LMFDB - Embedded newform 143.4.a.c.1.5

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			1.5
Root			$0.388321$ 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)

$f(q)$	$=$	$q+0.388321 q^{2} +3.09988 q^{3} -7.84921 q^{4} +16.8933 q^{5} +1.20375 q^{6} +26.1569 q^{7} -6.15457 q^{8} -17.3907 q^{9} +O(q^{10})$	\(q+0.388321 q^{2} +3.09988 q^{3} -7.84921 q^{4} +16.8933 q^{5} +1.20375 q^{6} +26.1569 q^{7} -6.15457 q^{8} -17.3907 q^{9} +6.56001 q^{10} -11.0000 q^{11} -24.3316 q^{12} -13.0000 q^{13} +10.1573 q^{14} +52.3671 q^{15} +60.4037 q^{16} +80.2409 q^{17} -6.75319 q^{18} +97.0754 q^{19} -132.599 q^{20} +81.0832 q^{21} -4.27153 q^{22} +173.956 q^{23} -19.0784 q^{24} +160.383 q^{25} -5.04817 q^{26} -137.606 q^{27} -205.311 q^{28} -40.5745 q^{29} +20.3352 q^{30} -234.483 q^{31} +72.6926 q^{32} -34.0987 q^{33} +31.1592 q^{34} +441.876 q^{35} +136.504 q^{36} -31.5992 q^{37} +37.6964 q^{38} -40.2984 q^{39} -103.971 q^{40} -447.194 q^{41} +31.4863 q^{42} -291.357 q^{43} +86.3413 q^{44} -293.787 q^{45} +67.5507 q^{46} +361.139 q^{47} +187.244 q^{48} +341.183 q^{49} +62.2801 q^{50} +248.737 q^{51} +102.040 q^{52} -313.121 q^{53} -53.4352 q^{54} -185.826 q^{55} -160.985 q^{56} +300.922 q^{57} -15.7559 q^{58} +27.1513 q^{59} -411.041 q^{60} +305.678 q^{61} -91.0544 q^{62} -454.888 q^{63} -455.002 q^{64} -219.613 q^{65} -13.2412 q^{66} -998.792 q^{67} -629.827 q^{68} +539.243 q^{69} +171.590 q^{70} +548.738 q^{71} +107.033 q^{72} -596.069 q^{73} -12.2706 q^{74} +497.168 q^{75} -761.965 q^{76} -287.726 q^{77} -15.6487 q^{78} -370.922 q^{79} +1020.42 q^{80} +42.9884 q^{81} -173.655 q^{82} -1383.29 q^{83} -636.439 q^{84} +1355.53 q^{85} -113.140 q^{86} -125.776 q^{87} +67.7003 q^{88} +928.836 q^{89} -114.084 q^{90} -340.040 q^{91} -1365.42 q^{92} -726.868 q^{93} +140.238 q^{94} +1639.92 q^{95} +225.338 q^{96} +1082.85 q^{97} +132.488 q^{98} +191.298 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	0.388321	0.137292	0.0686460	−	0.997641i	$-0.478132\pi$
$2$	0.388321	0.137292	0.0686460	+	0.997641i	$0.478132\pi$
$3$	3.09988	0.596572	0.298286	−	0.954477i	$-0.403585\pi$
$3$	3.09988	0.596572	0.298286	+	0.954477i	$0.403585\pi$
$4$	−7.84921	−0.981151
$5$	16.8933	1.51098	0.755491	−	0.655159i	$-0.227399\pi$
$5$	16.8933	1.51098	0.755491	+	0.655159i	$0.227399\pi$
$6$	1.20375	0.0819046
$7$	26.1569	1.41234	0.706170	−	0.708042i	$-0.250422\pi$
$7$	26.1569	1.41234	0.706170	+	0.708042i	$0.250422\pi$
$8$	−6.15457	−0.271996
$9$	−17.3907	−0.644102
$10$	6.56001	0.207446
$11$	−11.0000	−0.301511
$11$	−11.0000	−0.301511
$12$	−24.3316	−0.585327
$13$	−13.0000	−0.277350
$13$	−13.0000	−0.277350
$14$	10.1573	0.193903
$15$	52.3671	0.901409
$16$	60.4037	0.943808
$17$	80.2409	1.14478	0.572390	−	0.819981i	$-0.306016\pi$
$17$	80.2409	1.14478	0.572390	+	0.819981i	$0.306016\pi$
$18$	−6.75319	−0.0884301
$19$	97.0754	1.17214	0.586069	−	0.810261i	$-0.300675\pi$
$19$	97.0754	1.17214	0.586069	+	0.810261i	$0.300675\pi$
$20$	−132.599	−1.48250
$21$	81.0832	0.842562
$22$	−4.27153	−0.0413951
$23$	173.956	1.57706	0.788529	−	0.614997i	$-0.210843\pi$
$23$	173.956	1.57706	0.788529	+	0.614997i	$0.210843\pi$
$24$	−19.0784	−0.162265
$25$	160.383	1.28306
$26$	−5.04817	−0.0380780
$27$	−137.606	−0.980825
$28$	−205.311	−1.38572
$29$	−40.5745	−0.259810	−0.129905	−	0.991526i	$-0.541467\pi$
$29$	−40.5745	−0.259810	−0.129905	+	0.991526i	$0.541467\pi$
$30$	20.3352	0.123756
$31$	−234.483	−1.35853	−0.679263	−	0.733895i	$-0.737701\pi$
$31$	−234.483	−1.35853	−0.679263	+	0.733895i	$0.737701\pi$
$32$	72.6926	0.401574
$33$	−34.0987	−0.179873
$34$	31.1592	0.157169
$35$	441.876	2.13402
$36$	136.504	0.631961
$37$	−31.5992	−0.140402	−0.0702010	−	0.997533i	$-0.522364\pi$
$37$	−31.5992	−0.140402	−0.0702010	+	0.997533i	$0.522364\pi$
$38$	37.6964	0.160925
$39$	−40.2984	−0.165459
$40$	−103.971	−0.410981
$41$	−447.194	−1.70342	−0.851708	−	0.524017i	$-0.824433\pi$
$41$	−447.194	−1.70342	−0.851708	+	0.524017i	$0.824433\pi$
$42$	31.4863	0.115677
$43$	−291.357	−1.03329	−0.516646	−	0.856199i	$-0.672820\pi$
$43$	−291.357	−1.03329	−0.516646	+	0.856199i	$0.672820\pi$
$44$	86.3413	0.295828
$45$	−293.787	−0.973226
$46$	67.5507	0.216518
$47$	361.139	1.12080	0.560400	−	0.828222i	$-0.310647\pi$
$47$	361.139	1.12080	0.560400	+	0.828222i	$0.310647\pi$
$48$	187.244	0.563049
$49$	341.183	0.994703
$50$	62.2801	0.176155
$51$	248.737	0.682944
$52$	102.040	0.272122
$53$	−313.121	−0.811519	−0.405759	−	0.913980i	$-0.632993\pi$
$53$	−313.121	−0.811519	−0.405759	+	0.913980i	$0.632993\pi$
$54$	−53.4352	−0.134660
$55$	−185.826	−0.455578
$56$	−160.985	−0.384151
$57$	300.922	0.699265
$58$	−15.7559	−0.0356698
$59$	27.1513	0.0599118	0.0299559	−	0.999551i	$-0.490463\pi$
$59$	27.1513	0.0599118	0.0299559	+	0.999551i	$0.490463\pi$
$60$	−411.041	−0.884418
$61$	305.678	0.641608	0.320804	−	0.947146i	$-0.396047\pi$
$61$	305.678	0.641608	0.320804	+	0.947146i	$0.396047\pi$
$62$	−91.0544	−0.186515
$63$	−454.888	−0.909691
$64$	−455.002	−0.888675
$65$	−219.613	−0.419071
$66$	−13.2412	−0.0246952
$67$	−998.792	−1.82122	−0.910611	−	0.413264i	$-0.864389\pi$
$67$	−998.792	−1.82122	−0.910611	+	0.413264i	$0.864389\pi$
$68$	−629.827	−1.12320
$69$	539.243	0.940829
$70$	171.590	0.292984
$71$	548.738	0.917228	0.458614	−	0.888636i	$-0.348346\pi$
$71$	548.738	0.917228	0.458614	+	0.888636i	$0.348346\pi$
$72$	107.033	0.175193
$73$	−596.069	−0.955680	−0.477840	−	0.878447i	$-0.658580\pi$
$73$	−596.069	−0.955680	−0.477840	+	0.878447i	$0.658580\pi$
$74$	−12.2706	−0.0192761
$75$	497.168	0.765441
$76$	−761.965	−1.15004
$77$	−287.726	−0.425836
