LMFDB - Embedded newform 4001.2.a.b.1.10

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			1.10
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)

$f(q)$	$=$	$q-2.65266 q^{2} +3.05290 q^{3} +5.03661 q^{4} -1.94746 q^{5} -8.09830 q^{6} +2.48037 q^{7} -8.05510 q^{8} +6.32018 q^{9} +O(q^{10})$	\(q-2.65266 q^{2} +3.05290 q^{3} +5.03661 q^{4} -1.94746 q^{5} -8.09830 q^{6} +2.48037 q^{7} -8.05510 q^{8} +6.32018 q^{9} +5.16596 q^{10} -2.94497 q^{11} +15.3763 q^{12} +0.192789 q^{13} -6.57957 q^{14} -5.94540 q^{15} +11.2942 q^{16} +4.76794 q^{17} -16.7653 q^{18} -2.90135 q^{19} -9.80861 q^{20} +7.57230 q^{21} +7.81201 q^{22} -3.08821 q^{23} -24.5914 q^{24} -1.20739 q^{25} -0.511405 q^{26} +10.1362 q^{27} +12.4926 q^{28} +2.23235 q^{29} +15.7711 q^{30} -3.07974 q^{31} -13.8496 q^{32} -8.99069 q^{33} -12.6477 q^{34} -4.83042 q^{35} +31.8323 q^{36} +8.80848 q^{37} +7.69631 q^{38} +0.588566 q^{39} +15.6870 q^{40} -2.72877 q^{41} -20.0867 q^{42} +11.9799 q^{43} -14.8327 q^{44} -12.3083 q^{45} +8.19199 q^{46} -4.38663 q^{47} +34.4801 q^{48} -0.847785 q^{49} +3.20280 q^{50} +14.5560 q^{51} +0.971006 q^{52} +14.3594 q^{53} -26.8878 q^{54} +5.73522 q^{55} -19.9796 q^{56} -8.85753 q^{57} -5.92167 q^{58} -3.28792 q^{59} -29.9447 q^{60} +12.6102 q^{61} +8.16952 q^{62} +15.6764 q^{63} +14.1497 q^{64} -0.375450 q^{65} +23.8493 q^{66} +4.80775 q^{67} +24.0143 q^{68} -9.42800 q^{69} +12.8135 q^{70} +0.546449 q^{71} -50.9097 q^{72} +4.67236 q^{73} -23.3659 q^{74} -3.68604 q^{75} -14.6130 q^{76} -7.30461 q^{77} -1.56127 q^{78} -4.07327 q^{79} -21.9951 q^{80} +11.9841 q^{81} +7.23849 q^{82} -0.610918 q^{83} +38.1387 q^{84} -9.28538 q^{85} -31.7787 q^{86} +6.81513 q^{87} +23.7220 q^{88} +4.34903 q^{89} +32.6498 q^{90} +0.478188 q^{91} -15.5541 q^{92} -9.40214 q^{93} +11.6363 q^{94} +5.65028 q^{95} -42.2813 q^{96} +6.32560 q^{97} +2.24889 q^{98} -18.6127 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.65266	−1.87571	−0.937857	−	0.347021i	$-0.887193\pi$
$2$	−2.65266	−1.87571	−0.937857	+	0.347021i	$0.887193\pi$
$3$	3.05290	1.76259	0.881295	−	0.472566i	$-0.156672\pi$
$3$	3.05290	1.76259	0.881295	+	0.472566i	$0.156672\pi$
$4$	5.03661	2.51831
$5$	−1.94746	−0.870932	−0.435466	−	0.900205i	$-0.643416\pi$
$5$	−1.94746	−0.870932	−0.435466	+	0.900205i	$0.643416\pi$
$6$	−8.09830	−3.30612
$7$	2.48037	0.937490	0.468745	−	0.883333i	$-0.344706\pi$
$7$	2.48037	0.937490	0.468745	+	0.883333i	$0.344706\pi$
$8$	−8.05510	−2.84791
$9$	6.32018	2.10673
$10$	5.16596	1.63362
$11$	−2.94497	−0.887942	−0.443971	−	0.896041i	$-0.646431\pi$
$11$	−2.94497	−0.887942	−0.443971	+	0.896041i	$0.646431\pi$
$12$	15.3763	4.43874
$13$	0.192789	0.0534702	0.0267351	−	0.999643i	$-0.491489\pi$
$13$	0.192789	0.0534702	0.0267351	+	0.999643i	$0.491489\pi$
$14$	−6.57957	−1.75846
$15$	−5.94540	−1.53510
$16$	11.2942	2.82356
$17$	4.76794	1.15640	0.578198	−	0.815897i	$-0.303756\pi$
$17$	4.76794	1.15640	0.578198	+	0.815897i	$0.303756\pi$
$18$	−16.7653	−3.95162
$19$	−2.90135	−0.665616	−0.332808	−	0.942995i	$-0.607996\pi$
$19$	−2.90135	−0.665616	−0.332808	+	0.942995i	$0.607996\pi$
$20$	−9.80861	−2.19327
$21$	7.57230	1.65241
$22$	7.81201	1.66553
$23$	−3.08821	−0.643937	−0.321969	−	0.946750i	$-0.604345\pi$
$23$	−3.08821	−0.643937	−0.321969	+	0.946750i	$0.604345\pi$
$24$	−24.5914	−5.01970
$25$	−1.20739	−0.241478
$26$	−0.511405	−0.100295
$27$	10.1362	1.95070
$28$	12.4926	2.36089
$29$	2.23235	0.414537	0.207268	−	0.978284i	$-0.433543\pi$
$29$	2.23235	0.414537	0.207268	+	0.978284i	$0.433543\pi$
$30$	15.7711	2.87940
$31$	−3.07974	−0.553138	−0.276569	−	0.960994i	$-0.589197\pi$
$31$	−3.07974	−0.553138	−0.276569	+	0.960994i	$0.589197\pi$
$32$	−13.8496	−2.44828
$33$	−8.99069	−1.56508
$34$	−12.6477	−2.16907
$35$	−4.83042	−0.816490
$36$	31.8323	5.30538
$37$	8.80848	1.44810	0.724052	−	0.689745i	$-0.242277\pi$
$37$	8.80848	1.44810	0.724052	+	0.689745i	$0.242277\pi$
$38$	7.69631	1.24851
$39$	0.588566	0.0942460
$40$	15.6870	2.48033
$41$	−2.72877	−0.426162	−0.213081	−	0.977035i	$-0.568350\pi$
$41$	−2.72877	−0.426162	−0.213081	+	0.977035i	$0.568350\pi$
$42$	−20.0867	−3.09945
$43$	11.9799	1.82692	0.913460	−	0.406929i	$-0.133400\pi$
$43$	11.9799	1.82692	0.913460	+	0.406929i	$0.133400\pi$
$44$	−14.8327	−2.23611
$45$	−12.3083	−1.83481
$46$	8.19199	1.20784
$47$	−4.38663	−0.639856	−0.319928	−	0.947442i	$-0.603659\pi$
$47$	−4.38663	−0.639856	−0.319928	+	0.947442i	$0.603659\pi$
$48$	34.4801	4.97678
$49$	−0.847785	−0.121112
$50$	3.20280	0.452944
$51$	14.5560	2.03825
$52$	0.971006	0.134654
$53$	14.3594	1.97242	0.986209	−	0.165504i	$-0.0529250\pi$
$53$	14.3594	1.97242	0.986209	+	0.165504i	$0.0529250\pi$
$54$	−26.8878	−3.65896
$55$	5.73522	0.773337
$56$	−19.9796	−2.66989
$57$	−8.85753	−1.17321
$58$	−5.92167	−0.777553
$59$	−3.28792	−0.428050	−0.214025	−	0.976828i	$-0.568657\pi$
$59$	−3.28792	−0.428050	−0.214025	+	0.976828i	$0.568657\pi$
$60$	−29.9447	−3.86584
$61$	12.6102	1.61458	0.807288	−	0.590158i	$-0.200935\pi$
$61$	12.6102	1.61458	0.807288	+	0.590158i	$0.200935\pi$
$62$	8.16952	1.03753
$63$	15.6764	1.97503
$64$	14.1497	1.76872
$65$	−0.375450	−0.0465689
$66$	23.8493	2.93564
$67$	4.80775	0.587360	0.293680	−	0.955904i	$-0.405120\pi$
$67$	4.80775	0.587360	0.293680	+	0.955904i	$0.405120\pi$
$68$	24.0143	2.91216
$69$	−9.42800	−1.13500
$70$	12.8135	1.53150
$71$	0.546449	0.0648516	0.0324258	−	0.999474i	$-0.489677\pi$
$71$	0.546449	0.0648516	0.0324258	+	0.999474i	$0.489677\pi$
$72$	−50.9097	−5.99976
$73$	4.67236	0.546858	0.273429	−	0.961892i	$-0.411842\pi$
