LMFDB - Embedded newform 6005.2.a.g.1.4

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			1.4
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)

$f(q)$	$=$	$q-2.77794 q^{2} +1.80495 q^{3} +5.71693 q^{4} -1.00000 q^{5} -5.01404 q^{6} -4.50639 q^{7} -10.3254 q^{8} +0.257853 q^{9} +O(q^{10})$	\(q-2.77794 q^{2} +1.80495 q^{3} +5.71693 q^{4} -1.00000 q^{5} -5.01404 q^{6} -4.50639 q^{7} -10.3254 q^{8} +0.257853 q^{9} +2.77794 q^{10} -3.82146 q^{11} +10.3188 q^{12} +3.22881 q^{13} +12.5185 q^{14} -1.80495 q^{15} +17.2494 q^{16} -6.76827 q^{17} -0.716300 q^{18} -2.98224 q^{19} -5.71693 q^{20} -8.13381 q^{21} +10.6158 q^{22} -8.72908 q^{23} -18.6369 q^{24} +1.00000 q^{25} -8.96943 q^{26} -4.94944 q^{27} -25.7627 q^{28} -9.38365 q^{29} +5.01404 q^{30} -5.34477 q^{31} -27.2671 q^{32} -6.89755 q^{33} +18.8018 q^{34} +4.50639 q^{35} +1.47413 q^{36} -8.66468 q^{37} +8.28446 q^{38} +5.82785 q^{39} +10.3254 q^{40} -1.61256 q^{41} +22.5952 q^{42} +4.89625 q^{43} -21.8470 q^{44} -0.257853 q^{45} +24.2488 q^{46} +6.22302 q^{47} +31.1344 q^{48} +13.3075 q^{49} -2.77794 q^{50} -12.2164 q^{51} +18.4589 q^{52} -4.17004 q^{53} +13.7492 q^{54} +3.82146 q^{55} +46.5302 q^{56} -5.38280 q^{57} +26.0672 q^{58} +5.43215 q^{59} -10.3188 q^{60} +0.0769916 q^{61} +14.8474 q^{62} -1.16199 q^{63} +41.2473 q^{64} -3.22881 q^{65} +19.1610 q^{66} +3.13180 q^{67} -38.6937 q^{68} -15.7556 q^{69} -12.5185 q^{70} -2.79104 q^{71} -2.66244 q^{72} -13.6218 q^{73} +24.0699 q^{74} +1.80495 q^{75} -17.0492 q^{76} +17.2210 q^{77} -16.1894 q^{78} +9.88436 q^{79} -17.2494 q^{80} -9.70707 q^{81} +4.47960 q^{82} -15.7777 q^{83} -46.5005 q^{84} +6.76827 q^{85} -13.6015 q^{86} -16.9371 q^{87} +39.4581 q^{88} +11.9104 q^{89} +0.716300 q^{90} -14.5503 q^{91} -49.9035 q^{92} -9.64706 q^{93} -17.2872 q^{94} +2.98224 q^{95} -49.2158 q^{96} +0.645444 q^{97} -36.9674 q^{98} -0.985376 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.77794	−1.96430	−0.982149	−	0.188105i	$-0.939765\pi$
$2$	−2.77794	−1.96430	−0.982149	+	0.188105i	$0.939765\pi$
$3$	1.80495	1.04209	0.521045	−	0.853529i	$-0.325542\pi$
$3$	1.80495	1.04209	0.521045	+	0.853529i	$0.325542\pi$
$4$	5.71693	2.85847
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	−5.01404	−2.04697
$7$	−4.50639	−1.70325	−0.851627	−	0.524148i	$-0.824384\pi$
$7$	−4.50639	−1.70325	−0.851627	+	0.524148i	$0.824384\pi$
$8$	−10.3254	−3.65058
$9$	0.257853	0.0859511
$10$	2.77794	0.878461
$11$	−3.82146	−1.15221	−0.576107	−	0.817374i	$-0.695429\pi$
$11$	−3.82146	−1.15221	−0.576107	+	0.817374i	$0.695429\pi$
$12$	10.3188	2.97878
$13$	3.22881	0.895511	0.447756	−	0.894156i	$-0.352223\pi$
$13$	3.22881	0.895511	0.447756	+	0.894156i	$0.352223\pi$
$14$	12.5185	3.34570
$15$	−1.80495	−0.466037
$16$	17.2494	4.31236
$17$	−6.76827	−1.64155	−0.820774	−	0.571254i	$-0.806457\pi$
$17$	−6.76827	−1.64155	−0.820774	+	0.571254i	$0.806457\pi$
$18$	−0.716300	−0.168834
$19$	−2.98224	−0.684172	−0.342086	−	0.939669i	$-0.611133\pi$
$19$	−2.98224	−0.684172	−0.342086	+	0.939669i	$0.611133\pi$
$20$	−5.71693	−1.27834
$21$	−8.13381	−1.77494
$22$	10.6158	2.26329
$23$	−8.72908	−1.82014	−0.910069	−	0.414456i	$-0.863972\pi$
$23$	−8.72908	−1.82014	−0.910069	+	0.414456i	$0.863972\pi$
$24$	−18.6369	−3.80423
$25$	1.00000	0.200000
$26$	−8.96943	−1.75905
$27$	−4.94944	−0.952521
$28$	−25.7627	−4.86869
$29$	−9.38365	−1.74250	−0.871250	−	0.490839i	$-0.836690\pi$
$29$	−9.38365	−1.74250	−0.871250	+	0.490839i	$0.836690\pi$
$30$	5.01404	0.915435
$31$	−5.34477	−0.959949	−0.479975	−	0.877282i	$-0.659354\pi$
$31$	−5.34477	−0.959949	−0.479975	+	0.877282i	$0.659354\pi$
$32$	−27.2671	−4.82018
$33$	−6.89755	−1.20071
$34$	18.8018	3.22449
$35$	4.50639	0.761718
$36$	1.47413	0.245688
$37$	−8.66468	−1.42446	−0.712232	−	0.701944i	$-0.752316\pi$
$37$	−8.66468	−1.42446	−0.712232	+	0.701944i	$0.752316\pi$
$38$	8.28446	1.34392
$39$	5.82785	0.933203
$40$	10.3254	1.63259
$41$	−1.61256	−0.251840	−0.125920	−	0.992040i	$-0.540188\pi$
$41$	−1.61256	−0.251840	−0.125920	+	0.992040i	$0.540188\pi$
$42$	22.5952	3.48652
$43$	4.89625	0.746672	0.373336	−	0.927696i	$-0.378214\pi$
$43$	4.89625	0.746672	0.373336	+	0.927696i	$0.378214\pi$
$44$	−21.8470	−3.29356
$45$	−0.257853	−0.0384385
$46$	24.2488	3.57529
$47$	6.22302	0.907721	0.453860	−	0.891073i	$-0.350046\pi$
$47$	6.22302	0.907721	0.453860	+	0.891073i	$0.350046\pi$
$48$	31.1344	4.49387
$49$	13.3075	1.90107
$50$	−2.77794	−0.392860
$51$	−12.2164	−1.71064
$52$	18.4589	2.55979
$53$	−4.17004	−0.572799	−0.286400	−	0.958110i	$-0.592459\pi$
$53$	−4.17004	−0.572799	−0.286400	+	0.958110i	$0.592459\pi$
$54$	13.7492	1.87103
$55$	3.82146	0.515286
$56$	46.5302	6.21787
$57$	−5.38280	−0.712969
$58$	26.0672	3.42279
$59$	5.43215	0.707206	0.353603	−	0.935396i	$-0.384956\pi$
$59$	5.43215	0.707206	0.353603	+	0.935396i	$0.384956\pi$
$60$	−10.3188	−1.33215
$61$	0.0769916	0.00985777	0.00492888	−	0.999988i	$-0.498431\pi$
$61$	0.0769916	0.00985777	0.00492888	+	0.999988i	$0.498431\pi$
$62$	14.8474	1.88563
$63$	−1.16199	−0.146397
$64$	41.2473	5.15591
$65$	−3.22881	−0.400485
$66$	19.1610	2.35855
$67$	3.13180	0.382611	0.191305	−	0.981531i	$-0.438728\pi$
$67$	3.13180	0.382611	0.191305	+	0.981531i	$0.438728\pi$
$68$	−38.6937	−4.69231
$69$	−15.7556	−1.89675
$70$	−12.5185	−1.49624
$71$	−2.79104	−0.331235	−0.165618	−	0.986190i	$-0.552962\pi$
$71$	−2.79104	−0.331235	−0.165618	+	0.986190i	$0.552962\pi$
$72$	−2.66244	−0.313771
$73$	−13.6218	−1.59431	−0.797154	−	0.603776i	$-0.793662\pi$
$73$	−13.6218	−1.59431	−0.797154	+	0.603776i	$0.793662\pi$
