LMFDB - Embedded newform 2001.4.a.h.1.14

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:	$44$
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.14
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)

$f(q)$	$=$	$q-2.77019 q^{2} +3.00000 q^{3} -0.326072 q^{4} -1.57049 q^{5} -8.31056 q^{6} -15.6447 q^{7} +23.0648 q^{8} +9.00000 q^{9} +O(q^{10})$	\(q-2.77019 q^{2} +3.00000 q^{3} -0.326072 q^{4} -1.57049 q^{5} -8.31056 q^{6} -15.6447 q^{7} +23.0648 q^{8} +9.00000 q^{9} +4.35056 q^{10} -60.5147 q^{11} -0.978217 q^{12} -37.1303 q^{13} +43.3387 q^{14} -4.71148 q^{15} -61.2851 q^{16} -34.0795 q^{17} -24.9317 q^{18} -47.6755 q^{19} +0.512095 q^{20} -46.9341 q^{21} +167.637 q^{22} +23.0000 q^{23} +69.1943 q^{24} -122.534 q^{25} +102.858 q^{26} +27.0000 q^{27} +5.10131 q^{28} -29.0000 q^{29} +13.0517 q^{30} -194.784 q^{31} -14.7470 q^{32} -181.544 q^{33} +94.4065 q^{34} +24.5699 q^{35} -2.93465 q^{36} -114.207 q^{37} +132.070 q^{38} -111.391 q^{39} -36.2231 q^{40} -360.202 q^{41} +130.016 q^{42} +142.844 q^{43} +19.7322 q^{44} -14.1345 q^{45} -63.7143 q^{46} -81.1505 q^{47} -183.855 q^{48} -98.2431 q^{49} +339.441 q^{50} -102.238 q^{51} +12.1072 q^{52} -71.7966 q^{53} -74.7950 q^{54} +95.0381 q^{55} -360.842 q^{56} -143.026 q^{57} +80.3354 q^{58} +745.302 q^{59} +1.53628 q^{60} +446.394 q^{61} +539.587 q^{62} -140.802 q^{63} +531.133 q^{64} +58.3129 q^{65} +502.911 q^{66} -878.393 q^{67} +11.1124 q^{68} +69.0000 q^{69} -68.0633 q^{70} -742.454 q^{71} +207.583 q^{72} -521.669 q^{73} +316.375 q^{74} -367.601 q^{75} +15.5457 q^{76} +946.736 q^{77} +308.573 q^{78} -173.662 q^{79} +96.2479 q^{80} +81.0000 q^{81} +997.826 q^{82} +480.607 q^{83} +15.3039 q^{84} +53.5216 q^{85} -395.703 q^{86} -87.0000 q^{87} -1395.76 q^{88} +99.6673 q^{89} +39.1551 q^{90} +580.892 q^{91} -7.49966 q^{92} -584.351 q^{93} +224.802 q^{94} +74.8741 q^{95} -44.2411 q^{96} +1450.27 q^{97} +272.151 q^{98} -544.633 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 44 q + 6 q^{2} + 132 q^{3} + 210 q^{4} + 15 q^{5} + 18 q^{6} + 78 q^{7} + 12 q^{8} + 396 q^{9}+O(q^{10}) $ 44 * q + 6 * q^2 + 132 * q^3 + 210 * q^4 + 15 * q^5 + 18 * q^6 + 78 * q^7 + 12 * q^8 + 396 * q^9	\( 44 q + 6 q^{2} + 132 q^{3} + 210 q^{4} + 15 q^{5} + 18 q^{6} + 78 q^{7} + 12 q^{8} + 396 q^{9} + 214 q^{10} + 111 q^{11} + 630 q^{12} + 275 q^{13} + 104 q^{14} + 45 q^{15} + 1062 q^{16} - 58 q^{17} + 54 q^{18} + 331 q^{19} + 287 q^{20} + 234 q^{21} + 285 q^{22} + 1012 q^{23} + 36 q^{24} + 1903 q^{25} + 1084 q^{26} + 1188 q^{27} + 222 q^{28} - 1276 q^{29} + 642 q^{30} + 1394 q^{31} + 42 q^{32} + 333 q^{33} + 373 q^{34} + 567 q^{35} + 1890 q^{36} + 1229 q^{37} + 733 q^{38} + 825 q^{39} + 2483 q^{40} - 107 q^{41} + 312 q^{42} + 1165 q^{43} + 1639 q^{44} + 135 q^{45} + 138 q^{46} + 964 q^{47} + 3186 q^{48} + 4264 q^{49} + 495 q^{50} - 174 q^{51} + 2679 q^{52} - 380 q^{53} + 162 q^{54} + 1260 q^{55} + 2229 q^{56} + 993 q^{57} - 174 q^{58} + 897 q^{59} + 861 q^{60} + 2584 q^{61} + 3034 q^{62} + 702 q^{63} + 6866 q^{64} - 286 q^{65} + 855 q^{66} + 2277 q^{67} - 1554 q^{68} + 3036 q^{69} + 689 q^{70} + 4304 q^{71} + 108 q^{72} + 4712 q^{73} - 1005 q^{74} + 5709 q^{75} + 2877 q^{76} + 919 q^{77} + 3252 q^{78} + 3864 q^{79} + 2593 q^{80} + 3564 q^{81} + 3297 q^{82} - 540 q^{83} + 666 q^{84} + 6537 q^{85} + 3789 q^{86} - 3828 q^{87} + 1707 q^{88} - 331 q^{89} + 1926 q^{90} + 4311 q^{91} + 4830 q^{92} + 4182 q^{93} + 6189 q^{94} + 3267 q^{95} + 126 q^{96} + 5572 q^{97} + 2588 q^{98} + 999 q^{99}+O(q^{100}) \) 44 * q + 6 * q^2 + 132 * q^3 + 210 * q^4 + 15 * q^5 + 18 * q^6 + 78 * q^7 + 12 * q^8 + 396 * q^9 + 214 * q^10 + 111 * q^11 + 630 * q^12 + 275 * q^13 + 104 * q^14 + 45 * q^15 + 1062 * q^16 - 58 * q^17 + 54 * q^18 + 331 * q^19 + 287 * q^20 + 234 * q^21 + 285 * q^22 + 1012 * q^23 + 36 * q^24 + 1903 * q^25 + 1084 * q^26 + 1188 * q^27 + 222 * q^28 - 1276 * q^29 + 642 * q^30 + 1394 * q^31 + 42 * q^32 + 333 * q^33 + 373 * q^34 + 567 * q^35 + 1890 * q^36 + 1229 * q^37 + 733 * q^38 + 825 * q^39 + 2483 * q^40 - 107 * q^41 + 312 * q^42 + 1165 * q^43 + 1639 * q^44 + 135 * q^45 + 138 * q^46 + 964 * q^47 + 3186 * q^48 + 4264 * q^49 + 495 * q^50 - 174 * q^51 + 2679 * q^52 - 380 * q^53 + 162 * q^54 + 1260 * q^55 + 2229 * q^56 + 993 * q^57 - 174 * q^58 + 897 * q^59 + 861 * q^60 + 2584 * q^61 + 3034 * q^62 + 702 * q^63 + 6866 * q^64 - 286 * q^65 + 855 * q^66 + 2277 * q^67 - 1554 * q^68 + 3036 * q^69 + 689 * q^70 + 4304 * q^71 + 108 * q^72 + 4712 * q^73 - 1005 * q^74 + 5709 * q^75 + 2877 * q^76 + 919 * q^77 + 3252 * q^78 + 3864 * q^79 + 2593 * q^80 + 3564 * q^81 + 3297 * q^82 - 540 * q^83 + 666 * q^84 + 6537 * q^85 + 3789 * q^86 - 3828 * q^87 + 1707 * q^88 - 331 * q^89 + 1926 * q^90 + 4311 * q^91 + 4830 * q^92 + 4182 * q^93 + 6189 * q^94 + 3267 * q^95 + 126 * q^96 + 5572 * q^97 + 2588 * q^98 + 999 * 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 $

$2$	−2.77019	−0.979408	−0.489704	−	0.871889i	$-0.662895\pi$
$2$	−2.77019	−0.979408	−0.489704	+	0.871889i	$0.662895\pi$
$3$	3.00000	0.577350
$3$	3.00000	0.577350
$4$	−0.326072	−0.0407590
$5$	−1.57049	−0.140469	−0.0702347	−	0.997530i	$-0.522375\pi$
$5$	−1.57049	−0.140469	−0.0702347	+	0.997530i	$0.522375\pi$
$6$	−8.31056	−0.565462
$7$	−15.6447	−0.844735	−0.422367	−	0.906425i	$-0.638801\pi$
$7$	−15.6447	−0.844735	−0.422367	+	0.906425i	$0.638801\pi$
$8$	23.0648	1.01933
$9$	9.00000	0.333333
$10$	4.35056	0.137577
$11$	−60.5147	−1.65872	−0.829358	−	0.558717i	$-0.811294\pi$
$11$	−60.5147	−1.65872	−0.829358	+	0.558717i	$0.811294\pi$
$12$	−0.978217	−0.0235322
$13$	−37.1303	−0.792160	−0.396080	−	0.918216i	$-0.629630\pi$
$13$	−37.1303	−0.792160	−0.396080	+	0.918216i	$0.629630\pi$
$14$	43.3387	0.827341
$15$	−4.71148	−0.0811000
$16$	−61.2851	−0.957580
$17$	−34.0795	−0.486205	−0.243103	−	0.970001i	$-0.578165\pi$
$17$	−34.0795	−0.486205	−0.243103	+	0.970001i	$0.578165\pi$
$18$	−24.9317	−0.326469
$19$	−47.6755	−0.575658	−0.287829	−	0.957682i	$-0.592934\pi$
$19$	−47.6755	−0.575658	−0.287829	+	0.957682i	$0.592934\pi$
$20$	0.512095	0.00572539
$21$	−46.9341	−0.487708
$22$	167.637	1.62456
$23$	23.0000	0.208514
$23$	23.0000	0.208514
$24$	69.1943	0.588509
$25$	−122.534	−0.980268
$26$	102.858	0.775849
$27$	27.0000	0.192450
$28$	5.10131	0.0344306
