LMFDB - Embedded newform 6005.2.a.g.1.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6005,2,Mod(1,6005)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6005, 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("6005.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6005 = 5 \cdot 1201 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6005.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:	$47.9501664138$
Analytic rank:	$0$
Dimension:	$113$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
Character	$\chi$	$=$	6005.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.67625 q^{2} +1.85244 q^{3} +5.16230 q^{4} -1.00000 q^{5} -4.95758 q^{6} +4.71146 q^{7} -8.46311 q^{8} +0.431523 q^{9} +O(q^{10})$	\(q-2.67625 q^{2} +1.85244 q^{3} +5.16230 q^{4} -1.00000 q^{5} -4.95758 q^{6} +4.71146 q^{7} -8.46311 q^{8} +0.431523 q^{9} +2.67625 q^{10} -0.675782 q^{11} +9.56284 q^{12} +4.43357 q^{13} -12.6090 q^{14} -1.85244 q^{15} +12.3248 q^{16} +5.84507 q^{17} -1.15486 q^{18} -3.92531 q^{19} -5.16230 q^{20} +8.72768 q^{21} +1.80856 q^{22} -1.79497 q^{23} -15.6774 q^{24} +1.00000 q^{25} -11.8653 q^{26} -4.75794 q^{27} +24.3220 q^{28} -7.82389 q^{29} +4.95758 q^{30} -8.11966 q^{31} -16.0579 q^{32} -1.25184 q^{33} -15.6428 q^{34} -4.71146 q^{35} +2.22765 q^{36} +8.95483 q^{37} +10.5051 q^{38} +8.21291 q^{39} +8.46311 q^{40} +9.14103 q^{41} -23.3574 q^{42} +9.29996 q^{43} -3.48859 q^{44} -0.431523 q^{45} +4.80378 q^{46} -9.32022 q^{47} +22.8309 q^{48} +15.1978 q^{49} -2.67625 q^{50} +10.8276 q^{51} +22.8874 q^{52} -3.79904 q^{53} +12.7334 q^{54} +0.675782 q^{55} -39.8736 q^{56} -7.27140 q^{57} +20.9387 q^{58} +7.46425 q^{59} -9.56284 q^{60} +4.89906 q^{61} +21.7302 q^{62} +2.03310 q^{63} +18.3255 q^{64} -4.43357 q^{65} +3.35024 q^{66} -4.58490 q^{67} +30.1740 q^{68} -3.32506 q^{69} +12.6090 q^{70} +4.50062 q^{71} -3.65203 q^{72} +11.4025 q^{73} -23.9654 q^{74} +1.85244 q^{75} -20.2637 q^{76} -3.18392 q^{77} -21.9798 q^{78} -12.1697 q^{79} -12.3248 q^{80} -10.1084 q^{81} -24.4637 q^{82} +7.75506 q^{83} +45.0549 q^{84} -5.84507 q^{85} -24.8890 q^{86} -14.4933 q^{87} +5.71921 q^{88} -1.21619 q^{89} +1.15486 q^{90} +20.8886 q^{91} -9.26617 q^{92} -15.0412 q^{93} +24.9432 q^{94} +3.92531 q^{95} -29.7463 q^{96} +12.0444 q^{97} -40.6732 q^{98} -0.291615 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 113 q - 3 q^{2} + 6 q^{3} + 141 q^{4} - 113 q^{5} + 7 q^{6} + 7 q^{7} - 12 q^{8} + 141 q^{9}+O(q^{10}) $ 113 * q - 3 * q^2 + 6 * q^3 + 141 * q^4 - 113 * q^5 + 7 * q^6 + 7 * q^7 - 12 * q^8 + 141 * q^9	\( 113 q - 3 q^{2} + 6 q^{3} + 141 q^{4} - 113 q^{5} + 7 q^{6} + 7 q^{7} - 12 q^{8} + 141 q^{9} + 3 q^{10} + 38 q^{11} - 4 q^{12} + 17 q^{13} + 23 q^{14} - 6 q^{15} + 193 q^{16} - 11 q^{17} - 3 q^{18} + 76 q^{19} - 141 q^{20} + 19 q^{21} + 41 q^{22} - 28 q^{23} + 29 q^{24} + 113 q^{25} + 21 q^{26} + 18 q^{27} + 29 q^{28} + 24 q^{29} - 7 q^{30} + 59 q^{31} - 22 q^{32} + 3 q^{33} + 55 q^{34} - 7 q^{35} + 232 q^{36} + 41 q^{37} - 6 q^{38} + 55 q^{39} + 12 q^{40} + 24 q^{41} + 17 q^{42} + 136 q^{43} + 85 q^{44} - 141 q^{45} + 84 q^{46} - 91 q^{47} - 19 q^{48} + 198 q^{49} - 3 q^{50} + 97 q^{51} + 45 q^{52} + 9 q^{53} + 54 q^{54} - 38 q^{55} + 98 q^{56} + 22 q^{57} + 69 q^{58} + 59 q^{59} + 4 q^{60} + 51 q^{61} - 30 q^{62} - 22 q^{63} + 298 q^{64} - 17 q^{65} + 76 q^{66} + 201 q^{67} - 34 q^{68} + 42 q^{69} - 23 q^{70} + 69 q^{71} - 7 q^{72} + 30 q^{73} + 35 q^{74} + 6 q^{75} + 170 q^{76} - 37 q^{77} - 11 q^{78} + 143 q^{79} - 193 q^{80} + 197 q^{81} + 55 q^{82} - 15 q^{83} + 83 q^{84} + 11 q^{85} + 78 q^{86} - 51 q^{87} + 113 q^{88} + 53 q^{89} + 3 q^{90} + 217 q^{91} - 40 q^{92} + 36 q^{93} + 81 q^{94} - 76 q^{95} + 66 q^{96} + 63 q^{97} - 62 q^{98} + 184 q^{99}+O(q^{100}) \) 113 * q - 3 * q^2 + 6 * q^3 + 141 * q^4 - 113 * q^5 + 7 * q^6 + 7 * q^7 - 12 * q^8 + 141 * q^9 + 3 * q^10 + 38 * q^11 - 4 * q^12 + 17 * q^13 + 23 * q^14 - 6 * q^15 + 193 * q^16 - 11 * q^17 - 3 * q^18 + 76 * q^19 - 141 * q^20 + 19 * q^21 + 41 * q^22 - 28 * q^23 + 29 * q^24 + 113 * q^25 + 21 * q^26 + 18 * q^27 + 29 * q^28 + 24 * q^29 - 7 * q^30 + 59 * q^31 - 22 * q^32 + 3 * q^33 + 55 * q^34 - 7 * q^35 + 232 * q^36 + 41 * q^37 - 6 * q^38 + 55 * q^39 + 12 * q^40 + 24 * q^41 + 17 * q^42 + 136 * q^43 + 85 * q^44 - 141 * q^45 + 84 * q^46 - 91 * q^47 - 19 * q^48 + 198 * q^49 - 3 * q^50 + 97 * q^51 + 45 * q^52 + 9 * q^53 + 54 * q^54 - 38 * q^55 + 98 * q^56 + 22 * q^57 + 69 * q^58 + 59 * q^59 + 4 * q^60 + 51 * q^61 - 30 * q^62 - 22 * q^63 + 298 * q^64 - 17 * q^65 + 76 * q^66 + 201 * q^67 - 34 * q^68 + 42 * q^69 - 23 * q^70 + 69 * q^71 - 7 * q^72 + 30 * q^73 + 35 * q^74 + 6 * q^75 + 170 * q^76 - 37 * q^77 - 11 * q^78 + 143 * q^79 - 193 * q^80 + 197 * q^81 + 55 * q^82 - 15 * q^83 + 83 * q^84 + 11 * q^85 + 78 * q^86 - 51 * q^87 + 113 * q^88 + 53 * q^89 + 3 * q^90 + 217 * q^91 - 40 * q^92 + 36 * q^93 + 81 * q^94 - 76 * q^95 + 66 * q^96 + 63 * q^97 - 62 * q^98 + 184 * 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 $

$2$	−2.67625	−1.89239	−0.946197	−	0.323592i	$-0.895109\pi$
$2$	−2.67625	−1.89239	−0.946197	+	0.323592i	$0.895109\pi$
$3$	1.85244	1.06951	0.534753	−	0.845009i	$-0.320405\pi$
$3$	1.85244	1.06951	0.534753	+	0.845009i	$0.320405\pi$
$4$	5.16230	2.58115
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	−4.95758	−2.02392
$7$	4.71146	1.78076	0.890382	−	0.455214i	$-0.150437\pi$
$7$	4.71146	1.78076	0.890382	+	0.455214i	$0.150437\pi$
$8$	−8.46311	−2.99216
$9$	0.431523	0.143841
$10$	2.67625	0.846304
$11$	−0.675782	−0.203756	−0.101878	−	0.994797i	$-0.532485\pi$
$11$	−0.675782	−0.203756	−0.101878	+	0.994797i	$0.532485\pi$
$12$	9.56284	2.76055
$13$	4.43357	1.22965	0.614825	−	0.788663i	$-0.289227\pi$
$13$	4.43357	1.22965	0.614825	+	0.788663i	$0.289227\pi$
$14$	−12.6090	−3.36991
$15$	−1.85244	−0.478297
$16$	12.3248	3.08119
$17$	5.84507	1.41764	0.708818	−	0.705391i	$-0.249229\pi$
$17$	5.84507	1.41764	0.708818	+	0.705391i	$0.249229\pi$
$18$	−1.15486	−0.272204
$19$	−3.92531	−0.900529	−0.450264	−	0.892895i	$-0.648670\pi$
$19$	−3.92531	−0.900529	−0.450264	+	0.892895i	$0.648670\pi$
$20$	−5.16230	−1.15433
$21$	8.72768	1.90454
$22$	1.80856	0.385586
$23$	−1.79497	−0.374277	−0.187138	−	0.982334i	$-0.559921\pi$
