LMFDB - Embedded newform 6043.2.a.c.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6043,2,Mod(1,6043)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6043, 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("6043.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6043 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6043.a (trivial)

Newform invariants

comment: select newform

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

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

Self dual:	yes
Analytic conductor:	$48.2535979415$
Analytic rank:	$0$
Dimension:	$259$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	6043.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.74821 q^{2} +2.62862 q^{3} +5.55264 q^{4} +2.51369 q^{5} -7.22400 q^{6} -0.922798 q^{7} -9.76337 q^{8} +3.90966 q^{9} +O(q^{10})$	\(q-2.74821 q^{2} +2.62862 q^{3} +5.55264 q^{4} +2.51369 q^{5} -7.22400 q^{6} -0.922798 q^{7} -9.76337 q^{8} +3.90966 q^{9} -6.90814 q^{10} +3.31634 q^{11} +14.5958 q^{12} +4.36973 q^{13} +2.53604 q^{14} +6.60755 q^{15} +15.7265 q^{16} +3.50840 q^{17} -10.7446 q^{18} +0.325280 q^{19} +13.9576 q^{20} -2.42569 q^{21} -9.11397 q^{22} -6.26816 q^{23} -25.6642 q^{24} +1.31864 q^{25} -12.0089 q^{26} +2.39116 q^{27} -5.12396 q^{28} +7.04779 q^{29} -18.1589 q^{30} -4.55079 q^{31} -23.6929 q^{32} +8.71740 q^{33} -9.64182 q^{34} -2.31963 q^{35} +21.7089 q^{36} +5.99133 q^{37} -0.893936 q^{38} +11.4864 q^{39} -24.5421 q^{40} -5.33541 q^{41} +6.66629 q^{42} +6.97637 q^{43} +18.4144 q^{44} +9.82768 q^{45} +17.2262 q^{46} +8.54603 q^{47} +41.3390 q^{48} -6.14844 q^{49} -3.62390 q^{50} +9.22228 q^{51} +24.2635 q^{52} +3.44518 q^{53} -6.57141 q^{54} +8.33624 q^{55} +9.00962 q^{56} +0.855038 q^{57} -19.3688 q^{58} +3.17937 q^{59} +36.6893 q^{60} -9.32769 q^{61} +12.5065 q^{62} -3.60783 q^{63} +33.6599 q^{64} +10.9842 q^{65} -23.9572 q^{66} -7.00068 q^{67} +19.4809 q^{68} -16.4766 q^{69} +6.37481 q^{70} +5.54485 q^{71} -38.1715 q^{72} +2.50832 q^{73} -16.4654 q^{74} +3.46621 q^{75} +1.80616 q^{76} -3.06031 q^{77} -31.5670 q^{78} +10.2996 q^{79} +39.5315 q^{80} -5.44352 q^{81} +14.6628 q^{82} +8.55587 q^{83} -13.4690 q^{84} +8.81904 q^{85} -19.1725 q^{86} +18.5260 q^{87} -32.3786 q^{88} -7.86462 q^{89} -27.0085 q^{90} -4.03238 q^{91} -34.8048 q^{92} -11.9623 q^{93} -23.4863 q^{94} +0.817653 q^{95} -62.2797 q^{96} -8.68155 q^{97} +16.8972 q^{98} +12.9658 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 259 q + 39 q^{2} + 25 q^{3} + 271 q^{4} + 83 q^{5} + 18 q^{6} + 26 q^{7} + 111 q^{8} + 286 q^{9}+O(q^{10}) $ 259 * q + 39 * q^2 + 25 * q^3 + 271 * q^4 + 83 * q^5 + 18 * q^6 + 26 * q^7 + 111 * q^8 + 286 * q^9	\( 259 q + 39 q^{2} + 25 q^{3} + 271 q^{4} + 83 q^{5} + 18 q^{6} + 26 q^{7} + 111 q^{8} + 286 q^{9} + 36 q^{10} + 35 q^{11} + 58 q^{12} + 109 q^{13} + 31 q^{14} + 30 q^{15} + 287 q^{16} + 124 q^{17} + 97 q^{18} + 42 q^{19} + 149 q^{20} + 99 q^{21} + 22 q^{22} + 63 q^{23} + 53 q^{24} + 308 q^{25} + 86 q^{26} + 82 q^{27} + 52 q^{28} + 131 q^{29} + 6 q^{30} + 29 q^{31} + 251 q^{32} + 147 q^{33} + 24 q^{34} + 79 q^{35} + 315 q^{36} + 108 q^{37} + 124 q^{38} + 48 q^{39} + 87 q^{40} + 190 q^{41} + 28 q^{42} + 36 q^{43} + 70 q^{44} + 211 q^{45} + 19 q^{46} + 186 q^{47} + 103 q^{48} + 297 q^{49} + 161 q^{50} + 20 q^{51} + 173 q^{52} + 213 q^{53} + 56 q^{54} + 35 q^{55} + 99 q^{56} + 80 q^{57} + 32 q^{58} + 135 q^{59} + 23 q^{60} + 83 q^{61} + 172 q^{62} + 85 q^{63} + 297 q^{64} + 177 q^{65} + 41 q^{66} + 30 q^{67} + 271 q^{68} + 168 q^{69} + 24 q^{70} + 63 q^{71} + 241 q^{72} + 152 q^{73} + 32 q^{74} + 36 q^{75} + 92 q^{76} + 396 q^{77} + 21 q^{78} - 2 q^{79} + 242 q^{80} + 343 q^{81} + 40 q^{82} + 236 q^{83} + 92 q^{84} + 124 q^{85} + 55 q^{86} + 113 q^{87} + 7 q^{88} + 214 q^{89} + 100 q^{90} + 2 q^{91} + 176 q^{92} + 228 q^{93} + 51 q^{94} + 96 q^{95} + 48 q^{96} + 135 q^{97} + 261 q^{98} + 26 q^{99}+O(q^{100}) \) 259 * q + 39 * q^2 + 25 * q^3 + 271 * q^4 + 83 * q^5 + 18 * q^6 + 26 * q^7 + 111 * q^8 + 286 * q^9 + 36 * q^10 + 35 * q^11 + 58 * q^12 + 109 * q^13 + 31 * q^14 + 30 * q^15 + 287 * q^16 + 124 * q^17 + 97 * q^18 + 42 * q^19 + 149 * q^20 + 99 * q^21 + 22 * q^22 + 63 * q^23 + 53 * q^24 + 308 * q^25 + 86 * q^26 + 82 * q^27 + 52 * q^28 + 131 * q^29 + 6 * q^30 + 29 * q^31 + 251 * q^32 + 147 * q^33 + 24 * q^34 + 79 * q^35 + 315 * q^36 + 108 * q^37 + 124 * q^38 + 48 * q^39 + 87 * q^40 + 190 * q^41 + 28 * q^42 + 36 * q^43 + 70 * q^44 + 211 * q^45 + 19 * q^46 + 186 * q^47 + 103 * q^48 + 297 * q^49 + 161 * q^50 + 20 * q^51 + 173 * q^52 + 213 * q^53 + 56 * q^54 + 35 * q^55 + 99 * q^56 + 80 * q^57 + 32 * q^58 + 135 * q^59 + 23 * q^60 + 83 * q^61 + 172 * q^62 + 85 * q^63 + 297 * q^64 + 177 * q^65 + 41 * q^66 + 30 * q^67 + 271 * q^68 + 168 * q^69 + 24 * q^70 + 63 * q^71 + 241 * q^72 + 152 * q^73 + 32 * q^74 + 36 * q^75 + 92 * q^76 + 396 * q^77 + 21 * q^78 - 2 * q^79 + 242 * q^80 + 343 * q^81 + 40 * q^82 + 236 * q^83 + 92 * q^84 + 124 * q^85 + 55 * q^86 + 113 * q^87 + 7 * q^88 + 214 * q^89 + 100 * q^90 + 2 * q^91 + 176 * q^92 + 228 * q^93 + 51 * q^94 + 96 * q^95 + 48 * q^96 + 135 * q^97 + 261 * q^98 + 26 * 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 $

$2$	−2.74821	−1.94327	−0.971637	−	0.236475i	$-0.924008\pi$
$2$	−2.74821	−1.94327	−0.971637	+	0.236475i	$0.924008\pi$
$3$	2.62862	1.51764	0.758818	−	0.651302i	$-0.225777\pi$
$3$	2.62862	1.51764	0.758818	+	0.651302i	$0.225777\pi$
$4$	5.55264	2.77632
$5$	2.51369	1.12416	0.562078	−	0.827084i	$-0.310002\pi$
$5$	2.51369	1.12416	0.562078	+	0.827084i	$0.310002\pi$
$6$	−7.22400	−2.94919
$7$	−0.922798	−0.348785	−0.174392	−	0.984676i	$-0.555796\pi$
$7$	−0.922798	−0.348785	−0.174392	+	0.984676i	$0.555796\pi$
$8$	−9.76337	−3.45187
$9$	3.90966	1.30322
$10$	−6.90814	−2.18455
$11$	3.31634	0.999913	0.499956	−	0.866051i	$-0.333349\pi$
$11$	3.31634	0.999913	0.499956	+	0.866051i	$0.333349\pi$
$12$	14.5958	4.21344
$13$	4.36973	1.21195	0.605973	−	0.795485i	$-0.292784\pi$
$13$	4.36973	1.21195	0.605973	+	0.795485i	$0.292784\pi$
$14$	2.53604	0.677785
$15$	6.60755	1.70606
$16$	15.7265	3.93162
$17$	3.50840	0.850913	0.425457	−	0.904979i	$-0.360114\pi$
$17$	3.50840	0.850913	0.425457	+	0.904979i	$0.360114\pi$
