LMFDB - Embedded newform 143.4.a.c.1.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [143,4,Mod(1,143)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(143, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("143.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 143 = 11 \cdot 13 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	143.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:	$8.43727313082$
Analytic rank:	$0$
Dimension:	$9$
Coefficient field:	$\mathbb{Q}[x]/(x^{9} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{9} - 59x^{7} - 12x^{6} + 1144x^{5} + 345x^{4} - 7888x^{3} - 2245x^{2} + 9710x - 2988 $ x^9 - 59x^7 - 12x^6 + 1144x^5 + 345x^4 - 7888x^3 - 2245x^2 + 9710*x - 2988
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.9
Root			$5.41479$ of defining polynomial
Character	$\chi$	$=$	143.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+5.41479 q^{2} -1.18631 q^{3} +21.3199 q^{4} +5.73789 q^{5} -6.42360 q^{6} +3.58372 q^{7} +72.1247 q^{8} -25.5927 q^{9} +O(q^{10})$	\(q+5.41479 q^{2} -1.18631 q^{3} +21.3199 q^{4} +5.73789 q^{5} -6.42360 q^{6} +3.58372 q^{7} +72.1247 q^{8} -25.5927 q^{9} +31.0694 q^{10} -11.0000 q^{11} -25.2920 q^{12} -13.0000 q^{13} +19.4051 q^{14} -6.80689 q^{15} +219.981 q^{16} -7.29067 q^{17} -138.579 q^{18} +57.1435 q^{19} +122.331 q^{20} -4.25140 q^{21} -59.5627 q^{22} -73.6812 q^{23} -85.5620 q^{24} -92.0767 q^{25} -70.3923 q^{26} +62.3911 q^{27} +76.4048 q^{28} +84.9516 q^{29} -36.8579 q^{30} -98.0210 q^{31} +614.151 q^{32} +13.0494 q^{33} -39.4775 q^{34} +20.5630 q^{35} -545.634 q^{36} -49.2566 q^{37} +309.420 q^{38} +15.4220 q^{39} +413.843 q^{40} -213.532 q^{41} -23.0204 q^{42} +70.7399 q^{43} -234.519 q^{44} -146.848 q^{45} -398.968 q^{46} -624.502 q^{47} -260.964 q^{48} -330.157 q^{49} -498.576 q^{50} +8.64898 q^{51} -277.159 q^{52} +657.019 q^{53} +337.834 q^{54} -63.1167 q^{55} +258.475 q^{56} -67.7897 q^{57} +459.995 q^{58} -289.733 q^{59} -145.123 q^{60} +40.5324 q^{61} -530.763 q^{62} -91.7171 q^{63} +1565.65 q^{64} -74.5925 q^{65} +70.6596 q^{66} +866.684 q^{67} -155.437 q^{68} +87.4085 q^{69} +111.344 q^{70} +947.557 q^{71} -1845.86 q^{72} +919.099 q^{73} -266.714 q^{74} +109.231 q^{75} +1218.30 q^{76} -39.4210 q^{77} +83.5068 q^{78} -56.0379 q^{79} +1262.22 q^{80} +616.987 q^{81} -1156.23 q^{82} -1313.55 q^{83} -90.6395 q^{84} -41.8331 q^{85} +383.042 q^{86} -100.779 q^{87} -793.372 q^{88} +1072.13 q^{89} -795.150 q^{90} -46.5884 q^{91} -1570.88 q^{92} +116.283 q^{93} -3381.55 q^{94} +327.883 q^{95} -728.571 q^{96} -943.591 q^{97} -1787.73 q^{98} +281.519 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 9 q + 8 q^{3} + 46 q^{4} + 30 q^{5} + 34 q^{6} + 25 q^{7} + 36 q^{8} + 91 q^{9}+O(q^{10}) $ 9 * q + 8 * q^3 + 46 * q^4 + 30 * q^5 + 34 * q^6 + 25 * q^7 + 36 * q^8 + 91 * q^9	\( 9 q + 8 q^{3} + 46 q^{4} + 30 q^{5} + 34 q^{6} + 25 q^{7} + 36 q^{8} + 91 q^{9} - 22 q^{10} - 99 q^{11} + 181 q^{12} - 117 q^{13} + 351 q^{15} + 130 q^{16} + 53 q^{17} + 33 q^{18} + 69 q^{19} + 282 q^{20} + 463 q^{21} + 216 q^{23} - 121 q^{24} + 617 q^{25} + 275 q^{27} + 279 q^{28} - 91 q^{29} + 29 q^{30} + 636 q^{31} + 663 q^{32} - 88 q^{33} + 423 q^{34} - 358 q^{35} - 252 q^{36} + 967 q^{37} - 101 q^{38} - 104 q^{39} + 652 q^{40} - 226 q^{41} - 1186 q^{42} + 42 q^{43} - 506 q^{44} + 5 q^{45} - 1127 q^{46} - 269 q^{47} - 1820 q^{48} + 228 q^{49} - 1374 q^{50} - 589 q^{51} - 598 q^{52} + 1227 q^{53} - 2438 q^{54} - 330 q^{55} - 659 q^{56} - 71 q^{57} + 471 q^{58} - 613 q^{59} - 859 q^{60} + 427 q^{61} - 1714 q^{62} + 305 q^{63} - 1194 q^{64} - 390 q^{65} - 374 q^{66} - 271 q^{67} - 2835 q^{68} - 846 q^{69} - 102 q^{70} + 2279 q^{71} - 2400 q^{72} + 3602 q^{73} - 4955 q^{74} - 883 q^{75} + 1126 q^{76} - 275 q^{77} - 442 q^{78} - 1182 q^{79} - 2360 q^{80} + 2697 q^{81} + 1007 q^{82} - 1877 q^{83} + 1618 q^{84} - 441 q^{85} + 830 q^{86} + 1942 q^{87} - 396 q^{88} + 1258 q^{89} - 5669 q^{90} - 325 q^{91} + 1046 q^{92} + 1556 q^{93} + 1439 q^{94} + 2032 q^{95} - 3417 q^{96} + 4002 q^{97} - 1855 q^{98} - 1001 q^{99}+O(q^{100}) \) 9 * q + 8 * q^3 + 46 * q^4 + 30 * q^5 + 34 * q^6 + 25 * q^7 + 36 * q^8 + 91 * q^9 - 22 * q^10 - 99 * q^11 + 181 * q^12 - 117 * q^13 + 351 * q^15 + 130 * q^16 + 53 * q^17 + 33 * q^18 + 69 * q^19 + 282 * q^20 + 463 * q^21 + 216 * q^23 - 121 * q^24 + 617 * q^25 + 275 * q^27 + 279 * q^28 - 91 * q^29 + 29 * q^30 + 636 * q^31 + 663 * q^32 - 88 * q^33 + 423 * q^34 - 358 * q^35 - 252 * q^36 + 967 * q^37 - 101 * q^38 - 104 * q^39 + 652 * q^40 - 226 * q^41 - 1186 * q^42 + 42 * q^43 - 506 * q^44 + 5 * q^45 - 1127 * q^46 - 269 * q^47 - 1820 * q^48 + 228 * q^49 - 1374 * q^50 - 589 * q^51 - 598 * q^52 + 1227 * q^53 - 2438 * q^54 - 330 * q^55 - 659 * q^56 - 71 * q^57 + 471 * q^58 - 613 * q^59 - 859 * q^60 + 427 * q^61 - 1714 * q^62 + 305 * q^63 - 1194 * q^64 - 390 * q^65 - 374 * q^66 - 271 * q^67 - 2835 * q^68 - 846 * q^69 - 102 * q^70 + 2279 * q^71 - 2400 * q^72 + 3602 * q^73 - 4955 * q^74 - 883 * q^75 + 1126 * q^76 - 275 * q^77 - 442 * q^78 - 1182 * q^79 - 2360 * q^80 + 2697 * q^81 + 1007 * q^82 - 1877 * q^83 + 1618 * q^84 - 441 * q^85 + 830 * q^86 + 1942 * q^87 - 396 * q^88 + 1258 * q^89 - 5669 * q^90 - 325 * q^91 + 1046 * q^92 + 1556 * q^93 + 1439 * q^94 + 2032 * q^95 - 3417 * q^96 + 4002 * q^97 - 1855 * q^98 - 1001 * 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 $

$2$	5.41479	1.91442	0.957209	−	0.289399i	$-0.0934554\pi$
$2$	5.41479	1.91442	0.957209	+	0.289399i	$0.0934554\pi$
$3$	−1.18631	−0.228305	−0.114152	−	0.993463i	$-0.536415\pi$
$3$	−1.18631	−0.228305	−0.114152	+	0.993463i	$0.536415\pi$
$4$	21.3199	2.66499
$5$	5.73789	0.513212	0.256606	−	0.966516i	$-0.417396\pi$
$5$	5.73789	0.513212	0.256606	+	0.966516i	$0.417396\pi$
$6$	−6.42360	−0.437071
$7$	3.58372	0.193503	0.0967514	−	0.995309i	$-0.469155\pi$
$7$	3.58372	0.193503	0.0967514	+	0.995309i	$0.469155\pi$
$8$	72.1247	3.18749
$9$	−25.5927	−0.947877
$10$	31.0694	0.982502
$11$	−11.0000	−0.301511
$11$	−11.0000	−0.301511
$12$	−25.2920	−0.608431
$13$	−13.0000	−0.277350
$13$	−13.0000	−0.277350
$14$	19.4051	0.370445
$15$	−6.80689	−0.117169
$16$	219.981	3.43720
$17$	−7.29067	−0.104015	−0.0520073	−	0.998647i	$-0.516562\pi$
$17$	−7.29067	−0.104015	−0.0520073	+	0.998647i	$0.516562\pi$
$18$	−138.579	−1.81463
