LMFDB - Embedded newform 2011.2.a.b.1.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2011,2,Mod(1,2011)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2011, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("2011.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2011 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2011.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:	$16.0579158465$
Analytic rank:	$0$
Dimension:	$90$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.16
Character	$\chi$	$=$	2011.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.87387 q^{2} -0.640540 q^{3} +1.51138 q^{4} -2.41353 q^{5} +1.20029 q^{6} -1.29099 q^{7} +0.915613 q^{8} -2.58971 q^{9} +O(q^{10})$	\(q-1.87387 q^{2} -0.640540 q^{3} +1.51138 q^{4} -2.41353 q^{5} +1.20029 q^{6} -1.29099 q^{7} +0.915613 q^{8} -2.58971 q^{9} +4.52263 q^{10} +0.0249232 q^{11} -0.968098 q^{12} +5.07801 q^{13} +2.41915 q^{14} +1.54596 q^{15} -4.73849 q^{16} +5.12670 q^{17} +4.85277 q^{18} -2.94316 q^{19} -3.64775 q^{20} +0.826932 q^{21} -0.0467028 q^{22} -3.75869 q^{23} -0.586487 q^{24} +0.825119 q^{25} -9.51551 q^{26} +3.58043 q^{27} -1.95118 q^{28} -6.20109 q^{29} -2.89693 q^{30} -8.27031 q^{31} +7.04808 q^{32} -0.0159643 q^{33} -9.60676 q^{34} +3.11585 q^{35} -3.91403 q^{36} -7.02984 q^{37} +5.51509 q^{38} -3.25267 q^{39} -2.20986 q^{40} +0.584163 q^{41} -1.54956 q^{42} -3.27151 q^{43} +0.0376684 q^{44} +6.25033 q^{45} +7.04329 q^{46} -2.39670 q^{47} +3.03520 q^{48} -5.33334 q^{49} -1.54616 q^{50} -3.28386 q^{51} +7.67479 q^{52} +8.63985 q^{53} -6.70926 q^{54} -0.0601529 q^{55} -1.18205 q^{56} +1.88521 q^{57} +11.6200 q^{58} -4.41290 q^{59} +2.33653 q^{60} +12.3268 q^{61} +15.4975 q^{62} +3.34329 q^{63} -3.73018 q^{64} -12.2559 q^{65} +0.0299150 q^{66} -4.91599 q^{67} +7.74838 q^{68} +2.40759 q^{69} -5.83868 q^{70} +8.43151 q^{71} -2.37117 q^{72} -3.42450 q^{73} +13.1730 q^{74} -0.528522 q^{75} -4.44822 q^{76} -0.0321757 q^{77} +6.09507 q^{78} -1.27568 q^{79} +11.4365 q^{80} +5.47571 q^{81} -1.09464 q^{82} -8.24978 q^{83} +1.24981 q^{84} -12.3734 q^{85} +6.13038 q^{86} +3.97205 q^{87} +0.0228200 q^{88} +3.35816 q^{89} -11.7123 q^{90} -6.55567 q^{91} -5.68080 q^{92} +5.29747 q^{93} +4.49109 q^{94} +7.10339 q^{95} -4.51458 q^{96} +10.0320 q^{97} +9.99397 q^{98} -0.0645439 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 90 q + 11 q^{2} + 9 q^{3} + 95 q^{4} + 47 q^{5} + 20 q^{6} + 4 q^{7} + 33 q^{8} + 109 q^{9}+O(q^{10}) $ 90 * q + 11 * q^2 + 9 * q^3 + 95 * q^4 + 47 * q^5 + 20 * q^6 + 4 * q^7 + 33 * q^8 + 109 * q^9	\( 90 q + 11 q^{2} + 9 q^{3} + 95 q^{4} + 47 q^{5} + 20 q^{6} + 4 q^{7} + 33 q^{8} + 109 q^{9} + 19 q^{10} + 24 q^{11} + 14 q^{12} + 36 q^{13} + 43 q^{14} + 4 q^{15} + 93 q^{16} + 55 q^{17} + 18 q^{18} + 15 q^{19} + 76 q^{20} + 65 q^{21} - 3 q^{22} + 30 q^{23} + 46 q^{24} + 107 q^{25} + 38 q^{26} + 21 q^{27} + 2 q^{28} + 149 q^{29} + q^{30} + 33 q^{31} + 67 q^{32} + 13 q^{33} + 15 q^{34} + 34 q^{35} + 103 q^{36} + 23 q^{37} + 38 q^{38} + 32 q^{39} + 43 q^{40} + 144 q^{41} - 20 q^{42} - 5 q^{43} + 37 q^{44} + 103 q^{45} + 8 q^{46} + 28 q^{47} + 12 q^{48} + 114 q^{49} + 67 q^{50} + 11 q^{51} + 59 q^{52} + 59 q^{53} + 38 q^{54} + 3 q^{55} + 106 q^{56} + 2 q^{57} - 5 q^{58} + 86 q^{59} - 28 q^{60} + 113 q^{61} + 12 q^{62} - 29 q^{63} + 71 q^{64} + 51 q^{65} + 15 q^{66} - 14 q^{67} + 96 q^{68} + 116 q^{69} - 24 q^{70} + 47 q^{71} + 13 q^{72} + 22 q^{73} + 57 q^{74} + 7 q^{75} + 2 q^{76} + 100 q^{77} - 34 q^{78} + 18 q^{79} + 100 q^{80} + 154 q^{81} - 4 q^{82} + 24 q^{83} + 35 q^{84} + 30 q^{85} - q^{86} + 49 q^{87} - 74 q^{88} + 97 q^{89} + 22 q^{90} - 25 q^{91} + 23 q^{92} + 32 q^{93} + 21 q^{94} + 56 q^{95} + 29 q^{96} + 26 q^{97} + 15 q^{98} - 11 q^{99}+O(q^{100}) \) 90 * q + 11 * q^2 + 9 * q^3 + 95 * q^4 + 47 * q^5 + 20 * q^6 + 4 * q^7 + 33 * q^8 + 109 * q^9 + 19 * q^10 + 24 * q^11 + 14 * q^12 + 36 * q^13 + 43 * q^14 + 4 * q^15 + 93 * q^16 + 55 * q^17 + 18 * q^18 + 15 * q^19 + 76 * q^20 + 65 * q^21 - 3 * q^22 + 30 * q^23 + 46 * q^24 + 107 * q^25 + 38 * q^26 + 21 * q^27 + 2 * q^28 + 149 * q^29 + q^30 + 33 * q^31 + 67 * q^32 + 13 * q^33 + 15 * q^34 + 34 * q^35 + 103 * q^36 + 23 * q^37 + 38 * q^38 + 32 * q^39 + 43 * q^40 + 144 * q^41 - 20 * q^42 - 5 * q^43 + 37 * q^44 + 103 * q^45 + 8 * q^46 + 28 * q^47 + 12 * q^48 + 114 * q^49 + 67 * q^50 + 11 * q^51 + 59 * q^52 + 59 * q^53 + 38 * q^54 + 3 * q^55 + 106 * q^56 + 2 * q^57 - 5 * q^58 + 86 * q^59 - 28 * q^60 + 113 * q^61 + 12 * q^62 - 29 * q^63 + 71 * q^64 + 51 * q^65 + 15 * q^66 - 14 * q^67 + 96 * q^68 + 116 * q^69 - 24 * q^70 + 47 * q^71 + 13 * q^72 + 22 * q^73 + 57 * q^74 + 7 * q^75 + 2 * q^76 + 100 * q^77 - 34 * q^78 + 18 * q^79 + 100 * q^80 + 154 * q^81 - 4 * q^82 + 24 * q^83 + 35 * q^84 + 30 * q^85 - q^86 + 49 * q^87 - 74 * q^88 + 97 * q^89 + 22 * q^90 - 25 * q^91 + 23 * q^92 + 32 * q^93 + 21 * q^94 + 56 * q^95 + 29 * q^96 + 26 * q^97 + 15 * q^98 - 11 * 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 $

$2$	−1.87387	−1.32502	−0.662512	−	0.749051i	$-0.730510\pi$
$2$	−1.87387	−1.32502	−0.662512	+	0.749051i	$0.730510\pi$
$3$	−0.640540	−0.369816	−0.184908	−	0.982756i	$-0.559199\pi$
$3$	−0.640540	−0.369816	−0.184908	+	0.982756i	$0.559199\pi$
$4$	1.51138	0.755689
$5$	−2.41353	−1.07936	−0.539681	−	0.841869i	$-0.681455\pi$
$5$	−2.41353	−1.07936	−0.539681	+	0.841869i	$0.681455\pi$
$6$	1.20029	0.490015
$7$	−1.29099	−0.487949	−0.243975	−	0.969782i	$-0.578451\pi$
$7$	−1.29099	−0.487949	−0.243975	+	0.969782i	$0.578451\pi$
$8$	0.915613	0.323718
$9$	−2.58971	−0.863236
$10$	4.52263	1.43018
$11$	0.0249232	0.00751463	0.00375732	−	0.999993i	$-0.498804\pi$
$11$	0.0249232	0.00751463	0.00375732	+	0.999993i	$0.498804\pi$
$12$	−0.968098	−0.279466
$13$	5.07801	1.40839	0.704193	−	0.710008i	$-0.251309\pi$
$13$	5.07801	1.40839	0.704193	+	0.710008i	$0.251309\pi$
$14$	2.41915	0.646544
$15$	1.54596	0.399166
$16$	−4.73849	−1.18462
$17$	5.12670	1.24341	0.621704	−	0.783252i	$-0.286441\pi$
$17$	5.12670	1.24341	0.621704	+	0.783252i	$0.286441\pi$
$18$	4.85277	1.14381
$19$	−2.94316	−0.675207	−0.337603	−	0.941288i	$-0.609616\pi$
$19$	−2.94316	−0.675207	−0.337603	+	0.941288i	$0.609616\pi$
$20$	−3.64775	−0.815662
$21$	0.826932	0.180451
$22$	−0.0467028	−0.00995707
