LMFDB - Embedded newform 2005.2.a.g.1.11

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			1.11
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)

$f(q)$	$=$	$q-0.868310 q^{2} +2.12555 q^{3} -1.24604 q^{4} +1.00000 q^{5} -1.84564 q^{6} +3.66007 q^{7} +2.81857 q^{8} +1.51797 q^{9} +O(q^{10})$	\(q-0.868310 q^{2} +2.12555 q^{3} -1.24604 q^{4} +1.00000 q^{5} -1.84564 q^{6} +3.66007 q^{7} +2.81857 q^{8} +1.51797 q^{9} -0.868310 q^{10} -2.35694 q^{11} -2.64852 q^{12} +5.42263 q^{13} -3.17808 q^{14} +2.12555 q^{15} +0.0446870 q^{16} +4.31709 q^{17} -1.31807 q^{18} +2.73494 q^{19} -1.24604 q^{20} +7.77967 q^{21} +2.04655 q^{22} -3.59692 q^{23} +5.99101 q^{24} +1.00000 q^{25} -4.70852 q^{26} -3.15013 q^{27} -4.56059 q^{28} +4.30604 q^{29} -1.84564 q^{30} -4.74045 q^{31} -5.67594 q^{32} -5.00980 q^{33} -3.74857 q^{34} +3.66007 q^{35} -1.89145 q^{36} -5.76833 q^{37} -2.37478 q^{38} +11.5261 q^{39} +2.81857 q^{40} +4.86146 q^{41} -6.75517 q^{42} -6.75798 q^{43} +2.93684 q^{44} +1.51797 q^{45} +3.12324 q^{46} +8.03782 q^{47} +0.0949845 q^{48} +6.39612 q^{49} -0.868310 q^{50} +9.17620 q^{51} -6.75680 q^{52} +0.533240 q^{53} +2.73529 q^{54} -2.35694 q^{55} +10.3162 q^{56} +5.81326 q^{57} -3.73898 q^{58} +8.47885 q^{59} -2.64852 q^{60} -10.8483 q^{61} +4.11618 q^{62} +5.55589 q^{63} +4.83910 q^{64} +5.42263 q^{65} +4.35006 q^{66} +5.43203 q^{67} -5.37926 q^{68} -7.64545 q^{69} -3.17808 q^{70} +8.20947 q^{71} +4.27851 q^{72} -13.1221 q^{73} +5.00870 q^{74} +2.12555 q^{75} -3.40784 q^{76} -8.62657 q^{77} -10.0082 q^{78} -1.12752 q^{79} +0.0446870 q^{80} -11.2497 q^{81} -4.22125 q^{82} +2.14855 q^{83} -9.69377 q^{84} +4.31709 q^{85} +5.86802 q^{86} +9.15271 q^{87} -6.64319 q^{88} +2.59008 q^{89} -1.31807 q^{90} +19.8472 q^{91} +4.48190 q^{92} -10.0761 q^{93} -6.97932 q^{94} +2.73494 q^{95} -12.0645 q^{96} -8.77543 q^{97} -5.55381 q^{98} -3.57777 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 37 q + 11 q^{2} + 13 q^{3} + 43 q^{4} + 37 q^{5} - 2 q^{6} + 34 q^{7} + 27 q^{8} + 50 q^{9}+O(q^{10}) $ 37 * q + 11 * q^2 + 13 * q^3 + 43 * q^4 + 37 * q^5 - 2 * q^6 + 34 * q^7 + 27 * q^8 + 50 * q^9	\( 37 q + 11 q^{2} + 13 q^{3} + 43 q^{4} + 37 q^{5} - 2 q^{6} + 34 q^{7} + 27 q^{8} + 50 q^{9} + 11 q^{10} + 38 q^{11} + 24 q^{12} + 17 q^{13} + 14 q^{14} + 13 q^{15} + 47 q^{16} + 22 q^{17} + 18 q^{18} + 6 q^{19} + 43 q^{20} + 4 q^{21} + 18 q^{22} + 45 q^{23} - 19 q^{24} + 37 q^{25} - q^{26} + 43 q^{27} + 46 q^{28} + 17 q^{29} - 2 q^{30} - 13 q^{31} + 50 q^{32} + 12 q^{33} - 30 q^{34} + 34 q^{35} + 43 q^{36} + 9 q^{37} + q^{38} - 7 q^{39} + 27 q^{40} + 12 q^{41} - 38 q^{42} + 53 q^{43} + 36 q^{44} + 50 q^{45} - 15 q^{46} + 39 q^{47} - 6 q^{48} + 37 q^{49} + 11 q^{50} + 38 q^{51} + 17 q^{52} + 19 q^{53} - 62 q^{54} + 38 q^{55} + 18 q^{56} + 6 q^{57} - 13 q^{58} + 33 q^{59} + 24 q^{60} - 11 q^{61} + q^{62} + 98 q^{63} + 15 q^{64} + 17 q^{65} - 70 q^{66} + 49 q^{67} + 32 q^{68} - 36 q^{69} + 14 q^{70} + 19 q^{71} + 5 q^{72} + 39 q^{73} + 21 q^{74} + 13 q^{75} - 33 q^{76} + 34 q^{77} - 22 q^{78} - 9 q^{79} + 47 q^{80} + 49 q^{81} + 14 q^{82} + 114 q^{83} - 50 q^{84} + 22 q^{85} + 9 q^{86} + 56 q^{87} + 14 q^{88} + 2 q^{89} + 18 q^{90} - 29 q^{91} + 47 q^{92} - 7 q^{93} - 52 q^{94} + 6 q^{95} - 89 q^{96} + 4 q^{97} + 14 q^{98} + 57 q^{99}+O(q^{100}) \) 37 * q + 11 * q^2 + 13 * q^3 + 43 * q^4 + 37 * q^5 - 2 * q^6 + 34 * q^7 + 27 * q^8 + 50 * q^9 + 11 * q^10 + 38 * q^11 + 24 * q^12 + 17 * q^13 + 14 * q^14 + 13 * q^15 + 47 * q^16 + 22 * q^17 + 18 * q^18 + 6 * q^19 + 43 * q^20 + 4 * q^21 + 18 * q^22 + 45 * q^23 - 19 * q^24 + 37 * q^25 - q^26 + 43 * q^27 + 46 * q^28 + 17 * q^29 - 2 * q^30 - 13 * q^31 + 50 * q^32 + 12 * q^33 - 30 * q^34 + 34 * q^35 + 43 * q^36 + 9 * q^37 + q^38 - 7 * q^39 + 27 * q^40 + 12 * q^41 - 38 * q^42 + 53 * q^43 + 36 * q^44 + 50 * q^45 - 15 * q^46 + 39 * q^47 - 6 * q^48 + 37 * q^49 + 11 * q^50 + 38 * q^51 + 17 * q^52 + 19 * q^53 - 62 * q^54 + 38 * q^55 + 18 * q^56 + 6 * q^57 - 13 * q^58 + 33 * q^59 + 24 * q^60 - 11 * q^61 + q^62 + 98 * q^63 + 15 * q^64 + 17 * q^65 - 70 * q^66 + 49 * q^67 + 32 * q^68 - 36 * q^69 + 14 * q^70 + 19 * q^71 + 5 * q^72 + 39 * q^73 + 21 * q^74 + 13 * q^75 - 33 * q^76 + 34 * q^77 - 22 * q^78 - 9 * q^79 + 47 * q^80 + 49 * q^81 + 14 * q^82 + 114 * q^83 - 50 * q^84 + 22 * q^85 + 9 * q^86 + 56 * q^87 + 14 * q^88 + 2 * q^89 + 18 * q^90 - 29 * q^91 + 47 * q^92 - 7 * q^93 - 52 * q^94 + 6 * q^95 - 89 * q^96 + 4 * q^97 + 14 * q^98 + 57 * 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 $

$2$	−0.868310	−0.613988	−0.306994	−	0.951711i	$-0.599323\pi$
$2$	−0.868310	−0.613988	−0.306994	+	0.951711i	$0.599323\pi$
$3$	2.12555	1.22719	0.613594	−	0.789622i	$-0.289723\pi$
$3$	2.12555	1.22719	0.613594	+	0.789622i	$0.289723\pi$
$4$	−1.24604	−0.623019
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	−1.84564	−0.753479
$7$	3.66007	1.38338	0.691688	−	0.722196i	$-0.256867\pi$
$7$	3.66007	1.38338	0.691688	+	0.722196i	$0.256867\pi$
$8$	2.81857	0.996514
$9$	1.51797	0.505991
$10$	−0.868310	−0.274584
$11$	−2.35694	−0.710644	−0.355322	−	0.934744i	$-0.615629\pi$
$11$	−2.35694	−0.710644	−0.355322	+	0.934744i	$0.615629\pi$
$12$	−2.64852	−0.764562
$13$	5.42263	1.50397	0.751984	−	0.659182i	$-0.229097\pi$
$13$	5.42263	1.50397	0.751984	+	0.659182i	$0.229097\pi$
$14$	−3.17808	−0.849376
$15$	2.12555	0.548815
$16$	0.0446870	0.0111717
$17$	4.31709	1.04705	0.523524	−	0.852011i	$-0.324617\pi$
$17$	4.31709	1.04705	0.523524	+	0.852011i	$0.324617\pi$
$18$	−1.31807	−0.310672
$19$	2.73494	0.627438	0.313719	−	0.949516i	$-0.398425\pi$
$19$	2.73494	0.627438	0.313719	+	0.949516i	$0.398425\pi$
$20$	−1.24604	−0.278623
$21$	7.77967	1.69766
$22$	2.04655	0.436327
$23$	−3.59692	−0.750010	−0.375005	−	0.927023i	$-0.622359\pi$
$23$	−3.59692	−0.750010	−0.375005	+	0.927023i	$0.622359\pi$
$24$	5.99101	1.22291
$25$	1.00000	0.200000
$26$	−4.70852	−0.923417
$27$	−3.15013	−0.606242
$28$	−4.56059	−0.861870
$29$	4.30604	0.799611	0.399806	−	0.916600i	$-0.369078\pi$
$29$	4.30604	0.799611	0.399806	+	0.916600i	$0.369078\pi$
$30$	−1.84564	−0.336966
$31$	−4.74045	−0.851409	−0.425705	−	0.904862i	$-0.639974\pi$
