LMFDB - Embedded newform 4001.2.a.a.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:	$1$
Dimension:	$149$
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)

$f(q)$	$=$	$q-2.66308 q^{2} -1.99633 q^{3} +5.09200 q^{4} +2.13614 q^{5} +5.31640 q^{6} +2.50209 q^{7} -8.23426 q^{8} +0.985342 q^{9} +O(q^{10})$	\(q-2.66308 q^{2} -1.99633 q^{3} +5.09200 q^{4} +2.13614 q^{5} +5.31640 q^{6} +2.50209 q^{7} -8.23426 q^{8} +0.985342 q^{9} -5.68872 q^{10} -1.13086 q^{11} -10.1653 q^{12} -5.72273 q^{13} -6.66326 q^{14} -4.26444 q^{15} +11.7445 q^{16} -2.06977 q^{17} -2.62405 q^{18} -4.11827 q^{19} +10.8772 q^{20} -4.99500 q^{21} +3.01157 q^{22} +8.81523 q^{23} +16.4383 q^{24} -0.436906 q^{25} +15.2401 q^{26} +4.02193 q^{27} +12.7406 q^{28} +1.81282 q^{29} +11.3566 q^{30} -3.18227 q^{31} -14.8081 q^{32} +2.25757 q^{33} +5.51196 q^{34} +5.34481 q^{35} +5.01736 q^{36} +3.59551 q^{37} +10.9673 q^{38} +11.4245 q^{39} -17.5895 q^{40} -1.81015 q^{41} +13.3021 q^{42} +9.62461 q^{43} -5.75833 q^{44} +2.10483 q^{45} -23.4757 q^{46} +0.575319 q^{47} -23.4459 q^{48} -0.739563 q^{49} +1.16352 q^{50} +4.13194 q^{51} -29.1402 q^{52} -1.38701 q^{53} -10.7107 q^{54} -2.41567 q^{55} -20.6028 q^{56} +8.22143 q^{57} -4.82769 q^{58} -6.17050 q^{59} -21.7146 q^{60} +14.1039 q^{61} +8.47465 q^{62} +2.46541 q^{63} +15.9460 q^{64} -12.2246 q^{65} -6.01209 q^{66} -0.154659 q^{67} -10.5393 q^{68} -17.5981 q^{69} -14.2337 q^{70} -16.0527 q^{71} -8.11356 q^{72} -2.19401 q^{73} -9.57513 q^{74} +0.872210 q^{75} -20.9702 q^{76} -2.82950 q^{77} -30.4243 q^{78} +2.81036 q^{79} +25.0879 q^{80} -10.9851 q^{81} +4.82059 q^{82} +11.8144 q^{83} -25.4345 q^{84} -4.42131 q^{85} -25.6311 q^{86} -3.61899 q^{87} +9.31178 q^{88} +16.1642 q^{89} -5.60533 q^{90} -14.3188 q^{91} +44.8872 q^{92} +6.35287 q^{93} -1.53212 q^{94} -8.79719 q^{95} +29.5618 q^{96} -11.4660 q^{97} +1.96952 q^{98} -1.11428 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 149 q - 6 q^{2} - 28 q^{3} + 116 q^{4} - 19 q^{5} - 31 q^{6} - 47 q^{7} - 15 q^{8} + 115 q^{9}+O(q^{10}) $ 149 * q - 6 * q^2 - 28 * q^3 + 116 * q^4 - 19 * q^5 - 31 * q^6 - 47 * q^7 - 15 * q^8 + 115 * q^9	\( 149 q - 6 q^{2} - 28 q^{3} + 116 q^{4} - 19 q^{5} - 31 q^{6} - 47 q^{7} - 15 q^{8} + 115 q^{9} - 48 q^{10} - 31 q^{11} - 61 q^{12} - 54 q^{13} - 44 q^{14} - 65 q^{15} + 58 q^{16} - 26 q^{17} - 23 q^{18} - 86 q^{19} - 52 q^{20} - 30 q^{21} - 56 q^{22} - 63 q^{23} - 90 q^{24} + 92 q^{25} - 38 q^{26} - 103 q^{27} - 77 q^{28} - 51 q^{29} - 22 q^{30} - 256 q^{31} - 21 q^{32} - 36 q^{33} - 124 q^{34} - 50 q^{35} + 45 q^{36} - 42 q^{37} - 14 q^{38} - 119 q^{39} - 131 q^{40} - 55 q^{41} - 5 q^{42} - 55 q^{43} - 54 q^{44} - 68 q^{45} - 59 q^{46} - 82 q^{47} - 89 q^{48} + 30 q^{49} + 13 q^{50} - 83 q^{51} - 126 q^{52} - 23 q^{53} - 83 q^{54} - 244 q^{55} - 94 q^{56} - 14 q^{57} - 60 q^{58} - 93 q^{59} - 70 q^{60} - 139 q^{61} - 10 q^{62} - 120 q^{63} - 45 q^{64} - 37 q^{65} - 28 q^{66} - 110 q^{67} - 27 q^{68} - 79 q^{69} - 78 q^{70} - 123 q^{71} - 74 q^{73} - 25 q^{74} - 146 q^{75} - 192 q^{76} - q^{77} + 26 q^{78} - 273 q^{79} - 51 q^{80} + 41 q^{81} - 120 q^{82} - 27 q^{83} - 14 q^{84} - 71 q^{85} + 3 q^{86} - 98 q^{87} - 143 q^{88} - 70 q^{89} - 24 q^{90} - 256 q^{91} - 47 q^{92} + 16 q^{93} - 151 q^{94} - 83 q^{95} - 137 q^{96} - 108 q^{97} + 17 q^{98} - 131 q^{99}+O(q^{100}) \) 149 * q - 6 * q^2 - 28 * q^3 + 116 * q^4 - 19 * q^5 - 31 * q^6 - 47 * q^7 - 15 * q^8 + 115 * q^9 - 48 * q^10 - 31 * q^11 - 61 * q^12 - 54 * q^13 - 44 * q^14 - 65 * q^15 + 58 * q^16 - 26 * q^17 - 23 * q^18 - 86 * q^19 - 52 * q^20 - 30 * q^21 - 56 * q^22 - 63 * q^23 - 90 * q^24 + 92 * q^25 - 38 * q^26 - 103 * q^27 - 77 * q^28 - 51 * q^29 - 22 * q^30 - 256 * q^31 - 21 * q^32 - 36 * q^33 - 124 * q^34 - 50 * q^35 + 45 * q^36 - 42 * q^37 - 14 * q^38 - 119 * q^39 - 131 * q^40 - 55 * q^41 - 5 * q^42 - 55 * q^43 - 54 * q^44 - 68 * q^45 - 59 * q^46 - 82 * q^47 - 89 * q^48 + 30 * q^49 + 13 * q^50 - 83 * q^51 - 126 * q^52 - 23 * q^53 - 83 * q^54 - 244 * q^55 - 94 * q^56 - 14 * q^57 - 60 * q^58 - 93 * q^59 - 70 * q^60 - 139 * q^61 - 10 * q^62 - 120 * q^63 - 45 * q^64 - 37 * q^65 - 28 * q^66 - 110 * q^67 - 27 * q^68 - 79 * q^69 - 78 * q^70 - 123 * q^71 - 74 * q^73 - 25 * q^74 - 146 * q^75 - 192 * q^76 - q^77 + 26 * q^78 - 273 * q^79 - 51 * q^80 + 41 * q^81 - 120 * q^82 - 27 * q^83 - 14 * q^84 - 71 * q^85 + 3 * q^86 - 98 * q^87 - 143 * q^88 - 70 * q^89 - 24 * q^90 - 256 * q^91 - 47 * q^92 + 16 * q^93 - 151 * q^94 - 83 * q^95 - 137 * q^96 - 108 * q^97 + 17 * q^98 - 131 * 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 $

$2$	−2.66308	−1.88308	−0.941542	−	0.336897i	$-0.890623\pi$
$2$	−2.66308	−1.88308	−0.941542	+	0.336897i	$0.890623\pi$
$3$	−1.99633	−1.15258	−0.576291	−	0.817244i	$-0.695501\pi$
$3$	−1.99633	−1.15258	−0.576291	+	0.817244i	$0.695501\pi$
$4$	5.09200	2.54600
$5$	2.13614	0.955311	0.477655	−	0.878547i	$-0.341487\pi$
$5$	2.13614	0.955311	0.477655	+	0.878547i	$0.341487\pi$
$6$	5.31640	2.17041
$7$	2.50209	0.945700	0.472850	−	0.881143i	$-0.343225\pi$
$7$	2.50209	0.945700	0.472850	+	0.881143i	$0.343225\pi$
$8$	−8.23426	−2.91125
$9$	0.985342	0.328447
$10$	−5.68872	−1.79893
$11$	−1.13086	−0.340966	−0.170483	−	0.985361i	$-0.554533\pi$
$11$	−1.13086	−0.340966	−0.170483	+	0.985361i	$0.554533\pi$
$12$	−10.1653	−2.93448
$13$	−5.72273	−1.58720	−0.793600	−	0.608440i	$-0.791796\pi$
$13$	−5.72273	−1.58720	−0.793600	+	0.608440i	$0.791796\pi$
$14$	−6.66326	−1.78083
$15$	−4.26444	−1.10107
$16$	11.7445	2.93613
$17$	−2.06977	−0.501992	−0.250996	−	0.967988i	$-0.580758\pi$
$17$	−2.06977	−0.501992	−0.250996	+	0.967988i	$0.580758\pi$
$18$	−2.62405	−0.618493
$19$	−4.11827	−0.944795	−0.472397	−	0.881386i	$-0.656611\pi$
$19$	−4.11827	−0.944795	−0.472397	+	0.881386i	$0.656611\pi$
$20$	10.8772	2.43222
$21$	−4.99500	−1.09000
$22$	3.01157	0.642068
$23$	8.81523	1.83810	0.919051	−	0.394138i	$-0.128957\pi$
$23$	8.81523	1.83810	0.919051	+	0.394138i	$0.128957\pi$
$24$	16.4383	3.35546
$25$	−0.436906	−0.0873812
$26$	15.2401	2.98883
$27$	4.02193	0.774020
$28$	12.7406	2.40775
$29$	1.81282	0.336633	0.168316	−	0.985733i	$-0.446167\pi$
