LMFDB - Embedded newform 2005.2.a.f.1.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2005,2,Mod(1,2005)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2005, 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("2005.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2005 = 5 \cdot 401 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2005.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$16.0100056053$
Analytic rank:	$0$
Dimension:	$37$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.10
Character	$\chi$	$=$	2005.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.31166 q^{2} +2.95262 q^{3} -0.279548 q^{4} -1.00000 q^{5} -3.87283 q^{6} +1.12020 q^{7} +2.98999 q^{8} +5.71797 q^{9} +O(q^{10})$	\(q-1.31166 q^{2} +2.95262 q^{3} -0.279548 q^{4} -1.00000 q^{5} -3.87283 q^{6} +1.12020 q^{7} +2.98999 q^{8} +5.71797 q^{9} +1.31166 q^{10} +5.24765 q^{11} -0.825401 q^{12} -4.00469 q^{13} -1.46932 q^{14} -2.95262 q^{15} -3.36276 q^{16} -0.102994 q^{17} -7.50004 q^{18} +3.70762 q^{19} +0.279548 q^{20} +3.30752 q^{21} -6.88313 q^{22} -6.85967 q^{23} +8.82831 q^{24} +1.00000 q^{25} +5.25279 q^{26} +8.02515 q^{27} -0.313150 q^{28} +2.01465 q^{29} +3.87283 q^{30} +10.3186 q^{31} -1.56919 q^{32} +15.4943 q^{33} +0.135093 q^{34} -1.12020 q^{35} -1.59845 q^{36} +2.90510 q^{37} -4.86313 q^{38} -11.8243 q^{39} -2.98999 q^{40} +11.8745 q^{41} -4.33835 q^{42} +3.80514 q^{43} -1.46697 q^{44} -5.71797 q^{45} +8.99756 q^{46} +0.424427 q^{47} -9.92894 q^{48} -5.74515 q^{49} -1.31166 q^{50} -0.304103 q^{51} +1.11950 q^{52} -10.7332 q^{53} -10.5263 q^{54} -5.24765 q^{55} +3.34939 q^{56} +10.9472 q^{57} -2.64253 q^{58} -9.06941 q^{59} +0.825401 q^{60} -10.7000 q^{61} -13.5345 q^{62} +6.40527 q^{63} +8.78376 q^{64} +4.00469 q^{65} -20.3233 q^{66} +14.8990 q^{67} +0.0287919 q^{68} -20.2540 q^{69} +1.46932 q^{70} +9.72876 q^{71} +17.0967 q^{72} -7.13745 q^{73} -3.81050 q^{74} +2.95262 q^{75} -1.03646 q^{76} +5.87841 q^{77} +15.5095 q^{78} -7.65046 q^{79} +3.36276 q^{80} +6.54130 q^{81} -15.5753 q^{82} -8.28276 q^{83} -0.924613 q^{84} +0.102994 q^{85} -4.99105 q^{86} +5.94849 q^{87} +15.6904 q^{88} +9.60184 q^{89} +7.50004 q^{90} -4.48605 q^{91} +1.91761 q^{92} +30.4670 q^{93} -0.556705 q^{94} -3.70762 q^{95} -4.63323 q^{96} +5.34506 q^{97} +7.53569 q^{98} +30.0059 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 37 q + 7 q^{2} + 3 q^{3} + 43 q^{4} - 37 q^{5} + 8 q^{6} - 16 q^{7} + 21 q^{8} + 54 q^{9}+O(q^{10}) $ 37 * q + 7 * q^2 + 3 * q^3 + 43 * q^4 - 37 * q^5 + 8 * q^6 - 16 * q^7 + 21 * q^8 + 54 * q^9	\( 37 q + 7 q^{2} + 3 q^{3} + 43 q^{4} - 37 q^{5} + 8 q^{6} - 16 q^{7} + 21 q^{8} + 54 q^{9} - 7 q^{10} + 42 q^{11} - 13 q^{13} + 14 q^{14} - 3 q^{15} + 63 q^{16} + 18 q^{17} + 22 q^{18} + 22 q^{19} - 43 q^{20} + 16 q^{21} - 10 q^{22} + 23 q^{23} + 23 q^{24} + 37 q^{25} + 21 q^{26} + 3 q^{27} - 18 q^{28} + 33 q^{29} - 8 q^{30} + 11 q^{31} + 54 q^{32} + 2 q^{33} + 8 q^{34} + 16 q^{35} + 91 q^{36} - 11 q^{37} + 29 q^{38} + 25 q^{39} - 21 q^{40} + 24 q^{41} + 4 q^{42} + 25 q^{43} + 84 q^{44} - 54 q^{45} + 31 q^{46} + 7 q^{47} + 4 q^{48} + 45 q^{49} + 7 q^{50} + 94 q^{51} - 43 q^{52} + 49 q^{53} + 38 q^{54} - 42 q^{55} + 46 q^{56} + 6 q^{57} + 15 q^{58} + 69 q^{59} + 9 q^{61} + 17 q^{62} - 38 q^{63} + 107 q^{64} + 13 q^{65} + 74 q^{66} + 13 q^{67} + 86 q^{68} - 14 q^{70} + 51 q^{71} + 81 q^{72} - 47 q^{73} + 79 q^{74} + 3 q^{75} + 59 q^{76} + 2 q^{77} + 20 q^{78} + 67 q^{79} - 63 q^{80} + 125 q^{81} - 24 q^{82} + 80 q^{83} + 50 q^{84} - 18 q^{85} + 69 q^{86} - 32 q^{87} - 12 q^{88} + 34 q^{89} - 22 q^{90} + 39 q^{91} + 85 q^{92} + q^{93} + 12 q^{94} - 22 q^{95} + 77 q^{96} - 14 q^{97} + 40 q^{98} + 133 q^{99}+O(q^{100}) \) 37 * q + 7 * q^2 + 3 * q^3 + 43 * q^4 - 37 * q^5 + 8 * q^6 - 16 * q^7 + 21 * q^8 + 54 * q^9 - 7 * q^10 + 42 * q^11 - 13 * q^13 + 14 * q^14 - 3 * q^15 + 63 * q^16 + 18 * q^17 + 22 * q^18 + 22 * q^19 - 43 * q^20 + 16 * q^21 - 10 * q^22 + 23 * q^23 + 23 * q^24 + 37 * q^25 + 21 * q^26 + 3 * q^27 - 18 * q^28 + 33 * q^29 - 8 * q^30 + 11 * q^31 + 54 * q^32 + 2 * q^33 + 8 * q^34 + 16 * q^35 + 91 * q^36 - 11 * q^37 + 29 * q^38 + 25 * q^39 - 21 * q^40 + 24 * q^41 + 4 * q^42 + 25 * q^43 + 84 * q^44 - 54 * q^45 + 31 * q^46 + 7 * q^47 + 4 * q^48 + 45 * q^49 + 7 * q^50 + 94 * q^51 - 43 * q^52 + 49 * q^53 + 38 * q^54 - 42 * q^55 + 46 * q^56 + 6 * q^57 + 15 * q^58 + 69 * q^59 + 9 * q^61 + 17 * q^62 - 38 * q^63 + 107 * q^64 + 13 * q^65 + 74 * q^66 + 13 * q^67 + 86 * q^68 - 14 * q^70 + 51 * q^71 + 81 * q^72 - 47 * q^73 + 79 * q^74 + 3 * q^75 + 59 * q^76 + 2 * q^77 + 20 * q^78 + 67 * q^79 - 63 * q^80 + 125 * q^81 - 24 * q^82 + 80 * q^83 + 50 * q^84 - 18 * q^85 + 69 * q^86 - 32 * q^87 - 12 * q^88 + 34 * q^89 - 22 * q^90 + 39 * q^91 + 85 * q^92 + q^93 + 12 * q^94 - 22 * q^95 + 77 * q^96 - 14 * q^97 + 40 * q^98 + 133 * 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 $

$2$	−1.31166	−0.927484	−0.463742	−	0.885970i	$-0.653493\pi$
$2$	−1.31166	−0.927484	−0.463742	+	0.885970i	$0.653493\pi$
$3$	2.95262	1.70470	0.852348	−	0.522974i	$-0.175178\pi$
$3$	2.95262	1.70470	0.852348	+	0.522974i	$0.175178\pi$
$4$	−0.279548	−0.139774
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	−3.87283	−1.58108
$7$	1.12020	0.423395	0.211698	−	0.977335i	$-0.432101\pi$
$7$	1.12020	0.423395	0.211698	+	0.977335i	$0.432101\pi$
$8$	2.98999	1.05712
$9$	5.71797	1.90599
$10$	1.31166	0.414783
$11$	5.24765	1.58223	0.791113	−	0.611670i	$-0.209502\pi$
$11$	5.24765	1.58223	0.791113	+	0.611670i	$0.209502\pi$
$12$	−0.825401	−0.238273
$13$	−4.00469	−1.11070	−0.555350	−	0.831617i	$-0.687416\pi$
$13$	−4.00469	−1.11070	−0.555350	+	0.831617i	$0.687416\pi$
$14$	−1.46932	−0.392692
$15$	−2.95262	−0.762364
$16$	−3.36276	−0.840689
$17$	−0.102994	−0.0249798	−0.0124899	−	0.999922i	$-0.503976\pi$
$17$	−0.102994	−0.0249798	−0.0124899	+	0.999922i	$0.503976\pi$
$18$	−7.50004	−1.76778
$19$	3.70762	0.850586	0.425293	−	0.905056i	$-0.360171\pi$
$19$	3.70762	0.850586	0.425293	+	0.905056i	$0.360171\pi$
$20$	0.279548	0.0625089
$21$	3.30752	0.721761
$22$	−6.88313	−1.46749
$23$	−6.85967	−1.43034	−0.715171	−	0.698950i	$-0.753651\pi$
$23$	−6.85967	−1.43034	−0.715171	+	0.698950i	$0.753651\pi$
$24$	8.82831	1.80207
