LMFDB - Embedded newform 4013.2.a.c.1.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4013,2,Mod(1,4013)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4013, 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("4013.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4013 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4013.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:	$32.0439663311$
Analytic rank:	$0$
Dimension:	$176$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.7
Character	$\chi$	$=$	4013.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.63729 q^{2} +1.99604 q^{3} +4.95530 q^{4} -2.90741 q^{5} -5.26413 q^{6} +3.48548 q^{7} -7.79400 q^{8} +0.984162 q^{9} +O(q^{10})$	\(q-2.63729 q^{2} +1.99604 q^{3} +4.95530 q^{4} -2.90741 q^{5} -5.26413 q^{6} +3.48548 q^{7} -7.79400 q^{8} +0.984162 q^{9} +7.66769 q^{10} -4.95478 q^{11} +9.89097 q^{12} -4.04969 q^{13} -9.19222 q^{14} -5.80330 q^{15} +10.6444 q^{16} +0.154371 q^{17} -2.59552 q^{18} +0.682953 q^{19} -14.4071 q^{20} +6.95715 q^{21} +13.0672 q^{22} +0.607940 q^{23} -15.5571 q^{24} +3.45304 q^{25} +10.6802 q^{26} -4.02369 q^{27} +17.2716 q^{28} +0.135779 q^{29} +15.3050 q^{30} +3.48959 q^{31} -12.4845 q^{32} -9.88993 q^{33} -0.407121 q^{34} -10.1337 q^{35} +4.87682 q^{36} -3.57078 q^{37} -1.80115 q^{38} -8.08333 q^{39} +22.6604 q^{40} -2.02330 q^{41} -18.3480 q^{42} -1.01463 q^{43} -24.5525 q^{44} -2.86136 q^{45} -1.60332 q^{46} -0.259199 q^{47} +21.2467 q^{48} +5.14857 q^{49} -9.10666 q^{50} +0.308130 q^{51} -20.0674 q^{52} +9.03516 q^{53} +10.6116 q^{54} +14.4056 q^{55} -27.1658 q^{56} +1.36320 q^{57} -0.358088 q^{58} +6.98583 q^{59} -28.7571 q^{60} +8.08766 q^{61} -9.20307 q^{62} +3.43028 q^{63} +11.6363 q^{64} +11.7741 q^{65} +26.0826 q^{66} +13.0891 q^{67} +0.764954 q^{68} +1.21347 q^{69} +26.7256 q^{70} -11.1324 q^{71} -7.67056 q^{72} -8.45075 q^{73} +9.41719 q^{74} +6.89238 q^{75} +3.38424 q^{76} -17.2698 q^{77} +21.3181 q^{78} -0.383966 q^{79} -30.9477 q^{80} -10.9839 q^{81} +5.33604 q^{82} +9.61858 q^{83} +34.4748 q^{84} -0.448819 q^{85} +2.67587 q^{86} +0.271020 q^{87} +38.6176 q^{88} +5.16555 q^{89} +7.54625 q^{90} -14.1151 q^{91} +3.01253 q^{92} +6.96536 q^{93} +0.683583 q^{94} -1.98563 q^{95} -24.9195 q^{96} -2.46812 q^{97} -13.5783 q^{98} -4.87631 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 176 q + 11 q^{2} + 53 q^{3} + 191 q^{4} + 5 q^{5} + 19 q^{6} + 46 q^{7} + 36 q^{8} + 193 q^{9}+O(q^{10}) $ 176 * q + 11 * q^2 + 53 * q^3 + 191 * q^4 + 5 * q^5 + 19 * q^6 + 46 * q^7 + 36 * q^8 + 193 * q^9	\( 176 q + 11 q^{2} + 53 q^{3} + 191 q^{4} + 5 q^{5} + 19 q^{6} + 46 q^{7} + 36 q^{8} + 193 q^{9} + 43 q^{10} + 18 q^{11} + 95 q^{12} + 95 q^{13} + 2 q^{14} + 36 q^{15} + 225 q^{16} + 35 q^{17} + 46 q^{18} + 127 q^{19} + 4 q^{20} + 32 q^{21} + 60 q^{22} + 35 q^{23} + 26 q^{24} + 207 q^{25} + 19 q^{26} + 191 q^{27} + 87 q^{28} + 16 q^{29} + 28 q^{30} + 93 q^{31} + 73 q^{32} + 70 q^{33} + 45 q^{34} + 73 q^{35} + 206 q^{36} + 64 q^{37} + 35 q^{38} + 72 q^{39} + 139 q^{40} + 19 q^{41} + 35 q^{42} + 261 q^{43} + 11 q^{44} + 12 q^{45} + 58 q^{46} + 40 q^{47} + 130 q^{48} + 234 q^{49} - 14 q^{50} + 76 q^{51} + 263 q^{52} + 17 q^{53} + 28 q^{54} + 170 q^{55} - 10 q^{56} + 60 q^{57} + 52 q^{58} + 69 q^{59} + 37 q^{60} + 110 q^{61} + 71 q^{62} + 101 q^{63} + 250 q^{64} - q^{65} + 43 q^{66} + 190 q^{67} + 48 q^{68} + 45 q^{69} + 14 q^{70} + 9 q^{71} + 98 q^{72} + 182 q^{73} - 23 q^{74} + 219 q^{75} + 197 q^{76} + 25 q^{77} - 26 q^{78} + 105 q^{79} + 20 q^{80} + 236 q^{81} + 107 q^{82} + 130 q^{83} + 38 q^{84} + 73 q^{85} - 24 q^{86} + 171 q^{87} + 165 q^{88} + 40 q^{89} + 45 q^{90} + 182 q^{91} - 4 q^{92} + 23 q^{93} + 98 q^{94} + 30 q^{95} - 2 q^{96} + 168 q^{97} + 82 q^{98} + 50 q^{99}+O(q^{100}) \) 176 * q + 11 * q^2 + 53 * q^3 + 191 * q^4 + 5 * q^5 + 19 * q^6 + 46 * q^7 + 36 * q^8 + 193 * q^9 + 43 * q^10 + 18 * q^11 + 95 * q^12 + 95 * q^13 + 2 * q^14 + 36 * q^15 + 225 * q^16 + 35 * q^17 + 46 * q^18 + 127 * q^19 + 4 * q^20 + 32 * q^21 + 60 * q^22 + 35 * q^23 + 26 * q^24 + 207 * q^25 + 19 * q^26 + 191 * q^27 + 87 * q^28 + 16 * q^29 + 28 * q^30 + 93 * q^31 + 73 * q^32 + 70 * q^33 + 45 * q^34 + 73 * q^35 + 206 * q^36 + 64 * q^37 + 35 * q^38 + 72 * q^39 + 139 * q^40 + 19 * q^41 + 35 * q^42 + 261 * q^43 + 11 * q^44 + 12 * q^45 + 58 * q^46 + 40 * q^47 + 130 * q^48 + 234 * q^49 - 14 * q^50 + 76 * q^51 + 263 * q^52 + 17 * q^53 + 28 * q^54 + 170 * q^55 - 10 * q^56 + 60 * q^57 + 52 * q^58 + 69 * q^59 + 37 * q^60 + 110 * q^61 + 71 * q^62 + 101 * q^63 + 250 * q^64 - q^65 + 43 * q^66 + 190 * q^67 + 48 * q^68 + 45 * q^69 + 14 * q^70 + 9 * q^71 + 98 * q^72 + 182 * q^73 - 23 * q^74 + 219 * q^75 + 197 * q^76 + 25 * q^77 - 26 * q^78 + 105 * q^79 + 20 * q^80 + 236 * q^81 + 107 * q^82 + 130 * q^83 + 38 * q^84 + 73 * q^85 - 24 * q^86 + 171 * q^87 + 165 * q^88 + 40 * q^89 + 45 * q^90 + 182 * q^91 - 4 * q^92 + 23 * q^93 + 98 * q^94 + 30 * q^95 - 2 * q^96 + 168 * q^97 + 82 * q^98 + 50 * 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 $

$2$	−2.63729	−1.86485	−0.932423	−	0.361368i	$-0.882310\pi$
$2$	−2.63729	−1.86485	−0.932423	+	0.361368i	$0.882310\pi$
$3$	1.99604	1.15241	0.576206	−	0.817304i	$-0.304533\pi$
$3$	1.99604	1.15241	0.576206	+	0.817304i	$0.304533\pi$
$4$	4.95530	2.47765
$5$	−2.90741	−1.30023	−0.650117	−	0.759834i	$-0.725280\pi$
$5$	−2.90741	−1.30023	−0.650117	+	0.759834i	$0.725280\pi$
$6$	−5.26413	−2.14907
$7$	3.48548	1.31739	0.658694	−	0.752411i	$-0.271109\pi$
$7$	3.48548	1.31739	0.658694	+	0.752411i	$0.271109\pi$
$8$	−7.79400	−2.75559
$9$	0.984162	0.328054
$10$	7.66769	2.42474
$11$	−4.95478	−1.49392	−0.746961	−	0.664867i	$-0.768488\pi$
$11$	−4.95478	−1.49392	−0.746961	+	0.664867i	$0.768488\pi$
$12$	9.89097	2.85528
$13$	−4.04969	−1.12318	−0.561591	−	0.827415i	$-0.689811\pi$
$13$	−4.04969	−1.12318	−0.561591	+	0.827415i	$0.689811\pi$
$14$	−9.19222	−2.45673
$15$	−5.80330	−1.49841
$16$	10.6444	2.66111
$17$	0.154371	0.0374404	0.0187202	−	0.999825i	$-0.494041\pi$
$17$	0.154371	0.0374404	0.0187202	+	0.999825i	$0.494041\pi$
$18$	−2.59552	−0.611771
$19$	0.682953	0.156680	0.0783401	−	0.996927i	$-0.475038\pi$
$19$	0.682953	0.156680	0.0783401	+	0.996927i	$0.475038\pi$
$20$	−14.4071	−3.22153
