LMFDB - Embedded newform 6031.2.a.e.1.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6031,2,Mod(1,6031)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6031, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("6031.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6031 = 37 \cdot 163 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6031.a (trivial)

Newform invariants

comment: select newform

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

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

Self dual:	yes
Analytic conductor:	$48.1577774590$
Analytic rank:	$0$
Dimension:	$134$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.18
Character	$\chi$	$=$	6031.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.21168 q^{2} +1.70673 q^{3} +2.89152 q^{4} +4.27910 q^{5} -3.77473 q^{6} +1.99718 q^{7} -1.97176 q^{8} -0.0870880 q^{9} +O(q^{10})$	\(q-2.21168 q^{2} +1.70673 q^{3} +2.89152 q^{4} +4.27910 q^{5} -3.77473 q^{6} +1.99718 q^{7} -1.97176 q^{8} -0.0870880 q^{9} -9.46398 q^{10} -5.32704 q^{11} +4.93504 q^{12} -4.16406 q^{13} -4.41712 q^{14} +7.30324 q^{15} -1.42214 q^{16} -2.84299 q^{17} +0.192611 q^{18} +2.12931 q^{19} +12.3731 q^{20} +3.40863 q^{21} +11.7817 q^{22} -0.825143 q^{23} -3.36526 q^{24} +13.3107 q^{25} +9.20956 q^{26} -5.26881 q^{27} +5.77489 q^{28} +9.70279 q^{29} -16.1524 q^{30} +7.52169 q^{31} +7.08884 q^{32} -9.09179 q^{33} +6.28778 q^{34} +8.54611 q^{35} -0.251817 q^{36} +1.00000 q^{37} -4.70935 q^{38} -7.10691 q^{39} -8.43736 q^{40} +8.89058 q^{41} -7.53880 q^{42} -4.25757 q^{43} -15.4032 q^{44} -0.372658 q^{45} +1.82495 q^{46} -8.75496 q^{47} -2.42720 q^{48} -3.01128 q^{49} -29.4389 q^{50} -4.85220 q^{51} -12.0405 q^{52} +0.220627 q^{53} +11.6529 q^{54} -22.7949 q^{55} -3.93796 q^{56} +3.63415 q^{57} -21.4595 q^{58} +11.2887 q^{59} +21.1175 q^{60} +12.3776 q^{61} -16.6356 q^{62} -0.173930 q^{63} -12.8340 q^{64} -17.8184 q^{65} +20.1081 q^{66} +3.09466 q^{67} -8.22057 q^{68} -1.40829 q^{69} -18.9013 q^{70} +9.85416 q^{71} +0.171717 q^{72} -4.80350 q^{73} -2.21168 q^{74} +22.7176 q^{75} +6.15694 q^{76} -10.6390 q^{77} +15.7182 q^{78} -0.795480 q^{79} -6.08548 q^{80} -8.73115 q^{81} -19.6631 q^{82} +11.9973 q^{83} +9.85614 q^{84} -12.1654 q^{85} +9.41638 q^{86} +16.5600 q^{87} +10.5036 q^{88} +17.7896 q^{89} +0.824200 q^{90} -8.31637 q^{91} -2.38592 q^{92} +12.8375 q^{93} +19.3632 q^{94} +9.11151 q^{95} +12.0987 q^{96} -4.37815 q^{97} +6.65999 q^{98} +0.463921 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 134 q + 9 q^{2} + 7 q^{3} + 149 q^{4} + 22 q^{5} + 20 q^{6} + 11 q^{7} + 27 q^{8} + 181 q^{9}+O(q^{10}) $ 134 * q + 9 * q^2 + 7 * q^3 + 149 * q^4 + 22 * q^5 + 20 * q^6 + 11 * q^7 + 27 * q^8 + 181 * q^9	\( 134 q + 9 q^{2} + 7 q^{3} + 149 q^{4} + 22 q^{5} + 20 q^{6} + 11 q^{7} + 27 q^{8} + 181 q^{9} + 15 q^{10} + 20 q^{11} + 28 q^{12} + 11 q^{13} + 17 q^{14} - 13 q^{15} + 143 q^{16} + 76 q^{17} + 23 q^{18} + 15 q^{19} + 67 q^{20} + 63 q^{21} + 2 q^{22} + 22 q^{23} + 33 q^{24} + 160 q^{25} + 65 q^{26} + 31 q^{27} + 10 q^{28} + 73 q^{29} + 20 q^{30} + 10 q^{31} + 53 q^{32} + 72 q^{33} - 7 q^{34} + 52 q^{35} + 201 q^{36} + 134 q^{37} + 70 q^{38} + 6 q^{39} + 11 q^{40} + 182 q^{41} - 15 q^{42} + 12 q^{43} + 33 q^{44} + 29 q^{45} + 24 q^{46} + 80 q^{47} + 21 q^{48} + 229 q^{49} + 37 q^{50} + 57 q^{51} - 15 q^{52} + 75 q^{53} + 95 q^{54} - 9 q^{55} + 39 q^{56} + 19 q^{57} - 21 q^{58} + 91 q^{59} + 62 q^{60} + 58 q^{61} + 108 q^{62} + 9 q^{63} + 167 q^{64} + 76 q^{65} + 105 q^{66} - 17 q^{67} + 109 q^{68} + 48 q^{69} - 55 q^{70} + 56 q^{71} + 48 q^{72} + 54 q^{73} + 9 q^{74} + 28 q^{75} + 82 q^{76} + 156 q^{77} + 16 q^{78} - 2 q^{79} + 98 q^{80} + 270 q^{81} - 42 q^{82} + 130 q^{83} + 229 q^{84} + 22 q^{85} + 72 q^{86} + 22 q^{87} + 61 q^{88} + 157 q^{89} + 176 q^{90} + 31 q^{91} - 18 q^{92} + 36 q^{93} + 83 q^{94} + 98 q^{95} + 111 q^{96} + 35 q^{97} + 53 q^{98} + 55 q^{99}+O(q^{100}) \) 134 * q + 9 * q^2 + 7 * q^3 + 149 * q^4 + 22 * q^5 + 20 * q^6 + 11 * q^7 + 27 * q^8 + 181 * q^9 + 15 * q^10 + 20 * q^11 + 28 * q^12 + 11 * q^13 + 17 * q^14 - 13 * q^15 + 143 * q^16 + 76 * q^17 + 23 * q^18 + 15 * q^19 + 67 * q^20 + 63 * q^21 + 2 * q^22 + 22 * q^23 + 33 * q^24 + 160 * q^25 + 65 * q^26 + 31 * q^27 + 10 * q^28 + 73 * q^29 + 20 * q^30 + 10 * q^31 + 53 * q^32 + 72 * q^33 - 7 * q^34 + 52 * q^35 + 201 * q^36 + 134 * q^37 + 70 * q^38 + 6 * q^39 + 11 * q^40 + 182 * q^41 - 15 * q^42 + 12 * q^43 + 33 * q^44 + 29 * q^45 + 24 * q^46 + 80 * q^47 + 21 * q^48 + 229 * q^49 + 37 * q^50 + 57 * q^51 - 15 * q^52 + 75 * q^53 + 95 * q^54 - 9 * q^55 + 39 * q^56 + 19 * q^57 - 21 * q^58 + 91 * q^59 + 62 * q^60 + 58 * q^61 + 108 * q^62 + 9 * q^63 + 167 * q^64 + 76 * q^65 + 105 * q^66 - 17 * q^67 + 109 * q^68 + 48 * q^69 - 55 * q^70 + 56 * q^71 + 48 * q^72 + 54 * q^73 + 9 * q^74 + 28 * q^75 + 82 * q^76 + 156 * q^77 + 16 * q^78 - 2 * q^79 + 98 * q^80 + 270 * q^81 - 42 * q^82 + 130 * q^83 + 229 * q^84 + 22 * q^85 + 72 * q^86 + 22 * q^87 + 61 * q^88 + 157 * q^89 + 176 * q^90 + 31 * q^91 - 18 * q^92 + 36 * q^93 + 83 * q^94 + 98 * q^95 + 111 * q^96 + 35 * q^97 + 53 * q^98 + 55 * 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 $

$2$	−2.21168	−1.56389	−0.781947	−	0.623346i	$-0.785773\pi$
$2$	−2.21168	−1.56389	−0.781947	+	0.623346i	$0.785773\pi$
$3$	1.70673	0.985378	0.492689	−	0.870205i	$-0.336014\pi$
$3$	1.70673	0.985378	0.492689	+	0.870205i	$0.336014\pi$
$4$	2.89152	1.44576
$5$	4.27910	1.91367	0.956835	−	0.290632i	$-0.0938656\pi$
$5$	4.27910	1.91367	0.956835	+	0.290632i	$0.0938656\pi$
$6$	−3.77473	−1.54103
$7$	1.99718	0.754862	0.377431	−	0.926038i	$-0.376807\pi$
$7$	1.99718	0.754862	0.377431	+	0.926038i	$0.376807\pi$
$8$	−1.97176	−0.697123
$9$	−0.0870880	−0.0290293
$10$	−9.46398	−2.99277
$11$	−5.32704	−1.60616	−0.803081	−	0.595870i	$-0.796807\pi$
$11$	−5.32704	−1.60616	−0.803081	+	0.595870i	$0.796807\pi$
$12$	4.93504	1.42462
$13$	−4.16406	−1.15490	−0.577451	−	0.816425i	$-0.695953\pi$
$13$	−4.16406	−1.15490	−0.577451	+	0.816425i	$0.695953\pi$
$14$	−4.41712	−1.18052
$15$	7.30324	1.88569
$16$	−1.42214	−0.355535
$17$	−2.84299	−0.689526	−0.344763	−	0.938690i	$-0.612041\pi$
$17$	−2.84299	−0.689526	−0.344763	+	0.938690i	$0.612041\pi$
$18$	0.192611	0.0453988
