LMFDB - Embedded newform 4001.2.a.a.1.12

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			1.12
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)

$f(q)$	$=$	$q-2.44683 q^{2} -2.82076 q^{3} +3.98699 q^{4} +4.21697 q^{5} +6.90192 q^{6} -1.62820 q^{7} -4.86182 q^{8} +4.95666 q^{9} +O(q^{10})$	\(q-2.44683 q^{2} -2.82076 q^{3} +3.98699 q^{4} +4.21697 q^{5} +6.90192 q^{6} -1.62820 q^{7} -4.86182 q^{8} +4.95666 q^{9} -10.3182 q^{10} -2.90570 q^{11} -11.2463 q^{12} +1.01638 q^{13} +3.98394 q^{14} -11.8950 q^{15} +3.92209 q^{16} +4.18101 q^{17} -12.1281 q^{18} -4.76814 q^{19} +16.8130 q^{20} +4.59276 q^{21} +7.10975 q^{22} -2.69947 q^{23} +13.7140 q^{24} +12.7828 q^{25} -2.48691 q^{26} -5.51927 q^{27} -6.49162 q^{28} -3.99454 q^{29} +29.1051 q^{30} +4.07364 q^{31} +0.126946 q^{32} +8.19626 q^{33} -10.2302 q^{34} -6.86607 q^{35} +19.7622 q^{36} +2.23821 q^{37} +11.6668 q^{38} -2.86696 q^{39} -20.5021 q^{40} -4.93466 q^{41} -11.2377 q^{42} +4.87866 q^{43} -11.5850 q^{44} +20.9021 q^{45} +6.60516 q^{46} +12.9124 q^{47} -11.0633 q^{48} -4.34896 q^{49} -31.2774 q^{50} -11.7936 q^{51} +4.05229 q^{52} -10.4825 q^{53} +13.5047 q^{54} -12.2532 q^{55} +7.91603 q^{56} +13.4498 q^{57} +9.77397 q^{58} -5.91709 q^{59} -47.4253 q^{60} -2.95503 q^{61} -9.96751 q^{62} -8.07045 q^{63} -8.15480 q^{64} +4.28604 q^{65} -20.0549 q^{66} -10.5154 q^{67} +16.6696 q^{68} +7.61456 q^{69} +16.8001 q^{70} -0.749186 q^{71} -24.0984 q^{72} +1.56079 q^{73} -5.47653 q^{74} -36.0571 q^{75} -19.0105 q^{76} +4.73106 q^{77} +7.01497 q^{78} -8.24644 q^{79} +16.5393 q^{80} +0.698525 q^{81} +12.0743 q^{82} +6.54933 q^{83} +18.3113 q^{84} +17.6312 q^{85} -11.9373 q^{86} +11.2676 q^{87} +14.1270 q^{88} -2.97383 q^{89} -51.1439 q^{90} -1.65487 q^{91} -10.7628 q^{92} -11.4907 q^{93} -31.5946 q^{94} -20.1071 q^{95} -0.358083 q^{96} +4.94076 q^{97} +10.6412 q^{98} -14.4026 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.44683	−1.73017	−0.865086	−	0.501624i	$-0.832736\pi$
$2$	−2.44683	−1.73017	−0.865086	+	0.501624i	$0.832736\pi$
$3$	−2.82076	−1.62856	−0.814282	−	0.580469i	$-0.802869\pi$
$3$	−2.82076	−1.62856	−0.814282	+	0.580469i	$0.802869\pi$
$4$	3.98699	1.99349
$5$	4.21697	1.88588	0.942942	−	0.332957i	$-0.108046\pi$
$5$	4.21697	1.88588	0.942942	+	0.332957i	$0.108046\pi$
$6$	6.90192	2.81770
$7$	−1.62820	−0.615402	−0.307701	−	0.951483i	$-0.599560\pi$
$7$	−1.62820	−0.615402	−0.307701	+	0.951483i	$0.599560\pi$
$8$	−4.86182	−1.71891
$9$	4.95666	1.65222
$10$	−10.3182	−3.26290
$11$	−2.90570	−0.876101	−0.438050	−	0.898950i	$-0.644331\pi$
$11$	−2.90570	−0.876101	−0.438050	+	0.898950i	$0.644331\pi$
$12$	−11.2463	−3.24653
$13$	1.01638	0.281893	0.140947	−	0.990017i	$-0.454985\pi$
$13$	1.01638	0.281893	0.140947	+	0.990017i	$0.454985\pi$
$14$	3.98394	1.06475
$15$	−11.8950	−3.07128
$16$	3.92209	0.980523
$17$	4.18101	1.01404	0.507022	−	0.861933i	$-0.330746\pi$
$17$	4.18101	1.01404	0.507022	+	0.861933i	$0.330746\pi$
$18$	−12.1281	−2.85863
$19$	−4.76814	−1.09389	−0.546944	−	0.837169i	$-0.684209\pi$
$19$	−4.76814	−1.09389	−0.546944	+	0.837169i	$0.684209\pi$
$20$	16.8130	3.75950
$21$	4.59276	1.00222
$22$	7.10975	1.51580
$23$	−2.69947	−0.562879	−0.281440	−	0.959579i	$-0.590812\pi$
$23$	−2.69947	−0.562879	−0.281440	+	0.959579i	$0.590812\pi$
$24$	13.7140	2.79936
$25$	12.7828	2.55656
$26$	−2.48691	−0.487723
$27$	−5.51927	−1.06218
$28$	−6.49162	−1.22680
$29$	−3.99454	−0.741768	−0.370884	−	0.928679i	$-0.620945\pi$
$29$	−3.99454	−0.741768	−0.370884	+	0.928679i	$0.620945\pi$
$30$	29.1051	5.31385
$31$	4.07364	0.731647	0.365823	−	0.930684i	$-0.380787\pi$
$31$	4.07364	0.731647	0.365823	+	0.930684i	$0.380787\pi$
$32$	0.126946	0.0224410
$33$	8.19626	1.42679
$34$	−10.2302	−1.75447
$35$	−6.86607	−1.16058
$36$	19.7622	3.29369
$37$	2.23821	0.367960	0.183980	−	0.982930i	$-0.441102\pi$
$37$	2.23821	0.367960	0.183980	+	0.982930i	$0.441102\pi$
$38$	11.6668	1.89261
$39$	−2.86696	−0.459081
$40$	−20.5021	−3.24167
$41$	−4.93466	−0.770665	−0.385333	−	0.922778i	$-0.625913\pi$
$41$	−4.93466	−0.770665	−0.385333	+	0.922778i	$0.625913\pi$
$42$	−11.2377	−1.73402
$43$	4.87866	0.743989	0.371994	−	0.928235i	$-0.378674\pi$
$43$	4.87866	0.743989	0.371994	+	0.928235i	$0.378674\pi$
$44$	−11.5850	−1.74650
$45$	20.9021	3.11590
$46$	6.60516	0.973877
$47$	12.9124	1.88347	0.941736	−	0.336352i	$-0.109193\pi$
$47$	12.9124	1.88347	0.941736	+	0.336352i	$0.109193\pi$
$48$	−11.0633	−1.59684
$49$	−4.34896	−0.621280
$50$	−31.2774	−4.42329
$51$	−11.7936	−1.65144
$52$	4.05229	0.561952
$53$	−10.4825	−1.43988	−0.719941	−	0.694035i	$-0.755831\pi$
$53$	−10.4825	−1.43988	−0.719941	+	0.694035i	$0.755831\pi$
$54$	13.5047	1.83776
$55$	−12.2532	−1.65222
$56$	7.91603	1.05782
$57$	13.4498	1.78147
$58$	9.77397	1.28339
$59$	−5.91709	−0.770340	−0.385170	−	0.922846i	$-0.625857\pi$
$59$	−5.91709	−0.770340	−0.385170	+	0.922846i	$0.625857\pi$
$60$	−47.4253	−6.12258
$61$	−2.95503	−0.378352	−0.189176	−	0.981943i	$-0.560582\pi$
$61$	−2.95503	−0.378352	−0.189176	+	0.981943i	$0.560582\pi$
$62$	−9.96751	−1.26587
$63$	−8.07045	−1.01678
$64$	−8.15480	−1.01935
$65$	4.28604	0.531618
$66$	−20.0549	−2.46859
$67$	−10.5154	−1.28465	−0.642327	−	0.766430i	$-0.722031\pi$
$67$	−10.5154	−1.28465	−0.642327	+	0.766430i	$0.722031\pi$
$68$	16.6696	2.02149
$69$	7.61456	0.916685
$70$	16.8001	2.00800
$71$	−0.749186	−0.0889120	−0.0444560	−	0.999011i	$-0.514155\pi$
$71$	−0.749186	−0.0889120	−0.0444560	+	0.999011i	$0.514155\pi$
$72$	−24.0984	−2.84003
$73$	1.56079	0.182677	0.0913384	−	0.995820i	$-0.470885\pi$