$29$	1.81282	0.336633	0.168316	+	0.985733i	$0.446167\pi$
$30$	11.3566	2.07342
$31$	−3.18227	−0.571553	−0.285776	−	0.958296i	$-0.592251\pi$
$31$	−3.18227	−0.571553	−0.285776	+	0.958296i	$0.592251\pi$
$32$	−14.8081	−2.61772
$33$	2.25757	0.392992
$34$	5.51196	0.945293
$35$	5.34481	0.903437
$36$	5.01736	0.836227
$37$	3.59551	0.591098	0.295549	−	0.955328i	$-0.404497\pi$
$37$	3.59551	0.591098	0.295549	+	0.955328i	$0.404497\pi$
$38$	10.9673	1.77913
$39$	11.4245	1.82938
$40$	−17.5895	−2.78115
$41$	−1.81015	−0.282698	−0.141349	−	0.989960i	$-0.545144\pi$
$41$	−1.81015	−0.282698	−0.141349	+	0.989960i	$0.545144\pi$
$42$	13.3021	2.05256
$43$	9.62461	1.46774	0.733870	−	0.679290i	$-0.237712\pi$
$43$	9.62461	1.46774	0.733870	+	0.679290i	$0.237712\pi$
$44$	−5.75833	−0.868101
$45$	2.10483	0.313769
$46$	−23.4757	−3.46130
$47$	0.575319	0.0839189	0.0419595	−	0.999119i	$-0.486640\pi$
$47$	0.575319	0.0839189	0.0419595	+	0.999119i	$0.486640\pi$
$48$	−23.4459	−3.38413
$49$	−0.739563	−0.105652
$50$	1.16352	0.164546
$51$	4.13194	0.578588
$52$	−29.1402	−4.04101
$53$	−1.38701	−0.190520	−0.0952601	−	0.995452i	$-0.530368\pi$
$53$	−1.38701	−0.190520	−0.0952601	+	0.995452i	$0.530368\pi$
$54$	−10.7107	−1.45754
$55$	−2.41567	−0.325729
$56$	−20.6028	−2.75317
$57$	8.22143	1.08895
$58$	−4.82769	−0.633907
$59$	−6.17050	−0.803330	−0.401665	−	0.915787i	$-0.631568\pi$
$59$	−6.17050	−0.803330	−0.401665	+	0.915787i	$0.631568\pi$
$60$	−21.7146	−2.80334
$61$	14.1039	1.80583	0.902913	−	0.429824i	$-0.141424\pi$
$61$	14.1039	1.80583	0.902913	+	0.429824i	$0.141424\pi$
$62$	8.47465	1.07628
$63$	2.46541	0.310612
$64$	15.9460	1.99326
$65$	−12.2246	−1.51627
$66$	−6.01209	−0.740037
$67$	−0.154659	−0.0188947	−0.00944733	−	0.999955i	$-0.503007\pi$
$67$	−0.154659	−0.0188947	−0.00944733	+	0.999955i	$0.503007\pi$
$68$	−10.5393	−1.27807
$69$	−17.5981	−2.11857
$70$	−14.2337	−1.70125
$71$	−16.0527	−1.90510	−0.952550	−	0.304382i	$-0.901550\pi$
$71$	−16.0527	−1.90510	−0.952550	+	0.304382i	$0.901550\pi$
$72$	−8.11356	−0.956192
$73$	−2.19401	−0.256790	−0.128395	−	0.991723i	$-0.540983\pi$
$73$	−2.19401	−0.256790	−0.128395	+	0.991723i	$0.540983\pi$
$74$	−9.57513	−1.11309
$75$	0.872210	0.100714
$76$	−20.9702	−2.40545
$77$	−2.82950	−0.322452
$78$	−30.4243	−3.44487
$79$	2.81036	0.316190	0.158095	−	0.987424i	$-0.449465\pi$
$79$	2.81036	0.316190	0.158095	+	0.987424i	$0.449465\pi$
$80$	25.0879	2.80491
$81$	−10.9851	−1.22057
$82$	4.82059	0.532345
$83$	11.8144	1.29679	0.648397	−	0.761302i	$-0.275440\pi$
$83$	11.8144	1.29679	0.648397	+	0.761302i	$0.275440\pi$
$84$	−25.4345	−2.77514
$85$	−4.42131	−0.479559
$86$	−25.6311	−2.76388
$87$	−3.61899	−0.387997
$88$	9.31178	0.992639
$89$	16.1642	1.71340	0.856698	−	0.515818i	$-0.172512\pi$
$89$	16.1642	1.71340	0.856698	+	0.515818i	$0.172512\pi$
$90$	−5.60533	−0.590853
$91$	−14.3188	−1.50101
$92$	44.8872	4.67981
$93$	6.35287	0.658762
$94$	−1.53212	−0.158026
$95$	−8.79719	−0.902573
$96$	29.5618	3.01714
$97$	−11.4660	−1.16419	−0.582096	−	0.813120i	$-0.697767\pi$
$97$	−11.4660	−1.16419	−0.582096	+	0.813120i	$0.697767\pi$
$98$	1.96952	0.198951
$99$	−1.11428	−0.111989
$100$	−2.22473	−0.222473
$101$	14.6256	1.45531	0.727653	−	0.685946i	$-0.240611\pi$
$101$	14.6256	1.45531	0.727653	+	0.685946i	$0.240611\pi$
$102$	−11.0037	−1.08953
$103$	3.05932	0.301444	0.150722	−	0.988576i	$-0.451840\pi$
$103$	3.05932	0.301444	0.150722	+	0.988576i	$0.451840\pi$
$104$	47.1225	4.62074
$105$	−10.6700	−1.04129
$106$	3.69372	0.358765
$107$	−11.8177	−1.14246	−0.571230	−	0.820790i	$-0.693533\pi$
$107$	−11.8177	−1.14246	−0.571230	+	0.820790i	$0.693533\pi$
$108$	20.4797	1.97066
$109$	−19.5586	−1.87337	−0.936685	−	0.350172i	$-0.886123\pi$
$109$	−19.5586	−1.87337	−0.936685	+	0.350172i	$0.886123\pi$
$110$	6.43313	0.613375
$111$	−7.17783	−0.681289
$112$	29.3858	2.77669
$113$	10.2950	0.968469	0.484235	−	0.874938i	$-0.339098\pi$
$113$	10.2950	0.968469	0.484235	+	0.874938i	$0.339098\pi$
$114$	−21.8943	−2.05059
$115$	18.8306	1.75596
$116$	9.23090	0.857067
$117$	−5.63884	−0.521311
$118$	16.4325	1.51274
$119$	−5.17874	−0.474734
$120$	35.1146	3.20551
$121$	−9.72116	−0.883742
$122$	−37.5600	−3.40052
$123$	3.61367	0.325833
$124$	−16.2041	−1.45517
$125$	−11.6140	−1.03879
$126$	−6.56559	−0.584909
$127$	−10.8936	−0.966651	−0.483325	−	0.875441i	$-0.660571\pi$
$127$	−10.8936	−0.966651	−0.483325	+	0.875441i	$0.660571\pi$
$128$	−12.8495	−1.13575
$129$	−19.2139	−1.69169
$130$	32.5550	2.85526
$131$	−4.73348	−0.413566	−0.206783	−	0.978387i	$-0.566299\pi$
$131$	−4.73348	−0.413566	−0.206783	+	0.978387i	$0.566299\pi$
$132$	11.4955	1.00056
$133$	−10.3043	−0.893492
$134$	0.411871	0.0355802
$135$	8.59140	0.739430
$136$	17.0430	1.46143
$137$	6.58578	0.562661	0.281330	−	0.959611i	$-0.409224\pi$
$137$	6.58578	0.562661	0.281330	+	0.959611i	$0.409224\pi$
$138$	46.8653	3.98944
$139$	−7.23282	−0.613480	−0.306740	−	0.951793i	$-0.599238\pi$
$139$	−7.23282	−0.613480	−0.306740	+	0.951793i	$0.599238\pi$
$140$	27.2158	2.30015
$141$	−1.14853	−0.0967235
$142$	42.7496	3.58746
$143$	6.47159	0.541182
$144$	11.5723	0.964362
$145$	3.87244	0.321589
$146$	5.84284	0.483557
$147$	1.47641	0.121772
$148$	18.3083	1.50494
$149$	6.61593	0.541998	0.270999	−	0.962580i	$-0.412646\pi$
$149$	6.61593	0.541998	0.270999	+	0.962580i	$0.412646\pi$
$150$	−2.32277	−0.189653
$151$	5.17369	0.421029	0.210514	−	0.977591i	$-0.432486\pi$
$151$	5.17369	0.421029	0.210514	+	0.977591i	$0.432486\pi$
$152$	33.9109	2.75054
$153$	−2.03943	−0.164878
$154$	7.53520	0.607204
$155$	−6.79777	−0.546010
$156$	58.1735	4.65760
$157$	−17.9441	−1.43210	−0.716049	−	0.698050i	$-0.754051\pi$
$157$	−17.9441	−1.43210	−0.716049	+	0.698050i	$0.754051\pi$
$158$	−7.48421	−0.595412
$159$	2.76893	0.219590
$160$	−31.6321	−2.50073
$161$	22.0565	1.73829
$162$	29.2543	2.29843
$163$	−5.41435	−0.424085	−0.212042	−	0.977260i	$-0.568011\pi$
$163$	−5.41435	−0.424085	−0.212042	+	0.977260i	$0.568011\pi$
$164$	−9.21731	−0.719751
$165$	4.82248	0.375430
$166$	−31.4626	−2.44197
$167$	21.2349	1.64321	0.821605	−	0.570058i	$-0.193079\pi$
$167$	21.2349	1.64321	0.821605	+	0.570058i	$0.193079\pi$
$168$	41.1301	3.17326
$169$	19.7496	1.51920
$170$	11.7743	0.903049
$171$	−4.05790	−0.310315
$172$	49.0086	3.73687
