LMFDB - Embedded newform 6005.2.a.f.1.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6005,2,Mod(1,6005)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6005, 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("6005.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6005 = 5 \cdot 1201 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6005.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:	$47.9501664138$
Analytic rank:	$0$
Dimension:	$111$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.16
Character	$\chi$	$=$	6005.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.17647 q^{2} +1.64482 q^{3} +2.73702 q^{4} +1.00000 q^{5} -3.57990 q^{6} -1.13164 q^{7} -1.60410 q^{8} -0.294573 q^{9} +O(q^{10})$	\(q-2.17647 q^{2} +1.64482 q^{3} +2.73702 q^{4} +1.00000 q^{5} -3.57990 q^{6} -1.13164 q^{7} -1.60410 q^{8} -0.294573 q^{9} -2.17647 q^{10} +1.31009 q^{11} +4.50190 q^{12} +4.28700 q^{13} +2.46298 q^{14} +1.64482 q^{15} -1.98276 q^{16} -4.71547 q^{17} +0.641130 q^{18} -0.712364 q^{19} +2.73702 q^{20} -1.86134 q^{21} -2.85137 q^{22} -0.646819 q^{23} -2.63846 q^{24} +1.00000 q^{25} -9.33052 q^{26} -5.41897 q^{27} -3.09732 q^{28} -7.12065 q^{29} -3.57990 q^{30} +3.83645 q^{31} +7.52362 q^{32} +2.15486 q^{33} +10.2631 q^{34} -1.13164 q^{35} -0.806254 q^{36} -1.75632 q^{37} +1.55044 q^{38} +7.05133 q^{39} -1.60410 q^{40} +2.27756 q^{41} +4.05115 q^{42} +8.13683 q^{43} +3.58574 q^{44} -0.294573 q^{45} +1.40778 q^{46} -5.11822 q^{47} -3.26127 q^{48} -5.71939 q^{49} -2.17647 q^{50} -7.75609 q^{51} +11.7336 q^{52} -5.96794 q^{53} +11.7942 q^{54} +1.31009 q^{55} +1.81527 q^{56} -1.17171 q^{57} +15.4979 q^{58} +13.0264 q^{59} +4.50190 q^{60} +12.5056 q^{61} -8.34993 q^{62} +0.333351 q^{63} -12.4094 q^{64} +4.28700 q^{65} -4.68998 q^{66} +6.11219 q^{67} -12.9063 q^{68} -1.06390 q^{69} +2.46298 q^{70} +7.89927 q^{71} +0.472527 q^{72} +14.8581 q^{73} +3.82257 q^{74} +1.64482 q^{75} -1.94976 q^{76} -1.48255 q^{77} -15.3470 q^{78} -3.87006 q^{79} -1.98276 q^{80} -8.02951 q^{81} -4.95704 q^{82} +5.02342 q^{83} -5.09453 q^{84} -4.71547 q^{85} -17.7096 q^{86} -11.7122 q^{87} -2.10152 q^{88} +13.4038 q^{89} +0.641130 q^{90} -4.85133 q^{91} -1.77036 q^{92} +6.31027 q^{93} +11.1397 q^{94} -0.712364 q^{95} +12.3750 q^{96} +6.10495 q^{97} +12.4481 q^{98} -0.385917 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 111 q + 20 q^{2} + 40 q^{3} + 136 q^{4} + 111 q^{5} + 3 q^{6} + 39 q^{7} + 45 q^{8} + 139 q^{9}+O(q^{10}) $ 111 * q + 20 * q^2 + 40 * q^3 + 136 * q^4 + 111 * q^5 + 3 * q^6 + 39 * q^7 + 45 * q^8 + 139 * q^9	\( 111 q + 20 q^{2} + 40 q^{3} + 136 q^{4} + 111 q^{5} + 3 q^{6} + 39 q^{7} + 45 q^{8} + 139 q^{9} + 20 q^{10} + 36 q^{11} + 80 q^{12} + 36 q^{13} + 7 q^{14} + 40 q^{15} + 190 q^{16} + 38 q^{17} + 48 q^{18} + 77 q^{19} + 136 q^{20} + 11 q^{21} + 39 q^{22} + 82 q^{23} - 3 q^{24} + 111 q^{25} - 3 q^{26} + 130 q^{27} + 87 q^{28} + 20 q^{29} + 3 q^{30} + 41 q^{31} + 85 q^{32} + 33 q^{33} + 7 q^{34} + 39 q^{35} + 191 q^{36} + 80 q^{37} + 42 q^{38} + 21 q^{39} + 45 q^{40} + 16 q^{41} + 33 q^{42} + 164 q^{43} + 37 q^{44} + 139 q^{45} + 32 q^{46} + 148 q^{47} + 149 q^{48} + 160 q^{49} + 20 q^{50} + 51 q^{51} + 87 q^{52} + 83 q^{53} - 6 q^{54} + 36 q^{55} - 10 q^{56} + 28 q^{57} + 47 q^{58} + 14 q^{59} + 80 q^{60} + 20 q^{61} + 14 q^{62} + 120 q^{63} + 231 q^{64} + 36 q^{65} - 4 q^{66} + 253 q^{67} + 80 q^{68} + 6 q^{69} + 7 q^{70} + 5 q^{71} + 124 q^{72} + 64 q^{73} - 37 q^{74} + 40 q^{75} + 92 q^{76} + 63 q^{77} + 29 q^{78} + 91 q^{79} + 190 q^{80} + 187 q^{81} - 7 q^{82} + 63 q^{83} - 69 q^{84} + 38 q^{85} - 22 q^{86} + 57 q^{87} + 121 q^{88} - 6 q^{89} + 48 q^{90} + 119 q^{91} + 104 q^{92} + 14 q^{93} - q^{94} + 77 q^{95} - 38 q^{96} + 96 q^{97} + 81 q^{98} + 106 q^{99}+O(q^{100}) \) 111 * q + 20 * q^2 + 40 * q^3 + 136 * q^4 + 111 * q^5 + 3 * q^6 + 39 * q^7 + 45 * q^8 + 139 * q^9 + 20 * q^10 + 36 * q^11 + 80 * q^12 + 36 * q^13 + 7 * q^14 + 40 * q^15 + 190 * q^16 + 38 * q^17 + 48 * q^18 + 77 * q^19 + 136 * q^20 + 11 * q^21 + 39 * q^22 + 82 * q^23 - 3 * q^24 + 111 * q^25 - 3 * q^26 + 130 * q^27 + 87 * q^28 + 20 * q^29 + 3 * q^30 + 41 * q^31 + 85 * q^32 + 33 * q^33 + 7 * q^34 + 39 * q^35 + 191 * q^36 + 80 * q^37 + 42 * q^38 + 21 * q^39 + 45 * q^40 + 16 * q^41 + 33 * q^42 + 164 * q^43 + 37 * q^44 + 139 * q^45 + 32 * q^46 + 148 * q^47 + 149 * q^48 + 160 * q^49 + 20 * q^50 + 51 * q^51 + 87 * q^52 + 83 * q^53 - 6 * q^54 + 36 * q^55 - 10 * q^56 + 28 * q^57 + 47 * q^58 + 14 * q^59 + 80 * q^60 + 20 * q^61 + 14 * q^62 + 120 * q^63 + 231 * q^64 + 36 * q^65 - 4 * q^66 + 253 * q^67 + 80 * q^68 + 6 * q^69 + 7 * q^70 + 5 * q^71 + 124 * q^72 + 64 * q^73 - 37 * q^74 + 40 * q^75 + 92 * q^76 + 63 * q^77 + 29 * q^78 + 91 * q^79 + 190 * q^80 + 187 * q^81 - 7 * q^82 + 63 * q^83 - 69 * q^84 + 38 * q^85 - 22 * q^86 + 57 * q^87 + 121 * q^88 - 6 * q^89 + 48 * q^90 + 119 * q^91 + 104 * q^92 + 14 * q^93 - q^94 + 77 * q^95 - 38 * q^96 + 96 * q^97 + 81 * q^98 + 106 * 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 $

$2$	−2.17647	−1.53900	−0.769498	−	0.638649i	$-0.779494\pi$
$2$	−2.17647	−1.53900	−0.769498	+	0.638649i	$0.779494\pi$
$3$	1.64482	0.949636	0.474818	−	0.880084i	$-0.342514\pi$
$3$	1.64482	0.949636	0.474818	+	0.880084i	$0.342514\pi$
$4$	2.73702	1.36851
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	−3.57990	−1.46149
$7$	−1.13164	−0.427719	−0.213860	−	0.976864i	$-0.568603\pi$
$7$	−1.13164	−0.427719	−0.213860	+	0.976864i	$0.568603\pi$
$8$	−1.60410	−0.567137
$9$	−0.294573	−0.0981912
$10$	−2.17647	−0.688260
$11$	1.31009	0.395006	0.197503	−	0.980302i	$-0.436717\pi$
$11$	1.31009	0.395006	0.197503	+	0.980302i	$0.436717\pi$
$12$	4.50190	1.29959
$13$	4.28700	1.18900	0.594500	−	0.804096i	$-0.297350\pi$
$13$	4.28700	1.18900	0.594500	+	0.804096i	$0.297350\pi$
$14$	2.46298	0.658258
$15$	1.64482	0.424690
$16$	−1.98276	−0.495689
$17$	−4.71547	−1.14367	−0.571834	−	0.820369i	$-0.693768\pi$
$17$	−4.71547	−1.14367	−0.571834	+	0.820369i	$0.693768\pi$
$18$	0.641130	0.151116
$19$	−0.712364	−0.163428	−0.0817138	−	0.996656i	$-0.526039\pi$
$19$	−0.712364	−0.163428	−0.0817138	+	0.996656i	$0.526039\pi$
$20$	2.73702	0.612017
$21$	−1.86134	−0.406178
$22$	−2.85137	−0.607913