$18$	−10.7446	−2.53252
$19$	0.325280	0.0746243	0.0373122	−	0.999304i	$-0.488120\pi$
$19$	0.325280	0.0746243	0.0373122	+	0.999304i	$0.488120\pi$
$20$	13.9576	3.12102
$21$	−2.42569	−0.529328
$22$	−9.11397	−1.94311
$23$	−6.26816	−1.30700	−0.653501	−	0.756926i	$-0.726700\pi$
$23$	−6.26816	−1.30700	−0.653501	+	0.756926i	$0.726700\pi$
$24$	−25.6642	−5.23869
$25$	1.31864	0.263728
$26$	−12.0089	−2.35514
$27$	2.39116	0.460180
$28$	−5.12396	−0.968337
$29$	7.04779	1.30874	0.654371	−	0.756173i	$-0.272933\pi$
$29$	7.04779	1.30874	0.654371	+	0.756173i	$0.272933\pi$
$30$	−18.1589	−3.31535
$31$	−4.55079	−0.817346	−0.408673	−	0.912681i	$-0.634008\pi$
$31$	−4.55079	−0.817346	−0.408673	+	0.912681i	$0.634008\pi$
$32$	−23.6929	−4.18835
$33$	8.71740	1.51750
$34$	−9.64182	−1.65356
$35$	−2.31963	−0.392089
$36$	21.7089	3.61816
$37$	5.99133	0.984969	0.492484	−	0.870321i	$-0.336089\pi$
$37$	5.99133	0.984969	0.492484	+	0.870321i	$0.336089\pi$
$38$	−0.893936	−0.145016
$39$	11.4864	1.83929
$40$	−24.5421	−3.88045
$41$	−5.33541	−0.833251	−0.416625	−	0.909078i	$-0.636787\pi$
$41$	−5.33541	−0.833251	−0.416625	+	0.909078i	$0.636787\pi$
$42$	6.66629	1.02863
$43$	6.97637	1.06389	0.531943	−	0.846780i	$-0.321462\pi$
$43$	6.97637	1.06389	0.531943	+	0.846780i	$0.321462\pi$
$44$	18.4144	2.77608
$45$	9.82768	1.46502
$46$	17.2262	2.53986
$47$	8.54603	1.24657	0.623283	−	0.781996i	$-0.285798\pi$
$47$	8.54603	1.24657	0.623283	+	0.781996i	$0.285798\pi$
$48$	41.3390	5.96677
$49$	−6.14844	−0.878349
$50$	−3.62390	−0.512497
$51$	9.22228	1.29138
$52$	24.2635	3.36475
$53$	3.44518	0.473232	0.236616	−	0.971603i	$-0.423962\pi$
$53$	3.44518	0.473232	0.236616	+	0.971603i	$0.423962\pi$
$54$	−6.57141	−0.894255
$55$	8.33624	1.12406
$56$	9.00962	1.20396
$57$	0.855038	0.113253
$58$	−19.3688	−2.54325
$59$	3.17937	0.413919	0.206959	−	0.978350i	$-0.433643\pi$
$59$	3.17937	0.413919	0.206959	+	0.978350i	$0.433643\pi$
$60$	36.6893	4.73657
$61$	−9.32769	−1.19429	−0.597144	−	0.802134i	$-0.703698\pi$
$61$	−9.32769	−1.19429	−0.597144	+	0.802134i	$0.703698\pi$
$62$	12.5065	1.58833
$63$	−3.60783	−0.454544
$64$	33.6599	4.20749
$65$	10.9842	1.36242
$66$	−23.9572	−2.94893
$67$	−7.00068	−0.855269	−0.427635	−	0.903952i	$-0.640653\pi$
$67$	−7.00068	−0.855269	−0.427635	+	0.903952i	$0.640653\pi$
$68$	19.4809	2.36240
$69$	−16.4766	−1.98355
$70$	6.37481	0.761936
$71$	5.54485	0.658053	0.329027	−	0.944321i	$-0.393279\pi$
$71$	5.54485	0.658053	0.329027	+	0.944321i	$0.393279\pi$
$72$	−38.1715	−4.49855
$73$	2.50832	0.293576	0.146788	−	0.989168i	$-0.453106\pi$
$73$	2.50832	0.293576	0.146788	+	0.989168i	$0.453106\pi$
$74$	−16.4654	−1.91407
$75$	3.46621	0.400244
$76$	1.80616	0.207181
$77$	−3.06031	−0.348754
$78$	−31.5670	−3.57425
$79$	10.2996	1.15880	0.579399	−	0.815044i	$-0.303287\pi$
$79$	10.2996	1.15880	0.579399	+	0.815044i	$0.303287\pi$
$80$	39.5315	4.41976
$81$	−5.44352	−0.604836
$82$	14.6628	1.61924
$83$	8.55587	0.939128	0.469564	−	0.882898i	$-0.344411\pi$
$83$	8.55587	0.939128	0.469564	+	0.882898i	$0.344411\pi$
$84$	−13.4690	−1.46958
$85$	8.81904	0.956560
$86$	−19.1725	−2.06742
$87$	18.5260	1.98620
$88$	−32.3786	−3.45157
$89$	−7.86462	−0.833648	−0.416824	−	0.908987i	$-0.636857\pi$
$89$	−7.86462	−0.833648	−0.416824	+	0.908987i	$0.636857\pi$
$90$	−27.0085	−2.84695
$91$	−4.03238	−0.422708
$92$	−34.8048	−3.62865
$93$	−11.9623	−1.24043
$94$	−23.4863	−2.42242
$95$	0.817653	0.0838894
$96$	−62.2797	−6.35639
$97$	−8.68155	−0.881478	−0.440739	−	0.897635i	$-0.645283\pi$
$97$	−8.68155	−0.881478	−0.440739	+	0.897635i	$0.645283\pi$
$98$	16.8972	1.70687
$99$	12.9658	1.30311
$100$	7.32193	0.732193
$101$	−3.26844	−0.325222	−0.162611	−	0.986690i	$-0.551992\pi$
$101$	−3.26844	−0.325222	−0.162611	+	0.986690i	$0.551992\pi$
$102$	−25.3447	−2.50950
$103$	−9.23072	−0.909530	−0.454765	−	0.890612i	$-0.650277\pi$
$103$	−9.23072	−0.909530	−0.454765	+	0.890612i	$0.650277\pi$
$104$	−42.6633	−4.18348
$105$	−6.09743	−0.595048
$106$	−9.46807	−0.919620
$107$	10.8848	1.05227	0.526134	−	0.850401i	$-0.323641\pi$
$107$	10.8848	1.05227	0.526134	+	0.850401i	$0.323641\pi$
$108$	13.2773	1.27760
$109$	12.4018	1.18788	0.593939	−	0.804510i	$-0.297572\pi$
$109$	12.4018	1.18788	0.593939	+	0.804510i	$0.297572\pi$
$110$	−22.9097	−2.18436
$111$	15.7490	1.49482
$112$	−14.5124	−1.37129
$113$	−5.64250	−0.530802	−0.265401	−	0.964138i	$-0.585504\pi$
$113$	−5.64250	−0.530802	−0.265401	+	0.964138i	$0.585504\pi$
$114$	−2.34982	−0.220081
$115$	−15.7562	−1.46927
$116$	39.1338	3.63348
$117$	17.0842	1.57943
$118$	−8.73756	−0.804358
$119$	−3.23755	−0.296785
$120$	−64.5120	−5.88911
$121$	−0.00191475	−0.000174068 0
$122$	25.6344	2.32083
$123$	−14.0248	−1.26457
$124$	−25.2689	−2.26921
$125$	−9.25380	−0.827685
$126$	9.91505	0.883303
$127$	−8.55125	−0.758800	−0.379400	−	0.925233i	$-0.623870\pi$
$127$	−8.55125	−0.758800	−0.379400	+	0.925233i	$0.623870\pi$
$128$	−45.1187	−3.98796
$129$	18.3382	1.61459
$130$	−30.1867	−2.64755
$131$	12.1265	1.05950	0.529749	−	0.848155i	$-0.322286\pi$
$131$	12.1265	1.05950	0.529749	+	0.848155i	$0.322286\pi$
$132$	48.4045	4.21307
$133$	−0.300167	−0.0260278
$134$	19.2393	1.66202
$135$	6.01064	0.517314
$136$	−34.2539	−2.93724
$137$	−0.108905	−0.00930441	−0.00465220	−	0.999989i	$-0.501481\pi$
$137$	−0.108905	−0.00930441	−0.00465220	+	0.999989i	$0.501481\pi$
$138$	45.2812	3.85459
$139$	12.5523	1.06467	0.532335	−	0.846534i	$-0.321315\pi$
$139$	12.5523	1.06467	0.532335	+	0.846534i	$0.321315\pi$
$140$	−12.8800	−1.08856
$141$	22.4643	1.89184
$142$	−15.2384	−1.27878
$143$	14.4915	1.21184
$144$	61.4853	5.12377
$145$	17.7160	1.47123
$146$	−6.89338	−0.570500
$147$	−16.1619	−1.33302
$148$	33.2677	2.73459
$149$	11.7591	0.963343	0.481672	−	0.876352i	$-0.340030\pi$
$149$	11.7591	0.963343	0.481672	+	0.876352i	$0.340030\pi$
$150$	−9.52586	−0.777784
$151$	5.45352	0.443801	0.221900	−	0.975069i	$-0.428774\pi$
$151$	5.45352	0.443801	0.221900	+	0.975069i	$0.428774\pi$
$152$	−3.17583	−0.257594
$153$	13.7167	1.10893
$154$	8.41035	0.677726
$155$	−11.4393	−0.918825
$156$	63.7797	5.10646
$157$	−13.8266	−1.10348	−0.551740	−	0.834016i	$-0.686036\pi$
$157$	−13.8266	−1.10348	−0.551740	+	0.834016i	$0.686036\pi$
$158$	−28.3055	−2.25186
$159$	9.05609	0.718195
$160$	−59.5566	−4.70836
$161$	5.78424	0.455862
