−2657.40	−0.441281	−0.220640	+	0.975355i	$0.570815\pi$
$332$	859.920	0.142151
$333$	−227.601	−0.0374548
$334$	4227.65	0.692595
$335$	−10798.2	−1.76110
$336$	−336.000	−0.0545545
$337$	−5725.35	−0.925458	−0.462729	−	0.886500i	$-0.653130\pi$
$337$	−5725.35	−0.925458	−0.462729	+	0.886500i	$0.653130\pi$
$338$	316.095	0.0508678
$339$	755.460	0.121035
$340$	−5904.97	−0.941887
$341$	−3560.04	−0.565357
$342$	1573.14	0.248731
$343$	−343.000	−0.0539949
$344$	1584.02	0.248269
$345$	−1316.86	−0.205499
$346$	−3294.81	−0.511936
$347$	312.777	0.0483884	0.0241942	−	0.999707i	$-0.492298\pi$
$347$	312.777	0.0483884	0.0241942	+	0.999707i	$0.492298\pi$
$348$	−176.015	−0.0271133
$349$	−3405.18	−0.522278	−0.261139	−	0.965301i	$-0.584098\pi$
$349$	−3405.18	−0.522278	−0.261139	+	0.965301i	$0.584098\pi$
$350$	−3349.27	−0.511503
$351$	1310.28	0.199252
$352$	−579.679	−0.0877755
$353$	−364.088	−0.0548964	−0.0274482	−	0.999623i	$-0.508738\pi$
$353$	−364.088	−0.0548964	−0.0274482	+	0.999623i	$0.508738\pi$
$354$	354.184	0.0531771
$355$	2488.59	0.372058
$356$	2885.99	0.429655
$357$	1624.38	0.240815
$358$	−8584.02	−1.26726
$359$	2380.28	0.349935	0.174967	−	0.984574i	$-0.444018\pi$
$359$	2380.28	0.349935	0.174967	+	0.984574i	$0.444018\pi$
$360$	1374.11	0.201173
$361$	779.222	0.113606
$362$	9319.32	1.35307
$363$	−3008.54	−0.435007
$364$	−1358.81	−0.195662
$365$	−1131.76	−0.162299
$366$	676.432	0.0966056
$367$	−6732.20	−0.957542	−0.478771	−	0.877940i	$-0.658918\pi$
$367$	−6732.20	−0.957542	−0.478771	+	0.877940i	$0.658918\pi$
$368$	−368.000	−0.0521286
$369$	1875.23	0.264554
$370$	−965.276	−0.135628
$371$	4809.18	0.672992
$372$	2358.30	0.328688
$373$	8368.12	1.16162	0.580811	−	0.814039i	$-0.302736\pi$
$373$	8368.12	1.16162	0.580811	+	0.814039i	$0.302736\pi$
$374$	2802.43	0.387460
$375$	6540.42	0.900656
$376$	1763.58	0.241888
$377$	−711.818	−0.0972427
$378$	−378.000	−0.0514344
$379$	−7026.17	−0.952270	−0.476135	−	0.879372i	$-0.657963\pi$
$379$	−7026.17	−0.952270	−0.476135	+	0.879372i	$0.657963\pi$
$380$	6671.85	0.900681
$381$	−4930.09	−0.662930
$382$	5852.77	0.783911
$383$	−8588.37	−1.14581	−0.572905	−	0.819622i	$-0.694184\pi$
$383$	−8588.37	−1.14581	−0.572905	+	0.819622i	$0.694184\pi$
$384$	384.000	0.0510310
$385$	2420.06	0.320357
$386$	4010.35	0.528812
$387$	1782.02	0.234071
$388$	−5080.48	−0.664748
$389$	1850.46	0.241187	0.120594	−	0.992702i	$-0.461520\pi$
$389$	1850.46	0.241187	0.120594	+	0.992702i	$0.461520\pi$
$390$	5557.01	0.721513
$391$	1779.08	0.230107
$392$	392.000	0.0505076
$393$	6637.40	0.851941
$394$	5636.35	0.720699
$395$	−944.157	−0.120268
$396$	−652.138	−0.0827555
$397$	−4425.88	−0.559518	−0.279759	−	0.960070i	$-0.590254\pi$
$397$	−4425.88	−0.559518	−0.279759	+	0.960070i	$0.590254\pi$
$398$	−2832.18	−0.356694
$399$	−1835.34	−0.230280
$400$	3827.74	0.478467
$401$	5447.41	0.678381	0.339191	−	0.940718i	$-0.389847\pi$
$401$	5447.41	0.678381	0.339191	+	0.940718i	$0.389847\pi$
$402$	−3394.79	−0.421186
$403$	9537.12	1.17885
$404$	−6485.73	−0.798706
$405$	1545.88	0.189667
$406$	205.351	0.0251020
$407$	458.109	0.0557927
$408$	−1856.43	−0.225262
$409$	−14156.6	−1.71149	−0.855746	−	0.517397i	$-0.826901\pi$
$409$	−14156.6	−1.71149	−0.855746	+	0.517397i	$0.826901\pi$
$410$	7953.00	0.957978
$411$	−2462.56	−0.295546
$412$	4671.34	0.558593
$413$	−413.215	−0.0492324
$414$	−414.000	−0.0491473
$415$	4102.87	0.485306
$416$	1552.92	0.183025
$417$	7013.72	0.823654
$418$	−3166.38	−0.370509
$419$	2678.26	0.312271	0.156136	−	0.987736i	$-0.450096\pi$
$419$	2678.26	0.312271	0.156136	+	0.987736i	$0.450096\pi$
$420$	−1603.13	−0.186250
$421$	9566.13	1.10742	0.553711	−	0.832709i	$-0.313211\pi$
$421$	9566.13	1.10742	0.553711	+	0.832709i	$0.313211\pi$
$422$	7335.89	0.846222
$423$	1984.03	0.228054
$424$	−5496.21	−0.629527
$425$	−18505.0	−2.11206
$426$	782.374	0.0889815
$427$	−789.171	−0.0894394
$428$	−7313.16	−0.825923
