LMFDB - Embedded newform 4001.2.a.b.1.4

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			1.4
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)

$f(q)$	$=$	$q-2.76351 q^{2} -0.782711 q^{3} +5.63697 q^{4} +4.06144 q^{5} +2.16303 q^{6} +1.66325 q^{7} -10.0508 q^{8} -2.38736 q^{9} +O(q^{10})$	\(q-2.76351 q^{2} -0.782711 q^{3} +5.63697 q^{4} +4.06144 q^{5} +2.16303 q^{6} +1.66325 q^{7} -10.0508 q^{8} -2.38736 q^{9} -11.2238 q^{10} +5.36440 q^{11} -4.41212 q^{12} +4.72431 q^{13} -4.59641 q^{14} -3.17893 q^{15} +16.5015 q^{16} -0.338710 q^{17} +6.59749 q^{18} -2.39058 q^{19} +22.8942 q^{20} -1.30185 q^{21} -14.8246 q^{22} +1.52348 q^{23} +7.86687 q^{24} +11.4953 q^{25} -13.0557 q^{26} +4.21675 q^{27} +9.37571 q^{28} -2.87593 q^{29} +8.78500 q^{30} +7.10978 q^{31} -25.5004 q^{32} -4.19878 q^{33} +0.936028 q^{34} +6.75519 q^{35} -13.4575 q^{36} +7.03437 q^{37} +6.60640 q^{38} -3.69777 q^{39} -40.8207 q^{40} -7.06405 q^{41} +3.59766 q^{42} -10.7122 q^{43} +30.2390 q^{44} -9.69612 q^{45} -4.21015 q^{46} -7.82786 q^{47} -12.9159 q^{48} -4.23359 q^{49} -31.7672 q^{50} +0.265112 q^{51} +26.6308 q^{52} +13.0571 q^{53} -11.6530 q^{54} +21.7872 q^{55} -16.7170 q^{56} +1.87114 q^{57} +7.94766 q^{58} +0.352401 q^{59} -17.9195 q^{60} -2.23483 q^{61} -19.6479 q^{62} -3.97079 q^{63} +37.4676 q^{64} +19.1875 q^{65} +11.6034 q^{66} +8.18616 q^{67} -1.90930 q^{68} -1.19245 q^{69} -18.6680 q^{70} +9.16707 q^{71} +23.9949 q^{72} -9.95483 q^{73} -19.4395 q^{74} -8.99747 q^{75} -13.4757 q^{76} +8.92236 q^{77} +10.2188 q^{78} +14.1721 q^{79} +67.0198 q^{80} +3.86159 q^{81} +19.5216 q^{82} -2.57679 q^{83} -7.33847 q^{84} -1.37565 q^{85} +29.6032 q^{86} +2.25103 q^{87} -53.9165 q^{88} +15.4335 q^{89} +26.7953 q^{90} +7.85772 q^{91} +8.58783 q^{92} -5.56491 q^{93} +21.6323 q^{94} -9.70920 q^{95} +19.9595 q^{96} +2.79797 q^{97} +11.6996 q^{98} -12.8068 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.76351	−1.95409	−0.977047	−	0.213022i	$-0.931669\pi$
$2$	−2.76351	−1.95409	−0.977047	+	0.213022i	$0.931669\pi$
$3$	−0.782711	−0.451899	−0.225949	−	0.974139i	$-0.572548\pi$
$3$	−0.782711	−0.451899	−0.225949	+	0.974139i	$0.572548\pi$
$4$	5.63697	2.81849
$5$	4.06144	1.81633	0.908165	−	0.418613i	$-0.137484\pi$
$5$	4.06144	1.81633	0.908165	+	0.418613i	$0.137484\pi$
$6$	2.16303	0.883053
$7$	1.66325	0.628651	0.314325	−	0.949315i	$-0.398222\pi$
$7$	1.66325	0.628651	0.314325	+	0.949315i	$0.398222\pi$
$8$	−10.0508	−3.55349
$9$	−2.38736	−0.795788
$10$	−11.2238	−3.54928
$11$	5.36440	1.61743	0.808714	−	0.588202i	$-0.200164\pi$
$11$	5.36440	1.61743	0.808714	+	0.588202i	$0.200164\pi$
$12$	−4.41212	−1.27367
$13$	4.72431	1.31029	0.655144	−	0.755504i	$-0.272608\pi$
$13$	4.72431	1.31029	0.655144	+	0.755504i	$0.272608\pi$
$14$	−4.59641	−1.22844
$15$	−3.17893	−0.820797
$16$	16.5015	4.12538
$17$	−0.338710	−0.0821493	−0.0410746	−	0.999156i	$-0.513078\pi$
$17$	−0.338710	−0.0821493	−0.0410746	+	0.999156i	$0.513078\pi$
$18$	6.59749	1.55504
$19$	−2.39058	−0.548438	−0.274219	−	0.961667i	$-0.588419\pi$
$19$	−2.39058	−0.548438	−0.274219	+	0.961667i	$0.588419\pi$
$20$	22.8942	5.11930
$21$	−1.30185	−0.284086
$22$	−14.8246	−3.16061
$23$	1.52348	0.317668	0.158834	−	0.987305i	$-0.449227\pi$
$23$	1.52348	0.317668	0.158834	+	0.987305i	$0.449227\pi$
$24$	7.86687	1.60582
$25$	11.4953	2.29905
$26$	−13.0557	−2.56043
$27$	4.21675	0.811514
$28$	9.37571	1.77184
$29$	−2.87593	−0.534047	−0.267024	−	0.963690i	$-0.586040\pi$
$29$	−2.87593	−0.534047	−0.267024	+	0.963690i	$0.586040\pi$
$30$	8.78500	1.60391
$31$	7.10978	1.27695	0.638477	−	0.769641i	$-0.279565\pi$
$31$	7.10978	1.27695	0.638477	+	0.769641i	$0.279565\pi$
$32$	−25.5004	−4.50788
$33$	−4.19878	−0.730913
$34$	0.936028	0.160527
$35$	6.75519	1.14184
$36$	−13.4575	−2.24292
$37$	7.03437	1.15644	0.578221	−	0.815880i	$-0.303747\pi$
$37$	7.03437	1.15644	0.578221	+	0.815880i	$0.303747\pi$
$38$	6.60640	1.07170
$39$	−3.69777	−0.592117
$40$	−40.8207	−6.45431
$41$	−7.06405	−1.10322	−0.551610	−	0.834102i	$-0.685986\pi$
$41$	−7.06405	−1.10322	−0.551610	+	0.834102i	$0.685986\pi$
$42$	3.59766	0.555132
$43$	−10.7122	−1.63359	−0.816797	−	0.576925i	$-0.804253\pi$
$43$	−10.7122	−1.63359	−0.816797	+	0.576925i	$0.804253\pi$
$44$	30.2390	4.55870
$45$	−9.69612	−1.44541
$46$	−4.21015	−0.620753
$47$	−7.82786	−1.14181	−0.570905	−	0.821016i	$-0.693408\pi$
$47$	−7.82786	−1.14181	−0.570905	+	0.821016i	$0.693408\pi$
$48$	−12.9159	−1.86425
$49$	−4.23359	−0.604799
$50$	−31.7672	−4.49256
$51$	0.265112	0.0371231
$52$	26.6308	3.69303
$53$	13.0571	1.79353	0.896765	−	0.442508i	$-0.145911\pi$
$53$	13.0571	1.79353	0.896765	+	0.442508i	$0.145911\pi$
$54$	−11.6530	−1.58578
$55$	21.7872	2.93778
$56$	−16.7170	−2.23391
$57$	1.87114	0.247838
$58$	7.94766	1.04358
$59$	0.352401	0.0458786	0.0229393	−	0.999737i	$-0.492698\pi$
$59$	0.352401	0.0458786	0.0229393	+	0.999737i	$0.492698\pi$
$60$	−17.9195	−2.31340
$61$	−2.23483	−0.286140	−0.143070	−	0.989713i	$-0.545697\pi$
$61$	−2.23483	−0.286140	−0.143070	+	0.989713i	$0.545697\pi$
$62$	−19.6479	−2.49529
$63$	−3.97079	−0.500272
$64$	37.4676	4.68345
$65$	19.1875	2.37991
$66$	11.6034	1.42827
$67$	8.18616	1.00010	0.500049	−	0.865997i	$-0.333315\pi$
$67$	8.18616	1.00010	0.500049	+	0.865997i	$0.333315\pi$
$68$	−1.90930	−0.231537
$69$	−1.19245	−0.143554
$70$	−18.6680	−2.23126
$71$	9.16707	1.08793	0.543965	−	0.839108i	$-0.316922\pi$
$71$	9.16707	1.08793	0.543965	+	0.839108i	$0.316922\pi$
$72$	23.9949	2.82783
$73$	−9.95483	−1.16512	−0.582562	−	0.812786i	$-0.697950\pi$