$25$	1.00000	0.200000
$26$	5.25279	1.03016
$27$	8.02515	1.54444
$28$	−0.313150	−0.0591798
$29$	2.01465	0.374111	0.187055	−	0.982349i	$-0.440106\pi$
$29$	2.01465	0.374111	0.187055	+	0.982349i	$0.440106\pi$
$30$	3.87283	0.707080
$31$	10.3186	1.85328	0.926640	−	0.375950i	$-0.122684\pi$
$31$	10.3186	1.85328	0.926640	+	0.375950i	$0.122684\pi$
$32$	−1.56919	−0.277397
$33$	15.4943	2.69722
$34$	0.135093	0.0231683
$35$	−1.12020	−0.189348
$36$	−1.59845	−0.266408
$37$	2.90510	0.477596	0.238798	−	0.971069i	$-0.423247\pi$
$37$	2.90510	0.477596	0.238798	+	0.971069i	$0.423247\pi$
$38$	−4.86313	−0.788904
$39$	−11.8243	−1.89341
$40$	−2.98999	−0.472759
$41$	11.8745	1.85448	0.927241	−	0.374466i	$-0.122174\pi$
$41$	11.8745	1.85448	0.927241	+	0.374466i	$0.122174\pi$
$42$	−4.33835	−0.669421
$43$	3.80514	0.580279	0.290139	−	0.956984i	$-0.406298\pi$
$43$	3.80514	0.580279	0.290139	+	0.956984i	$0.406298\pi$
$44$	−1.46697	−0.221154
$45$	−5.71797	−0.852385
$46$	8.99756	1.32662
$47$	0.424427	0.0619091	0.0309546	−	0.999521i	$-0.490145\pi$
$47$	0.424427	0.0619091	0.0309546	+	0.999521i	$0.490145\pi$
$48$	−9.92894	−1.43312
$49$	−5.74515	−0.820736
$50$	−1.31166	−0.185497
$51$	−0.304103	−0.0425829
$52$	1.11950	0.155247
$53$	−10.7332	−1.47432	−0.737160	−	0.675718i	$-0.763834\pi$
$53$	−10.7332	−1.47432	−0.737160	+	0.675718i	$0.763834\pi$
$54$	−10.5263	−1.43244
$55$	−5.24765	−0.707593
$56$	3.34939	0.447581
$57$	10.9472	1.44999
$58$	−2.64253	−0.346982
$59$	−9.06941	−1.18074	−0.590369	−	0.807134i	$-0.701018\pi$
$59$	−9.06941	−1.18074	−0.590369	+	0.807134i	$0.701018\pi$
$60$	0.825401	0.106559
$61$	−10.7000	−1.37000	−0.685000	−	0.728543i	$-0.740198\pi$
$61$	−10.7000	−1.37000	−0.685000	+	0.728543i	$0.740198\pi$
$62$	−13.5345	−1.71889
$63$	6.40527	0.806988
$64$	8.78376	1.09797
$65$	4.00469	0.496720
$66$	−20.3233	−2.50162
$67$	14.8990	1.82021	0.910104	−	0.414380i	$-0.136002\pi$
$67$	14.8990	1.82021	0.910104	+	0.414380i	$0.136002\pi$
$68$	0.0287919	0.00349153
$69$	−20.2540	−2.43830
$70$	1.46932	0.175617
$71$	9.72876	1.15459	0.577296	−	0.816535i	$-0.304108\pi$
$71$	9.72876	1.15459	0.577296	+	0.816535i	$0.304108\pi$
$72$	17.0967	2.01486
$73$	−7.13745	−0.835375	−0.417688	−	0.908591i	$-0.637159\pi$
$73$	−7.13745	−0.835375	−0.417688	+	0.908591i	$0.637159\pi$
$74$	−3.81050	−0.442962
$75$	2.95262	0.340939
$76$	−1.03646	−0.118890
$77$	5.87841	0.669907
$78$	15.5095	1.75610
$79$	−7.65046	−0.860744	−0.430372	−	0.902652i	$-0.641618\pi$
$79$	−7.65046	−0.860744	−0.430372	+	0.902652i	$0.641618\pi$
$80$	3.36276	0.375968
$81$	6.54130	0.726811
$82$	−15.5753	−1.72000
$83$	−8.28276	−0.909151	−0.454575	−	0.890708i	$-0.650209\pi$
$83$	−8.28276	−0.909151	−0.454575	+	0.890708i	$0.650209\pi$
$84$	−0.924613	−0.100884
$85$	0.102994	0.0111713
$86$	−4.99105	−0.538199
$87$	5.94849	0.637746
$88$	15.6904	1.67261
$89$	9.60184	1.01779	0.508897	−	0.860828i	$-0.330053\pi$
$89$	9.60184	1.01779	0.508897	+	0.860828i	$0.330053\pi$
$90$	7.50004	0.790573
$91$	−4.48605	−0.470265
$92$	1.91761	0.199925
$93$	30.4670	3.15928
$94$	−0.556705	−0.0574197
$95$	−3.70762	−0.380394
$96$	−4.63323	−0.472877
$97$	5.34506	0.542709	0.271355	−	0.962479i	$-0.412528\pi$
$97$	5.34506	0.542709	0.271355	+	0.962479i	$0.412528\pi$
$98$	7.53569	0.761219
$99$	30.0059	3.01571
$100$	−0.279548	−0.0279548
$101$	6.15185	0.612132	0.306066	−	0.952010i	$-0.400987\pi$
$101$	6.15185	0.612132	0.306066	+	0.952010i	$0.400987\pi$
$102$	0.398880	0.0394950
$103$	7.55884	0.744794	0.372397	−	0.928073i	$-0.378536\pi$
$103$	7.55884	0.744794	0.372397	+	0.928073i	$0.378536\pi$
$104$	−11.9740	−1.17415
$105$	−3.30752	−0.322781
$106$	14.0783	1.36741
$107$	8.49086	0.820842	0.410421	−	0.911896i	$-0.365382\pi$
$107$	8.49086	0.820842	0.410421	+	0.911896i	$0.365382\pi$
$108$	−2.24342	−0.215873
$109$	1.88600	0.180646	0.0903230	−	0.995913i	$-0.471210\pi$
$109$	1.88600	0.180646	0.0903230	+	0.995913i	$0.471210\pi$
$110$	6.88313	0.656281
$111$	8.57766	0.814156
$112$	−3.76696	−0.355944
$113$	0.353818	0.0332844	0.0166422	−	0.999862i	$-0.494702\pi$
$113$	0.353818	0.0332844	0.0166422	+	0.999862i	$0.494702\pi$
$114$	−14.3590	−1.34484
$115$	6.85967	0.639668
$116$	−0.563192	−0.0522911
$117$	−22.8987	−2.11698
$118$	11.8960	1.09511
$119$	−0.115374	−0.0105763
$120$	−8.82831	−0.805911
$121$	16.5378	1.50344
$122$	14.0348	1.27065
$123$	35.0608	3.16133
$124$	−2.88456	−0.259041
$125$	−1.00000	−0.0894427
$126$	−8.40153	−0.748468
$127$	−12.2987	−1.09133	−0.545665	−	0.838003i	$-0.683723\pi$
$127$	−12.2987	−1.09133	−0.545665	+	0.838003i	$0.683723\pi$
$128$	−8.38292	−0.740952
$129$	11.2351	0.989199
$130$	−5.25279	−0.460700
$131$	16.1915	1.41466	0.707330	−	0.706883i	$-0.249899\pi$
$131$	16.1915	1.41466	0.707330	+	0.706883i	$0.249899\pi$
$132$	−4.33142	−0.377001
$133$	4.15327	0.360134
$134$	−19.5425	−1.68821
$135$	−8.02515	−0.690695
$136$	−0.307952	−0.0264067
$137$	−0.366552	−0.0313166	−0.0156583	−	0.999877i	$-0.504984\pi$
$137$	−0.366552	−0.0313166	−0.0156583	+	0.999877i	$0.504984\pi$
$138$	26.5664	2.26148
$139$	−4.28446	−0.363403	−0.181702	−	0.983354i	$-0.558160\pi$
$139$	−4.28446	−0.363403	−0.181702	+	0.983354i	$0.558160\pi$
$140$	0.313150	0.0264660
$141$	1.25317	0.105536
$142$	−12.7608	−1.07086
$143$	−21.0152	−1.75738
$144$	−19.2281	−1.60235
$145$	−2.01465	−0.167307
$146$	9.36191	0.774797
$147$	−16.9633	−1.39911
$148$	−0.812117	−0.0667556
$149$	20.2936	1.66252	0.831260	−	0.555883i	$-0.187620\pi$
$149$	20.2936	1.66252	0.831260	+	0.555883i	$0.187620\pi$
$150$	−3.87283	−0.316216
$151$	−1.34097	−0.109126	−0.0545632	−	0.998510i	$-0.517377\pi$
$151$	−1.34097	−0.109126	−0.0545632	+	0.998510i	$0.517377\pi$
$152$	11.0857	0.899173
$153$	−0.588918	−0.0476112
$154$	−7.71048	−0.621328
$155$	−10.3186	−0.828812
$156$	3.30547	0.264650
$157$	10.6689	0.851475	0.425737	−	0.904847i	$-0.360015\pi$
$157$	10.6689	0.851475	0.425737	+	0.904847i	$0.360015\pi$
$158$	10.0348	0.798326
$159$	−31.6911	−2.51327
$160$	1.56919	0.124056
$161$	−7.68420	−0.605600
$162$	−8.57996	−0.674105
$163$	−8.81319	−0.690302	−0.345151	−	0.938547i	$-0.612172\pi$
$163$	−8.81319	−0.690302	−0.345151	+	0.938547i	$0.612172\pi$
$164$	−3.31949	−0.259209
$165$	−15.4943	−1.20623
$166$	10.8642	0.843223
$167$	−15.6554	−1.21145	−0.605726	−	0.795673i	$-0.707117\pi$