$19$	2.12931	0.488497	0.244248	−	0.969713i	$-0.421459\pi$
$19$	2.12931	0.488497	0.244248	+	0.969713i	$0.421459\pi$
$20$	12.3731	2.76671
$21$	3.40863	0.743825
$22$	11.7817	2.51187
$23$	−0.825143	−0.172054	−0.0860271	−	0.996293i	$-0.527417\pi$
$23$	−0.825143	−0.172054	−0.0860271	+	0.996293i	$0.527417\pi$
$24$	−3.36526	−0.686930
$25$	13.3107	2.66213
$26$	9.20956	1.80614
$27$	−5.26881	−1.01398
$28$	5.77489	1.09135
$29$	9.70279	1.80176	0.900882	−	0.434065i	$-0.142921\pi$
$29$	9.70279	1.80176	0.900882	+	0.434065i	$0.142921\pi$
$30$	−16.1524	−2.94902
$31$	7.52169	1.35094	0.675468	−	0.737389i	$-0.263942\pi$
$31$	7.52169	1.35094	0.675468	+	0.737389i	$0.263942\pi$
$32$	7.08884	1.25314
$33$	−9.09179	−1.58268
$34$	6.28778	1.07835
$35$	8.54611	1.44456
$36$	−0.251817	−0.0419695
$37$	1.00000	0.164399
$37$	1.00000	0.164399
$38$	−4.70935	−0.763957
$39$	−7.10691	−1.13802
$40$	−8.43736	−1.33406
$41$	8.89058	1.38848	0.694238	−	0.719746i	$-0.255742\pi$
$41$	8.89058	1.38848	0.694238	+	0.719746i	$0.255742\pi$
$42$	−7.53880	−1.16326
$43$	−4.25757	−0.649273	−0.324637	−	0.945839i	$-0.605242\pi$
$43$	−4.25757	−0.649273	−0.324637	+	0.945839i	$0.605242\pi$
$44$	−15.4032	−2.32213
$45$	−0.372658	−0.0555526
$46$	1.82495	0.269075
$47$	−8.75496	−1.27704	−0.638521	−	0.769604i	$-0.720454\pi$
$47$	−8.75496	−1.27704	−0.638521	+	0.769604i	$0.720454\pi$
$48$	−2.42720	−0.350337
$49$	−3.01128	−0.430183
$50$	−29.4389	−4.16329
$51$	−4.85220	−0.679445
$52$	−12.0405	−1.66971
$53$	0.220627	0.0303054	0.0151527	−	0.999885i	$-0.495177\pi$
$53$	0.220627	0.0303054	0.0151527	+	0.999885i	$0.495177\pi$
$54$	11.6529	1.58576
$55$	−22.7949	−3.07366
$56$	−3.93796	−0.526232
$57$	3.63415	0.481354
$58$	−21.4595	−2.81777
$59$	11.2887	1.46967	0.734834	−	0.678247i	$-0.237260\pi$
$59$	11.2887	1.46967	0.734834	+	0.678247i	$0.237260\pi$
$60$	21.1175	2.72626
$61$	12.3776	1.58479	0.792395	−	0.610008i	$-0.208834\pi$
$61$	12.3776	1.58479	0.792395	+	0.610008i	$0.208834\pi$
$62$	−16.6356	−2.11272
$63$	−0.173930	−0.0219132
$64$	−12.8340	−1.60425
$65$	−17.8184	−2.21010
$66$	20.1081	2.47514
$67$	3.09466	0.378073	0.189036	−	0.981970i	$-0.439464\pi$
$67$	3.09466	0.378073	0.189036	+	0.981970i	$0.439464\pi$
$68$	−8.22057	−0.996891
$69$	−1.40829	−0.169539
$70$	−18.9013	−2.25913
$71$	9.85416	1.16947	0.584737	−	0.811223i	$-0.301198\pi$
$71$	9.85416	1.16947	0.584737	+	0.811223i	$0.301198\pi$
$72$	0.171717	0.0202370
$73$	−4.80350	−0.562207	−0.281104	−	0.959677i	$-0.590700\pi$
$73$	−4.80350	−0.562207	−0.281104	+	0.959677i	$0.590700\pi$
$74$	−2.21168	−0.257102
$75$	22.7176	2.62321
$76$	6.15694	0.706250
$77$	−10.6390	−1.21243
$78$	15.7182	1.77974
$79$	−0.795480	−0.0894985	−0.0447492	−	0.998998i	$-0.514249\pi$
$79$	−0.795480	−0.0894985	−0.0447492	+	0.998998i	$0.514249\pi$
$80$	−6.08548	−0.680377
$81$	−8.73115	−0.970128
$82$	−19.6631	−2.17143
$83$	11.9973	1.31687	0.658437	−	0.752636i	$-0.271218\pi$
$83$	11.9973	1.31687	0.658437	+	0.752636i	$0.271218\pi$
$84$	9.85614	1.07539
$85$	−12.1654	−1.31953
$86$	9.41638	1.01539
$87$	16.5600	1.77542
$88$	10.5036	1.11969
$89$	17.7896	1.88570	0.942849	−	0.333219i	$-0.108135\pi$
$89$	17.7896	1.88570	0.942849	+	0.333219i	$0.108135\pi$
$90$	0.824200	0.0868783
$91$	−8.31637	−0.871792
$92$	−2.38592	−0.248749
$93$	12.8375	1.33118
$94$	19.3632	1.99716
$95$	9.11151	0.934822
$96$	12.0987	1.23482
$97$	−4.37815	−0.444534	−0.222267	−	0.974986i	$-0.571346\pi$
$97$	−4.37815	−0.444534	−0.222267	+	0.974986i	$0.571346\pi$
$98$	6.65999	0.672760
$99$	0.463921	0.0466258
$100$	38.4881	3.84881
$101$	−8.96751	−0.892300	−0.446150	−	0.894958i	$-0.647205\pi$
$101$	−8.96751	−0.892300	−0.446150	+	0.894958i	$0.647205\pi$
$102$	10.7315	1.06258
$103$	9.77474	0.963134	0.481567	−	0.876409i	$-0.340068\pi$
$103$	9.77474	0.963134	0.481567	+	0.876409i	$0.340068\pi$
$104$	8.21054	0.805109
$105$	14.5859	1.42344
$106$	−0.487956	−0.0473945
$107$	−7.55846	−0.730704	−0.365352	−	0.930869i	$-0.619051\pi$
$107$	−7.55846	−0.730704	−0.365352	+	0.930869i	$0.619051\pi$
$108$	−15.2349	−1.46598
$109$	17.4565	1.67203	0.836013	−	0.548709i	$-0.184881\pi$
$109$	17.4565	1.67203	0.836013	+	0.548709i	$0.184881\pi$
$110$	50.4150	4.80688
$111$	1.70673	0.161995
$112$	−2.84027	−0.268380
$113$	−5.27101	−0.495855	−0.247928	−	0.968779i	$-0.579749\pi$
$113$	−5.27101	−0.495855	−0.247928	+	0.968779i	$0.579749\pi$
$114$	−8.03756	−0.752787
$115$	−3.53087	−0.329255
$116$	28.0558	2.60492
$117$	0.362640	0.0335260
$118$	−24.9671	−2.29840
$119$	−5.67796	−0.520497
$120$	−14.4003	−1.31456
$121$	17.3773	1.57976
$122$	−27.3753	−2.47844
$123$	15.1738	1.36817
$124$	21.7491	1.95313
$125$	35.5621	3.18077
$126$	0.384678	0.0342698
$127$	11.1189	0.986643	0.493322	−	0.869847i	$-0.335783\pi$
$127$	11.1189	0.986643	0.493322	+	0.869847i	$0.335783\pi$
$128$	14.2069	1.25573
$129$	−7.26650	−0.639780
$130$	39.4086	3.45636
$131$	−6.68574	−0.584136	−0.292068	−	0.956398i	$-0.594343\pi$
$131$	−6.68574	−0.584136	−0.292068	+	0.956398i	$0.594343\pi$
$132$	−26.2891	−2.28817
$133$	4.25261	0.368748
$134$	−6.84439	−0.591265
$135$	−22.5457	−1.94043
$136$	5.60570	0.480685
$137$	−2.01341	−0.172017	−0.0860087	−	0.996294i	$-0.527411\pi$
$137$	−2.01341	−0.172017	−0.0860087	+	0.996294i	$0.527411\pi$
$138$	3.11469	0.265140
$139$	10.8674	0.921762	0.460881	−	0.887462i	$-0.347534\pi$
$139$	10.8674	0.921762	0.460881	+	0.887462i	$0.347534\pi$
$140$	24.7113	2.08848
$141$	−14.9423	−1.25837
$142$	−21.7942	−1.82893
$143$	22.1821	1.85496
$144$	0.123851	0.0103210
$145$	41.5192	3.44798
$146$	10.6238	0.879232
$147$	−5.13943	−0.423893
$148$	2.89152	0.237682
$149$	4.85041	0.397361	0.198681	−	0.980064i	$-0.436334\pi$
$149$	4.85041	0.397361	0.198681	+	0.980064i	$0.436334\pi$
$150$	−50.2441	−4.10242
$151$	−8.70015	−0.708008	−0.354004	−	0.935244i	$-0.615180\pi$
$151$	−8.70015	−0.708008	−0.354004	+	0.935244i	$0.615180\pi$
$152$	−4.19849	−0.340543
$153$	0.247590	0.0200165
$154$	23.5301	1.89611
$155$	32.1860	2.58524
$156$	−20.5498	−1.64530
$157$	−21.7751	−1.73784	−0.868920	−	0.494953i	$-0.835185\pi$
$157$	−21.7751	−1.73784	−0.868920	+	0.494953i	$0.835185\pi$
$158$	1.75935	0.139966
$159$	0.376550	0.0298623
$160$	30.3338	2.39810
$161$	−1.64796	−0.129877
$162$	19.3105	1.51718
$163$	−1.00000	−0.0783260
$163$	−1.00000	−0.0783260
$164$	25.7073	2.00740
