LMFDB - Embedded newform 2645.2.a.y.1.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2645,2,Mod(1,2645)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2645, 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("2645.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2645 = 5 \cdot 23^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2645.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:	$21.1204313346$
Analytic rank:	$0$
Dimension:	$25$
Twist minimal:	no (minimal twist has level 115)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.10
Character	$\chi$	$=$	2645.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.898902 q^{2} -1.87885 q^{3} -1.19197 q^{4} +1.00000 q^{5} +1.68890 q^{6} -2.86688 q^{7} +2.86927 q^{8} +0.530083 q^{9} +O(q^{10})$	\(q-0.898902 q^{2} -1.87885 q^{3} -1.19197 q^{4} +1.00000 q^{5} +1.68890 q^{6} -2.86688 q^{7} +2.86927 q^{8} +0.530083 q^{9} -0.898902 q^{10} -0.808414 q^{11} +2.23954 q^{12} +5.52848 q^{13} +2.57705 q^{14} -1.87885 q^{15} -0.195247 q^{16} -6.64696 q^{17} -0.476493 q^{18} -2.77720 q^{19} -1.19197 q^{20} +5.38645 q^{21} +0.726686 q^{22} -5.39094 q^{24} +1.00000 q^{25} -4.96957 q^{26} +4.64061 q^{27} +3.41725 q^{28} -5.31155 q^{29} +1.68890 q^{30} +7.09853 q^{31} -5.56304 q^{32} +1.51889 q^{33} +5.97497 q^{34} -2.86688 q^{35} -0.631846 q^{36} -5.20340 q^{37} +2.49643 q^{38} -10.3872 q^{39} +2.86927 q^{40} -6.50772 q^{41} -4.84189 q^{42} +1.99472 q^{43} +0.963609 q^{44} +0.530083 q^{45} -1.53965 q^{47} +0.366841 q^{48} +1.21903 q^{49} -0.898902 q^{50} +12.4887 q^{51} -6.58981 q^{52} -4.05029 q^{53} -4.17145 q^{54} -0.808414 q^{55} -8.22588 q^{56} +5.21795 q^{57} +4.77457 q^{58} -2.09263 q^{59} +2.23954 q^{60} -12.2909 q^{61} -6.38088 q^{62} -1.51969 q^{63} +5.39112 q^{64} +5.52848 q^{65} -1.36533 q^{66} +9.84478 q^{67} +7.92301 q^{68} +2.57705 q^{70} +2.37438 q^{71} +1.52095 q^{72} -7.47700 q^{73} +4.67735 q^{74} -1.87885 q^{75} +3.31036 q^{76} +2.31763 q^{77} +9.33708 q^{78} -10.1256 q^{79} -0.195247 q^{80} -10.3093 q^{81} +5.84981 q^{82} -3.68561 q^{83} -6.42051 q^{84} -6.64696 q^{85} -1.79306 q^{86} +9.97962 q^{87} -2.31956 q^{88} -7.59548 q^{89} -0.476493 q^{90} -15.8495 q^{91} -13.3371 q^{93} +1.38399 q^{94} -2.77720 q^{95} +10.4521 q^{96} -5.45755 q^{97} -1.09579 q^{98} -0.428527 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 25 q + 3 q^{2} + 10 q^{3} + 33 q^{4} + 25 q^{5} + 22 q^{6} + 14 q^{7} + 21 q^{8} + 29 q^{9}+O(q^{10}) $ 25 * q + 3 * q^2 + 10 * q^3 + 33 * q^4 + 25 * q^5 + 22 * q^6 + 14 * q^7 + 21 * q^8 + 29 * q^9	\( 25 q + 3 q^{2} + 10 q^{3} + 33 q^{4} + 25 q^{5} + 22 q^{6} + 14 q^{7} + 21 q^{8} + 29 q^{9} + 3 q^{10} - 8 q^{11} + 34 q^{12} + 15 q^{13} - 6 q^{14} + 10 q^{15} + 41 q^{16} + 19 q^{17} + 23 q^{18} - 8 q^{19} + 33 q^{20} - 21 q^{21} + 3 q^{22} + 51 q^{24} + 25 q^{25} + 7 q^{26} + 64 q^{27} + 27 q^{28} + 3 q^{29} + 22 q^{30} + 34 q^{31} + 30 q^{32} - q^{33} - 21 q^{34} + 14 q^{35} + 31 q^{36} - q^{37} - 7 q^{38} + 49 q^{39} + 21 q^{40} - 29 q^{42} + 25 q^{43} - 33 q^{44} + 29 q^{45} - 5 q^{47} + 42 q^{48} + 33 q^{49} + 3 q^{50} + 23 q^{51} + 67 q^{52} + 24 q^{53} + 37 q^{54} - 8 q^{55} - 55 q^{56} - 19 q^{57} + 49 q^{58} + 41 q^{59} + 34 q^{60} - 31 q^{61} - 3 q^{62} + 37 q^{63} + 77 q^{64} + 15 q^{65} - 39 q^{66} - 5 q^{67} + 27 q^{68} - 6 q^{70} + 15 q^{71} + 48 q^{72} + 34 q^{73} - 29 q^{74} + 10 q^{75} - 24 q^{76} - 35 q^{77} - 45 q^{78} - 41 q^{79} + 41 q^{80} + 25 q^{81} + 33 q^{82} + 62 q^{83} - 126 q^{84} + 19 q^{85} - 10 q^{86} + 26 q^{87} - 50 q^{88} - 23 q^{89} + 23 q^{90} + 19 q^{91} + 50 q^{93} + 9 q^{94} - 8 q^{95} + 64 q^{96} + 37 q^{97} - 55 q^{98} - 48 q^{99}+O(q^{100}) \) 25 * q + 3 * q^2 + 10 * q^3 + 33 * q^4 + 25 * q^5 + 22 * q^6 + 14 * q^7 + 21 * q^8 + 29 * q^9 + 3 * q^10 - 8 * q^11 + 34 * q^12 + 15 * q^13 - 6 * q^14 + 10 * q^15 + 41 * q^16 + 19 * q^17 + 23 * q^18 - 8 * q^19 + 33 * q^20 - 21 * q^21 + 3 * q^22 + 51 * q^24 + 25 * q^25 + 7 * q^26 + 64 * q^27 + 27 * q^28 + 3 * q^29 + 22 * q^30 + 34 * q^31 + 30 * q^32 - q^33 - 21 * q^34 + 14 * q^35 + 31 * q^36 - q^37 - 7 * q^38 + 49 * q^39 + 21 * q^40 - 29 * q^42 + 25 * q^43 - 33 * q^44 + 29 * q^45 - 5 * q^47 + 42 * q^48 + 33 * q^49 + 3 * q^50 + 23 * q^51 + 67 * q^52 + 24 * q^53 + 37 * q^54 - 8 * q^55 - 55 * q^56 - 19 * q^57 + 49 * q^58 + 41 * q^59 + 34 * q^60 - 31 * q^61 - 3 * q^62 + 37 * q^63 + 77 * q^64 + 15 * q^65 - 39 * q^66 - 5 * q^67 + 27 * q^68 - 6 * q^70 + 15 * q^71 + 48 * q^72 + 34 * q^73 - 29 * q^74 + 10 * q^75 - 24 * q^76 - 35 * q^77 - 45 * q^78 - 41 * q^79 + 41 * q^80 + 25 * q^81 + 33 * q^82 + 62 * q^83 - 126 * q^84 + 19 * q^85 - 10 * q^86 + 26 * q^87 - 50 * q^88 - 23 * q^89 + 23 * q^90 + 19 * q^91 + 50 * q^93 + 9 * q^94 - 8 * q^95 + 64 * q^96 + 37 * q^97 - 55 * q^98 - 48 * 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 $

$2$	−0.898902	−0.635620	−0.317810	−	0.948154i	$-0.602947\pi$
$2$	−0.898902	−0.635620	−0.317810	+	0.948154i	$0.602947\pi$
$3$	−1.87885	−1.08476	−0.542378	−	0.840135i	$-0.682476\pi$
$3$	−1.87885	−1.08476	−0.542378	+	0.840135i	$0.682476\pi$
$4$	−1.19197	−0.595987
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	1.68890	0.689492
$7$	−2.86688	−1.08358	−0.541790	−	0.840514i	$-0.682253\pi$
$7$	−2.86688	−1.08358	−0.541790	+	0.840514i	$0.682253\pi$
$8$	2.86927	1.01444
$9$	0.530083	0.176694
$10$	−0.898902	−0.284258
$11$	−0.808414	−0.243746	−0.121873	−	0.992546i	$-0.538890\pi$
