LMFDB - Embedded newform 1339.2.a.g.1.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1339,2,Mod(1,1339)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1339, 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("1339.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1339 = 13 \cdot 103 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1339.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:	$10.6919688306$
Analytic rank:	$0$
Dimension:	$30$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
Character	$\chi$	$=$	1339.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.15890 q^{2} -0.0701034 q^{3} +2.66085 q^{4} -2.25465 q^{5} +0.151346 q^{6} -1.38084 q^{7} -1.42671 q^{8} -2.99509 q^{9} +O(q^{10})$	\(q-2.15890 q^{2} -0.0701034 q^{3} +2.66085 q^{4} -2.25465 q^{5} +0.151346 q^{6} -1.38084 q^{7} -1.42671 q^{8} -2.99509 q^{9} +4.86756 q^{10} -4.35836 q^{11} -0.186535 q^{12} -1.00000 q^{13} +2.98109 q^{14} +0.158058 q^{15} -2.24157 q^{16} +3.87232 q^{17} +6.46609 q^{18} -7.82697 q^{19} -5.99928 q^{20} +0.0968014 q^{21} +9.40927 q^{22} -2.49818 q^{23} +0.100017 q^{24} +0.0834429 q^{25} +2.15890 q^{26} +0.420276 q^{27} -3.67420 q^{28} +6.85927 q^{29} -0.341233 q^{30} -7.84742 q^{31} +7.69276 q^{32} +0.305536 q^{33} -8.35996 q^{34} +3.11331 q^{35} -7.96948 q^{36} +0.413746 q^{37} +16.8976 q^{38} +0.0701034 q^{39} +3.21673 q^{40} +10.1145 q^{41} -0.208985 q^{42} -3.34016 q^{43} -11.5969 q^{44} +6.75287 q^{45} +5.39333 q^{46} -8.45988 q^{47} +0.157142 q^{48} -5.09329 q^{49} -0.180145 q^{50} -0.271463 q^{51} -2.66085 q^{52} -2.05024 q^{53} -0.907333 q^{54} +9.82658 q^{55} +1.97006 q^{56} +0.548697 q^{57} -14.8085 q^{58} +10.0279 q^{59} +0.420570 q^{60} +6.57661 q^{61} +16.9418 q^{62} +4.13573 q^{63} -12.1247 q^{64} +2.25465 q^{65} -0.659621 q^{66} -12.9117 q^{67} +10.3037 q^{68} +0.175131 q^{69} -6.72132 q^{70} -1.00279 q^{71} +4.27312 q^{72} +5.11887 q^{73} -0.893236 q^{74} -0.00584963 q^{75} -20.8264 q^{76} +6.01819 q^{77} -0.151346 q^{78} +0.796172 q^{79} +5.05397 q^{80} +8.95579 q^{81} -21.8362 q^{82} +1.36103 q^{83} +0.257574 q^{84} -8.73073 q^{85} +7.21107 q^{86} -0.480858 q^{87} +6.21812 q^{88} -15.7028 q^{89} -14.5788 q^{90} +1.38084 q^{91} -6.64729 q^{92} +0.550131 q^{93} +18.2640 q^{94} +17.6471 q^{95} -0.539288 q^{96} +5.58675 q^{97} +10.9959 q^{98} +13.0537 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q + 5 q^{3} + 34 q^{4} + 17 q^{5} + 3 q^{6} + 2 q^{7} + 3 q^{8} + 49 q^{9}+O(q^{10}) $ 30 * q + 5 * q^3 + 34 * q^4 + 17 * q^5 + 3 * q^6 + 2 * q^7 + 3 * q^8 + 49 * q^9	\( 30 q + 5 q^{3} + 34 q^{4} + 17 q^{5} + 3 q^{6} + 2 q^{7} + 3 q^{8} + 49 q^{9} + 5 q^{10} + q^{11} + 15 q^{12} - 30 q^{13} + 24 q^{14} + 6 q^{15} + 38 q^{16} + 17 q^{17} + 8 q^{18} + 9 q^{19} + 31 q^{20} + 27 q^{21} + 2 q^{22} + 14 q^{23} + 26 q^{24} + 47 q^{25} + 14 q^{27} - 6 q^{28} + 53 q^{29} + 25 q^{30} + 19 q^{31} - 4 q^{32} + q^{33} - 22 q^{34} + 9 q^{35} + 61 q^{36} + 46 q^{38} - 5 q^{39} - 35 q^{40} + 28 q^{41} - 7 q^{42} + 6 q^{43} - 12 q^{44} + 68 q^{45} + 7 q^{46} + 12 q^{47} + 13 q^{48} + 54 q^{49} - 18 q^{50} + 10 q^{51} - 34 q^{52} + 37 q^{53} + 22 q^{54} + 11 q^{55} + 67 q^{56} - 57 q^{57} - 5 q^{58} + 61 q^{59} - 102 q^{60} + 16 q^{61} - 2 q^{62} - 7 q^{63} + 29 q^{64} - 17 q^{65} - 83 q^{66} - 2 q^{67} + 57 q^{68} + 98 q^{69} - 10 q^{70} + 50 q^{71} - 8 q^{72} - 10 q^{73} - 13 q^{74} + 5 q^{75} - 19 q^{76} + 54 q^{77} - 3 q^{78} + 3 q^{79} + 76 q^{80} + 118 q^{81} + 7 q^{82} + 6 q^{83} + 44 q^{84} + 33 q^{85} - 29 q^{86} - 10 q^{87} - 13 q^{88} + 77 q^{89} + 38 q^{90} - 2 q^{91} - 3 q^{92} + 34 q^{93} - 25 q^{94} + 24 q^{95} - 28 q^{96} + 12 q^{97} - 14 q^{98} - 58 q^{99}+O(q^{100}) \) 30 * q + 5 * q^3 + 34 * q^4 + 17 * q^5 + 3 * q^6 + 2 * q^7 + 3 * q^8 + 49 * q^9 + 5 * q^10 + q^11 + 15 * q^12 - 30 * q^13 + 24 * q^14 + 6 * q^15 + 38 * q^16 + 17 * q^17 + 8 * q^18 + 9 * q^19 + 31 * q^20 + 27 * q^21 + 2 * q^22 + 14 * q^23 + 26 * q^24 + 47 * q^25 + 14 * q^27 - 6 * q^28 + 53 * q^29 + 25 * q^30 + 19 * q^31 - 4 * q^32 + q^33 - 22 * q^34 + 9 * q^35 + 61 * q^36 + 46 * q^38 - 5 * q^39 - 35 * q^40 + 28 * q^41 - 7 * q^42 + 6 * q^43 - 12 * q^44 + 68 * q^45 + 7 * q^46 + 12 * q^47 + 13 * q^48 + 54 * q^49 - 18 * q^50 + 10 * q^51 - 34 * q^52 + 37 * q^53 + 22 * q^54 + 11 * q^55 + 67 * q^56 - 57 * q^57 - 5 * q^58 + 61 * q^59 - 102 * q^60 + 16 * q^61 - 2 * q^62 - 7 * q^63 + 29 * q^64 - 17 * q^65 - 83 * q^66 - 2 * q^67 + 57 * q^68 + 98 * q^69 - 10 * q^70 + 50 * q^71 - 8 * q^72 - 10 * q^73 - 13 * q^74 + 5 * q^75 - 19 * q^76 + 54 * q^77 - 3 * q^78 + 3 * q^79 + 76 * q^80 + 118 * q^81 + 7 * q^82 + 6 * q^83 + 44 * q^84 + 33 * q^85 - 29 * q^86 - 10 * q^87 - 13 * q^88 + 77 * q^89 + 38 * q^90 - 2 * q^91 - 3 * q^92 + 34 * q^93 - 25 * q^94 + 24 * q^95 - 28 * q^96 + 12 * q^97 - 14 * q^98 - 58 * 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 $

$2$	−2.15890	−1.52657	−0.763287	−	0.646060i	$-0.776416\pi$
$2$	−2.15890	−1.52657	−0.763287	+	0.646060i	$0.776416\pi$
$3$	−0.0701034	−0.0404742	−0.0202371	−	0.999795i	$-0.506442\pi$
$3$	−0.0701034	−0.0404742	−0.0202371	+	0.999795i	$0.506442\pi$
$4$	2.66085	1.33043
$5$	−2.25465	−1.00831	−0.504155	−	0.863613i	$-0.668196\pi$
$5$	−2.25465	−1.00831	−0.504155	+	0.863613i	$0.668196\pi$
$6$	0.151346	0.0617868
$7$	−1.38084	−0.521908	−0.260954	−	0.965351i	$-0.584037\pi$
$7$	−1.38084	−0.521908	−0.260954	+	0.965351i	$0.584037\pi$
$8$	−1.42671	−0.504418
$9$	−2.99509	−0.998362
$10$	4.86756	1.53926
$11$	−4.35836	−1.31410	−0.657048	−	0.753849i	$-0.728195\pi$
$11$	−4.35836	−1.31410	−0.657048	+	0.753849i	$0.728195\pi$
$12$	−0.186535	−0.0538479
$13$	−1.00000	−0.277350
$13$	−1.00000	−0.277350
$14$	2.98109	0.796730
$15$	0.158058	0.0408105
$16$	−2.24157	−0.560394
$17$	3.87232	0.939176	0.469588	−	0.882886i	$-0.344402\pi$
$17$	3.87232	0.939176	0.469588	+	0.882886i	$0.344402\pi$
$18$	6.46609	1.52407
$19$	−7.82697	−1.79563	−0.897815	−	0.440373i	$-0.854846\pi$
$19$	−7.82697	−1.79563	−0.897815	+	0.440373i	$0.854846\pi$
$20$	−5.99928	−1.34148
$21$	0.0968014	0.0211238
$22$	9.40927	2.00606
$23$	−2.49818	−0.520907	−0.260454	−	0.965486i	$-0.583872\pi$
$23$	−2.49818	−0.520907	−0.260454	+	0.965486i	$0.583872\pi$
$24$	0.100017	0.0204159
$25$	0.0834429	0.0166886
$26$	2.15890	0.423395
