LMFDB - Embedded newform 1849.4.a.l.1.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1849,4,Mod(1,1849)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1849, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("1849.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 1849 = 43^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	1849.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:	$109.094531601$
Analytic rank:	$0$
Dimension:	$60$
Twist minimal:	no (minimal twist has level 43)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.14
Character	$\chi$	$=$	1849.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-3.29999 q^{2} +5.03144 q^{3} +2.88991 q^{4} +8.27916 q^{5} -16.6037 q^{6} -12.1380 q^{7} +16.8632 q^{8} -1.68463 q^{9} +O(q^{10})$	\(q-3.29999 q^{2} +5.03144 q^{3} +2.88991 q^{4} +8.27916 q^{5} -16.6037 q^{6} -12.1380 q^{7} +16.8632 q^{8} -1.68463 q^{9} -27.3211 q^{10} -21.7668 q^{11} +14.5404 q^{12} +44.9239 q^{13} +40.0554 q^{14} +41.6561 q^{15} -78.7677 q^{16} +42.4177 q^{17} +5.55925 q^{18} -34.2760 q^{19} +23.9260 q^{20} -61.0718 q^{21} +71.8302 q^{22} +136.379 q^{23} +84.8463 q^{24} -56.4554 q^{25} -148.248 q^{26} -144.325 q^{27} -35.0778 q^{28} +31.7146 q^{29} -137.465 q^{30} +249.236 q^{31} +125.026 q^{32} -109.518 q^{33} -139.978 q^{34} -100.493 q^{35} -4.86842 q^{36} -20.9446 q^{37} +113.110 q^{38} +226.032 q^{39} +139.613 q^{40} -89.6713 q^{41} +201.536 q^{42} -62.9041 q^{44} -13.9473 q^{45} -450.049 q^{46} +229.845 q^{47} -396.315 q^{48} -195.668 q^{49} +186.302 q^{50} +213.422 q^{51} +129.826 q^{52} -674.595 q^{53} +476.270 q^{54} -180.211 q^{55} -204.687 q^{56} -172.458 q^{57} -104.658 q^{58} -370.448 q^{59} +120.382 q^{60} +797.326 q^{61} -822.476 q^{62} +20.4481 q^{63} +217.556 q^{64} +371.932 q^{65} +361.409 q^{66} +769.340 q^{67} +122.583 q^{68} +686.184 q^{69} +331.625 q^{70} -127.427 q^{71} -28.4083 q^{72} -80.4806 q^{73} +69.1168 q^{74} -284.052 q^{75} -99.0545 q^{76} +264.207 q^{77} -745.901 q^{78} -862.471 q^{79} -652.131 q^{80} -680.677 q^{81} +295.914 q^{82} +493.132 q^{83} -176.492 q^{84} +351.183 q^{85} +159.570 q^{87} -367.059 q^{88} +441.464 q^{89} +46.0259 q^{90} -545.288 q^{91} +394.123 q^{92} +1254.02 q^{93} -758.484 q^{94} -283.777 q^{95} +629.063 q^{96} +214.747 q^{97} +645.701 q^{98} +36.6690 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 60 q + 15 q^{2} + 37 q^{3} + 213 q^{4} + 51 q^{5} + 22 q^{6} + 54 q^{7} + 204 q^{8} + 387 q^{9}+O(q^{10}) $ 60 * q + 15 * q^2 + 37 * q^3 + 213 * q^4 + 51 * q^5 + 22 * q^6 + 54 * q^7 + 204 * q^8 + 387 * q^9	\( 60 q + 15 q^{2} + 37 q^{3} + 213 q^{4} + 51 q^{5} + 22 q^{6} + 54 q^{7} + 204 q^{8} + 387 q^{9} + 27 q^{10} + 43 q^{11} + 432 q^{12} + 13 q^{13} + 96 q^{14} + 65 q^{15} + 717 q^{16} - 138 q^{17} + 625 q^{18} + 610 q^{19} + 345 q^{20} + 611 q^{21} + 118 q^{22} - 243 q^{23} + 258 q^{24} + 899 q^{25} + 1071 q^{26} + 1609 q^{27} + 46 q^{28} + 773 q^{29} + 375 q^{30} - 97 q^{31} + 1967 q^{32} + 500 q^{33} + 217 q^{34} + 247 q^{35} + 175 q^{36} + 228 q^{37} + 1253 q^{38} + 1493 q^{39} + 2220 q^{40} - 951 q^{41} + 2643 q^{42} - 1378 q^{44} + 1086 q^{45} - 565 q^{46} - 2 q^{47} + 2303 q^{48} + 1264 q^{49} + 3273 q^{50} + 3076 q^{51} - 2825 q^{52} - 39 q^{53} + 5201 q^{54} + 1306 q^{55} + 3683 q^{56} + 1342 q^{57} + 2588 q^{58} - 1065 q^{59} + 2803 q^{60} + 2999 q^{61} + 5569 q^{62} + 2377 q^{63} + 2082 q^{64} + 5578 q^{65} + 3338 q^{66} + 961 q^{67} - 3754 q^{68} + 1817 q^{69} + 2738 q^{70} + 8003 q^{71} + 1412 q^{72} - 1011 q^{73} - 1413 q^{74} + 7457 q^{75} + 5516 q^{76} + 4052 q^{77} + 1091 q^{78} - 4422 q^{79} + 1610 q^{80} + 2108 q^{81} + 4676 q^{82} - 297 q^{83} - 54 q^{84} + 4333 q^{85} + 1377 q^{87} + 3652 q^{88} + 2480 q^{89} - 1414 q^{90} + 4551 q^{91} - 3286 q^{92} + 4 q^{93} + 4609 q^{94} - 835 q^{95} + 5864 q^{96} + 3785 q^{97} + 753 q^{98} + 5072 q^{99}+O(q^{100}) \) 60 * q + 15 * q^2 + 37 * q^3 + 213 * q^4 + 51 * q^5 + 22 * q^6 + 54 * q^7 + 204 * q^8 + 387 * q^9 + 27 * q^10 + 43 * q^11 + 432 * q^12 + 13 * q^13 + 96 * q^14 + 65 * q^15 + 717 * q^16 - 138 * q^17 + 625 * q^18 + 610 * q^19 + 345 * q^20 + 611 * q^21 + 118 * q^22 - 243 * q^23 + 258 * q^24 + 899 * q^25 + 1071 * q^26 + 1609 * q^27 + 46 * q^28 + 773 * q^29 + 375 * q^30 - 97 * q^31 + 1967 * q^32 + 500 * q^33 + 217 * q^34 + 247 * q^35 + 175 * q^36 + 228 * q^37 + 1253 * q^38 + 1493 * q^39 + 2220 * q^40 - 951 * q^41 + 2643 * q^42 - 1378 * q^44 + 1086 * q^45 - 565 * q^46 - 2 * q^47 + 2303 * q^48 + 1264 * q^49 + 3273 * q^50 + 3076 * q^51 - 2825 * q^52 - 39 * q^53 + 5201 * q^54 + 1306 * q^55 + 3683 * q^56 + 1342 * q^57 + 2588 * q^58 - 1065 * q^59 + 2803 * q^60 + 2999 * q^61 + 5569 * q^62 + 2377 * q^63 + 2082 * q^64 + 5578 * q^65 + 3338 * q^66 + 961 * q^67 - 3754 * q^68 + 1817 * q^69 + 2738 * q^70 + 8003 * q^71 + 1412 * q^72 - 1011 * q^73 - 1413 * q^74 + 7457 * q^75 + 5516 * q^76 + 4052 * q^77 + 1091 * q^78 - 4422 * q^79 + 1610 * q^80 + 2108 * q^81 + 4676 * q^82 - 297 * q^83 - 54 * q^84 + 4333 * q^85 + 1377 * q^87 + 3652 * q^88 + 2480 * q^89 - 1414 * q^90 + 4551 * q^91 - 3286 * q^92 + 4 * q^93 + 4609 * q^94 - 835 * q^95 + 5864 * q^96 + 3785 * q^97 + 753 * q^98 + 5072 * 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 $

$2$	−3.29999	−1.16672	−0.583361	−	0.812213i	$-0.698263\pi$
$2$	−3.29999	−1.16672	−0.583361	+	0.812213i	$0.698263\pi$
$3$	5.03144	0.968301	0.484150	−	0.874985i	$-0.339129\pi$
$3$	5.03144	0.968301	0.484150	+	0.874985i	$0.339129\pi$
$4$	2.88991	0.361239
$5$	8.27916	0.740511	0.370255	−	0.928930i	$-0.379270\pi$
$5$	8.27916	0.740511	0.370255	+	0.928930i	$0.379270\pi$
$6$	−16.6037	−1.12974
$7$	−12.1380	−0.655393	−0.327696	−	0.944783i	$-0.606272\pi$
$7$	−12.1380	−0.655393	−0.327696	+	0.944783i	$0.606272\pi$
$8$	16.8632	0.745257
$9$	−1.68463	−0.0623936
$10$	−27.3211	−0.863970
$11$	−21.7668	−0.596631	−0.298316	−	0.954467i	$-0.596425\pi$
$11$	−21.7668	−0.596631	−0.298316	+	0.954467i	$0.596425\pi$
$12$	14.5404	0.349788
$13$	44.9239	0.958434	0.479217	−	0.877697i	$-0.340921\pi$
$13$	44.9239	0.958434	0.479217	+	0.877697i	$0.340921\pi$
$14$	40.0554	0.764661
$15$	41.6561	0.717037
$16$	−78.7677	−1.23075
$17$	42.4177	0.605164	0.302582	−	0.953123i	$-0.402151\pi$
$17$	42.4177	0.605164	0.302582	+	0.953123i	$0.402151\pi$
$18$	5.55925	0.0727959