$31$	−4.74045	−0.851409	−0.425705	+	0.904862i	$0.639974\pi$
$32$	−5.67594	−1.00337
$33$	−5.00980	−0.872094
$34$	−3.74857	−0.642874
$35$	3.66007	0.618665
$36$	−1.89145	−0.315242
$37$	−5.76833	−0.948308	−0.474154	−	0.880442i	$-0.657246\pi$
$37$	−5.76833	−0.948308	−0.474154	+	0.880442i	$0.657246\pi$
$38$	−2.37478	−0.385239
$39$	11.5261	1.84565
$40$	2.81857	0.445655
$41$	4.86146	0.759233	0.379616	−	0.925144i	$-0.376056\pi$
$41$	4.86146	0.759233	0.379616	+	0.925144i	$0.376056\pi$
$42$	−6.75517	−1.04234
$43$	−6.75798	−1.03058	−0.515291	−	0.857015i	$-0.672316\pi$
$43$	−6.75798	−1.03058	−0.515291	+	0.857015i	$0.672316\pi$
$44$	2.93684	0.442745
$45$	1.51797	0.226286
$46$	3.12324	0.460497
$47$	8.03782	1.17244	0.586218	−	0.810153i	$-0.300616\pi$
$47$	8.03782	1.17244	0.586218	+	0.810153i	$0.300616\pi$
$48$	0.0949845	0.0137098
$49$	6.39612	0.913731
$50$	−0.868310	−0.122798
$51$	9.17620	1.28492
$52$	−6.75680	−0.937000
$53$	0.533240	0.0732461	0.0366231	−	0.999329i	$-0.488340\pi$
$53$	0.533240	0.0732461	0.0366231	+	0.999329i	$0.488340\pi$
$54$	2.73529	0.372225
$55$	−2.35694	−0.317810
$56$	10.3162	1.37855
$57$	5.81326	0.769985
$58$	−3.73898	−0.490952
$59$	8.47885	1.10385	0.551926	−	0.833893i	$-0.313893\pi$
$59$	8.47885	1.10385	0.551926	+	0.833893i	$0.313893\pi$
$60$	−2.64852	−0.341922
$61$	−10.8483	−1.38898	−0.694490	−	0.719503i	$-0.744370\pi$
$61$	−10.8483	−1.38898	−0.694490	+	0.719503i	$0.744370\pi$
$62$	4.11618	0.522755
$63$	5.55589	0.699976
$64$	4.83910	0.604887
$65$	5.42263	0.672595
$66$	4.35006	0.535455
$67$	5.43203	0.663628	0.331814	−	0.943345i	$-0.392339\pi$
$67$	5.43203	0.663628	0.331814	+	0.943345i	$0.392339\pi$
$68$	−5.37926	−0.652331
$69$	−7.64545	−0.920404
$70$	−3.17808	−0.379853
$71$	8.20947	0.974285	0.487142	−	0.873323i	$-0.338039\pi$
$71$	8.20947	0.974285	0.487142	+	0.873323i	$0.338039\pi$
$72$	4.27851	0.504227
$73$	−13.1221	−1.53582	−0.767910	−	0.640558i	$-0.778703\pi$
$73$	−13.1221	−1.53582	−0.767910	+	0.640558i	$0.778703\pi$
$74$	5.00870	0.582250
$75$	2.12555	0.245438
$76$	−3.40784	−0.390906
$77$	−8.62657	−0.983089
$78$	−10.0082	−1.13321
$79$	−1.12752	−0.126856	−0.0634280	−	0.997986i	$-0.520203\pi$
$79$	−1.12752	−0.126856	−0.0634280	+	0.997986i	$0.520203\pi$
$80$	0.0446870	0.00499615
$81$	−11.2497	−1.24996
$82$	−4.22125	−0.466160
$83$	2.14855	0.235834	0.117917	−	0.993023i	$-0.462378\pi$
$83$	2.14855	0.235834	0.117917	+	0.993023i	$0.462378\pi$
$84$	−9.69377	−1.05768
$85$	4.31709	0.468254
$86$	5.86802	0.632765
$87$	9.15271	0.981274
$88$	−6.64319	−0.708167
$89$	2.59008	0.274548	0.137274	−	0.990533i	$-0.456166\pi$
$89$	2.59008	0.274548	0.137274	+	0.990533i	$0.456166\pi$
$90$	−1.31807	−0.138937
$91$	19.8472	2.08055
$92$	4.48190	0.467271
$93$	−10.0761	−1.04484
$94$	−6.97932	−0.719862
$95$	2.73494	0.280599
$96$	−12.0645	−1.23133
$97$	−8.77543	−0.891010	−0.445505	−	0.895279i	$-0.646976\pi$
$97$	−8.77543	−0.891010	−0.445505	+	0.895279i	$0.646976\pi$
$98$	−5.55381	−0.561020
$99$	−3.57777	−0.359580
$100$	−1.24604	−0.124604
$101$	−6.80451	−0.677074	−0.338537	−	0.940953i	$-0.609932\pi$
$101$	−6.80451	−0.677074	−0.338537	+	0.940953i	$0.609932\pi$
$102$	−7.96778	−0.788928
$103$	10.7966	1.06382	0.531909	−	0.846801i	$-0.321475\pi$
$103$	10.7966	1.06382	0.531909	+	0.846801i	$0.321475\pi$
$104$	15.2840	1.49872
$105$	7.77967	0.759218
$106$	−0.463017	−0.0449722
$107$	−2.21863	−0.214483	−0.107242	−	0.994233i	$-0.534202\pi$
$107$	−2.21863	−0.214483	−0.107242	+	0.994233i	$0.534202\pi$
$108$	3.92518	0.377700
$109$	12.6378	1.21048	0.605241	−	0.796043i	$-0.293077\pi$
$109$	12.6378	1.21048	0.605241	+	0.796043i	$0.293077\pi$
$110$	2.04655	0.195131
$111$	−12.2609	−1.16375
$112$	0.163557	0.0154547
$113$	−0.475909	−0.0447698	−0.0223849	−	0.999749i	$-0.507126\pi$
$113$	−0.475909	−0.0447698	−0.0223849	+	0.999749i	$0.507126\pi$
$114$	−5.04771	−0.472761
$115$	−3.59692	−0.335415
$116$	−5.36549	−0.498173
$117$	8.23141	0.760994
$118$	−7.36227	−0.677752
$119$	15.8008	1.44846
$120$	5.99101	0.546902
$121$	−5.44483	−0.494985
$122$	9.41966	0.852816
$123$	10.3333	0.931721
$124$	5.90677	0.530444
$125$	1.00000	0.0894427
$126$	−4.82423	−0.429777
$127$	9.36646	0.831139	0.415569	−	0.909561i	$-0.363582\pi$
$127$	9.36646	0.831139	0.415569	+	0.909561i	$0.363582\pi$
$128$	7.15004	0.631980
$129$	−14.3644	−1.26472
$130$	−4.70852	−0.412965
$131$	−10.9721	−0.958638	−0.479319	−	0.877641i	$-0.659116\pi$
$131$	−10.9721	−0.958638	−0.479319	+	0.877641i	$0.659116\pi$
$132$	6.24240	0.543331
$133$	10.0101	0.867984
$134$	−4.71668	−0.407459
$135$	−3.15013	−0.271120
$136$	12.1680	1.04340
$137$	2.77874	0.237404	0.118702	−	0.992930i	$-0.462127\pi$
$137$	2.77874	0.237404	0.118702	+	0.992930i	$0.462127\pi$
$138$	6.63862	0.565117
$139$	16.8206	1.42670	0.713350	−	0.700808i	$-0.247177\pi$
$139$	16.8206	1.42670	0.713350	+	0.700808i	$0.247177\pi$
$140$	−4.56059	−0.385440
$141$	17.0848	1.43880
$142$	−7.12836	−0.598199
$143$	−12.7808	−1.06879
$144$	0.0678336	0.00565280
$145$	4.30604	0.357597
$146$	11.3940	0.942975
$147$	13.5953	1.12132
$148$	7.18756	0.590814
$149$	−6.60977	−0.541493	−0.270747	−	0.962651i	$-0.587271\pi$
$149$	−6.60977	−0.541493	−0.270747	+	0.962651i	$0.587271\pi$
$150$	−1.84564	−0.150696
$151$	−0.153493	−0.0124911	−0.00624555	−	0.999980i	$-0.501988\pi$
$151$	−0.153493	−0.0124911	−0.00624555	+	0.999980i	$0.501988\pi$
$152$	7.70861	0.625251
$153$	6.55322	0.529797
$154$	7.49053	0.603604
$155$	−4.74045	−0.380762
$156$	−14.3619	−1.14988
$157$	12.1713	0.971374	0.485687	−	0.874133i	$-0.338569\pi$
$157$	12.1713	0.971374	0.485687	+	0.874133i	$0.338569\pi$
$158$	0.979038	0.0778880
$159$	1.13343	0.0898868
$160$	−5.67594	−0.448722
$161$	−13.1650	−1.03755
$162$	9.76820	0.767463
$163$	−6.76843	−0.530144	−0.265072	−	0.964229i	$-0.585396\pi$
$163$	−6.76843	−0.530144	−0.265072	+	0.964229i	$0.585396\pi$
$164$	−6.05756	−0.473016
$165$	−5.00980	−0.390012
$166$	−1.86560	−0.144799
$167$	−4.50223	−0.348393	−0.174197	−	0.984711i	$-0.555733\pi$
$167$	−4.50223	−0.348393	−0.174197	+	0.984711i	$0.555733\pi$
$168$	21.9275	1.69175
$169$	16.4049	1.26192
$170$	−3.74857	−0.287502
$171$	4.15157	0.317478
$172$	8.42070	0.642073
$173$	19.4217	1.47660	0.738301	−	0.674471i	$-0.235628\pi$