$27$	0.420276	0.0808821
$28$	−3.67420	−0.694359
$29$	6.85927	1.27374	0.636868	−	0.770973i	$-0.280230\pi$
$29$	6.85927	1.27374	0.636868	+	0.770973i	$0.280230\pi$
$30$	−0.341233	−0.0623002
$31$	−7.84742	−1.40944	−0.704720	−	0.709486i	$-0.748927\pi$
$31$	−7.84742	−1.40944	−0.704720	+	0.709486i	$0.748927\pi$
$32$	7.69276	1.35990
$33$	0.305536	0.0531870
$34$	−8.35996	−1.43372
$35$	3.11331	0.526245
$36$	−7.96948	−1.32825
$37$	0.413746	0.0680194	0.0340097	−	0.999422i	$-0.489172\pi$
$37$	0.413746	0.0680194	0.0340097	+	0.999422i	$0.489172\pi$
$38$	16.8976	2.74116
$39$	0.0701034	0.0112255
$40$	3.21673	0.508610
$41$	10.1145	1.57962	0.789808	−	0.613354i	$-0.210180\pi$
$41$	10.1145	1.57962	0.789808	+	0.613354i	$0.210180\pi$
$42$	−0.208985	−0.0322470
$43$	−3.34016	−0.509370	−0.254685	−	0.967024i	$-0.581972\pi$
$43$	−3.34016	−0.509370	−0.254685	+	0.967024i	$0.581972\pi$
$44$	−11.5969	−1.74831
$45$	6.75287	1.00666
$46$	5.39333	0.795203
$47$	−8.45988	−1.23400	−0.617000	−	0.786963i	$-0.711652\pi$
$47$	−8.45988	−1.23400	−0.617000	+	0.786963i	$0.711652\pi$
$48$	0.157142	0.0226815
$49$	−5.09329	−0.727612
$50$	−0.180145	−0.0254763
$51$	−0.271463	−0.0380124
$52$	−2.66085	−0.368994
$53$	−2.05024	−0.281623	−0.140811	−	0.990036i	$-0.544971\pi$
$53$	−2.05024	−0.281623	−0.140811	+	0.990036i	$0.544971\pi$
$54$	−0.907333	−0.123472
$55$	9.82658	1.32502
$56$	1.97006	0.263260
$57$	0.548697	0.0726767
$58$	−14.8085	−1.94445
$59$	10.0279	1.30553	0.652763	−	0.757562i	$-0.273610\pi$
$59$	10.0279	1.30553	0.652763	+	0.757562i	$0.273610\pi$
$60$	0.420570	0.0542954
$61$	6.57661	0.842049	0.421025	−	0.907049i	$-0.361671\pi$
$61$	6.57661	0.842049	0.421025	+	0.907049i	$0.361671\pi$
$62$	16.9418	2.15161
$63$	4.13573	0.521053
$64$	−12.1247	−1.51559
$65$	2.25465	0.279655
$66$	−0.659621	−0.0811938
$67$	−12.9117	−1.57742	−0.788709	−	0.614767i	$-0.789250\pi$
$67$	−12.9117	−1.57742	−0.788709	+	0.614767i	$0.789250\pi$
$68$	10.3037	1.24950
$69$	0.175131	0.0210833
$70$	−6.72132	−0.803351
$71$	−1.00279	−0.119009	−0.0595044	−	0.998228i	$-0.518952\pi$
$71$	−1.00279	−0.119009	−0.0595044	+	0.998228i	$0.518952\pi$
$72$	4.27312	0.503592
$73$	5.11887	0.599119	0.299559	−	0.954078i	$-0.403160\pi$
$73$	5.11887	0.599119	0.299559	+	0.954078i	$0.403160\pi$
$74$	−0.893236	−0.103837
$75$	−0.00584963	−0.000675457 0
$76$	−20.8264	−2.38895
$77$	6.01819	0.685837
$78$	−0.151346	−0.0171366
$79$	0.796172	0.0895763	0.0447882	−	0.998997i	$-0.485739\pi$
$79$	0.796172	0.0895763	0.0447882	+	0.998997i	$0.485739\pi$
$80$	5.05397	0.565050
$81$	8.95579	0.995088
$82$	−21.8362	−2.41140
$83$	1.36103	0.149392	0.0746961	−	0.997206i	$-0.476201\pi$
$83$	1.36103	0.149392	0.0746961	+	0.997206i	$0.476201\pi$
$84$	0.257574	0.0281036
$85$	−8.73073	−0.946981
$86$	7.21107	0.777590
$87$	−0.480858	−0.0515534
$88$	6.21812	0.662854
$89$	−15.7028	−1.66449	−0.832247	−	0.554404i	$-0.812946\pi$
$89$	−15.7028	−1.66449	−0.832247	+	0.554404i	$0.812946\pi$
$90$	−14.5788	−1.53674
$91$	1.38084	0.144751
$92$	−6.64729	−0.693028
$93$	0.550131	0.0570459
$94$	18.2640	1.88379
$95$	17.6471	1.81055
$96$	−0.539288	−0.0550409
$97$	5.58675	0.567249	0.283624	−	0.958935i	$-0.408463\pi$
$97$	5.58675	0.567249	0.283624	+	0.958935i	$0.408463\pi$
$98$	10.9959	1.11075
$99$	13.0537	1.31194
$100$	0.222029	0.0222029
$101$	−13.7820	−1.37136	−0.685682	−	0.727901i	$-0.740496\pi$
$101$	−13.7820	−1.37136	−0.685682	+	0.727901i	$0.740496\pi$
$102$	0.586061	0.0580287
$103$	1.00000	0.0985329
$103$	1.00000	0.0985329
$104$	1.42671	0.139901
$105$	−0.218253	−0.0212993
$106$	4.42627	0.429917
$107$	15.3095	1.48002	0.740012	−	0.672594i	$-0.234820\pi$
$107$	15.3095	1.48002	0.740012	+	0.672594i	$0.234820\pi$
$108$	1.11829	0.107608
$109$	6.24993	0.598635	0.299317	−	0.954154i	$-0.403241\pi$
$109$	6.24993	0.598635	0.299317	+	0.954154i	$0.403241\pi$
$110$	−21.2146	−2.02273
$111$	−0.0290050	−0.00275303
$112$	3.09525	0.292474
$113$	5.11219	0.480914	0.240457	−	0.970660i	$-0.422703\pi$
$113$	5.11219	0.480914	0.240457	+	0.970660i	$0.422703\pi$
$114$	−1.18458	−0.110946
$115$	5.63253	0.525236
$116$	18.2515	1.69461
$117$	2.99509	0.276896
$118$	−21.6493	−1.99298
$119$	−5.34705	−0.490163
$120$	−0.225504	−0.0205856
$121$	7.99532	0.726847
$122$	−14.1983	−1.28545
$123$	−0.709059	−0.0639337
$124$	−20.8808	−1.87515
$125$	11.0851	0.991483
$126$	−8.92862	−0.795425
$127$	−0.811219	−0.0719840	−0.0359920	−	0.999352i	$-0.511459\pi$
$127$	−0.811219	−0.0719840	−0.0359920	+	0.999352i	$0.511459\pi$
$128$	10.7906	0.953764
$129$	0.234156	0.0206163
$130$	−4.86756	−0.426914
$131$	−7.50892	−0.656057	−0.328029	−	0.944668i	$-0.606384\pi$
$131$	−7.50892	−0.656057	−0.328029	+	0.944668i	$0.606384\pi$
$132$	0.812985	0.0707613
$133$	10.8078	0.937153
$134$	27.8751	2.40804
$135$	−0.947574	−0.0815542
$136$	−5.52469	−0.473738
$137$	0.372323	0.0318097	0.0159049	−	0.999874i	$-0.494937\pi$
$137$	0.372323	0.0318097	0.0159049	+	0.999874i	$0.494937\pi$
$138$	−0.378090	−0.0321852
$139$	19.2111	1.62946	0.814730	−	0.579840i	$-0.196885\pi$
$139$	19.2111	1.62946	0.814730	+	0.579840i	$0.196885\pi$
$140$	8.28404	0.700129
$141$	0.593066	0.0499451
$142$	2.16492	0.181676
$143$	4.35836	0.364465
$144$	6.71371	0.559476
$145$	−15.4653	−1.28432
$146$	−11.0511	−0.914599
$147$	0.357057	0.0294495
$148$	1.10092	0.0904947
$149$	15.9075	1.30320	0.651598	−	0.758564i	$-0.274099\pi$
$149$	15.9075	1.30320	0.651598	+	0.758564i	$0.274099\pi$
$150$	0.0126288	0.00103113
$151$	13.9012	1.13126	0.565630	−	0.824659i	$-0.308633\pi$
$151$	13.9012	1.13126	0.565630	+	0.824659i	$0.308633\pi$
$152$	11.1668	0.905749
$153$	−11.5979	−0.937638
$154$	−12.9927	−1.04698
$155$	17.6932	1.42115
$156$	0.186535	0.0149347
$157$	−6.61066	−0.527588	−0.263794	−	0.964579i	$-0.584974\pi$
$157$	−6.61066	−0.527588	−0.263794	+	0.964579i	$0.584974\pi$
$158$	−1.71886	−0.136745
$159$	0.143729	0.0113984
$160$	−17.3445	−1.37120
$161$	3.44959	0.271865
$162$	−19.3347	−1.51907
$163$	13.3508	1.04572	0.522858	−	0.852420i	$-0.324866\pi$
$163$	13.3508	1.04572	0.522858	+	0.852420i	$0.324866\pi$
$164$	26.9131	2.10156
$165$	−0.688876	−0.0536289
$166$	−2.93832	−0.228058
$167$	−3.94791	−0.305498	−0.152749	−	0.988265i	$-0.548813\pi$
$167$	−3.94791	−0.305498	−0.152749	+	0.988265i	$0.548813\pi$
$168$	−0.138108	−0.0106552
$169$	1.00000	0.0769231
$170$	18.8488	1.44564