$29$	−29.0000	−0.185695
$29$	−29.0000	−0.185695
$30$	13.0517	0.0794300
$31$	−194.784	−1.12852	−0.564261	−	0.825596i	$-0.690839\pi$
$31$	−194.784	−1.12852	−0.564261	+	0.825596i	$0.690839\pi$
$32$	−14.7470	−0.0814666
$33$	−181.544	−0.957660
$34$	94.4065	0.476194
$35$	24.5699	0.118659
$36$	−2.93465	−0.0135863
$37$	−114.207	−0.507447	−0.253723	−	0.967277i	$-0.581655\pi$
$37$	−114.207	−0.507447	−0.253723	+	0.967277i	$0.581655\pi$
$38$	132.070	0.563804
$39$	−111.391	−0.457354
$40$	−36.2231	−0.143184
$41$	−360.202	−1.37205	−0.686025	−	0.727578i	$-0.740646\pi$
$41$	−360.202	−1.37205	−0.686025	+	0.727578i	$0.740646\pi$
$42$	130.016	0.477665
$43$	142.844	0.506591	0.253296	−	0.967389i	$-0.418485\pi$
$43$	142.844	0.506591	0.253296	+	0.967389i	$0.418485\pi$
$44$	19.7322	0.0676077
$45$	−14.1345	−0.0468231
$46$	−63.7143	−0.204221
$47$	−81.1505	−0.251851	−0.125926	−	0.992040i	$-0.540190\pi$
$47$	−81.1505	−0.251851	−0.125926	+	0.992040i	$0.540190\pi$
$48$	−183.855	−0.552859
$49$	−98.2431	−0.286423
$50$	339.441	0.960083
$51$	−102.238	−0.280711
$52$	12.1072	0.0322877
$53$	−71.7966	−0.186076	−0.0930379	−	0.995663i	$-0.529658\pi$
$53$	−71.7966	−0.186076	−0.0930379	+	0.995663i	$0.529658\pi$
$54$	−74.7950	−0.188487
$55$	95.0381	0.232999
$56$	−360.842	−0.861062
$57$	−143.026	−0.332356
$58$	80.3354	0.181872
$59$	745.302	1.64458	0.822288	−	0.569071i	$-0.192697\pi$
$59$	745.302	1.64458	0.822288	+	0.569071i	$0.192697\pi$
$60$	1.53628	0.00330556
$61$	446.394	0.936966	0.468483	−	0.883473i	$-0.344801\pi$
$61$	446.394	0.936966	0.468483	+	0.883473i	$0.344801\pi$
$62$	539.587	1.10528
$63$	−140.802	−0.281578
$64$	531.133	1.03737
$65$	58.3129	0.111274
$66$	502.911	0.937941
$67$	−878.393	−1.60168	−0.800841	−	0.598876i	$-0.795614\pi$
$67$	−878.393	−1.60168	−0.800841	+	0.598876i	$0.795614\pi$
$68$	11.1124	0.0198173
$69$	69.0000	0.120386
$70$	−68.0633	−0.116216
$71$	−742.454	−1.24103	−0.620515	−	0.784195i	$-0.713076\pi$
$71$	−742.454	−1.24103	−0.620515	+	0.784195i	$0.713076\pi$
$72$	207.583	0.339776
$73$	−521.669	−0.836394	−0.418197	−	0.908356i	$-0.637338\pi$
$73$	−521.669	−0.836394	−0.418197	+	0.908356i	$0.637338\pi$
$74$	316.375	0.496998
$75$	−367.601	−0.565958
$76$	15.5457	0.0234633
$77$	946.736	1.40118
$78$	308.573	0.447936
$79$	−173.662	−0.247323	−0.123661	−	0.992324i	$-0.539464\pi$
$79$	−173.662	−0.247323	−0.123661	+	0.992324i	$0.539464\pi$
$80$	96.2479	0.134511
$81$	81.0000	0.111111
$82$	997.826	1.34380
$83$	480.607	0.635584	0.317792	−	0.948161i	$-0.397059\pi$
$83$	480.607	0.635584	0.317792	+	0.948161i	$0.397059\pi$
$84$	15.3039	0.0198785
$85$	53.5216	0.0682969
$86$	−395.703	−0.496160
$87$	−87.0000	−0.107211
$88$	−1395.76	−1.69078
$89$	99.6673	0.118705	0.0593523	−	0.998237i	$-0.481096\pi$
$89$	99.6673	0.118705	0.0593523	+	0.998237i	$0.481096\pi$
$90$	39.1551	0.0458589
$91$	580.892	0.669166
$92$	−7.49966	−0.00849885
$93$	−584.351	−0.651553
$94$	224.802	0.246665
$95$	74.8741	0.0808623
$96$	−44.2411	−0.0470348
$97$	1450.27	1.51807	0.759036	−	0.651049i	$-0.225671\pi$
$97$	1450.27	1.51807	0.759036	+	0.651049i	$0.225671\pi$
$98$	272.151	0.280525
$99$	−544.633	−0.552905
$100$	39.9548	0.0399548
$101$	−954.777	−0.940632	−0.470316	−	0.882498i	$-0.655860\pi$
$101$	−954.777	−0.940632	−0.470316	+	0.882498i	$0.655860\pi$
$102$	283.219	0.274930
$103$	−1197.10	−1.14518	−0.572591	−	0.819841i	$-0.694062\pi$
$103$	−1197.10	−1.14518	−0.572591	+	0.819841i	$0.694062\pi$
$104$	−856.401	−0.807471
$105$	73.7098	0.0685080
$106$	198.890	0.182244
$107$	90.9101	0.0821365	0.0410683	−	0.999156i	$-0.486924\pi$
$107$	90.9101	0.0821365	0.0410683	+	0.999156i	$0.486924\pi$
$108$	−8.80395	−0.00784408
$109$	−1068.48	−0.938915	−0.469458	−	0.882955i	$-0.655551\pi$
$109$	−1068.48	−0.938915	−0.469458	+	0.882955i	$0.655551\pi$
$110$	−263.273	−0.228201
$111$	−342.621	−0.292975
$112$	958.788	0.808901
$113$	−516.635	−0.430097	−0.215048	−	0.976603i	$-0.568991\pi$
$113$	−516.635	−0.430097	−0.215048	+	0.976603i	$0.568991\pi$
$114$	396.210	0.325513
$115$	−36.1214	−0.0292899
$116$	9.45610	0.00756876
$117$	−334.172	−0.264053
$118$	−2064.62	−1.61071
$119$	533.164	0.410715
$120$	−108.669	−0.0826675
$121$	2331.03	1.75134
$122$	−1236.59	−0.917672
$123$	−1080.61	−0.792154
$124$	63.5136	0.0459975
$125$	388.750	0.278167
$126$	390.049	0.275780
$127$	341.861	0.238860	0.119430	−	0.992843i	$-0.461893\pi$
$127$	341.861	0.238860	0.119430	+	0.992843i	$0.461893\pi$
$128$	−1353.36	−0.934541
$129$	428.531	0.292481
$130$	−161.538	−0.108983
$131$	−73.5629	−0.0490628	−0.0245314	−	0.999699i	$-0.507809\pi$
$131$	−73.5629	−0.0490628	−0.0245314	+	0.999699i	$0.507809\pi$
$132$	59.1965	0.0390333
$133$	745.869	0.486279
$134$	2433.31	1.56870
$135$	−42.4034	−0.0270333
$136$	−786.035	−0.495603
$137$	−1817.72	−1.13356	−0.566782	−	0.823868i	$-0.691812\pi$
$137$	−1817.72	−1.13356	−0.566782	+	0.823868i	$0.691812\pi$
$138$	−191.143	−0.117907
$139$	920.454	0.561668	0.280834	−	0.959756i	$-0.409389\pi$
$139$	920.454	0.561668	0.280834	+	0.959756i	$0.409389\pi$
$140$	−8.01157	−0.00483644
$141$	−243.451	−0.145406
$142$	2056.74	1.21547
$143$	2246.93	1.31397
$144$	−551.566	−0.319193
$145$	45.5443	0.0260845
$146$	1445.12	0.819171
$147$	−294.729	−0.165366
$148$	37.2398	0.0206830
$149$	−1406.17	−0.773141	−0.386571	−	0.922260i	$-0.626340\pi$
$149$	−1406.17	−0.773141	−0.386571	+	0.922260i	$0.626340\pi$
$150$	1018.32	0.554304
$151$	−2517.97	−1.35702	−0.678508	−	0.734593i	$-0.737373\pi$
$151$	−2517.97	−1.35702	−0.678508	+	0.734593i	$0.737373\pi$
$152$	−1099.62	−0.586785
$153$	−306.715	−0.162068
$154$	−2622.63	−1.37232
$155$	305.907	0.158523
$156$	36.3215	0.0186413
$157$	3194.69	1.62397	0.811987	−	0.583675i	$-0.198386\pi$
$157$	3194.69	1.62397	0.811987	+	0.583675i	$0.198386\pi$
$158$	481.076	0.242230
$159$	−215.390	−0.107431
$160$	23.1601	0.0114436
$161$	−359.828	−0.176139
$162$	−224.385	−0.108823
$163$	−1316.10	−0.632424	−0.316212	−	0.948689i	$-0.602411\pi$
$163$	−1316.10	−0.632424	−0.316212	+	0.948689i	$0.602411\pi$
$164$	117.452	0.0559235
$165$	285.114	0.134522
$166$	−1331.37	−0.622496
$167$	1921.87	0.890530	0.445265	−	0.895399i	$-0.353109\pi$
$167$	1921.87	0.890530	0.445265	+	0.895399i	$0.353109\pi$
$168$	−1082.52	−0.497134
$169$	−818.343	−0.372482
$170$	−148.265	−0.0668906
$171$	−429.079	−0.191886
$172$	−46.5773	−0.0206482
