LMFDB - Embedded newform 2013.4.a.c.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)

$f(q)$	$=$	$q-2.45234 q^{2} +3.00000 q^{3} -1.98602 q^{4} -1.35025 q^{5} -7.35703 q^{6} -17.8806 q^{7} +24.4891 q^{8} +9.00000 q^{9} +O(q^{10})$	\(q-2.45234 q^{2} +3.00000 q^{3} -1.98602 q^{4} -1.35025 q^{5} -7.35703 q^{6} -17.8806 q^{7} +24.4891 q^{8} +9.00000 q^{9} +3.31128 q^{10} -11.0000 q^{11} -5.95806 q^{12} +46.6419 q^{13} +43.8494 q^{14} -4.05075 q^{15} -44.1676 q^{16} -129.415 q^{17} -22.0711 q^{18} +101.836 q^{19} +2.68163 q^{20} -53.6419 q^{21} +26.9758 q^{22} +132.540 q^{23} +73.4674 q^{24} -123.177 q^{25} -114.382 q^{26} +27.0000 q^{27} +35.5113 q^{28} -53.0199 q^{29} +9.93383 q^{30} -20.7164 q^{31} -87.5991 q^{32} -33.0000 q^{33} +317.369 q^{34} +24.1434 q^{35} -17.8742 q^{36} -34.7960 q^{37} -249.736 q^{38} +139.926 q^{39} -33.0665 q^{40} -2.27637 q^{41} +131.548 q^{42} +21.1633 q^{43} +21.8462 q^{44} -12.1523 q^{45} -325.033 q^{46} +527.269 q^{47} -132.503 q^{48} -23.2827 q^{49} +302.072 q^{50} -388.244 q^{51} -92.6317 q^{52} +211.264 q^{53} -66.2132 q^{54} +14.8528 q^{55} -437.881 q^{56} +305.508 q^{57} +130.023 q^{58} -466.231 q^{59} +8.04488 q^{60} -61.0000 q^{61} +50.8037 q^{62} -160.926 q^{63} +568.163 q^{64} -62.9782 q^{65} +80.9273 q^{66} -76.8386 q^{67} +257.020 q^{68} +397.620 q^{69} -59.2078 q^{70} -638.972 q^{71} +220.402 q^{72} +659.749 q^{73} +85.3316 q^{74} -369.530 q^{75} -202.248 q^{76} +196.687 q^{77} -343.145 q^{78} +789.589 q^{79} +59.6373 q^{80} +81.0000 q^{81} +5.58243 q^{82} +1316.19 q^{83} +106.534 q^{84} +174.743 q^{85} -51.8995 q^{86} -159.060 q^{87} -269.380 q^{88} +711.938 q^{89} +29.8015 q^{90} -833.986 q^{91} -263.227 q^{92} -62.1492 q^{93} -1293.04 q^{94} -137.504 q^{95} -262.797 q^{96} +573.635 q^{97} +57.0970 q^{98} -99.0000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 37 q - 8 q^{2} + 111 q^{3} + 130 q^{4} - 35 q^{5} - 24 q^{6} - 35 q^{7} - 117 q^{8} + 333 q^{9}+O(q^{10}) $ 37 * q - 8 * q^2 + 111 * q^3 + 130 * q^4 - 35 * q^5 - 24 * q^6 - 35 * q^7 - 117 * q^8 + 333 * q^9	\( 37 q - 8 q^{2} + 111 q^{3} + 130 q^{4} - 35 q^{5} - 24 q^{6} - 35 q^{7} - 117 q^{8} + 333 q^{9} - 41 q^{10} - 407 q^{11} + 390 q^{12} + 51 q^{13} - 228 q^{14} - 105 q^{15} + 462 q^{16} - 190 q^{17} - 72 q^{18} - 51 q^{19} - 720 q^{20} - 105 q^{21} + 88 q^{22} - 583 q^{23} - 351 q^{24} + 598 q^{25} - 1019 q^{26} + 999 q^{27} - 498 q^{28} - 566 q^{29} - 123 q^{30} - 696 q^{31} - 859 q^{32} - 1221 q^{33} - 348 q^{34} - 1102 q^{35} + 1170 q^{36} - 1022 q^{37} - 455 q^{38} + 153 q^{39} - 503 q^{40} - 790 q^{41} - 684 q^{42} - 87 q^{43} - 1430 q^{44} - 315 q^{45} - 303 q^{46} - 1603 q^{47} + 1386 q^{48} + 110 q^{49} - 1926 q^{50} - 570 q^{51} + 736 q^{52} - 2619 q^{53} - 216 q^{54} + 385 q^{55} - 4937 q^{56} - 153 q^{57} - 1099 q^{58} - 2471 q^{59} - 2160 q^{60} - 2257 q^{61} - 2909 q^{62} - 315 q^{63} - 265 q^{64} - 1970 q^{65} + 264 q^{66} - 3033 q^{67} - 1956 q^{68} - 1749 q^{69} + 2410 q^{70} - 3891 q^{71} - 1053 q^{72} + 391 q^{73} - 532 q^{74} + 1794 q^{75} + 1554 q^{76} + 385 q^{77} - 3057 q^{78} + 67 q^{79} - 5111 q^{80} + 2997 q^{81} - 4818 q^{82} - 5315 q^{83} - 1494 q^{84} - 2747 q^{85} - 5195 q^{86} - 1698 q^{87} + 1287 q^{88} - 8945 q^{89} - 369 q^{90} - 4432 q^{91} - 4701 q^{92} - 2088 q^{93} - 372 q^{94} - 3388 q^{95} - 2577 q^{96} - 3784 q^{97} - 4502 q^{98} - 3663 q^{99}+O(q^{100}) \) 37 * q - 8 * q^2 + 111 * q^3 + 130 * q^4 - 35 * q^5 - 24 * q^6 - 35 * q^7 - 117 * q^8 + 333 * q^9 - 41 * q^10 - 407 * q^11 + 390 * q^12 + 51 * q^13 - 228 * q^14 - 105 * q^15 + 462 * q^16 - 190 * q^17 - 72 * q^18 - 51 * q^19 - 720 * q^20 - 105 * q^21 + 88 * q^22 - 583 * q^23 - 351 * q^24 + 598 * q^25 - 1019 * q^26 + 999 * q^27 - 498 * q^28 - 566 * q^29 - 123 * q^30 - 696 * q^31 - 859 * q^32 - 1221 * q^33 - 348 * q^34 - 1102 * q^35 + 1170 * q^36 - 1022 * q^37 - 455 * q^38 + 153 * q^39 - 503 * q^40 - 790 * q^41 - 684 * q^42 - 87 * q^43 - 1430 * q^44 - 315 * q^45 - 303 * q^46 - 1603 * q^47 + 1386 * q^48 + 110 * q^49 - 1926 * q^50 - 570 * q^51 + 736 * q^52 - 2619 * q^53 - 216 * q^54 + 385 * q^55 - 4937 * q^56 - 153 * q^57 - 1099 * q^58 - 2471 * q^59 - 2160 * q^60 - 2257 * q^61 - 2909 * q^62 - 315 * q^63 - 265 * q^64 - 1970 * q^65 + 264 * q^66 - 3033 * q^67 - 1956 * q^68 - 1749 * q^69 + 2410 * q^70 - 3891 * q^71 - 1053 * q^72 + 391 * q^73 - 532 * q^74 + 1794 * q^75 + 1554 * q^76 + 385 * q^77 - 3057 * q^78 + 67 * q^79 - 5111 * q^80 + 2997 * q^81 - 4818 * q^82 - 5315 * q^83 - 1494 * q^84 - 2747 * q^85 - 5195 * q^86 - 1698 * q^87 + 1287 * q^88 - 8945 * q^89 - 369 * q^90 - 4432 * q^91 - 4701 * q^92 - 2088 * q^93 - 372 * q^94 - 3388 * q^95 - 2577 * q^96 - 3784 * q^97 - 4502 * 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 $

$2$	−2.45234	−0.867034	−0.433517	−	0.901145i	$-0.642728\pi$
$2$	−2.45234	−0.867034	−0.433517	+	0.901145i	$0.642728\pi$
$3$	3.00000	0.577350
$3$	3.00000	0.577350
$4$	−1.98602	−0.248253
$5$	−1.35025	−0.120770	−0.0603851	−	0.998175i	$-0.519233\pi$
$5$	−1.35025	−0.120770	−0.0603851	+	0.998175i	$0.519233\pi$
$6$	−7.35703	−0.500582
$7$	−17.8806	−0.965464	−0.482732	−	0.875768i	$-0.660355\pi$
$7$	−17.8806	−0.965464	−0.482732	+	0.875768i	$0.660355\pi$
$8$	24.4891	1.08228
$9$	9.00000	0.333333
$10$	3.31128	0.104712
$11$	−11.0000	−0.301511
$11$	−11.0000	−0.301511
$12$	−5.95806	−0.143329
$13$	46.6419	0.995087	0.497543	−	0.867439i	$-0.334236\pi$
$13$	46.6419	0.995087	0.497543	+	0.867439i	$0.334236\pi$
$14$	43.8494	0.837090
$15$	−4.05075	−0.0697267
$16$	−44.1676	−0.690118
$17$	−129.415	−1.84634	−0.923168	−	0.384397i	$-0.874409\pi$
$17$	−129.415	−1.84634	−0.923168	+	0.384397i	$0.874409\pi$
$18$	−22.0711	−0.289011
$19$	101.836	1.22962	0.614809	−	0.788676i	$-0.289233\pi$
$19$	101.836	1.22962	0.614809	+	0.788676i	$0.289233\pi$
$20$	2.68163	0.0299815
$21$	−53.6419	−0.557411
$22$	26.9758	0.261421
$23$	132.540	1.20159	0.600793	−	0.799405i	$-0.294852\pi$
$23$	132.540	1.20159	0.600793	+	0.799405i	$0.294852\pi$
$24$	73.4674	0.624853
$25$	−123.177	−0.985415
$26$	−114.382	−0.862774
$27$	27.0000	0.192450
$28$	35.5113	0.239679
$29$	−53.0199	−0.339502	−0.169751	−	0.985487i	$-0.554296\pi$
$29$	−53.0199	−0.339502	−0.169751	+	0.985487i	$0.554296\pi$
$30$	9.93383	0.0604554