$429$	−2637.29	−0.296806
$430$	7557.72	0.847594
$431$	−11037.7	−1.23357	−0.616783	−	0.787133i	$-0.711565\pi$
$431$	−11037.7	−1.23357	−0.616783	+	0.787133i	$0.711565\pi$
$432$	432.000	0.0481125
$433$	5248.00	0.582455	0.291227	−	0.956654i	$-0.405936\pi$
$433$	5248.00	0.582455	0.291227	+	0.956654i	$0.405936\pi$
$434$	−2751.35	−0.304306
$435$	−839.809	−0.0925650
$436$	−4641.36	−0.509818
$437$	−2010.13	−0.220040
$438$	−355.808	−0.0388154
$439$	−9535.05	−1.03664	−0.518318	−	0.855188i	$-0.673442\pi$
$439$	−9535.05	−1.03664	−0.518318	+	0.855188i	$0.673442\pi$
$440$	−2765.78	−0.299667
$441$	441.000	0.0476190
$442$	−7507.53	−0.807911
$443$	11763.5	1.26163	0.630816	−	0.775932i	$-0.282720\pi$
$443$	11763.5	1.26163	0.630816	+	0.775932i	$0.282720\pi$
$444$	−303.468	−0.0324368
$445$	13769.7	1.46685
$446$	7777.60	0.825740
$447$	−2083.03	−0.220412
$448$	−448.000	−0.0472456
$449$	1623.63	0.170655	0.0853274	−	0.996353i	$-0.472806\pi$
$449$	1623.63	0.170655	0.0853274	+	0.996353i	$0.472806\pi$
$450$	4306.21	0.451103
$451$	−3774.40	−0.394079
$452$	1007.28	0.104820
$453$	9154.84	0.949519
$454$	−4400.36	−0.454888
$455$	−6483.18	−0.667991
$456$	2097.53	0.215407
$457$	13561.2	1.38811	0.694054	−	0.719923i	$-0.255823\pi$
$457$	13561.2	1.38811	0.694054	+	0.719923i	$0.255823\pi$
$458$	−6416.06	−0.654591
$459$	−2088.48	−0.212379
$460$	−1755.81	−0.177968
$461$	10202.0	1.03070	0.515351	−	0.856979i	$-0.327662\pi$
$461$	10202.0	1.03070	0.515351	+	0.856979i	$0.327662\pi$
$462$	760.828	0.0766167
$463$	−8616.02	−0.864839	−0.432419	−	0.901673i	$-0.642340\pi$
$463$	−8616.02	−0.864839	−0.432419	+	0.901673i	$0.642340\pi$
$464$	−234.687	−0.0234808
$465$	11252.0	1.12215
$466$	−12498.0	−1.24240
$467$	−6327.34	−0.626969	−0.313485	−	0.949593i	$-0.601496\pi$
$467$	−6327.34	−0.626969	−0.313485	+	0.949593i	$0.601496\pi$
$468$	1747.04	0.172557
$469$	3960.59	0.389942
$470$	8414.44	0.825807
$471$	−3406.79	−0.333284
$472$	472.246	0.0460527
$473$	−3586.81	−0.348671
$474$	−296.828	−0.0287633
$475$	20908.3	2.01966
$476$	2165.83	0.208552
$477$	−6183.23	−0.593524
$478$	−4298.48	−0.411314
$479$	−7158.87	−0.682875	−0.341438	−	0.939904i	$-0.610914\pi$
$479$	−7158.87	−0.682875	−0.341438	+	0.939904i	$0.610914\pi$
$480$	1832.15	0.174221
$481$	−1227.25	−0.116336
$482$	−3194.93	−0.301919
$483$	483.000	0.0455016
$484$	−4011.39	−0.376727
$485$	−24240.1	−2.26946
$486$	486.000	0.0453609
$487$	16994.8	1.58133	0.790667	−	0.612246i	$-0.209734\pi$
$487$	16994.8	1.58133	0.790667	+	0.612246i	$0.209734\pi$
$488$	901.909	0.0836629
$489$	−6998.78	−0.647231
$490$	1870.32	0.172434
$491$	−19700.1	−1.81070	−0.905350	−	0.424666i	$-0.860392\pi$
$491$	−19700.1	−1.81070	−0.905350	+	0.424666i	$0.860392\pi$
$492$	2500.30	0.229110
$493$	1134.58	0.103649
$494$	8482.54	0.772566
$495$	−3111.50	−0.282528
$496$	3144.40	0.284652
$497$	−912.769	−0.0823809
$498$	1289.88	0.116066
$499$	−15337.9	−1.37599	−0.687993	−	0.725718i	$-0.741508\pi$
$499$	−15337.9	−1.37599	−0.687993	+	0.725718i	$0.741508\pi$
$500$	8720.56	0.779991
$501$	6341.48	0.565501
$502$	95.8773	0.00852433
$503$	2602.26	0.230674	0.115337	−	0.993326i	$-0.463205\pi$
$503$	2602.26	0.230674	0.115337	+	0.993326i	$0.463205\pi$
$504$	−504.000	−0.0445435
$505$	−30944.9	−2.72679
$506$	833.288	0.0732098
$507$	474.143	0.0415334
$508$	−6573.46	−0.574114
$509$	−8365.88	−0.728509	−0.364254	−	0.931299i	$-0.618676\pi$
$509$	−8365.88	−0.728509	−0.364254	+	0.931299i	$0.618676\pi$
$510$	−8857.45	−0.769048
$511$	415.109	0.0359361
$512$	512.000	0.0441942
$513$	2359.72	0.203088
$514$	−12098.4	−1.03821
$515$	22288.0	1.90704
$516$	2376.03	0.202711
$517$	−3993.40	−0.339709
$518$	354.046	0.0300307
$519$	−4942.21	−0.417994
$520$	7409.35	0.624849
$521$	−20133.9	−1.69305	−0.846527	−	0.532347i	$-0.821310\pi$
$521$	−20133.9	−1.69305	−0.846527	+	0.532347i	$0.821310\pi$
$522$	−264.023	−0.0221379
