LMFDB - Embedded newform 1339.2.a.e.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1339,2,Mod(1,1339)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1339, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("1339.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1339 = 13 \cdot 103 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1339.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:	$10.6919688306$
Analytic rank:	$1$
Dimension:	$21$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Character	$\chi$	$=$	1339.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.12469 q^{2} +0.347667 q^{3} +2.51433 q^{4} -4.40399 q^{5} -0.738685 q^{6} -0.0796229 q^{7} -1.09279 q^{8} -2.87913 q^{9} +O(q^{10})$	\(q-2.12469 q^{2} +0.347667 q^{3} +2.51433 q^{4} -4.40399 q^{5} -0.738685 q^{6} -0.0796229 q^{7} -1.09279 q^{8} -2.87913 q^{9} +9.35713 q^{10} +4.35168 q^{11} +0.874148 q^{12} -1.00000 q^{13} +0.169174 q^{14} -1.53112 q^{15} -2.70681 q^{16} -0.234125 q^{17} +6.11727 q^{18} +7.31908 q^{19} -11.0731 q^{20} -0.0276822 q^{21} -9.24598 q^{22} -0.812188 q^{23} -0.379926 q^{24} +14.3951 q^{25} +2.12469 q^{26} -2.04398 q^{27} -0.200198 q^{28} -2.12916 q^{29} +3.25316 q^{30} -3.40165 q^{31} +7.93673 q^{32} +1.51293 q^{33} +0.497445 q^{34} +0.350658 q^{35} -7.23907 q^{36} +11.7481 q^{37} -15.5508 q^{38} -0.347667 q^{39} +4.81263 q^{40} -7.15208 q^{41} +0.0588163 q^{42} +6.12509 q^{43} +10.9415 q^{44} +12.6796 q^{45} +1.72565 q^{46} -0.190494 q^{47} -0.941068 q^{48} -6.99366 q^{49} -30.5852 q^{50} -0.0813975 q^{51} -2.51433 q^{52} -10.1519 q^{53} +4.34283 q^{54} -19.1647 q^{55} +0.0870111 q^{56} +2.54460 q^{57} +4.52382 q^{58} -2.95128 q^{59} -3.84974 q^{60} -7.49067 q^{61} +7.22748 q^{62} +0.229245 q^{63} -11.4495 q^{64} +4.40399 q^{65} -3.21452 q^{66} -8.85777 q^{67} -0.588667 q^{68} -0.282371 q^{69} -0.745042 q^{70} +7.80083 q^{71} +3.14628 q^{72} +12.8987 q^{73} -24.9612 q^{74} +5.00470 q^{75} +18.4026 q^{76} -0.346493 q^{77} +0.738685 q^{78} -8.22786 q^{79} +11.9208 q^{80} +7.92676 q^{81} +15.1960 q^{82} -13.2689 q^{83} -0.0696022 q^{84} +1.03108 q^{85} -13.0140 q^{86} -0.740238 q^{87} -4.75547 q^{88} -4.38958 q^{89} -26.9404 q^{90} +0.0796229 q^{91} -2.04211 q^{92} -1.18264 q^{93} +0.404741 q^{94} -32.2331 q^{95} +2.75934 q^{96} +1.24048 q^{97} +14.8594 q^{98} -12.5290 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 21 q - q^{2} - 6 q^{3} + 15 q^{4} - 18 q^{5} - 8 q^{6} - 2 q^{7} + 6 q^{8} + 11 q^{9}+O(q^{10}) $ 21 * q - q^2 - 6 * q^3 + 15 * q^4 - 18 * q^5 - 8 * q^6 - 2 * q^7 + 6 * q^8 + 11 * q^9	\( 21 q - q^{2} - 6 q^{3} + 15 q^{4} - 18 q^{5} - 8 q^{6} - 2 q^{7} + 6 q^{8} + 11 q^{9} - 10 q^{10} - 5 q^{11} - 22 q^{12} - 21 q^{13} - 24 q^{14} - q^{15} - 5 q^{16} - 18 q^{17} + 10 q^{18} - 6 q^{19} - 30 q^{20} - 17 q^{21} - 8 q^{22} - 14 q^{23} - 13 q^{24} + 11 q^{25} + q^{26} - 33 q^{27} - 2 q^{28} - 36 q^{29} + 2 q^{30} + q^{31} - 9 q^{32} - 11 q^{33} - 25 q^{34} - 37 q^{35} + 3 q^{36} + 5 q^{37} - 13 q^{38} + 6 q^{39} - 2 q^{40} - 32 q^{41} + 7 q^{42} + 2 q^{43} + 4 q^{44} - 32 q^{45} - 5 q^{46} - 12 q^{47} - 18 q^{48} + 5 q^{49} - 2 q^{50} - 27 q^{51} - 15 q^{52} - 49 q^{53} - 31 q^{54} - 9 q^{55} - 53 q^{56} + 14 q^{57} - 2 q^{58} - 34 q^{59} + 25 q^{60} - 27 q^{61} - 12 q^{62} + 41 q^{63} - 70 q^{64} + 18 q^{65} - 15 q^{66} - 12 q^{67} - 20 q^{68} - 70 q^{69} + 70 q^{70} - 26 q^{71} - 14 q^{72} + 23 q^{73} + 20 q^{74} - 9 q^{75} - 36 q^{76} - 62 q^{77} + 8 q^{78} - 7 q^{79} - 41 q^{80} - 3 q^{81} - 33 q^{82} - q^{83} - 48 q^{84} + 10 q^{85} - 23 q^{86} - 7 q^{87} + 9 q^{88} - 16 q^{89} - 30 q^{90} + 2 q^{91} - 27 q^{92} + 2 q^{93} - 37 q^{94} - 35 q^{95} + 55 q^{96} - 30 q^{97} - 43 q^{98} - 42 q^{99}+O(q^{100}) \) 21 * q - q^2 - 6 * q^3 + 15 * q^4 - 18 * q^5 - 8 * q^6 - 2 * q^7 + 6 * q^8 + 11 * q^9 - 10 * q^10 - 5 * q^11 - 22 * q^12 - 21 * q^13 - 24 * q^14 - q^15 - 5 * q^16 - 18 * q^17 + 10 * q^18 - 6 * q^19 - 30 * q^20 - 17 * q^21 - 8 * q^22 - 14 * q^23 - 13 * q^24 + 11 * q^25 + q^26 - 33 * q^27 - 2 * q^28 - 36 * q^29 + 2 * q^30 + q^31 - 9 * q^32 - 11 * q^33 - 25 * q^34 - 37 * q^35 + 3 * q^36 + 5 * q^37 - 13 * q^38 + 6 * q^39 - 2 * q^40 - 32 * q^41 + 7 * q^42 + 2 * q^43 + 4 * q^44 - 32 * q^45 - 5 * q^46 - 12 * q^47 - 18 * q^48 + 5 * q^49 - 2 * q^50 - 27 * q^51 - 15 * q^52 - 49 * q^53 - 31 * q^54 - 9 * q^55 - 53 * q^56 + 14 * q^57 - 2 * q^58 - 34 * q^59 + 25 * q^60 - 27 * q^61 - 12 * q^62 + 41 * q^63 - 70 * q^64 + 18 * q^65 - 15 * q^66 - 12 * q^67 - 20 * q^68 - 70 * q^69 + 70 * q^70 - 26 * q^71 - 14 * q^72 + 23 * q^73 + 20 * q^74 - 9 * q^75 - 36 * q^76 - 62 * q^77 + 8 * q^78 - 7 * q^79 - 41 * q^80 - 3 * q^81 - 33 * q^82 - q^83 - 48 * q^84 + 10 * q^85 - 23 * q^86 - 7 * q^87 + 9 * q^88 - 16 * q^89 - 30 * q^90 + 2 * q^91 - 27 * q^92 + 2 * q^93 - 37 * q^94 - 35 * q^95 + 55 * q^96 - 30 * q^97 - 43 * q^98 - 42 * 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 $

$2$	−2.12469	−1.50239	−0.751193	−	0.660083i	$-0.770521\pi$
$2$	−2.12469	−1.50239	−0.751193	+	0.660083i	$0.770521\pi$
$3$	0.347667	0.200725	0.100363	−	0.994951i	$-0.468000\pi$
$3$	0.347667	0.200725	0.100363	+	0.994951i	$0.468000\pi$
$4$	2.51433	1.25716
$5$	−4.40399	−1.96952	−0.984761	−	0.173910i	$-0.944360\pi$
$5$	−4.40399	−1.96952	−0.984761	+	0.173910i	$0.944360\pi$
$6$	−0.738685	−0.301567
$7$	−0.0796229	−0.0300946	−0.0150473	−	0.999887i	$-0.504790\pi$
$7$	−0.0796229	−0.0300946	−0.0150473	+	0.999887i	$0.504790\pi$
$8$	−1.09279	−0.386359
$9$	−2.87913	−0.959709
$10$	9.35713	2.95898
$11$	4.35168	1.31208	0.656040	−	0.754726i	$-0.272230\pi$
$11$	4.35168	1.31208	0.656040	+	0.754726i	$0.272230\pi$
$12$	0.874148	0.252345
$13$	−1.00000	−0.277350
$13$	−1.00000	−0.277350
$14$	0.169174	0.0452138
$15$	−1.53112	−0.395333
$16$	−2.70681	−0.676703
$17$	−0.234125	−0.0567837	−0.0283918	−	0.999597i	$-0.509039\pi$
$17$	−0.234125	−0.0567837	−0.0283918	+	0.999597i	$0.509039\pi$
$18$	6.11727	1.44185
$19$	7.31908	1.67911	0.839556	−	0.543272i	$-0.182815\pi$
$19$	7.31908	1.67911	0.839556	+	0.543272i	$0.182815\pi$
$20$	−11.0731	−2.47601
$21$	−0.0276822	−0.00604076
$22$	−9.24598	−1.97125
$23$	−0.812188	−0.169353	−0.0846764	−	0.996409i	$-0.526986\pi$
$23$	−0.812188	−0.169353	−0.0846764	+	0.996409i	$0.526986\pi$
$24$	−0.379926	−0.0775522
