LMFDB - Embedded newform 1573.4.a.b.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1573,4,Mod(1,1573)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1573, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("1573.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 1573 = 11^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	1573.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:	$92.8100044390$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\sqrt{17}) $
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 4 $ x^2 - x - 4
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 13)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$2.56155$ of defining polynomial
Character	$\chi$	$=$	1573.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.56155 q^{2} -3.68466 q^{3} -1.43845 q^{4} +0.561553 q^{5} +9.43845 q^{6} -18.1771 q^{7} +24.1771 q^{8} -13.4233 q^{9} +O(q^{10})$	\(q-2.56155 q^{2} -3.68466 q^{3} -1.43845 q^{4} +0.561553 q^{5} +9.43845 q^{6} -18.1771 q^{7} +24.1771 q^{8} -13.4233 q^{9} -1.43845 q^{10} +5.30019 q^{12} +13.0000 q^{13} +46.5616 q^{14} -2.06913 q^{15} -50.4233 q^{16} +25.5464 q^{17} +34.3845 q^{18} +107.970 q^{19} -0.807764 q^{20} +66.9763 q^{21} +73.2614 q^{23} -89.0843 q^{24} -124.685 q^{25} -33.3002 q^{26} +148.946 q^{27} +26.1468 q^{28} -175.909 q^{29} +5.30019 q^{30} -113.093 q^{31} -64.2547 q^{32} -65.4384 q^{34} -10.2074 q^{35} +19.3087 q^{36} +114.808 q^{37} -276.570 q^{38} -47.9006 q^{39} +13.5767 q^{40} +69.6458 q^{41} -171.563 q^{42} -438.302 q^{43} -7.53789 q^{45} -187.663 q^{46} -31.9479 q^{47} +185.793 q^{48} -12.5937 q^{49} +319.386 q^{50} -94.1298 q^{51} -18.6998 q^{52} +2.84658 q^{53} -381.533 q^{54} -439.469 q^{56} -397.831 q^{57} +450.600 q^{58} +71.6325 q^{59} +2.97633 q^{60} +920.695 q^{61} +289.693 q^{62} +243.996 q^{63} +567.978 q^{64} +7.30019 q^{65} -444.280 q^{67} -36.7471 q^{68} -269.943 q^{69} +26.1468 q^{70} -541.719 q^{71} -324.536 q^{72} -764.004 q^{73} -294.086 q^{74} +459.420 q^{75} -155.309 q^{76} +122.700 q^{78} +421.538 q^{79} -28.3153 q^{80} -186.386 q^{81} -178.401 q^{82} -603.797 q^{83} -96.3419 q^{84} +14.3457 q^{85} +1122.73 q^{86} +648.165 q^{87} -1159.88 q^{89} +19.3087 q^{90} -236.302 q^{91} -105.383 q^{92} +416.708 q^{93} +81.8362 q^{94} +60.6307 q^{95} +236.757 q^{96} +583.269 q^{97} +32.2595 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - q^{2} + 5 q^{3} - 7 q^{4} - 3 q^{5} + 23 q^{6} + 9 q^{7} + 3 q^{8} + 35 q^{9}+O(q^{10}) $ 2 * q - q^2 + 5 * q^3 - 7 * q^4 - 3 * q^5 + 23 * q^6 + 9 * q^7 + 3 * q^8 + 35 * q^9	\( 2 q - q^{2} + 5 q^{3} - 7 q^{4} - 3 q^{5} + 23 q^{6} + 9 q^{7} + 3 q^{8} + 35 q^{9} - 7 q^{10} - 43 q^{12} + 26 q^{13} + 89 q^{14} - 33 q^{15} - 39 q^{16} - 19 q^{17} + 110 q^{18} + 84 q^{19} + 19 q^{20} + 303 q^{21} + 196 q^{23} - 273 q^{24} - 237 q^{25} - 13 q^{26} + 335 q^{27} - 125 q^{28} + 44 q^{29} - 43 q^{30} - 86 q^{31} + 123 q^{32} - 135 q^{34} - 107 q^{35} - 250 q^{36} + 209 q^{37} - 314 q^{38} + 65 q^{39} + 89 q^{40} + 230 q^{41} + 197 q^{42} - 287 q^{43} - 180 q^{45} + 4 q^{46} + 435 q^{47} + 285 q^{48} + 383 q^{49} + 144 q^{50} - 481 q^{51} - 91 q^{52} - 118 q^{53} - 91 q^{54} - 1015 q^{56} - 606 q^{57} + 794 q^{58} - 368 q^{59} + 175 q^{60} + 1058 q^{61} + 332 q^{62} + 1560 q^{63} + 769 q^{64} - 39 q^{65} + 68 q^{67} + 211 q^{68} + 796 q^{69} - 125 q^{70} - 131 q^{71} - 1350 q^{72} - 456 q^{73} - 147 q^{74} - 516 q^{75} - 22 q^{76} + 299 q^{78} + 1008 q^{79} - 69 q^{80} + 122 q^{81} + 72 q^{82} - 1958 q^{83} - 1409 q^{84} + 173 q^{85} + 1359 q^{86} + 2558 q^{87} - 720 q^{89} - 250 q^{90} + 117 q^{91} - 788 q^{92} + 652 q^{93} + 811 q^{94} + 146 q^{95} + 1863 q^{96} - 928 q^{97} + 650 q^{98}+O(q^{100}) \) 2 * q - q^2 + 5 * q^3 - 7 * q^4 - 3 * q^5 + 23 * q^6 + 9 * q^7 + 3 * q^8 + 35 * q^9 - 7 * q^10 - 43 * q^12 + 26 * q^13 + 89 * q^14 - 33 * q^15 - 39 * q^16 - 19 * q^17 + 110 * q^18 + 84 * q^19 + 19 * q^20 + 303 * q^21 + 196 * q^23 - 273 * q^24 - 237 * q^25 - 13 * q^26 + 335 * q^27 - 125 * q^28 + 44 * q^29 - 43 * q^30 - 86 * q^31 + 123 * q^32 - 135 * q^34 - 107 * q^35 - 250 * q^36 + 209 * q^37 - 314 * q^38 + 65 * q^39 + 89 * q^40 + 230 * q^41 + 197 * q^42 - 287 * q^43 - 180 * q^45 + 4 * q^46 + 435 * q^47 + 285 * q^48 + 383 * q^49 + 144 * q^50 - 481 * q^51 - 91 * q^52 - 118 * q^53 - 91 * q^54 - 1015 * q^56 - 606 * q^57 + 794 * q^58 - 368 * q^59 + 175 * q^60 + 1058 * q^61 + 332 * q^62 + 1560 * q^63 + 769 * q^64 - 39 * q^65 + 68 * q^67 + 211 * q^68 + 796 * q^69 - 125 * q^70 - 131 * q^71 - 1350 * q^72 - 456 * q^73 - 147 * q^74 - 516 * q^75 - 22 * q^76 + 299 * q^78 + 1008 * q^79 - 69 * q^80 + 122 * q^81 + 72 * q^82 - 1958 * q^83 - 1409 * q^84 + 173 * q^85 + 1359 * q^86 + 2558 * q^87 - 720 * q^89 - 250 * q^90 + 117 * q^91 - 788 * q^92 + 652 * q^93 + 811 * q^94 + 146 * q^95 + 1863 * q^96 - 928 * q^97 + 650 * q^98

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 $

$2$	−2.56155	−0.905646	−0.452823	−	0.891601i	$-0.649583\pi$
$2$	−2.56155	−0.905646	−0.452823	+	0.891601i	$0.649583\pi$
$3$	−3.68466	−0.709113	−0.354556	−	0.935035i	$-0.615368\pi$
$3$	−3.68466	−0.709113	−0.354556	+	0.935035i	$0.615368\pi$
$4$	−1.43845	−0.179806
$5$	0.561553	0.0502268	0.0251134	−	0.999685i	$-0.492005\pi$
$5$	0.561553	0.0502268	0.0251134	+	0.999685i	$0.492005\pi$
$6$	9.43845	0.642205
$7$	−18.1771	−0.981470	−0.490735	−	0.871309i	$-0.663272\pi$
$7$	−18.1771	−0.981470	−0.490735	+	0.871309i	$0.663272\pi$
$8$	24.1771	1.06849
$9$	−13.4233	−0.497159
$10$	−1.43845	−0.0454877
$11$	0	0
$11$	0	0
$12$	5.30019	0.127503
$13$	13.0000	0.277350
$13$	13.0000	0.277350
$14$	46.5616	0.888864
$15$	−2.06913	−0.0356165
$16$	−50.4233	−0.787864
$17$	25.5464	0.364465	0.182233	−	0.983255i	$-0.441668\pi$
$17$	25.5464	0.364465	0.182233	+	0.983255i	$0.441668\pi$
$18$	34.3845	0.450250
$19$	107.970	1.30368	0.651841	−	0.758356i	$-0.273997\pi$
$19$	107.970	1.30368	0.651841	+	0.758356i	$0.273997\pi$
$20$	−0.807764	−0.00903108
$21$	66.9763	0.695973
$22$	0	0
$23$	73.2614	0.664176	0.332088	−	0.943248i	$-0.392247\pi$
$23$	73.2614	0.664176	0.332088	+	0.943248i	$0.392247\pi$
$24$	−89.0843	−0.757677
$25$	−124.685	−0.997477
$26$	−33.3002	−0.251181
$27$	148.946	1.06165
$28$	26.1468	0.176474
$29$	−175.909	−1.12640	−0.563198	−	0.826322i	$-0.690429\pi$
