LMFDB - Embedded newform 2001.4.a.d.1.31

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2001,4,Mod(1,2001)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2001, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("2001.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 2001 = 3 \cdot 23 \cdot 29 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	2001.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:	$118.062821921$
Analytic rank:	$0$
Dimension:	$37$
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.31
Character	$\chi$	$=$	2001.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+4.07939 q^{2} -3.00000 q^{3} +8.64144 q^{4} -17.0062 q^{5} -12.2382 q^{6} -11.0590 q^{7} +2.61667 q^{8} +9.00000 q^{9} +O(q^{10})$	\(q+4.07939 q^{2} -3.00000 q^{3} +8.64144 q^{4} -17.0062 q^{5} -12.2382 q^{6} -11.0590 q^{7} +2.61667 q^{8} +9.00000 q^{9} -69.3749 q^{10} -14.9299 q^{11} -25.9243 q^{12} -44.8878 q^{13} -45.1138 q^{14} +51.0186 q^{15} -58.4571 q^{16} -116.186 q^{17} +36.7145 q^{18} +49.4288 q^{19} -146.958 q^{20} +33.1769 q^{21} -60.9050 q^{22} -23.0000 q^{23} -7.85000 q^{24} +164.211 q^{25} -183.115 q^{26} -27.0000 q^{27} -95.5653 q^{28} -29.0000 q^{29} +208.125 q^{30} +44.6045 q^{31} -259.403 q^{32} +44.7898 q^{33} -473.966 q^{34} +188.071 q^{35} +77.7729 q^{36} -77.4319 q^{37} +201.639 q^{38} +134.663 q^{39} -44.4995 q^{40} -210.076 q^{41} +135.341 q^{42} -546.292 q^{43} -129.016 q^{44} -153.056 q^{45} -93.8260 q^{46} -277.718 q^{47} +175.371 q^{48} -220.699 q^{49} +669.880 q^{50} +348.557 q^{51} -387.895 q^{52} +648.765 q^{53} -110.144 q^{54} +253.901 q^{55} -28.9376 q^{56} -148.286 q^{57} -118.302 q^{58} +294.029 q^{59} +440.874 q^{60} -346.193 q^{61} +181.959 q^{62} -99.5306 q^{63} -590.548 q^{64} +763.371 q^{65} +182.715 q^{66} +428.421 q^{67} -1004.01 q^{68} +69.0000 q^{69} +767.215 q^{70} +617.193 q^{71} +23.5500 q^{72} +499.123 q^{73} -315.875 q^{74} -492.632 q^{75} +427.136 q^{76} +165.110 q^{77} +549.345 q^{78} +179.340 q^{79} +994.132 q^{80} +81.0000 q^{81} -856.984 q^{82} +531.302 q^{83} +286.696 q^{84} +1975.87 q^{85} -2228.54 q^{86} +87.0000 q^{87} -39.0667 q^{88} +980.717 q^{89} -624.374 q^{90} +496.413 q^{91} -198.753 q^{92} -133.813 q^{93} -1132.92 q^{94} -840.596 q^{95} +778.208 q^{96} +519.635 q^{97} -900.319 q^{98} -134.369 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 37 q + 4 q^{2} - 111 q^{3} + 146 q^{4} + 15 q^{5} - 12 q^{6} + 8 q^{7} + 3 q^{8} + 333 q^{9}+O(q^{10}) $ 37 * q + 4 * q^2 - 111 * q^3 + 146 * q^4 + 15 * q^5 - 12 * q^6 + 8 * q^7 + 3 * q^8 + 333 * q^9	\( 37 q + 4 q^{2} - 111 q^{3} + 146 q^{4} + 15 q^{5} - 12 q^{6} + 8 q^{7} + 3 q^{8} + 333 q^{9} - 136 q^{10} + 109 q^{11} - 438 q^{12} - 269 q^{13} + 121 q^{14} - 45 q^{15} + 390 q^{16} + 180 q^{17} + 36 q^{18} + 117 q^{19} + 287 q^{20} - 24 q^{21} - 128 q^{22} - 851 q^{23} - 9 q^{24} + 490 q^{25} + 677 q^{26} - 999 q^{27} + 775 q^{28} - 1073 q^{29} + 408 q^{30} - 194 q^{31} + 668 q^{32} - 327 q^{33} + 972 q^{34} - 309 q^{35} + 1314 q^{36} - 565 q^{37} + 725 q^{38} + 807 q^{39} + 263 q^{40} + 521 q^{41} - 363 q^{42} - 61 q^{43} + 2242 q^{44} + 135 q^{45} - 92 q^{46} + 1142 q^{47} - 1170 q^{48} + 919 q^{49} + 1833 q^{50} - 540 q^{51} - 10 q^{52} - 120 q^{53} - 108 q^{54} - 996 q^{55} + 1707 q^{56} - 351 q^{57} - 116 q^{58} + 1073 q^{59} - 861 q^{60} - 428 q^{61} + 174 q^{62} + 72 q^{63} + 1479 q^{64} + 1410 q^{65} + 384 q^{66} + 175 q^{67} + 1483 q^{68} + 2553 q^{69} + 675 q^{70} + 2236 q^{71} + 27 q^{72} - 1058 q^{73} - 695 q^{74} - 1470 q^{75} + 1345 q^{76} - 1547 q^{77} - 2031 q^{78} + 1972 q^{79} - 2017 q^{80} + 2997 q^{81} + 2429 q^{82} - 832 q^{83} - 2325 q^{84} + 2299 q^{85} + 1527 q^{86} + 3219 q^{87} + 2579 q^{88} + 2817 q^{89} - 1224 q^{90} + 3175 q^{91} - 3358 q^{92} + 582 q^{93} + 1900 q^{94} + 8017 q^{95} - 2004 q^{96} + 912 q^{97} - 2565 q^{98} + 981 q^{99}+O(q^{100}) \) 37 * q + 4 * q^2 - 111 * q^3 + 146 * q^4 + 15 * q^5 - 12 * q^6 + 8 * q^7 + 3 * q^8 + 333 * q^9 - 136 * q^10 + 109 * q^11 - 438 * q^12 - 269 * q^13 + 121 * q^14 - 45 * q^15 + 390 * q^16 + 180 * q^17 + 36 * q^18 + 117 * q^19 + 287 * q^20 - 24 * q^21 - 128 * q^22 - 851 * q^23 - 9 * q^24 + 490 * q^25 + 677 * q^26 - 999 * q^27 + 775 * q^28 - 1073 * q^29 + 408 * q^30 - 194 * q^31 + 668 * q^32 - 327 * q^33 + 972 * q^34 - 309 * q^35 + 1314 * q^36 - 565 * q^37 + 725 * q^38 + 807 * q^39 + 263 * q^40 + 521 * q^41 - 363 * q^42 - 61 * q^43 + 2242 * q^44 + 135 * q^45 - 92 * q^46 + 1142 * q^47 - 1170 * q^48 + 919 * q^49 + 1833 * q^50 - 540 * q^51 - 10 * q^52 - 120 * q^53 - 108 * q^54 - 996 * q^55 + 1707 * q^56 - 351 * q^57 - 116 * q^58 + 1073 * q^59 - 861 * q^60 - 428 * q^61 + 174 * q^62 + 72 * q^63 + 1479 * q^64 + 1410 * q^65 + 384 * q^66 + 175 * q^67 + 1483 * q^68 + 2553 * q^69 + 675 * q^70 + 2236 * q^71 + 27 * q^72 - 1058 * q^73 - 695 * q^74 - 1470 * q^75 + 1345 * q^76 - 1547 * q^77 - 2031 * q^78 + 1972 * q^79 - 2017 * q^80 + 2997 * q^81 + 2429 * q^82 - 832 * q^83 - 2325 * q^84 + 2299 * q^85 + 1527 * q^86 + 3219 * q^87 + 2579 * q^88 + 2817 * q^89 - 1224 * q^90 + 3175 * q^91 - 3358 * q^92 + 582 * q^93 + 1900 * q^94 + 8017 * q^95 - 2004 * q^96 + 912 * q^97 - 2565 * q^98 + 981 * 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 $

$2$	4.07939	1.44228	0.721141	−	0.692788i	$-0.243618\pi$
$2$	4.07939	1.44228	0.721141	+	0.692788i	$0.243618\pi$
$3$	−3.00000	−0.577350
$3$	−3.00000	−0.577350
$4$	8.64144	1.08018
$5$	−17.0062	−1.52108	−0.760540	−	0.649291i	$-0.775066\pi$
$5$	−17.0062	−1.52108	−0.760540	+	0.649291i	$0.775066\pi$
$6$	−12.2382	−0.832702
$7$	−11.0590	−0.597128	−0.298564	−	0.954390i	$-0.596508\pi$
$7$	−11.0590	−0.597128	−0.298564	+	0.954390i	$0.596508\pi$
$8$	2.61667	0.115641
$9$	9.00000	0.333333
$10$	−69.3749	−2.19383
$11$	−14.9299	−0.409231	−0.204616	−	0.978842i	$-0.565594\pi$
$11$	−14.9299	−0.409231	−0.204616	+	0.978842i	$0.565594\pi$
$12$	−25.9243	−0.623642
$13$	−44.8878	−0.957665	−0.478832	−	0.877906i	$-0.658940\pi$
$13$	−44.8878	−0.957665	−0.478832	+	0.877906i	$0.658940\pi$
$14$	−45.1138	−0.861227
$15$	51.0186	0.878196
$16$	−58.4571	−0.913392
$17$	−116.186	−1.65760	−0.828798	−	0.559548i	$-0.810975\pi$
$17$	−116.186	−1.65760	−0.828798	+	0.559548i	$0.810975\pi$
$18$	36.7145	0.480761
$19$	49.4288	0.596828	0.298414	−	0.954436i	$-0.403542\pi$