$165$	−38.9046	−3.02872
$166$	−26.5342	−2.05945
$167$	−6.59716	−0.510504	−0.255252	−	0.966875i	$-0.582158\pi$
$167$	−6.59716	−0.510504	−0.255252	+	0.966875i	$0.582158\pi$
$168$	−6.72102	−0.518538
$169$	4.33939	0.333799
$170$	26.9060	2.06360
$171$	−0.185437	−0.0141807
$172$	−12.3109	−0.938694
$173$	7.87657	0.598845	0.299422	−	0.954121i	$-0.403206\pi$
$173$	7.87657	0.598845	0.299422	+	0.954121i	$0.403206\pi$
$174$	−36.6254	−2.77656
$175$	26.5838	2.00954
$176$	7.57580	0.571047
$177$	19.2668	1.44818
$178$	−39.3450	−2.94903
$179$	−9.08911	−0.679352	−0.339676	−	0.940543i	$-0.610317\pi$
$179$	−9.08911	−0.679352	−0.339676	+	0.940543i	$0.610317\pi$
$180$	−1.07755	−0.0803158
$181$	5.18959	0.385739	0.192869	−	0.981224i	$-0.438221\pi$
$181$	5.18959	0.385739	0.192869	+	0.981224i	$0.438221\pi$
$182$	18.3931	1.36339
$183$	21.1252	1.56162
$184$	1.62699	0.119943
$185$	4.27910	0.314605
$186$	−28.3923	−2.08183
$187$	15.1447	1.10749
$188$	−25.3152	−1.84630
$189$	−10.5228	−0.765418
$190$	−20.1517	−1.46196
$191$	−7.02488	−0.508302	−0.254151	−	0.967164i	$-0.581796\pi$
$191$	−7.02488	−0.508302	−0.254151	+	0.967164i	$0.581796\pi$
$192$	−21.9041	−1.58079
$193$	−0.132602	−0.00954487	−0.00477244	−	0.999989i	$-0.501519\pi$
$193$	−0.132602	−0.00954487	−0.00477244	+	0.999989i	$0.501519\pi$
$194$	9.68306	0.695203
$195$	−30.4111	−2.17779
$196$	−8.70719	−0.621942
$197$	21.0459	1.49946	0.749728	−	0.661746i	$-0.230184\pi$
$197$	21.0459	1.49946	0.749728	+	0.661746i	$0.230184\pi$
$198$	−1.02604	−0.0729178
$199$	−12.2116	−0.865658	−0.432829	−	0.901476i	$-0.642485\pi$
$199$	−12.2116	−0.865658	−0.432829	+	0.901476i	$0.642485\pi$
$200$	−26.2455	−1.85583
$201$	5.28173	0.372545
$202$	19.8332	1.39546
$203$	19.3782	1.36008
$204$	−14.0303	−0.982315
$205$	38.0437	2.65708
$206$	−21.6186	−1.50624
$207$	0.0718601	0.00499462
$208$	5.92188	0.410609
$209$	−11.3429	−0.784605
$210$	−32.2593	−2.22610
$211$	6.12989	0.421999	0.210999	−	0.977486i	$-0.432328\pi$
$211$	6.12989	0.421999	0.210999	+	0.977486i	$0.432328\pi$
$212$	0.637948	0.0438144
$213$	16.8184	1.15237
$214$	16.7169	1.14274
$215$	−18.2186	−1.24249
$216$	10.3888	0.706871
$217$	15.0222	1.01977
$218$	−38.6081	−2.61487
$219$	−8.19826	−0.553987
$220$	−65.9120	−4.44378
$221$	11.8384	0.796336
$222$	−3.77473	−0.253343
$223$	−17.8370	−1.19445	−0.597226	−	0.802073i	$-0.703731\pi$
$223$	−17.8370	−1.19445	−0.597226	+	0.802073i	$0.703731\pi$
$224$	14.1577	0.945950
$225$	−1.15920	−0.0772799
$226$	11.6578	0.775464
$227$	−6.16068	−0.408898	−0.204449	−	0.978877i	$-0.565540\pi$
$227$	−6.16068	−0.408898	−0.204449	+	0.978877i	$0.565540\pi$
$228$	10.5082	0.695923
$229$	−1.28023	−0.0846002	−0.0423001	−	0.999105i	$-0.513469\pi$
$229$	−1.28023	−0.0846002	−0.0423001	+	0.999105i	$0.513469\pi$
$230$	7.80914	0.514920
$231$	−18.1579	−1.19470
$232$	−19.1316	−1.25605
$233$	2.17861	0.142725	0.0713626	−	0.997450i	$-0.477265\pi$
$233$	2.17861	0.142725	0.0713626	+	0.997450i	$0.477265\pi$
$234$	−0.802042	−0.0524312
$235$	−37.4633	−2.44384
$236$	32.6416	2.12479
$237$	−1.35767	−0.0881899
$238$	12.5578	0.814002
$239$	20.8425	1.34819	0.674096	−	0.738644i	$-0.264533\pi$
$239$	20.8425	1.34819	0.674096	+	0.738644i	$0.264533\pi$
$240$	−10.3862	−0.670429
$241$	3.64292	0.234661	0.117331	−	0.993093i	$-0.462566\pi$
$241$	3.64292	0.234661	0.117331	+	0.993093i	$0.462566\pi$
$242$	−38.4330	−2.47057
$243$	0.904756	0.0580401
$244$	35.7901	2.29123
$245$	−12.8856	−0.823228
$246$	−33.5595	−2.13968
$247$	−8.86657	−0.564166
$248$	−14.8310	−0.941769
$249$	20.4761	1.29762
$250$	−78.6520	−4.97439
$251$	−18.3503	−1.15826	−0.579129	−	0.815236i	$-0.696607\pi$
$251$	−18.3503	−1.15826	−0.579129	+	0.815236i	$0.696607\pi$
$252$	−0.502923	−0.0316812
$253$	4.39557	0.276347
$254$	−24.5914	−1.54300
$255$	−20.7630	−1.30023
$256$	−5.75321	−0.359575
$257$	20.3259	1.26789	0.633946	−	0.773377i	$-0.281434\pi$
$257$	20.3259	1.26789	0.633946	+	0.773377i	$0.281434\pi$
$258$	16.0712	1.00055
$259$	1.99718	0.124099
$260$	−51.5223	−3.19528
$261$	−0.844997	−0.0523040
$262$	14.7867	0.913526
$263$	−21.9268	−1.35206	−0.676031	−	0.736873i	$-0.736302\pi$
$263$	−21.9268	−1.35206	−0.676031	+	0.736873i	$0.736302\pi$
$264$	17.9268	1.10332
$265$	0.944084	0.0579946
$266$	−9.40540	−0.576682
$267$	30.3620	1.85813
$268$	8.94828	0.546603
$269$	27.1032	1.65251	0.826255	−	0.563296i	$-0.190467\pi$
$269$	27.1032	1.65251	0.826255	+	0.563296i	$0.190467\pi$
$270$	49.8640	3.03462
$271$	−2.13962	−0.129972	−0.0649862	−	0.997886i	$-0.520700\pi$
$271$	−2.13962	−0.129972	−0.0649862	+	0.997886i	$0.520700\pi$
$272$	4.04313	0.245151
$273$	−14.1938	−0.859045
$274$	4.45302	0.269017
$275$	−70.9064	−4.27582
$276$	−4.07211	−0.245112
$277$	20.2058	1.21405	0.607024	−	0.794683i	$-0.292363\pi$
$277$	20.2058	1.21405	0.607024	+	0.794683i	$0.292363\pi$
$278$	−24.0352	−1.44154
$279$	−0.655049	−0.0392168
$280$	−16.8509	−1.00703
$281$	−7.71911	−0.460483	−0.230242	−	0.973133i	$-0.573952\pi$
$281$	−7.71911	−0.460483	−0.230242	+	0.973133i	$0.573952\pi$
$282$	33.0476	1.96796
$283$	22.1135	1.31451	0.657256	−	0.753667i	$-0.271717\pi$
$283$	22.1135	1.31451	0.657256	+	0.753667i	$0.271717\pi$
$284$	28.4935	1.69078
$285$	15.5509	0.921153
$286$	−49.0597	−2.90096
$287$	17.7561	1.04811
$288$	−0.617353	−0.0363779
$289$	−8.91741	−0.524553
$290$	−91.8271	−5.39227
$291$	−7.47230	−0.438034
$292$	−13.8894	−0.812818
$293$	19.6333	1.14699	0.573494	−	0.819210i	$-0.305588\pi$
$293$	19.6333	1.14699	0.573494	+	0.819210i	$0.305588\pi$
$294$	11.3668	0.662923
$295$	48.3056	2.81246
$296$	−1.97176	−0.114606
$297$	28.0672	1.62862
$298$	−10.7276	−0.621430
$299$	3.43595	0.198706
$300$	65.6886	3.79253
$301$	−8.50312	−0.490112
$302$	19.2419	1.10725
$303$	−15.3051	−0.879254
$304$	−3.02818	−0.173678
$305$	52.9650	3.03277
$306$	−0.547590	−0.0313037
$307$	34.3770	1.96200	0.980998	−	0.194017i	$-0.0621518\pi$
$307$	34.3770	1.96200	0.980998	+	0.194017i	$0.0621518\pi$
$308$	−30.7630	−1.75289
$309$	16.6828	0.949051
$310$	−71.1852	−4.04305
$311$	−9.55955	−0.542072	−0.271036	−	0.962569i	$-0.587366\pi$
$311$	−9.55955	−0.542072	−0.271036	+	0.962569i	$0.587366\pi$
$312$	14.0131	0.793337
$313$	−34.4848	−1.94920	−0.974598	−	0.223960i	$-0.928102\pi$
$313$	−34.4848	−1.94920	−0.974598	+	0.223960i	$0.928102\pi$
$314$	48.1594	2.71779