$23$	−1.79497	−0.374277	−0.187138	+	0.982334i	$0.559921\pi$
$24$	−15.6774	−3.20013
$25$	1.00000	0.200000
$26$	−11.8653	−2.32698
$27$	−4.75794	−0.915666
$28$	24.3220	4.59642
$29$	−7.82389	−1.45286	−0.726430	−	0.687241i	$-0.758822\pi$
$29$	−7.82389	−1.45286	−0.726430	+	0.687241i	$0.758822\pi$
$30$	4.95758	0.905126
$31$	−8.11966	−1.45833	−0.729167	−	0.684336i	$-0.760092\pi$
$31$	−8.11966	−1.45833	−0.729167	+	0.684336i	$0.760092\pi$
$32$	−16.0579	−2.83867
$33$	−1.25184	−0.217918
$34$	−15.6428	−2.68273
$35$	−4.71146	−0.796382
$36$	2.22765	0.371275
$37$	8.95483	1.47217	0.736083	−	0.676891i	$-0.236673\pi$
$37$	8.95483	1.47217	0.736083	+	0.676891i	$0.236673\pi$
$38$	10.5051	1.70415
$39$	8.21291	1.31512
$40$	8.46311	1.33814
$41$	9.14103	1.42759	0.713795	−	0.700355i	$-0.246975\pi$
$41$	9.14103	1.42759	0.713795	+	0.700355i	$0.246975\pi$
$42$	−23.3574	−3.60413
$43$	9.29996	1.41823	0.709115	−	0.705093i	$-0.249095\pi$
$43$	9.29996	1.41823	0.709115	+	0.705093i	$0.249095\pi$
$44$	−3.48859	−0.525925
$45$	−0.431523	−0.0643276
$46$	4.80378	0.708278
$47$	−9.32022	−1.35949	−0.679747	−	0.733447i	$-0.737910\pi$
$47$	−9.32022	−1.35949	−0.679747	+	0.733447i	$0.737910\pi$
$48$	22.8309	3.29535
$49$	15.1978	2.17112
$50$	−2.67625	−0.378479
$51$	10.8276	1.51617
$52$	22.8874	3.17392
$53$	−3.79904	−0.521839	−0.260919	−	0.965361i	$-0.584026\pi$
$53$	−3.79904	−0.521839	−0.260919	+	0.965361i	$0.584026\pi$
$54$	12.7334	1.73280
$55$	0.675782	0.0911224
$56$	−39.8736	−5.32833
$57$	−7.27140	−0.963120
$58$	20.9387	2.74938
$59$	7.46425	0.971762	0.485881	−	0.874025i	$-0.338499\pi$
$59$	7.46425	0.971762	0.485881	+	0.874025i	$0.338499\pi$
$60$	−9.56284	−1.23456
$61$	4.89906	0.627261	0.313630	−	0.949545i	$-0.398455\pi$
$61$	4.89906	0.627261	0.313630	+	0.949545i	$0.398455\pi$
$62$	21.7302	2.75974
$63$	2.03310	0.256147
$64$	18.3255	2.29068
$65$	−4.43357	−0.549916
$66$	3.35024	0.412386
$67$	−4.58490	−0.560135	−0.280067	−	0.959980i	$-0.590357\pi$
$67$	−4.58490	−0.560135	−0.280067	+	0.959980i	$0.590357\pi$
$68$	30.1740	3.65914
$69$	−3.32506	−0.400291
$70$	12.6090	1.50707
$71$	4.50062	0.534125	0.267063	−	0.963679i	$-0.413947\pi$
$71$	4.50062	0.534125	0.267063	+	0.963679i	$0.413947\pi$
$72$	−3.65203	−0.430395
$73$	11.4025	1.33457	0.667284	−	0.744804i	$-0.267457\pi$
$73$	11.4025	1.33457	0.667284	+	0.744804i	$0.267457\pi$
$74$	−23.9654	−2.78592
$75$	1.85244	0.213901
$76$	−20.2637	−2.32440
$77$	−3.18392	−0.362841
$78$	−21.9798	−2.48872
$79$	−12.1697	−1.36920	−0.684600	−	0.728919i	$-0.740023\pi$
$79$	−12.1697	−1.36920	−0.684600	+	0.728919i	$0.740023\pi$
$80$	−12.3248	−1.37795
$81$	−10.1084	−1.12315
$82$	−24.4637	−2.70156
$83$	7.75506	0.851229	0.425614	−	0.904905i	$-0.360058\pi$
$83$	7.75506	0.851229	0.425614	+	0.904905i	$0.360058\pi$
$84$	45.0549	4.91590
$85$	−5.84507	−0.633986
$86$	−24.8890	−2.68385
$87$	−14.4933	−1.55384
$88$	5.71921	0.609670
$89$	−1.21619	−0.128916	−0.0644580	−	0.997920i	$-0.520532\pi$
$89$	−1.21619	−0.128916	−0.0644580	+	0.997920i	$0.520532\pi$
$90$	1.15486	0.121733
$91$	20.8886	2.18972
$92$	−9.26617	−0.966065
$93$	−15.0412	−1.55969
$94$	24.9432	2.57270
$95$	3.92531	0.402729
$96$	−29.7463	−3.03597
$97$	12.0444	1.22292	0.611460	−	0.791275i	$-0.290583\pi$
$97$	12.0444	1.22292	0.611460	+	0.791275i	$0.290583\pi$
$98$	−40.6732	−4.10861
$99$	−0.291615	−0.0293084
$100$	5.16230	0.516230
$101$	10.3165	1.02653	0.513265	−	0.858230i	$-0.328436\pi$
$101$	10.3165	1.02653	0.513265	+	0.858230i	$0.328436\pi$
$102$	−28.9774	−2.86919
$103$	−0.968500	−0.0954291	−0.0477145	−	0.998861i	$-0.515194\pi$
$103$	−0.968500	−0.0954291	−0.0477145	+	0.998861i	$0.515194\pi$
$104$	−37.5218	−3.67931
$105$	−8.72768	−0.851734
$106$	10.1672	0.987524
$107$	10.5285	1.01783	0.508913	−	0.860818i	$-0.330047\pi$
$107$	10.5285	1.01783	0.508913	+	0.860818i	$0.330047\pi$
$108$	−24.5619	−2.36347
$109$	−0.527865	−0.0505603	−0.0252801	−	0.999680i	$-0.508048\pi$
$109$	−0.527865	−0.0505603	−0.0252801	+	0.999680i	$0.508048\pi$
$110$	−1.80856	−0.172439
$111$	16.5883	1.57449
$112$	58.0677	5.48688
$113$	−6.74928	−0.634919	−0.317459	−	0.948272i	$-0.602830\pi$
$113$	−6.74928	−0.634919	−0.317459	+	0.948272i	$0.602830\pi$
$114$	19.4601	1.82260
$115$	1.79497	0.167382
$116$	−40.3893	−3.75005
$117$	1.91319	0.176874
$118$	−19.9762	−1.83896
$119$	27.5388	2.52448
$120$	15.6774	1.43114
$121$	−10.5433	−0.958484
$122$	−13.1111	−1.18702
$123$	16.9332	1.52681
$124$	−41.9161	−3.76418
$125$	−1.00000	−0.0894427
$126$	−5.44109	−0.484730
$127$	20.4211	1.81208	0.906038	−	0.423196i	$-0.139092\pi$
$127$	20.4211	1.81208	0.906038	+	0.423196i	$0.139092\pi$
$128$	−16.9276	−1.49621
$129$	17.2276	1.51680
$130$	11.8653	1.04066
$131$	11.5698	1.01086	0.505429	−	0.862868i	$-0.331334\pi$
$131$	11.5698	1.01086	0.505429	+	0.862868i	$0.331334\pi$
$132$	−6.46239	−0.562479
$133$	−18.4940	−1.60363
$134$	12.2703	1.05999
$135$	4.75794	0.409498
$136$	−49.4674	−4.24180
$137$	8.96485	0.765919	0.382960	−	0.923765i	$-0.374905\pi$
$137$	8.96485	0.765919	0.382960	+	0.923765i	$0.374905\pi$
$138$	8.89870	0.757507
$139$	20.7934	1.76367	0.881837	−	0.471554i	$-0.156307\pi$
$139$	20.7934	1.76367	0.881837	+	0.471554i	$0.156307\pi$
$140$	−24.3220	−2.05558
$141$	−17.2651	−1.45399
$142$	−12.0448	−1.01077
$143$	−2.99612	−0.250548
$144$	5.31842	0.443202
$145$	7.82389	0.649739
$146$	−30.5160	−2.52553
$147$	28.1530	2.32202
$148$	46.2276	3.79988
$149$	1.30248	0.106704	0.0533518	−	0.998576i	$-0.483010\pi$
$149$	1.30248	0.106704	0.0533518	+	0.998576i	$0.483010\pi$
$150$	−4.95758	−0.404785
$151$	−17.5149	−1.42534	−0.712671	−	0.701498i	$-0.752515\pi$
$151$	−17.5149	−1.42534	−0.712671	+	0.701498i	$0.752515\pi$
$152$	33.2204	2.69453
$153$	2.52228	0.203914
$154$	8.52095	0.686638
$155$	8.11966	0.652186
$156$	42.3975	3.39452
$157$	−20.3044	−1.62047	−0.810233	−	0.586109i	$-0.800659\pi$
$157$	−20.3044	−1.62047	−0.810233	+	0.586109i	$0.800659\pi$
$158$	32.5692	2.59107
$159$	−7.03749	−0.558109
$160$	16.0579	1.26949
$161$	−8.45691	−0.666498
$162$	27.0525	2.12544
$163$	−9.64555	−0.755498	−0.377749	−	0.925908i	$-0.623302\pi$
$163$	−9.64555	−0.755498	−0.377749	+	0.925908i	$0.623302\pi$
$164$	47.1888	3.68483
$165$	1.25184	0.0974558
$166$	−20.7545	−1.61086