$173$	19.4217	1.47660	0.738301	+	0.674471i	$0.235628\pi$
$174$	−7.94739	−0.602490
$175$	3.66007	0.276675
$176$	−0.105324	−0.00793913
$177$	18.0222	1.35464
$178$	−2.24899	−0.168569
$179$	−0.391322	−0.0292488	−0.0146244	−	0.999893i	$-0.504655\pi$
$179$	−0.391322	−0.0292488	−0.0146244	+	0.999893i	$0.504655\pi$
$180$	−1.89145	−0.140981
$181$	−13.6865	−1.01731	−0.508656	−	0.860970i	$-0.669857\pi$
$181$	−13.6865	−1.01731	−0.508656	+	0.860970i	$0.669857\pi$
$182$	−17.2335	−1.27743
$183$	−23.0586	−1.70454
$184$	−10.1382	−0.747396
$185$	−5.76833	−0.424096
$186$	8.74915	0.641519
$187$	−10.1751	−0.744078
$188$	−10.0154	−0.730451
$189$	−11.5297	−0.838661
$190$	−2.37478	−0.172284
$191$	5.64210	0.408248	0.204124	−	0.978945i	$-0.434565\pi$
$191$	5.64210	0.408248	0.204124	+	0.978945i	$0.434565\pi$
$192$	10.2858	0.742310
$193$	−22.6871	−1.63306	−0.816528	−	0.577306i	$-0.804104\pi$
$193$	−22.6871	−1.63306	−0.816528	+	0.577306i	$0.804104\pi$
$194$	7.61980	0.547069
$195$	11.5261	0.825400
$196$	−7.96981	−0.569272
$197$	2.02017	0.143931	0.0719654	−	0.997407i	$-0.477073\pi$
$197$	2.02017	0.143931	0.0719654	+	0.997407i	$0.477073\pi$
$198$	3.10661	0.220778
$199$	−24.3902	−1.72898	−0.864489	−	0.502651i	$-0.832358\pi$
$199$	−24.3902	−1.72898	−0.864489	+	0.502651i	$0.832358\pi$
$200$	2.81857	0.199303
$201$	11.5461	0.814396
$202$	5.90842	0.415715
$203$	15.7604	1.10616
$204$	−11.4339	−0.800533
$205$	4.86146	0.339539
$206$	−9.37477	−0.653171
$207$	−5.46003	−0.379499
$208$	0.242321	0.0168019
$209$	−6.44609	−0.445885
$210$	−6.75517	−0.466151
$211$	8.60060	0.592090	0.296045	−	0.955174i	$-0.404332\pi$
$211$	8.60060	0.592090	0.296045	+	0.955174i	$0.404332\pi$
$212$	−0.664437	−0.0456337
$213$	17.4497	1.19563
$214$	1.92646	0.131690
$215$	−6.75798	−0.460891
$216$	−8.87884	−0.604128
$217$	−17.3504	−1.17782
$218$	−10.9735	−0.743221
$219$	−27.8916	−1.88474
$220$	2.93684	0.198002
$221$	23.4100	1.57473
$222$	10.6463	0.714530
$223$	7.23294	0.484353	0.242177	−	0.970232i	$-0.422139\pi$
$223$	7.23294	0.484353	0.242177	+	0.970232i	$0.422139\pi$
$224$	−20.7743	−1.38804
$225$	1.51797	0.101198
$226$	0.413237	0.0274881
$227$	7.37615	0.489572	0.244786	−	0.969577i	$-0.421282\pi$
$227$	7.37615	0.489572	0.244786	+	0.969577i	$0.421282\pi$
$228$	−7.24354	−0.479715
$229$	16.3215	1.07855	0.539277	−	0.842129i	$-0.318698\pi$
$229$	16.3215	1.07855	0.539277	+	0.842129i	$0.318698\pi$
$230$	3.12324	0.205941
$231$	−18.3362	−1.20644
$232$	12.1369	0.796824
$233$	−12.7154	−0.833015	−0.416508	−	0.909132i	$-0.636746\pi$
$233$	−12.7154	−0.833015	−0.416508	+	0.909132i	$0.636746\pi$
$234$	−7.14741	−0.467241
$235$	8.03782	0.524330
$236$	−10.5650	−0.687721
$237$	−2.39660	−0.155676
$238$	−13.7200	−0.889338
$239$	24.7512	1.60102	0.800511	−	0.599318i	$-0.204561\pi$
$239$	24.7512	1.60102	0.800511	+	0.599318i	$0.204561\pi$
$240$	0.0949845	0.00613122
$241$	20.3568	1.31130	0.655650	−	0.755065i	$-0.272395\pi$
$241$	20.3568	1.31130	0.655650	+	0.755065i	$0.272395\pi$
$242$	4.72780	0.303915
$243$	−14.4614	−0.927699
$244$	13.5174	0.865361
$245$	6.39612	0.408633
$246$	−8.97250	−0.572066
$247$	14.8306	0.943647
$248$	−13.3613	−0.848441
$249$	4.56685	0.289412
$250$	−0.868310	−0.0549167
$251$	−9.62501	−0.607525	−0.303762	−	0.952748i	$-0.598243\pi$
$251$	−9.62501	−0.607525	−0.303762	+	0.952748i	$0.598243\pi$
$252$	−6.92285	−0.436099
$253$	8.47773	0.532991
$254$	−8.13299	−0.510309
$255$	9.17620	0.574636
$256$	−15.8866	−0.992915
$257$	2.25917	0.140923	0.0704615	−	0.997515i	$-0.477553\pi$
$257$	2.25917	0.140923	0.0704615	+	0.997515i	$0.477553\pi$
$258$	12.4728	0.776522
$259$	−21.1125	−1.31187
$260$	−6.75680	−0.419039
$261$	6.53645	0.404596
$262$	9.52719	0.588592
$263$	−10.8021	−0.666088	−0.333044	−	0.942911i	$-0.608076\pi$
$263$	−10.8021	−0.666088	−0.333044	+	0.942911i	$0.608076\pi$
$264$	−14.1205	−0.869054
$265$	0.533240	0.0327567
$266$	−8.69185	−0.532931
$267$	5.50535	0.336922
$268$	−6.76851	−0.413453
$269$	8.29185	0.505563	0.252782	−	0.967523i	$-0.418655\pi$
$269$	8.29185	0.505563	0.252782	+	0.967523i	$0.418655\pi$
$270$	2.73529	0.166464
$271$	−23.8768	−1.45041	−0.725207	−	0.688531i	$-0.758256\pi$
$271$	−23.8768	−1.45041	−0.725207	+	0.688531i	$0.758256\pi$
$272$	0.192918	0.0116973
$273$	42.1863	2.55323
$274$	−2.41281	−0.145763
$275$	−2.35694	−0.142129
$276$	9.52652	0.573429
$277$	−22.7352	−1.36603	−0.683013	−	0.730406i	$-0.739331\pi$
$277$	−22.7352	−1.36603	−0.683013	+	0.730406i	$0.739331\pi$
$278$	−14.6054	−0.875977
$279$	−7.19587	−0.430805
$280$	10.3162	0.616508
$281$	25.1415	1.49982	0.749909	−	0.661541i	$-0.230097\pi$
$281$	25.1415	1.49982	0.749909	+	0.661541i	$0.230097\pi$
$282$	−14.8349	−0.883406
$283$	−10.9528	−0.651075	−0.325537	−	0.945529i	$-0.605545\pi$
$283$	−10.9528	−0.651075	−0.325537	+	0.945529i	$0.605545\pi$
$284$	−10.2293	−0.606998
$285$	5.81326	0.344348
$286$	11.0977	0.656221
$287$	17.7933	1.05030
$288$	−8.61592	−0.507698
$289$	1.63725	0.0963088
$290$	−3.73898	−0.219560
$291$	−18.6526	−1.09344
$292$	16.3506	0.956845
$293$	−11.0998	−0.648458	−0.324229	−	0.945979i	$-0.605105\pi$
$293$	−11.0998	−0.648458	−0.324229	+	0.945979i	$0.605105\pi$
$294$	−11.8049	−0.688477
$295$	8.47885	0.493658
$296$	−16.2584	−0.945002
$297$	7.42466	0.430822
$298$	5.73932	0.332470
$299$	−19.5048	−1.12799
$300$	−2.64852	−0.152912
$301$	−24.7347	−1.42568
$302$	0.133280	0.00766939
$303$	−14.4633	−0.830897
$304$	0.122216	0.00700958
$305$	−10.8483	−0.621171
$306$	−5.69023	−0.325289
$307$	8.35918	0.477084	0.238542	−	0.971132i	$-0.423331\pi$
$307$	8.35918	0.477084	0.238542	+	0.971132i	$0.423331\pi$
$308$	10.7490	0.612483
$309$	22.9487	1.30551
$310$	4.11618	0.233783
$311$	26.3063	1.49169	0.745846	−	0.666118i	$-0.232045\pi$
$311$	26.3063	1.49169	0.745846	+	0.666118i	$0.232045\pi$
$312$	32.4870	1.83922
$313$	−10.3522	−0.585139	−0.292569	−	0.956244i	$-0.594510\pi$
$313$	−10.3522	−0.585139	−0.292569	+	0.956244i	$0.594510\pi$
$314$	−10.5684	−0.596412
$315$	5.55589	0.313039
$316$	1.40493	0.0790337
$317$	3.67233	0.206259	0.103129	−	0.994668i	$-0.467114\pi$
$317$	3.67233	0.206259	0.103129	+	0.994668i	$0.467114\pi$
$318$	−0.984168	−0.0551894
$319$	−10.1491	−0.568239
$320$	4.83910	0.270514
$321$	−4.71581	−0.263211