$19$	−34.2760	−0.413866	−0.206933	−	0.978355i	$-0.566348\pi$
$19$	−34.2760	−0.413866	−0.206933	+	0.978355i	$0.566348\pi$
$20$	23.9260	0.267501
$21$	−61.0718	−0.634618
$22$	71.8302	0.696102
$23$	136.379	1.23639	0.618196	−	0.786024i	$-0.287864\pi$
$23$	136.379	1.23639	0.618196	+	0.786024i	$0.287864\pi$
$24$	84.8463	0.721633
$25$	−56.4554	−0.451643
$26$	−148.248	−1.11822
$27$	−144.325	−1.02872
$28$	−35.0778	−0.236753
$29$	31.7146	0.203078	0.101539	−	0.994832i	$-0.467623\pi$
$29$	31.7146	0.203078	0.101539	+	0.994832i	$0.467623\pi$
$30$	−137.465	−0.836583
$31$	249.236	1.44400	0.722002	−	0.691891i	$-0.243222\pi$
$31$	249.236	1.44400	0.722002	+	0.691891i	$0.243222\pi$
$32$	125.026	0.690680
$33$	−109.518	−0.577719
$34$	−139.978	−0.706058
$35$	−100.493	−0.485326
$36$	−4.86842	−0.0225390
$37$	−20.9446	−0.0930612	−0.0465306	−	0.998917i	$-0.514817\pi$
$37$	−20.9446	−0.0930612	−0.0465306	+	0.998917i	$0.514817\pi$
$38$	113.110	0.482866
$39$	226.032	0.928052
$40$	139.613	0.551871
$41$	−89.6713	−0.341568	−0.170784	−	0.985308i	$-0.554630\pi$
$41$	−89.6713	−0.341568	−0.170784	+	0.985308i	$0.554630\pi$
$42$	201.536	0.740422
$43$	0	0
$43$	0	0
$44$	−62.9041	−0.215526
$45$	−13.9473	−0.0462032
$46$	−450.049	−1.44253
$47$	229.845	0.713325	0.356662	−	0.934233i	$-0.383915\pi$
$47$	229.845	0.713325	0.356662	+	0.934233i	$0.383915\pi$
$48$	−396.315	−1.19173
$49$	−195.668	−0.570460
$50$	186.302	0.526942
$51$	213.422	0.585981
$52$	129.826	0.346223
$53$	−674.595	−1.74835	−0.874177	−	0.485608i	$-0.838598\pi$
$53$	−674.595	−1.74835	−0.874177	+	0.485608i	$0.838598\pi$
$54$	476.270	1.20023
$55$	−180.211	−0.441812
$56$	−204.687	−0.488436
$57$	−172.458	−0.400747
$58$	−104.658	−0.236935
$59$	−370.448	−0.817427	−0.408714	−	0.912663i	$-0.634023\pi$
$59$	−370.448	−0.817427	−0.408714	+	0.912663i	$0.634023\pi$
$60$	120.382	0.259022
$61$	797.326	1.67356	0.836780	−	0.547539i	$-0.184435\pi$
$61$	797.326	1.67356	0.836780	+	0.547539i	$0.184435\pi$
$62$	−822.476	−1.68475
$63$	20.4481	0.0408923
$64$	217.556	0.424914
$65$	371.932	0.709731
$66$	361.409	0.674037
$67$	769.340	1.40283	0.701416	−	0.712752i	$-0.252551\pi$
$67$	769.340	1.40283	0.701416	+	0.712752i	$0.252551\pi$
$68$	122.583	0.218609
$69$	686.184	1.19720
$70$	331.625	0.566240
$71$	−127.427	−0.212996	−0.106498	−	0.994313i	$-0.533964\pi$
$71$	−127.427	−0.212996	−0.106498	+	0.994313i	$0.533964\pi$
$72$	−28.4083	−0.0464992
$73$	−80.4806	−0.129035	−0.0645174	−	0.997917i	$-0.520551\pi$
$73$	−80.4806	−0.129035	−0.0645174	+	0.997917i	$0.520551\pi$
$74$	69.1168	0.108577
$75$	−284.052	−0.437327
$76$	−99.0545	−0.149504
$77$	264.207	0.391028
$78$	−745.901	−1.08278
$79$	−862.471	−1.22830	−0.614149	−	0.789190i	$-0.710501\pi$
$79$	−862.471	−1.22830	−0.614149	+	0.789190i	$0.710501\pi$
$80$	−652.131	−0.911380
$81$	−680.677	−0.933713
$82$	295.914	0.398515
$83$	493.132	0.652148	0.326074	−	0.945344i	$-0.394274\pi$
$83$	493.132	0.652148	0.326074	+	0.945344i	$0.394274\pi$
$84$	−176.492	−0.229248
$85$	351.183	0.448131
$86$	0	0
$87$	159.570	0.196640
$88$	−367.059	−0.444643
$89$	441.464	0.525788	0.262894	−	0.964825i	$-0.415323\pi$
$89$	441.464	0.525788	0.262894	+	0.964825i	$0.415323\pi$
$90$	46.0259	0.0539062
$91$	−545.288	−0.628151
$92$	394.123	0.446633
$93$	1254.02	1.39823
$94$	−758.484	−0.832251
$95$	−283.777	−0.306472
$96$	629.063	0.668786
$97$	214.747	0.224786	0.112393	−	0.993664i	$-0.464148\pi$
$97$	214.747	0.224786	0.112393	+	0.993664i	$0.464148\pi$
$98$	645.701	0.665568
$99$	36.6690	0.0372260
$100$	−163.151	−0.163151
$101$	1761.56	1.73546	0.867730	−	0.497035i	$-0.165578\pi$
$101$	1761.56	1.73546	0.867730	+	0.497035i	$0.165578\pi$
$102$	−704.289	−0.683677
$103$	1902.83	1.82030	0.910152	−	0.414275i	$-0.135965\pi$
$103$	1902.83	1.82030	0.910152	+	0.414275i	$0.135965\pi$
$104$	757.561	0.714279
$105$	−505.624	−0.469941
$106$	2226.15	2.03984
$107$	−1243.31	−1.12332	−0.561659	−	0.827369i	$-0.689837\pi$
$107$	−1243.31	−1.12332	−0.561659	+	0.827369i	$0.689837\pi$
$108$	−417.086	−0.371612
$109$	−68.5719	−0.0602568	−0.0301284	−	0.999546i	$-0.509592\pi$
$109$	−68.5719	−0.0602568	−0.0301284	+	0.999546i	$0.509592\pi$
$110$	594.694	0.515471
$111$	−105.381	−0.0901113
$112$	956.086	0.806622
$113$	2315.63	1.92775	0.963875	−	0.266356i	$-0.0858196\pi$
$113$	2315.63	1.92775	0.963875	+	0.266356i	$0.0858196\pi$
$114$	569.107	0.467560
$115$	1129.11	0.915562
$116$	91.6522	0.0733595
$117$	−75.6800	−0.0598001
$118$	1222.47	0.953710
$119$	−514.868	−0.396620
$120$	702.457	0.534377
$121$	−857.205	−0.644031
$122$	−2631.17	−1.95258
$123$	−451.175	−0.330741
$124$	720.270	0.521630
$125$	−1502.30	−1.07496
$126$	−67.4784	−0.0477100
$127$	−1906.21	−1.33188	−0.665942	−	0.746004i	$-0.731970\pi$
$127$	−1906.21	−1.33188	−0.665942	+	0.746004i	$0.731970\pi$
$128$	−1718.14	−1.18644
$129$	0	0
$130$	−1227.37	−0.828058
$131$	−724.408	−0.483143	−0.241572	−	0.970383i	$-0.577663\pi$
$131$	−724.408	−0.483143	−0.241572	+	0.970383i	$0.577663\pi$
$132$	−316.498	−0.208694
$133$	416.044	0.271245
$134$	−2538.81	−1.63671
$135$	−1194.89	−0.761776
$136$	715.299	0.451003
$137$	2712.95	1.69185	0.845924	−	0.533303i	$-0.179050\pi$
$137$	2712.95	1.69185	0.845924	+	0.533303i	$0.179050\pi$
$138$	−2264.40	−1.39680
$139$	1577.35	0.962509	0.481255	−	0.876581i	$-0.340181\pi$
$139$	1577.35	0.962509	0.481255	+	0.876581i	$0.340181\pi$
$140$	−290.415	−0.175318
$141$	1156.45	0.690713
$142$	420.506	0.248507
$143$	−977.850	−0.571831
$144$	132.694	0.0767906
$145$	262.570	0.150381
$146$	265.585	0.150548
$147$	−984.491	−0.552377
$148$	−60.5279	−0.0336173
$149$	−594.237	−0.326723	−0.163362	−	0.986566i	$-0.552234\pi$
$149$	−594.237	−0.326723	−0.163362	+	0.986566i	$0.552234\pi$
$150$	937.368	0.510238
$151$	2398.47	1.29262	0.646308	−	0.763077i	$-0.276312\pi$
$151$	2398.47	1.29262	0.646308	+	0.763077i	$0.276312\pi$
$152$	−578.004	−0.308436
$153$	−71.4580	−0.0377584
$154$	−871.879	−0.456221
$155$	2063.47	1.06930
$156$	653.211	0.335248
$157$	1465.85	0.745143	0.372571	−	0.928004i	$-0.378476\pi$
$157$	1465.85	0.745143	0.372571	+	0.928004i	$0.378476\pi$
$158$	2846.14	1.43308
$159$	−3394.18	−1.69293
$160$	1035.11	0.511456
$161$	−1655.38	−0.810323
$162$	2246.22	1.08938
$163$	3269.21	1.57095	0.785474	−	0.618895i	$-0.212419\pi$
$163$	3269.21	1.57095	0.785474	+	0.618895i	$0.212419\pi$