$78$	−15.6487	−0.0227163
$79$	−370.922	−0.528254	−0.264127	−	0.964488i	$-0.585084\pi$
$79$	−370.922	−0.528254	−0.264127	+	0.964488i	$0.585084\pi$
$80$	1020.42	1.42608
$81$	42.9884	0.0589689
$82$	−173.655	−0.233865
$83$	−1383.29	−1.82934	−0.914671	−	0.404198i	$-0.867551\pi$
$83$	−1383.29	−1.82934	−0.914671	+	0.404198i	$0.867551\pi$
$84$	−636.439	−0.826681
$85$	1355.53	1.72974
$86$	−113.140	−0.141863
$87$	−125.776	−0.154995
$88$	67.7003	0.0820100
$89$	928.836	1.10625	0.553126	−	0.833098i	$-0.313435\pi$
$89$	928.836	1.10625	0.553126	+	0.833098i	$0.313435\pi$
$90$	−114.084	−0.133616
$91$	−340.040	−0.391713
$92$	−1365.42	−1.54733
$93$	−726.868	−0.810459
$94$	140.238	0.153877
$95$	1639.92	1.77108
$96$	225.338	0.239568
$97$	1082.85	1.13348	0.566738	−	0.823898i	$-0.308205\pi$
$97$	1082.85	1.13348	0.566738	+	0.823898i	$0.308205\pi$
$98$	132.488	0.136565
$99$	191.298	0.194204
$100$	−1258.88	−1.25888
$101$	143.629	0.141501	0.0707507	−	0.997494i	$-0.477461\pi$
$101$	143.629	0.141501	0.0707507	+	0.997494i	$0.477461\pi$
$102$	96.5897	0.0937628
$103$	1055.62	1.00984	0.504920	−	0.863166i	$-0.331522\pi$
$103$	1055.62	1.00984	0.504920	+	0.863166i	$0.331522\pi$
$104$	80.0095	0.0754382
$105$	1369.76	1.27310
$106$	−121.591	−0.111415
$107$	−1507.85	−1.36233	−0.681166	−	0.732129i	$-0.738527\pi$
$107$	−1507.85	−1.36233	−0.681166	+	0.732129i	$0.738527\pi$
$108$	1080.10	0.962337
$109$	40.3152	0.0354266	0.0177133	−	0.999843i	$-0.494361\pi$
$109$	40.3152	0.0354266	0.0177133	+	0.999843i	$0.494361\pi$
$110$	−72.1601	−0.0625472
$111$	−97.9536	−0.0837599
$112$	1579.97	1.33298
$113$	−1378.35	−1.14747	−0.573735	−	0.819041i	$-0.694506\pi$
$113$	−1378.35	−1.14747	−0.573735	+	0.819041i	$0.694506\pi$
$114$	116.854	0.0960035
$115$	2938.69	2.38291
$116$	318.477	0.254913
$117$	226.080	0.178642
$118$	10.5434	0.00822542
$119$	2098.85	1.61682
$120$	−322.297	−0.245180
$121$	121.000	0.0909091
$122$	118.701	0.0880876
$123$	−1386.25	−1.01621
$124$	1840.50	1.33292
$125$	597.737	0.427706
$126$	−176.642	−0.124893
$127$	413.487	0.288906	0.144453	−	0.989512i	$-0.453858\pi$
$127$	413.487	0.288906	0.144453	+	0.989512i	$0.453858\pi$
$128$	−758.227	−0.523582
$129$	−903.173	−0.616434
$130$	−85.2801	−0.0575351
$131$	−1905.08	−1.27059	−0.635296	−	0.772269i	$-0.719122\pi$
$131$	−1905.08	−1.27059	−0.635296	+	0.772269i	$0.719122\pi$
$132$	267.648	0.176483
$133$	2539.19	1.65546
$134$	−387.852	−0.250039
$135$	−2324.62	−1.48201
$136$	−493.848	−0.311376
$137$	−2360.37	−1.47197	−0.735985	−	0.676998i	$-0.763281\pi$
$137$	−2360.37	−1.47197	−0.735985	+	0.676998i	$0.763281\pi$
$138$	209.399	0.129168
$139$	2193.45	1.33846	0.669231	−	0.743054i	$-0.266623\pi$
$139$	2193.45	1.33846	0.669231	+	0.743054i	$0.266623\pi$
$140$	−3468.38	−2.09379
$141$	1119.49	0.668638
$142$	213.086	0.125928
$143$	143.000	0.0836242
$144$	−1050.47	−0.607908
$145$	−685.436	−0.392568
$146$	−231.466	−0.131207
$147$	1057.63	0.593412
$148$	248.028	0.137756
$149$	1722.29	0.946952	0.473476	−	0.880807i	$-0.342999\pi$
$149$	1722.29	0.946952	0.473476	+	0.880807i	$0.342999\pi$
$150$	193.061	0.105089
$151$	−1543.77	−0.831988	−0.415994	−	0.909367i	$-0.636566\pi$
$151$	−1543.77	−0.831988	−0.415994	+	0.909367i	$0.636566\pi$
$152$	−597.458	−0.318817
$153$	−1395.45	−0.737355
$154$	−111.730	−0.0584640
$155$	−3961.18	−2.05271
$156$	316.311	0.162341
$157$	626.041	0.318239	0.159120	−	0.987259i	$-0.449134\pi$
$157$	626.041	0.318239	0.159120	+	0.987259i	$0.449134\pi$
$158$	−144.037	−0.0725250
$159$	−970.637	−0.484129
$160$	1228.02	0.606770
$161$	4550.15	2.22734
$162$	16.6933	0.00809597
$163$	2287.19	1.09906	0.549530	−	0.835474i	$-0.314807\pi$
$163$	2287.19	1.09906	0.549530	+	0.835474i	$0.314807\pi$
$164$	3510.12	1.67131
$165$	−576.039	−0.271785
$166$	−537.159	−0.251154
$167$	−422.194	−0.195631	−0.0978154	−	0.995205i	$-0.531185\pi$
$167$	−422.194	−0.195631	−0.0978154	+	0.995205i	$0.531185\pi$
$168$	−499.033	−0.229174
$169$	169.000	0.0769231
$170$	526.381	0.237480
$171$	−1688.21	−0.754976
$172$	2286.92	1.01382
$173$	−94.3342	−0.0414572	−0.0207286	−	0.999785i	$-0.506599\pi$
$173$	−94.3342	−0.0414572	−0.0207286	+	0.999785i	$0.506599\pi$
$174$	−48.8414	−0.0212796
$175$	4195.12	1.81212
$176$	−664.441	−0.284569
$177$	84.1657	0.0357417
$178$	360.686	0.151880
$179$	−145.785	−0.0608741	−0.0304370	−	0.999537i	$-0.509690\pi$
$179$	−145.785	−0.0608741	−0.0304370	+	0.999537i	$0.509690\pi$
$180$	2305.99	0.954881
$181$	951.575	0.390774	0.195387	−	0.980726i	$-0.437404\pi$
$181$	951.575	0.390774	0.195387	+	0.980726i	$0.437404\pi$
$182$	−132.044	−0.0537790
$183$	947.565	0.382765
$184$	−1070.63	−0.428954
$185$	−533.814	−0.212145
$186$	−282.258	−0.111270
$187$	−882.650	−0.345164
$188$	−2834.66	−1.09967
$189$	−3599.34	−1.38526
$190$	636.816	0.243155
$191$	−804.423	−0.304744	−0.152372	−	0.988323i	$-0.548691\pi$
$191$	−804.423	−0.304744	−0.152372	+	0.988323i	$0.548691\pi$
$192$	−1410.45	−0.530159
$193$	2572.76	0.959541	0.479770	−	0.877394i	$-0.340720\pi$
$193$	2572.76	0.959541	0.479770	+	0.877394i	$0.340720\pi$
$194$	420.495	0.155617
$195$	−680.773	−0.250006
$196$	−2678.02	−0.975954
$197$	2841.12	1.02752	0.513761	−	0.857934i	$-0.328252\pi$
$197$	2841.12	1.02752	0.513761	+	0.857934i	$0.328252\pi$
$198$	74.2850	0.0266627
$199$	3073.36	1.09480	0.547399	−	0.836872i	$-0.315618\pi$
$199$	3073.36	1.09480	0.547399	+	0.836872i	$0.315618\pi$
$200$	−987.090	−0.348989
$201$	−3096.14	−1.08649
$202$	55.7741	0.0194270
$203$	−1061.30	−0.366940
$204$	−1952.39	−0.670071
$205$	−7554.58	−2.57383
$206$	409.920	0.138643
$207$	−3025.23	−1.01579
$208$	−785.248	−0.261765
