LMFDB - Embedded newform 6007.2.a.b.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6007,2,Mod(1,6007)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6007, 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("6007.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6007 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6007.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:	$47.9661364942$
Analytic rank:	$1$
Dimension:	$237$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Character	$\chi$	$=$	6007.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.78154 q^{2} +3.16840 q^{3} +5.73694 q^{4} -2.96782 q^{5} -8.81302 q^{6} +0.536102 q^{7} -10.3944 q^{8} +7.03875 q^{9} +O(q^{10})$	\(q-2.78154 q^{2} +3.16840 q^{3} +5.73694 q^{4} -2.96782 q^{5} -8.81302 q^{6} +0.536102 q^{7} -10.3944 q^{8} +7.03875 q^{9} +8.25511 q^{10} +2.61443 q^{11} +18.1769 q^{12} +1.94305 q^{13} -1.49119 q^{14} -9.40325 q^{15} +17.4386 q^{16} -6.57866 q^{17} -19.5785 q^{18} -2.47654 q^{19} -17.0262 q^{20} +1.69859 q^{21} -7.27214 q^{22} -8.23513 q^{23} -32.9337 q^{24} +3.80798 q^{25} -5.40467 q^{26} +12.7964 q^{27} +3.07559 q^{28} -6.60111 q^{29} +26.1555 q^{30} +9.62497 q^{31} -27.7173 q^{32} +8.28356 q^{33} +18.2988 q^{34} -1.59106 q^{35} +40.3809 q^{36} +5.71274 q^{37} +6.88859 q^{38} +6.15637 q^{39} +30.8489 q^{40} +2.22151 q^{41} -4.72468 q^{42} -6.38635 q^{43} +14.9988 q^{44} -20.8898 q^{45} +22.9063 q^{46} -7.50064 q^{47} +55.2525 q^{48} -6.71259 q^{49} -10.5920 q^{50} -20.8438 q^{51} +11.1472 q^{52} +10.8177 q^{53} -35.5936 q^{54} -7.75918 q^{55} -5.57248 q^{56} -7.84667 q^{57} +18.3612 q^{58} +11.5378 q^{59} -53.9459 q^{60} -7.86776 q^{61} -26.7722 q^{62} +3.77349 q^{63} +42.2194 q^{64} -5.76664 q^{65} -23.0410 q^{66} -3.51756 q^{67} -37.7414 q^{68} -26.0922 q^{69} +4.42558 q^{70} +9.20158 q^{71} -73.1639 q^{72} -6.74824 q^{73} -15.8902 q^{74} +12.0652 q^{75} -14.2078 q^{76} +1.40160 q^{77} -17.1242 q^{78} -10.1332 q^{79} -51.7548 q^{80} +19.4278 q^{81} -6.17921 q^{82} -6.81209 q^{83} +9.74469 q^{84} +19.5243 q^{85} +17.7639 q^{86} -20.9149 q^{87} -27.1756 q^{88} -11.8614 q^{89} +58.1057 q^{90} +1.04168 q^{91} -47.2445 q^{92} +30.4958 q^{93} +20.8633 q^{94} +7.34994 q^{95} -87.8194 q^{96} -11.1727 q^{97} +18.6713 q^{98} +18.4023 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 237 q - 26 q^{2} - 24 q^{3} + 226 q^{4} - 67 q^{5} - 30 q^{6} - 37 q^{7} - 75 q^{8} + 189 q^{9}+O(q^{10}) $ 237 * q - 26 * q^2 - 24 * q^3 + 226 * q^4 - 67 * q^5 - 30 * q^6 - 37 * q^7 - 75 * q^8 + 189 * q^9	\( 237 q - 26 q^{2} - 24 q^{3} + 226 q^{4} - 67 q^{5} - 30 q^{6} - 37 q^{7} - 75 q^{8} + 189 q^{9} - 39 q^{10} - 38 q^{11} - 67 q^{12} - 52 q^{13} - 54 q^{14} - 24 q^{15} + 208 q^{16} - 255 q^{17} - 71 q^{18} - 24 q^{19} - 154 q^{20} - 60 q^{21} - 39 q^{22} - 118 q^{23} - 85 q^{24} + 170 q^{25} - 61 q^{26} - 87 q^{27} - 99 q^{28} - 87 q^{29} - 30 q^{30} - 28 q^{31} - 156 q^{32} - 173 q^{33} - 4 q^{34} - 113 q^{35} + 152 q^{36} - 49 q^{37} - 145 q^{38} - 49 q^{39} - 91 q^{40} - 197 q^{41} - 61 q^{42} - 63 q^{43} - 106 q^{44} - 181 q^{45} - 2 q^{46} - 119 q^{47} - 142 q^{48} + 150 q^{49} - 89 q^{50} - 40 q^{51} - 97 q^{52} - 190 q^{53} - 97 q^{54} - 55 q^{55} - 154 q^{56} - 202 q^{57} - 27 q^{58} - 86 q^{59} - 48 q^{60} - 96 q^{61} - 239 q^{62} - 149 q^{63} + 183 q^{64} - 259 q^{65} - 72 q^{66} - 28 q^{67} - 482 q^{68} - 83 q^{69} + 20 q^{70} - 63 q^{71} - 193 q^{72} - 206 q^{73} - 132 q^{74} - 89 q^{75} - 11 q^{76} - 179 q^{77} - 58 q^{78} - 32 q^{79} - 320 q^{80} + 57 q^{81} - 77 q^{82} - 245 q^{83} - 133 q^{84} + q^{85} - 39 q^{86} - 179 q^{87} - 104 q^{88} - 227 q^{89} - 146 q^{90} - 36 q^{91} - 315 q^{92} - 87 q^{93} - 48 q^{94} - 111 q^{95} - 134 q^{96} - 221 q^{97} - 161 q^{98} - 68 q^{99}+O(q^{100}) \) 237 * q - 26 * q^2 - 24 * q^3 + 226 * q^4 - 67 * q^5 - 30 * q^6 - 37 * q^7 - 75 * q^8 + 189 * q^9 - 39 * q^10 - 38 * q^11 - 67 * q^12 - 52 * q^13 - 54 * q^14 - 24 * q^15 + 208 * q^16 - 255 * q^17 - 71 * q^18 - 24 * q^19 - 154 * q^20 - 60 * q^21 - 39 * q^22 - 118 * q^23 - 85 * q^24 + 170 * q^25 - 61 * q^26 - 87 * q^27 - 99 * q^28 - 87 * q^29 - 30 * q^30 - 28 * q^31 - 156 * q^32 - 173 * q^33 - 4 * q^34 - 113 * q^35 + 152 * q^36 - 49 * q^37 - 145 * q^38 - 49 * q^39 - 91 * q^40 - 197 * q^41 - 61 * q^42 - 63 * q^43 - 106 * q^44 - 181 * q^45 - 2 * q^46 - 119 * q^47 - 142 * q^48 + 150 * q^49 - 89 * q^50 - 40 * q^51 - 97 * q^52 - 190 * q^53 - 97 * q^54 - 55 * q^55 - 154 * q^56 - 202 * q^57 - 27 * q^58 - 86 * q^59 - 48 * q^60 - 96 * q^61 - 239 * q^62 - 149 * q^63 + 183 * q^64 - 259 * q^65 - 72 * q^66 - 28 * q^67 - 482 * q^68 - 83 * q^69 + 20 * q^70 - 63 * q^71 - 193 * q^72 - 206 * q^73 - 132 * q^74 - 89 * q^75 - 11 * q^76 - 179 * q^77 - 58 * q^78 - 32 * q^79 - 320 * q^80 + 57 * q^81 - 77 * q^82 - 245 * q^83 - 133 * q^84 + q^85 - 39 * q^86 - 179 * q^87 - 104 * q^88 - 227 * q^89 - 146 * q^90 - 36 * q^91 - 315 * q^92 - 87 * q^93 - 48 * q^94 - 111 * q^95 - 134 * q^96 - 221 * q^97 - 161 * q^98 - 68 * 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 $

$2$	−2.78154	−1.96684	−0.983422	−	0.181334i	$-0.941958\pi$
$2$	−2.78154	−1.96684	−0.983422	+	0.181334i	$0.941958\pi$
$3$	3.16840	1.82928	0.914638	−	0.404274i	$-0.132476\pi$
$3$	3.16840	1.82928	0.914638	+	0.404274i	$0.132476\pi$
$4$	5.73694	2.86847
$5$	−2.96782	−1.32725	−0.663626	−	0.748065i	$-0.730983\pi$
$5$	−2.96782	−1.32725	−0.663626	+	0.748065i	$0.730983\pi$
$6$	−8.81302	−3.59790
$7$	0.536102	0.202628	0.101314	−	0.994855i	$-0.467695\pi$
$7$	0.536102	0.202628	0.101314	+	0.994855i	$0.467695\pi$
$8$	−10.3944	−3.67499
$9$	7.03875	2.34625
$10$	8.25511	2.61050
$11$	2.61443	0.788281	0.394140	−	0.919050i	$-0.371042\pi$
$11$	2.61443	0.788281	0.394140	+	0.919050i	$0.371042\pi$
$12$	18.1769	5.24723
$13$	1.94305	0.538906	0.269453	−	0.963014i	$-0.413157\pi$
$13$	1.94305	0.538906	0.269453	+	0.963014i	$0.413157\pi$
$14$	−1.49119	−0.398537
$15$	−9.40325	−2.42791
$16$	17.4386	4.35966
$17$	−6.57866	−1.59556	−0.797780	−	0.602949i	$-0.793992\pi$
$17$	−6.57866	−1.59556	−0.797780	+	0.602949i	$0.793992\pi$
$18$	−19.5785	−4.61471
$19$	−2.47654	−0.568158	−0.284079	−	0.958801i	$-0.591688\pi$
$19$	−2.47654	−0.568158	−0.284079	+	0.958801i	$0.591688\pi$
