LMFDB - Embedded newform 6005.2.a.f.1.20

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			1.20
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)

$f(q)$	$=$	$q-1.91654 q^{2} -2.98629 q^{3} +1.67314 q^{4} +1.00000 q^{5} +5.72336 q^{6} +0.938196 q^{7} +0.626446 q^{8} +5.91794 q^{9} +O(q^{10})$	\(q-1.91654 q^{2} -2.98629 q^{3} +1.67314 q^{4} +1.00000 q^{5} +5.72336 q^{6} +0.938196 q^{7} +0.626446 q^{8} +5.91794 q^{9} -1.91654 q^{10} +0.820584 q^{11} -4.99648 q^{12} -1.40722 q^{13} -1.79809 q^{14} -2.98629 q^{15} -4.54689 q^{16} -0.705966 q^{17} -11.3420 q^{18} -3.67307 q^{19} +1.67314 q^{20} -2.80173 q^{21} -1.57268 q^{22} +3.10146 q^{23} -1.87075 q^{24} +1.00000 q^{25} +2.69699 q^{26} -8.71383 q^{27} +1.56973 q^{28} -10.0961 q^{29} +5.72336 q^{30} -6.02736 q^{31} +7.46141 q^{32} -2.45050 q^{33} +1.35301 q^{34} +0.938196 q^{35} +9.90153 q^{36} +6.08303 q^{37} +7.03959 q^{38} +4.20236 q^{39} +0.626446 q^{40} -2.27978 q^{41} +5.36963 q^{42} -4.98566 q^{43} +1.37295 q^{44} +5.91794 q^{45} -5.94409 q^{46} -3.38328 q^{47} +13.5783 q^{48} -6.11979 q^{49} -1.91654 q^{50} +2.10822 q^{51} -2.35447 q^{52} +7.57948 q^{53} +16.7004 q^{54} +0.820584 q^{55} +0.587729 q^{56} +10.9688 q^{57} +19.3497 q^{58} +5.04009 q^{59} -4.99648 q^{60} -14.0897 q^{61} +11.5517 q^{62} +5.55219 q^{63} -5.20634 q^{64} -1.40722 q^{65} +4.69650 q^{66} +10.1236 q^{67} -1.18118 q^{68} -9.26188 q^{69} -1.79809 q^{70} +8.37228 q^{71} +3.70727 q^{72} +9.19517 q^{73} -11.6584 q^{74} -2.98629 q^{75} -6.14554 q^{76} +0.769868 q^{77} -8.05401 q^{78} +10.7413 q^{79} -4.54689 q^{80} +8.26823 q^{81} +4.36931 q^{82} -7.56742 q^{83} -4.68767 q^{84} -0.705966 q^{85} +9.55524 q^{86} +30.1500 q^{87} +0.514052 q^{88} -12.6946 q^{89} -11.3420 q^{90} -1.32025 q^{91} +5.18918 q^{92} +17.9995 q^{93} +6.48421 q^{94} -3.67307 q^{95} -22.2820 q^{96} +5.51335 q^{97} +11.7288 q^{98} +4.85617 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−1.91654	−1.35520	−0.677600	−	0.735430i	$-0.736980\pi$
$2$	−1.91654	−1.35520	−0.677600	+	0.735430i	$0.736980\pi$
$3$	−2.98629	−1.72414	−0.862068	−	0.506792i	$-0.830831\pi$
$3$	−2.98629	−1.72414	−0.862068	+	0.506792i	$0.830831\pi$
$4$	1.67314	0.836569
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	5.72336	2.33655
$7$	0.938196	0.354605	0.177302	−	0.984156i	$-0.443263\pi$
$7$	0.938196	0.354605	0.177302	+	0.984156i	$0.443263\pi$
$8$	0.626446	0.221482
$9$	5.91794	1.97265
$10$	−1.91654	−0.606064
$11$	0.820584	0.247415	0.123708	−	0.992319i	$-0.460521\pi$
$11$	0.820584	0.247415	0.123708	+	0.992319i	$0.460521\pi$
$12$	−4.99648	−1.44236
$13$	−1.40722	−0.390292	−0.195146	−	0.980774i	$-0.562518\pi$
$13$	−1.40722	−0.390292	−0.195146	+	0.980774i	$0.562518\pi$
$14$	−1.79809	−0.480560
$15$	−2.98629	−0.771057
$16$	−4.54689	−1.13672
$17$	−0.705966	−0.171222	−0.0856109	−	0.996329i	$-0.527284\pi$
$17$	−0.705966	−0.171222	−0.0856109	+	0.996329i	$0.527284\pi$
$18$	−11.3420	−2.67333
$19$	−3.67307	−0.842659	−0.421330	−	0.906908i	$-0.638436\pi$
$19$	−3.67307	−0.842659	−0.421330	+	0.906908i	$0.638436\pi$
$20$	1.67314	0.374125
$21$	−2.80173	−0.611387
$22$	−1.57268	−0.335297
$23$	3.10146	0.646700	0.323350	−	0.946279i	$-0.395191\pi$
$23$	3.10146	0.646700	0.323350	+	0.946279i	$0.395191\pi$
$24$	−1.87075	−0.381866
$25$	1.00000	0.200000
$26$	2.69699	0.528924
$27$	−8.71383	−1.67698
$28$	1.56973	0.296651
$29$	−10.0961	−1.87480	−0.937402	−	0.348250i	$-0.886776\pi$
$29$	−10.0961	−1.87480	−0.937402	+	0.348250i	$0.886776\pi$
$30$	5.72336	1.04494
$31$	−6.02736	−1.08255	−0.541273	−	0.840847i	$-0.682057\pi$
$31$	−6.02736	−1.08255	−0.541273	+	0.840847i	$0.682057\pi$
$32$	7.46141	1.31900
$33$	−2.45050	−0.426578
$34$	1.35301	0.232040
$35$	0.938196	0.158584
$36$	9.90153	1.65026
$37$	6.08303	1.00004	0.500022	−	0.866013i	$-0.333325\pi$
$37$	6.08303	1.00004	0.500022	+	0.866013i	$0.333325\pi$
$38$	7.03959	1.14197
$39$	4.20236	0.672917
$40$	0.626446	0.0990498
$41$	−2.27978	−0.356043	−0.178021	−	0.984027i	$-0.556970\pi$
$41$	−2.27978	−0.356043	−0.178021	+	0.984027i	$0.556970\pi$
$42$	5.36963	0.828552
$43$	−4.98566	−0.760306	−0.380153	−	0.924924i	$-0.624129\pi$
$43$	−4.98566	−0.760306	−0.380153	+	0.924924i	$0.624129\pi$
$44$	1.37295	0.206980
$45$	5.91794	0.882195
$46$	−5.94409	−0.876408
$47$	−3.38328	−0.493502	−0.246751	−	0.969079i	$-0.579363\pi$
$47$	−3.38328	−0.493502	−0.246751	+	0.969079i	$0.579363\pi$
$48$	13.5783	1.95986
$49$	−6.11979	−0.874256
$50$	−1.91654	−0.271040
$51$	2.10822	0.295210
$52$	−2.35447	−0.326506
$53$	7.57948	1.04112	0.520561	−	0.853825i	$-0.325723\pi$
$53$	7.57948	1.04112	0.520561	+	0.853825i	$0.325723\pi$
$54$	16.7004	2.27264
$55$	0.820584	0.110647
$56$	0.587729	0.0785386
$57$	10.9688	1.45286
$58$	19.3497	2.54073
$59$	5.04009	0.656164	0.328082	−	0.944649i	$-0.393598\pi$
$59$	5.04009	0.656164	0.328082	+	0.944649i	$0.393598\pi$
$60$	−4.99648	−0.645043
$61$	−14.0897	−1.80401	−0.902003	−	0.431730i	$-0.857903\pi$
$61$	−14.0897	−1.80401	−0.902003	+	0.431730i	$0.857903\pi$
$62$	11.5517	1.46707
$63$	5.55219	0.699510
$64$	−5.20634	−0.650793
$65$	−1.40722	−0.174544
$66$	4.69650	0.578099
$67$	10.1236	1.23680	0.618399	−	0.785864i	$-0.287782\pi$
$67$	10.1236	1.23680	0.618399	+	0.785864i	$0.287782\pi$
$68$	−1.18118	−0.143239
$69$	−9.26188	−1.11500
$70$	−1.79809	−0.214913
$71$	8.37228	0.993607	0.496804	−	0.867863i	$-0.334507\pi$
$71$	8.37228	0.993607	0.496804	+	0.867863i	$0.334507\pi$
$72$	3.70727	0.436906
$73$	9.19517	1.07621	0.538106	−	0.842877i	$-0.319140\pi$
$73$	9.19517	1.07621	0.538106	+	0.842877i	$0.319140\pi$