$21$	6.95715	1.51817
$22$	13.0672	2.78594
$23$	0.607940	0.126764	0.0633822	−	0.997989i	$-0.479811\pi$
$23$	0.607940	0.126764	0.0633822	+	0.997989i	$0.479811\pi$
$24$	−15.5571	−3.17558
$25$	3.45304	0.690607
$26$	10.6802	2.09456
$27$	−4.02369	−0.774359
$28$	17.2716	3.26403
$29$	0.135779	0.0252135	0.0126067	−	0.999921i	$-0.495987\pi$
$29$	0.135779	0.0252135	0.0126067	+	0.999921i	$0.495987\pi$
$30$	15.3050	2.79430
$31$	3.48959	0.626750	0.313375	−	0.949630i	$-0.398540\pi$
$31$	3.48959	0.626750	0.313375	+	0.949630i	$0.398540\pi$
$32$	−12.4845	−2.20696
$33$	−9.88993	−1.72162
$34$	−0.407121	−0.0698206
$35$	−10.1337	−1.71291
$36$	4.87682	0.812804
$37$	−3.57078	−0.587033	−0.293516	−	0.955954i	$-0.594826\pi$
$37$	−3.57078	−0.587033	−0.293516	+	0.955954i	$0.594826\pi$
$38$	−1.80115	−0.292185
$39$	−8.08333	−1.29437
$40$	22.6604	3.58292
$41$	−2.02330	−0.315987	−0.157993	−	0.987440i	$-0.550502\pi$
$41$	−2.02330	−0.315987	−0.157993	+	0.987440i	$0.550502\pi$
$42$	−18.3480	−2.83116
$43$	−1.01463	−0.154729	−0.0773647	−	0.997003i	$-0.524651\pi$
$43$	−1.01463	−0.154729	−0.0773647	+	0.997003i	$0.524651\pi$
$44$	−24.5525	−3.70142
$45$	−2.86136	−0.426547
$46$	−1.60332	−0.236396
$47$	−0.259199	−0.0378081	−0.0189040	−	0.999821i	$-0.506018\pi$
$47$	−0.259199	−0.0378081	−0.0189040	+	0.999821i	$0.506018\pi$
$48$	21.2467	3.06669
$49$	5.14857	0.735510
$50$	−9.10666	−1.28788
$51$	0.308130	0.0431468
$52$	−20.0674	−2.78285
$53$	9.03516	1.24108	0.620538	−	0.784177i	$-0.286914\pi$
$53$	9.03516	1.24108	0.620538	+	0.784177i	$0.286914\pi$
$54$	10.6116	1.44406
$55$	14.4056	1.94245
$56$	−27.1658	−3.63019
$57$	1.36320	0.180560
$58$	−0.358088	−0.0470193
$59$	6.98583	0.909477	0.454739	−	0.890625i	$-0.349733\pi$
$59$	6.98583	0.909477	0.454739	+	0.890625i	$0.349733\pi$
$60$	−28.7571	−3.71253
$61$	8.08766	1.03552	0.517759	−	0.855526i	$-0.326766\pi$
$61$	8.08766	1.03552	0.517759	+	0.855526i	$0.326766\pi$
$62$	−9.20307	−1.16879
$63$	3.43028	0.432174
$64$	11.6363	1.45454
$65$	11.7741	1.46040
$66$	26.0826	3.21055
$67$	13.0891	1.59909	0.799545	−	0.600607i	$-0.205074\pi$
$67$	13.0891	1.59909	0.799545	+	0.600607i	$0.205074\pi$
$68$	0.764954	0.0927643
$69$	1.21347	0.146085
$70$	26.7256	3.19432
$71$	−11.1324	−1.32118	−0.660589	−	0.750748i	$-0.729693\pi$
$71$	−11.1324	−1.32118	−0.660589	+	0.750748i	$0.729693\pi$
$72$	−7.67056	−0.903984
$73$	−8.45075	−0.989086	−0.494543	−	0.869153i	$-0.664664\pi$
$73$	−8.45075	−0.989086	−0.494543	+	0.869153i	$0.664664\pi$
$74$	9.41719	1.09473
$75$	6.89238	0.795864
$76$	3.38424	0.388199
$77$	−17.2698	−1.96808
$78$	21.3181	2.41380
$79$	−0.383966	−0.0431996	−0.0215998	−	0.999767i	$-0.506876\pi$
$79$	−0.383966	−0.0431996	−0.0215998	+	0.999767i	$0.506876\pi$
$80$	−30.9477	−3.46006
$81$	−10.9839	−1.22043
$82$	5.33604	0.589267
$83$	9.61858	1.05578	0.527888	−	0.849314i	$-0.322984\pi$
$83$	9.61858	1.05578	0.527888	+	0.849314i	$0.322984\pi$
$84$	34.4748	3.76151
$85$	−0.448819	−0.0486813
$86$	2.67587	0.288547
$87$	0.271020	0.0290563
$88$	38.6176	4.11665
$89$	5.16555	0.547547	0.273774	−	0.961794i	$-0.411728\pi$
$89$	5.16555	0.547547	0.273774	+	0.961794i	$0.411728\pi$
$90$	7.54625	0.795445
$91$	−14.1151	−1.47967
$92$	3.01253	0.314078
$93$	6.96536	0.722274
$94$	0.683583	0.0705062
$95$	−1.98563	−0.203721
$96$	−24.9195	−2.54333
$97$	−2.46812	−0.250599	−0.125300	−	0.992119i	$-0.539989\pi$
$97$	−2.46812	−0.250599	−0.125300	+	0.992119i	$0.539989\pi$
$98$	−13.5783	−1.37161
$99$	−4.87631	−0.490088
$100$	17.1108	1.71108
$101$	−0.186225	−0.0185301	−0.00926504	−	0.999957i	$-0.502949\pi$
$101$	−0.186225	−0.0185301	−0.00926504	+	0.999957i	$0.502949\pi$
$102$	−0.812628	−0.0804621
$103$	4.51502	0.444878	0.222439	−	0.974947i	$-0.428598\pi$
$103$	4.51502	0.444878	0.222439	+	0.974947i	$0.428598\pi$
$104$	31.5633	3.09503
$105$	−20.2273	−1.97398
$106$	−23.8284	−2.31441
$107$	16.2234	1.56838	0.784189	−	0.620522i	$-0.213079\pi$
$107$	16.2234	1.56838	0.784189	+	0.620522i	$0.213079\pi$
$108$	−19.9386	−1.91859
$109$	7.92634	0.759206	0.379603	−	0.925150i	$-0.376061\pi$
$109$	7.92634	0.759206	0.379603	+	0.925150i	$0.376061\pi$
$110$	−37.9917	−3.62237
$111$	−7.12741	−0.676504
$112$	37.1010	3.50571
$113$	7.51012	0.706493	0.353246	−	0.935530i	$-0.385078\pi$
$113$	7.51012	0.706493	0.353246	+	0.935530i	$0.385078\pi$
$114$	−3.59515	−0.336717
$115$	−1.76753	−0.164823
$116$	0.672825	0.0624703
$117$	−3.98555	−0.368465
$118$	−18.4237	−1.69604
$119$	0.538056	0.0493235
$120$	45.2309	4.12900
$121$	13.5499	1.23181
$122$	−21.3295	−1.93108
$123$	−4.03859	−0.364147
$124$	17.2920	1.55287
$125$	4.49766	0.402283
$126$	−9.04664	−0.805939
$127$	9.47810	0.841045	0.420523	−	0.907282i	$-0.361847\pi$
$127$	9.47810	0.841045	0.420523	+	0.907282i	$0.361847\pi$
$128$	−5.71942	−0.505530
$129$	−2.02524	−0.178312
$130$	−31.0518	−2.72342
$131$	10.2774	0.897937	0.448969	−	0.893547i	$-0.351791\pi$
$131$	10.2774	0.897937	0.448969	+	0.893547i	$0.351791\pi$
$132$	−49.0076	−4.26556
$133$	2.38042	0.206409
$134$	−34.5198	−2.98206
$135$	11.6985	1.00685
$136$	−1.20317	−0.103171
$137$	−20.7474	−1.77257	−0.886285	−	0.463140i	$-0.846723\pi$
$137$	−20.7474	−1.77257	−0.886285	+	0.463140i	$0.846723\pi$
$138$	−3.20028	−0.272426
$139$	16.5124	1.40056	0.700281	−	0.713868i	$-0.253058\pi$
$139$	16.5124	1.40056	0.700281	+	0.713868i	$0.253058\pi$
$140$	−50.2157	−4.24400
$141$	−0.517371	−0.0435705
$142$	29.3595	2.46379
$143$	20.0653	1.67795
$144$	10.4759	0.872988
$145$	−0.394765	−0.0327834
$146$	22.2871	1.84449
$147$	10.2767	0.847611
$148$	−17.6943	−1.45446
$149$	17.8509	1.46240	0.731200	−	0.682163i	$-0.238960\pi$
$149$	17.8509	1.46240	0.731200	+	0.682163i	$0.238960\pi$
$150$	−18.1772	−1.48416
$151$	−12.2871	−0.999911	−0.499955	−	0.866051i	$-0.666650\pi$
$151$	−12.2871	−0.999911	−0.499955	+	0.866051i	$0.666650\pi$
$152$	−5.32294	−0.431747
$153$	0.151926	0.0122825
$154$	45.5455	3.67016
$155$	−10.1457	−0.814921
$156$	−40.0554	−3.20700
$157$	9.71208	0.775108	0.387554	−	0.921847i	$-0.373320\pi$
$157$	9.71208	0.775108	0.387554	+	0.921847i	$0.373320\pi$
$158$	1.01263	0.0805606
$159$	18.0345	1.43023
$160$	36.2975	2.86957
$161$	2.11896	0.166998
$162$	28.9678	2.27592
$163$	−3.91059	−0.306301	−0.153151	−	0.988203i	$-0.548942\pi$
$163$	−3.91059	−0.306301	−0.153151	+	0.988203i	$0.548942\pi$