$74$	24.0699	2.79807
$75$	1.80495	0.208418
$76$	−17.0492	−1.95568
$77$	17.2210	1.96251
$78$	−16.1894	−1.83309
$79$	9.88436	1.11208	0.556038	−	0.831157i	$-0.312321\pi$
$79$	9.88436	1.11208	0.556038	+	0.831157i	$0.312321\pi$
$80$	−17.2494	−1.92855
$81$	−9.70707	−1.07856
$82$	4.47960	0.494689
$83$	−15.7777	−1.73183	−0.865914	−	0.500192i	$-0.833263\pi$
$83$	−15.7777	−1.73183	−0.865914	+	0.500192i	$0.833263\pi$
$84$	−46.5005	−5.07362
$85$	6.76827	0.734122
$86$	−13.6015	−1.46669
$87$	−16.9371	−1.81584
$88$	39.4581	4.20625
$89$	11.9104	1.26250	0.631249	−	0.775580i	$-0.282542\pi$
$89$	11.9104	1.26250	0.631249	+	0.775580i	$0.282542\pi$
$90$	0.716300	0.0755047
$91$	−14.5503	−1.52528
$92$	−49.9035	−5.20280
$93$	−9.64706	−1.00035
$94$	−17.2872	−1.78303
$95$	2.98224	0.305971
$96$	−49.2158	−5.02306
$97$	0.645444	0.0655349	0.0327675	−	0.999463i	$-0.489568\pi$
$97$	0.645444	0.0655349	0.0327675	+	0.999463i	$0.489568\pi$
$98$	−36.9674	−3.73428
$99$	−0.985376	−0.0990340
$100$	5.71693	0.571693
$101$	14.1086	1.40385	0.701927	−	0.712249i	$-0.252323\pi$
$101$	14.1086	1.40385	0.701927	+	0.712249i	$0.252323\pi$
$102$	33.9364	3.36021
$103$	10.8010	1.06426	0.532129	−	0.846663i	$-0.321392\pi$
$103$	10.8010	1.06426	0.532129	+	0.846663i	$0.321392\pi$
$104$	−33.3388	−3.26914
$105$	8.13381	0.793779
$106$	11.5841	1.12515
$107$	6.42472	0.621101	0.310550	−	0.950557i	$-0.399487\pi$
$107$	6.42472	0.621101	0.310550	+	0.950557i	$0.399487\pi$
$108$	−28.2956	−2.72275
$109$	1.03244	0.0988900	0.0494450	−	0.998777i	$-0.484255\pi$
$109$	1.03244	0.0988900	0.0494450	+	0.998777i	$0.484255\pi$
$110$	−10.6158	−1.01217
$111$	−15.6393	−1.48442
$112$	−77.7327	−7.34505
$113$	15.7664	1.48318	0.741590	−	0.670853i	$-0.234072\pi$
$113$	15.7664	1.48318	0.741590	+	0.670853i	$0.234072\pi$
$114$	14.9531	1.40048
$115$	8.72908	0.813991
$116$	−53.6457	−4.98088
$117$	0.832560	0.0769702
$118$	−15.0902	−1.38916
$119$	30.5004	2.79597
$120$	18.6369	1.70130
$121$	3.60356	0.327596
$122$	−0.213878	−0.0193636
$123$	−2.91060	−0.262440
$124$	−30.5557	−2.74398
$125$	−1.00000	−0.0894427
$126$	3.22793	0.287566
$127$	−17.1713	−1.52370	−0.761852	−	0.647751i	$-0.775710\pi$
$127$	−17.1713	−1.52370	−0.761852	+	0.647751i	$0.775710\pi$
$128$	−60.0482	−5.30756
$129$	8.83751	0.778099
$130$	8.96943	0.786671
$131$	−1.50253	−0.131277	−0.0656385	−	0.997843i	$-0.520908\pi$
$131$	−1.50253	−0.131277	−0.0656385	+	0.997843i	$0.520908\pi$
$132$	−39.4328	−3.43219
$133$	13.4391	1.16532
$134$	−8.69995	−0.751562
$135$	4.94944	0.425980
$136$	69.8851	5.99260
$137$	10.7618	0.919441	0.459720	−	0.888064i	$-0.347950\pi$
$137$	10.7618	0.919441	0.459720	+	0.888064i	$0.347950\pi$
$138$	43.7680	3.72578
$139$	−0.440600	−0.0373712	−0.0186856	−	0.999825i	$-0.505948\pi$
$139$	−0.440600	−0.0373712	−0.0186856	+	0.999825i	$0.505948\pi$
$140$	25.7627	2.17735
$141$	11.2323	0.945927
$142$	7.75333	0.650645
$143$	−12.3388	−1.03182
$144$	4.44783	0.370652
$145$	9.38365	0.779270
$146$	37.8404	3.13169
$147$	24.0194	1.98109
$148$	−49.5354	−4.07178
$149$	−11.2525	−0.921838	−0.460919	−	0.887442i	$-0.652480\pi$
$149$	−11.2525	−0.921838	−0.460919	+	0.887442i	$0.652480\pi$
$150$	−5.01404	−0.409395
$151$	2.11501	0.172117	0.0860587	−	0.996290i	$-0.472573\pi$
$151$	2.11501	0.172117	0.0860587	+	0.996290i	$0.472573\pi$
$152$	30.7928	2.49763
$153$	−1.74522	−0.141093
$154$	−47.8388	−3.85496
$155$	5.34477	0.429302
$156$	33.3174	2.66753
$157$	−2.33441	−0.186306	−0.0931530	−	0.995652i	$-0.529695\pi$
$157$	−2.33441	−0.186306	−0.0931530	+	0.995652i	$0.529695\pi$
$158$	−27.4581	−2.18445
$159$	−7.52673	−0.596908
$160$	27.2671	2.15565
$161$	39.3366	3.10016
$162$	26.9656	2.11862
$163$	−6.10363	−0.478073	−0.239037	−	0.971011i	$-0.576832\pi$
$163$	−6.10363	−0.478073	−0.239037	+	0.971011i	$0.576832\pi$
$164$	−9.21892	−0.719876
$165$	6.89755	0.536974
$166$	43.8295	3.40183
$167$	−18.0928	−1.40006	−0.700030	−	0.714113i	$-0.746830\pi$
$167$	−18.0928	−1.40006	−0.700030	+	0.714113i	$0.746830\pi$
$168$	83.9849	6.47957
$169$	−2.57478	−0.198060
$170$	−18.8018	−1.44203
$171$	−0.768980	−0.0588053
$172$	27.9915	2.13434
$173$	−22.3258	−1.69740	−0.848699	−	0.528877i	$-0.822613\pi$
$173$	−22.3258	−1.69740	−0.848699	+	0.528877i	$0.822613\pi$
$174$	47.0501	3.56686
$175$	−4.50639	−0.340651
$176$	−65.9181	−4.96876
$177$	9.80477	0.736972
$178$	−33.0863	−2.47992
$179$	10.4841	0.783618	0.391809	−	0.920047i	$-0.371849\pi$
$179$	10.4841	0.783618	0.391809	+	0.920047i	$0.371849\pi$
$180$	−1.47413	−0.109875
$181$	−1.74538	−0.129733	−0.0648667	−	0.997894i	$-0.520662\pi$
$181$	−1.74538	−0.129733	−0.0648667	+	0.997894i	$0.520662\pi$
$182$	40.4197	2.99611
$183$	0.138966	0.0102727
$184$	90.1312	6.64456
$185$	8.66468	0.637040
$186$	26.7989	1.96499
$187$	25.8647	1.89141
$188$	35.5766	2.59469
$189$	22.3041	1.62239
$190$	−8.28446	−0.601018
$191$	−10.1529	−0.734641	−0.367321	−	0.930094i	$-0.619725\pi$
$191$	−10.1529	−0.734641	−0.367321	+	0.930094i	$0.619725\pi$
$192$	74.4494	5.37292
$193$	−20.7466	−1.49337	−0.746686	−	0.665176i	$-0.768356\pi$
$193$	−20.7466	−1.49337	−0.746686	+	0.665176i	$0.768356\pi$
$194$	−1.79300	−0.128730
$195$	−5.82785	−0.417341
$196$	76.0782	5.43415
$197$	16.4910	1.17494	0.587469	−	0.809247i	$-0.300125\pi$
$197$	16.4910	1.17494	0.587469	+	0.809247i	$0.300125\pi$
$198$	2.73731	0.194532
$199$	−2.92623	−0.207435	−0.103717	−	0.994607i	$-0.533074\pi$
$199$	−2.92623	−0.207435	−0.103717	+	0.994607i	$0.533074\pi$
$200$	−10.3254	−0.730116
$201$	5.65276	0.398715
$202$	−39.1927	−2.75759
$203$	42.2864	2.96792