$171$	23.4424	1.79269
$172$	−8.88767	−0.677678
$173$	16.9128	1.28586	0.642930	−	0.765925i	$-0.277719\pi$
$173$	16.9128	1.28586	0.642930	+	0.765925i	$0.277719\pi$
$174$	1.03812	0.0787000
$175$	−0.115221	−0.00870990
$176$	9.76959	0.736411
$177$	−0.702992	−0.0528401
$178$	33.9008	2.54097
$179$	−5.22247	−0.390345	−0.195173	−	0.980769i	$-0.562527\pi$
$179$	−5.22247	−0.390345	−0.195173	+	0.980769i	$0.562527\pi$
$180$	17.9684	1.33928
$181$	−2.83982	−0.211082	−0.105541	−	0.994415i	$-0.533657\pi$
$181$	−2.83982	−0.211082	−0.105541	+	0.994415i	$0.533657\pi$
$182$	−2.98109	−0.220973
$183$	−0.461043	−0.0340813
$184$	3.56418	0.262755
$185$	−0.932851	−0.0685846
$186$	−1.18768	−0.0870848
$187$	−16.8770	−1.23417
$188$	−22.5105	−1.64174
$189$	−0.580333	−0.0422130
$190$	−38.0983	−2.76394
$191$	−8.59581	−0.621971	−0.310985	−	0.950415i	$-0.600659\pi$
$191$	−8.59581	−0.621971	−0.310985	+	0.950415i	$0.600659\pi$
$192$	0.849986	0.0613424
$193$	−0.298363	−0.0214766	−0.0107383	−	0.999942i	$-0.503418\pi$
$193$	−0.298363	−0.0214766	−0.0107383	+	0.999942i	$0.503418\pi$
$194$	−12.0612	−0.865947
$195$	−0.158058	−0.0113188
$196$	−13.5525	−0.968034
$197$	−5.45305	−0.388514	−0.194257	−	0.980951i	$-0.562229\pi$
$197$	−5.45305	−0.388514	−0.194257	+	0.980951i	$0.562229\pi$
$198$	−28.1816	−2.00278
$199$	24.0519	1.70499	0.852497	−	0.522732i	$-0.175087\pi$
$199$	24.0519	1.70499	0.852497	+	0.522732i	$0.175087\pi$
$200$	−0.119049	−0.00841803
$201$	0.905155	0.0638447
$202$	29.7541	2.09349
$203$	−9.47155	−0.664772
$204$	−0.722322	−0.0505727
$205$	−22.8046	−1.59274
$206$	−2.15890	−0.150418
$207$	7.48227	0.520054
$208$	2.24157	0.155425
$209$	34.1128	2.35963
$210$	0.471187	0.0325150
$211$	6.73911	0.463939	0.231970	−	0.972723i	$-0.425483\pi$
$211$	6.73911	0.463939	0.231970	+	0.972723i	$0.425483\pi$
$212$	−5.45539	−0.374678
$213$	0.0702987	0.00481679
$214$	−33.0516	−2.25936
$215$	7.53089	0.513602
$216$	−0.599612	−0.0407984
$217$	10.8360	0.735597
$218$	−13.4930	−0.913859
$219$	−0.358850	−0.0242489
$220$	26.1471	1.76283
$221$	−3.87232	−0.260481
$222$	0.0626188	0.00420270
$223$	−16.1771	−1.08330	−0.541650	−	0.840604i	$-0.682200\pi$
$223$	−16.1771	−1.08330	−0.541650	+	0.840604i	$0.682200\pi$
$224$	−10.6225	−0.709742
$225$	−0.249919	−0.0166612
$226$	−11.0367	−0.734151
$227$	−26.1290	−1.73424	−0.867121	−	0.498098i	$-0.834032\pi$
$227$	−26.1290	−1.73424	−0.867121	+	0.498098i	$0.834032\pi$
$228$	1.46000	0.0966909
$229$	12.0119	0.793769	0.396884	−	0.917869i	$-0.370091\pi$
$229$	12.0119	0.793769	0.396884	+	0.917869i	$0.370091\pi$
$230$	−12.1601	−0.801811
$231$	−0.421895	−0.0277587
$232$	−9.78620	−0.642496
$233$	−13.6031	−0.891171	−0.445585	−	0.895239i	$-0.647004\pi$
$233$	−13.6031	−0.891171	−0.445585	+	0.895239i	$0.647004\pi$
$234$	−6.46609	−0.422702
$235$	19.0741	1.24425
$236$	26.6828	1.73690
$237$	−0.0558143	−0.00362553
$238$	11.5437	0.748270
$239$	7.64295	0.494382	0.247191	−	0.968967i	$-0.420493\pi$
$239$	7.64295	0.494382	0.247191	+	0.968967i	$0.420493\pi$
$240$	−0.354300	−0.0228700
$241$	−2.36458	−0.152316	−0.0761580	−	0.997096i	$-0.524265\pi$
$241$	−2.36458	−0.152316	−0.0761580	+	0.997096i	$0.524265\pi$
$242$	−17.2611	−1.10958
$243$	−1.88866	−0.121157
$244$	17.4994	1.12028
$245$	11.4836	0.733659
$246$	1.53079	0.0975995
$247$	7.82697	0.498018
$248$	11.1960	0.710947
$249$	−0.0954126	−0.00604653
$250$	−23.9317	−1.51357
$251$	24.7759	1.56384	0.781920	−	0.623379i	$-0.214241\pi$
$251$	24.7759	1.56384	0.781920	+	0.623379i	$0.214241\pi$
$252$	11.0046	0.693222
$253$	10.8880	0.684522
$254$	1.75134	0.109889
$255$	0.612054	0.0383283
$256$	0.953651	0.0596032
$257$	−5.60317	−0.349516	−0.174758	−	0.984611i	$-0.555914\pi$
$257$	−5.60317	−0.349516	−0.174758	+	0.984611i	$0.555914\pi$
$258$	−0.505520	−0.0314723
$259$	−0.571316	−0.0354998
$260$	5.99928	0.372060
$261$	−20.5441	−1.27165
$262$	16.2110	1.00152
$263$	−26.5222	−1.63543	−0.817715	−	0.575624i	$-0.804759\pi$
$263$	−26.5222	−1.63543	−0.817715	+	0.575624i	$0.804759\pi$
$264$	−0.435911	−0.0268285
$265$	4.62258	0.283963
$266$	−23.3329	−1.43063
$267$	1.10082	0.0673691
$268$	−34.3562	−2.09864
$269$	5.47546	0.333845	0.166922	−	0.985970i	$-0.446617\pi$
$269$	5.47546	0.333845	0.166922	+	0.985970i	$0.446617\pi$
$270$	2.04572	0.124498
$271$	−5.52672	−0.335724	−0.167862	−	0.985810i	$-0.553686\pi$
$271$	−5.52672	−0.335724	−0.167862	+	0.985810i	$0.553686\pi$
$272$	−8.68010	−0.526309
$273$	−0.0968014	−0.00585869
$274$	−0.803809	−0.0485599
$275$	−0.363674	−0.0219304
$276$	0.465998	0.0280498
$277$	−5.75528	−0.345801	−0.172901	−	0.984939i	$-0.555314\pi$
$277$	−5.75528	−0.345801	−0.172901	+	0.984939i	$0.555314\pi$
$278$	−41.4748	−2.48749
$279$	23.5037	1.40713
$280$	−4.44179	−0.265447
$281$	−21.8993	−1.30641	−0.653203	−	0.757183i	$-0.726575\pi$
$281$	−21.8993	−1.30641	−0.653203	+	0.757183i	$0.726575\pi$
$282$	−1.28037	−0.0762449
$283$	−4.31201	−0.256322	−0.128161	−	0.991753i	$-0.540907\pi$
$283$	−4.31201	−0.256322	−0.128161	+	0.991753i	$0.540907\pi$
$284$	−2.66827	−0.158332
$285$	−1.23712	−0.0732806
$286$	−9.40927	−0.556382
$287$	−13.9665	−0.824414
$288$	−23.0405	−1.35767
$289$	−2.00511	−0.117948
$290$	33.3879	1.96061
$291$	−0.391650	−0.0229589
$292$	13.6206	0.797083
$293$	8.12801	0.474844	0.237422	−	0.971407i	$-0.423698\pi$
$293$	8.12801	0.474844	0.237422	+	0.971407i	$0.423698\pi$
$294$	−0.770849	−0.0449569
$295$	−22.6095	−1.31637
$296$	−0.590295	−0.0343102
$297$	−1.83171	−0.106287
$298$	−34.3428	−1.98942
$299$	2.49818	0.144474
$300$	−0.0155650	−0.000898645 0
$301$	4.61222	0.265844
$302$	−30.0112	−1.72695
$303$	0.966168	0.0555049
$304$	17.5447	1.00626
$305$	−14.8280	−0.849046
$306$	25.0388	1.43137
$307$	−17.0601	−0.973672	−0.486836	−	0.873493i	$-0.661849\pi$
$307$	−17.0601	−0.973672	−0.486836	+	0.873493i	$0.661849\pi$
$308$	16.0135	0.912454
$309$	−0.0701034	−0.00398804
$310$	−38.1978	−2.16949
$311$	3.73209	0.211628	0.105814	−	0.994386i	$-0.466255\pi$
$311$	3.73209	0.211628	0.105814	+	0.994386i	$0.466255\pi$
$312$	−0.100017	−0.00566236
$313$	−29.2567	−1.65369	−0.826844	−	0.562431i	$-0.809866\pi$
$313$	−29.2567	−1.65369	−0.826844	+	0.562431i	$0.809866\pi$
$314$	14.2718	0.805402
$315$	−9.32462	−0.525383
$316$	2.11849	0.119175
$317$	−6.28990	−0.353276	−0.176638	−	0.984276i	$-0.556522\pi$