$164$	−10.0261	−0.782906
$165$	28.7541	2.23850
$166$	−25.3670	−1.96886
$167$	−1.22763	−0.0949971	−0.0474986	−	0.998871i	$-0.515125\pi$
$167$	−1.22763	−0.0949971	−0.0474986	+	0.998871i	$0.515125\pi$
$168$	−54.2240	−4.18347
$169$	3.39999	0.261538
$170$	1.18367	0.0907831
$171$	0.672137	0.0513996
$172$	−5.02779	−0.383366
$173$	−17.0253	−1.29441	−0.647205	−	0.762316i	$-0.724062\pi$
$173$	−17.0253	−1.29441	−0.647205	+	0.762316i	$0.724062\pi$
$174$	−0.714757	−0.0541856
$175$	12.0355	0.909797
$176$	−52.7408	−3.97549
$177$	13.9440	1.04809
$178$	−13.6231	−1.02109
$179$	−3.36050	−0.251175	−0.125588	−	0.992083i	$-0.540082\pi$
$179$	−3.36050	−0.251175	−0.125588	+	0.992083i	$0.540082\pi$
$180$	−14.1789	−1.05684
$181$	16.0099	1.19001	0.595004	−	0.803723i	$-0.297150\pi$
$181$	16.0099	1.19001	0.595004	+	0.803723i	$0.297150\pi$
$182$	37.2257	2.75935
$183$	16.1433	1.19334
$184$	−4.73829	−0.349311
$185$	10.3817	0.763280
$186$	−18.3697	−1.34693
$187$	−0.764873	−0.0559331
$188$	−1.28441	−0.0936753
$189$	−14.0245	−1.02013
$190$	5.23667	0.379908
$191$	15.5762	1.12706	0.563528	−	0.826097i	$-0.309444\pi$
$191$	15.5762	1.12706	0.563528	+	0.826097i	$0.309444\pi$
$192$	23.2265	1.67623
$193$	4.79230	0.344957	0.172479	−	0.985013i	$-0.444822\pi$
$193$	4.79230	0.344957	0.172479	+	0.985013i	$0.444822\pi$
$194$	6.50914	0.467329
$195$	23.5016	1.68298
$196$	25.5127	1.82234
$197$	−12.5379	−0.893287	−0.446643	−	0.894712i	$-0.647381\pi$
$197$	−12.5379	−0.893287	−0.446643	+	0.894712i	$0.647381\pi$
$198$	12.8602	0.913938
$199$	23.6326	1.67527	0.837636	−	0.546229i	$-0.183937\pi$
$199$	23.6326	1.67527	0.837636	+	0.546229i	$0.183937\pi$
$200$	−26.9129	−1.90303
$201$	26.1263	1.84281
$202$	0.491130	0.0345558
$203$	0.473254	0.0332159
$204$	1.52688	0.106903
$205$	5.88257	0.410857
$206$	−11.9074	−0.829629
$207$	0.598312	0.0415856
$208$	−43.1067	−2.98891
$209$	−3.38388	−0.234068
$210$	53.3452	3.68117
$211$	−18.1762	−1.25130	−0.625649	−	0.780105i	$-0.715166\pi$
$211$	−18.1762	−1.25130	−0.625649	+	0.780105i	$0.715166\pi$
$212$	44.7720	3.07495
$213$	−22.2208	−1.52254
$214$	−42.7859	−2.92478
$215$	2.94994	0.201184
$216$	31.3606	2.13382
$217$	12.1629	0.825672
$218$	−20.9041	−1.41580
$219$	−16.8680	−1.13983
$220$	71.3841	4.81271
$221$	−0.625154	−0.0420524
$222$	18.7971	1.26158
$223$	−17.6894	−1.18457	−0.592284	−	0.805729i	$-0.701774\pi$
$223$	−17.6894	−1.18457	−0.592284	+	0.805729i	$0.701774\pi$
$224$	−43.5144	−2.90743
$225$	3.39835	0.226557
$226$	−19.8064	−1.31750
$227$	10.0811	0.669104	0.334552	−	0.942377i	$-0.391415\pi$
$227$	10.0811	0.669104	0.334552	+	0.942377i	$0.391415\pi$
$228$	6.75507	0.447365
$229$	5.42671	0.358607	0.179304	−	0.983794i	$-0.442616\pi$
$229$	5.42671	0.358607	0.179304	+	0.983794i	$0.442616\pi$
$230$	4.66150	0.307370
$231$	−34.4711	−2.26803
$232$	−1.05826	−0.0694782
$233$	12.1459	0.795702	0.397851	−	0.917450i	$-0.369756\pi$
$233$	12.1459	0.795702	0.397851	+	0.917450i	$0.369756\pi$
$234$	10.5111	0.687130
$235$	0.753598	0.0491593
$236$	34.6169	2.25337
$237$	−0.766411	−0.0497837
$238$	−1.41901	−0.0919808
$239$	−0.0139699	−0.000903636 0	−0.000451818	−	1.00000i	$-0.500144\pi$
$239$	−0.0139699	−0.000903636 0	−0.000451818		1.00000i	$0.500144\pi$
$240$	−61.7728	−3.98742
$241$	−16.0391	−1.03317	−0.516586	−	0.856236i	$-0.672797\pi$
$241$	−16.0391	−1.03317	−0.516586	+	0.856236i	$0.672797\pi$
$242$	−35.7349	−2.29713
$243$	−9.85323	−0.632085
$244$	40.0768	2.56565
$245$	−14.9690	−0.956335
$246$	10.6509	0.679079
$247$	−2.76575	−0.175980
$248$	−27.1979	−1.72707
$249$	19.1990	1.21669
$250$	−11.8616	−0.750196
$251$	−4.43737	−0.280085	−0.140042	−	0.990146i	$-0.544724\pi$
$251$	−4.43737	−0.280085	−0.140042	+	0.990146i	$0.544724\pi$
$252$	16.9981	1.07078
$253$	−3.01221	−0.189376
$254$	−24.9965	−1.56842
$255$	−0.895859	−0.0561009
$256$	−8.18886	−0.511804
$257$	7.19000	0.448500	0.224250	−	0.974532i	$-0.428007\pi$
$257$	7.19000	0.448500	0.224250	+	0.974532i	$0.428007\pi$
$258$	5.34114	0.332525
$259$	−12.4459	−0.773350
$260$	58.3443	3.61836
$261$	0.133628	0.00827139
$262$	−27.1044	−1.67452
$263$	15.3493	0.946476	0.473238	−	0.880935i	$-0.343085\pi$
$263$	15.3493	0.946476	0.473238	+	0.880935i	$0.343085\pi$
$264$	77.0821	4.74407
$265$	−26.2689	−1.61369
$266$	−6.27786	−0.384920
$267$	10.3106	0.631000
$268$	64.8605	3.96199
$269$	−4.98255	−0.303792	−0.151896	−	0.988397i	$-0.548538\pi$
$269$	−4.98255	−0.303792	−0.151896	+	0.988397i	$0.548538\pi$
$270$	−30.8524	−1.87762
$271$	−4.94942	−0.300656	−0.150328	−	0.988636i	$-0.548033\pi$
$271$	−4.94942	−0.300656	−0.150328	+	0.988636i	$0.548033\pi$
$272$	1.64319	0.0996330
$273$	−28.1743	−1.70519
$274$	54.7169	3.30557
$275$	−17.1090	−1.03171
$276$	6.01312	0.361947
$277$	18.9701	1.13980	0.569902	−	0.821713i	$-0.306981\pi$
$277$	18.9701	1.13980	0.569902	+	0.821713i	$0.306981\pi$
$278$	−43.5479	−2.61183
$279$	3.43433	0.205608
$280$	78.9822	4.72009
$281$	21.2273	1.26632	0.633158	−	0.774022i	$-0.281758\pi$
$281$	21.2273	1.26632	0.633158	+	0.774022i	$0.281758\pi$
$282$	1.36446	0.0812523
$283$	−24.0345	−1.42870	−0.714351	−	0.699788i	$-0.753278\pi$
$283$	−24.0345	−1.42870	−0.714351	+	0.699788i	$0.753278\pi$
$284$	−55.1646	−3.27342
$285$	−3.96338	−0.234770
$286$	−52.9181	−3.12911
$287$	−7.05218	−0.416277
$288$	−12.2867	−0.724004
$289$	−16.9762	−0.998598
$290$	1.04111	0.0611361
$291$	−4.92645	−0.288794
$292$	−41.8760	−2.45061
$293$	−17.1490	−1.00185	−0.500927	−	0.865489i	$-0.667008\pi$
$293$	−17.1490	−1.00185	−0.500927	+	0.865489i	$0.667008\pi$
$294$	−27.1027	−1.58066
$295$	−20.3107	−1.18253
$296$	27.8307	1.61762
$297$	19.9365	1.15683
$298$	−47.0780	−2.72715
$299$	−2.46197	−0.142379
$300$	34.1539	1.97187
$301$	−3.53647	−0.203839
$302$	32.4047	1.86468
$303$	−0.371712	−0.0213543
$304$	7.26965	0.416943
$305$	−23.5141	−1.34642
$306$	−0.400673	−0.0229049
$307$	5.06111	0.288853	0.144426	−	0.989516i	$-0.453866\pi$
$307$	5.06111	0.288853	0.144426	+	0.989516i	$0.453866\pi$
$308$	−85.5771	−4.87621
$309$	9.01214	0.512683
$310$	26.7571	1.51970
$311$	−25.1255	−1.42474	−0.712369	−	0.701805i	$-0.752378\pi$
$311$	−25.1255	−1.42474	−0.712369	+	0.701805i	$0.752378\pi$
$312$	63.0015	3.56676
$313$	−11.9658	−0.676349	−0.338175	−	0.941083i	$-0.609809\pi$
$313$	−11.9658	−0.676349	−0.338175	+	0.941083i	$0.609809\pi$