$167$	−15.6554	−1.21145	−0.605726	+	0.795673i	$0.707117\pi$
$168$	9.88947	0.762989
$169$	3.03751	0.233655
$170$	−0.135093	−0.0103612
$171$	21.2001	1.62121
$172$	−1.06372	−0.0811080
$173$	23.0007	1.74871	0.874354	−	0.485289i	$-0.161285\pi$
$173$	23.0007	1.74871	0.874354	+	0.485289i	$0.161285\pi$
$174$	−7.80240	−0.591499
$175$	1.12020	0.0846791
$176$	−17.6466	−1.33016
$177$	−26.7785	−2.01280
$178$	−12.5944	−0.943987
$179$	11.4089	0.852742	0.426371	−	0.904548i	$-0.359792\pi$
$179$	11.4089	0.852742	0.426371	+	0.904548i	$0.359792\pi$
$180$	1.59845	0.119141
$181$	−17.8443	−1.32635	−0.663177	−	0.748463i	$-0.730792\pi$
$181$	−17.8443	−1.32635	−0.663177	+	0.748463i	$0.730792\pi$
$182$	5.88417	0.436163
$183$	−31.5932	−2.33544
$184$	−20.5104	−1.51204
$185$	−2.90510	−0.213587
$186$	−39.9623	−2.93018
$187$	−0.540478	−0.0395237
$188$	−0.118648	−0.00865330
$189$	8.98976	0.653909
$190$	4.86313	0.352809
$191$	12.0639	0.872916	0.436458	−	0.899725i	$-0.356233\pi$
$191$	12.0639	0.872916	0.436458	+	0.899725i	$0.356233\pi$
$192$	25.9351	1.87171
$193$	1.56199	0.112434	0.0562172	−	0.998419i	$-0.482096\pi$
$193$	1.56199	0.112434	0.0562172	+	0.998419i	$0.482096\pi$
$194$	−7.01091	−0.503354
$195$	11.8243	0.846757
$196$	1.60605	0.114718
$197$	17.7378	1.26376	0.631882	−	0.775064i	$-0.282283\pi$
$197$	17.7378	1.26376	0.631882	+	0.775064i	$0.282283\pi$
$198$	−39.3576	−2.79702
$199$	−15.0489	−1.06679	−0.533396	−	0.845866i	$-0.679084\pi$
$199$	−15.0489	−1.06679	−0.533396	+	0.845866i	$0.679084\pi$
$200$	2.98999	0.211424
$201$	43.9912	3.10290
$202$	−8.06914	−0.567742
$203$	2.25681	0.158397
$204$	0.0850115	0.00595200
$205$	−11.8745	−0.829349
$206$	−9.91462	−0.690785
$207$	−39.2234	−2.72622
$208$	13.4668	0.933753
$209$	19.4563	1.34582
$210$	4.33835	0.299374
$211$	−18.3114	−1.26061	−0.630305	−	0.776347i	$-0.717070\pi$
$211$	−18.3114	−1.26061	−0.630305	+	0.776347i	$0.717070\pi$
$212$	3.00045	0.206072
$213$	28.7254	1.96823
$214$	−11.1371	−0.761317
$215$	−3.80514	−0.259509
$216$	23.9951	1.63266
$217$	11.5589	0.784670
$218$	−2.47379	−0.167546
$219$	−21.0742	−1.42406
$220$	1.46697	0.0989033
$221$	0.412460	0.0277450
$222$	−11.2510	−0.755116
$223$	11.3880	0.762595	0.381298	−	0.924452i	$-0.375477\pi$
$223$	11.3880	0.762595	0.381298	+	0.924452i	$0.375477\pi$
$224$	−1.75781	−0.117448
$225$	5.71797	0.381198
$226$	−0.464089	−0.0308708
$227$	−0.442379	−0.0293617	−0.0146809	−	0.999892i	$-0.504673\pi$
$227$	−0.442379	−0.0293617	−0.0146809	+	0.999892i	$0.504673\pi$
$228$	−3.06027	−0.202671
$229$	3.16764	0.209323	0.104662	−	0.994508i	$-0.466624\pi$
$229$	3.16764	0.209323	0.104662	+	0.994508i	$0.466624\pi$
$230$	−8.99756	−0.593282
$231$	17.3567	1.14199
$232$	6.02378	0.395481
$233$	−8.26746	−0.541620	−0.270810	−	0.962633i	$-0.587291\pi$
$233$	−8.26746	−0.541620	−0.270810	+	0.962633i	$0.587291\pi$
$234$	30.0353	1.96347
$235$	−0.424427	−0.0276866
$236$	2.53534	0.165037
$237$	−22.5889	−1.46731
$238$	0.151332	0.00980937
$239$	16.6368	1.07615	0.538073	−	0.842898i	$-0.319152\pi$
$239$	16.6368	1.07615	0.538073	+	0.842898i	$0.319152\pi$
$240$	9.92894	0.640911
$241$	−18.0843	−1.16491	−0.582456	−	0.812862i	$-0.697908\pi$
$241$	−18.0843	−1.16491	−0.582456	+	0.812862i	$0.697908\pi$
$242$	−21.6920	−1.39442
$243$	−4.76146	−0.305448
$244$	2.99118	0.191491
$245$	5.74515	0.367044
$246$	−45.9879	−2.93208
$247$	−14.8478	−0.944746
$248$	30.8526	1.95914
$249$	−24.4559	−1.54983
$250$	1.31166	0.0829567
$251$	−3.85866	−0.243556	−0.121778	−	0.992557i	$-0.538860\pi$
$251$	−3.85866	−0.243556	−0.121778	+	0.992557i	$0.538860\pi$
$252$	−1.79058	−0.112796
$253$	−35.9972	−2.26312
$254$	16.1317	1.01219
$255$	0.304103	0.0190437
$256$	−6.57198	−0.410749
$257$	21.1549	1.31960	0.659802	−	0.751440i	$-0.270640\pi$
$257$	21.1549	1.31960	0.659802	+	0.751440i	$0.270640\pi$
$258$	−14.7367	−0.917466
$259$	3.25429	0.202212
$260$	−1.11950	−0.0694287
$261$	11.5197	0.713052
$262$	−21.2378	−1.31207
$263$	−16.0544	−0.989955	−0.494977	−	0.868906i	$-0.664824\pi$
$263$	−16.0544	−0.989955	−0.494977	+	0.868906i	$0.664824\pi$
$264$	46.3279	2.85129
$265$	10.7332	0.659336
$266$	−5.44768	−0.334018
$267$	28.3506	1.73503
$268$	−4.16500	−0.254418
$269$	−19.0490	−1.16144	−0.580720	−	0.814104i	$-0.697229\pi$
$269$	−19.0490	−1.16144	−0.580720	+	0.814104i	$0.697229\pi$
$270$	10.5263	0.640608
$271$	7.54554	0.458359	0.229180	−	0.973384i	$-0.426396\pi$
$271$	7.54554	0.458359	0.229180	+	0.973384i	$0.426396\pi$
$272$	0.346345	0.0210002
$273$	−13.2456	−0.801660
$274$	0.480791	0.0290456
$275$	5.24765	0.316445
$276$	5.66198	0.340811
$277$	−25.3251	−1.52164	−0.760819	−	0.648965i	$-0.775202\pi$
$277$	−25.3251	−1.52164	−0.760819	+	0.648965i	$0.775202\pi$
$278$	5.61975	0.337050
$279$	59.0016	3.53233
$280$	−3.34939	−0.200164
$281$	13.5852	0.810422	0.405211	−	0.914223i	$-0.367198\pi$
$281$	13.5852	0.810422	0.405211	+	0.914223i	$0.367198\pi$
$282$	−1.64374	−0.0978832
$283$	−0.838835	−0.0498636	−0.0249318	−	0.999689i	$-0.507937\pi$
$283$	−0.838835	−0.0498636	−0.0249318	+	0.999689i	$0.507937\pi$
$284$	−2.71966	−0.161382
$285$	−10.9472	−0.648456
$286$	27.5648	1.62994
$287$	13.3018	0.785179
$288$	−8.97260	−0.528716
$289$	−16.9894	−0.999376
$290$	2.64253	0.155175
$291$	15.7819	0.925154
$292$	1.99526	0.116764
$293$	17.9128	1.04648	0.523239	−	0.852186i	$-0.324724\pi$
$293$	17.9128	1.04648	0.523239	+	0.852186i	$0.324724\pi$
$294$	22.2500	1.29765
$295$	9.06941	0.528042
$296$	8.68623	0.504877
$297$	42.1132	2.44365
$298$	−26.6184	−1.54196
$299$	27.4708	1.58868
$300$	−0.825401	−0.0476545
$301$	4.26252	0.245687
$302$	1.75889	0.101213
$303$	18.1641	1.04350
$304$	−12.4678	−0.715078
$305$	10.7000	0.612683
$306$	0.772461	0.0441586
$307$	−30.4947	−1.74042	−0.870212	−	0.492677i	$-0.836019\pi$
$307$	−30.4947	−1.74042	−0.870212	+	0.492677i	$0.836019\pi$
$308$	−1.64330	−0.0936358
$309$	22.3184	1.26965
$310$	13.5345	0.768709
$311$	−20.9082	−1.18560	−0.592798	−	0.805351i	$-0.701977\pi$
$311$	−20.9082	−1.18560	−0.592798	+	0.805351i	$0.701977\pi$
$312$	−35.3546	−2.00156
$313$	6.17994	0.349311	0.174655	−	0.984630i	$-0.444119\pi$
$313$	6.17994	0.349311	0.174655	+	0.984630i	$0.444119\pi$
$314$	−13.9940	−0.789729
$315$	−6.40527	−0.360896
$316$	2.13867	0.120310
$317$	−24.2595	−1.36255	−0.681274	−	0.732028i	$-0.738574\pi$