$20$	−17.0262	−3.80718
$21$	1.69859	0.370662
$22$	−7.27214	−1.55042
$23$	−8.23513	−1.71714	−0.858572	−	0.512694i	$-0.828648\pi$
$23$	−8.23513	−1.71714	−0.858572	+	0.512694i	$0.828648\pi$
$24$	−32.9337	−6.72257
$25$	3.80798	0.761597
$26$	−5.40467	−1.05994
$27$	12.7964	2.46266
$28$	3.07559	0.581231
$29$	−6.60111	−1.22579	−0.612897	−	0.790163i	$-0.709996\pi$
$29$	−6.60111	−1.22579	−0.612897	+	0.790163i	$0.709996\pi$
$30$	26.1555	4.77532
$31$	9.62497	1.72870	0.864348	−	0.502894i	$-0.167731\pi$
$31$	9.62497	1.72870	0.864348	+	0.502894i	$0.167731\pi$
$32$	−27.7173	−4.89977
$33$	8.28356	1.44198
$34$	18.2988	3.13821
$35$	−1.59106	−0.268938
$36$	40.3809	6.73015
$37$	5.71274	0.939168	0.469584	−	0.882888i	$-0.344404\pi$
$37$	5.71274	0.939168	0.469584	+	0.882888i	$0.344404\pi$
$38$	6.88859	1.11748
$39$	6.15637	0.985808
$40$	30.8489	4.87764
$41$	2.22151	0.346942	0.173471	−	0.984839i	$-0.444502\pi$
$41$	2.22151	0.346942	0.173471	+	0.984839i	$0.444502\pi$
$42$	−4.72468	−0.729033
$43$	−6.38635	−0.973909	−0.486954	−	0.873427i	$-0.661892\pi$
$43$	−6.38635	−0.973909	−0.486954	+	0.873427i	$0.661892\pi$
$44$	14.9988	2.26116
$45$	−20.8898	−3.11406
$46$	22.9063	3.37735
$47$	−7.50064	−1.09408	−0.547040	−	0.837106i	$-0.684245\pi$
$47$	−7.50064	−1.09408	−0.547040	+	0.837106i	$0.684245\pi$
$48$	55.2525	7.97502
$49$	−6.71259	−0.958942
$50$	−10.5920	−1.49794
$51$	−20.8438	−2.91872
$52$	11.1472	1.54584
$53$	10.8177	1.48593	0.742966	−	0.669329i	$-0.233418\pi$
$53$	10.8177	1.48593	0.742966	+	0.669329i	$0.233418\pi$
$54$	−35.5936	−4.84367
$55$	−7.75918	−1.04625
$56$	−5.57248	−0.744654
$57$	−7.84667	−1.03932
$58$	18.3612	2.41095
$59$	11.5378	1.50209	0.751047	−	0.660248i	$-0.229549\pi$
$59$	11.5378	1.50209	0.751047	+	0.660248i	$0.229549\pi$
$60$	−53.9459	−6.96439
$61$	−7.86776	−1.00736	−0.503682	−	0.863889i	$-0.668021\pi$
$61$	−7.86776	−1.00736	−0.503682	+	0.863889i	$0.668021\pi$
$62$	−26.7722	−3.40007
$63$	3.77349	0.475415
$64$	42.2194	5.27742
$65$	−5.76664	−0.715264
$66$	−23.0410	−2.83615
$67$	−3.51756	−0.429739	−0.214869	−	0.976643i	$-0.568933\pi$
$67$	−3.51756	−0.429739	−0.214869	+	0.976643i	$0.568933\pi$
$68$	−37.7414	−4.57682
$69$	−26.0922	−3.14113
$70$	4.42558	0.528958
$71$	9.20158	1.09203	0.546013	−	0.837777i	$-0.316145\pi$
$71$	9.20158	1.09203	0.546013	+	0.837777i	$0.316145\pi$
$72$	−73.1639	−8.62245
$73$	−6.74824	−0.789822	−0.394911	−	0.918719i	$-0.629224\pi$
$73$	−6.74824	−0.789822	−0.394911	+	0.918719i	$0.629224\pi$
$74$	−15.8902	−1.84720
$75$	12.0652	1.39317
$76$	−14.2078	−1.62974
$77$	1.40160	0.159727
$78$	−17.1242	−1.93893
$79$	−10.1332	−1.14007	−0.570037	−	0.821619i	$-0.693071\pi$
$79$	−10.1332	−1.14007	−0.570037	+	0.821619i	$0.693071\pi$
$80$	−51.7548	−5.78636
$81$	19.4278	2.15864
$82$	−6.17921	−0.682380
$83$	−6.81209	−0.747724	−0.373862	−	0.927484i	$-0.621967\pi$
$83$	−6.81209	−0.747724	−0.373862	+	0.927484i	$0.621967\pi$
$84$	9.74469	1.06323
$85$	19.5243	2.11771
$86$	17.7639	1.91553
$87$	−20.9149	−2.24232
$88$	−27.1756	−2.89692
$89$	−11.8614	−1.25731	−0.628653	−	0.777686i	$-0.716393\pi$
$89$	−11.8614	−1.25731	−0.628653	+	0.777686i	$0.716393\pi$
$90$	58.1057	6.12488
$91$	1.04168	0.109197
$92$	−47.2445	−4.92558
$93$	30.4958	3.16226
$94$	20.8633	2.15188
$95$	7.34994	0.754088
$96$	−87.8194	−8.96303
$97$	−11.1727	−1.13442	−0.567210	−	0.823573i	$-0.691977\pi$
$97$	−11.1727	−1.13442	−0.567210	+	0.823573i	$0.691977\pi$
$98$	18.6713	1.88609
$99$	18.4023	1.84950
$100$	21.8462	2.18462
$101$	9.85969	0.981076	0.490538	−	0.871420i	$-0.336800\pi$
$101$	9.85969	0.981076	0.490538	+	0.871420i	$0.336800\pi$
$102$	57.9778	5.74066
$103$	−16.5719	−1.63288	−0.816440	−	0.577430i	$-0.804056\pi$
$103$	−16.5719	−1.63288	−0.816440	+	0.577430i	$0.804056\pi$
$104$	−20.1970	−1.98047
$105$	−5.04110	−0.491961
$106$	−30.0900	−2.92259
$107$	−8.76401	−0.847249	−0.423625	−	0.905838i	$-0.639242\pi$
$107$	−8.76401	−0.847249	−0.423625	+	0.905838i	$0.639242\pi$
$108$	73.4121	7.06408
$109$	0.343904	0.0329401	0.0164700	−	0.999864i	$-0.494757\pi$
$109$	0.343904	0.0329401	0.0164700	+	0.999864i	$0.494757\pi$
$110$	21.5824	2.05780
$111$	18.1002	1.71800
$112$	9.34889	0.883387
$113$	4.47816	0.421270	0.210635	−	0.977565i	$-0.432447\pi$
$113$	4.47816	0.421270	0.210635	+	0.977565i	$0.432447\pi$
$114$	21.8258	2.04417
$115$	24.4404	2.27908
$116$	−37.8702	−3.51616
$117$	13.6767	1.26441
$118$	−32.0928	−2.95438
$119$	−3.52683	−0.323304
$120$	97.7416	8.92254
$121$	−4.16474	−0.378613
$122$	21.8844	1.98132
$123$	7.03863	0.634652
$124$	55.2179	4.95872
$125$	3.53769	0.316421
$126$	−10.4961	−0.935067
$127$	5.67736	0.503784	0.251892	−	0.967755i	$-0.418947\pi$
$127$	5.67736	0.503784	0.251892	+	0.967755i	$0.418947\pi$
$128$	−62.0002	−5.48009
$129$	−20.2345	−1.78155
$130$	16.0401	1.40681
$131$	7.62093	0.665844	0.332922	−	0.942954i	$-0.391965\pi$
$131$	7.62093	0.665844	0.332922	+	0.942954i	$0.391965\pi$
$132$	47.5223	4.13629
$133$	−1.32768	−0.115124
$134$	9.78422	0.845228
$135$	−37.9774	−3.26857
$136$	68.3815	5.86366
$137$	−8.02473	−0.685599	−0.342800	−	0.939409i	$-0.611375\pi$
$137$	−8.02473	−0.685599	−0.342800	+	0.939409i	$0.611375\pi$
$138$	72.5763	6.17811
$139$	−3.53943	−0.300211	−0.150105	−	0.988670i	$-0.547961\pi$
$139$	−3.53943	−0.300211	−0.150105	+	0.988670i	$0.547961\pi$
$140$	−9.12780	−0.771440
$141$	−23.7650	−2.00137
$142$	−25.5945	−2.14784
$143$	5.07998	0.424809
$144$	122.746	10.2288
$145$	19.5909	1.62694
$146$	18.7705	1.55346
$147$	−21.2682	−1.75417
$148$	32.7736	2.69398
$149$	−1.27303	−0.104290	−0.0521452	−	0.998640i	$-0.516606\pi$
$149$	−1.27303	−0.104290	−0.0521452	+	0.998640i	$0.516606\pi$
$150$	−33.5598	−2.74015
$151$	−16.3185	−1.32798	−0.663990	−	0.747742i	$-0.731138\pi$
$151$	−16.3185	−1.32798	−0.663990	+	0.747742i	$0.731138\pi$
$152$	25.7423	2.08797
$153$	−46.3055	−3.74358
$154$	−3.89861	−0.314159
$155$	−28.5652	−2.29441
$156$	35.3187	2.82776
$157$	7.18561	0.573474	0.286737	−	0.958009i	$-0.407429\pi$
$157$	7.18561	0.573474	0.286737	+	0.958009i	$0.407429\pi$
$158$	28.1859	2.24235
$159$	34.2749	2.71818
$160$	82.2601	6.50323
$161$	−4.41487	−0.347941
$162$	−54.0390	−4.24571
$163$	−11.7009	−0.916486	−0.458243	−	0.888827i	$-0.651521\pi$
$163$	−11.7009	−0.916486	−0.458243	+	0.888827i	$0.651521\pi$