$314$	−25.6136	−1.44546
$315$	−9.97323	−0.561928
$316$	−1.90267	−0.107034
$317$	11.5993	0.651481	0.325741	−	0.945459i	$-0.394386\pi$
$317$	11.5993	0.651481	0.325741	+	0.945459i	$0.394386\pi$
$318$	−47.5623	−2.66716
$319$	−0.672754	−0.0376670
$320$	−33.8316	−1.89124
$321$	32.3826	1.80742
$322$	−5.58833	−0.311425
$323$	0.105428	0.00586617
$324$	−54.4286	−3.02381
$325$	−13.9837	−0.775677
$326$	10.3134	0.571205
$327$	15.8213	0.874918
$328$	15.7696	0.870732
$329$	−0.903433	−0.0498079
$330$	−75.8329	−4.17446
$331$	9.61198	0.528322	0.264161	−	0.964479i	$-0.414905\pi$
$331$	9.61198	0.528322	0.264161	+	0.964479i	$0.414905\pi$
$332$	47.6630	2.61585
$333$	−3.51423	−0.192579
$334$	3.23763	0.177155
$335$	−38.0554	−2.07919
$336$	74.0549	4.04002
$337$	−20.0283	−1.09101	−0.545504	−	0.838108i	$-0.683662\pi$
$337$	−20.0283	−1.09101	−0.545504	+	0.838108i	$0.683662\pi$
$338$	−8.96677	−0.487728
$339$	14.9905	0.814171
$340$	−2.22404	−0.120615
$341$	−17.2902	−0.936315
$342$	−1.77262	−0.0958524
$343$	−6.45312	−0.348436
$344$	7.90801	0.426371
$345$	−3.52806	−0.189944
$346$	44.9007	2.41388
$347$	−19.3733	−1.04001	−0.520006	−	0.854163i	$-0.674070\pi$
$347$	−19.3733	−1.04001	−0.520006	+	0.854163i	$0.674070\pi$
$348$	1.34298	0.0719915
$349$	−5.30816	−0.284140	−0.142070	−	0.989857i	$-0.545376\pi$
$349$	−5.30816	−0.284140	−0.142070	+	0.989857i	$0.545376\pi$
$350$	−31.7411	−1.69663
$351$	16.2947	0.869746
$352$	61.8578	3.29703
$353$	2.98686	0.158975	0.0794874	−	0.996836i	$-0.474672\pi$
$353$	2.98686	0.158975	0.0794874	+	0.996836i	$0.474672\pi$
$354$	−36.7743	−1.95453
$355$	32.3666	1.71784
$356$	25.5969	1.35663
$357$	1.07398	0.0568410
$358$	8.86261	0.468403
$359$	−13.5515	−0.715219	−0.357610	−	0.933871i	$-0.616408\pi$
$359$	−13.5515	−0.715219	−0.357610	+	0.933871i	$0.616408\pi$
$360$	22.3015	1.17539
$361$	−18.5336	−0.975451
$362$	−42.2228	−2.21918
$363$	27.0460	1.41955
$364$	−69.9447	−3.66610
$365$	24.5698	1.28604
$366$	−42.5745	−2.22540
$367$	25.0725	1.30878	0.654388	−	0.756159i	$-0.272926\pi$
$367$	25.0725	1.30878	0.654388	+	0.756159i	$0.272926\pi$
$368$	6.47118	0.337334
$369$	−1.99126	−0.103661
$370$	−27.3796	−1.42340
$371$	31.4919	1.63498
$372$	34.5155	1.78954
$373$	26.1180	1.35234	0.676169	−	0.736747i	$-0.263639\pi$
$373$	26.1180	1.35234	0.676169	+	0.736747i	$0.263639\pi$
$374$	2.01719	0.104307
$375$	8.97750	0.463596
$376$	2.02020	0.104184
$377$	−0.549862	−0.0283193
$378$	36.9866	1.90239
$379$	7.20275	0.369981	0.184990	−	0.982740i	$-0.440775\pi$
$379$	7.20275	0.369981	0.184990	+	0.982740i	$0.440775\pi$
$380$	−9.83938	−0.504749
$381$	18.9186	0.969231
$382$	−41.0790	−2.10179
$383$	−38.4884	−1.96666	−0.983332	−	0.181818i	$-0.941802\pi$
$383$	−38.4884	−1.96666	−0.983332	+	0.181818i	$0.941802\pi$
$384$	−11.4162	−0.582579
$385$	50.2104	2.55896
$386$	−12.6387	−0.643293
$387$	−0.998559	−0.0507596
$388$	−12.2303	−0.620898
$389$	32.8888	1.66753	0.833764	−	0.552121i	$-0.186181\pi$
$389$	32.8888	1.66753	0.833764	+	0.552121i	$0.186181\pi$
$390$	−61.9805	−3.13850
$391$	0.0938482	0.00474611
$392$	−40.1279	−2.02677
$393$	20.5140	1.03479
$394$	33.0660	1.66584
$395$	1.11635	0.0561695
$396$	−24.1636	−1.21427
$397$	−26.1246	−1.31116	−0.655578	−	0.755127i	$-0.727575\pi$
$397$	−26.1246	−1.31116	−0.655578	+	0.755127i	$0.727575\pi$
$398$	−62.3261	−3.12412
$399$	4.75140	0.237868
$400$	36.7556	1.83778
$401$	22.1022	1.10373	0.551865	−	0.833934i	$-0.313916\pi$
$401$	22.1022	1.10373	0.551865	+	0.833934i	$0.313916\pi$
$402$	−68.9028	−3.43656
$403$	−14.1318	−0.703954
$404$	−0.922802	−0.0459111
$405$	31.9347	1.58685
$406$	−1.24811	−0.0619426
$407$	17.6924	0.876982
$408$	−2.40156	−0.118895
$409$	19.8717	0.982590	0.491295	−	0.870993i	$-0.336524\pi$
$409$	19.8717	0.982590	0.491295	+	0.870993i	$0.336524\pi$
$410$	−15.5141	−0.766185
$411$	−41.4126	−2.04273
$412$	22.3733	1.10225
$413$	24.3490	1.19813
$414$	−1.57792	−0.0775507
$415$	−27.9651	−1.37276
$416$	50.5582	2.47882
$417$	32.9593	1.61402
$418$	8.92429	0.436501
$419$	12.7274	0.621774	0.310887	−	0.950447i	$-0.399374\pi$
$419$	12.7274	0.621774	0.310887	+	0.950447i	$0.399374\pi$
$420$	−100.232	−4.89084
$421$	26.9931	1.31556	0.657781	−	0.753209i	$-0.271495\pi$
$421$	26.9931	1.31556	0.657781	+	0.753209i	$0.271495\pi$
$422$	47.9358	2.33348
$423$	−0.255094	−0.0124031
$424$	−70.4201	−3.41990
$425$	0.533048	0.0258566
$426$	58.6026	2.83931
$427$	28.1894	1.36418
$428$	80.3920	3.88589
$429$	40.0511	1.93369
$430$	−7.77985	−0.375178
$431$	−22.4294	−1.08038	−0.540192	−	0.841542i	$-0.681648\pi$
$431$	−22.4294	−1.08038	−0.540192	+	0.841542i	$0.681648\pi$
$432$	−42.8299	−2.06065
$433$	12.3006	0.591131	0.295565	−	0.955322i	$-0.404492\pi$
$433$	12.3006	0.591131	0.295565	+	0.955322i	$0.404492\pi$
$434$	−32.0771	−1.53975
$435$	−0.787965	−0.0377800
$436$	39.2774	1.88105
$437$	0.415195	0.0198615
$438$	44.4858	2.12562
$439$	16.9150	0.807310	0.403655	−	0.914911i	$-0.367740\pi$
$439$	16.9150	0.807310	0.403655	+	0.914911i	$0.367740\pi$
$440$	−112.277	−5.35260
$441$	5.06703	0.241287
$442$	1.64871	0.0784212
$443$	34.1708	1.62350	0.811752	−	0.584003i	$-0.198514\pi$
$443$	34.1708	1.62350	0.811752	+	0.584003i	$0.198514\pi$
$444$	−35.3185	−1.67614
$445$	−15.0184	−0.711939
$446$	46.6520	2.20904
$447$	35.6310	1.68529
$448$	40.5582	1.91619
$449$	−1.75466	−0.0828078	−0.0414039	−	0.999142i	$-0.513183\pi$
$449$	−1.75466	−0.0828078	−0.0414039	+	0.999142i	$0.513183\pi$
$450$	−8.96243	−0.422493
$451$	10.0250	0.472060
$452$	37.2149	1.75044
$453$	−24.5255	−1.15231
$454$	−26.5867	−1.24778
$455$	41.0384	1.92391
$456$	−10.6248	−0.497551
$457$	39.2354	1.83535	0.917677	−	0.397326i	$-0.130062\pi$
$457$	39.2354	1.83535	0.917677	+	0.397326i	$0.130062\pi$
$458$	−14.3118	−0.668748
$459$	−0.621139	−0.0289923
$460$	−8.75866	−0.408375
$461$	21.9984	1.02457	0.512284	−	0.858816i	$-0.328799\pi$
$461$	21.9984	1.02457	0.512284	+	0.858816i	$0.328799\pi$
$462$	90.9104	4.22954
$463$	27.0710	1.25809	0.629047	−	0.777367i	$-0.283445\pi$
$463$	27.0710	1.25809	0.629047	+	0.777367i	$0.283445\pi$
$464$	1.44529	0.0670958
$465$	−20.2512	−0.939125
$466$	−32.0322	−1.48386
$467$	27.6910	1.28139	0.640694	−	0.767796i	$-0.278647\pi$
$467$	27.6910	1.28139	0.640694	+	0.767796i	$0.278647\pi$
$468$	−19.7496	−0.912927
$469$	45.6218	2.10662
$470$	−1.98746	−0.0916746
