LMFDB - Embedded newform 2013.4.a.d.1.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2013,4,Mod(1,2013)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2013, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("2013.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 2013 = 3 \cdot 11 \cdot 61 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	2013.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:	$118.770844842$
Analytic rank:	$1$
Dimension:	$37$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.12
Character	$\chi$	$=$	2013.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.70850 q^{2} -3.00000 q^{3} -0.664006 q^{4} +8.28724 q^{5} +8.12551 q^{6} -34.8516 q^{7} +23.4665 q^{8} +9.00000 q^{9} +O(q^{10})$	\(q-2.70850 q^{2} -3.00000 q^{3} -0.664006 q^{4} +8.28724 q^{5} +8.12551 q^{6} -34.8516 q^{7} +23.4665 q^{8} +9.00000 q^{9} -22.4460 q^{10} +11.0000 q^{11} +1.99202 q^{12} +57.5764 q^{13} +94.3957 q^{14} -24.8617 q^{15} -58.2471 q^{16} +40.3137 q^{17} -24.3765 q^{18} -38.1981 q^{19} -5.50278 q^{20} +104.555 q^{21} -29.7935 q^{22} -42.0267 q^{23} -70.3995 q^{24} -56.3216 q^{25} -155.946 q^{26} -27.0000 q^{27} +23.1417 q^{28} -227.111 q^{29} +67.3381 q^{30} -29.0034 q^{31} -29.9696 q^{32} -33.0000 q^{33} -109.190 q^{34} -288.824 q^{35} -5.97605 q^{36} +218.707 q^{37} +103.460 q^{38} -172.729 q^{39} +194.473 q^{40} +17.3721 q^{41} -283.187 q^{42} -213.269 q^{43} -7.30406 q^{44} +74.5852 q^{45} +113.830 q^{46} +157.860 q^{47} +174.741 q^{48} +871.633 q^{49} +152.547 q^{50} -120.941 q^{51} -38.2311 q^{52} +410.384 q^{53} +73.1296 q^{54} +91.1597 q^{55} -817.845 q^{56} +114.594 q^{57} +615.131 q^{58} -467.703 q^{59} +16.5083 q^{60} -61.0000 q^{61} +78.5557 q^{62} -313.664 q^{63} +547.149 q^{64} +477.150 q^{65} +89.3806 q^{66} +1073.76 q^{67} -26.7685 q^{68} +126.080 q^{69} +782.280 q^{70} -1170.62 q^{71} +211.198 q^{72} +852.024 q^{73} -592.369 q^{74} +168.965 q^{75} +25.3637 q^{76} -383.367 q^{77} +467.838 q^{78} -1181.60 q^{79} -482.707 q^{80} +81.0000 q^{81} -47.0524 q^{82} +571.012 q^{83} -69.4250 q^{84} +334.089 q^{85} +577.639 q^{86} +681.333 q^{87} +258.131 q^{88} +1642.02 q^{89} -202.014 q^{90} -2006.63 q^{91} +27.9060 q^{92} +87.0101 q^{93} -427.564 q^{94} -316.557 q^{95} +89.9088 q^{96} +493.887 q^{97} -2360.82 q^{98} +99.0000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 37 q - 4 q^{2} - 111 q^{3} + 158 q^{4} - 15 q^{5} + 12 q^{6} - 77 q^{7} - 69 q^{8} + 333 q^{9}+O(q^{10}) $ 37 * q - 4 * q^2 - 111 * q^3 + 158 * q^4 - 15 * q^5 + 12 * q^6 - 77 * q^7 - 69 * q^8 + 333 * q^9	\( 37 q - 4 q^{2} - 111 q^{3} + 158 q^{4} - 15 q^{5} + 12 q^{6} - 77 q^{7} - 69 q^{8} + 333 q^{9} - 45 q^{10} + 407 q^{11} - 474 q^{12} - 169 q^{13} + 102 q^{14} + 45 q^{15} + 598 q^{16} - 338 q^{17} - 36 q^{18} - 235 q^{19} - 550 q^{20} + 231 q^{21} - 44 q^{22} - 53 q^{23} + 207 q^{24} + 750 q^{25} - 75 q^{26} - 999 q^{27} - 1378 q^{28} - 30 q^{29} + 135 q^{30} - 506 q^{31} - 841 q^{32} - 1221 q^{33} - 316 q^{34} - 822 q^{35} + 1422 q^{36} - 830 q^{37} - 371 q^{38} + 507 q^{39} - 613 q^{40} + 16 q^{41} - 306 q^{42} - 1137 q^{43} + 1738 q^{44} - 135 q^{45} - 659 q^{46} - 489 q^{47} - 1794 q^{48} + 2214 q^{49} + 1066 q^{50} + 1014 q^{51} - 2342 q^{52} + 731 q^{53} + 108 q^{54} - 165 q^{55} + 3051 q^{56} + 705 q^{57} - 611 q^{58} - 425 q^{59} + 1650 q^{60} - 2257 q^{61} + 453 q^{62} - 693 q^{63} + 4919 q^{64} + 1346 q^{65} + 132 q^{66} - 1907 q^{67} - 3236 q^{68} + 159 q^{69} - 1050 q^{70} - 561 q^{71} - 621 q^{72} - 2397 q^{73} - 1840 q^{74} - 2250 q^{75} - 3868 q^{76} - 847 q^{77} + 225 q^{78} + 393 q^{79} - 4031 q^{80} + 2997 q^{81} - 1946 q^{82} - 4191 q^{83} + 4134 q^{84} - 2667 q^{85} + 2405 q^{86} + 90 q^{87} - 759 q^{88} + 1437 q^{89} - 405 q^{90} - 5192 q^{91} - 737 q^{92} + 1518 q^{93} - 1960 q^{94} + 1356 q^{95} + 2523 q^{96} - 2368 q^{97} - 3014 q^{98} + 3663 q^{99}+O(q^{100}) \) 37 * q - 4 * q^2 - 111 * q^3 + 158 * q^4 - 15 * q^5 + 12 * q^6 - 77 * q^7 - 69 * q^8 + 333 * q^9 - 45 * q^10 + 407 * q^11 - 474 * q^12 - 169 * q^13 + 102 * q^14 + 45 * q^15 + 598 * q^16 - 338 * q^17 - 36 * q^18 - 235 * q^19 - 550 * q^20 + 231 * q^21 - 44 * q^22 - 53 * q^23 + 207 * q^24 + 750 * q^25 - 75 * q^26 - 999 * q^27 - 1378 * q^28 - 30 * q^29 + 135 * q^30 - 506 * q^31 - 841 * q^32 - 1221 * q^33 - 316 * q^34 - 822 * q^35 + 1422 * q^36 - 830 * q^37 - 371 * q^38 + 507 * q^39 - 613 * q^40 + 16 * q^41 - 306 * q^42 - 1137 * q^43 + 1738 * q^44 - 135 * q^45 - 659 * q^46 - 489 * q^47 - 1794 * q^48 + 2214 * q^49 + 1066 * q^50 + 1014 * q^51 - 2342 * q^52 + 731 * q^53 + 108 * q^54 - 165 * q^55 + 3051 * q^56 + 705 * q^57 - 611 * q^58 - 425 * q^59 + 1650 * q^60 - 2257 * q^61 + 453 * q^62 - 693 * q^63 + 4919 * q^64 + 1346 * q^65 + 132 * q^66 - 1907 * q^67 - 3236 * q^68 + 159 * q^69 - 1050 * q^70 - 561 * q^71 - 621 * q^72 - 2397 * q^73 - 1840 * q^74 - 2250 * q^75 - 3868 * q^76 - 847 * q^77 + 225 * q^78 + 393 * q^79 - 4031 * q^80 + 2997 * q^81 - 1946 * q^82 - 4191 * q^83 + 4134 * q^84 - 2667 * q^85 + 2405 * q^86 + 90 * q^87 - 759 * q^88 + 1437 * q^89 - 405 * q^90 - 5192 * q^91 - 737 * q^92 + 1518 * q^93 - 1960 * q^94 + 1356 * q^95 + 2523 * q^96 - 2368 * q^97 - 3014 * q^98 + 3663 * 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 $

$2$	−2.70850	−0.957601	−0.478800	−	0.877924i	$-0.658928\pi$
$2$	−2.70850	−0.957601	−0.478800	+	0.877924i	$0.658928\pi$
$3$	−3.00000	−0.577350
$3$	−3.00000	−0.577350
$4$	−0.664006	−0.0830007
$5$	8.28724	0.741233	0.370617	−	0.928786i	$-0.379146\pi$
$5$	8.28724	0.741233	0.370617	+	0.928786i	$0.379146\pi$
$6$	8.12551	0.552871
$7$	−34.8516	−1.88181	−0.940904	−	0.338672i	$-0.890022\pi$
$7$	−34.8516	−1.88181	−0.940904	+	0.338672i	$0.890022\pi$
$8$	23.4665	1.03708
$9$	9.00000	0.333333
$10$	−22.4460	−0.709806
$11$	11.0000	0.301511
$11$	11.0000	0.301511
$12$	1.99202	0.0479205
$13$	57.5764	1.22837	0.614186	−	0.789162i	$-0.289485\pi$
$13$	57.5764	1.22837	0.614186	+	0.789162i	$0.289485\pi$
$14$	94.3957	1.80202
$15$	−24.8617	−0.427951
$16$	−58.2471	−0.910110
$17$	40.3137	0.575147	0.287574	−	0.957759i	$-0.407151\pi$
$17$	40.3137	0.575147	0.287574	+	0.957759i	$0.407151\pi$
$18$	−24.3765	−0.319200
$19$	−38.1981	−0.461223	−0.230611	−	0.973046i	$-0.574073\pi$
$19$	−38.1981	−0.461223	−0.230611	+	0.973046i	$0.574073\pi$