$204$	−69.8404	−4.88980
$205$	1.61256	0.112626
$206$	−30.0046	−2.09052
$207$	−2.25082	−0.156443
$208$	55.6952	3.86177
$209$	11.3965	0.788312
$210$	−22.5952	−1.55922
$211$	7.00190	0.482031	0.241015	−	0.970521i	$-0.422520\pi$
$211$	7.00190	0.482031	0.241015	+	0.970521i	$0.422520\pi$
$212$	−23.8398	−1.63733
$213$	−5.03769	−0.345177
$214$	−17.8475	−1.22003
$215$	−4.89625	−0.333922
$216$	51.1050	3.47725
$217$	24.0856	1.63504
$218$	−2.86806	−0.194249
$219$	−24.5866	−1.66141
$220$	21.8470	1.47293
$221$	−21.8535	−1.47002
$222$	43.4451	2.91584
$223$	−15.8140	−1.05898	−0.529492	−	0.848315i	$-0.677618\pi$
$223$	−15.8140	−1.05898	−0.529492	+	0.848315i	$0.677618\pi$
$224$	122.876	8.20999
$225$	0.257853	0.0171902
$226$	−43.7981	−2.91341
$227$	11.6272	0.771725	0.385862	−	0.922556i	$-0.373904\pi$
$227$	11.6272	0.771725	0.385862	+	0.922556i	$0.373904\pi$
$228$	−30.7731	−2.03800
$229$	−27.9606	−1.84769	−0.923846	−	0.382765i	$-0.874972\pi$
$229$	−27.9606	−1.84769	−0.923846	+	0.382765i	$0.874972\pi$
$230$	−24.2488	−1.59892
$231$	31.0830	2.04511
$232$	96.8900	6.36114
$233$	−28.9474	−1.89641	−0.948203	−	0.317665i	$-0.897101\pi$
$233$	−28.9474	−1.89641	−0.948203	+	0.317665i	$0.897101\pi$
$234$	−2.31280	−0.151192
$235$	−6.22302	−0.405945
$236$	31.0552	2.02152
$237$	17.8408	1.15888
$238$	−84.7283	−5.49212
$239$	0.451279	0.0291908	0.0145954	−	0.999893i	$-0.495354\pi$
$239$	0.451279	0.0291908	0.0145954	+	0.999893i	$0.495354\pi$
$240$	−31.1344	−2.00972
$241$	−21.5542	−1.38843	−0.694214	−	0.719768i	$-0.744248\pi$
$241$	−21.5542	−1.38843	−0.694214	+	0.719768i	$0.744248\pi$
$242$	−10.0104	−0.643496
$243$	−2.67247	−0.171439
$244$	0.440156	0.0281781
$245$	−13.3075	−0.850186
$246$	8.08546	0.515510
$247$	−9.62908	−0.612684
$248$	55.1869	3.50437
$249$	−28.4780	−1.80472
$250$	2.77794	0.175692
$251$	−2.52511	−0.159384	−0.0796918	−	0.996820i	$-0.525394\pi$
$251$	−2.52511	−0.159384	−0.0796918	+	0.996820i	$0.525394\pi$
$252$	−6.64300	−0.418470
$253$	33.3578	2.09719
$254$	47.7007	2.99301
$255$	12.2164	0.765021
$256$	84.3156	5.26972
$257$	−4.72444	−0.294703	−0.147351	−	0.989084i	$-0.547075\pi$
$257$	−4.72444	−0.294703	−0.147351	+	0.989084i	$0.547075\pi$
$258$	−24.5500	−1.52842
$259$	39.0464	2.42622
$260$	−18.4589	−1.14477
$261$	−2.41961	−0.149770
$262$	4.17394	0.257867
$263$	−2.87136	−0.177055	−0.0885277	−	0.996074i	$-0.528216\pi$
$263$	−2.87136	−0.177055	−0.0885277	+	0.996074i	$0.528216\pi$
$264$	71.2200	4.38329
$265$	4.17004	0.256164
$266$	−37.3330	−2.28903
$267$	21.4977	1.31564
$268$	17.9043	1.09368
$269$	−16.4426	−1.00252	−0.501261	−	0.865296i	$-0.667131\pi$
$269$	−16.4426	−1.00252	−0.501261	+	0.865296i	$0.667131\pi$
$270$	−13.7492	−0.836752
$271$	6.75112	0.410101	0.205051	−	0.978751i	$-0.434264\pi$
$271$	6.75112	0.410101	0.205051	+	0.978751i	$0.434264\pi$
$272$	−116.749	−7.07894
$273$	−26.2625	−1.58948
$274$	−29.8955	−1.80606
$275$	−3.82146	−0.230443
$276$	−90.0735	−5.42179
$277$	26.9560	1.61963	0.809815	−	0.586685i	$-0.199567\pi$
$277$	26.9560	1.61963	0.809815	+	0.586685i	$0.199567\pi$
$278$	1.22396	0.0734081
$279$	−1.37817	−0.0825087
$280$	−46.5302	−2.78071
$281$	19.3056	1.15167	0.575837	−	0.817564i	$-0.304676\pi$
$281$	19.3056	1.15167	0.575837	+	0.817564i	$0.304676\pi$
$282$	−31.2025	−1.85808
$283$	−6.61622	−0.393293	−0.196647	−	0.980474i	$-0.563005\pi$
$283$	−6.61622	−0.393293	−0.196647	+	0.980474i	$0.563005\pi$
$284$	−15.9562	−0.946825
$285$	5.38280	0.318849
$286$	34.2763	2.02680
$287$	7.26684	0.428948
$288$	−7.03090	−0.414300
$289$	28.8095	1.69468
$290$	−26.0672	−1.53072
$291$	1.16500	0.0682933
$292$	−77.8747	−4.55727
$293$	9.07355	0.530083	0.265041	−	0.964237i	$-0.414614\pi$
$293$	9.07355	0.530083	0.265041	+	0.964237i	$0.414614\pi$
$294$	−66.7245	−3.89145
$295$	−5.43215	−0.316272
$296$	89.4663	5.20012
$297$	18.9141	1.09751
$298$	31.2586	1.81076
$299$	−28.1845	−1.62995
$300$	10.3188	0.595756
$301$	−22.0644	−1.27177
$302$	−5.87537	−0.338090
$303$	25.4653	1.46294
$304$	−51.4419	−2.95040
$305$	−0.0769916	−0.00440853
$306$	4.84811	0.277148
$307$	−14.2457	−0.813044	−0.406522	−	0.913641i	$-0.633259\pi$
$307$	−14.2457	−0.813044	−0.406522	+	0.913641i	$0.633259\pi$
$308$	98.4511	5.60977
$309$	19.4954	1.10905
$310$	−14.8474	−0.843278
$311$	17.8390	1.01156	0.505780	−	0.862663i	$-0.331205\pi$
$311$	17.8390	1.01156	0.505780	+	0.862663i	$0.331205\pi$
$312$	−60.1749	−3.40673
$313$	−34.7589	−1.96469	−0.982344	−	0.187084i	$-0.940096\pi$
$313$	−34.7589	−1.96469	−0.982344	+	0.187084i	$0.940096\pi$
$314$	6.48483	0.365960
$315$	1.16199	0.0654705
$316$	56.5082	3.17883
$317$	6.13788	0.344738	0.172369	−	0.985032i	$-0.444858\pi$
$317$	6.13788	0.344738	0.172369	+	0.985032i	$0.444858\pi$
$318$	20.9088	1.17251
$319$	35.8593	2.00773
$320$	−41.2473	−2.30579
$321$	11.5963	0.647243
$322$	−109.275	−6.08963
$323$	20.1846	1.12310
$324$	−55.4947	−3.08304
$325$	3.22881	0.179102
$326$	16.9555	0.939078
$327$	1.86351	0.103052
$328$	16.6504	0.919363
$329$	−28.0433	−1.54608
$330$	−19.1610	−1.05478
$331$	8.32442	0.457552	0.228776	−	0.973479i	$-0.426528\pi$
$331$	8.32442	0.457552	0.228776	+	0.973479i	$0.426528\pi$
$332$	−90.2001	−4.95037
$333$	−2.23422	−0.122434
$334$	50.2606	2.75014
$335$	−3.13180	−0.171109
$336$	−140.304	−7.65420
$337$	10.3926	0.566122	0.283061	−	0.959102i	$-0.408650\pi$
$337$	10.3926	0.566122	0.283061	+	0.959102i	$0.408650\pi$
$338$	7.15258	0.389049
$339$	28.4576	1.54561
$340$	38.6937	2.09846
$341$	20.4248	1.10607
$342$	2.13618	0.115511
$343$	−28.4241	−1.53476
$344$	−50.5558	−2.72579
$345$	15.7556	0.848252
