LMFDB - Embedded newform 6007.2.a.b.1.17

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			1.17
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)

$f(q)$	$=$	$q-2.54661 q^{2} +1.71939 q^{3} +4.48524 q^{4} -4.31092 q^{5} -4.37861 q^{6} +4.46436 q^{7} -6.32895 q^{8} -0.0437112 q^{9} +O(q^{10})$	\(q-2.54661 q^{2} +1.71939 q^{3} +4.48524 q^{4} -4.31092 q^{5} -4.37861 q^{6} +4.46436 q^{7} -6.32895 q^{8} -0.0437112 q^{9} +10.9783 q^{10} -0.155812 q^{11} +7.71186 q^{12} -0.436879 q^{13} -11.3690 q^{14} -7.41214 q^{15} +7.14691 q^{16} +3.48074 q^{17} +0.111315 q^{18} +0.681898 q^{19} -19.3355 q^{20} +7.67596 q^{21} +0.396793 q^{22} -4.29179 q^{23} -10.8819 q^{24} +13.5840 q^{25} +1.11256 q^{26} -5.23331 q^{27} +20.0237 q^{28} +1.12436 q^{29} +18.8759 q^{30} -7.57812 q^{31} -5.54251 q^{32} -0.267901 q^{33} -8.86411 q^{34} -19.2455 q^{35} -0.196055 q^{36} +3.22015 q^{37} -1.73653 q^{38} -0.751163 q^{39} +27.2836 q^{40} -4.19515 q^{41} -19.5477 q^{42} -2.77354 q^{43} -0.698854 q^{44} +0.188435 q^{45} +10.9295 q^{46} +7.35940 q^{47} +12.2883 q^{48} +12.9305 q^{49} -34.5933 q^{50} +5.98474 q^{51} -1.95951 q^{52} +0.457493 q^{53} +13.3272 q^{54} +0.671693 q^{55} -28.2547 q^{56} +1.17245 q^{57} -2.86332 q^{58} -6.26236 q^{59} -33.2452 q^{60} -11.4614 q^{61} +19.2985 q^{62} -0.195142 q^{63} -0.179174 q^{64} +1.88335 q^{65} +0.682240 q^{66} +11.7935 q^{67} +15.6120 q^{68} -7.37925 q^{69} +49.0109 q^{70} -6.09317 q^{71} +0.276646 q^{72} +2.97623 q^{73} -8.20047 q^{74} +23.3562 q^{75} +3.05848 q^{76} -0.695600 q^{77} +1.91292 q^{78} -6.85478 q^{79} -30.8098 q^{80} -8.86696 q^{81} +10.6834 q^{82} -0.0781677 q^{83} +34.4285 q^{84} -15.0052 q^{85} +7.06313 q^{86} +1.93321 q^{87} +0.986126 q^{88} -1.39426 q^{89} -0.479872 q^{90} -1.95038 q^{91} -19.2497 q^{92} -13.0297 q^{93} -18.7415 q^{94} -2.93961 q^{95} -9.52972 q^{96} -18.9612 q^{97} -32.9290 q^{98} +0.00681072 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.54661	−1.80073	−0.900364	−	0.435138i	$-0.856700\pi$
$2$	−2.54661	−1.80073	−0.900364	+	0.435138i	$0.856700\pi$
$3$	1.71939	0.992688	0.496344	−	0.868126i	$-0.334675\pi$
$3$	1.71939	0.992688	0.496344	+	0.868126i	$0.334675\pi$
$4$	4.48524	2.24262
$5$	−4.31092	−1.92790	−0.963951	−	0.266079i	$-0.914272\pi$
$5$	−4.31092	−1.92790	−0.963951	+	0.266079i	$0.914272\pi$
$6$	−4.37861	−1.78756
$7$	4.46436	1.68737	0.843685	−	0.536839i	$-0.180382\pi$
$7$	4.46436	1.68737	0.843685	+	0.536839i	$0.180382\pi$
$8$	−6.32895	−2.23762
$9$	−0.0437112	−0.0145704
$10$	10.9783	3.47163
$11$	−0.155812	−0.0469791	−0.0234895	−	0.999724i	$-0.507478\pi$
$11$	−0.155812	−0.0469791	−0.0234895	+	0.999724i	$0.507478\pi$
$12$	7.71186	2.22622
$13$	−0.436879	−0.121168	−0.0605842	−	0.998163i	$-0.519296\pi$
$13$	−0.436879	−0.121168	−0.0605842	+	0.998163i	$0.519296\pi$
$14$	−11.3690	−3.03849
$15$	−7.41214	−1.91381
$16$	7.14691	1.78673
$17$	3.48074	0.844204	0.422102	−	0.906548i	$-0.361292\pi$
$17$	3.48074	0.844204	0.422102	+	0.906548i	$0.361292\pi$
$18$	0.111315	0.0262373
$19$	0.681898	0.156438	0.0782191	−	0.996936i	$-0.475077\pi$
$19$	0.681898	0.156438	0.0782191	+	0.996936i	$0.475077\pi$
$20$	−19.3355	−4.32355
$21$	7.67596	1.67503
$22$	0.396793	0.0845965
$23$	−4.29179	−0.894901	−0.447450	−	0.894309i	$-0.647668\pi$
$23$	−4.29179	−0.894901	−0.447450	+	0.894309i	$0.647668\pi$
$24$	−10.8819	−2.22126
$25$	13.5840	2.71681
$26$	1.11256	0.218191
$27$	−5.23331	−1.00715
$28$	20.0237	3.78413
$29$	1.12436	0.208789	0.104394	−	0.994536i	$-0.466710\pi$
$29$	1.12436	0.208789	0.104394	+	0.994536i	$0.466710\pi$
$30$	18.8759	3.44624
$31$	−7.57812	−1.36107	−0.680535	−	0.732716i	$-0.738253\pi$
$31$	−7.57812	−1.36107	−0.680535	+	0.732716i	$0.738253\pi$
$32$	−5.54251	−0.979787
$33$	−0.267901	−0.0466356
$34$	−8.86411	−1.52018
$35$	−19.2455	−3.25308
$36$	−0.196055	−0.0326759
$37$	3.22015	0.529389	0.264694	−	0.964332i	$-0.414729\pi$
$37$	3.22015	0.529389	0.264694	+	0.964332i	$0.414729\pi$
$38$	−1.73653	−0.281702
$39$	−0.751163	−0.120282
$40$	27.2836	4.31392
$41$	−4.19515	−0.655172	−0.327586	−	0.944821i	$-0.606235\pi$
$41$	−4.19515	−0.655172	−0.327586	+	0.944821i	$0.606235\pi$
$42$	−19.5477	−3.01628
$43$	−2.77354	−0.422961	−0.211480	−	0.977382i	$-0.567828\pi$
$43$	−2.77354	−0.422961	−0.211480	+	0.977382i	$0.567828\pi$
$44$	−0.698854	−0.105356
$45$	0.188435	0.0280903
$46$	10.9295	1.61147
$47$	7.35940	1.07348	0.536739	−	0.843748i	$-0.319656\pi$
$47$	7.35940	1.07348	0.536739	+	0.843748i	$0.319656\pi$
$48$	12.2883	1.77366
$49$	12.9305	1.84722
$50$	−34.5933	−4.89223
$51$	5.98474	0.838032
$52$	−1.95951	−0.271735
$53$	0.457493	0.0628415	0.0314207	−	0.999506i	$-0.489997\pi$
$53$	0.457493	0.0628415	0.0314207	+	0.999506i	$0.489997\pi$
$54$	13.3272	1.81361
$55$	0.671693	0.0905710
$56$	−28.2547	−3.77569
$57$	1.17245	0.155294
$58$	−2.86332	−0.375972
$59$	−6.26236	−0.815290	−0.407645	−	0.913141i	$-0.633650\pi$
$59$	−6.26236	−0.815290	−0.407645	+	0.913141i	$0.633650\pi$
$60$	−33.2452	−4.29194
$61$	−11.4614	−1.46749	−0.733743	−	0.679427i	$-0.762228\pi$
$61$	−11.4614	−1.46749	−0.733743	+	0.679427i	$0.762228\pi$
$62$	19.2985	2.45092
$63$	−0.195142	−0.0245856
$64$	−0.179174	−0.0223968
$65$	1.88335	0.233601
$66$	0.682240	0.0839779
$67$	11.7935	1.44080	0.720402	−	0.693557i	$-0.243958\pi$
$67$	11.7935	1.44080	0.720402	+	0.693557i	$0.243958\pi$
$68$	15.6120	1.89323
$69$	−7.37925	−0.888358
$70$	49.0109	5.85792
$71$	−6.09317	−0.723127	−0.361563	−	0.932348i	$-0.617757\pi$
$71$	−6.09317	−0.723127	−0.361563	+	0.932348i	$0.617757\pi$
$72$	0.276646	0.0326030
$73$	2.97623	0.348342	0.174171	−	0.984715i	$-0.444276\pi$