$20$	−5.50278	−0.0615229
$21$	104.555	1.08646
$22$	−29.7935	−0.288728
$23$	−42.0267	−0.381008	−0.190504	−	0.981686i	$-0.561012\pi$
$23$	−42.0267	−0.381008	−0.190504	+	0.981686i	$0.561012\pi$
$24$	−70.3995	−0.598760
$25$	−56.3216	−0.450573
$26$	−155.946	−1.17629
$27$	−27.0000	−0.192450
$28$	23.1417	0.156191
$29$	−227.111	−1.45426	−0.727129	−	0.686501i	$-0.759146\pi$
$29$	−227.111	−1.45426	−0.727129	+	0.686501i	$0.759146\pi$
$30$	67.3381	0.409807
$31$	−29.0034	−0.168037	−0.0840187	−	0.996464i	$-0.526776\pi$
$31$	−29.0034	−0.168037	−0.0840187	+	0.996464i	$0.526776\pi$
$32$	−29.9696	−0.165560
$33$	−33.0000	−0.174078
$34$	−109.190	−0.550761
$35$	−288.824	−1.39486
$36$	−5.97605	−0.0276669
$37$	218.707	0.971763	0.485882	−	0.874025i	$-0.338499\pi$
$37$	218.707	0.971763	0.485882	+	0.874025i	$0.338499\pi$
$38$	103.460	0.441667
$39$	−172.729	−0.709200
$40$	194.473	0.768720
$41$	17.3721	0.0661723	0.0330862	−	0.999453i	$-0.489466\pi$
$41$	17.3721	0.0661723	0.0330862	+	0.999453i	$0.489466\pi$
$42$	−283.187	−1.04040
$43$	−213.269	−0.756353	−0.378176	−	0.925734i	$-0.623449\pi$
$43$	−213.269	−0.756353	−0.378176	+	0.925734i	$0.623449\pi$
$44$	−7.30406	−0.0250257
$45$	74.5852	0.247078
$46$	113.830	0.364853
$47$	157.860	0.489919	0.244960	−	0.969533i	$-0.421225\pi$
$47$	157.860	0.489919	0.244960	+	0.969533i	$0.421225\pi$
$48$	174.741	0.525452
$49$	871.633	2.54120
$50$	152.547	0.431469
$51$	−120.941	−0.332061
$52$	−38.2311	−0.101956
$53$	410.384	1.06359	0.531797	−	0.846872i	$-0.321517\pi$
$53$	410.384	1.06359	0.531797	+	0.846872i	$0.321517\pi$
$54$	73.1296	0.184290
$55$	91.1597	0.223490
$56$	−817.845	−1.95159
$57$	114.594	0.266287
$58$	615.131	1.39260
$59$	−467.703	−1.03203	−0.516015	−	0.856580i	$-0.672585\pi$
$59$	−467.703	−1.03203	−0.516015	+	0.856580i	$0.672585\pi$
$60$	16.5083	0.0355203
$61$	−61.0000	−0.128037
$61$	−61.0000	−0.128037
$62$	78.5557	0.160913
$63$	−313.664	−0.627270
$64$	547.149	1.06865
$65$	477.150	0.910510
$66$	89.3806	0.166697
$67$	1073.76	1.95792	0.978958	−	0.204063i	$-0.0654146\pi$
$67$	1073.76	1.95792	0.978958	+	0.204063i	$0.0654146\pi$
$68$	−26.7685	−0.0477376
$69$	126.080	0.219975
$70$	782.280	1.33572
$71$	−1170.62	−1.95672	−0.978361	−	0.206904i	$-0.933661\pi$
$71$	−1170.62	−1.95672	−0.978361	+	0.206904i	$0.933661\pi$
$72$	211.198	0.345694
$73$	852.024	1.36605	0.683026	−	0.730394i	$-0.260663\pi$
$73$	852.024	1.36605	0.683026	+	0.730394i	$0.260663\pi$
$74$	−592.369	−0.930561
$75$	168.965	0.260138
$76$	25.3637	0.0382818
$77$	−383.367	−0.567387
$78$	467.838	0.679131
$79$	−1181.60	−1.68280	−0.841398	−	0.540415i	$-0.818267\pi$
$79$	−1181.60	−1.68280	−0.841398	+	0.540415i	$0.818267\pi$
$80$	−482.707	−0.674604
$81$	81.0000	0.111111
$82$	−47.0524	−0.0633667
$83$	571.012	0.755141	0.377570	−	0.925981i	$-0.376760\pi$
$83$	571.012	0.755141	0.377570	+	0.925981i	$0.376760\pi$
$84$	−69.4250	−0.0901772
$85$	334.089	0.426318
$86$	577.639	0.724284
$87$	681.333	0.839616
$88$	258.131	0.312692
$89$	1642.02	1.95566	0.977830	−	0.209401i	$-0.0671513\pi$
$89$	1642.02	1.95566	0.977830	+	0.209401i	$0.0671513\pi$
$90$	−202.014	−0.236602
$91$	−2006.63	−2.31156
$92$	27.9060	0.0316239
$93$	87.0101	0.0970164
$94$	−427.564	−0.469147
$95$	−316.557	−0.341874
$96$	89.9088	0.0955862
$97$	493.887	0.516975	0.258488	−	0.966015i	$-0.416776\pi$
$97$	493.887	0.516975	0.258488	+	0.966015i	$0.416776\pi$
$98$	−2360.82	−2.43346
$99$	99.0000	0.100504
$100$	37.3979	0.0373979
$101$	−490.489	−0.483222	−0.241611	−	0.970373i	$-0.577676\pi$
$101$	−490.489	−0.483222	−0.241611	+	0.970373i	$0.577676\pi$
$102$	327.569	0.317982
$103$	−548.626	−0.524833	−0.262416	−	0.964955i	$-0.584519\pi$
$103$	−548.626	−0.524833	−0.262416	+	0.964955i	$0.584519\pi$
$104$	1351.12	1.27392
$105$	866.471	0.805323
$106$	−1111.53	−1.01850
$107$	−1172.76	−1.05958	−0.529790	−	0.848129i	$-0.677729\pi$
$107$	−1172.76	−1.05958	−0.529790	+	0.848129i	$0.677729\pi$
$108$	17.9282	0.0159735
$109$	375.101	0.329616	0.164808	−	0.986326i	$-0.447300\pi$
$109$	375.101	0.329616	0.164808	+	0.986326i	$0.447300\pi$
$110$	−246.906	−0.214014
$111$	−656.122	−0.561048
$112$	2030.00	1.71265
$113$	368.486	0.306763	0.153382	−	0.988167i	$-0.450984\pi$
$113$	368.486	0.306763	0.153382	+	0.988167i	$0.450984\pi$
$114$	−310.379	−0.254997
$115$	−348.286	−0.282416
$116$	150.803	0.120704
$117$	518.188	0.409457
$118$	1266.78	0.988272
$119$	−1405.00	−1.08232
$120$	−583.418	−0.443821
$121$	121.000	0.0909091
$122$	165.219	0.122608
$123$	−52.1163	−0.0382046
$124$	19.2584	0.0139472
$125$	−1502.66	−1.07521
$126$	849.561	0.600674
$127$	2274.83	1.58944	0.794718	−	0.606979i	$-0.207619\pi$
$127$	2274.83	1.58944	0.794718	+	0.606979i	$0.207619\pi$
$128$	−1242.20	−0.857781
$129$	639.806	0.436680
$130$	−1292.36	−0.871905
$131$	957.827	0.638822	0.319411	−	0.947616i	$-0.396515\pi$
$131$	957.827	0.638822	0.319411	+	0.947616i	$0.396515\pi$
$132$	21.9122	0.0144486
$133$	1331.26	0.867933
$134$	−2908.28	−1.87490
$135$	−223.756	−0.142650
$136$	946.021	0.596475
$137$	−635.331	−0.396204	−0.198102	−	0.980181i	$-0.563478\pi$
$137$	−635.331	−0.396204	−0.198102	+	0.980181i	$0.563478\pi$
$138$	−341.489	−0.210648
$139$	1149.01	0.701133	0.350566	−	0.936538i	$-0.385989\pi$
$139$	1149.01	0.701133	0.350566	+	0.936538i	$0.385989\pi$
$140$	191.781	0.115774
$141$	−473.579	−0.282855
$142$	3170.64	1.87376
$143$	633.341	0.370368
$144$	−524.223	−0.303370
$145$	−1882.12	−1.07794
$146$	−2307.71	−1.30813
$147$	−2614.90	−1.46717
$148$	−145.223	−0.0806570
$149$	2533.73	1.39310	0.696548	−	0.717510i	$-0.254718\pi$
$149$	2533.73	1.39310	0.696548	+	0.717510i	$0.254718\pi$
$150$	−457.642	−0.249109
$151$	2004.26	1.08016	0.540080	−	0.841614i	$-0.318394\pi$
$151$	2004.26	1.08016	0.540080	+	0.841614i	$0.318394\pi$
$152$	−896.374	−0.478326
$153$	362.823	0.191716
$154$	1038.35	0.543330
$155$	−240.358	−0.124555
$156$	114.693	0.0588641
$157$	−2723.73	−1.38457	−0.692284	−	0.721625i	$-0.743395\pi$
$157$	−2723.73	−1.38457	−0.692284	+	0.721625i	$0.743395\pi$
$158$	3200.38	1.61145
$159$	−1231.15	−0.614067
$160$	−248.365	−0.122719
$161$	1464.70	0.716984
$162$	−219.389	−0.106400
$163$	−3399.18	−1.63340	−0.816700	−	0.577062i	$-0.804199\pi$
$163$	−3399.18	−1.63340	−0.816700	+	0.577062i	$0.804199\pi$
$164$	−11.5352	−0.00549235
$165$	−273.479	−0.129032
$166$	−1546.59	−0.723123
$167$	3307.24	1.53247	0.766234	−	0.642562i	$-0.222128\pi$
