LMFDB - Embedded newform 4007.2.a.b.1.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4007,2,Mod(1,4007)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4007, 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("4007.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4007 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4007.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:	$31.9960560899$
Analytic rank:	$0$
Dimension:	$195$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
Character	$\chi$	$=$	4007.1

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.71610 q^{2} -2.73922 q^{3} +5.37720 q^{4} -0.158886 q^{5} +7.44001 q^{6} +4.34515 q^{7} -9.17282 q^{8} +4.50335 q^{9} +O(q^{10})$	\(q-2.71610 q^{2} -2.73922 q^{3} +5.37720 q^{4} -0.158886 q^{5} +7.44001 q^{6} +4.34515 q^{7} -9.17282 q^{8} +4.50335 q^{9} +0.431551 q^{10} -2.09710 q^{11} -14.7294 q^{12} +5.88350 q^{13} -11.8019 q^{14} +0.435225 q^{15} +14.1599 q^{16} -5.37844 q^{17} -12.2316 q^{18} -8.03540 q^{19} -0.854363 q^{20} -11.9023 q^{21} +5.69594 q^{22} -0.874997 q^{23} +25.1264 q^{24} -4.97476 q^{25} -15.9802 q^{26} -4.11802 q^{27} +23.3647 q^{28} -7.79035 q^{29} -1.18211 q^{30} +6.81658 q^{31} -20.1141 q^{32} +5.74443 q^{33} +14.6084 q^{34} -0.690384 q^{35} +24.2154 q^{36} -8.21577 q^{37} +21.8249 q^{38} -16.1162 q^{39} +1.45743 q^{40} +3.46115 q^{41} +32.3279 q^{42} -12.4941 q^{43} -11.2765 q^{44} -0.715520 q^{45} +2.37658 q^{46} +6.24253 q^{47} -38.7872 q^{48} +11.8803 q^{49} +13.5119 q^{50} +14.7328 q^{51} +31.6368 q^{52} -0.254886 q^{53} +11.1850 q^{54} +0.333200 q^{55} -39.8573 q^{56} +22.0108 q^{57} +21.1594 q^{58} +0.432677 q^{59} +2.34029 q^{60} +7.57216 q^{61} -18.5145 q^{62} +19.5677 q^{63} +26.3120 q^{64} -0.934807 q^{65} -15.6025 q^{66} -2.64809 q^{67} -28.9210 q^{68} +2.39681 q^{69} +1.87515 q^{70} -5.34691 q^{71} -41.3084 q^{72} +7.92762 q^{73} +22.3149 q^{74} +13.6270 q^{75} -43.2080 q^{76} -9.11222 q^{77} +43.7733 q^{78} -2.83415 q^{79} -2.24981 q^{80} -2.22988 q^{81} -9.40082 q^{82} +8.57001 q^{83} -64.0013 q^{84} +0.854560 q^{85} +33.9352 q^{86} +21.3395 q^{87} +19.2363 q^{88} -0.266916 q^{89} +1.94342 q^{90} +25.5647 q^{91} -4.70503 q^{92} -18.6721 q^{93} -16.9553 q^{94} +1.27671 q^{95} +55.0970 q^{96} +9.67998 q^{97} -32.2681 q^{98} -9.44399 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 195 q + 14 q^{2} + 22 q^{3} + 220 q^{4} + 14 q^{5} + 13 q^{6} + 48 q^{7} + 39 q^{8} + 245 q^{9}+O(q^{10}) $ 195 * q + 14 * q^2 + 22 * q^3 + 220 * q^4 + 14 * q^5 + 13 * q^6 + 48 * q^7 + 39 * q^8 + 245 * q^9	\( 195 q + 14 q^{2} + 22 q^{3} + 220 q^{4} + 14 q^{5} + 13 q^{6} + 48 q^{7} + 39 q^{8} + 245 q^{9} + 40 q^{10} + 13 q^{11} + 57 q^{12} + 97 q^{13} + 9 q^{14} + 23 q^{15} + 270 q^{16} + 66 q^{17} + 60 q^{18} + 33 q^{19} + 24 q^{20} + 27 q^{21} + 127 q^{22} + 42 q^{23} + 33 q^{24} + 357 q^{25} + 8 q^{26} + 79 q^{27} + 131 q^{28} + 57 q^{29} + 51 q^{30} + 41 q^{31} + 67 q^{32} + 74 q^{33} + 26 q^{34} + 14 q^{35} + 279 q^{36} + 133 q^{37} + 7 q^{38} + 28 q^{39} + 97 q^{40} + 64 q^{41} - q^{42} + 123 q^{43} + 21 q^{44} + 40 q^{45} + 84 q^{46} + 14 q^{47} + 122 q^{48} + 335 q^{49} + 35 q^{50} + 37 q^{51} + 220 q^{52} + 83 q^{53} + 21 q^{54} + 47 q^{55} + q^{56} + 235 q^{57} + 138 q^{58} + 18 q^{59} - 4 q^{60} + 81 q^{61} + 39 q^{62} + 102 q^{63} + 343 q^{64} + 165 q^{65} - 54 q^{66} + 147 q^{67} + 74 q^{68} - 2 q^{69} + 13 q^{70} + 31 q^{71} + 112 q^{72} + 300 q^{73} + 5 q^{74} + 84 q^{75} + 64 q^{76} + 67 q^{77} + 61 q^{78} + 144 q^{79} - 8 q^{80} + 359 q^{81} + 85 q^{82} + 26 q^{83} + 12 q^{84} + 201 q^{85} - 2 q^{86} + 80 q^{87} + 347 q^{88} + 29 q^{89} + 62 q^{90} + 70 q^{91} + 79 q^{92} + 76 q^{93} + 72 q^{94} + 71 q^{95} + 31 q^{96} + 264 q^{97} + 30 q^{98} + 19 q^{99}+O(q^{100}) \) 195 * q + 14 * q^2 + 22 * q^3 + 220 * q^4 + 14 * q^5 + 13 * q^6 + 48 * q^7 + 39 * q^8 + 245 * q^9 + 40 * q^10 + 13 * q^11 + 57 * q^12 + 97 * q^13 + 9 * q^14 + 23 * q^15 + 270 * q^16 + 66 * q^17 + 60 * q^18 + 33 * q^19 + 24 * q^20 + 27 * q^21 + 127 * q^22 + 42 * q^23 + 33 * q^24 + 357 * q^25 + 8 * q^26 + 79 * q^27 + 131 * q^28 + 57 * q^29 + 51 * q^30 + 41 * q^31 + 67 * q^32 + 74 * q^33 + 26 * q^34 + 14 * q^35 + 279 * q^36 + 133 * q^37 + 7 * q^38 + 28 * q^39 + 97 * q^40 + 64 * q^41 - q^42 + 123 * q^43 + 21 * q^44 + 40 * q^45 + 84 * q^46 + 14 * q^47 + 122 * q^48 + 335 * q^49 + 35 * q^50 + 37 * q^51 + 220 * q^52 + 83 * q^53 + 21 * q^54 + 47 * q^55 + q^56 + 235 * q^57 + 138 * q^58 + 18 * q^59 - 4 * q^60 + 81 * q^61 + 39 * q^62 + 102 * q^63 + 343 * q^64 + 165 * q^65 - 54 * q^66 + 147 * q^67 + 74 * q^68 - 2 * q^69 + 13 * q^70 + 31 * q^71 + 112 * q^72 + 300 * q^73 + 5 * q^74 + 84 * q^75 + 64 * q^76 + 67 * q^77 + 61 * q^78 + 144 * q^79 - 8 * q^80 + 359 * q^81 + 85 * q^82 + 26 * q^83 + 12 * q^84 + 201 * q^85 - 2 * q^86 + 80 * q^87 + 347 * q^88 + 29 * q^89 + 62 * q^90 + 70 * q^91 + 79 * q^92 + 76 * q^93 + 72 * q^94 + 71 * q^95 + 31 * q^96 + 264 * q^97 + 30 * q^98 + 19 * 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 $

$2$	−2.71610	−1.92057	−0.960287	−	0.279016i	$-0.909992\pi$
$2$	−2.71610	−1.92057	−0.960287	+	0.279016i	$0.909992\pi$
$3$	−2.73922	−1.58149	−0.790746	−	0.612144i	$-0.790307\pi$
$3$	−2.73922	−1.58149	−0.790746	+	0.612144i	$0.790307\pi$
$4$	5.37720	2.68860
$5$	−0.158886	−0.0710560	−0.0355280	−	0.999369i	$-0.511311\pi$
$5$	−0.158886	−0.0710560	−0.0355280	+	0.999369i	$0.511311\pi$
$6$	7.44001	3.03737
$7$	4.34515	1.64231	0.821156	−	0.570704i	$-0.193330\pi$
$7$	4.34515	1.64231	0.821156	+	0.570704i	$0.193330\pi$
$8$	−9.17282	−3.24308
$9$	4.50335	1.50112
$10$	0.431551	0.136468
$11$	−2.09710	−0.632300	−0.316150	−	0.948709i	$-0.602390\pi$
$11$	−2.09710	−0.632300	−0.316150	+	0.948709i	$0.602390\pi$
$12$	−14.7294	−4.25200
$13$	5.88350	1.63179	0.815895	−	0.578200i	$-0.196245\pi$
$13$	5.88350	1.63179	0.815895	+	0.578200i	$0.196245\pi$
$14$	−11.8019	−3.15418
$15$	0.435225	0.112375
$16$	14.1599	3.53998
$17$	−5.37844	−1.30446	−0.652232	−	0.758019i	$-0.726167\pi$
$17$	−5.37844	−1.30446	−0.652232	+	0.758019i	$0.726167\pi$
$18$	−12.2316	−2.88301
$19$	−8.03540	−1.84345	−0.921723	−	0.387848i	$-0.873219\pi$
$19$	−8.03540	−1.84345	−0.921723	+	0.387848i	$0.873219\pi$