$31$	−20.7164	−0.120025	−0.0600125	−	0.998198i	$-0.519114\pi$
$31$	−20.7164	−0.120025	−0.0600125	+	0.998198i	$0.519114\pi$
$32$	−87.5991	−0.483921
$33$	−33.0000	−0.174078
$34$	317.369	1.60084
$35$	24.1434	0.116599
$36$	−17.8742	−0.0827508
$37$	−34.7960	−0.154606	−0.0773030	−	0.997008i	$-0.524631\pi$
$37$	−34.7960	−0.154606	−0.0773030	+	0.997008i	$0.524631\pi$
$38$	−249.736	−1.06612
$39$	139.926	0.574513
$40$	−33.0665	−0.130707
$41$	−2.27637	−0.00867094	−0.00433547	−	0.999991i	$-0.501380\pi$
$41$	−2.27637	−0.00867094	−0.00433547	+	0.999991i	$0.501380\pi$
$42$	131.548	0.483294
$43$	21.1633	0.0750550	0.0375275	−	0.999296i	$-0.488052\pi$
$43$	21.1633	0.0750550	0.0375275	+	0.999296i	$0.488052\pi$
$44$	21.8462	0.0748509
$45$	−12.1523	−0.0402567
$46$	−325.033	−1.04182
$47$	527.269	1.63638	0.818192	−	0.574945i	$-0.194977\pi$
$47$	527.269	1.63638	0.818192	+	0.574945i	$0.194977\pi$
$48$	−132.503	−0.398440
$49$	−23.2827	−0.0678795
$50$	302.072	0.854388
$51$	−388.244	−1.06598
$52$	−92.6317	−0.247033
$53$	211.264	0.547535	0.273767	−	0.961796i	$-0.411730\pi$
$53$	211.264	0.547535	0.273767	+	0.961796i	$0.411730\pi$
$54$	−66.2132	−0.166861
$55$	14.8528	0.0364136
$56$	−437.881	−1.04490
$57$	305.508	0.709921
$58$	130.023	0.294359
$59$	−466.231	−1.02878	−0.514391	−	0.857556i	$-0.671982\pi$
$59$	−466.231	−1.02878	−0.514391	+	0.857556i	$0.671982\pi$
$60$	8.04488	0.0173098
$61$	−61.0000	−0.128037
$61$	−61.0000	−0.128037
$62$	50.8037	0.104066
$63$	−160.926	−0.321821
$64$	568.163	1.10969
$65$	−62.9782	−0.120177
$66$	80.9273	0.150931
$67$	−76.8386	−0.140109	−0.0700547	−	0.997543i	$-0.522317\pi$
$67$	−76.8386	−0.140109	−0.0700547	+	0.997543i	$0.522317\pi$
$68$	257.020	0.458357
$69$	397.620	0.693736
$70$	−59.2078	−0.101095
$71$	−638.972	−1.06806	−0.534029	−	0.845466i	$-0.679323\pi$
$71$	−638.972	−1.06806	−0.534029	+	0.845466i	$0.679323\pi$
$72$	220.402	0.360759
$73$	659.749	1.05778	0.528889	−	0.848691i	$-0.322609\pi$
$73$	659.749	1.05778	0.528889	+	0.848691i	$0.322609\pi$
$74$	85.3316	0.134049
$75$	−369.530	−0.568929
$76$	−202.248	−0.305256
$77$	196.687	0.291098
$78$	−343.145	−0.498123
$79$	789.589	1.12450	0.562251	−	0.826967i	$-0.309935\pi$
$79$	789.589	1.12450	0.562251	+	0.826967i	$0.309935\pi$
$80$	59.6373	0.0833457
$81$	81.0000	0.111111
$82$	5.58243	0.00751800
$83$	1316.19	1.74061	0.870306	−	0.492511i	$-0.163921\pi$
$83$	1316.19	1.74061	0.870306	+	0.492511i	$0.163921\pi$
$84$	106.534	0.138379
$85$	174.743	0.222982
$86$	−51.8995	−0.0650752
$87$	−159.060	−0.196011
$88$	−269.380	−0.326319
$89$	711.938	0.847924	0.423962	−	0.905680i	$-0.360639\pi$
$89$	711.938	0.847924	0.423962	+	0.905680i	$0.360639\pi$
$90$	29.8015	0.0349039
$91$	−833.986	−0.960720
$92$	−263.227	−0.298297
$93$	−62.1492	−0.0692965
$94$	−1293.04	−1.41880
$95$	−137.504	−0.148501
$96$	−262.797	−0.279392
$97$	573.635	0.600452	0.300226	−	0.953868i	$-0.402938\pi$
$97$	573.635	0.600452	0.300226	+	0.953868i	$0.402938\pi$
$98$	57.0970	0.0588538
$99$	−99.0000	−0.100504
$100$	244.632	0.244632
$101$	−755.283	−0.744093	−0.372047	−	0.928214i	$-0.621344\pi$
$101$	−755.283	−0.744093	−0.372047	+	0.928214i	$0.621344\pi$
$102$	952.108	0.924243
$103$	−31.7202	−0.0303445	−0.0151722	−	0.999885i	$-0.504830\pi$
$103$	−31.7202	−0.0303445	−0.0151722	+	0.999885i	$0.504830\pi$
$104$	1142.22	1.07696
$105$	72.4301	0.0673186
$106$	−518.091	−0.474731
$107$	94.4474	0.0853325	0.0426662	−	0.999089i	$-0.486415\pi$
$107$	94.4474	0.0853325	0.0426662	+	0.999089i	$0.486415\pi$
$108$	−53.6225	−0.0477762
$109$	−2129.92	−1.87164	−0.935822	−	0.352473i	$-0.885341\pi$
$109$	−2129.92	−1.87164	−0.935822	+	0.352473i	$0.885341\pi$
$110$	−36.4241	−0.0315718
$111$	−104.388	−0.0892618
$112$	789.744	0.666284
$113$	−1251.98	−1.04227	−0.521133	−	0.853475i	$-0.674491\pi$
$113$	−1251.98	−1.04227	−0.521133	+	0.853475i	$0.674491\pi$
$114$	−749.209	−0.615525
$115$	−178.962	−0.145116
$116$	105.299	0.0842822
$117$	419.777	0.331696
$118$	1143.36	0.891989
$119$	2314.02	1.78257
$120$	−99.1995	−0.0754636
$121$	121.000	0.0909091
$122$	149.593	0.111012
$123$	−6.82910	−0.00500617
$124$	41.1432	0.0297965
$125$	335.101	0.239779
$126$	394.645	0.279030
$127$	682.165	0.476633	0.238316	−	0.971188i	$-0.423404\pi$
$127$	682.165	0.476633	0.238316	+	0.971188i	$0.423404\pi$
$128$	−692.538	−0.478221
$129$	63.4898	0.0433330
$130$	154.444	0.104197
$131$	1663.46	1.10944	0.554722	−	0.832036i	$-0.312825\pi$
$131$	1663.46	1.10944	0.554722	+	0.832036i	$0.312825\pi$
$132$	65.5387	0.0432152
$133$	−1820.89	−1.18715
$134$	188.434	0.121480
$135$	−36.4568	−0.0232422
$136$	−3169.26	−1.99825
$137$	−1200.68	−0.748767	−0.374383	−	0.927274i	$-0.622146\pi$
$137$	−1200.68	−0.748767	−0.374383	+	0.927274i	$0.622146\pi$
$138$	−975.099	−0.601493
$139$	−1540.27	−0.939886	−0.469943	−	0.882697i	$-0.655726\pi$
$139$	−1540.27	−0.939886	−0.469943	+	0.882697i	$0.655726\pi$
$140$	−47.9492	−0.0289461
$141$	1581.81	0.944767
$142$	1566.98	0.926041
$143$	−513.060	−0.300030
$144$	−397.508	−0.230039
$145$	71.5902	0.0410017
$146$	−1617.93	−0.917129
$147$	−69.8480	−0.0391902
$148$	69.1055	0.0383813
$149$	875.099	0.481147	0.240574	−	0.970631i	$-0.422664\pi$
$149$	875.099	0.481147	0.240574	+	0.970631i	$0.422664\pi$
$150$	906.215	0.493281
$151$	459.543	0.247663	0.123831	−	0.992303i	$-0.460482\pi$
$151$	459.543	0.247663	0.123831	+	0.992303i	$0.460482\pi$
$152$	2493.87	1.33079
$153$	−1164.73	−0.615445
$154$	−482.344	−0.252392
$155$	27.9724	0.0144954
$156$	−277.895	−0.142624
$157$	−1009.90	−0.513369	−0.256685	−	0.966495i	$-0.582630\pi$
$157$	−1009.90	−0.513369	−0.256685	+	0.966495i	$0.582630\pi$
$158$	−1936.34	−0.974981
$159$	633.792	0.316119
$160$	118.281	0.0584433
$161$	−2369.90	−1.16009
$162$	−198.640	−0.0963371
$163$	531.620	0.255458	0.127729	−	0.991809i	$-0.459231\pi$
$163$	531.620	0.255458	0.127729	+	0.991809i	$0.459231\pi$
$164$	4.52091	0.00215258
$165$	44.5583	0.0210234
$166$	−3227.75	−1.50917
$167$	−1574.79	−0.729704	−0.364852	−	0.931065i	$-0.618880\pi$
$167$	−1574.79	−0.729704	−0.364852	+	0.931065i	$0.618880\pi$
$168$	−1313.64	−0.603273
$169$	−21.5366	−0.00980275
$170$	−428.528	−0.193333
$171$	916.523	0.409873
$172$	−42.0306	−0.0186326
$173$	−2116.10	−0.929965	−0.464982	−	0.885320i	$-0.653939\pi$
$173$	−2116.10	−0.929965	−0.464982	+	0.885320i	$0.653939\pi$