$73$	2.97623	0.348342	0.174171	+	0.984715i	$0.444276\pi$
$74$	−8.20047	−0.953285
$75$	23.3562	2.69694
$76$	3.05848	0.350831
$77$	−0.695600	−0.0792710
$78$	1.91292	0.216596
$79$	−6.85478	−0.771223	−0.385612	−	0.922661i	$-0.626010\pi$
$79$	−6.85478	−0.771223	−0.385612	+	0.922661i	$0.626010\pi$
$80$	−30.8098	−3.44464
$81$	−8.86696	−0.985217
$82$	10.6834	1.17979
$83$	−0.0781677	−0.00858002	−0.00429001	−	0.999991i	$-0.501366\pi$
$83$	−0.0781677	−0.00858002	−0.00429001	+	0.999991i	$0.501366\pi$
$84$	34.4285	3.75646
$85$	−15.0052	−1.62754
$86$	7.06313	0.761637
$87$	1.93321	0.207262
$88$	0.986126	0.105121
$89$	−1.39426	−0.147791	−0.0738954	−	0.997266i	$-0.523543\pi$
$89$	−1.39426	−0.147791	−0.0738954	+	0.997266i	$0.523543\pi$
$90$	−0.479872	−0.0505830
$91$	−1.95038	−0.204456
$92$	−19.2497	−2.00692
$93$	−13.0297	−1.35112
$94$	−18.7415	−1.93304
$95$	−2.93961	−0.301597
$96$	−9.52972	−0.972623
$97$	−18.9612	−1.92522	−0.962610	−	0.270892i	$-0.912681\pi$
$97$	−18.9612	−1.92522	−0.962610	+	0.270892i	$0.912681\pi$
$98$	−32.9290	−3.32633
$99$	0.00681072	0.000684503 0
$100$	60.9277	6.09277
$101$	4.58900	0.456623	0.228311	−	0.973588i	$-0.426680\pi$
$101$	4.58900	0.456623	0.228311	+	0.973588i	$0.426680\pi$
$102$	−15.2408	−1.50907
$103$	8.87742	0.874719	0.437359	−	0.899287i	$-0.355914\pi$
$103$	8.87742	0.874719	0.437359	+	0.899287i	$0.355914\pi$
$104$	2.76498	0.271129
$105$	−33.0904	−3.22930
$106$	−1.16506	−0.113160
$107$	−8.14273	−0.787187	−0.393594	−	0.919285i	$-0.628768\pi$
$107$	−8.14273	−0.787187	−0.393594	+	0.919285i	$0.628768\pi$
$108$	−23.4727	−2.25866
$109$	13.7273	1.31484	0.657419	−	0.753525i	$-0.271648\pi$
$109$	13.7273	1.31484	0.657419	+	0.753525i	$0.271648\pi$
$110$	−1.71054	−0.163094
$111$	5.53668	0.525518
$112$	31.9064	3.01487
$113$	6.47600	0.609211	0.304606	−	0.952479i	$-0.401475\pi$
$113$	6.47600	0.609211	0.304606	+	0.952479i	$0.401475\pi$
$114$	−2.98577	−0.279643
$115$	18.5016	1.72528
$116$	5.04303	0.468234
$117$	0.0190965	0.00176547
$118$	15.9478	1.46811
$119$	15.5393	1.42448
$120$	46.9110	4.28237
$121$	−10.9757	−0.997793
$122$	29.1878	2.64254
$123$	−7.21308	−0.650382
$124$	−33.9897	−3.05236
$125$	−37.0051	−3.30984
$126$	0.496952	0.0442720
$127$	6.69406	0.594001	0.297001	−	0.954877i	$-0.404014\pi$
$127$	6.69406	0.594001	0.297001	+	0.954877i	$0.404014\pi$
$128$	11.5413	1.02012
$129$	−4.76878	−0.419868
$130$	−4.79616	−0.420651
$131$	−2.48444	−0.217067	−0.108533	−	0.994093i	$-0.534615\pi$
$131$	−2.48444	−0.217067	−0.108533	+	0.994093i	$0.534615\pi$
$132$	−1.20160	−0.104586
$133$	3.04424	0.263969
$134$	−30.0334	−2.59449
$135$	22.5604	1.94169
$136$	−22.0295	−1.88901
$137$	−11.9477	−1.02076	−0.510381	−	0.859949i	$-0.670496\pi$
$137$	−11.9477	−1.02076	−0.510381	+	0.859949i	$0.670496\pi$
$138$	18.7921	1.59969
$139$	8.19457	0.695054	0.347527	−	0.937670i	$-0.387021\pi$
$139$	8.19457	0.695054	0.347527	+	0.937670i	$0.387021\pi$
$140$	−86.3207	−7.29543
$141$	12.6536	1.06563
$142$	15.5170	1.30215
$143$	0.0680709	0.00569238
$144$	−0.312400	−0.0260333
$145$	−4.84703	−0.402524
$146$	−7.57931	−0.627269
$147$	22.2325	1.83371
$148$	14.4431	1.18722
$149$	16.2130	1.32822	0.664111	−	0.747634i	$-0.268810\pi$
$149$	16.2130	1.32822	0.664111	+	0.747634i	$0.268810\pi$
$150$	−59.4792	−4.85646
$151$	15.0378	1.22376	0.611880	−	0.790951i	$-0.290414\pi$
$151$	15.0378	1.22376	0.611880	+	0.790951i	$0.290414\pi$
$152$	−4.31570	−0.350049
$153$	−0.152147	−0.0123004
$154$	1.77143	0.142746
$155$	32.6687	2.62401
$156$	−3.36915	−0.269748
$157$	−4.30053	−0.343220	−0.171610	−	0.985165i	$-0.554897\pi$
$157$	−4.30053	−0.343220	−0.171610	+	0.985165i	$0.554897\pi$
$158$	17.4565	1.38876
$159$	0.786607	0.0623820
$160$	23.8933	1.88893
$161$	−19.1601	−1.51003
$162$	22.5807	1.77411
$163$	9.83704	0.770497	0.385248	−	0.922813i	$-0.374116\pi$
$163$	9.83704	0.770497	0.385248	+	0.922813i	$0.374116\pi$
$164$	−18.8163	−1.46930
$165$	1.15490	0.0899088
$166$	0.199063	0.0154503
$167$	−12.8501	−0.994367	−0.497184	−	0.867645i	$-0.665632\pi$
$167$	−12.8501	−0.994367	−0.497184	+	0.867645i	$0.665632\pi$
$168$	−48.5808	−3.74809
$169$	−12.8091	−0.985318
$170$	38.2125	2.93076
$171$	−0.0298066	−0.00227936
$172$	−12.4400	−0.948540
$173$	−3.12351	−0.237476	−0.118738	−	0.992926i	$-0.537885\pi$
$173$	−3.12351	−0.237476	−0.118738	+	0.992926i	$0.537885\pi$
$174$	−4.92314	−0.373223
$175$	60.6440	4.58426
$176$	−1.11357	−0.0839388
$177$	−10.7674	−0.809328
$178$	3.55063	0.266131
$179$	6.96186	0.520354	0.260177	−	0.965561i	$-0.416219\pi$
$179$	6.96186	0.520354	0.260177	+	0.965561i	$0.416219\pi$
$180$	0.845178	0.0629959
$181$	−16.9489	−1.25980	−0.629901	−	0.776675i	$-0.716905\pi$
$181$	−16.9489	−1.25980	−0.629901	+	0.776675i	$0.716905\pi$
$182$	4.96687	0.368169
$183$	−19.7066	−1.45676
$184$	27.1626	2.00245
$185$	−13.8818	−1.02061
$186$	33.1816	2.43300
$187$	−0.542341	−0.0396599
$188$	33.0087	2.40740
$189$	−23.3634	−1.69944
$190$	7.48605	0.543095
$191$	−5.08923	−0.368244	−0.184122	−	0.982903i	$-0.558944\pi$
$191$	−5.08923	−0.368244	−0.184122	+	0.982903i	$0.558944\pi$
$192$	−0.308070	−0.0222330
$193$	6.32419	0.455225	0.227612	−	0.973752i	$-0.426908\pi$
$193$	6.32419	0.455225	0.227612	+	0.973752i	$0.426908\pi$
$194$	48.2869	3.46680
$195$	3.23821	0.231893
$196$	57.9964	4.14260
$197$	21.8297	1.55530	0.777650	−	0.628697i	$-0.216412\pi$
$197$	21.8297	1.55530	0.777650	+	0.628697i	$0.216412\pi$
$198$	−0.0173443	−0.00123260
$199$	−19.0430	−1.34992	−0.674962	−	0.737852i	$-0.735840\pi$
$199$	−19.0430	−1.34992	−0.674962	+	0.737852i	$0.735840\pi$
$200$	−85.9727	−6.07919
$201$	20.2775	1.43027