$73$	−9.95483	−1.16512	−0.582562	+	0.812786i	$0.697950\pi$
$74$	−19.4395	−2.25980
$75$	−8.99747	−1.03894
$76$	−13.4757	−1.54576
$77$	8.92236	1.01680
$78$	10.2188	1.15705
$79$	14.1721	1.59449	0.797245	−	0.603656i	$-0.206290\pi$
$79$	14.1721	1.59449	0.797245	+	0.603656i	$0.206290\pi$
$80$	67.0198	7.49304
$81$	3.86159	0.429066
$82$	19.5216	2.15580
$83$	−2.57679	−0.282840	−0.141420	−	0.989950i	$-0.545167\pi$
$83$	−2.57679	−0.282840	−0.141420	+	0.989950i	$0.545167\pi$
$84$	−7.33847	−0.800693
$85$	−1.37565	−0.149210
$86$	29.6032	3.19220
$87$	2.25103	0.241335
$88$	−53.9165	−5.74752
$89$	15.4335	1.63594	0.817972	−	0.575257i	$-0.195098\pi$
$89$	15.4335	1.63594	0.817972	+	0.575257i	$0.195098\pi$
$90$	26.7953	2.82447
$91$	7.85772	0.823713
$92$	8.58783	0.895343
$93$	−5.56491	−0.577054
$94$	21.6323	2.23121
$95$	−9.70920	−0.996143
$96$	19.9595	2.03711
$97$	2.79797	0.284091	0.142045	−	0.989860i	$-0.454632\pi$
$97$	2.79797	0.284091	0.142045	+	0.989860i	$0.454632\pi$
$98$	11.6996	1.18183
$99$	−12.8068	−1.28713
$100$	64.7984	6.47984
$101$	−4.14013	−0.411959	−0.205979	−	0.978556i	$-0.566038\pi$
$101$	−4.14013	−0.411959	−0.205979	+	0.978556i	$0.566038\pi$
$102$	−0.732640	−0.0725421
$103$	−1.85446	−0.182725	−0.0913627	−	0.995818i	$-0.529122\pi$
$103$	−1.85446	−0.182725	−0.0913627	+	0.995818i	$0.529122\pi$
$104$	−47.4831	−4.65610
$105$	−5.28737	−0.515994
$106$	−36.0834	−3.50473
$107$	1.72169	0.166442	0.0832211	−	0.996531i	$-0.473479\pi$
$107$	1.72169	0.166442	0.0832211	+	0.996531i	$0.473479\pi$
$108$	23.7697	2.28724
$109$	9.70657	0.929721	0.464860	−	0.885384i	$-0.346105\pi$
$109$	9.70657	0.929721	0.464860	+	0.885384i	$0.346105\pi$
$110$	−60.2090	−5.74070
$111$	−5.50588	−0.522595
$112$	27.4462	2.59342
$113$	−18.1225	−1.70482	−0.852410	−	0.522873i	$-0.824860\pi$
$113$	−18.1225	−1.70482	−0.852410	+	0.522873i	$0.824860\pi$
$114$	−5.17090	−0.484299
$115$	6.18753	0.576990
$116$	−16.2116	−1.50521
$117$	−11.2786	−1.04271
$118$	−0.973861	−0.0896512
$119$	−0.563361	−0.0516432
$120$	31.9508	2.91670
$121$	17.7768	1.61607
$122$	6.17596	0.559145
$123$	5.52912	0.498544
$124$	40.0776	3.59908
$125$	26.3801	2.35950
$126$	10.9733	0.977579
$127$	−10.3281	−0.916475	−0.458238	−	0.888830i	$-0.651519\pi$
$127$	−10.3281	−0.916475	−0.458238	+	0.888830i	$0.651519\pi$
$128$	−52.5412	−4.64403
$129$	8.38456	0.738219
$130$	−53.0247	−4.65058
$131$	5.47824	0.478636	0.239318	−	0.970941i	$-0.423076\pi$
$131$	5.47824	0.478636	0.239318	+	0.970941i	$0.423076\pi$
$132$	−23.6684	−2.06007
$133$	−3.97615	−0.344776
$134$	−22.6225	−1.95429
$135$	17.1261	1.47398
$136$	3.40431	0.291917
$137$	−9.05252	−0.773409	−0.386704	−	0.922204i	$-0.626387\pi$
$137$	−9.05252	−0.773409	−0.386704	+	0.922204i	$0.626387\pi$
$138$	3.29534	0.280518
$139$	9.89452	0.839242	0.419621	−	0.907699i	$-0.362163\pi$
$139$	9.89452	0.839242	0.419621	+	0.907699i	$0.362163\pi$
$140$	38.0788	3.21825
$141$	6.12695	0.515983
$142$	−25.3333	−2.12592
$143$	25.3431	2.11930
$144$	−39.3951	−3.28292
$145$	−11.6804	−0.970006
$146$	27.5102	2.27676
$147$	3.31368	0.273308
$148$	39.6525	3.25942
$149$	−7.08093	−0.580092	−0.290046	−	0.957013i	$-0.593671\pi$
$149$	−7.08093	−0.580092	−0.290046	+	0.957013i	$0.593671\pi$
$150$	24.8646	2.03018
$151$	10.4528	0.850634	0.425317	−	0.905044i	$-0.360163\pi$
$151$	10.4528	0.850634	0.425317	+	0.905044i	$0.360163\pi$
$152$	24.0273	1.94887
$153$	0.808624	0.0653734
$154$	−24.6570	−1.98692
$155$	28.8759	2.31937
$156$	−20.8442	−1.66887
$157$	−17.6811	−1.41111	−0.705555	−	0.708656i	$-0.749302\pi$
$157$	−17.6811	−1.41111	−0.705555	+	0.708656i	$0.749302\pi$
$158$	−39.1648	−3.11578
$159$	−10.2199	−0.810493
$160$	−103.568	−8.18780
$161$	2.53394	0.199702
$162$	−10.6715	−0.838435
$163$	−10.3629	−0.811682	−0.405841	−	0.913944i	$-0.633021\pi$
$163$	−10.3629	−0.811682	−0.405841	+	0.913944i	$0.633021\pi$
$164$	−39.8199	−3.10941
$165$	−17.0531	−1.32758
$166$	7.12098	0.552695
$167$	−12.2731	−0.949722	−0.474861	−	0.880061i	$-0.657502\pi$
$167$	−12.2731	−0.949722	−0.474861	+	0.880061i	$0.657502\pi$
$168$	13.0846	1.00950
$169$	9.31909	0.716853
$170$	3.80162	0.291571
$171$	5.70719	0.436440
$172$	−60.3844	−4.60426
$173$	2.67855	0.203646	0.101823	−	0.994803i	$-0.467532\pi$
$173$	2.67855	0.203646	0.101823	+	0.994803i	$0.467532\pi$
$174$	−6.22073	−0.471592
$175$	19.1195	1.44530
$176$	88.5207	6.67250
$177$	−0.275828	−0.0207325
$178$	−42.6505	−3.19679
$179$	−3.39805	−0.253982	−0.126991	−	0.991904i	$-0.540532\pi$
$179$	−3.39805	−0.253982	−0.126991	+	0.991904i	$0.540532\pi$
$180$	−54.6568	−4.07387
$181$	6.63490	0.493168	0.246584	−	0.969121i	$-0.420692\pi$
$181$	6.63490	0.493168	0.246584	+	0.969121i	$0.420692\pi$
$182$	−21.7149	−1.60961
$183$	1.74922	0.129306
$184$	−15.3122	−1.12883
$185$	28.5696	2.10048
$186$	15.3787	1.12762
$187$	−1.81698	−0.132871
$188$	−44.1254	−3.21818
$189$	7.01352	0.510159
$190$	26.8314	1.94656
$191$	2.13831	0.154723	0.0773614	−	0.997003i	$-0.475350\pi$
$191$	2.13831	0.154723	0.0773614	+	0.997003i	$0.475350\pi$
$192$	−29.3263	−2.11645
$193$	4.94193	0.355728	0.177864	−	0.984055i	$-0.443081\pi$
$193$	4.94193	0.355728	0.177864	+	0.984055i	$0.443081\pi$
$194$	−7.73221	−0.555140
$195$	−15.0183	−1.07548
$196$	−23.8646	−1.70462
$197$	−15.6568	−1.11550	−0.557751	−	0.830008i	$-0.688336\pi$
$197$	−15.6568	−1.11550	−0.557751	+	0.830008i	$0.688336\pi$
$198$	35.3916	2.51517
$199$	−5.62420	−0.398689	−0.199344	−	0.979929i	$-0.563881\pi$
$199$	−5.62420	−0.398689	−0.199344	+	0.979929i	$0.563881\pi$
$200$	−115.536	−8.16966
$201$	−6.40740	−0.451943