$73$	1.56079	0.182677	0.0913384	+	0.995820i	$0.470885\pi$
$74$	−5.47653	−0.636634
$75$	−36.0571	−4.16352
$76$	−19.0105	−2.18066
$77$	4.73106	0.539155
$78$	7.01497	0.794289
$79$	−8.24644	−0.927797	−0.463899	−	0.885888i	$-0.653550\pi$
$79$	−8.24644	−0.927797	−0.463899	+	0.885888i	$0.653550\pi$
$80$	16.5393	1.84915
$81$	0.698525	0.0776139
$82$	12.0743	1.33338
$83$	6.54933	0.718883	0.359441	−	0.933168i	$-0.382967\pi$
$83$	6.54933	0.718883	0.359441	+	0.933168i	$0.382967\pi$
$84$	18.3113	1.99792
$85$	17.6312	1.91237
$86$	−11.9373	−1.28723
$87$	11.2676	1.20802
$88$	14.1270	1.50594
$89$	−2.97383	−0.315225	−0.157613	−	0.987501i	$-0.550380\pi$
$89$	−2.97383	−0.315225	−0.157613	+	0.987501i	$0.550380\pi$
$90$	−51.1439	−5.39104
$91$	−1.65487	−0.173478
$92$	−10.7628	−1.12210
$93$	−11.4907	−1.19153
$94$	−31.5946	−3.25873
$95$	−20.1071	−2.06294
$96$	−0.358083	−0.0365467
$97$	4.94076	0.501659	0.250829	−	0.968031i	$-0.419297\pi$
$97$	4.94076	0.501659	0.250829	+	0.968031i	$0.419297\pi$
$98$	10.6412	1.07492
$99$	−14.4026	−1.44751
$100$	50.9648	5.09648
$101$	−4.89836	−0.487405	−0.243702	−	0.969850i	$-0.578362\pi$
$101$	−4.89836	−0.487405	−0.243702	+	0.969850i	$0.578362\pi$
$102$	28.8570	2.85727
$103$	−9.71538	−0.957285	−0.478642	−	0.878010i	$-0.658871\pi$
$103$	−9.71538	−0.957285	−0.478642	+	0.878010i	$0.658871\pi$
$104$	−4.94146	−0.484550
$105$	19.3675	1.89008
$106$	25.6489	2.49124
$107$	−6.53958	−0.632205	−0.316103	−	0.948725i	$-0.602374\pi$
$107$	−6.53958	−0.632205	−0.316103	+	0.948725i	$0.602374\pi$
$108$	−22.0053	−2.11746
$109$	16.0317	1.53556	0.767778	−	0.640717i	$-0.221363\pi$
$109$	16.0317	1.53556	0.767778	+	0.640717i	$0.221363\pi$
$110$	29.9816	2.85863
$111$	−6.31346	−0.599247
$112$	−6.38596	−0.603416
$113$	−13.9016	−1.30775	−0.653876	−	0.756602i	$-0.726858\pi$
$113$	−13.9016	−1.30775	−0.653876	+	0.756602i	$0.726858\pi$
$114$	−32.9093	−3.08224
$115$	−11.3836	−1.06152
$116$	−15.9262	−1.47871
$117$	5.03785	0.465750
$118$	14.4781	1.33282
$119$	−6.80753	−0.624045
$120$	57.8315	5.27927
$121$	−2.55692	−0.232447
$122$	7.23046	0.654615
$123$	13.9195	1.25508
$124$	16.2415	1.45853
$125$	32.8198	2.93549
$126$	19.7470	1.75921
$127$	21.0857	1.87105	0.935525	−	0.353260i	$-0.114927\pi$
$127$	21.0857	1.87105	0.935525	+	0.353260i	$0.114927\pi$
$128$	19.6995	1.74121
$129$	−13.7615	−1.21163
$130$	−10.4872	−0.919790
$131$	15.8200	1.38220	0.691099	−	0.722760i	$-0.257127\pi$
$131$	15.8200	1.38220	0.691099	+	0.722760i	$0.257127\pi$
$132$	32.6784	2.84429
$133$	7.76350	0.673181
$134$	25.7293	2.22267
$135$	−23.2746	−2.00316
$136$	−20.3273	−1.74305
$137$	−10.5486	−0.901227	−0.450614	−	0.892719i	$-0.648795\pi$
$137$	−10.5486	−0.901227	−0.450614	+	0.892719i	$0.648795\pi$
$138$	−18.6315	−1.58602
$139$	−0.889216	−0.0754223	−0.0377111	−	0.999289i	$-0.512007\pi$
$139$	−0.889216	−0.0754223	−0.0377111	+	0.999289i	$0.512007\pi$
$140$	−27.3749	−2.31360
$141$	−36.4228	−3.06736
$142$	1.83313	0.153833
$143$	−2.95329	−0.246967
$144$	19.4405	1.62004
$145$	−16.8448	−1.39889
$146$	−3.81900	−0.316062
$147$	12.2674	1.01179
$148$	8.92373	0.733526
$149$	4.07234	0.333619	0.166810	−	0.985989i	$-0.446653\pi$
$149$	4.07234	0.333619	0.166810	+	0.985989i	$0.446653\pi$
$150$	88.2258	7.20360
$151$	4.60002	0.374344	0.187172	−	0.982327i	$-0.440068\pi$
$151$	4.60002	0.374344	0.187172	+	0.982327i	$0.440068\pi$
$152$	23.1819	1.88030
$153$	20.7239	1.67542
$154$	−11.5761	−0.932830
$155$	17.1784	1.37980
$156$	−11.4305	−0.915175
$157$	19.8221	1.58197	0.790987	−	0.611833i	$-0.209568\pi$
$157$	19.8221	1.58197	0.790987	+	0.611833i	$0.209568\pi$
$158$	20.1777	1.60525
$159$	29.5686	2.34494
$160$	0.535325	0.0423212
$161$	4.39529	0.346397
$162$	−1.70917	−0.134285
$163$	−17.5203	−1.37229	−0.686147	−	0.727463i	$-0.740699\pi$
$163$	−17.5203	−1.37229	−0.686147	+	0.727463i	$0.740699\pi$
$164$	−19.6744	−1.53632
$165$	34.5634	2.69075
$166$	−16.0251	−1.24379
$167$	−13.0981	−1.01356	−0.506782	−	0.862074i	$-0.669165\pi$
$167$	−13.0981	−1.01356	−0.506782	+	0.862074i	$0.669165\pi$
$168$	−22.3292	−1.72273
$169$	−11.9670	−0.920536
$170$	−43.1405	−3.30873
$171$	−23.6341	−1.80734
$172$	19.4512	1.48314
$173$	17.5937	1.33762	0.668812	−	0.743431i	$-0.266803\pi$
$173$	17.5937	1.33762	0.668812	+	0.743431i	$0.266803\pi$
$174$	−27.5700	−2.09008
$175$	−20.8130	−1.57331
$176$	−11.3964	−0.859037
$177$	16.6907	1.25455
$178$	7.27646	0.545394
$179$	9.24355	0.690895	0.345448	−	0.938438i	$-0.387727\pi$
$179$	9.24355	0.690895	0.345448	+	0.938438i	$0.387727\pi$
$180$	83.3363	6.21152
$181$	3.15308	0.234366	0.117183	−	0.993110i	$-0.462614\pi$
$181$	3.15308	0.234366	0.117183	+	0.993110i	$0.462614\pi$
$182$	4.04919	0.300146
$183$	8.33541	0.616171
$184$	13.1244	0.967541
$185$	9.43847	0.693930
$186$	28.1159	2.06156
$187$	−12.1487	−0.888405
$188$	51.4817	3.75469
$189$	8.98649	0.653671
$190$	49.1987	3.56925
$191$	−2.00030	−0.144737	−0.0723684	−	0.997378i	$-0.523056\pi$
$191$	−2.00030	−0.144737	−0.0723684	+	0.997378i	$0.523056\pi$
$192$	23.0027	1.66008
$193$	−14.8894	−1.07176	−0.535881	−	0.844294i	$-0.680020\pi$
$193$	−14.8894	−1.07176	−0.535881	+	0.844294i	$0.680020\pi$
$194$	−12.0892	−0.867955
$195$	−12.0899	−0.865774
$196$	−17.3392	−1.23852
$197$	19.1274	1.36277	0.681384	−	0.731926i	$-0.261379\pi$
$197$	19.1274	1.36277	0.681384	+	0.731926i	$0.261379\pi$
$198$	35.2407	2.50444
$199$	−26.4725	−1.87659	−0.938293	−	0.345840i	$-0.887594\pi$
$199$	−26.4725	−1.87659	−0.938293	+	0.345840i	$0.887594\pi$
$200$	−62.1477	−4.39451
$201$	29.6612	2.09214
$202$	11.9855	0.843293
