LMFDB - Embedded newform 4001.2.a.b.1.1

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			1.1
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)

$f(q)$	$=$	$q-2.80114 q^{2} -3.24231 q^{3} +5.84639 q^{4} -0.362239 q^{5} +9.08218 q^{6} +0.683027 q^{7} -10.7743 q^{8} +7.51260 q^{9} +O(q^{10})$	\(q-2.80114 q^{2} -3.24231 q^{3} +5.84639 q^{4} -0.362239 q^{5} +9.08218 q^{6} +0.683027 q^{7} -10.7743 q^{8} +7.51260 q^{9} +1.01468 q^{10} -2.13162 q^{11} -18.9558 q^{12} -1.68516 q^{13} -1.91326 q^{14} +1.17449 q^{15} +18.4875 q^{16} -5.09163 q^{17} -21.0439 q^{18} -0.801920 q^{19} -2.11779 q^{20} -2.21459 q^{21} +5.97097 q^{22} -8.57971 q^{23} +34.9336 q^{24} -4.86878 q^{25} +4.72037 q^{26} -14.6313 q^{27} +3.99325 q^{28} -3.50963 q^{29} -3.28992 q^{30} +1.80809 q^{31} -30.2376 q^{32} +6.91138 q^{33} +14.2624 q^{34} -0.247419 q^{35} +43.9216 q^{36} -5.00800 q^{37} +2.24629 q^{38} +5.46382 q^{39} +3.90287 q^{40} -9.31222 q^{41} +6.20338 q^{42} -7.60034 q^{43} -12.4623 q^{44} -2.72136 q^{45} +24.0330 q^{46} +1.24331 q^{47} -59.9424 q^{48} -6.53347 q^{49} +13.6381 q^{50} +16.5087 q^{51} -9.85210 q^{52} +7.78403 q^{53} +40.9843 q^{54} +0.772157 q^{55} -7.35914 q^{56} +2.60008 q^{57} +9.83096 q^{58} -1.98291 q^{59} +6.86655 q^{60} -3.99389 q^{61} -5.06473 q^{62} +5.13131 q^{63} +47.7248 q^{64} +0.610431 q^{65} -19.3598 q^{66} +5.71728 q^{67} -29.7677 q^{68} +27.8181 q^{69} +0.693057 q^{70} +8.29768 q^{71} -80.9430 q^{72} -1.66674 q^{73} +14.0281 q^{74} +15.7861 q^{75} -4.68834 q^{76} -1.45595 q^{77} -15.3049 q^{78} +1.42417 q^{79} -6.69691 q^{80} +24.9014 q^{81} +26.0849 q^{82} -1.86129 q^{83} -12.9474 q^{84} +1.84439 q^{85} +21.2896 q^{86} +11.3793 q^{87} +22.9667 q^{88} -6.35369 q^{89} +7.62291 q^{90} -1.15101 q^{91} -50.1604 q^{92} -5.86241 q^{93} -3.48270 q^{94} +0.290487 q^{95} +98.0399 q^{96} +10.6003 q^{97} +18.3012 q^{98} -16.0140 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.80114	−1.98071	−0.990353	−	0.138567i	$-0.955750\pi$
$2$	−2.80114	−1.98071	−0.990353	+	0.138567i	$0.955750\pi$
$3$	−3.24231	−1.87195	−0.935975	−	0.352065i	$-0.885480\pi$
$3$	−3.24231	−1.87195	−0.935975	+	0.352065i	$0.885480\pi$
$4$	5.84639	2.92320
$5$	−0.362239	−0.161998	−0.0809992	−	0.996714i	$-0.525811\pi$
$5$	−0.362239	−0.161998	−0.0809992	+	0.996714i	$0.525811\pi$
$6$	9.08218	3.70778
$7$	0.683027	0.258160	0.129080	−	0.991634i	$-0.458798\pi$
$7$	0.683027	0.258160	0.129080	+	0.991634i	$0.458798\pi$
$8$	−10.7743	−3.80929
$9$	7.51260	2.50420
$10$	1.01468	0.320871
$11$	−2.13162	−0.642708	−0.321354	−	0.946959i	$-0.604138\pi$
$11$	−2.13162	−0.642708	−0.321354	+	0.946959i	$0.604138\pi$
$12$	−18.9558	−5.47208
$13$	−1.68516	−0.467379	−0.233690	−	0.972311i	$-0.575080\pi$
$13$	−1.68516	−0.467379	−0.233690	+	0.972311i	$0.575080\pi$
$14$	−1.91326	−0.511339
$15$	1.17449	0.303253
$16$	18.4875	4.62188
$17$	−5.09163	−1.23490	−0.617450	−	0.786610i	$-0.711834\pi$
$17$	−5.09163	−1.23490	−0.617450	+	0.786610i	$0.711834\pi$
$18$	−21.0439	−4.96009
$19$	−0.801920	−0.183973	−0.0919865	−	0.995760i	$-0.529322\pi$
$19$	−0.801920	−0.183973	−0.0919865	+	0.995760i	$0.529322\pi$
$20$	−2.11779	−0.473553
$21$	−2.21459	−0.483263
$22$	5.97097	1.27302
$23$	−8.57971	−1.78899	−0.894497	−	0.447075i	$-0.852466\pi$
$23$	−8.57971	−1.78899	−0.894497	+	0.447075i	$0.852466\pi$
$24$	34.9336	7.13080
$25$	−4.86878	−0.973757
$26$	4.72037	0.925741
$27$	−14.6313	−2.81579
$28$	3.99325	0.754653
$29$	−3.50963	−0.651721	−0.325861	−	0.945418i	$-0.605654\pi$
$29$	−3.50963	−0.651721	−0.325861	+	0.945418i	$0.605654\pi$
$30$	−3.28992	−0.600655
$31$	1.80809	0.324743	0.162372	−	0.986730i	$-0.448086\pi$
$31$	1.80809	0.324743	0.162372	+	0.986730i	$0.448086\pi$
$32$	−30.2376	−5.34531
$33$	6.91138	1.20312
$34$	14.2624	2.44598
$35$	−0.247419	−0.0418215
$36$	43.9216	7.32027
$37$	−5.00800	−0.823310	−0.411655	−	0.911340i	$-0.635049\pi$
$37$	−5.00800	−0.823310	−0.411655	+	0.911340i	$0.635049\pi$
$38$	2.24629	0.364396
$39$	5.46382	0.874911
$40$	3.90287	0.617098
$41$	−9.31222	−1.45432	−0.727162	−	0.686465i	$-0.759161\pi$
$41$	−9.31222	−1.45432	−0.727162	+	0.686465i	$0.759161\pi$
$42$	6.20338	0.957202
$43$	−7.60034	−1.15904	−0.579520	−	0.814958i	$-0.696760\pi$
$43$	−7.60034	−1.15904	−0.579520	+	0.814958i	$0.696760\pi$
$44$	−12.4623	−1.87876
$45$	−2.72136	−0.405676
$46$	24.0330	3.54347
$47$	1.24331	0.181356	0.0906780	−	0.995880i	$-0.471097\pi$
$47$	1.24331	0.181356	0.0906780	+	0.995880i	$0.471097\pi$
$48$	−59.9424	−8.65194
$49$	−6.53347	−0.933353
$50$	13.6381	1.92873
$51$	16.5087	2.31167
$52$	−9.85210	−1.36624
$53$	7.78403	1.06922	0.534609	−	0.845099i	$-0.320459\pi$
$53$	7.78403	1.06922	0.534609	+	0.845099i	$0.320459\pi$
$54$	40.9843	5.57725
$55$	0.772157	0.104118
$56$	−7.35914	−0.983406
$57$	2.60008	0.344388
$58$	9.83096	1.29087
$59$	−1.98291	−0.258153	−0.129076	−	0.991635i	$-0.541201\pi$
$59$	−1.98291	−0.258153	−0.129076	+	0.991635i	$0.541201\pi$
$60$	6.86655	0.886468
$61$	−3.99389	−0.511366	−0.255683	−	0.966761i	$-0.582300\pi$
$61$	−3.99389	−0.511366	−0.255683	+	0.966761i	$0.582300\pi$
$62$	−5.06473	−0.643221
$63$	5.13131	0.646484
$64$	47.7248	5.96560
$65$	0.610431	0.0757146
$66$	−19.3598	−2.38302
$67$	5.71728	0.698476	0.349238	−	0.937034i	$-0.386440\pi$
$67$	5.71728	0.698476	0.349238	+	0.937034i	$0.386440\pi$
$68$	−29.7677	−3.60986
$69$	27.8181	3.34891
$70$	0.693057	0.0828361
$71$	8.29768	0.984753	0.492377	−	0.870382i	$-0.336128\pi$
$71$	8.29768	0.984753	0.492377	+	0.870382i	$0.336128\pi$
$72$	−80.9430	−9.53922