$23$	−3.75869	−0.783741	−0.391871	−	0.920020i	$-0.628172\pi$
$23$	−3.75869	−0.783741	−0.391871	+	0.920020i	$0.628172\pi$
$24$	−0.586487	−0.119716
$25$	0.825119	0.165024
$26$	−9.51551	−1.86615
$27$	3.58043	0.689055
$28$	−1.95118	−0.368738
$29$	−6.20109	−1.15151	−0.575757	−	0.817621i	$-0.695293\pi$
$29$	−6.20109	−1.15151	−0.575757	+	0.817621i	$0.695293\pi$
$30$	−2.89693	−0.528904
$31$	−8.27031	−1.48539	−0.742696	−	0.669629i	$-0.766453\pi$
$31$	−8.27031	−1.48539	−0.742696	+	0.669629i	$0.766453\pi$
$32$	7.04808	1.24594
$33$	−0.0159643	−0.00277903
$34$	−9.60676	−1.64755
$35$	3.11585	0.526674
$36$	−3.91403	−0.652338
$37$	−7.02984	−1.15570	−0.577849	−	0.816143i	$-0.696108\pi$
$37$	−7.02984	−1.15570	−0.577849	+	0.816143i	$0.696108\pi$
$38$	5.51509	0.894665
$39$	−3.25267	−0.520844
$40$	−2.20986	−0.349409
$41$	0.584163	0.0912309	0.0456154	−	0.998959i	$-0.485475\pi$
$41$	0.584163	0.0912309	0.0456154	+	0.998959i	$0.485475\pi$
$42$	−1.54956	−0.239102
$43$	−3.27151	−0.498901	−0.249450	−	0.968388i	$-0.580250\pi$
$43$	−3.27151	−0.498901	−0.249450	+	0.968388i	$0.580250\pi$
$44$	0.0376684	0.00567872
$45$	6.25033	0.931745
$46$	7.04329	1.03848
$47$	−2.39670	−0.349594	−0.174797	−	0.984604i	$-0.555927\pi$
$47$	−2.39670	−0.349594	−0.174797	+	0.984604i	$0.555927\pi$
$48$	3.03520	0.438093
$49$	−5.33334	−0.761906
$50$	−1.54616	−0.218660
$51$	−3.28386	−0.459832
$52$	7.67479	1.06430
$53$	8.63985	1.18678	0.593388	−	0.804917i	$-0.297790\pi$
$53$	8.63985	1.18678	0.593388	+	0.804917i	$0.297790\pi$
$54$	−6.70926	−0.913014
$55$	−0.0601529	−0.00811101
$56$	−1.18205	−0.157958
$57$	1.88521	0.249702
$58$	11.6200	1.52578
$59$	−4.41290	−0.574511	−0.287255	−	0.957854i	$-0.592743\pi$
$59$	−4.41290	−0.574511	−0.287255	+	0.957854i	$0.592743\pi$
$60$	2.33653	0.301645
$61$	12.3268	1.57828	0.789141	−	0.614212i	$-0.210526\pi$
$61$	12.3268	1.57828	0.789141	+	0.614212i	$0.210526\pi$
$62$	15.4975	1.96818
$63$	3.34329	0.421215
$64$	−3.73018	−0.466272
$65$	−12.2559	−1.52016
$66$	0.0299150	0.00368228
$67$	−4.91599	−0.600584	−0.300292	−	0.953847i	$-0.597084\pi$
$67$	−4.91599	−0.600584	−0.300292	+	0.953847i	$0.597084\pi$
$68$	7.74838	0.939630
$69$	2.40759	0.289840
$70$	−5.83868	−0.697856
$71$	8.43151	1.00064	0.500318	−	0.865842i	$-0.333216\pi$
$71$	8.43151	1.00064	0.500318	+	0.865842i	$0.333216\pi$
$72$	−2.37117	−0.279445
$73$	−3.42450	−0.400808	−0.200404	−	0.979713i	$-0.564225\pi$
$73$	−3.42450	−0.400808	−0.200404	+	0.979713i	$0.564225\pi$
$74$	13.1730	1.53133
$75$	−0.528522	−0.0610284
$76$	−4.44822	−0.510246
$77$	−0.0321757	−0.00366676
$78$	6.09507	0.690131
$79$	−1.27568	−0.143525	−0.0717627	−	0.997422i	$-0.522862\pi$
$79$	−1.27568	−0.143525	−0.0717627	+	0.997422i	$0.522862\pi$
$80$	11.4365	1.27864
$81$	5.47571	0.608413
$82$	−1.09464	−0.120883
$83$	−8.24978	−0.905531	−0.452766	−	0.891630i	$-0.649563\pi$
$83$	−8.24978	−0.905531	−0.452766	+	0.891630i	$0.649563\pi$
$84$	1.24981	0.136365
$85$	−12.3734	−1.34209
$86$	6.13038	0.661056
$87$	3.97205	0.425848
$88$	0.0228200	0.00243262
$89$	3.35816	0.355964	0.177982	−	0.984034i	$-0.443043\pi$
$89$	3.35816	0.355964	0.177982	+	0.984034i	$0.443043\pi$
$90$	−11.7123	−1.23458
$91$	−6.55567	−0.687221
$92$	−5.68080	−0.592265
$93$	5.29747	0.549322
$94$	4.49109	0.463221
$95$	7.10339	0.728793
$96$	−4.51458	−0.460767
$97$	10.0320	1.01860	0.509298	−	0.860590i	$-0.329905\pi$
$97$	10.0320	1.01860	0.509298	+	0.860590i	$0.329905\pi$
$98$	9.99397	1.00954
$99$	−0.0645439	−0.00648690
$100$	1.24707	0.124707
$101$	1.59774	0.158981	0.0794907	−	0.996836i	$-0.474671\pi$
$101$	1.59774	0.158981	0.0794907	+	0.996836i	$0.474671\pi$
$102$	6.15352	0.609289
$103$	−7.46435	−0.735484	−0.367742	−	0.929928i	$-0.619869\pi$
$103$	−7.46435	−0.735484	−0.367742	+	0.929928i	$0.619869\pi$
$104$	4.64949	0.455920
$105$	−1.99582	−0.194772
$106$	−16.1899	−1.57251
$107$	16.6999	1.61444	0.807221	−	0.590249i	$-0.200971\pi$
$107$	16.6999	1.61444	0.807221	+	0.590249i	$0.200971\pi$
$108$	5.41139	0.520711
$109$	−6.62333	−0.634400	−0.317200	−	0.948359i	$-0.602743\pi$
$109$	−6.62333	−0.634400	−0.317200	+	0.948359i	$0.602743\pi$
$110$	0.112719	0.0107473
$111$	4.50290	0.427396
$112$	6.11736	0.578036
$113$	9.11962	0.857901	0.428951	−	0.903328i	$-0.358883\pi$
$113$	9.11962	0.857901	0.428951	+	0.903328i	$0.358883\pi$
$114$	−3.53263	−0.330862
$115$	9.07171	0.845941
$116$	−9.37220	−0.870186
$117$	−13.1506	−1.21577
$118$	8.26919	0.761241
$119$	−6.61853	−0.606720
$120$	1.41550	0.129217
$121$	−10.9994	−0.999944
$122$	−23.0987	−2.09126
$123$	−0.374180	−0.0337386
$124$	−12.4996	−1.12249
$125$	10.0762	0.901242
$126$	−6.26488	−0.558120
$127$	9.58949	0.850929	0.425465	−	0.904975i	$-0.360111\pi$
$127$	9.58949	0.850929	0.425465	+	0.904975i	$0.360111\pi$
$128$	−7.10630	−0.628114
$129$	2.09553	0.184502
$130$	22.9660	2.01425
$131$	−9.37945	−0.819487	−0.409743	−	0.912201i	$-0.634382\pi$
$131$	−9.37945	−0.819487	−0.409743	+	0.912201i	$0.634382\pi$
$132$	−0.0241281	−0.00210008
$133$	3.79959	0.329466
$134$	9.21191	0.795788
$135$	−8.64148	−0.743740
$136$	4.69408	0.402514
$137$	10.3550	0.884687	0.442344	−	0.896846i	$-0.354147\pi$
$137$	10.3550	0.884687	0.442344	+	0.896846i	$0.354147\pi$
$138$	−4.51151	−0.384045
$139$	−6.13655	−0.520495	−0.260248	−	0.965542i	$-0.583804\pi$
$139$	−6.13655	−0.520495	−0.260248	+	0.965542i	$0.583804\pi$
$140$	4.70922	0.398002
$141$	1.53518	0.129286
$142$	−15.7995	−1.32587
$143$	0.126560	0.0105835
$144$	12.2713	1.02261
$145$	14.9665	1.24290
$146$	6.41706	0.531080
$147$	3.41622	0.281765
$148$	−10.6247	−0.873349
$149$	12.6612	1.03725	0.518624	−	0.855003i	$-0.326445\pi$
$149$	12.6612	1.03725	0.518624	+	0.855003i	$0.326445\pi$
$150$	0.990380	0.0808642
$151$	22.8552	1.85993	0.929964	−	0.367650i	$-0.119837\pi$
$151$	22.8552	1.85993	0.929964	+	0.367650i	$0.119837\pi$
$152$	−2.69479	−0.218577
$153$	−13.2767	−1.07335
$154$	0.0602929	0.00485854
$155$	19.9606	1.60328
$156$	−4.91601	−0.393596
$157$	−18.2931	−1.45994	−0.729972	−	0.683477i	$-0.760467\pi$
$157$	−18.2931	−1.45994	−0.729972	+	0.683477i	$0.760467\pi$
$158$	2.39046	0.190175
$159$	−5.53417	−0.438888
$160$	−17.0107	−1.34482
$161$	4.85244	0.382426
$162$	−10.2608	−0.806161
$163$	−7.69296	−0.602559	−0.301280	−	0.953536i	$-0.597414\pi$
$163$	−7.69296	−0.602559	−0.301280	+	0.953536i	$0.597414\pi$
$164$	0.882891	0.0689422
$165$	0.0385303	0.00299958