$29$	−175.909	−1.12640	−0.563198	+	0.826322i	$0.690429\pi$
$30$	5.30019	0.0322559
$31$	−113.093	−0.655228	−0.327614	−	0.944812i	$-0.606245\pi$
$31$	−113.093	−0.655228	−0.327614	+	0.944812i	$0.606245\pi$
$32$	−64.2547	−0.354961
$33$	0	0
$34$	−65.4384	−0.330077
$35$	−10.2074	−0.0492961
$36$	19.3087	0.0893921
$37$	114.808	0.510116	0.255058	−	0.966926i	$-0.417905\pi$
$37$	114.808	0.510116	0.255058	+	0.966926i	$0.417905\pi$
$38$	−276.570	−1.18067
$39$	−47.9006	−0.196673
$40$	13.5767	0.0536666
$41$	69.6458	0.265289	0.132645	−	0.991164i	$-0.457653\pi$
$41$	69.6458	0.265289	0.132645	+	0.991164i	$0.457653\pi$
$42$	−171.563	−0.630305
$43$	−438.302	−1.55443	−0.777214	−	0.629236i	$-0.783368\pi$
$43$	−438.302	−1.55443	−0.777214	+	0.629236i	$0.783368\pi$
$44$	0	0
$45$	−7.53789	−0.0249707
$46$	−187.663	−0.601508
$47$	−31.9479	−0.0991506	−0.0495753	−	0.998770i	$-0.515787\pi$
$47$	−31.9479	−0.0991506	−0.0495753	+	0.998770i	$0.515787\pi$
$48$	185.793	0.558684
$49$	−12.5937	−0.0367164
$50$	319.386	0.903361
$51$	−94.1298	−0.258447
$52$	−18.6998	−0.0498692
$53$	2.84658	0.00737752	0.00368876	−	0.999993i	$-0.498826\pi$
$53$	2.84658	0.00737752	0.00368876	+	0.999993i	$0.498826\pi$
$54$	−381.533	−0.961483
$55$	0	0
$56$	−439.469	−1.04869
$57$	−397.831	−0.924457
$58$	450.600	1.02012
$59$	71.6325	0.158064	0.0790319	−	0.996872i	$-0.474817\pi$
$59$	71.6325	0.158064	0.0790319	+	0.996872i	$0.474817\pi$
$60$	2.97633	0.00640405
$61$	920.695	1.93251	0.966253	−	0.257593i	$-0.0829295\pi$
$61$	920.695	1.93251	0.966253	+	0.257593i	$0.0829295\pi$
$62$	289.693	0.593404
$63$	243.996	0.487947
$64$	567.978	1.10933
$65$	7.30019	0.0139304
$66$	0	0
$67$	−444.280	−0.810112	−0.405056	−	0.914292i	$-0.632748\pi$
$67$	−444.280	−0.810112	−0.405056	+	0.914292i	$0.632748\pi$
$68$	−36.7471	−0.0655330
$69$	−269.943	−0.470976
$70$	26.1468	0.0446448
$71$	−541.719	−0.905496	−0.452748	−	0.891639i	$-0.649556\pi$
$71$	−541.719	−0.905496	−0.452748	+	0.891639i	$0.649556\pi$
$72$	−324.536	−0.531207
$73$	−764.004	−1.22493	−0.612465	−	0.790498i	$-0.709822\pi$
$73$	−764.004	−1.22493	−0.612465	+	0.790498i	$0.709822\pi$
$74$	−294.086	−0.461984
$75$	459.420	0.707324
$76$	−155.309	−0.234410
$77$	0	0
$78$	122.700	0.178116
$79$	421.538	0.600338	0.300169	−	0.953886i	$-0.402957\pi$
$79$	421.538	0.600338	0.300169	+	0.953886i	$0.402957\pi$
$80$	−28.3153	−0.0395719
$81$	−186.386	−0.255674
$82$	−178.401	−0.240258
$83$	−603.797	−0.798498	−0.399249	−	0.916842i	$-0.630729\pi$
$83$	−603.797	−0.798498	−0.399249	+	0.916842i	$0.630729\pi$
$84$	−96.3419	−0.125140
$85$	14.3457	0.0183059
$86$	1122.73	1.40776
$87$	648.165	0.798742
$88$	0	0
$89$	−1159.88	−1.38143	−0.690715	−	0.723127i	$-0.742704\pi$
$89$	−1159.88	−1.38143	−0.690715	+	0.723127i	$0.742704\pi$
$90$	19.3087	0.0226146
$91$	−236.302	−0.272211
$92$	−105.383	−0.119423
$93$	416.708	0.464631
$94$	81.8362	0.0897953
$95$	60.6307	0.0654798
$96$	236.757	0.251707
$97$	583.269	0.610536	0.305268	−	0.952267i	$-0.401254\pi$
$97$	583.269	0.610536	0.305268	+	0.952267i	$0.401254\pi$
$98$	32.2595	0.0332521
$99$	0	0
$100$	179.352	0.179352
$101$	−921.740	−0.908085	−0.454043	−	0.890980i	$-0.650019\pi$
$101$	−921.740	−0.908085	−0.454043	+	0.890980i	$0.650019\pi$
$102$	241.118	0.234061
$103$	−930.712	−0.890347	−0.445174	−	0.895444i	$-0.646858\pi$
$103$	−930.712	−0.890347	−0.445174	+	0.895444i	$0.646858\pi$
$104$	314.302	0.296345
$105$	37.6107	0.0349565
$106$	−7.29168	−0.00668142
$107$	−857.383	−0.774638	−0.387319	−	0.921946i	$-0.626599\pi$
$107$	−857.383	−0.774638	−0.387319	+	0.921946i	$0.626599\pi$
$108$	−214.251	−0.190892
$109$	−671.853	−0.590384	−0.295192	−	0.955438i	$-0.595384\pi$
$109$	−671.853	−0.590384	−0.295192	+	0.955438i	$0.595384\pi$
$110$	0	0
$111$	−423.027	−0.361730
$112$	916.548	0.773265
$113$	641.474	0.534024	0.267012	−	0.963693i	$-0.413964\pi$
$113$	641.474	0.534024	0.267012	+	0.963693i	$0.413964\pi$
$114$	1019.07	0.837231
$115$	41.1401	0.0333594
$116$	253.036	0.202533
$117$	−174.503	−0.137887
$118$	−183.491	−0.143150
$119$	−464.359	−0.357712
$120$	−50.0255	−0.0380557
$121$	0	0
$122$	−2358.41	−1.75017
$123$	−256.621	−0.188120
$124$	162.678	0.117814
$125$	−140.211	−0.100327
$126$	−625.009	−0.441907
$127$	553.174	0.386506	0.193253	−	0.981149i	$-0.438096\pi$
$127$	553.174	0.386506	0.193253	+	0.981149i	$0.438096\pi$
$128$	−940.868	−0.649702
$129$	1614.99	1.10227
$130$	−18.6998	−0.0126160
$131$	−2056.40	−1.37152	−0.685758	−	0.727830i	$-0.740529\pi$
$131$	−2056.40	−1.37152	−0.685758	+	0.727830i	$0.740529\pi$
$132$	0	0
$133$	−1962.57	−1.27952
$134$	1138.05	0.733674
$135$	83.6411	0.0533235
$136$	617.637	0.389426
$137$	−1808.57	−1.12786	−0.563928	−	0.825824i	$-0.690710\pi$
$137$	−1808.57	−1.12786	−0.563928	+	0.825824i	$0.690710\pi$
$138$	691.474	0.426537
$139$	−1493.64	−0.911428	−0.455714	−	0.890126i	$-0.650616\pi$
$139$	−1493.64	−0.911428	−0.455714	+	0.890126i	$0.650616\pi$
$140$	14.6828	0.00886373
$141$	117.717	0.0703090
$142$	1387.64	0.820058
$143$	0	0
$144$	676.847	0.391694
$145$	−98.7822	−0.0565753
$146$	1957.04	1.10935
$147$	46.4036	0.0260361
$148$	−165.145	−0.0917218
$149$	2759.02	1.51696	0.758482	−	0.651694i	$-0.225941\pi$
$149$	2759.02	1.51696	0.758482	+	0.651694i	$0.225941\pi$
$150$	−1176.83	−0.640585
$151$	976.355	0.526190	0.263095	−	0.964770i	$-0.415257\pi$
$151$	976.355	0.526190	0.263095	+	0.964770i	$0.415257\pi$
$152$	2610.39	1.39297
$153$	−342.917	−0.181197
$154$	0	0
$155$	−63.5076	−0.0329100
$156$	68.9024	0.0353629
$157$	−564.875	−0.287146	−0.143573	−	0.989640i	$-0.545859\pi$
$157$	−564.875	−0.287146	−0.143573	+	0.989640i	$0.545859\pi$
$158$	−1079.79	−0.543694
$159$	−10.4887	−0.00523149
$160$	−36.0824	−0.0178285
$161$	−1331.68	−0.651869
$162$	477.438	0.231550
$163$	1508.53	0.724892	0.362446	−	0.932005i	$-0.381942\pi$
$163$	1508.53	0.724892	0.362446	+	0.932005i	$0.381942\pi$
$164$	−100.182	−0.0477005
$165$	0	0
$166$	1546.66	0.723157
$167$	−592.521	−0.274555	−0.137277	−	0.990533i	$-0.543835\pi$
$167$	−592.521	−0.274555	−0.137277	+	0.990533i	$0.543835\pi$
$168$	1619.29	0.743638
$169$	169.000	0.0769231
$170$	−36.7471	−0.0165787
$171$	−1449.31	−0.648137
$172$	630.474	0.279495
$173$	4495.57	1.97568	0.987838	−	0.155488i	$-0.0496952\pi$
$173$	4495.57	1.97568	0.987838	+	0.155488i	$0.0496952\pi$
