LMFDB - Embedded newform 6041.2.a.c.1.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6041,2,Mod(1,6041)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6041, 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("6041.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6041 = 7 \cdot 863 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6041.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:	$48.2376278611$
Analytic rank:	$1$
Dimension:	$83$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.12
Character	$\chi$	$=$	6041.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.15056 q^{2} -0.709425 q^{3} +2.62493 q^{4} -2.42733 q^{5} +1.52566 q^{6} +1.00000 q^{7} -1.34395 q^{8} -2.49672 q^{9} +O(q^{10})$	\(q-2.15056 q^{2} -0.709425 q^{3} +2.62493 q^{4} -2.42733 q^{5} +1.52566 q^{6} +1.00000 q^{7} -1.34395 q^{8} -2.49672 q^{9} +5.22013 q^{10} -3.03448 q^{11} -1.86219 q^{12} +0.169680 q^{13} -2.15056 q^{14} +1.72201 q^{15} -2.35960 q^{16} -0.458209 q^{17} +5.36935 q^{18} -5.85207 q^{19} -6.37157 q^{20} -0.709425 q^{21} +6.52585 q^{22} +2.61609 q^{23} +0.953433 q^{24} +0.891926 q^{25} -0.364907 q^{26} +3.89951 q^{27} +2.62493 q^{28} +4.07553 q^{29} -3.70329 q^{30} +2.13180 q^{31} +7.76238 q^{32} +2.15274 q^{33} +0.985407 q^{34} -2.42733 q^{35} -6.55370 q^{36} -2.37718 q^{37} +12.5853 q^{38} -0.120375 q^{39} +3.26221 q^{40} +8.10017 q^{41} +1.52566 q^{42} -6.79849 q^{43} -7.96531 q^{44} +6.06035 q^{45} -5.62608 q^{46} +0.100377 q^{47} +1.67396 q^{48} +1.00000 q^{49} -1.91815 q^{50} +0.325065 q^{51} +0.445397 q^{52} +0.543932 q^{53} -8.38615 q^{54} +7.36569 q^{55} -1.34395 q^{56} +4.15161 q^{57} -8.76470 q^{58} +11.9928 q^{59} +4.52015 q^{60} +9.67031 q^{61} -4.58457 q^{62} -2.49672 q^{63} -11.9743 q^{64} -0.411868 q^{65} -4.62960 q^{66} +7.89885 q^{67} -1.20277 q^{68} -1.85592 q^{69} +5.22013 q^{70} -2.96615 q^{71} +3.35546 q^{72} -10.8959 q^{73} +5.11228 q^{74} -0.632755 q^{75} -15.3613 q^{76} -3.03448 q^{77} +0.258874 q^{78} +7.92535 q^{79} +5.72754 q^{80} +4.72374 q^{81} -17.4199 q^{82} -13.2366 q^{83} -1.86219 q^{84} +1.11222 q^{85} +14.6206 q^{86} -2.89129 q^{87} +4.07820 q^{88} -7.37530 q^{89} -13.0332 q^{90} +0.169680 q^{91} +6.86706 q^{92} -1.51235 q^{93} -0.215867 q^{94} +14.2049 q^{95} -5.50683 q^{96} -10.1427 q^{97} -2.15056 q^{98} +7.57624 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 83 q - 8 q^{2} - 12 q^{3} + 48 q^{4} - 11 q^{5} - 8 q^{6} + 83 q^{7} - 18 q^{8} + 39 q^{9}+O(q^{10}) $ 83 * q - 8 * q^2 - 12 * q^3 + 48 * q^4 - 11 * q^5 - 8 * q^6 + 83 * q^7 - 18 * q^8 + 39 * q^9	\( 83 q - 8 q^{2} - 12 q^{3} + 48 q^{4} - 11 q^{5} - 8 q^{6} + 83 q^{7} - 18 q^{8} + 39 q^{9} - 20 q^{10} - 26 q^{11} - 14 q^{12} - 22 q^{13} - 8 q^{14} - 37 q^{15} - 10 q^{16} - 9 q^{17} - 27 q^{18} - 42 q^{19} - 22 q^{20} - 12 q^{21} - 44 q^{22} - 46 q^{23} - 24 q^{24} - 20 q^{25} - 9 q^{26} - 39 q^{27} + 48 q^{28} - 36 q^{29} - 11 q^{30} - 107 q^{31} - 19 q^{32} - 25 q^{33} - 24 q^{34} - 11 q^{35} - 32 q^{36} - 75 q^{37} - 16 q^{38} - 78 q^{39} - 34 q^{40} - 17 q^{41} - 8 q^{42} - 87 q^{43} - 32 q^{44} - 17 q^{45} - 56 q^{46} - 39 q^{47} - 16 q^{48} + 83 q^{49} - 26 q^{50} - 71 q^{51} - 53 q^{52} - 28 q^{53} - 25 q^{54} - 94 q^{55} - 18 q^{56} - 79 q^{57} - 69 q^{58} - 26 q^{59} - 43 q^{60} - 56 q^{61} - 6 q^{62} + 39 q^{63} - 108 q^{64} - 26 q^{65} + 10 q^{66} - 123 q^{67} - 11 q^{68} + 2 q^{69} - 20 q^{70} - 96 q^{71} - 11 q^{72} - 53 q^{73} - 26 q^{74} - 27 q^{75} - 65 q^{76} - 26 q^{77} - 43 q^{78} - 160 q^{79} + 12 q^{80} - 53 q^{81} - 20 q^{82} - 2 q^{83} - 14 q^{84} - 110 q^{85} + 24 q^{86} - 52 q^{87} - 79 q^{88} - 5 q^{89} - 4 q^{90} - 22 q^{91} - 51 q^{92} - 30 q^{93} - 9 q^{94} - 76 q^{95} - 3 q^{96} - 44 q^{97} - 8 q^{98} - 82 q^{99}+O(q^{100}) \) 83 * q - 8 * q^2 - 12 * q^3 + 48 * q^4 - 11 * q^5 - 8 * q^6 + 83 * q^7 - 18 * q^8 + 39 * q^9 - 20 * q^10 - 26 * q^11 - 14 * q^12 - 22 * q^13 - 8 * q^14 - 37 * q^15 - 10 * q^16 - 9 * q^17 - 27 * q^18 - 42 * q^19 - 22 * q^20 - 12 * q^21 - 44 * q^22 - 46 * q^23 - 24 * q^24 - 20 * q^25 - 9 * q^26 - 39 * q^27 + 48 * q^28 - 36 * q^29 - 11 * q^30 - 107 * q^31 - 19 * q^32 - 25 * q^33 - 24 * q^34 - 11 * q^35 - 32 * q^36 - 75 * q^37 - 16 * q^38 - 78 * q^39 - 34 * q^40 - 17 * q^41 - 8 * q^42 - 87 * q^43 - 32 * q^44 - 17 * q^45 - 56 * q^46 - 39 * q^47 - 16 * q^48 + 83 * q^49 - 26 * q^50 - 71 * q^51 - 53 * q^52 - 28 * q^53 - 25 * q^54 - 94 * q^55 - 18 * q^56 - 79 * q^57 - 69 * q^58 - 26 * q^59 - 43 * q^60 - 56 * q^61 - 6 * q^62 + 39 * q^63 - 108 * q^64 - 26 * q^65 + 10 * q^66 - 123 * q^67 - 11 * q^68 + 2 * q^69 - 20 * q^70 - 96 * q^71 - 11 * q^72 - 53 * q^73 - 26 * q^74 - 27 * q^75 - 65 * q^76 - 26 * q^77 - 43 * q^78 - 160 * q^79 + 12 * q^80 - 53 * q^81 - 20 * q^82 - 2 * q^83 - 14 * q^84 - 110 * q^85 + 24 * q^86 - 52 * q^87 - 79 * q^88 - 5 * q^89 - 4 * q^90 - 22 * q^91 - 51 * q^92 - 30 * q^93 - 9 * q^94 - 76 * q^95 - 3 * q^96 - 44 * q^97 - 8 * q^98 - 82 * 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 $

$2$	−2.15056	−1.52068	−0.760340	−	0.649526i	$-0.774967\pi$
$2$	−2.15056	−1.52068	−0.760340	+	0.649526i	$0.774967\pi$
$3$	−0.709425	−0.409587	−0.204793	−	0.978805i	$-0.565652\pi$
$3$	−0.709425	−0.409587	−0.204793	+	0.978805i	$0.565652\pi$
$4$	2.62493	1.31246
$5$	−2.42733	−1.08553	−0.542767	−	0.839883i	$-0.682623\pi$
$5$	−2.42733	−1.08553	−0.542767	+	0.839883i	$0.682623\pi$
$6$	1.52566	0.622850
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	−1.34395	−0.475159
$9$	−2.49672	−0.832239
$10$	5.22013	1.65075
$11$	−3.03448	−0.914931	−0.457466	−	0.889227i	$-0.651243\pi$
$11$	−3.03448	−0.914931	−0.457466	+	0.889227i	$0.651243\pi$
$12$	−1.86219	−0.537568
$13$	0.169680	0.0470606	0.0235303	−	0.999723i	$-0.492509\pi$
$13$	0.169680	0.0470606	0.0235303	+	0.999723i	$0.492509\pi$
$14$	−2.15056	−0.574763
$15$	1.72201	0.444621
$16$	−2.35960	−0.589901
$17$	−0.458209	−0.111132	−0.0555659	−	0.998455i	$-0.517696\pi$
$17$	−0.458209	−0.111132	−0.0555659	+	0.998455i	$0.517696\pi$
$18$	5.36935	1.26557
$19$	−5.85207	−1.34256	−0.671279	−	0.741205i	$-0.734255\pi$
$19$	−5.85207	−1.34256	−0.671279	+	0.741205i	$0.734255\pi$
$20$	−6.37157	−1.42473
$21$	−0.709425	−0.154809
$22$	6.52585	1.39132
$23$	2.61609	0.545493	0.272747	−	0.962086i	$-0.412068\pi$