$74$	−11.6584	−1.35526
$75$	−2.98629	−0.344827
$76$	−6.14554	−0.704942
$77$	0.769868	0.0877346
$78$	−8.05401	−0.911937
$79$	10.7413	1.20849	0.604243	−	0.796800i	$-0.293476\pi$
$79$	10.7413	1.20849	0.604243	+	0.796800i	$0.293476\pi$
$80$	−4.54689	−0.508357
$81$	8.26823	0.918692
$82$	4.36931	0.482509
$83$	−7.56742	−0.830632	−0.415316	−	0.909677i	$-0.636329\pi$
$83$	−7.56742	−0.830632	−0.415316	+	0.909677i	$0.636329\pi$
$84$	−4.68767	−0.511467
$85$	−0.705966	−0.0765727
$86$	9.55524	1.03037
$87$	30.1500	3.23242
$88$	0.514052	0.0547981
$89$	−12.6946	−1.34563	−0.672815	−	0.739811i	$-0.734915\pi$
$89$	−12.6946	−1.34563	−0.672815	+	0.739811i	$0.734915\pi$
$90$	−11.3420	−1.19555
$91$	−1.32025	−0.138399
$92$	5.18918	0.541009
$93$	17.9995	1.86646
$94$	6.48421	0.668795
$95$	−3.67307	−0.376849
$96$	−22.2820	−2.27414
$97$	5.51335	0.559796	0.279898	−	0.960030i	$-0.409699\pi$
$97$	5.51335	0.559796	0.279898	+	0.960030i	$0.409699\pi$
$98$	11.7288	1.18479
$99$	4.85617	0.488063
$100$	1.67314	0.167314
$101$	16.8695	1.67858	0.839288	−	0.543688i	$-0.182972\pi$
$101$	16.8695	1.67858	0.839288	+	0.543688i	$0.182972\pi$
$102$	−4.04050	−0.400069
$103$	0.633483	0.0624189	0.0312095	−	0.999513i	$-0.490064\pi$
$103$	0.633483	0.0624189	0.0312095	+	0.999513i	$0.490064\pi$
$104$	−0.881546	−0.0864427
$105$	−2.80173	−0.273420
$106$	−14.5264	−1.41093
$107$	2.72015	0.262967	0.131483	−	0.991318i	$-0.458026\pi$
$107$	2.72015	0.262967	0.131483	+	0.991318i	$0.458026\pi$
$108$	−14.5794	−1.40291
$109$	−5.44188	−0.521237	−0.260619	−	0.965442i	$-0.583927\pi$
$109$	−5.44188	−0.521237	−0.260619	+	0.965442i	$0.583927\pi$
$110$	−1.57268	−0.149950
$111$	−18.1657	−1.72421
$112$	−4.26587	−0.403087
$113$	−0.272660	−0.0256497	−0.0128249	−	0.999918i	$-0.504082\pi$
$113$	−0.272660	−0.0256497	−0.0128249	+	0.999918i	$0.504082\pi$
$114$	−21.0223	−1.96892
$115$	3.10146	0.289213
$116$	−16.8922	−1.56840
$117$	−8.32783	−0.769909
$118$	−9.65956	−0.889234
$119$	−0.662334	−0.0607160
$120$	−1.87075	−0.170775
$121$	−10.3266	−0.938786
$122$	27.0036	2.44479
$123$	6.80810	0.613866
$124$	−10.0846	−0.905624
$125$	1.00000	0.0894427
$126$	−10.6410	−0.947976
$127$	0.141801	0.0125828	0.00629141	−	0.999980i	$-0.497997\pi$
$127$	0.141801	0.0125828	0.00629141	+	0.999980i	$0.497997\pi$
$128$	−4.94464	−0.437049
$129$	14.8886	1.31087
$130$	2.69699	0.236542
$131$	17.1969	1.50250	0.751249	−	0.660019i	$-0.229452\pi$
$131$	17.1969	1.50250	0.751249	+	0.660019i	$0.229452\pi$
$132$	−4.10003	−0.356862
$133$	−3.44605	−0.298811
$134$	−19.4024	−1.67611
$135$	−8.71383	−0.749968
$136$	−0.442250	−0.0379226
$137$	−8.39373	−0.717125	−0.358563	−	0.933506i	$-0.616733\pi$
$137$	−8.39373	−0.717125	−0.358563	+	0.933506i	$0.616733\pi$
$138$	17.7508	1.51105
$139$	14.5210	1.23165	0.615827	−	0.787881i	$-0.288822\pi$
$139$	14.5210	1.23165	0.615827	+	0.787881i	$0.288822\pi$
$140$	1.56973	0.132666
$141$	10.1035	0.850866
$142$	−16.0458	−1.34654
$143$	−1.15474	−0.0965642
$144$	−26.9082	−2.24235
$145$	−10.0961	−0.838437
$146$	−17.6229	−1.45848
$147$	18.2755	1.50734
$148$	10.1777	0.836606
$149$	−8.84992	−0.725014	−0.362507	−	0.931981i	$-0.618079\pi$
$149$	−8.84992	−0.725014	−0.362507	+	0.931981i	$0.618079\pi$
$150$	5.72336	0.467310
$151$	−19.3356	−1.57351	−0.786754	−	0.617267i	$-0.788240\pi$
$151$	−19.3356	−1.57351	−0.786754	+	0.617267i	$0.788240\pi$
$152$	−2.30098	−0.186634
$153$	−4.17787	−0.337760
$154$	−1.47549	−0.118898
$155$	−6.02736	−0.484129
$156$	7.03113	0.562941
$157$	−21.6202	−1.72548	−0.862740	−	0.505649i	$-0.831253\pi$
$157$	−21.6202	−1.72548	−0.862740	+	0.505649i	$0.831253\pi$
$158$	−20.5861	−1.63774
$159$	−22.6345	−1.79504
$160$	7.46141	0.589876
$161$	2.90978	0.229323
$162$	−15.8464	−1.24501
$163$	8.14550	0.638005	0.319002	−	0.947754i	$-0.396652\pi$
$163$	8.14550	0.638005	0.319002	+	0.947754i	$0.396652\pi$
$164$	−3.81439	−0.297854
$165$	−2.45050	−0.190771
$166$	14.5033	1.12567
$167$	−0.901622	−0.0697696	−0.0348848	−	0.999391i	$-0.511106\pi$
$167$	−0.901622	−0.0697696	−0.0348848	+	0.999391i	$0.511106\pi$
$168$	−1.75513	−0.135411
$169$	−11.0197	−0.847672
$170$	1.35301	0.103771
$171$	−21.7370	−1.66227
$172$	−8.34170	−0.636048
$173$	−14.2605	−1.08420	−0.542102	−	0.840313i	$-0.682371\pi$
$173$	−14.2605	−1.08420	−0.542102	+	0.840313i	$0.682371\pi$
$174$	−57.7837	−4.38057
$175$	0.938196	0.0709209
$176$	−3.73110	−0.281242
$177$	−15.0512	−1.13132
$178$	24.3298	1.82360
$179$	3.08376	0.230491	0.115245	−	0.993337i	$-0.463235\pi$
$179$	3.08376	0.230491	0.115245	+	0.993337i	$0.463235\pi$
$180$	9.90153	0.738017
$181$	25.3574	1.88480	0.942400	−	0.334487i	$-0.108563\pi$
$181$	25.3574	1.88480	0.942400	+	0.334487i	$0.108563\pi$
$182$	2.53031	0.187559
$183$	42.0761	3.11035
$184$	1.94290	0.143233
$185$	6.08303	0.447233
$186$	−34.4967	−2.52942
$187$	−0.579304	−0.0423629
$188$	−5.66070	−0.412849
$189$	−8.17528	−0.594664
$190$	7.03959	0.510705
$191$	−1.60182	−0.115903	−0.0579517	−	0.998319i	$-0.518457\pi$
$191$	−1.60182	−0.115903	−0.0579517	+	0.998319i	$0.518457\pi$
$192$	15.5477	1.12206
$193$	7.07774	0.509467	0.254733	−	0.967011i	$-0.418012\pi$
$193$	7.07774	0.509467	0.254733	+	0.967011i	$0.418012\pi$
$194$	−10.5666	−0.758636
$195$	4.20236	0.300937
$196$	−10.2392	−0.731375
$197$	17.4177	1.24096	0.620478	−	0.784224i	$-0.286939\pi$
$197$	17.4177	1.24096	0.620478	+	0.784224i	$0.286939\pi$
$198$	−9.30706	−0.661424
$199$	−6.66638	−0.472567	−0.236284	−	0.971684i	$-0.575929\pi$
$199$	−6.66638	−0.472567	−0.236284	+	0.971684i	$0.575929\pi$
$200$	0.626446	0.0442964
$201$	−30.2321	−2.13241
$202$	−32.3311	−2.27481