$174$	390.069	0.169949
$175$	2202.48	0.951382
$176$	485.843	0.208078
$177$	−1398.69	−0.593968
$178$	−1745.92	−0.735179
$179$	1414.68	0.590716	0.295358	−	0.955387i	$-0.404561\pi$
$179$	1414.68	0.590716	0.295358	+	0.955387i	$0.404561\pi$
$180$	24.1346	0.00999383
$181$	−1589.72	−0.652834	−0.326417	−	0.945226i	$-0.605841\pi$
$181$	−1589.72	−0.652834	−0.326417	+	0.945226i	$0.605841\pi$
$182$	2045.22	0.832977
$183$	−183.000	−0.0739221
$184$	3245.79	1.30045
$185$	46.9833	0.0186718
$186$	152.411	0.0600824
$187$	1423.56	0.556691
$188$	−1047.17	−0.406236
$189$	−482.777	−0.185804
$190$	337.207	0.128756
$191$	−3412.39	−1.29273	−0.646366	−	0.763027i	$-0.723712\pi$
$191$	−3412.39	−1.29273	−0.646366	+	0.763027i	$0.723712\pi$
$192$	1704.49	0.640682
$193$	−1980.23	−0.738548	−0.369274	−	0.929321i	$-0.620394\pi$
$193$	−1980.23	−0.738548	−0.369274	+	0.929321i	$0.620394\pi$
$194$	−1406.75	−0.520612
$195$	−188.935	−0.0693841
$196$	46.2398	0.0168512
$197$	−3256.83	−1.17787	−0.588934	−	0.808181i	$-0.700452\pi$
$197$	−3256.83	−1.17787	−0.588934	+	0.808181i	$0.700452\pi$
$198$	242.782	0.0871402
$199$	1598.53	0.569430	0.284715	−	0.958612i	$-0.408101\pi$
$199$	1598.53	0.569430	0.284715	+	0.958612i	$0.408101\pi$
$200$	−3016.49	−1.06649
$201$	−230.516	−0.0808922
$202$	1852.21	0.645154
$203$	948.030	0.327777
$204$	771.061	0.264633
$205$	3.07367	0.00104719
$206$	77.7887	0.0263097
$207$	1192.86	0.400529
$208$	−2060.06	−0.686727
$209$	−1120.19	−0.370744
$210$	−177.623	−0.0583675
$211$	−5081.76	−1.65802	−0.829011	−	0.559232i	$-0.811096\pi$
$211$	−5081.76	−1.65802	−0.829011	+	0.559232i	$0.811096\pi$
$212$	−419.574	−0.135927
$213$	−1916.92	−0.616643
$214$	−231.617	−0.0739862
$215$	−28.5757	−0.00906441
$216$	661.207	0.208284
$217$	370.423	0.115880
$218$	5223.29	1.62278
$219$	1979.25	0.610708
$220$	−29.4979	−0.00903976
$221$	−6036.15	−1.83726
$222$	255.995	0.0773930
$223$	3908.70	1.17375	0.586874	−	0.809678i	$-0.300358\pi$
$223$	3908.70	1.17375	0.586874	+	0.809678i	$0.300358\pi$
$224$	1566.33	0.467209
$225$	−1108.59	−0.328472
$226$	3070.28	0.903680
$227$	1240.52	0.362714	0.181357	−	0.983417i	$-0.441951\pi$
$227$	1240.52	0.362714	0.181357	+	0.983417i	$0.441951\pi$
$228$	−606.744	−0.176240
$229$	−3567.35	−1.02942	−0.514709	−	0.857365i	$-0.672100\pi$
$229$	−3567.35	−1.02942	−0.514709	+	0.857365i	$0.672100\pi$
$230$	438.877	0.125820
$231$	590.061	0.168066
$232$	−1298.41	−0.367435
$233$	2530.96	0.711624	0.355812	−	0.934558i	$-0.384204\pi$
$233$	2530.96	0.711624	0.355812	+	0.934558i	$0.384204\pi$
$234$	−1029.44	−0.287591
$235$	−711.945	−0.197626
$236$	925.945	0.255398
$237$	2368.77	0.649232
$238$	−5674.77	−1.54555
$239$	1676.33	0.453695	0.226847	−	0.973930i	$-0.427158\pi$
$239$	1676.33	0.453695	0.226847	+	0.973930i	$0.427158\pi$
$240$	178.912	0.0481197
$241$	4699.60	1.25613	0.628066	−	0.778160i	$-0.283847\pi$
$241$	4699.60	1.25613	0.628066	+	0.778160i	$0.283847\pi$
$242$	−296.733	−0.0788212
$243$	243.000	0.0641500
$244$	121.147	0.0317855
$245$	31.4374	0.00819781
$246$	16.7473	0.00434052
$247$	4749.82	1.22358
$248$	−507.327	−0.129900
$249$	3948.58	1.00494
$250$	−821.783	−0.207896
$251$	4059.61	1.02088	0.510439	−	0.859914i	$-0.329483\pi$
$251$	4059.61	1.02088	0.510439	+	0.859914i	$0.329483\pi$
$252$	319.602	0.0798929
$253$	−1457.94	−0.362292
$254$	−1672.90	−0.413257
$255$	524.228	0.128739
$256$	−2846.97	−0.695060
$257$	−379.907	−0.0922098	−0.0461049	−	0.998937i	$-0.514681\pi$
$257$	−379.907	−0.0922098	−0.0461049	+	0.998937i	$0.514681\pi$
$258$	−155.699	−0.0375712
$259$	622.174	0.149267
$260$	125.076	0.0298342
$261$	−477.179	−0.113167
$262$	−4079.37	−0.961925
$263$	−7303.05	−1.71226	−0.856132	−	0.516757i	$-0.827139\pi$
$263$	−7303.05	−1.71226	−0.856132	+	0.516757i	$0.827139\pi$
$264$	−808.141	−0.188400
$265$	−285.259	−0.0661259
$266$	4465.45	1.02930
$267$	2135.81	0.489549
$268$	152.603	0.0347825
$269$	−1300.18	−0.294696	−0.147348	−	0.989085i	$-0.547074\pi$
$269$	−1300.18	−0.294696	−0.147348	+	0.989085i	$0.547074\pi$
$270$	89.4045	0.0201518
$271$	−1442.24	−0.323282	−0.161641	−	0.986850i	$-0.551679\pi$
$271$	−1442.24	−0.323282	−0.161641	+	0.986850i	$0.551679\pi$
$272$	5715.94	1.27419
$273$	−2501.96	−0.554672
$274$	2944.48	0.649206
$275$	1354.95	0.297114
$276$	−789.681	−0.172222
$277$	−2087.24	−0.452745	−0.226372	−	0.974041i	$-0.572687\pi$
$277$	−2087.24	−0.452745	−0.226372	+	0.974041i	$0.572687\pi$
$278$	3777.27	0.814913
$279$	−186.448	−0.0400083
$280$	591.250	0.126193
$281$	−5716.21	−1.21353	−0.606763	−	0.794883i	$-0.707532\pi$
$281$	−5716.21	−1.21353	−0.606763	+	0.794883i	$0.707532\pi$
$282$	−3879.13	−0.819145
$283$	1857.10	0.390081	0.195041	−	0.980795i	$-0.437516\pi$
$283$	1857.10	0.390081	0.195041	+	0.980795i	$0.437516\pi$
$284$	1269.01	0.265148
$285$	−412.512	−0.0857373
$286$	1258.20	0.260136
$287$	40.7029	0.00837148
$288$	−788.392	−0.161307
$289$	11835.2	2.40895
$290$	−175.564	−0.0355498
$291$	1720.91	0.346671
$292$	−1310.27	−0.262596
$293$	−4284.33	−0.854243	−0.427121	−	0.904194i	$-0.640472\pi$
$293$	−4284.33	−0.854243	−0.427121	+	0.904194i	$0.640472\pi$
$294$	171.291	0.0339792
$295$	629.530	0.124246
$296$	−852.123	−0.167327
$297$	−297.000	−0.0580259
$298$	−2146.04	−0.417171
$299$	6181.91	1.19568
$300$	733.895	0.141238
$301$	−378.413	−0.0724629
$302$	−1126.96	−0.214732
$303$	−2265.85	−0.429602
$304$	−4497.84	−0.848582
$305$	82.3653	0.0154630
$306$	2856.32	0.533612
$307$	5309.72	0.987107	0.493553	−	0.869716i	$-0.335698\pi$
$307$	5309.72	0.987107	0.493553	+	0.869716i	$0.335698\pi$
$308$	−390.624	−0.0722659
$309$	−95.1605	−0.0175194
$310$	−68.5978	−0.0125680
$311$	−6717.69	−1.22484	−0.612420	−	0.790532i	$-0.709804\pi$
$311$	−6717.69	−1.22484	−0.612420	+	0.790532i	$0.709804\pi$
$312$	3426.66	0.621783
$313$	6970.88	1.25884	0.629421	−	0.777065i	$-0.283292\pi$
$313$	6970.88	1.25884	0.629421	+	0.777065i	$0.283292\pi$
$314$	2476.63	0.445109
$315$	217.290	0.0388664
$316$	−1568.14	−0.279160
$317$	−3905.53	−0.691977	−0.345988	−	0.938239i	$-0.612456\pi$
$317$	−3905.53	−0.691977	−0.345988	+	0.938239i	$0.612456\pi$
$318$	−1554.27	−0.274086
$319$	583.219	0.102364
$320$	−767.164	−0.134018
$321$	283.342	0.0492667
$322$	5811.80	1.00584
$323$	−13179.1	−2.27029
$324$	−160.868	−0.0275836