$164$	12.7447	0.995193
$165$	−24.5842	−1.91387
$166$	18.9481	1.47065
$167$	3.44211	0.266359	0.133179	−	0.991092i	$-0.457481\pi$
$167$	3.44211	0.266359	0.133179	+	0.991092i	$0.457481\pi$
$168$	−17.6558	−1.36218
$169$	−9.22454	−0.709580
$170$	−54.3076	−4.16520
$171$	−17.4318	−1.33304
$172$	−36.6381	−2.79363
$173$	−9.77956	−0.743526	−0.371763	−	0.928328i	$-0.621247\pi$
$173$	−9.77956	−0.743526	−0.371763	+	0.928328i	$0.621247\pi$
$174$	58.1757	4.41029
$175$	2.04147	0.154321
$176$	45.5921	3.43663
$177$	36.5564	2.74775
$178$	32.9929	2.47292
$179$	−8.06200	−0.602582	−0.301291	−	0.953532i	$-0.597418\pi$
$179$	−8.06200	−0.602582	−0.301291	+	0.953532i	$0.597418\pi$
$180$	−119.843	−8.93261
$181$	−23.5519	−1.75060	−0.875301	−	0.483579i	$-0.839337\pi$
$181$	−23.5519	−1.75060	−0.875301	+	0.483579i	$0.839337\pi$
$182$	−2.89746	−0.214774
$183$	−24.9282	−1.84274
$184$	85.5996	6.31048
$185$	−16.9544	−1.24651
$186$	−84.8250	−6.21967
$187$	−17.1995	−1.25775
$188$	−43.0307	−3.13834
$189$	6.86016	0.499003
$190$	−20.4441	−1.48317
$191$	12.9501	0.937036	0.468518	−	0.883454i	$-0.344788\pi$
$191$	12.9501	0.937036	0.468518	+	0.883454i	$0.344788\pi$
$192$	133.768	9.65386
$193$	11.5773	0.833355	0.416678	−	0.909054i	$-0.363194\pi$
$193$	11.5773	0.833355	0.416678	+	0.909054i	$0.363194\pi$
$194$	31.0774	2.23123
$195$	−18.2710	−1.30842
$196$	−38.5098	−2.75070
$197$	2.57532	0.183484	0.0917419	−	0.995783i	$-0.470757\pi$
$197$	2.57532	0.183484	0.0917419	+	0.995783i	$0.470757\pi$
$198$	−51.1868	−3.63768
$199$	18.7437	1.32870	0.664352	−	0.747420i	$-0.268708\pi$
$199$	18.7437	1.32870	0.664352	+	0.747420i	$0.268708\pi$
$200$	−39.5819	−2.79886
$201$	−11.1450	−0.786110
$202$	−27.4251	−1.92962
$203$	−3.53887	−0.248380
$204$	−119.580	−8.37226
$205$	−6.59306	−0.460479
$206$	46.0954	3.21162
$207$	−57.9650	−4.02885
$208$	33.8842	2.34945
$209$	−6.47475	−0.447868
$210$	14.0220	0.967611
$211$	−13.4829	−0.928200	−0.464100	−	0.885783i	$-0.653622\pi$
$211$	−13.4829	−0.928200	−0.464100	+	0.885783i	$0.653622\pi$
$212$	62.0608	4.26235
$213$	29.1543	1.99762
$214$	24.3774	1.66641
$215$	18.9536	1.29262
$216$	−133.011	−9.05026
$217$	5.15997	0.350281
$218$	−0.956582	−0.0647879
$219$	−21.3811	−1.44480
$220$	−44.5140	−3.00113
$221$	−12.7827	−0.859857
$222$	−50.3464	−3.37903
$223$	2.31096	0.154753	0.0773767	−	0.997002i	$-0.475346\pi$
$223$	2.31096	0.154753	0.0773767	+	0.997002i	$0.475346\pi$
$224$	−14.8593	−0.992829
$225$	26.8035	1.78690
$226$	−12.4562	−0.828572
$227$	21.4593	1.42430	0.712151	−	0.702027i	$-0.247721\pi$
$227$	21.4593	1.42430	0.712151	+	0.702027i	$0.247721\pi$
$228$	−45.0159	−2.98125
$229$	−9.17690	−0.606427	−0.303213	−	0.952923i	$-0.598060\pi$
$229$	−9.17690	−0.606427	−0.303213	+	0.952923i	$0.598060\pi$
$230$	−67.9819	−4.48259
$231$	4.44084	0.292186
$232$	68.6148	4.50478
$233$	−19.7857	−1.29621	−0.648103	−	0.761553i	$-0.724437\pi$
$233$	−19.7857	−1.29621	−0.648103	+	0.761553i	$0.724437\pi$
$234$	−38.0422	−2.48689
$235$	22.2606	1.45212
$236$	66.1918	4.30872
$237$	−32.1060	−2.08551
$238$	9.81001	0.635889
$239$	13.8543	0.896157	0.448079	−	0.893994i	$-0.352108\pi$
$239$	13.8543	0.896157	0.448079	+	0.893994i	$0.352108\pi$
$240$	−163.980	−10.5849
$241$	16.7784	1.08079	0.540396	−	0.841411i	$-0.318274\pi$
$241$	16.7784	1.08079	0.540396	+	0.841411i	$0.318274\pi$
$242$	11.5844	0.744673
$243$	23.1658	1.48609
$244$	−45.1369	−2.88959
$245$	19.9218	1.27276
$246$	−19.5782	−1.24826
$247$	−4.81205	−0.306184
$248$	−100.046	−6.35294
$249$	−21.5834	−1.36779
$250$	−9.84022	−0.622350
$251$	−14.3341	−0.904759	−0.452380	−	0.891826i	$-0.649425\pi$
$251$	−14.3341	−0.904759	−0.452380	+	0.891826i	$0.649425\pi$
$252$	21.6483	1.36371
$253$	−21.5302	−1.35359
$254$	−15.7918	−0.990864
$255$	61.8608	3.87387
$256$	88.0169	5.50106
$257$	20.1487	1.25684	0.628421	−	0.777873i	$-0.283701\pi$
$257$	20.1487	1.25684	0.628421	+	0.777873i	$0.283701\pi$
$258$	56.2830	3.50403
$259$	3.06261	0.190301
$260$	−33.0829	−2.05171
$261$	−46.4635	−2.87602
$262$	−21.1979	−1.30961
$263$	−5.52192	−0.340496	−0.170248	−	0.985401i	$-0.554457\pi$
$263$	−5.52192	−0.340496	−0.170248	+	0.985401i	$0.554457\pi$
$264$	−86.1030	−5.29927
$265$	−32.1052	−1.97221
$266$	3.69299	0.226432
$267$	−37.5817	−2.29996
$268$	−20.1801	−1.23269
$269$	12.7851	0.779519	0.389760	−	0.920917i	$-0.372558\pi$
$269$	12.7851	0.779519	0.389760	+	0.920917i	$0.372558\pi$
$270$	105.635	6.42877
$271$	31.7248	1.92714	0.963572	−	0.267450i	$-0.0861812\pi$
$271$	31.7248	1.92714	0.963572	+	0.267450i	$0.0861812\pi$
$272$	−114.723	−6.95609
$273$	3.30044	0.199752
$274$	22.3211	1.34847
$275$	9.95572	0.600352
$276$	−149.689	−9.01024
$277$	23.7207	1.42524	0.712619	−	0.701551i	$-0.247509\pi$
$277$	23.7207	1.42524	0.712619	+	0.701551i	$0.247509\pi$
$278$	9.84506	0.590468
$279$	67.7478	4.05595
$280$	16.5382	0.988344
$281$	22.3750	1.33478	0.667392	−	0.744707i	$-0.267411\pi$
$281$	22.3750	1.33478	0.667392	+	0.744707i	$0.267411\pi$
$282$	66.1032	3.93639
$283$	−21.5715	−1.28229	−0.641145	−	0.767420i	$-0.721540\pi$
$283$	−21.5715	−1.28229	−0.641145	+	0.767420i	$0.721540\pi$
$284$	52.7889	3.13245
$285$	23.2876	1.37944
$286$	−14.1302	−0.835533
$287$	1.19096	0.0703000
$288$	−195.095	−11.4961
$289$	26.2788	1.54581
$290$	−54.4929	−3.19993
$291$	−35.3997	−2.07517
$292$	−38.7143	−2.26558
$293$	−24.3985	−1.42537	−0.712687	−	0.701482i	$-0.752522\pi$
$293$	−24.3985	−1.42537	−0.712687	+	0.701482i	$0.752522\pi$
$294$	59.1582	3.45018
$295$	−34.2422	−1.99366
$296$	−59.3807	−3.45143
$297$	33.4553	1.94127
$298$	3.54097	0.205123
$299$	−16.0013	−0.925379
$300$	69.2174	3.99627
$301$	−3.42373	−0.197341
$302$	45.3904	2.61193
$303$	31.2394	1.79466
$304$	−43.1875	−2.47697
$305$	23.3501	1.33702
$306$	128.801	7.36304
$307$	−12.5695	−0.717380	−0.358690	−	0.933457i	$-0.616776\pi$
$307$	−12.5695	−0.717380	−0.358690	+	0.933457i	$0.616776\pi$
$308$	8.04091	0.458174
$309$	−52.5065	−2.98699
$310$	79.4552	4.51275
$311$	0.858286	0.0486690	0.0243345	−	0.999704i	$-0.492253\pi$
$311$	0.858286	0.0486690	0.0243345	+	0.999704i	$0.492253\pi$
$312$	−63.9920	−3.62283
$313$	−1.73431	−0.0980292	−0.0490146	−	0.998798i	$-0.515608\pi$
$313$	−1.73431	−0.0980292	−0.0490146	+	0.998798i	$0.515608\pi$
$314$	−19.9870	−1.12793