$166$	15.4590	1.19985
$167$	−14.8254	−1.14722	−0.573611	−	0.819128i	$-0.694458\pi$
$167$	−14.8254	−1.14722	−0.573611	+	0.819128i	$0.694458\pi$
$168$	0.757150	0.0584154
$169$	12.7862	0.983552
$170$	23.1862	1.77830
$171$	7.62192	0.582863
$172$	−4.94449	−0.377014
$173$	−1.29339	−0.0983345	−0.0491672	−	0.998791i	$-0.515657\pi$
$173$	−1.29339	−0.0983345	−0.0491672	+	0.998791i	$0.515657\pi$
$174$	−7.44309	−0.564259
$175$	−1.06522	−0.0805232
$176$	−0.118098	−0.00890201
$177$	2.82664	0.212463
$178$	−6.29275	−0.471661
$179$	1.28210	0.0958289	0.0479145	−	0.998851i	$-0.484743\pi$
$179$	1.28210	0.0958289	0.0479145	+	0.998851i	$0.484743\pi$
$180$	9.44662	0.704109
$181$	−7.29613	−0.542317	−0.271159	−	0.962535i	$-0.587407\pi$
$181$	−7.29613	−0.542317	−0.271159	+	0.962535i	$0.587407\pi$
$182$	12.2845	0.910584
$183$	−7.89580	−0.583674
$184$	−3.44151	−0.253711
$185$	16.9667	1.24742
$186$	−9.92675	−0.727864
$187$	0.127774	0.00934376
$188$	−3.62231	−0.264184
$189$	−4.62231	−0.336224
$190$	−13.3108	−0.965668
$191$	23.0281	1.66625	0.833126	−	0.553084i	$-0.186549\pi$
$191$	23.0281	1.66625	0.833126	+	0.553084i	$0.186549\pi$
$192$	2.38933	0.172435
$193$	11.2658	0.810928	0.405464	−	0.914111i	$-0.367110\pi$
$193$	11.2658	0.810928	0.405464	+	0.914111i	$0.367110\pi$
$194$	−18.7987	−1.34967
$195$	7.85041	0.562179
$196$	−8.06069	−0.575764
$197$	19.2454	1.37118	0.685588	−	0.727990i	$-0.259545\pi$
$197$	19.2454	1.37118	0.685588	+	0.727990i	$0.259545\pi$
$198$	0.120947	0.00859530
$199$	21.5378	1.52678	0.763388	−	0.645940i	$-0.223534\pi$
$199$	21.5378	1.52678	0.763388	+	0.645940i	$0.223534\pi$
$200$	0.755490	0.0534212
$201$	3.14889	0.222105
$202$	−2.99396	−0.210654
$203$	8.00556	0.561880
$204$	−4.96315	−0.347490
$205$	−1.40989	−0.0984712
$206$	13.9872	0.974534
$207$	9.73391	0.676554
$208$	−24.0621	−1.66841
$209$	−0.0733530	−0.00507393
$210$	3.73991	0.258078
$211$	6.97014	0.479844	0.239922	−	0.970792i	$-0.422878\pi$
$211$	6.97014	0.479844	0.239922	+	0.970792i	$0.422878\pi$
$212$	13.0581	0.896833
$213$	−5.40072	−0.370051
$214$	−31.2934	−2.13917
$215$	7.89588	0.538495
$216$	3.27829	0.223059
$217$	10.6769	0.724795
$218$	12.4112	0.840596
$219$	2.19353	0.148225
$220$	−0.0909137	−0.00612940
$221$	26.0334	1.75120
$222$	−8.43783	−0.566310
$223$	2.92526	0.195890	0.0979451	−	0.995192i	$-0.468773\pi$
$223$	2.92526	0.195890	0.0979451	+	0.995192i	$0.468773\pi$
$224$	−9.09901	−0.607953
$225$	−2.13682	−0.142454
$226$	−17.0890	−1.13674
$227$	0.670831	0.0445246	0.0222623	−	0.999752i	$-0.492913\pi$
$227$	0.670831	0.0445246	0.0222623	+	0.999752i	$0.492913\pi$
$228$	2.84927	0.188697
$229$	−13.4907	−0.891491	−0.445745	−	0.895160i	$-0.647061\pi$
$229$	−13.4907	−0.891491	−0.445745	+	0.895160i	$0.647061\pi$
$230$	−16.9992	−1.12089
$231$	0.0206098	0.00135603
$232$	−5.67780	−0.372766
$233$	−28.2851	−1.85302	−0.926509	−	0.376272i	$-0.877206\pi$
$233$	−28.2851	−1.85302	−0.926509	+	0.376272i	$0.877206\pi$
$234$	24.6424	1.61092
$235$	5.78450	0.377339
$236$	−6.66956	−0.434152
$237$	0.817125	0.0530780
$238$	12.4022	0.803918
$239$	−17.3377	−1.12148	−0.560742	−	0.827990i	$-0.689484\pi$
$239$	−17.3377	−1.12148	−0.560742	+	0.827990i	$0.689484\pi$
$240$	−7.32553	−0.472861
$241$	27.5323	1.77351	0.886754	−	0.462241i	$-0.152954\pi$
$241$	27.5323	1.77351	0.886754	+	0.462241i	$0.152954\pi$
$242$	20.6114	1.32495
$243$	−14.2487	−0.914055
$244$	18.6304	1.19269
$245$	12.8722	0.822373
$246$	0.701163	0.0447045
$247$	−14.9454	−0.950952
$248$	−7.57240	−0.480848
$249$	5.28432	0.334880
$250$	−18.8814	−1.19417
$251$	21.7165	1.37073	0.685365	−	0.728199i	$-0.259643\pi$
$251$	21.7165	1.37073	0.685365	+	0.728199i	$0.259643\pi$
$252$	5.05298	0.318308
$253$	−0.0936787	−0.00588953
$254$	−17.9694	−1.12750
$255$	7.92569	0.496326
$256$	20.7766	1.29854
$257$	18.7829	1.17165	0.585823	−	0.810439i	$-0.300771\pi$
$257$	18.7829	1.17165	0.585823	+	0.810439i	$0.300771\pi$
$258$	−3.92675	−0.244469
$259$	9.07547	0.563922
$260$	−18.5233	−1.14877
$261$	16.0590	0.994029
$262$	17.5759	1.08584
$263$	18.5898	1.14630	0.573149	−	0.819451i	$-0.305721\pi$
$263$	18.5898	1.14630	0.573149	+	0.819451i	$0.305721\pi$
$264$	−0.0146171	−0.000899623 0
$265$	−20.8525	−1.28096
$266$	−7.11993	−0.436551
$267$	−2.15104	−0.131641
$268$	−7.42991	−0.453854
$269$	−3.55496	−0.216750	−0.108375	−	0.994110i	$-0.534565\pi$
$269$	−3.55496	−0.216750	−0.108375	+	0.994110i	$0.534565\pi$
$270$	16.1930	0.985473
$271$	−17.5494	−1.06605	−0.533025	−	0.846100i	$-0.678945\pi$
$271$	−17.5494	−1.06605	−0.533025	+	0.846100i	$0.678945\pi$
$272$	−24.2928	−1.47297
$273$	4.19917	0.254145
$274$	−19.4039	−1.17223
$275$	0.0205646	0.00124009
$276$	3.63878	0.219029
$277$	−1.44472	−0.0868047	−0.0434023	−	0.999058i	$-0.513820\pi$
$277$	−1.44472	−0.0868047	−0.0434023	+	0.999058i	$0.513820\pi$
$278$	11.4991	0.689669
$279$	21.4177	1.28224
$280$	2.85291	0.170494
$281$	8.33007	0.496931	0.248465	−	0.968641i	$-0.420074\pi$
$281$	8.33007	0.496931	0.248465	+	0.968641i	$0.420074\pi$
$282$	−2.87672	−0.171306
$283$	28.3429	1.68481	0.842405	−	0.538845i	$-0.181139\pi$
$283$	28.3429	1.68481	0.842405	+	0.538845i	$0.181139\pi$
$284$	12.7432	0.756169
$285$	−4.55001	−0.269519
$286$	−0.237157	−0.0140234
$287$	−0.754149	−0.0445160
$288$	−18.2525	−1.07554
$289$	9.28308	0.546064
$290$	−28.0453	−1.64687
$291$	−6.42591	−0.376693
$292$	−5.17571	−0.302886
$293$	5.98046	0.349382	0.174691	−	0.984623i	$-0.444107\pi$
$293$	5.98046	0.349382	0.174691	+	0.984623i	$0.444107\pi$
$294$	−6.40154	−0.373345
$295$	10.6507	0.620106
$296$	−6.43662	−0.374121
$297$	0.0892359	0.00517799
$298$	−23.7254	−1.37438
$299$	−19.0867	−1.10381
$300$	−0.798796	−0.0461185
$301$	4.22349	0.243438
$302$	−42.8276	−2.46445
$303$	−1.02342	−0.0587939
$304$	13.9461	0.799866
$305$	−29.7510	−1.70354
$306$	24.8787	1.42222
$307$	−11.4597	−0.654038	−0.327019	−	0.945018i	$-0.606044\pi$
$307$	−11.4597	−0.654038	−0.327019	+	0.945018i	$0.606044\pi$
$308$	−0.0486296	−0.00277093
$309$	4.78121	0.271994
$310$	−37.4036	−2.12438
$311$	4.42874	0.251131	0.125565	−	0.992085i	$-0.459926\pi$
$311$	4.42874	0.251131	0.125565	+	0.992085i	$0.459926\pi$
$312$	−2.97819	−0.168607
$313$	23.1651	1.30937	0.654685	−	0.755902i	$-0.272801\pi$
$313$	23.1651	1.30937	0.654685	+	0.755902i	$0.272801\pi$
$314$	34.2788	1.93446
$315$	−8.06913	−0.454644
$316$	−1.92804	−0.108461