$203$	−9.47214	−0.664814
$204$	3.52734	0.246963
$205$	−2.27978	−0.159227
$206$	−1.21410	−0.0845901
$207$	18.3543	1.27571
$208$	6.39846	0.443653
$209$	−3.01406	−0.208487
$210$	5.36963	0.370540
$211$	7.76967	0.534886	0.267443	−	0.963574i	$-0.413821\pi$
$211$	7.76967	0.534886	0.267443	+	0.963574i	$0.413821\pi$
$212$	12.6815	0.870970
$213$	−25.0021	−1.71311
$214$	−5.21328	−0.356373
$215$	−4.98566	−0.340019
$216$	−5.45875	−0.371421
$217$	−5.65484	−0.383876
$218$	10.4296	0.706381
$219$	−27.4595	−1.85554
$220$	1.37295	0.0925642
$221$	0.993447	0.0668265
$222$	34.8154	2.33666
$223$	−16.8159	−1.12608	−0.563038	−	0.826431i	$-0.690367\pi$
$223$	−16.8159	−1.12608	−0.563038	+	0.826431i	$0.690367\pi$
$224$	7.00026	0.467725
$225$	5.91794	0.394530
$226$	0.522565	0.0347605
$227$	−8.81993	−0.585399	−0.292700	−	0.956204i	$-0.594554\pi$
$227$	−8.81993	−0.585399	−0.292700	+	0.956204i	$0.594554\pi$
$228$	18.3524	1.21542
$229$	16.2242	1.07212	0.536062	−	0.844179i	$-0.319911\pi$
$229$	16.2242	1.07212	0.536062	+	0.844179i	$0.319911\pi$
$230$	−5.94409	−0.391942
$231$	−2.29905	−0.151266
$232$	−6.32468	−0.415235
$233$	−25.6838	−1.68260	−0.841300	−	0.540568i	$-0.818209\pi$
$233$	−25.6838	−1.68260	−0.841300	+	0.540568i	$0.818209\pi$
$234$	15.9607	1.04338
$235$	−3.38328	−0.220701
$236$	8.43277	0.548927
$237$	−32.0765	−2.08359
$238$	1.26939	0.0822824
$239$	1.55915	0.100853	0.0504267	−	0.998728i	$-0.483942\pi$
$239$	1.55915	0.100853	0.0504267	+	0.998728i	$0.483942\pi$
$240$	13.5783	0.876478
$241$	−9.23388	−0.594806	−0.297403	−	0.954752i	$-0.596121\pi$
$241$	−9.23388	−0.594806	−0.297403	+	0.954752i	$0.596121\pi$
$242$	19.7915	1.27224
$243$	1.45015	0.0930273
$244$	−23.5741	−1.50917
$245$	−6.11979	−0.390979
$246$	−13.0480	−0.831912
$247$	5.16880	0.328883
$248$	−3.77582	−0.239765
$249$	22.5985	1.43212
$250$	−1.91654	−0.121213
$251$	10.3034	0.650342	0.325171	−	0.945655i	$-0.394578\pi$
$251$	10.3034	0.650342	0.325171	+	0.945655i	$0.394578\pi$
$252$	9.28957	0.585188
$253$	2.54501	0.160003
$254$	−0.271768	−0.0170522
$255$	2.10822	0.132022
$256$	19.8893	1.24308
$257$	−13.3551	−0.833065	−0.416533	−	0.909121i	$-0.636755\pi$
$257$	−13.3551	−0.833065	−0.416533	+	0.909121i	$0.636755\pi$
$258$	−28.5347	−1.77649
$259$	5.70707	0.354620
$260$	−2.35447	−0.146018
$261$	−59.7483	−3.69833
$262$	−32.9585	−2.03619
$263$	−8.21629	−0.506638	−0.253319	−	0.967383i	$-0.581522\pi$
$263$	−8.21629	−0.506638	−0.253319	+	0.967383i	$0.581522\pi$
$264$	−1.53511	−0.0944794
$265$	7.57948	0.465604
$266$	6.60451	0.404949
$267$	37.9099	2.32005
$268$	16.9382	1.03467
$269$	17.1250	1.04413	0.522064	−	0.852906i	$-0.325162\pi$
$269$	17.1250	1.04413	0.522064	+	0.852906i	$0.325162\pi$
$270$	16.7004	1.01636
$271$	12.8282	0.779259	0.389629	−	0.920972i	$-0.372603\pi$
$271$	12.8282	0.779259	0.389629	+	0.920972i	$0.372603\pi$
$272$	3.20995	0.194632
$273$	3.94264	0.238619
$274$	16.0870	0.971848
$275$	0.820584	0.0494831
$276$	−15.4964	−0.932774
$277$	18.7495	1.12655	0.563273	−	0.826271i	$-0.309542\pi$
$277$	18.7495	1.12655	0.563273	+	0.826271i	$0.309542\pi$
$278$	−27.8301	−1.66914
$279$	−35.6696	−2.13548
$280$	0.587729	0.0351235
$281$	−12.7643	−0.761453	−0.380727	−	0.924688i	$-0.624326\pi$
$281$	−12.7643	−0.761453	−0.380727	+	0.924688i	$0.624326\pi$
$282$	−19.3637	−1.15309
$283$	0.455158	0.0270563	0.0135282	−	0.999908i	$-0.495694\pi$
$283$	0.455158	0.0270563	0.0135282	+	0.999908i	$0.495694\pi$
$284$	14.0080	0.831221
$285$	10.9688	0.649739
$286$	2.21311	0.130864
$287$	−2.13888	−0.126254
$288$	44.1562	2.60193
$289$	−16.5016	−0.970683
$290$	19.3497	1.13625
$291$	−16.4645	−0.965165
$292$	15.3848	0.900326
$293$	−3.56243	−0.208120	−0.104060	−	0.994571i	$-0.533183\pi$
$293$	−3.56243	−0.208120	−0.104060	+	0.994571i	$0.533183\pi$
$294$	−35.0257	−2.04274
$295$	5.04009	0.293446
$296$	3.81069	0.221492
$297$	−7.15043	−0.414910
$298$	16.9613	0.982539
$299$	−4.36443	−0.252402
$300$	−4.99648	−0.288472
$301$	−4.67753	−0.269608
$302$	37.0575	2.13242
$303$	−50.3772	−2.89409
$304$	16.7010	0.957869
$305$	−14.0897	−0.806776
$306$	8.00706	0.457733
$307$	31.6120	1.80419	0.902097	−	0.431534i	$-0.142028\pi$
$307$	31.6120	1.80419	0.902097	+	0.431534i	$0.142028\pi$
$308$	1.28810	0.0733960
$309$	−1.89176	−0.107619
$310$	11.5517	0.656092
$311$	17.7913	1.00885	0.504426	−	0.863455i	$-0.331704\pi$
$311$	17.7913	1.00885	0.504426	+	0.863455i	$0.331704\pi$
$312$	2.63255	0.149039
$313$	12.2780	0.693996	0.346998	−	0.937866i	$-0.387201\pi$
$313$	12.2780	0.693996	0.346998	+	0.937866i	$0.387201\pi$
$314$	41.4360	2.33837
$315$	5.55219	0.312830
$316$	17.9716	1.01098
$317$	24.9851	1.40330	0.701652	−	0.712520i	$-0.252446\pi$
$317$	24.9851	1.40330	0.701652	+	0.712520i	$0.252446\pi$
$318$	43.3801	2.43263
$319$	−8.28472	−0.463855
$320$	−5.20634	−0.291043
$321$	−8.12316	−0.453391
$322$	−5.57672	−0.310778
$323$	2.59306	0.144282
$324$	13.8339	0.768549
$325$	−1.40722	−0.0780584
$326$	−15.6112	−0.864624
$327$	16.2510	0.898685
$328$	−1.42816	−0.0788571
$329$	−3.17418	−0.174998
$330$	4.69650	0.258534
$331$	18.9808	1.04328	0.521640	−	0.853166i	$-0.325320\pi$
$331$	18.9808	1.04328	0.521640	+	0.853166i	$0.325320\pi$
$332$	−12.6613	−0.694881
$333$	35.9990	1.97274
$334$	1.72800	0.0945518
$335$	10.1236	0.553113
$336$	12.7391	0.694977
$337$	25.9307	1.41254	0.706268	−	0.707944i	$-0.250377\pi$
$337$	25.9307	1.41254	0.706268	+	0.707944i	$0.250377\pi$
$338$	21.1198	1.14877
$339$	0.814243	0.0442236
$340$	−1.18118	−0.0640584
$341$	−4.94595	−0.267838
$342$	41.6599	2.25271
$343$	−12.3089	−0.664620
$344$	−3.12325	−0.168394