$11$	−0.808414	−0.243746	−0.121873	+	0.992546i	$0.538890\pi$
$12$	2.23954	0.646500
$13$	5.52848	1.53333	0.766663	−	0.642050i	$-0.221916\pi$
$13$	5.52848	1.53333	0.766663	+	0.642050i	$0.221916\pi$
$14$	2.57705	0.688745
$15$	−1.87885	−0.485117
$16$	−0.195247	−0.0488119
$17$	−6.64696	−1.61213	−0.806063	−	0.591830i	$-0.798406\pi$
$17$	−6.64696	−1.61213	−0.806063	+	0.591830i	$0.798406\pi$
$18$	−0.476493	−0.112310
$19$	−2.77720	−0.637134	−0.318567	−	0.947900i	$-0.603202\pi$
$19$	−2.77720	−0.637134	−0.318567	+	0.947900i	$0.603202\pi$
$20$	−1.19197	−0.266534
$21$	5.38645	1.17542
$22$	0.726686	0.154930
$23$	0	0
$23$	0	0
$24$	−5.39094	−1.10042
$25$	1.00000	0.200000
$26$	−4.96957	−0.974612
$27$	4.64061	0.893085
$28$	3.41725	0.645800
$29$	−5.31155	−0.986330	−0.493165	−	0.869936i	$-0.664160\pi$
$29$	−5.31155	−0.986330	−0.493165	+	0.869936i	$0.664160\pi$
$30$	1.68890	0.308350
$31$	7.09853	1.27493	0.637467	−	0.770478i	$-0.279982\pi$
$31$	7.09853	1.27493	0.637467	+	0.770478i	$0.279982\pi$
$32$	−5.56304	−0.983416
$33$	1.51889	0.264405
$34$	5.97497	1.02470
$35$	−2.86688	−0.484592
$36$	−0.631846	−0.105308
$37$	−5.20340	−0.855433	−0.427717	−	0.903913i	$-0.640682\pi$
$37$	−5.20340	−0.855433	−0.427717	+	0.903913i	$0.640682\pi$
$38$	2.49643	0.404975
$39$	−10.3872	−1.66328
$40$	2.86927	0.453672
$41$	−6.50772	−1.01634	−0.508168	−	0.861258i	$-0.669677\pi$
$41$	−6.50772	−1.01634	−0.508168	+	0.861258i	$0.669677\pi$
$42$	−4.84189	−0.747120
$43$	1.99472	0.304192	0.152096	−	0.988366i	$-0.451398\pi$
$43$	1.99472	0.304192	0.152096	+	0.988366i	$0.451398\pi$
$44$	0.963609	0.145270
$45$	0.530083	0.0790201
$46$	0	0
$47$	−1.53965	−0.224581	−0.112290	−	0.993675i	$-0.535819\pi$
$47$	−1.53965	−0.224581	−0.112290	+	0.993675i	$0.535819\pi$
$48$	0.366841	0.0529489
$49$	1.21903	0.174147
$50$	−0.898902	−0.127124
$51$	12.4887	1.74876
$52$	−6.58981	−0.913843
$53$	−4.05029	−0.556351	−0.278175	−	0.960530i	$-0.589730\pi$
$53$	−4.05029	−0.556351	−0.278175	+	0.960530i	$0.589730\pi$
$54$	−4.17145	−0.567663
$55$	−0.808414	−0.109007
$56$	−8.22588	−1.09923
$57$	5.21795	0.691135
$58$	4.77457	0.626931
$59$	−2.09263	−0.272437	−0.136219	−	0.990679i	$-0.543495\pi$
$59$	−2.09263	−0.272437	−0.136219	+	0.990679i	$0.543495\pi$
$60$	2.23954	0.289124
$61$	−12.2909	−1.57369	−0.786846	−	0.617150i	$-0.788287\pi$
$61$	−12.2909	−1.57369	−0.786846	+	0.617150i	$0.788287\pi$
$62$	−6.38088	−0.810373
$63$	−1.51969	−0.191463
$64$	5.39112	0.673890
$65$	5.52848	0.685724
$66$	−1.36533	−0.168061
$67$	9.84478	1.20273	0.601366	−	0.798974i	$-0.294623\pi$
$67$	9.84478	1.20273	0.601366	+	0.798974i	$0.294623\pi$
$68$	7.92301	0.960806
$69$	0	0
$70$	2.57705	0.308016
$71$	2.37438	0.281787	0.140893	−	0.990025i	$-0.455003\pi$
$71$	2.37438	0.281787	0.140893	+	0.990025i	$0.455003\pi$
$72$	1.52095	0.179246
$73$	−7.47700	−0.875117	−0.437559	−	0.899190i	$-0.644157\pi$
$73$	−7.47700	−0.875117	−0.437559	+	0.899190i	$0.644157\pi$
$74$	4.67735	0.543730
$75$	−1.87885	−0.216951
$76$	3.31036	0.379724
$77$	2.31763	0.264119
$78$	9.33708	1.05722
$79$	−10.1256	−1.13922	−0.569609	−	0.821916i	$-0.692905\pi$
$79$	−10.1256	−1.13922	−0.569609	+	0.821916i	$0.692905\pi$
$80$	−0.195247	−0.0218293
$81$	−10.3093	−1.14547
$82$	5.84981	0.646003
$83$	−3.68561	−0.404548	−0.202274	−	0.979329i	$-0.564833\pi$
$83$	−3.68561	−0.404548	−0.202274	+	0.979329i	$0.564833\pi$
$84$	−6.42051	−0.700535
$85$	−6.64696	−0.720964
$86$	−1.79306	−0.193351
$87$	9.97962	1.06993
$88$	−2.31956	−0.247266
$89$	−7.59548	−0.805119	−0.402559	−	0.915394i	$-0.631879\pi$
$89$	−7.59548	−0.805119	−0.402559	+	0.915394i	$0.631879\pi$
$90$	−0.476493	−0.0502268
$91$	−15.8495	−1.66148
$92$	0	0
$93$	−13.3371	−1.38299
$94$	1.38399	0.142748
$95$	−2.77720	−0.284935
$96$	10.4521	1.06677
$97$	−5.45755	−0.554130	−0.277065	−	0.960851i	$-0.589362\pi$
$97$	−5.45755	−0.554130	−0.277065	+	0.960851i	$0.589362\pi$
$98$	−1.09579	−0.110691
$99$	−0.428527	−0.0430686
$100$	−1.19197	−0.119197
$101$	14.3083	1.42373	0.711864	−	0.702317i	$-0.247851\pi$
$101$	14.3083	1.42373	0.711864	+	0.702317i	$0.247851\pi$
$102$	−11.2261	−1.11155
$103$	12.4232	1.22409	0.612046	−	0.790822i	$-0.290347\pi$
$103$	12.4232	1.22409	0.612046	+	0.790822i	$0.290347\pi$
$104$	15.8627	1.55547
$105$	5.38645	0.525664
$106$	3.64082	0.353628
$107$	4.21785	0.407755	0.203877	−	0.978996i	$-0.434646\pi$
$107$	4.21785	0.407755	0.203877	+	0.978996i	$0.434646\pi$
$108$	−5.53149	−0.532267
$109$	12.8873	1.23438	0.617189	−	0.786815i	$-0.288271\pi$
$109$	12.8873	1.23438	0.617189	+	0.786815i	$0.288271\pi$
$110$	0.726686	0.0692868
$111$	9.77641	0.927936
$112$	0.559752	0.0528916
$113$	19.8625	1.86851	0.934254	−	0.356608i	$-0.116067\pi$
$113$	19.8625	1.86851	0.934254	+	0.356608i	$0.116067\pi$
$114$	−4.69043	−0.439299
$115$	0	0
$116$	6.33123	0.587840
$117$	2.93056	0.270930
$118$	1.88107	0.173166
$119$	19.0561	1.74687
$120$	−5.39094	−0.492123
$121$	−10.3465	−0.940588
$122$	11.0483	1.00027
$123$	12.2270	1.10248
$124$	−8.46126	−0.759844
$125$	1.00000	0.0894427
$126$	1.36605	0.121697
$127$	16.1732	1.43514	0.717568	−	0.696488i	$-0.245255\pi$
$127$	16.1732	1.43514	0.717568	+	0.696488i	$0.245255\pi$
$128$	6.27998	0.555077
$129$	−3.74779	−0.329974
$130$	−4.96957	−0.435860
$131$	7.07834	0.618437	0.309219	−	0.950991i	$-0.399933\pi$
$131$	7.07834	0.618437	0.309219	+	0.950991i	$0.399933\pi$
$132$	−1.81048	−0.157582
$133$	7.96192	0.690386
$134$	−8.84950	−0.764480
$135$	4.64061	0.399400
$136$	−19.0720	−1.63541
