LMFDB - Embedded newform 6029.2.a.a.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6029,2,Mod(1,6029)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6029, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("6029.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6029 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6029.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:	$48.1418073786$
Analytic rank:	$1$
Dimension:	$234$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Character	$\chi$	$=$	6029.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.69522 q^{2} -2.18729 q^{3} +5.26421 q^{4} -2.45102 q^{5} +5.89522 q^{6} -1.76465 q^{7} -8.79776 q^{8} +1.78423 q^{9} +O(q^{10})$	\(q-2.69522 q^{2} -2.18729 q^{3} +5.26421 q^{4} -2.45102 q^{5} +5.89522 q^{6} -1.76465 q^{7} -8.79776 q^{8} +1.78423 q^{9} +6.60605 q^{10} +2.16166 q^{11} -11.5143 q^{12} +3.56301 q^{13} +4.75613 q^{14} +5.36110 q^{15} +13.1835 q^{16} +6.91723 q^{17} -4.80889 q^{18} -6.09777 q^{19} -12.9027 q^{20} +3.85980 q^{21} -5.82615 q^{22} +4.86473 q^{23} +19.2432 q^{24} +1.00752 q^{25} -9.60308 q^{26} +2.65924 q^{27} -9.28950 q^{28} -7.34296 q^{29} -14.4493 q^{30} +4.06634 q^{31} -17.9368 q^{32} -4.72818 q^{33} -18.6434 q^{34} +4.32520 q^{35} +9.39256 q^{36} -5.33908 q^{37} +16.4348 q^{38} -7.79332 q^{39} +21.5635 q^{40} -8.06769 q^{41} -10.4030 q^{42} -10.1761 q^{43} +11.3794 q^{44} -4.37319 q^{45} -13.1115 q^{46} +1.75055 q^{47} -28.8361 q^{48} -3.88600 q^{49} -2.71548 q^{50} -15.1300 q^{51} +18.7564 q^{52} -0.144480 q^{53} -7.16723 q^{54} -5.29828 q^{55} +15.5250 q^{56} +13.3376 q^{57} +19.7909 q^{58} +9.34328 q^{59} +28.2219 q^{60} +0.561444 q^{61} -10.9597 q^{62} -3.14855 q^{63} +21.9768 q^{64} -8.73301 q^{65} +12.7435 q^{66} -2.85566 q^{67} +36.4137 q^{68} -10.6406 q^{69} -11.6574 q^{70} +11.0336 q^{71} -15.6972 q^{72} -8.85218 q^{73} +14.3900 q^{74} -2.20373 q^{75} -32.0999 q^{76} -3.81458 q^{77} +21.0047 q^{78} -17.0575 q^{79} -32.3130 q^{80} -11.1692 q^{81} +21.7442 q^{82} +15.2952 q^{83} +20.3188 q^{84} -16.9543 q^{85} +27.4269 q^{86} +16.0612 q^{87} -19.0178 q^{88} +11.9907 q^{89} +11.7867 q^{90} -6.28747 q^{91} +25.6090 q^{92} -8.89426 q^{93} -4.71811 q^{94} +14.9458 q^{95} +39.2330 q^{96} +15.7367 q^{97} +10.4736 q^{98} +3.85691 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 234 q - 10 q^{2} - 43 q^{3} + 202 q^{4} - 24 q^{5} - 40 q^{6} - 61 q^{7} - 27 q^{8} + 203 q^{9}+O(q^{10}) $ 234 * q - 10 * q^2 - 43 * q^3 + 202 * q^4 - 24 * q^5 - 40 * q^6 - 61 * q^7 - 27 * q^8 + 203 * q^9	\( 234 q - 10 q^{2} - 43 q^{3} + 202 q^{4} - 24 q^{5} - 40 q^{6} - 61 q^{7} - 27 q^{8} + 203 q^{9} - 89 q^{10} - 55 q^{11} - 75 q^{12} - 49 q^{13} - 42 q^{14} - 43 q^{15} + 142 q^{16} - 40 q^{17} - 30 q^{18} - 235 q^{19} - 62 q^{20} - 62 q^{21} - 63 q^{22} - 30 q^{23} - 108 q^{24} + 170 q^{25} - 44 q^{26} - 160 q^{27} - 147 q^{28} - 76 q^{29} - 15 q^{30} - 175 q^{31} - 49 q^{32} - 43 q^{33} - 104 q^{34} - 87 q^{35} + 124 q^{36} - 77 q^{37} - 18 q^{38} - 104 q^{39} - 247 q^{40} - 60 q^{41} - 6 q^{42} - 201 q^{43} - 89 q^{44} - 102 q^{45} - 128 q^{46} - 27 q^{47} - 130 q^{48} + 123 q^{49} - 33 q^{50} - 220 q^{51} - 125 q^{52} - 34 q^{53} - 126 q^{54} - 176 q^{55} - 125 q^{56} - 17 q^{57} - 46 q^{58} - 172 q^{59} - 61 q^{60} - 243 q^{61} - 37 q^{62} - 137 q^{63} + 39 q^{64} - 31 q^{65} - 142 q^{66} - 132 q^{67} - 106 q^{68} - 115 q^{69} - 60 q^{70} - 68 q^{71} - 66 q^{72} - 109 q^{73} - 74 q^{74} - 256 q^{75} - 412 q^{76} - 32 q^{77} - 38 q^{78} - 297 q^{79} - 111 q^{80} + 142 q^{81} - 94 q^{82} - 100 q^{83} - 134 q^{84} - 90 q^{85} + q^{86} - 103 q^{87} - 143 q^{88} - 77 q^{89} - 181 q^{90} - 418 q^{91} - 19 q^{92} + 5 q^{93} - 231 q^{94} - 92 q^{95} - 189 q^{96} - 141 q^{97} - 25 q^{98} - 244 q^{99}+O(q^{100}) \) 234 * q - 10 * q^2 - 43 * q^3 + 202 * q^4 - 24 * q^5 - 40 * q^6 - 61 * q^7 - 27 * q^8 + 203 * q^9 - 89 * q^10 - 55 * q^11 - 75 * q^12 - 49 * q^13 - 42 * q^14 - 43 * q^15 + 142 * q^16 - 40 * q^17 - 30 * q^18 - 235 * q^19 - 62 * q^20 - 62 * q^21 - 63 * q^22 - 30 * q^23 - 108 * q^24 + 170 * q^25 - 44 * q^26 - 160 * q^27 - 147 * q^28 - 76 * q^29 - 15 * q^30 - 175 * q^31 - 49 * q^32 - 43 * q^33 - 104 * q^34 - 87 * q^35 + 124 * q^36 - 77 * q^37 - 18 * q^38 - 104 * q^39 - 247 * q^40 - 60 * q^41 - 6 * q^42 - 201 * q^43 - 89 * q^44 - 102 * q^45 - 128 * q^46 - 27 * q^47 - 130 * q^48 + 123 * q^49 - 33 * q^50 - 220 * q^51 - 125 * q^52 - 34 * q^53 - 126 * q^54 - 176 * q^55 - 125 * q^56 - 17 * q^57 - 46 * q^58 - 172 * q^59 - 61 * q^60 - 243 * q^61 - 37 * q^62 - 137 * q^63 + 39 * q^64 - 31 * q^65 - 142 * q^66 - 132 * q^67 - 106 * q^68 - 115 * q^69 - 60 * q^70 - 68 * q^71 - 66 * q^72 - 109 * q^73 - 74 * q^74 - 256 * q^75 - 412 * q^76 - 32 * q^77 - 38 * q^78 - 297 * q^79 - 111 * q^80 + 142 * q^81 - 94 * q^82 - 100 * q^83 - 134 * q^84 - 90 * q^85 + q^86 - 103 * q^87 - 143 * q^88 - 77 * q^89 - 181 * q^90 - 418 * q^91 - 19 * q^92 + 5 * q^93 - 231 * q^94 - 92 * q^95 - 189 * q^96 - 141 * q^97 - 25 * q^98 - 244 * 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 $

$2$	−2.69522	−1.90581	−0.952904	−	0.303272i	$-0.901921\pi$
$2$	−2.69522	−1.90581	−0.952904	+	0.303272i	$0.901921\pi$
$3$	−2.18729	−1.26283	−0.631416	−	0.775444i	$-0.717526\pi$
$3$	−2.18729	−1.26283	−0.631416	+	0.775444i	$0.717526\pi$
$4$	5.26421	2.63210
$5$	−2.45102	−1.09613	−0.548065	−	0.836435i	$-0.684636\pi$
$5$	−2.45102	−1.09613	−0.548065	+	0.836435i	$0.684636\pi$
$6$	5.89522	2.40671
$7$	−1.76465	−0.666976	−0.333488	−	0.942754i	$-0.608226\pi$
$7$	−1.76465	−0.666976	−0.333488	+	0.942754i	$0.608226\pi$
$8$	−8.79776	−3.11048
$9$	1.78423	0.594744
$10$	6.60605	2.08902
$11$	2.16166	0.651766	0.325883	−	0.945410i	$-0.394339\pi$
$11$	2.16166	0.651766	0.325883	+	0.945410i	$0.394339\pi$
$12$	−11.5143	−3.32390
$13$	3.56301	0.988200	0.494100	−	0.869405i	$-0.335498\pi$
$13$	3.56301	0.988200	0.494100	+	0.869405i	$0.335498\pi$
$14$	4.75613	1.27113
$15$	5.36110	1.38423
$16$	13.1835	3.29587
$17$	6.91723	1.67767	0.838837	−	0.544383i	$-0.183236\pi$
$17$	6.91723	1.67767	0.838837	+	0.544383i	$0.183236\pi$
$18$	−4.80889	−1.13347
$19$	−6.09777	−1.39892	−0.699462	−	0.714669i	$-0.746577\pi$
$19$	−6.09777	−1.39892	−0.699462	+	0.714669i	$0.746577\pi$