$322$	11.4313	0.637041
$323$	11.8070	0.656958
$324$	14.0175	0.778751
$325$	5.42263	0.300793
$326$	5.87709	0.325502
$327$	26.8623	1.48549
$328$	13.7024	0.756586
$329$	29.4190	1.62192
$330$	4.35006	0.239463
$331$	−18.4103	−1.01192	−0.505960	−	0.862557i	$-0.668862\pi$
$331$	−18.4103	−1.01192	−0.505960	+	0.862557i	$0.668862\pi$
$332$	−2.67717	−0.146929
$333$	−8.75617	−0.479835
$334$	3.90933	0.213909
$335$	5.43203	0.296783
$336$	0.347650	0.0189659
$337$	−26.5449	−1.44599	−0.722996	−	0.690853i	$-0.757235\pi$
$337$	−26.5449	−1.44599	−0.722996	+	0.690853i	$0.757235\pi$
$338$	−14.2446	−0.774802
$339$	−1.01157	−0.0549409
$340$	−5.37926	−0.291731
$341$	11.1729	0.605049
$342$	−3.60485	−0.194928
$343$	−2.21024	−0.119342
$344$	−19.0478	−1.02699
$345$	−7.64545	−0.411617
$346$	−16.8640	−0.906616
$347$	7.36120	0.395170	0.197585	−	0.980286i	$-0.436690\pi$
$347$	7.36120	0.395170	0.197585	+	0.980286i	$0.436690\pi$
$348$	−11.4046	−0.611352
$349$	−33.4339	−1.78968	−0.894838	−	0.446391i	$-0.852709\pi$
$349$	−33.4339	−1.78968	−0.894838	+	0.446391i	$0.852709\pi$
$350$	−3.17808	−0.169875
$351$	−17.0820	−0.911768
$352$	13.3778	0.713041
$353$	−17.4012	−0.926173	−0.463087	−	0.886313i	$-0.653258\pi$
$353$	−17.4012	−0.926173	−0.463087	+	0.886313i	$0.653258\pi$
$354$	−15.6489	−0.831729
$355$	8.20947	0.435713
$356$	−3.22734	−0.171049
$357$	33.5855	1.77753
$358$	0.339789	0.0179584
$359$	−5.26396	−0.277821	−0.138911	−	0.990305i	$-0.544360\pi$
$359$	−5.26396	−0.277821	−0.138911	+	0.990305i	$0.544360\pi$
$360$	4.27851	0.225497
$361$	−11.5201	−0.606321
$362$	11.8842	0.624617
$363$	−11.5733	−0.607440
$364$	−24.7304	−1.29622
$365$	−13.1221	−0.686840
$366$	20.0220	1.04657
$367$	33.0912	1.72735	0.863674	−	0.504052i	$-0.168158\pi$
$367$	33.0912	1.72735	0.863674	+	0.504052i	$0.168158\pi$
$368$	−0.160736	−0.00837892
$369$	7.37957	0.384165
$370$	5.00870	0.260390
$371$	1.95170	0.101327
$372$	12.5552	0.650955
$373$	−15.7897	−0.817560	−0.408780	−	0.912633i	$-0.634046\pi$
$373$	−15.7897	−0.817560	−0.408780	+	0.912633i	$0.634046\pi$
$374$	8.83516	0.456855
$375$	2.12555	0.109763
$376$	22.6551	1.16835
$377$	23.3501	1.20259
$378$	10.0113	0.514928
$379$	8.18394	0.420381	0.210190	−	0.977660i	$-0.432592\pi$
$379$	8.18394	0.420381	0.210190	+	0.977660i	$0.432592\pi$
$380$	−3.40784	−0.174818
$381$	19.9089	1.01996
$382$	−4.89909	−0.250659
$383$	−15.7414	−0.804346	−0.402173	−	0.915564i	$-0.631745\pi$
$383$	−15.7414	−0.804346	−0.402173	+	0.915564i	$0.631745\pi$
$384$	15.1978	0.775558
$385$	−8.62657	−0.439651
$386$	19.6995	1.00268
$387$	−10.2584	−0.521466
$388$	10.9345	0.555116
$389$	−1.04982	−0.0532279	−0.0266139	−	0.999646i	$-0.508472\pi$
$389$	−1.04982	−0.0532279	−0.0266139	+	0.999646i	$0.508472\pi$
$390$	−10.0082	−0.506786
$391$	−15.5282	−0.785297
$392$	18.0279	0.910546
$393$	−23.3218	−1.17643
$394$	−1.75413	−0.0883718
$395$	−1.12752	−0.0567317
$396$	4.45804	0.224025
$397$	−16.7266	−0.839484	−0.419742	−	0.907644i	$-0.637879\pi$
$397$	−16.7266	−0.839484	−0.419742	+	0.907644i	$0.637879\pi$
$398$	21.1783	1.06157
$399$	21.2769	1.06518
$400$	0.0446870	0.00223435
$401$	−1.00000	−0.0499376
$401$	−1.00000	−0.0499376
$402$	−10.0256	−0.500029
$403$	−25.7057	−1.28049
$404$	8.47868	0.421830
$405$	−11.2497	−0.559001
$406$	−13.6849	−0.679171
$407$	13.5956	0.673910
$408$	25.8637	1.28045
$409$	30.3916	1.50277	0.751384	−	0.659865i	$-0.229386\pi$
$409$	30.3916	1.50277	0.751384	+	0.659865i	$0.229386\pi$
$410$	−4.22125	−0.208473
$411$	5.90636	0.291339
$412$	−13.4529	−0.662779
$413$	31.0332	1.52704
$414$	4.74100	0.233007
$415$	2.14855	0.105468
$416$	−30.7785	−1.50904
$417$	35.7530	1.75083
$418$	5.59720	0.273768
$419$	6.02316	0.294251	0.147125	−	0.989118i	$-0.452998\pi$
$419$	6.02316	0.294251	0.147125	+	0.989118i	$0.452998\pi$
$420$	−9.69377	−0.473007
$421$	3.97214	0.193590	0.0967951	−	0.995304i	$-0.469141\pi$
$421$	3.97214	0.193590	0.0967951	+	0.995304i	$0.469141\pi$
$422$	−7.46799	−0.363536
$423$	12.2012	0.593243
$424$	1.50297	0.0729908
$425$	4.31709	0.209410
$426$	−15.1517	−0.734103
$427$	−39.7055	−1.92148
$428$	2.76450	0.133627
$429$	−27.1663	−1.31160
$430$	5.86802	0.282981
$431$	−21.4949	−1.03537	−0.517686	−	0.855571i	$-0.673206\pi$
$431$	−21.4949	−1.03537	−0.517686	+	0.855571i	$0.673206\pi$
$432$	−0.140770	−0.00677278
$433$	23.9833	1.15257	0.576283	−	0.817250i	$-0.304503\pi$
$433$	23.9833	1.15257	0.576283	+	0.817250i	$0.304503\pi$
$434$	15.0655	0.723167
$435$	9.15271	0.438839
$436$	−15.7472	−0.754153
$437$	−9.83737	−0.470585
$438$	24.2186	1.15721
$439$	30.7735	1.46874	0.734371	−	0.678749i	$-0.237477\pi$
$439$	30.7735	1.46874	0.734371	+	0.678749i	$0.237477\pi$
$440$	−6.64319	−0.316702
$441$	9.70914	0.462340
$442$	−20.3271	−0.966862
$443$	−16.0675	−0.763390	−0.381695	−	0.924288i	$-0.624660\pi$
$443$	−16.0675	−0.763390	−0.381695	+	0.924288i	$0.624660\pi$
$444$	15.2775	0.725040
$445$	2.59008	0.122782
$446$	−6.28043	−0.297387
$447$	−14.0494	−0.664514
$448$	17.7114	0.836787
$449$	−5.85673	−0.276396	−0.138198	−	0.990405i	$-0.544131\pi$
$449$	−5.85673	−0.276396	−0.138198	+	0.990405i	$0.544131\pi$
$450$	−1.31807	−0.0621345
$451$	−11.4582	−0.539544
$452$	0.593001	0.0278924
$453$	−0.326258	−0.0153289
$454$	−6.40478	−0.300591
$455$	19.8472	0.930452
$456$	16.3851	0.767301
$457$	−38.6258	−1.80684	−0.903418	−	0.428760i	$-0.858951\pi$
$457$	−38.6258	−1.80684	−0.903418	+	0.428760i	$0.858951\pi$
$458$	−14.1721	−0.662219
$459$	−13.5994	−0.634764
$460$	4.48190	0.208970
$461$	−26.7652	−1.24658	−0.623289	−	0.781991i	$-0.714204\pi$
$461$	−26.7652	−1.24658	−0.623289	+	0.781991i	$0.714204\pi$
$462$	15.9215	0.740736
$463$	−20.1899	−0.938304	−0.469152	−	0.883117i	$-0.655440\pi$
$463$	−20.1899	−0.938304	−0.469152	+	0.883117i	$0.655440\pi$
$464$	0.192424	0.00893305
$465$	−10.0761	−0.467266
$466$	11.0409	0.511461
$467$	−20.3267	−0.940607	−0.470304	−	0.882505i	$-0.655856\pi$
$467$	−20.3267	−0.940607	−0.470304	+	0.882505i	$0.655856\pi$
$468$	−10.2566	−0.474114
$469$	19.8816	0.918047
$470$	−6.97932	−0.321932
$471$	25.8707	1.19206
$472$	23.8982	1.10000
$473$	15.9282	0.732378
$474$	2.08100	0.0955833
$475$	2.73494	0.125488
$476$	−19.6885	−0.902419
$477$	0.809444	0.0370619
$478$	−21.4917	−0.983008