$20$	−0.854363	−0.191041
$21$	−11.9023	−2.59730
$22$	5.69594	1.21438
$23$	−0.874997	−0.182449	−0.0912247	−	0.995830i	$-0.529078\pi$
$23$	−0.874997	−0.182449	−0.0912247	+	0.995830i	$0.529078\pi$
$24$	25.1264	5.12891
$25$	−4.97476	−0.994951
$26$	−15.9802	−3.13397
$27$	−4.11802	−0.792513
$28$	23.3647	4.41552
$29$	−7.79035	−1.44663	−0.723316	−	0.690518i	$-0.757383\pi$
$29$	−7.79035	−1.44663	−0.723316	+	0.690518i	$0.757383\pi$
$30$	−1.18211	−0.215824
$31$	6.81658	1.22429	0.612147	−	0.790744i	$-0.290306\pi$
$31$	6.81658	1.22429	0.612147	+	0.790744i	$0.290306\pi$
$32$	−20.1141	−3.55570
$33$	5.74443	0.999977
$34$	14.6084	2.50532
$35$	−0.690384	−0.116696
$36$	24.2154	4.03591
$37$	−8.21577	−1.35066	−0.675332	−	0.737514i	$-0.736000\pi$
$37$	−8.21577	−1.35066	−0.675332	+	0.737514i	$0.736000\pi$
$38$	21.8249	3.54047
$39$	−16.1162	−2.58066
$40$	1.45743	0.230441
$41$	3.46115	0.540540	0.270270	−	0.962785i	$-0.412887\pi$
$41$	3.46115	0.540540	0.270270	+	0.962785i	$0.412887\pi$
$42$	32.3279	4.98831
$43$	−12.4941	−1.90533	−0.952666	−	0.304020i	$-0.901671\pi$
$43$	−12.4941	−1.90533	−0.952666	+	0.304020i	$0.901671\pi$
$44$	−11.2765	−1.70000
$45$	−0.715520	−0.106663
$46$	2.37658	0.350407
$47$	6.24253	0.910567	0.455283	−	0.890347i	$-0.349538\pi$
$47$	6.24253	0.910567	0.455283	+	0.890347i	$0.349538\pi$
$48$	−38.7872	−5.59844
$49$	11.8803	1.69719
$50$	13.5119	1.91088
$51$	14.7328	2.06300
$52$	31.6368	4.38723
$53$	−0.254886	−0.0350113	−0.0175057	−	0.999847i	$-0.505573\pi$
$53$	−0.254886	−0.0350113	−0.0175057	+	0.999847i	$0.505573\pi$
$54$	11.1850	1.52208
$55$	0.333200	0.0449287
$56$	−39.8573	−5.32615
$57$	22.0108	2.91540
$58$	21.1594	2.77836
$59$	0.432677	0.0563297	0.0281648	−	0.999603i	$-0.491034\pi$
$59$	0.432677	0.0563297	0.0281648	+	0.999603i	$0.491034\pi$
$60$	2.34029	0.302130
$61$	7.57216	0.969516	0.484758	−	0.874648i	$-0.338908\pi$
$61$	7.57216	0.969516	0.484758	+	0.874648i	$0.338908\pi$
$62$	−18.5145	−2.35134
$63$	19.5677	2.46530
$64$	26.3120	3.28901
$65$	−0.934807	−0.115949
$66$	−15.6025	−1.92053
$67$	−2.64809	−0.323515	−0.161758	−	0.986831i	$-0.551716\pi$
$67$	−2.64809	−0.323515	−0.161758	+	0.986831i	$0.551716\pi$
$68$	−28.9210	−3.50718
$69$	2.39681	0.288542
$70$	1.87515	0.224123
$71$	−5.34691	−0.634561	−0.317281	−	0.948332i	$-0.602770\pi$
$71$	−5.34691	−0.634561	−0.317281	+	0.948332i	$0.602770\pi$
$72$	−41.3084	−4.86825
$73$	7.92762	0.927857	0.463929	−	0.885873i	$-0.346439\pi$
$73$	7.92762	0.927857	0.463929	+	0.885873i	$0.346439\pi$
$74$	22.3149	2.59405
$75$	13.6270	1.57351
$76$	−43.2080	−4.95629
$77$	−9.11222	−1.03843
$78$	43.7733	4.95635
$79$	−2.83415	−0.318867	−0.159433	−	0.987209i	$-0.550967\pi$
$79$	−2.83415	−0.318867	−0.159433	+	0.987209i	$0.550967\pi$
$80$	−2.24981	−0.251537
$81$	−2.22988	−0.247764
$82$	−9.40082	−1.03815
$83$	8.57001	0.940681	0.470340	−	0.882485i	$-0.344131\pi$
$83$	8.57001	0.940681	0.470340	+	0.882485i	$0.344131\pi$
$84$	−64.0013	−6.98311
$85$	0.854560	0.0926901
$86$	33.9352	3.65933
$87$	21.3395	2.28784
$88$	19.2363	2.05060
$89$	−0.266916	−0.0282930	−0.0141465	−	0.999900i	$-0.504503\pi$
$89$	−0.266916	−0.0282930	−0.0141465	+	0.999900i	$0.504503\pi$
$90$	1.94342	0.204855
$91$	25.5647	2.67991
$92$	−4.70503	−0.490534
$93$	−18.6721	−1.93621
$94$	−16.9553	−1.74881
$95$	1.27671	0.130988
$96$	55.0970	5.62331
$97$	9.67998	0.982853	0.491427	−	0.870919i	$-0.336476\pi$
$97$	9.67998	0.982853	0.491427	+	0.870919i	$0.336476\pi$
$98$	−32.2681	−3.25957
$99$	−9.44399	−0.949156
$100$	−26.7503	−2.67503
$101$	1.80945	0.180047	0.0900233	−	0.995940i	$-0.471306\pi$
$101$	1.80945	0.180047	0.0900233	+	0.995940i	$0.471306\pi$
$102$	−40.0157	−3.96214
$103$	5.31558	0.523760	0.261880	−	0.965100i	$-0.415658\pi$
$103$	5.31558	0.523760	0.261880	+	0.965100i	$0.415658\pi$
$104$	−53.9683	−5.29203
$105$	1.89112	0.184554
$106$	0.692297	0.0672418
$107$	18.5246	1.79084	0.895418	−	0.445226i	$-0.146877\pi$
$107$	18.5246	1.79084	0.895418	+	0.445226i	$0.146877\pi$
$108$	−22.1434	−2.13075
$109$	−16.2647	−1.55787	−0.778937	−	0.627102i	$-0.784241\pi$
$109$	−16.2647	−1.55787	−0.778937	+	0.627102i	$0.784241\pi$
$110$	−0.905006	−0.0862889
$111$	22.5048	2.13607
$112$	61.5269	5.81374
$113$	16.2223	1.52607	0.763033	−	0.646360i	$-0.223710\pi$
$113$	16.2223	1.52607	0.763033	+	0.646360i	$0.223710\pi$
$114$	−59.7834	−5.59923
$115$	0.139025	0.0129641
$116$	−41.8903	−3.88941
$117$	26.4955	2.44951
$118$	−1.17519	−0.108185
$119$	−23.3701	−2.14234
$120$	−3.99224	−0.364440
$121$	−6.60217	−0.600197
$122$	−20.5667	−1.86203
$123$	−9.48086	−0.854860
$124$	36.6541	3.29164
$125$	1.58485	0.141753
$126$	−53.1479	−4.73479
$127$	14.3745	1.27553	0.637767	−	0.770229i	$-0.279858\pi$
$127$	14.3745	1.27553	0.637767	+	0.770229i	$0.279858\pi$
$128$	−31.2380	−2.76108
$129$	34.2241	3.01327
$130$	2.53903	0.222688
$131$	−16.4860	−1.44039	−0.720194	−	0.693772i	$-0.755947\pi$
$131$	−16.4860	−1.44039	−0.720194	+	0.693772i	$0.755947\pi$
$132$	30.8890	2.68854
$133$	−34.9150	−3.02751
$134$	7.19247	0.621335
$135$	0.654296	0.0563128
$136$	49.3355	4.23049
$137$	7.76688	0.663570	0.331785	−	0.943355i	$-0.392349\pi$
$137$	7.76688	0.663570	0.331785	+	0.943355i	$0.392349\pi$
$138$	−6.50998	−0.554167
$139$	3.23015	0.273978	0.136989	−	0.990573i	$-0.456258\pi$
$139$	3.23015	0.273978	0.136989	+	0.990573i	$0.456258\pi$
$140$	−3.71233	−0.313749
$141$	−17.0997	−1.44005
$142$	14.5227	1.21872
$143$	−12.3383	−1.03178
$144$	63.7670	5.31392
$145$	1.23778	0.102792
$146$	−21.5322	−1.78202
$147$	−32.5428	−2.68409
$148$	−44.1779	−3.63140
$149$	2.30470	0.188808	0.0944042	−	0.995534i	$-0.469905\pi$
$149$	2.30470	0.188808	0.0944042	+	0.995534i	$0.469905\pi$
$150$	−37.0122	−3.02204
$151$	−10.7828	−0.877491	−0.438745	−	0.898611i	$-0.644577\pi$
$151$	−10.7828	−0.877491	−0.438745	+	0.898611i	$0.644577\pi$
$152$	73.7073	5.97845
$153$	−24.2210	−1.95815
$154$	24.7497	1.99439
$155$	−1.08306	−0.0869934
$156$	−86.6603	−6.93837
$157$	−4.48263	−0.357753	−0.178876	−	0.983872i	$-0.557246\pi$
$157$	−4.48263	−0.357753	−0.178876	+	0.983872i	$0.557246\pi$
$158$	7.69783	0.612406
$159$	0.698191	0.0553701
$160$	3.19585	0.252654
$161$	−3.80199	−0.299639
$162$	6.05657	0.475849
$163$	−13.3444	−1.04521	−0.522606	−	0.852574i	$-0.675040\pi$
$163$	−13.3444	−1.04521	−0.522606	+	0.852574i	$0.675040\pi$