$25$	14.3951	2.87902
$26$	2.12469	0.416687
$27$	−2.04398	−0.393363
$28$	−0.200198	−0.0378339
$29$	−2.12916	−0.395375	−0.197688	−	0.980265i	$-0.563343\pi$
$29$	−2.12916	−0.395375	−0.197688	+	0.980265i	$0.563343\pi$
$30$	3.25316	0.593943
$31$	−3.40165	−0.610955	−0.305478	−	0.952199i	$-0.598816\pi$
$31$	−3.40165	−0.610955	−0.305478	+	0.952199i	$0.598816\pi$
$32$	7.93673	1.40303
$33$	1.51293	0.263368
$34$	0.497445	0.0853110
$35$	0.350658	0.0592721
$36$	−7.23907	−1.20651
$37$	11.7481	1.93138	0.965691	−	0.259692i	$-0.0836210\pi$
$37$	11.7481	1.93138	0.965691	+	0.259692i	$0.0836210\pi$
$38$	−15.5508	−2.52268
$39$	−0.347667	−0.0556712
$40$	4.81263	0.760944
$41$	−7.15208	−1.11697	−0.558484	−	0.829515i	$-0.688617\pi$
$41$	−7.15208	−1.11697	−0.558484	+	0.829515i	$0.688617\pi$
$42$	0.0588163	0.00907555
$43$	6.12509	0.934068	0.467034	−	0.884239i	$-0.345323\pi$
$43$	6.12509	0.934068	0.467034	+	0.884239i	$0.345323\pi$
$44$	10.9415	1.64950
$45$	12.6796	1.89017
$46$	1.72565	0.254433
$47$	−0.190494	−0.0277864	−0.0138932	−	0.999903i	$-0.504422\pi$
$47$	−0.190494	−0.0277864	−0.0138932	+	0.999903i	$0.504422\pi$
$48$	−0.941068	−0.135831
$49$	−6.99366	−0.999094
$50$	−30.5852	−4.32540
$51$	−0.0813975	−0.0113979
$52$	−2.51433	−0.348675
$53$	−10.1519	−1.39447	−0.697236	−	0.716842i	$-0.745587\pi$
$53$	−10.1519	−1.39447	−0.697236	+	0.716842i	$0.745587\pi$
$54$	4.34283	0.590984
$55$	−19.1647	−2.58417
$56$	0.0870111	0.0116273
$57$	2.54460	0.337041
$58$	4.52382	0.594006
$59$	−2.95128	−0.384224	−0.192112	−	0.981373i	$-0.561534\pi$
$59$	−2.95128	−0.384224	−0.192112	+	0.981373i	$0.561534\pi$
$60$	−3.84974	−0.496999
$61$	−7.49067	−0.959082	−0.479541	−	0.877519i	$-0.659197\pi$
$61$	−7.49067	−0.959082	−0.479541	+	0.877519i	$0.659197\pi$
$62$	7.22748	0.917890
$63$	0.229245	0.0288821
$64$	−11.4495	−1.43119
$65$	4.40399	0.546247
$66$	−3.21452	−0.395680
$67$	−8.85777	−1.08215	−0.541075	−	0.840975i	$-0.681982\pi$
$67$	−8.85777	−1.08215	−0.541075	+	0.840975i	$0.681982\pi$
$68$	−0.588667	−0.0713864
$69$	−0.282371	−0.0339934
$70$	−0.745042	−0.0890495
$71$	7.80083	0.925789	0.462894	−	0.886414i	$-0.346811\pi$
$71$	7.80083	0.925789	0.462894	+	0.886414i	$0.346811\pi$
$72$	3.14628	0.370793
$73$	12.8987	1.50968	0.754838	−	0.655912i	$-0.227716\pi$
$73$	12.8987	1.50968	0.754838	+	0.655912i	$0.227716\pi$
$74$	−24.9612	−2.90168
$75$	5.00470	0.577893
$76$	18.4026	2.11092
$77$	−0.346493	−0.0394866
$78$	0.738685	0.0836397
$79$	−8.22786	−0.925706	−0.462853	−	0.886435i	$-0.653174\pi$
$79$	−8.22786	−0.925706	−0.462853	+	0.886435i	$0.653174\pi$
$80$	11.9208	1.33278
$81$	7.92676	0.880751
$82$	15.1960	1.67812
$83$	−13.2689	−1.45645	−0.728224	−	0.685339i	$-0.759654\pi$
$83$	−13.2689	−1.45645	−0.728224	+	0.685339i	$0.759654\pi$
$84$	−0.0696022	−0.00759422
$85$	1.03108	0.111837
$86$	−13.0140	−1.40333
$87$	−0.740238	−0.0793618
$88$	−4.75547	−0.506934
$89$	−4.38958	−0.465294	−0.232647	−	0.972561i	$-0.574739\pi$
$89$	−4.38958	−0.465294	−0.232647	+	0.972561i	$0.574739\pi$
$90$	−26.9404	−2.83976
$91$	0.0796229	0.00834675
$92$	−2.04211	−0.212904
$93$	−1.18264	−0.122634
$94$	0.404741	0.0417459
$95$	−32.2331	−3.30705
$96$	2.75934	0.281623
$97$	1.24048	0.125952	0.0629759	−	0.998015i	$-0.479941\pi$
$97$	1.24048	0.125952	0.0629759	+	0.998015i	$0.479941\pi$
$98$	14.8594	1.50103
$99$	−12.5290	−1.25922
$100$	36.1940	3.61940
$101$	4.62820	0.460523	0.230262	−	0.973129i	$-0.426042\pi$
$101$	4.62820	0.460523	0.230262	+	0.973129i	$0.426042\pi$
$102$	0.172945	0.0171241
$103$	−1.00000	−0.0985329
$103$	−1.00000	−0.0985329
$104$	1.09279	0.107157
$105$	0.121912	0.0118974
$106$	21.5697	2.09504
$107$	7.56534	0.731369	0.365684	−	0.930739i	$-0.380835\pi$
$107$	7.56534	0.731369	0.365684	+	0.930739i	$0.380835\pi$
$108$	−5.13923	−0.494522
$109$	3.69301	0.353727	0.176863	−	0.984235i	$-0.443405\pi$
$109$	3.69301	0.353727	0.176863	+	0.984235i	$0.443405\pi$
$110$	40.7192	3.88242
$111$	4.08444	0.387678
$112$	0.215524	0.0203651
$113$	−3.07852	−0.289602	−0.144801	−	0.989461i	$-0.546254\pi$
$113$	−3.07852	−0.289602	−0.144801	+	0.989461i	$0.546254\pi$
$114$	−5.40650	−0.506365
$115$	3.57686	0.333544
$116$	−5.35341	−0.497051
$117$	2.87913	0.266175
$118$	6.27058	0.577253
$119$	0.0186417	0.00170888
$120$	1.67319	0.152741
$121$	7.93709	0.721554
$122$	15.9154	1.44091
$123$	−2.48654	−0.224204
$124$	−8.55287	−0.768071
$125$	−41.3759	−3.70077
$126$	−0.487075	−0.0433921
$127$	−13.0765	−1.16035	−0.580177	−	0.814490i	$-0.697017\pi$
$127$	−13.0765	−1.16035	−0.580177	+	0.814490i	$0.697017\pi$
$128$	8.45324	0.747168
$129$	2.12949	0.187491
$130$	−9.35713	−0.820674
$131$	0.456614	0.0398945	0.0199473	−	0.999801i	$-0.493650\pi$
$131$	0.456614	0.0398945	0.0199473	+	0.999801i	$0.493650\pi$
$132$	3.80401	0.331096
$133$	−0.582767	−0.0505323
$134$	18.8201	1.62581
$135$	9.00165	0.774738
$136$	0.255849	0.0219389
$137$	−6.34942	−0.542467	−0.271234	−	0.962514i	$-0.587432\pi$
$137$	−6.34942	−0.542467	−0.271234	+	0.962514i	$0.587432\pi$
$138$	0.599951	0.0510712
$139$	−20.3812	−1.72871	−0.864353	−	0.502885i	$-0.832272\pi$
$139$	−20.3812	−1.72871	−0.864353	+	0.502885i	$0.832272\pi$
$140$	0.881670	0.0745147
$141$	−0.0662284	−0.00557744
$142$	−16.5744	−1.39089
$143$	−4.35168	−0.363905
$144$	7.79326	0.649438
$145$	9.37679	0.778700
$146$	−27.4057	−2.26811
$147$	−2.43146	−0.200544
$148$	29.5387	2.42806
$149$	0.447699	0.0366770	0.0183385	−	0.999832i	$-0.494162\pi$
$149$	0.447699	0.0366770	0.0183385	+	0.999832i	$0.494162\pi$
$150$	−10.6335	−0.868218
$151$	−15.0734	−1.22665	−0.613326	−	0.789830i	$-0.710169\pi$
$151$	−15.0734	−1.22665	−0.613326	+	0.789830i	$0.710169\pi$
$152$	−7.99822	−0.648741
$153$	0.674076	0.0544958
$154$	0.736192	0.0593241
$155$	14.9808	1.20329
$156$	−0.874148	−0.0699878
$157$	13.3213	1.06315	0.531577	−	0.847010i	$-0.321599\pi$
$157$	13.3213	1.06315	0.531577	+	0.847010i	$0.321599\pi$
$158$	17.4817	1.39077
$159$	−3.52948	−0.279906
$160$	−34.9532	−2.76330
$161$	0.0646688	0.00509661
$162$	−16.8419	−1.32323
$163$	14.0688	1.10195	0.550977	−	0.834521i	$-0.314255\pi$
$163$	14.0688	1.10195	0.550977	+	0.834521i	$0.314255\pi$
$164$	−17.9827	−1.40421
$165$	−6.66294	−0.518709
$166$	28.1923	2.18815
$167$	−21.6116	−1.67236	−0.836179	−	0.548456i	$-0.815216\pi$
$167$	−21.6116	−1.67236	−0.836179	+	0.548456i	$0.815216\pi$