$174$	−1660.31	−0.723377
$175$	2266.40	0.978994
$176$	0	0
$177$	−263.941	−0.112085
$178$	2971.10	1.25109
$179$	−154.285	−0.0644235	−0.0322117	−	0.999481i	$-0.510255\pi$
$179$	−154.285	−0.0644235	−0.0322117	+	0.999481i	$0.510255\pi$
$180$	10.8429	0.00448988
$181$	1071.35	0.439959	0.219979	−	0.975505i	$-0.429401\pi$
$181$	1071.35	0.439959	0.219979	+	0.975505i	$0.429401\pi$
$182$	605.300	0.246527
$183$	−3392.45	−1.37037
$184$	1771.25	0.709663
$185$	64.4706	0.0256215
$186$	−1067.42	−0.420791
$187$	0	0
$188$	45.9554	0.0178279
$189$	−2707.40	−1.04198
$190$	−155.309	−0.0593015
$191$	677.203	0.256548	0.128274	−	0.991739i	$-0.459056\pi$
$191$	677.203	0.256548	0.128274	+	0.991739i	$0.459056\pi$
$192$	−2092.81	−0.786642
$193$	−1321.68	−0.492936	−0.246468	−	0.969151i	$-0.579270\pi$
$193$	−1321.68	−0.492936	−0.246468	+	0.969151i	$0.579270\pi$
$194$	−1494.07	−0.552929
$195$	−26.8987	−0.00987823
$196$	18.1154	0.00660183
$197$	−1267.37	−0.458356	−0.229178	−	0.973385i	$-0.573604\pi$
$197$	−1267.37	−0.458356	−0.229178	+	0.973385i	$0.573604\pi$
$198$	0	0
$199$	2396.24	0.853593	0.426796	−	0.904348i	$-0.359642\pi$
$199$	2396.24	0.853593	0.426796	+	0.904348i	$0.359642\pi$
$200$	−3014.51	−1.06579
$201$	1637.02	0.574460
$202$	2361.09	0.822403
$203$	3197.51	1.10552
$204$	135.401	0.0464703
$205$	39.1098	0.0133246
$206$	2384.07	0.806339
$207$	−983.409	−0.330201
$208$	−655.503	−0.218514
$209$	0	0
$210$	−96.3419	−0.0316582
$211$	91.5539	0.0298712	0.0149356	−	0.999888i	$-0.495246\pi$
$211$	91.5539	0.0298712	0.0149356	+	0.999888i	$0.495246\pi$
$212$	−4.09466	−0.00132652
$213$	1996.05	0.642099
$214$	2196.23	0.701548
$215$	−246.130	−0.0780740
$216$	3601.08	1.13436
$217$	2055.70	0.643087
$218$	1720.99	0.534679
$219$	2815.09	0.868613
$220$	0	0
$221$	332.103	0.101085
$222$	1083.61	0.327599
$223$	1235.42	0.370985	0.185493	−	0.982646i	$-0.440612\pi$
$223$	1235.42	0.370985	0.185493	+	0.982646i	$0.440612\pi$
$224$	1167.96	0.348383
$225$	1673.68	0.495905
$226$	−1643.17	−0.483637
$227$	−3301.66	−0.965370	−0.482685	−	0.875794i	$-0.660338\pi$
$227$	−3301.66	−0.965370	−0.482685	+	0.875794i	$0.660338\pi$
$228$	572.260	0.166223
$229$	211.283	0.0609694	0.0304847	−	0.999535i	$-0.490295\pi$
$229$	211.283	0.0609694	0.0304847	+	0.999535i	$0.490295\pi$
$230$	−105.383	−0.0302118
$231$	0	0
$232$	−4252.97	−1.20354
$233$	256.724	0.0721827	0.0360913	−	0.999348i	$-0.488509\pi$
$233$	256.724	0.0721827	0.0360913	+	0.999348i	$0.488509\pi$
$234$	446.998	0.124877
$235$	−17.9404	−0.00498002
$236$	−103.040	−0.0284208
$237$	−1553.22	−0.425708
$238$	1189.48	0.323960
$239$	3549.62	0.960694	0.480347	−	0.877078i	$-0.340511\pi$
$239$	3549.62	0.960694	0.480347	+	0.877078i	$0.340511\pi$
$240$	104.332	0.0280609
$241$	5030.10	1.34447	0.672235	−	0.740338i	$-0.265335\pi$
$241$	5030.10	1.34447	0.672235	+	0.740338i	$0.265335\pi$
$242$	0	0
$243$	−3334.77	−0.880353
$244$	−1324.37	−0.347476
$245$	−7.07204	−0.00184415
$246$	657.349	0.170370
$247$	1403.61	0.361576
$248$	−2734.25	−0.700102
$249$	2224.79	0.566226
$250$	359.158	0.0908606
$251$	−718.784	−0.180754	−0.0903770	−	0.995908i	$-0.528807\pi$
$251$	−718.784	−0.180754	−0.0903770	+	0.995908i	$0.528807\pi$
$252$	−350.976	−0.0877357
$253$	0	0
$254$	−1416.98	−0.350038
$255$	−52.8588	−0.0129810
$256$	−2133.74	−0.520933
$257$	1280.79	0.310871	0.155435	−	0.987846i	$-0.450322\pi$
$257$	1280.79	0.310871	0.155435	+	0.987846i	$0.450322\pi$
$258$	−4136.89	−0.998262
$259$	−2086.87	−0.500663
$260$	−10.5009	−0.00250477
$261$	2361.28	0.559998
$262$	5267.58	1.24211
$263$	−5225.55	−1.22517	−0.612587	−	0.790403i	$-0.709871\pi$
$263$	−5225.55	−1.22517	−0.612587	+	0.790403i	$0.709871\pi$
$264$	0	0
$265$	1.59851	0.000370549 0
$266$	5027.24	1.15880
$267$	4273.77	0.979590
$268$	639.074	0.145663
$269$	6443.80	1.46054	0.730270	−	0.683158i	$-0.239394\pi$
$269$	6443.80	1.46054	0.730270	+	0.683158i	$0.239394\pi$
$270$	−214.251	−0.0482922
$271$	3929.93	0.880909	0.440455	−	0.897775i	$-0.354817\pi$
$271$	3929.93	0.880909	0.440455	+	0.897775i	$0.354817\pi$
$272$	−1288.13	−0.287149
$273$	870.692	0.193028
$274$	4632.74	1.02144
$275$	0	0
$276$	388.299	0.0846842
$277$	5884.40	1.27639	0.638194	−	0.769876i	$-0.279682\pi$
$277$	5884.40	1.27639	0.638194	+	0.769876i	$0.279682\pi$
$278$	3826.03	0.825431
$279$	1518.08	0.325752
$280$	−246.785	−0.0526722
$281$	−3529.79	−0.749358	−0.374679	−	0.927155i	$-0.622247\pi$
$281$	−3529.79	−0.749358	−0.374679	+	0.927155i	$0.622247\pi$
$282$	−301.538	−0.0636750
$283$	2611.00	0.548438	0.274219	−	0.961667i	$-0.411581\pi$
$283$	2611.00	0.548438	0.274219	+	0.961667i	$0.411581\pi$
$284$	779.234	0.162813
$285$	−223.403	−0.0464325
$286$	0	0
$287$	−1265.96	−0.260373
$288$	862.510	0.176472
$289$	−4260.38	−0.867165
$290$	253.036	0.0512372
$291$	−2149.15	−0.432939
$292$	1098.98	0.220250
$293$	5491.03	1.09484	0.547422	−	0.836857i	$-0.315609\pi$
$293$	5491.03	1.09484	0.547422	+	0.836857i	$0.315609\pi$
$294$	−118.865	−0.0235795
$295$	40.2255	0.00793904
$296$	2775.72	0.545052
$297$	0	0
$298$	−7067.37	−1.37383
$299$	952.398	0.184209
$300$	−660.852	−0.127181
$301$	7967.05	1.52563
$302$	−2500.99	−0.476542
$303$	3396.30	0.643935
$304$	−5444.19	−1.02712
$305$	517.019	0.0970637
$306$	878.399	0.164100
$307$	7307.59	1.35852	0.679261	−	0.733897i	$-0.262300\pi$
$307$	7307.59	1.35852	0.679261	+	0.733897i	$0.262300\pi$
$308$	0	0
$309$	3429.36	0.631357
$310$	162.678	0.0298048
$311$	7904.92	1.44131	0.720654	−	0.693295i	$-0.243842\pi$
$311$	7904.92	1.44131	0.720654	+	0.693295i	$0.243842\pi$
$312$	−1158.10	−0.210142
$313$	10002.4	1.80629	0.903145	−	0.429336i	$-0.141252\pi$
$313$	10002.4	1.80629	0.903145	+	0.429336i	$0.141252\pi$
$314$	1446.96	0.260053
$315$	137.017	0.0245080
$316$	−606.360	−0.107944
$317$	−6230.81	−1.10397	−0.551983	−	0.833856i	$-0.686129\pi$
$317$	−6230.81	−1.10397	−0.551983	+	0.833856i	$0.686129\pi$
$318$	26.8673	0.00473788
$319$	0	0
$320$	318.950	0.0557182
$321$	3159.16	0.549306
$322$	3411.16	0.590362
$323$	2758.24	0.475147
$324$	268.107	0.0459717
$325$	−1620.90	−0.276650
$326$	−3864.19	−0.656495
$327$	2475.55	0.418649
$328$	1683.83	0.283458
$329$	580.719	0.0973134
$330$	0	0
$331$	−4634.51	−0.769594	−0.384797	−	0.923001i	$-0.625729\pi$
$331$	−4634.51	−0.769594	−0.384797	+	0.923001i	$0.625729\pi$
