LMFDB - Embedded newform 6017.2.a.c.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6017,2,Mod(1,6017)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6017, 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("6017.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6017 = 11 \cdot 547 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6017.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$48.0459868962$
Analytic rank:	$1$
Dimension:	$106$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Character	$\chi$	$=$	6017.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.73187 q^{2} -0.157601 q^{3} +5.46313 q^{4} +2.56928 q^{5} +0.430546 q^{6} -5.24072 q^{7} -9.46082 q^{8} -2.97516 q^{9} +O(q^{10})$	\(q-2.73187 q^{2} -0.157601 q^{3} +5.46313 q^{4} +2.56928 q^{5} +0.430546 q^{6} -5.24072 q^{7} -9.46082 q^{8} -2.97516 q^{9} -7.01894 q^{10} +1.00000 q^{11} -0.860994 q^{12} -5.86953 q^{13} +14.3170 q^{14} -0.404921 q^{15} +14.9195 q^{16} +0.0371539 q^{17} +8.12776 q^{18} +7.34848 q^{19} +14.0363 q^{20} +0.825943 q^{21} -2.73187 q^{22} -3.50507 q^{23} +1.49103 q^{24} +1.60119 q^{25} +16.0348 q^{26} +0.941692 q^{27} -28.6307 q^{28} +0.837837 q^{29} +1.10619 q^{30} +1.36511 q^{31} -21.8365 q^{32} -0.157601 q^{33} -0.101500 q^{34} -13.4649 q^{35} -16.2537 q^{36} +5.04931 q^{37} -20.0751 q^{38} +0.925043 q^{39} -24.3075 q^{40} -2.95624 q^{41} -2.25637 q^{42} +5.22482 q^{43} +5.46313 q^{44} -7.64402 q^{45} +9.57541 q^{46} +6.75107 q^{47} -2.35133 q^{48} +20.4652 q^{49} -4.37424 q^{50} -0.00585550 q^{51} -32.0660 q^{52} +4.83982 q^{53} -2.57258 q^{54} +2.56928 q^{55} +49.5815 q^{56} -1.15813 q^{57} -2.28886 q^{58} +6.77803 q^{59} -2.21213 q^{60} -4.16001 q^{61} -3.72931 q^{62} +15.5920 q^{63} +29.8156 q^{64} -15.0804 q^{65} +0.430546 q^{66} +8.81152 q^{67} +0.202977 q^{68} +0.552403 q^{69} +36.7843 q^{70} -10.2332 q^{71} +28.1475 q^{72} +0.960007 q^{73} -13.7941 q^{74} -0.252349 q^{75} +40.1457 q^{76} -5.24072 q^{77} -2.52710 q^{78} -2.38437 q^{79} +38.3323 q^{80} +8.77707 q^{81} +8.07608 q^{82} +6.92736 q^{83} +4.51223 q^{84} +0.0954587 q^{85} -14.2735 q^{86} -0.132044 q^{87} -9.46082 q^{88} +3.29656 q^{89} +20.8825 q^{90} +30.7606 q^{91} -19.1486 q^{92} -0.215143 q^{93} -18.4430 q^{94} +18.8803 q^{95} +3.44146 q^{96} +10.2366 q^{97} -55.9082 q^{98} -2.97516 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 106 q - 13 q^{2} - 15 q^{3} + 93 q^{4} - 12 q^{5} - 22 q^{6} - 66 q^{7} - 39 q^{8} + 97 q^{9}+O(q^{10}) $ 106 * q - 13 * q^2 - 15 * q^3 + 93 * q^4 - 12 * q^5 - 22 * q^6 - 66 * q^7 - 39 * q^8 + 97 * q^9	\( 106 q - 13 q^{2} - 15 q^{3} + 93 q^{4} - 12 q^{5} - 22 q^{6} - 66 q^{7} - 39 q^{8} + 97 q^{9} - 30 q^{10} + 106 q^{11} - 26 q^{12} - 72 q^{13} + 3 q^{14} - 46 q^{15} + 75 q^{16} - 65 q^{17} - 37 q^{18} - 63 q^{19} - 25 q^{20} - 27 q^{21} - 13 q^{22} - 23 q^{23} - 56 q^{24} + 74 q^{25} + 2 q^{26} - 54 q^{27} - 115 q^{28} - 45 q^{29} - 14 q^{30} - 89 q^{31} - 96 q^{32} - 15 q^{33} - 26 q^{34} - 52 q^{35} + 91 q^{36} - 35 q^{37} + 7 q^{38} - 34 q^{39} - 74 q^{40} - 32 q^{41} - 94 q^{43} + 93 q^{44} - 46 q^{45} - 20 q^{46} - 105 q^{47} - 57 q^{48} + 80 q^{49} - 60 q^{50} - 36 q^{51} - 137 q^{52} - 61 q^{54} - 12 q^{55} + 32 q^{56} - 71 q^{57} - 28 q^{58} - 15 q^{59} - 21 q^{60} - 80 q^{61} - 84 q^{62} - 182 q^{63} + 55 q^{64} - 73 q^{65} - 22 q^{66} - 58 q^{67} - 145 q^{68} - 8 q^{69} - 39 q^{70} - 11 q^{71} - 100 q^{72} - 155 q^{73} - 15 q^{74} - 15 q^{75} - 132 q^{76} - 66 q^{77} - 45 q^{78} - 50 q^{79} - 28 q^{80} + 114 q^{81} - 57 q^{82} - 96 q^{83} - 27 q^{84} - 74 q^{85} + 54 q^{86} - 182 q^{87} - 39 q^{88} + 9 q^{89} - 53 q^{90} + 6 q^{91} - 18 q^{92} - 26 q^{93} - 33 q^{94} - 49 q^{95} - 56 q^{96} - 102 q^{97} - 76 q^{98} + 97 q^{99}+O(q^{100}) \) 106 * q - 13 * q^2 - 15 * q^3 + 93 * q^4 - 12 * q^5 - 22 * q^6 - 66 * q^7 - 39 * q^8 + 97 * q^9 - 30 * q^10 + 106 * q^11 - 26 * q^12 - 72 * q^13 + 3 * q^14 - 46 * q^15 + 75 * q^16 - 65 * q^17 - 37 * q^18 - 63 * q^19 - 25 * q^20 - 27 * q^21 - 13 * q^22 - 23 * q^23 - 56 * q^24 + 74 * q^25 + 2 * q^26 - 54 * q^27 - 115 * q^28 - 45 * q^29 - 14 * q^30 - 89 * q^31 - 96 * q^32 - 15 * q^33 - 26 * q^34 - 52 * q^35 + 91 * q^36 - 35 * q^37 + 7 * q^38 - 34 * q^39 - 74 * q^40 - 32 * q^41 - 94 * q^43 + 93 * q^44 - 46 * q^45 - 20 * q^46 - 105 * q^47 - 57 * q^48 + 80 * q^49 - 60 * q^50 - 36 * q^51 - 137 * q^52 - 61 * q^54 - 12 * q^55 + 32 * q^56 - 71 * q^57 - 28 * q^58 - 15 * q^59 - 21 * q^60 - 80 * q^61 - 84 * q^62 - 182 * q^63 + 55 * q^64 - 73 * q^65 - 22 * q^66 - 58 * q^67 - 145 * q^68 - 8 * q^69 - 39 * q^70 - 11 * q^71 - 100 * q^72 - 155 * q^73 - 15 * q^74 - 15 * q^75 - 132 * q^76 - 66 * q^77 - 45 * q^78 - 50 * q^79 - 28 * q^80 + 114 * q^81 - 57 * q^82 - 96 * q^83 - 27 * q^84 - 74 * q^85 + 54 * q^86 - 182 * q^87 - 39 * q^88 + 9 * q^89 - 53 * q^90 + 6 * q^91 - 18 * q^92 - 26 * q^93 - 33 * q^94 - 49 * q^95 - 56 * q^96 - 102 * q^97 - 76 * q^98 + 97 * 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 $

$2$	−2.73187	−1.93173	−0.965863	−	0.259055i	$-0.916589\pi$
$2$	−2.73187	−1.93173	−0.965863	+	0.259055i	$0.916589\pi$
$3$	−0.157601	−0.0909910	−0.0454955	−	0.998965i	$-0.514487\pi$
$3$	−0.157601	−0.0909910	−0.0454955	+	0.998965i	$0.514487\pi$
$4$	5.46313	2.73156
$5$	2.56928	1.14902	0.574508	−	0.818499i	$-0.305193\pi$
$5$	2.56928	1.14902	0.574508	+	0.818499i	$0.305193\pi$
$6$	0.430546	0.175770
$7$	−5.24072	−1.98081	−0.990403	−	0.138208i	$-0.955866\pi$
$7$	−5.24072	−1.98081	−0.990403	+	0.138208i	$0.955866\pi$
$8$	−9.46082	−3.34490
$9$	−2.97516	−0.991721
$10$	−7.01894	−2.21958
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	−0.860994	−0.248548
$13$	−5.86953	−1.62791	−0.813957	−	0.580925i	$-0.802691\pi$
$13$	−5.86953	−1.62791	−0.813957	+	0.580925i	$0.802691\pi$
$14$	14.3170	3.82637
$15$	−0.404921	−0.104550
$16$	14.9195	3.72987
$17$	0.0371539	0.00901115	0.00450557	−	0.999990i	$-0.498566\pi$
$17$	0.0371539	0.00901115	0.00450557	+	0.999990i	$0.498566\pi$
$18$	8.12776	1.91573
$19$	7.34848	1.68586	0.842929	−	0.538025i	$-0.180829\pi$
$19$	7.34848	1.68586	0.842929	+	0.538025i	$0.180829\pi$
$20$	14.0363	3.13861
$21$	0.825943	0.180236
$22$	−2.73187	−0.582437
$23$	−3.50507	−0.730858	−0.365429	−	0.930839i	$-0.619078\pi$
