LMFDB - Embedded newform 6001.2.a.a.1.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6001,2,Mod(1,6001)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6001, 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("6001.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6001 = 17 \cdot 353 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6001.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:	$47.9182262530$
Analytic rank:	$1$
Dimension:	$113$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.10
Character	$\chi$	$=$	6001.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.49624 q^{2} +1.48745 q^{3} +4.23122 q^{4} -3.58200 q^{5} -3.71302 q^{6} +1.79069 q^{7} -5.56966 q^{8} -0.787505 q^{9} +O(q^{10})$	\(q-2.49624 q^{2} +1.48745 q^{3} +4.23122 q^{4} -3.58200 q^{5} -3.71302 q^{6} +1.79069 q^{7} -5.56966 q^{8} -0.787505 q^{9} +8.94153 q^{10} +2.74388 q^{11} +6.29371 q^{12} +6.81757 q^{13} -4.46999 q^{14} -5.32803 q^{15} +5.44078 q^{16} -1.00000 q^{17} +1.96580 q^{18} -0.434175 q^{19} -15.1562 q^{20} +2.66355 q^{21} -6.84940 q^{22} -1.97418 q^{23} -8.28457 q^{24} +7.83072 q^{25} -17.0183 q^{26} -5.63371 q^{27} +7.57680 q^{28} -3.49833 q^{29} +13.3000 q^{30} +4.44454 q^{31} -2.44217 q^{32} +4.08138 q^{33} +2.49624 q^{34} -6.41425 q^{35} -3.33210 q^{36} -11.1235 q^{37} +1.08381 q^{38} +10.1408 q^{39} +19.9505 q^{40} -0.275218 q^{41} -6.64887 q^{42} +0.924990 q^{43} +11.6100 q^{44} +2.82084 q^{45} +4.92802 q^{46} -2.44235 q^{47} +8.09286 q^{48} -3.79343 q^{49} -19.5474 q^{50} -1.48745 q^{51} +28.8466 q^{52} -1.31889 q^{53} +14.0631 q^{54} -9.82859 q^{55} -9.97354 q^{56} -0.645812 q^{57} +8.73267 q^{58} -7.90477 q^{59} -22.5441 q^{60} -12.6824 q^{61} -11.0946 q^{62} -1.41018 q^{63} -4.78531 q^{64} -24.4205 q^{65} -10.1881 q^{66} -1.78241 q^{67} -4.23122 q^{68} -2.93648 q^{69} +16.0115 q^{70} +14.1871 q^{71} +4.38613 q^{72} -3.18785 q^{73} +27.7670 q^{74} +11.6478 q^{75} -1.83709 q^{76} +4.91345 q^{77} -25.3138 q^{78} +3.21890 q^{79} -19.4889 q^{80} -6.01732 q^{81} +0.687010 q^{82} -2.32445 q^{83} +11.2701 q^{84} +3.58200 q^{85} -2.30900 q^{86} -5.20358 q^{87} -15.2825 q^{88} -17.5695 q^{89} -7.04150 q^{90} +12.2082 q^{91} -8.35318 q^{92} +6.61101 q^{93} +6.09670 q^{94} +1.55521 q^{95} -3.63260 q^{96} +7.12310 q^{97} +9.46931 q^{98} -2.16082 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 113 q - 11 q^{2} - 11 q^{3} + 103 q^{4} - 19 q^{5} - 13 q^{6} + 11 q^{7} - 36 q^{8} + 94 q^{9}+O(q^{10}) $ 113 * q - 11 * q^2 - 11 * q^3 + 103 * q^4 - 19 * q^5 - 13 * q^6 + 11 * q^7 - 36 * q^8 + 94 * q^9	\( 113 q - 11 q^{2} - 11 q^{3} + 103 q^{4} - 19 q^{5} - 13 q^{6} + 11 q^{7} - 36 q^{8} + 94 q^{9} - 5 q^{10} - 40 q^{11} - 19 q^{12} - 18 q^{13} - 48 q^{14} - 63 q^{15} + 79 q^{16} - 113 q^{17} - 32 q^{18} - 46 q^{19} - 56 q^{20} - 46 q^{21} + 14 q^{22} - 35 q^{23} - 42 q^{24} + 88 q^{25} - 89 q^{26} - 41 q^{27} + 20 q^{28} - 51 q^{29} - 18 q^{30} - 57 q^{31} - 93 q^{32} - 40 q^{33} + 11 q^{34} - 69 q^{35} + 18 q^{36} + 16 q^{37} - 74 q^{38} - 51 q^{39} + 2 q^{40} - 87 q^{41} - 23 q^{42} - 32 q^{43} - 110 q^{44} - 17 q^{45} - 17 q^{46} - 161 q^{47} - 36 q^{48} + 56 q^{49} - 69 q^{50} + 11 q^{51} - 49 q^{52} - 48 q^{53} - 38 q^{54} - 79 q^{55} - 171 q^{56} + 20 q^{57} + 13 q^{58} - 174 q^{59} - 146 q^{60} - 34 q^{61} - 34 q^{62} - 14 q^{63} + 62 q^{64} - 22 q^{65} - 60 q^{66} - 50 q^{67} - 103 q^{68} - 59 q^{69} - 58 q^{70} - 189 q^{71} - 123 q^{72} - 4 q^{73} - 24 q^{74} - 106 q^{75} - 92 q^{76} - 78 q^{77} - 42 q^{78} + 8 q^{79} - 150 q^{80} + 13 q^{81} + 6 q^{82} - 109 q^{83} - 114 q^{84} + 19 q^{85} - 116 q^{86} - 106 q^{87} + 54 q^{88} - 170 q^{89} - q^{90} - 43 q^{91} - 94 q^{92} - 69 q^{93} - 35 q^{94} - 78 q^{95} - 44 q^{96} - 3 q^{97} - 68 q^{98} - 119 q^{99}+O(q^{100}) \) 113 * q - 11 * q^2 - 11 * q^3 + 103 * q^4 - 19 * q^5 - 13 * q^6 + 11 * q^7 - 36 * q^8 + 94 * q^9 - 5 * q^10 - 40 * q^11 - 19 * q^12 - 18 * q^13 - 48 * q^14 - 63 * q^15 + 79 * q^16 - 113 * q^17 - 32 * q^18 - 46 * q^19 - 56 * q^20 - 46 * q^21 + 14 * q^22 - 35 * q^23 - 42 * q^24 + 88 * q^25 - 89 * q^26 - 41 * q^27 + 20 * q^28 - 51 * q^29 - 18 * q^30 - 57 * q^31 - 93 * q^32 - 40 * q^33 + 11 * q^34 - 69 * q^35 + 18 * q^36 + 16 * q^37 - 74 * q^38 - 51 * q^39 + 2 * q^40 - 87 * q^41 - 23 * q^42 - 32 * q^43 - 110 * q^44 - 17 * q^45 - 17 * q^46 - 161 * q^47 - 36 * q^48 + 56 * q^49 - 69 * q^50 + 11 * q^51 - 49 * q^52 - 48 * q^53 - 38 * q^54 - 79 * q^55 - 171 * q^56 + 20 * q^57 + 13 * q^58 - 174 * q^59 - 146 * q^60 - 34 * q^61 - 34 * q^62 - 14 * q^63 + 62 * q^64 - 22 * q^65 - 60 * q^66 - 50 * q^67 - 103 * q^68 - 59 * q^69 - 58 * q^70 - 189 * q^71 - 123 * q^72 - 4 * q^73 - 24 * q^74 - 106 * q^75 - 92 * q^76 - 78 * q^77 - 42 * q^78 + 8 * q^79 - 150 * q^80 + 13 * q^81 + 6 * q^82 - 109 * q^83 - 114 * q^84 + 19 * q^85 - 116 * q^86 - 106 * q^87 + 54 * q^88 - 170 * q^89 - q^90 - 43 * q^91 - 94 * q^92 - 69 * q^93 - 35 * q^94 - 78 * q^95 - 44 * q^96 - 3 * q^97 - 68 * q^98 - 119 * 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 $

$2$	−2.49624	−1.76511	−0.882554	−	0.470210i	$-0.844178\pi$
$2$	−2.49624	−1.76511	−0.882554	+	0.470210i	$0.844178\pi$
$3$	1.48745	0.858777	0.429389	−	0.903120i	$-0.358729\pi$
$3$	1.48745	0.858777	0.429389	+	0.903120i	$0.358729\pi$
$4$	4.23122	2.11561
$5$	−3.58200	−1.60192	−0.800959	−	0.598719i	$-0.795677\pi$
$5$	−3.58200	−1.60192	−0.800959	+	0.598719i	$0.795677\pi$
$6$	−3.71302	−1.51584
$7$	1.79069	0.676817	0.338409	−	0.940999i	$-0.390111\pi$
$7$	1.79069	0.676817	0.338409	+	0.940999i	$0.390111\pi$
$8$	−5.56966	−1.96917
$9$	−0.787505	−0.262502
$10$	8.94153	2.82756
$11$	2.74388	0.827312	0.413656	−	0.910433i	$-0.364252\pi$
$11$	2.74388	0.827312	0.413656	+	0.910433i	$0.364252\pi$
$12$	6.29371	1.81684
$13$	6.81757	1.89085	0.945426	−	0.325836i	$-0.105646\pi$
$13$	6.81757	1.89085	0.945426	+	0.325836i	$0.105646\pi$
$14$	−4.46999	−1.19466
$15$	−5.32803	−1.37569
$16$	5.44078	1.36019
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	1.96580	0.463344
$19$	−0.434175	−0.0996066	−0.0498033	−	0.998759i	$-0.515859\pi$
$19$	−0.434175	−0.0996066	−0.0498033	+	0.998759i	$0.515859\pi$
$20$	−15.1562	−3.38904
$21$	2.66355	0.581235
$22$	−6.84940	−1.46030