$345$	−9.26188	−0.498643
$346$	27.3308	1.46931
$347$	−22.3837	−1.20162	−0.600809	−	0.799393i	$-0.705155\pi$
$347$	−22.3837	−1.20162	−0.600809	+	0.799393i	$0.705155\pi$
$348$	50.4451	2.70414
$349$	−25.7921	−1.38062	−0.690310	−	0.723514i	$-0.742526\pi$
$349$	−25.7921	−1.38062	−0.690310	+	0.723514i	$0.742526\pi$
$350$	−1.79809	−0.0961121
$351$	12.2623	0.654511
$352$	6.12271	0.326342
$353$	−3.16653	−0.168537	−0.0842686	−	0.996443i	$-0.526855\pi$
$353$	−3.16653	−0.168537	−0.0842686	+	0.996443i	$0.526855\pi$
$354$	28.8463	1.53316
$355$	8.37228	0.444355
$356$	−21.2399	−1.12571
$357$	1.97792	0.104683
$358$	−5.91016	−0.312361
$359$	25.4180	1.34151	0.670755	−	0.741679i	$-0.265970\pi$
$359$	25.4180	1.34151	0.670755	+	0.741679i	$0.265970\pi$
$360$	3.70727	0.195390
$361$	−5.50859	−0.289926
$362$	−48.5986	−2.55428
$363$	30.8384	1.61859
$364$	−2.20895	−0.115781
$365$	9.19517	0.481297
$366$	−80.6406	−4.21515
$367$	−6.15777	−0.321433	−0.160716	−	0.987001i	$-0.551380\pi$
$367$	−6.15777	−0.321433	−0.160716	+	0.987001i	$0.551380\pi$
$368$	−14.1020	−0.735118
$369$	−13.4916	−0.702347
$370$	−11.6584	−0.606091
$371$	7.11103	0.369186
$372$	30.1156	1.56142
$373$	23.2698	1.20486	0.602431	−	0.798171i	$-0.294199\pi$
$373$	23.2698	1.20486	0.602431	+	0.798171i	$0.294199\pi$
$374$	1.11026	0.0574102
$375$	−2.98629	−0.154211
$376$	−2.11944	−0.109302
$377$	14.2074	0.731721
$378$	15.6683	0.805889
$379$	28.0051	1.43853	0.719263	−	0.694738i	$-0.244480\pi$
$379$	28.0051	1.43853	0.719263	+	0.694738i	$0.244480\pi$
$380$	−6.14554	−0.315260
$381$	−0.423460	−0.0216945
$382$	3.06995	0.157072
$383$	−19.7420	−1.00877	−0.504383	−	0.863480i	$-0.668280\pi$
$383$	−19.7420	−1.00877	−0.504383	+	0.863480i	$0.668280\pi$
$384$	14.7661	0.753532
$385$	0.769868	0.0392361
$386$	−13.5648	−0.690430
$387$	−29.5049	−1.49982
$388$	9.22460	0.468308
$389$	−13.4239	−0.680619	−0.340310	−	0.940313i	$-0.610532\pi$
$389$	−13.4239	−0.680619	−0.340310	+	0.940313i	$0.610532\pi$
$390$	−8.05401	−0.407831
$391$	−2.18953	−0.110729
$392$	−3.83372	−0.193632
$393$	−51.3549	−2.59051
$394$	−33.3817	−1.68175
$395$	10.7413	0.540451
$396$	8.12504	0.408299
$397$	10.5888	0.531436	0.265718	−	0.964051i	$-0.414391\pi$
$397$	10.5888	0.531436	0.265718	+	0.964051i	$0.414391\pi$
$398$	12.7764	0.640423
$399$	10.2909	0.515191
$400$	−4.54689	−0.227344
$401$	5.45837	0.272578	0.136289	−	0.990669i	$-0.456482\pi$
$401$	5.45837	0.272578	0.136289	+	0.990669i	$0.456482\pi$
$402$	57.9411	2.88984
$403$	8.48180	0.422509
$404$	28.2249	1.40424
$405$	8.26823	0.410852
$406$	18.1538	0.900956
$407$	4.99164	0.247426
$408$	1.32069	0.0653837
$409$	−30.1617	−1.49140	−0.745701	−	0.666281i	$-0.767885\pi$
$409$	−30.1617	−1.49140	−0.745701	+	0.666281i	$0.767885\pi$
$410$	4.36931	0.215785
$411$	25.0661	1.23642
$412$	1.05990	0.0522177
$413$	4.72859	0.232679
$414$	−35.1768	−1.72884
$415$	−7.56742	−0.371470
$416$	−10.4998	−0.514796
$417$	−43.3639	−2.12354
$418$	5.77657	0.282541
$419$	−13.9172	−0.679901	−0.339950	−	0.940443i	$-0.610410\pi$
$419$	−13.9172	−0.679901	−0.339950	+	0.940443i	$0.610410\pi$
$420$	−4.68767	−0.228735
$421$	21.9526	1.06990	0.534952	−	0.844883i	$-0.320330\pi$
$421$	21.9526	1.06990	0.534952	+	0.844883i	$0.320330\pi$
$422$	−14.8909	−0.724878
$423$	−20.0221	−0.973506
$424$	4.74813	0.230590
$425$	−0.705966	−0.0342444
$426$	47.9176	2.32161
$427$	−13.2189	−0.639709
$428$	4.55118	0.219990
$429$	3.44839	0.166490
$430$	9.55524	0.460794
$431$	−1.20599	−0.0580903	−0.0290452	−	0.999578i	$-0.509247\pi$
$431$	−1.20599	−0.0580903	−0.0290452	+	0.999578i	$0.509247\pi$
$432$	39.6208	1.90626
$433$	21.4161	1.02919	0.514596	−	0.857433i	$-0.327942\pi$
$433$	21.4161	1.02919	0.514596	+	0.857433i	$0.327942\pi$
$434$	10.8377	0.520228
$435$	30.1500	1.44558
$436$	−9.10501	−0.436051
$437$	−11.3919	−0.544948
$438$	52.6272	2.51463
$439$	9.06068	0.432443	0.216221	−	0.976344i	$-0.430627\pi$
$439$	9.06068	0.432443	0.216221	+	0.976344i	$0.430627\pi$
$440$	0.514052	0.0245064
$441$	−36.2166	−1.72460
$442$	−1.90398	−0.0905633
$443$	25.9230	1.23164	0.615819	−	0.787888i	$-0.288825\pi$
$443$	25.9230	1.23164	0.615819	+	0.787888i	$0.288825\pi$
$444$	−30.3937	−1.44242
$445$	−12.6946	−0.601784
$446$	32.2284	1.52606
$447$	26.4285	1.25002
$448$	−4.88457	−0.230774
$449$	−15.0955	−0.712402	−0.356201	−	0.934409i	$-0.615928\pi$
$449$	−15.0955	−0.712402	−0.356201	+	0.934409i	$0.615928\pi$
$450$	−11.3420	−0.534667
$451$	−1.87075	−0.0880904
$452$	−0.456198	−0.0214577
$453$	57.7417	2.71294
$454$	16.9038	0.793333
$455$	−1.32025	−0.0618940
$456$	6.87139	0.321782
$457$	35.2759	1.65014	0.825069	−	0.565032i	$-0.191136\pi$
$457$	35.2759	1.65014	0.825069	+	0.565032i	$0.191136\pi$
$458$	−31.0943	−1.45294
$459$	6.15167	0.287135
$460$	5.18918	0.241947
$461$	−13.0024	−0.605580	−0.302790	−	0.953057i	$-0.597918\pi$
$461$	−13.0024	−0.605580	−0.302790	+	0.953057i	$0.597918\pi$
$462$	4.40623	0.204996
$463$	20.2996	0.943402	0.471701	−	0.881758i	$-0.343640\pi$
$463$	20.2996	0.943402	0.471701	+	0.881758i	$0.343640\pi$
$464$	45.9059	2.13113
$465$	17.9995	0.834705
$466$	49.2241	2.28026
$467$	−19.5889	−0.906466	−0.453233	−	0.891392i	$-0.649729\pi$
$467$	−19.5889	−0.906466	−0.453233	+	0.891392i	$0.649729\pi$
$468$	−13.9336	−0.644081
$469$	9.49794	0.438574
$470$	6.48421	0.299094
$471$	64.5642	2.97496
$472$	3.15735	0.145329
$473$	−4.09115	−0.188111
$474$	61.4760	2.82369
$475$	−3.67307	−0.168532
$476$	−1.10818	−0.0507931
$477$	44.8549	2.05377
$478$	−2.98819	−0.136676
$479$	−19.7659	−0.903129	−0.451564	−	0.892239i	$-0.649134\pi$
