LMFDB - Embedded newform 4001.2.a.b.1.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4001,2,Mod(1,4001)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4001, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("4001.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4001 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4001.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:	$31.9481458487$
Analytic rank:	$0$
Dimension:	$184$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
Character	$\chi$	$=$	4001.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.71583 q^{2} +2.95270 q^{3} +5.37572 q^{4} +2.81232 q^{5} -8.01903 q^{6} -1.71576 q^{7} -9.16786 q^{8} +5.71846 q^{9} +O(q^{10})$	\(q-2.71583 q^{2} +2.95270 q^{3} +5.37572 q^{4} +2.81232 q^{5} -8.01903 q^{6} -1.71576 q^{7} -9.16786 q^{8} +5.71846 q^{9} -7.63778 q^{10} +3.65762 q^{11} +15.8729 q^{12} -5.54091 q^{13} +4.65970 q^{14} +8.30396 q^{15} +14.1469 q^{16} -2.82348 q^{17} -15.5304 q^{18} +2.81693 q^{19} +15.1183 q^{20} -5.06613 q^{21} -9.93345 q^{22} +3.39196 q^{23} -27.0700 q^{24} +2.90916 q^{25} +15.0481 q^{26} +8.02681 q^{27} -9.22343 q^{28} +7.16279 q^{29} -22.5521 q^{30} +1.41203 q^{31} -20.0848 q^{32} +10.7999 q^{33} +7.66807 q^{34} -4.82527 q^{35} +30.7408 q^{36} +10.6344 q^{37} -7.65029 q^{38} -16.3607 q^{39} -25.7830 q^{40} +4.06503 q^{41} +13.7587 q^{42} +5.63493 q^{43} +19.6623 q^{44} +16.0822 q^{45} -9.21198 q^{46} -1.75490 q^{47} +41.7716 q^{48} -4.05617 q^{49} -7.90078 q^{50} -8.33689 q^{51} -29.7864 q^{52} +2.98389 q^{53} -21.7994 q^{54} +10.2864 q^{55} +15.7298 q^{56} +8.31756 q^{57} -19.4529 q^{58} -3.05256 q^{59} +44.6397 q^{60} -6.68573 q^{61} -3.83484 q^{62} -9.81150 q^{63} +26.2530 q^{64} -15.5828 q^{65} -29.3305 q^{66} -13.2281 q^{67} -15.1782 q^{68} +10.0155 q^{69} +13.1046 q^{70} -0.844264 q^{71} -52.4261 q^{72} +3.44574 q^{73} -28.8812 q^{74} +8.58989 q^{75} +15.1430 q^{76} -6.27558 q^{77} +44.4327 q^{78} +2.22690 q^{79} +39.7856 q^{80} +6.54541 q^{81} -11.0399 q^{82} -1.22741 q^{83} -27.2341 q^{84} -7.94053 q^{85} -15.3035 q^{86} +21.1496 q^{87} -33.5325 q^{88} -6.85737 q^{89} -43.6764 q^{90} +9.50686 q^{91} +18.2342 q^{92} +4.16932 q^{93} +4.76601 q^{94} +7.92211 q^{95} -59.3045 q^{96} +17.8276 q^{97} +11.0159 q^{98} +20.9159 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 184 q + 3 q^{2} + 28 q^{3} + 217 q^{4} + 15 q^{5} + 31 q^{6} + 49 q^{7} + 6 q^{8} + 210 q^{9}+O(q^{10}) $ 184 * q + 3 * q^2 + 28 * q^3 + 217 * q^4 + 15 * q^5 + 31 * q^6 + 49 * q^7 + 6 * q^8 + 210 * q^9	\( 184 q + 3 q^{2} + 28 q^{3} + 217 q^{4} + 15 q^{5} + 31 q^{6} + 49 q^{7} + 6 q^{8} + 210 q^{9} + 46 q^{10} + 25 q^{11} + 61 q^{12} + 52 q^{13} + 28 q^{14} + 59 q^{15} + 279 q^{16} + 16 q^{17} - 2 q^{18} + 86 q^{19} + 26 q^{20} + 22 q^{21} + 54 q^{22} + 55 q^{23} + 72 q^{24} + 241 q^{25} + 32 q^{26} + 97 q^{27} + 75 q^{28} + 27 q^{29} - 10 q^{30} + 276 q^{31} + 20 q^{33} + 122 q^{34} + 30 q^{35} + 278 q^{36} + 42 q^{37} + 14 q^{38} + 113 q^{39} + 115 q^{40} + 39 q^{41} + 15 q^{42} + 65 q^{43} + 32 q^{44} + 54 q^{45} + 65 q^{46} + 82 q^{47} + 117 q^{48} + 297 q^{49} + 4 q^{50} + 45 q^{51} + 136 q^{52} + 21 q^{53} + 93 q^{54} + 252 q^{55} + 74 q^{56} + 14 q^{57} + 54 q^{58} + 95 q^{59} + 58 q^{60} + 131 q^{61} + 14 q^{62} + 88 q^{63} + 368 q^{64} - 9 q^{65} + 52 q^{66} + 90 q^{67} + 27 q^{68} + 101 q^{69} + 18 q^{70} + 117 q^{71} - 15 q^{72} + 72 q^{73} + 7 q^{74} + 150 q^{75} + 148 q^{76} + 7 q^{77} + 22 q^{78} + 287 q^{79} + 43 q^{80} + 244 q^{81} + 86 q^{82} + 25 q^{83} + 14 q^{84} + 41 q^{85} + 25 q^{86} + 82 q^{87} + 115 q^{88} + 48 q^{89} + 78 q^{90} + 272 q^{91} + 69 q^{92} + 44 q^{93} + 161 q^{94} + 37 q^{95} + 129 q^{96} + 106 q^{97} - 46 q^{98} + 53 q^{99}+O(q^{100}) \) 184 * q + 3 * q^2 + 28 * q^3 + 217 * q^4 + 15 * q^5 + 31 * q^6 + 49 * q^7 + 6 * q^8 + 210 * q^9 + 46 * q^10 + 25 * q^11 + 61 * q^12 + 52 * q^13 + 28 * q^14 + 59 * q^15 + 279 * q^16 + 16 * q^17 - 2 * q^18 + 86 * q^19 + 26 * q^20 + 22 * q^21 + 54 * q^22 + 55 * q^23 + 72 * q^24 + 241 * q^25 + 32 * q^26 + 97 * q^27 + 75 * q^28 + 27 * q^29 - 10 * q^30 + 276 * q^31 + 20 * q^33 + 122 * q^34 + 30 * q^35 + 278 * q^36 + 42 * q^37 + 14 * q^38 + 113 * q^39 + 115 * q^40 + 39 * q^41 + 15 * q^42 + 65 * q^43 + 32 * q^44 + 54 * q^45 + 65 * q^46 + 82 * q^47 + 117 * q^48 + 297 * q^49 + 4 * q^50 + 45 * q^51 + 136 * q^52 + 21 * q^53 + 93 * q^54 + 252 * q^55 + 74 * q^56 + 14 * q^57 + 54 * q^58 + 95 * q^59 + 58 * q^60 + 131 * q^61 + 14 * q^62 + 88 * q^63 + 368 * q^64 - 9 * q^65 + 52 * q^66 + 90 * q^67 + 27 * q^68 + 101 * q^69 + 18 * q^70 + 117 * q^71 - 15 * q^72 + 72 * q^73 + 7 * q^74 + 150 * q^75 + 148 * q^76 + 7 * q^77 + 22 * q^78 + 287 * q^79 + 43 * q^80 + 244 * q^81 + 86 * q^82 + 25 * q^83 + 14 * q^84 + 41 * q^85 + 25 * q^86 + 82 * q^87 + 115 * q^88 + 48 * q^89 + 78 * q^90 + 272 * q^91 + 69 * q^92 + 44 * q^93 + 161 * q^94 + 37 * q^95 + 129 * q^96 + 106 * q^97 - 46 * q^98 + 53 * 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 $

$2$	−2.71583	−1.92038	−0.960190	−	0.279348i	$-0.909882\pi$
$2$	−2.71583	−1.92038	−0.960190	+	0.279348i	$0.909882\pi$
$3$	2.95270	1.70474	0.852372	−	0.522936i	$-0.175163\pi$
$3$	2.95270	1.70474	0.852372	+	0.522936i	$0.175163\pi$
$4$	5.37572	2.68786
$5$	2.81232	1.25771	0.628855	−	0.777523i	$-0.283524\pi$
$5$	2.81232	1.25771	0.628855	+	0.777523i	$0.283524\pi$
$6$	−8.01903	−3.27376
$7$	−1.71576	−0.648496	−0.324248	−	0.945972i	$-0.605111\pi$
$7$	−1.71576	−0.648496	−0.324248	+	0.945972i	$0.605111\pi$
$8$	−9.16786	−3.24133
$9$	5.71846	1.90615
$10$	−7.63778	−2.41528
$11$	3.65762	1.10281	0.551406	−	0.834237i	$-0.314091\pi$
$11$	3.65762	1.10281	0.551406	+	0.834237i	$0.314091\pi$
$12$	15.8729	4.58211
$13$	−5.54091	−1.53677	−0.768386	−	0.639987i	$-0.778940\pi$
$13$	−5.54091	−1.53677	−0.768386	+	0.639987i	$0.778940\pi$
$14$	4.65970	1.24536
$15$	8.30396	2.14407
$16$	14.1469	3.53672
$17$	−2.82348	−0.684793	−0.342397	−	0.939555i	$-0.611239\pi$
$17$	−2.82348	−0.684793	−0.342397	+	0.939555i	$0.611239\pi$
$18$	−15.5304	−3.66054
$19$	2.81693	0.646248	0.323124	−	0.946357i	$-0.395267\pi$
$19$	2.81693	0.646248	0.323124	+	0.946357i	$0.395267\pi$
$20$	15.1183	3.38054