$23$	−1.97418	−0.411644	−0.205822	−	0.978589i	$-0.565987\pi$
$23$	−1.97418	−0.411644	−0.205822	+	0.978589i	$0.565987\pi$
$24$	−8.28457	−1.69108
$25$	7.83072	1.56614
$26$	−17.0183	−3.33756
$27$	−5.63371	−1.08421
$28$	7.57680	1.43188
$29$	−3.49833	−0.649623	−0.324812	−	0.945779i	$-0.605301\pi$
$29$	−3.49833	−0.649623	−0.324812	+	0.945779i	$0.605301\pi$
$30$	13.3000	2.42825
$31$	4.44454	0.798263	0.399132	−	0.916894i	$-0.369312\pi$
$31$	4.44454	0.798263	0.399132	+	0.916894i	$0.369312\pi$
$32$	−2.44217	−0.431719
$33$	4.08138	0.710477
$34$	2.49624	0.428102
$35$	−6.41425	−1.08421
$36$	−3.33210	−0.555351
$37$	−11.1235	−1.82869	−0.914347	−	0.404932i	$-0.867295\pi$
$37$	−11.1235	−1.82869	−0.914347	+	0.404932i	$0.867295\pi$
$38$	1.08381	0.175816
$39$	10.1408	1.62382
$40$	19.9505	3.15445
$41$	−0.275218	−0.0429818	−0.0214909	−	0.999769i	$-0.506841\pi$
$41$	−0.275218	−0.0429818	−0.0214909	+	0.999769i	$0.506841\pi$
$42$	−6.64887	−1.02594
$43$	0.924990	0.141060	0.0705298	−	0.997510i	$-0.477531\pi$
$43$	0.924990	0.141060	0.0705298	+	0.997510i	$0.477531\pi$
$44$	11.6100	1.75027
$45$	2.82084	0.420506
$46$	4.92802	0.726597
$47$	−2.44235	−0.356254	−0.178127	−	0.984008i	$-0.557004\pi$
$47$	−2.44235	−0.356254	−0.178127	+	0.984008i	$0.557004\pi$
$48$	8.09286	1.16810
$49$	−3.79343	−0.541918
$50$	−19.5474	−2.76442
$51$	−1.48745	−0.208284
$52$	28.8466	4.00031
$53$	−1.31889	−0.181164	−0.0905818	−	0.995889i	$-0.528873\pi$
$53$	−1.31889	−0.181164	−0.0905818	+	0.995889i	$0.528873\pi$
$54$	14.0631	1.91374
$55$	−9.82859	−1.32529
$56$	−9.97354	−1.33277
$57$	−0.645812	−0.0855399
$58$	8.73267	1.14666
$59$	−7.90477	−1.02911	−0.514557	−	0.857456i	$-0.672044\pi$
$59$	−7.90477	−1.02911	−0.514557	+	0.857456i	$0.672044\pi$
$60$	−22.5441	−2.91043
$61$	−12.6824	−1.62382	−0.811908	−	0.583785i	$-0.801571\pi$
$61$	−12.6824	−1.62382	−0.811908	+	0.583785i	$0.801571\pi$
$62$	−11.0946	−1.40902
$63$	−1.41018	−0.177666
$64$	−4.78531	−0.598164
$65$	−24.4205	−3.02899
$66$	−10.1881	−1.25407
$67$	−1.78241	−0.217757	−0.108878	−	0.994055i	$-0.534726\pi$
$67$	−1.78241	−0.217757	−0.108878	+	0.994055i	$0.534726\pi$
$68$	−4.23122	−0.513111
$69$	−2.93648	−0.353511
$70$	16.0115	1.91374
$71$	14.1871	1.68370	0.841849	−	0.539713i	$-0.181467\pi$
$71$	14.1871	1.68370	0.841849	+	0.539713i	$0.181467\pi$
$72$	4.38613	0.516911
$73$	−3.18785	−0.373109	−0.186555	−	0.982445i	$-0.559732\pi$
$73$	−3.18785	−0.373109	−0.186555	+	0.982445i	$0.559732\pi$
$74$	27.7670	3.22784
$75$	11.6478	1.34497
$76$	−1.83709	−0.210729
$77$	4.91345	0.559939
$78$	−25.3138	−2.86622
$79$	3.21890	0.362155	0.181077	−	0.983469i	$-0.442042\pi$
$79$	3.21890	0.362155	0.181077	+	0.983469i	$0.442042\pi$
$80$	−19.4889	−2.17892
$81$	−6.01732	−0.668591
$82$	0.687010	0.0758675
$83$	−2.32445	−0.255142	−0.127571	−	0.991829i	$-0.540718\pi$
$83$	−2.32445	−0.255142	−0.127571	+	0.991829i	$0.540718\pi$
$84$	11.2701	1.22967
$85$	3.58200	0.388522
$86$	−2.30900	−0.248986
$87$	−5.20358	−0.557882
$88$	−15.2825	−1.62912
$89$	−17.5695	−1.86236	−0.931180	−	0.364561i	$-0.881219\pi$
$89$	−17.5695	−1.86236	−0.931180	+	0.364561i	$0.881219\pi$
$90$	−7.04150	−0.742239
$91$	12.2082	1.27976
$92$	−8.35318	−0.870879
$93$	6.61101	0.685530
$94$	6.09670	0.628827
$95$	1.55521	0.159562
$96$	−3.63260	−0.370750
$97$	7.12310	0.723241	0.361620	−	0.932325i	$-0.382224\pi$
$97$	7.12310	0.723241	0.361620	+	0.932325i	$0.382224\pi$
$98$	9.46931	0.956545
$99$	−2.16082	−0.217171
$100$	33.1335	3.31335
$101$	14.5553	1.44831	0.724154	−	0.689638i	$-0.242230\pi$
$101$	14.5553	1.44831	0.724154	+	0.689638i	$0.242230\pi$
$102$	3.71302	0.367644
$103$	14.2127	1.40042	0.700209	−	0.713938i	$-0.253090\pi$
$103$	14.2127	1.40042	0.700209	+	0.713938i	$0.253090\pi$
$104$	−37.9715	−3.72342
$105$	−9.54085	−0.931092
$106$	3.29227	0.319773
$107$	−7.45110	−0.720325	−0.360162	−	0.932890i	$-0.617279\pi$
$107$	−7.45110	−0.720325	−0.360162	+	0.932890i	$0.617279\pi$
$108$	−23.8375	−2.29376
$109$	19.3827	1.85652	0.928261	−	0.371930i	$-0.121304\pi$
$109$	19.3827	1.85652	0.928261	+	0.371930i	$0.121304\pi$
$110$	24.5345	2.33928
$111$	−16.5456	−1.57044
$112$	9.74275	0.920603
$113$	8.12030	0.763893	0.381947	−	0.924184i	$-0.375254\pi$
$113$	8.12030	0.763893	0.381947	+	0.924184i	$0.375254\pi$
$114$	1.61210	0.150987
$115$	7.07150	0.659421
$116$	−14.8022	−1.37435
$117$	−5.36887	−0.496352
$118$	19.7322	1.81650
$119$	−1.79069	−0.164152
$120$	29.6753	2.70897
$121$	−3.47110	−0.315555
$122$	31.6584	2.86621
$123$	−0.409372	−0.0369118
$124$	18.8058	1.68881
$125$	−10.1396	−0.906917
$126$	3.52014	0.313599
$127$	−10.0481	−0.891627	−0.445813	−	0.895126i	$-0.647086\pi$
$127$	−10.0481	−0.891627	−0.445813	+	0.895126i	$0.647086\pi$
$128$	16.8296	1.48754
$129$	1.37587	0.121139
$130$	60.9595	5.34650
$131$	−15.2051	−1.32848	−0.664238	−	0.747521i	$-0.731244\pi$
$131$	−15.2051	−1.32848	−0.664238	+	0.747521i	$0.731244\pi$
$132$	17.2692	1.50309
$133$	−0.777473	−0.0674155
$134$	4.44934	0.384364
$135$	20.1799	1.73681
$136$	5.56966	0.477594
$137$	−8.60799	−0.735430	−0.367715	−	0.929939i	$-0.619860\pi$
$137$	−8.60799	−0.735430	−0.367715	+	0.929939i	$0.619860\pi$
$138$	7.33017	0.623985
$139$	12.3062	1.04380	0.521898	−	0.853008i	$-0.325224\pi$
$139$	12.3062	1.04380	0.521898	+	0.853008i	$0.325224\pi$
$140$	−27.1401	−2.29376
$141$	−3.63287	−0.305943
$142$	−35.4144	−2.97191
$143$	18.7066	1.56433
$144$	−4.28464	−0.357053
$145$	12.5310	1.04064
$146$	7.95764	0.658579
$147$	−5.64252	−0.465387
$148$	−47.0660	−3.86880
$149$	1.00203	0.0820893	0.0410446	−	0.999157i	$-0.486931\pi$
$149$	1.00203	0.0820893	0.0410446	+	0.999157i	$0.486931\pi$
$150$	−29.0757	−2.37402
$151$	−10.5438	−0.858045	−0.429023	−	0.903294i	$-0.641142\pi$
$151$	−10.5438	−0.858045	−0.429023	+	0.903294i	$0.641142\pi$
$152$	2.41821	0.196143
$153$	0.787505	0.0636660
$154$	−12.2651	−0.988354
$155$	−15.9203	−1.27875
$156$	42.9078	3.43537
$157$	14.7080	1.17383	0.586913	−	0.809650i	$-0.300343\pi$
$157$	14.7080	1.17383	0.586913	+	0.809650i	$0.300343\pi$
$158$	−8.03515	−0.639242
$159$	−1.96178	−0.155579
$160$	8.74785	0.691578
$161$	−3.53514	−0.278608
$162$	15.0207	1.18014
$163$	17.0731	1.33727	0.668634	−	0.743591i	$-0.266879\pi$
$163$	17.0731	1.33727	0.668634	+	0.743591i	$0.266879\pi$
$164$	−1.16451	−0.0909327
$165$	−14.6195	−1.13813