$164$	18.6113	1.45330
$165$	−0.912711	−0.0710544
$166$	−23.2770	−1.80665
$167$	−8.61000	−0.666262	−0.333131	−	0.942881i	$-0.608105\pi$
$167$	−8.61000	−0.666262	−0.333131	+	0.942881i	$0.608105\pi$
$168$	109.178	8.42327
$169$	21.6156	1.66274
$170$	−2.32107	−0.178018
$171$	−36.1862	−2.76723
$172$	−67.1833	−5.12268
$173$	21.2772	1.61767	0.808837	−	0.588033i	$-0.200097\pi$
$173$	21.2772	1.61767	0.808837	+	0.588033i	$0.200097\pi$
$174$	−57.9603	−4.39396
$175$	−21.6160	−1.63402
$176$	−29.6948	−2.23833
$177$	−1.18520	−0.0890850
$178$	0.724971	0.0543389
$179$	−6.25167	−0.467272	−0.233636	−	0.972324i	$-0.575062\pi$
$179$	−6.25167	−0.467272	−0.233636	+	0.972324i	$0.575062\pi$
$180$	−3.84750	−0.286775
$181$	12.9977	0.966111	0.483056	−	0.875590i	$-0.339527\pi$
$181$	12.9977	0.966111	0.483056	+	0.875590i	$0.339527\pi$
$182$	−69.4363	−5.14696
$183$	−20.7418	−1.53328
$184$	8.02619	0.591699
$185$	1.30537	0.0959729
$186$	50.7154	3.71863
$187$	11.2791	0.824813
$188$	33.5674	2.44815
$189$	−17.8934	−1.30155
$190$	−3.46768	−0.251572
$191$	−9.16552	−0.663194	−0.331597	−	0.943421i	$-0.607587\pi$
$191$	−9.16552	−0.663194	−0.331597	+	0.943421i	$0.607587\pi$
$192$	−72.0746	−5.20154
$193$	20.1051	1.44720	0.723598	−	0.690221i	$-0.242487\pi$
$193$	20.1051	1.44720	0.723598	+	0.690221i	$0.242487\pi$
$194$	−26.2918	−1.88764
$195$	2.56065	0.183372
$196$	63.8828	4.56306
$197$	23.0781	1.64425	0.822123	−	0.569310i	$-0.192790\pi$
$197$	23.0781	1.64425	0.822123	+	0.569310i	$0.192790\pi$
$198$	25.6508	1.82292
$199$	−14.1066	−0.999992	−0.499996	−	0.866028i	$-0.666665\pi$
$199$	−14.1066	−0.999992	−0.499996	+	0.866028i	$0.666665\pi$
$200$	45.6325	3.22671
$201$	7.25371	0.511637
$202$	−4.91464	−0.345793
$203$	−33.8502	−2.37582
$204$	79.2211	5.54659
$205$	−0.549928	−0.0384086
$206$	−14.4377	−1.00592
$207$	−3.94042	−0.273878
$208$	83.3098	5.77650
$209$	16.8510	1.16561
$210$	−5.13646	−0.354450
$211$	−3.36160	−0.231422	−0.115711	−	0.993283i	$-0.536915\pi$
$211$	−3.36160	−0.231422	−0.115711	+	0.993283i	$0.536915\pi$
$212$	−1.37058	−0.0941315
$213$	14.6464	1.00355
$214$	−50.3146	−3.43943
$215$	1.98514	0.135385
$216$	37.7739	2.57019
$217$	29.6190	2.01067
$218$	44.1765	2.99201
$219$	−21.7155	−1.46740
$220$	1.79169	0.120795
$221$	−31.6441	−2.12861
$222$	−61.1254	−4.10247
$223$	−18.0190	−1.20664	−0.603321	−	0.797498i	$-0.706156\pi$
$223$	−18.0190	−1.20664	−0.603321	+	0.797498i	$0.706156\pi$
$224$	−87.3986	−5.83957
$225$	−22.4031	−1.49354
$226$	−44.0614	−2.93092
$227$	23.1080	1.53373	0.766865	−	0.641809i	$-0.221816\pi$
$227$	23.1080	1.53373	0.766865	+	0.641809i	$0.221816\pi$
$228$	118.356	7.83834
$229$	−5.03677	−0.332839	−0.166420	−	0.986055i	$-0.553221\pi$
$229$	−5.03677	−0.332839	−0.166420	+	0.986055i	$0.553221\pi$
$230$	−0.377605	−0.0248986
$231$	24.9604	1.64227
$232$	71.4595	4.69154
$233$	−24.5164	−1.60612	−0.803060	−	0.595898i	$-0.796796\pi$
$233$	−24.5164	−1.60612	−0.803060	+	0.595898i	$0.796796\pi$
$234$	−71.9644	−4.70446
$235$	−0.991852	−0.0647013
$236$	2.32659	0.151448
$237$	7.76337	0.504285
$238$	63.4756	4.11452
$239$	5.93713	0.384041	0.192021	−	0.981391i	$-0.438496\pi$
$239$	5.93713	0.384041	0.192021	+	0.981391i	$0.438496\pi$
$240$	6.16274	0.397803
$241$	18.2102	1.17302	0.586511	−	0.809941i	$-0.300501\pi$
$241$	18.2102	1.17302	0.586511	+	0.809941i	$0.300501\pi$
$242$	17.9321	1.15272
$243$	18.4622	1.18435
$244$	40.7170	2.60664
$245$	−1.88762	−0.120595
$246$	25.7510	1.64182
$247$	−47.2763	−3.00812
$248$	−62.5272	−3.97048
$249$	−23.4752	−1.48768
$250$	−4.30461	−0.272248
$251$	3.47795	0.219526	0.109763	−	0.993958i	$-0.464991\pi$
$251$	3.47795	0.219526	0.109763	+	0.993958i	$0.464991\pi$
$252$	105.220	6.62821
$253$	1.83496	0.115363
$254$	−39.0427	−2.44976
$255$	−2.34083	−0.146589
$256$	32.2215	2.01384
$257$	4.20818	0.262499	0.131250	−	0.991349i	$-0.458101\pi$
$257$	4.20818	0.262499	0.131250	+	0.991349i	$0.458101\pi$
$258$	−92.9562	−5.78720
$259$	−35.6987	−2.21821
$260$	−5.02665	−0.311739
$261$	−35.0827	−2.17156
$262$	44.7776	2.76637
$263$	11.7892	0.726951	0.363476	−	0.931604i	$-0.381590\pi$
$263$	11.7892	0.726951	0.363476	+	0.931604i	$0.381590\pi$
$264$	−52.6927	−3.24301
$265$	0.0404979	0.00248777
$266$	94.8326	5.81456
$267$	0.731143	0.0447452
$268$	−14.2393	−0.869804
$269$	9.52674	0.580856	0.290428	−	0.956897i	$-0.406202\pi$
$269$	9.52674	0.580856	0.290428	+	0.956897i	$0.406202\pi$
$270$	−1.77713	−0.108153
$271$	13.1530	0.798988	0.399494	−	0.916736i	$-0.369186\pi$
$271$	13.1530	0.798988	0.399494	+	0.916736i	$0.369186\pi$
$272$	−76.1583	−4.61777
$273$	−70.0274	−4.23825
$274$	−21.0956	−1.27443
$275$	10.4326	0.629107
$276$	12.8881	0.775775
$277$	7.94272	0.477232	0.238616	−	0.971114i	$-0.423306\pi$
$277$	7.94272	0.477232	0.238616	+	0.971114i	$0.423306\pi$
$278$	−8.77342	−0.526195
$279$	30.6974	1.83781
$280$	6.33277	0.378455
$281$	−6.47960	−0.386540	−0.193270	−	0.981146i	$-0.561909\pi$
$281$	−6.47960	−0.386540	−0.193270	+	0.981146i	$0.561909\pi$
$282$	46.4445	2.76573
$283$	−7.17048	−0.426241	−0.213120	−	0.977026i	$-0.568363\pi$
$283$	−7.17048	−0.426241	−0.213120	+	0.977026i	$0.568363\pi$
$284$	−28.7514	−1.70608
$285$	−3.49720	−0.207157
$286$	33.5121	1.98161
$287$	15.0392	0.887735
$288$	−90.5808	−5.33752
$289$	11.9277	0.701628
$290$	−3.36193	−0.197419
$291$	−26.5156	−1.55437
$292$	42.6284	2.49464
$293$	18.6202	1.08780	0.543901	−	0.839150i	$-0.316947\pi$
$293$	18.6202	1.08780	0.543901	+	0.839150i	$0.316947\pi$
$294$	88.3896	5.15499
$295$	−0.0687463	−0.00400257
$296$	75.3618	4.38032
$297$	8.63590	0.501106
$298$	−6.25979	−0.362620
$299$	−5.14804	−0.297719
$300$	73.2750	4.23053
$301$	−54.2887	−3.12915
$302$	29.2871	1.68529
$303$	−4.95648	−0.284742
$304$	−113.780	−6.52576
$305$	−1.20311	−0.0688899
$306$	65.7868	3.76078
$307$	6.89468	0.393500	0.196750	−	0.980454i	$-0.436961\pi$
$307$	6.89468	0.393500	0.196750	+	0.980454i	$0.436961\pi$
$308$	−48.9982	−2.79193
$309$	−14.5606	−0.828322
$310$	2.94170	0.167077
$311$	11.1576	0.632690	0.316345	−	0.948644i	$-0.397544\pi$
$311$	11.1576	0.632690	0.316345	+	0.948644i	$0.397544\pi$
$312$	147.831	8.36930
$313$	5.69843	0.322094	0.161047	−	0.986947i	$-0.448513\pi$
$313$	5.69843	0.322094	0.161047	+	0.986947i	$0.448513\pi$
