LMFDB - Embedded newform 6017.2.a.f.1.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6017,2,Mod(1,6017)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6017, 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("6017.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6017 = 11 \cdot 547 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6017.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:	$48.0459868962$
Analytic rank:	$0$
Dimension:	$121$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.19
Character	$\chi$	$=$	6017.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.22670 q^{2} +0.200688 q^{3} +2.95817 q^{4} +3.39958 q^{5} -0.446870 q^{6} -0.867591 q^{7} -2.13356 q^{8} -2.95972 q^{9} +O(q^{10})$	\(q-2.22670 q^{2} +0.200688 q^{3} +2.95817 q^{4} +3.39958 q^{5} -0.446870 q^{6} -0.867591 q^{7} -2.13356 q^{8} -2.95972 q^{9} -7.56983 q^{10} -1.00000 q^{11} +0.593668 q^{12} -5.52527 q^{13} +1.93186 q^{14} +0.682253 q^{15} -1.16556 q^{16} +3.54049 q^{17} +6.59040 q^{18} +0.206834 q^{19} +10.0565 q^{20} -0.174115 q^{21} +2.22670 q^{22} +6.80589 q^{23} -0.428178 q^{24} +6.55714 q^{25} +12.3031 q^{26} -1.19604 q^{27} -2.56648 q^{28} +3.50942 q^{29} -1.51917 q^{30} +3.97784 q^{31} +6.86247 q^{32} -0.200688 q^{33} -7.88359 q^{34} -2.94944 q^{35} -8.75537 q^{36} +5.88133 q^{37} -0.460555 q^{38} -1.10885 q^{39} -7.25320 q^{40} -0.545479 q^{41} +0.387700 q^{42} -9.67460 q^{43} -2.95817 q^{44} -10.0618 q^{45} -15.1546 q^{46} +12.1133 q^{47} -0.233914 q^{48} -6.24729 q^{49} -14.6008 q^{50} +0.710532 q^{51} -16.3447 q^{52} -4.89427 q^{53} +2.66322 q^{54} -3.39958 q^{55} +1.85105 q^{56} +0.0415089 q^{57} -7.81440 q^{58} +6.94782 q^{59} +2.01822 q^{60} +0.613662 q^{61} -8.85743 q^{62} +2.56783 q^{63} -12.9495 q^{64} -18.7836 q^{65} +0.446870 q^{66} -12.1450 q^{67} +10.4734 q^{68} +1.36586 q^{69} +6.56751 q^{70} +2.13501 q^{71} +6.31474 q^{72} -0.891895 q^{73} -13.0959 q^{74} +1.31594 q^{75} +0.611849 q^{76} +0.867591 q^{77} +2.46908 q^{78} -8.08839 q^{79} -3.96242 q^{80} +8.63914 q^{81} +1.21462 q^{82} -0.211727 q^{83} -0.515061 q^{84} +12.0362 q^{85} +21.5424 q^{86} +0.704296 q^{87} +2.13356 q^{88} -6.97044 q^{89} +22.4046 q^{90} +4.79367 q^{91} +20.1330 q^{92} +0.798302 q^{93} -26.9725 q^{94} +0.703147 q^{95} +1.37721 q^{96} -3.76158 q^{97} +13.9108 q^{98} +2.95972 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 121 q + 2 q^{2} + 18 q^{3} + 138 q^{4} + 13 q^{5} + 10 q^{6} + 56 q^{7} + 12 q^{8} + 143 q^{9}+O(q^{10}) $ 121 * q + 2 * q^2 + 18 * q^3 + 138 * q^4 + 13 * q^5 + 10 * q^6 + 56 * q^7 + 12 * q^8 + 143 * q^9	\( 121 q + 2 q^{2} + 18 q^{3} + 138 q^{4} + 13 q^{5} + 10 q^{6} + 56 q^{7} + 12 q^{8} + 143 q^{9} + 20 q^{10} - 121 q^{11} + 40 q^{12} + 31 q^{13} + 7 q^{14} + 53 q^{15} + 164 q^{16} - 23 q^{17} + 14 q^{18} + 62 q^{19} + 53 q^{20} + 19 q^{21} - 2 q^{22} + 34 q^{23} + 34 q^{24} + 172 q^{25} + 34 q^{26} + 87 q^{27} + 91 q^{28} - 30 q^{29} + 2 q^{30} + 102 q^{31} + 31 q^{32} - 18 q^{33} + 30 q^{34} + 20 q^{35} + 164 q^{36} + 58 q^{37} + 35 q^{38} + 42 q^{39} + 52 q^{40} - 12 q^{41} + 56 q^{42} + 96 q^{43} - 138 q^{44} + 72 q^{45} + 48 q^{46} + 136 q^{47} + 99 q^{48} + 199 q^{49} - 7 q^{50} + 22 q^{51} + 81 q^{52} + 24 q^{53} + 37 q^{54} - 13 q^{55} + 28 q^{56} + 25 q^{57} + 76 q^{58} + 58 q^{59} + 81 q^{60} + 14 q^{61} - 2 q^{62} + 152 q^{63} + 236 q^{64} - 29 q^{65} - 10 q^{66} + 112 q^{67} - 61 q^{68} + 41 q^{69} + 105 q^{70} + 56 q^{71} + 71 q^{72} + 113 q^{73} - 23 q^{74} + 111 q^{75} + 144 q^{76} - 56 q^{77} + 59 q^{78} + 80 q^{79} + 100 q^{80} + 177 q^{81} + 123 q^{82} + 6 q^{83} + 79 q^{84} + 26 q^{85} + 14 q^{86} + 180 q^{87} - 12 q^{88} + 26 q^{89} + 75 q^{90} + 72 q^{91} + 58 q^{92} + 139 q^{93} + 37 q^{94} + 39 q^{95} + 66 q^{96} + 136 q^{97} + 7 q^{98} - 143 q^{99}+O(q^{100}) \) 121 * q + 2 * q^2 + 18 * q^3 + 138 * q^4 + 13 * q^5 + 10 * q^6 + 56 * q^7 + 12 * q^8 + 143 * q^9 + 20 * q^10 - 121 * q^11 + 40 * q^12 + 31 * q^13 + 7 * q^14 + 53 * q^15 + 164 * q^16 - 23 * q^17 + 14 * q^18 + 62 * q^19 + 53 * q^20 + 19 * q^21 - 2 * q^22 + 34 * q^23 + 34 * q^24 + 172 * q^25 + 34 * q^26 + 87 * q^27 + 91 * q^28 - 30 * q^29 + 2 * q^30 + 102 * q^31 + 31 * q^32 - 18 * q^33 + 30 * q^34 + 20 * q^35 + 164 * q^36 + 58 * q^37 + 35 * q^38 + 42 * q^39 + 52 * q^40 - 12 * q^41 + 56 * q^42 + 96 * q^43 - 138 * q^44 + 72 * q^45 + 48 * q^46 + 136 * q^47 + 99 * q^48 + 199 * q^49 - 7 * q^50 + 22 * q^51 + 81 * q^52 + 24 * q^53 + 37 * q^54 - 13 * q^55 + 28 * q^56 + 25 * q^57 + 76 * q^58 + 58 * q^59 + 81 * q^60 + 14 * q^61 - 2 * q^62 + 152 * q^63 + 236 * q^64 - 29 * q^65 - 10 * q^66 + 112 * q^67 - 61 * q^68 + 41 * q^69 + 105 * q^70 + 56 * q^71 + 71 * q^72 + 113 * q^73 - 23 * q^74 + 111 * q^75 + 144 * q^76 - 56 * q^77 + 59 * q^78 + 80 * q^79 + 100 * q^80 + 177 * q^81 + 123 * q^82 + 6 * q^83 + 79 * q^84 + 26 * q^85 + 14 * q^86 + 180 * q^87 - 12 * q^88 + 26 * q^89 + 75 * q^90 + 72 * q^91 + 58 * q^92 + 139 * q^93 + 37 * q^94 + 39 * q^95 + 66 * q^96 + 136 * q^97 + 7 * q^98 - 143 * 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 $

$2$	−2.22670	−1.57451	−0.787256	−	0.616627i	$-0.788499\pi$
$2$	−2.22670	−1.57451	−0.787256	+	0.616627i	$0.788499\pi$
$3$	0.200688	0.115867	0.0579335	−	0.998320i	$-0.481549\pi$
$3$	0.200688	0.115867	0.0579335	+	0.998320i	$0.481549\pi$
$4$	2.95817	1.47909
$5$	3.39958	1.52034	0.760169	−	0.649725i	$-0.225116\pi$
$5$	3.39958	1.52034	0.760169	+	0.649725i	$0.225116\pi$
$6$	−0.446870	−0.182434
$7$	−0.867591	−0.327918	−0.163959	−	0.986467i	$-0.552427\pi$
$7$	−0.867591	−0.327918	−0.163959	+	0.986467i	$0.552427\pi$
$8$	−2.13356	−0.754326
$9$	−2.95972	−0.986575
$10$	−7.56983	−2.39379
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	0.593668	0.171377
$13$	−5.52527	−1.53243	−0.766217	−	0.642582i	$-0.777863\pi$
$13$	−5.52527	−1.53243	−0.766217	+	0.642582i	$0.777863\pi$
$14$	1.93186	0.516311
$15$	0.682253	0.176157
$16$	−1.16556	−0.291391
$17$	3.54049	0.858695	0.429347	−	0.903139i	$-0.358744\pi$
$17$	3.54049	0.858695	0.429347	+	0.903139i	$0.358744\pi$
$18$	6.59040	1.55337
$19$	0.206834	0.0474509	0.0237254	−	0.999719i	$-0.492447\pi$
$19$	0.206834	0.0474509	0.0237254	+	0.999719i	$0.492447\pi$
$20$	10.0565	2.24871
$21$	−0.174115	−0.0379949
$22$	2.22670	0.474733