$23$	−0.646819	−0.134871	−0.0674355	−	0.997724i	$-0.521482\pi$
$23$	−0.646819	−0.134871	−0.0674355	+	0.997724i	$0.521482\pi$
$24$	−2.63846	−0.538573
$25$	1.00000	0.200000
$26$	−9.33052	−1.82987
$27$	−5.41897	−1.04288
$28$	−3.09732	−0.585338
$29$	−7.12065	−1.32227	−0.661135	−	0.750267i	$-0.729925\pi$
$29$	−7.12065	−1.32227	−0.661135	+	0.750267i	$0.729925\pi$
$30$	−3.57990	−0.653597
$31$	3.83645	0.689048	0.344524	−	0.938778i	$-0.388040\pi$
$31$	3.83645	0.689048	0.344524	+	0.938778i	$0.388040\pi$
$32$	7.52362	1.33000
$33$	2.15486	0.375112
$34$	10.2631	1.76010
$35$	−1.13164	−0.191282
$36$	−0.806254	−0.134376
$37$	−1.75632	−0.288737	−0.144368	−	0.989524i	$-0.546115\pi$
$37$	−1.75632	−0.288737	−0.144368	+	0.989524i	$0.546115\pi$
$38$	1.55044	0.251514
$39$	7.05133	1.12912
$40$	−1.60410	−0.253631
$41$	2.27756	0.355695	0.177847	−	0.984058i	$-0.443087\pi$
$41$	2.27756	0.355695	0.177847	+	0.984058i	$0.443087\pi$
$42$	4.05115	0.625106
$43$	8.13683	1.24085	0.620427	−	0.784264i	$-0.286959\pi$
$43$	8.13683	1.24085	0.620427	+	0.784264i	$0.286959\pi$
$44$	3.58574	0.540570
$45$	−0.294573	−0.0439124
$46$	1.40778	0.207566
$47$	−5.11822	−0.746569	−0.373285	−	0.927717i	$-0.621768\pi$
$47$	−5.11822	−0.746569	−0.373285	+	0.927717i	$0.621768\pi$
$48$	−3.26127	−0.470724
$49$	−5.71939	−0.817056
$50$	−2.17647	−0.307799
$51$	−7.75609	−1.08607
$52$	11.7336	1.62716
$53$	−5.96794	−0.819760	−0.409880	−	0.912139i	$-0.634429\pi$
$53$	−5.96794	−0.819760	−0.409880	+	0.912139i	$0.634429\pi$
$54$	11.7942	1.60499
$55$	1.31009	0.176652
$56$	1.81527	0.242575
$57$	−1.17171	−0.155197
$58$	15.4979	2.03497
$59$	13.0264	1.69589	0.847943	−	0.530087i	$-0.177841\pi$
$59$	13.0264	1.69589	0.847943	+	0.530087i	$0.177841\pi$
$60$	4.50190	0.581193
$61$	12.5056	1.60117	0.800587	−	0.599217i	$-0.204521\pi$
$61$	12.5056	1.60117	0.800587	+	0.599217i	$0.204521\pi$
$62$	−8.34993	−1.06044
$63$	0.333351	0.0419982
$64$	−12.4094	−1.55118
$65$	4.28700	0.531737
$66$	−4.68998	−0.577297
$67$	6.11219	0.746723	0.373361	−	0.927686i	$-0.378205\pi$
$67$	6.11219	0.746723	0.373361	+	0.927686i	$0.378205\pi$
$68$	−12.9063	−1.56512
$69$	−1.06390	−0.128078
$70$	2.46298	0.294382
$71$	7.89927	0.937470	0.468735	−	0.883339i	$-0.344710\pi$
$71$	7.89927	0.937470	0.468735	+	0.883339i	$0.344710\pi$
$72$	0.472527	0.0556878
$73$	14.8581	1.73901	0.869503	−	0.493927i	$-0.164439\pi$
$73$	14.8581	1.73901	0.869503	+	0.493927i	$0.164439\pi$
$74$	3.82257	0.444365
$75$	1.64482	0.189927
$76$	−1.94976	−0.223652
$77$	−1.48255	−0.168952
$78$	−15.3470	−1.73771
$79$	−3.87006	−0.435416	−0.217708	−	0.976014i	$-0.569858\pi$
$79$	−3.87006	−0.435416	−0.217708	+	0.976014i	$0.569858\pi$
$80$	−1.98276	−0.221679
$81$	−8.02951	−0.892167
$82$	−4.95704	−0.547413
$83$	5.02342	0.551392	0.275696	−	0.961245i	$-0.411092\pi$
$83$	5.02342	0.551392	0.275696	+	0.961245i	$0.411092\pi$
$84$	−5.09453	−0.555858
$85$	−4.71547	−0.511464
$86$	−17.7096	−1.90967
$87$	−11.7122	−1.25568
$88$	−2.10152	−0.224023
$89$	13.4038	1.42080	0.710398	−	0.703801i	$-0.248515\pi$
$89$	13.4038	1.42080	0.710398	+	0.703801i	$0.248515\pi$
$90$	0.641130	0.0675811
$91$	−4.85133	−0.508558
$92$	−1.77036	−0.184572
$93$	6.31027	0.654344
$94$	11.1397	1.14897
$95$	−0.712364	−0.0730870
$96$	12.3750	1.26302
$97$	6.10495	0.619864	0.309932	−	0.950759i	$-0.399694\pi$
$97$	6.10495	0.619864	0.309932	+	0.950759i	$0.399694\pi$
$98$	12.4481	1.25745
$99$	−0.385917	−0.0387861
$100$	2.73702	0.273702
$101$	0.920226	0.0915659	0.0457829	−	0.998951i	$-0.485422\pi$
$101$	0.920226	0.0915659	0.0457829	+	0.998951i	$0.485422\pi$
$102$	16.8809	1.67146
$103$	−10.5953	−1.04399	−0.521995	−	0.852949i	$-0.674812\pi$
$103$	−10.5953	−1.04399	−0.521995	+	0.852949i	$0.674812\pi$
$104$	−6.87679	−0.674325
$105$	−1.86134	−0.181648
$106$	12.9890	1.26161
$107$	0.0213886	0.00206771	0.00103386	−	0.999999i	$-0.499671\pi$
$107$	0.0213886	0.00206771	0.00103386	+	0.999999i	$0.499671\pi$
$108$	−14.8318	−1.42720
$109$	2.52954	0.242286	0.121143	−	0.992635i	$-0.461344\pi$
$109$	2.52954	0.242286	0.121143	+	0.992635i	$0.461344\pi$
$110$	−2.85137	−0.271867
$111$	−2.88882	−0.274195
$112$	2.24376	0.212016
$113$	10.8185	1.01772	0.508861	−	0.860849i	$-0.330067\pi$
$113$	10.8185	1.01772	0.508861	+	0.860849i	$0.330067\pi$
$114$	2.55019	0.238847
$115$	−0.646819	−0.0603161
$116$	−19.4894	−1.80954
$117$	−1.26284	−0.116749
$118$	−28.3515	−2.60996
$119$	5.33620	0.489169
$120$	−2.63846	−0.240857
$121$	−9.28367	−0.843970
$122$	−27.2180	−2.46420
$123$	3.74617	0.337781
$124$	10.5005	0.942969
$125$	1.00000	0.0894427
$126$	−0.725528	−0.0646351
$127$	−13.2018	−1.17147	−0.585733	−	0.810504i	$-0.699193\pi$
$127$	−13.2018	−1.17147	−0.585733	+	0.810504i	$0.699193\pi$
$128$	11.9615	1.05726
$129$	13.3836	1.17836
$130$	−9.33052	−0.818341
$131$	−0.216187	−0.0188883	−0.00944417	−	0.999955i	$-0.503006\pi$
$131$	−0.216187	−0.0188883	−0.00944417	+	0.999955i	$0.503006\pi$
$132$	5.89789	0.513345
$133$	0.806139	0.0699011
$134$	−13.3030	−1.14920
$135$	−5.41897	−0.466391
$136$	7.56410	0.648617
$137$	7.22761	0.617496	0.308748	−	0.951144i	$-0.400090\pi$
$137$	7.22761	0.617496	0.308748	+	0.951144i	$0.400090\pi$
$138$	2.31554	0.197112
$139$	−13.3567	−1.13290	−0.566451	−	0.824095i	$-0.691684\pi$
$139$	−13.3567	−1.13290	−0.566451	+	0.824095i	$0.691684\pi$
$140$	−3.09732	−0.261771
$141$	−8.41854	−0.708969
$142$	−17.1925	−1.44276
$143$	5.61634	0.469662
$144$	0.584068	0.0486723
$145$	−7.12065	−0.591338
$146$	−32.3382	−2.67632
$147$	−9.40736	−0.775906
$148$	−4.80708	−0.395139
$149$	−9.89582	−0.810697	−0.405349	−	0.914162i	$-0.632850\pi$
$149$	−9.89582	−0.810697	−0.405349	+	0.914162i	$0.632850\pi$
$150$	−3.57990	−0.292297
$151$	18.9596	1.54291	0.771456	−	0.636283i	$-0.219529\pi$
$151$	18.9596	1.54291	0.771456	+	0.636283i	$0.219529\pi$
$152$	1.14271	0.0926857
$153$	1.38905	0.112298
$154$	3.22672	0.260016
$155$	3.83645	0.308151
$156$	19.2996	1.54521
$157$	22.7344	1.81440	0.907201	−	0.420697i	$-0.138214\pi$
$157$	22.7344	1.81440	0.907201	+	0.420697i	$0.138214\pi$
$158$	8.42307	0.670103
$159$	−9.81618	−0.778474
$160$	7.52362	0.594794
$161$	0.731965	0.0576869
$162$	17.4760	1.37304
$163$	15.1388	1.18576	0.592880	−	0.805291i	$-0.297991\pi$
$163$	15.1388	1.18576	0.592880	+	0.805291i	$0.297991\pi$
$164$	6.23373	0.486772
$165$	2.15486	0.167755
$166$	−10.9333	−0.848591