$317$	−6.28990	−0.353276	−0.176638	+	0.984276i	$0.556522\pi$
$318$	−0.310297	−0.0174006
$319$	−29.8952	−1.67381
$320$	27.3371	1.52819
$321$	−1.07325	−0.0599028
$322$	−7.44731	−0.415022
$323$	−30.3086	−1.68641
$324$	23.8300	1.32389
$325$	−0.0834429	−0.00462858
$326$	−28.8230	−1.59636
$327$	−0.438141	−0.0242293
$328$	−14.4304	−0.796788
$329$	11.6817	0.644034
$330$	1.48721	0.0818685
$331$	−31.0623	−1.70734	−0.853670	−	0.520815i	$-0.825628\pi$
$331$	−31.0623	−1.70734	−0.853670	+	0.520815i	$0.825628\pi$
$332$	3.62149	0.198755
$333$	−1.23920	−0.0679079
$334$	8.52314	0.466365
$335$	29.1114	1.59053
$336$	−0.216988	−0.0118376
$337$	7.11760	0.387720	0.193860	−	0.981029i	$-0.437899\pi$
$337$	7.11760	0.387720	0.193860	+	0.981029i	$0.437899\pi$
$338$	−2.15890	−0.117429
$339$	−0.358382	−0.0194646
$340$	−23.2312	−1.25989
$341$	34.2019	1.85214
$342$	−50.6099	−2.73667
$343$	16.6989	0.901654
$344$	4.76544	0.256935
$345$	−0.394859	−0.0212585
$346$	−36.5131	−1.96296
$347$	27.1881	1.45954	0.729768	−	0.683695i	$-0.239628\pi$
$347$	27.1881	1.45954	0.729768	+	0.683695i	$0.239628\pi$
$348$	−1.27949	−0.0685880
$349$	−14.4384	−0.772867	−0.386434	−	0.922317i	$-0.626293\pi$
$349$	−14.4384	−0.772867	−0.386434	+	0.922317i	$0.626293\pi$
$350$	0.248751	0.0132963
$351$	−0.420276	−0.0224327
$352$	−33.5278	−1.78704
$353$	−13.1331	−0.699004	−0.349502	−	0.936936i	$-0.613649\pi$
$353$	−13.1331	−0.699004	−0.349502	+	0.936936i	$0.613649\pi$
$354$	1.51769	0.0806643
$355$	2.26093	0.119998
$356$	−41.7828	−2.21449
$357$	0.374846	0.0198390
$358$	11.2748	0.595891
$359$	4.10037	0.216409	0.108205	−	0.994129i	$-0.465490\pi$
$359$	4.10037	0.216409	0.108205	+	0.994129i	$0.465490\pi$
$360$	−9.63439	−0.507777
$361$	42.2614	2.22429
$362$	6.13089	0.322232
$363$	−0.560499	−0.0294185
$364$	3.67420	0.192581
$365$	−11.5413	−0.604097
$366$	0.995345	0.0520275
$367$	−32.1460	−1.67801	−0.839003	−	0.544127i	$-0.816861\pi$
$367$	−32.1460	−1.67801	−0.839003	+	0.544127i	$0.816861\pi$
$368$	5.59986	0.291913
$369$	−30.2937	−1.57703
$370$	2.01393	0.104699
$371$	2.83105	0.146981
$372$	1.46382	0.0758953
$373$	−31.5589	−1.63406	−0.817029	−	0.576597i	$-0.804380\pi$
$373$	−31.5589	−1.63406	−0.817029	+	0.576597i	$0.804380\pi$
$374$	36.4357	1.88405
$375$	−0.777104	−0.0401295
$376$	12.0698	0.622452
$377$	−6.85927	−0.353271
$378$	1.25288	0.0644412
$379$	−2.24523	−0.115330	−0.0576649	−	0.998336i	$-0.518366\pi$
$379$	−2.24523	−0.115330	−0.0576649	+	0.998336i	$0.518366\pi$
$380$	46.9562	2.40880
$381$	0.0568692	0.00291350
$382$	18.5575	0.949484
$383$	−26.6328	−1.36087	−0.680437	−	0.732807i	$-0.738210\pi$
$383$	−26.6328	−1.36087	−0.680437	+	0.732807i	$0.738210\pi$
$384$	−0.756458	−0.0386028
$385$	−13.5689	−0.691536
$386$	0.644136	0.0327857
$387$	10.0041	0.508535
$388$	14.8655	0.754682
$389$	10.3356	0.524036	0.262018	−	0.965063i	$-0.415612\pi$
$389$	10.3356	0.524036	0.262018	+	0.965063i	$0.415612\pi$
$390$	0.341233	0.0172790
$391$	−9.67377	−0.489224
$392$	7.26665	0.367021
$393$	0.526400	0.0265534
$394$	11.7726	0.593094
$395$	−1.79509	−0.0903207
$396$	34.7339	1.74544
$397$	−5.60341	−0.281227	−0.140614	−	0.990065i	$-0.544907\pi$
$397$	−5.60341	−0.281227	−0.140614	+	0.990065i	$0.544907\pi$
$398$	−51.9257	−2.60280
$399$	−0.757661	−0.0379305
$400$	−0.187044	−0.00935218
$401$	18.0055	0.899150	0.449575	−	0.893243i	$-0.351575\pi$
$401$	18.0055	0.899150	0.449575	+	0.893243i	$0.351575\pi$
$402$	−1.95414	−0.0974636
$403$	7.84742	0.390908
$404$	−36.6720	−1.82450
$405$	−20.1922	−1.00336
$406$	20.4481	1.01482
$407$	−1.80325	−0.0893839
$408$	0.387299	0.0191742
$409$	−19.8899	−0.983490	−0.491745	−	0.870739i	$-0.663641\pi$
$409$	−19.8899	−0.983490	−0.491745	+	0.870739i	$0.663641\pi$
$410$	49.2329	2.43144
$411$	−0.0261011	−0.00128747
$412$	2.66085	0.131091
$413$	−13.8470	−0.681364
$414$	−16.1535	−0.793900
$415$	−3.06864	−0.150634
$416$	−7.69276	−0.377169
$417$	−1.34676	−0.0659511
$418$	−73.6460	−3.60215
$419$	22.7963	1.11367	0.556836	−	0.830622i	$-0.312015\pi$
$419$	22.7963	1.11367	0.556836	+	0.830622i	$0.312015\pi$
$420$	−0.580739	−0.0283372
$421$	−1.80632	−0.0880349	−0.0440174	−	0.999031i	$-0.514016\pi$
$421$	−1.80632	−0.0880349	−0.0440174	+	0.999031i	$0.514016\pi$
$422$	−14.5491	−0.708237
$423$	25.3381	1.23198
$424$	2.92510	0.142056
$425$	0.323118	0.0156735
$426$	−0.151768	−0.00735318
$427$	−9.08124	−0.439472
$428$	40.7362	1.96906
$429$	−0.305536	−0.0147514
$430$	−16.2584	−0.784052
$431$	−31.0473	−1.49550	−0.747748	−	0.663982i	$-0.768865\pi$
$431$	−31.0473	−1.49550	−0.747748	+	0.663982i	$0.768865\pi$
$432$	−0.942079	−0.0453258
$433$	−8.71565	−0.418848	−0.209424	−	0.977825i	$-0.567159\pi$
$433$	−8.71565	−0.418848	−0.209424	+	0.977825i	$0.567159\pi$
$434$	−23.3939	−1.12294
$435$	1.08417	0.0519818
$436$	16.6301	0.796439
$437$	19.5532	0.935356
$438$	0.774722	0.0370176
$439$	11.2569	0.537262	0.268631	−	0.963243i	$-0.413429\pi$
$439$	11.2569	0.537262	0.268631	+	0.963243i	$0.413429\pi$
$440$	−14.0197	−0.668362
$441$	15.2548	0.726420
$442$	8.35996	0.397643
$443$	−9.98243	−0.474280	−0.237140	−	0.971476i	$-0.576210\pi$
$443$	−9.98243	−0.474280	−0.237140	+	0.971476i	$0.576210\pi$
$444$	−0.0771779	−0.00366270
$445$	35.4043	1.67833
$446$	34.9248	1.65374
$447$	−1.11517	−0.0527458
$448$	16.7423	0.791000
$449$	21.3256	1.00642	0.503209	−	0.864165i	$-0.332152\pi$
$449$	21.3256	1.00642	0.503209	+	0.864165i	$0.332152\pi$
$450$	0.539550	0.0254346
$451$	−44.0826	−2.07577
$452$	13.6028	0.639821
$453$	−0.974518	−0.0457868
$454$	56.4099	2.64745
$455$	−3.11331	−0.145954
$456$	−0.782832	−0.0366595
$457$	34.4973	1.61372	0.806859	−	0.590744i	$-0.201166\pi$
$457$	34.4973	1.61372	0.806859	+	0.590744i	$0.201166\pi$
$458$	−25.9325	−1.21175
$459$	1.62744	0.0759625
$460$	14.9873	0.698787
$461$	12.6810	0.590613	0.295306	−	0.955403i	$-0.404578\pi$
$461$	12.6810	0.590613	0.295306	+	0.955403i	$0.404578\pi$
$462$	0.910830	0.0423757
$463$	0.635241	0.0295222	0.0147611	−	0.999891i	$-0.495301\pi$
$463$	0.635241	0.0295222	0.0147611	+	0.999891i	$0.495301\pi$
$464$	−15.3756	−0.713793
$465$	−1.24035	−0.0575200
$466$	29.3678	1.36044
$467$	5.55253	0.256941	0.128470	−	0.991713i	$-0.458993\pi$
$467$	5.55253	0.256941	0.128470	+	0.991713i	$0.458993\pi$
$468$	7.96948	0.368389
$469$	17.8290	0.823266
$470$	−41.1790	−1.89944
$471$	0.463430	0.0213537