$23$	2.61609	0.545493	0.272747	+	0.962086i	$0.412068\pi$
$24$	0.953433	0.194619
$25$	0.891926	0.178385
$26$	−0.364907	−0.0715641
$27$	3.89951	0.750461
$28$	2.62493	0.496065
$29$	4.07553	0.756808	0.378404	−	0.925641i	$-0.376473\pi$
$29$	4.07553	0.756808	0.378404	+	0.925641i	$0.376473\pi$
$30$	−3.70329	−0.676125
$31$	2.13180	0.382882	0.191441	−	0.981504i	$-0.438684\pi$
$31$	2.13180	0.382882	0.191441	+	0.981504i	$0.438684\pi$
$32$	7.76238	1.37221
$33$	2.15274	0.374744
$34$	0.985407	0.168996
$35$	−2.42733	−0.410293
$36$	−6.55370	−1.09228
$37$	−2.37718	−0.390806	−0.195403	−	0.980723i	$-0.562601\pi$
$37$	−2.37718	−0.390806	−0.195403	+	0.980723i	$0.562601\pi$
$38$	12.5853	2.04160
$39$	−0.120375	−0.0192754
$40$	3.26221	0.515801
$41$	8.10017	1.26503	0.632517	−	0.774547i	$-0.282022\pi$
$41$	8.10017	1.26503	0.632517	+	0.774547i	$0.282022\pi$
$42$	1.52566	0.235415
$43$	−6.79849	−1.03676	−0.518380	−	0.855151i	$-0.673465\pi$
$43$	−6.79849	−1.03676	−0.518380	+	0.855151i	$0.673465\pi$
$44$	−7.96531	−1.20081
$45$	6.06035	0.903424
$46$	−5.62608	−0.829520
$47$	0.100377	0.0146415	0.00732073	−	0.999973i	$-0.497670\pi$
$47$	0.100377	0.0146415	0.00732073	+	0.999973i	$0.497670\pi$
$48$	1.67396	0.241616
$49$	1.00000	0.142857
$50$	−1.91815	−0.271267
$51$	0.325065	0.0455182
$52$	0.445397	0.0617654
$53$	0.543932	0.0747148	0.0373574	−	0.999302i	$-0.488106\pi$
$53$	0.543932	0.0747148	0.0373574	+	0.999302i	$0.488106\pi$
$54$	−8.38615	−1.14121
$55$	7.36569	0.993189
$56$	−1.34395	−0.179593
$57$	4.15161	0.549894
$58$	−8.76470	−1.15086
$59$	11.9928	1.56133	0.780664	−	0.624951i	$-0.214881\pi$
$59$	11.9928	1.56133	0.780664	+	0.624951i	$0.214881\pi$
$60$	4.52015	0.583549
$61$	9.67031	1.23816	0.619078	−	0.785330i	$-0.287507\pi$
$61$	9.67031	1.23816	0.619078	+	0.785330i	$0.287507\pi$
$62$	−4.58457	−0.582241
$63$	−2.49672	−0.314557
$64$	−11.9743	−1.49679
$65$	−0.411868	−0.0510859
$66$	−4.62960	−0.569865
$67$	7.89885	0.964999	0.482499	−	0.875896i	$-0.339729\pi$
$67$	7.89885	0.964999	0.482499	+	0.875896i	$0.339729\pi$
$68$	−1.20277	−0.145857
$69$	−1.85592	−0.223427
$70$	5.22013	0.623925
$71$	−2.96615	−0.352018	−0.176009	−	0.984389i	$-0.556319\pi$
$71$	−2.96615	−0.352018	−0.176009	+	0.984389i	$0.556319\pi$
$72$	3.35546	0.395445
$73$	−10.8959	−1.27526	−0.637632	−	0.770341i	$-0.720086\pi$
$73$	−10.8959	−1.27526	−0.637632	+	0.770341i	$0.720086\pi$
$74$	5.11228	0.594291
$75$	−0.632755	−0.0730642
$76$	−15.3613	−1.76206
$77$	−3.03448	−0.345812
$78$	0.258874	0.0293117
$79$	7.92535	0.891672	0.445836	−	0.895115i	$-0.352906\pi$
$79$	7.92535	0.891672	0.445836	+	0.895115i	$0.352906\pi$
$80$	5.72754	0.640358
$81$	4.72374	0.524860
$82$	−17.4199	−1.92371
$83$	−13.2366	−1.45291	−0.726454	−	0.687215i	$-0.758833\pi$
$83$	−13.2366	−1.45291	−0.726454	+	0.687215i	$0.758833\pi$
$84$	−1.86219	−0.203182
$85$	1.11222	0.120638
$86$	14.6206	1.57658
$87$	−2.89129	−0.309978
$88$	4.07820	0.434737
$89$	−7.37530	−0.781780	−0.390890	−	0.920437i	$-0.627833\pi$
$89$	−7.37530	−0.781780	−0.390890	+	0.920437i	$0.627833\pi$
$90$	−13.0332	−1.37382
$91$	0.169680	0.0177872
$92$	6.86706	0.715940
$93$	−1.51235	−0.156823
$94$	−0.215867	−0.0222650
$95$	14.2049	1.45739
$96$	−5.50683	−0.562039
$97$	−10.1427	−1.02984	−0.514920	−	0.857238i	$-0.672178\pi$
$97$	−10.1427	−1.02984	−0.514920	+	0.857238i	$0.672178\pi$
$98$	−2.15056	−0.217240
$99$	7.57624	0.761441
$100$	2.34124	0.234124
$101$	12.7697	1.27064	0.635319	−	0.772250i	$-0.280869\pi$
$101$	12.7697	1.27064	0.635319	+	0.772250i	$0.280869\pi$
$102$	−0.699073	−0.0692185
$103$	−6.01075	−0.592257	−0.296129	−	0.955148i	$-0.595696\pi$
$103$	−6.01075	−0.592257	−0.296129	+	0.955148i	$0.595696\pi$
$104$	−0.228041	−0.0223613
$105$	1.72201	0.168051
$106$	−1.16976	−0.113617
$107$	3.26335	0.315480	0.157740	−	0.987481i	$-0.449579\pi$
$107$	3.26335	0.315480	0.157740	+	0.987481i	$0.449579\pi$
$108$	10.2359	0.984953
$109$	−5.23484	−0.501406	−0.250703	−	0.968064i	$-0.580662\pi$
$109$	−5.23484	−0.501406	−0.250703	+	0.968064i	$0.580662\pi$
$110$	−15.8404	−1.51032
$111$	1.68643	0.160069
$112$	−2.35960	−0.222962
$113$	13.2438	1.24587	0.622936	−	0.782273i	$-0.285940\pi$
$113$	13.2438	1.24587	0.622936	+	0.782273i	$0.285940\pi$
$114$	−8.92830	−0.836212
$115$	−6.35012	−0.592152
$116$	10.6980	0.993283
$117$	−0.423642	−0.0391657
$118$	−25.7913	−2.37428
$119$	−0.458209	−0.0420039
$120$	−2.31429	−0.211265
$121$	−1.79191	−0.162901
$122$	−20.7966	−1.88284
$123$	−5.74646	−0.518141
$124$	5.59582	0.502519
$125$	9.97165	0.891891
$126$	5.36935	0.478340
$127$	−0.505529	−0.0448585	−0.0224292	−	0.999748i	$-0.507140\pi$
$127$	−0.505529	−0.0448585	−0.0224292	+	0.999748i	$0.507140\pi$
$128$	10.2267	0.903925
$129$	4.82302	0.424643
$130$	0.885749	0.0776853
$131$	−6.96083	−0.608171	−0.304085	−	0.952645i	$-0.598351\pi$
$131$	−6.96083	−0.608171	−0.304085	+	0.952645i	$0.598351\pi$
$132$	5.65079	0.491838
$133$	−5.85207	−0.507439
$134$	−16.9870	−1.46745
$135$	−9.46539	−0.814651
$136$	0.615810	0.0528053
$137$	20.4879	1.75040	0.875202	−	0.483758i	$-0.160729\pi$
$137$	20.4879	1.75040	0.875202	+	0.483758i	$0.160729\pi$
$138$	3.99128	0.339760
$139$	8.06353	0.683940	0.341970	−	0.939711i	$-0.388906\pi$
$139$	8.06353	0.683940	0.341970	+	0.939711i	$0.388906\pi$
$140$	−6.37157	−0.538496
$141$	−0.0712099	−0.00599695
$142$	6.37891	0.535306
$143$	−0.514890	−0.0430572
$144$	5.89126	0.490939
$145$	−9.89266	−0.821541
$146$	23.4322	1.93927
$147$	−0.709425	−0.0585124
$148$	−6.23993	−0.512919
$149$	10.3390	0.847001	0.423501	−	0.905896i	$-0.360801\pi$
$149$	10.3390	0.847001	0.423501	+	0.905896i	$0.360801\pi$
$150$	1.36078	0.111107
$151$	2.54405	0.207032	0.103516	−	0.994628i	$-0.466991\pi$
$151$	2.54405	0.207032	0.103516	+	0.994628i	$0.466991\pi$
$152$	7.86490	0.637928
$153$	1.14402	0.0924883
$154$	6.52585	0.525868
$155$	−5.17457	−0.415632
$156$	−0.315976	−0.0252983
$157$	−4.95177	−0.395194	−0.197597	−	0.980283i	$-0.563314\pi$
$157$	−4.95177	−0.395194	−0.197597	+	0.980283i	$0.563314\pi$
$158$	−17.0440	−1.35595
$159$	−0.385879	−0.0306022
$160$	−18.8419	−1.48958
$161$	2.61609	0.206177
$162$	−10.1587	−0.798143
$163$	11.9407	0.935269	0.467635	−	0.883922i	$-0.345106\pi$
$163$	11.9407	0.935269	0.467635	+	0.883922i	$0.345106\pi$
$164$	21.2624	1.66031
$165$	−5.22541	−0.406797
$166$	28.4662	2.20941