$167$	3.12264	0.241637	0.120818	−	0.992675i	$-0.461448\pi$
$167$	3.12264	0.241637	0.120818	+	0.992675i	$0.461448\pi$
$168$	2.98578	0.230358
$169$	5.37835	0.413719
$170$	10.2631	0.787142
$171$	0.209844	0.0160471
$172$	22.2707	1.69812
$173$	16.8400	1.28032	0.640161	−	0.768241i	$-0.278868\pi$
$173$	16.8400	1.28032	0.640161	+	0.768241i	$0.278868\pi$
$174$	25.4912	1.93248
$175$	−1.13164	−0.0855438
$176$	−2.59759	−0.195800
$177$	21.4260	1.61048
$178$	−29.1729	−2.18660
$179$	10.3414	0.772949	0.386475	−	0.922300i	$-0.373693\pi$
$179$	10.3414	0.772949	0.386475	+	0.922300i	$0.373693\pi$
$180$	−0.806254	−0.0600946
$181$	2.73888	0.203580	0.101790	−	0.994806i	$-0.467543\pi$
$181$	2.73888	0.203580	0.101790	+	0.994806i	$0.467543\pi$
$182$	10.5588	0.782669
$183$	20.5694	1.52053
$184$	1.03756	0.0764903
$185$	−1.75632	−0.129127
$186$	−13.7341	−1.00703
$187$	−6.17768	−0.451756
$188$	−14.0087	−1.02169
$189$	6.13232	0.446061
$190$	1.55044	0.112481
$191$	−13.5758	−0.982309	−0.491155	−	0.871072i	$-0.663425\pi$
$191$	−13.5758	−0.982309	−0.491155	+	0.871072i	$0.663425\pi$
$192$	−20.4112	−1.47305
$193$	22.0022	1.58375	0.791877	−	0.610680i	$-0.209104\pi$
$193$	22.0022	1.58375	0.791877	+	0.610680i	$0.209104\pi$
$194$	−13.2872	−0.953968
$195$	7.05133	0.504956
$196$	−15.6541	−1.11815
$197$	16.2998	1.16131	0.580656	−	0.814149i	$-0.302796\pi$
$197$	16.2998	1.16131	0.580656	+	0.814149i	$0.302796\pi$
$198$	0.839937	0.0596917
$199$	−0.941347	−0.0667303	−0.0333651	−	0.999443i	$-0.510622\pi$
$199$	−0.941347	−0.0667303	−0.0333651	+	0.999443i	$0.510622\pi$
$200$	−1.60410	−0.113427
$201$	10.0534	0.709115
$202$	−2.00284	−0.140920
$203$	8.05800	0.565561
$204$	−21.2286	−1.48630
$205$	2.27756	0.159072
$206$	23.0604	1.60670
$207$	0.190536	0.0132431
$208$	−8.50008	−0.589374
$209$	−0.933259	−0.0645549
$210$	4.05115	0.279556
$211$	6.73418	0.463600	0.231800	−	0.972763i	$-0.425538\pi$
$211$	6.73418	0.463600	0.231800	+	0.972763i	$0.425538\pi$
$212$	−16.3344	−1.12185
$213$	12.9929	0.890256
$214$	−0.0465516	−0.00318220
$215$	8.13683	0.554927
$216$	8.69260	0.591457
$217$	−4.34148	−0.294719
$218$	−5.50547	−0.372878
$219$	24.4388	1.65142
$220$	3.58574	0.241750
$221$	−20.2152	−1.35982
$222$	6.28743	0.421985
$223$	16.7283	1.12021	0.560105	−	0.828422i	$-0.310761\pi$
$223$	16.7283	1.12021	0.560105	+	0.828422i	$0.310761\pi$
$224$	−8.51402	−0.568867
$225$	−0.294573	−0.0196382
$226$	−23.5462	−1.56627
$227$	−16.0767	−1.06705	−0.533523	−	0.845786i	$-0.679132\pi$
$227$	−16.0767	−1.06705	−0.533523	+	0.845786i	$0.679132\pi$
$228$	−3.20699	−0.212388
$229$	6.40548	0.423286	0.211643	−	0.977347i	$-0.432119\pi$
$229$	6.40548	0.423286	0.211643	+	0.977347i	$0.432119\pi$
$230$	1.40778	0.0928263
$231$	−2.43852	−0.160443
$232$	11.4223	0.749908
$233$	19.6184	1.28524	0.642621	−	0.766184i	$-0.277847\pi$
$233$	19.6184	1.28524	0.642621	+	0.766184i	$0.277847\pi$
$234$	2.74852	0.179677
$235$	−5.11822	−0.333876
$236$	35.6534	2.32084
$237$	−6.36554	−0.413486
$238$	−11.6141	−0.752830
$239$	−28.0125	−1.81198	−0.905990	−	0.423298i	$-0.860872\pi$
$239$	−28.0125	−1.81198	−0.905990	+	0.423298i	$0.860872\pi$
$240$	−3.26127	−0.210514
$241$	−22.0268	−1.41887	−0.709435	−	0.704771i	$-0.751050\pi$
$241$	−22.0268	−1.41887	−0.709435	+	0.704771i	$0.751050\pi$
$242$	20.2056	1.29887
$243$	3.04985	0.195648
$244$	34.2280	2.19122
$245$	−5.71939	−0.365399
$246$	−8.15343	−0.519843
$247$	−3.05390	−0.194315
$248$	−6.15407	−0.390784
$249$	8.26262	0.523622
$250$	−2.17647	−0.137652
$251$	16.2921	1.02835	0.514173	−	0.857687i	$-0.328099\pi$
$251$	16.2921	1.02835	0.514173	+	0.857687i	$0.328099\pi$
$252$	0.912388	0.0574750
$253$	−0.847389	−0.0532749
$254$	28.7332	1.80288
$255$	−7.75609	−0.485705
$256$	−1.21498	−0.0759361
$257$	−12.5408	−0.782271	−0.391136	−	0.920333i	$-0.627918\pi$
$257$	−12.5408	−0.782271	−0.391136	+	0.920333i	$0.627918\pi$
$258$	−29.1290	−1.81349
$259$	1.98752	0.123498
$260$	11.7336	0.727687
$261$	2.09755	0.129835
$262$	0.470524	0.0290691
$263$	−23.8176	−1.46866	−0.734328	−	0.678795i	$-0.762502\pi$
$263$	−23.8176	−1.46866	−0.734328	+	0.678795i	$0.762502\pi$
$264$	−3.45661	−0.212740
$265$	−5.96794	−0.366608
$266$	−1.75454	−0.107578
$267$	22.0467	1.34924
$268$	16.7292	1.02190
$269$	16.9338	1.03248	0.516238	−	0.856445i	$-0.327332\pi$
$269$	16.9338	1.03248	0.516238	+	0.856445i	$0.327332\pi$
$270$	11.7942	0.717774
$271$	26.6652	1.61979	0.809897	−	0.586573i	$-0.199523\pi$
$271$	26.6652	1.61979	0.809897	+	0.586573i	$0.199523\pi$
$272$	9.34963	0.566904
$273$	−7.97956	−0.482945
$274$	−15.7307	−0.950324
$275$	1.31009	0.0790013
$276$	−2.91191	−0.175277
$277$	4.82219	0.289738	0.144869	−	0.989451i	$-0.453724\pi$
$277$	4.82219	0.289738	0.144869	+	0.989451i	$0.453724\pi$
$278$	29.0705	1.74353
$279$	−1.13012	−0.0676584
$280$	1.81527	0.108483
$281$	12.2601	0.731375	0.365688	−	0.930738i	$-0.380834\pi$
$281$	12.2601	0.731375	0.365688	+	0.930738i	$0.380834\pi$
$282$	18.3227	1.09110
$283$	−10.2142	−0.607172	−0.303586	−	0.952804i	$-0.598184\pi$
$283$	−10.2142	−0.607172	−0.303586	+	0.952804i	$0.598184\pi$
$284$	21.6205	1.28294
$285$	−1.17171	−0.0694061
$286$	−12.2238	−0.722809
$287$	−2.57737	−0.152138
$288$	−2.21626	−0.130594
$289$	5.23564	0.307979
$290$	15.4979	0.910066
$291$	10.0415	0.588645
$292$	40.6669	2.37985
$293$	−11.4031	−0.666174	−0.333087	−	0.942896i	$-0.608090\pi$
$293$	−11.4031	−0.666174	−0.333087	+	0.942896i	$0.608090\pi$
$294$	20.4748	1.19412
$295$	13.0264	0.758424
$296$	2.81732	0.163753
$297$	−7.09933	−0.411945
$298$	21.5380	1.24766
$299$	−2.77291	−0.160362
$300$	4.50190	0.259917
$301$	−9.20795	−0.530737
$302$	−41.2650	−2.37453
$303$	1.51360	0.0869543
$304$	1.41244	0.0810093
$305$	12.5056	0.716067
$306$	−3.02323	−0.172827
$307$	11.8507	0.676355	0.338178	−	0.941082i	$-0.390190\pi$
$307$	11.8507	0.676355	0.338178	+	0.941082i	$0.390190\pi$
$308$	−4.05776	−0.231212
$309$	−17.4274	−0.991410
$310$	−8.34993	−0.474244
$311$	−18.3993	−1.04333	−0.521664	−	0.853151i	$-0.674689\pi$
$311$	−18.3993	−1.04333	−0.521664	+	0.853151i	$0.674689\pi$
$312$	−11.3111	−0.640363
$313$	11.8573	0.670215	0.335107	−	0.942180i	$-0.391227\pi$
$313$	11.8573	0.670215	0.335107	+	0.942180i	$0.391227\pi$
$314$	−49.4807	−2.79236
$315$	0.333351	0.0187822
$316$	−10.5924	−0.595871
$317$	−29.4055	−1.65158	−0.825789	−	0.563979i	$-0.809270\pi$