$203$	6.50392	0.456486
$204$	−47.0210	−3.29213
$205$	−20.8093	−1.45338
$206$	23.7719	1.65627
$207$	−13.3804	−0.930001
$208$	3.98634	0.276403
$209$	13.8548	0.958356
$210$	−47.3890	−3.27015
$211$	0.834879	0.0574755	0.0287377	−	0.999587i	$-0.490851\pi$
$211$	0.834879	0.0574755	0.0287377	+	0.999587i	$0.490851\pi$
$212$	−41.7936	−2.87039
$213$	2.11327	0.144799
$214$	16.0013	1.09382
$215$	20.5731	1.40308
$216$	26.8337	1.82580
$217$	−6.63270	−0.450257
$218$	−39.2268	−2.65677
$219$	−4.40261	−0.297501
$220$	−48.8535	−3.29370
$221$	4.24949	0.285852
$222$	15.4480	1.03680
$223$	−19.9604	−1.33665	−0.668323	−	0.743871i	$-0.732988\pi$
$223$	−19.9604	−1.33665	−0.668323	+	0.743871i	$0.732988\pi$
$224$	−0.206693	−0.0138103
$225$	63.3600	4.22400
$226$	34.0149	2.26264
$227$	13.7414	0.912051	0.456025	−	0.889967i	$-0.349273\pi$
$227$	13.7414	0.912051	0.456025	+	0.889967i	$0.349273\pi$
$228$	53.6241	3.55134
$229$	−14.7968	−0.977800	−0.488900	−	0.872340i	$-0.662602\pi$
$229$	−14.7968	−0.977800	−0.488900	+	0.872340i	$0.662602\pi$
$230$	27.8537	1.83662
$231$	−13.3452	−0.878048
$232$	19.4208	1.27504
$233$	−14.9344	−0.978386	−0.489193	−	0.872176i	$-0.662709\pi$
$233$	−14.9344	−0.978386	−0.489193	+	0.872176i	$0.662709\pi$
$234$	−12.3268	−0.805827
$235$	54.4513	3.55201
$236$	−23.5914	−1.53567
$237$	23.2612	1.51098
$238$	16.6569	1.07970
$239$	−11.3078	−0.731440	−0.365720	−	0.930725i	$-0.619177\pi$
$239$	−11.3078	−0.731440	−0.365720	+	0.930725i	$0.619177\pi$
$240$	−46.6534	−3.01146
$241$	−21.0177	−1.35387	−0.676933	−	0.736044i	$-0.736692\pi$
$241$	−21.0177	−1.35387	−0.676933	+	0.736044i	$0.736692\pi$
$242$	6.25636	0.402174
$243$	14.5874	0.935785
$244$	−11.7817	−0.754243
$245$	−18.3394	−1.17166
$246$	−34.0586	−2.17150
$247$	−4.84625	−0.308359
$248$	−19.8053	−1.25764
$249$	−18.4741	−1.17075
$250$	−80.3045	−5.07890
$251$	16.1410	1.01881	0.509405	−	0.860527i	$-0.329866\pi$
$251$	16.1410	1.01881	0.509405	+	0.860527i	$0.329866\pi$
$252$	−32.1768	−2.02695
$253$	7.84385	0.493139
$254$	−51.5931	−3.23724
$255$	−49.7332	−3.11442
$256$	−31.8919	−1.99324
$257$	5.32541	0.332190	0.166095	−	0.986110i	$-0.446884\pi$
$257$	5.32541	0.332190	0.166095	+	0.986110i	$0.446884\pi$
$258$	33.6721	2.09633
$259$	−3.64426	−0.226444
$260$	17.0884	1.05978
$261$	−19.7996	−1.22556
$262$	−38.7088	−2.39144
$263$	15.9596	0.984108	0.492054	−	0.870565i	$-0.336246\pi$
$263$	15.9596	0.984108	0.492054	+	0.870565i	$0.336246\pi$
$264$	−39.8488	−2.45252
$265$	−44.2043	−2.71545
$266$	−18.9960	−1.16472
$267$	8.38845	0.513365
$268$	−41.9246	−2.56095
$269$	−0.339374	−0.0206920	−0.0103460	−	0.999946i	$-0.503293\pi$
$269$	−0.339374	−0.0206920	−0.0103460	+	0.999946i	$0.503293\pi$
$270$	56.9490	3.46580
$271$	4.98333	0.302716	0.151358	−	0.988479i	$-0.451635\pi$
$271$	4.98333	0.302716	0.151358	+	0.988479i	$0.451635\pi$
$272$	16.3983	0.994293
$273$	4.66799	0.282520
$274$	25.8106	1.55928
$275$	−37.1429	−2.23980
$276$	30.3591	1.82741
$277$	0.532529	0.0319966	0.0159983	−	0.999872i	$-0.494907\pi$
$277$	0.532529	0.0319966	0.0159983	+	0.999872i	$0.494907\pi$
$278$	2.17576	0.130494
$279$	20.1916	1.20884
$280$	33.3816	1.99493
$281$	−12.0344	−0.717911	−0.358956	−	0.933355i	$-0.616867\pi$
$281$	−12.0344	−0.717911	−0.358956	+	0.933355i	$0.616867\pi$
$282$	89.1206	5.30705
$283$	−4.58935	−0.272809	−0.136404	−	0.990653i	$-0.543555\pi$
$283$	−4.58935	−0.272809	−0.136404	+	0.990653i	$0.543555\pi$
$284$	−2.98699	−0.177245
$285$	56.7172	3.35964
$286$	7.22621	0.427295
$287$	8.03463	0.474269
$288$	0.629227	0.0370776
$289$	0.480840	0.0282847
$290$	41.2165	2.42032
$291$	−13.9367	−0.816983
$292$	6.22286	0.364165
$293$	1.84623	0.107858	0.0539290	−	0.998545i	$-0.482826\pi$
$293$	1.84623	0.107858	0.0539290	+	0.998545i	$0.482826\pi$
$294$	−30.0161	−1.75058
$295$	−24.9522	−1.45277
$296$	−10.8818	−0.632492
$297$	16.0373	0.930580
$298$	−9.96433	−0.577218
$299$	−2.74369	−0.158672
$300$	−143.759	−8.29995
$301$	−7.94344	−0.457852
$302$	−11.2555	−0.647680
$303$	13.8171	0.793770
$304$	−18.7011	−1.07258
$305$	−12.4612	−0.713529
$306$	−50.7078	−2.89877
$307$	−23.7289	−1.35428	−0.677139	−	0.735855i	$-0.736780\pi$
$307$	−23.7289	−1.35428	−0.677139	+	0.735855i	$0.736780\pi$
$308$	18.8627	1.07480
$309$	27.4047	1.55900
$310$	−42.0326	−2.38729
$311$	21.7923	1.23573	0.617864	−	0.786285i	$-0.287998\pi$
$311$	21.7923	1.23573	0.617864	+	0.786285i	$0.287998\pi$
$312$	13.9387	0.789121
$313$	15.5710	0.880123	0.440061	−	0.897968i	$-0.354957\pi$
$313$	15.5710	0.880123	0.440061	+	0.897968i	$0.354957\pi$
$314$	−48.5013	−2.73709
$315$	−34.0328	−1.91753
$316$	−32.8785	−1.84956
$317$	−4.34508	−0.244044	−0.122022	−	0.992527i	$-0.538938\pi$
$317$	−4.34508	−0.244044	−0.122022	+	0.992527i	$0.538938\pi$
$318$	−72.3493	−4.05715
$319$	11.6069	0.649863
$320$	−34.3885	−1.92238
$321$	18.4466	1.02959
$322$	−10.7545	−0.599327
$323$	−19.9357	−1.10925
$324$	2.78501	0.154723
$325$	12.9922	0.720676
$326$	42.8692	2.37430
$327$	−45.2214	−2.50075
$328$	23.9915	1.32471
$329$	−21.0241	−1.15909
$330$	−84.5707	−4.65547
$331$	−26.7280	−1.46910	−0.734552	−	0.678553i	$-0.762607\pi$
$331$	−26.7280	−1.46910	−0.734552	+	0.678553i	$0.762607\pi$
$332$	26.1121	1.43309
$333$	11.0941	0.607952
$334$	32.0490	1.75364
$335$	−44.3429	−2.42271
$336$	18.0132	0.982702
$337$	14.5860	0.794549	0.397274	−	0.917700i	$-0.369956\pi$
$337$	14.5860	0.794549	0.397274	+	0.917700i	$0.369956\pi$
$338$	29.2812	1.59269
$339$	39.2130	2.12976
$340$	70.2953	3.81230
$341$	−11.8368	−0.640996
$342$	57.8286	3.12702
$343$	18.4784	0.997740