$73$	−1.66674	−0.195077	−0.0975385	−	0.995232i	$-0.531097\pi$
$73$	−1.66674	−0.195077	−0.0975385	+	0.995232i	$0.531097\pi$
$74$	14.0281	1.63074
$75$	15.7861	1.82282
$76$	−4.68834	−0.537789
$77$	−1.45595	−0.165921
$78$	−15.3049	−1.73294
$79$	1.42417	0.160232	0.0801160	−	0.996786i	$-0.474471\pi$
$79$	1.42417	0.160232	0.0801160	+	0.996786i	$0.474471\pi$
$80$	−6.69691	−0.748738
$81$	24.9014	2.76682
$82$	26.0849	2.88059
$83$	−1.86129	−0.204303	−0.102152	−	0.994769i	$-0.532573\pi$
$83$	−1.86129	−0.204303	−0.102152	+	0.994769i	$0.532573\pi$
$84$	−12.9474	−1.41267
$85$	1.84439	0.200052
$86$	21.2896	2.29572
$87$	11.3793	1.21999
$88$	22.9667	2.44826
$89$	−6.35369	−0.673490	−0.336745	−	0.941596i	$-0.609326\pi$
$89$	−6.35369	−0.673490	−0.336745	+	0.941596i	$0.609326\pi$
$90$	7.62291	0.803526
$91$	−1.15101	−0.120659
$92$	−50.1604	−5.22958
$93$	−5.86241	−0.607904
$94$	−3.48270	−0.359213
$95$	0.290487	0.0298033
$96$	98.0399	10.0062
$97$	10.6003	1.07630	0.538150	−	0.842849i	$-0.319123\pi$
$97$	10.6003	1.07630	0.538150	+	0.842849i	$0.319123\pi$
$98$	18.3012	1.84870
$99$	−16.0140	−1.60947
$100$	−28.4648	−2.84648
$101$	−13.7583	−1.36900	−0.684500	−	0.729013i	$-0.739980\pi$
$101$	−13.7583	−1.36900	−0.684500	+	0.729013i	$0.739980\pi$
$102$	−46.2431	−4.57875
$103$	2.15900	0.212732	0.106366	−	0.994327i	$-0.466078\pi$
$103$	2.15900	0.212732	0.106366	+	0.994327i	$0.466078\pi$
$104$	18.1564	1.78038
$105$	0.802211	0.0782878
$106$	−21.8042	−2.11781
$107$	−8.78706	−0.849477	−0.424738	−	0.905316i	$-0.639634\pi$
$107$	−8.78706	−0.849477	−0.424738	+	0.905316i	$0.639634\pi$
$108$	−85.5402	−8.23111
$109$	−15.6529	−1.49928	−0.749638	−	0.661848i	$-0.769772\pi$
$109$	−15.6529	−1.49928	−0.749638	+	0.661848i	$0.769772\pi$
$110$	−2.16292	−0.206226
$111$	16.2375	1.54120
$112$	12.6275	1.19319
$113$	−8.99890	−0.846545	−0.423273	−	0.906002i	$-0.639119\pi$
$113$	−8.99890	−0.846545	−0.423273	+	0.906002i	$0.639119\pi$
$114$	−7.28318	−0.682132
$115$	3.10791	0.289814
$116$	−20.5187	−1.90511
$117$	−12.6599	−1.17041
$118$	5.55441	0.511324
$119$	−3.47772	−0.318802
$120$	−12.6543	−1.15518
$121$	−6.45619	−0.586927
$122$	11.1875	1.01287
$123$	30.1931	2.72242
$124$	10.5708	0.949289
$125$	3.57486	0.319745
$126$	−14.3735	−1.28050
$127$	13.3030	1.18045	0.590227	−	0.807237i	$-0.299038\pi$
$127$	13.3030	1.18045	0.590227	+	0.807237i	$0.299038\pi$
$128$	−73.2086	−6.47079
$129$	24.6427	2.16967
$130$	−1.70990	−0.149968
$131$	−2.62380	−0.229242	−0.114621	−	0.993409i	$-0.536565\pi$
$131$	−2.62380	−0.229242	−0.114621	+	0.993409i	$0.536565\pi$
$132$	40.4067	3.51695
$133$	−0.547733	−0.0474945
$134$	−16.0149	−1.38348
$135$	5.30002	0.456153
$136$	54.8587	4.70409
$137$	5.48350	0.468487	0.234244	−	0.972178i	$-0.424739\pi$
$137$	5.48350	0.468487	0.234244	+	0.972178i	$0.424739\pi$
$138$	−77.9225	−6.63320
$139$	−20.8221	−1.76611	−0.883055	−	0.469269i	$-0.844518\pi$
$139$	−20.8221	−1.76611	−0.883055	+	0.469269i	$0.844518\pi$
$140$	−1.44651	−0.122252
$141$	−4.03122	−0.339490
$142$	−23.2430	−1.95051
$143$	3.59212	0.300388
$144$	138.889	11.5741
$145$	1.27132	0.105578
$146$	4.66877	0.386390
$147$	21.1836	1.74719
$148$	−29.2788	−2.40670
$149$	−13.3985	−1.09765	−0.548826	−	0.835937i	$-0.684925\pi$
$149$	−13.3985	−1.09765	−0.548826	+	0.835937i	$0.684925\pi$
$150$	−44.2192	−3.61048
$151$	−14.7845	−1.20315	−0.601573	−	0.798818i	$-0.705459\pi$
$151$	−14.7845	−1.20315	−0.601573	+	0.798818i	$0.705459\pi$
$152$	8.64012	0.700806
$153$	−38.2514	−3.09244
$154$	4.07834	0.328642
$155$	−0.654963	−0.0526079
$156$	31.9436	2.55754
$157$	−13.8881	−1.10839	−0.554195	−	0.832387i	$-0.686974\pi$
$157$	−13.8881	−1.10839	−0.554195	+	0.832387i	$0.686974\pi$
$158$	−3.98931	−0.317373
$159$	−25.2383	−2.00152
$160$	10.9533	0.865931
$161$	−5.86018	−0.461847
$162$	−69.7523	−5.48026
$163$	7.74695	0.606788	0.303394	−	0.952865i	$-0.401880\pi$
$163$	7.74695	0.606788	0.303394	+	0.952865i	$0.401880\pi$
$164$	−54.4429	−4.25128
$165$	−2.50357	−0.194903
$166$	5.21373	0.404664
$167$	13.7092	1.06085	0.530424	−	0.847732i	$-0.322033\pi$
$167$	13.7092	1.06085	0.530424	+	0.847732i	$0.322033\pi$
$168$	23.8606	1.84089
$169$	−10.1602	−0.781557
$170$	−5.16639	−0.396244
$171$	−6.02450	−0.460705
$172$	−44.4346	−3.38810
$173$	19.1159	1.45335	0.726677	−	0.686979i	$-0.241064\pi$
$173$	19.1159	1.45335	0.726677	+	0.686979i	$0.241064\pi$
$174$	−31.8751	−2.41644
$175$	−3.32551	−0.251385
$176$	−39.4084	−2.97052
$177$	6.42921	0.483249
$178$	17.7976	1.33399
$179$	16.0029	1.19611	0.598055	−	0.801455i	$-0.295940\pi$
$179$	16.0029	1.19611	0.598055	+	0.801455i	$0.295940\pi$
$180$	−15.9101	−1.18587
$181$	6.21687	0.462096	0.231048	−	0.972942i	$-0.425785\pi$
$181$	6.21687	0.462096	0.231048	+	0.972942i	$0.425785\pi$
$182$	3.22414	0.238989
$183$	12.9495	0.957251
$184$	92.4403	6.81479
$185$	1.81410	0.133375
$186$	16.4214	1.20408
$187$	10.8534	0.793680
$188$	7.26891	0.530140
$189$	−9.99356	−0.726924
$190$	−0.813695	−0.0590316
$191$	−16.3139	−1.18043	−0.590215	−	0.807246i	$-0.700957\pi$
$191$	−16.3139	−1.18043	−0.590215	+	0.807246i	$0.700957\pi$
$192$	−154.739	−11.1673
$193$	−0.312001	−0.0224583	−0.0112291	−	0.999937i	$-0.503574\pi$
$193$	−0.312001	−0.0224583	−0.0112291	+	0.999937i	$0.503574\pi$
$194$	−29.6930	−2.13183
$195$	−1.97921	−0.141734
$196$	−38.1973	−2.72838
$197$	−19.5223	−1.39091	−0.695453	−	0.718571i	$-0.744796\pi$
$197$	−19.5223	−1.39091	−0.695453	+	0.718571i	$0.744796\pi$
$198$	44.8575	3.18789
$199$	16.3357	1.15801	0.579003	−	0.815326i	$-0.303442\pi$
$199$	16.3357	1.15801	0.579003	+	0.815326i	$0.303442\pi$