$73$	4.67236	0.546858	0.273429	+	0.961892i	$0.411842\pi$
$74$	−23.3659	−2.71623
$75$	−3.68604	−0.425627
$76$	−14.6130	−1.67622
$77$	−7.30461	−0.832437
$78$	−1.56127	−0.176779
$79$	−4.07327	−0.458279	−0.229140	−	0.973394i	$-0.573591\pi$
$79$	−4.07327	−0.458279	−0.229140	+	0.973394i	$0.573591\pi$
$80$	−21.9951	−2.45913
$81$	11.9841	1.33157
$82$	7.23849	0.799357
$83$	−0.610918	−0.0670570	−0.0335285	−	0.999438i	$-0.510674\pi$
$83$	−0.610918	−0.0670570	−0.0335285	+	0.999438i	$0.510674\pi$
$84$	38.1387	4.16128
$85$	−9.28538	−1.00714
$86$	−31.7787	−3.42678
$87$	6.81513	0.730659
$88$	23.7220	2.52878
$89$	4.34903	0.460996	0.230498	−	0.973073i	$-0.425965\pi$
$89$	4.34903	0.460996	0.230498	+	0.973073i	$0.425965\pi$
$90$	32.6498	3.44159
$91$	0.478188	0.0501278
$92$	−15.5541	−1.62163
$93$	−9.40214	−0.974956
$94$	11.6363	1.20019
$95$	5.65028	0.579706
$96$	−42.2813	−4.31532
$97$	6.32560	0.642267	0.321134	−	0.947034i	$-0.395936\pi$
$97$	6.32560	0.642267	0.321134	+	0.947034i	$0.395936\pi$
$98$	2.24889	0.227172
$99$	−18.6127	−1.87065
$100$	−6.08115	−0.608115
$101$	−4.28037	−0.425912	−0.212956	−	0.977062i	$-0.568309\pi$
$101$	−4.28037	−0.425912	−0.212956	+	0.977062i	$0.568309\pi$
$102$	−38.6122	−3.82318
$103$	−2.94064	−0.289750	−0.144875	−	0.989450i	$-0.546278\pi$
$103$	−2.94064	−0.289750	−0.144875	+	0.989450i	$0.546278\pi$
$104$	−1.55294	−0.152278
$105$	−14.7468	−1.43914
$106$	−38.0907	−3.69969
$107$	2.21393	0.214028	0.107014	−	0.994257i	$-0.465871\pi$
$107$	2.21393	0.214028	0.107014	+	0.994257i	$0.465871\pi$
$108$	51.0519	4.91247
$109$	8.23984	0.789234	0.394617	−	0.918846i	$-0.370877\pi$
$109$	8.23984	0.789234	0.394617	+	0.918846i	$0.370877\pi$
$110$	−15.2136	−1.45056
$111$	26.8914	2.55242
$112$	28.0138	2.64706
$113$	7.94211	0.747131	0.373566	−	0.927604i	$-0.378135\pi$
$113$	7.94211	0.747131	0.373566	+	0.927604i	$0.378135\pi$
$114$	23.4960	2.20060
$115$	6.01418	0.560825
$116$	11.2435	1.04393
$117$	1.21846	0.112647
$118$	8.72173	0.802900
$119$	11.8262	1.08411
$120$	47.8908	4.37181
$121$	−2.32714	−0.211558
$122$	−33.4507	−3.02848
$123$	−8.33064	−0.751148
$124$	−15.5115	−1.39297
$125$	12.0887	1.08124
$126$	−41.5840	−3.70460
$127$	0.723073	0.0641623	0.0320812	−	0.999485i	$-0.489786\pi$
$127$	0.723073	0.0641623	0.0320812	+	0.999485i	$0.489786\pi$
$128$	−9.83535	−0.869330
$129$	36.5734	3.22011
$130$	0.995942	0.0873499
$131$	−4.71928	−0.412325	−0.206163	−	0.978518i	$-0.566098\pi$
$131$	−4.71928	−0.412325	−0.206163	+	0.978518i	$0.566098\pi$
$132$	−45.2826	−3.94135
$133$	−7.19642	−0.624008
$134$	−12.7533	−1.10172
$135$	−19.7398	−1.69893
$136$	−38.4062	−3.29331
$137$	8.90380	0.760703	0.380351	−	0.924842i	$-0.375803\pi$
$137$	8.90380	0.760703	0.380351	+	0.924842i	$0.375803\pi$
$138$	25.0093	2.12893
$139$	14.5272	1.23219	0.616093	−	0.787674i	$-0.288715\pi$
$139$	14.5272	1.23219	0.616093	+	0.787674i	$0.288715\pi$
$140$	−24.3289	−2.05617
$141$	−13.3919	−1.12780
$142$	−1.44954	−0.121643
$143$	−0.567760	−0.0474784
$144$	71.3815	5.94846
$145$	−4.34742	−0.361033
$146$	−12.3942	−1.02575
$147$	−2.58820	−0.213471
$148$	44.3649	3.64677
$149$	−8.73860	−0.715894	−0.357947	−	0.933742i	$-0.616523\pi$
$149$	−8.73860	−0.715894	−0.357947	+	0.933742i	$0.616523\pi$
$150$	9.77780	0.798354
$151$	17.6680	1.43781	0.718903	−	0.695111i	$-0.244645\pi$
$151$	17.6680	1.43781	0.718903	+	0.695111i	$0.244645\pi$
$152$	23.3707	1.89561
$153$	30.1342	2.43621
$154$	19.3767	1.56142
$155$	5.99769	0.481746
$156$	2.96438	0.237340
$157$	10.0397	0.801253	0.400627	−	0.916241i	$-0.368792\pi$
$157$	10.0397	0.801253	0.400627	+	0.916241i	$0.368792\pi$
$158$	10.8050	0.859601
$159$	43.8378	3.47657
$160$	26.9715	2.13229
$161$	−7.65990	−0.603685
$162$	−31.7898	−2.49764
$163$	13.5668	1.06263	0.531316	−	0.847174i	$-0.321698\pi$
$163$	13.5668	1.06263	0.531316	+	0.847174i	$0.321698\pi$
$164$	−13.7437	−1.07321
$165$	17.5090	1.36308
$166$	1.62056	0.125780
$167$	−10.5826	−0.818910	−0.409455	−	0.912330i	$-0.634281\pi$
$167$	−10.5826	−0.818910	−0.409455	+	0.912330i	$0.634281\pi$
$168$	−60.9956	−4.70592
$169$	−12.9628	−0.997141
$170$	24.6310	1.88911
$171$	−18.3371	−1.40227
$172$	60.3382	4.60074
$173$	−18.4685	−1.40414	−0.702068	−	0.712110i	$-0.747740\pi$
$173$	−18.4685	−1.40414	−0.702068	+	0.712110i	$0.747740\pi$
$174$	−18.0782	−1.37051
$175$	−2.99477	−0.226383
$176$	−33.2612	−2.50716
$177$	−10.0377	−0.754477
$178$	−11.5365	−0.864697
$179$	22.2879	1.66588	0.832938	−	0.553366i	$-0.186657\pi$
$179$	22.2879	1.66588	0.832938	+	0.553366i	$0.186657\pi$
$180$	−61.9922	−4.62062
$181$	−7.48911	−0.556661	−0.278331	−	0.960485i	$-0.589781\pi$
$181$	−7.48911	−0.556661	−0.278331	+	0.960485i	$0.589781\pi$
$182$	−1.26847	−0.0940254
$183$	38.4977	2.84584
$184$	24.8759	1.83387
$185$	−17.1542	−1.26120
$186$	24.9407	1.82874
$187$	−14.0414	−1.02681
$188$	−22.0938	−1.61135
$189$	25.1414	1.82877
$190$	−14.9883	−1.08736
$191$	22.8566	1.65385	0.826923	−	0.562315i	$-0.190089\pi$
$191$	22.8566	1.65385	0.826923	+	0.562315i	$0.190089\pi$
$192$	43.1977	3.11753
$193$	20.0189	1.44099	0.720496	−	0.693459i	$-0.243914\pi$
$193$	20.0189	1.44099	0.720496	+	0.693459i	$0.243914\pi$
$194$	−16.7797	−1.20471
$195$	−1.14621	−0.0820819
$196$	−4.26996	−0.304997
$197$	−13.5736	−0.967079	−0.483540	−	0.875322i	$-0.660649\pi$
$197$	−13.5736	−0.967079	−0.483540	+	0.875322i	$0.660649\pi$
$198$	49.3733	3.50881
$199$	13.6861	0.970183	0.485091	−	0.874464i	$-0.338786\pi$
$199$	13.6861	0.970183	0.485091	+	0.874464i	$0.338786\pi$
$200$	9.72565	0.687707
$201$	14.6776	1.03528