$209$	−1067.83	−0.353413
$210$	531.907	0.174786
$211$	−4014.76	−1.30989	−0.654946	−	0.755676i	$-0.727309\pi$
$211$	−4014.76	−1.30989	−0.654946	+	0.755676i	$0.727309\pi$
$212$	2457.75	0.796222
$213$	1701.02	0.547192
$214$	−585.530	−0.187037
$215$	−4921.98	−1.56129
$216$	846.906	0.266781
$217$	−6133.34	−1.91870
$218$	15.6552	0.00486379
$219$	−1847.74	−0.570132
$220$	1458.59	0.446991
$221$	−1043.13	−0.317505
$222$	−38.0374	−0.0114996
$223$	−1161.62	−0.348825	−0.174413	−	0.984673i	$-0.555803\pi$
$223$	−1161.62	−0.348825	−0.174413	+	0.984673i	$0.555803\pi$
$224$	1901.41	0.567158
$225$	−2789.18	−0.826424
$226$	−535.241	−0.157539
$227$	834.066	0.243872	0.121936	−	0.992538i	$-0.461090\pi$
$227$	834.066	0.243872	0.121936	+	0.992538i	$0.461090\pi$
$228$	−2362.00	−0.686084
$229$	6536.75	1.88629	0.943146	−	0.332379i	$-0.107851\pi$
$229$	6536.75	1.88629	0.943146	+	0.332379i	$0.107851\pi$
$230$	1141.15	0.327154
$231$	−891.915	−0.254042
$232$	249.719	0.0706673
$233$	651.253	0.183112	0.0915558	−	0.995800i	$-0.470816\pi$
$233$	651.253	0.183112	0.0915558	+	0.995800i	$0.470816\pi$
$234$	87.7914	0.0245261
$235$	6100.83	1.69351
$236$	−213.116	−0.0587825
$237$	−1149.81	−0.315141
$238$	815.028	0.221976
$239$	−2659.32	−0.719738	−0.359869	−	0.933003i	$-0.617179\pi$
$239$	−2659.32	−0.719738	−0.359869	+	0.933003i	$0.617179\pi$
$240$	3163.17	0.850757
$241$	−4013.82	−1.07283	−0.536417	−	0.843953i	$-0.680222\pi$
$241$	−4013.82	−1.07283	−0.536417	+	0.843953i	$0.680222\pi$
$242$	46.9868	0.0124811
$243$	3848.62	1.01600
$244$	−2399.33	−0.629514
$245$	5763.71	1.50298
$246$	−538.309	−0.139518
$247$	−1261.98	−0.325093
$248$	1443.14	0.369514
$249$	−4288.02	−1.09133
$250$	232.114	0.0587206
$251$	−342.694	−0.0861779	−0.0430889	−	0.999071i	$-0.513720\pi$
$251$	−342.694	−0.0861779	−0.0430889	+	0.999071i	$0.513720\pi$
$252$	3570.51	0.892544
$253$	−1913.52	−0.475501
$254$	160.566	0.0396645
$255$	4201.99	1.03192
$256$	3345.58	0.816791
$257$	2210.79	0.536597	0.268299	−	0.963336i	$-0.413539\pi$
$257$	2210.79	0.536597	0.268299	+	0.963336i	$0.413539\pi$
$258$	−350.721	−0.0846314
$259$	−826.536	−0.198295
$260$	1723.79	0.411172
$261$	705.620	0.167344
$262$	−739.781	−0.174442
$263$	−1806.70	−0.423597	−0.211799	−	0.977313i	$-0.567932\pi$
$263$	−1806.70	−0.423597	−0.211799	+	0.977313i	$0.567932\pi$
$264$	209.863	0.0489249
$265$	−5289.64	−1.22619
$266$	986.020	0.227281
$267$	2879.28	0.659959
$268$	7839.73	1.78689
$269$	7775.99	1.76249	0.881246	−	0.472657i	$-0.156705\pi$
$269$	7775.99	1.76249	0.881246	+	0.472657i	$0.156705\pi$
$270$	−902.697	−0.203468
$271$	4238.19	0.950007	0.475004	−	0.879984i	$-0.342447\pi$
$271$	4238.19	0.950007	0.475004	+	0.879984i	$0.342447\pi$
$272$	4846.85	1.08045
$273$	−1054.08	−0.233685
$274$	−916.580	−0.202090
$275$	−1764.21	−0.386859
$276$	−4232.63	−0.923095
$277$	1673.47	0.362993	0.181497	−	0.983392i	$-0.441906\pi$
$277$	1673.47	0.362993	0.181497	+	0.983392i	$0.441906\pi$
$278$	851.763	0.183760
$279$	4077.83	0.875029
$280$	−2719.56	−0.580445
$281$	−4575.71	−0.971401	−0.485701	−	0.874125i	$-0.661436\pi$
$281$	−4575.71	−0.971401	−0.485701	+	0.874125i	$0.661436\pi$
$282$	434.720	0.0917987
$283$	−253.322	−0.0532100	−0.0266050	−	0.999646i	$-0.508470\pi$
$283$	−253.322	−0.0532100	−0.0266050	+	0.999646i	$0.508470\pi$
$284$	−4307.16	−0.899939
$285$	5083.56	1.05658
$286$	55.5298	0.0114809
$287$	−11697.2	−2.40580
$288$	−1264.18	−0.258654
$289$	1525.60	0.310523
$290$	−266.169	−0.0538965
$291$	3356.72	0.676200
$292$	4678.67	0.937666
$293$	1573.27	0.313690	0.156845	−	0.987623i	$-0.449868\pi$
$293$	1573.27	0.313690	0.156845	+	0.987623i	$0.449868\pi$
$294$	410.698	0.0814708
$295$	458.674	0.0905256
$296$	194.479	0.0381888
$297$	1513.67	0.295730
$298$	668.803	0.130009
$299$	−2261.43	−0.437397
$300$	−3902.38	−0.751013
$301$	−7621.01	−1.45936
$302$	−599.478	−0.114225
$303$	445.233	0.0844157
$304$	5863.71	1.10627
$305$	5163.91	0.969457
$306$	−541.882	−0.101233
$307$	−8406.39	−1.56280	−0.781398	−	0.624033i	$-0.785493\pi$
$307$	−8406.39	−1.56280	−0.781398	+	0.624033i	$0.785493\pi$
$308$	2258.42	0.417810
$309$	3272.30	0.602442
$310$	−1538.21	−0.281821
$311$	4745.50	0.865249	0.432624	−	0.901574i	$-0.357588\pi$
$311$	4745.50	0.865249	0.432624	+	0.901574i	$0.357588\pi$
$312$	248.020	0.0450043
$313$	9805.81	1.77079	0.885395	−	0.464840i	$-0.153888\pi$
$313$	9805.81	1.77079	0.885395	+	0.464840i	$0.153888\pi$
$314$	243.105	0.0436917
$315$	−7684.55	−1.37453
$316$	2911.45	0.518296
$317$	2770.42	0.490859	0.245429	−	0.969414i	$-0.421071\pi$
$317$	2770.42	0.490859	0.245429	+	0.969414i	$0.421071\pi$
$318$	−376.919	−0.0664671
$319$	446.319	0.0783356
$320$	−7686.47	−1.34277
$321$	−4674.16	−0.812729
$322$	1766.92	0.305796
$323$	7789.41	1.34184
$324$	−337.425	−0.0578574
$325$	−2084.98	−0.355858
$326$	888.164	0.150892
$327$	124.972	0.0211345
$328$	2752.29	0.463323
$329$	9446.28	1.58295
$330$	−223.688	−0.0373139
$331$	−3336.72	−0.554086	−0.277043	−	0.960858i	$-0.589354\pi$
$331$	−3336.72	−0.554086	−0.277043	+	0.960858i	$0.589354\pi$
$332$	10857.7	1.79486
$333$	549.533	0.0904332
$334$	−163.947	−0.0268586
$335$	−16872.9	−2.75183
$336$	4897.73	0.795217
$337$	3687.31	0.596025	0.298013	−	0.954562i	$-0.403676\pi$
$337$	3687.31	0.596025	0.298013	+	0.954562i	$0.403676\pi$
$338$	65.6262	0.0105609
$339$	−4272.72	−0.684549
$340$	−10639.9	−1.69714
$341$	2579.31	0.409611
$342$	−655.568	−0.103652
$343$	−47.5212	−0.00748077
$344$	1793.18	0.281052
$345$	9109.58	1.42158
$346$	−36.6319	−0.00569175
$347$	−4234.07	−0.655034	−0.327517	−	0.944845i	$-0.606212\pi$
$347$	−4234.07	−0.655034	−0.327517	+	0.944845i	$0.606212\pi$