$471$	19.3857	0.893244
$472$	−54.4475	−2.50615
$473$	5.02726	0.231154
$474$	2.02125	0.0928390
$475$	2.35826	0.108204
$476$	2.66623	0.122207
$477$	8.89207	0.407140
$478$	0.0368426	0.00168514
$479$	27.8490	1.27245	0.636226	−	0.771502i	$-0.280494\pi$
$479$	27.8490	1.27245	0.636226	+	0.771502i	$0.280494\pi$
$480$	72.4511	3.30693
$481$	14.4606	0.659345
$482$	42.2998	1.92671
$483$	4.22953	0.192450
$484$	67.1437	3.05199
$485$	7.17583	0.325838
$486$	25.9858	1.17874
$487$	9.46325	0.428821	0.214410	−	0.976744i	$-0.431217\pi$
$487$	9.46325	0.428821	0.214410	+	0.976744i	$0.431217\pi$
$488$	−63.0352	−2.85347
$489$	−7.80569	−0.352986
$490$	39.4776	1.78342
$491$	25.5374	1.15249	0.576243	−	0.817279i	$-0.304518\pi$
$491$	25.5374	1.15249	0.576243	+	0.817279i	$0.304518\pi$
$492$	−20.0124	−0.902230
$493$	0.0209603	0.000944004 0
$494$	7.29409	0.328176
$495$	14.1774	0.637228
$496$	37.1447	1.66785
$497$	−38.8019	−1.74050
$498$	−50.6334	−2.26894
$499$	−26.6371	−1.19244	−0.596220	−	0.802821i	$-0.703331\pi$
$499$	−26.6371	−1.19244	−0.596220	+	0.802821i	$0.703331\pi$
$500$	22.2873	0.996718
$501$	−2.45040	−0.109476
$502$	11.7026	0.522315
$503$	−10.4117	−0.464236	−0.232118	−	0.972688i	$-0.574566\pi$
$503$	−10.4117	−0.464236	−0.232118	+	0.972688i	$0.574566\pi$
$504$	−26.7356	−1.19090
$505$	0.541433	0.0240934
$506$	7.94408	0.353157
$507$	6.78651	0.301399
$508$	46.9669	2.08382
$509$	−28.1055	−1.24576	−0.622878	−	0.782319i	$-0.714037\pi$
$509$	−28.1055	−1.24576	−0.622878	+	0.782319i	$0.714037\pi$
$510$	2.36264	0.104620
$511$	−29.4549	−1.30301
$512$	33.0353	1.45997
$513$	−2.74799	−0.121327
$514$	−18.9621	−0.836384
$515$	−13.1270	−0.578445
$516$	−10.0357	−0.441795
$517$	1.28427	0.0564823
$518$	32.8234	1.44218
$519$	−33.9831	−1.49169
$520$	−91.7674	−4.02427
$521$	−23.0015	−1.00772	−0.503858	−	0.863787i	$-0.668086\pi$
$521$	−23.0015	−1.00772	−0.503858	+	0.863787i	$0.668086\pi$
$522$	−0.352417	−0.0154249
$523$	−7.80221	−0.341167	−0.170583	−	0.985343i	$-0.554565\pi$
$523$	−7.80221	−0.341167	−0.170583	+	0.985343i	$0.554565\pi$
$524$	50.9275	2.22478
$525$	24.0233	1.04846
$526$	−40.4805	−1.76503
$527$	0.538691	0.0234658
$528$	−105.273	−4.58140
$529$	−22.6304	−0.983931
$530$	69.2788	3.00928
$531$	6.87519	0.298358
$532$	11.7957	0.511409
$533$	8.19375	0.354911
$534$	−27.1921	−1.17672
$535$	−47.1682	−2.03926
$536$	−102.016	−4.40644
$537$	−6.70767	−0.289457
$538$	13.1404	0.566525
$539$	−25.5100	−1.09880
$540$	57.9697	2.49462
$541$	22.3560	0.961159	0.480580	−	0.876951i	$-0.340426\pi$
$541$	22.3560	0.961159	0.480580	+	0.876951i	$0.340426\pi$
$542$	13.0531	0.560677
$543$	31.9564	1.37138
$544$	−1.92724	−0.0826296
$545$	−23.0451	−0.987144
$546$	74.3038	3.17991
$547$	−21.5007	−0.919304	−0.459652	−	0.888099i	$-0.652026\pi$
$547$	−21.5007	−0.919304	−0.459652	+	0.888099i	$0.652026\pi$
$548$	−102.810	−4.39181
$549$	7.95957	0.339706
$550$	45.1215	1.92399
$551$	0.0927306	0.00395046
$552$	−9.45779	−0.402550
$553$	−1.33831	−0.0569106
$554$	−50.0297	−2.12556
$555$	20.7223	0.879613
$556$	81.8238	3.47010
$557$	−31.5554	−1.33705	−0.668523	−	0.743691i	$-0.733073\pi$
$557$	−31.5554	−1.33705	−0.668523	+	0.743691i	$0.733073\pi$
$558$	−9.05732	−0.383427
$559$	4.10893	0.173789
$560$	−107.868	−4.55824
$561$	−1.52672	−0.0644580
$562$	−55.9827	−2.36149
$563$	15.2317	0.641941	0.320971	−	0.947089i	$-0.395991\pi$
$563$	15.2317	0.641941	0.320971	+	0.947089i	$0.395991\pi$
$564$	−2.56373	−0.107953
$565$	−21.8350	−0.918606
$566$	63.3859	2.66431
$567$	−38.2842	−1.60779
$568$	86.7662	3.64063
$569$	25.8001	1.08160	0.540799	−	0.841152i	$-0.318122\pi$
$569$	25.8001	1.08160	0.540799	+	0.841152i	$0.318122\pi$
$570$	10.4526	0.437811
$571$	−20.4726	−0.856750	−0.428375	−	0.903601i	$-0.640914\pi$
$571$	−20.4726	−0.856750	−0.428375	+	0.903601i	$0.640914\pi$
$572$	99.4298	4.15737
$573$	31.0907	1.29883
$574$	18.5987	0.776293
$575$	2.09924	0.0875444
$576$	11.4520	0.477168
$577$	36.6337	1.52508	0.762540	−	0.646942i	$-0.223952\pi$
$577$	36.6337	1.52508	0.762540	+	0.646942i	$0.223952\pi$
$578$	44.7711	1.86223
$579$	9.56561	0.397533
$580$	−1.95618	−0.0812259
$581$	33.5254	1.39087
$582$	12.9925	0.538556
$583$	−44.7673	−1.85407
$584$	65.8651	2.72552
$585$	11.5876	0.479090
$586$	45.2269	1.86831
$587$	−0.928581	−0.0383267	−0.0191633	−	0.999816i	$-0.506100\pi$
$587$	−0.928581	−0.0383267	−0.0191633	+	0.999816i	$0.506100\pi$
$588$	50.9243	2.10008
$589$	2.38323	0.0981992
$590$	53.5651	2.20524
$591$	−25.0261	−1.02943
$592$	−38.0089	−1.56216
$593$	42.8223	1.75850	0.879251	−	0.476359i	$-0.158044\pi$
$593$	42.8223	1.75850	0.879251	+	0.476359i	$0.158044\pi$
$594$	−52.5783	−2.15731
$595$	−1.56435	−0.0641321
$596$	88.4565	3.62332
$597$	47.1716	1.93060
$598$	6.49293	0.265516
$599$	−33.8960	−1.38495	−0.692476	−	0.721441i	$-0.743480\pi$
$599$	−33.8960	−1.38495	−0.692476	+	0.721441i	$0.743480\pi$
$600$	−53.7192	−2.19308
$601$	27.3368	1.11509	0.557545	−	0.830147i	$-0.311743\pi$
$601$	27.3368	1.11509	0.557545	+	0.830147i	$0.311743\pi$
$602$	9.32669	0.380128
$603$	12.8818	0.524588
$604$	−60.8864	−2.47743
$605$	−39.3950	−1.60163
$606$	0.980313	0.0398225
$607$	−34.3409	−1.39385	−0.696926	−	0.717143i	$-0.745450\pi$
$607$	−34.3409	−1.39385	−0.696926	+	0.717143i	$0.745450\pi$
$608$	−8.52631	−0.345788
$609$	0.944633	0.0382785
$610$	62.0136	2.51086
$611$	1.04968	0.0424653
$612$	0.752839	0.0304317
$613$	31.8122	1.28488	0.642442	−	0.766334i	$-0.277921\pi$
$613$	31.8122	1.28488	0.642442	+	0.766334i	$0.277921\pi$
$614$	−13.3476	−0.538666
$615$	11.7418	0.473476
$616$	134.601	5.42322
$617$	27.3971	1.10297	0.551483	−	0.834186i	$-0.314062\pi$
$617$	27.3971	1.10297	0.551483	+	0.834186i	$0.314062\pi$
$618$	−23.7676	−0.956074
$619$	20.4135	0.820486	0.410243	−	0.911976i	$-0.365444\pi$
$619$	20.4135	0.820486	0.410243	+	0.911976i	$0.365444\pi$
$620$	−50.2749	−2.01909
$621$	−2.44616	−0.0981611
$622$	66.2633	2.65692
$623$	18.0044	0.721332
$624$	−86.0425	−3.44446
$625$	−30.3417	−1.21367
$626$	31.5574	1.26129
$627$	−6.75436	−0.269743
$628$	48.1263	1.92045
$629$	−0.551224	−0.0219787
$630$	26.3023	1.04791
$631$	−28.0587	−1.11700	−0.558499	−	0.829505i	$-0.688623\pi$
$631$	−28.0587	−1.11700	−0.558499	+	0.829505i	$0.688623\pi$
$632$	2.99263	0.119041
$633$	−36.2803	−1.44201
$634$	−30.5907	−1.21491