$202$	11.3544	0.798890
$203$	5.53704	0.388624
$204$	73.3130	5.13294
$205$	5.31417	0.371158
$206$	7.80053	0.543489
$207$	−19.5181	−1.35660
$208$	2.17741	0.150976
$209$	8.54440	0.591029
$210$	39.1182	2.69941
$211$	−24.1510	−1.66262	−0.831312	−	0.555805i	$-0.812410\pi$
$211$	−24.1510	−1.66262	−0.831312	+	0.555805i	$0.812410\pi$
$212$	72.3228	4.96715
$213$	1.66825	0.114307
$214$	−5.87280	−0.401456
$215$	−23.3304	−1.59112
$216$	−81.6477	−5.55543
$217$	−7.63889	−0.518562
$218$	−21.8575	−1.48038
$219$	14.2642	0.963887
$220$	28.8861	1.94750
$221$	0.919209	0.0618327
$222$	−71.3337	−4.78760
$223$	19.6211	1.31393	0.656964	−	0.753922i	$-0.271840\pi$
$223$	19.6211	1.31393	0.656964	+	0.753922i	$0.271840\pi$
$224$	−34.3520	−2.29524
$225$	−7.63092	−0.508728
$226$	−21.0677	−1.40141
$227$	17.1133	1.13585	0.567926	−	0.823080i	$-0.307746\pi$
$227$	17.1133	1.13585	0.567926	+	0.823080i	$0.307746\pi$
$228$	−44.6119	−2.95450
$229$	−19.4868	−1.28773	−0.643863	−	0.765141i	$-0.722669\pi$
$229$	−19.4868	−1.28773	−0.643863	+	0.765141i	$0.722669\pi$
$230$	−15.9536	−1.05195
$231$	−22.3002	−1.46725
$232$	−17.9818	−1.18056
$233$	−25.1005	−1.64439	−0.822196	−	0.569205i	$-0.807251\pi$
$233$	−25.1005	−1.64439	−0.822196	+	0.569205i	$0.807251\pi$
$234$	−3.23217	−0.211294
$235$	8.54281	0.557271
$236$	−16.5600	−1.07796
$237$	−12.4353	−0.807758
$238$	−31.3710	−2.03348
$239$	3.75871	0.243130	0.121565	−	0.992583i	$-0.461209\pi$
$239$	3.75871	0.243130	0.121565	+	0.992583i	$0.461209\pi$
$240$	−67.1487	−4.33443
$241$	−21.4799	−1.38364	−0.691820	−	0.722070i	$-0.743191\pi$
$241$	−21.4799	−1.38364	−0.691820	+	0.722070i	$0.743191\pi$
$242$	6.17311	0.396823
$243$	6.17775	0.396303
$244$	63.5129	4.06599
$245$	1.65103	0.105480
$246$	22.0984	1.40894
$247$	−0.559350	−0.0355906
$248$	24.8076	1.57529
$249$	−1.86507	−0.118194
$250$	−32.0671	−2.02810
$251$	13.8248	0.872617	0.436308	−	0.899797i	$-0.356286\pi$
$251$	13.8248	0.872617	0.436308	+	0.899797i	$0.356286\pi$
$252$	78.9557	4.97374
$253$	9.09470	0.571779
$254$	−1.91807	−0.120350
$255$	−28.3473	−1.77518
$256$	−2.20965	−0.138103
$257$	−25.7785	−1.60802	−0.804010	−	0.594615i	$-0.797304\pi$
$257$	−25.7785	−1.60802	−0.804010	+	0.594615i	$0.797304\pi$
$258$	−97.0169	−6.04001
$259$	21.8482	1.35758
$260$	−1.89100	−0.117275
$261$	14.1088	0.873315
$262$	12.5187	0.773405
$263$	−9.63979	−0.594415	−0.297208	−	0.954813i	$-0.596055\pi$
$263$	−9.63979	−0.594415	−0.297208	+	0.954813i	$0.596055\pi$
$264$	72.4210	4.45720
$265$	−27.9644	−1.71784
$266$	19.0897	1.17046
$267$	13.2771	0.812547
$268$	24.2148	1.47915
$269$	3.78475	0.230760	0.115380	−	0.993321i	$-0.463191\pi$
$269$	3.78475	0.230760	0.115380	+	0.993321i	$0.463191\pi$
$270$	52.3630	3.18671
$271$	7.70490	0.468040	0.234020	−	0.972232i	$-0.424812\pi$
$271$	7.70490	0.468040	0.234020	+	0.972232i	$0.424812\pi$
$272$	53.8502	3.26515
$273$	1.45986	0.0883547
$274$	−23.6188	−1.42686
$275$	3.55573	0.214419
$276$	−47.4852	−2.85827
$277$	−20.1388	−1.21003	−0.605013	−	0.796216i	$-0.706832\pi$
$277$	−20.1388	−1.21003	−0.605013	+	0.796216i	$0.706832\pi$
$278$	−38.5359	−2.31123
$279$	−19.4645	−1.16531
$280$	38.9095	2.32529
$281$	−22.7383	−1.35645	−0.678225	−	0.734854i	$-0.737251\pi$
$281$	−22.7383	−1.35645	−0.678225	+	0.734854i	$0.737251\pi$
$282$	35.5243	2.11544
$283$	3.82502	0.227374	0.113687	−	0.993517i	$-0.463734\pi$
$283$	3.82502	0.227374	0.113687	+	0.993517i	$0.463734\pi$
$284$	2.75225	0.163316
$285$	17.2497	1.02178
$286$	1.50607	0.0890560
$287$	−6.76834	−0.399522
$288$	−87.5317	−5.15786
$289$	5.73325	0.337250
$290$	11.5322	0.677195
$291$	19.3114	1.13205
$292$	23.5329	1.37716
$293$	−8.91049	−0.520556	−0.260278	−	0.965534i	$-0.583814\pi$
$293$	−8.91049	−0.520556	−0.260278	+	0.965534i	$0.583814\pi$
$294$	6.86562	0.400411
$295$	6.40309	0.372803
$296$	−70.9532	−4.12407
$297$	−29.8507	−1.73211
$298$	23.1805	1.34281
$299$	−0.595375	−0.0344314
$300$	−18.5651	−1.07186
$301$	29.7146	1.71272
$302$	−46.8673	−2.69691
$303$	−13.0675	−0.750709
$304$	−32.7686	−1.87941
$305$	−24.5580	−1.40618
$306$	−79.9359	−4.56963
$307$	−22.9425	−1.30940	−0.654698	−	0.755891i	$-0.727204\pi$
$307$	−22.9425	−1.30940	−0.654698	+	0.755891i	$0.727204\pi$
$308$	−36.7905	−2.09633
$309$	−8.97748	−0.510711
$310$	−15.9098	−0.903618
$311$	13.8497	0.785346	0.392673	−	0.919678i	$-0.371550\pi$
$311$	13.8497	0.785346	0.392673	+	0.919678i	$0.371550\pi$
$312$	−4.74096	−0.268404
$313$	18.9952	1.07367	0.536837	−	0.843686i	$-0.319619\pi$
$313$	18.9952	1.07367	0.536837	+	0.843686i	$0.319619\pi$
$314$	−26.6319	−1.50292
$315$	−30.5291	−1.72012
$316$	−20.5155	−1.15409
$317$	−8.11643	−0.455864	−0.227932	−	0.973677i	$-0.573196\pi$
$317$	−8.11643	−0.455864	−0.227932	+	0.973677i	$0.573196\pi$
$318$	−116.287	−6.52105
$319$	−6.57421	−0.368085
$320$	−27.5561	−1.54043
$321$	6.75889	0.377244
$322$	20.3191	1.13234
$323$	−13.8335	−0.769715
$324$	60.3593	3.35329
$325$	−0.232772	−0.0129119
$326$	−35.9881	−1.99319
$327$	25.1554	1.39110
$328$	21.9805	1.21367
$329$	−10.8805	−0.599859
$330$	−46.4456	−2.55674
$331$	−16.8979	−0.928792	−0.464396	−	0.885628i	$-0.653729\pi$
$331$	−16.8979	−0.928792	−0.464396	+	0.885628i	$0.653729\pi$
$332$	−3.07696	−0.168870
$333$	55.6711	3.05076
$334$	28.0722	1.53604
$335$	−9.36292	−0.511551
$336$	85.5233	4.66568
$337$	−13.9713	−0.761068	−0.380534	−	0.924767i	$-0.624260\pi$
$337$	−13.9713	−0.761068	−0.380534	+	0.924767i	$0.624260\pi$
$338$	34.3860	1.87035
$339$	24.2465	1.31689
$340$	−46.7669	−2.53629
$341$	9.06976	0.491155
$342$	48.6420	2.63026
$343$	−19.4654	−1.05103