$166$	5.80239	0.450353
$167$	−12.6471	−0.978665	−0.489333	−	0.872097i	$-0.662760\pi$
$167$	−12.6471	−0.978665	−0.489333	+	0.872097i	$0.662760\pi$
$168$	−14.8351	−1.14455
$169$	33.4792	2.57532
$170$	−8.94153	−0.685784
$171$	0.341915	0.0261469
$172$	3.91383	0.298427
$173$	−11.3704	−0.864474	−0.432237	−	0.901760i	$-0.642276\pi$
$173$	−11.3704	−0.864474	−0.432237	+	0.901760i	$0.642276\pi$
$174$	12.9894	0.984722
$175$	14.0224	1.05999
$176$	14.9289	1.12531
$177$	−11.7579	−0.883779
$178$	43.8576	3.28727
$179$	20.5453	1.53563	0.767813	−	0.640674i	$-0.221345\pi$
$179$	20.5453	1.53563	0.767813	+	0.640674i	$0.221345\pi$
$180$	11.9356	0.889627
$181$	2.50257	0.186015	0.0930074	−	0.995665i	$-0.470352\pi$
$181$	2.50257	0.186015	0.0930074	+	0.995665i	$0.470352\pi$
$182$	−30.4745	−2.25892
$183$	−18.8644	−1.39450
$184$	10.9955	0.810599
$185$	39.8444	2.92942
$186$	−16.5027	−1.21004
$187$	−2.74388	−0.200653
$188$	−10.3341	−0.753694
$189$	−10.0882	−0.733811
$190$	−3.88219	−0.281644
$191$	−11.3958	−0.824570	−0.412285	−	0.911055i	$-0.635269\pi$
$191$	−11.3958	−0.824570	−0.412285	+	0.911055i	$0.635269\pi$
$192$	−7.11789	−0.513689
$193$	−15.6800	−1.12867	−0.564336	−	0.825545i	$-0.690868\pi$
$193$	−15.6800	−1.12867	−0.564336	+	0.825545i	$0.690868\pi$
$194$	−17.7810	−1.27660
$195$	−36.3242	−2.60123
$196$	−16.0508	−1.14649
$197$	−8.62286	−0.614353	−0.307177	−	0.951653i	$-0.599384\pi$
$197$	−8.62286	−0.614353	−0.307177	+	0.951653i	$0.599384\pi$
$198$	5.39393	0.383330
$199$	−22.9959	−1.63013	−0.815067	−	0.579366i	$-0.803300\pi$
$199$	−22.9959	−1.63013	−0.815067	+	0.579366i	$0.803300\pi$
$200$	−43.6145	−3.08401
$201$	−2.65125	−0.187004
$202$	−36.3336	−2.55642
$203$	−6.26442	−0.439676
$204$	−6.29371	−0.440648
$205$	0.985830	0.0688533
$206$	−35.4783	−2.47189
$207$	1.55467	0.108057
$208$	37.0929	2.57193
$209$	−1.19133	−0.0824057
$210$	23.8163	1.64348
$211$	9.38030	0.645767	0.322883	−	0.946439i	$-0.395348\pi$
$211$	9.38030	0.645767	0.322883	+	0.946439i	$0.395348\pi$
$212$	−5.58051	−0.383271
$213$	21.1025	1.44592
$214$	18.5997	1.27145
$215$	−3.31331	−0.225966
$216$	31.3778	2.13499
$217$	7.95880	0.540278
$218$	−48.3838	−3.27696
$219$	−4.74175	−0.320418
$220$	−41.5869	−2.80379
$221$	−6.81757	−0.458599
$222$	41.3018	2.77200
$223$	−20.0474	−1.34247	−0.671235	−	0.741244i	$-0.734236\pi$
$223$	−20.0474	−1.34247	−0.671235	+	0.741244i	$0.734236\pi$
$224$	−4.37317	−0.292195
$225$	−6.16673	−0.411115
$226$	−20.2702	−1.34835
$227$	−15.1119	−1.00301	−0.501506	−	0.865154i	$-0.667221\pi$
$227$	−15.1119	−1.00301	−0.501506	+	0.865154i	$0.667221\pi$
$228$	−2.73257	−0.180969
$229$	−10.3006	−0.680686	−0.340343	−	0.940301i	$-0.610543\pi$
$229$	−10.3006	−0.680686	−0.340343	+	0.940301i	$0.610543\pi$
$230$	−17.6522	−1.16395
$231$	7.30849	0.480863
$232$	19.4845	1.27922
$233$	−9.27697	−0.607754	−0.303877	−	0.952711i	$-0.598281\pi$
$233$	−9.27697	−0.607754	−0.303877	+	0.952711i	$0.598281\pi$
$234$	13.4020	0.876115
$235$	8.74851	0.570690
$236$	−33.4468	−2.17720
$237$	4.78794	0.311010
$238$	4.46999	0.289747
$239$	−4.52603	−0.292764	−0.146382	−	0.989228i	$-0.546763\pi$
$239$	−4.52603	−0.292764	−0.146382	+	0.989228i	$0.546763\pi$
$240$	−28.9886	−1.87121
$241$	−9.43016	−0.607450	−0.303725	−	0.952760i	$-0.598230\pi$
$241$	−9.43016	−0.607450	−0.303725	+	0.952760i	$0.598230\pi$
$242$	8.66470	0.556988
$243$	7.95068	0.510037
$244$	−53.6621	−3.43536
$245$	13.5881	0.868109
$246$	1.02189	0.0651533
$247$	−2.96002	−0.188341
$248$	−24.7546	−1.57192
$249$	−3.45749	−0.219110
$250$	25.3110	1.60081
$251$	14.2810	0.901412	0.450706	−	0.892673i	$-0.351172\pi$
$251$	14.2810	0.901412	0.450706	+	0.892673i	$0.351172\pi$
$252$	−5.96677	−0.375871
$253$	−5.41691	−0.340558
$254$	25.0825	1.57382
$255$	5.32803	0.333654
$256$	−32.4402	−2.02751
$257$	10.5772	0.659788	0.329894	−	0.944018i	$-0.392987\pi$
$257$	10.5772	0.659788	0.329894	+	0.944018i	$0.392987\pi$
$258$	−3.43451	−0.213823
$259$	−19.9188	−1.23769
$260$	−103.329	−6.40817
$261$	2.75495	0.170527
$262$	37.9556	2.34490
$263$	−9.66688	−0.596086	−0.298043	−	0.954553i	$-0.596334\pi$
$263$	−9.66688	−0.596086	−0.298043	+	0.954553i	$0.596334\pi$
$264$	−22.7319	−1.39905
$265$	4.72426	0.290209
$266$	1.94076	0.118996
$267$	−26.1336	−1.59935
$268$	−7.54179	−0.460688
$269$	−24.0979	−1.46928	−0.734638	−	0.678459i	$-0.762648\pi$
$269$	−24.0979	−1.46928	−0.734638	+	0.678459i	$0.762648\pi$
$270$	−50.3740	−3.06566
$271$	−8.09852	−0.491950	−0.245975	−	0.969276i	$-0.579108\pi$
$271$	−8.09852	−0.491950	−0.245975	+	0.969276i	$0.579108\pi$
$272$	−5.44078	−0.329896
$273$	18.1590	1.09903
$274$	21.4876	1.29811
$275$	21.4866	1.29569
$276$	−12.4249	−0.747891
$277$	−23.2425	−1.39651	−0.698254	−	0.715850i	$-0.746040\pi$
$277$	−23.2425	−1.39651	−0.698254	+	0.715850i	$0.746040\pi$
$278$	−30.7192	−1.84241
$279$	−3.50010	−0.209545
$280$	35.7252	2.13499
$281$	−9.42405	−0.562191	−0.281096	−	0.959680i	$-0.590698\pi$
$281$	−9.42405	−0.562191	−0.281096	+	0.959680i	$0.590698\pi$
$282$	9.06852	0.540022
$283$	8.54936	0.508207	0.254103	−	0.967177i	$-0.418220\pi$
$283$	8.54936	0.508207	0.254103	+	0.967177i	$0.418220\pi$
$284$	60.0287	3.56205
$285$	2.31330	0.137028
$286$	−46.6962	−2.76120
$287$	−0.492830	−0.0290908
$288$	1.92322	0.113327
$289$	1.00000	0.0588235
$290$	−31.2804	−1.83685
$291$	10.5952	0.621103
$292$	−13.4885	−0.789354
$293$	17.6636	1.03192	0.515958	−	0.856614i	$-0.327436\pi$
$293$	17.6636	1.03192	0.515958	+	0.856614i	$0.327436\pi$
$294$	14.0851	0.821459
$295$	28.3149	1.64856
$296$	61.9542	3.60101
$297$	−15.4582	−0.896978
$298$	−2.50130	−0.144897
$299$	−13.4591	−0.778359
$300$	49.2843	2.84543
$301$	1.65637	0.0954716
$302$	26.3200	1.51454
$303$	21.6502	1.24377
$304$	−2.36225	−0.135484
$305$	45.4284	2.60122
$306$	−1.96580	−0.112377
$307$	0.605986	0.0345855	0.0172927	−	0.999850i	$-0.494495\pi$
$307$	0.605986	0.0345855	0.0172927	+	0.999850i	$0.494495\pi$
$308$	20.7899	1.18461
$309$	21.1406	1.20265
$310$	39.7410	2.25714
$311$	17.0603	0.967400	0.483700	−	0.875234i	$-0.339293\pi$
$311$	17.0603	0.967400	0.483700	+	0.875234i	$0.339293\pi$
$312$	−56.4806	−3.19758
$313$	−2.87981	−0.162776	−0.0813881	−	0.996682i	$-0.525935\pi$
$313$	−2.87981	−0.162776	−0.0813881	+	0.996682i	$0.525935\pi$
$314$	−36.7147	−2.07193
$315$	5.05125	0.284606