$19$	57.1435	0.689980	0.344990	−	0.938606i	$-0.387882\pi$
$19$	57.1435	0.689980	0.344990	+	0.938606i	$0.387882\pi$
$20$	122.331	1.36771
$21$	−4.25140	−0.0441777
$22$	−59.5627	−0.577219
$23$	−73.6812	−0.667982	−0.333991	−	0.942576i	$-0.608396\pi$
$23$	−73.6812	−0.667982	−0.333991	+	0.942576i	$0.608396\pi$
$24$	−85.5620	−0.727720
$25$	−92.0767	−0.736613
$26$	−70.3923	−0.530964
$27$	62.3911	0.444710
$28$	76.4048	0.515684
$29$	84.9516	0.543970	0.271985	−	0.962302i	$-0.412320\pi$
$29$	84.9516	0.543970	0.271985	+	0.962302i	$0.412320\pi$
$30$	−36.8579	−0.224310
$31$	−98.0210	−0.567906	−0.283953	−	0.958838i	$-0.591646\pi$
$31$	−98.0210	−0.567906	−0.283953	+	0.958838i	$0.591646\pi$
$32$	614.151	3.39273
$33$	13.0494	0.0688365
$34$	−39.4775	−0.199127
$35$	20.5630	0.0993080
$36$	−545.634	−2.52609
$37$	−49.2566	−0.218858	−0.109429	−	0.993995i	$-0.534902\pi$
$37$	−49.2566	−0.218858	−0.109429	+	0.993995i	$0.534902\pi$
$38$	309.420	1.32091
$39$	15.4220	0.0633204
$40$	413.843	1.63586
$41$	−213.532	−0.813368	−0.406684	−	0.913569i	$-0.633315\pi$
$41$	−213.532	−0.813368	−0.406684	+	0.913569i	$0.633315\pi$
$42$	−23.0204	−0.0845745
$43$	70.7399	0.250878	0.125439	−	0.992101i	$-0.459966\pi$
$43$	70.7399	0.250878	0.125439	+	0.992101i	$0.459966\pi$
$44$	−234.519	−0.803526
$45$	−146.848	−0.486462
$46$	−398.968	−1.27880
$47$	−624.502	−1.93815	−0.969074	−	0.246769i	$-0.920631\pi$
$47$	−624.502	−1.93815	−0.969074	+	0.246769i	$0.920631\pi$
$48$	−260.964	−0.784729
$49$	−330.157	−0.962557
$50$	−498.576	−1.41019
$51$	8.64898	0.0237470
$52$	−277.159	−0.739136
$53$	657.019	1.70280	0.851401	−	0.524515i	$-0.175753\pi$
$53$	657.019	1.70280	0.851401	+	0.524515i	$0.175753\pi$
$54$	337.834	0.851360
$55$	−63.1167	−0.154739
$56$	258.475	0.616789
$57$	−67.7897	−0.157526
$58$	459.995	1.04138
$59$	−289.733	−0.639322	−0.319661	−	0.947532i	$-0.603569\pi$
$59$	−289.733	−0.639322	−0.319661	+	0.947532i	$0.603569\pi$
$60$	−145.123	−0.312254
$61$	40.5324	0.0850761	0.0425380	−	0.999095i	$-0.486456\pi$
$61$	40.5324	0.0850761	0.0425380	+	0.999095i	$0.486456\pi$
$62$	−530.763	−1.08721
$63$	−91.7171	−0.183417
$64$	1565.65	3.05791
$65$	−74.5925	−0.142339
$66$	70.6596	0.131782
$67$	866.684	1.58033	0.790166	−	0.612893i	$-0.209994\pi$
$67$	866.684	1.58033	0.790166	+	0.612893i	$0.209994\pi$
$68$	−155.437	−0.277198
$69$	87.4085	0.152504
$70$	111.344	0.190117
$71$	947.557	1.58386	0.791932	−	0.610610i	$-0.209076\pi$
$71$	947.557	1.58386	0.791932	+	0.610610i	$0.209076\pi$
$72$	−1845.86	−3.02135
$73$	919.099	1.47359	0.736797	−	0.676114i	$-0.236337\pi$
$73$	919.099	1.47359	0.736797	+	0.676114i	$0.236337\pi$
$74$	−266.714	−0.418985
$75$	109.231	0.168172
$76$	1218.30	1.83879
$77$	−39.4210	−0.0583433
$78$	83.5068	0.121222
$79$	−56.0379	−0.0798071	−0.0399035	−	0.999204i	$-0.512705\pi$
$79$	−56.0379	−0.0798071	−0.0399035	+	0.999204i	$0.512705\pi$
$80$	1262.22	1.76401
$81$	616.987	0.846347
$82$	−1156.23	−1.55712
$83$	−1313.55	−1.73712	−0.868559	−	0.495586i	$-0.834953\pi$
$83$	−1313.55	−1.73712	−0.868559	+	0.495586i	$0.834953\pi$
$84$	−90.6395	−0.117733
$85$	−41.8331	−0.0533816
$86$	383.042	0.480284
$87$	−100.779	−0.124191
$88$	−793.372	−0.961065
$89$	1072.13	1.27691	0.638457	−	0.769657i	$-0.279573\pi$
$89$	1072.13	1.27691	0.638457	+	0.769657i	$0.279573\pi$
$90$	−795.150	−0.931291
$91$	−46.5884	−0.0536680
$92$	−1570.88	−1.78017
$93$	116.283	0.129656
$94$	−3381.55	−3.71043
$95$	327.883	0.354106
$96$	−728.571	−0.774578
$97$	−943.591	−0.987703	−0.493852	−	0.869546i	$-0.664411\pi$
$97$	−943.591	−0.987703	−0.493852	+	0.869546i	$0.664411\pi$
$98$	−1787.73	−1.84273
$99$	281.519	0.285796
$100$	−1963.07	−1.96307
$101$	1223.86	1.20573	0.602863	−	0.797845i	$-0.294027\pi$
$101$	1223.86	1.20573	0.602863	+	0.797845i	$0.294027\pi$
$102$	46.8324	0.0454617
$103$	−231.408	−0.221372	−0.110686	−	0.993855i	$-0.535305\pi$
$103$	−231.408	−0.221372	−0.110686	+	0.993855i	$0.535305\pi$
$104$	−937.621	−0.884051
$105$	−24.3940	−0.0226725
$106$	3557.62	3.25987
$107$	177.090	0.159999	0.0799996	−	0.996795i	$-0.474508\pi$
$107$	177.090	0.159999	0.0799996	+	0.996795i	$0.474508\pi$
$108$	1330.17	1.18515
$109$	729.672	0.641191	0.320596	−	0.947216i	$-0.396117\pi$
$109$	729.672	0.641191	0.320596	+	0.947216i	$0.396117\pi$
$110$	−341.764	−0.296236
$111$	58.4334	0.0499662
$112$	788.349	0.665107
$113$	840.502	0.699715	0.349857	−	0.936803i	$-0.386230\pi$
$113$	840.502	0.699715	0.349857	+	0.936803i	$0.386230\pi$
$114$	−367.067	−0.301570
$115$	−422.774	−0.342817
$116$	1811.16	1.44968
$117$	332.705	0.262894
$118$	−1568.84	−1.22393
$119$	−26.1278	−0.0201271
$120$	−490.945	−0.373475
$121$	121.000	0.0909091
$122$	219.474	0.162871
$123$	253.314	0.185696
$124$	−2089.80	−1.51347
$125$	−1245.56	−0.891251
$126$	−496.629	−0.351137
$127$	1821.07	1.27239	0.636195	−	0.771528i	$-0.280507\pi$
$127$	1821.07	1.27239	0.636195	+	0.771528i	$0.280507\pi$
$128$	3564.47	2.46139
$129$	−83.9193	−0.0572766
$130$	−403.903	−0.272497
$131$	411.950	0.274750	0.137375	−	0.990519i	$-0.456133\pi$
$131$	411.950	0.274750	0.137375	+	0.990519i	$0.456133\pi$
$132$	278.212	0.183449
$133$	204.787	0.133513
$134$	4692.91	3.02542
$135$	357.993	0.228230
$136$	−525.838	−0.331546
$137$	−24.7820	−0.0154546	−0.00772728	−	0.999970i	$-0.502460\pi$
$137$	−24.7820	−0.0154546	−0.00772728	+	0.999970i	$0.502460\pi$
$138$	473.299	0.291956
$139$	−2070.83	−1.26364	−0.631818	−	0.775117i	$-0.717691\pi$
$139$	−2070.83	−1.26364	−0.631818	+	0.775117i	$0.717691\pi$
$140$	438.402	0.264655
$141$	740.851	0.442489
$142$	5130.82	3.03217
$143$	143.000	0.0836242
$144$	−5629.89	−3.25804
$145$	487.443	0.279172
$146$	4976.73	2.82107
$147$	391.667	0.219756
$148$	−1050.15	−0.583254
$149$	2754.88	1.51469	0.757345	−	0.653015i	$-0.226496\pi$
$149$	2754.88	1.51469	0.757345	+	0.653015i	$0.226496\pi$
$150$	591.464	0.321952
$151$	−2345.35	−1.26399	−0.631994	−	0.774974i	$-0.717763\pi$
$151$	−2345.35	−1.26399	−0.631994	+	0.774974i	$0.717763\pi$
$152$	4121.46	2.19931
$153$	186.588	0.0985930
$154$	−213.456	−0.111693
$155$	−562.433	−0.291456
$156$	328.796	0.168748
$157$	−422.144	−0.214591	−0.107295	−	0.994227i	$-0.534219\pi$
$157$	−422.144	−0.214591	−0.107295	+	0.994227i	$0.534219\pi$
$158$	−303.434	−0.152784
$159$	−779.426	−0.388758
$160$	3523.93	1.74119
$161$	−264.053	−0.129256
$162$	3340.86	1.62026
$163$	1281.43	0.615765	0.307882	−	0.951424i	$-0.400380\pi$