$162$	14.9599	1.17536
$163$	10.3571	0.811231	0.405616	−	0.914044i	$-0.367057\pi$
$163$	10.3571	0.811231	0.405616	+	0.914044i	$0.367057\pi$
$164$	−29.6256	−2.31337
$165$	21.9128	1.70591
$166$	−23.5133	−1.82498
$167$	−4.33970	−0.335816	−0.167908	−	0.985803i	$-0.553701\pi$
$167$	−4.33970	−0.335816	−0.167908	+	0.985803i	$0.553701\pi$
$168$	23.6829	1.82717
$169$	6.09457	0.468813
$170$	−24.2365	−1.85886
$171$	1.27173	0.0972520
$172$	38.7372	2.95369
$173$	−12.8258	−0.975129	−0.487564	−	0.873087i	$-0.662115\pi$
$173$	−12.8258	−0.975129	−0.487564	+	0.873087i	$0.662115\pi$
$174$	−50.9133	−3.85972
$175$	−1.21684	−0.0919844
$176$	52.1543	3.93128
$177$	8.35736	0.628178
$178$	21.6136	1.62001
$179$	9.88069	0.738518	0.369259	−	0.929327i	$-0.379612\pi$
$179$	9.88069	0.738518	0.369259	+	0.929327i	$0.379612\pi$
$180$	54.5695	4.06737
$181$	−6.89058	−0.512173	−0.256086	−	0.966654i	$-0.582433\pi$
$181$	−6.89058	−0.512173	−0.256086	+	0.966654i	$0.582433\pi$
$182$	11.0818	0.821438
$183$	−24.5190	−1.81250
$184$	61.1984	4.51160
$185$	15.0604	1.10726
$186$	32.8749	2.41050
$187$	11.6350	0.850839
$188$	47.4530	3.46087
$189$	−2.20656	−0.160504
$190$	−2.24708	−0.163020
$191$	−18.7659	−1.35786	−0.678928	−	0.734205i	$-0.737555\pi$
$191$	−18.7659	−1.35786	−0.678928	+	0.734205i	$0.737555\pi$
$192$	88.4793	6.38544
$193$	20.2815	1.45989	0.729946	−	0.683505i	$-0.239545\pi$
$193$	20.2815	1.45989	0.729946	+	0.683505i	$0.239545\pi$
$194$	23.8587	1.71295
$195$	28.8732	2.06765
$196$	−34.1401	−2.43858
$197$	5.45965	0.388984	0.194492	−	0.980904i	$-0.437694\pi$
$197$	5.45965	0.388984	0.194492	+	0.980904i	$0.437694\pi$
$198$	−35.6326	−2.53230
$199$	−24.1510	−1.71202	−0.856011	−	0.516958i	$-0.827064\pi$
$199$	−24.1510	−1.71202	−0.856011	+	0.516958i	$0.827064\pi$
$200$	−12.8744	−0.910357
$201$	−18.4022	−1.29799
$202$	8.98235	0.631996
$203$	−6.50369	−0.456469
$204$	51.2079	3.58527
$205$	−13.4116	−0.936704
$206$	25.3679	1.76747
$207$	−24.5064	−1.70331
$208$	68.7206	4.76491
$209$	1.07874	0.0746178
$210$	16.7570	1.15634
$211$	−16.2608	−1.11944	−0.559721	−	0.828681i	$-0.689092\pi$
$211$	−16.2608	−1.11944	−0.559721	+	0.828681i	$0.689092\pi$
$212$	19.1298	1.31384
$213$	14.5753	0.998686
$214$	−29.9135	−2.04485
$215$	17.5364	1.19597
$216$	−23.3458	−1.58848
$217$	4.19946	0.285078
$218$	−34.0827	−2.30837
$219$	6.59343	0.445542
$220$	46.2881	3.12074
$221$	15.3308	1.03126
$222$	−43.2814	−2.90486
$223$	−6.57679	−0.440415	−0.220207	−	0.975453i	$-0.570673\pi$
$223$	−6.57679	−0.440415	−0.220207	+	0.975453i	$0.570673\pi$
$224$	21.8637	1.46083
$225$	5.15544	0.343696
$226$	15.5068	1.03149
$227$	16.1375	1.07108	0.535542	−	0.844508i	$-0.320107\pi$
$227$	16.1375	1.07108	0.535542	+	0.844508i	$0.320107\pi$
$228$	4.74772	0.314425
$229$	20.7159	1.36895	0.684473	−	0.729038i	$-0.260032\pi$
$229$	20.7159	1.36895	0.684473	+	0.729038i	$0.260032\pi$
$230$	43.3013	2.85520
$231$	−8.04440	−0.529282
$232$	−68.8102	−4.51761
$233$	9.53097	0.624395	0.312197	−	0.950017i	$-0.398935\pi$
$233$	9.53097	0.624395	0.312197	+	0.950017i	$0.398935\pi$
$234$	−46.9509	−3.06927
$235$	21.4821	1.40134
$236$	17.6539	1.14917
$237$	27.0739	1.75864
$238$	8.89744	0.576736
$239$	−29.6712	−1.91927	−0.959636	−	0.281244i	$-0.909253\pi$
$239$	−29.6712	−1.91927	−0.959636	+	0.281244i	$0.909253\pi$
$240$	103.914	6.70759
$241$	−11.3199	−0.729181	−0.364590	−	0.931168i	$-0.618791\pi$
$241$	−11.3199	−0.729181	−0.364590	+	0.931168i	$0.618791\pi$
$242$	0.00526212	0.000338262 0
$243$	−21.4825	−1.37810
$244$	−51.7932	−3.31572
$245$	−15.4553	−0.987402
$246$	38.5430	2.45741
$247$	1.42139	0.0904406
$248$	44.4310	2.82137
$249$	22.4902	1.42526
$250$	25.4313	1.60842
$251$	−16.0044	−1.01019	−0.505094	−	0.863065i	$-0.668542\pi$
$251$	−16.0044	−1.01019	−0.505094	+	0.863065i	$0.668542\pi$
$252$	−20.0330	−1.26196
$253$	−20.7873	−1.30689
$254$	23.5006	1.47456
$255$	23.1819	1.45171
$256$	56.6755	3.54222
$257$	21.2130	1.32323	0.661617	−	0.749842i	$-0.269871\pi$
$257$	21.2130	1.32323	0.661617	+	0.749842i	$0.269871\pi$
$258$	−50.3973	−3.13760
$259$	−5.52879	−0.343542
$260$	60.9910	3.78250
$261$	27.5545	1.70558
$262$	−33.3261	−2.05890
$263$	6.85994	0.423002	0.211501	−	0.977378i	$-0.432165\pi$
$263$	6.85994	0.423002	0.211501	+	0.977378i	$0.432165\pi$
$264$	−85.1112	−5.23823
$265$	8.66012	0.531987
$266$	0.824922	0.0505792
$267$	−20.6731	−1.26517
$268$	−38.8722	−2.37450
$269$	10.4016	0.634194	0.317097	−	0.948393i	$-0.397292\pi$
$269$	10.4016	0.634194	0.317097	+	0.948393i	$0.397292\pi$
$270$	−16.5185	−1.00528
$271$	2.93133	0.178066	0.0890329	−	0.996029i	$-0.471622\pi$
$271$	2.93133	0.178066	0.0890329	+	0.996029i	$0.471622\pi$
$272$	55.1749	3.34547
$273$	−10.5996	−0.641518
$274$	0.299294	0.0180810
$275$	4.37306	0.263705
$276$	−91.4887	−5.50697
$277$	1.70900	0.102684	0.0513420	−	0.998681i	$-0.483650\pi$
$277$	1.70900	0.102684	0.0513420	+	0.998681i	$0.483650\pi$
$278$	−34.4963	−2.06895
$279$	−17.7920	−1.06518
$280$	22.6474	1.35344
$281$	−5.52163	−0.329393	−0.164697	−	0.986344i	$-0.552664\pi$
$281$	−5.52163	−0.329393	−0.164697	+	0.986344i	$0.552664\pi$
$282$	−61.7365	−3.67636
$283$	−9.21549	−0.547804	−0.273902	−	0.961758i	$-0.588314\pi$
$283$	−9.21549	−0.547804	−0.273902	+	0.961758i	$0.588314\pi$
$284$	30.7886	1.82696
$285$	2.14930	0.127314
$286$	−39.8256	−2.35494
$287$	4.92350	0.290625
$288$	−92.6312	−5.45834
$289$	−4.69110	−0.275947
$290$	−48.6871	−2.85901
$291$	−22.8205	−1.33776
$292$	13.9278	0.815062
$293$	10.2561	0.599170	0.299585	−	0.954070i	$-0.403152\pi$
$293$	10.2561	0.599170	0.299585	+	0.954070i	$0.403152\pi$
$294$	44.4164	2.59041
$295$	7.99195	0.465309
$296$	−58.4956	−3.39999
$297$	7.92990	0.460139
$298$	−32.3164	−1.87204
$299$	−27.3902	−1.58402
$300$	19.2466	1.11120
$301$	−6.43777	−0.371067
$302$	−14.9874	−0.862427
$303$	−8.59150	−0.493569
$304$	5.11551	0.293395
$305$	−23.4469	−1.34257
$306$	−37.6963	−2.15495
$307$	−33.1200	−1.89026	−0.945128	−	0.326701i	$-0.894063\pi$
$307$	−33.1200	−1.89026	−0.945128	+	0.326701i	$0.894063\pi$
$308$	−16.9928	−0.968253
$309$	−24.2641	−1.38034
$310$	31.4375	1.78553
$311$	−22.1588	−1.25651	−0.628257	−	0.778006i	$-0.716231\pi$
$311$	−22.1588	−1.25651	−0.628257	+	0.778006i	$0.716231\pi$
$312$	−112.146	−6.34901
$313$	19.4380	1.09870	0.549349	−	0.835593i	$-0.314876\pi$