$317$	24.0371	1.35006	0.675029	−	0.737791i	$-0.264131\pi$
$317$	24.0371	1.35006	0.675029	+	0.737791i	$0.264131\pi$
$318$	10.3703	0.581538
$319$	−0.154551	−0.00865321
$320$	9.00289	0.503277
$321$	−10.6970	−0.597047
$322$	−9.09283	−0.506723
$323$	−15.0887	−0.839557
$324$	8.27587	0.459771
$325$	4.18996	0.232417
$326$	14.4156	0.798405
$327$	4.24251	0.234611
$328$	0.534867	0.0295331
$329$	3.09412	0.170584
$330$	−0.0722007	−0.00397452
$331$	−8.34130	−0.458479	−0.229240	−	0.973370i	$-0.573624\pi$
$331$	−8.34130	−0.458479	−0.229240	+	0.973370i	$0.573624\pi$
$332$	−12.4685	−0.684300
$333$	18.2052	0.997641
$334$	27.7808	1.52010
$335$	11.8649	0.648247
$336$	−3.91841	−0.213767
$337$	−19.9768	−1.08821	−0.544103	−	0.839019i	$-0.683130\pi$
$337$	−19.9768	−1.08821	−0.544103	+	0.839019i	$0.683130\pi$
$338$	−23.9596	−1.30323
$339$	−5.84148	−0.317266
$340$	−18.7009	−1.01420
$341$	−0.206123	−0.0111622
$342$	−14.2825	−0.772307
$343$	15.9222	0.859720
$344$	−2.99544	−0.161503
$345$	−5.81079	−0.312843
$346$	2.42364	0.130296
$347$	−24.9563	−1.33973	−0.669863	−	0.742485i	$-0.733647\pi$
$347$	−24.9563	−1.33973	−0.669863	+	0.742485i	$0.733647\pi$
$348$	6.00327	0.321809
$349$	−12.8017	−0.685259	−0.342629	−	0.939471i	$-0.611318\pi$
$349$	−12.8017	−0.685259	−0.342629	+	0.939471i	$0.611318\pi$
$350$	1.99608	0.106695
$351$	18.1815	0.970455
$352$	0.175661	0.00936275
$353$	−21.0231	−1.11895	−0.559474	−	0.828848i	$-0.688997\pi$
$353$	−21.0231	−1.11895	−0.559474	+	0.828848i	$0.688997\pi$
$354$	−5.29675	−0.281519
$355$	−20.3497	−1.08005
$356$	5.07545	0.268998
$357$	4.23944	0.224375
$358$	−2.40249	−0.126976
$359$	18.1177	0.956216	0.478108	−	0.878301i	$-0.341323\pi$
$359$	18.1177	0.956216	0.478108	+	0.878301i	$0.341323\pi$
$360$	5.72289	0.301623
$361$	−10.3378	−0.544096
$362$	13.6720	0.718584
$363$	7.04554	0.369795
$364$	−9.90809	−0.519325
$365$	8.26513	0.432617
$366$	14.7957	0.773382
$367$	31.2981	1.63375	0.816873	−	0.576817i	$-0.195706\pi$
$367$	31.2981	1.63375	0.816873	+	0.576817i	$0.195706\pi$
$368$	17.8105	0.928438
$369$	−1.51281	−0.0787538
$370$	−31.7934	−1.65286
$371$	−11.1540	−0.579086
$372$	8.00647	0.415116
$373$	14.0024	0.725018	0.362509	−	0.931980i	$-0.381920\pi$
$373$	14.0024	0.725018	0.362509	+	0.931980i	$0.381920\pi$
$374$	−0.239431	−0.0123807
$375$	−6.45421	−0.333294
$376$	−2.19445	−0.113170
$377$	−31.4892	−1.62178
$378$	8.66159	0.445504
$379$	24.5664	1.26189	0.630947	−	0.775826i	$-0.282667\pi$
$379$	24.5664	1.26189	0.630947	+	0.775826i	$0.282667\pi$
$380$	10.7359	0.550741
$381$	−6.14245	−0.314687
$382$	−43.1515	−2.20782
$383$	−18.2312	−0.931568	−0.465784	−	0.884898i	$-0.654228\pi$
$383$	−18.2312	−0.931568	−0.465784	+	0.884898i	$0.654228\pi$
$384$	4.55187	0.232287
$385$	0.0776569	0.00395776
$386$	−21.1106	−1.07450
$387$	8.47226	0.430669
$388$	15.1622	0.769742
$389$	30.2644	1.53447	0.767233	−	0.641368i	$-0.221633\pi$
$389$	30.2644	1.53447	0.767233	+	0.641368i	$0.221633\pi$
$390$	−14.7106	−0.744901
$391$	−19.2697	−0.974510
$392$	−4.88328	−0.246643
$393$	6.00792	0.303059
$394$	−36.0633	−1.81684
$395$	3.07889	0.154916
$396$	−0.0975502	−0.00490208
$397$	−20.4281	−1.02526	−0.512630	−	0.858610i	$-0.671329\pi$
$397$	−20.4281	−1.02526	−0.512630	+	0.858610i	$0.671329\pi$
$398$	−40.3590	−2.02302
$399$	−2.43379	−0.121842
$400$	−3.90982	−0.195491
$401$	39.1418	1.95465	0.977324	−	0.211751i	$-0.0679167\pi$
$401$	39.1418	1.95465	0.977324	+	0.211751i	$0.0679167\pi$
$402$	−5.90060	−0.294295
$403$	−41.9967	−2.09201
$404$	2.41479	0.120140
$405$	−13.2158	−0.656698
$406$	−15.0014	−0.744505
$407$	−0.175206	−0.00868465
$408$	−3.00674	−0.148856
$409$	−35.4466	−1.75272	−0.876360	−	0.481656i	$-0.840035\pi$
$409$	−35.4466	−1.75272	−0.876360	+	0.481656i	$0.840035\pi$
$410$	2.64195	0.130477
$411$	−6.63279	−0.327171
$412$	−11.2814	−0.555797
$413$	5.69702	0.280332
$414$	−18.2401	−0.896450
$415$	19.9111	0.977396
$416$	35.7902	1.75476
$417$	3.93071	0.192487
$418$	0.137454	0.00672308
$419$	21.7963	1.06482	0.532411	−	0.846486i	$-0.321286\pi$
$419$	21.7963	1.06482	0.532411	+	0.846486i	$0.321286\pi$
$420$	−3.01644	−0.147187
$421$	18.6909	0.910937	0.455469	−	0.890252i	$-0.349472\pi$
$421$	18.6909	0.910937	0.455469	+	0.890252i	$0.349472\pi$
$422$	−13.0611	−0.635805
$423$	6.20675	0.301782
$424$	7.91076	0.384181
$425$	4.23014	0.205192
$426$	10.1202	0.490327
$427$	−15.9138	−0.770121
$428$	25.2399	1.22002
$429$	−0.0810670	−0.00391395
$430$	−14.7958	−0.713519
$431$	−28.9718	−1.39552	−0.697761	−	0.716330i	$-0.745820\pi$
$431$	−28.9718	−1.39552	−0.697761	+	0.716330i	$0.745820\pi$
$432$	−16.9659	−0.816270
$433$	−3.26549	−0.156929	−0.0784647	−	0.996917i	$-0.525002\pi$
$433$	−3.26549	−0.156929	−0.0784647	+	0.996917i	$0.525002\pi$
$434$	−20.0071	−0.960371
$435$	−9.58665	−0.459645
$436$	−10.0104	−0.479409
$437$	11.0624	0.529187
$438$	−4.11038	−0.196402
$439$	22.9707	1.09633	0.548167	−	0.836369i	$-0.315326\pi$
$439$	22.9707	1.09633	0.548167	+	0.836369i	$0.315326\pi$
$440$	−0.0550768	−0.00262568
$441$	13.8118	0.657705
$442$	−48.7832	−2.32038
$443$	−16.2814	−0.773551	−0.386775	−	0.922174i	$-0.626411\pi$
$443$	−16.2814	−0.773551	−0.386775	+	0.922174i	$0.626411\pi$
$444$	6.80558	0.322978
$445$	−8.10502	−0.384215
$446$	−5.48156	−0.259559
$447$	−8.11002	−0.383591
$448$	4.81563	0.227517
$449$	−14.7971	−0.698318	−0.349159	−	0.937064i	$-0.613533\pi$
$449$	−14.7971	−0.698318	−0.349159	+	0.937064i	$0.613533\pi$
$450$	4.00411	0.188756
$451$	0.0145592	0.000685567 0
$452$	13.7832	0.648307
$453$	−14.6397	−0.687831
$454$	−1.25705	−0.0589962
$455$	15.8223	0.741760
$456$	1.72612	0.0808332
$457$	−38.2428	−1.78892	−0.894461	−	0.447146i	$-0.852440\pi$
$457$	−38.2428	−1.78892	−0.894461	+	0.447146i	$0.852440\pi$
$458$	25.2798	1.18125
$459$	18.3558	0.856776
$460$	13.7108	0.639268
$461$	16.8923	0.786754	0.393377	−	0.919377i	$-0.371307\pi$
$461$	16.8923	0.786754	0.393377	+	0.919377i	$0.371307\pi$
$462$	−0.0386200	−0.00179677
$463$	−15.8337	−0.735856	−0.367928	−	0.929854i	$-0.619933\pi$
$463$	−15.8337	−0.735856	−0.367928	+	0.929854i	$0.619933\pi$
$464$	29.3838	1.36411
$465$	−12.7856	−0.592917
$466$	53.0025	2.45529
$467$	19.8714	0.919541	0.459770	−	0.888038i	$-0.347932\pi$
$467$	19.8714	0.919541	0.459770	+	0.888038i	$0.347932\pi$
$468$	−19.8755	−0.918744
$469$	6.34650	0.293054
$470$	−10.8394	−0.499983