$164$	−259.142	−0.123388
$165$	−906.721	−0.427807
$166$	−1627.33	−0.760874
$167$	−3255.61	−1.50854	−0.754272	−	0.656562i	$-0.772010\pi$
$167$	−3255.61	−1.50854	−0.754272	+	0.656562i	$0.772010\pi$
$168$	−1029.87	−0.472953
$169$	−178.847	−0.0814052
$170$	−1158.90	−0.522844
$171$	57.7423	0.0258226
$172$	0	0
$173$	808.144	0.355156	0.177578	−	0.984107i	$-0.443174\pi$
$173$	808.144	0.355156	0.177578	+	0.984107i	$0.443174\pi$
$174$	−526.579	−0.229424
$175$	685.259	0.296004
$176$	1714.52	0.734301
$177$	−1863.89	−0.791515
$178$	−1456.83	−0.613448
$179$	−155.735	−0.0650290	−0.0325145	−	0.999471i	$-0.510352\pi$
$179$	−155.735	−0.0650290	−0.0325145	+	0.999471i	$0.510352\pi$
$180$	−40.3064	−0.0166904
$181$	−892.265	−0.366417	−0.183209	−	0.983074i	$-0.558648\pi$
$181$	−892.265	−0.366417	−0.183209	+	0.983074i	$0.558648\pi$
$182$	1799.44	0.732877
$183$	4011.70	1.62051
$184$	2299.79	0.921430
$185$	−173.404	−0.0689129
$186$	−4138.24	−1.63135
$187$	−923.298	−0.361060
$188$	664.230	0.257680
$189$	1751.82	0.674214
$190$	936.459	0.357568
$191$	−4328.59	−1.63982	−0.819910	−	0.572493i	$-0.805976\pi$
$191$	−4328.59	−1.63982	−0.819910	+	0.572493i	$0.805976\pi$
$192$	1094.62	0.411445
$193$	2235.40	0.833718	0.416859	−	0.908971i	$-0.363131\pi$
$193$	2235.40	0.833718	0.416859	+	0.908971i	$0.363131\pi$
$194$	−708.662	−0.262263
$195$	1871.35	0.687233
$196$	−565.462	−0.206072
$197$	9.21411	0.00333237	0.00166619	−	0.999999i	$-0.499470\pi$
$197$	9.21411	0.00333237	0.00166619	+	0.999999i	$0.499470\pi$
$198$	−121.007	−0.0434323
$199$	−810.712	−0.288793	−0.144397	−	0.989520i	$-0.546124\pi$
$199$	−810.712	−0.288793	−0.144397	+	0.989520i	$0.546124\pi$
$200$	−952.021	−0.336590
$201$	3870.89	1.35836
$202$	−5813.11	−2.02480
$203$	−384.953	−0.133096
$204$	616.770	0.211679
$205$	−742.403	−0.252935
$206$	−6279.31	−2.12379
$207$	−229.748	−0.0771430
$208$	−3538.55	−1.17959
$209$	746.079	0.246925
$210$	1668.55	0.548290
$211$	1555.00	0.507350	0.253675	−	0.967289i	$-0.418361\pi$
$211$	1555.00	0.507350	0.253675	+	0.967289i	$0.418361\pi$
$212$	−1949.52	−0.631573
$213$	−641.139	−0.206245
$214$	4102.89	1.31060
$215$	0	0
$216$	−2433.78	−0.766658
$217$	−3025.24	−0.946391
$218$	226.286	0.0703029
$219$	−404.933	−0.124944
$220$	−520.794	−0.159600
$221$	1905.57	0.580010
$222$	347.757	0.105135
$223$	4107.38	1.23341	0.616705	−	0.787194i	$-0.288467\pi$
$223$	4107.38	1.23341	0.616705	+	0.787194i	$0.288467\pi$
$224$	−1517.58	−0.452667
$225$	95.1064	0.0281797
$226$	−7641.53	−2.24915
$227$	2219.87	0.649065	0.324533	−	0.945875i	$-0.394793\pi$
$227$	2219.87	0.649065	0.324533	+	0.945875i	$0.394793\pi$
$228$	−498.386	−0.144765
$229$	−2477.13	−0.714819	−0.357410	−	0.933948i	$-0.616340\pi$
$229$	−2477.13	−0.714819	−0.357410	+	0.933948i	$0.616340\pi$
$230$	−3726.03	−1.06821
$231$	1329.34	0.378633
$232$	534.810	0.151345
$233$	4888.64	1.37453	0.687264	−	0.726407i	$-0.258811\pi$
$233$	4888.64	1.37453	0.687264	+	0.726407i	$0.258811\pi$
$234$	249.743	0.0697701
$235$	1902.92	0.528225
$236$	−1070.56	−0.295286
$237$	−4339.47	−1.18936
$238$	1699.06	0.462746
$239$	−3150.85	−0.852768	−0.426384	−	0.904542i	$-0.640213\pi$
$239$	−3150.85	−0.852768	−0.426384	+	0.904542i	$0.640213\pi$
$240$	−3281.16	−0.882490
$241$	−2792.03	−0.746269	−0.373134	−	0.927777i	$-0.621717\pi$
$241$	−2792.03	−0.746269	−0.373134	+	0.927777i	$0.621717\pi$
$242$	2828.77	0.751405
$243$	471.988	0.124601
$244$	2304.20	0.604554
$245$	−1619.97	−0.422432
$246$	1488.87	0.385882
$247$	−1539.81	−0.396663
$248$	4202.93	1.07615
$249$	2481.16	0.631475
$250$	4957.57	1.25418
$251$	−1479.36	−0.372018	−0.186009	−	0.982548i	$-0.559555\pi$
$251$	−1479.36	−0.372018	−0.186009	+	0.982548i	$0.559555\pi$
$252$	59.0931	0.0147719
$253$	−2968.54	−0.737671
$254$	6290.48	1.55394
$255$	1766.95	0.433925
$256$	3929.40	0.959326
$257$	5399.30	1.31050	0.655251	−	0.755412i	$-0.272563\pi$
$257$	5399.30	1.31050	0.655251	+	0.755412i	$0.272563\pi$
$258$	0	0
$259$	254.226	0.0609917
$260$	1074.85	0.256382
$261$	−53.4273	−0.0126707
$262$	2390.53	0.563694
$263$	2285.92	0.535954	0.267977	−	0.963425i	$-0.413645\pi$
$263$	2285.92	0.535954	0.267977	+	0.963425i	$0.413645\pi$
$264$	−1846.83	−0.430549
$265$	−5585.08	−1.29468
$266$	−1372.94	−0.316467
$267$	2221.20	0.509121
$268$	2223.32	0.506757
$269$	−7346.40	−1.66512	−0.832561	−	0.553933i	$-0.813126\pi$
$269$	−7346.40	−1.66512	−0.832561	+	0.553933i	$0.813126\pi$
$270$	3943.12	0.888780
$271$	1714.63	0.384342	0.192171	−	0.981361i	$-0.438447\pi$
$271$	1714.63	0.384342	0.192171	+	0.981361i	$0.438447\pi$
$272$	−3341.14	−0.744803
$273$	−2743.58	−0.608239
$274$	−8952.71	−1.97392
$275$	1228.86	0.269465
$276$	1983.01	0.432475
$277$	−2412.89	−0.523382	−0.261691	−	0.965152i	$-0.584280\pi$
$277$	−2412.89	−0.523382	−0.261691	+	0.965152i	$0.584280\pi$
$278$	−5205.22	−1.12298
$279$	−419.870	−0.0900967
$280$	−1694.63	−0.361692
$281$	7379.38	1.56661	0.783305	−	0.621638i	$-0.213533\pi$
$281$	7379.38	1.56661	0.783305	+	0.621638i	$0.213533\pi$
$282$	−3816.26	−0.805870
$283$	1782.25	0.374361	0.187180	−	0.982326i	$-0.440065\pi$
$283$	1782.25	0.374361	0.187180	+	0.982326i	$0.440065\pi$
$284$	−368.251	−0.0769425
$285$	−1427.80	−0.296757
$286$	3226.89	0.667168
$287$	1088.43	0.223861
$288$	−210.623	−0.0430940
$289$	−3113.74	−0.633776
$290$	−866.478	−0.175453
$291$	1080.49	0.217661
$292$	−232.581	−0.0466123
$293$	1862.00	0.371261	0.185631	−	0.982620i	$-0.440567\pi$
$293$	1862.00	0.371261	0.185631	+	0.982620i	$0.440567\pi$
$294$	3248.80	0.644470
$295$	−3067.00	−0.605314
$296$	−353.193	−0.0693545
$297$	3141.50	0.613764
$298$	1960.97	0.381195
$299$	6126.68	1.18500
$300$	−820.884	−0.157979
$301$	0	0
$302$	−7914.93	−1.50812
$303$	8863.17	1.68045
$304$	2699.84	0.509363
$305$	6601.19	1.23929
$306$	235.810	0.0440535
$307$	9971.32	1.85372	0.926862	−	0.375403i	$-0.122496\pi$
$307$	9971.32	1.85372	0.926862	+	0.375403i	$0.122496\pi$
$308$	763.533	0.141254
$309$	9573.96	1.76260
$310$	−6809.41	−1.24758
$311$	1200.78	0.218939	0.109469	−	0.993990i	$-0.465085\pi$
$311$	1200.78	0.218939	0.109469	+	0.993990i	$0.465085\pi$
$312$	3811.62	0.691637
$313$	1935.57	0.349536	0.174768	−	0.984610i	$-0.444083\pi$
$313$	1935.57	0.349536	0.174768	+	0.984610i	$0.444083\pi$
$314$	−4837.28	−0.869374
$315$	169.293	0.0302812
$316$	−2492.46	−0.443708