$332$	868.531	0.143575
$333$	−1541.10	−0.253609
$334$	1517.77	0.248649
$335$	−249.487	−0.0406893
$336$	−3377.17	−0.548332
$337$	−3029.82	−0.489747	−0.244874	−	0.969555i	$-0.578746\pi$
$337$	−3029.82	−0.489747	−0.244874	+	0.969555i	$0.578746\pi$
$338$	−432.902	−0.0696651
$339$	−2363.61	−0.378684
$340$	−20.6355	−0.00329151
$341$	0	0
$342$	3712.48	0.586982
$343$	6463.66	1.01751
$344$	−10596.9	−1.66089
$345$	−151.587	−0.0236556
$346$	−11515.6	−1.78926
$347$	−2841.60	−0.439611	−0.219805	−	0.975544i	$-0.570542\pi$
$347$	−2841.60	−0.439611	−0.219805	+	0.975544i	$0.570542\pi$
$348$	−932.351	−0.143619
$349$	−7565.68	−1.16040	−0.580202	−	0.814472i	$-0.697027\pi$
$349$	−7565.68	−1.16040	−0.580202	+	0.814472i	$0.697027\pi$
$350$	−5805.51	−0.886622
$351$	1936.30	0.294450
$352$	0	0
$353$	−2339.44	−0.352736	−0.176368	−	0.984324i	$-0.556435\pi$
$353$	−2339.44	−0.352736	−0.176368	+	0.984324i	$0.556435\pi$
$354$	676.100	0.101509
$355$	−304.204	−0.0454802
$356$	1668.43	0.248389
$357$	1711.00	0.253658
$358$	395.209	0.0583449
$359$	2531.68	0.372192	0.186096	−	0.982532i	$-0.440417\pi$
$359$	2531.68	0.372192	0.186096	+	0.982532i	$0.440417\pi$
$360$	−182.244	−0.0266809
$361$	4798.45	0.699585
$362$	−2744.31	−0.398447
$363$	0	0
$364$	339.908	0.0489451
$365$	−429.028	−0.0615243
$366$	8689.93	1.24107
$367$	6577.81	0.935583	0.467792	−	0.883839i	$-0.345050\pi$
$367$	6577.81	0.935583	0.467792	+	0.883839i	$0.345050\pi$
$368$	−3694.08	−0.523280
$369$	−934.876	−0.131891
$370$	−165.145	−0.0232040
$371$	−51.7426	−0.00724081
$372$	−599.413	−0.0835433
$373$	−2902.72	−0.402942	−0.201471	−	0.979495i	$-0.564572\pi$
$373$	−2902.72	−0.402942	−0.201471	+	0.979495i	$0.564572\pi$
$374$	0	0
$375$	516.630	0.0711431
$376$	−772.407	−0.105941
$377$	−2286.82	−0.312406
$378$	6935.16	0.943667
$379$	−1865.73	−0.252866	−0.126433	−	0.991975i	$-0.540353\pi$
$379$	−1865.73	−0.252866	−0.126433	+	0.991975i	$0.540353\pi$
$380$	−87.2140	−0.0117736
$381$	−2038.26	−0.274076
$382$	−1734.69	−0.232342
$383$	10836.0	1.44567	0.722837	−	0.691019i	$-0.242838\pi$
$383$	10836.0	1.44567	0.722837	+	0.691019i	$0.242838\pi$
$384$	3466.78	0.460712
$385$	0	0
$386$	3385.55	0.446425
$387$	5883.46	0.772798
$388$	−839.001	−0.109778
$389$	−9520.34	−1.24088	−0.620438	−	0.784256i	$-0.713045\pi$
$389$	−9520.34	−1.24088	−0.620438	+	0.784256i	$0.713045\pi$
$390$	68.9024	0.00894618
$391$	1871.56	0.242069
$392$	−304.480	−0.0392310
$393$	7577.13	0.972559
$394$	3246.43	0.415108
$395$	236.716	0.0301531
$396$	0	0
$397$	−10108.8	−1.27796	−0.638978	−	0.769225i	$-0.720642\pi$
$397$	−10108.8	−1.27796	−0.638978	+	0.769225i	$0.720642\pi$
$398$	−6138.10	−0.773053
$399$	7231.41	0.907327
$400$	6287.01	0.785876
$401$	2084.38	0.259573	0.129787	−	0.991542i	$-0.458571\pi$
$401$	2084.38	0.259573	0.129787	+	0.991542i	$0.458571\pi$
$402$	−4193.32	−0.520258
$403$	−1470.21	−0.181728
$404$	1325.88	0.163279
$405$	−104.666	−0.0128417
$406$	−8190.60	−1.00121
$407$	0	0
$408$	−2275.78	−0.276147
$409$	9716.53	1.17470	0.587349	−	0.809334i	$-0.300172\pi$
$409$	9716.53	1.17470	0.587349	+	0.809334i	$0.300172\pi$
$410$	−100.182	−0.0120674
$411$	6663.95	0.799777
$412$	1338.78	0.160090
$413$	−1302.07	−0.155135
$414$	2519.05	0.299045
$415$	−339.064	−0.0401060
$416$	−835.311	−0.0984483
$417$	5503.54	0.646305
$418$	0	0
$419$	13381.9	1.56026	0.780129	−	0.625619i	$-0.215153\pi$
$419$	13381.9	1.56026	0.780129	+	0.625619i	$0.215153\pi$
$420$	−54.1011	−0.00628539
$421$	−9463.37	−1.09553	−0.547763	−	0.836633i	$-0.684521\pi$
$421$	−9463.37	−1.09553	−0.547763	+	0.836633i	$0.684521\pi$
$422$	−234.520	−0.0270527
$423$	428.846	0.0492936
$424$	68.8221	0.00788278
$425$	−3185.24	−0.363546
$426$	−5112.98	−0.581514
$427$	−16735.5	−1.89670
$428$	1233.30	0.139285
$429$	0	0
$430$	630.474	0.0707074
$431$	−4852.28	−0.542288	−0.271144	−	0.962539i	$-0.587402\pi$
$431$	−4852.28	−0.542288	−0.271144	+	0.962539i	$0.587402\pi$
$432$	−7510.35	−0.836439
$433$	−8208.00	−0.910973	−0.455486	−	0.890243i	$-0.650535\pi$
$433$	−8208.00	−0.910973	−0.455486	+	0.890243i	$0.650535\pi$
$434$	−5265.78	−0.582409
$435$	363.979	0.0401183
$436$	966.425	0.106155
$437$	7910.01	0.865874
$438$	−7211.01	−0.786656
$439$	2993.80	0.325481	0.162741	−	0.986669i	$-0.447967\pi$
$439$	2993.80	0.325481	0.162741	+	0.986669i	$0.447967\pi$
$440$	0	0
$441$	169.049	0.0182539
$442$	−850.700	−0.0915468
$443$	9743.67	1.04500	0.522501	−	0.852639i	$-0.324999\pi$
$443$	9743.67	1.04500	0.522501	+	0.852639i	$0.324999\pi$
$444$	608.503	0.0650411
$445$	−651.335	−0.0693848
$446$	−3164.59	−0.335981
$447$	−10166.0	−1.07570
$448$	−10324.2	−1.08878
$449$	−561.459	−0.0590131	−0.0295065	−	0.999565i	$-0.509394\pi$
$449$	−561.459	−0.0590131	−0.0295065	+	0.999565i	$0.509394\pi$
$450$	−4287.22	−0.449114
$451$	0	0
$452$	−922.726	−0.0960207
$453$	−3597.54	−0.373128
$454$	8457.38	0.874283
$455$	−132.696	−0.0136723
$456$	−9618.40	−0.987770
$457$	−13758.4	−1.40830	−0.704148	−	0.710054i	$-0.748671\pi$
$457$	−13758.4	−1.40830	−0.704148	+	0.710054i	$0.748671\pi$
$458$	−541.213	−0.0552166
$459$	3805.03	0.386936
$460$	−59.1779	−0.00599823
$461$	−12009.2	−1.21329	−0.606644	−	0.794974i	$-0.707485\pi$
$461$	−12009.2	−1.21329	−0.606644	+	0.794974i	$0.707485\pi$
$462$	0	0
$463$	13635.7	1.36870	0.684348	−	0.729156i	$-0.260087\pi$
$463$	13635.7	1.36870	0.684348	+	0.729156i	$0.260087\pi$
$464$	8869.91	0.887447
$465$	234.004	0.0233369
$466$	−657.613	−0.0653719
$467$	8821.95	0.874157	0.437079	−	0.899423i	$-0.356013\pi$
$467$	8821.95	0.874157	0.437079	+	0.899423i	$0.356013\pi$
$468$	251.013	0.0247929
$469$	8075.72	0.795100
$470$	45.9554	0.00451013
$471$	2081.37	0.203619
$472$	1731.87	0.168889
$473$	0	0
$474$	3978.66	0.385540
$475$	−13462.2	−1.30039
$476$	667.956	0.0643187
$477$	−38.2105	−0.00366780
$478$	−9092.54	−0.870049
$479$	14620.0	1.39459	0.697293	−	0.716786i	$-0.254388\pi$
$479$	14620.0	1.39459	0.697293	+	0.716786i	$0.254388\pi$
$480$	132.951	0.0126424
$481$	1492.50	0.141481
$482$	−12884.9	−1.21761
$483$	4906.78	0.462249
$484$	0	0
$485$	327.536	0.0306653
$486$	8542.20	0.797288
$487$	−9798.86	−0.911763	−0.455882	−	0.890040i	$-0.650676\pi$
$487$	−9798.86	−0.911763	−0.455882	+	0.890040i	$0.650676\pi$
$488$	22259.7	2.06486
$489$	−5558.43	−0.514030
$490$	18.1154	0.00167014
$491$	10836.1	0.995977	0.497989	−	0.867184i	$-0.334072\pi$