$23$	6.80589	1.41913	0.709563	−	0.704642i	$-0.248892\pi$
$23$	6.80589	1.41913	0.709563	+	0.704642i	$0.248892\pi$
$24$	−0.428178	−0.0874016
$25$	6.55714	1.31143
$26$	12.3031	2.41283
$27$	−1.19604	−0.230179
$28$	−2.56648	−0.485020
$29$	3.50942	0.651682	0.325841	−	0.945425i	$-0.394353\pi$
$29$	3.50942	0.651682	0.325841	+	0.945425i	$0.394353\pi$
$30$	−1.51917	−0.277361
$31$	3.97784	0.714441	0.357220	−	0.934020i	$-0.383725\pi$
$31$	3.97784	0.714441	0.357220	+	0.934020i	$0.383725\pi$
$32$	6.86247	1.21312
$33$	−0.200688	−0.0349352
$34$	−7.88359	−1.35202
$35$	−2.94944	−0.498547
$36$	−8.75537	−1.45923
$37$	5.88133	0.966885	0.483442	−	0.875376i	$-0.339386\pi$
$37$	5.88133	0.966885	0.483442	+	0.875376i	$0.339386\pi$
$38$	−0.460555	−0.0747119
$39$	−1.10885	−0.177559
$40$	−7.25320	−1.14683
$41$	−0.545479	−0.0851895	−0.0425948	−	0.999092i	$-0.513562\pi$
$41$	−0.545479	−0.0851895	−0.0425948	+	0.999092i	$0.513562\pi$
$42$	0.387700	0.0598235
$43$	−9.67460	−1.47536	−0.737682	−	0.675149i	$-0.764079\pi$
$43$	−9.67460	−1.47536	−0.737682	+	0.675149i	$0.764079\pi$
$44$	−2.95817	−0.445961
$45$	−10.0618	−1.49993
$46$	−15.1546	−2.23443
$47$	12.1133	1.76690	0.883450	−	0.468526i	$-0.155215\pi$
$47$	12.1133	1.76690	0.883450	+	0.468526i	$0.155215\pi$
$48$	−0.233914	−0.0337626
$49$	−6.24729	−0.892470
$50$	−14.6008	−2.06486
$51$	0.710532	0.0994944
$52$	−16.3447	−2.26660
$53$	−4.89427	−0.672280	−0.336140	−	0.941812i	$-0.609121\pi$
$53$	−4.89427	−0.672280	−0.336140	+	0.941812i	$0.609121\pi$
$54$	2.66322	0.362419
$55$	−3.39958	−0.458399
$56$	1.85105	0.247358
$57$	0.0415089	0.00549799
$58$	−7.81440	−1.02608
$59$	6.94782	0.904529	0.452264	−	0.891884i	$-0.350616\pi$
$59$	6.94782	0.904529	0.452264	+	0.891884i	$0.350616\pi$
$60$	2.01822	0.260551
$61$	0.613662	0.0785714	0.0392857	−	0.999228i	$-0.487492\pi$
$61$	0.613662	0.0785714	0.0392857	+	0.999228i	$0.487492\pi$
$62$	−8.85743	−1.12489
$63$	2.56783	0.323516
$64$	−12.9495	−1.61869
$65$	−18.7836	−2.32982
$66$	0.446870	0.0550059
$67$	−12.1450	−1.48375	−0.741876	−	0.670537i	$-0.766064\pi$
$67$	−12.1450	−1.48375	−0.741876	+	0.670537i	$0.766064\pi$
$68$	10.4734	1.27008
$69$	1.36586	0.164430
$70$	6.56751	0.784968
$71$	2.13501	0.253378	0.126689	−	0.991942i	$-0.459565\pi$
$71$	2.13501	0.253378	0.126689	+	0.991942i	$0.459565\pi$
$72$	6.31474	0.744199
$73$	−0.891895	−0.104388	−0.0521942	−	0.998637i	$-0.516621\pi$
$73$	−0.891895	−0.104388	−0.0521942	+	0.998637i	$0.516621\pi$
$74$	−13.0959	−1.52237
$75$	1.31594	0.151951
$76$	0.611849	0.0701839
$77$	0.867591	0.0988711
$78$	2.46908	0.279568
$79$	−8.08839	−0.910015	−0.455007	−	0.890488i	$-0.650363\pi$
$79$	−8.08839	−0.910015	−0.455007	+	0.890488i	$0.650363\pi$
$80$	−3.96242	−0.443012
$81$	8.63914	0.959905
$82$	1.21462	0.134132
$83$	−0.211727	−0.0232401	−0.0116200	−	0.999932i	$-0.503699\pi$
$83$	−0.211727	−0.0232401	−0.0116200	+	0.999932i	$0.503699\pi$
$84$	−0.515061	−0.0561978
$85$	12.0362	1.30551
$86$	21.5424	2.32298
$87$	0.704296	0.0755085
$88$	2.13356	0.227438
$89$	−6.97044	−0.738865	−0.369432	−	0.929258i	$-0.620448\pi$
$89$	−6.97044	−0.738865	−0.369432	+	0.929258i	$0.620448\pi$
$90$	22.4046	2.36165
$91$	4.79367	0.502513
$92$	20.1330	2.09901
$93$	0.798302	0.0827801
$94$	−26.9725	−2.78200
$95$	0.703147	0.0721414
$96$	1.37721	0.140561
$97$	−3.76158	−0.381931	−0.190966	−	0.981597i	$-0.561162\pi$
$97$	−3.76158	−0.381931	−0.190966	+	0.981597i	$0.561162\pi$
$98$	13.9108	1.40520
$99$	2.95972	0.297464
$100$	19.3971	1.93971
$101$	12.6052	1.25426	0.627130	−	0.778915i	$-0.284229\pi$
$101$	12.6052	1.25426	0.627130	+	0.778915i	$0.284229\pi$
$102$	−1.58214	−0.156655
$103$	5.51936	0.543838	0.271919	−	0.962320i	$-0.412342\pi$
$103$	5.51936	0.543838	0.271919	+	0.962320i	$0.412342\pi$
$104$	11.7885	1.15596
$105$	−0.591917	−0.0577651
$106$	10.8980	1.05851
$107$	−11.8705	−1.14756	−0.573780	−	0.819009i	$-0.694524\pi$
$107$	−11.8705	−1.14756	−0.573780	+	0.819009i	$0.694524\pi$
$108$	−3.53810	−0.340454
$109$	6.29863	0.603299	0.301650	−	0.953419i	$-0.402463\pi$
$109$	6.29863	0.603299	0.301650	+	0.953419i	$0.402463\pi$
$110$	7.56983	0.721755
$111$	1.18031	0.112030
$112$	1.01123	0.0955523
$113$	0.891285	0.0838450	0.0419225	−	0.999121i	$-0.486652\pi$
$113$	0.891285	0.0838450	0.0419225	+	0.999121i	$0.486652\pi$
$114$	−0.0924277	−0.00865665
$115$	23.1372	2.15755
$116$	10.3815	0.963894
$117$	16.3533	1.51186
$118$	−15.4707	−1.42419
$119$	−3.07169	−0.281582
$120$	−1.45563	−0.132880
$121$	1.00000	0.0909091
$122$	−1.36644	−0.123712
$123$	−0.109471	−0.00987066
$124$	11.7671	1.05672
$125$	5.29362	0.473476
$126$	−5.71777	−0.509380
$127$	−13.1468	−1.16659	−0.583296	−	0.812259i	$-0.698237\pi$
$127$	−13.1468	−1.16659	−0.583296	+	0.812259i	$0.698237\pi$
$128$	15.1097	1.33552
$129$	−1.94157	−0.170946
$130$	41.8253	3.66832
$131$	9.90183	0.865127	0.432564	−	0.901603i	$-0.357609\pi$
$131$	9.90183	0.865127	0.432564	+	0.901603i	$0.357609\pi$
$132$	−0.593668	−0.0516722
$133$	−0.179447	−0.0155600
$134$	27.0433	2.33618
$135$	−4.06604	−0.349949
$136$	−7.55384	−0.647736
$137$	16.1414	1.37906	0.689528	−	0.724259i	$-0.257818\pi$
$137$	16.1414	1.37906	0.689528	+	0.724259i	$0.257818\pi$
$138$	−3.04135	−0.258897
$139$	1.53194	0.129937	0.0649687	−	0.997887i	$-0.479305\pi$
$139$	1.53194	0.129937	0.0649687	+	0.997887i	$0.479305\pi$
$140$	−8.72496	−0.737394
$141$	2.43098	0.204725
$142$	−4.75401	−0.398947
$143$	5.52527	0.462046
$144$	3.44974	0.287479
$145$	11.9305	0.990777
$146$	1.98598	0.164361
$147$	−1.25375	−0.103408
$148$	17.3980	1.43011
$149$	1.77842	0.145694	0.0728469	−	0.997343i	$-0.476792\pi$
$149$	1.77842	0.145694	0.0728469	+	0.997343i	$0.476792\pi$
$150$	−2.93019	−0.239249
$151$	−1.31045	−0.106643	−0.0533215	−	0.998577i	$-0.516981\pi$
$151$	−1.31045	−0.106643	−0.0533215	+	0.998577i	$0.516981\pi$
$152$	−0.441291	−0.0357934
$153$	−10.4789	−0.847166
$154$	−1.93186	−0.155674
$155$	13.5230	1.08619
$156$	−3.28018	−0.262624
$157$	4.29705	0.342942	0.171471	−	0.985189i	$-0.445148\pi$
$157$	4.29705	0.342942	0.171471	+	0.985189i	$0.445148\pi$
$158$	18.0104	1.43283
$159$	−0.982219	−0.0778950
$160$	23.3295	1.84436
$161$	−5.90473	−0.465358
$162$	−19.2367	−1.51138
$163$	−16.9369	−1.32660	−0.663298	−	0.748355i	$-0.730844\pi$
$163$	−16.9369	−1.32660	−0.663298	+	0.748355i	$0.730844\pi$
$164$	−1.61362	−0.126003
$165$	−0.682253	−0.0531134