$317$	−24.2595	−1.36255	−0.681274	+	0.732028i	$0.738574\pi$
$318$	41.5680	2.33101
$319$	10.5722	0.591928
$320$	−8.78376	−0.491027
$321$	25.0703	1.39929
$322$	10.0791	0.561684
$323$	−0.381863	−0.0212474
$324$	−1.82861	−0.101589
$325$	−4.00469	−0.222140
$326$	11.5599	0.640244
$327$	5.56864	0.307947
$328$	35.5046	1.96041
$329$	0.475443	0.0262120
$330$	20.3233	1.11876
$331$	30.2806	1.66437	0.832187	−	0.554495i	$-0.187088\pi$
$331$	30.2806	1.66437	0.832187	+	0.554495i	$0.187088\pi$
$332$	2.31543	0.127076
$333$	16.6113	0.910293
$334$	20.5346	1.12360
$335$	−14.8990	−0.814022
$336$	−11.1224	−0.606776
$337$	−3.38169	−0.184212	−0.0921061	−	0.995749i	$-0.529360\pi$
$337$	−3.38169	−0.184212	−0.0921061	+	0.995749i	$0.529360\pi$
$338$	−3.98419	−0.216711
$339$	1.04469	0.0567399
$340$	−0.0287919	−0.00156146
$341$	54.1485	2.93231
$342$	−27.8073	−1.50364
$343$	−14.2771	−0.770891
$344$	11.3773	0.613425
$345$	20.2540	1.09044
$346$	−30.1690	−1.62190
$347$	−21.7217	−1.16608	−0.583040	−	0.812443i	$-0.698137\pi$
$347$	−21.7217	−1.16608	−0.583040	+	0.812443i	$0.698137\pi$
$348$	−1.66289	−0.0891404
$349$	16.7496	0.896583	0.448291	−	0.893887i	$-0.352033\pi$
$349$	16.7496	0.896583	0.448291	+	0.893887i	$0.352033\pi$
$350$	−1.46932	−0.0785385
$351$	−32.1382	−1.71541
$352$	−8.23458	−0.438904
$353$	−7.16595	−0.381405	−0.190702	−	0.981648i	$-0.561077\pi$
$353$	−7.16595	−0.381405	−0.190702	+	0.981648i	$0.561077\pi$
$354$	35.1243	1.86684
$355$	−9.72876	−0.516349
$356$	−2.68418	−0.142261
$357$	−0.340656	−0.0180294
$358$	−14.9646	−0.790904
$359$	−29.9874	−1.58267	−0.791337	−	0.611380i	$-0.790615\pi$
$359$	−29.9874	−1.58267	−0.791337	+	0.611380i	$0.790615\pi$
$360$	−17.0967	−0.901075
$361$	−5.25357	−0.276504
$362$	23.4056	1.23017
$363$	48.8300	2.56291
$364$	1.25407	0.0657310
$365$	7.13745	0.373591
$366$	41.4395	2.16608
$367$	−13.2168	−0.689913	−0.344957	−	0.938619i	$-0.612106\pi$
$367$	−13.2168	−0.689913	−0.344957	+	0.938619i	$0.612106\pi$
$368$	23.0674	1.20247
$369$	67.8979	3.53462
$370$	3.81050	0.198099
$371$	−12.0233	−0.624220
$372$	−8.51700	−0.441586
$373$	12.4538	0.644833	0.322417	−	0.946598i	$-0.395505\pi$
$373$	12.4538	0.644833	0.322417	+	0.946598i	$0.395505\pi$
$374$	0.708923	0.0366575
$375$	−2.95262	−0.152473
$376$	1.26903	0.0654455
$377$	−8.06804	−0.415525
$378$	−11.7915	−0.606490
$379$	−30.9159	−1.58804	−0.794022	−	0.607889i	$-0.792017\pi$
$379$	−30.9159	−1.58804	−0.794022	+	0.607889i	$0.792017\pi$
$380$	1.03646	0.0531692
$381$	−36.3133	−1.86039
$382$	−15.8238	−0.809615
$383$	−22.1134	−1.12994	−0.564970	−	0.825112i	$-0.691112\pi$
$383$	−22.1134	−1.12994	−0.564970	+	0.825112i	$0.691112\pi$
$384$	−24.7516	−1.26310
$385$	−5.87841	−0.299592
$386$	−2.04880	−0.104281
$387$	21.7577	1.10601
$388$	−1.49420	−0.0758567
$389$	5.41675	0.274640	0.137320	−	0.990527i	$-0.456151\pi$
$389$	5.41675	0.274640	0.137320	+	0.990527i	$0.456151\pi$
$390$	−15.5095	−0.785354
$391$	0.706507	0.0357296
$392$	−17.1780	−0.867618
$393$	47.8075	2.41157
$394$	−23.2659	−1.17212
$395$	7.65046	0.384936
$396$	−8.38811	−0.421518
$397$	−27.6601	−1.38822	−0.694110	−	0.719868i	$-0.744202\pi$
$397$	−27.6601	−1.38822	−0.694110	+	0.719868i	$0.744202\pi$
$398$	19.7391	0.989432
$399$	12.2630	0.613919
$400$	−3.36276	−0.168138
$401$	1.00000	0.0499376
$401$	1.00000	0.0499376
$402$	−57.7015	−2.87789
$403$	−41.3229	−2.05844
$404$	−1.71974	−0.0855603
$405$	−6.54130	−0.325040
$406$	−2.96016	−0.146910
$407$	15.2450	0.755664
$408$	−0.909266	−0.0450154
$409$	14.9181	0.737653	0.368827	−	0.929498i	$-0.379760\pi$
$409$	14.9181	0.737653	0.368827	+	0.929498i	$0.379760\pi$
$410$	15.5753	0.769208
$411$	−1.08229	−0.0533853
$412$	−2.11306	−0.104103
$413$	−10.1595	−0.499919
$414$	51.4478	2.52852
$415$	8.28276	0.406585
$416$	6.28413	0.308105
$417$	−12.6504	−0.619492
$418$	−25.5200	−1.24823
$419$	−7.93403	−0.387602	−0.193801	−	0.981041i	$-0.562082\pi$
$419$	−7.93403	−0.387602	−0.193801	+	0.981041i	$0.562082\pi$
$420$	0.924613	0.0451165
$421$	−35.5210	−1.73119	−0.865594	−	0.500746i	$-0.833059\pi$
$421$	−35.5210	−1.73119	−0.865594	+	0.500746i	$0.833059\pi$
$422$	24.0184	1.16920
$423$	2.42686	0.117998
$424$	−32.0922	−1.55854
$425$	−0.102994	−0.00499596
$426$	−37.6779	−1.82550
$427$	−11.9862	−0.580052
$428$	−2.37361	−0.114733
$429$	−62.0499	−2.99580
$430$	4.99105	0.240690
$431$	−5.44307	−0.262183	−0.131092	−	0.991370i	$-0.541848\pi$
$431$	−5.44307	−0.262183	−0.131092	+	0.991370i	$0.541848\pi$
$432$	−26.9866	−1.29839
$433$	−37.9201	−1.82232	−0.911162	−	0.412048i	$-0.864813\pi$
$433$	−37.9201	−1.82232	−0.911162	+	0.412048i	$0.864813\pi$
$434$	−15.1614	−0.727769
$435$	−5.94849	−0.285208
$436$	−0.527228	−0.0252497
$437$	−25.4331	−1.21663
$438$	27.6422	1.32079
$439$	−3.28382	−0.156728	−0.0783642	−	0.996925i	$-0.524970\pi$
$439$	−3.28382	−0.156728	−0.0783642	+	0.996925i	$0.524970\pi$
$440$	−15.6904	−0.748012
$441$	−32.8506	−1.56432
$442$	−0.541007	−0.0257331
$443$	25.0669	1.19096	0.595481	−	0.803369i	$-0.296961\pi$
$443$	25.0669	1.19096	0.595481	+	0.803369i	$0.296961\pi$
$444$	−2.39787	−0.113798
$445$	−9.60184	−0.455171
$446$	−14.9372	−0.707295
$447$	59.9195	2.83409
$448$	9.83956	0.464875
$449$	−11.4057	−0.538269	−0.269134	−	0.963103i	$-0.586738\pi$
$449$	−11.4057	−0.538269	−0.269134	+	0.963103i	$0.586738\pi$
$450$	−7.50004	−0.353555
$451$	62.3131	2.93421
$452$	−0.0989094	−0.00465231
$453$	−3.95937	−0.186028
$454$	0.580251	0.0272325
$455$	4.48605	0.210309
$456$	32.7320	1.53282
$457$	8.33186	0.389748	0.194874	−	0.980828i	$-0.437570\pi$
$457$	8.33186	0.389748	0.194874	+	0.980828i	$0.437570\pi$
$458$	−4.15486	−0.194144
$459$	−0.826544	−0.0385798
$460$	−1.91761	−0.0894091
$461$	−20.0008	−0.931531	−0.465766	−	0.884908i	$-0.654221\pi$
$461$	−20.0008	−0.931531	−0.465766	+	0.884908i	$0.654221\pi$
$462$	−22.7661	−1.05918
$463$	35.2227	1.63694	0.818469	−	0.574550i	$-0.194823\pi$
$463$	35.2227	1.63694	0.818469	+	0.574550i	$0.194823\pi$
$464$	−6.77477	−0.314511
$465$	−30.4670	−1.41287
$466$	10.8441	0.502343
$467$	−1.89807	−0.0878321	−0.0439160	−	0.999035i	$-0.513983\pi$
$467$	−1.89807	−0.0878321	−0.0439160	+	0.999035i	$0.513983\pi$
$468$	6.40129	0.295900
$469$	16.6899	0.770668
$470$	0.556705	0.0256789
$471$	31.5014	1.45151