$21$	−5.06613	−1.10552
$22$	−9.93345	−2.11782
$23$	3.39196	0.707273	0.353636	−	0.935383i	$-0.384945\pi$
$23$	3.39196	0.707273	0.353636	+	0.935383i	$0.384945\pi$
$24$	−27.0700	−5.52564
$25$	2.90916	0.581832
$26$	15.0481	2.95118
$27$	8.02681	1.54476
$28$	−9.22343	−1.74306
$29$	7.16279	1.33010	0.665048	−	0.746801i	$-0.268411\pi$
$29$	7.16279	1.33010	0.665048	+	0.746801i	$0.268411\pi$
$30$	−22.5521	−4.11743
$31$	1.41203	0.253609	0.126804	−	0.991928i	$-0.459528\pi$
$31$	1.41203	0.253609	0.126804	+	0.991928i	$0.459528\pi$
$32$	−20.0848	−3.55052
$33$	10.7999	1.88001
$34$	7.66807	1.31506
$35$	−4.82527	−0.815619
$36$	30.7408	5.12347
$37$	10.6344	1.74828	0.874141	−	0.485672i	$-0.161425\pi$
$37$	10.6344	1.74828	0.874141	+	0.485672i	$0.161425\pi$
$38$	−7.65029	−1.24104
$39$	−16.3607	−2.61980
$40$	−25.7830	−4.07665
$41$	4.06503	0.634850	0.317425	−	0.948283i	$-0.397182\pi$
$41$	4.06503	0.634850	0.317425	+	0.948283i	$0.397182\pi$
$42$	13.7587	2.12302
$43$	5.63493	0.859319	0.429659	−	0.902991i	$-0.358634\pi$
$43$	5.63493	0.859319	0.429659	+	0.902991i	$0.358634\pi$
$44$	19.6623	2.96420
$45$	16.0822	2.39739
$46$	−9.21198	−1.35823
$47$	−1.75490	−0.255979	−0.127989	−	0.991776i	$-0.540852\pi$
$47$	−1.75490	−0.255979	−0.127989	+	0.991776i	$0.540852\pi$
$48$	41.7716	6.02921
$49$	−4.05617	−0.579454
$50$	−7.90078	−1.11734
$51$	−8.33689	−1.16740
$52$	−29.7864	−4.13062
$53$	2.98389	0.409869	0.204934	−	0.978776i	$-0.434302\pi$
$53$	2.98389	0.409869	0.204934	+	0.978776i	$0.434302\pi$
$54$	−21.7994	−2.96653
$55$	10.2864	1.38702
$56$	15.7298	2.10199
$57$	8.31756	1.10169
$58$	−19.4529	−2.55429
$59$	−3.05256	−0.397409	−0.198705	−	0.980059i	$-0.563673\pi$
$59$	−3.05256	−0.397409	−0.198705	+	0.980059i	$0.563673\pi$
$60$	44.6397	5.76296
$61$	−6.68573	−0.856019	−0.428010	−	0.903774i	$-0.640785\pi$
$61$	−6.68573	−0.856019	−0.428010	+	0.903774i	$0.640785\pi$
$62$	−3.83484	−0.487025
$63$	−9.81150	−1.23613
$64$	26.2530	3.28163
$65$	−15.5828	−1.93281
$66$	−29.3305	−3.61034
$67$	−13.2281	−1.61607	−0.808033	−	0.589138i	$-0.799468\pi$
$67$	−13.2281	−1.61607	−0.808033	+	0.589138i	$0.799468\pi$
$68$	−15.1782	−1.84063
$69$	10.0155	1.20572
$70$	13.1046	1.56630
$71$	−0.844264	−0.100196	−0.0500979	−	0.998744i	$-0.515953\pi$
$71$	−0.844264	−0.100196	−0.0500979	+	0.998744i	$0.515953\pi$
$72$	−52.4261	−6.17847
$73$	3.44574	0.403293	0.201646	−	0.979458i	$-0.435371\pi$
$73$	3.44574	0.403293	0.201646	+	0.979458i	$0.435371\pi$
$74$	−28.8812	−3.35737
$75$	8.58989	0.991875
$76$	15.1430	1.73702
$77$	−6.27558	−0.715169
$78$	44.4327	5.03102
$79$	2.22690	0.250545	0.125273	−	0.992122i	$-0.460019\pi$
$79$	2.22690	0.250545	0.125273	+	0.992122i	$0.460019\pi$
$80$	39.7856	4.44817
$81$	6.54541	0.727268
$82$	−11.0399	−1.21915
$83$	−1.22741	−0.134726	−0.0673630	−	0.997729i	$-0.521459\pi$
$83$	−1.22741	−0.134726	−0.0673630	+	0.997729i	$0.521459\pi$
$84$	−27.2341	−2.97148
$85$	−7.94053	−0.861271
$86$	−15.3035	−1.65022
$87$	21.1496	2.26747
$88$	−33.5325	−3.57458
$89$	−6.85737	−0.726880	−0.363440	−	0.931618i	$-0.618398\pi$
$89$	−6.85737	−0.726880	−0.363440	+	0.931618i	$0.618398\pi$
$90$	−43.6764	−4.60389
$91$	9.50686	0.996589
$92$	18.2342	1.90105
$93$	4.16932	0.432338
$94$	4.76601	0.491576
$95$	7.92211	0.812792
$96$	−59.3045	−6.05274
$97$	17.8276	1.81011	0.905057	−	0.425290i	$-0.139828\pi$
$97$	17.8276	1.81011	0.905057	+	0.425290i	$0.139828\pi$
$98$	11.0159	1.11277
$99$	20.9159	2.10213
$100$	15.6388	1.56388
$101$	5.32425	0.529783	0.264891	−	0.964278i	$-0.414664\pi$
$101$	5.32425	0.529783	0.264891	+	0.964278i	$0.414664\pi$
$102$	22.6415	2.24185
$103$	16.1650	1.59279	0.796394	−	0.604779i	$-0.206738\pi$
$103$	16.1650	1.59279	0.796394	+	0.604779i	$0.206738\pi$
$104$	50.7983	4.98118
$105$	−14.2476	−1.39042
$106$	−8.10373	−0.787104
$107$	−8.94141	−0.864399	−0.432199	−	0.901778i	$-0.642262\pi$
$107$	−8.94141	−0.864399	−0.432199	+	0.901778i	$0.642262\pi$
$108$	43.1499	4.15210
$109$	−2.22899	−0.213499	−0.106749	−	0.994286i	$-0.534044\pi$
$109$	−2.22899	−0.213499	−0.106749	+	0.994286i	$0.534044\pi$
$110$	−27.9361	−2.66360
$111$	31.4002	2.98037
$112$	−24.2726	−2.29355
$113$	−9.07479	−0.853684	−0.426842	−	0.904326i	$-0.640374\pi$
$113$	−9.07479	−0.853684	−0.426842	+	0.904326i	$0.640374\pi$
$114$	−22.5890	−2.11566
$115$	9.53929	0.889543
$116$	38.5051	3.57511
$117$	−31.6855	−2.92932
$118$	8.29023	0.763177
$119$	4.84440	0.444086
$120$	−76.1295	−6.94964
$121$	2.37815	0.216196
$122$	18.1573	1.64388
$123$	12.0028	1.08226
$124$	7.59069	0.681664
$125$	−5.88011	−0.525933
$126$	26.6463	2.37384
$127$	13.9986	1.24217	0.621086	−	0.783743i	$-0.286692\pi$
$127$	13.9986	1.24217	0.621086	+	0.783743i	$0.286692\pi$
$128$	−31.1291	−2.75145
$129$	16.6383	1.46492
$130$	42.3203	3.71173
$131$	19.4044	1.69537	0.847684	−	0.530502i	$-0.177996\pi$
$131$	19.4044	1.69537	0.847684	+	0.530502i	$0.177996\pi$
$132$	58.0570	5.05321
$133$	−4.83317	−0.419089
$134$	35.9251	3.10346
$135$	22.5740	1.94286
$136$	25.8852	2.21964
$137$	−6.09324	−0.520580	−0.260290	−	0.965530i	$-0.583818\pi$
$137$	−6.09324	−0.520580	−0.260290	+	0.965530i	$0.583818\pi$
$138$	−27.2003	−2.31544
$139$	5.01392	0.425275	0.212638	−	0.977131i	$-0.431795\pi$
$139$	5.01392	0.425275	0.212638	+	0.977131i	$0.431795\pi$
$140$	−25.9393	−2.19227
$141$	−5.18170	−0.436378
$142$	2.29288	0.192414
$143$	−20.2665	−1.69477
$144$	80.8985	6.74154
$145$	20.1441	1.67287
$146$	−9.35802	−0.774475
$147$	−11.9767	−0.987820
$148$	57.1675	4.69914
$149$	17.3213	1.41902	0.709509	−	0.704697i	$-0.248917\pi$
$149$	17.3213	1.41902	0.709509	+	0.704697i	$0.248917\pi$
$150$	−23.3287	−1.90478
$151$	−11.4933	−0.935308	−0.467654	−	0.883912i	$-0.654901\pi$
$151$	−11.4933	−0.935308	−0.467654	+	0.883912i	$0.654901\pi$
$152$	−25.8252	−2.09470
$153$	−16.1459	−1.30532
$154$	17.0434	1.37340
$155$	3.97110	0.318966
$156$	−87.9503	−7.04166
$157$	−6.86774	−0.548106	−0.274053	−	0.961715i	$-0.588364\pi$
$157$	−6.86774	−0.548106	−0.274053	+	0.961715i	$0.588364\pi$
$158$	−6.04786	−0.481142
$159$	8.81054	0.698722
$160$	−56.4849	−4.46553
$161$	−5.81978	−0.458663
$162$	−17.7762	−1.39663
$163$	−2.51271	−0.196810	−0.0984052	−	0.995146i	$-0.531374\pi$
$163$	−2.51271	−0.196810	−0.0984052	+	0.995146i	$0.531374\pi$