$166$	0.471452	0.0365918
$167$	−19.2890	−1.49263	−0.746315	−	0.665592i	$-0.768179\pi$
$167$	−19.2890	−1.49263	−0.746315	+	0.665592i	$0.768179\pi$
$168$	0.371484	0.0286606
$169$	17.5286	1.34835
$170$	−26.8009	−2.05553
$171$	−0.612170	−0.0468138
$172$	−28.6191	−2.18219
$173$	7.62786	0.579936	0.289968	−	0.957036i	$-0.406355\pi$
$173$	7.62786	0.579936	0.289968	+	0.957036i	$0.406355\pi$
$174$	−1.56825	−0.118889
$175$	−5.68891	−0.430041
$176$	1.16556	0.0878575
$177$	1.39434	0.104805
$178$	15.5210	1.16335
$179$	24.1711	1.80663	0.903315	−	0.428978i	$-0.141126\pi$
$179$	24.1711	1.80663	0.903315	+	0.428978i	$0.141126\pi$
$180$	−29.7646	−2.21852
$181$	−0.0778879	−0.00578936	−0.00289468	−	0.999996i	$-0.500921\pi$
$181$	−0.0778879	−0.00578936	−0.00289468	+	0.999996i	$0.500921\pi$
$182$	−10.6740	−0.791213
$183$	0.123154	0.00910384
$184$	−14.5208	−1.07048
$185$	19.9941	1.46999
$186$	−1.77758	−0.130338
$187$	−3.54049	−0.258906
$188$	35.8331	2.61340
$189$	1.03768	0.0754798
$190$	−1.56569	−0.113587
$191$	13.3915	0.968976	0.484488	−	0.874798i	$-0.339006\pi$
$191$	13.3915	0.968976	0.484488	+	0.874798i	$0.339006\pi$
$192$	−2.59880	−0.187552
$193$	19.1370	1.37751	0.688754	−	0.724995i	$-0.258158\pi$
$193$	19.1370	1.37751	0.688754	+	0.724995i	$0.258158\pi$
$194$	8.37590	0.601355
$195$	−3.76963	−0.269949
$196$	−18.4805	−1.32004
$197$	−4.16251	−0.296566	−0.148283	−	0.988945i	$-0.547375\pi$
$197$	−4.16251	−0.296566	−0.148283	+	0.988945i	$0.547375\pi$
$198$	−6.59040	−0.468360
$199$	18.2806	1.29588	0.647938	−	0.761693i	$-0.275632\pi$
$199$	18.2806	1.29588	0.647938	+	0.761693i	$0.275632\pi$
$200$	−13.9900	−0.989245
$201$	−2.43736	−0.171918
$202$	−28.0678	−1.97485
$203$	−3.04474	−0.213699
$204$	2.10188	0.147161
$205$	−1.85440	−0.129517
$206$	−12.2899	−0.856280
$207$	−20.1436	−1.40007
$208$	6.44004	0.446537
$209$	−0.206834	−0.0143070
$210$	1.31802	0.0909519
$211$	6.48189	0.446232	0.223116	−	0.974792i	$-0.428377\pi$
$211$	6.48189	0.446232	0.223116	+	0.974792i	$0.428377\pi$
$212$	−14.4781	−0.994359
$213$	0.428469	0.0293582
$214$	26.4319	1.80685
$215$	−32.8896	−2.24305
$216$	2.55183	0.173630
$217$	−3.45113	−0.234278
$218$	−14.0251	−0.949902
$219$	−0.178992	−0.0120952
$220$	−10.0565	−0.678012
$221$	−19.5622	−1.31589
$222$	−2.62819	−0.176393
$223$	2.33809	0.156570	0.0782849	−	0.996931i	$-0.475056\pi$
$223$	2.33809	0.156570	0.0782849	+	0.996931i	$0.475056\pi$
$224$	−5.95381	−0.397806
$225$	−19.4073	−1.29382
$226$	−1.98462	−0.132015
$227$	14.5517	0.965833	0.482916	−	0.875666i	$-0.339577\pi$
$227$	14.5517	0.965833	0.482916	+	0.875666i	$0.339577\pi$
$228$	0.122791	0.00813200
$229$	−10.6450	−0.703440	−0.351720	−	0.936105i	$-0.614403\pi$
$229$	−10.6450	−0.703440	−0.351720	+	0.936105i	$0.614403\pi$
$230$	−51.5194	−3.39709
$231$	0.174115	0.0114559
$232$	−7.48754	−0.491581
$233$	21.1216	1.38372	0.691861	−	0.722031i	$-0.256791\pi$
$233$	21.1216	1.38372	0.691861	+	0.722031i	$0.256791\pi$
$234$	−36.4138	−2.38044
$235$	41.1800	2.68628
$236$	20.5528	1.33788
$237$	−1.62324	−0.105441
$238$	6.83973	0.443354
$239$	11.7416	0.759503	0.379752	−	0.925088i	$-0.376009\pi$
$239$	11.7416	0.759503	0.379752	+	0.925088i	$0.376009\pi$
$240$	−0.795209	−0.0513305
$241$	−11.0347	−0.710807	−0.355404	−	0.934713i	$-0.615657\pi$
$241$	−11.0347	−0.710807	−0.355404	+	0.934713i	$0.615657\pi$
$242$	−2.22670	−0.143137
$243$	5.32190	0.341400
$244$	1.81532	0.116214
$245$	−21.2381	−1.35686
$246$	0.243758	0.0155415
$247$	−1.14281	−0.0727153
$248$	−8.48694	−0.538921
$249$	−0.0424910	−0.00269276
$250$	−11.7873	−0.745493
$251$	−14.4514	−0.912163	−0.456081	−	0.889938i	$-0.650747\pi$
$251$	−14.4514	−0.912163	−0.456081	+	0.889938i	$0.650747\pi$
$252$	7.59608	0.478508
$253$	−6.80589	−0.427883
$254$	29.2740	1.83681
$255$	2.41551	0.151265
$256$	−7.74560	−0.484100
$257$	29.7081	1.85314	0.926570	−	0.376122i	$-0.122743\pi$
$257$	29.7081	1.85314	0.926570	+	0.376122i	$0.122743\pi$
$258$	4.32329	0.269156
$259$	−5.10259	−0.317059
$260$	−55.5651	−3.44600
$261$	−10.3869	−0.642933
$262$	−22.0484	−1.36215
$263$	−5.13200	−0.316453	−0.158226	−	0.987403i	$-0.550578\pi$
$263$	−5.13200	−0.316453	−0.158226	+	0.987403i	$0.550578\pi$
$264$	0.428178	0.0263526
$265$	−16.6385	−1.02209
$266$	0.399573	0.0244994
$267$	−1.39888	−0.0856101
$268$	−35.9271	−2.19460
$269$	−1.71440	−0.104529	−0.0522643	−	0.998633i	$-0.516644\pi$
$269$	−1.71440	−0.104529	−0.0522643	+	0.998633i	$0.516644\pi$
$270$	9.05384	0.550999
$271$	−6.55748	−0.398339	−0.199169	−	0.979965i	$-0.563824\pi$
$271$	−6.55748	−0.398339	−0.199169	+	0.979965i	$0.563824\pi$
$272$	−4.12666	−0.250215
$273$	0.962030	0.0582247
$274$	−35.9420	−2.17134
$275$	−6.55714	−0.395410
$276$	4.04044	0.243206
$277$	−4.60961	−0.276965	−0.138482	−	0.990365i	$-0.544222\pi$
$277$	−4.60961	−0.276965	−0.138482	+	0.990365i	$0.544222\pi$
$278$	−3.41116	−0.204588
$279$	−11.7733	−0.704849
$280$	6.29281	0.376067
$281$	−0.333156	−0.0198744	−0.00993721	−	0.999951i	$-0.503163\pi$
$281$	−0.333156	−0.0198744	−0.00993721	+	0.999951i	$0.503163\pi$
$282$	−5.41305	−0.322342
$283$	30.9189	1.83794	0.918969	−	0.394330i	$-0.129023\pi$
$283$	30.9189	1.83794	0.918969	+	0.394330i	$0.129023\pi$
$284$	6.31571	0.374769
$285$	0.141113	0.00835880
$286$	−12.3031	−0.727497
$287$	0.473252	0.0279352
$288$	−20.3110	−1.19684
$289$	−4.46494	−0.262644
$290$	−26.5657	−1.55999
$291$	−0.754903	−0.0442532
$292$	−2.63838	−0.154399
$293$	−15.5290	−0.907212	−0.453606	−	0.891202i	$-0.649863\pi$
$293$	−15.5290	−0.907212	−0.453606	+	0.891202i	$0.649863\pi$
$294$	2.79173	0.162817
$295$	23.6197	1.37519
$296$	−12.5482	−0.729347
$297$	1.19604	0.0694014
$298$	−3.96000	−0.229397
$299$	−37.6044	−2.17472
$300$	3.89277	0.224749
$301$	8.39359	0.483799
$302$	2.91798	0.167911
$303$	2.52970	0.145327
$304$	−0.241077	−0.0138267
$305$	2.08619	0.119455
$306$	23.3333	1.33387
$307$	24.1617	1.37898	0.689491	−	0.724294i	$-0.257834\pi$
$307$	24.1617	1.37898	0.689491	+	0.724294i	$0.257834\pi$
$308$	2.56648	0.146239
$309$	1.10767	0.0630129
$310$	−30.1115	−1.71022
$311$	1.57570	0.0893498	0.0446749	−	0.999002i	$-0.485775\pi$
$311$	1.57570	0.0893498	0.0446749	+	0.999002i	$0.485775\pi$
$312$	2.36580	0.133937
$313$	30.2000	1.70701	0.853504	−	0.521087i	$-0.174473\pi$
$313$	30.2000	1.70701	0.853504	+	0.521087i	$0.174473\pi$
$314$	−9.56822	−0.539966
$315$	8.72954	0.491854