$173$	11.8886	0.903871	0.451935	−	0.892051i	$-0.350734\pi$
$173$	11.8886	0.903871	0.451935	+	0.892051i	$0.350734\pi$
$174$	9.63768	0.730630
$175$	−1.09318	−0.0826364
$176$	−13.2814	−1.00112
$177$	12.3184	0.925905
$178$	−43.0465	−3.22647
$179$	−9.07719	−0.678461	−0.339230	−	0.940703i	$-0.610167\pi$
$179$	−9.07719	−0.678461	−0.339230	+	0.940703i	$0.610167\pi$
$180$	10.7178	0.798857
$181$	−12.6089	−0.937212	−0.468606	−	0.883407i	$-0.655244\pi$
$181$	−12.6089	−0.937212	−0.468606	+	0.883407i	$0.655244\pi$
$182$	38.1320	2.82654
$183$	−28.1562	−2.08136
$184$	−72.5869	−5.35118
$185$	7.68051	0.564682
$186$	−16.9182	−1.24050
$187$	2.34061	0.171163
$188$	2.92953	0.213658
$189$	10.0632	0.731991
$190$	23.4276	1.69962
$191$	−7.94315	−0.574746	−0.287373	−	0.957819i	$-0.592782\pi$
$191$	−7.94315	−0.574746	−0.287373	+	0.957819i	$0.592782\pi$
$192$	−31.8336	−2.29739
$193$	−8.12156	−0.584603	−0.292301	−	0.956326i	$-0.594421\pi$
$193$	−8.12156	−0.584603	−0.292301	+	0.956326i	$0.594421\pi$
$194$	30.5348	2.19227
$195$	24.4043	1.74763
$196$	−3.76586	−0.268990
$197$	0.587027	0.0418240	0.0209120	−	0.999781i	$-0.493343\pi$
$197$	0.587027	0.0418240	0.0209120	+	0.999781i	$0.493343\pi$
$198$	2.96742	0.210885
$199$	−17.5660	−1.24522	−0.622611	−	0.782532i	$-0.713928\pi$
$199$	−17.5660	−1.24522	−0.622611	+	0.782532i	$0.713928\pi$
$200$	3.59760	0.254389
$201$	0.308752	0.0217777
$202$	−38.9493	−2.74046
$203$	4.53584	0.318353
$204$	21.0399	1.47309
$205$	−3.86674	−0.270065
$206$	−8.14723	−0.567645
$207$	8.68601	0.603720
$208$	−67.2106	−4.66022
$209$	4.65717	0.322143
$210$	28.4151	1.96083
$211$	−17.9031	−1.23250	−0.616250	−	0.787550i	$-0.711349\pi$
$211$	−17.9031	−1.23250	−0.616250	+	0.787550i	$0.711349\pi$
$212$	−7.06265	−0.485065
$213$	32.0464	2.19579
$214$	31.4715	2.15135
$215$	20.5595	1.40215
$216$	−33.1176	−2.25337
$217$	−7.96232	−0.540517
$218$	52.0861	3.52771
$219$	4.37998	0.295972
$220$	−12.3006	−0.829307
$221$	11.8447	0.796762
$222$	19.1151	1.28292
$223$	−10.6474	−0.713003	−0.356501	−	0.934295i	$-0.616030\pi$
$223$	−10.6474	−0.713003	−0.356501	+	0.934295i	$0.616030\pi$
$224$	−37.0510	−2.47558
$225$	−0.430502	−0.0287001
$226$	−27.4163	−1.82371
$227$	23.7316	1.57512	0.787560	−	0.616238i	$-0.211344\pi$
$227$	23.7316	1.57512	0.787560	+	0.616238i	$0.211344\pi$
$228$	41.8635	2.77248
$229$	−6.78233	−0.448189	−0.224095	−	0.974567i	$-0.571942\pi$
$229$	−6.78233	−0.448189	−0.224095	+	0.974567i	$0.571942\pi$
$230$	−50.1473	−3.30662
$231$	5.64863	0.371653
$232$	−14.9272	−0.980022
$233$	−18.3864	−1.20454	−0.602268	−	0.798294i	$-0.705736\pi$
$233$	−18.3864	−1.20454	−0.602268	+	0.798294i	$0.705736\pi$
$234$	15.0167	0.981673
$235$	1.22896	0.0801687
$236$	−31.4202	−2.04528
$237$	−5.61041	−0.364435
$238$	13.7914	0.893964
$239$	13.9492	0.902302	0.451151	−	0.892448i	$-0.351014\pi$
$239$	13.9492	0.902302	0.451151	+	0.892448i	$0.351014\pi$
$240$	−50.0838	−3.23289
$241$	−8.73697	−0.562798	−0.281399	−	0.959591i	$-0.590798\pi$
$241$	−8.73697	−0.562798	−0.281399	+	0.959591i	$0.590798\pi$
$242$	25.8882	1.66416
$243$	9.86418	0.632787
$244$	71.8174	4.59764
$245$	−1.57981	−0.100930
$246$	−9.62349	−0.613571
$247$	23.5677	1.49958
$248$	26.2036	1.66393
$249$	−23.5854	−1.49466
$250$	30.9290	1.95612
$251$	−10.7387	−0.677819	−0.338910	−	0.940819i	$-0.610058\pi$
$251$	−10.7387	−0.677819	−0.338910	+	0.940819i	$0.610058\pi$
$252$	12.5539	0.790820
$253$	−9.96877	−0.626731
$254$	29.0106	1.82028
$255$	8.82641	0.552731
$256$	2.32723	0.145452
$257$	−0.155844	−0.00972128	−0.00486064	−	0.999988i	$-0.501547\pi$
$257$	−0.155844	−0.00972128	−0.00486064	+	0.999988i	$0.501547\pi$
$258$	51.1682	3.18560
$259$	8.99627	0.559001
$260$	−62.2475	−3.86043
$261$	1.78625	0.110566
$262$	12.6056	0.778780
$263$	−29.7490	−1.83440	−0.917201	−	0.398425i	$-0.869557\pi$
$263$	−29.7490	−1.83440	−0.917201	+	0.398425i	$0.869557\pi$
$264$	−18.5894	−1.14410
$265$	−2.96284	−0.182006
$266$	27.4411	1.68252
$267$	−32.2690	−1.97483
$268$	−0.787527	−0.0481059
$269$	−17.3149	−1.05571	−0.527853	−	0.849335i	$-0.677003\pi$
$269$	−17.3149	−1.05571	−0.527853	+	0.849335i	$0.677003\pi$
$270$	−22.8796	−1.39241
$271$	12.7149	0.772376	0.386188	−	0.922420i	$-0.373792\pi$
$271$	12.7149	0.772376	0.386188	+	0.922420i	$0.373792\pi$
$272$	−24.3084	−1.47391
$273$	28.5850	1.73004
$274$	−17.5385	−1.05954
$275$	0.494079	0.0297941
$276$	−89.6098	−5.39387
$277$	−8.46860	−0.508829	−0.254414	−	0.967095i	$-0.581883\pi$
$277$	−8.46860	−0.508829	−0.254414	+	0.967095i	$0.581883\pi$
$278$	19.2616	1.15523
$279$	−3.13562	−0.187725
$280$	−44.0105	−2.63013
$281$	−5.73166	−0.341922	−0.170961	−	0.985278i	$-0.554687\pi$
$281$	−5.73166	−0.341922	−0.170961	+	0.985278i	$0.554687\pi$
$282$	3.05862	0.182138
$283$	−19.3227	−1.14862	−0.574308	−	0.818640i	$-0.694729\pi$
$283$	−19.3227	−1.14862	−0.574308	+	0.818640i	$0.694729\pi$
$284$	−81.7402	−4.85039
$285$	17.5621	1.04029
$286$	−17.2344	−1.01909
$287$	−4.52916	−0.267348
$288$	−14.5910	−0.859782
$289$	−12.7161	−0.748004
$290$	−10.3126	−0.605578
$291$	22.8899	1.34183
$292$	−11.1719	−0.653788
$293$	24.8787	1.45343	0.726716	−	0.686938i	$-0.241046\pi$
$293$	24.8787	1.45343	0.726716	+	0.686938i	$0.241046\pi$
$294$	−3.93181	−0.229308
$295$	−13.1810	−0.767430
$296$	−29.6064	−1.72083
$297$	−4.54823	−0.263915
$298$	−17.6188	−1.02063
$299$	−50.4472	−2.91744
$300$	4.44130	0.256418
$301$	24.0816	1.38804
$302$	−13.7780	−0.792832
$303$	−29.1976	−1.67736
$304$	−48.3670	−2.77404
$305$	30.1280	1.72512
$306$	5.43116	0.310479
$307$	29.4630	1.68154	0.840771	−	0.541391i	$-0.182102\pi$
$307$	29.4630	1.68154	0.840771	+	0.541391i	$0.182102\pi$
$308$	−14.4078	−0.820963
$309$	−6.10743	−0.347439
$310$	18.1030	1.02818
$311$	−22.0574	−1.25076	−0.625381	−	0.780319i	$-0.715057\pi$
$311$	−22.0574	−1.25076	−0.625381	+	0.780319i	$0.715057\pi$
$312$	−94.0721	−5.32578
$313$	18.4997	1.04566	0.522832	−	0.852436i	$-0.324875\pi$
$313$	18.4997	1.04566	0.522832	+	0.852436i	$0.324875\pi$
$314$	47.7867	2.69676
$315$	5.26646	0.296731
$316$	14.3104	0.805021
$317$	16.0684	0.902492	0.451246	−	0.892400i	$-0.350980\pi$
$317$	16.0684	0.902492	0.451246	+	0.892400i	$0.350980\pi$
$318$	−7.37388	−0.413507
$319$	−2.05004	−0.114780