$200$	52.4577	3.70932
$201$	−18.5372	−1.30751
$202$	38.5389	2.71159
$203$	−2.39717	−0.168248
$204$	96.5161	6.75748
$205$	3.37325	0.235598
$206$	−6.04766	−0.421360
$207$	−64.4559	−4.48000
$208$	−31.1544	−2.16017
$209$	1.70939	0.118241
$210$	−2.24711	−0.155065
$211$	−25.7810	−1.77484	−0.887418	−	0.460966i	$-0.847503\pi$
$211$	−25.7810	−1.77484	−0.887418	+	0.460966i	$0.847503\pi$
$212$	45.5085	3.12554
$213$	−26.9037	−1.84341
$214$	24.6138	1.68256
$215$	2.75314	0.187763
$216$	157.642	10.7262
$217$	1.23498	0.0838358
$218$	43.8460	2.96962
$219$	5.40409	0.365175
$220$	4.51433	0.304356
$221$	8.58020	0.577167
$222$	−45.4836	−3.05266
$223$	−1.23190	−0.0824938	−0.0412469	−	0.999149i	$-0.513133\pi$
$223$	−1.23190	−0.0824938	−0.0412469	+	0.999149i	$0.513133\pi$
$224$	−20.6531	−1.37994
$225$	−36.5772	−2.43848
$226$	25.2072	1.67676
$227$	−4.81199	−0.319383	−0.159692	−	0.987167i	$-0.551050\pi$
$227$	−4.81199	−0.319383	−0.159692	+	0.987167i	$0.551050\pi$
$228$	15.2011	1.00672
$229$	−22.2208	−1.46839	−0.734195	−	0.678938i	$-0.762440\pi$
$229$	−22.2208	−1.46839	−0.734195	+	0.678938i	$0.762440\pi$
$230$	−8.70569	−0.574036
$231$	4.72066	0.310597
$232$	37.8138	2.48259
$233$	−12.3169	−0.806910	−0.403455	−	0.914999i	$-0.632191\pi$
$233$	−12.3169	−0.806910	−0.403455	+	0.914999i	$0.632191\pi$
$234$	35.4623	2.31824
$235$	−0.450378	−0.0293794
$236$	−11.5929	−0.754631
$237$	−4.61762	−0.299946
$238$	9.74158	0.631453
$239$	6.39467	0.413637	0.206818	−	0.978379i	$-0.433689\pi$
$239$	6.39467	0.413637	0.206818	+	0.978379i	$0.433689\pi$
$240$	21.7135	1.40160
$241$	16.5963	1.06906	0.534531	−	0.845149i	$-0.320488\pi$
$241$	16.5963	1.06906	0.534531	+	0.845149i	$0.320488\pi$
$242$	18.0847	1.16253
$243$	−36.8443	−2.36356
$244$	−23.3499	−1.49482
$245$	2.36668	0.151202
$246$	−84.5753	−5.39232
$247$	1.35136	0.0859851
$248$	−19.4809	−1.23704
$249$	6.03488	0.382445
$250$	−10.0137	−0.633322
$251$	3.92502	0.247745	0.123873	−	0.992298i	$-0.460469\pi$
$251$	3.92502	0.247745	0.123873	+	0.992298i	$0.460469\pi$
$252$	29.9997	1.88980
$253$	18.2887	1.14980
$254$	−37.2637	−2.33813
$255$	−5.98008	−0.374487
$256$	109.618	6.85113
$257$	−29.1741	−1.81983	−0.909916	−	0.414792i	$-0.863854\pi$
$257$	−29.1741	−1.81983	−0.909916	+	0.414792i	$0.863854\pi$
$258$	−69.0276	−4.29747
$259$	−3.42060	−0.212546
$260$	3.56882	0.221329
$261$	−26.3664	−1.63204
$262$	7.34962	0.454061
$263$	−15.1007	−0.931152	−0.465576	−	0.885008i	$-0.654153\pi$
$263$	−15.1007	−0.931152	−0.465576	+	0.885008i	$0.654153\pi$
$264$	−74.4653	−4.58302
$265$	−2.81968	−0.173212
$266$	1.53428	0.0940726
$267$	20.6007	1.26074
$268$	33.4254	2.04178
$269$	21.7530	1.32631	0.663153	−	0.748484i	$-0.269218\pi$
$269$	21.7530	1.32631	0.663153	+	0.748484i	$0.269218\pi$
$270$	−14.8461	−0.903506
$271$	−22.4406	−1.36317	−0.681583	−	0.731741i	$-0.738708\pi$
$271$	−22.4406	−1.36317	−0.681583	+	0.731741i	$0.738708\pi$
$272$	−94.1316	−5.70757
$273$	3.73193	0.225867
$274$	−15.3601	−0.927936
$275$	10.3784	0.625841
$276$	162.636	9.78952
$277$	−22.3480	−1.34276	−0.671382	−	0.741112i	$-0.734299\pi$
$277$	−22.3480	−1.34276	−0.671382	+	0.741112i	$0.734299\pi$
$278$	58.3258	3.49815
$279$	13.5835	0.813222
$280$	2.66577	0.159310
$281$	30.8208	1.83861	0.919307	−	0.393542i	$-0.128750\pi$
$281$	30.8208	1.83861	0.919307	+	0.393542i	$0.128750\pi$
$282$	11.2920	0.672429
$283$	17.7865	1.05730	0.528649	−	0.848841i	$-0.322699\pi$
$283$	17.7865	1.05730	0.528649	+	0.848841i	$0.322699\pi$
$284$	48.5115	2.87863
$285$	−0.941849	−0.0557903
$286$	−10.0620	−0.594981
$287$	−6.36050	−0.375449
$288$	−227.163	−13.3857
$289$	8.92466	0.524980
$290$	−3.56116	−0.209119
$291$	−34.3696	−2.01478
$292$	−9.74441	−0.570249
$293$	−21.5171	−1.25704	−0.628522	−	0.777792i	$-0.716340\pi$
$293$	−21.5171	−1.25704	−0.628522	+	0.777792i	$0.716340\pi$
$294$	−59.3382	−3.46067
$295$	0.718287	0.0418203
$296$	53.9577	3.13623
$297$	31.1883	1.80973
$298$	37.5312	2.17413
$299$	14.4582	0.836138
$300$	92.2919	5.32848
$301$	−5.19124	−0.299218
$302$	41.4135	2.38308
$303$	44.6087	2.56270
$304$	−14.8255	−0.850302
$305$	1.44675	0.0828404
$306$	107.147	6.12521
$307$	−20.6707	−1.17974	−0.589869	−	0.807499i	$-0.700821\pi$
$307$	−20.6707	−1.17974	−0.589869	+	0.807499i	$0.700821\pi$
$308$	−8.51209	−0.485021
$309$	−7.00015	−0.398225
$310$	1.83464	0.104201
$311$	4.80834	0.272656	0.136328	−	0.990664i	$-0.456470\pi$
$311$	4.80834	0.272656	0.136328	+	0.990664i	$0.456470\pi$
$312$	−58.8688	−3.33279
$313$	13.7358	0.776396	0.388198	−	0.921576i	$-0.373098\pi$
$313$	13.7358	0.776396	0.388198	+	0.921576i	$0.373098\pi$
$314$	38.9025	2.19539
$315$	−1.85876	−0.104729
$316$	8.32628	0.468390
$317$	2.59886	0.145966	0.0729832	−	0.997333i	$-0.476748\pi$
$317$	2.59886	0.145966	0.0729832	+	0.997333i	$0.476748\pi$
$318$	70.6959	3.96443
$319$	7.48119	0.418866
$320$	−17.2878	−0.966417
$321$	28.4904	1.59018
$322$	16.4152	0.914782
$323$	4.08307	0.227188
$324$	145.583	8.08796
$325$	8.20467	0.455113
$326$	−21.7003	−1.20187
$327$	50.7516	2.80657
$328$	100.333	5.53994
$329$	0.849218	0.0468189
$330$	7.01287	0.386046
$331$	16.5472	0.909516	0.454758	−	0.890615i	$-0.349726\pi$
$331$	16.5472	0.909516	0.454758	+	0.890615i	$0.349726\pi$
$332$	−10.8818	−0.597218
$333$	−37.6231	−2.06173
$334$	−38.4014	−2.10123
$335$	−2.07102	−0.113152
$336$	−40.9423	−2.23359
$337$	30.7087	1.67281	0.836405	−	0.548112i	$-0.184653\pi$
$337$	30.7087	1.67281	0.836405	+	0.548112i	$0.184653\pi$
$338$	28.4603	1.54803
$339$	29.1773	1.58469
$340$	10.7830	0.584791
$341$	−3.85417	−0.208715
$342$	16.8755	0.912522