$202$	−11.6864	−0.822253
$203$	5.01956	0.352304
$204$	26.8430	1.87939
$205$	18.0850	1.26311
$206$	−22.6074	−1.57513
$207$	0.187599	0.0130391
$208$	−3.12233	−0.216495
$209$	−0.106248	−0.00734932
$210$	84.2686	5.81509
$211$	−21.4135	−1.47416	−0.737082	−	0.675803i	$-0.763797\pi$
$211$	−21.4135	−1.47416	−0.737082	+	0.675803i	$0.763797\pi$
$212$	2.05197	0.140930
$213$	−10.4765	−0.717839
$214$	20.7364	1.41751
$215$	11.9565	0.815427
$216$	33.1214	2.25362
$217$	−33.8314	−2.29663
$218$	−34.9582	−2.36767
$219$	5.11729	0.345795
$220$	3.01270	0.203116
$221$	−1.52066	−0.102291
$222$	−14.0998	−0.946315
$223$	−3.11932	−0.208885	−0.104442	−	0.994531i	$-0.533306\pi$
$223$	−3.11932	−0.208885	−0.104442	+	0.994531i	$0.533306\pi$
$224$	−24.7438	−1.65326
$225$	−0.593774	−0.0395850
$226$	−16.4919	−1.09702
$227$	−17.1011	−1.13504	−0.567520	−	0.823359i	$-0.692097\pi$
$227$	−17.1011	−1.13504	−0.567520	+	0.823359i	$0.692097\pi$
$228$	5.25870	0.348266
$229$	−0.329860	−0.0217978	−0.0108989	−	0.999941i	$-0.503469\pi$
$229$	−0.329860	−0.0217978	−0.0108989	+	0.999941i	$0.503469\pi$
$230$	−47.1164	−3.10676
$231$	−1.19601	−0.0786914
$232$	−7.11603	−0.467190
$233$	−10.3289	−0.676670	−0.338335	−	0.941026i	$-0.609864\pi$
$233$	−10.3289	−0.676670	−0.338335	+	0.941026i	$0.609864\pi$
$234$	−0.0486314	−0.00317913
$235$	−31.7258	−2.06956
$236$	−28.0882	−1.82839
$237$	−11.7860	−0.765584
$238$	−39.5726	−2.56511
$239$	17.2434	1.11538	0.557691	−	0.830049i	$-0.311688\pi$
$239$	17.2434	1.11538	0.557691	+	0.830049i	$0.311688\pi$
$240$	−52.9739	−3.41945
$241$	−7.54120	−0.485771	−0.242886	−	0.970055i	$-0.578094\pi$
$241$	−7.54120	−0.485771	−0.242886	+	0.970055i	$0.578094\pi$
$242$	27.9509	1.79675
$243$	0.454224	0.0291385
$244$	−51.4073	−3.29102
$245$	−55.7424	−3.56125
$246$	18.3689	1.17116
$247$	−0.297907	−0.0189554
$248$	47.9615	3.04556
$249$	−0.134401	−0.00851729
$250$	94.2377	5.96012
$251$	−19.2254	−1.21350	−0.606748	−	0.794894i	$-0.707526\pi$
$251$	−19.2254	−1.21350	−0.606748	+	0.794894i	$0.707526\pi$
$252$	−0.875261	−0.0551362
$253$	0.668713	0.0420416
$254$	−17.0472	−1.06964
$255$	−25.7998	−1.61564
$256$	−29.0329	−1.81456
$257$	−12.0426	−0.751197	−0.375599	−	0.926782i	$-0.622563\pi$
$257$	−12.0426	−0.751197	−0.375599	+	0.926782i	$0.622563\pi$
$258$	12.1442	0.756068
$259$	14.3759	0.893275
$260$	8.44728	0.523878
$261$	−0.0491472	−0.00304213
$262$	6.32691	0.390878
$263$	−0.0508724	−0.00313693	−0.00156846	−	0.999999i	$-0.500499\pi$
$263$	−0.0508724	−0.00313693	−0.00156846	+	0.999999i	$0.500499\pi$
$264$	1.69553	0.104353
$265$	−1.97222	−0.121152
$266$	−7.75250	−0.475336
$267$	−2.39726	−0.146710
$268$	52.8966	3.23117
$269$	−22.7253	−1.38559	−0.692793	−	0.721137i	$-0.743620\pi$
$269$	−22.7253	−1.38559	−0.692793	+	0.721137i	$0.743620\pi$
$270$	−57.4526	−3.49646
$271$	−12.8301	−0.779375	−0.389687	−	0.920947i	$-0.627417\pi$
$271$	−12.8301	−0.779375	−0.389687	+	0.920947i	$0.627417\pi$
$272$	24.8766	1.50836
$273$	−3.35346	−0.202961
$274$	30.4262	1.83811
$275$	−2.11656	−0.127633
$276$	−33.0977	−1.99225
$277$	7.95890	0.478204	0.239102	−	0.970994i	$-0.423147\pi$
$277$	7.95890	0.478204	0.239102	+	0.970994i	$0.423147\pi$
$278$	−20.8684	−1.25160
$279$	0.331248	0.0198313
$280$	121.804	7.27917
$281$	7.22535	0.431028	0.215514	−	0.976501i	$-0.430857\pi$
$281$	7.22535	0.431028	0.215514	+	0.976501i	$0.430857\pi$
$282$	−32.2239	−1.91891
$283$	−24.2886	−1.44381	−0.721905	−	0.691993i	$-0.756733\pi$
$283$	−24.2886	−1.44381	−0.721905	+	0.691993i	$0.756733\pi$
$284$	−27.3294	−1.62170
$285$	−5.05432	−0.299392
$286$	−0.173350	−0.0102504
$287$	−18.7287	−1.10552
$288$	0.242270	0.0142759
$289$	−4.88442	−0.287319
$290$	12.3435	0.724837
$291$	−32.6016	−1.91114
$292$	13.3491	0.781198
$293$	20.1589	1.17770	0.588848	−	0.808244i	$-0.299582\pi$
$293$	20.1589	1.17770	0.588848	+	0.808244i	$0.299582\pi$
$294$	−56.6177	−3.30201
$295$	26.9965	1.57180
$296$	−20.3802	−1.18457
$297$	0.815413	0.0473151
$298$	−41.2883	−2.39176
$299$	1.87499	0.108434
$300$	104.758	6.04822
$301$	−12.3821	−0.713691
$302$	−38.2955	−2.20366
$303$	7.89026	0.453284
$304$	4.87346	0.279512
$305$	49.4093	2.82917
$306$	0.387461	0.0221497
$307$	23.2331	1.32598	0.662990	−	0.748628i	$-0.269287\pi$
$307$	23.2331	1.32598	0.662990	+	0.748628i	$0.269287\pi$
$308$	−3.11994	−0.177775
$309$	15.2637	0.868323
$310$	−83.1945	−4.72513
$311$	18.6506	1.05758	0.528789	−	0.848753i	$-0.322646\pi$
$311$	18.6506	1.05758	0.528789	+	0.848753i	$0.322646\pi$
$312$	4.75408	0.269146
$313$	−15.0178	−0.848854	−0.424427	−	0.905462i	$-0.639525\pi$
$313$	−15.0178	−0.848854	−0.424427	+	0.905462i	$0.639525\pi$
$314$	10.9518	0.618045
$315$	0.841243	0.0473987
$316$	−30.7454	−1.72956
$317$	23.0548	1.29489	0.647443	−	0.762114i	$-0.275838\pi$
$317$	23.0548	1.29489	0.647443	+	0.762114i	$0.275838\pi$
$318$	−2.00318	−0.112333
$319$	−0.175189	−0.00980870
$320$	0.772407	0.0431789
$321$	−14.0005	−0.781431
$322$	48.7934	2.71915
$323$	2.37351	0.132066
$324$	−39.7704	−2.20947
$325$	−5.93458	−0.329191
$326$	−25.0512	−1.38746
$327$	23.6026	1.30522
$328$	26.5509	1.46603
$329$	32.8550	1.81135
$330$	−2.94108	−0.161901
$331$	−14.3133	−0.786731	−0.393366	−	0.919382i	$-0.628689\pi$
$331$	−14.3133	−0.786731	−0.393366	+	0.919382i	$0.628689\pi$
$332$	−0.350601	−0.0192417
$333$	−0.140756	−0.00771340
$334$	32.7241	1.79058
$335$	−50.8408	−2.77773
$336$	54.8594	2.99282
$337$	−8.01496	−0.436603	−0.218301	−	0.975881i	$-0.570052\pi$
$337$	−8.01496	−0.436603	−0.218301	+	0.975881i	$0.570052\pi$
$338$	32.6199	1.77429
$339$	11.1347	0.604757
$340$	−67.3020	−3.64996
$341$	1.18076	0.0639418
$342$	0.0759058	0.00410452