$164$	21.8524	1.70639
$165$	30.3727	2.36451
$166$	3.33344	0.258725
$167$	−22.4497	−1.73721	−0.868606	−	0.495503i	$-0.834984\pi$
$167$	−22.4497	−1.73721	−0.868606	+	0.495503i	$0.834984\pi$
$168$	46.4455	3.58335
$169$	17.7017	1.36167
$170$	21.5651	1.65397
$171$	16.1085	1.23185
$172$	30.2918	2.30973
$173$	13.2760	1.00936	0.504679	−	0.863307i	$-0.331611\pi$
$173$	13.2760	1.00936	0.504679	+	0.863307i	$0.331611\pi$
$174$	−57.4386	−4.35441
$175$	−4.99142	−0.377316
$176$	51.7439	3.90034
$177$	−9.01331	−0.677482
$178$	18.6234	1.39589
$179$	8.42656	0.629831	0.314915	−	0.949120i	$-0.398024\pi$
$179$	8.42656	0.629831	0.314915	+	0.949120i	$0.398024\pi$
$180$	86.4531	6.44384
$181$	5.77855	0.429516	0.214758	−	0.976667i	$-0.431104\pi$
$181$	5.77855	0.429516	0.214758	+	0.976667i	$0.431104\pi$
$182$	−25.8190	−1.91383
$183$	−19.7410	−1.45929
$184$	−31.0970	−2.29250
$185$	29.9073	2.19883
$186$	−11.3231	−0.830253
$187$	−10.3272	−0.755199
$188$	−9.43385	−0.688034
$189$	−13.7721	−1.00177
$190$	−21.5151	−1.56087
$191$	−14.8363	−1.07352	−0.536759	−	0.843735i	$-0.680352\pi$
$191$	−14.8363	−1.07352	−0.536759	+	0.843735i	$0.680352\pi$
$192$	77.5175	5.59434
$193$	27.0321	1.94582	0.972908	−	0.231192i	$-0.0742624\pi$
$193$	27.0321	1.94582	0.972908	+	0.231192i	$0.0742624\pi$
$194$	−48.4166	−3.47611
$195$	−46.0115	−3.29495
$196$	−21.8048	−1.55749
$197$	−24.9267	−1.77595	−0.887976	−	0.459890i	$-0.847889\pi$
$197$	−24.9267	−1.77595	−0.887976	+	0.459890i	$0.847889\pi$
$198$	−56.8041	−4.03689
$199$	18.9616	1.34415	0.672075	−	0.740483i	$-0.265403\pi$
$199$	18.9616	1.34415	0.672075	+	0.740483i	$0.265403\pi$
$200$	−26.6708	−1.88591
$201$	−39.0586	−2.75498
$202$	−14.4597	−1.01738
$203$	−12.2896	−0.862561
$204$	−44.8167	−3.13780
$205$	11.4322	0.798457
$206$	−43.9014	−3.05876
$207$	19.3968	1.34817
$208$	−78.3867	−5.43514
$209$	10.3032	0.712690
$210$	38.6940	2.67014
$211$	16.8967	1.16322	0.581609	−	0.813469i	$-0.302423\pi$
$211$	16.8967	1.16322	0.581609	+	0.813469i	$0.302423\pi$
$212$	16.0405	1.10167
$213$	−2.49286	−0.170808
$214$	24.2833	1.65997
$215$	15.8472	1.08077
$216$	−73.5887	−5.00708
$217$	−2.42271	−0.164464
$218$	6.05356	0.409999
$219$	10.1742	0.687511
$220$	55.2968	3.72811
$221$	15.6446	1.05237
$222$	−85.2775	−5.72345
$223$	−9.15887	−0.613323	−0.306662	−	0.951819i	$-0.599212\pi$
$223$	−9.15887	−0.613323	−0.306662	+	0.951819i	$0.599212\pi$
$224$	34.4607	2.30250
$225$	16.6359	1.10906
$226$	24.6455	1.63940
$227$	−25.1501	−1.66927	−0.834634	−	0.550804i	$-0.814321\pi$
$227$	−25.1501	−1.66927	−0.834634	+	0.550804i	$0.814321\pi$
$228$	44.7128	2.96118
$229$	26.6281	1.75963	0.879816	−	0.475315i	$-0.157666\pi$
$229$	26.6281	1.75963	0.879816	+	0.475315i	$0.157666\pi$
$230$	−25.9071	−1.70826
$231$	−18.5299	−1.21918
$232$	−65.6674	−4.31128
$233$	−23.7779	−1.55774	−0.778870	−	0.627186i	$-0.784207\pi$
$233$	−23.7779	−1.55774	−0.778870	+	0.627186i	$0.784207\pi$
$234$	86.0523	5.62541
$235$	−4.93535	−0.321947
$236$	−16.4097	−1.06818
$237$	6.57536	0.427116
$238$	−13.1566	−0.852813
$239$	4.75724	0.307720	0.153860	−	0.988093i	$-0.450829\pi$
$239$	4.75724	0.307720	0.153860	+	0.988093i	$0.450829\pi$
$240$	117.475	7.58299
$241$	−6.77899	−0.436673	−0.218337	−	0.975874i	$-0.570063\pi$
$241$	−6.77899	−0.436673	−0.218337	+	0.975874i	$0.570063\pi$
$242$	−6.45866	−0.415178
$243$	−4.75376	−0.304954
$244$	−35.9406	−2.30086
$245$	−11.4073	−0.728784
$246$	−32.5976	−2.07835
$247$	−15.6083	−0.993135
$248$	−12.9453	−0.822029
$249$	−3.62418	−0.229673
$250$	15.9694	1.00999
$251$	3.56812	0.225218	0.112609	−	0.993639i	$-0.464079\pi$
$251$	3.56812	0.225218	0.112609	+	0.993639i	$0.464079\pi$
$252$	−52.7438	−3.32255
$253$	12.4065	0.779989
$254$	−38.0177	−2.38544
$255$	−23.4460	−1.46825
$256$	32.0353	2.00220
$257$	20.3210	1.26759	0.633796	−	0.773500i	$-0.281496\pi$
$257$	20.3210	1.26759	0.633796	+	0.773500i	$0.281496\pi$
$258$	−45.1867	−2.81320
$259$	−18.2460	−1.13375
$260$	−83.7689	−5.19512
$261$	40.9601	2.53537
$262$	−52.6989	−3.25575
$263$	24.3778	1.50320	0.751600	−	0.659619i	$-0.229282\pi$
$263$	24.3778	1.50320	0.751600	+	0.659619i	$0.229282\pi$
$264$	−99.0116	−6.09374
$265$	8.39166	0.515496
$266$	13.1260	0.804810
$267$	−20.2478	−1.23914
$268$	−71.1103	−4.34376
$269$	22.1062	1.34784	0.673919	−	0.738805i	$-0.264610\pi$
$269$	22.1062	1.34784	0.673919	+	0.738805i	$0.264610\pi$
$270$	−61.3070	−3.73103
$271$	−15.4232	−0.936893	−0.468447	−	0.883492i	$-0.655186\pi$
$271$	−15.4232	−0.936893	−0.468447	+	0.883492i	$0.655186\pi$
$272$	−39.9434	−2.42193
$273$	28.0709	1.69893
$274$	16.5482	0.999712
$275$	10.6406	0.641652
$276$	53.8403	3.24080
$277$	−8.17413	−0.491136	−0.245568	−	0.969379i	$-0.578974\pi$
$277$	−8.17413	−0.491136	−0.245568	+	0.969379i	$0.578974\pi$
$278$	−13.6169	−0.816690
$279$	8.07466	0.483417
$280$	44.2374	2.64369
$281$	15.7815	0.941443	0.470721	−	0.882282i	$-0.343994\pi$
$281$	15.7815	0.941443	0.470721	+	0.882282i	$0.343994\pi$
$282$	14.0726	0.838011
$283$	−25.8041	−1.53390	−0.766948	−	0.641709i	$-0.778226\pi$
$283$	−25.8041	−1.53390	−0.766948	+	0.641709i	$0.778226\pi$
$284$	−4.53853	−0.269312
$285$	23.3917	1.38560
$286$	55.0404	3.25460
$287$	−6.97460	−0.411698
$288$	−114.854	−6.76784
$289$	−9.02798	−0.531058
$290$	−54.7078	−3.21255
$291$	52.6395	3.08578
$292$	18.5233	1.08399
$293$	−20.1442	−1.17683	−0.588417	−	0.808558i	$-0.700249\pi$
$293$	−20.1442	−1.17683	−0.588417	+	0.808558i	$0.700249\pi$
$294$	32.5266	1.89699
$295$	−8.58479	−0.499826
$296$	−97.4946	−5.66676
$297$	29.3590	1.70358
$298$	−47.0417	−2.72505
$299$	−18.7945	−1.08692
$300$	46.1768	2.66602
$301$	−9.66818	−0.557265
$302$	31.2137	1.79615
$303$	15.7209	0.903144
$304$	39.8508	2.28560
$305$	−18.8024	−1.07662
$306$	43.8496	2.50671
$307$	17.7020	1.01031	0.505154	−	0.863029i	$-0.331436\pi$
$307$	17.7020	1.01031	0.505154	+	0.863029i	$0.331436\pi$
$308$	−33.7358	−1.92227
$309$	47.7305	2.71529
$310$	−10.7848	−0.612536
$311$	−28.8578	−1.63638	−0.818188	−	0.574951i	$-0.805021\pi$
$311$	−28.8578	−1.63638	−0.818188	+	0.574951i	$0.805021\pi$
$312$	149.992	8.49164
$313$	−12.9829	−0.733836	−0.366918	−	0.930253i	$-0.619587\pi$
$313$	−12.9829	−0.733836	−0.366918	+	0.930253i	$0.619587\pi$
$314$	18.6516	1.05257
$315$	−27.5931	−1.55469