$20$	−12.9027	−2.88513
$21$	3.85980	0.842278
$22$	−5.82615	−1.24214
$23$	4.86473	1.01437	0.507183	−	0.861838i	$-0.330687\pi$
$23$	4.86473	1.01437	0.507183	+	0.861838i	$0.330687\pi$
$24$	19.2432	3.92801
$25$	1.00752	0.201503
$26$	−9.60308	−1.88332
$27$	2.65924	0.511770
$28$	−9.28950	−1.75555
$29$	−7.34296	−1.36355	−0.681777	−	0.731561i	$-0.738792\pi$
$29$	−7.34296	−1.36355	−0.681777	+	0.731561i	$0.738792\pi$
$30$	−14.4493	−2.63807
$31$	4.06634	0.730337	0.365168	−	0.930942i	$-0.381011\pi$
$31$	4.06634	0.730337	0.365168	+	0.930942i	$0.381011\pi$
$32$	−17.9368	−3.17081
$33$	−4.72818	−0.823070
$34$	−18.6434	−3.19732
$35$	4.32520	0.731093
$36$	9.39256	1.56543
$37$	−5.33908	−0.877739	−0.438869	−	0.898551i	$-0.644621\pi$
$37$	−5.33908	−0.877739	−0.438869	+	0.898551i	$0.644621\pi$
$38$	16.4348	2.66608
$39$	−7.79332	−1.24793
$40$	21.5635	3.40949
$41$	−8.06769	−1.25996	−0.629981	−	0.776611i	$-0.716937\pi$
$41$	−8.06769	−1.25996	−0.629981	+	0.776611i	$0.716937\pi$
$42$	−10.4030	−1.60522
$43$	−10.1761	−1.55184	−0.775922	−	0.630829i	$-0.782715\pi$
$43$	−10.1761	−1.55184	−0.775922	+	0.630829i	$0.782715\pi$
$44$	11.3794	1.71552
$45$	−4.37319	−0.651917
$46$	−13.1115	−1.93319
$47$	1.75055	0.255343	0.127672	−	0.991816i	$-0.459250\pi$
$47$	1.75055	0.255343	0.127672	+	0.991816i	$0.459250\pi$
$48$	−28.8361	−4.16213
$49$	−3.88600	−0.555143
$50$	−2.71548	−0.384026
$51$	−15.1300	−2.11862
$52$	18.7564	2.60104
$53$	−0.144480	−0.0198458	−0.00992291	−	0.999951i	$-0.503159\pi$
$53$	−0.144480	−0.0198458	−0.00992291	+	0.999951i	$0.503159\pi$
$54$	−7.16723	−0.975336
$55$	−5.29828	−0.714421
$56$	15.5250	2.07461
$57$	13.3376	1.76661
$58$	19.7909	2.59867
$59$	9.34328	1.21639	0.608196	−	0.793787i	$-0.291893\pi$
$59$	9.34328	1.21639	0.608196	+	0.793787i	$0.291893\pi$
$60$	28.2219	3.64343
$61$	0.561444	0.0718856	0.0359428	−	0.999354i	$-0.488557\pi$
$61$	0.561444	0.0718856	0.0359428	+	0.999354i	$0.488557\pi$
$62$	−10.9597	−1.39188
$63$	−3.14855	−0.396680
$64$	21.9768	2.74709
$65$	−8.73301	−1.08320
$66$	12.7435	1.56861
$67$	−2.85566	−0.348874	−0.174437	−	0.984668i	$-0.555811\pi$
$67$	−2.85566	−0.348874	−0.174437	+	0.984668i	$0.555811\pi$
$68$	36.4137	4.41581
$69$	−10.6406	−1.28097
$70$	−11.6574	−1.39332
$71$	11.0336	1.30945	0.654724	−	0.755868i	$-0.272785\pi$
$71$	11.0336	1.30945	0.654724	+	0.755868i	$0.272785\pi$
$72$	−15.6972	−1.84994
$73$	−8.85218	−1.03607	−0.518035	−	0.855359i	$-0.673336\pi$
$73$	−8.85218	−1.03607	−0.518035	+	0.855359i	$0.673336\pi$
$74$	14.3900	1.67280
$75$	−2.20373	−0.254465
$76$	−32.0999	−3.68212
$77$	−3.81458	−0.434712
$78$	21.0047	2.37831
$79$	−17.0575	−1.91912	−0.959558	−	0.281511i	$-0.909165\pi$
$79$	−17.0575	−1.91912	−0.959558	+	0.281511i	$0.909165\pi$
$80$	−32.3130	−3.61270
$81$	−11.1692	−1.24102
$82$	21.7442	2.40124
$83$	15.2952	1.67886	0.839431	−	0.543466i	$-0.182888\pi$
$83$	15.2952	1.67886	0.839431	+	0.543466i	$0.182888\pi$
$84$	20.3188	2.21696
$85$	−16.9543	−1.83895
$86$	27.4269	2.95752
$87$	16.0612	1.72194
$88$	−19.0178	−2.02730
$89$	11.9907	1.27102	0.635508	−	0.772094i	$-0.280791\pi$
$89$	11.9907	1.27102	0.635508	+	0.772094i	$0.280791\pi$
$90$	11.7867	1.24243
$91$	−6.28747	−0.659106
$92$	25.6090	2.66992
$93$	−8.89426	−0.922292
$94$	−4.71811	−0.486635
$95$	14.9458	1.53340
$96$	39.2330	4.00420
$97$	15.7367	1.59782	0.798908	−	0.601453i	$-0.205411\pi$
$97$	15.7367	1.59782	0.798908	+	0.601453i	$0.205411\pi$
$98$	10.4736	1.05800
$99$	3.85691	0.387634
$100$	5.30377	0.530377
$101$	−8.07093	−0.803088	−0.401544	−	0.915840i	$-0.631526\pi$
$101$	−8.07093	−0.803088	−0.401544	+	0.915840i	$0.631526\pi$
$102$	40.7786	4.03768
$103$	12.0728	1.18957	0.594786	−	0.803884i	$-0.297237\pi$
$103$	12.0728	1.18957	0.594786	+	0.803884i	$0.297237\pi$
$104$	−31.3465	−3.07377
$105$	−9.46047	−0.923247
$106$	0.389405	0.0378223
$107$	5.59548	0.540935	0.270468	−	0.962729i	$-0.412822\pi$
$107$	5.59548	0.540935	0.270468	+	0.962729i	$0.412822\pi$
$108$	13.9988	1.34703
$109$	12.9103	1.23658	0.618289	−	0.785951i	$-0.287826\pi$
$109$	12.9103	1.23658	0.618289	+	0.785951i	$0.287826\pi$
$110$	14.2800	1.36155
$111$	11.6781	1.10844
$112$	−23.2642	−2.19826
$113$	−10.2311	−0.962460	−0.481230	−	0.876594i	$-0.659810\pi$
$113$	−10.2311	−0.962460	−0.481230	+	0.876594i	$0.659810\pi$
$114$	−35.9477	−3.36681
$115$	−11.9236	−1.11188
$116$	−38.6549	−3.58901
$117$	6.35723	0.587726
$118$	−25.1822	−2.31821
$119$	−12.2065	−1.11897
$120$	−47.1656	−4.30561
$121$	−6.32722	−0.575202
$122$	−1.51322	−0.137000
$123$	17.6464	1.59112
$124$	21.4061	1.92232
$125$	9.78567	0.875257
$126$	8.48603	0.755996
$127$	6.76904	0.600655	0.300327	−	0.953836i	$-0.402904\pi$
$127$	6.76904	0.600655	0.300327	+	0.953836i	$0.402904\pi$
$128$	−23.3585	−2.06462
$129$	22.2581	1.95972
$130$	23.5374	2.06436
$131$	−9.88925	−0.864027	−0.432014	−	0.901867i	$-0.642197\pi$
$131$	−9.88925	−0.864027	−0.432014	+	0.901867i	$0.642197\pi$
$132$	−24.8901	−2.16641
$133$	10.7604	0.933049
$134$	7.69662	0.664887
$135$	−6.51785	−0.560967
$136$	−60.8561	−5.21837
$137$	14.8734	1.27072	0.635360	−	0.772216i	$-0.280852\pi$
$137$	14.8734	1.27072	0.635360	+	0.772216i	$0.280852\pi$
$138$	28.6787	2.44129
$139$	−12.9495	−1.09836	−0.549181	−	0.835704i	$-0.685060\pi$
$139$	−12.9495	−1.09836	−0.549181	+	0.835704i	$0.685060\pi$
$140$	22.7688	1.92431
$141$	−3.82895	−0.322456
$142$	−29.7380	−2.49556
$143$	7.70201	0.644075
$144$	23.5224	1.96020
$145$	17.9978	1.49463
$146$	23.8586	1.97455
$147$	8.49981	0.701052
$148$	−28.1060	−2.31030
$149$	−4.79969	−0.393206	−0.196603	−	0.980483i	$-0.562991\pi$
$149$	−4.79969	−0.393206	−0.196603	+	0.980483i	$0.562991\pi$
$150$	5.93953	0.484961
$151$	−20.6424	−1.67986	−0.839928	−	0.542698i	$-0.817403\pi$
$151$	−20.6424	−1.67986	−0.839928	+	0.542698i	$0.817403\pi$
$152$	53.6467	4.35132
$153$	12.3419	0.997786
$154$	10.2811	0.828478
$155$	−9.96670	−0.800545
$156$	−41.0257	−3.28468
$157$	−1.60533	−0.128119	−0.0640596	−	0.997946i	$-0.520405\pi$
$157$	−1.60533	−0.128119	−0.0640596	+	0.997946i	$0.520405\pi$
$158$	45.9736	3.65747
$159$	0.316019	0.0250619
$160$	43.9636	3.47563
$161$	−8.58456	−0.676558
$162$	30.1035	2.36515
$163$	8.42007	0.659511	0.329755	−	0.944066i	$-0.393034\pi$
$163$	8.42007	0.659511	0.329755	+	0.944066i	$0.393034\pi$