$167$	11.8349	0.915809	0.457905	−	0.889001i	$-0.348600\pi$
$167$	11.8349	0.915809	0.457905	+	0.889001i	$0.348600\pi$
$168$	0.953433	0.0735589
$169$	−12.9712	−0.997785
$170$	−2.39191	−0.183451
$171$	14.6110	1.11733
$172$	−17.8455	−1.36071
$173$	−1.20029	−0.0912565	−0.0456282	−	0.998958i	$-0.514529\pi$
$173$	−1.20029	−0.0912565	−0.0456282	+	0.998958i	$0.514529\pi$
$174$	6.21790	0.471378
$175$	0.891926	0.0674233
$176$	7.16018	0.539719
$177$	−8.50798	−0.639499
$178$	15.8611	1.18884
$179$	−11.7840	−0.880779	−0.440389	−	0.897807i	$-0.645160\pi$
$179$	−11.7840	−0.880779	−0.440389	+	0.897807i	$0.645160\pi$
$180$	15.9080	1.18571
$181$	2.41552	0.179544	0.0897720	−	0.995962i	$-0.471386\pi$
$181$	2.41552	0.179544	0.0897720	+	0.995962i	$0.471386\pi$
$182$	−0.364907	−0.0270487
$183$	−6.86036	−0.507132
$184$	−3.51590	−0.259196
$185$	5.77020	0.424233
$186$	3.25241	0.238478
$187$	1.39043	0.101678
$188$	0.263482	0.0192164
$189$	3.89951	0.283647
$190$	−30.5486	−2.21623
$191$	−22.7948	−1.64937	−0.824685	−	0.565592i	$-0.808648\pi$
$191$	−22.7948	−1.64937	−0.824685	+	0.565592i	$0.808648\pi$
$192$	8.49487	0.613065
$193$	6.54920	0.471422	0.235711	−	0.971823i	$-0.424258\pi$
$193$	6.54920	0.471422	0.235711	+	0.971823i	$0.424258\pi$
$194$	21.8126	1.56606
$195$	0.292190	0.0209241
$196$	2.62493	0.187495
$197$	5.51400	0.392856	0.196428	−	0.980518i	$-0.437066\pi$
$197$	5.51400	0.392856	0.196428	+	0.980518i	$0.437066\pi$
$198$	−16.2932	−1.15791
$199$	1.02053	0.0723436	0.0361718	−	0.999346i	$-0.488484\pi$
$199$	1.02053	0.0723436	0.0361718	+	0.999346i	$0.488484\pi$
$200$	−1.19871	−0.0847613
$201$	−5.60365	−0.395251
$202$	−27.4622	−1.93223
$203$	4.07553	0.286046
$204$	0.853272	0.0597410
$205$	−19.6618	−1.37324
$206$	12.9265	0.900633
$207$	−6.53164	−0.453980
$208$	−0.400377	−0.0277611
$209$	17.7580	1.22835
$210$	−3.70329	−0.255551
$211$	4.21446	0.290136	0.145068	−	0.989422i	$-0.453660\pi$
$211$	4.21446	0.290136	0.145068	+	0.989422i	$0.453660\pi$
$212$	1.42778	0.0980606
$213$	2.10426	0.144182
$214$	−7.01806	−0.479744
$215$	16.5022	1.12544
$216$	−5.24075	−0.356588
$217$	2.13180	0.144716
$218$	11.2579	0.762478
$219$	7.72979	0.522331
$220$	19.3344	1.30353
$221$	−0.0777486	−0.00522994
$222$	−3.62678	−0.243414
$223$	0.216106	0.0144716	0.00723578	−	0.999974i	$-0.497697\pi$
$223$	0.216106	0.0144716	0.00723578	+	0.999974i	$0.497697\pi$
$224$	7.76238	0.518646
$225$	−2.22689	−0.148459
$226$	−28.4817	−1.89457
$227$	13.5349	0.898342	0.449171	−	0.893446i	$-0.351719\pi$
$227$	13.5349	0.898342	0.449171	+	0.893446i	$0.351719\pi$
$228$	10.8977	0.721716
$229$	20.2187	1.33609	0.668043	−	0.744122i	$-0.267132\pi$
$229$	20.2187	1.33609	0.668043	+	0.744122i	$0.267132\pi$
$230$	13.6563	0.900473
$231$	2.15274	0.141640
$232$	−5.47732	−0.359604
$233$	−3.17449	−0.207968	−0.103984	−	0.994579i	$-0.533159\pi$
$233$	−3.17449	−0.207968	−0.103984	+	0.994579i	$0.533159\pi$
$234$	0.911069	0.0595584
$235$	−0.243648	−0.0158938
$236$	31.4802	2.04919
$237$	−5.62244	−0.365217
$238$	0.985407	0.0638745
$239$	16.0984	1.04132	0.520659	−	0.853765i	$-0.325686\pi$
$239$	16.0984	1.04132	0.520659	+	0.853765i	$0.325686\pi$
$240$	−4.06326	−0.262282
$241$	−2.01603	−0.129864	−0.0649319	−	0.997890i	$-0.520683\pi$
$241$	−2.01603	−0.129864	−0.0649319	+	0.997890i	$0.520683\pi$
$242$	3.85362	0.247720
$243$	−15.0497	−0.965436
$244$	25.3839	1.62504
$245$	−2.42733	−0.155076
$246$	12.3581	0.787926
$247$	−0.992977	−0.0631816
$248$	−2.86503	−0.181930
$249$	9.39040	0.595092
$250$	−21.4447	−1.35628
$251$	−6.37682	−0.402501	−0.201251	−	0.979540i	$-0.564501\pi$
$251$	−6.37682	−0.402501	−0.201251	+	0.979540i	$0.564501\pi$
$252$	−6.55370	−0.412845
$253$	−7.93849	−0.499089
$254$	1.08717	0.0682154
$255$	−0.789039	−0.0494115
$256$	1.95532	0.122208
$257$	−19.4220	−1.21151	−0.605754	−	0.795652i	$-0.707128\pi$
$257$	−19.4220	−1.21151	−0.605754	+	0.795652i	$0.707128\pi$
$258$	−10.3722	−0.645746
$259$	−2.37718	−0.147711
$260$	−1.08112	−0.0670485
$261$	−10.1755	−0.629845
$262$	14.9697	0.924832
$263$	−12.1426	−0.748746	−0.374373	−	0.927278i	$-0.622142\pi$
$263$	−12.1426	−0.748746	−0.374373	+	0.927278i	$0.622142\pi$
$264$	−2.89318	−0.178063
$265$	−1.32030	−0.0811055
$266$	12.5853	0.771652
$267$	5.23222	0.320207
$268$	20.7339	1.26653
$269$	0.538448	0.0328298	0.0164149	−	0.999865i	$-0.494775\pi$
$269$	0.538448	0.0328298	0.0164149	+	0.999865i	$0.494775\pi$
$270$	20.3559	1.23882
$271$	−29.3278	−1.78154	−0.890770	−	0.454455i	$-0.849834\pi$
$271$	−29.3278	−1.78154	−0.890770	+	0.454455i	$0.849834\pi$
$272$	1.08119	0.0655568
$273$	−0.120375	−0.00728542
$274$	−44.0607	−2.66180
$275$	−2.70654	−0.163210
$276$	−4.87166	−0.293240
$277$	18.2464	1.09632	0.548159	−	0.836374i	$-0.315329\pi$
$277$	18.2464	1.09632	0.548159	+	0.836374i	$0.315329\pi$
$278$	−17.3411	−1.04005
$279$	−5.32249	−0.318649
$280$	3.26221	0.194954
$281$	−14.8442	−0.885529	−0.442764	−	0.896638i	$-0.646002\pi$
$281$	−14.8442	−0.885529	−0.442764	+	0.896638i	$0.646002\pi$
$282$	0.153141	0.00911944
$283$	−7.03319	−0.418080	−0.209040	−	0.977907i	$-0.567034\pi$
$283$	−7.03319	−0.418080	−0.209040	+	0.977907i	$0.567034\pi$
$284$	−7.78594	−0.462011
$285$	−10.0773	−0.596929
$286$	1.10730	0.0654763
$287$	8.10017	0.478138
$288$	−19.3805	−1.14201
$289$	−16.7900	−0.987650
$290$	21.2748	1.24930
$291$	7.19551	0.421809
$292$	−28.6008	−1.67374
$293$	28.7792	1.68130	0.840650	−	0.541578i	$-0.182173\pi$
$293$	28.7792	1.68130	0.840650	+	0.541578i	$0.182173\pi$
$294$	1.52566	0.0889786
$295$	−29.1104	−1.69488
$296$	3.19481	0.185695
$297$	−11.8330	−0.686620
$298$	−22.2346	−1.28802
$299$	0.443897	0.0256713
$300$	−1.66094	−0.0958942
$301$	−6.79849	−0.391858
$302$	−5.47116	−0.314830
$303$	−9.05918	−0.520436
$304$	13.8086	0.791976
$305$	−23.4730	−1.34406
$306$	−2.46028	−0.140645
$307$	19.5395	1.11518	0.557589	−	0.830117i	$-0.311726\pi$
$307$	19.5395	1.11518	0.557589	+	0.830117i	$0.311726\pi$
$308$	−7.96531	−0.453865
$309$	4.26418	0.242581
$310$	11.1283	0.632042
$311$	23.5406	1.33487	0.667433	−	0.744670i	$-0.267393\pi$
$311$	23.5406	1.33487	0.667433	+	0.744670i	$0.267393\pi$
$312$	0.161778	0.00915888
$313$	15.9898	0.903797	0.451898	−	0.892069i	$-0.350747\pi$
$313$	15.9898	0.903797	0.451898	+	0.892069i	$0.350747\pi$
$314$	10.6491	0.600964
$315$	6.06035	0.341462
$316$	20.8035	1.17029