$167$	11.6294	0.899907	0.449953	−	0.893052i	$-0.351441\pi$
$167$	11.6294	0.899907	0.449953	+	0.893052i	$0.351441\pi$
$168$	−73.8633	−5.69868
$169$	6.65653	0.512041
$170$	15.6428	1.19975
$171$	−1.69386	−0.129533
$172$	48.0092	3.66067
$173$	−10.3448	−0.786498	−0.393249	−	0.919432i	$-0.628649\pi$
$173$	−10.3448	−0.786498	−0.393249	+	0.919432i	$0.628649\pi$
$174$	38.7876	2.94048
$175$	4.71146	0.356153
$176$	−8.32885	−0.627811
$177$	13.8270	1.03930
$178$	3.25483	0.243960
$179$	9.53713	0.712838	0.356419	−	0.934326i	$-0.383998\pi$
$179$	9.53713	0.712838	0.356419	+	0.934326i	$0.383998\pi$
$180$	−2.22765	−0.166039
$181$	8.37727	0.622678	0.311339	−	0.950299i	$-0.399223\pi$
$181$	8.37727	0.622678	0.311339	+	0.950299i	$0.399223\pi$
$182$	−55.9030	−4.14381
$183$	9.07520	0.670858
$184$	15.1910	1.11990
$185$	−8.95483	−0.658373
$186$	40.2539	2.95156
$187$	−3.94999	−0.288852
$188$	−48.1138	−3.50906
$189$	−22.4168	−1.63059
$190$	−10.5051	−0.762121
$191$	2.28490	0.165329	0.0826647	−	0.996577i	$-0.473657\pi$
$191$	2.28490	0.165329	0.0826647	+	0.996577i	$0.473657\pi$
$192$	33.9468	2.44990
$193$	−15.0747	−1.08510	−0.542549	−	0.840024i	$-0.682541\pi$
$193$	−15.0747	−1.08510	−0.542549	+	0.840024i	$0.682541\pi$
$194$	−32.2337	−2.31424
$195$	−8.21291	−0.588138
$196$	78.4558	5.60399
$197$	−2.51625	−0.179276	−0.0896379	−	0.995974i	$-0.528571\pi$
$197$	−2.51625	−0.179276	−0.0896379	+	0.995974i	$0.528571\pi$
$198$	0.780435	0.0554631
$199$	15.9489	1.13058	0.565292	−	0.824891i	$-0.308763\pi$
$199$	15.9489	1.13058	0.565292	+	0.824891i	$0.308763\pi$
$200$	−8.46311	−0.598432
$201$	−8.49324	−0.599067
$202$	−27.6095	−1.94260
$203$	−36.8619	−2.58720
$204$	55.8954	3.91346
$205$	−9.14103	−0.638438
$206$	2.59195	0.180589
$207$	−0.774570	−0.0538363
$208$	54.6427	3.78879
$209$	2.65265	0.183488
$210$	23.3574	1.61182
$211$	26.9525	1.85549	0.927744	−	0.373218i	$-0.121746\pi$
$211$	26.9525	1.85549	0.927744	+	0.373218i	$0.121746\pi$
$212$	−19.6118	−1.34695
$213$	8.33711	0.571250
$214$	−28.1768	−1.92613
$215$	−9.29996	−0.634252
$216$	40.2670	2.73982
$217$	−38.2554	−2.59695
$218$	1.41270	0.0956799
$219$	21.1225	1.42733
$220$	3.48859	0.235201
$221$	25.9145	1.74320
$222$	−44.3943	−2.97955
$223$	−0.379911	−0.0254407	−0.0127204	−	0.999919i	$-0.504049\pi$
$223$	−0.379911	−0.0254407	−0.0127204	+	0.999919i	$0.504049\pi$
$224$	−75.6563	−5.05500
$225$	0.431523	0.0287682
$226$	18.0627	1.20152
$227$	2.82037	0.187194	0.0935972	−	0.995610i	$-0.470163\pi$
$227$	2.82037	0.187194	0.0935972	+	0.995610i	$0.470163\pi$
$228$	−37.5372	−2.48596
$229$	−3.37049	−0.222728	−0.111364	−	0.993780i	$-0.535522\pi$
$229$	−3.37049	−0.222728	−0.111364	+	0.993780i	$0.535522\pi$
$230$	−4.80378	−0.316752
$231$	−5.89800	−0.388060
$232$	66.2144	4.34719
$233$	11.9997	0.786128	0.393064	−	0.919511i	$-0.371415\pi$
$233$	11.9997	0.786128	0.393064	+	0.919511i	$0.371415\pi$
$234$	−5.12016	−0.334715
$235$	9.32022	0.607984
$236$	38.5327	2.50827
$237$	−22.5436	−1.46437
$238$	−73.7006	−4.77730
$239$	−0.00858157	−0.000555096 0	−0.000277548	−	1.00000i	$-0.500088\pi$
$239$	−0.00858157	−0.000555096 0	−0.000277548		1.00000i	$0.500088\pi$
$240$	−22.8309	−1.47373
$241$	26.6009	1.71352	0.856758	−	0.515719i	$-0.172475\pi$
$241$	26.6009	1.71352	0.856758	+	0.515719i	$0.172475\pi$
$242$	28.2165	1.81383
$243$	−4.45127	−0.285549
$244$	25.2904	1.61905
$245$	−15.1978	−0.970954
$246$	−45.3174	−2.88933
$247$	−17.4031	−1.10734
$248$	68.7175	4.36357
$249$	14.3658	0.910394
$250$	2.67625	0.169261
$251$	−10.2889	−0.649431	−0.324716	−	0.945812i	$-0.605269\pi$
$251$	−10.2889	−0.649431	−0.324716	+	0.945812i	$0.605269\pi$
$252$	10.4955	0.661154
$253$	1.21301	0.0762610
$254$	−54.6518	−3.42916
$255$	−10.8276	−0.678052
$256$	8.65160	0.540725
$257$	20.1654	1.25788	0.628941	−	0.777453i	$-0.283489\pi$
$257$	20.1654	1.25788	0.628941	+	0.777453i	$0.283489\pi$
$258$	−46.1053	−2.87039
$259$	42.1903	2.62158
$260$	−22.8874	−1.41942
$261$	−3.37619	−0.208981
$262$	−30.9637	−1.91294
$263$	−9.99314	−0.616203	−0.308102	−	0.951353i	$-0.599694\pi$
$263$	−9.99314	−0.616203	−0.308102	+	0.951353i	$0.599694\pi$
$264$	10.5945	0.652045
$265$	3.79904	0.233373
$266$	49.4944	3.03470
$267$	−2.25292	−0.137876
$268$	−23.6686	−1.44579
$269$	10.6721	0.650689	0.325344	−	0.945596i	$-0.394520\pi$
$269$	10.6721	0.650689	0.325344	+	0.945596i	$0.394520\pi$
$270$	−12.7334	−0.774932
$271$	−16.9910	−1.03213	−0.516064	−	0.856550i	$-0.672603\pi$
$271$	−16.9910	−1.03213	−0.516064	+	0.856550i	$0.672603\pi$
$272$	72.0391	4.36801
$273$	38.6948	2.34191
$274$	−23.9922	−1.44942
$275$	−0.675782	−0.0407512
$276$	−17.1650	−1.03321
$277$	−29.2297	−1.75624	−0.878120	−	0.478440i	$-0.841202\pi$
$277$	−29.2297	−1.75624	−0.878120	+	0.478440i	$0.841202\pi$
$278$	−55.6483	−3.33757
$279$	−3.50382	−0.209768
$280$	39.8736	2.38290
$281$	−11.4842	−0.685093	−0.342546	−	0.939501i	$-0.611289\pi$
$281$	−11.4842	−0.685093	−0.342546	+	0.939501i	$0.611289\pi$
$282$	46.2057	2.75151
$283$	6.42244	0.381774	0.190887	−	0.981612i	$-0.438864\pi$
$283$	6.42244	0.381774	0.190887	+	0.981612i	$0.438864\pi$
$284$	23.2336	1.37866
$285$	7.27140	0.430720
$286$	8.01837	0.474136
$287$	43.0676	2.54220
$288$	−6.92937	−0.408317
$289$	17.1648	1.00969
$290$	−20.9387	−1.22956
$291$	22.3114	1.30792
$292$	58.8634	3.44472
$293$	−11.8887	−0.694548	−0.347274	−	0.937764i	$-0.612893\pi$
$293$	−11.8887	−0.694548	−0.347274	+	0.937764i	$0.612893\pi$
$294$	−75.3445	−4.39418
$295$	−7.46425	−0.434585
$296$	−75.7857	−4.40496
$297$	3.21533	0.186572
$298$	−3.48577	−0.201925
$299$	−7.95811	−0.460229
$300$	9.56284	0.552111
$301$	43.8163	2.52553
$302$	46.8742	2.69731
$303$	19.1106	1.09788
$304$	−48.3786	−2.77470
$305$	−4.89906	−0.280519
$306$	−6.75025	−0.385886
$307$	28.9288	1.65105	0.825526	−	0.564364i	$-0.190878\pi$
$307$	28.9288	1.65105	0.825526	+	0.564364i	$0.190878\pi$
$308$	−16.4363	−0.936548
$309$	−1.79408	−0.102062
$310$	−21.7302	−1.23419
$311$	15.0063	0.850929	0.425465	−	0.904975i	$-0.360111\pi$
$311$	15.0063	0.850929	0.425465	+	0.904975i	$0.360111\pi$
$312$	−69.5067	−3.93504
$313$	−26.3769	−1.49091	−0.745454	−	0.666557i	$-0.767767\pi$
$313$	−26.3769	−1.49091	−0.745454	+	0.666557i	$0.767767\pi$
$314$	54.3395	3.06656
$315$	−2.03310	−0.114552
$316$	−62.8238	−3.53412