$168$	0.0302508	0.00233390
$169$	1.00000	0.0769231
$170$	−2.19074	−0.168022
$171$	−21.0726	−1.61146
$172$	15.4005	1.17428
$173$	−24.6186	−1.87171	−0.935857	−	0.352380i	$-0.885373\pi$
$173$	−24.6186	−1.87171	−0.935857	+	0.352380i	$0.885373\pi$
$174$	1.57278	0.119232
$175$	−1.14618	−0.0866431
$176$	−11.7792	−0.887888
$177$	−1.02606	−0.0771236
$178$	9.32651	0.699052
$179$	−14.5038	−1.08406	−0.542031	−	0.840359i	$-0.682344\pi$
$179$	−14.5038	−1.08406	−0.542031	+	0.840359i	$0.682344\pi$
$180$	31.8808	2.37625
$181$	−12.3689	−0.919376	−0.459688	−	0.888080i	$-0.652039\pi$
$181$	−12.3689	−0.919376	−0.459688	+	0.888080i	$0.652039\pi$
$182$	−0.169174	−0.0125400
$183$	−2.60426	−0.192512
$184$	0.887550	0.0654311
$185$	−51.7387	−3.80390
$186$	2.51275	0.184244
$187$	−1.01884	−0.0745047
$188$	−0.478964	−0.0349320
$189$	0.162747	0.0118381
$190$	68.4856	4.96847
$191$	−5.99185	−0.433555	−0.216778	−	0.976221i	$-0.569555\pi$
$191$	−5.99185	−0.433555	−0.216778	+	0.976221i	$0.569555\pi$
$192$	−3.98061	−0.287276
$193$	10.3561	0.745446	0.372723	−	0.927943i	$-0.378424\pi$
$193$	10.3561	0.745446	0.372723	+	0.927943i	$0.378424\pi$
$194$	−2.63564	−0.189228
$195$	1.53112	0.109646
$196$	−17.5844	−1.25603
$197$	16.4487	1.17192	0.585960	−	0.810340i	$-0.300717\pi$
$197$	16.4487	1.17192	0.585960	+	0.810340i	$0.300717\pi$
$198$	26.6204	1.89183
$199$	−17.9973	−1.27580	−0.637899	−	0.770120i	$-0.720196\pi$
$199$	−17.9973	−1.27580	−0.637899	+	0.770120i	$0.720196\pi$
$200$	−15.7308	−1.11234
$201$	−3.07955	−0.217215
$202$	−9.83352	−0.691884
$203$	0.169530	0.0118987
$204$	−0.204660	−0.0143291
$205$	31.4977	2.19989
$206$	2.12469	0.148034
$207$	2.33839	0.162529
$208$	2.70681	0.187684
$209$	31.8503	2.20313
$210$	−0.259026	−0.0178745
$211$	−3.01947	−0.207869	−0.103934	−	0.994584i	$-0.533143\pi$
$211$	−3.01947	−0.207869	−0.103934	+	0.994584i	$0.533143\pi$
$212$	−25.5252	−1.75308
$213$	2.71209	0.185829
$214$	−16.0740	−1.09880
$215$	−26.9748	−1.83967
$216$	2.23364	0.151980
$217$	0.270850	0.0183865
$218$	−7.84653	−0.531434
$219$	4.48444	0.303030
$220$	−48.1864	−3.24873
$221$	0.234125	0.0157490
$222$	−8.67818	−0.582442
$223$	1.39518	0.0934282	0.0467141	−	0.998908i	$-0.485125\pi$
$223$	1.39518	0.0934282	0.0467141	+	0.998908i	$0.485125\pi$
$224$	−0.631945	−0.0422236
$225$	−41.4453	−2.76302
$226$	6.54091	0.435095
$227$	−6.45055	−0.428138	−0.214069	−	0.976819i	$-0.568672\pi$
$227$	−6.45055	−0.428138	−0.214069	+	0.976819i	$0.568672\pi$
$228$	6.39796	0.423715
$229$	12.4041	0.819689	0.409844	−	0.912155i	$-0.365583\pi$
$229$	12.4041	0.819689	0.409844	+	0.912155i	$0.365583\pi$
$230$	−7.59974	−0.501112
$231$	−0.120464	−0.00792596
$232$	2.32672	0.152757
$233$	3.30455	0.216488	0.108244	−	0.994124i	$-0.465477\pi$
$233$	3.30455	0.216488	0.108244	+	0.994124i	$0.465477\pi$
$234$	−6.11727	−0.399898
$235$	0.838933	0.0547259
$236$	−7.42049	−0.483033
$237$	−2.86055	−0.185813
$238$	−0.0396080	−0.00256740
$239$	−21.2730	−1.37603	−0.688016	−	0.725695i	$-0.741518\pi$
$239$	−21.2730	−1.37603	−0.688016	+	0.725695i	$0.741518\pi$
$240$	4.14445	0.267523
$241$	−20.3632	−1.31171	−0.655856	−	0.754886i	$-0.727692\pi$
$241$	−20.3632	−1.31171	−0.655856	+	0.754886i	$0.727692\pi$
$242$	−16.8639	−1.08405
$243$	8.88780	0.570153
$244$	−18.8340	−1.20572
$245$	30.8000	1.96774
$246$	5.28314	0.336841
$247$	−7.31908	−0.465702
$248$	3.71729	0.236048
$249$	−4.61314	−0.292346
$250$	87.9112	5.55999
$251$	5.38432	0.339855	0.169928	−	0.985457i	$-0.445647\pi$
$251$	5.38432	0.339855	0.169928	+	0.985457i	$0.445647\pi$
$252$	0.576396	0.0363095
$253$	−3.53438	−0.222204
$254$	27.7836	1.74330
$255$	0.358474	0.0224485
$256$	4.93845	0.308653
$257$	2.43409	0.151834	0.0759172	−	0.997114i	$-0.475812\pi$
$257$	2.43409	0.151834	0.0759172	+	0.997114i	$0.475812\pi$
$258$	−4.52452	−0.281684
$259$	−0.935422	−0.0581243
$260$	11.0731	0.686722
$261$	6.13012	0.379445
$262$	−0.970165	−0.0599370
$263$	21.4956	1.32548	0.662739	−	0.748850i	$-0.269394\pi$
$263$	21.4956	1.32548	0.662739	+	0.748850i	$0.269394\pi$
$264$	−1.65332	−0.101755
$265$	44.7089	2.74645
$266$	1.23820	0.0759190
$267$	−1.52611	−0.0933964
$268$	−22.2713	−1.36044
$269$	14.6147	0.891074	0.445537	−	0.895264i	$-0.353013\pi$
$269$	14.6147	0.891074	0.445537	+	0.895264i	$0.353013\pi$
$270$	−19.1258	−1.16396
$271$	21.7192	1.31935	0.659674	−	0.751552i	$-0.270694\pi$
$271$	21.7192	1.31935	0.659674	+	0.751552i	$0.270694\pi$
$272$	0.633733	0.0384257
$273$	0.0276822	0.00167540
$274$	13.4906	0.814996
$275$	62.6428	3.77750
$276$	−0.709972	−0.0427353
$277$	−13.2554	−0.796440	−0.398220	−	0.917290i	$-0.630372\pi$
$277$	−13.2554	−0.796440	−0.398220	+	0.917290i	$0.630372\pi$
$278$	43.3037	2.59719
$279$	9.79380	0.586339
$280$	−0.383196	−0.0229003
$281$	23.6783	1.41253	0.706266	−	0.707947i	$-0.250378\pi$
$281$	23.6783	1.41253	0.706266	+	0.707947i	$0.250378\pi$
$282$	0.140715	0.00837946
$283$	−3.54996	−0.211023	−0.105512	−	0.994418i	$-0.533648\pi$
$283$	−3.54996	−0.211023	−0.105512	+	0.994418i	$0.533648\pi$
$284$	19.6139	1.16387
$285$	−11.2064	−0.663809
$286$	9.24598	0.546727
$287$	0.569470	0.0336147
$288$	−22.8509	−1.34650
$289$	−16.9452	−0.996776
$290$	−19.9228	−1.16991
$291$	0.431274	0.0252817
$292$	32.4315	1.89791
$293$	−7.06359	−0.412659	−0.206330	−	0.978483i	$-0.566152\pi$
$293$	−7.06359	−0.412659	−0.206330	+	0.978483i	$0.566152\pi$
$294$	5.16612	0.301294
$295$	12.9974	0.756739
$296$	−12.8382	−0.746208
$297$	−8.89472	−0.516124
$298$	−0.951224	−0.0551030
$299$	0.812188	0.0469700
$300$	12.5834	0.726506
$301$	−0.487698	−0.0281104
$302$	32.0263	1.84290
$303$	1.60907	0.0924388
$304$	−19.8114	−1.13626
$305$	32.9888	1.88893
$306$	−1.43221	−0.0818738
$307$	23.7956	1.35809	0.679043	−	0.734098i	$-0.262395\pi$
$307$	23.7956	1.35809	0.679043	+	0.734098i	$0.262395\pi$
$308$	−0.871197	−0.0496411
$309$	−0.347667	−0.0197781
$310$	−31.8297	−1.80781
$311$	15.6868	0.889518	0.444759	−	0.895650i	$-0.353289\pi$
$311$	15.6868	0.889518	0.444759	+	0.895650i	$0.353289\pi$
$312$	0.379926	0.0215091
$313$	21.1388	1.19484	0.597419	−	0.801929i	$-0.296193\pi$
$313$	21.1388	1.19484	0.597419	+	0.801929i	$0.296193\pi$
$314$	−28.3037	−1.59727
$315$	−1.00959	−0.0568840
$316$	−20.6875	−1.16376
$317$	−5.74644	−0.322752	−0.161376	−	0.986893i	$-0.551593\pi$