$316$	11.9712	0.673430
$317$	−20.0248	−1.12471	−0.562353	−	0.826898i	$-0.690104\pi$
$317$	−20.0248	−1.12471	−0.562353	+	0.826898i	$0.690104\pi$
$318$	−23.9279	−1.34181
$319$	26.1987	1.46685
$320$	73.8320	4.12734
$321$	−26.4013	−1.47358
$322$	15.8055	0.880808
$323$	−7.95353	−0.442546
$324$	35.1863	1.95479
$325$	−16.1194	−0.894143
$326$	6.82408	0.377951
$327$	−6.58156	−0.363961
$328$	−37.2676	−2.05776
$329$	3.01098	0.166001
$330$	−82.4870	−4.54076
$331$	−27.5209	−1.51269	−0.756343	−	0.654176i	$-0.773016\pi$
$331$	−27.5209	−1.51269	−0.756343	+	0.654176i	$0.773016\pi$
$332$	−6.59822	−0.362124
$333$	60.8123	3.33250
$334$	60.9696	3.33611
$335$	−37.2016	−2.03254
$336$	−71.6699	−3.90992
$337$	23.2219	1.26498	0.632488	−	0.774570i	$-0.282034\pi$
$337$	23.2219	1.26498	0.632488	+	0.774570i	$0.282034\pi$
$338$	−48.0747	−2.61492
$339$	−26.7952	−1.45531
$340$	−42.6860	−2.31497
$341$	5.16468	0.279683
$342$	−43.7479	−2.36562
$343$	18.9697	1.02427
$344$	−51.6603	−2.78534
$345$	28.1667	1.51644
$346$	−36.0554	−1.93835
$347$	20.8700	1.12036	0.560181	−	0.828371i	$-0.310732\pi$
$347$	20.8700	1.12036	0.560181	+	0.828371i	$0.310732\pi$
$348$	113.694	6.09465
$349$	15.7027	0.840544	0.420272	−	0.907398i	$-0.361935\pi$
$349$	15.7027	0.840544	0.420272	+	0.907398i	$0.361935\pi$
$350$	13.5558	0.724589
$351$	−44.4758	−2.37394
$352$	−73.4625	−3.91556
$353$	−21.7834	−1.15941	−0.579706	−	0.814826i	$-0.696832\pi$
$353$	−21.7834	−1.15941	−0.579706	+	0.814826i	$0.696832\pi$
$354$	24.4786	1.30102
$355$	−2.37434	−0.126017
$356$	−36.8633	−1.95375
$357$	14.3041	0.757052
$358$	−22.8851	−1.20951
$359$	−3.63583	−0.191892	−0.0959460	−	0.995387i	$-0.530588\pi$
$359$	−3.63583	−0.191892	−0.0959460	+	0.995387i	$0.530588\pi$
$360$	−147.439	−7.77072
$361$	−11.0649	−0.582364
$362$	−15.6935	−0.824834
$363$	7.02199	0.368559
$364$	51.1062	2.67869
$365$	9.69052	0.507225
$366$	53.6131	2.80240
$367$	10.1501	0.529829	0.264914	−	0.964272i	$-0.414656\pi$
$367$	10.1501	0.529829	0.264914	+	0.964272i	$0.414656\pi$
$368$	47.9857	2.50143
$369$	23.2457	1.21012
$370$	−81.2231	−4.22259
$371$	−5.11963	−0.265798
$372$	22.4131	1.16206
$373$	−25.8142	−1.33661	−0.668304	−	0.743889i	$-0.732979\pi$
$373$	−25.8142	−1.33661	−0.668304	+	0.743889i	$0.732979\pi$
$374$	28.0469	1.45027
$375$	−17.3622	−0.896582
$376$	16.0887	0.829711
$377$	−39.6883	−2.04405
$378$	37.4025	1.92378
$379$	−31.6525	−1.62588	−0.812941	−	0.582346i	$-0.802135\pi$
$379$	−31.6525	−1.62588	−0.812941	+	0.582346i	$0.802135\pi$
$380$	42.5870	2.18467
$381$	41.3336	2.11758
$382$	40.2929	2.06156
$383$	−3.60025	−0.183964	−0.0919821	−	0.995761i	$-0.529320\pi$
$383$	−3.60025	−0.183964	−0.0919821	+	0.995761i	$0.529320\pi$
$384$	−91.9151	−4.69052
$385$	−17.6490	−0.899475
$386$	−73.4146	−3.73671
$387$	32.2231	1.63799
$388$	95.8359	4.86533
$389$	−37.0436	−1.87819	−0.939093	−	0.343664i	$-0.888332\pi$
$389$	−37.0436	−1.87819	−0.939093	+	0.343664i	$0.888332\pi$
$390$	124.959	6.32755
$391$	−9.57712	−0.484336
$392$	37.1865	1.87820
$393$	57.2954	2.89017
$394$	67.6965	3.41050
$395$	6.26275	0.315113
$396$	112.438	5.65023
$397$	36.9316	1.85355	0.926773	−	0.375622i	$-0.122571\pi$
$397$	36.9316	1.85355	0.926773	+	0.375622i	$0.122571\pi$
$398$	−51.4963	−2.58128
$399$	−14.2709	−0.714439
$400$	41.1556	2.05778
$401$	12.7490	0.636653	0.318327	−	0.947981i	$-0.396879\pi$
$401$	12.7490	0.636653	0.318327	+	0.947981i	$0.396879\pi$
$402$	106.076	5.29061
$403$	−7.82395	−0.389739
$404$	28.6217	1.42398
$405$	18.4078	0.914692
$406$	33.3764	1.65645
$407$	38.8965	1.92803
$408$	76.4314	3.78392
$409$	29.6555	1.46637	0.733186	−	0.680028i	$-0.238033\pi$
$409$	29.6555	1.46637	0.733186	+	0.680028i	$0.238033\pi$
$410$	−31.0478	−1.53334
$411$	−17.9915	−0.887456
$412$	86.8986	4.28119
$413$	5.23745	0.257718
$414$	−52.6783	−2.58900
$415$	−3.45188	−0.169446
$416$	111.288	5.45634
$417$	14.8046	0.724986
$418$	−27.9818	−1.36864
$419$	−4.89842	−0.239304	−0.119652	−	0.992816i	$-0.538178\pi$
$419$	−4.89842	−0.239304	−0.119652	+	0.992816i	$0.538178\pi$
$420$	−76.5910	−3.73726
$421$	19.5305	0.951860	0.475930	−	0.879483i	$-0.342112\pi$
$421$	19.5305	0.951860	0.475930	+	0.879483i	$0.342112\pi$
$422$	−45.8885	−2.23382
$423$	−10.0353	−0.487934
$424$	−27.3559	−1.32852
$425$	−8.21395	−0.398435
$426$	6.77019	0.328017
$427$	11.4711	0.555125
$428$	−48.0665	−2.32338
$429$	−59.8410	−2.88915
$430$	−43.0384	−2.07550
$431$	−12.7328	−0.613318	−0.306659	−	0.951819i	$-0.599211\pi$
$431$	−12.7328	−0.613318	−0.306659	+	0.951819i	$0.599211\pi$
$432$	113.554	5.46339
$433$	−6.85055	−0.329217	−0.164608	−	0.986359i	$-0.552636\pi$
$433$	−6.85055	−0.329217	−0.164608	+	0.986359i	$0.552636\pi$
$434$	6.57966	0.315834
$435$	59.4795	2.85182
$436$	−11.9824	−0.573855
$437$	9.55491	0.457073
$438$	−27.6315	−1.32028
$439$	24.3037	1.15995	0.579976	−	0.814633i	$-0.303062\pi$
$439$	24.3037	1.15995	0.579976	+	0.814633i	$0.303062\pi$
$440$	−94.3043	−4.49578
$441$	−23.1951	−1.10453
$442$	−42.4881	−2.02095
$443$	−33.6172	−1.59720	−0.798600	−	0.601862i	$-0.794426\pi$
$443$	−33.6172	−1.59720	−0.798600	+	0.601862i	$0.794426\pi$
$444$	168.799	8.01083
$445$	−19.2851	−0.914204
$446$	24.8739	1.17781
$447$	51.1447	2.41906
$448$	−45.0439	−2.12812
$449$	3.66652	0.173034	0.0865169	−	0.996250i	$-0.472426\pi$
$449$	3.66652	0.173034	0.0865169	+	0.996250i	$0.472426\pi$
$450$	−45.1803	−2.12982
$451$	14.8683	0.700121
$452$	−48.7835	−2.29458
$453$	−33.9362	−1.59446
$454$	68.3032	3.20563
$455$	26.7364	1.25342
$456$	−76.2542	−3.57093
$457$	−13.9056	−0.650474	−0.325237	−	0.945632i	$-0.605444\pi$
$457$	−13.9056	−0.650474	−0.325237	+	0.945632i	$0.605444\pi$
$458$	−72.3172	−3.37916
$459$	−22.6635	−1.05784
$460$	51.2805	2.39097
$461$	25.7272	1.19823	0.599117	−	0.800662i	$-0.295518\pi$
$461$	25.7272	1.19823	0.599117	+	0.800662i	$0.295518\pi$
$462$	50.3241	2.34129
$463$	−8.24942	−0.383383	−0.191692	−	0.981455i	$-0.561397\pi$
$463$	−8.24942	−0.383383	−0.191692	+	0.981455i	$0.561397\pi$
$464$	101.331	4.70418
$465$	11.7255	0.543756
$466$	64.5765	2.99145
$467$	20.3318	0.940842	0.470421	−	0.882442i	$-0.344102\pi$
$467$	20.3318	0.940842	0.470421	+	0.882442i	$0.344102\pi$
$468$	−170.332	−7.87360
$469$	22.6962	1.04801
$470$	13.4035	0.618260