$491$	10836.1	0.995977	0.497989	+	0.867184i	$0.334072\pi$
$492$	369.136	0.0338251
$493$	−4493.84	−0.410532
$494$	−3595.41	−0.327460
$495$	0	0
$496$	5702.51	0.516230
$497$	9846.86	0.888717
$498$	−5698.91	−0.512800
$499$	2589.96	0.232349	0.116175	−	0.993229i	$-0.462937\pi$
$499$	2589.96	0.232349	0.116175	+	0.993229i	$0.462937\pi$
$500$	201.686	0.0180394
$501$	2183.24	0.194690
$502$	1841.20	0.163699
$503$	17067.5	1.51292	0.756462	−	0.654038i	$-0.226926\pi$
$503$	17067.5	1.51292	0.756462	+	0.654038i	$0.226926\pi$
$504$	5899.12	0.521364
$505$	−517.606	−0.0456102
$506$	0	0
$507$	−622.707	−0.0545471
$508$	−795.712	−0.0694961
$509$	−1012.89	−0.0882038	−0.0441019	−	0.999027i	$-0.514043\pi$
$509$	−1012.89	−0.0882038	−0.0441019	+	0.999027i	$0.514043\pi$
$510$	135.401	0.0117562
$511$	13887.4	1.20223
$512$	12992.6	1.12148
$513$	16081.7	1.38406
$514$	−3280.82	−0.281539
$515$	−522.644	−0.0447193
$516$	−2323.08	−0.198194
$517$	0	0
$518$	5345.63	0.453424
$519$	−16564.6	−1.40098
$520$	176.497	0.0148845
$521$	−14367.7	−1.20818	−0.604089	−	0.796917i	$-0.706463\pi$
$521$	−14367.7	−1.20818	−0.604089	+	0.796917i	$0.706463\pi$
$522$	−6048.54	−0.507160
$523$	16219.9	1.35611	0.678057	−	0.735010i	$-0.262822\pi$
$523$	16219.9	1.35611	0.678057	+	0.735010i	$0.262822\pi$
$524$	2958.02	0.246607
$525$	−8350.92	−0.694217
$526$	13385.5	1.10957
$527$	−2889.11	−0.238808
$528$	0	0
$529$	−6799.77	−0.558870
$530$	−4.09466	−0.000335586 0
$531$	−961.545	−0.0785828
$532$	2823.06	0.230066
$533$	905.396	0.0735780
$534$	−10947.5	−0.887161
$535$	−481.466	−0.0389076
$536$	−10741.4	−0.865593
$537$	568.488	0.0456835
$538$	−16506.1	−1.32273
$539$	0	0
$540$	−120.313	−0.00958788
$541$	−17592.2	−1.39806	−0.699029	−	0.715094i	$-0.746384\pi$
$541$	−17592.2	−1.39806	−0.699029	+	0.715094i	$0.746384\pi$
$542$	−10066.7	−0.797792
$543$	−3947.55	−0.311980
$544$	−1641.48	−0.129371
$545$	−377.281	−0.0296531
$546$	−2230.32	−0.174815
$547$	−10504.6	−0.821103	−0.410552	−	0.911837i	$-0.634664\pi$
$547$	−10504.6	−0.821103	−0.410552	+	0.911837i	$0.634664\pi$
$548$	2601.53	0.202795
$549$	−12358.8	−0.960763
$550$	0	0
$551$	−18992.8	−1.46846
$552$	−6526.44	−0.503231
$553$	−7662.33	−0.589214
$554$	−15073.2	−1.15596
$555$	−237.552	−0.0181685
$556$	2148.52	0.163880
$557$	507.558	0.0386102	0.0193051	−	0.999814i	$-0.493855\pi$
$557$	507.558	0.0386102	0.0193051	+	0.999814i	$0.493855\pi$
$558$	−3888.64	−0.295016
$559$	−5697.93	−0.431121
$560$	514.690	0.0388386
$561$	0	0
$562$	9041.75	0.678653
$563$	3443.14	0.257746	0.128873	−	0.991661i	$-0.458864\pi$
$563$	3443.14	0.257746	0.128873	+	0.991661i	$0.458864\pi$
$564$	−169.330	−0.0126420
$565$	360.221	0.0268223
$566$	−6688.21	−0.496690
$567$	3387.96	0.250936
$568$	−13097.2	−0.967509
$569$	−23972.2	−1.76620	−0.883098	−	0.469189i	$-0.844546\pi$
$569$	−23972.2	−1.76620	−0.883098	+	0.469189i	$0.844546\pi$
$570$	572.260	0.0420514
$571$	7458.32	0.546622	0.273311	−	0.961926i	$-0.411881\pi$
$571$	7458.32	0.546622	0.273311	+	0.961926i	$0.411881\pi$
$572$	0	0
$573$	−2495.26	−0.181922
$574$	3242.82	0.235806
$575$	−9134.57	−0.662501
$576$	−7624.14	−0.551515
$577$	5669.57	0.409059	0.204530	−	0.978860i	$-0.434434\pi$
$577$	5669.57	0.409059	0.204530	+	0.978860i	$0.434434\pi$
$578$	10913.2	0.785344
$579$	4869.94	0.349547
$580$	142.093	0.0101726
$581$	10975.3	0.783702
$582$	5505.15	0.392089
$583$	0	0
$584$	−18471.4	−1.30882
$585$	−97.9925	−0.00692563
$586$	−14065.6	−0.991541
$587$	1017.39	0.0715371	0.0357685	−	0.999360i	$-0.488612\pi$
$587$	1017.39	0.0715371	0.0357685	+	0.999360i	$0.488612\pi$
$588$	−66.7491	−0.00468144
$589$	−12210.6	−0.854208
$590$	−103.040	−0.00718996
$591$	4669.81	0.325026
$592$	−5788.99	−0.401902
$593$	10198.2	0.706221	0.353111	−	0.935582i	$-0.385124\pi$
$593$	10198.2	0.706221	0.353111	+	0.935582i	$0.385124\pi$
$594$	0	0
$595$	−260.762	−0.0179667
$596$	−3968.70	−0.272759
$597$	−8829.33	−0.605294
$598$	−2439.62	−0.166828
$599$	12516.3	0.853763	0.426881	−	0.904308i	$-0.359612\pi$
$599$	12516.3	0.853763	0.426881	+	0.904308i	$0.359612\pi$
$600$	11107.4	0.755766
$601$	−9627.46	−0.653431	−0.326716	−	0.945123i	$-0.605942\pi$
$601$	−9627.46	−0.653431	−0.326716	+	0.945123i	$0.605942\pi$
$602$	−20408.0	−1.38168
$603$	5963.70	0.402754
$604$	−1404.44	−0.0946120
$605$	0	0
$606$	−8699.80	−0.583177
$607$	−6667.20	−0.445821	−0.222910	−	0.974839i	$-0.571556\pi$
$607$	−6667.20	−0.445821	−0.222910	+	0.974839i	$0.571556\pi$
$608$	−6937.56	−0.462755
$609$	−11781.7	−0.783942
$610$	−1324.37	−0.0879053
$611$	−415.323	−0.0274994
$612$	493.268	0.0325803
$613$	23085.4	1.52106	0.760530	−	0.649302i	$-0.224939\pi$
$613$	23085.4	1.52106	0.760530	+	0.649302i	$0.224939\pi$
$614$	−18718.8	−1.23034
$615$	−144.106	−0.00944866
$616$	0	0
$617$	3049.24	0.198959	0.0994796	−	0.995040i	$-0.468282\pi$
$617$	3049.24	0.198959	0.0994796	+	0.995040i	$0.468282\pi$
$618$	−8784.48	−0.571786
$619$	7296.58	0.473787	0.236894	−	0.971536i	$-0.423871\pi$
$619$	7296.58	0.473787	0.236894	+	0.971536i	$0.423871\pi$
$620$	91.3523	0.00591741
$621$	10912.0	0.705126
$622$	−20248.9	−1.30531
$623$	21083.3	1.35583
$624$	2415.30	0.154951
$625$	15506.8	0.992438
$626$	−25621.7	−1.63586
$627$	0	0
$628$	812.543	0.0516305
$629$	2932.92	0.185920
$630$	−350.976	−0.0221956
$631$	−23829.5	−1.50339	−0.751694	−	0.659512i	$-0.770763\pi$
$631$	−23829.5	−1.50339	−0.751694	+	0.659512i	$0.770763\pi$
$632$	10191.6	0.641453
$633$	−337.345	−0.0211821
$634$	15960.5	0.999801
$635$	310.637	0.0194130
$636$	15.0874	0.000940653 0
$637$	−163.718	−0.0101833
$638$	0	0
$639$	7271.65	0.450175
$640$	−528.347	−0.0326324
$641$	13405.3	0.826016	0.413008	−	0.910727i	$-0.364478\pi$
$641$	13405.3	0.826016	0.413008	+	0.910727i	$0.364478\pi$
$642$	−8092.36	−0.497477
$643$	5251.51	0.322083	0.161042	−	0.986948i	$-0.448515\pi$
$643$	5251.51	0.322083	0.161042	+	0.986948i	$0.448515\pi$
$644$	1915.55	0.117210
$645$	906.904	0.0553633
$646$	−7065.37	−0.430315
$647$	21611.4	1.31319	0.656595	−	0.754244i	$-0.271996\pi$
$647$	21611.4	1.31319	0.656595	+	0.754244i	$0.271996\pi$
$648$	−4506.28	−0.273184
$649$	0	0
$650$	4152.02	0.250547
$651$	−7574.54	−0.456021
$652$	−2169.94	−0.130340
$653$	−21595.8	−1.29420	−0.647099	−	0.762406i	$-0.724018\pi$
$653$	−21595.8	−1.29420	−0.647099	+	0.762406i	$0.724018\pi$