$315$	−11.1991	−0.630995
$316$	−58.1336	−3.27027
$317$	−9.59137	−0.538705	−0.269352	−	0.963042i	$-0.586810\pi$
$317$	−9.59137	−0.538705	−0.269352	+	0.963042i	$0.586810\pi$
$318$	−95.3370	−5.34623
$319$	−17.2581	−0.966271
$320$	−125.300	−7.00447
$321$	−27.7679	−1.54985
$322$	12.2801	0.684344
$323$	16.2923	0.906529
$324$	111.456	6.19200
$325$	7.39912	0.410429
$326$	32.5465	1.80258
$327$	1.08963	0.0602565
$328$	−23.0914	−1.27501
$329$	−4.02111	−0.221691
$330$	68.3817	3.76429
$331$	−8.00461	−0.439973	−0.219987	−	0.975503i	$-0.570601\pi$
$331$	−8.00461	−0.439973	−0.219987	+	0.975503i	$0.570601\pi$
$332$	−39.0805	−2.14482
$333$	40.2105	2.20352
$334$	−9.57436	−0.523885
$335$	10.4395	0.570371
$336$	29.6210	1.61596
$337$	−25.4723	−1.38756	−0.693782	−	0.720185i	$-0.744057\pi$
$337$	−25.4723	−1.38756	−0.693782	+	0.720185i	$0.744057\pi$
$338$	25.6584	1.39563
$339$	14.1886	0.770619
$340$	112.010	6.07459
$341$	25.1638	1.36270
$342$	48.4871	2.62188
$343$	−7.35135	−0.396936
$344$	66.3825	3.57911
$345$	77.4370	4.16907
$346$	27.2022	1.46240
$347$	−0.696267	−0.0373776	−0.0186888	−	0.999825i	$-0.505949\pi$
$347$	−0.696267	−0.0373776	−0.0186888	+	0.999825i	$0.505949\pi$
$348$	−119.988	−6.43202
$349$	−20.7178	−1.10900	−0.554499	−	0.832184i	$-0.687090\pi$
$349$	−20.7178	−1.10900	−0.554499	+	0.832184i	$0.687090\pi$
$350$	−5.67842	−0.303524
$351$	24.8640	1.32714
$352$	−72.4650	−3.86240
$353$	−16.6328	−0.885273	−0.442636	−	0.896701i	$-0.645957\pi$
$353$	−16.6328	−0.885273	−0.442636	+	0.896701i	$0.645957\pi$
$354$	−101.683	−5.40438
$355$	−27.3087	−1.44939
$356$	−68.0482	−3.60655
$357$	−11.1744	−0.591413
$358$	22.4247	1.18518
$359$	31.4569	1.66023	0.830115	−	0.557592i	$-0.188274\pi$
$359$	31.4569	1.66023	0.830115	+	0.557592i	$0.188274\pi$
$360$	217.138	11.4442
$361$	−12.8667	−0.677197
$362$	65.5106	3.44316
$363$	−13.1956	−0.692588
$364$	5.97603	0.313229
$365$	20.0276	1.04829
$366$	69.3387	3.62439
$367$	9.08253	0.474104	0.237052	−	0.971497i	$-0.423819\pi$
$367$	9.08253	0.474104	0.237052	+	0.971497i	$0.423819\pi$
$368$	−143.609	−7.48616
$369$	15.6367	0.814012
$370$	47.1593	2.45169
$371$	5.79942	0.301091
$372$	174.952	9.07086
$373$	−15.1610	−0.785006	−0.392503	−	0.919751i	$-0.628391\pi$
$373$	−15.1610	−0.785006	−0.392503	+	0.919751i	$0.628391\pi$
$374$	47.8409	2.47379
$375$	11.2088	0.578821
$376$	77.9649	4.02073
$377$	−12.8263	−0.660588
$378$	−19.0818	−0.981461
$379$	−2.81141	−0.144412	−0.0722062	−	0.997390i	$-0.523004\pi$
$379$	−2.81141	−0.144412	−0.0722062	+	0.997390i	$0.523004\pi$
$380$	42.1662	2.16308
$381$	17.9881	0.921560
$382$	−36.0211	−1.84300
$383$	−1.12925	−0.0577022	−0.0288511	−	0.999584i	$-0.509185\pi$
$383$	−1.12925	−0.0577022	−0.0288511	+	0.999584i	$0.509185\pi$
$384$	−196.441	−10.0246
$385$	−4.15971	−0.211999
$386$	−32.2028	−1.63908
$387$	−44.9519	−2.28503
$388$	−64.0974	−3.25405
$389$	−12.6245	−0.640087	−0.320043	−	0.947403i	$-0.603698\pi$
$389$	−12.6245	−0.640087	−0.320043	+	0.947403i	$0.603698\pi$
$390$	50.8215	2.57345
$391$	54.1761	2.73980
$392$	69.7737	3.52410
$393$	24.1462	1.21801
$394$	−7.16334	−0.360884
$395$	30.0736	1.51316
$396$	105.573	5.30525
$397$	−14.7845	−0.742013	−0.371006	−	0.928630i	$-0.620987\pi$
$397$	−14.7845	−0.742013	−0.371006	+	0.928630i	$0.620987\pi$
$398$	−52.1362	−2.61335
$399$	−4.20662	−0.210594
$400$	66.4060	3.32030
$401$	−28.1853	−1.40751	−0.703754	−	0.710443i	$-0.748494\pi$
$401$	−28.1853	−1.40751	−0.703754	+	0.710443i	$0.748494\pi$
$402$	31.0003	1.54616
$403$	18.7018	0.931605
$404$	56.5645	2.81419
$405$	−57.6582	−2.86506
$406$	9.84349	0.488524
$407$	14.9356	0.740328
$408$	216.660	10.7263
$409$	5.94876	0.294147	0.147074	−	0.989126i	$-0.453015\pi$
$409$	5.94876	0.294147	0.147074	+	0.989126i	$0.453015\pi$
$410$	18.3388	0.905690
$411$	−25.4255	−1.25415
$412$	−95.0722	−4.68387
$413$	6.18544	0.304366
$414$	161.232	7.92411
$415$	20.2171	0.992417
$416$	−53.8562	−2.64052
$417$	−11.2143	−0.549168
$418$	18.0098	0.880886
$419$	17.8819	0.873586	0.436793	−	0.899562i	$-0.356114\pi$
$419$	17.8819	0.873586	0.436793	+	0.899562i	$0.356114\pi$
$420$	−28.9205	−1.41118
$421$	−13.4222	−0.654156	−0.327078	−	0.944997i	$-0.606064\pi$
$421$	−13.4222	−0.654156	−0.327078	+	0.944997i	$0.606064\pi$
$422$	37.5031	1.82562
$423$	−52.7951	−2.56699
$424$	−112.444	−5.46078
$425$	−25.0514	−1.21517
$426$	−81.0936	−3.92900
$427$	−4.21792	−0.204120
$428$	−50.2786	−2.43031
$429$	16.0954	0.777094
$430$	−52.7200	−2.54238
$431$	1.63574	0.0787906	0.0393953	−	0.999224i	$-0.487457\pi$
$431$	1.63574	0.0787906	0.0393953	+	0.999224i	$0.487457\pi$
$432$	223.151	10.7364
$433$	32.9034	1.58124	0.790618	−	0.612309i	$-0.209759\pi$
$433$	32.9034	1.58124	0.790618	+	0.612309i	$0.209759\pi$
$434$	−14.3526	−0.688949
$435$	62.0719	2.97612
$436$	1.97296	0.0944876
$437$	20.3946	0.975608
$438$	59.4723	2.84170
$439$	−28.9362	−1.38105	−0.690525	−	0.723309i	$-0.742620\pi$
$439$	−28.9362	−1.38105	−0.690525	+	0.723309i	$0.742620\pi$
$440$	80.6523	3.84495
$441$	−47.2483	−2.24992
$442$	35.5555	1.69120
$443$	27.0683	1.28605	0.643026	−	0.765844i	$-0.277679\pi$
$443$	27.0683	1.28605	0.643026	+	0.765844i	$0.277679\pi$
$444$	103.840	4.92803
$445$	35.2026	1.66876
$446$	−6.42802	−0.304375
$447$	−4.03346	−0.190776
$448$	22.6339	1.06935
$449$	20.0665	0.946995	0.473498	−	0.880795i	$-0.342991\pi$
$449$	20.0665	0.946995	0.473498	+	0.880795i	$0.342991\pi$
$450$	−74.5548	−3.51455
$451$	5.80799	0.273488
$452$	25.6910	1.20840
$453$	−51.7035	−2.42924
$454$	−59.6897	−2.80138
$455$	−3.09151	−0.144932
$456$	81.5618	3.81948
$457$	35.5258	1.66182	0.830912	−	0.556403i	$-0.187819\pi$
$457$	35.5258	1.66182	0.830912	+	0.556403i	$0.187819\pi$
$458$	25.5259	1.19275
$459$	−84.1830	−3.92932
$460$	140.213	6.53748
$461$	−2.01612	−0.0939001	−0.0469500	−	0.998897i	$-0.514950\pi$
$461$	−2.01612	−0.0939001	−0.0469500	+	0.998897i	$0.514950\pi$
$462$	−12.3523	−0.574683
$463$	4.21000	0.195655	0.0978277	−	0.995203i	$-0.468811\pi$
$463$	4.21000	0.195655	0.0978277	+	0.995203i	$0.468811\pi$
$464$	−115.114	−5.34404
$465$	−90.5061	−4.19712
$466$	55.0347	2.54943
$467$	−23.6872	−1.09611	−0.548055	−	0.836442i	$-0.684632\pi$
$467$	−23.6872	−1.09611	−0.548055	+	0.836442i	$0.684632\pi$
$468$	78.4623	3.62692
$469$	−1.88577	−0.0870769