$343$	−9.24373	−0.499115
$344$	81.8883	4.41512
$345$	−10.0768	−0.542518
$346$	−53.5463	−2.87867
$347$	30.0224	1.61169	0.805843	−	0.592129i	$-0.201712\pi$
$347$	30.0224	1.61169	0.805843	+	0.592129i	$0.201712\pi$
$348$	66.5279	3.56627
$349$	15.6654	0.838550	0.419275	−	0.907859i	$-0.362284\pi$
$349$	15.6654	0.838550	0.419275	+	0.907859i	$0.362284\pi$
$350$	9.31523	0.497920
$351$	24.6560	1.31604
$352$	64.4551	3.43547
$353$	5.19326	0.276409	0.138205	−	0.990404i	$-0.455867\pi$
$353$	5.19326	0.276409	0.138205	+	0.990404i	$0.455867\pi$
$354$	−18.0091	−0.957174
$355$	−3.00574	−0.159528
$356$	−37.1462	−1.96874
$357$	11.2759	0.596782
$358$	−44.8263	−2.36914
$359$	14.1782	0.748297	0.374148	−	0.927369i	$-0.377935\pi$
$359$	14.1782	0.748297	0.374148	+	0.927369i	$0.377935\pi$
$360$	29.3207	1.54534
$361$	−18.3569	−0.966154
$362$	−17.4143	−0.915276
$363$	20.9330	1.09870
$364$	−6.72926	−0.352709
$365$	0.603758	0.0316022
$366$	−36.2733	−1.89603
$367$	36.4637	1.90339	0.951696	−	0.307043i	$-0.0993396\pi$
$367$	36.4637	1.90339	0.951696	+	0.307043i	$0.0993396\pi$
$368$	−158.618	−8.26852
$369$	−69.9590	−3.64192
$370$	−5.08154	−0.264177
$371$	5.31670	0.276029
$372$	−34.2740	−1.77702
$373$	7.99296	0.413860	0.206930	−	0.978356i	$-0.433653\pi$
$373$	7.99296	0.413860	0.206930	+	0.978356i	$0.433653\pi$
$374$	−30.4019	−1.57205
$375$	−11.5908	−0.598548
$376$	−13.3958	−0.690838
$377$	5.91428	0.304601
$378$	27.9934	1.43982
$379$	−24.3021	−1.24832	−0.624158	−	0.781298i	$-0.714558\pi$
$379$	−24.3021	−1.24832	−0.624158	+	0.781298i	$0.714558\pi$
$380$	1.69830	0.0871210
$381$	−43.1326	−2.20975
$382$	45.6975	2.33809
$383$	−10.8819	−0.556038	−0.278019	−	0.960576i	$-0.589678\pi$
$383$	−10.8819	−0.556038	−0.278019	+	0.960576i	$0.589678\pi$
$384$	237.365	12.1130
$385$	0.527404	0.0268790
$386$	0.873958	0.0444833
$387$	−57.0983	−2.90247
$388$	61.9737	3.14624
$389$	−38.8963	−1.97212	−0.986061	−	0.166387i	$-0.946790\pi$
$389$	−38.8963	−1.97212	−0.986061	+	0.166387i	$0.946790\pi$
$390$	5.54404	0.280734
$391$	43.6847	2.20923
$392$	70.3936	3.55541
$393$	8.50717	0.429130
$394$	54.6847	2.75498
$395$	−0.515892	−0.0259573
$396$	−93.6242	−4.70480
$397$	−27.3289	−1.37160	−0.685800	−	0.727790i	$-0.740547\pi$
$397$	−27.3289	−1.37160	−0.685800	+	0.727790i	$0.740547\pi$
$398$	−45.7585	−2.29367
$399$	1.77592	0.0889073
$400$	−90.0118	−4.50059
$401$	18.3083	0.914272	0.457136	−	0.889397i	$-0.348875\pi$
$401$	18.3083	0.914272	0.457136	+	0.889397i	$0.348875\pi$
$402$	51.9253	2.58980
$403$	−3.04693	−0.151778
$404$	−80.4364	−4.00186
$405$	−9.02026	−0.448220
$406$	6.71481	0.333251
$407$	10.6752	0.529148
$408$	−177.869	−8.80583
$409$	−2.75652	−0.136301	−0.0681505	−	0.997675i	$-0.521710\pi$
$409$	−2.75652	−0.136301	−0.0681505	+	0.997675i	$0.521710\pi$
$410$	−9.44896	−0.466651
$411$	−17.7792	−0.876985
$412$	12.6224	0.621859
$413$	−1.35438	−0.0666447
$414$	180.550	8.87356
$415$	0.674232	0.0330968
$416$	50.9552	2.49828
$417$	67.5119	3.30607
$418$	−4.78824	−0.234200
$419$	35.9064	1.75414	0.877071	−	0.480360i	$-0.159494\pi$
$419$	35.9064	1.75414	0.877071	+	0.480360i	$0.159494\pi$
$420$	4.69004	0.228851
$421$	−30.0350	−1.46382	−0.731908	−	0.681403i	$-0.761370\pi$
$421$	−30.0350	−1.46382	−0.731908	+	0.681403i	$0.761370\pi$
$422$	72.2162	3.51543
$423$	9.34053	0.454152
$424$	−83.8674	−4.07296
$425$	24.7900	1.20249
$426$	75.3610	3.65125
$427$	−2.72794	−0.132014
$428$	−51.3726	−2.48319
$429$	−11.6468	−0.562312
$430$	−7.71194	−0.371903
$431$	−25.4638	−1.22655	−0.613273	−	0.789871i	$-0.710148\pi$
$431$	−25.4638	−1.22655	−0.613273	+	0.789871i	$0.710148\pi$
$432$	−270.496	−13.0143
$433$	−15.6738	−0.753233	−0.376616	−	0.926369i	$-0.622913\pi$
$433$	−15.6738	−0.753233	−0.376616	+	0.926369i	$0.622913\pi$
$434$	−3.45935	−0.166054
$435$	−4.12203	−0.197636
$436$	−91.5130	−4.38268
$437$	6.88024	0.329126
$438$	−15.1376	−0.723304
$439$	1.10537	0.0527567	0.0263783	−	0.999652i	$-0.491603\pi$
$439$	1.10537	0.0527567	0.0263783	+	0.999652i	$0.491603\pi$
$440$	−8.31944	−0.396614
$441$	−49.0834	−2.33730
$442$	−24.0344	−1.14320
$443$	−26.2214	−1.24581	−0.622907	−	0.782296i	$-0.714049\pi$
$443$	−26.2214	−1.24581	−0.622907	+	0.782296i	$0.714049\pi$
$444$	94.9309	4.50522
$445$	2.30156	0.109104
$446$	3.45071	0.163396
$447$	43.4423	2.05475
$448$	32.5973	1.54008
$449$	6.25150	0.295027	0.147513	−	0.989060i	$-0.452873\pi$
$449$	6.25150	0.295027	0.147513	+	0.989060i	$0.452873\pi$
$450$	102.458	4.82992
$451$	19.8501	0.934706
$452$	−52.6111	−2.47462
$453$	47.9360	2.25223
$454$	13.4791	0.632604
$455$	0.416941	0.0195465
$456$	−28.0140	−1.31187
$457$	26.6932	1.24866	0.624328	−	0.781163i	$-0.285373\pi$
$457$	26.6932	1.24866	0.624328	+	0.781163i	$0.285373\pi$
$458$	62.2436	2.90845
$459$	74.4970	3.47722
$460$	18.1701	0.847183
$461$	16.2849	0.758464	0.379232	−	0.925302i	$-0.376188\pi$
$461$	16.2849	0.758464	0.379232	+	0.925302i	$0.376188\pi$
$462$	−13.2232	−0.615201
$463$	−0.447975	−0.0208191	−0.0104096	−	0.999946i	$-0.503314\pi$
$463$	−0.447975	−0.0208191	−0.0104096	+	0.999946i	$0.503314\pi$
$464$	−64.8844	−3.01218
$465$	2.12360	0.0984794
$466$	34.5015	1.59825
$467$	27.7029	1.28194	0.640970	−	0.767566i	$-0.278532\pi$
$467$	27.7029	1.28194	0.640970	+	0.767566i	$0.278532\pi$
$468$	−74.0149	−3.42134
$469$	3.90505	0.180319
$470$	1.26157	0.0581919
$471$	45.0295	2.07485
$472$	21.3644	0.983378
$473$	16.2010	0.744924
$474$	12.9346	0.594106
$475$	3.90437	0.179145
$476$	−20.3321	−0.931921
$477$	58.4783	2.67754
$478$	−17.9124	−0.819293
$479$	25.3320	1.15745	0.578725	−	0.815523i	$-0.303550\pi$