$167$	3307.24	1.53247	0.766234	+	0.642562i	$0.222128\pi$
$168$	2453.53	1.12675
$169$	1118.04	0.508896
$170$	−904.882	−0.408243
$171$	−343.782	−0.153741
$172$	141.612	0.0627778
$173$	−1720.32	−0.756031	−0.378015	−	0.925799i	$-0.623393\pi$
$173$	−1720.32	−0.756031	−0.378015	+	0.925799i	$0.623393\pi$
$174$	−1845.39	−0.804017
$175$	1962.90	0.847892
$176$	−640.718	−0.274409
$177$	1403.11	0.595842
$178$	−4447.42	−1.87274
$179$	−1432.91	−0.598327	−0.299164	−	0.954202i	$-0.596708\pi$
$179$	−1432.91	−0.598327	−0.299164	+	0.954202i	$0.596708\pi$
$180$	−49.5250	−0.0205076
$181$	1627.99	0.668550	0.334275	−	0.942476i	$-0.391509\pi$
$181$	1627.99	0.668550	0.334275	+	0.942476i	$0.391509\pi$
$182$	5434.96	2.21355
$183$	183.000	0.0739221
$184$	−986.220	−0.395137
$185$	1812.48	0.720303
$186$	−235.667	−0.0929030
$187$	443.450	0.173413
$188$	−104.820	−0.0406637
$189$	940.993	0.362154
$190$	857.395	0.327379
$191$	4314.47	1.63447	0.817236	−	0.576303i	$-0.195505\pi$
$191$	4314.47	1.63447	0.817236	+	0.576303i	$0.195505\pi$
$192$	−1641.45	−0.616986
$193$	−4911.09	−1.83165	−0.915824	−	0.401580i	$-0.868461\pi$
$193$	−4911.09	−1.83165	−0.915824	+	0.401580i	$0.868461\pi$
$194$	−1337.69	−0.495056
$195$	−1431.45	−0.525683
$196$	−578.770	−0.210922
$197$	1868.10	0.675619	0.337809	−	0.941215i	$-0.390314\pi$
$197$	1868.10	0.675619	0.337809	+	0.941215i	$0.390314\pi$
$198$	−268.142	−0.0962425
$199$	647.498	0.230653	0.115326	−	0.993328i	$-0.463209\pi$
$199$	647.498	0.230653	0.115326	+	0.993328i	$0.463209\pi$
$200$	−1321.67	−0.467281
$201$	−3221.27	−1.13040
$202$	1328.49	0.462734
$203$	7915.18	2.73663
$204$	80.3055	0.0275613
$205$	143.967	0.0490492
$206$	1485.96	0.502580
$207$	−378.241	−0.127003
$208$	−3353.66	−1.11795
$209$	−420.179	−0.139064
$210$	−2346.84	−0.771178
$211$	−141.044	−0.0460182	−0.0230091	−	0.999735i	$-0.507325\pi$
$211$	−141.044	−0.0460182	−0.0230091	+	0.999735i	$0.507325\pi$
$212$	−272.497	−0.0882791
$213$	3511.87	1.12971
$214$	3176.42	1.01465
$215$	−1767.41	−0.560634
$216$	−633.595	−0.199587
$217$	1010.81	0.316214
$218$	−1015.96	−0.315640
$219$	−2556.07	−0.788691
$220$	−60.5305	−0.0185499
$221$	2321.12	0.706494
$222$	1777.11	0.537260
$223$	2680.85	0.805037	0.402519	−	0.915412i	$-0.368135\pi$
$223$	2680.85	0.805037	0.402519	+	0.915412i	$0.368135\pi$
$224$	1044.49	0.311553
$225$	−506.895	−0.150191
$226$	−998.046	−0.293757
$227$	−3641.90	−1.06485	−0.532426	−	0.846477i	$-0.678719\pi$
$227$	−3641.90	−1.06485	−0.532426	+	0.846477i	$0.678719\pi$
$228$	−76.0912	−0.0221020
$229$	1667.16	0.481088	0.240544	−	0.970638i	$-0.422674\pi$
$229$	1667.16	0.481088	0.240544	+	0.970638i	$0.422674\pi$
$230$	943.333	0.270442
$231$	1150.10	0.327581
$232$	−5329.50	−1.50818
$233$	−3286.51	−0.924062	−0.462031	−	0.886864i	$-0.652879\pi$
$233$	−3286.51	−0.924062	−0.462031	+	0.886864i	$0.652879\pi$
$234$	−1403.51	−0.392096
$235$	1308.22	0.363145
$236$	310.557	0.0856592
$237$	3544.81	0.971563
$238$	3805.44	1.03643
$239$	−1202.85	−0.325549	−0.162774	−	0.986663i	$-0.552044\pi$
$239$	−1202.85	−0.325549	−0.162774	+	0.986663i	$0.552044\pi$
$240$	1448.12	0.389483
$241$	305.130	0.0815568	0.0407784	−	0.999168i	$-0.487016\pi$
$241$	305.130	0.0815568	0.0407784	+	0.999168i	$0.487016\pi$
$242$	−327.729	−0.0870546
$243$	−243.000	−0.0641500
$244$	40.5044	0.0106272
$245$	7223.44	1.88363
$246$	141.157	0.0365848
$247$	−2199.31	−0.566553
$248$	−680.607	−0.174269
$249$	−1713.03	−0.435981
$250$	4069.95	1.02963
$251$	−5801.29	−1.45886	−0.729431	−	0.684054i	$-0.760215\pi$
$251$	−5801.29	−1.45886	−0.729431	+	0.684054i	$0.760215\pi$
$252$	208.275	0.0520638
$253$	−462.294	−0.114878
$254$	−6161.38	−1.52204
$255$	−1002.27	−0.246135
$256$	−1012.69	−0.247239
$257$	3240.48	0.786520	0.393260	−	0.919427i	$-0.371347\pi$
$257$	3240.48	0.786520	0.393260	+	0.919427i	$0.371347\pi$
$258$	−1732.92	−0.418165
$259$	−7622.29	−1.82867
$260$	−316.830	−0.0755730
$261$	−2044.00	−0.484752
$262$	−2594.28	−0.611737
$263$	−985.234	−0.230997	−0.115498	−	0.993308i	$-0.536847\pi$
$263$	−985.234	−0.230997	−0.115498	+	0.993308i	$0.536847\pi$
$264$	−774.394	−0.180533
$265$	3400.95	0.788372
$266$	−3605.73	−0.831134
$267$	−4926.06	−1.12910
$268$	−712.981	−0.162508
$269$	830.916	0.188334	0.0941670	−	0.995556i	$-0.469981\pi$
$269$	830.916	0.188334	0.0941670	+	0.995556i	$0.469981\pi$
$270$	606.043	0.136602
$271$	6178.17	1.38486	0.692430	−	0.721485i	$-0.256540\pi$
$271$	6178.17	1.38486	0.692430	+	0.721485i	$0.256540\pi$
$272$	−2348.15	−0.523447
$273$	6019.89	1.33458
$274$	1720.80	0.379406
$275$	−619.538	−0.135853
$276$	−83.7180	−0.0182581
$277$	−5389.76	−1.16910	−0.584548	−	0.811359i	$-0.698728\pi$
$277$	−5389.76	−1.16910	−0.584548	+	0.811359i	$0.698728\pi$
$278$	−3112.09	−0.671405
$279$	−261.030	−0.0560125
$280$	−6777.68	−1.44658
$281$	1361.67	0.289076	0.144538	−	0.989499i	$-0.453830\pi$
$281$	1361.67	0.289076	0.144538	+	0.989499i	$0.453830\pi$
$282$	1282.69	0.270862
$283$	1746.22	0.366791	0.183396	−	0.983039i	$-0.441291\pi$
$283$	1746.22	0.366791	0.183396	+	0.983039i	$0.441291\pi$
$284$	777.300	0.162409
$285$	949.670	0.197381
$286$	−1715.41	−0.354665
$287$	−605.445	−0.124524
$288$	−269.726	−0.0551867
$289$	−3287.81	−0.669206
$290$	5097.74	1.03224
$291$	−1481.66	−0.298476
$292$	−565.749	−0.113383
$293$	−9065.99	−1.80765	−0.903824	−	0.427905i	$-0.859252\pi$
$293$	−9065.99	−1.80765	−0.903824	+	0.427905i	$0.859252\pi$
$294$	7082.47	1.40496
$295$	−3875.97	−0.764975
$296$	5132.29	1.00780
$297$	−297.000	−0.0580259
$298$	−6862.62	−1.33403
$299$	−2419.75	−0.468019
$300$	−112.194	−0.0215917
$301$	7432.75	1.42331
$302$	−5428.54	−1.03436
$303$	1471.47	0.278988
$304$	2224.92	0.419764
$305$	−505.522	−0.0949052
$306$	−982.708	−0.183587
$307$	3362.59	0.625124	0.312562	−	0.949897i	$-0.398813\pi$
$307$	3362.59	0.625124	0.312562	+	0.949897i	$0.398813\pi$
$308$	254.558	0.0470935
$309$	1645.88	0.303012
$310$	651.010	0.119274
$311$	−2027.53	−0.369682	−0.184841	−	0.982768i	$-0.559177\pi$
$311$	−2027.53	−0.369682	−0.184841	+	0.982768i	$0.559177\pi$
$312$	−4053.35	−0.735499
$313$	−6311.24	−1.13972	−0.569860	−	0.821742i	$-0.693003\pi$
$313$	−6311.24	−1.13972	−0.569860	+	0.821742i	$0.693003\pi$
$314$	7377.23	1.32586
$315$	−2599.41	−0.464953
$316$	784.592	0.139673
$317$	1005.70	0.178189	0.0890945	−	0.996023i	$-0.471603\pi$