$320$	34.0630	1.90418
$321$	23.5920	1.31678
$322$	−58.7382	−3.27335
$323$	8.52385	0.474280
$324$	−55.9363	−3.10757
$325$	2.50030	0.138691
$326$	14.4189	0.798587
$327$	39.0454	2.15922
$328$	14.9053	0.823006
$329$	1.43950	0.0793621
$330$	−12.8427	−0.706965
$331$	1.66201	0.0913521	0.0456760	−	0.998956i	$-0.485456\pi$
$331$	1.66201	0.0913521	0.0456760	+	0.998956i	$0.485456\pi$
$332$	60.1588	3.30164
$333$	3.54280	0.194144
$334$	−56.5504	−3.09430
$335$	−0.330374	−0.0180503
$336$	−58.6637	−3.20037
$337$	32.3461	1.76200	0.881002	−	0.473113i	$-0.156870\pi$
$337$	32.3461	1.76200	0.881002	+	0.473113i	$0.156870\pi$
$338$	−52.5949	−2.86079
$339$	−20.5522	−1.11624
$340$	−22.5133	−1.22096
$341$	3.59869	0.194880
$342$	10.8065	0.584349
$343$	−19.3651	−1.04561
$344$	−79.2516	−4.27296
$345$	−37.5921	−2.02389
$346$	−31.6602	−1.70206
$347$	25.4753	1.36758	0.683792	−	0.729677i	$-0.260329\pi$
$347$	25.4753	1.36758	0.683792	+	0.729677i	$0.260329\pi$
$348$	−18.4279	−0.987841
$349$	8.35544	0.447256	0.223628	−	0.974675i	$-0.428210\pi$
$349$	8.35544	0.447256	0.223628	+	0.974675i	$0.428210\pi$
$350$	2.91122	0.155611
$351$	−23.0164	−1.22852
$352$	16.7458	0.892554
$353$	−25.8261	−1.37458	−0.687292	−	0.726381i	$-0.741201\pi$
$353$	−25.8261	−1.37458	−0.687292	+	0.726381i	$0.741201\pi$
$354$	−32.8048	−1.74356
$355$	−34.2907	−1.81996
$356$	82.3080	4.36231
$357$	10.3385	0.547170
$358$	24.1733	1.27760
$359$	21.7296	1.14684	0.573422	−	0.819260i	$-0.305616\pi$
$359$	21.7296	1.14684	0.573422	+	0.819260i	$0.305616\pi$
$360$	−17.3317	−0.913461
$361$	−2.03989	−0.107363
$362$	33.5785	1.76485
$363$	19.4067	1.01859
$364$	−72.9112	−3.82159
$365$	−4.68672	−0.245314
$366$	74.9822	3.91938
$367$	−7.40161	−0.386361	−0.193181	−	0.981163i	$-0.561880\pi$
$367$	−7.40161	−0.386361	−0.193181	+	0.981163i	$0.561880\pi$
$368$	103.531	5.39690
$369$	−1.78362	−0.0928515
$370$	−20.4538	−1.06334
$371$	−3.47041	−0.180175
$372$	32.3488	1.67721
$373$	−2.93008	−0.151714	−0.0758570	−	0.997119i	$-0.524169\pi$
$373$	−2.93008	−0.151714	−0.0758570	+	0.997119i	$0.524169\pi$
$374$	−6.23324	−0.322313
$375$	23.1854	1.19729
$376$	−4.73733	−0.244309
$377$	−10.3743	−0.534303
$378$	−26.7992	−1.37840
$379$	−22.7233	−1.16722	−0.583610	−	0.812034i	$-0.698360\pi$
$379$	−22.7233	−1.16722	−0.583610	+	0.812034i	$0.698360\pi$
$380$	−44.7953	−2.29795
$381$	21.7472	1.11415
$382$	21.1533	1.08230
$383$	−31.9205	−1.63106	−0.815530	−	0.578715i	$-0.803554\pi$
$383$	−31.9205	−1.63106	−0.815530	+	0.578715i	$0.803554\pi$
$384$	25.6519	1.30904
$385$	−6.04422	−0.308042
$386$	21.6284	1.10086
$387$	9.48353	0.482075
$388$	−58.3847	−2.96403
$389$	25.5135	1.29358	0.646792	−	0.762666i	$-0.276110\pi$
$389$	25.5135	1.29358	0.646792	+	0.762666i	$0.276110\pi$
$390$	−64.9906	−3.29092
$391$	−18.2455	−0.922714
$392$	6.08975	0.307579
$393$	9.44960	0.476669
$394$	−1.56330	−0.0787580
$395$	6.00332	0.302060
$396$	−5.67392	−0.285125
$397$	−30.5141	−1.53146	−0.765730	−	0.643163i	$-0.777622\pi$
$397$	−30.5141	−1.53146	−0.765730	+	0.643163i	$0.777622\pi$
$398$	46.7797	2.34486
$399$	20.5707	1.02982
$400$	−5.13125	−0.256562
$401$	5.18307	0.258830	0.129415	−	0.991590i	$-0.458690\pi$
$401$	5.18307	0.258830	0.129415	+	0.991590i	$0.458690\pi$
$402$	−0.822231	−0.0410092
$403$	18.2113	0.907168
$404$	74.4738	3.70521
$405$	−23.4658	−1.16602
$406$	−12.0793	−0.599486
$407$	−4.06601	−0.201545
$408$	−34.0235	−1.68441
$409$	−28.3356	−1.40110	−0.700552	−	0.713602i	$-0.747063\pi$
$409$	−28.3356	−1.40110	−0.700552	+	0.713602i	$0.747063\pi$
$410$	10.2974	0.508555
$411$	−13.1474	−0.648513
$412$	15.5781	0.767478
$413$	−15.4391	−0.759709
$414$	−23.1316	−1.13685
$415$	25.2371	1.23884
$416$	84.7425	4.15484
$417$	14.4391	0.707086
$418$	−12.4024	−0.606623
$419$	−36.1292	−1.76503	−0.882513	−	0.470288i	$-0.844150\pi$
$419$	−36.1292	−1.76503	−0.882513	+	0.470288i	$0.844150\pi$
$420$	−54.3317	−2.65112
$421$	18.4054	0.897023	0.448512	−	0.893777i	$-0.351954\pi$
$421$	18.4054	0.897023	0.448512	+	0.893777i	$0.351954\pi$
$422$	47.6774	2.32090
$423$	0.566886	0.0275629
$424$	11.4210	0.554652
$425$	0.904294	0.0438647
$426$	−85.3423	−4.13485
$427$	35.2893	1.70777
$428$	−60.1757	−2.90870
$429$	−12.9194	−0.623757
$430$	−54.7517	−2.64036
$431$	−5.80624	−0.279677	−0.139838	−	0.990174i	$-0.544658\pi$
$431$	−5.80624	−0.279677	−0.139838	+	0.990174i	$0.544658\pi$
$432$	47.2355	2.27262
$433$	3.41917	0.164315	0.0821575	−	0.996619i	$-0.473819\pi$
$433$	3.41917	0.164315	0.0821575	+	0.996619i	$0.473819\pi$
$434$	21.2043	1.01784
$435$	−7.73068	−0.370658
$436$	−99.5923	−4.76961
$437$	−36.3035	−1.73663
$438$	−11.6642	−0.557339
$439$	−10.3107	−0.492103	−0.246051	−	0.969257i	$-0.579133\pi$
$439$	−10.3107	−0.492103	−0.246051	+	0.969257i	$0.579133\pi$
$440$	19.8913	0.948279
$441$	−0.728722	−0.0347010
$442$	−31.5435	−1.50037
$443$	−15.4932	−0.736102	−0.368051	−	0.929806i	$-0.619975\pi$
$443$	−15.4932	−0.736102	−0.368051	+	0.929806i	$0.619975\pi$
$444$	−36.5495	−1.73456
$445$	34.5289	1.63683
$446$	28.3549	1.34264
$447$	−13.2076	−0.624698
$448$	39.8984	1.88502
$449$	−27.8014	−1.31203	−0.656016	−	0.754747i	$-0.727759\pi$
$449$	−27.8014	−1.31203	−0.656016	+	0.754747i	$0.727759\pi$
$450$	1.14646	0.0540447
$451$	2.04703	0.0963907
$452$	52.4220	2.46573
$453$	−10.3284	−0.485271
$454$	−63.1991	−2.96608
$455$	−30.5869	−1.43394
$456$	−67.6974	−3.17022
$457$	16.6197	0.777437	0.388718	−	0.921357i	$-0.372918\pi$
$457$	16.6197	0.777437	0.388718	+	0.921357i	$0.372918\pi$
$458$	18.0619	0.843978
$459$	−8.32445	−0.388552
$460$	95.8854	4.47068
$461$	12.0696	0.562136	0.281068	−	0.959688i	$-0.409311\pi$
$461$	12.0696	0.562136	0.281068	+	0.959688i	$0.409311\pi$
$462$	−15.0428	−0.699853
$463$	−18.0877	−0.840608	−0.420304	−	0.907383i	$-0.638077\pi$
$463$	−18.0877	−0.840608	−0.420304	+	0.907383i	$0.638077\pi$
$464$	21.2907	0.988395
$465$	13.5706	0.629322
$466$	48.9646	2.26824
$467$	−7.10049	−0.328572	−0.164286	−	0.986413i	$-0.552532\pi$
$467$	−7.10049	−0.328572	−0.164286	+	0.986413i	$0.552532\pi$
$468$	−28.7130	−1.32726
$469$	−0.386971	−0.0178687
$470$	−3.27283	−0.150964
$471$	35.8224	1.65061
$472$	50.8095	2.33870
$473$	−10.8841	−0.500450
$474$	14.9410	0.686262
$475$	1.79930	0.0825573