$314$	12.1753	0.687090
$315$	−3.10904	−0.175175
$316$	−15.2398	−0.857305
$317$	4.43863	0.249298	0.124649	−	0.992201i	$-0.460220\pi$
$317$	4.43863	0.249298	0.124649	+	0.992201i	$0.460220\pi$
$318$	−1.89636	−0.106342
$319$	16.3371	0.914705
$320$	−4.18062	−0.233704
$321$	−50.7429	−2.83219
$322$	10.3266	0.575478
$323$	43.2179	2.40471
$324$	−11.9905	−0.666139
$325$	−29.2690	−1.62355
$326$	36.2447	2.00741
$327$	44.5526	2.46377
$328$	−31.7485	−1.75302
$329$	27.1247	1.49543
$330$	2.47901	0.136465
$331$	17.0950	0.939626	0.469813	−	0.882766i	$-0.344321\pi$
$331$	17.0950	0.939626	0.469813	+	0.882766i	$0.344321\pi$
$332$	46.0827	2.52912
$333$	−36.9985	−2.02751
$334$	23.3856	1.27960
$335$	0.420744	0.0229877
$336$	−168.536	−9.19439
$337$	2.15292	0.117277	0.0586384	−	0.998279i	$-0.481324\pi$
$337$	2.15292	0.117277	0.0586384	+	0.998279i	$0.481324\pi$
$338$	−58.7101	−3.19341
$339$	−44.4365	−2.41346
$340$	4.59514	0.249207
$341$	−14.2951	−0.774120
$342$	98.2854	5.31467
$343$	21.2057	1.14500
$344$	114.606	6.17915
$345$	−0.380820	−0.0205027
$346$	−57.7910	−3.10686
$347$	12.2524	0.657745	0.328872	−	0.944374i	$-0.393331\pi$
$347$	12.2524	0.657745	0.328872	+	0.944374i	$0.393331\pi$
$348$	114.747	6.15108
$349$	17.5542	0.939657	0.469829	−	0.882758i	$-0.344316\pi$
$349$	17.5542	0.939657	0.469829	+	0.882758i	$0.344316\pi$
$350$	58.7114	3.13825
$351$	−24.2284	−1.29321
$352$	42.1813	2.24827
$353$	22.1319	1.17796	0.588981	−	0.808147i	$-0.299529\pi$
$353$	22.1319	1.17796	0.588981	+	0.808147i	$0.299529\pi$
$354$	3.21912	0.171094
$355$	0.849550	0.0450894
$356$	−1.43526	−0.0760687
$357$	64.0161	3.38809
$358$	16.9802	0.897429
$359$	12.3276	0.650627	0.325313	−	0.945606i	$-0.394530\pi$
$359$	12.3276	0.650627	0.325313	+	0.945606i	$0.394530\pi$
$360$	6.56334	0.345918
$361$	45.5676	2.39830
$362$	−35.3031	−1.85549
$363$	18.0848	0.949207
$364$	137.466	7.20520
$365$	−1.25959	−0.0659299
$366$	56.3369	2.94478
$367$	−8.36092	−0.436437	−0.218218	−	0.975900i	$-0.570024\pi$
$367$	−8.36092	−0.436437	−0.218218	+	0.975900i	$0.570024\pi$
$368$	−12.3899	−0.645867
$369$	15.5868	0.811414
$370$	−3.54552	−0.184323
$371$	−1.10752	−0.0574995
$372$	−100.404	−5.20570
$373$	−0.438331	−0.0226959	−0.0113479	−	0.999936i	$-0.503612\pi$
$373$	−0.438331	−0.0226959	−0.0113479	+	0.999936i	$0.503612\pi$
$374$	−30.6353	−1.58411
$375$	−4.34126	−0.224182
$376$	−57.2616	−2.95304
$377$	−45.8345	−2.36060
$378$	48.6003	2.49973
$379$	14.5368	0.746706	0.373353	−	0.927689i	$-0.378208\pi$
$379$	14.5368	0.746706	0.373353	+	0.927689i	$0.378208\pi$
$380$	6.86515	0.352175
$381$	−39.3751	−2.01725
$382$	24.8945	1.27371
$383$	−3.58417	−0.183142	−0.0915712	−	0.995799i	$-0.529189\pi$
$383$	−3.58417	−0.183142	−0.0915712	+	0.995799i	$0.529189\pi$
$384$	85.5679	4.36662
$385$	1.44780	0.0737870
$386$	−54.6075	−2.77945
$387$	−56.2653	−2.86013
$388$	52.0512	2.64250
$389$	2.73717	0.138780	0.0693901	−	0.997590i	$-0.477895\pi$
$389$	2.73717	0.138780	0.0693901	+	0.997590i	$0.477895\pi$
$390$	−6.95497	−0.352179
$391$	4.70612	0.237999
$392$	−108.976	−5.50412
$393$	45.1589	2.27796
$394$	−62.6824	−3.15789
$395$	0.450307	0.0226574
$396$	−50.7822	−2.55190
$397$	−34.7307	−1.74308	−0.871542	−	0.490320i	$-0.836880\pi$
$397$	−34.7307	−1.74308	−0.871542	+	0.490320i	$0.836880\pi$
$398$	38.3150	1.92056
$399$	95.6400	4.78799
$400$	−70.4420	−3.52210
$401$	23.8490	1.19096	0.595481	−	0.803370i	$-0.296962\pi$
$401$	23.8490	1.19096	0.595481	+	0.803370i	$0.296962\pi$
$402$	−19.7018	−0.982637
$403$	40.1053	1.99779
$404$	9.72976	0.484074
$405$	0.354296	0.0176051
$406$	91.9406	4.56293
$407$	17.2293	0.854025
$408$	−135.141	−6.69048
$409$	−6.85962	−0.339187	−0.169593	−	0.985514i	$-0.554245\pi$
$409$	−6.85962	−0.339187	−0.169593	+	0.985514i	$0.554245\pi$
$410$	1.49366	0.0737666
$411$	−21.2752	−1.04943
$412$	28.5830	1.40818
$413$	1.88004	0.0925109
$414$	10.7026	0.526003
$415$	−1.36166	−0.0668410
$416$	−118.341	−5.80215
$417$	−8.84811	−0.433294
$418$	−45.7691	−2.23864
$419$	−15.8682	−0.775210	−0.387605	−	0.921826i	$-0.626698\pi$
$419$	−15.8682	−0.775210	−0.387605	+	0.921826i	$0.626698\pi$
$420$	10.1689	0.496192
$421$	26.6544	1.29905	0.649527	−	0.760338i	$-0.274967\pi$
$421$	26.6544	1.29905	0.649527	+	0.760338i	$0.274967\pi$
$422$	9.13046	0.444464
$423$	28.1123	1.36687
$424$	2.33803	0.113545
$425$	26.7564	1.29788
$426$	−39.7811	−1.92740
$427$	32.9022	1.59225
$428$	99.6103	4.81485
$429$	33.7974	1.63175
$430$	−5.39184	−0.260017
$431$	2.88383	0.138909	0.0694546	−	0.997585i	$-0.477874\pi$
$431$	2.88383	0.138909	0.0694546	+	0.997585i	$0.477874\pi$
$432$	−58.3107	−2.80548
$433$	16.6886	0.802002	0.401001	−	0.916078i	$-0.368662\pi$
$433$	16.6886	0.802002	0.401001	+	0.916078i	$0.368662\pi$
$434$	−80.4483	−3.86164
$435$	−3.39055	−0.162565
$436$	−87.4585	−4.18850
$437$	7.03095	0.336336
$438$	58.9815	2.81825
$439$	−25.7573	−1.22933	−0.614665	−	0.788788i	$-0.710709\pi$
$439$	−25.7573	−1.22933	−0.614665	+	0.788788i	$0.710709\pi$
$440$	−3.05639	−0.145708
$441$	53.5012	2.54768
$442$	85.9485	4.08815
$443$	−38.9215	−1.84921	−0.924607	−	0.380922i	$-0.875607\pi$
$443$	−38.9215	−1.84921	−0.924607	+	0.380922i	$0.875607\pi$
$444$	121.013	5.74303
$445$	0.0424092	0.00201039
$446$	48.9414	2.31744
$447$	−6.31309	−0.298599
$448$	114.330	5.40157
$449$	−26.6822	−1.25921	−0.629606	−	0.776915i	$-0.716784\pi$
$449$	−26.6822	−1.25921	−0.629606	+	0.776915i	$0.716784\pi$
$450$	60.8490	2.86845
$451$	−7.25837	−0.341783
$452$	87.2306	4.10298
$453$	29.5365	1.38774
$454$	−62.7635	−2.94564
$455$	−4.06187	−0.190424
$456$	−201.901	−9.45487
$457$	39.9242	1.86758	0.933788	−	0.357826i	$-0.116482\pi$
$457$	39.9242	1.86758	0.933788	+	0.357826i	$0.116482\pi$
$458$	13.6804	0.639242
$459$	22.1485	1.03381
$460$	0.747565	0.0348554
$461$	17.6172	0.820517	0.410258	−	0.911969i	$-0.365439\pi$
$461$	17.6172	0.820517	0.410258	+	0.911969i	$0.365439\pi$
$462$	−67.7950	−3.15411
$463$	27.7219	1.28835	0.644173	−	0.764880i	$-0.277202\pi$
$463$	27.7219	1.28835	0.644173	+	0.764880i	$0.277202\pi$
$464$	−110.311	−5.12104
$465$	2.96674	0.137579
$466$	66.5889	3.08467
$467$	−7.98073	−0.369304	−0.184652	−	0.982804i	$-0.559116\pi$
$467$	−7.98073	−0.369304	−0.184652	+	0.982804i	$0.559116\pi$
$468$	142.472	6.58575
$469$	−11.5063	−0.531313