$654$	−6341.25	−0.379148
$655$	−1154.78	−0.0688869
$656$	−3511.77	−0.209012
$657$	10255.4	0.608985
$658$	−1487.54	−0.0881314
$659$	16642.6	0.983768	0.491884	−	0.870661i	$-0.336308\pi$
$659$	16642.6	0.983768	0.491884	+	0.870661i	$0.336308\pi$
$660$	0	0
$661$	26981.1	1.58766	0.793831	−	0.608139i	$-0.208084\pi$
$661$	26981.1	1.58766	0.793831	+	0.608139i	$0.208084\pi$
$662$	11871.5	0.696980
$663$	−1223.69	−0.0716803
$664$	−14598.1	−0.853185
$665$	−1102.09	−0.0642664
$666$	3947.60	0.229680
$667$	−12887.3	−0.748126
$668$	852.310	0.0493665
$669$	−4552.09	−0.263070
$670$	639.074	0.0368501
$671$	0	0
$672$	−4303.55	−0.247043
$673$	−11149.2	−0.638591	−0.319296	−	0.947655i	$-0.603446\pi$
$673$	−11149.2	−0.638591	−0.319296	+	0.947655i	$0.603446\pi$
$674$	7761.04	0.443537
$675$	−18571.3	−1.05898
$676$	−243.098	−0.0138312
$677$	−3314.33	−0.188154	−0.0940769	−	0.995565i	$-0.529990\pi$
$677$	−3314.33	−0.188154	−0.0940769	+	0.995565i	$0.529990\pi$
$678$	6054.51	0.342953
$679$	−10602.1	−0.599223
$680$	346.836	0.0195596
$681$	12165.5	0.684556
$682$	0	0
$683$	24505.2	1.37287	0.686433	−	0.727193i	$-0.259176\pi$
$683$	24505.2	1.37287	0.686433	+	0.727193i	$0.259176\pi$
$684$	2084.75	0.116539
$685$	−1015.61	−0.0566486
$686$	−16557.0	−0.921500
$687$	−778.506	−0.0432342
$688$	22100.6	1.22468
$689$	37.0056	0.00204616
$690$	388.299	0.0214236
$691$	−21752.8	−1.19756	−0.598782	−	0.800912i	$-0.704348\pi$
$691$	−21752.8	−1.19756	−0.598782	+	0.800912i	$0.704348\pi$
$692$	−6466.64	−0.355238
$693$	0	0
$694$	7278.90	0.398132
$695$	−838.755	−0.0457781
$696$	15670.7	0.853445
$697$	1779.20	0.0966887
$698$	19379.9	1.05092
$699$	−945.941	−0.0511857
$700$	−3260.10	−0.176029
$701$	−34250.9	−1.84542	−0.922709	−	0.385496i	$-0.874030\pi$
$701$	−34250.9	−1.84542	−0.922709	+	0.385496i	$0.874030\pi$
$702$	−4959.93	−0.266667
$703$	12395.8	0.665028
$704$	0	0
$705$	66.1043	0.00353140
$706$	5992.59	0.319454
$707$	16754.6	0.891259
$708$	379.666	0.0201536
$709$	−5527.11	−0.292771	−0.146386	−	0.989228i	$-0.546764\pi$
$709$	−5527.11	−0.292771	−0.146386	+	0.989228i	$0.546764\pi$
$710$	779.234	0.0411889
$711$	−5658.43	−0.298464
$712$	−28042.6	−1.47604
$713$	−8285.33	−0.435187
$714$	−4382.83	−0.229724
$715$	0	0
$716$	221.931	0.0115837
$717$	−13079.1	−0.681241
$718$	−6485.02	−0.337074
$719$	−3777.78	−0.195949	−0.0979745	−	0.995189i	$-0.531236\pi$
$719$	−3777.78	−0.195949	−0.0979745	+	0.995189i	$0.531236\pi$
$720$	380.085	0.0196735
$721$	16917.6	0.873849
$722$	−12291.5	−0.633576
$723$	−18534.2	−0.953380
$724$	−1541.08	−0.0791072
$725$	21933.2	1.12355
$726$	0	0
$727$	19076.8	0.973204	0.486602	−	0.873624i	$-0.338236\pi$
$727$	19076.8	0.973204	0.486602	+	0.873624i	$0.338236\pi$
$728$	−5713.09	−0.290853
$729$	17319.9	0.879944
$730$	1098.98	0.0557192
$731$	−11197.0	−0.566535
$732$	4879.86	0.246400
$733$	−7997.30	−0.402984	−0.201492	−	0.979490i	$-0.564579\pi$
$733$	−7997.30	−0.402984	−0.201492	+	0.979490i	$0.564579\pi$
$734$	−16849.4	−0.847307
$735$	26.0581	0.00130771
$736$	−4707.39	−0.235756
$737$	0	0
$738$	2394.74	0.119446
$739$	−28983.6	−1.44273	−0.721367	−	0.692553i	$-0.756486\pi$
$739$	−28983.6	−1.44273	−0.721367	+	0.692553i	$0.756486\pi$
$740$	−92.7376	−0.00460689
$741$	−5171.81	−0.256398
$742$	132.541	0.00655761
$743$	19145.4	0.945324	0.472662	−	0.881244i	$-0.343293\pi$
$743$	19145.4	0.945324	0.472662	+	0.881244i	$0.343293\pi$
$744$	10074.8	0.496451
$745$	1549.33	0.0761923
$746$	7435.47	0.364922
$747$	8104.95	0.396981
$748$	0	0
$749$	15584.7	0.760284
$750$	−1323.38	−0.0644304
$751$	−25516.9	−1.23985	−0.619923	−	0.784663i	$-0.712836\pi$
$751$	−25516.9	−1.23985	−0.619923	+	0.784663i	$0.712836\pi$
$752$	1610.92	0.0781172
$753$	2648.47	0.128175
$754$	5857.80	0.282929
$755$	548.275	0.0264288
$756$	3894.46	0.187355
$757$	−17230.6	−0.827289	−0.413645	−	0.910438i	$-0.635744\pi$
$757$	−17230.6	−0.827289	−0.413645	+	0.910438i	$0.635744\pi$
$758$	4779.17	0.229007
$759$	0	0
$760$	1465.87	0.0699642
$761$	2343.06	0.111611	0.0558053	−	0.998442i	$-0.482227\pi$
$761$	2343.06	0.111611	0.0558053	+	0.998442i	$0.482227\pi$
$762$	5221.11	0.248216
$763$	12212.3	0.579444
$764$	−974.121	−0.0461289
$765$	−192.566	−0.00910096
$766$	−27756.9	−1.30927
$767$	931.223	0.0438390
$768$	7862.11	0.369400
$769$	7100.18	0.332950	0.166475	−	0.986046i	$-0.446761\pi$
$769$	7100.18	0.332950	0.166475	+	0.986046i	$0.446761\pi$
$770$	0	0
$771$	−4719.29	−0.220442
$772$	1901.17	0.0886328
$773$	12270.4	0.570940	0.285470	−	0.958388i	$-0.407850\pi$
$773$	12270.4	0.570940	0.285470	+	0.958388i	$0.407850\pi$
$774$	−15070.8	−0.699881
$775$	14100.9	0.653575
$776$	14101.7	0.652349
$777$	7689.40	0.355027
$778$	24386.9	1.12379
$779$	7519.64	0.345852
$780$	38.6924	0.00177616
$781$	0	0
$782$	−4794.11	−0.219229
$783$	−26201.0	−1.19584
$784$	635.017	0.0289275
$785$	−317.207	−0.0144224
$786$	−19409.2	−0.880794
$787$	−3425.04	−0.155133	−0.0775663	−	0.996987i	$-0.524715\pi$
$787$	−3425.04	−0.155133	−0.0775663	+	0.996987i	$0.524715\pi$
$788$	1823.04	0.0824151
$789$	19254.3	0.868787
$790$	−606.360	−0.0273080
$791$	−11660.1	−0.524129
$792$	0	0
$793$	11969.0	0.535981
$794$	25894.3	1.15737
$795$	−5.88995	−0.000262761 0
$796$	−3446.87	−0.153481
$797$	−11781.1	−0.523600	−0.261800	−	0.965122i	$-0.584316\pi$
$797$	−11781.1	−0.523600	−0.261800	+	0.965122i	$0.584316\pi$
$798$	−18523.6	−0.821717
$799$	−816.154	−0.0361370
$800$	8011.58	0.354065
$801$	15569.4	0.686790
$802$	−5339.24	−0.235081
$803$	0	0
$804$	−2354.77	−0.103291
$805$	−747.807	−0.0327413
$806$	3766.01	0.164581
$807$	−23743.2	−1.03569
$808$	−22285.0	−0.970276
$809$	−18910.1	−0.821810	−0.410905	−	0.911678i	$-0.634787\pi$
$809$	−18910.1	−0.821810	−0.410905	+	0.911678i	$0.634787\pi$
$810$	268.107	0.0116300
$811$	−12803.3	−0.554359	−0.277180	−	0.960818i	$-0.589400\pi$
$811$	−12803.3	−0.554359	−0.277180	+	0.960818i	$0.589400\pi$
$812$	−4599.45	−0.198780
$813$	−14480.5	−0.624664
$814$	0	0
$815$	847.121	0.0364090
$816$	4746.33	0.203621
$817$	−47323.3	−2.02648
$818$	−24889.4	−1.06386
$819$	3171.95	0.135332
$820$	−56.2574	−0.00239585
$821$	−19335.1	−0.821923	−0.410962	−	0.911653i	$-0.634807\pi$
$821$	−19335.1	−0.821923	−0.410962	+	0.911653i	$0.634807\pi$
$822$	−17070.1	−0.724315
$823$	−2125.90	−0.0900417	−0.0450209	−	0.998986i	$-0.514335\pi$