$471$	−20.2784	−0.934380
$472$	27.9855	1.28813
$473$	20.6104	0.947668
$474$	−17.8575	−0.820224
$475$	8.19490	0.376008
$476$	26.0421	1.19364
$477$	17.0633	0.781273
$478$	−12.9198	−0.590940
$479$	−25.4481	−1.16276	−0.581378	−	0.813634i	$-0.697486\pi$
$479$	−25.4481	−1.16276	−0.581378	+	0.813634i	$0.697486\pi$
$480$	−166.783	−7.61258
$481$	−58.9242	−2.68671
$482$	18.4106	0.838578
$483$	−17.1841	−0.781904
$484$	12.7843	0.581104
$485$	50.1368	2.27660
$486$	12.9104	0.585628
$487$	33.5049	1.51825	0.759125	−	0.650944i	$-0.225627\pi$
$487$	33.5049	1.51825	0.759125	+	0.650944i	$0.225627\pi$
$488$	61.2938	2.77464
$489$	−7.41928	−0.335511
$490$	30.9802	1.39954
$491$	24.0563	1.08564	0.542822	−	0.839848i	$-0.317356\pi$
$491$	24.0563	1.08564	0.542822	+	0.839848i	$0.317356\pi$
$492$	64.5237	2.90895
$493$	−20.2240	−0.910841
$494$	42.3896	1.90720
$495$	58.8224	2.64387
$496$	19.9759	0.896944
$497$	1.44855	0.0649765
$498$	9.84265	0.441060
$499$	5.88501	0.263449	0.131725	−	0.991286i	$-0.457949\pi$
$499$	5.88501	0.263449	0.131725	+	0.991286i	$0.457949\pi$
$500$	−31.6098	−1.41363
$501$	−66.2874	−2.96150
$502$	−9.69041	−0.432504
$503$	15.2084	0.678109	0.339055	−	0.940767i	$-0.389893\pi$
$503$	15.2084	0.678109	0.339055	+	0.940767i	$0.389893\pi$
$504$	89.9504	4.00671
$505$	14.9735	0.666312
$506$	−33.6939	−1.49788
$507$	52.2678	2.32129
$508$	75.2523	3.33878
$509$	−24.1779	−1.07167	−0.535834	−	0.844323i	$-0.680003\pi$
$509$	−24.1779	−1.07167	−0.535834	+	0.844323i	$0.680003\pi$
$510$	63.6753	2.81959
$511$	−5.91205	−0.261534
$512$	−24.7439	−1.09354
$513$	22.6110	0.998298
$514$	−55.1884	−2.43426
$515$	45.4613	2.00326
$516$	89.4427	3.93750
$517$	−6.41875	−0.282296
$518$	49.5531	2.17724
$519$	39.2002	1.72070
$520$	142.861	6.26488
$521$	−28.8546	−1.26414	−0.632072	−	0.774909i	$-0.717795\pi$
$521$	−28.8546	−1.26414	−0.632072	+	0.774909i	$0.717795\pi$
$522$	−111.241	−4.86887
$523$	19.0566	0.833287	0.416643	−	0.909070i	$-0.363206\pi$
$523$	19.0566	0.833287	0.416643	+	0.909070i	$0.363206\pi$
$524$	104.312	4.55691
$525$	−14.7382	−0.643227
$526$	−66.2059	−2.88671
$527$	−3.98684	−0.173670
$528$	152.784	6.64909
$529$	−11.4946	−0.499765
$530$	−22.7903	−0.989948
$531$	−17.4559	−0.757524
$532$	−25.9817	−1.12645
$533$	−22.5239	−0.975620
$534$	54.9895	2.37963
$535$	−25.1461	−1.08716
$536$	121.273	5.23820
$537$	24.8811	1.07370
$538$	−60.0366	−2.58836
$539$	−14.8359	−0.639029
$540$	121.351	5.22213
$541$	20.6455	0.887621	0.443811	−	0.896121i	$-0.353626\pi$
$541$	20.6455	0.887621	0.443811	+	0.896121i	$0.353626\pi$
$542$	41.8868	1.79919
$543$	17.0623	0.732215
$544$	56.7089	2.43138
$545$	−6.26865	−0.268520
$546$	−76.2358	−3.26259
$547$	−46.4380	−1.98555	−0.992773	−	0.120008i	$-0.961708\pi$
$547$	−46.4380	−1.98555	−0.992773	+	0.120008i	$0.961708\pi$
$548$	−32.7555	−1.39925
$549$	−38.2321	−1.63170
$550$	−28.8980	−1.23222
$551$	20.1771	0.859571
$552$	−91.8203	−3.90813
$553$	−3.82081	−0.162478
$554$	22.1995	0.943167
$555$	88.3075	3.74844
$556$	26.9534	1.14308
$557$	−25.5779	−1.08377	−0.541886	−	0.840452i	$-0.682289\pi$
$557$	−25.5779	−1.08377	−0.541886	+	0.840452i	$0.682289\pi$
$558$	−21.9294	−0.928345
$559$	−31.2226	−1.32058
$560$	−68.2625	−2.88462
$561$	−30.4931	−1.28742
$562$	−42.8597	−1.80793
$563$	7.63528	0.321789	0.160894	−	0.986972i	$-0.448562\pi$
$563$	7.63528	0.321789	0.160894	+	0.986972i	$0.448562\pi$
$564$	−27.8554	−1.17292
$565$	−25.5212	−1.07369
$566$	70.0796	2.94566
$567$	−11.2303	−0.471630
$568$	7.74010	0.324767
$569$	2.02462	0.0848766	0.0424383	−	0.999099i	$-0.486487\pi$
$569$	2.02462	0.0848766	0.0424383	+	0.999099i	$0.486487\pi$
$570$	−63.5277	−2.66088
$571$	−0.614429	−0.0257131	−0.0128565	−	0.999917i	$-0.504092\pi$
$571$	−0.614429	−0.0257131	−0.0128565	+	0.999917i	$0.504092\pi$
$572$	−108.947	−4.55530
$573$	−43.8073	−1.83008
$574$	18.9418	0.790616
$575$	9.86776	0.411514
$576$	150.127	6.25529
$577$	−10.5013	−0.437176	−0.218588	−	0.975817i	$-0.570145\pi$
$577$	−10.5013	−0.437176	−0.218588	+	0.975817i	$0.570145\pi$
$578$	24.5184	1.01983
$579$	79.8179	3.31712
$580$	108.289	4.49645
$581$	2.10594	0.0873692
$582$	−142.960	−5.92587
$583$	10.9139	0.452009
$584$	−31.5900	−1.30720
$585$	−89.1098	−3.68424
$586$	54.7080	2.25997
$587$	−28.3464	−1.16998	−0.584990	−	0.811040i	$-0.698902\pi$
$587$	−28.3464	−1.16998	−0.584990	+	0.811040i	$0.698902\pi$
$588$	−64.3833	−2.65512
$589$	3.97760	0.163894
$590$	23.3148	0.959855
$591$	−73.6011	−3.02754
$592$	150.444	6.18319
$593$	−29.7173	−1.22034	−0.610172	−	0.792269i	$-0.708900\pi$
$593$	−29.7173	−1.22034	−0.610172	+	0.792269i	$0.708900\pi$
$594$	−79.7339	−3.27152
$595$	13.6240	0.558530
$596$	93.1145	3.81412
$597$	55.9879	2.29143
$598$	51.0427	2.08729
$599$	−11.9241	−0.487204	−0.243602	−	0.969875i	$-0.578329\pi$
$599$	−11.9241	−0.487204	−0.243602	+	0.969875i	$0.578329\pi$
$600$	−78.7510	−3.21499
$601$	−9.62727	−0.392704	−0.196352	−	0.980533i	$-0.562910\pi$
$601$	−9.62727	−0.392704	−0.196352	+	0.980533i	$0.562910\pi$
$602$	26.2571	1.07016
$603$	−75.6442	−3.08047
$604$	−61.7845	−2.51398
$605$	6.68814	0.271912
$606$	−42.6953	−1.73438
$607$	−11.6875	−0.474380	−0.237190	−	0.971463i	$-0.576226\pi$
$607$	−11.6875	−0.474380	−0.237190	+	0.971463i	$0.576226\pi$
$608$	−56.5774	−2.29452
$609$	−36.2876	−1.47045
$610$	51.0641	2.06753
$611$	9.72374	0.393380
$612$	−86.7960	−3.50852
$613$	1.89587	0.0765734	0.0382867	−	0.999267i	$-0.487810\pi$
$613$	1.89587	0.0765734	0.0382867	+	0.999267i	$0.487810\pi$
$614$	−48.0756	−1.94017
$615$	33.7558	1.36117
$616$	57.5337	2.31810
$617$	−31.5420	−1.26983	−0.634917	−	0.772580i	$-0.718966\pi$
$617$	−31.5420	−1.26983	−0.634917	+	0.772580i	$0.718966\pi$
$618$	−129.628	−5.21440
$619$	−10.5542	−0.424208	−0.212104	−	0.977247i	$-0.568032\pi$
$619$	−10.5542	−0.424208	−0.212104	+	0.977247i	$0.568032\pi$
$620$	21.3475	0.857336
$621$	27.2266	1.09257
$622$	78.3728	3.14246
$623$	11.7656	0.471378
$624$	−231.453	−9.26552
$625$	−31.0826	−1.24330
$626$	35.2593	1.40924
$627$	30.4224	1.21495
$628$	−36.9190	−1.47323
$629$	−30.0259	−1.19721
$630$	74.9381	2.98560
$631$	11.6821	0.465057	0.232529	−	0.972590i	$-0.425300\pi$
$631$	11.6821	0.465057	0.232529	+	0.972590i	$0.425300\pi$
$632$	−20.4159	−0.812100
$633$	49.8910	1.98299