$173$	2806.39	1.23333	0.616664	−	0.787227i	$-0.288484\pi$
$173$	2806.39	1.23333	0.616664	+	0.787227i	$0.288484\pi$
$174$	241.006	0.105004
$175$	1917.00	0.828067
$176$	3708.65	1.58835
$177$	2235.90	0.949497
$178$	−276.097	−0.116260
$179$	−1295.93	−0.541129	−0.270565	−	0.962702i	$-0.587210\pi$
$179$	−1295.93	−0.541129	−0.270565	+	0.962702i	$0.587210\pi$
$180$	4.60885	0.00190846
$181$	2472.01	1.01515	0.507577	−	0.861606i	$-0.330541\pi$
$181$	2472.01	1.01515	0.507577	+	0.861606i	$0.330541\pi$
$182$	−1609.18	−0.655386
$183$	1339.18	0.540957
$184$	530.490	0.212545
$185$	179.362	0.0712807
$186$	1618.76	0.638136
$187$	2062.31	0.806477
$188$	26.4609	0.0102652
$189$	−422.407	−0.162569
$190$	−207.415	−0.0791972
$191$	−847.545	−0.321079	−0.160540	−	0.987029i	$-0.551323\pi$
$191$	−847.545	−0.321079	−0.160540	+	0.987029i	$0.551323\pi$
$192$	1593.40	0.598925
$193$	846.717	0.315793	0.157896	−	0.987456i	$-0.449529\pi$
$193$	846.717	0.315793	0.157896	+	0.987456i	$0.449529\pi$
$194$	−4017.53	−1.48681
$195$	174.939	0.0642442
$196$	32.0343	0.0116743
$197$	−308.603	−0.111610	−0.0558048	−	0.998442i	$-0.517772\pi$
$197$	−308.603	−0.111610	−0.0558048	+	0.998442i	$0.517772\pi$
$198$	1508.73	0.541520
$199$	530.327	0.188914	0.0944570	−	0.995529i	$-0.469889\pi$
$199$	530.327	0.188914	0.0944570	+	0.995529i	$0.469889\pi$
$200$	−2826.21	−0.999215
$201$	−2635.18	−0.924732
$202$	2644.91	0.921263
$203$	453.697	0.156863
$204$	33.3371	0.0114415
$205$	565.695	0.192731
$206$	3316.19	1.12160
$207$	207.000	0.0695048
$208$	2275.53	0.758557
$209$	2885.07	0.954854
$210$	−204.190	−0.0670973
$211$	−3440.93	−1.12267	−0.561336	−	0.827588i	$-0.689712\pi$
$211$	−3440.93	−1.12267	−0.561336	+	0.827588i	$0.689712\pi$
$212$	23.4109	0.00758427
$213$	−2227.36	−0.716509
$214$	−251.838	−0.0804452
$215$	−224.335	−0.0711605
$216$	622.749	0.196170
$217$	3047.34	0.953302
$218$	2959.89	0.919582
$219$	−1565.01	−0.482892
$220$	−30.9893	−0.00949680
$221$	1265.38	0.385153
$222$	949.125	0.286942
$223$	−3254.88	−0.977412	−0.488706	−	0.872449i	$-0.662531\pi$
$223$	−3254.88	−0.977412	−0.488706	+	0.872449i	$0.662531\pi$
$224$	230.713	0.0688177
$225$	−1102.80	−0.326756
$226$	1431.18	0.421241
$227$	−1335.86	−0.390590	−0.195295	−	0.980745i	$-0.562566\pi$
$227$	−1335.86	−0.390590	−0.195295	+	0.980745i	$0.562566\pi$
$228$	46.6370	0.0135465
$229$	−576.477	−0.166352	−0.0831762	−	0.996535i	$-0.526506\pi$
$229$	−576.477	−0.166352	−0.0831762	+	0.996535i	$0.526506\pi$
$230$	100.063	0.0286868
$231$	2840.21	0.808969
$232$	−668.878	−0.189284
$233$	3408.11	0.958252	0.479126	−	0.877746i	$-0.340954\pi$
$233$	3408.11	0.958252	0.479126	+	0.877746i	$0.340954\pi$
$234$	925.720	0.258616
$235$	127.446	0.0353774
$236$	−243.022	−0.0670313
$237$	−520.986	−0.142792
$238$	−1476.96	−0.402257
$239$	−6777.27	−1.83425	−0.917124	−	0.398603i	$-0.869495\pi$
$239$	−6777.27	−1.83425	−0.917124	+	0.398603i	$0.869495\pi$
$240$	288.744	0.0776597
$241$	−3359.14	−0.897847	−0.448923	−	0.893570i	$-0.648192\pi$
$241$	−3359.14	−0.897847	−0.448923	+	0.893570i	$0.648192\pi$
$242$	−6457.40	−1.71528
$243$	243.000	0.0641500
$244$	−145.557	−0.0381898
$245$	154.290	0.0402336
$246$	2993.48	0.775842
$247$	1770.20	0.456014
$248$	−4492.64	−1.15033
$249$	1441.82	0.366954
$250$	−1076.91	−0.272439
$251$	1394.43	0.350660	0.175330	−	0.984510i	$-0.443901\pi$
$251$	1394.43	0.350660	0.175330	+	0.984510i	$0.443901\pi$
$252$	45.9118	0.0114769
$253$	−1391.84	−0.345866
$254$	−947.017	−0.233942
$255$	160.565	0.0394312
$256$	−500.004	−0.122071
$257$	−1715.80	−0.416454	−0.208227	−	0.978081i	$-0.566769\pi$
$257$	−1715.80	−0.416454	−0.208227	+	0.978081i	$0.566769\pi$
$258$	−1187.11	−0.286458
$259$	1786.74	0.428658
$260$	−19.0142	−0.00453543
$261$	−261.000	−0.0618984
$262$	203.783	0.0480525
$263$	−5347.88	−1.25386	−0.626929	−	0.779076i	$-0.715688\pi$
$263$	−5347.88	−1.25386	−0.626929	+	0.779076i	$0.715688\pi$
$264$	−4187.27	−0.976170
$265$	112.756	0.0261379
$266$	−2066.20	−0.476265
$267$	299.002	0.0685342
$268$	286.420	0.0652831
$269$	−195.857	−0.0443925	−0.0221963	−	0.999754i	$-0.507066\pi$
$269$	−195.857	−0.0443925	−0.0221963	+	0.999754i	$0.507066\pi$
$270$	117.465	0.0264767
$271$	7196.76	1.61318	0.806591	−	0.591110i	$-0.201310\pi$
$271$	7196.76	1.61318	0.806591	+	0.591110i	$0.201310\pi$
$272$	2088.56	0.465580
$273$	1742.68	0.386343
$274$	5035.42	1.11022
$275$	7415.09	1.62599
$276$	−22.4990	−0.00490681
$277$	7913.12	1.71644	0.858219	−	0.513283i	$-0.171571\pi$
$277$	7913.12	1.71644	0.858219	+	0.513283i	$0.171571\pi$
$278$	−2549.83	−0.550103
$279$	−1753.05	−0.376174
$280$	566.700	0.120953
$281$	−6668.54	−1.41570	−0.707851	−	0.706362i	$-0.750335\pi$
$281$	−6668.54	−1.41570	−0.707851	+	0.706362i	$0.750335\pi$
$282$	674.405	0.142412
$283$	2460.91	0.516911	0.258455	−	0.966023i	$-0.416786\pi$
$283$	2460.91	0.516911	0.258455	+	0.966023i	$0.416786\pi$
$284$	242.094	0.0505832
$285$	224.622	0.0466859
$286$	−6224.41	−1.28691
$287$	5635.25	1.15902
$288$	−132.723	−0.0271555
$289$	−3751.59	−0.763604
$290$	−126.166	−0.0255474
$291$	4350.82	0.876459
$292$	170.102	0.0340906
$293$	5792.28	1.15491	0.577455	−	0.816422i	$-0.304046\pi$
$293$	5792.28	1.15491	0.577455	+	0.816422i	$0.304046\pi$
$294$	816.454	0.161961
$295$	−1170.49	−0.231013
$296$	−2634.16	−0.517255
$297$	−1633.90	−0.319220
$298$	3895.36	0.757221
$299$	−853.996	−0.165177
$300$	119.864	0.0230679
$301$	−2234.75	−0.427935
$302$	6975.24	1.32907
$303$	−2864.33	−0.543074
$304$	2921.80	0.551239
$305$	−701.059	−0.131615
$306$	849.658	0.158731
$307$	9614.86	1.78746	0.893728	−	0.448609i	$-0.148080\pi$
$307$	9614.86	1.78746	0.893728	+	0.448609i	$0.148080\pi$
$308$	−308.704	−0.0571106
$309$	−3591.30	−0.661171
$310$	−847.419	−0.155259
$311$	3322.04	0.605709	0.302855	−	0.953037i	$-0.402060\pi$
$311$	3322.04	0.605709	0.302855	+	0.953037i	$0.402060\pi$
$312$	−2569.20	−0.466194
$313$	5887.22	1.06315	0.531574	−	0.847012i	$-0.321601\pi$
$313$	5887.22	1.06315	0.531574	+	0.847012i	$0.321601\pi$
$314$	−8849.88	−1.59053
$315$	221.129	0.0395531
$316$	56.6264	0.0100806
$317$	−5266.62	−0.933132	−0.466566	−	0.884486i	$-0.654509\pi$
$317$	−5266.62	−0.933132	−0.466566	+	0.884486i	$0.654509\pi$
$318$	596.670	0.105219
$319$	1754.93	0.308016
$320$	−834.141	−0.145718
$321$	272.730	0.0474215
$322$	996.791	0.172512