$164$	−42.4700	−3.31635
$165$	11.5889	0.902193
$166$	−41.2238	−3.19959
$167$	−25.0762	−1.94045	−0.970226	−	0.242200i	$-0.922131\pi$
$167$	−25.0762	−1.94045	−0.970226	+	0.242200i	$0.922131\pi$
$168$	−33.9576	−2.61989
$169$	−0.304995	−0.0234611
$170$	45.6955	3.50469
$171$	−10.8798	−0.832002
$172$	−53.5692	−4.08462
$173$	17.3827	1.32158	0.660790	−	0.750571i	$-0.270222\pi$
$173$	17.3827	1.32158	0.660790	+	0.750571i	$0.270222\pi$
$174$	−43.2884	−3.28168
$175$	−1.77792	−0.134398
$176$	28.4982	2.14813
$177$	−20.4365	−1.53610
$178$	−32.3177	−2.42231
$179$	−3.33634	−0.249370	−0.124685	−	0.992196i	$-0.539792\pi$
$179$	−3.33634	−0.249370	−0.124685	+	0.992196i	$0.539792\pi$
$180$	−23.0214	−1.71591
$181$	16.3763	1.21724	0.608622	−	0.793460i	$-0.291723\pi$
$181$	16.3763	1.21724	0.608622	+	0.793460i	$0.291723\pi$
$182$	16.9461	1.25613
$183$	−1.22804	−0.0907794
$184$	−42.7987	−3.15516
$185$	13.0862	0.962116
$186$	23.9720	1.75771
$187$	14.9527	1.09345
$188$	9.21524	0.672090
$189$	−4.69263	−0.341339
$190$	−40.2822	−2.92238
$191$	24.4937	1.77230	0.886152	−	0.463394i	$-0.153369\pi$
$191$	24.4937	1.77230	0.886152	+	0.463394i	$0.153369\pi$
$192$	−48.0695	−3.46912
$193$	20.3387	1.46401	0.732006	−	0.681298i	$-0.238584\pi$
$193$	20.3387	1.46401	0.732006	+	0.681298i	$0.238584\pi$
$194$	−42.4138	−3.04513
$195$	19.1016	1.36789
$196$	−20.4567	−1.46119
$197$	−24.5064	−1.74601	−0.873004	−	0.487713i	$-0.837831\pi$
$197$	−24.5064	−1.74601	−0.873004	+	0.487713i	$0.837831\pi$
$198$	−10.3952	−0.738755
$199$	−8.50989	−0.603250	−0.301625	−	0.953427i	$-0.597529\pi$
$199$	−8.50989	−0.603250	−0.301625	+	0.953427i	$0.597529\pi$
$200$	−8.86388	−0.626771
$201$	6.24615	0.440569
$202$	21.7529	1.53053
$203$	12.9578	0.909457
$204$	−79.6473	−5.57643
$205$	19.7741	1.38108
$206$	−32.5390	−2.26710
$207$	8.67981	0.603288
$208$	46.9728	3.25698
$209$	−13.1813	−0.911771
$210$	25.4980	1.75953
$211$	−11.5448	−0.794778	−0.397389	−	0.917650i	$-0.630084\pi$
$211$	−11.5448	−0.794778	−0.397389	+	0.917650i	$0.630084\pi$
$212$	−0.760571	−0.0522363
$213$	−24.1337	−1.65361
$214$	−15.0810	−1.03092
$215$	24.9419	1.70102
$216$	−23.3953	−1.59185
$217$	−7.17568	−0.487117
$218$	−34.7960	−2.35668
$219$	19.3623	1.30838
$220$	−27.8913	−1.88043
$221$	24.6461	1.65788
$222$	−31.4750	−2.11247
$223$	11.3279	0.758571	0.379286	−	0.925280i	$-0.376170\pi$
$223$	11.3279	0.758571	0.379286	+	0.925280i	$0.376170\pi$
$224$	31.6523	2.11486
$225$	1.79764	0.119843
$226$	27.5750	1.83426
$227$	−6.41287	−0.425637	−0.212819	−	0.977092i	$-0.568264\pi$
$227$	−6.41287	−0.425637	−0.212819	+	0.977092i	$0.568264\pi$
$228$	70.2118	4.64989
$229$	16.7725	1.10836	0.554180	−	0.832397i	$-0.313032\pi$
$229$	16.7725	1.10836	0.554180	+	0.832397i	$0.313032\pi$
$230$	32.1366	2.11903
$231$	8.34359	0.548968
$232$	64.6016	4.24130
$233$	23.8437	1.56205	0.781027	−	0.624497i	$-0.214696\pi$
$233$	23.8437	1.56205	0.781027	+	0.624497i	$0.214696\pi$
$234$	−17.1341	−1.12009
$235$	−4.29063	−0.279890
$236$	49.1850	3.20167
$237$	37.3096	2.42352
$238$	32.8992	2.13254
$239$	2.77828	0.179712	0.0898559	−	0.995955i	$-0.471359\pi$
$239$	2.77828	0.179712	0.0898559	+	0.995955i	$0.471359\pi$
$240$	70.6778	4.56224
$241$	17.7206	1.14148	0.570741	−	0.821130i	$-0.306656\pi$
$241$	17.7206	1.14148	0.570741	+	0.821130i	$0.306656\pi$
$242$	17.0532	1.09622
$243$	16.4526	1.05543
$244$	2.95556	0.189210
$245$	9.52468	0.608509
$246$	−47.5608	−3.03237
$247$	−21.7264	−1.38242
$248$	−35.7747	−2.27169
$249$	−33.4549	−2.12012
$250$	−26.3745	−1.66807
$251$	−5.90839	−0.372934	−0.186467	−	0.982461i	$-0.559704\pi$
$251$	−5.90839	−0.372934	−0.186467	+	0.982461i	$0.559704\pi$
$252$	−16.5746	−1.04410
$253$	10.5159	0.661129
$254$	−18.2440	−1.14473
$255$	37.0839	2.32228
$256$	19.0028	1.18768
$257$	−3.30784	−0.206337	−0.103169	−	0.994664i	$-0.532898\pi$
$257$	−3.30784	−0.206337	−0.103169	+	0.994664i	$0.532898\pi$
$258$	−59.9905	−3.73485
$259$	9.42161	0.585431
$260$	−45.9724	−2.85109
$261$	−13.1015	−0.810965
$262$	26.6537	1.64667
$263$	−12.5330	−0.772817	−0.386408	−	0.922328i	$-0.626284\pi$
$263$	−12.5330	−0.772817	−0.386408	+	0.922328i	$0.626284\pi$
$264$	41.5974	2.56014
$265$	0.354123	0.0217536
$266$	−29.0018	−1.77821
$267$	−26.2272	−1.60508
$268$	−15.0328	−0.918273
$269$	−18.9544	−1.15567	−0.577835	−	0.816154i	$-0.696102\pi$
$269$	−18.9544	−1.15567	−0.577835	+	0.816154i	$0.696102\pi$
$270$	17.5670	1.06910
$271$	3.76982	0.229000	0.114500	−	0.993423i	$-0.463473\pi$
$271$	3.76982	0.229000	0.114500	+	0.993423i	$0.463473\pi$
$272$	91.1931	5.52939
$273$	13.7525	0.832339
$274$	−40.0871	−2.42175
$275$	2.17791	0.131333
$276$	−56.0142	−3.37166
$277$	18.7263	1.12515	0.562576	−	0.826746i	$-0.309810\pi$
$277$	18.7263	1.12515	0.562576	+	0.826746i	$0.309810\pi$
$278$	34.9017	2.09327
$279$	7.25529	0.434363
$280$	−38.0521	−2.27405
$281$	25.2151	1.50420	0.752102	−	0.659046i	$-0.229040\pi$
$281$	25.2151	1.50420	0.752102	+	0.659046i	$0.229040\pi$
$282$	10.3199	0.614539
$283$	−9.87062	−0.586747	−0.293374	−	0.955998i	$-0.594778\pi$
$283$	−9.87062	−0.586747	−0.293374	+	0.955998i	$0.594778\pi$
$284$	58.0832	3.44660
$285$	−32.6907	−1.93643
$286$	−20.7586	−1.22748
$287$	14.2367	0.840364
$288$	−32.0035	−1.88582
$289$	30.8480	1.81459
$290$	−48.5079	−2.84848
$291$	−34.4206	−2.01777
$292$	−46.5997	−2.72704
$293$	−12.2711	−0.716888	−0.358444	−	0.933551i	$-0.616693\pi$
$293$	−12.2711	−0.716888	−0.358444	+	0.933551i	$0.616693\pi$
$294$	−22.9088	−1.33607
$295$	−22.9006	−1.33333
$296$	46.9719	2.73019
$297$	5.74837	0.333554
$298$	12.9362	0.749376
$299$	17.3331	1.00240
$300$	−11.6009	−0.669777
$301$	17.9573	1.03504
$302$	55.6359	3.20148
$303$	17.6535	1.01416
$304$	−80.3898	−4.61067
$305$	−1.37611	−0.0787960
$306$	−33.2642	−1.90159
$307$	−26.4908	−1.51191	−0.755955	−	0.654623i	$-0.772827\pi$
$307$	−26.4908	−1.51191	−0.755955	+	0.654623i	$0.772827\pi$
$308$	−20.0808	−1.14421
$309$	−26.4068	−1.50223
$310$	26.8624	1.52568
$311$	−0.849182	−0.0481527	−0.0240763	−	0.999710i	$-0.507664\pi$
$311$	−0.849182	−0.0481527	−0.0240763	+	0.999710i	$0.507664\pi$
$312$	68.5637	3.88166
$313$	30.3944	1.71799	0.858997	−	0.511981i	$-0.171088\pi$
$313$	30.3944	1.71799	0.858997	+	0.511981i	$0.171088\pi$
$314$	4.32671	0.244171