$316$	13.6199	0.766178
$317$	6.89436	0.387226	0.193613	−	0.981078i	$-0.437979\pi$
$317$	6.89436	0.387226	0.193613	+	0.981078i	$0.437979\pi$
$318$	4.89707	0.274614
$319$	−9.59901	−0.537441
$320$	17.1410	0.958210
$321$	−11.0831	−0.618599
$322$	8.82456	0.491774
$323$	0.434175	0.0241581
$324$	−25.4606	−1.41448
$325$	53.3865	2.96135
$326$	−42.6186	−2.36042
$327$	28.8307	1.59434
$328$	1.53287	0.0846386
$329$	−4.37350	−0.241119
$330$	36.4938	2.00892
$331$	−7.66289	−0.421191	−0.210595	−	0.977573i	$-0.567540\pi$
$331$	−7.66289	−0.421191	−0.210595	+	0.977573i	$0.567540\pi$
$332$	−9.83526	−0.539780
$333$	8.75982	0.480035
$334$	31.5703	1.72745
$335$	6.38461	0.348828
$336$	14.4918	0.790593
$337$	18.0613	0.983860	0.491930	−	0.870635i	$-0.336292\pi$
$337$	18.0613	0.983860	0.491930	+	0.870635i	$0.336292\pi$
$338$	−83.5722	−4.54573
$339$	12.0785	0.656014
$340$	15.1562	0.821962
$341$	12.1953	0.660413
$342$	−0.853502	−0.0461521
$343$	−19.3277	−1.04360
$344$	−5.15188	−0.277771
$345$	10.5185	0.566296
$346$	28.3832	1.52589
$347$	−32.5563	−1.74772	−0.873858	−	0.486182i	$-0.838389\pi$
$347$	−32.5563	−1.74772	−0.873858	+	0.486182i	$0.838389\pi$
$348$	−22.0175	−1.18026
$349$	−18.8456	−1.00878	−0.504391	−	0.863476i	$-0.668283\pi$
$349$	−18.8456	−1.00878	−0.504391	+	0.863476i	$0.668283\pi$
$350$	−35.0033	−1.87100
$351$	−38.4082	−2.05008
$352$	−6.70103	−0.357166
$353$	−1.00000	−0.0532246
$353$	−1.00000	−0.0532246
$354$	29.3506	1.55997
$355$	−50.8182	−2.69715
$356$	−74.3402	−3.94002
$357$	−2.66355	−0.140970
$358$	−51.2860	−2.71055
$359$	0.403568	0.0212995	0.0106497	−	0.999943i	$-0.496610\pi$
$359$	0.403568	0.0212995	0.0106497	+	0.999943i	$0.496610\pi$
$360$	−15.7111	−0.828049
$361$	−18.8115	−0.990079
$362$	−6.24703	−0.328336
$363$	−5.16307	−0.270991
$364$	51.6554	2.70748
$365$	11.4189	0.597691
$366$	47.0901	2.46144
$367$	20.1614	1.05242	0.526208	−	0.850356i	$-0.323613\pi$
$367$	20.1614	1.05242	0.526208	+	0.850356i	$0.323613\pi$
$368$	−10.7411	−0.559916
$369$	0.216735	0.0112828
$370$	−99.4612	−5.17074
$371$	−2.36172	−0.122615
$372$	27.9727	1.45031
$373$	−18.9808	−0.982787	−0.491394	−	0.870938i	$-0.663512\pi$
$373$	−18.9808	−0.982787	−0.491394	+	0.870938i	$0.663512\pi$
$374$	6.84940	0.354174
$375$	−15.0822	−0.778840
$376$	13.6031	0.701525
$377$	−23.8501	−1.22834
$378$	25.1826	1.29526
$379$	−24.3015	−1.24829	−0.624143	−	0.781310i	$-0.714552\pi$
$379$	−24.3015	−1.24829	−0.624143	+	0.781310i	$0.714552\pi$
$380$	6.58045	0.337570
$381$	−14.9460	−0.765709
$382$	28.4466	1.45546
$383$	−10.3472	−0.528719	−0.264359	−	0.964424i	$-0.585161\pi$
$383$	−10.3472	−0.528719	−0.264359	+	0.964424i	$0.585161\pi$
$384$	25.0332	1.27747
$385$	−17.6000	−0.896977
$386$	39.1411	1.99223
$387$	−0.728434	−0.0370284
$388$	30.1394	1.53010
$389$	−0.309777	−0.0157063	−0.00785316	−	0.999969i	$-0.502500\pi$
$389$	−0.309777	−0.0157063	−0.00785316	+	0.999969i	$0.502500\pi$
$390$	90.6740	4.59145
$391$	1.97418	0.0998384
$392$	21.1281	1.06713
$393$	−22.6168	−1.14087
$394$	21.5247	1.08440
$395$	−11.5301	−0.580142
$396$	−9.14291	−0.459448
$397$	−30.9616	−1.55392	−0.776958	−	0.629552i	$-0.783238\pi$
$397$	−30.9616	−1.55392	−0.776958	+	0.629552i	$0.783238\pi$
$398$	57.4032	2.87736
$399$	−1.15645	−0.0578949
$400$	42.6052	2.13026
$401$	14.4213	0.720167	0.360084	−	0.932920i	$-0.382748\pi$
$401$	14.4213	0.720167	0.360084	+	0.932920i	$0.382748\pi$
$402$	6.61815	0.330083
$403$	30.3010	1.50940
$404$	61.5867	3.06405
$405$	21.5540	1.07103
$406$	15.6375	0.776077
$407$	−30.5216	−1.51290
$408$	8.28457	0.410147
$409$	−35.7369	−1.76708	−0.883538	−	0.468360i	$-0.844845\pi$
$409$	−35.7369	−1.76708	−0.883538	+	0.468360i	$0.844845\pi$
$410$	−2.46087	−0.121534
$411$	−12.8039	−0.631570
$412$	60.1370	2.96274
$413$	−14.1550	−0.696522
$414$	−3.88084	−0.190733
$415$	8.32618	0.408716
$416$	−16.6497	−0.816317
$417$	18.3048	0.896388
$418$	2.97384	0.145455
$419$	18.3900	0.898412	0.449206	−	0.893428i	$-0.351707\pi$
$419$	18.3900	0.898412	0.449206	+	0.893428i	$0.351707\pi$
$420$	−40.3694	−1.96983
$421$	−20.2530	−0.987069	−0.493535	−	0.869726i	$-0.664295\pi$
$421$	−20.2530	−0.987069	−0.493535	+	0.869726i	$0.664295\pi$
$422$	−23.4155	−1.13985
$423$	1.92337	0.0935172
$424$	7.34577	0.356742
$425$	−7.83072	−0.379846
$426$	−52.6770	−2.55221
$427$	−22.7103	−1.09903
$428$	−31.5272	−1.52393
$429$	27.8251	1.34341
$430$	8.27083	0.398855
$431$	40.6492	1.95800	0.979001	−	0.203854i	$-0.0653469\pi$
$431$	40.6492	1.95800	0.979001	+	0.203854i	$0.0653469\pi$
$432$	−30.6518	−1.47473
$433$	−8.59126	−0.412870	−0.206435	−	0.978460i	$-0.566186\pi$
$433$	−8.59126	−0.412870	−0.206435	+	0.978460i	$0.566186\pi$
$434$	−19.8671	−0.953650
$435$	18.6392	0.893681
$436$	82.0123	3.92768
$437$	0.857138	0.0410025
$438$	11.8366	0.565573
$439$	24.6621	1.17706	0.588530	−	0.808475i	$-0.299707\pi$
$439$	24.6621	1.17706	0.588530	+	0.808475i	$0.299707\pi$
$440$	54.7419	2.60972
$441$	2.98734	0.142254
$442$	17.0183	0.809478
$443$	−10.6048	−0.503847	−0.251924	−	0.967747i	$-0.581063\pi$
$443$	−10.6048	−0.503847	−0.251924	+	0.967747i	$0.581063\pi$
$444$	−70.0081	−3.32244
$445$	62.9338	2.98335
$446$	50.0431	2.36961
$447$	1.49046	0.0704964
$448$	−8.56901	−0.404848
$449$	2.23265	0.105365	0.0526826	−	0.998611i	$-0.483223\pi$
$449$	2.23265	0.105365	0.0526826	+	0.998611i	$0.483223\pi$
$450$	15.3936	0.725663
$451$	−0.755166	−0.0355594
$452$	34.3588	1.61610
$453$	−15.6834	−0.736870
$454$	37.7230	1.77043
$455$	−43.7296	−2.05007
$456$	3.59695	0.168443
$457$	42.4676	1.98655	0.993276	−	0.115773i	$-0.0369346\pi$
$457$	42.4676	1.98655	0.993276	+	0.115773i	$0.0369346\pi$
$458$	25.7129	1.20148
$459$	5.63371	0.262959
$460$	29.9211	1.39508
$461$	6.82757	0.317992	0.158996	−	0.987279i	$-0.449174\pi$
$461$	6.82757	0.317992	0.158996	+	0.987279i	$0.449174\pi$
$462$	−18.2437	−0.848776
$463$	−5.68353	−0.264136	−0.132068	−	0.991241i	$-0.542162\pi$
$463$	−5.68353	−0.264136	−0.132068	+	0.991241i	$0.542162\pi$
$464$	−19.0336	−0.883614
$465$	−23.6807	−1.09816
$466$	23.1575	1.07275
$467$	15.2729	0.706747	0.353373	−	0.935482i	$-0.385035\pi$
$467$	15.2729	0.706747	0.353373	+	0.935482i	$0.385035\pi$
$468$	−22.7168	−1.05009
$469$	−3.19175	−0.147381
$470$	−21.8384	−1.00733
$471$	21.8773	1.00805
$472$	44.0269	2.02650