$479$	−41.7218	−1.90632	−0.953159	−	0.302470i	$-0.902189\pi$
$479$	−41.7218	−1.90632	−0.953159	+	0.302470i	$0.902189\pi$
$480$	−12.0645	−0.550667
$481$	−31.2795	−1.42622
$482$	−17.6760	−0.805122
$483$	−27.9829	−1.27327
$484$	6.78447	0.308385
$485$	−8.77543	−0.398472
$486$	12.5570	0.569596
$487$	12.9926	0.588752	0.294376	−	0.955690i	$-0.404888\pi$
$487$	12.9926	0.588752	0.294376	+	0.955690i	$0.404888\pi$
$488$	−30.5766	−1.38414
$489$	−14.3866	−0.650587
$490$	−5.55381	−0.250896
$491$	−11.2370	−0.507120	−0.253560	−	0.967320i	$-0.581601\pi$
$491$	−11.2370	−0.507120	−0.253560	+	0.967320i	$0.581601\pi$
$492$	−12.8757	−0.580480
$493$	18.5896	0.837231
$494$	−12.8775	−0.579387
$495$	−3.57777	−0.160809
$496$	−0.211836	−0.00951172
$497$	30.0472	1.34780
$498$	−3.96544	−0.177695
$499$	−26.0823	−1.16760	−0.583802	−	0.811896i	$-0.698435\pi$
$499$	−26.0823	−1.16760	−0.583802	+	0.811896i	$0.698435\pi$
$500$	−1.24604	−0.0557245
$501$	−9.56973	−0.427544
$502$	8.35749	0.373013
$503$	19.7313	0.879774	0.439887	−	0.898053i	$-0.355019\pi$
$503$	19.7313	0.879774	0.439887	+	0.898053i	$0.355019\pi$
$504$	15.6596	0.697536
$505$	−6.80451	−0.302797
$506$	−7.36130	−0.327250
$507$	34.8695	1.54861
$508$	−11.6710	−0.517815
$509$	14.9633	0.663235	0.331618	−	0.943414i	$-0.392406\pi$
$509$	14.9633	0.663235	0.331618	+	0.943414i	$0.392406\pi$
$510$	−7.96778	−0.352819
$511$	−48.0277	−2.12462
$512$	−0.505547	−0.0223422
$513$	−8.61541	−0.380379
$514$	−1.96166	−0.0865250
$515$	10.7966	0.475754
$516$	17.8986	0.787944
$517$	−18.9447	−0.833186
$518$	18.3322	0.805470
$519$	41.2818	1.81207
$520$	15.2840	0.670250
$521$	−7.09679	−0.310916	−0.155458	−	0.987842i	$-0.549685\pi$
$521$	−7.09679	−0.310916	−0.155458	+	0.987842i	$0.549685\pi$
$522$	−5.67567	−0.248417
$523$	−28.6227	−1.25158	−0.625792	−	0.779990i	$-0.715224\pi$
$523$	−28.6227	−1.25158	−0.625792	+	0.779990i	$0.715224\pi$
$524$	13.6717	0.597249
$525$	7.77967	0.339533
$526$	9.37960	0.408970
$527$	−20.4649	−0.891466
$528$	−0.223873	−0.00974281
$529$	−10.0621	−0.437485
$530$	−0.463017	−0.0201122
$531$	12.8707	0.558540
$532$	−12.4729	−0.540770
$533$	26.3619	1.14186
$534$	−4.78035	−0.206866
$535$	−2.21863	−0.0959197
$536$	15.3105	0.661314
$537$	−0.831776	−0.0358938
$538$	−7.19989	−0.310409
$539$	−15.0753	−0.649338
$540$	3.92518	0.168913
$541$	−15.6756	−0.673945	−0.336972	−	0.941515i	$-0.609403\pi$
$541$	−15.6756	−0.673945	−0.336972	+	0.941515i	$0.609403\pi$
$542$	20.7325	0.890536
$543$	−29.0914	−1.24843
$544$	−24.5035	−1.05058
$545$	12.6378	0.541344
$546$	−36.6308	−1.56765
$547$	16.9787	0.725957	0.362979	−	0.931797i	$-0.381760\pi$
$547$	16.9787	0.725957	0.362979	+	0.931797i	$0.381760\pi$
$548$	−3.46242	−0.147907
$549$	−16.4674	−0.702811
$550$	2.04655	0.0872654
$551$	11.7768	0.501707
$552$	−21.5492	−0.917195
$553$	−4.12681	−0.175490
$554$	19.7412	0.838724
$555$	−12.2609	−0.520446
$556$	−20.9590	−0.888862
$557$	13.7174	0.581227	0.290613	−	0.956841i	$-0.406141\pi$
$557$	13.7174	0.581227	0.290613	+	0.956841i	$0.406141\pi$
$558$	6.24824	0.264509
$559$	−36.6460	−1.54996
$560$	0.163557	0.00691156
$561$	−21.6277	−0.913124
$562$	−21.8306	−0.920870
$563$	−7.44213	−0.313648	−0.156824	−	0.987627i	$-0.550126\pi$
$563$	−7.44213	−0.313648	−0.156824	+	0.987627i	$0.550126\pi$
$564$	−21.2883	−0.896400
$565$	−0.475909	−0.0200217
$566$	9.51040	0.399752
$567$	−41.1746	−1.72917
$568$	23.1389	0.970888
$569$	−39.6070	−1.66041	−0.830207	−	0.557455i	$-0.811778\pi$
$569$	−39.6070	−1.66041	−0.830207	+	0.557455i	$0.811778\pi$
$570$	−5.04771	−0.211425
$571$	−12.2135	−0.511119	−0.255559	−	0.966793i	$-0.582260\pi$
$571$	−12.2135	−0.511119	−0.255559	+	0.966793i	$0.582260\pi$
$572$	15.9254	0.665874
$573$	11.9926	0.500998
$574$	−15.4501	−0.644874
$575$	−3.59692	−0.150002
$576$	7.34562	0.306067
$577$	−40.5402	−1.68771	−0.843855	−	0.536572i	$-0.819719\pi$
$577$	−40.5402	−1.68771	−0.843855	+	0.536572i	$0.819719\pi$
$578$	−1.42164	−0.0591325
$579$	−48.2227	−2.00407
$580$	−5.36549	−0.222790
$581$	7.86383	0.326247
$582$	16.1963	0.671357
$583$	−1.25681	−0.0520519
$584$	−36.9854	−1.53047
$585$	8.23141	0.340327
$586$	9.63807	0.398145
$587$	25.4070	1.04866	0.524329	−	0.851515i	$-0.324316\pi$
$587$	25.4070	1.04866	0.524329	+	0.851515i	$0.324316\pi$
$588$	−16.9402	−0.698604
$589$	−12.9648	−0.534207
$590$	−7.36227	−0.303100
$591$	4.29397	0.176630
$592$	−0.257769	−0.0105942
$593$	4.09335	0.168094	0.0840470	−	0.996462i	$-0.473215\pi$
$593$	4.09335	0.168094	0.0840470	+	0.996462i	$0.473215\pi$
$594$	−6.44690	−0.264520
$595$	15.8008	0.647772
$596$	8.23602	0.337361
$597$	−51.8428	−2.12178
$598$	16.9362	0.692573
$599$	1.04484	0.0426908	0.0213454	−	0.999772i	$-0.493205\pi$
$599$	1.04484	0.0426908	0.0213454	+	0.999772i	$0.493205\pi$
$600$	5.99101	0.244582
$601$	−27.7092	−1.13028	−0.565142	−	0.824994i	$-0.691179\pi$
$601$	−27.7092	−1.13028	−0.565142	+	0.824994i	$0.691179\pi$
$602$	21.4774	0.875353
$603$	8.24567	0.335790
$604$	0.191258	0.00778220
$605$	−5.44483	−0.221364
$606$	12.5587	0.510161
$607$	18.6227	0.755873	0.377936	−	0.925832i	$-0.376634\pi$
$607$	18.6227	0.755873	0.377936	+	0.925832i	$0.376634\pi$
$608$	−15.5233	−0.629555
$609$	33.4996	1.35747
$610$	9.41966	0.381391
$611$	43.5861	1.76331
$612$	−8.16557	−0.330073
$613$	35.4283	1.43094	0.715468	−	0.698645i	$-0.246213\pi$
$613$	35.4283	1.43094	0.715468	+	0.698645i	$0.246213\pi$
$614$	−7.25836	−0.292923
$615$	10.3333	0.416678
$616$	−24.3146	−0.979662
$617$	−27.4131	−1.10361	−0.551805	−	0.833973i	$-0.686061\pi$
$617$	−27.4131	−1.10361	−0.551805	+	0.833973i	$0.686061\pi$
$618$	−19.9266	−0.801564
$619$	19.0024	0.763769	0.381884	−	0.924210i	$-0.375275\pi$
$619$	19.0024	0.763769	0.381884	+	0.924210i	$0.375275\pi$
$620$	5.90677	0.237222
$621$	11.3308	0.454688
$622$	−22.8420	−0.915881
$623$	9.47987	0.379803
$624$	0.515066	0.0206191
$625$	1.00000	0.0400000
$626$	8.98888	0.359268
$627$	−13.7015	−0.547185
$628$	−15.1659	−0.605185
$629$	−24.9024	−0.992924
$630$	−4.82423	−0.192202
$631$	−8.88372	−0.353655	−0.176828	−	0.984242i	$-0.556584\pi$
$631$	−8.88372	−0.353655	−0.176828	+	0.984242i	$0.556584\pi$
$632$	−3.17799	−0.126414
$633$	18.2810	0.726606
$634$	−3.18872	−0.126640
$635$	9.36646	0.371697