$472$	−27.1175	−1.24818
$473$	19.9681	0.918132
$474$	29.6290	1.36090
$475$	3.70762	0.170117
$476$	0.0322526	0.00147830
$477$	−61.3722	−2.81004
$478$	−21.8219	−0.998108
$479$	−7.43067	−0.339516	−0.169758	−	0.985486i	$-0.554299\pi$
$479$	−7.43067	−0.339516	−0.169758	+	0.985486i	$0.554299\pi$
$480$	4.63323	0.211477
$481$	−11.6340	−0.530466
$482$	23.7205	1.08044
$483$	−22.6885	−1.03236
$484$	−4.62313	−0.210142
$485$	−5.34506	−0.242707
$486$	6.24542	0.283298
$487$	−25.5659	−1.15850	−0.579250	−	0.815150i	$-0.696654\pi$
$487$	−25.5659	−1.15850	−0.579250	+	0.815150i	$0.696654\pi$
$488$	−31.9931	−1.44826
$489$	−26.0220	−1.17676
$490$	−7.53569	−0.340428
$491$	−35.2099	−1.58900	−0.794500	−	0.607264i	$-0.792267\pi$
$491$	−35.2099	−1.58900	−0.794500	+	0.607264i	$0.792267\pi$
$492$	−9.80120	−0.441872
$493$	−0.207497	−0.00934521
$494$	19.4753	0.876236
$495$	−30.0059	−1.34867
$496$	−34.6990	−1.55803
$497$	10.8982	0.488849
$498$	32.0778	1.43744
$499$	−16.9597	−0.759221	−0.379611	−	0.925146i	$-0.623942\pi$
$499$	−16.9597	−0.759221	−0.379611	+	0.925146i	$0.623942\pi$
$500$	0.279548	0.0125018
$501$	−46.2245	−2.06516
$502$	5.06125	0.225895
$503$	−42.5281	−1.89623	−0.948116	−	0.317923i	$-0.897015\pi$
$503$	−42.5281	−1.89623	−0.948116	+	0.317923i	$0.897015\pi$
$504$	19.1517	0.853085
$505$	−6.15185	−0.273754
$506$	47.2161	2.09901
$507$	8.96863	0.398311
$508$	3.43807	0.152540
$509$	34.1314	1.51285	0.756424	−	0.654082i	$-0.226945\pi$
$509$	34.1314	1.51285	0.756424	+	0.654082i	$0.226945\pi$
$510$	−0.398880	−0.0176627
$511$	−7.99537	−0.353694
$512$	25.3860	1.12191
$513$	29.7542	1.31368
$514$	−27.7480	−1.22391
$515$	−7.55884	−0.333082
$516$	−3.14077	−0.138265
$517$	2.22725	0.0979542
$518$	−4.26852	−0.187548
$519$	67.9123	2.98102
$520$	11.9740	0.525094
$521$	−3.90241	−0.170967	−0.0854837	−	0.996340i	$-0.527244\pi$
$521$	−3.90241	−0.170967	−0.0854837	+	0.996340i	$0.527244\pi$
$522$	−15.1099	−0.661344
$523$	−21.0587	−0.920832	−0.460416	−	0.887703i	$-0.652300\pi$
$523$	−21.0587	−0.920832	−0.460416	+	0.887703i	$0.652300\pi$
$524$	−4.52632	−0.197733
$525$	3.30752	0.144352
$526$	21.0579	0.918167
$527$	−1.06276	−0.0462945
$528$	−52.1036	−2.26752
$529$	24.0551	1.04588
$530$	−14.0783	−0.611523
$531$	−51.8587	−2.25047
$532$	−1.16104	−0.0503375
$533$	−47.5535	−2.05977
$534$	−37.1864	−1.60921
$535$	−8.49086	−0.367092
$536$	44.5480	1.92418
$537$	33.6862	1.45367
$538$	24.9858	1.07722
$539$	−30.1486	−1.29859
$540$	2.24342	0.0965413
$541$	−19.6785	−0.846044	−0.423022	−	0.906119i	$-0.639031\pi$
$541$	−19.6785	−0.846044	−0.423022	+	0.906119i	$0.639031\pi$
$542$	−9.89719	−0.425121
$543$	−52.6874	−2.26103
$544$	0.161618	0.00692931
$545$	−1.88600	−0.0807873
$546$	17.3737	0.743526
$547$	17.0049	0.727079	0.363539	−	0.931579i	$-0.381568\pi$
$547$	17.0049	0.727079	0.363539	+	0.931579i	$0.381568\pi$
$548$	0.102469	0.00437726
$549$	−61.1826	−2.61121
$550$	−6.88313	−0.293498
$551$	7.46955	0.318213
$552$	−60.5594	−2.57758
$553$	−8.57004	−0.364435
$554$	33.2179	1.41129
$555$	−8.57766	−0.364102
$556$	1.19771	0.0507944
$557$	15.0575	0.638008	0.319004	−	0.947753i	$-0.396652\pi$
$557$	15.0575	0.638008	0.319004	+	0.947753i	$0.396652\pi$
$558$	−77.3901	−3.27618
$559$	−15.2384	−0.644516
$560$	3.76696	0.159183
$561$	−1.59583	−0.0673759
$562$	−17.8191	−0.751653
$563$	−25.6669	−1.08173	−0.540866	−	0.841109i	$-0.681904\pi$
$563$	−25.6669	−1.08173	−0.540866	+	0.841109i	$0.681904\pi$
$564$	−0.350323	−0.0147513
$565$	−0.353818	−0.0148852
$566$	1.10027	0.0462477
$567$	7.32755	0.307728
$568$	29.0889	1.22054
$569$	37.7537	1.58272	0.791359	−	0.611351i	$-0.209374\pi$
$569$	37.7537	1.58272	0.791359	+	0.611351i	$0.209374\pi$
$570$	14.3590	0.601432
$571$	−17.9191	−0.749891	−0.374946	−	0.927047i	$-0.622339\pi$
$571$	−17.9191	−0.749891	−0.374946	+	0.927047i	$0.622339\pi$
$572$	5.87477	0.245636
$573$	35.6202	1.48806
$574$	−17.4474	−0.728241
$575$	−6.85967	−0.286068
$576$	50.2253	2.09272
$577$	−20.0016	−0.832678	−0.416339	−	0.909209i	$-0.636687\pi$
$577$	−20.0016	−0.832678	−0.416339	+	0.909209i	$0.636687\pi$
$578$	22.2843	0.926905
$579$	4.61196	0.191666
$580$	0.563192	0.0233853
$581$	−9.27834	−0.384930
$582$	−20.7005	−0.858065
$583$	−56.3241	−2.33271
$584$	−21.3409	−0.883094
$585$	22.8987	0.946744
$586$	−23.4955	−0.970591
$587$	−13.8063	−0.569847	−0.284923	−	0.958550i	$-0.591968\pi$
$587$	−13.8063	−0.569847	−0.284923	+	0.958550i	$0.591968\pi$
$588$	4.74205	0.195559
$589$	38.2575	1.57637
$590$	−11.8960	−0.489750
$591$	52.3730	2.15434
$592$	−9.76915	−0.401509
$593$	19.5358	0.802241	0.401121	−	0.916025i	$-0.368621\pi$
$593$	19.5358	0.802241	0.401121	+	0.916025i	$0.368621\pi$
$594$	−55.2381	−2.26645
$595$	0.115374	0.00472988
$596$	−5.67306	−0.232378
$597$	−44.4338	−1.81856
$598$	−36.0324	−1.47347
$599$	18.3723	0.750674	0.375337	−	0.926889i	$-0.377527\pi$
$599$	18.3723	0.750674	0.375337	+	0.926889i	$0.377527\pi$
$600$	8.82831	0.360414
$601$	38.3482	1.56426	0.782129	−	0.623117i	$-0.214134\pi$
$601$	38.3482	1.56426	0.782129	+	0.623117i	$0.214134\pi$
$602$	−5.59097	−0.227871
$603$	85.1923	3.46930
$604$	0.374866	0.0152531
$605$	−16.5378	−0.672359
$606$	−23.8251	−0.967829
$607$	12.3601	0.501682	0.250841	−	0.968028i	$-0.419293\pi$
$607$	12.3601	0.501682	0.250841	+	0.968028i	$0.419293\pi$
$608$	−5.81797	−0.235950
$609$	6.66350	0.270019
$610$	−14.0348	−0.568253
$611$	−1.69970	−0.0687625
$612$	0.164631	0.00665482
$613$	15.6683	0.632836	0.316418	−	0.948620i	$-0.397520\pi$
$613$	15.6683	0.632836	0.316418	+	0.948620i	$0.397520\pi$
$614$	39.9987	1.61422
$615$	−35.0608	−1.41379
$616$	17.5764	0.708174
$617$	5.19870	0.209292	0.104646	−	0.994510i	$-0.466629\pi$
$617$	5.19870	0.209292	0.104646	+	0.994510i	$0.466629\pi$
$618$	−29.2741	−1.17758
$619$	34.0375	1.36808	0.684041	−	0.729444i	$-0.260221\pi$
$619$	34.0375	1.36808	0.684041	+	0.729444i	$0.260221\pi$
$620$	2.88456	0.115847
$621$	−55.0499	−2.20908
$622$	27.4245	1.09962
$623$	10.7560	0.430929
$624$	39.7623	1.59177
$625$	1.00000	0.0400000
$626$	−8.10598	−0.323980
$627$	57.4470	2.29421
$628$	−2.98249	−0.119014
$629$	−0.299209	−0.0119302
$630$	8.40153	0.334725
$631$	34.7015	1.38144	0.690722	−	0.723120i	$-0.257293\pi$
$631$	34.7015	1.38144	0.690722	+	0.723120i	$0.257293\pi$
$632$	−22.8748	−0.909911