$316$	−23.9268	−1.34599
$317$	18.1383	1.01875	0.509375	−	0.860545i	$-0.329877\pi$
$317$	18.1383	1.01875	0.509375	+	0.860545i	$0.329877\pi$
$318$	2.18710	0.122647
$319$	−3.50942	−0.196490
$320$	−44.0228	−2.46095
$321$	−2.38225	−0.132964
$322$	13.1480	0.732711
$323$	0.732292	0.0407458
$324$	25.5561	1.41978
$325$	−36.2300	−2.00968
$326$	37.7132	2.08874
$327$	1.26406	0.0699025
$328$	1.16381	0.0642607
$329$	−10.5093	−0.579399
$330$	1.51917	0.0836276
$331$	24.0653	1.32275	0.661374	−	0.750056i	$-0.269974\pi$
$331$	24.0653	1.32275	0.661374	+	0.750056i	$0.269974\pi$
$332$	−0.626326	−0.0343741
$333$	−17.4071	−0.953904
$334$	42.9508	2.35016
$335$	−41.2880	−2.25580
$336$	0.202941	0.0110714
$337$	29.4864	1.60623	0.803113	−	0.595826i	$-0.203175\pi$
$337$	29.4864	1.60623	0.803113	+	0.595826i	$0.203175\pi$
$338$	−39.0308	−2.12300
$339$	0.178870	0.00971487
$340$	35.6051	1.93096
$341$	−3.97784	−0.215412
$342$	1.36312	0.0737089
$343$	11.4932	0.620576
$344$	20.6413	1.11291
$345$	4.64334	0.249989
$346$	−16.9849	−0.913115
$347$	11.4900	0.616817	0.308408	−	0.951254i	$-0.400204\pi$
$347$	11.4900	0.616817	0.308408	+	0.951254i	$0.400204\pi$
$348$	2.08343	0.111684
$349$	−34.6108	−1.85267	−0.926337	−	0.376695i	$-0.877060\pi$
$349$	−34.6108	−1.85267	−0.926337	+	0.376695i	$0.877060\pi$
$350$	12.6675	0.677105
$351$	6.60846	0.352733
$352$	−6.86247	−0.365771
$353$	35.6310	1.89644	0.948222	−	0.317607i	$-0.102879\pi$
$353$	35.6310	1.89644	0.948222	+	0.317607i	$0.102879\pi$
$354$	−3.10477	−0.165017
$355$	7.25812	0.385221
$356$	−20.6198	−1.09284
$357$	−0.616451	−0.0326260
$358$	−53.8216	−2.84456
$359$	22.0620	1.16439	0.582193	−	0.813051i	$-0.302195\pi$
$359$	22.0620	1.16439	0.582193	+	0.813051i	$0.302195\pi$
$360$	21.4675	1.13143
$361$	−18.9572	−0.997748
$362$	0.173433	0.00911541
$363$	0.200688	0.0105334
$364$	14.1805	0.743260
$365$	−3.03207	−0.158706
$366$	−0.274227	−0.0143341
$367$	21.1231	1.10262	0.551308	−	0.834302i	$-0.314129\pi$
$367$	21.1231	1.10262	0.551308	+	0.834302i	$0.314129\pi$
$368$	−7.93269	−0.413520
$369$	1.61447	0.0840458
$370$	−44.5207	−2.31452
$371$	4.24622	0.220453
$372$	2.36152	0.122439
$373$	−2.33252	−0.120774	−0.0603868	−	0.998175i	$-0.519233\pi$
$373$	−2.33252	−0.120774	−0.0603868	+	0.998175i	$0.519233\pi$
$374$	7.88359	0.407651
$375$	1.06236	0.0548602
$376$	−25.8443	−1.33282
$377$	−19.3905	−0.998660
$378$	−2.31059	−0.118844
$379$	29.0418	1.49178	0.745890	−	0.666070i	$-0.232025\pi$
$379$	29.0418	1.49178	0.745890	+	0.666070i	$0.232025\pi$
$380$	2.08003	0.106703
$381$	−2.63841	−0.135170
$382$	−29.8188	−1.52566
$383$	−7.20579	−0.368199	−0.184099	−	0.982908i	$-0.558937\pi$
$383$	−7.20579	−0.368199	−0.184099	+	0.982908i	$0.558937\pi$
$384$	3.03232	0.154742
$385$	2.94944	0.150318
$386$	−42.6122	−2.16890
$387$	28.6342	1.45556
$388$	−11.1274	−0.564909
$389$	−32.3934	−1.64241	−0.821205	−	0.570634i	$-0.806698\pi$
$389$	−32.3934	−1.64241	−0.821205	+	0.570634i	$0.806698\pi$
$390$	8.39383	0.425038
$391$	24.0962	1.21860
$392$	13.3289	0.673213
$393$	1.98718	0.100240
$394$	9.26863	0.466947
$395$	−27.4971	−1.38353
$396$	8.75537	0.439974
$397$	2.63480	0.132237	0.0661184	−	0.997812i	$-0.478939\pi$
$397$	2.63480	0.132237	0.0661184	+	0.997812i	$0.478939\pi$
$398$	−40.7053	−2.04037
$399$	−0.0360127	−0.00180289
$400$	−7.64275	−0.382138
$401$	5.89790	0.294527	0.147264	−	0.989097i	$-0.452953\pi$
$401$	5.89790	0.294527	0.147264	+	0.989097i	$0.452953\pi$
$402$	5.42725	0.270687
$403$	−21.9786	−1.09483
$404$	37.2882	1.85516
$405$	29.3695	1.45938
$406$	6.77970	0.336471
$407$	−5.88133	−0.291527
$408$	−1.51596	−0.0750513
$409$	−2.42631	−0.119973	−0.0599865	−	0.998199i	$-0.519106\pi$
$409$	−2.42631	−0.119973	−0.0599865	+	0.998199i	$0.519106\pi$
$410$	4.12918	0.203926
$411$	3.23938	0.159787
$412$	16.3272	0.804384
$413$	−6.02786	−0.296612
$414$	44.8536	2.20443
$415$	−0.719784	−0.0353328
$416$	−37.9170	−1.85903
$417$	0.307441	0.0150555
$418$	0.460555	0.0225265
$419$	−1.98956	−0.0971965	−0.0485982	−	0.998818i	$-0.515475\pi$
$419$	−1.98956	−0.0971965	−0.0485982	+	0.998818i	$0.515475\pi$
$420$	−1.75099	−0.0854396
$421$	5.05322	0.246279	0.123139	−	0.992389i	$-0.460704\pi$
$421$	5.05322	0.246279	0.123139	+	0.992389i	$0.460704\pi$
$422$	−14.4332	−0.702597
$423$	−35.8519	−1.74318
$424$	10.4422	0.507118
$425$	23.2155	1.12612
$426$	−0.954070	−0.0462248
$427$	−0.532408	−0.0257650
$428$	−35.1149	−1.69734
$429$	1.10885	0.0535359
$430$	73.2351	3.53171
$431$	19.1611	0.922957	0.461479	−	0.887151i	$-0.347319\pi$
$431$	19.1611	0.922957	0.461479	+	0.887151i	$0.347319\pi$
$432$	1.39406	0.0670718
$433$	−7.38041	−0.354680	−0.177340	−	0.984150i	$-0.556749\pi$
$433$	−7.38041	−0.354680	−0.177340	+	0.984150i	$0.556749\pi$
$434$	7.68462	0.368874
$435$	2.39431	0.114798
$436$	18.6324	0.892331
$437$	1.40769	0.0673388
$438$	0.398561	0.0190440
$439$	−14.7902	−0.705900	−0.352950	−	0.935642i	$-0.614821\pi$
$439$	−14.7902	−0.705900	−0.352950	+	0.935642i	$0.614821\pi$
$440$	7.25320	0.345783
$441$	18.4902	0.880488
$442$	43.5590	2.07189
$443$	3.39973	0.161526	0.0807631	−	0.996733i	$-0.474264\pi$
$443$	3.39973	0.161526	0.0807631	+	0.996733i	$0.474264\pi$
$444$	3.49156	0.165702
$445$	−23.6966	−1.12332
$446$	−5.20621	−0.246521
$447$	0.356907	0.0168811
$448$	11.2349	0.530797
$449$	−24.4752	−1.15506	−0.577529	−	0.816370i	$-0.695983\pi$
$449$	−24.4752	−1.15506	−0.577529	+	0.816370i	$0.695983\pi$
$450$	43.2142	2.03714
$451$	0.545479	0.0256856
$452$	2.63657	0.124014
$453$	−0.262991	−0.0123564
$454$	−32.4023	−1.52071
$455$	16.2965	0.763990
$456$	−0.0885617	−0.00414728
$457$	31.2420	1.46144	0.730719	−	0.682678i	$-0.239185\pi$
$457$	31.2420	1.46144	0.730719	+	0.682678i	$0.239185\pi$
$458$	23.7031	1.10757
$459$	−4.23458	−0.197653
$460$	68.4437	3.19120
$461$	4.82516	0.224730	0.112365	−	0.993667i	$-0.464157\pi$
$461$	4.82516	0.224730	0.112365	+	0.993667i	$0.464157\pi$
$462$	−0.387700	−0.0180375
$463$	39.9837	1.85820	0.929101	−	0.369826i	$-0.120583\pi$
$463$	39.9837	1.85820	0.929101	+	0.369826i	$0.120583\pi$
$464$	−4.09044	−0.189894
$465$	2.71389	0.125854
$466$	−47.0314	−2.17869
$467$	36.3976	1.68428	0.842141	−	0.539258i	$-0.181295\pi$
$467$	36.3976	1.68428	0.842141	+	0.539258i	$0.181295\pi$
$468$	48.3758	2.23617
$469$	10.5369	0.486550
$470$	−91.6952	−4.22959
$471$	0.862364	0.0397357