$346$	62.0196	3.33419
$347$	2.86341	0.153716	0.0768581	−	0.997042i	$-0.475511\pi$
$347$	2.86341	0.153716	0.0768581	+	0.997042i	$0.475511\pi$
$348$	−96.8280	−5.19052
$349$	3.24573	0.173740	0.0868699	−	0.996220i	$-0.472314\pi$
$349$	3.24573	0.173740	0.0868699	+	0.996220i	$0.472314\pi$
$350$	12.5185	0.669140
$351$	−15.9808	−0.852993
$352$	104.200	5.55388
$353$	−16.2957	−0.867332	−0.433666	−	0.901074i	$-0.642780\pi$
$353$	−16.2957	−0.867332	−0.433666	+	0.901074i	$0.642780\pi$
$354$	−27.2370	−1.44763
$355$	2.79104	0.148133
$356$	68.0909	3.60881
$357$	55.0519	2.91365
$358$	−29.1241	−1.53926
$359$	−25.1507	−1.32740	−0.663702	−	0.747997i	$-0.731016\pi$
$359$	−25.1507	−1.32740	−0.663702	+	0.747997i	$0.731016\pi$
$360$	2.66244	0.140323
$361$	−10.1063	−0.531909
$362$	4.84857	0.254835
$363$	6.50425	0.341384
$364$	−83.1829	−4.35997
$365$	13.6218	0.712996
$366$	−0.386039	−0.0201786
$367$	−8.24996	−0.430644	−0.215322	−	0.976543i	$-0.569080\pi$
$367$	−8.24996	−0.430644	−0.215322	+	0.976543i	$0.569080\pi$
$368$	−150.572	−7.84910
$369$	−0.415805	−0.0216459
$370$	−24.0699	−1.25134
$371$	18.7918	0.975623
$372$	−55.1516	−2.85948
$373$	−17.1152	−0.886189	−0.443095	−	0.896475i	$-0.646119\pi$
$373$	−17.1152	−0.886189	−0.443095	+	0.896475i	$0.646119\pi$
$374$	−71.8504	−3.71530
$375$	−1.80495	−0.0932073
$376$	−64.2552	−3.31371
$377$	−30.2980	−1.56043
$378$	−61.9594	−3.18685
$379$	25.2648	1.29777	0.648883	−	0.760888i	$-0.275236\pi$
$379$	25.2648	1.29777	0.648883	+	0.760888i	$0.275236\pi$
$380$	17.0492	0.874608
$381$	−30.9933	−1.58784
$382$	28.2042	1.44305
$383$	−24.6345	−1.25877	−0.629383	−	0.777095i	$-0.716692\pi$
$383$	−24.6345	−1.25877	−0.629383	+	0.777095i	$0.716692\pi$
$384$	−108.384	−5.53096
$385$	−17.2210	−0.877662
$386$	57.6327	2.93343
$387$	1.26252	0.0641773
$388$	3.68996	0.187329
$389$	5.67003	0.287482	0.143741	−	0.989615i	$-0.454087\pi$
$389$	5.67003	0.287482	0.143741	+	0.989615i	$0.454087\pi$
$390$	16.1894	0.819782
$391$	59.0808	2.98784
$392$	−137.405	−6.94002
$393$	−2.71200	−0.136802
$394$	−45.8110	−2.30793
$395$	−9.88436	−0.497336
$396$	−5.63333	−0.283085
$397$	−4.83365	−0.242594	−0.121297	−	0.992616i	$-0.538705\pi$
$397$	−4.83365	−0.242594	−0.121297	+	0.992616i	$0.538705\pi$
$398$	8.12888	0.407464
$399$	24.2570	1.21437
$400$	17.2494	0.862472
$401$	−29.4098	−1.46866	−0.734329	−	0.678794i	$-0.762503\pi$
$401$	−29.4098	−1.46866	−0.734329	+	0.678794i	$0.762503\pi$
$402$	−15.7030	−0.783195
$403$	−17.2573	−0.859645
$404$	80.6577	4.01287
$405$	9.70707	0.482348
$406$	−117.469	−5.82988
$407$	33.1117	1.64129
$408$	126.139	6.24483
$409$	7.45471	0.368612	0.184306	−	0.982869i	$-0.440996\pi$
$409$	7.45471	0.368612	0.184306	+	0.982869i	$0.440996\pi$
$410$	−4.47960	−0.221232
$411$	19.4245	0.958140
$412$	61.7488	3.04215
$413$	−24.4794	−1.20455
$414$	6.25264	0.307301
$415$	15.7777	0.774497
$416$	−88.0402	−4.31653
$417$	−0.795262	−0.0389441
$418$	−31.6588	−1.54848
$419$	14.3749	0.702259	0.351129	−	0.936327i	$-0.385798\pi$
$419$	14.3749	0.702259	0.351129	+	0.936327i	$0.385798\pi$
$420$	46.5005	2.26899
$421$	4.62235	0.225280	0.112640	−	0.993636i	$-0.464069\pi$
$421$	4.62235	0.225280	0.112640	+	0.993636i	$0.464069\pi$
$422$	−19.4508	−0.946852
$423$	1.60463	0.0780196
$424$	43.0574	2.09105
$425$	−6.76827	−0.328309
$426$	13.9944	0.678030
$427$	−0.346954	−0.0167903
$428$	36.7297	1.77539
$429$	−22.2709	−1.07525
$430$	13.6015	0.655922
$431$	−12.6505	−0.609355	−0.304678	−	0.952456i	$-0.598549\pi$
$431$	−12.6505	−0.609355	−0.304678	+	0.952456i	$0.598549\pi$
$432$	−85.3752	−4.10761
$433$	12.4382	0.597740	0.298870	−	0.954294i	$-0.403390\pi$
$433$	12.4382	0.597740	0.298870	+	0.954294i	$0.403390\pi$
$434$	−66.9083	−3.21170
$435$	16.9371	0.812069
$436$	5.90240	0.282674
$437$	26.0322	1.24529
$438$	68.3001	3.26351
$439$	30.7475	1.46750	0.733749	−	0.679420i	$-0.237769\pi$
$439$	30.7475	1.46750	0.733749	+	0.679420i	$0.237769\pi$
$440$	−39.4581	−1.88109
$441$	3.43139	0.163399
$442$	60.7076	2.88756
$443$	2.54920	0.121116	0.0605582	−	0.998165i	$-0.480712\pi$
$443$	2.54920	0.121116	0.0605582	+	0.998165i	$0.480712\pi$
$444$	−89.4090	−4.24316
$445$	−11.9104	−0.564607
$446$	43.9303	2.08016
$447$	−20.3102	−0.960638
$448$	−185.876	−8.78182
$449$	−27.2553	−1.28626	−0.643128	−	0.765758i	$-0.722364\pi$
$449$	−27.2553	−1.28626	−0.643128	+	0.765758i	$0.722364\pi$
$450$	−0.716300	−0.0337667
$451$	6.16235	0.290174
$452$	90.1356	4.23962
$453$	3.81750	0.179362
$454$	−32.2996	−1.51590
$455$	14.5503	0.682127
$456$	55.5795	2.60275
$457$	−7.54444	−0.352914	−0.176457	−	0.984308i	$-0.556464\pi$
$457$	−7.54444	−0.352914	−0.176457	+	0.984308i	$0.556464\pi$
$458$	77.6729	3.62942
$459$	33.4992	1.56361
$460$	49.9035	2.32676
$461$	−22.8032	−1.06205	−0.531025	−	0.847356i	$-0.678193\pi$
$461$	−22.8032	−1.06205	−0.531025	+	0.847356i	$0.678193\pi$
$462$	−86.3467	−4.01721
$463$	25.2255	1.17233	0.586163	−	0.810193i	$-0.300638\pi$
$463$	25.2255	1.17233	0.586163	+	0.810193i	$0.300638\pi$
$464$	−161.863	−7.51429
$465$	9.64706	0.447372
$466$	80.4140	3.72511
$467$	17.5467	0.811964	0.405982	−	0.913881i	$-0.366930\pi$
$467$	17.5467	0.811964	0.405982	+	0.913881i	$0.366930\pi$
$468$	4.75969	0.220017
$469$	−14.1131	−0.651683
$470$	17.2872	0.797397
$471$	−4.21349	−0.194148
$472$	−56.0891	−2.58171
$473$	−18.7108	−0.860325
$474$	−49.5606	−2.27639
$475$	−2.98224	−0.136834
$476$	174.369	7.99219
$477$	−1.07526	−0.0492327
$478$	−1.25362	−0.0573395
$479$	−15.8960	−0.726307	−0.363154	−	0.931729i	$-0.618300\pi$
$479$	−15.8960	−0.726307	−0.363154	+	0.931729i	$0.618300\pi$