$323$	1624.76	0.279888
$324$	−26.4119	−0.00452878
$325$	4549.70	0.776530
$326$	3645.85	0.619401
$327$	−3205.44	−0.542083
$328$	−8307.97	−1.39857
$329$	1269.58	0.212748
$330$	−789.819	−0.131752
$331$	4649.87	0.772145	0.386072	−	0.922468i	$-0.373831\pi$
$331$	4649.87	0.772145	0.386072	+	0.922468i	$0.373831\pi$
$332$	−156.712	−0.0259058
$333$	−1027.86	−0.169149
$334$	−5323.93	−0.872192
$335$	1379.51	0.224987
$336$	2876.36	0.467019
$337$	−11235.5	−1.81613	−0.908063	−	0.418833i	$-0.862439\pi$
$337$	−11235.5	−1.81613	−0.908063	+	0.418833i	$0.862439\pi$
$338$	2266.96	0.364812
$339$	−1549.91	−0.248317
$340$	−17.4519	−0.00278372
$341$	11787.3	1.87190
$342$	1188.63	0.187935
$343$	6903.12	1.08669
$344$	3294.65	0.516383
$345$	−108.364	−0.0169105
$346$	−7774.21	−1.20793
$347$	−1976.90	−0.305838	−0.152919	−	0.988239i	$-0.548867\pi$
$347$	−1976.90	−0.305838	−0.152919	+	0.988239i	$0.548867\pi$
$348$	28.3683	0.00436983
$349$	10124.9	1.55294	0.776470	−	0.630155i	$-0.217008\pi$
$349$	10124.9	1.55294	0.776470	+	0.630155i	$0.217008\pi$
$350$	−5310.45	−0.811016
$351$	−1002.52	−0.152451
$352$	892.412	0.135130
$353$	−12569.5	−1.89521	−0.947604	−	0.319446i	$-0.896503\pi$
$353$	−12569.5	−1.89521	−0.947604	+	0.319446i	$0.896503\pi$
$354$	−6193.87	−0.929945
$355$	1166.02	0.174327
$356$	−32.4987	−0.00483829
$357$	1599.49	0.237126
$358$	3589.96	0.529987
$359$	5305.60	0.779997	0.389998	−	0.920816i	$-0.372476\pi$
$359$	5305.60	0.779997	0.389998	+	0.920816i	$0.372476\pi$
$360$	−326.008	−0.0477281
$361$	−4586.05	−0.668618
$362$	−6847.92	−0.994250
$363$	6993.10	1.01114
$364$	−189.413	−0.0272745
$365$	819.278	0.117488
$366$	−3709.78	−0.529818
$367$	9773.49	1.39011	0.695057	−	0.718955i	$-0.255379\pi$
$367$	9773.49	1.39011	0.695057	+	0.718955i	$0.255379\pi$
$368$	−1409.56	−0.199669
$369$	−3241.82	−0.457350
$370$	−496.865	−0.0698129
$371$	1123.24	0.157185
$372$	190.541	0.0265567
$373$	5434.49	0.754389	0.377194	−	0.926134i	$-0.376889\pi$
$373$	5434.49	0.754389	0.377194	+	0.926134i	$0.376889\pi$
$374$	−5712.98	−0.789870
$375$	1166.25	0.160600
$376$	−1871.72	−0.256719
$377$	1076.78	0.147100
$378$	1170.15	0.159222
$379$	12431.9	1.68492	0.842461	−	0.538758i	$-0.181106\pi$
$379$	12431.9	1.68492	0.842461	+	0.538758i	$0.181106\pi$
$380$	−24.4144	−0.00329587
$381$	1025.58	0.137906
$382$	2347.86	0.314468
$383$	−8664.50	−1.15597	−0.577984	−	0.816048i	$-0.696160\pi$
$383$	−8664.50	−1.15597	−0.577984	+	0.816048i	$0.696160\pi$
$384$	−4060.08	−0.539558
$385$	−1486.84	−0.196822
$386$	−2345.56	−0.309290
$387$	1285.59	0.168864
$388$	−472.894	−0.0618752
$389$	−358.614	−0.0467415	−0.0233708	−	0.999727i	$-0.507440\pi$
$389$	−358.614	−0.0467415	−0.0233708	+	0.999727i	$0.507440\pi$
$390$	−484.613	−0.0629213
$391$	−783.828	−0.101381
$392$	−2265.95	−0.291959
$393$	−220.689	−0.0283264
$394$	854.888	0.109311
$395$	272.735	0.0347413
$396$	177.590	0.0225359
$397$	9129.48	1.15414	0.577072	−	0.816693i	$-0.304195\pi$
$397$	9129.48	1.15414	0.577072	+	0.816693i	$0.304195\pi$
$398$	−1469.10	−0.185024
$399$	2237.61	0.280753
$400$	7509.48	0.938685
$401$	6128.26	0.763169	0.381584	−	0.924334i	$-0.375379\pi$
$401$	6128.26	0.763169	0.381584	+	0.924334i	$0.375379\pi$
$402$	7299.93	0.905690
$403$	7232.37	0.893971
$404$	311.326	0.0383392
$405$	−127.210	−0.0156077
$406$	−1256.82	−0.153633
$407$	6911.22	0.841711
$408$	−2358.11	−0.286136
$409$	9633.31	1.16464	0.582319	−	0.812961i	$-0.302146\pi$
$409$	9633.31	1.16464	0.582319	+	0.812961i	$0.302146\pi$
$410$	−1567.08	−0.188762
$411$	−5453.16	−0.654463
$412$	390.341	0.0466765
$413$	−11660.0	−1.38923
$414$	−573.428	−0.0680736
$415$	−754.790	−0.0892800
$416$	547.561	0.0645346
$417$	2761.36	0.324279
$418$	−7992.18	−0.935192
$419$	15252.5	1.77836	0.889182	−	0.457554i	$-0.151274\pi$
$419$	15252.5	1.77836	0.889182	+	0.457554i	$0.151274\pi$
$420$	−24.0347	−0.00279232
$421$	−15681.4	−1.81536	−0.907679	−	0.419664i	$-0.862148\pi$
$421$	−15681.4	−1.81536	−0.907679	+	0.419664i	$0.862148\pi$
$422$	9532.02	1.09955
$423$	−730.354	−0.0839504
$424$	−1655.97	−0.189672
$425$	4175.88	0.476612
$426$	6170.21	0.701755
$427$	−6983.71	−0.791488
$428$	−29.6433	−0.00334781
$429$	6740.79	0.758621
$430$	621.449	0.0696952
$431$	−6798.59	−0.759806	−0.379903	−	0.925026i	$-0.624043\pi$
$431$	−6798.59	−0.759806	−0.379903	+	0.925026i	$0.624043\pi$
$432$	−1654.70	−0.184286
$433$	4406.67	0.489079	0.244539	−	0.969639i	$-0.421363\pi$
$433$	4406.67	0.489079	0.244539	+	0.969639i	$0.421363\pi$
$434$	−8441.68	−0.933672
$435$	136.633	0.0150599
$436$	348.402	0.0382693
$437$	−1096.54	−0.120033
$438$	4335.36	0.472949
$439$	−10499.7	−1.14151	−0.570757	−	0.821119i	$-0.693350\pi$
$439$	−10499.7	−1.14151	−0.570757	+	0.821119i	$0.693350\pi$
$440$	2192.03	0.237502
$441$	−884.188	−0.0954743
$442$	−3505.34	−0.377222
$443$	−11508.5	−1.23428	−0.617141	−	0.786852i	$-0.711709\pi$
$443$	−11508.5	−1.23428	−0.617141	+	0.786852i	$0.711709\pi$
$444$	111.719	0.0119414
$445$	−156.527	−0.0166744
$446$	9016.62	0.957286
$447$	−4218.52	−0.446373
$448$	−8309.42	−0.876302
$449$	6148.81	0.646281	0.323141	−	0.946351i	$-0.395261\pi$
$449$	6148.81	0.646281	0.323141	+	0.946351i	$0.395261\pi$
$450$	3054.97	0.320028
$451$	21797.5	2.27584
$452$	168.460	0.0175303
$453$	−7553.90	−0.783473
$454$	3700.57	0.382547
$455$	−912.288	−0.0939972
$456$	−3298.87	−0.338780
$457$	1590.22	0.162774	0.0813868	−	0.996683i	$-0.474065\pi$
$457$	1590.22	0.162774	0.0813868	+	0.996683i	$0.474065\pi$
$458$	1596.95	0.162927
$459$	−920.146	−0.0935702
$460$	11.7782	0.00119383
$461$	−17713.1	−1.78954	−0.894772	−	0.446524i	$-0.852662\pi$
$461$	−17713.1	−1.78954	−0.894772	+	0.446524i	$0.852662\pi$
$462$	−7867.90	−0.792311
$463$	8183.19	0.821393	0.410697	−	0.911772i	$-0.365286\pi$
$463$	8183.19	0.821393	0.410697	+	0.911772i	$0.365286\pi$
$464$	1777.27	0.177818
$465$	917.721	0.0915232
$466$	−9441.10	−0.938521
$467$	6666.29	0.660555	0.330277	−	0.943884i	$-0.392858\pi$
$467$	6666.29	0.660555	0.330277	+	0.943884i	$0.392858\pi$
$468$	108.964	0.0107626
$469$	13742.2	1.35300
$470$	−353.050	−0.0346489
$471$	9584.07	0.937602
$472$	17190.2	1.67636
$473$	−8644.14	−0.840291
$474$	1443.23	0.139852
$475$	5841.85	0.564299
$476$	−173.850	−0.0167403
$477$	−646.169	−0.0620253
$478$	18774.3	1.79648
$479$	−11282.4	−1.07621	−0.538107	−	0.842877i	$-0.680860\pi$