$476$	−26.3702	−1.20867
$477$	−1.36668	−0.0625758
$478$	−37.1480	−1.69911
$479$	10.9486	0.500255	0.250127	−	0.968213i	$-0.419528\pi$
$479$	10.9486	0.500255	0.250127	+	0.968213i	$0.419528\pi$
$480$	63.1481	2.88230
$481$	−20.5761	−0.938191
$482$	23.2673	1.05979
$483$	−44.0320	−2.00353
$484$	−49.5002	−2.25001
$485$	−24.4929	−1.11216
$486$	−26.2691	−1.19159
$487$	7.56385	0.342751	0.171375	−	0.985206i	$-0.445179\pi$
$487$	7.56385	0.342751	0.171375	+	0.985206i	$0.445179\pi$
$488$	−116.136	−5.25721
$489$	10.8088	0.488793
$490$	4.20716	0.190060
$491$	−9.21658	−0.415938	−0.207969	−	0.978135i	$-0.566685\pi$
$491$	−9.21658	−0.415938	−0.207969	+	0.978135i	$0.566685\pi$
$492$	18.4008	0.829572
$493$	−3.75212	−0.168987
$494$	−62.7628	−2.82383
$495$	−2.38026	−0.106985
$496$	−37.3742	−1.67815
$497$	−40.1651	−1.80165
$498$	62.8098	2.81457
$499$	−39.4250	−1.76491	−0.882453	−	0.470401i	$-0.844109\pi$
$499$	−39.4250	−1.76491	−0.882453	+	0.470401i	$0.844109\pi$
$500$	−59.1385	−2.64475
$501$	−42.3920	−1.89394
$502$	28.5980	1.27639
$503$	−26.2515	−1.17050	−0.585249	−	0.810854i	$-0.699003\pi$
$503$	−26.2515	−1.17050	−0.585249	+	0.810854i	$0.699003\pi$
$504$	−20.3008	−0.904271
$505$	31.2424	1.39027
$506$	26.5477	1.18019
$507$	−39.4268	−1.75101
$508$	−55.4703	−2.46110
$509$	32.7175	1.45018	0.725088	−	0.688656i	$-0.241799\pi$
$509$	32.7175	1.45018	0.725088	+	0.688656i	$0.241799\pi$
$510$	−23.5055	−1.04084
$511$	−5.48961	−0.242846
$512$	19.5014	0.861850
$513$	−16.5634	−0.731290
$514$	0.415025	0.0183060
$515$	6.53515	0.287973
$516$	−97.8374	−4.30705
$517$	−0.650604	−0.0286135
$518$	−23.9578	−1.05265
$519$	−23.7335	−1.04179
$520$	100.660	4.41424
$521$	−7.45115	−0.326441	−0.163220	−	0.986590i	$-0.552188\pi$
$521$	−7.45115	−0.326441	−0.163220	+	0.986590i	$0.552188\pi$
$522$	−4.75693	−0.208205
$523$	−39.4489	−1.72498	−0.862490	−	0.506074i	$-0.831096\pi$
$523$	−39.4489	−1.72498	−0.862490	+	0.506074i	$0.831096\pi$
$524$	−24.1029	−1.05294
$525$	2.18234	0.0952453
$526$	79.2240	3.45433
$527$	6.58656	0.286915
$528$	26.5140	1.15387
$529$	54.7083	2.37862
$530$	7.89029	0.342732
$531$	−6.08005	−0.263852
$532$	−52.4693	−2.27483
$533$	10.3590	0.448699
$534$	85.9350	3.71877
$535$	−25.2442	−1.09140
$536$	1.27351	0.0550071
$537$	18.1211	0.781982
$538$	46.1109	1.98798
$539$	0.836340	0.0360237
$540$	43.7474	1.88259
$541$	4.22135	0.181490	0.0907450	−	0.995874i	$-0.471075\pi$
$541$	4.22135	0.181490	0.0907450	+	0.995874i	$0.471075\pi$
$542$	−33.8608	−1.45445
$543$	25.1715	1.08021
$544$	30.6492	1.31407
$545$	−41.7798	−1.78965
$546$	−76.1242	−3.25782
$547$	25.5810	1.09377	0.546883	−	0.837209i	$-0.315814\pi$
$547$	25.5810	1.09377	0.546883	+	0.837209i	$0.315814\pi$
$548$	33.5348	1.43254
$549$	13.8972	0.593118
$550$	−1.31577	−0.0561047
$551$	−7.46568	−0.318049
$552$	144.908	6.16768
$553$	7.03176	0.299021
$554$	22.5526	0.958167
$555$	−15.3328	−0.650843
$556$	−36.8296	−1.56192
$557$	11.7722	0.498803	0.249402	−	0.968400i	$-0.419766\pi$
$557$	11.7722	0.498803	0.249402	+	0.968400i	$0.419766\pi$
$558$	8.35042	0.353502
$559$	−55.0791	−2.32960
$560$	62.7721	2.65261
$561$	−4.67264	−0.197279
$562$	15.2639	0.643868
$563$	7.69730	0.324403	0.162201	−	0.986758i	$-0.448141\pi$
$563$	7.69730	0.324403	0.162201	+	0.986758i	$0.448141\pi$
$564$	−5.84831	−0.246258
$565$	21.9915	0.925189
$566$	51.4579	2.16294
$567$	−27.4857	−1.15429
$568$	132.182	5.54623
$569$	21.0272	0.881507	0.440753	−	0.897628i	$-0.354711\pi$
$569$	21.0272	0.881507	0.440753	+	0.897628i	$0.354711\pi$
$570$	−46.7694	−1.95895
$571$	27.9421	1.16934	0.584671	−	0.811271i	$-0.301224\pi$
$571$	27.9421	1.16934	0.584671	+	0.811271i	$0.301224\pi$
$572$	32.9534	1.37785
$573$	15.8572	0.662443
$574$	12.0615	0.503438
$575$	−3.85143	−0.160616
$576$	15.7123	0.654679
$577$	−21.0663	−0.877000	−0.438500	−	0.898731i	$-0.644490\pi$
$577$	−21.0663	−0.877000	−0.438500	+	0.898731i	$0.644490\pi$
$578$	33.8639	1.40855
$579$	16.2133	0.673803
$580$	19.7185	0.818766
$581$	29.5605	1.22638
$582$	−60.9575	−2.52677
$583$	1.56851	0.0649610
$584$	18.0661	0.747580
$585$	−12.0454	−0.498014
$586$	−66.2541	−2.73693
$587$	−47.3409	−1.95397	−0.976985	−	0.213310i	$-0.931576\pi$
$587$	−47.3409	−1.95397	−0.976985	+	0.213310i	$0.931576\pi$
$588$	7.51790	0.310033
$589$	13.1054	0.540000
$590$	35.1022	1.44513
$591$	−1.17190	−0.0482056
$592$	42.2275	1.73554
$593$	−3.98176	−0.163511	−0.0817557	−	0.996652i	$-0.526053\pi$
$593$	−3.98176	−0.163511	−0.0817557	+	0.996652i	$0.526053\pi$
$594$	12.1123	0.496974
$595$	−11.0625	−0.453519
$596$	33.6884	1.37993
$597$	35.0676	1.43522
$598$	134.345	5.49378
$599$	−31.3569	−1.28121	−0.640604	−	0.767871i	$-0.721316\pi$
$599$	−31.3569	−1.28121	−0.640604	+	0.767871i	$0.721316\pi$
$600$	−7.18200	−0.293204
$601$	12.7065	0.518307	0.259154	−	0.965836i	$-0.416556\pi$
$601$	12.7065	0.518307	0.259154	+	0.965836i	$0.416556\pi$
$602$	−64.1313	−2.61380
$603$	−0.152392	−0.00620590
$604$	26.3444	1.07194
$605$	−20.7658	−0.844248
$606$	77.7557	3.15861
$607$	−17.2602	−0.700570	−0.350285	−	0.936643i	$-0.613915\pi$
$607$	−17.2602	−0.700570	−0.350285	+	0.936643i	$0.613915\pi$
$608$	60.9835	2.47321
$609$	−9.05504	−0.366929
$610$	−80.2334	−3.24855
$611$	−3.29240	−0.133196
$612$	−10.3848	−0.419780
$613$	43.4737	1.75589	0.877943	−	0.478765i	$-0.158915\pi$
$613$	43.4737	1.75589	0.877943	+	0.478765i	$0.158915\pi$
$614$	−78.4624	−3.16648
$615$	7.71930	0.311272
$616$	23.2989	0.938739
$617$	14.5210	0.584595	0.292298	−	0.956327i	$-0.405580\pi$
$617$	14.5210	0.584595	0.292298	+	0.956327i	$0.405580\pi$
$618$	16.2646	0.654257
$619$	21.2306	0.853329	0.426664	−	0.904410i	$-0.359689\pi$
$619$	21.2306	0.853329	0.426664	+	0.904410i	$0.359689\pi$
$620$	−34.6143	−1.39014
$621$	35.4542	1.42273
$622$	58.7408	2.35529
$623$	40.4441	1.62036
$624$	134.175	5.37129
$625$	−22.6246	−0.904983
$626$	−49.2662	−1.96907
$627$	−9.29726	−0.371297
$628$	−91.3716	−3.64612
$629$	−7.44187	−0.296727
$630$	−14.0250	−0.558770
$631$	8.83227	0.351607	0.175803	−	0.984425i	$-0.443748\pi$
$631$	8.83227	0.351607	0.175803	+	0.984425i	$0.443748\pi$
$632$	−23.1412	−0.920509
$633$	35.7405	1.42056
$634$	−42.7915	−1.69947
$635$	−23.2703	−0.923452
$636$	14.0994	0.559077
$637$	4.23232	0.167691