$472$	−14.8236	−0.682310
$473$	9.67460	0.444839
$474$	3.61446	0.166018
$475$	1.35624	0.0622284
$476$	−9.08660	−0.416484
$477$	14.4857	0.663254
$478$	−26.1450	−1.19585
$479$	−13.8960	−0.634926	−0.317463	−	0.948271i	$-0.602831\pi$
$479$	−13.8960	−0.634926	−0.317463	+	0.948271i	$0.602831\pi$
$480$	4.68194	0.213700
$481$	−32.4959	−1.48169
$482$	24.5709	1.11917
$483$	−1.18501	−0.0539196
$484$	2.95817	0.134462
$485$	−12.7878	−0.580664
$486$	−11.8502	−0.537538
$487$	14.4811	0.656201	0.328101	−	0.944643i	$-0.393592\pi$
$487$	14.4811	0.656201	0.328101	+	0.944643i	$0.393592\pi$
$488$	−1.30928	−0.0592685
$489$	−3.39902	−0.153709
$490$	47.2909	2.13638
$491$	16.9051	0.762917	0.381458	−	0.924386i	$-0.375422\pi$
$491$	16.9051	0.762917	0.381458	+	0.924386i	$0.375422\pi$
$492$	−0.323834	−0.0145995
$493$	12.4250	0.559596
$494$	2.54469	0.114491
$495$	10.0618	0.452245
$496$	−4.63642	−0.208181
$497$	−1.85231	−0.0830875
$498$	0.0946146	0.00423978
$499$	−26.4697	−1.18495	−0.592474	−	0.805589i	$-0.701849\pi$
$499$	−26.4697	−1.18495	−0.592474	+	0.805589i	$0.701849\pi$
$500$	15.6594	0.700311
$501$	−3.87107	−0.172947
$502$	32.1788	1.43621
$503$	−8.81374	−0.392985	−0.196493	−	0.980505i	$-0.562955\pi$
$503$	−8.81374	−0.392985	−0.196493	+	0.980505i	$0.562955\pi$
$504$	−5.47861	−0.244037
$505$	42.8522	1.90690
$506$	15.1546	0.673706
$507$	3.51777	0.156230
$508$	−38.8906	−1.72549
$509$	−19.9660	−0.884976	−0.442488	−	0.896774i	$-0.645904\pi$
$509$	−19.9660	−0.884976	−0.442488	+	0.896774i	$0.645904\pi$
$510$	−5.37861	−0.238169
$511$	0.773800	0.0342309
$512$	−12.9722	−0.573296
$513$	−0.247382	−0.0109222
$514$	−66.1509	−2.91779
$515$	18.7635	0.826818
$516$	−5.74351	−0.252844
$517$	−12.1133	−0.532740
$518$	11.3619	0.499214
$519$	1.53082	0.0671954
$520$	40.0759	1.75744
$521$	17.2473	0.755618	0.377809	−	0.925884i	$-0.376678\pi$
$521$	17.2473	0.755618	0.377809	+	0.925884i	$0.376678\pi$
$522$	23.1285	1.01231
$523$	−4.71318	−0.206093	−0.103047	−	0.994677i	$-0.532859\pi$
$523$	−4.71318	−0.206093	−0.103047	+	0.994677i	$0.532859\pi$
$524$	29.2913	1.27960
$525$	−1.14169	−0.0498276
$526$	11.4274	0.498259
$527$	14.0835	0.613486
$528$	0.233914	0.0101798
$529$	23.3201	1.01392
$530$	37.0488	1.60930
$531$	−20.5636	−0.892386
$532$	−0.530835	−0.0230146
$533$	3.01392	0.130547
$534$	3.11488	0.134794
$535$	−40.3546	−1.74468
$536$	25.9121	1.11923
$537$	4.85083	0.209329
$538$	3.81744	0.164582
$539$	6.24729	0.269090
$540$	−12.0281	−0.517605
$541$	1.86579	0.0802166	0.0401083	−	0.999195i	$-0.487230\pi$
$541$	1.86579	0.0802166	0.0401083	+	0.999195i	$0.487230\pi$
$542$	14.6015	0.627189
$543$	−0.0156311	−0.000670796 0
$544$	24.2965	1.04170
$545$	21.4127	0.917219
$546$	−2.14215	−0.0916755
$547$	1.00000	0.0427569
$547$	1.00000	0.0427569
$548$	47.7491	2.03974
$549$	−1.81627	−0.0775166
$550$	14.6008	0.622578
$551$	0.725865	0.0309229
$552$	−2.91414	−0.124034
$553$	7.01741	0.298411
$554$	10.2642	0.436084
$555$	4.01256	0.170324
$556$	4.53174	0.192189
$557$	−20.8609	−0.883904	−0.441952	−	0.897039i	$-0.645714\pi$
$557$	−20.8609	−0.883904	−0.441952	+	0.897039i	$0.645714\pi$
$558$	26.2156	1.10979
$559$	53.4548	2.26090
$560$	3.43776	0.145272
$561$	−0.710532	−0.0299987
$562$	0.741837	0.0312925
$563$	−18.7401	−0.789801	−0.394901	−	0.918724i	$-0.629221\pi$
$563$	−18.7401	−0.789801	−0.394901	+	0.918724i	$0.629221\pi$
$564$	7.19126	0.302807
$565$	3.02999	0.127473
$566$	−68.8470	−2.89385
$567$	−7.49524	−0.314770
$568$	−4.55516	−0.191130
$569$	−17.2556	−0.723394	−0.361697	−	0.932296i	$-0.617803\pi$
$569$	−17.2556	−0.723394	−0.361697	+	0.932296i	$0.617803\pi$
$570$	−0.314215	−0.0131610
$571$	−7.22806	−0.302485	−0.151242	−	0.988497i	$-0.548327\pi$
$571$	−7.22806	−0.302485	−0.151242	+	0.988497i	$0.548327\pi$
$572$	16.3447	0.683406
$573$	2.68751	0.112272
$574$	−1.05379	−0.0439843
$575$	44.6272	1.86108
$576$	38.3269	1.59696
$577$	−6.06438	−0.252464	−0.126232	−	0.992001i	$-0.540288\pi$
$577$	−6.06438	−0.252464	−0.126232	+	0.992001i	$0.540288\pi$
$578$	9.94206	0.413535
$579$	3.84055	0.159608
$580$	35.2926	1.46544
$581$	0.183693	0.00762085
$582$	1.68094	0.0696772
$583$	4.89427	0.202700
$584$	1.90291	0.0787430
$585$	55.5943	2.29854
$586$	34.5783	1.42842
$587$	−30.9404	−1.27705	−0.638524	−	0.769602i	$-0.720455\pi$
$587$	−30.9404	−1.27705	−0.638524	+	0.769602i	$0.720455\pi$
$588$	−3.70882	−0.152949
$589$	0.822750	0.0339008
$590$	−52.5938	−2.16525
$591$	−0.835363	−0.0343622
$592$	−6.85506	−0.281741
$593$	8.18850	0.336261	0.168131	−	0.985765i	$-0.446227\pi$
$593$	8.18850	0.336261	0.168131	+	0.985765i	$0.446227\pi$
$594$	−2.66322	−0.109273
$595$	−10.4425	−0.428100
$596$	5.26087	0.215494
$597$	3.66868	0.150149
$598$	83.7335	3.42412
$599$	32.1275	1.31270	0.656348	−	0.754458i	$-0.272100\pi$
$599$	32.1275	1.31270	0.656348	+	0.754458i	$0.272100\pi$
$600$	−2.80763	−0.114621
$601$	−23.1252	−0.943297	−0.471648	−	0.881787i	$-0.656341\pi$
$601$	−23.1252	−0.943297	−0.471648	+	0.881787i	$0.656341\pi$
$602$	−18.6900	−0.761747
$603$	35.9459	1.46383
$604$	−3.87654	−0.157734
$605$	3.39958	0.138213
$606$	−5.63287	−0.228820
$607$	18.9949	0.770981	0.385491	−	0.922712i	$-0.374032\pi$
$607$	18.9949	0.770981	0.385491	+	0.922712i	$0.374032\pi$
$608$	1.41939	0.0575638
$609$	−0.611041	−0.0247606
$610$	−4.64532	−0.188083
$611$	−66.9290	−2.70766
$612$	−30.9983	−1.25303
$613$	9.30281	0.375737	0.187869	−	0.982194i	$-0.439842\pi$
$613$	9.30281	0.375737	0.187869	+	0.982194i	$0.439842\pi$
$614$	−53.8008	−2.17122
$615$	−0.372155	−0.0150067
$616$	−1.85105	−0.0745811
$617$	18.9104	0.761302	0.380651	−	0.924719i	$-0.375700\pi$
$617$	18.9104	0.761302	0.380651	+	0.924719i	$0.375700\pi$
$618$	−2.46644	−0.0992146
$619$	26.4456	1.06294	0.531470	−	0.847077i	$-0.321640\pi$
$619$	26.4456	1.06294	0.531470	+	0.847077i	$0.321640\pi$
$620$	40.0033	1.60657
$621$	−8.14013	−0.326652
$622$	−3.50861	−0.140682
$623$	6.04749	0.242287
$624$	1.29244	0.0517389
$625$	−14.7896	−0.591585
$626$	−67.2463	−2.68770
$627$	−0.0415089	−0.00165771
$628$	12.7114	0.507241
$629$	20.8228	0.830259
$630$	−19.4380	−0.774429
$631$	3.72567	0.148317	0.0741583	−	0.997246i	$-0.476373\pi$
$631$	3.72567	0.148317	0.0741583	+	0.997246i	$0.476373\pi$
$632$	17.2570	0.686448
$633$	1.30084	0.0517036
$634$	−40.3885	−1.60403
$635$	−44.6937	−1.77362
$636$	−2.90557	−0.115213
$637$	34.5179	1.36765