$472$	−14.3070	−0.658531
$473$	14.5576	0.669360
$474$	0.120498	0.00553464
$475$	−0.653105	−0.0299665
$476$	−14.2277	−0.652126
$477$	6.14065	0.281161
$478$	−16.5004	−0.754710
$479$	21.7252	0.992652	0.496326	−	0.868136i	$-0.334682\pi$
$479$	21.7252	0.992652	0.496326	+	0.868136i	$0.334682\pi$
$480$	1.21591	0.0554983
$481$	−0.413746	−0.0188652
$482$	5.10490	0.232522
$483$	−0.241828	−0.0110035
$484$	21.2743	0.967016
$485$	−12.5962	−0.571963
$486$	4.07742	0.184956
$487$	−4.95032	−0.224320	−0.112160	−	0.993690i	$-0.535777\pi$
$487$	−4.95032	−0.224320	−0.112160	+	0.993690i	$0.535777\pi$
$488$	−9.38292	−0.424745
$489$	−0.935936	−0.0423245
$490$	−24.7919	−1.11998
$491$	−20.3257	−0.917285	−0.458643	−	0.888621i	$-0.651664\pi$
$491$	−20.3257	−0.917285	−0.458643	+	0.888621i	$0.651664\pi$
$492$	−1.88670	−0.0850590
$493$	26.5613	1.19626
$494$	−16.8976	−0.760261
$495$	−29.4314	−1.32284
$496$	17.5906	0.789841
$497$	1.38469	0.0621116
$498$	0.205986	0.00923047
$499$	22.1478	0.991471	0.495736	−	0.868473i	$-0.334898\pi$
$499$	22.1478	0.991471	0.495736	+	0.868473i	$0.334898\pi$
$500$	29.4958	1.31909
$501$	0.276761	0.0123648
$502$	−53.4887	−2.38732
$503$	19.3200	0.861437	0.430718	−	0.902486i	$-0.358260\pi$
$503$	19.3200	0.861437	0.430718	+	0.902486i	$0.358260\pi$
$504$	−5.90049	−0.262829
$505$	31.0737	1.38276
$506$	−23.5061	−1.04497
$507$	−0.0701034	−0.00311340
$508$	−2.15853	−0.0957694
$509$	25.8979	1.14791	0.573953	−	0.818888i	$-0.305409\pi$
$509$	25.8979	1.14791	0.573953	+	0.818888i	$0.305409\pi$
$510$	−1.32136	−0.0585109
$511$	−7.06833	−0.312685
$512$	−23.6401	−1.04475
$513$	−3.28948	−0.145234
$514$	12.0967	0.533562
$515$	−2.25465	−0.0993517
$516$	0.623055	0.0274285
$517$	36.8712	1.62159
$518$	1.23341	0.0541931
$519$	−1.18565	−0.0520441
$520$	−3.21673	−0.141063
$521$	−39.3982	−1.72606	−0.863032	−	0.505149i	$-0.831438\pi$
$521$	−39.3982	−1.72606	−0.863032	+	0.505149i	$0.831438\pi$
$522$	44.3527	1.94126
$523$	29.5576	1.29246	0.646231	−	0.763142i	$-0.276344\pi$
$523$	29.5576	1.29246	0.646231	+	0.763142i	$0.276344\pi$
$524$	−19.9801	−0.872835
$525$	0.00807739	0.000352526 0
$526$	57.2588	2.49660
$527$	−30.3878	−1.32371
$528$	−0.684881	−0.0298056
$529$	−16.7591	−0.728656
$530$	−9.97969	−0.433490
$531$	−30.0345	−1.30339
$532$	28.7579	1.24681
$533$	−10.1145	−0.438107
$534$	−2.37656	−0.102844
$535$	−34.5175	−1.49232
$536$	18.4213	0.795678
$537$	0.366112	0.0157989
$538$	−11.8210	−0.509638
$539$	22.1984	0.956152
$540$	−2.52135	−0.108502
$541$	42.1053	1.81025	0.905124	−	0.425149i	$-0.139778\pi$
$541$	42.1053	1.81025	0.905124	+	0.425149i	$0.139778\pi$
$542$	11.9316	0.512508
$543$	0.199081	0.00854338
$544$	29.7888	1.27719
$545$	−14.0914	−0.603609
$546$	0.208985	0.00894371
$547$	−16.6100	−0.710191	−0.355096	−	0.934830i	$-0.615552\pi$
$547$	−16.6100	−0.710191	−0.355096	+	0.934830i	$0.615552\pi$
$548$	0.990697	0.0423205
$549$	−19.6975	−0.840670
$550$	0.785137	0.0334784
$551$	−53.6873	−2.28716
$552$	−0.249861	−0.0106348
$553$	−1.09938	−0.0467506
$554$	12.4251	0.527891
$555$	0.0653960	0.00277591
$556$	51.1178	2.16788
$557$	2.20856	0.0935798	0.0467899	−	0.998905i	$-0.485101\pi$
$557$	2.20856	0.0935798	0.0467899	+	0.998905i	$0.485101\pi$
$558$	−50.7422	−2.14809
$559$	3.34016	0.141274
$560$	−6.97871	−0.294904
$561$	1.18313	0.0499519
$562$	47.2785	1.99432
$563$	43.2897	1.82444	0.912222	−	0.409697i	$-0.134366\pi$
$563$	43.2897	1.82444	0.912222	+	0.409697i	$0.134366\pi$
$564$	1.57806	0.0664483
$565$	−11.5262	−0.484911
$566$	9.30919	0.391295
$567$	−12.3665	−0.519344
$568$	1.43069	0.0600303
$569$	27.7343	1.16268	0.581341	−	0.813660i	$-0.302528\pi$
$569$	27.7343	1.16268	0.581341	+	0.813660i	$0.302528\pi$
$570$	2.67082	0.111868
$571$	−37.3705	−1.56390	−0.781952	−	0.623338i	$-0.785776\pi$
$571$	−37.3705	−1.56390	−0.781952	+	0.623338i	$0.785776\pi$
$572$	11.5969	0.484893
$573$	0.602595	0.0251738
$574$	30.1522	1.25853
$575$	−0.208456	−0.00869320
$576$	36.3147	1.51311
$577$	−38.3145	−1.59506	−0.797528	−	0.603283i	$-0.793859\pi$
$577$	−38.3145	−1.59506	−0.797528	+	0.603283i	$0.793859\pi$
$578$	4.32884	0.180056
$579$	0.0209162	0.000869249 0
$580$	−41.1507	−1.70869
$581$	−1.87936	−0.0779690
$582$	0.845534	0.0350485
$583$	8.93570	0.370079
$584$	−7.30315	−0.302207
$585$	−6.75287	−0.279197
$586$	−17.5476	−0.724883
$587$	40.3147	1.66397	0.831984	−	0.554800i	$-0.187205\pi$
$587$	40.3147	1.66397	0.831984	+	0.554800i	$0.187205\pi$
$588$	0.950074	0.0391804
$589$	61.4215	2.53083
$590$	48.8116	2.00954
$591$	0.382277	0.0157248
$592$	−0.927442	−0.0381176
$593$	13.9522	0.572948	0.286474	−	0.958088i	$-0.407517\pi$
$593$	13.9522	0.572948	0.286474	+	0.958088i	$0.407517\pi$
$594$	3.95449	0.162255
$595$	12.0557	0.494236
$596$	42.3276	1.73381
$597$	−1.68612	−0.0690083
$598$	−5.39333	−0.220550
$599$	15.1904	0.620663	0.310332	−	0.950628i	$-0.399560\pi$
$599$	15.1904	0.620663	0.310332	+	0.950628i	$0.399560\pi$
$600$	0.00834573	0.000340713 0
$601$	−12.8225	−0.523043	−0.261521	−	0.965198i	$-0.584224\pi$
$601$	−12.8225	−0.523043	−0.261521	+	0.965198i	$0.584224\pi$
$602$	−9.95732	−0.405830
$603$	38.6717	1.57483
$604$	36.9889	1.50506
$605$	−18.0266	−0.732887
$606$	−2.08586	−0.0847323
$607$	48.7292	1.97786	0.988928	−	0.148393i	$-0.0474100\pi$
$607$	48.7292	1.97786	0.988928	+	0.148393i	$0.0474100\pi$
$608$	−60.2110	−2.44188
$609$	0.663987	0.0269061
$610$	32.0121	1.29613
$611$	8.45988	0.342250
$612$	−30.8604	−1.24746
$613$	35.2860	1.42519	0.712593	−	0.701578i	$-0.247521\pi$
$613$	35.2860	1.42519	0.712593	+	0.701578i	$0.247521\pi$
$614$	36.8311	1.48638
$615$	1.59868	0.0644650
$616$	−8.58622	−0.345949
$617$	8.34215	0.335842	0.167921	−	0.985800i	$-0.446295\pi$
$617$	8.34215	0.335842	0.167921	+	0.985800i	$0.446295\pi$
$618$	0.151346	0.00608804
$619$	−11.4138	−0.458759	−0.229380	−	0.973337i	$-0.573670\pi$
$619$	−11.4138	−0.458759	−0.229380	+	0.973337i	$0.573670\pi$
$620$	47.0789	1.89074
$621$	−1.04993	−0.0421321
$622$	−8.05722	−0.323065
$623$	21.6830	0.868713
$624$	−0.157142	−0.00629071
$625$	−25.4103	−1.01641
$626$	63.1624	2.52448
$627$	−2.39142	−0.0955041
$628$	−17.5900	−0.701917
$629$	1.60216	0.0638822
$630$	20.1309	0.802035
$631$	−7.87844	−0.313636	−0.156818	−	0.987628i	$-0.550124\pi$
$631$	−7.87844	−0.313636	−0.156818	+	0.987628i	$0.550124\pi$
$632$	−1.13591	−0.0451840