$638$	5.45943	0.216141
$639$	−15.8174	−0.625725
$640$	−27.4484	−1.08499
$641$	10.7200	0.423414	0.211707	−	0.977333i	$-0.432098\pi$
$641$	10.7200	0.423414	0.211707	+	0.977333i	$0.432098\pi$
$642$	−62.8275	−2.47960
$643$	0.556904	0.0219621	0.0109811	−	0.999940i	$-0.496505\pi$
$643$	0.556904	0.0219621	0.0109811	+	0.999940i	$0.496505\pi$
$644$	112.312	4.42570
$645$	−41.0436	−1.61609
$646$	−22.6997	−0.893108
$647$	−24.6144	−0.967693	−0.483847	−	0.875153i	$-0.660761\pi$
$647$	−24.6144	−0.967693	−0.483847	+	0.875153i	$0.660761\pi$
$648$	90.4544	3.55338
$649$	6.97795	0.273909
$650$	−6.65849	−0.261168
$651$	15.8954	0.622991
$652$	−27.5699	−1.07972
$653$	−26.4132	−1.03363	−0.516815	−	0.856097i	$-0.672883\pi$
$653$	−26.4132	−1.03363	−0.516815	+	0.856097i	$0.672883\pi$
$654$	−103.981	−4.06598
$655$	−10.1114	−0.395084
$656$	−21.2593	−0.830038
$657$	−2.16185	−0.0843419
$658$	−3.83350	−0.149445
$659$	−6.43633	−0.250724	−0.125362	−	0.992111i	$-0.540009\pi$
$659$	−6.43633	−0.250724	−0.125362	+	0.992111i	$0.540009\pi$
$660$	24.5561	0.955845
$661$	−3.53561	−0.137519	−0.0687596	−	0.997633i	$-0.521904\pi$
$661$	−3.53561	−0.137519	−0.0687596	+	0.997633i	$0.521904\pi$
$662$	−4.42606	−0.172024
$663$	−23.6460	−0.918334
$664$	−97.2825	−3.77529
$665$	−22.0113	−0.853563
$666$	−9.43478	−0.365590
$667$	15.9804	0.618765
$668$	108.128	4.18362
$669$	21.2557	0.821794
$670$	0.879814	0.0339902
$671$	−15.9496	−0.615726
$672$	73.9662	2.85331
$673$	−7.82665	−0.301695	−0.150848	−	0.988557i	$-0.548200\pi$
$673$	−7.82665	−0.301695	−0.150848	+	0.988557i	$0.548200\pi$
$674$	−86.1403	−3.31800
$675$	−1.75720	−0.0676348
$676$	100.565	3.86790
$677$	−15.0225	−0.577363	−0.288681	−	0.957425i	$-0.593217\pi$
$677$	−15.0225	−0.577363	−0.288681	+	0.957425i	$0.593217\pi$
$678$	54.7321	2.10197
$679$	−28.6888	−1.10098
$680$	36.4063	1.39612
$681$	−47.3761	−1.81546
$682$	−9.58362	−0.366976
$683$	−16.7879	−0.642372	−0.321186	−	0.947016i	$-0.604081\pi$
$683$	−16.7879	−0.642372	−0.321186	+	0.947016i	$0.604081\pi$
$684$	−20.6628	−0.790063
$685$	14.0681	0.537516
$686$	51.5707	1.96898
$687$	13.5398	0.516575
$688$	113.036	4.30947
$689$	7.93747	0.302394
$690$	100.111	3.81115
$691$	−1.63934	−0.0623634	−0.0311817	−	0.999514i	$-0.509927\pi$
$691$	−1.63934	−0.0623634	−0.0311817	+	0.999514i	$0.509927\pi$
$692$	60.5366	2.30126
$693$	−2.78803	−0.105908
$694$	−67.8427	−2.57528
$695$	−15.4503	−0.586064
$696$	29.7997	1.12956
$697$	3.74660	0.141912
$698$	−22.2512	−0.842221
$699$	36.7054	1.38833
$700$	−5.56646	−0.210393
$701$	−6.21388	−0.234695	−0.117348	−	0.993091i	$-0.537439\pi$
$701$	−6.21388	−0.234695	−0.117348	+	0.993091i	$0.537439\pi$
$702$	61.2946	2.31341
$703$	−14.8073	−0.558466
$704$	−18.0327	−0.679633
$705$	−2.45342	−0.0924010
$706$	68.7770	2.58846
$707$	36.5946	1.37628
$708$	62.7252	2.35736
$709$	2.99766	0.112579	0.0562896	−	0.998414i	$-0.482073\pi$
$709$	2.99766	0.112579	0.0562896	+	0.998414i	$0.482073\pi$
$710$	91.3190	3.42714
$711$	2.76916	0.103852
$712$	−133.100	−4.98813
$713$	−28.0525	−1.05057
$714$	−27.5322	−1.03037
$715$	13.8242	0.516997
$716$	−46.2211	−1.72736
$717$	−27.8473	−1.03998
$718$	−57.8677	−2.15960
$719$	14.0152	0.522679	0.261339	−	0.965247i	$-0.415836\pi$
$719$	14.0152	0.522679	0.261339	+	0.965247i	$0.415836\pi$
$720$	24.7202	0.921266
$721$	7.65470	0.285076
$722$	5.43239	0.202173
$723$	17.4419	0.648671
$724$	−64.2046	−2.38614
$725$	−0.792033	−0.0294154
$726$	−51.6815	−1.91808
$727$	−6.70108	−0.248529	−0.124265	−	0.992249i	$-0.539657\pi$
$727$	−6.70108	−0.248529	−0.124265	+	0.992249i	$0.539657\pi$
$728$	117.904	4.36983
$729$	13.2632	0.491230
$730$	12.4811	0.461947
$731$	−19.9207	−0.736794
$732$	−143.371	−5.29916
$733$	24.5735	0.907642	0.453821	−	0.891093i	$-0.350061\pi$
$733$	24.5735	0.907642	0.453821	+	0.891093i	$0.350061\pi$
$734$	19.7111	0.727550
$735$	3.15382	0.116331
$736$	−130.536	−4.81164
$737$	0.174898	0.00644245
$738$	4.74992	0.174847
$739$	14.7224	0.541573	0.270786	−	0.962639i	$-0.412716\pi$
$739$	14.7224	0.541573	0.270786	+	0.962639i	$0.412716\pi$
$740$	39.1092	1.43768
$741$	−47.0490	−1.72839
$742$	9.24200	0.339284
$743$	−43.5716	−1.59849	−0.799244	−	0.601007i	$-0.794766\pi$
$743$	−43.5716	−1.59849	−0.799244	+	0.601007i	$0.794766\pi$
$744$	−52.3112	−1.91782
$745$	14.1326	0.517777
$746$	7.80305	0.285690
$747$	11.6412	0.425928
$748$	11.9184	0.435780
$749$	−29.5689	−1.08042
$750$	−61.7446	−2.25459
$751$	−16.4283	−0.599476	−0.299738	−	0.954022i	$-0.596899\pi$
$751$	−16.4283	−0.599476	−0.299738	+	0.954022i	$0.596899\pi$
$752$	6.75684	0.246397
$753$	21.4380	0.781243
$754$	27.6276	1.00614
$755$	11.0517	0.402213
$756$	51.2419	1.86365
$757$	3.64409	0.132447	0.0662234	−	0.997805i	$-0.478905\pi$
$757$	3.64409	0.132447	0.0662234	+	0.997805i	$0.478905\pi$
$758$	60.5141	2.19797
$759$	19.9010	0.722360
$760$	72.4384	2.62762
$761$	−9.18415	−0.332925	−0.166463	−	0.986048i	$-0.553234\pi$
$761$	−9.18415	−0.332925	−0.166463	+	0.986048i	$0.553234\pi$
$762$	−57.9147	−2.09803
$763$	−48.9372	−1.77165
$764$	−40.4466	−1.46331
$765$	−4.35650	−0.157510
$766$	85.0068	3.07142
$767$	35.3121	1.27505
$768$	−4.64593	−0.167645
$769$	8.11513	0.292639	0.146320	−	0.989237i	$-0.453257\pi$
$769$	8.11513	0.292639	0.146320	+	0.989237i	$0.453257\pi$
$770$	16.0962	0.580068
$771$	0.311116	0.0112046
$772$	−41.3550	−1.48840
$773$	−32.8761	−1.18247	−0.591236	−	0.806499i	$-0.701360\pi$
$773$	−32.8761	−1.18247	−0.591236	+	0.806499i	$0.701360\pi$
$774$	−25.2554	−0.907787
$775$	1.39035	0.0499430
$776$	94.4137	3.38925
$777$	−17.9596	−0.644295
$778$	−67.9445	−2.43593
$779$	7.45469	0.267092
$780$	124.267	4.44946
$781$	18.1533	0.649575
$782$	48.5892	1.73755
$783$	7.29104	0.260560
$784$	−8.68580	−0.310207
$785$	−38.3312	−1.36810
$786$	−25.1651	−0.897608
$787$	−16.6935	−0.595060	−0.297530	−	0.954713i	$-0.596163\pi$
$787$	−16.6935	−0.595060	−0.297530	+	0.954713i	$0.596163\pi$
$788$	2.98915	0.106484
$789$	59.3889	2.11430
$790$	−15.9873	−0.568804
$791$	25.7589	0.915881
$792$	9.17528	0.326029
$793$	−80.7131	−2.86621
$794$	81.2616	2.88387
$795$	5.91482	0.209777
$796$	−89.4462	−3.17034
$797$	55.5009	1.96594	0.982972	−	0.183757i	$-0.0588259\pi$
$797$	55.5009	1.96594	0.982972	+	0.183757i	$0.0588259\pi$