$343$	26.4759	1.42957
$344$	17.5536	0.946426
$345$	31.8114	1.71267
$346$	7.95438	0.427630
$347$	25.8345	1.38687	0.693436	−	0.720519i	$-0.256096\pi$
$347$	25.8345	1.38687	0.693436	+	0.720519i	$0.256096\pi$
$348$	8.67092	0.464810
$349$	33.4547	1.79079	0.895395	−	0.445272i	$-0.146893\pi$
$349$	33.4547	1.79079	0.895395	+	0.445272i	$0.146893\pi$
$350$	−154.437	−8.25500
$351$	2.28632	0.122035
$352$	0.863590	0.0460295
$353$	−32.0997	−1.70849	−0.854247	−	0.519867i	$-0.825981\pi$
$353$	−32.0997	−1.70849	−0.854247	+	0.519867i	$0.825981\pi$
$354$	27.4204	1.45738
$355$	26.2672	1.39412
$356$	−6.25358	−0.331439
$357$	26.7180	1.41407
$358$	−17.7292	−0.937016
$359$	−32.1664	−1.69768	−0.848838	−	0.528653i	$-0.822697\pi$
$359$	−32.1664	−1.69768	−0.848838	+	0.528653i	$0.822697\pi$
$360$	−1.19260	−0.0628554
$361$	−18.5350	−0.975527
$362$	43.1623	2.26856
$363$	−18.8715	−0.990497
$364$	−8.74794	−0.458517
$365$	−12.8303	−0.671569
$366$	50.1852	2.62322
$367$	−4.11261	−0.214676	−0.107338	−	0.994223i	$-0.534233\pi$
$367$	−4.11261	−0.214676	−0.107338	+	0.994223i	$0.534233\pi$
$368$	−30.6731	−1.59894
$369$	0.183375	0.00954612
$370$	35.3516	1.83784
$371$	2.04241	0.106037
$372$	−58.4414	−3.03005
$373$	28.5797	1.47980	0.739899	−	0.672718i	$-0.234873\pi$
$373$	28.5797	1.47980	0.739899	+	0.672718i	$0.234873\pi$
$374$	1.38113	0.0714167
$375$	−63.6261	−3.28564
$376$	−46.5773	−2.40204
$377$	−0.491210	−0.0252986
$378$	59.4976	3.06022
$379$	−19.4671	−0.999959	−0.499979	−	0.866037i	$-0.666659\pi$
$379$	−19.4671	−0.999959	−0.499979	+	0.866037i	$0.666659\pi$
$380$	−13.1849	−0.676369
$381$	11.5097	0.589658
$382$	12.9603	0.663107
$383$	−21.2999	−1.08837	−0.544186	−	0.838964i	$-0.683161\pi$
$383$	−21.2999	−1.08837	−0.544186	+	0.838964i	$0.683161\pi$
$384$	19.8440	1.01266
$385$	2.99868	0.152827
$386$	−16.1053	−0.819736
$387$	0.121235	0.00616270
$388$	−85.0456	−4.31754
$389$	−19.5983	−0.993671	−0.496836	−	0.867845i	$-0.665505\pi$
$389$	−19.5983	−0.993671	−0.496836	+	0.867845i	$0.665505\pi$
$390$	−8.24646	−0.417576
$391$	−14.9386	−0.755479
$392$	−81.8365	−4.13337
$393$	−4.27172	−0.215480
$394$	−55.5918	−2.80067
$395$	29.5504	1.48684
$396$	0.0305477	0.00153508
$397$	−2.46792	−0.123862	−0.0619308	−	0.998080i	$-0.519726\pi$
$397$	−2.46792	−0.123862	−0.0619308	+	0.998080i	$0.519726\pi$
$398$	48.4952	2.43085
$399$	5.23422	0.262039
$400$	97.0839	4.85419
$401$	−13.0254	−0.650456	−0.325228	−	0.945636i	$-0.605441\pi$
$401$	−13.0254	−0.650456	−0.325228	+	0.945636i	$0.605441\pi$
$402$	−51.6391	−2.57552
$403$	3.31072	0.164919
$404$	20.5828	1.02403
$405$	38.2247	1.89940
$406$	−12.7829	−0.634403
$407$	−0.501737	−0.0248702
$408$	−37.8771	−1.87520
$409$	−7.93232	−0.392228	−0.196114	−	0.980581i	$-0.562832\pi$
$409$	−7.93232	−0.392228	−0.196114	+	0.980581i	$0.562832\pi$
$410$	−46.0554	−2.27451
$411$	−20.5427	−1.01330
$412$	39.8174	1.96166
$413$	−27.9574	−1.37569
$414$	−0.477743	−0.0234798
$415$	0.336975	0.0165414
$416$	2.42141	0.118719
$417$	14.0896	0.689972
$418$	0.270572	0.0132341
$419$	−13.1684	−0.643317	−0.321659	−	0.946856i	$-0.604240\pi$
$419$	−13.1684	−0.643317	−0.321659	+	0.946856i	$0.604240\pi$
$420$	−148.419	−7.24209
$421$	−3.79830	−0.185118	−0.0925588	−	0.995707i	$-0.529505\pi$
$421$	−3.79830	−0.185118	−0.0925588	+	0.995707i	$0.529505\pi$
$422$	54.5318	2.65457
$423$	−0.321688	−0.0156410
$424$	−2.89545	−0.140615
$425$	47.2826	2.29354
$426$	26.6796	1.29263
$427$	−51.1680	−2.47619
$428$	−36.5221	−1.76536
$429$	0.117040	0.00565075
$430$	−30.4486	−1.46836
$431$	29.1643	1.40480	0.702398	−	0.711784i	$-0.252112\pi$
$431$	29.1643	1.40480	0.702398	+	0.711784i	$0.252112\pi$
$432$	−37.4020	−1.79951
$433$	−20.7942	−0.999304	−0.499652	−	0.866226i	$-0.666539\pi$
$433$	−20.7942	−0.999304	−0.499652	+	0.866226i	$0.666539\pi$
$434$	86.1556	4.13560
$435$	−8.33392	−0.399581
$436$	61.5703	2.94868
$437$	−2.92657	−0.139997
$438$	−13.0318	−0.622682
$439$	32.4031	1.54651	0.773257	−	0.634092i	$-0.218626\pi$
$439$	32.4031	1.54651	0.773257	+	0.634092i	$0.218626\pi$
$440$	−4.25111	−0.202664
$441$	−0.565208	−0.0269146
$442$	3.87254	0.184198
$443$	35.9067	1.70598	0.852989	−	0.521929i	$-0.174787\pi$
$443$	35.9067	1.70598	0.852989	+	0.521929i	$0.174787\pi$
$444$	24.8333	1.17854
$445$	6.01053	0.284926
$446$	7.94370	0.376145
$447$	27.8764	1.31851
$448$	−0.799899	−0.0377917
$449$	5.42497	0.256020	0.128010	−	0.991773i	$-0.459141\pi$
$449$	5.42497	0.256020	0.128010	+	0.991773i	$0.459141\pi$
$450$	1.51211	0.0712817
$451$	0.653654	0.0307794
$452$	29.0464	1.36623
$453$	25.8558	1.21481
$454$	43.5499	2.04390
$455$	8.40795	0.394171
$456$	−7.42035	−0.347490
$457$	18.1855	0.850682	0.425341	−	0.905033i	$-0.360154\pi$
$457$	18.1855	0.850682	0.425341	+	0.905033i	$0.360154\pi$
$458$	0.840026	0.0392518
$459$	−18.2158	−0.850242
$460$	82.9841	3.86915
$461$	8.22812	0.383222	0.191611	−	0.981471i	$-0.438629\pi$
$461$	8.22812	0.383222	0.191611	+	0.981471i	$0.438629\pi$
$462$	3.04576	0.141702
$463$	−35.9428	−1.67040	−0.835201	−	0.549945i	$-0.814649\pi$
$463$	−35.9428	−1.67040	−0.835201	+	0.549945i	$0.814649\pi$
$464$	8.03571	0.373048
$465$	56.1701	2.60482
$466$	26.3038	1.21850
$467$	5.41877	0.250751	0.125375	−	0.992109i	$-0.459986\pi$
$467$	5.41877	0.250751	0.125375	+	0.992109i	$0.459986\pi$
$468$	0.0856523	0.00395928
$469$	52.6503	2.43117
$470$	80.7933	3.72672
$471$	−7.39427	−0.340710
$472$	39.6341	1.82431
$473$	0.432150	0.0198703
$474$	30.0144	1.37861
$475$	9.26293	0.425012
$476$	69.6975	3.19458
$477$	−0.0199976	−0.000915625 0
$478$	−43.9122	−2.00850
$479$	−18.8062	−0.859275	−0.429638	−	0.903001i	$-0.641359\pi$