$634$	54.3839	2.15986
$635$	39.3685	1.56229
$636$	47.3630	1.87806
$637$	22.4749	0.890488
$638$	−71.1512	−2.81690
$639$	−4.82789	−0.190989
$640$	−87.5452	−3.46053
$641$	5.14460	0.203200	0.101600	−	0.994825i	$-0.467604\pi$
$641$	5.14460	0.203200	0.101600	+	0.994825i	$0.467604\pi$
$642$	71.7015	2.82983
$643$	−9.75823	−0.384827	−0.192413	−	0.981314i	$-0.561631\pi$
$643$	−9.75823	−0.384827	−0.192413	+	0.981314i	$0.561631\pi$
$644$	−31.2855	−1.23282
$645$	46.7922	1.84244
$646$	21.6004	0.849857
$647$	−43.1676	−1.69709	−0.848546	−	0.529121i	$-0.822522\pi$
$647$	−43.1676	−1.69709	−0.848546	+	0.529121i	$0.822522\pi$
$648$	−60.0075	−2.35732
$649$	−11.1651	−0.438268
$650$	43.7775	1.71709
$651$	−7.15354	−0.280369
$652$	−13.5076	−0.528998
$653$	21.0234	0.822711	0.411355	−	0.911475i	$-0.365056\pi$
$653$	21.0234	0.822711	0.411355	+	0.911475i	$0.365056\pi$
$654$	17.8744	0.698943
$655$	54.5714	2.13228
$656$	57.5075	2.24529
$657$	19.7043	0.768738
$658$	−8.17731	−0.318785
$659$	40.0959	1.56192	0.780958	−	0.624584i	$-0.214731\pi$
$659$	40.0959	1.56192	0.780958	+	0.624584i	$0.214731\pi$
$660$	163.275	6.35547
$661$	−28.8232	−1.12109	−0.560546	−	0.828123i	$-0.689409\pi$
$661$	−28.8232	−1.12109	−0.560546	+	0.828123i	$0.689409\pi$
$662$	74.7420	2.90493
$663$	46.1939	1.79402
$664$	11.2527	0.436691
$665$	−13.5924	−0.527092
$666$	−165.156	−6.39966
$667$	24.2959	0.940741
$668$	−120.683	−4.66938
$669$	−27.0434	−1.04556
$670$	101.033	3.90325
$671$	−24.4538	−0.944029
$672$	101.752	3.92517
$673$	17.7253	0.683260	0.341630	−	0.939835i	$-0.389021\pi$
$673$	17.7253	0.683260	0.341630	+	0.939835i	$0.389021\pi$
$674$	−63.0666	−2.42923
$675$	23.3513	0.898792
$676$	95.1591	3.65997
$677$	5.97463	0.229624	0.114812	−	0.993387i	$-0.463374\pi$
$677$	5.97463	0.229624	0.114812	+	0.993387i	$0.463374\pi$
$678$	72.7710	2.79475
$679$	−30.5878	−1.17385
$680$	72.7977	2.79166
$681$	−74.2607	−2.84568
$682$	−14.0264	−0.537098
$683$	−29.4294	−1.12608	−0.563042	−	0.826428i	$-0.690369\pi$
$683$	−29.4294	−1.12608	−0.563042	+	0.826428i	$0.690369\pi$
$684$	86.5947	3.31103
$685$	−17.1361	−0.654739
$686$	−51.5185	−1.96698
$687$	78.6248	2.99972
$688$	79.7168	3.03917
$689$	−16.5335	−0.629875
$690$	−76.4959	−2.91215
$691$	2.26725	0.0862502	0.0431251	−	0.999070i	$-0.486269\pi$
$691$	2.26725	0.0862502	0.0431251	+	0.999070i	$0.486269\pi$
$692$	71.3682	2.71301
$693$	−35.8867	−1.36322
$694$	−56.6794	−2.15152
$695$	14.1008	0.534873
$696$	−193.896	−7.34963
$697$	−11.4775	−0.434741
$698$	−42.6457	−1.61416
$699$	−70.2090	−2.65555
$700$	−26.8324	−1.01417
$701$	−4.72948	−0.178630	−0.0893151	−	0.996003i	$-0.528468\pi$
$701$	−4.72948	−0.178630	−0.0893151	+	0.996003i	$0.528468\pi$
$702$	120.789	4.55887
$703$	29.9563	1.12982
$704$	96.0236	3.61902
$705$	−14.5726	−0.548837
$706$	59.1598	2.22651
$707$	−9.13512	−0.343562
$708$	−48.4530	−1.82097
$709$	3.09344	0.116177	0.0580883	−	0.998311i	$-0.481500\pi$
$709$	3.09344	0.116177	0.0580883	+	0.998311i	$0.481500\pi$
$710$	6.44831	0.242001
$711$	12.7344	0.477578
$712$	62.8674	2.35606
$713$	4.78956	0.179371
$714$	−38.8474	−1.45383
$715$	−56.9960	−2.13153
$716$	45.2988	1.69290
$717$	14.0467	0.524585
$718$	9.87430	0.368506
$719$	12.1672	0.453762	0.226881	−	0.973923i	$-0.427147\pi$
$719$	12.1672	0.453762	0.226881	+	0.973923i	$0.427147\pi$
$720$	227.513	8.47890
$721$	−27.7353	−1.03292
$722$	30.0504	1.11836
$723$	−20.0164	−0.744416
$724$	31.0638	1.15448
$725$	20.8377	0.773893
$726$	−19.0705	−0.707773
$727$	18.7141	0.694069	0.347034	−	0.937852i	$-0.387189\pi$
$727$	18.7141	0.694069	0.347034	+	0.937852i	$0.387189\pi$
$728$	−87.1576	−3.23027
$729$	−33.6727	−1.24714
$730$	−26.3178	−0.974065
$731$	−15.9101	−0.588456
$732$	−106.122	−3.92238
$733$	−39.0505	−1.44236	−0.721182	−	0.692746i	$-0.756401\pi$
$733$	−39.0505	−1.44236	−0.721182	+	0.692746i	$0.756401\pi$
$734$	−27.5658	−1.01747
$735$	−33.6823	−1.24239
$736$	−68.1269	−2.51119
$737$	−48.3832	−1.78222
$738$	−63.1313	−2.32389
$739$	−42.9004	−1.57812	−0.789058	−	0.614319i	$-0.789431\pi$
$739$	−42.9004	−1.57812	−0.789058	+	0.614319i	$0.789431\pi$
$740$	160.773	5.91015
$741$	−46.0868	−1.69304
$742$	13.9040	0.510433
$743$	−38.4000	−1.40876	−0.704380	−	0.709823i	$-0.748775\pi$
$743$	−38.4000	−1.40876	−0.704380	+	0.709823i	$0.748775\pi$
$744$	−38.2237	−1.40135
$745$	48.7131	1.78471
$746$	70.1068	2.56679
$747$	−7.01891	−0.256808
$748$	−55.5160	−2.02987
$749$	15.3413	0.560559
$750$	47.1528	1.72178
$751$	33.8803	1.23631	0.618155	−	0.786056i	$-0.287881\pi$
$751$	33.8803	1.23631	0.618155	+	0.786056i	$0.287881\pi$
$752$	−24.8264	−0.905325
$753$	10.5356	0.383939
$754$	107.787	3.92536
$755$	−32.3228	−1.17635
$756$	−74.0347	−2.69262
$757$	49.4773	1.79828	0.899142	−	0.437657i	$-0.144191\pi$
$757$	49.4773	1.79828	0.899142	+	0.437657i	$0.144191\pi$
$758$	85.9628	3.12231
$759$	36.6327	1.32968
$760$	−72.6289	−2.63453
$761$	−28.8392	−1.04542	−0.522711	−	0.852510i	$-0.675079\pi$
$761$	−28.8392	−1.04542	−0.522711	+	0.852510i	$0.675079\pi$
$762$	−112.255	−4.06657
$763$	3.82441	0.138453
$764$	−79.7559	−2.88547
$765$	−45.4076	−1.64171
$766$	9.77765	0.353281
$767$	16.9140	0.610728
$768$	94.5906	3.41325
$769$	−28.8418	−1.04006	−0.520032	−	0.854147i	$-0.674080\pi$
$769$	−28.8418	−1.04006	−0.520032	+	0.854147i	$0.674080\pi$
$770$	47.9315	1.72733
$771$	60.0020	2.16092
$772$	145.317	5.23008
$773$	−5.67686	−0.204183	−0.102091	−	0.994775i	$-0.532553\pi$
$773$	−5.67686	−0.204183	−0.102091	+	0.994775i	$0.532553\pi$
$774$	−87.5125	−3.14557
$775$	4.10783	0.147558
$776$	−163.441	−5.86717
$777$	−53.8751	−1.93276
$778$	100.604	3.60683
$779$	11.4509	0.410271
$780$	−247.345	−8.85636
$781$	−3.08800	−0.110497
$782$	26.0098	0.930109
$783$	57.4943	2.05468
$784$	−57.3823	−2.04937
$785$	−19.3143	−0.689358
$786$	−155.604	−5.55022
$787$	−16.0070	−0.570587	−0.285294	−	0.958440i	$-0.592091\pi$
$787$	−16.0070	−0.570587	−0.285294	+	0.958440i	$0.592091\pi$
$788$	−133.999	−4.77351
$789$	71.9805	2.56257
$790$	−17.0085	−0.605137
$791$	15.5701	0.553610
$792$	−191.754	−6.81370
$793$	37.0450	1.31551
$794$	−100.300	−3.55951
$795$	24.7781	0.878789
$796$	101.932	3.61288
$797$	−25.0754	−0.888217	−0.444109	−	0.895973i	$-0.646480\pi$
$797$	−25.0754	−0.888217	−0.444109	+	0.895973i	$0.646480\pi$