$317$	−29.4055	−1.65158	−0.825789	+	0.563979i	$0.809270\pi$
$318$	21.3646	1.19807
$319$	−9.32867	−0.522305
$320$	−12.4094	−0.693708
$321$	0.0351803	0.00196357
$322$	−1.59310	−0.0887799
$323$	3.35913	0.186907
$324$	−21.9769	−1.22094
$325$	4.28700	0.237800
$326$	−32.9491	−1.82488
$327$	4.16064	0.230084
$328$	−3.65344	−0.201728
$329$	5.79198	0.319322
$330$	−4.68998	−0.258175
$331$	−30.7589	−1.69066	−0.845330	−	0.534245i	$-0.820596\pi$
$331$	−30.7589	−1.69066	−0.845330	+	0.534245i	$0.820596\pi$
$332$	13.7492	0.754586
$333$	0.517364	0.0283514
$334$	−6.79633	−0.371878
$335$	6.11219	0.333945
$336$	3.69058	0.201338
$337$	−27.9145	−1.52060	−0.760299	−	0.649574i	$-0.774947\pi$
$337$	−27.9145	−1.52060	−0.760299	+	0.649574i	$0.774947\pi$
$338$	−11.7058	−0.636713
$339$	17.7945	0.966466
$340$	−12.9063	−0.699944
$341$	5.02609	0.272178
$342$	−0.456718	−0.0246965
$343$	14.3938	0.777190
$344$	−13.0523	−0.703734
$345$	−1.06390	−0.0572784
$346$	−36.6518	−1.97041
$347$	−23.7613	−1.27557	−0.637785	−	0.770214i	$-0.720149\pi$
$347$	−23.7613	−1.27557	−0.637785	+	0.770214i	$0.720149\pi$
$348$	−32.0565	−1.71841
$349$	−8.16149	−0.436874	−0.218437	−	0.975851i	$-0.570096\pi$
$349$	−8.16149	−0.436874	−0.218437	+	0.975851i	$0.570096\pi$
$350$	2.46298	0.131652
$351$	−23.2311	−1.23999
$352$	9.85660	0.525359
$353$	24.5073	1.30439	0.652197	−	0.758050i	$-0.273848\pi$
$353$	24.5073	1.30439	0.652197	+	0.758050i	$0.273848\pi$
$354$	−46.6330	−2.47852
$355$	7.89927	0.419250
$356$	36.6864	1.94437
$357$	8.77709	0.464533
$358$	−22.5077	−1.18957
$359$	14.3513	0.757433	0.378716	−	0.925513i	$-0.376366\pi$
$359$	14.3513	0.757433	0.378716	+	0.925513i	$0.376366\pi$
$360$	0.472527	0.0249043
$361$	−18.4925	−0.973291
$362$	−5.96110	−0.313308
$363$	−15.2699	−0.801464
$364$	−13.2782	−0.695967
$365$	14.8581	0.777707
$366$	−44.7686	−2.34009
$367$	37.6440	1.96500	0.982501	−	0.186257i	$-0.0596358\pi$
$367$	37.6440	1.96500	0.982501	+	0.186257i	$0.0596358\pi$
$368$	1.28248	0.0668541
$369$	−0.670908	−0.0349261
$370$	3.82257	0.198726
$371$	6.75355	0.350627
$372$	17.2713	0.895477
$373$	−2.38949	−0.123723	−0.0618615	−	0.998085i	$-0.519704\pi$
$373$	−2.38949	−0.123723	−0.0618615	+	0.998085i	$0.519704\pi$
$374$	13.4455	0.695252
$375$	1.64482	0.0849380
$376$	8.21016	0.423407
$377$	−30.5262	−1.57218
$378$	−13.3468	−0.686486
$379$	−14.4812	−0.743850	−0.371925	−	0.928263i	$-0.621302\pi$
$379$	−14.4812	−0.743850	−0.371925	+	0.928263i	$0.621302\pi$
$380$	−1.94976	−0.100020
$381$	−21.7145	−1.11247
$382$	29.5473	1.51177
$383$	−2.78519	−0.142316	−0.0711582	−	0.997465i	$-0.522670\pi$
$383$	−2.78519	−0.142316	−0.0711582	+	0.997465i	$0.522670\pi$
$384$	19.6745	1.00401
$385$	−1.48255	−0.0755575
$386$	−47.8872	−2.43739
$387$	−2.39689	−0.121841
$388$	16.7094	0.848290
$389$	−0.974575	−0.0494129	−0.0247065	−	0.999695i	$-0.507865\pi$
$389$	−0.974575	−0.0494129	−0.0247065	+	0.999695i	$0.507865\pi$
$390$	−15.3470	−0.777126
$391$	3.05005	0.154248
$392$	9.17451	0.463383
$393$	−0.355588	−0.0179371
$394$	−35.4760	−1.78725
$395$	−3.87006	−0.194724
$396$	−1.05626	−0.0530792
$397$	−11.7006	−0.587238	−0.293619	−	0.955923i	$-0.594860\pi$
$397$	−11.7006	−0.587238	−0.293619	+	0.955923i	$0.594860\pi$
$398$	2.04881	0.102698
$399$	1.32595	0.0663806
$400$	−1.98276	−0.0991379
$401$	−30.1914	−1.50769	−0.753843	−	0.657054i	$-0.771802\pi$
$401$	−30.1914	−1.50769	−0.753843	+	0.657054i	$0.771802\pi$
$402$	−21.8810	−1.09133
$403$	16.4469	0.819277
$404$	2.51868	0.125309
$405$	−8.02951	−0.398989
$406$	−17.5380	−0.870396
$407$	−2.30093	−0.114053
$408$	12.4416	0.615950
$409$	−3.15389	−0.155950	−0.0779749	−	0.996955i	$-0.524845\pi$
$409$	−3.15389	−0.155950	−0.0779749	+	0.996955i	$0.524845\pi$
$410$	−4.95704	−0.244811
$411$	11.8881	0.586397
$412$	−28.9997	−1.42871
$413$	−14.7411	−0.725363
$414$	−0.414695	−0.0203811
$415$	5.02342	0.246590
$416$	32.2537	1.58137
$417$	−21.9694	−1.07585
$418$	2.03121	0.0993498
$419$	−18.2589	−0.892005	−0.446002	−	0.895032i	$-0.647153\pi$
$419$	−18.2589	−0.892005	−0.446002	+	0.895032i	$0.647153\pi$
$420$	−5.09453	−0.248587
$421$	20.6668	1.00724	0.503620	−	0.863925i	$-0.332001\pi$
$421$	20.6668	1.00724	0.503620	+	0.863925i	$0.332001\pi$
$422$	−14.6567	−0.713479
$423$	1.50769	0.0733065
$424$	9.57320	0.464916
$425$	−4.71547	−0.228734
$426$	−28.2786	−1.37010
$427$	−14.1518	−0.684853
$428$	0.0585410	0.00282969
$429$	9.23786	0.446008
$430$	−17.7096	−0.854031
$431$	21.3703	1.02937	0.514685	−	0.857379i	$-0.327909\pi$
$431$	21.3703	1.02937	0.514685	+	0.857379i	$0.327909\pi$
$432$	10.7445	0.516945
$433$	13.6867	0.657743	0.328872	−	0.944375i	$-0.393332\pi$
$433$	13.6867	0.657743	0.328872	+	0.944375i	$0.393332\pi$
$434$	9.44910	0.453571
$435$	−11.7122	−0.561555
$436$	6.92341	0.331571
$437$	0.460770	0.0220416
$438$	−53.1904	−2.54153
$439$	28.9170	1.38013	0.690067	−	0.723745i	$-0.257581\pi$
$439$	28.9170	1.38013	0.690067	+	0.723745i	$0.257581\pi$
$440$	−2.10152	−0.100186
$441$	1.68478	0.0802277
$442$	43.9978	2.09276
$443$	−30.0485	−1.42765	−0.713825	−	0.700324i	$-0.753039\pi$
$443$	−30.0485	−1.42765	−0.713825	+	0.700324i	$0.753039\pi$
$444$	−7.90677	−0.375239
$445$	13.4038	0.635399
$446$	−36.4086	−1.72400
$447$	−16.2768	−0.769867
$448$	14.0430	0.663468
$449$	−17.7936	−0.839733	−0.419867	−	0.907586i	$-0.637923\pi$
$449$	−17.7936	−0.839733	−0.419867	+	0.907586i	$0.637923\pi$
$450$	0.641130	0.0302232
$451$	2.98380	0.140502
$452$	29.6106	1.39276
$453$	31.1851	1.46520
$454$	34.9904	1.64218
$455$	−4.85133	−0.227434
$456$	1.87954	0.0880177
$457$	18.3276	0.857330	0.428665	−	0.903463i	$-0.358984\pi$
$457$	18.3276	0.857330	0.428665	+	0.903463i	$0.358984\pi$
$458$	−13.9413	−0.651436
$459$	25.5530	1.19271
$460$	−1.77036	−0.0825433
$461$	12.6966	0.591341	0.295671	−	0.955290i	$-0.404457\pi$
$461$	12.6966	0.591341	0.295671	+	0.955290i	$0.404457\pi$
$462$	5.30736	0.246921
$463$	16.2981	0.757435	0.378718	−	0.925512i	$-0.376365\pi$
$463$	16.2981	0.757435	0.378718	+	0.925512i	$0.376365\pi$
$464$	14.1185	0.655436
$465$	6.31027	0.292632
$466$	−42.6988	−1.97798
$467$	4.67028	0.216115	0.108057	−	0.994145i	$-0.465537\pi$
$467$	4.67028	0.216115	0.108057	+	0.994145i	$0.465537\pi$
$468$	−3.45641	−0.159773
$469$	−6.91679	−0.319388
$470$	11.1397	0.513834
$471$	37.3940	1.72302