$344$	−23.7192	−1.27885
$345$	32.1103	1.72876
$346$	−43.0488	−2.31432
$347$	−22.6558	−1.21623	−0.608113	−	0.793850i	$-0.708073\pi$
$347$	−22.6558	−1.21623	−0.608113	+	0.793850i	$0.708073\pi$
$348$	44.9239	2.40817
$349$	33.1899	1.77661	0.888306	−	0.459251i	$-0.151882\pi$
$349$	33.1899	1.77661	0.888306	+	0.459251i	$0.151882\pi$
$350$	50.9258	2.72210
$351$	−5.60968	−0.299422
$352$	−0.368866	−0.0196606
$353$	−20.4666	−1.08933	−0.544664	−	0.838654i	$-0.683343\pi$
$353$	−20.4666	−1.08933	−0.544664	+	0.838654i	$0.683343\pi$
$354$	−40.8393	−2.17058
$355$	−3.15929	−0.167678
$356$	−11.8566	−0.628400
$357$	19.2024	1.01630
$358$	−22.6174	−1.19537
$359$	2.74540	0.144897	0.0724484	−	0.997372i	$-0.476919\pi$
$359$	2.74540	0.144897	0.0724484	+	0.997372i	$0.476919\pi$
$360$	−101.622	−5.35596
$361$	3.73520	0.196590
$362$	−7.71505	−0.405494
$363$	7.21245	0.378555
$364$	−6.59795	−0.345827
$365$	6.58181	0.344507
$366$	−20.3954	−1.06608
$367$	−29.5257	−1.54123	−0.770614	−	0.637302i	$-0.780050\pi$
$367$	−29.5257	−1.54123	−0.770614	+	0.637302i	$0.780050\pi$
$368$	−10.5876	−0.551916
$369$	−24.4595	−1.27331
$370$	−23.0944	−1.20062
$371$	17.0676	0.886107
$372$	−45.8134	−2.37531
$373$	6.76740	0.350403	0.175201	−	0.984533i	$-0.443942\pi$
$373$	6.76740	0.350403	0.175201	+	0.984533i	$0.443942\pi$
$374$	29.7260	1.53709
$375$	−92.5766	−4.78063
$376$	−62.7780	−3.23753
$377$	−4.05997	−0.209099
$378$	−21.9884	−1.13096
$379$	−21.6553	−1.11236	−0.556178	−	0.831063i	$-0.687733\pi$
$379$	−21.6553	−1.11236	−0.556178	+	0.831063i	$0.687733\pi$
$380$	−80.1668	−4.11247
$381$	−59.4775	−3.04713
$382$	4.89441	0.250420
$383$	26.0462	1.33090	0.665448	−	0.746444i	$-0.268240\pi$
$383$	26.0462	1.33090	0.665448	+	0.746444i	$0.268240\pi$
$384$	−55.5676	−2.83567
$385$	19.9507	1.01678
$386$	36.4318	1.85433
$387$	24.1819	1.22923
$388$	19.6988	1.00005
$389$	−19.6243	−0.994991	−0.497496	−	0.867467i	$-0.665747\pi$
$389$	−19.6243	−0.994991	−0.497496	+	0.867467i	$0.665747\pi$
$390$	29.5819	1.49794
$391$	−11.2865	−0.570784
$392$	21.1439	1.06793
$393$	−44.6243	−2.25100
$394$	−46.8014	−2.35782
$395$	−34.7750	−1.74972
$396$	−57.4229	−2.88561
$397$	33.4742	1.68002	0.840011	−	0.542570i	$-0.182549\pi$
$397$	33.4742	1.68002	0.840011	+	0.542570i	$0.182549\pi$
$398$	64.7738	3.24682
$399$	−21.8989	−1.09632
$400$	50.1353	2.50677
$401$	9.14779	0.456819	0.228409	−	0.973565i	$-0.426648\pi$
$401$	9.14779	0.456819	0.228409	+	0.973565i	$0.426648\pi$
$402$	−72.5761	−3.61977
$403$	4.14036	0.206246
$404$	−19.5297	−0.971638
$405$	2.94566	0.146371
$406$	−15.9140	−0.789799
$407$	−6.50357	−0.322370
$408$	57.3384	2.83868
$409$	−20.1053	−0.994144	−0.497072	−	0.867709i	$-0.665592\pi$
$409$	−20.1053	−0.994144	−0.497072	+	0.867709i	$0.665592\pi$
$410$	50.9169	2.51461
$411$	29.7550	1.46771
$412$	−38.7351	−1.90834
$413$	9.63422	0.474069
$414$	32.7395	1.60906
$415$	27.6183	1.35573
$416$	0.129025	0.00632597
$417$	2.50826	0.122830
$418$	−33.9003	−1.65812
$419$	−32.0227	−1.56441	−0.782207	−	0.623019i	$-0.785906\pi$
$419$	−32.0227	−1.56441	−0.782207	+	0.623019i	$0.785906\pi$
$420$	77.2180	3.76785
$421$	−3.69037	−0.179858	−0.0899289	−	0.995948i	$-0.528664\pi$
$421$	−3.69037	−0.179858	−0.0899289	+	0.995948i	$0.528664\pi$
$422$	−2.04281	−0.0994424
$423$	64.0026	3.11191
$424$	50.9641	2.47503
$425$	53.4450	2.59246
$426$	−5.17082	−0.250527
$427$	4.81138	0.232839
$428$	−26.0732	−1.26030
$429$	8.33052	0.402201
$430$	−50.3390	−2.42756
$431$	21.6196	1.04138	0.520690	−	0.853746i	$-0.325675\pi$
$431$	21.6196	1.04138	0.520690	+	0.853746i	$0.325675\pi$
$432$	−21.6471	−1.04150
$433$	17.5363	0.842741	0.421371	−	0.906888i	$-0.361549\pi$
$433$	17.5363	0.842741	0.421371	+	0.906888i	$0.361549\pi$
$434$	16.2291	0.779022
$435$	47.5152	2.27818
$436$	63.9180	3.06112
$437$	12.8715	0.615726
$438$	10.7725	0.514728
$439$	15.3280	0.731566	0.365783	−	0.930700i	$-0.380801\pi$
$439$	15.3280	0.731566	0.365783	+	0.930700i	$0.380801\pi$
$440$	59.5730	2.84003
$441$	−21.5563	−1.02649
$442$	−10.3978	−0.494573
$443$	5.69141	0.270407	0.135203	−	0.990818i	$-0.456831\pi$
$443$	5.69141	0.270407	0.135203	+	0.990818i	$0.456831\pi$
$444$	−25.1717	−1.19459
$445$	−12.5405	−0.594478
$446$	48.8397	2.31263
$447$	−11.4871	−0.543320
$448$	13.2777	0.627311
$449$	8.55759	0.403858	0.201929	−	0.979400i	$-0.435279\pi$
$449$	8.55759	0.403858	0.201929	+	0.979400i	$0.435279\pi$
$450$	−155.031	−7.30825
$451$	14.3386	0.675180
$452$	−55.4255	−2.60700
$453$	−12.9755	−0.609644
$454$	−33.6230	−1.57800
$455$	−6.97854	−0.327159
$456$	−65.3904	−3.06219
$457$	−8.37124	−0.391590	−0.195795	−	0.980645i	$-0.562729\pi$
$457$	−8.37124	−0.391590	−0.195795	+	0.980645i	$0.562729\pi$
$458$	36.2053	1.69176
$459$	−23.0761	−1.07710
$460$	−45.3862	−2.11614
$461$	23.7037	1.10399	0.551997	−	0.833846i	$-0.313866\pi$
$461$	23.7037	1.10399	0.551997	+	0.833846i	$0.313866\pi$
$462$	32.6534	1.51917
$463$	−40.8832	−1.90001	−0.950003	−	0.312242i	$-0.898920\pi$
$463$	−40.8832	−1.90001	−0.950003	+	0.312242i	$0.898920\pi$
$464$	−15.6670	−0.727321
$465$	−48.4560	−2.24709
$466$	36.5420	1.69278
$467$	12.4467	0.575965	0.287983	−	0.957636i	$-0.407015\pi$
$467$	12.4467	0.575965	0.287983	+	0.957636i	$0.407015\pi$
$468$	20.0859	0.928469
$469$	17.1211	0.790580
$470$	−133.233	−6.14559
$471$	−55.9132	−2.57635
$472$	28.7679	1.32415
$473$	−14.1759	−0.651809
$474$	−56.9163	−2.61425
$475$	−60.9502	−2.79659
$476$	−27.1415	−1.24403
$477$	−51.9582	−2.37900
$478$	27.6683	1.26552
$479$	−14.7077	−0.672010	−0.336005	−	0.941860i	$-0.609076\pi$