$798$	−54.7815	−1.93924
$799$	−1.19078	−0.0421267
$800$	6.46973	0.228739
$801$	15.9272	0.562760
$802$	−13.8029	−0.487399
$803$	2.48112	0.0875568
$804$	1.57217	0.0554460
$805$	47.1157	1.66061
$806$	−48.4981	−1.70827
$807$	34.5663	1.21679
$808$	−120.431	−4.23676
$809$	−27.7951	−0.977222	−0.488611	−	0.872502i	$-0.662496\pi$
$809$	−27.7951	−0.977222	−0.488611	+	0.872502i	$0.662496\pi$
$810$	62.4913	2.19572
$811$	32.3664	1.13654	0.568269	−	0.822843i	$-0.307613\pi$
$811$	32.3664	1.13654	0.568269	+	0.822843i	$0.307613\pi$
$812$	23.0965	0.810528
$813$	−25.3832	−0.890227
$814$	10.8281	0.379525
$815$	−11.5658	−0.405133
$816$	48.5276	1.69881
$817$	−39.6367	−1.38671
$818$	75.4599	2.63839
$819$	−14.1089	−0.493004
$820$	−19.6895	−0.687586
$821$	−45.4246	−1.58533	−0.792665	−	0.609657i	$-0.791307\pi$
$821$	−45.4246	−1.58533	−0.792665	+	0.609657i	$0.791307\pi$
$822$	35.0126	1.22120
$823$	27.2251	0.949007	0.474504	−	0.880254i	$-0.342628\pi$
$823$	27.2251	0.949007	0.474504	+	0.880254i	$0.342628\pi$
$824$	−25.1913	−0.877580
$825$	−0.986345	−0.0343401
$826$	41.1156	1.43060
$827$	−20.2019	−0.702489	−0.351245	−	0.936284i	$-0.614241\pi$
$827$	−20.2019	−0.702489	−0.351245	+	0.936284i	$0.614241\pi$
$828$	44.2292	1.53707
$829$	19.0276	0.660857	0.330429	−	0.943831i	$-0.392807\pi$
$829$	19.0276	0.660857	0.330429	+	0.943831i	$0.392807\pi$
$830$	−67.2085	−2.33284
$831$	16.9061	0.586467
$832$	−91.2549	−3.16369
$833$	1.53072	0.0530364
$834$	−38.4525	−1.33150
$835$	45.3608	1.56978
$836$	23.7143	0.820178
$837$	−12.7989	−0.442393
$838$	96.2150	3.32369
$839$	−27.4874	−0.948970	−0.474485	−	0.880264i	$-0.657366\pi$
$839$	−27.4874	−0.948970	−0.474485	+	0.880264i	$0.657366\pi$
$840$	87.8597	3.03145
$841$	−25.7137	−0.886679
$842$	−49.0150	−1.68917
$843$	11.4423	0.394094
$844$	−91.1627	−3.13795
$845$	42.1880	1.45131
$846$	−1.50966	−0.0519033
$847$	−24.3232	−0.835755
$848$	−16.2897	−0.559391
$849$	38.5745	1.32387
$850$	−2.40821	−0.0826009
$851$	31.6952	1.08650
$852$	163.181	5.59048
$853$	−30.6938	−1.05094	−0.525468	−	0.850813i	$-0.676110\pi$
$853$	−30.6938	−1.05094	−0.525468	+	0.850813i	$0.676110\pi$
$854$	−93.9783	−3.21587
$855$	−8.66824	−0.296448
$856$	97.3100	3.32599
$857$	−24.2072	−0.826902	−0.413451	−	0.910526i	$-0.635677\pi$
$857$	−24.2072	−0.826902	−0.413451	+	0.910526i	$0.635677\pi$
$858$	34.4056	1.17459
$859$	−4.18327	−0.142731	−0.0713657	−	0.997450i	$-0.522736\pi$
$859$	−4.18327	−0.142731	−0.0713657	+	0.997450i	$0.522736\pi$
$860$	104.689	3.56987
$861$	9.04171	0.308141
$862$	15.4625	0.526655
$863$	30.0131	1.02166	0.510828	−	0.859683i	$-0.329339\pi$
$863$	30.0131	1.02166	0.510828	+	0.859683i	$0.329339\pi$
$864$	−59.5569	−2.02617
$865$	25.3956	0.863477
$866$	−9.10554	−0.309419
$867$	25.3855	0.862136
$868$	−40.5442	−1.37616
$869$	−3.17812	−0.107810
$870$	20.5874	0.697979
$871$	0.885075	0.0299896
$872$	161.050	5.45385
$873$	−11.2979	−0.382375
$874$	96.6791	3.27022
$875$	−29.0592	−0.982381
$876$	22.3029	0.753545
$877$	47.1910	1.59353	0.796763	−	0.604292i	$-0.206544\pi$
$877$	47.1910	1.59353	0.796763	+	0.604292i	$0.206544\pi$
$878$	27.4582	0.926670
$879$	−49.6662	−1.67520
$880$	−28.3709	−0.956381
$881$	−14.7324	−0.496348	−0.248174	−	0.968716i	$-0.579830\pi$
$881$	−14.7324	−0.496348	−0.248174	+	0.968716i	$0.579830\pi$
$882$	1.94065	0.0653449
$883$	45.8246	1.54212	0.771060	−	0.636763i	$-0.219727\pi$
$883$	45.8246	1.54212	0.771060	+	0.636763i	$0.219727\pi$
$884$	60.3134	2.02856
$885$	26.3137	0.884527
$886$	41.2595	1.38614
$887$	−25.0175	−0.840007	−0.420003	−	0.907523i	$-0.637971\pi$
$887$	−25.0175	−0.840007	−0.420003	+	0.907523i	$0.637971\pi$
$888$	59.1041	1.98340
$889$	−27.2567	−0.914162
$890$	−91.9533	−3.08228
$891$	12.4226	0.416173
$892$	−54.2166	−1.81531
$893$	−2.36932	−0.0792862
$894$	35.1729	1.17636
$895$	−19.3901	−0.648141
$896$	−32.1506	−1.07408
$897$	100.709	3.36259
$898$	74.0375	2.47066
$899$	−5.76889	−0.192403
$900$	−2.19212	−0.0730706
$901$	2.87078	0.0956397
$902$	−5.45140	−0.181512
$903$	−48.0749	−1.59983
$904$	−84.7715	−2.81946
$905$	−26.9344	−0.895329
$906$	27.5054	0.913805
$907$	−18.3212	−0.608345	−0.304173	−	0.952617i	$-0.598380\pi$
$907$	−18.3212	−0.608345	−0.304173	+	0.952617i	$0.598380\pi$
$908$	120.841	4.01026
$909$	14.4112	0.477991
$910$	81.4554	2.70022
$911$	1.40280	0.0464767	0.0232384	−	0.999730i	$-0.492602\pi$
$911$	1.40280	0.0464767	0.0232384	+	0.999730i	$0.492602\pi$
$912$	96.5566	3.19731
$913$	−13.3604	−0.442163
$914$	−44.2596	−1.46398
$915$	−60.1455	−1.98835
$916$	−34.5357	−1.14109
$917$	−11.8436	−0.391110
$918$	22.1687	0.731676
$919$	13.1646	0.434261	0.217131	−	0.976143i	$-0.430330\pi$
$919$	13.1646	0.434261	0.217131	+	0.976143i	$0.430330\pi$
$920$	−155.056	−5.11204
$921$	−58.8179	−1.93812
$922$	−32.1422	−1.05855
$923$	91.8651	3.02378
$924$	28.7628	0.946228
$925$	−1.57090	−0.0516509
$926$	48.1691	1.58293
$927$	3.01448	0.0990085
$928$	−26.8444	−0.881209
$929$	26.2705	0.861908	0.430954	−	0.902374i	$-0.358177\pi$
$929$	26.2705	0.861908	0.430954	+	0.902374i	$0.358177\pi$
$930$	−36.1397	−1.18507
$931$	3.04571	0.0998193
$932$	−93.6239	−3.06675
$933$	44.0340	1.44161
$934$	18.9092	0.618728
$935$	4.99988	0.163513
$936$	46.4317	1.51767
$937$	−34.0155	−1.11124	−0.555619	−	0.831437i	$-0.687519\pi$
$937$	−34.0155	−1.11124	−0.555619	+	0.831437i	$0.687519\pi$
$938$	1.03054	0.0336482
$939$	−36.9315	−1.20521
$940$	6.25788	0.204110
$941$	13.9867	0.455955	0.227977	−	0.973666i	$-0.426789\pi$
$941$	13.9867	0.455955	0.227977	+	0.973666i	$0.426789\pi$
$942$	−95.3981	−3.10824
$943$	−15.9569	−0.519629
$944$	−72.4694	−2.35868
$945$	21.4964	0.699279
$946$	28.9852	0.942389
$947$	−27.9501	−0.908255	−0.454128	−	0.890937i	$-0.650049\pi$
$947$	−27.9501	−0.908255	−0.454128	+	0.890937i	$0.650049\pi$
$948$	−28.5682	−0.927853
$949$	12.5558	0.407577
$950$	−4.79167	−0.155462
$951$	−32.0779	−1.04020
$952$	42.6431	1.38207
$953$	28.0122	0.907406	0.453703	−	0.891153i	$-0.350103\pi$
$953$	28.0122	0.907406	0.453703	+	0.891153i	$0.350103\pi$
$954$	3.63957	0.117835
$955$	−16.9677	−0.549062
$956$	71.0296	2.29726
$957$	4.09257	0.132294
$958$	−29.1570	−0.942021
$959$	16.4782	0.532108
$960$	−68.0010	−2.19472
$961$	−20.8732	−0.673328