$313$	19.4380	1.09870	0.549349	+	0.835593i	$0.314876\pi$
$314$	37.9982	2.14436
$315$	−9.06896	−0.510978
$316$	57.1901	3.21719
$317$	31.6859	1.77966	0.889829	−	0.456295i	$-0.150824\pi$
$317$	31.6859	1.77966	0.889829	+	0.456295i	$0.150824\pi$
$318$	−24.8880	−1.39565
$319$	23.3729	1.30863
$320$	84.6107	4.72988
$321$	28.6119	1.59696
$322$	−15.8963	−0.885865
$323$	1.14121	0.0634988
$324$	−30.2259	−1.67922
$325$	5.76211	0.319624
$326$	−28.4635	−1.57645
$327$	32.5997	1.80277
$328$	52.0916	2.87628
$329$	−7.88626	−0.434783
$330$	−60.2210	−3.31506
$331$	−12.5007	−0.687100	−0.343550	−	0.939134i	$-0.611630\pi$
$331$	−12.5007	−0.687100	−0.343550	+	0.939134i	$0.611630\pi$
$332$	47.5076	2.60732
$333$	23.4241	1.28363
$334$	11.9264	0.652583
$335$	−17.5975	−0.961457
$336$	−38.1475	−2.08112
$337$	11.2841	0.614685	0.307342	−	0.951599i	$-0.400560\pi$
$337$	11.2841	0.614685	0.307342	+	0.951599i	$0.400560\pi$
$338$	−16.7491	−0.911033
$339$	−14.8320	−0.805564
$340$	48.9689	2.65571
$341$	−15.0919	−0.817274
$342$	−3.49499	−0.188987
$343$	12.1334	0.655139
$344$	−68.1129	−3.67240
$345$	−41.4171	−2.22982
$346$	35.2480	1.89494
$347$	20.4061	1.09546	0.547729	−	0.836656i	$-0.315492\pi$
$347$	20.4061	1.09546	0.547729	+	0.836656i	$0.315492\pi$
$348$	102.868	5.51431
$349$	−4.29364	−0.229833	−0.114917	−	0.993375i	$-0.536660\pi$
$349$	−4.29364	−0.229833	−0.114917	+	0.993375i	$0.536660\pi$
$350$	3.34412	0.178751
$351$	10.4487	0.557713
$352$	−78.5736	−4.18798
$353$	11.9829	0.637787	0.318893	−	0.947791i	$-0.396689\pi$
$353$	11.9829	0.637787	0.318893	+	0.947791i	$0.396689\pi$
$354$	−22.9678	−1.22072
$355$	13.9380	0.739755
$356$	−43.6694	−2.31447
$357$	−8.51029	−0.450412
$358$	−27.1542	−1.43514
$359$	−25.0699	−1.32314	−0.661570	−	0.749884i	$-0.730109\pi$
$359$	−25.0699	−1.32314	−0.661570	+	0.749884i	$0.730109\pi$
$360$	−95.9514	−5.05708
$361$	−18.8942	−0.994431
$362$	18.9367	0.995292
$363$	−0.00503315	−0.000264172 0
$364$	−22.3903	−1.17357
$365$	6.30514	0.330026
$366$	67.3832	3.52218
$367$	20.8443	1.08806	0.544031	−	0.839065i	$-0.316897\pi$
$367$	20.8443	1.08806	0.544031	+	0.839065i	$0.316897\pi$
$368$	−98.5761	−5.13863
$369$	−20.8596	−1.08591
$370$	−41.3890	−2.15171
$371$	−3.17921	−0.165056
$372$	−66.4223	−3.44384
$373$	−21.3326	−1.10456	−0.552280	−	0.833658i	$-0.686242\pi$
$373$	−21.3326	−1.10456	−0.552280	+	0.833658i	$0.686242\pi$
$374$	−31.9755	−1.65341
$375$	−24.3248	−1.25612
$376$	−83.4381	−4.30299
$377$	30.7970	1.58613
$378$	6.06408	0.311903
$379$	23.2334	1.19342	0.596710	−	0.802457i	$-0.296474\pi$
$379$	23.2334	1.19342	0.596710	+	0.802457i	$0.296474\pi$
$380$	4.54013	0.232904
$381$	−22.4780	−1.15158
$382$	51.5727	2.63869
$383$	−2.48568	−0.127012	−0.0635062	−	0.997981i	$-0.520228\pi$
$383$	−2.48568	−0.127012	−0.0635062	+	0.997981i	$0.520228\pi$
$384$	−118.600	−6.05228
$385$	−7.69266	−0.392055
$386$	−55.7377	−2.83697
$387$	27.2752	1.38648
$388$	−48.2055	−2.44726
$389$	32.3646	1.64095	0.820475	−	0.571682i	$-0.193709\pi$
$389$	32.3646	1.64095	0.820475	+	0.571682i	$0.193709\pi$
$390$	−79.3496	−4.01802
$391$	−21.9912	−1.11214
$392$	60.0296	3.03195
$393$	31.8760	1.60793
$394$	−15.0042	−0.755903
$395$	25.8901	1.30267
$396$	71.9941	3.61784
$397$	−10.2995	−0.516916	−0.258458	−	0.966022i	$-0.583214\pi$
$397$	−10.2995	−0.516916	−0.258458	+	0.966022i	$0.583214\pi$
$398$	66.3720	3.32693
$399$	−0.789027	−0.0395008
$400$	20.7376	1.03688
$401$	18.9468	0.946158	0.473079	−	0.881020i	$-0.343143\pi$
$401$	18.9468	0.946158	0.473079	+	0.881020i	$0.343143\pi$
$402$	50.5729	2.52235
$403$	−19.8857	−0.990579
$404$	−18.1485	−0.902919
$405$	−13.6833	−0.679930
$406$	17.8735	0.887045
$407$	19.8693	0.984883
$408$	−90.0405	−4.45767
$409$	−2.54727	−0.125954	−0.0629771	−	0.998015i	$-0.520060\pi$
$409$	−2.54727	−0.125954	−0.0629771	+	0.998015i	$0.520060\pi$
$410$	36.8577	1.82027
$411$	−0.286271	−0.0141207
$412$	−51.2548	−2.52514
$413$	−2.93391	−0.144368
$414$	67.3486	3.31000
$415$	21.5068	1.05573
$416$	−103.532	−5.07605
$417$	32.9952	1.61578
$418$	−2.96459	−0.145003
$419$	−37.0630	−1.81065	−0.905323	−	0.424723i	$-0.860371\pi$
$419$	−37.0630	−1.81065	−0.905323	+	0.424723i	$0.860371\pi$
$420$	−33.8568	−1.65204
$421$	14.0892	0.686664	0.343332	−	0.939214i	$-0.388444\pi$
$421$	14.0892	0.686664	0.343332	+	0.939214i	$0.388444\pi$
$422$	44.6881	2.17538
$423$	33.4121	1.62455
$424$	−33.6366	−1.63354
$425$	4.62633	0.224410
$426$	−40.0560	−1.94072
$427$	8.60757	0.416549
$428$	60.4391	2.92143
$429$	38.0927	1.83913
$430$	−48.1937	−2.32411
$431$	18.3029	0.881621	0.440810	−	0.897600i	$-0.354691\pi$
$431$	18.3029	0.881621	0.440810	+	0.897600i	$0.354691\pi$
$432$	37.6046	1.80925
$433$	−24.2149	−1.16370	−0.581848	−	0.813298i	$-0.697670\pi$
$433$	−24.2149	−1.16370	−0.581848	+	0.813298i	$0.697670\pi$
$434$	−11.5410	−0.553984
$435$	46.5686	2.23279
$436$	68.8627	3.29793
$437$	−2.03890	−0.0975341
$438$	−18.1201	−0.865812
$439$	−11.9885	−0.572181	−0.286090	−	0.958203i	$-0.592356\pi$
$439$	−11.9885	−0.572181	−0.286090	+	0.958203i	$0.592356\pi$
$440$	−81.3899	−3.88011
$441$	−24.0383	−1.14468
$442$	−42.1322	−2.00402
$443$	34.7067	1.64897	0.824483	−	0.565887i	$-0.191466\pi$
$443$	34.7067	1.64897	0.824483	+	0.565887i	$0.191466\pi$
$444$	87.4482	4.15011
$445$	−19.7692	−0.937151
$446$	18.0744	0.855847
$447$	30.9103	1.46201
$448$	−31.0613	−1.46751
$449$	−39.6784	−1.87254	−0.936271	−	0.351280i	$-0.885747\pi$
$449$	−39.6784	−1.87254	−0.936271	+	0.351280i	$0.885747\pi$
$450$	−14.1682	−0.667896
$451$	−17.6940	−0.833178
$452$	−31.3307	−1.47367
$453$	14.3352	0.673529
$454$	−44.3492	−2.08141
$455$	−10.1362	−0.475190
$456$	−8.34806	−0.390934
$457$	−28.5124	−1.33375	−0.666876	−	0.745169i	$-0.732369\pi$
$457$	−28.5124	−1.33375	−0.666876	+	0.745169i	$0.732369\pi$
$458$	−56.9316	−2.66024
$459$	8.38917	0.391573
$460$	−87.4885	−4.07917
$461$	39.2812	1.82951	0.914755	−	0.404010i	$-0.132384\pi$
$461$	39.2812	1.82951	0.914755	+	0.404010i	$0.132384\pi$
$462$	22.1077	1.02854
$463$	−36.3487	−1.68927	−0.844634	−	0.535344i	$-0.820182\pi$
$463$	−36.3487	−1.68927	−0.844634	+	0.535344i	$0.820182\pi$
$464$	110.837	5.14548
$465$	−30.0695	−1.39444
$466$	−26.1931	−1.21337
$467$	20.1926	0.934402	0.467201	−	0.884151i	$-0.345262\pi$
$467$	20.1926	0.934402	0.467201	+	0.884151i	$0.345262\pi$