$636$	−1.41230	−0.0560012
$637$	34.6838	1.37422
$638$	8.81254	0.348892
$639$	12.4618	0.492979
$640$	7.15004	0.282630
$641$	15.9748	0.630966	0.315483	−	0.948931i	$-0.397833\pi$
$641$	15.9748	0.630966	0.315483	+	0.948931i	$0.397833\pi$
$642$	4.09479	0.161608
$643$	17.6326	0.695362	0.347681	−	0.937613i	$-0.386969\pi$
$643$	17.6326	0.695362	0.347681	+	0.937613i	$0.386969\pi$
$644$	16.4041	0.646411
$645$	−14.3644	−0.565600
$646$	−10.2521	−0.403364
$647$	−11.0577	−0.434723	−0.217362	−	0.976091i	$-0.569745\pi$
$647$	−11.0577	−0.434723	−0.217362	+	0.976091i	$0.569745\pi$
$648$	−31.7080	−1.24561
$649$	−19.9842	−0.784447
$650$	−4.70852	−0.184683
$651$	−36.8791	−1.44541
$652$	8.43372	0.330290
$653$	−3.75374	−0.146895	−0.0734477	−	0.997299i	$-0.523400\pi$
$653$	−3.75374	−0.146895	−0.0734477	+	0.997299i	$0.523400\pi$
$654$	−23.3248	−0.912072
$655$	−10.9721	−0.428716
$656$	0.217244	0.00848195
$657$	−19.9189	−0.777111
$658$	−25.5448	−0.995840
$659$	−39.0047	−1.51941	−0.759703	−	0.650270i	$-0.774656\pi$
$659$	−39.0047	−1.51941	−0.759703	+	0.650270i	$0.774656\pi$
$660$	6.24240	0.242985
$661$	−27.6348	−1.07487	−0.537434	−	0.843306i	$-0.680606\pi$
$661$	−27.6348	−1.07487	−0.537434	+	0.843306i	$0.680606\pi$
$662$	15.9858	0.621307
$663$	49.7591	1.93248
$664$	6.05582	0.235011
$665$	10.0101	0.388174
$666$	7.60307	0.294613
$667$	−15.4885	−0.599717
$668$	5.60995	0.217056
$669$	15.3740	0.594393
$670$	−4.71668	−0.182221
$671$	25.5687	0.987070
$672$	−44.1569	−1.70339
$673$	−8.50769	−0.327947	−0.163974	−	0.986465i	$-0.552431\pi$
$673$	−8.50769	−0.327947	−0.163974	+	0.986465i	$0.552431\pi$
$674$	23.0492	0.887821
$675$	−3.15013	−0.121248
$676$	−20.4412	−0.786199
$677$	5.73777	0.220521	0.110260	−	0.993903i	$-0.464832\pi$
$677$	5.73777	0.220521	0.110260	+	0.993903i	$0.464832\pi$
$678$	0.878356	0.0337331
$679$	−32.1187	−1.23260
$680$	12.1680	0.466622
$681$	15.6784	0.600797
$682$	−9.70158	−0.371493
$683$	38.8598	1.48693	0.743465	−	0.668775i	$-0.233181\pi$
$683$	38.8598	1.48693	0.743465	+	0.668775i	$0.233181\pi$
$684$	−5.17301	−0.197795
$685$	2.77874	0.106170
$686$	1.91918	0.0732745
$687$	34.6922	1.32359
$688$	−0.301994	−0.0115134
$689$	2.89156	0.110160
$690$	6.63862	0.252728
$691$	29.4938	1.12200	0.560999	−	0.827816i	$-0.310417\pi$
$691$	29.4938	1.12200	0.560999	+	0.827816i	$0.310417\pi$
$692$	−24.2001	−0.919952
$693$	−13.0949	−0.497434
$694$	−6.39180	−0.242629
$695$	16.8206	0.638040
$696$	25.7975	0.977853
$697$	20.9874	0.794953
$698$	29.0310	1.09884
$699$	−27.0273	−1.02227
$700$	−4.56059	−0.172374
$701$	−51.7715	−1.95538	−0.977691	−	0.210050i	$-0.932637\pi$
$701$	−51.7715	−1.95538	−0.977691	+	0.210050i	$0.932637\pi$
$702$	14.8324	0.559814
$703$	−15.7760	−0.595005
$704$	−11.4055	−0.429860
$705$	17.0848	0.643451
$706$	15.1096	0.568659
$707$	−24.9050	−0.936649
$708$	−22.4564	−0.843963
$709$	39.1333	1.46968	0.734841	−	0.678239i	$-0.237257\pi$
$709$	39.1333	1.46968	0.734841	+	0.678239i	$0.237257\pi$
$710$	−7.12836	−0.267523
$711$	−1.71155	−0.0641880
$712$	7.30031	0.273591
$713$	17.0510	0.638566
$714$	−29.1626	−1.09138
$715$	−12.7808	−0.477975
$716$	0.487602	0.0182226
$717$	52.6100	1.96476
$718$	4.57075	0.170579
$719$	−49.4125	−1.84277	−0.921387	−	0.388646i	$-0.872943\pi$
$719$	−49.4125	−1.84277	−0.921387	+	0.388646i	$0.872943\pi$
$720$	0.0678336	0.00252801
$721$	39.5162	1.47166
$722$	10.0030	0.372274
$723$	43.2695	1.60921
$724$	17.0539	0.633805
$725$	4.30604	0.159922
$726$	10.0492	0.372960
$727$	4.22057	0.156532	0.0782661	−	0.996933i	$-0.475062\pi$
$727$	4.22057	0.156532	0.0782661	+	0.996933i	$0.475062\pi$
$728$	55.9407	2.07330
$729$	3.01056	0.111502
$730$	11.3940	0.421711
$731$	−29.1748	−1.07907
$732$	28.7319	1.06196
$733$	37.1836	1.37341	0.686703	−	0.726938i	$-0.259057\pi$
$733$	37.1836	1.37341	0.686703	+	0.726938i	$0.259057\pi$
$734$	−28.7334	−1.06057
$735$	13.5953	0.501470
$736$	20.4159	0.752540
$737$	−12.8030	−0.471603
$738$	−6.40775	−0.235873
$739$	−27.9739	−1.02904	−0.514519	−	0.857479i	$-0.672029\pi$
$739$	−27.9739	−1.02904	−0.514519	+	0.857479i	$0.672029\pi$
$740$	7.18756	0.264220
$741$	31.5232	1.15803
$742$	−1.69468	−0.0622135
$743$	38.6705	1.41868	0.709341	−	0.704865i	$-0.248993\pi$
$743$	38.6705	1.41868	0.709341	+	0.704865i	$0.248993\pi$
$744$	−28.4001	−1.04120
$745$	−6.60977	−0.242163
$746$	13.7104	0.501972
$747$	3.26143	0.119330
$748$	12.6786	0.463575
$749$	−8.12034	−0.296711
$750$	−1.84564	−0.0673932
$751$	7.18768	0.262282	0.131141	−	0.991364i	$-0.458136\pi$
$751$	7.18768	0.262282	0.131141	+	0.991364i	$0.458136\pi$
$752$	0.359186	0.0130982
$753$	−20.4585	−0.745547
$754$	−20.2751	−0.738375
$755$	−0.153493	−0.00558619
$756$	14.3664	0.522502
$757$	−14.0718	−0.511449	−0.255724	−	0.966750i	$-0.582314\pi$
$757$	−14.0718	−0.511449	−0.255724	+	0.966750i	$0.582314\pi$
$758$	−7.10619	−0.258109
$759$	18.0199	0.654080
$760$	7.70861	0.279621
$761$	44.7222	1.62118	0.810590	−	0.585614i	$-0.199147\pi$
$761$	44.7222	1.62118	0.810590	+	0.585614i	$0.199147\pi$
$762$	−17.2871	−0.626245
$763$	46.2552	1.67455
$764$	−7.03028	−0.254346
$765$	6.55322	0.236932
$766$	13.6684	0.493859
$767$	45.9777	1.66016
$768$	−33.7679	−1.21849
$769$	10.7452	0.387482	0.193741	−	0.981053i	$-0.437938\pi$
$769$	10.7452	0.387482	0.193741	+	0.981053i	$0.437938\pi$
$770$	7.49053	0.269940
$771$	4.80198	0.172939
$772$	28.2690	1.01742
$773$	6.66113	0.239584	0.119792	−	0.992799i	$-0.461777\pi$
$773$	6.66113	0.239584	0.119792	+	0.992799i	$0.461777\pi$
$774$	8.90750	0.320174
$775$	−4.74045	−0.170282
$776$	−24.7341	−0.887904
$777$	−44.8757	−1.60991
$778$	0.911567	0.0326813
$779$	13.2958	0.476372
$780$	−14.3619	−0.514240
$781$	−19.3492	−0.692370
$782$	13.4833	0.482162
$783$	−13.5646	−0.484758
$784$	0.285823	0.0102080
$785$	12.1713	0.434412
$786$	20.2505	0.722313
$787$	11.7392	0.418456	0.209228	−	0.977867i	$-0.432905\pi$
$787$	11.7392	0.418456	0.209228	+	0.977867i	$0.432905\pi$
$788$	−2.51720	−0.0896716
$789$	−22.9605	−0.817415
$790$	0.979038	0.0348326
$791$	−1.74186	−0.0619335
$792$	−10.0842	−0.358326
$793$	−58.8262	−2.08898
$794$	14.5239	0.515433
$795$	1.13343	0.0401986
$796$	30.3912	1.07719
$797$	−33.0141	−1.16942	−0.584709	−	0.811243i	$-0.698791\pi$