$348$	987.241	0.152074
$349$	−960.345	−0.147295	−0.0736477	−	0.997284i	$-0.523464\pi$
$349$	−960.345	−0.147295	−0.0736477	+	0.997284i	$0.523464\pi$
$350$	1629.05	0.248790
$351$	1788.88	0.272032
$352$	−799.619	−0.121079
$353$	−6308.96	−0.951253	−0.475626	−	0.879647i	$-0.657779\pi$
$353$	−6308.96	−0.951253	−0.475626	+	0.879647i	$0.657779\pi$
$354$	32.6833	0.00490705
$355$	9269.98	1.38591
$356$	−7290.63	−1.08540
$357$	6506.19	0.964549
$358$	−56.6112	−0.00835753
$359$	−4547.64	−0.668566	−0.334283	−	0.942473i	$-0.608494\pi$
$359$	−4547.64	−0.668566	−0.334283	+	0.942473i	$0.608494\pi$
$360$	1808.13	0.264714
$361$	2564.63	0.373907
$362$	369.516	0.0536501
$363$	375.085	0.0542338
$364$	2669.04	0.384329
$365$	−10069.6	−1.44401
$366$	367.959	0.0525506
$367$	−1485.93	−0.211348	−0.105674	−	0.994401i	$-0.533700\pi$
$367$	−1485.93	−0.211348	−0.105674	+	0.994401i	$0.533700\pi$
$368$	10507.6	1.48844
$369$	7777.05	1.09717
$370$	−207.291	−0.0291258
$371$	−8190.27	−1.14614
$372$	5705.34	0.795182
$373$	−12173.5	−1.68987	−0.844933	−	0.534871i	$-0.820360\pi$
$373$	−12173.5	−1.68987	−0.844933	+	0.534871i	$0.820360\pi$
$374$	−342.751	−0.0473883
$375$	1852.91	0.255157
$376$	−2222.66	−0.304853
$377$	527.468	0.0720583
$378$	−1397.70	−0.190185
$379$	−5305.96	−0.719127	−0.359563	−	0.933121i	$-0.617074\pi$
$379$	−5305.96	−0.719127	−0.359563	+	0.933121i	$0.617074\pi$
$380$	−12872.1	−1.73770
$381$	1281.76	0.172353
$382$	−312.374	−0.0418389
$383$	−6021.94	−0.803412	−0.401706	−	0.915769i	$-0.631583\pi$
$383$	−6021.94	−0.803412	−0.401706	+	0.915769i	$0.631583\pi$
$384$	−2350.41	−0.312354
$385$	−4860.64	−0.643431
$386$	999.056	0.131737
$387$	5066.92	0.665546
$388$	−8499.55	−1.11211
$389$	−10050.1	−1.30993	−0.654963	−	0.755661i	$-0.727316\pi$
$389$	−10050.1	−1.30993	−0.654963	+	0.755661i	$0.727316\pi$
$390$	−264.358	−0.0343238
$391$	13958.4	1.80539
$392$	−2099.84	−0.270556
$393$	−5905.51	−0.757999
$394$	1103.27	0.141071
$395$	−6266.10	−0.798181
$396$	−1501.54	−0.190543
$397$	10158.2	1.28420	0.642099	−	0.766622i	$-0.278064\pi$
$397$	10158.2	1.28420	0.642099	+	0.766622i	$0.278064\pi$
$398$	1193.45	0.150307
$399$	7871.18	0.987599
$400$	9687.73	1.21097
$401$	−6932.82	−0.863362	−0.431681	−	0.902026i	$-0.642079\pi$
$401$	−6932.82	−0.863362	−0.431681	+	0.902026i	$0.642079\pi$
$402$	−1202.29	−0.149166
$403$	3048.27	0.376787
$404$	−1127.37	−0.138834
$405$	726.215	0.0891010
$406$	−412.125	−0.0503779
$407$	347.591	0.0423328
$408$	−1530.87	−0.185758
$409$	11451.0	1.38439	0.692196	−	0.721709i	$-0.256643\pi$
$409$	11451.0	1.38439	0.692196	+	0.721709i	$0.256643\pi$
$410$	−2933.60	−0.353366
$411$	−7316.86	−0.878136
$412$	−8285.79	−0.990805
$413$	710.193	0.0846158
$414$	−1174.76	−0.139459
$415$	−23368.3	−2.76410
$416$	−945.004	−0.111376
$417$	6799.44	0.798489
$418$	−414.660	−0.0485208
$419$	−4201.20	−0.489838	−0.244919	−	0.969543i	$-0.578761\pi$
$419$	−4201.20	−0.489838	−0.244919	+	0.969543i	$0.578761\pi$
$420$	−10751.5	−1.24910
$421$	13940.1	1.61377	0.806885	−	0.590709i	$-0.201152\pi$
$421$	13940.1	1.61377	0.806885	+	0.590709i	$0.201152\pi$
$422$	−1559.01	−0.179838
$423$	−6280.48	−0.721909
$424$	1927.13	0.220730
$425$	12869.3	1.46883
$426$	660.541	0.0751252
$427$	7995.59	0.906168
$428$	11835.4	1.33665
$429$	443.283	0.0498879
$430$	−1911.31	−0.214352
$431$	−1690.07	−0.188882	−0.0944409	−	0.995530i	$-0.530106\pi$
$431$	−1690.07	−0.188882	−0.0944409	+	0.995530i	$0.530106\pi$
$432$	−8311.91	−0.925711
$433$	2726.88	0.302646	0.151323	−	0.988484i	$-0.451647\pi$
$433$	2726.88	0.302646	0.151323	+	0.988484i	$0.451647\pi$
$434$	−2381.70	−0.263422
$435$	−2124.77	−0.234195
$436$	−316.442	−0.0347588
$437$	16886.9	1.84853
$438$	−717.516	−0.0782746
$439$	−17479.5	−1.90034	−0.950171	−	0.311729i	$-0.899092\pi$
$439$	−17479.5	−1.90034	−0.950171	+	0.311729i	$0.899092\pi$
$440$	1143.68	0.123916
$441$	−5933.43	−0.640690
$442$	−405.069	−0.0435909
$443$	−17567.5	−1.88411	−0.942053	−	0.335465i	$-0.891107\pi$
$443$	−17567.5	−1.88411	−0.942053	+	0.335465i	$0.891107\pi$
$444$	768.858	0.0821811
$445$	15691.1	1.67153
$446$	−451.082	−0.0478909
$447$	5338.91	0.564925
$448$	−11901.4	−1.25511
$449$	574.698	0.0604046	0.0302023	−	0.999544i	$-0.490385\pi$
$449$	574.698	0.0604046	0.0302023	+	0.999544i	$0.490385\pi$
$450$	−1083.10	−0.113462
$451$	4919.14	0.513599
$452$	10818.9	1.12584
$453$	−4785.50	−0.496341
$454$	323.885	0.0334817
$455$	−5744.39	−0.591870
$456$	−1852.05	−0.190197
$457$	18260.0	1.86907	0.934535	−	0.355871i	$-0.115816\pi$
$457$	18260.0	1.86907	0.934535	+	0.355871i	$0.115816\pi$
$458$	2538.36	0.258973
$459$	−11041.6	−1.12283
$460$	−23066.4	−2.33799
$461$	5790.45	0.585007	0.292504	−	0.956264i	$-0.405512\pi$
$461$	5790.45	0.585007	0.292504	+	0.956264i	$0.405512\pi$
$462$	−346.349	−0.0348780
$463$	10900.8	1.09418	0.547088	−	0.837075i	$-0.315736\pi$
$463$	10900.8	1.09418	0.547088	+	0.837075i	$0.315736\pi$
$464$	−2450.85	−0.245211
$465$	−12279.2	−1.22459
$466$	252.895	0.0251398
$467$	5359.64	0.531080	0.265540	−	0.964100i	$-0.414450\pi$
$467$	5359.64	0.531080	0.265540	+	0.964100i	$0.414450\pi$
$468$	−1774.55	−0.175274
$469$	−26125.3	−2.57218
$470$	2369.08	0.232505
$471$	1940.65	0.189853
$472$	−167.105	−0.0162958
$473$	3204.93	0.311549
$474$	−446.497	−0.0432664
$475$	15569.3	1.50393
$476$	−16474.3	−1.58634
$477$	5445.41	0.522701
$478$	−1032.67	−0.0988143
$479$	9865.45	0.941052	0.470526	−	0.882386i	$-0.344064\pi$
$479$	9865.45	0.941052	0.470526	+	0.882386i	$0.344064\pi$
$480$	3806.70	0.361982
$481$	410.789	0.0389405
$482$	−1558.65	−0.147292
$483$	14104.9	1.32877