$163$	1281.43	0.615765	0.307882	+	0.951424i	$0.400380\pi$
$164$	−4552.49	−2.16762
$165$	74.8758	0.0353277
$166$	−7112.59	−3.32557
$167$	610.521	0.282895	0.141448	−	0.989946i	$-0.454824\pi$
$167$	610.521	0.282895	0.141448	+	0.989946i	$0.454824\pi$
$168$	−306.631	−0.140816
$169$	169.000	0.0769231
$170$	−226.517	−0.102195
$171$	−1462.46	−0.654016
$172$	1508.17	0.668587
$173$	1810.85	0.795816	0.397908	−	0.917425i	$-0.369736\pi$
$173$	1810.85	0.795816	0.397908	+	0.917425i	$0.369736\pi$
$174$	−545.695	−0.237753
$175$	−329.977	−0.142537
$176$	−2419.79	−1.03635
$177$	343.712	0.145960
$178$	5805.35	2.44455
$179$	−2383.33	−0.995186	−0.497593	−	0.867411i	$-0.665783\pi$
$179$	−2383.33	−0.995186	−0.497593	+	0.867411i	$0.665783\pi$
$180$	−3130.79	−1.29642
$181$	3943.98	1.61963	0.809817	−	0.586683i	$-0.199567\pi$
$181$	3943.98	1.61963	0.809817	+	0.586683i	$0.199567\pi$
$182$	−252.266	−0.102743
$183$	−48.0839	−0.0194233
$184$	−5314.23	−2.12919
$185$	−282.628	−0.112320
$186$	629.648	0.248215
$187$	80.1974	0.0313616
$188$	−13314.4	−5.16515
$189$	223.592	0.0860526
$190$	1775.42	0.677907
$191$	786.517	0.297960	0.148980	−	0.988840i	$-0.452401\pi$
$191$	786.517	0.297960	0.148980	+	0.988840i	$0.452401\pi$
$192$	−1857.34	−0.698137
$193$	−4034.43	−1.50469	−0.752344	−	0.658770i	$-0.771077\pi$
$193$	−4034.43	−1.50469	−0.752344	+	0.658770i	$0.771077\pi$
$194$	−5109.35	−1.89088
$195$	88.4896	0.0324968
$196$	−7038.93	−2.56521
$197$	−1378.00	−0.498369	−0.249185	−	0.968456i	$-0.580163\pi$
$197$	−1378.00	−0.498369	−0.249185	+	0.968456i	$0.580163\pi$
$198$	1524.37	0.547132
$199$	−1459.10	−0.519763	−0.259882	−	0.965640i	$-0.583684\pi$
$199$	−1459.10	−0.519763	−0.259882	+	0.965640i	$0.583684\pi$
$200$	−6641.00	−2.34795
$201$	−1028.15	−0.360798
$202$	6626.93	2.30826
$203$	304.443	0.105260
$204$	184.396	0.0632857
$205$	−1225.22	−0.417430
$206$	−1253.02	−0.423797
$207$	1885.70	0.633165
$208$	−2859.75	−0.953307
$209$	−628.579	−0.208037
$210$	−132.089	−0.0434046
$211$	4949.83	1.61498	0.807488	−	0.589884i	$-0.200826\pi$
$211$	4949.83	1.61498	0.807488	+	0.589884i	$0.200826\pi$
$212$	14007.6	4.53796
$213$	−1124.09	−0.361604
$214$	958.903	0.306305
$215$	405.898	0.128753
$216$	4499.94	1.41751
$217$	−351.280	−0.109891
$218$	3951.02	1.22751
$219$	−1090.33	−0.336429
$220$	−1345.65	−0.412379
$221$	94.7788	0.0288485
$222$	316.405	0.0956562
$223$	1864.52	0.559898	0.279949	−	0.960015i	$-0.409682\pi$
$223$	1864.52	0.559898	0.279949	+	0.960015i	$0.409682\pi$
$224$	2200.95	0.656504
$225$	2356.49	0.698219
$226$	4551.14	1.33955
$227$	−4911.50	−1.43607	−0.718035	−	0.696007i	$-0.754958\pi$
$227$	−4911.50	−1.43607	−0.718035	+	0.696007i	$0.754958\pi$
$228$	−1445.27	−0.419805
$229$	−5439.72	−1.56972	−0.784862	−	0.619671i	$-0.787266\pi$
$229$	−5439.72	−1.56972	−0.784862	+	0.619671i	$0.787266\pi$
$230$	−2289.23	−0.656294
$231$	46.7654	0.0133201
$232$	6127.11	1.73390
$233$	−6679.30	−1.87801	−0.939004	−	0.343907i	$-0.888250\pi$
$233$	−6679.30	−1.87801	−0.939004	+	0.343907i	$0.888250\pi$
$234$	1801.53	0.503288
$235$	−3583.32	−0.994681
$236$	−6177.08	−1.70379
$237$	66.4782	0.0182203
$238$	−141.476	−0.0385317
$239$	−4850.14	−1.31268	−0.656338	−	0.754467i	$-0.727895\pi$
$239$	−4850.14	−1.31268	−0.656338	+	0.754467i	$0.727895\pi$
$240$	−1497.38	−0.402732
$241$	7293.87	1.94954	0.974770	−	0.223210i	$-0.0716535\pi$
$241$	7293.87	1.94954	0.974770	+	0.223210i	$0.0716535\pi$
$242$	655.190	0.174038
$243$	−2416.49	−0.637935
$244$	864.149	0.226727
$245$	−1894.40	−0.493996
$246$	1371.64	0.355499
$247$	−742.866	−0.191366
$248$	−7069.73	−1.81020
$249$	1558.27	0.396593
$250$	−6744.45	−1.70623
$251$	−5041.10	−1.26769	−0.633847	−	0.773458i	$-0.718525\pi$
$251$	−5041.10	−1.26769	−0.633847	+	0.773458i	$0.718525\pi$
$252$	−1955.40	−0.488805
$253$	810.493	0.201404
$254$	9860.70	2.43589
$255$	49.6268	0.0121873
$256$	6775.65	1.65421
$257$	672.854	0.163313	0.0816566	−	0.996661i	$-0.473979\pi$
$257$	672.854	0.163313	0.0816566	+	0.996661i	$0.473979\pi$
$258$	−454.405	−0.109651
$259$	−176.522	−0.0423496
$260$	−1590.31	−0.379334
$261$	−2174.14	−0.515616
$262$	2230.62	0.525986
$263$	−4302.43	−1.00874	−0.504372	−	0.863487i	$-0.668276\pi$
$263$	−4302.43	−1.00874	−0.504372	+	0.863487i	$0.668276\pi$
$264$	941.182	0.219416
$265$	3769.90	0.873899
$266$	1108.88	0.255600
$267$	−1271.87	−0.291526
$268$	18477.7	4.21158
$269$	−603.338	−0.136751	−0.0683757	−	0.997660i	$-0.521782\pi$
$269$	−603.338	−0.136751	−0.0683757	+	0.997660i	$0.521782\pi$
$270$	1938.46	0.436928
$271$	4596.03	1.03022	0.515109	−	0.857125i	$-0.327752\pi$
$271$	4596.03	1.03022	0.515109	+	0.857125i	$0.327752\pi$
$272$	−1603.81	−0.357519
$273$	55.2682	0.0122527
$274$	−134.190	−0.0295865
$275$	1012.84	0.222097
$276$	1863.54	0.406421
$277$	3602.36	0.781388	0.390694	−	0.920521i	$-0.372235\pi$
$277$	3602.36	0.781388	0.390694	+	0.920521i	$0.372235\pi$
$278$	−11213.1	−2.41913
$279$	2508.62	0.538305
$280$	1483.10	0.316544
$281$	−6795.69	−1.44269	−0.721347	−	0.692574i	$-0.756477\pi$
$281$	−6795.69	−1.44269	−0.721347	+	0.692574i	$0.756477\pi$
$282$	4011.55	0.847108
$283$	798.045	0.167628	0.0838142	−	0.996481i	$-0.473290\pi$
$283$	798.045	0.167628	0.0838142	+	0.996481i	$0.473290\pi$
$284$	20201.9	4.22098
$285$	−388.970	−0.0808441
$286$	774.315	0.160092
$287$	−765.239	−0.157389
$288$	−15717.8	−3.21589
$289$	−4859.85	−0.989181
$290$	2639.40	0.534451
$291$	1119.39	0.225497
$292$	19595.1	3.92712
$293$	−2291.71	−0.456938	−0.228469	−	0.973551i	$-0.573372\pi$
$293$	−2291.71	−0.456938	−0.228469	+	0.973551i	$0.573372\pi$
$294$	2120.80	0.420705
$295$	−1662.45	−0.328108
$296$	−3552.61	−0.697606
$297$	−686.302	−0.134085
$298$	14917.1	2.89975
$299$	957.856	0.185265
$300$	2328.80	0.448178
$301$	253.512	0.0485455
$302$	−12699.6	−2.41980
$303$	−1451.87	−0.275273
$304$	12570.5	2.37160
$305$	232.570	0.0436621
$306$	1010.33	0.188748
$307$	−4757.10	−0.884372	−0.442186	−	0.896923i	$-0.645797\pi$
$307$	−4757.10	−0.884372	−0.442186	+	0.896923i	$0.645797\pi$
$308$	−840.453	−0.155485
$309$	274.520	0.0505402
$310$	−3045.46	−0.557969
$311$	−7780.52	−1.41863	−0.709314	−	0.704893i	$-0.750995\pi$
$311$	−7780.52	−1.41863	−0.709314	+	0.704893i	$0.750995\pi$
$312$	1112.31	0.201833
$313$	8183.89	1.47789	0.738947	−	0.673764i	$-0.235323\pi$
$313$	8183.89	1.47789	0.738947	+	0.673764i	$0.235323\pi$
$314$	−2285.82	−0.410816
$315$	−526.262	−0.0941318