$479$	−19.7659	−0.903129	−0.451564	+	0.892239i	$0.649134\pi$
$480$	−22.2820	−1.01703
$481$	−8.56015	−0.390309
$482$	17.6971	0.806082
$483$	−8.68945	−0.395384
$484$	−17.2779	−0.785359
$485$	5.51335	0.250348
$486$	−2.77928	−0.126071
$487$	37.5409	1.70114	0.850570	−	0.525862i	$-0.176257\pi$
$487$	37.5409	1.70114	0.850570	+	0.525862i	$0.176257\pi$
$488$	−8.82646	−0.399555
$489$	−24.3248	−1.10001
$490$	11.7288	0.529855
$491$	−8.14785	−0.367707	−0.183854	−	0.982954i	$-0.558857\pi$
$491$	−8.14785	−0.367707	−0.183854	+	0.982954i	$0.558857\pi$
$492$	11.3909	0.513541
$493$	7.12752	0.321007
$494$	−9.90623	−0.445702
$495$	4.85617	0.218269
$496$	27.4057	1.23055
$497$	7.85484	0.352338
$498$	−43.3111	−1.94082
$499$	36.2504	1.62279	0.811395	−	0.584499i	$-0.198709\pi$
$499$	36.2504	1.62279	0.811395	+	0.584499i	$0.198709\pi$
$500$	1.67314	0.0748250
$501$	2.69251	0.120292
$502$	−19.7468	−0.881344
$503$	−8.04451	−0.358687	−0.179344	−	0.983787i	$-0.557397\pi$
$503$	−8.04451	−0.358687	−0.179344	+	0.983787i	$0.557397\pi$
$504$	3.47815	0.154929
$505$	16.8695	0.750682
$506$	−4.87762	−0.216837
$507$	32.9082	1.46150
$508$	0.237253	0.0105264
$509$	−13.5769	−0.601786	−0.300893	−	0.953658i	$-0.597285\pi$
$509$	−13.5769	−0.601786	−0.300893	+	0.953658i	$0.597285\pi$
$510$	−4.04050	−0.178916
$511$	8.62686	0.381630
$512$	−28.2294	−1.24758
$513$	32.0065	1.41312
$514$	25.5955	1.12897
$515$	0.633483	0.0279146
$516$	24.9108	1.09663
$517$	−2.77627	−0.122100
$518$	−10.9379	−0.480582
$519$	42.5859	1.86932
$520$	−0.881546	−0.0386583
$521$	−26.4664	−1.15951	−0.579757	−	0.814789i	$-0.696853\pi$
$521$	−26.4664	−1.15951	−0.579757	+	0.814789i	$0.696853\pi$
$522$	114.510	5.01197
$523$	−38.3396	−1.67648	−0.838238	−	0.545305i	$-0.816414\pi$
$523$	−38.3396	−1.67648	−0.838238	+	0.545305i	$0.816414\pi$
$524$	28.7727	1.25694
$525$	−2.80173	−0.122277
$526$	15.7469	0.686596
$527$	4.25511	0.185355
$528$	11.1422	0.484900
$529$	−13.3809	−0.581779
$530$	−14.5264	−0.630986
$531$	29.8270	1.29438
$532$	−5.76572	−0.249976
$533$	3.20815	0.138961
$534$	−72.6560	−3.14413
$535$	2.72015	0.117602
$536$	6.34191	0.273929
$537$	−9.20901	−0.397398
$538$	−32.8208	−1.41500
$539$	−5.02180	−0.216304
$540$	−14.5794	−0.627399
$541$	−11.5221	−0.495375	−0.247687	−	0.968840i	$-0.579671\pi$
$541$	−11.5221	−0.495375	−0.247687	+	0.968840i	$0.579671\pi$
$542$	−24.5858	−1.05605
$543$	−75.7246	−3.24965
$544$	−5.26750	−0.225842
$545$	−5.44188	−0.233104
$546$	−7.55624	−0.323377
$547$	38.0113	1.62524	0.812622	−	0.582791i	$-0.198039\pi$
$547$	38.0113	1.62524	0.812622	+	0.582791i	$0.198039\pi$
$548$	−14.0439	−0.599924
$549$	−83.3823	−3.55867
$550$	−1.57268	−0.0670595
$551$	37.0837	1.57982
$552$	−5.80207	−0.246952
$553$	10.0774	0.428534
$554$	−35.9342	−1.52670
$555$	−18.1657	−0.771092
$556$	24.2956	1.03036
$557$	24.7937	1.05054	0.525271	−	0.850935i	$-0.323964\pi$
$557$	24.7937	1.05054	0.525271	+	0.850935i	$0.323964\pi$
$558$	68.3623	2.89401
$559$	7.01591	0.296741
$560$	−4.26587	−0.180266
$561$	1.72997	0.0730394
$562$	24.4633	1.03192
$563$	−23.4656	−0.988957	−0.494478	−	0.869190i	$-0.664641\pi$
$563$	−23.4656	−0.988957	−0.494478	+	0.869190i	$0.664641\pi$
$564$	16.9045	0.711808
$565$	−0.272660	−0.0114709
$566$	−0.872330	−0.0366668
$567$	7.75722	0.325772
$568$	5.24478	0.220066
$569$	23.4397	0.982644	0.491322	−	0.870978i	$-0.336514\pi$
$569$	23.4397	0.982644	0.491322	+	0.870978i	$0.336514\pi$
$570$	−21.0223	−0.880526
$571$	−36.3271	−1.52024	−0.760122	−	0.649781i	$-0.774861\pi$
$571$	−36.3271	−1.52024	−0.760122	+	0.649781i	$0.774861\pi$
$572$	−1.93204	−0.0807826
$573$	4.78349	0.199833
$574$	4.09926	0.171100
$575$	3.10146	0.129340
$576$	−30.8108	−1.28379
$577$	−19.3392	−0.805100	−0.402550	−	0.915398i	$-0.631876\pi$
$577$	−19.3392	−0.805100	−0.402550	+	0.915398i	$0.631876\pi$
$578$	31.6261	1.31547
$579$	−21.1362	−0.878391
$580$	−16.8922	−0.701411
$581$	−7.09972	−0.294546
$582$	31.5549	1.30799
$583$	6.21960	0.257589
$584$	5.76028	0.238362
$585$	−8.32783	−0.344314
$586$	6.82756	0.282044
$587$	7.56566	0.312268	0.156134	−	0.987736i	$-0.450097\pi$
$587$	7.56566	0.312268	0.156134	+	0.987736i	$0.450097\pi$
$588$	30.5774	1.26099
$589$	22.1389	0.912217
$590$	−9.65956	−0.397678
$591$	−52.0142	−2.13958
$592$	−27.6589	−1.13677
$593$	−6.21205	−0.255098	−0.127549	−	0.991832i	$-0.540711\pi$
$593$	−6.21205	−0.255098	−0.127549	+	0.991832i	$0.540711\pi$
$594$	13.7041	0.562286
$595$	−0.662334	−0.0271530
$596$	−14.8071	−0.606524
$597$	19.9078	0.814770
$598$	8.36463	0.342055
$599$	−11.7891	−0.481691	−0.240846	−	0.970563i	$-0.577425\pi$
$599$	−11.7891	−0.481691	−0.240846	+	0.970563i	$0.577425\pi$
$600$	−1.87075	−0.0763731
$601$	18.7274	0.763905	0.381953	−	0.924182i	$-0.375252\pi$
$601$	18.7274	0.763905	0.381953	+	0.924182i	$0.375252\pi$
$602$	8.96468	0.365373
$603$	59.9110	2.43977
$604$	−32.3511	−1.31635
$605$	−10.3266	−0.419838
$606$	96.5500	3.92208
$607$	5.14967	0.209018	0.104509	−	0.994524i	$-0.466673\pi$
$607$	5.14967	0.209018	0.104509	+	0.994524i	$0.466673\pi$
$608$	−27.4063	−1.11147
$609$	28.2866	1.14623
$610$	27.0036	1.09334
$611$	4.76101	0.192610
$612$	−6.99014	−0.282560
$613$	−22.2795	−0.899860	−0.449930	−	0.893064i	$-0.648551\pi$
$613$	−22.2795	−0.899860	−0.449930	+	0.893064i	$0.648551\pi$
$614$	−60.5858	−2.44504
$615$	6.80810	0.274529
$616$	0.482281	0.0194316
$617$	11.7716	0.473907	0.236953	−	0.971521i	$-0.423851\pi$
$617$	11.7716	0.473907	0.236953	+	0.971521i	$0.423851\pi$
$618$	3.62565	0.145845
$619$	2.79259	0.112244	0.0561218	−	0.998424i	$-0.482126\pi$
$619$	2.79259	0.112244	0.0561218	+	0.998424i	$0.482126\pi$