$325$	−5745.20	−0.980573
$326$	−1303.71	−0.221491
$327$	−6389.75	−1.08059
$328$	−55.7462	−0.00938436
$329$	−9427.90	−1.57987
$330$	−109.272	−0.0182280
$331$	−196.557	−0.0326398	−0.0163199	−	0.999867i	$-0.505195\pi$
$331$	−196.557	−0.0326398	−0.0163199	+	0.999867i	$0.505195\pi$
$332$	−2613.98	−0.432111
$333$	−313.164	−0.0515353
$334$	3861.91	0.632678
$335$	103.751	0.0169210
$336$	2369.23	0.384679
$337$	−6914.61	−1.11769	−0.558847	−	0.829271i	$-0.688756\pi$
$337$	−6914.61	−1.11769	−0.558847	+	0.829271i	$0.688756\pi$
$338$	52.8152	0.00849931
$339$	−3755.93	−0.601753
$340$	−347.042	−0.0553559
$341$	227.880	0.0361889
$342$	−2247.63	−0.355374
$343$	6549.37	1.03100
$344$	518.270	0.0812303
$345$	−536.887	−0.0837826
$346$	5189.39	0.806311
$347$	−8901.82	−1.37716	−0.688581	−	0.725160i	$-0.741766\pi$
$347$	−8901.82	−1.37716	−0.688581	+	0.725160i	$0.741766\pi$
$348$	315.896	0.0486603
$349$	10463.6	1.60488	0.802438	−	0.596735i	$-0.203536\pi$
$349$	10463.6	1.60488	0.802438	+	0.596735i	$0.203536\pi$
$350$	−5401.24	−0.824880
$351$	1259.33	0.191504
$352$	963.590	0.145908
$353$	−10269.9	−1.54847	−0.774236	−	0.632897i	$-0.781866\pi$
$353$	−10269.9	−1.54847	−0.774236	+	0.632897i	$0.781866\pi$
$354$	3430.08	0.514990
$355$	862.773	0.128989
$356$	−1413.92	−0.210499
$357$	6942.06	1.02917
$358$	−3469.28	−0.512171
$359$	−6610.22	−0.971794	−0.485897	−	0.874016i	$-0.661507\pi$
$359$	−6610.22	−0.971794	−0.485897	+	0.874016i	$0.661507\pi$
$360$	−297.598	−0.0435689
$361$	3511.55	0.511962
$362$	3898.54	0.566029
$363$	363.000	0.0524864
$364$	1656.31	0.238501
$365$	−890.827	−0.127748
$366$	448.779	0.0640930
$367$	−2917.74	−0.414999	−0.207499	−	0.978235i	$-0.566533\pi$
$367$	−2917.74	−0.414999	−0.207499	+	0.978235i	$0.566533\pi$
$368$	−5853.97	−0.829236
$369$	−20.4873	−0.00289031
$370$	−115.219	−0.0161891
$371$	−3777.54	−0.528625
$372$	123.430	0.0172030
$373$	−7184.01	−0.997249	−0.498624	−	0.866818i	$-0.666161\pi$
$373$	−7184.01	−0.997249	−0.498624	+	0.866818i	$0.666161\pi$
$374$	−3491.06	−0.482670
$375$	1005.30	0.138436
$376$	12912.4	1.77102
$377$	−2472.95	−0.337834
$378$	1183.93	0.161098
$379$	−8450.64	−1.14533	−0.572665	−	0.819789i	$-0.694091\pi$
$379$	−8450.64	−1.14533	−0.572665	+	0.819789i	$0.694091\pi$
$380$	273.086	0.0368658
$381$	2046.50	0.275184
$382$	8368.35	1.12084
$383$	−14573.1	−1.94425	−0.972127	−	0.234455i	$-0.924670\pi$
$383$	−14573.1	−1.94425	−0.972127	+	0.234455i	$0.924670\pi$
$384$	−2077.61	−0.276101
$385$	−265.577	−0.0351560
$386$	4856.19	0.640346
$387$	190.469	0.0250183
$388$	−1139.25	−0.149064
$389$	−12847.9	−1.67459	−0.837294	−	0.546753i	$-0.815864\pi$
$389$	−12847.9	−1.67459	−0.837294	+	0.546753i	$0.815864\pi$
$390$	463.333	0.0601583
$391$	−17152.6	−2.21853
$392$	−570.172	−0.0734644
$393$	4990.38	0.640537
$394$	7986.87	1.02125
$395$	−1066.14	−0.135806
$396$	196.616	0.0249503
$397$	−1155.81	−0.146117	−0.0730583	−	0.997328i	$-0.523276\pi$
$397$	−1155.81	−0.146117	−0.0730583	+	0.997328i	$0.523276\pi$
$398$	−3920.14	−0.493715
$399$	−5462.67	−0.685403
$400$	5440.42	0.680052
$401$	−12172.1	−1.51582	−0.757910	−	0.652359i	$-0.773779\pi$
$401$	−12172.1	−1.51582	−0.757910	+	0.652359i	$0.773779\pi$
$402$	565.303	0.0701362
$403$	−966.251	−0.119435
$404$	1500.01	0.184723
$405$	−109.370	−0.0134189
$406$	−2324.89	−0.284193
$407$	382.756	0.0466155
$408$	−9507.77	−1.15369
$409$	−1855.87	−0.224369	−0.112185	−	0.993687i	$-0.535785\pi$
$409$	−1855.87	−0.224369	−0.112185	+	0.993687i	$0.535785\pi$
$410$	−7.53768	−0.000907950 0
$411$	−3602.04	−0.432301
$412$	62.9969	0.00753310
$413$	8336.51	0.993252
$414$	−2925.30	−0.347272
$415$	−1777.19	−0.210214
$416$	−4085.79	−0.481544
$417$	−4620.82	−0.542643
$418$	2747.10	0.321448
$419$	−8579.86	−1.00037	−0.500183	−	0.865920i	$-0.666734\pi$
$419$	−8579.86	−1.00037	−0.500183	+	0.865920i	$0.666734\pi$
$420$	−143.848	−0.0167120
$421$	10206.1	1.18151	0.590755	−	0.806851i	$-0.298830\pi$
$421$	10206.1	1.18151	0.590755	+	0.806851i	$0.298830\pi$
$422$	12462.2	1.43756
$423$	4745.42	0.545461
$424$	5173.67	0.592584
$425$	15940.9	1.81941
$426$	4700.93	0.534650
$427$	1090.72	0.123615
$428$	−187.574	−0.0211840
$429$	−1539.18	−0.173222
$430$	70.0774	0.00785915
$431$	12501.6	1.39717	0.698583	−	0.715529i	$-0.253814\pi$
$431$	12501.6	1.39717	0.698583	+	0.715529i	$0.253814\pi$
$432$	−1192.52	−0.132813
$433$	−6013.00	−0.667359	−0.333679	−	0.942687i	$-0.608290\pi$
$433$	−6013.00	−0.667359	−0.333679	+	0.942687i	$0.608290\pi$
$434$	−908.403	−0.100472
$435$	214.771	0.0236723
$436$	4230.06	0.464640
$437$	13497.3	1.47749
$438$	−4853.79	−0.529505
$439$	13191.1	1.43411	0.717055	−	0.697016i	$-0.245490\pi$
$439$	13191.1	1.43411	0.717055	+	0.697016i	$0.245490\pi$
$440$	363.731	0.0394096
$441$	−209.544	−0.0226265
$442$	14802.7	1.59297
$443$	−10528.3	−1.12915	−0.564574	−	0.825382i	$-0.690960\pi$
$443$	−10528.3	−1.12915	−0.564574	+	0.825382i	$0.690960\pi$
$444$	207.317	0.0221595
$445$	−961.295	−0.102404
$446$	−9585.47	−1.01768
$447$	2625.30	0.277790
$448$	−10159.1	−1.07137
$449$	3876.01	0.407395	0.203697	−	0.979034i	$-0.434704\pi$
$449$	3876.01	0.407395	0.203697	+	0.979034i	$0.434704\pi$
$450$	2718.64	0.284796
$451$	25.0400	0.00261439
$452$	2486.45	0.258745
$453$	1378.63	0.142988
$454$	−3042.17	−0.314485
$455$	1126.09	0.116026
$456$	7481.62	0.768331
$457$	14612.9	1.49576	0.747882	−	0.663831i	$-0.231071\pi$
$457$	14612.9	1.49576	0.747882	+	0.663831i	$0.231071\pi$
$458$	8748.35	0.892540
$459$	−3494.20	−0.355327
$460$	355.423	0.0360254
$461$	−10019.1	−1.01222	−0.506111	−	0.862469i	$-0.668917\pi$
$461$	−10019.1	−1.01222	−0.506111	+	0.862469i	$0.668917\pi$
$462$	−1447.03	−0.145719
$463$	−8862.69	−0.889599	−0.444799	−	0.895630i	$-0.646725\pi$
$463$	−8862.69	−0.889599	−0.444799	+	0.895630i	$0.646725\pi$
$464$	2341.76	0.234296
$465$	83.9171	0.00836895
$466$	−6206.77	−0.617002
$467$	−9240.10	−0.915590	−0.457795	−	0.889058i	$-0.651361\pi$
$467$	−9240.10	−0.915590	−0.457795	+	0.889058i	$0.651361\pi$
$468$	−833.685	−0.0823442
$469$	1373.92	0.135270
$470$	1745.93	0.171349
$471$	−3029.71	−0.296394
$472$	−11417.6	−1.11343
$473$	−232.796	−0.0226299
$474$	−5809.02	−0.562906
$475$	−12543.8	−1.21168
$476$	−4595.69	−0.442528
$477$	1901.38	0.182512
$478$	−4110.94	−0.393369
$479$	−9972.01	−0.951217	−0.475608	−	0.879657i	$-0.657772\pi$