$317$	2732.03	0.484057	0.242029	−	0.970269i	$-0.422187\pi$
$317$	2732.03	0.484057	0.242029	+	0.970269i	$0.422187\pi$
$318$	11200.8	1.97518
$319$	−690.326	−0.121162
$320$	1801.18	0.314654
$321$	−6255.62	−1.08771
$322$	5462.72	0.945421
$323$	−1453.91	−0.250457
$324$	−1967.09	−0.337293
$325$	−2536.20	−0.432870
$326$	−10788.4	−1.83286
$327$	−345.015	−0.0583467
$328$	−1512.15	−0.254556
$329$	−2789.86	−0.467508
$330$	2992.17	0.499131
$331$	−4089.91	−0.679159	−0.339580	−	0.940577i	$-0.610285\pi$
$331$	−4089.91	−0.679159	−0.339580	+	0.940577i	$0.610285\pi$
$332$	1425.11	0.235581
$333$	35.2838	0.00580643
$334$	10743.5	1.76005
$335$	6369.49	1.03881
$336$	4810.49	0.781052
$337$	6972.49	1.12705	0.563525	−	0.826099i	$-0.309445\pi$
$337$	6972.49	1.12705	0.563525	+	0.826099i	$0.309445\pi$
$338$	590.193	0.0949771
$339$	11650.9	1.86664
$340$	1014.89	0.161882
$341$	−5425.08	−0.861538
$342$	−190.549	−0.0301278
$343$	6538.38	1.02927
$344$	0	0
$345$	5681.03	0.886540
$346$	−2666.86	−0.414368
$347$	5083.28	0.786411	0.393206	−	0.919451i	$-0.371366\pi$
$347$	5083.28	0.786411	0.393206	+	0.919451i	$0.371366\pi$
$348$	461.143	0.0710340
$349$	−53.7603	−0.00824562	−0.00412281	−	0.999992i	$-0.501312\pi$
$349$	−53.7603	−0.00824562	−0.00412281	+	0.999992i	$0.501312\pi$
$350$	−2261.34	−0.345354
$351$	−6483.63	−0.985956
$352$	−2721.43	−0.412081
$353$	−2762.47	−0.416520	−0.208260	−	0.978074i	$-0.566780\pi$
$353$	−2762.47	−0.416520	−0.208260	+	0.978074i	$0.566780\pi$
$354$	6150.80	0.923478
$355$	−1054.99	−0.157726
$356$	1275.79	0.189935
$357$	−2590.52	−0.384048
$358$	513.924	0.0758707
$359$	−1463.00	−0.215082	−0.107541	−	0.994201i	$-0.534298\pi$
$359$	−1463.00	−0.215082	−0.107541	+	0.994201i	$0.534298\pi$
$360$	−235.197	−0.0344332
$361$	−5684.16	−0.828715
$362$	2944.46	0.427507
$363$	−4312.98	−0.623616
$364$	−1575.83	−0.226912
$365$	−666.312	−0.0955517
$366$	−13238.5	−1.89068
$367$	6824.12	0.970616	0.485308	−	0.874343i	$-0.338707\pi$
$367$	6824.12	0.970616	0.485308	+	0.874343i	$0.338707\pi$
$368$	−10742.3	−1.52168
$369$	151.063	0.0213117
$370$	572.229	0.0804021
$371$	8188.27	1.14586
$372$	3623.99	0.505095
$373$	−7220.23	−1.00228	−0.501138	−	0.865367i	$-0.667085\pi$
$373$	−7220.23	−1.00228	−0.501138	+	0.865367i	$0.667085\pi$
$374$	3046.87	0.421256
$375$	−7558.73	−1.04088
$376$	3875.92	0.531610
$377$	1424.74	0.194636
$378$	−5780.99	−0.786619
$379$	2522.66	0.341901	0.170950	−	0.985280i	$-0.445316\pi$
$379$	2522.66	0.341901	0.170950	+	0.985280i	$0.445316\pi$
$380$	−820.088	−0.110710
$381$	−9591.00	−1.28966
$382$	14284.3	1.91321
$383$	2421.94	0.323121	0.161561	−	0.986863i	$-0.448347\pi$
$383$	2421.94	0.323121	0.161561	+	0.986863i	$0.448347\pi$
$384$	−8644.73	−1.14883
$385$	2187.41	0.289560
$386$	−7376.79	−0.972717
$387$	0	0
$388$	620.599	0.0812014
$389$	10280.8	1.33999	0.669993	−	0.742367i	$-0.266297\pi$
$389$	10280.8	1.33999	0.669993	+	0.742367i	$0.266297\pi$
$390$	−6175.44	−0.801809
$391$	5784.89	0.748221
$392$	−3299.59	−0.425139
$393$	−3644.81	−0.467828
$394$	−30.4064	−0.00388795
$395$	−7140.54	−0.909568
$396$	105.970	0.0134475
$397$	13220.2	1.67130	0.835648	−	0.549266i	$-0.185092\pi$
$397$	13220.2	1.67130	0.835648	+	0.549266i	$0.185092\pi$
$398$	2675.34	0.336941
$399$	2093.30	0.262647
$400$	4446.86	0.555858
$401$	2266.54	0.282258	0.141129	−	0.989991i	$-0.454927\pi$
$401$	2266.54	0.282258	0.141129	+	0.989991i	$0.454927\pi$
$402$	−12773.9	−1.58483
$403$	11196.7	1.38398
$404$	5090.74	0.626915
$405$	−5635.44	−0.691425
$406$	1270.34	0.155286
$407$	455.897	0.0555232
$408$	3598.98	0.436706
$409$	8566.55	1.03567	0.517835	−	0.855481i	$-0.326738\pi$
$409$	8566.55	1.03567	0.517835	+	0.855481i	$0.326738\pi$
$410$	2449.92	0.295105
$411$	13650.1	1.63822
$412$	5499.00	0.657564
$413$	4496.51	0.535736
$414$	758.166	0.0900044
$415$	4082.72	0.482922
$416$	5616.67	0.661971
$417$	7936.32	0.931998
$418$	−2462.05	−0.288093
$419$	5771.91	0.672974	0.336487	−	0.941688i	$-0.390761\pi$
$419$	5771.91	0.672974	0.336487	+	0.941688i	$0.390761\pi$
$420$	−1461.21	−0.169761
$421$	−11677.1	−1.35180	−0.675899	−	0.736994i	$-0.736245\pi$
$421$	−11677.1	−1.35180	−0.675899	+	0.736994i	$0.736245\pi$
$422$	−5131.49	−0.591937
$423$	−387.202	−0.0445069
$424$	−11375.9	−1.30297
$425$	−2394.71	−0.273319
$426$	2115.75	0.240630
$427$	−9677.98	−1.09684
$428$	−3593.04	−0.405785
$429$	−4919.99	−0.553705
$430$	0	0
$431$	841.434	0.0940382	0.0470191	−	0.998894i	$-0.485028\pi$
$431$	841.434	0.0940382	0.0470191	+	0.998894i	$0.485028\pi$
$432$	11368.1	1.26609
$433$	16667.1	1.84981	0.924907	−	0.380194i	$-0.124143\pi$
$433$	16667.1	1.84981	0.924907	+	0.380194i	$0.124143\pi$
$434$	9983.25	1.10417
$435$	1321.11	0.145614
$436$	−198.166	−0.0217671
$437$	−4674.53	−0.511701
$438$	1336.27	0.145775
$439$	5511.91	0.599246	0.299623	−	0.954058i	$-0.403139\pi$
$439$	5511.91	0.599246	0.299623	+	0.954058i	$0.403139\pi$
$440$	−3038.94	−0.329263
$441$	329.627	0.0355931
$442$	−6288.34	−0.676710
$443$	10220.7	1.09616	0.548080	−	0.836426i	$-0.315359\pi$
$443$	10220.7	1.09616	0.548080	+	0.836426i	$0.315359\pi$
$444$	−304.542	−0.0325517
$445$	3654.95	0.389352
$446$	−13554.3	−1.43905
$447$	−2989.87	−0.316366
$448$	−2640.71	−0.278486
$449$	9377.34	0.985621	0.492811	−	0.870137i	$-0.335970\pi$
$449$	9377.34	0.985621	0.492811	+	0.870137i	$0.335970\pi$
$450$	−313.850	−0.0328778
$451$	1951.86	0.203790
$452$	6691.94	0.696377
$453$	12067.8	1.25164
$454$	−7325.53	−0.757278
$455$	−4514.53	−0.465152
$456$	−2908.19	−0.298659
$457$	4907.82	0.502359	0.251180	−	0.967941i	$-0.419182\pi$
$457$	4907.82	0.502359	0.251180	+	0.967941i	$0.419182\pi$
$458$	8174.51	0.833995
$459$	−6121.93	−0.622543
$460$	3263.01	0.330736
$461$	−11678.8	−1.17991	−0.589953	−	0.807438i	$-0.700854\pi$
$461$	−11678.8	−1.17991	−0.589953	+	0.807438i	$0.700854\pi$
$462$	−4386.80	−0.441759
$463$	13092.8	1.31420	0.657100	−	0.753804i	$-0.271783\pi$
$463$	13092.8	1.31420	0.657100	+	0.753804i	$0.271783\pi$
$464$	−2498.08	−0.249937
$465$	10382.2	1.03541
$466$	−16132.4	−1.60369
$467$	7904.09	0.783207	0.391604	−	0.920134i	$-0.371920\pi$
$467$	7904.09	0.783207	0.391604	+	0.920134i	$0.371920\pi$
$468$	−218.708	−0.0216021
$469$	−9338.28	−0.919407
$470$	−6279.61	−0.616291
$471$	7375.32	0.721522
$472$	−6246.95	−0.609193
$473$	0	0
$474$	14320.2	1.38765
$475$	1935.07	0.186920
$476$	−1487.92	−0.143275