$471$	11.7174	0.539911
$472$	−4.04051	−0.185980
$473$	−0.0815366	−0.00374906
$474$	−1.53118	−0.0703296
$475$	−2.42846	−0.111425
$476$	−10.0031	−0.458491
$477$	−22.3747	−1.02447
$478$	32.4886	1.48599
$479$	−19.9146	−0.909923	−0.454962	−	0.890511i	$-0.650347\pi$
$479$	−19.9146	−0.909923	−0.454962	+	0.890511i	$0.650347\pi$
$480$	10.8961	0.497335
$481$	−35.6976	−1.62767
$482$	−51.5918	−2.34994
$483$	−3.10818	−0.141427
$484$	−16.6242	−0.755646
$485$	−24.2125	−1.09944
$486$	26.7002	1.21115
$487$	−0.795335	−0.0360401	−0.0180200	−	0.999838i	$-0.505736\pi$
$487$	−0.795335	−0.0360401	−0.0180200	+	0.999838i	$0.505736\pi$
$488$	11.2866	0.510918
$489$	4.92765	0.222836
$490$	−24.1207	−1.08966
$491$	21.3963	0.965600	0.482800	−	0.875731i	$-0.339620\pi$
$491$	21.3963	0.965600	0.482800	+	0.875731i	$0.339620\pi$
$492$	−0.565527	−0.0254959
$493$	−31.7912	−1.43180
$494$	28.0057	1.26003
$495$	0.155778	0.00700172
$496$	39.1888	1.75963
$497$	−10.8850	−0.488259
$498$	−9.90211	−0.443724
$499$	0.950668	0.0425577	0.0212789	−	0.999774i	$-0.493226\pi$
$499$	0.950668	0.0425577	0.0212789	+	0.999774i	$0.493226\pi$
$500$	15.2289	0.681059
$501$	9.49625	0.424261
$502$	−40.6938	−1.81625
$503$	−4.65600	−0.207601	−0.103800	−	0.994598i	$-0.533100\pi$
$503$	−4.65600	−0.207601	−0.103800	+	0.994598i	$0.533100\pi$
$504$	3.06116	0.136355
$505$	−3.85620	−0.171599
$506$	0.175541	0.00780377
$507$	−8.19006	−0.363733
$508$	14.4933	0.643038
$509$	5.18141	0.229662	0.114831	−	0.993385i	$-0.463367\pi$
$509$	5.18141	0.229662	0.114831	+	0.993385i	$0.463367\pi$
$510$	−14.8517	−0.657644
$511$	4.42100	0.195574
$512$	−24.7200	−1.09248
$513$	−10.5378	−0.465254
$514$	−35.1967	−1.55246
$515$	18.0154	0.793854
$516$	3.16714	0.139426
$517$	−0.0597334	−0.00262707
$518$	−17.0062	−0.747210
$519$	0.828467	0.0363657
$520$	−11.2217	−0.492103
$521$	12.7999	0.560773	0.280387	−	0.959887i	$-0.409537\pi$
$521$	12.7999	0.560773	0.280387	+	0.959887i	$0.409537\pi$
$522$	−30.0925	−1.31711
$523$	−15.7260	−0.687649	−0.343825	−	0.939034i	$-0.611723\pi$
$523$	−15.7260	−0.687649	−0.343825	+	0.939034i	$0.611723\pi$
$524$	−14.1759	−0.619277
$525$	0.682317	0.0297788
$526$	−34.8349	−1.51887
$527$	−42.3994	−1.84695
$528$	0.0756468	0.00329211
$529$	−8.87224	−0.385749
$530$	39.0749	1.69730
$531$	11.4281	0.495939
$532$	5.74262	0.248974
$533$	2.96638	0.128488
$534$	4.03076	0.174428
$535$	−40.3057	−1.74257
$536$	−4.50114	−0.194420
$537$	−0.821239	−0.0354391
$538$	6.66152	0.287198
$539$	−0.132924	−0.00572544
$540$	−13.0605	−0.562036
$541$	20.2783	0.871832	0.435916	−	0.899987i	$-0.356425\pi$
$541$	20.2783	0.871832	0.435916	+	0.899987i	$0.356425\pi$
$542$	32.8852	1.41254
$543$	4.67347	0.200558
$544$	36.1334	1.54921
$545$	15.9856	0.684748
$546$	−7.86868	−0.336749
$547$	−10.7327	−0.458898	−0.229449	−	0.973321i	$-0.573692\pi$
$547$	−10.7327	−0.458898	−0.229449	+	0.973321i	$0.573692\pi$
$548$	15.6503	0.668548
$549$	−31.9228	−1.36243
$550$	−0.0385354	−0.00164315
$551$	18.2508	0.777510
$552$	2.20442	0.0938265
$553$	1.64689	0.0700331
$554$	2.70721	0.115018
$555$	−10.8679	−0.461315
$556$	−9.27464	−0.393332
$557$	9.05002	0.383462	0.191731	−	0.981448i	$-0.438590\pi$
$557$	9.05002	0.383462	0.191731	+	0.981448i	$0.438590\pi$
$558$	−40.1339	−1.69900
$559$	−16.6128	−0.702645
$560$	−14.7644	−0.623910
$561$	−0.0818443	−0.00345547
$562$	−15.6095	−0.658445
$563$	19.2175	0.809919	0.404960	−	0.914335i	$-0.367286\pi$
$563$	19.2175	0.809919	0.404960	+	0.914335i	$0.367286\pi$
$564$	2.32024	0.0976996
$565$	−22.0105	−0.925987
$566$	−53.1108	−2.23241
$567$	−7.06910	−0.296874
$568$	7.72000	0.323924
$569$	−8.03757	−0.336952	−0.168476	−	0.985706i	$-0.553885\pi$
$569$	−8.03757	−0.336952	−0.168476	+	0.985706i	$0.553885\pi$
$570$	8.52611	0.357120
$571$	12.8334	0.537059	0.268530	−	0.963271i	$-0.413462\pi$
$571$	12.8334	0.537059	0.268530	+	0.963271i	$0.413462\pi$
$572$	0.191280	0.00799784
$573$	−14.7504	−0.616207
$574$	1.41318	0.0589848
$575$	−3.10137	−0.129336
$576$	9.66007	0.402503
$577$	−5.23978	−0.218135	−0.109067	−	0.994034i	$-0.534786\pi$
$577$	−5.23978	−0.218135	−0.109067	+	0.994034i	$0.534786\pi$
$578$	−17.3953	−0.723548
$579$	−7.21618	−0.299894
$580$	22.6201	0.939247
$581$	10.6504	0.441853
$582$	12.0413	0.499128
$583$	0.215333	0.00891818
$584$	−3.13552	−0.129749
$585$	31.7393	1.31226
$586$	−11.2066	−0.462940
$587$	2.14227	0.0884208	0.0442104	−	0.999022i	$-0.485923\pi$
$587$	2.14227	0.0884208	0.0442104	+	0.999022i	$0.485923\pi$
$588$	5.16320	0.212927
$589$	24.3408	1.00295
$590$	−19.9579	−0.821655
$591$	−12.3274	−0.507083
$592$	33.3109	1.36907
$593$	−1.95393	−0.0802381	−0.0401190	−	0.999195i	$-0.512774\pi$
$593$	−1.95393	−0.0802381	−0.0401190	+	0.999195i	$0.512774\pi$
$594$	−0.167216	−0.00686096
$595$	15.9740	0.654871
$596$	19.1359	0.783836
$597$	−13.7959	−0.564627
$598$	35.7659	1.46258
$599$	−10.6591	−0.435518	−0.217759	−	0.976003i	$-0.569875\pi$
$599$	−10.6591	−0.435518	−0.217759	+	0.976003i	$0.569875\pi$
$600$	−0.483922	−0.0197560
$601$	−1.26253	−0.0514997	−0.0257498	−	0.999668i	$-0.508197\pi$
$601$	−1.26253	−0.0514997	−0.0257498	+	0.999668i	$0.508197\pi$
$602$	−7.91427	−0.322561
$603$	12.7310	0.518445
$604$	34.5428	1.40553
$605$	26.5473	1.07930
$606$	1.91775	0.0779033
$607$	−31.6153	−1.28323	−0.641613	−	0.767029i	$-0.721734\pi$
$607$	−31.6153	−1.28323	−0.641613	+	0.767029i	$0.721734\pi$
$608$	−20.7436	−0.841264
$609$	−5.12788	−0.207792
$610$	55.7495	2.25723
$611$	−12.1704	−0.492364
$612$	−20.0661	−0.811122
$613$	43.2243	1.74581	0.872906	−	0.487888i	$-0.162233\pi$
$613$	43.2243	1.74581	0.872906	+	0.487888i	$0.162233\pi$
$614$	21.4739	0.866616
$615$	0.903093	0.0364162
$616$	−0.0294605	−0.00118700
$617$	14.2627	0.574195	0.287098	−	0.957901i	$-0.407310\pi$
$617$	14.2627	0.574195	0.287098	+	0.957901i	$0.407310\pi$
$618$	−8.95936	−0.360398
$619$	11.4339	0.459566	0.229783	−	0.973242i	$-0.426198\pi$
$619$	11.4339	0.459566	0.229783	+	0.973242i	$0.426198\pi$
$620$	30.1680	1.21158
$621$	−13.4577	−0.540041
$622$	−8.29887	−0.332754
$623$	−4.33536	−0.173692
$624$	15.4127	0.617004
$625$	−28.4448	−1.13779
$626$	−43.4083	−1.73495
$627$	0.0469855	0.00187642
$628$	−27.6477	−1.10326
$629$	−36.0399	−1.43701
$630$	15.1205	0.602414
$631$	−12.2003	−0.485686	−0.242843	−	0.970066i	$-0.578080\pi$
$631$	−12.2003	−0.485686	−0.242843	+	0.970066i	$0.578080\pi$