$470$	2.69397	0.124264
$471$	12.2789	0.565783
$472$	−3.96887	−0.182682
$473$	26.2014	1.20474
$474$	−21.0861	−0.968516
$475$	39.9741	1.83414
$476$	−125.666	−5.75989
$477$	−1.14784	−0.0525561
$478$	−16.1259	−0.737579
$479$	20.3175	0.928328	0.464164	−	0.885749i	$-0.346355\pi$
$479$	20.3175	0.928328	0.464164	+	0.885749i	$0.346355\pi$
$480$	−8.75414	−0.399570
$481$	−48.3375	−2.20400
$482$	−49.4608	−2.25288
$483$	10.4145	0.473876
$484$	−35.5012	−1.61369
$485$	−1.53802	−0.0698377
$486$	−50.1452	−2.27463
$487$	−16.3427	−0.740558	−0.370279	−	0.928921i	$-0.620738\pi$
$487$	−16.3427	−0.740558	−0.370279	+	0.928921i	$0.620738\pi$
$488$	−69.4581	−3.14422
$489$	36.5532	1.65299
$490$	5.12696	0.231612
$491$	15.3953	0.694781	0.347390	−	0.937721i	$-0.387068\pi$
$491$	15.3953	0.694781	0.347390	+	0.937721i	$0.387068\pi$
$492$	−50.9805	−2.29838
$493$	41.9000	1.88708
$494$	128.407	5.77731
$495$	1.50052	0.0674433
$496$	96.5220	4.33397
$497$	−23.2331	−1.04215
$498$	63.7609	2.85720
$499$	−25.3641	−1.13545	−0.567727	−	0.823217i	$-0.692177\pi$
$499$	−25.3641	−1.13545	−0.567727	+	0.823217i	$0.692177\pi$
$500$	8.52206	0.381118
$501$	23.5847	1.05369
$502$	−9.44646	−0.421616
$503$	8.69734	0.387795	0.193898	−	0.981022i	$-0.437887\pi$
$503$	8.69734	0.387795	0.193898	+	0.981022i	$0.437887\pi$
$504$	−179.491	−7.99518
$505$	−0.287496	−0.0127934
$506$	−4.98393	−0.221563
$507$	−59.2100	−2.62961
$508$	77.2948	3.42940
$509$	24.4401	1.08329	0.541645	−	0.840607i	$-0.317802\pi$
$509$	24.4401	1.08329	0.541645	+	0.840607i	$0.317802\pi$
$510$	6.35794	0.281534
$511$	34.4467	1.52383
$512$	−25.0408	−1.10666
$513$	33.0899	1.46096
$514$	−11.4298	−0.504149
$515$	−0.844572	−0.0372163
$516$	184.030	8.10147
$517$	−13.0912	−0.575751
$518$	96.9614	4.26024
$519$	−58.2830	−2.55834
$520$	8.57482	0.376031
$521$	−26.6533	−1.16770	−0.583851	−	0.811861i	$-0.698455\pi$
$521$	−26.6533	−1.16770	−0.583851	+	0.811861i	$0.698455\pi$
$522$	95.2881	4.17065
$523$	7.41158	0.324086	0.162043	−	0.986784i	$-0.448192\pi$
$523$	7.41158	0.324086	0.162043	+	0.986784i	$0.448192\pi$
$524$	−88.6486	−3.87263
$525$	59.2112	2.58419
$526$	−32.0206	−1.39616
$527$	−36.6626	−1.59705
$528$	81.3406	3.53990
$529$	−22.2344	−0.966712
$530$	−0.109996	−0.00477794
$531$	1.94850	0.0845575
$532$	−187.745	−8.13978
$533$	20.3637	0.882048
$534$	−1.98586	−0.0859365
$535$	−2.94329	−0.127250
$536$	24.2904	1.04919
$537$	17.1247	0.738986
$538$	−25.8756	−1.11558
$539$	−24.9142	−1.07313
$540$	3.51828	0.151403
$541$	−0.482338	−0.0207373	−0.0103687	−	0.999946i	$-0.503301\pi$
$541$	−0.482338	−0.0207373	−0.0103687	+	0.999946i	$0.503301\pi$
$542$	−35.7249	−1.53452
$543$	−35.6036	−1.52790
$544$	108.182	4.63828
$545$	2.58423	0.110696
$546$	190.202	8.13987
$547$	−20.6506	−0.882955	−0.441478	−	0.897272i	$-0.645546\pi$
$547$	−20.6506	−0.882955	−0.441478	+	0.897272i	$0.645546\pi$
$548$	41.7641	1.78407
$549$	34.1001	1.45536
$550$	−28.3359	−1.20825
$551$	62.5985	2.66679
$552$	−21.9855	−0.935767
$553$	−12.3148	−0.523678
$554$	−21.5732	−0.916559
$555$	−3.57571	−0.151780
$556$	17.3692	0.736617
$557$	−35.3579	−1.49816	−0.749082	−	0.662477i	$-0.769505\pi$
$557$	−35.3579	−1.49816	−0.749082	+	0.662477i	$0.769505\pi$
$558$	−83.3773	−3.52964
$559$	−73.5090	−3.10910
$560$	−9.77577	−0.413101
$561$	−30.8961	−1.30443
$562$	17.5992	0.742379
$563$	2.72443	0.114821	0.0574105	−	0.998351i	$-0.481716\pi$
$563$	2.72443	0.114821	0.0574105	+	0.998351i	$0.481716\pi$
$564$	−91.9485	−3.87173
$565$	−2.57750	−0.108436
$566$	19.4757	0.818627
$567$	−9.68914	−0.406906
$568$	49.0462	2.05793
$569$	31.4176	1.31710	0.658548	−	0.752539i	$-0.271171\pi$
$569$	31.4176	1.31710	0.658548	+	0.752539i	$0.271171\pi$
$570$	9.49876	0.397859
$571$	−42.8357	−1.79262	−0.896309	−	0.443429i	$-0.853762\pi$
$571$	−42.8357	−1.79262	−0.896309	+	0.443429i	$0.853762\pi$
$572$	−66.3455	−2.77405
$573$	25.1064	1.04884
$574$	−40.8480	−1.70496
$575$	4.35289	0.181528
$576$	118.492	4.93718
$577$	−26.6744	−1.11047	−0.555235	−	0.831693i	$-0.687372\pi$
$577$	−26.6744	−1.11047	−0.555235	+	0.831693i	$0.687372\pi$
$578$	−32.3968	−1.34753
$579$	−55.0724	−2.28873
$580$	6.65578	0.276366
$581$	37.2380	1.54489
$582$	72.0192	2.98529
$583$	0.534522	0.0221377
$584$	−72.7186	−3.00912
$585$	−4.20976	−0.174052
$586$	−50.5742	−2.08920
$587$	11.0427	0.455783	0.227891	−	0.973687i	$-0.426817\pi$
$587$	11.0427	0.455783	0.227891	+	0.973687i	$0.426817\pi$
$588$	−174.989	−7.21644
$589$	−54.7739	−2.25692
$590$	0.186722	0.00768722
$591$	−63.2161	−2.60036
$592$	−116.335	−4.78132
$593$	−20.5543	−0.844065	−0.422032	−	0.906581i	$-0.638683\pi$
$593$	−20.5543	−0.844065	−0.422032	+	0.906581i	$0.638683\pi$
$594$	−23.4560	−0.962411
$595$	3.71319	0.152226
$596$	12.3928	0.507630
$597$	38.6412	1.58148
$598$	13.9826	0.571791
$599$	10.4358	0.426394	0.213197	−	0.977009i	$-0.431612\pi$
$599$	10.4358	0.426394	0.213197	+	0.977009i	$0.431612\pi$
$600$	−124.998	−5.10301
$601$	−15.2257	−0.621070	−0.310535	−	0.950562i	$-0.600508\pi$
$601$	−15.2257	−0.621070	−0.310535	+	0.950562i	$0.600508\pi$
$602$	147.454	6.00976
$603$	−11.9253	−0.485635
$604$	−57.9812	−2.35922
$605$	1.04899	0.0426476
$606$	13.4623	0.546868
$607$	12.4996	0.507345	0.253673	−	0.967290i	$-0.418361\pi$
$607$	12.4996	0.507345	0.253673	+	0.967290i	$0.418361\pi$
$608$	161.625	6.55474
$609$	92.7233	3.75734
$610$	3.26777	0.132308
$611$	36.7280	1.48585
$612$	−130.241	−5.26470
$613$	−36.2795	−1.46532	−0.732658	−	0.680597i	$-0.761721\pi$
$613$	−36.2795	−1.46532	−0.732658	+	0.680597i	$0.761721\pi$
$614$	−18.7266	−0.755746
$615$	1.50638	0.0607430
$616$	83.5847	3.36772
$617$	−32.1822	−1.29561	−0.647804	−	0.761807i	$-0.724313\pi$
$617$	−32.1822	−1.29561	−0.647804	+	0.761807i	$0.724313\pi$
$618$	39.5480	1.59085
$619$	−8.32153	−0.334470	−0.167235	−	0.985917i	$-0.553484\pi$
$619$	−8.32153	−0.334470	−0.167235	+	0.985917i	$0.553484\pi$
$620$	−5.82383	−0.233891
$621$	3.60325	0.144594
$622$	−30.3052	−1.21513
$623$	−1.15979	−0.0464660
$624$	−228.204	−9.13548
$625$	24.6220	0.984879
$626$	−15.4775	−0.618606
$627$	−46.1588	−1.84340
$628$	−24.1040	−0.961854
$629$	44.1881	1.76189
$630$	8.44447	0.336436
$631$	27.3877	1.09029	0.545143	−	0.838343i	$-0.316475\pi$
$631$	27.3877	1.09029	0.545143	+	0.838343i	$0.316475\pi$
$632$	25.9971	1.03411