$470$	−61.9186	−2.85609
$471$	22.7669	1.04904
$472$	−119.929	−5.52018
$473$	−16.6967	−0.767714
$474$	89.3040	4.10187
$475$	−9.43063	−0.432707
$476$	−20.2332	−0.927389
$477$	76.1434	3.48637
$478$	−38.5361	−1.76260
$479$	−15.3615	−0.701885	−0.350943	−	0.936397i	$-0.614139\pi$
$479$	−15.3615	−0.701885	−0.350943	+	0.936397i	$0.614139\pi$
$480$	260.633	11.8962
$481$	11.1002	0.506123
$482$	−46.6697	−2.12575
$483$	−13.9881	−0.636479
$484$	−23.8929	−1.08604
$485$	33.1587	1.50566
$486$	−64.4364	−2.92290
$487$	27.2208	1.23349	0.616745	−	0.787163i	$-0.288451\pi$
$487$	27.2208	1.23349	0.616745	+	0.787163i	$0.288451\pi$
$488$	81.7809	3.70205
$489$	−37.0732	−1.67651
$490$	−55.4132	−2.50331
$491$	−23.6590	−1.06772	−0.533858	−	0.845574i	$-0.679258\pi$
$491$	−23.6590	−1.06772	−0.533858	+	0.845574i	$0.679258\pi$
$492$	40.3802	1.82048
$493$	43.4264	1.95583
$494$	13.3849	0.602215
$495$	−54.6149	−2.45476
$496$	167.846	7.53652
$497$	4.93298	0.221275
$498$	60.0350	2.69023
$499$	−25.9481	−1.16160	−0.580799	−	0.814047i	$-0.697260\pi$
$499$	−25.9481	−1.16160	−0.580799	+	0.814047i	$0.697260\pi$
$500$	20.2956	0.907645
$501$	10.9060	0.487243
$502$	39.8708	1.77952
$503$	−1.18707	−0.0529290	−0.0264645	−	0.999650i	$-0.508425\pi$
$503$	−1.18707	−0.0529290	−0.0264645	+	0.999650i	$0.508425\pi$
$504$	−39.2233	−1.74715
$505$	−29.2618	−1.30213
$506$	59.8870	2.66230
$507$	−29.2270	−1.29802
$508$	32.5707	1.44509
$509$	−36.0165	−1.59640	−0.798201	−	0.602391i	$-0.794215\pi$
$509$	−36.0165	−1.59640	−0.798201	+	0.602391i	$0.794215\pi$
$510$	−172.068	−7.61930
$511$	−3.61774	−0.160040
$512$	−120.822	−5.33963
$513$	−31.6908	−1.39918
$514$	−56.0444	−2.47201
$515$	49.1826	2.16724
$516$	−116.084	−5.11032
$517$	−19.6099	−0.862443
$518$	−8.51876	−0.374293
$519$	−30.9856	−1.36011
$520$	59.9410	2.62859
$521$	−25.9406	−1.13648	−0.568239	−	0.822863i	$-0.692375\pi$
$521$	−25.9406	−1.13648	−0.568239	+	0.822863i	$0.692375\pi$
$522$	129.240	5.65668
$523$	−17.6536	−0.771940	−0.385970	−	0.922511i	$-0.626133\pi$
$523$	−17.6536	−0.771940	−0.385970	+	0.922511i	$0.626133\pi$
$524$	43.7209	1.90995
$525$	6.46819	0.282295
$526$	15.3594	0.669702
$527$	−63.3194	−2.75824
$528$	144.454	6.28655
$529$	44.8174	1.94858
$530$	89.3017	3.87902
$531$	81.2118	3.52429
$532$	−7.61682	−0.330231
$533$	4.31652	0.186969
$534$	104.535	4.52366
$535$	26.0101	1.12451
$536$	36.5631	1.57928
$537$	−25.5436	−1.10229
$538$	−35.5621	−1.53319
$539$	−17.5496	−0.755916
$540$	−217.874	−9.37581
$541$	37.4973	1.61213	0.806066	−	0.591825i	$-0.201592\pi$
$541$	37.4973	1.61213	0.806066	+	0.591825i	$0.201592\pi$
$542$	−88.2436	−3.79039
$543$	−74.6219	−3.20233
$544$	182.343	7.81787
$545$	−1.02065	−0.0437197
$546$	−9.18030	−0.392881
$547$	−2.73743	−0.117044	−0.0585220	−	0.998286i	$-0.518639\pi$
$547$	−2.73743	−0.117044	−0.0585220	+	0.998286i	$0.518639\pi$
$548$	−46.0374	−1.96662
$549$	−55.3792	−2.36353
$550$	−27.6922	−1.18080
$551$	16.3479	0.696445
$552$	271.214	11.5436
$553$	−5.43243	−0.231010
$554$	−65.9799	−2.80322
$555$	−53.7183	−2.28021
$556$	−20.3055	−0.861146
$557$	−5.84327	−0.247587	−0.123794	−	0.992308i	$-0.539506\pi$
$557$	−5.84327	−0.247587	−0.123794	+	0.992308i	$0.539506\pi$
$558$	−188.443	−7.97742
$559$	−12.4090	−0.524845
$560$	−27.7459	−1.17248
$561$	−54.4947	−2.30077
$562$	−62.2370	−2.62531
$563$	−24.7183	−1.04175	−0.520876	−	0.853633i	$-0.674394\pi$
$563$	−24.7183	−1.04175	−0.520876	+	0.853633i	$0.674394\pi$
$564$	−136.338	−5.74089
$565$	−13.2904	−0.559131
$566$	60.0018	2.52206
$567$	10.4153	0.437400
$568$	−95.6452	−4.01319
$569$	−5.64324	−0.236577	−0.118288	−	0.992979i	$-0.537741\pi$
$569$	−5.64324	−0.236577	−0.118288	+	0.992979i	$0.537741\pi$
$570$	−64.7752	−2.71313
$571$	6.87413	0.287673	0.143837	−	0.989601i	$-0.454056\pi$
$571$	6.87413	0.287673	0.143837	+	0.989601i	$0.454056\pi$
$572$	29.1436	1.21855
$573$	41.0310	1.71410
$574$	−3.31269	−0.138269
$575$	−31.3592	−1.30777
$576$	297.172	12.3822
$577$	−33.9099	−1.41169	−0.705843	−	0.708368i	$-0.749432\pi$
$577$	−33.9099	−1.41169	−0.705843	+	0.708368i	$0.749432\pi$
$578$	−73.0953	−3.04036
$579$	36.6816	1.52444
$580$	112.392	4.66683
$581$	−3.65197	−0.151509
$582$	98.4655	4.08153
$583$	28.2823	1.17133
$584$	70.1442	2.90259
$585$	−40.5900	−1.67819
$586$	67.8653	2.80349
$587$	35.8620	1.48018	0.740092	−	0.672506i	$-0.234782\pi$
$587$	35.8620	1.48018	0.740092	+	0.672506i	$0.234782\pi$
$588$	−122.014	−5.03179
$589$	−23.8367	−0.982172
$590$	95.2459	3.92121
$591$	8.15963	0.335642
$592$	99.6223	4.09445
$593$	9.90557	0.406773	0.203387	−	0.979099i	$-0.434805\pi$
$593$	9.90557	0.406773	0.203387	+	0.979099i	$0.434805\pi$
$594$	−93.0570	−3.81817
$595$	10.4670	0.429106
$596$	−7.30328	−0.299154
$597$	59.3874	2.43057
$598$	44.5082	1.82008
$599$	−28.3312	−1.15758	−0.578790	−	0.815476i	$-0.696475\pi$
$599$	−28.3312	−1.15758	−0.578790	+	0.815476i	$0.696475\pi$
$600$	−125.411	−5.11989
$601$	−6.75006	−0.275340	−0.137670	−	0.990478i	$-0.543961\pi$
$601$	−6.75006	−0.275340	−0.137670	+	0.990478i	$0.543961\pi$
$602$	9.52324	0.388138
$603$	−24.7592	−1.00827
$604$	−93.6182	−3.80927
$605$	12.3602	0.502515
$606$	−86.8936	−3.52981
$607$	11.4298	0.463922	0.231961	−	0.972725i	$-0.425486\pi$
$607$	11.4298	0.463922	0.231961	+	0.972725i	$0.425486\pi$
$608$	68.6430	2.78384
$609$	−11.2125	−0.454355
$610$	−64.9492	−2.62972
$611$	−14.5741	−0.589607
$612$	−265.652	−10.7384
$613$	4.08833	0.165126	0.0825630	−	0.996586i	$-0.473689\pi$
$613$	4.08833	0.165126	0.0825630	+	0.996586i	$0.473689\pi$
$614$	34.9625	1.41097
$615$	−20.8894	−0.842343
$616$	−14.5689	−0.586997
$617$	21.3844	0.860904	0.430452	−	0.902613i	$-0.358354\pi$
$617$	21.3844	0.860904	0.430452	+	0.902613i	$0.358354\pi$
$618$	146.049	5.87494
$619$	11.6855	0.469678	0.234839	−	0.972034i	$-0.424544\pi$
$619$	11.6855	0.469678	0.234839	+	0.972034i	$0.424544\pi$
$620$	−163.877	−6.58146
$621$	−105.380	−4.22875
$622$	−2.38735	−0.0957242
$623$	−6.35892	−0.254765
$624$	107.359	4.29778
$625$	−29.5392	−1.18157
$626$	4.82406	0.192808
$627$	−20.5146	−0.819274
$628$	41.2234	1.64499
$629$	−37.5821	−1.49850
$630$	31.1506	1.24107
$631$	30.2709	1.20506	0.602532	−	0.798095i	$-0.294159\pi$
$631$	30.2709	1.20506	0.602532	+	0.798095i	$0.294159\pi$
$632$	105.329	4.18976