$479$	−11282.4	−1.07621	−0.538107	+	0.842877i	$0.680860\pi$
$480$	69.4804	0.00660694
$481$	4240.54	0.401979
$482$	9305.43	0.879359
$483$	−1079.48	−0.101694
$484$	−760.085	−0.0713829
$485$	−2277.65	−0.213243
$486$	−673.155	−0.0628291
$487$	9350.21	0.870017	0.435009	−	0.900426i	$-0.356745\pi$
$487$	9350.21	0.870017	0.435009	+	0.900426i	$0.356745\pi$
$488$	10296.0	0.955076
$489$	−3948.30	−0.365130
$490$	−427.412	−0.0394052
$491$	12402.2	1.13992	0.569962	−	0.821671i	$-0.306958\pi$
$491$	12402.2	1.13992	0.569962	+	0.821671i	$0.306958\pi$
$492$	352.356	0.0322874
$493$	988.305	0.0902861
$494$	−4903.79	−0.446624
$495$	855.343	0.0776662
$496$	11937.3	1.08065
$497$	11615.5	1.04834
$498$	−3994.11	−0.359398
$499$	14246.4	1.27807	0.639034	−	0.769179i	$-0.279334\pi$
$499$	14246.4	1.27807	0.639034	+	0.769179i	$0.279334\pi$
$500$	−126.761	−0.0113378
$501$	5765.60	0.514148
$502$	−3862.83	−0.343440
$503$	3188.39	0.282631	0.141316	−	0.989965i	$-0.454867\pi$
$503$	3188.39	0.282631	0.141316	+	0.989965i	$0.454867\pi$
$504$	−3247.57	−0.287021
$505$	1499.47	0.132130
$506$	3855.65	0.338744
$507$	−2455.03	−0.215053
$508$	−111.471	−0.00973571
$509$	17375.8	1.51310	0.756550	−	0.653935i	$-0.226883\pi$
$509$	17375.8	1.51310	0.756550	+	0.653935i	$0.226883\pi$
$510$	−444.795	−0.0386193
$511$	8161.36	0.706531
$512$	12212.0	1.05410
$513$	−1287.24	−0.110785
$514$	4753.09	0.407879
$515$	1880.04	0.160863
$516$	−139.732	−0.0119212
$517$	4910.80	0.417750
$518$	−4949.59	−0.419831
$519$	8419.16	0.712062
$520$	1344.97	0.113425
$521$	−7486.85	−0.629568	−0.314784	−	0.949163i	$-0.601932\pi$
$521$	−7486.85	−0.629568	−0.314784	+	0.949163i	$0.601932\pi$
$522$	723.018	0.0606239
$523$	8143.37	0.680850	0.340425	−	0.940272i	$-0.389429\pi$
$523$	8143.37	0.680850	0.340425	+	0.940272i	$0.389429\pi$
$524$	23.9868	0.00199975
$525$	5751.01	0.478085
$526$	14814.6	1.22804
$527$	6638.13	0.548694
$528$	11126.0	0.917036
$529$	529.000	0.0434783
$530$	−312.356	−0.0255997
$531$	6707.71	0.548192
$532$	−243.207	−0.0198202
$533$	13374.4	1.08688
$534$	−828.291	−0.0671229
$535$	−142.774	−0.0115377
$536$	−20259.9	−1.63264
$537$	−3887.78	−0.312421
$538$	542.559	0.0434784
$539$	5945.15	0.475094
$540$	13.8266	0.00110185
$541$	15143.7	1.20347	0.601736	−	0.798695i	$-0.294476\pi$
$541$	15143.7	1.20347	0.601736	+	0.798695i	$0.294476\pi$
$542$	−19936.4	−1.57996
$543$	7416.02	0.586099
$544$	502.571	0.0396095
$545$	1678.04	0.131889
$546$	−4827.54	−0.378388
$547$	20336.2	1.58961	0.794804	−	0.606867i	$-0.207574\pi$
$547$	20336.2	1.58961	0.794804	+	0.606867i	$0.207574\pi$
$548$	592.708	0.0462030
$549$	4017.55	0.312322
$550$	−20541.2	−1.59251
$551$	1382.59	0.106897
$552$	1591.47	0.122713
$553$	2716.89	0.208922
$554$	−21920.8	−1.68109
$555$	538.085	0.0411539
$556$	−300.134	−0.0228931
$557$	−17780.8	−1.35259	−0.676297	−	0.736629i	$-0.736416\pi$
$557$	−17780.8	−1.35259	−0.676297	+	0.736629i	$0.736416\pi$
$558$	4856.28	0.368428
$559$	−5303.82	−0.401302
$560$	−1505.77	−0.113626
$561$	6186.93	0.465620
$562$	18473.1	1.38655
$563$	−3318.92	−0.248447	−0.124224	−	0.992254i	$-0.539644\pi$
$563$	−3318.92	−0.248447	−0.124224	+	0.992254i	$0.539644\pi$
$564$	79.3827	0.00592663
$565$	811.373	0.0604154
$566$	−6817.17	−0.506267
$567$	−1267.22	−0.0938594
$568$	−17124.5	−1.26502
$569$	−12117.5	−0.892779	−0.446389	−	0.894839i	$-0.647290\pi$
$569$	−12117.5	−0.892779	−0.446389	+	0.894839i	$0.647290\pi$
$570$	−622.245	−0.0457245
$571$	−19183.4	−1.40596	−0.702979	−	0.711211i	$-0.748147\pi$
$571$	−19183.4	−1.40596	−0.702979	+	0.711211i	$0.748147\pi$
$572$	−732.661	−0.0535561
$573$	−2542.63	−0.185375
$574$	−15610.7	−1.13515
$575$	−2818.27	−0.204400
$576$	4780.20	0.345790
$577$	23201.6	1.67399	0.836996	−	0.547209i	$-0.184310\pi$
$577$	23201.6	1.67399	0.836996	+	0.547209i	$0.184310\pi$
$578$	10392.6	0.747881
$579$	2540.15	0.182323
$580$	−14.8507	−0.00106318
$581$	−7518.95	−0.536900
$582$	−12052.6	−0.858412
$583$	4344.75	0.308647
$584$	−12032.2	−0.852560
$585$	524.816	0.0370914
$586$	−16045.7	−1.13113
$587$	2133.57	0.150020	0.0750100	−	0.997183i	$-0.476101\pi$
$587$	2133.57	0.150020	0.0750100	+	0.997183i	$0.476101\pi$
$588$	96.1030	0.00674017
$589$	9286.41	0.649643
$590$	3242.48	0.226256
$591$	−925.810	−0.0644378
$592$	6999.20	0.485921
$593$	8251.93	0.571444	0.285722	−	0.958313i	$-0.407767\pi$
$593$	8251.93	0.571444	0.285722	+	0.958313i	$0.407767\pi$
$594$	4526.20	0.312647
$595$	−837.331	−0.0576928
$596$	458.514	0.0315125
$597$	1590.98	0.109070
$598$	2365.73	0.161776
$599$	−4222.06	−0.287995	−0.143997	−	0.989578i	$-0.545996\pi$
$599$	−4222.06	−0.287995	−0.143997	+	0.989578i	$0.545996\pi$
$600$	−8478.62	−0.576897
$601$	4494.71	0.305063	0.152532	−	0.988299i	$-0.451257\pi$
$601$	4494.71	0.305063	0.152532	+	0.988299i	$0.451257\pi$
$602$	6190.66	0.419124
$603$	−7905.54	−0.533894
$604$	821.040	0.0553106
$605$	−3660.88	−0.246010
$606$	7934.73	0.531891
$607$	4274.73	0.285842	0.142921	−	0.989734i	$-0.454351\pi$
$607$	4274.73	0.285842	0.142921	+	0.989734i	$0.454351\pi$
$608$	703.072	0.0468969
$609$	1361.09	0.0905651
$610$	1942.06	0.128905
$611$	3013.14	0.199507
$612$	100.011	0.00660575
$613$	10884.3	0.717146	0.358573	−	0.933502i	$-0.383263\pi$
$613$	10884.3	0.717146	0.358573	+	0.933502i	$0.383263\pi$
$614$	−26635.0	−1.75065
$615$	1697.09	0.111273
$616$	21836.2	1.42826
$617$	−21166.2	−1.38107	−0.690533	−	0.723301i	$-0.742624\pi$
$617$	−21166.2	−1.38107	−0.690533	+	0.723301i	$0.742624\pi$
$618$	9948.57	0.647557
$619$	−23624.0	−1.53397	−0.766985	−	0.641665i	$-0.778244\pi$
$619$	−23624.0	−1.53397	−0.766985	+	0.641665i	$0.778244\pi$
$620$	−99.7477	−0.00646124
$621$	621.000	0.0401286
$622$	−9202.66	−0.593237
$623$	−1559.27	−0.100274
$624$	6826.60	0.437953
$625$	14706.2	0.941194
$626$	−16308.7	−1.04126
$627$	8655.21	0.551285
$628$	−1041.70	−0.0661916
$629$	3892.12	0.246723
$630$	−612.569	−0.0387386
$631$	2908.76	0.183511	0.0917557	−	0.995782i	$-0.470752\pi$
$631$	2908.76	0.183511	0.0917557	+	0.995782i	$0.470752\pi$
$632$	−4005.47	−0.252103
$633$	−10322.8	−0.648175
$634$	14589.5	0.913918
$635$	−536.890	−0.0335525
$636$	70.2326	0.00437878
$637$	3647.79	0.226893
$638$	−4861.47	−0.301673
$639$	−6682.09	−0.413676
$640$	2125.44	0.131274
$641$	22326.5	1.37573	0.687866	−	0.725838i	$-0.258548\pi$