$484$	−949.754	−0.0891955
$485$	18293.0	1.71266
$486$	1494.50	0.139489
$487$	−1295.82	−0.120573	−0.0602865	−	0.998181i	$-0.519201\pi$
$487$	−1295.82	−0.120573	−0.0602865	+	0.998181i	$0.519201\pi$
$488$	−1881.32	−0.174515
$489$	7090.02	0.655668
$490$	2238.17	0.206347
$491$	8703.05	0.799925	0.399962	−	0.916532i	$-0.369023\pi$
$491$	8703.05	0.799925	0.399962	+	0.916532i	$0.369023\pi$
$492$	10881.0	0.997055
$493$	−3255.73	−0.297425
$494$	−490.053	−0.0446326
$495$	3231.66	0.293439
$496$	−14163.6	−1.28219
$497$	14353.3	1.29544
$498$	−1665.13	−0.149832
$499$	−18369.1	−1.64793	−0.823963	−	0.566643i	$-0.808242\pi$
$499$	−18369.1	−1.64793	−0.823963	+	0.566643i	$0.808242\pi$
$500$	−4691.76	−0.419644
$501$	−1308.75	−0.116708
$502$	−133.075	−0.0118315
$503$	−15592.1	−1.38214	−0.691071	−	0.722787i	$-0.742861\pi$
$503$	−15592.1	−1.38214	−0.691071	+	0.722787i	$0.742861\pi$
$504$	2799.64	0.247432
$505$	2426.37	0.213806
$506$	−743.058	−0.0652825
$507$	523.880	0.0458902
$508$	−3245.55	−0.283460
$509$	5263.23	0.458327	0.229164	−	0.973388i	$-0.426401\pi$
$509$	5263.23	0.458327	0.229164	+	0.973388i	$0.426401\pi$
$510$	1631.72	0.141674
$511$	−15591.3	−1.34974
$512$	7364.97	0.635721
$513$	−13358.2	−1.14966
$514$	858.497	0.0736706
$515$	17832.9	1.52585
$516$	7089.19	0.604814
$517$	−3972.53	−0.337934
$518$	−320.961	−0.0272244
$519$	−292.425	−0.0247322
$520$	1351.62	0.113986
$521$	−5050.74	−0.424716	−0.212358	−	0.977192i	$-0.568114\pi$
$521$	−5050.74	−0.424716	−0.212358	+	0.977192i	$0.568114\pi$
$522$	274.007	0.0229750
$523$	9314.66	0.778779	0.389390	−	0.921073i	$-0.372686\pi$
$523$	9314.66	0.778779	0.389390	+	0.921073i	$0.372686\pi$
$524$	14953.4	1.24664
$525$	13004.4	1.08106
$526$	−701.580	−0.0581566
$527$	−18815.1	−1.55521
$528$	−2059.69	−0.169766
$529$	18093.7	1.48711
$530$	−2054.08	−0.168346
$531$	−472.181	−0.0385893
$532$	−19930.6	−1.62425
$533$	5813.53	0.472442
$534$	1118.08	0.0906072
$535$	−25472.6	−2.05846
$536$	6147.14	0.495366
$537$	−451.915	−0.0363158
$538$	3019.58	0.241976
$539$	−3753.02	−0.299914
$540$	18246.4	1.45407
$541$	12179.3	0.967889	0.483944	−	0.875099i	$-0.339204\pi$
$541$	12179.3	0.967889	0.483944	+	0.875099i	$0.339204\pi$
$542$	1645.78	0.130428
$543$	2949.77	0.233125
$544$	5832.92	0.459714
$545$	681.056	0.0535289
$546$	−409.322	−0.0320831
$547$	19581.3	1.53060	0.765298	−	0.643676i	$-0.222592\pi$
$547$	19581.3	1.53060	0.765298	+	0.643676i	$0.222592\pi$
$548$	18527.0	1.44423
$549$	−5315.97	−0.413261
$550$	−685.081	−0.0531126
$551$	−3938.78	−0.304533
$552$	−3318.81	−0.255902
$553$	−9702.18	−0.746073
$554$	649.843	0.0498361
$555$	−1654.76	−0.126560
$556$	−17216.9	−1.31323
$557$	−8584.07	−0.652996	−0.326498	−	0.945198i	$-0.605869\pi$
$557$	−8584.07	−0.652996	−0.326498	+	0.945198i	$0.605869\pi$
$558$	1583.50	0.120135
$559$	3787.65	0.286584
$560$	26690.9	2.01410
$561$	−2736.11	−0.205915
$562$	−1776.84	−0.133366
$563$	−1319.00	−0.0987375	−0.0493688	−	0.998781i	$-0.515721\pi$
$563$	−1319.00	−0.0987375	−0.0493688	+	0.998781i	$0.515721\pi$
$564$	−8787.10	−0.656035
$565$	−23284.8	−1.73381
$566$	−98.3702	−0.00730531
$567$	1124.44	0.0832842
$568$	−3377.25	−0.249483
$569$	7345.65	0.541205	0.270603	−	0.962691i	$-0.412777\pi$
$569$	7345.65	0.541205	0.270603	+	0.962691i	$0.412777\pi$
$570$	1974.05	0.145059
$571$	−7322.64	−0.536678	−0.268339	−	0.963325i	$-0.586475\pi$
$571$	−7322.64	−0.536678	−0.268339	+	0.963325i	$0.586475\pi$
$572$	−1122.44	−0.0820480
$573$	−2493.61	−0.181801
$574$	−4542.27	−0.330297
$575$	27899.6	2.02347
$576$	7912.82	0.572397
$577$	8781.69	0.633599	0.316799	−	0.948493i	$-0.397392\pi$
$577$	8781.69	0.633599	0.316799	+	0.948493i	$0.397392\pi$
$578$	592.422	0.0426324
$579$	7975.25	0.572435
$580$	5380.13	0.385168
$581$	−36182.5	−2.58365
$582$	1303.48	0.0928369
$583$	3444.33	0.244682
$584$	3668.55	0.259941
$585$	3819.23	0.269924
$586$	610.931	0.0430671
$587$	23072.1	1.62229	0.811147	−	0.584842i	$-0.198843\pi$
$587$	23072.1	1.62229	0.811147	+	0.584842i	$0.198843\pi$
$588$	−8301.53	−0.582227
$589$	−22762.5	−1.59238
$590$	178.113	0.0124284
$591$	8807.14	0.612990
$592$	−1908.71	−0.132512
$593$	4835.36	0.334848	0.167424	−	0.985885i	$-0.446455\pi$
$593$	4835.36	0.334848	0.167424	+	0.985885i	$0.446455\pi$
$594$	587.788	0.0406014
$595$	35456.5	2.44298
$596$	−13518.6	−0.929103
$597$	9527.05	0.653126
$598$	−878.160	−0.0600512
$599$	18398.9	1.25502	0.627512	−	0.778607i	$-0.284073\pi$
$599$	18398.9	1.25502	0.627512	+	0.778607i	$0.284073\pi$
$600$	−3059.86	−0.208197
$601$	4647.76	0.315451	0.157726	−	0.987483i	$-0.449584\pi$
$601$	4647.76	0.315451	0.157726	+	0.987483i	$0.449584\pi$
$602$	−2959.39	−0.200359
$603$	17369.7	1.17305
$604$	12117.4	0.816306
$605$	2044.09	0.137362
$606$	172.893	0.0115896
$607$	−23180.5	−1.55003	−0.775015	−	0.631943i	$-0.782258\pi$
$607$	−23180.5	−1.55003	−0.775015	+	0.631943i	$0.782258\pi$
$608$	7056.66	0.470700
$609$	−3289.91	−0.218906
$610$	2005.25	0.133099
$611$	−4694.81	−0.310854
$612$	10953.2	0.723457
$613$	14114.2	0.929965	0.464982	−	0.885320i	$-0.346061\pi$
$613$	14114.2	0.929965	0.464982	+	0.885320i	$0.346061\pi$
$614$	−3264.38	−0.214559
$615$	−23418.3	−1.53547
$616$	1770.83	0.115826
$617$	−7122.52	−0.464735	−0.232368	−	0.972628i	$-0.574647\pi$
$617$	−7122.52	−0.464735	−0.232368	+	0.972628i	$0.574647\pi$
$618$	1270.70	0.0827105
$619$	5509.59	0.357753	0.178877	−	0.983872i	$-0.442754\pi$
$619$	5509.59	0.357753	0.178877	+	0.983872i	$0.442754\pi$
$620$	31092.1	2.01402
$621$	−23937.4	−1.54682
$622$	1842.77	0.118792
$623$	24295.5	1.56240
$624$	−2434.17	−0.156162
$625$	−9950.15	−0.636810
$626$	3807.80	0.243115