$620$	−10.0846	−0.405007
$621$	−27.0256	−1.08450
$622$	−34.0978	−1.36720
$623$	−11.9101	−0.477167
$624$	−19.1077	−0.764919
$625$	1.00000	0.0400000
$626$	−23.5314	−0.940504
$627$	9.00086	0.359460
$628$	−36.1736	−1.44348
$629$	−4.29441	−0.171229
$630$	−10.6410	−0.423948
$631$	2.74906	0.109438	0.0547192	−	0.998502i	$-0.482574\pi$
$631$	2.74906	0.109438	0.0547192	+	0.998502i	$0.482574\pi$
$632$	6.72882	0.267658
$633$	−23.2025	−0.922217
$634$	−47.8850	−1.90176
$635$	0.141801	0.00562721
$636$	−37.8707	−1.50167
$637$	8.61187	0.341215
$638$	15.8780	0.628617
$639$	49.5467	1.96004
$640$	−4.94464	−0.195454
$641$	45.9786	1.81605	0.908024	−	0.418919i	$-0.137591\pi$
$641$	45.9786	1.81605	0.908024	+	0.418919i	$0.137591\pi$
$642$	15.5684	0.614435
$643$	−28.5942	−1.12765	−0.563823	−	0.825896i	$-0.690670\pi$
$643$	−28.5942	−1.12765	−0.563823	+	0.825896i	$0.690670\pi$
$644$	4.86846	0.191844
$645$	14.8886	0.586240
$646$	−4.96971	−0.195531
$647$	10.2310	0.402222	0.201111	−	0.979568i	$-0.435545\pi$
$647$	10.2310	0.402222	0.201111	+	0.979568i	$0.435545\pi$
$648$	5.17960	0.203474
$649$	4.13582	0.162345
$650$	2.69699	0.105785
$651$	16.8870	0.661854
$652$	13.6285	0.533735
$653$	12.8092	0.501262	0.250631	−	0.968083i	$-0.419362\pi$
$653$	12.8092	0.501262	0.250631	+	0.968083i	$0.419362\pi$
$654$	−31.1458	−1.21790
$655$	17.1969	0.671937
$656$	10.3659	0.404721
$657$	54.4165	2.12299
$658$	6.08345	0.237158
$659$	−23.1921	−0.903438	−0.451719	−	0.892160i	$-0.649189\pi$
$659$	−23.1921	−0.903438	−0.451719	+	0.892160i	$0.649189\pi$
$660$	−4.10003	−0.159593
$661$	−37.3786	−1.45386	−0.726929	−	0.686712i	$-0.759053\pi$
$661$	−37.3786	−1.45386	−0.726929	+	0.686712i	$0.759053\pi$
$662$	−36.3775	−1.41385
$663$	−2.96672	−0.115218
$664$	−4.74058	−0.183970
$665$	−3.44605	−0.133632
$666$	−68.9937	−2.67345
$667$	−31.3128	−1.21244
$668$	−1.50854	−0.0583671
$669$	50.2172	1.94151
$670$	−19.4024	−0.749579
$671$	−11.5618	−0.446339
$672$	−20.9048	−0.806421
$673$	−30.1147	−1.16084	−0.580419	−	0.814318i	$-0.697111\pi$
$673$	−30.1147	−1.16084	−0.580419	+	0.814318i	$0.697111\pi$
$674$	−49.6974	−1.91427
$675$	−8.71383	−0.335396
$676$	−18.4375	−0.709136
$677$	32.4800	1.24831	0.624154	−	0.781302i	$-0.285444\pi$
$677$	32.4800	1.24831	0.624154	+	0.781302i	$0.285444\pi$
$678$	−1.56053	−0.0599319
$679$	5.17260	0.198506
$680$	−0.442250	−0.0169595
$681$	26.3389	1.00931
$682$	9.47913	0.362975
$683$	29.2631	1.11972	0.559860	−	0.828587i	$-0.310855\pi$
$683$	29.2631	1.11972	0.559860	+	0.828587i	$0.310855\pi$
$684$	−36.3690	−1.39060
$685$	−8.39373	−0.320708
$686$	23.5906	0.900693
$687$	−48.4501	−1.84849
$688$	22.6692	0.864257
$689$	−10.6660	−0.406341
$690$	17.7508	0.675761
$691$	20.9871	0.798386	0.399193	−	0.916867i	$-0.369290\pi$
$691$	20.9871	0.798386	0.399193	+	0.916867i	$0.369290\pi$
$692$	−23.8597	−0.907011
$693$	4.55604	0.173069
$694$	42.8992	1.62843
$695$	14.5210	0.550812
$696$	18.8873	0.715923
$697$	1.60945	0.0609623
$698$	49.4317	1.87102
$699$	76.6993	2.90103
$700$	1.56973	0.0593302
$701$	15.6796	0.592209	0.296105	−	0.955155i	$-0.404312\pi$
$701$	15.6796	0.592209	0.296105	+	0.955155i	$0.404312\pi$
$702$	−23.5012	−0.886994
$703$	−22.3434	−0.842696
$704$	−4.27224	−0.161016
$705$	10.1035	0.380519
$706$	6.06879	0.228402
$707$	15.8269	0.595230
$708$	−25.1827	−0.946425
$709$	−23.5391	−0.884028	−0.442014	−	0.897008i	$-0.645736\pi$
$709$	−23.5391	−0.884028	−0.442014	+	0.897008i	$0.645736\pi$
$710$	−16.0458	−0.602190
$711$	63.5661	2.38392
$712$	−7.95251	−0.298033
$713$	−18.6936	−0.700082
$714$	−3.79077	−0.141866
$715$	−1.15474	−0.0431848
$716$	5.15955	0.192822
$717$	−4.65609	−0.173885
$718$	−48.7146	−1.81801
$719$	2.53215	0.0944334	0.0472167	−	0.998885i	$-0.484965\pi$
$719$	2.53215	0.0944334	0.0472167	+	0.998885i	$0.484965\pi$
$720$	−26.9082	−1.00281
$721$	0.594331	0.0221340
$722$	10.5574	0.392908
$723$	27.5751	1.02553
$724$	42.4264	1.57677
$725$	−10.0961	−0.374961
$726$	−59.1031	−2.19352
$727$	−3.49408	−0.129588	−0.0647942	−	0.997899i	$-0.520639\pi$
$727$	−3.49408	−0.129588	−0.0647942	+	0.997899i	$0.520639\pi$
$728$	−0.827063	−0.0306530
$729$	−29.1353	−1.07908
$730$	−17.6229	−0.652254
$731$	3.51971	0.130181
$732$	70.3991	2.60202
$733$	48.4358	1.78902	0.894509	−	0.447051i	$-0.147526\pi$
$733$	48.4358	1.78902	0.894509	+	0.447051i	$0.147526\pi$
$734$	11.8016	0.435606
$735$	18.2755	0.674101
$736$	23.1413	0.853000
$737$	8.30728	0.306003
$738$	25.8573	0.951820
$739$	29.1669	1.07292	0.536460	−	0.843926i	$-0.319761\pi$
$739$	29.1669	1.07292	0.536460	+	0.843926i	$0.319761\pi$
$740$	10.1777	0.374142
$741$	−15.4356	−0.567039
$742$	−13.6286	−0.500322
$743$	−29.7336	−1.09082	−0.545411	−	0.838169i	$-0.683626\pi$
$743$	−29.7336	−1.09082	−0.545411	+	0.838169i	$0.683626\pi$
$744$	11.2757	0.413387
$745$	−8.84992	−0.324236
$746$	−44.5975	−1.63283
$747$	−44.7836	−1.63855
$748$	−0.969255	−0.0354395
$749$	2.55203	0.0932492
$750$	5.72336	0.208988
$751$	−0.902486	−0.0329322	−0.0164661	−	0.999864i	$-0.505242\pi$
$751$	−0.902486	−0.0329322	−0.0164661	+	0.999864i	$0.505242\pi$
$752$	15.3834	0.560975
$753$	−30.7688	−1.12128
$754$	−27.2292	−0.991628
$755$	−19.3356	−0.703694
$756$	−13.6784	−0.497477
$757$	3.24069	0.117785	0.0588924	−	0.998264i	$-0.481243\pi$
$757$	3.24069	0.117785	0.0588924	+	0.998264i	$0.481243\pi$
$758$	−53.6730	−1.94949
$759$	−7.60015	−0.275868
$760$	−2.30098	−0.0834652
$761$	6.64849	0.241007	0.120504	−	0.992713i	$-0.461549\pi$
$761$	6.64849	0.241007	0.120504	+	0.992713i	$0.461549\pi$
$762$	0.811579	0.0294004
$763$	−5.10555	−0.184833