$633$	9.20819	0.365993
$634$	−12.0558	−0.478795
$635$	−2.28391	−0.0906344
$636$	3.75431	0.148868
$637$	69.8978	2.76945
$638$	−44.3733	−1.75676
$639$	−24.0790	−0.952551
$640$	4.96329	0.196191
$641$	21.0321	0.830718	0.415359	−	0.909658i	$-0.363656\pi$
$641$	21.0321	0.830718	0.415359	+	0.909658i	$0.363656\pi$
$642$	137.823	5.43944
$643$	−14.1154	−0.556655	−0.278328	−	0.960486i	$-0.589780\pi$
$643$	−14.1154	−0.556655	−0.278328	+	0.960486i	$0.589780\pi$
$644$	−20.4441	−0.805609
$645$	−5.43774	−0.214111
$646$	−117.384	−4.61842
$647$	−38.1827	−1.50112	−0.750559	−	0.660803i	$-0.770216\pi$
$647$	−38.1827	−1.50112	−0.750559	+	0.660803i	$0.770216\pi$
$648$	20.4543	0.803519
$649$	−0.907367	−0.0356173
$650$	79.4975	3.11815
$651$	−81.1332	−3.17986
$652$	−71.7554	−2.81016
$653$	−43.1170	−1.68730	−0.843650	−	0.536893i	$-0.819598\pi$
$653$	−43.1170	−1.68730	−0.843650	+	0.536893i	$0.819598\pi$
$654$	−121.009	−4.73184
$655$	2.61940	0.102348
$656$	49.0095	1.91350
$657$	35.7008	1.39282
$658$	−73.6735	−2.87209
$659$	31.5378	1.22854	0.614269	−	0.789097i	$-0.289451\pi$
$659$	31.5378	1.22854	0.614269	+	0.789097i	$0.289451\pi$
$660$	−4.90783	−0.191037
$661$	20.1123	0.782276	0.391138	−	0.920332i	$-0.372081\pi$
$661$	20.1123	0.782276	0.391138	+	0.920332i	$0.372081\pi$
$662$	−46.4317	−1.80462
$663$	86.6803	3.36638
$664$	−78.6112	−3.05070
$665$	5.54751	0.215123
$666$	100.492	3.89397
$667$	6.81653	0.263937
$668$	−46.2977	−1.79131
$669$	49.3581	1.90829
$670$	−1.14278	−0.0441496
$671$	−15.8796	−0.613025
$672$	239.404	9.23523
$673$	38.1061	1.46888	0.734441	−	0.678673i	$-0.237444\pi$
$673$	38.1061	1.46888	0.734441	+	0.678673i	$0.237444\pi$
$674$	−5.84753	−0.225239
$675$	20.4861	0.788512
$676$	116.231	4.47044
$677$	−43.0476	−1.65445	−0.827226	−	0.561869i	$-0.810082\pi$
$677$	−43.0476	−1.65445	−0.827226	+	0.561869i	$0.810082\pi$
$678$	120.694	4.63523
$679$	42.0610	1.61415
$680$	−7.83873	−0.300602
$681$	−63.2979	−2.42558
$682$	38.8268	1.48675
$683$	−12.5972	−0.482018	−0.241009	−	0.970523i	$-0.577478\pi$
$683$	−12.5972	−0.482018	−0.241009	+	0.970523i	$0.577478\pi$
$684$	−194.581	−7.43998
$685$	−1.23405	−0.0471506
$686$	−57.5967	−2.19905
$687$	13.7968	0.526382
$688$	−176.915	−6.74483
$689$	−1.49962	−0.0571311
$690$	1.03435	0.0393769
$691$	13.3706	0.508642	0.254321	−	0.967120i	$-0.418148\pi$
$691$	13.3706	0.508642	0.254321	+	0.967120i	$0.418148\pi$
$692$	114.412	4.34928
$693$	−41.0355	−1.55881
$694$	−33.2788	−1.26325
$695$	−0.513226	−0.0194678
$696$	−195.744	−7.41964
$697$	−18.6156	−0.705115
$698$	−47.6791	−1.80468
$699$	67.1558	2.54007
$700$	−116.234	−4.39323
$701$	−31.6835	−1.19667	−0.598335	−	0.801246i	$-0.704171\pi$
$701$	−31.6835	−1.19667	−0.598335	+	0.801246i	$0.704171\pi$
$702$	65.8067	2.48371
$703$	66.0170	2.48988
$704$	−55.1790	−2.07964
$705$	2.71690	0.102325
$706$	−60.1125	−2.26236
$707$	7.86231	0.295693
$708$	−6.37305	−0.239514
$709$	18.4930	0.694517	0.347259	−	0.937769i	$-0.387113\pi$
$709$	18.4930	0.694517	0.347259	+	0.937769i	$0.387113\pi$
$710$	−2.30746	−0.0865975
$711$	−12.7632	−0.478656
$712$	2.44837	0.0917567
$713$	−5.96448	−0.223372
$714$	−173.874	−6.50707
$715$	1.96038	0.0733142
$716$	−33.6165	−1.25631
$717$	−16.2631	−0.607358
$718$	−33.4831	−1.24958
$719$	24.6704	0.920052	0.460026	−	0.887905i	$-0.347840\pi$
$719$	24.6704	0.920052	0.460026	+	0.887905i	$0.347840\pi$
$720$	−10.1317	−0.377586
$721$	23.0970	0.860177
$722$	−123.766	−4.60610
$723$	−49.8819	−1.85513
$724$	69.8913	2.59749
$725$	38.7551	1.43933
$726$	−49.1202	−1.82302
$727$	41.9802	1.55696	0.778479	−	0.627670i	$-0.215991\pi$
$727$	41.9802	1.55696	0.778479	+	0.627670i	$0.215991\pi$
$728$	−234.500	−8.69116
$729$	−43.8825	−1.62528
$730$	3.42117	0.126623
$731$	67.1988	2.48544
$732$	−111.533	−4.12238
$733$	17.9149	0.661701	0.330850	−	0.943683i	$-0.392664\pi$
$733$	17.9149	0.661701	0.330850	+	0.943683i	$0.392664\pi$
$734$	22.7091	0.838208
$735$	5.17061	0.190721
$736$	17.5997	0.648735
$737$	5.55331	0.204559
$738$	−42.3352	−1.55838
$739$	2.90594	0.106897	0.0534484	−	0.998571i	$-0.482979\pi$
$739$	2.90594	0.106897	0.0534484	+	0.998571i	$0.482979\pi$
$740$	7.01925	0.258033
$741$	129.500	4.75731
$742$	3.00813	0.110432
$743$	−6.16836	−0.226295	−0.113148	−	0.993578i	$-0.536093\pi$
$743$	−6.16836	−0.226295	−0.113148	+	0.993578i	$0.536093\pi$
$744$	171.276	6.27929
$745$	−0.366185	−0.0134160
$746$	1.19055	0.0435891
$747$	38.5938	1.41207
$748$	60.6502	2.21759
$749$	80.4919	2.94111
$750$	11.7913	0.430557
$751$	20.5733	0.750729	0.375365	−	0.926877i	$-0.377517\pi$
$751$	20.5733	0.750729	0.375365	+	0.926877i	$0.377517\pi$
$752$	88.3936	3.22338
$753$	−9.52689	−0.347179
$754$	124.491	4.53370
$755$	1.71324	0.0623510
$756$	−96.2164	−3.49936
$757$	29.4228	1.06939	0.534695	−	0.845045i	$-0.320427\pi$
$757$	29.4228	1.06939	0.534695	+	0.845045i	$0.320427\pi$
$758$	−39.4835	−1.43410
$759$	−5.02636	−0.182445
$760$	−11.7111	−0.424805
$761$	32.6594	1.18390	0.591951	−	0.805974i	$-0.298358\pi$
$761$	32.6594	1.18390	0.591951	+	0.805974i	$0.298358\pi$
$762$	106.947	3.87427
$763$	−70.6725	−2.55852
$764$	−49.2848	−1.78306
$765$	3.84839	0.139139
$766$	9.73496	0.351738
$767$	2.54565	0.0919182
$768$	−88.2619	−3.18488
$769$	−31.3234	−1.12955	−0.564776	−	0.825244i	$-0.691037\pi$
$769$	−31.3234	−1.12955	−0.564776	+	0.825244i	$0.691037\pi$
$770$	−3.93238	−0.141713
$771$	−11.5272	−0.415140
$772$	108.109	3.89094
$773$	50.2265	1.80652	0.903260	−	0.429093i	$-0.141167\pi$
$773$	50.2265	1.80652	0.903260	+	0.429093i	$0.141167\pi$
$774$	152.822	5.49308
$775$	−33.9108	−1.21811
$776$	−88.7928	−3.18747
$777$	97.7869	3.50809
$778$	−7.43444	−0.266538
$779$	−27.8117	−0.996457
$780$	13.7691	0.493013
$781$	11.2130	0.401233
$782$	−12.7823	−0.457094
$783$	32.0808	1.14647
$784$	168.224	6.00800
$785$	0.712227	0.0254205
$786$	−122.656	−4.37500
$787$	−31.1359	−1.10988	−0.554938	−	0.831892i	$-0.687258\pi$
$787$	−31.1359	−1.10988	−0.554938	+	0.831892i	$0.687258\pi$
$788$	124.096	4.42072
$789$	−32.2932	−1.14967
$790$	−1.22308	−0.0435152
$791$	70.4883	2.50627
$792$	86.6280	3.07819
$793$	44.5508	1.58205
$794$	94.3321	3.34772
$795$	−0.110933	−0.00393438
$796$	−75.8542	−2.68858
$797$	25.9842	0.920408	0.460204	−	0.887813i	$-0.347776\pi$
$797$	25.9842	0.920408	0.460204	+	0.887813i	$0.347776\pi$