$316$	−1194.73	−0.212685
$317$	8916.78	1.57986	0.789931	−	0.613196i	$-0.210116\pi$
$317$	8916.78	1.57986	0.789931	+	0.613196i	$0.210116\pi$
$318$	−4220.43	−0.744245
$319$	−934.468	−0.164013
$320$	8983.53	1.56936
$321$	−210.083	−0.0365286
$322$	−1429.79	−0.247451
$323$	−416.615	−0.0717680
$324$	13154.1	2.25551
$325$	1197.00	0.204300
$326$	6938.70	1.17883
$327$	−865.614	−0.146387
$328$	−15400.9	−2.59260
$329$	−2238.04	−0.375037
$330$	405.437	0.0676320
$331$	243.768	0.0404794	0.0202397	−	0.999795i	$-0.493557\pi$
$331$	243.768	0.0404794	0.0202397	+	0.999795i	$0.493557\pi$
$332$	−28004.8	−4.62941
$333$	1260.61	0.207450
$334$	3305.84	0.541580
$335$	4972.93	0.811046
$336$	−935.224	−0.151847
$337$	−4611.91	−0.745480	−0.372740	−	0.927936i	$-0.621582\pi$
$337$	−4611.91	−0.745480	−0.372740	+	0.927936i	$0.621582\pi$
$338$	915.099	0.147263
$339$	−997.093	−0.159748
$340$	−891.878	−0.142261
$341$	1078.23	0.171230
$342$	−7918.89	−1.25206
$343$	−2412.41	−0.379760
$344$	5102.10	0.799670
$345$	501.540	0.0782667
$346$	9805.36	1.52352
$347$	−3756.54	−0.581158	−0.290579	−	0.956851i	$-0.593848\pi$
$347$	−3756.54	−0.581158	−0.290579	+	0.956851i	$0.593848\pi$
$348$	−2148.60	−0.330968
$349$	−625.209	−0.0958930	−0.0479465	−	0.998850i	$-0.515268\pi$
$349$	−625.209	−0.0958930	−0.0479465	+	0.998850i	$0.515268\pi$
$350$	−1786.76	−0.272875
$351$	−811.084	−0.123340
$352$	−6755.66	−1.02295
$353$	349.129	0.0526410	0.0263205	−	0.999654i	$-0.491621\pi$
$353$	349.129	0.0526410	0.0263205	+	0.999654i	$0.491621\pi$
$354$	1861.13	0.279429
$355$	5436.97	0.812858
$356$	22857.7	3.40297
$357$	30.9955	0.00459512
$358$	−12905.2	−1.90520
$359$	−9576.27	−1.40784	−0.703922	−	0.710277i	$-0.748570\pi$
$359$	−9576.27	−1.40784	−0.703922	+	0.710277i	$0.748570\pi$
$360$	−10591.4	−1.55059
$361$	−3593.62	−0.523928
$362$	21355.8	3.10065
$363$	−143.543	−0.0207550
$364$	−993.262	−0.143025
$365$	5273.68	0.756266
$366$	−260.364	−0.0371843
$367$	−3557.11	−0.505939	−0.252970	−	0.967474i	$-0.581407\pi$
$367$	−3557.11	−0.505939	−0.252970	+	0.967474i	$0.581407\pi$
$368$	−16208.4	−2.29599
$369$	5464.85	0.770972
$370$	−1530.37	−0.215028
$371$	2354.58	0.329497
$372$	2479.15	0.345532
$373$	2859.54	0.396947	0.198474	−	0.980106i	$-0.436402\pi$
$373$	2859.54	0.396947	0.198474	+	0.980106i	$0.436402\pi$
$374$	434.252	0.0600392
$375$	1477.62	0.203477
$376$	−45042.0	−6.17783
$377$	−1104.37	−0.150870
$378$	1210.71	0.164741
$379$	6630.12	0.898592	0.449296	−	0.893383i	$-0.351675\pi$
$379$	6630.12	0.898592	0.449296	+	0.893383i	$0.351675\pi$
$380$	6990.45	0.943690
$381$	−2160.35	−0.290493
$382$	4258.82	0.570420
$383$	−2525.38	−0.336921	−0.168461	−	0.985708i	$-0.553880\pi$
$383$	−2525.38	−0.336921	−0.168461	+	0.985708i	$0.553880\pi$
$384$	−4228.56	−0.561947
$385$	−226.193	−0.0299425
$386$	−21845.6	−2.88060
$387$	−1810.42	−0.237801
$388$	−20117.3	−2.63222
$389$	8099.35	1.05566	0.527832	−	0.849349i	$-0.323005\pi$
$389$	8099.35	1.05566	0.527832	+	0.849349i	$0.323005\pi$
$390$	479.153	0.0622124
$391$	537.186	0.0694799
$392$	−23812.5	−3.06814
$393$	−488.699	−0.0627268
$394$	−7461.61	−0.954087
$395$	−321.539	−0.0409579
$396$	6001.98	0.761643
$397$	6538.75	0.826626	0.413313	−	0.910589i	$-0.364372\pi$
$397$	6538.75	0.826626	0.413313	+	0.910589i	$0.364372\pi$
$398$	−7900.72	−0.995044
$399$	−242.940	−0.0304817
$400$	−20255.1	−2.53188
$401$	12965.8	1.61466	0.807331	−	0.590099i	$-0.200911\pi$
$401$	12965.8	1.61466	0.807331	+	0.590099i	$0.200911\pi$
$402$	−5567.23	−0.690717
$403$	1274.27	0.157509
$404$	26092.6	3.21325
$405$	3540.20	0.434356
$406$	1648.50	0.201511
$407$	541.822	0.0659880
$408$	623.805	0.0756935
$409$	10898.1	1.31755	0.658775	−	0.752340i	$-0.271075\pi$
$409$	10898.1	1.31755	0.658775	+	0.752340i	$0.271075\pi$
$410$	−6634.32	−0.799135
$411$	29.3991	0.00352835
$412$	−4933.60	−0.589954
$413$	−1038.32	−0.123711
$414$	10210.7	1.21214
$415$	−7537.00	−0.891510
$416$	−7983.96	−0.940975
$417$	2456.64	0.288494
$418$	−3403.62	−0.398269
$419$	−7403.48	−0.863206	−0.431603	−	0.902064i	$-0.642052\pi$
$419$	−7403.48	−0.863206	−0.431603	+	0.902064i	$0.642052\pi$
$420$	−520.079	−0.0604221
$421$	−4834.35	−0.559648	−0.279824	−	0.960051i	$-0.590276\pi$
$421$	−4834.35	−0.559648	−0.279824	+	0.960051i	$0.590276\pi$
$422$	26802.3	3.09174
$423$	15982.7	1.83713
$424$	47387.3	5.42767
$425$	671.301	0.0766185
$426$	−6086.73	−0.692260
$427$	145.257	0.0164625
$428$	3775.54	0.426397
$429$	−169.642	−0.0190918
$430$	2197.85	0.246488
$431$	7418.45	0.829082	0.414541	−	0.910031i	$-0.363942\pi$
$431$	7418.45	0.829082	0.414541	+	0.910031i	$0.363942\pi$
$432$	13724.8	1.52855
$433$	5888.85	0.653580	0.326790	−	0.945097i	$-0.394033\pi$
$433$	5888.85	0.653580	0.326790	+	0.945097i	$0.394033\pi$
$434$	−1902.11	−0.210378
$435$	−578.257	−0.0637363
$436$	15556.6	1.70877
$437$	−4210.40	−0.460894
$438$	−5903.93	−0.644065
$439$	760.850	0.0827184	0.0413592	−	0.999144i	$-0.486831\pi$
$439$	760.850	0.0827184	0.0413592	+	0.999144i	$0.486831\pi$
$440$	−4552.28	−0.493230
$441$	8449.60	0.912385
$442$	513.207	0.0552280
$443$	1853.06	0.198740	0.0993699	−	0.995051i	$-0.468317\pi$
$443$	1853.06	0.198740	0.0993699	+	0.995051i	$0.468317\pi$
$444$	1245.80	0.133160
$445$	6151.75	0.655328
$446$	10096.0	1.07188
$447$	−3268.14	−0.345811
$448$	5610.86	0.591715
$449$	11275.2	1.18510	0.592549	−	0.805534i	$-0.298122\pi$
$449$	11275.2	1.18510	0.592549	+	0.805534i	$0.298122\pi$
$450$	12759.9	1.33668
$451$	2348.85	0.245240
$452$	17919.5	1.86474
$453$	2782.31	0.288574
$454$	−26594.7	−2.74924
$455$	−267.319	−0.0275431
$456$	−4889.31	−0.502112
$457$	15380.1	1.57429	0.787145	−	0.616768i	$-0.211558\pi$
$457$	15380.1	1.57429	0.787145	+	0.616768i	$0.211558\pi$
$458$	−29454.9	−3.00511
$459$	−454.873	−0.0462563
$460$	−9013.52	−0.913604
$461$	−8981.94	−0.907441	−0.453721	−	0.891144i	$-0.649904\pi$
$461$	−8981.94	−0.907441	−0.453721	+	0.891144i	$0.649904\pi$
$462$	253.225	0.0255002
$463$	520.531	0.0522486	0.0261243	−	0.999659i	$-0.491683\pi$
$463$	520.531	0.0522486	0.0261243	+	0.999659i	$0.491683\pi$
$464$	18687.7	1.86973
$465$	667.218	0.0665409
$466$	−36167.0	−3.59529
$467$	−5181.94	−0.513472	−0.256736	−	0.966482i	$-0.582647\pi$
$467$	−5181.94	−0.513472	−0.256736	+	0.966482i	$0.582647\pi$
$468$	7093.25	0.700610
$469$	3105.96	0.305799
$470$	−19402.9	−1.90424
$471$	500.792	0.0489921
$472$	−20896.9	−2.03783
