LMFDB - Embedded newform 1587.4.a.v.1.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1587,4,Mod(1,1587)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1587, 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("1587.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 1587 = 3 \cdot 23^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	1587.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:	$93.6360311791$
Analytic rank:	$1$
Dimension:	$30$
Twist minimal:	no (minimal twist has level 69)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
Character	$\chi$	$=$	1587.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-3.90585 q^{2} -3.00000 q^{3} +7.25568 q^{4} -2.82752 q^{5} +11.7176 q^{6} -35.5408 q^{7} +2.90722 q^{8} +9.00000 q^{9} +O(q^{10})$	\(q-3.90585 q^{2} -3.00000 q^{3} +7.25568 q^{4} -2.82752 q^{5} +11.7176 q^{6} -35.5408 q^{7} +2.90722 q^{8} +9.00000 q^{9} +11.0439 q^{10} +40.3700 q^{11} -21.7670 q^{12} -29.0330 q^{13} +138.817 q^{14} +8.48256 q^{15} -69.4006 q^{16} -19.2789 q^{17} -35.1527 q^{18} +19.8758 q^{19} -20.5156 q^{20} +106.622 q^{21} -157.679 q^{22} -8.72165 q^{24} -117.005 q^{25} +113.399 q^{26} -27.0000 q^{27} -257.872 q^{28} +56.4991 q^{29} -33.1316 q^{30} -259.418 q^{31} +247.811 q^{32} -121.110 q^{33} +75.3004 q^{34} +100.492 q^{35} +65.3011 q^{36} -118.199 q^{37} -77.6318 q^{38} +87.0990 q^{39} -8.22021 q^{40} +470.661 q^{41} -416.451 q^{42} +239.516 q^{43} +292.912 q^{44} -25.4477 q^{45} -260.363 q^{47} +208.202 q^{48} +920.146 q^{49} +457.005 q^{50} +57.8366 q^{51} -210.654 q^{52} -479.196 q^{53} +105.458 q^{54} -114.147 q^{55} -103.325 q^{56} -59.6273 q^{57} -220.677 q^{58} +163.687 q^{59} +61.5467 q^{60} +588.275 q^{61} +1013.25 q^{62} -319.867 q^{63} -412.707 q^{64} +82.0913 q^{65} +473.038 q^{66} -365.791 q^{67} -139.881 q^{68} -392.508 q^{70} +725.866 q^{71} +26.1650 q^{72} +187.095 q^{73} +461.668 q^{74} +351.015 q^{75} +144.212 q^{76} -1434.78 q^{77} -340.196 q^{78} +431.132 q^{79} +196.231 q^{80} +81.0000 q^{81} -1838.33 q^{82} +423.214 q^{83} +773.617 q^{84} +54.5114 q^{85} -935.516 q^{86} -169.497 q^{87} +117.364 q^{88} -710.344 q^{89} +99.3948 q^{90} +1031.85 q^{91} +778.255 q^{93} +1016.94 q^{94} -56.1991 q^{95} -743.432 q^{96} +511.178 q^{97} -3593.95 q^{98} +363.330 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q + 2 q^{2} - 90 q^{3} + 118 q^{4} - 52 q^{5} - 6 q^{6} + 2 q^{7} + 18 q^{8} + 270 q^{9}+O(q^{10}) $ 30 * q + 2 * q^2 - 90 * q^3 + 118 * q^4 - 52 * q^5 - 6 * q^6 + 2 * q^7 + 18 * q^8 + 270 * q^9	\( 30 q + 2 q^{2} - 90 q^{3} + 118 q^{4} - 52 q^{5} - 6 q^{6} + 2 q^{7} + 18 q^{8} + 270 q^{9} + 39 q^{10} - 126 q^{11} - 354 q^{12} + 14 q^{13} - 42 q^{14} + 156 q^{15} + 438 q^{16} - 340 q^{17} + 18 q^{18} + 156 q^{19} - 617 q^{20} - 6 q^{21} - 311 q^{22} - 54 q^{24} + 624 q^{25} + 398 q^{26} - 810 q^{27} - 468 q^{28} - 196 q^{29} - 117 q^{30} - 380 q^{31} + 46 q^{32} + 378 q^{33} - 64 q^{34} - 636 q^{35} + 1062 q^{36} - 1082 q^{37} - 747 q^{38} - 42 q^{39} + 623 q^{40} + 768 q^{41} + 126 q^{42} - 68 q^{43} - 1657 q^{44} - 468 q^{45} - 720 q^{47} - 1314 q^{48} + 2926 q^{49} - 1008 q^{50} + 1020 q^{51} + 482 q^{52} - 2720 q^{53} - 54 q^{54} - 336 q^{55} - 576 q^{56} - 468 q^{57} - 690 q^{58} + 80 q^{59} + 1851 q^{60} - 906 q^{61} - 110 q^{62} + 18 q^{63} + 5740 q^{64} - 3490 q^{65} + 933 q^{66} - 1294 q^{67} - 2802 q^{68} + 1492 q^{70} - 1350 q^{71} + 162 q^{72} - 1824 q^{73} - 2629 q^{74} - 1872 q^{75} + 585 q^{76} - 864 q^{77} - 1194 q^{78} + 3540 q^{79} - 5233 q^{80} + 2430 q^{81} + 2166 q^{82} - 1410 q^{83} + 1404 q^{84} + 2468 q^{85} - 1597 q^{86} + 588 q^{87} - 5645 q^{88} - 2022 q^{89} + 351 q^{90} + 2718 q^{91} + 1140 q^{93} - 1548 q^{94} + 9230 q^{95} - 138 q^{96} - 2926 q^{97} - 11775 q^{98} - 1134 q^{99}+O(q^{100}) \) 30 * q + 2 * q^2 - 90 * q^3 + 118 * q^4 - 52 * q^5 - 6 * q^6 + 2 * q^7 + 18 * q^8 + 270 * q^9 + 39 * q^10 - 126 * q^11 - 354 * q^12 + 14 * q^13 - 42 * q^14 + 156 * q^15 + 438 * q^16 - 340 * q^17 + 18 * q^18 + 156 * q^19 - 617 * q^20 - 6 * q^21 - 311 * q^22 - 54 * q^24 + 624 * q^25 + 398 * q^26 - 810 * q^27 - 468 * q^28 - 196 * q^29 - 117 * q^30 - 380 * q^31 + 46 * q^32 + 378 * q^33 - 64 * q^34 - 636 * q^35 + 1062 * q^36 - 1082 * q^37 - 747 * q^38 - 42 * q^39 + 623 * q^40 + 768 * q^41 + 126 * q^42 - 68 * q^43 - 1657 * q^44 - 468 * q^45 - 720 * q^47 - 1314 * q^48 + 2926 * q^49 - 1008 * q^50 + 1020 * q^51 + 482 * q^52 - 2720 * q^53 - 54 * q^54 - 336 * q^55 - 576 * q^56 - 468 * q^57 - 690 * q^58 + 80 * q^59 + 1851 * q^60 - 906 * q^61 - 110 * q^62 + 18 * q^63 + 5740 * q^64 - 3490 * q^65 + 933 * q^66 - 1294 * q^67 - 2802 * q^68 + 1492 * q^70 - 1350 * q^71 + 162 * q^72 - 1824 * q^73 - 2629 * q^74 - 1872 * q^75 + 585 * q^76 - 864 * q^77 - 1194 * q^78 + 3540 * q^79 - 5233 * q^80 + 2430 * q^81 + 2166 * q^82 - 1410 * q^83 + 1404 * q^84 + 2468 * q^85 - 1597 * q^86 + 588 * q^87 - 5645 * q^88 - 2022 * q^89 + 351 * q^90 + 2718 * q^91 + 1140 * q^93 - 1548 * q^94 + 9230 * q^95 - 138 * q^96 - 2926 * q^97 - 11775 * q^98 - 1134 * 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 $

$2$	−3.90585	−1.38093	−0.690464	−	0.723367i	$-0.742593\pi$
$2$	−3.90585	−1.38093	−0.690464	+	0.723367i	$0.742593\pi$
$3$	−3.00000	−0.577350
$3$	−3.00000	−0.577350
$4$	7.25568	0.906960
$5$	−2.82752	−0.252901	−0.126451	−	0.991973i	$-0.540358\pi$
$5$	−2.82752	−0.252901	−0.126451	+	0.991973i	$0.540358\pi$
$6$	11.7176	0.797279
$7$	−35.5408	−1.91902	−0.959510	−	0.281673i	$-0.909111\pi$
$7$	−35.5408	−1.91902	−0.959510	+	0.281673i	$0.909111\pi$
$8$	2.90722	0.128482
$9$	9.00000	0.333333
$10$	11.0439	0.349238
$11$	40.3700	1.10655	0.553274	−	0.833000i	$-0.313378\pi$
$11$	40.3700	1.10655	0.553274	+	0.833000i	$0.313378\pi$
$12$	−21.7670	−0.523633
$13$	−29.0330	−0.619408	−0.309704	−	0.950833i	$-0.600230\pi$
$13$	−29.0330	−0.619408	−0.309704	+	0.950833i	$0.600230\pi$
$14$	138.817	2.65003
$15$	8.48256	0.146012
$16$	−69.4006	−1.08438
$17$	−19.2789	−0.275048	−0.137524	−	0.990498i	$-0.543914\pi$
$17$	−19.2789	−0.275048	−0.137524	+	0.990498i	$0.543914\pi$
$18$	−35.1527	−0.460309
$19$	19.8758	0.239990	0.119995	−	0.992774i	$-0.461712\pi$
$19$	19.8758	0.239990	0.119995	+	0.992774i	$0.461712\pi$