$315$	7.71717	0.434813
$316$	−89.7941	−5.05131
$317$	−9.15552	−0.514225	−0.257112	−	0.966381i	$-0.582771\pi$
$317$	−9.15552	−0.514225	−0.257112	+	0.966381i	$0.582771\pi$
$318$	−0.851740	−0.0477632
$319$	−15.8730	−0.888717
$320$	−53.8655	−3.01118
$321$	−12.2389	−0.683110
$322$	23.1373	1.28939
$323$	−42.1797	−2.34694
$324$	−58.7971	−3.26650
$325$	3.58978	0.199125
$326$	−22.6939	−1.25690
$327$	−28.2384	−1.56159
$328$	70.9776	3.91908
$329$	−3.08911	−0.170308
$330$	−31.2346	−1.71941
$331$	−13.8968	−0.763837	−0.381919	−	0.924196i	$-0.624737\pi$
$331$	−13.8968	−0.763837	−0.381919	+	0.924196i	$0.624737\pi$
$332$	80.5169	4.41894
$333$	−9.52615	−0.522030
$334$	67.5858	3.69813
$335$	6.99928	0.382412
$336$	50.8856	2.77604
$337$	−25.0622	−1.36523	−0.682613	−	0.730780i	$-0.739156\pi$
$337$	−25.0622	−1.36523	−0.682613	+	0.730780i	$0.739156\pi$
$338$	0.822028	0.0447124
$339$	22.3783	1.21542
$340$	−89.2509	−4.84031
$341$	8.79006	0.476008
$342$	29.3235	1.58564
$343$	19.2100	1.03724
$344$	89.5271	4.82698
$345$	26.0803	1.40412
$346$	−46.8501	−2.51868
$347$	−2.95589	−0.158680	−0.0793402	−	0.996848i	$-0.525281\pi$
$347$	−2.95589	−0.158680	−0.0793402	+	0.996848i	$0.525281\pi$
$348$	84.5493	4.53232
$349$	14.0627	0.752758	0.376379	−	0.926466i	$-0.377169\pi$
$349$	14.0627	0.752758	0.376379	+	0.926466i	$0.377169\pi$
$350$	4.79187	0.256136
$351$	9.47488	0.505731
$352$	−38.7734	−2.06663
$353$	27.6623	1.47231	0.736157	−	0.676811i	$-0.236639\pi$
$353$	27.6623	1.47231	0.736157	+	0.676811i	$0.236639\pi$
$354$	55.0807	2.92751
$355$	−27.0436	−1.43533
$356$	63.1218	3.34545
$357$	26.6991	1.41307
$358$	8.99217	0.475251
$359$	−26.9064	−1.42007	−0.710033	−	0.704169i	$-0.751320\pi$
$359$	−26.9064	−1.42007	−0.710033	+	0.704169i	$0.751320\pi$
$360$	38.4743	2.02777
$361$	18.1828	0.956991
$362$	−44.1378	−2.31983
$363$	13.8394	0.726383
$364$	−33.0985	−1.73483
$365$	21.6969	1.13567
$366$	3.30984	0.173008
$367$	23.3739	1.22011	0.610053	−	0.792361i	$-0.291148\pi$
$367$	23.3739	1.22011	0.610053	+	0.792361i	$0.291148\pi$
$368$	64.1340	3.34322
$369$	−14.3946	−0.749354
$370$	−35.2702	−1.83361
$371$	0.254957	0.0132367
$372$	−46.8213	−2.42757
$373$	4.93598	0.255576	0.127788	−	0.991802i	$-0.459212\pi$
$373$	4.93598	0.255576	0.127788	+	0.991802i	$0.459212\pi$
$374$	−40.3008	−2.08391
$375$	−21.4041	−1.10530
$376$	−15.4009	−0.794240
$377$	−26.1630	−1.34746
$378$	12.6477	0.650526
$379$	16.5121	0.848171	0.424085	−	0.905622i	$-0.360596\pi$
$379$	16.5121	0.848171	0.424085	+	0.905622i	$0.360596\pi$
$380$	78.6777	4.03608
$381$	−14.8058	−0.758526
$382$	−66.0160	−3.37767
$383$	−2.12204	−0.108431	−0.0542157	−	0.998529i	$-0.517266\pi$
$383$	−2.12204	−0.108431	−0.0542157	+	0.998529i	$0.517266\pi$
$384$	51.0918	2.60727
$385$	9.34963	0.476501
$386$	−54.8173	−2.79013
$387$	−18.1566	−0.922950
$388$	82.8411	4.20562
$389$	30.2801	1.53526	0.767630	−	0.640893i	$-0.221436\pi$
$389$	30.2801	1.53526	0.767630	+	0.640893i	$0.221436\pi$
$390$	−51.4830	−2.60694
$391$	33.6505	1.70178
$392$	34.1881	1.72676
$393$	21.6306	1.09112
$394$	66.0501	3.32756
$395$	41.8083	2.10360
$396$	20.3036	1.02029
$397$	−18.3779	−0.922362	−0.461181	−	0.887306i	$-0.652574\pi$
$397$	−18.3779	−0.922362	−0.461181	+	0.887306i	$0.652574\pi$
$398$	22.9360	1.14968
$399$	−23.5362	−1.17828
$400$	13.2826	0.664128
$401$	28.5817	1.42730	0.713651	−	0.700502i	$-0.247040\pi$
$401$	28.5817	1.42730	0.713651	+	0.700502i	$0.247040\pi$
$402$	−16.8347	−0.839640
$403$	14.4884	0.721718
$404$	−42.4871	−2.11381
$405$	27.3760	1.36032
$406$	−34.9240	−1.73325
$407$	−11.5413	−0.572080
$408$	133.110	6.58992
$409$	2.78358	0.137639	0.0688197	−	0.997629i	$-0.478077\pi$
$409$	2.78358	0.137639	0.0688197	+	0.997629i	$0.478077\pi$
$410$	−53.2955	−2.63208
$411$	−32.5324	−1.60471
$412$	63.5540	3.13108
$413$	−16.4877	−0.811304
$414$	−23.3940	−1.14975
$415$	−37.4888	−1.84025
$416$	−63.9090	−3.13340
$417$	28.3243	1.38705
$418$	35.5266	1.73766
$419$	−19.9095	−0.972641	−0.486320	−	0.873781i	$-0.661661\pi$
$419$	−19.9095	−0.972641	−0.486320	+	0.873781i	$0.661661\pi$
$420$	−49.8019	−2.43008
$421$	14.2612	0.695047	0.347524	−	0.937671i	$-0.387023\pi$
$421$	14.2612	0.695047	0.347524	+	0.937671i	$0.387023\pi$
$422$	31.1158	1.51470
$423$	3.12338	0.151864
$424$	1.27110	0.0617300
$425$	6.96922	0.338057
$426$	65.0456	3.15147
$427$	−0.990754	−0.0479460
$428$	29.4558	1.42380
$429$	−16.8465	−0.813358
$430$	−67.2239	−3.24183
$431$	1.53277	0.0738307	0.0369153	−	0.999318i	$-0.488247\pi$
$431$	1.53277	0.0738307	0.0369153	+	0.999318i	$0.488247\pi$
$432$	35.0580	1.68673
$433$	−17.2145	−0.827276	−0.413638	−	0.910441i	$-0.635742\pi$
$433$	−17.2145	−0.827276	−0.413638	+	0.910441i	$0.635742\pi$
$434$	19.3400	0.928351
$435$	−39.3663	−1.88747
$436$	67.9622	3.25480
$437$	−29.6640	−1.41902
$438$	−52.1856	−2.49352
$439$	−29.6511	−1.41517	−0.707585	−	0.706628i	$-0.750215\pi$
$439$	−29.6511	−1.41517	−0.707585	+	0.706628i	$0.750215\pi$
$440$	46.6130	2.22219
$441$	−6.93352	−0.330168
$442$	−66.4267	−3.15960
$443$	−11.3749	−0.540439	−0.270219	−	0.962799i	$-0.587096\pi$
$443$	−11.3749	−0.540439	−0.270219	+	0.962799i	$0.587096\pi$
$444$	61.4759	2.91752
$445$	−29.3896	−1.39320
$446$	−30.5311	−1.44569
$447$	10.4983	0.496553
$448$	−38.7813	−1.83225
$449$	−18.4010	−0.868398	−0.434199	−	0.900817i	$-0.642969\pi$
$449$	−18.4010	−0.868398	−0.434199	+	0.900817i	$0.642969\pi$
$450$	−4.84504	−0.228397
$451$	−17.4396	−0.821200
$452$	−53.8586	−2.53329
$453$	45.1509	2.12138
$454$	17.2841	0.811183
$455$	15.4107	0.722466
$456$	−117.341	−5.49499
$457$	16.7714	0.784535	0.392267	−	0.919851i	$-0.371691\pi$
$457$	16.7714	0.784535	0.392267	+	0.919851i	$0.371691\pi$
$458$	−45.2056	−2.11232
$459$	18.3945	0.858584
$460$	−62.7682	−2.92658
$461$	−31.8151	−1.48178	−0.740890	−	0.671627i	$-0.765596\pi$
$461$	−31.8151	−1.48178	−0.740890	+	0.671627i	$0.765596\pi$
$462$	−22.4878	−1.04623
$463$	−8.90398	−0.413803	−0.206902	−	0.978362i	$-0.566338\pi$
$463$	−8.90398	−0.413803	−0.206902	+	0.978362i	$0.566338\pi$
$464$	−96.8057	−4.49409
$465$	21.8000	1.01095
$466$	−64.2641	−2.97698
$467$	19.1912	0.888064	0.444032	−	0.896011i	$-0.353548\pi$
$467$	19.1912	0.888064	0.444032	+	0.896011i	$0.353548\pi$
$468$	33.4658	1.54696
$469$	5.03924	0.232691
$470$	11.5642	0.533416