$23$	−3.50507	−0.730858	−0.365429	+	0.930839i	$0.619078\pi$
$24$	1.49103	0.304356
$25$	1.60119	0.320238
$26$	16.0348	3.14468
$27$	0.941692	0.181229
$28$	−28.6307	−5.41070
$29$	0.837837	0.155582	0.0777912	−	0.996970i	$-0.475213\pi$
$29$	0.837837	0.155582	0.0777912	+	0.996970i	$0.475213\pi$
$30$	1.10619	0.201962
$31$	1.36511	0.245181	0.122591	−	0.992457i	$-0.460880\pi$
$31$	1.36511	0.245181	0.122591	+	0.992457i	$0.460880\pi$
$32$	−21.8365	−3.86019
$33$	−0.157601	−0.0274348
$34$	−0.101500	−0.0174071
$35$	−13.4649	−2.27598
$36$	−16.2537	−2.70895
$37$	5.04931	0.830102	0.415051	−	0.909798i	$-0.363764\pi$
$37$	5.04931	0.830102	0.415051	+	0.909798i	$0.363764\pi$
$38$	−20.0751	−3.25661
$39$	0.925043	0.148125
$40$	−24.3075	−3.84335
$41$	−2.95624	−0.461688	−0.230844	−	0.972991i	$-0.574149\pi$
$41$	−2.95624	−0.461688	−0.230844	+	0.972991i	$0.574149\pi$
$42$	−2.25637	−0.348166
$43$	5.22482	0.796777	0.398389	−	0.917217i	$-0.369570\pi$
$43$	5.22482	0.796777	0.398389	+	0.917217i	$0.369570\pi$
$44$	5.46313	0.823597
$45$	−7.64402	−1.13950
$46$	9.57541	1.41182
$47$	6.75107	0.984744	0.492372	−	0.870385i	$-0.336130\pi$
$47$	6.75107	0.984744	0.492372	+	0.870385i	$0.336130\pi$
$48$	−2.35133	−0.339385
$49$	20.4652	2.92359
$50$	−4.37424	−0.618611
$51$	−0.00585550	−0.000819933 0
$52$	−32.0660	−4.44675
$53$	4.83982	0.664800	0.332400	−	0.943138i	$-0.392142\pi$
$53$	4.83982	0.664800	0.332400	+	0.943138i	$0.392142\pi$
$54$	−2.57258	−0.350084
$55$	2.56928	0.346441
$56$	49.5815	6.62561
$57$	−1.15813	−0.153398
$58$	−2.28886	−0.300542
$59$	6.77803	0.882425	0.441212	−	0.897403i	$-0.354549\pi$
$59$	6.77803	0.882425	0.441212	+	0.897403i	$0.354549\pi$
$60$	−2.21213	−0.285585
$61$	−4.16001	−0.532635	−0.266317	−	0.963885i	$-0.585807\pi$
$61$	−4.16001	−0.532635	−0.266317	+	0.963885i	$0.585807\pi$
$62$	−3.72931	−0.473623
$63$	15.5920	1.96441
$64$	29.8156	3.72695
$65$	−15.0804	−1.87050
$66$	0.430546	0.0529965
$67$	8.81152	1.07650	0.538249	−	0.842786i	$-0.319086\pi$
$67$	8.81152	1.07650	0.538249	+	0.842786i	$0.319086\pi$
$68$	0.202977	0.0246145
$69$	0.552403	0.0665015
$70$	36.7843	4.39656
$71$	−10.2332	−1.21446	−0.607230	−	0.794526i	$-0.707719\pi$
$71$	−10.2332	−1.21446	−0.607230	+	0.794526i	$0.707719\pi$
$72$	28.1475	3.31721
$73$	0.960007	0.112360	0.0561801	−	0.998421i	$-0.482108\pi$
$73$	0.960007	0.112360	0.0561801	+	0.998421i	$0.482108\pi$
$74$	−13.7941	−1.60353
$75$	−0.252349	−0.0291387
$76$	40.1457	4.60503
$77$	−5.24072	−0.597236
$78$	−2.52710	−0.286138
$79$	−2.38437	−0.268263	−0.134131	−	0.990964i	$-0.542824\pi$
$79$	−2.38437	−0.268263	−0.134131	+	0.990964i	$0.542824\pi$
$80$	38.3323	4.28568
$81$	8.77707	0.975230
$82$	8.07608	0.891854
$83$	6.92736	0.760377	0.380188	−	0.924909i	$-0.375859\pi$
$83$	6.92736	0.760377	0.380188	+	0.924909i	$0.375859\pi$
$84$	4.51223	0.492325
$85$	0.0954587	0.0103540
$86$	−14.2735	−1.53916
$87$	−0.132044	−0.0141566
$88$	−9.46082	−1.00853
$89$	3.29656	0.349434	0.174717	−	0.984619i	$-0.444099\pi$
$89$	3.29656	0.349434	0.174717	+	0.984619i	$0.444099\pi$
$90$	20.8825	2.20121
$91$	30.7606	3.22458
$92$	−19.1486	−1.99638
$93$	−0.215143	−0.0223093
$94$	−18.4430	−1.90226
$95$	18.8803	1.93708
$96$	3.44146	0.351242
$97$	10.2366	1.03937	0.519683	−	0.854359i	$-0.326050\pi$
$97$	10.2366	1.03937	0.519683	+	0.854359i	$0.326050\pi$
$98$	−55.9082	−5.64758
$99$	−2.97516	−0.299015
$100$	8.74749	0.874749
$101$	−1.42485	−0.141778	−0.0708889	−	0.997484i	$-0.522584\pi$
$101$	−1.42485	−0.141778	−0.0708889	+	0.997484i	$0.522584\pi$
$102$	0.0159965	0.00158389
$103$	−10.0955	−0.994739	−0.497370	−	0.867539i	$-0.665701\pi$
$103$	−10.0955	−0.994739	−0.497370	+	0.867539i	$0.665701\pi$
$104$	55.5305	5.44521
$105$	2.12208	0.207094
$106$	−13.2218	−1.28421
$107$	9.55763	0.923971	0.461985	−	0.886888i	$-0.347137\pi$
$107$	9.55763	0.923971	0.461985	+	0.886888i	$0.347137\pi$
$108$	5.14458	0.495037
$109$	2.36305	0.226339	0.113169	−	0.993576i	$-0.463900\pi$
$109$	2.36305	0.226339	0.113169	+	0.993576i	$0.463900\pi$
$110$	−7.01894	−0.669230
$111$	−0.795777	−0.0755318
$112$	−78.1889	−7.38816
$113$	−11.7275	−1.10323	−0.551613	−	0.834100i	$-0.685988\pi$
$113$	−11.7275	−1.10323	−0.551613	+	0.834100i	$0.685988\pi$
$114$	3.16386	0.296323
$115$	−9.00550	−0.839767
$116$	4.57721	0.424983
$117$	17.4628	1.61444
$118$	−18.5167	−1.70460
$119$	−0.194713	−0.0178493
$120$	3.83088	0.349710
$121$	1.00000	0.0909091
$122$	11.3646	1.02890
$123$	0.465907	0.0420094
$124$	7.45777	0.669728
$125$	−8.73249	−0.781058
$126$	−42.5953	−3.79469
$127$	−15.6522	−1.38891	−0.694453	−	0.719538i	$-0.744354\pi$
$127$	−15.6522	−1.38891	−0.694453	+	0.719538i	$0.744354\pi$
$128$	−37.7793	−3.33925
$129$	−0.823437	−0.0724996
$130$	41.1978	3.61329
$131$	−5.17965	−0.452548	−0.226274	−	0.974064i	$-0.572654\pi$
$131$	−5.17965	−0.452548	−0.226274	+	0.974064i	$0.572654\pi$
$132$	−0.860994	−0.0749399
$133$	−38.5114	−3.33936
$134$	−24.0719	−2.07950
$135$	2.41947	0.208235
$136$	−0.351506	−0.0301414
$137$	−12.0733	−1.03149	−0.515746	−	0.856741i	$-0.672485\pi$
$137$	−12.0733	−1.03149	−0.515746	+	0.856741i	$0.672485\pi$
$138$	−1.50909	−0.128463
$139$	20.7489	1.75990	0.879951	−	0.475065i	$-0.157576\pi$
$139$	20.7489	1.75990	0.879951	+	0.475065i	$0.157576\pi$
$140$	−73.5603	−6.21698
$141$	−1.06397	−0.0896029
$142$	27.9559	2.34600
$143$	−5.86953	−0.490834
$144$	−44.3879	−3.69899
$145$	2.15263	0.178767
$146$	−2.62262	−0.217049
$147$	−3.22533	−0.266021
$148$	27.5850	2.26748
$149$	−5.61262	−0.459804	−0.229902	−	0.973214i	$-0.573841\pi$
$149$	−5.61262	−0.459804	−0.229902	+	0.973214i	$0.573841\pi$
$150$	0.689385	0.0562880
$151$	−5.89696	−0.479888	−0.239944	−	0.970787i	$-0.577129\pi$
$151$	−5.89696	−0.479888	−0.239944	+	0.970787i	$0.577129\pi$
$152$	−69.5227	−5.63903
$153$	−0.110539	−0.00893654
$154$	14.3170	1.15370
$155$	3.50735	0.281717
$156$	5.05363	0.404614
$157$	−24.0535	−1.91968	−0.959840	−	0.280549i	$-0.909483\pi$
$157$	−24.0535	−1.91968	−0.959840	+	0.280549i	$0.909483\pi$
$158$	6.51380	0.518210
$159$	−0.762760	−0.0604908
$160$	−56.1041	−4.43542
$161$	18.3691	1.44769
$162$	−23.9778	−1.88388
$163$	−16.5039	−1.29268	−0.646341	−	0.763049i	$-0.723702\pi$
$163$	−16.5039	−1.29268	−0.646341	+	0.763049i	$0.723702\pi$
$164$	−16.1503	−1.26113
$165$	−0.404921	−0.0315230
$166$	−18.9247	−1.46884