$635$	−27.5567	−1.09356
$636$	89.3665	3.54361
$637$	−20.8501	−0.826112
$638$	1.77425	0.0702432
$639$	−10.9561	−0.433418
$640$	16.6287	0.657308
$641$	24.8337	0.980874	0.490437	−	0.871477i	$-0.336837\pi$
$641$	24.8337	0.980874	0.490437	+	0.871477i	$0.336837\pi$
$642$	−85.4022	−3.37056
$643$	19.5294	0.770163	0.385081	−	0.922883i	$-0.374173\pi$
$643$	19.5294	0.770163	0.385081	+	0.922883i	$0.374173\pi$
$644$	10.5001	0.413762
$645$	5.88819	0.231847
$646$	−0.278044	−0.0109395
$647$	16.2936	0.640566	0.320283	−	0.947322i	$-0.396222\pi$
$647$	16.2936	0.640566	0.320283	+	0.947322i	$0.396222\pi$
$648$	85.6086	3.36302
$649$	−34.6132	−1.35869
$650$	36.8791	1.44652
$651$	24.2776	0.951515
$652$	−19.3782	−0.758908
$653$	−6.85713	−0.268340	−0.134170	−	0.990958i	$-0.542837\pi$
$653$	−6.85713	−0.268340	−0.134170	+	0.990958i	$0.542837\pi$
$654$	−41.7253	−1.63159
$655$	−29.8805	−1.16753
$656$	−21.5369	−0.840875
$657$	−8.31691	−0.324474
$658$	2.38262	0.0928841
$659$	20.8861	0.813609	0.406804	−	0.913515i	$-0.366643\pi$
$659$	20.8861	0.813609	0.406804	+	0.913515i	$0.366643\pi$
$660$	142.485	5.54623
$661$	−24.6725	−0.959648	−0.479824	−	0.877365i	$-0.659299\pi$
$661$	−24.6725	−0.959648	−0.479824	+	0.877365i	$0.659299\pi$
$662$	−25.3496	−0.985240
$663$	−1.24783	−0.0484617
$664$	−74.9672	−2.90929
$665$	−6.92086	−0.268379
$666$	9.26804	0.359129
$667$	0.0825455	0.00319617
$668$	−6.08330	−0.235370
$669$	−35.3086	−1.36511
$670$	100.363	3.87737
$671$	−40.0726	−1.54698
$672$	−86.8563	−3.35055
$673$	6.51326	0.251068	0.125534	−	0.992089i	$-0.459936\pi$
$673$	6.51326	0.251068	0.125534	+	0.992089i	$0.459936\pi$
$674$	52.8203	2.03456
$675$	−13.8939	−0.534778
$676$	16.8480	0.648000
$677$	22.8151	0.876856	0.438428	−	0.898766i	$-0.355535\pi$
$677$	22.8151	0.876856	0.438428	+	0.898766i	$0.355535\pi$
$678$	−39.5343	−1.51830
$679$	−8.60257	−0.330136
$680$	3.49810	0.134146
$681$	20.1222	0.771084
$682$	45.5992	1.74608
$683$	27.9282	1.06864	0.534321	−	0.845282i	$-0.320567\pi$
$683$	27.9282	1.06864	0.534321	+	0.845282i	$0.320567\pi$
$684$	3.33064	0.127350
$685$	60.3212	2.30475
$686$	17.0188	0.649779
$687$	10.8319	0.413263
$688$	−10.8001	−0.411752
$689$	−36.5896	−1.39395
$690$	9.30452	0.354217
$691$	−15.0130	−0.571122	−0.285561	−	0.958361i	$-0.592180\pi$
$691$	−15.0130	−0.571122	−0.285561	+	0.958361i	$0.592180\pi$
$692$	−84.3656	−3.20710
$693$	−16.9963	−0.645635
$694$	51.0929	1.93946
$695$	−48.0082	−1.82106
$696$	−2.11233	−0.0800675
$697$	−0.312339	−0.0118307
$698$	13.9992	0.529877
$699$	24.2436	0.916977
$700$	59.6395	2.25416
$701$	29.6151	1.11855	0.559273	−	0.828983i	$-0.311080\pi$
$701$	29.6151	1.11855	0.559273	+	0.828983i	$0.311080\pi$
$702$	−42.9738	−1.62194
$703$	−2.43868	−0.0919764
$704$	−57.6554	−2.17297
$705$	1.50421	0.0566518
$706$	−7.87723	−0.296464
$707$	−0.649084	−0.0244113
$708$	69.0966	2.59681
$709$	−37.7070	−1.41612	−0.708058	−	0.706154i	$-0.750429\pi$
$709$	−37.7070	−1.41612	−0.708058	+	0.706154i	$0.750429\pi$
$710$	−85.3601	−3.20351
$711$	−0.377885	−0.0141718
$712$	−40.2603	−1.50882
$713$	2.12147	0.0794495
$714$	−2.83240	−0.106000
$715$	−58.3382	−2.18172
$716$	−16.6523	−0.622325
$717$	−0.0278844	−0.00104136
$718$	35.7392	1.33377
$719$	−14.2728	−0.532286	−0.266143	−	0.963933i	$-0.585749\pi$
$719$	−14.2728	−0.532286	−0.266143	+	0.963933i	$0.585749\pi$
$720$	−30.4576	−1.13509
$721$	15.7370	0.586076
$722$	48.8784	1.81907
$723$	−32.0147	−1.19064
$724$	79.3341	2.94843
$725$	0.468849	0.0174126
$726$	−71.3282	−2.64724
$727$	30.5702	1.13379	0.566894	−	0.823791i	$-0.308145\pi$
$727$	30.5702	1.13379	0.566894	+	0.823791i	$0.308145\pi$
$728$	110.013	4.07736
$729$	13.2843	0.492012
$730$	−64.7977	−2.39827
$731$	−0.156629	−0.00579313
$732$	79.9948	2.95669
$733$	4.84002	0.178770	0.0893851	−	0.995997i	$-0.471510\pi$
$733$	4.84002	0.178770	0.0893851	+	0.995997i	$0.471510\pi$
$734$	−66.1236	−2.44067
$735$	−29.8787	−1.10209
$736$	−7.58982	−0.279764
$737$	−64.8537	−2.38892
$738$	5.25153	0.193312
$739$	−25.8870	−0.952267	−0.476134	−	0.879373i	$-0.657962\pi$
$739$	−25.8870	−0.952267	−0.476134	+	0.879373i	$0.657962\pi$
$740$	51.4446	1.89114
$741$	−5.52054	−0.202802
$742$	−83.0533	−3.04898
$743$	10.4101	0.381910	0.190955	−	0.981599i	$-0.438842\pi$
$743$	10.4101	0.381910	0.190955	+	0.981599i	$0.438842\pi$
$744$	−54.2880	−1.99029
$745$	−51.8998	−1.90146
$746$	−68.8807	−2.52190
$747$	9.46624	0.346352
$748$	−3.79018	−0.138583
$749$	56.5464	2.06616
$750$	−23.6763	−0.864535
$751$	−2.90026	−0.105832	−0.0529160	−	0.998599i	$-0.516852\pi$
$751$	−2.90026	−0.105832	−0.0529160	+	0.998599i	$0.516852\pi$
$752$	−2.75903	−0.100611
$753$	−8.85716	−0.322773
$754$	1.45015	0.0528112
$755$	35.7237	1.30012
$756$	−69.4955	−2.52753
$757$	−20.0209	−0.727672	−0.363836	−	0.931463i	$-0.618533\pi$
$757$	−20.0209	−0.727672	−0.363836	+	0.931463i	$0.618533\pi$
$758$	−18.9958	−0.689957
$759$	−6.01249	−0.218239
$760$	15.4760	0.561372
$761$	−3.24170	−0.117512	−0.0587558	−	0.998272i	$-0.518713\pi$
$761$	−3.24170	−0.117512	−0.0587558	+	0.998272i	$0.518713\pi$
$762$	−49.8939	−1.80747
$763$	27.6271	1.00017
$764$	77.1849	2.79245
$765$	−0.441711	−0.0159701
$766$	101.505	3.66753
$767$	−28.2904	−1.02151
$768$	−16.3453	−0.589809
$769$	19.0249	0.686056	0.343028	−	0.939325i	$-0.388547\pi$
$769$	19.0249	0.686056	0.343028	+	0.939325i	$0.388547\pi$
$770$	−132.419	−4.77206
$771$	14.3515	0.516857
$772$	23.7473	0.854684
$773$	−30.5793	−1.09986	−0.549931	−	0.835210i	$-0.685346\pi$
$773$	−30.5793	−1.09986	−0.549931	+	0.835210i	$0.685346\pi$
$774$	2.63349	0.0946589
$775$	12.0497	0.432838
$776$	19.2365	0.690550
$777$	−24.8424	−0.891218
$778$	−86.7373	−3.10968
$779$	−1.38182	−0.0495089
$780$	116.457	4.16984
$781$	55.1588	1.97374
$782$	−0.247505	−0.00885076
$783$	−0.546331	−0.0195243
$784$	54.8036	1.95727
$785$	−28.2370	−1.00782
$786$	−54.1014	−1.92973
$787$	−33.3331	−1.18820	−0.594098	−	0.804393i	$-0.702491\pi$
$787$	−33.3331	−1.18820	−0.594098	+	0.804393i	$0.702491\pi$
$788$	−62.1290	−2.21325
$789$	30.6377	1.09073
$790$	−2.94413	−0.104748
$791$	26.1764	0.930725
$792$	38.0060	1.35048
$793$	−32.7525	−1.16308
$794$	68.8982	2.44511
$795$	−52.4337	−1.85963
$796$	117.107	4.15074
$797$	41.0279	1.45328	0.726642	−	0.687017i	$-0.241080\pi$
$797$	41.0279	1.45328	0.726642	+	0.687017i	$0.241080\pi$