$477$	1136.44	0.109086
$478$	10397.8	0.994943
$479$	15995.1	1.52575	0.762877	−	0.646544i	$-0.223786\pi$
$479$	15995.1	1.52575	0.762877	+	0.646544i	$0.223786\pi$
$480$	5208.11	0.495243
$481$	−940.911	−0.0891930
$482$	9213.67	0.870688
$483$	−8328.93	−0.784636
$484$	−2477.24	−0.232649
$485$	1777.93	0.166457
$486$	−1557.56	−0.145375
$487$	−3597.03	−0.334696	−0.167348	−	0.985898i	$-0.553520\pi$
$487$	−3597.03	−0.334696	−0.167348	+	0.985898i	$0.553520\pi$
$488$	13445.5	1.24723
$489$	16448.8	1.52115
$490$	5345.87	0.492860
$491$	−1684.84	−0.154859	−0.0774296	−	0.996998i	$-0.524671\pi$
$491$	−1684.84	−0.154859	−0.0774296	+	0.996998i	$0.524671\pi$
$492$	−1303.86	−0.119476
$493$	1345.26	0.122895
$494$	5081.35	0.462795
$495$	303.589	0.0275662
$496$	−19631.8	−1.77720
$497$	1546.71	0.139596
$498$	−8187.80	−0.736755
$499$	118.197	0.0106037	0.00530185	−	0.999986i	$-0.498312\pi$
$499$	118.197	0.0106037	0.00530185	+	0.999986i	$0.498312\pi$
$500$	−4341.51	−0.388316
$501$	−16380.4	−1.46073
$502$	4881.87	0.434041
$503$	18063.5	1.60122	0.800609	−	0.599187i	$-0.204509\pi$
$503$	18063.5	1.60122	0.800609	+	0.599187i	$0.204509\pi$
$504$	344.821	0.0304753
$505$	14584.2	1.28513
$506$	9796.15	0.860656
$507$	−899.858	−0.0788247
$508$	−5508.78	−0.481127
$509$	13505.3	1.17605	0.588026	−	0.808842i	$-0.299905\pi$
$509$	13505.3	1.17605	0.588026	+	0.808842i	$0.299905\pi$
$510$	−5830.93	−0.506270
$511$	976.877	0.0845685
$512$	778.179	0.0671699
$513$	4946.88	0.425751
$514$	−17817.6	−1.52899
$515$	15753.8	1.34795
$516$	0	0
$517$	−5002.99	−0.425592
$518$	−838.943	−0.0711603
$519$	4066.12	0.343898
$520$	6271.98	0.528931
$521$	−10357.5	−0.870958	−0.435479	−	0.900199i	$-0.643421\pi$
$521$	−10357.5	−0.870958	−0.435479	+	0.900199i	$0.643421\pi$
$522$	176.309	0.0147832
$523$	78.4052	0.00655530	0.00327765	−	0.999995i	$-0.498957\pi$
$523$	78.4052	0.00655530	0.00327765	+	0.999995i	$0.498957\pi$
$524$	−2093.47	−0.174530
$525$	3447.84	0.286621
$526$	−7543.50	−0.625309
$527$	10572.0	0.873860
$528$	8626.51	0.711024
$529$	6432.29	0.528667
$530$	18430.7	1.51053
$531$	624.067	0.0510022
$532$	1202.33	0.0979841
$533$	−4028.38	−0.327370
$534$	−7329.93	−0.594002
$535$	−10293.5	−0.831829
$536$	12973.6	1.04547
$537$	−783.572	−0.0629676
$538$	24243.0	1.94273
$539$	4259.07	0.340354
$540$	−3453.12	−0.275183
$541$	16422.2	1.30508	0.652539	−	0.757755i	$-0.273704\pi$
$541$	16422.2	1.30508	0.652539	+	0.757755i	$0.273704\pi$
$542$	−5658.27	−0.448420
$543$	−4489.38	−0.354802
$544$	5303.33	0.417975
$545$	−567.718	−0.0446208
$546$	9053.78	0.709645
$547$	−2935.23	−0.229436	−0.114718	−	0.993398i	$-0.536596\pi$
$547$	−2935.23	−0.229436	−0.114718	+	0.993398i	$0.536596\pi$
$548$	7840.18	0.611161
$549$	−1343.20	−0.104419
$550$	−4055.21	−0.314390
$551$	−1087.05	−0.0840469
$552$	11571.3	0.892221
$553$	10468.7	0.805018
$554$	7962.52	0.610641
$555$	−872.469	−0.0667284
$556$	4558.39	0.347695
$557$	6806.76	0.517795	0.258897	−	0.965905i	$-0.416641\pi$
$557$	6806.76	0.517795	0.258897	+	0.965905i	$0.416641\pi$
$558$	1385.57	0.105118
$559$	0	0
$560$	7915.59	0.597312
$561$	−4645.52	−0.349615
$562$	−24351.9	−1.82780
$563$	171.554	0.0128422	0.00642108	−	0.999979i	$-0.497956\pi$
$563$	171.554	0.0128422	0.00642108	+	0.999979i	$0.497956\pi$
$564$	3342.03	0.249512
$565$	19171.4	1.42752
$566$	−5881.42	−0.436774
$567$	8262.09	0.611949
$568$	−2148.82	−0.158737
$569$	−15590.5	−1.14866	−0.574329	−	0.818624i	$-0.694737\pi$
$569$	−15590.5	−1.14866	−0.574329	+	0.818624i	$0.694737\pi$
$570$	4711.73	0.346233
$571$	−20811.4	−1.52527	−0.762637	−	0.646827i	$-0.776096\pi$
$571$	−20811.4	−1.52527	−0.762637	+	0.646827i	$0.776096\pi$
$572$	−2825.90	−0.206568
$573$	−21779.0	−1.58784
$574$	−3591.82	−0.261184
$575$	−7699.35	−0.558409
$576$	−366.501	−0.0265119
$577$	−18893.4	−1.36316	−0.681580	−	0.731744i	$-0.738707\pi$
$577$	−18893.4	−1.36316	−0.681580	+	0.731744i	$0.738707\pi$
$578$	10275.3	0.739440
$579$	11247.3	0.807290
$580$	758.804	0.0543235
$581$	−5985.66	−0.427413
$582$	−3565.59	−0.253949
$583$	14683.8	1.04312
$584$	−1357.16	−0.0961640
$585$	−626.567	−0.0442827
$586$	−6144.59	−0.433158
$587$	313.601	0.0220506	0.0110253	−	0.999939i	$-0.496490\pi$
$587$	313.601	0.0220506	0.0110253	+	0.999939i	$0.496490\pi$
$588$	−2845.09	−0.199540
$589$	−8542.82	−0.597624
$590$	10121.1	0.706233
$591$	46.3602	0.00322674
$592$	1649.76	0.114535
$593$	16354.7	1.13256	0.566280	−	0.824213i	$-0.308382\pi$
$593$	16354.7	1.13256	0.566280	+	0.824213i	$0.308382\pi$
$594$	−10366.9	−0.716092
$595$	−4262.67	−0.293702
$596$	−1717.29	−0.118025
$597$	−4079.05	−0.279639
$598$	−20218.0	−1.38256
$599$	−6463.05	−0.440857	−0.220428	−	0.975403i	$-0.570746\pi$
$599$	−6463.05	−0.440857	−0.220428	+	0.975403i	$0.570746\pi$
$600$	−4790.04	−0.325921
$601$	−13862.4	−0.940864	−0.470432	−	0.882436i	$-0.655902\pi$
$601$	−13862.4	−0.940864	−0.470432	+	0.882436i	$0.655902\pi$
$602$	0	0
$603$	−1296.05	−0.0875278
$604$	6931.37	0.466943
$605$	−7096.94	−0.476912
$606$	−29248.3	−1.96061
$607$	−968.595	−0.0647678	−0.0323839	−	0.999476i	$-0.510310\pi$
$607$	−968.595	−0.0647678	−0.0323839	+	0.999476i	$0.510310\pi$
$608$	−4285.40	−0.285849
$609$	−1936.87	−0.128877
$610$	−21783.9	−1.44591
$611$	10325.5	0.683674
$612$	−206.507	−0.0136398
$613$	−15918.1	−1.04882	−0.524411	−	0.851465i	$-0.675714\pi$
$613$	−15918.1	−1.04882	−0.524411	+	0.851465i	$0.675714\pi$
$614$	−32905.2	−2.16278
$615$	−3735.36	−0.244917
$616$	4455.38	0.291416
$617$	−4544.12	−0.296498	−0.148249	−	0.988950i	$-0.547364\pi$
$617$	−4544.12	−0.296498	−0.148249	+	0.988950i	$0.547364\pi$
$618$	−31593.9	−2.05646
$619$	−22300.5	−1.44803	−0.724017	−	0.689782i	$-0.757706\pi$
$619$	−22300.5	−1.44803	−0.724017	+	0.689782i	$0.757706\pi$
$620$	5963.23	0.386273
$621$	−19682.9	−1.27190
$622$	−3962.55	−0.255440
$623$	−5358.51	−0.344598
$624$	−17804.0	−1.14220
$625$	−5380.85	−0.344375
$626$	−6387.34	−0.407811
$627$	3753.85	0.239098
$628$	4236.17	0.269174
$629$	−888.420	−0.0563173
$630$	−558.665	−0.0353297
$631$	328.745	0.0207403	0.0103701	−	0.999946i	$-0.496699\pi$
$631$	328.745	0.0207403	0.0103701	+	0.999946i	$0.496699\pi$
$632$	−14544.0	−0.915397
$633$	7823.91	0.491268
$634$	−9015.66	−0.564760
$635$	−15781.9	−0.986274
$636$	−9808.88	−0.611552
$637$	−8790.15	−0.546748
$638$	2278.07	0.141363
$639$	214.666	0.0132896