$315$	−0.744264	−0.0419345
$316$	−2.30015	−0.129393
$317$	7.95368	0.446723	0.223362	−	0.974736i	$-0.428297\pi$
$317$	7.95368	0.446723	0.223362	+	0.974736i	$0.428297\pi$
$318$	−0.832807	−0.0467015
$319$	−51.6871	−2.89392
$320$	−54.9178	−3.07000
$321$	−12.9002	−0.720020
$322$	3.64475	0.203114
$323$	−6.05360	−0.336832
$324$	−25.2463	−1.40257
$325$	−55.4264	−3.07450
$326$	2.21168	0.122494
$327$	29.7934	1.64758
$328$	−17.5301	−0.967939
$329$	−17.4852	−0.963991
$330$	86.0446	4.73660
$331$	11.6031	0.637766	0.318883	−	0.947794i	$-0.396692\pi$
$331$	11.6031	0.637766	0.318883	+	0.947794i	$0.396692\pi$
$332$	34.6904	1.90389
$333$	−0.0870880	−0.00477239
$334$	14.5908	0.798373
$335$	13.2423	0.723506
$336$	−4.84756	−0.264456
$337$	−34.7526	−1.89310	−0.946548	−	0.322564i	$-0.895455\pi$
$337$	−34.7526	−1.89310	−0.946548	+	0.322564i	$0.895455\pi$
$338$	−9.59734	−0.522027
$339$	−8.99617	−0.488605
$340$	−35.1766	−1.90772
$341$	−40.0683	−2.16982
$342$	0.410128	0.0221772
$343$	−19.9943	−1.07959
$344$	8.39492	0.452624
$345$	−6.02622	−0.324441
$346$	−17.4204	−0.936529
$347$	7.72513	0.414707	0.207353	−	0.978266i	$-0.433515\pi$
$347$	7.72513	0.414707	0.207353	+	0.978266i	$0.433515\pi$
$348$	47.8836	2.56683
$349$	−8.02039	−0.429322	−0.214661	−	0.976689i	$-0.568865\pi$
$349$	−8.02039	−0.429322	−0.214661	+	0.976689i	$0.568865\pi$
$350$	−58.7947	−3.14271
$351$	21.9396	1.17105
$352$	−37.7625	−2.01275
$353$	6.42814	0.342136	0.171068	−	0.985259i	$-0.445278\pi$
$353$	6.42814	0.342136	0.171068	+	0.985259i	$0.445278\pi$
$354$	−42.6119	−2.26480
$355$	42.1669	2.23799
$356$	51.4392	2.72627
$357$	−9.69071	−0.512887
$358$	20.1022	1.06243
$359$	21.4969	1.13456	0.567282	−	0.823524i	$-0.307995\pi$
$359$	21.4969	1.13456	0.567282	+	0.823524i	$0.307995\pi$
$360$	0.734793	0.0387270
$361$	−14.4660	−0.761371
$362$	−11.4777	−0.603254
$363$	29.6583	1.55666
$364$	−24.0470	−1.26040
$365$	−20.5546	−1.07588
$366$	−46.7221	−2.44220
$367$	−26.0667	−1.36067	−0.680335	−	0.732902i	$-0.738166\pi$
$367$	−26.0667	−1.36067	−0.680335	+	0.732902i	$0.738166\pi$
$368$	1.17347	0.0611714
$369$	−0.774263	−0.0403065
$370$	−9.46398	−0.492009
$371$	0.440631	0.0228764
$372$	37.1198	1.92457
$373$	36.2332	1.87608	0.938042	−	0.346521i	$-0.112637\pi$
$373$	36.2332	1.87608	0.938042	+	0.346521i	$0.112637\pi$
$374$	−33.4952	−1.73200
$375$	60.6948	3.13426
$376$	17.2627	0.890256
$377$	−40.4030	−2.08086
$378$	23.2730	1.19703
$379$	7.73314	0.397225	0.198612	−	0.980078i	$-0.436357\pi$
$379$	7.73314	0.397225	0.198612	+	0.980078i	$0.436357\pi$
$380$	26.3462	1.35153
$381$	18.9769	0.972217
$382$	15.5368	0.794931
$383$	−28.3077	−1.44646	−0.723229	−	0.690609i	$-0.757343\pi$
$383$	−28.3077	−1.44646	−0.723229	+	0.690609i	$0.757343\pi$
$384$	24.2473	1.23737
$385$	−45.5255	−2.32019
$386$	0.293272	0.0149272
$387$	0.370783	0.0188480
$388$	−12.6595	−0.642690
$389$	11.8464	0.600638	0.300319	−	0.953839i	$-0.402907\pi$
$389$	11.8464	0.600638	0.300319	+	0.953839i	$0.402907\pi$
$390$	67.2597	3.40583
$391$	2.34587	0.118636
$392$	5.93753	0.299891
$393$	−11.4107	−0.575595
$394$	−46.5467	−2.34499
$395$	−3.40393	−0.171271
$396$	1.34144	0.0674098
$397$	−10.5610	−0.530042	−0.265021	−	0.964243i	$-0.585379\pi$
$397$	−10.5610	−0.530042	−0.265021	+	0.964243i	$0.585379\pi$
$398$	27.0082	1.35380
$399$	7.25803	0.363356
$400$	−18.9296	−0.946482
$401$	−6.42865	−0.321031	−0.160516	−	0.987033i	$-0.551316\pi$
$401$	−6.42865	−0.321031	−0.160516	+	0.987033i	$0.551316\pi$
$402$	−11.6815	−0.582620
$403$	−31.3208	−1.56020
$404$	−25.9298	−1.29005
$405$	−37.3614	−1.85650
$406$	−42.8584	−2.12702
$407$	−5.32704	−0.264051
$408$	9.56739	0.473657
$409$	8.22169	0.406536	0.203268	−	0.979123i	$-0.434844\pi$
$409$	8.22169	0.406536	0.203268	+	0.979123i	$0.434844\pi$
$410$	−84.1403	−4.15540
$411$	−3.43634	−0.169502
$412$	28.2639	1.39246
$413$	22.5456	1.10940
$414$	−0.158931	−0.00781105
$415$	51.3376	2.52006
$416$	−29.5184	−1.44726
$417$	18.5477	0.908284
$418$	25.0869	1.22704
$419$	−31.3447	−1.53129	−0.765645	−	0.643263i	$-0.777580\pi$
$419$	−31.3447	−1.53129	−0.765645	+	0.643263i	$0.777580\pi$
$420$	42.1754	2.05795
$421$	−3.71538	−0.181076	−0.0905382	−	0.995893i	$-0.528859\pi$
$421$	−3.71538	−0.181076	−0.0905382	+	0.995893i	$0.528859\pi$
$422$	−13.5573	−0.659961
$423$	0.762452	0.0370717
$424$	−0.435024	−0.0211266
$425$	−37.8421	−1.83561
$426$	−37.1968	−1.80219
$427$	24.7203	1.19630
$428$	−21.8555	−1.05642
$429$	37.8588	1.82784
$430$	40.2936	1.94313
$431$	11.4825	0.553093	0.276547	−	0.961000i	$-0.410810\pi$
$431$	11.4825	0.553093	0.276547	+	0.961000i	$0.410810\pi$
$432$	7.49299	0.360507
$433$	−26.7485	−1.28545	−0.642726	−	0.766096i	$-0.722197\pi$
$433$	−26.7485	−1.28545	−0.642726	+	0.766096i	$0.722197\pi$
$434$	−33.2242	−1.59481
$435$	70.8618	3.39757
$436$	50.4758	2.41735
$437$	−1.75698	−0.0840480
$438$	18.1319	0.866376
$439$	31.2878	1.49328	0.746642	−	0.665227i	$-0.231665\pi$
$439$	31.2878	1.49328	0.746642	+	0.665227i	$0.231665\pi$
$440$	44.9461	2.14272
$441$	0.262246	0.0124879
$442$	−26.1827	−1.24538
$443$	34.8255	1.65461	0.827304	−	0.561755i	$-0.189874\pi$
$443$	34.8255	1.65461	0.827304	+	0.561755i	$0.189874\pi$
$444$	4.93504	0.234206
$445$	76.1236	3.60860
$446$	39.4497	1.86800
$447$	8.27832	0.391551
$448$	−25.6317	−1.21098
$449$	28.1130	1.32674	0.663368	−	0.748294i	$-0.269127\pi$
$449$	28.1130	1.32674	0.663368	+	0.748294i	$0.269127\pi$
$450$	2.56378	0.120858
$451$	−47.3605	−2.23012
$452$	−15.2412	−0.716888
$453$	−14.8488	−0.697656
$454$	13.6254	0.639473
$455$	−35.5865	−1.66832
$456$	−7.16567	−0.335563
$457$	−23.6664	−1.10707	−0.553534	−	0.832827i	$-0.686721\pi$
$457$	−23.6664	−1.10707	−0.553534	+	0.832827i	$0.686721\pi$
$458$	2.83147	0.132306
$459$	14.9792	0.699168
$460$	−10.2096	−0.476024
$461$	−1.40511	−0.0654426	−0.0327213	−	0.999465i	$-0.510417\pi$
$461$	−1.40511	−0.0654426	−0.0327213	+	0.999465i	$0.510417\pi$
$462$	40.1595	1.86839
$463$	10.1286	0.470717	0.235359	−	0.971909i	$-0.424374\pi$
$463$	10.1286	0.470717	0.235359	+	0.971909i	$0.424374\pi$
$464$	−13.7987	−0.640590
$465$	54.9327	2.54744
$466$	−4.81837	−0.223207
$467$	−24.2642	−1.12282	−0.561408	−	0.827539i	$-0.689740\pi$
$467$	−24.2642	−1.12282	−0.561408	+	0.827539i	$0.689740\pi$
$468$	1.04858	0.0484707
$469$	6.18058	0.285393