$627$	−3310.14	−0.210836
$628$	−4913.93	−0.312241
$629$	−2535.55	−0.160729
$630$	−2984.07	−0.188711
$631$	7677.54	0.484371	0.242185	−	0.970230i	$-0.422136\pi$
$631$	7677.54	0.484371	0.242185	+	0.970230i	$0.422136\pi$
$632$	2282.87	0.143683
$633$	−12445.3	−0.781445
$634$	1075.81	0.0673910
$635$	6985.15	0.436531
$636$	7618.73	0.475004
$637$	−4435.38	−0.275881
$638$	173.315	0.0107549
$639$	−9542.96	−0.590788
$640$	−12808.9	−0.791122
$641$	−17836.4	−1.09906	−0.549530	−	0.835474i	$-0.685193\pi$
$641$	−17836.4	−1.09906	−0.549530	+	0.835474i	$0.685193\pi$
$642$	−1815.07	−0.111581
$643$	20385.9	1.25030	0.625148	−	0.780506i	$-0.285039\pi$
$643$	20385.9	1.25030	0.625148	+	0.780506i	$0.285039\pi$
$644$	−35715.1	−2.18536
$645$	−15257.6	−0.931420
$646$	3024.79	0.184224
$647$	−16906.7	−1.02731	−0.513656	−	0.857997i	$-0.671709\pi$
$647$	−16906.7	−1.02731	−0.513656	+	0.857997i	$0.671709\pi$
$648$	−264.575	−0.0160393
$649$	−298.664	−0.0180641
$650$	−809.641	−0.0488565
$651$	−19012.6	−1.14464
$652$	−17952.6	−1.07834
$653$	−23768.4	−1.42439	−0.712196	−	0.701981i	$-0.752299\pi$
$653$	−23768.4	−1.42439	−0.712196	+	0.701981i	$0.752299\pi$
$654$	48.5293	0.00290160
$655$	−32183.0	−1.91984
$656$	−27012.2	−1.60770
$657$	10366.1	0.615555
$658$	3668.19	0.217326
$659$	12086.8	0.714469	0.357234	−	0.934015i	$-0.383720\pi$
$659$	12086.8	0.714469	0.357234	+	0.934015i	$0.383720\pi$
$660$	4521.45	0.266662
$661$	−27808.1	−1.63632	−0.818162	−	0.574987i	$-0.805007\pi$
$661$	−27808.1	−1.63632	−0.818162	+	0.574987i	$0.805007\pi$
$662$	−1295.72	−0.0760716
$663$	−3233.58	−0.189415
$664$	8513.54	0.497575
$665$	42895.3	2.50136
$666$	213.395	0.0124158
$667$	−7058.17	−0.409736
$668$	3313.89	0.191943
$669$	−3600.89	−0.208099
$670$	−6552.09	−0.377805
$671$	−3362.46	−0.193452
$672$	5894.15	0.338351
$673$	23925.2	1.37036	0.685178	−	0.728375i	$-0.259724\pi$
$673$	23925.2	1.37036	0.685178	+	0.728375i	$0.259724\pi$
$674$	1431.86	0.0818296
$675$	−22069.7	−1.25846
$676$	−1326.52	−0.0754731
$677$	14944.4	0.848387	0.424194	−	0.905571i	$-0.360558\pi$
$677$	14944.4	0.848387	0.424194	+	0.905571i	$0.360558\pi$
$678$	−1659.18	−0.0939831
$679$	28324.1	1.60085
$680$	−8342.72	−0.470484
$681$	2585.50	0.145487
$682$	1001.60	0.0562364
$683$	−1419.94	−0.0795499	−0.0397749	−	0.999209i	$-0.512664\pi$
$683$	−1419.94	−0.0795499	−0.0397749	+	0.999209i	$0.512664\pi$
$684$	13251.1	0.740745
$685$	−39874.4	−2.22412
$686$	−18.4535	−0.00102705
$687$	20263.1	1.12531
$688$	−17599.1	−0.975230
$689$	4070.57	0.225075
$690$	3537.44	0.195171
$691$	12724.8	0.700540	0.350270	−	0.936649i	$-0.386090\pi$
$691$	12724.8	0.700540	0.350270	+	0.936649i	$0.386090\pi$
$692$	740.449	0.0406758
$693$	5003.77	0.274282
$694$	−1644.18	−0.0899309
$695$	37054.6	2.02239
$696$	774.097	0.0421582
$697$	−35883.3	−1.95004
$698$	−372.922	−0.0202225
$699$	2018.81	0.109239
$700$	−32928.4	−1.77797
$701$	828.514	0.0446399	0.0223199	−	0.999751i	$-0.492895\pi$
$701$	828.514	0.0446399	0.0223199	+	0.999751i	$0.492895\pi$
$702$	694.658	0.0373478
$703$	−3067.50	−0.164570
$704$	5005.02	0.267946
$705$	18911.8	1.01030
$706$	−2449.90	−0.130599
$707$	3756.89	0.199848
$708$	−660.634	−0.0350680
$709$	−12499.3	−0.662087	−0.331044	−	0.943615i	$-0.607401\pi$
$709$	−12499.3	−0.662087	−0.331044	+	0.943615i	$0.607401\pi$
$710$	3599.72	0.190275
$711$	6450.62	0.340249
$712$	−5716.59	−0.300897
$713$	−40789.7	−2.14248
$714$	2526.49	0.132425
$715$	2415.74	0.126355
$716$	1144.29	0.0597266
$717$	−8243.58	−0.429376
$718$	−1765.94	−0.0917889
$719$	−29160.2	−1.51251	−0.756254	−	0.654278i	$-0.772972\pi$
$719$	−29160.2	−1.51251	−0.756254	+	0.654278i	$0.772972\pi$
$720$	−17745.8	−0.918538
$721$	27611.8	1.42624
$722$	995.898	0.0513345
$723$	−12442.4	−0.640022
$724$	−7469.11	−0.383408
$725$	−6507.46	−0.333353
$726$	145.653	0.00744587
$727$	16792.6	0.856676	0.428338	−	0.903619i	$-0.359099\pi$
$727$	16792.6	0.856676	0.428338	+	0.903619i	$0.359099\pi$
$728$	2092.80	0.106544
$729$	10769.6	0.547151
$730$	−3910.22	−0.198252
$731$	−23378.8	−1.18289
$732$	−7437.64	−0.375550
$733$	13898.3	0.700333	0.350167	−	0.936687i	$-0.386125\pi$
$733$	13898.3	0.700333	0.350167	+	0.936687i	$0.386125\pi$
$734$	−577.016	−0.0290164
$735$	17866.8	0.896635
$736$	12645.3	0.633305
$737$	10986.7	0.549119
$738$	3019.99	0.150633
$739$	18553.3	0.923536	0.461768	−	0.887001i	$-0.347215\pi$
$739$	18553.3	0.923536	0.461768	+	0.887001i	$0.347215\pi$
$740$	4190.02	0.208146
$741$	−3911.99	−0.193941
$742$	−3180.45	−0.157356
$743$	6605.17	0.326138	0.163069	−	0.986615i	$-0.447861\pi$
$743$	6605.17	0.326138	0.163069	+	0.986615i	$0.447861\pi$
$744$	4473.56	0.220442
$745$	29095.2	1.43083
$746$	−4727.22	−0.232005
$747$	24056.4	1.17828
$748$	6928.10	0.338658
$749$	−39440.7	−1.92408
$750$	719.524	0.0350311
$751$	27529.8	1.33765	0.668827	−	0.743418i	$-0.266797\pi$
$751$	27529.8	1.33765	0.668827	+	0.743418i	$0.266797\pi$
$752$	21814.2	1.05782
$753$	−1062.31	−0.0514113
$754$	204.827	0.00989303
$755$	−26079.4	−1.25712
$756$	28252.0	1.35915
$757$	3426.76	0.164528	0.0822641	−	0.996611i	$-0.473785\pi$
$757$	3426.76	0.164528	0.0822641	+	0.996611i	$0.473785\pi$
$758$	−2060.42	−0.0987304
$759$	−5931.67	−0.283671
$760$	−10093.0	−0.481727
$761$	−27501.2	−1.31001	−0.655005	−	0.755625i	$-0.727333\pi$
$761$	−27501.2	−1.31001	−0.655005	+	0.755625i	$0.727333\pi$
$762$	497.734	0.0236627
$763$	1054.52	0.0500343
$764$	6314.08	0.298999
$765$	−23573.7	−1.11413
$766$	−2338.44	−0.110302
$767$	−352.967	−0.0166165
$768$	10370.9	0.487275
$769$	−4717.83	−0.221234	−0.110617	−	0.993863i	$-0.535283\pi$