$798$	−259.768	−9.19568
$799$	−33.5751	−1.18780
$800$	100.063	3.53775
$801$	−1.20202	−0.0424712
$802$	−64.7762	−2.28733
$803$	−16.6250	−0.586684
$804$	39.0047	1.37559
$805$	0.604083	0.0212911
$806$	−108.930	−3.83690
$807$	−26.0959	−0.918618
$808$	−16.5977	−0.583906
$809$	−48.3395	−1.69953	−0.849764	−	0.527164i	$-0.823255\pi$
$809$	−48.3395	−1.69953	−0.849764	+	0.527164i	$0.823255\pi$
$810$	−0.962305	−0.0338119
$811$	47.9040	1.68214	0.841068	−	0.540929i	$-0.181927\pi$
$811$	47.9040	1.68214	0.841068	+	0.540929i	$0.181927\pi$
$812$	−182.019	−6.38763
$813$	−36.0290	−1.26359
$814$	−46.7965	−1.64022
$815$	2.12024	0.0742686
$816$	208.615	7.30297
$817$	100.395	3.51238
$818$	18.6314	0.651433
$819$	115.127	4.02286
$820$	−2.95707	−0.103266
$821$	15.8562	0.553384	0.276692	−	0.960959i	$-0.410762\pi$
$821$	15.8562	0.553384	0.276692	+	0.960959i	$0.410762\pi$
$822$	57.7857	2.01551
$823$	16.5329	0.576299	0.288149	−	0.957585i	$-0.406960\pi$
$823$	16.5329	0.576299	0.288149	+	0.957585i	$0.406960\pi$
$824$	−48.7589	−1.69860
$825$	−28.5771	−0.994928
$826$	−5.10639	−0.177674
$827$	−34.9963	−1.21694	−0.608470	−	0.793577i	$-0.708217\pi$
$827$	−34.9963	−1.21694	−0.608470	+	0.793577i	$0.708217\pi$
$828$	−21.1884	−0.736349
$829$	−15.3071	−0.531637	−0.265819	−	0.964023i	$-0.585642\pi$
$829$	−15.3071	−0.531637	−0.265819	+	0.964023i	$0.585642\pi$
$830$	3.69839	0.128373
$831$	−21.7569	−0.754739
$832$	154.807	5.36697
$833$	−63.8976	−2.21392
$834$	24.0324	0.832172
$835$	1.36801	0.0473419
$836$	90.6115	3.13386
$837$	−28.0708	−0.970268
$838$	43.0995	1.48885
$839$	−41.0614	−1.41760	−0.708798	−	0.705412i	$-0.750762\pi$
$839$	−41.0614	−1.41760	−0.708798	+	0.705412i	$0.750762\pi$
$840$	−17.3469	−0.598524
$841$	31.6895	1.09274
$842$	−72.3959	−2.49493
$843$	17.7491	0.611311
$844$	−18.0760	−0.622203
$845$	−3.43442	−0.118148
$846$	−76.3559	−2.62517
$847$	−28.6874	−0.985710
$848$	−3.60916	−0.123939
$849$	19.6416	0.674096
$850$	−72.6732	−2.49267
$851$	7.18877	0.246428
$852$	78.7566	2.69816
$853$	54.4976	1.86596	0.932981	−	0.359926i	$-0.117198\pi$
$853$	54.4976	1.86596	0.932981	+	0.359926i	$0.117198\pi$
$854$	−89.3656	−3.05803
$855$	5.74949	0.196628
$856$	−169.922	−5.80783
$857$	24.4830	0.836325	0.418162	−	0.908372i	$-0.362674\pi$
$857$	24.4830	0.836325	0.418162	+	0.908372i	$0.362674\pi$
$858$	−91.7971	−3.13390
$859$	−52.6580	−1.79667	−0.898335	−	0.439312i	$-0.855222\pi$
$859$	−52.6580	−1.79667	−0.898335	+	0.439312i	$0.855222\pi$
$860$	10.6745	0.363997
$861$	−41.1957	−1.40395
$862$	−7.83278	−0.266785
$863$	−3.32743	−0.113267	−0.0566335	−	0.998395i	$-0.518037\pi$
$863$	−3.32743	−0.113267	−0.0566335	+	0.998395i	$0.518037\pi$
$864$	82.8301	2.81794
$865$	−3.38065	−0.114945
$866$	−45.3279	−1.54030
$867$	−32.6726	−1.10962
$868$	159.268	5.40589
$869$	5.94350	0.201619
$870$	9.20908	0.312217
$871$	−15.5800	−0.527909
$872$	149.193	5.05232
$873$	43.5924	1.47538
$874$	−19.0968	−0.645958
$875$	6.88641	0.232803
$876$	−116.769	−3.94525
$877$	12.4528	0.420501	0.210250	−	0.977648i	$-0.432572\pi$
$877$	12.4528	0.420501	0.210250	+	0.977648i	$0.432572\pi$
$878$	69.9595	2.36102
$879$	−51.0048	−1.72035
$880$	4.71808	0.159047
$881$	−0.212056	−0.00714433	−0.00357217	−	0.999994i	$-0.501137\pi$
$881$	−0.212056	−0.00714433	−0.00357217	+	0.999994i	$0.501137\pi$
$882$	−145.315	−4.89300
$883$	56.5320	1.90245	0.951226	−	0.308493i	$-0.0998248\pi$
$883$	56.5320	1.90245	0.951226	+	0.308493i	$0.0998248\pi$
$884$	−170.157	−5.72299
$885$	0.188312	0.00633003
$886$	105.715	3.55155
$887$	9.08386	0.305006	0.152503	−	0.988303i	$-0.451267\pi$
$887$	9.08386	0.305006	0.152503	+	0.988303i	$0.451267\pi$
$888$	−206.433	−6.92744
$889$	62.4595	2.09482
$890$	−0.115188	−0.00386110
$891$	4.67628	0.156661
$892$	−96.8918	−3.24418
$893$	−50.1612	−1.67858
$894$	17.1470	0.573481
$895$	0.993303	0.0332025
$896$	−135.734	−4.53455
$897$	14.1017	0.470840
$898$	72.4716	2.41841
$899$	−53.1035	−1.77110
$900$	−120.466	−4.01553
$901$	1.37089	0.0456710
$902$	19.7145	0.656420
$903$	148.709	4.94872
$904$	−148.804	−4.94916
$905$	−2.06515	−0.0686481
$906$	−80.2241	−2.66527
$907$	−52.1443	−1.73142	−0.865712	−	0.500542i	$-0.833134\pi$
$907$	−52.1443	−1.73142	−0.865712	+	0.500542i	$0.833134\pi$
$908$	124.256	4.12359
$909$	8.14857	0.270271
$910$	11.0325	0.365722
$911$	−25.0649	−0.830436	−0.415218	−	0.909722i	$-0.636295\pi$
$911$	−25.0649	−0.830436	−0.415218	+	0.909722i	$0.636295\pi$
$912$	311.670	10.3204
$913$	−17.9722	−0.594792
$914$	−108.438	−3.58682
$915$	3.29559	0.108949
$916$	−27.0837	−0.894872
$917$	−71.6341	−2.36557
$918$	−60.1577	−1.98550
$919$	35.7128	1.17806	0.589029	−	0.808112i	$-0.299510\pi$
$919$	35.7128	1.17806	0.589029	+	0.808112i	$0.299510\pi$
$920$	−1.27525	−0.0420437
$921$	−18.8861	−0.622317
$922$	−47.8502	−1.57586
$923$	−31.4585	−1.03547
$924$	134.217	4.41542
$925$	40.8715	1.34385
$926$	−75.2955	−2.47436
$927$	23.9379	0.786225
$928$	156.696	5.14379
$929$	13.3232	0.437121	0.218561	−	0.975823i	$-0.429864\pi$
$929$	13.3232	0.437121	0.218561	+	0.975823i	$0.429864\pi$
$930$	−8.05797	−0.264231
$931$	−95.4630	−3.12867
$932$	−131.829	−4.31822
$933$	−30.5632	−1.00060
$934$	21.6765	0.709276
$935$	−1.79210	−0.0586079
$936$	−243.038	−7.94396
$937$	15.7207	0.513572	0.256786	−	0.966468i	$-0.417336\pi$
$937$	15.7207	0.513572	0.256786	+	0.966468i	$0.417336\pi$
$938$	31.2524	1.02043
$939$	−15.6093	−0.509390
$940$	−5.33339	−0.173956
$941$	−53.9557	−1.75891	−0.879453	−	0.475985i	$-0.842092\pi$
$941$	−53.9557	−1.75891	−0.879453	+	0.475985i	$0.842092\pi$
$942$	−33.3508	−1.08663
$943$	−3.02849	−0.0986212
$944$	6.12666	0.199406
$945$	2.84301	0.0924832
$946$	−71.1656	−2.31379
$947$	2.89042	0.0939260	0.0469630	−	0.998897i	$-0.485046\pi$
$947$	2.89042	0.0939260	0.0469630	+	0.998897i	$0.485046\pi$
$948$	41.7452	1.35582
$949$	46.6421	1.51407
$950$	−108.574	−3.52260
$951$	−12.1584	−0.394263
$952$	214.370	6.94778
$953$	24.4542	0.792150	0.396075	−	0.918218i	$-0.370372\pi$
$953$	24.4542	0.792150	0.396075	+	0.918218i	$0.370372\pi$
$954$	3.11766	0.100938
$955$	1.45627	0.0471239
$956$	31.9252	1.03253
$957$	−44.7511	−1.44660
$958$	−55.1842	−1.78292
$959$	33.7483	1.08979
$960$	11.4517	0.369601
$961$	15.4657	0.498894
$962$	131.290	4.23295
$963$	83.4226	2.68826