$344$	−96.4994	−5.20290
$345$	18.3607	0.988505
$346$	48.9907	2.63376
$347$	7.97316	0.428022	0.214011	−	0.976831i	$-0.431347\pi$
$347$	7.97316	0.428022	0.214011	+	0.976831i	$0.431347\pi$
$348$	34.3252	1.84002
$349$	−17.7457	−0.949908	−0.474954	−	0.880011i	$-0.657535\pi$
$349$	−17.7457	−0.949908	−0.474954	+	0.880011i	$0.657535\pi$
$350$	7.94411	0.424630
$351$	1.95414	0.104304
$352$	40.7866	2.17393
$353$	−8.17292	−0.435001	−0.217500	−	0.976060i	$-0.569790\pi$
$353$	−8.17292	−0.435001	−0.217500	+	0.976060i	$0.569790\pi$
$354$	26.6265	1.41518
$355$	−1.06419	−0.0564813
$356$	21.9044	1.16093
$357$	36.1043	1.91084
$358$	−59.1223	−3.12471
$359$	11.1681	0.589427	0.294714	−	0.955586i	$-0.404776\pi$
$359$	11.1681	0.589427	0.294714	+	0.955586i	$0.404776\pi$
$360$	99.1447	5.22538
$361$	−10.5822	−0.556955
$362$	19.8661	1.04414
$363$	−7.10452	−0.372890
$364$	2.40845	0.126237
$365$	−9.09925	−0.476276
$366$	−102.121	−5.33798
$367$	31.1719	1.62716	0.813580	−	0.581453i	$-0.197516\pi$
$367$	31.1719	1.62716	0.813580	+	0.581453i	$0.197516\pi$
$368$	−34.8790	−1.81819
$369$	−17.2463	−0.897805
$370$	45.5042	2.36565
$371$	35.6166	1.84912
$372$	−47.3549	−2.45524
$373$	20.2679	1.04943	0.524716	−	0.851277i	$-0.324172\pi$
$373$	20.2679	1.04943	0.524716	+	0.851277i	$0.324172\pi$
$374$	37.2472	1.92601
$375$	36.9054	1.90579
$376$	35.3348	1.82225
$377$	0.430373	0.0221654
$378$	−66.6915	−3.43024
$379$	−25.1834	−1.29358	−0.646792	−	0.762667i	$-0.723890\pi$
$379$	−25.1834	−1.29358	−0.646792	+	0.762667i	$0.723890\pi$
$380$	28.4582	1.45988
$381$	2.20747	0.113092
$382$	−60.6309	−3.10214
$383$	12.7415	0.651059	0.325530	−	0.945532i	$-0.394457\pi$
$383$	12.7415	0.651059	0.325530	+	0.945532i	$0.394457\pi$
$384$	−30.0263	−1.53227
$385$	14.2255	0.724996
$386$	−53.1034	−2.70289
$387$	75.7152	3.84882
$388$	31.8596	1.61743
$389$	15.4663	0.784172	0.392086	−	0.919929i	$-0.371754\pi$
$389$	15.4663	0.784172	0.392086	+	0.919929i	$0.371754\pi$
$390$	3.04051	0.153962
$391$	−14.7244	−0.744646
$392$	6.82899	0.344916
$393$	−14.4075	−0.726761
$394$	36.0062	1.81396
$395$	7.93255	0.399130
$396$	−93.7452	−4.71087
$397$	−3.06504	−0.153830	−0.0769150	−	0.997038i	$-0.524507\pi$
$397$	−3.06504	−0.153830	−0.0769150	+	0.997038i	$0.524507\pi$
$398$	−36.3046	−1.81979
$399$	−21.9699	−1.09987
$400$	−13.6365	−0.681827
$401$	0.0629464	0.00314339	0.00157170	−	0.999999i	$-0.499500\pi$
$401$	0.0629464	0.00314339	0.00157170	+	0.999999i	$0.499500\pi$
$402$	−38.9346	−1.94188
$403$	−0.593742	−0.0295764
$404$	−21.5585	−1.07258
$405$	−23.3386	−1.15970
$406$	−14.6879	−0.728948
$407$	−25.9407	−1.28583
$408$	−117.250	−5.80475
$409$	2.35100	0.116250	0.0581248	−	0.998309i	$-0.481488\pi$
$409$	2.35100	0.116250	0.0581248	+	0.998309i	$0.481488\pi$
$410$	−14.0967	−0.696186
$411$	27.1824	1.34081
$412$	−14.8109	−0.729680
$413$	−8.15524	−0.401293
$414$	51.7748	2.54459
$415$	1.18974	0.0584021
$416$	−2.67005	−0.130910
$417$	44.3502	2.17184
$418$	−22.6654	−1.10860
$419$	8.56477	0.418417	0.209208	−	0.977871i	$-0.432911\pi$
$419$	8.56477	0.418417	0.209208	+	0.977871i	$0.432911\pi$
$420$	−74.2738	−3.62419
$421$	23.3286	1.13696	0.568482	−	0.822695i	$-0.307531\pi$
$421$	23.3286	1.13696	0.568482	+	0.822695i	$0.307531\pi$
$422$	64.0645	3.11861
$423$	−27.7243	−1.34800
$424$	−115.667	−5.61727
$425$	−5.75676	−0.279244
$426$	−4.42531	−0.214407
$427$	31.2780	1.51365
$428$	11.1507	0.538989
$429$	−1.73331	−0.0836851
$430$	61.8877	2.98449
$431$	16.4071	0.790300	0.395150	−	0.918617i	$-0.370693\pi$
$431$	16.4071	0.790300	0.395150	+	0.918617i	$0.370693\pi$
$432$	114.480	5.50793
$433$	15.6613	0.752632	0.376316	−	0.926491i	$-0.377191\pi$
$433$	15.6613	0.752632	0.376316	+	0.926491i	$0.377191\pi$
$434$	20.2634	0.972674
$435$	−13.2722	−0.636354
$436$	41.5009	1.98753
$437$	8.96000	0.428615
$438$	−37.8382	−1.80798
$439$	−33.3839	−1.59333	−0.796663	−	0.604424i	$-0.793404\pi$
$439$	−33.3839	−1.59333	−0.796663	+	0.604424i	$0.793404\pi$
$440$	−46.1978	−2.20239
$441$	−5.35815	−0.255150
$442$	−2.43835	−0.115980
$443$	28.2026	1.33995	0.669973	−	0.742385i	$-0.266306\pi$
$443$	28.2026	1.33995	0.669973	+	0.742385i	$0.266306\pi$
$444$	135.441	6.42776
$445$	−8.46957	−0.401496
$446$	−52.0482	−2.46455
$447$	−26.6780	−1.26183
$448$	35.0965	1.65816
$449$	31.4341	1.48347	0.741734	−	0.670694i	$-0.234004\pi$
$449$	31.4341	1.48347	0.741734	+	0.670694i	$0.234004\pi$
$450$	20.2422	0.954228
$451$	8.03614	0.378407
$452$	40.0013	1.88150
$453$	53.9387	2.53426
$454$	−45.3958	−2.13053
$455$	−0.931254	−0.0436579
$456$	71.3483	3.34119
$457$	14.4247	0.674760	0.337380	−	0.941369i	$-0.390459\pi$
$457$	14.4247	0.674760	0.337380	+	0.941369i	$0.390459\pi$
$458$	51.6919	2.41541
$459$	48.3286	2.25578
$460$	30.2911	1.41233
$461$	23.2219	1.08155	0.540775	−	0.841167i	$-0.318131\pi$
$461$	23.2219	1.08155	0.540775	+	0.841167i	$0.318131\pi$
$462$	59.1549	2.75214
$463$	−26.5874	−1.23562	−0.617811	−	0.786327i	$-0.711980\pi$
$463$	−26.5874	−1.23562	−0.617811	+	0.786327i	$0.711980\pi$
$464$	25.2127	1.17047
$465$	18.3103	0.849120
$466$	66.5832	3.08441
$467$	5.02961	0.232743	0.116371	−	0.993206i	$-0.462874\pi$
$467$	5.02961	0.232743	0.116371	+	0.993206i	$0.462874\pi$
$468$	6.13693	0.283680
$469$	11.9250	0.550645
$470$	−22.6612	−1.04528
$471$	30.6501	1.41228
$472$	26.4845	1.21905
$473$	−35.2805	−1.62220
$474$	32.9866	1.51512
$475$	3.50306	0.160732
$476$	59.5642	2.73012
$477$	90.7541	4.15534
$478$	−9.97057	−0.456043
$479$	19.0655	0.871126	0.435563	−	0.900158i	$-0.356549\pi$
$479$	19.0655	0.871126	0.435563	+	0.900158i	$0.356549\pi$