$523$	1532.57	0.128135	0.0640676	−	0.997946i	$-0.479593\pi$
$523$	1532.57	0.128135	0.0640676	+	0.997946i	$0.479593\pi$
$524$	8849.87	0.737802
$525$	−5023.91	−0.417641
$526$	1894.40	0.157034
$527$	−15201.4	−1.25652
$528$	−869.518	−0.0716684
$529$	529.000	0.0434783
$530$	−26223.6	−2.14921
$531$	531.277	0.0434189
$532$	−2447.11	−0.199428
$533$	10111.4	0.821713
$534$	4328.98	0.350811
$535$	−34892.8	−2.81971
$536$	−4526.39	−0.364758
$537$	−12876.0	−1.03471
$538$	−5237.02	−0.419673
$539$	−887.633	−0.0709333
$540$	2061.17	0.164257
$541$	12784.4	1.01598	0.507988	−	0.861364i	$-0.330390\pi$
$541$	12784.4	1.01598	0.507988	+	0.861364i	$0.330390\pi$
$542$	507.668	0.0402328
$543$	13979.0	1.10478
$544$	−2475.24	−0.195083
$545$	−22145.0	−1.74053
$546$	−2038.21	−0.159757
$547$	−21540.6	−1.68375	−0.841873	−	0.539676i	$-0.818547\pi$
$547$	−21540.6	−1.68375	−0.841873	+	0.539676i	$0.818547\pi$
$548$	−3283.42	−0.255950
$549$	1014.65	0.0788782
$550$	−8667.42	−0.671964
$551$	−1281.93	−0.0991147
$552$	−552.000	−0.0425628
$553$	346.300	0.0266296
$554$	−15539.2	−1.19169
$555$	−1447.91	−0.110740
$556$	9351.63	0.713305
$557$	3514.56	0.267355	0.133677	−	0.991025i	$-0.457321\pi$
$557$	3514.56	0.267355	0.133677	+	0.991025i	$0.457321\pi$
$558$	3537.45	0.268373
$559$	9608.83	0.727031
$560$	−2137.51	−0.161297
$561$	4203.64	0.316360
$562$	6023.19	0.452087
$563$	12725.4	0.952593	0.476297	−	0.879285i	$-0.341979\pi$
$563$	12725.4	0.952593	0.476297	+	0.879285i	$0.341979\pi$
$564$	2645.37	0.197500
$565$	4805.96	0.357856
$566$	−16965.3	−1.25991
$567$	−567.000	−0.0419961
$568$	1043.17	0.0770603
$569$	−3594.00	−0.264795	−0.132397	−	0.991197i	$-0.542268\pi$
$569$	−3594.00	−0.264795	−0.132397	+	0.991197i	$0.542268\pi$
$570$	10007.8	0.735403
$571$	−16909.7	−1.23932	−0.619659	−	0.784871i	$-0.712729\pi$
$571$	−16909.7	−1.23932	−0.619659	+	0.784871i	$0.712729\pi$
$572$	−3516.39	−0.257041
$573$	8779.16	0.640061
$574$	−2917.02	−0.212115
$575$	−5502.38	−0.399069
$576$	576.000	0.0416667
$577$	11676.1	0.842429	0.421214	−	0.906961i	$-0.361604\pi$
$577$	11676.1	0.842429	0.421214	+	0.906961i	$0.361604\pi$
$578$	2140.43	0.154031
$579$	6015.53	0.431774
$580$	−1119.75	−0.0801636
$581$	−1504.86	−0.107456
$582$	−7620.72	−0.542764
$583$	12445.4	0.884112
$584$	−474.410	−0.0336151
$585$	8335.52	0.589113
$586$	−234.612	−0.0165388
$587$	3140.61	0.220829	0.110415	−	0.993886i	$-0.464782\pi$
$587$	3140.61	0.220829	0.110415	+	0.993886i	$0.464782\pi$
$588$	588.000	0.0412393
$589$	17175.7	1.20155
$590$	2253.19	0.157225
$591$	8454.53	0.588448
$592$	−404.624	−0.0280911
$593$	−21338.3	−1.47767	−0.738834	−	0.673887i	$-0.764623\pi$
$593$	−21338.3	−1.47767	−0.738834	+	0.673887i	$0.764623\pi$
$594$	−978.208	−0.0675696
$595$	10333.7	0.712000
$596$	−2777.38	−0.190882
$597$	−4248.27	−0.291240
$598$	−2232.33	−0.152653
$599$	23432.2	1.59835	0.799176	−	0.601097i	$-0.205269\pi$
$599$	23432.2	1.59835	0.799176	+	0.601097i	$0.205269\pi$
$600$	5741.61	0.390667
$601$	20009.9	1.35810	0.679051	−	0.734091i	$-0.262391\pi$
$601$	20009.9	1.35810	0.679051	+	0.734091i	$0.262391\pi$
$602$	−2772.04	−0.187674
$603$	−5092.18	−0.343897
$604$	12206.5	0.822307
$605$	−19139.3	−1.28615
$606$	−9728.59	−0.652140
$607$	29229.2	1.95449	0.977246	−	0.212109i	$-0.0680333\pi$
$607$	29229.2	1.95449	0.977246	+	0.212109i	$0.0680333\pi$
$608$	2796.70	0.186548
$609$	308.027	0.0204957
$610$	4303.21	0.285626
$611$	10698.1	0.708343
$612$	−2784.64	−0.183926
$613$	−5470.76	−0.360460	−0.180230	−	0.983624i	$-0.557684\pi$
$613$	−5470.76	−0.360460	−0.180230	+	0.983624i	$0.557684\pi$
$614$	6522.52	0.428709
$615$	11929.5	0.782185
$616$	1014.44	0.0663520
$617$	6531.75	0.426189	0.213094	−	0.977032i	$-0.431646\pi$
$617$	6531.75	0.426189	0.213094	+	0.977032i	$0.431646\pi$
$618$	7007.01	0.456089
$619$	9295.06	0.603554	0.301777	−	0.953379i	$-0.402420\pi$
$619$	9295.06	0.603554	0.301777	+	0.953379i	$0.402420\pi$