$167$	−14.0421	−1.08661	−0.543306	−	0.839534i	$-0.682828\pi$
$167$	−14.0421	−1.08661	−0.543306	+	0.839534i	$0.682828\pi$
$168$	−7.81410	−0.602871
$169$	21.4513	1.65010
$170$	−0.260781	−0.0200010
$171$	−21.8629	−1.67190
$172$	28.5438	2.17645
$173$	22.7459	1.72934	0.864668	−	0.502343i	$-0.167528\pi$
$173$	22.7459	1.72934	0.864668	+	0.502343i	$0.167528\pi$
$174$	0.360727	0.0273466
$175$	−8.39138	−0.634329
$176$	14.9195	1.12460
$177$	−1.06823	−0.0802927
$178$	−9.00577	−0.675011
$179$	−7.90539	−0.590876	−0.295438	−	0.955362i	$-0.595466\pi$
$179$	−7.90539	−0.590876	−0.295438	+	0.955362i	$0.595466\pi$
$180$	−41.7602	−3.11262
$181$	−24.4062	−1.81410	−0.907048	−	0.421027i	$-0.861670\pi$
$181$	−24.4062	−1.81410	−0.907048	+	0.421027i	$0.861670\pi$
$182$	−84.0339	−6.22901
$183$	0.655622	0.0484650
$184$	33.1608	2.44465
$185$	12.9731	0.953800
$186$	0.587743	0.0430954
$187$	0.0371539	0.00271696
$188$	36.8819	2.68989
$189$	−4.93514	−0.358979
$190$	−51.5786	−3.74190
$191$	3.82760	0.276956	0.138478	−	0.990366i	$-0.455779\pi$
$191$	3.82760	0.276956	0.138478	+	0.990366i	$0.455779\pi$
$192$	−4.69896	−0.339119
$193$	3.80124	0.273619	0.136810	−	0.990597i	$-0.456315\pi$
$193$	3.80124	0.273619	0.136810	+	0.990597i	$0.456315\pi$
$194$	−27.9650	−2.00777
$195$	2.37669	0.170199
$196$	111.804	7.98598
$197$	14.8583	1.05861	0.529303	−	0.848433i	$-0.322453\pi$
$197$	14.8583	1.05861	0.529303	+	0.848433i	$0.322453\pi$
$198$	8.12776	0.577615
$199$	−23.5277	−1.66783	−0.833917	−	0.551890i	$-0.813907\pi$
$199$	−23.5277	−1.66783	−0.833917	+	0.551890i	$0.813907\pi$
$200$	−15.1485	−1.07116
$201$	−1.38870	−0.0979516
$202$	3.89250	0.273876
$203$	−4.39087	−0.308179
$204$	−0.0319893	−0.00223970
$205$	−7.59541	−0.530486
$206$	27.5796	1.92156
$207$	10.4282	0.724807
$208$	−87.5703	−6.07191
$209$	7.34848	0.508305
$210$	−5.79724	−0.400048
$211$	−5.00325	−0.344438	−0.172219	−	0.985059i	$-0.555094\pi$
$211$	−5.00325	−0.344438	−0.172219	+	0.985059i	$0.555094\pi$
$212$	26.4405	1.81594
$213$	1.61277	0.110505
$214$	−26.1102	−1.78486
$215$	13.4240	0.915510
$216$	−8.90917	−0.606192
$217$	−7.15417	−0.485657
$218$	−6.45555	−0.437225
$219$	−0.151298	−0.0102238
$220$	14.0363	0.946326
$221$	−0.218076	−0.0146694
$222$	2.17396	0.145907
$223$	−26.3785	−1.76643	−0.883217	−	0.468965i	$-0.844627\pi$
$223$	−26.3785	−1.76643	−0.883217	+	0.468965i	$0.844627\pi$
$224$	114.439	7.64628
$225$	−4.76379	−0.317586
$226$	32.0379	2.13113
$227$	−26.5402	−1.76153	−0.880766	−	0.473552i	$-0.842972\pi$
$227$	−26.5402	−1.76153	−0.880766	+	0.473552i	$0.842972\pi$
$228$	−6.32700	−0.419016
$229$	11.8693	0.784343	0.392172	−	0.919892i	$-0.371724\pi$
$229$	11.8693	0.784343	0.392172	+	0.919892i	$0.371724\pi$
$230$	24.6019	1.62220
$231$	0.825943	0.0543431
$232$	−7.92662	−0.520408
$233$	1.28760	0.0843536	0.0421768	−	0.999110i	$-0.486571\pi$
$233$	1.28760	0.0843536	0.0421768	+	0.999110i	$0.486571\pi$
$234$	−47.7061	−3.11865
$235$	17.3454	1.13149
$236$	37.0293	2.41040
$237$	0.375779	0.0244095
$238$	0.531932	0.0344800
$239$	−20.7077	−1.33947	−0.669734	−	0.742601i	$-0.733592\pi$
$239$	−20.7077	−1.33947	−0.669734	+	0.742601i	$0.733592\pi$
$240$	−6.04121	−0.389959
$241$	−12.6613	−0.815585	−0.407792	−	0.913075i	$-0.633701\pi$
$241$	−12.6613	−0.815585	−0.407792	+	0.913075i	$0.633701\pi$
$242$	−2.73187	−0.175611
$243$	−4.20835	−0.269966
$244$	−22.7267	−1.45493
$245$	52.5807	3.35926
$246$	−1.27280	−0.0811506
$247$	−43.1321	−2.74443
$248$	−12.9151	−0.820108
$249$	−1.09176	−0.0691875
$250$	23.8561	1.50879
$251$	10.8385	0.684121	0.342060	−	0.939678i	$-0.388875\pi$
$251$	10.8385	0.684121	0.342060	+	0.939678i	$0.388875\pi$
$252$	85.1810	5.36590
$253$	−3.50507	−0.220362
$254$	42.7598	2.68299
$255$	−0.0150444	−0.000942117 0
$256$	43.5771	2.72357
$257$	27.1587	1.69411	0.847057	−	0.531502i	$-0.178372\pi$
$257$	27.1587	1.69411	0.847057	+	0.531502i	$0.178372\pi$
$258$	2.24952	0.140049
$259$	−26.4620	−1.64427
$260$	−82.3864	−5.10938
$261$	−2.49270	−0.154294
$262$	14.1501	0.874198
$263$	23.4738	1.44745	0.723727	−	0.690086i	$-0.242427\pi$
$263$	23.4738	1.44745	0.723727	+	0.690086i	$0.242427\pi$
$264$	1.49103	0.0917668
$265$	12.4348	0.763866
$266$	105.208	6.45072
$267$	−0.519541	−0.0317954
$268$	48.1384	2.94052
$269$	15.0039	0.914807	0.457403	−	0.889259i	$-0.348780\pi$
$269$	15.0039	0.914807	0.457403	+	0.889259i	$0.348780\pi$
$270$	−6.60968	−0.402252
$271$	−11.2002	−0.680363	−0.340182	−	0.940360i	$-0.610489\pi$
$271$	−11.2002	−0.680363	−0.340182	+	0.940360i	$0.610489\pi$
$272$	0.554318	0.0336104
$273$	−4.84789	−0.293408
$274$	32.9827	1.99256
$275$	1.60119	0.0965553
$276$	3.01785	0.181653
$277$	−26.1664	−1.57219	−0.786095	−	0.618106i	$-0.787900\pi$
$277$	−26.1664	−1.57219	−0.786095	+	0.618106i	$0.787900\pi$
$278$	−56.6834	−3.39965
$279$	−4.06143	−0.243151
$280$	127.389	7.61293
$281$	26.2595	1.56651	0.783255	−	0.621701i	$-0.213558\pi$
$281$	26.2595	1.56651	0.783255	+	0.621701i	$0.213558\pi$
$282$	2.90664	0.173088
$283$	−24.5286	−1.45807	−0.729036	−	0.684475i	$-0.760031\pi$
$283$	−24.5286	−1.45807	−0.729036	+	0.684475i	$0.760031\pi$
$284$	−55.9054	−3.31738
$285$	−2.97555	−0.176257
$286$	16.0348	0.948157
$287$	15.4928	0.914514
$288$	64.9671	3.82823
$289$	−16.9986	−0.999919
$290$	−5.88072	−0.345328
$291$	−1.61329	−0.0945730
$292$	5.24464	0.306919
$293$	23.6369	1.38088	0.690441	−	0.723389i	$-0.257416\pi$
$293$	23.6369	1.38088	0.690441	+	0.723389i	$0.257416\pi$
$294$	8.81119	0.513879
$295$	17.4147	1.01392
$296$	−47.7706	−2.77661
$297$	0.941692	0.0546425
$298$	15.3330	0.888214
$299$	20.5731	1.18977
$300$	−1.37861	−0.0795943
$301$	−27.3818	−1.57826
$302$	16.1098	0.927012
$303$	0.224558	0.0129005
$304$	109.636	6.28804
$305$	−10.6882	−0.612006
$306$	0.301978	0.0172629
$307$	17.1691	0.979891	0.489945	−	0.871753i	$-0.337017\pi$
$307$	17.1691	0.979891	0.489945	+	0.871753i	$0.337017\pi$
$308$	−28.6307	−1.63139
$309$	1.59106	0.0905123
$310$	−9.58163	−0.544200
$311$	−18.5309	−1.05079	−0.525395	−	0.850858i	$-0.676083\pi$
$311$	−18.5309	−1.05079	−0.525395	+	0.850858i	$0.676083\pi$
$312$	−8.75167	−0.495466
$313$	−24.2433	−1.37031	−0.685157	−	0.728395i	$-0.740266\pi$
$313$	−24.2433	−1.37031	−0.685157	+	0.728395i	$0.740266\pi$
$314$	65.7111	3.70829
$315$	40.0602	2.25713
$316$	−13.0261	−0.732776