$317$	−19.5662	−1.09895	−0.549475	−	0.835510i	$-0.685172\pi$
$317$	−19.5662	−1.09895	−0.549475	+	0.835510i	$0.685172\pi$
$318$	18.8341	1.05616
$319$	5.28724	0.296029
$320$	−18.3255	−1.02442
$321$	19.5033	1.08857
$322$	22.6328	1.26128
$323$	−22.9437	−1.27662
$324$	−52.1824	−2.89902
$325$	4.43357	0.245930
$326$	25.8139	1.42970
$327$	−0.977836	−0.0540744
$328$	−77.3616	−4.27158
$329$	−43.9118	−2.42094
$330$	−3.35024	−0.184425
$331$	−2.38123	−0.130884	−0.0654420	−	0.997856i	$-0.520846\pi$
$331$	−2.38123	−0.130884	−0.0654420	+	0.997856i	$0.520846\pi$
$332$	40.0340	2.19715
$333$	3.86422	0.211758
$334$	−31.1230	−1.70298
$335$	4.58490	0.250500
$336$	107.567	5.86824
$337$	17.8081	0.970069	0.485035	−	0.874495i	$-0.338807\pi$
$337$	17.8081	0.970069	0.485035	+	0.874495i	$0.338807\pi$
$338$	−17.8145	−0.968982
$339$	−12.5026	−0.679049
$340$	−30.1740	−1.63642
$341$	5.48711	0.297144
$342$	4.53320	0.245127
$343$	38.6238	2.08549
$344$	−78.7065	−4.24357
$345$	3.32506	0.179015
$346$	27.6852	1.48836
$347$	−29.4843	−1.58280	−0.791401	−	0.611297i	$-0.790648\pi$
$347$	−29.4843	−1.58280	−0.791401	+	0.611297i	$0.790648\pi$
$348$	−74.8186	−4.01070
$349$	−28.2670	−1.51310	−0.756549	−	0.653937i	$-0.773116\pi$
$349$	−28.2670	−1.51310	−0.756549	+	0.653937i	$0.773116\pi$
$350$	−12.6090	−0.673981
$351$	−21.0947	−1.12595
$352$	10.8517	0.578395
$353$	−8.63374	−0.459528	−0.229764	−	0.973246i	$-0.573795\pi$
$353$	−8.63374	−0.459528	−0.229764	+	0.973246i	$0.573795\pi$
$354$	−37.0046	−1.96677
$355$	−4.50062	−0.238868
$356$	−6.27835	−0.332752
$357$	51.0139	2.69994
$358$	−25.5237	−1.34897
$359$	−14.7260	−0.777210	−0.388605	−	0.921404i	$-0.627043\pi$
$359$	−14.7260	−0.777210	−0.388605	+	0.921404i	$0.627043\pi$
$360$	3.65203	0.192479
$361$	−3.59191	−0.189048
$362$	−22.4197	−1.17835
$363$	−19.5308	−1.02510
$364$	107.833	5.65199
$365$	−11.4025	−0.596837
$366$	−24.2875	−1.26953
$367$	14.2994	0.746423	0.373211	−	0.927746i	$-0.378257\pi$
$367$	14.2994	0.746423	0.373211	+	0.927746i	$0.378257\pi$
$368$	−22.1226	−1.15322
$369$	3.94457	0.205346
$370$	23.9654	1.24590
$371$	−17.8990	−0.929272
$372$	−77.6470	−4.02581
$373$	32.3946	1.67733	0.838664	−	0.544649i	$-0.183337\pi$
$373$	32.3946	1.67733	0.838664	+	0.544649i	$0.183337\pi$
$374$	10.5711	0.546621
$375$	−1.85244	−0.0956594
$376$	78.8781	4.06782
$377$	−34.6877	−1.78651
$378$	59.9930	3.08571
$379$	−6.50005	−0.333885	−0.166943	−	0.985967i	$-0.553389\pi$
$379$	−6.50005	−0.333885	−0.166943	+	0.985967i	$0.553389\pi$
$380$	20.2637	1.03950
$381$	37.8287	1.93802
$382$	−6.11495	−0.312868
$383$	10.8301	0.553394	0.276697	−	0.960957i	$-0.410760\pi$
$383$	10.8301	0.553394	0.276697	+	0.960957i	$0.410760\pi$
$384$	−31.3574	−1.60020
$385$	3.18392	0.162267
$386$	40.3436	2.05343
$387$	4.01314	0.204000
$388$	62.1767	3.15654
$389$	−10.5725	−0.536047	−0.268024	−	0.963412i	$-0.586370\pi$
$389$	−10.5725	−0.536047	−0.268024	+	0.963412i	$0.586370\pi$
$390$	21.9798	1.11299
$391$	−10.4917	−0.530588
$392$	−128.621	−6.49634
$393$	21.4323	1.08112
$394$	6.73412	0.339260
$395$	12.1697	0.612325
$396$	−1.50541	−0.0756495
$397$	−25.9826	−1.30403	−0.652013	−	0.758207i	$-0.726075\pi$
$397$	−25.9826	−1.30403	−0.652013	+	0.758207i	$0.726075\pi$
$398$	−42.6831	−2.13951
$399$	−34.2589	−1.71509
$400$	12.3248	0.616239
$401$	9.96196	0.497476	0.248738	−	0.968571i	$-0.419984\pi$
$401$	9.96196	0.497476	0.248738	+	0.968571i	$0.419984\pi$
$402$	22.7300	1.13367
$403$	−35.9991	−1.79324
$404$	53.2569	2.64963
$405$	10.1084	0.502288
$406$	98.6516	4.89600
$407$	−6.05151	−0.299962
$408$	−91.6353	−4.53662
$409$	−12.7583	−0.630858	−0.315429	−	0.948949i	$-0.602148\pi$
$409$	−12.7583	−0.630858	−0.315429	+	0.948949i	$0.602148\pi$
$410$	24.4637	1.20817
$411$	16.6068	0.819154
$412$	−4.99969	−0.246317
$413$	35.1675	1.73048
$414$	2.07294	0.101879
$415$	−7.75506	−0.380681
$416$	−71.1940	−3.49057
$417$	38.5185	1.88626
$418$	−7.09916	−0.347231
$419$	−36.2232	−1.76962	−0.884810	−	0.465952i	$-0.845712\pi$
$419$	−36.2232	−1.76962	−0.884810	+	0.465952i	$0.845712\pi$
$420$	−45.0549	−2.19846
$421$	−3.48655	−0.169924	−0.0849620	−	0.996384i	$-0.527077\pi$
$421$	−3.48655	−0.169924	−0.0849620	+	0.996384i	$0.527077\pi$
$422$	−72.1316	−3.51131
$423$	−4.02189	−0.195551
$424$	32.1517	1.56143
$425$	5.84507	0.283527
$426$	−22.3122	−1.08103
$427$	23.0817	1.11700
$428$	54.3512	2.62716
$429$	−5.55013	−0.267963
$430$	24.8890	1.20025
$431$	4.69783	0.226287	0.113143	−	0.993579i	$-0.463908\pi$
$431$	4.69783	0.226287	0.113143	+	0.993579i	$0.463908\pi$
$432$	−58.6406	−2.82135
$433$	19.5871	0.941298	0.470649	−	0.882321i	$-0.344020\pi$
$433$	19.5871	0.941298	0.470649	+	0.882321i	$0.344020\pi$
$434$	102.381	4.91444
$435$	14.4933	0.694899
$436$	−2.72500	−0.130504
$437$	7.04581	0.337047
$438$	−56.5290	−2.70106
$439$	15.6432	0.746608	0.373304	−	0.927709i	$-0.378225\pi$
$439$	15.6432	0.746608	0.373304	+	0.927709i	$0.378225\pi$
$440$	−5.71921	−0.272653
$441$	6.55821	0.312296
$442$	−69.3536	−3.29882
$443$	−9.94490	−0.472496	−0.236248	−	0.971693i	$-0.575918\pi$
$443$	−9.94490	−0.472496	−0.236248	+	0.971693i	$0.575918\pi$
$444$	85.6337	4.06399
$445$	1.21619	0.0576530
$446$	1.01674	0.0481438
$447$	2.41277	0.114120
$448$	86.3397	4.07917
$449$	−28.6860	−1.35377	−0.676887	−	0.736087i	$-0.736672\pi$
$449$	−28.6860	−1.35377	−0.676887	+	0.736087i	$0.736672\pi$
$450$	−1.15486	−0.0544407
$451$	−6.17734	−0.290880
$452$	−34.8418	−1.63882
$453$	−32.4453	−1.52441
$454$	−7.54800	−0.354245
$455$	−20.8886	−0.979271
$456$	61.5386	2.88181
$457$	−34.5092	−1.61427	−0.807136	−	0.590366i	$-0.798984\pi$
$457$	−34.5092	−1.61427	−0.807136	+	0.590366i	$0.798984\pi$
$458$	9.02026	0.421489
$459$	−27.8105	−1.29808
$460$	9.26617	0.432037
$461$	21.4960	1.00117	0.500584	−	0.865688i	$-0.333119\pi$
$461$	21.4960	1.00117	0.500584	+	0.865688i	$0.333119\pi$
$462$	15.7845	0.734362
$463$	0.807596	0.0375322	0.0187661	−	0.999824i	$-0.494026\pi$
$463$	0.807596	0.0375322	0.0187661	+	0.999824i	$0.494026\pi$
$464$	−96.4277	−4.47654
$465$	15.0412	0.697517
$466$	−32.1142	−1.48766
$467$	3.52815	0.163263	0.0816317	−	0.996663i	$-0.473987\pi$
$467$	3.52815	0.163263	0.0816317	+	0.996663i	$0.473987\pi$
$468$	9.87645	0.456539
$469$	−21.6016	−0.997467
$470$	−24.9432	−1.15055
$471$	−37.6126	−1.73310