$317$	−5.74644	−0.322752	−0.161376	+	0.986893i	$0.551593\pi$
$318$	7.49907	0.420527
$319$	−9.26542	−0.518764
$320$	50.4234	2.81876
$321$	2.63022	0.146804
$322$	−0.137401	−0.00765708
$323$	−1.71358	−0.0953462
$324$	19.9305	1.10725
$325$	−14.3951	−0.798497
$326$	−29.8919	−1.65556
$327$	1.28394	0.0710019
$328$	7.81572	0.431551
$329$	0.0151677	0.000836221 0
$330$	14.1567	0.779301
$331$	6.95990	0.382551	0.191275	−	0.981536i	$-0.438738\pi$
$331$	6.95990	0.382551	0.191275	+	0.981536i	$0.438738\pi$
$332$	−33.3623	−1.83099
$333$	−33.8244	−1.85357
$334$	45.9181	2.51253
$335$	39.0095	2.13132
$336$	0.0749306	0.00408780
$337$	−9.42275	−0.513290	−0.256645	−	0.966506i	$-0.582617\pi$
$337$	−9.42275	−0.513290	−0.256645	+	0.966506i	$0.582617\pi$
$338$	−2.12469	−0.115568
$339$	−1.07030	−0.0581306
$340$	2.59248	0.140597
$341$	−14.8029	−0.801622
$342$	44.7728	2.42104
$343$	1.11422	0.0601620
$344$	−6.69344	−0.360886
$345$	1.24356	0.0669508
$346$	52.3069	2.81204
$347$	12.4096	0.666184	0.333092	−	0.942894i	$-0.391908\pi$
$347$	12.4096	0.666184	0.333092	+	0.942894i	$0.391908\pi$
$348$	−1.86120	−0.0997708
$349$	−28.2661	−1.51305	−0.756526	−	0.653964i	$-0.773105\pi$
$349$	−28.2661	−1.51305	−0.756526	+	0.653964i	$0.773105\pi$
$350$	2.43528	0.130171
$351$	2.04398	0.109099
$352$	34.5381	1.84089
$353$	−5.89853	−0.313947	−0.156973	−	0.987603i	$-0.550174\pi$
$353$	−5.89853	−0.313947	−0.156973	+	0.987603i	$0.550174\pi$
$354$	2.18007	0.115869
$355$	−34.3548	−1.82336
$356$	−11.0368	−0.584951
$357$	0.00648111	0.000343017 0
$358$	30.8160	1.62868
$359$	−19.9140	−1.05102	−0.525510	−	0.850787i	$-0.676126\pi$
$359$	−19.9140	−1.05102	−0.525510	+	0.850787i	$0.676126\pi$
$360$	−13.8562	−0.730285
$361$	34.5690	1.81942
$362$	26.2802	1.38126
$363$	2.75946	0.144834
$364$	0.200198	0.0104932
$365$	−56.8056	−2.97334
$366$	5.53325	0.289228
$367$	−21.6579	−1.13053	−0.565267	−	0.824908i	$-0.691227\pi$
$367$	−21.6579	−1.13053	−0.565267	+	0.824908i	$0.691227\pi$
$368$	2.19844	0.114602
$369$	20.5918	1.07196
$370$	109.929	5.71493
$371$	0.808325	0.0419661
$372$	−2.97355	−0.154171
$373$	−30.5325	−1.58092	−0.790458	−	0.612517i	$-0.790157\pi$
$373$	−30.5325	−1.58092	−0.790458	+	0.612517i	$0.790157\pi$
$374$	2.16472	0.111935
$375$	−14.3850	−0.742839
$376$	0.208170	0.0107355
$377$	2.12916	0.109657
$378$	−0.345789	−0.0177854
$379$	4.75205	0.244096	0.122048	−	0.992524i	$-0.461054\pi$
$379$	4.75205	0.244096	0.122048	+	0.992524i	$0.461054\pi$
$380$	−81.0447	−4.15751
$381$	−4.54627	−0.232913
$382$	12.7309	0.651367
$383$	3.08594	0.157684	0.0788421	−	0.996887i	$-0.474878\pi$
$383$	3.08594	0.157684	0.0788421	+	0.996887i	$0.474878\pi$
$384$	2.93891	0.149976
$385$	1.52595	0.0777697
$386$	−22.0035	−1.11995
$387$	−17.6349	−0.896434
$388$	3.11898	0.158342
$389$	3.48736	0.176816	0.0884082	−	0.996084i	$-0.471822\pi$
$389$	3.48736	0.176816	0.0884082	+	0.996084i	$0.471822\pi$
$390$	−3.25316	−0.164730
$391$	0.190154	0.00961648
$392$	7.64260	0.386009
$393$	0.158749	0.00800785
$394$	−34.9485	−1.76068
$395$	36.2354	1.82320
$396$	−31.5021	−1.58304
$397$	−14.0470	−0.704999	−0.352499	−	0.935812i	$-0.614668\pi$
$397$	−14.0470	−0.704999	−0.352499	+	0.935812i	$0.614668\pi$
$398$	38.2388	1.91674
$399$	−0.202609	−0.0101431
$400$	−38.9648	−1.94824
$401$	28.4574	1.42110	0.710548	−	0.703649i	$-0.248447\pi$
$401$	28.4574	1.42110	0.710548	+	0.703649i	$0.248447\pi$
$402$	6.54311	0.326341
$403$	3.40165	0.169448
$404$	11.6368	0.578953
$405$	−34.9094	−1.73466
$406$	−0.360199	−0.0178764
$407$	51.1241	2.53413
$408$	0.0889503	0.00440370
$409$	−34.2315	−1.69264	−0.846320	−	0.532674i	$-0.821187\pi$
$409$	−34.2315	−1.69264	−0.846320	+	0.532674i	$0.821187\pi$
$410$	−66.9229	−3.30509
$411$	−2.20748	−0.108887
$412$	−2.51433	−0.123872
$413$	0.234990	0.0115631
$414$	−4.96837	−0.244182
$415$	58.4359	2.86851
$416$	−7.93673	−0.389130
$417$	−7.08585	−0.346995
$418$	−67.6721	−3.30995
$419$	17.8158	0.870358	0.435179	−	0.900344i	$-0.356685\pi$
$419$	17.8158	0.870358	0.435179	+	0.900344i	$0.356685\pi$
$420$	0.306527	0.0149570
$421$	−7.73691	−0.377074	−0.188537	−	0.982066i	$-0.560375\pi$
$421$	−7.73691	−0.377074	−0.188537	+	0.982066i	$0.560375\pi$
$422$	6.41545	0.312299
$423$	0.548456	0.0266669
$424$	11.0939	0.538767
$425$	−3.37026	−0.163481
$426$	−5.76236	−0.279187
$427$	0.596429	0.0288632
$428$	19.0217	0.919451
$429$	−1.51293	−0.0730451
$430$	57.3133	2.76389
$431$	−18.3936	−0.885989	−0.442994	−	0.896524i	$-0.646084\pi$
$431$	−18.3936	−0.885989	−0.442994	+	0.896524i	$0.646084\pi$
$432$	5.53266	0.266190
$433$	10.2159	0.490944	0.245472	−	0.969404i	$-0.421057\pi$
$433$	10.2159	0.490944	0.245472	+	0.969404i	$0.421057\pi$
$434$	−0.575473	−0.0276236
$435$	3.26000	0.156305
$436$	9.28545	0.444692
$437$	−5.94447	−0.284363
$438$	−9.52806	−0.455268
$439$	−35.3388	−1.68663	−0.843314	−	0.537420i	$-0.819399\pi$
$439$	−35.3388	−1.68663	−0.843314	+	0.537420i	$0.819399\pi$
$440$	20.9430	0.998419
$441$	20.1356	0.958840
$442$	−0.497445	−0.0236610
$443$	−11.1458	−0.529553	−0.264776	−	0.964310i	$-0.585298\pi$
$443$	−11.1458	−0.529553	−0.264776	+	0.964310i	$0.585298\pi$
$444$	10.2696	0.487374
$445$	19.3316	0.916408
$446$	−2.96433	−0.140365
$447$	0.155650	0.00736200
$448$	0.911643	0.0430711
$449$	−34.9339	−1.64863	−0.824316	−	0.566130i	$-0.808440\pi$
$449$	−34.9339	−1.64863	−0.824316	+	0.566130i	$0.808440\pi$
$450$	88.0587	4.15113
$451$	−31.1235	−1.46555
$452$	−7.74040	−0.364078
$453$	−5.24050	−0.246220
$454$	13.7054	0.643228
$455$	−0.350658	−0.0164391
$456$	−2.78071	−0.130219
$457$	18.1491	0.848977	0.424489	−	0.905433i	$-0.360454\pi$
$457$	18.1491	0.848977	0.424489	+	0.905433i	$0.360454\pi$
$458$	−26.3550	−1.23149
$459$	0.478546	0.0223366
$460$	8.99341	0.419320
$461$	−4.87828	−0.227204	−0.113602	−	0.993526i	$-0.536239\pi$
$461$	−4.87828	−0.227204	−0.113602	+	0.993526i	$0.536239\pi$
$462$	0.255949	0.0119078
$463$	31.1985	1.44992	0.724959	−	0.688792i	$-0.241859\pi$
$463$	31.1985	1.44992	0.724959	+	0.688792i	$0.241859\pi$
$464$	5.76324	0.267551
$465$	5.20834	0.241531
$466$	−7.02115	−0.325249
$467$	36.0265	1.66711	0.833555	−	0.552437i	$-0.186302\pi$
$467$	36.0265	1.66711	0.833555	+	0.552437i	$0.186302\pi$
$468$	7.23907	0.334626
$469$	0.705282	0.0325669
$470$	−1.78248	−0.0822195
$471$	4.63137	0.213402
$472$	3.22513	0.148449