$633$	−0.472434	−0.0187776
$634$	13.5793	0.539301
$635$	1.82901	0.0725822
$636$	0.382441	0.0151648
$637$	5.09329	0.201803
$638$	64.5408	2.55519
$639$	3.00343	0.118814
$640$	−24.3290	−0.961690
$641$	−13.9523	−0.551082	−0.275541	−	0.961289i	$-0.588857\pi$
$641$	−13.9523	−0.551082	−0.275541	+	0.961289i	$0.588857\pi$
$642$	2.31703	0.0914459
$643$	−3.74049	−0.147510	−0.0737552	−	0.997276i	$-0.523498\pi$
$643$	−3.74049	−0.147510	−0.0737552	+	0.997276i	$0.523498\pi$
$644$	9.17883	0.361697
$645$	−0.527941	−0.0207876
$646$	65.4331	2.57443
$647$	−37.5837	−1.47757	−0.738784	−	0.673942i	$-0.764600\pi$
$647$	−37.5837	−1.47757	−0.738784	+	0.673942i	$0.764600\pi$
$648$	−12.7773	−0.501941
$649$	−43.7054	−1.71559
$650$	0.180145	0.00706587
$651$	−0.759642	−0.0297727
$652$	35.5245	1.39125
$653$	−6.74154	−0.263817	−0.131908	−	0.991262i	$-0.542110\pi$
$653$	−6.74154	−0.263817	−0.131908	+	0.991262i	$0.542110\pi$
$654$	0.945903	0.0369877
$655$	16.9300	0.661509
$656$	−22.6724	−0.885207
$657$	−15.3315	−0.598137
$658$	−25.2197	−0.983165
$659$	−10.8066	−0.420965	−0.210483	−	0.977598i	$-0.567504\pi$
$659$	−10.8066	−0.420965	−0.210483	+	0.977598i	$0.567504\pi$
$660$	−1.83300	−0.0713493
$661$	39.3533	1.53067	0.765333	−	0.643634i	$-0.222574\pi$
$661$	39.3533	1.53067	0.765333	+	0.643634i	$0.222574\pi$
$662$	67.0604	2.60638
$663$	0.271463	0.0105427
$664$	−1.94179	−0.0753562
$665$	−24.3677	−0.944940
$666$	2.67532	0.103666
$667$	−17.1357	−0.663498
$668$	−10.5048	−0.406442
$669$	1.13407	0.0438457
$670$	−62.8486	−2.42805
$671$	−28.6633	−1.10653
$672$	0.744670	0.0287263
$673$	−11.0523	−0.426034	−0.213017	−	0.977048i	$-0.568329\pi$
$673$	−11.0523	−0.426034	−0.213017	+	0.977048i	$0.568329\pi$
$674$	−15.3662	−0.591884
$675$	0.0350690	0.00134981
$676$	2.66085	0.102340
$677$	26.0074	0.999545	0.499773	−	0.866157i	$-0.333417\pi$
$677$	26.0074	0.999545	0.499773	+	0.866157i	$0.333417\pi$
$678$	0.773711	0.0297142
$679$	−7.71440	−0.296052
$680$	12.4562	0.477675
$681$	1.83173	0.0701920
$682$	−73.8385	−2.82742
$683$	48.6879	1.86299	0.931495	−	0.363755i	$-0.118505\pi$
$683$	48.6879	1.86299	0.931495	+	0.363755i	$0.118505\pi$
$684$	62.3768	2.38504
$685$	−0.839459	−0.0320741
$686$	−36.0512	−1.37644
$687$	−0.842075	−0.0321272
$688$	7.48722	0.285448
$689$	2.05024	0.0781081
$690$	0.852461	0.0324526
$691$	−43.0322	−1.63702	−0.818511	−	0.574492i	$-0.805200\pi$
$691$	−43.0322	−1.63702	−0.818511	+	0.574492i	$0.805200\pi$
$692$	45.0025	1.71074
$693$	−18.0250	−0.684713
$694$	−58.6965	−2.22809
$695$	−43.3142	−1.64300
$696$	0.686046	0.0260045
$697$	39.1665	1.48354
$698$	31.1710	1.17984
$699$	0.953625	0.0360694
$700$	−0.306586	−0.0115879
$701$	−43.0872	−1.62738	−0.813691	−	0.581297i	$-0.802545\pi$
$701$	−43.0872	−1.62738	−0.813691	+	0.581297i	$0.802545\pi$
$702$	0.907333	0.0342451
$703$	−3.23837	−0.122138
$704$	52.8440	1.99163
$705$	−1.33716	−0.0503602
$706$	28.3531	1.06708
$707$	19.0308	0.715726
$708$	−1.87056	−0.0702998
$709$	14.2202	0.534051	0.267026	−	0.963689i	$-0.413959\pi$
$709$	14.2202	0.534051	0.267026	+	0.963689i	$0.413959\pi$
$710$	−4.88113	−0.183185
$711$	−2.38460	−0.0894296
$712$	22.4034	0.839602
$713$	19.6043	0.734187
$714$	−0.809256	−0.0302856
$715$	−9.82658	−0.367493
$716$	−13.8962	−0.519325
$717$	−0.535797	−0.0200097
$718$	−8.85228	−0.330364
$719$	23.1318	0.862672	0.431336	−	0.902191i	$-0.358042\pi$
$719$	23.1318	0.862672	0.431336	+	0.902191i	$0.358042\pi$
$720$	−15.1371	−0.564125
$721$	−1.38084	−0.0514251
$722$	−91.2382	−3.39554
$723$	0.165765	0.00616487
$724$	−7.55634	−0.280829
$725$	0.572358	0.0212568
$726$	1.21006	0.0449096
$727$	−12.3408	−0.457696	−0.228848	−	0.973462i	$-0.573496\pi$
$727$	−12.3408	−0.457696	−0.228848	+	0.973462i	$0.573496\pi$
$728$	−1.97006	−0.0730151
$729$	−26.7350	−0.990184
$730$	24.9164	0.922199
$731$	−12.9342	−0.478388
$732$	−1.22677	−0.0453426
$733$	−33.2848	−1.22940	−0.614702	−	0.788760i	$-0.710724\pi$
$733$	−33.2848	−1.22940	−0.614702	+	0.788760i	$0.710724\pi$
$734$	69.3999	2.56160
$735$	−0.805037	−0.0296942
$736$	−19.2179	−0.708382
$737$	56.2739	2.07288
$738$	65.4012	2.40745
$739$	21.6499	0.796404	0.398202	−	0.917298i	$-0.369634\pi$
$739$	21.6499	0.796404	0.398202	+	0.917298i	$0.369634\pi$
$740$	−2.48218	−0.0912467
$741$	−0.548697	−0.0201569
$742$	−6.11196	−0.224377
$743$	−4.76646	−0.174865	−0.0874323	−	0.996170i	$-0.527866\pi$
$743$	−4.76646	−0.174865	−0.0874323	+	0.996170i	$0.527866\pi$
$744$	−0.784878	−0.0287750
$745$	−35.8659	−1.31403
$746$	68.1325	2.49451
$747$	−4.07640	−0.149147
$748$	−44.9071	−1.64197
$749$	−21.1399	−0.772436
$750$	1.67769	0.0612605
$751$	7.04305	0.257005	0.128502	−	0.991709i	$-0.458983\pi$
$751$	7.04305	0.257005	0.128502	+	0.991709i	$0.458983\pi$
$752$	18.9634	0.691526
$753$	−1.73687	−0.0632952
$754$	14.8085	0.539293
$755$	−31.3422	−1.14066
$756$	−1.54418	−0.0561612
$757$	−49.4103	−1.79585	−0.897924	−	0.440150i	$-0.854925\pi$
$757$	−49.4103	−1.79585	−0.897924	+	0.440150i	$0.854925\pi$
$758$	4.84723	0.176059
$759$	−0.763284	−0.0277055
$760$	−25.1773	−0.913275
$761$	36.2519	1.31413	0.657065	−	0.753834i	$-0.271798\pi$
$761$	36.2519	1.31413	0.657065	+	0.753834i	$0.271798\pi$
$762$	−0.122775	−0.00444766
$763$	−8.63014	−0.312432
$764$	−22.8722	−0.827486
$765$	26.1493	0.945429
$766$	57.4976	2.07747
$767$	−10.0279	−0.362088
$768$	−0.0668541	−0.00241239
$769$	−6.76393	−0.243913	−0.121957	−	0.992535i	$-0.538917\pi$
$769$	−6.76393	−0.243913	−0.121957	+	0.992535i	$0.538917\pi$
$770$	29.2939	1.05568
$771$	0.392801	0.0141464
$772$	−0.793899	−0.0285731
$773$	18.4946	0.665205	0.332602	−	0.943067i	$-0.392073\pi$
$773$	18.4946	0.665205	0.332602	+	0.943067i	$0.392073\pi$
$774$	−21.5978	−0.776316
$775$	−0.654812	−0.0235215
$776$	−7.97068	−0.286131
$777$	0.0400511	0.00143683
$778$	−22.3135	−0.799979
$779$	−79.1657	−2.83641
$780$	−0.420570	−0.0150588
$781$	4.37051	0.156389
$782$	20.8847	0.746836
$783$	2.88279	0.103022
$784$	11.4170	0.407749
$785$	14.9047	0.531972
$786$	−1.13645	−0.0405357
$787$	−18.0781	−0.644413	−0.322206	−	0.946669i	$-0.604425\pi$
$787$	−18.0781	−0.644413	−0.322206	+	0.946669i	$0.604425\pi$
$788$	−14.5097	−0.516888
$789$	1.85930	0.0661927
$790$	3.87542	0.137881
$791$	−7.05911	−0.250993
$792$	−18.6238	−0.661768
$793$	−6.57661	−0.233542
$794$	12.0972	0.429314
$795$	−0.324058	−0.0114932