$470$	82.8568	3.82190
$471$	−37.1641	−1.71243
$472$	−22.2587	−1.02454
$473$	22.6802	1.04284
$474$	3.00272	0.137920
$475$	28.3425	1.30044
$476$	−16.4179	−0.752515
$477$	−0.0192140	−0.000879747 0
$478$	−46.0970	−2.10843
$479$	−12.5854	−0.575043	−0.287522	−	0.957774i	$-0.592831\pi$
$479$	−12.5854	−0.575043	−0.287522	+	0.957774i	$0.592831\pi$
$480$	51.7715	2.36304
$481$	−4.16406	−0.189865
$482$	−8.05697	−0.366985
$483$	−2.81261	−0.127978
$484$	50.2469	2.28395
$485$	−18.7345	−0.850691
$486$	−2.00103	−0.0907686
$487$	7.51325	0.340458	0.170229	−	0.985405i	$-0.445549\pi$
$487$	7.51325	0.340458	0.170229	+	0.985405i	$0.445549\pi$
$488$	−24.4057	−1.10479
$489$	−1.70673	−0.0771808
$490$	28.4987	1.28744
$491$	−19.7839	−0.892836	−0.446418	−	0.894825i	$-0.647300\pi$
$491$	−19.7839	−0.892836	−0.446418	+	0.894825i	$0.647300\pi$
$492$	43.8753	1.97805
$493$	−27.5849	−1.24236
$494$	19.6100	0.882296
$495$	1.98516	0.0892264
$496$	−10.6969	−0.480305
$497$	19.6805	0.882792
$498$	−45.2865	−2.02934
$499$	−15.1644	−0.678851	−0.339425	−	0.940633i	$-0.610233\pi$
$499$	−15.1644	−0.678851	−0.339425	+	0.940633i	$0.610233\pi$
$500$	102.829	4.59864
$501$	−11.2595	−0.503039
$502$	40.5849	1.81139
$503$	6.76563	0.301665	0.150832	−	0.988559i	$-0.451805\pi$
$503$	6.76563	0.301665	0.150832	+	0.988559i	$0.451805\pi$
$504$	0.342949	0.0152762
$505$	−38.3728	−1.70757
$506$	−9.72159	−0.432177
$507$	7.40615	0.328919
$508$	32.1506	1.42645
$509$	9.22773	0.409012	0.204506	−	0.978865i	$-0.434441\pi$
$509$	9.22773	0.409012	0.204506	+	0.978865i	$0.434441\pi$
$510$	45.9212	2.03342
$511$	−9.59345	−0.424389
$512$	−15.6896	−0.693388
$513$	−11.2189	−0.495328
$514$	−44.9543	−1.98285
$515$	41.8271	1.84312
$516$	−21.0113	−0.924969
$517$	46.6380	2.05114
$518$	−4.41712	−0.194077
$519$	13.4431	0.590089
$520$	35.1337	1.54071
$521$	18.5630	0.813259	0.406629	−	0.913593i	$-0.366704\pi$
$521$	18.5630	0.813259	0.406629	+	0.913593i	$0.366704\pi$
$522$	1.86886	0.0817979
$523$	−15.5970	−0.682011	−0.341005	−	0.940061i	$-0.610767\pi$
$523$	−15.5970	−0.682011	−0.341005	+	0.940061i	$0.610767\pi$
$524$	−19.3320	−0.844521
$525$	45.3712	1.98016
$526$	48.4950	2.11448
$527$	−21.3841	−0.931506
$528$	12.9298	0.562698
$529$	−22.3191	−0.970397
$530$	−2.08801	−0.0906973
$531$	−0.983113	−0.0426635
$532$	12.2965	0.533121
$533$	−37.0209	−1.60355
$534$	−67.1511	−2.90591
$535$	−32.3434	−1.39833
$536$	−6.10193	−0.263563
$537$	−15.5126	−0.669419
$538$	−59.9435	−2.58435
$539$	16.0412	0.690944
$540$	−65.1916	−2.80540
$541$	−10.7342	−0.461500	−0.230750	−	0.973013i	$-0.574118\pi$
$541$	−10.7342	−0.461500	−0.230750	+	0.973013i	$0.574118\pi$
$542$	4.73214	0.203263
$543$	8.85720	0.380099
$544$	−20.1535	−0.864075
$545$	74.6979	3.19971
$546$	31.3920	1.34345
$547$	−14.3916	−0.615340	−0.307670	−	0.951493i	$-0.599549\pi$
$547$	−14.3916	−0.615340	−0.307670	+	0.951493i	$0.599549\pi$
$548$	−5.82183	−0.248696
$549$	−1.07794	−0.0460054
$550$	156.822	6.68692
$551$	20.6602	0.880156
$552$	2.77682	0.118189
$553$	−1.58871	−0.0675590
$554$	−44.6887	−1.89864
$555$	7.30324	0.310005
$556$	31.4234	1.33265
$557$	−12.6978	−0.538025	−0.269013	−	0.963137i	$-0.586697\pi$
$557$	−12.6978	−0.538025	−0.269013	+	0.963137i	$0.586697\pi$
$558$	1.44876	0.0613308
$559$	17.7288	0.749847
$560$	−12.1538	−0.513591
$561$	25.8479	1.09130
$562$	17.0722	0.720147
$563$	2.30841	0.0972881	0.0486440	−	0.998816i	$-0.484510\pi$
$563$	2.30841	0.0972881	0.0486440	+	0.998816i	$0.484510\pi$
$564$	−43.2060	−1.81930
$565$	−22.5552	−0.948903
$566$	−48.9080	−2.05576
$567$	−17.4377	−0.732313
$568$	−19.4301	−0.815267
$569$	−13.5432	−0.567760	−0.283880	−	0.958860i	$-0.591622\pi$
$569$	−13.5432	−0.567760	−0.283880	+	0.958860i	$0.591622\pi$
$570$	−34.3935	−1.44058
$571$	4.47122	0.187115	0.0935574	−	0.995614i	$-0.470176\pi$
$571$	4.47122	0.187115	0.0935574	+	0.995614i	$0.470176\pi$
$572$	64.1400	2.68183
$573$	−11.9895	−0.500870
$574$	−39.2707	−1.63913
$575$	−10.9832	−0.458031
$576$	1.11768	0.0465702
$577$	17.0987	0.711827	0.355913	−	0.934519i	$-0.384170\pi$
$577$	17.0987	0.711827	0.355913	+	0.934519i	$0.384170\pi$
$578$	19.7224	0.820345
$579$	−0.226315	−0.00940531
$580$	120.054	4.98496
$581$	23.9607	0.994058
$582$	16.5263	0.685039
$583$	−1.17529	−0.0486754
$584$	9.47136	0.391928
$585$	1.55177	0.0641578
$586$	−43.4225	−1.79377
$587$	1.97434	0.0814897	0.0407449	−	0.999170i	$-0.487027\pi$
$587$	1.97434	0.0814897	0.0407449	+	0.999170i	$0.487027\pi$
$588$	−14.8608	−0.612848
$589$	16.0160	0.659928
$590$	−106.836	−4.39839
$591$	35.9195	1.47753
$592$	−1.42214	−0.0584496
$593$	18.2209	0.748244	0.374122	−	0.927379i	$-0.377944\pi$
$593$	18.2209	0.748244	0.374122	+	0.927379i	$0.377944\pi$
$594$	−62.0755	−2.54699
$595$	−24.2965	−0.996060
$596$	14.0251	0.574490
$597$	−20.8419	−0.853001
$598$	−7.59921	−0.310755
$599$	2.10920	0.0861796	0.0430898	−	0.999071i	$-0.486280\pi$
$599$	2.10920	0.0861796	0.0430898	+	0.999071i	$0.486280\pi$
$600$	−44.7938	−1.82870
$601$	−35.8341	−1.46171	−0.730853	−	0.682535i	$-0.760877\pi$
$601$	−35.8341	−1.46171	−0.730853	+	0.682535i	$0.760877\pi$
$602$	18.8062	0.766483
$603$	−0.269508	−0.0109752
$604$	−25.1567	−1.02361
$605$	74.3592	3.02313
$606$	33.8499	1.37506
$607$	−47.7670	−1.93880	−0.969402	−	0.245480i	$-0.921054\pi$
$607$	−47.7670	−1.93880	−0.969402	+	0.245480i	$0.921054\pi$
$608$	15.0943	0.612156
$609$	33.0733	1.34020
$610$	−117.142	−4.74292
$611$	36.4562	1.47486
$612$	0.715913	0.0289391
$613$	14.1052	0.569704	0.284852	−	0.958572i	$-0.408056\pi$
$613$	14.1052	0.569704	0.284852	+	0.958572i	$0.408056\pi$
$614$	−76.0308	−3.06835
$615$	64.9301	2.61823
$616$	20.9777	0.845214
$617$	−38.5034	−1.55009	−0.775044	−	0.631908i	$-0.782272\pi$
$617$	−38.5034	−1.55009	−0.775044	+	0.631908i	$0.782272\pi$
$618$	−36.8970	−1.48421
$619$	−38.7122	−1.55597	−0.777987	−	0.628280i	$-0.783759\pi$
$619$	−38.7122	−1.55597	−0.777987	+	0.628280i	$0.783759\pi$
$620$	93.0667	3.73765
$621$	4.34753	0.174460
$622$	21.1426	0.847743
$623$	35.5291	1.42344
$624$	10.1070	0.404605
$625$	85.6204	3.42481
$626$	76.2693	3.04834
$627$	−19.3592	−0.773133
$628$	−62.9631	−2.51250
$629$	−2.84299	−0.113357
$630$	1.64607	0.0655811
$631$	42.1951	1.67976	0.839881	−	0.542771i	$-0.182625\pi$
$631$	42.1951	1.67976	0.839881	+	0.542771i	$0.182625\pi$
$632$	1.56850	0.0623915