$798$	38.7573	1.37199
$799$	4.95492	0.175292
$800$	−58.4299	−2.06581
$801$	−39.2136	−1.38554
$802$	−34.6240	−1.22262
$803$	12.6032	0.444756
$804$	−209.968	−7.40499
$805$	−16.3671	−0.576865
$806$	21.2485	0.748446
$807$	65.2731	2.29772
$808$	−48.8120	−1.71720
$809$	18.7998	0.660965	0.330482	−	0.943812i	$-0.392789\pi$
$809$	18.7998	0.660965	0.330482	+	0.943812i	$0.392789\pi$
$810$	−49.9925	−1.75656
$811$	−51.2943	−1.80119	−0.900593	−	0.434664i	$-0.856867\pi$
$811$	−51.2943	−1.80119	−0.900593	+	0.434664i	$0.856867\pi$
$812$	−66.0654	−2.31844
$813$	−45.5402	−1.59716
$814$	−105.636	−3.70255
$815$	−7.06654	−0.247530
$816$	−117.941	−4.12876
$817$	15.8732	0.555333
$818$	−80.5393	−2.81599
$819$	54.3646	1.89965
$820$	61.4561	2.14614
$821$	37.3283	1.30277	0.651383	−	0.758749i	$-0.274189\pi$
$821$	37.3283	1.30277	0.651383	+	0.758749i	$0.274189\pi$
$822$	48.8619	1.70425
$823$	2.01536	0.0702511	0.0351256	−	0.999383i	$-0.488817\pi$
$823$	2.01536	0.0702511	0.0351256	+	0.999383i	$0.488817\pi$
$824$	−148.199	−5.16275
$825$	31.4185	1.09385
$826$	−14.2240	−0.494917
$827$	−8.76679	−0.304851	−0.152426	−	0.988315i	$-0.548708\pi$
$827$	−8.76679	−0.304851	−0.152426	+	0.988315i	$0.548708\pi$
$828$	104.272	3.62369
$829$	38.9283	1.35204	0.676019	−	0.736885i	$-0.263704\pi$
$829$	38.9283	1.35204	0.676019	+	0.736885i	$0.263704\pi$
$830$	9.37470	0.325401
$831$	−24.1358	−0.837261
$832$	−145.466	−5.04312
$833$	11.4525	0.396806
$834$	−40.2068	−1.39225
$835$	−63.1359	−2.18491
$836$	55.3873	1.91561
$837$	11.3341	0.391765
$838$	13.3033	0.459554
$839$	27.4957	0.949255	0.474628	−	0.880187i	$-0.342583\pi$
$839$	27.4957	0.949255	0.474628	+	0.880187i	$0.342583\pi$
$840$	130.620	4.50681
$841$	22.3055	0.769155
$842$	−53.0415	−1.82793
$843$	46.5980	1.60492
$844$	90.8319	3.12656
$845$	49.7828	1.71258
$846$	27.2542	0.937019
$847$	−4.08034	−0.140202
$848$	42.2128	1.44959
$849$	−76.1920	−2.61490
$850$	22.3077	0.765146
$851$	36.0714	1.23651
$852$	−13.4009	−0.459108
$853$	31.3886	1.07473	0.537363	−	0.843351i	$-0.319420\pi$
$853$	31.3886	1.07473	0.537363	+	0.843351i	$0.319420\pi$
$854$	−31.1535	−1.06605
$855$	45.3023	1.54931
$856$	81.9736	2.80180
$857$	48.6419	1.66158	0.830789	−	0.556588i	$-0.187890\pi$
$857$	48.6419	1.66158	0.830789	+	0.556588i	$0.187890\pi$
$858$	162.518	5.54827
$859$	17.5211	0.597813	0.298907	−	0.954282i	$-0.403378\pi$
$859$	17.5211	0.597813	0.298907	+	0.954282i	$0.403378\pi$
$860$	85.1903	2.90497
$861$	−20.5939	−0.701839
$862$	34.5801	1.17780
$863$	−13.3175	−0.453334	−0.226667	−	0.973972i	$-0.572783\pi$
$863$	−13.3175	−0.453334	−0.226667	+	0.973972i	$0.572783\pi$
$864$	−161.217	−5.48471
$865$	37.3365	1.26948
$866$	18.6049	0.632221
$867$	−26.6570	−0.905318
$868$	−13.0238	−0.442056
$869$	8.14513	0.276305
$870$	−161.536	−5.47658
$871$	73.2955	2.48352
$872$	20.4351	0.692020
$873$	101.946	3.45036
$874$	−25.9495	−0.877755
$875$	10.0889	0.341065
$876$	54.6938	1.84793
$877$	4.64343	0.156797	0.0783987	−	0.996922i	$-0.475019\pi$
$877$	4.64343	0.156797	0.0783987	+	0.996922i	$0.475019\pi$
$878$	−66.0047	−2.22755
$879$	−59.4797	−2.00620
$880$	145.521	4.90550
$881$	−20.5831	−0.693461	−0.346730	−	0.937965i	$-0.612708\pi$
$881$	−20.5831	−0.693461	−0.346730	+	0.937965i	$0.612708\pi$
$882$	62.9938	2.12111
$883$	−18.4577	−0.621152	−0.310576	−	0.950549i	$-0.600522\pi$
$883$	−18.4577	−0.621152	−0.310576	+	0.950549i	$0.600522\pi$
$884$	84.1010	2.82862
$885$	−25.3483	−0.852075
$886$	91.2985	3.06723
$887$	28.3527	0.951990	0.475995	−	0.879448i	$-0.342088\pi$
$887$	28.3527	0.951990	0.475995	+	0.879448i	$0.342088\pi$
$888$	−287.873	−9.66038
$889$	−24.0181	−0.805542
$890$	52.3751	1.75562
$891$	23.9406	0.802041
$892$	−49.2355	−1.64853
$893$	−4.94343	−0.165426
$894$	−138.900	−4.64552
$895$	23.6982	0.792144
$896$	53.4101	1.78430
$897$	−55.4947	−1.85292
$898$	−9.95764	−0.332291
$899$	10.1141	0.337324
$900$	89.4300	2.98100
$901$	−8.42494	−0.280675
$902$	−40.3797	−1.34450
$903$	−28.5473	−0.949994
$904$	83.1964	2.76707
$905$	16.2511	0.540206
$906$	92.1648	3.06197
$907$	−2.91474	−0.0967822	−0.0483911	−	0.998828i	$-0.515409\pi$
$907$	−2.91474	−0.0967822	−0.0483911	+	0.998828i	$0.515409\pi$
$908$	−135.200	−4.48676
$909$	30.4465	1.00985
$910$	−72.6113	−2.40704
$911$	29.3058	0.970945	0.485472	−	0.874252i	$-0.338648\pi$
$911$	29.3058	0.970945	0.485472	+	0.874252i	$0.338648\pi$
$912$	117.668	3.89636
$913$	−4.48940	−0.148577
$914$	37.7651	1.24916
$915$	−55.5180	−1.83537
$916$	143.145	4.72964
$917$	−33.2932	−1.09944
$918$	61.5502	2.03146
$919$	−55.6778	−1.83664	−0.918320	−	0.395838i	$-0.870454\pi$
$919$	−55.6778	−1.83664	−0.918320	+	0.395838i	$0.870454\pi$
$920$	−87.4549	−2.88330
$921$	52.2688	1.72232
$922$	−69.8705	−2.30106
$923$	4.67799	0.153978
$924$	−99.6117	−3.27698
$925$	30.9372	1.01721
$926$	22.4040	0.736241
$927$	92.4391	3.03610
$928$	−143.863	−4.72254
$929$	56.2466	1.84539	0.922696	−	0.385528i	$-0.125981\pi$
$929$	56.2466	1.84539	0.922696	+	0.385528i	$0.125981\pi$
$930$	−31.8443	−1.04422
$931$	−11.4260	−0.374471
$932$	−127.823	−4.18698
$933$	−85.2086	−2.78960
$934$	−55.2175	−1.80677
$935$	−29.0434	−0.949821
$936$	290.488	9.49490
$937$	−30.8278	−1.00710	−0.503550	−	0.863966i	$-0.667973\pi$
$937$	−30.8278	−1.00710	−0.503550	+	0.863966i	$0.667973\pi$
$938$	−61.6388	−2.01258
$939$	−38.3346	−1.25100
$940$	−26.5310	−0.865347
$941$	−24.8662	−0.810614	−0.405307	−	0.914181i	$-0.632835\pi$
$941$	−24.8662	−0.810614	−0.405307	+	0.914181i	$0.632835\pi$
$942$	55.0727	1.79436
$943$	13.7884	0.449012
$944$	−43.1842	−1.40553
$945$	−38.7315	−1.25994
$946$	−55.9743	−1.81988
$947$	30.5992	0.994339	0.497170	−	0.867653i	$-0.334373\pi$
$947$	30.5992	0.994339	0.497170	+	0.867653i	$0.334373\pi$
$948$	35.3473	1.14803
$949$	−19.0925	−0.619769
$950$	−22.2559	−0.722078
$951$	−59.1273	−1.91734
$952$	−44.4128	−1.43943
$953$	36.4778	1.18163	0.590816	−	0.806807i	$-0.298806\pi$
$953$	36.4778	1.18163	0.590816	+	0.806807i	$0.298806\pi$
$954$	−46.3409	−1.50034
$955$	−41.7245	−1.35017
$956$	25.5736	0.827109
$957$	77.3571	2.50060
$958$	69.1128	2.23293
$959$	10.4545	0.337594
$960$	218.004	7.03605
$961$	−29.0062	−0.935683
$962$	160.028	5.15950
$963$	−51.1311	−1.64768
$964$	−36.4419	−1.17372