$479$	−14.7077	−0.672010	−0.336005	+	0.941860i	$0.609076\pi$
$480$	−1.51002	−0.0689228
$481$	2.27488	0.103725
$482$	51.4267	2.34242
$483$	−12.3980	−0.564130
$484$	−10.1944	−0.463382
$485$	20.8350	0.946070
$486$	−35.6930	−1.61907
$487$	−42.0511	−1.90552	−0.952758	−	0.303729i	$-0.901768\pi$
$487$	−42.0511	−1.90552	−0.952758	+	0.303729i	$0.901768\pi$
$488$	14.3668	0.650356
$489$	49.4204	2.23487
$490$	44.8734	2.02718
$491$	25.6833	1.15907	0.579534	−	0.814948i	$-0.303234\pi$
$491$	25.6833	1.15907	0.579534	+	0.814948i	$0.303234\pi$
$492$	55.4968	2.50199
$493$	−16.7012	−0.752185
$494$	11.8580	0.533514
$495$	−60.7351	−2.72984
$496$	15.9772	0.717397
$497$	1.21983	0.0547166
$498$	45.2029	2.02559
$499$	−20.6881	−0.926127	−0.463064	−	0.886325i	$-0.653250\pi$
$499$	−20.6881	−0.926127	−0.463064	+	0.886325i	$0.653250\pi$
$500$	130.852	5.85188
$501$	36.9467	1.65066
$502$	−39.4943	−1.76272
$503$	8.35285	0.372435	0.186218	−	0.982509i	$-0.440377\pi$
$503$	8.35285	0.372435	0.186218	+	0.982509i	$0.440377\pi$
$504$	39.2371	1.74776
$505$	−20.6562	−0.919188
$506$	−19.1926	−0.853215
$507$	33.7559	1.49915
$508$	84.0683	3.72993
$509$	−20.1247	−0.892013	−0.446007	−	0.895030i	$-0.647154\pi$
$509$	−20.1247	−0.892013	−0.446007	+	0.895030i	$0.647154\pi$
$510$	121.689	5.38847
$511$	−2.54128	−0.112420
$512$	38.6349	1.70744
$513$	26.3167	1.16191
$514$	−13.0304	−0.574746
$515$	−40.9694	−1.80533
$516$	−54.8670	−2.41538
$517$	−37.5196	−1.65011
$518$	8.91690	0.391786
$519$	−49.6275	−2.17841
$520$	−20.8380	−0.913805
$521$	−39.5014	−1.73059	−0.865294	−	0.501264i	$-0.832869\pi$
$521$	−39.5014	−1.73059	−0.865294	+	0.501264i	$0.832869\pi$
$522$	48.4463	2.12044
$523$	−21.6274	−0.945702	−0.472851	−	0.881142i	$-0.656775\pi$
$523$	−21.6274	−0.945702	−0.472851	+	0.881142i	$0.656775\pi$
$524$	63.0741	2.75540
$525$	58.7083	2.56224
$526$	−39.0503	−1.70268
$527$	17.0319	0.741922
$528$	32.1465	1.39900
$529$	−15.7128	−0.683167
$530$	108.161	4.69819
$531$	−29.3290	−1.27277
$532$	30.9530	1.34198
$533$	−5.01549	−0.217245
$534$	−20.5251	−0.888209
$535$	−27.5772	−1.19227
$536$	51.1238	2.20821
$537$	−26.0738	−1.12517
$538$	0.830392	0.0358007
$539$	12.6368	0.544304
$540$	−92.7954	−3.99328
$541$	−26.7541	−1.15025	−0.575125	−	0.818066i	$-0.695046\pi$
$541$	−26.7541	−1.15025	−0.575125	+	0.818066i	$0.695046\pi$
$542$	−12.1934	−0.523750
$543$	−8.89406	−0.381681
$544$	0.530761	0.0227562
$545$	67.6050	2.89588
$546$	−11.4218	−0.488807
$547$	−26.8417	−1.14767	−0.573835	−	0.818971i	$-0.694545\pi$
$547$	−26.8417	−1.14767	−0.573835	+	0.818971i	$0.694545\pi$
$548$	−42.0571	−1.79659
$549$	−14.6471	−0.625122
$550$	90.8825	3.87524
$551$	19.0466	0.811410
$552$	−37.0206	−1.57570
$553$	13.4269	0.570969
$554$	−1.30301	−0.0553595
$555$	−26.6236	−1.13011
$556$	−3.54529	−0.150354
$557$	−23.2458	−0.984955	−0.492477	−	0.870325i	$-0.663909\pi$
$557$	−23.2458	−0.984955	−0.492477	+	0.870325i	$0.663909\pi$
$558$	−49.4056	−2.09150
$559$	4.95857	0.209725
$560$	−26.9294	−1.13797
$561$	34.2687	1.44682
$562$	29.4461	1.24211
$563$	0.549515	0.0231593	0.0115796	−	0.999933i	$-0.496314\pi$
$563$	0.549515	0.0231593	0.0115796	+	0.999933i	$0.496314\pi$
$564$	−145.217	−6.11475
$565$	−58.6225	−2.46627
$566$	11.2294	0.472006
$567$	−1.13734	−0.0477638
$568$	3.64241	0.152832
$569$	21.4019	0.897214	0.448607	−	0.893729i	$-0.351920\pi$
$569$	21.4019	0.897214	0.448607	+	0.893729i	$0.351920\pi$
$570$	−138.778	−5.81275
$571$	−4.04438	−0.169252	−0.0846259	−	0.996413i	$-0.526970\pi$
$571$	−4.04438	−0.169252	−0.0846259	+	0.996413i	$0.526970\pi$
$572$	−11.7747	−0.492327
$573$	5.64237	0.235713
$574$	−19.6594	−0.820567
$575$	−34.5068	−1.43903
$576$	−40.4206	−1.68419
$577$	21.2616	0.885134	0.442567	−	0.896735i	$-0.354068\pi$
$577$	21.2616	0.885134	0.442567	+	0.896735i	$0.354068\pi$
$578$	−1.17654	−0.0489374
$579$	41.9993	1.74543
$580$	−67.1602	−2.78867
$581$	−10.6636	−0.442402
$582$	34.1007	1.41352
$583$	30.4590	1.26148
$584$	−7.58830	−0.314006
$585$	21.2445	0.878350
$586$	−4.51742	−0.186613
$587$	29.8455	1.23186	0.615928	−	0.787802i	$-0.288781\pi$
$587$	29.8455	1.23186	0.615928	+	0.787802i	$0.288781\pi$
$588$	48.9098	2.01700
$589$	−19.4237	−0.800339
$590$	61.0538	2.51355
$591$	−53.9536	−2.21935
$592$	8.77848	0.360793
$593$	24.2935	0.997614	0.498807	−	0.866713i	$-0.333772\pi$
$593$	24.2935	0.997614	0.498807	+	0.866713i	$0.333772\pi$
$594$	−39.2407	−1.61006
$595$	−28.7071	−1.17688
$596$	16.2364	0.665067
$597$	74.6725	3.05614
$598$	6.71335	0.274529
$599$	23.8275	0.973567	0.486783	−	0.873523i	$-0.338170\pi$
$599$	23.8275	0.973567	0.486783	+	0.873523i	$0.338170\pi$
$600$	175.303	7.15674
$601$	17.8701	0.728936	0.364468	−	0.931216i	$-0.381251\pi$
$601$	17.8701	0.728936	0.364468	+	0.931216i	$0.381251\pi$
$602$	19.4363	0.792163
$603$	−52.1211	−2.12253
$604$	18.3402	0.746253
$605$	−10.7824	−0.438369
$606$	−33.8080	−1.37336
$607$	−45.3916	−1.84239	−0.921194	−	0.389103i	$-0.872785\pi$
$607$	−45.3916	−1.84239	−0.921194	+	0.389103i	$0.872785\pi$
$608$	−0.605295	−0.0245480
$609$	−18.3460	−0.743416
$610$	30.4906	1.23453
$611$	13.1239	0.530938
$612$	82.6258	3.33995
$613$	−16.3421	−0.660050	−0.330025	−	0.943972i	$-0.607057\pi$
$613$	−16.3421	−0.660050	−0.330025	+	0.943972i	$0.607057\pi$
$614$	58.0606	2.34313
$615$	58.6980	2.36693
$616$	−23.0016	−0.926761
$617$	−46.5940	−1.87580	−0.937901	−	0.346902i	$-0.887234\pi$
$617$	−46.5940	−1.87580	−0.937901	+	0.346902i	$0.887234\pi$
$618$	−67.0547	−2.69734
$619$	24.4145	0.981301	0.490650	−	0.871356i	$-0.336759\pi$
$619$	24.4145	0.981301	0.490650	+	0.871356i	$0.336759\pi$