$473$	−778.139	−0.0756425
$474$	359.965	0.0348813
$475$	−5261.58	−0.508248
$476$	−557.042	−0.0536387
$477$	−16814.9	−1.61405
$478$	−26262.5	−2.51301
$479$	−14631.0	−1.39563	−0.697817	−	0.716276i	$-0.745845\pi$
$479$	−14631.0	−1.39563	−0.697817	+	0.716276i	$0.745845\pi$
$480$	−4180.46	−0.397523
$481$	640.335	0.0607002
$482$	39494.8	3.73223
$483$	313.248	0.0295099
$484$	2579.71	0.242272
$485$	−5414.22	−0.506901
$486$	−13084.8	−1.22127
$487$	21353.8	1.98693	0.993464	−	0.114144i	$-0.0364126\pi$
$487$	21353.8	1.98693	0.993464	+	0.114144i	$0.0364126\pi$
$488$	2923.39	0.271179
$489$	−1520.17	−0.140582
$490$	−10257.8	−0.945714
$491$	787.577	0.0723887	0.0361943	−	0.999345i	$-0.488476\pi$
$491$	787.577	0.0723887	0.0361943	+	0.999345i	$0.488476\pi$
$492$	5400.65	0.494878
$493$	−619.355	−0.0565808
$494$	−4022.46	−0.366354
$495$	1615.33	0.146674
$496$	−21562.7	−1.95200
$497$	3395.78	0.306482
$498$	8437.72	0.759244
$499$	19269.6	1.72871	0.864355	−	0.502882i	$-0.167727\pi$
$499$	19269.6	1.72871	0.864355	+	0.502882i	$0.167727\pi$
$500$	−26555.3	−2.37518
$501$	−724.266	−0.0645864
$502$	−27296.5	−2.42690
$503$	−17160.7	−1.52119	−0.760595	−	0.649227i	$-0.775093\pi$
$503$	−17160.7	−1.52119	−0.760595	+	0.649227i	$0.775093\pi$
$504$	−6615.07	−0.584640
$505$	7022.35	0.618793
$506$	4388.65	0.385572
$507$	−200.486	−0.0175619
$508$	38825.1	3.39091
$509$	−12767.1	−1.11177	−0.555886	−	0.831258i	$-0.687621\pi$
$509$	−12767.1	−1.11177	−0.555886	+	0.831258i	$0.687621\pi$
$510$	268.719	0.0233315
$511$	3293.80	0.285145
$512$	8172.93	0.705461
$513$	3565.24	0.306841
$514$	3643.36	0.312649
$515$	−1327.79	−0.113611
$516$	−1789.15	−0.152642
$517$	6869.52	0.584374
$518$	−955.829	−0.0810747
$519$	−2148.22	−0.181689
$520$	−5379.96	−0.453706
$521$	−10281.1	−0.864538	−0.432269	−	0.901745i	$-0.642287\pi$
$521$	−10281.1	−0.864538	−0.432269	+	0.901745i	$0.642287\pi$
$522$	−11772.5	−0.987105
$523$	−6023.80	−0.503638	−0.251819	−	0.967774i	$-0.581029\pi$
$523$	−6023.80	−0.503638	−0.251819	+	0.967774i	$0.581029\pi$
$524$	8782.75	0.732207
$525$	391.454	0.0325419
$526$	−23296.8	−1.93116
$527$	714.639	0.0590705
$528$	2870.61	0.236605
$529$	−6738.08	−0.553800
$530$	20413.2	1.67301
$531$	7415.03	0.605998
$532$	4366.04	0.355812
$533$	2775.91	0.225588
$534$	−6886.93	−0.558102
$535$	1016.12	0.0821135
$536$	62509.3	5.03730
$537$	2827.36	0.227206
$538$	−3266.95	−0.261799
$539$	3631.73	0.290222
$540$	7632.39	0.608233
$541$	−7574.93	−0.601981	−0.300991	−	0.953627i	$-0.597317\pi$
$541$	−7574.93	−0.601981	−0.300991	+	0.953627i	$0.597317\pi$
$542$	24886.5	1.97227
$543$	−4678.77	−0.369770
$544$	−4477.57	−0.352894
$545$	4186.77	0.329067
$546$	299.265	0.0234567
$547$	−17066.8	−1.33405	−0.667023	−	0.745037i	$-0.732432\pi$
$547$	−17066.8	−1.33405	−0.667023	+	0.745037i	$0.732432\pi$
$548$	−528.352	−0.0411863
$549$	−1037.33	−0.0806417
$550$	5484.33	0.425187
$551$	4854.43	0.375328
$552$	6304.31	0.486104
$553$	−200.824	−0.0154429
$554$	19506.0	1.49590
$555$	335.284	0.0256433
$556$	−44150.0	−3.36758
$557$	−9502.76	−0.722882	−0.361441	−	0.932395i	$-0.617715\pi$
$557$	−9502.76	−0.722882	−0.361441	+	0.932395i	$0.617715\pi$
$558$	13583.6	1.03054
$559$	−919.619	−0.0695809
$560$	4523.46	0.341341
$561$	−95.1388	−0.00716000
$562$	−36797.2	−2.76192
$563$	19445.5	1.45565	0.727824	−	0.685764i	$-0.240532\pi$
$563$	19445.5	1.45565	0.727824	+	0.685764i	$0.240532\pi$
$564$	15794.9	1.17923
$565$	4822.70	0.359102
$566$	4321.24	0.320911
$567$	2211.11	0.163771
$568$	68342.2	5.04855
$569$	−14955.4	−1.10187	−0.550935	−	0.834548i	$-0.685729\pi$
$569$	−14955.4	−1.10187	−0.550935	+	0.834548i	$0.685729\pi$
$570$	−2106.19	−0.154769
$571$	−25453.0	−1.86545	−0.932727	−	0.360582i	$-0.882578\pi$
$571$	−25453.0	−1.86545	−0.932727	+	0.360582i	$0.882578\pi$
$572$	3048.75	0.222858
$573$	−933.050	−0.0680257
$574$	−4143.61	−0.301308
$575$	6784.32	0.492045
$576$	−40069.2	−2.89853
$577$	19316.8	1.39371	0.696855	−	0.717212i	$-0.254582\pi$
$577$	19316.8	1.39371	0.696855	+	0.717212i	$0.254582\pi$
$578$	−26315.0	−1.89371
$579$	4786.08	0.343528
$580$	10392.3	0.743991
$581$	−4707.40	−0.336137
$582$	6061.26	0.431696
$583$	−7227.21	−0.513414
$584$	66289.7	4.69707
$585$	1909.02	0.134920
$586$	−12409.1	−0.874770
$587$	−1285.50	−0.0903890	−0.0451945	−	0.998978i	$-0.514391\pi$
$587$	−1285.50	−0.0903890	−0.0451945	+	0.998978i	$0.514391\pi$
$588$	8350.33	0.585649
$589$	−5601.26	−0.391844
$590$	−9001.83	−0.628135
$591$	1634.74	0.113780
$592$	−10835.5	−0.752256
$593$	−15481.3	−1.07207	−0.536037	−	0.844194i	$-0.680079\pi$
$593$	−15481.3	−1.07207	−0.536037	+	0.844194i	$0.680079\pi$
$594$	−3716.18	−0.256695
$595$	−149.918	−0.0103295
$596$	58733.9	4.03664
$597$	1730.94	0.118665
$598$	5186.59	0.354674
$599$	−18057.2	−1.23172	−0.615858	−	0.787857i	$-0.711190\pi$
$599$	−18057.2	−1.23172	−0.615858	+	0.787857i	$0.711190\pi$
$600$	7878.27	0.536048
$601$	−3083.99	−0.209315	−0.104658	−	0.994508i	$-0.533375\pi$
$601$	−3083.99	−0.209315	−0.104658	+	0.994508i	$0.533375\pi$
$602$	1372.72	0.0929364
$603$	−22180.8	−1.49796
$604$	−50002.8	−3.36852
$605$	694.284	0.0466556
$606$	−7861.57	−0.526988
$607$	24394.1	1.63118	0.815589	−	0.578632i	$-0.196413\pi$
$607$	24394.1	1.63118	0.815589	+	0.578632i	$0.196413\pi$
$608$	35094.7	2.34092
$609$	−361.163	−0.0240313
$610$	1259.32	0.0835874
$611$	8118.53	0.537546
$612$	3978.04	0.262750
$613$	2912.38	0.191892	0.0959461	−	0.995387i	$-0.469412\pi$
$613$	2912.38	0.191892	0.0959461	+	0.995387i	$0.469412\pi$
$614$	−25758.7	−1.69306
$615$	1453.49	0.0953013
$616$	−2843.23	−0.185969
$617$	19235.4	1.25508	0.627542	−	0.778583i	$-0.284061\pi$
$617$	19235.4	1.25508	0.627542	+	0.778583i	$0.284061\pi$
$618$	1486.47	0.0967550
$619$	−20306.1	−1.31853	−0.659265	−	0.751911i	$-0.729132\pi$
$619$	−20306.1	−1.31853	−0.659265	+	0.751911i	$0.729132\pi$
$620$	−11991.0	−0.776729
$621$	−4597.05	−0.297058
$622$	−42129.9	−2.71584
$623$	3842.21	0.247087
$624$	3392.54	0.217645
$625$	4362.70	0.279213
$626$	44314.0	2.82930
$627$	745.687	0.0474958
$628$	−9000.09	−0.571883
$629$	359.113	0.0227644
$630$	−2849.60	−0.180208
$631$	14435.5	0.910729	0.455364	−	0.890305i	$-0.349509\pi$
$631$	14435.5	0.910729	0.455364	+	0.890305i	$0.349509\pi$
$632$	−4041.72	−0.254384
$633$	−5872.01	−0.368707
$634$	48282.5	3.02452
$635$	10449.1	0.653006
$636$	−16617.3	−1.03604
$637$	4292.04	0.266965