$471$	3.51132	0.161793
$472$	−82.2000	−3.78356
$473$	−21.9973	−1.01144
$474$	−100.558	−4.61877
$475$	−6.14360	−0.281888
$476$	−64.2576	−2.94524
$477$	−0.257785	−0.0118032
$478$	−7.48806	−0.342496
$479$	6.39311	0.292109	0.146054	−	0.989277i	$-0.453343\pi$
$479$	6.39311	0.292109	0.146054	+	0.989277i	$0.453343\pi$
$480$	−96.1611	−4.38913
$481$	−19.0232	−0.867381
$482$	−47.7608	−2.17545
$483$	18.7769	0.854379
$484$	−33.3078	−1.51399
$485$	−38.5710	−1.75142
$486$	−44.3433	−2.01145
$487$	−7.45732	−0.337923	−0.168962	−	0.985623i	$-0.554041\pi$
$487$	−7.45732	−0.337923	−0.168962	+	0.985623i	$0.554041\pi$
$488$	−4.93945	−0.223598
$489$	−18.4171	−0.832851
$490$	−25.6711	−1.15970
$491$	−28.9325	−1.30571	−0.652853	−	0.757485i	$-0.726428\pi$
$491$	−28.9325	−1.30571	−0.652853	+	0.757485i	$0.726428\pi$
$492$	92.8941	4.18799
$493$	−50.7929	−2.28760
$494$	58.5574	2.63462
$495$	−9.45336	−0.424897
$496$	53.6085	2.40709
$497$	−19.4705	−0.873371
$498$	90.1684	4.04054
$499$	41.8159	1.87194	0.935969	−	0.352082i	$-0.114526\pi$
$499$	41.8159	1.87194	0.935969	+	0.352082i	$0.114526\pi$
$500$	51.5138	2.30377
$501$	54.8488	2.45046
$502$	15.9244	0.710741
$503$	30.4264	1.35664	0.678322	−	0.734765i	$-0.262707\pi$
$503$	30.4264	1.35664	0.678322	+	0.734765i	$0.262707\pi$
$504$	27.7002	1.23386
$505$	19.7820	0.880289
$506$	−28.3427	−1.25999
$507$	0.667112	0.0296275
$508$	35.6336	1.58099
$509$	−41.3973	−1.83490	−0.917452	−	0.397847i	$-0.869758\pi$
$509$	−41.3973	−1.83490	−0.917452	+	0.397847i	$0.869758\pi$
$510$	−99.9493	−4.42583
$511$	15.6210	0.691034
$512$	−4.49975	−0.198863
$513$	−16.2154	−0.715928
$514$	8.91535	0.393239
$515$	−29.5908	−1.30393
$516$	117.171	5.15818
$517$	3.78409	0.166424
$518$	−25.3933	−1.11572
$519$	−38.0209	−1.66893
$520$	76.8309	3.36926
$521$	5.87892	0.257560	0.128780	−	0.991673i	$-0.458894\pi$
$521$	5.87892	0.257560	0.128780	+	0.991673i	$0.458894\pi$
$522$	35.3115	1.54554
$523$	−19.6248	−0.858133	−0.429066	−	0.903273i	$-0.641157\pi$
$523$	−19.6248	−0.858133	−0.429066	+	0.903273i	$0.641157\pi$
$524$	−52.0591	−2.27421
$525$	3.88881	0.169722
$526$	33.7791	1.47284
$527$	28.1278	1.22527
$528$	−62.3338	−2.71273
$529$	0.665612	0.0289397
$530$	−0.954440	−0.0414582
$531$	16.6706	0.723442
$532$	56.6452	2.45588
$533$	−28.7452	−1.24509
$534$	70.6881	3.05897
$535$	−13.7147	−0.592936
$536$	25.1234	1.08516
$537$	7.29754	0.314912
$538$	51.0863	2.20249
$539$	−8.40022	−0.361823
$540$	−34.3113	−1.47652
$541$	10.9616	0.471276	0.235638	−	0.971841i	$-0.424282\pi$
$541$	10.9616	0.471276	0.235638	+	0.971841i	$0.424282\pi$
$542$	−10.1605	−0.436431
$543$	−35.8198	−1.53717
$544$	−124.073	−5.31959
$545$	−31.6433	−1.35545
$546$	−37.0660	−1.58628
$547$	−10.4957	−0.448763	−0.224382	−	0.974501i	$-0.572036\pi$
$547$	−10.4957	−0.448763	−0.224382	+	0.974501i	$0.572036\pi$
$548$	78.2967	3.34467
$549$	1.00175	0.0427535
$550$	−5.86994	−0.250295
$551$	44.7757	1.90751
$552$	93.6132	3.98444
$553$	30.1005	1.28000
$554$	−50.4714	−2.14432
$555$	−28.6233	−1.21499
$556$	−68.1688	−2.89100
$557$	29.5879	1.25368	0.626840	−	0.779148i	$-0.284348\pi$
$557$	29.5879	1.25368	0.626840	+	0.779148i	$0.284348\pi$
$558$	−19.5546	−0.827813
$559$	−36.2576	−1.53353
$560$	57.0212	2.40959
$561$	−32.7059	−1.38084
$562$	−67.9601	−2.86673
$563$	−42.2386	−1.78014	−0.890072	−	0.455819i	$-0.849346\pi$
$563$	−42.2386	−1.78014	−0.890072	+	0.455819i	$0.849346\pi$
$564$	−20.1564	−0.848737
$565$	25.0766	1.05498
$566$	26.6035	1.11823
$567$	19.7098	0.827733
$568$	−97.0710	−4.07301
$569$	−0.670103	−0.0280922	−0.0140461	−	0.999901i	$-0.504471\pi$
$569$	−0.670103	−0.0280922	−0.0140461	+	0.999901i	$0.504471\pi$
$570$	88.1087	3.69047
$571$	24.0392	1.00601	0.503004	−	0.864284i	$-0.332228\pi$
$571$	24.0392	1.00601	0.503004	+	0.864284i	$0.332228\pi$
$572$	40.5450	1.69527
$573$	−53.5749	−2.23812
$574$	−38.3710	−1.60157
$575$	4.90129	0.204398
$576$	39.2116	1.63382
$577$	−38.8275	−1.61641	−0.808204	−	0.588902i	$-0.799560\pi$
$577$	−38.8275	−1.61641	−0.808204	+	0.588902i	$0.799560\pi$
$578$	−83.1422	−3.45826
$579$	−44.4866	−1.84880
$580$	94.7440	3.93403
$581$	−26.9906	−1.11976
$582$	92.7712	3.84549
$583$	−0.312316	−0.0129348
$584$	77.8794	3.22267
$585$	−15.5817	−0.644224
$586$	33.0734	1.36625
$587$	10.6807	0.440841	0.220420	−	0.975405i	$-0.429257\pi$
$587$	10.6807	0.440841	0.220420	+	0.975405i	$0.429257\pi$
$588$	44.7447	1.84524
$589$	−24.7956	−1.02169
$590$	61.7222	2.54106
$591$	53.6026	2.20491
$592$	−70.3875	−2.89291
$593$	39.5837	1.62551	0.812754	−	0.582607i	$-0.197967\pi$
$593$	39.5837	1.62551	0.812754	+	0.582607i	$0.197967\pi$
$594$	−15.4931	−0.635691
$595$	29.9184	1.22654
$596$	−25.2666	−1.03496
$597$	18.6136	0.761804
$598$	−46.7164	−1.91038
$599$	−4.09682	−0.167392	−0.0836958	−	0.996491i	$-0.526672\pi$
$599$	−4.09682	−0.167392	−0.0836958	+	0.996491i	$0.526672\pi$
$600$	19.3879	0.791506
$601$	−2.08552	−0.0850700	−0.0425350	−	0.999095i	$-0.513543\pi$
$601$	−2.08552	−0.0850700	−0.0425350	+	0.999095i	$0.513543\pi$
$602$	−48.3989	−1.97259
$603$	−5.09515	−0.207491
$604$	−108.666	−4.42156
$605$	15.5082	0.630496
$606$	−47.5799	−1.93280
$607$	−29.6131	−1.20196	−0.600979	−	0.799265i	$-0.705223\pi$
$607$	−29.6131	−1.20196	−0.600979	+	0.799265i	$0.705223\pi$
$608$	109.375	4.43573
$609$	−28.3424	−1.14849
$610$	3.70893	0.150170
$611$	6.23720	0.252330
$612$	64.9705	2.62628
$613$	−25.6803	−1.03722	−0.518608	−	0.855012i	$-0.673550\pi$
$613$	−25.6803	−1.03722	−0.518608	+	0.855012i	$0.673550\pi$
$614$	71.3986	2.88141
$615$	−43.2517	−1.74408
$616$	33.5598	1.35216
$617$	−46.3763	−1.86704	−0.933519	−	0.358527i	$-0.883279\pi$
$617$	−46.3763	−1.86704	−0.933519	+	0.358527i	$0.883279\pi$
$618$	71.1721	2.86296
$619$	−18.8579	−0.757963	−0.378981	−	0.925404i	$-0.623726\pi$
$619$	−18.8579	−0.757963	−0.378981	+	0.925404i	$0.623726\pi$
$620$	−52.4668	−2.10712
$621$	12.9365	0.519123
$622$	2.28873	0.0917698
$623$	−21.1595	−0.847738
$624$	−102.743	−4.11301
$625$	−29.0225	−1.16090
$626$	−81.9196	−3.27417
$627$	28.8314	1.15141
$628$	−8.45079	−0.337223
$629$	−36.9316	−1.47256
$630$	−20.7995	−0.828670
$631$	18.1091	0.720911	0.360455	−	0.932776i	$-0.382621\pi$
$631$	18.1091	0.720911	0.360455	+	0.932776i	$0.382621\pi$
$632$	150.068	5.96937
$633$	25.2519	1.00367