$620$	68.4900	2.75062
$621$	14.8991	0.597881
$622$	−53.3221	−2.13802
$623$	4.84200	0.193990
$624$	−11.2445	−0.450140
$625$	74.4859	2.97944
$626$	−38.0995	−1.52276
$627$	−39.0810	−1.56074
$628$	79.0303	3.15365
$629$	9.35800	0.373128
$630$	83.2726	3.31766
$631$	2.02675	0.0806837	0.0403418	−	0.999186i	$-0.487155\pi$
$631$	2.02675	0.0806837	0.0403418	+	0.999186i	$0.487155\pi$
$632$	40.0928	1.59480
$633$	−2.35499	−0.0936025
$634$	10.6317	0.422238
$635$	88.9175	3.52858
$636$	117.889	4.67462
$637$	−4.42019	−0.175134
$638$	−28.4002	−1.12438
$639$	−3.71346	−0.146902
$640$	83.0723	3.28372
$641$	−36.4891	−1.44123	−0.720617	−	0.693333i	$-0.756141\pi$
$641$	−36.4891	−1.44123	−0.720617	+	0.693333i	$0.756141\pi$
$642$	−45.1357	−1.78136
$643$	−22.4921	−0.887002	−0.443501	−	0.896274i	$-0.646264\pi$
$643$	−22.4921	−0.887002	−0.443501	+	0.896274i	$0.646264\pi$
$644$	17.5240	0.690541
$645$	−58.0318	−2.28500
$646$	48.7792	1.91919
$647$	12.7766	0.502300	0.251150	−	0.967948i	$-0.419191\pi$
$647$	12.7766	0.502300	0.251150	+	0.967948i	$0.419191\pi$
$648$	−3.39611	−0.133412
$649$	17.1933	0.674896
$650$	−31.7897	−1.24689
$651$	18.7092	0.733273
$652$	−69.8531	−2.73566
$653$	33.4617	1.30946	0.654728	−	0.755864i	$-0.272783\pi$
$653$	33.4617	1.30946	0.654728	+	0.755864i	$0.272783\pi$
$654$	110.649	4.32673
$655$	66.7123	2.60667
$656$	−19.3542	−0.755655
$657$	7.73632	0.301823
$658$	51.4423	2.00543
$659$	9.63239	0.375225	0.187612	−	0.982243i	$-0.439925\pi$
$659$	9.63239	0.375225	0.187612	+	0.982243i	$0.439925\pi$
$660$	137.804	5.36400
$661$	−21.1703	−0.823430	−0.411715	−	0.911313i	$-0.635070\pi$
$661$	−21.1703	−0.823430	−0.411715	+	0.911313i	$0.635070\pi$
$662$	65.3989	2.54180
$663$	−11.9868	−0.465528
$664$	−31.8417	−1.23570
$665$	32.7384	1.26954
$666$	−27.1453	−1.05186
$667$	10.7832	0.417526
$668$	−52.2221	−2.02054
$669$	56.3034	2.17681
$670$	108.500	4.19170
$671$	8.58642	0.331475
$672$	0.583031	0.0224909
$673$	−7.37721	−0.284370	−0.142185	−	0.989840i	$-0.545413\pi$
$673$	−7.37721	−0.284370	−0.142185	+	0.989840i	$0.545413\pi$
$674$	−35.6894	−1.37471
$675$	−70.5517	−2.71554
$676$	−47.7122	−1.83508
$677$	−14.9519	−0.574648	−0.287324	−	0.957834i	$-0.592766\pi$
$677$	−14.9519	−0.574648	−0.287324	+	0.957834i	$0.592766\pi$
$678$	−95.9476	−3.68485
$679$	−8.04456	−0.308722
$680$	−85.7197	−3.28720
$681$	−38.7612	−1.48533
$682$	28.9626	1.10903
$683$	25.4019	0.971977	0.485989	−	0.873965i	$-0.338460\pi$
$683$	25.4019	0.971977	0.485989	+	0.873965i	$0.338460\pi$
$684$	−94.2288	−3.60293
$685$	−44.4831	−1.69961
$686$	−45.2135	−1.72626
$687$	41.7382	1.59241
$688$	19.1346	0.729498
$689$	−10.6542	−0.405893
$690$	−78.5685	−2.99105
$691$	24.6581	0.938039	0.469019	−	0.883188i	$-0.344607\pi$
$691$	24.6581	0.938039	0.469019	+	0.883188i	$0.344607\pi$
$692$	70.1459	2.66655
$693$	23.4503	0.890803
$694$	55.4349	2.10428
$695$	−3.74979	−0.142238
$696$	−54.7812	−2.07648
$697$	−20.6319	−0.781488
$698$	−81.2100	−3.07385
$699$	42.1263	1.59336
$700$	−82.9810	−3.13639
$701$	−35.0306	−1.32309	−0.661544	−	0.749906i	$-0.730099\pi$
$701$	−35.0306	−1.32309	−0.661544	+	0.749906i	$0.730099\pi$
$702$	13.7259	0.518052
$703$	−10.6721	−0.402507
$704$	23.6954	0.893053
$705$	−153.594	−5.78468
$706$	50.0784	1.88472
$707$	7.97551	0.299950
$708$	66.5455	2.50093
$709$	−6.03879	−0.226791	−0.113396	−	0.993550i	$-0.536173\pi$
$709$	−6.03879	−0.226791	−0.113396	+	0.993550i	$0.536173\pi$
$710$	7.73025	0.290111
$711$	−40.8748	−1.53293
$712$	14.4582	0.541845
$713$	−10.9967	−0.411829
$714$	−46.9850	−1.75837
$715$	−12.4539	−0.465751
$716$	36.8539	1.37730
$717$	31.8965	1.19120
$718$	−6.71754	−0.250696
$719$	0.757479	0.0282492	0.0141246	−	0.999900i	$-0.495504\pi$
$719$	0.757479	0.0282492	0.0141246	+	0.999900i	$0.495504\pi$
$720$	81.9799	3.05521
$721$	15.8186	0.589115
$722$	−9.13941	−0.340134
$723$	59.2857	2.20486
$724$	12.5713	0.467208
$725$	−51.0614	−1.89637
$726$	−17.6477	−0.654966
$727$	7.41938	0.275170	0.137585	−	0.990490i	$-0.456066\pi$
$727$	7.41938	0.275170	0.137585	+	0.990490i	$0.456066\pi$
$728$	8.04570	0.298193
$729$	−43.2432	−1.60160
$730$	−16.1046	−0.596057
$731$	20.3977	0.754437
$732$	33.2332	1.22833
$733$	15.5999	0.576196	0.288098	−	0.957601i	$-0.406977\pi$
$733$	15.5999	0.576196	0.288098	+	0.957601i	$0.406977\pi$
$734$	72.2444	2.66659
$735$	51.7310	1.90813
$736$	−0.342686	−0.0126316
$737$	30.5544	1.12549
$738$	59.8482	2.20304
$739$	−4.76320	−0.175217	−0.0876086	−	0.996155i	$-0.527922\pi$
$739$	−4.76320	−0.175217	−0.0876086	+	0.996155i	$0.527922\pi$
$740$	37.6311	1.38335
$741$	13.6701	0.502183
$742$	−41.7616	−1.53312
$743$	11.7006	0.429254	0.214627	−	0.976696i	$-0.431146\pi$
$743$	11.7006	0.429254	0.214627	+	0.976696i	$0.431146\pi$
$744$	55.8659	2.04814
$745$	17.1729	0.629167
$746$	−16.5587	−0.606257
$747$	32.4628	1.18775
$748$	−48.4369	−1.77103
$749$	10.6478	0.389061
$750$	226.519	8.27132
$751$	−10.3628	−0.378143	−0.189071	−	0.981963i	$-0.560548\pi$
$751$	−10.3628	−0.378143	−0.189071	+	0.981963i	$0.560548\pi$
$752$	50.6438	1.84679
$753$	−45.5298	−1.65920
$754$	9.93407	0.361778
$755$	19.3981	0.705970
$756$	35.8290	1.30309
$757$	−37.3974	−1.35923	−0.679615	−	0.733569i	$-0.737853\pi$
$757$	−37.3974	−1.35923	−0.679615	+	0.733569i	$0.737853\pi$
$758$	52.9868	1.92457
$759$	−22.1256	−0.803108
$760$	97.7572	3.54603
$761$	−36.2144	−1.31277	−0.656385	−	0.754426i	$-0.727915\pi$
$761$	−36.2144	−1.31277	−0.656385	+	0.754426i	$0.727915\pi$
$762$	145.532	5.27205
$763$	−26.1028	−0.944984
$764$	−7.97519	−0.288532
$765$	87.3918	3.15966