$202$	11.4413	0.805006
$203$	−4.78340	−0.335729
$204$	1.49443	0.104631
$205$	−28.6902	−2.00381
$206$	5.12481	0.357063
$207$	−3.63711	−0.252796
$208$	77.9582	5.40543
$209$	−12.8241	−0.887058
$210$	14.6117	1.00830
$211$	3.22729	0.222176	0.111088	−	0.993811i	$-0.464567\pi$
$211$	3.22729	0.222176	0.111088	+	0.993811i	$0.464567\pi$
$212$	73.6024	5.05504
$213$	−7.17517	−0.491634
$214$	−4.75791	−0.325244
$215$	−43.5069	−2.96715
$216$	−42.3817	−2.88371
$217$	11.8254	0.802758
$218$	−26.8242	−1.81676
$219$	7.79176	0.526518
$220$	122.814	8.28010
$221$	−1.60017	−0.107639
$222$	15.2155	1.02120
$223$	7.22423	0.483770	0.241885	−	0.970305i	$-0.422234\pi$
$223$	7.22423	0.483770	0.241885	+	0.970305i	$0.422234\pi$
$224$	−42.4137	−2.83388
$225$	−27.4433	−1.82956
$226$	50.0816	3.33138
$227$	−20.4699	−1.35864	−0.679318	−	0.733844i	$-0.737724\pi$
$227$	−20.4699	−1.35864	−0.679318	+	0.733844i	$0.737724\pi$
$228$	10.5475	0.698528
$229$	14.5928	0.964319	0.482160	−	0.876083i	$-0.339853\pi$
$229$	14.5928	0.964319	0.482160	+	0.876083i	$0.339853\pi$
$230$	−17.0993	−1.12749
$231$	−6.98363	−0.459489
$232$	28.9054	1.89773
$233$	6.75231	0.442359	0.221179	−	0.975233i	$-0.429009\pi$
$233$	6.75231	0.442359	0.221179	+	0.975233i	$0.429009\pi$
$234$	31.1686	2.03755
$235$	−31.7923	−2.07390
$236$	1.98647	0.129308
$237$	−11.0927	−0.720548
$238$	1.55685	0.100916
$239$	−20.7729	−1.34368	−0.671842	−	0.740694i	$-0.734497\pi$
$239$	−20.7729	−1.34368	−0.671842	+	0.740694i	$0.734497\pi$
$240$	−52.4572	−3.38610
$241$	7.74442	0.498862	0.249431	−	0.968393i	$-0.419756\pi$
$241$	7.74442	0.498862	0.249431	+	0.968393i	$0.419756\pi$
$242$	−49.1263	−3.15796
$243$	−15.6728	−1.00541
$244$	−12.5977	−0.806482
$245$	−17.1945	−1.09851
$246$	−15.2798	−0.974201
$247$	−11.2939	−0.718611
$248$	−71.4590	−4.53765
$249$	2.01688	0.127815
$250$	−72.9015	−4.61070
$251$	−1.07922	−0.0681195	−0.0340597	−	0.999420i	$-0.510844\pi$
$251$	−1.07922	−0.0681195	−0.0340597	+	0.999420i	$0.510844\pi$
$252$	−22.3832	−1.41001
$253$	8.17257	0.513805
$254$	28.5419	1.79088
$255$	1.07674	0.0674278
$256$	70.2627	4.39142
$257$	−21.0808	−1.31498	−0.657491	−	0.753462i	$-0.728382\pi$
$257$	−21.0808	−1.31498	−0.657491	+	0.753462i	$0.728382\pi$
$258$	−23.1708	−1.44255
$259$	11.6999	0.726998
$260$	108.159	6.70775
$261$	6.86590	0.424988
$262$	−15.1391	−0.935299
$263$	−6.07480	−0.374588	−0.187294	−	0.982304i	$-0.559972\pi$
$263$	−6.07480	−0.374588	−0.187294	+	0.982304i	$0.559972\pi$
$264$	42.2011	2.59730
$265$	53.0305	3.25764
$266$	10.9881	0.673724
$267$	−12.0800	−0.739281
$268$	46.1452	2.81876
$269$	−29.7060	−1.81121	−0.905603	−	0.424127i	$-0.860581\pi$
$269$	−29.7060	−1.81121	−0.905603	+	0.424127i	$0.860581\pi$
$270$	−47.3280	−2.88029
$271$	21.0614	1.27939	0.639696	−	0.768628i	$-0.279060\pi$
$271$	21.0614	1.27939	0.639696	+	0.768628i	$0.279060\pi$
$272$	−5.58923	−0.338897
$273$	−6.15033	−0.372235
$274$	25.0167	1.51131
$275$	61.6652	3.71855
$276$	−6.72179	−0.404604
$277$	0.00821825	0.000493787 0	0.000246894	−	1.00000i	$-0.499921\pi$
$277$	0.00821825	0.000493787 0	0.000246894		1.00000i	$0.499921\pi$
$278$	−27.3436	−1.63996
$279$	−16.9736	−1.01618
$280$	−67.8951	−4.05751
$281$	−15.7183	−0.937677	−0.468839	−	0.883284i	$-0.655327\pi$
$281$	−15.7183	−0.937677	−0.468839	+	0.883284i	$0.655327\pi$
$282$	−16.9319	−1.00828
$283$	16.9512	1.00765	0.503823	−	0.863807i	$-0.331926\pi$
$283$	16.9512	1.00765	0.503823	+	0.863807i	$0.331926\pi$
$284$	51.6745	3.06632
$285$	7.59950	0.450156
$286$	−70.0358	−4.14130
$287$	−11.7493	−0.693540
$288$	60.8788	3.58732
$289$	−16.8853	−0.993251
$290$	32.2789	1.89548
$291$	−2.19000	−0.128380
$292$	−56.1151	−3.28389
$293$	25.9396	1.51541	0.757703	−	0.652600i	$-0.226322\pi$
$293$	25.9396	1.51541	0.757703	+	0.652600i	$0.226322\pi$
$294$	−9.15738	−0.534069
$295$	1.43125	0.0833307
$296$	−70.7010	−4.10941
$297$	22.6203	1.31257
$298$	19.5682	1.13356
$299$	7.19740	0.416236
$300$	−50.7185	−2.92823
$301$	−17.8171	−1.02696
$302$	−28.8863	−1.66222
$303$	3.24053	0.186164
$304$	−39.4482	−2.26251
$305$	−9.07660	−0.519725
$306$	−2.23464	−0.127746
$307$	9.02991	0.515364	0.257682	−	0.966230i	$-0.417041\pi$
$307$	9.02991	0.515364	0.257682	+	0.966230i	$0.417041\pi$
$308$	50.2951	2.86583
$309$	1.45151	0.0825734
$310$	−79.7988	−4.53227
$311$	23.9710	1.35927	0.679634	−	0.733551i	$-0.262138\pi$
$311$	23.9710	1.35927	0.679634	+	0.733551i	$0.262138\pi$
$312$	37.1655	2.10408
$313$	27.1495	1.53458	0.767291	−	0.641299i	$-0.221604\pi$
$313$	27.1495	1.53458	0.767291	+	0.641299i	$0.221604\pi$
$314$	48.8620	2.75744
$315$	−16.1271	−0.908659
$316$	79.8879	4.49405
$317$	−29.6221	−1.66374	−0.831872	−	0.554967i	$-0.812731\pi$
$317$	−29.6221	−1.66374	−0.831872	+	0.554967i	$0.812731\pi$
$318$	28.2429	1.58378
$319$	−15.4277	−0.863783
$320$	152.172	8.50669
$321$	−1.34759	−0.0752150
$322$	−7.00255	−0.390237
$323$	0.809715	0.0450537
$324$	21.7677	1.20932
$325$	54.3071	3.01242
$326$	28.6379	1.58610
$327$	−7.59744	−0.420140
$328$	70.9994	3.92029
$329$	−13.0197	−0.717800
$330$	47.1263	2.59422
$331$	1.53106	0.0841546	0.0420773	−	0.999114i	$-0.486602\pi$
$331$	1.53106	0.0841546	0.0420773	+	0.999114i	$0.486602\pi$
$332$	−14.5253	−0.797179
$333$	−16.7936	−0.920283
$334$	33.9168	1.85585
$335$	33.2476	1.81651
$336$	−21.4824	−1.17196
$337$	−28.1458	−1.53320	−0.766600	−	0.642125i	$-0.778053\pi$
$337$	−28.1458	−1.53320	−0.766600	+	0.642125i	$0.778053\pi$
$338$	−25.7534	−1.40080
$339$	14.1847	0.770406
$340$	−7.75450	−0.420547
$341$	38.1397	2.06538
$342$	−15.7719	−0.852845