$769$	−4717.83	−0.221234	−0.110617	+	0.993863i	$0.535283\pi$
$770$	−1887.48	−0.0883380
$771$	6853.20	0.320119
$772$	−20194.1	−0.941454
$773$	−11526.9	−0.536344	−0.268172	−	0.963371i	$-0.586419\pi$
$773$	−11526.9	−0.536344	−0.268172	+	0.963371i	$0.586419\pi$
$774$	1967.59	0.0913742
$775$	−37607.0	−1.74308
$776$	−6664.51	−0.308301
$777$	−2562.16	−0.118297
$778$	−3902.67	−0.179842
$779$	−43411.6	−1.99664
$780$	5343.53	0.245294
$781$	−6036.11	−0.276555
$782$	5420.33	0.247865
$783$	5583.29	0.254828
$784$	20608.7	0.938809
$785$	10575.9	0.480853
$786$	−2293.23	−0.104067
$787$	6868.27	0.311090	0.155545	−	0.987829i	$-0.450287\pi$
$787$	6868.27	0.311090	0.155545	+	0.987829i	$0.450287\pi$
$788$	−22300.6	−1.00815
$789$	−5600.56	−0.252706
$790$	−2433.26	−0.109584
$791$	−36053.3	−1.62062
$792$	−1177.36	−0.0528228
$793$	−3973.82	−0.177950
$794$	3944.65	0.176310
$795$	−16397.3	−0.731510
$796$	−24123.5	−1.07416
$797$	−13049.8	−0.579983	−0.289991	−	0.957029i	$-0.593652\pi$
$797$	−13049.8	−0.579983	−0.289991	+	0.957029i	$0.593652\pi$
$798$	3056.54	0.135590
$799$	28978.1	1.28307
$800$	11658.7	0.515245
$801$	−16153.2	−0.712539
$802$	−2692.16	−0.118533
$803$	6556.76	0.288148
$804$	24302.2	1.06601
$805$	76867.0	3.36547
$806$	1183.71	0.0517299
$807$	24104.6	1.05145
$808$	−883.976	−0.0384878
$809$	13499.8	0.586685	0.293343	−	0.956007i	$-0.405232\pi$
$809$	13499.8	0.586685	0.293343	+	0.956007i	$0.405232\pi$
$810$	282.004	0.0122329
$811$	−13092.8	−0.566893	−0.283447	−	0.958988i	$-0.591478\pi$
$811$	−13092.8	−0.566893	−0.283447	+	0.958988i	$0.591478\pi$
$812$	8330.38	0.360023
$813$	13137.9	0.566748
$814$	134.977	0.00581196
$815$	38638.2	1.66066
$816$	15024.6	0.644568
$817$	−28283.6	−1.21116
$818$	4446.67	0.190066
$819$	5913.54	0.252303
$820$	59297.5	2.52531
$821$	−19444.8	−0.826588	−0.413294	−	0.910598i	$-0.635622\pi$
$821$	−19444.8	−0.826588	−0.413294	+	0.910598i	$0.635622\pi$
$822$	−2841.29	−0.120561
$823$	−9237.46	−0.391249	−0.195624	−	0.980679i	$-0.562673\pi$
$823$	−9237.46	−0.391249	−0.195624	+	0.980679i	$0.562673\pi$
$824$	−6496.90	−0.274673
$825$	−5468.85	−0.230789
$826$	275.783	0.0116171
$827$	−24430.4	−1.02724	−0.513620	−	0.858018i	$-0.671696\pi$
$827$	−24430.4	−1.02724	−0.513620	+	0.858018i	$0.671696\pi$
$828$	23745.6	0.996640
$829$	19965.7	0.836473	0.418237	−	0.908338i	$-0.362648\pi$
$829$	19965.7	0.836473	0.418237	+	0.908338i	$0.362648\pi$
$830$	−9074.38	−0.379489
$831$	5187.55	0.216551
$832$	5915.02	0.246474
$833$	27376.8	1.13872
$834$	2640.36	0.109626
$835$	−7132.24	−0.295595
$836$	8381.61	0.346751
$837$	32266.2	1.33248
$838$	−1631.41	−0.0672509
$839$	43310.0	1.78216	0.891078	−	0.453851i	$-0.149950\pi$
$839$	43310.0	1.78216	0.891078	+	0.453851i	$0.149950\pi$
$840$	−8430.30	−0.346277
$841$	−22742.7	−0.932499
$842$	5413.21	0.221558
$843$	−14184.1	−0.579511
$844$	31512.6	1.28520
$845$	2854.97	0.116229
$846$	−2438.84	−0.0991124
$847$	3164.98	0.128395
$848$	−18913.7	−0.765918
$849$	−785.268	−0.0317436
$850$	4997.41	0.201658
$851$	−5496.87	−0.221422
$852$	−13351.7	−0.536878
$853$	−38615.6	−1.55003	−0.775014	−	0.631944i	$-0.782257\pi$
$853$	−38615.6	−1.55003	−0.775014	+	0.631944i	$0.782257\pi$
$854$	3104.85	0.124410
$855$	−28519.5	−1.14075
$856$	9280.18	0.370549
$857$	35769.1	1.42573	0.712863	−	0.701303i	$-0.247398\pi$
$857$	35769.1	1.42573	0.712863	+	0.701303i	$0.247398\pi$
$858$	172.136	0.00684921
$859$	−45037.0	−1.78887	−0.894437	−	0.447194i	$-0.852423\pi$
$859$	−45037.0	−1.78887	−0.894437	+	0.447194i	$0.852423\pi$
$860$	38633.7	1.53186
$861$	−36260.0	−1.43523
$862$	−656.291	−0.0259320
$863$	−1064.65	−0.0419941	−0.0209971	−	0.999780i	$-0.506684\pi$
$863$	−1064.65	−0.0419941	−0.0209971	+	0.999780i	$0.506684\pi$
$864$	−10002.9	−0.393874
$865$	−1593.61	−0.0626411
$866$	1058.91	0.0415509
$867$	4729.18	0.185249
$868$	48141.8	1.88253
$869$	4080.15	0.159274
$870$	−825.091	−0.0321531
$871$	12984.3	0.505116
$872$	−248.123	−0.00963589
$873$	−18831.7	−0.730074
$874$	6557.51	0.253789
$875$	15634.9	0.604066
$876$	14503.3	0.559385
$877$	−20297.2	−0.781513	−0.390757	−	0.920494i	$-0.627787\pi$
$877$	−20297.2	−0.781513	−0.390757	+	0.920494i	$0.627787\pi$
$878$	−6787.64	−0.260902
$879$	4876.93	0.187139
$880$	−11224.6	−0.429978
$881$	38070.2	1.45586	0.727932	−	0.685649i	$-0.240481\pi$
$881$	38070.2	1.45586	0.727932	+	0.685649i	$0.240481\pi$
$882$	−2304.07	−0.0879617
$883$	−40484.9	−1.54295	−0.771476	−	0.636258i	$-0.780481\pi$
$883$	−40484.9	−1.54295	−0.771476	+	0.636258i	$0.780481\pi$
$884$	8187.76	0.311520
$885$	1421.84	0.0540051
$886$	−6821.84	−0.258673
$887$	11696.1	0.442748	0.221374	−	0.975189i	$-0.428946\pi$
$887$	11696.1	0.442748	0.221374	+	0.975189i	$0.428946\pi$
$888$	602.863	0.0227824
$889$	10815.5	0.408033
$890$	6093.18	0.229487
$891$	−472.872	−0.0177798
$892$	9117.82	0.342250
$893$	35057.7	1.31373
$894$	2073.21	0.0775597
$895$	−2462.78	−0.0919796
$896$	−19832.9	−0.739475
$897$	−7010.16	−0.260939
$898$	223.167	0.00829308
$899$	9514.00	0.352959
$900$	21892.9	0.810847
$901$	−25125.1	−0.929011
$902$	1910.20	0.0705131
$903$	−23624.2	−0.870614
$904$	8483.15	0.312108
$905$	16075.2	0.590452
$906$	−1858.31	−0.0681437
$907$	659.923	0.0241592	0.0120796	−	0.999927i	$-0.496155\pi$
$907$	659.923	0.0241592	0.0120796	+	0.999927i	$0.496155\pi$
$908$	−6546.76	−0.239275
$909$	−2497.82	−0.0911412
$910$	−2230.66	−0.0812591
$911$	−10817.0	−0.393396	−0.196698	−	0.980464i	$-0.563022\pi$
$911$	−10817.0	−0.393396	−0.196698	+	0.980464i	$0.563022\pi$
$912$	18176.8	0.659972
$913$	15216.2	0.551568
$914$	7090.72	0.256609
$915$	16007.5	0.578351
$916$	−51308.3	−1.85074
$917$	−49830.9	−1.79451