$479$	25.3320	1.15745	0.578725	+	0.815523i	$0.303550\pi$
$480$	−35.5139	−1.62098
$481$	8.43928	0.384798
$482$	−46.4886	−2.11750
$483$	19.0005	0.864554
$484$	−37.7455	−1.71570
$485$	−3.83986	−0.174359
$486$	103.206	4.68152
$487$	−36.4431	−1.65139	−0.825697	−	0.564113i	$-0.809218\pi$
$487$	−36.4431	−1.65139	−0.825697	+	0.564113i	$0.809218\pi$
$488$	43.0314	1.94794
$489$	−25.1181	−1.13588
$490$	−6.62941	−0.299486
$491$	−21.3805	−0.964887	−0.482443	−	0.875927i	$-0.660251\pi$
$491$	−21.3805	−0.964887	−0.482443	+	0.875927i	$0.660251\pi$
$492$	176.521	7.95818
$493$	17.8697	0.804811
$494$	−3.78536	−0.170311
$495$	5.80091	0.260731
$496$	33.4272	1.50093
$497$	5.66754	0.254224
$498$	−16.9046	−0.757512
$499$	7.43051	0.332635	0.166318	−	0.986072i	$-0.446812\pi$
$499$	7.43051	0.332635	0.166318	+	0.986072i	$0.446812\pi$
$500$	20.9000	0.934679
$501$	−44.4495	−1.98586
$502$	−10.9945	−0.490710
$503$	12.0516	0.537355	0.268677	−	0.963230i	$-0.413413\pi$
$503$	12.0516	0.537355	0.268677	+	0.963230i	$0.413413\pi$
$504$	−55.2863	−2.46265
$505$	4.98379	0.221776
$506$	−51.2292	−2.27742
$507$	32.9427	1.46304
$508$	77.7748	3.45070
$509$	18.4659	0.818488	0.409244	−	0.912425i	$-0.365792\pi$
$509$	18.4659	0.818488	0.409244	+	0.912425i	$0.365792\pi$
$510$	16.7511	0.741749
$511$	−1.13843	−0.0503611
$512$	−160.639	−7.09930
$513$	11.7331	0.518029
$514$	81.7209	3.60455
$515$	−0.782074	−0.0344623
$516$	144.071	6.34236
$517$	−2.65028	−0.116559
$518$	9.58159	0.420991
$519$	−61.9797	−2.72061
$520$	−6.57696	−0.288419
$521$	−27.5513	−1.20704	−0.603522	−	0.797346i	$-0.706237\pi$
$521$	−27.5513	−1.20704	−0.603522	+	0.797346i	$0.706237\pi$
$522$	73.8561	3.23259
$523$	18.7489	0.819831	0.409916	−	0.912123i	$-0.365558\pi$
$523$	18.7489	0.819831	0.409916	+	0.912123i	$0.365558\pi$
$524$	−15.3397	−0.670120
$525$	10.7824	0.470580
$526$	42.2993	1.84434
$527$	−9.20614	−0.401026
$528$	127.774	5.56067
$529$	50.6114	2.20050
$530$	7.89833	0.343081
$531$	−14.8968	−0.646466
$532$	−3.20226	−0.138836
$533$	15.6926	0.679721
$534$	−57.7054	−2.49716
$535$	3.18302	0.137614
$536$	−61.5996	−2.66070
$537$	−51.8863	−2.23906
$538$	−60.9334	−2.62702
$539$	13.9269	0.599873
$540$	30.9860	1.33343
$541$	−30.0662	−1.29265	−0.646323	−	0.763064i	$-0.723694\pi$
$541$	−30.0662	−1.29265	−0.646323	+	0.763064i	$0.723694\pi$
$542$	62.8592	2.70003
$543$	−20.1570	−0.865021
$544$	153.959	6.60092
$545$	5.67010	0.242880
$546$	−10.4537	−0.447376
$547$	−39.9761	−1.70925	−0.854627	−	0.519242i	$-0.826214\pi$
$547$	−39.9761	−1.70925	−0.854627	+	0.519242i	$0.826214\pi$
$548$	32.0587	1.36948
$549$	−30.0045	−1.28056
$550$	−29.0714	−1.23961
$551$	2.81444	0.119899
$552$	−299.721	−12.7570
$553$	0.972749	0.0413655
$554$	62.6000	2.65962
$555$	−5.88187	−0.249671
$556$	−121.734	−5.16269
$557$	−12.4425	−0.527204	−0.263602	−	0.964631i	$-0.584911\pi$
$557$	−12.4425	−0.527204	−0.263602	+	0.964631i	$0.584911\pi$
$558$	−38.0493	−1.61075
$559$	12.8078	0.541711
$560$	−4.57417	−0.193294
$561$	−35.1902	−1.48573
$562$	−86.3334	−3.64175
$563$	−11.0166	−0.464294	−0.232147	−	0.972681i	$-0.574575\pi$
$563$	−11.0166	−0.464294	−0.232147	+	0.972681i	$0.574575\pi$
$564$	−23.5681	−0.992395
$565$	3.25976	0.137139
$566$	−49.8225	−2.09420
$567$	17.0083	0.714282
$568$	−89.4016	−3.75121
$569$	11.3267	0.474839	0.237420	−	0.971407i	$-0.423698\pi$
$569$	11.3267	0.474839	0.237420	+	0.971407i	$0.423698\pi$
$570$	2.63825	0.110504
$571$	−14.5739	−0.609899	−0.304949	−	0.952369i	$-0.598640\pi$
$571$	−14.5739	−0.609899	−0.304949	+	0.952369i	$0.598640\pi$
$572$	21.0009	0.878094
$573$	52.8947	2.20971
$574$	17.8167	0.743653
$575$	41.7727	1.74204
$576$	358.537	14.9390
$577$	−44.5889	−1.85626	−0.928131	−	0.372254i	$-0.878585\pi$
$577$	−44.5889	−1.85626	−0.928131	+	0.372254i	$0.878585\pi$
$578$	−24.9992	−1.03983
$579$	1.01160	0.0420408
$580$	7.43267	0.308625
$581$	−1.27131	−0.0527429
$582$	96.2741	3.99069
$583$	−16.5926	−0.687195
$584$	17.9579	0.743105
$585$	4.58592	0.189605
$586$	60.2726	2.48984
$587$	−3.53774	−0.146018	−0.0730091	−	0.997331i	$-0.523260\pi$
$587$	−3.53774	−0.146018	−0.0730091	+	0.997331i	$0.523260\pi$
$588$	123.848	5.10739
$589$	−1.44995	−0.0597440
$590$	−2.01202	−0.0828337
$591$	63.2974	2.60371
$592$	−92.5856	−3.80525
$593$	−33.6146	−1.38038	−0.690192	−	0.723626i	$-0.742474\pi$
$593$	−33.6146	−1.38038	−0.690192	+	0.723626i	$0.742474\pi$
$594$	−87.3629	−3.58454
$595$	1.25977	0.0516454
$596$	−78.3332	−3.20865
$597$	−52.9654	−2.16773
$598$	−40.4994	−1.65614
$599$	−26.8304	−1.09626	−0.548130	−	0.836393i	$-0.684660\pi$
$599$	−26.8304	−1.09626	−0.548130	+	0.836393i	$0.684660\pi$
$600$	−170.084	−6.94366
$601$	31.0040	1.26468	0.632339	−	0.774692i	$-0.282095\pi$
$601$	31.0040	1.26468	0.632339	+	0.774692i	$0.282095\pi$
$602$	14.5414	0.592663
$603$	42.9516	1.74912
$604$	−86.4361	−3.51703
$605$	2.33869	0.0950812
$606$	−124.955	−5.07596
$607$	11.6366	0.472316	0.236158	−	0.971715i	$-0.424112\pi$
$607$	11.6366	0.472316	0.236158	+	0.971715i	$0.424112\pi$
$608$	24.2481	0.983392
$609$	7.77238	0.314953
$610$	−4.05254	−0.164082
$611$	−2.09518	−0.0847620
$612$	−223.633	−9.03981
$613$	23.0572	0.931270	0.465635	−	0.884977i	$-0.345826\pi$
$613$	23.0572	0.931270	0.465635	+	0.884977i	$0.345826\pi$
$614$	57.9015	2.33672
$615$	−10.9371	−0.441028
$616$	15.6869	0.632043
$617$	18.5259	0.745824	0.372912	−	0.927867i	$-0.378359\pi$
$617$	18.5259	0.745824	0.372912	+	0.927867i	$0.378359\pi$
$618$	19.6084	0.788766
$619$	10.3076	0.414297	0.207148	−	0.978310i	$-0.433582\pi$