$479$	−18.8062	−0.859275	−0.429638	+	0.903001i	$0.641359\pi$
$480$	41.0819	1.87512
$481$	−1.40681	−0.0641452
$482$	19.2045	0.874742
$483$	−32.9436	−1.49899
$484$	−49.2288	−2.23767
$485$	81.7403	3.71164
$486$	−1.15673	−0.0524704
$487$	−13.7559	−0.623339	−0.311670	−	0.950191i	$-0.600888\pi$
$487$	−13.7559	−0.623339	−0.311670	+	0.950191i	$0.600888\pi$
$488$	72.5388	3.28368
$489$	16.9137	0.764863
$490$	141.954	6.41284
$491$	−16.5665	−0.747637	−0.373818	−	0.927502i	$-0.621952\pi$
$491$	−16.5665	−0.747637	−0.373818	+	0.927502i	$0.621952\pi$
$492$	−32.3524	−1.45856
$493$	3.91362	0.176260
$494$	0.758653	0.0341334
$495$	−0.0293605	−0.00131966
$496$	−54.1601	−2.43186
$497$	−27.2021	−1.22018
$498$	0.342266	0.0153373
$499$	28.3700	1.27001	0.635007	−	0.772506i	$-0.280997\pi$
$499$	28.3700	1.27001	0.635007	+	0.772506i	$0.280997\pi$
$500$	−165.977	−7.42271
$501$	−22.0942	−0.987096
$502$	48.9597	2.18518
$503$	−17.5439	−0.782242	−0.391121	−	0.920339i	$-0.627913\pi$
$503$	−17.5439	−0.782242	−0.391121	+	0.920339i	$0.627913\pi$
$504$	1.23505	0.0550133
$505$	−19.7828	−0.880324
$506$	−1.70295	−0.0757055
$507$	−22.0239	−0.978114
$508$	30.0245	1.33212
$509$	−23.2075	−1.02865	−0.514326	−	0.857595i	$-0.671958\pi$
$509$	−23.2075	−1.02865	−0.514326	+	0.857595i	$0.671958\pi$
$510$	65.7020	2.90933
$511$	13.2870	0.587781
$512$	50.8530	2.24741
$513$	−3.56859	−0.157557
$514$	30.6679	1.35270
$515$	−38.2699	−1.68637
$516$	−21.3891	−0.941604
$517$	−1.14668	−0.0504310
$518$	−36.6099	−1.60854
$519$	−5.37052	−0.235740
$520$	−11.9196	−0.522710
$521$	25.5879	1.12103	0.560513	−	0.828146i	$-0.310604\pi$
$521$	25.5879	1.12103	0.560513	+	0.828146i	$0.310604\pi$
$522$	0.125159	0.00547805
$523$	−13.6458	−0.596690	−0.298345	−	0.954458i	$-0.596435\pi$
$523$	−13.6458	−0.596690	−0.298345	+	0.954458i	$0.596435\pi$
$524$	−11.1433	−0.486798
$525$	104.271	4.55074
$526$	0.129552	0.00564875
$527$	−26.3775	−1.14902
$528$	−1.91466	−0.0833250
$529$	−4.58050	−0.199152
$530$	5.02247	0.218162
$531$	0.273735	0.0118791
$532$	13.6541	0.591982
$533$	1.83277	0.0793861
$534$	6.10491	0.264185
$535$	35.1026	1.51762
$536$	−74.6404	−3.22397
$537$	11.9701	0.516549
$538$	57.8725	2.49506
$539$	−2.01473	−0.0867804
$540$	101.189	4.35448
$541$	23.2866	1.00117	0.500584	−	0.865688i	$-0.333118\pi$
$541$	23.2866	1.00117	0.500584	+	0.865688i	$0.333118\pi$
$542$	32.6734	1.40344
$543$	−29.1417	−1.25059
$544$	−19.2921	−0.827141
$545$	−59.1774	−2.53488
$546$	8.53998	0.365477
$547$	−2.12062	−0.0906710	−0.0453355	−	0.998972i	$-0.514436\pi$
$547$	−2.12062	−0.0906710	−0.0453355	+	0.998972i	$0.514436\pi$
$548$	−53.5884	−2.28918
$549$	0.500993	0.0213818
$550$	5.39005	0.229832
$551$	0.766700	0.0326625
$552$	46.7029	1.98781
$553$	−30.6022	−1.30134
$554$	−20.2682	−0.861115
$555$	−23.8682	−1.01315
$556$	36.7546	1.55874
$557$	−30.9628	−1.31193	−0.655967	−	0.754789i	$-0.727739\pi$
$557$	−30.9628	−1.31193	−0.655967	+	0.754789i	$0.727739\pi$
$558$	−0.843562	−0.0357108
$559$	1.21170	0.0512494
$560$	−137.546	−5.81237
$561$	−0.932494	−0.0393699
$562$	−18.4002	−0.776164
$563$	23.3051	0.982193	0.491097	−	0.871105i	$-0.336596\pi$
$563$	23.3051	0.982193	0.491097	+	0.871105i	$0.336596\pi$
$564$	56.7546	2.38980
$565$	−27.9175	−1.17450
$566$	61.8538	2.59991
$567$	−39.5853	−1.66243
$568$	38.5634	1.61808
$569$	11.5852	0.485677	0.242839	−	0.970067i	$-0.421921\pi$
$569$	11.5852	0.485677	0.242839	+	0.970067i	$0.421921\pi$
$570$	12.8714	0.539124
$571$	−20.3310	−0.850825	−0.425412	−	0.905000i	$-0.639871\pi$
$571$	−20.3310	−0.850825	−0.425412	+	0.905000i	$0.639871\pi$
$572$	0.305315	0.0127658
$573$	−8.75035	−0.365551
$574$	47.6946	1.99074
$575$	−58.2999	−2.43127
$576$	0.00783193	0.000326330 0
$577$	−14.8300	−0.617380	−0.308690	−	0.951163i	$-0.599891\pi$
$577$	−14.8300	−0.617380	−0.308690	+	0.951163i	$0.599891\pi$
$578$	12.4387	0.517383
$579$	10.8737	0.451896
$580$	−21.7401	−0.902709
$581$	−0.348969	−0.0144777
$582$	83.0238	3.44145
$583$	−0.0712829	−0.00295223
$584$	−18.8364	−0.779457
$585$	−0.0823234	−0.00340366
$586$	−51.3370	−2.12071
$587$	31.1884	1.28728	0.643641	−	0.765327i	$-0.277423\pi$
$587$	31.1884	1.28728	0.643641	+	0.765327i	$0.277423\pi$
$588$	99.7183	4.11231
$589$	−5.16750	−0.212923
$590$	−68.7497	−2.83038
$591$	37.5336	1.54393
$592$	23.0141	0.945873
$593$	−35.0642	−1.43992	−0.719958	−	0.694018i	$-0.755839\pi$
$593$	−35.0642	−1.43992	−0.719958	+	0.694018i	$0.755839\pi$
$594$	−2.07654	−0.0852015
$595$	−66.9887	−2.74627
$596$	72.7192	2.97870
$597$	−32.7423	−1.34005
$598$	−4.77489	−0.195260
$599$	11.7271	0.479158	0.239579	−	0.970877i	$-0.422991\pi$
$599$	11.7271	0.479158	0.239579	+	0.970877i	$0.422991\pi$
$600$	−147.820	−6.03474
$601$	−31.6062	−1.28924	−0.644621	−	0.764502i	$-0.722985\pi$
$601$	−31.6062	−1.28924	−0.644621	+	0.764502i	$0.722985\pi$
$602$	31.5323	1.28516
$603$	−0.515507	−0.0209931
$604$	67.4482	2.74443
$605$	47.3155	1.92365
$606$	−20.0935	−0.816241
$607$	−11.7346	−0.476291	−0.238145	−	0.971229i	$-0.576540\pi$
$607$	−11.7346	−0.476291	−0.238145	+	0.971229i	$0.576540\pi$
$608$	−3.77943	−0.153276
$609$	8.63055	0.349728
$610$	−125.826	−5.09457
$611$	−3.21516	−0.130072
$612$	−0.682418	−0.0275851
$613$	−31.0777	−1.25522	−0.627608	−	0.778530i	$-0.715966\pi$
$613$	−31.0777	−1.25522	−0.627608	+	0.778530i	$0.715966\pi$
$614$	−59.1656	−2.38773
$615$	31.0950	1.25387
$616$	4.40242	0.177379
$617$	−13.3807	−0.538686	−0.269343	−	0.963044i	$-0.586807\pi$
$617$	−13.3807	−0.538686	−0.269343	+	0.963044i	$0.586807\pi$
$618$	−38.8708	−1.56361
$619$	32.2521	1.29632	0.648161	−	0.761504i	$-0.275539\pi$
$619$	32.2521	1.29632	0.648161	+	0.761504i	$0.275539\pi$