$766$	−63.7306	−2.30268
$767$	−6.01402	−0.217154
$768$	89.9591	3.24612
$769$	0.736566	0.0265612	0.0132806	−	0.999912i	$-0.495773\pi$
$769$	0.736566	0.0265612	0.0132806	+	0.999912i	$0.495773\pi$
$770$	−48.8161	−1.75921
$771$	−15.0217	−0.540993
$772$	−59.3638	−2.13655
$773$	−42.6533	−1.53413	−0.767066	−	0.641568i	$-0.778284\pi$
$773$	−42.6533	−1.53413	−0.767066	+	0.641568i	$0.778284\pi$
$774$	−59.1690	−2.12679
$775$	52.0725	1.87050
$776$	−24.0211	−0.862308
$777$	10.2796	0.368778
$778$	48.0174	1.72151
$779$	23.5292	0.843021
$780$	−48.2022	−1.72591
$781$	2.17691	0.0778959
$782$	27.6162	0.987554
$783$	22.0470	0.787894
$784$	−17.0570	−0.609179
$785$	83.5890	2.98342
$786$	109.188	3.89461
$787$	50.6686	1.80614	0.903070	−	0.429494i	$-0.141308\pi$
$787$	50.6686	1.80614	0.903070	+	0.429494i	$0.141308\pi$
$788$	76.2605	2.71667
$789$	−45.0180	−1.60268
$790$	85.0885	3.02731
$791$	22.6346	0.804794
$792$	70.0227	2.48815
$793$	−3.00343	−0.106655
$794$	−81.9057	−2.90673
$795$	124.690	4.42228
$796$	−105.546	−3.74096
$797$	−21.5993	−0.765087	−0.382543	−	0.923938i	$-0.624952\pi$
$797$	−21.5993	−0.765087	−0.382543	+	0.923938i	$0.624952\pi$
$798$	53.5830	1.89682
$799$	53.9870	1.90992
$800$	1.62272	0.0573718
$801$	−14.7403	−0.520822
$802$	−22.3831	−0.790375
$803$	−4.53519	−0.160043
$804$	118.259	4.17067
$805$	18.5348	0.653265
$806$	−10.1308	−0.356841
$807$	0.957292	0.0336983
$808$	23.8149	0.837807
$809$	11.2084	0.394068	0.197034	−	0.980397i	$-0.436869\pi$
$809$	11.2084	0.394068	0.197034	+	0.980397i	$0.436869\pi$
$810$	−7.20752	−0.253247
$811$	16.7003	0.586428	0.293214	−	0.956047i	$-0.405275\pi$
$811$	16.7003	0.586428	0.293214	+	0.956047i	$0.405275\pi$
$812$	25.9310	0.910001
$813$	−14.0568	−0.492992
$814$	15.9132	0.557756
$815$	−73.8824	−2.58799
$816$	−46.2556	−1.61927
$817$	−23.2622	−0.813840
$818$	49.1943	1.72004
$819$	−8.20264	−0.286624
$820$	−82.9664	−2.89731
$821$	−9.22830	−0.322070	−0.161035	−	0.986949i	$-0.551483\pi$
$821$	−9.22830	−0.322070	−0.161035	+	0.986949i	$0.551483\pi$
$822$	−72.8055	−2.53938
$823$	−6.98735	−0.243564	−0.121782	−	0.992557i	$-0.538861\pi$
$823$	−6.98735	−0.243564	−0.121782	+	0.992557i	$0.538861\pi$
$824$	47.2345	1.64549
$825$	104.771	3.64766
$826$	−23.5733	−0.820221
$827$	5.98959	0.208278	0.104139	−	0.994563i	$-0.466791\pi$
$827$	5.98959	0.208278	0.104139	+	0.994563i	$0.466791\pi$
$828$	−53.3474	−1.85395
$829$	−42.2662	−1.46797	−0.733983	−	0.679167i	$-0.762341\pi$
$829$	−42.2662	−1.46797	−0.733983	+	0.679167i	$0.762341\pi$
$830$	−67.5773	−2.34564
$831$	−1.50213	−0.0521085
$832$	−8.28838	−0.287348
$833$	−18.1830	−0.630005
$834$	−6.13729	−0.212517
$835$	−55.2344	−1.91147
$836$	55.2389	1.91048
$837$	−22.4835	−0.777144
$838$	78.3543	2.70670
$839$	−42.4245	−1.46466	−0.732328	−	0.680952i	$-0.761566\pi$
$839$	−42.4245	−1.46466	−0.732328	+	0.680952i	$0.761566\pi$
$840$	−94.1614	−3.24888
$841$	−13.0436	−0.449781
$842$	9.02972	0.311185
$843$	33.9461	1.16916
$844$	3.32865	0.114577
$845$	−50.4643	−1.73602
$846$	−156.604	−5.38414
$847$	4.16318	0.143049
$848$	−41.1133	−1.41184
$849$	12.9455	0.444287
$850$	−130.771	−4.48541
$851$	−6.04200	−0.207117
$852$	8.42558	0.288656
$853$	−27.3204	−0.935433	−0.467716	−	0.883879i	$-0.654923\pi$
$853$	−27.3204	−0.935433	−0.467716	+	0.883879i	$0.654923\pi$
$854$	−11.7726	−0.402851
$855$	−99.6641	−3.40844
$856$	31.7943	1.08671
$857$	−47.9903	−1.63932	−0.819659	−	0.572852i	$-0.805837\pi$
$857$	−47.9903	−1.63932	−0.819659	+	0.572852i	$0.805837\pi$
$858$	−20.3834	−0.695877
$859$	−31.4486	−1.07301	−0.536505	−	0.843897i	$-0.680256\pi$
$859$	−31.4486	−1.07301	−0.536505	+	0.843897i	$0.680256\pi$
$860$	82.0248	2.79702
$861$	−22.6637	−0.772378
$862$	−52.8995	−1.80177
$863$	−9.65277	−0.328584	−0.164292	−	0.986412i	$-0.552534\pi$
$863$	−9.65277	−0.328584	−0.164292	+	0.986412i	$0.552534\pi$
$864$	−0.700647	−0.0238365
$865$	74.1920	2.52260
$866$	−42.9084	−1.45809
$867$	−1.35633	−0.0460635
$868$	−26.4445	−0.897585
$869$	23.9617	0.812844
$870$	−116.262	−3.94164
$871$	−10.6876	−0.362135
$872$	−77.9431	−2.63949
$873$	24.4897	0.828851
$874$	−31.4943	−1.06531
$875$	−53.4372	−1.80651
$876$	−17.5532	−0.593066
$877$	23.2579	0.785362	0.392681	−	0.919675i	$-0.371548\pi$
$877$	23.2579	0.785362	0.392681	+	0.919675i	$0.371548\pi$
$878$	−37.5051	−1.26573
$879$	−5.20777	−0.175654
$880$	−48.0583	−1.62004
$881$	6.15696	0.207433	0.103717	−	0.994607i	$-0.466927\pi$
$881$	6.15696	0.207433	0.103717	+	0.994607i	$0.466927\pi$
$882$	52.7447	1.77601
$883$	−49.4419	−1.66385	−0.831926	−	0.554886i	$-0.812762\pi$
$883$	−49.4419	−1.66385	−0.831926	+	0.554886i	$0.812762\pi$
$884$	16.9427	0.569844
$885$	70.3840	2.36593
$886$	−13.9259	−0.467850
$887$	18.2218	0.611827	0.305914	−	0.952059i	$-0.401038\pi$
$887$	18.2218	0.611827	0.305914	+	0.952059i	$0.401038\pi$
$888$	30.6949	1.03005
$889$	−34.3317	−1.15145
$890$	30.6846	1.02855
$891$	−2.02970	−0.0679976
$892$	−79.5818	−2.66459
$893$	−61.5684	−2.06031
$894$	28.1069	0.940037
$895$	38.9797	1.30295
$896$	−32.0748	−1.07154
$897$	7.73928	0.258407
$898$	−20.9390	−0.698743
$899$	−16.2723	−0.542712
$900$	252.616	8.42052
$901$	−43.8274	−1.46010
$902$	−35.0842	−1.16818
$903$	22.4065	0.745642
$904$	67.5871	2.24791
$905$	13.2964	0.441988
$906$	31.7490	1.05479
$907$	−20.8551	−0.692481	−0.346240	−	0.938146i	$-0.612542\pi$
$907$	−20.8551	−0.692481	−0.346240	+	0.938146i	$0.612542\pi$
$908$	54.7869	1.81817
$909$	−24.2795	−0.805300
$910$	17.0753	0.566041
$911$	12.3956	0.410685	0.205343	−	0.978690i	$-0.434169\pi$
$911$	12.3956	0.410685	0.205343	+	0.978690i	$0.434169\pi$