$317$	1005.70	0.178189	0.0890945	+	0.996023i	$0.471603\pi$
$318$	3334.58	0.588031
$319$	−2498.22	−0.438475
$320$	4534.36	0.792120
$321$	3518.28	0.611748
$322$	−3967.14	−0.686585
$323$	−1539.90	−0.265271
$324$	−53.7845	−0.00922230
$325$	−3242.80	−0.553471
$326$	9206.69	1.56415
$327$	−1125.30	−0.190304
$328$	407.662	0.0686262
$329$	−5501.66	−0.921935
$330$	740.719	0.123561
$331$	−5778.01	−0.959480	−0.479740	−	0.877411i	$-0.659269\pi$
$331$	−5778.01	−0.959480	−0.479740	+	0.877411i	$0.659269\pi$
$332$	−379.155	−0.0626772
$333$	1968.36	0.323921
$334$	−8957.68	−1.46749
$335$	8898.49	1.45127
$336$	−6090.01	−0.988801
$337$	−5061.18	−0.818101	−0.409050	−	0.912512i	$-0.634140\pi$
$337$	−5061.18	−0.818101	−0.409050	+	0.912512i	$0.634140\pi$
$338$	−3028.23	−0.487319
$339$	−1105.46	−0.177110
$340$	−221.837	−0.0353847
$341$	−319.037	−0.0506652
$342$	931.136	0.147222
$343$	−18423.7	−2.90025
$344$	−5004.67	−0.784400
$345$	1044.86	0.163053
$346$	4659.49	0.723976
$347$	−3954.33	−0.611757	−0.305879	−	0.952071i	$-0.598950\pi$
$347$	−3954.33	−0.611757	−0.305879	+	0.952071i	$0.598950\pi$
$348$	−452.409	−0.0696887
$349$	−7924.40	−1.21542	−0.607712	−	0.794157i	$-0.707913\pi$
$349$	−7924.40	−1.21542	−0.607712	+	0.794157i	$0.707913\pi$
$350$	−5316.52	−0.811942
$351$	−1554.56	−0.236400
$352$	−329.665	−0.0499183
$353$	−4678.50	−0.705415	−0.352707	−	0.935734i	$-0.614739\pi$
$353$	−4678.50	−0.705415	−0.352707	+	0.935734i	$0.614739\pi$
$354$	−3800.33	−0.570579
$355$	−9701.23	−1.45039
$356$	−1090.31	−0.162321
$357$	4214.99	0.624876
$358$	3881.04	0.572959
$359$	−8798.20	−1.29346	−0.646729	−	0.762720i	$-0.723863\pi$
$359$	−8798.20	−1.29346	−0.646729	+	0.762720i	$0.723863\pi$
$360$	1750.25	0.256240
$361$	−5399.91	−0.787273
$362$	−4409.42	−0.640204
$363$	−363.000	−0.0524864
$364$	1332.41	0.191861
$365$	7060.93	1.01256
$366$	−495.656	−0.0707879
$367$	−10668.7	−1.51744	−0.758720	−	0.651417i	$-0.774175\pi$
$367$	−10668.7	−1.51744	−0.758720	+	0.651417i	$0.774175\pi$
$368$	2447.93	0.346759
$369$	156.349	0.0220574
$370$	−4909.11	−0.689763
$371$	−14302.5	−2.00148
$372$	−57.7752	−0.00805243
$373$	−8812.75	−1.22334	−0.611671	−	0.791112i	$-0.709502\pi$
$373$	−8812.75	−1.22334	−0.611671	+	0.791112i	$0.709502\pi$
$374$	−1201.09	−0.166061
$375$	4507.97	0.620775
$376$	3704.41	0.508087
$377$	−13076.2	−1.78637
$378$	−2548.68	−0.346799
$379$	6670.50	0.904064	0.452032	−	0.892002i	$-0.350699\pi$
$379$	6670.50	0.904064	0.452032	+	0.892002i	$0.350699\pi$
$380$	210.195	0.0283758
$381$	−6824.48	−0.917661
$382$	−11685.8	−1.56517
$383$	−1116.30	−0.148930	−0.0744652	−	0.997224i	$-0.523725\pi$
$383$	−1116.30	−0.148930	−0.0744652	+	0.997224i	$0.523725\pi$
$384$	3726.60	0.495240
$385$	−3177.06	−0.420566
$386$	13301.7	1.75399
$387$	−1919.42	−0.252118
$388$	−327.944	−0.0429093
$389$	4949.74	0.645146	0.322573	−	0.946545i	$-0.395452\pi$
$389$	4949.74	0.645146	0.322573	+	0.946545i	$0.395452\pi$
$390$	3877.09	0.503395
$391$	−1694.25	−0.219136
$392$	20454.2	2.63544
$393$	−2873.48	−0.368824
$394$	−5059.77	−0.646973
$395$	−9792.25	−1.24735
$396$	−65.7366	−0.00834189
$397$	6744.32	0.852613	0.426307	−	0.904579i	$-0.359814\pi$
$397$	6744.32	0.852613	0.426307	+	0.904579i	$0.359814\pi$
$398$	−1753.75	−0.220873
$399$	−3993.79	−0.501102
$400$	3280.57	0.410071
$401$	9210.68	1.14703	0.573515	−	0.819195i	$-0.305579\pi$
$401$	9210.68	1.14703	0.573515	+	0.819195i	$0.305579\pi$
$402$	8724.83	1.08247
$403$	−1669.91	−0.206412
$404$	325.687	0.0401078
$405$	671.267	0.0823593
$406$	−21438.3	−2.62060
$407$	2405.78	0.292998
$408$	−2838.06	−0.344375
$409$	−2716.47	−0.328413	−0.164206	−	0.986426i	$-0.552506\pi$
$409$	−2716.47	−0.328413	−0.164206	+	0.986426i	$0.552506\pi$
$410$	−389.935	−0.0469695
$411$	1905.99	0.228749
$412$	364.291	0.0435615
$413$	16300.2	1.94208
$414$	1024.47	0.121618
$415$	4732.11	0.559735
$416$	−1725.54	−0.203369
$417$	−3447.02	−0.404799
$418$	1138.06	0.133168
$419$	15197.4	1.77193	0.885967	−	0.463748i	$-0.153496\pi$
$419$	15197.4	1.77193	0.885967	+	0.463748i	$0.153496\pi$
$420$	−575.342	−0.0668424
$421$	−5429.32	−0.628525	−0.314262	−	0.949336i	$-0.601757\pi$
$421$	−5429.32	−0.628525	−0.314262	+	0.949336i	$0.601757\pi$
$422$	382.017	0.0440671
$423$	1420.74	0.163306
$424$	9630.27	1.10304
$425$	−2270.53	−0.259146
$426$	−9511.91	−1.08182
$427$	2125.95	0.240941
$428$	778.719	0.0879458
$429$	−1900.02	−0.213832
$430$	4787.03	0.536863
$431$	15630.6	1.74687	0.873436	−	0.486940i	$-0.161887\pi$
$431$	15630.6	1.74687	0.873436	+	0.486940i	$0.161887\pi$
$432$	1572.67	0.175151
$433$	17620.4	1.95562	0.977811	−	0.209491i	$-0.0671808\pi$
$433$	17620.4	1.95562	0.977811	+	0.209491i	$0.0671808\pi$
$434$	−2737.79	−0.302807
$435$	5646.37	0.622351
$436$	−249.069	−0.0273584
$437$	1605.34	0.175730
$438$	6923.13	0.755251
$439$	−8565.42	−0.931219	−0.465610	−	0.884990i	$-0.654165\pi$
$439$	−8565.42	−0.931219	−0.465610	+	0.884990i	$0.654165\pi$
$440$	2139.20	0.231778
$441$	7844.70	0.847068
$442$	−6286.75	−0.676539
$443$	−3903.27	−0.418623	−0.209311	−	0.977849i	$-0.567122\pi$
$443$	−3903.27	−0.418623	−0.209311	+	0.977849i	$0.567122\pi$
$444$	435.668	0.0465674
$445$	13607.8	1.44960
$446$	−7261.10	−0.770904
$447$	−7601.19	−0.804304
$448$	−19069.0	−2.01100
$449$	−18262.5	−1.91951	−0.959753	−	0.280844i	$-0.909385\pi$
$449$	−18262.5	−1.91951	−0.959753	+	0.280844i	$0.909385\pi$
$450$	1372.93	0.143823
$451$	191.093	0.0199517
$452$	−244.677	−0.0254616
$453$	−6012.77	−0.623631
$454$	9864.10	1.01970
$455$	−16629.4	−1.71341
$456$	2689.12	0.276162
$457$	−7656.63	−0.783724	−0.391862	−	0.920024i	$-0.628169\pi$
$457$	−7656.63	−0.783724	−0.391862	+	0.920024i	$0.628169\pi$
$458$	−4515.52	−0.460690
$459$	−1088.47	−0.110687
$460$	231.264	0.0234407
$461$	8309.50	0.839505	0.419753	−	0.907639i	$-0.362117\pi$
$461$	8309.50	0.839505	0.419753	+	0.907639i	$0.362117\pi$
$462$	−3115.06	−0.313692
$463$	−15787.7	−1.58470	−0.792351	−	0.610065i	$-0.791143\pi$
$463$	−15787.7	−1.58470	−0.792351	+	0.610065i	$0.791143\pi$
$464$	13228.5	1.32353
$465$	721.074	0.0719118
$466$	8901.53	0.884883
$467$	1295.81	0.128400	0.0641999	−	0.997937i	$-0.479550\pi$
$467$	1295.81	0.128400	0.0641999	+	0.997937i	$0.479550\pi$
$468$	−344.080	−0.0339852
$469$	−37422.2	−3.68442
$470$	−3543.32	−0.347748
$471$	8171.18	0.799381
$472$	−10975.3	−1.07030
$473$	−2345.95	−0.228049
$474$	−9601.14	−0.930370