$633$	10.4620	0.415829
$634$	−17.5910	−0.698627
$635$	47.5789	1.88811
$636$	1.08880	0.0431738
$637$	12.5392	0.496819
$638$	114.315	4.52579
$639$	−0.858179	−0.0339491
$640$	60.7927	2.40304
$641$	−21.4022	−0.845336	−0.422668	−	0.906285i	$-0.638906\pi$
$641$	−21.4022	−0.845336	−0.422668	+	0.906285i	$0.638906\pi$
$642$	28.5311	1.12603
$643$	6.81209	0.268642	0.134321	−	0.990938i	$-0.457115\pi$
$643$	6.81209	0.268642	0.134321	+	0.990938i	$0.457115\pi$
$644$	−4.76511	−0.187772
$645$	−31.0941	−1.22433
$646$	13.3886	0.526768
$647$	13.3460	0.524687	0.262344	−	0.964975i	$-0.415505\pi$
$647$	13.3460	0.524687	0.262344	+	0.964975i	$0.415505\pi$
$648$	17.2158	0.676299
$649$	−60.1355	−2.36052
$650$	122.585	4.80819
$651$	25.6387	1.00486
$652$	−2.89152	−0.113241
$653$	−42.3481	−1.65721	−0.828604	−	0.559836i	$-0.810864\pi$
$653$	−42.3481	−1.65721	−0.828604	+	0.559836i	$0.810864\pi$
$654$	−65.8934	−2.57664
$655$	−28.6089	−1.11784
$656$	−12.6437	−0.493652
$657$	0.418327	0.0163205
$658$	38.6717	1.50758
$659$	−41.3182	−1.60953	−0.804765	−	0.593594i	$-0.797709\pi$
$659$	−41.3182	−1.60953	−0.804765	+	0.593594i	$0.797709\pi$
$660$	−112.494	−4.37881
$661$	11.1873	0.435136	0.217568	−	0.976045i	$-0.430188\pi$
$661$	11.1873	0.435136	0.217568	+	0.976045i	$0.430188\pi$
$662$	−25.6624	−0.997398
$663$	20.2049	0.784692
$664$	−23.6558	−0.918023
$665$	18.1973	0.705662
$666$	0.192611	0.00746351
$667$	−8.00620	−0.310001
$668$	−19.0758	−0.738067
$669$	−30.4428	−1.17699
$670$	−29.2878	−1.13149
$671$	−65.9360	−2.54543
$672$	24.1633	0.932119
$673$	−40.4866	−1.56065	−0.780323	−	0.625377i	$-0.784945\pi$
$673$	−40.4866	−1.56065	−0.780323	+	0.625377i	$0.784945\pi$
$674$	76.8616	2.96060
$675$	−70.1314	−2.69936
$676$	12.5475	0.482594
$677$	7.42405	0.285330	0.142665	−	0.989771i	$-0.454433\pi$
$677$	7.42405	0.285330	0.142665	+	0.989771i	$0.454433\pi$
$678$	19.8966	0.764126
$679$	−8.74395	−0.335562
$680$	23.9873	0.919872
$681$	−10.5146	−0.402920
$682$	88.6183	3.39337
$683$	−21.5005	−0.822693	−0.411347	−	0.911479i	$-0.634941\pi$
$683$	−21.5005	−0.822693	−0.411347	+	0.911479i	$0.634941\pi$
$684$	−0.536196	−0.0205020
$685$	−8.61558	−0.329184
$686$	44.2210	1.68837
$687$	−2.18501	−0.0833632
$688$	6.05487	0.230840
$689$	−0.918704	−0.0349998
$690$	13.3281	0.507391
$691$	−29.6017	−1.12610	−0.563051	−	0.826422i	$-0.690373\pi$
$691$	−29.6017	−1.12610	−0.563051	+	0.826422i	$0.690373\pi$
$692$	22.7753	0.865787
$693$	0.926533	0.0351961
$694$	−17.0855	−0.648557
$695$	46.5027	1.76395
$696$	−32.6524	−1.23769
$697$	−25.2758	−0.957391
$698$	17.7385	0.671414
$699$	3.71828	0.140638
$700$	76.8675	2.90532
$701$	22.3851	0.845472	0.422736	−	0.906253i	$-0.361070\pi$
$701$	22.3851	0.845472	0.422736	+	0.906253i	$0.361070\pi$
$702$	−48.5235	−1.83140
$703$	2.12931	0.0803084
$704$	68.3670	2.57668
$705$	−63.9396	−2.40810
$706$	−14.2170	−0.535063
$707$	−17.9097	−0.673564
$708$	55.7103	2.09372
$709$	3.41463	0.128239	0.0641195	−	0.997942i	$-0.479576\pi$
$709$	3.41463	0.128239	0.0641195	+	0.997942i	$0.479576\pi$
$710$	−93.2596	−3.49997
$711$	0.0692768	0.00259808
$712$	−35.0769	−1.31456
$713$	−6.20647	−0.232434
$714$	21.4327	0.802100
$715$	94.9193	3.54978
$716$	−26.2814	−0.982181
$717$	35.5725	1.32848
$718$	−47.5443	−1.77434
$719$	19.5962	0.730815	0.365408	−	0.930848i	$-0.380930\pi$
$719$	19.5962	0.730815	0.365408	+	0.930848i	$0.380930\pi$
$720$	0.529972	0.0197509
$721$	19.5219	0.727033
$722$	31.9942	1.19070
$723$	6.21747	0.231230
$724$	15.0058	0.557686
$725$	129.151	4.79653
$726$	−65.5947	−2.43445
$727$	15.1537	0.562021	0.281010	−	0.959705i	$-0.409331\pi$
$727$	15.1537	0.562021	0.281010	+	0.959705i	$0.409331\pi$
$728$	16.3979	0.607747
$729$	27.7376	1.02732
$730$	45.4603	1.68256
$731$	12.1042	0.447691
$732$	61.0840	2.25773
$733$	−20.7833	−0.767650	−0.383825	−	0.923406i	$-0.625393\pi$
$733$	−20.7833	−0.767650	−0.383825	+	0.923406i	$0.625393\pi$
$734$	57.6511	2.12794
$735$	−21.9921	−0.811191
$736$	−5.84931	−0.215609
$737$	−16.4854	−0.607246
$738$	1.71242	0.0630351
$739$	−14.7961	−0.544285	−0.272143	−	0.962257i	$-0.587732\pi$
$739$	−14.7961	−0.544285	−0.272143	+	0.962257i	$0.587732\pi$
$740$	12.3731	0.454844
$741$	−15.1328	−0.555917
$742$	−0.974535	−0.0357763
$743$	36.7767	1.34921	0.674603	−	0.738181i	$-0.264315\pi$
$743$	36.7767	1.34921	0.674603	+	0.738181i	$0.264315\pi$
$744$	−25.3124	−0.927998
$745$	20.7554	0.760418
$746$	−80.1362	−2.93400
$747$	−1.04482	−0.0382280
$748$	43.7913	1.60117
$749$	−15.0956	−0.551581
$750$	−134.237	−4.90165
$751$	−23.9488	−0.873904	−0.436952	−	0.899485i	$-0.643942\pi$
$751$	−23.9488	−0.873904	−0.436952	+	0.899485i	$0.643942\pi$
$752$	12.4508	0.454034
$753$	−31.3188	−1.14132
$754$	89.3585	3.25424
$755$	−37.2288	−1.35489
$756$	−30.4268	−1.10661
$757$	−19.6046	−0.712540	−0.356270	−	0.934383i	$-0.615952\pi$
$757$	−19.6046	−0.712540	−0.356270	+	0.934383i	$0.615952\pi$
$758$	−17.1032	−0.621217
$759$	7.50203	0.272306
$760$	−17.9657	−0.651686
$761$	26.0182	0.943158	0.471579	−	0.881824i	$-0.343684\pi$
$761$	26.0182	0.943158	0.471579	+	0.881824i	$0.343684\pi$
$762$	−41.9708	−1.52044
$763$	34.8637	1.26215
$764$	−20.3126	−0.734884
$765$	1.05946	0.0383050
$766$	62.6076	2.26210
$767$	−47.0070	−1.69732
$768$	−9.81914	−0.354318
$769$	−26.7393	−0.964244	−0.482122	−	0.876104i	$-0.660134\pi$
$769$	−26.7393	−0.964244	−0.482122	+	0.876104i	$0.660134\pi$
$770$	100.688	3.62853
$771$	34.6907	1.24935
$772$	−0.383421	−0.0137996
$773$	42.7618	1.53803	0.769017	−	0.639228i	$-0.220746\pi$
$773$	42.7618	1.53803	0.769017	+	0.639228i	$0.220746\pi$
$774$	−0.820054	−0.0294762
$775$	100.119	3.59637
$776$	8.63267	0.309895
$777$	3.40863	0.122284
$778$	−26.2005	−0.939333
$779$	18.9308	0.678266
$780$	−87.9345	−3.14856
$781$	−52.4935	−1.87836
$782$	−5.18832	−0.185534
$783$	−51.1222	−1.82696
$784$	4.28247	0.152945
$785$	−93.1776	−3.32565
$786$	25.2369	0.900169
$787$	−12.7078	−0.452983	−0.226491	−	0.974013i	$-0.572725\pi$
$787$	−12.7078	−0.452983	−0.226491	+	0.974013i	$0.572725\pi$
$788$	60.8546	2.16786
$789$	−37.4230	−1.33229
$790$	7.52841	0.267849
$791$	−10.5271	−0.374302
$792$	−0.914742	−0.0325039
$793$	−51.5411	−1.83028
$794$	23.3576	0.828929
$795$	1.61129	0.0571466
$796$	−35.3102	−1.25154
$797$	35.2688	1.24928	0.624642	−	0.780911i	$-0.285245\pi$