$620$	15002.6	0.971807
$621$	−621.000	−0.0401286
$622$	2949.20	0.190116
$623$	−5050.48	−0.324788
$624$	2329.38	0.149439
$625$	11703.6	0.749028
$626$	11406.6	0.728272
$627$	−4749.57	−0.302520
$628$	−4542.39	−0.288632
$629$	1956.13	0.124000
$630$	−2404.70	−0.152072
$631$	8952.90	0.564832	0.282416	−	0.959292i	$-0.408864\pi$
$631$	8952.90	0.564832	0.282416	+	0.959292i	$0.408864\pi$
$632$	−395.771	−0.0249097
$633$	11003.8	0.690937
$634$	−6372.02	−0.399156
$635$	−31363.5	−1.96003
$636$	−8244.31	−0.514006
$637$	2377.91	0.147906
$638$	531.418	0.0329766
$639$	1173.56	0.0726531
$640$	2442.87	0.150879
$641$	−17476.0	−1.07685	−0.538424	−	0.842674i	$-0.680980\pi$
$641$	−17476.0	−1.07685	−0.538424	+	0.842674i	$0.680980\pi$
$642$	−10969.7	−0.674363
$643$	−15659.1	−0.960394	−0.480197	−	0.877161i	$-0.659435\pi$
$643$	−15659.1	−0.960394	−0.480197	+	0.877161i	$0.659435\pi$
$644$	644.000	0.0394055
$645$	11336.6	0.692058
$646$	−13520.5	−0.823464
$647$	−20090.9	−1.22080	−0.610399	−	0.792094i	$-0.708991\pi$
$647$	−20090.9	−1.22080	−0.610399	+	0.792094i	$0.708991\pi$
$648$	648.000	0.0392837
$649$	−1069.34	−0.0646768
$650$	23219.5	1.40114
$651$	−4127.02	−0.248465
$652$	−9331.71	−0.560518
$653$	−2356.46	−0.141218	−0.0706090	−	0.997504i	$-0.522494\pi$
$653$	−2356.46	−0.141218	−0.0706090	+	0.997504i	$0.522494\pi$
$654$	−6962.04	−0.416265
$655$	42224.7	2.51887
$656$	3333.73	0.198415
$657$	−533.712	−0.0316927
$658$	−3086.27	−0.182850
$659$	2452.43	0.144967	0.0724833	−	0.997370i	$-0.476908\pi$
$659$	2452.43	0.144967	0.0724833	+	0.997370i	$0.476908\pi$
$660$	−4148.67	−0.244677
$661$	13404.8	0.788782	0.394391	−	0.918943i	$-0.370956\pi$
$661$	13404.8	0.788782	0.394391	+	0.918943i	$0.370956\pi$
$662$	−5314.80	−0.312032
$663$	−11261.3	−0.659657
$664$	1719.84	0.100516
$665$	−11675.7	−0.680851
$666$	−455.202	−0.0264846
$667$	337.363	0.0195843
$668$	8455.30	0.489739
$669$	11666.4	0.674214
$670$	−21596.4	−1.24529
$671$	−2042.26	−0.117497
$672$	−672.000	−0.0385758
$673$	1530.70	0.0876735	0.0438368	−	0.999039i	$-0.486042\pi$
$673$	1530.70	0.0876735	0.0438368	+	0.999039i	$0.486042\pi$
$674$	−11450.7	−0.654398
$675$	6459.31	0.368324
$676$	632.191	0.0359690
$677$	−19307.7	−1.09609	−0.548046	−	0.836448i	$-0.684628\pi$
$677$	−19307.7	−1.09609	−0.548046	+	0.836448i	$0.684628\pi$
$678$	1510.92	0.0855849
$679$	8890.84	0.502502
$680$	−11809.9	−0.666015
$681$	−6600.54	−0.371414
$682$	−7120.08	−0.399768
$683$	20705.4	1.15998	0.579992	−	0.814623i	$-0.303056\pi$
$683$	20705.4	1.15998	0.579992	+	0.814623i	$0.303056\pi$
$684$	3146.29	0.175879
$685$	−15665.9	−0.873817
$686$	−686.000	−0.0381802
$687$	−9624.09	−0.534471
$688$	3168.04	0.175553
$689$	−33340.6	−1.84350
$690$	−2633.72	−0.145310
$691$	13480.6	0.742150	0.371075	−	0.928603i	$-0.378989\pi$
$691$	13480.6	0.742150	0.371075	+	0.928603i	$0.378989\pi$
$692$	−6589.62	−0.361994
$693$	1141.24	0.0625573
$694$	625.554	0.0342157
$695$	44618.8	2.43523
$696$	−352.031	−0.0191720
$697$	−16116.8	−0.875849
$698$	−6810.36	−0.369306
$699$	−18747.0	−1.01442
$700$	−6698.54	−0.361687
$701$	−3364.38	−0.181271	−0.0906355	−	0.995884i	$-0.528890\pi$
$701$	−3364.38	−0.181271	−0.0906355	+	0.995884i	$0.528890\pi$
$702$	2620.56	0.140893
$703$	−2210.18	−0.118575
$704$	−1159.36	−0.0620666
$705$	12621.7	0.674269
$706$	−728.176	−0.0388176
$707$	11350.0	0.603765
$708$	708.369	0.0376019
$709$	26130.6	1.38414	0.692069	−	0.721831i	$-0.256699\pi$
$709$	26130.6	1.38414	0.692069	+	0.721831i	$0.256699\pi$
$710$	4977.18	0.263085
$711$	−445.243	−0.0234851
$712$	5771.97	0.303812
$713$	−4520.07	−0.237416
$714$	3248.75	0.170282
$715$	−16777.5	−0.877543
$716$	−17168.0	−0.896089
$717$	−6447.72	−0.335836
$718$	4760.57	0.247441
$719$	−1212.19	−0.0628749	−0.0314375	−	0.999506i	$-0.510009\pi$
$719$	−1212.19	−0.0628749	−0.0314375	+	0.999506i	$0.510009\pi$
$720$	2748.23	0.142251
$721$	−8174.84	−0.422257