$634$	24.6761	0.980014
$635$	−16.5911	−0.658396
$636$	1.66359	0.0659656
$637$	−13.8458	−0.548592
$638$	42.7812	1.69372
$639$	19.6865	0.778786
$640$	57.2523	2.26310
$641$	3.73162	0.147390	0.0736950	−	0.997281i	$-0.476521\pi$
$641$	3.73162	0.147390	0.0736950	+	0.997281i	$0.476521\pi$
$642$	32.9866	1.30188
$643$	−31.2610	−1.23281	−0.616407	−	0.787427i	$-0.711413\pi$
$643$	−31.2610	−1.23281	−0.616407	+	0.787427i	$0.711413\pi$
$644$	−45.1909	−1.78077
$645$	−54.5552	−2.14811
$646$	113.683	4.47282
$647$	−0.665112	−0.0261483	−0.0130741	−	0.999915i	$-0.504162\pi$
$647$	−0.665112	−0.0261483	−0.0130741	+	0.999915i	$0.504162\pi$
$648$	98.2640	3.86018
$649$	20.1970	0.792803
$650$	−9.67526	−0.379495
$651$	15.6953	0.615147
$652$	44.3250	1.73590
$653$	5.77493	0.225990	0.112995	−	0.993596i	$-0.463956\pi$
$653$	5.77493	0.225990	0.112995	+	0.993596i	$0.463956\pi$
$654$	76.1088	2.97609
$655$	24.2388	0.947087
$656$	−106.360	−4.15267
$657$	−15.7943	−0.616196
$658$	8.32582	0.324574
$659$	4.33673	0.168935	0.0844674	−	0.996426i	$-0.473081\pi$
$659$	4.33673	0.168935	0.0844674	+	0.996426i	$0.473081\pi$
$660$	61.0063	2.37467
$661$	−26.0740	−1.01416	−0.507081	−	0.861898i	$-0.669276\pi$
$661$	−26.0740	−1.01416	−0.507081	+	0.861898i	$0.669276\pi$
$662$	37.4549	1.45573
$663$	−53.9082	−2.09362
$664$	−134.563	−5.22206
$665$	−26.3741	−1.02274
$666$	25.6751	0.994888
$667$	−35.7215	−1.38314
$668$	−132.006	−5.10747
$669$	−24.7774	−0.957948
$670$	−18.8646	−0.728803
$671$	1.21365	0.0468526
$672$	−69.2327	−2.67071
$673$	−7.61796	−0.293651	−0.146825	−	0.989162i	$-0.546906\pi$
$673$	−7.61796	−0.293651	−0.146825	+	0.989162i	$0.546906\pi$
$674$	67.5481	2.60186
$675$	2.67922	0.103123
$676$	−1.60556	−0.0617522
$677$	−35.5651	−1.36688	−0.683440	−	0.730007i	$-0.739517\pi$
$677$	−35.5651	−1.36688	−0.683440	+	0.730007i	$0.739517\pi$
$678$	−60.3146	−2.31637
$679$	−27.7698	−1.06571
$680$	149.160	5.72001
$681$	14.0268	0.537508
$682$	−23.6911	−0.907180
$683$	36.1416	1.38292	0.691461	−	0.722414i	$-0.256968\pi$
$683$	36.1416	1.38292	0.691461	+	0.722414i	$0.256968\pi$
$684$	−57.2737	−2.18992
$685$	−36.4550	−1.39288
$686$	−51.7752	−1.97679
$687$	−36.6864	−1.39967
$688$	−134.157	−5.11467
$689$	−0.514782	−0.0196116
$690$	−70.2921	−2.67597
$691$	−29.7422	−1.13145	−0.565723	−	0.824595i	$-0.691403\pi$
$691$	−29.7422	−1.13145	−0.565723	+	0.824595i	$0.691403\pi$
$692$	91.5059	3.47853
$693$	−6.80610	−0.258542
$694$	7.96677	0.302415
$695$	31.7395	1.20395
$696$	−141.302	−5.35605
$697$	−55.8060	−2.11380
$698$	−37.9020	−1.43461
$699$	−52.1531	−1.97261
$700$	−9.35932	−0.353749
$701$	43.1571	1.63002	0.815011	−	0.579445i	$-0.196731\pi$
$701$	43.1571	1.63002	0.815011	+	0.579445i	$0.196731\pi$
$702$	−25.5369	−0.963827
$703$	32.5565	1.22789
$704$	47.5063	1.79046
$705$	9.38484	0.353454
$706$	−74.5559	−2.80595
$707$	14.2424	0.535640
$708$	−107.582	−4.04317
$709$	−23.9614	−0.899890	−0.449945	−	0.893056i	$-0.648557\pi$
$709$	−23.9614	−0.899890	−0.449945	+	0.893056i	$0.648557\pi$
$710$	72.8885	2.73546
$711$	−30.4345	−1.14138
$712$	−105.492	−3.95347
$713$	19.7817	0.740829
$714$	−71.9601	−2.69304
$715$	−18.8778	−0.705990
$716$	−17.5632	−0.656368
$717$	−6.07689	−0.226946
$718$	72.5186	2.70637
$719$	5.60724	0.209115	0.104557	−	0.994519i	$-0.466657\pi$
$719$	5.60724	0.209115	0.104557	+	0.994519i	$0.466657\pi$
$720$	−57.6539	−2.14863
$721$	−21.3044	−0.793416
$722$	−49.0067	−1.82384
$723$	−38.7600	−1.44150
$724$	86.2085	3.20391
$725$	−7.39815	−0.274760
$726$	−37.3004	−1.38435
$727$	0.0379132	0.00140612	0.000703061	−	1.00000i	$-0.499776\pi$
$727$	0.0379132	0.00140612	0.000703061		1.00000i	$0.499776\pi$
$728$	55.3156	2.05013
$729$	−2.47890	−0.0918112
$730$	−58.4779	−2.16437
$731$	−70.3906	−2.60349
$732$	−6.46466	−0.238941
$733$	8.06571	0.297914	0.148957	−	0.988844i	$-0.452408\pi$
$733$	8.06571	0.297914	0.148957	+	0.988844i	$0.452408\pi$
$734$	−62.9977	−2.32529
$735$	−20.8332	−0.768445
$736$	−87.2579	−3.21637
$737$	−6.17297	−0.227384
$738$	38.7967	1.42813
$739$	−26.0612	−0.958676	−0.479338	−	0.877630i	$-0.659123\pi$
$739$	−26.0612	−0.958676	−0.479338	+	0.877630i	$0.659123\pi$
$740$	68.8885	2.53239
$741$	47.5219	1.74576
$742$	−0.687164	−0.0252266
$743$	32.7766	1.20246	0.601228	−	0.799078i	$-0.294678\pi$
$743$	32.7766	1.20246	0.601228	+	0.799078i	$0.294678\pi$
$744$	78.2496	2.86877
$745$	11.7642	0.431006
$746$	−13.3036	−0.487078
$747$	27.2901	0.998493
$748$	78.7142	2.87807
$749$	−9.87408	−0.360791
$750$	57.6887	2.10649
$751$	−17.1076	−0.624264	−0.312132	−	0.950039i	$-0.601043\pi$
$751$	−17.1076	−0.624264	−0.312132	+	0.950039i	$0.601043\pi$
$752$	23.0783	0.841578
$753$	12.9233	0.470953
$754$	70.5150	2.56801
$755$	50.5951	1.84134
$756$	−24.7030	−0.898439
$757$	−15.6760	−0.569755	−0.284878	−	0.958564i	$-0.591953\pi$
$757$	−15.6760	−0.569755	−0.284878	+	0.958564i	$0.591953\pi$
$758$	−44.5038	−1.61645
$759$	−23.0013	−0.834895
$760$	−131.489	−4.76962
$761$	30.8335	1.11771	0.558856	−	0.829265i	$-0.311240\pi$
$761$	30.8335	1.11771	0.558856	+	0.829265i	$0.311240\pi$
$762$	39.9050	1.44560
$763$	−22.7821	−0.824768
$764$	128.940	4.66489
$765$	−30.2504	−1.09370
$766$	5.71937	0.206649
$767$	33.2902	1.20204
$768$	−41.5647	−1.49984
$769$	8.45401	0.304859	0.152430	−	0.988314i	$-0.451290\pi$
$769$	8.45401	0.304859	0.152430	+	0.988314i	$0.451290\pi$
$770$	−25.1993	−0.908120
$771$	7.23520	0.260569
$772$	107.067	3.85343
$773$	37.7603	1.35814	0.679071	−	0.734072i	$-0.262383\pi$
$773$	37.7603	1.35814	0.679071	+	0.734072i	$0.262383\pi$
$774$	48.9359	1.75896
$775$	4.09690	0.147165
$776$	−138.447	−4.96997
$777$	−20.6078	−0.739300
$778$	−81.6114	−2.92591
$779$	49.1949	1.76259
$780$	100.555	3.60044
$781$	23.8509	0.853454
$782$	−90.6954	−3.24326
$783$	−19.5267	−0.697826
$784$	−51.2310	−1.82968
$785$	3.93470	0.140435
$786$	−58.2993	−2.07947
$787$	−20.6529	−0.736198	−0.368099	−	0.929787i	$-0.619991\pi$
$787$	−20.6529	−0.736198	−0.368099	+	0.929787i	$0.619991\pi$
$788$	−129.007	−4.59568
$789$	27.4132	0.975937
$790$	−112.682	−4.00906
$791$	18.0543	0.641938
$792$	−33.9321	−1.20573
$793$	2.00043	0.0710373
$794$	49.5326	1.75784
$795$	−0.774570	−0.0274712
$796$	−44.7979	−1.58782
$797$	15.3016	0.542011	0.271006	−	0.962578i	$-0.412644\pi$