$473$	26.6544	1.22557
$474$	6.07780	0.279163
$475$	105.359	4.83420
$476$	0.0468714	0.00214835
$477$	29.2287	1.33829
$478$	45.1985	2.06733
$479$	17.6933	0.808427	0.404213	−	0.914665i	$-0.367545\pi$
$479$	17.6933	0.808427	0.404213	+	0.914665i	$0.367545\pi$
$480$	−12.1521	−0.554664
$481$	−11.7481	−0.535669
$482$	43.2657	1.97070
$483$	0.0224832	0.00102302
$484$	19.9564	0.907111
$485$	−5.46306	−0.248065
$486$	−18.8839	−0.856589
$487$	−5.33224	−0.241627	−0.120813	−	0.992675i	$-0.538550\pi$
$487$	−5.33224	−0.241627	−0.120813	+	0.992675i	$0.538550\pi$
$488$	8.18573	0.370550
$489$	4.89125	0.221190
$490$	−65.4406	−2.95630
$491$	14.4276	0.651107	0.325554	−	0.945524i	$-0.394449\pi$
$491$	14.4276	0.651107	0.325554	+	0.945524i	$0.394449\pi$
$492$	−6.25198	−0.281861
$493$	0.498490	0.0224509
$494$	15.5508	0.699664
$495$	55.1777	2.48005
$496$	9.20764	0.413435
$497$	−0.621125	−0.0278613
$498$	9.80152	0.439217
$499$	−38.9455	−1.74344	−0.871719	−	0.490006i	$-0.836995\pi$
$499$	−38.9455	−1.74344	−0.871719	+	0.490006i	$0.836995\pi$
$500$	−104.033	−4.65248
$501$	−7.51364	−0.335685
$502$	−11.4400	−0.510594
$503$	−11.7102	−0.522133	−0.261066	−	0.965321i	$-0.584074\pi$
$503$	−11.7102	−0.522133	−0.261066	+	0.965321i	$0.584074\pi$
$504$	−0.250516	−0.0111589
$505$	−20.3825	−0.907011
$506$	7.50947	0.333837
$507$	0.347667	0.0154404
$508$	−32.8787	−1.45876
$509$	33.5533	1.48722	0.743612	−	0.668612i	$-0.233111\pi$
$509$	33.5533	1.48722	0.743612	+	0.668612i	$0.233111\pi$
$510$	−0.761647	−0.0337263
$511$	−1.02703	−0.0454331
$512$	−27.3992	−1.21088
$513$	−14.9600	−0.660502
$514$	−5.17170	−0.228114
$515$	4.40399	0.194063
$516$	5.35424	0.235707
$517$	−0.828968	−0.0364580
$518$	1.98749	0.0873251
$519$	−8.55905	−0.375701
$520$	−4.81263	−0.211048
$521$	14.3735	0.629714	0.314857	−	0.949139i	$-0.398043\pi$
$521$	14.3735	0.629714	0.314857	+	0.949139i	$0.398043\pi$
$522$	−13.0246	−0.570073
$523$	−44.0725	−1.92715	−0.963577	−	0.267431i	$-0.913825\pi$
$523$	−44.0725	−1.92715	−0.963577	+	0.267431i	$0.913825\pi$
$524$	1.14808	0.0501540
$525$	−0.398489	−0.0173915
$526$	−45.6717	−1.99138
$527$	0.796413	0.0346923
$528$	−4.09522	−0.178222
$529$	−22.3404	−0.971320
$530$	−94.9927	−4.12622
$531$	8.49712	0.368744
$532$	−1.46527	−0.0635274
$533$	7.15208	0.309791
$534$	3.24252	0.140317
$535$	−33.3177	−1.44045
$536$	9.67968	0.418098
$537$	−5.04247	−0.217599
$538$	−31.0518	−1.33874
$539$	−30.4341	−1.31089
$540$	22.6331	0.973973
$541$	−7.61426	−0.327363	−0.163681	−	0.986513i	$-0.552337\pi$
$541$	−7.61426	−0.327363	−0.163681	+	0.986513i	$0.552337\pi$
$542$	−46.1467	−1.98217
$543$	−4.30027	−0.184542
$544$	−1.85819	−0.0796691
$545$	−16.2640	−0.696672
$546$	−0.0588163	−0.00251710
$547$	38.6295	1.65168	0.825839	−	0.563907i	$-0.190702\pi$
$547$	38.6295	1.65168	0.825839	+	0.563907i	$0.190702\pi$
$548$	−15.9645	−0.681970
$549$	21.5666	0.920440
$550$	−133.097	−5.67527
$551$	−15.5835	−0.663879
$552$	0.308572	0.0131337
$553$	0.655126	0.0278588
$554$	28.1637	1.19656
$555$	−17.9878	−0.763540
$556$	−51.2449	−2.17327
$557$	10.0828	0.427224	0.213612	−	0.976919i	$-0.431477\pi$
$557$	10.0828	0.427224	0.213612	+	0.976919i	$0.431477\pi$
$558$	−20.8088	−0.880908
$559$	−6.12509	−0.259064
$560$	−0.949166	−0.0401096
$561$	−0.354216	−0.0149550
$562$	−50.3093	−2.12217
$563$	23.7018	0.998911	0.499455	−	0.866340i	$-0.333533\pi$
$563$	23.7018	0.998911	0.499455	+	0.866340i	$0.333533\pi$
$564$	−0.166520	−0.00701175
$565$	13.5577	0.570379
$566$	7.54259	0.317039
$567$	−0.631152	−0.0265059
$568$	−8.52467	−0.357687
$569$	−27.4143	−1.14927	−0.574634	−	0.818411i	$-0.694856\pi$
$569$	−27.4143	−1.14927	−0.574634	+	0.818411i	$0.694856\pi$
$570$	23.8102	0.997298
$571$	−8.18092	−0.342361	−0.171180	−	0.985240i	$-0.554758\pi$
$571$	−8.18092	−0.342361	−0.171180	+	0.985240i	$0.554758\pi$
$572$	−10.9415	−0.457489
$573$	−2.08317	−0.0870256
$574$	−1.20995	−0.0505023
$575$	−11.6915	−0.487570
$576$	32.9646	1.37352
$577$	−3.24262	−0.134992	−0.0674961	−	0.997720i	$-0.521501\pi$
$577$	−3.24262	−0.134992	−0.0674961	+	0.997720i	$0.521501\pi$
$578$	36.0033	1.49754
$579$	3.60046	0.149630
$580$	23.5763	0.978954
$581$	1.05651	0.0438313
$582$	−0.916325	−0.0379829
$583$	−44.1778	−1.82966
$584$	−14.0955	−0.583277
$585$	−12.6796	−0.524239
$586$	15.0080	0.619973
$587$	−22.2782	−0.919520	−0.459760	−	0.888043i	$-0.652065\pi$
$587$	−22.2782	−0.919520	−0.459760	+	0.888043i	$0.652065\pi$
$588$	−6.11349	−0.252116
$589$	−24.8970	−1.02586
$590$	−27.6155	−1.13691
$591$	5.71866	0.235234
$592$	−31.8000	−1.30697
$593$	6.70531	0.275354	0.137677	−	0.990477i	$-0.456036\pi$
$593$	6.70531	0.275354	0.137677	+	0.990477i	$0.456036\pi$
$594$	18.8986	0.775418
$595$	−0.0820979	−0.00336569
$596$	1.12566	0.0461089
$597$	−6.25707	−0.256085
$598$	−1.72565	−0.0705671
$599$	2.75990	0.112766	0.0563832	−	0.998409i	$-0.482043\pi$
$599$	2.75990	0.112766	0.0563832	+	0.998409i	$0.482043\pi$
$600$	−5.46908	−0.223274
$601$	−25.3307	−1.03326	−0.516631	−	0.856208i	$-0.672814\pi$
$601$	−25.3307	−1.03326	−0.516631	+	0.856208i	$0.672814\pi$
$602$	1.03621	0.0422327
$603$	25.5027	1.03855
$604$	−37.8993	−1.54210
$605$	−34.9548	−1.42112
$606$	−3.41879	−0.138879
$607$	32.6577	1.32554	0.662768	−	0.748825i	$-0.269382\pi$
$607$	32.6577	1.32554	0.662768	+	0.748825i	$0.269382\pi$
$608$	58.0896	2.35584
$609$	0.0589399	0.00238837
$610$	−70.0912	−2.83791
$611$	0.190494	0.00770656
$612$	1.69485	0.0685102
$613$	−5.00903	−0.202313	−0.101156	−	0.994871i	$-0.532254\pi$
$613$	−5.00903	−0.202313	−0.101156	+	0.994871i	$0.532254\pi$
$614$	−50.5584	−2.04037
$615$	10.9507	0.441574
$616$	0.378644	0.0152560
$617$	−27.6858	−1.11459	−0.557295	−	0.830315i	$-0.688161\pi$
$617$	−27.6858	−1.11459	−0.557295	+	0.830315i	$0.688161\pi$
$618$	0.738685	0.0297143
$619$	−38.4261	−1.54448	−0.772238	−	0.635333i	$-0.780863\pi$
$619$	−38.4261	−1.54448	−0.772238	+	0.635333i	$0.780863\pi$
$620$	37.6667	1.51273
$621$	1.66009	0.0666172
$622$	−33.3297	−1.33640
$623$	0.349511	0.0140029
$624$	0.941068	0.0376729
$625$	110.243	4.40974
$626$	−44.9136	−1.79511
$627$	11.0733	0.442224
$628$	33.4941	1.33656
$629$	−2.75054	−0.109671
$630$	2.14507	0.0854617
$631$	3.96557	0.157867	0.0789334	−	0.996880i	$-0.474849\pi$
$631$	3.96557	0.157867	0.0789334	+	0.996880i	$0.474849\pi$
$632$	8.99131	0.357655