$797$	35.2688	1.24928	0.624642	+	0.780911i	$0.285245\pi$
$798$	−16.0524	−0.568250
$799$	24.8903	0.880554
$800$	94.3572	3.33603
$801$	−1.54926	−0.0547406
$802$	14.2181	0.502059
$803$	25.5884	0.902996
$804$	15.2723	0.538611
$805$	−7.05177	−0.248542
$806$	69.2715	2.43998
$807$	46.2577	1.62835
$808$	17.6818	0.622043
$809$	4.52404	0.159057	0.0795284	−	0.996833i	$-0.474659\pi$
$809$	4.52404	0.159057	0.0795284	+	0.996833i	$0.474659\pi$
$810$	82.6315	2.90337
$811$	7.50514	0.263541	0.131771	−	0.991280i	$-0.457934\pi$
$811$	7.50514	0.263541	0.131771	+	0.991280i	$0.457934\pi$
$812$	56.0325	1.96636
$813$	−3.65174	−0.128072
$814$	11.7817	0.412948
$815$	−4.27910	−0.149890
$816$	6.90052	0.241567
$817$	−9.06568	−0.317168
$818$	−18.1837	−0.635779
$819$	0.724256	0.0253075
$820$	110.004	3.84151
$821$	−26.8711	−0.937809	−0.468905	−	0.883249i	$-0.655351\pi$
$821$	−26.8711	−0.937809	−0.468905	+	0.883249i	$0.655351\pi$
$822$	7.60008	0.265083
$823$	8.09915	0.282319	0.141159	−	0.989987i	$-0.454917\pi$
$823$	8.09915	0.282319	0.141159	+	0.989987i	$0.454917\pi$
$824$	−19.2735	−0.671423
$825$	−121.018	−4.21330
$826$	−49.8636	−1.73498
$827$	28.1743	0.979716	0.489858	−	0.871802i	$-0.337049\pi$
$827$	28.1743	0.979716	0.489858	+	0.871802i	$0.337049\pi$
$828$	0.207785	0.00722103
$829$	25.5807	0.888455	0.444228	−	0.895914i	$-0.353478\pi$
$829$	25.5807	0.888455	0.444228	+	0.895914i	$0.353478\pi$
$830$	−113.542	−3.94111
$831$	34.4857	1.19630
$832$	53.4414	1.85275
$833$	8.56104	0.296623
$834$	−41.0215	−1.42046
$835$	−28.2299	−0.976935
$836$	−32.7983	−1.13435
$837$	−39.6304	−1.36983
$838$	69.3245	2.39478
$839$	36.3199	1.25390	0.626951	−	0.779058i	$-0.284302\pi$
$839$	36.3199	1.25390	0.626951	+	0.779058i	$0.284302\pi$
$840$	−28.7599	−0.992310
$841$	65.1442	2.24635
$842$	8.21722	0.283184
$843$	−13.1744	−0.453750
$844$	17.7247	0.610110
$845$	18.5687	0.638782
$846$	−1.68630	−0.0579762
$847$	34.7056	1.19250
$848$	−0.313763	−0.0107747
$849$	37.7417	1.29529
$850$	83.6945	2.87070
$851$	−0.825143	−0.0282856
$852$	48.6306	1.66606
$853$	−54.2212	−1.85650	−0.928249	−	0.371960i	$-0.878686\pi$
$853$	−54.2212	−1.85650	−0.928249	+	0.371960i	$0.878686\pi$
$854$	−54.6733	−1.87088
$855$	−0.793504	−0.0271373
$856$	14.9035	0.509391
$857$	−21.7559	−0.743168	−0.371584	−	0.928399i	$-0.621185\pi$
$857$	−21.7559	−0.743168	−0.371584	+	0.928399i	$0.621185\pi$
$858$	−83.7314	−2.85854
$859$	−25.8341	−0.881450	−0.440725	−	0.897642i	$-0.645279\pi$
$859$	−25.8341	−0.881450	−0.440725	+	0.897642i	$0.645279\pi$
$860$	−52.6794	−1.79635
$861$	30.3047	1.03278
$862$	−25.3956	−0.864979
$863$	6.42527	0.218719	0.109359	−	0.994002i	$-0.465120\pi$
$863$	6.42527	0.218719	0.109359	+	0.994002i	$0.465120\pi$
$864$	−37.3498	−1.27067
$865$	33.7046	1.14599
$866$	59.1592	2.01031
$867$	−15.2196	−0.516883
$868$	43.4369	1.47434
$869$	4.23755	0.143749
$870$	−156.724	−5.31343
$871$	−12.8863	−0.436637
$872$	−34.4200	−1.16561
$873$	0.381284	0.0129045
$874$	3.88589	0.131442
$875$	71.0239	2.40104
$876$	−23.7055	−0.800933
$877$	−34.0223	−1.14885	−0.574426	−	0.818557i	$-0.694775\pi$
$877$	−34.0223	−1.14885	−0.574426	+	0.818557i	$0.694775\pi$
$878$	−69.1985	−2.33534
$879$	33.5086	1.13022
$880$	32.4176	1.09280
$881$	45.1724	1.52190	0.760948	−	0.648813i	$-0.224734\pi$
$881$	45.1724	1.52190	0.760948	+	0.648813i	$0.224734\pi$
$882$	−0.580005	−0.0195298
$883$	−43.6755	−1.46980	−0.734898	−	0.678178i	$-0.762770\pi$
$883$	−43.6755	−1.46980	−0.734898	+	0.678178i	$0.762770\pi$
$884$	34.2310	1.15131
$885$	82.4444	2.77134
$886$	−77.0227	−2.58763
$887$	17.4215	0.584955	0.292478	−	0.956272i	$-0.405520\pi$
$887$	17.4215	0.584955	0.292478	+	0.956272i	$0.405520\pi$
$888$	−3.36526	−0.112931
$889$	22.2064	0.744780
$890$	−168.361	−5.64347
$891$	46.5112	1.55818
$892$	−51.5760	−1.72689
$893$	−18.6420	−0.623831
$894$	−18.3090	−0.612344
$895$	−38.8932	−1.30006
$896$	28.3737	0.947900
$897$	5.86422	0.195801
$898$	−62.1770	−2.07487
$899$	72.9814	2.43407
$900$	−3.35185	−0.111728
$901$	−0.627240	−0.0208964
$902$	104.746	3.48766
$903$	−14.5125	−0.482946
$904$	10.3932	0.345672
$905$	22.2067	0.738177
$906$	32.8407	1.09106
$907$	14.2233	0.472276	0.236138	−	0.971720i	$-0.424118\pi$
$907$	14.2233	0.472276	0.236138	+	0.971720i	$0.424118\pi$
$908$	−17.8137	−0.591170
$909$	0.780962	0.0259029
$910$	78.7060	2.60908
$911$	6.59854	0.218619	0.109310	−	0.994008i	$-0.465136\pi$
$911$	6.59854	0.218619	0.109310	+	0.994008i	$0.465136\pi$
$912$	−5.16827	−0.171138
$913$	−63.9100	−2.11511
$914$	52.3425	1.73133
$915$	90.3967	2.98842
$916$	−3.70183	−0.122312
$917$	−13.3526	−0.440942
$918$	−33.1291	−1.09342
$919$	−43.6531	−1.43998	−0.719991	−	0.693984i	$-0.755854\pi$
$919$	−43.6531	−1.43998	−0.719991	+	0.693984i	$0.755854\pi$
$920$	6.96203	0.229531
$921$	58.6720	1.93331
$922$	3.10766	0.102345
$923$	−41.0333	−1.35063
$924$	−52.5040	−1.72726
$925$	13.3107	0.437652
$926$	−22.4013	−0.736151
$927$	−0.851263	−0.0279591
$928$	68.7816	2.25787
$929$	13.2695	0.435358	0.217679	−	0.976020i	$-0.430151\pi$
$929$	13.2695	0.435358	0.217679	+	0.976020i	$0.430151\pi$
$930$	−121.494	−3.98393
$931$	−6.41195	−0.210143
$932$	6.29949	0.206347
$933$	−16.3155	−0.534146
$934$	53.6647	1.75596
$935$	64.8057	2.11937
$936$	−0.715039	−0.0233718
$937$	17.1465	0.560151	0.280076	−	0.959978i	$-0.409640\pi$
$937$	17.1465	0.560151	0.280076	+	0.959978i	$0.409640\pi$
$938$	−13.6695	−0.446324
$939$	−58.8561	−1.92070
$940$	−108.326	−3.53321
$941$	2.87840	0.0938333	0.0469166	−	0.998899i	$-0.485060\pi$
$941$	2.87840	0.0938333	0.0469166	+	0.998899i	$0.485060\pi$
$942$	82.1950	2.67806
$943$	−7.33601	−0.238893
$944$	−16.0542	−0.522519
$945$	−45.0279	−1.46476
$946$	−50.1614	−1.63089
$947$	−1.90609	−0.0619397	−0.0309698	−	0.999520i	$-0.509860\pi$
$947$	−1.90609	−0.0619397	−0.0309698	+	0.999520i	$0.509860\pi$
$948$	−3.92572	−0.127502
$949$	20.0021	0.649295
$950$	−62.6845	−2.03375
$951$	13.5748	0.440192
$952$	11.1956	0.362851
$953$	−46.1369	−1.49452	−0.747260	−	0.664532i	$-0.768631\pi$
$953$	−46.1369	−1.49452	−0.747260	+	0.664532i	$0.768631\pi$
$954$	0.0424951	0.00137583
$955$	−30.0601	−0.972723
$956$	60.2667	1.94916
$957$	−88.2157	−2.85161
$958$	27.8349	0.899306
$959$	−4.02114	−0.129849
$960$	−93.7295	−3.02511
$961$	25.5758	0.825027
$962$	9.20956	0.296928