$137$	6.90047	0.589547	0.294774	−	0.955567i	$-0.404756\pi$
$137$	6.90047	0.589547	0.294774	+	0.955567i	$0.404756\pi$
$138$	0	0
$139$	4.01862	0.340855	0.170428	−	0.985370i	$-0.445485\pi$
$139$	4.01862	0.340855	0.170428	+	0.985370i	$0.445485\pi$
$140$	3.41725	0.288811
$141$	2.89277	0.243615
$142$	−2.13433	−0.179109
$143$	−4.46931	−0.373742
$144$	−0.103497	−0.00862478
$145$	−5.31155	−0.441100
$146$	6.72110	0.556242
$147$	−2.29037	−0.188907
$148$	6.20232	0.509827
$149$	−7.48083	−0.612853	−0.306427	−	0.951894i	$-0.599133\pi$
$149$	−7.48083	−0.612853	−0.306427	+	0.951894i	$0.599133\pi$
$150$	1.68890	0.137898
$151$	−13.7665	−1.12030	−0.560152	−	0.828390i	$-0.689257\pi$
$151$	−13.7665	−1.12030	−0.560152	+	0.828390i	$0.689257\pi$
$152$	−7.96855	−0.646335
$153$	−3.52344	−0.284853
$154$	−2.08332	−0.167879
$155$	7.09853	0.570167
$156$	12.3813	0.991296
$157$	−7.98351	−0.637153	−0.318577	−	0.947897i	$-0.603205\pi$
$157$	−7.98351	−0.637153	−0.318577	+	0.947897i	$0.603205\pi$
$158$	9.10191	0.724109
$159$	7.60990	0.603504
$160$	−5.56304	−0.439797
$161$	0	0
$162$	9.26702	0.728086
$163$	5.16805	0.404793	0.202396	−	0.979304i	$-0.435127\pi$
$163$	5.16805	0.404793	0.202396	+	0.979304i	$0.435127\pi$
$164$	7.75704	0.605723
$165$	1.51889	0.118245
$166$	3.31300	0.257139
$167$	22.2431	1.72122	0.860610	−	0.509265i	$-0.170083\pi$
$167$	22.2431	1.72122	0.860610	+	0.509265i	$0.170083\pi$
$168$	15.4552	1.19239
$169$	17.5641	1.35109
$170$	5.97497	0.458259
$171$	−1.47215	−0.112578
$172$	−2.37766	−0.181295
$173$	−7.23559	−0.550111	−0.275056	−	0.961428i	$-0.588696\pi$
$173$	−7.23559	−0.550111	−0.275056	+	0.961428i	$0.588696\pi$
$174$	−8.97070	−0.680067
$175$	−2.86688	−0.216716
$176$	0.157841	0.0118977
$177$	3.93174	0.295528
$178$	6.82759	0.511750
$179$	−22.8751	−1.70977	−0.854884	−	0.518819i	$-0.826372\pi$
$179$	−22.8751	−1.70977	−0.854884	+	0.518819i	$0.826372\pi$
$180$	−0.631846	−0.0470950
$181$	−18.3540	−1.36424	−0.682119	−	0.731241i	$-0.738942\pi$
$181$	−18.3540	−1.36424	−0.682119	+	0.731241i	$0.738942\pi$
$182$	14.2472	1.05607
$183$	23.0928	1.70707
$184$	0	0
$185$	−5.20340	−0.382561
$186$	11.9887	0.879056
$187$	5.37350	0.392949
$188$	1.83522	0.133847
$189$	−13.3041	−0.967730
$190$	2.49643	0.181110
$191$	−5.67322	−0.410500	−0.205250	−	0.978710i	$-0.565801\pi$
$191$	−5.67322	−0.410500	−0.205250	+	0.978710i	$0.565801\pi$
$192$	−10.1291	−0.731006
$193$	21.1943	1.52560	0.762800	−	0.646635i	$-0.223824\pi$
$193$	21.1943	1.52560	0.762800	+	0.646635i	$0.223824\pi$
$194$	4.90580	0.352216
$195$	−10.3872	−0.743843
$196$	−1.45305	−0.103789
$197$	−5.71154	−0.406931	−0.203465	−	0.979082i	$-0.565220\pi$
$197$	−5.71154	−0.406931	−0.203465	+	0.979082i	$0.565220\pi$
$198$	0.385204	0.0273752
$199$	14.9011	1.05631	0.528155	−	0.849148i	$-0.322884\pi$
$199$	14.9011	1.05631	0.528155	+	0.849148i	$0.322884\pi$
$200$	2.86927	0.202888
$201$	−18.4969	−1.30467
$202$	−12.8618	−0.904950
$203$	15.2276	1.06877
$204$	−14.8862	−1.04224
$205$	−6.50772	−0.454519
$206$	−11.1672	−0.778057
$207$	0	0
$208$	−1.07942	−0.0748445
$209$	2.24513	0.155299
$210$	−4.84189	−0.334122
$211$	19.6267	1.35116	0.675578	−	0.737288i	$-0.263894\pi$
$211$	19.6267	1.35116	0.675578	+	0.737288i	$0.263894\pi$
$212$	4.82785	0.331578
$213$	−4.46110	−0.305669
$214$	−3.79143	−0.259177
$215$	1.99472	0.136039
$216$	13.3152	0.905983
$217$	−20.3507	−1.38149
$218$	−11.5844	−0.784595
$219$	14.0482	0.949288
$220$	0.963609	0.0649665
$221$	−36.7476	−2.47191
$222$	−8.78804	−0.589815
$223$	22.7125	1.52094	0.760471	−	0.649372i	$-0.224968\pi$
$223$	22.7125	1.52094	0.760471	+	0.649372i	$0.224968\pi$
$224$	15.9486	1.06561
$225$	0.530083	0.0353389
$226$	−17.8545	−1.18766
$227$	8.17674	0.542709	0.271355	−	0.962479i	$-0.412528\pi$
$227$	8.17674	0.542709	0.271355	+	0.962479i	$0.412528\pi$
$228$	−6.21967	−0.411907
$229$	16.5764	1.09540	0.547701	−	0.836674i	$-0.315503\pi$
$229$	16.5764	1.09540	0.547701	+	0.836674i	$0.315503\pi$
$230$	0	0
$231$	−4.35448	−0.286504
$232$	−15.2403	−1.00057
$233$	−10.6718	−0.699132	−0.349566	−	0.936912i	$-0.613671\pi$
$233$	−10.6718	−0.699132	−0.349566	+	0.936912i	$0.613671\pi$
$234$	−2.63428	−0.172209
$235$	−1.53965	−0.100436
$236$	2.49436	0.162369
$237$	19.0245	1.23577
$238$	−17.1295	−1.11034
$239$	15.5592	1.00644	0.503221	−	0.864158i	$-0.332148\pi$
$239$	15.5592	1.00644	0.503221	+	0.864158i	$0.332148\pi$
$240$	0.366841	0.0236795
$241$	6.21641	0.400434	0.200217	−	0.979752i	$-0.435835\pi$
$241$	6.21641	0.400434	0.200217	+	0.979752i	$0.435835\pi$
$242$	9.30046	0.597856
$243$	5.44775	0.349473
$244$	14.6505	0.937900
$245$	1.21903	0.0778808
$246$	−10.9909	−0.700755
$247$	−15.3537	−0.976934
$248$	20.3676	1.29334
$249$	6.92471	0.438835
$250$	−0.898902	−0.0568516
$251$	7.74211	0.488677	0.244339	−	0.969690i	$-0.421429\pi$
$251$	7.74211	0.488677	0.244339	+	0.969690i	$0.421429\pi$
$252$	1.81143	0.114109
$253$	0	0
$254$	−14.5381	−0.912202
$255$	12.4887	0.782070
$256$	−16.4273	−1.02671
$257$	18.2781	1.14016	0.570079	−	0.821590i	$-0.306913\pi$
$257$	18.2781	1.14016	0.570079	+	0.821590i	$0.306913\pi$
$258$	3.36889	0.209738
$259$	14.9175	0.926931
$260$	−6.58981	−0.408683
$261$	−2.81556	−0.174279
$262$	−6.36273	−0.393091
$263$	15.9528	0.983693	0.491846	−	0.870682i	$-0.336322\pi$
$263$	15.9528	0.983693	0.491846	+	0.870682i	$0.336322\pi$
$264$	4.35811	0.268223
$265$	−4.05029	−0.248808
$266$	−7.15699	−0.438823
$267$	14.2708	0.873357
$268$	−11.7347	−0.716813
$269$	18.8599	1.14991	0.574954	−	0.818186i	$-0.305020\pi$