$317$	16.9726	0.953275	0.476637	−	0.879100i	$-0.341855\pi$
$317$	16.9726	0.953275	0.476637	+	0.879100i	$0.341855\pi$
$318$	0.829858	0.0465361
$319$	−12.3671	−0.692427
$320$	29.0656	1.62482
$321$	−2.31511	−0.129217
$322$	−5.62608	−0.313529
$323$	2.68147	0.149201
$324$	12.3995	0.688860
$325$	0.151342	0.00839492
$326$	−25.6793	−1.42224
$327$	3.71372	0.205369
$328$	−10.8862	−0.601092
$329$	0.100377	0.00553396
$330$	11.2376	0.618608
$331$	−33.7914	−1.85734	−0.928671	−	0.370904i	$-0.879048\pi$
$331$	−33.7914	−1.85734	−0.928671	+	0.370904i	$0.879048\pi$
$332$	−34.7452	−1.90689
$333$	5.93514	0.325244
$334$	−25.4516	−1.39265
$335$	−19.1731	−1.04754
$336$	1.67396	0.0913221
$337$	−29.8096	−1.62383	−0.811916	−	0.583774i	$-0.801575\pi$
$337$	−29.8096	−1.62383	−0.811916	+	0.583774i	$0.801575\pi$
$338$	27.8954	1.51731
$339$	−9.39549	−0.510293
$340$	2.91951	0.158332
$341$	−6.46890	−0.350311
$342$	−31.4218	−1.69910
$343$	1.00000	0.0539949
$344$	9.13684	0.492625
$345$	4.50493	0.242537
$346$	2.58131	0.138772
$347$	−9.76473	−0.524198	−0.262099	−	0.965041i	$-0.584415\pi$
$347$	−9.76473	−0.524198	−0.262099	+	0.965041i	$0.584415\pi$
$348$	−7.58942	−0.406836
$349$	9.56968	0.512253	0.256127	−	0.966643i	$-0.417554\pi$
$349$	9.56968	0.512253	0.256127	+	0.966643i	$0.417554\pi$
$350$	−1.91815	−0.102529
$351$	0.661667	0.0353172
$352$	−23.5548	−1.25548
$353$	−12.1448	−0.646402	−0.323201	−	0.946330i	$-0.604759\pi$
$353$	−12.1448	−0.646402	−0.323201	+	0.946330i	$0.604759\pi$
$354$	18.2970	0.972473
$355$	7.19983	0.382127
$356$	−19.3596	−1.02606
$357$	0.325065	0.0172042
$358$	25.3423	1.33938
$359$	12.4067	0.654802	0.327401	−	0.944885i	$-0.393827\pi$
$359$	12.4067	0.654802	0.327401	+	0.944885i	$0.393827\pi$
$360$	−8.14482	−0.429270
$361$	15.2467	0.802460
$362$	−5.19472	−0.273029
$363$	1.27123	0.0667220
$364$	0.445397	0.0233451
$365$	26.4478	1.38434
$366$	14.7536	0.771185
$367$	−14.1093	−0.736498	−0.368249	−	0.929727i	$-0.620043\pi$
$367$	−14.1093	−0.736498	−0.368249	+	0.929727i	$0.620043\pi$
$368$	−6.17294	−0.321787
$369$	−20.2238	−1.05281
$370$	−12.4092	−0.645123
$371$	0.543932	0.0282396
$372$	−3.96981	−0.205825
$373$	−6.31940	−0.327206	−0.163603	−	0.986526i	$-0.552312\pi$
$373$	−6.31940	−0.327206	−0.163603	+	0.986526i	$0.552312\pi$
$374$	−2.99020	−0.154620
$375$	−7.07414	−0.365307
$376$	−0.134902	−0.00695702
$377$	0.691535	0.0356159
$378$	−8.38615	−0.431337
$379$	26.8403	1.37869	0.689346	−	0.724433i	$-0.257898\pi$
$379$	26.8403	1.37869	0.689346	+	0.724433i	$0.257898\pi$
$380$	37.2869	1.91278
$381$	0.358635	0.0183734
$382$	49.0216	2.50816
$383$	−7.20877	−0.368351	−0.184175	−	0.982893i	$-0.558961\pi$
$383$	−7.20877	−0.368351	−0.184175	+	0.982893i	$0.558961\pi$
$384$	−7.25511	−0.370236
$385$	7.36569	0.375390
$386$	−14.0845	−0.716881
$387$	16.9739	0.862831
$388$	−26.6240	−1.35163
$389$	20.0956	1.01889	0.509444	−	0.860504i	$-0.329851\pi$
$389$	20.0956	1.01889	0.509444	+	0.860504i	$0.329851\pi$
$390$	−0.628373	−0.0318189
$391$	−1.19872	−0.0606217
$392$	−1.34395	−0.0678798
$393$	4.93819	0.249099
$394$	−11.8582	−0.597408
$395$	−19.2374	−0.967941
$396$	19.8871	0.999365
$397$	−28.3171	−1.42120	−0.710598	−	0.703598i	$-0.751576\pi$
$397$	−28.3171	−1.42120	−0.710598	+	0.703598i	$0.751576\pi$
$398$	−2.19472	−0.110011
$399$	4.15161	0.207840
$400$	−2.10459	−0.105230
$401$	−8.56825	−0.427878	−0.213939	−	0.976847i	$-0.568629\pi$
$401$	−8.56825	−0.427878	−0.213939	+	0.976847i	$0.568629\pi$
$402$	12.0510	0.601049
$403$	0.361722	0.0180187
$404$	33.5197	1.66767
$405$	−11.4661	−0.569754
$406$	−8.76470	−0.434985
$407$	7.21352	0.357561
$408$	−0.436871	−0.0216283
$409$	−36.3173	−1.79578	−0.897888	−	0.440224i	$-0.854899\pi$
$409$	−36.3173	−1.79578	−0.897888	+	0.440224i	$0.854899\pi$
$410$	42.2839	2.08825
$411$	−14.5347	−0.716942
$412$	−15.7778	−0.777317
$413$	11.9928	0.590127
$414$	14.0467	0.690359
$415$	32.1297	1.57718
$416$	1.31712	0.0645770
$417$	−5.72047	−0.280133
$418$	−38.1898	−1.86792
$419$	−0.846386	−0.0413487	−0.0206743	−	0.999786i	$-0.506581\pi$
$419$	−0.846386	−0.0413487	−0.0206743	+	0.999786i	$0.506581\pi$
$420$	4.52015	0.220561
$421$	−12.1068	−0.590047	−0.295024	−	0.955490i	$-0.595328\pi$
$421$	−12.1068	−0.590047	−0.295024	+	0.955490i	$0.595328\pi$
$422$	−9.06348	−0.441203
$423$	−0.250613	−0.0121852
$424$	−0.731018	−0.0355014
$425$	−0.408688	−0.0198243
$426$	−4.52536	−0.219254
$427$	9.67031	0.467979
$428$	8.56608	0.414057
$429$	0.365276	0.0176357
$430$	−35.4890	−1.71143
$431$	34.0047	1.63795	0.818975	−	0.573829i	$-0.194543\pi$
$431$	34.0047	1.63795	0.818975	+	0.573829i	$0.194543\pi$
$432$	−9.20130	−0.442698
$433$	15.6377	0.751498	0.375749	−	0.926722i	$-0.377386\pi$
$433$	15.6377	0.751498	0.375749	+	0.926722i	$0.377386\pi$
$434$	−4.58457	−0.220066
$435$	7.01810	0.336492
$436$	−13.7411	−0.658078
$437$	−15.3096	−0.732356
$438$	−16.6234	−0.794298
$439$	16.1771	0.772093	0.386046	−	0.922479i	$-0.373840\pi$
$439$	16.1771	0.772093	0.386046	+	0.922479i	$0.373840\pi$
$440$	−9.89913	−0.471922
$441$	−2.49672	−0.118891
$442$	0.167203	0.00795306
$443$	−3.08656	−0.146647	−0.0733235	−	0.997308i	$-0.523361\pi$
$443$	−3.08656	−0.146647	−0.0733235	+	0.997308i	$0.523361\pi$
$444$	4.42676	0.210085
$445$	17.9023	0.848650
$446$	−0.464751	−0.0220066
$447$	−7.33472	−0.346921
$448$	−11.9743	−0.565733
$449$	−34.1082	−1.60966	−0.804832	−	0.593503i	$-0.797745\pi$
$449$	−34.1082	−1.60966	−0.804832	+	0.593503i	$0.797745\pi$
$450$	4.78906	0.225759
$451$	−24.5798	−1.15742
$452$	34.7640	1.63516
$453$	−1.80482	−0.0847977
$454$	−29.1077	−1.36609
$455$	−0.411868	−0.0193087
$456$	−5.57956	−0.261287
$457$	9.45073	0.442086	0.221043	−	0.975264i	$-0.429054\pi$
$457$	9.45073	0.442086	0.221043	+	0.975264i	$0.429054\pi$
$458$	−43.4815	−2.03176
$459$	−1.78679	−0.0834001
$460$	−16.6686	−0.777178
$461$	8.49428	0.395618	0.197809	−	0.980241i	$-0.436617\pi$
$461$	8.49428	0.395618	0.197809	+	0.980241i	$0.436617\pi$
$462$	−4.62960	−0.215389
$463$	−14.7404	−0.685044	−0.342522	−	0.939510i	$-0.611281\pi$
$463$	−14.7404	−0.685044	−0.342522	+	0.939510i	$0.611281\pi$
$464$	−9.61665	−0.446442
$465$	3.67097	0.170237
$466$	6.82696	0.316253
$467$	7.21659	0.333944	0.166972	−	0.985962i	$-0.446601\pi$
$467$	7.21659	0.333944	0.166972	+	0.985962i	$0.446601\pi$
$468$	−1.11203	−0.0514036
$469$	7.89885	0.364735
$470$	0.523980	0.0241694