$965$	76.0231	2.44727
$966$	46.6690	1.50155
$967$	−1.32277	−0.0425373	−0.0212687	−	0.999774i	$-0.506771\pi$
$967$	−1.32277	−0.0425373	−0.0212687	+	0.999774i	$0.506771\pi$
$968$	−21.8026	−0.700762
$969$	−23.4844	−0.754428
$970$	−136.163	−4.37193
$971$	−23.2369	−0.745709	−0.372855	−	0.927890i	$-0.621621\pi$
$971$	−23.2369	−0.745709	−0.372855	+	0.927890i	$0.621621\pi$
$972$	−25.5549	−0.819673
$973$	−8.60267	−0.275789
$974$	−90.9934	−2.91562
$975$	−47.5958	−1.52429
$976$	−94.5823	−3.02750
$977$	16.0601	0.513808	0.256904	−	0.966437i	$-0.417298\pi$
$977$	16.0601	0.513808	0.256904	+	0.966437i	$0.417298\pi$
$978$	20.1495	0.644309
$979$	−25.0816	−0.801613
$980$	−61.3223	−1.95887
$981$	−12.7464	−0.406962
$982$	−65.3327	−2.08485
$983$	−28.3881	−0.905439	−0.452719	−	0.891653i	$-0.649546\pi$
$983$	−28.3881	−0.905439	−0.452719	+	0.891653i	$0.649546\pi$
$984$	−110.040	−3.50795
$985$	−70.1019	−2.23363
$986$	54.9248	1.74916
$987$	8.89054	0.282989
$988$	−83.9060	−2.66941
$989$	19.1135	0.607773
$990$	−159.751	−5.07723
$991$	16.6732	0.529643	0.264822	−	0.964297i	$-0.414687\pi$
$991$	16.6732	0.529643	0.264822	+	0.964297i	$0.414687\pi$
$992$	−28.3604	−0.900444
$993$	−81.2611	−2.57874
$994$	−3.93402	−0.124780
$995$	53.3260	1.69055
$996$	−19.4826	−0.617329
$997$	16.1415	0.511207	0.255604	−	0.966782i	$-0.417726\pi$
$997$	16.1415	0.511207	0.255604	+	0.966782i	$0.417726\pi$
$998$	−15.9827	−0.505922
$999$	85.3602	2.70068

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4001.2.a.b.1.6	✓	184

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4001.2.a.b.1.6	✓	184	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:	\( N \)	\(=\)	\( 4001 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4001.a (trivial)

\(f(q)\)	\(=\)	\(q-2.71583 q^{2} +2.95270 q^{3} +5.37572 q^{4} +2.81232 q^{5} -8.01903 q^{6} -1.71576 q^{7} -9.16786 q^{8} +5.71846 q^{9} +O(q^{10})\)	\(q-2.71583 q^{2} +2.95270 q^{3} +5.37572 q^{4} +2.81232 q^{5} -8.01903 q^{6} -1.71576 q^{7} -9.16786 q^{8} +5.71846 q^{9} -7.63778 q^{10} +3.65762 q^{11} +15.8729 q^{12} -5.54091 q^{13} +4.65970 q^{14} +8.30396 q^{15} +14.1469 q^{16} -2.82348 q^{17} -15.5304 q^{18} +2.81693 q^{19} +15.1183 q^{20} -5.06613 q^{21} -9.93345 q^{22} +3.39196 q^{23} -27.0700 q^{24} +2.90916 q^{25} +15.0481 q^{26} +8.02681 q^{27} -9.22343 q^{28} +7.16279 q^{29} -22.5521 q^{30} +1.41203 q^{31} -20.0848 q^{32} +10.7999 q^{33} +7.66807 q^{34} -4.82527 q^{35} +30.7408 q^{36} +10.6344 q^{37} -7.65029 q^{38} -16.3607 q^{39} -25.7830 q^{40} +4.06503 q^{41} +13.7587 q^{42} +5.63493 q^{43} +19.6623 q^{44} +16.0822 q^{45} -9.21198 q^{46} -1.75490 q^{47} +41.7716 q^{48} -4.05617 q^{49} -7.90078 q^{50} -8.33689 q^{51} -29.7864 q^{52} +2.98389 q^{53} -21.7994 q^{54} +10.2864 q^{55} +15.7298 q^{56} +8.31756 q^{57} -19.4529 q^{58} -3.05256 q^{59} +44.6397 q^{60} -6.68573 q^{61} -3.83484 q^{62} -9.81150 q^{63} +26.2530 q^{64} -15.5828 q^{65} -29.3305 q^{66} -13.2281 q^{67} -15.1782 q^{68} +10.0155 q^{69} +13.1046 q^{70} -0.844264 q^{71} -52.4261 q^{72} +3.44574 q^{73} -28.8812 q^{74} +8.58989 q^{75} +15.1430 q^{76} -6.27558 q^{77} +44.4327 q^{78} +2.22690 q^{79} +39.7856 q^{80} +6.54541 q^{81} -11.0399 q^{82} -1.22741 q^{83} -27.2341 q^{84} -7.94053 q^{85} -15.3035 q^{86} +21.1496 q^{87} -33.5325 q^{88} -6.85737 q^{89} -43.6764 q^{90} +9.50686 q^{91} +18.2342 q^{92} +4.16932 q^{93} +4.76601 q^{94} +7.92211 q^{95} -59.3045 q^{96} +17.8276 q^{97} +11.0159 q^{98} +20.9159 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 184 q + 3 q^{2} + 28 q^{3} + 217 q^{4} + 15 q^{5} + 31 q^{6} + 49 q^{7} + 6 q^{8} + 210 q^{9}+O(q^{10}) \) 184 * q + 3 * q^2 + 28 * q^3 + 217 * q^4 + 15 * q^5 + 31 * q^6 + 49 * q^7 + 6 * q^8 + 210 * q^9	\( 184 q + 3 q^{2} + 28 q^{3} + 217 q^{4} + 15 q^{5} + 31 q^{6} + 49 q^{7} + 6 q^{8} + 210 q^{9} + 46 q^{10} + 25 q^{11} + 61 q^{12} + 52 q^{13} + 28 q^{14} + 59 q^{15} + 279 q^{16} + 16 q^{17} - 2 q^{18} + 86 q^{19} + 26 q^{20} + 22 q^{21} + 54 q^{22} + 55 q^{23} + 72 q^{24} + 241 q^{25} + 32 q^{26} + 97 q^{27} + 75 q^{28} + 27 q^{29} - 10 q^{30} + 276 q^{31} + 20 q^{33} + 122 q^{34} + 30 q^{35} + 278 q^{36} + 42 q^{37} + 14 q^{38} + 113 q^{39} + 115 q^{40} + 39 q^{41} + 15 q^{42} + 65 q^{43} + 32 q^{44} + 54 q^{45} + 65 q^{46} + 82 q^{47} + 117 q^{48} + 297 q^{49} + 4 q^{50} + 45 q^{51} + 136 q^{52} + 21 q^{53} + 93 q^{54} + 252 q^{55} + 74 q^{56} + 14 q^{57} + 54 q^{58} + 95 q^{59} + 58 q^{60} + 131 q^{61} + 14 q^{62} + 88 q^{63} + 368 q^{64} - 9 q^{65} + 52 q^{66} + 90 q^{67} + 27 q^{68} + 101 q^{69} + 18 q^{70} + 117 q^{71} - 15 q^{72} + 72 q^{73} + 7 q^{74} + 150 q^{75} + 148 q^{76} + 7 q^{77} + 22 q^{78} + 287 q^{79} + 43 q^{80} + 244 q^{81} + 86 q^{82} + 25 q^{83} + 14 q^{84} + 41 q^{85} + 25 q^{86} + 82 q^{87} + 115 q^{88} + 48 q^{89} + 78 q^{90} + 272 q^{91} + 69 q^{92} + 44 q^{93} + 161 q^{94} + 37 q^{95} + 129 q^{96} + 106 q^{97} - 46 q^{98} + 53 q^{99}+O(q^{100}) \) 184 * q + 3 * q^2 + 28 * q^3 + 217 * q^4 + 15 * q^5 + 31 * q^6 + 49 * q^7 + 6 * q^8 + 210 * q^9 + 46 * q^10 + 25 * q^11 + 61 * q^12 + 52 * q^13 + 28 * q^14 + 59 * q^15 + 279 * q^16 + 16 * q^17 - 2 * q^18 + 86 * q^19 + 26 * q^20 + 22 * q^21 + 54 * q^22 + 55 * q^23 + 72 * q^24 + 241 * q^25 + 32 * q^26 + 97 * q^27 + 75 * q^28 + 27 * q^29 - 10 * q^30 + 276 * q^31 + 20 * q^33 + 122 * q^34 + 30 * q^35 + 278 * q^36 + 42 * q^37 + 14 * q^38 + 113 * q^39 + 115 * q^40 + 39 * q^41 + 15 * q^42 + 65 * q^43 + 32 * q^44 + 54 * q^45 + 65 * q^46 + 82 * q^47 + 117 * q^48 + 297 * q^49 + 4 * q^50 + 45 * q^51 + 136 * q^52 + 21 * q^53 + 93 * q^54 + 252 * q^55 + 74 * q^56 + 14 * q^57 + 54 * q^58 + 95 * q^59 + 58 * q^60 + 131 * q^61 + 14 * q^62 + 88 * q^63 + 368 * q^64 - 9 * q^65 + 52 * q^66 + 90 * q^67 + 27 * q^68 + 101 * q^69 + 18 * q^70 + 117 * q^71 - 15 * q^72 + 72 * q^73 + 7 * q^74 + 150 * q^75 + 148 * q^76 + 7 * q^77 + 22 * q^78 + 287 * q^79 + 43 * q^80 + 244 * q^81 + 86 * q^82 + 25 * q^83 + 14 * q^84 + 41 * q^85 + 25 * q^86 + 82 * q^87 + 115 * q^88 + 48 * q^89 + 78 * q^90 + 272 * q^91 + 69 * q^92 + 44 * q^93 + 161 * q^94 + 37 * q^95 + 129 * q^96 + 106 * q^97 - 46 * q^98 + 53 * q^99

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