$19$	49.4288	0.596828	0.298414	+	0.954436i	$0.403542\pi$
$20$	−146.958	−1.64304
$21$	33.1769	0.344752
$22$	−60.9050	−0.590227
$23$	−23.0000	−0.208514
$23$	−23.0000	−0.208514
$24$	−7.85000	−0.0667656
$25$	164.211	1.31369
$26$	−183.115	−1.38122
$27$	−27.0000	−0.192450
$28$	−95.5653	−0.645005
$29$	−29.0000	−0.185695
$29$	−29.0000	−0.185695
$30$	208.125	1.26661
$31$	44.6045	0.258426	0.129213	−	0.991617i	$-0.458755\pi$
$31$	44.6045	0.258426	0.129213	+	0.991617i	$0.458755\pi$
$32$	−259.403	−1.43301
$33$	44.7898	0.236270
$34$	−473.966	−2.39072
$35$	188.071	0.908279
$36$	77.7729	0.360060
$37$	−77.4319	−0.344047	−0.172023	−	0.985093i	$-0.555030\pi$
$37$	−77.4319	−0.344047	−0.172023	+	0.985093i	$0.555030\pi$
$38$	201.639	0.860795
$39$	134.663	0.552908
$40$	−44.4995	−0.175900
$41$	−210.076	−0.800205	−0.400103	−	0.916470i	$-0.631025\pi$
$41$	−210.076	−0.800205	−0.400103	+	0.916470i	$0.631025\pi$
$42$	135.341	0.497230
$43$	−546.292	−1.93741	−0.968706	−	0.248209i	$-0.920158\pi$
$43$	−546.292	−1.93741	−0.968706	+	0.248209i	$0.920158\pi$
$44$	−129.016	−0.442043
$45$	−153.056	−0.507027
$46$	−93.8260	−0.300737
$47$	−277.718	−0.861900	−0.430950	−	0.902376i	$-0.641821\pi$
$47$	−277.718	−0.861900	−0.430950	+	0.902376i	$0.641821\pi$
$48$	175.371	0.527347
$49$	−220.699	−0.643438
$50$	669.880	1.89471
$51$	348.557	0.957013
$52$	−387.895	−1.03445
$53$	648.765	1.68141	0.840705	−	0.541493i	$-0.182141\pi$
$53$	648.765	1.68141	0.840705	+	0.541493i	$0.182141\pi$
$54$	−110.144	−0.277567
$55$	253.901	0.622474
$56$	−28.9376	−0.0690527
$57$	−148.286	−0.344579
$58$	−118.302	−0.267825
$59$	294.029	0.648801	0.324400	−	0.945920i	$-0.394837\pi$
$59$	294.029	0.648801	0.324400	+	0.945920i	$0.394837\pi$
$60$	440.874	0.948609
$61$	−346.193	−0.726647	−0.363324	−	0.931663i	$-0.618358\pi$
$61$	−346.193	−0.726647	−0.363324	+	0.931663i	$0.618358\pi$
$62$	181.959	0.372723
$63$	−99.5306	−0.199043
$64$	−590.548	−1.15341
$65$	763.371	1.45669
$66$	182.715	0.340768
$67$	428.421	0.781194	0.390597	−	0.920562i	$-0.372269\pi$
$67$	428.421	0.781194	0.390597	+	0.920562i	$0.372269\pi$
$68$	−1004.01	−1.79050
$69$	69.0000	0.120386
$70$	767.215	1.31000
$71$	617.193	1.03165	0.515827	−	0.856693i	$-0.327485\pi$
$71$	617.193	1.03165	0.515827	+	0.856693i	$0.327485\pi$
$72$	23.5500	0.0385471
$73$	499.123	0.800246	0.400123	−	0.916461i	$-0.368967\pi$
$73$	499.123	0.800246	0.400123	+	0.916461i	$0.368967\pi$
$74$	−315.875	−0.496213
$75$	−492.632	−0.758457
$76$	427.136	0.644682
$77$	165.110	0.244363
$78$	549.345	0.797450
$79$	179.340	0.255409	0.127704	−	0.991812i	$-0.459239\pi$
$79$	179.340	0.255409	0.127704	+	0.991812i	$0.459239\pi$
$80$	994.132	1.38934
$81$	81.0000	0.111111
$82$	−856.984	−1.15412
$83$	531.302	0.702626	0.351313	−	0.936258i	$-0.385735\pi$
$83$	531.302	0.702626	0.351313	+	0.936258i	$0.385735\pi$
$84$	286.696	0.372394
$85$	1975.87	2.52134
$86$	−2228.54	−2.79430
$87$	87.0000	0.107211
$88$	−39.0667	−0.0473241
$89$	980.717	1.16804	0.584021	−	0.811739i	$-0.301479\pi$
$89$	980.717	1.16804	0.584021	+	0.811739i	$0.301479\pi$
$90$	−624.374	−0.731276
$91$	496.413	0.571848
$92$	−198.753	−0.225233
$93$	−133.813	−0.149202
$94$	−1132.92	−1.24310
$95$	−840.596	−0.907824
$96$	778.208	0.827349
$97$	519.635	0.543927	0.271964	−	0.962308i	$-0.412327\pi$
$97$	519.635	0.543927	0.271964	+	0.962308i	$0.412327\pi$
$98$	−900.319	−0.928020
$99$	−134.369	−0.136410
$100$	1419.02	1.41902
$101$	−513.681	−0.506071	−0.253036	−	0.967457i	$-0.581429\pi$
$101$	−513.681	−0.506071	−0.253036	+	0.967457i	$0.581429\pi$
$102$	1421.90	1.38028
$103$	−2.63408	−0.00251984	−0.00125992	−	0.999999i	$-0.500401\pi$
$103$	−2.63408	−0.00251984	−0.00125992	+	0.999999i	$0.500401\pi$
$104$	−117.456	−0.110746
$105$	−564.213	−0.524395
$106$	2646.57	2.42507
$107$	133.634	0.120737	0.0603687	−	0.998176i	$-0.480772\pi$
$107$	133.634	0.120737	0.0603687	+	0.998176i	$0.480772\pi$
$108$	−233.319	−0.207881
$109$	−274.720	−0.241407	−0.120704	−	0.992689i	$-0.538515\pi$
$109$	−274.720	−0.241407	−0.120704	+	0.992689i	$0.538515\pi$
$110$	1035.76	0.897783
$111$	232.296	0.198635
$112$	646.474	0.545412
$113$	123.558	0.102861	0.0514306	−	0.998677i	$-0.483622\pi$
$113$	123.558	0.102861	0.0514306	+	0.998677i	$0.483622\pi$
$114$	−604.918	−0.496980
$115$	391.143	0.317167
$116$	−250.602	−0.200584
$117$	−403.990	−0.319222
$118$	1199.46	0.935754
$119$	1284.89	0.989796
$120$	133.499	0.101556
$121$	−1108.10	−0.832530
$122$	−1412.26	−1.04803
$123$	630.229	0.461999
$124$	385.447	0.279146
$125$	−666.825	−0.477141
$126$	−406.024	−0.287076
$127$	−1561.30	−1.09089	−0.545445	−	0.838146i	$-0.683639\pi$
$127$	−1561.30	−1.09089	−0.545445	+	0.838146i	$0.683639\pi$
$128$	−333.857	−0.230539
$129$	1638.88	1.11857
$130$	3114.09	2.10095
$131$	−1486.90	−0.991685	−0.495842	−	0.868413i	$-0.665141\pi$
$131$	−1486.90	−0.991685	−0.495842	+	0.868413i	$0.665141\pi$
$132$	387.048	0.255214
$133$	−546.631	−0.356383
$134$	1747.70	1.12670
$135$	459.167	0.292732
$136$	−304.019	−0.191687
$137$	−1004.01	−0.626121	−0.313061	−	0.949733i	$-0.601354\pi$
$137$	−1004.01	−0.626121	−0.313061	+	0.949733i	$0.601354\pi$
$138$	281.478	0.173630
$139$	−1284.13	−0.783589	−0.391794	−	0.920053i	$-0.628146\pi$
$139$	−1284.13	−0.783589	−0.391794	+	0.920053i	$0.628146\pi$
$140$	1625.20	0.981105
$141$	833.153	0.497618
$142$	2517.77	1.48794
$143$	670.172	0.391906
$144$	−526.114	−0.304464
$145$	493.180	0.282458
$146$	2036.12	1.15418
$147$	662.098	0.371489
$148$	−669.123	−0.371632
$149$	2704.83	1.48717	0.743584	−	0.668643i	$-0.233125\pi$
$149$	2704.83	1.48717	0.743584	+	0.668643i	$0.233125\pi$
$150$	−2009.64	−1.09391
$151$	−1155.55	−0.622764	−0.311382	−	0.950285i	$-0.600792\pi$
$151$	−1155.55	−0.622764	−0.311382	+	0.950285i	$0.600792\pi$
$152$	129.339	0.0690181
$153$	−1045.67	−0.552532
$154$	673.546	0.352441
$155$	−758.552	−0.393086
$156$	1163.69	0.597240
$157$	−532.855	−0.270869	−0.135435	−	0.990786i	$-0.543243\pi$
$157$	−532.855	−0.270869	−0.135435	+	0.990786i	$0.543243\pi$
$158$	731.597	0.368372
$159$	−1946.30	−0.970763
$160$	4411.45	2.17972
$161$	254.356	0.124510
$162$	330.431	0.160254
$163$	2082.69	1.00079	0.500396	−	0.865796i	$-0.333188\pi$
$163$	2082.69	1.00079	0.500396	+	0.865796i	$0.333188\pi$
$164$	−1815.36	−0.864365
$165$	−761.704	−0.359385
$166$	2167.39	1.01339