$620$	146.527	5.88466
$621$	22.4603	0.901301
$622$	−47.4959	−1.90441
$623$	−6.22446	−0.249378
$624$	−5.36849	−0.214912
$625$	91.6059	3.66424
$626$	38.2444	1.52856
$627$	−0.182681	−0.00729558
$628$	−19.2889	−0.769711
$629$	11.2085	0.446912
$630$	−2.14232	−0.0853522
$631$	−48.0002	−1.91086	−0.955430	−	0.295219i	$-0.904607\pi$
$631$	−48.0002	−1.91086	−0.955430	+	0.295219i	$0.904607\pi$
$632$	43.3836	1.72571
$633$	−36.8180	−1.46338
$634$	−58.7117	−2.33174
$635$	−28.8575	−1.14518
$636$	3.52812	0.139899
$637$	−5.64906	−0.223824
$638$	0.446139	0.0176628
$639$	0.266340	0.0105362
$640$	−49.7537	−1.96669
$641$	−39.3040	−1.55241	−0.776207	−	0.630478i	$-0.782859\pi$
$641$	−39.3040	−1.55241	−0.776207	+	0.630478i	$0.782859\pi$
$642$	35.6538	1.40714
$643$	−37.2896	−1.47056	−0.735279	−	0.677764i	$-0.762949\pi$
$643$	−37.2896	−1.47056	−0.735279	+	0.677764i	$0.762949\pi$
$644$	−85.9377	−3.38642
$645$	20.5578	0.809464
$646$	−6.04442	−0.237814
$647$	−7.44045	−0.292514	−0.146257	−	0.989247i	$-0.546723\pi$
$647$	−7.44045	−0.292514	−0.146257	+	0.989247i	$0.546723\pi$
$648$	56.1185	2.20454
$649$	0.975750	0.0383015
$650$	15.1131	0.592784
$651$	−58.1693	−2.27984
$652$	44.1215	1.72793
$653$	32.9842	1.29077	0.645385	−	0.763857i	$-0.276697\pi$
$653$	32.9842	1.29077	0.645385	+	0.763857i	$0.276697\pi$
$654$	−60.1066	−2.35035
$655$	10.7102	0.418483
$656$	−29.9823	−1.17061
$657$	−0.130095	−0.00507547
$658$	−83.6690	−3.26176
$659$	−31.9547	−1.24478	−0.622390	−	0.782708i	$-0.713838\pi$
$659$	−31.9547	−1.24478	−0.622390	+	0.782708i	$0.713838\pi$
$660$	5.18000	0.201631
$661$	−12.7241	−0.494910	−0.247455	−	0.968899i	$-0.579594\pi$
$661$	−12.7241	−0.494910	−0.247455	+	0.968899i	$0.579594\pi$
$662$	36.4505	1.41669
$663$	−2.61461	−0.101543
$664$	0.494720	0.0191988
$665$	−13.1235	−0.508906
$666$	0.358452	0.0138897
$667$	−4.82553	−0.186845
$668$	−57.6356	−2.22999
$669$	−5.36331	−0.207358
$670$	129.472	5.00193
$671$	1.78583	0.0689411
$672$	−42.5441	−1.64117
$673$	5.27935	0.203504	0.101752	−	0.994810i	$-0.467555\pi$
$673$	5.27935	0.203504	0.101752	+	0.994810i	$0.467555\pi$
$674$	20.4110	0.786203
$675$	−71.0896	−2.73624
$676$	−57.4521	−2.20970
$677$	3.99594	0.153576	0.0767882	−	0.997047i	$-0.475533\pi$
$677$	3.99594	0.153576	0.0767882	+	0.997047i	$0.475533\pi$
$678$	−28.3559	−1.08900
$679$	−84.6497	−3.24856
$680$	94.9672	3.64183
$681$	−29.4034	−1.12674
$682$	−3.00694	−0.115142
$683$	−49.0102	−1.87532	−0.937661	−	0.347552i	$-0.887013\pi$
$683$	−49.0102	−1.87532	−0.937661	+	0.347552i	$0.887013\pi$
$684$	−0.133690	−0.00511175
$685$	51.5056	1.96793
$686$	−67.4239	−2.57426
$687$	−0.567157	−0.0216384
$688$	−19.8222	−0.755715
$689$	−0.199869	−0.00761440
$690$	−81.0113	−3.08405
$691$	28.8571	1.09778	0.548888	−	0.835896i	$-0.315051\pi$
$691$	28.8571	1.09778	0.548888	+	0.835896i	$0.315051\pi$
$692$	−14.0097	−0.532569
$693$	0.0304055	0.00115501
$694$	−65.7906	−2.49738
$695$	−35.3261	−1.34000
$696$	−12.2352	−0.463774
$697$	−14.6022	−0.553099
$698$	−85.1963	−3.22473
$699$	−17.7594	−0.671722
$700$	272.003	10.2808
$701$	−4.15400	−0.156895	−0.0784473	−	0.996918i	$-0.524996\pi$
$701$	−4.15400	−0.156895	−0.0784473	+	0.996918i	$0.524996\pi$
$702$	−5.82238	−0.219752
$703$	2.19581	0.0828166
$704$	0.0279175	0.00105218
$705$	−54.5489	−2.05443
$706$	81.7455	3.07653
$707$	20.4869	0.770491
$708$	−48.2944	−1.81502
$709$	−26.0206	−0.977224	−0.488612	−	0.872501i	$-0.662497\pi$
$709$	−26.0206	−0.977224	−0.488612	+	0.872501i	$0.662497\pi$
$710$	−66.8924	−2.51043
$711$	0.299631	0.0112370
$712$	8.82418	0.330700
$713$	32.5237	1.21802
$714$	−68.0405	−2.54635
$715$	−0.293448	−0.0109743
$716$	31.2256	1.16696
$717$	29.6480	1.10723
$718$	81.9153	3.05705
$719$	−41.0509	−1.53094	−0.765471	−	0.643471i	$-0.777494\pi$
$719$	−41.0509	−1.53094	−0.765471	+	0.643471i	$0.777494\pi$
$720$	1.34673	0.0501897
$721$	39.6320	1.47597
$722$	47.2015	1.75666
$723$	−12.9662	−0.482220
$724$	−76.0200	−2.82526
$725$	15.2734	0.567239
$726$	48.0584	1.78362
$727$	46.2007	1.71349	0.856745	−	0.515740i	$-0.172483\pi$
$727$	46.2007	1.71349	0.856745	+	0.515740i	$0.172483\pi$
$728$	12.3439	0.457495
$729$	27.3819	1.01414
$730$	32.6738	1.20931
$731$	−9.65397	−0.357065
$732$	−88.3890	−3.26695
$733$	−0.0509781	−0.00188292	−0.000941460	−	1.00000i	$-0.500300\pi$
$733$	−0.0509781	−0.00188292	−0.000941460		1.00000i	$0.500300\pi$
$734$	10.4732	0.386573
$735$	−95.8427	−3.53521
$736$	23.7873	0.876813
$737$	−1.83756	−0.0676876
$738$	−0.466985	−0.0171900
$739$	−30.8006	−1.13302	−0.566509	−	0.824055i	$-0.691706\pi$
$739$	−30.8006	−1.13302	−0.566509	+	0.824055i	$0.691706\pi$
$740$	−62.2632	−2.28884
$741$	−0.512217	−0.0188168
$742$	−5.20124	−0.190943
$743$	42.0469	1.54255	0.771276	−	0.636501i	$-0.219619\pi$
$743$	42.0469	1.54255	0.771276	+	0.636501i	$0.219619\pi$
$744$	82.4644	3.02329
$745$	−69.8930	−2.56068
$746$	−72.7813	−2.66471
$747$	0.00341680	0.000125014 0
$748$	−2.43253	−0.0889422
$749$	−36.3521	−1.32828
$750$	162.031	5.91654
$751$	−13.6457	−0.497937	−0.248969	−	0.968512i	$-0.580092\pi$
$751$	−13.6457	−0.497937	−0.248969	+	0.968512i	$0.580092\pi$
$752$	52.5969	1.91801
$753$	−33.0559	−1.20462
$754$	1.25092	0.0455559
$755$	−64.8268	−2.35929
$756$	−104.790	−3.81119
$757$	−17.9290	−0.651640	−0.325820	−	0.945432i	$-0.605640\pi$
$757$	−17.9290	−0.651640	−0.325820	+	0.945432i	$0.605640\pi$
$758$	49.5752	1.80065
$759$	1.14978	0.0417342
$760$	18.6046	0.674861
$761$	−25.5211	−0.925138	−0.462569	−	0.886583i	$-0.653072\pi$
$761$	−25.5211	−0.925138	−0.462569	+	0.886583i	$0.653072\pi$
$762$	−29.3107	−1.06181
$763$	61.2837	2.21862