$641$	22326.5	1.37573	0.687866	+	0.725838i	$0.258548\pi$
$642$	−755.513	−0.0464451
$643$	−3528.88	−0.216431	−0.108216	−	0.994127i	$-0.534514\pi$
$643$	−3528.88	−0.216431	−0.108216	+	0.994127i	$0.534514\pi$
$644$	117.330	0.00717927
$645$	−673.005	−0.0410846
$646$	−4500.88	−0.274125
$647$	28121.8	1.70878	0.854391	−	0.519630i	$-0.173930\pi$
$647$	28121.8	1.70878	0.854391	+	0.519630i	$0.173930\pi$
$648$	1868.25	0.113259
$649$	−45101.7	−2.72789
$650$	−12603.5	−0.760540
$651$	9142.01	0.550389
$652$	429.144	0.0257770
$653$	−27912.9	−1.67276	−0.836382	−	0.548147i	$-0.815333\pi$
$653$	−27912.9	−1.67276	−0.836382	+	0.548147i	$0.815333\pi$
$654$	8879.66	0.530921
$655$	115.530	0.00689181
$656$	22075.0	1.31385
$657$	−4695.02	−0.278798
$658$	−3516.96	−0.208367
$659$	−3517.96	−0.207952	−0.103976	−	0.994580i	$-0.533157\pi$
$659$	−3517.96	−0.207952	−0.103976	+	0.994580i	$0.533157\pi$
$660$	−92.9678	−0.00548298
$661$	−9845.64	−0.579351	−0.289676	−	0.957125i	$-0.593547\pi$
$661$	−9845.64	−0.579351	−0.289676	+	0.957125i	$0.593547\pi$
$662$	−12881.0	−0.756245
$663$	3796.14	0.222368
$664$	11085.1	0.647868
$665$	−1171.38	−0.0683072
$666$	2847.37	0.165666
$667$	−667.000	−0.0387202
$668$	−626.667	−0.0362971
$669$	−9764.64	−0.564309
$670$	−3821.50	−0.220354
$671$	−27013.4	−1.55416
$672$	692.139	0.0397319
$673$	−22237.5	−1.27369	−0.636845	−	0.770992i	$-0.719761\pi$
$673$	−22237.5	−1.27369	−0.636845	+	0.770992i	$0.719761\pi$
$674$	31124.3	1.77873
$675$	−3308.41	−0.188653
$676$	266.839	0.0151820
$677$	−30362.2	−1.72365	−0.861827	−	0.507203i	$-0.830679\pi$
$677$	−30362.2	−1.72365	−0.861827	+	0.507203i	$0.830679\pi$
$678$	4293.53	0.243203
$679$	−22689.1	−1.28237
$680$	1234.46	0.0696170
$681$	−4007.57	−0.225507
$682$	−32653.0	−1.83335
$683$	−29444.4	−1.64957	−0.824786	−	0.565444i	$-0.808705\pi$
$683$	−29444.4	−1.64957	−0.824786	+	0.565444i	$0.808705\pi$
$684$	139.911	0.00782109
$685$	2854.72	0.159231
$686$	−19122.9	−1.06431
$687$	−1729.43	−0.0960436
$688$	−8754.18	−0.485102
$689$	2665.83	0.147402
$690$	300.189	0.0165623
$691$	−25904.8	−1.42614	−0.713072	−	0.701091i	$-0.752697\pi$
$691$	−25904.8	−1.42614	−0.713072	+	0.701091i	$0.752697\pi$
$692$	−915.085	−0.0502692
$693$	8520.62	0.467059
$694$	5476.39	0.299540
$695$	−1445.57	−0.0788971
$696$	−2006.63	−0.109283
$697$	12275.5	0.667098
$698$	−28048.0	−1.52096
$699$	10224.3	0.553247
$700$	−625.081	−0.0337512
$701$	22936.0	1.23578	0.617888	−	0.786266i	$-0.287988\pi$
$701$	22936.0	1.23578	0.617888	+	0.786266i	$0.287988\pi$
$702$	2777.16	0.149312
$703$	5444.88	0.292116
$704$	−32141.4	−1.72070
$705$	382.339	0.0204251
$706$	34819.9	1.85618
$707$	14937.2	0.794585
$708$	−729.067	−0.0387006
$709$	−32743.9	−1.73445	−0.867223	−	0.497921i	$-0.834097\pi$
$709$	−32743.9	−1.73445	−0.867223	+	0.497921i	$0.834097\pi$
$710$	−3230.09	−0.170737
$711$	−1562.96	−0.0824409
$712$	2298.80	0.120999
$713$	−4480.03	−0.235313
$714$	−4430.89	−0.232243
$715$	−3528.79	−0.184572
$716$	422.566	0.0220559
$717$	−20331.8	−1.05900
$718$	−14697.5	−0.763936
$719$	−1174.08	−0.0608983	−0.0304491	−	0.999536i	$-0.509694\pi$
$719$	−1174.08	−0.0608983	−0.0304491	+	0.999536i	$0.509694\pi$
$720$	866.231	0.0448368
$721$	18728.3	0.967375
$722$	12704.2	0.654850
$723$	−10077.4	−0.518372
$724$	−806.053	−0.0413767
$725$	3553.47	0.182031
$726$	−19372.2	−0.990316
$727$	−25756.3	−1.31396	−0.656979	−	0.753909i	$-0.728166\pi$
$727$	−25756.3	−1.31396	−0.656979	+	0.753909i	$0.728166\pi$
$728$	13398.1	0.682099
$729$	729.000	0.0370370
$730$	−2269.55	−0.115068
$731$	−4868.03	−0.246307
$732$	−436.670	−0.0220489
$733$	−35720.8	−1.79997	−0.899986	−	0.435919i	$-0.856423\pi$
$733$	−35720.8	−1.79997	−0.899986	+	0.435919i	$0.856423\pi$
$734$	−27074.4	−1.36149
$735$	462.871	0.0232289
$736$	−339.182	−0.0169870
$737$	53155.7	2.65674
$738$	8980.43	0.447933
$739$	3511.39	0.174789	0.0873943	−	0.996174i	$-0.472146\pi$
$739$	3511.39	0.174789	0.0873943	+	0.996174i	$0.472146\pi$
$740$	−58.4849	−0.00290533
$741$	5310.61	0.263280
$742$	−3111.57	−0.153948
$743$	5174.99	0.255521	0.127760	−	0.991805i	$-0.459221\pi$
$743$	5174.99	0.255521	0.127760	+	0.991805i	$0.459221\pi$
$744$	−13477.9	−0.664146
$745$	2208.38	0.108603
$746$	−15054.5	−0.738855
$747$	4325.46	0.211861
$748$	−672.463	−0.0328712
$749$	−1422.26	−0.0693836
$750$	−3230.73	−0.157293
$751$	−34385.2	−1.67075	−0.835374	−	0.549682i	$-0.814749\pi$
$751$	−34385.2	−1.67075	−0.835374	+	0.549682i	$0.814749\pi$
$752$	4973.31	0.241168
$753$	4183.30	0.202454
$754$	−2982.87	−0.144071
$755$	3954.45	0.190619
$756$	137.735	0.00662617
$757$	−26086.3	−1.25247	−0.626236	−	0.779634i	$-0.715405\pi$
$757$	−26086.3	−1.25247	−0.626236	+	0.779634i	$0.715405\pi$
$758$	−34438.7	−1.65023
$759$	−4175.52	−0.199686
$760$	1726.95	0.0824252
$761$	−7397.94	−0.352398	−0.176199	−	0.984355i	$-0.556380\pi$
$761$	−7397.94	−0.352398	−0.176199	+	0.984355i	$0.556380\pi$
$762$	−2841.05	−0.135066
$763$	16716.1	0.793135
$764$	276.361	0.0130869
$765$	481.695	0.0227656
$766$	24002.3	1.13216
$767$	−27673.3	−1.30277
$768$	−1500.01	−0.0704778
$769$	1747.82	0.0819611	0.0409805	−	0.999160i	$-0.486952\pi$
$769$	1747.82	0.0819611	0.0409805	+	0.999160i	$0.486952\pi$
$770$	4118.83	0.192769
$771$	−5147.40	−0.240440
$772$	−276.091	−0.0128714
$773$	−10.1578	−0.000472642 0	−0.000236321	−	1.00000i	$-0.500075\pi$
$773$	−10.1578	−0.000472642 0	−0.000236321		1.00000i	$0.500075\pi$
$774$	−3561.33	−0.165387
$775$	23867.5	1.10625
$776$	33450.2	1.54741
$777$	5360.21	0.247486
$778$	993.428	0.0457791
$779$	17172.8	0.789832
$780$	−57.0427	−0.00261853
$781$	44929.4	2.05852
$782$	2171.35	0.0992932
$783$	−783.000	−0.0357371
$784$	6020.84	0.274273
$785$	−5017.24	−0.228119
$786$	611.349	0.0277431
$787$	−7488.92	−0.339201	−0.169600	−	0.985513i	$-0.554248\pi$
$787$	−7488.92	−0.339201	−0.169600	+	0.985513i	$0.554248\pi$
$788$	100.627	0.00454910
$789$	−16043.7	−0.723915
$790$	−755.527	−0.0340259
$791$	8082.61	0.363318
$792$	−12561.8	−0.563592
$793$	−16574.7	−0.742227
$794$	−25290.3	−1.13038
$795$	338.269	0.0150908
$796$	−172.925	−0.00769995
$797$	29921.3	1.32982	0.664910	−	0.746924i	$-0.268470\pi$
$797$	29921.3	1.32982	0.664910	+	0.746924i	$0.268470\pi$
$798$	−6198.59	−0.274972
$799$	2765.57	0.122451
$800$	1807.01	0.0798591
$801$	897.006	0.0395682
$802$	−16976.4	−0.747454
$803$	31568.7	1.38734