$797$	15.3016	0.542011	0.271006	+	0.962578i	$0.412644\pi$
$798$	63.4352	2.24558
$799$	12.1089	0.428383
$800$	−18.0716	−0.638929
$801$	21.3943	0.755929
$802$	−77.0339	−2.72016
$803$	−19.1354	−0.675275
$804$	32.8810	1.15962
$805$	21.0410	0.741596
$806$	−39.0494	−1.37546
$807$	41.4587	1.45942
$808$	71.0061	2.49799
$809$	18.2518	0.641697	0.320849	−	0.947130i	$-0.396032\pi$
$809$	18.2518	0.641697	0.320849	+	0.947130i	$0.396032\pi$
$810$	−73.7843	−2.59252
$811$	−13.0234	−0.457315	−0.228657	−	0.973507i	$-0.573434\pi$
$811$	−13.0234	−0.457315	−0.228657	+	0.973507i	$0.573434\pi$
$812$	68.2124	2.39379
$813$	−8.24568	−0.289189
$814$	31.1063	1.09027
$815$	−20.6378	−0.722910
$816$	−199.466	−6.98269
$817$	62.0517	2.17091
$818$	−7.50237	−0.262314
$819$	−11.2183	−0.391999
$820$	104.095	3.63515
$821$	−20.9592	−0.731481	−0.365740	−	0.930717i	$-0.619184\pi$
$821$	−20.9592	−0.731481	−0.365740	+	0.930717i	$0.619184\pi$
$822$	87.6820	3.05826
$823$	13.4908	0.470260	0.235130	−	0.971964i	$-0.424448\pi$
$823$	13.4908	0.470260	0.235130	+	0.971964i	$0.424448\pi$
$824$	−106.214	−3.70014
$825$	−4.76371	−0.165851
$826$	44.4378	1.54619
$827$	−8.36506	−0.290882	−0.145441	−	0.989367i	$-0.546460\pi$
$827$	−8.36506	−0.290882	−0.145441	+	0.989367i	$0.546460\pi$
$828$	45.6923	1.58792
$829$	−23.6694	−0.822073	−0.411037	−	0.911619i	$-0.634833\pi$
$829$	−23.6694	−0.822073	−0.411037	+	0.911619i	$0.634833\pi$
$830$	101.041	3.50717
$831$	−40.9597	−1.42088
$832$	78.3033	2.71468
$833$	−26.8804	−0.931349
$834$	−76.3401	−2.64344
$835$	61.4623	2.12699
$836$	−69.3892	−2.39988
$837$	10.8134	0.373765
$838$	53.6604	1.85367
$839$	4.49423	0.155158	0.0775790	−	0.996986i	$-0.475281\pi$
$839$	4.49423	0.155158	0.0775790	+	0.996986i	$0.475281\pi$
$840$	83.2309	2.87174
$841$	24.9190	0.859277
$842$	−38.4370	−1.32463
$843$	−55.1526	−1.89956
$844$	−60.7744	−2.09194
$845$	0.747550	0.0257165
$846$	−8.41819	−0.289423
$847$	11.1653	0.383646
$848$	−1.90474	−0.0654092
$849$	21.5899	0.740963
$850$	−18.7836	−0.644271
$851$	−25.9732	−0.890349
$852$	−127.045	−4.35248
$853$	20.9525	0.717399	0.358699	−	0.933453i	$-0.383220\pi$
$853$	20.9525	0.717399	0.358699	+	0.933453i	$0.383220\pi$
$854$	2.67030	0.0913758
$855$	26.6667	0.911983
$856$	−49.2277	−1.68257
$857$	3.09597	0.105756	0.0528782	−	0.998601i	$-0.483160\pi$
$857$	3.09597	0.105756	0.0528782	+	0.998601i	$0.483160\pi$
$858$	45.4051	1.55010
$859$	51.9293	1.77180	0.885902	−	0.463872i	$-0.153540\pi$
$859$	51.9293	1.77180	0.885902	+	0.463872i	$0.153540\pi$
$860$	131.299	4.47727
$861$	−31.1397	−1.06124
$862$	−4.13114	−0.140707
$863$	−36.7057	−1.24948	−0.624739	−	0.780834i	$-0.714795\pi$
$863$	−36.7057	−1.24948	−0.624739	+	0.780834i	$0.714795\pi$
$864$	−47.6983	−1.62273
$865$	−42.6053	−1.44862
$866$	46.3968	1.57663
$867$	−67.4735	−2.29152
$868$	−37.7743	−1.28214
$869$	−36.8725	−1.25081
$870$	106.101	3.59715
$871$	−10.1747	−0.344757
$872$	−113.581	−3.84635
$873$	28.0779	0.950292
$874$	79.9511	2.70438
$875$	−17.2683	−0.583776
$876$	101.927	3.44380
$877$	11.3895	0.384595	0.192297	−	0.981337i	$-0.438406\pi$
$877$	11.3895	0.384595	0.192297	+	0.981337i	$0.438406\pi$
$878$	79.9162	2.69704
$879$	26.8405	0.905309
$880$	−69.8498	−2.35464
$881$	54.1544	1.82451	0.912254	−	0.409625i	$-0.134340\pi$
$881$	54.1544	1.82451	0.912254	+	0.409625i	$0.134340\pi$
$882$	18.6874	0.629236
$883$	23.1936	0.780528	0.390264	−	0.920703i	$-0.372384\pi$
$883$	23.1936	0.780528	0.390264	+	0.920703i	$0.372384\pi$
$884$	129.742	4.36371
$885$	50.0902	1.68377
$886$	30.6579	1.02997
$887$	−20.7615	−0.697104	−0.348552	−	0.937289i	$-0.613327\pi$
$887$	−20.7615	−0.697104	−0.348552	+	0.937289i	$0.613327\pi$
$888$	−102.741	−3.44776
$889$	−11.9450	−0.400622
$890$	79.2114	2.65517
$891$	−24.1441	−0.808857
$892$	59.6323	1.99664
$893$	−10.6744	−0.357206
$894$	−28.2953	−0.946335
$895$	8.17745	0.273342
$896$	41.2197	1.37705
$897$	−37.9124	−1.26586
$898$	49.5948	1.65500
$899$	−29.8590	−0.995853
$900$	9.46316	0.315439
$901$	−0.999399	−0.0332948
$902$	47.0036	1.56505
$903$	−39.2778	−1.30708
$904$	90.0106	2.99371
$905$	−40.1388	−1.33426
$906$	−121.692	−4.04293
$907$	22.6756	0.752932	0.376466	−	0.926430i	$-0.377139\pi$
$907$	22.6756	0.752932	0.376466	+	0.926430i	$0.377139\pi$
$908$	−33.7587	−1.12032
$909$	−14.4004	−0.477631
$910$	−41.5353	−1.37688
$911$	−34.3245	−1.13722	−0.568611	−	0.822606i	$-0.692519\pi$
$911$	−34.3245	−1.13722	−0.568611	+	0.822606i	$0.692519\pi$
$912$	175.836	5.82250
$913$	33.0630	1.09422
$914$	−45.2027	−1.49517
$915$	3.00996	0.0995061
$916$	88.2941	2.91732
$917$	17.4511	0.576286
$918$	−49.5773	−1.63630
$919$	−45.4762	−1.50012	−0.750061	−	0.661369i	$-0.769976\pi$
$919$	−45.4762	−1.50012	−0.750061	+	0.661369i	$0.769976\pi$
$920$	104.901	3.45847
$921$	57.9431	1.90929
$922$	85.7488	2.82399
$923$	39.3128	1.29400
$924$	43.9224	1.44494
$925$	−5.37920	−0.176867
$926$	23.9982	0.788629
$927$	21.5407	0.707491
$928$	131.709	4.32357
$929$	27.1823	0.891822	0.445911	−	0.895077i	$-0.352880\pi$
$929$	27.1823	0.891822	0.445911	+	0.895077i	$0.352880\pi$
$930$	−58.7559	−1.92668
$931$	23.6959	0.776603
$932$	125.518	4.11149
$933$	1.85741	0.0608088
$934$	−51.7246	−1.69248
$935$	−36.6494	−1.19856
$936$	−55.9293	−1.82811
$937$	−3.69129	−0.120589	−0.0602946	−	0.998181i	$-0.519204\pi$
$937$	−3.69129	−0.120589	−0.0602946	+	0.998181i	$0.519204\pi$
$938$	−13.5819	−0.443464
$939$	−66.4813	−2.16954
$940$	−22.5868	−0.736699
$941$	12.5120	0.407880	0.203940	−	0.978983i	$-0.434625\pi$
$941$	12.5120	0.407880	0.203940	+	0.978983i	$0.434625\pi$
$942$	−9.46377	−0.308346
$943$	−39.2471	−1.27806
$944$	123.177	4.00907
$945$	11.5017	0.374152
$946$	59.2877	1.92761
$947$	29.1174	0.946189	0.473094	−	0.881012i	$-0.343137\pi$
$947$	29.1174	0.946189	0.473094	+	0.881012i	$0.343137\pi$
$948$	196.406	6.37896
$949$	−31.5404	−1.02384
$950$	16.5584	0.537224
$951$	20.0258	0.649380
$952$	107.390	3.48053
$953$	−21.5485	−0.698026	−0.349013	−	0.937118i	$-0.613483\pi$
$953$	−21.5485	−0.698026	−0.349013	+	0.937118i	$0.613483\pi$
$954$	0.694788	0.0224946
$955$	−60.0347	−1.94268
$956$	14.6254	0.473020
$957$	34.7188	1.12230
$958$	−17.2308	−0.556703
$959$	−26.2464	−0.847540
$960$	117.819	3.80261
$961$	−14.4649	−0.466609
$962$	51.2716	1.65306
$963$	9.98363	0.321718
$964$	93.2848	3.00450