$472$	−20.8956	−0.961800
$473$	10.6600	0.490145
$474$	13.8544	0.636354
$475$	−0.712364	−0.0326855
$476$	14.6053	0.669433
$477$	1.75800	0.0804932
$478$	60.9685	2.78863
$479$	−40.1061	−1.83250	−0.916248	−	0.400611i	$-0.868798\pi$
$479$	−40.1061	−1.83250	−0.916248	+	0.400611i	$0.868798\pi$
$480$	12.3750	0.564838
$481$	−7.52933	−0.343308
$482$	47.9407	2.18364
$483$	1.20395	0.0547816
$484$	−25.4096	−1.15498
$485$	6.10495	0.277212
$486$	−6.63790	−0.301101
$487$	41.4318	1.87746	0.938728	−	0.344660i	$-0.112006\pi$
$487$	41.4318	1.87746	0.938728	+	0.344660i	$0.112006\pi$
$488$	−20.0602	−0.908084
$489$	24.9005	1.12604
$490$	12.4481	0.562347
$491$	−20.6256	−0.930822	−0.465411	−	0.885095i	$-0.654093\pi$
$491$	−20.6256	−0.930822	−0.465411	+	0.885095i	$0.654093\pi$
$492$	10.2533	0.462257
$493$	33.5772	1.51224
$494$	6.64673	0.299050
$495$	−0.385917	−0.0173457
$496$	−7.60676	−0.341553
$497$	−8.93911	−0.400974
$498$	−17.9833	−0.805852
$499$	22.8567	1.02321	0.511604	−	0.859221i	$-0.329052\pi$
$499$	22.8567	1.02321	0.511604	+	0.859221i	$0.329052\pi$
$500$	2.73702	0.122403
$501$	5.13617	0.229467
$502$	−35.4592	−1.58262
$503$	−5.02214	−0.223926	−0.111963	−	0.993712i	$-0.535714\pi$
$503$	−5.02214	−0.223926	−0.111963	+	0.993712i	$0.535714\pi$
$504$	−0.534729	−0.0238187
$505$	0.920226	0.0409495
$506$	1.84432	0.0819899
$507$	8.84641	0.392883
$508$	−36.1335	−1.60316
$509$	23.9278	1.06058	0.530292	−	0.847815i	$-0.322082\pi$
$509$	23.9278	1.06058	0.530292	+	0.847815i	$0.322082\pi$
$510$	16.8809	0.747498
$511$	−16.8140	−0.743806
$512$	−21.2786	−0.940391
$513$	3.86028	0.170436
$514$	27.2946	1.20391
$515$	−10.5953	−0.466886
$516$	36.6312	1.61260
$517$	−6.70532	−0.294900
$518$	−4.32577	−0.190063
$519$	27.6988	1.21584
$520$	−6.87679	−0.301567
$521$	−12.2579	−0.537029	−0.268514	−	0.963276i	$-0.586533\pi$
$521$	−12.2579	−0.537029	−0.268514	+	0.963276i	$0.586533\pi$
$522$	−4.56526	−0.199816
$523$	39.9969	1.74894	0.874472	−	0.485076i	$-0.161208\pi$
$523$	39.9969	1.74894	0.874472	+	0.485076i	$0.161208\pi$
$524$	−0.591708	−0.0258489
$525$	−1.86134	−0.0812355
$526$	51.8383	2.26026
$527$	−18.0907	−0.788042
$528$	−4.27256	−0.185939
$529$	−22.5816	−0.981810
$530$	12.9890	0.564208
$531$	−3.83722	−0.166521
$532$	2.20642	0.0956604
$533$	9.76389	0.422921
$534$	−47.9841	−2.07647
$535$	0.0213886	0.000924709 0
$536$	−9.80459	−0.423494
$537$	17.0097	0.734021
$538$	−36.8560	−1.58898
$539$	−7.49291	−0.322742
$540$	−14.8318	−0.638261
$541$	−41.6798	−1.79195	−0.895977	−	0.444099i	$-0.853524\pi$
$541$	−41.6798	−1.79195	−0.895977	+	0.444099i	$0.853524\pi$
$542$	−58.0359	−2.49286
$543$	4.50497	0.193327
$544$	−35.4774	−1.52108
$545$	2.52954	0.108354
$546$	17.3673	0.743251
$547$	39.6139	1.69377	0.846883	−	0.531779i	$-0.178476\pi$
$547$	39.6139	1.69377	0.846883	+	0.531779i	$0.178476\pi$
$548$	19.7821	0.845050
$549$	−3.68381	−0.157221
$550$	−2.85137	−0.121583
$551$	5.07249	0.216095
$552$	1.70660	0.0726379
$553$	4.37951	0.186236
$554$	−10.4954	−0.445905
$555$	−2.88882	−0.122624
$556$	−36.5576	−1.55039
$557$	35.8791	1.52025	0.760124	−	0.649778i	$-0.225138\pi$
$557$	35.8791	1.52025	0.760124	+	0.649778i	$0.225138\pi$
$558$	2.45967	0.104126
$559$	34.8826	1.47537
$560$	2.24376	0.0948163
$561$	−10.1612	−0.429004
$562$	−26.6837	−1.12558
$563$	−2.12247	−0.0894516	−0.0447258	−	0.998999i	$-0.514241\pi$
$563$	−2.12247	−0.0894516	−0.0447258	+	0.998999i	$0.514241\pi$
$564$	−23.0417	−0.970232
$565$	10.8185	0.455139
$566$	22.2309	0.934436
$567$	9.08650	0.381597
$568$	−12.6712	−0.531674
$569$	−21.3403	−0.894631	−0.447315	−	0.894376i	$-0.647620\pi$
$569$	−21.3403	−0.894631	−0.447315	+	0.894376i	$0.647620\pi$
$570$	2.55019	0.106816
$571$	17.5525	0.734551	0.367276	−	0.930112i	$-0.380291\pi$
$571$	17.5525	0.734551	0.367276	+	0.930112i	$0.380291\pi$
$572$	15.3721	0.642738
$573$	−22.3297	−0.932837
$574$	5.60958	0.234139
$575$	−0.646819	−0.0269742
$576$	3.65549	0.152312
$577$	36.9659	1.53891	0.769455	−	0.638700i	$-0.220528\pi$
$577$	36.9659	1.53891	0.769455	+	0.638700i	$0.220528\pi$
$578$	−11.3952	−0.473978
$579$	36.1897	1.50399
$580$	−19.4894	−0.809252
$581$	−5.68470	−0.235841
$582$	−21.8551	−0.905923
$583$	−7.81853	−0.323810
$584$	−23.8339	−0.986254
$585$	−1.26284	−0.0522118
$586$	24.8184	1.02524
$587$	42.9047	1.77087	0.885434	−	0.464766i	$-0.153862\pi$
$587$	42.9047	1.77087	0.885434	+	0.464766i	$0.153862\pi$
$588$	−25.7482	−1.06184
$589$	−2.73295	−0.112609
$590$	−28.3515	−1.16721
$591$	26.8102	1.10282
$592$	3.48235	0.143124
$593$	−25.4577	−1.04542	−0.522712	−	0.852509i	$-0.675080\pi$
$593$	−25.4577	−1.04542	−0.522712	+	0.852509i	$0.675080\pi$
$594$	15.4515	0.633982
$595$	5.33620	0.218763
$596$	−27.0851	−1.10945
$597$	−1.54834	−0.0633695
$598$	6.03515	0.246796
$599$	−25.1012	−1.02561	−0.512803	−	0.858506i	$-0.671393\pi$
$599$	−25.1012	−1.02561	−0.512803	+	0.858506i	$0.671393\pi$
$600$	−2.63846	−0.107715
$601$	−14.9385	−0.609353	−0.304677	−	0.952456i	$-0.598548\pi$
$601$	−14.9385	−0.609353	−0.304677	+	0.952456i	$0.598548\pi$
$602$	20.0408	0.816803
$603$	−1.80049	−0.0733216
$604$	51.8929	2.11149
$605$	−9.28367	−0.377435
$606$	−3.29431	−0.133822
$607$	15.6962	0.637090	0.318545	−	0.947908i	$-0.396806\pi$
$607$	15.6962	0.637090	0.318545	+	0.947908i	$0.396806\pi$
$608$	−5.35956	−0.217359
$609$	13.2539	0.537077
$610$	−27.2180	−1.10202
$611$	−21.9418	−0.887670
$612$	3.80186	0.153681
$613$	20.1797	0.815050	0.407525	−	0.913194i	$-0.366392\pi$
$613$	20.1797	0.815050	0.407525	+	0.913194i	$0.366392\pi$
$614$	−25.7927	−1.04091
$615$	3.74617	0.151060
$616$	2.37816	0.0958187
$617$	20.0582	0.807512	0.403756	−	0.914867i	$-0.367704\pi$
$617$	20.0582	0.807512	0.403756	+	0.914867i	$0.367704\pi$
$618$	37.9302	1.52578
$619$	11.2218	0.451042	0.225521	−	0.974238i	$-0.427592\pi$
$619$	11.2218	0.451042	0.225521	+	0.974238i	$0.427592\pi$
$620$	10.5005	0.421709
$621$	3.50509	0.140655
$622$	40.0455	1.60568
$623$	−15.1682	−0.607701
$624$	−13.9811	−0.559691
$625$	1.00000	0.0400000
$626$	−25.8071	−1.03146
$627$	−1.53504	−0.0613037
$628$	62.2245	2.48303
$629$	8.28186	0.330219
$630$	−0.725528	−0.0289057
$631$	−17.0497	−0.678739	−0.339370	−	0.940653i	$-0.610214\pi$
$631$	−17.0497	−0.678739	−0.339370	+	0.940653i	$0.610214\pi$
$632$	6.20798	0.246940
$633$	11.0765	0.440251
$634$	64.0002	2.54177