$167$	−2047.13	−0.948574	−0.474287	−	0.880370i	$-0.657294\pi$
$167$	−2047.13	−0.948574	−0.474287	+	0.880370i	$0.657294\pi$
$168$	86.8128	0.0398676
$169$	−182.083	−0.0828779
$170$	8060.36	3.63648
$171$	444.859	0.198943
$172$	−4720.75	−2.09275
$173$	2527.67	1.11084	0.555420	−	0.831570i	$-0.312558\pi$
$173$	2527.67	1.11084	0.555420	+	0.831570i	$0.312558\pi$
$174$	354.907	0.154629
$175$	−1816.00	−0.784438
$176$	872.760	0.373789
$177$	−882.086	−0.374585
$178$	4000.73	1.68465
$179$	−3911.33	−1.63322	−0.816610	−	0.577189i	$-0.804149\pi$
$179$	−3911.33	−1.63322	−0.816610	+	0.577189i	$0.804149\pi$
$180$	−1322.62	−0.547680
$181$	−858.721	−0.352642	−0.176321	−	0.984333i	$-0.556420\pi$
$181$	−858.721	−0.352642	−0.176321	+	0.984333i	$0.556420\pi$
$182$	2025.06	0.824767
$183$	1038.58	0.419530
$184$	−60.1833	−0.0241129
$185$	1316.82	0.523323
$186$	−545.877	−0.215192
$187$	1734.64	0.678340
$188$	−2399.88	−0.931006
$189$	298.592	0.114917
$190$	−3429.12	−1.30934
$191$	2926.08	1.10850	0.554251	−	0.832349i	$-0.313005\pi$
$191$	2926.08	1.10850	0.554251	+	0.832349i	$0.313005\pi$
$192$	1771.64	0.665924
$193$	1657.94	0.618347	0.309173	−	0.951006i	$-0.399948\pi$
$193$	1657.94	0.618347	0.309173	+	0.951006i	$0.399948\pi$
$194$	2119.79	0.784497
$195$	−2290.11	−0.841018
$196$	−1907.16	−0.695029
$197$	−1131.07	−0.409061	−0.204531	−	0.978860i	$-0.565567\pi$
$197$	−1131.07	−0.409061	−0.204531	+	0.978860i	$0.565567\pi$
$198$	−548.145	−0.196742
$199$	−3941.32	−1.40398	−0.701992	−	0.712185i	$-0.747706\pi$
$199$	−3941.32	−1.40398	−0.701992	+	0.712185i	$0.747706\pi$
$200$	429.685	0.151916
$201$	−1285.26	−0.451023
$202$	−2095.51	−0.729897
$203$	320.710	0.110884
$204$	3012.03	1.03375
$205$	3572.60	1.21718
$206$	−10.7454	−0.00363432
$207$	−207.000	−0.0695048
$208$	2624.01	0.874723
$209$	−737.968	−0.244241
$210$	−2301.64	−0.756326
$211$	2697.92	0.880249	0.440124	−	0.897937i	$-0.354934\pi$
$211$	2697.92	0.880249	0.440124	+	0.897937i	$0.354934\pi$
$212$	5606.26	1.81623
$213$	−1851.58	−0.595625
$214$	545.146	0.174138
$215$	9290.35	2.94696
$216$	−70.6500	−0.0222552
$217$	−493.279	−0.154313
$218$	−1120.69	−0.348177
$219$	−1497.37	−0.462022
$220$	2194.07	0.672383
$221$	5215.32	1.58742
$222$	947.625	0.286488
$223$	−4974.68	−1.49385	−0.746926	−	0.664907i	$-0.768471\pi$
$223$	−4974.68	−1.49385	−0.746926	+	0.664907i	$0.768471\pi$
$224$	2868.72	0.855690
$225$	1477.90	0.437895
$226$	504.040	0.148355
$227$	2846.71	0.832346	0.416173	−	0.909285i	$-0.363371\pi$
$227$	2846.71	0.832346	0.416173	+	0.909285i	$0.363371\pi$
$228$	−1281.41	−0.372207
$229$	−469.098	−0.135366	−0.0676831	−	0.997707i	$-0.521561\pi$
$229$	−469.098	−0.135366	−0.0676831	+	0.997707i	$0.521561\pi$
$230$	1595.62	0.457445
$231$	−495.329	−0.141083
$232$	−75.8833	−0.0214741
$233$	1050.36	0.295328	0.147664	−	0.989038i	$-0.452825\pi$
$233$	1050.36	0.295328	0.147664	+	0.989038i	$0.452825\pi$
$234$	−1648.04	−0.460408
$235$	4722.92	1.31102
$236$	2540.83	0.700821
$237$	−538.019	−0.147460
$238$	5241.57	1.42757
$239$	3877.14	1.04934	0.524669	−	0.851307i	$-0.324189\pi$
$239$	3877.14	1.04934	0.524669	+	0.851307i	$0.324189\pi$
$240$	−2982.40	−0.802137
$241$	2030.20	0.542642	0.271321	−	0.962489i	$-0.412539\pi$
$241$	2030.20	0.542642	0.271321	+	0.962489i	$0.412539\pi$
$242$	−4520.36	−1.20074
$243$	−243.000	−0.0641500
$244$	−2991.60	−0.784909
$245$	3753.26	0.978722
$246$	2570.95	0.666333
$247$	−2218.75	−0.571562
$248$	116.715	0.0298847
$249$	−1593.91	−0.405661
$250$	−2720.24	−0.688172
$251$	−6466.94	−1.62625	−0.813126	−	0.582087i	$-0.802236\pi$
$251$	−6466.94	−1.62625	−0.813126	+	0.582087i	$0.802236\pi$
$252$	−860.088	−0.215002
$253$	343.388	0.0853306
$254$	−6369.16	−1.57337
$255$	−5927.62	−1.45569
$256$	3362.45	0.820912
$257$	3412.34	0.828233	0.414116	−	0.910224i	$-0.364091\pi$
$257$	3412.34	0.828233	0.414116	+	0.910224i	$0.364091\pi$
$258$	6685.62	1.61329
$259$	856.316	0.205440
$260$	6596.62	1.57348
$261$	−261.000	−0.0618984
$262$	−6065.63	−1.43029
$263$	3878.44	0.909334	0.454667	−	0.890661i	$-0.349758\pi$
$263$	3878.44	0.909334	0.454667	+	0.890661i	$0.349758\pi$
$264$	117.200	0.0273226
$265$	−11033.0	−2.55756
$266$	−2229.92	−0.514005
$267$	−2942.15	−0.674369
$268$	3702.17	0.843830
$269$	−1989.83	−0.451010	−0.225505	−	0.974242i	$-0.572403\pi$
$269$	−1989.83	−0.451010	−0.225505	+	0.974242i	$0.572403\pi$
$270$	1873.12	0.422202
$271$	498.208	0.111675	0.0558376	−	0.998440i	$-0.482217\pi$
$271$	498.208	0.111675	0.0558376	+	0.998440i	$0.482217\pi$
$272$	6791.87	1.51403
$273$	−1489.24	−0.330157
$274$	−4095.76	−0.903044
$275$	−2451.65	−0.537601
$276$	596.259	0.130038
$277$	−6560.66	−1.42308	−0.711538	−	0.702648i	$-0.752001\pi$
$277$	−6560.66	−1.42308	−0.711538	+	0.702648i	$0.752001\pi$
$278$	−5238.49	−1.13016
$279$	401.440	0.0861419
$280$	492.119	0.105035
$281$	260.001	0.0551970	0.0275985	−	0.999619i	$-0.491214\pi$
$281$	260.001	0.0551970	0.0275985	+	0.999619i	$0.491214\pi$
$282$	3398.76	0.717706
$283$	−4622.40	−0.970929	−0.485465	−	0.874256i	$-0.661350\pi$
$283$	−4622.40	−0.970929	−0.485465	+	0.874256i	$0.661350\pi$
$284$	5333.44	1.11437
$285$	2521.79	0.524132
$286$	2733.90	0.565240
$287$	2323.23	0.477825
$288$	−2334.62	−0.477670
$289$	8586.07	1.74762
$290$	2011.87	0.407384
$291$	−1558.90	−0.314037
$292$	4313.14	0.864410
$293$	−1554.26	−0.309900	−0.154950	−	0.987922i	$-0.549522\pi$
$293$	−1554.26	−0.309900	−0.154950	+	0.987922i	$0.549522\pi$
$294$	2700.96	0.535793
$295$	−5000.31	−0.986878
$296$	−202.614	−0.0397861
$297$	403.108	0.0787566
$298$	11034.0	2.14492
$299$	1032.42	0.199687
$300$	−4257.05	−0.819269
$301$	6041.42	1.15688
$302$	−4713.95	−0.898202
$303$	1541.04	0.292180
$304$	−2889.46	−0.545138
$305$	5887.43	1.10529
$306$	−4265.70	−0.796907
$307$	−8366.37	−1.55535	−0.777677	−	0.628663i	$-0.783602\pi$
$307$	−8366.37	−1.55535	−0.777677	+	0.628663i	$0.783602\pi$
$308$	1426.78	0.263956
$309$	7.90223	0.00145483
$310$	−3094.43	−0.566942
$311$	−1448.81	−0.264162	−0.132081	−	0.991239i	$-0.542166\pi$
$311$	−1448.81	−0.264162	−0.132081	+	0.991239i	$0.542166\pi$
$312$	352.369	0.0639391
$313$	−3778.58	−0.682358	−0.341179	−	0.939998i	$-0.610826\pi$
$313$	−3778.58	−0.682358	−0.341179	+	0.939998i	$0.610826\pi$
$314$	−2173.73	−0.390670
$315$	1692.64	0.302760
$316$	1549.75	0.275887
$317$	4466.29	0.791331	0.395666	−	0.918395i	$-0.370514\pi$