$269$	18.8599	1.14991	0.574954	+	0.818186i	$0.305020\pi$
$270$	−4.17145	−0.253867
$271$	27.5808	1.67541	0.837707	−	0.546120i	$-0.183896\pi$
$271$	27.5808	1.67541	0.837707	+	0.546120i	$0.183896\pi$
$272$	1.29780	0.0786908
$273$	29.7789	1.80230
$274$	−6.20285	−0.374728
$275$	−0.808414	−0.0487492
$276$	0	0
$277$	0.230620	0.0138566	0.00692831	−	0.999976i	$-0.497795\pi$
$277$	0.230620	0.0138566	0.00692831	+	0.999976i	$0.497795\pi$
$278$	−3.61235	−0.216654
$279$	3.76281	0.225274
$280$	−8.22588	−0.491590
$281$	−8.79634	−0.524746	−0.262373	−	0.964967i	$-0.584505\pi$
$281$	−8.79634	−0.524746	−0.262373	+	0.964967i	$0.584505\pi$
$282$	−2.60032	−0.154847
$283$	−10.6824	−0.635002	−0.317501	−	0.948258i	$-0.602844\pi$
$283$	−10.6824	−0.635002	−0.317501	+	0.948258i	$0.602844\pi$
$284$	−2.83020	−0.167941
$285$	5.21795	0.309085
$286$	4.01747	0.237558
$287$	18.6569	1.10128
$288$	−2.94887	−0.173764
$289$	27.1821	1.59895
$290$	4.77457	0.280372
$291$	10.2539	0.601096
$292$	8.91240	0.521559
$293$	10.9312	0.638605	0.319302	−	0.947653i	$-0.396551\pi$
$293$	10.9312	0.638605	0.319302	+	0.947653i	$0.396551\pi$
$294$	2.05882	0.120073
$295$	−2.09263	−0.121838
$296$	−14.9300	−0.867787
$297$	−3.75153	−0.217686
$298$	6.72454	0.389542
$299$	0	0
$300$	2.23954	0.129300
$301$	−5.71864	−0.329617
$302$	12.3748	0.712088
$303$	−26.8832	−1.54440
$304$	0.542242	0.0310997
$305$	−12.2909	−0.703776
$306$	3.16723	0.181059
$307$	5.52465	0.315309	0.157654	−	0.987494i	$-0.449607\pi$
$307$	5.52465	0.315309	0.157654	+	0.987494i	$0.449607\pi$
$308$	−2.76256	−0.157411
$309$	−23.3413	−1.32784
$310$	−6.38088	−0.362410
$311$	−25.3097	−1.43518	−0.717592	−	0.696464i	$-0.754756\pi$
$311$	−25.3097	−1.43518	−0.717592	+	0.696464i	$0.754756\pi$
$312$	−29.8037	−1.68730
$313$	32.6954	1.84805	0.924027	−	0.382327i	$-0.124877\pi$
$313$	32.6954	1.84805	0.924027	+	0.382327i	$0.124877\pi$
$314$	7.17640	0.404987
$315$	−1.51969	−0.0856247
$316$	12.0694	0.678959
$317$	−11.5202	−0.647039	−0.323520	−	0.946221i	$-0.604866\pi$
$317$	−11.5202	−0.647039	−0.323520	+	0.946221i	$0.604866\pi$
$318$	−6.84056	−0.383599
$319$	4.29393	0.240414
$320$	5.39112	0.301373
$321$	−7.92471	−0.442314
$322$	0	0
$323$	18.4600	1.02714
$324$	12.2884	0.682688
$325$	5.52848	0.306665
$326$	−4.64557	−0.257294
$327$	−24.2133	−1.33900
$328$	−18.6724	−1.03101
$329$	4.41400	0.243352
$330$	−1.36533	−0.0751592
$331$	−19.8433	−1.09069	−0.545343	−	0.838213i	$-0.683601\pi$
$331$	−19.8433	−1.09069	−0.545343	+	0.838213i	$0.683601\pi$
$332$	4.39315	0.241105
$333$	−2.75823	−0.151150
$334$	−19.9943	−1.09404
$335$	9.84478	0.537878
$336$	−1.05169	−0.0573744
$337$	27.2455	1.48416	0.742078	−	0.670313i	$-0.233840\pi$
$337$	27.2455	1.48416	0.742078	+	0.670313i	$0.233840\pi$
$338$	−15.7884	−0.858778
$339$	−37.3187	−2.02687
$340$	7.92301	0.429686
$341$	−5.73855	−0.310760
$342$	1.32332	0.0715568
$343$	16.5734	0.894879
$344$	5.72340	0.308585
$345$	0	0
$346$	6.50409	0.349662
$347$	−6.06063	−0.325352	−0.162676	−	0.986680i	$-0.552012\pi$
$347$	−6.06063	−0.325352	−0.162676	+	0.986680i	$0.552012\pi$
$348$	−11.8954	−0.637663
$349$	−0.0963116	−0.00515544	−0.00257772	−	0.999997i	$-0.500821\pi$
$349$	−0.0963116	−0.00515544	−0.00257772	+	0.999997i	$0.500821\pi$
$350$	2.57705	0.137749
$351$	25.6555	1.36939
$352$	4.49724	0.239704
$353$	−18.8927	−1.00556	−0.502778	−	0.864415i	$-0.667689\pi$
$353$	−18.8927	−1.00556	−0.502778	+	0.864415i	$0.667689\pi$
$354$	−3.53425	−0.187843
$355$	2.37438	0.126019
$356$	9.05361	0.479841
$357$	−35.8035	−1.89492
$358$	20.5625	1.08676
$359$	7.34972	0.387903	0.193952	−	0.981011i	$-0.437870\pi$
$359$	7.34972	0.387903	0.193952	+	0.981011i	$0.437870\pi$
$360$	1.52095	0.0801613
$361$	−11.2871	−0.594060
$362$	16.4984	0.867137
$363$	19.4395	1.02031
$364$	18.8922	0.990222
$365$	−7.47700	−0.391364
$366$	−20.7582	−1.08505
$367$	2.76963	0.144574	0.0722868	−	0.997384i	$-0.476970\pi$
$367$	2.76963	0.144574	0.0722868	+	0.997384i	$0.476970\pi$
$368$	0	0
$369$	−3.44963	−0.179581
$370$	4.67735	0.243164
$371$	11.6117	0.602851
$372$	15.8975	0.824245
$373$	15.6752	0.811632	0.405816	−	0.913955i	$-0.366987\pi$
$373$	15.6752	0.811632	0.405816	+	0.913955i	$0.366987\pi$
$374$	−4.83025	−0.249766
$375$	−1.87885	−0.0970235
$376$	−4.41768	−0.227824
$377$	−29.3648	−1.51237
$378$	11.9591	0.615108
$379$	−15.9147	−0.817485	−0.408743	−	0.912650i	$-0.634033\pi$
$379$	−15.9147	−0.817485	−0.408743	+	0.912650i	$0.634033\pi$
$380$	3.31036	0.169818
$381$	−30.3870	−1.55677
$382$	5.09967	0.260922
$383$	−16.5944	−0.847935	−0.423967	−	0.905677i	$-0.639363\pi$
$383$	−16.5944	−0.847935	−0.423967	+	0.905677i	$0.639363\pi$
$384$	−11.7992	−0.602123
$385$	2.31763	0.118117
$386$	−19.0516	−0.969702
$387$	1.05737	0.0537491
$388$	6.50526	0.330254
$389$	−3.68691	−0.186934	−0.0934669	−	0.995622i	$-0.529795\pi$
$389$	−3.68691	−0.186934	−0.0934669	+	0.995622i	$0.529795\pi$
$390$	9.33708	0.472801
$391$	0	0
$392$	3.49772	0.176662
$393$	−13.2991	−0.670853
$394$	5.13412	0.258653
$395$	−10.1256	−0.509474
$396$	0.510793	0.0256683
$397$	11.1938	0.561803	0.280901	−	0.959737i	$-0.409367\pi$
$397$	11.1938	0.561803	0.280901	+	0.959737i	$0.409367\pi$
$398$	−13.3946	−0.671411
$399$	−14.9593	−0.748900
$400$	−0.195247	−0.00976237
$401$	14.7167	0.734915	0.367458	−	0.930040i	$-0.380228\pi$
$401$	14.7167	0.734915	0.367458	+	0.930040i	$0.380228\pi$
$402$	16.6269	0.829274
$403$	39.2441	1.95489
$404$	−17.0551	−0.848524
$405$	−10.3093	−0.512271
$406$	−13.6881	−0.679330