$638$	7.81440	0.309375
$639$	−6.31903	−0.249977
$640$	51.3665	2.03044
$641$	−32.3257	−1.27679	−0.638394	−	0.769710i	$-0.720401\pi$
$641$	−32.3257	−1.27679	−0.638394	+	0.769710i	$0.720401\pi$
$642$	5.30455	0.209354
$643$	14.9790	0.590713	0.295357	−	0.955387i	$-0.404562\pi$
$643$	14.9790	0.590713	0.295357	+	0.955387i	$0.404562\pi$
$644$	−17.4672	−0.688304
$645$	−6.60053	−0.259896
$646$	−1.63059	−0.0641547
$647$	39.0331	1.53455	0.767275	−	0.641318i	$-0.221612\pi$
$647$	39.0331	1.53455	0.767275	+	0.641318i	$0.221612\pi$
$648$	−18.4321	−0.724081
$649$	−6.94782	−0.272726
$650$	80.6731	3.16426
$651$	−0.692600	−0.0271451
$652$	−50.1021	−1.96215
$653$	23.0434	0.901756	0.450878	−	0.892586i	$-0.351111\pi$
$653$	23.0434	0.901756	0.450878	+	0.892586i	$0.351111\pi$
$654$	−2.81467	−0.110062
$655$	33.6621	1.31529
$656$	0.635790	0.0248234
$657$	2.63976	0.102987
$658$	23.4011	0.912270
$659$	35.5500	1.38483	0.692415	−	0.721499i	$-0.256547\pi$
$659$	35.5500	1.38483	0.692415	+	0.721499i	$0.256547\pi$
$660$	−2.01822	−0.0785592
$661$	−21.5004	−0.836267	−0.418133	−	0.908386i	$-0.637316\pi$
$661$	−21.5004	−0.836267	−0.418133	+	0.908386i	$0.637316\pi$
$662$	−53.5861	−2.08268
$663$	−3.92588	−0.152469
$664$	0.451732	0.0175306
$665$	−0.610044	−0.0236565
$666$	38.7603	1.50193
$667$	23.8847	0.924819
$668$	−57.0603	−2.20773
$669$	0.469225	0.0181413
$670$	91.9358	3.55179
$671$	−0.613662	−0.0236902
$672$	−1.19486	−0.0460926
$673$	−0.0598608	−0.00230746	−0.00115373	−	0.999999i	$-0.500367\pi$
$673$	−0.0598608	−0.00230746	−0.00115373	+	0.999999i	$0.500367\pi$
$674$	−65.6572	−2.52902
$675$	−7.84262	−0.301863
$676$	51.8526	1.99433
$677$	−2.11168	−0.0811584	−0.0405792	−	0.999176i	$-0.512920\pi$
$677$	−2.11168	−0.0811584	−0.0405792	+	0.999176i	$0.512920\pi$
$678$	−0.398288	−0.0152962
$679$	3.26352	0.125242
$680$	−25.6799	−0.984778
$681$	2.92035	0.111908
$682$	8.85743	0.339169
$683$	31.7498	1.21487	0.607435	−	0.794369i	$-0.292198\pi$
$683$	31.7498	1.21487	0.607435	+	0.794369i	$0.292198\pi$
$684$	−1.81090	−0.0692417
$685$	54.8741	2.09663
$686$	−25.5919	−0.977103
$687$	−2.13631	−0.0815055
$688$	11.2764	0.429907
$689$	27.0422	1.03022
$690$	−10.3393	−0.393611
$691$	−3.00187	−0.114197	−0.0570983	−	0.998369i	$-0.518185\pi$
$691$	−3.00187	−0.114197	−0.0570983	+	0.998369i	$0.518185\pi$
$692$	22.5645	0.857775
$693$	−2.56783	−0.0975438
$694$	−25.5848	−0.971185
$695$	5.20795	0.197549
$696$	−1.50266	−0.0569580
$697$	−1.93126	−0.0731518
$698$	77.0677	2.91706
$699$	4.23884	0.160328
$700$	−16.8288	−0.636068
$701$	21.8108	0.823783	0.411892	−	0.911233i	$-0.364868\pi$
$701$	21.8108	0.823783	0.411892	+	0.911233i	$0.364868\pi$
$702$	−14.7150	−0.555383
$703$	1.21646	0.0458795
$704$	12.9495	0.488053
$705$	8.26431	0.311252
$706$	−79.3393	−2.98597
$707$	−10.9361	−0.411295
$708$	4.12470	0.155016
$709$	2.83035	0.106296	0.0531480	−	0.998587i	$-0.483075\pi$
$709$	2.83035	0.106296	0.0531480	+	0.998587i	$0.483075\pi$
$710$	−16.1616	−0.606535
$711$	23.9394	0.897798
$712$	14.8718	0.557345
$713$	27.0727	1.01388
$714$	1.37265	0.0513701
$715$	18.7836	0.702466
$716$	71.5022	2.67216
$717$	2.35640	0.0880014
$718$	−49.1253	−1.83334
$719$	4.48456	0.167246	0.0836230	−	0.996497i	$-0.473351\pi$
$719$	4.48456	0.167246	0.0836230	+	0.996497i	$0.473351\pi$
$720$	11.7277	0.437065
$721$	−4.78854	−0.178335
$722$	42.2120	1.57097
$723$	−2.21453	−0.0823591
$724$	−0.230406	−0.00856296
$725$	23.0117	0.854634
$726$	−0.446870	−0.0165849
$727$	−5.59601	−0.207545	−0.103772	−	0.994601i	$-0.533091\pi$
$727$	−5.59601	−0.207545	−0.103772	+	0.994601i	$0.533091\pi$
$728$	−10.2276	−0.379059
$729$	−24.8494	−0.920348
$730$	6.75149	0.249884
$731$	−34.2528	−1.26689
$732$	0.364312	0.0134654
$733$	−11.6629	−0.430780	−0.215390	−	0.976528i	$-0.569102\pi$
$733$	−11.6629	−0.430780	−0.215390	+	0.976528i	$0.569102\pi$
$734$	−47.0347	−1.73608
$735$	−4.26223	−0.157215
$736$	46.7052	1.72158
$737$	12.1450	0.447368
$738$	−3.59493	−0.132331
$739$	−39.1508	−1.44019	−0.720094	−	0.693877i	$-0.755901\pi$
$739$	−39.1508	−1.44019	−0.720094	+	0.693877i	$0.755901\pi$
$740$	59.1458	2.17424
$741$	−0.229348	−0.00842531
$742$	−9.45504	−0.347106
$743$	−32.7690	−1.20218	−0.601090	−	0.799181i	$-0.705267\pi$
$743$	−32.7690	−1.20218	−0.601090	+	0.799181i	$0.705267\pi$
$744$	−1.70322	−0.0624432
$745$	6.04588	0.221504
$746$	5.19382	0.190159
$747$	0.626654	0.0229281
$748$	−10.4734	−0.382944
$749$	10.2987	0.376306
$750$	−2.36556	−0.0863781
$751$	18.1478	0.662223	0.331111	−	0.943592i	$-0.392576\pi$
$751$	18.1478	0.662223	0.331111	+	0.943592i	$0.392576\pi$
$752$	−14.1187	−0.514858
$753$	−2.90021	−0.105690
$754$	43.1767	1.57240
$755$	−4.45498	−0.162133
$756$	3.06962	0.111641
$757$	−17.9111	−0.650989	−0.325494	−	0.945544i	$-0.605531\pi$
$757$	−17.9111	−0.650989	−0.325494	+	0.945544i	$0.605531\pi$
$758$	−64.6673	−2.34882
$759$	−1.36586	−0.0495775
$760$	−1.50020	−0.0544181
$761$	24.5640	0.890443	0.445222	−	0.895420i	$-0.353125\pi$
$761$	24.5640	0.890443	0.445222	+	0.895420i	$0.353125\pi$
$762$	5.87493	0.212826
$763$	−5.46463	−0.197833
$764$	39.6144	1.43320
$765$	−35.6238	−1.28798
$766$	16.0451	0.579733
$767$	−38.3886	−1.38613
$768$	−1.55445	−0.0560912
$769$	−3.14368	−0.113364	−0.0566820	−	0.998392i	$-0.518052\pi$
$769$	−3.14368	−0.113364	−0.0566820	+	0.998392i	$0.518052\pi$
$770$	−6.56751	−0.236677
$771$	5.96205	0.214718
$772$	56.6104	2.03745
$773$	−30.8113	−1.10821	−0.554103	−	0.832448i	$-0.686939\pi$
$773$	−30.8113	−1.10821	−0.554103	+	0.832448i	$0.686939\pi$
$774$	−63.7595	−2.29179
$775$	26.0832	0.936937
$776$	8.02556	0.288101
$777$	−1.02403	−0.0367367
$778$	72.1302	2.58599
$779$	−0.112823	−0.00404232
$780$	−11.1512	−0.399278
$781$	−2.13501	−0.0763965
$782$	−53.6548	−1.91869
$783$	−4.19741	−0.150003
$784$	7.28160	0.260057
$785$	14.6082	0.521388
$786$	−4.42483	−0.157829
$787$	30.7840	1.09733	0.548665	−	0.836042i	$-0.315136\pi$
$787$	30.7840	1.09733	0.548665	+	0.836042i	$0.315136\pi$
$788$	−12.3134	−0.438647
$789$	−1.02993	−0.0366664
$790$	61.2277	2.17838
$791$	−0.773270	−0.0274943
$792$	−6.31474	−0.224385
$793$	−3.39065	−0.120406
$794$	−5.86689	−0.208208
$795$	−3.33913	−0.118427
$796$	54.0771	1.91671
$797$	14.3420	0.508019	0.254009	−	0.967202i	$-0.418251\pi$
$797$	14.3420	0.508019	0.254009	+	0.967202i	$0.418251\pi$
$798$	0.0801894	0.00283867