$638$	−5059.95	−0.313989
$639$	−24250.5	−1.50131
$640$	20452.5	1.26321
$641$	17669.2	1.08876	0.544378	−	0.838840i	$-0.316766\pi$
$641$	17669.2	1.08876	0.544378	+	0.838840i	$0.316766\pi$
$642$	−1137.55	−0.0699309
$643$	8929.43	0.547655	0.273828	−	0.961779i	$-0.411710\pi$
$643$	8929.43	0.547655	0.273828	+	0.961779i	$0.411710\pi$
$644$	−5629.60	−0.344468
$645$	−481.519	−0.0293950
$646$	−2255.88	−0.137394
$647$	20460.3	1.24324	0.621619	−	0.783319i	$-0.286475\pi$
$647$	20460.3	1.24324	0.621619	+	0.783319i	$0.286475\pi$
$648$	44500.0	2.69773
$649$	3187.06	0.192763
$650$	6481.49	0.391115
$651$	416.726	0.0250888
$652$	27320.1	1.64101
$653$	−9943.60	−0.595901	−0.297950	−	0.954581i	$-0.596303\pi$
$653$	−9943.60	−0.595901	−0.297950	+	0.954581i	$0.596303\pi$
$654$	−4687.12	−0.280246
$655$	2363.72	0.141005
$656$	−46972.8	−2.79570
$657$	−23522.2	−1.39679
$658$	−12118.5	−0.717978
$659$	−29671.5	−1.75393	−0.876963	−	0.480557i	$-0.840434\pi$
$659$	−29671.5	−1.75393	−0.876963	+	0.480557i	$0.840434\pi$
$660$	1596.35	0.0941482
$661$	−6601.14	−0.388434	−0.194217	−	0.980959i	$-0.562217\pi$
$661$	−6601.14	−0.388434	−0.194217	+	0.980959i	$0.562217\pi$
$662$	1319.95	0.0774945
$663$	−112.437	−0.00658624
$664$	−94739.4	−5.53705
$665$	1175.04	0.0685205
$666$	6825.92	0.397146
$667$	−6259.34	−0.363362
$668$	13016.3	0.753915
$669$	−2211.89	−0.127828
$670$	26927.4	1.55268
$671$	−445.856	−0.0256514
$672$	−2611.00	−0.149883
$673$	12079.9	0.691895	0.345947	−	0.938254i	$-0.387558\pi$
$673$	12079.9	0.691895	0.345947	+	0.938254i	$0.387558\pi$
$674$	−24972.5	−1.42716
$675$	−5744.76	−0.327579
$676$	3603.07	0.204999
$677$	−21903.7	−1.24347	−0.621734	−	0.783228i	$-0.713572\pi$
$677$	−21903.7	−1.24347	−0.621734	+	0.783228i	$0.713572\pi$
$678$	−5399.05	−0.305825
$679$	−3381.57	−0.191123
$680$	−3017.20	−0.170153
$681$	5826.55	0.327862
$682$	5838.39	0.327806
$683$	−171.190	−0.00959062	−0.00479531	−	0.999989i	$-0.501526\pi$
$683$	−171.190	−0.00959062	−0.00479531	+	0.999989i	$0.501526\pi$
$684$	−31179.5	−1.74295
$685$	−142.197	−0.00793146
$686$	−13062.7	−0.727020
$687$	6453.18	0.358376
$688$	15561.4	0.862316
$689$	−8541.25	−0.472272
$690$	2715.73	0.149835
$691$	29459.5	1.62184	0.810921	−	0.585156i	$-0.198967\pi$
$691$	29459.5	1.62184	0.810921	+	0.585156i	$0.198967\pi$
$692$	38607.2	2.12084
$693$	1008.89	0.0553023
$694$	−20340.9	−1.11258
$695$	−11882.2	−0.648513
$696$	−7268.63	−0.395858
$697$	1556.79	0.0846021
$698$	−3385.37	−0.183579
$699$	7923.70	0.428758
$700$	−7035.10	−0.379860
$701$	−15584.6	−0.839691	−0.419845	−	0.907596i	$-0.637916\pi$
$701$	−15584.6	−0.839691	−0.419845	+	0.907596i	$0.637916\pi$
$702$	−4391.85	−0.236125
$703$	−2814.69	−0.151007
$704$	−17222.2	−0.921996
$705$	4250.92	0.227091
$706$	1890.46	0.100777
$707$	4385.97	0.233311
$708$	7327.92	0.388983
$709$	−1601.65	−0.0848393	−0.0424196	−	0.999100i	$-0.513507\pi$
$709$	−1601.65	−0.0848393	−0.0424196	+	0.999100i	$0.513507\pi$
$710$	29440.1	1.55615
$711$	1434.16	0.0756473
$712$	77327.0	4.07016
$713$	7222.30	0.379351
$714$	167.834	0.00879698
$715$	820.518	0.0429170
$716$	−50812.4	−2.65217
$717$	5753.75	0.299690
$718$	−51853.5	−2.69520
$719$	−20345.2	−1.05528	−0.527640	−	0.849468i	$-0.676923\pi$
$719$	−20345.2	−1.05528	−0.527640	+	0.849468i	$0.676923\pi$
$720$	−32303.7	−1.67206
$721$	−829.301	−0.0428360
$722$	−19458.7	−1.00302
$723$	−8652.77	−0.445090
$724$	84085.4	4.31631
$725$	−7822.06	−0.400695
$726$	−777.256	−0.0397337
$727$	56.9580	0.00290571	0.00145286	−	0.999999i	$-0.499538\pi$
$727$	56.9580	0.00290571	0.00145286	+	0.999999i	$0.499538\pi$
$728$	−3360.18	−0.171066
$729$	−13792.0	−0.700704
$730$	28555.9	1.44781
$731$	−515.742	−0.0260949
$732$	−1025.15	−0.0517629
$733$	10912.4	0.549876	0.274938	−	0.961462i	$-0.411343\pi$
$733$	10912.4	0.549876	0.274938	+	0.961462i	$0.411343\pi$
$734$	−19261.0	−0.968578
$735$	2247.34	0.112782
$736$	−45251.3	−2.26629
$737$	−9533.52	−0.476488
$738$	29591.0	1.47596
$739$	17979.6	0.894981	0.447490	−	0.894289i	$-0.352318\pi$
$739$	17979.6	0.894981	0.447490	+	0.894289i	$0.352318\pi$
$740$	−6025.62	−0.299333
$741$	881.267	0.0436898
$742$	12749.5	0.630795
$743$	10755.8	0.531078	0.265539	−	0.964100i	$-0.414450\pi$
$743$	10755.8	0.531078	0.265539	+	0.964100i	$0.414450\pi$
$744$	8386.87	0.413277
$745$	15807.2	0.777357
$746$	15483.8	0.759922
$747$	33617.2	1.64657
$748$	1709.80	0.0835784
$749$	634.641	0.0309603
$750$	8000.99	0.389540
$751$	−18138.2	−0.881323	−0.440661	−	0.897673i	$-0.645256\pi$
$751$	−18138.2	−0.881323	−0.440661	+	0.897673i	$0.645256\pi$
$752$	−137378.	−6.66180
$753$	5980.29	0.289421
$754$	−5979.94	−0.288828
$755$	−13457.4	−0.648694
$756$	4766.98	0.229330
$757$	−1918.52	−0.0921133	−0.0460566	−	0.998939i	$-0.514665\pi$
$757$	−1918.52	−0.0921133	−0.0460566	+	0.998939i	$0.514665\pi$
$758$	35900.7	1.72028
$759$	−961.494	−0.0459816
$760$	23648.5	1.12871
$761$	10828.3	0.515804	0.257902	−	0.966171i	$-0.416969\pi$
$761$	10828.3	0.515804	0.257902	+	0.966171i	$0.416969\pi$
$762$	−11697.8	−0.556125
$763$	2614.94	0.124072
$764$	16768.5	0.794061
$765$	1070.62	0.0505991
$766$	−13674.4	−0.645007
$767$	3766.52	0.177316
$768$	−8038.00	−0.377664
$769$	−30126.8	−1.41274	−0.706372	−	0.707841i	$-0.749669\pi$
$769$	−30126.8	−1.41274	−0.706372	+	0.707841i	$0.749669\pi$
$770$	−1224.79	−0.0573224
$771$	−798.211	−0.0372852
$772$	−86013.9	−4.00998
$773$	−15799.9	−0.735167	−0.367583	−	0.929991i	$-0.619815\pi$
$773$	−15799.9	−0.735167	−0.367583	+	0.929991i	$0.619815\pi$
$774$	−9803.07	−0.455251
$775$	9025.45	0.418327
$776$	−68056.3	−3.14830
$777$	209.409	0.00966861
$778$	43856.3	2.02098
$779$	−12202.0	−0.561207
$780$	1886.59	0.0866037
$781$	−10423.1	−0.477553
$782$	2908.75	0.133014
$783$	5300.22	0.241909
$784$	−72628.1	−3.30850
$785$	−2422.21	−0.110131
$786$	−2646.20	−0.120085
$787$	27005.9	1.22320	0.611600	−	0.791167i	$-0.290526\pi$
$787$	27005.9	1.22320	0.611600	+	0.791167i	$0.290526\pi$
$788$	−29379.0	−1.32815
$789$	5104.01	0.230301
$790$	−1741.07	−0.0784106
$791$	3012.13	0.135397
$792$	20304.5	0.910971
$793$	−526.921	−0.0235959
$794$	35406.0	1.58251
$795$	−4472.26	−0.199515
$796$	−31108.0	−1.38517
$797$	39693.4	1.76413	0.882067	−	0.471125i	$-0.156152\pi$
$797$	39693.4	1.76413	0.882067	+	0.471125i	$0.156152\pi$
$798$	−1315.47	−0.0583547
$799$	4553.04	0.201596
$800$	−56548.9	−2.49913
$801$	−27438.6	−1.21036