$798$	−12.5308	−0.443587
$799$	−0.0400128	−0.00141555
$800$	−43.1093	−1.52414
$801$	5.08374	0.179625
$802$	−58.2899	−2.05829
$803$	41.8716	1.47762
$804$	129.464	4.56584
$805$	−6.16070	−0.217136
$806$	37.2696	1.31277
$807$	−9.94536	−0.350093
$808$	1.45144	0.0510614
$809$	17.6275	0.619750	0.309875	−	0.950777i	$-0.399713\pi$
$809$	17.6275	0.619750	0.309875	+	0.950777i	$0.399713\pi$
$810$	−84.2212	−2.95923
$811$	−21.6049	−0.758652	−0.379326	−	0.925263i	$-0.623844\pi$
$811$	−21.6049	−0.758652	−0.379326	+	0.925263i	$0.623844\pi$
$812$	2.34512	0.0822976
$813$	−9.87923	−0.346480
$814$	−46.6601	−1.63544
$815$	11.3697	0.398263
$816$	3.27987	0.114818
$817$	−0.692944	−0.0242430
$818$	−52.4073	−1.83238
$819$	−13.8916	−0.485411
$820$	29.1499	1.01796
$821$	−54.7645	−1.91130	−0.955648	−	0.294513i	$-0.904843\pi$
$821$	−54.7645	−1.91130	−0.955648	+	0.294513i	$0.904843\pi$
$822$	109.217	3.80938
$823$	−9.10628	−0.317425	−0.158712	−	0.987325i	$-0.550734\pi$
$823$	−9.10628	−0.317425	−0.158712	+	0.987325i	$0.550734\pi$
$824$	−35.1900	−1.22590
$825$	−34.1503	−1.18896
$826$	−64.2153	−2.23434
$827$	−16.1228	−0.560644	−0.280322	−	0.959906i	$-0.590441\pi$
$827$	−16.1228	−0.560644	−0.280322	+	0.959906i	$0.590441\pi$
$828$	2.96482	0.103035
$829$	−5.95725	−0.206904	−0.103452	−	0.994634i	$-0.532989\pi$
$829$	−5.95725	−0.206904	−0.103452	+	0.994634i	$0.532989\pi$
$830$	73.7522	2.55998
$831$	37.8650	1.31352
$832$	−47.1235	−1.63371
$833$	0.794789	0.0275378
$834$	−86.9233	−3.00991
$835$	3.56923	0.123518
$836$	−16.7682	−0.579939
$837$	−14.0410	−0.485329
$838$	−33.5659	−1.15951
$839$	1.66229	0.0573887	0.0286944	−	0.999588i	$-0.490865\pi$
$839$	1.66229	0.0573887	0.0286944	+	0.999588i	$0.490865\pi$
$840$	157.651	5.43949
$841$	−28.9816	−0.999364
$842$	−71.1886	−2.45332
$843$	42.3705	1.45932
$844$	−90.0684	−3.10028
$845$	−9.88517	−0.340060
$846$	0.672757	0.0231299
$847$	47.2278	1.62277
$848$	96.1742	3.30264
$849$	−47.9737	−1.64645
$850$	−1.40580	−0.0482186
$851$	−2.17082	−0.0744148
$852$	−110.111	−3.77233
$853$	46.6355	1.59677	0.798384	−	0.602148i	$-0.205688\pi$
$853$	46.6355	1.59677	0.798384	+	0.602148i	$0.205688\pi$
$854$	−74.3436	−2.54398
$855$	−1.95418	−0.0668315
$856$	−126.445	−4.32181
$857$	−35.3101	−1.20617	−0.603085	−	0.797677i	$-0.706062\pi$
$857$	−35.3101	−1.20617	−0.603085	+	0.797677i	$0.706062\pi$
$858$	−105.627	−3.60603
$859$	−48.4098	−1.65172	−0.825861	−	0.563873i	$-0.809311\pi$
$859$	−48.4098	−1.65172	−0.825861	+	0.563873i	$0.809311\pi$
$860$	14.6179	0.498465
$861$	−14.0764	−0.479723
$862$	59.1527	2.01475
$863$	3.82206	0.130104	0.0650522	−	0.997882i	$-0.479279\pi$
$863$	3.82206	0.130104	0.0650522	+	0.997882i	$0.479279\pi$
$864$	50.2336	1.70898
$865$	49.4995	1.68304
$866$	−32.4404	−1.10237
$867$	−33.8851	−1.15080
$868$	60.2709	2.04573
$869$	1.90247	0.0645369
$870$	2.07809	0.0704540
$871$	−53.0068	−1.79607
$872$	−61.7779	−2.09206
$873$	−2.42903	−0.0822101
$874$	−1.09499	−0.0370386
$875$	15.6765	0.529963
$876$	−83.5861	−2.82411
$877$	31.2125	1.05397	0.526985	−	0.849874i	$-0.323322\pi$
$877$	31.2125	1.05397	0.526985	+	0.849874i	$0.323322\pi$
$878$	−44.6098	−1.50551
$879$	−34.2300	−1.15455
$880$	153.339	5.16907
$881$	22.0770	0.743791	0.371896	−	0.928275i	$-0.378708\pi$
$881$	22.0770	0.743791	0.371896	+	0.928275i	$0.378708\pi$
$882$	−13.3632	−0.449963
$883$	13.1851	0.443714	0.221857	−	0.975079i	$-0.428788\pi$
$883$	13.1851	0.443714	0.221857	+	0.975079i	$0.428788\pi$
$884$	−3.09783	−0.104191
$885$	−40.5408	−1.36277
$886$	−90.1183	−3.02758
$887$	44.4006	1.49082	0.745412	−	0.666604i	$-0.232253\pi$
$887$	44.4006	1.49082	0.745412	+	0.666604i	$0.232253\pi$
$888$	55.5510	1.86417
$889$	33.0357	1.10798
$890$	39.6078	1.32766
$891$	54.4229	1.82324
$892$	−87.6562	−2.93495
$893$	−0.177021	−0.00592378
$894$	−93.9693	−3.14280
$895$	9.77034	0.326586
$896$	−19.9349	−0.665979
$897$	−4.91418	−0.164080
$898$	4.62756	0.154424
$899$	0.473813	0.0158025
$900$	16.8398	0.561328
$901$	1.39477	0.0464664
$902$	−26.4389	−0.880320
$903$	−7.05892	−0.234906
$904$	−58.5339	−1.94681
$905$	−46.5474	−1.54729
$906$	64.6809	2.14888
$907$	−0.0574867	−0.00190881	−0.000954407	−	1.00000i	$-0.500304\pi$
$907$	−0.0574867	−0.00190881	−0.000954407		1.00000i	$0.500304\pi$
$908$	49.9548	1.65781
$909$	−0.183276	−0.00607887
$910$	−108.230	−3.58780
$911$	−33.5536	−1.11168	−0.555841	−	0.831289i	$-0.687604\pi$
$911$	−33.5536	−1.11168	−0.555841	+	0.831289i	$0.687604\pi$
$912$	14.5105	0.480490
$913$	−47.6579	−1.57725
$914$	−103.475	−3.42265
$915$	−46.9351	−1.55163
$916$	26.8910	0.888504
$917$	35.8215	1.18293
$918$	1.63813	0.0540662
$919$	−39.7205	−1.31026	−0.655129	−	0.755517i	$-0.727386\pi$
$919$	−39.7205	−1.31026	−0.655129	+	0.755517i	$0.727386\pi$
$920$	13.7761	0.454186
$921$	10.1022	0.332878
$922$	−58.0162	−1.91066
$923$	45.0829	1.48392
$924$	−170.815	−5.61940
$925$	−12.3300	−0.405409
$926$	−71.3940	−2.34615
$927$	4.44351	0.145944
$928$	−1.69513	−0.0556453
$929$	−34.3982	−1.12857	−0.564284	−	0.825581i	$-0.690848\pi$
$929$	−34.3982	−1.12857	−0.564284	+	0.825581i	$0.690848\pi$
$930$	53.4082	1.75132
$931$	3.51623	0.115240
$932$	60.1865	1.97147
$933$	−50.1515	−1.64189
$934$	−73.0293	−2.38959
$935$	2.22380	0.0727261
$936$	31.0634	1.01534
$937$	14.9917	0.489757	0.244879	−	0.969554i	$-0.421252\pi$
$937$	14.9917	0.489757	0.244879	+	0.969554i	$0.421252\pi$
$938$	−120.318	−3.92852
$939$	−23.8842	−0.779433
$940$	3.73431	0.121800
$941$	36.5885	1.19275	0.596375	−	0.802706i	$-0.296607\pi$
$941$	36.5885	1.19275	0.596375	+	0.802706i	$0.296607\pi$
$942$	−51.1256	−1.66576
$943$	−1.23005	−0.0400559
$944$	74.3602	2.42022
$945$	40.7749	1.32641
$946$	−13.2584	−0.431066
$947$	22.8767	0.743392	0.371696	−	0.928355i	$-0.378776\pi$
$947$	22.8767	0.743392	0.371696	+	0.928355i	$0.378776\pi$
$948$	−3.79780	−0.123347
$949$	34.2229	1.11092
$950$	−6.21942	−0.201785
$951$	23.1526	0.750775
$952$	−4.19361	−0.135916
$953$	41.6773	1.35006	0.675031	−	0.737790i	$-0.264130\pi$
$953$	41.6773	1.35006	0.675031	+	0.737790i	$0.264130\pi$
$954$	−23.4510	−0.759253
$955$	−45.2865	−1.46544
$956$	−0.0692250	−0.00223890
$957$	−1.34284	−0.0434079
$958$	−73.4459	−2.37293
$959$	−72.3146	−2.33516
$960$	−67.5290	−2.17949
$961$	−18.8227	−0.607185
$962$	−38.1367	−1.22958
$963$	15.9665	0.514513