$471$	3.51291	0.161866
$472$	−16.1177	−0.741878
$473$	20.6299	0.948564
$474$	12.0914	0.555378
$475$	−5.21962	−0.239492
$476$	−1.20277	−0.0551286
$477$	−1.35804	−0.0621806
$478$	−34.6206	−1.58351
$479$	−17.4261	−0.796219	−0.398109	−	0.917338i	$-0.630334\pi$
$479$	−17.4261	−0.796219	−0.398109	+	0.917338i	$0.630334\pi$
$480$	13.3669	0.610112
$481$	−0.403359	−0.0183916
$482$	4.33560	0.197481
$483$	−1.85592	−0.0844474
$484$	−4.70363	−0.213802
$485$	24.6198	1.11793
$486$	32.3653	1.46812
$487$	12.1033	0.548454	0.274227	−	0.961665i	$-0.411578\pi$
$487$	12.1033	0.548454	0.274227	+	0.961665i	$0.411578\pi$
$488$	−12.9964	−0.588320
$489$	−8.47104	−0.383074
$490$	5.22013	0.235821
$491$	−41.3652	−1.86679	−0.933393	−	0.358856i	$-0.883167\pi$
$491$	−41.3652	−1.86679	−0.933393	+	0.358856i	$0.883167\pi$
$492$	−15.0841	−0.680042
$493$	−1.86744	−0.0841055
$494$	2.13546	0.0960789
$495$	−18.3900	−0.826571
$496$	−5.03020	−0.225863
$497$	−2.96615	−0.133050
$498$	−20.1947	−0.904944
$499$	−3.44675	−0.154298	−0.0771489	−	0.997020i	$-0.524582\pi$
$499$	−3.44675	−0.154298	−0.0771489	+	0.997020i	$0.524582\pi$
$500$	26.1749	1.17058
$501$	−8.39595	−0.375103
$502$	13.7138	0.612075
$503$	35.2895	1.57348	0.786739	−	0.617285i	$-0.211768\pi$
$503$	35.2895	1.57348	0.786739	+	0.617285i	$0.211768\pi$
$504$	3.35546	0.149464
$505$	−30.9964	−1.37932
$506$	17.0722	0.758954
$507$	9.20210	0.408680
$508$	−1.32698	−0.0588752
$509$	28.9865	1.28480	0.642402	−	0.766368i	$-0.277938\pi$
$509$	28.9865	1.28480	0.642402	+	0.766368i	$0.277938\pi$
$510$	1.69688	0.0751391
$511$	−10.8959	−0.482004
$512$	−24.6585	−1.08976
$513$	−22.8202	−1.00754
$514$	41.7682	1.84231
$515$	14.5901	0.642916
$516$	12.6601	0.557329
$517$	−0.304592	−0.0133959
$518$	5.11228	0.224621
$519$	0.851517	0.0373774
$520$	0.553531	0.0242739
$521$	−15.0141	−0.657780	−0.328890	−	0.944368i	$-0.606674\pi$
$521$	−15.0141	−0.657780	−0.328890	+	0.944368i	$0.606674\pi$
$522$	21.8830	0.957792
$523$	−8.93861	−0.390858	−0.195429	−	0.980718i	$-0.562610\pi$
$523$	−8.93861	−0.390858	−0.195429	+	0.980718i	$0.562610\pi$
$524$	−18.2717	−0.798203
$525$	−0.632755	−0.0276157
$526$	26.1135	1.13860
$527$	−0.976808	−0.0425504
$528$	−5.07961	−0.221062
$529$	−16.1561	−0.702437
$530$	2.83940	0.123335
$531$	−29.9426	−1.29940
$532$	−15.3613	−0.665996
$533$	1.37443	0.0595333
$534$	−11.2522	−0.486932
$535$	−7.92124	−0.342465
$536$	−10.6157	−0.458527
$537$	8.35988	0.360755
$538$	−1.15797	−0.0499235
$539$	−3.03448	−0.130704
$540$	−24.8460	−1.06920
$541$	−26.6671	−1.14651	−0.573253	−	0.819378i	$-0.694319\pi$
$541$	−26.6671	−1.14651	−0.573253	+	0.819378i	$0.694319\pi$
$542$	63.0714	2.70915
$543$	−1.71363	−0.0735388
$544$	−3.55679	−0.152496
$545$	12.7067	0.544294
$546$	0.258874	0.0110788
$547$	−16.2994	−0.696912	−0.348456	−	0.937325i	$-0.613294\pi$
$547$	−16.2994	−0.696912	−0.348456	+	0.937325i	$0.613294\pi$
$548$	53.7794	2.29734
$549$	−24.1440	−1.03044
$550$	5.82058	0.248190
$551$	−23.8503	−1.01606
$552$	2.49427	0.106163
$553$	7.92535	0.337020
$554$	−39.2400	−1.66715
$555$	−4.09352	−0.173760
$556$	21.1662	0.897647
$557$	−2.30003	−0.0974555	−0.0487277	−	0.998812i	$-0.515517\pi$
$557$	−2.30003	−0.0974555	−0.0487277	+	0.998812i	$0.515517\pi$
$558$	11.4464	0.484563
$559$	−1.15356	−0.0487906
$560$	5.72754	0.242033
$561$	−0.986403	−0.0416460
$562$	31.9233	1.34660
$563$	13.7003	0.577399	0.288700	−	0.957420i	$-0.406777\pi$
$563$	13.7003	0.577399	0.288700	+	0.957420i	$0.406777\pi$
$564$	−0.186921	−0.00787079
$565$	−32.1471	−1.35244
$566$	15.1253	0.635766
$567$	4.72374	0.198378
$568$	3.98637	0.167264
$569$	−35.3753	−1.48301	−0.741504	−	0.670948i	$-0.765887\pi$
$569$	−35.3753	−1.48301	−0.741504	+	0.670948i	$0.765887\pi$
$570$	21.6719	0.907737
$571$	−23.5364	−0.984968	−0.492484	−	0.870321i	$-0.663911\pi$
$571$	−23.5364	−0.984968	−0.492484	+	0.870321i	$0.663911\pi$
$572$	−1.35155	−0.0565111
$573$	16.1712	0.675560
$574$	−17.4199	−0.727094
$575$	2.33336	0.0973079
$576$	29.8964	1.24568
$577$	16.1722	0.673259	0.336630	−	0.941637i	$-0.390713\pi$
$577$	16.1722	0.673259	0.336630	+	0.941637i	$0.390713\pi$
$578$	36.1081	1.50190
$579$	−4.64617	−0.193088
$580$	−25.9675	−1.07824
$581$	−13.2366	−0.549148
$582$	−15.4744	−0.641435
$583$	−1.65055	−0.0683589
$584$	14.6435	0.605952
$585$	1.02832	0.0425157
$586$	−61.8916	−2.55672
$587$	−15.6060	−0.644129	−0.322064	−	0.946718i	$-0.604377\pi$
$587$	−15.6060	−0.644129	−0.322064	+	0.946718i	$0.604377\pi$
$588$	−1.86219	−0.0767954
$589$	−12.4754	−0.514041
$590$	62.6039	2.57736
$591$	−3.91177	−0.160909
$592$	5.60921	0.230537
$593$	−11.9835	−0.492102	−0.246051	−	0.969257i	$-0.579133\pi$
$593$	−11.9835	−0.492102	−0.246051	+	0.969257i	$0.579133\pi$
$594$	25.4476	1.04413
$595$	1.11222	0.0455967
$596$	27.1391	1.11166
$597$	−0.723991	−0.0296310
$598$	−0.954630	−0.0390377
$599$	−27.4503	−1.12159	−0.560794	−	0.827956i	$-0.689504\pi$
$599$	−27.4503	−1.12159	−0.560794	+	0.827956i	$0.689504\pi$
$600$	0.850392	0.0347171
$601$	−4.47738	−0.182636	−0.0913181	−	0.995822i	$-0.529108\pi$
$601$	−4.47738	−0.182636	−0.0913181	+	0.995822i	$0.529108\pi$
$602$	14.6206	0.595891
$603$	−19.7212	−0.803109
$604$	6.67796	0.271723
$605$	4.34955	0.176834
$606$	19.4824	0.791417
$607$	−7.47050	−0.303218	−0.151609	−	0.988441i	$-0.548445\pi$
$607$	−7.47050	−0.303218	−0.151609	+	0.988441i	$0.548445\pi$
$608$	−45.4260	−1.84227
$609$	−2.89129	−0.117161
$610$	50.4802	2.04389
$611$	0.0170319	0.000689037 0
$612$	3.00296	0.121388
$613$	−27.1366	−1.09604	−0.548018	−	0.836467i	$-0.684617\pi$
$613$	−27.1366	−1.09604	−0.548018	+	0.836467i	$0.684617\pi$
$614$	−42.0210	−1.69583
$615$	13.9486	0.562460
$616$	4.07820	0.164315
$617$	−41.9810	−1.69009	−0.845046	−	0.534693i	$-0.820427\pi$
$617$	−41.9810	−1.69009	−0.845046	+	0.534693i	$0.820427\pi$
$618$	−9.17039	−0.368887
$619$	11.6993	0.470236	0.235118	−	0.971967i	$-0.424452\pi$
$619$	11.6993	0.470236	0.235118	+	0.971967i	$0.424452\pi$
$620$	−13.5829	−0.545502
$621$	10.2015	0.409371
$622$	−50.6256	−2.02990
$623$	−7.37530	−0.295485
$624$	0.284037	0.0113706
$625$	−28.6641	−1.14656
$626$	−34.3871	−1.37438
$627$	−12.5980	−0.503115
$628$	−12.9980	−0.518679
$629$	1.08924	0.0434310
$630$	−13.0332	−0.519254
$631$	12.9702	0.516336	0.258168	−	0.966100i	$-0.416881\pi$
$631$	12.9702	0.516336	0.258168	+	0.966100i	$0.416881\pi$