$965$	−49.8506	−1.60475
$966$	−50.6079	−1.62828
$967$	7.88364	0.253521	0.126760	−	0.991933i	$-0.459542\pi$
$967$	7.88364	0.253521	0.126760	+	0.991933i	$0.459542\pi$
$968$	55.6653	1.78915
$969$	92.2591	2.96379
$970$	103.957	3.33786
$971$	32.4079	1.04002	0.520009	−	0.854161i	$-0.325929\pi$
$971$	32.4079	1.04002	0.520009	+	0.854161i	$0.325929\pi$
$972$	86.6098	2.77801
$973$	22.8514	0.732581
$974$	20.0991	0.644017
$975$	−7.85189	−0.251462
$976$	7.40179	0.236925
$977$	−52.0985	−1.66678	−0.833389	−	0.552687i	$-0.813602\pi$
$977$	−52.0985	−1.66678	−0.833389	+	0.552687i	$0.813602\pi$
$978$	49.6382	1.58725
$979$	25.9199	0.828405
$980$	50.1399	1.60166
$981$	23.0349	0.735447
$982$	77.9795	2.48842
$983$	−21.6082	−0.689196	−0.344598	−	0.938750i	$-0.611985\pi$
$983$	−21.6082	−0.689196	−0.344598	+	0.938750i	$0.611985\pi$
$984$	−155.248	−4.94914
$985$	60.0658	1.91385
$986$	136.898	4.35972
$987$	6.75676	0.215070
$988$	−114.372	−3.63867
$989$	−49.5041	−1.57414
$990$	25.4789	0.809772
$991$	−52.1960	−1.65806	−0.829030	−	0.559205i	$-0.811107\pi$
$991$	−52.1960	−1.65806	−0.829030	+	0.559205i	$0.811107\pi$
$992$	−72.9373	−2.31576
$993$	30.3963	0.964598
$994$	52.4772	1.66448
$995$	20.8579	0.661241
$996$	−176.114	−5.58038
$997$	36.9553	1.17038	0.585192	−	0.810895i	$-0.301019\pi$
$997$	36.9553	1.17038	0.585192	+	0.810895i	$0.301019\pi$
$998$	−112.703	−3.56755
$999$	−14.1979	−0.449201

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6029.2.a.a.1.4	✓	234

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6029.2.a.a.1.4	✓	234	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:	\( N \)	\(=\)	\( 6029 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6029.a (trivial)

\(f(q)\)	\(=\)	\(q-2.69522 q^{2} -2.18729 q^{3} +5.26421 q^{4} -2.45102 q^{5} +5.89522 q^{6} -1.76465 q^{7} -8.79776 q^{8} +1.78423 q^{9} +O(q^{10})\)	\(q-2.69522 q^{2} -2.18729 q^{3} +5.26421 q^{4} -2.45102 q^{5} +5.89522 q^{6} -1.76465 q^{7} -8.79776 q^{8} +1.78423 q^{9} +6.60605 q^{10} +2.16166 q^{11} -11.5143 q^{12} +3.56301 q^{13} +4.75613 q^{14} +5.36110 q^{15} +13.1835 q^{16} +6.91723 q^{17} -4.80889 q^{18} -6.09777 q^{19} -12.9027 q^{20} +3.85980 q^{21} -5.82615 q^{22} +4.86473 q^{23} +19.2432 q^{24} +1.00752 q^{25} -9.60308 q^{26} +2.65924 q^{27} -9.28950 q^{28} -7.34296 q^{29} -14.4493 q^{30} +4.06634 q^{31} -17.9368 q^{32} -4.72818 q^{33} -18.6434 q^{34} +4.32520 q^{35} +9.39256 q^{36} -5.33908 q^{37} +16.4348 q^{38} -7.79332 q^{39} +21.5635 q^{40} -8.06769 q^{41} -10.4030 q^{42} -10.1761 q^{43} +11.3794 q^{44} -4.37319 q^{45} -13.1115 q^{46} +1.75055 q^{47} -28.8361 q^{48} -3.88600 q^{49} -2.71548 q^{50} -15.1300 q^{51} +18.7564 q^{52} -0.144480 q^{53} -7.16723 q^{54} -5.29828 q^{55} +15.5250 q^{56} +13.3376 q^{57} +19.7909 q^{58} +9.34328 q^{59} +28.2219 q^{60} +0.561444 q^{61} -10.9597 q^{62} -3.14855 q^{63} +21.9768 q^{64} -8.73301 q^{65} +12.7435 q^{66} -2.85566 q^{67} +36.4137 q^{68} -10.6406 q^{69} -11.6574 q^{70} +11.0336 q^{71} -15.6972 q^{72} -8.85218 q^{73} +14.3900 q^{74} -2.20373 q^{75} -32.0999 q^{76} -3.81458 q^{77} +21.0047 q^{78} -17.0575 q^{79} -32.3130 q^{80} -11.1692 q^{81} +21.7442 q^{82} +15.2952 q^{83} +20.3188 q^{84} -16.9543 q^{85} +27.4269 q^{86} +16.0612 q^{87} -19.0178 q^{88} +11.9907 q^{89} +11.7867 q^{90} -6.28747 q^{91} +25.6090 q^{92} -8.89426 q^{93} -4.71811 q^{94} +14.9458 q^{95} +39.2330 q^{96} +15.7367 q^{97} +10.4736 q^{98} +3.85691 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 234 q - 10 q^{2} - 43 q^{3} + 202 q^{4} - 24 q^{5} - 40 q^{6} - 61 q^{7} - 27 q^{8} + 203 q^{9}+O(q^{10}) \) 234 * q - 10 * q^2 - 43 * q^3 + 202 * q^4 - 24 * q^5 - 40 * q^6 - 61 * q^7 - 27 * q^8 + 203 * q^9	\( 234 q - 10 q^{2} - 43 q^{3} + 202 q^{4} - 24 q^{5} - 40 q^{6} - 61 q^{7} - 27 q^{8} + 203 q^{9} - 89 q^{10} - 55 q^{11} - 75 q^{12} - 49 q^{13} - 42 q^{14} - 43 q^{15} + 142 q^{16} - 40 q^{17} - 30 q^{18} - 235 q^{19} - 62 q^{20} - 62 q^{21} - 63 q^{22} - 30 q^{23} - 108 q^{24} + 170 q^{25} - 44 q^{26} - 160 q^{27} - 147 q^{28} - 76 q^{29} - 15 q^{30} - 175 q^{31} - 49 q^{32} - 43 q^{33} - 104 q^{34} - 87 q^{35} + 124 q^{36} - 77 q^{37} - 18 q^{38} - 104 q^{39} - 247 q^{40} - 60 q^{41} - 6 q^{42} - 201 q^{43} - 89 q^{44} - 102 q^{45} - 128 q^{46} - 27 q^{47} - 130 q^{48} + 123 q^{49} - 33 q^{50} - 220 q^{51} - 125 q^{52} - 34 q^{53} - 126 q^{54} - 176 q^{55} - 125 q^{56} - 17 q^{57} - 46 q^{58} - 172 q^{59} - 61 q^{60} - 243 q^{61} - 37 q^{62} - 137 q^{63} + 39 q^{64} - 31 q^{65} - 142 q^{66} - 132 q^{67} - 106 q^{68} - 115 q^{69} - 60 q^{70} - 68 q^{71} - 66 q^{72} - 109 q^{73} - 74 q^{74} - 256 q^{75} - 412 q^{76} - 32 q^{77} - 38 q^{78} - 297 q^{79} - 111 q^{80} + 142 q^{81} - 94 q^{82} - 100 q^{83} - 134 q^{84} - 90 q^{85} + q^{86} - 103 q^{87} - 143 q^{88} - 77 q^{89} - 181 q^{90} - 418 q^{91} - 19 q^{92} + 5 q^{93} - 231 q^{94} - 92 q^{95} - 189 q^{96} - 141 q^{97} - 25 q^{98} - 244 q^{99}+O(q^{100}) \) 234 * q - 10 * q^2 - 43 * q^3 + 202 * q^4 - 24 * q^5 - 40 * q^6 - 61 * q^7 - 27 * q^8 + 203 * q^9 - 89 * q^10 - 55 * q^11 - 75 * q^12 - 49 * q^13 - 42 * q^14 - 43 * q^15 + 142 * q^16 - 40 * q^17 - 30 * q^18 - 235 * q^19 - 62 * q^20 - 62 * q^21 - 63 * q^22 - 30 * q^23 - 108 * q^24 + 170 * q^25 - 44 * q^26 - 160 * q^27 - 147 * q^28 - 76 * q^29 - 15 * q^30 - 175 * q^31 - 49 * q^32 - 43 * q^33 - 104 * q^34 - 87 * q^35 + 124 * q^36 - 77 * q^37 - 18 * q^38 - 104 * q^39 - 247 * q^40 - 60 * q^41 - 6 * q^42 - 201 * q^43 - 89 * q^44 - 102 * q^45 - 128 * q^46 - 27 * q^47 - 130 * q^48 + 123 * q^49 - 33 * q^50 - 220 * q^51 - 125 * q^52 - 34 * q^53 - 126 * q^54 - 176 * q^55 - 125 * q^56 - 17 * q^57 - 46 * q^58 - 172 * q^59 - 61 * q^60 - 243 * q^61 - 37 * q^62 - 137 * q^63 + 39 * q^64 - 31 * q^65 - 142 * q^66 - 132 * q^67 - 106 * q^68 - 115 * q^69 - 60 * q^70 - 68 * q^71 - 66 * q^72 - 109 * q^73 - 74 * q^74 - 256 * q^75 - 412 * q^76 - 32 * q^77 - 38 * q^78 - 297 * q^79 - 111 * q^80 + 142 * q^81 - 94 * q^82 - 100 * q^83 - 134 * q^84 - 90 * q^85 + q^86 - 103 * q^87 - 143 * q^88 - 77 * q^89 - 181 * q^90 - 418 * q^91 - 19 * q^92 + 5 * q^93 - 231 * q^94 - 92 * q^95 - 189 * q^96 - 141 * q^97 - 25 * q^98 - 244 * q^99

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