$407$	4.20650	0.208509
$408$	35.8334	1.77402
$409$	−26.1960	−1.29531	−0.647655	−	0.761933i	$-0.724250\pi$
$409$	−26.1960	−1.29531	−0.647655	+	0.761933i	$0.724250\pi$
$410$	5.84981	0.288901
$411$	−12.9650	−0.639514
$412$	−14.8081	−0.729543
$413$	5.99933	0.295208
$414$	0	0
$415$	−3.68561	−0.180919
$416$	−30.7552	−1.50790
$417$	−7.55040	−0.369745
$418$	−2.01815	−0.0987111
$419$	2.99384	0.146259	0.0731293	−	0.997322i	$-0.476701\pi$
$419$	2.99384	0.146259	0.0731293	+	0.997322i	$0.476701\pi$
$420$	−6.42051	−0.313289
$421$	−18.3495	−0.894299	−0.447150	−	0.894459i	$-0.647561\pi$
$421$	−18.3495	−0.894299	−0.447150	+	0.894459i	$0.647561\pi$
$422$	−17.6425	−0.858822
$423$	−0.816142	−0.0396822
$424$	−11.6214	−0.564385
$425$	−6.64696	−0.322425
$426$	4.01009	0.194290
$427$	35.2367	1.70522
$428$	−5.02757	−0.243017
$429$	8.39716	0.405419
$430$	−1.79306	−0.0864691
$431$	−1.59045	−0.0766091	−0.0383046	−	0.999266i	$-0.512196\pi$
$431$	−1.59045	−0.0766091	−0.0383046	+	0.999266i	$0.512196\pi$
$432$	−0.906067	−0.0435932
$433$	−27.8383	−1.33782	−0.668912	−	0.743342i	$-0.733240\pi$
$433$	−27.8383	−1.33782	−0.668912	+	0.743342i	$0.733240\pi$
$434$	18.2933	0.878104
$435$	9.97962	0.478486
$436$	−15.3613	−0.735674
$437$	0	0
$438$	−12.6279	−0.603387
$439$	25.5038	1.21723	0.608614	−	0.793466i	$-0.291726\pi$
$439$	25.5038	1.21723	0.608614	+	0.793466i	$0.291726\pi$
$440$	−2.31956	−0.110581
$441$	0.646186	0.0307707
$442$	33.0325	1.57120
$443$	−8.29735	−0.394219	−0.197109	−	0.980381i	$-0.563155\pi$
$443$	−8.29735	−0.394219	−0.197109	+	0.980381i	$0.563155\pi$
$444$	−11.6532	−0.553038
$445$	−7.59548	−0.360060
$446$	−20.4163	−0.966740
$447$	14.0554	0.664796
$448$	−15.4557	−0.730214
$449$	−22.7503	−1.07365	−0.536826	−	0.843693i	$-0.680377\pi$
$449$	−22.7503	−1.07365	−0.536826	+	0.843693i	$0.680377\pi$
$450$	−0.476493	−0.0224621
$451$	5.26094	0.247728
$452$	−23.6756	−1.11361
$453$	25.8653	1.21526
$454$	−7.35009	−0.344957
$455$	−15.8495	−0.743037
$456$	14.9717	0.701116
$457$	−19.8147	−0.926890	−0.463445	−	0.886126i	$-0.653387\pi$
$457$	−19.8147	−0.926890	−0.463445	+	0.886126i	$0.653387\pi$
$458$	−14.9006	−0.696260
$459$	−30.8459	−1.43977
$460$	0	0
$461$	37.2696	1.73582	0.867909	−	0.496724i	$-0.165464\pi$
$461$	37.2696	1.73582	0.867909	+	0.496724i	$0.165464\pi$
$462$	3.91426	0.182108
$463$	−19.5030	−0.906382	−0.453191	−	0.891413i	$-0.649714\pi$
$463$	−19.5030	−0.906382	−0.453191	+	0.891413i	$0.649714\pi$
$464$	1.03707	0.0481446
$465$	−13.3371	−0.618492
$466$	9.59290	0.444382
$467$	−37.4507	−1.73301	−0.866505	−	0.499169i	$-0.833639\pi$
$467$	−37.4507	−1.73301	−0.866505	+	0.499169i	$0.833639\pi$
$468$	−3.49315	−0.161471
$469$	−28.2239	−1.30326
$470$	1.38399	0.0638389
$471$	14.9998	0.691156
$472$	−6.00433	−0.276371
$473$	−1.61256	−0.0741457
$474$	−17.1011	−0.785482
$475$	−2.77720	−0.127427
$476$	−22.7144	−1.04111
$477$	−2.14699	−0.0983041
$478$	−13.9862	−0.639714
$479$	−19.8888	−0.908741	−0.454370	−	0.890813i	$-0.650136\pi$
$479$	−19.8888	−0.908741	−0.454370	+	0.890813i	$0.650136\pi$
$480$	10.4521	0.477072
$481$	−28.7669	−1.31166
$482$	−5.58794	−0.254524
$483$	0	0
$484$	12.3327	0.560578
$485$	−5.45755	−0.247814
$486$	−4.89700	−0.222132
$487$	−21.2484	−0.962858	−0.481429	−	0.876485i	$-0.659882\pi$
$487$	−21.2484	−0.962858	−0.481429	+	0.876485i	$0.659882\pi$
$488$	−35.2660	−1.59642
$489$	−9.71000	−0.439101
$490$	−1.09579	−0.0495026
$491$	0.488343	0.0220386	0.0110193	−	0.999939i	$-0.496492\pi$
$491$	0.488343	0.0220386	0.0110193	+	0.999939i	$0.496492\pi$
$492$	−14.5743	−0.657061
$493$	35.3057	1.59009
$494$	13.8015	0.620959
$495$	−0.428527	−0.0192609
$496$	−1.38597	−0.0622319
$497$	−6.80706	−0.305338
$498$	−6.22463	−0.278933
$499$	5.18326	0.232035	0.116017	−	0.993247i	$-0.462987\pi$
$499$	5.18326	0.232035	0.116017	+	0.993247i	$0.462987\pi$
$500$	−1.19197	−0.0533067
$501$	−41.7914	−1.86710
$502$	−6.95940	−0.310613
$503$	32.2440	1.43769	0.718845	−	0.695171i	$-0.244671\pi$
$503$	32.2440	1.43769	0.718845	+	0.695171i	$0.244671\pi$
$504$	−4.36040	−0.194228
$505$	14.3083	0.636711
$506$	0	0
$507$	−33.0004	−1.46560
$508$	−19.2780	−0.855323
$509$	9.33792	0.413896	0.206948	−	0.978352i	$-0.433647\pi$
$509$	9.33792	0.413896	0.206948	+	0.978352i	$0.433647\pi$
$510$	−11.2261	−0.497099
$511$	21.4357	0.948260
$512$	2.20661	0.0975191
$513$	−12.8879	−0.569015
$514$	−16.4302	−0.724707
$515$	12.4232	0.547431
$516$	4.46727	0.196660
$517$	1.24467	0.0547407
$518$	−13.4094	−0.589176
$519$	13.5946	0.596736
$520$	15.8627	0.695627
$521$	19.6206	0.859592	0.429796	−	0.902926i	$-0.358585\pi$
$521$	19.6206	0.859592	0.429796	+	0.902926i	$0.358585\pi$
$522$	2.53092	0.110775
$523$	−21.1423	−0.924486	−0.462243	−	0.886753i	$-0.652955\pi$
$523$	−21.1423	−0.924486	−0.462243	+	0.886753i	$0.652955\pi$
$524$	−8.43720	−0.368581
$525$	5.38645	0.235084
$526$	−14.3400	−0.625255
$527$	−47.1836	−2.05535
$528$	−0.296560	−0.0129061
$529$	0	0
$530$	3.64082	0.158147
$531$	−1.10927	−0.0481381
$532$	−9.49041	−0.411461
$533$	−35.9778	−1.55837
$534$	−12.8280	−0.555123
$535$	4.21785	0.182353
$536$	28.2474	1.22010
$537$	42.9790	1.85468
$538$	−16.9532	−0.730905
$539$	−0.985479	−0.0424476
$540$	−5.53149	−0.238037
$541$	32.9219	1.41542	0.707712	−	0.706501i	$-0.249727\pi$
$541$	32.9219	1.41542	0.707712	+	0.706501i	$0.249727\pi$
$542$	−24.7924	−1.06493
$543$	34.4844	1.47987
$544$	36.9773	1.58539
$545$	12.8873	0.552031
$546$	−26.7683	−1.14558
$547$	10.3355	0.441915	0.220957	−	0.975283i	$-0.429082\pi$