$343$	−18.6843	−1.00886
$344$	107.666	5.80497
$345$	−4.84305	−0.260741
$346$	−7.40219	−0.397944
$347$	23.9352	1.28491	0.642455	−	0.766324i	$-0.277916\pi$
$347$	23.9352	1.28491	0.642455	+	0.766324i	$0.277916\pi$
$348$	12.6890	0.680200
$349$	−21.3570	−1.14321	−0.571607	−	0.820527i	$-0.693680\pi$
$349$	−21.3570	−1.14321	−0.571607	+	0.820527i	$0.693680\pi$
$350$	−52.8369	−2.82425
$351$	19.9212	1.06332
$352$	−136.795	−7.29118
$353$	−5.01320	−0.266826	−0.133413	−	0.991061i	$-0.542594\pi$
$353$	−5.01320	−0.266826	−0.133413	+	0.991061i	$0.542594\pi$
$354$	0.762252	0.0405133
$355$	37.2314	1.97604
$356$	86.9981	4.61089
$357$	0.440949	0.0233375
$358$	9.39054	0.496306
$359$	11.1548	0.588730	0.294365	−	0.955693i	$-0.404892\pi$
$359$	11.1548	0.588730	0.294365	+	0.955693i	$0.404892\pi$
$360$	97.4537	5.13626
$361$	−13.2851	−0.699216
$362$	−18.3356	−0.963697
$363$	−13.9141	−0.730301
$364$	44.2937	2.32162
$365$	−40.4309	−2.11625
$366$	−4.83399	−0.252677
$367$	−20.7089	−1.08099	−0.540497	−	0.841346i	$-0.681764\pi$
$367$	−20.7089	−1.08099	−0.540497	+	0.841346i	$0.681764\pi$
$368$	25.1398	1.31050
$369$	16.8645	0.877929
$370$	−78.9523	−4.10454
$371$	21.7172	1.12750
$372$	−31.3692	−1.62642
$373$	4.96448	0.257051	0.128525	−	0.991706i	$-0.458976\pi$
$373$	4.96448	0.257051	0.128525	+	0.991706i	$0.458976\pi$
$374$	5.02123	0.259642
$375$	−20.6480	−1.06626
$376$	78.6762	4.05742
$377$	−13.5868	−0.699755
$378$	−19.3819	−0.996898
$379$	16.8520	0.865627	0.432813	−	0.901484i	$-0.357521\pi$
$379$	16.8520	0.865627	0.432813	+	0.901484i	$0.357521\pi$
$380$	−54.7305	−2.80761
$381$	8.08396	0.414154
$382$	−5.90924	−0.302343
$383$	−26.6989	−1.36425	−0.682126	−	0.731235i	$-0.738944\pi$
$383$	−26.6989	−1.36425	−0.682126	+	0.731235i	$0.738944\pi$
$384$	41.1246	2.09863
$385$	36.2376	1.84684
$386$	−13.6571	−0.695126
$387$	25.5739	1.29999
$388$	15.7721	0.800706
$389$	−25.2176	−1.27859	−0.639293	−	0.768964i	$-0.720773\pi$
$389$	−25.2176	−1.27859	−0.639293	+	0.768964i	$0.720773\pi$
$390$	41.5030	2.10159
$391$	−0.516019	−0.0260962
$392$	42.5510	2.14915
$393$	−4.28788	−0.216295
$394$	43.2678	2.17980
$395$	57.5592	2.89612
$396$	−72.1914	−3.62776
$397$	30.2673	1.51907	0.759536	−	0.650465i	$-0.225426\pi$
$397$	30.2673	1.51907	0.759536	+	0.650465i	$0.225426\pi$
$398$	15.5425	0.779076
$399$	3.11217	0.155804
$400$	189.689	9.48445
$401$	−21.4227	−1.06980	−0.534900	−	0.844915i	$-0.679651\pi$
$401$	−21.4227	−1.06980	−0.534900	+	0.844915i	$0.679651\pi$
$402$	17.7069	0.883140
$403$	33.5888	1.67318
$404$	−23.3378	−1.16110
$405$	15.6836	0.779324
$406$	13.2190	0.656047
$407$	37.7352	1.87046
$408$	−2.66459	−0.131917
$409$	19.1628	0.947537	0.473769	−	0.880649i	$-0.342893\pi$
$409$	19.1628	0.947537	0.473769	+	0.880649i	$0.342893\pi$
$410$	79.2856	3.91564
$411$	7.08551	0.349502
$412$	−10.4535	−0.515009
$413$	0.586131	0.0288416
$414$	10.0512	0.493988
$415$	−10.4655	−0.513730
$416$	−120.472	−5.90662
$417$	−7.74455	−0.379252
$418$	35.4394	1.73340
$419$	−2.00076	−0.0977436	−0.0488718	−	0.998805i	$-0.515563\pi$
$419$	−2.00076	−0.0977436	−0.0488718	+	0.998805i	$0.515563\pi$
$420$	−29.8047	−1.45432
$421$	32.6067	1.58915	0.794577	−	0.607163i	$-0.207693\pi$
$421$	32.6067	1.58915	0.794577	+	0.607163i	$0.207693\pi$
$422$	−8.91863	−0.434152
$423$	18.6879	0.908639
$424$	−131.234	−6.37329
$425$	−3.89356	−0.188865
$426$	19.8286	0.960700
$427$	−3.71708	−0.179882
$428$	9.70512	0.469115
$429$	−19.8363	−0.957707
$430$	120.232	5.79808
$431$	17.8223	0.858469	0.429235	−	0.903193i	$-0.358783\pi$
$431$	17.8223	0.858469	0.429235	+	0.903193i	$0.358783\pi$
$432$	69.5827	3.34780
$433$	−13.8895	−0.667486	−0.333743	−	0.942664i	$-0.608312\pi$
$433$	−13.8895	−0.667486	−0.333743	+	0.942664i	$0.608312\pi$
$434$	−32.6795	−1.56866
$435$	9.14240	0.438344
$436$	54.7157	2.62040
$437$	−3.64201	−0.174221
$438$	−21.5326	−1.02887
$439$	19.4677	0.929140	0.464570	−	0.885536i	$-0.346209\pi$
$439$	19.4677	0.929140	0.464570	+	0.885536i	$0.346209\pi$
$440$	−218.978	−10.4394
$441$	10.1071	0.481291
$442$	4.42208	0.210337
$443$	16.8827	0.802121	0.401060	−	0.916052i	$-0.368642\pi$
$443$	16.8827	0.802121	0.401060	+	0.916052i	$0.368642\pi$
$444$	−31.0365	−1.47293
$445$	62.6821	2.97141
$446$	−19.9642	−0.945333
$447$	5.54232	0.262143
$448$	62.3181	2.94426
$449$	−30.4303	−1.43609	−0.718047	−	0.695994i	$-0.754964\pi$
$449$	−30.4303	−1.43609	−0.718047	+	0.695994i	$0.754964\pi$
$450$	75.8399	3.57513
$451$	−37.8944	−1.78438
$452$	−102.156	−4.80501
$453$	−8.18150	−0.384400
$454$	56.5687	2.65490
$455$	31.9136	1.49613
$456$	−18.8064	−0.880691
$457$	−29.7230	−1.39038	−0.695192	−	0.718824i	$-0.744681\pi$
$457$	−29.7230	−1.39038	−0.695192	+	0.718824i	$0.744681\pi$
$458$	−40.3273	−1.88437
$459$	−1.42826	−0.0666653
$460$	34.8789	1.62624
$461$	34.5537	1.60933	0.804664	−	0.593731i	$-0.202346\pi$
$461$	34.5537	1.60933	0.804664	+	0.593731i	$0.202346\pi$
$462$	19.2993	0.897885
$463$	7.94873	0.369409	0.184704	−	0.982794i	$-0.440867\pi$
$463$	7.94873	0.369409	0.184704	+	0.982794i	$0.440867\pi$
$464$	−47.4572	−2.20315
$465$	−22.6015	−1.04812
$466$	−18.6601	−0.864411
$467$	4.59106	0.212449	0.106224	−	0.994342i	$-0.466124\pi$
$467$	4.59106	0.212449	0.106224	+	0.994342i	$0.466124\pi$
$468$	−63.5774	−2.93886
$469$	13.6157	0.628713
$470$	87.8584	4.05260
$471$	13.8392	0.637678
$472$	−3.54191	−0.163029
$473$	−57.4645	−2.64222
$474$	30.6547	1.40802
$475$	−27.4804	−1.26089
$476$	−3.17565	−0.145556
$477$	−31.1720	−1.42727
$478$	57.4059	2.62569
$479$	15.1938	0.694220	0.347110	−	0.937824i	$-0.387163\pi$