$468$	94.8623	4.38501
$469$	6.46021	0.298305
$470$	−59.0372	−2.72318
$471$	−36.3448	−1.67468
$472$	−31.0414	−1.42879
$473$	23.1360	1.06379
$474$	−74.4045	−3.41751
$475$	0.428927	0.0196805
$476$	−17.9769	−0.823971
$477$	13.4695	0.616726
$478$	81.5427	3.72967
$479$	−25.6644	−1.17264	−0.586318	−	0.810081i	$-0.699423\pi$
$479$	−25.6644	−1.17264	−0.586318	+	0.810081i	$0.699423\pi$
$480$	−156.552	−7.14558
$481$	26.1805	1.19373
$482$	31.1095	1.41700
$483$	15.2046	0.691833
$484$	−0.0106319	−0.000483268 0
$485$	−21.8227	−0.990919
$486$	59.0382	2.67803
$487$	18.0450	0.817699	0.408849	−	0.912602i	$-0.365930\pi$
$487$	18.0450	0.817699	0.408849	+	0.912602i	$0.365930\pi$
$488$	91.0697	4.12253
$489$	27.2249	1.23115
$490$	42.4743	1.91879
$491$	−31.2762	−1.41147	−0.705737	−	0.708474i	$-0.749384\pi$
$491$	−31.2762	−1.41147	−0.705737	+	0.708474i	$0.749384\pi$
$492$	−77.8745	−3.51085
$493$	24.7265	1.11363
$494$	−3.90626	−0.175751
$495$	32.5919	1.46490
$496$	−71.5679	−3.21349
$497$	−5.11678	−0.229519
$498$	−61.8076	−2.76966
$499$	8.28200	0.370753	0.185377	−	0.982668i	$-0.440649\pi$
$499$	8.28200	0.370753	0.185377	+	0.982668i	$0.440649\pi$
$500$	−51.3830	−2.29792
$501$	−11.4074	−0.509647
$502$	43.9833	1.96307
$503$	9.56435	0.426453	0.213227	−	0.977003i	$-0.431603\pi$
$503$	9.56435	0.426453	0.213227	+	0.977003i	$0.431603\pi$
$504$	35.2246	1.56903
$505$	−8.21585	−0.365600
$506$	57.1278	2.53964
$507$	16.0203	0.711488
$508$	−47.4820	−2.10667
$509$	26.2453	1.16330	0.581651	−	0.813438i	$-0.302407\pi$
$509$	26.2453	1.16330	0.581651	+	0.813438i	$0.302407\pi$
$510$	−63.7088	−2.82107
$511$	−2.31467	−0.102395
$512$	−65.5186	−2.89554
$513$	0.777797	0.0343406
$514$	−58.2978	−2.57141
$515$	−23.2032	−1.02245
$516$	101.826	4.48262
$517$	28.3415	1.24646
$518$	15.1942	0.667597
$519$	−33.7142	−1.47989
$520$	−107.242	−4.70289
$521$	−8.30757	−0.363961	−0.181981	−	0.983302i	$-0.558251\pi$
$521$	−8.30757	−0.363961	−0.181981	+	0.983302i	$0.558251\pi$
$522$	−75.7254	−3.31441
$523$	−27.7112	−1.21173	−0.605863	−	0.795569i	$-0.707172\pi$
$523$	−27.7112	−1.21173	−0.605863	+	0.795569i	$0.707172\pi$
$524$	67.3341	2.94150
$525$	−3.19861	−0.139599
$526$	−18.8525	−0.822010
$527$	−15.9660	−0.695490
$528$	137.094	5.96625
$529$	16.2898	0.708252
$530$	−23.7998	−1.03380
$531$	12.4303	0.539427
$532$	−1.66672	−0.0722615
$533$	−23.3143	−1.00985
$534$	56.8140	2.45858
$535$	27.3609	1.18292
$536$	68.3503	2.95228
$537$	25.9726	1.12080
$538$	−28.5856	−1.23241
$539$	−20.3903	−0.878273
$540$	33.3749	1.43623
$541$	−0.691183	−0.0297163	−0.0148581	−	0.999890i	$-0.504730\pi$
$541$	−0.691183	−0.0297163	−0.0148581	+	0.999890i	$0.504730\pi$
$542$	−8.05591	−0.346031
$543$	−18.1127	−0.777292
$544$	−83.1242	−3.56392
$545$	31.1743	1.33536
$546$	29.1299	1.24664
$547$	−10.6701	−0.456219	−0.228109	−	0.973636i	$-0.573254\pi$
$547$	−10.6701	−0.456219	−0.228109	+	0.973636i	$0.573254\pi$
$548$	−0.604711	−0.0258320
$549$	−36.4681	−1.55642
$550$	−12.0181	−0.512452
$551$	2.29250	0.0976640
$552$	160.867	6.84697
$553$	−9.50447	−0.404171
$554$	−4.69669	−0.199543
$555$	39.5880	1.68042
$556$	69.6983	2.95586
$557$	−3.70007	−0.156777	−0.0783885	−	0.996923i	$-0.524977\pi$
$557$	−3.70007	−0.156777	−0.0783885	+	0.996923i	$0.524977\pi$
$558$	48.8962	2.06994
$559$	30.4849	1.28937
$560$	−36.4796	−1.54154
$561$	30.5842	1.29126
$562$	15.1746	0.640101
$563$	−33.6085	−1.41643	−0.708215	−	0.705997i	$-0.750499\pi$
$563$	−33.6085	−1.41643	−0.708215	+	0.705997i	$0.750499\pi$
$564$	124.736	5.25234
$565$	−14.1835	−0.596704
$566$	25.3261	1.06453
$567$	5.02327	0.210957
$568$	−54.1365	−2.27152
$569$	−26.0591	−1.09245	−0.546227	−	0.837637i	$-0.683936\pi$
$569$	−26.0591	−1.09245	−0.546227	+	0.837637i	$0.683936\pi$
$570$	−5.90672	−0.247405
$571$	6.65298	0.278419	0.139209	−	0.990263i	$-0.455544\pi$
$571$	6.65298	0.278419	0.139209	+	0.990263i	$0.455544\pi$
$572$	80.4660	3.36445
$573$	−49.3286	−2.06073
$574$	−13.5308	−0.564764
$575$	−8.26545	−0.344693
$576$	131.599	5.48329
$577$	5.55262	0.231159	0.115579	−	0.993298i	$-0.463128\pi$
$577$	5.55262	0.231159	0.115579	+	0.993298i	$0.463128\pi$
$578$	12.8921	0.536241
$579$	53.3124	2.21559
$580$	98.3703	4.08461
$581$	−7.89533	−0.327554
$582$	62.7155	2.59964
$583$	11.4254	0.473191
$584$	−24.4897	−1.01339
$585$	42.9444	1.77553
$586$	−28.1860	−1.16435
$587$	34.3351	1.41716	0.708581	−	0.705630i	$-0.249336\pi$
$587$	34.3351	1.41716	0.708581	+	0.705630i	$0.249336\pi$
$588$	−89.7414	−3.70087
$589$	−1.48028	−0.0609938
$590$	−21.9635	−0.904224
$591$	14.3514	0.590336
$592$	94.2226	3.87252
$593$	7.64949	0.314127	0.157064	−	0.987589i	$-0.449797\pi$
$593$	7.64949	0.314127	0.157064	+	0.987589i	$0.449797\pi$
$594$	−21.7930	−0.894177
$595$	−8.13819	−0.333633
$596$	65.2940	2.67455
$597$	−63.4840	−2.59823
$598$	75.2739	3.07818
$599$	−18.7512	−0.766155	−0.383077	−	0.923716i	$-0.625136\pi$
$599$	−18.7512	−0.766155	−0.383077	+	0.923716i	$0.625136\pi$
$600$	−33.8419	−1.38159
$601$	25.2412	1.02961	0.514805	−	0.857307i	$-0.327864\pi$
$601$	25.2412	1.02961	0.514805	+	0.857307i	$0.327864\pi$
$602$	17.6923	0.721085
$603$	−27.3703	−1.11461
$604$	30.2814	1.23213
$605$	−0.00481308	−0.000195680 0
$606$	23.6112	0.959140
$607$	−26.9719	−1.09476	−0.547378	−	0.836886i	$-0.684374\pi$
$607$	−26.9719	−1.09476	−0.547378	+	0.836886i	$0.684374\pi$
$608$	−7.70681	−0.312553
$609$	−17.0957	−0.692755
$610$	64.4370	2.60898
$611$	37.3439	1.51077
$612$	76.1637	3.07874
$613$	−9.83588	−0.397267	−0.198634	−	0.980074i	$-0.563650\pi$
$613$	−9.83588	−0.397267	−0.198634	+	0.980074i	$0.563650\pi$
$614$	91.0205	3.67329
$615$	−35.2540	−1.42158
$616$	29.8789	1.20386
$617$	−3.43188	−0.138162	−0.0690812	−	0.997611i	$-0.522007\pi$
$617$	−3.43188	−0.138162	−0.0690812	+	0.997611i	$0.522007\pi$
$618$	66.6827	2.68237
$619$	−32.7739	−1.31729	−0.658647	−	0.752452i	$-0.728871\pi$
$619$	−32.7739	−1.31729	−0.658647	+	0.752452i	$0.728871\pi$
$620$	−63.5181	−2.55095
$621$	−14.9882	−0.601455
$622$	60.8971	2.44175
$623$	7.25745	0.290764
$624$	180.641	7.23141
$625$	−29.8544	−1.19418
$626$	−53.4195	−2.13507
$627$	2.83559	0.113243
$628$	−76.7739	−3.06361
$629$	21.0200	0.838123
$630$	24.9234	0.992971
$631$	−21.5281	−0.857021	−0.428511	−	0.903537i	$-0.640962\pi$