$635$	−13.2018	−0.523896
$636$	−26.8671	−1.06535
$637$	−24.5190	−0.971479
$638$	20.3036	0.803826
$639$	−2.32691	−0.0920513
$640$	11.9615	0.472819
$641$	27.2326	1.07562	0.537811	−	0.843066i	$-0.319251\pi$
$641$	27.2326	1.07562	0.537811	+	0.843066i	$0.319251\pi$
$642$	−0.0765689	−0.00302193
$643$	34.5984	1.36443	0.682214	−	0.731153i	$-0.261017\pi$
$643$	34.5984	1.36443	0.682214	+	0.731153i	$0.261017\pi$
$644$	2.00340	0.0789451
$645$	13.3836	0.526979
$646$	−7.31105	−0.287649
$647$	9.75992	0.383702	0.191851	−	0.981424i	$-0.438551\pi$
$647$	9.75992	0.383702	0.191851	+	0.981424i	$0.438551\pi$
$648$	12.8802	0.505981
$649$	17.0657	0.669886
$650$	−9.33052	−0.365973
$651$	−7.14094	−0.279876
$652$	41.4351	1.62272
$653$	−15.5413	−0.608177	−0.304089	−	0.952644i	$-0.598352\pi$
$653$	−15.5413	−0.608177	−0.304089	+	0.952644i	$0.598352\pi$
$654$	−9.05550	−0.354098
$655$	−0.216187	−0.00844712
$656$	−4.51585	−0.176314
$657$	−4.37680	−0.170755
$658$	−12.6061	−0.491435
$659$	17.4606	0.680169	0.340084	−	0.940395i	$-0.389544\pi$
$659$	17.4606	0.680169	0.340084	+	0.940395i	$0.389544\pi$
$660$	5.89789	0.229575
$661$	25.3343	0.985392	0.492696	−	0.870202i	$-0.336012\pi$
$661$	25.3343	0.985392	0.492696	+	0.870202i	$0.336012\pi$
$662$	66.9457	2.60192
$663$	−33.2503	−1.29134
$664$	−8.05809	−0.312715
$665$	0.806139	0.0312607
$666$	−1.12603	−0.0436327
$667$	4.60577	0.178336
$668$	8.54673	0.330683
$669$	27.5150	1.06379
$670$	−13.3030	−0.513939
$671$	16.3834	0.632474
$672$	−14.0040	−0.540216
$673$	−47.0792	−1.81477	−0.907385	−	0.420301i	$-0.861925\pi$
$673$	−47.0792	−1.81477	−0.907385	+	0.420301i	$0.861925\pi$
$674$	60.7550	2.34019
$675$	−5.41897	−0.208576
$676$	14.7207	0.566179
$677$	−9.88273	−0.379824	−0.189912	−	0.981801i	$-0.560820\pi$
$677$	−9.88273	−0.379824	−0.189912	+	0.981801i	$0.560820\pi$
$678$	−38.7292	−1.48739
$679$	−6.90860	−0.265128
$680$	7.56410	0.290070
$681$	−26.4432	−1.01331
$682$	−10.9391	−0.418881
$683$	−26.8367	−1.02688	−0.513438	−	0.858127i	$-0.671628\pi$
$683$	−26.8367	−1.02688	−0.513438	+	0.858127i	$0.671628\pi$
$684$	0.574346	0.0219607
$685$	7.22761	0.276153
$686$	−31.3276	−1.19609
$687$	10.5358	0.401968
$688$	−16.1333	−0.615078
$689$	−25.5846	−0.974694
$690$	2.31554	0.0881512
$691$	4.61496	0.175561	0.0877807	−	0.996140i	$-0.472023\pi$
$691$	4.61496	0.175561	0.0877807	+	0.996140i	$0.472023\pi$
$692$	46.0915	1.75213
$693$	0.436719	0.0165896
$694$	51.7157	1.96310
$695$	−13.3567	−0.506649
$696$	18.7875	0.712140
$697$	−10.7398	−0.406797
$698$	17.7632	0.672348
$699$	32.2686	1.22051
$700$	−3.09732	−0.117068
$701$	−0.356330	−0.0134584	−0.00672920	−	0.999977i	$-0.502142\pi$
$701$	−0.356330	−0.0134584	−0.00672920	+	0.999977i	$0.502142\pi$
$702$	50.5619	1.90833
$703$	1.25114	0.0471875
$704$	−16.2574	−0.612725
$705$	−8.41854	−0.317061
$706$	−53.3395	−2.00746
$707$	−1.04136	−0.0391645
$708$	58.6434	2.20395
$709$	17.5551	0.659295	0.329647	−	0.944104i	$-0.393070\pi$
$709$	17.5551	0.659295	0.329647	+	0.944104i	$0.393070\pi$
$710$	−17.1925	−0.645224
$711$	1.14002	0.0427540
$712$	−21.5010	−0.805785
$713$	−2.48149	−0.0929325
$714$	−19.1031	−0.714914
$715$	5.61634	0.210039
$716$	28.3045	1.05779
$717$	−46.0755	−1.72072
$718$	−31.2352	−1.16569
$719$	17.9365	0.668920	0.334460	−	0.942410i	$-0.391446\pi$
$719$	17.9365	0.668920	0.334460	+	0.942410i	$0.391446\pi$
$720$	0.584068	0.0217669
$721$	11.9901	0.446534
$722$	40.2485	1.49789
$723$	−36.2301	−1.34741
$724$	7.49638	0.278601
$725$	−7.12065	−0.264454
$726$	33.2346	1.23345
$727$	16.2587	0.603002	0.301501	−	0.953466i	$-0.402512\pi$
$727$	16.2587	0.603002	0.301501	+	0.953466i	$0.402512\pi$
$728$	7.78204	0.288422
$729$	29.1050	1.07796
$730$	−32.3382	−1.19689
$731$	−38.3689	−1.41913
$732$	56.2988	2.08086
$733$	−1.23431	−0.0455904	−0.0227952	−	0.999740i	$-0.507257\pi$
$733$	−1.23431	−0.0455904	−0.0227952	+	0.999740i	$0.507257\pi$
$734$	−81.9311	−3.02413
$735$	−9.40736	−0.346996
$736$	−4.86642	−0.179379
$737$	8.00750	0.294960
$738$	1.46021	0.0537511
$739$	−27.1843	−0.999991	−0.499995	−	0.866028i	$-0.666665\pi$
$739$	−27.1843	−0.999991	−0.499995	+	0.866028i	$0.666665\pi$
$740$	−4.80708	−0.176712
$741$	−5.02312	−0.184529
$742$	−14.6989	−0.539614
$743$	−37.7876	−1.38629	−0.693146	−	0.720797i	$-0.743776\pi$
$743$	−37.7876	−1.38629	−0.693146	+	0.720797i	$0.743776\pi$
$744$	−10.1223	−0.371103
$745$	−9.89582	−0.362555
$746$	5.20065	0.190409
$747$	−1.47977	−0.0541418
$748$	−16.9084	−0.618234
$749$	−0.0242041	−0.000884400 0
$750$	−3.57990	−0.130719
$751$	−23.9011	−0.872164	−0.436082	−	0.899907i	$-0.643634\pi$
$751$	−23.9011	−0.872164	−0.436082	+	0.899907i	$0.643634\pi$
$752$	10.1482	0.370066
$753$	26.7975	0.976554
$754$	66.4394	2.41958
$755$	18.9596	0.690011
$756$	16.7843	0.610439
$757$	7.46987	0.271497	0.135749	−	0.990743i	$-0.456656\pi$
$757$	7.46987	0.271497	0.135749	+	0.990743i	$0.456656\pi$
$758$	31.5179	1.14478
$759$	−1.39380	−0.0505918
$760$	1.14271	0.0414503
$761$	4.91572	0.178195	0.0890973	−	0.996023i	$-0.471602\pi$
$761$	4.91572	0.178195	0.0890973	+	0.996023i	$0.471602\pi$
$762$	47.2609	1.71208
$763$	−2.86253	−0.103630
$764$	−37.1572	−1.34430
$765$	1.38905	0.0502213
$766$	6.06188	0.219025
$767$	55.8440	2.01641
$768$	−1.99842	−0.0721116
$769$	−25.3441	−0.913932	−0.456966	−	0.889484i	$-0.651064\pi$
$769$	−25.3441	−0.913932	−0.456966	+	0.889484i	$0.651064\pi$
$770$	3.22672	0.116283
$771$	−20.6273	−0.742873
$772$	60.2205	2.16738
$773$	−24.2285	−0.871437	−0.435719	−	0.900083i	$-0.643506\pi$
$773$	−24.2285	−0.871437	−0.435719	+	0.900083i	$0.643506\pi$
$774$	5.21677	0.187513
$775$	3.83645	0.137810
$776$	−9.79298	−0.351548
$777$	3.26910	0.117278
$778$	2.12113	0.0760463
$779$	−1.62245	−0.0581303
$780$	19.2996	0.691038
$781$	10.3487	0.370307
$782$	−6.63835	−0.237387
$783$	38.5866	1.37897
$784$	11.3402	0.405006
$785$	22.7344	0.811426
$786$	0.773927	0.0276051
$787$	−9.92614	−0.353829	−0.176914	−	0.984226i	$-0.556612\pi$
$787$	−9.92614	−0.353829	−0.176914	+	0.984226i	$0.556612\pi$
$788$	44.6129	1.58927
$789$	−39.1756	−1.39469
$790$	8.42307	0.299679
$791$	−12.2427	−0.435299
$792$	0.619051	0.0219970
$793$	53.6113	1.90379
$794$	25.4661	0.903757
$795$	−9.81618	−0.348144
$796$	−2.57649	−0.0913211
$797$	14.8400	0.525659	0.262829	−	0.964842i	$-0.415344\pi$