$722$	1558.44	0.0803314
$723$	−4792.39	−0.246516
$724$	18638.6	0.956768
$725$	−3509.07	−0.179757
$726$	−6017.09	−0.307597
$727$	−7251.96	−0.369959	−0.184980	−	0.982742i	$-0.559222\pi$
$727$	−7251.96	−0.369959	−0.184980	+	0.982742i	$0.559222\pi$
$728$	−2717.61	−0.138354
$729$	729.000	0.0370370
$730$	−2263.52	−0.114762
$731$	−15315.7	−0.774929
$732$	1352.86	0.0683105
$733$	25389.4	1.27937	0.639685	−	0.768637i	$-0.279065\pi$
$733$	25389.4	1.27937	0.639685	+	0.768637i	$0.279065\pi$
$734$	−13464.4	−0.677084
$735$	2805.48	0.140791
$736$	−736.000	−0.0368605
$737$	10249.4	0.512269
$738$	3750.45	0.187068
$739$	30374.5	1.51197	0.755984	−	0.654590i	$-0.227159\pi$
$739$	30374.5	1.51197	0.755984	+	0.654590i	$0.227159\pi$
$740$	−1930.55	−0.0959034
$741$	12723.8	0.630797
$742$	9618.36	0.475878
$743$	7433.00	0.367013	0.183506	−	0.983019i	$-0.441255\pi$
$743$	7433.00	0.367013	0.183506	+	0.983019i	$0.441255\pi$
$744$	4716.60	0.232418
$745$	−13251.5	−0.651675
$746$	16736.2	0.821390
$747$	1934.82	0.0947675
$748$	5604.86	0.273976
$749$	12798.0	0.624339
$750$	13080.8	0.636860
$751$	15829.7	0.769154	0.384577	−	0.923093i	$-0.374347\pi$
$751$	15829.7	0.769154	0.384577	+	0.923093i	$0.374347\pi$
$752$	3527.16	0.171040
$753$	143.816	0.00696009
$754$	−1423.64	−0.0687610
$755$	58239.8	2.80737
$756$	−756.000	−0.0363696
$757$	−33120.1	−1.59018	−0.795092	−	0.606489i	$-0.792577\pi$
$757$	−33120.1	−1.59018	−0.795092	+	0.606489i	$0.792577\pi$
$758$	−14052.3	−0.673356
$759$	1249.93	0.0597756
$760$	13343.7	0.636877
$761$	29811.1	1.42004	0.710020	−	0.704182i	$-0.248686\pi$
$761$	29811.1	1.42004	0.710020	+	0.704182i	$0.248686\pi$
$762$	−9860.19	−0.468762
$763$	8122.38	0.385386
$764$	11705.5	0.554309
$765$	−13286.2	−0.627925
$766$	−17176.7	−0.810210
$767$	2864.69	0.134861
$768$	768.000	0.0360844
$769$	31782.2	1.49037	0.745187	−	0.666856i	$-0.232360\pi$
$769$	31782.2	1.49037	0.745187	+	0.666856i	$0.232360\pi$
$770$	4840.11	0.226527
$771$	−18147.6	−0.847691
$772$	8020.71	0.373927
$773$	−18982.3	−0.883243	−0.441622	−	0.897201i	$-0.645597\pi$
$773$	−18982.3	−0.883243	−0.441622	+	0.897201i	$0.645597\pi$
$774$	3564.05	0.165513
$775$	47015.4	2.17915
$776$	−10161.0	−0.470048
$777$	531.069	0.0245199
$778$	3700.92	0.170545
$779$	18209.9	0.837531
$780$	11114.0	0.510187
$781$	−2362.11	−0.108224
$782$	3558.16	0.162710
$783$	−396.035	−0.0180755
$784$	784.000	0.0357143
$785$	−21672.8	−0.985394
$786$	13274.8	0.602413
$787$	15164.4	0.686853	0.343426	−	0.939180i	$-0.388412\pi$
$787$	15164.4	0.686853	0.343426	+	0.939180i	$0.388412\pi$
$788$	11272.7	0.509611
$789$	2841.61	0.128218
$790$	−1888.31	−0.0850421
$791$	−1762.74	−0.0792362
$792$	−1304.28	−0.0585170
$793$	5471.08	0.244998
$794$	−8851.76	−0.395639
$795$	−39335.5	−1.75482
$796$	−5664.36	−0.252221
$797$	−24697.2	−1.09764	−0.548820	−	0.835941i	$-0.684923\pi$
$797$	−24697.2	−1.09764	−0.548820	+	0.835941i	$0.684923\pi$
$798$	−3670.67	−0.162833
$799$	−17051.9	−0.755009
$800$	7655.48	0.338328
$801$	6493.47	0.286436
$802$	10894.8	0.479688
$803$	1074.24	0.0472094
$804$	−6789.58	−0.297823
$805$	3072.67	0.134531
$806$	19074.2	0.833575
$807$	−7855.53	−0.342662
$808$	−12971.5	−0.564770
$809$	44917.3	1.95205	0.976025	−	0.217660i	$-0.0698423\pi$
$809$	44917.3	1.95205	0.976025	+	0.217660i	$0.0698423\pi$
$810$	3091.76	0.134115
$811$	−12484.3	−0.540546	−0.270273	−	0.962784i	$-0.587114\pi$
$811$	−12484.3	−0.540546	−0.270273	+	0.962784i	$0.587114\pi$
$812$	410.702	0.0177498
$813$	761.501	0.0328500
$814$	916.218	0.0394514
$815$	−44523.7	−1.91362
$816$	−3712.86	−0.159284
$817$	17304.8	0.741027
$818$	−28313.2	−1.21021
$819$	−3057.32	−0.130441
$820$	15906.0	0.677393
$821$	39839.2	1.69354	0.846771	−	0.531957i	$-0.178543\pi$
$821$	39839.2	1.69354	0.846771	+	0.531957i	$0.178543\pi$
$822$	−4925.13	−0.208982
$823$	20505.8	0.868515	0.434257	−	0.900789i	$-0.357011\pi$