$633$	−42.7192	−1.69793
$634$	26.6787	1.05955
$635$	−16.8494	−0.668648
$636$	196.633	7.79702
$637$	−13.0429	−0.516780
$638$	48.0042	1.90050
$639$	64.7676	2.56217
$640$	184.006	7.27346
$641$	−45.6961	−1.80489	−0.902444	−	0.430808i	$-0.858229\pi$
$641$	−45.6961	−1.80489	−0.902444	+	0.430808i	$0.858229\pi$
$642$	77.2374	3.04832
$643$	−28.5831	−1.12721	−0.563603	−	0.826046i	$-0.690585\pi$
$643$	−28.5831	−1.12721	−0.563603	+	0.826046i	$0.690585\pi$
$644$	−25.3279	−0.998058
$645$	60.0524	2.36456
$646$	−45.3177	−1.78300
$647$	−5.35695	−0.210603	−0.105302	−	0.994440i	$-0.533581\pi$
$647$	−5.35695	−0.210603	−0.105302	+	0.994440i	$0.533581\pi$
$648$	−201.941	−7.93298
$649$	30.1648	1.18407
$650$	−20.5809	−0.807250
$651$	16.3488	0.640762
$652$	−67.1275	−2.62891
$653$	−28.9041	−1.13111	−0.565553	−	0.824712i	$-0.691337\pi$
$653$	−28.9041	−1.13111	−0.565553	+	0.824712i	$0.691337\pi$
$654$	−3.03083	−0.118515
$655$	−22.6176	−0.883743
$656$	38.7401	1.51255
$657$	−47.4992	−1.85312
$658$	11.1849	0.436031
$659$	−36.4534	−1.42002	−0.710012	−	0.704190i	$-0.751310\pi$
$659$	−36.4534	−1.42002	−0.710012	+	0.704190i	$0.751310\pi$
$660$	−141.038	−5.48990
$661$	27.1945	1.05774	0.528871	−	0.848702i	$-0.322615\pi$
$661$	27.1945	1.05774	0.528871	+	0.848702i	$0.322615\pi$
$662$	22.2651	0.865359
$663$	−40.5006	−1.57291
$664$	70.8078	2.74788
$665$	3.94032	0.152799
$666$	−111.847	−4.33398
$667$	54.3610	2.10487
$668$	19.7472	0.764042
$669$	7.32204	0.283087
$670$	−29.0379	−1.12183
$671$	−20.5697	−0.794085
$672$	−47.0802	−1.81616
$673$	4.09424	0.157821	0.0789107	−	0.996882i	$-0.474856\pi$
$673$	4.09424	0.157821	0.0789107	+	0.996882i	$0.474856\pi$
$674$	70.8521	2.72912
$675$	48.7284	1.87556
$676$	−52.9207	−2.03541
$677$	47.8439	1.83879	0.919396	−	0.393334i	$-0.128678\pi$
$677$	47.8439	1.83879	0.919396	+	0.393334i	$0.128678\pi$
$678$	−39.4661	−1.51569
$679$	−5.98973	−0.229865
$680$	−202.944	−7.78256
$681$	67.9915	2.60544
$682$	−69.9941	−2.68021
$683$	−40.6157	−1.55412	−0.777058	−	0.629429i	$-0.783289\pi$
$683$	−40.6157	−1.55412	−0.777058	+	0.629429i	$0.783289\pi$
$684$	−100.005	−3.82379
$685$	23.8160	0.909962
$686$	20.4480	0.780710
$687$	−29.0761	−1.10932
$688$	−111.369	−4.24591
$689$	21.0195	0.800778
$690$	−215.394	−8.19990
$691$	8.23572	0.313302	0.156651	−	0.987654i	$-0.449930\pi$
$691$	8.23572	0.313302	0.156651	+	0.987654i	$0.449930\pi$
$692$	−56.1048	−2.13278
$693$	9.86553	0.374761
$694$	1.93669	0.0735158
$695$	10.5044	0.398455
$696$	217.399	8.24049
$697$	−14.6146	−0.553566
$698$	57.6273	2.18123
$699$	−62.6890	−2.37112
$700$	11.7118	0.442664
$701$	17.3679	0.655976	0.327988	−	0.944682i	$-0.393629\pi$
$701$	17.3679	0.655976	0.327988	+	0.944682i	$0.393629\pi$
$702$	−69.1602	−2.61028
$703$	−14.1478	−0.533596
$704$	110.380	4.16009
$705$	70.5304	2.65633
$706$	46.2646	1.74119
$707$	5.28580	0.198793
$708$	209.722	7.88183
$709$	−45.7456	−1.71801	−0.859006	−	0.511966i	$-0.828917\pi$
$709$	−45.7456	−1.71801	−0.859006	+	0.511966i	$0.828917\pi$
$710$	75.9600	2.85073
$711$	−71.3251	−2.67490
$712$	123.293	4.62059
$713$	−79.2629	−2.96842
$714$	31.0820	1.16322
$715$	−15.0765	−0.563829
$716$	−46.2512	−1.72849
$717$	43.8958	1.63932
$718$	−87.4985	−3.26541
$719$	18.5491	0.691766	0.345883	−	0.938278i	$-0.387579\pi$
$719$	18.5491	0.691766	0.345883	+	0.938278i	$0.387579\pi$
$720$	−364.289	−13.5763
$721$	−8.88425	−0.330867
$722$	35.7893	1.33194
$723$	53.1607	1.97707
$724$	−135.116	−5.02155
$725$	−25.1369	−0.933561
$726$	36.7040	1.36221
$727$	−46.2827	−1.71653	−0.858265	−	0.513207i	$-0.828457\pi$
$727$	−46.2827	−1.71653	−0.858265	+	0.513207i	$0.828457\pi$
$728$	−10.8276	−0.401299
$729$	15.1151	0.559820
$730$	−55.7075	−2.06183
$731$	42.0136	1.55393
$732$	−143.012	−5.28586
$733$	−16.1611	−0.596925	−0.298463	−	0.954421i	$-0.596474\pi$
$733$	−16.1611	−0.596925	−0.298463	+	0.954421i	$0.596474\pi$
$734$	−25.2634	−0.932489
$735$	63.1202	2.32822
$736$	228.255	8.41361
$737$	−9.19643	−0.338755
$738$	−43.4939	−1.60103
$739$	−33.3110	−1.22536	−0.612682	−	0.790330i	$-0.709909\pi$
$739$	−33.3110	−1.22536	−0.612682	+	0.790330i	$0.709909\pi$
$740$	−97.2664	−3.57558
$741$	−15.2465	−0.560094
$742$	−16.1313	−0.592198
$743$	−7.45220	−0.273395	−0.136697	−	0.990613i	$-0.543649\pi$
$743$	−7.45220	−0.273395	−0.136697	+	0.990613i	$0.543649\pi$
$744$	−316.986	−11.6213
$745$	3.77812	0.138420
$746$	42.1708	1.54398
$747$	−47.9486	−1.75435
$748$	−98.6723	−3.60782
$749$	−4.69841	−0.171676
$750$	−31.1778	−1.13845
$751$	26.4133	0.963835	0.481917	−	0.876217i	$-0.339941\pi$
$751$	26.4133	0.963835	0.481917	+	0.876217i	$0.339941\pi$
$752$	−130.801	−4.76981
$753$	−45.4161	−1.65505
$754$	35.6768	1.29927
$755$	48.4304	1.76256
$756$	39.3564	1.43138
$757$	14.5984	0.530589	0.265295	−	0.964167i	$-0.414531\pi$
$757$	14.5984	0.530589	0.265295	+	0.964167i	$0.414531\pi$
$758$	7.82004	0.284037
$759$	−68.2162	−2.47609
$760$	−76.3986	−2.77127
$761$	−20.9259	−0.758564	−0.379282	−	0.925281i	$-0.623829\pi$
$761$	−20.9259	−0.758564	−0.379282	+	0.925281i	$0.623829\pi$
$762$	−50.0347	−1.81256
$763$	0.184368	0.00667456
$764$	74.2939	2.68786
$765$	137.427	4.96867
$766$	3.14106	0.113491
$767$	22.4186	0.809488
$768$	278.873	10.0630
$769$	21.5753	0.778026	0.389013	−	0.921232i	$-0.372816\pi$
$769$	21.5753	0.778026	0.389013	+	0.921232i	$0.372816\pi$
$770$	11.5704	0.416968
$771$	63.8392	2.29911
$772$	66.4185	2.39046
$773$	−26.4476	−0.951254	−0.475627	−	0.879647i	$-0.657779\pi$
$773$	−26.4476	−0.951254	−0.475627	+	0.879647i	$0.657779\pi$
$774$	125.035	4.49430
$775$	36.6517	1.31657
$776$	116.134	4.16898
$777$	9.70357	0.348114
$778$	35.1155	1.25895
$779$	−5.50167	−0.197118
$780$	−104.820	−3.75315
$781$	24.0569	0.860823
$782$	−150.693	−5.38876
$783$	−84.4702	−3.01872
$784$	−117.058	−4.18066
$785$	−21.3256	−0.761144
$786$	−67.1634	−2.39564
$787$	11.4291	0.407403	0.203702	−	0.979033i	$-0.434703\pi$
$787$	11.4291	0.407403	0.203702	+	0.979033i	$0.434703\pi$
$788$	14.7744	0.526318
$789$	−17.4956	−0.622861
$790$	−83.6507	−2.97616
$791$	2.40075	0.0853609
$792$	−191.282	−6.79691
$793$	−15.2875	−0.542874
$794$	41.1236	1.45942
$795$	−101.722	−3.60771
$796$	107.531	3.81135
$797$	8.62441	0.305492	0.152746	−	0.988265i	$-0.451188\pi$
$797$	8.62441	0.305492	0.152746	+	0.988265i	$0.451188\pi$