$796$	63.9985	2.26837
$797$	−14.4778	−0.512830	−0.256415	−	0.966567i	$-0.582541\pi$
$797$	−14.4778	−0.512830	−0.256415	+	0.966567i	$0.582541\pi$
$798$	1.63572	0.0579037
$799$	−32.7594	−1.15894
$800$	0.641906	0.0226948
$801$	47.0313	1.66177
$802$	−38.8720	−1.37262
$803$	−22.3099	−0.787299
$804$	2.40848	0.0849406
$805$	−7.77761	−0.274125
$806$	−16.9418	−0.596750
$807$	−0.383848	−0.0135121
$808$	19.6630	0.691742
$809$	−15.2361	−0.535672	−0.267836	−	0.963464i	$-0.586309\pi$
$809$	−15.2361	−0.535672	−0.267836	+	0.963464i	$0.586309\pi$
$810$	43.5929	1.53170
$811$	−17.4066	−0.611227	−0.305614	−	0.952156i	$-0.598862\pi$
$811$	−17.4066	−0.611227	−0.305614	+	0.952156i	$0.598862\pi$
$812$	−25.2024	−0.884430
$813$	0.387442	0.0135882
$814$	3.89304	0.136451
$815$	−30.1014	−1.05440
$816$	0.608504	0.0213019
$817$	26.1433	0.914639
$818$	42.9402	1.50137
$819$	−4.13573	−0.144514
$820$	−60.6797	−2.11903
$821$	−28.3139	−0.988162	−0.494081	−	0.869416i	$-0.664495\pi$
$821$	−28.3139	−0.988162	−0.494081	+	0.869416i	$0.664495\pi$
$822$	0.0563497	0.00196542
$823$	−21.9297	−0.764423	−0.382211	−	0.924075i	$-0.624837\pi$
$823$	−21.9297	−0.764423	−0.382211	+	0.924075i	$0.624837\pi$
$824$	−1.42671	−0.0497018
$825$	0.0254948	0.000887615 0
$826$	29.8942	1.04015
$827$	18.9314	0.658309	0.329154	−	0.944276i	$-0.393236\pi$
$827$	18.9314	0.658309	0.329154	+	0.944276i	$0.393236\pi$
$828$	19.9092	0.691893
$829$	11.6327	0.404021	0.202011	−	0.979383i	$-0.435252\pi$
$829$	11.6327	0.404021	0.202011	+	0.979383i	$0.435252\pi$
$830$	6.62489	0.229953
$831$	0.403465	0.0139960
$832$	12.1247	0.420350
$833$	−19.7229	−0.683356
$834$	2.90752	0.100679
$835$	8.90114	0.308037
$836$	90.7690	3.13931
$837$	−3.29808	−0.113998
$838$	−49.2149	−1.70010
$839$	−17.4479	−0.602370	−0.301185	−	0.953566i	$-0.597382\pi$
$839$	−17.4479	−0.602370	−0.301185	+	0.953566i	$0.597382\pi$
$840$	0.311384	0.0107438
$841$	18.0496	0.622401
$842$	3.89967	0.134392
$843$	1.53522	0.0528757
$844$	17.9318	0.617236
$845$	−2.25465	−0.0775623
$846$	−54.7023	−1.88070
$847$	−11.0402	−0.379347
$848$	4.59577	0.157820
$849$	0.302286	0.0103744
$850$	−0.697580	−0.0239268
$851$	−1.03361	−0.0354318
$852$	0.187054	0.00640838
$853$	47.6542	1.63165	0.815825	−	0.578299i	$-0.196283\pi$
$853$	47.6542	1.63165	0.815825	+	0.578299i	$0.196283\pi$
$854$	19.6055	0.670886
$855$	−52.8545	−1.80759
$856$	−21.8422	−0.746551
$857$	22.7170	0.775998	0.387999	−	0.921660i	$-0.373166\pi$
$857$	22.7170	0.775998	0.387999	+	0.921660i	$0.373166\pi$
$858$	0.659621	0.0225191
$859$	−49.1655	−1.67751	−0.838753	−	0.544512i	$-0.816715\pi$
$859$	−49.1655	−1.67751	−0.838753	+	0.544512i	$0.816715\pi$
$860$	20.0386	0.683310
$861$	0.979096	0.0333675
$862$	67.0281	2.28299
$863$	−14.9380	−0.508494	−0.254247	−	0.967139i	$-0.581828\pi$
$863$	−14.9380	−0.508494	−0.254247	+	0.967139i	$0.581828\pi$
$864$	3.23308	0.109992
$865$	−38.1325	−1.29654
$866$	18.8162	0.639401
$867$	0.140565	0.00477384
$868$	28.8330	0.978657
$869$	−3.47001	−0.117712
$870$	−2.34061	−0.0793540
$871$	12.9117	0.437497
$872$	−8.91684	−0.301962
$873$	−16.7328	−0.566320
$874$	−42.2134	−1.42789
$875$	−15.3067	−0.517462
$876$	−0.954847	−0.0322613
$877$	−16.8230	−0.568074	−0.284037	−	0.958813i	$-0.591674\pi$
$877$	−16.8230	−0.568074	−0.284037	+	0.958813i	$0.591674\pi$
$878$	−24.3025	−0.820170
$879$	−0.569801	−0.0192189
$880$	−22.0270	−0.742530
$881$	20.4681	0.689587	0.344794	−	0.938679i	$-0.387949\pi$
$881$	20.4681	0.689587	0.344794	+	0.938679i	$0.387949\pi$
$882$	−32.9337	−1.10893
$883$	−47.9523	−1.61372	−0.806861	−	0.590742i	$-0.798835\pi$
$883$	−47.9523	−1.61372	−0.806861	+	0.590742i	$0.798835\pi$
$884$	−10.3037	−0.346550
$885$	1.58500	0.0532792
$886$	21.5511	0.724023
$887$	−22.2898	−0.748417	−0.374208	−	0.927345i	$-0.622086\pi$
$887$	−22.2898	−0.748417	−0.374208	+	0.927345i	$0.622086\pi$
$888$	0.0413817	0.00138868
$889$	1.12016	0.0375690
$890$	−76.4344	−2.56209
$891$	−39.0326	−1.30764
$892$	−43.0449	−1.44125
$893$	66.2152	2.21581
$894$	2.40754	0.0805203
$895$	11.7748	0.393589
$896$	−14.9001	−0.497777
$897$	−0.175131	−0.00584745
$898$	−46.0399	−1.53637
$899$	−53.8276	−1.79525
$900$	−0.664996	−0.0221665
$901$	−7.93921	−0.264493
$902$	95.1699	3.16881
$903$	−0.323332	−0.0107598
$904$	−7.29362	−0.242582
$905$	6.40280	0.212836
$906$	2.10389	0.0698970
$907$	−12.4035	−0.411852	−0.205926	−	0.978568i	$-0.566021\pi$
$907$	−12.4035	−0.411852	−0.205926	+	0.978568i	$0.566021\pi$
$908$	−69.5253	−2.30728
$909$	41.2784	1.36912
$910$	6.72132	0.222809
$911$	30.6481	1.01542	0.507709	−	0.861529i	$-0.330492\pi$
$911$	30.6481	1.01542	0.507709	+	0.861529i	$0.330492\pi$
$912$	−1.22995	−0.0407275
$913$	−5.93185	−0.196316
$914$	−74.4763	−2.46346
$915$	1.03949	0.0343645
$916$	31.9619	1.05605
$917$	10.3686	0.342401
$918$	−3.51349	−0.115962
$919$	51.6532	1.70388	0.851941	−	0.523638i	$-0.175426\pi$
$919$	51.6532	1.70388	0.851941	+	0.523638i	$0.175426\pi$
$920$	−8.03599	−0.264939
$921$	1.19597	0.0394086
$922$	−27.3770	−0.901613
$923$	1.00279	0.0330071
$924$	−1.12260	−0.0369309
$925$	0.0345242	0.00113515
$926$	−1.37142	−0.0450677
$927$	−2.99509	−0.0983715
$928$	52.7667	1.73215
$929$	48.0864	1.57766	0.788832	−	0.614608i	$-0.210686\pi$
$929$	48.0864	1.57766	0.788832	+	0.614608i	$0.210686\pi$
$930$	2.67780	0.0878084
$931$	39.8650	1.30652
$932$	−36.1959	−1.18564
$933$	−0.261632	−0.00856546
$934$	−11.9874	−0.392239
$935$	38.0517	1.24442
$936$	−4.27312	−0.139671
$937$	50.8862	1.66238	0.831190	−	0.555989i	$-0.187660\pi$
$937$	50.8862	1.66238	0.831190	+	0.555989i	$0.187660\pi$
$938$	−38.4910	−1.25678
$939$	2.05099	0.0669317
$940$	50.7532	1.65539
$941$	−19.6597	−0.640888	−0.320444	−	0.947267i	$-0.603832\pi$
$941$	−19.6597	−0.640888	−0.320444	+	0.947267i	$0.603832\pi$
$942$	−1.00050	−0.0325980
$943$	−25.2678	−0.822834
$944$	−22.4784	−0.731609
$945$	1.30845	0.0425638
$946$	−31.4285	−1.02183
$947$	8.89692	0.289111	0.144556	−	0.989497i	$-0.453825\pi$
$947$	8.89692	0.289111	0.144556	+	0.989497i	$0.453825\pi$
$948$	−0.148514	−0.00482350
$949$	−5.11887	−0.166166
$950$	1.40999	0.0457461
$951$	0.440943	0.0142985
$952$	7.62870	0.247247
$953$	−38.1889	−1.23706	−0.618530	−	0.785761i	$-0.712271\pi$
$953$	−38.1889	−1.23706	−0.618530	+	0.785761i	$0.712271\pi$
$954$	−13.2571	−0.429213
$955$	19.3805	0.627139