$797$	−33.0141	−1.16942	−0.584709	+	0.811243i	$0.698791\pi$
$798$	−18.4750	−0.654007
$799$	34.7000	1.22760
$800$	−5.67594	−0.200675
$801$	3.93167	0.138919
$802$	0.868310	0.0306611
$803$	30.9279	1.09142
$804$	−14.3868	−0.507384
$805$	−13.1650	−0.464005
$806$	22.3205	0.786206
$807$	17.6248	0.620421
$808$	−19.1790	−0.674714
$809$	−45.1181	−1.58627	−0.793135	−	0.609046i	$-0.791552\pi$
$809$	−45.1181	−1.58627	−0.793135	+	0.609046i	$0.791552\pi$
$810$	9.76820	0.343220
$811$	12.7597	0.448054	0.224027	−	0.974583i	$-0.428080\pi$
$811$	12.7597	0.448054	0.224027	+	0.974583i	$0.428080\pi$
$812$	−19.6381	−0.689161
$813$	−50.7514	−1.77993
$814$	−11.8052	−0.413772
$815$	−6.76843	−0.237088
$816$	0.410056	0.0143548
$817$	−18.4827	−0.646627
$818$	−26.3893	−0.922682
$819$	30.1275	1.05274
$820$	−6.05756	−0.211539
$821$	51.2083	1.78718	0.893591	−	0.448882i	$-0.148178\pi$
$821$	51.2083	1.78718	0.893591	+	0.448882i	$0.148178\pi$
$822$	−5.12855	−0.178879
$823$	−42.7772	−1.49112	−0.745559	−	0.666439i	$-0.767818\pi$
$823$	−42.7772	−1.49112	−0.745559	+	0.666439i	$0.767818\pi$
$824$	30.4309	1.06011
$825$	−5.00980	−0.174419
$826$	−26.9464	−0.937586
$827$	−13.4084	−0.466254	−0.233127	−	0.972446i	$-0.574896\pi$
$827$	−13.4084	−0.466254	−0.233127	+	0.972446i	$0.574896\pi$
$828$	6.80341	0.236435
$829$	−23.5205	−0.816900	−0.408450	−	0.912781i	$-0.633931\pi$
$829$	−23.5205	−0.816900	−0.408450	+	0.912781i	$0.633931\pi$
$830$	−1.86560	−0.0647560
$831$	−48.3249	−1.67637
$832$	26.2406	0.909730
$833$	27.6126	0.956720
$834$	−31.0446	−1.07499
$835$	−4.50223	−0.155806
$836$	8.03207	0.277795
$837$	14.9330	0.516160
$838$	−5.22997	−0.180666
$839$	18.1500	0.626609	0.313304	−	0.949653i	$-0.398564\pi$
$839$	18.1500	0.626609	0.313304	+	0.949653i	$0.398564\pi$
$840$	21.9275	0.756572
$841$	−10.4580	−0.360621
$842$	−3.44905	−0.118862
$843$	53.4396	1.84056
$844$	−10.7167	−0.368883
$845$	16.4049	0.564347
$846$	−10.5944	−0.364244
$847$	−19.9285	−0.684750
$848$	0.0238289	0.000818287 0
$849$	−23.2807	−0.798991
$850$	−3.74857	−0.128575
$851$	20.7482	0.711241
$852$	−21.7429	−0.744901
$853$	−22.2352	−0.761318	−0.380659	−	0.924715i	$-0.624303\pi$
$853$	−22.2352	−0.761318	−0.380659	+	0.924715i	$0.624303\pi$
$854$	34.4766	1.17977
$855$	4.15157	0.141981
$856$	−6.25336	−0.213735
$857$	0.431613	0.0147436	0.00737181	−	0.999973i	$-0.497653\pi$
$857$	0.431613	0.0147436	0.00737181	+	0.999973i	$0.497653\pi$
$858$	23.5888	0.805307
$859$	49.1705	1.67768	0.838838	−	0.544382i	$-0.183236\pi$
$859$	49.1705	1.67768	0.838838	+	0.544382i	$0.183236\pi$
$860$	8.42070	0.287144
$861$	37.8206	1.28892
$862$	18.6642	0.635706
$863$	21.6119	0.735677	0.367839	−	0.929890i	$-0.380098\pi$
$863$	21.6119	0.735677	0.367839	+	0.929890i	$0.380098\pi$
$864$	17.8799	0.608287
$865$	19.4217	0.660357
$866$	−20.8250	−0.707661
$867$	3.48006	0.118189
$868$	21.6192	0.733804
$869$	2.65750	0.0901495
$870$	−7.94739	−0.269442
$871$	29.4559	0.998074
$872$	35.6205	1.20626
$873$	−13.3209	−0.450843
$874$	8.54188	0.288934
$875$	3.66007	0.123733
$876$	34.7540	1.17423
$877$	−35.5879	−1.20172	−0.600859	−	0.799355i	$-0.705175\pi$
$877$	−35.5879	−1.20172	−0.600859	+	0.799355i	$0.705175\pi$
$878$	−26.7210	−0.901789
$879$	−23.5932	−0.795779
$880$	−0.105324	−0.00355049
$881$	45.6599	1.53832	0.769161	−	0.639055i	$-0.220675\pi$
$881$	45.6599	1.53832	0.769161	+	0.639055i	$0.220675\pi$
$882$	−8.43054	−0.283871
$883$	42.4769	1.42946	0.714731	−	0.699399i	$-0.246549\pi$
$883$	42.4769	1.42946	0.714731	+	0.699399i	$0.246549\pi$
$884$	−29.1697	−0.981084
$885$	18.0222	0.605811
$886$	13.9516	0.468712
$887$	5.30216	0.178029	0.0890146	−	0.996030i	$-0.471628\pi$
$887$	5.30216	0.178029	0.0890146	+	0.996030i	$0.471628\pi$
$888$	−34.5581	−1.15970
$889$	34.2819	1.14978
$890$	−2.24899	−0.0753864
$891$	26.5148	0.888280
$892$	−9.01251	−0.301761
$893$	21.9830	0.735632
$894$	12.1992	0.408003
$895$	−0.391322	−0.0130805
$896$	26.1696	0.874266
$897$	−41.4584	−1.38426
$898$	5.08546	0.169704
$899$	−20.4125	−0.680796
$900$	−1.89145	−0.0630484
$901$	2.30204	0.0766922
$902$	9.94924	0.331274
$903$	−52.5749	−1.74958
$904$	−1.34138	−0.0446137
$905$	−13.6865	−0.454956
$906$	0.283293	0.00941178
$907$	9.32720	0.309705	0.154852	−	0.987938i	$-0.450510\pi$
$907$	9.32720	0.309705	0.154852	+	0.987938i	$0.450510\pi$
$908$	−9.19096	−0.305013
$909$	−10.3291	−0.342593
$910$	−17.2335	−0.571286
$911$	8.74468	0.289724	0.144862	−	0.989452i	$-0.453726\pi$
$911$	8.74468	0.289724	0.144862	+	0.989452i	$0.453726\pi$
$912$	0.259777	0.00860207
$913$	−5.06399	−0.167594
$914$	33.5391	1.10938
$915$	−23.0586	−0.762293
$916$	−20.3372	−0.671959
$917$	−40.1587	−1.32616
$918$	11.8085	0.389737
$919$	23.5798	0.777825	0.388912	−	0.921275i	$-0.372851\pi$
$919$	23.5798	0.777825	0.388912	+	0.921275i	$0.372851\pi$
$920$	−10.1382	−0.334246
$921$	17.7679	0.585471
$922$	23.2405	0.765384
$923$	44.5169	1.46529
$924$	22.8476	0.751632
$925$	−5.76833	−0.189662
$926$	17.5311	0.576107
$927$	16.3889	0.538283
$928$	−24.4408	−0.802309
$929$	−30.7211	−1.00793	−0.503963	−	0.863725i	$-0.668125\pi$
$929$	−30.7211	−1.00793	−0.503963	+	0.863725i	$0.668125\pi$
$930$	8.74915	0.286896
$931$	17.4930	0.573310
$932$	15.8439	0.518984
$933$	55.9154	1.83059
$934$	17.6499	0.577521
$935$	−10.1751	−0.332762
$936$	23.2008	0.758341
$937$	−35.6529	−1.16473	−0.582364	−	0.812928i	$-0.697872\pi$
$937$	−35.6529	−1.16473	−0.582364	+	0.812928i	$0.697872\pi$
$938$	−17.2634	−0.563670
$939$	−22.0041	−0.718075
$940$	−10.0154	−0.326667
$941$	−0.633391	−0.0206480	−0.0103240	−	0.999947i	$-0.503286\pi$
$941$	−0.633391	−0.0206480	−0.0103240	+	0.999947i	$0.503286\pi$
$942$	−22.4638	−0.731910
$943$	−17.4863	−0.569432
$944$	0.378894	0.0123320
$945$	−11.5297	−0.375061
$946$	−13.8306	−0.449671
$947$	−55.9974	−1.81967	−0.909835	−	0.414969i	$-0.863792\pi$
$947$	−55.9974	−1.81967	−0.909835	+	0.414969i	$0.863792\pi$
$948$	2.98626	0.0969892
$949$	−71.1561	−2.30982
$950$	−2.37478	−0.0770479
$951$	7.80574	0.253118
$952$	44.5357	1.44341
$953$	11.0898	0.359235	0.179617	−	0.983737i	$-0.442514\pi$
$953$	11.0898	0.359235	0.179617	+	0.983737i	$0.442514\pi$
$954$	−0.702848	−0.0227555
$955$	5.64210	0.182574
$956$	−30.8410	−0.997468
$957$	−21.5724	−0.697337