$764$	−22.8264	−0.825831
$765$	0.655895	0.0237139
$766$	54.2425	1.95986
$767$	2.73589	0.0987873
$768$	−49.9188	−1.80129
$769$	9.48352	0.341985	0.170992	−	0.985272i	$-0.445303\pi$
$769$	9.48352	0.341985	0.170992	+	0.985272i	$0.445303\pi$
$770$	−7.63648	−0.275199
$771$	−20.7059	−0.745705
$772$	28.3655	1.02090
$773$	−43.8396	−1.57680	−0.788400	−	0.615163i	$-0.789090\pi$
$773$	−43.8396	−1.57680	−0.788400	+	0.615163i	$0.789090\pi$
$774$	−0.308738	−0.0110973
$775$	−102.941	−3.69777
$776$	120.005	4.30791
$777$	24.7177	0.886743
$778$	49.9092	1.78933
$779$	−2.86066	−0.102494
$780$	14.5241	0.520047
$781$	0.949389	0.0339718
$782$	38.0429	1.36041
$783$	−5.88414	−0.210282
$784$	92.4131	3.30047
$785$	18.5392	0.661694
$786$	10.8784	0.388020
$787$	33.2337	1.18465	0.592327	−	0.805698i	$-0.298209\pi$
$787$	33.2337	1.18465	0.592327	+	0.805698i	$0.298209\pi$
$788$	97.9114	3.48795
$789$	−0.0874693	−0.00311399
$790$	−75.2535	−2.67740
$791$	28.9112	1.02796
$792$	−0.0431047	−0.00153166
$793$	5.00726	0.177813
$794$	6.28485	0.223041
$795$	−3.39100	−0.120266
$796$	−85.4126	−3.02737
$797$	−12.1800	−0.431439	−0.215720	−	0.976455i	$-0.569210\pi$
$797$	−12.1800	−0.431439	−0.215720	+	0.976455i	$0.569210\pi$
$798$	−13.3295	−0.471860
$799$	25.6162	0.906235
$800$	−75.2897	−2.66189
$801$	0.0609446	0.00215337
$802$	33.1706	1.17129
$803$	−0.463732	−0.0163648
$804$	90.9497	3.20755
$805$	82.5977	2.91119
$806$	−8.43112	−0.296974
$807$	−39.0735	−1.37545
$808$	−29.0436	−1.02175
$809$	−30.2868	−1.06483	−0.532413	−	0.846485i	$-0.678715\pi$
$809$	−30.2868	−1.06483	−0.532413	+	0.846485i	$0.678715\pi$
$810$	−97.3437	−3.42031
$811$	−43.0138	−1.51042	−0.755209	−	0.655484i	$-0.772465\pi$
$811$	−43.0138	−1.51042	−0.755209	+	0.655484i	$0.772465\pi$
$812$	22.5139	0.790084
$813$	−22.0599	−0.773676
$814$	1.27773	0.0447845
$815$	−42.4067	−1.48544
$816$	42.7724	1.49733
$817$	−1.89127	−0.0661671
$818$	20.2006	0.706296
$819$	0.0852536	0.00297900
$820$	81.1154	2.83267
$821$	0.153553	0.00535904	0.00267952	−	0.999996i	$-0.499147\pi$
$821$	0.153553	0.00535904	0.00267952	+	0.999996i	$0.499147\pi$
$822$	52.3144	1.82467
$823$	−25.1858	−0.877923	−0.438961	−	0.898506i	$-0.644653\pi$
$823$	−25.1858	−0.877923	−0.438961	+	0.898506i	$0.644653\pi$
$824$	−56.1848	−1.95729
$825$	−3.63918	−0.126700
$826$	71.1967	2.47725
$827$	11.6048	0.403540	0.201770	−	0.979433i	$-0.435331\pi$
$827$	11.6048	0.403540	0.201770	+	0.979433i	$0.435331\pi$
$828$	0.841428	0.0292417
$829$	−7.75696	−0.269410	−0.134705	−	0.990886i	$-0.543009\pi$
$829$	−7.75696	−0.269410	−0.134705	+	0.990886i	$0.543009\pi$
$830$	−0.858145	−0.0297866
$831$	13.6844	0.474707
$832$	0.0782775	0.00271378
$833$	45.0078	1.55943
$834$	−35.8808	−1.24245
$835$	55.3956	1.91704
$836$	−0.476547	−0.0164817
$837$	39.6587	1.37080
$838$	33.5348	1.15844
$839$	−12.0287	−0.415275	−0.207638	−	0.978206i	$-0.566577\pi$
$839$	−12.0287	−0.415275	−0.207638	+	0.978206i	$0.566577\pi$
$840$	209.428	7.22595
$841$	−27.7358	−0.956407
$842$	9.67279	0.333346
$843$	12.4232	0.427876
$844$	−96.0446	−3.30599
$845$	55.2192	1.89960
$846$	0.819215	0.0281652
$847$	−48.9996	−1.68365
$848$	3.26966	0.112281
$849$	−41.7615	−1.43325
$850$	−120.410	−4.13004
$851$	−13.8202	−0.473751
$852$	−46.9897	−1.60984
$853$	43.1426	1.47717	0.738587	−	0.674159i	$-0.235494\pi$
$853$	43.1426	1.47717	0.738587	+	0.674159i	$0.235494\pi$
$854$	130.305	4.45895
$855$	0.128494	0.00439439
$856$	51.5349	1.76143
$857$	−51.8371	−1.77072	−0.885360	−	0.464905i	$-0.846088\pi$
$857$	−51.8371	−1.77072	−0.885360	+	0.464905i	$0.846088\pi$
$858$	−0.298056	−0.0101755
$859$	11.3159	0.386094	0.193047	−	0.981190i	$-0.438163\pi$
$859$	11.3159	0.386094	0.193047	+	0.981190i	$0.438163\pi$
$860$	53.6278	1.82869
$861$	−32.2018	−1.09743
$862$	−74.2703	−2.52966
$863$	−20.5336	−0.698973	−0.349487	−	0.936941i	$-0.613644\pi$
$863$	−20.5336	−0.698973	−0.349487	+	0.936941i	$0.613644\pi$
$864$	29.0057	0.986795
$865$	13.4652	0.457831
$866$	52.9547	1.79947
$867$	−8.39821	−0.285218
$868$	−151.742	−5.15047
$869$	1.06806	0.0362313
$870$	21.2233	0.719537
$871$	−5.15232	−0.174580
$872$	−86.8795	−2.94211
$873$	0.828817	0.0280512
$874$	7.45283	0.252096
$875$	−165.204	−5.58492
$876$	22.9523	0.775486
$877$	−41.2162	−1.39177	−0.695887	−	0.718152i	$-0.744988\pi$
$877$	−41.2162	−1.39177	−0.695887	+	0.718152i	$0.744988\pi$
$878$	−82.5181	−2.78485
$879$	34.6610	1.16909
$880$	4.80053	0.161826
$881$	−18.6329	−0.627759	−0.313879	−	0.949463i	$-0.601629\pi$
$881$	−18.6329	−0.627759	−0.313879	+	0.949463i	$0.601629\pi$
$882$	1.43937	0.0484660
$883$	−27.1431	−0.913439	−0.456719	−	0.889611i	$-0.650976\pi$
$883$	−27.1431	−0.913439	−0.456719	+	0.889611i	$0.650976\pi$
$884$	−6.82054	−0.229400
$885$	46.4175	1.56031
$886$	−91.4405	−3.07200
$887$	−45.6728	−1.53354	−0.766771	−	0.641921i	$-0.778138\pi$
$887$	−45.6728	−1.53354	−0.766771	+	0.641921i	$0.778138\pi$
$888$	−35.0413	−1.17591
$889$	29.8847	1.00230
$890$	−15.3065	−0.513075
$891$	1.38158	0.0462846
$892$	−13.9909	−0.468450
$893$	5.01836	0.167933
$894$	−70.9905	−2.37428
$895$	−30.0120	−1.00319
$896$	51.5246	1.72132
$897$	3.22384	0.107641
$898$	−13.8153	−0.461023
$899$	−8.52055	−0.284176
$900$	−2.66322	−0.0887740
$901$	1.59242	0.0530511
$902$	−1.66460	−0.0554253
$903$	−21.2896	−0.708472
$904$	−40.9863	−1.36318
$905$	73.0654	2.42878
$906$	−65.8447	−2.18754
$907$	11.5849	0.384671	0.192336	−	0.981329i	$-0.438394\pi$
$907$	11.5849	0.384671	0.192336	+	0.981329i	$0.438394\pi$
$908$	−76.7026	−2.54547
$909$	−0.200591	−0.00665317
$910$	−21.4118	−0.709794
$911$	47.0987	1.56045	0.780224	−	0.625500i	$-0.215105\pi$