$956$	20.3368	0.657738
$957$	2.09575	0.0677461
$958$	−46.9026	−1.51536
$959$	−0.514118	−0.0166017
$960$	−1.91642	−0.0618522
$961$	30.5821	0.986519
$962$	0.893236	0.0287991
$963$	−45.8532	−1.47760
$964$	−6.29180	−0.202645
$965$	0.672704	0.0216551
$966$	0.522082	0.0167977
$967$	46.7747	1.50417	0.752087	−	0.659064i	$-0.229048\pi$
$967$	46.7747	1.50417	0.752087	+	0.659064i	$0.229048\pi$
$968$	−11.4070	−0.366635
$969$	2.12473	0.0682562
$970$	27.1939	0.873143
$971$	23.6460	0.758836	0.379418	−	0.925225i	$-0.376124\pi$
$971$	23.6460	0.758836	0.379418	+	0.925225i	$0.376124\pi$
$972$	−5.02544	−0.161191
$973$	−26.5274	−0.850428
$974$	10.6872	0.342441
$975$	0.00584963	0.000187338 0
$976$	−14.7420	−0.471879
$977$	4.27066	0.136631	0.0683153	−	0.997664i	$-0.478238\pi$
$977$	4.27066	0.136631	0.0683153	+	0.997664i	$0.478238\pi$
$978$	2.02059	0.0646114
$979$	68.4385	2.18731
$980$	30.5561	0.976078
$981$	−18.7191	−0.597654
$982$	43.8811	1.40030
$983$	4.64348	0.148104	0.0740520	−	0.997254i	$-0.476407\pi$
$983$	4.64348	0.148104	0.0740520	+	0.997254i	$0.476407\pi$
$984$	1.01162	0.0322493
$985$	12.2947	0.391742
$986$	−57.3433	−1.82618
$987$	−0.818928	−0.0260668
$988$	20.8264	0.662576
$989$	8.34433	0.265334
$990$	63.5395	2.01942
$991$	38.3186	1.21723	0.608615	−	0.793466i	$-0.291726\pi$
$991$	38.3186	1.21723	0.608615	+	0.793466i	$0.291726\pi$
$992$	−60.3683	−1.91670
$993$	2.17757	0.0691032
$994$	−2.98940	−0.0948180
$995$	−54.2286	−1.71916
$996$	−0.253879	−0.00804446
$997$	−17.1515	−0.543194	−0.271597	−	0.962411i	$-0.587552\pi$
$997$	−17.1515	−0.543194	−0.271597	+	0.962411i	$0.587552\pi$
$998$	−47.8149	−1.51355
$999$	0.173887	0.00550155

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1339.2.a.g.1.6	✓	30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1339.2.a.g.1.6	✓	30	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:	\( N \)	\(=\)	\( 1339 = 13 \cdot 103 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1339.a (trivial)

\(f(q)\)	\(=\)	\(q-2.15890 q^{2} -0.0701034 q^{3} +2.66085 q^{4} -2.25465 q^{5} +0.151346 q^{6} -1.38084 q^{7} -1.42671 q^{8} -2.99509 q^{9} +O(q^{10})\)	\(q-2.15890 q^{2} -0.0701034 q^{3} +2.66085 q^{4} -2.25465 q^{5} +0.151346 q^{6} -1.38084 q^{7} -1.42671 q^{8} -2.99509 q^{9} +4.86756 q^{10} -4.35836 q^{11} -0.186535 q^{12} -1.00000 q^{13} +2.98109 q^{14} +0.158058 q^{15} -2.24157 q^{16} +3.87232 q^{17} +6.46609 q^{18} -7.82697 q^{19} -5.99928 q^{20} +0.0968014 q^{21} +9.40927 q^{22} -2.49818 q^{23} +0.100017 q^{24} +0.0834429 q^{25} +2.15890 q^{26} +0.420276 q^{27} -3.67420 q^{28} +6.85927 q^{29} -0.341233 q^{30} -7.84742 q^{31} +7.69276 q^{32} +0.305536 q^{33} -8.35996 q^{34} +3.11331 q^{35} -7.96948 q^{36} +0.413746 q^{37} +16.8976 q^{38} +0.0701034 q^{39} +3.21673 q^{40} +10.1145 q^{41} -0.208985 q^{42} -3.34016 q^{43} -11.5969 q^{44} +6.75287 q^{45} +5.39333 q^{46} -8.45988 q^{47} +0.157142 q^{48} -5.09329 q^{49} -0.180145 q^{50} -0.271463 q^{51} -2.66085 q^{52} -2.05024 q^{53} -0.907333 q^{54} +9.82658 q^{55} +1.97006 q^{56} +0.548697 q^{57} -14.8085 q^{58} +10.0279 q^{59} +0.420570 q^{60} +6.57661 q^{61} +16.9418 q^{62} +4.13573 q^{63} -12.1247 q^{64} +2.25465 q^{65} -0.659621 q^{66} -12.9117 q^{67} +10.3037 q^{68} +0.175131 q^{69} -6.72132 q^{70} -1.00279 q^{71} +4.27312 q^{72} +5.11887 q^{73} -0.893236 q^{74} -0.00584963 q^{75} -20.8264 q^{76} +6.01819 q^{77} -0.151346 q^{78} +0.796172 q^{79} +5.05397 q^{80} +8.95579 q^{81} -21.8362 q^{82} +1.36103 q^{83} +0.257574 q^{84} -8.73073 q^{85} +7.21107 q^{86} -0.480858 q^{87} +6.21812 q^{88} -15.7028 q^{89} -14.5788 q^{90} +1.38084 q^{91} -6.64729 q^{92} +0.550131 q^{93} +18.2640 q^{94} +17.6471 q^{95} -0.539288 q^{96} +5.58675 q^{97} +10.9959 q^{98} +13.0537 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q + 5 q^{3} + 34 q^{4} + 17 q^{5} + 3 q^{6} + 2 q^{7} + 3 q^{8} + 49 q^{9}+O(q^{10}) \) 30 * q + 5 * q^3 + 34 * q^4 + 17 * q^5 + 3 * q^6 + 2 * q^7 + 3 * q^8 + 49 * q^9	\( 30 q + 5 q^{3} + 34 q^{4} + 17 q^{5} + 3 q^{6} + 2 q^{7} + 3 q^{8} + 49 q^{9} + 5 q^{10} + q^{11} + 15 q^{12} - 30 q^{13} + 24 q^{14} + 6 q^{15} + 38 q^{16} + 17 q^{17} + 8 q^{18} + 9 q^{19} + 31 q^{20} + 27 q^{21} + 2 q^{22} + 14 q^{23} + 26 q^{24} + 47 q^{25} + 14 q^{27} - 6 q^{28} + 53 q^{29} + 25 q^{30} + 19 q^{31} - 4 q^{32} + q^{33} - 22 q^{34} + 9 q^{35} + 61 q^{36} + 46 q^{38} - 5 q^{39} - 35 q^{40} + 28 q^{41} - 7 q^{42} + 6 q^{43} - 12 q^{44} + 68 q^{45} + 7 q^{46} + 12 q^{47} + 13 q^{48} + 54 q^{49} - 18 q^{50} + 10 q^{51} - 34 q^{52} + 37 q^{53} + 22 q^{54} + 11 q^{55} + 67 q^{56} - 57 q^{57} - 5 q^{58} + 61 q^{59} - 102 q^{60} + 16 q^{61} - 2 q^{62} - 7 q^{63} + 29 q^{64} - 17 q^{65} - 83 q^{66} - 2 q^{67} + 57 q^{68} + 98 q^{69} - 10 q^{70} + 50 q^{71} - 8 q^{72} - 10 q^{73} - 13 q^{74} + 5 q^{75} - 19 q^{76} + 54 q^{77} - 3 q^{78} + 3 q^{79} + 76 q^{80} + 118 q^{81} + 7 q^{82} + 6 q^{83} + 44 q^{84} + 33 q^{85} - 29 q^{86} - 10 q^{87} - 13 q^{88} + 77 q^{89} + 38 q^{90} - 2 q^{91} - 3 q^{92} + 34 q^{93} - 25 q^{94} + 24 q^{95} - 28 q^{96} + 12 q^{97} - 14 q^{98} - 58 q^{99}+O(q^{100}) \) 30 * q + 5 * q^3 + 34 * q^4 + 17 * q^5 + 3 * q^6 + 2 * q^7 + 3 * q^8 + 49 * q^9 + 5 * q^10 + q^11 + 15 * q^12 - 30 * q^13 + 24 * q^14 + 6 * q^15 + 38 * q^16 + 17 * q^17 + 8 * q^18 + 9 * q^19 + 31 * q^20 + 27 * q^21 + 2 * q^22 + 14 * q^23 + 26 * q^24 + 47 * q^25 + 14 * q^27 - 6 * q^28 + 53 * q^29 + 25 * q^30 + 19 * q^31 - 4 * q^32 + q^33 - 22 * q^34 + 9 * q^35 + 61 * q^36 + 46 * q^38 - 5 * q^39 - 35 * q^40 + 28 * q^41 - 7 * q^42 + 6 * q^43 - 12 * q^44 + 68 * q^45 + 7 * q^46 + 12 * q^47 + 13 * q^48 + 54 * q^49 - 18 * q^50 + 10 * q^51 - 34 * q^52 + 37 * q^53 + 22 * q^54 + 11 * q^55 + 67 * q^56 - 57 * q^57 - 5 * q^58 + 61 * q^59 - 102 * q^60 + 16 * q^61 - 2 * q^62 - 7 * q^63 + 29 * q^64 - 17 * q^65 - 83 * q^66 - 2 * q^67 + 57 * q^68 + 98 * q^69 - 10 * q^70 + 50 * q^71 - 8 * q^72 - 10 * q^73 - 13 * q^74 + 5 * q^75 - 19 * q^76 + 54 * q^77 - 3 * q^78 + 3 * q^79 + 76 * q^80 + 118 * q^81 + 7 * q^82 + 6 * q^83 + 44 * q^84 + 33 * q^85 - 29 * q^86 - 10 * q^87 - 13 * q^88 + 77 * q^89 + 38 * q^90 - 2 * q^91 - 3 * q^92 + 34 * q^93 - 25 * q^94 + 24 * q^95 - 28 * q^96 + 12 * q^97 - 14 * q^98 - 58 * q^99

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