$799$	42.8868	1.51723
$800$	44.9982	1.59092
$801$	20.6306	0.728945
$802$	−13.1328	−0.463737
$803$	0.891895	0.0314743
$804$	−7.21012	−0.254281
$805$	−20.0736	−0.707501
$806$	48.9397	1.72383
$807$	−0.344058	−0.0121114
$808$	−26.8938	−0.946122
$809$	16.1758	0.568711	0.284355	−	0.958719i	$-0.408220\pi$
$809$	16.1758	0.568711	0.284355	+	0.958719i	$0.408220\pi$
$810$	−65.3968	−2.29781
$811$	−41.2489	−1.44844	−0.724222	−	0.689567i	$-0.757801\pi$
$811$	−41.2489	−1.44844	−0.724222	+	0.689567i	$0.757801\pi$
$812$	−9.00685	−0.316079
$813$	−1.31601	−0.0461543
$814$	13.0959	0.459012
$815$	−57.5782	−2.01688
$816$	−0.828169	−0.0289917
$817$	−2.00103	−0.0700073
$818$	5.40264	0.188899
$819$	−14.1879	−0.495767
$820$	−5.48563	−0.191567
$821$	16.5848	0.578812	0.289406	−	0.957206i	$-0.406542\pi$
$821$	16.5848	0.578812	0.289406	+	0.957206i	$0.406542\pi$
$822$	−7.21312	−0.251587
$823$	37.2624	1.29889	0.649443	−	0.760410i	$-0.275002\pi$
$823$	37.2624	1.29889	0.649443	+	0.760410i	$0.275002\pi$
$824$	−11.7759	−0.410232
$825$	−1.31594	−0.0458150
$826$	13.4222	0.467019
$827$	−40.3798	−1.40414	−0.702071	−	0.712107i	$-0.747741\pi$
$827$	−40.3798	−1.40414	−0.702071	+	0.712107i	$0.747741\pi$
$828$	−59.5881	−2.07083
$829$	−40.7782	−1.41628	−0.708142	−	0.706070i	$-0.750466\pi$
$829$	−40.7782	−1.41628	−0.708142	+	0.706070i	$0.750466\pi$
$830$	1.60274	0.0556319
$831$	−0.925092	−0.0320911
$832$	71.5495	2.48053
$833$	−22.1184	−0.766359
$834$	−0.684578	−0.0237050
$835$	−65.5746	−2.26930
$836$	−0.611849	−0.0211612
$837$	−4.75766	−0.164449
$838$	4.43015	0.153037
$839$	55.0965	1.90214	0.951072	−	0.308971i	$-0.0999845\pi$
$839$	55.0965	1.90214	0.951072	+	0.308971i	$0.0999845\pi$
$840$	1.26289	0.0435738
$841$	−16.6840	−0.575310
$842$	−11.2520	−0.387769
$843$	−0.0668603	−0.00230279
$844$	19.1746	0.660015
$845$	59.5899	2.04995
$846$	79.8312	2.74465
$847$	−0.867591	−0.0298108
$848$	5.70457	0.195896
$849$	6.20504	0.212956
$850$	−51.6938	−1.77308
$851$	40.0277	1.37213
$852$	1.26749	0.0434233
$853$	−35.5855	−1.21842	−0.609211	−	0.793008i	$-0.708514\pi$
$853$	−35.5855	−1.21842	−0.609211	+	0.793008i	$0.708514\pi$
$854$	1.18551	0.0405673
$855$	−2.08112	−0.0711728
$856$	25.3263	0.865635
$857$	23.4393	0.800672	0.400336	−	0.916368i	$-0.368893\pi$
$857$	23.4393	0.800672	0.400336	+	0.916368i	$0.368893\pi$
$858$	−2.46908	−0.0842929
$859$	−5.29623	−0.180705	−0.0903525	−	0.995910i	$-0.528799\pi$
$859$	−5.29623	−0.180705	−0.0903525	+	0.995910i	$0.528799\pi$
$860$	−97.2930	−3.31767
$861$	0.0949759	0.00323677
$862$	−42.6659	−1.45321
$863$	−4.16711	−0.141850	−0.0709250	−	0.997482i	$-0.522595\pi$
$863$	−4.16711	−0.141850	−0.0709250	+	0.997482i	$0.522595\pi$
$864$	−8.20780	−0.279235
$865$	25.9315	0.881698
$866$	16.4339	0.558447
$867$	−0.896058	−0.0304317
$868$	−10.2090	−0.346518
$869$	8.08839	0.274380
$870$	−5.33140	−0.180751
$871$	67.1046	2.27375
$872$	−13.4385	−0.455085
$873$	11.1333	0.376804
$874$	−3.13449	−0.106026
$875$	−4.59270	−0.155261
$876$	−0.529490	−0.0178898
$877$	−39.1819	−1.32308	−0.661539	−	0.749911i	$-0.730096\pi$
$877$	−39.1819	−1.32308	−0.661539	+	0.749911i	$0.730096\pi$
$878$	32.9334	1.11145
$879$	−3.11647	−0.105116
$880$	3.96242	0.133573
$881$	−35.5080	−1.19630	−0.598148	−	0.801386i	$-0.704096\pi$
$881$	−35.5080	−1.19630	−0.598148	+	0.801386i	$0.704096\pi$
$882$	−41.1721	−1.38634
$883$	28.5051	0.959273	0.479637	−	0.877467i	$-0.340768\pi$
$883$	28.5051	0.959273	0.479637	+	0.877467i	$0.340768\pi$
$884$	−57.8682	−1.94632
$885$	4.74017	0.159339
$886$	−7.57017	−0.254325
$887$	−17.9442	−0.602507	−0.301253	−	0.953544i	$-0.597405\pi$
$887$	−17.9442	−0.602507	−0.301253	+	0.953544i	$0.597405\pi$
$888$	−2.51826	−0.0845072
$889$	11.4061	0.382547
$890$	52.7650	1.76869
$891$	−8.63914	−0.289422
$892$	6.91646	0.231580
$893$	2.50543	0.0838409
$894$	−0.794723	−0.0265795
$895$	82.1715	2.74669
$896$	−13.1090	−0.437941
$897$	−7.54673	−0.251978
$898$	54.4989	1.81865
$899$	13.9599	0.465588
$900$	−57.4102	−1.91367
$901$	−17.3281	−0.577283
$902$	−1.21462	−0.0404423
$903$	1.68449	0.0560563
$904$	−1.90161	−0.0632465
$905$	−0.264786	−0.00880178
$906$	0.585601	0.0194553
$907$	12.0757	0.400966	0.200483	−	0.979697i	$-0.435749\pi$
$907$	12.0757	0.400966	0.200483	+	0.979697i	$0.435749\pi$
$908$	43.0465	1.42855
$909$	−37.3078	−1.23742
$910$	−36.2873	−1.20291
$911$	−7.33155	−0.242905	−0.121452	−	0.992597i	$-0.538755\pi$
$911$	−7.33155	−0.242905	−0.121452	+	0.992597i	$0.538755\pi$
$912$	−0.0483812	−0.00160206
$913$	0.211727	0.00700715
$914$	−69.5664	−2.30105
$915$	0.418673	0.0138409
$916$	−31.4897	−1.04045
$917$	−8.59074	−0.283691
$918$	9.42911	0.311207
$919$	2.59188	0.0854982	0.0427491	−	0.999086i	$-0.486388\pi$
$919$	2.59188	0.0854982	0.0427491	+	0.999086i	$0.486388\pi$
$920$	−49.3645	−1.62750
$921$	4.84896	0.159779
$922$	−10.7442	−0.353840
$923$	−11.7965	−0.388286
$924$	0.515061	0.0169443
$925$	38.5647	1.26800
$926$	−89.0316	−2.92576
$927$	−16.3358	−0.536537
$928$	24.0832	0.790571
$929$	−40.7807	−1.33797	−0.668986	−	0.743275i	$-0.733271\pi$
$929$	−40.7807	−1.33797	−0.668986	+	0.743275i	$0.733271\pi$
$930$	−6.04301	−0.198158
$931$	−1.29215	−0.0423484
$932$	62.4813	2.04664
$933$	0.316224	0.0103527
$934$	−81.0464	−2.65192
$935$	−12.0362	−0.393625
$936$	−34.8906	−1.14044
$937$	44.0812	1.44007	0.720034	−	0.693938i	$-0.244126\pi$
$937$	44.0812	1.44007	0.720034	+	0.693938i	$0.244126\pi$
$938$	−23.4625	−0.766078
$939$	6.06077	0.197786
$940$	121.817	3.97325
$941$	−16.7531	−0.546134	−0.273067	−	0.961995i	$-0.588038\pi$
$941$	−16.7531	−0.546134	−0.273067	+	0.961995i	$0.588038\pi$
$942$	−1.92022	−0.0625642
$943$	−3.71247	−0.120895
$944$	−8.09811	−0.263571
$945$	3.52766	0.114755
$946$	−21.5424	−0.700404
$947$	−49.5329	−1.60960	−0.804802	−	0.593543i	$-0.797729\pi$
$947$	−49.5329	−1.60960	−0.804802	+	0.593543i	$0.797729\pi$
$948$	−4.80182	−0.155956
$949$	4.92796	0.159968
$950$	−3.01993	−0.0979793
$951$	3.64014	0.118040
$952$	6.55364	0.212405
$953$	−47.2104	−1.52930	−0.764648	−	0.644448i	$-0.777087\pi$
$953$	−47.2104	−1.52930	−0.764648	+	0.644448i	$0.777087\pi$
$954$	−32.2552	−1.04430
$955$	45.5255	1.47317
$956$	34.7338	1.12337
$957$	−0.704296	−0.0227667
$958$	30.9423	0.999699
$959$	−14.0042	−0.452218
$960$	−8.83484	−0.285143
$961$	−15.1768	−0.489575
$962$	72.3585	2.33293
$963$	35.1333	1.13215