$640$	−14224.8	−0.878569
$641$	29957.7	1.84595	0.922977	−	0.384855i	$-0.125749\pi$
$641$	29957.7	1.84595	0.922977	+	0.384855i	$0.125749\pi$
$642$	20643.5	1.26905
$643$	−9666.34	−0.592851	−0.296426	−	0.955056i	$-0.595795\pi$
$643$	−9666.34	−0.592851	−0.296426	+	0.955056i	$0.595795\pi$
$644$	−4783.89	−0.292720
$645$	0	0
$646$	4797.87	0.292213
$647$	−16226.9	−0.986004	−0.493002	−	0.870028i	$-0.664100\pi$
$647$	−16226.9	−0.986004	−0.493002	+	0.870028i	$0.664100\pi$
$648$	−11478.4	−0.695856
$649$	8063.47	0.487703
$650$	8369.41	0.505039
$651$	−15221.3	−0.916391
$652$	9447.72	0.567487
$653$	3595.76	0.215487	0.107743	−	0.994179i	$-0.465637\pi$
$653$	3595.76	0.215487	0.107743	+	0.994179i	$0.465637\pi$
$654$	1138.55	0.0680744
$655$	−5997.49	−0.357773
$656$	7063.20	0.420383
$657$	135.580	0.00805095
$658$	9206.51	0.545452
$659$	18664.7	1.10330	0.551648	−	0.834077i	$-0.313999\pi$
$659$	18664.7	1.10330	0.551648	+	0.834077i	$0.313999\pi$
$660$	−2620.34	−0.154540
$661$	20339.2	1.19683	0.598413	−	0.801188i	$-0.295798\pi$
$661$	20339.2	1.19683	0.598413	+	0.801188i	$0.295798\pi$
$662$	13496.6	0.792390
$663$	9587.73	0.561624
$664$	8315.80	0.486017
$665$	3444.49	0.200860
$666$	−116.436	−0.00677448
$667$	4325.21	0.251084
$668$	−9408.43	−0.544945
$669$	20666.0	1.19431
$670$	−21019.2	−1.21201
$671$	−17355.3	−0.998498
$672$	−7635.59	−0.438318
$673$	−10057.9	−0.576083	−0.288042	−	0.957618i	$-0.593004\pi$
$673$	−10057.9	−0.576083	−0.288042	+	0.957618i	$0.593004\pi$
$674$	−23009.1	−1.31495
$675$	8147.93	0.464613
$676$	−516.852	−0.0294067
$677$	−21717.7	−1.23291	−0.616454	−	0.787391i	$-0.711431\pi$
$677$	−21717.7	−1.23291	−0.616454	+	0.787391i	$0.711431\pi$
$678$	−38447.9	−2.17785
$679$	−2606.61	−0.147323
$680$	5922.08	0.333973
$681$	11169.1	0.628490
$682$	17902.7	1.00518
$683$	−26605.1	−1.49050	−0.745252	−	0.666783i	$-0.767671\pi$
$683$	−26605.1	−1.49050	−0.745252	+	0.666783i	$0.767671\pi$
$684$	166.870	0.00932811
$685$	22461.0	1.25283
$686$	−21576.5	−1.20087
$687$	−12463.5	−0.692160
$688$	0	0
$689$	−30305.4	−1.67568
$690$	−18747.3	−1.03434
$691$	22701.2	1.24978	0.624888	−	0.780715i	$-0.285145\pi$
$691$	22701.2	1.24978	0.624888	+	0.780715i	$0.285145\pi$
$692$	2335.46	0.128296
$693$	−445.090	−0.0243976
$694$	−16774.7	−0.917523
$695$	13059.1	0.712749
$696$	2690.87	0.146547
$697$	−3803.65	−0.206705
$698$	177.408	0.00962034
$699$	24596.9	1.33096
$700$	1980.33	0.106928
$701$	−21442.0	−1.15528	−0.577641	−	0.816291i	$-0.696026\pi$
$701$	−21442.0	−1.15528	−0.577641	+	0.816291i	$0.696026\pi$
$702$	21395.9	1.15034
$703$	717.896	0.0385149
$704$	−4735.50	−0.253517
$705$	9574.43	0.511481
$706$	9116.11	0.485962
$707$	−21381.9	−1.13741
$708$	−5386.46	−0.285926
$709$	−1419.07	−0.0751682	−0.0375841	−	0.999293i	$-0.511966\pi$
$709$	−1419.07	−0.0751682	−0.0375841	+	0.999293i	$0.511966\pi$
$710$	3481.44	0.184023
$711$	1452.94	0.0766379
$712$	7444.51	0.391847
$713$	33990.6	1.78536
$714$	8548.70	0.448077
$715$	−8095.78	−0.423447
$716$	−450.060	−0.0234910
$717$	−15853.3	−0.825736
$718$	4827.89	0.250940
$719$	2924.35	0.151683	0.0758413	−	0.997120i	$-0.475836\pi$
$719$	2924.35	0.151683	0.0758413	+	0.997120i	$0.475836\pi$
$720$	1098.60	0.0568643
$721$	−23096.6	−1.19301
$722$	18757.6	0.966879
$723$	−14047.9	−0.722613
$724$	−2578.56	−0.132364
$725$	−1790.46	−0.0917187
$726$	14232.8	0.727586
$727$	−29066.1	−1.48281	−0.741405	−	0.671058i	$-0.765840\pi$
$727$	−29066.1	−1.48281	−0.741405	+	0.671058i	$0.765840\pi$
$728$	−9195.32	−0.468133
$729$	20753.1	1.05436
$730$	2198.82	0.111482
$731$	0	0
$732$	11593.4	0.585390
$733$	−36280.3	−1.82816	−0.914082	−	0.405530i	$-0.867087\pi$
$733$	−36280.3	−1.82816	−0.914082	+	0.405530i	$0.867087\pi$
$734$	−22519.5	−1.13244
$735$	−8150.76	−0.409041
$736$	17051.0	0.853952
$737$	−16746.1	−0.836974
$738$	−498.505	−0.0248648
$739$	3392.34	0.168862	0.0844312	−	0.996429i	$-0.473093\pi$
$739$	3392.34	0.168862	0.0844312	+	0.996429i	$0.473093\pi$
$740$	−501.120	−0.0248940
$741$	−7747.46	−0.384089
$742$	−27021.2	−1.33690
$743$	14133.8	0.697870	0.348935	−	0.937147i	$-0.386543\pi$
$743$	14133.8	0.697870	0.348935	+	0.937147i	$0.386543\pi$
$744$	21146.8	1.04204
$745$	−4919.78	−0.241942
$746$	23826.6	1.16938
$747$	−830.743	−0.0406898
$748$	−2668.25	−0.130429
$749$	15091.3	0.736214
$750$	24943.7	1.21442
$751$	28790.0	1.39889	0.699443	−	0.714688i	$-0.253431\pi$
$751$	28790.0	1.39889	0.699443	+	0.714688i	$0.253431\pi$
$752$	−18104.3	−0.877921
$753$	−7443.32	−0.360225
$754$	−4701.63	−0.227086
$755$	19857.4	0.957197
$756$	5062.61	0.243552
$757$	10323.5	0.495657	0.247829	−	0.968804i	$-0.420283\pi$
$757$	10323.5	0.495657	0.247829	+	0.968804i	$0.420283\pi$
$758$	−8324.75	−0.398903
$759$	−14936.0	−0.714287
$760$	−4785.39	−0.228400
$761$	−23500.4	−1.11944	−0.559718	−	0.828683i	$-0.689090\pi$
$761$	−23500.4	−1.11944	−0.559718	+	0.828683i	$0.689090\pi$
$762$	31650.2	1.50468
$763$	832.329	0.0394919
$764$	−12509.2	−0.592366
$765$	−591.612	−0.0279605
$766$	−7992.37	−0.376992
$767$	−16641.9	−0.783450
$768$	19770.5	0.928917
$769$	−27214.3	−1.27617	−0.638083	−	0.769968i	$-0.720272\pi$
$769$	−27214.3	−1.27617	−0.638083	+	0.769968i	$0.720272\pi$
$770$	−7218.43	−0.337836
$771$	27166.2	1.26896
$772$	6460.10	0.301171
$773$	23293.4	1.08383	0.541917	−	0.840432i	$-0.317699\pi$
$773$	23293.4	1.08383	0.541917	+	0.840432i	$0.317699\pi$
$774$	0	0
$775$	−14070.7	−0.652175
$776$	3621.33	0.167523
$777$	1279.12	0.0590583
$778$	−33926.3	−1.56339
$779$	3073.57	0.141363
$780$	5408.04	0.248255
$781$	2773.67	0.127080
$782$	−19090.0	−0.872965
$783$	−4577.21	−0.208909
$784$	15412.3	0.702091
$785$	12136.0	0.551786
$786$	12027.8	0.545825
$787$	−27483.2	−1.24482	−0.622408	−	0.782693i	$-0.713845\pi$
$787$	−27483.2	−1.24482	−0.622408	+	0.782693i	$0.713845\pi$
$788$	26.6279	0.00120378
$789$	11501.5	0.518965
$790$	23563.7	1.06121
$791$	−28107.2	−1.26343
$792$	618.358	0.0277429
$793$	35819.0	1.60400
$794$	−43626.6	−1.94994
$795$	−28101.0	−1.25363
$796$	−2342.88	−0.104323
$797$	−27108.2	−1.20480	−0.602398	−	0.798196i	$-0.705788\pi$
$797$	−27108.2	−1.20480	−0.602398	+	0.798196i	$0.705788\pi$
$798$	−6907.85	−0.306435
$799$	9749.47	0.431679
$800$	−7058.42	−0.311941
$801$	−743.703	−0.0328058
$802$	−7479.55	−0.329317
$803$	1751.81	0.0769862
$804$	11186.5	0.490693
$805$	−13705.1	−0.600053