$964$	97.9200	3.15379
$965$	−3.19442	−0.102832
$966$	−28.2868	−0.910114
$967$	3.28436	0.105618	0.0528090	−	0.998605i	$-0.483183\pi$
$967$	3.28436	0.105618	0.0528090	+	0.998605i	$0.483183\pi$
$968$	60.5605	1.94649
$969$	−118.384	−3.80303
$970$	4.17740	0.134128
$971$	−4.90323	−0.157352	−0.0786760	−	0.996900i	$-0.525069\pi$
$971$	−4.90323	−0.157352	−0.0786760	+	0.996900i	$0.525069\pi$
$972$	99.2749	3.18425
$973$	14.0355	0.449957
$974$	44.3884	1.42230
$975$	80.1743	2.56763
$976$	107.221	3.43206
$977$	−8.66558	−0.277237	−0.138618	−	0.990346i	$-0.544266\pi$
$977$	−8.66558	−0.277237	−0.138618	+	0.990346i	$0.544266\pi$
$978$	−99.2823	−3.17470
$979$	0.559750	0.0178897
$980$	−10.1501	−0.324233
$981$	−73.2456	−2.33855
$982$	−41.8152	−1.33438
$983$	−44.6584	−1.42438	−0.712191	−	0.701986i	$-0.752297\pi$
$983$	−44.6584	−1.42438	−0.712191	+	0.701986i	$0.752297\pi$
$984$	86.9662	2.77238
$985$	−3.66679	−0.116834
$986$	−113.804	−3.62427
$987$	−74.3007	−2.36502
$988$	−254.214	−8.08763
$989$	10.9323	0.347627
$990$	−4.07556	−0.129530
$991$	29.3430	0.932112	0.466056	−	0.884755i	$-0.345675\pi$
$991$	29.3430	0.932112	0.466056	+	0.884755i	$0.345675\pi$
$992$	−137.109	−4.35322
$993$	−46.8271	−1.48601
$994$	63.1035	2.00152
$995$	2.24135	0.0710554
$996$	−126.231	−3.99978
$997$	14.1244	0.447324	0.223662	−	0.974667i	$-0.428199\pi$
$997$	14.1244	0.447324	0.223662	+	0.974667i	$0.428199\pi$
$998$	68.8915	2.18072
$999$	33.8327	1.07042

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4007.2.a.b.1.6	✓	195

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4007.2.a.b.1.6	✓	195	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:	\( N \)	\(=\)	\( 4007 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4007.a (trivial)

\(f(q)\)	\(=\)	\(q-2.71610 q^{2} -2.73922 q^{3} +5.37720 q^{4} -0.158886 q^{5} +7.44001 q^{6} +4.34515 q^{7} -9.17282 q^{8} +4.50335 q^{9} +O(q^{10})\)	\(q-2.71610 q^{2} -2.73922 q^{3} +5.37720 q^{4} -0.158886 q^{5} +7.44001 q^{6} +4.34515 q^{7} -9.17282 q^{8} +4.50335 q^{9} +0.431551 q^{10} -2.09710 q^{11} -14.7294 q^{12} +5.88350 q^{13} -11.8019 q^{14} +0.435225 q^{15} +14.1599 q^{16} -5.37844 q^{17} -12.2316 q^{18} -8.03540 q^{19} -0.854363 q^{20} -11.9023 q^{21} +5.69594 q^{22} -0.874997 q^{23} +25.1264 q^{24} -4.97476 q^{25} -15.9802 q^{26} -4.11802 q^{27} +23.3647 q^{28} -7.79035 q^{29} -1.18211 q^{30} +6.81658 q^{31} -20.1141 q^{32} +5.74443 q^{33} +14.6084 q^{34} -0.690384 q^{35} +24.2154 q^{36} -8.21577 q^{37} +21.8249 q^{38} -16.1162 q^{39} +1.45743 q^{40} +3.46115 q^{41} +32.3279 q^{42} -12.4941 q^{43} -11.2765 q^{44} -0.715520 q^{45} +2.37658 q^{46} +6.24253 q^{47} -38.7872 q^{48} +11.8803 q^{49} +13.5119 q^{50} +14.7328 q^{51} +31.6368 q^{52} -0.254886 q^{53} +11.1850 q^{54} +0.333200 q^{55} -39.8573 q^{56} +22.0108 q^{57} +21.1594 q^{58} +0.432677 q^{59} +2.34029 q^{60} +7.57216 q^{61} -18.5145 q^{62} +19.5677 q^{63} +26.3120 q^{64} -0.934807 q^{65} -15.6025 q^{66} -2.64809 q^{67} -28.9210 q^{68} +2.39681 q^{69} +1.87515 q^{70} -5.34691 q^{71} -41.3084 q^{72} +7.92762 q^{73} +22.3149 q^{74} +13.6270 q^{75} -43.2080 q^{76} -9.11222 q^{77} +43.7733 q^{78} -2.83415 q^{79} -2.24981 q^{80} -2.22988 q^{81} -9.40082 q^{82} +8.57001 q^{83} -64.0013 q^{84} +0.854560 q^{85} +33.9352 q^{86} +21.3395 q^{87} +19.2363 q^{88} -0.266916 q^{89} +1.94342 q^{90} +25.5647 q^{91} -4.70503 q^{92} -18.6721 q^{93} -16.9553 q^{94} +1.27671 q^{95} +55.0970 q^{96} +9.67998 q^{97} -32.2681 q^{98} -9.44399 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 195 q + 14 q^{2} + 22 q^{3} + 220 q^{4} + 14 q^{5} + 13 q^{6} + 48 q^{7} + 39 q^{8} + 245 q^{9}+O(q^{10}) \) 195 * q + 14 * q^2 + 22 * q^3 + 220 * q^4 + 14 * q^5 + 13 * q^6 + 48 * q^7 + 39 * q^8 + 245 * q^9	\( 195 q + 14 q^{2} + 22 q^{3} + 220 q^{4} + 14 q^{5} + 13 q^{6} + 48 q^{7} + 39 q^{8} + 245 q^{9} + 40 q^{10} + 13 q^{11} + 57 q^{12} + 97 q^{13} + 9 q^{14} + 23 q^{15} + 270 q^{16} + 66 q^{17} + 60 q^{18} + 33 q^{19} + 24 q^{20} + 27 q^{21} + 127 q^{22} + 42 q^{23} + 33 q^{24} + 357 q^{25} + 8 q^{26} + 79 q^{27} + 131 q^{28} + 57 q^{29} + 51 q^{30} + 41 q^{31} + 67 q^{32} + 74 q^{33} + 26 q^{34} + 14 q^{35} + 279 q^{36} + 133 q^{37} + 7 q^{38} + 28 q^{39} + 97 q^{40} + 64 q^{41} - q^{42} + 123 q^{43} + 21 q^{44} + 40 q^{45} + 84 q^{46} + 14 q^{47} + 122 q^{48} + 335 q^{49} + 35 q^{50} + 37 q^{51} + 220 q^{52} + 83 q^{53} + 21 q^{54} + 47 q^{55} + q^{56} + 235 q^{57} + 138 q^{58} + 18 q^{59} - 4 q^{60} + 81 q^{61} + 39 q^{62} + 102 q^{63} + 343 q^{64} + 165 q^{65} - 54 q^{66} + 147 q^{67} + 74 q^{68} - 2 q^{69} + 13 q^{70} + 31 q^{71} + 112 q^{72} + 300 q^{73} + 5 q^{74} + 84 q^{75} + 64 q^{76} + 67 q^{77} + 61 q^{78} + 144 q^{79} - 8 q^{80} + 359 q^{81} + 85 q^{82} + 26 q^{83} + 12 q^{84} + 201 q^{85} - 2 q^{86} + 80 q^{87} + 347 q^{88} + 29 q^{89} + 62 q^{90} + 70 q^{91} + 79 q^{92} + 76 q^{93} + 72 q^{94} + 71 q^{95} + 31 q^{96} + 264 q^{97} + 30 q^{98} + 19 q^{99}+O(q^{100}) \) 195 * q + 14 * q^2 + 22 * q^3 + 220 * q^4 + 14 * q^5 + 13 * q^6 + 48 * q^7 + 39 * q^8 + 245 * q^9 + 40 * q^10 + 13 * q^11 + 57 * q^12 + 97 * q^13 + 9 * q^14 + 23 * q^15 + 270 * q^16 + 66 * q^17 + 60 * q^18 + 33 * q^19 + 24 * q^20 + 27 * q^21 + 127 * q^22 + 42 * q^23 + 33 * q^24 + 357 * q^25 + 8 * q^26 + 79 * q^27 + 131 * q^28 + 57 * q^29 + 51 * q^30 + 41 * q^31 + 67 * q^32 + 74 * q^33 + 26 * q^34 + 14 * q^35 + 279 * q^36 + 133 * q^37 + 7 * q^38 + 28 * q^39 + 97 * q^40 + 64 * q^41 - q^42 + 123 * q^43 + 21 * q^44 + 40 * q^45 + 84 * q^46 + 14 * q^47 + 122 * q^48 + 335 * q^49 + 35 * q^50 + 37 * q^51 + 220 * q^52 + 83 * q^53 + 21 * q^54 + 47 * q^55 + q^56 + 235 * q^57 + 138 * q^58 + 18 * q^59 - 4 * q^60 + 81 * q^61 + 39 * q^62 + 102 * q^63 + 343 * q^64 + 165 * q^65 - 54 * q^66 + 147 * q^67 + 74 * q^68 - 2 * q^69 + 13 * q^70 + 31 * q^71 + 112 * q^72 + 300 * q^73 + 5 * q^74 + 84 * q^75 + 64 * q^76 + 67 * q^77 + 61 * q^78 + 144 * q^79 - 8 * q^80 + 359 * q^81 + 85 * q^82 + 26 * q^83 + 12 * q^84 + 201 * q^85 - 2 * q^86 + 80 * q^87 + 347 * q^88 + 29 * q^89 + 62 * q^90 + 70 * q^91 + 79 * q^92 + 76 * q^93 + 72 * q^94 + 71 * q^95 + 31 * q^96 + 264 * q^97 + 30 * q^98 + 19 * q^99

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