$797$	14.8400	0.525659	0.262829	+	0.964842i	$0.415344\pi$
$798$	−2.88589	−0.102160
$799$	24.1348	0.853828
$800$	7.52362	0.266000
$801$	−3.94839	−0.139510
$802$	65.7107	2.32032
$803$	19.4654	0.686918
$804$	27.5165	0.970431
$805$	0.731965	0.0257984
$806$	−35.7961	−1.26086
$807$	27.8531	0.980476
$808$	−1.47614	−0.0519304
$809$	−3.87086	−0.136092	−0.0680461	−	0.997682i	$-0.521677\pi$
$809$	−3.87086	−0.136092	−0.0680461	+	0.997682i	$0.521677\pi$
$810$	17.4760	0.614043
$811$	17.6599	0.620122	0.310061	−	0.950717i	$-0.399651\pi$
$811$	17.6599	0.620122	0.310061	+	0.950717i	$0.399651\pi$
$812$	22.0549	0.773976
$813$	43.8593	1.53821
$814$	5.00790	0.175527
$815$	15.1388	0.530288
$816$	15.3784	0.538353
$817$	−5.79638	−0.202790
$818$	6.86435	0.240006
$819$	1.42907	0.0499359
$820$	6.23373	0.217691
$821$	45.1636	1.57622	0.788110	−	0.615535i	$-0.211060\pi$
$821$	45.1636	1.57622	0.788110	+	0.615535i	$0.211060\pi$
$822$	−25.8741	−0.902462
$823$	21.5959	0.752784	0.376392	−	0.926460i	$-0.377165\pi$
$823$	21.5959	0.752784	0.376392	+	0.926460i	$0.377165\pi$
$824$	16.9960	0.592085
$825$	2.15486	0.0750225
$826$	32.0836	1.11633
$827$	37.2091	1.29389	0.646944	−	0.762537i	$-0.276047\pi$
$827$	37.2091	1.29389	0.646944	+	0.762537i	$0.276047\pi$
$828$	0.521500	0.0181234
$829$	−6.00371	−0.208518	−0.104259	−	0.994550i	$-0.533247\pi$
$829$	−6.00371	−0.208518	−0.104259	+	0.994550i	$0.533247\pi$
$830$	−10.9333	−0.379501
$831$	7.93163	0.275145
$832$	−53.1992	−1.84435
$833$	26.9696	0.934442
$834$	47.8157	1.65572
$835$	3.12264	0.108063
$836$	−2.55435	−0.0883441
$837$	−20.7896	−0.718595
$838$	39.7399	1.37279
$839$	21.0489	0.726689	0.363344	−	0.931655i	$-0.381635\pi$
$839$	21.0489	0.726689	0.363344	+	0.931655i	$0.381635\pi$
$840$	2.98578	0.103019
$841$	21.7036	0.748400
$842$	−44.9807	−1.55014
$843$	20.1656	0.694540
$844$	18.4316	0.634442
$845$	5.37835	0.185021
$846$	−3.28145	−0.112818
$847$	10.5058	0.360982
$848$	11.8330	0.406346
$849$	−16.8005	−0.576593
$850$	10.2631	0.352021
$851$	1.13602	0.0389422
$852$	35.5617	1.21832
$853$	−22.6090	−0.774117	−0.387058	−	0.922055i	$-0.626509\pi$
$853$	−22.6090	−0.774117	−0.387058	+	0.922055i	$0.626509\pi$
$854$	30.8009	1.05399
$855$	0.209844	0.00717650
$856$	−0.0343095	−0.00117268
$857$	−46.4266	−1.58590	−0.792952	−	0.609284i	$-0.791457\pi$
$857$	−46.4266	−1.58590	−0.792952	+	0.609284i	$0.791457\pi$
$858$	−20.1059	−0.686405
$859$	−11.2111	−0.382518	−0.191259	−	0.981540i	$-0.561257\pi$
$859$	−11.2111	−0.382518	−0.191259	+	0.981540i	$0.561257\pi$
$860$	22.2707	0.759423
$861$	−4.23931	−0.144475
$862$	−46.5117	−1.58420
$863$	−10.9127	−0.371473	−0.185736	−	0.982600i	$-0.559467\pi$
$863$	−10.9127	−0.371473	−0.185736	+	0.982600i	$0.559467\pi$
$864$	−40.7703	−1.38703
$865$	16.8400	0.572578
$866$	−29.7888	−1.01226
$867$	8.61167	0.292468
$868$	−11.8827	−0.403326
$869$	−5.07012	−0.171992
$870$	25.4912	0.864232
$871$	26.2029	0.887853
$872$	−4.05765	−0.137409
$873$	−1.79836	−0.0608652
$874$	−1.00285	−0.0339220
$875$	−1.13164	−0.0382564
$876$	66.8896	2.25999
$877$	38.3839	1.29613	0.648066	−	0.761584i	$-0.275578\pi$
$877$	38.3839	1.29613	0.648066	+	0.761584i	$0.275578\pi$
$878$	−62.9371	−2.12402
$879$	−18.7560	−0.632623
$880$	−2.59759	−0.0875646
$881$	16.4373	0.553787	0.276893	−	0.960901i	$-0.410695\pi$
$881$	16.4373	0.553787	0.276893	+	0.960901i	$0.410695\pi$
$882$	−3.66688	−0.123470
$883$	−5.57949	−0.187765	−0.0938824	−	0.995583i	$-0.529928\pi$
$883$	−5.57949	−0.187765	−0.0938824	+	0.995583i	$0.529928\pi$
$884$	−55.3294	−1.86093
$885$	21.4260	0.720227
$886$	65.3998	2.19715
$887$	−29.4206	−0.987847	−0.493923	−	0.869505i	$-0.664438\pi$
$887$	−29.4206	−0.987847	−0.493923	+	0.869505i	$0.664438\pi$
$888$	4.63397	0.155506
$889$	14.9396	0.501059
$890$	−29.1729	−0.977877
$891$	−10.5194	−0.352412
$892$	45.7857	1.53302
$893$	3.64604	0.122010
$894$	35.4260	1.18482
$895$	10.3414	0.345674
$896$	−13.5361	−0.452209
$897$	−4.56093	−0.152285
$898$	38.7273	1.29235
$899$	−27.3180	−0.911108
$900$	−0.806254	−0.0268751
$901$	28.1416	0.937534
$902$	−6.49416	−0.216232
$903$	−15.1454	−0.504007
$904$	−17.3541	−0.577187
$905$	2.73888	0.0910436
$906$	−67.8734	−2.25494
$907$	−56.3253	−1.87025	−0.935125	−	0.354318i	$-0.884713\pi$
$907$	−56.3253	−1.87025	−0.935125	+	0.354318i	$0.884713\pi$
$908$	−44.0022	−1.46026
$909$	−0.271074	−0.00899096
$910$	10.5588	0.350020
$911$	12.5032	0.414251	0.207125	−	0.978314i	$-0.433589\pi$
$911$	12.5032	0.414251	0.207125	+	0.978314i	$0.433589\pi$
$912$	2.32321	0.0769293
$913$	6.58112	0.217803
$914$	−39.8895	−1.31943
$915$	20.5694	0.680003
$916$	17.5319	0.579271
$917$	0.244645	0.00807891
$918$	−55.6153	−1.83558
$919$	−52.8245	−1.74252	−0.871260	−	0.490822i	$-0.836697\pi$
$919$	−52.8245	−1.74252	−0.871260	+	0.490822i	$0.836697\pi$
$920$	1.03756	0.0342075
$921$	19.4922	0.642291
$922$	−27.6338	−0.910072
$923$	33.8641	1.11465
$924$	−6.67428	−0.219568
$925$	−1.75632	−0.0577473
$926$	−35.4722	−1.16569
$927$	3.12111	0.102511
$928$	−53.5730	−1.75862
$929$	49.7969	1.63378	0.816892	−	0.576791i	$-0.195695\pi$
$929$	49.7969	1.63378	0.816892	+	0.576791i	$0.195695\pi$
$930$	−13.7341	−0.450359
$931$	4.07429	0.133529
$932$	53.6959	1.75887
$933$	−30.2635	−0.990783
$934$	−10.1647	−0.332600
$935$	−6.17768	−0.202032
$936$	2.02572	0.0662128
$937$	35.7866	1.16910	0.584548	−	0.811359i	$-0.301272\pi$
$937$	35.7866	1.16910	0.584548	+	0.811359i	$0.301272\pi$
$938$	15.0542	0.491536
$939$	19.5031	0.636460
$940$	−14.0087	−0.456913
$941$	−45.5331	−1.48434	−0.742168	−	0.670213i	$-0.766203\pi$
$941$	−45.5331	−1.48434	−0.742168	+	0.670213i	$0.766203\pi$
$942$	−81.3868	−2.65173
$943$	−1.47317	−0.0479729
$944$	−25.8281	−0.840633
$945$	6.13232	0.199484
$946$	−23.2011	−0.754332
$947$	39.4689	1.28257	0.641284	−	0.767304i	$-0.278402\pi$
$947$	39.4689	1.28257	0.641284	+	0.767304i	$0.278402\pi$
$948$	−17.4226	−0.565860
$949$	63.6965	2.06768
$950$	1.55044	0.0503029
$951$	−48.3667	−1.56840
$952$	−8.55983	−0.277426
$953$	49.1084	1.59078	0.795388	−	0.606100i	$-0.207267\pi$
$953$	49.1084	1.59078	0.795388	+	0.606100i	$0.207267\pi$
$954$	−3.82623	−0.123879
$955$	−13.5758	−0.439302
$956$	−76.6709	−2.47972
$957$	−15.3440	−0.496000
$958$	87.2898	2.82021
$959$	−8.17904	−0.264115
$960$	−20.4112	−0.658770
$961$	−16.2816	−0.525213
$962$	16.3874	0.528349