$912$	52.7513	1.74677
$913$	−19.0304	−0.629814
$914$	20.4830	0.677518
$915$	35.1501	1.16203
$916$	−58.9947	−1.94924
$917$	−25.7581	−0.850608
$918$	56.4634	1.86357
$919$	26.5841	0.876930	0.438465	−	0.898748i	$-0.355522\pi$
$919$	26.5841	0.876930	0.438465	+	0.898748i	$0.355522\pi$
$920$	55.3450	1.82467
$921$	66.9333	2.20553
$922$	−57.9991	−1.91010
$923$	−0.761457	−0.0250637
$924$	−53.2070	−1.75038
$925$	28.6106	0.940712
$926$	100.034	3.28734
$927$	−48.1559	−1.58165
$928$	−0.507090	−0.0166460
$929$	6.65926	0.218483	0.109242	−	0.994015i	$-0.465158\pi$
$929$	6.65926	0.218483	0.109242	+	0.994015i	$0.465158\pi$
$930$	118.564	3.88786
$931$	20.7365	0.679610
$932$	−59.5433	−1.95041
$933$	−61.4707	−2.01246
$934$	−30.4550	−0.996518
$935$	−51.2309	−1.67543
$936$	−24.4932	−0.800584
$937$	−53.6550	−1.75283	−0.876416	−	0.481554i	$-0.840072\pi$
$937$	−53.6550	−1.75283	−0.876416	+	0.481554i	$0.840072\pi$
$938$	−41.8925	−1.36784
$939$	−43.9219	−1.43334
$940$	217.097	7.08091
$941$	34.7733	1.13358	0.566788	−	0.823863i	$-0.308186\pi$
$941$	34.7733	1.13358	0.566788	+	0.823863i	$0.308186\pi$
$942$	136.810	4.45752
$943$	13.3210	0.433791
$944$	−23.2074	−0.755336
$945$	37.8957	1.23275
$946$	34.6861	1.12774
$947$	−21.7915	−0.708130	−0.354065	−	0.935221i	$-0.615201\pi$
$947$	−21.7915	−0.708130	−0.354065	+	0.935221i	$0.615201\pi$
$948$	92.7421	3.01212
$949$	1.58636	0.0514954
$950$	149.135	4.83858
$951$	12.2564	0.397442
$952$	33.0970	1.07268
$953$	−1.62106	−0.0525111	−0.0262556	−	0.999655i	$-0.508358\pi$
$953$	−1.62106	−0.0525111	−0.0262556	+	0.999655i	$0.508358\pi$
$954$	127.133	4.11608
$955$	−8.43521	−0.272957
$956$	−45.0840	−1.45812
$957$	−32.7403	−1.05834
$958$	35.9872	1.16269
$959$	17.1752	0.554618
$960$	97.0016	3.13071
$961$	−14.4055	−0.464693
$962$	−5.56624	−0.179463
$963$	−32.4145	−1.04454
$964$	−83.7972	−2.69893
$965$	−62.7880	−2.02122
$966$	30.3359	0.976042
$967$	−30.0072	−0.964965	−0.482483	−	0.875906i	$-0.660265\pi$
$967$	−30.0072	−0.964965	−0.482483	+	0.875906i	$0.660265\pi$
$968$	12.4313	0.399557
$969$	56.2336	1.80648
$970$	−50.9798	−1.63686
$971$	−48.5017	−1.55649	−0.778247	−	0.627958i	$-0.783891\pi$
$971$	−48.5017	−1.55649	−0.778247	+	0.627958i	$0.783891\pi$
$972$	58.1600	1.86548
$973$	1.44782	0.0464151
$974$	102.892	3.29687
$975$	−36.6478	−1.17367
$976$	−11.5899	−0.370983
$977$	−1.34278	−0.0429595	−0.0214797	−	0.999769i	$-0.506838\pi$
$977$	−1.34278	−0.0429595	−0.0214797	+	0.999769i	$0.506838\pi$
$978$	−120.924	−3.86671
$979$	8.64105	0.276169
$980$	−73.1190	−2.33570
$981$	79.4636	2.53708
$982$	−62.8426	−2.00539
$983$	−28.0305	−0.894034	−0.447017	−	0.894525i	$-0.647514\pi$
$983$	−28.0305	−0.894034	−0.447017	+	0.894525i	$0.647514\pi$
$984$	−67.6741	−2.15737
$985$	80.6594	2.57002
$986$	40.8651	1.30141
$987$	59.3037	1.88766
$988$	−19.3219	−0.614712
$989$	−13.1698	−0.418776
$990$	148.609	4.72309
$991$	0.377564	0.0119937	0.00599685	−	0.999982i	$-0.498091\pi$
$991$	0.377564	0.0119937	0.00599685	+	0.999982i	$0.498091\pi$
$992$	0.517130	0.0164189
$993$	75.3931	2.39253
$994$	−2.98471	−0.0946692
$995$	−111.634	−3.53903
$996$	−73.6559	−2.33388
$997$	−32.1891	−1.01944	−0.509719	−	0.860341i	$-0.670251\pi$
$997$	−32.1891	−1.01944	−0.509719	+	0.860341i	$0.670251\pi$
$998$	50.6204	1.60236
$999$	−12.3533	−0.390841

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4001.2.a.a.1.12	✓	149

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4001.2.a.a.1.12	✓	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)

\(f(q)\)	\(=\)	\(q-2.44683 q^{2} -2.82076 q^{3} +3.98699 q^{4} +4.21697 q^{5} +6.90192 q^{6} -1.62820 q^{7} -4.86182 q^{8} +4.95666 q^{9} +O(q^{10})\)	\(q-2.44683 q^{2} -2.82076 q^{3} +3.98699 q^{4} +4.21697 q^{5} +6.90192 q^{6} -1.62820 q^{7} -4.86182 q^{8} +4.95666 q^{9} -10.3182 q^{10} -2.90570 q^{11} -11.2463 q^{12} +1.01638 q^{13} +3.98394 q^{14} -11.8950 q^{15} +3.92209 q^{16} +4.18101 q^{17} -12.1281 q^{18} -4.76814 q^{19} +16.8130 q^{20} +4.59276 q^{21} +7.10975 q^{22} -2.69947 q^{23} +13.7140 q^{24} +12.7828 q^{25} -2.48691 q^{26} -5.51927 q^{27} -6.49162 q^{28} -3.99454 q^{29} +29.1051 q^{30} +4.07364 q^{31} +0.126946 q^{32} +8.19626 q^{33} -10.2302 q^{34} -6.86607 q^{35} +19.7622 q^{36} +2.23821 q^{37} +11.6668 q^{38} -2.86696 q^{39} -20.5021 q^{40} -4.93466 q^{41} -11.2377 q^{42} +4.87866 q^{43} -11.5850 q^{44} +20.9021 q^{45} +6.60516 q^{46} +12.9124 q^{47} -11.0633 q^{48} -4.34896 q^{49} -31.2774 q^{50} -11.7936 q^{51} +4.05229 q^{52} -10.4825 q^{53} +13.5047 q^{54} -12.2532 q^{55} +7.91603 q^{56} +13.4498 q^{57} +9.77397 q^{58} -5.91709 q^{59} -47.4253 q^{60} -2.95503 q^{61} -9.96751 q^{62} -8.07045 q^{63} -8.15480 q^{64} +4.28604 q^{65} -20.0549 q^{66} -10.5154 q^{67} +16.6696 q^{68} +7.61456 q^{69} +16.8001 q^{70} -0.749186 q^{71} -24.0984 q^{72} +1.56079 q^{73} -5.47653 q^{74} -36.0571 q^{75} -19.0105 q^{76} +4.73106 q^{77} +7.01497 q^{78} -8.24644 q^{79} +16.5393 q^{80} +0.698525 q^{81} +12.0743 q^{82} +6.54933 q^{83} +18.3113 q^{84} +17.6312 q^{85} -11.9373 q^{86} +11.2676 q^{87} +14.1270 q^{88} -2.97383 q^{89} -51.1439 q^{90} -1.65487 q^{91} -10.7628 q^{92} -11.4907 q^{93} -31.5946 q^{94} -20.1071 q^{95} -0.358083 q^{96} +4.94076 q^{97} +10.6412 q^{98} -14.4026 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 149 q - 6 q^{2} - 28 q^{3} + 116 q^{4} - 19 q^{5} - 31 q^{6} - 47 q^{7} - 15 q^{8} + 115 q^{9}+O(q^{10}) \) 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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