$317$	4466.29	0.791331	0.395666	+	0.918395i	$0.370514\pi$
$318$	−7939.70	−1.40011
$319$	432.968	0.0759923
$320$	10043.0	1.75444
$321$	−400.903	−0.0697078
$322$	1037.62	0.179578
$323$	−5742.91	−0.989300
$324$	699.956	0.120020
$325$	−7371.06	−1.25807
$326$	8496.13	1.44343
$327$	824.159	0.139376
$328$	−549.700	−0.0925369
$329$	3071.27	0.514664
$330$	−3107.29	−0.518335
$331$	5451.73	0.905300	0.452650	−	0.891688i	$-0.350479\pi$
$331$	5451.73	0.905300	0.452650	+	0.891688i	$0.350479\pi$
$332$	4591.21	0.758962
$333$	−696.887	−0.114682
$334$	−8351.06	−1.36811
$335$	−7285.82	−1.18826
$336$	−1939.42	−0.314894
$337$	1291.65	0.208785	0.104392	−	0.994536i	$-0.466710\pi$
$337$	1291.65	0.208785	0.104392	+	0.994536i	$0.466710\pi$
$338$	−742.787	−0.119533
$339$	−370.673	−0.0593870
$340$	17074.4	2.72350
$341$	−665.942	−0.105756
$342$	1814.75	0.286932
$343$	6233.93	0.981343
$344$	−1429.46	−0.224045
$345$	−1173.43	−0.183117
$346$	10311.4	1.60214
$347$	250.167	0.0387021	0.0193511	−	0.999813i	$-0.493840\pi$
$347$	250.167	0.0387021	0.0193511	+	0.999813i	$0.493840\pi$
$348$	751.805	0.115807
$349$	−4185.59	−0.641976	−0.320988	−	0.947083i	$-0.604015\pi$
$349$	−4185.59	−0.641976	−0.320988	+	0.947083i	$0.604015\pi$
$350$	−7408.17	−1.13138
$351$	1211.97	0.184303
$352$	3872.86	0.586433
$353$	−7421.38	−1.11898	−0.559491	−	0.828837i	$-0.689003\pi$
$353$	−7421.38	−1.11898	−0.559491	+	0.828837i	$0.689003\pi$
$354$	−3598.37	−0.540258
$355$	−10496.1	−1.56923
$356$	8474.80	1.26170
$357$	−3854.67	−0.571459
$358$	−15955.8	−2.35557
$359$	170.827	0.0251139	0.0125569	−	0.999921i	$-0.496003\pi$
$359$	170.827	0.0251139	0.0125569	+	0.999921i	$0.496003\pi$
$360$	−400.496	−0.0586333
$361$	−4415.80	−0.643796
$362$	−3503.06	−0.508610
$363$	3324.29	0.480661
$364$	4289.72	0.617699
$365$	−8488.19	−1.21724
$366$	4236.77	0.605081
$367$	−1835.50	−0.261070	−0.130535	−	0.991444i	$-0.541669\pi$
$367$	−1835.50	−0.261070	−0.130535	+	0.991444i	$0.541669\pi$
$368$	1344.51	0.190455
$369$	−1890.69	−0.266735
$370$	5371.83	0.754779
$371$	−7174.67	−1.00402
$372$	−1156.34	−0.161165
$373$	1801.39	0.250060	0.125030	−	0.992153i	$-0.460097\pi$
$373$	1801.39	0.250060	0.125030	+	0.992153i	$0.460097\pi$
$374$	7076.28	0.978358
$375$	2000.47	0.275478
$376$	−726.695	−0.0996713
$377$	1301.75	0.177834
$378$	1218.07	0.165743
$379$	6649.79	0.901259	0.450629	−	0.892711i	$-0.351200\pi$
$379$	6649.79	0.901259	0.450629	+	0.892711i	$0.351200\pi$
$380$	−7263.95	−0.980613
$381$	4683.91	0.629826
$382$	11936.6	1.59877
$383$	−5825.71	−0.777232	−0.388616	−	0.921400i	$-0.627047\pi$
$383$	−5825.71	−0.777232	−0.388616	+	0.921400i	$0.627047\pi$
$384$	1001.57	0.133102
$385$	−2807.89	−0.371696
$386$	6763.37	0.891831
$387$	−4916.63	−0.645804
$388$	4490.39	0.587539
$389$	−9338.74	−1.21720	−0.608602	−	0.793475i	$-0.708270\pi$
$389$	−9338.74	−1.21720	−0.608602	+	0.793475i	$0.708270\pi$
$390$	−9342.27	−1.21299
$391$	2672.27	0.345633
$392$	−577.497	−0.0744081
$393$	4460.69	0.572549
$394$	−4614.06	−0.589982
$395$	−3049.89	−0.388497
$396$	−1161.14	−0.147348
$397$	−6510.63	−0.823071	−0.411536	−	0.911394i	$-0.635007\pi$
$397$	−6510.63	−0.823071	−0.411536	+	0.911394i	$0.635007\pi$
$398$	−16078.2	−2.02494
$399$	1639.89	0.205758
$400$	−9599.28	−1.19991
$401$	−6783.77	−0.844801	−0.422400	−	0.906409i	$-0.638812\pi$
$401$	−6783.77	−0.844801	−0.422400	+	0.906409i	$0.638812\pi$
$402$	−5243.09	−0.650502
$403$	−2002.20	−0.247485
$404$	−4438.94	−0.546648
$405$	−1377.50	−0.169009
$406$	1308.30	0.159926
$407$	1156.05	0.140795
$408$	912.056	0.110670
$409$	−3846.20	−0.464993	−0.232497	−	0.972597i	$-0.574689\pi$
$409$	−3846.20	−0.464993	−0.232497	+	0.972597i	$0.574689\pi$
$410$	14574.0	1.75551
$411$	3012.04	0.361491
$412$	−22.7622	−0.00272188
$413$	−3251.65	−0.387417
$414$	−844.434	−0.100246
$415$	−9035.43	−1.06875
$416$	11644.0	1.37234
$417$	3852.40	0.452405
$418$	−3010.46	−0.352264
$419$	−4048.92	−0.472083	−0.236041	−	0.971743i	$-0.575850\pi$
$419$	−4048.92	−0.472083	−0.236041	+	0.971743i	$0.575850\pi$
$420$	−4875.61	−0.566441
$421$	6708.63	0.776624	0.388312	−	0.921528i	$-0.373058\pi$
$421$	6708.63	0.776624	0.388312	+	0.921528i	$0.373058\pi$
$422$	11005.9	1.26957
$423$	−2499.46	−0.287300
$424$	1697.60	0.194441
$425$	−19078.9	−2.17756
$426$	−7553.32	−0.859060
$427$	3828.53	0.433901
$428$	1154.79	0.130418
$429$	−2010.52	−0.226267
$430$	37899.0	4.25035
$431$	−2770.53	−0.309633	−0.154816	−	0.987943i	$-0.549479\pi$
$431$	−2770.53	−0.309633	−0.154816	+	0.987943i	$0.549479\pi$
$432$	1578.34	0.175782
$433$	13946.5	1.54786	0.773931	−	0.633270i	$-0.218288\pi$
$433$	13946.5	1.54786	0.773931	+	0.633270i	$0.218288\pi$
$434$	−2012.28	−0.222563
$435$	−1479.54	−0.163077
$436$	−2373.97	−0.260763
$437$	−1136.86	−0.124447
$438$	−6108.36	−0.666367
$439$	−4789.86	−0.520746	−0.260373	−	0.965508i	$-0.583846\pi$
$439$	−4789.86	−0.520746	−0.260373	+	0.965508i	$0.583846\pi$
$440$	664.375	0.0719838
$441$	−1986.29	−0.214479
$442$	21275.3	2.28951
$443$	973.679	0.104426	0.0522132	−	0.998636i	$-0.483372\pi$
$443$	973.679	0.104426	0.0522132	+	0.998636i	$0.483372\pi$
$444$	2007.37	0.214562
$445$	−16678.3	−1.77669
$446$	−20293.7	−2.15456
$447$	−8114.48	−0.858616
$448$	6530.85	0.688736
$449$	16586.1	1.74331	0.871654	−	0.490122i	$-0.163048\pi$
$449$	16586.1	1.74331	0.871654	+	0.490122i	$0.163048\pi$
$450$	6028.92	0.631569
$451$	3136.43	0.327469
$452$	1067.71	0.111109
$453$	3466.65	0.359553
$454$	11612.8	1.20048
$455$	−8442.09	−0.869827
$456$	−388.016	−0.0398476
$457$	−2517.62	−0.257701	−0.128851	−	0.991664i	$-0.541129\pi$
$457$	−2517.62	−0.257701	−0.128851	+	0.991664i	$0.541129\pi$
$458$	−1913.64	−0.195236
$459$	3137.01	0.319004
$460$	3380.03	0.342597
$461$	−2984.98	−0.301571	−0.150786	−	0.988566i	$-0.548180\pi$
$461$	−2984.98	−0.301571	−0.150786	+	0.988566i	$0.548180\pi$
$462$	−2020.64	−0.203482
$463$	−4963.27	−0.498191	−0.249096	−	0.968479i	$-0.580133\pi$
$463$	−4963.27	−0.498191	−0.249096	+	0.968479i	$0.580133\pi$
$464$	1695.26	0.169613
$465$	2275.66	0.226949
$466$	4284.84	0.425947
$467$	9079.37	0.899664	0.449832	−	0.893113i	$-0.351484\pi$
$467$	9079.37	0.899664	0.449832	+	0.893113i	$0.351484\pi$
$468$	−3491.06	−0.344817
$469$	−4737.89	−0.466473
$470$	19266.6	1.89086
$471$	1598.57	0.156386
$472$	769.375	0.0750283
$473$	8156.10	0.792850