$958$	36.2275	1.17046
$959$	10.1704	0.328419
$960$	10.2858	0.331971
$961$	−8.52818	−0.275103
$962$	27.1603	0.875684
$963$	−3.36782	−0.108526
$964$	−25.3654	−0.816964
$965$	−22.6871	−0.730325
$966$	24.2978	0.781769
$967$	29.0586	0.934462	0.467231	−	0.884135i	$-0.345252\pi$
$967$	29.0586	0.934462	0.467231	+	0.884135i	$0.345252\pi$
$968$	−15.3466	−0.493259
$969$	25.0964	0.806211
$970$	7.61980	0.244657
$971$	56.5451	1.81462	0.907310	−	0.420462i	$-0.138132\pi$
$971$	56.5451	1.81462	0.907310	+	0.420462i	$0.138132\pi$
$972$	18.0195	0.577974
$973$	61.5644	1.97366
$974$	−11.2816	−0.361487
$975$	11.5261	0.369130
$976$	−0.484776	−0.0155173
$977$	43.1287	1.37981	0.689905	−	0.723900i	$-0.257652\pi$
$977$	43.1287	1.37981	0.689905	+	0.723900i	$0.257652\pi$
$978$	12.4921	0.399452
$979$	−6.10466	−0.195106
$980$	−7.96981	−0.254586
$981$	19.1838	0.612493
$982$	9.75722	0.311365
$983$	45.7318	1.45862	0.729309	−	0.684185i	$-0.239842\pi$
$983$	45.7318	1.45862	0.729309	+	0.684185i	$0.239842\pi$
$984$	29.1251	0.928473
$985$	2.02017	0.0643678
$986$	−16.1415	−0.514050
$987$	62.5316	1.99040
$988$	−18.4795	−0.587910
$989$	24.3079	0.772948
$990$	3.10661	0.0987347
$991$	−35.9590	−1.14228	−0.571138	−	0.820854i	$-0.693498\pi$
$991$	−35.9590	−1.14228	−0.571138	+	0.820854i	$0.693498\pi$
$992$	26.9065	0.854281
$993$	−39.1320	−1.24182
$994$	−26.0903	−0.827534
$995$	−24.3902	−0.773223
$996$	−5.69046	−0.180309
$997$	40.9342	1.29640	0.648199	−	0.761471i	$-0.275523\pi$
$997$	40.9342	1.29640	0.648199	+	0.761471i	$0.275523\pi$
$998$	22.6475	0.716894
$999$	18.1710	0.574904

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2005.2.a.g.1.11	✓	37

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2005.2.a.g.1.11	✓	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)

\(f(q)\)	\(=\)	\(q-0.868310 q^{2} +2.12555 q^{3} -1.24604 q^{4} +1.00000 q^{5} -1.84564 q^{6} +3.66007 q^{7} +2.81857 q^{8} +1.51797 q^{9} +O(q^{10})\)	\(q-0.868310 q^{2} +2.12555 q^{3} -1.24604 q^{4} +1.00000 q^{5} -1.84564 q^{6} +3.66007 q^{7} +2.81857 q^{8} +1.51797 q^{9} -0.868310 q^{10} -2.35694 q^{11} -2.64852 q^{12} +5.42263 q^{13} -3.17808 q^{14} +2.12555 q^{15} +0.0446870 q^{16} +4.31709 q^{17} -1.31807 q^{18} +2.73494 q^{19} -1.24604 q^{20} +7.77967 q^{21} +2.04655 q^{22} -3.59692 q^{23} +5.99101 q^{24} +1.00000 q^{25} -4.70852 q^{26} -3.15013 q^{27} -4.56059 q^{28} +4.30604 q^{29} -1.84564 q^{30} -4.74045 q^{31} -5.67594 q^{32} -5.00980 q^{33} -3.74857 q^{34} +3.66007 q^{35} -1.89145 q^{36} -5.76833 q^{37} -2.37478 q^{38} +11.5261 q^{39} +2.81857 q^{40} +4.86146 q^{41} -6.75517 q^{42} -6.75798 q^{43} +2.93684 q^{44} +1.51797 q^{45} +3.12324 q^{46} +8.03782 q^{47} +0.0949845 q^{48} +6.39612 q^{49} -0.868310 q^{50} +9.17620 q^{51} -6.75680 q^{52} +0.533240 q^{53} +2.73529 q^{54} -2.35694 q^{55} +10.3162 q^{56} +5.81326 q^{57} -3.73898 q^{58} +8.47885 q^{59} -2.64852 q^{60} -10.8483 q^{61} +4.11618 q^{62} +5.55589 q^{63} +4.83910 q^{64} +5.42263 q^{65} +4.35006 q^{66} +5.43203 q^{67} -5.37926 q^{68} -7.64545 q^{69} -3.17808 q^{70} +8.20947 q^{71} +4.27851 q^{72} -13.1221 q^{73} +5.00870 q^{74} +2.12555 q^{75} -3.40784 q^{76} -8.62657 q^{77} -10.0082 q^{78} -1.12752 q^{79} +0.0446870 q^{80} -11.2497 q^{81} -4.22125 q^{82} +2.14855 q^{83} -9.69377 q^{84} +4.31709 q^{85} +5.86802 q^{86} +9.15271 q^{87} -6.64319 q^{88} +2.59008 q^{89} -1.31807 q^{90} +19.8472 q^{91} +4.48190 q^{92} -10.0761 q^{93} -6.97932 q^{94} +2.73494 q^{95} -12.0645 q^{96} -8.77543 q^{97} -5.55381 q^{98} -3.57777 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 37 q + 11 q^{2} + 13 q^{3} + 43 q^{4} + 37 q^{5} - 2 q^{6} + 34 q^{7} + 27 q^{8} + 50 q^{9}+O(q^{10}) \) 37 * q + 11 * q^2 + 13 * q^3 + 43 * q^4 + 37 * q^5 - 2 * q^6 + 34 * q^7 + 27 * q^8 + 50 * q^9	\( 37 q + 11 q^{2} + 13 q^{3} + 43 q^{4} + 37 q^{5} - 2 q^{6} + 34 q^{7} + 27 q^{8} + 50 q^{9} + 11 q^{10} + 38 q^{11} + 24 q^{12} + 17 q^{13} + 14 q^{14} + 13 q^{15} + 47 q^{16} + 22 q^{17} + 18 q^{18} + 6 q^{19} + 43 q^{20} + 4 q^{21} + 18 q^{22} + 45 q^{23} - 19 q^{24} + 37 q^{25} - q^{26} + 43 q^{27} + 46 q^{28} + 17 q^{29} - 2 q^{30} - 13 q^{31} + 50 q^{32} + 12 q^{33} - 30 q^{34} + 34 q^{35} + 43 q^{36} + 9 q^{37} + q^{38} - 7 q^{39} + 27 q^{40} + 12 q^{41} - 38 q^{42} + 53 q^{43} + 36 q^{44} + 50 q^{45} - 15 q^{46} + 39 q^{47} - 6 q^{48} + 37 q^{49} + 11 q^{50} + 38 q^{51} + 17 q^{52} + 19 q^{53} - 62 q^{54} + 38 q^{55} + 18 q^{56} + 6 q^{57} - 13 q^{58} + 33 q^{59} + 24 q^{60} - 11 q^{61} + q^{62} + 98 q^{63} + 15 q^{64} + 17 q^{65} - 70 q^{66} + 49 q^{67} + 32 q^{68} - 36 q^{69} + 14 q^{70} + 19 q^{71} + 5 q^{72} + 39 q^{73} + 21 q^{74} + 13 q^{75} - 33 q^{76} + 34 q^{77} - 22 q^{78} - 9 q^{79} + 47 q^{80} + 49 q^{81} + 14 q^{82} + 114 q^{83} - 50 q^{84} + 22 q^{85} + 9 q^{86} + 56 q^{87} + 14 q^{88} + 2 q^{89} + 18 q^{90} - 29 q^{91} + 47 q^{92} - 7 q^{93} - 52 q^{94} + 6 q^{95} - 89 q^{96} + 4 q^{97} + 14 q^{98} + 57 q^{99}+O(q^{100}) \) 37 * q + 11 * q^2 + 13 * q^3 + 43 * q^4 + 37 * q^5 - 2 * q^6 + 34 * q^7 + 27 * q^8 + 50 * q^9 + 11 * q^10 + 38 * q^11 + 24 * q^12 + 17 * q^13 + 14 * q^14 + 13 * q^15 + 47 * q^16 + 22 * q^17 + 18 * q^18 + 6 * q^19 + 43 * q^20 + 4 * q^21 + 18 * q^22 + 45 * q^23 - 19 * q^24 + 37 * q^25 - q^26 + 43 * q^27 + 46 * q^28 + 17 * q^29 - 2 * q^30 - 13 * q^31 + 50 * q^32 + 12 * q^33 - 30 * q^34 + 34 * q^35 + 43 * q^36 + 9 * q^37 + q^38 - 7 * q^39 + 27 * q^40 + 12 * q^41 - 38 * q^42 + 53 * q^43 + 36 * q^44 + 50 * q^45 - 15 * q^46 + 39 * q^47 - 6 * q^48 + 37 * q^49 + 11 * q^50 + 38 * q^51 + 17 * q^52 + 19 * q^53 - 62 * q^54 + 38 * q^55 + 18 * q^56 + 6 * q^57 - 13 * q^58 + 33 * q^59 + 24 * q^60 - 11 * q^61 + q^62 + 98 * q^63 + 15 * q^64 + 17 * q^65 - 70 * q^66 + 49 * q^67 + 32 * q^68 - 36 * q^69 + 14 * q^70 + 19 * q^71 + 5 * q^72 + 39 * q^73 + 21 * q^74 + 13 * q^75 - 33 * q^76 + 34 * q^77 - 22 * q^78 - 9 * q^79 + 47 * q^80 + 49 * q^81 + 14 * q^82 + 114 * q^83 - 50 * q^84 + 22 * q^85 + 9 * q^86 + 56 * q^87 + 14 * q^88 + 2 * q^89 + 18 * q^90 - 29 * q^91 + 47 * q^92 - 7 * q^93 - 52 * q^94 + 6 * q^95 - 89 * q^96 + 4 * q^97 + 14 * q^98 + 57 * q^99

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