$473$	2.53806	0.116700
$474$	−11.9519	−0.548967
$475$	−3.39990	−0.155998
$476$	−7.57680	−0.347282
$477$	1.03863	0.0475557
$478$	11.2980	0.516761
$479$	39.6391	1.81116	0.905579	−	0.424177i	$-0.139437\pi$
$479$	39.6391	1.81116	0.905579	+	0.424177i	$0.139437\pi$
$480$	13.0120	0.593912
$481$	−75.8353	−3.45779
$482$	23.5400	1.07222
$483$	−5.25833	−0.239262
$484$	−14.6870	−0.667590
$485$	−25.5149	−1.15857
$486$	−19.8468	−0.900270
$487$	−19.2969	−0.874426	−0.437213	−	0.899358i	$-0.644034\pi$
$487$	−19.2969	−0.874426	−0.437213	+	0.899358i	$0.644034\pi$
$488$	70.6367	3.19757
$489$	25.3953	1.14842
$490$	−33.9191	−1.53231
$491$	−12.5122	−0.564666	−0.282333	−	0.959316i	$-0.591108\pi$
$491$	−12.5122	−0.564666	−0.282333	+	0.959316i	$0.591108\pi$
$492$	−1.73214	−0.0780909
$493$	3.49833	0.157557
$494$	7.38892	0.332443
$495$	7.74006	0.347890
$496$	24.1818	1.08579
$497$	25.4047	1.13956
$498$	8.63074	0.386753
$499$	2.43106	0.108829	0.0544145	−	0.998518i	$-0.482671\pi$
$499$	2.43106	0.108829	0.0544145	+	0.998518i	$0.482671\pi$
$500$	−42.9030	−1.91868
$501$	−18.8119	−0.840456
$502$	−35.6489	−1.59109
$503$	−24.0498	−1.07233	−0.536165	−	0.844114i	$-0.680127\pi$
$503$	−24.0498	−1.07233	−0.536165	+	0.844114i	$0.680127\pi$
$504$	7.85421	0.349854
$505$	−52.1371	−2.32007
$506$	13.5219	0.601123
$507$	49.7985	2.21163
$508$	−42.5158	−1.88633
$509$	−11.5911	−0.513764	−0.256882	−	0.966443i	$-0.582695\pi$
$509$	−11.5911	−0.513764	−0.256882	+	0.966443i	$0.582695\pi$
$510$	−13.3000	−0.588936
$511$	−5.70845	−0.252527
$512$	47.3193	2.09124
$513$	2.44602	0.107994
$514$	−26.4032	−1.16460
$515$	−50.9099	−2.24336
$516$	5.82162	0.256282
$517$	−6.70154	−0.294733
$518$	49.7220	2.18466
$519$	−16.9128	−0.742390
$520$	136.014	5.96461
$521$	18.4563	0.808586	0.404293	−	0.914630i	$-0.367518\pi$
$521$	18.4563	0.808586	0.404293	+	0.914630i	$0.367518\pi$
$522$	−6.87702	−0.300999
$523$	−9.23046	−0.403620	−0.201810	−	0.979425i	$-0.564682\pi$
$523$	−9.23046	−0.403620	−0.201810	+	0.979425i	$0.564682\pi$
$524$	−64.3361	−2.81054
$525$	20.8576	0.910298
$526$	24.1309	1.05216
$527$	−4.44454	−0.193607
$528$	22.2059	0.966387
$529$	−19.1026	−0.830549
$530$	−11.7929	−0.512251
$531$	6.22505	0.270144
$532$	−3.28966	−0.142625
$533$	−1.87632	−0.0812722
$534$	65.2358	2.82303
$535$	26.6898	1.15390
$536$	9.92745	0.428800
$537$	30.5600	1.31876
$538$	60.1542	2.59343
$539$	−10.4087	−0.448336
$540$	85.3858	3.67442
$541$	24.6775	1.06097	0.530485	−	0.847694i	$-0.322010\pi$
$541$	24.6775	1.06097	0.530485	+	0.847694i	$0.322010\pi$
$542$	20.2158	0.868345
$543$	3.72244	0.159745
$544$	2.44217	0.104707
$545$	−69.4287	−2.97400
$546$	−45.3291	−1.93991
$547$	−0.500672	−0.0214072	−0.0107036	−	0.999943i	$-0.503407\pi$
$547$	−0.500672	−0.0214072	−0.0107036	+	0.999943i	$0.503407\pi$
$548$	−36.4223	−1.55588
$549$	9.98746	0.426254
$550$	−53.6357	−2.28703
$551$	1.51889	0.0647068
$552$	16.3552	0.696124
$553$	5.76405	0.245112
$554$	58.0190	2.46499
$555$	59.2664	2.51572
$556$	52.0701	2.20826
$557$	−0.608488	−0.0257824	−0.0128912	−	0.999917i	$-0.504104\pi$
$557$	−0.608488	−0.0257824	−0.0128912	+	0.999917i	$0.504104\pi$
$558$	8.73709	0.369870
$559$	6.30618	0.266723
$560$	−34.8985	−1.47473
$561$	−4.08138	−0.172316
$562$	23.5247	0.992329
$563$	27.2923	1.15023	0.575116	−	0.818072i	$-0.304957\pi$
$563$	27.2923	1.15023	0.575116	+	0.818072i	$0.304957\pi$
$564$	−15.3715	−0.647255
$565$	−29.0869	−1.22370
$566$	−21.3413	−0.897041
$567$	−10.7752	−0.452514
$568$	−79.0173	−3.31549
$569$	−38.0395	−1.59470	−0.797349	−	0.603518i	$-0.793765\pi$
$569$	−38.0395	−1.59470	−0.797349	+	0.603518i	$0.793765\pi$
$570$	−5.77455	−0.241869
$571$	9.30332	0.389332	0.194666	−	0.980870i	$-0.437638\pi$
$571$	9.30332	0.389332	0.194666	+	0.980870i	$0.437638\pi$
$572$	79.1518	3.30950
$573$	−16.9506	−0.708122
$574$	1.23022	0.0513485
$575$	−15.4592	−0.644694
$576$	3.76845	0.157019
$577$	−20.9058	−0.870318	−0.435159	−	0.900354i	$-0.643308\pi$
$577$	−20.9058	−0.870318	−0.435159	+	0.900354i	$0.643308\pi$
$578$	−2.49624	−0.103830
$579$	−23.3232	−0.969278
$580$	53.0215	2.20160
$581$	−4.16237	−0.172684
$582$	−26.4482	−1.09631
$583$	−3.61888	−0.149879
$584$	17.7552	0.734717
$585$	19.2313	0.795115
$586$	−44.0925	−1.82145
$587$	3.10828	0.128292	0.0641462	−	0.997941i	$-0.479568\pi$
$587$	3.10828	0.128292	0.0641462	+	0.997941i	$0.479568\pi$
$588$	−23.8747	−0.984578
$589$	−1.92971	−0.0795123
$590$	−70.6808	−2.90988
$591$	−12.8260	−0.527593
$592$	−60.5205	−2.48738
$593$	17.6057	0.722981	0.361491	−	0.932376i	$-0.382268\pi$
$593$	17.6057	0.722981	0.361491	+	0.932376i	$0.382268\pi$
$594$	38.5875	1.58326
$595$	6.41425	0.262959
$596$	4.23980	0.173669
$597$	−34.2051	−1.39992
$598$	33.5971	1.37389
$599$	17.5588	0.717431	0.358716	−	0.933447i	$-0.383215\pi$
$599$	17.5588	0.717431	0.358716	+	0.933447i	$0.383215\pi$
$600$	−64.8742	−2.64848
$601$	−31.6167	−1.28967	−0.644837	−	0.764320i	$-0.723075\pi$
$601$	−31.6167	−1.28967	−0.644837	+	0.764320i	$0.723075\pi$
$602$	−4.13470	−0.168518
$603$	1.40366	0.0571615
$604$	−44.6133	−1.81529
$605$	12.4335	0.505493
$606$	−54.0442	−2.19540
$607$	36.9973	1.50167	0.750836	−	0.660488i	$-0.229651\pi$
$607$	36.9973	1.50167	0.750836	+	0.660488i	$0.229651\pi$
$608$	1.06033	0.0430020
$609$	−9.31799	−0.377584
$610$	−113.400	−4.59144
$611$	−16.6509	−0.673624
$612$	3.33210	0.134692
$613$	−44.3492	−1.79125	−0.895623	−	0.444814i	$-0.853270\pi$
$613$	−44.3492	−1.79125	−0.895623	+	0.444814i	$0.853270\pi$
$614$	−1.51269	−0.0610471
$615$	1.46637	0.0591297
$616$	−27.3662	−1.10262
$617$	−42.0808	−1.69411	−0.847054	−	0.531507i	$-0.821626\pi$
$617$	−42.0808	−1.69411	−0.847054	+	0.531507i	$0.821626\pi$
$618$	−52.7721	−2.12280
$619$	−11.2127	−0.450677	−0.225339	−	0.974280i	$-0.572349\pi$
$619$	−11.2127	−0.450677	−0.225339	+	0.974280i	$0.572349\pi$
$620$	−67.3625	−2.70534
$621$	11.1219	0.446308
$622$	−42.5866	−1.70757
$623$	−31.4615	−1.26048
$624$	55.1736	2.20871
$625$	−2.83341	−0.113336
$626$	7.18869	0.287318
$627$	−1.77203	−0.0707682
$628$	62.2327	2.48336
$629$	11.1235	0.443523
$630$	−12.6091	−0.502360
$631$	−19.2926	−0.768025	−0.384013	−	0.923328i	$-0.625458\pi$
$631$	−19.2926	−0.768025	−0.384013	+	0.923328i	$0.625458\pi$
$632$	−17.9282	−0.713145
$633$	13.9527	0.554570
$634$	−17.2100	−0.683496