$317$	−0.180553	−0.0101409	−0.00507043	−	0.999987i	$-0.501614\pi$
$317$	−0.180553	−0.0101409	−0.00507043	+	0.999987i	$0.501614\pi$
$318$	2.08376	0.116852
$319$	0.837837	0.0469098
$320$	76.6045	4.28232
$321$	−1.50629	−0.0840730
$322$	−50.1820	−2.79654
$323$	0.273025	0.0151915
$324$	47.9503	2.66390
$325$	−9.39822	−0.521319
$326$	45.0864	2.49711
$327$	−0.372419	−0.0205948
$328$	27.9685	1.54430
$329$	−35.3805	−1.95059
$330$	1.10619	0.0608939
$331$	2.08357	0.114523	0.0572617	−	0.998359i	$-0.481763\pi$
$331$	2.08357	0.114523	0.0572617	+	0.998359i	$0.481763\pi$
$332$	37.8451	2.07702
$333$	−15.0225	−0.823229
$334$	38.3613	2.09904
$335$	22.6392	1.23691
$336$	12.3227	0.672256
$337$	5.70795	0.310932	0.155466	−	0.987841i	$-0.450312\pi$
$337$	5.70795	0.310932	0.155466	+	0.987841i	$0.450312\pi$
$338$	−58.6023	−3.18755
$339$	1.84826	0.100384
$340$	0.521503	0.0282825
$341$	1.36511	0.0739249
$342$	59.7267	3.22965
$343$	−70.5672	−3.81027
$344$	−49.4311	−2.66514
$345$	1.41928	0.0764113
$346$	−62.1388	−3.34060
$347$	−29.2406	−1.56972	−0.784859	−	0.619675i	$-0.787264\pi$
$347$	−29.2406	−1.56972	−0.784859	+	0.619675i	$0.787264\pi$
$348$	−0.721372	−0.0386696
$349$	−5.34262	−0.285984	−0.142992	−	0.989724i	$-0.545672\pi$
$349$	−5.34262	−0.285984	−0.142992	+	0.989724i	$0.545672\pi$
$350$	22.9242	1.22535
$351$	−5.52728	−0.295025
$352$	−21.8365	−1.16389
$353$	−15.7190	−0.836638	−0.418319	−	0.908300i	$-0.637381\pi$
$353$	−15.7190	−0.836638	−0.418319	+	0.908300i	$0.637381\pi$
$354$	2.91825	0.155103
$355$	−26.2920	−1.39543
$356$	18.0095	0.954502
$357$	0.0306870	0.00162413
$358$	21.5965	1.14141
$359$	−0.343054	−0.0181057	−0.00905284	−	0.999959i	$-0.502882\pi$
$359$	−0.343054	−0.0181057	−0.00905284	+	0.999959i	$0.502882\pi$
$360$	72.3186	3.81153
$361$	35.0002	1.84212
$362$	66.6745	3.50434
$363$	−0.157601	−0.00827191
$364$	168.049	8.80815
$365$	2.46652	0.129104
$366$	−1.79108	−0.0936210
$367$	20.0334	1.04574	0.522868	−	0.852414i	$-0.324862\pi$
$367$	20.0334	1.04574	0.522868	+	0.852414i	$0.324862\pi$
$368$	−52.2939	−2.72601
$369$	8.79530	0.457865
$370$	−35.4408	−1.84248
$371$	−25.3641	−1.31684
$372$	−1.17535	−0.0609392
$373$	−13.1037	−0.678486	−0.339243	−	0.940699i	$-0.610171\pi$
$373$	−13.1037	−0.678486	−0.339243	+	0.940699i	$0.610171\pi$
$374$	−0.101500	−0.00524843
$375$	1.37625	0.0710692
$376$	−63.8706	−3.29387
$377$	−4.91770	−0.253275
$378$	13.4822	0.693449
$379$	−0.966986	−0.0496707	−0.0248354	−	0.999692i	$-0.507906\pi$
$379$	−0.966986	−0.0496707	−0.0248354	+	0.999692i	$0.507906\pi$
$380$	103.145	5.29125
$381$	2.46680	0.126378
$382$	−10.4565	−0.535002
$383$	−22.6049	−1.15506	−0.577529	−	0.816370i	$-0.695983\pi$
$383$	−22.6049	−1.15506	−0.577529	+	0.816370i	$0.695983\pi$
$384$	5.95406	0.303842
$385$	−13.4649	−0.686233
$386$	−10.3845	−0.528557
$387$	−15.5447	−0.790181
$388$	55.9237	2.83910
$389$	−27.3335	−1.38586	−0.692931	−	0.721004i	$-0.743681\pi$
$389$	−27.3335	−1.38586	−0.692931	+	0.721004i	$0.743681\pi$
$390$	−6.49282	−0.328777
$391$	−0.130227	−0.00658587
$392$	−193.617	−9.77914
$393$	0.816318	0.0411778
$394$	−40.5909	−2.04494
$395$	−6.12611	−0.308238
$396$	−16.2537	−0.816778
$397$	24.8277	1.24606	0.623032	−	0.782196i	$-0.285901\pi$
$397$	24.8277	1.24606	0.623032	+	0.782196i	$0.285901\pi$
$398$	64.2747	3.22180
$399$	6.06943	0.303852
$400$	23.8889	1.19445
$401$	−24.6724	−1.23208	−0.616040	−	0.787715i	$-0.711264\pi$
$401$	−24.6724	−1.23208	−0.616040	+	0.787715i	$0.711264\pi$
$402$	3.79376	0.189216
$403$	−8.01256	−0.399134
$404$	−7.78413	−0.387275
$405$	22.5507	1.12056
$406$	11.9953	0.595316
$407$	5.04931	0.250285
$408$	0.0553978	0.00274260
$409$	−5.03835	−0.249130	−0.124565	−	0.992211i	$-0.539754\pi$
$409$	−5.03835	−0.249130	−0.124565	+	0.992211i	$0.539754\pi$
$410$	20.7497	1.02475
$411$	1.90277	0.0938566
$412$	−55.1530	−2.71719
$413$	−35.5218	−1.74791
$414$	−28.4884	−1.40013
$415$	17.7983	0.873685
$416$	128.170	6.28405
$417$	−3.27005	−0.160135
$418$	−20.0751	−0.981906
$419$	−11.0465	−0.539654	−0.269827	−	0.962909i	$-0.586967\pi$
$419$	−11.0465	−0.539654	−0.269827	+	0.962909i	$0.586967\pi$
$420$	11.5932	0.565689
$421$	27.4976	1.34015	0.670076	−	0.742293i	$-0.266262\pi$
$421$	27.4976	1.34015	0.670076	+	0.742293i	$0.266262\pi$
$422$	13.6682	0.665359
$423$	−20.0855	−0.976591
$424$	−45.7886	−2.22369
$425$	0.0594904	0.00288571
$426$	−4.40587	−0.213465
$427$	21.8015	1.05505
$428$	52.2145	2.52388
$429$	0.925043	0.0446615
$430$	−36.6727	−1.76851
$431$	−22.5048	−1.08402	−0.542010	−	0.840372i	$-0.682337\pi$
$431$	−22.5048	−1.08402	−0.542010	+	0.840372i	$0.682337\pi$
$432$	14.0496	0.675960
$433$	27.9936	1.34529	0.672644	−	0.739966i	$-0.265159\pi$
$433$	27.9936	1.34529	0.672644	+	0.739966i	$0.265159\pi$
$434$	19.5443	0.938155
$435$	−0.339257	−0.0162661
$436$	12.9096	0.618259
$437$	−25.7570	−1.23212
$438$	0.413327	0.0197495
$439$	5.00556	0.238902	0.119451	−	0.992840i	$-0.461887\pi$
$439$	5.00556	0.238902	0.119451	+	0.992840i	$0.461887\pi$
$440$	−24.3075	−1.15881
$441$	−60.8872	−2.89939
$442$	0.595755	0.0283372
$443$	−3.95941	−0.188117	−0.0940587	−	0.995567i	$-0.529984\pi$
$443$	−3.95941	−0.188117	−0.0940587	+	0.995567i	$0.529984\pi$
$444$	−4.34743	−0.206320
$445$	8.46977	0.401506
$446$	72.0626	3.41226
$447$	0.884554	0.0418380
$448$	−156.255	−7.38236
$449$	33.9166	1.60063	0.800313	−	0.599583i	$-0.204667\pi$
$449$	33.9166	1.60063	0.800313	+	0.599583i	$0.204667\pi$
$450$	13.0141	0.613489
$451$	−2.95624	−0.139204
$452$	−64.0686	−3.01353
$453$	0.929368	0.0436655
$454$	72.5043	3.40280
$455$	79.0324	3.70510
$456$	10.9568	0.513101
$457$	−23.3153	−1.09064	−0.545321	−	0.838227i	$-0.683592\pi$
$457$	−23.3153	−1.09064	−0.545321	+	0.838227i	$0.683592\pi$
$458$	−32.4253	−1.51514
$459$	0.0349875	0.00163308
$460$	−49.1982	−2.29388
$461$	−26.9218	−1.25387	−0.626936	−	0.779070i	$-0.715691\pi$
$461$	−26.9218	−1.25387	−0.626936	+	0.779070i	$0.715691\pi$
$462$	−2.25637	−0.104976
$463$	−19.1265	−0.888886	−0.444443	−	0.895807i	$-0.646598\pi$
$463$	−19.1265	−0.888886	−0.444443	+	0.895807i	$0.646598\pi$
$464$	12.5001	0.580302
$465$	−0.552762	−0.0256337
$466$	−3.51756	−0.162948
$467$	34.4993	1.59644	0.798220	−	0.602367i	$-0.205775\pi$
$467$	34.4993	1.59644	0.798220	+	0.602367i	$0.205775\pi$
$468$	95.4014	4.40993
$469$	−46.1787	−2.13233