$633$	−1.04977	−0.0417246
$634$	12.2094	0.484899
$635$	57.5889	2.28534
$636$	−8.87427	−0.351888
$637$	6.99366	0.277099
$638$	19.6862	0.779383
$639$	−22.4596	−0.888488
$640$	−37.2279	−1.47156
$641$	21.4430	0.846949	0.423474	−	0.905908i	$-0.360810\pi$
$641$	21.4430	0.846949	0.423474	+	0.905908i	$0.360810\pi$
$642$	−5.58841	−0.220557
$643$	−29.1106	−1.14801	−0.574005	−	0.818852i	$-0.694611\pi$
$643$	−29.1106	−1.14801	−0.574005	+	0.818852i	$0.694611\pi$
$644$	0.162598	0.00640728
$645$	−9.37825	−0.369268
$646$	3.64084	0.143247
$647$	19.9729	0.785216	0.392608	−	0.919706i	$-0.371573\pi$
$647$	19.9729	0.785216	0.392608	+	0.919706i	$0.371573\pi$
$648$	−8.66228	−0.340287
$649$	−12.8430	−0.504133
$650$	30.5852	1.19965
$651$	0.0941654	0.00369063
$652$	35.3736	1.38534
$653$	−16.9086	−0.661684	−0.330842	−	0.943686i	$-0.607333\pi$
$653$	−16.9086	−0.661684	−0.330842	+	0.943686i	$0.607333\pi$
$654$	−2.72798	−0.106672
$655$	−2.01092	−0.0785732
$656$	19.3593	0.755855
$657$	−37.1369	−1.44885
$658$	−0.0322267	−0.00125633
$659$	−32.1437	−1.25214	−0.626071	−	0.779766i	$-0.715338\pi$
$659$	−32.1437	−1.25214	−0.626071	+	0.779766i	$0.715338\pi$
$660$	−16.7528	−0.652102
$661$	−38.5876	−1.50088	−0.750442	−	0.660936i	$-0.770159\pi$
$661$	−38.5876	−1.50088	−0.750442	+	0.660936i	$0.770159\pi$
$662$	−14.7877	−0.574739
$663$	0.0813975	0.00316122
$664$	14.5001	0.562712
$665$	2.56650	0.0995245
$666$	71.8665	2.78477
$667$	1.72928	0.0669579
$668$	−54.3387	−2.10243
$669$	0.485058	0.0187534
$670$	−82.8833	−3.20206
$671$	−32.5970	−1.25839
$672$	−0.219706	−0.00847536
$673$	38.6728	1.49073	0.745363	−	0.666659i	$-0.232276\pi$
$673$	38.6728	1.49073	0.745363	+	0.666659i	$0.232276\pi$
$674$	20.0205	0.771160
$675$	−29.4233	−1.13250
$676$	2.51433	0.0967049
$677$	−30.7111	−1.18032	−0.590162	−	0.807285i	$-0.700936\pi$
$677$	−30.7111	−1.18032	−0.590162	+	0.807285i	$0.700936\pi$
$678$	2.27406	0.0873346
$679$	−0.0987707	−0.00379047
$680$	−1.12676	−0.0432092
$681$	−2.24264	−0.0859381
$682$	31.4516	1.20435
$683$	10.7419	0.411027	0.205514	−	0.978654i	$-0.434114\pi$
$683$	10.7419	0.411027	0.205514	+	0.978654i	$0.434114\pi$
$684$	−52.9834	−2.02587
$685$	27.9628	1.06840
$686$	−2.36737	−0.0903866
$687$	4.31251	0.164532
$688$	−16.5795	−0.632087
$689$	10.1519	0.386757
$690$	−2.64218	−0.100586
$691$	5.00554	0.190420	0.0952098	−	0.995457i	$-0.469648\pi$
$691$	5.00554	0.190420	0.0952098	+	0.995457i	$0.469648\pi$
$692$	−61.8991	−2.35305
$693$	0.997598	0.0378956
$694$	−26.3667	−1.00086
$695$	89.7583	3.40473
$696$	0.808924	0.0306622
$697$	1.67448	0.0634255
$698$	60.0569	2.27319
$699$	1.14888	0.0434547
$700$	−2.88187	−0.108925
$701$	12.7225	0.480522	0.240261	−	0.970708i	$-0.422767\pi$
$701$	12.7225	0.480522	0.240261	+	0.970708i	$0.422767\pi$
$702$	−4.34283	−0.163909
$703$	85.9856	3.24301
$704$	−49.8245	−1.87783
$705$	0.291669	0.0109849
$706$	12.5326	0.471669
$707$	−0.368511	−0.0138593
$708$	−2.57986	−0.0969570
$709$	−17.7530	−0.666727	−0.333364	−	0.942798i	$-0.608184\pi$
$709$	−17.7530	−0.666727	−0.333364	+	0.942798i	$0.608184\pi$
$710$	72.9934	2.73939
$711$	23.6891	0.888409
$712$	4.79689	0.179771
$713$	2.76278	0.103467
$714$	−0.0137704	−0.000515343 0
$715$	19.1647	0.716720
$716$	−36.4672	−1.36284
$717$	−7.39589	−0.276205
$718$	42.3112	1.57904
$719$	−38.0906	−1.42054	−0.710270	−	0.703929i	$-0.751427\pi$
$719$	−38.0906	−1.42054	−0.710270	+	0.703929i	$0.751427\pi$
$720$	−34.3214	−1.27908
$721$	0.0796229	0.00296531
$722$	−73.4485	−2.73347
$723$	−7.07962	−0.263294
$724$	−31.0996	−1.15581
$725$	−30.6495	−1.13829
$726$	−5.86301	−0.217597
$727$	1.04435	0.0387327	0.0193664	−	0.999812i	$-0.493835\pi$
$727$	1.04435	0.0387327	0.0193664	+	0.999812i	$0.493835\pi$
$728$	−0.0870111	−0.00322485
$729$	−20.6903	−0.766307
$730$	120.695	4.46710
$731$	−1.43404	−0.0530398
$732$	−6.54796	−0.242019
$733$	−2.66573	−0.0984610	−0.0492305	−	0.998787i	$-0.515677\pi$
$733$	−2.66573	−0.0984610	−0.0492305	+	0.998787i	$0.515677\pi$
$734$	46.0165	1.69850
$735$	10.7081	0.394975
$736$	−6.44611	−0.237607
$737$	−38.5462	−1.41987
$738$	−43.7512	−1.61050
$739$	−48.0160	−1.76630	−0.883149	−	0.469093i	$-0.844581\pi$
$739$	−48.0160	−1.76630	−0.883149	+	0.469093i	$0.844581\pi$
$740$	−130.088	−4.78213
$741$	−2.54460	−0.0934783
$742$	−1.71744	−0.0630493
$743$	−38.1746	−1.40049	−0.700244	−	0.713903i	$-0.746926\pi$
$743$	−38.1746	−1.40049	−0.700244	+	0.713903i	$0.746926\pi$
$744$	1.29238	0.0473809
$745$	−1.97166	−0.0722361
$746$	64.8723	2.37514
$747$	38.2028	1.39777
$748$	−2.56169	−0.0936647
$749$	−0.602374	−0.0220103
$750$	30.5638	1.11603
$751$	26.7205	0.975045	0.487522	−	0.873110i	$-0.337901\pi$
$751$	26.7205	0.975045	0.487522	+	0.873110i	$0.337901\pi$
$752$	0.515631	0.0188031
$753$	1.87195	0.0682176
$754$	−4.52382	−0.164748
$755$	66.3828	2.41592
$756$	0.409200	0.0148825
$757$	31.8604	1.15799	0.578994	−	0.815332i	$-0.303446\pi$
$757$	31.8604	1.15799	0.578994	+	0.815332i	$0.303446\pi$
$758$	−10.0967	−0.366727
$759$	−1.22879	−0.0446021
$760$	35.2240	1.27771
$761$	31.0716	1.12634	0.563172	−	0.826340i	$-0.309581\pi$
$761$	31.0716	1.12634	0.563172	+	0.826340i	$0.309581\pi$
$762$	9.65944	0.349925
$763$	−0.294048	−0.0106453
$764$	−15.0655	−0.545050
$765$	−2.96862	−0.107331
$766$	−6.55668	−0.236902
$767$	2.95128	0.106565
$768$	1.71693	0.0619546
$769$	13.7245	0.494919	0.247460	−	0.968898i	$-0.420404\pi$
$769$	13.7245	0.494919	0.247460	+	0.968898i	$0.420404\pi$
$770$	−3.24218	−0.116840
$771$	0.846253	0.0304770
$772$	26.0386	0.937148
$773$	−32.8114	−1.18014	−0.590072	−	0.807351i	$-0.700901\pi$
$773$	−32.8114	−1.18014	−0.590072	+	0.807351i	$0.700901\pi$
$774$	37.4688	1.34679
$775$	−48.9672	−1.75895
$776$	−1.35558	−0.0486626
$777$	−0.325215	−0.0116670
$778$	−7.40958	−0.265646
$779$	−52.3467	−1.87551
$780$	3.84974	0.137843
$781$	33.9467	1.21471
$782$	−0.404018	−0.0144477
$783$	4.35195	0.155526
$784$	18.9305	0.676090
$785$	−58.6668	−2.09391
$786$	−0.337294	−0.0120309
$787$	23.4696	0.836602	0.418301	−	0.908309i	$-0.362626\pi$
$787$	23.4696	0.836602	0.418301	+	0.908309i	$0.362626\pi$
$788$	41.3574	1.47330
$789$	7.47332	0.266057
$790$	−76.9891	−2.73915
$791$	0.245120	0.00871548
$792$	13.6916	0.486510
$793$	7.49067	0.266002
$794$	29.8456	1.05918
$795$	15.5438	0.551281
$796$	−45.2512	−1.60389