$20$	−20.5156	−0.229371
$21$	106.622	1.10795
$22$	−157.679	−1.52806
$23$	0	0
$23$	0	0
$24$	−8.72165	−0.0741792
$25$	−117.005	−0.936041
$26$	113.399	0.855357
$27$	−27.0000	−0.192450
$28$	−257.872	−1.74047
$29$	56.4991	0.361780	0.180890	−	0.983503i	$-0.442102\pi$
$29$	56.4991	0.361780	0.180890	+	0.983503i	$0.442102\pi$
$30$	−33.1316	−0.201633
$31$	−259.418	−1.50300	−0.751499	−	0.659734i	$-0.770669\pi$
$31$	−259.418	−1.50300	−0.751499	+	0.659734i	$0.770669\pi$
$32$	247.811	1.36897
$33$	−121.110	−0.638865
$34$	75.3004	0.379821
$35$	100.492	0.485322
$36$	65.3011	0.302320
$37$	−118.199	−0.525184	−0.262592	−	0.964907i	$-0.584577\pi$
$37$	−118.199	−0.525184	−0.262592	+	0.964907i	$0.584577\pi$
$38$	−77.6318	−0.331409
$39$	87.0990	0.357615
$40$	−8.22021	−0.0324933
$41$	470.661	1.79280	0.896402	−	0.443242i	$-0.146172\pi$
$41$	470.661	1.79280	0.896402	+	0.443242i	$0.146172\pi$
$42$	−416.451	−1.52999
$43$	239.516	0.849440	0.424720	−	0.905325i	$-0.360373\pi$
$43$	239.516	0.849440	0.424720	+	0.905325i	$0.360373\pi$
$44$	292.912	1.00359
$45$	−25.4477	−0.0843003
$46$	0	0
$47$	−260.363	−0.808038	−0.404019	−	0.914751i	$-0.632387\pi$
$47$	−260.363	−0.808038	−0.404019	+	0.914751i	$0.632387\pi$
$48$	208.202	0.626069
$49$	920.146	2.68264
$50$	457.005	1.29260
$51$	57.8366	0.158799
$52$	−210.654	−0.561778
$53$	−479.196	−1.24194	−0.620968	−	0.783836i	$-0.713260\pi$
$53$	−479.196	−1.24194	−0.620968	+	0.783836i	$0.713260\pi$
$54$	105.458	0.265760
$55$	−114.147	−0.279847
$56$	−103.325	−0.246560
$57$	−59.6273	−0.138558
$58$	−220.677	−0.499592
$59$	163.687	0.361191	0.180595	−	0.983557i	$-0.442198\pi$
$59$	163.687	0.361191	0.180595	+	0.983557i	$0.442198\pi$
$60$	61.5467	0.132427
$61$	588.275	1.23477	0.617385	−	0.786662i	$-0.288192\pi$
$61$	588.275	1.23477	0.617385	+	0.786662i	$0.288192\pi$
$62$	1013.25	2.07553
$63$	−319.867	−0.639674
$64$	−412.707	−0.806068
$65$	82.0913	0.156649
$66$	473.038	0.882227
$67$	−365.791	−0.666993	−0.333497	−	0.942751i	$-0.608229\pi$
$67$	−365.791	−0.666993	−0.333497	+	0.942751i	$0.608229\pi$
$68$	−139.881	−0.249457
$69$	0	0
$70$	−392.508	−0.670195
$71$	725.866	1.21330	0.606651	−	0.794968i	$-0.292513\pi$
$71$	725.866	1.21330	0.606651	+	0.794968i	$0.292513\pi$
$72$	26.1650	0.0428274
$73$	187.095	0.299971	0.149985	−	0.988688i	$-0.452077\pi$
$73$	187.095	0.299971	0.149985	+	0.988688i	$0.452077\pi$
$74$	461.668	0.725240
$75$	351.015	0.540424
$76$	144.212	0.217661
$77$	−1434.78	−2.12349
$78$	−340.196	−0.493841
$79$	431.132	0.614002	0.307001	−	0.951709i	$-0.400674\pi$
$79$	431.132	0.614002	0.307001	+	0.951709i	$0.400674\pi$
$80$	196.231	0.274242
$81$	81.0000	0.111111
$82$	−1838.33	−2.47573
$83$	423.214	0.559684	0.279842	−	0.960046i	$-0.409718\pi$
$83$	423.214	0.559684	0.279842	+	0.960046i	$0.409718\pi$
$84$	773.617	1.00486
$85$	54.5114	0.0695599
$86$	−935.516	−1.17301
$87$	−169.497	−0.208874
$88$	117.364	0.142172
$89$	−710.344	−0.846026	−0.423013	−	0.906124i	$-0.639028\pi$
$89$	−710.344	−0.846026	−0.423013	+	0.906124i	$0.639028\pi$
$90$	99.3948	0.116413
$91$	1031.85	1.18866
$92$	0	0
$93$	778.255	0.867756
$94$	1016.94	1.11584
$95$	−56.1991	−0.0606937
$96$	−743.432	−0.790377
$97$	511.178	0.535075	0.267538	−	0.963547i	$-0.413790\pi$
$97$	511.178	0.535075	0.267538	+	0.963547i	$0.413790\pi$
$98$	−3593.95	−3.70453
$99$	363.330	0.368849
$100$	−848.951	−0.848951
$101$	396.125	0.390256	0.195128	−	0.980778i	$-0.437488\pi$
$101$	396.125	0.390256	0.195128	+	0.980778i	$0.437488\pi$
$102$	−225.901	−0.219290
$103$	1564.79	1.49692	0.748462	−	0.663178i	$-0.230793\pi$
$103$	1564.79	1.49692	0.748462	+	0.663178i	$0.230793\pi$
$104$	−84.4052	−0.0795828
$105$	−301.477	−0.280201
$106$	1871.67	1.71502
$107$	151.769	0.137122	0.0685611	−	0.997647i	$-0.478159\pi$
$107$	151.769	0.137122	0.0685611	+	0.997647i	$0.478159\pi$
$108$	−195.903	−0.174544
$109$	−2133.05	−1.87439	−0.937197	−	0.348799i	$-0.886589\pi$
$109$	−2133.05	−1.87439	−0.937197	+	0.348799i	$0.886589\pi$
$110$	445.841	0.386448
$111$	354.597	0.303215
$112$	2466.55	2.08096
$113$	142.608	0.118721	0.0593604	−	0.998237i	$-0.481094\pi$
$113$	142.608	0.118721	0.0593604	+	0.998237i	$0.481094\pi$
$114$	232.895	0.191339
$115$	0	0
$116$	409.939	0.328120
$117$	−261.297	−0.206469
$118$	−639.338	−0.498778
$119$	685.186	0.527823
$120$	24.6606	0.0187600
$121$	298.739	0.224447
$122$	−2297.72	−1.70513
$123$	−1411.98	−1.03508
$124$	−1882.26	−1.36316
$125$	684.274	0.489627
$126$	1249.35	0.883343
$127$	−208.893	−0.145955	−0.0729773	−	0.997334i	$-0.523250\pi$
$127$	−208.893	−0.145955	−0.0729773	+	0.997334i	$0.523250\pi$
$128$	−370.513	−0.255852
$129$	−718.549	−0.490424
$130$	−320.637	−0.216321
$131$	2007.28	1.33875	0.669377	−	0.742923i	$-0.266561\pi$
$131$	2007.28	1.33875	0.669377	+	0.742923i	$0.266561\pi$
$132$	−878.736	−0.579425
$133$	−706.400	−0.460546
$134$	1428.73	0.921069
$135$	76.3430	0.0486708
$136$	−56.0479	−0.0353387
$137$	2966.11	1.84972	0.924862	−	0.380303i	$-0.124180\pi$
$137$	2966.11	1.84972	0.924862	+	0.380303i	$0.124180\pi$
$138$	0	0
$139$	876.374	0.534770	0.267385	−	0.963590i	$-0.413840\pi$
$139$	876.374	0.534770	0.267385	+	0.963590i	$0.413840\pi$
$140$	729.139	0.440168
$141$	781.088	0.466521
$142$	−2835.12	−1.67548
$143$	−1172.06	−0.685404
$144$	−624.605	−0.361461
$145$	−159.752	−0.0914946
$146$	−730.767	−0.414237
$147$	−2760.44	−1.54882
$148$	−857.614	−0.476320
$149$	−617.234	−0.339368	−0.169684	−	0.985499i	$-0.554275\pi$
$149$	−617.234	−0.339368	−0.169684	+	0.985499i	$0.554275\pi$
$150$	−1371.01	−0.746286
$151$	2965.77	1.59835	0.799174	−	0.601100i	$-0.205270\pi$
$151$	2965.77	1.59835	0.799174	+	0.601100i	$0.205270\pi$
$152$	57.7832	0.0308344
$153$	−173.510	−0.0916826
$154$	5604.04	2.93238
$155$	733.511	0.380110
$156$	631.962	0.324343
$157$	−2876.92	−1.46244	−0.731220	−	0.682141i	$-0.761049\pi$
$157$	−2876.92	−1.46244	−0.731220	+	0.682141i	$0.761049\pi$
$158$	−1683.94	−0.847892
$159$	1437.59	0.717033
$160$	−700.689	−0.346215
$161$	0	0
$162$	−316.374	−0.153436
$163$	3019.84	1.45112	0.725558	−	0.688161i	$-0.241582\pi$
$163$	3019.84	1.45112	0.725558	+	0.688161i	$0.241582\pi$
$164$	3414.97	1.62600
$165$	342.441	0.161570
$166$	−1653.01	−0.772883
$167$	−2184.76	−1.01235	−0.506173	−	0.862432i	$-0.668940\pi$