$479$	15.1938	0.694220	0.347110	+	0.937824i	$0.387163\pi$
$480$	81.0642	3.70006
$481$	33.2325	1.51527
$482$	−21.4018	−0.974823
$483$	−1.98334	−0.0902451
$484$	100.207	4.55488
$485$	11.3638	0.516002
$486$	43.3118	1.96466
$487$	13.9988	0.634345	0.317173	−	0.948368i	$-0.397267\pi$
$487$	13.9988	0.634345	0.317173	+	0.948368i	$0.397267\pi$
$488$	22.4618	1.01680
$489$	8.11113	0.366798
$490$	47.5170	2.14660
$491$	0.753044	0.0339844	0.0169922	−	0.999856i	$-0.494591\pi$
$491$	0.753044	0.0339844	0.0169922	+	0.999856i	$0.494591\pi$
$492$	31.1675	1.40514
$493$	0.974108	0.0438716
$494$	31.2106	1.40423
$495$	−52.0139	−2.33785
$496$	117.322	5.26792
$497$	15.2471	0.683928
$498$	−5.57367	−0.249762
$499$	−24.4995	−1.09675	−0.548375	−	0.836233i	$-0.684753\pi$
$499$	−24.4995	−1.09675	−0.548375	+	0.836233i	$0.684753\pi$
$500$	148.704	6.65023
$501$	9.60631	0.429178
$502$	2.98242	0.133112
$503$	−38.8310	−1.73139	−0.865695	−	0.500572i	$-0.833123\pi$
$503$	−38.8310	−1.73139	−0.865695	+	0.500572i	$0.833123\pi$
$504$	39.9096	1.77771
$505$	−16.8149	−0.748252
$506$	−22.5850	−1.00402
$507$	−7.29415	−0.323945
$508$	−58.2195	−2.58307
$509$	30.7290	1.36204	0.681020	−	0.732265i	$-0.261537\pi$
$509$	30.7290	1.36204	0.681020	+	0.732265i	$0.261537\pi$
$510$	−2.97557	−0.131760
$511$	−16.5574	−0.732456
$512$	−89.0891	−3.93722
$513$	−10.0805	−0.445065
$514$	58.2569	2.56960
$515$	−7.53177	−0.331889
$516$	47.2635	2.08066
$517$	−41.9918	−1.84680
$518$	−32.3328	−1.42062
$519$	−2.09653	−0.0920275
$520$	−192.849	−8.45701
$521$	−22.3321	−0.978387	−0.489194	−	0.872175i	$-0.662709\pi$
$521$	−22.3321	−0.978387	−0.489194	+	0.872175i	$0.662709\pi$
$522$	−18.9740	−0.830467
$523$	−25.2009	−1.10196	−0.550980	−	0.834518i	$-0.685746\pi$
$523$	−25.2009	−1.10196	−0.550980	+	0.834518i	$0.685746\pi$
$524$	30.8807	1.34903
$525$	−14.9651	−0.653129
$526$	16.7878	0.731981
$527$	−2.40815	−0.104901
$528$	−69.2862	−3.01529
$529$	−20.6790	−0.899087
$530$	−146.550	−6.36574
$531$	−0.841308	−0.0365097
$532$	−22.4134	−0.971745
$533$	−33.3728	−1.44554
$534$	33.3830	1.44463
$535$	6.99254	0.302314
$536$	−82.2775	−3.55384
$537$	2.65969	0.114774
$538$	82.0927	3.53927
$539$	−22.7107	−0.978218
$540$	96.5391	4.15438
$541$	−10.5358	−0.452970	−0.226485	−	0.974015i	$-0.572723\pi$
$541$	−10.5358	−0.452970	−0.226485	+	0.974015i	$0.572723\pi$
$542$	−58.2034	−2.50005
$543$	−5.19321	−0.222862
$544$	8.63726	0.370319
$545$	39.4226	1.68868
$546$	16.9965	0.727382
$547$	11.0105	0.470774	0.235387	−	0.971902i	$-0.424364\pi$
$547$	11.0105	0.470774	0.235387	+	0.971902i	$0.424364\pi$
$548$	−51.0288	−2.17984
$549$	5.33534	0.227707
$550$	−170.412	−7.26640
$551$	6.87516	0.292892
$552$	11.9850	0.510117
$553$	23.5718	1.00238
$554$	−0.0227112	−0.000964907 0
$555$	−22.3618	−0.949204
$556$	55.7751	2.36539
$557$	30.5916	1.29621	0.648104	−	0.761552i	$-0.275562\pi$
$557$	30.5916	1.29621	0.648104	+	0.761552i	$0.275562\pi$
$558$	46.9067	1.98572
$559$	−50.6077	−2.14048
$560$	111.471	4.71050
$561$	1.42217	0.0600440
$562$	43.4377	1.83231
$563$	−43.8493	−1.84803	−0.924014	−	0.382359i	$-0.875112\pi$
$563$	−43.8493	−1.84803	−0.924014	+	0.382359i	$0.875112\pi$
$564$	34.5375	1.45429
$565$	−73.6033	−3.09652
$566$	−46.8449	−1.96904
$567$	6.42280	0.269732
$568$	−92.1363	−3.86595
$569$	−28.2582	−1.18465	−0.592323	−	0.805700i	$-0.701789\pi$
$569$	−28.2582	−1.18465	−0.592323	+	0.805700i	$0.701789\pi$
$570$	−21.0013	−0.879647
$571$	21.0355	0.880309	0.440155	−	0.897922i	$-0.354924\pi$
$571$	21.0355	0.880309	0.440155	+	0.897922i	$0.354924\pi$
$572$	142.858	5.97320
$573$	−1.67368	−0.0699191
$574$	32.4693	1.35524
$575$	17.5128	0.730335
$576$	−89.4488	−3.72703
$577$	−12.0054	−0.499793	−0.249896	−	0.968273i	$-0.580397\pi$
$577$	−12.0054	−0.499793	−0.249896	+	0.968273i	$0.580397\pi$
$578$	46.6626	1.94091
$579$	−3.86811	−0.160753
$580$	−65.8422	−2.73395
$581$	−4.28586	−0.177807
$582$	6.05209	0.250867
$583$	70.0435	2.90090
$584$	100.054	4.14026
$585$	−45.8075	−1.89391
$586$	−71.6842	−2.96125
$587$	3.53289	0.145818	0.0729091	−	0.997339i	$-0.476772\pi$
$587$	3.53289	0.145818	0.0729091	+	0.997339i	$0.476772\pi$
$588$	18.6791	0.770314
$589$	−16.9965	−0.700330
$590$	−3.95527	−0.162836
$591$	12.2548	0.504094
$592$	116.078	4.77076
$593$	−28.6561	−1.17677	−0.588383	−	0.808582i	$-0.700235\pi$
$593$	−28.6561	−1.17677	−0.588383	+	0.808582i	$0.700235\pi$
$594$	−62.5115	−2.56488
$595$	−2.28805	−0.0938010
$596$	−39.9150	−1.63498
$597$	4.40212	0.180167
$598$	−19.8901	−0.813365
$599$	−26.4908	−1.08238	−0.541191	−	0.840899i	$-0.682027\pi$
$599$	−26.4908	−1.08238	−0.541191	+	0.840899i	$0.682027\pi$
$600$	90.4317	3.69186
$601$	3.91365	0.159641	0.0798206	−	0.996809i	$-0.474565\pi$
$601$	3.91365	0.159641	0.0798206	+	0.996809i	$0.474565\pi$
$602$	49.2377	2.00678
$603$	−19.5433	−0.795866
$604$	58.9219	2.39750
$605$	72.1993	2.93532
$606$	−8.95522	−0.363781
$607$	23.1746	0.940627	0.470314	−	0.882499i	$-0.344141\pi$
$607$	23.1746	0.940627	0.470314	+	0.882499i	$0.344141\pi$
$608$	60.9609	2.47229
$609$	3.74403	0.151716
$610$	25.0833	1.01559
$611$	−36.9812	−1.49610
$612$	4.55819	0.184254
$613$	32.8080	1.32510	0.662552	−	0.749016i	$-0.269473\pi$
$613$	32.8080	1.32510	0.662552	+	0.749016i	$0.269473\pi$
$614$	−24.9542	−1.00707
$615$	22.4561	0.905519
$616$	−89.6768	−3.61318
$617$	32.1439	1.29406	0.647032	−	0.762463i	$-0.276010\pi$
$617$	32.1439	1.29406	0.647032	+	0.762463i	$0.276010\pi$
$618$	−4.01125	−0.161356
$619$	48.0341	1.93065	0.965327	−	0.261042i	$-0.0840662\pi$
$619$	48.0341	1.93065	0.965327	+	0.261042i	$0.0840662\pi$