$633$	−54.0667	−2.14896
$634$	31.8202	1.26374
$635$	12.2987	0.488058
$636$	8.85920	0.351290
$637$	23.0075	0.911592
$638$	−13.8671	−0.549004
$639$	55.6288	2.20064
$640$	8.38292	0.331364
$641$	−24.2449	−0.957615	−0.478807	−	0.877920i	$-0.658931\pi$
$641$	−24.2449	−0.957615	−0.478807	+	0.877920i	$0.658931\pi$
$642$	−32.8837	−1.29782
$643$	−25.2367	−0.995239	−0.497620	−	0.867395i	$-0.665792\pi$
$643$	−25.2367	−0.995239	−0.497620	+	0.867395i	$0.665792\pi$
$644$	2.14811	0.0846473
$645$	−11.2351	−0.442383
$646$	0.500875	0.0197067
$647$	−27.7290	−1.09014	−0.545070	−	0.838390i	$-0.683497\pi$
$647$	−27.7290	−1.09014	−0.545070	+	0.838390i	$0.683497\pi$
$648$	19.5584	0.768327
$649$	−47.5931	−1.86819
$650$	5.25279	0.206031
$651$	34.1291	1.33762
$652$	2.46371	0.0964865
$653$	−9.29853	−0.363880	−0.181940	−	0.983310i	$-0.558238\pi$
$653$	−9.29853	−0.363880	−0.181940	+	0.983310i	$0.558238\pi$
$654$	−7.30416	−0.285615
$655$	−16.1915	−0.632655
$656$	−39.9310	−1.55904
$657$	−40.8118	−1.59222
$658$	−0.623620	−0.0243112
$659$	30.2329	1.17771	0.588854	−	0.808240i	$-0.299579\pi$
$659$	30.2329	1.17771	0.588854	+	0.808240i	$0.299579\pi$
$660$	4.33142	0.168600
$661$	12.3739	0.481289	0.240644	−	0.970613i	$-0.422641\pi$
$661$	12.3739	0.481289	0.240644	+	0.970613i	$0.422641\pi$
$662$	−39.7179	−1.54368
$663$	1.21784	0.0472969
$664$	−24.7654	−0.961083
$665$	−4.15327	−0.161057
$666$	−21.7884	−0.844282
$667$	−13.8198	−0.535106
$668$	4.37644	0.169330
$669$	33.6244	1.29999
$670$	19.5425	0.754992
$671$	−56.1501	−2.16765
$672$	−5.19014	−0.200214
$673$	38.5219	1.48491	0.742454	−	0.669897i	$-0.233662\pi$
$673$	38.5219	1.48491	0.742454	+	0.669897i	$0.233662\pi$
$674$	4.43562	0.170854
$675$	8.02515	0.308888
$676$	−0.849133	−0.0326589
$677$	27.0845	1.04094	0.520472	−	0.853879i	$-0.325756\pi$
$677$	27.0845	1.04094	0.520472	+	0.853879i	$0.325756\pi$
$678$	−1.37028	−0.0526253
$679$	5.98754	0.229781
$680$	0.307952	0.0118094
$681$	−1.30618	−0.0500529
$682$	−71.0245	−2.71967
$683$	−50.5323	−1.93357	−0.966783	−	0.255598i	$-0.917728\pi$
$683$	−50.5323	−1.93357	−0.966783	+	0.255598i	$0.917728\pi$
$684$	−5.92644	−0.226603
$685$	0.366552	0.0140052
$686$	18.7267	0.714989
$687$	9.35283	0.356833
$688$	−12.7958	−0.487834
$689$	42.9831	1.63753
$690$	−26.5664	−1.01137
$691$	25.5088	0.970401	0.485200	−	0.874403i	$-0.338747\pi$
$691$	25.5088	0.970401	0.485200	+	0.874403i	$0.338747\pi$
$692$	−6.42980	−0.244424
$693$	33.6126	1.27684
$694$	28.4915	1.08152
$695$	4.28446	0.162519
$696$	17.7860	0.674175
$697$	−1.22300	−0.0463245
$698$	−21.9697	−0.831566
$699$	−24.4107	−0.923297
$700$	−0.313150	−0.0118360
$701$	4.59081	0.173392	0.0866962	−	0.996235i	$-0.472369\pi$
$701$	4.59081	0.173392	0.0866962	+	0.996235i	$0.472369\pi$
$702$	42.1544	1.59101
$703$	10.7710	0.406236
$704$	46.0941	1.73724
$705$	−1.25317	−0.0471973
$706$	9.39929	0.353747
$707$	6.89130	0.259174
$708$	7.48590	0.281337
$709$	−33.9739	−1.27592	−0.637958	−	0.770071i	$-0.720221\pi$
$709$	−33.9739	−1.27592	−0.637958	+	0.770071i	$0.720221\pi$
$710$	12.7608	0.478905
$711$	−43.7451	−1.64057
$712$	28.7094	1.07593
$713$	−70.7824	−2.65082
$714$	0.446825	0.0167220
$715$	21.0152	0.785924
$716$	−3.18934	−0.119191
$717$	49.1222	1.83450
$718$	39.3333	1.46790
$719$	−3.87065	−0.144351	−0.0721754	−	0.997392i	$-0.522994\pi$
$719$	−3.87065	−0.144351	−0.0721754	+	0.997392i	$0.522994\pi$
$720$	19.2281	0.716591
$721$	8.46740	0.315343
$722$	6.89090	0.256453
$723$	−53.3961	−1.98582
$724$	4.98834	0.185390
$725$	2.01465	0.0748222
$726$	−64.0483	−2.37706
$727$	3.67911	0.136451	0.0682254	−	0.997670i	$-0.478266\pi$
$727$	3.67911	0.136451	0.0682254	+	0.997670i	$0.478266\pi$
$728$	−13.4132	−0.497128
$729$	−33.6827	−1.24751
$730$	−9.36191	−0.346500
$731$	−0.391908	−0.0144952
$732$	8.83183	0.326434
$733$	33.8609	1.25068	0.625340	−	0.780352i	$-0.284960\pi$
$733$	33.8609	1.25068	0.625340	+	0.780352i	$0.284960\pi$
$734$	17.3360	0.639883
$735$	16.9633	0.625699
$736$	10.7642	0.396772
$737$	78.1850	2.87998
$738$	−89.0590	−3.27831
$739$	−33.8315	−1.24451	−0.622256	−	0.782814i	$-0.713784\pi$
$739$	−33.8315	−1.24451	−0.622256	+	0.782814i	$0.713784\pi$
$740$	0.812117	0.0298540
$741$	−43.8401	−1.61051
$742$	15.7705	0.578954
$743$	28.1847	1.03400	0.516998	−	0.855986i	$-0.327049\pi$
$743$	28.1847	1.03400	0.516998	+	0.855986i	$0.327049\pi$
$744$	91.0961	3.33974
$745$	−20.2936	−0.743502
$746$	−16.3351	−0.598072
$747$	−47.3606	−1.73283
$748$	0.151090	0.00552439
$749$	9.51145	0.347541
$750$	3.87283	0.141416
$751$	−31.7761	−1.15953	−0.579764	−	0.814784i	$-0.696855\pi$
$751$	−31.7761	−1.15953	−0.579764	+	0.814784i	$0.696855\pi$
$752$	−1.42725	−0.0520463
$753$	−11.3932	−0.415190
$754$	10.5825	0.385393
$755$	1.34097	0.0488028
$756$	−2.51307	−0.0913996
$757$	20.2483	0.735937	0.367968	−	0.929838i	$-0.380053\pi$
$757$	20.2483	0.735937	0.367968	+	0.929838i	$0.380053\pi$
$758$	40.5512	1.47288
$759$	−106.286	−3.85794
$760$	−11.0857	−0.402122
$761$	29.8354	1.08153	0.540766	−	0.841173i	$-0.318135\pi$
$761$	29.8354	1.08153	0.540766	+	0.841173i	$0.318135\pi$
$762$	47.6307	1.72548
$763$	2.11269	0.0764847
$764$	−3.37246	−0.122011
$765$	0.588918	0.0212924
$766$	29.0052	1.04800
$767$	36.3202	1.31145
$768$	−19.4046	−0.700202
$769$	−51.3272	−1.85091	−0.925453	−	0.378861i	$-0.876316\pi$
$769$	−51.3272	−1.85091	−0.925453	+	0.378861i	$0.876316\pi$
$770$	7.71048	0.277866
$771$	62.4623	2.24952
$772$	−0.436651	−0.0157154
$773$	−8.19135	−0.294622	−0.147311	−	0.989090i	$-0.547062\pi$
$773$	−8.19135	−0.294622	−0.147311	+	0.989090i	$0.547062\pi$
$774$	−28.5387	−1.02580
$775$	10.3186	0.370656
$776$	15.9817	0.573710
$777$	9.60869	0.344710
$778$	−7.10493	−0.254724
$779$	44.0260	1.57740
$780$	−3.30547	−0.118355
$781$	51.0532	1.82683
$782$	−0.926697	−0.0331386
$783$	16.1678	0.577792
$784$	19.3196	0.689984
$785$	−10.6689	−0.380791
$786$	−62.7071	−2.23669
$787$	11.1704	0.398180	0.199090	−	0.979981i	$-0.436201\pi$
$787$	11.1704	0.398180	0.199090	+	0.979981i	$0.436201\pi$
$788$	−4.95857	−0.176642
$789$	−47.4025	−1.68757
$790$	−10.0348	−0.357022
$791$	0.396347	0.0140925
$792$	89.7175	3.18797
$793$	42.8503	1.52166
$794$	36.2807	1.28755
$795$	31.6911	1.12397
$796$	4.20691	0.149110
$797$	22.2139	0.786857	0.393429	−	0.919355i	$-0.371289\pi$