$823$	20505.8	0.868515	0.434257	+	0.900789i	$0.357011\pi$
$824$	9342.68	0.394985
$825$	−13001.1	−0.548656
$826$	−826.430	−0.0348126
$827$	35663.4	1.49956	0.749781	−	0.661686i	$-0.230159\pi$
$827$	35663.4	1.49956	0.749781	+	0.661686i	$0.230159\pi$
$828$	−828.000	−0.0347524
$829$	−13720.9	−0.574846	−0.287423	−	0.957804i	$-0.592799\pi$
$829$	−13720.9	−0.574846	−0.287423	+	0.957804i	$0.592799\pi$
$830$	8205.75	0.343163
$831$	−23308.7	−0.973010
$832$	3105.85	0.129418
$833$	−3790.21	−0.157651
$834$	14027.4	0.582411
$835$	40342.2	1.67197
$836$	−6332.77	−0.261990
$837$	5306.17	0.219126
$838$	5356.52	0.220809
$839$	−26621.5	−1.09544	−0.547720	−	0.836661i	$-0.684504\pi$
$839$	−26621.5	−1.09544	−0.547720	+	0.836661i	$0.684504\pi$
$840$	−3206.26	−0.131698
$841$	−24173.9	−0.991178
$842$	19132.3	0.783066
$843$	9034.79	0.369128
$844$	14671.8	0.598369
$845$	3016.33	0.122799
$846$	3968.06	0.161258
$847$	7019.94	0.284779
$848$	−10992.4	−0.445143
$849$	−25448.0	−1.02871
$850$	−37010.0	−1.49345
$851$	581.647	0.0234296
$852$	1564.75	0.0629194
$853$	13447.5	0.539782	0.269891	−	0.962891i	$-0.413012\pi$
$853$	13447.5	0.539782	0.269891	+	0.962891i	$0.413012\pi$
$854$	−1578.34	−0.0632432
$855$	15011.7	0.600454
$856$	−14626.3	−0.584016
$857$	6915.81	0.275659	0.137829	−	0.990456i	$-0.455987\pi$
$857$	6915.81	0.275659	0.137829	+	0.990456i	$0.455987\pi$
$858$	−5274.59	−0.209873
$859$	−17873.3	−0.709930	−0.354965	−	0.934880i	$-0.615507\pi$
$859$	−17873.3	−0.709930	−0.354965	+	0.934880i	$0.615507\pi$
$860$	15115.4	0.599340
$861$	−4375.53	−0.173191
$862$	−22075.4	−0.872263
$863$	−29206.5	−1.15203	−0.576015	−	0.817439i	$-0.695393\pi$
$863$	−29206.5	−1.15203	−0.576015	+	0.817439i	$0.695393\pi$
$864$	864.000	0.0340207
$865$	−31440.6	−1.23585
$866$	10496.0	0.411858
$867$	3210.64	0.125766
$868$	−5502.69	−0.215177
$869$	896.172	0.0349834
$870$	−1679.62	−0.0654533
$871$	−27457.5	−1.06815
$872$	−9282.71	−0.360496
$873$	−11431.1	−0.443165
$874$	−4020.26	−0.155592
$875$	−15261.0	−0.589618
$876$	−711.615	−0.0274466
$877$	37044.4	1.42634	0.713170	−	0.700991i	$-0.247259\pi$
$877$	37044.4	1.42634	0.713170	+	0.700991i	$0.247259\pi$
$878$	−19070.1	−0.733012
$879$	−351.918	−0.0135039
$880$	−5531.56	−0.211896
$881$	−30756.6	−1.17618	−0.588091	−	0.808795i	$-0.700120\pi$
$881$	−30756.6	−1.17618	−0.588091	+	0.808795i	$0.700120\pi$
$882$	882.000	0.0336718
$883$	4528.98	0.172607	0.0863036	−	0.996269i	$-0.472494\pi$
$883$	4528.98	0.172607	0.0863036	+	0.996269i	$0.472494\pi$
$884$	−15015.1	−0.571280
$885$	3379.79	0.128373
$886$	23527.1	0.892109
$887$	−31277.6	−1.18399	−0.591995	−	0.805942i	$-0.701659\pi$
$887$	−31277.6	−1.18399	−0.591995	+	0.805942i	$0.701659\pi$
$888$	−606.936	−0.0229363
$889$	11503.6	0.433990
$890$	27539.4	1.03722
$891$	−1467.31	−0.0551704
$892$	15555.2	0.583886
$893$	19266.4	0.721979
$894$	−4166.07	−0.155855
$895$	−81912.6	−3.05926
$896$	−896.000	−0.0334077
$897$	−3348.49	−0.124641
$898$	3247.27	0.120671
$899$	−2882.61	−0.106942
$900$	8612.41	0.318978
$901$	53142.3	1.96496
$902$	−7548.81	−0.278656
$903$	−4158.05	−0.153235
$904$	2014.56	0.0741187
$905$	88929.2	3.26642
$906$	18309.7	0.671411
$907$	−21275.3	−0.778870	−0.389435	−	0.921054i	$-0.627330\pi$
$907$	−21275.3	−0.778870	−0.389435	+	0.921054i	$0.627330\pi$
$908$	−8800.71	−0.321654
$909$	−14592.9	−0.532470
$910$	−12966.4	−0.472341
$911$	8074.24	0.293646	0.146823	−	0.989163i	$-0.453095\pi$
$911$	8074.24	0.293646	0.146823	+	0.989163i	$0.453095\pi$
$912$	4195.05	0.152316
$913$	−3894.35	−0.141166
$914$	27122.4	0.981540
$915$	6454.82	0.233213
$916$	−12832.1	−0.462866
$917$	−15487.3	−0.557726
$918$	−4176.97	−0.150175
$919$	11046.3	0.396501	0.198250	−	0.980151i	$-0.436474\pi$
$919$	11046.3	0.396501	0.198250	+	0.980151i	$0.436474\pi$
$920$	−3511.62	−0.125842
$921$	9783.77	0.350039
$922$	20404.0	0.728816
$923$	6327.95	0.225663
$924$	1521.66	0.0541762