$167$	−2184.76	−1.01235	−0.506173	+	0.862432i	$0.668940\pi$
$168$	309.974	0.142351
$169$	−1354.09	−0.616334
$170$	−212.913	−0.0960571
$171$	178.882	0.0799967
$172$	1737.85	0.770408
$173$	2609.17	1.14666	0.573329	−	0.819325i	$-0.305652\pi$
$173$	2609.17	1.14666	0.573329	+	0.819325i	$0.305652\pi$
$174$	662.032	0.288440
$175$	4158.45	1.79628
$176$	−2801.70	−1.19992
$177$	−491.062	−0.208534
$178$	2774.50	1.16830
$179$	−717.807	−0.299729	−0.149864	−	0.988707i	$-0.547884\pi$
$179$	−717.807	−0.299729	−0.149864	+	0.988707i	$0.547884\pi$
$180$	−184.640	−0.0764570
$181$	4035.10	1.65705	0.828527	−	0.559949i	$-0.189179\pi$
$181$	4035.10	1.65705	0.828527	+	0.559949i	$0.189179\pi$
$182$	−4030.27	−1.64145
$183$	−1764.83	−0.712894
$184$	0	0
$185$	334.210	0.132819
$186$	−3039.75	−1.19831
$187$	−778.289	−0.304354
$188$	−1889.11	−0.732858
$189$	959.601	0.369316
$190$	219.505	0.0838136
$191$	−2718.14	−1.02972	−0.514862	−	0.857273i	$-0.672157\pi$
$191$	−2718.14	−1.02972	−0.514862	+	0.857273i	$0.672157\pi$
$192$	1238.12	0.465384
$193$	3920.30	1.46212	0.731060	−	0.682314i	$-0.239026\pi$
$193$	3920.30	1.46212	0.731060	+	0.682314i	$0.239026\pi$
$194$	−1996.59	−0.738900
$195$	−246.274	−0.0904413
$196$	6676.28	2.43305
$197$	3966.11	1.43438	0.717192	−	0.696876i	$-0.245427\pi$
$197$	3966.11	1.43438	0.717192	+	0.696876i	$0.245427\pi$
$198$	−1419.11	−0.509354
$199$	−946.437	−0.337141	−0.168571	−	0.985690i	$-0.553915\pi$
$199$	−946.437	−0.337141	−0.168571	+	0.985690i	$0.553915\pi$
$200$	−340.159	−0.120265
$201$	1097.37	0.385089
$202$	−1547.20	−0.538915
$203$	−2008.02	−0.694264
$204$	419.644	0.144024
$205$	−1330.80	−0.453402
$206$	−6111.83	−2.06714
$207$	0	0
$208$	2014.91	0.671676
$209$	802.385	0.265560
$210$	1177.52	0.386937
$211$	1149.06	0.374903	0.187452	−	0.982274i	$-0.439977\pi$
$211$	1149.06	0.374903	0.187452	+	0.982274i	$0.439977\pi$
$212$	−3476.89	−1.12639
$213$	−2177.60	−0.700500
$214$	−592.787	−0.189356
$215$	−677.238	−0.214824
$216$	−78.4949	−0.0247264
$217$	9219.93	2.88428
$218$	8331.37	2.58840
$219$	−561.286	−0.173188
$220$	−828.214	−0.253810
$221$	559.723	0.170367
$222$	−1385.00	−0.418718
$223$	−3627.66	−1.08935	−0.544677	−	0.838646i	$-0.683348\pi$
$223$	−3627.66	−1.08935	−0.544677	+	0.838646i	$0.683348\pi$
$224$	−8807.38	−2.62709
$225$	−1053.05	−0.312014
$226$	−557.006	−0.163945
$227$	−2348.67	−0.686726	−0.343363	−	0.939203i	$-0.611566\pi$
$227$	−2348.67	−0.686726	−0.343363	+	0.939203i	$0.611566\pi$
$228$	−432.636	−0.125667
$229$	−4589.89	−1.32449	−0.662246	−	0.749286i	$-0.730397\pi$
$229$	−4589.89	−1.32449	−0.662246	+	0.749286i	$0.730397\pi$
$230$	0	0
$231$	4304.35	1.22600
$232$	164.255	0.0464823
$233$	−4125.18	−1.15987	−0.579935	−	0.814663i	$-0.696922\pi$
$233$	−4125.18	−1.15987	−0.579935	+	0.814663i	$0.696922\pi$
$234$	1020.59	0.285119
$235$	736.180	0.204354
$236$	1187.66	0.327586
$237$	−1293.40	−0.354494
$238$	−2676.23	−0.728885
$239$	−2476.29	−0.670200	−0.335100	−	0.942183i	$-0.608770\pi$
$239$	−2476.29	−0.670200	−0.335100	+	0.942183i	$0.608770\pi$
$240$	−588.694	−0.158334
$241$	2598.75	0.694606	0.347303	−	0.937753i	$-0.387098\pi$
$241$	2598.75	0.694606	0.347303	+	0.937753i	$0.387098\pi$
$242$	−1166.83	−0.309945
$243$	−243.000	−0.0641500
$244$	4268.33	1.11989
$245$	−2601.73	−0.678443
$246$	5515.00	1.42936
$247$	−577.053	−0.148652
$248$	−754.186	−0.193108
$249$	−1269.64	−0.323134
$250$	−2672.67	−0.676139
$251$	2414.20	0.607103	0.303552	−	0.952815i	$-0.401828\pi$
$251$	2414.20	0.607103	0.303552	+	0.952815i	$0.401828\pi$
$252$	−2320.85	−0.580158
$253$	0	0
$254$	815.904	0.201553
$255$	−163.534	−0.0401604
$256$	4748.82	1.15938
$257$	−4596.20	−1.11558	−0.557788	−	0.829984i	$-0.688350\pi$
$257$	−4596.20	−1.11558	−0.557788	+	0.829984i	$0.688350\pi$
$258$	2806.55	0.677240
$259$	4200.88	1.00784
$260$	595.628	0.142074
$261$	508.492	0.120593
$262$	−7840.14	−1.84872
$263$	−7776.73	−1.82332	−0.911661	−	0.410942i	$-0.865200\pi$
$263$	−7776.73	−1.82332	−0.911661	+	0.410942i	$0.865200\pi$
$264$	−352.093	−0.0820828
$265$	1354.94	0.314087
$266$	2759.09	0.635981
$267$	2131.03	0.488453
$268$	−2654.06	−0.604936
$269$	−1755.53	−0.397906	−0.198953	−	0.980009i	$-0.563754\pi$
$269$	−1755.53	−0.397906	−0.198953	+	0.980009i	$0.563754\pi$
$270$	−298.185	−0.0672109
$271$	−1372.80	−0.307718	−0.153859	−	0.988093i	$-0.549170\pi$
$271$	−1372.80	−0.307718	−0.153859	+	0.988093i	$0.549170\pi$
$272$	1337.97	0.298258
$273$	−3095.56	−0.686271
$274$	−11585.2	−2.55433
$275$	−4723.50	−1.03577
$276$	0	0
$277$	−4955.58	−1.07492	−0.537458	−	0.843290i	$-0.680615\pi$
$277$	−4955.58	−1.07492	−0.537458	+	0.843290i	$0.680615\pi$
$278$	−3422.99	−0.738479
$279$	−2334.77	−0.500999
$280$	292.153	0.0623552
$281$	442.446	0.0939292	0.0469646	−	0.998897i	$-0.485045\pi$
$281$	442.446	0.0939292	0.0469646	+	0.998897i	$0.485045\pi$
$282$	−3050.81	−0.644231
$283$	−2674.91	−0.561863	−0.280931	−	0.959728i	$-0.590643\pi$
$283$	−2674.91	−0.561863	−0.280931	+	0.959728i	$0.590643\pi$
$284$	5266.65	1.10042
$285$	168.597	0.0350415
$286$	4577.90	0.946493
$287$	−16727.7	−3.44043
$288$	2230.30	0.456324
$289$	−4541.32	−0.924349
$290$	623.969	0.126347
$291$	−1533.54	−0.308926
$292$	1357.50	0.272061
$293$	−6815.57	−1.35894	−0.679471	−	0.733702i	$-0.737791\pi$
$293$	−6815.57	−1.35894	−0.679471	+	0.733702i	$0.737791\pi$
$294$	10781.9	2.13881
$295$	−462.829	−0.0913456
$296$	−343.630	−0.0674767
$297$	−1089.99	−0.212955
$298$	2410.83	0.468642
$299$	0	0
$300$	2546.85	0.490142
$301$	−8512.60	−1.63009
$302$	−11583.8	−2.20720
$303$	−1188.37	−0.225315
$304$	−1379.39	−0.260241
$305$	−1663.36	−0.312274
$306$	677.704	0.126607
$307$	−2452.68	−0.455967	−0.227983	−	0.973665i	$-0.573213\pi$
$307$	−2452.68	−0.455967	−0.227983	+	0.973665i	$0.573213\pi$
$308$	−10410.3	−1.92592
$309$	−4694.36	−0.864249
$310$	−2864.98	−0.524904
$311$	−2339.92	−0.426639	−0.213320	−	0.976982i	$-0.568428\pi$
$311$	−2339.92	−0.426639	−0.213320	+	0.976982i	$0.568428\pi$
$312$	253.216	0.0459472
$313$	−2648.02	−0.478195	−0.239097	−	0.970996i	$-0.576851\pi$
$313$	−2648.02	−0.478195	−0.239097	+	0.970996i	$0.576851\pi$
$314$	11236.8	2.01952
$315$	904.430	0.161774
$316$	3128.16	0.556875
$317$	9914.78	1.75669	0.878343	−	0.478031i	$-0.158649\pi$
$317$	9914.78	1.75669	0.878343	+	0.478031i	$0.158649\pi$