$470$	−47.3853	−2.18572
$471$	3.79086	0.174674
$472$	−64.1257	−2.95163
$473$	5.22482	0.240237
$474$	−1.02658	−0.0471524
$475$	11.7663	0.539875
$476$	−1.06374	−0.0487566
$477$	−14.3992	−0.659296
$478$	56.5707	2.58749
$479$	19.2630	0.880151	0.440076	−	0.897961i	$-0.354952\pi$
$479$	19.2630	0.880151	0.440076	+	0.897961i	$0.354952\pi$
$480$	8.84206	0.403583
$481$	−29.6371	−1.35133
$482$	34.5890	1.57549
$483$	−2.89499	−0.131727
$484$	5.46313	0.248324
$485$	26.3006	1.19425
$486$	11.4967	0.521500
$487$	−1.31178	−0.0594424	−0.0297212	−	0.999558i	$-0.509462\pi$
$487$	−1.31178	−0.0594424	−0.0297212	+	0.999558i	$0.509462\pi$
$488$	39.3571	1.78161
$489$	2.60102	0.117622
$490$	−143.644	−6.48916
$491$	39.3594	1.77627	0.888133	−	0.459586i	$-0.152002\pi$
$491$	39.3594	1.77627	0.888133	+	0.459586i	$0.152002\pi$
$492$	2.54531	0.114751
$493$	0.0311289	0.00140198
$494$	117.831	5.30149
$495$	−7.64402	−0.343573
$496$	20.3668	0.914495
$497$	53.6295	2.40561
$498$	2.98255	0.133651
$499$	−11.5307	−0.516185	−0.258092	−	0.966120i	$-0.583094\pi$
$499$	−11.5307	−0.516185	−0.258092	+	0.966120i	$0.583094\pi$
$500$	−47.7067	−2.13351
$501$	2.21305	0.0988720
$502$	−29.6094	−1.32153
$503$	34.0563	1.51849	0.759247	−	0.650802i	$-0.225567\pi$
$503$	34.0563	1.51849	0.759247	+	0.650802i	$0.225567\pi$
$504$	−147.513	−6.57075
$505$	−3.66083	−0.162905
$506$	9.57541	0.425679
$507$	−3.38075	−0.150145
$508$	−85.5099	−3.79389
$509$	31.6683	1.40367	0.701837	−	0.712338i	$-0.252364\pi$
$509$	31.6683	1.40367	0.701837	+	0.712338i	$0.252364\pi$
$510$	0.0410994	0.00181991
$511$	−5.03113	−0.222564
$512$	−43.4885	−1.92194
$513$	6.92001	0.305526
$514$	−74.1941	−3.27256
$515$	−25.9381	−1.14297
$516$	−4.49854	−0.198037
$517$	6.75107	0.296912
$518$	72.2909	3.17628
$519$	−3.58477	−0.157354
$520$	142.673	6.25664
$521$	15.5890	0.682966	0.341483	−	0.939888i	$-0.389071\pi$
$521$	15.5890	0.682966	0.341483	+	0.939888i	$0.389071\pi$
$522$	6.80974	0.298054
$523$	28.4761	1.24517	0.622587	−	0.782550i	$-0.286082\pi$
$523$	28.4761	1.24517	0.622587	+	0.782550i	$0.286082\pi$
$524$	−28.2971	−1.23616
$525$	1.32249	0.0577182
$526$	−64.1273	−2.79608
$527$	0.0507192	0.00220936
$528$	−2.35133	−0.102328
$529$	−10.7145	−0.465847
$530$	−33.9704	−1.47558
$531$	−20.1658	−0.875119
$532$	−210.392	−9.12167
$533$	17.3517	0.751587
$534$	1.41932	0.0614199
$535$	24.5562	1.06166
$536$	−83.3641	−3.60078
$537$	1.24590	0.0537644
$538$	−40.9889	−1.76716
$539$	20.4652	0.881497
$540$	13.2179	0.568806
$541$	30.6768	1.31890	0.659448	−	0.751750i	$-0.270790\pi$
$541$	30.6768	1.31890	0.659448	+	0.751750i	$0.270790\pi$
$542$	30.5975	1.31428
$543$	3.84644	0.165066
$544$	−0.811312	−0.0347847
$545$	6.07133	0.260067
$546$	13.2438	0.566784
$547$	1.00000	0.0427569
$547$	1.00000	0.0427569
$548$	−65.9580	−2.81759
$549$	12.3767	0.528225
$550$	−4.37424	−0.186518
$551$	6.15683	0.262290
$552$	−5.22618	−0.222441
$553$	12.4958	0.531377
$554$	71.4834	3.03704
$555$	−2.04457	−0.0867872
$556$	113.354	4.80728
$557$	−16.9107	−0.716530	−0.358265	−	0.933620i	$-0.616632\pi$
$557$	−16.9107	−0.716530	−0.358265	+	0.933620i	$0.616632\pi$
$558$	11.0953	0.469701
$559$	−30.6672	−1.29708
$560$	−200.889	−8.48911
$561$	−0.00585550	−0.000247219 0
$562$	−71.7376	−3.02607
$563$	−14.4225	−0.607837	−0.303919	−	0.952698i	$-0.598295\pi$
$563$	−14.4225	−0.607837	−0.303919	+	0.952698i	$0.598295\pi$
$564$	−5.81263	−0.244756
$565$	−30.1311	−1.26763
$566$	67.0089	2.81659
$567$	−45.9982	−1.93174
$568$	96.8147	4.06225
$569$	−34.7394	−1.45635	−0.728175	−	0.685391i	$-0.759631\pi$
$569$	−34.7394	−1.45635	−0.728175	+	0.685391i	$0.759631\pi$
$570$	8.12883	0.340479
$571$	11.4336	0.478481	0.239241	−	0.970960i	$-0.423102\pi$
$571$	11.4336	0.478481	0.239241	+	0.970960i	$0.423102\pi$
$572$	−32.0660	−1.34075
$573$	−0.603234	−0.0252005
$574$	−42.3245	−1.76659
$575$	−5.61228	−0.234048
$576$	−88.7061	−3.69609
$577$	3.65403	0.152119	0.0760596	−	0.997103i	$-0.475766\pi$
$577$	3.65403	0.152119	0.0760596	+	0.997103i	$0.475766\pi$
$578$	46.4381	1.93157
$579$	−0.599080	−0.0248969
$580$	11.7601	0.488312
$581$	−36.3044	−1.50616
$582$	4.40731	0.182689
$583$	4.83982	0.200445
$584$	−9.08245	−0.375834
$585$	44.8668	1.85501
$586$	−64.5730	−2.66749
$587$	−20.4690	−0.844844	−0.422422	−	0.906399i	$-0.638820\pi$
$587$	−20.4690	−0.844844	−0.422422	+	0.906399i	$0.638820\pi$
$588$	−17.6204	−0.726652
$589$	10.0315	0.413341
$590$	−47.5746	−1.95862
$591$	−2.34168	−0.0963237
$592$	75.3332	3.09617
$593$	−12.8228	−0.526571	−0.263285	−	0.964718i	$-0.584806\pi$
$593$	−12.8228	−0.526571	−0.263285	+	0.964718i	$0.584806\pi$
$594$	−2.57258	−0.105554
$595$	−0.500273	−0.0205092
$596$	−30.6624	−1.25598
$597$	3.70799	0.151758
$598$	−56.2031	−2.29832
$599$	−16.8927	−0.690217	−0.345108	−	0.938563i	$-0.612158\pi$
$599$	−16.8927	−0.690217	−0.345108	+	0.938563i	$0.612158\pi$
$600$	2.38743	0.0974663
$601$	34.0593	1.38931	0.694655	−	0.719343i	$-0.255557\pi$
$601$	34.0593	1.38931	0.694655	+	0.719343i	$0.255557\pi$
$602$	74.8036	3.04877
$603$	−26.2157	−1.06759
$604$	−32.2159	−1.31084
$605$	2.56928	0.104456
$606$	−0.613463	−0.0249202
$607$	−11.2167	−0.455274	−0.227637	−	0.973746i	$-0.573100\pi$
$607$	−11.2167	−0.455274	−0.227637	+	0.973746i	$0.573100\pi$
$608$	−160.465	−6.50772
$609$	0.692005	0.0280415
$610$	29.1989	1.18223
$611$	−39.6256	−1.60308
$612$	−0.603888	−0.0244107
$613$	10.4189	0.420815	0.210408	−	0.977614i	$-0.432521\pi$
$613$	10.4189	0.420815	0.210408	+	0.977614i	$0.432521\pi$
$614$	−46.9037	−1.89288
$615$	1.19704	0.0482695
$616$	49.5815	1.99770
$617$	25.1418	1.01217	0.506086	−	0.862483i	$-0.331092\pi$
$617$	25.1418	1.01217	0.506086	+	0.862483i	$0.331092\pi$
$618$	−4.34658	−0.174845
$619$	−5.44850	−0.218994	−0.109497	−	0.993987i	$-0.534924\pi$
$619$	−5.44850	−0.218994	−0.109497	+	0.993987i	$0.534924\pi$
$620$	19.1611	0.769528
$621$	−3.30070	−0.132452
$622$	50.6241	2.02984
$623$	−17.2763	−0.692162
$624$	13.8012	0.552489
$625$	−30.4421	−1.21769
$626$	66.2297	2.64707
$627$	−1.15813	−0.0462512
$628$	−131.407	−5.24372
$629$	0.187602	0.00748017
$630$	−109.439	−4.36016
$631$	2.32525	0.0925669	0.0462834	−	0.998928i	$-0.485262\pi$
$631$	2.32525	0.0925669	0.0462834	+	0.998928i	$0.485262\pi$
$632$	22.5581	0.897313
$633$	0.788517	0.0313407
$634$	0.493247	0.0195893