$925$	−6049.98	−0.215051
$926$	−17232.0	−0.611533
$927$	10510.5	0.372395
$928$	−469.374	−0.0166034
$929$	36735.8	1.29738	0.648688	−	0.761055i	$-0.275318\pi$
$929$	36735.8	1.29738	0.648688	+	0.761055i	$0.275318\pi$
$930$	22503.9	0.793477
$931$	4282.45	0.150754
$932$	−24996.0	−0.878510
$933$	4423.79	0.155229
$934$	−12654.7	−0.443334
$935$	26742.0	0.935357
$936$	3494.08	0.122017
$937$	5313.54	0.185257	0.0926285	−	0.995701i	$-0.470473\pi$
$937$	5313.54	0.185257	0.0926285	+	0.995701i	$0.470473\pi$
$938$	7921.18	0.275731
$939$	17109.9	0.594632
$940$	16828.9	0.583934
$941$	6223.35	0.215595	0.107798	−	0.994173i	$-0.465620\pi$
$941$	6223.35	0.215595	0.107798	+	0.994173i	$0.465620\pi$
$942$	−6813.58	−0.235667
$943$	−4792.24	−0.165490
$944$	944.492	0.0325642
$945$	−3607.05	−0.124166
$946$	−7173.61	−0.246548
$947$	37973.8	1.30304	0.651522	−	0.758630i	$-0.274131\pi$
$947$	37973.8	1.30304	0.651522	+	0.758630i	$0.274131\pi$
$948$	−593.657	−0.0203387
$949$	−2877.82	−0.0984384
$950$	41816.6	1.42811
$951$	−9558.02	−0.325910
$952$	4331.67	0.147469
$953$	−37631.1	−1.27911	−0.639554	−	0.768746i	$-0.720881\pi$
$953$	−37631.1	−1.27911	−0.639554	+	0.768746i	$0.720881\pi$
$954$	−12366.5	−0.419685
$955$	55849.8	1.89242
$956$	−8596.96	−0.290843
$957$	797.128	0.0269253
$958$	−14317.7	−0.482866
$959$	5745.98	0.193480
$960$	3664.30	0.123193
$961$	8831.00	0.296432
$962$	−2454.49	−0.0822619
$963$	−16454.6	−0.550615
$964$	−6389.85	−0.213489
$965$	38268.6	1.27659
$966$	966.000	0.0321745
$967$	53714.9	1.78630	0.893151	−	0.449757i	$-0.148489\pi$
$967$	53714.9	1.78630	0.893151	+	0.449757i	$0.148489\pi$
$968$	−8022.79	−0.266386
$969$	−20280.8	−0.672356
$970$	−48480.2	−1.60475
$971$	9471.53	0.313034	0.156517	−	0.987675i	$-0.449973\pi$
$971$	9471.53	0.313034	0.156517	+	0.987675i	$0.449973\pi$
$972$	972.000	0.0320750
$973$	−16365.4	−0.539208
$974$	33989.7	1.11817
$975$	34829.2	1.14403
$976$	1803.82	0.0591586
$977$	16151.4	0.528894	0.264447	−	0.964400i	$-0.414811\pi$
$977$	16151.4	0.528894	0.264447	+	0.964400i	$0.414811\pi$
$978$	−13997.6	−0.457661
$979$	−13069.9	−0.426676
$980$	3740.64	0.121929
$981$	−10443.1	−0.339879
$982$	−39400.2	−1.28036
$983$	8001.49	0.259622	0.129811	−	0.991539i	$-0.458563\pi$
$983$	8001.49	0.259622	0.129811	+	0.991539i	$0.458563\pi$
$984$	5000.60	0.162005
$985$	53784.6	1.73982
$986$	2269.17	0.0732911
$987$	−4629.40	−0.149296
$988$	16965.1	0.546287
$989$	−4554.06	−0.146421
$990$	−6223.00	−0.199778
$991$	10185.2	0.326483	0.163242	−	0.986586i	$-0.447805\pi$
$991$	10185.2	0.326483	0.163242	+	0.986586i	$0.447805\pi$
$992$	6288.79	0.201280
$993$	−7972.20	−0.254773
$994$	−1825.54	−0.0582521
$995$	−27025.9	−0.861085
$996$	2579.76	0.0820711
$997$	35170.0	1.11720	0.558598	−	0.829439i	$-0.311340\pi$
$997$	35170.0	1.11720	0.558598	+	0.829439i	$0.311340\pi$
$998$	−30675.7	−0.972968
$999$	−682.803	−0.0216245

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	966.4.a.q.1.5	✓	5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
966.4.a.q.1.5	✓	5	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:	\( N \)	\(=\)	\( 966 = 2 \cdot 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	966.a (trivial)

\(f(q)\)	\(=\)	\(q+2.00000 q^{2} +3.00000 q^{3} +4.00000 q^{4} +19.0849 q^{5} +6.00000 q^{6} -7.00000 q^{7} +8.00000 q^{8} +9.00000 q^{9} +O(q^{10})\)	\(q+2.00000 q^{2} +3.00000 q^{3} +4.00000 q^{4} +19.0849 q^{5} +6.00000 q^{6} -7.00000 q^{7} +8.00000 q^{8} +9.00000 q^{9} +38.1698 q^{10} -18.1150 q^{11} +12.0000 q^{12} +48.5288 q^{13} -14.0000 q^{14} +57.2547 q^{15} +16.0000 q^{16} -77.3512 q^{17} +18.0000 q^{18} +87.3969 q^{19} +76.3396 q^{20} -21.0000 q^{21} -36.2299 q^{22} -23.0000 q^{23} +24.0000 q^{24} +239.234 q^{25} +97.0577 q^{26} +27.0000 q^{27} -28.0000 q^{28} -14.6679 q^{29} +114.509 q^{30} +196.525 q^{31} +32.0000 q^{32} -54.3449 q^{33} -154.702 q^{34} -133.594 q^{35} +36.0000 