$472$	−63.1708	−2.90767
$473$	−6.28474	−0.288973
$474$	60.3324	2.77116
$475$	−3.92531	−0.180106
$476$	142.164	6.51606
$477$	−1.63937	−0.0750618
$478$	0.0229664	0.00105046
$479$	6.82551	0.311866	0.155933	−	0.987768i	$-0.450162\pi$
$479$	6.82551	0.311866	0.155933	+	0.987768i	$0.450162\pi$
$480$	29.7463	1.35773
$481$	39.7019	1.81025
$482$	−71.1907	−3.24265
$483$	−15.6659	−0.712823
$484$	−54.4278	−2.47399
$485$	−12.0444	−0.546906
$486$	11.9127	0.540371
$487$	8.26194	0.374384	0.187192	−	0.982323i	$-0.440061\pi$
$487$	8.26194	0.374384	0.187192	+	0.982323i	$0.440061\pi$
$488$	−41.4613	−1.87686
$489$	−17.8678	−0.808009
$490$	40.6732	1.83743
$491$	−29.6477	−1.33798	−0.668990	−	0.743271i	$-0.733273\pi$
$491$	−29.6477	−1.33798	−0.668990	+	0.743271i	$0.733273\pi$
$492$	87.4143	3.94094
$493$	−45.7311	−2.05963
$494$	46.5751	2.09551
$495$	0.291615	0.0131071
$496$	−100.073	−4.49341
$497$	21.2045	0.951151
$498$	−38.4464	−1.72282
$499$	−11.3170	−0.506618	−0.253309	−	0.967385i	$-0.581519\pi$
$499$	−11.3170	−0.506618	−0.253309	+	0.967385i	$0.581519\pi$
$500$	−5.16230	−0.230865
$501$	21.5427	0.962455
$502$	27.5357	1.22898
$503$	36.2856	1.61789	0.808947	−	0.587882i	$-0.200038\pi$
$503$	36.2856	1.61789	0.808947	+	0.587882i	$0.200038\pi$
$504$	−17.2064	−0.766432
$505$	−10.3165	−0.459078
$506$	−3.24630	−0.144316
$507$	12.3308	0.547630
$508$	105.420	4.67724
$509$	14.8868	0.659847	0.329924	−	0.944008i	$-0.392977\pi$
$509$	14.8868	0.659847	0.329924	+	0.944008i	$0.392977\pi$
$510$	28.9774	1.28314
$511$	53.7226	2.37655
$512$	10.7014	0.472941
$513$	18.6764	0.824584
$514$	−53.9676	−2.38041
$515$	0.968500	0.0426772
$516$	88.9340	3.91510
$517$	6.29843	0.277005
$518$	−112.912	−4.96106
$519$	−19.1630	−0.841164
$520$	37.5218	1.64544
$521$	0.445552	0.0195200	0.00975999	−	0.999952i	$-0.496893\pi$
$521$	0.445552	0.0195200	0.00975999	+	0.999952i	$0.496893\pi$
$522$	9.03551	0.395474
$523$	−10.6506	−0.465720	−0.232860	−	0.972510i	$-0.574808\pi$
$523$	−10.6506	−0.465720	−0.232860	+	0.972510i	$0.574808\pi$
$524$	59.7269	2.60918
$525$	8.72768	0.380907
$526$	26.7441	1.16610
$527$	−47.4599	−2.06739
$528$	−15.4287	−0.671447
$529$	−19.7781	−0.859917
$530$	−10.1672	−0.441634
$531$	3.22099	0.139779
$532$	−95.4714	−4.13921
$533$	40.5274	1.75544
$534$	6.02937	0.260916
$535$	−10.5285	−0.455186
$536$	38.8025	1.67601
$537$	17.6669	0.762384
$538$	−28.5611	−1.23136
$539$	−10.2704	−0.442378
$540$	24.5619	1.05698
$541$	−17.8185	−0.766076	−0.383038	−	0.923733i	$-0.625122\pi$
$541$	−17.8185	−0.766076	−0.383038	+	0.923733i	$0.625122\pi$
$542$	45.4720	1.95319
$543$	15.5184	0.665957
$544$	−93.8597	−4.02420
$545$	0.527865	0.0226112
$546$	−103.557	−4.43182
$547$	19.8733	0.849721	0.424861	−	0.905259i	$-0.360323\pi$
$547$	19.8733	0.849721	0.424861	+	0.905259i	$0.360323\pi$
$548$	46.2793	1.97695
$549$	2.11406	0.0902258
$550$	1.80856	0.0771172
$551$	30.7112	1.30834
$552$	28.1404	1.19773
$553$	−57.3371	−2.43822
$554$	78.2258	3.32350
$555$	−16.5883	−0.704133
$556$	107.342	4.55231
$557$	31.7650	1.34593	0.672964	−	0.739676i	$-0.265021\pi$
$557$	31.7650	1.34593	0.672964	+	0.739676i	$0.265021\pi$
$558$	9.37709	0.396964
$559$	41.2320	1.74393
$560$	−58.0677	−2.45381
$561$	−7.31710	−0.308928
$562$	30.7347	1.29646
$563$	24.8346	1.04665	0.523327	−	0.852132i	$-0.324691\pi$
$563$	24.8346	1.04665	0.523327	+	0.852132i	$0.324691\pi$
$564$	−89.1278	−3.75296
$565$	6.74928	0.283944
$566$	−17.1880	−0.722467
$567$	−47.6251	−2.00007
$568$	−38.0892	−1.59819
$569$	−14.8874	−0.624113	−0.312056	−	0.950064i	$-0.601018\pi$
$569$	−14.8874	−0.624113	−0.312056	+	0.950064i	$0.601018\pi$
$570$	−19.4601	−0.815092
$571$	−0.178772	−0.00748138	−0.00374069	−	0.999993i	$-0.501191\pi$
$571$	−0.178772	−0.00748138	−0.00374069	+	0.999993i	$0.501191\pi$
$572$	−15.4669	−0.646704
$573$	4.23263	0.176821
$574$	−115.260	−4.81084
$575$	−1.79497	−0.0748553
$576$	7.90786	0.329494
$577$	−23.9515	−0.997112	−0.498556	−	0.866858i	$-0.666136\pi$
$577$	−23.9515	−0.997112	−0.498556	+	0.866858i	$0.666136\pi$
$578$	−45.9372	−1.91074
$579$	−27.9249	−1.16052
$580$	40.3893	1.67707
$581$	36.5377	1.51584
$582$	−59.7109	−2.47510
$583$	2.56732	0.106328
$584$	−96.5010	−3.99324
$585$	−1.91319	−0.0791005
$586$	31.8172	1.31436
$587$	36.2294	1.49535	0.747674	−	0.664066i	$-0.231171\pi$
$587$	36.2294	1.49535	0.747674	+	0.664066i	$0.231171\pi$
$588$	145.335	5.99349
$589$	31.8722	1.31327
$590$	19.9762	0.822406
$591$	−4.66120	−0.191736
$592$	110.366	4.53603
$593$	−19.6228	−0.805811	−0.402905	−	0.915242i	$-0.632000\pi$
$593$	−19.6228	−0.805811	−0.402905	+	0.915242i	$0.632000\pi$
$594$	−8.60502	−0.353068
$595$	−27.5388	−1.12898
$596$	6.72382	0.275418
$597$	29.5442	1.20917
$598$	21.2979	0.870935
$599$	45.0413	1.84034	0.920170	−	0.391520i	$-0.128051\pi$
$599$	45.0413	1.84034	0.920170	+	0.391520i	$0.128051\pi$
$600$	−15.6774	−0.640026
$601$	30.5511	1.24621	0.623103	−	0.782140i	$-0.285872\pi$
$601$	30.5511	1.24621	0.623103	+	0.782140i	$0.285872\pi$
$602$	−117.263	−4.77930
$603$	−1.97849	−0.0805703
$604$	−90.4173	−3.67903
$605$	10.5433	0.428647
$606$	−51.1448	−2.07762
$607$	−37.4858	−1.52150	−0.760751	−	0.649044i	$-0.775169\pi$
$607$	−37.4858	−1.52150	−0.760751	+	0.649044i	$0.775169\pi$
$608$	63.0324	2.55630
$609$	−68.2844	−2.76702
$610$	13.1111	0.530853
$611$	−41.3218	−1.67170
$612$	13.0208	0.526334
$613$	−2.45374	−0.0991055	−0.0495527	−	0.998772i	$-0.515780\pi$
$613$	−2.45374	−0.0991055	−0.0495527	+	0.998772i	$0.515780\pi$
$614$	−77.4206	−3.12444
$615$	−16.9332	−0.682812
$616$	26.9458	1.08568
$617$	−6.31471	−0.254221	−0.127110	−	0.991889i	$-0.540570\pi$
$617$	−6.31471	−0.254221	−0.127110	+	0.991889i	$0.540570\pi$
$618$	4.80141	0.193141
$619$	43.5017	1.74848	0.874240	−	0.485494i	$-0.161360\pi$
$619$	43.5017	1.74848	0.874240	+	0.485494i	$0.161360\pi$
$620$	41.9161	1.68339
$621$	8.54035	0.342712
$622$	−40.1606	−1.61029
$623$	−5.73004	−0.229569
$624$	101.222	4.05213
$625$	1.00000	0.0400000
$626$	70.5910	2.82138
$627$	4.91388	0.196241
$628$	−104.817	−4.18267
$629$	52.3416	2.08700
$630$	5.44109	0.216778
$631$	−6.56203	−0.261230	−0.130615	−	0.991433i	$-0.541695\pi$
$631$	−6.56203	−0.261230	−0.130615	+	0.991433i	$0.541695\pi$
$632$	102.994	4.09687
$633$	49.9278	1.98445
$634$	52.3641	2.07964