$635$	−40.2148	−1.59588
$636$	−4.16706	−0.165235
$637$	−120.121	−4.75936
$638$	−2.28886	−0.0906169
$639$	30.4455	1.20441
$640$	−97.0655	−3.83685
$641$	46.3201	1.82953	0.914767	−	0.403981i	$-0.132374\pi$
$641$	46.3201	1.82953	0.914767	+	0.403981i	$0.132374\pi$
$642$	4.11500	0.162406
$643$	−12.6051	−0.497096	−0.248548	−	0.968620i	$-0.579953\pi$
$643$	−12.6051	−0.497096	−0.248548	+	0.968620i	$0.579953\pi$
$644$	100.353	3.95445
$645$	−2.11564	−0.0833032
$646$	−0.745869	−0.0293458
$647$	28.4620	1.11896	0.559479	−	0.828845i	$-0.311001\pi$
$647$	28.4620	1.11896	0.559479	+	0.828845i	$0.311001\pi$
$648$	−83.0383	−3.26205
$649$	6.77803	0.266061
$650$	25.6747	1.00705
$651$	1.12750	0.0441904
$652$	−90.1626	−3.53104
$653$	26.7712	1.04764	0.523819	−	0.851830i	$-0.324507\pi$
$653$	26.7712	1.04764	0.523819	+	0.851830i	$0.324507\pi$
$654$	1.01740	0.0397835
$655$	−13.3080	−0.519985
$656$	−44.1056	−1.72204
$657$	−2.85618	−0.111430
$658$	96.6549	3.76800
$659$	−19.2650	−0.750460	−0.375230	−	0.926932i	$-0.622436\pi$
$659$	−19.2650	−0.750460	−0.375230	+	0.926932i	$0.622436\pi$
$660$	−2.21213	−0.0861072
$661$	−23.7344	−0.923161	−0.461580	−	0.887098i	$-0.652717\pi$
$661$	−23.7344	−0.923161	−0.461580	+	0.887098i	$0.652717\pi$
$662$	−5.69205	−0.221228
$663$	0.0343690	0.00133478
$664$	−65.5385	−2.54339
$665$	−98.9464	−3.83698
$666$	41.0396	1.59025
$667$	−2.93668	−0.113709
$668$	−76.7139	−2.96815
$669$	4.15727	0.160730
$670$	−61.8475	−2.38938
$671$	−4.16001	−0.160595
$672$	−18.0357	−0.695743
$673$	−11.4270	−0.440477	−0.220239	−	0.975446i	$-0.570684\pi$
$673$	−11.4270	−0.440477	−0.220239	+	0.975446i	$0.570684\pi$
$674$	−15.5934	−0.600635
$675$	1.50783	0.0580362
$676$	117.191	4.50736
$677$	7.14029	0.274424	0.137212	−	0.990542i	$-0.456186\pi$
$677$	7.14029	0.274424	0.137212	+	0.990542i	$0.456186\pi$
$678$	−5.04921	−0.193914
$679$	−53.6470	−2.05878
$680$	−0.903118	−0.0346330
$681$	4.18276	0.160284
$682$	−3.72931	−0.142803
$683$	23.2320	0.888946	0.444473	−	0.895792i	$-0.353391\pi$
$683$	23.2320	0.888946	0.444473	+	0.895792i	$0.353391\pi$
$684$	−119.440	−4.56690
$685$	−31.0197	−1.18520
$686$	192.780	7.36039
$687$	−1.87061	−0.0713682
$688$	77.9516	2.97188
$689$	−28.4074	−1.08224
$690$	−3.87728	−0.147606
$691$	−42.1437	−1.60322	−0.801612	−	0.597845i	$-0.796024\pi$
$691$	−42.1437	−1.60322	−0.801612	+	0.597845i	$0.796024\pi$
$692$	124.264	4.72379
$693$	15.5920	0.592291
$694$	79.8816	3.03226
$695$	53.3098	2.02215
$696$	1.24924	0.0473524
$697$	−0.109836	−0.00416034
$698$	14.5954	0.552443
$699$	−0.202927	−0.00767542
$700$	−45.8432	−1.73271
$701$	−20.0383	−0.756837	−0.378419	−	0.925635i	$-0.623532\pi$
$701$	−20.0383	−0.756837	−0.378419	+	0.925635i	$0.623532\pi$
$702$	15.0998	0.569906
$703$	37.1048	1.39943
$704$	29.8156	1.12372
$705$	−2.73365	−0.102955
$706$	42.9423	1.61615
$707$	7.46723	0.280834
$708$	−5.83585	−0.219325
$709$	18.4645	0.693449	0.346724	−	0.937967i	$-0.387294\pi$
$709$	18.4645	0.693449	0.346724	+	0.937967i	$0.387294\pi$
$710$	71.8264	2.69560
$711$	7.09389	0.266042
$712$	−31.1881	−1.16882
$713$	−4.78481	−0.179193
$714$	−0.0838330	−0.00313737
$715$	−15.0804	−0.563977
$716$	−43.1881	−1.61402
$717$	3.26355	0.121880
$718$	0.937179	0.0349752
$719$	−33.9169	−1.26489	−0.632444	−	0.774606i	$-0.717948\pi$
$719$	−33.9169	−1.26489	−0.632444	+	0.774606i	$0.717948\pi$
$720$	−114.045	−4.25020
$721$	52.9077	1.97039
$722$	−95.6161	−3.55846
$723$	1.99543	0.0742109
$724$	−133.334	−4.95532
$725$	1.34153	0.0498233
$726$	0.430546	0.0159791
$727$	−0.642922	−0.0238447	−0.0119223	−	0.999929i	$-0.503795\pi$
$727$	−0.642922	−0.0238447	−0.0119223	+	0.999929i	$0.503795\pi$
$728$	−291.020	−10.7859
$729$	−25.6680	−0.950666
$730$	−6.73823	−0.249393
$731$	0.194122	0.00717988
$732$	3.58174	0.132385
$733$	9.28785	0.343055	0.171527	−	0.985179i	$-0.445130\pi$
$733$	9.28785	0.343055	0.171527	+	0.985179i	$0.445130\pi$
$734$	−54.7287	−2.02007
$735$	−8.28677	−0.305662
$736$	76.5385	2.82125
$737$	8.81152	0.324576
$738$	−24.0276	−0.884470
$739$	−4.98727	−0.183460	−0.0917298	−	0.995784i	$-0.529240\pi$
$739$	−4.98727	−0.183460	−0.0917298	+	0.995784i	$0.529240\pi$
$740$	70.8736	2.60537
$741$	6.79767	0.249719
$742$	69.2916	2.54377
$743$	−6.16632	−0.226220	−0.113110	−	0.993582i	$-0.536081\pi$
$743$	−6.16632	−0.226220	−0.113110	+	0.993582i	$0.536081\pi$
$744$	2.03543	0.0746224
$745$	−14.4204	−0.528322
$746$	35.7977	1.31065
$747$	−20.6100	−0.754081
$748$	0.202977	0.00742156
$749$	−50.0889	−1.83021
$750$	−3.75974	−0.137286
$751$	7.36737	0.268839	0.134420	−	0.990925i	$-0.457083\pi$
$751$	7.36737	0.268839	0.134420	+	0.990925i	$0.457083\pi$
$752$	100.722	3.67297
$753$	−1.70816	−0.0622488
$754$	13.4345	0.489257
$755$	−15.1509	−0.551399
$756$	−26.9613	−0.980573
$757$	−15.0272	−0.546173	−0.273086	−	0.961990i	$-0.588044\pi$
$757$	−15.0272	−0.546173	−0.273086	+	0.961990i	$0.588044\pi$
$758$	2.64168	0.0959502
$759$	0.552403	0.0200510
$760$	−178.623	−6.47934
$761$	−21.7547	−0.788609	−0.394304	−	0.918980i	$-0.629014\pi$
$761$	−21.7547	−0.788609	−0.394304	+	0.918980i	$0.629014\pi$
$762$	−6.73898	−0.244128
$763$	−12.3841	−0.448334
$764$	20.9107	0.756521
$765$	−0.284005	−0.0102682
$766$	61.7538	2.23126
$767$	−39.7839	−1.43651
$768$	−6.86780	−0.247820
$769$	−4.92494	−0.177598	−0.0887989	−	0.996050i	$-0.528303\pi$
$769$	−4.92494	−0.177598	−0.0887989	+	0.996050i	$0.528303\pi$
$770$	36.7843	1.32561
$771$	−4.28024	−0.154149
$772$	20.7667	0.747408
$773$	9.65747	0.347355	0.173678	−	0.984803i	$-0.444435\pi$
$773$	9.65747	0.347355	0.173678	+	0.984803i	$0.444435\pi$
$774$	42.4661	1.52641
$775$	2.18580	0.0785163
$776$	−96.8464	−3.47658
$777$	4.17044	0.149614
$778$	74.6716	2.67711
$779$	−21.7239	−0.778340
$780$	12.9842	0.464908
$781$	−10.2332	−0.366174
$782$	0.355764	0.0127221
$783$	0.788984	0.0281960
$784$	305.330	10.9046
$785$	−61.8002	−2.20574
$786$	−2.23008	−0.0795442
$787$	29.0273	1.03471	0.517355	−	0.855771i	$-0.326917\pi$
$787$	29.0273	1.03471	0.517355	+	0.855771i	$0.326917\pi$
$788$	81.1725	2.89165
$789$	−3.69949	−0.131705
$790$	16.7358	0.595431
$791$	61.4604	2.18528
$792$	28.1475	1.00018
$793$	24.4173	0.867083
$794$	−67.8260	−2.40705
$795$	−1.95974	−0.0695049
$796$	−128.535	−4.55579
$797$	52.2291	1.85005	0.925025	−	0.379905i	$-0.124043\pi$