$480$	82.3412	3.75835
$481$	1.69818	0.0774304
$482$	56.9788	2.59532
$483$	−23.3849	−1.06405
$484$	−11.7209	−0.532768
$485$	−12.3189	−0.559371
$486$	−16.3875	−0.743351
$487$	10.5597	0.478504	0.239252	−	0.970957i	$-0.423098\pi$
$487$	10.5597	0.478504	0.239252	+	0.970957i	$0.423098\pi$
$488$	−101.577	−4.59816
$489$	41.4180	1.87299
$490$	−4.37962	−0.197851
$491$	−19.7303	−0.890416	−0.445208	−	0.895427i	$-0.646870\pi$
$491$	−19.7303	−0.890416	−0.445208	+	0.895427i	$0.646870\pi$
$492$	−41.9582	−1.89162
$493$	10.6437	0.479368
$494$	1.48377	0.0667578
$495$	36.2476	1.62921
$496$	−34.7833	−1.56182
$497$	1.35539	0.0607977
$498$	4.94740	0.221698
$499$	−36.7245	−1.64401	−0.822007	−	0.569477i	$-0.807146\pi$
$499$	−36.7245	−1.64401	−0.822007	+	0.569477i	$0.807146\pi$
$500$	60.8859	2.72290
$501$	−32.3077	−1.44340
$502$	−36.6726	−1.63678
$503$	17.0151	0.758664	0.379332	−	0.925261i	$-0.376154\pi$
$503$	17.0151	0.758664	0.379332	+	0.925261i	$0.376154\pi$
$504$	−126.275	−5.62472
$505$	8.33585	0.370941
$506$	−24.1252	−1.07249
$507$	−39.5742	−1.75755
$508$	3.64184	0.161580
$509$	23.0865	1.02329	0.511647	−	0.859196i	$-0.329036\pi$
$509$	23.0865	1.02329	0.511647	+	0.859196i	$0.329036\pi$
$510$	75.1958	3.32973
$511$	11.5892	0.512674
$512$	25.5321	1.12837
$513$	−29.4086	−1.29842
$514$	68.3817	3.01619
$515$	5.72679	0.252353
$516$	184.206	8.10922
$517$	12.9185	0.568156
$518$	−57.9560	−2.54644
$519$	−56.3825	−2.47492
$520$	3.02429	0.132624
$521$	10.9621	0.480260	0.240130	−	0.970741i	$-0.422810\pi$
$521$	10.9621	0.480260	0.240130	+	0.970741i	$0.422810\pi$
$522$	−37.4260	−1.63809
$523$	9.53969	0.417141	0.208571	−	0.978007i	$-0.433119\pi$
$523$	9.53969	0.417141	0.208571	+	0.978007i	$0.433119\pi$
$524$	−23.7692	−1.03836
$525$	−9.14272	−0.399021
$526$	25.5711	1.11495
$527$	−14.6840	−0.639647
$528$	−101.543	−4.41909
$529$	−13.4629	−0.585345
$530$	74.1802	3.22218
$531$	−20.7802	−0.901784
$532$	−36.2456	−1.57144
$533$	−0.526077	−0.0227869
$534$	−35.2197	−1.52411
$535$	−4.31154	−0.186404
$536$	−38.7269	−1.67275
$537$	68.0427	2.93626
$538$	−10.0397	−0.432841
$539$	2.49670	0.107541
$540$	−99.4216	−4.27842
$541$	−42.0727	−1.80885	−0.904423	−	0.426637i	$-0.859698\pi$
$541$	−42.0727	−1.80885	−0.904423	+	0.426637i	$0.859698\pi$
$542$	−20.4385	−0.877909
$543$	−22.8635	−0.981166
$544$	−66.0339	−2.83118
$545$	−16.0468	−0.687369
$546$	−3.87251	−0.165728
$547$	−14.8311	−0.634132	−0.317066	−	0.948403i	$-0.602698\pi$
$547$	−14.8311	−0.634132	−0.317066	+	0.948403i	$0.602698\pi$
$548$	44.8450	1.91568
$549$	79.6989	3.40147
$550$	−9.43214	−0.402188
$551$	−6.47683	−0.275922
$552$	75.9435	3.23237
$553$	−10.1032	−0.429632
$554$	53.4215	2.26966
$555$	−52.3699	−2.22298
$556$	73.1681	3.10302
$557$	1.04920	0.0444562	0.0222281	−	0.999753i	$-0.492924\pi$
$557$	1.04920	0.0444562	0.0222281	+	0.999753i	$0.492924\pi$
$558$	51.6328	2.18579
$559$	2.30960	0.0976857
$560$	−54.5559	−2.30541
$561$	−42.8671	−1.80985
$562$	60.3169	2.54431
$563$	−30.8680	−1.30093	−0.650465	−	0.759536i	$-0.725426\pi$
$563$	−30.8680	−1.30093	−0.650465	+	0.759536i	$0.725426\pi$
$564$	−67.4500	−2.84016
$565$	−15.4670	−0.650700
$566$	−10.1465	−0.426488
$567$	29.7250	1.24833
$568$	−4.40170	−0.184691
$569$	−40.4706	−1.69662	−0.848308	−	0.529502i	$-0.822379\pi$
$569$	−40.4706	−1.69662	−0.848308	+	0.529502i	$0.822379\pi$
$570$	−45.7576	−1.91658
$571$	0.232265	0.00971999	0.00485999	−	0.999988i	$-0.498453\pi$
$571$	0.232265	0.00971999	0.00485999	+	0.999988i	$0.498453\pi$
$572$	−2.85958	−0.119565
$573$	69.7789	2.91505
$574$	17.9541	0.749390
$575$	3.72868	0.155497
$576$	89.4289	3.72620
$577$	−6.15819	−0.256369	−0.128184	−	0.991750i	$-0.540915\pi$
$577$	−6.15819	−0.256369	−0.128184	+	0.991750i	$0.540915\pi$
$578$	−15.2084	−0.632585
$579$	61.1156	2.53988
$580$	−21.8962	−0.909192
$581$	−1.51530	−0.0628653
$582$	−51.2266	−2.12341
$583$	−42.2881	−1.75139
$584$	−37.6363	−1.55740
$585$	−2.37291	−0.0981078
$586$	23.6365	0.976415
$587$	36.2164	1.49481	0.747405	−	0.664368i	$-0.231299\pi$
$587$	36.2164	1.49481	0.747405	+	0.664368i	$0.231299\pi$
$588$	−13.0358	−0.537585
$589$	8.93542	0.368178
$590$	−16.9852	−0.699271
$591$	−41.4388	−1.70456
$592$	99.4850	4.08881
$593$	−46.6241	−1.91462	−0.957312	−	0.289058i	$-0.906658\pi$
$593$	−46.6241	−1.91462	−0.957312	+	0.289058i	$0.906658\pi$
$594$	79.1838	3.24895
$595$	−23.0312	−0.944185
$596$	−44.0129	−1.80284
$597$	41.7823	1.71003
$598$	1.57933	0.0645836
$599$	16.5338	0.675551	0.337776	−	0.941227i	$-0.390326\pi$
$599$	16.5338	0.675551	0.337776	+	0.941227i	$0.390326\pi$
$600$	29.6914	1.21215
$601$	22.3970	0.913593	0.456797	−	0.889571i	$-0.348997\pi$
$601$	22.3970	0.913593	0.456797	+	0.889571i	$0.348997\pi$
$602$	−78.8227	−3.21257
$603$	30.3858	1.23741
$604$	88.9871	3.62083
$605$	4.53202	0.184253
$606$	34.6637	1.40812
$607$	2.43468	0.0988205	0.0494103	−	0.998779i	$-0.484266\pi$
$607$	2.43468	0.0988205	0.0494103	+	0.998779i	$0.484266\pi$
$608$	40.1825	1.62961
$609$	16.9040	0.684985
$610$	65.1440	2.63760
$611$	−0.845697	−0.0342132
$612$	151.774	6.13511
$613$	−12.1857	−0.492177	−0.246089	−	0.969247i	$-0.579145\pi$
$613$	−12.1857	−0.492177	−0.246089	+	0.969247i	$0.579145\pi$
$614$	60.8586	2.45605
$615$	16.2236	0.654199
$616$	58.8394	2.37071
$617$	5.63392	0.226813	0.113407	−	0.993549i	$-0.463824\pi$
$617$	5.63392	0.226813	0.113407	+	0.993549i	$0.463824\pi$
$618$	23.8142	0.957948
$619$	−17.8395	−0.717028	−0.358514	−	0.933524i	$-0.616716\pi$
$619$	−17.8395	−0.717028	−0.358514	+	0.933524i	$0.616716\pi$