$547$	10.3355	0.441915	0.220957	+	0.975283i	$0.429082\pi$
$548$	−8.22519	−0.351363
$549$	−6.51521	−0.278062
$550$	0.726686	0.0309860
$551$	14.7513	0.628425
$552$	0	0
$553$	29.0289	1.23443
$554$	−0.207305	−0.00880755
$555$	9.77641	0.414986
$556$	−4.79010	−0.203145
$557$	20.2564	0.858289	0.429145	−	0.903236i	$-0.358815\pi$
$557$	20.2564	0.858289	0.429145	+	0.903236i	$0.358815\pi$
$558$	−3.38240	−0.143188
$559$	11.0278	0.466426
$560$	0.559752	0.0236538
$561$	−10.0960	−0.426254
$562$	7.90705	0.333539
$563$	−41.7555	−1.75978	−0.879892	−	0.475174i	$-0.842385\pi$
$563$	−41.7555	−1.75978	−0.879892	+	0.475174i	$0.842385\pi$
$564$	−3.44811	−0.145192
$565$	19.8625	0.835622
$566$	9.60242	0.403620
$567$	29.5555	1.24121
$568$	6.81273	0.285856
$569$	10.6925	0.448251	0.224125	−	0.974560i	$-0.428047\pi$
$569$	10.6925	0.448251	0.224125	+	0.974560i	$0.428047\pi$
$570$	−4.69043	−0.196460
$571$	12.7521	0.533660	0.266830	−	0.963744i	$-0.414024\pi$
$571$	12.7521	0.533660	0.266830	+	0.963744i	$0.414024\pi$
$572$	5.32730	0.222746
$573$	10.6591	0.445292
$574$	−16.7707	−0.699996
$575$	0	0
$576$	2.85774	0.119073
$577$	−0.215423	−0.00896817	−0.00448409	−	0.999990i	$-0.501427\pi$
$577$	−0.215423	−0.00896817	−0.00448409	+	0.999990i	$0.501427\pi$
$578$	−24.4341	−1.01632
$579$	−39.8210	−1.65490
$580$	6.33123	0.262890
$581$	10.5662	0.438360
$582$	−9.21727	−0.382068
$583$	3.27432	0.135608
$584$	−21.4536	−0.887755
$585$	2.93056	0.121164
$586$	−9.82604	−0.405910
$587$	19.5311	0.806136	0.403068	−	0.915170i	$-0.367944\pi$
$587$	19.5311	0.806136	0.403068	+	0.915170i	$0.367944\pi$
$588$	2.73006	0.112586
$589$	−19.7141	−0.812303
$590$	1.88107	0.0774424
$591$	10.7311	0.441420
$592$	1.01595	0.0417553
$593$	−15.0434	−0.617759	−0.308879	−	0.951101i	$-0.599954\pi$
$593$	−15.0434	−0.617759	−0.308879	+	0.951101i	$0.599954\pi$
$594$	3.37226	0.138366
$595$	19.0561	0.781223
$596$	8.91696	0.365253
$597$	−27.9969	−1.14584
$598$	0	0
$599$	−18.9446	−0.774057	−0.387028	−	0.922068i	$-0.626498\pi$
$599$	−18.9446	−0.774057	−0.387028	+	0.922068i	$0.626498\pi$
$600$	−5.39094	−0.220084
$601$	36.9163	1.50585	0.752923	−	0.658109i	$-0.228643\pi$
$601$	36.9163	1.50585	0.752923	+	0.658109i	$0.228643\pi$
$602$	5.14050	0.209511
$603$	5.21855	0.212516
$604$	16.4094	0.667687
$605$	−10.3465	−0.420644
$606$	24.1653	0.981650
$607$	18.3248	0.743781	0.371891	−	0.928277i	$-0.378710\pi$
$607$	18.3248	0.743781	0.371891	+	0.928277i	$0.378710\pi$
$608$	15.4497	0.626568
$609$	−28.6104	−1.15935
$610$	11.0483	0.447334
$611$	−8.51193	−0.344356
$612$	4.19985	0.169769
$613$	23.3513	0.943150	0.471575	−	0.881826i	$-0.343686\pi$
$613$	23.3513	0.943150	0.471575	+	0.881826i	$0.343686\pi$
$614$	−4.96612	−0.200416
$615$	12.2270	0.493042
$616$	6.64992	0.267933
$617$	22.4316	0.903064	0.451532	−	0.892255i	$-0.350878\pi$
$617$	22.4316	0.903064	0.451532	+	0.892255i	$0.350878\pi$
$618$	20.9816	0.844002
$619$	−22.3734	−0.899264	−0.449632	−	0.893214i	$-0.648445\pi$
$619$	−22.3734	−0.899264	−0.449632	+	0.893214i	$0.648445\pi$
$620$	−8.46126	−0.339813
$621$	0	0
$622$	22.7510	0.912231
$623$	21.7754	0.872411
$624$	2.02807	0.0811880
$625$	1.00000	0.0400000
$626$	−29.3900	−1.17466
$627$	−4.21827	−0.168461
$628$	9.51614	0.379735
$629$	34.5868	1.37907
$630$	1.36605	0.0544248
$631$	−21.2674	−0.846641	−0.423321	−	0.905980i	$-0.639136\pi$
$631$	−21.2674	−0.846641	−0.423321	+	0.905980i	$0.639136\pi$
$632$	−29.0531	−1.15567
$633$	−36.8756	−1.46567
$634$	10.3555	0.411271
$635$	16.1732	0.641813
$636$	−9.07081	−0.359681
$637$	6.73937	0.267024
$638$	−3.85983	−0.152812
$639$	1.25862	0.0497901
$640$	6.27998	0.248238
$641$	−15.9591	−0.630347	−0.315173	−	0.949034i	$-0.602063\pi$
$641$	−15.9591	−0.630347	−0.315173	+	0.949034i	$0.602063\pi$
$642$	7.12354	0.281144
$643$	8.51331	0.335732	0.167866	−	0.985810i	$-0.446312\pi$
$643$	8.51331	0.335732	0.167866	+	0.985810i	$0.446312\pi$
$644$	0	0
$645$	−3.74779	−0.147569
$646$	−16.5937	−0.652871
$647$	5.79981	0.228014	0.114007	−	0.993480i	$-0.463631\pi$
$647$	5.79981	0.228014	0.114007	+	0.993480i	$0.463631\pi$
$648$	−29.5801	−1.16202
$649$	1.69171	0.0664055
$650$	−4.96957	−0.194922
$651$	38.2359	1.49858
$652$	−6.16018	−0.241251
$653$	14.4983	0.567361	0.283681	−	0.958919i	$-0.408444\pi$
$653$	14.4983	0.567361	0.283681	+	0.958919i	$0.408444\pi$
$654$	21.7654	0.851094
$655$	7.07834	0.276574
$656$	1.27062	0.0496092
$657$	−3.96343	−0.154628
$658$	−3.96775	−0.154679
$659$	−34.1740	−1.33123	−0.665615	−	0.746295i	$-0.731831\pi$
$659$	−34.1740	−1.33123	−0.665615	+	0.746295i	$0.731831\pi$
$660$	−1.81048	−0.0704728
$661$	−18.5243	−0.720513	−0.360256	−	0.932853i	$-0.617311\pi$
$661$	−18.5243	−0.720513	−0.360256	+	0.932853i	$0.617311\pi$
$662$	17.8372	0.693262
$663$	69.0433	2.68142
$664$	−10.5750	−0.410390
$665$	7.96192	0.308750
$666$	2.47938	0.0960741
$667$	0	0
$668$	−26.5132	−1.02583
$669$	−42.6734	−1.64985
$670$	−8.84950	−0.341886
$671$	9.93616	0.383581
$672$	−29.9650	−1.15593
$673$	−38.1762	−1.47158	−0.735791	−	0.677208i	$-0.763190\pi$
$673$	−38.1762	−1.47158	−0.735791	+	0.677208i	$0.763190\pi$
$674$	−24.4910	−0.943360
$675$	4.64061	0.178617
$676$	−20.9360	−0.805231
$677$	34.3559	1.32040	0.660202	−	0.751088i	$-0.270471\pi$
$677$	34.3559	1.32040	0.660202	+	0.751088i	$0.270471\pi$
$678$	33.5459	1.28832
$679$	15.6462	0.600444
$680$	−19.0720	−0.731376
$681$	−15.3629	−0.588707
$682$	5.15840	0.197525
$683$	−9.17694	−0.351146	−0.175573	−	0.984466i	$-0.556178\pi$