$804$	859.259	0.0376912
$805$	565.108	0.0247422
$806$	−20035.0	−0.875563
$807$	−587.570	−0.0256301
$808$	−22021.7	−0.958813
$809$	−25262.5	−1.09788	−0.548938	−	0.835863i	$-0.684968\pi$
$809$	−25262.5	−1.09788	−0.548938	+	0.835863i	$0.684968\pi$
$810$	352.395	0.0152863
$811$	30182.8	1.30686	0.653429	−	0.756988i	$-0.273330\pi$
$811$	30182.8	1.30686	0.653429	+	0.756988i	$0.273330\pi$
$812$	−147.938	−0.00639360
$813$	21590.3	0.931371
$814$	−19145.3	−0.824379
$815$	2066.93	0.0888361
$816$	6265.69	0.268803
$817$	−6810.13	−0.291623
$818$	−26686.1	−1.14066
$819$	5228.03	0.223055
$820$	−184.457	−0.00785553
$821$	−9221.29	−0.391992	−0.195996	−	0.980605i	$-0.562794\pi$
$821$	−9221.29	−0.391992	−0.195996	+	0.980605i	$0.562794\pi$
$822$	15106.3	0.640987
$823$	−5977.66	−0.253181	−0.126591	−	0.991955i	$-0.540403\pi$
$823$	−5977.66	−0.253181	−0.126591	+	0.991955i	$0.540403\pi$
$824$	−27610.8	−1.16732
$825$	22245.3	0.938764
$826$	32300.4	1.36062
$827$	−11659.1	−0.490236	−0.245118	−	0.969493i	$-0.578827\pi$
$827$	−11659.1	−0.490236	−0.245118	+	0.969493i	$0.578827\pi$
$828$	−67.4970	−0.00283295
$829$	−35538.6	−1.48891	−0.744454	−	0.667674i	$-0.767290\pi$
$829$	−35538.6	−1.48891	−0.744454	+	0.667674i	$0.767290\pi$
$830$	2090.91	0.0874416
$831$	23739.4	0.990986
$832$	−19721.1	−0.821762
$833$	3348.07	0.139260
$834$	−7649.48	−0.317602
$835$	−3018.28	−0.125092
$836$	−940.741	−0.0389189
$837$	−5259.16	−0.217184
$838$	−42252.3	−1.74174
$839$	6726.58	0.276791	0.138395	−	0.990377i	$-0.455806\pi$
$839$	6726.58	0.276791	0.138395	+	0.990377i	$0.455806\pi$
$840$	1700.10	0.0698321
$841$	841.000	0.0344828
$842$	43440.5	1.77798
$843$	−20005.6	−0.817355
$844$	1121.99	0.0457590
$845$	1285.20	0.0523223
$846$	2023.22	0.0822218
$847$	−36468.3	−1.47942
$848$	4400.06	0.178182
$849$	7382.72	0.298439
$850$	−11568.0	−0.466797
$851$	−2626.76	−0.105810
$852$	726.281	0.0292042
$853$	−31447.7	−1.26231	−0.631153	−	0.775658i	$-0.717418\pi$
$853$	−31447.7	−1.26231	−0.631153	+	0.775658i	$0.717418\pi$
$854$	19346.2	0.775190
$855$	673.867	0.0269541
$856$	2096.82	0.0837241
$857$	15554.9	0.620007	0.310003	−	0.950735i	$-0.399670\pi$
$857$	15554.9	0.620007	0.310003	+	0.950735i	$0.399670\pi$
$858$	−18673.2	−0.742999
$859$	21430.9	0.851238	0.425619	−	0.904902i	$-0.360056\pi$
$859$	21430.9	0.851238	0.425619	+	0.904902i	$0.360056\pi$
$860$	73.1494	0.00290044
$861$	16905.8	0.669160
$862$	18833.3	0.744161
$863$	36099.2	1.42391	0.711954	−	0.702226i	$-0.247811\pi$
$863$	36099.2	1.42391	0.711954	+	0.702226i	$0.247811\pi$
$864$	−398.170	−0.0156783
$865$	−4407.42	−0.173245
$866$	−12207.3	−0.479008
$867$	−11254.8	−0.440867
$868$	−993.652	−0.0388557
$869$	10509.1	0.410238
$870$	−378.499	−0.0147498
$871$	32615.0	1.26879
$872$	−24644.2	−0.957063
$873$	13052.5	0.506024
$874$	3037.61	0.117561
$875$	−6081.88	−0.234977
$876$	510.305	0.0196822
$877$	−27152.2	−1.04546	−0.522728	−	0.852499i	$-0.675086\pi$
$877$	−27152.2	−1.04546	−0.522728	+	0.852499i	$0.675086\pi$
$878$	29086.2	1.11801
$879$	17376.8	0.666788
$880$	−5824.42	−0.223115
$881$	18133.1	0.693438	0.346719	−	0.937969i	$-0.387296\pi$
$881$	18133.1	0.693438	0.346719	+	0.937969i	$0.387296\pi$
$882$	2449.36	0.0935083
$883$	32381.0	1.23410	0.617048	−	0.786926i	$-0.288329\pi$
$883$	32381.0	1.23410	0.617048	+	0.786926i	$0.288329\pi$
$884$	−412.606	−0.0156984
$885$	−3511.48	−0.133375
$886$	31880.8	1.20887
$887$	−13794.6	−0.522184	−0.261092	−	0.965314i	$-0.584083\pi$
$887$	−13794.6	−0.522184	−0.261092	+	0.965314i	$0.584083\pi$
$888$	−7902.48	−0.298637
$889$	−5348.31	−0.201773
$890$	433.609	0.0163310
$891$	−4901.69	−0.184302
$892$	1061.33	0.0398384
$893$	3868.89	0.144980
$894$	11686.1	0.437182
$895$	2035.25	0.0760120
$896$	21172.9	0.789440
$897$	−2561.99	−0.0953649
$898$	−17033.3	−0.632973
$899$	5648.73	0.209561
$900$	359.593	0.0133183
$901$	2446.79	0.0904711
$902$	−60383.2	−2.22898
$903$	−6704.24	−0.247069
$904$	−11916.1	−0.438410
$905$	−3882.27	−0.142598
$906$	20925.7	0.767340
$907$	−5460.00	−0.199886	−0.0999429	−	0.994993i	$-0.531866\pi$
$907$	−5460.00	−0.199886	−0.0999429	+	0.994993i	$0.531866\pi$
$908$	435.585	0.0159201
$909$	−8592.99	−0.313544
$910$	2527.21	0.0920617
$911$	−2924.67	−0.106365	−0.0531826	−	0.998585i	$-0.516937\pi$
$911$	−2924.67	−0.106365	−0.0531826	+	0.998585i	$0.516937\pi$
$912$	8765.39	0.318258
$913$	−29083.8	−1.05425
$914$	−4405.21	−0.159422
$915$	−2103.18	−0.0759879
$916$	187.973	0.00678036
$917$	1150.87	0.0414450
$918$	2548.98	0.0916435
$919$	−3379.35	−0.121300	−0.0606499	−	0.998159i	$-0.519317\pi$
$919$	−3379.35	−0.121300	−0.0606499	+	0.998159i	$0.519317\pi$
$920$	−833.131	−0.0298560
$921$	28844.6	1.03199
$922$	49068.5	1.75269
$923$	27567.5	0.983094
$924$	−926.113	−0.0329728
$925$	13994.2	0.497434
$926$	−22669.0	−0.804479
$927$	−10773.9	−0.381727
$928$	427.664	0.0151280
$929$	−49518.1	−1.74880	−0.874400	−	0.485206i	$-0.838745\pi$
$929$	−49518.1	−1.74880	−0.874400	+	0.485206i	$0.838745\pi$
$930$	−2542.26	−0.0896386
$931$	4683.78	0.164882
$932$	−1111.29	−0.0390574
$933$	9966.12	0.349706
$934$	−18466.9	−0.646953
$935$	−3238.85	−0.113285
$936$	−7707.61	−0.269157
$937$	−50907.5	−1.77489	−0.887447	−	0.460911i	$-0.847523\pi$
$937$	−50907.5	−1.77489	−0.887447	+	0.460911i	$0.847523\pi$
$938$	−38068.4	−1.32514
$939$	17661.6	0.613808
$940$	−41.5567	−0.00144195
$941$	−34614.9	−1.19916	−0.599582	−	0.800313i	$-0.704666\pi$
$941$	−34614.9	−1.19916	−0.599582	+	0.800313i	$0.704666\pi$
$942$	−26549.6	−0.918295
$943$	−8284.64	−0.286092
$944$	−45675.9	−1.57481
$945$	663.388	0.0228360
$946$	23945.9	0.822989
$947$	−31239.5	−1.07196	−0.535980	−	0.844231i	$-0.680058\pi$
$947$	−31239.5	−1.07196	−0.535980	+	0.844231i	$0.680058\pi$
$948$	169.879	0.00582006
$949$	19369.7	0.662558
$950$	−16183.0	−0.552680
$951$	−15799.9	−0.538744
$952$	12297.3	0.418653
$953$	4450.64	0.151281	0.0756403	−	0.997135i	$-0.475900\pi$
$953$	4450.64	0.151281	0.0756403	+	0.997135i	$0.475900\pi$
$954$	1790.01	0.0607481
$955$	1331.06	0.0451018
$956$	2209.88	0.0747621
$957$	5264.78	0.177833
$958$	31254.3	1.05405
$959$	28437.7	0.957561
$960$	−2502.42	−0.0841306
$961$	8149.72	0.273563
$962$	−11747.1	−0.393702
$963$	818.191	0.0273788
$964$	1095.32	0.0365954
$965$	−1329.76	−0.0443592
$966$	2990.37	0.0996001
$967$	−4615.26	−0.153482	−0.0767408	−	0.997051i	$-0.524451\pi$