$806$	−36948.8	−1.61472
$807$	−36963.0	−1.61234
$808$	29705.6	1.29336
$809$	−2729.12	−0.118604	−0.0593020	−	0.998240i	$-0.518887\pi$
$809$	−2729.12	−0.118604	−0.0593020	+	0.998240i	$0.518887\pi$
$810$	18596.9	0.806700
$811$	7382.40	0.319644	0.159822	−	0.987146i	$-0.448908\pi$
$811$	7382.40	0.319644	0.159822	+	0.987146i	$0.448908\pi$
$812$	−1112.48	−0.0480793
$813$	8627.07	0.372158
$814$	−1504.45	−0.0647801
$815$	27066.3	1.16330
$816$	−16810.7	−0.721194
$817$	0	0
$818$	−28269.5	−1.20834
$819$	918.607	0.0391926
$820$	−2145.48	−0.0913699
$821$	−41135.6	−1.74865	−0.874326	−	0.485339i	$-0.838696\pi$
$821$	−41135.6	−1.74865	−0.874326	+	0.485339i	$0.838696\pi$
$822$	−45045.0	−1.91134
$823$	−7081.66	−0.299941	−0.149970	−	0.988690i	$-0.547918\pi$
$823$	−7081.66	−0.299941	−0.149970	+	0.988690i	$0.547918\pi$
$824$	32087.8	1.35659
$825$	6182.91	0.260923
$826$	−14838.4	−0.625055
$827$	−18013.8	−0.757438	−0.378719	−	0.925512i	$-0.623635\pi$
$827$	−18013.8	−0.757438	−0.378719	+	0.925512i	$0.623635\pi$
$828$	−663.951	−0.0278670
$829$	9722.43	0.407327	0.203663	−	0.979041i	$-0.434715\pi$
$829$	9722.43	0.407327	0.203663	+	0.979041i	$0.434715\pi$
$830$	−13472.9	−0.563436
$831$	−12140.3	−0.506791
$832$	9773.46	0.407252
$833$	−8299.77	−0.345222
$834$	−26189.7	−1.08738
$835$	−26953.8	−1.11709
$836$	2156.10	0.0891989
$837$	−35971.0	−1.48547
$838$	−19047.2	−0.785174
$839$	19102.1	0.786030	0.393015	−	0.919532i	$-0.371432\pi$
$839$	19102.1	0.786030	0.393015	+	0.919532i	$0.371432\pi$
$840$	−8526.45	−0.350227
$841$	−23383.2	−0.958759
$842$	38534.3	1.57717
$843$	37128.9	1.51695
$844$	4493.82	0.183275
$845$	−1480.70	−0.0602814
$846$	1277.76	0.0519272
$847$	10404.8	0.422093
$848$	53136.3	2.15178
$849$	8967.30	0.362494
$850$	7902.50	0.318887
$851$	−2856.40	−0.115060
$852$	−1852.83	−0.0745035
$853$	−41712.7	−1.67434	−0.837171	−	0.546941i	$-0.815792\pi$
$853$	−41712.7	−1.67434	−0.837171	+	0.546941i	$0.815792\pi$
$854$	31937.2	1.27971
$855$	478.058	0.0191219
$856$	−20966.2	−0.837160
$857$	28910.6	1.15235	0.576177	−	0.817325i	$-0.304544\pi$
$857$	28910.6	1.15235	0.576177	+	0.817325i	$0.304544\pi$
$858$	16235.9	0.646019
$859$	−14437.6	−0.573463	−0.286731	−	0.958011i	$-0.592569\pi$
$859$	−14437.6	−0.573463	−0.286731	+	0.958011i	$0.592569\pi$
$860$	0	0
$861$	5476.39	0.216765
$862$	−2776.72	−0.109716
$863$	28743.9	1.13378	0.566891	−	0.823793i	$-0.308146\pi$
$863$	28743.9	1.13378	0.566891	+	0.823793i	$0.308146\pi$
$864$	−18044.4	−0.710514
$865$	6690.75	0.262997
$866$	−55001.2	−2.15822
$867$	−15666.6	−0.613686
$868$	−8742.67	−0.341873
$869$	18773.2	0.732841
$870$	−4359.63	−0.169891
$871$	34561.7	1.34452
$872$	−1156.34	−0.0449068
$873$	−361.769	−0.0140252
$874$	15425.9	0.597012
$875$	18235.0	0.704520
$876$	−1170.22	−0.0451348
$877$	−43256.2	−1.66552	−0.832758	−	0.553637i	$-0.813240\pi$
$877$	−43256.2	−1.66552	−0.832758	+	0.553637i	$0.813240\pi$
$878$	−18189.2	−0.699153
$879$	9368.56	0.359492
$880$	14194.8	0.543758
$881$	−5092.66	−0.194752	−0.0973758	−	0.995248i	$-0.531045\pi$
$881$	−5092.66	−0.194752	−0.0973758	+	0.995248i	$0.531045\pi$
$882$	−1087.77	−0.0415272
$883$	2510.31	0.0956725	0.0478362	−	0.998855i	$-0.484767\pi$
$883$	2510.31	0.0956725	0.0478362	+	0.998855i	$0.484767\pi$
$884$	5506.91	0.209522
$885$	−15431.4	−0.586126
$886$	−33728.1	−1.27891
$887$	47927.5	1.81426	0.907130	−	0.420852i	$-0.138269\pi$
$887$	47927.5	1.81426	0.907130	+	0.420852i	$0.138269\pi$
$888$	−1777.07	−0.0671560
$889$	23137.7	0.872907
$890$	−12061.3	−0.454265
$891$	14816.2	0.557083
$892$	11870.0	0.445555
$893$	−7878.15	−0.295221
$894$	9866.51	0.369111
$895$	−1289.36	−0.0481547
$896$	20854.9	0.777582
$897$	30826.0	1.14744
$898$	−30945.1	−1.14995
$899$	7904.42	0.293245
$900$	274.849	0.0101796
$901$	−28614.7	−1.05804
$902$	−6441.11	−0.237766
$903$	0	0
$904$	39048.9	1.43667
$905$	−7387.21	−0.271336
$906$	−39823.5	−1.46032
$907$	−43372.3	−1.58782	−0.793910	−	0.608036i	$-0.791958\pi$
$907$	−43372.3	−1.58782	−0.793910	+	0.608036i	$0.791958\pi$
$908$	6415.21	0.234467
$909$	−2967.57	−0.108282
$910$	14897.9	0.542703
$911$	−13523.3	−0.491820	−0.245910	−	0.969293i	$-0.579087\pi$
$911$	−13523.3	−0.491820	−0.245910	+	0.969293i	$0.579087\pi$
$912$	13584.1	0.493217
$913$	−10733.9	−0.389092
$914$	−16195.7	−0.586113
$915$	33213.5	1.20001
$916$	−7158.69	−0.258220
$917$	8792.89	0.316649
$918$	20202.3	0.726334
$919$	39954.8	1.43415	0.717076	−	0.696995i	$-0.245480\pi$
$919$	39954.8	1.43415	0.717076	+	0.696995i	$0.245480\pi$
$920$	19040.4	0.682329
$921$	50170.1	1.79496
$922$	38539.9	1.37662
$923$	−5724.49	−0.204143
$924$	3841.67	0.136777
$925$	1182.43	0.0420305
$926$	−43206.1	−1.53330
$927$	−3205.56	−0.113575
$928$	3965.16	0.140262
$929$	3658.49	0.129205	0.0646023	−	0.997911i	$-0.479422\pi$
$929$	3658.49	0.129205	0.0646023	+	0.997911i	$0.479422\pi$
$930$	−34261.1	−1.20803
$931$	6706.71	0.236094
$932$	14127.7	0.496533
$933$	6041.64	0.211998
$934$	−26083.4	−0.913784
$935$	−7644.13	−0.267369
$936$	−1276.21	−0.0445664
$937$	12451.7	0.434130	0.217065	−	0.976157i	$-0.430352\pi$
$937$	12451.7	0.434130	0.217065	+	0.976157i	$0.430352\pi$
$938$	30816.2	1.07269
$939$	9738.68	0.338456
$940$	5499.27	0.190815
$941$	−5850.61	−0.202683	−0.101341	−	0.994852i	$-0.532313\pi$
$941$	−5850.61	−0.202683	−0.101341	+	0.994852i	$0.532313\pi$
$942$	−24338.5	−0.841815
$943$	−12229.3	−0.422312
$944$	29179.3	1.00604
$945$	14503.6	0.499263
$946$	0	0
$947$	46867.8	1.60824	0.804118	−	0.594470i	$-0.202638\pi$
$947$	46867.8	1.60824	0.804118	+	0.594470i	$0.202638\pi$
$948$	−12540.7	−0.429643
$949$	−3615.50	−0.123671
$950$	−6385.69	−0.218083
$951$	13746.0	0.468713
$952$	−8682.33	−0.295584
$953$	44105.5	1.49918	0.749589	−	0.661904i	$-0.230251\pi$
$953$	44105.5	1.49918	0.749589	+	0.661904i	$0.230251\pi$
$954$	−3750.24	−0.127273
$955$	−35837.1	−1.21430
$956$	−9105.67	−0.308053
$957$	−3473.33	−0.117322
$958$	−52783.7	−1.78013
$959$	−32930.0	−1.10883
$960$	9062.54	0.304679
$961$	32327.7	1.08515
$962$	3104.99	0.104063
$963$	2094.51	0.0700878
$964$	−8068.72	−0.269581
$965$	18507.3	0.617378
$966$	27485.3	0.915452
$967$	43513.4	1.44705	0.723525	−	0.690298i	$-0.242521\pi$
$967$	43513.4	1.44705	0.723525	+	0.690298i	$0.242521\pi$
$968$	−14455.3	−0.479968
$969$	−7315.25	−0.242518
$970$	−5867.13	−0.194208