$683$	−9.17694	−0.351146	−0.175573	+	0.984466i	$0.556178\pi$
$684$	1.75476	0.0670951
$685$	6.90047	0.263653
$686$	−14.8979	−0.568803
$687$	−31.1447	−1.18824
$688$	−0.389464	−0.0148482
$689$	−22.3920	−0.853067
$690$	0	0
$691$	−14.2825	−0.543333	−0.271666	−	0.962392i	$-0.587575\pi$
$691$	−14.2825	−0.543333	−0.271666	+	0.962392i	$0.587575\pi$
$692$	8.62464	0.327859
$693$	1.22854	0.0466683
$694$	5.44791	0.206800
$695$	4.01862	0.152435
$696$	28.6342	1.08538
$697$	43.2566	1.63846
$698$	0.0865748	0.00327690
$699$	20.0507	0.758387
$700$	3.41725	0.129160
$701$	40.7374	1.53863	0.769315	−	0.638870i	$-0.220598\pi$
$701$	40.7374	1.53863	0.769315	+	0.638870i	$0.220598\pi$
$702$	−23.0618	−0.870412
$703$	14.4509	0.545026
$704$	−4.35826	−0.164258
$705$	2.89277	0.108948
$706$	16.9827	0.639152
$707$	−41.0202	−1.54272
$708$	−4.68653	−0.176131
$709$	25.3819	0.953237	0.476618	−	0.879110i	$-0.341862\pi$
$709$	25.3819	0.953237	0.476618	+	0.879110i	$0.341862\pi$
$710$	−2.13433	−0.0801000
$711$	−5.36740	−0.201293
$712$	−21.7935	−0.816746
$713$	0	0
$714$	32.1839	1.20445
$715$	−4.46931	−0.167143
$716$	27.2666	1.01900
$717$	−29.2334	−1.09174
$718$	−6.60668	−0.246559
$719$	9.03209	0.336840	0.168420	−	0.985715i	$-0.446134\pi$
$719$	9.03209	0.336840	0.168420	+	0.985715i	$0.446134\pi$
$720$	−0.103497	−0.00385712
$721$	−35.6158	−1.32640
$722$	10.1460	0.377597
$723$	−11.6797	−0.434373
$724$	21.8774	0.813069
$725$	−5.31155	−0.197266
$726$	−17.4742	−0.648528
$727$	−36.3041	−1.34644	−0.673222	−	0.739440i	$-0.735090\pi$
$727$	−36.3041	−1.34644	−0.673222	+	0.739440i	$0.735090\pi$
$728$	−45.4766	−1.68548
$729$	20.6923	0.766380
$730$	6.72110	0.248759
$731$	−13.2588	−0.490396
$732$	−27.5261	−1.01739
$733$	2.43074	0.0897815	0.0448908	−	0.998992i	$-0.485706\pi$
$733$	2.43074	0.0897815	0.0448908	+	0.998992i	$0.485706\pi$
$734$	−2.48963	−0.0918939
$735$	−2.29037	−0.0844816
$736$	0	0
$737$	−7.95866	−0.293161
$738$	3.10088	0.114145
$739$	28.8962	1.06296	0.531482	−	0.847069i	$-0.321635\pi$
$739$	28.8962	1.06296	0.531482	+	0.847069i	$0.321635\pi$
$740$	6.20232	0.228002
$741$	28.8474	1.05973
$742$	−10.4378	−0.383184
$743$	10.9589	0.402044	0.201022	−	0.979587i	$-0.435574\pi$
$743$	10.9589	0.402044	0.201022	+	0.979587i	$0.435574\pi$
$744$	−38.2677	−1.40296
$745$	−7.48083	−0.274076
$746$	−14.0905	−0.515889
$747$	−1.95368	−0.0714813
$748$	−6.40507	−0.234193
$749$	−12.0921	−0.441835
$750$	1.68890	0.0616701
$751$	42.3613	1.54578	0.772892	−	0.634537i	$-0.218809\pi$
$751$	42.3613	1.54578	0.772892	+	0.634537i	$0.218809\pi$
$752$	0.300613	0.0109622
$753$	−14.5463	−0.530095
$754$	26.3961	0.961290
$755$	−13.7665	−0.501015
$756$	15.8581	0.576755
$757$	−37.0209	−1.34555	−0.672773	−	0.739849i	$-0.734897\pi$
$757$	−37.0209	−1.34555	−0.672773	+	0.739849i	$0.734897\pi$
$758$	14.3058	0.519610
$759$	0	0
$760$	−7.96855	−0.289050
$761$	−13.9476	−0.505599	−0.252800	−	0.967519i	$-0.581351\pi$
$761$	−13.9476	−0.505599	−0.252800	+	0.967519i	$0.581351\pi$
$762$	27.3149	0.989516
$763$	−36.9464	−1.33755
$764$	6.76233	0.244653
$765$	−3.52344	−0.127390
$766$	14.9168	0.538964
$767$	−11.5691	−0.417735
$768$	30.8645	1.11373
$769$	16.1501	0.582387	0.291193	−	0.956664i	$-0.405948\pi$
$769$	16.1501	0.582387	0.291193	+	0.956664i	$0.405948\pi$
$770$	−2.08332	−0.0750778
$771$	−34.3419	−1.23679
$772$	−25.2631	−0.909238
$773$	−36.8847	−1.32665	−0.663326	−	0.748331i	$-0.730856\pi$
$773$	−36.8847	−1.32665	−0.663326	+	0.748331i	$0.730856\pi$
$774$	−0.950471	−0.0341640
$775$	7.09853	0.254987
$776$	−15.6592	−0.562132
$777$	−28.0278	−1.00549
$778$	3.31417	0.118819
$779$	18.0733	0.647542
$780$	12.3813	0.443321
$781$	−1.91948	−0.0686844
$782$	0	0
$783$	−24.6488	−0.880877
$784$	−0.238012	−0.00850043
$785$	−7.98351	−0.284944
$786$	11.9546	0.426408
$787$	29.0947	1.03711	0.518557	−	0.855043i	$-0.326470\pi$
$787$	29.0947	1.03711	0.518557	+	0.855043i	$0.326470\pi$
$788$	6.80802	0.242526
$789$	−29.9730	−1.06707
$790$	9.10191	0.323832
$791$	−56.9435	−2.02468
$792$	−1.22956	−0.0436905
$793$	−67.9502	−2.41298
$794$	−10.0622	−0.357093
$795$	7.60990	0.269895
$796$	−17.7617	−0.629547
$797$	6.33692	0.224465	0.112233	−	0.993682i	$-0.464200\pi$
$797$	6.33692	0.224465	0.112233	+	0.993682i	$0.464200\pi$
$798$	13.4469	0.476016
$799$	10.2340	0.362053
$800$	−5.56304	−0.196683
$801$	−4.02623	−0.142260
$802$	−13.2288	−0.467127
$803$	6.04452	0.213306
$804$	22.0478	0.777567
$805$	0	0
$806$	−35.2766	−1.24257
$807$	−35.4350	−1.24737
$808$	41.0544	1.44429
$809$	29.3852	1.03313	0.516564	−	0.856248i	$-0.327211\pi$
$809$	29.3852	1.03313	0.516564	+	0.856248i	$0.327211\pi$
$810$	9.26702	0.325610
$811$	−1.36095	−0.0477895	−0.0238947	−	0.999714i	$-0.507607\pi$
$811$	−1.36095	−0.0477895	−0.0238947	+	0.999714i	$0.507607\pi$
$812$	−18.1509	−0.636972
$813$	−51.8202	−1.81741
$814$	−3.78123	−0.132532
$815$	5.16805	0.181029
$816$	−2.43838	−0.0853603
$817$	−5.53975	−0.193811
$818$	23.5477	0.823325
$819$	−8.40157	−0.293575
$820$	7.75704	0.270888
$821$	35.5430	1.24046	0.620230	−	0.784420i	$-0.287039\pi$
$821$	35.5430	1.24046	0.620230	+	0.784420i	$0.287039\pi$
$822$	11.6542	0.406488
$823$	45.9222	1.60075	0.800373	−	0.599502i	$-0.204635\pi$
$823$	45.9222	1.60075	0.800373	+	0.599502i	$0.204635\pi$
$824$	35.6455	1.24177
$825$	1.51889	0.0528810
$826$	−5.39281	−0.187640
$827$	−16.0726	−0.558900	−0.279450	−	0.960160i	$-0.590152\pi$
$827$	−16.0726	−0.558900	−0.279450	+	0.960160i	$0.590152\pi$
$828$	0	0