$632$	−10.6513	−0.423685
$633$	−2.98985	−0.118836
$634$	−36.5006	−1.44962
$635$	1.22709	0.0486954
$636$	−1.01291	−0.0401643
$637$	0.169680	0.00672295
$638$	26.5963	1.05296
$639$	7.40564	0.292963
$640$	−24.8237	−0.981242
$641$	−10.3140	−0.407379	−0.203690	−	0.979036i	$-0.565293\pi$
$641$	−10.3140	−0.407379	−0.203690	+	0.979036i	$0.565293\pi$
$642$	4.97878	0.196497
$643$	25.8776	1.02051	0.510256	−	0.860022i	$-0.329550\pi$
$643$	25.8776	1.02051	0.510256	+	0.860022i	$0.329550\pi$
$644$	6.86706	0.270600
$645$	−11.7070	−0.460965
$646$	−5.76667	−0.226887
$647$	−1.36161	−0.0535303	−0.0267652	−	0.999642i	$-0.508521\pi$
$647$	−1.36161	−0.0535303	−0.0267652	+	0.999642i	$0.508521\pi$
$648$	−6.34848	−0.249392
$649$	−36.3919	−1.42851
$650$	−0.325470	−0.0127660
$651$	−1.51235	−0.0592737
$652$	31.3435	1.22751
$653$	20.7458	0.811844	0.405922	−	0.913908i	$-0.366950\pi$
$653$	20.7458	0.811844	0.405922	+	0.913908i	$0.366950\pi$
$654$	−7.98661	−0.312301
$655$	16.8962	0.660190
$656$	−19.1132	−0.746245
$657$	27.2039	1.06132
$658$	−0.215867	−0.00841537
$659$	−1.34272	−0.0523049	−0.0261524	−	0.999658i	$-0.508326\pi$
$659$	−1.34272	−0.0523049	−0.0261524	+	0.999658i	$0.508326\pi$
$660$	−13.7163	−0.533907
$661$	1.03170	0.0401284	0.0200642	−	0.999799i	$-0.493613\pi$
$661$	1.03170	0.0401284	0.0200642	+	0.999799i	$0.493613\pi$
$662$	72.6705	2.82442
$663$	0.0551568	0.00214211
$664$	17.7894	0.690362
$665$	14.2049	0.550843
$666$	−12.7639	−0.494592
$667$	10.6620	0.412833
$668$	31.0657	1.20197
$669$	−0.153311	−0.00592736
$670$	41.2330	1.59297
$671$	−29.3444	−1.13283
$672$	−5.50683	−0.212431
$673$	−4.47645	−0.172554	−0.0862772	−	0.996271i	$-0.527497\pi$
$673$	−4.47645	−0.172554	−0.0862772	+	0.996271i	$0.527497\pi$
$674$	64.1075	2.46933
$675$	3.47807	0.133871
$676$	−34.0485	−1.30956
$677$	−38.2947	−1.47179	−0.735893	−	0.677098i	$-0.763237\pi$
$677$	−38.2947	−1.47179	−0.735893	+	0.677098i	$0.763237\pi$
$678$	20.2056	0.775991
$679$	−10.1427	−0.389243
$680$	−1.49477	−0.0573219
$681$	−9.60199	−0.367949
$682$	13.9118	0.532710
$683$	−32.3712	−1.23865	−0.619324	−	0.785135i	$-0.712593\pi$
$683$	−32.3712	−1.23865	−0.619324	+	0.785135i	$0.712593\pi$
$684$	38.3527	1.46645
$685$	−49.7310	−1.90012
$686$	−2.15056	−0.0821089
$687$	−14.3436	−0.547243
$688$	16.0417	0.611586
$689$	0.0922942	0.00351613
$690$	−9.68815	−0.368822
$691$	35.0805	1.33452	0.667262	−	0.744823i	$-0.267466\pi$
$691$	35.0805	1.33452	0.667262	+	0.744823i	$0.267466\pi$
$692$	−3.15068	−0.119771
$693$	7.57624	0.287798
$694$	20.9997	0.797137
$695$	−19.5728	−0.742440
$696$	3.88575	0.147289
$697$	−3.71157	−0.140586
$698$	−20.5802	−0.778973
$699$	2.25207	0.0851809
$700$	2.34124	0.0884907
$701$	−48.9339	−1.84821	−0.924104	−	0.382142i	$-0.875187\pi$
$701$	−48.9339	−1.84821	−0.924104	+	0.382142i	$0.875187\pi$
$702$	−1.42296	−0.0537061
$703$	13.9114	0.524680
$704$	36.3358	1.36946
$705$	0.172850	0.00650990
$706$	26.1182	0.982970
$707$	12.7697	0.480256
$708$	−22.3329	−0.839320
$709$	4.81420	0.180801	0.0904006	−	0.995905i	$-0.471185\pi$
$709$	4.81420	0.180801	0.0904006	+	0.995905i	$0.471185\pi$
$710$	−15.4837	−0.581093
$711$	−19.7874	−0.742084
$712$	9.91205	0.371470
$713$	5.57698	0.208859
$714$	−0.699073	−0.0261621
$715$	1.24981	0.0467401
$716$	−30.9322	−1.15599
$717$	−11.4206	−0.426510
$718$	−26.6815	−0.995744
$719$	25.7634	0.960813	0.480407	−	0.877046i	$-0.340489\pi$
$719$	25.7634	0.960813	0.480407	+	0.877046i	$0.340489\pi$
$720$	−14.3000	−0.532931
$721$	−6.01075	−0.223852
$722$	−32.7891	−1.22028
$723$	1.43022	0.0531905
$724$	6.34056	0.235645
$725$	3.63508	0.135003
$726$	−2.73385	−0.101463
$727$	35.6644	1.32272	0.661360	−	0.750069i	$-0.269980\pi$
$727$	35.6644	1.32272	0.661360	+	0.750069i	$0.269980\pi$
$728$	−0.228041	−0.00845176
$729$	−3.49461	−0.129430
$730$	−56.8778	−2.10514
$731$	3.11512	0.115217
$732$	−18.0080	−0.665593
$733$	−47.2197	−1.74410	−0.872051	−	0.489416i	$-0.837210\pi$
$733$	−47.2197	−1.74410	−0.872051	+	0.489416i	$0.837210\pi$
$734$	30.3429	1.11998
$735$	1.72201	0.0635172
$736$	20.3071	0.748530
$737$	−23.9689	−0.882907
$738$	43.4926	1.60099
$739$	−7.15421	−0.263172	−0.131586	−	0.991305i	$-0.542007\pi$
$739$	−7.15421	−0.263172	−0.131586	+	0.991305i	$0.542007\pi$
$740$	15.1464	0.556791
$741$	0.704443	0.0258783
$742$	−1.16976	−0.0429433
$743$	−21.7623	−0.798381	−0.399191	−	0.916868i	$-0.630709\pi$
$743$	−21.7623	−0.798381	−0.399191	+	0.916868i	$0.630709\pi$
$744$	2.03252	0.0745160
$745$	−25.0961	−0.919449
$746$	13.5903	0.497575
$747$	33.0481	1.20917
$748$	3.64977	0.133449
$749$	3.26335	0.119240
$750$	15.2134	0.555514
$751$	4.51946	0.164917	0.0824587	−	0.996594i	$-0.473723\pi$
$751$	4.51946	0.164917	0.0824587	+	0.996594i	$0.473723\pi$
$752$	−0.236850	−0.00863702
$753$	4.52388	0.164859
$754$	−1.48719	−0.0541603
$755$	−6.17526	−0.224741
$756$	10.2359	0.372277
$757$	23.9385	0.870059	0.435029	−	0.900416i	$-0.356738\pi$
$757$	23.9385	0.870059	0.435029	+	0.900416i	$0.356738\pi$
$758$	−57.7217	−2.09655
$759$	5.63176	0.204420
$760$	−19.0907	−0.692492
$761$	−43.8038	−1.58789	−0.793944	−	0.607991i	$-0.791976\pi$
$761$	−43.8038	−1.58789	−0.793944	+	0.607991i	$0.791976\pi$
$762$	−0.771268	−0.0279401
$763$	−5.23484	−0.189514
$764$	−59.8346	−2.16474
$765$	−2.77690	−0.100399
$766$	15.5029	0.560143
$767$	2.03493	0.0734771
$768$	−1.38716	−0.0500547
$769$	−32.7448	−1.18081	−0.590404	−	0.807108i	$-0.701032\pi$
$769$	−32.7448	−1.18081	−0.590404	+	0.807108i	$0.701032\pi$
$770$	−15.8404	−0.570848
$771$	13.7784	0.496218
$772$	17.1912	0.618724
$773$	−31.7775	−1.14296	−0.571479	−	0.820617i	$-0.693630\pi$
$773$	−31.7775	−1.14296	−0.571479	+	0.820617i	$0.693630\pi$
$774$	−36.5035	−1.31209
$775$	1.90141	0.0683005
$776$	13.6313	0.489337
$777$	1.68643	0.0605004
$778$	−43.2169	−1.54940
$779$	−47.4028	−1.69838
$780$	0.766977	0.0274622
$781$	9.00075	0.322072
$782$	2.57792	0.0921861
$783$	15.8926	0.567954
$784$	−2.35960	−0.0842716
$785$	12.0196	0.428997
$786$	−10.6199	−0.378799
$787$	−21.7490	−0.775267	−0.387634	−	0.921813i	$-0.626707\pi$
$787$	−21.7490	−0.775267	−0.387634	+	0.921813i	$0.626707\pi$
$788$	14.4739	0.515610
$789$	8.61428	0.306677
$790$	41.3714	1.47193
$791$	13.2438	0.470895
$792$	−10.1821	−0.361805
$793$	1.64085	0.0582684
$794$	60.8978	2.16118
$795$	0.936656	0.0332198