$632$	−1.16803	−0.0464618
$633$	−4.46466	−0.177454
$634$	−45.0423	−1.78886
$635$	−23.1445	−0.918461
$636$	−8.36423	−0.331663
$637$	−27.0828	−1.07306
$638$	0.289608	0.0114657
$639$	−21.8351	−0.863785
$640$	17.1513	0.677963
$641$	−31.7666	−1.25471	−0.627353	−	0.778735i	$-0.715862\pi$
$641$	−31.7666	−1.25471	−0.627353	+	0.778735i	$0.715862\pi$
$642$	20.0447	0.791101
$643$	11.8850	0.468697	0.234349	−	0.972153i	$-0.424704\pi$
$643$	11.8850	0.468697	0.234349	+	0.972153i	$0.424704\pi$
$644$	7.33387	0.288995
$645$	−5.05763	−0.199144
$646$	28.2742	1.11243
$647$	8.09843	0.318382	0.159191	−	0.987248i	$-0.449111\pi$
$647$	8.09843	0.318382	0.159191	+	0.987248i	$0.449111\pi$
$648$	5.01364	0.196954
$649$	−0.109984	−0.00431724
$650$	−7.85143	−0.307958
$651$	−6.83898	−0.268041
$652$	−11.6270	−0.455347
$653$	44.3185	1.73432	0.867159	−	0.498031i	$-0.165943\pi$
$653$	44.3185	1.73432	0.867159	+	0.498031i	$0.165943\pi$
$654$	−7.94990	−0.310866
$655$	22.6376	0.884523
$656$	−2.76805	−0.108074
$657$	8.86846	0.345992
$658$	−5.79796	−0.226028
$659$	−41.4330	−1.61400	−0.807000	−	0.590551i	$-0.798911\pi$
$659$	−41.4330	−1.61400	−0.807000	+	0.590551i	$0.798911\pi$
$660$	0.0582339	0.00226675
$661$	21.4695	0.835066	0.417533	−	0.908662i	$-0.362895\pi$
$661$	21.4695	0.835066	0.417533	+	0.908662i	$0.362895\pi$
$662$	15.6305	0.607496
$663$	−16.6755	−0.647621
$664$	−7.55361	−0.293137
$665$	−9.17042	−0.355614
$666$	−34.1142	−1.32190
$667$	23.3080	0.902489
$668$	−22.4067	−0.866943
$669$	−1.87375	−0.0724433
$670$	−22.2332	−0.858944
$671$	0.307223	0.0118602
$672$	5.82828	0.224831
$673$	−23.1779	−0.893442	−0.446721	−	0.894673i	$-0.647408\pi$
$673$	−23.1779	−0.893442	−0.446721	+	0.894673i	$0.647408\pi$
$674$	37.4339	1.44190
$675$	2.95428	0.113710
$676$	19.3247	0.743259
$677$	−18.6971	−0.718589	−0.359294	−	0.933224i	$-0.616983\pi$
$677$	−18.6971	−0.718589	−0.359294	+	0.933224i	$0.616983\pi$
$678$	10.9462	0.420385
$679$	−12.9512	−0.497023
$680$	−11.3293	−0.434458
$681$	−0.429694	−0.0164659
$682$	0.386247	0.0147901
$683$	−22.9902	−0.879694	−0.439847	−	0.898073i	$-0.644967\pi$
$683$	−22.9902	−0.879694	−0.439847	+	0.898073i	$0.644967\pi$
$684$	11.5196	0.440463
$685$	−24.9921	−0.954898
$686$	−29.8362	−1.13915
$687$	8.64134	0.329688
$688$	15.5020	0.591009
$689$	43.8733	1.67144
$690$	10.8887	0.414524
$691$	0.339621	0.0129198	0.00645989	−	0.999979i	$-0.497944\pi$
$691$	0.339621	0.0129198	0.00645989	+	0.999979i	$0.497944\pi$
$692$	−1.95480	−0.0743103
$693$	0.0833256	0.00316528
$694$	46.7649	1.77517
$695$	14.8107	0.561803
$696$	3.63686	0.137855
$697$	2.99483	0.113437
$698$	23.9887	0.907984
$699$	18.1177	0.685276
$700$	−1.60995	−0.0608505
$701$	7.81410	0.295135	0.147567	−	0.989052i	$-0.452856\pi$
$701$	7.81410	0.295135	0.147567	+	0.989052i	$0.452856\pi$
$702$	−34.0697	−1.28588
$703$	20.6899	0.780336
$704$	−0.0929680	−0.00350386
$705$	−3.70520	−0.139546
$706$	39.3945	1.48263
$707$	−2.06267	−0.0775748
$708$	4.27212	0.160556
$709$	−18.4302	−0.692162	−0.346081	−	0.938205i	$-0.612488\pi$
$709$	−18.4302	−0.692162	−0.346081	+	0.938205i	$0.612488\pi$
$710$	38.1326	1.43109
$711$	3.30364	0.123896
$712$	3.07478	0.115232
$713$	31.0855	1.16416
$714$	−7.94414	−0.297302
$715$	−0.305457	−0.0114234
$716$	1.93774	0.0724169
$717$	11.1055	0.414743
$718$	−33.9502	−1.26701
$719$	24.2161	0.903108	0.451554	−	0.892244i	$-0.350870\pi$
$719$	24.2161	0.903108	0.451554	+	0.892244i	$0.350870\pi$
$720$	−29.6172	−1.10377
$721$	9.63641	0.358879
$722$	19.3717	0.720940
$723$	−17.6355	−0.655872
$724$	−11.0272	−0.409823
$725$	−5.11664	−0.190027
$726$	−13.2024	−0.489988
$727$	23.6415	0.876816	0.438408	−	0.898776i	$-0.355542\pi$
$727$	23.6415	0.876816	0.438408	+	0.898776i	$0.355542\pi$
$728$	−6.00246	−0.222466
$729$	−7.30027	−0.270380
$730$	−15.4878	−0.573228
$731$	−16.7721	−0.620337
$732$	−11.9335	−0.441076
$733$	42.5519	1.57169	0.785845	−	0.618423i	$-0.212228\pi$
$733$	42.5519	1.57169	0.785845	+	0.618423i	$0.212228\pi$
$734$	−58.6484	−2.16475
$735$	−8.24514	−0.304127
$736$	−26.4916	−0.976492
$737$	−0.122522	−0.00451316
$738$	2.83481	0.104351
$739$	−15.0869	−0.554980	−0.277490	−	0.960728i	$-0.589503\pi$
$739$	−15.0869	−0.554980	−0.277490	+	0.960728i	$0.589503\pi$
$740$	25.6431	0.942660
$741$	9.57312	0.351677
$742$	20.9011	0.767303
$743$	−6.23091	−0.228590	−0.114295	−	0.993447i	$-0.536461\pi$
$743$	−6.23091	−0.228590	−0.114295	+	0.993447i	$0.536461\pi$
$744$	4.85043	0.177825
$745$	−30.5582	−1.11957
$746$	−26.2387	−0.960667
$747$	21.3645	0.781687
$748$	0.193115	0.00706097
$749$	−21.5595	−0.787765
$750$	12.0943	0.441622
$751$	6.52890	0.238243	0.119122	−	0.992880i	$-0.461992\pi$
$751$	6.52890	0.238243	0.119122	+	0.992880i	$0.461992\pi$
$752$	11.3567	0.414137
$753$	−13.9103	−0.506918
$754$	59.0066	2.14889
$755$	−55.1616	−2.00754
$756$	−6.98606	−0.254080
$757$	42.5076	1.54497	0.772483	−	0.635036i	$-0.219015\pi$
$757$	42.5076	1.54497	0.772483	+	0.635036i	$0.219015\pi$
$758$	−46.0343	−1.67204
$759$	0.0600050	0.00217804
$760$	6.50396	0.235923
$761$	−6.90594	−0.250340	−0.125170	−	0.992135i	$-0.539948\pi$
$761$	−6.90594	−0.250340	−0.125170	+	0.992135i	$0.539948\pi$
$762$	11.5101	0.416968
$763$	8.55067	0.309555
$764$	34.8041	1.25917
$765$	32.0436	1.15854
$766$	34.1628	1.23435
$767$	−22.4088	−0.809133
$768$	−13.3083	−0.480220
$769$	38.7085	1.39586	0.697931	−	0.716165i	$-0.254104\pi$
$769$	38.7085	1.39586	0.697931	+	0.716165i	$0.254104\pi$
$770$	−0.145519	−0.00524413
$771$	−12.0312	−0.433293
$772$	17.0268	0.612810
$773$	−2.68828	−0.0966908	−0.0483454	−	0.998831i	$-0.515395\pi$
$773$	−2.68828	−0.0966908	−0.0483454	+	0.998831i	$0.515395\pi$
$774$	−15.8759	−0.570647
$775$	−6.82399	−0.245125
$776$	9.18544	0.329738
$777$	−5.81320	−0.208547
$778$	−56.7115	−2.03320
$779$	−1.71928	−0.0615997
$780$	11.8649	0.424833
$781$	0.210140	0.00751941
$782$	36.1088	1.29125
$783$	−22.2026	−0.793456
$784$	25.2720	0.902571
$785$	44.1508	1.57581
$786$	−11.2580	−0.401561
$787$	−1.80591	−0.0643738	−0.0321869	−	0.999482i	$-0.510247\pi$
$787$	−1.80591	−0.0643738	−0.0321869	+	0.999482i	$0.510247\pi$
$788$	29.0870	1.03618
$789$	−11.9075	−0.423920
$790$	−5.76944	−0.205267
$791$	−11.7734	−0.418612
$792$	−0.0590972	−0.00209993
$793$	62.5955	2.22283
$794$	38.2796	1.35849
$795$	13.3569	0.473720
$796$	32.5518	1.15377