$620$	30.2080	1.21318
$621$	−31.3026	−1.25613
$622$	−36.7387	−1.47309
$623$	10.7872	0.432179
$624$	6.64740	0.266109
$625$	−17.5053	−0.700210
$626$	−50.3879	−2.01391
$627$	26.0852	1.04174
$628$	50.5659	2.01780
$629$	41.9983	1.67458
$630$	80.9834	3.22645
$631$	−13.0005	−0.517544	−0.258772	−	0.965938i	$-0.583318\pi$
$631$	−13.0005	−0.517544	−0.258772	+	0.965938i	$0.583318\pi$
$632$	32.8106	1.30514
$633$	−73.7306	−2.93053
$634$	21.5301	0.855071
$635$	−1.40816	−0.0558810
$636$	220.794	8.75506
$637$	−0.163444	−0.00647589
$638$	17.4391	0.690422
$639$	3.45366	0.136625
$640$	19.1540	0.757127
$641$	29.2012	1.15338	0.576690	−	0.816963i	$-0.304344\pi$
$641$	29.2012	1.15338	0.576690	+	0.816963i	$0.304344\pi$
$642$	−17.9290	−0.707603
$643$	25.6030	1.00968	0.504841	−	0.863212i	$-0.331551\pi$
$643$	25.6030	1.00968	0.504841	+	0.863212i	$0.331551\pi$
$644$	−38.5799	−1.52026
$645$	−71.2254	−2.80450
$646$	36.6955	1.44377
$647$	31.7663	1.24886	0.624432	−	0.781080i	$-0.285331\pi$
$647$	31.7663	1.24886	0.624432	+	0.781080i	$0.285331\pi$
$648$	−96.5331	−3.79218
$649$	9.68282	0.380084
$650$	0.617465	0.0242190
$651$	−23.3207	−0.914012
$652$	68.3306	2.67603
$653$	0.771188	0.0301789	0.0150895	−	0.999886i	$-0.495197\pi$
$653$	0.771188	0.0301789	0.0150895	+	0.999886i	$0.495197\pi$
$654$	−66.7287	−2.60930
$655$	9.19062	0.359107
$656$	−30.8193	−1.20329
$657$	29.5301	1.15208
$658$	28.8622	1.12516
$659$	−35.1877	−1.37072	−0.685359	−	0.728205i	$-0.740355\pi$
$659$	−35.1877	−1.37072	−0.685359	+	0.728205i	$0.740355\pi$
$660$	88.1862	3.43264
$661$	−11.3851	−0.442829	−0.221415	−	0.975180i	$-0.571067\pi$
$661$	−11.3851	−0.442829	−0.221415	+	0.975180i	$0.571067\pi$
$662$	44.8244	1.74215
$663$	2.80625	0.108986
$664$	4.92101	0.190972
$665$	14.0148	0.543469
$666$	−147.677	−5.72235
$667$	−6.89397	−0.266936
$668$	−53.3007	−2.06227
$669$	59.9013	2.31592
$670$	24.8366	0.959523
$671$	−37.1368	−1.43365
$672$	−104.873	−4.04557
$673$	−33.2938	−1.28338	−0.641690	−	0.766964i	$-0.721766\pi$
$673$	−33.2938	−1.28338	−0.641690	+	0.766964i	$0.721766\pi$
$674$	37.0613	1.42755
$675$	−12.2383	−0.471052
$676$	−65.2887	−2.51111
$677$	47.7487	1.83513	0.917566	−	0.397583i	$-0.130151\pi$
$677$	47.7487	1.83513	0.917566	+	0.397583i	$0.130151\pi$
$678$	−64.3176	−2.47010
$679$	15.6898	0.602119
$680$	74.7947	2.86825
$681$	52.2452	2.00204
$682$	−24.0590	−0.921267
$683$	−18.2576	−0.698608	−0.349304	−	0.937010i	$-0.613582\pi$
$683$	−18.2576	−0.698608	−0.349304	+	0.937010i	$0.613582\pi$
$684$	−92.3567	−3.53134
$685$	−17.3398	−0.662520
$686$	51.6351	1.97144
$687$	−59.4912	−2.26973
$688$	135.304	5.15841
$689$	2.76835	0.105466
$690$	−48.7046	−1.85415
$691$	26.2426	0.998317	0.499159	−	0.866511i	$-0.333643\pi$
$691$	26.2426	0.998317	0.499159	+	0.866511i	$0.333643\pi$
$692$	−93.0188	−3.53604
$693$	−46.1664	−1.75372
$694$	−21.1501	−0.802846
$695$	−28.2913	−1.07315
$696$	−54.8966	−2.08085
$697$	−13.0106	−0.492811
$698$	47.0734	1.78176
$699$	−76.6293	−2.89839
$700$	−15.0835	−0.570102
$701$	25.3670	0.958100	0.479050	−	0.877788i	$-0.340981\pi$
$701$	25.3670	0.958100	0.479050	+	0.877788i	$0.340981\pi$
$702$	−5.18368	−0.195645
$703$	−25.5565	−0.963881
$704$	−41.6706	−1.57052
$705$	26.0803	0.982241
$706$	21.6800	0.815937
$707$	−10.6169	−0.399289
$708$	−50.5558	−1.90000
$709$	−10.6978	−0.401764	−0.200882	−	0.979615i	$-0.564381\pi$
$709$	−10.6978	−0.401764	−0.200882	+	0.979615i	$0.564381\pi$
$710$	2.82293	0.105943
$711$	−25.7438	−0.965468
$712$	−35.0318	−1.31287
$713$	9.51091	0.356186
$714$	−95.7724	−3.58419
$715$	1.10569	0.0413505
$716$	112.256	4.19519
$717$	11.4749	0.428539
$718$	−29.6251	−1.10560
$719$	15.7594	0.587726	0.293863	−	0.955848i	$-0.405059\pi$
$719$	15.7594	0.587726	0.293863	+	0.955848i	$0.405059\pi$
$720$	−139.013	−5.18070
$721$	−7.29387	−0.271638
$722$	28.0709	1.04469
$723$	−65.5759	−2.43879
$724$	−37.7197	−1.40184
$725$	−2.69532	−0.100101
$726$	18.8459	0.699436
$727$	−28.4397	−1.05477	−0.527386	−	0.849626i	$-0.676828\pi$
$727$	−28.4397	−1.05477	−0.527386	+	0.849626i	$0.676828\pi$
$728$	−3.85186	−0.142759
$729$	−17.0923	−0.633047
$730$	24.1372	0.893359
$731$	57.1195	2.11264
$732$	193.898	7.16668
$733$	12.5454	0.463377	0.231688	−	0.972790i	$-0.425575\pi$
$733$	12.5454	0.463377	0.231688	+	0.972790i	$0.425575\pi$
$734$	−82.6885	−3.05209
$735$	5.04042	0.185919
$736$	42.7704	1.57654
$737$	−14.1587	−0.521542
$738$	45.7485	1.68403
$739$	27.6264	1.01625	0.508126	−	0.861282i	$-0.330338\pi$
$739$	27.6264	1.01625	0.508126	+	0.861282i	$0.330338\pi$
$740$	−86.3989	−3.17609
$741$	−1.70764	−0.0627317
$742$	−94.4788	−3.46843
$743$	36.1684	1.32689	0.663444	−	0.748226i	$-0.269094\pi$
$743$	36.1684	1.32689	0.663444	+	0.748226i	$0.269094\pi$
$744$	75.7352	2.77659
$745$	17.0181	0.623495
$746$	−53.7639	−1.96843
$747$	−3.86111	−0.141271
$748$	−70.7213	−2.58583
$749$	5.49135	0.200649
$750$	−97.8976	−3.57471
$751$	−35.1141	−1.28133	−0.640667	−	0.767819i	$-0.721342\pi$
$751$	−35.1141	−1.28133	−0.640667	+	0.767819i	$0.721342\pi$
$752$	−49.5437	−1.80667
$753$	42.2058	1.53807
$754$	−1.14163	−0.0415759
$755$	−34.4079	−1.25223
$756$	126.627	4.60539
$757$	−33.3690	−1.21282	−0.606409	−	0.795153i	$-0.707391\pi$
$757$	−33.3690	−1.21282	−0.606409	+	0.795153i	$0.707391\pi$
$758$	66.8030	2.42639
$759$	27.7652	1.00781
$760$	−45.5135	−1.65095
$761$	8.83761	0.320363	0.160182	−	0.987088i	$-0.448792\pi$
$761$	8.83761	0.320363	0.160182	+	0.987088i	$0.448792\pi$
$762$	−5.85566	−0.212128
$763$	20.4378	0.739899
$764$	115.120	4.16489
$765$	−58.6853	−2.12177