$631$	−21.5281	−0.857021	−0.428511	+	0.903537i	$0.640962\pi$
$632$	−100.559	−4.00003
$633$	−42.7436	−1.69891
$634$	−87.0794	−3.45836
$635$	−21.4952	−0.853011
$636$	50.2852	1.99394
$637$	−26.8671	−1.06451
$638$	−64.2334	−2.54303
$639$	21.6785	0.857589
$640$	−113.414	−4.48310
$641$	2.36425	0.0933824	0.0466912	−	0.998909i	$-0.485132\pi$
$641$	2.36425	0.0933824	0.0466912	+	0.998909i	$0.485132\pi$
$642$	−78.6315	−3.10334
$643$	24.3639	0.960818	0.480409	−	0.877044i	$-0.340488\pi$
$643$	24.3639	0.960818	0.480409	+	0.877044i	$0.340488\pi$
$644$	32.1178	1.26562
$645$	46.0967	1.81505
$646$	−3.13629	−0.123396
$647$	12.8901	0.506762	0.253381	−	0.967367i	$-0.418457\pi$
$647$	12.8901	0.506762	0.253381	+	0.967367i	$0.418457\pi$
$648$	53.1471	2.08782
$649$	10.5439	0.413883
$650$	−15.8355	−0.621118
$651$	11.0388	0.432644
$652$	57.5092	2.25224
$653$	32.0137	1.25279	0.626396	−	0.779505i	$-0.284529\pi$
$653$	32.0137	1.25279	0.626396	+	0.779505i	$0.284529\pi$
$654$	−89.5907	−3.50327
$655$	30.4823	1.19104
$656$	−83.9072	−3.27603
$657$	9.80668	0.382595
$658$	21.6731	0.844904
$659$	12.4806	0.486174	0.243087	−	0.970005i	$-0.421840\pi$
$659$	12.4806	0.486174	0.243087	+	0.970005i	$0.421840\pi$
$660$	121.674	4.73616
$661$	−12.2392	−0.476048	−0.238024	−	0.971259i	$-0.576500\pi$
$661$	−12.2392	−0.476048	−0.238024	+	0.971259i	$0.576500\pi$
$662$	34.3545	1.33522
$663$	40.2989	1.56508
$664$	−83.5341	−3.24175
$665$	−0.754528	−0.0292593
$666$	−64.3742	−2.49445
$667$	−44.1767	−1.71053
$668$	−24.0968	−0.932332
$669$	−17.2879	−0.668389
$670$	48.3617	1.86837
$671$	−30.9337	−1.19418
$672$	57.4715	2.21701
$673$	−25.0234	−0.964581	−0.482291	−	0.876011i	$-0.660195\pi$
$673$	−25.0234	−0.964581	−0.482291	+	0.876011i	$0.660195\pi$
$674$	−31.0111	−1.19450
$675$	3.15309	0.121362
$676$	33.8409	1.30157
$677$	−21.9053	−0.841890	−0.420945	−	0.907086i	$-0.638302\pi$
$677$	−21.9053	−0.841890	−0.420945	+	0.907086i	$0.638302\pi$
$678$	40.7614	1.56543
$679$	8.01131	0.307446
$680$	−86.1036	−3.30192
$681$	42.4195	1.62552
$682$	41.4758	1.58819
$683$	13.0445	0.499135	0.249567	−	0.968357i	$-0.419712\pi$
$683$	13.0445	0.499135	0.249567	+	0.968357i	$0.419712\pi$
$684$	7.06148	0.270002
$685$	−0.273754	−0.0104596
$686$	−33.3449	−1.27312
$687$	54.4543	2.07756
$688$	109.714	4.18280
$689$	15.0545	0.573532
$690$	113.823	4.33316
$691$	−24.0646	−0.915459	−0.457729	−	0.889092i	$-0.651337\pi$
$691$	−24.0646	−0.915459	−0.457729	+	0.889092i	$0.651337\pi$
$692$	−71.2171	−2.70727
$693$	−11.9648	−0.454504
$694$	−56.0803	−2.12878
$695$	31.5526	1.19686
$696$	−180.876	−6.85610
$697$	−18.7188	−0.709024
$698$	11.7998	0.446629
$699$	25.0533	0.947604
$700$	−6.75666	−0.255378
$701$	−29.5218	−1.11502	−0.557511	−	0.830170i	$-0.688244\pi$
$701$	−29.5218	−1.11502	−0.557511	+	0.830170i	$0.688244\pi$
$702$	−28.7153	−1.08379
$703$	1.94886	0.0735026
$704$	111.628	4.20713
$705$	56.4683	2.12672
$706$	−32.9316	−1.23940
$707$	3.01611	0.113432
$708$	46.4054	1.74402
$709$	−37.1182	−1.39400	−0.697001	−	0.717070i	$-0.745483\pi$
$709$	−37.1182	−1.39400	−0.697001	+	0.717070i	$0.745483\pi$
$710$	−38.3046	−1.43755
$711$	40.2681	1.51017
$712$	76.7852	2.87765
$713$	28.5251	1.06827
$714$	23.3880	0.875275
$715$	36.4272	1.36230
$716$	54.8639	2.05036
$717$	−77.9945	−2.91276
$718$	68.8973	2.57122
$719$	23.8631	0.889943	0.444971	−	0.895545i	$-0.353214\pi$
$719$	23.8631	0.889943	0.444971	+	0.895545i	$0.353214\pi$
$720$	154.555	5.75992
$721$	8.51808	0.317230
$722$	51.9251	1.93245
$723$	−29.7558	−1.10663
$724$	−38.2609	−1.42195
$725$	9.29351	0.345152
$726$	0.0138321	0.000513359 0
$727$	−18.9882	−0.704232	−0.352116	−	0.935956i	$-0.614538\pi$
$727$	−18.9882	−0.704232	−0.352116	+	0.935956i	$0.614538\pi$
$728$	39.3696	1.45914
$729$	−40.1387	−1.48662
$730$	−17.3278	−0.641331
$731$	24.4759	0.905274
$732$	−136.145	−5.03206
$733$	−40.4508	−1.49408	−0.747041	−	0.664777i	$-0.768526\pi$
$733$	−40.4508	−1.49408	−0.747041	+	0.664777i	$0.768526\pi$
$734$	−57.2843	−2.11440
$735$	−40.6261	−1.49852
$736$	148.511	5.47418
$737$	−23.2166	−0.855195
$738$	57.3266	2.11022
$739$	−27.6994	−1.01894	−0.509469	−	0.860489i	$-0.670158\pi$
$739$	−27.6994	−1.01894	−0.509469	+	0.860489i	$0.670158\pi$
$740$	83.6247	3.07410
$741$	3.73629	0.137256
$742$	8.73711	0.320749
$743$	−20.3770	−0.747561	−0.373780	−	0.927517i	$-0.621939\pi$
$743$	−20.3770	−0.747561	−0.373780	+	0.927517i	$0.621939\pi$
$744$	116.792	4.28182
$745$	29.5588	1.08295
$746$	58.6264	2.14647
$747$	33.4506	1.22389
$748$	64.6052	2.36220
$749$	−10.0444	−0.367015
$750$	66.8494	2.44100
$751$	29.7041	1.08392	0.541959	−	0.840405i	$-0.317683\pi$
$751$	29.7041	1.08392	0.541959	+	0.840405i	$0.317683\pi$
$752$	134.399	4.90103
$753$	−42.0695	−1.53310
$754$	−84.6364	−3.08228
$755$	13.7085	0.498902
$756$	−12.2522	−0.445609
$757$	38.1402	1.38623	0.693115	−	0.720827i	$-0.256238\pi$
$757$	38.1402	1.38623	0.693115	+	0.720827i	$0.256238\pi$
$758$	−63.8502	−2.31914
$759$	−54.6420	−1.98338
$760$	−7.98305	−0.289576
$761$	50.1828	1.81912	0.909562	−	0.415567i	$-0.136417\pi$
$761$	50.1828	1.81912	0.909562	+	0.415567i	$0.136417\pi$
$762$	61.7742	2.23784
$763$	−11.4444	−0.414314
$764$	−104.200	−3.76984
$765$	34.4795	1.24661
$766$	6.83116	0.246820
$767$	13.8930	0.501647
$768$	148.979	5.37580
$769$	17.5631	0.633342	0.316671	−	0.948535i	$-0.397435\pi$
$769$	17.5631	0.633342	0.316671	+	0.948535i	$0.397435\pi$
$770$	21.1410	0.761870
$771$	55.7611	2.00819
$772$	112.616	4.05312
$773$	−1.31372	−0.0472514	−0.0236257	−	0.999721i	$-0.507521\pi$
$773$	−1.31372	−0.0472514	−0.0236257	+	0.999721i	$0.507521\pi$
$774$	−74.9580	−2.69431
$775$	−6.00086	−0.215557
$776$	84.7612	3.04275
$777$	−14.5331	−0.521372
$778$	−88.9446	−3.18882
$779$	−1.73550	−0.0621808
$780$	160.322	5.74047
$781$	18.3886	0.657996
$782$	60.4364	2.16120
$783$	16.8524	0.602256
$784$	−96.6934	−3.45334
$785$	−34.7557	−1.24048
$786$	−87.6019	−3.12465
$787$	55.2471	1.96935	0.984674	−	0.174406i	$-0.0558007\pi$
$787$	55.2471	1.96935	0.984674	+	0.174406i	$0.0558007\pi$
$788$	30.3154	1.07994
$789$	18.0322	0.641964
$790$	−71.1513	−2.53145
$791$	5.20689	0.185136
$792$	−126.590	−4.49816
$793$	−40.7595	−1.44741
$794$	28.3051	1.00451
$795$	22.7642	0.807363
$796$	−134.102	−4.75312
$797$	19.2643	0.682375	0.341188	−	0.939995i	$-0.389171\pi$