$480$	49.2158	2.24638
$481$	−27.9766	−1.27562
$482$	59.8762	2.72729
$483$	71.0007	3.23064
$484$	20.6013	0.936422
$485$	−0.645444	−0.0293081
$486$	7.42395	0.336757
$487$	−12.7140	−0.576127	−0.288063	−	0.957611i	$-0.593011\pi$
$487$	−12.7140	−0.576127	−0.288063	+	0.957611i	$0.593011\pi$
$488$	−0.794969	−0.0359866
$489$	−11.0168	−0.498195
$490$	36.9674	1.67002
$491$	−30.0874	−1.35782	−0.678912	−	0.734219i	$-0.737548\pi$
$491$	−30.0874	−1.35782	−0.678912	+	0.734219i	$0.737548\pi$
$492$	−16.6397	−0.750176
$493$	63.5111	2.86040
$494$	26.7490	1.20349
$495$	0.985376	0.0442894
$496$	−92.1944	−4.13965
$497$	12.5775	0.564178
$498$	79.1101	3.54501
$499$	−32.5616	−1.45766	−0.728829	−	0.684696i	$-0.759935\pi$
$499$	−32.5616	−1.45766	−0.728829	+	0.684696i	$0.759935\pi$
$500$	−5.71693	−0.255669
$501$	−32.6566	−1.45899
$502$	7.01460	0.313077
$503$	24.3576	1.08605	0.543026	−	0.839716i	$-0.317279\pi$
$503$	24.3576	1.08605	0.543026	+	0.839716i	$0.317279\pi$
$504$	11.9980	0.534432
$505$	−14.1086	−0.627823
$506$	−92.6659	−4.11950
$507$	−4.64736	−0.206396
$508$	−98.1670	−4.35546
$509$	−15.6976	−0.695783	−0.347892	−	0.937535i	$-0.613102\pi$
$509$	−15.6976	−0.695783	−0.347892	+	0.937535i	$0.613102\pi$
$510$	−33.9364	−1.50273
$511$	61.3849	2.71551
$512$	−114.127	−5.04374
$513$	14.7604	0.651688
$514$	13.1242	0.578883
$515$	−10.8010	−0.475951
$516$	50.5234	2.22417
$517$	−23.7810	−1.04589
$518$	−108.468	−4.76583
$519$	−40.2970	−1.76884
$520$	33.3388	1.46200
$521$	29.5173	1.29318	0.646589	−	0.762839i	$-0.276195\pi$
$521$	29.5173	1.29318	0.646589	+	0.762839i	$0.276195\pi$
$522$	6.72151	0.294193
$523$	6.73193	0.294367	0.147183	−	0.989109i	$-0.452979\pi$
$523$	6.73193	0.294367	0.147183	+	0.989109i	$0.452979\pi$
$524$	−8.58988	−0.375251
$525$	−8.13381	−0.354989
$526$	7.97645	0.347790
$527$	36.1749	1.57580
$528$	−118.979	−5.17789
$529$	53.1968	2.31291
$530$	−11.5841	−0.503182
$531$	1.40070	0.0607851
$532$	76.8305	3.33102
$533$	−5.20666	−0.225526
$534$	−59.7192	−2.58430
$535$	−6.42472	−0.277765
$536$	−32.3371	−1.39675
$537$	18.9233	0.816600
$538$	45.6765	1.96925
$539$	−50.8541	−2.19044
$540$	28.2956	1.21765
$541$	−11.8842	−0.510944	−0.255472	−	0.966816i	$-0.582231\pi$
$541$	−11.8842	−0.510944	−0.255472	+	0.966816i	$0.582231\pi$
$542$	−18.7542	−0.805561
$543$	−3.15033	−0.135194
$544$	184.551	7.91255
$545$	−1.03244	−0.0442249
$546$	72.9557	3.12221
$547$	33.1035	1.41540	0.707701	−	0.706512i	$-0.249732\pi$
$547$	33.1035	1.41540	0.707701	+	0.706512i	$0.249732\pi$
$548$	61.5243	2.62819
$549$	0.0198525	0.000847286 0
$550$	10.6158	0.452658
$551$	27.9843	1.19217
$552$	162.683	6.92423
$553$	−44.5427	−1.89415
$554$	−74.8821	−3.18144
$555$	15.6393	0.663853
$556$	−2.51888	−0.106824
$557$	−16.5850	−0.702731	−0.351365	−	0.936238i	$-0.614282\pi$
$557$	−16.5850	−0.702731	−0.351365	+	0.936238i	$0.614282\pi$
$558$	3.82846	0.162072
$559$	15.8091	0.668653
$560$	77.7327	3.28480
$561$	46.6845	1.97102
$562$	−53.6297	−2.26223
$563$	−34.4719	−1.45282	−0.726408	−	0.687264i	$-0.758812\pi$
$563$	−34.4719	−1.45282	−0.726408	+	0.687264i	$0.758812\pi$
$564$	64.2141	2.70390
$565$	−15.7664	−0.663298
$566$	18.3794	0.772545
$567$	43.7438	1.83707
$568$	28.8186	1.20920
$569$	17.3574	0.727662	0.363831	−	0.931465i	$-0.381469\pi$
$569$	17.3574	0.727662	0.363831	+	0.931465i	$0.381469\pi$
$570$	−14.9531	−0.626315
$571$	−40.3467	−1.68846	−0.844228	−	0.535985i	$-0.819940\pi$
$571$	−40.3467	−1.68846	−0.844228	+	0.535985i	$0.819940\pi$
$572$	−70.5399	−2.94942
$573$	−18.3256	−0.765562
$574$	−20.1868	−0.842581
$575$	−8.72908	−0.364028
$576$	10.6357	0.443156
$577$	−30.7537	−1.28029	−0.640147	−	0.768252i	$-0.721127\pi$
$577$	−30.7537	−1.28029	−0.640147	+	0.768252i	$0.721127\pi$
$578$	−80.0310	−3.32885
$579$	−37.4466	−1.55623
$580$	53.6457	2.22752
$581$	71.1005	2.94974
$582$	−3.23628	−0.134148
$583$	15.9356	0.659987
$584$	140.650	5.82015
$585$	−0.832560	−0.0344221
$586$	−25.2058	−1.04124
$587$	−0.618576	−0.0255314	−0.0127657	−	0.999919i	$-0.504064\pi$
$587$	−0.618576	−0.0255314	−0.0127657	+	0.999919i	$0.504064\pi$
$588$	137.317	5.66288
$589$	15.9394	0.656771
$590$	15.0902	0.621252
$591$	29.7655	1.22439
$592$	−149.461	−6.14281
$593$	−15.5587	−0.638921	−0.319460	−	0.947600i	$-0.603502\pi$
$593$	−15.5587	−0.638921	−0.319460	+	0.947600i	$0.603502\pi$
$594$	−52.5422	−2.15583
$595$	−30.5004	−1.25040
$596$	−64.3296	−2.63504
$597$	−5.28170	−0.216166
$598$	78.2949	3.20172
$599$	9.73002	0.397558	0.198779	−	0.980044i	$-0.436302\pi$
$599$	9.73002	0.397558	0.198779	+	0.980044i	$0.436302\pi$
$600$	−18.6369	−0.760847
$601$	−18.5267	−0.755719	−0.377860	−	0.925863i	$-0.623340\pi$
$601$	−18.5267	−0.755719	−0.377860	+	0.925863i	$0.623340\pi$
$602$	61.2935	2.49814
$603$	0.807546	0.0328858
$604$	12.0914	0.491992
$605$	−3.60356	−0.146505
$606$	−70.7409	−2.87365
$607$	−23.8538	−0.968198	−0.484099	−	0.875013i	$-0.660853\pi$
$607$	−23.8538	−0.968198	−0.484099	+	0.875013i	$0.660853\pi$
$608$	81.3168	3.29783
$609$	76.3249	3.09284
$610$	0.213878	0.00865966
$611$	20.0930	0.812874
$612$	−9.97731	−0.403309
$613$	−22.9630	−0.927468	−0.463734	−	0.885974i	$-0.653491\pi$
$613$	−22.9630	−0.927468	−0.463734	+	0.885974i	$0.653491\pi$
$614$	39.5736	1.59706
$615$	2.91060	0.117367
$616$	−177.813	−7.16431
$617$	7.50544	0.302158	0.151079	−	0.988522i	$-0.451725\pi$
$617$	7.50544	0.302158	0.151079	+	0.988522i	$0.451725\pi$
$618$	−54.1569	−2.17851
$619$	18.9611	0.762113	0.381056	−	0.924552i	$-0.375560\pi$
$619$	18.9611	0.762113	0.381056	+	0.924552i	$0.375560\pi$
$620$	30.5557	1.22715