$479$	−9972.01	−0.951217	−0.475608	+	0.879657i	$0.657772\pi$
$480$	354.843	0.0337422
$481$	−1622.95	−0.153846
$482$	−11525.0	−1.08911
$483$	−7109.70	−0.669777
$484$	−240.308	−0.0225684
$485$	−774.552	−0.0725167
$486$	−595.919	−0.0556202
$487$	6807.47	0.633421	0.316710	−	0.948522i	$-0.397422\pi$
$487$	6807.47	0.633421	0.316710	+	0.948522i	$0.397422\pi$
$488$	−1493.84	−0.138571
$489$	1594.86	0.147489
$490$	−77.0954	−0.00710778
$491$	15915.5	1.46284	0.731422	−	0.681925i	$-0.238857\pi$
$491$	15915.5	1.46284	0.731422	+	0.681925i	$0.238857\pi$
$492$	13.5627	0.00124279
$493$	6861.56	0.626834
$494$	−11648.2	−1.06088
$495$	133.675	0.0121379
$496$	914.993	0.0828314
$497$	11425.2	1.03117
$498$	−9683.26	−0.871319
$499$	−3906.33	−0.350444	−0.175222	−	0.984529i	$-0.556064\pi$
$499$	−3906.33	−0.350444	−0.175222	+	0.984529i	$0.556064\pi$
$500$	−665.518	−0.0595257
$501$	−4724.36	−0.421295
$502$	−9955.55	−0.885135
$503$	−12666.3	−1.12279	−0.561396	−	0.827548i	$-0.689735\pi$
$503$	−12666.3	−1.12279	−0.561396	+	0.827548i	$0.689735\pi$
$504$	−3940.93	−0.348300
$505$	1019.82	0.0898643
$506$	3575.36	0.314119
$507$	−64.6099	−0.00565962
$508$	−1354.79	−0.118325
$509$	−5257.23	−0.457804	−0.228902	−	0.973449i	$-0.573514\pi$
$509$	−5257.23	−0.457804	−0.228902	+	0.973449i	$0.573514\pi$
$510$	−1285.59	−0.111621
$511$	−11796.7	−1.02125
$512$	12522.0	1.08086
$513$	2749.57	0.236640
$514$	931.661	0.0799490
$515$	42.8302	0.00366471
$516$	−126.092	−0.0107575
$517$	−5799.96	−0.493388
$518$	−1525.78	−0.129419
$519$	−6348.29	−0.536915
$520$	−1542.28	−0.130065
$521$	−13977.0	−1.17532	−0.587661	−	0.809108i	$-0.699951\pi$
$521$	−13977.0	−1.17532	−0.587661	+	0.809108i	$0.699951\pi$
$522$	1170.21	0.0981198
$523$	−11760.2	−0.983247	−0.491624	−	0.870808i	$-0.663596\pi$
$523$	−11760.2	−0.983247	−0.491624	+	0.870808i	$0.663596\pi$
$524$	−3303.66	−0.275422
$525$	6607.44	0.549281
$526$	17909.6	1.48459
$527$	2681.01	0.221606
$528$	1457.53	0.120134
$529$	5399.83	0.443809
$530$	699.554	0.0573333
$531$	−4196.08	−0.342927
$532$	3616.33	0.294714
$533$	−106.174	−0.00862834
$534$	−5237.75	−0.424456
$535$	−127.528	−0.0103056
$536$	−1881.71	−0.151637
$537$	4244.04	0.341050
$538$	3188.48	0.255511
$539$	256.109	0.0204664
$540$	72.4039	0.00576994
$541$	−20526.4	−1.63124	−0.815620	−	0.578588i	$-0.803604\pi$
$541$	−20526.4	−1.63124	−0.815620	+	0.578588i	$0.803604\pi$
$542$	3536.85	0.280297
$543$	−4769.16	−0.376914
$544$	11336.6	0.893481
$545$	2875.93	0.226039
$546$	6135.66	0.480919
$547$	−18681.2	−1.46024	−0.730119	−	0.683320i	$-0.760535\pi$
$547$	−18681.2	−1.46024	−0.730119	+	0.683320i	$0.760535\pi$
$548$	2384.58	0.185883
$549$	−549.000	−0.0426790
$550$	−3322.79	−0.257608
$551$	−5399.33	−0.417458
$552$	9737.36	0.750815
$553$	−14118.4	−1.08567
$554$	5118.63	0.392545
$555$	140.950	0.0107802
$556$	3059.01	0.233329
$557$	11381.5	0.865799	0.432900	−	0.901442i	$-0.357490\pi$
$557$	11381.5	0.865799	0.432900	+	0.901442i	$0.357490\pi$
$558$	457.233	0.0346886
$559$	987.094	0.0746862
$560$	−1066.35	−0.0804673
$561$	4270.69	0.321406
$562$	14018.1	1.05217
$563$	−5100.74	−0.381830	−0.190915	−	0.981607i	$-0.561146\pi$
$563$	−5100.74	−0.381830	−0.190915	+	0.981607i	$0.561146\pi$
$564$	−3141.50	−0.234541
$565$	1690.48	0.125875
$566$	−4554.24	−0.338214
$567$	−1448.33	−0.107274
$568$	−15647.9	−1.15593
$569$	−25161.8	−1.85384	−0.926922	−	0.375253i	$-0.877556\pi$
$569$	−25161.8	−1.85384	−0.926922	+	0.375253i	$0.877556\pi$
$570$	1011.62	0.0743371
$571$	−7290.66	−0.534334	−0.267167	−	0.963650i	$-0.586087\pi$
$571$	−7290.66	−0.534334	−0.267167	+	0.963650i	$0.586087\pi$
$572$	1018.95	0.0744832
$573$	−10237.2	−0.746359
$574$	−99.8173	−0.00725835
$575$	−16325.8	−1.18406
$576$	5113.47	0.369898
$577$	−6078.42	−0.438558	−0.219279	−	0.975662i	$-0.570370\pi$
$577$	−6078.42	−0.438558	−0.219279	+	0.975662i	$0.570370\pi$
$578$	−29023.9	−2.08865
$579$	−5940.68	−0.426401
$580$	−142.180	−0.0101788
$581$	−23534.4	−1.68050
$582$	−4220.25	−0.300576
$583$	−2323.90	−0.165088
$584$	16156.7	1.14481
$585$	−566.804	−0.0400589
$586$	10506.6	0.740657
$587$	17961.1	1.26292	0.631460	−	0.775408i	$-0.282456\pi$
$587$	17961.1	1.26292	0.631460	+	0.775408i	$0.282456\pi$
$588$	138.719	0.00972907
$589$	−2109.67	−0.147585
$590$	−1543.82	−0.107726
$591$	−9770.50	−0.680042
$592$	1536.85	0.106696
$593$	6795.63	0.470596	0.235298	−	0.971923i	$-0.424393\pi$
$593$	6795.63	0.470596	0.235298	+	0.971923i	$0.424393\pi$
$594$	728.345	0.0503104
$595$	−3124.51	−0.215281
$596$	−1737.96	−0.119446
$597$	4795.58	0.328761
$598$	−15160.2	−1.03670
$599$	−26840.9	−1.83086	−0.915432	−	0.402473i	$-0.868151\pi$
$599$	−26840.9	−1.83086	−0.915432	+	0.402473i	$0.868151\pi$
$600$	−9049.48	−0.615739
$601$	23658.3	1.60573	0.802865	−	0.596161i	$-0.203308\pi$
$601$	23658.3	1.60573	0.802865	+	0.596161i	$0.203308\pi$
$602$	927.997	0.0628278
$603$	−691.547	−0.0467031
$604$	−912.661	−0.0614829
$605$	−163.380	−0.0109791
$606$	5556.63	0.372480
$607$	1829.47	0.122332	0.0611662	−	0.998128i	$-0.480518\pi$
$607$	1829.47	0.122332	0.0611662	+	0.998128i	$0.480518\pi$
$608$	−8920.73	−0.595039
$609$	2844.09	0.189242
$610$	−201.988	−0.0134070
$611$	24592.8	1.62834
$612$	2313.18	0.152786
$613$	−5107.63	−0.336534	−0.168267	−	0.985741i	$-0.553817\pi$
$613$	−5107.63	−0.336534	−0.168267	+	0.985741i	$0.553817\pi$
$614$	−13021.2	−0.855855
$615$	9.22100	0.000604596 0
$616$	4816.70	0.315049
$617$	19067.9	1.24416	0.622078	−	0.782955i	$-0.286288\pi$
$617$	19067.9	1.24416	0.622078	+	0.782955i	$0.286288\pi$
$618$	233.366	0.0151899
$619$	21621.4	1.40394	0.701969	−	0.712208i	$-0.252305\pi$
$619$	21621.4	1.40394	0.701969	+	0.712208i	$0.252305\pi$
$620$	−55.5537	−0.00359853
$621$	3578.58	0.231245
$622$	16474.1	1.06198
$623$	−12729.9	−0.818640
$624$	−6180.17	−0.396482
$625$	14944.6	0.956456
$626$	−17095.0	−1.09146
$627$	−3360.58	−0.214049
$628$	2005.69	0.127445
$629$	4503.11	0.285455
$630$	−532.870	−0.0336985
$631$	−2140.30	−0.135030	−0.0675150	−	0.997718i	$-0.521507\pi$
$631$	−2140.30	−0.135030	−0.0675150	+	0.997718i	$0.521507\pi$
$632$	19336.3	1.21702
$633$	−15245.3	−0.957260
$634$	9577.70	0.599967
$635$	−921.095	−0.0575630
$636$	−1258.72	−0.0784774
$637$	−1085.95	−0.0675459
$638$	−1430.25	−0.0887527
$639$	−5750.75	−0.356019