$318$	−5615.01	−0.990170
$319$	2280.87	0.400327
$320$	1166.94	0.203855
$321$	−455.307	−0.0791675
$322$	0	0
$323$	−383.182	−0.0660088
$324$	587.710	0.100773
$325$	3397.01	0.579791
$326$	−11795.0	−2.00388
$327$	6399.15	1.08218
$328$	1368.32	0.230343
$329$	9253.48	1.55064
$330$	−1337.52	−0.223116
$331$	6560.48	1.08942	0.544708	−	0.838626i	$-0.316640\pi$
$331$	6560.48	1.08942	0.544708	+	0.838626i	$0.316640\pi$
$332$	3070.70	0.507611
$333$	−1063.79	−0.175061
$334$	8533.35	1.39798
$335$	1034.28	0.168683
$336$	−7399.65	−1.20144
$337$	−3434.92	−0.555228	−0.277614	−	0.960693i	$-0.589544\pi$
$337$	−3434.92	−0.555228	−0.277614	+	0.960693i	$0.589544\pi$
$338$	5288.86	0.851112
$339$	−427.824	−0.0685435
$340$	395.517	0.0630880
$341$	−10472.7	−1.66314
$342$	−698.686	−0.110470
$343$	−20512.2	−3.22902
$344$	696.327	0.109138
$345$	0	0
$346$	−10191.0	−1.58345
$347$	3239.47	0.501163	0.250582	−	0.968095i	$-0.419378\pi$
$347$	3239.47	0.501163	0.250582	+	0.968095i	$0.419378\pi$
$348$	−1229.82	−0.189440
$349$	−4627.68	−0.709782	−0.354891	−	0.934908i	$-0.615482\pi$
$349$	−4627.68	−0.709782	−0.354891	+	0.934908i	$0.615482\pi$
$350$	−16242.3	−2.48053
$351$	783.891	0.119205
$352$	10004.1	1.51483
$353$	7625.61	1.14977	0.574887	−	0.818233i	$-0.305046\pi$
$353$	7625.61	1.14977	0.574887	+	0.818233i	$0.305046\pi$
$354$	1918.01	0.287970
$355$	−2052.40	−0.306845
$356$	−5154.03	−0.767312
$357$	−2055.56	−0.304739
$358$	2803.65	0.413903
$359$	−2795.67	−0.411002	−0.205501	−	0.978657i	$-0.565882\pi$
$359$	−2795.67	−0.411002	−0.205501	+	0.978657i	$0.565882\pi$
$360$	−73.9819	−0.0108311
$361$	−6463.95	−0.942405
$362$	−15760.5	−2.28827
$363$	−896.218	−0.129585
$364$	7486.80	1.07806
$365$	−529.016	−0.0758629
$366$	6893.15	0.984455
$367$	−4203.81	−0.597921	−0.298960	−	0.954266i	$-0.596640\pi$
$367$	−4203.81	−0.597921	−0.298960	+	0.954266i	$0.596640\pi$
$368$	0	0
$369$	4235.95	0.597601
$370$	−1305.37	−0.183414
$371$	17031.0	2.38330
$372$	5646.77	0.787020
$373$	10216.0	1.41813	0.709064	−	0.705144i	$-0.249118\pi$
$373$	10216.0	1.41813	0.709064	+	0.705144i	$0.249118\pi$
$374$	3039.88	0.420290
$375$	−2052.82	−0.282686
$376$	−756.931	−0.103818
$377$	−1640.34	−0.224090
$378$	−3748.06	−0.509998
$379$	−7802.50	−1.05749	−0.528743	−	0.848782i	$-0.677337\pi$
$379$	−7802.50	−1.05749	−0.528743	+	0.848782i	$0.677337\pi$
$380$	−407.762	−0.0550468
$381$	626.678	0.0842669
$382$	10616.6	1.42198
$383$	−2500.03	−0.333540	−0.166770	−	0.985996i	$-0.553334\pi$
$383$	−2500.03	−0.333540	−0.166770	+	0.985996i	$0.553334\pi$
$384$	1111.54	0.147716
$385$	4056.87	0.537032
$386$	−15312.1	−2.01908
$387$	2155.65	0.283147
$388$	3708.94	0.485292
$389$	−14366.9	−1.87258	−0.936289	−	0.351230i	$-0.885764\pi$
$389$	−14366.9	−1.87258	−0.936289	+	0.351230i	$0.885764\pi$
$390$	961.910	0.124893
$391$	0	0
$392$	2675.06	0.344671
$393$	−6021.84	−0.772930
$394$	−15491.0	−1.98078
$395$	−1219.04	−0.155282
$396$	2636.21	0.334531
$397$	−944.270	−0.119374	−0.0596871	−	0.998217i	$-0.519010\pi$
$397$	−944.270	−0.119374	−0.0596871	+	0.998217i	$0.519010\pi$
$398$	3696.64	0.465568
$399$	2119.20	0.265896
$400$	8120.22	1.01503
$401$	−5248.39	−0.653596	−0.326798	−	0.945094i	$-0.605970\pi$
$401$	−5248.39	−0.653596	−0.326798	+	0.945094i	$0.605970\pi$
$402$	−4286.18	−0.531779
$403$	7531.69	0.930969
$404$	2874.15	0.353947
$405$	−229.029	−0.0281001
$406$	7843.04	0.958728
$407$	−4771.70	−0.581141
$408$	168.144	0.0204028
$409$	−6175.69	−0.746622	−0.373311	−	0.927706i	$-0.621778\pi$
$409$	−6175.69	−0.746622	−0.373311	+	0.927706i	$0.621778\pi$
$410$	5197.92	0.626115
$411$	−8898.34	−1.06794
$412$	11353.6	1.35765
$413$	−5817.57	−0.693133
$414$	0	0
$415$	−1196.65	−0.141545
$416$	−7194.68	−0.847953
$417$	−2629.12	−0.308750
$418$	−3134.00	−0.366720
$419$	4869.45	0.567752	0.283876	−	0.958861i	$-0.408380\pi$
$419$	4869.45	0.567752	0.283876	+	0.958861i	$0.408380\pi$
$420$	−2187.42	−0.254131
$421$	−4465.00	−0.516890	−0.258445	−	0.966026i	$-0.583210\pi$
$421$	−4465.00	−0.516890	−0.258445	+	0.966026i	$0.583210\pi$
$422$	−4488.06	−0.517714
$423$	−2343.26	−0.269346
$424$	−1393.13	−0.159567
$425$	2255.73	0.257456
$426$	8505.37	0.967340
$427$	−20907.7	−2.36955
$428$	1101.19	0.124364
$429$	3516.19	0.395718
$430$	2645.19	0.296657
$431$	10016.1	1.11940	0.559699	−	0.828696i	$-0.310917\pi$
$431$	10016.1	1.11940	0.559699	+	0.828696i	$0.310917\pi$
$432$	1873.82	0.208690
$433$	−9778.37	−1.08526	−0.542631	−	0.839971i	$-0.682572\pi$
$433$	−9778.37	−1.08526	−0.542631	+	0.839971i	$0.682572\pi$
$434$	−36011.7	−3.98299
$435$	479.257	0.0528244
$436$	−15476.7	−1.70000
$437$	0	0
$438$	2192.30	0.239160
$439$	12863.8	1.39853	0.699265	−	0.714863i	$-0.253511\pi$
$439$	12863.8	1.39853	0.699265	+	0.714863i	$0.253511\pi$
$440$	−331.850	−0.0359553
$441$	8281.31	0.894214
$442$	−2186.20	−0.235264
$443$	14162.4	1.51891	0.759453	−	0.650562i	$-0.225467\pi$
$443$	14162.4	1.51891	0.759453	+	0.650562i	$0.225467\pi$
$444$	2572.84	0.275004
$445$	2008.51	0.213961
$446$	14169.1	1.50432
$447$	1851.70	0.195934
$448$	14667.9	1.54686
$449$	−11162.3	−1.17323	−0.586615	−	0.809866i	$-0.699540\pi$
$449$	−11162.3	−1.17323	−0.586615	+	0.809866i	$0.699540\pi$
$450$	4113.04	0.430868
$451$	19000.6	1.98382
$452$	1034.72	0.107675
$453$	−8897.30	−0.922807
$454$	9173.56	0.948318
$455$	−2917.59	−0.300612
$456$	−173.350	−0.0178023
$457$	889.118	0.0910092	0.0455046	−	0.998964i	$-0.485510\pi$
$457$	889.118	0.0910092	0.0455046	+	0.998964i	$0.485510\pi$
$458$	17927.4	1.82903
$459$	520.530	0.0529330
$460$	0	0
$461$	3838.43	0.387795	0.193897	−	0.981022i	$-0.437887\pi$
$461$	3838.43	0.387795	0.193897	+	0.981022i	$0.437887\pi$
$462$	−16812.1	−1.69301
$463$	−14.6056	−0.00146605	−0.000733023	−	1.00000i	$-0.500233\pi$
$463$	−14.6056	−0.00146605	−0.000733023		1.00000i	$0.500233\pi$
$464$	−3921.07	−0.392309
$465$	−2200.53	−0.219456
$466$	16112.4	1.60170
$467$	1242.50	0.123117	0.0615587	−	0.998103i	$-0.480393\pi$
$467$	1242.50	0.123117	0.0615587	+	0.998103i	$0.480393\pi$
$468$	−1895.89	−0.187259
$469$	13000.5	1.27997
$470$	−2875.41	−0.282197
$471$	8630.76	0.844340
$472$	475.875	0.0464066
$473$	9669.29	0.939946
$474$	5051.82	0.489531
$475$	−2325.57	−0.224641
$476$	4971.49	0.478714
$477$	−4312.77	−0.413979
$478$	9672.02	0.925498