$621$	43.2041	1.73372
$622$	−49.5557	−1.98700
$623$	−53.6728	−2.15036
$624$	100.527	4.02431
$625$	1.00000	0.0400000
$626$	96.5580	3.85923
$627$	20.5701	0.821492
$628$	−13.3456	−0.532549
$629$	58.6449	2.33833
$630$	−3.22793	−0.128604
$631$	−30.2281	−1.20336	−0.601681	−	0.798736i	$-0.705502\pi$
$631$	−30.2281	−1.20336	−0.601681	+	0.798736i	$0.705502\pi$
$632$	−102.060	−4.05973
$633$	12.6381	0.502319
$634$	−17.0506	−0.677167
$635$	17.1713	0.681421
$636$	−43.0298	−1.70624
$637$	42.9675	1.70243
$638$	−99.6148	−3.94379
$639$	−0.719679	−0.0284700
$640$	60.0482	2.37361
$641$	−16.8315	−0.664804	−0.332402	−	0.943138i	$-0.607859\pi$
$641$	−16.8315	−0.664804	−0.332402	+	0.943138i	$0.607859\pi$
$642$	−32.2138	−1.27138
$643$	−4.06744	−0.160404	−0.0802021	−	0.996779i	$-0.525557\pi$
$643$	−4.06744	−0.160404	−0.0802021	+	0.996779i	$0.525557\pi$
$644$	224.885	8.86170
$645$	−8.83751	−0.347976
$646$	−56.0715	−2.20610
$647$	39.2081	1.54143	0.770714	−	0.637181i	$-0.219900\pi$
$647$	39.2081	1.54143	0.770714	+	0.637181i	$0.219900\pi$
$648$	100.229	3.93738
$649$	−20.7587	−0.814852
$650$	−8.96943	−0.351810
$651$	43.4734	1.70386
$652$	−34.8940	−1.36656
$653$	−33.7685	−1.32146	−0.660731	−	0.750623i	$-0.729754\pi$
$653$	−33.7685	−1.32146	−0.660731	+	0.750623i	$0.729754\pi$
$654$	−5.17671	−0.202425
$655$	1.50253	0.0587088
$656$	−27.8158	−1.08603
$657$	−3.51242	−0.137032
$658$	77.9026	3.03696
$659$	−2.26242	−0.0881314	−0.0440657	−	0.999029i	$-0.514031\pi$
$659$	−2.26242	−0.0881314	−0.0440657	+	0.999029i	$0.514031\pi$
$660$	39.4328	1.53492
$661$	10.0675	0.391580	0.195790	−	0.980646i	$-0.437273\pi$
$661$	10.0675	0.391580	0.195790	+	0.980646i	$0.437273\pi$
$662$	−23.1247	−0.898768
$663$	−39.4445	−1.53190
$664$	162.911	6.32218
$665$	−13.4391	−0.521146
$666$	6.20651	0.240497
$667$	81.9107	3.17159
$668$	−103.435	−4.00202
$669$	−28.5435	−1.10356
$670$	8.69995	0.336109
$671$	−0.294220	−0.0113583
$672$	221.785	8.55555
$673$	40.1002	1.54575	0.772874	−	0.634559i	$-0.218818\pi$
$673$	40.1002	1.54575	0.772874	+	0.634559i	$0.218818\pi$
$674$	−28.8701	−1.11203
$675$	−4.94944	−0.190504
$676$	−14.7198	−0.566148
$677$	−7.24747	−0.278543	−0.139271	−	0.990254i	$-0.544476\pi$
$677$	−7.24747	−0.278543	−0.139271	+	0.990254i	$0.544476\pi$
$678$	−79.0535	−3.03603
$679$	−2.90862	−0.111623
$680$	−69.8851	−2.67997
$681$	20.9866	0.804206
$682$	−56.7389	−2.17264
$683$	6.20714	0.237510	0.118755	−	0.992924i	$-0.462110\pi$
$683$	6.20714	0.237510	0.118755	+	0.992924i	$0.462110\pi$
$684$	−4.39620	−0.168093
$685$	−10.7618	−0.411186
$686$	78.9604	3.01472
$687$	−50.4676	−1.92546
$688$	84.4577	3.21992
$689$	−13.4643	−0.512948
$690$	−43.7680	−1.66622
$691$	−29.5877	−1.12557	−0.562784	−	0.826604i	$-0.690270\pi$
$691$	−29.5877	−1.12557	−0.562784	+	0.826604i	$0.690270\pi$
$692$	−127.635	−4.85195
$693$	4.44049	0.168680
$694$	−7.95438	−0.301944
$695$	0.440600	0.0167129
$696$	174.882	6.62888
$697$	10.9143	0.413407
$698$	−9.01643	−0.341277
$699$	−52.2487	−1.97623
$700$	−25.7627	−0.973739
$701$	−2.13797	−0.0807499	−0.0403750	−	0.999185i	$-0.512855\pi$
$701$	−2.13797	−0.0807499	−0.0403750	+	0.999185i	$0.512855\pi$
$702$	44.3937	1.67553
$703$	25.8401	0.974579
$704$	−157.625	−5.94071
$705$	−11.2323	−0.423031
$706$	45.2684	1.70370
$707$	−63.5786	−2.39112
$708$	56.0532	2.10661
$709$	−36.4655	−1.36949	−0.684745	−	0.728783i	$-0.740087\pi$
$709$	−36.4655	−1.36949	−0.684745	+	0.728783i	$0.740087\pi$
$710$	−7.75333	−0.290977
$711$	2.54871	0.0955842
$712$	−122.980	−4.60885
$713$	46.6549	1.74724
$714$	−152.931	−5.72328
$715$	12.3388	0.461444
$716$	59.9368	2.23994
$717$	0.814537	0.0304195
$718$	69.8670	2.60742
$719$	43.7346	1.63102	0.815512	−	0.578740i	$-0.196456\pi$
$719$	43.7346	1.63102	0.815512	+	0.578740i	$0.196456\pi$
$720$	−4.44783	−0.165761
$721$	−48.6737	−1.81270
$722$	28.0746	1.04483
$723$	−38.9043	−1.44687
$724$	−9.97824	−0.370838
$725$	−9.38365	−0.348500
$726$	−18.0684	−0.670581
$727$	50.5726	1.87563	0.937817	−	0.347131i	$-0.112844\pi$
$727$	50.5726	1.87563	0.937817	+	0.347131i	$0.112844\pi$
$728$	150.237	5.56817
$729$	24.2975	0.899909
$730$	−37.8404	−1.40054
$731$	−33.1392	−1.22570
$732$	0.794460	0.0293641
$733$	41.5425	1.53441	0.767204	−	0.641403i	$-0.221647\pi$
$733$	41.5425	1.53441	0.767204	+	0.641403i	$0.221647\pi$
$734$	22.9179	0.845914
$735$	−24.0194	−0.885970
$736$	238.016	8.77340
$737$	−11.9681	−0.440849
$738$	1.15508	0.0425191
$739$	34.4594	1.26761	0.633805	−	0.773493i	$-0.281492\pi$
$739$	34.4594	1.26761	0.633805	+	0.773493i	$0.281492\pi$
$740$	49.5354	1.82096
$741$	−17.3800	−0.638471
$742$	−52.2025	−1.91641
$743$	−2.08852	−0.0766202	−0.0383101	−	0.999266i	$-0.512197\pi$
$743$	−2.08852	−0.0766202	−0.0383101	+	0.999266i	$0.512197\pi$
$744$	99.6098	3.65187
$745$	11.2525	0.412259
$746$	47.5448	1.74074
$747$	−4.06834	−0.148853
$748$	147.867	5.40654
$749$	−28.9522	−1.05789
$750$	5.01404	0.183087
$751$	7.03031	0.256540	0.128270	−	0.991739i	$-0.459058\pi$
$751$	7.03031	0.256540	0.128270	+	0.991739i	$0.459058\pi$
$752$	107.344	3.91442
$753$	−4.55771	−0.166092
$754$	84.1661	3.06515
$755$	−2.11501	−0.0769732
$756$	127.511	4.63753
$757$	−0.191204	−0.00694943	−0.00347472	−	0.999994i	$-0.501106\pi$
$757$	−0.191204	−0.00694943	−0.00347472	+	0.999994i	$0.501106\pi$
$758$	−70.1840	−2.54920
$759$	60.2093	2.18546
$760$	−30.7928	−1.11697
$761$	36.7121	1.33081	0.665407	−	0.746481i	$-0.268258\pi$
$761$	36.7121	1.33081	0.665407	+	0.746481i	$0.268258\pi$
$762$	86.0975	3.11898
$763$	−4.65258	−0.168435
$764$	−58.0437	−2.09995
$765$	1.74522	0.0630986