$640$	935.101	0.0577548
$641$	−26163.1	−1.61214	−0.806070	−	0.591820i	$-0.798410\pi$
$641$	−26163.1	−1.61214	−0.806070	+	0.591820i	$0.798410\pi$
$642$	−694.852	−0.0427159
$643$	11327.5	0.694732	0.347366	−	0.937730i	$-0.387076\pi$
$643$	11327.5	0.694732	0.347366	+	0.937730i	$0.387076\pi$
$644$	4706.67	0.287995
$645$	−85.7272	−0.00523334
$646$	32319.6	1.96842
$647$	15943.3	0.968775	0.484388	−	0.874854i	$-0.339042\pi$
$647$	15943.3	0.968775	0.484388	+	0.874854i	$0.339042\pi$
$648$	1983.62	0.120253
$649$	5128.54	0.310189
$650$	14089.2	0.850190
$651$	1111.27	0.0669032
$652$	−1055.81	−0.0634181
$653$	−15658.1	−0.938361	−0.469181	−	0.883102i	$-0.655451\pi$
$653$	−15658.1	−0.938361	−0.469181	+	0.883102i	$0.655451\pi$
$654$	15669.9	0.936911
$655$	−2246.09	−0.133988
$656$	100.542	0.00598397
$657$	5937.74	0.352593
$658$	23120.4	1.36980
$659$	5692.81	0.336511	0.168255	−	0.985743i	$-0.446187\pi$
$659$	5692.81	0.336511	0.168255	+	0.985743i	$0.446187\pi$
$660$	−88.4937	−0.00521911
$661$	−18428.9	−1.08442	−0.542209	−	0.840243i	$-0.682412\pi$
$661$	−18428.9	−1.08442	−0.542209	+	0.840243i	$0.682412\pi$
$662$	482.026	0.0282998
$663$	−18108.4	−1.06074
$664$	32232.4	1.88382
$665$	2458.66	0.143373
$666$	767.985	0.0446829
$667$	−7027.25	−0.407941
$668$	3127.56	0.181151
$669$	11726.1	0.677664
$670$	−254.434	−0.0146711
$671$	671.000	0.0386046
$672$	4698.98	0.269743
$673$	10809.0	0.619101	0.309551	−	0.950883i	$-0.399821\pi$
$673$	10809.0	0.619101	0.309551	+	0.950883i	$0.399821\pi$
$674$	16957.0	0.969078
$675$	−3325.77	−0.189643
$676$	42.7722	0.00243356
$677$	22295.8	1.26573	0.632864	−	0.774263i	$-0.281879\pi$
$677$	22295.8	1.26573	0.632864	+	0.774263i	$0.281879\pi$
$678$	9210.83	0.521740
$679$	−10257.0	−0.579715
$680$	4279.29	0.241329
$681$	3721.55	0.209413
$682$	−558.841	−0.0313770
$683$	13376.9	0.749416	0.374708	−	0.927143i	$-0.377743\pi$
$683$	13376.9	0.749416	0.374708	+	0.927143i	$0.377743\pi$
$684$	−1820.23	−0.101752
$685$	1621.22	0.0904287
$686$	−16061.3	−0.893911
$687$	−10702.0	−0.594335
$688$	−934.729	−0.0517968
$689$	9853.74	0.544844
$690$	1316.63	0.0726424
$691$	8830.65	0.486156	0.243078	−	0.970007i	$-0.421843\pi$
$691$	8830.65	0.486156	0.243078	+	0.970007i	$0.421843\pi$
$692$	4202.61	0.230866
$693$	1770.18	0.0970328
$694$	21830.3	1.19405
$695$	2079.75	0.113510
$696$	−3895.23	−0.212139
$697$	294.595	0.0160095
$698$	−25660.2	−1.39148
$699$	7592.87	0.410856
$700$	−4374.17	−0.236183
$701$	10595.5	0.570881	0.285440	−	0.958396i	$-0.407860\pi$
$701$	10595.5	0.570881	0.285440	+	0.958396i	$0.407860\pi$
$702$	−3088.31	−0.166041
$703$	−3543.48	−0.190106
$704$	−6249.80	−0.334585
$705$	−2135.84	−0.114100
$706$	25185.3	1.34258
$707$	13504.9	0.718395
$708$	2777.83	0.147454
$709$	−16651.1	−0.882012	−0.441006	−	0.897504i	$-0.645378\pi$
$709$	−16651.1	−0.882012	−0.441006	+	0.897504i	$0.645378\pi$
$710$	−2115.81	−0.111838
$711$	7106.30	0.374834
$712$	17434.7	0.917689
$713$	−2745.75	−0.144220
$714$	−17024.3	−0.892323
$715$	692.761	0.0362347
$716$	−2809.58	−0.146647
$717$	5029.00	0.261941
$718$	16210.5	0.842578
$719$	16007.4	0.830285	0.415143	−	0.909756i	$-0.363732\pi$
$719$	16007.4	0.830285	0.415143	+	0.909756i	$0.363732\pi$
$720$	536.736	0.0277819
$721$	567.177	0.0292965
$722$	−8611.52	−0.443889
$723$	14098.8	0.725228
$724$	3157.22	0.162068
$725$	6530.82	0.334550
$726$	−890.200	−0.0455075
$727$	−26843.1	−1.36940	−0.684701	−	0.728824i	$-0.740067\pi$
$727$	−26843.1	−1.36940	−0.684701	+	0.728824i	$0.740067\pi$
$728$	−20423.6	−1.03977
$729$	729.000	0.0370370
$730$	2184.61	0.110762
$731$	−2738.84	−0.138577
$732$	363.442	0.0183514
$733$	24613.0	1.24025	0.620124	−	0.784504i	$-0.287082\pi$
$733$	24613.0	1.24025	0.620124	+	0.784504i	$0.287082\pi$
$734$	7155.29	0.359818
$735$	94.3123	0.00473301
$736$	−11610.4	−0.581473
$737$	845.224	0.0422446
$738$	50.2418	0.00250600
$739$	−17938.2	−0.892919	−0.446460	−	0.894804i	$-0.647315\pi$
$739$	−17938.2	−0.892919	−0.446460	+	0.894804i	$0.647315\pi$
$740$	−93.3098	−0.00463532
$741$	14249.4	0.706433
$742$	9263.81	0.458336
$743$	30064.1	1.48445	0.742224	−	0.670152i	$-0.233771\pi$
$743$	30064.1	1.48445	0.742224	+	0.670152i	$0.233771\pi$
$744$	−1521.98	−0.0749980
$745$	−1181.60	−0.0581082
$746$	17617.6	0.864648
$747$	11845.7	0.580204
$748$	−2827.22	−0.138200
$749$	−1688.78	−0.0823854
$750$	−2465.35	−0.120029
$751$	−8419.05	−0.409075	−0.204538	−	0.978859i	$-0.565569\pi$
$751$	−8419.05	−0.409075	−0.204538	+	0.978859i	$0.565569\pi$
$752$	−23288.2	−1.12930
$753$	12178.8	0.589404
$754$	6064.51	0.292913
$755$	−620.498	−0.0299103
$756$	958.805	0.0461262
$757$	27781.7	1.33387	0.666937	−	0.745114i	$-0.267605\pi$
$757$	27781.7	1.33387	0.666937	+	0.745114i	$0.267605\pi$
$758$	20723.9	0.993040
$759$	−4373.82	−0.209169
$760$	−3367.36	−0.160720
$761$	−4290.87	−0.204394	−0.102197	−	0.994764i	$-0.532587\pi$
$761$	−4290.87	−0.204394	−0.102197	+	0.994764i	$0.532587\pi$
$762$	−5018.71	−0.238594
$763$	38084.3	1.80700
$764$	6777.07	0.320924
$765$	1572.68	0.0743274
$766$	35738.2	1.68573
$767$	−21745.9	−1.02373
$768$	−8540.90	−0.401293
$769$	7397.70	0.346902	0.173451	−	0.984842i	$-0.444508\pi$
$769$	7397.70	0.346902	0.173451	+	0.984842i	$0.444508\pi$
$770$	651.286	0.0304814
$771$	−1139.72	−0.0532374
$772$	3932.77	0.183346
$773$	−9498.98	−0.441985	−0.220993	−	0.975276i	$-0.570930\pi$
$773$	−9498.98	−0.441985	−0.220993	+	0.975276i	$0.570930\pi$
$774$	−467.096	−0.0216917
$775$	2551.78	0.118274
$776$	14047.8	0.649856
$777$	1866.52	0.0861791
$778$	31507.5	1.45192
$779$	−231.816	−0.0106620
$780$	375.228	0.0172248
$781$	7028.69	0.322031
$782$	42064.1	1.92354
$783$	−1431.54	−0.0653371
$784$	1028.34	0.0468449
$785$	1363.62	0.0619997
$786$	−12238.1	−0.555368
$787$	−30272.6	−1.37116	−0.685579	−	0.727998i	$-0.740451\pi$
$787$	−30272.6	−1.37116	−0.685579	+	0.727998i	$0.740451\pi$
$788$	6468.14	0.292409
$789$	−21909.2	−0.988576
$790$	2614.55	0.117749
$791$	22386.2	1.00627
$792$	−2424.42	−0.108773
$793$	−2845.15	−0.127408
$794$	2834.43	0.126688
$795$	−855.778	−0.0381778
$796$	−3174.71	−0.141363
$797$	318.026	0.0141343	0.00706717	−	0.999975i	$-0.497750\pi$
$797$	318.026	0.0141343	0.00706717	+	0.999975i	$0.497750\pi$
$798$	13396.3	0.594267
$799$	−68236.4	−3.02131
$800$	10790.2	0.476863
$801$	6407.44	0.282641