$971$	−2044.41	−0.0675677	−0.0337838	−	0.999429i	$-0.510756\pi$
$971$	−2044.41	−0.0675677	−0.0337838	+	0.999429i	$0.510756\pi$
$972$	1364.00	0.0450107
$973$	−19145.9	−0.630822
$974$	11870.1	0.390497
$975$	−12760.7	−0.419149
$976$	−62803.5	−2.05973
$977$	−54670.3	−1.79023	−0.895117	−	0.445832i	$-0.852908\pi$
$977$	−54670.3	−1.79023	−0.895117	+	0.445832i	$0.852908\pi$
$978$	−54280.9	−1.77476
$979$	−9609.27	−0.313701
$980$	−4681.55	−0.152599
$981$	115.518	0.00375964
$982$	5559.96	0.180678
$983$	−13334.1	−0.432646	−0.216323	−	0.976322i	$-0.569406\pi$
$983$	−13334.1	−0.432646	−0.216323	+	0.976322i	$0.569406\pi$
$984$	−7608.28	−0.246487
$985$	76.2851	0.00246766
$986$	−4439.34	−0.143385
$987$	−14037.0	−0.452688
$988$	−4449.91	−0.143290
$989$	0	0
$990$	−1001.84	−0.0321621
$991$	−8701.70	−0.278929	−0.139464	−	0.990227i	$-0.544538\pi$
$991$	−8701.70	−0.278929	−0.139464	+	0.990227i	$0.544538\pi$
$992$	31161.1	0.997345
$993$	−20578.1	−0.657630
$994$	−5104.12	−0.162870
$995$	−6712.02	−0.213855
$996$	7170.33	0.228113
$997$	36430.6	1.15724	0.578621	−	0.815597i	$-0.303591\pi$
$997$	36430.6	1.15724	0.578621	+	0.815597i	$0.303591\pi$
$998$	−390.050	−0.0123716
$999$	3022.82	0.0957336

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1849.4.a.l.1.14		60
43.17	even	21		43.4.g.a.31.9	yes	120
43.38	even	21		43.4.g.a.25.9	✓	120
43.42	odd	2		1849.4.a.k.1.47		60

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
43.4.g.a.25.9	✓	120	43.38	even	21
43.4.g.a.31.9	yes	120	43.17	even	21
1849.4.a.k.1.47		60	43.42	odd	2
1849.4.a.l.1.14		60	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 1849 = 43^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1849.a (trivial)

\(f(q)\)	\(=\)	\(q-3.29999 q^{2} +5.03144 q^{3} +2.88991 q^{4} +8.27916 q^{5} -16.6037 q^{6} -12.1380 q^{7} +16.8632 q^{8} -1.68463 q^{9} +O(q^{10})\)	\(q-3.29999 q^{2} +5.03144 q^{3} +2.88991 q^{4} +8.27916 q^{5} -16.6037 q^{6} -12.1380 q^{7} +16.8632 q^{8} -1.68463 q^{9} -27.3211 q^{10} -21.7668 q^{11} +14.5404 q^{12} +44.9239 q^{13} +40.0554 q^{14} +41.6561 q^{15} -78.7677 q^{16} +42.4177 q^{17} +5.55925 q^{18} -34.2760 q^{19} +23.9260 q^{20} -61.0718 q^{21} +71.8302 q^{22} +136.379 q^{23} +84.8463 q^{24} -56.4554 q^{25} -148.248 q^{26} -144.325 q^{27} -35.0778 q^{28} +31.7146 q^{29} -137.465 q^{30} +249.236 q^{31} +125.026 q^{32} -109.518 q^{33} -139.978 q^{34} -100.493 q^{35} -4.86842 q^{36} -20.9446 q^{37} +113.110 q^{38} +226.032 q^{39} +139.613 q^{40} -89.6713 q^{41} +201.536 q^{42} -62.9041 q^{44} -13.9473 q^{45} -450.049 q^{46} +229.845 q^{47} -396.315 q^{48} -195.668 q^{49} +186.302 q^{50} +213.422 q^{51} +129.826 q^{52} -674.595 q^{53} +476.270 q^{54} -180.211 q^{55} -204.687 q^{56} -172.458 q^{57} -104.658 q^{58} -370.448 q^{59} +120.382 q^{60} +797.326 q^{61} -822.476 q^{62} +20.4481 q^{63} +217.556 q^{64} +371.932 q^{65} +361.409 q^{66} +769.340 q^{67} +122.583 q^{68} +686.184 q^{69} +331.625 q^{70} -127.427 q^{71} -28.4083 q^{72} -80.4806 q^{73} +69.1168 q^{74} -284.052 q^{75} -99.0545 q^{76} +264.207 q^{77} -745.901 q^{78} -862.471 q^{79} -652.131 q^{80} -680.677 q^{81} +295.914 q^{82} +493.132 q^{83} -176.492 q^{84} +351.183 q^{85} +159.570 q^{87} -367.059 q^{88} +441.464 q^{89} +46.0259 q^{90} -545.288 q^{91} +394.123 q^{92} +1254.02 q^{93} -758.484 q^{94} -283.777 q^{95} +629.063 q^{96} +214.747 q^{97} +645.701 q^{98} +36.6690 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 60 q + 15 q^{2} + 37 q^{3} + 213 q^{4} + 51 q^{5} + 22 q^{6} + 54 q^{7} + 204 q^{8} + 387 q^{9}+O(q^{10}) \) 60 * q + 15 * q^2 + 37 * q^3 + 213 * q^4 + 51 * q^5 + 22 * q^6 + 54 * q^7 + 204 * q^8 + 387 * q^9	\( 60 q + 15 q^{2} + 37 q^{3} + 213 q^{4} + 51 q^{5} + 22 q^{6} + 54 q^{7} + 204 q^{8} + 387 q^{9} + 27 q^{10} + 43 q^{11} + 432 q^{12} + 13 q^{13} + 96 q^{14} + 65 q^{15} + 717 q^{16} - 138 q^{17} + 625 q^{18} + 610 q^{19} + 345 q^{20} + 611 q^{21} + 118 q^{22} - 243 q^{23} + 258 q^{24} + 899 q^{25} + 1071 q^{26} + 1609 q^{27} + 46 q^{28} + 773 q^{29} + 375 q^{30} - 97 q^{31} + 1967 q^{32} + 500 q^{33} + 217 q^{34} + 247 q^{35} + 175 q^{36} + 228 q^{37} + 1253 q^{38} + 1493 q^{39} + 2220 q^{40} - 951 q^{41} + 2643 q^{42} - 1378 q^{44} + 1086 q^{45} - 565 q^{46} - 2 q^{47} + 2303 q^{48} + 1264 q^{49} + 3273 q^{50} + 3076 q^{51} - 2825 q^{52} - 39 q^{53} + 5201 q^{54} + 1306 q^{55} + 3683 q^{56} + 1342 q^{57} + 2588 q^{58} - 1065 q^{59} + 2803 q^{60} + 2999 q^{61} + 5569 q^{62} + 2377 q^{63} + 2082 q^{64} + 5578 q^{65} + 3338 q^{66} + 961 q^{67} - 3754 q^{68} + 1817 q^{69} + 2738 q^{70} + 8003 q^{71} + 1412 q^{72} - 1011 q^{73} - 1413 q^{74} + 7457 q^{75} + 5516 q^{76} + 4052 q^{77} + 1091 q^{78} - 4422 q^{79} + 1610 q^{80} + 2108 q^{81} + 4676 q^{82} - 297 q^{83} - 54 q^{84} + 4333 q^{85} + 1377 q^{87} + 3652 q^{88} + 2480 q^{89} - 1414 q^{90} + 4551 q^{91} - 3286 q^{92} + 4 q^{93} + 4609 q^{94} - 835 q^{95} + 5864 q^{96} + 3785 q^{97} + 753 q^{98} + 5072 q^{99}+O(q^{100}) \) 60 * q + 15 * q^2 + 37 * q^3 + 213 * q^4 + 51 * q^5 + 22 * q^6 + 54 * q^7 + 204 * q^8 + 387 * q^9 + 27 * q^10 + 43 * q^11 + 432 * q^12 + 13 * q^13 + 96 * q^14 + 65 * q^15 + 717 * q^16 - 138 * q^17 + 625 * q^18 + 610 * q^19 + 345 * q^20 + 611 * q^21 + 118 * q^22 - 243 * q^23 + 258 * q^24 + 899 * q^25 + 1071 * q^26 + 1609 * q^27 + 46 * q^28 + 773 * q^29 + 375 * q^30 - 97 * q^31 + 1967 * q^32 + 500 * q^33 + 217 * q^34 + 247 * q^35 + 175 * q^36 + 228 * q^37 + 1253 * q^38 + 1493 * q^39 + 2220 * q^40 - 951 * q^41 + 2643 * q^42 - 1378 * q^44 + 1086 * q^45 - 565 * q^46 - 2 * q^47 + 2303 * q^48 + 1264 * q^49 + 3273 * q^50 + 3076 * q^51 - 2825 * q^52 - 39 * q^53 + 5201 * q^54 + 1306 * q^55 + 3683 * q^56 + 1342 * q^57 + 2588 * q^58 - 1065 * q^59 + 2803 * q^60 + 2999 * q^61 + 5569 * q^62 + 2377 * q^63 + 2082 * q^64 + 5578 * q^65 + 3338 * q^66 + 961 * q^67 - 3754 * q^68 + 1817 * q^69 + 2738 * q^70 + 8003 * q^71 + 1412 * q^72 - 1011 * q^73 - 1413 * q^74 + 7457 * q^75 + 5516 * q^76 + 4052 * q^77 + 1091 * q^78 - 4422 * q^79 + 1610 * q^80 + 2108 * q^81 + 4676 * q^82 - 297 * q^83 - 54 * q^84 + 4333 * q^85 + 1377 * q^87 + 3652 * q^88 + 2480 * q^89 - 1414 * q^90 + 4551 * q^91 - 3286 * q^92 + 4 * q^93 + 4609 * q^94 - 835 * q^95 + 5864 * q^96 + 3785 * q^97 + 753 * q^98 + 5072 * q^99

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