$797$	−23.9320	−0.847713	−0.423857	−	0.905729i	$-0.639324\pi$
$797$	−23.9320	−0.847713	−0.423857	+	0.905729i	$0.639324\pi$
$798$	4.56060	0.161444
$799$	−12.2872	−0.434688
$800$	5.81550	0.205609
$801$	−8.69666	−0.307281
$802$	−73.3465	−2.58995
$803$	−0.0853496	−0.00301192
$804$	4.75916	0.167843
$805$	−11.7115	−0.412776
$806$	78.6962	2.77196
$807$	2.27709	0.0801575
$808$	1.46291	0.0514652
$809$	19.1678	0.673905	0.336952	−	0.941522i	$-0.390604\pi$
$809$	19.1678	0.673905	0.336952	+	0.941522i	$0.390604\pi$
$810$	24.7646	0.870141
$811$	34.1913	1.20062	0.600310	−	0.799768i	$-0.295044\pi$
$811$	34.1913	1.20062	0.600310	+	0.799768i	$0.295044\pi$
$812$	12.0994	0.424607
$813$	11.2411	0.394242
$814$	0.328313	0.0115074
$815$	18.5672	0.650380
$816$	15.5605	0.544728
$817$	9.62857	0.336861
$818$	66.4222	2.32240
$819$	16.9773	0.593234
$820$	−2.13088	−0.0744136
$821$	45.1613	1.57614	0.788069	−	0.615587i	$-0.211081\pi$
$821$	45.1613	1.57614	0.788069	+	0.615587i	$0.211081\pi$
$822$	12.4290	0.433510
$823$	−30.8627	−1.07581	−0.537903	−	0.843007i	$-0.680783\pi$
$823$	−30.8627	−1.07581	−0.537903	+	0.843007i	$0.680783\pi$
$824$	−6.83446	−0.238090
$825$	−0.0131725	−0.000458606 0
$826$	−10.6755	−0.371447
$827$	−6.29537	−0.218911	−0.109456	−	0.993992i	$-0.534911\pi$
$827$	−6.29537	−0.218911	−0.109456	+	0.993992i	$0.534911\pi$
$828$	14.7116	0.511264
$829$	34.9966	1.21548	0.607741	−	0.794136i	$-0.292076\pi$
$829$	34.9966	1.21548	0.607741	+	0.794136i	$0.292076\pi$
$830$	−37.3107	−1.29507
$831$	0.925400	0.0321018
$832$	−18.9419	−0.656691
$833$	−27.3425	−0.947360
$834$	−7.36562	−0.255051
$835$	35.7815	1.23827
$836$	−0.110864	−0.00383431
$837$	−29.6113	−1.02352
$838$	−40.8435	−1.41091
$839$	−28.6033	−0.987494	−0.493747	−	0.869606i	$-0.664373\pi$
$839$	−28.6033	−0.987494	−0.493747	+	0.869606i	$0.664373\pi$
$840$	−1.82740	−0.0630514
$841$	9.45357	0.325985
$842$	−35.0242	−1.20701
$843$	−5.33575	−0.183773
$844$	10.5345	0.362613
$845$	−30.8598	−1.06161
$846$	−11.6306	−0.399869
$847$	14.2001	0.487921
$848$	−40.9399	−1.40588
$849$	−18.1548	−0.623070
$850$	−7.92672	−0.271884
$851$	26.4230	0.905769
$852$	−8.16253	−0.279644
$853$	37.0633	1.26902	0.634512	−	0.772913i	$-0.281201\pi$
$853$	37.0633	1.26902	0.634512	+	0.772913i	$0.281201\pi$
$854$	29.8203	1.02043
$855$	−18.3957	−0.629120
$856$	15.2907	0.522624
$857$	−4.80610	−0.164173	−0.0820867	−	0.996625i	$-0.526158\pi$
$857$	−4.80610	−0.164173	−0.0820867	+	0.996625i	$0.526158\pi$
$858$	0.151909	0.00518608
$859$	−26.6083	−0.907865	−0.453932	−	0.891036i	$-0.649979\pi$
$859$	−26.6083	−0.907865	−0.453932	+	0.891036i	$0.649979\pi$
$860$	11.9337	0.406935
$861$	0.483063	0.0164627
$862$	54.2893	1.84910
$863$	11.6216	0.395605	0.197803	−	0.980242i	$-0.436619\pi$
$863$	11.6216	0.395605	0.197803	+	0.980242i	$0.436619\pi$
$864$	25.2352	0.858518
$865$	3.12163	0.106139
$866$	6.11909	0.207935
$867$	−5.94619	−0.201943
$868$	16.1368	0.547720
$869$	−0.0317941	−0.00107854
$870$	17.9641	0.609041
$871$	−24.9634	−0.845854
$872$	−6.06441	−0.205367
$873$	−25.9800	−0.879289
$874$	−20.7295	−0.701186
$875$	−13.0083	−0.439760
$876$	3.31525	0.112012
$877$	48.5109	1.63810	0.819049	−	0.573724i	$-0.194502\pi$
$877$	48.5109	1.63810	0.819049	+	0.573724i	$0.194502\pi$
$878$	−43.0441	−1.45267
$879$	−3.83073	−0.129207
$880$	0.285034	0.00960850
$881$	34.1497	1.15053	0.575267	−	0.817966i	$-0.304898\pi$
$881$	34.1497	1.15053	0.575267	+	0.817966i	$0.304898\pi$
$882$	−25.8815	−0.871474
$883$	−20.3495	−0.684814	−0.342407	−	0.939552i	$-0.611242\pi$
$883$	−20.3495	−0.684814	−0.342407	+	0.939552i	$0.611242\pi$
$884$	39.3464	1.32336
$885$	−6.82218	−0.229325
$886$	30.5091	1.02497
$887$	−7.87056	−0.264268	−0.132134	−	0.991232i	$-0.542183\pi$
$887$	−7.87056	−0.264268	−0.132134	+	0.991232i	$0.542183\pi$
$888$	4.12291	0.138356
$889$	−12.3799	−0.415210
$890$	15.1877	0.509094
$891$	0.136472	0.00457200
$892$	4.42118	0.148032
$893$	7.05386	0.236048
$894$	15.1971	0.508267
$895$	−3.09439	−0.103434
$896$	9.17418	0.306488
$897$	12.2258	0.408207
$898$	27.7278	0.925288
$899$	51.2850	1.71045
$900$	−3.22954	−0.107651
$901$	44.2940	1.47565
$902$	−0.0272820	−0.000908392 0
$903$	−2.70532	−0.0900273
$904$	8.35004	0.277718
$905$	17.6094	0.585357
$906$	27.4328	0.911393
$907$	31.7995	1.05588	0.527942	−	0.849280i	$-0.322964\pi$
$907$	31.7995	1.05588	0.527942	+	0.849280i	$0.322964\pi$
$908$	1.01388	0.0336467
$909$	−4.13769	−0.137238
$910$	−29.6489	−0.982850
$911$	−55.8204	−1.84941	−0.924706	−	0.380681i	$-0.875689\pi$
$911$	−55.8204	−1.84941	−0.924706	+	0.380681i	$0.875689\pi$
$912$	−8.93306	−0.295803
$913$	−0.205611	−0.00680473
$914$	71.6619	2.37036
$915$	19.0567	0.629996
$916$	−20.3895	−0.673690
$917$	12.1088	0.399868
$918$	−34.3964	−1.13525
$919$	15.6360	0.515783	0.257892	−	0.966174i	$-0.416972\pi$
$919$	15.6360	0.515783	0.257892	+	0.966174i	$0.416972\pi$
$920$	8.30618	0.273847
$921$	7.34038	0.241874
$922$	−31.6540	−1.04247
$923$	42.8153	1.40928
$924$	0.0311492	0.00102473
$925$	−5.80046	−0.190718
$926$	29.6703	0.975027
$927$	19.3305	0.634896
$928$	−43.7058	−1.43471
$929$	37.8287	1.24112	0.620560	−	0.784159i	$-0.286905\pi$
$929$	37.8287	1.24112	0.620560	+	0.784159i	$0.286905\pi$
$930$	23.9585	0.785630
$931$	15.6969	0.514444
$932$	−42.7495	−1.40031
$933$	−2.83679	−0.0928722
$934$	−37.2364	−1.21841
$935$	−0.308386	−0.0100853
$936$	−12.0408	−0.393567
$937$	50.3359	1.64440	0.822201	−	0.569197i	$-0.192746\pi$
$937$	50.3359	1.64440	0.822201	+	0.569197i	$0.192746\pi$
$938$	−11.8925	−0.388304
$939$	−14.8382	−0.484226
$940$	8.74256	0.285151
$941$	−34.3119	−1.11854	−0.559269	−	0.828986i	$-0.688918\pi$
$941$	−34.3119	−1.11854	−0.559269	+	0.828986i	$0.688918\pi$
$942$	−21.9569	−0.715395
$943$	−2.19569	−0.0715014
$944$	20.9105	0.680579
$945$	11.1561	0.362907
$946$	0.152789	0.00496759
$947$	40.3582	1.31146	0.655732	−	0.754993i	$-0.272360\pi$
$947$	40.3582	1.31146	0.655732	+	0.754993i	$0.272360\pi$
$948$	1.23499	0.0401105
$949$	−17.3896	−0.564492
$950$	4.55060	0.147641
$951$	−15.3967	−0.499273
$952$	−6.06001	−0.196406
$953$	0.902813	0.0292450	0.0146225	−	0.999893i	$-0.495345\pi$
$953$	0.902813	0.0292450	0.0146225	+	0.999893i	$0.495345\pi$
$954$	41.9272	1.35744
$955$	−55.5789	−1.79849
$956$	−26.2039	−0.847494
$957$	0.0989963	0.00320009
$958$	37.3174	1.20567
$959$	−13.3682	−0.431682