$620$	162.773	6.53711
$621$	6.42414	0.257792
$622$	−66.2439	−2.65614
$623$	25.6698	1.02844
$624$	−61.0188	−2.44271
$625$	49.6646	1.98659
$626$	−75.0280	−2.99872
$627$	10.0375	0.400860
$628$	−99.6681	−3.97719
$629$	−2.38261	−0.0950009
$630$	44.5674	1.77561
$631$	−10.2415	−0.407708	−0.203854	−	0.979001i	$-0.565347\pi$
$631$	−10.2415	−0.407708	−0.203854	+	0.979001i	$0.565347\pi$
$632$	−142.441	−5.66601
$633$	−2.52603	−0.100401
$634$	81.8610	3.25111
$635$	−41.9471	−1.66462
$636$	−57.6095	−2.28436
$637$	−20.0008	−0.792460
$638$	42.6345	1.68791
$639$	−21.8851	−0.865762
$640$	−213.393	−8.43508
$641$	28.3695	1.12053	0.560263	−	0.828315i	$-0.310700\pi$
$641$	28.3695	1.12053	0.560263	+	0.828315i	$0.310700\pi$
$642$	3.72407	0.146977
$643$	0.811429	0.0319996	0.0159998	−	0.999872i	$-0.494907\pi$
$643$	0.811429	0.0319996	0.0159998	+	0.999872i	$0.494907\pi$
$644$	14.2837	0.562858
$645$	34.0533	1.34085
$646$	−2.23765	−0.0880393
$647$	15.3549	0.603664	0.301832	−	0.953361i	$-0.402402\pi$
$647$	15.3549	0.603664	0.301832	+	0.953361i	$0.402402\pi$
$648$	−38.8121	−1.52468
$649$	1.89042	0.0742054
$650$	−150.078	−5.88655
$651$	−9.25585	−0.362765
$652$	−58.4152	−2.28771
$653$	43.7304	1.71130	0.855651	−	0.517553i	$-0.173157\pi$
$653$	43.7304	1.71130	0.855651	+	0.517553i	$0.173157\pi$
$654$	20.9956	0.820992
$655$	22.2495	0.869360
$656$	−116.568	−4.55120
$657$	23.7658	0.927192
$658$	35.9801	1.40265
$659$	−41.5489	−1.61852	−0.809258	−	0.587454i	$-0.800130\pi$
$659$	−41.5489	−1.61852	−0.809258	+	0.587454i	$0.800130\pi$
$660$	−96.1277	−3.74176
$661$	−9.19150	−0.357508	−0.178754	−	0.983894i	$-0.557207\pi$
$661$	−9.19150	−0.357508	−0.178754	+	0.983894i	$0.557207\pi$
$662$	−4.23109	−0.164446
$663$	1.25247	0.0486420
$664$	25.8988	1.00507
$665$	−16.1489	−0.626226
$666$	46.4092	1.79832
$667$	−4.38143	−0.169650
$668$	−69.1832	−2.67678
$669$	−5.65449	−0.218615
$670$	−91.8799	−3.54963
$671$	−11.9885	−0.462811
$672$	33.1977	1.28063
$673$	39.2929	1.51463	0.757316	−	0.653049i	$-0.226510\pi$
$673$	39.2929	1.51463	0.757316	+	0.653049i	$0.226510\pi$
$674$	77.7811	2.99602
$675$	48.4726	1.86571
$676$	52.5314	2.02044
$677$	20.8353	0.800766	0.400383	−	0.916348i	$-0.368877\pi$
$677$	20.8353	0.800766	0.400383	+	0.916348i	$0.368877\pi$
$678$	−39.1995	−1.50545
$679$	4.65373	0.178594
$680$	13.8264	0.530217
$681$	16.0220	0.613965
$682$	−105.399	−4.03595
$683$	42.9185	1.64223	0.821116	−	0.570762i	$-0.193352\pi$
$683$	42.9185	1.64223	0.821116	+	0.570762i	$0.193352\pi$
$684$	32.1713	1.23010
$685$	−36.7662	−1.40477
$686$	51.6342	1.97140
$687$	−11.4219	−0.435774
$688$	−176.767	−6.73919
$689$	61.6857	2.35004
$690$	13.3838	0.509512
$691$	15.6720	0.596190	0.298095	−	0.954536i	$-0.403649\pi$
$691$	15.6720	0.596190	0.298095	+	0.954536i	$0.403649\pi$
$692$	15.0989	0.573974
$693$	−21.3009	−0.809154
$694$	−66.1451	−2.51083
$695$	40.1860	1.52434
$696$	−22.6246	−0.857583
$697$	2.39267	0.0906287
$698$	59.0202	2.23395
$699$	−5.28511	−0.199901
$700$	107.776	4.07356
$701$	−32.7422	−1.23666	−0.618329	−	0.785920i	$-0.712190\pi$
$701$	−32.7422	−1.23666	−0.618329	+	0.785920i	$0.712190\pi$
$702$	−55.0525	−2.07782
$703$	−16.8162	−0.634236
$704$	200.991	7.57515
$705$	24.8842	0.937194
$706$	13.8540	0.521403
$707$	−6.88609	−0.258978
$708$	−1.55483	−0.0584342
$709$	−39.5594	−1.48568	−0.742842	−	0.669467i	$-0.766523\pi$
$709$	−39.5594	−1.48568	−0.742842	+	0.669467i	$0.766523\pi$
$710$	−102.889	−3.86137
$711$	−33.8340	−1.26888
$712$	−155.119	−5.81332
$713$	10.8316	0.405648
$714$	−1.21856	−0.0456036
$715$	102.929	3.84934
$716$	−19.1547	−0.715846
$717$	16.2592	0.607209
$718$	−30.8265	−1.15043
$719$	−31.1541	−1.16185	−0.580926	−	0.813956i	$-0.697310\pi$
$719$	−31.1541	−1.16185	−0.580926	+	0.813956i	$0.697310\pi$
$720$	−160.001	−5.96287
$721$	−3.08444	−0.114870
$722$	36.7135	1.36633
$723$	−6.06164	−0.225435
$724$	37.4007	1.38999
$725$	−33.0596	−1.22780
$726$	38.4517	1.42708
$727$	11.0199	0.408705	0.204352	−	0.978897i	$-0.434491\pi$
$727$	11.0199	0.408705	0.204352	+	0.978897i	$0.434491\pi$
$728$	−78.9763	−2.92706
$729$	0.682478	0.0252770
$730$	111.731	4.13535
$731$	3.62833	0.134199
$732$	9.86033	0.364448
$733$	−6.99113	−0.258223	−0.129112	−	0.991630i	$-0.541213\pi$
$733$	−6.99113	−0.258223	−0.129112	+	0.991630i	$0.541213\pi$
$734$	57.2291	2.11237
$735$	13.4583	0.496417
$736$	−38.8495	−1.43201
$737$	43.9139	1.61759
$738$	−46.6051	−1.71556
$739$	14.2422	0.523906	0.261953	−	0.965081i	$-0.415633\pi$
$739$	14.2422	0.523906	0.261953	+	0.965081i	$0.415633\pi$
$740$	161.046	5.92017
$741$	8.83983	0.324739
$742$	−60.0158	−2.20325
$743$	−13.4898	−0.494891	−0.247446	−	0.968902i	$-0.579591\pi$
$743$	−13.4898	−0.494891	−0.247446	+	0.968902i	$0.579591\pi$
$744$	55.9317	2.05056
$745$	−28.7587	−1.05364
$746$	−13.7194	−0.502302
$747$	6.15174	0.225080
$748$	−10.2422	−0.374494
$749$	2.86361	0.104634
$750$	57.0608	2.08357
$751$	−27.4570	−1.00192	−0.500959	−	0.865471i	$-0.667019\pi$
$751$	−27.4570	−1.00192	−0.500959	+	0.865471i	$0.667019\pi$
$752$	−129.171	−4.71040
$753$	0.844714	0.0307831
$754$	37.5472	1.36739
$755$	42.4532	1.54503
$756$	39.5350	1.43788
$757$	−44.9270	−1.63290	−0.816449	−	0.577417i	$-0.804061\pi$
$757$	−44.9270	−1.63290	−0.816449	+	0.577417i	$0.804061\pi$
$758$	−46.5705	−1.69152
$759$	−6.39676	−0.232188
$760$	97.5852	3.53979
$761$	0.783707	0.0284094	0.0142047	−	0.999899i	$-0.495478\pi$
$761$	0.783707	0.0284094	0.0142047	+	0.999899i	$0.495478\pi$
$762$	−22.3401	−0.809296
$763$	16.1445	0.584469
$764$	12.0536	0.436084