$797$	22.2139	0.786857	0.393429	+	0.919355i	$0.371289\pi$
$798$	−16.0849	−0.569400
$799$	−0.0437136	−0.00154648
$800$	−1.56919	−0.0554793
$801$	54.9031	1.93991
$802$	−1.31166	−0.0463163
$803$	−37.4549	−1.32175
$804$	−12.2977	−0.433706
$805$	7.68420	0.270832
$806$	54.2015	1.90917
$807$	−56.2445	−1.97990
$808$	18.3940	0.647098
$809$	−38.5322	−1.35472	−0.677360	−	0.735652i	$-0.736876\pi$
$809$	−38.5322	−1.35472	−0.677360	+	0.735652i	$0.736876\pi$
$810$	8.57996	0.301469
$811$	18.6415	0.654590	0.327295	−	0.944922i	$-0.393863\pi$
$811$	18.6415	0.654590	0.327295	+	0.944922i	$0.393863\pi$
$812$	−0.630887	−0.0221398
$813$	22.2791	0.781363
$814$	−19.9962	−0.700866
$815$	8.81319	0.308713
$816$	1.02262	0.0357990
$817$	14.1080	0.493577
$818$	−19.5675	−0.684161
$819$	−25.6511	−0.896322
$820$	3.31949	0.115922
$821$	12.6137	0.440220	0.220110	−	0.975475i	$-0.429358\pi$
$821$	12.6137	0.440220	0.220110	+	0.975475i	$0.429358\pi$
$822$	1.41959	0.0495140
$823$	−8.66816	−0.302153	−0.151077	−	0.988522i	$-0.548274\pi$
$823$	−8.66816	−0.302153	−0.151077	+	0.988522i	$0.548274\pi$
$824$	22.6009	0.787338
$825$	15.4943	0.539443
$826$	13.3259	0.463666
$827$	−4.85609	−0.168863	−0.0844314	−	0.996429i	$-0.526907\pi$
$827$	−4.85609	−0.168863	−0.0844314	+	0.996429i	$0.526907\pi$
$828$	10.9649	0.381055
$829$	−5.89432	−0.204718	−0.102359	−	0.994748i	$-0.532639\pi$
$829$	−5.89432	−0.204718	−0.102359	+	0.994748i	$0.532639\pi$
$830$	−10.8642	−0.377101
$831$	−74.7754	−2.59393
$832$	−35.1762	−1.21952
$833$	0.591718	0.0205018
$834$	16.5930	0.574569
$835$	15.6554	0.541778
$836$	−5.43897	−0.188111
$837$	82.8085	2.86228
$838$	10.4067	0.359495
$839$	−3.99703	−0.137993	−0.0689965	−	0.997617i	$-0.521980\pi$
$839$	−3.99703	−0.137993	−0.0689965	+	0.997617i	$0.521980\pi$
$840$	−9.88947	−0.341219
$841$	−24.9412	−0.860041
$842$	46.5915	1.60565
$843$	40.1118	1.38152
$844$	5.11893	0.176201
$845$	−3.03751	−0.104494
$846$	−3.18322	−0.109441
$847$	18.5257	0.636550
$848$	36.0932	1.23944
$849$	−2.47676	−0.0850023
$850$	0.135093	0.00463367
$851$	−19.9280	−0.683125
$852$	−8.03013	−0.275108
$853$	−19.1938	−0.657183	−0.328591	−	0.944472i	$-0.606574\pi$
$853$	−19.1938	−0.657183	−0.328591	+	0.944472i	$0.606574\pi$
$854$	15.7218	0.537989
$855$	−21.2001	−0.725027
$856$	25.3876	0.867730
$857$	−31.1318	−1.06344	−0.531721	−	0.846919i	$-0.678455\pi$
$857$	−31.1318	−1.06344	−0.531721	+	0.846919i	$0.678455\pi$
$858$	81.3884	2.77855
$859$	−38.7622	−1.32255	−0.661275	−	0.750143i	$-0.729984\pi$
$859$	−38.7622	−1.32255	−0.661275	+	0.750143i	$0.729984\pi$
$860$	1.06372	0.0362726
$861$	39.2751	1.33849
$862$	7.13945	0.243171
$863$	46.4700	1.58186	0.790929	−	0.611908i	$-0.209598\pi$
$863$	46.4700	1.58186	0.790929	+	0.611908i	$0.209598\pi$
$864$	−12.5930	−0.428423
$865$	−23.0007	−0.782046
$866$	49.7383	1.69018
$867$	−50.1632	−1.70363
$868$	−3.23128	−0.109677
$869$	−40.1470	−1.36189
$870$	7.80240	0.264526
$871$	−59.6660	−2.02171
$872$	5.63912	0.190965
$873$	30.5629	1.03440
$874$	33.3595	1.12840
$875$	−1.12020	−0.0378696
$876$	5.89126	0.199047
$877$	22.1272	0.747181	0.373590	−	0.927594i	$-0.378127\pi$
$877$	22.1272	0.747181	0.373590	+	0.927594i	$0.378127\pi$
$878$	4.30726	0.145363
$879$	52.8897	1.78393
$880$	17.6466	0.594866
$881$	12.9222	0.435362	0.217681	−	0.976020i	$-0.430151\pi$
$881$	12.9222	0.435362	0.217681	+	0.976020i	$0.430151\pi$
$882$	43.0889	1.45088
$883$	−25.7684	−0.867176	−0.433588	−	0.901111i	$-0.642753\pi$
$883$	−25.7684	−0.867176	−0.433588	+	0.901111i	$0.642753\pi$
$884$	−0.115302	−0.00387804
$885$	26.7785	0.900151
$886$	−32.8792	−1.10460
$887$	44.1896	1.48374	0.741871	−	0.670543i	$-0.233939\pi$
$887$	44.1896	1.48374	0.741871	+	0.670543i	$0.233939\pi$
$888$	25.6471	0.860662
$889$	−13.7770	−0.462064
$890$	12.5944	0.422164
$891$	34.3264	1.14998
$892$	−3.18349	−0.106591
$893$	1.57361	0.0526590
$894$	−78.5940	−2.62857
$895$	−11.4089	−0.381358
$896$	−9.39054	−0.313716
$897$	81.1110	2.70822
$898$	14.9604	0.499236
$899$	20.7884	0.693332
$900$	−1.59845	−0.0532817
$901$	1.10546	0.0368282
$902$	−81.7336	−2.72143
$903$	12.5856	0.418823
$904$	1.05791	0.0351857
$905$	17.8443	0.593164
$906$	5.19335	0.172537
$907$	27.8458	0.924606	0.462303	−	0.886722i	$-0.347023\pi$
$907$	27.8458	0.924606	0.462303	+	0.886722i	$0.347023\pi$
$908$	0.123666	0.00410401
$909$	35.1761	1.16672
$910$	−5.88417	−0.195058
$911$	−42.2415	−1.39952	−0.699761	−	0.714377i	$-0.746710\pi$
$911$	−42.2415	−1.39952	−0.699761	+	0.714377i	$0.746710\pi$
$912$	−36.8127	−1.21899
$913$	−43.4650	−1.43848
$914$	−10.9286	−0.361485
$915$	31.5932	1.04444
$916$	−0.885508	−0.0292580
$917$	18.1377	0.598961
$918$	1.08414	0.0357821
$919$	−12.8142	−0.422703	−0.211351	−	0.977410i	$-0.567786\pi$
$919$	−12.8142	−0.422703	−0.211351	+	0.977410i	$0.567786\pi$
$920$	20.5104	0.676207
$921$	−90.0393	−2.96690
$922$	26.2343	0.863980
$923$	−38.9606	−1.28241
$924$	−4.85205	−0.159621
$925$	2.90510	0.0955191
$926$	−46.2002	−1.51823
$927$	43.2212	1.41957
$928$	−3.16137	−0.103777
$929$	−7.00382	−0.229788	−0.114894	−	0.993378i	$-0.536653\pi$
$929$	−7.00382	−0.229788	−0.114894	+	0.993378i	$0.536653\pi$
$930$	39.9623	1.31042
$931$	−21.3008	−0.698107
$932$	2.31116	0.0757045
$933$	−61.7340	−2.02108
$934$	2.48962	0.0814628
$935$	0.540478	0.0176755
$936$	−68.4669	−2.23791
$937$	−18.2939	−0.597636	−0.298818	−	0.954310i	$-0.596592\pi$
$937$	−18.2939	−0.597636	−0.298818	+	0.954310i	$0.596592\pi$
$938$	−21.8915	−0.714782
$939$	18.2470	0.595469
$940$	0.118648	0.00386987
$941$	−13.0533	−0.425525	−0.212762	−	0.977104i	$-0.568246\pi$
$941$	−13.0533	−0.425525	−0.212762	+	0.977104i	$0.568246\pi$
$942$	−41.3191	−1.34625
$943$	−81.4550	−2.65254
$944$	30.4982	0.992633
$945$	−8.98976	−0.292437
$946$	−26.1913	−0.851553
$947$	−30.7936	−1.00066	−0.500329	−	0.865835i	$-0.666788\pi$
$947$	−30.7936	−1.00066	−0.500329	+	0.865835i	$0.666788\pi$
$948$	6.31470	0.205092
$949$	28.5833	0.927852
$950$	−4.86313	−0.157781
$951$	−71.6291	−2.32273
$952$	−0.344968	−0.0111805
$953$	−21.7833	−0.705629	−0.352815	−	0.935693i	$-0.614775\pi$
$953$	−21.7833	−0.705629	−0.352815	+	0.935693i	$0.614775\pi$
$954$	80.4995	2.60627
$955$	−12.0639	−0.390380
$956$	−4.65080	−0.150418
$957$	31.2156	1.00906
$958$	9.74652	0.314896