$479$	14192.9	1.35384	0.676919	−	0.736058i	$-0.263315\pi$
$479$	14192.9	1.35384	0.676919	+	0.736058i	$0.263315\pi$
$480$	2102.07	0.199887
$481$	3431.67	0.325303
$482$	−10150.3	−0.959200
$483$	0	0
$484$	2167.56	0.203565
$485$	−1445.37	−0.135321
$486$	949.122	0.0885865
$487$	353.618	0.0329035	0.0164517	−	0.999865i	$-0.494763\pi$
$487$	353.618	0.0329035	0.0164517	+	0.999865i	$0.494763\pi$
$488$	1710.24	0.158646
$489$	−9059.51	−0.837802
$490$	10162.0	0.936880
$491$	−770.460	−0.0708154	−0.0354077	−	0.999373i	$-0.511273\pi$
$491$	−770.460	−0.0708154	−0.0354077	+	0.999373i	$0.511273\pi$
$492$	−10244.9	−0.938772
$493$	−1089.24	−0.0995069
$494$	2253.88	0.205277
$495$	−1027.32	−0.0932823
$496$	18003.8	1.62983
$497$	−25797.8	−2.32835
$498$	4959.03	0.446224
$499$	−6765.22	−0.606919	−0.303460	−	0.952844i	$-0.598142\pi$
$499$	−6765.22	−0.606919	−0.303460	+	0.952844i	$0.598142\pi$
$500$	4964.87	0.444072
$501$	6554.28	0.584479
$502$	−9429.50	−0.838365
$503$	4619.05	0.409450	0.204725	−	0.978820i	$-0.434370\pi$
$503$	4619.05	0.409450	0.204725	+	0.978820i	$0.434370\pi$
$504$	−929.923	−0.0821866
$505$	−1120.05	−0.0986962
$506$	0	0
$507$	4062.26	0.355840
$508$	−1515.66	−0.132375
$509$	17842.7	1.55376	0.776878	−	0.629651i	$-0.216802\pi$
$509$	17842.7	1.55376	0.776878	+	0.629651i	$0.216802\pi$
$510$	638.740	0.0554586
$511$	−6649.51	−0.575650
$512$	−15584.1	−1.34517
$513$	−536.646	−0.0461861
$514$	17952.1	1.54053
$515$	−4424.47	−0.378574
$516$	−5213.56	−0.444795
$517$	−10510.8	−0.894132
$518$	−16408.0	−1.39175
$519$	−7827.52	−0.662023
$520$	238.657	0.0201266
$521$	−19513.8	−1.64091	−0.820455	−	0.571711i	$-0.806280\pi$
$521$	−19513.8	−1.64091	−0.820455	+	0.571711i	$0.806280\pi$
$522$	−1986.09	−0.166531
$523$	15895.2	1.32896	0.664480	−	0.747306i	$-0.268653\pi$
$523$	15895.2	1.32896	0.664480	+	0.747306i	$0.268653\pi$
$524$	14564.2	1.21420
$525$	−12475.4	−1.03708
$526$	30374.8	2.51788
$527$	5001.30	0.413396
$528$	8405.11	0.692775
$529$	0	0
$530$	−5292.18	−0.433731
$531$	1473.19	0.120397
$532$	−5125.41	−0.417697
$533$	−13664.7	−1.11048
$534$	−8323.50	−0.674519
$535$	−429.130	−0.0346783
$536$	−1063.44	−0.0856967
$537$	2153.42	0.173048
$538$	6856.84	0.549479
$539$	37146.3	2.96847
$540$	553.920	0.0441425
$541$	7164.33	0.569350	0.284675	−	0.958624i	$-0.408114\pi$
$541$	7164.33	0.569350	0.284675	+	0.958624i	$0.408114\pi$
$542$	5361.94	0.424936
$543$	−12105.3	−0.956700
$544$	−4777.51	−0.376533
$545$	6031.24	0.474036
$546$	12090.8	0.947691
$547$	−6577.39	−0.514130	−0.257065	−	0.966394i	$-0.582755\pi$
$547$	−6577.39	−0.514130	−0.257065	+	0.966394i	$0.582755\pi$
$548$	21521.2	1.67762
$549$	5294.48	0.411590
$550$	18449.3	1.43033
$551$	1122.96	0.0868237
$552$	0	0
$553$	−15322.8	−1.17828
$554$	19355.7	1.48438
$555$	−1002.63	−0.0766834
$556$	6358.68	0.485015
$557$	1080.13	0.0821664	0.0410832	−	0.999156i	$-0.486919\pi$
$557$	1080.13	0.0821664	0.0410832	+	0.999156i	$0.486919\pi$
$558$	9119.25	0.691843
$559$	−6953.88	−0.526150
$560$	−6974.22	−0.526276
$561$	2334.87	0.175719
$562$	−1728.13	−0.129709
$563$	−20549.7	−1.53830	−0.769151	−	0.639067i	$-0.779321\pi$
$563$	−20549.7	−1.53830	−0.769151	+	0.639067i	$0.779321\pi$
$564$	5667.32	0.423116
$565$	−403.227	−0.0300246
$566$	10447.8	0.775891
$567$	−2878.80	−0.213225
$568$	2110.25	0.155888
$569$	4180.19	0.307983	0.153992	−	0.988072i	$-0.450787\pi$
$569$	4180.19	0.307983	0.153992	+	0.988072i	$0.450787\pi$
$570$	−658.516	−0.0483898
$571$	100.487	0.00736472	0.00368236	−	0.999993i	$-0.498828\pi$
$571$	100.487	0.00736472	0.00368236	+	0.999993i	$0.498828\pi$
$572$	−8504.11	−0.621634
$573$	8154.41	0.594512
$574$	65335.8	4.75098
$575$	0	0
$576$	−3714.36	−0.268689
$577$	8049.79	0.580793	0.290396	−	0.956906i	$-0.406213\pi$
$577$	8049.79	0.580793	0.290396	+	0.956906i	$0.406213\pi$
$578$	17737.7	1.27646
$579$	−11760.9	−0.844155
$580$	−1159.11	−0.0829819
$581$	−15041.3	−1.07405
$582$	5989.76	0.426604
$583$	−19345.2	−1.37426
$584$	543.927	0.0385408
$585$	738.822	0.0522163
$586$	26620.6	1.87660
$587$	−16932.2	−1.19058	−0.595288	−	0.803512i	$-0.702962\pi$
$587$	−16932.2	−1.19058	−0.595288	+	0.803512i	$0.702962\pi$
$588$	−20028.8	−1.40472
$589$	−5156.14	−0.360705
$590$	1807.74	0.126142
$591$	−11898.3	−0.828142
$592$	8203.08	0.569501
$593$	−4588.01	−0.317718	−0.158859	−	0.987301i	$-0.550782\pi$
$593$	−4588.01	−0.317718	−0.158859	+	0.987301i	$0.550782\pi$
$594$	4257.34	0.294076
$595$	−1937.38	−0.133487
$596$	−4478.45	−0.307793
$597$	2839.31	0.194649
$598$	0	0
$599$	1406.87	0.0959649	0.0479824	−	0.998848i	$-0.484721\pi$
$599$	1406.87	0.0959649	0.0479824	+	0.998848i	$0.484721\pi$
$600$	1020.48	0.0694348
$601$	−6348.90	−0.430911	−0.215455	−	0.976514i	$-0.569124\pi$
$601$	−6348.90	−0.430911	−0.215455	+	0.976514i	$0.569124\pi$
$602$	33248.9	2.25104
$603$	−3292.12	−0.222331
$604$	21518.6	1.44964
$605$	−844.691	−0.0567629
$606$	4641.61	0.311143
$607$	−25961.2	−1.73596	−0.867982	−	0.496595i	$-0.834583\pi$
$607$	−25961.2	−1.73596	−0.867982	+	0.496595i	$0.834583\pi$
$608$	4925.42	0.328540
$609$	6024.07	0.400833
$610$	6496.83	0.431228
$611$	7559.10	0.500505
$612$	−1258.93	−0.0831524
$613$	−5614.27	−0.369915	−0.184958	−	0.982746i	$-0.559215\pi$
$613$	−5614.27	−0.369915	−0.184958	+	0.982746i	$0.559215\pi$
$614$	9579.81	0.629657
$615$	3992.41	0.261772
$616$	−4171.22	−0.272830
$617$	−19293.8	−1.25890	−0.629449	−	0.777042i	$-0.716719\pi$
$617$	−19293.8	−1.25890	−0.629449	+	0.777042i	$0.716719\pi$
$618$	18335.5	1.19347
$619$	9189.22	0.596682	0.298341	−	0.954459i	$-0.403567\pi$
$619$	9189.22	0.596682	0.298341	+	0.954459i	$0.403567\pi$
$620$	5322.12	0.344744
$621$	0	0
$622$	9139.39	0.589158
$623$	25246.2	1.62354
$624$	−6044.72	−0.387792
$625$	12690.8	0.812214
$626$	10342.8	0.660352
$627$	−2407.16	−0.153321
$628$	−20874.0	−1.32637
$629$	2278.74	0.144451
$630$	−3532.57	−0.223398
$631$	−2511.60	−0.158455	−0.0792276	−	0.996857i	$-0.525245\pi$
$631$	−2511.60	−0.158455	−0.0792276	+	0.996857i	$0.525245\pi$
$632$	1253.40	0.0788883
$633$	−3447.18	−0.216451
$634$	−38725.6	−2.42585
$635$	590.648	0.0369121
$636$	10430.7	0.650320
$637$	−26714.6	−1.66165
$638$	−8908.75	−0.552822
$639$	6532.79	0.404434
$640$	1047.63	0.0647052
$641$	−1614.84	−0.0995045	−0.0497522	−	0.998762i	$-0.515843\pi$