$964$	−32.6425	−1.05134
$965$	65.0576	2.09428
$966$	2.63865	0.0848970
$967$	−30.6831	−0.986701	−0.493350	−	0.869831i	$-0.664228\pi$
$967$	−30.6831	−0.986701	−0.493350	+	0.869831i	$0.664228\pi$
$968$	−2.13356	−0.0685751
$969$	0.146962	0.00472110
$970$	28.4745	0.914263
$971$	−56.1396	−1.80161	−0.900803	−	0.434229i	$-0.857021\pi$
$971$	−56.1396	−1.80161	−0.900803	+	0.434229i	$0.857021\pi$
$972$	15.7431	0.504960
$973$	−1.32910	−0.0426089
$974$	−32.2450	−1.03320
$975$	−7.27090	−0.232855
$976$	−0.715262	−0.0228950
$977$	24.5356	0.784964	0.392482	−	0.919760i	$-0.371617\pi$
$977$	24.5356	0.784964	0.392482	+	0.919760i	$0.371617\pi$
$978$	7.56857	0.242016
$979$	6.97044	0.222776
$980$	−62.8261	−2.00691
$981$	−18.6422	−0.595200
$982$	−37.6425	−1.20122
$983$	7.15067	0.228071	0.114035	−	0.993477i	$-0.463622\pi$
$983$	7.15067	0.228071	0.114035	+	0.993477i	$0.463622\pi$
$984$	0.233562	0.00744570
$985$	−14.1508	−0.450881
$986$	−27.6668	−0.881090
$987$	−2.10910	−0.0671332
$988$	−3.38063	−0.107552
$989$	−65.8443	−2.09373
$990$	−22.4046	−0.712065
$991$	−49.6523	−1.57726	−0.788628	−	0.614870i	$-0.789208\pi$
$991$	−49.6523	−1.57726	−0.788628	+	0.614870i	$0.789208\pi$
$992$	27.2978	0.866705
$993$	4.82960	0.153263
$994$	4.12453	0.130822
$995$	62.1462	1.97017
$996$	−0.125696	−0.00398282
$997$	−10.3325	−0.327232	−0.163616	−	0.986524i	$-0.552316\pi$
$997$	−10.3325	−0.327232	−0.163616	+	0.986524i	$0.552316\pi$
$998$	58.9401	1.86572
$999$	−7.03432	−0.222556

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6017.2.a.f.1.19	✓	121

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6017.2.a.f.1.19	✓	121	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:	\( N \)	\(=\)	\( 6017 = 11 \cdot 547 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6017.a (trivial)

\(f(q)\)	\(=\)	\(q-2.22670 q^{2} +0.200688 q^{3} +2.95817 q^{4} +3.39958 q^{5} -0.446870 q^{6} -0.867591 q^{7} -2.13356 q^{8} -2.95972 q^{9} +O(q^{10})\)	\(q-2.22670 q^{2} +0.200688 q^{3} +2.95817 q^{4} +3.39958 q^{5} -0.446870 q^{6} -0.867591 q^{7} -2.13356 q^{8} -2.95972 q^{9} -7.56983 q^{10} -1.00000 q^{11} +0.593668 q^{12} -5.52527 q^{13} +1.93186 q^{14} +0.682253 q^{15} -1.16556 q^{16} +3.54049 q^{17} +6.59040 q^{18} +0.206834 q^{19} +10.0565 q^{20} -0.174115 q^{21} +2.22670 q^{22} +6.80589 q^{23} -0.428178 q^{24} +6.55714 q^{25} +12.3031 q^{26} -1.19604 q^{27} -2.56648 q^{28} +3.50942 q^{29} -1.51917 q^{30} +3.97784 q^{31} +6.86247 q^{32} -0.200688 q^{33} -7.88359 q^{34} -2.94944 q^{35} -8.75537 q^{36} +5.88133 q^{37} -0.460555 q^{38} -1.10885 q^{39} -7.25320 q^{40} -0.545479 q^{41} +0.387700 q^{42} -9.67460 q^{43} -2.95817 q^{44} -10.0618 q^{45} -15.1546 q^{46} +12.1133 q^{47} -0.233914 q^{48} -6.24729 q^{49} -14.6008 q^{50} +0.710532 q^{51} -16.3447 q^{52} -4.89427 q^{53} +2.66322 q^{54} -3.39958 q^{55} +1.85105 q^{56} +0.0415089 q^{57} -7.81440 q^{58} +6.94782 q^{59} +2.01822 q^{60} +0.613662 q^{61} -8.85743 q^{62} +2.56783 q^{63} -12.9495 q^{64} -18.7836 q^{65} +0.446870 q^{66} -12.1450 q^{67} +10.4734 q^{68} +1.36586 q^{69} +6.56751 q^{70} +2.13501 q^{71} +6.31474 q^{72} -0.891895 q^{73} -13.0959 q^{74} +1.31594 q^{75} +0.611849 q^{76} +0.867591 q^{77} +2.46908 q^{78} -8.08839 q^{79} -3.96242 q^{80} +8.63914 q^{81} +1.21462 q^{82} -0.211727 q^{83} -0.515061 q^{84} +12.0362 q^{85} +21.5424 q^{86} +0.704296 q^{87} +2.13356 q^{88} -6.97044 q^{89} +22.4046 q^{90} +4.79367 q^{91} +20.1330 q^{92} +0.798302 q^{93} -26.9725 q^{94} +0.703147 q^{95} +1.37721 q^{96} -3.76158 q^{97} +13.9108 q^{98} +2.95972 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 121 q + 2 q^{2} + 18 q^{3} + 138 q^{4} + 13 q^{5} + 10 q^{6} + 56 q^{7} + 12 q^{8} + 143 q^{9}+O(q^{10}) \) 121 * q + 2 * q^2 + 18 * q^3 + 138 * q^4 + 13 * q^5 + 10 * q^6 + 56 * q^7 + 12 * q^8 + 143 * q^9	\( 121 q + 2 q^{2} + 18 q^{3} + 138 q^{4} + 13 q^{5} + 10 q^{6} + 56 q^{7} + 12 q^{8} + 143 q^{9} + 20 q^{10} - 121 q^{11} + 40 q^{12} + 31 q^{13} + 7 q^{14} + 53 q^{15} + 164 q^{16} - 23 q^{17} + 14 q^{18} + 62 q^{19} + 53 q^{20} + 19 q^{21} - 2 q^{22} + 34 q^{23} + 34 q^{24} + 172 q^{25} + 34 q^{26} + 87 q^{27} + 91 q^{28} - 30 q^{29} + 2 q^{30} + 102 q^{31} + 31 q^{32} - 18 q^{33} + 30 q^{34} + 20 q^{35} + 164 q^{36} + 58 q^{37} + 35 q^{38} + 42 q^{39} + 52 q^{40} - 12 q^{41} + 56 q^{42} + 96 q^{43} - 138 q^{44} + 72 q^{45} + 48 q^{46} + 136 q^{47} + 99 q^{48} + 199 q^{49} - 7 q^{50} + 22 q^{51} + 81 q^{52} + 24 q^{53} + 37 q^{54} - 13 q^{55} + 28 q^{56} + 25 q^{57} + 76 q^{58} + 58 q^{59} + 81 q^{60} + 14 q^{61} - 2 q^{62} + 152 q^{63} + 236 q^{64} - 29 q^{65} - 10 q^{66} + 112 q^{67} - 61 q^{68} + 41 q^{69} + 105 q^{70} + 56 q^{71} + 71 q^{72} + 113 q^{73} - 23 q^{74} + 111 q^{75} + 144 q^{76} - 56 q^{77} + 59 q^{78} + 80 q^{79} + 100 q^{80} + 177 q^{81} + 123 q^{82} + 6 q^{83} + 79 q^{84} + 26 q^{85} + 14 q^{86} + 180 q^{87} - 12 q^{88} + 26 q^{89} + 75 q^{90} + 72 q^{91} + 58 q^{92} + 139 q^{93} + 37 q^{94} + 39 q^{95} + 66 q^{96} + 136 q^{97} + 7 q^{98} - 143 q^{99}+O(q^{100}) \) 121 * q + 2 * q^2 + 18 * q^3 + 138 * q^4 + 13 * q^5 + 10 * q^6 + 56 * q^7 + 12 * q^8 + 143 * q^9 + 20 * q^10 - 121 * q^11 + 40 * q^12 + 31 * q^13 + 7 * q^14 + 53 * q^15 + 164 * q^16 - 23 * q^17 + 14 * q^18 + 62 * q^19 + 53 * q^20 + 19 * q^21 - 2 * q^22 + 34 * q^23 + 34 * q^24 + 172 * q^25 + 34 * q^26 + 87 * q^27 + 91 * q^28 - 30 * q^29 + 2 * q^30 + 102 * q^31 + 31 * q^32 - 18 * q^33 + 30 * q^34 + 20 * q^35 + 164 * q^36 + 58 * q^37 + 35 * q^38 + 42 * q^39 + 52 * q^40 - 12 * q^41 + 56 * q^42 + 96 * q^43 - 138 * q^44 + 72 * q^45 + 48 * q^46 + 136 * q^47 + 99 * q^48 + 199 * q^49 - 7 * q^50 + 22 * q^51 + 81 * q^52 + 24 * q^53 + 37 * q^54 - 13 * q^55 + 28 * q^56 + 25 * q^57 + 76 * q^58 + 58 * q^59 + 81 * q^60 + 14 * q^61 - 2 * q^62 + 152 * q^63 + 236 * q^64 - 29 * q^65 - 10 * q^66 + 112 * q^67 - 61 * q^68 + 41 * q^69 + 105 * q^70 + 56 * q^71 + 71 * q^72 + 113 * q^73 - 23 * q^74 + 111 * q^75 + 144 * q^76 - 56 * q^77 + 59 * q^78 + 80 * q^79 + 100 * q^80 + 177 * q^81 + 123 * q^82 + 6 * q^83 + 79 * q^84 + 26 * q^85 + 14 * q^86 + 180 * q^87 - 12 * q^88 + 26 * q^89 + 75 * q^90 + 72 * q^91 + 58 * q^92 + 139 * q^93 + 37 * q^94 + 39 * q^95 + 66 * q^96 + 136 * q^97 + 7 * q^98 - 143 * q^99

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