$635$	−20.4211	−0.810385
$636$	−36.3297	−1.44056
$637$	67.3806	2.66972
$638$	−14.1500	−0.560202
$639$	1.94212	0.0768291
$640$	16.9276	0.669123
$641$	−1.53339	−0.0605654	−0.0302827	−	0.999541i	$-0.509641\pi$
$641$	−1.53339	−0.0605654	−0.0302827	+	0.999541i	$0.509641\pi$
$642$	−52.1958	−2.06000
$643$	−20.7533	−0.818430	−0.409215	−	0.912438i	$-0.634197\pi$
$643$	−20.7533	−0.818430	−0.409215	+	0.912438i	$0.634197\pi$
$644$	−43.6572	−1.72033
$645$	−17.2276	−0.678335
$646$	61.4031	2.41587
$647$	−11.3289	−0.445386	−0.222693	−	0.974889i	$-0.571485\pi$
$647$	−11.3289	−0.445386	−0.222693	+	0.974889i	$0.571485\pi$
$648$	85.5481	3.36065
$649$	−5.04420	−0.198002
$650$	−11.8653	−0.465397
$651$	−70.8658	−2.77745
$652$	−49.7933	−1.95006
$653$	1.98573	0.0777075	0.0388537	−	0.999245i	$-0.487629\pi$
$653$	1.98573	0.0777075	0.0388537	+	0.999245i	$0.487629\pi$
$654$	2.61693	0.102330
$655$	−11.5698	−0.452070
$656$	112.661	4.39868
$657$	4.92046	0.191965
$658$	117.519	4.58137
$659$	34.9789	1.36258	0.681292	−	0.732012i	$-0.261419\pi$
$659$	34.9789	1.36258	0.681292	+	0.732012i	$0.261419\pi$
$660$	6.46239	0.251548
$661$	−37.2105	−1.44732	−0.723660	−	0.690156i	$-0.757542\pi$
$661$	−37.2105	−1.44732	−0.723660	+	0.690156i	$0.757542\pi$
$662$	6.37275	0.247684
$663$	48.0050	1.86436
$664$	−65.6320	−2.54701
$665$	18.4940	0.717165
$666$	−10.3416	−0.400729
$667$	14.0436	0.543771
$668$	60.0343	2.32280
$669$	−0.703761	−0.0272090
$670$	−12.2703	−0.474044
$671$	−3.31070	−0.127808
$672$	−140.148	−5.40635
$673$	42.0955	1.62266	0.811330	−	0.584588i	$-0.198744\pi$
$673$	42.0955	1.62266	0.811330	+	0.584588i	$0.198744\pi$
$674$	−47.6589	−1.83575
$675$	−4.75794	−0.183133
$676$	34.3630	1.32165
$677$	50.2204	1.93013	0.965063	−	0.262018i	$-0.0843881\pi$
$677$	50.2204	1.93013	0.965063	+	0.262018i	$0.0843881\pi$
$678$	33.4601	1.28503
$679$	56.7465	2.17773
$680$	49.4674	1.89699
$681$	5.22455	0.200205
$682$	−14.6849	−0.562313
$683$	−17.0538	−0.652546	−0.326273	−	0.945276i	$-0.605793\pi$
$683$	−17.0538	−0.652546	−0.326273	+	0.945276i	$0.605793\pi$
$684$	−8.74424	−0.334344
$685$	−8.96485	−0.342529
$686$	−103.367	−3.94656
$687$	−6.24362	−0.238209
$688$	114.620	4.36984
$689$	−16.8433	−0.641679
$690$	−8.89870	−0.338768
$691$	50.1940	1.90947	0.954735	−	0.297457i	$-0.0961385\pi$
$691$	50.1940	1.90947	0.954735	+	0.297457i	$0.0961385\pi$
$692$	−53.4029	−2.03007
$693$	−1.37393	−0.0521914
$694$	78.9074	2.99528
$695$	−20.7934	−0.788739
$696$	122.658	4.64934
$697$	53.4299	2.02380
$698$	75.6495	2.86338
$699$	22.2287	0.840768
$700$	24.3220	0.919284
$701$	−23.8826	−0.902032	−0.451016	−	0.892516i	$-0.648938\pi$
$701$	−23.8826	−0.902032	−0.451016	+	0.892516i	$0.648938\pi$
$702$	56.4545	2.13074
$703$	−35.1505	−1.32573
$704$	−12.3840	−0.466740
$705$	17.2651	0.650242
$706$	23.1060	0.869607
$707$	48.6057	1.82801
$708$	71.3794	2.68260
$709$	−22.1085	−0.830302	−0.415151	−	0.909753i	$-0.636271\pi$
$709$	−22.1085	−0.830302	−0.415151	+	0.909753i	$0.636271\pi$
$710$	12.0448	0.452032
$711$	−5.25151	−0.196947
$712$	10.2928	0.385738
$713$	14.5745	0.545820
$714$	−136.526	−5.10935
$715$	2.99612	0.112049
$716$	49.2335	1.83994
$717$	−0.0158968	−0.000593677 0
$718$	39.4105	1.47079
$719$	−11.0672	−0.412737	−0.206368	−	0.978474i	$-0.566165\pi$
$719$	−11.0672	−0.412737	−0.206368	+	0.978474i	$0.566165\pi$
$720$	−5.31842	−0.198206
$721$	−4.56304	−0.169937
$722$	9.61284	0.357753
$723$	49.2765	1.83261
$724$	43.2460	1.60723
$725$	−7.82389	−0.290572
$726$	52.2694	1.93990
$727$	4.05166	0.150268	0.0751339	−	0.997173i	$-0.476062\pi$
$727$	4.05166	0.150268	0.0751339	+	0.997173i	$0.476062\pi$
$728$	−176.782	−6.55199
$729$	22.0794	0.817755
$730$	30.5160	1.12945
$731$	54.3588	2.01053
$732$	46.8490	1.73159
$733$	−25.9253	−0.957571	−0.478786	−	0.877932i	$-0.658923\pi$
$733$	−25.9253	−0.957571	−0.478786	+	0.877932i	$0.658923\pi$
$734$	−38.2687	−1.41253
$735$	−28.1530	−1.03844
$736$	28.8235	1.06245
$737$	3.09839	0.114131
$738$	−10.5566	−0.388595
$739$	4.93273	0.181453	0.0907267	−	0.995876i	$-0.471081\pi$
$739$	4.93273	0.181453	0.0907267	+	0.995876i	$0.471081\pi$
$740$	−46.2276	−1.69936
$741$	−32.2382	−1.18430
$742$	47.9023	1.75855
$743$	−16.7351	−0.613952	−0.306976	−	0.951717i	$-0.599317\pi$
$743$	−16.7351	−0.613952	−0.306976	+	0.951717i	$0.599317\pi$
$744$	127.295	4.66686
$745$	−1.30248	−0.0477193
$746$	−86.6959	−3.17416
$747$	3.34649	0.122442
$748$	−20.3910	−0.745570
$749$	49.6045	1.81251
$750$	4.95758	0.181025
$751$	43.3539	1.58201	0.791003	−	0.611813i	$-0.209559\pi$
$751$	43.3539	1.58201	0.791003	+	0.611813i	$0.209559\pi$
$752$	−114.870	−4.18886
$753$	−19.0596	−0.694570
$754$	92.8330	3.38078
$755$	17.5149	0.637433
$756$	−115.723	−4.20879
$757$	−31.3120	−1.13805	−0.569027	−	0.822319i	$-0.692680\pi$
$757$	−31.3120	−1.13805	−0.569027	+	0.822319i	$0.692680\pi$
$758$	17.3958	0.631842
$759$	2.24702	0.0815615
$760$	−33.2204	−1.20503
$761$	−46.6450	−1.69088	−0.845440	−	0.534070i	$-0.820662\pi$
$761$	−46.6450	−1.69088	−0.845440	+	0.534070i	$0.820662\pi$
$762$	−101.239	−3.66750
$763$	−2.48701	−0.0900359
$764$	11.7953	0.426740
$765$	−2.52228	−0.0911932
$766$	−28.9842	−1.04724
$767$	33.0933	1.19493
$768$	16.0265	0.578308
$769$	−15.7633	−0.568441	−0.284220	−	0.958759i	$-0.591735\pi$
$769$	−15.7633	−0.568441	−0.284220	+	0.958759i	$0.591735\pi$
$770$	−8.52095	−0.307074
$771$	37.3551	1.34531
$772$	−77.8201	−2.80081
$773$	−35.9094	−1.29157	−0.645786	−	0.763519i	$-0.723470\pi$
$773$	−35.9094	−1.29157	−0.645786	+	0.763519i	$0.723470\pi$
$774$	−10.7402	−0.386047
$775$	−8.11966	−0.291667
$776$	−101.933	−3.65917
$777$	78.1549	2.80379
$778$	28.2946	1.01441
$779$	−35.8814	−1.28559
$780$	−42.3975	−1.51807
$781$	−3.04144	−0.108831
$782$	28.0784	1.00408
$783$	37.2256	1.33033
$784$	187.310	6.68964
$785$	20.3044	0.724694
$786$	−57.3583	−2.04590
$787$	−7.74031	−0.275912	−0.137956	−	0.990438i	$-0.544053\pi$
$787$	−7.74031	−0.275912	−0.137956	+	0.990438i	$0.544053\pi$
$788$	−12.9897	−0.462738
$789$	−18.5117	−0.659033
$790$	−32.5692	−1.15876
$791$	−31.7990	−1.13064
$792$	2.46797	0.0876956
$793$	21.7203	0.771311
$794$	69.5358	2.46773
$795$	7.03749	0.249594
$796$	82.3328	2.91821
$797$	47.9208	1.69744	0.848722	−	0.528840i	$-0.177373\pi$
$797$	47.9208	1.69744	0.848722	+	0.528840i	$0.177373\pi$