$823$	−2125.90	−0.0900417	−0.0450209	+	0.998986i	$0.514335\pi$
$824$	−22501.9	−0.951324
$825$	0	0
$826$	3335.32	0.140497
$827$	6989.24	0.293881	0.146941	−	0.989145i	$-0.453057\pi$
$827$	6989.24	0.293881	0.146941	+	0.989145i	$0.453057\pi$
$828$	1414.58	0.0593721
$829$	−32649.7	−1.36788	−0.683938	−	0.729540i	$-0.739734\pi$
$829$	−32649.7	−1.36788	−0.683938	+	0.729540i	$0.739734\pi$
$830$	868.531	0.0363219
$831$	−21682.0	−0.905103
$832$	7383.72	0.307673
$833$	−321.724	−0.0133819
$834$	−14097.6	−0.585324
$835$	−332.732	−0.0137900
$836$	0	0
$837$	−16844.7	−0.695626
$838$	−34278.4	−1.41304
$839$	−4038.23	−0.166168	−0.0830841	−	0.996543i	$-0.526477\pi$
$839$	−4038.23	−0.166168	−0.0830841	+	0.996543i	$0.526477\pi$
$840$	909.318	0.0373505
$841$	6555.00	0.268769
$842$	24240.9	0.992159
$843$	13006.1	0.531380
$844$	−131.695	−0.00537102
$845$	94.9024	0.00386360
$846$	−1098.51	−0.0446426
$847$	0	0
$848$	−143.534	−0.00581248
$849$	−9620.64	−0.388904
$850$	8159.17	0.329244
$851$	8410.97	0.338807
$852$	−2871.21	−0.115453
$853$	−8114.12	−0.325700	−0.162850	−	0.986651i	$-0.552069\pi$
$853$	−8114.12	−0.325700	−0.162850	+	0.986651i	$0.552069\pi$
$854$	42869.0	1.71774
$855$	−813.863	−0.0325538
$856$	−20729.0	−0.827690
$857$	22298.1	0.888786	0.444393	−	0.895832i	$-0.353419\pi$
$857$	22298.1	0.888786	0.444393	+	0.895832i	$0.353419\pi$
$858$	0	0
$859$	33550.5	1.33263	0.666315	−	0.745670i	$-0.267870\pi$
$859$	33550.5	1.33263	0.666315	+	0.745670i	$0.267870\pi$
$860$	354.045	0.0140382
$861$	4664.62	0.184634
$862$	12429.4	0.491121
$863$	−14120.5	−0.556972	−0.278486	−	0.960440i	$-0.589833\pi$
$863$	−14120.5	−0.556972	−0.278486	+	0.960440i	$0.589833\pi$
$864$	−9570.49	−0.376846
$865$	2524.50	0.0992319
$866$	21025.2	0.825018
$867$	15698.1	0.614918
$868$	−2957.01	−0.115631
$869$	0	0
$870$	−932.351	−0.0363329
$871$	−5775.64	−0.224685
$872$	−16243.4	−0.630817
$873$	−7829.39	−0.303533
$874$	−20261.9	−0.784175
$875$	2548.63	0.0984679
$876$	−4049.36	−0.156182
$877$	1941.69	0.0747619	0.0373809	−	0.999301i	$-0.488099\pi$
$877$	1941.69	0.0747619	0.0373809	+	0.999301i	$0.488099\pi$
$878$	−7668.78	−0.294771
$879$	−20232.6	−0.776368
$880$	0	0
$881$	−790.231	−0.0302197	−0.0151099	−	0.999886i	$-0.504810\pi$
$881$	−790.231	−0.0302197	−0.0151099	+	0.999886i	$0.504810\pi$
$882$	−433.029	−0.0165316
$883$	−36638.6	−1.39636	−0.698180	−	0.715922i	$-0.746007\pi$
$883$	−36638.6	−1.39636	−0.698180	+	0.715922i	$0.746007\pi$
$884$	−477.713	−0.0181756
$885$	−148.217	−0.00562968
$886$	−24958.9	−0.946401
$887$	40686.3	1.54015	0.770075	−	0.637954i	$-0.220219\pi$
$887$	40686.3	1.54015	0.770075	+	0.637954i	$0.220219\pi$
$888$	−10227.6	−0.386503
$889$	−10055.1	−0.379344
$890$	1668.43	0.0628381
$891$	0	0
$892$	−1777.08	−0.0667053
$893$	−3449.40	−0.129261
$894$	26040.9	0.974202
$895$	−86.6392	−0.00323579
$896$	17102.2	0.637663
$897$	−3509.26	−0.130625
$898$	1438.21	0.0534449
$899$	19894.0	0.738046
$900$	−2407.50	−0.0891666
$901$	72.7200	0.00268885
$902$	0	0
$903$	−29355.9	−1.08184
$904$	15509.0	0.570598
$905$	601.618	0.0220977
$906$	9215.28	0.337922
$907$	−10464.4	−0.383093	−0.191547	−	0.981484i	$-0.561350\pi$
$907$	−10464.4	−0.383093	−0.191547	+	0.981484i	$0.561350\pi$
$908$	4749.26	0.173579
$909$	12372.8	0.451463
$910$	339.908	0.0123822
$911$	−35611.5	−1.29513	−0.647563	−	0.762011i	$-0.724212\pi$
$911$	−35611.5	−1.29513	−0.647563	+	0.762011i	$0.724212\pi$
$912$	20060.0	0.728346
$913$	0	0
$914$	35242.9	1.27542
$915$	−1905.04	−0.0688291
$916$	−303.920	−0.0109627
$917$	37379.4	1.34610
$918$	−9746.80	−0.350427
$919$	−1077.25	−0.0386674	−0.0193337	−	0.999813i	$-0.506154\pi$
$919$	−1077.25	−0.0386674	−0.0193337	+	0.999813i	$0.506154\pi$
$920$	994.648	0.0356441
$921$	−26926.0	−0.963346
$922$	30762.3	1.09881
$923$	−7042.34	−0.251139
$924$	0	0
$925$	−14314.8	−0.508829
$926$	−34928.6	−1.23955
$927$	12493.2	0.442644
$928$	11303.0	0.399826
$929$	55733.8	1.96832	0.984159	−	0.177290i	$-0.0567330\pi$
$929$	55733.8	1.96832	0.984159	+	0.177290i	$0.0567330\pi$
$930$	−599.413	−0.0211350
$931$	−1359.74	−0.0478665
$932$	−369.284	−0.0129789
$933$	−29126.9	−1.02205
$934$	−22597.9	−0.791677
$935$	0	0
$936$	−4218.97	−0.147330
$937$	3198.60	0.111519	0.0557596	−	0.998444i	$-0.482242\pi$
$937$	3198.60	0.111519	0.0557596	+	0.998444i	$0.482242\pi$
$938$	−20686.4	−0.720079
$939$	−36855.4	−1.28086
$940$	25.8064	0.000895437 0
$941$	−8823.35	−0.305667	−0.152834	−	0.988252i	$-0.548840\pi$
$941$	−8823.35	−0.305667	−0.152834	+	0.988252i	$0.548840\pi$
$942$	−5331.54	−0.184407
$943$	5102.35	0.176199
$944$	−3611.95	−0.124533
$945$	−1520.35	−0.0523354
$946$	0	0
$947$	28290.4	0.970766	0.485383	−	0.874301i	$-0.338680\pi$
$947$	28290.4	0.970766	0.485383	+	0.874301i	$0.338680\pi$
$948$	2234.23	0.0765447
$949$	−9932.05	−0.339734
$950$	34484.0	1.17769
$951$	22958.4	0.782836
$952$	−11226.8	−0.382210
$953$	12399.0	0.421452	0.210726	−	0.977545i	$-0.432417\pi$
$953$	12399.0	0.421452	0.210726	+	0.977545i	$0.432417\pi$
$954$	97.8783	0.00332173
$955$	380.285	0.0128856
$956$	−5105.94	−0.172739
$957$	0	0
$958$	−37450.0	−1.26300
$959$	32874.5	1.10696
$960$	−1175.22	−0.0395105
$961$	−17001.0	−0.570676
$962$	−3823.12	−0.128131
$963$	11508.9	0.385118
$964$	−7235.53	−0.241744
$965$	−742.193	−0.0247586
$966$	−12569.0	−0.418634
$967$	26667.1	0.886820	0.443410	−	0.896319i	$-0.353769\pi$
$967$	26667.1	0.886820	0.443410	+	0.896319i	$0.353769\pi$
$968$	0	0
$969$	−10163.2	−0.336933
$970$	−839.001	−0.0277719
$971$	49420.7	1.63335	0.816676	−	0.577096i	$-0.195814\pi$
$971$	49420.7	1.63335	0.816676	+	0.577096i	$0.195814\pi$
$972$	4796.89	0.158293
$973$	27149.9	0.894539
$974$	25100.3	0.825735
$975$	5972.46	0.196176
$976$	−46424.5	−1.52255
$977$	778.759	0.0255012	0.0127506	−	0.999919i	$-0.495941\pi$
$977$	778.759	0.0255012	0.0127506	+	0.999919i	$0.495941\pi$
$978$	14238.2	0.465529
$979$	0	0
$980$	10.1728	0.000331589 0
$981$	9018.48	0.293515
$982$	−27757.2	−0.902003
$983$	5997.90	0.194612	0.0973059	−	0.995255i	$-0.468977\pi$
$983$	5997.90	0.194612	0.0973059	+	0.995255i	$0.468977\pi$
$984$	−6204.35	−0.201004
$985$	−711.693	−0.0230218
$986$	11511.2	0.371797
$987$	−2139.75	−0.0690062
$988$	−2019.01	−0.0650135
$989$	−32110.6	−1.03241
$990$	0	0
$991$	8974.94	0.287688	0.143844	−	0.989600i	$-0.454054\pi$