$797$	−17.0380	−0.603518	−0.301759	−	0.953384i	$-0.597574\pi$
$797$	−17.0380	−0.603518	−0.301759	+	0.953384i	$0.597574\pi$
$798$	0.430481	0.0152389
$799$	0.0445994	0.00157781
$800$	114.250	4.03935
$801$	12.6382	0.446547
$802$	−60.4634	−2.13504
$803$	56.1308	1.98081
$804$	−7.74300	−0.273075
$805$	−0.284800	−0.0100379
$806$	−7.22748	−0.254577
$807$	5.08104	0.178861
$808$	−5.05765	−0.177928
$809$	32.7837	1.15261	0.576307	−	0.817233i	$-0.304493\pi$
$809$	32.7837	1.15261	0.576307	+	0.817233i	$0.304493\pi$
$810$	74.1717	2.60613
$811$	−1.73982	−0.0610934	−0.0305467	−	0.999533i	$-0.509725\pi$
$811$	−1.73982	−0.0610934	−0.0305467	+	0.999533i	$0.509725\pi$
$812$	0.426254	0.0149586
$813$	7.55105	0.264827
$814$	−108.623	−3.80724
$815$	−61.9588	−2.17032
$816$	0.220328	0.00771301
$817$	44.8301	1.56841
$818$	72.7316	2.54300
$819$	−0.229245	−0.00801045
$820$	79.1955	2.76563
$821$	−11.9370	−0.416602	−0.208301	−	0.978065i	$-0.566793\pi$
$821$	−11.9370	−0.416602	−0.208301	+	0.978065i	$0.566793\pi$
$822$	4.69022	0.163590
$823$	−3.08174	−0.107423	−0.0537113	−	0.998557i	$-0.517105\pi$
$823$	−3.08174	−0.107423	−0.0537113	+	0.998557i	$0.517105\pi$
$824$	1.09279	0.0380691
$825$	21.7788	0.758241
$826$	−0.499282	−0.0173722
$827$	−30.2734	−1.05271	−0.526355	−	0.850265i	$-0.676442\pi$
$827$	−30.2734	−1.05271	−0.526355	+	0.850265i	$0.676442\pi$
$828$	5.87948	0.204326
$829$	13.4587	0.467441	0.233721	−	0.972304i	$-0.424910\pi$
$829$	13.4587	0.467441	0.233721	+	0.972304i	$0.424910\pi$
$830$	−124.159	−4.30960
$831$	−4.60846	−0.159866
$832$	11.4495	0.396940
$833$	1.63739	0.0567323
$834$	15.0553	0.521321
$835$	95.1774	3.29375
$836$	80.0821	2.76970
$837$	6.95290	0.240327
$838$	−37.8531	−1.30761
$839$	−20.6609	−0.713295	−0.356647	−	0.934239i	$-0.616080\pi$
$839$	−20.6609	−0.713295	−0.356647	+	0.934239i	$0.616080\pi$
$840$	−0.133224	−0.00459668
$841$	−24.4667	−0.843679
$842$	16.4386	0.566511
$843$	8.23217	0.283531
$844$	−7.59193	−0.261325
$845$	−4.40399	−0.151502
$846$	−1.16530	−0.0400639
$847$	−0.631974	−0.0217149
$848$	27.4793	0.943643
$849$	−1.23420	−0.0423577
$850$	7.16076	0.245612
$851$	−9.54170	−0.327085
$852$	6.81908	0.233618
$853$	31.3786	1.07438	0.537191	−	0.843461i	$-0.319485\pi$
$853$	31.3786	1.07438	0.537191	+	0.843461i	$0.319485\pi$
$854$	−1.26723	−0.0433637
$855$	92.8034	3.17381
$856$	−8.26732	−0.282571
$857$	8.53046	0.291395	0.145697	−	0.989329i	$-0.453457\pi$
$857$	8.53046	0.291395	0.145697	+	0.989329i	$0.453457\pi$
$858$	3.21452	0.109742
$859$	−28.4208	−0.969705	−0.484853	−	0.874596i	$-0.661127\pi$
$859$	−28.4208	−0.969705	−0.484853	+	0.874596i	$0.661127\pi$
$860$	−67.8236	−2.31277
$861$	0.197986	0.00674733
$862$	39.0808	1.33110
$863$	0.831224	0.0282952	0.0141476	−	0.999900i	$-0.495497\pi$
$863$	0.831224	0.0282952	0.0141476	+	0.999900i	$0.495497\pi$
$864$	−16.2225	−0.551900
$865$	108.420	3.68638
$866$	−21.7056	−0.737587
$867$	−5.89128	−0.200078
$868$	0.681005	0.0231148
$869$	−35.8050	−1.21460
$870$	−6.92650	−0.234830
$871$	8.85777	0.300134
$872$	−4.03569	−0.136666
$873$	−3.57150	−0.120877
$874$	12.6302	0.427222
$875$	3.29447	0.111373
$876$	11.2753	0.380959
$877$	−46.2609	−1.56212	−0.781059	−	0.624457i	$-0.785320\pi$
$877$	−46.2609	−1.56212	−0.781059	+	0.624457i	$0.785320\pi$
$878$	75.0842	2.53397
$879$	−2.45577	−0.0828312
$880$	51.8753	1.74872
$881$	−32.0373	−1.07936	−0.539681	−	0.841869i	$-0.681455\pi$
$881$	−32.0373	−1.07936	−0.539681	+	0.841869i	$0.681455\pi$
$882$	−42.7821	−1.44055
$883$	−29.8609	−1.00490	−0.502450	−	0.864606i	$-0.667568\pi$
$883$	−29.8609	−1.00490	−0.502450	+	0.864606i	$0.667568\pi$
$884$	0.588667	0.0197990
$885$	4.51877	0.151897
$886$	23.6814	0.795593
$887$	51.2181	1.71974	0.859868	−	0.510517i	$-0.170546\pi$
$887$	51.2181	1.71974	0.859868	+	0.510517i	$0.170546\pi$
$888$	−4.46343	−0.149783
$889$	1.04119	0.0349204
$890$	−41.0739	−1.37680
$891$	34.4947	1.15562
$892$	3.50794	0.117455
$893$	−1.39424	−0.0466565
$894$	−0.330709	−0.0110606
$895$	63.8743	2.13508
$896$	−0.673071	−0.0224857
$897$	0.282371	0.00942808
$898$	74.2239	2.47688
$899$	7.24266	0.241556
$900$	−104.207	−3.47357
$901$	2.37682	0.0791833
$902$	66.1280	2.20182
$903$	−0.169556	−0.00564248
$904$	3.36417	0.111891
$905$	54.4727	1.81073
$906$	11.1345	0.369918
$907$	−59.5562	−1.97753	−0.988765	−	0.149476i	$-0.952241\pi$
$907$	−59.5562	−1.97753	−0.988765	+	0.149476i	$0.952241\pi$
$908$	−16.2188	−0.538239
$909$	−13.3252	−0.441969
$910$	0.745042	0.0246979
$911$	6.26086	0.207432	0.103716	−	0.994607i	$-0.466927\pi$
$911$	6.26086	0.207432	0.103716	+	0.994607i	$0.466927\pi$
$912$	−6.88776	−0.228076
$913$	−57.7418	−1.91098
$914$	−38.5612	−1.27549
$915$	11.4691	0.379157
$916$	31.1881	1.03048
$917$	−0.0363569	−0.00120061
$918$	−1.01676	−0.0335582
$919$	−10.4816	−0.345755	−0.172878	−	0.984943i	$-0.555307\pi$
$919$	−10.4816	−0.345755	−0.172878	+	0.984943i	$0.555307\pi$
$920$	−3.90876	−0.128868
$921$	8.27293	0.272602
$922$	10.3649	0.341348
$923$	−7.80083	−0.256768
$924$	−0.302886	−0.00996423
$925$	169.116	5.56049
$926$	−66.2873	−2.17834
$927$	2.87913	0.0945630
$928$	−16.8986	−0.554722
$929$	17.8443	0.585454	0.292727	−	0.956196i	$-0.405437\pi$
$929$	17.8443	0.585454	0.292727	+	0.956196i	$0.405437\pi$
$930$	−11.0661	−0.362873
$931$	−51.1872	−1.67759
$932$	8.30871	0.272161
$933$	5.45378	0.178549
$934$	−76.5454	−2.50464
$935$	4.48695	0.146739
$936$	−3.14628	−0.102839
$937$	−54.1589	−1.76929	−0.884647	−	0.466262i	$-0.845600\pi$
$937$	−54.1589	−1.76929	−0.884647	+	0.466262i	$0.845600\pi$
$938$	−1.49851	−0.0489280
$939$	7.34927	0.239834
$940$	2.10935	0.0687995
$941$	48.8039	1.59096	0.795480	−	0.605979i	$-0.207219\pi$
$941$	48.8039	1.59096	0.795480	+	0.605979i	$0.207219\pi$
$942$	−9.84024	−0.320613
$943$	5.80883	0.189162
$944$	7.98857	0.260006
$945$	−0.716737	−0.0233155
$946$	−56.6325	−1.84128
$947$	11.7587	0.382107	0.191053	−	0.981580i	$-0.438810\pi$
$947$	11.7587	0.382107	0.191053	+	0.981580i	$0.438810\pi$
$948$	−7.19236	−0.233597
$949$	−12.8987	−0.418709
$950$	−223.856	−7.26284
$951$	−1.99785	−0.0647846
$952$	−0.0203715	−0.000660244 0
$953$	2.81451	0.0911708	0.0455854	−	0.998960i	$-0.485485\pi$
$953$	2.81451	0.0911708	0.0455854	+	0.998960i	$0.485485\pi$
$954$	−62.1020	−2.01063
$955$	26.3880	0.853897
$956$	−53.4872	−1.72990
$957$	−3.22128	−0.104129
$958$	−37.5928	−1.21457