$475$	2151.38	0.207815
$476$	932.925	0.0898331
$477$	3693.45	0.354532
$478$	3257.93	0.311746
$479$	13108.7	1.25042	0.625211	−	0.780456i	$-0.285013\pi$
$479$	13108.7	1.25042	0.625211	+	0.780456i	$0.285013\pi$
$480$	745.096	0.0708517
$481$	12592.4	1.19369
$482$	−826.447	−0.0780988
$483$	−4394.10	−0.413951
$484$	−80.3447	−0.00754552
$485$	4092.96	0.383199
$486$	658.166	0.0614301
$487$	1879.69	0.174901	0.0874506	−	0.996169i	$-0.472128\pi$
$487$	1879.69	0.174901	0.0874506	+	0.996169i	$0.472128\pi$
$488$	−1431.46	−0.132785
$489$	10197.5	0.943044
$490$	−19564.7	−1.80376
$491$	−18987.1	−1.74516	−0.872582	−	0.488467i	$-0.837556\pi$
$491$	−18987.1	−1.74516	−0.872582	+	0.488467i	$0.837556\pi$
$492$	34.6055	0.00317101
$493$	−9155.68	−0.836412
$494$	5956.83	0.542532
$495$	820.437	0.0744968
$496$	1689.36	0.152933
$497$	40798.0	3.68218
$498$	4639.76	0.417495
$499$	4424.86	0.396962	0.198481	−	0.980105i	$-0.436399\pi$
$499$	4424.86	0.396962	0.198481	+	0.980105i	$0.436399\pi$
$500$	997.772	0.0892435
$501$	−9921.73	−0.884771
$502$	15712.8	1.39701
$503$	−13033.5	−1.15534	−0.577670	−	0.816271i	$-0.696038\pi$
$503$	−13033.5	−1.15534	−0.577670	+	0.816271i	$0.696038\pi$
$504$	−7360.60	−0.650530
$505$	−4064.80	−0.358180
$506$	1252.13	0.110007
$507$	−3354.13	−0.293811
$508$	−1510.50	−0.131924
$509$	15796.4	1.37556	0.687782	−	0.725917i	$-0.258584\pi$
$509$	15796.4	1.37556	0.687782	+	0.725917i	$0.258584\pi$
$510$	2714.65	0.235699
$511$	−29694.4	−2.57065
$512$	12680.5	1.09454
$513$	1031.35	0.0887624
$514$	−8776.85	−0.753172
$515$	−4546.60	−0.389024
$516$	−424.835	−0.0362448
$517$	1736.46	0.147716
$518$	20645.0	1.75114
$519$	5160.95	0.436495
$520$	11197.0	0.944274
$521$	−8291.74	−0.697251	−0.348625	−	0.937262i	$-0.613351\pi$
$521$	−8291.74	−0.697251	−0.348625	+	0.937262i	$0.613351\pi$
$522$	5536.18	0.464199
$523$	−2300.38	−0.192330	−0.0961651	−	0.995365i	$-0.530658\pi$
$523$	−2300.38	−0.192330	−0.0961651	+	0.995365i	$0.530658\pi$
$524$	−636.002	−0.0530227
$525$	−5888.69	−0.489531
$526$	2668.51	0.221203
$527$	−1169.23	−0.0966462
$528$	1922.15	0.158430
$529$	−10400.8	−0.854833
$530$	−9211.48	−0.754946
$531$	−4209.33	−0.344010
$532$	−883.966	−0.0720391
$533$	1000.22	0.0812842
$534$	13342.3	1.08123
$535$	−9718.94	−0.785395
$536$	25197.3	2.03052
$537$	4298.72	0.345444
$538$	−2250.54	−0.180349
$539$	9587.97	0.766202
$540$	148.575	0.0118401
$541$	3146.21	0.250030	0.125015	−	0.992155i	$-0.460102\pi$
$541$	3146.21	0.250030	0.125015	+	0.992155i	$0.460102\pi$
$542$	−16733.6	−1.32614
$543$	−4883.97	−0.385988
$544$	−1208.18	−0.0952214
$545$	3108.55	0.244322
$546$	−16304.9	−1.27799
$547$	−3974.03	−0.310635	−0.155317	−	0.987865i	$-0.549640\pi$
$547$	−3974.03	−0.310635	−0.155317	+	0.987865i	$0.549640\pi$
$548$	421.864	0.0328853
$549$	−549.000	−0.0426790
$550$	1678.02	0.130093
$551$	8675.20	0.670737
$552$	2958.66	0.228132
$553$	41180.8	3.16670
$554$	14598.2	1.11953
$555$	−5437.44	−0.415867
$556$	−762.947	−0.0581945
$557$	10175.6	0.774061	0.387031	−	0.922067i	$-0.373501\pi$
$557$	10175.6	0.774061	0.387031	+	0.922067i	$0.373501\pi$
$558$	707.002	0.0536376
$559$	−12279.2	−0.929082
$560$	16823.1	1.26948
$561$	−1330.35	−0.100120
$562$	−3688.09	−0.276819
$563$	−19183.7	−1.43605	−0.718027	−	0.696015i	$-0.754955\pi$
$563$	−19183.7	−1.43605	−0.718027	+	0.696015i	$0.754955\pi$
$564$	314.459	0.0234772
$565$	3053.73	0.227383
$566$	−4729.64	−0.351239
$567$	−2822.98	−0.209090
$568$	−27470.4	−2.02928
$569$	−18264.3	−1.34566	−0.672830	−	0.739797i	$-0.734921\pi$
$569$	−18264.3	−1.34566	−0.672830	+	0.739797i	$0.734921\pi$
$570$	−2572.18	−0.189012
$571$	−6065.07	−0.444510	−0.222255	−	0.974989i	$-0.571342\pi$
$571$	−6065.07	−0.444510	−0.222255	+	0.974989i	$0.571342\pi$
$572$	−420.542	−0.0307408
$573$	−12943.4	−0.943663
$574$	1639.85	0.119244
$575$	2367.01	0.171672
$576$	4924.34	0.356217
$577$	2455.40	0.177157	0.0885786	−	0.996069i	$-0.471768\pi$
$577$	2455.40	0.177157	0.0885786	+	0.996069i	$0.471768\pi$
$578$	8905.04	0.640832
$579$	14733.3	1.05750
$580$	1249.74	0.0894701
$581$	−19900.7	−1.42103
$582$	4013.08	0.285821
$583$	4514.22	0.320686
$584$	19994.0	1.41671
$585$	4294.35	0.303503
$586$	24555.3	1.73100
$587$	−15399.9	−1.08283	−0.541415	−	0.840755i	$-0.682111\pi$
$587$	−15399.9	−1.08283	−0.541415	+	0.840755i	$0.682111\pi$
$588$	1736.31	0.121776
$589$	1107.87	0.0775027
$590$	10498.1	0.732540
$591$	−5604.31	−0.390069
$592$	−12739.0	−0.884412
$593$	−755.537	−0.0523207	−0.0261604	−	0.999658i	$-0.508328\pi$
$593$	−755.537	−0.0523207	−0.0261604	+	0.999658i	$0.508328\pi$
$594$	804.426	0.0555656
$595$	−11643.5	−0.802250
$596$	−1682.41	−0.115628
$597$	−1942.49	−0.133167
$598$	6553.90	0.448176
$599$	−13869.3	−0.946049	−0.473025	−	0.881049i	$-0.656838\pi$
$599$	−13869.3	−0.946049	−0.473025	+	0.881049i	$0.656838\pi$
$600$	3965.01	0.269785
$601$	−26467.4	−1.79639	−0.898193	−	0.439602i	$-0.855119\pi$
$601$	−26467.4	−1.79639	−0.898193	+	0.439602i	$0.855119\pi$
$602$	−20131.6	−1.36296
$603$	9663.82	0.652639
$604$	−1330.84	−0.0896541
$605$	1002.76	0.0673849
$606$	−3985.47	−0.267160
$607$	8268.79	0.552916	0.276458	−	0.961026i	$-0.410839\pi$
$607$	8268.79	0.552916	0.276458	+	0.961026i	$0.410839\pi$
$608$	1144.78	0.0763601
$609$	−23745.5	−1.58000
$610$	1369.21	0.0908813
$611$	9089.00	0.601803
$612$	−240.917	−0.0159125
$613$	6610.23	0.435538	0.217769	−	0.976000i	$-0.430122\pi$
$613$	6610.23	0.435538	0.217769	+	0.976000i	$0.430122\pi$
$614$	−9107.58	−0.598619
$615$	−431.900	−0.0283185
$616$	−8996.29	−0.588427
$617$	3534.17	0.230600	0.115300	−	0.993331i	$-0.463217\pi$
$617$	3534.17	0.230600	0.115300	+	0.993331i	$0.463217\pi$
$618$	−4457.87	−0.290165
$619$	26870.0	1.74475	0.872373	−	0.488840i	$-0.162580\pi$
$619$	26870.0	1.74475	0.872373	+	0.488840i	$0.162580\pi$
$620$	159.599	0.0103381
$621$	1134.72	0.0733250
$622$	5491.59	0.354007
$623$	−57227.0	−3.68018
$624$	10061.0	0.645451
$625$	−5412.67	−0.346411
$626$	17094.0	1.09140
$627$	1260.54	0.0802886
$628$	1808.57	0.114920
$629$	8816.89	0.558907
$630$	7040.52	0.445240
$631$	27301.8	1.72245	0.861226	−	0.508222i	$-0.169697\pi$
$631$	27301.8	1.72245	0.861226	+	0.508222i	$0.169697\pi$
$632$	−27728.1	−1.74520
$633$	423.131	0.0265686
$634$	−2723.95	−0.170634
$635$	18852.0	1.17814
$636$	817.491	0.0509680
$637$	50185.5	3.12154
$638$	6766.44	0.419884