$797$	19.2643	0.682375	0.341188	+	0.939995i	$0.389171\pi$
$798$	2.16841	0.0767608
$799$	29.9829	1.06072
$800$	−31.2424	−1.10459
$801$	−30.7480	−1.08643
$802$	−52.0697	−1.83865
$803$	8.31843	0.293551
$804$	−102.180	−3.60363
$805$	14.5398	0.512460
$806$	54.6501	1.92497
$807$	27.3418	0.962476
$808$	31.9110	1.12262
$809$	−13.1010	−0.460607	−0.230304	−	0.973119i	$-0.573972\pi$
$809$	−13.1010	−0.460607	−0.230304	+	0.973119i	$0.573972\pi$
$810$	37.6046	1.32129
$811$	40.1284	1.40910	0.704549	−	0.709656i	$-0.251150\pi$
$811$	40.1284	1.40910	0.704549	+	0.709656i	$0.251150\pi$
$812$	−36.1126	−1.26730
$813$	7.70537	0.270239
$814$	−54.6048	−1.91390
$815$	26.0346	0.911951
$816$	145.034	5.07721
$817$	2.26927	0.0793917
$818$	7.00042	0.244764
$819$	−15.7652	−0.550882
$820$	−74.4695	−2.60059
$821$	26.1359	0.912148	0.456074	−	0.889942i	$-0.349255\pi$
$821$	26.1359	0.912148	0.456074	+	0.889942i	$0.349255\pi$
$822$	0.786732	0.0274404
$823$	−50.7793	−1.77005	−0.885027	−	0.465540i	$-0.845860\pi$
$823$	−50.7793	−1.77005	−0.885027	+	0.465540i	$0.845860\pi$
$824$	90.1229	3.13958
$825$	11.4951	0.400209
$826$	8.06300	0.280548
$827$	−38.3426	−1.33330	−0.666651	−	0.745370i	$-0.732273\pi$
$827$	−38.3426	−1.33330	−0.666651	+	0.745370i	$0.732273\pi$
$828$	−136.075	−4.72893
$829$	8.47834	0.294465	0.147232	−	0.989102i	$-0.452963\pi$
$829$	8.47834	0.294465	0.147232	+	0.989102i	$0.452963\pi$
$830$	−59.1051	−2.05157
$831$	4.49232	0.155837
$832$	147.085	5.09925
$833$	−21.5712	−0.747399
$834$	−90.6777	−3.13991
$835$	−10.9087	−0.377510
$836$	5.98983	0.207163
$837$	−10.8817	−0.376126
$838$	101.857	3.51858
$839$	14.2315	0.491324	0.245662	−	0.969356i	$-0.420995\pi$
$839$	14.2315	0.491324	0.245662	+	0.969356i	$0.420995\pi$
$840$	59.5315	2.05403
$841$	20.6714	0.712807
$842$	−38.7200	−1.33438
$843$	−14.5143	−0.499899
$844$	−90.2905	−3.10793
$845$	15.3199	0.527020
$846$	−91.8234	−3.15695
$847$	0.00176692	6.07122e−5 0
$848$	54.1806	1.86057
$849$	−24.2240	−0.831367
$850$	−12.7141	−0.436090
$851$	−37.5546	−1.28736
$852$	80.9315	2.77267
$853$	25.1430	0.860880	0.430440	−	0.902619i	$-0.358358\pi$
$853$	25.1430	0.860880	0.430440	+	0.902619i	$0.358358\pi$
$854$	−23.6554	−0.809470
$855$	3.19675	0.109326
$856$	−106.272	−3.63230
$857$	6.41948	0.219285	0.109643	−	0.993971i	$-0.465029\pi$
$857$	6.41948	0.219285	0.109643	+	0.993971i	$0.465029\pi$
$858$	−104.687	−3.57394
$859$	−51.3153	−1.75085	−0.875427	−	0.483350i	$-0.839420\pi$
$859$	−51.3153	−1.75085	−0.875427	+	0.483350i	$0.839420\pi$
$860$	97.3734	3.32040
$861$	12.9420	0.441063
$862$	−50.3002	−1.71323
$863$	23.4900	0.799607	0.399804	−	0.916601i	$-0.369078\pi$
$863$	23.4900	0.799607	0.399804	+	0.916601i	$0.369078\pi$
$864$	−56.6535	−1.92739
$865$	−32.2401	−1.09620
$866$	66.5476	2.26138
$867$	−12.3311	−0.418787
$868$	23.3180	0.791466
$869$	34.1570	1.15870
$870$	−127.980	−4.33893
$871$	−30.5911	−1.03654
$872$	−121.084	−4.10041
$873$	−33.9419	−1.14876
$874$	5.60333	0.189535
$875$	8.53938	0.288684
$876$	36.6109	1.23697
$877$	27.3495	0.923529	0.461764	−	0.887003i	$-0.347217\pi$
$877$	27.3495	0.923529	0.461764	+	0.887003i	$0.347217\pi$
$878$	32.9469	1.11190
$879$	26.9595	0.909322
$880$	131.100	4.41937
$881$	−4.38114	−0.147604	−0.0738022	−	0.997273i	$-0.523513\pi$
$881$	−4.38114	−0.147604	−0.0738022	+	0.997273i	$0.523513\pi$
$882$	66.0623	2.22443
$883$	−40.5728	−1.36538	−0.682692	−	0.730706i	$-0.739191\pi$
$883$	−40.5728	−1.36538	−0.682692	+	0.730706i	$0.739191\pi$
$884$	85.1263	2.86311
$885$	21.0078	0.706171
$886$	−95.3812	−3.20439
$887$	−51.1305	−1.71680	−0.858398	−	0.512985i	$-0.828540\pi$
$887$	−51.1305	−1.71680	−0.858398	+	0.512985i	$0.828540\pi$
$888$	−153.763	−5.15995
$889$	7.89107	0.264658
$890$	54.3299	1.82114
$891$	−18.0525	−0.604783
$892$	−36.5185	−1.22273
$893$	2.77985	0.0930242
$894$	−84.9478	−2.84108
$895$	24.8370	0.830210
$896$	41.6354	1.39094
$897$	−71.9985	−2.40396
$898$	109.045	3.63886
$899$	−32.0730	−1.06969
$900$	28.6263	0.954210
$901$	12.0871	0.402679
$902$	48.6268	1.61909
$903$	−16.9225	−0.563145
$904$	55.0898	1.83226
$905$	−17.3208	−0.575762
$906$	−39.3962	−1.30885
$907$	−7.06665	−0.234644	−0.117322	−	0.993094i	$-0.537431\pi$
$907$	−7.06665	−0.234644	−0.117322	+	0.993094i	$0.537431\pi$
$908$	89.6057	2.97367
$909$	−12.7785	−0.423836
$910$	27.8562	0.923425
$911$	30.6034	1.01394	0.506969	−	0.861964i	$-0.330766\pi$
$911$	30.6034	1.01394	0.506969	+	0.861964i	$0.330766\pi$
$912$	13.4467	0.445266
$913$	28.3741	0.939047
$914$	78.3578	2.59185
$915$	−61.6331	−2.03753
$916$	115.028	3.80063
$917$	−11.1903	−0.369537
$918$	−23.0552	−0.760934
$919$	35.2418	1.16252	0.581259	−	0.813718i	$-0.302560\pi$
$919$	35.2418	1.16252	0.581259	+	0.813718i	$0.302560\pi$
$920$	153.834	5.07175
$921$	−87.0599	−2.86872
$922$	−107.953	−3.55524
$923$	24.2295	0.797525
$924$	−44.6676	−1.46946
$925$	7.90042	0.259764
$926$	99.8937	3.28271
$927$	−36.0890	−1.18532
$928$	−166.983	−5.48147
$929$	27.8982	0.915310	0.457655	−	0.889130i	$-0.348689\pi$
$929$	27.8982	0.915310	0.457655	+	0.889130i	$0.348689\pi$
$930$	82.6373	2.70978
$931$	−1.99996	−0.0655462
$932$	52.9220	1.73352
$933$	−58.2473	−1.90693
$934$	−55.4934	−1.81580
$935$	29.2469	0.956476
$936$	−166.799	−5.45201
$937$	59.0849	1.93022	0.965110	−	0.261844i	$-0.0843305\pi$
$937$	59.0849	1.93022	0.965110	+	0.261844i	$0.0843305\pi$
$938$	−17.7540	−0.579688
$939$	51.0951	1.66742
$940$	119.282	3.89056
$941$	20.8953	0.681169	0.340584	−	0.940214i	$-0.389375\pi$
$941$	20.8953	0.681169	0.340584	+	0.940214i	$0.389375\pi$
$942$	99.8831	3.25437
$943$	33.4432	1.08906
$944$	50.0003	1.62737
$945$	−5.54661	−0.180431
$946$	−63.5824	−2.06724
$947$	−53.8938	−1.75131	−0.875656	−	0.482935i	$-0.839571\pi$
$947$	−53.8938	−1.75131	−0.875656	+	0.482935i	$0.839571\pi$
$948$	150.331	4.88253
$949$	10.9607	0.355799
$950$	−1.17878	−0.0382447
$951$	83.2903	2.70087
$952$	31.6094	1.02447
$953$	24.1663	0.782822	0.391411	−	0.920216i	$-0.371987\pi$
$953$	24.1663	0.782822	0.391411	+	0.920216i	$0.371987\pi$
$954$	−37.0170	−1.19847
$955$	−47.1718	−1.52644
$956$	−164.754	−5.32851
$957$	61.4384	1.98602
$958$	70.5310	2.27875
$959$	0.100498	0.00324523
$960$	222.410	7.17824
$961$	−10.2903	−0.331946
$962$	−71.9495	−2.31974
$963$	42.5557	1.37134
$964$	−62.8554	−2.02444
$965$	50.9813	1.64115