$798$	91.6853	3.24562
$799$	−54.4773	−1.92727
$800$	−16.0579	−0.567734
$801$	−0.524815	−0.0185434
$802$	−26.6607	−0.941421
$803$	−7.70563	−0.271926
$804$	−43.8447	−1.54628
$805$	8.45691	0.298067
$806$	96.3424	3.39352
$807$	19.7694	0.695915
$808$	−87.3096	−3.07154
$809$	−18.3014	−0.643444	−0.321722	−	0.946834i	$-0.604262\pi$
$809$	−18.3014	−0.643444	−0.321722	+	0.946834i	$0.604262\pi$
$810$	−27.0525	−0.950527
$811$	50.5396	1.77469	0.887343	−	0.461110i	$-0.152549\pi$
$811$	50.5396	1.77469	0.887343	+	0.461110i	$0.152549\pi$
$812$	−190.292	−6.67796
$813$	−31.4747	−1.10387
$814$	16.1953	0.567647
$815$	9.64555	0.337869
$816$	133.448	4.67161
$817$	−36.5052	−1.27716
$818$	34.1444	1.19383
$819$	9.01390	0.314971
$820$	−47.1888	−1.64790
$821$	−41.9763	−1.46498	−0.732492	−	0.680776i	$-0.761643\pi$
$821$	−41.9763	−1.46498	−0.732492	+	0.680776i	$0.761643\pi$
$822$	−44.4440	−1.55016
$823$	35.9852	1.25437	0.627183	−	0.778872i	$-0.284208\pi$
$823$	35.9852	1.25437	0.627183	+	0.778872i	$0.284208\pi$
$824$	8.19652	0.285539
$825$	−1.25184	−0.0435836
$826$	−94.1169	−3.27475
$827$	9.13514	0.317660	0.158830	−	0.987306i	$-0.449228\pi$
$827$	9.13514	0.317660	0.158830	+	0.987306i	$0.449228\pi$
$828$	−3.99856	−0.138960
$829$	−0.665801	−0.0231242	−0.0115621	−	0.999933i	$-0.503680\pi$
$829$	−0.665801	−0.0231242	−0.0115621	+	0.999933i	$0.503680\pi$
$830$	20.7545	0.720398
$831$	−54.1461	−1.87831
$832$	81.2472	2.81674
$833$	88.8323	3.07786
$834$	−103.085	−3.56954
$835$	−11.6294	−0.402451
$836$	13.6938	0.473610
$837$	38.6329	1.33535
$838$	96.9423	3.34882
$839$	27.2851	0.941987	0.470993	−	0.882137i	$-0.343896\pi$
$839$	27.2851	0.941987	0.470993	+	0.882137i	$0.343896\pi$
$840$	73.8633	2.54853
$841$	32.2132	1.11080
$842$	9.33087	0.321563
$843$	−21.2738	−0.732710
$844$	139.137	4.78929
$845$	−6.65653	−0.228992
$846$	10.7636	0.370059
$847$	−49.6744	−1.70683
$848$	−46.8224	−1.60789
$849$	11.8972	0.408310
$850$	−15.6428	−0.536545
$851$	−16.0736	−0.550997
$852$	43.0387	1.47448
$853$	−13.6553	−0.467550	−0.233775	−	0.972291i	$-0.575108\pi$
$853$	−13.6553	−0.467550	−0.233775	+	0.972291i	$0.575108\pi$
$854$	−61.7724	−2.11381
$855$	1.69386	0.0579289
$856$	−89.1037	−3.04550
$857$	19.9725	0.682249	0.341125	−	0.940018i	$-0.389192\pi$
$857$	19.9725	0.682249	0.341125	+	0.940018i	$0.389192\pi$
$858$	14.8535	0.507091
$859$	−33.6286	−1.14739	−0.573697	−	0.819068i	$-0.694491\pi$
$859$	−33.6286	−1.14739	−0.573697	+	0.819068i	$0.694491\pi$
$860$	−48.0092	−1.63710
$861$	79.7800	2.71890
$862$	−12.5726	−0.428223
$863$	−37.9536	−1.29195	−0.645977	−	0.763357i	$-0.723550\pi$
$863$	−37.9536	−1.29195	−0.645977	+	0.763357i	$0.723550\pi$
$864$	76.4027	2.59927
$865$	10.3448	0.351733
$866$	−52.4201	−1.78131
$867$	31.7967	1.07987
$868$	−197.486	−6.70311
$869$	8.22407	0.278983
$870$	−38.7876	−1.31502
$871$	−20.3275	−0.688770
$872$	4.46738	0.151284
$873$	5.19742	0.175906
$874$	−18.8563	−0.637825
$875$	−4.71146	−0.159276
$876$	109.041	3.68415
$877$	−2.63278	−0.0889025	−0.0444513	−	0.999012i	$-0.514154\pi$
$877$	−2.63278	−0.0889025	−0.0444513	+	0.999012i	$0.514154\pi$
$878$	−41.8650	−1.41288
$879$	−22.0231	−0.742822
$880$	8.32885	0.280766
$881$	−3.58025	−0.120622	−0.0603109	−	0.998180i	$-0.519209\pi$
$881$	−3.58025	−0.120622	−0.0603109	+	0.998180i	$0.519209\pi$
$882$	−17.5514	−0.590987
$883$	−14.6350	−0.492509	−0.246254	−	0.969205i	$-0.579200\pi$
$883$	−14.6350	−0.492509	−0.246254	+	0.969205i	$0.579200\pi$
$884$	133.779	4.49946
$885$	−13.8270	−0.464791
$886$	26.6150	0.894149
$887$	4.30941	0.144696	0.0723480	−	0.997379i	$-0.476951\pi$
$887$	4.30941	0.144696	0.0723480	+	0.997379i	$0.476951\pi$
$888$	−140.388	−4.71112
$889$	96.2130	3.22688
$890$	−3.25483	−0.109102
$891$	6.83104	0.228848
$892$	−1.96121	−0.0656663
$893$	36.5848	1.22426
$894$	−6.45717	−0.215960
$895$	−9.53713	−0.318791
$896$	−79.7538	−2.66439
$897$	−14.7419	−0.492218
$898$	76.7708	2.56187
$899$	63.5273	2.11875
$900$	2.22765	0.0742551
$901$	−22.2057	−0.739778
$902$	16.5321	0.550459
$903$	81.1670	2.70107
$904$	57.1199	1.89978
$905$	−8.37727	−0.278470
$906$	86.8316	2.88479
$907$	−24.4175	−0.810770	−0.405385	−	0.914146i	$-0.632863\pi$
$907$	−24.4175	−0.810770	−0.405385	+	0.914146i	$0.632863\pi$
$908$	14.5596	0.483177
$909$	4.45180	0.147657
$910$	55.9030	1.85317
$911$	7.48264	0.247911	0.123955	−	0.992288i	$-0.460442\pi$
$911$	7.48264	0.247911	0.123955	+	0.992288i	$0.460442\pi$
$912$	−89.6183	−2.96756
$913$	−5.24073	−0.173443
$914$	92.3552	3.05484
$915$	−9.07520	−0.300017
$916$	−17.3995	−0.574895
$917$	54.5107	1.80010
$918$	74.4277	2.45648
$919$	18.6941	0.616660	0.308330	−	0.951279i	$-0.400230\pi$
$919$	18.6941	0.616660	0.308330	+	0.951279i	$0.400230\pi$
$920$	−15.1910	−0.500833
$921$	53.5887	1.76581
$922$	−57.5286	−1.89460
$923$	19.9538	0.656787
$924$	−30.4473	−1.00164
$925$	8.95483	0.294433
$926$	−2.16133	−0.0710256
$927$	−0.417930	−0.0137266
$928$	125.635	4.12419
$929$	13.1664	0.431977	0.215989	−	0.976396i	$-0.430703\pi$
$929$	13.1664	0.431977	0.215989	+	0.976396i	$0.430703\pi$
$930$	−40.2539	−1.31998
$931$	−59.6563	−1.95516
$932$	61.9462	2.02912
$933$	27.7982	0.910073
$934$	−9.44221	−0.308959
$935$	3.94999	0.129178
$936$	−16.1915	−0.529236
$937$	−5.87978	−0.192084	−0.0960421	−	0.995377i	$-0.530618\pi$
$937$	−5.87978	−0.192084	−0.0960421	+	0.995377i	$0.530618\pi$
$938$	57.8111	1.88760
$939$	−48.8615	−1.59453
$940$	48.1138	1.56930
$941$	51.7545	1.68715	0.843575	−	0.537011i	$-0.180447\pi$
$941$	51.7545	1.68715	0.843575	+	0.537011i	$0.180447\pi$
$942$	100.661	3.27970
$943$	−16.4079	−0.534313
$944$	91.9952	2.99419
$945$	22.4168	0.729220
$946$	16.8195	0.546850
$947$	6.23180	0.202506	0.101253	−	0.994861i	$-0.467715\pi$
$947$	6.23180	0.202506	0.101253	+	0.994861i	$0.467715\pi$
$948$	−116.377	−3.77975
$949$	50.5540	1.64105
$950$	10.5051	0.340831
$951$	−36.2452	−1.17533
$952$	−233.064	−7.55364
$953$	25.2573	0.818165	0.409083	−	0.912497i	$-0.365849\pi$
$953$	25.2573	0.818165	0.409083	+	0.912497i	$0.365849\pi$
$954$	4.38737	0.142046
$955$	−2.28490	−0.0739375
$956$	−0.0443007	−0.00143279
$957$	9.79428	0.316604
$958$	−18.2668	−0.590172
$959$	42.2375	1.36392
$960$	−33.9468	−1.09563
$961$	34.9288	1.12674
$962$	−106.252	−3.42570