$619$	10.3076	0.414297	0.207148	+	0.978310i	$0.433582\pi$
$620$	−3.82917	−0.153783
$621$	125.532	5.03743
$622$	−13.4689	−0.540052
$623$	−4.33974	−0.173868
$624$	101.012	4.04374
$625$	23.0490	0.921958
$626$	−38.4761	−1.53781
$627$	−5.54237	−0.221341
$628$	−81.1952	−3.24004
$629$	25.4989	1.01671
$630$	5.20666	0.207438
$631$	15.6901	0.624612	0.312306	−	0.949982i	$-0.398899\pi$
$631$	15.6901	0.624612	0.312306	+	0.949982i	$0.398899\pi$
$632$	−15.3445	−0.610370
$633$	83.5900	3.32241
$634$	−7.27977	−0.289116
$635$	−4.81889	−0.191232
$636$	−147.553	−5.85085
$637$	11.0099	0.436230
$638$	−20.9559	−0.829651
$639$	62.3371	2.46602
$640$	26.5190	1.04826
$641$	−10.8883	−0.430061	−0.215030	−	0.976607i	$-0.568985\pi$
$641$	−10.8883	−0.430061	−0.215030	+	0.976607i	$0.568985\pi$
$642$	−79.8056	−3.14968
$643$	30.5679	1.20548	0.602740	−	0.797937i	$-0.294075\pi$
$643$	30.5679	1.20548	0.602740	+	0.797937i	$0.294075\pi$
$644$	−34.2609	−1.35007
$645$	−8.92655	−0.351482
$646$	−11.4373	−0.449993
$647$	−40.1376	−1.57797	−0.788986	−	0.614411i	$-0.789394\pi$
$647$	−40.1376	−1.57797	−0.788986	+	0.614411i	$0.789394\pi$
$648$	−268.295	−10.5396
$649$	4.22681	0.165917
$650$	−22.9825	−0.901446
$651$	−4.00419	−0.156936
$652$	45.2917	1.77376
$653$	−32.3278	−1.26509	−0.632543	−	0.774525i	$-0.717989\pi$
$653$	−32.3278	−1.26509	−0.632543	+	0.774525i	$0.717989\pi$
$654$	−142.162	−5.55899
$655$	0.950442	0.0371369
$656$	−172.160	−6.72172
$657$	−12.5215	−0.488512
$658$	−2.37878	−0.0927345
$659$	25.0061	0.974099	0.487049	−	0.873374i	$-0.338073\pi$
$659$	25.0061	0.974099	0.487049	+	0.873374i	$0.338073\pi$
$660$	−14.6369	−0.569740
$661$	12.0993	0.470607	0.235304	−	0.971922i	$-0.424392\pi$
$661$	12.0993	0.470607	0.235304	+	0.971922i	$0.424392\pi$
$662$	−46.3510	−1.80148
$663$	−27.8197	−1.08043
$664$	20.0541	0.778249
$665$	0.198410	0.00769402
$666$	105.388	4.08369
$667$	30.1116	1.16593
$668$	80.1493	3.10107
$669$	3.99419	0.154424
$670$	5.80123	0.224121
$671$	8.51347	0.328659
$672$	66.9639	2.58319
$673$	6.14022	0.236688	0.118344	−	0.992973i	$-0.462241\pi$
$673$	6.14022	0.236688	0.118344	+	0.992973i	$0.462241\pi$
$674$	−86.0195	−3.31335
$675$	71.2365	2.74189
$676$	−59.4008	−2.28464
$677$	−7.12019	−0.273651	−0.136826	−	0.990595i	$-0.543690\pi$
$677$	−7.12019	−0.273651	−0.136826	+	0.990595i	$0.543690\pi$
$678$	−81.7296	−3.13881
$679$	7.24031	0.277858
$680$	−19.8720	−0.762055
$681$	15.6020	0.597870
$682$	10.7961	0.413403
$683$	−38.5686	−1.47579	−0.737893	−	0.674917i	$-0.764179\pi$
$683$	−38.5686	−1.47579	−0.737893	+	0.674917i	$0.764179\pi$
$684$	−35.2216	−1.34673
$685$	−1.98634	−0.0758942
$686$	25.8930	0.988599
$687$	72.0468	2.74875
$688$	−140.511	−5.35695
$689$	−13.1173	−0.499730
$690$	28.2266	1.07457
$691$	−46.1305	−1.75489	−0.877443	−	0.479681i	$-0.840752\pi$
$691$	−46.1305	−1.75489	−0.877443	+	0.479681i	$0.840752\pi$
$692$	111.759	4.24844
$693$	−10.9380	−0.415501
$694$	−84.0970	−3.19228
$695$	7.54260	0.286107
$696$	−122.604	−4.64730
$697$	47.4144	1.79595
$698$	−43.8810	−1.66092
$699$	39.9354	1.51050
$700$	−19.4422	−0.734848
$701$	−9.24854	−0.349312	−0.174656	−	0.984629i	$-0.555881\pi$
$701$	−9.24854	−0.349312	−0.174656	+	0.984629i	$0.555881\pi$
$702$	−69.0650	−2.60669
$703$	4.01601	0.151467
$704$	−101.731	−3.83414
$705$	1.46027	0.0549968
$706$	−14.5471	−0.547485
$707$	−9.39728	−0.353421
$708$	37.5877	1.41263
$709$	11.6155	0.436231	0.218115	−	0.975923i	$-0.430009\pi$
$709$	11.6155	0.436231	0.218115	+	0.975923i	$0.430009\pi$
$710$	8.41952	0.315979
$711$	10.6992	0.401253
$712$	68.4565	2.56552
$713$	−15.5129	−0.580964
$714$	−31.5853	−1.18205
$715$	−1.30121	−0.0486624
$716$	93.5591	3.49647
$717$	−20.7335	−0.774308
$718$	−39.7152	−1.48216
$719$	−11.1114	−0.414387	−0.207193	−	0.978300i	$-0.566433\pi$
$719$	−11.1114	−0.414387	−0.207193	+	0.978300i	$0.566433\pi$
$720$	−50.3112	−1.87499
$721$	1.47465	0.0549190
$722$	51.4203	1.91367
$723$	−53.8104	−2.00123
$724$	36.3462	1.35080
$725$	17.0876	0.634618
$726$	−58.6363	−2.17620
$727$	19.1828	0.711449	0.355725	−	0.934591i	$-0.384234\pi$
$727$	19.1828	0.711449	0.355725	+	0.934591i	$0.384234\pi$
$728$	12.4013	0.459623
$729$	44.7566	1.65765
$730$	−1.69121	−0.0625946
$731$	38.6981	1.43130
$732$	75.7076	2.79823
$733$	2.39648	0.0885161	0.0442580	−	0.999020i	$-0.485908\pi$
$733$	2.39648	0.0885161	0.0442580	+	0.999020i	$0.485908\pi$
$734$	−102.140	−3.77006
$735$	−7.67352	−0.283042
$736$	259.430	9.56272
$737$	−12.1871	−0.448916
$738$	195.965	7.21357
$739$	44.8936	1.65144	0.825720	−	0.564081i	$-0.190769\pi$
$739$	44.8936	1.65144	0.825720	+	0.564081i	$0.190769\pi$
$740$	10.6059	0.389881
$741$	−4.38154	−0.160960
$742$	−14.8928	−0.546733
$743$	13.0768	0.479741	0.239870	−	0.970805i	$-0.422895\pi$
$743$	13.0768	0.479741	0.239870	+	0.970805i	$0.422895\pi$
$744$	63.1633	2.31568
$745$	4.85348	0.177818
$746$	−22.3894	−0.819735
$747$	−13.9831	−0.511616
$748$	63.4533	2.32008
$749$	−6.00180	−0.219301
$750$	32.4675	1.18555
$751$	44.4244	1.62107	0.810535	−	0.585691i	$-0.199177\pi$
$751$	44.4244	1.62107	0.810535	+	0.585691i	$0.199177\pi$
$752$	22.9858	0.838207
$753$	−12.7261	−0.463767
$754$	−16.5667	−0.603325
$755$	5.35553	0.194908
$756$	−58.4263	−2.12494
$757$	−26.8094	−0.974404	−0.487202	−	0.873289i	$-0.661982\pi$
$757$	−26.8094	−0.974404	−0.487202	+	0.873289i	$0.661982\pi$
$758$	68.0737	2.47255
$759$	−59.2977	−2.15237
$760$	−3.12979	−0.113529
$761$	−43.1614	−1.56460	−0.782299	−	0.622903i	$-0.785953\pi$
$761$	−43.1614	−1.56460	−0.782299	+	0.622903i	$0.785953\pi$
$762$	120.821	4.37687