$635$	35.9924	1.42831
$636$	−8.30071	−0.329145
$637$	−25.8620	−1.02469
$638$	23.9614	0.948643
$639$	−11.1724	−0.441974
$640$	−60.2837	−2.38292
$641$	14.3004	0.564830	0.282415	−	0.959292i	$-0.408864\pi$
$641$	14.3004	0.564830	0.282415	+	0.959292i	$0.408864\pi$
$642$	27.6661	1.09189
$643$	36.1350	1.42503	0.712514	−	0.701658i	$-0.247557\pi$
$643$	36.1350	1.42503	0.712514	+	0.701658i	$0.247557\pi$
$644$	−14.9579	−0.589426
$645$	−4.92837	−0.194055
$646$	−1.08381	−0.0426418
$647$	−2.97841	−0.117094	−0.0585468	−	0.998285i	$-0.518647\pi$
$647$	−2.97841	−0.117094	−0.0585468	+	0.998285i	$0.518647\pi$
$648$	33.5144	1.31657
$649$	−21.6898	−0.851398
$650$	−133.265	−5.22710
$651$	11.8383	0.463979
$652$	72.2400	2.82914
$653$	44.6443	1.74707	0.873533	−	0.486765i	$-0.161823\pi$
$653$	44.6443	1.74707	0.873533	+	0.486765i	$0.161823\pi$
$654$	−71.9683	−2.81418
$655$	54.4647	2.12811
$656$	−1.49740	−0.0584636
$657$	2.51045	0.0979418
$658$	10.9173	0.425601
$659$	−11.3813	−0.443353	−0.221677	−	0.975120i	$-0.571153\pi$
$659$	−11.3813	−0.443353	−0.221677	+	0.975120i	$0.571153\pi$
$660$	−61.8583	−2.40783
$661$	−30.4431	−1.18410	−0.592049	−	0.805902i	$-0.701681\pi$
$661$	−30.4431	−1.18410	−0.592049	+	0.805902i	$0.701681\pi$
$662$	19.1284	0.743447
$663$	−10.1408	−0.393835
$664$	12.9464	0.502418
$665$	2.78491	0.107994
$666$	−21.8666	−0.847314
$667$	6.90632	0.267414
$668$	−53.5128	−2.07047
$669$	−29.8194	−1.15288
$670$	−15.9375	−0.615720
$671$	−34.7991	−1.34340
$672$	−6.50485	−0.250930
$673$	29.5382	1.13861	0.569307	−	0.822125i	$-0.307212\pi$
$673$	29.5382	1.13861	0.569307	+	0.822125i	$0.307212\pi$
$674$	−45.0853	−1.73662
$675$	−44.1160	−1.69803
$676$	141.658	5.44838
$677$	−29.6816	−1.14076	−0.570378	−	0.821383i	$-0.693203\pi$
$677$	−29.6816	−1.14076	−0.570378	+	0.821383i	$0.693203\pi$
$678$	−30.1509	−1.15794
$679$	12.7553	0.489502
$680$	−19.9505	−0.765068
$681$	−22.4781	−0.861365
$682$	−30.4424	−1.16570
$683$	28.6233	1.09524	0.547620	−	0.836727i	$-0.315534\pi$
$683$	28.6233	1.09524	0.547620	+	0.836727i	$0.315534\pi$
$684$	1.44672	0.0553166
$685$	30.8338	1.17810
$686$	48.2466	1.84206
$687$	−15.3217	−0.584558
$688$	5.03266	0.191869
$689$	−8.99162	−0.342554
$690$	−26.2566	−0.999574
$691$	−37.1539	−1.41340	−0.706700	−	0.707513i	$-0.749817\pi$
$691$	−37.1539	−1.41340	−0.706700	+	0.707513i	$0.749817\pi$
$692$	−48.1106	−1.82889
$693$	−3.86936	−0.146985
$694$	81.2684	3.08491
$695$	−44.0807	−1.67208
$696$	28.9822	1.09857
$697$	0.275218	0.0104246
$698$	47.0431	1.78061
$699$	−13.7990	−0.521926
$700$	59.3318	2.24253
$701$	−44.2798	−1.67242	−0.836212	−	0.548406i	$-0.815235\pi$
$701$	−44.2798	−1.67242	−0.836212	+	0.548406i	$0.815235\pi$
$702$	95.8761	3.61861
$703$	4.82955	0.182150
$704$	−13.1303	−0.494868
$705$	13.0129	0.490095
$706$	2.49624	0.0939473
$707$	26.0641	0.980240
$708$	−49.7503	−1.86973
$709$	−38.0476	−1.42891	−0.714453	−	0.699683i	$-0.753324\pi$
$709$	−38.0476	−1.42891	−0.714453	+	0.699683i	$0.753324\pi$
$710$	126.854	4.76076
$711$	−2.53490	−0.0950661
$712$	97.8559	3.66731
$713$	−8.77431	−0.328601
$714$	6.64887	0.248828
$715$	−67.0071	−2.50592
$716$	86.9316	3.24879
$717$	−6.73222	−0.251419
$718$	−1.00740	−0.0375959
$719$	28.3026	1.05551	0.527755	−	0.849397i	$-0.323034\pi$
$719$	28.3026	1.05551	0.527755	+	0.849397i	$0.323034\pi$
$720$	15.3476	0.571970
$721$	25.4505	0.947828
$722$	46.9580	1.74760
$723$	−14.0269	−0.521664
$724$	10.5889	0.393535
$725$	−27.3944	−1.01740
$726$	12.8883	0.478329
$727$	−48.3771	−1.79421	−0.897103	−	0.441821i	$-0.854333\pi$
$727$	−48.3771	−1.79421	−0.897103	+	0.441821i	$0.854333\pi$
$728$	−67.9953	−2.52007
$729$	29.8782	1.10660
$730$	−28.5043	−1.05499
$731$	−0.924990	−0.0342120
$732$	−79.8194	−2.95021
$733$	1.23612	0.0456572	0.0228286	−	0.999739i	$-0.492733\pi$
$733$	1.23612	0.0456572	0.0228286	+	0.999739i	$0.492733\pi$
$734$	−50.3277	−1.85763
$735$	20.2115	0.745512
$736$	4.82128	0.177715
$737$	−4.89074	−0.180153
$738$	−0.541023	−0.0199154
$739$	15.8300	0.582315	0.291157	−	0.956675i	$-0.405960\pi$
$739$	15.8300	0.582315	0.291157	+	0.956675i	$0.405960\pi$
$740$	168.590	6.19751
$741$	−4.40287	−0.161743
$742$	5.89543	0.216428
$743$	−22.3184	−0.818782	−0.409391	−	0.912359i	$-0.634259\pi$
$743$	−22.3184	−0.818782	−0.409391	+	0.912359i	$0.634259\pi$
$744$	−36.8211	−1.34993
$745$	−3.58926	−0.131500
$746$	47.3806	1.73473
$747$	1.83052	0.0669751
$748$	−11.6100	−0.424503
$749$	−13.3426	−0.487528
$750$	37.6487	1.37474
$751$	47.2793	1.72525	0.862623	−	0.505847i	$-0.168820\pi$
$751$	47.2793	1.72525	0.862623	+	0.505847i	$0.168820\pi$
$752$	−13.2883	−0.484575
$753$	21.2423	0.774112
$754$	59.5356	2.16816
$755$	37.7680	1.37452
$756$	−42.6855	−1.55246
$757$	20.5615	0.747319	0.373660	−	0.927566i	$-0.378103\pi$
$757$	20.5615	0.747319	0.373660	+	0.927566i	$0.378103\pi$
$758$	60.6625	2.20336
$759$	−8.05736	−0.292464
$760$	−8.66202	−0.314204
$761$	−44.5601	−1.61530	−0.807651	−	0.589661i	$-0.799261\pi$
$761$	−44.5601	−1.61530	−0.807651	+	0.589661i	$0.799261\pi$
$762$	37.3089	1.35156
$763$	34.7083	1.25653
$764$	−48.2180	−1.74447
$765$	−2.82084	−0.101988
$766$	25.8292	0.933246
$767$	−53.8913	−1.94590
$768$	−48.2530	−1.74118
$769$	−27.2166	−0.981455	−0.490728	−	0.871313i	$-0.663269\pi$
$769$	−27.2166	−0.981455	−0.490728	+	0.871313i	$0.663269\pi$
$770$	43.9337	1.58326
$771$	15.7330	0.566611
$772$	−66.3456	−2.38783
$773$	−26.7955	−0.963767	−0.481883	−	0.876235i	$-0.660047\pi$
$773$	−26.7955	−0.963767	−0.481883	+	0.876235i	$0.660047\pi$
$774$	1.81835	0.0653591
$775$	34.8040	1.25020
$776$	−39.6732	−1.42419
$777$	−29.6281	−1.06290
$778$	0.773278	0.0277234
$779$	0.119493	0.00428127
$780$	−153.696	−5.50319
$781$	38.9277	1.39294
$782$	−4.92802	−0.176226
$783$	19.7086	0.704327
$784$	−20.6392	−0.737114
$785$	−52.6840	−1.88037
$786$	56.4569	2.01375
$787$	−2.32624	−0.0829214	−0.0414607	−	0.999140i	$-0.513201\pi$
$787$	−2.32624	−0.0829214	−0.0414607	+	0.999140i	$0.513201\pi$
$788$	−36.4852	−1.29973
$789$	−14.3790	−0.511905
$790$	28.7819	1.02401
$791$	14.5409	0.517016
$792$	12.0350	0.427647
$793$	−86.4632	−3.07040
$794$	77.2875	2.74283
$795$	7.02709	0.249225
$796$	−97.3006	−3.44873
$797$	−29.2927	−1.03760	−0.518800	−	0.854896i	$-0.673621\pi$
$797$	−29.2927	−1.03760	−0.518800	+	0.854896i	$0.673621\pi$