$964$	−79.4788	−2.55984
$965$	−13.9332	−0.448525
$966$	−11.1545	−0.358890
$967$	−28.7176	−0.923495	−0.461747	−	0.887012i	$-0.652777\pi$
$967$	−28.7176	−0.923495	−0.461747	+	0.887012i	$0.652777\pi$
$968$	−105.608	−3.39436
$969$	0.210438	0.00676025
$970$	−18.9247	−0.607637
$971$	−22.2210	−0.713105	−0.356552	−	0.934275i	$-0.616048\pi$
$971$	−22.2210	−0.713105	−0.356552	+	0.934275i	$0.616048\pi$
$972$	−48.8258	−1.56609
$973$	57.5535	1.84508
$974$	−24.9573	−0.799685
$975$	−27.9120	−0.893900
$976$	86.0885	2.75563
$977$	0.0112943	0.000361336 0	0.000180668	−	1.00000i	$-0.499942\pi$
$977$	0.0112943	0.000361336 0	0.000180668		1.00000i	$0.499942\pi$
$978$	20.5859	0.658264
$979$	−25.5942	−0.817993
$980$	−74.1760	−2.36946
$981$	7.80081	0.249061
$982$	−67.3495	−2.14921
$983$	31.3987	1.00146	0.500732	−	0.865603i	$-0.333064\pi$
$983$	31.3987	1.00146	0.500732	+	0.865603i	$0.333064\pi$
$984$	31.4767	1.00344
$985$	36.4527	1.16148
$986$	−0.0552784	−0.00176042
$987$	−1.80329	−0.0573992
$988$	−13.7051	−0.436018
$989$	−0.616834	−0.0196142
$990$	−37.3900	−1.18833
$991$	22.6112	0.718270	0.359135	−	0.933286i	$-0.383072\pi$
$991$	22.6112	0.718270	0.359135	+	0.933286i	$0.383072\pi$
$992$	−43.5657	−1.38321
$993$	19.1859	0.608845
$994$	102.332	3.24577
$995$	−68.7097	−2.17824
$996$	95.1370	3.01453
$997$	59.1186	1.87230	0.936152	−	0.351595i	$-0.114361\pi$
$997$	59.1186	1.87230	0.936152	+	0.351595i	$0.114361\pi$
$998$	70.2497	2.22372
$999$	14.3677	0.454574

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4013.2.a.c.1.7	✓	176

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4013.2.a.c.1.7	✓	176	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:	\( N \)	\(=\)	\( 4013 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4013.a (trivial)

\(f(q)\)	\(=\)	\(q-2.63729 q^{2} +1.99604 q^{3} +4.95530 q^{4} -2.90741 q^{5} -5.26413 q^{6} +3.48548 q^{7} -7.79400 q^{8} +0.984162 q^{9} +O(q^{10})\)	\(q-2.63729 q^{2} +1.99604 q^{3} +4.95530 q^{4} -2.90741 q^{5} -5.26413 q^{6} +3.48548 q^{7} -7.79400 q^{8} +0.984162 q^{9} +7.66769 q^{10} -4.95478 q^{11} +9.89097 q^{12} -4.04969 q^{13} -9.19222 q^{14} -5.80330 q^{15} +10.6444 q^{16} +0.154371 q^{17} -2.59552 q^{18} +0.682953 q^{19} -14.4071 q^{20} +6.95715 q^{21} +13.0672 q^{22} +0.607940 q^{23} -15.5571 q^{24} +3.45304 q^{25} +10.6802 q^{26} -4.02369 q^{27} +17.2716 q^{28} +0.135779 q^{29} +15.3050 q^{30} +3.48959 q^{31} -12.4845 q^{32} -9.88993 q^{33} -0.407121 q^{34} -10.1337 q^{35} +4.87682 q^{36} -3.57078 q^{37} -1.80115 q^{38} -8.08333 q^{39} +22.6604 q^{40} -2.02330 q^{41} -18.3480 q^{42} -1.01463 q^{43} -24.5525 q^{44} -2.86136 q^{45} -1.60332 q^{46} -0.259199 q^{47} +21.2467 q^{48} +5.14857 q^{49} -9.10666 q^{50} +0.308130 q^{51} -20.0674 q^{52} +9.03516 q^{53} +10.6116 q^{54} +14.4056 q^{55} -27.1658 q^{56} +1.36320 q^{57} -0.358088 q^{58} +6.98583 q^{59} -28.7571 q^{60} +8.08766 q^{61} -9.20307 q^{62} +3.43028 q^{63} +11.6363 q^{64} +11.7741 q^{65} +26.0826 q^{66} +13.0891 q^{67} +0.764954 q^{68} +1.21347 q^{69} +26.7256 q^{70} -11.1324 q^{71} -7.67056 q^{72} -8.45075 q^{73} +9.41719 q^{74} +6.89238 q^{75} +3.38424 q^{76} -17.2698 q^{77} +21.3181 q^{78} -0.383966 q^{79} -30.9477 q^{80} -10.9839 q^{81} +5.33604 q^{82} +9.61858 q^{83} +34.4748 q^{84} -0.448819 q^{85} +2.67587 q^{86} +0.271020 q^{87} +38.6176 q^{88} +5.16555 q^{89} +7.54625 q^{90} -14.1151 q^{91} +3.01253 q^{92} +6.96536 q^{93} +0.683583 q^{94} -1.98563 q^{95} -24.9195 q^{96} -2.46812 q^{97} -13.5783 q^{98} -4.87631 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 176 q + 11 q^{2} + 53 q^{3} + 191 q^{4} + 5 q^{5} + 19 q^{6} + 46 q^{7} + 36 q^{8} + 193 q^{9}+O(q^{10}) \) 176 * q + 11 * q^2 + 53 * q^3 + 191 * q^4 + 5 * q^5 + 19 * q^6 + 46 * q^7 + 36 * q^8 + 193 * q^9	\( 176 q + 11 q^{2} + 53 q^{3} + 191 q^{4} + 5 q^{5} + 19 q^{6} + 46 q^{7} + 36 q^{8} + 193 q^{9} + 43 q^{10} + 18 q^{11} + 95 q^{12} + 95 q^{13} + 2 q^{14} + 36 q^{15} + 225 q^{16} + 35 q^{17} + 46 q^{18} + 127 q^{19} + 4 q^{20} + 32 q^{21} + 60 q^{22} + 35 q^{23} + 26 q^{24} + 207 q^{25} + 19 q^{26} + 191 q^{27} + 87 q^{28} + 16 q^{29} + 28 q^{30} + 93 q^{31} + 73 q^{32} + 70 q^{33} + 45 q^{34} + 73 q^{35} + 206 q^{36} + 64 q^{37} + 35 q^{38} + 72 q^{39} + 139 q^{40} + 19 q^{41} + 35 q^{42} + 261 q^{43} + 11 q^{44} + 12 q^{45} + 58 q^{46} + 40 q^{47} + 130 q^{48} + 234 q^{49} - 14 q^{50} + 76 q^{51} + 263 q^{52} + 17 q^{53} + 28 q^{54} + 170 q^{55} - 10 q^{56} + 60 q^{57} + 52 q^{58} + 69 q^{59} + 37 q^{60} + 110 q^{61} + 71 q^{62} + 101 q^{63} + 250 q^{64} - q^{65} + 43 q^{66} + 190 q^{67} + 48 q^{68} + 45 q^{69} + 14 q^{70} + 9 q^{71} + 98 q^{72} + 182 q^{73} - 23 q^{74} + 219 q^{75} + 197 q^{76} + 25 q^{77} - 26 q^{78} + 105 q^{79} + 20 q^{80} + 236 q^{81} + 107 q^{82} + 130 q^{83} + 38 q^{84} + 73 q^{85} - 24 q^{86} + 171 q^{87} + 165 q^{88} + 40 q^{89} + 45 q^{90} + 182 q^{91} - 4 q^{92} + 23 q^{93} + 98 q^{94} + 30 q^{95} - 2 q^{96} + 168 q^{97} + 82 q^{98} + 50 q^{99}+O(q^{100}) \) 176 * q + 11 * q^2 + 53 * q^3 + 191 * q^4 + 5 * q^5 + 19 * q^6 + 46 * q^7 + 36 * q^8 + 193 * q^9 + 43 * q^10 + 18 * q^11 + 95 * q^12 + 95 * q^13 + 2 * q^14 + 36 * q^15 + 225 * q^16 + 35 * q^17 + 46 * q^18 + 127 * q^19 + 4 * q^20 + 32 * q^21 + 60 * q^22 + 35 * q^23 + 26 * q^24 + 207 * q^25 + 19 * q^26 + 191 * q^27 + 87 * q^28 + 16 * q^29 + 28 * q^30 + 93 * q^31 + 73 * q^32 + 70 * q^33 + 45 * q^34 + 73 * q^35 + 206 * q^36 + 64 * q^37 + 35 * q^38 + 72 * q^39 + 139 * q^40 + 19 * q^41 + 35 * q^42 + 261 * q^43 + 11 * q^44 + 12 * q^45 + 58 * q^46 + 40 * q^47 + 130 * q^48 + 234 * q^49 - 14 * q^50 + 76 * q^51 + 263 * q^52 + 17 * q^53 + 28 * q^54 + 170 * q^55 - 10 * q^56 + 60 * q^57 + 52 * q^58 + 69 * q^59 + 37 * q^60 + 110 * q^61 + 71 * q^62 + 101 * q^63 + 250 * q^64 - q^65 + 43 * q^66 + 190 * q^67 + 48 * q^68 + 45 * q^69 + 14 * q^70 + 9 * q^71 + 98 * q^72 + 182 * q^73 - 23 * q^74 + 219 * q^75 + 197 * q^76 + 25 * q^77 - 26 * q^78 + 105 * q^79 + 20 * q^80 + 236 * q^81 + 107 * q^82 + 130 * q^83 + 38 * q^84 + 73 * q^85 - 24 * q^86 + 171 * q^87 + 165 * q^88 + 40 * q^89 + 45 * q^90 + 182 * q^91 - 4 * q^92 + 23 * q^93 + 98 * q^94 + 30 * q^95 - 2 * q^96 + 168 * q^97 + 82 * q^98 + 50 * q^99

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