$959$	0.505559	0.0163254
$960$	17.5305	0.565796
$961$	−19.4288	−0.626734
$962$	24.9612	0.804782
$963$	−21.7816	−0.701902
$964$	−51.1999	−1.64904
$965$	−45.6080	−1.46817
$966$	−0.0477699	−0.00153697
$967$	8.44736	0.271649	0.135824	−	0.990733i	$-0.456632\pi$
$967$	8.44736	0.271649	0.135824	+	0.990733i	$0.456632\pi$
$968$	−8.67357	−0.278779
$969$	−0.595755	−0.0191384
$970$	11.6073	0.372689
$971$	−50.8535	−1.63197	−0.815984	−	0.578074i	$-0.803804\pi$
$971$	−50.8535	−1.63197	−0.815984	+	0.578074i	$0.803804\pi$
$972$	22.3468	0.716775
$973$	1.62281	0.0520248
$974$	11.3294	0.363017
$975$	−5.00470	−0.160279
$976$	20.2758	0.649014
$977$	48.4595	1.55036	0.775179	−	0.631742i	$-0.217660\pi$
$977$	48.4595	1.55036	0.775179	+	0.631742i	$0.217660\pi$
$978$	−10.3924	−0.332313
$979$	−19.1020	−0.610503
$980$	77.4413	2.47377
$981$	−10.6327	−0.339475
$982$	−30.6542	−0.978215
$983$	30.5216	0.973488	0.486744	−	0.873545i	$-0.338185\pi$
$983$	30.5216	0.973488	0.486744	+	0.873545i	$0.338185\pi$
$984$	2.71726	0.0866232
$985$	−72.4398	−2.30813
$986$	−1.05914	−0.0337299
$987$	0.00527330	0.000167851 0
$988$	−18.4026	−0.585464
$989$	−4.97473	−0.158187
$990$	−117.236	−3.72600
$991$	26.8815	0.853920	0.426960	−	0.904270i	$-0.359584\pi$
$991$	26.8815	0.853920	0.426960	+	0.904270i	$0.359584\pi$
$992$	−26.9980	−0.857187
$993$	2.41972	0.0767876
$994$	1.31970	0.0418584
$995$	79.2600	2.51271
$996$	−11.5990	−0.367527
$997$	−40.3733	−1.27864	−0.639318	−	0.768943i	$-0.720783\pi$
$997$	−40.3733	−1.27864	−0.639318	+	0.768943i	$0.720783\pi$
$998$	82.7472	2.61932
$999$	−24.0129	−0.759736

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1339.2.a.e.1.3	✓	21

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1339.2.a.e.1.3	✓	21	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:	\( N \)	\(=\)	\( 1339 = 13 \cdot 103 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1339.a (trivial)

\(f(q)\)	\(=\)	\(q-2.12469 q^{2} +0.347667 q^{3} +2.51433 q^{4} -4.40399 q^{5} -0.738685 q^{6} -0.0796229 q^{7} -1.09279 q^{8} -2.87913 q^{9} +O(q^{10})\)	\(q-2.12469 q^{2} +0.347667 q^{3} +2.51433 q^{4} -4.40399 q^{5} -0.738685 q^{6} -0.0796229 q^{7} -1.09279 q^{8} -2.87913 q^{9} +9.35713 q^{10} +4.35168 q^{11} +0.874148 q^{12} -1.00000 q^{13} +0.169174 q^{14} -1.53112 q^{15} -2.70681 q^{16} -0.234125 q^{17} +6.11727 q^{18} +7.31908 q^{19} -11.0731 q^{20} -0.0276822 q^{21} -9.24598 q^{22} -0.812188 q^{23} -0.379926 q^{24} +14.3951 q^{25} +2.12469 q^{26} -2.04398 q^{27} -0.200198 q^{28} -2.12916 q^{29} +3.25316 q^{30} -3.40165 q^{31} +7.93673 q^{32} +1.51293 q^{33} +0.497445 q^{34} +0.350658 q^{35} -7.23907 q^{36} +11.7481 q^{37} -15.5508 q^{38} -0.347667 q^{39} +4.81263 q^{40} -7.15208 q^{41} +0.0588163 q^{42} +6.12509 q^{43} +10.9415 q^{44} +12.6796 q^{45} +1.72565 q^{46} -0.190494 q^{47} -0.941068 q^{48} -6.99366 q^{49} -30.5852 q^{50} -0.0813975 q^{51} -2.51433 q^{52} -10.1519 q^{53} +4.34283 q^{54} -19.1647 q^{55} +0.0870111 q^{56} +2.54460 q^{57} +4.52382 q^{58} -2.95128 q^{59} -3.84974 q^{60} -7.49067 q^{61} +7.22748 q^{62} +0.229245 q^{63} -11.4495 q^{64} +4.40399 q^{65} -3.21452 q^{66} -8.85777 q^{67} -0.588667 q^{68} -0.282371 q^{69} -0.745042 q^{70} +7.80083 q^{71} +3.14628 q^{72} +12.8987 q^{73} -24.9612 q^{74} +5.00470 q^{75} +18.4026 q^{76} -0.346493 q^{77} +0.738685 q^{78} -8.22786 q^{79} +11.9208 q^{80} +7.92676 q^{81} +15.1960 q^{82} -13.2689 q^{83} -0.0696022 q^{84} +1.03108 q^{85} -13.0140 q^{86} -0.740238 q^{87} -4.75547 q^{88} -4.38958 q^{89} -26.9404 q^{90} +0.0796229 q^{91} -2.04211 q^{92} -1.18264 q^{93} +0.404741 q^{94} -32.2331 q^{95} +2.75934 q^{96} +1.24048 q^{97} +14.8594 q^{98} -12.5290 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 21 q - q^{2} - 6 q^{3} + 15 q^{4} - 18 q^{5} - 8 q^{6} - 2 q^{7} + 6 q^{8} + 11 q^{9}+O(q^{10}) \) 21 * q - q^2 - 6 * q^3 + 15 * q^4 - 18 * q^5 - 8 * q^6 - 2 * q^7 + 6 * q^8 + 11 * q^9	\( 21 q - q^{2} - 6 q^{3} + 15 q^{4} - 18 q^{5} - 8 q^{6} - 2 q^{7} + 6 q^{8} + 11 q^{9} - 10 q^{10} - 5 q^{11} - 22 q^{12} - 21 q^{13} - 24 q^{14} - q^{15} - 5 q^{16} - 18 q^{17} + 10 q^{18} - 6 q^{19} - 30 q^{20} - 17 q^{21} - 8 q^{22} - 14 q^{23} - 13 q^{24} + 11 q^{25} + q^{26} - 33 q^{27} - 2 q^{28} - 36 q^{29} + 2 q^{30} + q^{31} - 9 q^{32} - 11 q^{33} - 25 q^{34} - 37 q^{35} + 3 q^{36} + 5 q^{37} - 13 q^{38} + 6 q^{39} - 2 q^{40} - 32 q^{41} + 7 q^{42} + 2 q^{43} + 4 q^{44} - 32 q^{45} - 5 q^{46} - 12 q^{47} - 18 q^{48} + 5 q^{49} - 2 q^{50} - 27 q^{51} - 15 q^{52} - 49 q^{53} - 31 q^{54} - 9 q^{55} - 53 q^{56} + 14 q^{57} - 2 q^{58} - 34 q^{59} + 25 q^{60} - 27 q^{61} - 12 q^{62} + 41 q^{63} - 70 q^{64} + 18 q^{65} - 15 q^{66} - 12 q^{67} - 20 q^{68} - 70 q^{69} + 70 q^{70} - 26 q^{71} - 14 q^{72} + 23 q^{73} + 20 q^{74} - 9 q^{75} - 36 q^{76} - 62 q^{77} + 8 q^{78} - 7 q^{79} - 41 q^{80} - 3 q^{81} - 33 q^{82} - q^{83} - 48 q^{84} + 10 q^{85} - 23 q^{86} - 7 q^{87} + 9 q^{88} - 16 q^{89} - 30 q^{90} + 2 q^{91} - 27 q^{92} + 2 q^{93} - 37 q^{94} - 35 q^{95} + 55 q^{96} - 30 q^{97} - 43 q^{98} - 42 q^{99}+O(q^{100}) \) 21 * q - q^2 - 6 * q^3 + 15 * q^4 - 18 * q^5 - 8 * q^6 - 2 * q^7 + 6 * q^8 + 11 * q^9 - 10 * q^10 - 5 * q^11 - 22 * q^12 - 21 * q^13 - 24 * q^14 - q^15 - 5 * q^16 - 18 * q^17 + 10 * q^18 - 6 * q^19 - 30 * q^20 - 17 * q^21 - 8 * q^22 - 14 * q^23 - 13 * q^24 + 11 * q^25 + q^26 - 33 * q^27 - 2 * q^28 - 36 * q^29 + 2 * q^30 + q^31 - 9 * q^32 - 11 * q^33 - 25 * q^34 - 37 * q^35 + 3 * q^36 + 5 * q^37 - 13 * q^38 + 6 * q^39 - 2 * q^40 - 32 * q^41 + 7 * q^42 + 2 * q^43 + 4 * q^44 - 32 * q^45 - 5 * q^46 - 12 * q^47 - 18 * q^48 + 5 * q^49 - 2 * q^50 - 27 * q^51 - 15 * q^52 - 49 * q^53 - 31 * q^54 - 9 * q^55 - 53 * q^56 + 14 * q^57 - 2 * q^58 - 34 * q^59 + 25 * q^60 - 27 * q^61 - 12 * q^62 + 41 * q^63 - 70 * q^64 + 18 * q^65 - 15 * q^66 - 12 * q^67 - 20 * q^68 - 70 * q^69 + 70 * q^70 - 26 * q^71 - 14 * q^72 + 23 * q^73 + 20 * q^74 - 9 * q^75 - 36 * q^76 - 62 * q^77 + 8 * q^78 - 7 * q^79 - 41 * q^80 - 3 * q^81 - 33 * q^82 - q^83 - 48 * q^84 + 10 * q^85 - 23 * q^86 - 7 * q^87 + 9 * q^88 - 16 * q^89 - 30 * q^90 + 2 * q^91 - 27 * q^92 + 2 * q^93 - 37 * q^94 - 35 * q^95 + 55 * q^96 - 30 * q^97 - 43 * q^98 - 42 * q^99

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