$802$	70206.9	3.09114
$803$	−10110.1	−0.444305
$804$	−21920.2	−0.961523
$805$	−1515.11	−0.0663360
$806$	6899.92	0.301538
$807$	715.744	0.0312210
$808$	88270.3	3.84324
$809$	32848.6	1.42756	0.713779	−	0.700371i	$-0.246982\pi$
$809$	32848.6	1.42756	0.713779	+	0.700371i	$0.246982\pi$
$810$	19169.5	0.831538
$811$	−11904.1	−0.515425	−0.257712	−	0.966222i	$-0.582969\pi$
$811$	−11904.1	−0.515425	−0.257712	+	0.966222i	$0.582969\pi$
$812$	6490.71	0.280516
$813$	−5452.30	−0.235204
$814$	2933.85	0.126329
$815$	7352.72	0.316018
$816$	1902.61	0.0816232
$817$	4042.33	0.173101
$818$	59011.1	2.52234
$819$	1192.32	0.0508707
$820$	−26121.7	−1.11245
$821$	8859.38	0.376607	0.188304	−	0.982111i	$-0.439701\pi$
$821$	8859.38	0.376607	0.188304	+	0.982111i	$0.439701\pi$
$822$	159.190	0.00675473
$823$	1431.94	0.0606493	0.0303246	−	0.999540i	$-0.490346\pi$
$823$	1431.94	0.0606493	0.0303246	+	0.999540i	$0.490346\pi$
$824$	−16690.2	−0.705620
$825$	−1201.54	−0.0507059
$826$	−5622.29	−0.236834
$827$	−34746.9	−1.46103	−0.730513	−	0.682898i	$-0.760719\pi$
$827$	−34746.9	−1.46103	−0.730513	+	0.682898i	$0.760719\pi$
$828$	40203.0	1.68738
$829$	−22909.0	−0.959786	−0.479893	−	0.877327i	$-0.659324\pi$
$829$	−22909.0	−0.959786	−0.479893	+	0.877327i	$0.659324\pi$
$830$	−40811.3	−1.70672
$831$	−4273.50	−0.178395
$832$	−20353.5	−0.848113
$833$	2407.07	0.100120
$834$	13302.2	0.552298
$835$	3503.10	0.145185
$836$	−13401.3	−0.554417
$837$	−6115.63	−0.252553
$838$	−40088.3	−1.65254
$839$	−5564.10	−0.228956	−0.114478	−	0.993426i	$-0.536520\pi$
$839$	−5564.10	−0.228956	−0.114478	+	0.993426i	$0.536520\pi$
$840$	−1759.41	−0.0722684
$841$	−17172.2	−0.704097
$842$	−26177.0	−1.07140
$843$	8061.77	0.329374
$844$	105530.	4.30390
$845$	969.703	0.0394779
$846$	86542.9	3.51703
$847$	433.631	0.0175912
$848$	144531.	5.85287
$849$	−946.726	−0.0382704
$850$	3634.95	0.146680
$851$	3629.28	0.146193
$852$	−23965.6	−0.963671
$853$	−32871.0	−1.31944	−0.659719	−	0.751513i	$-0.729325\pi$
$853$	−32871.0	−1.31944	−0.659719	+	0.751513i	$0.729325\pi$
$854$	786.536	0.0315160
$855$	−8391.40	−0.335649
$856$	12772.5	0.509996
$857$	8739.62	0.348354	0.174177	−	0.984714i	$-0.444273\pi$
$857$	8739.62	0.348354	0.174177	+	0.984714i	$0.444273\pi$
$858$	−918.575	−0.0365497
$859$	25202.4	1.00104	0.500522	−	0.865724i	$-0.333142\pi$
$859$	25202.4	1.00104	0.500522	+	0.865724i	$0.333142\pi$
$860$	8653.72	0.343127
$861$	907.808	0.0359327
$862$	40169.4	1.58721
$863$	17282.4	0.681693	0.340847	−	0.940119i	$-0.389286\pi$
$863$	17282.4	0.681693	0.340847	+	0.940119i	$0.389286\pi$
$864$	38317.5	1.50878
$865$	10390.4	0.408422
$866$	31886.9	1.25123
$867$	5765.27	0.225835
$868$	−7489.27	−0.292860
$869$	616.417	0.0240627
$870$	−3131.14	−0.122018
$871$	−11266.9	−0.438305
$872$	52627.3	2.04379
$873$	24149.0	0.936221
$874$	−22798.4	−0.882344
$875$	−4463.75	−0.172460
$876$	−23245.9	−0.896580
$877$	4234.10	0.163028	0.0815138	−	0.996672i	$-0.474025\pi$
$877$	4234.10	0.163028	0.0815138	+	0.996672i	$0.474025\pi$
$878$	4119.84	0.158357
$879$	2718.67	0.104321
$880$	−13884.5	−0.531869
$881$	−1542.44	−0.0589855	−0.0294928	−	0.999565i	$-0.509389\pi$
$881$	−1542.44	−0.0589855	−0.0294928	+	0.999565i	$0.509389\pi$
$882$	45752.8	1.74669
$883$	35944.4	1.36990	0.684951	−	0.728589i	$-0.259823\pi$
$883$	35944.4	1.36990	0.684951	+	0.728589i	$0.259823\pi$
$884$	2020.68	0.0768809
$885$	1972.18	0.0749086
$886$	10034.0	0.380471
$887$	13531.7	0.512232	0.256116	−	0.966646i	$-0.417557\pi$
$887$	13531.7	0.512232	0.256116	+	0.966646i	$0.417557\pi$
$888$	4214.49	0.159267
$889$	6526.20	0.246211
$890$	33310.4	1.25457
$891$	−6786.86	−0.255183
$892$	39751.4	1.49213
$893$	−35686.2	−1.33728
$894$	−17696.3	−0.662027
$895$	−13675.3	−0.510742
$896$	12774.1	0.476286
$897$	−1136.31	−0.0422969
$898$	61052.8	2.26877
$899$	−8327.04	−0.308924
$900$	50240.2	1.86075
$901$	−4790.11	−0.177116
$902$	12718.5	0.469491
$903$	−300.743	−0.0110832
$904$	60621.0	2.23033
$905$	22630.1	0.831215
$906$	15065.6	0.552452
$907$	12684.2	0.464356	0.232178	−	0.972673i	$-0.425415\pi$
$907$	12684.2	0.464356	0.232178	+	0.972673i	$0.425415\pi$
$908$	−104713.	−3.82712
$909$	−31321.8	−1.14288
$910$	−1447.48	−0.0527290
$911$	20863.9	0.758782	0.379391	−	0.925236i	$-0.376133\pi$
$911$	20863.9	0.758782	0.379391	+	0.925236i	$0.376133\pi$
$912$	−14912.4	−0.541447
$913$	14449.0	0.523761
$914$	83280.0	3.01385
$915$	−275.900	−0.00996827
$916$	−115975.	−4.18330
$917$	1476.32	0.0531649
$918$	−2463.04	−0.0885539
$919$	−22461.0	−0.806224	−0.403112	−	0.915151i	$-0.632071\pi$
$919$	−22461.0	−0.806224	−0.403112	+	0.915151i	$0.632071\pi$
$920$	−30492.5	−1.09272
$921$	5643.38	0.201906
$922$	−48635.3	−1.73722
$923$	−12318.2	−0.439285
$924$	997.035	0.0354979
$925$	4535.38	0.161213
$926$	2818.57	0.100026
$927$	5922.34	0.209833
$928$	52173.1	1.84554
$929$	38102.6	1.34565	0.672823	−	0.739804i	$-0.265082\pi$
$929$	38102.6	1.34565	0.672823	+	0.739804i	$0.265082\pi$
$930$	3612.85	0.127387
$931$	−18866.3	−0.664145
$932$	−142402.	−5.00488
$933$	9230.09	0.323880
$934$	−28059.1	−0.982999
$935$	460.164	0.0160951
$936$	23996.2	0.837972
$937$	7054.62	0.245960	0.122980	−	0.992409i	$-0.460755\pi$
$937$	7054.62	0.245960	0.122980	+	0.992409i	$0.460755\pi$
$938$	16818.1	0.585427
$939$	−9708.60	−0.337410
$940$	−76396.2	−2.65082
$941$	25287.4	0.876031	0.438015	−	0.898968i	$-0.355682\pi$
$941$	25287.4	0.876031	0.438015	+	0.898968i	$0.355682\pi$
$942$	2711.68	0.0937914
$943$	15733.3	0.543315
$944$	−63735.5	−2.19747
$945$	1282.95	0.0441633
$946$	−4213.46	−0.144811
$947$	−1273.65	−0.0437043	−0.0218521	−	0.999761i	$-0.506956\pi$
$947$	−1273.65	−0.0437043	−0.0218521	+	0.999761i	$0.506956\pi$
$948$	1417.31	0.0485571
$949$	−11948.3	−0.408702
$950$	−28490.4	−0.973000
$951$	−10578.0	−0.360690
$952$	−1884.46	−0.0641550
$953$	−18550.8	−0.630556	−0.315278	−	0.948999i	$-0.602098\pi$
$953$	−18550.8	−0.630556	−0.315278	+	0.948999i	$0.602098\pi$
$954$	−91049.0	−3.08996
$955$	4512.94	0.152917
$956$	−103405.	−3.49827
$957$	1108.57	0.0374450
$958$	−79224.0	−2.67183
$959$	−88.8120	−0.00299050
$960$	−10657.2	−0.358292
$961$	−20182.9	−0.677483
$962$	3467.28	0.116205
$963$	−4532.20	−0.151659
$964$	155505.	5.19551
$965$	−23149.1	−0.772224
$966$	1696.17	0.0564942
$967$	−34324.8	−1.14148	−0.570740	−	0.821131i	$-0.693343\pi$
$967$	−34324.8	−1.14148	−0.570740	+	0.821131i	$0.693343\pi$