$763$	−10.6914	−0.387053
$764$	−95.3773	−3.45063
$765$	13.8561	0.500970
$766$	30.4817	1.10135
$767$	3.34152	0.120655
$768$	−355.416	−12.8250
$769$	39.3145	1.41772	0.708858	−	0.705351i	$-0.249210\pi$
$769$	39.3145	1.41772	0.708858	+	0.705351i	$0.249210\pi$
$770$	−1.47733	−0.0532394
$771$	94.5917	3.40664
$772$	−1.82408	−0.0656500
$773$	−3.66142	−0.131692	−0.0658461	−	0.997830i	$-0.520975\pi$
$773$	−3.66142	−0.131692	−0.0658461	+	0.997830i	$0.520975\pi$
$774$	159.940	5.74894
$775$	−8.80322	−0.316221
$776$	−114.211	−4.09994
$777$	11.0907	0.397875
$778$	108.954	3.90619
$779$	7.46765	0.267556
$780$	−11.5712	−0.414317
$781$	−17.6875	−0.632908
$782$	−122.367	−4.37583
$783$	51.3503	1.83511
$784$	−120.788	−4.31385
$785$	5.03081	0.179557
$786$	−23.8298	−0.849981
$787$	−11.0215	−0.392875	−0.196438	−	0.980516i	$-0.562937\pi$
$787$	−11.0215	−0.392875	−0.196438	+	0.980516i	$0.562937\pi$
$788$	−114.135	−4.06589
$789$	48.9614	1.74307
$790$	1.44509	0.0514138
$791$	−6.14649	−0.218544
$792$	172.540	6.13093
$793$	6.73035	0.239002
$794$	76.5522	2.71674
$795$	9.14229	0.324244
$796$	95.5048	3.38508
$797$	−20.3549	−0.721008	−0.360504	−	0.932758i	$-0.617395\pi$
$797$	−20.3549	−0.721008	−0.360504	+	0.932758i	$0.617395\pi$
$798$	−4.97461	−0.176099
$799$	−6.33049	−0.223957
$800$	147.220	5.20503
$801$	−47.7327	−1.68655
$802$	−51.2841	−1.81090
$803$	3.55285	0.125378
$804$	−108.376	−3.82212
$805$	2.12279	0.0748184
$806$	8.53487	0.300628
$807$	−70.5302	−2.48278
$808$	148.236	5.21492
$809$	−13.7301	−0.482723	−0.241362	−	0.970435i	$-0.577594\pi$
$809$	−13.7301	−0.482723	−0.241362	+	0.970435i	$0.577594\pi$
$810$	25.2670	0.887793
$811$	−24.5967	−0.863705	−0.431853	−	0.901944i	$-0.642140\pi$
$811$	−24.5967	−0.863705	−0.431853	+	0.901944i	$0.642140\pi$
$812$	−14.0148	−0.491823
$813$	72.7593	2.55178
$814$	−29.9026	−1.04809
$815$	−2.80625	−0.0982987
$816$	305.204	10.6843
$817$	6.09486	0.213232
$818$	7.72139	0.269972
$819$	−8.64708	−0.302153
$820$	19.7214	0.688700
$821$	−15.9617	−0.557067	−0.278534	−	0.960427i	$-0.589848\pi$
$821$	−15.9617	−0.557067	−0.278534	+	0.960427i	$0.589848\pi$
$822$	49.8022	1.73705
$823$	−53.1865	−1.85396	−0.926982	−	0.375106i	$-0.877606\pi$
$823$	−53.1865	−1.85396	−0.926982	+	0.375106i	$0.877606\pi$
$824$	−23.2617	−0.810359
$825$	−33.6500	−1.17154
$826$	3.79381	0.132004
$827$	33.9173	1.17942	0.589711	−	0.807615i	$-0.299242\pi$
$827$	33.9173	1.17942	0.589711	+	0.807615i	$0.299242\pi$
$828$	−376.835	−13.0959
$829$	14.4787	0.502866	0.251433	−	0.967875i	$-0.419098\pi$
$829$	14.4787	0.502866	0.251433	+	0.967875i	$0.419098\pi$
$830$	−1.88862	−0.0655549
$831$	72.4594	2.51359
$832$	−80.4238	−2.78819
$833$	33.2660	1.15260
$834$	−189.110	−6.54836
$835$	−4.96601	−0.171856
$836$	9.99376	0.345641
$837$	−26.4547	−0.914409
$838$	−100.579	−3.47444
$839$	−26.1228	−0.901859	−0.450929	−	0.892560i	$-0.648907\pi$
$839$	−26.1228	−0.901859	−0.450929	+	0.892560i	$0.648907\pi$
$840$	−8.64326	−0.298221
$841$	−16.6825	−0.575259
$842$	84.1323	2.89939
$843$	−99.9307	−3.44179
$844$	−150.726	−5.18819
$845$	3.68044	0.126611
$846$	−26.1641	−0.899542
$847$	−4.40976	−0.151521
$848$	143.907	4.94180
$849$	−57.6694	−1.97921
$850$	−69.4404	−2.38178
$851$	42.9672	1.47290
$852$	−157.289	−5.38865
$853$	41.5148	1.42144	0.710719	−	0.703476i	$-0.248370\pi$
$853$	41.5148	1.42144	0.710719	+	0.703476i	$0.248370\pi$
$854$	7.64134	0.261481
$855$	2.18231	0.0746335
$856$	94.6743	3.23590
$857$	−18.7795	−0.641496	−0.320748	−	0.947165i	$-0.603934\pi$
$857$	−18.7795	−0.641496	−0.320748	+	0.947165i	$0.603934\pi$
$858$	32.6243	1.11377
$859$	8.94616	0.305239	0.152619	−	0.988285i	$-0.451229\pi$
$859$	8.94616	0.305239	0.152619	+	0.988285i	$0.451229\pi$
$860$	16.0959	0.548867
$861$	20.6227	0.702821
$862$	71.3276	2.42943
$863$	−4.20772	−0.143232	−0.0716161	−	0.997432i	$-0.522816\pi$
$863$	−4.20772	−0.143232	−0.0716161	+	0.997432i	$0.522816\pi$
$864$	442.415	15.0513
$865$	−6.92453	−0.235441
$866$	43.9044	1.49193
$867$	−28.9365	−0.982736
$868$	7.22017	0.245068
$869$	−3.03580	−0.102982
$870$	11.5464	0.391460
$871$	−9.63452	−0.326453
$872$	168.649	5.71117
$873$	79.6360	2.69527
$874$	−19.2725	−0.651903
$875$	2.44173	0.0825455
$876$	31.5944	1.06748
$877$	12.4072	0.418960	0.209480	−	0.977813i	$-0.432823\pi$
$877$	12.4072	0.418960	0.209480	+	0.977813i	$0.432823\pi$
$878$	−3.09631	−0.104495
$879$	69.7653	2.35313
$880$	14.2753	0.481219
$881$	43.0471	1.45029	0.725147	−	0.688594i	$-0.241772\pi$
$881$	43.0471	1.45029	0.725147	+	0.688594i	$0.241772\pi$
$882$	137.490	4.62951
$883$	−12.9742	−0.436618	−0.218309	−	0.975880i	$-0.570054\pi$
$883$	−12.9742	−0.436618	−0.218309	+	0.975880i	$0.570054\pi$
$884$	50.1632	1.68717
$885$	−2.32891	−0.0782855
$886$	73.4497	2.46759
$887$	−34.3568	−1.15359	−0.576794	−	0.816890i	$-0.695696\pi$
$887$	−34.3568	−1.15359	−0.576794	+	0.816890i	$0.695696\pi$
$888$	−174.948	−5.87086
$889$	9.08634	0.304746
$890$	−6.44698	−0.216103
$891$	−53.0803	−1.77826
$892$	−7.20214	−0.241146
$893$	−0.997038	−0.0333646
$894$	−121.688	−4.06986
$895$	−5.79687	−0.193768
$896$	−50.0035	−1.67050
$897$	−46.8780	−1.56521
$898$	−17.5113	−0.584361
$899$	−6.34574	−0.211642
$900$	−213.845	−7.12816
$901$	−39.6334	−1.32038
$902$	−55.6030	−1.85138
$903$	16.8316	0.560121
$904$	96.9568	3.22474
$905$	−2.25199	−0.0748588
$906$	−134.276	−4.46101
$907$	12.9011	0.428374	0.214187	−	0.976793i	$-0.431290\pi$
$907$	12.9011	0.428374	0.214187	+	0.976793i	$0.431290\pi$
$908$	−28.1328	−0.933620
$909$	−103.361	−3.42825
$910$	−1.16791	−0.0387159