$963$	0.658252	0.0212119
$964$	10.5336	0.339264
$965$	−0.567415	−0.0182657
$966$	6.22059	0.200144
$967$	43.9212	1.41241	0.706205	−	0.708007i	$-0.250406\pi$
$967$	43.9212	1.41241	0.706205	+	0.708007i	$0.250406\pi$
$968$	−34.2639	−1.10128
$969$	−10.3318	−0.331907
$970$	41.4348	1.33039
$971$	16.1623	0.518672	0.259336	−	0.965787i	$-0.416496\pi$
$971$	16.1623	0.518672	0.259336	+	0.965787i	$0.416496\pi$
$972$	2.61612	0.0839122
$973$	21.7042	0.695803
$974$	−16.6169	−0.532440
$975$	−94.5976	−3.02955
$976$	−17.6027	−0.563449
$977$	27.9365	0.893769	0.446884	−	0.894592i	$-0.352534\pi$
$977$	27.9365	0.893769	0.446884	+	0.894592i	$0.352534\pi$
$978$	3.77473	0.120703
$979$	−94.7661	−3.02874
$980$	−37.2589	−1.19019
$981$	−1.52025	−0.0485378
$982$	43.7557	1.39630
$983$	−34.4889	−1.10003	−0.550013	−	0.835156i	$-0.685377\pi$
$983$	−34.4889	−1.10003	−0.550013	+	0.835156i	$0.685377\pi$
$984$	−29.9191	−0.953786
$985$	90.0573	2.86947
$986$	61.0090	1.94292
$987$	−29.8425	−0.949896
$988$	−25.6379	−0.815650
$989$	3.51311	0.111710
$990$	−4.39054	−0.139541
$991$	−5.80213	−0.184311	−0.0921553	−	0.995745i	$-0.529376\pi$
$991$	−5.80213	−0.184311	−0.0921553	+	0.995745i	$0.529376\pi$
$992$	53.3201	1.69291
$993$	19.8034	0.628441
$994$	−43.5270	−1.38059
$995$	−52.2547	−1.65658
$996$	59.2071	1.87605
$997$	39.5752	1.25336	0.626679	−	0.779277i	$-0.284414\pi$
$997$	39.5752	1.25336	0.626679	+	0.779277i	$0.284414\pi$
$998$	33.5387	1.06165
$999$	−5.26881	−0.166698

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6031.2.a.e.1.18	✓	134

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6031.2.a.e.1.18	✓	134	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:	\( N \)	\(=\)	\( 6031 = 37 \cdot 163 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6031.a (trivial)

\(f(q)\)	\(=\)	\(q-2.21168 q^{2} +1.70673 q^{3} +2.89152 q^{4} +4.27910 q^{5} -3.77473 q^{6} +1.99718 q^{7} -1.97176 q^{8} -0.0870880 q^{9} +O(q^{10})\)	\(q-2.21168 q^{2} +1.70673 q^{3} +2.89152 q^{4} +4.27910 q^{5} -3.77473 q^{6} +1.99718 q^{7} -1.97176 q^{8} -0.0870880 q^{9} -9.46398 q^{10} -5.32704 q^{11} +4.93504 q^{12} -4.16406 q^{13} -4.41712 q^{14} +7.30324 q^{15} -1.42214 q^{16} -2.84299 q^{17} +0.192611 q^{18} +2.12931 q^{19} +12.3731 q^{20} +3.40863 q^{21} +11.7817 q^{22} -0.825143 q^{23} -3.36526 q^{24} +13.3107 q^{25} +9.20956 q^{26} -5.26881 q^{27} +5.77489 q^{28} +9.70279 q^{29} -16.1524 q^{30} +7.52169 q^{31} +7.08884 q^{32} -9.09179 q^{33} +6.28778 q^{34} +8.54611 q^{35} -0.251817 q^{36} +1.00000 q^{37} -4.70935 q^{38} -7.10691 q^{39} -8.43736 q^{40} +8.89058 q^{41} -7.53880 q^{42} -4.25757 q^{43} -15.4032 q^{44} -0.372658 q^{45} +1.82495 q^{46} -8.75496 q^{47} -2.42720 q^{48} -3.01128 q^{49} -29.4389 q^{50} -4.85220 q^{51} -12.0405 q^{52} +0.220627 q^{53} +11.6529 q^{54} -22.7949 q^{55} -3.93796 q^{56} +3.63415 q^{57} -21.4595 q^{58} +11.2887 q^{59} +21.1175 q^{60} +12.3776 q^{61} -16.6356 q^{62} -0.173930 q^{63} -12.8340 q^{64} -17.8184 q^{65} +20.1081 q^{66} +3.09466 q^{67} -8.22057 q^{68} -1.40829 q^{69} -18.9013 q^{70} +9.85416 q^{71} +0.171717 q^{72} -4.80350 q^{73} -2.21168 q^{74} +22.7176 q^{75} +6.15694 q^{76} -10.6390 q^{77} +15.7182 q^{78} -0.795480 q^{79} -6.08548 q^{80} -8.73115 q^{81} -19.6631 q^{82} +11.9973 q^{83} +9.85614 q^{84} -12.1654 q^{85} +9.41638 q^{86} +16.5600 q^{87} +10.5036 q^{88} +17.7896 q^{89} +0.824200 q^{90} -8.31637 q^{91} -2.38592 q^{92} +12.8375 q^{93} +19.3632 q^{94} +9.11151 q^{95} +12.0987 q^{96} -4.37815 q^{97} +6.65999 q^{98} +0.463921 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 134 q + 9 q^{2} + 7 q^{3} + 149 q^{4} + 22 q^{5} + 20 q^{6} + 11 q^{7} + 27 q^{8} + 181 q^{9}+O(q^{10}) \) 134 * q + 9 * q^2 + 7 * q^3 + 149 * q^4 + 22 * q^5 + 20 * q^6 + 11 * q^7 + 27 * q^8 + 181 * q^9	\( 134 q + 9 q^{2} + 7 q^{3} + 149 q^{4} + 22 q^{5} + 20 q^{6} + 11 q^{7} + 27 q^{8} + 181 q^{9} + 15 q^{10} + 20 q^{11} + 28 q^{12} + 11 q^{13} + 17 q^{14} - 13 q^{15} + 143 q^{16} + 76 q^{17} + 23 q^{18} + 15 q^{19} + 67 q^{20} + 63 q^{21} + 2 q^{22} + 22 q^{23} + 33 q^{24} + 160 q^{25} + 65 q^{26} + 31 q^{27} + 10 q^{28} + 73 q^{29} + 20 q^{30} + 10 q^{31} + 53 q^{32} + 72 q^{33} - 7 q^{34} + 52 q^{35} + 201 q^{36} + 134 q^{37} + 70 q^{38} + 6 q^{39} + 11 q^{40} + 182 q^{41} - 15 q^{42} + 12 q^{43} + 33 q^{44} + 29 q^{45} + 24 q^{46} + 80 q^{47} + 21 q^{48} + 229 q^{49} + 37 q^{50} + 57 q^{51} - 15 q^{52} + 75 q^{53} + 95 q^{54} - 9 q^{55} + 39 q^{56} + 19 q^{57} - 21 q^{58} + 91 q^{59} + 62 q^{60} + 58 q^{61} + 108 q^{62} + 9 q^{63} + 167 q^{64} + 76 q^{65} + 105 q^{66} - 17 q^{67} + 109 q^{68} + 48 q^{69} - 55 q^{70} + 56 q^{71} + 48 q^{72} + 54 q^{73} + 9 q^{74} + 28 q^{75} + 82 q^{76} + 156 q^{77} + 16 q^{78} - 2 q^{79} + 98 q^{80} + 270 q^{81} - 42 q^{82} + 130 q^{83} + 229 q^{84} + 22 q^{85} + 72 q^{86} + 22 q^{87} + 61 q^{88} + 157 q^{89} + 176 q^{90} + 31 q^{91} - 18 q^{92} + 36 q^{93} + 83 q^{94} + 98 q^{95} + 111 q^{96} + 35 q^{97} + 53 q^{98} + 55 q^{99}+O(q^{100}) \) 134 * q + 9 * q^2 + 7 * q^3 + 149 * q^4 + 22 * q^5 + 20 * q^6 + 11 * q^7 + 27 * q^8 + 181 * q^9 + 15 * q^10 + 20 * q^11 + 28 * q^12 + 11 * q^13 + 17 * q^14 - 13 * q^15 + 143 * q^16 + 76 * q^17 + 23 * q^18 + 15 * q^19 + 67 * q^20 + 63 * q^21 + 2 * q^22 + 22 * q^23 + 33 * q^24 + 160 * q^25 + 65 * q^26 + 31 * q^27 + 10 * q^28 + 73 * q^29 + 20 * q^30 + 10 * q^31 + 53 * q^32 + 72 * q^33 - 7 * q^34 + 52 * q^35 + 201 * q^36 + 134 * q^37 + 70 * q^38 + 6 * q^39 + 11 * q^40 + 182 * q^41 - 15 * q^42 + 12 * q^43 + 33 * q^44 + 29 * q^45 + 24 * q^46 + 80 * q^47 + 21 * q^48 + 229 * q^49 + 37 * q^50 + 57 * q^51 - 15 * q^52 + 75 * q^53 + 95 * q^54 - 9 * q^55 + 39 * q^56 + 19 * q^57 - 21 * q^58 + 91 * q^59 + 62 * q^60 + 58 * q^61 + 108 * q^62 + 9 * q^63 + 167 * q^64 + 76 * q^65 + 105 * q^66 - 17 * q^67 + 109 * q^68 + 48 * q^69 - 55 * q^70 + 56 * q^71 + 48 * q^72 + 54 * q^73 + 9 * q^74 + 28 * q^75 + 82 * q^76 + 156 * q^77 + 16 * q^78 - 2 * q^79 + 98 * q^80 + 270 * q^81 - 42 * q^82 + 130 * q^83 + 229 * q^84 + 22 * q^85 + 72 * q^86 + 22 * q^87 + 61 * q^88 + 157 * q^89 + 176 * q^90 + 31 * q^91 - 18 * q^92 + 36 * q^93 + 83 * q^94 + 98 * q^95 + 111 * q^96 + 35 * q^97 + 53 * q^98 + 55 * q^99

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