$802$	29850.1	1.31427
$803$	−7257.24	−0.318932
$804$	457.809	0.0200817
$805$	3199.96	0.140104
$806$	2369.58	0.103554
$807$	−3900.53	−0.170143
$808$	−18496.2	−0.805315
$809$	−26558.5	−1.15420	−0.577101	−	0.816673i	$-0.695816\pi$
$809$	−26558.5	−1.15420	−0.577101	+	0.816673i	$0.695816\pi$
$810$	268.214	0.0116346
$811$	9377.84	0.406043	0.203021	−	0.979174i	$-0.434924\pi$
$811$	9377.84	0.406043	0.203021	+	0.979174i	$0.434924\pi$
$812$	−1882.81	−0.0813714
$813$	−4326.71	−0.186647
$814$	−938.648	−0.0404172
$815$	−717.820	−0.0308517
$816$	17147.8	0.735654
$817$	2155.18	0.0922891
$818$	4551.24	0.194536
$819$	−7505.88	−0.320240
$820$	−6.10436	−0.000259968 0
$821$	33371.1	1.41858	0.709292	−	0.704915i	$-0.249015\pi$
$821$	33371.1	1.41858	0.709292	+	0.704915i	$0.249015\pi$
$822$	8833.44	0.374819
$823$	−38262.7	−1.62060	−0.810300	−	0.586015i	$-0.800696\pi$
$823$	−38262.7	−1.62060	−0.810300	+	0.586015i	$0.800696\pi$
$824$	−776.800	−0.0328411
$825$	4064.84	0.171539
$826$	−20444.0	−0.861183
$827$	12085.4	0.508164	0.254082	−	0.967183i	$-0.418227\pi$
$827$	12085.4	0.508164	0.254082	+	0.967183i	$0.418227\pi$
$828$	−2369.04	−0.0994323
$829$	29461.6	1.23431	0.617156	−	0.786841i	$-0.288285\pi$
$829$	29461.6	1.23431	0.617156	+	0.786841i	$0.288285\pi$
$830$	4358.28	0.182263
$831$	−6261.73	−0.261392
$832$	26500.2	1.10424
$833$	3013.12	0.125328
$834$	11331.8	0.470490
$835$	2126.36	0.0881265
$836$	2224.73	0.0920381
$837$	−559.343	−0.0230988
$838$	21040.7	0.867352
$839$	−14750.8	−0.606978	−0.303489	−	0.952835i	$-0.598152\pi$
$839$	−14750.8	−0.606978	−0.303489	+	0.952835i	$0.598152\pi$
$840$	1773.75	0.0728574
$841$	−21577.9	−0.884739
$842$	−25028.9	−1.02441
$843$	−17148.6	−0.700629
$844$	10092.5	0.411608
$845$	29.0799	0.00118388
$846$	−11637.4	−0.472933
$847$	−2163.56	−0.0877694
$848$	−9331.01	−0.377864
$849$	5571.30	0.225214
$850$	−39092.5	−1.57749
$851$	−4611.86	−0.185772
$852$	3807.03	0.153083
$853$	9121.48	0.366136	0.183068	−	0.983100i	$-0.441397\pi$
$853$	9121.48	0.366136	0.183068	+	0.983100i	$0.441397\pi$
$854$	−2674.82	−0.107178
$855$	−1237.54	−0.0495004
$856$	2312.94	0.0923534
$857$	17159.2	0.683950	0.341975	−	0.939709i	$-0.388904\pi$
$857$	17159.2	0.683950	0.341975	+	0.939709i	$0.388904\pi$
$858$	3774.60	0.150190
$859$	37354.4	1.48372	0.741859	−	0.670556i	$-0.233944\pi$
$859$	37354.4	1.48372	0.741859	+	0.670556i	$0.233944\pi$
$860$	56.7519	0.00225026
$861$	122.109	0.00483328
$862$	−30658.1	−1.21139
$863$	16407.9	0.647198	0.323599	−	0.946194i	$-0.395107\pi$
$863$	16407.9	0.647198	0.323599	+	0.946194i	$0.395107\pi$
$864$	−2365.18	−0.0931307
$865$	2857.26	0.112312
$866$	14745.9	0.578623
$867$	35505.6	1.39081
$868$	−735.667	−0.0287675
$869$	−8685.47	−0.339050
$870$	−526.691	−0.0205247
$871$	−3583.89	−0.139421
$872$	−52159.9	−2.02564
$873$	5162.72	0.200151
$874$	−33100.0	−1.28104
$875$	−5991.82	−0.231498
$876$	−3930.82	−0.151610
$877$	17872.7	0.688161	0.344080	−	0.938940i	$-0.388191\pi$
$877$	17872.7	0.688161	0.344080	+	0.938940i	$0.388191\pi$
$878$	−32349.0	−1.24342
$879$	−12853.0	−0.493197
$880$	−656.011	−0.0251297
$881$	−22504.2	−0.860597	−0.430298	−	0.902687i	$-0.641592\pi$
$881$	−22504.2	−0.860597	−0.430298	+	0.902687i	$0.641592\pi$
$882$	513.873	0.0196179
$883$	12919.7	0.492393	0.246197	−	0.969220i	$-0.420819\pi$
$883$	12919.7	0.492393	0.246197	+	0.969220i	$0.420819\pi$
$884$	11987.9	0.456105
$885$	1888.59	0.0717336
$886$	25818.9	0.979010
$887$	35712.3	1.35186	0.675931	−	0.736965i	$-0.263742\pi$
$887$	35712.3	1.35186	0.675931	+	0.736965i	$0.263742\pi$
$888$	−2556.37	−0.0966060
$889$	−12197.6	−0.460172
$890$	2357.42	0.0887877
$891$	−891.000	−0.0335013
$892$	−7762.76	−0.291386
$893$	53694.9	2.01213
$894$	−6438.13	−0.240854
$895$	−1910.18	−0.0713409
$896$	12383.0	0.461705
$897$	18545.7	0.690327
$898$	−9505.31	−0.353225
$899$	1098.38	0.0407487
$900$	2201.68	0.0815439
$901$	−27340.7	−1.01093
$902$	−61.4067	−0.00226676
$903$	−1135.24	−0.0418365
$904$	−30659.8	−1.12802
$905$	2146.52	0.0788429
$906$	−3380.87	−0.123975
$907$	2743.28	0.100429	0.0502146	−	0.998738i	$-0.484009\pi$
$907$	2743.28	0.100429	0.0502146	+	0.998738i	$0.484009\pi$
$908$	−2463.69	−0.0900446
$909$	−6797.54	−0.248031
$910$	−2761.56	−0.100599
$911$	−2067.75	−0.0752004	−0.0376002	−	0.999293i	$-0.511971\pi$
$911$	−2067.75	−0.0752004	−0.0376002	+	0.999293i	$0.511971\pi$
$912$	−13493.5	−0.489929
$913$	−14478.1	−0.524814
$914$	−35835.9	−1.29688
$915$	247.096	0.00892759
$916$	7084.82	0.255556
$917$	−29743.7	−1.07113
$918$	8568.97	0.308081
$919$	22309.8	0.800795	0.400398	−	0.916341i	$-0.368872\pi$
$919$	22309.8	0.800795	0.400398	+	0.916341i	$0.368872\pi$
$920$	−4382.63	−0.157055
$921$	15929.2	0.569906
$922$	24570.2	0.877630
$923$	−29802.9	−1.06281
$924$	−1171.87	−0.0417227
$925$	4286.06	0.152351
$926$	21734.4	0.771312
$927$	−285.482	−0.0101148
$928$	4644.50	0.164292
$929$	−13955.6	−0.492861	−0.246431	−	0.969160i	$-0.579258\pi$
$929$	−13955.6	−0.492861	−0.246431	+	0.969160i	$0.579258\pi$
$930$	−205.793	−0.00725616
$931$	−2371.01	−0.0834659
$932$	−5026.53	−0.176662
$933$	−20153.1	−0.707162
$934$	22659.9	0.793848
$935$	−1922.17	−0.0672317
$936$	10280.0	0.358986
$937$	10457.6	0.364605	0.182303	−	0.983242i	$-0.441645\pi$
$937$	10457.6	0.364605	0.182303	+	0.983242i	$0.441645\pi$
$938$	−3369.33	−0.117284
$939$	20912.6	0.726792
$940$	1413.94	0.0490612
$941$	−7613.62	−0.263759	−0.131879	−	0.991266i	$-0.542101\pi$
$941$	−7613.62	−0.263759	−0.131879	+	0.991266i	$0.542101\pi$
$942$	7429.88	0.256984
$943$	−301.709	−0.0104189
$944$	20592.3	0.709981
$945$	651.871	0.0224395
$946$	570.895	0.0196209
$947$	−45597.7	−1.56465	−0.782327	−	0.622868i	$-0.785967\pi$
$947$	−45597.7	−1.56465	−0.782327	+	0.622868i	$0.785967\pi$
$948$	−4704.42	−0.161173
$949$	30771.9	1.05258
$950$	30761.7	1.05057
$951$	−11716.6	−0.399513
$952$	56668.3	1.92923
$953$	16722.8	0.568420	0.284210	−	0.958762i	$-0.408269\pi$
$953$	16722.8	0.568420	0.284210	+	0.958762i	$0.408269\pi$
$954$	−4662.82	−0.158244
$955$	4607.58	0.156123
$956$	−3329.23	−0.112631
$957$	1749.66	0.0590997
$958$	24454.8	0.824737
$959$	21468.9	0.722907
$960$	−2301.49	−0.0773753
$961$	−29361.8	−0.985594
$962$	3980.03	0.133390
$963$	850.027	0.0284442
$964$	−9333.50	−0.311838
$965$	2673.80	0.0891946
$966$	17435.4	0.580719