$911$	31.6977	1.05019	0.525096	−	0.851043i	$-0.324030\pi$
$911$	31.6977	1.05019	0.525096	+	0.851043i	$0.324030\pi$
$912$	48.0690	1.59172
$913$	3.96756	0.131307
$914$	−74.7714	−2.47322
$915$	−4.69080	−0.155073
$916$	−129.911	−4.29239
$917$	−1.79212	−0.0591812
$918$	−208.677	−6.88735
$919$	−22.1725	−0.731402	−0.365701	−	0.930732i	$-0.619171\pi$
$919$	−22.1725	−0.731402	−0.365701	+	0.930732i	$0.619171\pi$
$920$	−33.4855	−1.10399
$921$	67.0209	2.20841
$922$	−45.6164	−1.50229
$923$	−13.9829	−0.460253
$924$	27.5989	0.907936
$925$	24.3829	0.801704
$926$	1.25484	0.0412366
$927$	16.2197	0.532725
$928$	106.123	3.48365
$929$	35.0901	1.15127	0.575635	−	0.817707i	$-0.304755\pi$
$929$	35.0901	1.15127	0.575635	+	0.817707i	$0.304755\pi$
$930$	−5.94849	−0.195059
$931$	5.23932	0.171712
$932$	−72.0097	−2.35876
$933$	−15.5902	−0.510399
$934$	−77.5999	−2.53914
$935$	−3.93153	−0.128575
$936$	136.402	4.45843
$937$	−41.6743	−1.36144	−0.680720	−	0.732544i	$-0.738333\pi$
$937$	−41.6743	−1.36144	−0.680720	+	0.732544i	$0.738333\pi$
$938$	−10.9386	−0.357158
$939$	−44.5359	−1.45338
$940$	−2.63308	−0.0858817
$941$	−30.5881	−0.997142	−0.498571	−	0.866849i	$-0.666142\pi$
$941$	−30.5881	−0.997142	−0.498571	+	0.866849i	$0.666142\pi$
$942$	−126.134	−4.10967
$943$	79.8962	2.60178
$944$	−36.6591	−1.19315
$945$	3.62006	0.117761
$946$	−45.3814	−1.47548
$947$	3.41766	0.111059	0.0555295	−	0.998457i	$-0.482315\pi$
$947$	3.41766	0.111059	0.0555295	+	0.998457i	$0.482315\pi$
$948$	−26.9964	−0.876803
$949$	2.80872	0.0911749
$950$	−10.9367	−0.354833
$951$	−8.42631	−0.273242
$952$	37.4700	1.21441
$953$	−39.4300	−1.27726	−0.638631	−	0.769513i	$-0.720499\pi$
$953$	−39.4300	−1.27726	−0.638631	+	0.769513i	$0.720499\pi$
$954$	−163.806	−5.30341
$955$	5.90952	0.191228
$956$	37.3858	1.20914
$957$	−24.2564	−0.784097
$958$	−70.9586	−2.29257
$959$	3.74538	0.120945
$960$	56.0524	1.80908
$961$	−27.7308	−0.894542
$962$	−23.6396	−0.762172
$963$	−66.0136	−2.12726
$964$	97.0285	3.12508
$965$	0.113019	0.00363821
$966$	−53.2232	−1.71243
$967$	−4.46965	−0.143734	−0.0718672	−	0.997414i	$-0.522896\pi$
$967$	−4.46965	−0.143734	−0.0718672	+	0.997414i	$0.522896\pi$
$968$	69.5609	2.23577
$969$	−13.2386	−0.425285
$970$	10.7560	0.345354
$971$	15.6251	0.501434	0.250717	−	0.968060i	$-0.419334\pi$
$971$	15.6251	0.501434	0.250717	+	0.968060i	$0.419334\pi$
$972$	−215.406	−6.90915
$973$	−14.2221	−0.455939
$974$	102.082	3.27093
$975$	−26.6021	−0.851950
$976$	−73.8373	−2.36347
$977$	42.7389	1.36734	0.683669	−	0.729792i	$-0.260383\pi$
$977$	42.7389	1.36734	0.683669	+	0.729792i	$0.260383\pi$
$978$	70.3592	2.24984
$979$	13.5437	0.432857
$980$	13.8366	0.441992
$981$	−117.594	−3.75449
$982$	59.8897	1.91116
$983$	30.1285	0.960948	0.480474	−	0.877009i	$-0.340465\pi$
$983$	30.1285	0.960948	0.480474	+	0.877009i	$0.340465\pi$
$984$	−325.310	−10.3705
$985$	7.07175	0.225325
$986$	−50.0556	−1.59409
$987$	−2.75343	−0.0876427
$988$	7.90060	0.251351
$989$	65.2087	2.07352
$990$	−16.2492	−0.516432
$991$	−33.5491	−1.06572	−0.532861	−	0.846203i	$-0.678883\pi$
$991$	−33.5491	−1.06572	−0.532861	+	0.846203i	$0.678883\pi$
$992$	−54.6725	−1.73585
$993$	−53.6512	−1.70257
$994$	−15.8756	−0.503543
$995$	−5.91743	−0.187595
$996$	35.2823	1.11796
$997$	−22.5615	−0.714531	−0.357266	−	0.934003i	$-0.616291\pi$
$997$	−22.5615	−0.714531	−0.357266	+	0.934003i	$0.616291\pi$
$998$	−20.8139	−0.658853
$999$	73.2734	2.31827

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4001.2.a.b.1.1	✓	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)

\(f(q)\)	\(=\)	\(q-2.80114 q^{2} -3.24231 q^{3} +5.84639 q^{4} -0.362239 q^{5} +9.08218 q^{6} +0.683027 q^{7} -10.7743 q^{8} +7.51260 q^{9} +O(q^{10})\)	\(q-2.80114 q^{2} -3.24231 q^{3} +5.84639 q^{4} -0.362239 q^{5} +9.08218 q^{6} +0.683027 q^{7} -10.7743 q^{8} +7.51260 q^{9} +1.01468 q^{10} -2.13162 q^{11} -18.9558 q^{12} -1.68516 q^{13} -1.91326 q^{14} +1.17449 q^{15} +18.4875 q^{16} -5.09163 q^{17} -21.0439 q^{18} -0.801920 q^{19} -2.11779 q^{20} -2.21459 q^{21} +5.97097 q^{22} -8.57971 q^{23} +34.9336 q^{24} -4.86878 q^{25} +4.72037 q^{26} -14.6313 q^{27} +3.99325 q^{28} -3.50963 q^{29} -3.28992 q^{30} +1.80809 q^{31} -30.2376 q^{32} +6.91138 q^{33} +14.2624 q^{34} -0.247419 q^{35} +43.9216 q^{36} -5.00800 q^{37} +2.24629 q^{38} +5.46382 q^{39} +3.90287 q^{40} -9.31222 q^{41} +6.20338 q^{42} -7.60034 q^{43} -12.4623 q^{44} -2.72136 q^{45} +24.0330 q^{46} +1.24331 q^{47} -59.9424 q^{48} -6.53347 q^{49} +13.6381 q^{50} +16.5087 q^{51} -9.85210 q^{52} +7.78403 q^{53} +40.9843 q^{54} +0.772157 q^{55} -7.35914 q^{56} +2.60008 q^{57} +9.83096 q^{58} -1.98291 q^{59} +6.86655 q^{60} -3.99389 q^{61} -5.06473 q^{62} +5.13131 q^{63} +47.7248 q^{64} +0.610431 q^{65} -19.3598 q^{66} +5.71728 q^{67} -29.7677 q^{68} +27.8181 q^{69} +0.693057 q^{70} +8.29768 q^{71} -80.9430 q^{72} -1.66674 q^{73} +14.0281 q^{74} +15.7861 q^{75} -4.68834 q^{76} -1.45595 q^{77} -15.3049 q^{78} +1.42417 q^{79} -6.69691 q^{80} +24.9014 q^{81} +26.0849 q^{82} -1.86129 q^{83} -12.9474 q^{84} +1.84439 q^{85} +21.2896 q^{86} +11.3793 q^{87} +22.9667 q^{88} -6.35369 q^{89} +7.62291 q^{90} -1.15101 q^{91} -50.1604 q^{92} -5.86241 q^{93} -3.48270 q^{94} +0.290487 q^{95} +98.0399 q^{96} +10.6003 q^{97} +18.3012 q^{98} -16.0140 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 184 q + 3 q^{2} + 28 q^{3} + 217 q^{4} + 15 q^{5} + 31 q^{6} + 49 q^{7} + 6 q^{8} + 210 q^{9}+O(q^{10}) \) 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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