$967$	−4615.26	−0.153482	−0.0767408	+	0.997051i	$0.524451\pi$
$968$	53764.7	1.78519
$969$	4874.27	0.161593
$970$	6309.50	0.208852
$971$	−36670.5	−1.21196	−0.605979	−	0.795481i	$-0.707218\pi$
$971$	−36670.5	−1.21196	−0.605979	+	0.795481i	$0.707218\pi$
$972$	−79.2356	−0.00261469
$973$	−14400.2	−0.474461
$974$	−25901.8	−0.852102
$975$	13649.1	0.448330
$976$	−27357.3	−0.897219
$977$	36407.5	1.19220	0.596100	−	0.802910i	$-0.296716\pi$
$977$	36407.5	1.19220	0.596100	+	0.802910i	$0.296716\pi$
$978$	10937.5	0.357611
$979$	−6031.34	−0.196897
$980$	−50.3098	−0.00163988
$981$	−9616.32	−0.312972
$982$	−34356.3	−1.11645
$983$	−271.680	−0.00881511	−0.00440755	−	0.999990i	$-0.501403\pi$
$983$	−271.680	−0.00881511	−0.00440755	+	0.999990i	$0.501403\pi$
$984$	−24923.9	−0.807465
$985$	484.660	0.0156777
$986$	−2737.79	−0.0884269
$987$	3808.73	0.122830
$988$	−577.214	−0.0185867
$989$	3285.40	0.105632
$990$	−2369.46	−0.0760670
$991$	−11518.5	−0.369221	−0.184610	−	0.982812i	$-0.559102\pi$
$991$	−11518.5	−0.369221	−0.184610	+	0.982812i	$0.559102\pi$
$992$	2872.48	0.0919369
$993$	13949.6	0.445798
$994$	−32177.0	−1.02675
$995$	−832.876	−0.0265366
$996$	−470.137	−0.0149567
$997$	46432.3	1.47495	0.737475	−	0.675375i	$-0.236018\pi$
$997$	46432.3	1.47495	0.737475	+	0.675375i	$0.236018\pi$
$998$	−39465.1	−1.25175
$999$	−3083.59	−0.0976582

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2001.4.a.h.1.14	✓	44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2001.4.a.h.1.14	✓	44	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)

\(f(q)\)	\(=\)	\(q-2.77019 q^{2} +3.00000 q^{3} -0.326072 q^{4} -1.57049 q^{5} -8.31056 q^{6} -15.6447 q^{7} +23.0648 q^{8} +9.00000 q^{9} +O(q^{10})\)	\(q-2.77019 q^{2} +3.00000 q^{3} -0.326072 q^{4} -1.57049 q^{5} -8.31056 q^{6} -15.6447 q^{7} +23.0648 q^{8} +9.00000 q^{9} +4.35056 q^{10} -60.5147 q^{11} -0.978217 q^{12} -37.1303 q^{13} +43.3387 q^{14} -4.71148 q^{15} -61.2851 q^{16} -34.0795 q^{17} -24.9317 q^{18} -47.6755 q^{19} +0.512095 q^{20} -46.9341 q^{21} +167.637 q^{22} +23.0000 q^{23} +69.1943 q^{24} -122.534 q^{25} +102.858 q^{26} +27.0000 q^{27} +5.10131 q^{28} -29.0000 q^{29} +13.0517 q^{30} -194.784 q^{31} -14.7470 q^{32} -181.544 q^{33} +94.4065 q^{34} +24.5699 q^{35} -2.93465 q^{36} -114.207 q^{37} +132.070 q^{38} -111.391 q^{39} -36.2231 q^{40} -360.202 q^{41} +130.016 q^{42} +142.844 q^{43} +19.7322 q^{44} -14.1345 q^{45} -63.7143 q^{46} -81.1505 q^{47} -183.855 q^{48} -98.2431 q^{49} +339.441 q^{50} -102.238 q^{51} +12.1072 q^{52} -71.7966 q^{53} -74.7950 q^{54} +95.0381 q^{55} -360.842 q^{56} -143.026 q^{57} +80.3354 q^{58} +745.302 q^{59} +1.53628 q^{60} +446.394 q^{61} +539.587 q^{62} -140.802 q^{63} +531.133 q^{64} +58.3129 q^{65} +502.911 q^{66} -878.393 q^{67} +11.1124 q^{68} +69.0000 q^{69} -68.0633 q^{70} -742.454 q^{71} +207.583 q^{72} -521.669 q^{73} +316.375 q^{74} -367.601 q^{75} +15.5457 q^{76} +946.736 q^{77} +308.573 q^{78} -173.662 q^{79} +96.2479 q^{80} +81.0000 q^{81} +997.826 q^{82} +480.607 q^{83} +15.3039 q^{84} +53.5216 q^{85} -395.703 q^{86} -87.0000 q^{87} -1395.76 q^{88} +99.6673 q^{89} +39.1551 q^{90} +580.892 q^{91} -7.49966 q^{92} -584.351 q^{93} +224.802 q^{94} +74.8741 q^{95} -44.2411 q^{96} +1450.27 q^{97} +272.151 q^{98} -544.633 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q + 6 q^{2} + 132 q^{3} + 210 q^{4} + 15 q^{5} + 18 q^{6} + 78 q^{7} + 12 q^{8} + 396 q^{9}+O(q^{10}) \) 44 * q + 6 * q^2 + 132 * q^3 + 210 * q^4 + 15 * q^5 + 18 * q^6 + 78 * q^7 + 12 * q^8 + 396 * q^9	\( 44 q + 6 q^{2} + 132 q^{3} + 210 q^{4} + 15 q^{5} + 18 q^{6} + 78 q^{7} + 12 q^{8} + 396 q^{9} + 214 q^{10} + 111 q^{11} + 630 q^{12} + 275 q^{13} + 104 q^{14} + 45 q^{15} + 1062 q^{16} - 58 q^{17} + 54 q^{18} + 331 q^{19} + 287 q^{20} + 234 q^{21} + 285 q^{22} + 1012 q^{23} + 36 q^{24} + 1903 q^{25} + 1084 q^{26} + 1188 q^{27} + 222 q^{28} - 1276 q^{29} + 642 q^{30} + 1394 q^{31} + 42 q^{32} + 333 q^{33} + 373 q^{34} + 567 q^{35} + 1890 q^{36} + 1229 q^{37} + 733 q^{38} + 825 q^{39} + 2483 q^{40} - 107 q^{41} + 312 q^{42} + 1165 q^{43} + 1639 q^{44} + 135 q^{45} + 138 q^{46} + 964 q^{47} + 3186 q^{48} + 4264 q^{49} + 495 q^{50} - 174 q^{51} + 2679 q^{52} - 380 q^{53} + 162 q^{54} + 1260 q^{55} + 2229 q^{56} + 993 q^{57} - 174 q^{58} + 897 q^{59} + 861 q^{60} + 2584 q^{61} + 3034 q^{62} + 702 q^{63} + 6866 q^{64} - 286 q^{65} + 855 q^{66} + 2277 q^{67} - 1554 q^{68} + 3036 q^{69} + 689 q^{70} + 4304 q^{71} + 108 q^{72} + 4712 q^{73} - 1005 q^{74} + 5709 q^{75} + 2877 q^{76} + 919 q^{77} + 3252 q^{78} + 3864 q^{79} + 2593 q^{80} + 3564 q^{81} + 3297 q^{82} - 540 q^{83} + 666 q^{84} + 6537 q^{85} + 3789 q^{86} - 3828 q^{87} + 1707 q^{88} - 331 q^{89} + 1926 q^{90} + 4311 q^{91} + 4830 q^{92} + 4182 q^{93} + 6189 q^{94} + 3267 q^{95} + 126 q^{96} + 5572 q^{97} + 2588 q^{98} + 999 q^{99}+O(q^{100}) \) 44 * q + 6 * q^2 + 132 * q^3 + 210 * q^4 + 15 * q^5 + 18 * q^6 + 78 * q^7 + 12 * q^8 + 396 * q^9 + 214 * q^10 + 111 * q^11 + 630 * q^12 + 275 * q^13 + 104 * q^14 + 45 * q^15 + 1062 * q^16 - 58 * q^17 + 54 * q^18 + 331 * q^19 + 287 * q^20 + 234 * q^21 + 285 * q^22 + 1012 * q^23 + 36 * q^24 + 1903 * q^25 + 1084 * q^26 + 1188 * q^27 + 222 * q^28 - 1276 * q^29 + 642 * q^30 + 1394 * q^31 + 42 * q^32 + 333 * q^33 + 373 * q^34 + 567 * q^35 + 1890 * q^36 + 1229 * q^37 + 733 * q^38 + 825 * q^39 + 2483 * q^40 - 107 * q^41 + 312 * q^42 + 1165 * q^43 + 1639 * q^44 + 135 * q^45 + 138 * q^46 + 964 * q^47 + 3186 * q^48 + 4264 * q^49 + 495 * q^50 - 174 * q^51 + 2679 * q^52 - 380 * q^53 + 162 * q^54 + 1260 * q^55 + 2229 * q^56 + 993 * q^57 - 174 * q^58 + 897 * q^59 + 861 * q^60 + 2584 * q^61 + 3034 * q^62 + 702 * q^63 + 6866 * q^64 - 286 * q^65 + 855 * q^66 + 2277 * q^67 - 1554 * q^68 + 3036 * q^69 + 689 * q^70 + 4304 * q^71 + 108 * q^72 + 4712 * q^73 - 1005 * q^74 + 5709 * q^75 + 2877 * q^76 + 919 * q^77 + 3252 * q^78 + 3864 * q^79 + 2593 * q^80 + 3564 * q^81 + 3297 * q^82 - 540 * q^83 + 666 * q^84 + 6537 * q^85 + 3789 * q^86 - 3828 * q^87 + 1707 * q^88 - 331 * q^89 + 1926 * q^90 + 4311 * q^91 + 4830 * q^92 + 4182 * q^93 + 6189 * q^94 + 3267 * q^95 + 126 * q^96 + 5572 * q^97 + 2588 * q^98 + 999 * q^99

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