$474$	−2194.79	−0.212680
$475$	8116.74	0.784045
$476$	11103.3	1.06916
$477$	5838.89	0.560470
$478$	15816.4	1.51344
$479$	4512.03	0.430397	0.215198	−	0.976570i	$-0.430960\pi$
$479$	4512.03	0.430397	0.215198	+	0.976570i	$0.430960\pi$
$480$	−13234.4	−1.25846
$481$	3475.75	0.329481
$482$	8281.99	0.782643
$483$	−763.068	−0.0718857
$484$	−9575.55	−0.899282
$485$	−8837.01	−0.827357
$486$	−991.292	−0.0925225
$487$	4030.83	0.375060	0.187530	−	0.982259i	$-0.439952\pi$
$487$	4030.83	0.375060	0.187530	+	0.982259i	$0.439952\pi$
$488$	−905.872	−0.0840305
$489$	−6248.08	−0.577808
$490$	15311.0	1.41159
$491$	−10387.9	−0.954781	−0.477391	−	0.878691i	$-0.658417\pi$
$491$	−10387.9	−0.954781	−0.477391	+	0.878691i	$0.658417\pi$
$492$	5446.08	0.499041
$493$	3369.38	0.307808
$494$	−9051.15	−0.824354
$495$	2285.11	0.207491
$496$	−2607.45	−0.236044
$497$	−6825.52	−0.616029
$498$	−6502.17	−0.585078
$499$	15051.7	1.35031	0.675157	−	0.737674i	$-0.264076\pi$
$499$	15051.7	1.35031	0.675157	+	0.737674i	$0.264076\pi$
$500$	−5762.32	−0.515398
$501$	6141.40	0.547660
$502$	−26381.2	−2.34552
$503$	12.8305	0.00113734	0.000568671	−	1.00000i	$-0.499819\pi$
$503$	12.8305	0.00113734	0.000568671		1.00000i	$0.499819\pi$
$504$	−260.439	−0.0230176
$505$	8735.76	0.769775
$506$	1400.82	0.123071
$507$	546.248	0.0478496
$508$	−13491.9	−1.17836
$509$	20405.8	1.77696	0.888479	−	0.458917i	$-0.151762\pi$
$509$	20405.8	1.77696	0.888479	+	0.458917i	$0.151762\pi$
$510$	−24181.1	−2.09952
$511$	−5519.79	−0.477849
$512$	16387.6	1.41453
$513$	−1334.58	−0.114860
$514$	13920.3	1.19455
$515$	44.7956	0.00383288
$516$	14162.2	1.20825
$517$	4146.31	0.352716
$518$	3493.25	0.296302
$519$	−7583.01	−0.641344
$520$	1997.49	0.168453
$521$	12193.8	1.02538	0.512688	−	0.858575i	$-0.328650\pi$
$521$	12193.8	1.02538	0.512688	+	0.858575i	$0.328650\pi$
$522$	−1064.72	−0.0892751
$523$	−16913.9	−1.41413	−0.707066	−	0.707148i	$-0.749982\pi$
$523$	−16913.9	−1.41413	−0.707066	+	0.707148i	$0.749982\pi$
$524$	−12848.9	−1.07120
$525$	5448.00	0.452896
$526$	15821.7	1.31152
$527$	−5182.39	−0.428365
$528$	−2618.28	−0.215807
$529$	529.000	0.0434783
$530$	−45008.1	−3.68873
$531$	2646.26	0.216267
$532$	−4723.68	−0.384957
$533$	9429.87	0.766328
$534$	−12002.2	−0.972631
$535$	−2272.61	−0.183651
$536$	1121.04	0.0903384
$537$	11734.0	0.942940
$538$	−8117.28	−0.650484
$539$	3295.03	0.263315
$540$	3967.86	0.316203
$541$	635.592	0.0505106	0.0252553	−	0.999681i	$-0.491960\pi$
$541$	635.592	0.0505106	0.0252553	+	0.999681i	$0.491960\pi$
$542$	2032.38	0.161067
$543$	2576.16	0.203598
$544$	30138.8	2.37535
$545$	4671.94	0.367200
$546$	−6075.19	−0.476179
$547$	−13783.8	−1.07743	−0.538715	−	0.842488i	$-0.681090\pi$
$547$	−13783.8	−1.07743	−0.538715	+	0.842488i	$0.681090\pi$
$548$	−8676.11	−0.676323
$549$	−3115.74	−0.242216
$550$	−10001.3	−0.775373
$551$	−1433.43	−0.110828
$552$	180.550	0.0139216
$553$	−1983.31	−0.152512
$554$	−26763.5	−2.05248
$555$	−3950.47	−0.302141
$556$	−11096.8	−0.846416
$557$	8271.99	0.629256	0.314628	−	0.949215i	$-0.398120\pi$
$557$	8271.99	0.629256	0.314628	+	0.949215i	$0.398120\pi$
$558$	1637.63	0.124241
$559$	24521.9	1.85539
$560$	−10994.1	−0.829615
$561$	−5203.93	−0.391640
$562$	1060.65	0.0796097
$563$	−1228.14	−0.0919360	−0.0459680	−	0.998943i	$-0.514637\pi$
$563$	−1228.14	−0.0919360	−0.0459680	+	0.998943i	$0.514637\pi$
$564$	7199.64	0.537517
$565$	−2101.24	−0.156460
$566$	−18856.6	−1.40035
$567$	−895.776	−0.0663475
$568$	1614.99	0.119302
$569$	6091.90	0.448833	0.224416	−	0.974493i	$-0.427952\pi$
$569$	6091.90	0.448833	0.224416	+	0.974493i	$0.427952\pi$
$570$	10287.4	0.755947
$571$	25361.1	1.85872	0.929361	−	0.369172i	$-0.120359\pi$
$571$	25361.1	1.85872	0.929361	+	0.369172i	$0.120359\pi$
$572$	5791.25	0.423329
$573$	−8778.25	−0.639994
$574$	9477.35	0.689158
$575$	−3776.85	−0.273922
$576$	−5314.93	−0.384472
$577$	−16642.3	−1.20075	−0.600373	−	0.799720i	$-0.704981\pi$
$577$	−16642.3	−1.20075	−0.600373	+	0.799720i	$0.704981\pi$
$578$	35026.0	2.52057
$579$	−4973.81	−0.357003
$580$	4261.78	0.305105
$581$	−5875.65	−0.419558
$582$	−6359.38	−0.452929
$583$	−9686.02	−0.688086
$584$	1306.04	0.0925416
$585$	6870.34	0.485562
$586$	−6340.43	−0.446964
$587$	−18738.8	−1.31760	−0.658801	−	0.752317i	$-0.728936\pi$
$587$	−18738.8	−1.31760	−0.658801	+	0.752317i	$0.728936\pi$
$588$	5721.48	0.401275
$589$	2204.74	0.154236
$590$	−20398.2	−1.42336
$591$	3393.20	0.236172
$592$	4526.44	0.314249
$593$	8433.66	0.584029	0.292014	−	0.956414i	$-0.405675\pi$
$593$	8433.66	0.584029	0.292014	+	0.956414i	$0.405675\pi$
$594$	1644.44	0.113589
$595$	−21851.1	−1.50556
$596$	23373.6	1.60641
$597$	11824.0	0.810591
$598$	4211.65	0.288005
$599$	5341.29	0.364339	0.182170	−	0.983267i	$-0.441688\pi$
$599$	5341.29	0.364339	0.182170	+	0.983267i	$0.441688\pi$
$600$	−1289.05	−0.0877090
$601$	16380.7	1.11179	0.555893	−	0.831254i	$-0.312377\pi$
$601$	16380.7	1.11179	0.555893	+	0.831254i	$0.312377\pi$
$602$	24645.3	1.66855
$603$	3855.79	0.260398
$604$	−9985.62	−0.672697
$605$	18844.5	1.26634
$606$	6286.52	0.421407
$607$	10758.4	0.719393	0.359697	−	0.933069i	$-0.382880\pi$
$607$	10758.4	0.719393	0.359697	+	0.933069i	$0.382880\pi$
$608$	−12822.0	−0.855262
$609$	−962.130	−0.0640188
$610$	24017.1	1.59414
$611$	12466.1	0.825411
$612$	−9036.09	−0.596834
$613$	20147.3	1.32748	0.663738	−	0.747965i	$-0.268969\pi$
$613$	20147.3	1.32748	0.663738	+	0.747965i	$0.268969\pi$
$614$	−34129.7	−2.24326
$615$	−10717.8	−0.702737
$616$	432.037	0.0282585
$617$	−9131.99	−0.595851	−0.297925	−	0.954589i	$-0.596295\pi$
$617$	−9131.99	−0.595851	−0.297925	+	0.954589i	$0.596295\pi$
$618$	32.2363	0.00209827
$619$	−12965.3	−0.841872	−0.420936	−	0.907090i	$-0.638298\pi$
$619$	−12965.3	−0.841872	−0.420936	+	0.907090i	$0.638298\pi$
$620$	−6554.98	−0.424604
$621$	621.000	0.0401286
$622$	−5910.25	−0.380996
$623$	−10845.7	−0.697470
$624$	−7872.03	−0.505022
$625$	−9186.18	−0.587916
$626$	−15414.3	−0.984153
$627$	2213.91	0.141013
$628$	−4604.63	−0.292587
$629$	8996.47	0.570290
$630$	6904.93	0.436665
$631$	17175.5	1.08359	0.541795	−	0.840511i	$-0.317745\pi$
$631$	17175.5	1.08359	0.541795	+	0.840511i	$0.317745\pi$
$632$	469.272	0.0295358
$633$	−8093.76	−0.508212
$634$	18219.8	1.14132
$635$	26551.8	1.65933
$636$	−16818.8	−1.04860
$637$	9906.72	0.616198
$638$	1766.25	0.109602