$960$	−5.76671	−0.186120
$961$	37.3980	1.20639
$962$	66.8926	2.15670
$963$	−43.2479	−1.39364
$964$	41.6116	1.34022
$965$	−27.1903	−0.875286
$966$	5.82432	0.187394
$967$	22.1767	0.713154	0.356577	−	0.934266i	$-0.383944\pi$
$967$	22.1767	0.713154	0.356577	+	0.934266i	$0.383944\pi$
$968$	−10.0712	−0.323700
$969$	9.66492	0.310482
$970$	45.3711	1.45678
$971$	39.1666	1.25691	0.628457	−	0.777844i	$-0.283687\pi$
$971$	39.1666	1.25691	0.628457	+	0.777844i	$0.283687\pi$
$972$	−21.5352	−0.690741
$973$	7.92223	0.253975
$974$	1.49035	0.0477539
$975$	−2.68384	−0.0859516
$976$	−58.4103	−1.86967
$977$	42.6536	1.36461	0.682304	−	0.731068i	$-0.260978\pi$
$977$	42.6536	1.36461	0.682304	+	0.731068i	$0.260978\pi$
$978$	−9.23376	−0.295263
$979$	0.0836962	0.00267494
$980$	19.4547	0.621458
$981$	17.1525	0.547637
$982$	−40.0938	−1.27944
$983$	−16.5299	−0.527221	−0.263611	−	0.964629i	$-0.584913\pi$
$983$	−16.5299	−0.527221	−0.263611	+	0.964629i	$0.584913\pi$
$984$	−0.342604	−0.0109218
$985$	−46.4493	−1.48000
$986$	59.5724	1.89717
$987$	−1.98191	−0.0630848
$988$	−22.5881	−0.718624
$989$	12.2966	0.391009
$990$	−0.291908	−0.00927745
$991$	−37.2739	−1.18405	−0.592023	−	0.805921i	$-0.701671\pi$
$991$	−37.2739	−1.18405	−0.592023	+	0.805921i	$0.701671\pi$
$992$	−58.2898	−1.85070
$993$	5.34294	0.169553
$994$	20.3971	0.646955
$995$	−51.9822	−1.64795
$996$	7.98660	0.253065
$997$	−25.8496	−0.818664	−0.409332	−	0.912385i	$-0.634238\pi$
$997$	−25.8496	−0.818664	−0.409332	+	0.912385i	$0.634238\pi$
$998$	−1.78143	−0.0563900
$999$	−25.1699	−0.796340

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2011.2.a.b.1.16	✓	90

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2011.2.a.b.1.16	✓	90	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:	\( N \)	\(=\)	\( 2011 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2011.a (trivial)

\(f(q)\)	\(=\)	\(q-1.87387 q^{2} -0.640540 q^{3} +1.51138 q^{4} -2.41353 q^{5} +1.20029 q^{6} -1.29099 q^{7} +0.915613 q^{8} -2.58971 q^{9} +O(q^{10})\)	\(q-1.87387 q^{2} -0.640540 q^{3} +1.51138 q^{4} -2.41353 q^{5} +1.20029 q^{6} -1.29099 q^{7} +0.915613 q^{8} -2.58971 q^{9} +4.52263 q^{10} +0.0249232 q^{11} -0.968098 q^{12} +5.07801 q^{13} +2.41915 q^{14} +1.54596 q^{15} -4.73849 q^{16} +5.12670 q^{17} +4.85277 q^{18} -2.94316 q^{19} -3.64775 q^{20} +0.826932 q^{21} -0.0467028 q^{22} -3.75869 q^{23} -0.586487 q^{24} +0.825119 q^{25} -9.51551 q^{26} +3.58043 q^{27} -1.95118 q^{28} -6.20109 q^{29} -2.89693 q^{30} -8.27031 q^{31} +7.04808 q^{32} -0.0159643 q^{33} -9.60676 q^{34} +3.11585 q^{35} -3.91403 q^{36} -7.02984 q^{37} +5.51509 q^{38} -3.25267 q^{39} -2.20986 q^{40} +0.584163 q^{41} -1.54956 q^{42} -3.27151 q^{43} +0.0376684 q^{44} +6.25033 q^{45} +7.04329 q^{46} -2.39670 q^{47} +3.03520 q^{48} -5.33334 q^{49} -1.54616 q^{50} -3.28386 q^{51} +7.67479 q^{52} +8.63985 q^{53} -6.70926 q^{54} -0.0601529 q^{55} -1.18205 q^{56} +1.88521 q^{57} +11.6200 q^{58} -4.41290 q^{59} +2.33653 q^{60} +12.3268 q^{61} +15.4975 q^{62} +3.34329 q^{63} -3.73018 q^{64} -12.2559 q^{65} +0.0299150 q^{66} -4.91599 q^{67} +7.74838 q^{68} +2.40759 q^{69} -5.83868 q^{70} +8.43151 q^{71} -2.37117 q^{72} -3.42450 q^{73} +13.1730 q^{74} -0.528522 q^{75} -4.44822 q^{76} -0.0321757 q^{77} +6.09507 q^{78} -1.27568 q^{79} +11.4365 q^{80} +5.47571 q^{81} -1.09464 q^{82} -8.24978 q^{83} +1.24981 q^{84} -12.3734 q^{85} +6.13038 q^{86} +3.97205 q^{87} +0.0228200 q^{88} +3.35816 q^{89} -11.7123 q^{90} -6.55567 q^{91} -5.68080 q^{92} +5.29747 q^{93} +4.49109 q^{94} +7.10339 q^{95} -4.51458 q^{96} +10.0320 q^{97} +9.99397 q^{98} -0.0645439 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 90 q + 11 q^{2} + 9 q^{3} + 95 q^{4} + 47 q^{5} + 20 q^{6} + 4 q^{7} + 33 q^{8} + 109 q^{9}+O(q^{10}) \) 90 * q + 11 * q^2 + 9 * q^3 + 95 * q^4 + 47 * q^5 + 20 * q^6 + 4 * q^7 + 33 * q^8 + 109 * q^9	\( 90 q + 11 q^{2} + 9 q^{3} + 95 q^{4} + 47 q^{5} + 20 q^{6} + 4 q^{7} + 33 q^{8} + 109 q^{9} + 19 q^{10} + 24 q^{11} + 14 q^{12} + 36 q^{13} + 43 q^{14} + 4 q^{15} + 93 q^{16} + 55 q^{17} + 18 q^{18} + 15 q^{19} + 76 q^{20} + 65 q^{21} - 3 q^{22} + 30 q^{23} + 46 q^{24} + 107 q^{25} + 38 q^{26} + 21 q^{27} + 2 q^{28} + 149 q^{29} + q^{30} + 33 q^{31} + 67 q^{32} + 13 q^{33} + 15 q^{34} + 34 q^{35} + 103 q^{36} + 23 q^{37} + 38 q^{38} + 32 q^{39} + 43 q^{40} + 144 q^{41} - 20 q^{42} - 5 q^{43} + 37 q^{44} + 103 q^{45} + 8 q^{46} + 28 q^{47} + 12 q^{48} + 114 q^{49} + 67 q^{50} + 11 q^{51} + 59 q^{52} + 59 q^{53} + 38 q^{54} + 3 q^{55} + 106 q^{56} + 2 q^{57} - 5 q^{58} + 86 q^{59} - 28 q^{60} + 113 q^{61} + 12 q^{62} - 29 q^{63} + 71 q^{64} + 51 q^{65} + 15 q^{66} - 14 q^{67} + 96 q^{68} + 116 q^{69} - 24 q^{70} + 47 q^{71} + 13 q^{72} + 22 q^{73} + 57 q^{74} + 7 q^{75} + 2 q^{76} + 100 q^{77} - 34 q^{78} + 18 q^{79} + 100 q^{80} + 154 q^{81} - 4 q^{82} + 24 q^{83} + 35 q^{84} + 30 q^{85} - q^{86} + 49 q^{87} - 74 q^{88} + 97 q^{89} + 22 q^{90} - 25 q^{91} + 23 q^{92} + 32 q^{93} + 21 q^{94} + 56 q^{95} + 29 q^{96} + 26 q^{97} + 15 q^{98} - 11 q^{99}+O(q^{100}) \) 90 * q + 11 * q^2 + 9 * q^3 + 95 * q^4 + 47 * q^5 + 20 * q^6 + 4 * q^7 + 33 * q^8 + 109 * q^9 + 19 * q^10 + 24 * q^11 + 14 * q^12 + 36 * q^13 + 43 * q^14 + 4 * q^15 + 93 * q^16 + 55 * q^17 + 18 * q^18 + 15 * q^19 + 76 * q^20 + 65 * q^21 - 3 * q^22 + 30 * q^23 + 46 * q^24 + 107 * q^25 + 38 * q^26 + 21 * q^27 + 2 * q^28 + 149 * q^29 + q^30 + 33 * q^31 + 67 * q^32 + 13 * q^33 + 15 * q^34 + 34 * q^35 + 103 * q^36 + 23 * q^37 + 38 * q^38 + 32 * q^39 + 43 * q^40 + 144 * q^41 - 20 * q^42 - 5 * q^43 + 37 * q^44 + 103 * q^45 + 8 * q^46 + 28 * q^47 + 12 * q^48 + 114 * q^49 + 67 * q^50 + 11 * q^51 + 59 * q^52 + 59 * q^53 + 38 * q^54 + 3 * q^55 + 106 * q^56 + 2 * q^57 - 5 * q^58 + 86 * q^59 - 28 * q^60 + 113 * q^61 + 12 * q^62 - 29 * q^63 + 71 * q^64 + 51 * q^65 + 15 * q^66 - 14 * q^67 + 96 * q^68 + 116 * q^69 - 24 * q^70 + 47 * q^71 + 13 * q^72 + 22 * q^73 + 57 * q^74 + 7 * q^75 + 2 * q^76 + 100 * q^77 - 34 * q^78 + 18 * q^79 + 100 * q^80 + 154 * q^81 - 4 * q^82 + 24 * q^83 + 35 * q^84 + 30 * q^85 - q^86 + 49 * q^87 - 74 * q^88 + 97 * q^89 + 22 * q^90 - 25 * q^91 + 23 * q^92 + 32 * q^93 + 21 * q^94 + 56 * q^95 + 29 * q^96 + 26 * q^97 + 15 * q^98 - 11 * q^99

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