$959$	−0.410611	−0.0132593
$960$	−25.9351	−0.837052
$961$	75.4740	2.43465
$962$	15.2599	0.491998
$963$	48.5505	1.56452
$964$	5.05544	0.162825
$965$	−1.56199	−0.0502822
$966$	29.7596	0.957501
$967$	−12.7163	−0.408927	−0.204464	−	0.978874i	$-0.565545\pi$
$967$	−12.7163	−0.408927	−0.204464	+	0.978874i	$0.565545\pi$
$968$	49.4480	1.58932
$969$	−1.12750	−0.0362204
$970$	7.01091	0.225107
$971$	−20.2344	−0.649353	−0.324676	−	0.945825i	$-0.605255\pi$
$971$	−20.2344	−0.649353	−0.324676	+	0.945825i	$0.605255\pi$
$972$	1.33106	0.0426938
$973$	−4.79945	−0.153863
$974$	33.5337	1.07449
$975$	−11.8243	−0.378681
$976$	35.9816	1.15174
$977$	−25.4266	−0.813469	−0.406734	−	0.913546i	$-0.633333\pi$
$977$	−25.4266	−0.813469	−0.406734	+	0.913546i	$0.633333\pi$
$978$	34.1320	1.09142
$979$	50.3871	1.61038
$980$	−1.60605	−0.0513034
$981$	10.7841	0.344310
$982$	46.1834	1.47377
$983$	−10.2794	−0.327862	−0.163931	−	0.986472i	$-0.552417\pi$
$983$	−10.2794	−0.327862	−0.163931	+	0.986472i	$0.552417\pi$
$984$	104.832	3.34191
$985$	−17.7378	−0.565173
$986$	0.272166	0.00866752
$987$	1.40380	0.0446836
$988$	4.15069	0.132051
$989$	−26.1020	−0.829997
$990$	39.3576	1.25087
$991$	−19.3592	−0.614966	−0.307483	−	0.951554i	$-0.599487\pi$
$991$	−19.3592	−0.614966	−0.307483	+	0.951554i	$0.599487\pi$
$992$	−16.1919	−0.514094
$993$	89.4073	2.83725
$994$	−14.2947	−0.453399
$995$	15.0489	0.477084
$996$	6.83660	0.216626
$997$	−26.8624	−0.850741	−0.425371	−	0.905019i	$-0.639856\pi$
$997$	−26.8624	−0.850741	−0.425371	+	0.905019i	$0.639856\pi$
$998$	22.2454	0.704165
$999$	23.3139	0.737618

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2005.2.a.f.1.10	✓	37

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2005.2.a.f.1.10	✓	37	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:	\( N \)	\(=\)	\( 2005 = 5 \cdot 401 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2005.a (trivial)

\(f(q)\)	\(=\)	\(q-1.31166 q^{2} +2.95262 q^{3} -0.279548 q^{4} -1.00000 q^{5} -3.87283 q^{6} +1.12020 q^{7} +2.98999 q^{8} +5.71797 q^{9} +O(q^{10})\)	\(q-1.31166 q^{2} +2.95262 q^{3} -0.279548 q^{4} -1.00000 q^{5} -3.87283 q^{6} +1.12020 q^{7} +2.98999 q^{8} +5.71797 q^{9} +1.31166 q^{10} +5.24765 q^{11} -0.825401 q^{12} -4.00469 q^{13} -1.46932 q^{14} -2.95262 q^{15} -3.36276 q^{16} -0.102994 q^{17} -7.50004 q^{18} +3.70762 q^{19} +0.279548 q^{20} +3.30752 q^{21} -6.88313 q^{22} -6.85967 q^{23} +8.82831 q^{24} +1.00000 q^{25} +5.25279 q^{26} +8.02515 q^{27} -0.313150 q^{28} +2.01465 q^{29} +3.87283 q^{30} +10.3186 q^{31} -1.56919 q^{32} +15.4943 q^{33} +0.135093 q^{34} -1.12020 q^{35} -1.59845 q^{36} +2.90510 q^{37} -4.86313 q^{38} -11.8243 q^{39} -2.98999 q^{40} +11.8745 q^{41} -4.33835 q^{42} +3.80514 q^{43} -1.46697 q^{44} -5.71797 q^{45} +8.99756 q^{46} +0.424427 q^{47} -9.92894 q^{48} -5.74515 q^{49} -1.31166 q^{50} -0.304103 q^{51} +1.11950 q^{52} -10.7332 q^{53} -10.5263 q^{54} -5.24765 q^{55} +3.34939 q^{56} +10.9472 q^{57} -2.64253 q^{58} -9.06941 q^{59} +0.825401 q^{60} -10.7000 q^{61} -13.5345 q^{62} +6.40527 q^{63} +8.78376 q^{64} +4.00469 q^{65} -20.3233 q^{66} +14.8990 q^{67} +0.0287919 q^{68} -20.2540 q^{69} +1.46932 q^{70} +9.72876 q^{71} +17.0967 q^{72} -7.13745 q^{73} -3.81050 q^{74} +2.95262 q^{75} -1.03646 q^{76} +5.87841 q^{77} +15.5095 q^{78} -7.65046 q^{79} +3.36276 q^{80} +6.54130 q^{81} -15.5753 q^{82} -8.28276 q^{83} -0.924613 q^{84} +0.102994 q^{85} -4.99105 q^{86} +5.94849 q^{87} +15.6904 q^{88} +9.60184 q^{89} +7.50004 q^{90} -4.48605 q^{91} +1.91761 q^{92} +30.4670 q^{93} -0.556705 q^{94} -3.70762 q^{95} -4.63323 q^{96} +5.34506 q^{97} +7.53569 q^{98} +30.0059 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 37 q + 7 q^{2} + 3 q^{3} + 43 q^{4} - 37 q^{5} + 8 q^{6} - 16 q^{7} + 21 q^{8} + 54 q^{9}+O(q^{10}) \) 37 * q + 7 * q^2 + 3 * q^3 + 43 * q^4 - 37 * q^5 + 8 * q^6 - 16 * q^7 + 21 * q^8 + 54 * q^9	\( 37 q + 7 q^{2} + 3 q^{3} + 43 q^{4} - 37 q^{5} + 8 q^{6} - 16 q^{7} + 21 q^{8} + 54 q^{9} - 7 q^{10} + 42 q^{11} - 13 q^{13} + 14 q^{14} - 3 q^{15} + 63 q^{16} + 18 q^{17} + 22 q^{18} + 22 q^{19} - 43 q^{20} + 16 q^{21} - 10 q^{22} + 23 q^{23} + 23 q^{24} + 37 q^{25} + 21 q^{26} + 3 q^{27} - 18 q^{28} + 33 q^{29} - 8 q^{30} + 11 q^{31} + 54 q^{32} + 2 q^{33} + 8 q^{34} + 16 q^{35} + 91 q^{36} - 11 q^{37} + 29 q^{38} + 25 q^{39} - 21 q^{40} + 24 q^{41} + 4 q^{42} + 25 q^{43} + 84 q^{44} - 54 q^{45} + 31 q^{46} + 7 q^{47} + 4 q^{48} + 45 q^{49} + 7 q^{50} + 94 q^{51} - 43 q^{52} + 49 q^{53} + 38 q^{54} - 42 q^{55} + 46 q^{56} + 6 q^{57} + 15 q^{58} + 69 q^{59} + 9 q^{61} + 17 q^{62} - 38 q^{63} + 107 q^{64} + 13 q^{65} + 74 q^{66} + 13 q^{67} + 86 q^{68} - 14 q^{70} + 51 q^{71} + 81 q^{72} - 47 q^{73} + 79 q^{74} + 3 q^{75} + 59 q^{76} + 2 q^{77} + 20 q^{78} + 67 q^{79} - 63 q^{80} + 125 q^{81} - 24 q^{82} + 80 q^{83} + 50 q^{84} - 18 q^{85} + 69 q^{86} - 32 q^{87} - 12 q^{88} + 34 q^{89} - 22 q^{90} + 39 q^{91} + 85 q^{92} + q^{93} + 12 q^{94} - 22 q^{95} + 77 q^{96} - 14 q^{97} + 40 q^{98} + 133 q^{99}+O(q^{100}) \) 37 * q + 7 * q^2 + 3 * q^3 + 43 * q^4 - 37 * q^5 + 8 * q^6 - 16 * q^7 + 21 * q^8 + 54 * q^9 - 7 * q^10 + 42 * q^11 - 13 * q^13 + 14 * q^14 - 3 * q^15 + 63 * q^16 + 18 * q^17 + 22 * q^18 + 22 * q^19 - 43 * q^20 + 16 * q^21 - 10 * q^22 + 23 * q^23 + 23 * q^24 + 37 * q^25 + 21 * q^26 + 3 * q^27 - 18 * q^28 + 33 * q^29 - 8 * q^30 + 11 * q^31 + 54 * q^32 + 2 * q^33 + 8 * q^34 + 16 * q^35 + 91 * q^36 - 11 * q^37 + 29 * q^38 + 25 * q^39 - 21 * q^40 + 24 * q^41 + 4 * q^42 + 25 * q^43 + 84 * q^44 - 54 * q^45 + 31 * q^46 + 7 * q^47 + 4 * q^48 + 45 * q^49 + 7 * q^50 + 94 * q^51 - 43 * q^52 + 49 * q^53 + 38 * q^54 - 42 * q^55 + 46 * q^56 + 6 * q^57 + 15 * q^58 + 69 * q^59 + 9 * q^61 + 17 * q^62 - 38 * q^63 + 107 * q^64 + 13 * q^65 + 74 * q^66 + 13 * q^67 + 86 * q^68 - 14 * q^70 + 51 * q^71 + 81 * q^72 - 47 * q^73 + 79 * q^74 + 3 * q^75 + 59 * q^76 + 2 * q^77 + 20 * q^78 + 67 * q^79 - 63 * q^80 + 125 * q^81 - 24 * q^82 + 80 * q^83 + 50 * q^84 - 18 * q^85 + 69 * q^86 - 32 * q^87 - 12 * q^88 + 34 * q^89 - 22 * q^90 + 39 * q^91 + 85 * q^92 + q^93 + 12 * q^94 - 22 * q^95 + 77 * q^96 - 14 * q^97 + 40 * q^98 + 133 * q^99

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