$639$	5554.74	0.343884
$640$	5677.63	0.350669
$641$	−26528.0	−1.63462	−0.817310	−	0.576198i	$-0.804536\pi$
$641$	−26528.0	−1.63462	−0.817310	+	0.576198i	$0.804536\pi$
$642$	−1635.44	−0.100538
$643$	3325.19	0.203939	0.101969	−	0.994788i	$-0.467486\pi$
$643$	3325.19	0.203939	0.101969	+	0.994788i	$0.467486\pi$
$644$	2198.00	0.134493
$645$	−27871.0	−1.70143
$646$	−23427.6	−1.42685
$647$	−24569.0	−1.49290	−0.746450	−	0.665442i	$-0.768243\pi$
$647$	−24569.0	−1.49290	−0.746450	+	0.665442i	$0.768243\pi$
$648$	211.950	0.0128490
$649$	−4389.83	−0.265510
$650$	−30069.4	−1.81449
$651$	1479.84	0.0890928
$652$	17997.5	1.08104
$653$	−24378.3	−1.46094	−0.730472	−	0.682943i	$-0.760700\pi$
$653$	−24378.3	−1.46094	−0.730472	+	0.682943i	$0.760700\pi$
$654$	3362.07	0.201020
$655$	25286.4	1.50843
$656$	12280.4	0.730901
$657$	4492.11	0.266749
$658$	12528.9	0.742291
$659$	−22329.6	−1.31994	−0.659968	−	0.751293i	$-0.729430\pi$
$659$	−22329.6	−1.31994	−0.659968	+	0.751293i	$0.729430\pi$
$660$	−6582.22	−0.388201
$661$	9050.09	0.532538	0.266269	−	0.963899i	$-0.414209\pi$
$661$	9050.09	0.532538	0.266269	+	0.963899i	$0.414209\pi$
$662$	22239.8	1.30570
$663$	−15645.9	−0.916498
$664$	1390.24	0.0812527
$665$	9296.11	0.542087
$666$	−2842.88	−0.165404
$667$	667.000	0.0387202
$668$	−17690.2	−1.02463
$669$	14924.0	0.862476
$670$	−29721.7	−1.71381
$671$	5168.64	0.297367
$672$	−8606.17	−0.494033
$673$	−16698.4	−0.956428	−0.478214	−	0.878243i	$-0.658716\pi$
$673$	−16698.4	−0.956428	−0.478214	+	0.878243i	$0.658716\pi$
$674$	5269.13	0.301127
$675$	−4433.69	−0.252819
$676$	−1573.46	−0.0895230
$677$	−29230.1	−1.65939	−0.829693	−	0.558220i	$-0.811485\pi$
$677$	−29230.1	−1.65939	−0.829693	+	0.558220i	$0.811485\pi$
$678$	−1512.12	−0.0856528
$679$	−5746.62	−0.324794
$680$	5170.20	0.291571
$681$	−8540.12	−0.480555
$682$	−2716.64	−0.152530
$683$	−23659.4	−1.32548	−0.662740	−	0.748849i	$-0.730607\pi$
$683$	−23659.4	−1.32548	−0.662740	+	0.748849i	$0.730607\pi$
$684$	3844.22	0.214894
$685$	17074.4	0.952380
$686$	25430.6	1.41537
$687$	1407.29	0.0781538
$688$	31934.6	1.76962
$689$	−29121.7	−1.61023
$690$	−4786.87	−0.264106
$691$	−8049.50	−0.443151	−0.221576	−	0.975143i	$-0.571120\pi$
$691$	−8049.50	−0.443151	−0.221576	+	0.975143i	$0.571120\pi$
$692$	21842.7	1.19991
$693$	1485.99	0.0814545
$694$	1020.53	0.0558194
$695$	21838.2	1.19190
$696$	227.650	0.0123981
$697$	24407.8	1.32642
$698$	−17074.7	−0.925911
$699$	−3151.09	−0.170508
$700$	−15692.8	−0.847334
$701$	6983.50	0.376267	0.188133	−	0.982143i	$-0.439756\pi$
$701$	6983.50	0.376267	0.188133	+	0.982143i	$0.439756\pi$
$702$	4944.11	0.265817
$703$	−3827.37	−0.205337
$704$	8816.85	0.472013
$705$	−14168.8	−0.756917
$706$	−30274.7	−1.61389
$707$	5680.78	0.302189
$708$	−7622.49	−0.404619
$709$	−35234.2	−1.86636	−0.933179	−	0.359412i	$-0.882977\pi$
$709$	−35234.2	−1.86636	−0.933179	+	0.359412i	$0.882977\pi$
$710$	−42817.7	−2.26327
$711$	1614.06	0.0851363
$712$	2566.21	0.135074
$713$	−1025.90	−0.0538855
$714$	−15724.7	−0.824206
$715$	−11397.1	−0.596121
$716$	−33799.5	−1.76417
$717$	−11631.4	−0.605835
$718$	696.868	0.0362213
$719$	−21926.5	−1.13730	−0.568650	−	0.822579i	$-0.692534\pi$
$719$	−21926.5	−1.13730	−0.568650	+	0.822579i	$0.692534\pi$
$720$	8947.19	0.463114
$721$	29.1301	0.00150466
$722$	−18013.8	−0.928536
$723$	−6090.60	−0.313295
$724$	−7420.58	−0.380917
$725$	−4762.11	−0.243945
$726$	13561.1	0.693249
$727$	−9293.45	−0.474106	−0.237053	−	0.971497i	$-0.576182\pi$
$727$	−9293.45	−0.474106	−0.237053	+	0.971497i	$0.576182\pi$
$728$	1298.95	0.0661294
$729$	729.000	0.0370370
$730$	−34626.7	−1.75560
$731$	63471.2	3.21145
$732$	8974.81	0.453168
$733$	−30916.4	−1.55788	−0.778939	−	0.627100i	$-0.784242\pi$
$733$	−30916.4	−1.55788	−0.778939	+	0.627100i	$0.784242\pi$
$734$	−7487.74	−0.376536
$735$	−11259.8	−0.565065
$736$	5966.26	0.298803
$737$	−6396.30	−0.319689
$738$	−7712.85	−0.384707
$739$	−23332.7	−1.16144	−0.580721	−	0.814102i	$-0.697229\pi$
$739$	−23332.7	−1.16144	−0.580721	+	0.814102i	$0.697229\pi$
$740$	11379.2	0.565282
$741$	6656.25	0.329991
$742$	−29268.3	−1.44808
$743$	−4113.41	−0.203104	−0.101552	−	0.994830i	$-0.532381\pi$
$743$	−4113.41	−0.203104	−0.101552	+	0.994830i	$0.532381\pi$
$744$	−350.145	−0.0172540
$745$	−45998.8	−2.26210
$746$	7348.58	0.360658
$747$	4781.72	0.234209
$748$	14989.8	0.732729
$749$	−1477.86	−0.0720957
$750$	8160.72	0.397316
$751$	14224.7	0.691168	0.345584	−	0.938388i	$-0.387681\pi$
$751$	14224.7	0.691168	0.345584	+	0.938388i	$0.387681\pi$
$752$	16234.6	0.787252
$753$	19400.8	0.938918
$754$	5310.34	0.256487
$755$	19651.5	0.947275
$756$	2580.26	0.124131
$757$	−18478.5	−0.887205	−0.443602	−	0.896224i	$-0.646300\pi$
$757$	−18478.5	−0.887205	−0.443602	+	0.896224i	$0.646300\pi$
$758$	27127.1	1.29987
$759$	−1030.17	−0.0492657
$760$	−2199.56	−0.104982
$761$	20833.7	0.992406	0.496203	−	0.868207i	$-0.334727\pi$
$761$	20833.7	0.992406	0.496203	+	0.868207i	$0.334727\pi$
$762$	19107.5	0.908387
$763$	3038.11	0.144151
$764$	25285.6	1.19738
$765$	17782.9	0.840445
$766$	−23765.4	−1.12099
$767$	−13198.3	−0.621334
$768$	−10087.4	−0.473954
$769$	32514.0	1.52469	0.762345	−	0.647171i	$-0.224048\pi$
$769$	32514.0	1.52469	0.762345	+	0.647171i	$0.224048\pi$
$770$	−11454.5	−0.536091
$771$	−10237.0	−0.478180
$772$	14327.0	0.667925
$773$	13436.1	0.625178	0.312589	−	0.949888i	$-0.398804\pi$
$773$	13436.1	0.625178	0.312589	+	0.949888i	$0.398804\pi$
$774$	−20056.9	−0.931432
$775$	7324.53	0.339490
$776$	1359.71	0.0629005
$777$	−2568.95	−0.118611
$778$	−38096.4	−1.75555
$779$	−10383.8	−0.477585
$780$	−19789.9	−0.908450
$781$	−9214.66	−0.422185
$782$	10901.2	0.498500
$783$	783.000	0.0357371
$784$	12901.4	0.587711
$785$	9061.84	0.412014
$786$	18196.9	0.825778
$787$	7979.53	0.361422	0.180711	−	0.983536i	$-0.442160\pi$
$787$	7979.53	0.361422	0.180711	+	0.983536i	$0.442160\pi$
$788$	−9774.03	−0.441860
$789$	−11635.3	−0.525004
$790$	−12441.7	−0.560323
$791$	−1366.42	−0.0614213
$792$	−351.600	−0.0157747
$793$	15539.9	0.695884
$794$	−26559.4	−1.18710
$795$	33099.1	1.47661
$796$	−34058.7	−1.51655
$797$	−3170.39	−0.140904	−0.0704522	−	0.997515i	$-0.522444\pi$
$797$	−3170.39	−0.140904	−0.0704522	+	0.997515i	$0.522444\pi$
$798$	6689.76	0.296761
$799$	32266.8	1.42868
$800$	−42596.7	−1.88253
$801$	8826.45	0.389347