$967$	−15588.3	−0.518392	−0.259196	−	0.965825i	$-0.583458\pi$
$967$	−15588.3	−0.518392	−0.259196	+	0.965825i	$0.583458\pi$
$968$	2963.19	0.0983888
$969$	−39537.2	−1.31075
$970$	1899.47	0.0628744
$971$	−723.987	−0.0239277	−0.0119639	−	0.999928i	$-0.503808\pi$
$971$	−723.987	−0.0239277	−0.0119639	+	0.999928i	$0.503808\pi$
$972$	−482.603	−0.0159254
$973$	27541.1	0.907426
$974$	−16694.2	−0.549197
$975$	−17235.6	−0.566134
$976$	2694.22	0.0883606
$977$	−10832.7	−0.354727	−0.177364	−	0.984145i	$-0.556757\pi$
$977$	−10832.7	−0.354727	−0.177364	+	0.984145i	$0.556757\pi$
$978$	−3911.14	−0.127878
$979$	−7831.32	−0.255659
$980$	−62.4354	−0.00203513
$981$	−19169.3	−0.623881
$982$	−39030.2	−1.26834
$983$	10412.3	0.337844	0.168922	−	0.985629i	$-0.445971\pi$
$983$	10412.3	0.337844	0.168922	+	0.985629i	$0.445971\pi$
$984$	−167.239	−0.00541806
$985$	4397.55	0.142251
$986$	−16826.9	−0.543486
$987$	−28283.7	−0.912138
$988$	−9433.23	−0.303756
$989$	2804.98	0.0901851
$990$	−327.817	−0.0105239
$991$	−22302.9	−0.714908	−0.357454	−	0.933931i	$-0.616355\pi$
$991$	−22302.9	−0.714908	−0.357454	+	0.933931i	$0.616355\pi$
$992$	1814.74	0.0580827
$993$	−589.672	−0.0188446
$994$	−28018.6	−0.894060
$995$	−2158.41	−0.0687702
$996$	−7841.95	−0.249480
$997$	26990.7	0.857375	0.428688	−	0.903453i	$-0.358976\pi$
$997$	26990.7	0.857375	0.428688	+	0.903453i	$0.358976\pi$
$998$	9579.67	0.303847
$999$	−939.491	−0.0297539

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2013.4.a.c.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)

\(f(q)\)	\(=\)	\(q-2.45234 q^{2} +3.00000 q^{3} -1.98602 q^{4} -1.35025 q^{5} -7.35703 q^{6} -17.8806 q^{7} +24.4891 q^{8} +9.00000 q^{9} +O(q^{10})\)	\(q-2.45234 q^{2} +3.00000 q^{3} -1.98602 q^{4} -1.35025 q^{5} -7.35703 q^{6} -17.8806 q^{7} +24.4891 q^{8} +9.00000 q^{9} +3.31128 q^{10} -11.0000 q^{11} -5.95806 q^{12} +46.6419 q^{13} +43.8494 q^{14} -4.05075 q^{15} -44.1676 q^{16} -129.415 q^{17} -22.0711 q^{18} +101.836 q^{19} +2.68163 q^{20} -53.6419 q^{21} +26.9758 q^{22} +132.540 q^{23} +73.4674 q^{24} -123.177 q^{25} -114.382 q^{26} +27.0000 q^{27} +35.5113 q^{28} -53.0199 q^{29} +9.93383 q^{30} -20.7164 q^{31} -87.5991 q^{32} -33.0000 q^{33} +317.369 q^{34} +24.1434 q^{35} -17.8742 q^{36} -34.7960 q^{37} -249.736 q^{38} +139.926 q^{39} -33.0665 q^{40} -2.27637 q^{41} +131.548 q^{42} +21.1633 q^{43} +21.8462 q^{44} -12.1523 q^{45} -325.033 q^{46} +527.269 q^{47} -132.503 q^{48} -23.2827 q^{49} +302.072 q^{50} -388.244 q^{51} -92.6317 q^{52} +211.264 q^{53} -66.2132 q^{54} +14.8528 q^{55} -437.881 q^{56} +305.508 q^{57} +130.023 q^{58} -466.231 q^{59} +8.04488 q^{60} -61.0000 q^{61} +50.8037 q^{62} -160.926 q^{63} +568.163 q^{64} -62.9782 q^{65} +80.9273 q^{66} -76.8386 q^{67} +257.020 q^{68} +397.620 q^{69} -59.2078 q^{70} -638.972 q^{71} +220.402 q^{72} +659.749 q^{73} +85.3316 q^{74} -369.530 q^{75} -202.248 q^{76} +196.687 q^{77} -343.145 q^{78} +789.589 q^{79} +59.6373 q^{80} +81.0000 q^{81} +5.58243 q^{82} +1316.19 q^{83} +106.534 q^{84} +174.743 q^{85} -51.8995 q^{86} -159.060 q^{87} -269.380 q^{88} +711.938 q^{89} +29.8015 q^{90} -833.986 q^{91} -263.227 q^{92} -62.1492 q^{93} -1293.04 q^{94} -137.504 q^{95} -262.797 q^{96} +573.635 q^{97} +57.0970 q^{98} -99.0000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 37 q - 8 q^{2} + 111 q^{3} + 130 q^{4} - 35 q^{5} - 24 q^{6} - 35 q^{7} - 117 q^{8} + 333 q^{9}+O(q^{10}) \) 37 * q - 8 * q^2 + 111 * q^3 + 130 * q^4 - 35 * q^5 - 24 * q^6 - 35 * q^7 - 117 * q^8 + 333 * q^9	\( 37 q - 8 q^{2} + 111 q^{3} + 130 q^{4} - 35 q^{5} - 24 q^{6} - 35 q^{7} - 117 q^{8} + 333 q^{9} - 41 q^{10} - 407 q^{11} + 390 q^{12} + 51 q^{13} - 228 q^{14} - 105 q^{15} + 462 q^{16} - 190 q^{17} - 72 q^{18} - 51 q^{19} - 720 q^{20} - 105 q^{21} + 88 q^{22} - 583 q^{23} - 351 q^{24} + 598 q^{25} - 1019 q^{26} + 999 q^{27} - 498 q^{28} - 566 q^{29} - 123 q^{30} - 696 q^{31} - 859 q^{32} - 1221 q^{33} - 348 q^{34} - 1102 q^{35} + 1170 q^{36} - 1022 q^{37} - 455 q^{38} + 153 q^{39} - 503 q^{40} - 790 q^{41} - 684 q^{42} - 87 q^{43} - 1430 q^{44} - 315 q^{45} - 303 q^{46} - 1603 q^{47} + 1386 q^{48} + 110 q^{49} - 1926 q^{50} - 570 q^{51} + 736 q^{52} - 2619 q^{53} - 216 q^{54} + 385 q^{55} - 4937 q^{56} - 153 q^{57} - 1099 q^{58} - 2471 q^{59} - 2160 q^{60} - 2257 q^{61} - 2909 q^{62} - 315 q^{63} - 265 q^{64} - 1970 q^{65} + 264 q^{66} - 3033 q^{67} - 1956 q^{68} - 1749 q^{69} + 2410 q^{70} - 3891 q^{71} - 1053 q^{72} + 391 q^{73} - 532 q^{74} + 1794 q^{75} + 1554 q^{76} + 385 q^{77} - 3057 q^{78} + 67 q^{79} - 5111 q^{80} + 2997 q^{81} - 4818 q^{82} - 5315 q^{83} - 1494 q^{84} - 2747 q^{85} - 5195 q^{86} - 1698 q^{87} + 1287 q^{88} - 8945 q^{89} - 369 q^{90} - 4432 q^{91} - 4701 q^{92} - 2088 q^{93} - 372 q^{94} - 3388 q^{95} - 2577 q^{96} - 3784 q^{97} - 4502 q^{98} - 3663 q^{99}+O(q^{100}) \) 37 * q - 8 * q^2 + 111 * q^3 + 130 * q^4 - 35 * q^5 - 24 * q^6 - 35 * q^7 - 117 * q^8 + 333 * q^9 - 41 * q^10 - 407 * q^11 + 390 * q^12 + 51 * q^13 - 228 * q^14 - 105 * q^15 + 462 * q^16 - 190 * q^17 - 72 * q^18 - 51 * q^19 - 720 * q^20 - 105 * q^21 + 88 * q^22 - 583 * q^23 - 351 * q^24 + 598 * q^25 - 1019 * q^26 + 999 * q^27 - 498 * q^28 - 566 * q^29 - 123 * q^30 - 696 * q^31 - 859 * q^32 - 1221 * q^33 - 348 * q^34 - 1102 * q^35 + 1170 * q^36 - 1022 * q^37 - 455 * q^38 + 153 * q^39 - 503 * q^40 - 790 * q^41 - 684 * q^42 - 87 * q^43 - 1430 * q^44 - 315 * q^45 - 303 * q^46 - 1603 * q^47 + 1386 * q^48 + 110 * q^49 - 1926 * q^50 - 570 * q^51 + 736 * q^52 - 2619 * q^53 - 216 * q^54 + 385 * q^55 - 4937 * q^56 - 153 * q^57 - 1099 * q^58 - 2471 * q^59 - 2160 * q^60 - 2257 * q^61 - 2909 * q^62 - 315 * q^63 - 265 * q^64 - 1970 * q^65 + 264 * q^66 - 3033 * q^67 - 1956 * q^68 - 1749 * q^69 + 2410 * q^70 - 3891 * q^71 - 1053 * q^72 + 391 * q^73 - 532 * q^74 + 1794 * q^75 + 1554 * q^76 + 385 * q^77 - 3057 * q^78 + 67 * q^79 - 5111 * q^80 + 2997 * q^81 - 4818 * q^82 - 5315 * q^83 - 1494 * q^84 - 2747 * q^85 - 5195 * q^86 - 1698 * q^87 + 1287 * q^88 - 8945 * q^89 - 369 * q^90 - 4432 * q^91 - 4701 * q^92 - 2088 * q^93 - 372 * q^94 - 3388 * q^95 - 2577 * q^96 - 3784 * q^97 - 4502 * q^98 - 3663 * q^99

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