$639$	−10535.6	−0.652241
$640$	−10294.4	−0.635816
$641$	29657.3	1.82744	0.913722	−	0.406341i	$-0.133195\pi$
$641$	29657.3	1.82744	0.913722	+	0.406341i	$0.133195\pi$
$642$	−9529.27	−0.585811
$643$	−7860.27	−0.482082	−0.241041	−	0.970515i	$-0.577489\pi$
$643$	−7860.27	−0.482082	−0.241041	+	0.970515i	$0.577489\pi$
$644$	−972.568	−0.0595102
$645$	5302.23	0.323682
$646$	4170.84	0.254024
$647$	803.170	0.0488035	0.0244018	−	0.999702i	$-0.492232\pi$
$647$	803.170	0.0488035	0.0244018	+	0.999702i	$0.492232\pi$
$648$	1900.79	0.115231
$649$	−5144.73	−0.311169
$650$	8783.13	0.530004
$651$	−3032.44	−0.182566
$652$	2257.07	0.135573
$653$	−12647.0	−0.757909	−0.378954	−	0.925415i	$-0.623716\pi$
$653$	−12647.0	−0.757909	−0.378954	+	0.925415i	$0.623716\pi$
$654$	3047.89	0.182235
$655$	7937.74	0.473516
$656$	−1011.87	−0.0602241
$657$	7668.22	0.455351
$658$	14901.3	0.882845
$659$	656.397	0.0388006	0.0194003	−	0.999812i	$-0.493824\pi$
$659$	656.397	0.0388006	0.0194003	+	0.999812i	$0.493824\pi$
$660$	181.592	0.0107098
$661$	−14195.6	−0.835319	−0.417660	−	0.908604i	$-0.637150\pi$
$661$	−14195.6	−0.835319	−0.417660	+	0.908604i	$0.637150\pi$
$662$	15649.8	0.918799
$663$	−6963.35	−0.407895
$664$	13399.6	0.783143
$665$	11032.5	0.643341
$666$	−5331.32	−0.310187
$667$	9544.74	0.554084
$668$	−2196.03	−0.127196
$669$	−8042.56	−0.464788
$670$	−24101.6	−1.38974
$671$	−671.000	−0.0386046
$672$	−3133.46	−0.179875
$673$	−8308.23	−0.475867	−0.237934	−	0.971281i	$-0.576470\pi$
$673$	−8308.23	−0.475867	−0.237934	+	0.971281i	$0.576470\pi$
$674$	13708.2	0.783414
$675$	1520.68	0.0867128
$676$	−742.388	−0.0422387
$677$	−8937.46	−0.507377	−0.253689	−	0.967286i	$-0.581644\pi$
$677$	−8937.46	−0.507377	−0.253689	+	0.967286i	$0.581644\pi$
$678$	2994.14	0.169601
$679$	−17212.7	−0.972848
$680$	7839.90	0.442127
$681$	10925.7	0.614792
$682$	864.113	0.0485170
$683$	−14110.0	−0.790487	−0.395244	−	0.918576i	$-0.629340\pi$
$683$	−14110.0	−0.790487	−0.395244	+	0.918576i	$0.629340\pi$
$684$	228.274	0.0127606
$685$	−5265.14	−0.293680
$686$	49900.7	2.77728
$687$	−5001.49	−0.277756
$688$	12422.3	0.688364
$689$	23628.4	1.30649
$690$	−2830.00	−0.156140
$691$	−9033.05	−0.497299	−0.248649	−	0.968594i	$-0.579987\pi$
$691$	−9033.05	−0.497299	−0.248649	+	0.968594i	$0.579987\pi$
$692$	1142.30	0.0627511
$693$	−3450.31	−0.189129
$694$	10710.3	0.585819
$695$	9522.09	0.519703
$696$	15988.5	0.870751
$697$	700.333	0.0380588
$698$	21463.3	1.16389
$699$	9859.53	0.533508
$700$	−1303.38	−0.0703757
$701$	−9776.00	−0.526725	−0.263363	−	0.964697i	$-0.584832\pi$
$701$	−9776.00	−0.526725	−0.263363	+	0.964697i	$0.584832\pi$
$702$	4210.54	0.226377
$703$	−8354.19	−0.448199
$704$	6018.64	0.322210
$705$	−3924.67	−0.209662
$706$	12671.7	0.675506
$707$	17094.3	0.909332
$708$	−931.672	−0.0494554
$709$	−7661.56	−0.405834	−0.202917	−	0.979196i	$-0.565042\pi$
$709$	−7661.56	−0.405834	−0.202917	+	0.979196i	$0.565042\pi$
$710$	26275.8	1.38889
$711$	−10634.4	−0.560932
$712$	38532.4	2.02818
$713$	1218.92	0.0640236
$714$	−11416.3	−0.598382
$715$	5248.65	0.274529
$716$	951.459	0.0496616
$717$	3608.56	0.187956
$718$	23830.0	1.23862
$719$	−2629.82	−0.136406	−0.0682030	−	0.997671i	$-0.521727\pi$
$719$	−2629.82	−0.136406	−0.0682030	+	0.997671i	$0.521727\pi$
$720$	−4344.37	−0.224868
$721$	19120.5	0.987635
$722$	14625.7	0.753894
$723$	−915.391	−0.0470868
$724$	−1081.00	−0.0554901
$725$	12791.3	0.655249
$726$	983.187	0.0502610
$727$	14323.3	0.730706	0.365353	−	0.930869i	$-0.380948\pi$
$727$	14323.3	0.730706	0.365353	+	0.930869i	$0.380948\pi$
$728$	−47088.6	−2.39728
$729$	729.000	0.0370370
$730$	−19124.6	−0.969632
$731$	−8597.64	−0.435014
$732$	−121.513	−0.00613559
$733$	−1128.59	−0.0568694	−0.0284347	−	0.999596i	$-0.509052\pi$
$733$	−1128.59	−0.0568694	−0.0284347	+	0.999596i	$0.509052\pi$
$734$	28896.1	1.45310
$735$	−21670.3	−1.08751
$736$	1259.52	0.0630797
$737$	11811.3	0.590334
$738$	−423.472	−0.0211222
$739$	−28752.7	−1.43124	−0.715619	−	0.698491i	$-0.753855\pi$
$739$	−28752.7	−1.43124	−0.715619	+	0.698491i	$0.753855\pi$
$740$	−1203.50	−0.0597857
$741$	6597.92	0.327099
$742$	38738.4	1.91662
$743$	−20579.2	−1.01612	−0.508061	−	0.861321i	$-0.669637\pi$
$743$	−20579.2	−1.01612	−0.508061	+	0.861321i	$0.669637\pi$
$744$	2041.82	0.100614
$745$	20997.6	1.03261
$746$	23869.4	1.17147
$747$	5139.10	0.251714
$748$	−294.454	−0.0143934
$749$	40872.5	1.99393
$750$	−12209.9	−0.594454
$751$	7055.99	0.342845	0.171423	−	0.985198i	$-0.445164\pi$
$751$	7055.99	0.342845	0.171423	+	0.985198i	$0.445164\pi$
$752$	−9194.86	−0.445881
$753$	17403.9	0.842275
$754$	35417.1	1.71063
$755$	16609.8	0.800651
$756$	−624.825	−0.0300591
$757$	3722.92	0.178747	0.0893736	−	0.995998i	$-0.471513\pi$
$757$	3722.92	0.178747	0.0893736	+	0.995998i	$0.471513\pi$
$758$	−18067.1	−0.865733
$759$	1386.88	0.0663250
$760$	−7428.47	−0.354551
$761$	2561.36	0.122010	0.0610048	−	0.998137i	$-0.480570\pi$
$761$	2561.36	0.122010	0.0610048	+	0.998137i	$0.480570\pi$
$762$	18484.1	0.878753
$763$	−13072.9	−0.620274
$764$	−2864.83	−0.135662
$765$	3006.80	0.142106
$766$	3023.51	0.142616
$767$	−26928.7	−1.26772
$768$	3038.08	0.142744
$769$	17086.1	0.801221	0.400611	−	0.916248i	$-0.368798\pi$
$769$	17086.1	0.801221	0.400611	+	0.916248i	$0.368798\pi$
$770$	8605.08	0.402734
$771$	−9721.44	−0.454097
$772$	3260.99	0.152028
$773$	−18486.7	−0.860183	−0.430092	−	0.902785i	$-0.641519\pi$
$773$	−18486.7	−0.860183	−0.430092	+	0.902785i	$0.641519\pi$
$774$	5198.75	0.241428
$775$	1633.52	0.0757131
$776$	11589.8	0.536146
$777$	22866.9	1.05578
$778$	−13406.4	−0.617792
$779$	−663.580	−0.0305202
$780$	950.490	0.0436321
$781$	−12876.8	−0.589974
$782$	4588.89	0.209844
$783$	6132.00	0.279872
$784$	−50770.1	−2.31278
$785$	−22572.2	−1.02629
$786$	7782.83	0.353186
$787$	36003.0	1.63071	0.815355	−	0.578961i	$-0.196542\pi$
$787$	36003.0	1.63071	0.815355	+	0.578961i	$0.196542\pi$
$788$	−1240.43	−0.0560768
$789$	2955.70	0.133366
$790$	26522.3	1.19446
$791$	−12842.3	−0.577270
$792$	2323.18	0.104231
$793$	−3512.16	−0.157277
$794$	−18267.0	−0.816463
$795$	−10202.8	−0.455167
$796$	−429.942	−0.0191443
$797$	17324.0	0.769948	0.384974	−	0.922927i	$-0.374210\pi$
$797$	17324.0	0.769948	0.384974	+	0.922927i	$0.374210\pi$
$798$	10817.2	0.479855
$799$	6363.90	0.281776
$800$	1687.94	0.0745969
$801$	14778.2	0.651887
$802$	−24947.2	−1.09840