$798$	2.88678	0.102191
$799$	2.44235	0.0864043
$800$	−19.1240	−0.676134
$801$	13.8360	0.488872
$802$	−35.9991	−1.27117
$803$	−8.74709	−0.308678
$804$	−11.2180	−0.395628
$805$	12.6629	0.446307
$806$	−75.6385	−2.66425
$807$	−35.8444	−1.26178
$808$	−81.0682	−2.85197
$809$	−54.8276	−1.92763	−0.963817	−	0.266565i	$-0.914111\pi$
$809$	−54.8276	−1.92763	−0.963817	+	0.266565i	$0.914111\pi$
$810$	−53.8041	−1.89048
$811$	13.4009	0.470569	0.235284	−	0.971927i	$-0.424398\pi$
$811$	13.4009	0.470569	0.235284	+	0.971927i	$0.424398\pi$
$812$	−26.5062	−0.930184
$813$	−12.0461	−0.422475
$814$	76.1893	2.67043
$815$	−61.1558	−2.14220
$816$	−8.09286	−0.283307
$817$	−0.401608	−0.0140505
$818$	89.2079	3.11908
$819$	−9.61398	−0.335940
$820$	4.17126	0.145667
$821$	−3.84430	−0.134167	−0.0670836	−	0.997747i	$-0.521369\pi$
$821$	−3.84430	−0.134167	−0.0670836	+	0.997747i	$0.521369\pi$
$822$	31.9617	1.11479
$823$	−26.0485	−0.907994	−0.453997	−	0.891003i	$-0.650002\pi$
$823$	−26.0485	−0.907994	−0.453997	+	0.891003i	$0.650002\pi$
$824$	−79.1599	−2.75767
$825$	31.9601	1.11271
$826$	35.3343	1.22944
$827$	9.25510	0.321831	0.160916	−	0.986968i	$-0.448555\pi$
$827$	9.25510	0.321831	0.160916	+	0.986968i	$0.448555\pi$
$828$	6.57816	0.228607
$829$	20.2145	0.702079	0.351039	−	0.936361i	$-0.385828\pi$
$829$	20.2145	0.702079	0.351039	+	0.936361i	$0.385828\pi$
$830$	−20.7842	−0.721429
$831$	−34.5720	−1.19929
$832$	−32.6242	−1.13104
$833$	3.79343	0.131435
$834$	−45.6931	−1.58222
$835$	45.3021	1.56774
$836$	−5.04076	−0.174338
$837$	−25.0392	−0.865483
$838$	−45.9060	−1.58579
$839$	−26.1397	−0.902442	−0.451221	−	0.892412i	$-0.649011\pi$
$839$	−26.1397	−0.902442	−0.451221	+	0.892412i	$0.649011\pi$
$840$	53.1393	1.83348
$841$	−16.7617	−0.577989
$842$	50.5563	1.74228
$843$	−14.0178	−0.482797
$844$	39.6901	1.36619
$845$	−119.923	−4.12546
$846$	−4.80118	−0.165068
$847$	−6.21567	−0.213573
$848$	−7.17579	−0.246418
$849$	12.7167	0.436437
$850$	19.5474	0.670469
$851$	21.9598	0.752771
$852$	89.2895	3.05901
$853$	40.2101	1.37677	0.688384	−	0.725346i	$-0.258320\pi$
$853$	40.2101	1.37677	0.688384	+	0.725346i	$0.258320\pi$
$854$	56.6903	1.93990
$855$	−1.22474	−0.0418852
$856$	41.5001	1.41844
$857$	8.04847	0.274931	0.137465	−	0.990507i	$-0.456104\pi$
$857$	8.04847	0.274931	0.137465	+	0.990507i	$0.456104\pi$
$858$	−69.4581	−2.37126
$859$	−2.56013	−0.0873506	−0.0436753	−	0.999046i	$-0.513907\pi$
$859$	−2.56013	−0.0873506	−0.0436753	+	0.999046i	$0.513907\pi$
$860$	−14.0194	−0.478056
$861$	−0.733058	−0.0249825
$862$	−101.470	−3.45609
$863$	18.5971	0.633052	0.316526	−	0.948584i	$-0.397484\pi$
$863$	18.5971	0.633052	0.316526	+	0.948584i	$0.397484\pi$
$864$	13.7585	0.468073
$865$	40.7287	1.38482
$866$	21.4459	0.728760
$867$	1.48745	0.0505163
$868$	33.6754	1.14302
$869$	8.83229	0.299615
$870$	−46.5279	−1.57745
$871$	−12.1517	−0.411746
$872$	−107.955	−3.65581
$873$	−5.60947	−0.189852
$874$	−2.13962	−0.0723739
$875$	−18.1570	−0.613817
$876$	−20.0634	−0.677879
$877$	24.5358	0.828515	0.414258	−	0.910160i	$-0.364041\pi$
$877$	24.5358	0.828515	0.414258	+	0.910160i	$0.364041\pi$
$878$	−61.5627	−2.07764
$879$	26.2736	0.886187
$880$	−53.4752	−1.80265
$881$	−8.32002	−0.280308	−0.140154	−	0.990130i	$-0.544760\pi$
$881$	−8.32002	−0.280308	−0.140154	+	0.990130i	$0.544760\pi$
$882$	−7.45713	−0.251095
$883$	28.7327	0.966933	0.483466	−	0.875363i	$-0.339378\pi$
$883$	28.7327	0.966933	0.483466	+	0.875363i	$0.339378\pi$
$884$	−28.8466	−0.970217
$885$	42.1169	1.41574
$886$	26.4720	0.889346
$887$	−1.55693	−0.0522766	−0.0261383	−	0.999658i	$-0.508321\pi$
$887$	−1.55693	−0.0522766	−0.0261383	+	0.999658i	$0.508321\pi$
$888$	92.1535	3.09247
$889$	−17.9931	−0.603468
$890$	−157.098	−5.26594
$891$	−16.5108	−0.553134
$892$	−84.8248	−2.84014
$893$	1.06041	0.0354852
$894$	−3.72055	−0.124434
$895$	−73.5932	−2.45995
$896$	30.1366	1.00679
$897$	−20.0197	−0.668437
$898$	−5.57323	−0.185981
$899$	−15.5485	−0.518570
$900$	−26.0928	−0.869760
$901$	1.31889	0.0439386
$902$	1.88508	0.0627661
$903$	2.46376	0.0819888
$904$	−45.2273	−1.50424
$905$	−8.96422	−0.297981
$906$	39.1495	1.30066
$907$	8.22020	0.272947	0.136474	−	0.990644i	$-0.456423\pi$
$907$	8.22020	0.272947	0.136474	+	0.990644i	$0.456423\pi$
$908$	−63.9418	−2.12198
$909$	−11.4624	−0.380183
$910$	109.160	3.61861
$911$	44.2052	1.46458	0.732292	−	0.680991i	$-0.238451\pi$
$911$	44.2052	1.46458	0.732292	+	0.680991i	$0.238451\pi$
$912$	−3.51372	−0.116351
$913$	−6.37802	−0.211082
$914$	−106.009	−3.50648
$915$	67.5723	2.23387
$916$	−43.5843	−1.44007
$917$	−27.2276	−0.899136
$918$	−14.0631	−0.464151
$919$	−37.9385	−1.25148	−0.625738	−	0.780034i	$-0.715202\pi$
$919$	−37.9385	−1.25148	−0.625738	+	0.780034i	$0.715202\pi$
$920$	−39.3859	−1.29851
$921$	0.901372	0.0297012
$922$	−17.0433	−0.561290
$923$	96.7215	3.18363
$924$	30.9238	1.01732
$925$	−87.1051	−2.86400
$926$	14.1875	0.466229
$927$	−11.1926	−0.367612
$928$	8.54351	0.280455
$929$	2.08742	0.0684859	0.0342430	−	0.999414i	$-0.489098\pi$
$929$	2.08742	0.0684859	0.0342430	+	0.999414i	$0.489098\pi$
$930$	59.1126	1.93838
$931$	1.64701	0.0539786
$932$	−39.2529	−1.28577
$933$	25.3763	0.830782
$934$	−38.1249	−1.24749
$935$	9.82859	0.321429
$936$	29.9028	0.977402
$937$	41.2803	1.34857	0.674285	−	0.738472i	$-0.264452\pi$
$937$	41.2803	1.34857	0.674285	+	0.738472i	$0.264452\pi$
$938$	7.96738	0.260144
$939$	−4.28356	−0.139789
$940$	37.0169	1.20736
$941$	−37.9706	−1.23781	−0.618903	−	0.785467i	$-0.712423\pi$
$941$	−37.9706	−1.23781	−0.618903	+	0.785467i	$0.712423\pi$
$942$	−54.6111	−1.77933
$943$	0.543329	0.0176932
$944$	−43.0081	−1.39979
$945$	36.1360	1.17550
$946$	−6.33562	−0.205989
$947$	−15.3048	−0.497340	−0.248670	−	0.968588i	$-0.579994\pi$
$947$	−15.3048	−0.497340	−0.248670	+	0.968588i	$0.579994\pi$
$948$	20.2588	0.657976
$949$	−21.7334	−0.705495
$950$	8.48698	0.275354
$951$	10.2550	0.332541
$952$	9.97354	0.323244
$953$	20.3936	0.660612	0.330306	−	0.943874i	$-0.392848\pi$
$953$	20.3936	0.660612	0.330306	+	0.943874i	$0.392848\pi$
$954$	−2.59268	−0.0839410
$955$	40.8197	1.32089
$956$	−19.1506	−0.619375
$957$	−14.2780	−0.461542
$958$	−98.9488	−3.19689
$959$	−15.4142	−0.497752
$960$	25.4963	0.822889
$961$	−11.2461	−0.362776
$962$	189.303	6.10338
$963$	5.86778	0.189086