$802$	−27673.6	−1.21844
$803$	−7451.88	−0.327486
$804$	−11106.5	−0.487185
$805$	−4325.63	−0.189389
$806$	−8167.75	−0.356944
$807$	5969.48	0.260391
$808$	−1344.13	−0.0585228
$809$	34173.2	1.48512	0.742562	−	0.669778i	$-0.233611\pi$
$809$	34173.2	1.48512	0.742562	+	0.669778i	$0.233611\pi$
$810$	−5619.37	−0.243759
$811$	34307.4	1.48545	0.742723	−	0.669599i	$-0.233534\pi$
$811$	34307.4	1.48545	0.742723	+	0.669599i	$0.233534\pi$
$812$	2771.39	0.119774
$813$	−1494.62	−0.0644757
$814$	4715.99	0.203066
$815$	−35418.7	−1.52229
$816$	−20375.6	−0.874128
$817$	−27002.5	−1.15630
$818$	−15690.1	−0.670652
$819$	4467.71	0.190616
$820$	30872.4	1.31477
$821$	33368.1	1.41846	0.709229	−	0.704978i	$-0.249043\pi$
$821$	33368.1	1.41846	0.709229	+	0.704978i	$0.249043\pi$
$822$	12287.3	0.521372
$823$	34077.8	1.44335	0.721674	−	0.692233i	$-0.243373\pi$
$823$	34077.8	1.44335	0.721674	+	0.692233i	$0.243373\pi$
$824$	−6.89250	−0.000291398 0
$825$	7354.96	0.310384
$826$	−13264.8	−0.558765
$827$	21683.0	0.911718	0.455859	−	0.890052i	$-0.349332\pi$
$827$	21683.0	0.911718	0.455859	+	0.890052i	$0.349332\pi$
$828$	−1788.78	−0.0750777
$829$	3330.93	0.139551	0.0697756	−	0.997563i	$-0.477772\pi$
$829$	3330.93	0.139551	0.0697756	+	0.997563i	$0.477772\pi$
$830$	−36859.0	−1.54144
$831$	19682.0	0.821613
$832$	26508.4	1.10458
$833$	25642.1	1.06656
$834$	15715.5	0.652496
$835$	34813.9	1.44286
$836$	−6377.11	−0.263824
$837$	−1204.32	−0.0497341
$838$	−16517.1	−0.680877
$839$	43872.0	1.80528	0.902639	−	0.430398i	$-0.141627\pi$
$839$	43872.0	1.80528	0.902639	+	0.430398i	$0.141627\pi$
$840$	−1476.36	−0.0606418
$841$	841.000	0.0344828
$842$	27367.1	1.12011
$843$	−780.003	−0.0318680
$844$	23313.9	0.950826
$845$	3096.53	0.126064
$846$	−10196.3	−0.414368
$847$	12254.4	0.497127
$848$	−37924.9	−1.53579
$849$	13867.2	0.560566
$850$	−77830.3	−3.14066
$851$	1780.93	0.0717387
$852$	−16000.3	−0.643382
$853$	−11503.3	−0.461742	−0.230871	−	0.972984i	$-0.574157\pi$
$853$	−11503.3	−0.461742	−0.230871	+	0.972984i	$0.574157\pi$
$854$	15618.1	0.625808
$855$	−7565.36	−0.302608
$856$	349.676	0.0139623
$857$	−18269.0	−0.728189	−0.364094	−	0.931362i	$-0.618621\pi$
$857$	−18269.0	−0.728189	−0.364094	+	0.931362i	$0.618621\pi$
$858$	−8201.69	−0.326341
$859$	−6074.79	−0.241291	−0.120646	−	0.992696i	$-0.538496\pi$
$859$	−6074.79	−0.241291	−0.120646	+	0.992696i	$0.538496\pi$
$860$	80282.0	3.18325
$861$	−6969.68	−0.275872
$862$	−11302.1	−0.446578
$863$	14894.9	0.587518	0.293759	−	0.955880i	$-0.405094\pi$
$863$	14894.9	0.587518	0.293759	+	0.955880i	$0.405094\pi$
$864$	7003.87	0.275783
$865$	−42986.1	−1.68968
$866$	56893.1	2.23246
$867$	−25758.2	−1.00899
$868$	−4262.64	−0.166686
$869$	−2677.53	−0.104521
$870$	−6035.62	−0.235203
$871$	−19230.9	−0.748122
$872$	−718.850	−0.0279167
$873$	4676.71	0.181309
$874$	−4637.71	−0.179488
$875$	7374.39	0.284914
$876$	−12939.4	−0.499067
$877$	10505.5	0.404501	0.202250	−	0.979334i	$-0.435175\pi$
$877$	10505.5	0.404501	0.202250	+	0.979334i	$0.435175\pi$
$878$	−19539.7	−0.751063
$879$	4662.77	0.178921
$880$	−14842.3	−0.568562
$881$	241.233	0.00922515	0.00461258	−	0.999989i	$-0.498532\pi$
$881$	241.233	0.00922515	0.00461258	+	0.999989i	$0.498532\pi$
$882$	−8102.87	−0.309340
$883$	−42547.3	−1.62155	−0.810777	−	0.585355i	$-0.800955\pi$
$883$	−42547.3	−1.62155	−0.810777	+	0.585355i	$0.800955\pi$
$884$	45067.8	1.71470
$885$	15000.9	0.569774
$886$	3972.02	0.150612
$887$	46147.2	1.74687	0.873434	−	0.486943i	$-0.161888\pi$
$887$	46147.2	1.74687	0.873434	+	0.486943i	$0.161888\pi$
$888$	607.841	0.0229705
$889$	17266.4	0.651401
$890$	−68037.1	−2.56248
$891$	−1209.32	−0.0454701
$892$	−42988.4	−1.61363
$893$	−13727.2	−0.514406
$894$	−33102.1	−1.23837
$895$	66516.8	2.48426
$896$	3692.11	0.137661
$897$	−3097.26	−0.115289
$898$	67661.1	2.51434
$899$	−1293.53	−0.0479885
$900$	12771.1	0.473005
$901$	−75377.1	−2.78710
$902$	12794.7	0.472303
$903$	−18124.3	−0.667927
$904$	323.309	0.0118950
$905$	14603.6	0.536397
$906$	14141.8	0.518577
$907$	43585.7	1.59563	0.797817	−	0.602900i	$-0.205988\pi$
$907$	43585.7	1.59563	0.797817	+	0.602900i	$0.205988\pi$
$908$	24599.6	0.899083
$909$	−4623.13	−0.168690
$910$	−34438.6	−1.25454
$911$	−23758.0	−0.864036	−0.432018	−	0.901865i	$-0.642198\pi$
$911$	−23758.0	−0.864036	−0.432018	+	0.901865i	$0.642198\pi$
$912$	8668.39	0.314736
$913$	−7932.30	−0.287537
$914$	−10270.4	−0.371678
$915$	−17662.3	−0.638139
$916$	−4053.68	−0.146220
$917$	16443.5	0.592162
$918$	12797.1	0.460095
$919$	−20972.1	−0.752780	−0.376390	−	0.926461i	$-0.622835\pi$
$919$	−20972.1	−0.752780	−0.376390	+	0.926461i	$0.622835\pi$
$920$	1023.49	0.0366777
$921$	25099.1	0.897985
$922$	−12176.9	−0.434951
$923$	−27704.5	−0.987978
$924$	−4280.35	−0.152395
$925$	−12715.1	−0.451969
$926$	−20247.1	−0.718532
$927$	−23.7067	−0.000839946 0
$928$	7522.68	0.266103
$929$	1565.85	0.0553001	0.0276501	−	0.999618i	$-0.491198\pi$
$929$	1565.85	0.0553001	0.0276501	+	0.999618i	$0.491198\pi$
$930$	9283.30	0.327324
$931$	−10908.9	−0.384022
$932$	9076.64	0.319008
$933$	4346.42	0.152514
$934$	37038.3	1.29757
$935$	−29499.7	−1.03181
$936$	−1057.11	−0.0369152
$937$	−4640.25	−0.161783	−0.0808913	−	0.996723i	$-0.525777\pi$
$937$	−4640.25	−0.161783	−0.0808913	+	0.996723i	$0.525777\pi$
$938$	−19327.7	−0.672785
$939$	11335.7	0.393959
$940$	40812.8	1.41614
$941$	23425.8	0.811541	0.405770	−	0.913975i	$-0.367003\pi$
$941$	23425.8	0.811541	0.405770	+	0.913975i	$0.367003\pi$
$942$	6521.18	0.225553
$943$	4831.76	0.166854
$944$	−17188.0	−0.592609
$945$	−5077.91	−0.174798
$946$	33271.9	1.14351
$947$	36553.1	1.25429	0.627146	−	0.778901i	$-0.284223\pi$
$947$	36553.1	1.25429	0.627146	+	0.778901i	$0.284223\pi$
$948$	−4649.26	−0.159284
$949$	−22404.6	−0.766368
$950$	33111.3	1.13081
$951$	−13398.9	−0.456875
$952$	3362.13	0.114461
$953$	2058.33	0.0699641	0.0349821	−	0.999388i	$-0.488863\pi$
$953$	2058.33	0.0699641	0.0349821	+	0.999388i	$0.488863\pi$
$954$	23819.1	0.808357
$955$	−49761.6	−1.68612
$956$	33504.1	1.13347
$957$	−1298.90	−0.0438742
$958$	18406.3	0.620754
$959$	11103.3	0.373874
$960$	−30128.9	−1.01292
$961$	−27801.4	−0.933216
$962$	14178.9	0.475205
$963$	1202.71	0.0402458
$964$	17543.9	0.586151
$965$	−28195.2	−0.940555
$966$	−3112.85	−0.103680
$967$	30766.5	1.02315	0.511575	−	0.859239i	$-0.329062\pi$