$797$	52.2291	1.85005	0.925025	+	0.379905i	$0.124043\pi$
$798$	−16.5809	−0.586958
$799$	0.250829	0.00887368
$800$	−34.9644	−1.23618
$801$	−9.80779	−0.346541
$802$	67.4018	2.38004
$803$	0.960007	0.0338779
$804$	−7.58666	−0.267561
$805$	47.1953	1.66342
$806$	21.8893	0.771017
$807$	−2.36464	−0.0832392
$808$	13.4802	0.474233
$809$	51.7190	1.81834	0.909171	−	0.416423i	$-0.136717\pi$
$809$	51.7190	1.81834	0.909171	+	0.416423i	$0.136717\pi$
$810$	−61.6057	−2.16461
$811$	−29.4723	−1.03491	−0.517456	−	0.855710i	$-0.673121\pi$
$811$	−29.4723	−1.03491	−0.517456	+	0.855710i	$0.673121\pi$
$812$	−23.9879	−0.841809
$813$	1.76516	0.0619069
$814$	−13.7941	−0.483482
$815$	−42.4030	−1.48531
$816$	−0.0873610	−0.00305825
$817$	38.3945	1.34325
$818$	13.7641	0.481252
$819$	−91.5176	−3.19788
$820$	−41.4947	−1.44906
$821$	7.21594	0.251838	0.125919	−	0.992041i	$-0.459812\pi$
$821$	7.21594	0.251838	0.125919	+	0.992041i	$0.459812\pi$
$822$	−5.19811	−0.181305
$823$	37.0057	1.28994	0.644970	−	0.764208i	$-0.276870\pi$
$823$	37.0057	1.28994	0.644970	+	0.764208i	$0.276870\pi$
$824$	95.5117	3.32731
$825$	−0.252349	−0.00878566
$826$	97.0410	3.37649
$827$	0.602123	0.0209379	0.0104689	−	0.999945i	$-0.496668\pi$
$827$	0.602123	0.0209379	0.0104689	+	0.999945i	$0.496668\pi$
$828$	56.9703	1.97986
$829$	1.43310	0.0497735	0.0248867	−	0.999690i	$-0.492077\pi$
$829$	1.43310	0.0497735	0.0248867	+	0.999690i	$0.492077\pi$
$830$	−48.6227	−1.68772
$831$	4.12386	0.143055
$832$	−175.003	−6.06715
$833$	0.760361	0.0263449
$834$	8.93336	0.309337
$835$	−36.0781	−1.24854
$836$	40.1457	1.38847
$837$	1.28551	0.0444339
$838$	30.1775	1.04246
$839$	−25.2488	−0.871687	−0.435843	−	0.900023i	$-0.643550\pi$
$839$	−25.2488	−0.871687	−0.435843	+	0.900023i	$0.643550\pi$
$840$	−20.0766	−0.692708
$841$	−28.2980	−0.975794
$842$	−75.1199	−2.58880
$843$	−4.13852	−0.142538
$844$	−27.3334	−0.940854
$845$	55.1144	1.89599
$846$	54.8711	1.88651
$847$	−5.24072	−0.180073
$848$	72.2076	2.47962
$849$	3.86573	0.132671
$850$	−0.162520	−0.00557440
$851$	−17.6982	−0.606686
$852$	8.81075	0.301851
$853$	−9.91043	−0.339327	−0.169663	−	0.985502i	$-0.554268\pi$
$853$	−9.91043	−0.339327	−0.169663	+	0.985502i	$0.554268\pi$
$854$	−59.5588	−2.03806
$855$	−56.1719	−1.92104
$856$	−90.4229	−3.09059
$857$	−45.4206	−1.55154	−0.775770	−	0.631016i	$-0.782638\pi$
$857$	−45.4206	−1.55154	−0.775770	+	0.631016i	$0.782638\pi$
$858$	−2.52710	−0.0862738
$859$	−8.84740	−0.301869	−0.150935	−	0.988544i	$-0.548228\pi$
$859$	−8.84740	−0.301869	−0.150935	+	0.988544i	$0.548228\pi$
$860$	73.3371	2.50077
$861$	−2.44169	−0.0832125
$862$	61.4804	2.09403
$863$	20.6639	0.703406	0.351703	−	0.936112i	$-0.385603\pi$
$863$	20.6639	0.703406	0.351703	+	0.936112i	$0.385603\pi$
$864$	−20.5633	−0.699576
$865$	58.4405	1.98704
$866$	−76.4750	−2.59873
$867$	2.67900	0.0909836
$868$	−39.0841	−1.32660
$869$	−2.38437	−0.0808842
$870$	0.926808	0.0314217
$871$	−51.7194	−1.75245
$872$	−22.3564	−0.757082
$873$	−30.4555	−1.03076
$874$	70.3647	2.38012
$875$	45.7646	1.54712
$876$	−0.826560	−0.0279269
$877$	25.0428	0.845636	0.422818	−	0.906215i	$-0.361041\pi$
$877$	25.0428	0.845636	0.422818	+	0.906215i	$0.361041\pi$
$878$	−13.6745	−0.461493
$879$	−3.72520	−0.125648
$880$	38.3323	1.29218
$881$	−4.69467	−0.158168	−0.0790838	−	0.996868i	$-0.525199\pi$
$881$	−4.69467	−0.158168	−0.0790838	+	0.996868i	$0.525199\pi$
$882$	166.336	5.60082
$883$	−30.6830	−1.03257	−0.516283	−	0.856418i	$-0.672685\pi$
$883$	−30.6830	−1.03257	−0.516283	+	0.856418i	$0.672685\pi$
$884$	−1.19138	−0.0400703
$885$	−2.74457	−0.0922576
$886$	10.8166	0.363391
$887$	−32.2433	−1.08262	−0.541312	−	0.840822i	$-0.682072\pi$
$887$	−32.2433	−1.08262	−0.541312	+	0.840822i	$0.682072\pi$
$888$	7.52870	0.252647
$889$	82.0287	2.75116
$890$	−23.1383	−0.775598
$891$	8.77707	0.294043
$892$	−144.109	−4.82512
$893$	49.6101	1.66014
$894$	−2.41649	−0.0808195
$895$	−20.3111	−0.678926
$896$	197.991	6.61441
$897$	−3.24234	−0.108259
$898$	−92.6559	−3.09197
$899$	1.14374	0.0381459
$900$	−26.0252	−0.867507
$901$	0.179818	0.00599061
$902$	8.07608	0.268904
$903$	4.31540	0.143608
$904$	110.951	3.69019
$905$	−62.7062	−2.08443
$906$	−2.53891	−0.0843498
$907$	1.51259	0.0502248	0.0251124	−	0.999685i	$-0.492006\pi$
$907$	1.51259	0.0502248	0.0251124	+	0.999685i	$0.492006\pi$
$908$	−144.992	−4.81174
$909$	4.23916	0.140604
$910$	−215.906	−7.15723
$911$	−19.5471	−0.647623	−0.323811	−	0.946122i	$-0.604964\pi$
$911$	−19.5471	−0.647623	−0.323811	+	0.946122i	$0.604964\pi$
$912$	−17.2787	−0.572155
$913$	6.92736	0.229262
$914$	63.6943	2.10682
$915$	1.68447	0.0556870
$916$	64.8433	2.14248
$917$	27.1451	0.896410
$918$	−0.0955815	−0.00315466
$919$	53.9399	1.77931	0.889657	−	0.456629i	$-0.150943\pi$
$919$	53.9399	1.77931	0.889657	+	0.456629i	$0.150943\pi$
$920$	85.1994	2.80894
$921$	−2.70586	−0.0891612
$922$	73.5469	2.42214
$923$	60.0642	1.97704
$924$	4.51223	0.148441
$925$	8.08490	0.265830
$926$	52.2513	1.71708
$927$	30.0357	0.986503
$928$	−18.2954	−0.600577
$929$	4.12701	0.135403	0.0677014	−	0.997706i	$-0.478433\pi$
$929$	4.12701	0.135403	0.0677014	+	0.997706i	$0.478433\pi$
$930$	1.51007	0.0495173
$931$	150.388	4.92876
$932$	7.03433	0.230417
$933$	2.92049	0.0956125
$934$	−94.2478	−3.08388
$935$	0.0954587	0.00312183
$936$	−165.212	−5.40013
$937$	29.5399	0.965026	0.482513	−	0.875889i	$-0.339724\pi$
$937$	29.5399	0.965026	0.482513	+	0.875889i	$0.339724\pi$
$938$	126.154	4.11908
$939$	3.82077	0.124686
$940$	94.7599	3.09073
$941$	−23.5330	−0.767154	−0.383577	−	0.923509i	$-0.625308\pi$
$941$	−23.5330	−0.767154	−0.383577	+	0.923509i	$0.625308\pi$
$942$	−10.3561	−0.337421
$943$	10.3618	0.337428
$944$	101.125	3.29133
$945$	−12.6798	−0.412472
$946$	−14.2735	−0.464073
$947$	−1.06140	−0.0344909	−0.0172454	−	0.999851i	$-0.505490\pi$
$947$	−1.06140	−0.0344909	−0.0172454	+	0.999851i	$0.505490\pi$
$948$	2.05293	0.0666761
$949$	−5.63479	−0.182913
$950$	−32.1440	−1.04289
$951$	0.0284553	0.000922727 0
$952$	1.84215	0.0597043
$953$	60.4873	1.95938	0.979688	−	0.200526i	$-0.0642651\pi$
$953$	60.4873	1.95938	0.979688	+	0.200526i	$0.0642651\pi$
$954$	39.3369	1.27358
$955$	9.83417	0.318226
$956$	−113.129	−3.65884
$957$	−0.132044	−0.00426837
$958$	−52.6242	−1.70021
$959$	63.2729	2.04319
$960$	−12.0729	−0.389653
$961$	−29.1365	−0.939886