$796$	2.67882	0.0949484
$797$	3.10426	0.109959	0.0549793	−	0.998487i	$-0.482491\pi$
$797$	3.10426	0.109959	0.0549793	+	0.998487i	$0.482491\pi$
$798$	−8.92830	−0.316058
$799$	−0.0459935	−0.00162713
$800$	6.92348	0.244782
$801$	18.4140	0.650628
$802$	18.4266	0.650665
$803$	33.0633	1.16678
$804$	−14.7092	−0.518753
$805$	−6.35012	−0.223812
$806$	−0.777907	−0.0274006
$807$	−0.381989	−0.0134466
$808$	−17.1619	−0.603754
$809$	1.26185	0.0443644	0.0221822	−	0.999754i	$-0.492939\pi$
$809$	1.26185	0.0443644	0.0221822	+	0.999754i	$0.492939\pi$
$810$	24.6585	0.866412
$811$	3.00585	0.105550	0.0527749	−	0.998606i	$-0.483193\pi$
$811$	3.00585	0.105550	0.0527749	+	0.998606i	$0.483193\pi$
$812$	10.6980	0.375426
$813$	20.8059	0.729695
$814$	−15.5131	−0.543735
$815$	−28.9840	−1.01527
$816$	−0.767024	−0.0268512
$817$	39.7852	1.39191
$818$	78.1028	2.73080
$819$	−0.423642	−0.0148032
$820$	−51.6108	−1.80233
$821$	16.5966	0.579227	0.289613	−	0.957144i	$-0.406473\pi$
$821$	16.5966	0.579227	0.289613	+	0.957144i	$0.406473\pi$
$822$	31.2577	1.09024
$823$	−8.58777	−0.299351	−0.149675	−	0.988735i	$-0.547823\pi$
$823$	−8.58777	−0.299351	−0.149675	+	0.988735i	$0.547823\pi$
$824$	8.07816	0.281416
$825$	1.92008	0.0668488
$826$	−25.7913	−0.897393
$827$	32.2605	1.12181	0.560905	−	0.827881i	$-0.310453\pi$
$827$	32.2605	1.12181	0.560905	+	0.827881i	$0.310453\pi$
$828$	−17.1451	−0.595833
$829$	−11.8908	−0.412985	−0.206492	−	0.978448i	$-0.566205\pi$
$829$	−11.8908	−0.412985	−0.206492	+	0.978448i	$0.566205\pi$
$830$	−69.0969	−2.39839
$831$	−12.9444	−0.449038
$832$	−2.03179	−0.0704398
$833$	−0.458209	−0.0158760
$834$	12.3022	0.425992
$835$	−28.7271	−0.994142
$836$	46.6135	1.61216
$837$	8.31296	0.287338
$838$	1.82021	0.0628780
$839$	−48.7173	−1.68191	−0.840953	−	0.541108i	$-0.818005\pi$
$839$	−48.7173	−1.68191	−0.840953	+	0.541108i	$0.818005\pi$
$840$	−2.31429	−0.0798508
$841$	−12.3900	−0.427242
$842$	26.0364	0.897272
$843$	10.5308	0.362701
$844$	11.0627	0.380793
$845$	31.4854	1.08313
$846$	0.538958	0.0185298
$847$	−1.79191	−0.0615707
$848$	−1.28346	−0.0440744
$849$	4.98952	0.171240
$850$	0.878911	0.0301464
$851$	−6.21892	−0.213182
$852$	5.52354	0.189233
$853$	35.7530	1.22416	0.612079	−	0.790796i	$-0.290333\pi$
$853$	35.7530	1.22416	0.612079	+	0.790796i	$0.290333\pi$
$854$	−20.7966	−0.711646
$855$	−35.4656	−1.21290
$856$	−4.38579	−0.149903
$857$	−54.2294	−1.85244	−0.926221	−	0.376981i	$-0.876962\pi$
$857$	−54.2294	−1.85244	−0.926221	+	0.376981i	$0.876962\pi$
$858$	−0.785549	−0.0268182
$859$	−15.7846	−0.538562	−0.269281	−	0.963062i	$-0.586786\pi$
$859$	−15.7846	−0.538562	−0.269281	+	0.963062i	$0.586786\pi$
$860$	43.3170	1.47710
$861$	−5.74646	−0.195839
$862$	−73.1294	−2.49080
$863$	1.00000	0.0340404
$863$	1.00000	0.0340404
$864$	30.2695	1.02979
$865$	2.91350	0.0990621
$866$	−33.6298	−1.14279
$867$	11.9113	0.404528
$868$	5.59582	0.189934
$869$	−24.0494	−0.815818
$870$	−15.0929	−0.511697
$871$	1.34027	0.0454135
$872$	7.03537	0.238248
$873$	25.3235	0.857072
$874$	32.9242	1.11368
$875$	9.97165	0.337103
$876$	20.2902	0.685541
$877$	57.9253	1.95600	0.977999	−	0.208608i	$-0.0668934\pi$
$877$	57.9253	1.95600	0.977999	+	0.208608i	$0.0668934\pi$
$878$	−34.7900	−1.17411
$879$	−20.4167	−0.688638
$880$	−17.3801	−0.585884
$881$	17.5794	0.592266	0.296133	−	0.955147i	$-0.404303\pi$
$881$	17.5794	0.592266	0.296133	+	0.955147i	$0.404303\pi$
$882$	5.36935	0.180795
$883$	−24.8527	−0.836361	−0.418181	−	0.908364i	$-0.637332\pi$
$883$	−24.8527	−0.836361	−0.418181	+	0.908364i	$0.637332\pi$
$884$	−0.204085	−0.00686411
$885$	20.6517	0.694199
$886$	6.63786	0.223003
$887$	−47.4254	−1.59239	−0.796195	−	0.605041i	$-0.793157\pi$
$887$	−47.4254	−1.59239	−0.796195	+	0.605041i	$0.793157\pi$
$888$	−2.26648	−0.0760581
$889$	−0.505529	−0.0169549
$890$	−38.5000	−1.29052
$891$	−14.3341	−0.480211
$892$	0.567264	0.0189934
$893$	−0.587413	−0.0196570
$894$	15.7738	0.527555
$895$	28.6037	0.956116
$896$	10.2267	0.341652
$897$	−0.314912	−0.0105146
$898$	73.3518	2.44778
$899$	8.68821	0.289768
$900$	−5.84542	−0.194847
$901$	−0.249234	−0.00830320
$902$	52.8605	1.76006
$903$	4.82302	0.160500
$904$	−17.7990	−0.591987
$905$	−5.86325	−0.194901
$906$	3.88137	0.128950
$907$	−15.3115	−0.508411	−0.254205	−	0.967150i	$-0.581814\pi$
$907$	−15.3115	−0.508411	−0.254205	+	0.967150i	$0.581814\pi$
$908$	35.5281	1.17904
$909$	−31.8824	−1.05747
$910$	0.885749	0.0293623
$911$	−12.3593	−0.409483	−0.204742	−	0.978816i	$-0.565635\pi$
$911$	−12.3593	−0.409483	−0.204742	+	0.978816i	$0.565635\pi$
$912$	−9.79615	−0.324383
$913$	40.1663	1.32931
$914$	−20.3244	−0.672272
$915$	16.6523	0.550510
$916$	53.0726	1.75357
$917$	−6.96083	−0.229867
$918$	3.84260	0.126825
$919$	38.7904	1.27958	0.639789	−	0.768550i	$-0.279022\pi$
$919$	38.7904	1.27958	0.639789	+	0.768550i	$0.279022\pi$
$920$	8.53425	0.281366
$921$	−13.8618	−0.456762
$922$	−18.2675	−0.601608
$923$	−0.503296	−0.0165662
$924$	5.65079	0.185897
$925$	−2.12027	−0.0697140
$926$	31.7002	1.04173
$927$	15.0071	0.492899
$928$	31.6359	1.03850
$929$	52.6828	1.72847	0.864233	−	0.503092i	$-0.167804\pi$
$929$	52.6828	1.72847	0.864233	+	0.503092i	$0.167804\pi$
$930$	−7.89466	−0.258876
$931$	−5.85207	−0.191794
$932$	−8.33282	−0.272951
$933$	−16.7003	−0.546743
$934$	−15.5197	−0.507821
$935$	−3.37502	−0.110375
$936$	0.569354	0.0186099
$937$	40.4223	1.32054	0.660269	−	0.751029i	$-0.270442\pi$
$937$	40.4223	1.32054	0.660269	+	0.751029i	$0.270442\pi$
$938$	−16.9870	−0.554645
$939$	−11.3436	−0.370183
$940$	−0.639558	−0.0208601
$941$	22.9460	0.748019	0.374010	−	0.927425i	$-0.377983\pi$
$941$	22.9460	0.748019	0.374010	+	0.927425i	$0.377983\pi$
$942$	−7.55474	−0.246147
$943$	21.1908	0.690067
$944$	−28.2982	−0.921029
$945$	−9.46539	−0.307909
$946$	−44.3659	−1.44246
$947$	43.1646	1.40266	0.701330	−	0.712836i	$-0.252590\pi$
$947$	43.1646	1.40266	0.701330	+	0.712836i	$0.252590\pi$
$948$	−14.7585	−0.479334
$949$	−1.84880	−0.0600147
$950$	11.2251	0.364191
$951$	−12.0408	−0.390449
$952$	0.615810	0.0199585
$953$	−4.70155	−0.152298	−0.0761491	−	0.997096i	$-0.524263\pi$
$953$	−4.70155	−0.152298	−0.0761491	+	0.997096i	$0.524263\pi$
$954$	2.92056	0.0945567
$955$	55.3304	1.79045
$956$	42.2571	1.36669
$957$	8.77356	0.283609
$958$	37.4760	1.21079
$959$	20.4879	0.661590
$960$	−20.6198	−0.665503