$964$	−39.9011	−1.28513
$965$	56.1658	1.80804
$966$	13.1261	0.422324
$967$	−42.3139	−1.36072	−0.680361	−	0.732877i	$-0.738177\pi$
$967$	−42.3139	−1.36072	−0.680361	+	0.732877i	$0.738177\pi$
$968$	19.3329	0.621381
$969$	0.645812	0.0207465
$970$	63.6914	2.04501
$971$	11.9655	0.383990	0.191995	−	0.981396i	$-0.438504\pi$
$971$	11.9655	0.383990	0.191995	+	0.981396i	$0.438504\pi$
$972$	33.6411	1.07904
$973$	22.0365	0.706459
$974$	48.1697	1.54346
$975$	79.4095	2.54314
$976$	−69.0022	−2.20871
$977$	27.8585	0.891274	0.445637	−	0.895214i	$-0.352977\pi$
$977$	27.8585	0.891274	0.445637	+	0.895214i	$0.352977\pi$
$978$	−63.3928	−2.02708
$979$	−48.2086	−1.54075
$980$	57.4941	1.83658
$981$	−15.2639	−0.487340
$982$	31.2334	0.996698
$983$	5.17151	0.164945	0.0824727	−	0.996593i	$-0.473718\pi$
$983$	5.17151	0.164945	0.0824727	+	0.996593i	$0.473718\pi$
$984$	2.28006	0.0726857
$985$	30.8871	0.984144
$986$	−8.73267	−0.278105
$987$	−6.50534	−0.207067
$988$	−12.5245	−0.398457
$989$	−1.82609	−0.0580664
$990$	−19.3211	−0.614064
$991$	−23.5755	−0.748901	−0.374450	−	0.927247i	$-0.622169\pi$
$991$	−23.5755	−0.748901	−0.374450	+	0.927247i	$0.622169\pi$
$992$	−10.8543	−0.344625
$993$	−11.3981	−0.361709
$994$	−63.4162	−2.01144
$995$	82.3712	2.61134
$996$	−14.6294	−0.463551
$997$	−32.3884	−1.02575	−0.512875	−	0.858463i	$-0.671420\pi$
$997$	−32.3884	−1.02575	−0.512875	+	0.858463i	$0.671420\pi$
$998$	−6.06851	−0.192095
$999$	62.6666	1.98268

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6001.2.a.a.1.10	✓	113

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6001.2.a.a.1.10	✓	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:	\( N \)	\(=\)	\( 6001 = 17 \cdot 353 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6001.a (trivial)

\(f(q)\)	\(=\)	\(q-2.49624 q^{2} +1.48745 q^{3} +4.23122 q^{4} -3.58200 q^{5} -3.71302 q^{6} +1.79069 q^{7} -5.56966 q^{8} -0.787505 q^{9} +O(q^{10})\)	\(q-2.49624 q^{2} +1.48745 q^{3} +4.23122 q^{4} -3.58200 q^{5} -3.71302 q^{6} +1.79069 q^{7} -5.56966 q^{8} -0.787505 q^{9} +8.94153 q^{10} +2.74388 q^{11} +6.29371 q^{12} +6.81757 q^{13} -4.46999 q^{14} -5.32803 q^{15} +5.44078 q^{16} -1.00000 q^{17} +1.96580 q^{18} -0.434175 q^{19} -15.1562 q^{20} +2.66355 q^{21} -6.84940 q^{22} -1.97418 q^{23} -8.28457 q^{24} +7.83072 q^{25} -17.0183 q^{26} -5.63371 q^{27} +7.57680 q^{28} -3.49833 q^{29} +13.3000 q^{30} +4.44454 q^{31} -2.44217 q^{32} +4.08138 q^{33} +2.49624 q^{34} -6.41425 q^{35} -3.33210 q^{36} -11.1235 q^{37} +1.08381 q^{38} +10.1408 q^{39} +19.9505 q^{40} -0.275218 q^{41} -6.64887 q^{42} +0.924990 q^{43} +11.6100 q^{44} +2.82084 q^{45} +4.92802 q^{46} -2.44235 q^{47} +8.09286 q^{48} -3.79343 q^{49} -19.5474 q^{50} -1.48745 q^{51} +28.8466 q^{52} -1.31889 q^{53} +14.0631 q^{54} -9.82859 q^{55} -9.97354 q^{56} -0.645812 q^{57} +8.73267 q^{58} -7.90477 q^{59} -22.5441 q^{60} -12.6824 q^{61} -11.0946 q^{62} -1.41018 q^{63} -4.78531 q^{64} -24.4205 q^{65} -10.1881 q^{66} -1.78241 q^{67} -4.23122 q^{68} -2.93648 q^{69} +16.0115 q^{70} +14.1871 q^{71} +4.38613 q^{72} -3.18785 q^{73} +27.7670 q^{74} +11.6478 q^{75} -1.83709 q^{76} +4.91345 q^{77} -25.3138 q^{78} +3.21890 q^{79} -19.4889 q^{80} -6.01732 q^{81} +0.687010 q^{82} -2.32445 q^{83} +11.2701 q^{84} +3.58200 q^{85} -2.30900 q^{86} -5.20358 q^{87} -15.2825 q^{88} -17.5695 q^{89} -7.04150 q^{90} +12.2082 q^{91} -8.35318 q^{92} +6.61101 q^{93} +6.09670 q^{94} +1.55521 q^{95} -3.63260 q^{96} +7.12310 q^{97} +9.46931 q^{98} -2.16082 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 113 q - 11 q^{2} - 11 q^{3} + 103 q^{4} - 19 q^{5} - 13 q^{6} + 11 q^{7} - 36 q^{8} + 94 q^{9}+O(q^{10}) \) 113 * q - 11 * q^2 - 11 * q^3 + 103 * q^4 - 19 * q^5 - 13 * q^6 + 11 * q^7 - 36 * q^8 + 94 * q^9	\( 113 q - 11 q^{2} - 11 q^{3} + 103 q^{4} - 19 q^{5} - 13 q^{6} + 11 q^{7} - 36 q^{8} + 94 q^{9} - 5 q^{10} - 40 q^{11} - 19 q^{12} - 18 q^{13} - 48 q^{14} - 63 q^{15} + 79 q^{16} - 113 q^{17} - 32 q^{18} - 46 q^{19} - 56 q^{20} - 46 q^{21} + 14 q^{22} - 35 q^{23} - 42 q^{24} + 88 q^{25} - 89 q^{26} - 41 q^{27} + 20 q^{28} - 51 q^{29} - 18 q^{30} - 57 q^{31} - 93 q^{32} - 40 q^{33} + 11 q^{34} - 69 q^{35} + 18 q^{36} + 16 q^{37} - 74 q^{38} - 51 q^{39} + 2 q^{40} - 87 q^{41} - 23 q^{42} - 32 q^{43} - 110 q^{44} - 17 q^{45} - 17 q^{46} - 161 q^{47} - 36 q^{48} + 56 q^{49} - 69 q^{50} + 11 q^{51} - 49 q^{52} - 48 q^{53} - 38 q^{54} - 79 q^{55} - 171 q^{56} + 20 q^{57} + 13 q^{58} - 174 q^{59} - 146 q^{60} - 34 q^{61} - 34 q^{62} - 14 q^{63} + 62 q^{64} - 22 q^{65} - 60 q^{66} - 50 q^{67} - 103 q^{68} - 59 q^{69} - 58 q^{70} - 189 q^{71} - 123 q^{72} - 4 q^{73} - 24 q^{74} - 106 q^{75} - 92 q^{76} - 78 q^{77} - 42 q^{78} + 8 q^{79} - 150 q^{80} + 13 q^{81} + 6 q^{82} - 109 q^{83} - 114 q^{84} + 19 q^{85} - 116 q^{86} - 106 q^{87} + 54 q^{88} - 170 q^{89} - q^{90} - 43 q^{91} - 94 q^{92} - 69 q^{93} - 35 q^{94} - 78 q^{95} - 44 q^{96} - 3 q^{97} - 68 q^{98} - 119 q^{99}+O(q^{100}) \) 113 * q - 11 * q^2 - 11 * q^3 + 103 * q^4 - 19 * q^5 - 13 * q^6 + 11 * q^7 - 36 * q^8 + 94 * q^9 - 5 * q^10 - 40 * q^11 - 19 * q^12 - 18 * q^13 - 48 * q^14 - 63 * q^15 + 79 * q^16 - 113 * q^17 - 32 * q^18 - 46 * q^19 - 56 * q^20 - 46 * q^21 + 14 * q^22 - 35 * q^23 - 42 * q^24 + 88 * q^25 - 89 * q^26 - 41 * q^27 + 20 * q^28 - 51 * q^29 - 18 * q^30 - 57 * q^31 - 93 * q^32 - 40 * q^33 + 11 * q^34 - 69 * q^35 + 18 * q^36 + 16 * q^37 - 74 * q^38 - 51 * q^39 + 2 * q^40 - 87 * q^41 - 23 * q^42 - 32 * q^43 - 110 * q^44 - 17 * q^45 - 17 * q^46 - 161 * q^47 - 36 * q^48 + 56 * q^49 - 69 * q^50 + 11 * q^51 - 49 * q^52 - 48 * q^53 - 38 * q^54 - 79 * q^55 - 171 * q^56 + 20 * q^57 + 13 * q^58 - 174 * q^59 - 146 * q^60 - 34 * q^61 - 34 * q^62 - 14 * q^63 + 62 * q^64 - 22 * q^65 - 60 * q^66 - 50 * q^67 - 103 * q^68 - 59 * q^69 - 58 * q^70 - 189 * q^71 - 123 * q^72 - 4 * q^73 - 24 * q^74 - 106 * q^75 - 92 * q^76 - 78 * q^77 - 42 * q^78 + 8 * q^79 - 150 * q^80 + 13 * q^81 + 6 * q^82 - 109 * q^83 - 114 * q^84 + 19 * q^85 - 116 * q^86 - 106 * q^87 + 54 * q^88 - 170 * q^89 - q^90 - 43 * q^91 - 94 * q^92 - 69 * q^93 - 35 * q^94 - 78 * q^95 - 44 * q^96 - 3 * q^97 - 68 * q^98 - 119 * q^99

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