$766$	68.4332	2.47259
$767$	17.5394	0.633310
$768$	152.186	5.49152
$769$	−20.6475	−0.744569	−0.372284	−	0.928119i	$-0.621425\pi$
$769$	−20.6475	−0.744569	−0.372284	+	0.928119i	$0.621425\pi$
$770$	47.8388	1.72399
$771$	−8.52739	−0.307106
$772$	−118.607	−4.26875
$773$	10.5973	0.381159	0.190579	−	0.981672i	$-0.438963\pi$
$773$	10.5973	0.381159	0.190579	+	0.981672i	$0.438963\pi$
$774$	−3.50719	−0.126063
$775$	−5.34477	−0.191990
$776$	−6.66447	−0.239240
$777$	70.4769	2.52834
$778$	−15.7510	−0.564701
$779$	4.80905	0.172302
$780$	−33.3174	−1.19296
$781$	10.6658	0.381654
$782$	−164.123	−5.86901
$783$	46.4439	1.65977
$784$	229.547	8.19812
$785$	2.33441	0.0833185
$786$	7.53377	0.268721
$787$	31.4625	1.12152	0.560759	−	0.827979i	$-0.310509\pi$
$787$	31.4625	1.12152	0.560759	+	0.827979i	$0.310509\pi$
$788$	94.2781	3.35852
$789$	−5.18266	−0.184508
$790$	27.4581	0.976916
$791$	−71.0496	−2.52623
$792$	10.1744	0.361532
$793$	0.248591	0.00882774
$794$	13.4276	0.476527
$795$	7.52673	0.266946
$796$	−16.7291	−0.592946
$797$	−2.08809	−0.0739639	−0.0369820	−	0.999316i	$-0.511774\pi$
$797$	−2.08809	−0.0739639	−0.0369820	+	0.999316i	$0.511774\pi$
$798$	−67.3843	−2.38538
$799$	−42.1191	−1.49007
$800$	−27.2671	−0.964036
$801$	3.07113	0.108513
$802$	81.6987	2.88488
$803$	52.0550	1.83698
$804$	32.3164	1.13971
$805$	−39.3366	−1.38643
$806$	47.9396	1.68860
$807$	−29.6781	−1.04472
$808$	−145.676	−5.12488
$809$	19.3554	0.680498	0.340249	−	0.940335i	$-0.389489\pi$
$809$	19.3554	0.680498	0.340249	+	0.940335i	$0.389489\pi$
$810$	−26.9656	−0.947476
$811$	−38.9318	−1.36708	−0.683541	−	0.729912i	$-0.739561\pi$
$811$	−38.9318	−1.36708	−0.683541	+	0.729912i	$0.739561\pi$
$812$	241.748	8.48370
$813$	12.1855	0.427363
$814$	−91.9823	−3.22398
$815$	6.10363	0.213801
$816$	−210.726	−7.37690
$817$	−14.6018	−0.510852
$818$	−20.7087	−0.724064
$819$	−3.75184	−0.131100
$820$	9.21892	0.321939
$821$	−32.9686	−1.15061	−0.575306	−	0.817939i	$-0.695117\pi$
$821$	−32.9686	−1.15061	−0.575306	+	0.817939i	$0.695117\pi$
$822$	−53.9600	−1.88207
$823$	13.1209	0.457365	0.228683	−	0.973501i	$-0.426558\pi$
$823$	13.1209	0.457365	0.228683	+	0.973501i	$0.426558\pi$
$824$	−111.525	−3.88516
$825$	−6.89755	−0.240142
$826$	68.0021	2.36610
$827$	33.4180	1.16206	0.581029	−	0.813882i	$-0.302650\pi$
$827$	33.4180	1.16206	0.581029	+	0.813882i	$0.302650\pi$
$828$	−12.8678	−0.447187
$829$	−8.12793	−0.282295	−0.141147	−	0.989989i	$-0.545079\pi$
$829$	−8.12793	−0.282295	−0.141147	+	0.989989i	$0.545079\pi$
$830$	−43.8295	−1.52134
$831$	48.6543	1.68780
$832$	133.180	4.61717
$833$	−90.0689	−3.12070
$834$	2.20919	0.0764979
$835$	18.0928	0.626126
$836$	65.1530	2.25336
$837$	26.4537	0.914372
$838$	−39.9325	−1.37945
$839$	2.71322	0.0936708	0.0468354	−	0.998903i	$-0.485086\pi$
$839$	2.71322	0.0936708	0.0468354	+	0.998903i	$0.485086\pi$
$840$	−83.9849	−2.89775
$841$	59.0530	2.03631
$842$	−12.8406	−0.442517
$843$	34.8457	1.20015
$844$	40.0294	1.37787
$845$	2.57478	0.0885751
$846$	−4.45755	−0.153254
$847$	−16.2390	−0.557979
$848$	−71.9309	−2.47012
$849$	−11.9420	−0.409847
$850$	18.8018	0.644897
$851$	75.6347	2.59272
$852$	−28.8001	−0.986677
$853$	7.50424	0.256940	0.128470	−	0.991713i	$-0.458993\pi$
$853$	7.50424	0.256940	0.128470	+	0.991713i	$0.458993\pi$
$854$	0.963816	0.0329811
$855$	0.768980	0.0262985
$856$	−66.3378	−2.26738
$857$	11.8630	0.405234	0.202617	−	0.979258i	$-0.435055\pi$
$857$	11.8630	0.405234	0.202617	+	0.979258i	$0.435055\pi$
$858$	61.8671	2.11211
$859$	−23.5075	−0.802065	−0.401033	−	0.916064i	$-0.631349\pi$
$859$	−23.5075	−0.802065	−0.401033	+	0.916064i	$0.631349\pi$
$860$	−27.9915	−0.954504
$861$	13.1163	0.447002
$862$	35.1424	1.19696
$863$	35.1285	1.19579	0.597895	−	0.801575i	$-0.296004\pi$
$863$	35.1285	1.19579	0.597895	+	0.801575i	$0.296004\pi$
$864$	134.957	4.59132
$865$	22.3258	0.759099
$866$	−34.5524	−1.17414
$867$	51.9998	1.76601
$868$	137.696	4.67370
$869$	−37.7727	−1.28135
$870$	−47.0501	−1.59515
$871$	10.1120	0.342632
$872$	−10.6604	−0.361006
$873$	0.166430	0.00563280
$874$	−72.3157	−2.44612
$875$	4.50639	0.152344
$876$	−140.560	−4.74909
$877$	−45.0601	−1.52157	−0.760785	−	0.649004i	$-0.775186\pi$
$877$	−45.0601	−1.52157	−0.760785	+	0.649004i	$0.775186\pi$
$878$	−85.4147	−2.88260
$879$	16.3773	0.552394
$880$	65.9181	2.22210
$881$	−37.6472	−1.26837	−0.634184	−	0.773182i	$-0.718664\pi$
$881$	−37.6472	−1.26837	−0.634184	+	0.773182i	$0.718664\pi$
$882$	−9.53218	−0.320965
$883$	−31.3193	−1.05398	−0.526989	−	0.849872i	$-0.676679\pi$
$883$	−31.3193	−1.05398	−0.526989	+	0.849872i	$0.676679\pi$
$884$	−124.935	−4.20201
$885$	−9.80477	−0.329584
$886$	−7.08153	−0.237909
$887$	−45.8810	−1.54053	−0.770266	−	0.637723i	$-0.779877\pi$
$887$	−45.8810	−1.54053	−0.770266	+	0.637723i	$0.779877\pi$
$888$	161.482	5.41899
$889$	77.3804	2.59526
$890$	33.0863	1.10906
$891$	37.0952	1.24274
$892$	−90.4076	−3.02707
$893$	−18.5585	−0.621037
$894$	56.4204	1.88698
$895$	−10.4841	−0.350445
$896$	270.600	9.04013
$897$	−50.8718	−1.69856
$898$	75.7135	2.52659
$899$	50.1535	1.67271
$900$	1.47413	0.0491377
$901$	28.2240	0.940277
$902$	−17.1186	−0.569987
$903$	−39.8252	−1.32530
$904$	−162.795	−5.41447
$905$	1.74538	0.0580185
$906$	−10.6048	−0.352320
$907$	5.10816	0.169614	0.0848068	−	0.996397i	$-0.472973\pi$
$907$	5.10816	0.169614	0.0848068	+	0.996397i	$0.472973\pi$
$908$	66.4719	2.20595
$909$	3.63794	0.120663
$910$	−40.4197	−1.33990
$911$	−56.6010	−1.87527	−0.937637	−	0.347615i	$-0.886992\pi$
$911$	−56.6010	−1.87527	−0.937637	+	0.347615i	$0.886992\pi$