$766$	−33.7988	−1.22120
$767$	−0.633876	−0.0228879
$768$	−6.74582	−0.243419
$769$	−6.33489	−0.228442	−0.114221	−	0.993455i	$-0.536437\pi$
$769$	−6.33489	−0.228442	−0.114221	+	0.993455i	$0.536437\pi$
$770$	−37.7353	−1.35989
$771$	−78.6992	−2.83428
$772$	100.827	3.62886
$773$	−36.3218	−1.30641	−0.653203	−	0.757183i	$-0.726575\pi$
$773$	−36.3218	−1.30641	−0.653203	+	0.757183i	$0.726575\pi$
$774$	−200.847	−7.21928
$775$	3.71845	0.133571
$776$	−50.9533	−1.82912
$777$	66.7004	2.39286
$778$	−41.0268	−1.47088
$779$	7.91711	0.283660
$780$	−5.77302	−0.206707
$781$	−1.60928	−0.0575845
$782$	39.0589	1.39674
$783$	22.6274	0.808639
$784$	−9.57508	−0.341967
$785$	−19.5519	−0.697837
$786$	38.2182	1.36320
$787$	−12.2804	−0.437750	−0.218875	−	0.975753i	$-0.570239\pi$
$787$	−12.2804	−0.437750	−0.218875	+	0.975753i	$0.570239\pi$
$788$	−68.3650	−2.43540
$789$	−29.4293	−1.04771
$790$	−21.0424	−0.748654
$791$	19.6993	0.700428
$792$	149.928	5.32744
$793$	2.43112	0.0863316
$794$	8.13052	0.288541
$795$	−85.3725	−3.02785
$796$	68.9316	2.44322
$797$	7.89371	0.279610	0.139805	−	0.990179i	$-0.455352\pi$
$797$	7.89371	0.279610	0.139805	+	0.990179i	$0.455352\pi$
$798$	58.2787	2.06305
$799$	−20.9152	−0.739927
$800$	16.7218	0.591206
$801$	27.4866	0.971192
$802$	−0.166975	−0.00589611
$803$	−13.7600	−0.485579
$804$	73.9252	2.60714
$805$	14.9174	0.525768
$806$	1.57500	0.0554769
$807$	11.5545	0.406736
$808$	34.4788	1.21296
$809$	36.9078	1.29761	0.648804	−	0.760956i	$-0.275269\pi$
$809$	36.9078	1.29761	0.648804	+	0.760956i	$0.275269\pi$
$810$	61.9094	2.17527
$811$	0.639212	0.0224458	0.0112229	−	0.999937i	$-0.496428\pi$
$811$	0.639212	0.0224458	0.0112229	+	0.999937i	$0.496428\pi$
$812$	27.8879	0.978674
$813$	23.5223	0.824962
$814$	68.8119	2.41186
$815$	−26.4208	−0.925480
$816$	164.399	5.75512
$817$	−34.7580	−1.21603
$818$	−6.23642	−0.218051
$819$	3.02224	0.105605
$820$	26.7654	0.934688
$821$	11.7143	0.408833	0.204416	−	0.978884i	$-0.434470\pi$
$821$	11.7143	0.408833	0.204416	+	0.978884i	$0.434470\pi$
$822$	−72.1056	−2.51497
$823$	−27.2835	−0.951044	−0.475522	−	0.879704i	$-0.657741\pi$
$823$	−27.2835	−0.951044	−0.475522	+	0.879704i	$0.657741\pi$
$824$	23.6872	0.825182
$825$	10.8553	0.377932
$826$	21.6331	0.752711
$827$	−44.5108	−1.54779	−0.773895	−	0.633314i	$-0.781694\pi$
$827$	−44.5108	−1.54779	−0.773895	+	0.633314i	$0.781694\pi$
$828$	−98.3049	−3.41633
$829$	−35.5248	−1.23383	−0.616913	−	0.787031i	$-0.711617\pi$
$829$	−35.5248	−1.23383	−0.616913	+	0.787031i	$0.711617\pi$
$830$	−3.15598	−0.109546
$831$	−61.4818	−2.13278
$832$	2.72792	0.0945737
$833$	−4.04219	−0.140053
$834$	−117.646	−4.07375
$835$	20.6093	0.713215
$836$	43.0348	1.48839
$837$	−31.2168	−1.07901
$838$	−22.7194	−0.784830
$839$	27.0186	0.932784	0.466392	−	0.884578i	$-0.345554\pi$
$839$	27.0186	0.932784	0.466392	+	0.884578i	$0.345554\pi$
$840$	118.787	4.09853
$841$	−24.0166	−0.828159
$842$	−61.8828	−2.13262
$843$	−69.4175	−2.39087
$844$	−121.639	−4.18700
$845$	25.2446	0.868442
$846$	73.5432	2.52847
$847$	−5.77216	−0.198334
$848$	162.179	5.56924
$849$	11.6774	0.400766
$850$	15.2707	0.523782
$851$	−27.2025	−0.932488
$852$	8.40234	0.287860
$853$	37.9312	1.29874	0.649369	−	0.760474i	$-0.275033\pi$
$853$	37.9312	1.29874	0.649369	+	0.760474i	$0.275033\pi$
$854$	−82.9699	−2.83917
$855$	35.7107	1.22128
$856$	−17.8334	−0.609533
$857$	−31.0229	−1.05972	−0.529862	−	0.848084i	$-0.677756\pi$
$857$	−31.0229	−1.05972	−0.529862	+	0.848084i	$0.677756\pi$
$858$	4.59789	0.156969
$859$	25.8123	0.880703	0.440351	−	0.897826i	$-0.354854\pi$
$859$	25.8123	0.880703	0.440351	+	0.897826i	$0.354854\pi$
$860$	−117.506	−4.00693
$861$	−20.6630	−0.704194
$862$	−43.5224	−1.48238
$863$	−7.14893	−0.243352	−0.121676	−	0.992570i	$-0.538827\pi$
$863$	−7.14893	−0.243352	−0.121676	+	0.992570i	$0.538827\pi$
$864$	−140.381	−4.77587
$865$	35.9668	1.22291
$866$	−41.5440	−1.41172
$867$	17.5030	0.594434
$868$	−38.4741	−1.30590
$869$	11.9957	0.406925
$870$	35.2067	1.19362
$871$	0.926884	0.0314063
$872$	−66.3728	−2.24767
$873$	39.9789	1.35308
$874$	−23.7678	−0.803959
$875$	29.9843	1.01365
$876$	71.8434	2.42736
$877$	−12.0065	−0.405431	−0.202716	−	0.979238i	$-0.564977\pi$
$877$	−12.0065	−0.405431	−0.202716	+	0.979238i	$0.564977\pi$
$878$	88.5562	2.98863
$879$	−27.2028	−0.917528
$880$	64.7749	2.18356
$881$	−32.1303	−1.08250	−0.541249	−	0.840862i	$-0.682049\pi$
$881$	−32.1303	−1.08250	−0.541249	+	0.840862i	$0.682049\pi$
$882$	14.2134	0.478589
$883$	−19.6821	−0.662356	−0.331178	−	0.943568i	$-0.607446\pi$
$883$	−19.6821	−0.662356	−0.331178	+	0.943568i	$0.607446\pi$
$884$	4.62970	0.155714
$885$	19.5480	0.657098
$886$	−74.8120	−2.51336
$887$	−1.13995	−0.0382759	−0.0191379	−	0.999817i	$-0.506092\pi$
$887$	−1.13995	−0.0382759	−0.0191379	+	0.999817i	$0.506092\pi$
$888$	−216.613	−7.26904
$889$	1.79349	0.0601516
$890$	22.4669	0.753092
$891$	−35.2928	−1.18235
$892$	98.8240	3.30887
$893$	12.7272	0.425899
$894$	70.7678	2.36683
$895$	−43.4049	−1.45086
$896$	−24.3953	−0.814988
$897$	−1.81762	−0.0606885
$898$	−83.3841	−2.78256
$899$	−6.87506	−0.229296
$900$	−38.4340	−1.28113
$901$	68.4649	2.28090
$902$	−21.3172	−0.709783
$903$	90.7155	3.01882
$904$	−63.9745	−2.12776
$905$	14.5848	0.484814
$906$	−143.081	−4.75355
$907$	−36.9999	−1.22856	−0.614281	−	0.789088i	$-0.710554\pi$
$907$	−36.9999	−1.22856	−0.614281	+	0.789088i	$0.710554\pi$
$908$	86.1932	2.86042
$909$	−27.0527	−0.897280
$910$	2.47030	0.0818897
$911$	49.1117	1.62714	0.813572	−	0.581465i	$-0.197520\pi$
$911$	49.1117	1.62714	0.813572	+	0.581465i	$0.197520\pi$