$918$	−4287.69	−0.154156
$919$	52996.0	1.90226	0.951129	−	0.308794i	$-0.0999252\pi$
$919$	52996.0	1.90226	0.951129	+	0.308794i	$0.0999252\pi$
$920$	−18086.4	−0.648142
$921$	−26058.8	−0.932320
$922$	2248.55	0.0803168
$923$	−7133.59	−0.254393
$924$	7000.83	0.249254
$925$	−5067.97	−0.180145
$926$	4233.01	0.150222
$927$	−18358.1	−0.650440
$928$	−2949.46	−0.104333
$929$	27996.7	0.988743	0.494371	−	0.869251i	$-0.335398\pi$
$929$	27996.7	0.988743	0.494371	+	0.869251i	$0.335398\pi$
$930$	−4768.26	−0.168126
$931$	33120.5	1.16593
$932$	−5111.82	−0.179660
$933$	14710.5	0.516183
$934$	2081.26	0.0729131
$935$	−14910.9	−0.521537
$936$	−1391.42	−0.0485899
$937$	−6544.13	−0.228161	−0.114081	−	0.993471i	$-0.536392\pi$
$937$	−6544.13	−0.228161	−0.114081	+	0.993471i	$0.536392\pi$
$938$	−10145.0	−0.353140
$939$	30396.8	1.05640
$940$	−47886.7	−1.66159
$941$	16898.1	0.585402	0.292701	−	0.956204i	$-0.405446\pi$
$941$	16898.1	0.585402	0.292701	+	0.956204i	$0.405446\pi$
$942$	753.595	0.0260652
$943$	−77792.2	−2.68639
$944$	1640.04	0.0565452
$945$	−60804.8	−2.09310
$946$	1244.54	0.0427733
$947$	23070.4	0.791643	0.395822	−	0.918327i	$-0.370460\pi$
$947$	23070.4	0.791643	0.395822	+	0.918327i	$0.370460\pi$
$948$	9025.13	0.309201
$949$	7748.90	0.265058
$950$	6045.86	0.206477
$951$	8587.97	0.292833
$952$	−12917.5	−0.439769
$953$	2759.61	0.0938013	0.0469006	−	0.998900i	$-0.485066\pi$
$953$	2759.61	0.0938013	0.0469006	+	0.998900i	$0.485066\pi$
$954$	2114.56	0.0717626
$955$	−13589.3	−0.460462
$956$	20873.6	0.706172
$957$	1383.54	0.0467329
$958$	3830.96	0.129199
$959$	−61739.9	−2.07892
$960$	−23827.1	−0.801060
$961$	25191.1	0.845594
$962$	159.518	0.00534622
$963$	26222.7	0.877480
$964$	31505.3	1.05261
$965$	43462.4	1.44985
$966$	5477.23	0.182430
$967$	20005.3	0.665281	0.332641	−	0.943054i	$-0.392060\pi$
$967$	20005.3	0.665281	0.332641	+	0.943054i	$0.392060\pi$
$968$	−744.703	−0.0247269
$969$	24146.2	0.800505
$970$	7103.54	0.235135
$971$	30229.1	0.999071	0.499536	−	0.866293i	$-0.333504\pi$
$971$	30229.1	0.999071	0.499536	+	0.866293i	$0.333504\pi$
$972$	−30208.6	−0.996854
$973$	57373.9	1.89036
$974$	−503.192	−0.0165537
$975$	−6463.19	−0.212295
$976$	18464.1	0.605554
$977$	−32984.9	−1.08012	−0.540061	−	0.841626i	$-0.681599\pi$
$977$	−32984.9	−1.08012	−0.540061	+	0.841626i	$0.681599\pi$
$978$	2753.20	0.0900180
$979$	−10217.2	−0.333548
$980$	−45240.5	−1.47465
$981$	−701.111	−0.0228183
$982$	3379.57	0.109823
$983$	−19452.7	−0.631173	−0.315587	−	0.948897i	$-0.602201\pi$
$983$	−19452.7	−0.631173	−0.315587	+	0.948897i	$0.602201\pi$
$984$	8531.77	0.276405
$985$	47995.9	1.55257
$986$	−1264.27	−0.0408342
$987$	29282.3	0.944344
$988$	9905.54	0.318965
$989$	−50683.4	−1.62956
$990$	1254.92	0.0402868
$991$	46420.8	1.48800	0.743999	−	0.668181i	$-0.232927\pi$
$991$	46420.8	1.48800	0.743999	+	0.668181i	$0.232927\pi$
$992$	−17045.1	−0.545548
$993$	−10343.4	−0.330552
$994$	5573.67	0.177853
$995$	51919.2	1.65422
$996$	33657.6	1.07076
$997$	6479.05	0.205811	0.102906	−	0.994691i	$-0.467186\pi$
$997$	6479.05	0.205811	0.102906	+	0.994691i	$0.467186\pi$
$998$	−7133.11	−0.226247
$999$	4348.24	0.137710

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	143.4.a.c.1.5	✓	9
3.2	odd	2		1287.4.a.k.1.5		9
4.3	odd	2		2288.4.a.r.1.4		9
11.10	odd	2		1573.4.a.e.1.5		9
13.12	even	2		1859.4.a.d.1.5		9

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
143.4.a.c.1.5	✓	9	1.1	even	1	trivial
1287.4.a.k.1.5		9	3.2	odd	2
1573.4.a.e.1.5		9	11.10	odd	2
1859.4.a.d.1.5		9	13.12	even	2
2288.4.a.r.1.4		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)

\(f(q)\)	\(=\)	\(q+0.388321 q^{2} +3.09988 q^{3} -7.84921 q^{4} +16.8933 q^{5} +1.20375 q^{6} +26.1569 q^{7} -6.15457 q^{8} -17.3907 q^{9} +O(q^{10})\)	\(q+0.388321 q^{2} +3.09988 q^{3} -7.84921 q^{4} +16.8933 q^{5} +1.20375 q^{6} +26.1569 q^{7} -6.15457 q^{8} -17.3907 q^{9} +6.56001 q^{10} -11.0000 q^{11} -24.3316 q^{12} -13.0000 q^{13} +10.1573 q^{14} +52.3671 q^{15} +60.4037 q^{16} +80.2409 q^{17} -6.75319 q^{18} +97.0754 q^{19} -132.599 q^{20} +81.0832 q^{21} -4.27153 q^{22} +173.956 q^{23} -19.0784 q^{24} +160.383 q^{25} -5.04817 q^{26} -137.606 q^{27} -205.311 q^{28} -40.5745 q^{29} +20.3352 q^{30} -234.483 q^{31} +72.6926 q^{32} -34.0987 q^{33} +31.1592 q^{34} +441.876 q^{35} +136.504 q^{36} -31.5992 q^{37} +37.6964 q^{38} -40.2984 q^{39} -103.971 q^{40} -447.194 q^{41} +31.4863 q^{42} -291.357 q^{43} +86.3413 q^{44} -293.787 q^{45} +67.5507 q^{46} +361.139 q^{47} +187.244 q^{48} +341.183 q^{49} +62.2801 q^{50} +248.737 q^{51} +102.040 q^{52} -313.121 q^{53} -53.4352 q^{54} -185.826 q^{55} -160.985 q^{56} +300.922 q^{57} -15.7559 q^{58} +27.1513 q^{59} -411.041 q^{60} +305.678 q^{61} -91.0544 q^{62} -454.888 q^{63} -455.002 q^{64} -219.613 q^{65} -13.2412 q^{66} -998.792 q^{67} -629.827 q^{68} +539.243 q^{69} +171.590 q^{70} +548.738 q^{71} +107.033 q^{72} -596.069 q^{73} -12.2706 q^{74} +497.168 q^{75} -761.965 q^{76} -287.726 q^{77} -15.6487 q^{78} -370.922 q^{79} +1020.42 q^{80} +42.9884 q^{81} -173.655 q^{82} -1383.29 q^{83} -636.439 q^{84} +1355.53 q^{85} -113.140 q^{86} -125.776 q^{87} +67.7003 q^{88} +928.836 q^{89} -114.084 q^{90} -340.040 q^{91} -1365.42 q^{92} -726.868 q^{93} +140.238 q^{94} +1639.92 q^{95} +225.338 q^{96} +1082.85 q^{97} +132.488 q^{98} +191.298 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 9 q + 8 q^{3} + 46 q^{4} + 30 q^{5} + 34 q^{6} + 25 q^{7} + 36 q^{8} + 91 q^{9}+O(q^{10}) \) 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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