$991$	8974.94	0.287688	0.143844	+	0.989600i	$0.454054\pi$
$992$	7266.75	0.232580
$993$	17076.6	0.545729
$994$	−25223.3	−0.804863
$995$	1345.62	0.0428732
$996$	−3200.24	−0.101811
$997$	−28530.2	−0.906280	−0.453140	−	0.891439i	$-0.649696\pi$
$997$	−28530.2	−0.906280	−0.453140	+	0.891439i	$0.649696\pi$
$998$	−6634.31	−0.210426
$999$	17100.2	0.541567

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1573.4.a.b.1.1		2
11.10	odd	2		13.4.a.b.1.2	✓	2
33.32	even	2		117.4.a.d.1.1		2
44.43	even	2		208.4.a.h.1.2		2
55.32	even	4		325.4.b.e.274.4		4
55.43	even	4		325.4.b.e.274.1		4
55.54	odd	2		325.4.a.f.1.1		2
77.76	even	2		637.4.a.b.1.2		2
88.21	odd	2		832.4.a.s.1.2		2
88.43	even	2		832.4.a.z.1.1		2
132.131	odd	2		1872.4.a.bb.1.1		2
143.10	odd	6		169.4.c.j.22.2		4
143.21	even	4		169.4.b.f.168.4		4
143.32	even	12		169.4.e.f.23.1		8
143.43	odd	6		169.4.c.j.146.2		4
143.54	even	12		169.4.e.f.147.4		8
143.76	even	12		169.4.e.f.147.1		8
143.87	odd	6		169.4.c.g.146.1		4
143.98	even	12		169.4.e.f.23.4		8
143.109	even	4		169.4.b.f.168.1		4
143.120	odd	6		169.4.c.g.22.1		4
143.142	odd	2		169.4.a.g.1.1		2
429.428	even	2		1521.4.a.r.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
13.4.a.b.1.2	✓	2	11.10	odd	2
117.4.a.d.1.1		2	33.32	even	2
169.4.a.g.1.1		2	143.142	odd	2
169.4.b.f.168.1		4	143.109	even	4
169.4.b.f.168.4		4	143.21	even	4
169.4.c.g.22.1		4	143.120	odd	6
169.4.c.g.146.1		4	143.87	odd	6
169.4.c.j.22.2		4	143.10	odd	6
169.4.c.j.146.2		4	143.43	odd	6
169.4.e.f.23.1		8	143.32	even	12
169.4.e.f.23.4		8	143.98	even	12
169.4.e.f.147.1		8	143.76	even	12
169.4.e.f.147.4		8	143.54	even	12
208.4.a.h.1.2		2	44.43	even	2
325.4.a.f.1.1		2	55.54	odd	2
325.4.b.e.274.1		4	55.43	even	4
325.4.b.e.274.4		4	55.32	even	4
637.4.a.b.1.2		2	77.76	even	2
832.4.a.s.1.2		2	88.21	odd	2
832.4.a.z.1.1		2	88.43	even	2
1521.4.a.r.1.2		2	429.428	even	2
1573.4.a.b.1.1		2	1.1	even	1	trivial
1872.4.a.bb.1.1		2	132.131	odd	2

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:	\( N \)	\(=\)	\( 1573 = 11^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1573.a (trivial)

\(f(q)\)	\(=\)	\(q-2.56155 q^{2} -3.68466 q^{3} -1.43845 q^{4} +0.561553 q^{5} +9.43845 q^{6} -18.1771 q^{7} +24.1771 q^{8} -13.4233 q^{9} +O(q^{10})\)	\(q-2.56155 q^{2} -3.68466 q^{3} -1.43845 q^{4} +0.561553 q^{5} +9.43845 q^{6} -18.1771 q^{7} +24.1771 q^{8} -13.4233 q^{9} -1.43845 q^{10} +5.30019 q^{12} +13.0000 q^{13} +46.5616 q^{14} -2.06913 q^{15} -50.4233 q^{16} +25.5464 q^{17} +34.3845 q^{18} +107.970 q^{19} -0.807764 q^{20} +66.9763 q^{21} +73.2614 q^{23} -89.0843 q^{24} -124.685 q^{25} -33.3002 q^{26} +148.946 q^{27} +26.1468 q^{28} -175.909 q^{29} +5.30019 q^{30} -113.093 q^{31} -64.2547 q^{32} -65.4384 q^{34} -10.2074 q^{35} +19.3087 q^{36} +114.808 q^{37} -276.570 q^{38} -47.9006 q^{39} +13.5767 q^{40} +69.6458 q^{41} -171.563 q^{42} -438.302 q^{43} -7.53789 q^{45} -187.663 q^{46} -31.9479 q^{47} +185.793 q^{48} -12.5937 q^{49} +319.386 q^{50} -94.1298 q^{51} -18.6998 q^{52} +2.84658 q^{53} -381.533 q^{54} -439.469 q^{56} -397.831 q^{57} +450.600 q^{58} +71.6325 q^{59} +2.97633 q^{60} +920.695 q^{61} +289.693 q^{62} +243.996 q^{63} +567.978 q^{64} +7.30019 q^{65} -444.280 q^{67} -36.7471 q^{68} -269.943 q^{69} +26.1468 q^{70} -541.719 q^{71} -324.536 q^{72} -764.004 q^{73} -294.086 q^{74} +459.420 q^{75} -155.309 q^{76} +122.700 q^{78} +421.538 q^{79} -28.3153 q^{80} -186.386 q^{81} -178.401 q^{82} -603.797 q^{83} -96.3419 q^{84} +14.3457 q^{85} +1122.73 q^{86} +648.165 q^{87} -1159.88 q^{89} +19.3087 q^{90} -236.302 q^{91} -105.383 q^{92} +416.708 q^{93} +81.8362 q^{94} +60.6307 q^{95} +236.757 q^{96} +583.269 q^{97} +32.2595 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - q^{2} + 5 q^{3} - 7 q^{4} - 3 q^{5} + 23 q^{6} + 9 q^{7} + 3 q^{8} + 35 q^{9}+O(q^{10}) \) 2 * q - q^2 + 5 * q^3 - 7 * q^4 - 3 * q^5 + 23 * q^6 + 9 * q^7 + 3 * q^8 + 35 * q^9	\( 2 q - q^{2} + 5 q^{3} - 7 q^{4} - 3 q^{5} + 23 q^{6} + 9 q^{7} + 3 q^{8} + 35 q^{9} - 7 q^{10} - 43 q^{12} + 26 q^{13} + 89 q^{14} - 33 q^{15} - 39 q^{16} - 19 q^{17} + 110 q^{18} + 84 q^{19} + 19 q^{20} + 303 q^{21} + 196 q^{23} - 273 q^{24} - 237 q^{25} - 13 q^{26} + 335 q^{27} - 125 q^{28} + 44 q^{29} - 43 q^{30} - 86 q^{31} + 123 q^{32} - 135 q^{34} - 107 q^{35} - 250 q^{36} + 209 q^{37} - 314 q^{38} + 65 q^{39} + 89 q^{40} + 230 q^{41} + 197 q^{42} - 287 q^{43} - 180 q^{45} + 4 q^{46} + 435 q^{47} + 285 q^{48} + 383 q^{49} + 144 q^{50} - 481 q^{51} - 91 q^{52} - 118 q^{53} - 91 q^{54} - 1015 q^{56} - 606 q^{57} + 794 q^{58} - 368 q^{59} + 175 q^{60} + 1058 q^{61} + 332 q^{62} + 1560 q^{63} + 769 q^{64} - 39 q^{65} + 68 q^{67} + 211 q^{68} + 796 q^{69} - 125 q^{70} - 131 q^{71} - 1350 q^{72} - 456 q^{73} - 147 q^{74} - 516 q^{75} - 22 q^{76} + 299 q^{78} + 1008 q^{79} - 69 q^{80} + 122 q^{81} + 72 q^{82} - 1958 q^{83} - 1409 q^{84} + 173 q^{85} + 1359 q^{86} + 2558 q^{87} - 720 q^{89} - 250 q^{90} + 117 q^{91} - 788 q^{92} + 652 q^{93} + 811 q^{94} + 146 q^{95} + 1863 q^{96} - 928 q^{97} + 650 q^{98}+O(q^{100}) \) 2 * q - q^2 + 5 * q^3 - 7 * q^4 - 3 * q^5 + 23 * q^6 + 9 * q^7 + 3 * q^8 + 35 * q^9 - 7 * q^10 - 43 * q^12 + 26 * q^13 + 89 * q^14 - 33 * q^15 - 39 * q^16 - 19 * q^17 + 110 * q^18 + 84 * q^19 + 19 * q^20 + 303 * q^21 + 196 * q^23 - 273 * q^24 - 237 * q^25 - 13 * q^26 + 335 * q^27 - 125 * q^28 + 44 * q^29 - 43 * q^30 - 86 * q^31 + 123 * q^32 - 135 * q^34 - 107 * q^35 - 250 * q^36 + 209 * q^37 - 314 * q^38 + 65 * q^39 + 89 * q^40 + 230 * q^41 + 197 * q^42 - 287 * q^43 - 180 * q^45 + 4 * q^46 + 435 * q^47 + 285 * q^48 + 383 * q^49 + 144 * q^50 - 481 * q^51 - 91 * q^52 - 118 * q^53 - 91 * q^54 - 1015 * q^56 - 606 * q^57 + 794 * q^58 - 368 * q^59 + 175 * q^60 + 1058 * q^61 + 332 * q^62 + 1560 * q^63 + 769 * q^64 - 39 * q^65 + 68 * q^67 + 211 * q^68 + 796 * q^69 - 125 * q^70 - 131 * q^71 - 1350 * q^72 - 456 * q^73 - 147 * q^74 - 516 * q^75 - 22 * q^76 + 299 * q^78 + 1008 * q^79 - 69 * q^80 + 122 * q^81 + 72 * q^82 - 1958 * q^83 - 1409 * q^84 + 173 * q^85 + 1359 * q^86 + 2558 * q^87 - 720 * q^89 - 250 * q^90 + 117 * q^91 - 788 * q^92 + 652 * q^93 + 811 * q^94 + 146 * q^95 + 1863 * q^96 - 928 * q^97 + 650 * q^98

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