$966$	−41.7853	−1.34442
$967$	5.86911	0.188738	0.0943690	−	0.995537i	$-0.469917\pi$
$967$	5.86911	0.188738	0.0943690	+	0.995537i	$0.469917\pi$
$968$	0.0186944	0.000600860 0
$969$	2.99982	0.0963681
$970$	59.9733	1.92563
$971$	4.37585	0.140428	0.0702138	−	0.997532i	$-0.477632\pi$
$971$	4.37585	0.140428	0.0702138	+	0.997532i	$0.477632\pi$
$972$	−119.284	−3.82604
$973$	−11.5832	−0.371341
$974$	−49.5915	−1.58901
$975$	15.1464	0.485074
$976$	−146.692	−4.69549
$977$	−6.35142	−0.203200	−0.101600	−	0.994825i	$-0.532396\pi$
$977$	−6.35142	−0.203200	−0.101600	+	0.994825i	$0.532396\pi$
$978$	−74.8197	−2.39247
$979$	−26.0817	−0.833575
$980$	−85.8176	−2.74134
$981$	48.4869	1.54807
$982$	85.9534	2.74288
$983$	21.9089	0.698784	0.349392	−	0.936977i	$-0.386388\pi$
$983$	21.9089	0.698784	0.349392	+	0.936977i	$0.386388\pi$
$984$	136.929	4.36514
$985$	13.7239	0.437279
$986$	−67.9535	−2.16408
$987$	−20.7300	−0.659843
$988$	7.89244	0.251092
$989$	−43.7290	−1.39050
$990$	−89.5693	−2.84670
$991$	36.8363	1.17014	0.585072	−	0.810981i	$-0.301066\pi$
$991$	36.8363	1.17014	0.585072	+	0.810981i	$0.301066\pi$
$992$	107.821	3.42333
$993$	−32.8596	−1.04277
$994$	14.0620	0.446018
$995$	−60.7083	−1.92458
$996$	124.880	3.95696
$997$	−1.74513	−0.0552690	−0.0276345	−	0.999618i	$-0.508797\pi$
$997$	−1.74513	−0.0552690	−0.0276345	+	0.999618i	$0.508797\pi$
$998$	−22.7607	−0.720476
$999$	14.3262	0.453262

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6043.2.a.c.1.1	✓	259

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6043.2.a.c.1.1	✓	259	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:	\( N \)	\(=\)	\( 6043 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6043.a (trivial)

\(f(q)\)	\(=\)	\(q-2.74821 q^{2} +2.62862 q^{3} +5.55264 q^{4} +2.51369 q^{5} -7.22400 q^{6} -0.922798 q^{7} -9.76337 q^{8} +3.90966 q^{9} +O(q^{10})\)	\(q-2.74821 q^{2} +2.62862 q^{3} +5.55264 q^{4} +2.51369 q^{5} -7.22400 q^{6} -0.922798 q^{7} -9.76337 q^{8} +3.90966 q^{9} -6.90814 q^{10} +3.31634 q^{11} +14.5958 q^{12} +4.36973 q^{13} +2.53604 q^{14} +6.60755 q^{15} +15.7265 q^{16} +3.50840 q^{17} -10.7446 q^{18} +0.325280 q^{19} +13.9576 q^{20} -2.42569 q^{21} -9.11397 q^{22} -6.26816 q^{23} -25.6642 q^{24} +1.31864 q^{25} -12.0089 q^{26} +2.39116 q^{27} -5.12396 q^{28} +7.04779 q^{29} -18.1589 q^{30} -4.55079 q^{31} -23.6929 q^{32} +8.71740 q^{33} -9.64182 q^{34} -2.31963 q^{35} +21.7089 q^{36} +5.99133 q^{37} -0.893936 q^{38} +11.4864 q^{39} -24.5421 q^{40} -5.33541 q^{41} +6.66629 q^{42} +6.97637 q^{43} +18.4144 q^{44} +9.82768 q^{45} +17.2262 q^{46} +8.54603 q^{47} +41.3390 q^{48} -6.14844 q^{49} -3.62390 q^{50} +9.22228 q^{51} +24.2635 q^{52} +3.44518 q^{53} -6.57141 q^{54} +8.33624 q^{55} +9.00962 q^{56} +0.855038 q^{57} -19.3688 q^{58} +3.17937 q^{59} +36.6893 q^{60} -9.32769 q^{61} +12.5065 q^{62} -3.60783 q^{63} +33.6599 q^{64} +10.9842 q^{65} -23.9572 q^{66} -7.00068 q^{67} +19.4809 q^{68} -16.4766 q^{69} +6.37481 q^{70} +5.54485 q^{71} -38.1715 q^{72} +2.50832 q^{73} -16.4654 q^{74} +3.46621 q^{75} +1.80616 q^{76} -3.06031 q^{77} -31.5670 q^{78} +10.2996 q^{79} +39.5315 q^{80} -5.44352 q^{81} +14.6628 q^{82} +8.55587 q^{83} -13.4690 q^{84} +8.81904 q^{85} -19.1725 q^{86} +18.5260 q^{87} -32.3786 q^{88} -7.86462 q^{89} -27.0085 q^{90} -4.03238 q^{91} -34.8048 q^{92} -11.9623 q^{93} -23.4863 q^{94} +0.817653 q^{95} -62.2797 q^{96} -8.68155 q^{97} +16.8972 q^{98} +12.9658 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 259 q + 39 q^{2} + 25 q^{3} + 271 q^{4} + 83 q^{5} + 18 q^{6} + 26 q^{7} + 111 q^{8} + 286 q^{9}+O(q^{10}) \) 259 * q + 39 * q^2 + 25 * q^3 + 271 * q^4 + 83 * q^5 + 18 * q^6 + 26 * q^7 + 111 * q^8 + 286 * q^9	\( 259 q + 39 q^{2} + 25 q^{3} + 271 q^{4} + 83 q^{5} + 18 q^{6} + 26 q^{7} + 111 q^{8} + 286 q^{9} + 36 q^{10} + 35 q^{11} + 58 q^{12} + 109 q^{13} + 31 q^{14} + 30 q^{15} + 287 q^{16} + 124 q^{17} + 97 q^{18} + 42 q^{19} + 149 q^{20} + 99 q^{21} + 22 q^{22} + 63 q^{23} + 53 q^{24} + 308 q^{25} + 86 q^{26} + 82 q^{27} + 52 q^{28} + 131 q^{29} + 6 q^{30} + 29 q^{31} + 251 q^{32} + 147 q^{33} + 24 q^{34} + 79 q^{35} + 315 q^{36} + 108 q^{37} + 124 q^{38} + 48 q^{39} + 87 q^{40} + 190 q^{41} + 28 q^{42} + 36 q^{43} + 70 q^{44} + 211 q^{45} + 19 q^{46} + 186 q^{47} + 103 q^{48} + 297 q^{49} + 161 q^{50} + 20 q^{51} + 173 q^{52} + 213 q^{53} + 56 q^{54} + 35 q^{55} + 99 q^{56} + 80 q^{57} + 32 q^{58} + 135 q^{59} + 23 q^{60} + 83 q^{61} + 172 q^{62} + 85 q^{63} + 297 q^{64} + 177 q^{65} + 41 q^{66} + 30 q^{67} + 271 q^{68} + 168 q^{69} + 24 q^{70} + 63 q^{71} + 241 q^{72} + 152 q^{73} + 32 q^{74} + 36 q^{75} + 92 q^{76} + 396 q^{77} + 21 q^{78} - 2 q^{79} + 242 q^{80} + 343 q^{81} + 40 q^{82} + 236 q^{83} + 92 q^{84} + 124 q^{85} + 55 q^{86} + 113 q^{87} + 7 q^{88} + 214 q^{89} + 100 q^{90} + 2 q^{91} + 176 q^{92} + 228 q^{93} + 51 q^{94} + 96 q^{95} + 48 q^{96} + 135 q^{97} + 261 q^{98} + 26 q^{99}+O(q^{100}) \) 259 * q + 39 * q^2 + 25 * q^3 + 271 * q^4 + 83 * q^5 + 18 * q^6 + 26 * q^7 + 111 * q^8 + 286 * q^9 + 36 * q^10 + 35 * q^11 + 58 * q^12 + 109 * q^13 + 31 * q^14 + 30 * q^15 + 287 * q^16 + 124 * q^17 + 97 * q^18 + 42 * q^19 + 149 * q^20 + 99 * q^21 + 22 * q^22 + 63 * q^23 + 53 * q^24 + 308 * q^25 + 86 * q^26 + 82 * q^27 + 52 * q^28 + 131 * q^29 + 6 * q^30 + 29 * q^31 + 251 * q^32 + 147 * q^33 + 24 * q^34 + 79 * q^35 + 315 * q^36 + 108 * q^37 + 124 * q^38 + 48 * q^39 + 87 * q^40 + 190 * q^41 + 28 * q^42 + 36 * q^43 + 70 * q^44 + 211 * q^45 + 19 * q^46 + 186 * q^47 + 103 * q^48 + 297 * q^49 + 161 * q^50 + 20 * q^51 + 173 * q^52 + 213 * q^53 + 56 * q^54 + 35 * q^55 + 99 * q^56 + 80 * q^57 + 32 * q^58 + 135 * q^59 + 23 * q^60 + 83 * q^61 + 172 * q^62 + 85 * q^63 + 297 * q^64 + 177 * q^65 + 41 * q^66 + 30 * q^67 + 271 * q^68 + 168 * q^69 + 24 * q^70 + 63 * q^71 + 241 * q^72 + 152 * q^73 + 32 * q^74 + 36 * q^75 + 92 * q^76 + 396 * q^77 + 21 * q^78 - 2 * q^79 + 242 * q^80 + 343 * q^81 + 40 * q^82 + 236 * q^83 + 92 * q^84 + 124 * q^85 + 55 * q^86 + 113 * q^87 + 7 * q^88 + 214 * q^89 + 100 * q^90 + 2 * q^91 + 176 * q^92 + 228 * q^93 + 51 * q^94 + 96 * q^95 + 48 * q^96 + 135 * q^97 + 261 * q^98 + 26 * q^99

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