$798$	11.7009	0.414206
$799$	49.3441	1.74567
$800$	−105.547	−3.73165
$801$	−83.4895	−2.94995
$802$	78.3985	2.76835
$803$	−17.6428	−0.622601
$804$	−63.9384	−2.25494
$805$	13.1026	0.461805
$806$	−52.0198	−1.83232
$807$	40.5082	1.42596
$808$	−102.486	−3.60544
$809$	11.7034	0.411469	0.205735	−	0.978608i	$-0.434042\pi$
$809$	11.7034	0.411469	0.205735	+	0.978608i	$0.434042\pi$
$810$	160.378	5.63512
$811$	17.9429	0.630060	0.315030	−	0.949082i	$-0.397985\pi$
$811$	17.9429	0.630060	0.315030	+	0.949082i	$0.397985\pi$
$812$	−20.3023	−0.712470
$813$	100.517	3.52528
$814$	−41.5438	−1.45611
$815$	34.7263	1.21641
$816$	−363.488	−12.7246
$817$	15.8161	0.553334
$818$	−16.5467	−0.578542
$819$	7.33209	0.256204
$820$	−37.8240	−1.32087
$821$	34.0691	1.18902	0.594510	−	0.804088i	$-0.297346\pi$
$821$	34.0691	1.18902	0.594510	+	0.804088i	$0.297346\pi$
$822$	70.7221	2.46672
$823$	11.7411	0.409269	0.204635	−	0.978838i	$-0.434399\pi$
$823$	11.7411	0.409269	0.204635	+	0.978838i	$0.434399\pi$
$824$	172.256	6.00082
$825$	31.5437	1.09821
$826$	−17.2050	−0.598640
$827$	−2.51603	−0.0874908	−0.0437454	−	0.999043i	$-0.513929\pi$
$827$	−2.51603	−0.0874908	−0.0437454	+	0.999043i	$0.513929\pi$
$828$	−332.542	−11.5566
$829$	38.0484	1.32148	0.660738	−	0.750616i	$-0.270243\pi$
$829$	38.0484	1.32148	0.660738	+	0.750616i	$0.270243\pi$
$830$	−56.2345	−1.95193
$831$	75.1566	2.60715
$832$	82.0345	2.84404
$833$	44.1599	1.53005
$834$	31.1931	1.08013
$835$	−10.2156	−0.353525
$836$	−37.1453	−1.28470
$837$	123.165	4.25720
$838$	−49.7390	−1.71821
$839$	−37.4548	−1.29308	−0.646542	−	0.762878i	$-0.723786\pi$
$839$	−37.4548	−1.29308	−0.646542	+	0.762878i	$0.723786\pi$
$840$	52.3995	1.80795
$841$	14.5746	0.502573
$842$	37.3342	1.28662
$843$	70.8931	2.44169
$844$	−77.3505	−2.66252
$845$	27.3768	0.941791
$846$	146.852	5.04886
$847$	−2.23273	−0.0767174
$848$	188.647	6.47815
$849$	−68.3470	−2.34566
$850$	69.6815	2.39005
$851$	−47.0451	−1.61269
$852$	167.256	5.73011
$853$	31.3664	1.07396	0.536982	−	0.843594i	$-0.319564\pi$
$853$	31.3664	1.07396	0.536982	+	0.843594i	$0.319564\pi$
$854$	11.7323	0.401471
$855$	51.7344	1.76928
$856$	91.0970	3.11363
$857$	8.36436	0.285721	0.142860	−	0.989743i	$-0.454370\pi$
$857$	8.36436	0.285721	0.142860	+	0.989743i	$0.454370\pi$
$858$	−44.7700	−1.52842
$859$	35.2187	1.20164	0.600822	−	0.799382i	$-0.294840\pi$
$859$	35.2187	1.20164	0.600822	+	0.799382i	$0.294840\pi$
$860$	108.736	3.70785
$861$	3.77343	0.128598
$862$	−4.54986	−0.154969
$863$	39.0520	1.32934	0.664672	−	0.747135i	$-0.268571\pi$
$863$	39.0520	1.32934	0.664672	+	0.747135i	$0.268571\pi$
$864$	−354.681	−12.0665
$865$	29.0240	0.986846
$866$	−91.5220	−3.11004
$867$	83.2616	2.82771
$868$	29.6024	1.00477
$869$	−26.4926	−0.898699
$870$	−172.655	−5.85356
$871$	−6.83481	−0.231589
$872$	−3.57469	−0.121054
$873$	−78.6421	−2.66163
$874$	−56.7284	−1.91887
$875$	1.89657	0.0641156
$876$	−122.662	−4.14437
$877$	24.8863	0.840351	0.420175	−	0.907443i	$-0.361969\pi$
$877$	24.8863	0.840351	0.420175	+	0.907443i	$0.361969\pi$
$878$	80.4871	2.71631
$879$	−77.3041	−2.60740
$880$	−135.309	−4.56128
$881$	39.5556	1.33266	0.666331	−	0.745656i	$-0.267864\pi$
$881$	39.5556	1.33266	0.666331	+	0.745656i	$0.267864\pi$
$882$	131.423	4.42524
$883$	−1.15227	−0.0387768	−0.0193884	−	0.999812i	$-0.506172\pi$
$883$	−1.15227	−0.0387768	−0.0193884	+	0.999812i	$0.506172\pi$
$884$	−73.3335	−2.46647
$885$	−108.493	−3.64695
$886$	−75.2914	−2.52946
$887$	−25.1057	−0.842967	−0.421484	−	0.906836i	$-0.638491\pi$
$887$	−25.1057	−0.842967	−0.421484	+	0.906836i	$0.638491\pi$
$888$	−188.142	−6.31362
$889$	3.04364	0.102081
$890$	−97.9172	−3.28219
$891$	50.7926	1.70161
$892$	13.2578	0.443905
$893$	18.5756	0.621610
$894$	11.2192	0.375226
$895$	23.9266	0.799778
$896$	−33.2384	−1.11042
$897$	−50.6985	−1.69277
$898$	−55.8156	−1.86259
$899$	−63.5355	−2.11903
$900$	153.770	5.12566
$901$	−71.1663	−2.37089
$902$	−16.1551	−0.537907
$903$	−10.8478	−0.360991
$904$	−46.5480	−1.54816
$905$	69.8980	2.32349
$906$	143.815	4.77793
$907$	23.1375	0.768270	0.384135	−	0.923277i	$-0.374500\pi$
$907$	23.1375	0.768270	0.384135	+	0.923277i	$0.374500\pi$
$908$	123.111	4.08557
$909$	69.3999	2.30185
$910$	8.59914	0.285059
$911$	30.9758	1.02627	0.513136	−	0.858307i	$-0.328483\pi$
$911$	30.9758	1.02627	0.513136	+	0.858307i	$0.328483\pi$
$912$	−136.835	−4.53107
$913$	−17.8097	−0.589416
$914$	−98.8162	−3.26855
$915$	73.9825	2.44579
$916$	−52.6474	−1.73952
$917$	4.08560	0.134918
$918$	234.158	7.72837
$919$	−36.2361	−1.19532	−0.597659	−	0.801751i	$-0.703902\pi$
$919$	−36.2361	−1.19532	−0.597659	+	0.801751i	$0.703902\pi$
$920$	−254.045	−8.37560
$921$	−39.8252	−1.31229
$922$	5.60791	0.184687
$923$	17.8792	0.588500
$924$	25.4768	0.838126
$925$	21.7540	0.715267
$926$	−11.7103	−0.384824
$927$	−116.646	−3.83115
$928$	182.965	6.00611
$929$	−6.93983	−0.227688	−0.113844	−	0.993499i	$-0.536316\pi$
$929$	−6.93983	−0.227688	−0.113844	+	0.993499i	$0.536316\pi$
$930$	251.746	8.25507
$931$	16.6240	0.544830
$932$	−113.510	−3.71813
$933$	2.71939	0.0890289
$934$	65.8867	2.15588
$935$	51.0450	1.66935
$936$	−142.161	−4.64669
$937$	−11.9472	−0.390297	−0.195149	−	0.980774i	$-0.562519\pi$
$937$	−11.9472	−0.390297	−0.195149	+	0.980774i	$0.562519\pi$
$938$	5.24534	0.171267
$939$	−5.49500	−0.179323
$940$	127.708	4.16536
$941$	−46.7895	−1.52529	−0.762647	−	0.646815i	$-0.776101\pi$
$941$	−46.7895	−1.52529	−0.762647	+	0.646815i	$0.776101\pi$
$942$	−63.3269	−2.06330
$943$	−18.2944	−0.595749
$944$	201.204	6.54862
$945$	−20.3598	−0.662303
$946$	46.4424	1.50997
$947$	−17.5721	−0.571018	−0.285509	−	0.958376i	$-0.592163\pi$
$947$	−17.5721	−0.571018	−0.285509	+	0.958376i	$0.592163\pi$
$948$	−184.190	−5.98222
$949$	−13.1122	−0.425640
$950$	26.2316	0.851067
$951$	−30.3893	−0.985440
$952$	36.6595	1.18814
$953$	−46.7033	−1.51287	−0.756435	−	0.654069i	$-0.773060\pi$
$953$	−46.7033	−1.51287	−0.756435	+	0.654069i	$0.773060\pi$
$954$	−211.796	−6.85714
$955$	−38.4336	−1.24368
$956$	79.4811	2.57060
$957$	−54.6807	−1.76758
$958$	42.7286	1.38050
$959$	−4.30208	−0.138921
$960$	−397.000	−12.8131
$961$	61.6401	1.98839
$962$	−30.8755	−0.995465
$963$	−61.6877	−1.98786
$964$	96.2568	3.10022
$965$	−34.3595	−1.10607