$803$	9372.26	0.411880
$804$	2138.94	0.0938243
$805$	12138.3	0.531453
$806$	4522.96	0.197661
$807$	−2492.75	−0.108735
$808$	−11510.0	−0.501141
$809$	−42252.2	−1.83623	−0.918115	−	0.396315i	$-0.870289\pi$
$809$	−42252.2	−1.83623	−0.918115	+	0.396315i	$0.870289\pi$
$810$	−1818.13	−0.0788673
$811$	−38594.0	−1.67105	−0.835524	−	0.549454i	$-0.814836\pi$
$811$	−38594.0	−1.67105	−0.835524	+	0.549454i	$0.814836\pi$
$812$	−5255.73	−0.227143
$813$	−18534.5	−0.799549
$814$	−6516.06	−0.280575
$815$	−28169.8	−1.21073
$816$	7044.46	0.302212
$817$	8146.45	0.348847
$818$	7357.57	0.314488
$819$	−18059.7	−0.770520
$820$	−95.5948	−0.00407111
$821$	−41057.1	−1.74531	−0.872657	−	0.488334i	$-0.837605\pi$
$821$	−41057.1	−1.74531	−0.872657	+	0.488334i	$0.837605\pi$
$822$	−5162.39	−0.219050
$823$	−39609.6	−1.67765	−0.838824	−	0.544403i	$-0.816756\pi$
$823$	−39609.6	−1.67765	−0.838824	+	0.544403i	$0.816756\pi$
$824$	−12874.3	−0.544295
$825$	1858.61	0.0784347
$826$	−44149.1	−1.85974
$827$	−7685.04	−0.323138	−0.161569	−	0.986861i	$-0.551655\pi$
$827$	−7685.04	−0.323138	−0.161569	+	0.986861i	$0.551655\pi$
$828$	251.154	0.0105413
$829$	2900.90	0.121535	0.0607675	−	0.998152i	$-0.480645\pi$
$829$	2900.90	0.121535	0.0607675	+	0.998152i	$0.480645\pi$
$830$	−12816.9	−0.536003
$831$	16169.3	0.674978
$832$	31502.9	1.31270
$833$	35138.7	1.46157
$834$	9336.27	0.387636
$835$	27407.9	1.13592
$836$	279.001	0.0115424
$837$	783.091	0.0323388
$838$	−41162.2	−1.69681
$839$	10968.5	0.451339	0.225670	−	0.974204i	$-0.427543\pi$
$839$	10968.5	0.451339	0.225670	+	0.974204i	$0.427543\pi$
$840$	20333.0	0.835186
$841$	27190.4	1.11486
$842$	14705.3	0.601876
$843$	−4085.01	−0.166898
$844$	93.6538	0.00381954
$845$	9265.50	0.377211
$846$	−3848.07	−0.156382
$847$	−4217.04	−0.171074
$848$	−23903.6	−0.967988
$849$	−5238.65	−0.211767
$850$	6149.74	0.248158
$851$	−9191.55	−0.370249
$852$	−2331.90	−0.0937671
$853$	−29137.9	−1.16959	−0.584796	−	0.811180i	$-0.698825\pi$
$853$	−29137.9	−1.16959	−0.584796	+	0.811180i	$0.698825\pi$
$854$	−5758.14	−0.230725
$855$	−2849.01	−0.113958
$856$	−27520.6	−1.09887
$857$	−8801.35	−0.350815	−0.175408	−	0.984496i	$-0.556124\pi$
$857$	−8801.35	−0.350815	−0.175408	+	0.984496i	$0.556124\pi$
$858$	5146.22	0.204766
$859$	39138.2	1.55457	0.777286	−	0.629147i	$-0.216596\pi$
$859$	39138.2	1.55457	0.777286	+	0.629147i	$0.216596\pi$
$860$	1173.57	0.0465330
$861$	1816.34	0.0718938
$862$	−42335.7	−1.67281
$863$	−38362.3	−1.51317	−0.756587	−	0.653893i	$-0.773134\pi$
$863$	−38362.3	−1.51317	−0.756587	+	0.653893i	$0.773134\pi$
$864$	809.179	0.0318621
$865$	−14256.7	−0.560395
$866$	−47725.0	−1.87270
$867$	9863.42	0.386366
$868$	−671.186	−0.0262460
$869$	−12997.7	−0.507382
$870$	−15293.2	−0.595964
$871$	61823.1	2.40505
$872$	8802.30	0.341839
$873$	4444.98	0.172325
$874$	−4348.07	−0.168279
$875$	52370.0	2.02335
$876$	1697.25	0.0654619
$877$	17891.6	0.688889	0.344444	−	0.938807i	$-0.388067\pi$
$877$	17891.6	0.688889	0.344444	+	0.938807i	$0.388067\pi$
$878$	23199.5	0.891736
$879$	27198.0	1.04365
$880$	−5309.78	−0.203401
$881$	−11901.5	−0.455133	−0.227566	−	0.973763i	$-0.573077\pi$
$881$	−11901.5	−0.455133	−0.227566	+	0.973763i	$0.573077\pi$
$882$	−21247.4	−0.811153
$883$	−23469.2	−0.894454	−0.447227	−	0.894421i	$-0.647588\pi$
$883$	−23469.2	−0.894454	−0.447227	+	0.894421i	$0.647588\pi$
$884$	−1541.23	−0.0586395
$885$	11627.9	0.441658
$886$	10572.0	0.400873
$887$	−6176.58	−0.233810	−0.116905	−	0.993143i	$-0.537297\pi$
$887$	−6176.58	−0.233810	−0.116905	+	0.993143i	$0.537297\pi$
$888$	−15396.9	−0.581853
$889$	−79281.3	−2.99101
$890$	−36856.8	−1.38814
$891$	891.000	0.0335013
$892$	−1780.10	−0.0668187
$893$	−6029.93	−0.225962
$894$	20587.9	0.770202
$895$	−11874.9	−0.443500
$896$	43292.6	1.61418
$897$	7259.25	0.270211
$898$	49463.9	1.83812
$899$	6586.99	0.244370
$900$	336.581	0.0124660
$901$	16544.1	0.611724
$902$	−517.576	−0.0191058
$903$	−22298.3	−0.821749
$904$	8647.08	0.318139
$905$	13491.6	0.495552
$906$	16285.6	0.597189
$907$	12114.8	0.443512	0.221756	−	0.975102i	$-0.428821\pi$
$907$	12114.8	0.443512	0.221756	+	0.975102i	$0.428821\pi$
$908$	2418.24	0.0883834
$909$	−4414.40	−0.161074
$910$	45040.9	1.64076
$911$	−18960.2	−0.689548	−0.344774	−	0.938686i	$-0.612044\pi$
$911$	−18960.2	−0.689548	−0.344774	+	0.938686i	$0.612044\pi$
$912$	−6674.77	−0.242351
$913$	6281.13	0.227683
$914$	20738.0	0.750495
$915$	1516.57	0.0547936
$916$	−1107.01	−0.0399307
$917$	−33381.8	−1.20214
$918$	2948.12	0.105994
$919$	52340.1	1.87872	0.939359	−	0.342936i	$-0.111421\pi$
$919$	52340.1	1.87872	0.939359	+	0.342936i	$0.111421\pi$
$920$	−8173.05	−0.292888
$921$	−10087.8	−0.360915
$922$	−22506.3	−0.803911
$923$	−67400.2	−2.40358
$924$	−763.675	−0.0271895
$925$	−12317.9	−0.437850
$926$	42761.1	1.51751
$927$	−4937.64	−0.174944
$928$	6806.42	0.240767
$929$	3899.41	0.137713	0.0688566	−	0.997627i	$-0.478065\pi$
$929$	3899.41	0.137713	0.0688566	+	0.997627i	$0.478065\pi$
$930$	−1953.03	−0.0688628
$931$	−33294.7	−1.17206
$932$	2182.26	0.0766978
$933$	6082.60	0.213436
$934$	−3509.69	−0.122956
$935$	3674.98	0.128540
$936$	12160.1	0.424641
$937$	−36793.9	−1.28282	−0.641411	−	0.767197i	$-0.721651\pi$
$937$	−36793.9	−1.28282	−0.641411	+	0.767197i	$0.721651\pi$
$938$	101358.	3.52821
$939$	18933.7	0.658018
$940$	−868.667	−0.0301413
$941$	16189.9	0.560865	0.280433	−	0.959874i	$-0.409522\pi$
$941$	16189.9	0.560865	0.280433	+	0.959874i	$0.409522\pi$
$942$	−22131.7	−0.765488
$943$	−730.093	−0.0252122
$944$	27242.3	0.939260
$945$	7798.24	0.268441
$946$	6354.03	0.218380
$947$	44613.5	1.53088	0.765441	−	0.643506i	$-0.222521\pi$
$947$	44613.5	1.53088	0.765441	+	0.643506i	$0.222521\pi$
$948$	−2353.78	−0.0806404
$949$	49056.5	1.67802
$950$	−5827.01	−0.199003
$951$	−3017.11	−0.102877
$952$	−32970.3	−1.12245
$953$	−12620.8	−0.428989	−0.214495	−	0.976725i	$-0.568810\pi$
$953$	−12620.8	−0.428989	−0.214495	+	0.976725i	$0.568810\pi$
$954$	−10003.7	−0.339500
$955$	35755.1	1.21153
$956$	798.702	0.0270208
$957$	7494.66	0.253154
$958$	−35505.0	−1.19740
$959$	22142.3	0.745581
$960$	−13603.1	−0.457330
$961$	−28949.8	−0.971763
$962$	−34106.5	−1.14307
$963$	−10554.8	−0.353193
$964$	−202.608	−0.00676927
$965$	−40699.4	−1.35768
$966$	11901.4	0.396400
$967$	−4974.65	−0.165433	−0.0827166	−	0.996573i	$-0.526360\pi$