$963$	4.54328	0.146405
$964$	137.322	4.42284
$965$	15.0747	0.485271
$966$	41.9258	1.34894
$967$	0.367181	0.0118077	0.00590387	−	0.999983i	$-0.498121\pi$
$967$	0.367181	0.0118077	0.00590387	+	0.999983i	$0.498121\pi$
$968$	89.2293	2.86794
$969$	−42.5018	−1.36535
$970$	32.2337	1.03496
$971$	−11.9243	−0.382668	−0.191334	−	0.981525i	$-0.561281\pi$
$971$	−11.9243	−0.382668	−0.191334	+	0.981525i	$0.561281\pi$
$972$	−22.9788	−0.737045
$973$	97.9673	3.14069
$974$	−22.1110	−0.708482
$975$	8.21291	0.263024
$976$	60.3798	1.93271
$977$	35.8138	1.14579	0.572893	−	0.819630i	$-0.305821\pi$
$977$	35.8138	1.14579	0.572893	+	0.819630i	$0.305821\pi$
$978$	47.8186	1.52907
$979$	0.821880	0.0262674
$980$	−78.4558	−2.50618
$981$	−0.227786	−0.00727264
$982$	79.3445	2.53199
$983$	2.09230	0.0667339	0.0333669	−	0.999443i	$-0.489377\pi$
$983$	2.09230	0.0667339	0.0333669	+	0.999443i	$0.489377\pi$
$984$	−143.307	−4.56848
$985$	2.51625	0.0801745
$986$	122.388	3.89762
$987$	−81.3439	−2.58920
$988$	−89.8403	−2.85820
$989$	−16.6931	−0.530810
$990$	−0.780435	−0.0248038
$991$	50.4454	1.60245	0.801226	−	0.598362i	$-0.204182\pi$
$991$	50.4454	1.60245	0.801226	+	0.598362i	$0.204182\pi$
$992$	130.385	4.13972
$993$	−4.41107	−0.139981
$994$	−56.7484	−1.79995
$995$	−15.9489	−0.505613
$996$	74.1605	2.34986
$997$	19.5351	0.618683	0.309342	−	0.950951i	$-0.399891\pi$
$997$	19.5351	0.618683	0.309342	+	0.950951i	$0.399891\pi$
$998$	30.2871	0.958720
$999$	−42.6066	−1.34801

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6005.2.a.g.1.6	✓	113

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6005.2.a.g.1.6	✓	113	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:	\( N \)	\(=\)	\( 6005 = 5 \cdot 1201 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6005.a (trivial)

\(f(q)\)	\(=\)	\(q-2.67625 q^{2} +1.85244 q^{3} +5.16230 q^{4} -1.00000 q^{5} -4.95758 q^{6} +4.71146 q^{7} -8.46311 q^{8} +0.431523 q^{9} +O(q^{10})\)	\(q-2.67625 q^{2} +1.85244 q^{3} +5.16230 q^{4} -1.00000 q^{5} -4.95758 q^{6} +4.71146 q^{7} -8.46311 q^{8} +0.431523 q^{9} +2.67625 q^{10} -0.675782 q^{11} +9.56284 q^{12} +4.43357 q^{13} -12.6090 q^{14} -1.85244 q^{15} +12.3248 q^{16} +5.84507 q^{17} -1.15486 q^{18} -3.92531 q^{19} -5.16230 q^{20} +8.72768 q^{21} +1.80856 q^{22} -1.79497 q^{23} -15.6774 q^{24} +1.00000 q^{25} -11.8653 q^{26} -4.75794 q^{27} +24.3220 q^{28} -7.82389 q^{29} +4.95758 q^{30} -8.11966 q^{31} -16.0579 q^{32} -1.25184 q^{33} -15.6428 q^{34} -4.71146 q^{35} +2.22765 q^{36} +8.95483 q^{37} +10.5051 q^{38} +8.21291 q^{39} +8.46311 q^{40} +9.14103 q^{41} -23.3574 q^{42} +9.29996 q^{43} -3.48859 q^{44} -0.431523 q^{45} +4.80378 q^{46} -9.32022 q^{47} +22.8309 q^{48} +15.1978 q^{49} -2.67625 q^{50} +10.8276 q^{51} +22.8874 q^{52} -3.79904 q^{53} +12.7334 q^{54} +0.675782 q^{55} -39.8736 q^{56} -7.27140 q^{57} +20.9387 q^{58} +7.46425 q^{59} -9.56284 q^{60} +4.89906 q^{61} +21.7302 q^{62} +2.03310 q^{63} +18.3255 q^{64} -4.43357 q^{65} +3.35024 q^{66} -4.58490 q^{67} +30.1740 q^{68} -3.32506 q^{69} +12.6090 q^{70} +4.50062 q^{71} -3.65203 q^{72} +11.4025 q^{73} -23.9654 q^{74} +1.85244 q^{75} -20.2637 q^{76} -3.18392 q^{77} -21.9798 q^{78} -12.1697 q^{79} -12.3248 q^{80} -10.1084 q^{81} -24.4637 q^{82} +7.75506 q^{83} +45.0549 q^{84} -5.84507 q^{85} -24.8890 q^{86} -14.4933 q^{87} +5.71921 q^{88} -1.21619 q^{89} +1.15486 q^{90} +20.8886 q^{91} -9.26617 q^{92} -15.0412 q^{93} +24.9432 q^{94} +3.92531 q^{95} -29.7463 q^{96} +12.0444 q^{97} -40.6732 q^{98} -0.291615 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 113 q - 3 q^{2} + 6 q^{3} + 141 q^{4} - 113 q^{5} + 7 q^{6} + 7 q^{7} - 12 q^{8} + 141 q^{9}+O(q^{10}) \) 113 * q - 3 * q^2 + 6 * q^3 + 141 * q^4 - 113 * q^5 + 7 * q^6 + 7 * q^7 - 12 * q^8 + 141 * q^9	\( 113 q - 3 q^{2} + 6 q^{3} + 141 q^{4} - 113 q^{5} + 7 q^{6} + 7 q^{7} - 12 q^{8} + 141 q^{9} + 3 q^{10} + 38 q^{11} - 4 q^{12} + 17 q^{13} + 23 q^{14} - 6 q^{15} + 193 q^{16} - 11 q^{17} - 3 q^{18} + 76 q^{19} - 141 q^{20} + 19 q^{21} + 41 q^{22} - 28 q^{23} + 29 q^{24} + 113 q^{25} + 21 q^{26} + 18 q^{27} + 29 q^{28} + 24 q^{29} - 7 q^{30} + 59 q^{31} - 22 q^{32} + 3 q^{33} + 55 q^{34} - 7 q^{35} + 232 q^{36} + 41 q^{37} - 6 q^{38} + 55 q^{39} + 12 q^{40} + 24 q^{41} + 17 q^{42} + 136 q^{43} + 85 q^{44} - 141 q^{45} + 84 q^{46} - 91 q^{47} - 19 q^{48} + 198 q^{49} - 3 q^{50} + 97 q^{51} + 45 q^{52} + 9 q^{53} + 54 q^{54} - 38 q^{55} + 98 q^{56} + 22 q^{57} + 69 q^{58} + 59 q^{59} + 4 q^{60} + 51 q^{61} - 30 q^{62} - 22 q^{63} + 298 q^{64} - 17 q^{65} + 76 q^{66} + 201 q^{67} - 34 q^{68} + 42 q^{69} - 23 q^{70} + 69 q^{71} - 7 q^{72} + 30 q^{73} + 35 q^{74} + 6 q^{75} + 170 q^{76} - 37 q^{77} - 11 q^{78} + 143 q^{79} - 193 q^{80} + 197 q^{81} + 55 q^{82} - 15 q^{83} + 83 q^{84} + 11 q^{85} + 78 q^{86} - 51 q^{87} + 113 q^{88} + 53 q^{89} + 3 q^{90} + 217 q^{91} - 40 q^{92} + 36 q^{93} + 81 q^{94} - 76 q^{95} + 66 q^{96} + 63 q^{97} - 62 q^{98} + 184 q^{99}+O(q^{100}) \) 113 * q - 3 * q^2 + 6 * q^3 + 141 * q^4 - 113 * q^5 + 7 * q^6 + 7 * q^7 - 12 * q^8 + 141 * q^9 + 3 * q^10 + 38 * q^11 - 4 * q^12 + 17 * q^13 + 23 * q^14 - 6 * q^15 + 193 * q^16 - 11 * q^17 - 3 * q^18 + 76 * q^19 - 141 * q^20 + 19 * q^21 + 41 * q^22 - 28 * q^23 + 29 * q^24 + 113 * q^25 + 21 * q^26 + 18 * q^27 + 29 * q^28 + 24 * q^29 - 7 * q^30 + 59 * q^31 - 22 * q^32 + 3 * q^33 + 55 * q^34 - 7 * q^35 + 232 * q^36 + 41 * q^37 - 6 * q^38 + 55 * q^39 + 12 * q^40 + 24 * q^41 + 17 * q^42 + 136 * q^43 + 85 * q^44 - 141 * q^45 + 84 * q^46 - 91 * q^47 - 19 * q^48 + 198 * q^49 - 3 * q^50 + 97 * q^51 + 45 * q^52 + 9 * q^53 + 54 * q^54 - 38 * q^55 + 98 * q^56 + 22 * q^57 + 69 * q^58 + 59 * q^59 + 4 * q^60 + 51 * q^61 - 30 * q^62 - 22 * q^63 + 298 * q^64 - 17 * q^65 + 76 * q^66 + 201 * q^67 - 34 * q^68 + 42 * q^69 - 23 * q^70 + 69 * q^71 - 7 * q^72 + 30 * q^73 + 35 * q^74 + 6 * q^75 + 170 * q^76 - 37 * q^77 - 11 * q^78 + 143 * q^79 - 193 * q^80 + 197 * q^81 + 55 * q^82 - 15 * q^83 + 83 * q^84 + 11 * q^85 + 78 * q^86 - 51 * q^87 + 113 * q^88 + 53 * q^89 + 3 * q^90 + 217 * q^91 - 40 * q^92 + 36 * q^93 + 81 * q^94 - 76 * q^95 + 66 * q^96 + 63 * q^97 - 62 * q^98 + 184 * q^99

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