$968$	8727.09	0.289772
$969$	494.233	0.0163850
$970$	−29316.9	−0.970420
$971$	4974.61	0.164411	0.0822054	−	0.996615i	$-0.473804\pi$
$971$	4974.61	0.164411	0.0822054	+	0.996615i	$0.473804\pi$
$972$	−51519.5	−1.70009
$973$	−7421.28	−0.244517
$974$	115626.	3.80381
$975$	−1420.01	−0.0466426
$976$	8916.34	0.292423
$977$	−53426.2	−1.74949	−0.874747	−	0.484580i	$-0.838972\pi$
$977$	−53426.2	−1.74949	−0.874747	+	0.484580i	$0.838972\pi$
$978$	−8231.42	−0.269133
$979$	−11793.4	−0.385004
$980$	−40388.6	−1.31650
$981$	−18674.2	−0.607771
$982$	4264.56	0.138582
$983$	54152.3	1.75706	0.878531	−	0.477686i	$-0.158524\pi$
$983$	54152.3	1.75706	0.878531	+	0.477686i	$0.158524\pi$
$984$	18270.2	0.591904
$985$	−7906.83	−0.255769
$986$	−3353.67	−0.108319
$987$	2655.01	0.0856229
$988$	−15837.9	−0.509989
$989$	−5212.20	−0.167582
$990$	8746.65	0.280795
$991$	51906.5	1.66384	0.831919	−	0.554897i	$-0.187243\pi$
$991$	51906.5	1.66384	0.831919	+	0.554897i	$0.187243\pi$
$992$	−60199.6	−1.92675
$993$	−289.183	−0.00924165
$994$	18387.4	0.586735
$995$	−8372.15	−0.266749
$996$	33222.3	1.05692
$997$	5067.74	0.160980	0.0804899	−	0.996755i	$-0.474352\pi$
$997$	5067.74	0.160980	0.0804899	+	0.996755i	$0.474352\pi$
$998$	104341.	3.30947
$999$	−3073.17	−0.0973281

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	143.4.a.c.1.9	✓	9
3.2	odd	2		1287.4.a.k.1.1		9
4.3	odd	2		2288.4.a.r.1.6		9
11.10	odd	2		1573.4.a.e.1.1		9
13.12	even	2		1859.4.a.d.1.1		9

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
143.4.a.c.1.9	✓	9	1.1	even	1	trivial
1287.4.a.k.1.1		9	3.2	odd	2
1573.4.a.e.1.1		9	11.10	odd	2
1859.4.a.d.1.1		9	13.12	even	2
2288.4.a.r.1.6		9	4.3	odd	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:	\( N \)	\(=\)	\( 143 = 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	143.a (trivial)

\(f(q)\)	\(=\)	\(q+5.41479 q^{2} -1.18631 q^{3} +21.3199 q^{4} +5.73789 q^{5} -6.42360 q^{6} +3.58372 q^{7} +72.1247 q^{8} -25.5927 q^{9} +O(q^{10})\)	\(q+5.41479 q^{2} -1.18631 q^{3} +21.3199 q^{4} +5.73789 q^{5} -6.42360 q^{6} +3.58372 q^{7} +72.1247 q^{8} -25.5927 q^{9} +31.0694 q^{10} -11.0000 q^{11} -25.2920 q^{12} -13.0000 q^{13} +19.4051 q^{14} -6.80689 q^{15} +219.981 q^{16} -7.29067 q^{17} -138.579 q^{18} +57.1435 q^{19} +122.331 q^{20} -4.25140 q^{21} -59.5627 q^{22} -73.6812 q^{23} -85.5620 q^{24} -92.0767 q^{25} -70.3923 q^{26} +62.3911 q^{27} +76.4048 q^{28} +84.9516 q^{29} -36.8579 q^{30} -98.0210 q^{31} +614.151 q^{32} +13.0494 q^{33} -39.4775 q^{34} +20.5630 q^{35} -545.634 q^{36} -49.2566 q^{37} +309.420 q^{38} +15.4220 q^{39} +413.843 q^{40} -213.532 q^{41} -23.0204 q^{42} +70.7399 q^{43} -234.519 q^{44} -146.848 q^{45} -398.968 q^{46} -624.502 q^{47} -260.964 q^{48} -330.157 q^{49} -498.576 q^{50} +8.64898 q^{51} -277.159 q^{52} +657.019 q^{53} +337.834 q^{54} -63.1167 q^{55} +258.475 q^{56} -67.7897 q^{57} +459.995 q^{58} -289.733 q^{59} -145.123 q^{60} +40.5324 q^{61} -530.763 q^{62} -91.7171 q^{63} +1565.65 q^{64} -74.5925 q^{65} +70.6596 q^{66} +866.684 q^{67} -155.437 q^{68} +87.4085 q^{69} +111.344 q^{70} +947.557 q^{71} -1845.86 q^{72} +919.099 q^{73} -266.714 q^{74} +109.231 q^{75} +1218.30 q^{76} -39.4210 q^{77} +83.5068 q^{78} -56.0379 q^{79} +1262.22 q^{80} +616.987 q^{81} -1156.23 q^{82} -1313.55 q^{83} -90.6395 q^{84} -41.8331 q^{85} +383.042 q^{86} -100.779 q^{87} -793.372 q^{88} +1072.13 q^{89} -795.150 q^{90} -46.5884 q^{91} -1570.88 q^{92} +116.283 q^{93} -3381.55 q^{94} +327.883 q^{95} -728.571 q^{96} -943.591 q^{97} -1787.73 q^{98} +281.519 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 9 q + 8 q^{3} + 46 q^{4} + 30 q^{5} + 34 q^{6} + 25 q^{7} + 36 q^{8} + 91 q^{9}+O(q^{10}) \) 9 * q + 8 * q^3 + 46 * q^4 + 30 * q^5 + 34 * q^6 + 25 * q^7 + 36 * q^8 + 91 * q^9	\( 9 q + 8 q^{3} + 46 q^{4} + 30 q^{5} + 34 q^{6} + 25 q^{7} + 36 q^{8} + 91 q^{9} - 22 q^{10} - 99 q^{11} + 181 q^{12} - 117 q^{13} + 351 q^{15} + 130 q^{16} + 53 q^{17} + 33 q^{18} + 69 q^{19} + 282 q^{20} + 463 q^{21} + 216 q^{23} - 121 q^{24} + 617 q^{25} + 275 q^{27} + 279 q^{28} - 91 q^{29} + 29 q^{30} + 636 q^{31} + 663 q^{32} - 88 q^{33} + 423 q^{34} - 358 q^{35} - 252 q^{36} + 967 q^{37} - 101 q^{38} - 104 q^{39} + 652 q^{40} - 226 q^{41} - 1186 q^{42} + 42 q^{43} - 506 q^{44} + 5 q^{45} - 1127 q^{46} - 269 q^{47} - 1820 q^{48} + 228 q^{49} - 1374 q^{50} - 589 q^{51} - 598 q^{52} + 1227 q^{53} - 2438 q^{54} - 330 q^{55} - 659 q^{56} - 71 q^{57} + 471 q^{58} - 613 q^{59} - 859 q^{60} + 427 q^{61} - 1714 q^{62} + 305 q^{63} - 1194 q^{64} - 390 q^{65} - 374 q^{66} - 271 q^{67} - 2835 q^{68} - 846 q^{69} - 102 q^{70} + 2279 q^{71} - 2400 q^{72} + 3602 q^{73} - 4955 q^{74} - 883 q^{75} + 1126 q^{76} - 275 q^{77} - 442 q^{78} - 1182 q^{79} - 2360 q^{80} + 2697 q^{81} + 1007 q^{82} - 1877 q^{83} + 1618 q^{84} - 441 q^{85} + 830 q^{86} + 1942 q^{87} - 396 q^{88} + 1258 q^{89} - 5669 q^{90} - 325 q^{91} + 1046 q^{92} + 1556 q^{93} + 1439 q^{94} + 2032 q^{95} - 3417 q^{96} + 4002 q^{97} - 1855 q^{98} - 1001 q^{99}+O(q^{100}) \) 9 * q + 8 * q^3 + 46 * q^4 + 30 * q^5 + 34 * q^6 + 25 * q^7 + 36 * q^8 + 91 * q^9 - 22 * q^10 - 99 * q^11 + 181 * q^12 - 117 * q^13 + 351 * q^15 + 130 * q^16 + 53 * q^17 + 33 * q^18 + 69 * q^19 + 282 * q^20 + 463 * q^21 + 216 * q^23 - 121 * q^24 + 617 * q^25 + 275 * q^27 + 279 * q^28 - 91 * q^29 + 29 * q^30 + 636 * q^31 + 663 * q^32 - 88 * q^33 + 423 * q^34 - 358 * q^35 - 252 * q^36 + 967 * q^37 - 101 * q^38 - 104 * q^39 + 652 * q^40 - 226 * q^41 - 1186 * q^42 + 42 * q^43 - 506 * q^44 + 5 * q^45 - 1127 * q^46 - 269 * q^47 - 1820 * q^48 + 228 * q^49 - 1374 * q^50 - 589 * q^51 - 598 * q^52 + 1227 * q^53 - 2438 * q^54 - 330 * q^55 - 659 * q^56 - 71 * q^57 + 471 * q^58 - 613 * q^59 - 859 * q^60 + 427 * q^61 - 1714 * q^62 + 305 * q^63 - 1194 * q^64 - 390 * q^65 - 374 * q^66 - 271 * q^67 - 2835 * q^68 - 846 * q^69 - 102 * q^70 + 2279 * q^71 - 2400 * q^72 + 3602 * q^73 - 4955 * q^74 - 883 * q^75 + 1126 * q^76 - 275 * q^77 - 442 * q^78 - 1182 * q^79 - 2360 * q^80 + 2697 * q^81 + 1007 * q^82 - 1877 * q^83 + 1618 * q^84 - 441 * q^85 + 830 * q^86 + 1942 * q^87 - 396 * q^88 + 1258 * q^89 - 5669 * q^90 - 325 * q^91 + 1046 * q^92 + 1556 * q^93 + 1439 * q^94 + 2032 * q^95 - 3417 * q^96 + 4002 * q^97 - 1855 * q^98 - 1001 * q^99

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