$641$	−1614.84	−0.0995045	−0.0497522	+	0.998762i	$0.515843\pi$
$642$	1778.36	0.109325
$643$	7455.77	0.457274	0.228637	−	0.973512i	$-0.426573\pi$
$643$	7455.77	0.457274	0.228637	+	0.973512i	$0.426573\pi$
$644$	0	0
$645$	2031.71	0.124029
$646$	1496.65	0.0911533
$647$	−31485.9	−1.91319	−0.956597	−	0.291414i	$-0.905874\pi$
$647$	−31485.9	−1.91319	−0.956597	+	0.291414i	$0.905874\pi$
$648$	235.485	0.0142758
$649$	6608.06	0.399675
$650$	−13268.2	−0.800649
$651$	−27659.8	−1.66524
$652$	21911.0	1.31610
$653$	15252.0	0.914021	0.457011	−	0.889461i	$-0.348920\pi$
$653$	15252.0	0.914021	0.457011	+	0.889461i	$0.348920\pi$
$654$	−24994.1	−1.49441
$655$	−5675.62	−0.338572
$656$	−32664.2	−1.94409
$657$	1683.86	0.0999902
$658$	−36142.7	−2.14132
$659$	1224.60	0.0723879	0.0361939	−	0.999345i	$-0.488477\pi$
$659$	1224.60	0.0723879	0.0361939	+	0.999345i	$0.488477\pi$
$660$	2484.64	0.146537
$661$	−17236.2	−1.01424	−0.507120	−	0.861876i	$-0.669290\pi$
$661$	−17236.2	−1.01424	−0.507120	+	0.861876i	$0.669290\pi$
$662$	−25624.3	−1.50440
$663$	−1679.17	−0.0983613
$664$	1230.38	0.0719094
$665$	1997.36	0.116473
$666$	4155.01	0.241747
$667$	0	0
$668$	−15851.9	−0.918157
$669$	10883.0	0.628939
$670$	−4039.75	−0.232939
$671$	23748.7	1.36633
$672$	26422.1	1.51675
$673$	−2925.34	−0.167554	−0.0837768	−	0.996485i	$-0.526698\pi$
$673$	−2925.34	−0.167554	−0.0837768	+	0.996485i	$0.526698\pi$
$674$	13416.3	0.766729
$675$	3159.14	0.180141
$676$	−9824.81	−0.558990
$677$	23430.7	1.33015	0.665077	−	0.746775i	$-0.268399\pi$
$677$	23430.7	1.33015	0.665077	+	0.746775i	$0.268399\pi$
$678$	1671.02	0.0946535
$679$	−18167.7	−1.02682
$680$	158.477	0.00893720
$681$	7046.01	0.396481
$682$	40904.9	2.29667
$683$	4200.31	0.235315	0.117658	−	0.993054i	$-0.462461\pi$
$683$	4200.31	0.235315	0.117658	+	0.993054i	$0.462461\pi$
$684$	1297.91	0.0725538
$685$	−8386.74	−0.467797
$686$	80117.6	4.45905
$687$	13769.7	0.764696
$688$	−16622.6	−0.921119
$689$	13912.5	0.769266
$690$	0	0
$691$	18363.9	1.01099	0.505497	−	0.862829i	$-0.331309\pi$
$691$	18363.9	1.01099	0.505497	+	0.862829i	$0.331309\pi$
$692$	18931.3	1.03997
$693$	−12913.0	−0.707829
$694$	−12652.9	−0.692070
$695$	−2477.96	−0.135244
$696$	−492.766	−0.0268366
$697$	−9073.82	−0.493107
$698$	18075.0	0.980157
$699$	12375.6	0.669651
$700$	30172.4	1.62916
$701$	16099.1	0.867413	0.433706	−	0.901054i	$-0.357206\pi$
$701$	16099.1	0.867413	0.433706	+	0.901054i	$0.357206\pi$
$702$	−3061.76	−0.164614
$703$	−2349.30	−0.126039
$704$	−16661.0	−0.891952
$705$	−2208.54	−0.117984
$706$	−29784.5	−1.58775
$707$	−14078.6	−0.748910
$708$	−3562.99	−0.189132
$709$	−13030.7	−0.690235	−0.345118	−	0.938559i	$-0.612161\pi$
$709$	−13030.7	−0.690235	−0.345118	+	0.938559i	$0.612161\pi$
$710$	8016.37	0.423731
$711$	3880.19	0.204667
$712$	−2065.13	−0.108699
$713$	0	0
$714$	8028.70	0.420822
$715$	3314.03	0.173339
$716$	−5208.18	−0.271842
$717$	7428.87	0.386940
$718$	10919.5	0.567564
$719$	9086.17	0.471289	0.235645	−	0.971839i	$-0.424280\pi$
$719$	9086.17	0.471289	0.235645	+	0.971839i	$0.424280\pi$
$720$	1766.08	0.0914139
$721$	−55613.8	−2.87263
$722$	25247.2	1.30139
$723$	−7796.24	−0.401031
$724$	29277.4	1.50288
$725$	−6610.69	−0.338641
$726$	3500.49	0.178947
$727$	−9367.97	−0.477908	−0.238954	−	0.971031i	$-0.576804\pi$
$727$	−9367.97	−0.477908	−0.238954	+	0.971031i	$0.576804\pi$
$728$	2999.83	0.152721
$729$	729.000	0.0370370
$730$	2066.26	0.104761
$731$	−4617.61	−0.233637
$732$	−12805.0	−0.646566
$733$	329.039	0.0165803	0.00829014	−	0.999966i	$-0.497361\pi$
$733$	329.039	0.0165803	0.00829014	+	0.999966i	$0.497361\pi$
$734$	16419.4	0.825685
$735$	7805.19	0.391699
$736$	0	0
$737$	−14767.0	−0.738060
$738$	−16545.0	−0.825244
$739$	26207.3	1.30453	0.652267	−	0.757990i	$-0.273818\pi$
$739$	26207.3	1.30453	0.652267	+	0.757990i	$0.273818\pi$
$740$	2424.92	0.120462
$741$	1731.16	0.0858241
$742$	−66520.5	−3.29117
$743$	−20425.9	−1.00855	−0.504276	−	0.863543i	$-0.668241\pi$
$743$	−20425.9	−1.00855	−0.504276	+	0.863543i	$0.668241\pi$
$744$	2262.56	0.111491
$745$	1745.24	0.0858264
$746$	−39902.0	−1.95833
$747$	3808.93	0.186561
$748$	−5647.01	−0.276036
$749$	−5393.99	−0.263140
$750$	8018.02	0.390369
$751$	7670.84	0.372720	0.186360	−	0.982482i	$-0.440331\pi$
$751$	7670.84	0.372720	0.186360	+	0.982482i	$0.440331\pi$
$752$	18069.3	0.876223
$753$	−7242.60	−0.350511
$754$	6406.92	0.309451
$755$	−8385.76	−0.404224
$756$	6962.55	0.334954
$757$	21269.1	1.02119	0.510593	−	0.859823i	$-0.329426\pi$
$757$	21269.1	1.02119	0.510593	+	0.859823i	$0.329426\pi$
$758$	30475.4	1.46031
$759$	0	0
$760$	−163.383	−0.00779806
$761$	23817.1	1.13452	0.567260	−	0.823539i	$-0.308004\pi$
$761$	23817.1	1.13452	0.567260	+	0.823539i	$0.308004\pi$
$762$	−2447.71	−0.116366
$763$	75810.2	3.59700
$764$	−19721.9	−0.933919
$765$	490.603	0.0231866
$766$	9764.76	0.460594
$767$	−4752.33	−0.223725
$768$	−14246.5	−0.669369
$769$	−31207.4	−1.46342	−0.731709	−	0.681617i	$-0.761277\pi$
$769$	−31207.4	−1.46342	−0.731709	+	0.681617i	$0.761277\pi$
$770$	−15845.5	−0.741602
$771$	13788.6	0.644078
$772$	28444.4	1.32608
$773$	−16873.1	−0.785102	−0.392551	−	0.919730i	$-0.628407\pi$
$773$	−16873.1	−0.785102	−0.392551	+	0.919730i	$0.628407\pi$
$774$	−8419.64	−0.391005
$775$	30353.3	1.40687
$776$	1486.11	0.0687476
$777$	−12602.6	−0.581876
$778$	56115.2	2.58589
$779$	9354.75	0.430255
$780$	−1786.88	−0.0820266
$781$	29303.2	1.34258
$782$	0	0
$783$	−1525.48	−0.0696246
$784$	−63858.7	−2.90901
$785$	8134.55	0.369853
$786$	23520.4	1.06736
$787$	−8327.89	−0.377201	−0.188600	−	0.982054i	$-0.560395\pi$
$787$	−8327.89	−0.377201	−0.188600	+	0.982054i	$0.560395\pi$
$788$	28776.8	1.30093
$789$	23330.2	1.05270
$790$	4761.37	0.214433
$791$	−5068.40	−0.227828
$792$	1056.28	0.0473905
$793$	−17079.4	−0.764826
$794$	3688.18	0.164847
$795$	−4064.81	−0.181338
$796$	−6867.04	−0.305774
$797$	−16352.1	−0.726752	−0.363376	−	0.931643i	$-0.618376\pi$
$797$	−16352.1	−0.726752	−0.363376	+	0.931643i	$0.618376\pi$
$798$	−8277.28	−0.367184
$799$	5019.50	0.222249
$800$	−28995.1	−1.28141
$801$	−6393.10	−0.282009
$802$	20499.4	0.902568
$803$	7553.04	0.331932
$804$	7962.19	0.349260
$805$	0	0
$806$	−29417.7	−1.28560
$807$	5266.59	0.229731
$808$	1151.62	0.0501409
$809$	−13640.8	−0.592813	−0.296406	−	0.955062i	$-0.595788\pi$