q^{36} -25.2890 q^{37} +174.794 q^{38} +145.587 q^{39} +152.679 q^{40} +208.358 q^{41} -42.0000 q^{42} +198.003 q^{43} -72.4598 q^{44} +171.764 q^{45} -46.0000 q^{46} +220.448 q^{47} +48.0000 q^{48} +49.0000 q^{49} +478.467 q^{50} -232.054 q^{51} +194.115 q^{52} -687.026 q^{53} +54.0000 q^{54} -345.722 q^{55} -56.0000 q^{56} +262.191 q^{57} -29.3359 q^{58} +59.0307 q^{59} +229.019 q^{60} +112.739 q^{61} +393.050 q^{62} -63.0000 q^{63} +64.0000 q^{64} +926.168 q^{65} -108.690 q^{66} -565.798 q^{67} -309.405 q^{68} -69.0000 q^{69} -267.189 q^{70} +130.396 q^{71} +72.0000 q^{72} -59.3013 q^{73} -50.5780 q^{74} +717.701 q^{75} +349.588 q^{76} +126.805 q^{77} +291.173 q^{78} -49.4714 q^{79} +305.359 q^{80} +81.0000 q^{81} +416.717 q^{82} +214.980 q^{83} -84.0000 q^{84} -1476.24 q^{85} +396.005 q^{86} -44.0038 q^{87} -144.920 q^{88} +721.497 q^{89} +343.528 q^{90} -339.702 q^{91} -92.0000 q^{92} +589.574 q^{93} +440.895 q^{94} +1667.96 q^{95} +96.0000 q^{96} -1270.12 q^{97} +98.0000 q^{98} -163.035 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q + 10 q^{2} + 15 q^{3} + 20 q^{4} - 10 q^{5} + 30 q^{6} - 35 q^{7} + 40 q^{8} + 45 q^{9}+O(q^{10}) \) 5 * q + 10 * q^2 + 15 * q^3 + 20 * q^4 - 10 * q^5 + 30 * q^6 - 35 * q^7 + 40 * q^8 + 45 * q^9	\( 5 q + 10 q^{2} + 15 q^{3} + 20 q^{4} - 10 q^{5} + 30 q^{6} - 35 q^{7} + 40 q^{8} + 45 q^{9} - 20 q^{10} + 47 q^{11} + 60 q^{12} + 74 q^{13} - 70 q^{14} - 30 q^{15} + 80 q^{16} - 4 q^{17} + 90 q^{18} + 215 q^{19} - 40 q^{20} - 105 q^{21} + 94 q^{22} - 115 q^{23} + 120 q^{24} + 535 q^{25} + 148 q^{26} + 135 q^{27} - 140 q^{28} + 273 q^{29} - 60 q^{30} + 660 q^{31} + 160 q^{32} + 141 q^{33} - 8 q^{34} + 70 q^{35} + 180 q^{36} - 71 q^{37} + 430 q^{38} + 222 q^{39} - 80 q^{40} + 428 q^{41} - 210 q^{42} + 606 q^{43} + 188 q^{44} - 90 q^{45} - 230 q^{46} + 514 q^{47} + 240 q^{48} + 245 q^{49} + 1070 q^{50} - 12 q^{51} + 296 q^{52} + 376 q^{53} + 270 q^{54} - 395 q^{55} - 280 q^{56} + 645 q^{57} + 546 q^{58} + 1062 q^{59} - 120 q^{60} + 60 q^{61} + 1320 q^{62} - 315 q^{63} + 320 q^{64} + 1755 q^{65} + 282 q^{66} + 671 q^{67} - 16 q^{68} - 345 q^{69} + 140 q^{70} + 1885 q^{71} + 360 q^{72} + 790 q^{73} - 142 q^{74} + 1605 q^{75} + 860 q^{76} - 329 q^{77} + 444 q^{78} + 738 q^{79} - 160 q^{80} + 405 q^{81} + 856 q^{82} + 774 q^{83} - 420 q^{84} + 781 q^{85} + 1212 q^{86} + 819 q^{87} + 376 q^{88} + 131 q^{89} - 180 q^{90} - 518 q^{91} - 460 q^{92} + 1980 q^{93} + 1028 q^{94} + 625 q^{95} + 480 q^{96} - 51 q^{97} + 490 q^{98} + 423 q^{99}+O(q^{100}) \) 5 * q + 10 * q^2 + 15 * q^3 + 20 * q^4 - 10 * q^5 + 30 * q^6 - 35 * q^7 + 40 * q^8 + 45 * q^9 - 20 * q^10 + 47 * q^11 + 60 * q^12 + 74 * q^13 - 70 * q^14 - 30 * q^15 + 80 * q^16 - 4 * q^17 + 90 * q^18 + 215 * q^19 - 40 * q^20 - 105 * q^21 + 94 * q^22 - 115 * q^23 + 120 * q^24 + 535 * q^25 + 148 * q^26 + 135 * q^27 - 140 * q^28 + 273 * q^29 - 60 * q^30 + 660 * q^31 + 160 * q^32 + 141 * q^33 - 8 * q^34 + 70 * q^35 + 180 * q^36 - 71 * q^37 + 430 * q^38 + 222 * q^39 - 80 * q^40 + 428 * q^41 - 210 * q^42 + 606 * q^43 + 188 * q^44 - 90 * q^45 - 230 * q^46 + 514 * q^47 + 240 * q^48 + 245 * q^49 + 1070 * q^50 - 12 * q^51 + 296 * q^52 + 376 * q^53 + 270 * q^54 - 395 * q^55 - 280 * q^56 + 645 * q^57 + 546 * q^58 + 1062 * q^59 - 120 * q^60 + 60 * q^61 + 1320 * q^62 - 315 * q^63 + 320 * q^64 + 1755 * q^65 + 282 * q^66 + 671 * q^67 - 16 * q^68 - 345 * q^69 + 140 * q^70 + 1885 * q^71 + 360 * q^72 + 790 * q^73 - 142 * q^74 + 1605 * q^75 + 860 * q^76 - 329 * q^77 + 444 * q^78 + 738 * q^79 - 160 * q^80 + 405 * q^81 + 856 * q^82 + 774 * q^83 - 420 * q^84 + 781 * q^85 + 1212 * q^86 + 819 * q^87 + 376 * q^88 + 131 * q^89 - 180 * q^90 - 518 * q^91 - 460 * q^92 + 1980 * q^93 + 1028 * q^94 + 625 * q^95 + 480 * q^96 - 51 * q^97 + 490 * q^98 + 423 * q^99

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