$961$	−26.4554	−0.853401
$962$	0.867449	0.0279677
$963$	−8.14767	−0.262555
$964$	−5.29193	−0.170442
$965$	−15.8971	−0.511744
$966$	3.99128	0.128417
$967$	−25.5355	−0.821166	−0.410583	−	0.911823i	$-0.634675\pi$
$967$	−25.5355	−0.821166	−0.410583	+	0.911823i	$0.634675\pi$
$968$	2.40824	0.0774037
$969$	−1.90230	−0.0611107
$970$	−52.9464	−1.70001
$971$	−40.3578	−1.29514	−0.647572	−	0.762004i	$-0.724215\pi$
$971$	−40.3578	−1.29514	−0.647572	+	0.762004i	$0.724215\pi$
$972$	−39.5043	−1.26710
$973$	8.06353	0.258505
$974$	−26.0290	−0.834022
$975$	−0.107366	−0.00343845
$976$	−22.8181	−0.730389
$977$	−26.5715	−0.850097	−0.425048	−	0.905171i	$-0.639743\pi$
$977$	−26.5715	−0.850097	−0.425048	+	0.905171i	$0.639743\pi$
$978$	18.2175	0.582532
$979$	22.3802	0.715275
$980$	−6.37157	−0.203532
$981$	13.0699	0.417290
$982$	88.9586	2.83878
$983$	58.4961	1.86574	0.932868	−	0.360217i	$-0.117297\pi$
$983$	58.4961	1.86574	0.932868	+	0.360217i	$0.117297\pi$
$984$	7.72297	0.246199
$985$	−13.3843	−0.426459
$986$	4.01606	0.127897
$987$	−0.0712099	−0.00226663
$988$	−2.60649	−0.0829236
$989$	−17.7855	−0.565545
$990$	39.5490	1.25695
$991$	−35.8911	−1.14012	−0.570058	−	0.821604i	$-0.693079\pi$
$991$	−35.8911	−1.14012	−0.570058	+	0.821604i	$0.693079\pi$
$992$	16.5478	0.525394
$993$	23.9724	0.760743
$994$	6.37891	0.202327
$995$	−2.47717	−0.0785314
$996$	24.6491	0.781037
$997$	12.3886	0.392350	0.196175	−	0.980569i	$-0.437148\pi$
$997$	12.3886	0.392350	0.196175	+	0.980569i	$0.437148\pi$
$998$	7.41246	0.234637
$999$	−9.26983	−0.293285

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6041.2.a.c.1.12	✓	83

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6041.2.a.c.1.12	✓	83	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:	\( N \)	\(=\)	\( 6041 = 7 \cdot 863 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6041.a (trivial)

\(f(q)\)	\(=\)	\(q-2.15056 q^{2} -0.709425 q^{3} +2.62493 q^{4} -2.42733 q^{5} +1.52566 q^{6} +1.00000 q^{7} -1.34395 q^{8} -2.49672 q^{9} +O(q^{10})\)	\(q-2.15056 q^{2} -0.709425 q^{3} +2.62493 q^{4} -2.42733 q^{5} +1.52566 q^{6} +1.00000 q^{7} -1.34395 q^{8} -2.49672 q^{9} +5.22013 q^{10} -3.03448 q^{11} -1.86219 q^{12} +0.169680 q^{13} -2.15056 q^{14} +1.72201 q^{15} -2.35960 q^{16} -0.458209 q^{17} +5.36935 q^{18} -5.85207 q^{19} -6.37157 q^{20} -0.709425 q^{21} +6.52585 q^{22} +2.61609 q^{23} +0.953433 q^{24} +0.891926 q^{25} -0.364907 q^{26} +3.89951 q^{27} +2.62493 q^{28} +4.07553 q^{29} -3.70329 q^{30} +2.13180 q^{31} +7.76238 q^{32} +2.15274 q^{33} +0.985407 q^{34} -2.42733 q^{35} -6.55370 q^{36} -2.37718 q^{37} +12.5853 q^{38} -0.120375 q^{39} +3.26221 q^{40} +8.10017 q^{41} +1.52566 q^{42} -6.79849 q^{43} -7.96531 q^{44} +6.06035 q^{45} -5.62608 q^{46} +0.100377 q^{47} +1.67396 q^{48} +1.00000 q^{49} -1.91815 q^{50} +0.325065 q^{51} +0.445397 q^{52} +0.543932 q^{53} -8.38615 q^{54} +7.36569 q^{55} -1.34395 q^{56} +4.15161 q^{57} -8.76470 q^{58} +11.9928 q^{59} +4.52015 q^{60} +9.67031 q^{61} -4.58457 q^{62} -2.49672 q^{63} -11.9743 q^{64} -0.411868 q^{65} -4.62960 q^{66} +7.89885 q^{67} -1.20277 q^{68} -1.85592 q^{69} +5.22013 q^{70} -2.96615 q^{71} +3.35546 q^{72} -10.8959 q^{73} +5.11228 q^{74} -0.632755 q^{75} -15.3613 q^{76} -3.03448 q^{77} +0.258874 q^{78} +7.92535 q^{79} +5.72754 q^{80} +4.72374 q^{81} -17.4199 q^{82} -13.2366 q^{83} -1.86219 q^{84} +1.11222 q^{85} +14.6206 q^{86} -2.89129 q^{87} +4.07820 q^{88} -7.37530 q^{89} -13.0332 q^{90} +0.169680 q^{91} +6.86706 q^{92} -1.51235 q^{93} -0.215867 q^{94} +14.2049 q^{95} -5.50683 q^{96} -10.1427 q^{97} -2.15056 q^{98} +7.57624 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 83 q - 8 q^{2} - 12 q^{3} + 48 q^{4} - 11 q^{5} - 8 q^{6} + 83 q^{7} - 18 q^{8} + 39 q^{9}+O(q^{10}) \) 83 * q - 8 * q^2 - 12 * q^3 + 48 * q^4 - 11 * q^5 - 8 * q^6 + 83 * q^7 - 18 * q^8 + 39 * q^9	\( 83 q - 8 q^{2} - 12 q^{3} + 48 q^{4} - 11 q^{5} - 8 q^{6} + 83 q^{7} - 18 q^{8} + 39 q^{9} - 20 q^{10} - 26 q^{11} - 14 q^{12} - 22 q^{13} - 8 q^{14} - 37 q^{15} - 10 q^{16} - 9 q^{17} - 27 q^{18} - 42 q^{19} - 22 q^{20} - 12 q^{21} - 44 q^{22} - 46 q^{23} - 24 q^{24} - 20 q^{25} - 9 q^{26} - 39 q^{27} + 48 q^{28} - 36 q^{29} - 11 q^{30} - 107 q^{31} - 19 q^{32} - 25 q^{33} - 24 q^{34} - 11 q^{35} - 32 q^{36} - 75 q^{37} - 16 q^{38} - 78 q^{39} - 34 q^{40} - 17 q^{41} - 8 q^{42} - 87 q^{43} - 32 q^{44} - 17 q^{45} - 56 q^{46} - 39 q^{47} - 16 q^{48} + 83 q^{49} - 26 q^{50} - 71 q^{51} - 53 q^{52} - 28 q^{53} - 25 q^{54} - 94 q^{55} - 18 q^{56} - 79 q^{57} - 69 q^{58} - 26 q^{59} - 43 q^{60} - 56 q^{61} - 6 q^{62} + 39 q^{63} - 108 q^{64} - 26 q^{65} + 10 q^{66} - 123 q^{67} - 11 q^{68} + 2 q^{69} - 20 q^{70} - 96 q^{71} - 11 q^{72} - 53 q^{73} - 26 q^{74} - 27 q^{75} - 65 q^{76} - 26 q^{77} - 43 q^{78} - 160 q^{79} + 12 q^{80} - 53 q^{81} - 20 q^{82} - 2 q^{83} - 14 q^{84} - 110 q^{85} + 24 q^{86} - 52 q^{87} - 79 q^{88} - 5 q^{89} - 4 q^{90} - 22 q^{91} - 51 q^{92} - 30 q^{93} - 9 q^{94} - 76 q^{95} - 3 q^{96} - 44 q^{97} - 8 q^{98} - 82 q^{99}+O(q^{100}) \) 83 * q - 8 * q^2 - 12 * q^3 + 48 * q^4 - 11 * q^5 - 8 * q^6 + 83 * q^7 - 18 * q^8 + 39 * q^9 - 20 * q^10 - 26 * q^11 - 14 * q^12 - 22 * q^13 - 8 * q^14 - 37 * q^15 - 10 * q^16 - 9 * q^17 - 27 * q^18 - 42 * q^19 - 22 * q^20 - 12 * q^21 - 44 * q^22 - 46 * q^23 - 24 * q^24 - 20 * q^25 - 9 * q^26 - 39 * q^27 + 48 * q^28 - 36 * q^29 - 11 * q^30 - 107 * q^31 - 19 * q^32 - 25 * q^33 - 24 * q^34 - 11 * q^35 - 32 * q^36 - 75 * q^37 - 16 * q^38 - 78 * q^39 - 34 * q^40 - 17 * q^41 - 8 * q^42 - 87 * q^43 - 32 * q^44 - 17 * q^45 - 56 * q^46 - 39 * q^47 - 16 * q^48 + 83 * q^49 - 26 * q^50 - 71 * q^51 - 53 * q^52 - 28 * q^53 - 25 * q^54 - 94 * q^55 - 18 * q^56 - 79 * q^57 - 69 * q^58 - 26 * q^59 - 43 * q^60 - 56 * q^61 - 6 * q^62 + 39 * q^63 - 108 * q^64 - 26 * q^65 + 10 * q^66 - 123 * q^67 - 11 * q^68 + 2 * q^69 - 20 * q^70 - 96 * q^71 - 11 * q^72 - 53 * q^73 - 26 * q^74 - 27 * q^75 - 65 * q^76 - 26 * q^77 - 43 * q^78 - 160 * q^79 + 12 * q^80 - 53 * q^81 - 20 * q^82 - 2 * q^83 - 14 * q^84 - 110 * q^85 + 24 * q^86 - 52 * q^87 - 79 * q^88 - 5 * q^89 - 4 * q^90 - 22 * q^91 - 51 * q^92 - 30 * q^93 - 9 * q^94 - 76 * q^95 - 3 * q^96 - 44 * q^97 - 8 * q^98 - 82 * q^99

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