$912$	−92.8502	−3.07458
$913$	60.2939	1.99544
$914$	20.9580	0.693228
$915$	−0.138966	−0.00459408
$916$	−159.849	−5.28156
$917$	6.77099	0.223598
$918$	−93.0586	−3.07139
$919$	−0.150509	−0.00496484	−0.00248242	−	0.999997i	$-0.500790\pi$
$919$	−0.150509	−0.00496484	−0.00248242	+	0.999997i	$0.500790\pi$
$920$	−90.1312	−2.97154
$921$	−25.7128	−0.847265
$922$	63.3458	2.08618
$923$	−9.01174	−0.296625
$924$	177.700	5.84589
$925$	−8.66468	−0.284893
$926$	−70.0747	−2.30280
$927$	2.78509	0.0914742
$928$	255.865	8.39917
$929$	−21.1462	−0.693784	−0.346892	−	0.937905i	$-0.612763\pi$
$929$	−21.1462	−0.693784	−0.346892	+	0.937905i	$0.612763\pi$
$930$	−26.7989	−0.878771
$931$	−39.6862	−1.30066
$932$	−165.490	−5.42081
$933$	32.1986	1.05414
$934$	−48.7436	−1.59494
$935$	−25.8647	−0.845865
$936$	−8.59651	−0.280986
$937$	15.8149	0.516651	0.258325	−	0.966058i	$-0.416829\pi$
$937$	15.8149	0.516651	0.258325	+	0.966058i	$0.416829\pi$
$938$	39.2054	1.28010
$939$	−62.7381	−2.04738
$940$	−35.5766	−1.16038
$941$	24.7171	0.805756	0.402878	−	0.915254i	$-0.368010\pi$
$941$	24.7171	0.805756	0.402878	+	0.915254i	$0.368010\pi$
$942$	11.7048	0.381364
$943$	14.0762	0.458384
$944$	93.7016	3.04973
$945$	−22.3041	−0.725553
$946$	51.9775	1.68993
$947$	−7.06263	−0.229504	−0.114752	−	0.993394i	$-0.536607\pi$
$947$	−7.06263	−0.229504	−0.114752	+	0.993394i	$0.536607\pi$
$948$	101.995	3.31263
$949$	−43.9821	−1.42772
$950$	8.28446	0.268784
$951$	11.0786	0.359248
$952$	−314.929	−10.2069
$953$	−28.6678	−0.928642	−0.464321	−	0.885667i	$-0.653702\pi$
$953$	−28.6678	−0.928642	−0.464321	+	0.885667i	$0.653702\pi$
$954$	2.98700	0.0967078
$955$	10.1529	0.328542
$956$	2.57993	0.0834410
$957$	64.7243	2.09224
$958$	44.1581	1.42668
$959$	−48.4967	−1.56604
$960$	−74.4494	−2.40284
$961$	−2.43341	−0.0784970
$962$	77.7173	2.50570
$963$	1.65663	0.0533843
$964$	−123.224	−3.96878
$965$	20.7466	0.667856
$966$	−197.235	−6.34595
$967$	−6.46582	−0.207927	−0.103963	−	0.994581i	$-0.533153\pi$
$967$	−6.46582	−0.207927	−0.103963	+	0.994581i	$0.533153\pi$
$968$	−37.2082	−1.19592
$969$	36.4322	1.17037
$970$	1.79300	0.0575698
$971$	36.7542	1.17950	0.589749	−	0.807586i	$-0.299227\pi$
$971$	36.7542	1.17950	0.589749	+	0.807586i	$0.299227\pi$
$972$	−15.2783	−0.490053
$973$	1.98551	0.0636526
$974$	35.3187	1.13168
$975$	5.82785	0.186641
$976$	1.32806	0.0425103
$977$	−37.4655	−1.19863	−0.599315	−	0.800514i	$-0.704560\pi$
$977$	−37.4655	−1.19863	−0.599315	+	0.800514i	$0.704560\pi$
$978$	30.6039	0.978603
$979$	−45.5151	−1.45467
$980$	−76.0782	−2.43023
$981$	0.266219	0.00849970
$982$	83.5808	2.66717
$983$	−1.20434	−0.0384126	−0.0192063	−	0.999816i	$-0.506114\pi$
$983$	−1.20434	−0.0384126	−0.0192063	+	0.999816i	$0.506114\pi$
$984$	30.0531	0.958058
$985$	−16.4910	−0.525448
$986$	−176.430	−5.61867
$987$	−50.6169	−1.61115
$988$	−55.0488	−1.75134
$989$	−42.7398	−1.35905
$990$	−2.73731	−0.0869975
$991$	−27.1511	−0.862482	−0.431241	−	0.902237i	$-0.641924\pi$
$991$	−27.1511	−0.862482	−0.431241	+	0.902237i	$0.641924\pi$
$992$	145.736	4.62713
$993$	15.0252	0.476810
$994$	−34.9395	−1.10821
$995$	2.92623	0.0927677
$996$	−162.807	−5.15873
$997$	−40.6951	−1.28883	−0.644413	−	0.764678i	$-0.722898\pi$
$997$	−40.6951	−1.28883	−0.644413	+	0.764678i	$0.722898\pi$
$998$	90.4541	2.86327
$999$	42.8853	1.35683

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6005.2.a.g.1.4	✓	113

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6005.2.a.g.1.4	✓	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)

\(f(q)\)	\(=\)	\(q-2.77794 q^{2} +1.80495 q^{3} +5.71693 q^{4} -1.00000 q^{5} -5.01404 q^{6} -4.50639 q^{7} -10.3254 q^{8} +0.257853 q^{9} +O(q^{10})\)	\(q-2.77794 q^{2} +1.80495 q^{3} +5.71693 q^{4} -1.00000 q^{5} -5.01404 q^{6} -4.50639 q^{7} -10.3254 q^{8} +0.257853 q^{9} +2.77794 q^{10} -3.82146 q^{11} +10.3188 q^{12} +3.22881 q^{13} +12.5185 q^{14} -1.80495 q^{15} +17.2494 q^{16} -6.76827 q^{17} -0.716300 q^{18} -2.98224 q^{19} -5.71693 q^{20} -8.13381 q^{21} +10.6158 q^{22} -8.72908 q^{23} -18.6369 q^{24} +1.00000 q^{25} -8.96943 q^{26} -4.94944 q^{27} -25.7627 q^{28} -9.38365 q^{29} +5.01404 q^{30} -5.34477 q^{31} -27.2671 q^{32} -6.89755 q^{33} +18.8018 q^{34} +4.50639 q^{35} +1.47413 q^{36} -8.66468 q^{37} +8.28446 q^{38} +5.82785 q^{39} +10.3254 q^{40} -1.61256 q^{41} +22.5952 q^{42} +4.89625 q^{43} -21.8470 q^{44} -0.257853 q^{45} +24.2488 q^{46} +6.22302 q^{47} +31.1344 q^{48} +13.3075 q^{49} -2.77794 q^{50} -12.2164 q^{51} +18.4589 q^{52} -4.17004 q^{53} +13.7492 q^{54} +3.82146 q^{55} +46.5302 q^{56} -5.38280 q^{57} +26.0672 q^{58} +5.43215 q^{59} -10.3188 q^{60} +0.0769916 q^{61} +14.8474 q^{62} -1.16199 q^{63} +41.2473 q^{64} -3.22881 q^{65} +19.1610 q^{66} +3.13180 q^{67} -38.6937 q^{68} -15.7556 q^{69} -12.5185 q^{70} -2.79104 q^{71} -2.66244 q^{72} -13.6218 q^{73} +24.0699 q^{74} +1.80495 q^{75} -17.0492 q^{76} +17.2210 q^{77} -16.1894 q^{78} +9.88436 q^{79} -17.2494 q^{80} -9.70707 q^{81} +4.47960 q^{82} -15.7777 q^{83} -46.5005 q^{84} +6.76827 q^{85} -13.6015 q^{86} -16.9371 q^{87} +39.4581 q^{88} +11.9104 q^{89} +0.716300 q^{90} -14.5503 q^{91} -49.9035 q^{92} -9.64706 q^{93} -17.2872 q^{94} +2.98224 q^{95} -49.2158 q^{96} +0.645444 q^{97} -36.9674 q^{98} -0.985376 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 113 q - 3 q^{2} + 6 q^{3} + 141 q^{4} - 113 q^{5} + 7 q^{6} + 7 q^{7} - 12 q^{8} + 141 q^{9}+O(q^{10}) \) 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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