$962$	80.9647	2.61041
$963$	−28.4355	−0.916321
$964$	−69.1701	−2.22782
$965$	9.76644	0.314393
$966$	7.90874	0.254460
$967$	−28.4188	−0.913888	−0.456944	−	0.889496i	$-0.651056\pi$
$967$	−28.4188	−0.913888	−0.456944	+	0.889496i	$0.651056\pi$
$968$	−9.46082	−0.304082
$969$	−0.0430290	−0.00138229
$970$	−71.8499	−2.30696
$971$	56.2449	1.80498	0.902492	−	0.430706i	$-0.141735\pi$
$971$	56.2449	1.80498	0.902492	+	0.430706i	$0.141735\pi$
$972$	−22.9907	−0.737429
$973$	−108.739	−3.48602
$974$	3.58361	0.114826
$975$	1.48117	0.0474354
$976$	−62.0652	−1.98666
$977$	−37.2944	−1.19315	−0.596576	−	0.802556i	$-0.703473\pi$
$977$	−37.2944	−1.19315	−0.596576	+	0.802556i	$0.703473\pi$
$978$	−7.10567	−0.227214
$979$	3.29656	0.105358
$980$	287.255	9.17602
$981$	−7.03045	−0.224465
$982$	−107.525	−3.43126
$983$	20.3664	0.649587	0.324794	−	0.945785i	$-0.394705\pi$
$983$	20.3664	0.649587	0.324794	+	0.945785i	$0.394705\pi$
$984$	−4.40786	−0.140517
$985$	38.1750	1.21636
$986$	−0.0850402	−0.00270823
$987$	5.57600	0.177486
$988$	−235.636	−7.49659
$989$	−18.3134	−0.582331
$990$	20.8825	0.663689
$991$	4.30846	0.136863	0.0684313	−	0.997656i	$-0.478201\pi$
$991$	4.30846	0.136863	0.0684313	+	0.997656i	$0.478201\pi$
$992$	−29.8093	−0.946445
$993$	−0.328373	−0.0104206
$994$	−146.509	−4.64698
$995$	−60.4492	−1.91637
$996$	−5.96442	−0.188990
$997$	56.3954	1.78606	0.893030	−	0.449997i	$-0.148575\pi$
$997$	56.3954	1.78606	0.893030	+	0.449997i	$0.148575\pi$
$998$	31.5004	0.997127
$999$	4.75490	0.150438

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6017.2.a.c.1.3	✓	106

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6017.2.a.c.1.3	✓	106	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:	\( N \)	\(=\)	\( 6017 = 11 \cdot 547 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6017.a (trivial)

\(f(q)\)	\(=\)	\(q-2.73187 q^{2} -0.157601 q^{3} +5.46313 q^{4} +2.56928 q^{5} +0.430546 q^{6} -5.24072 q^{7} -9.46082 q^{8} -2.97516 q^{9} +O(q^{10})\)	\(q-2.73187 q^{2} -0.157601 q^{3} +5.46313 q^{4} +2.56928 q^{5} +0.430546 q^{6} -5.24072 q^{7} -9.46082 q^{8} -2.97516 q^{9} -7.01894 q^{10} +1.00000 q^{11} -0.860994 q^{12} -5.86953 q^{13} +14.3170 q^{14} -0.404921 q^{15} +14.9195 q^{16} +0.0371539 q^{17} +8.12776 q^{18} +7.34848 q^{19} +14.0363 q^{20} +0.825943 q^{21} -2.73187 q^{22} -3.50507 q^{23} +1.49103 q^{24} +1.60119 q^{25} +16.0348 q^{26} +0.941692 q^{27} -28.6307 q^{28} +0.837837 q^{29} +1.10619 q^{30} +1.36511 q^{31} -21.8365 q^{32} -0.157601 q^{33} -0.101500 q^{34} -13.4649 q^{35} -16.2537 q^{36} +5.04931 q^{37} -20.0751 q^{38} +0.925043 q^{39} -24.3075 q^{40} -2.95624 q^{41} -2.25637 q^{42} +5.22482 q^{43} +5.46313 q^{44} -7.64402 q^{45} +9.57541 q^{46} +6.75107 q^{47} -2.35133 q^{48} +20.4652 q^{49} -4.37424 q^{50} -0.00585550 q^{51} -32.0660 q^{52} +4.83982 q^{53} -2.57258 q^{54} +2.56928 q^{55} +49.5815 q^{56} -1.15813 q^{57} -2.28886 q^{58} +6.77803 q^{59} -2.21213 q^{60} -4.16001 q^{61} -3.72931 q^{62} +15.5920 q^{63} +29.8156 q^{64} -15.0804 q^{65} +0.430546 q^{66} +8.81152 q^{67} +0.202977 q^{68} +0.552403 q^{69} +36.7843 q^{70} -10.2332 q^{71} +28.1475 q^{72} +0.960007 q^{73} -13.7941 q^{74} -0.252349 q^{75} +40.1457 q^{76} -5.24072 q^{77} -2.52710 q^{78} -2.38437 q^{79} +38.3323 q^{80} +8.77707 q^{81} +8.07608 q^{82} +6.92736 q^{83} +4.51223 q^{84} +0.0954587 q^{85} -14.2735 q^{86} -0.132044 q^{87} -9.46082 q^{88} +3.29656 q^{89} +20.8825 q^{90} +30.7606 q^{91} -19.1486 q^{92} -0.215143 q^{93} -18.4430 q^{94} +18.8803 q^{95} +3.44146 q^{96} +10.2366 q^{97} -55.9082 q^{98} -2.97516 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 106 q - 13 q^{2} - 15 q^{3} + 93 q^{4} - 12 q^{5} - 22 q^{6} - 66 q^{7} - 39 q^{8} + 97 q^{9}+O(q^{10}) \) 106 * q - 13 * q^2 - 15 * q^3 + 93 * q^4 - 12 * q^5 - 22 * q^6 - 66 * q^7 - 39 * q^8 + 97 * q^9	\( 106 q - 13 q^{2} - 15 q^{3} + 93 q^{4} - 12 q^{5} - 22 q^{6} - 66 q^{7} - 39 q^{8} + 97 q^{9} - 30 q^{10} + 106 q^{11} - 26 q^{12} - 72 q^{13} + 3 q^{14} - 46 q^{15} + 75 q^{16} - 65 q^{17} - 37 q^{18} - 63 q^{19} - 25 q^{20} - 27 q^{21} - 13 q^{22} - 23 q^{23} - 56 q^{24} + 74 q^{25} + 2 q^{26} - 54 q^{27} - 115 q^{28} - 45 q^{29} - 14 q^{30} - 89 q^{31} - 96 q^{32} - 15 q^{33} - 26 q^{34} - 52 q^{35} + 91 q^{36} - 35 q^{37} + 7 q^{38} - 34 q^{39} - 74 q^{40} - 32 q^{41} - 94 q^{43} + 93 q^{44} - 46 q^{45} - 20 q^{46} - 105 q^{47} - 57 q^{48} + 80 q^{49} - 60 q^{50} - 36 q^{51} - 137 q^{52} - 61 q^{54} - 12 q^{55} + 32 q^{56} - 71 q^{57} - 28 q^{58} - 15 q^{59} - 21 q^{60} - 80 q^{61} - 84 q^{62} - 182 q^{63} + 55 q^{64} - 73 q^{65} - 22 q^{66} - 58 q^{67} - 145 q^{68} - 8 q^{69} - 39 q^{70} - 11 q^{71} - 100 q^{72} - 155 q^{73} - 15 q^{74} - 15 q^{75} - 132 q^{76} - 66 q^{77} - 45 q^{78} - 50 q^{79} - 28 q^{80} + 114 q^{81} - 57 q^{82} - 96 q^{83} - 27 q^{84} - 74 q^{85} + 54 q^{86} - 182 q^{87} - 39 q^{88} + 9 q^{89} - 53 q^{90} + 6 q^{91} - 18 q^{92} - 26 q^{93} - 33 q^{94} - 49 q^{95} - 56 q^{96} - 102 q^{97} - 76 q^{98} + 97 q^{99}+O(q^{100}) \) 106 * q - 13 * q^2 - 15 * q^3 + 93 * q^4 - 12 * q^5 - 22 * q^6 - 66 * q^7 - 39 * q^8 + 97 * q^9 - 30 * q^10 + 106 * q^11 - 26 * q^12 - 72 * q^13 + 3 * q^14 - 46 * q^15 + 75 * q^16 - 65 * q^17 - 37 * q^18 - 63 * q^19 - 25 * q^20 - 27 * q^21 - 13 * q^22 - 23 * q^23 - 56 * q^24 + 74 * q^25 + 2 * q^26 - 54 * q^27 - 115 * q^28 - 45 * q^29 - 14 * q^30 - 89 * q^31 - 96 * q^32 - 15 * q^33 - 26 * q^34 - 52 * q^35 + 91 * q^36 - 35 * q^37 + 7 * q^38 - 34 * q^39 - 74 * q^40 - 32 * q^41 - 94 * q^43 + 93 * q^44 - 46 * q^45 - 20 * q^46 - 105 * q^47 - 57 * q^48 + 80 * q^49 - 60 * q^50 - 36 * q^51 - 137 * q^52 - 61 * q^54 - 12 * q^55 + 32 * q^56 - 71 * q^57 - 28 * q^58 - 15 * q^59 - 21 * q^60 - 80 * q^61 - 84 * q^62 - 182 * q^63 + 55 * q^64 - 73 * q^65 - 22 * q^66 - 58 * q^67 - 145 * q^68 - 8 * q^69 - 39 * q^70 - 11 * q^71 - 100 * q^72 - 155 * q^73 - 15 * q^74 - 15 * q^75 - 132 * q^76 - 66 * q^77 - 45 * q^78 - 50 * q^79 - 28 * q^80 + 114 * q^81 - 57 * q^82 - 96 * q^83 - 27 * q^84 - 74 * q^85 + 54 * q^86 - 182 * q^87 - 39 * q^88 + 9 * q^89 - 53 * q^90 + 6 * q^91 - 18 * q^92 - 26 * q^93 - 33 * q^94 - 49 * q^95 - 56 * q^96 - 102 * q^97 - 76 * q^98 + 97 * q^99

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