$912$	−100.039	−3.31262
$913$	1.79914	0.0595428
$914$	−38.2639	−1.26566
$915$	−74.9729	−2.47853
$916$	−98.1475	−3.24289
$917$	−11.7055	−0.386551
$918$	−128.199	−4.23121
$919$	36.1027	1.19092	0.595459	−	0.803386i	$-0.296970\pi$
$919$	36.1027	1.19092	0.595459	+	0.803386i	$0.296970\pi$
$920$	−48.4448	−1.59718
$921$	−70.0410	−2.30793
$922$	−61.5997	−2.02868
$923$	0.105350	0.00346763
$924$	−112.318	−3.69497
$925$	−10.6353	−0.349685
$926$	70.5274	2.31767
$927$	−18.5854	−0.610424
$928$	−30.9171	−1.01490
$929$	35.9924	1.18087	0.590436	−	0.807084i	$-0.298956\pi$
$929$	35.9924	1.18087	0.590436	+	0.807084i	$0.298956\pi$
$930$	−48.5711	−1.59271
$931$	2.45972	0.0806142
$932$	−126.422	−4.14108
$933$	42.2818	1.38424
$934$	−13.3419	−0.436559
$935$	27.3452	0.894284
$936$	−9.81485	−0.320808
$937$	0.368168	0.0120275	0.00601377	−	0.999982i	$-0.498086\pi$
$937$	0.368168	0.0120275	0.00601377	+	0.999982i	$0.498086\pi$
$938$	−31.6329	−1.03285
$939$	57.9904	1.89245
$940$	43.0268	1.40338
$941$	10.1487	0.330837	0.165418	−	0.986223i	$-0.447103\pi$
$941$	10.1487	0.330837	0.165418	+	0.986223i	$0.447103\pi$
$942$	−81.3043	−2.64904
$943$	8.42701	0.274421
$944$	−37.1345	−1.20862
$945$	−48.9619	−1.59273
$946$	93.5872	3.04278
$947$	5.78211	0.187893	0.0939467	−	0.995577i	$-0.470052\pi$
$947$	5.78211	0.187893	0.0939467	+	0.995577i	$0.470052\pi$
$948$	−62.6317	−2.03418
$949$	0.900782	0.0292406
$950$	−9.29244	−0.301487
$951$	−24.7786	−0.803502
$952$	−95.2615	−3.08744
$953$	35.5792	1.15252	0.576262	−	0.817265i	$-0.304511\pi$
$953$	35.5792	1.15252	0.576262	+	0.817265i	$0.304511\pi$
$954$	−240.740	−7.79424
$955$	−44.5124	−1.44039
$956$	18.9311	0.612277
$957$	−20.0704	−0.648783
$958$	−50.5744	−1.63398
$959$	22.0847	0.713151
$960$	−84.1259	−2.71515
$961$	−21.5152	−0.694038
$962$	−4.50470	−0.145237
$963$	13.9924	0.450899
$964$	−108.186	−3.48443
$965$	−38.9861	−1.25501
$966$	62.0322	1.99585
$967$	54.9249	1.76626	0.883132	−	0.469124i	$-0.155430\pi$
$967$	54.9249	1.76626	0.883132	+	0.469124i	$0.155430\pi$
$968$	18.7453	0.602498
$969$	−42.2322	−1.35669
$970$	32.6778	1.04922
$971$	−24.6072	−0.789682	−0.394841	−	0.918749i	$-0.629200\pi$
$971$	−24.6072	−0.789682	−0.394841	+	0.918749i	$0.629200\pi$
$972$	31.1149	0.998012
$973$	36.0329	1.15516
$974$	−28.0112	−0.897537
$975$	−0.710629	−0.0227583
$976$	142.423	4.55885
$977$	39.1338	1.25200	0.626001	−	0.779822i	$-0.284691\pi$
$977$	39.1338	1.25200	0.626001	+	0.779822i	$0.284691\pi$
$978$	−109.868	−3.51319
$979$	−12.8078	−0.409338
$980$	8.31559	0.265632
$981$	52.0773	1.66270
$982$	52.3378	1.67017
$983$	−5.02643	−0.160318	−0.0801591	−	0.996782i	$-0.525543\pi$
$983$	−5.02643	−0.160318	−0.0801591	+	0.996782i	$0.525543\pi$
$984$	67.1041	2.13920
$985$	26.4341	0.842260
$986$	−28.2341	−0.899158
$987$	−33.2169	−1.05731
$988$	−2.81723	−0.0896280
$989$	−36.9965	−1.17642
$990$	−96.1527	−3.05593
$991$	12.3304	0.391688	0.195844	−	0.980635i	$-0.437255\pi$
$991$	12.3304	0.391688	0.195844	+	0.980635i	$0.437255\pi$
$992$	42.6531	1.35424
$993$	−51.5875	−1.63708
$994$	−3.59540	−0.114039
$995$	−26.6532	−0.844963
$996$	−9.39364	−0.297649
$997$	−51.5304	−1.63198	−0.815991	−	0.578064i	$-0.803808\pi$
$997$	−51.5304	−1.63198	−0.815991	+	0.578064i	$0.803808\pi$
$998$	97.4176	3.08370
$999$	89.2841	2.82482

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4001.2.a.b.1.10	✓	184

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4001.2.a.b.1.10	✓	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)

\(f(q)\)	\(=\)	\(q-2.65266 q^{2} +3.05290 q^{3} +5.03661 q^{4} -1.94746 q^{5} -8.09830 q^{6} +2.48037 q^{7} -8.05510 q^{8} +6.32018 q^{9} +O(q^{10})\)	\(q-2.65266 q^{2} +3.05290 q^{3} +5.03661 q^{4} -1.94746 q^{5} -8.09830 q^{6} +2.48037 q^{7} -8.05510 q^{8} +6.32018 q^{9} +5.16596 q^{10} -2.94497 q^{11} +15.3763 q^{12} +0.192789 q^{13} -6.57957 q^{14} -5.94540 q^{15} +11.2942 q^{16} +4.76794 q^{17} -16.7653 q^{18} -2.90135 q^{19} -9.80861 q^{20} +7.57230 q^{21} +7.81201 q^{22} -3.08821 q^{23} -24.5914 q^{24} -1.20739 q^{25} -0.511405 q^{26} +10.1362 q^{27} +12.4926 q^{28} +2.23235 q^{29} +15.7711 q^{30} -3.07974 q^{31} -13.8496 q^{32} -8.99069 q^{33} -12.6477 q^{34} -4.83042 q^{35} +31.8323 q^{36} +8.80848 q^{37} +7.69631 q^{38} +0.588566 q^{39} +15.6870 q^{40} -2.72877 q^{41} -20.0867 q^{42} +11.9799 q^{43} -14.8327 q^{44} -12.3083 q^{45} +8.19199 q^{46} -4.38663 q^{47} +34.4801 q^{48} -0.847785 q^{49} +3.20280 q^{50} +14.5560 q^{51} +0.971006 q^{52} +14.3594 q^{53} -26.8878 q^{54} +5.73522 q^{55} -19.9796 q^{56} -8.85753 q^{57} -5.92167 q^{58} -3.28792 q^{59} -29.9447 q^{60} +12.6102 q^{61} +8.16952 q^{62} +15.6764 q^{63} +14.1497 q^{64} -0.375450 q^{65} +23.8493 q^{66} +4.80775 q^{67} +24.0143 q^{68} -9.42800 q^{69} +12.8135 q^{70} +0.546449 q^{71} -50.9097 q^{72} +4.67236 q^{73} -23.3659 q^{74} -3.68604 q^{75} -14.6130 q^{76} -7.30461 q^{77} -1.56127 q^{78} -4.07327 q^{79} -21.9951 q^{80} +11.9841 q^{81} +7.23849 q^{82} -0.610918 q^{83} +38.1387 q^{84} -9.28538 q^{85} -31.7787 q^{86} +6.81513 q^{87} +23.7220 q^{88} +4.34903 q^{89} +32.6498 q^{90} +0.478188 q^{91} -15.5541 q^{92} -9.40214 q^{93} +11.6363 q^{94} +5.65028 q^{95} -42.2813 q^{96} +6.32560 q^{97} +2.24889 q^{98} -18.6127 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 184 q + 3 q^{2} + 28 q^{3} + 217 q^{4} + 15 q^{5} + 31 q^{6} + 49 q^{7} + 6 q^{8} + 210 q^{9}+O(q^{10}) \) 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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