$764$	−2.68006	−0.0969611
$765$	−4.17787	−0.151051
$766$	37.8363	1.36708
$767$	−7.09251	−0.256096
$768$	−59.3953	−2.14324
$769$	38.0002	1.37032	0.685162	−	0.728391i	$-0.259731\pi$
$769$	38.0002	1.37032	0.685162	+	0.728391i	$0.259731\pi$
$770$	−1.47549	−0.0531728
$771$	39.8821	1.43632
$772$	11.8420	0.426204
$773$	−10.5964	−0.381125	−0.190563	−	0.981675i	$-0.561031\pi$
$773$	−10.5964	−0.381125	−0.190563	+	0.981675i	$0.561031\pi$
$774$	56.5474	2.03255
$775$	−6.02736	−0.216509
$776$	3.45382	0.123985
$777$	−17.0430	−0.611414
$778$	25.7275	0.922375
$779$	8.37380	0.300022
$780$	7.03113	0.251755
$781$	6.87016	0.245834
$782$	4.19632	0.150060
$783$	87.9760	3.14400
$784$	27.8260	0.993785
$785$	−21.6202	−0.771658
$786$	98.4238	3.51066
$787$	−3.47762	−0.123964	−0.0619820	−	0.998077i	$-0.519742\pi$
$787$	−3.47762	−0.123964	−0.0619820	+	0.998077i	$0.519742\pi$
$788$	29.1421	1.03815
$789$	24.5363	0.873514
$790$	−20.5861	−0.732420
$791$	−0.255809	−0.00909550
$792$	3.04213	0.108097
$793$	19.8273	0.704089
$794$	−20.2939	−0.720202
$795$	−22.6345	−0.802764
$796$	−11.1538	−0.395335
$797$	48.7719	1.72759	0.863795	−	0.503844i	$-0.168081\pi$
$797$	48.7719	1.72759	0.863795	+	0.503844i	$0.168081\pi$
$798$	−19.7230	−0.698187
$799$	2.38848	0.0844984
$800$	7.46141	0.263801
$801$	−75.1262	−2.65445
$802$	−10.4612	−0.369398
$803$	7.54540	0.266272
$804$	−50.5825	−1.78391
$805$	2.90978	0.102556
$806$	−16.2557	−0.572584
$807$	−51.1402	−1.80022
$808$	10.5678	0.371774
$809$	6.19979	0.217973	0.108987	−	0.994043i	$-0.465239\pi$
$809$	6.19979	0.217973	0.108987	+	0.994043i	$0.465239\pi$
$810$	−15.8464	−0.556786
$811$	24.7428	0.868838	0.434419	−	0.900711i	$-0.356954\pi$
$811$	24.7428	0.868838	0.434419	+	0.900711i	$0.356954\pi$
$812$	−15.8482	−0.556162
$813$	−38.3088	−1.34355
$814$	−9.56669	−0.335312
$815$	8.14550	0.285324
$816$	−9.58584	−0.335571
$817$	18.3127	0.640679
$818$	57.8062	2.02115
$819$	−7.81314	−0.273013
$820$	−3.81439	−0.133204
$821$	−48.9019	−1.70669	−0.853345	−	0.521347i	$-0.825430\pi$
$821$	−48.9019	−1.70669	−0.853345	+	0.521347i	$0.825430\pi$
$822$	−48.0403	−1.67560
$823$	17.5460	0.611616	0.305808	−	0.952093i	$-0.401073\pi$
$823$	17.5460	0.611616	0.305808	+	0.952093i	$0.401073\pi$
$824$	0.396843	0.0138247
$825$	−2.45050	−0.0853156
$826$	−9.06255	−0.315327
$827$	4.81551	0.167452	0.0837259	−	0.996489i	$-0.473318\pi$
$827$	4.81551	0.167452	0.0837259	+	0.996489i	$0.473318\pi$
$828$	30.7093	1.06722
$829$	−9.16058	−0.318160	−0.159080	−	0.987266i	$-0.550853\pi$
$829$	−9.16058	−0.318160	−0.159080	+	0.987266i	$0.550853\pi$
$830$	14.5033	0.503417
$831$	−55.9914	−1.94232
$832$	7.32646	0.253999
$833$	4.32036	0.149692
$834$	83.1088	2.87782
$835$	−0.901622	−0.0312019
$836$	−5.04293	−0.174414
$837$	52.5214	1.81541
$838$	26.6730	0.921402
$839$	29.1279	1.00561	0.502803	−	0.864401i	$-0.332302\pi$
$839$	29.1279	1.00561	0.502803	+	0.864401i	$0.332302\pi$
$840$	−1.75513	−0.0605578
$841$	72.9317	2.51489
$842$	−42.0731	−1.44993
$843$	38.1179	1.31285
$844$	12.9997	0.447469
$845$	−11.0197	−0.379091
$846$	38.3732	1.31930
$847$	−9.68841	−0.332898
$848$	−34.4630	−1.18347
$849$	−1.35923	−0.0466488
$850$	1.35301	0.0464080
$851$	18.8663	0.646729
$852$	−41.8319	−1.43314
$853$	−36.2101	−1.23981	−0.619905	−	0.784677i	$-0.712829\pi$
$853$	−36.2101	−1.23981	−0.619905	+	0.784677i	$0.712829\pi$
$854$	25.3346	0.866934
$855$	−21.7370	−0.743390
$856$	1.70403	0.0582425
$857$	−21.6435	−0.739329	−0.369665	−	0.929165i	$-0.620527\pi$
$857$	−21.6435	−0.739329	−0.369665	+	0.929165i	$0.620527\pi$
$858$	−6.60899	−0.225627
$859$	50.3528	1.71802	0.859008	−	0.511961i	$-0.171081\pi$
$859$	50.3528	1.71802	0.859008	+	0.511961i	$0.171081\pi$
$860$	−8.34170	−0.284450
$861$	6.38733	0.217680
$862$	2.31133	0.0787240
$863$	4.05460	0.138020	0.0690101	−	0.997616i	$-0.478016\pi$
$863$	4.05460	0.138020	0.0690101	+	0.997616i	$0.478016\pi$
$864$	−65.0175	−2.21194
$865$	−14.2605	−0.484871
$866$	−41.0449	−1.39476
$867$	49.2786	1.67359
$868$	−9.46133	−0.321138
$869$	8.81410	0.298998
$870$	−57.7837	−1.95905
$871$	−14.2461	−0.482712
$872$	−3.40904	−0.115445
$873$	32.6277	1.10428
$874$	21.8330	0.738513
$875$	0.938196	0.0317168
$876$	−45.9434	−1.55229
$877$	54.1161	1.82737	0.913686	−	0.406421i	$-0.133223\pi$
$877$	54.1161	1.82737	0.913686	+	0.406421i	$0.133223\pi$
$878$	−17.3652	−0.586047
$879$	10.6385	0.358827
$880$	−3.73110	−0.125775
$881$	34.0035	1.14561	0.572803	−	0.819693i	$-0.305856\pi$
$881$	34.0035	1.14561	0.572803	+	0.819693i	$0.305856\pi$
$882$	69.4106	2.33718
$883$	45.4315	1.52889	0.764446	−	0.644688i	$-0.223013\pi$
$883$	45.4315	1.52889	0.764446	+	0.644688i	$0.223013\pi$
$884$	1.66217	0.0559050
$885$	−15.0512	−0.505940
$886$	−49.6825	−1.66912
$887$	−41.3819	−1.38947	−0.694734	−	0.719267i	$-0.744478\pi$
$887$	−41.3819	−1.38947	−0.694734	+	0.719267i	$0.744478\pi$
$888$	−11.3798	−0.381883
$889$	0.133037	0.00446193
$890$	24.3298	0.815538
$891$	6.78477	0.227299
$892$	−28.1353	−0.942040
$893$	12.4270	0.415854
$894$	−50.6513	−1.69403
$895$	3.08376	0.103079
$896$	−4.63904	−0.154979
$897$	13.0335	0.435175
$898$	28.9312	0.965448
$899$	60.8530	2.02956
$900$	9.90153	0.330051
$901$	−5.35085	−0.178263
$902$	3.58538	0.119380
$903$	13.9685	0.464841
$904$	−0.170807	−0.00568095
$905$	25.3574	0.842909
$906$	−110.664	−3.67658
$907$	35.2978	1.17204	0.586022	−	0.810295i	$-0.300693\pi$
$907$	35.2978	1.17204	0.586022	+	0.810295i	$0.300693\pi$
$908$	−14.7570	−0.489727
$909$	99.8326	3.31124
$910$	2.53031	0.0838789
$911$	9.28722	0.307699	0.153850	−	0.988094i	$-0.450833\pi$