$962$	54.7959	1.76669
$963$	−11.6445	−0.375238
$964$	−44.4887	−1.43288
$965$	−17.3488	−0.558477
$966$	117.261	3.77281
$967$	−42.1423	−1.35521	−0.677603	−	0.735428i	$-0.736981\pi$
$967$	−42.1423	−1.35521	−0.677603	+	0.735428i	$0.736981\pi$
$968$	80.0466	2.57279
$969$	−17.0164	−0.546647
$970$	65.2265	2.09430
$971$	5.07582	0.162891	0.0814454	−	0.996678i	$-0.474046\pi$
$971$	5.07582	0.162891	0.0814454	+	0.996678i	$0.474046\pi$
$972$	50.2284	1.61108
$973$	−18.0971	−0.580168
$974$	−20.1431	−0.645428
$975$	−4.99142	−0.159853
$976$	165.644	5.30213
$977$	22.0051	0.704005	0.352002	−	0.935999i	$-0.385501\pi$
$977$	22.0051	0.704005	0.352002	+	0.935999i	$0.385501\pi$
$978$	−28.7848	−0.920437
$979$	−18.2794	−0.584211
$980$	−8.04440	−0.256969
$981$	−19.2719	−0.615303
$982$	24.5445	0.783246
$983$	−8.71938	−0.278105	−0.139052	−	0.990285i	$-0.544406\pi$
$983$	−8.71938	−0.278105	−0.139052	+	0.990285i	$0.544406\pi$
$984$	−29.7559	−0.948583
$985$	1.25397	0.0399549
$986$	9.99220	0.318216
$987$	−2.87372	−0.0914714
$988$	120.007	3.81793
$989$	84.8432	2.69786
$990$	6.33883	0.201461
$991$	−21.4912	−0.682691	−0.341345	−	0.939938i	$-0.610883\pi$
$991$	−21.4912	−0.682691	−0.341345	+	0.939938i	$0.610883\pi$
$992$	47.1232	1.49616
$993$	−3.31791	−0.105291
$994$	106.963	3.39266
$995$	−37.5235	−1.18957
$996$	−120.097	−3.80541
$997$	−45.3270	−1.43552	−0.717760	−	0.696291i	$-0.754832\pi$
$997$	−45.3270	−1.43552	−0.717760	+	0.696291i	$0.754832\pi$
$998$	104.992	3.32346
$999$	14.4609	0.457522

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4001.2.a.a.1.4	✓	149

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4001.2.a.a.1.4	✓	149	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)

\(f(q)\)	\(=\)	\(q-2.66308 q^{2} -1.99633 q^{3} +5.09200 q^{4} +2.13614 q^{5} +5.31640 q^{6} +2.50209 q^{7} -8.23426 q^{8} +0.985342 q^{9} +O(q^{10})\)	\(q-2.66308 q^{2} -1.99633 q^{3} +5.09200 q^{4} +2.13614 q^{5} +5.31640 q^{6} +2.50209 q^{7} -8.23426 q^{8} +0.985342 q^{9} -5.68872 q^{10} -1.13086 q^{11} -10.1653 q^{12} -5.72273 q^{13} -6.66326 q^{14} -4.26444 q^{15} +11.7445 q^{16} -2.06977 q^{17} -2.62405 q^{18} -4.11827 q^{19} +10.8772 q^{20} -4.99500 q^{21} +3.01157 q^{22} +8.81523 q^{23} +16.4383 q^{24} -0.436906 q^{25} +15.2401 q^{26} +4.02193 q^{27} +12.7406 q^{28} +1.81282 q^{29} +11.3566 q^{30} -3.18227 q^{31} -14.8081 q^{32} +2.25757 q^{33} +5.51196 q^{34} +5.34481 q^{35} +5.01736 q^{36} +3.59551 q^{37} +10.9673 q^{38} +11.4245 q^{39} -17.5895 q^{40} -1.81015 q^{41} +13.3021 q^{42} +9.62461 q^{43} -5.75833 q^{44} +2.10483 q^{45} -23.4757 q^{46} +0.575319 q^{47} -23.4459 q^{48} -0.739563 q^{49} +1.16352 q^{50} +4.13194 q^{51} -29.1402 q^{52} -1.38701 q^{53} -10.7107 q^{54} -2.41567 q^{55} -20.6028 q^{56} +8.22143 q^{57} -4.82769 q^{58} -6.17050 q^{59} -21.7146 q^{60} +14.1039 q^{61} +8.47465 q^{62} +2.46541 q^{63} +15.9460 q^{64} -12.2246 q^{65} -6.01209 q^{66} -0.154659 q^{67} -10.5393 q^{68} -17.5981 q^{69} -14.2337 q^{70} -16.0527 q^{71} -8.11356 q^{72} -2.19401 q^{73} -9.57513 q^{74} +0.872210 q^{75} -20.9702 q^{76} -2.82950 q^{77} -30.4243 q^{78} +2.81036 q^{79} +25.0879 q^{80} -10.9851 q^{81} +4.82059 q^{82} +11.8144 q^{83} -25.4345 q^{84} -4.42131 q^{85} -25.6311 q^{86} -3.61899 q^{87} +9.31178 q^{88} +16.1642 q^{89} -5.60533 q^{90} -14.3188 q^{91} +44.8872 q^{92} +6.35287 q^{93} -1.53212 q^{94} -8.79719 q^{95} +29.5618 q^{96} -11.4660 q^{97} +1.96952 q^{98} -1.11428 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 149 q - 6 q^{2} - 28 q^{3} + 116 q^{4} - 19 q^{5} - 31 q^{6} - 47 q^{7} - 15 q^{8} + 115 q^{9}+O(q^{10}) \) 149 * q - 6 * q^2 - 28 * q^3 + 116 * q^4 - 19 * q^5 - 31 * q^6 - 47 * q^7 - 15 * q^8 + 115 * q^9	\( 149 q - 6 q^{2} - 28 q^{3} + 116 q^{4} - 19 q^{5} - 31 q^{6} - 47 q^{7} - 15 q^{8} + 115 q^{9} - 48 q^{10} - 31 q^{11} - 61 q^{12} - 54 q^{13} - 44 q^{14} - 65 q^{15} + 58 q^{16} - 26 q^{17} - 23 q^{18} - 86 q^{19} - 52 q^{20} - 30 q^{21} - 56 q^{22} - 63 q^{23} - 90 q^{24} + 92 q^{25} - 38 q^{26} - 103 q^{27} - 77 q^{28} - 51 q^{29} - 22 q^{30} - 256 q^{31} - 21 q^{32} - 36 q^{33} - 124 q^{34} - 50 q^{35} + 45 q^{36} - 42 q^{37} - 14 q^{38} - 119 q^{39} - 131 q^{40} - 55 q^{41} - 5 q^{42} - 55 q^{43} - 54 q^{44} - 68 q^{45} - 59 q^{46} - 82 q^{47} - 89 q^{48} + 30 q^{49} + 13 q^{50} - 83 q^{51} - 126 q^{52} - 23 q^{53} - 83 q^{54} - 244 q^{55} - 94 q^{56} - 14 q^{57} - 60 q^{58} - 93 q^{59} - 70 q^{60} - 139 q^{61} - 10 q^{62} - 120 q^{63} - 45 q^{64} - 37 q^{65} - 28 q^{66} - 110 q^{67} - 27 q^{68} - 79 q^{69} - 78 q^{70} - 123 q^{71} - 74 q^{73} - 25 q^{74} - 146 q^{75} - 192 q^{76} - q^{77} + 26 q^{78} - 273 q^{79} - 51 q^{80} + 41 q^{81} - 120 q^{82} - 27 q^{83} - 14 q^{84} - 71 q^{85} + 3 q^{86} - 98 q^{87} - 143 q^{88} - 70 q^{89} - 24 q^{90} - 256 q^{91} - 47 q^{92} + 16 q^{93} - 151 q^{94} - 83 q^{95} - 137 q^{96} - 108 q^{97} + 17 q^{98} - 131 q^{99}+O(q^{100}) \) 149 * q - 6 * q^2 - 28 * q^3 + 116 * q^4 - 19 * q^5 - 31 * q^6 - 47 * q^7 - 15 * q^8 + 115 * q^9 - 48 * q^10 - 31 * q^11 - 61 * q^12 - 54 * q^13 - 44 * q^14 - 65 * q^15 + 58 * q^16 - 26 * q^17 - 23 * q^18 - 86 * q^19 - 52 * q^20 - 30 * q^21 - 56 * q^22 - 63 * q^23 - 90 * q^24 + 92 * q^25 - 38 * q^26 - 103 * q^27 - 77 * q^28 - 51 * q^29 - 22 * q^30 - 256 * q^31 - 21 * q^32 - 36 * q^33 - 124 * q^34 - 50 * q^35 + 45 * q^36 - 42 * q^37 - 14 * q^38 - 119 * q^39 - 131 * q^40 - 55 * q^41 - 5 * q^42 - 55 * q^43 - 54 * q^44 - 68 * q^45 - 59 * q^46 - 82 * q^47 - 89 * q^48 + 30 * q^49 + 13 * q^50 - 83 * q^51 - 126 * q^52 - 23 * q^53 - 83 * q^54 - 244 * q^55 - 94 * q^56 - 14 * q^57 - 60 * q^58 - 93 * q^59 - 70 * q^60 - 139 * q^61 - 10 * q^62 - 120 * q^63 - 45 * q^64 - 37 * q^65 - 28 * q^66 - 110 * q^67 - 27 * q^68 - 79 * q^69 - 78 * q^70 - 123 * q^71 - 74 * q^73 - 25 * q^74 - 146 * q^75 - 192 * q^76 - q^77 + 26 * q^78 - 273 * q^79 - 51 * q^80 + 41 * q^81 - 120 * q^82 - 27 * q^83 - 14 * q^84 - 71 * q^85 + 3 * q^86 - 98 * q^87 - 143 * q^88 - 70 * q^89 - 24 * q^90 - 256 * q^91 - 47 * q^92 + 16 * q^93 - 151 * q^94 - 83 * q^95 - 137 * q^96 - 108 * q^97 + 17 * q^98 - 131 * q^99

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