$765$	3.28417	0.118740
$766$	73.7827	2.66588
$767$	1.66485	0.0601142
$768$	−54.9954	−1.98448
$769$	42.6574	1.53827	0.769133	−	0.639089i	$-0.220689\pi$
$769$	42.6574	1.53827	0.769133	+	0.639089i	$0.220689\pi$
$770$	−100.143	−3.60890
$771$	16.5002	0.594239
$772$	27.8575	1.00261
$773$	30.8780	1.11061	0.555303	−	0.831648i	$-0.312602\pi$
$773$	30.8780	1.11061	0.555303	+	0.831648i	$0.312602\pi$
$774$	−70.6737	−2.54031
$775$	81.7287	2.93578
$776$	−28.1218	−1.00951
$777$	−9.15767	−0.328529
$778$	69.6891	2.49848
$779$	16.8872	0.605047
$780$	−84.6575	−3.03122
$781$	49.1758	1.75965
$782$	1.42602	0.0509944
$783$	−12.1271	−0.433387
$784$	−69.8606	−2.49502
$785$	−71.8108	−2.56304
$786$	11.8496	0.422661
$787$	49.2454	1.75541	0.877704	−	0.479204i	$-0.159074\pi$
$787$	49.2454	1.75541	0.877704	+	0.479204i	$0.159074\pi$
$788$	−88.2571	−3.14403
$789$	4.75482	0.169276
$790$	−159.065	−5.65929
$791$	−30.1423	−1.07174
$792$	128.718	4.57381
$793$	−10.5580	−0.374926
$794$	−83.6439	−2.96841
$795$	−41.5076	−1.47212
$796$	−31.7034	−1.12370
$797$	33.1919	1.17572	0.587858	−	0.808964i	$-0.299971\pi$
$797$	33.1919	1.17572	0.587858	+	0.808964i	$0.299971\pi$
$798$	−8.60052	−0.304455
$799$	2.65137	0.0937989
$800$	−293.134	−10.3639
$801$	−36.8453	−1.30186
$802$	59.2019	2.09049
$803$	−53.4017	−1.88450
$804$	−36.1183	−1.27380
$805$	10.2914	0.362725
$806$	−92.8229	−3.26955
$807$	23.2512	0.818481
$808$	41.6116	1.46389
$809$	31.3586	1.10251	0.551256	−	0.834336i	$-0.314149\pi$
$809$	31.3586	1.10251	0.551256	+	0.834336i	$0.314149\pi$
$810$	−43.3417	−1.52287
$811$	30.4805	1.07032	0.535158	−	0.844752i	$-0.320252\pi$
$811$	30.4805	1.07032	0.535158	+	0.844752i	$0.320252\pi$
$812$	−26.9639	−0.946248
$813$	−16.4850	−0.578155
$814$	−104.281	−3.65506
$815$	−42.0881	−1.47428
$816$	4.37475	0.153147
$817$	25.6084	0.895925
$818$	−52.9564	−1.85158
$819$	−18.7592	−0.655500
$820$	−161.726	−5.64771
$821$	16.8756	0.588964	0.294482	−	0.955657i	$-0.404853\pi$
$821$	16.8756	0.588964	0.294482	+	0.955657i	$0.404853\pi$
$822$	−19.5809	−0.682961
$823$	−20.4063	−0.711318	−0.355659	−	0.934616i	$-0.615743\pi$
$823$	−20.4063	−0.711318	−0.355659	+	0.934616i	$0.615743\pi$
$824$	18.6388	0.649313
$825$	−48.2660	−1.68041
$826$	−1.61978	−0.0563593
$827$	44.6763	1.55355	0.776774	−	0.629779i	$-0.216855\pi$
$827$	44.6763	1.55355	0.776774	+	0.629779i	$0.216855\pi$
$828$	−20.5023	−0.712503
$829$	−16.3367	−0.567399	−0.283699	−	0.958913i	$-0.591562\pi$
$829$	−16.3367	−0.567399	−0.283699	+	0.958913i	$0.591562\pi$
$830$	28.9214	1.00388
$831$	−0.00643252	−0.000223142 0
$832$	177.009	6.13667
$833$	1.43396	0.0496838
$834$	21.4021	0.741095
$835$	−49.8465	−1.72501
$836$	−72.2888	−2.50016
$837$	29.9802	1.03627
$838$	5.52912	0.191000
$839$	−7.37673	−0.254673	−0.127337	−	0.991860i	$-0.540643\pi$
$839$	−7.37673	−0.254673	−0.127337	+	0.991860i	$0.540643\pi$
$840$	53.1423	1.83358
$841$	−20.7290	−0.714793
$842$	−90.1089	−3.10536
$843$	12.3029	0.423735
$844$	18.1921	0.626199
$845$	37.8489	1.30204
$846$	−51.6442	−1.77557
$847$	29.5673	1.01595
$848$	215.462	7.39898
$849$	−13.2679	−0.455354
$850$	10.7599	0.369061
$851$	10.7167	0.367365
$852$	−40.4462	−1.38566
$853$	−7.83121	−0.268136	−0.134068	−	0.990972i	$-0.542804\pi$
$853$	−7.83121	−0.268136	−0.134068	+	0.990972i	$0.542804\pi$
$854$	10.2722	0.351507
$855$	23.1794	0.792718
$856$	−17.3044	−0.591451
$857$	−49.2792	−1.68335	−0.841674	−	0.539987i	$-0.818429\pi$
$857$	−49.2792	−1.68335	−0.841674	+	0.539987i	$0.818429\pi$
$858$	54.8178	1.87145
$859$	5.61259	0.191499	0.0957496	−	0.995405i	$-0.469475\pi$
$859$	5.61259	0.191499	0.0957496	+	0.995405i	$0.469475\pi$
$860$	−245.247	−8.36286
$861$	9.19632	0.313410
$862$	−49.2520	−1.67753
$863$	−9.18501	−0.312661	−0.156331	−	0.987705i	$-0.549967\pi$
$863$	−9.18501	−0.312661	−0.156331	+	0.987705i	$0.549967\pi$
$864$	−107.529	−3.65821
$865$	10.8788	0.369889
$866$	38.3837	1.30433
$867$	13.2163	0.448849
$868$	66.6592	2.26256
$869$	76.0250	2.57897
$870$	−25.2651	−0.856566
$871$	38.6739	1.31042
$872$	−97.5588	−3.30376
$873$	−6.67977	−0.226076
$874$	10.0647	0.340444
$875$	43.8767	1.48330
$876$	43.9219	1.48398
$877$	−43.8343	−1.48018	−0.740090	−	0.672508i	$-0.765217\pi$
$877$	−43.8343	−1.48018	−0.740090	+	0.672508i	$0.765217\pi$
$878$	−53.7990	−1.81563
$879$	−20.3032	−0.684810
$880$	359.521	12.1195
$881$	−15.3025	−0.515556	−0.257778	−	0.966204i	$-0.582990\pi$
$881$	−15.3025	−0.515556	−0.257778	+	0.966204i	$0.582990\pi$
$882$	−27.9311	−0.940489
$883$	−2.80979	−0.0945571	−0.0472786	−	0.998882i	$-0.515055\pi$
$883$	−2.80979	−0.0945571	−0.0472786	+	0.998882i	$0.515055\pi$
$884$	−9.02012	−0.303379
$885$	−1.12026	−0.0376570
$886$	−46.6554	−1.56742
$887$	32.5514	1.09297	0.546485	−	0.837469i	$-0.315965\pi$
$887$	32.5514	1.09297	0.546485	+	0.837469i	$0.315965\pi$
$888$	55.3385	1.85704
$889$	−17.1783	−0.576143
$890$	−173.222	−5.80642
$891$	20.7151	0.693983
$892$	40.7228	1.36350
$893$	18.7131	0.626212
$894$	−15.3162	−0.512252
$895$	−13.8010	−0.461316
$896$	−87.3893	−2.91947
$897$	−5.63349	−0.188097
$898$	84.0943	2.80626
$899$	−20.4473	−0.681954
$900$	−154.697	−5.15658
$901$	−4.42257	−0.147337
$902$	104.722	3.48685
$903$	13.9456	0.464082
$904$	182.146	6.05807
$905$	26.9472	0.895755
$906$	22.6096	0.751155
$907$	30.5867	1.01561	0.507807	−	0.861471i	$-0.330456\pi$
$907$	30.5867	1.01561	0.507807	+	0.861471i	$0.330456\pi$
$908$	−115.388	−3.82929
$909$	9.88400	0.327832
$910$	−88.1935	−2.92359
$911$	35.5124	1.17658	0.588289	−	0.808651i	$-0.299802\pi$