$967$	30766.5	1.02315	0.511575	+	0.859239i	$0.329062\pi$
$968$	−2899.52	−0.0962749
$969$	17228.7	0.571173
$970$	−36049.6	−1.19328
$971$	28853.4	0.953603	0.476802	−	0.879011i	$-0.341796\pi$
$971$	28853.4	0.953603	0.476802	+	0.879011i	$0.341796\pi$
$972$	−2099.87	−0.0692935
$973$	14201.2	0.467903
$974$	16443.3	0.540943
$975$	22113.2	0.726347
$976$	20237.4	0.663713
$977$	22814.2	0.747073	0.373537	−	0.927615i	$-0.378145\pi$
$977$	22814.2	0.747073	0.373537	+	0.927615i	$0.378145\pi$
$978$	−25488.4	−0.833362
$979$	−14642.0	−0.477999
$980$	32433.5	1.05720
$981$	−2472.48	−0.0804690
$982$	−42376.2	−1.37706
$983$	−2068.44	−0.0671139	−0.0335569	−	0.999437i	$-0.510684\pi$
$983$	−2068.44	−0.0671139	−0.0335569	+	0.999437i	$0.510684\pi$
$984$	1649.10	0.0534262
$985$	19235.1	0.622215
$986$	13745.0	0.443946
$987$	−9213.81	−0.297142
$988$	−19173.2	−0.617389
$989$	12564.7	0.403978
$990$	9321.87	0.299261
$991$	42627.0	1.36639	0.683195	−	0.730236i	$-0.260590\pi$
$991$	42627.0	1.36639	0.683195	+	0.730236i	$0.260590\pi$
$992$	−11570.5	−0.370327
$993$	−16355.2	−0.522675
$994$	−27844.0	−0.888488
$995$	67026.9	2.13557
$996$	−13773.6	−0.438187
$997$	33194.6	1.05445	0.527224	−	0.849726i	$-0.323233\pi$
$997$	33194.6	1.05445	0.527224	+	0.849726i	$0.323233\pi$
$998$	61401.8	1.94753
$999$	2090.66	0.0662118

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2001.4.a.d.1.31	✓	37

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2001.4.a.d.1.31	✓	37	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:	\( N \)	\(=\)	\( 2001 = 3 \cdot 23 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	2001.a (trivial)

\(f(q)\)	\(=\)	\(q+4.07939 q^{2} -3.00000 q^{3} +8.64144 q^{4} -17.0062 q^{5} -12.2382 q^{6} -11.0590 q^{7} +2.61667 q^{8} +9.00000 q^{9} +O(q^{10})\)	\(q+4.07939 q^{2} -3.00000 q^{3} +8.64144 q^{4} -17.0062 q^{5} -12.2382 q^{6} -11.0590 q^{7} +2.61667 q^{8} +9.00000 q^{9} -69.3749 q^{10} -14.9299 q^{11} -25.9243 q^{12} -44.8878 q^{13} -45.1138 q^{14} +51.0186 q^{15} -58.4571 q^{16} -116.186 q^{17} +36.7145 q^{18} +49.4288 q^{19} -146.958 q^{20} +33.1769 q^{21} -60.9050 q^{22} -23.0000 q^{23} -7.85000 q^{24} +164.211 q^{25} -183.115 q^{26} -27.0000 q^{27} -95.5653 q^{28} -29.0000 q^{29} +208.125 q^{30} +44.6045 q^{31} -259.403 q^{32} +44.7898 q^{33} -473.966 q^{34} +188.071 q^{35} +77.7729 q^{36} -77.4319 q^{37} +201.639 q^{38} +134.663 q^{39} -44.4995 q^{40} -210.076 q^{41} +135.341 q^{42} -546.292 q^{43} -129.016 q^{44} -153.056 q^{45} -93.8260 q^{46} -277.718 q^{47} +175.371 q^{48} -220.699 q^{49} +669.880 q^{50} +348.557 q^{51} -387.895 q^{52} +648.765 q^{53} -110.144 q^{54} +253.901 q^{55} -28.9376 q^{56} -148.286 q^{57} -118.302 q^{58} +294.029 q^{59} +440.874 q^{60} -346.193 q^{61} +181.959 q^{62} -99.5306 q^{63} -590.548 q^{64} +763.371 q^{65} +182.715 q^{66} +428.421 q^{67} -1004.01 q^{68} +69.0000 q^{69} +767.215 q^{70} +617.193 q^{71} +23.5500 q^{72} +499.123 q^{73} -315.875 q^{74} -492.632 q^{75} +427.136 q^{76} +165.110 q^{77} +549.345 q^{78} +179.340 q^{79} +994.132 q^{80} +81.0000 q^{81} -856.984 q^{82} +531.302 q^{83} +286.696 q^{84} +1975.87 q^{85} -2228.54 q^{86} +87.0000 q^{87} -39.0667 q^{88} +980.717 q^{89} -624.374 q^{90} +496.413 q^{91} -198.753 q^{92} -133.813 q^{93} -1132.92 q^{94} -840.596 q^{95} +778.208 q^{96} +519.635 q^{97} -900.319 q^{98} -134.369 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 37 q + 4 q^{2} - 111 q^{3} + 146 q^{4} + 15 q^{5} - 12 q^{6} + 8 q^{7} + 3 q^{8} + 333 q^{9}+O(q^{10}) \) 37 * q + 4 * q^2 - 111 * q^3 + 146 * q^4 + 15 * q^5 - 12 * q^6 + 8 * q^7 + 3 * q^8 + 333 * q^9	\( 37 q + 4 q^{2} - 111 q^{3} + 146 q^{4} + 15 q^{5} - 12 q^{6} + 8 q^{7} + 3 q^{8} + 333 q^{9} - 136 q^{10} + 109 q^{11} - 438 q^{12} - 269 q^{13} + 121 q^{14} - 45 q^{15} + 390 q^{16} + 180 q^{17} + 36 q^{18} + 117 q^{19} + 287 q^{20} - 24 q^{21} - 128 q^{22} - 851 q^{23} - 9 q^{24} + 490 q^{25} + 677 q^{26} - 999 q^{27} + 775 q^{28} - 1073 q^{29} + 408 q^{30} - 194 q^{31} + 668 q^{32} - 327 q^{33} + 972 q^{34} - 309 q^{35} + 1314 q^{36} - 565 q^{37} + 725 q^{38} + 807 q^{39} + 263 q^{40} + 521 q^{41} - 363 q^{42} - 61 q^{43} + 2242 q^{44} + 135 q^{45} - 92 q^{46} + 1142 q^{47} - 1170 q^{48} + 919 q^{49} + 1833 q^{50} - 540 q^{51} - 10 q^{52} - 120 q^{53} - 108 q^{54} - 996 q^{55} + 1707 q^{56} - 351 q^{57} - 116 q^{58} + 1073 q^{59} - 861 q^{60} - 428 q^{61} + 174 q^{62} + 72 q^{63} + 1479 q^{64} + 1410 q^{65} + 384 q^{66} + 175 q^{67} + 1483 q^{68} + 2553 q^{69} + 675 q^{70} + 2236 q^{71} + 27 q^{72} - 1058 q^{73} - 695 q^{74} - 1470 q^{75} + 1345 q^{76} - 1547 q^{77} - 2031 q^{78} + 1972 q^{79} - 2017 q^{80} + 2997 q^{81} + 2429 q^{82} - 832 q^{83} - 2325 q^{84} + 2299 q^{85} + 1527 q^{86} + 3219 q^{87} + 2579 q^{88} + 2817 q^{89} - 1224 q^{90} + 3175 q^{91} - 3358 q^{92} + 582 q^{93} + 1900 q^{94} + 8017 q^{95} - 2004 q^{96} + 912 q^{97} - 2565 q^{98} + 981 q^{99}+O(q^{100}) \) 37 * q + 4 * q^2 - 111 * q^3 + 146 * q^4 + 15 * q^5 - 12 * q^6 + 8 * q^7 + 3 * q^8 + 333 * q^9 - 136 * q^10 + 109 * q^11 - 438 * q^12 - 269 * q^13 + 121 * q^14 - 45 * q^15 + 390 * q^16 + 180 * q^17 + 36 * q^18 + 117 * q^19 + 287 * q^20 - 24 * q^21 - 128 * q^22 - 851 * q^23 - 9 * q^24 + 490 * q^25 + 677 * q^26 - 999 * q^27 + 775 * q^28 - 1073 * q^29 + 408 * q^30 - 194 * q^31 + 668 * q^32 - 327 * q^33 + 972 * q^34 - 309 * q^35 + 1314 * q^36 - 565 * q^37 + 725 * q^38 + 807 * q^39 + 263 * q^40 + 521 * q^41 - 363 * q^42 - 61 * q^43 + 2242 * q^44 + 135 * q^45 - 92 * q^46 + 1142 * q^47 - 1170 * q^48 + 919 * q^49 + 1833 * q^50 - 540 * q^51 - 10 * q^52 - 120 * q^53 - 108 * q^54 - 996 * q^55 + 1707 * q^56 - 351 * q^57 - 116 * q^58 + 1073 * q^59 - 861 * q^60 - 428 * q^61 + 174 * q^62 + 72 * q^63 + 1479 * q^64 + 1410 * q^65 + 384 * q^66 + 175 * q^67 + 1483 * q^68 + 2553 * q^69 + 675 * q^70 + 2236 * q^71 + 27 * q^72 - 1058 * q^73 - 695 * q^74 - 1470 * q^75 + 1345 * q^76 - 1547 * q^77 - 2031 * q^78 + 1972 * q^79 - 2017 * q^80 + 2997 * q^81 + 2429 * q^82 - 832 * q^83 - 2325 * q^84 + 2299 * q^85 + 1527 * q^86 + 3219 * q^87 + 2579 * q^88 + 2817 * q^89 - 1224 * q^90 + 3175 * q^91 - 3358 * q^92 + 582 * q^93 + 1900 * q^94 + 8017 * q^95 - 2004 * q^96 + 912 * q^97 - 2565 * q^98 + 981 * q^99

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