$963$	−0.00630051	−0.000203031 0
$964$	−60.2878	−1.94174
$965$	22.0022	0.708277
$966$	−2.62036	−0.0843086
$967$	39.5391	1.27149	0.635746	−	0.771898i	$-0.280692\pi$
$967$	39.5391	1.27149	0.635746	+	0.771898i	$0.280692\pi$
$968$	14.8920	0.478646
$969$	5.52516	0.177494
$970$	−13.2872	−0.426628
$971$	28.6080	0.918076	0.459038	−	0.888417i	$-0.348194\pi$
$971$	28.6080	0.918076	0.459038	+	0.888417i	$0.348194\pi$
$972$	8.34749	0.267746
$973$	15.1150	0.484564
$974$	−90.1751	−2.88940
$975$	7.05133	0.225823
$976$	−24.7955	−0.793685
$977$	−5.36041	−0.171495	−0.0857474	−	0.996317i	$-0.527328\pi$
$977$	−5.36041	−0.171495	−0.0857474	+	0.996317i	$0.527328\pi$
$978$	−54.1952	−1.73297
$979$	17.5601	0.561223
$980$	−15.6541	−0.500052
$981$	−0.745136	−0.0237904
$982$	44.8911	1.43253
$983$	18.9986	0.605960	0.302980	−	0.952997i	$-0.402019\pi$
$983$	18.9986	0.605960	0.302980	+	0.952997i	$0.402019\pi$
$984$	−6.00925	−0.191568
$985$	16.2998	0.519354
$986$	−73.0797	−2.32733
$987$	9.52675	0.303240
$988$	−8.35860	−0.265922
$989$	−5.26305	−0.167355
$990$	0.839937	0.0266949
$991$	22.2598	0.707104	0.353552	−	0.935415i	$-0.384974\pi$
$991$	22.2598	0.707104	0.353552	+	0.935415i	$0.384974\pi$
$992$	28.8640	0.916434
$993$	−50.5927	−1.60551
$994$	19.4557	0.617098
$995$	−0.941347	−0.0298427
$996$	22.6150	0.716582
$997$	49.9885	1.58315	0.791576	−	0.611071i	$-0.209261\pi$
$997$	49.9885	1.58315	0.791576	+	0.611071i	$0.209261\pi$
$998$	−49.7470	−1.57471
$999$	9.51744	0.301118

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6005.2.a.f.1.16	✓	111

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6005.2.a.f.1.16	✓	111	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:	\( N \)	\(=\)	\( 6005 = 5 \cdot 1201 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6005.a (trivial)

\(f(q)\)	\(=\)	\(q-2.17647 q^{2} +1.64482 q^{3} +2.73702 q^{4} +1.00000 q^{5} -3.57990 q^{6} -1.13164 q^{7} -1.60410 q^{8} -0.294573 q^{9} +O(q^{10})\)	\(q-2.17647 q^{2} +1.64482 q^{3} +2.73702 q^{4} +1.00000 q^{5} -3.57990 q^{6} -1.13164 q^{7} -1.60410 q^{8} -0.294573 q^{9} -2.17647 q^{10} +1.31009 q^{11} +4.50190 q^{12} +4.28700 q^{13} +2.46298 q^{14} +1.64482 q^{15} -1.98276 q^{16} -4.71547 q^{17} +0.641130 q^{18} -0.712364 q^{19} +2.73702 q^{20} -1.86134 q^{21} -2.85137 q^{22} -0.646819 q^{23} -2.63846 q^{24} +1.00000 q^{25} -9.33052 q^{26} -5.41897 q^{27} -3.09732 q^{28} -7.12065 q^{29} -3.57990 q^{30} +3.83645 q^{31} +7.52362 q^{32} +2.15486 q^{33} +10.2631 q^{34} -1.13164 q^{35} -0.806254 q^{36} -1.75632 q^{37} +1.55044 q^{38} +7.05133 q^{39} -1.60410 q^{40} +2.27756 q^{41} +4.05115 q^{42} +8.13683 q^{43} +3.58574 q^{44} -0.294573 q^{45} +1.40778 q^{46} -5.11822 q^{47} -3.26127 q^{48} -5.71939 q^{49} -2.17647 q^{50} -7.75609 q^{51} +11.7336 q^{52} -5.96794 q^{53} +11.7942 q^{54} +1.31009 q^{55} +1.81527 q^{56} -1.17171 q^{57} +15.4979 q^{58} +13.0264 q^{59} +4.50190 q^{60} +12.5056 q^{61} -8.34993 q^{62} +0.333351 q^{63} -12.4094 q^{64} +4.28700 q^{65} -4.68998 q^{66} +6.11219 q^{67} -12.9063 q^{68} -1.06390 q^{69} +2.46298 q^{70} +7.89927 q^{71} +0.472527 q^{72} +14.8581 q^{73} +3.82257 q^{74} +1.64482 q^{75} -1.94976 q^{76} -1.48255 q^{77} -15.3470 q^{78} -3.87006 q^{79} -1.98276 q^{80} -8.02951 q^{81} -4.95704 q^{82} +5.02342 q^{83} -5.09453 q^{84} -4.71547 q^{85} -17.7096 q^{86} -11.7122 q^{87} -2.10152 q^{88} +13.4038 q^{89} +0.641130 q^{90} -4.85133 q^{91} -1.77036 q^{92} +6.31027 q^{93} +11.1397 q^{94} -0.712364 q^{95} +12.3750 q^{96} +6.10495 q^{97} +12.4481 q^{98} -0.385917 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 111 q + 20 q^{2} + 40 q^{3} + 136 q^{4} + 111 q^{5} + 3 q^{6} + 39 q^{7} + 45 q^{8} + 139 q^{9}+O(q^{10}) \) 111 * q + 20 * q^2 + 40 * q^3 + 136 * q^4 + 111 * q^5 + 3 * q^6 + 39 * q^7 + 45 * q^8 + 139 * q^9	\( 111 q + 20 q^{2} + 40 q^{3} + 136 q^{4} + 111 q^{5} + 3 q^{6} + 39 q^{7} + 45 q^{8} + 139 q^{9} + 20 q^{10} + 36 q^{11} + 80 q^{12} + 36 q^{13} + 7 q^{14} + 40 q^{15} + 190 q^{16} + 38 q^{17} + 48 q^{18} + 77 q^{19} + 136 q^{20} + 11 q^{21} + 39 q^{22} + 82 q^{23} - 3 q^{24} + 111 q^{25} - 3 q^{26} + 130 q^{27} + 87 q^{28} + 20 q^{29} + 3 q^{30} + 41 q^{31} + 85 q^{32} + 33 q^{33} + 7 q^{34} + 39 q^{35} + 191 q^{36} + 80 q^{37} + 42 q^{38} + 21 q^{39} + 45 q^{40} + 16 q^{41} + 33 q^{42} + 164 q^{43} + 37 q^{44} + 139 q^{45} + 32 q^{46} + 148 q^{47} + 149 q^{48} + 160 q^{49} + 20 q^{50} + 51 q^{51} + 87 q^{52} + 83 q^{53} - 6 q^{54} + 36 q^{55} - 10 q^{56} + 28 q^{57} + 47 q^{58} + 14 q^{59} + 80 q^{60} + 20 q^{61} + 14 q^{62} + 120 q^{63} + 231 q^{64} + 36 q^{65} - 4 q^{66} + 253 q^{67} + 80 q^{68} + 6 q^{69} + 7 q^{70} + 5 q^{71} + 124 q^{72} + 64 q^{73} - 37 q^{74} + 40 q^{75} + 92 q^{76} + 63 q^{77} + 29 q^{78} + 91 q^{79} + 190 q^{80} + 187 q^{81} - 7 q^{82} + 63 q^{83} - 69 q^{84} + 38 q^{85} - 22 q^{86} + 57 q^{87} + 121 q^{88} - 6 q^{89} + 48 q^{90} + 119 q^{91} + 104 q^{92} + 14 q^{93} - q^{94} + 77 q^{95} - 38 q^{96} + 96 q^{97} + 81 q^{98} + 106 q^{99}+O(q^{100}) \) 111 * q + 20 * q^2 + 40 * q^3 + 136 * q^4 + 111 * q^5 + 3 * q^6 + 39 * q^7 + 45 * q^8 + 139 * q^9 + 20 * q^10 + 36 * q^11 + 80 * q^12 + 36 * q^13 + 7 * q^14 + 40 * q^15 + 190 * q^16 + 38 * q^17 + 48 * q^18 + 77 * q^19 + 136 * q^20 + 11 * q^21 + 39 * q^22 + 82 * q^23 - 3 * q^24 + 111 * q^25 - 3 * q^26 + 130 * q^27 + 87 * q^28 + 20 * q^29 + 3 * q^30 + 41 * q^31 + 85 * q^32 + 33 * q^33 + 7 * q^34 + 39 * q^35 + 191 * q^36 + 80 * q^37 + 42 * q^38 + 21 * q^39 + 45 * q^40 + 16 * q^41 + 33 * q^42 + 164 * q^43 + 37 * q^44 + 139 * q^45 + 32 * q^46 + 148 * q^47 + 149 * q^48 + 160 * q^49 + 20 * q^50 + 51 * q^51 + 87 * q^52 + 83 * q^53 - 6 * q^54 + 36 * q^55 - 10 * q^56 + 28 * q^57 + 47 * q^58 + 14 * q^59 + 80 * q^60 + 20 * q^61 + 14 * q^62 + 120 * q^63 + 231 * q^64 + 36 * q^65 - 4 * q^66 + 253 * q^67 + 80 * q^68 + 6 * q^69 + 7 * q^70 + 5 * q^71 + 124 * q^72 + 64 * q^73 - 37 * q^74 + 40 * q^75 + 92 * q^76 + 63 * q^77 + 29 * q^78 + 91 * q^79 + 190 * q^80 + 187 * q^81 - 7 * q^82 + 63 * q^83 - 69 * q^84 + 38 * q^85 - 22 * q^86 + 57 * q^87 + 121 * q^88 - 6 * q^89 + 48 * q^90 + 119 * q^91 + 104 * q^92 + 14 * q^93 - q^94 + 77 * q^95 - 38 * q^96 + 96 * q^97 + 81 * q^98 + 106 * q^99

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