$809$	−13640.8	−0.592813	−0.296406	+	0.955062i	$0.595788\pi$
$810$	894.554	0.0388042
$811$	32535.7	1.40874	0.704368	−	0.709835i	$-0.251231\pi$
$811$	32535.7	1.40874	0.704368	+	0.709835i	$0.251231\pi$
$812$	−14569.6	−0.629669
$813$	4118.39	0.177661
$814$	18637.5	0.802513
$815$	−8538.64	−0.366989
$816$	−4013.90	−0.172199
$817$	4760.57	0.203857
$818$	24121.3	1.03103
$819$	9286.69	0.396219
$820$	−9655.88	−0.411217
$821$	−3469.01	−0.147466	−0.0737329	−	0.997278i	$-0.523491\pi$
$821$	−3469.01	−0.147466	−0.0737329	+	0.997278i	$0.523491\pi$
$822$	34755.6	1.47475
$823$	38316.5	1.62288	0.811438	−	0.584438i	$-0.198685\pi$
$823$	38316.5	1.62288	0.811438	+	0.584438i	$0.198685\pi$
$824$	4549.18	0.192328
$825$	14170.5	0.598004
$826$	22722.6	0.957166
$827$	−18851.3	−0.792651	−0.396325	−	0.918110i	$-0.629715\pi$
$827$	−18851.3	−0.792651	−0.396325	+	0.918110i	$0.629715\pi$
$828$	0	0
$829$	−2598.99	−0.108886	−0.0544430	−	0.998517i	$-0.517338\pi$
$829$	−2598.99	−0.108886	−0.0544430	+	0.998517i	$0.517338\pi$
$830$	4673.92	0.195463
$831$	14866.7	0.620603
$832$	11982.1	0.499285
$833$	−17739.4	−0.737855
$834$	10269.0	0.426361
$835$	6177.45	0.256024
$836$	5821.85	0.240853
$837$	7004.30	0.289252
$838$	−19019.4	−0.784025
$839$	9510.43	0.391343	0.195671	−	0.980670i	$-0.437311\pi$
$839$	9510.43	0.391343	0.195671	+	0.980670i	$0.437311\pi$
$840$	−876.458	−0.0360008
$841$	−21196.8	−0.869115
$842$	17439.6	0.713787
$843$	−1327.34	−0.0542300
$844$	8337.21	0.340022
$845$	3828.70	0.155871
$846$	9152.44	0.371947
$847$	−10617.4	−0.430719
$848$	33256.5	1.34674
$849$	8024.74	0.324392
$850$	−8810.54	−0.355528
$851$	0	0
$852$	−15799.9	−0.635325
$853$	−12825.6	−0.514820	−0.257410	−	0.966302i	$-0.582869\pi$
$853$	−12825.6	−0.514820	−0.257410	+	0.966302i	$0.582869\pi$
$854$	81662.6	3.27217
$855$	−505.792	−0.0202312
$856$	441.226	0.0176177
$857$	29220.4	1.16470	0.582352	−	0.812937i	$-0.302133\pi$
$857$	29220.4	1.16470	0.582352	+	0.812937i	$0.302133\pi$
$858$	−13733.7	−0.546458
$859$	32553.2	1.29301	0.646507	−	0.762908i	$-0.276229\pi$
$859$	32553.2	1.29301	0.646507	+	0.762908i	$0.276229\pi$
$860$	−4913.82	−0.194837
$861$	50183.0	1.98633
$862$	−39121.5	−1.54581
$863$	7038.26	0.277619	0.138809	−	0.990319i	$-0.455672\pi$
$863$	7038.26	0.277619	0.138809	+	0.990319i	$0.455672\pi$
$864$	−6690.89	−0.263459
$865$	−7377.49	−0.289991
$866$	38192.9	1.49867
$867$	13624.0	0.533673
$868$	66896.8	2.61593
$869$	17404.8	0.679423
$870$	−1871.91	−0.0729467
$871$	10620.0	0.413141
$872$	−6201.24	−0.240826
$873$	4600.61	0.178358
$874$	0	0
$875$	−24319.6	−0.939604
$876$	−4072.51	−0.157075
$877$	4356.74	0.167750	0.0838749	−	0.996476i	$-0.473270\pi$
$877$	4356.74	0.167750	0.0838749	+	0.996476i	$0.473270\pi$
$878$	−50244.0	−1.93127
$879$	20446.7	0.784586
$880$	7921.87	0.303462
$881$	−14343.6	−0.548521	−0.274261	−	0.961655i	$-0.588433\pi$
$881$	−14343.6	−0.548521	−0.274261	+	0.961655i	$0.588433\pi$
$882$	−32345.6	−1.23484
$883$	11530.0	0.439430	0.219715	−	0.975564i	$-0.429487\pi$
$883$	11530.0	0.439430	0.219715	+	0.975564i	$0.429487\pi$
$884$	4061.17	0.154516
$885$	1388.49	0.0527384
$886$	−55316.2	−2.09750
$887$	26911.3	1.01871	0.509354	−	0.860557i	$-0.329884\pi$
$887$	26911.3	1.01871	0.509354	+	0.860557i	$0.329884\pi$
$888$	1030.89	0.0389577
$889$	7424.21	0.280090
$890$	−7844.95	−0.295464
$891$	3269.97	0.122950
$892$	−26321.1	−0.988001
$893$	−5174.90	−0.193921
$894$	−7232.48	−0.270571
$895$	2029.61	0.0758017
$896$	13168.3	0.490985
$897$	0	0
$898$	43598.2	1.62015
$899$	−14656.9	−0.543755
$900$	−7640.56	−0.282984
$901$	9238.36	0.341592
$902$	−74213.6	−2.73951
$903$	25537.8	0.941135
$904$	414.593	0.0152535
$905$	−11409.3	−0.419071
$906$	34751.5	1.27433
$907$	−19527.2	−0.714874	−0.357437	−	0.933937i	$-0.616349\pi$
$907$	−19527.2	−0.714874	−0.357437	+	0.933937i	$0.616349\pi$
$908$	−17041.2	−0.622833
$909$	3565.12	0.130085
$910$	11395.7	0.415124
$911$	20712.4	0.753274	0.376637	−	0.926361i	$-0.377080\pi$
$911$	20712.4	0.753274	0.376637	+	0.926361i	$0.377080\pi$
$912$	4138.17	0.150250
$913$	17085.2	0.619317
$914$	−3472.76	−0.125677
$915$	4990.08	0.180292
$916$	−33302.8	−1.20126
$917$	−71340.3	−2.56910
$918$	−2033.11	−0.0730966
$919$	−44407.6	−1.59399	−0.796993	−	0.603989i	$-0.793577\pi$
$919$	−44407.6	−1.59399	−0.796993	+	0.603989i	$0.793577\pi$
$920$	0	0
$921$	7358.04	0.263253
$922$	−14992.3	−0.535516
$923$	−21074.1	−0.751529
$924$	31230.9	1.11193
$925$	13829.9	0.491594
$926$	57.0473	0.00202450
$927$	14083.1	0.498975
$928$	14001.1	0.495267
$929$	−5057.36	−0.178608	−0.0893038	−	0.996004i	$-0.528464\pi$
$929$	−5057.36	−0.178608	−0.0893038	+	0.996004i	$0.528464\pi$
$930$	8594.95	0.303053
$931$	18288.6	0.643807
$932$	−29931.0	−1.05196
$933$	7019.76	0.246320
$934$	−4853.00	−0.170016
$935$	2200.63	0.0769713
$936$	−759.647	−0.0265276
$937$	−29113.2	−1.01503	−0.507517	−	0.861642i	$-0.669436\pi$
$937$	−29113.2	−1.01503	−0.507517	+	0.861642i	$0.669436\pi$
$938$	−50778.1	−1.76755
$939$	7944.06	0.276086
$940$	5341.48	0.185340
$941$	−16122.4	−0.558529	−0.279264	−	0.960214i	$-0.590091\pi$
$941$	−16122.4	−0.558529	−0.279264	+	0.960214i	$0.590091\pi$
$942$	−33710.5	−1.16597
$943$	0	0
$944$	−11360.0	−0.391670
$945$	−2713.29	−0.0934003
$946$	−37766.8	−1.29800
$947$	−7390.32	−0.253594	−0.126797	−	0.991929i	$-0.540470\pi$
$947$	−7390.32	−0.253594	−0.126797	+	0.991929i	$0.540470\pi$
$948$	−9384.47	−0.321512
$949$	−5431.94	−0.185804
$950$	9083.32	0.310212
$951$	−29744.3	−1.01422
$952$	1991.99	0.0678158
$953$	−18564.1	−0.631007	−0.315503	−	0.948924i	$-0.602173\pi$
$953$	−18564.1	−0.631007	−0.315503	+	0.948924i	$0.602173\pi$
$954$	16845.0	0.571675
$955$	7685.58	0.260418
$956$	−17967.2	−0.607845
$957$	−6842.61	−0.231129
$958$	−55435.2	−1.86955
$959$	−105418.	−3.54966
$960$	−3500.81	−0.117696
$961$	37506.9	1.25900
$962$	−13403.6	−0.449220
$963$	1365.92	0.0457074
$964$	18855.7	0.629980
$965$	−11084.7	−0.369771
$966$	0	0
$967$	−8814.70	−0.293135	−0.146568	−	0.989201i	$-0.546823\pi$
$967$	−8814.70	−0.293135	−0.146568	+	0.989201i	$0.546823\pi$
$968$	868.500	0.0288375
$969$	1149.55	0.0381102
$970$	5645.39	0.186869
$971$	−26850.6	−0.887410	−0.443705	−	0.896173i	$-0.646336\pi$
$971$	−26850.6	−0.887410	−0.443705	+	0.896173i	$0.646336\pi$