$911$	47.0987	1.56045	0.780224	+	0.625500i	$0.215105\pi$
$912$	8.37936	0.277468
$913$	0.0121795	0.000403081 0
$914$	−46.3115	−1.53185
$915$	84.9537	2.80848
$916$	−1.47950	−0.0488841
$917$	−11.0914	−0.366272
$918$	46.3887	1.53105
$919$	−40.1343	−1.32391	−0.661955	−	0.749544i	$-0.730273\pi$
$919$	−40.1343	−1.32391	−0.661955	+	0.749544i	$0.730273\pi$
$920$	−117.096	−3.86053
$921$	39.9466	1.31629
$922$	−20.9538	−0.690078
$923$	2.66198	0.0876201
$924$	−5.36437	−0.176475
$925$	43.7426	1.43825
$926$	91.5324	3.00794
$927$	−0.388043	−0.0127450
$928$	−6.23179	−0.204569
$929$	23.0405	0.755934	0.377967	−	0.925819i	$-0.376623\pi$
$929$	23.0405	0.755934	0.377967	+	0.925819i	$0.376623\pi$
$930$	−143.043	−4.69058
$931$	8.81729	0.288975
$932$	−46.3277	−1.51751
$933$	32.0676	1.04985
$934$	−13.7995	−0.451534
$935$	2.33799	0.0764605
$936$	−0.120861	−0.00395046
$937$	−17.4347	−0.569566	−0.284783	−	0.958592i	$-0.591922\pi$
$937$	−17.4347	−0.569566	−0.284783	+	0.958592i	$0.591922\pi$
$938$	−134.080	−4.37787
$939$	−25.8213	−0.842648
$940$	−142.298	−4.64124
$941$	53.1087	1.73129	0.865646	−	0.500656i	$-0.166908\pi$
$941$	53.1087	1.73129	0.865646	+	0.500656i	$0.166908\pi$
$942$	18.8303	0.613526
$943$	18.0047	0.586314
$944$	−44.7565	−1.45670
$945$	100.718	3.27635
$946$	−1.10052	−0.0357810
$947$	37.3833	1.21479	0.607397	−	0.794398i	$-0.292214\pi$
$947$	37.3833	1.21479	0.607397	+	0.794398i	$0.292214\pi$
$948$	−52.8631	−1.71691
$949$	−1.30025	−0.0422080
$950$	−23.5891	−0.765331
$951$	39.6401	1.28542
$952$	−98.3474	−3.18746
$953$	42.5536	1.37844	0.689222	−	0.724550i	$-0.257952\pi$
$953$	42.5536	1.37844	0.689222	+	0.724550i	$0.257952\pi$
$954$	0.0509261	0.00164879
$955$	21.9393	0.709938
$956$	77.3407	2.50138
$957$	−0.301217	−0.00973698
$958$	47.8920	1.54732
$959$	−53.3389	−1.72240
$960$	1.32807	0.0428631
$961$	26.4279	0.852512
$962$	3.58261	0.115508
$963$	0.355928	0.0114696
$964$	−33.8241	−1.08940
$965$	−27.2631	−0.877629
$966$	83.8947	2.69927
$967$	−50.8508	−1.63525	−0.817625	−	0.575751i	$-0.804710\pi$
$967$	−50.8508	−1.63525	−0.817625	+	0.575751i	$0.804710\pi$
$968$	69.4648	2.23268
$969$	4.08098	0.131100
$970$	−208.161	−6.68364
$971$	−30.5656	−0.980898	−0.490449	−	0.871470i	$-0.663167\pi$
$971$	−30.5656	−0.980898	−0.490449	+	0.871470i	$0.663167\pi$
$972$	2.03730	0.0653465
$973$	36.5835	1.17281
$974$	35.0310	1.12246
$975$	−10.2038	−0.326784
$976$	−81.9138	−2.62200
$977$	60.6995	1.94195	0.970974	−	0.239184i	$-0.0768800\pi$
$977$	60.6995	1.94195	0.970974	+	0.239184i	$0.0768800\pi$
$978$	−43.0726	−1.37731
$979$	0.217242	0.00694308
$980$	−250.018	−7.98653
$981$	−0.600037	−0.0191577
$982$	42.1885	1.34629
$983$	12.4331	0.396555	0.198278	−	0.980146i	$-0.436465\pi$
$983$	12.4331	0.396555	0.198278	+	0.980146i	$0.436465\pi$
$984$	45.6512	1.45531
$985$	−94.1060	−2.99847
$986$	−9.96647	−0.317397
$987$	56.4904	1.79811
$988$	−1.33618	−0.0425097
$989$	11.9035	0.378508
$990$	0.0747698	0.00237634
$991$	57.2074	1.81725	0.908627	−	0.417609i	$-0.137132\pi$
$991$	57.2074	1.81725	0.908627	+	0.417609i	$0.137132\pi$
$992$	42.0018	1.33356
$993$	−24.6101	−0.780979
$994$	69.2733	2.19721
$995$	82.0930	2.60252
$996$	−0.602819	−0.0191010
$997$	0.00274358	8.68900e−5 0	4.34450e−5	−	1.00000i	$-0.499986\pi$
$997$	0.00274358	8.68900e−5 0	4.34450e−5		1.00000i	$0.499986\pi$
$998$	−72.2474	−2.28695
$999$	−16.8520	−0.533175

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6007.2.a.b.1.17	✓	237

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6007.2.a.b.1.17	✓	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)

\(f(q)\)	\(=\)	\(q-2.54661 q^{2} +1.71939 q^{3} +4.48524 q^{4} -4.31092 q^{5} -4.37861 q^{6} +4.46436 q^{7} -6.32895 q^{8} -0.0437112 q^{9} +O(q^{10})\)	\(q-2.54661 q^{2} +1.71939 q^{3} +4.48524 q^{4} -4.31092 q^{5} -4.37861 q^{6} +4.46436 q^{7} -6.32895 q^{8} -0.0437112 q^{9} +10.9783 q^{10} -0.155812 q^{11} +7.71186 q^{12} -0.436879 q^{13} -11.3690 q^{14} -7.41214 q^{15} +7.14691 q^{16} +3.48074 q^{17} +0.111315 q^{18} +0.681898 q^{19} -19.3355 q^{20} +7.67596 q^{21} +0.396793 q^{22} -4.29179 q^{23} -10.8819 q^{24} +13.5840 q^{25} +1.11256 q^{26} -5.23331 q^{27} +20.0237 q^{28} +1.12436 q^{29} +18.8759 q^{30} -7.57812 q^{31} -5.54251 q^{32} -0.267901 q^{33} -8.86411 q^{34} -19.2455 q^{35} -0.196055 q^{36} +3.22015 q^{37} -1.73653 q^{38} -0.751163 q^{39} +27.2836 q^{40} -4.19515 q^{41} -19.5477 q^{42} -2.77354 q^{43} -0.698854 q^{44} +0.188435 q^{45} +10.9295 q^{46} +7.35940 q^{47} +12.2883 q^{48} +12.9305 q^{49} -34.5933 q^{50} +5.98474 q^{51} -1.95951 q^{52} +0.457493 q^{53} +13.3272 q^{54} +0.671693 q^{55} -28.2547 q^{56} +1.17245 q^{57} -2.86332 q^{58} -6.26236 q^{59} -33.2452 q^{60} -11.4614 q^{61} +19.2985 q^{62} -0.195142 q^{63} -0.179174 q^{64} +1.88335 q^{65} +0.682240 q^{66} +11.7935 q^{67} +15.6120 q^{68} -7.37925 q^{69} +49.0109 q^{70} -6.09317 q^{71} +0.276646 q^{72} +2.97623 q^{73} -8.20047 q^{74} +23.3562 q^{75} +3.05848 q^{76} -0.695600 q^{77} +1.91292 q^{78} -6.85478 q^{79} -30.8098 q^{80} -8.86696 q^{81} +10.6834 q^{82} -0.0781677 q^{83} +34.4285 q^{84} -15.0052 q^{85} +7.06313 q^{86} +1.93321 q^{87} +0.986126 q^{88} -1.39426 q^{89} -0.479872 q^{90} -1.95038 q^{91} -19.2497 q^{92} -13.0297 q^{93} -18.7415 q^{94} -2.93961 q^{95} -9.52972 q^{96} -18.9612 q^{97} -32.9290 q^{98} +0.00681072 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 237 q - 26 q^{2} - 24 q^{3} + 226 q^{4} - 67 q^{5} - 30 q^{6} - 37 q^{7} - 75 q^{8} + 189 q^{9}+O(q^{10}) \) 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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