$967$	−4974.65	−0.165433	−0.0827166	+	0.996573i	$0.526360\pi$
$968$	2839.45	0.0942802
$969$	4619.71	0.153154
$970$	−11085.8	−0.366952
$971$	40427.6	1.33613	0.668066	−	0.744102i	$-0.267122\pi$
$971$	40427.6	1.33613	0.668066	+	0.744102i	$0.267122\pi$
$972$	161.353	0.00532450
$973$	−40044.7	−1.31940
$974$	−5091.15	−0.167486
$975$	9728.39	0.319547
$976$	3553.07	0.116528
$977$	−6896.81	−0.225843	−0.112921	−	0.993604i	$-0.536021\pi$
$977$	−6896.81	−0.225843	−0.112921	+	0.993604i	$0.536021\pi$
$978$	−27620.1	−0.903060
$979$	18062.2	0.589654
$980$	−4796.40	−0.156342
$981$	3375.91	0.109872
$982$	51426.6	1.67117
$983$	42429.9	1.37671	0.688354	−	0.725375i	$-0.258333\pi$
$983$	42429.9	1.37671	0.688354	+	0.725375i	$0.258333\pi$
$984$	−1222.99	−0.0396213
$985$	15481.4	0.500791
$986$	24798.2	0.800949
$987$	16505.0	0.532279
$988$	1460.35	0.0470243
$989$	8962.99	0.288176
$990$	−2222.16	−0.0713382
$991$	−26586.9	−0.852230	−0.426115	−	0.904669i	$-0.640118\pi$
$991$	−26586.9	−0.852230	−0.426115	+	0.904669i	$0.640118\pi$
$992$	869.219	0.0278203
$993$	17334.0	0.553956
$994$	−110502.	−3.52606
$995$	5365.97	0.170968
$996$	1137.46	0.0361867
$997$	−53809.0	−1.70928	−0.854639	−	0.519223i	$-0.826221\pi$
$997$	−53809.0	−1.70928	−0.854639	+	0.519223i	$0.826221\pi$
$998$	−11984.8	−0.380131
$999$	−5905.09	−0.187016

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2013.4.a.d.1.12	✓	37

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2013.4.a.d.1.12	✓	37	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:	\( N \)	\(=\)	\( 2013 = 3 \cdot 11 \cdot 61 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	2013.a (trivial)

\(f(q)\)	\(=\)	\(q-2.70850 q^{2} -3.00000 q^{3} -0.664006 q^{4} +8.28724 q^{5} +8.12551 q^{6} -34.8516 q^{7} +23.4665 q^{8} +9.00000 q^{9} +O(q^{10})\)	\(q-2.70850 q^{2} -3.00000 q^{3} -0.664006 q^{4} +8.28724 q^{5} +8.12551 q^{6} -34.8516 q^{7} +23.4665 q^{8} +9.00000 q^{9} -22.4460 q^{10} +11.0000 q^{11} +1.99202 q^{12} +57.5764 q^{13} +94.3957 q^{14} -24.8617 q^{15} -58.2471 q^{16} +40.3137 q^{17} -24.3765 q^{18} -38.1981 q^{19} -5.50278 q^{20} +104.555 q^{21} -29.7935 q^{22} -42.0267 q^{23} -70.3995 q^{24} -56.3216 q^{25} -155.946 q^{26} -27.0000 q^{27} +23.1417 q^{28} -227.111 q^{29} +67.3381 q^{30} -29.0034 q^{31} -29.9696 q^{32} -33.0000 q^{33} -109.190 q^{34} -288.824 q^{35} -5.97605 q^{36} +218.707 q^{37} +103.460 q^{38} -172.729 q^{39} +194.473 q^{40} +17.3721 q^{41} -283.187 q^{42} -213.269 q^{43} -7.30406 q^{44} +74.5852 q^{45} +113.830 q^{46} +157.860 q^{47} +174.741 q^{48} +871.633 q^{49} +152.547 q^{50} -120.941 q^{51} -38.2311 q^{52} +410.384 q^{53} +73.1296 q^{54} +91.1597 q^{55} -817.845 q^{56} +114.594 q^{57} +615.131 q^{58} -467.703 q^{59} +16.5083 q^{60} -61.0000 q^{61} +78.5557 q^{62} -313.664 q^{63} +547.149 q^{64} +477.150 q^{65} +89.3806 q^{66} +1073.76 q^{67} -26.7685 q^{68} +126.080 q^{69} +782.280 q^{70} -1170.62 q^{71} +211.198 q^{72} +852.024 q^{73} -592.369 q^{74} +168.965 q^{75} +25.3637 q^{76} -383.367 q^{77} +467.838 q^{78} -1181.60 q^{79} -482.707 q^{80} +81.0000 q^{81} -47.0524 q^{82} +571.012 q^{83} -69.4250 q^{84} +334.089 q^{85} +577.639 q^{86} +681.333 q^{87} +258.131 q^{88} +1642.02 q^{89} -202.014 q^{90} -2006.63 q^{91} +27.9060 q^{92} +87.0101 q^{93} -427.564 q^{94} -316.557 q^{95} +89.9088 q^{96} +493.887 q^{97} -2360.82 q^{98} +99.0000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 37 q - 4 q^{2} - 111 q^{3} + 158 q^{4} - 15 q^{5} + 12 q^{6} - 77 q^{7} - 69 q^{8} + 333 q^{9}+O(q^{10}) \) 37 * q - 4 * q^2 - 111 * q^3 + 158 * q^4 - 15 * q^5 + 12 * q^6 - 77 * q^7 - 69 * q^8 + 333 * q^9	\( 37 q - 4 q^{2} - 111 q^{3} + 158 q^{4} - 15 q^{5} + 12 q^{6} - 77 q^{7} - 69 q^{8} + 333 q^{9} - 45 q^{10} + 407 q^{11} - 474 q^{12} - 169 q^{13} + 102 q^{14} + 45 q^{15} + 598 q^{16} - 338 q^{17} - 36 q^{18} - 235 q^{19} - 550 q^{20} + 231 q^{21} - 44 q^{22} - 53 q^{23} + 207 q^{24} + 750 q^{25} - 75 q^{26} - 999 q^{27} - 1378 q^{28} - 30 q^{29} + 135 q^{30} - 506 q^{31} - 841 q^{32} - 1221 q^{33} - 316 q^{34} - 822 q^{35} + 1422 q^{36} - 830 q^{37} - 371 q^{38} + 507 q^{39} - 613 q^{40} + 16 q^{41} - 306 q^{42} - 1137 q^{43} + 1738 q^{44} - 135 q^{45} - 659 q^{46} - 489 q^{47} - 1794 q^{48} + 2214 q^{49} + 1066 q^{50} + 1014 q^{51} - 2342 q^{52} + 731 q^{53} + 108 q^{54} - 165 q^{55} + 3051 q^{56} + 705 q^{57} - 611 q^{58} - 425 q^{59} + 1650 q^{60} - 2257 q^{61} + 453 q^{62} - 693 q^{63} + 4919 q^{64} + 1346 q^{65} + 132 q^{66} - 1907 q^{67} - 3236 q^{68} + 159 q^{69} - 1050 q^{70} - 561 q^{71} - 621 q^{72} - 2397 q^{73} - 1840 q^{74} - 2250 q^{75} - 3868 q^{76} - 847 q^{77} + 225 q^{78} + 393 q^{79} - 4031 q^{80} + 2997 q^{81} - 1946 q^{82} - 4191 q^{83} + 4134 q^{84} - 2667 q^{85} + 2405 q^{86} + 90 q^{87} - 759 q^{88} + 1437 q^{89} - 405 q^{90} - 5192 q^{91} - 737 q^{92} + 1518 q^{93} - 1960 q^{94} + 1356 q^{95} + 2523 q^{96} - 2368 q^{97} - 3014 q^{98} + 3663 q^{99}+O(q^{100}) \) 37 * q - 4 * q^2 - 111 * q^3 + 158 * q^4 - 15 * q^5 + 12 * q^6 - 77 * q^7 - 69 * q^8 + 333 * q^9 - 45 * q^10 + 407 * q^11 - 474 * q^12 - 169 * q^13 + 102 * q^14 + 45 * q^15 + 598 * q^16 - 338 * q^17 - 36 * q^18 - 235 * q^19 - 550 * q^20 + 231 * q^21 - 44 * q^22 - 53 * q^23 + 207 * q^24 + 750 * q^25 - 75 * q^26 - 999 * q^27 - 1378 * q^28 - 30 * q^29 + 135 * q^30 - 506 * q^31 - 841 * q^32 - 1221 * q^33 - 316 * q^34 - 822 * q^35 + 1422 * q^36 - 830 * q^37 - 371 * q^38 + 507 * q^39 - 613 * q^40 + 16 * q^41 - 306 * q^42 - 1137 * q^43 + 1738 * q^44 - 135 * q^45 - 659 * q^46 - 489 * q^47 - 1794 * q^48 + 2214 * q^49 + 1066 * q^50 + 1014 * q^51 - 2342 * q^52 + 731 * q^53 + 108 * q^54 - 165 * q^55 + 3051 * q^56 + 705 * q^57 - 611 * q^58 - 425 * q^59 + 1650 * q^60 - 2257 * q^61 + 453 * q^62 - 693 * q^63 + 4919 * q^64 + 1346 * q^65 + 132 * q^66 - 1907 * q^67 - 3236 * q^68 + 159 * q^69 - 1050 * q^70 - 561 * q^71 - 621 * q^72 - 2397 * q^73 - 1840 * q^74 - 2250 * q^75 - 3868 * q^76 - 847 * q^77 + 225 * q^78 + 393 * q^79 - 4031 * q^80 + 2997 * q^81 - 1946 * q^82 - 4191 * q^83 + 4134 * q^84 - 2667 * q^85 + 2405 * q^86 + 90 * q^87 - 759 * q^88 + 1437 * q^89 - 405 * q^90 - 5192 * q^91 - 737 * q^92 + 1518 * q^93 - 1960 * q^94 + 1356 * q^95 + 2523 * q^96 - 2368 * q^97 - 3014 * q^98 + 3663 * q^99

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