$966$	38.9083	1.25185
$967$	32.6814	1.05096	0.525481	−	0.850805i	$-0.323885\pi$
$967$	32.6814	1.05096	0.525481	+	0.850805i	$0.323885\pi$
$968$	43.2902	1.39140
$969$	51.6206	1.65829
$970$	−92.2322	−2.96140
$971$	−6.94499	−0.222875	−0.111438	−	0.993771i	$-0.535546\pi$
$971$	−6.94499	−0.222875	−0.111438	+	0.993771i	$0.535546\pi$
$972$	132.901	4.26279
$973$	−1.89750	−0.0608310
$974$	−75.7155	−2.42608
$975$	23.4434	0.750788
$976$	−137.203	−4.39176
$977$	26.4797	0.847161	0.423580	−	0.905858i	$-0.360773\pi$
$977$	26.4797	0.847161	0.423580	+	0.905858i	$0.360773\pi$
$978$	103.120	3.29742
$979$	−31.0108	−0.991110
$980$	114.290	3.65087
$981$	2.42066	0.0772856
$982$	65.8083	2.10003
$983$	13.8854	0.442875	0.221438	−	0.975175i	$-0.428925\pi$
$983$	13.8854	0.442875	0.221438	+	0.975175i	$0.428925\pi$
$984$	−73.1627	−2.33234
$985$	−7.64309	−0.243529
$986$	−120.792	−3.84681
$987$	−12.7405	−0.405534
$988$	−27.6065	−0.878279
$989$	52.5924	1.67234
$990$	151.913	4.82812
$991$	−21.9120	−0.696056	−0.348028	−	0.937484i	$-0.613149\pi$
$991$	−21.9120	−0.696056	−0.348028	+	0.937484i	$0.613149\pi$
$992$	−266.778	−8.47022
$993$	−25.3618	−0.804833
$994$	−13.7213	−0.435212
$995$	−55.6279	−1.76352
$996$	−123.823	−3.92347
$997$	−4.62243	−0.146394	−0.0731969	−	0.997318i	$-0.523320\pi$
$997$	−4.62243	−0.146394	−0.0731969	+	0.997318i	$0.523320\pi$
$998$	72.1756	2.28468
$999$	73.1023	2.31285

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6007.2.a.b.1.2	✓	237

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6007.2.a.b.1.2	✓	237	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:	\( N \)	\(=\)	\( 6007 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6007.a (trivial)

\(f(q)\)	\(=\)	\(q-2.78154 q^{2} +3.16840 q^{3} +5.73694 q^{4} -2.96782 q^{5} -8.81302 q^{6} +0.536102 q^{7} -10.3944 q^{8} +7.03875 q^{9} +O(q^{10})\)	\(q-2.78154 q^{2} +3.16840 q^{3} +5.73694 q^{4} -2.96782 q^{5} -8.81302 q^{6} +0.536102 q^{7} -10.3944 q^{8} +7.03875 q^{9} +8.25511 q^{10} +2.61443 q^{11} +18.1769 q^{12} +1.94305 q^{13} -1.49119 q^{14} -9.40325 q^{15} +17.4386 q^{16} -6.57866 q^{17} -19.5785 q^{18} -2.47654 q^{19} -17.0262 q^{20} +1.69859 q^{21} -7.27214 q^{22} -8.23513 q^{23} -32.9337 q^{24} +3.80798 q^{25} -5.40467 q^{26} +12.7964 q^{27} +3.07559 q^{28} -6.60111 q^{29} +26.1555 q^{30} +9.62497 q^{31} -27.7173 q^{32} +8.28356 q^{33} +18.2988 q^{34} -1.59106 q^{35} +40.3809 q^{36} +5.71274 q^{37} +6.88859 q^{38} +6.15637 q^{39} +30.8489 q^{40} +2.22151 q^{41} -4.72468 q^{42} -6.38635 q^{43} +14.9988 q^{44} -20.8898 q^{45} +22.9063 q^{46} -7.50064 q^{47} +55.2525 q^{48} -6.71259 q^{49} -10.5920 q^{50} -20.8438 q^{51} +11.1472 q^{52} +10.8177 q^{53} -35.5936 q^{54} -7.75918 q^{55} -5.57248 q^{56} -7.84667 q^{57} +18.3612 q^{58} +11.5378 q^{59} -53.9459 q^{60} -7.86776 q^{61} -26.7722 q^{62} +3.77349 q^{63} +42.2194 q^{64} -5.76664 q^{65} -23.0410 q^{66} -3.51756 q^{67} -37.7414 q^{68} -26.0922 q^{69} +4.42558 q^{70} +9.20158 q^{71} -73.1639 q^{72} -6.74824 q^{73} -15.8902 q^{74} +12.0652 q^{75} -14.2078 q^{76} +1.40160 q^{77} -17.1242 q^{78} -10.1332 q^{79} -51.7548 q^{80} +19.4278 q^{81} -6.17921 q^{82} -6.81209 q^{83} +9.74469 q^{84} +19.5243 q^{85} +17.7639 q^{86} -20.9149 q^{87} -27.1756 q^{88} -11.8614 q^{89} +58.1057 q^{90} +1.04168 q^{91} -47.2445 q^{92} +30.4958 q^{93} +20.8633 q^{94} +7.34994 q^{95} -87.8194 q^{96} -11.1727 q^{97} +18.6713 q^{98} +18.4023 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 237 q - 26 q^{2} - 24 q^{3} + 226 q^{4} - 67 q^{5} - 30 q^{6} - 37 q^{7} - 75 q^{8} + 189 q^{9}+O(q^{10}) \) 237 * q - 26 * q^2 - 24 * q^3 + 226 * q^4 - 67 * q^5 - 30 * q^6 - 37 * q^7 - 75 * q^8 + 189 * q^9	\( 237 q - 26 q^{2} - 24 q^{3} + 226 q^{4} - 67 q^{5} - 30 q^{6} - 37 q^{7} - 75 q^{8} + 189 q^{9} - 39 q^{10} - 38 q^{11} - 67 q^{12} - 52 q^{13} - 54 q^{14} - 24 q^{15} + 208 q^{16} - 255 q^{17} - 71 q^{18} - 24 q^{19} - 154 q^{20} - 60 q^{21} - 39 q^{22} - 118 q^{23} - 85 q^{24} + 170 q^{25} - 61 q^{26} - 87 q^{27} - 99 q^{28} - 87 q^{29} - 30 q^{30} - 28 q^{31} - 156 q^{32} - 173 q^{33} - 4 q^{34} - 113 q^{35} + 152 q^{36} - 49 q^{37} - 145 q^{38} - 49 q^{39} - 91 q^{40} - 197 q^{41} - 61 q^{42} - 63 q^{43} - 106 q^{44} - 181 q^{45} - 2 q^{46} - 119 q^{47} - 142 q^{48} + 150 q^{49} - 89 q^{50} - 40 q^{51} - 97 q^{52} - 190 q^{53} - 97 q^{54} - 55 q^{55} - 154 q^{56} - 202 q^{57} - 27 q^{58} - 86 q^{59} - 48 q^{60} - 96 q^{61} - 239 q^{62} - 149 q^{63} + 183 q^{64} - 259 q^{65} - 72 q^{66} - 28 q^{67} - 482 q^{68} - 83 q^{69} + 20 q^{70} - 63 q^{71} - 193 q^{72} - 206 q^{73} - 132 q^{74} - 89 q^{75} - 11 q^{76} - 179 q^{77} - 58 q^{78} - 32 q^{79} - 320 q^{80} + 57 q^{81} - 77 q^{82} - 245 q^{83} - 133 q^{84} + q^{85} - 39 q^{86} - 179 q^{87} - 104 q^{88} - 227 q^{89} - 146 q^{90} - 36 q^{91} - 315 q^{92} - 87 q^{93} - 48 q^{94} - 111 q^{95} - 134 q^{96} - 221 q^{97} - 161 q^{98} - 68 q^{99}+O(q^{100}) \) 237 * q - 26 * q^2 - 24 * q^3 + 226 * q^4 - 67 * q^5 - 30 * q^6 - 37 * q^7 - 75 * q^8 + 189 * q^9 - 39 * q^10 - 38 * q^11 - 67 * q^12 - 52 * q^13 - 54 * q^14 - 24 * q^15 + 208 * q^16 - 255 * q^17 - 71 * q^18 - 24 * q^19 - 154 * q^20 - 60 * q^21 - 39 * q^22 - 118 * q^23 - 85 * q^24 + 170 * q^25 - 61 * q^26 - 87 * q^27 - 99 * q^28 - 87 * q^29 - 30 * q^30 - 28 * q^31 - 156 * q^32 - 173 * q^33 - 4 * q^34 - 113 * q^35 + 152 * q^36 - 49 * q^37 - 145 * q^38 - 49 * q^39 - 91 * q^40 - 197 * q^41 - 61 * q^42 - 63 * q^43 - 106 * q^44 - 181 * q^45 - 2 * q^46 - 119 * q^47 - 142 * q^48 + 150 * q^49 - 89 * q^50 - 40 * q^51 - 97 * q^52 - 190 * q^53 - 97 * q^54 - 55 * q^55 - 154 * q^56 - 202 * q^57 - 27 * q^58 - 86 * q^59 - 48 * q^60 - 96 * q^61 - 239 * q^62 - 149 * q^63 + 183 * q^64 - 259 * q^65 - 72 * q^66 - 28 * q^67 - 482 * q^68 - 83 * q^69 + 20 * q^70 - 63 * q^71 - 193 * q^72 - 206 * q^73 - 132 * q^74 - 89 * q^75 - 11 * q^76 - 179 * q^77 - 58 * q^78 - 32 * q^79 - 320 * q^80 + 57 * q^81 - 77 * q^82 - 245 * q^83 - 133 * q^84 + q^85 - 39 * q^86 - 179 * q^87 - 104 * q^88 - 227 * q^89 - 146 * q^90 - 36 * q^91 - 315 * q^92 - 87 * q^93 - 48 * q^94 - 111 * q^95 - 134 * q^96 - 221 * q^97 - 161 * q^98 - 68 * q^99

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