$911$	9.28722	0.307699	0.153850	+	0.988094i	$0.450833\pi$
$912$	−49.8741	−1.65150
$913$	−6.20970	−0.205511
$914$	−67.6078	−2.23627
$915$	42.0761	1.39099
$916$	27.1453	0.896905
$917$	16.1340	0.532792
$918$	−11.7899	−0.389126
$919$	−37.6061	−1.24051	−0.620256	−	0.784400i	$-0.712971\pi$
$919$	−37.6061	−1.24051	−0.620256	+	0.784400i	$0.712971\pi$
$920$	1.94290	0.0640555
$921$	−94.4027	−3.11068
$922$	24.9196	0.820683
$923$	−11.7816	−0.387797
$924$	−3.84663	−0.126545
$925$	6.08303	0.200009
$926$	−38.9051	−1.27850
$927$	3.74892	0.123131
$928$	−75.3313	−2.47287
$929$	11.4639	0.376118	0.188059	−	0.982158i	$-0.439780\pi$
$929$	11.4639	0.376118	0.188059	+	0.982158i	$0.439780\pi$
$930$	−34.4967	−1.13119
$931$	22.4784	0.736699
$932$	−42.9725	−1.40761
$933$	−53.1301	−1.73940
$934$	37.5430	1.22844
$935$	−0.579304	−0.0189453
$936$	−5.21694	−0.170521
$937$	−24.2003	−0.790590	−0.395295	−	0.918554i	$-0.629358\pi$
$937$	−24.2003	−0.790590	−0.395295	+	0.918554i	$0.629358\pi$
$938$	−18.2032	−0.594356
$939$	−36.6658	−1.19654
$940$	−5.66070	−0.184632
$941$	−44.2250	−1.44169	−0.720847	−	0.693094i	$-0.756247\pi$
$941$	−44.2250	−1.44169	−0.720847	+	0.693094i	$0.756247\pi$
$942$	−123.740	−4.03167
$943$	−7.07067	−0.230253
$944$	−22.9167	−0.745876
$945$	−8.17528	−0.265942
$946$	7.84087	0.254929
$947$	−36.7109	−1.19294	−0.596472	−	0.802634i	$-0.703431\pi$
$947$	−36.7109	−1.19294	−0.596472	+	0.802634i	$0.703431\pi$
$948$	−53.6684	−1.74307
$949$	−12.9396	−0.420037
$950$	7.03959	0.228394
$951$	−74.6128	−2.41949
$952$	−0.414916	−0.0134475
$953$	−43.1141	−1.39660	−0.698301	−	0.715804i	$-0.746060\pi$
$953$	−43.1141	−1.39660	−0.698301	+	0.715804i	$0.746060\pi$
$954$	−85.9664	−2.78326
$955$	−1.60182	−0.0518335
$956$	2.60868	0.0843707
$957$	24.7406	0.799750
$958$	37.8823	1.22392
$959$	−7.87496	−0.254296
$960$	15.5477	0.501799
$961$	5.32905	0.171905
$962$	16.4059	0.528947
$963$	16.0977	0.518741
$964$	−15.4495	−0.497596
$965$	7.07774	0.227841
$966$	16.6537	0.535824
$967$	30.7776	0.989741	0.494871	−	0.868967i	$-0.335215\pi$
$967$	30.7776	0.989741	0.494871	+	0.868967i	$0.335215\pi$
$968$	−6.46909	−0.207924
$969$	−7.74363	−0.248761
$970$	−10.5666	−0.339272
$971$	1.76280	0.0565710	0.0282855	−	0.999600i	$-0.490995\pi$
$971$	1.76280	0.0565710	0.0282855	+	0.999600i	$0.490995\pi$
$972$	2.42630	0.0778237
$973$	13.6235	0.436750
$974$	−71.9487	−2.30539
$975$	4.20236	0.134583
$976$	64.0644	2.05065
$977$	28.5726	0.914117	0.457059	−	0.889437i	$-0.348903\pi$
$977$	28.5726	0.914117	0.457059	+	0.889437i	$0.348903\pi$
$978$	46.6196	1.49073
$979$	−10.4170	−0.332929
$980$	−10.2392	−0.327081
$981$	−32.2047	−1.02822
$982$	15.6157	0.498317
$983$	53.5433	1.70777	0.853883	−	0.520465i	$-0.174241\pi$
$983$	53.5433	1.70777	0.853883	+	0.520465i	$0.174241\pi$
$984$	4.26491	0.135960
$985$	17.4177	0.554973
$986$	−13.6602	−0.435029
$987$	9.47903	0.301721
$988$	8.64812	0.275133
$989$	−15.4629	−0.491690
$990$	−9.30706	−0.295798
$991$	6.26258	0.198937	0.0994686	−	0.995041i	$-0.468286\pi$
$991$	6.26258	0.198937	0.0994686	+	0.995041i	$0.468286\pi$
$992$	−44.9726	−1.42788
$993$	−56.6823	−1.79876
$994$	−15.0541	−0.477488
$995$	−6.66638	−0.211338
$996$	37.8105	1.19807
$997$	52.9026	1.67544	0.837721	−	0.546098i	$-0.183888\pi$
$997$	52.9026	1.67544	0.837721	+	0.546098i	$0.183888\pi$
$998$	−69.4754	−2.19920
$999$	−53.0065	−1.67705

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6005.2.a.f.1.20	✓	111

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6005.2.a.f.1.20	✓	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)

\(f(q)\)	\(=\)	\(q-1.91654 q^{2} -2.98629 q^{3} +1.67314 q^{4} +1.00000 q^{5} +5.72336 q^{6} +0.938196 q^{7} +0.626446 q^{8} +5.91794 q^{9} +O(q^{10})\)	\(q-1.91654 q^{2} -2.98629 q^{3} +1.67314 q^{4} +1.00000 q^{5} +5.72336 q^{6} +0.938196 q^{7} +0.626446 q^{8} +5.91794 q^{9} -1.91654 q^{10} +0.820584 q^{11} -4.99648 q^{12} -1.40722 q^{13} -1.79809 q^{14} -2.98629 q^{15} -4.54689 q^{16} -0.705966 q^{17} -11.3420 q^{18} -3.67307 q^{19} +1.67314 q^{20} -2.80173 q^{21} -1.57268 q^{22} +3.10146 q^{23} -1.87075 q^{24} +1.00000 q^{25} +2.69699 q^{26} -8.71383 q^{27} +1.56973 q^{28} -10.0961 q^{29} +5.72336 q^{30} -6.02736 q^{31} +7.46141 q^{32} -2.45050 q^{33} +1.35301 q^{34} +0.938196 q^{35} +9.90153 q^{36} +6.08303 q^{37} +7.03959 q^{38} +4.20236 q^{39} +0.626446 q^{40} -2.27978 q^{41} +5.36963 q^{42} -4.98566 q^{43} +1.37295 q^{44} +5.91794 q^{45} -5.94409 q^{46} -3.38328 q^{47} +13.5783 q^{48} -6.11979 q^{49} -1.91654 q^{50} +2.10822 q^{51} -2.35447 q^{52} +7.57948 q^{53} +16.7004 q^{54} +0.820584 q^{55} +0.587729 q^{56} +10.9688 q^{57} +19.3497 q^{58} +5.04009 q^{59} -4.99648 q^{60} -14.0897 q^{61} +11.5517 q^{62} +5.55219 q^{63} -5.20634 q^{64} -1.40722 q^{65} +4.69650 q^{66} +10.1236 q^{67} -1.18118 q^{68} -9.26188 q^{69} -1.79809 q^{70} +8.37228 q^{71} +3.70727 q^{72} +9.19517 q^{73} -11.6584 q^{74} -2.98629 q^{75} -6.14554 q^{76} +0.769868 q^{77} -8.05401 q^{78} +10.7413 q^{79} -4.54689 q^{80} +8.26823 q^{81} +4.36931 q^{82} -7.56742 q^{83} -4.68767 q^{84} -0.705966 q^{85} +9.55524 q^{86} +30.1500 q^{87} +0.514052 q^{88} -12.6946 q^{89} -11.3420 q^{90} -1.32025 q^{91} +5.18918 q^{92} +17.9995 q^{93} +6.48421 q^{94} -3.67307 q^{95} -22.2820 q^{96} +5.51335 q^{97} +11.7288 q^{98} +4.85617 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 111 q + 20 q^{2} + 40 q^{3} + 136 q^{4} + 111 q^{5} + 3 q^{6} + 39 q^{7} + 45 q^{8} + 139 q^{9}+O(q^{10}) \) 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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