$972$	−1763.13	−0.0581815
$973$	−31147.0	−1.02624
$974$	−1381.18	−0.0454373
$975$	−10191.0	−0.334743
$976$	−40826.6	−1.33896
$977$	−2939.87	−0.0962690	−0.0481345	−	0.998841i	$-0.515328\pi$
$977$	−2939.87	−0.0962690	−0.0481345	+	0.998841i	$0.515328\pi$
$978$	35385.1	1.15694
$979$	−28676.6	−0.936168
$980$	−18877.3	−0.615320
$981$	−19197.4	−0.624798
$982$	3009.30	0.0977909
$983$	−9075.34	−0.294464	−0.147232	−	0.989102i	$-0.547036\pi$
$983$	−9075.34	−0.294464	−0.147232	+	0.989102i	$0.547036\pi$
$984$	−4104.95	−0.132989
$985$	−11214.2	−0.362757
$986$	4254.41	0.137412
$987$	−27760.4	−0.895263
$988$	−4186.91	−0.134821
$989$	0	0
$990$	4012.57	0.128816
$991$	29242.1	0.937342	0.468671	−	0.883373i	$-0.344733\pi$
$991$	29242.1	0.937342	0.468671	+	0.883373i	$0.344733\pi$
$992$	−64286.6	−2.05756
$993$	−19681.5	−0.628975
$994$	100762.	3.21528
$995$	2676.07	0.0852634
$996$	−9212.11	−0.293069
$997$	31103.4	0.988019	0.494010	−	0.869456i	$-0.335531\pi$
$997$	31103.4	0.988019	0.494010	+	0.869456i	$0.335531\pi$
$998$	26423.9	0.838111
$999$	3191.37	0.101072

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1587.4.a.v.1.6		30
23.11	odd	22		69.4.e.b.52.1	yes	60
23.21	odd	22		69.4.e.b.4.1	✓	60
23.22	odd	2		1587.4.a.w.1.6		30
69.11	even	22		207.4.i.b.190.6		60
69.44	even	22		207.4.i.b.73.6		60

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
69.4.e.b.4.1	✓	60	23.21	odd	22
69.4.e.b.52.1	yes	60	23.11	odd	22
207.4.i.b.73.6		60	69.44	even	22
207.4.i.b.190.6		60	69.11	even	22
1587.4.a.v.1.6		30	1.1	even	1	trivial
1587.4.a.w.1.6		30	23.22	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:	\( N \)	\(=\)	\( 1587 = 3 \cdot 23^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1587.a (trivial)

\(f(q)\)	\(=\)	\(q-3.90585 q^{2} -3.00000 q^{3} +7.25568 q^{4} -2.82752 q^{5} +11.7176 q^{6} -35.5408 q^{7} +2.90722 q^{8} +9.00000 q^{9} +O(q^{10})\)	\(q-3.90585 q^{2} -3.00000 q^{3} +7.25568 q^{4} -2.82752 q^{5} +11.7176 q^{6} -35.5408 q^{7} +2.90722 q^{8} +9.00000 q^{9} +11.0439 q^{10} +40.3700 q^{11} -21.7670 q^{12} -29.0330 q^{13} +138.817 q^{14} +8.48256 q^{15} -69.4006 q^{16} -19.2789 q^{17} -35.1527 q^{18} +19.8758 q^{19} -20.5156 q^{20} +106.622 q^{21} -157.679 q^{22} -8.72165 q^{24} -117.005 q^{25} +113.399 q^{26} -27.0000 q^{27} -257.872 q^{28} +56.4991 q^{29} -33.1316 q^{30} -259.418 q^{31} +247.811 q^{32} -121.110 q^{33} +75.3004 q^{34} +100.492 q^{35} +65.3011 q^{36} -118.199 q^{37} -77.6318 q^{38} +87.0990 q^{39} -8.22021 q^{40} +470.661 q^{41} -416.451 q^{42} +239.516 q^{43} +292.912 q^{44} -25.4477 q^{45} -260.363 q^{47} +208.202 q^{48} +920.146 q^{49} +457.005 q^{50} +57.8366 q^{51} -210.654 q^{52} -479.196 q^{53} +105.458 q^{54} -114.147 q^{55} -103.325 q^{56} -59.6273 q^{57} -220.677 q^{58} +163.687 q^{59} +61.5467 q^{60} +588.275 q^{61} +1013.25 q^{62} -319.867 q^{63} -412.707 q^{64} +82.0913 q^{65} +473.038 q^{66} -365.791 q^{67} -139.881 q^{68} -392.508 q^{70} +725.866 q^{71} +26.1650 q^{72} +187.095 q^{73} +461.668 q^{74} +351.015 q^{75} +144.212 q^{76} -1434.78 q^{77} -340.196 q^{78} +431.132 q^{79} +196.231 q^{80} +81.0000 q^{81} -1838.33 q^{82} +423.214 q^{83} +773.617 q^{84} +54.5114 q^{85} -935.516 q^{86} -169.497 q^{87} +117.364 q^{88} -710.344 q^{89} +99.3948 q^{90} +1031.85 q^{91} +778.255 q^{93} +1016.94 q^{94} -56.1991 q^{95} -743.432 q^{96} +511.178 q^{97} -3593.95 q^{98} +363.330 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q + 2 q^{2} - 90 q^{3} + 118 q^{4} - 52 q^{5} - 6 q^{6} + 2 q^{7} + 18 q^{8} + 270 q^{9}+O(q^{10}) \) 30 * q + 2 * q^2 - 90 * q^3 + 118 * q^4 - 52 * q^5 - 6 * q^6 + 2 * q^7 + 18 * q^8 + 270 * q^9	\( 30 q + 2 q^{2} - 90 q^{3} + 118 q^{4} - 52 q^{5} - 6 q^{6} + 2 q^{7} + 18 q^{8} + 270 q^{9} + 39 q^{10} - 126 q^{11} - 354 q^{12} + 14 q^{13} - 42 q^{14} + 156 q^{15} + 438 q^{16} - 340 q^{17} + 18 q^{18} + 156 q^{19} - 617 q^{20} - 6 q^{21} - 311 q^{22} - 54 q^{24} + 624 q^{25} + 398 q^{26} - 810 q^{27} - 468 q^{28} - 196 q^{29} - 117 q^{30} - 380 q^{31} + 46 q^{32} + 378 q^{33} - 64 q^{34} - 636 q^{35} + 1062 q^{36} - 1082 q^{37} - 747 q^{38} - 42 q^{39} + 623 q^{40} + 768 q^{41} + 126 q^{42} - 68 q^{43} - 1657 q^{44} - 468 q^{45} - 720 q^{47} - 1314 q^{48} + 2926 q^{49} - 1008 q^{50} + 1020 q^{51} + 482 q^{52} - 2720 q^{53} - 54 q^{54} - 336 q^{55} - 576 q^{56} - 468 q^{57} - 690 q^{58} + 80 q^{59} + 1851 q^{60} - 906 q^{61} - 110 q^{62} + 18 q^{63} + 5740 q^{64} - 3490 q^{65} + 933 q^{66} - 1294 q^{67} - 2802 q^{68} + 1492 q^{70} - 1350 q^{71} + 162 q^{72} - 1824 q^{73} - 2629 q^{74} - 1872 q^{75} + 585 q^{76} - 864 q^{77} - 1194 q^{78} + 3540 q^{79} - 5233 q^{80} + 2430 q^{81} + 2166 q^{82} - 1410 q^{83} + 1404 q^{84} + 2468 q^{85} - 1597 q^{86} + 588 q^{87} - 5645 q^{88} - 2022 q^{89} + 351 q^{90} + 2718 q^{91} + 1140 q^{93} - 1548 q^{94} + 9230 q^{95} - 138 q^{96} - 2926 q^{97} - 11775 q^{98} - 1134 q^{99}+O(q^{100}) \) 30 * q + 2 * q^2 - 90 * q^3 + 118 * q^4 - 52 * q^5 - 6 * q^6 + 2 * q^7 + 18 * q^8 + 270 * q^9 + 39 * q^10 - 126 * q^11 - 354 * q^12 + 14 * q^13 - 42 * q^14 + 156 * q^15 + 438 * q^16 - 340 * q^17 + 18 * q^18 + 156 * q^19 - 617 * q^20 - 6 * q^21 - 311 * q^22 - 54 * q^24 + 624 * q^25 + 398 * q^26 - 810 * q^27 - 468 * q^28 - 196 * q^29 - 117 * q^30 - 380 * q^31 + 46 * q^32 + 378 * q^33 - 64 * q^34 - 636 * q^35 + 1062 * q^36 - 1082 * q^37 - 747 * q^38 - 42 * q^39 + 623 * q^40 + 768 * q^41 + 126 * q^42 - 68 * q^43 - 1657 * q^44 - 468 * q^45 - 720 * q^47 - 1314 * q^48 + 2926 * q^49 - 1008 * q^50 + 1020 * q^51 + 482 * q^52 - 2720 * q^53 - 54 * q^54 - 336 * q^55 - 576 * q^56 - 468 * q^57 - 690 * q^58 + 80 * q^59 + 1851 * q^60 - 906 * q^61 - 110 * q^62 + 18 * q^63 + 5740 * q^64 - 3490 * q^65 + 933 * q^66 - 1294 * q^67 - 2802 * q^68 + 1492 * q^70 - 1350 * q^71 + 162 * q^72 - 1824 * q^73 - 2629 * q^74 - 1872 * q^75 + 585 * q^76 - 864 * q^77 - 1194 * q^78 + 3540 * q^79 - 5233 * q^80 + 2430 * q^81 + 2166 * q^82 - 1410 * q^83 + 1404 * q^84 + 2468 * q^85 - 1597 * q^86 + 588 * q^87 - 5645 * q^88 - 2022 * q^89 + 351 * q^90 + 2718 * q^91 + 1140 * q^93 - 1548 * q^94 + 9230 * q^95 - 138 * q^96 - 2926 * q^97 - 11775 * q^98 - 1134 * q^99

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