$911$	35.5124	1.17658	0.588289	+	0.808651i	$0.299802\pi$
$912$	30.8766	1.02243
$913$	−13.8229	−0.457473
$914$	82.1398	2.71694
$915$	7.10436	0.234863
$916$	82.2592	2.71792
$917$	9.11169	0.300895
$918$	3.94700	0.130270
$919$	4.70643	0.155251	0.0776254	−	0.996983i	$-0.475266\pi$
$919$	4.70643	0.155251	0.0776254	+	0.996983i	$0.475266\pi$
$920$	−62.1896	−2.05033
$921$	−7.06781	−0.232892
$922$	−95.4895	−3.14478
$923$	43.3080	1.42550
$924$	−39.3665	−1.29506
$925$	80.8618	2.65872
$926$	−21.9664	−0.721860
$927$	4.42727	0.145411
$928$	73.3376	2.40742
$929$	−15.1605	−0.497401	−0.248700	−	0.968580i	$-0.580003\pi$
$929$	−15.1605	−0.497401	−0.248700	+	0.968580i	$0.580003\pi$
$930$	62.4594	2.04812
$931$	10.1208	0.331694
$932$	38.0626	1.24678
$933$	−18.7624	−0.614252
$934$	−12.6874	−0.415145
$935$	−7.37953	−0.241337
$936$	113.359	3.70526
$937$	−31.3094	−1.02283	−0.511417	−	0.859333i	$-0.670879\pi$
$937$	−31.3094	−1.02283	−0.511417	+	0.859333i	$0.670879\pi$
$938$	−37.6270	−1.22856
$939$	−21.2503	−0.693476
$940$	−179.213	−5.84527
$941$	−57.5159	−1.87497	−0.937483	−	0.348032i	$-0.886850\pi$
$941$	−57.5159	−1.87497	−0.937483	+	0.348032i	$0.886850\pi$
$942$	−38.2448	−1.24608
$943$	−10.7620	−0.350458
$944$	5.81514	0.189267
$945$	28.4850	0.926616
$946$	158.804	5.16315
$947$	38.3279	1.24549	0.622745	−	0.782425i	$-0.286017\pi$
$947$	38.3279	1.24549	0.622745	+	0.782425i	$0.286017\pi$
$948$	−62.5292	−2.03085
$949$	−47.0297	−1.52665
$950$	75.9422	2.46389
$951$	23.1856	0.751844
$952$	5.66222	0.183514
$953$	22.3289	0.723304	0.361652	−	0.932313i	$-0.382213\pi$
$953$	22.3289	0.723304	0.361652	+	0.932313i	$0.382213\pi$
$954$	86.1441	2.78902
$955$	8.68462	0.281028
$956$	−117.096	−3.78716
$957$	12.0754	0.390342
$958$	−41.9880	−1.35657
$959$	−15.0566	−0.486204
$960$	−119.107	−3.84416
$961$	19.5490	0.630612
$962$	−91.8383	−2.96098
$963$	−4.11030	−0.132453
$964$	43.6551	1.40604
$965$	20.0713	0.646119
$966$	5.48098	0.176348
$967$	−34.2936	−1.10281	−0.551404	−	0.834239i	$-0.685908\pi$
$967$	−34.2936	−1.10281	−0.551404	+	0.834239i	$0.685908\pi$
$968$	−178.671	−5.74271
$969$	−0.633773	−0.0203597
$970$	−31.4039	−1.00832
$971$	30.9617	0.993608	0.496804	−	0.867863i	$-0.334507\pi$
$971$	30.9617	0.993608	0.496804	+	0.867863i	$0.334507\pi$
$972$	−88.3469	−2.83373
$973$	16.4571	0.527590
$974$	−38.6857	−1.23957
$975$	−42.5068	−1.36131
$976$	−36.8780	−1.18044
$977$	53.6337	1.71589	0.857947	−	0.513738i	$-0.171740\pi$
$977$	53.6337	1.71589	0.857947	+	0.513738i	$0.171740\pi$
$978$	−22.4152	−0.716758
$979$	82.7913	2.64602
$980$	−96.9246	−3.09614
$981$	−23.1731	−0.739860
$982$	−2.08104	−0.0664087
$983$	−9.78945	−0.312235	−0.156117	−	0.987738i	$-0.549898\pi$
$983$	−9.78945	−0.312235	−0.156117	+	0.987738i	$0.549898\pi$
$984$	−55.5720	−1.77157
$985$	−63.5892	−2.02612
$986$	−2.69195	−0.0857293
$987$	10.1907	0.324373
$988$	−63.6631	−2.02539
$989$	−16.3198	−0.518941
$990$	143.741	4.56838
$991$	8.69726	0.276278	0.138139	−	0.990413i	$-0.455888\pi$
$991$	8.69726	0.276278	0.138139	+	0.990413i	$0.455888\pi$
$992$	−181.302	−5.75636
$993$	−1.19838	−0.0380294
$994$	−42.1356	−1.33646
$995$	−22.8423	−0.724150
$996$	11.3691	0.360244
$997$	−57.7051	−1.82754	−0.913770	−	0.406232i	$-0.866842\pi$
$997$	−57.7051	−1.82754	−0.913770	+	0.406232i	$0.866842\pi$
$998$	67.7047	2.14315
$999$	29.6622	0.938469

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4001.2.a.b.1.4	✓	184

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4001.2.a.b.1.4	✓	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)

\(f(q)\)	\(=\)	\(q-2.76351 q^{2} -0.782711 q^{3} +5.63697 q^{4} +4.06144 q^{5} +2.16303 q^{6} +1.66325 q^{7} -10.0508 q^{8} -2.38736 q^{9} +O(q^{10})\)	\(q-2.76351 q^{2} -0.782711 q^{3} +5.63697 q^{4} +4.06144 q^{5} +2.16303 q^{6} +1.66325 q^{7} -10.0508 q^{8} -2.38736 q^{9} -11.2238 q^{10} +5.36440 q^{11} -4.41212 q^{12} +4.72431 q^{13} -4.59641 q^{14} -3.17893 q^{15} +16.5015 q^{16} -0.338710 q^{17} +6.59749 q^{18} -2.39058 q^{19} +22.8942 q^{20} -1.30185 q^{21} -14.8246 q^{22} +1.52348 q^{23} +7.86687 q^{24} +11.4953 q^{25} -13.0557 q^{26} +4.21675 q^{27} +9.37571 q^{28} -2.87593 q^{29} +8.78500 q^{30} +7.10978 q^{31} -25.5004 q^{32} -4.19878 q^{33} +0.936028 q^{34} +6.75519 q^{35} -13.4575 q^{36} +7.03437 q^{37} +6.60640 q^{38} -3.69777 q^{39} -40.8207 q^{40} -7.06405 q^{41} +3.59766 q^{42} -10.7122 q^{43} +30.2390 q^{44} -9.69612 q^{45} -4.21015 q^{46} -7.82786 q^{47} -12.9159 q^{48} -4.23359 q^{49} -31.7672 q^{50} +0.265112 q^{51} +26.6308 q^{52} +13.0571 q^{53} -11.6530 q^{54} +21.7872 q^{55} -16.7170 q^{56} +1.87114 q^{57} +7.94766 q^{58} +0.352401 q^{59} -17.9195 q^{60} -2.23483 q^{61} -19.6479 q^{62} -3.97079 q^{63} +37.4676 q^{64} +19.1875 q^{65} +11.6034 q^{66} +8.18616 q^{67} -1.90930 q^{68} -1.19245 q^{69} -18.6680 q^{70} +9.16707 q^{71} +23.9949 q^{72} -9.95483 q^{73} -19.4395 q^{74} -8.99747 q^{75} -13.4757 q^{76} +8.92236 q^{77} +10.2188 q^{78} +14.1721 q^{79} +67.0198 q^{80} +3.86159 q^{81} +19.5216 q^{82} -2.57679 q^{83} -7.33847 q^{84} -1.37565 q^{85} +29.6032 q^{86} +2.25103 q^{87} -53.9165 q^{88} +15.4335 q^{89} +26.7953 q^{90} +7.85772 q^{91} +8.58783 q^{92} -5.56491 q^{93} +21.6323 q^{94} -9.70920 q^{95} +19.9595 q^{96} +2.79797 q^{97} +11.6996 q^{98} -12.8068 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 184 q + 3 q^{2} + 28 q^{3} + 217 q^{4} + 15 q^{5} + 31 q^{6} + 49 q^{7} + 6 q^{8} + 210 q^{9}+O(q^{10}) \) 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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