$829$	25.1985	0.875179	0.437589	−	0.899175i	$-0.355832\pi$
$829$	25.1985	0.875179	0.437589	+	0.899175i	$0.355832\pi$
$830$	3.31300	0.114996
$831$	−0.433301	−0.0150311
$832$	29.8047	1.03329
$833$	−8.10283	−0.280746
$834$	6.78707	0.235017
$835$	22.2431	0.769753
$836$	−2.67614	−0.0925562
$837$	32.9415	1.13862
$838$	−2.69117	−0.0929649
$839$	−47.0623	−1.62477	−0.812386	−	0.583120i	$-0.801832\pi$
$839$	−47.0623	−1.62477	−0.812386	+	0.583120i	$0.801832\pi$
$840$	15.4552	0.533255
$841$	−0.787424	−0.0271526
$842$	16.4944	0.568434
$843$	16.5270	0.569221
$844$	−23.3945	−0.805272
$845$	17.5641	0.604225
$846$	0.733632	0.0252228
$847$	29.6621	1.01920
$848$	0.790810	0.0271565
$849$	20.0706	0.688822
$850$	5.97497	0.204940
$851$	0	0
$852$	5.31752	0.182175
$853$	39.8516	1.36449	0.682247	−	0.731122i	$-0.261003\pi$
$853$	39.8516	1.36449	0.682247	+	0.731122i	$0.261003\pi$
$854$	−31.6743	−1.08387
$855$	−1.47215	−0.0503464
$856$	12.1022	0.413643
$857$	3.08274	0.105304	0.0526522	−	0.998613i	$-0.483233\pi$
$857$	3.08274	0.105304	0.0526522	+	0.998613i	$0.483233\pi$
$858$	−7.54823	−0.257692
$859$	−3.09274	−0.105523	−0.0527614	−	0.998607i	$-0.516802\pi$
$859$	−3.09274	−0.105523	−0.0527614	+	0.998607i	$0.516802\pi$
$860$	−2.37766	−0.0810775
$861$	−35.0535	−1.19462
$862$	1.42966	0.0486943
$863$	16.0204	0.545342	0.272671	−	0.962107i	$-0.412093\pi$
$863$	16.0204	0.545342	0.272671	+	0.962107i	$0.412093\pi$
$864$	−25.8159	−0.878274
$865$	−7.23559	−0.246017
$866$	25.0239	0.850348
$867$	−51.0711	−1.73447
$868$	24.2575	0.823352
$869$	8.18567	0.277680
$870$	−8.97070	−0.304135
$871$	54.4267	1.84418
$872$	36.9772	1.25220
$873$	−2.89295	−0.0979117
$874$	0	0
$875$	−2.86688	−0.0969184
$876$	−16.7451	−0.565764
$877$	8.23037	0.277920	0.138960	−	0.990298i	$-0.455624\pi$
$877$	8.23037	0.277920	0.138960	+	0.990298i	$0.455624\pi$
$878$	−22.9254	−0.773695
$879$	−20.5380	−0.692730
$880$	0.157841	0.00532081
$881$	−2.58489	−0.0870870	−0.0435435	−	0.999052i	$-0.513865\pi$
$881$	−2.58489	−0.0870870	−0.0435435	+	0.999052i	$0.513865\pi$
$882$	−0.580858	−0.0195585
$883$	28.4853	0.958608	0.479304	−	0.877649i	$-0.340889\pi$
$883$	28.4853	0.958608	0.479304	+	0.877649i	$0.340889\pi$
$884$	43.8022	1.47323
$885$	3.93174	0.132164
$886$	7.45851	0.250573
$887$	−57.0558	−1.91575	−0.957873	−	0.287193i	$-0.907278\pi$
$887$	−57.0558	−1.91575	−0.957873	+	0.287193i	$0.907278\pi$
$888$	28.0512	0.941337
$889$	−46.3666	−1.55509
$890$	6.82759	0.228861
$891$	8.33416	0.279205
$892$	−27.0727	−0.906462
$893$	4.27592	0.143088
$894$	−12.6344	−0.422558
$895$	−22.8751	−0.764632
$896$	−18.0040	−0.601471
$897$	0	0
$898$	20.4503	0.682434
$899$	−37.7042	−1.25751
$900$	−0.631846	−0.0210615
$901$	26.9222	0.896907
$902$	−4.72907	−0.157461
$903$	10.7445	0.357554
$904$	56.9910	1.89549
$905$	−18.3540	−0.610106
$906$	−23.2503	−0.772441
$907$	−11.6389	−0.386464	−0.193232	−	0.981153i	$-0.561897\pi$
$907$	−11.6389	−0.386464	−0.193232	+	0.981153i	$0.561897\pi$
$908$	−9.74646	−0.323448
$909$	7.58459	0.251565
$910$	14.2472	0.472289
$911$	26.0769	0.863965	0.431982	−	0.901882i	$-0.357814\pi$
$911$	26.0769	0.863965	0.431982	+	0.901882i	$0.357814\pi$
$912$	−1.01879	−0.0337356
$913$	2.97950	0.0986069
$914$	17.8114	0.589150
$915$	23.0928	0.763425
$916$	−19.7587	−0.652846
$917$	−20.2928	−0.670126
$918$	27.7275	0.915143
$919$	−9.60201	−0.316741	−0.158371	−	0.987380i	$-0.550624\pi$
$919$	−9.60201	−0.316741	−0.158371	+	0.987380i	$0.550624\pi$
$920$	0	0
$921$	−10.3800	−0.342033
$922$	−33.5017	−1.10332
$923$	13.1267	0.432071
$924$	5.19043	0.170753
$925$	−5.20340	−0.171087
$926$	17.5313	0.576114
$927$	6.58532	0.216290
$928$	29.5484	0.969973
$929$	−6.74887	−0.221423	−0.110712	−	0.993853i	$-0.535313\pi$
$929$	−6.74887	−0.221423	−0.110712	+	0.993853i	$0.535313\pi$
$930$	11.9887	0.393126
$931$	−3.38549	−0.110955
$932$	12.7205	0.416674
$933$	47.5532	1.55682
$934$	33.6645	1.10154
$935$	5.37350	0.175732
$936$	8.40857	0.274843
$937$	48.0371	1.56930	0.784652	−	0.619937i	$-0.212842\pi$
$937$	48.0371	1.56930	0.784652	+	0.619937i	$0.212842\pi$
$938$	25.3705	0.828376
$939$	−61.4298	−2.00469
$940$	1.83522	0.0598584
$941$	52.2630	1.70372	0.851862	−	0.523766i	$-0.175473\pi$
$941$	52.2630	1.70372	0.851862	+	0.523766i	$0.175473\pi$
$942$	−13.4834	−0.439312
$943$	0	0
$944$	0.408581	0.0132982
$945$	−13.3041	−0.432782
$946$	1.44954	0.0471285
$947$	8.45510	0.274754	0.137377	−	0.990519i	$-0.456133\pi$
$947$	8.45510	0.274754	0.137377	+	0.990519i	$0.456133\pi$
$948$	−22.6767	−0.736505
$949$	−41.3365	−1.34184
$950$	2.49643	0.0809950
$951$	21.6448	0.701880
$952$	54.6771	1.77209
$953$	31.4414	1.01849	0.509244	−	0.860622i	$-0.329925\pi$
$953$	31.4414	1.01849	0.509244	+	0.860622i	$0.329925\pi$
$954$	1.92994	0.0624840
$955$	−5.67322	−0.183581
$956$	−18.5462	−0.599826
$957$	−8.06767	−0.260791
$958$	17.8781	0.577614
$959$	−19.7829	−0.638822
$960$	−10.1291	−0.326916
$961$	19.3891	0.625454
$962$	25.8586	0.833716
$963$	2.23581	0.0720480
$964$	−7.40980	−0.238654
$965$	21.1943	0.682269
$966$	0	0
$967$	37.7078	1.21260	0.606300	−	0.795236i	$-0.292653\pi$
$967$	37.7078	1.21260	0.606300	+	0.795236i	$0.292653\pi$
$968$	−29.6868	−0.954171
$969$	−34.6835	−1.11420
$970$	4.90580	0.157516
$971$	−14.5374	−0.466528	−0.233264	−	0.972413i	$-0.574941\pi$
$971$	−14.5374	−0.466528	−0.233264	+	0.972413i	$0.574941\pi$
$972$	−6.49358	−0.208282
$973$	−11.5209	−0.369344
$974$	19.1003	0.612011
$975$	−10.3872	−0.332657
$976$	2.39977	0.0768148
$977$	8.69125	0.278058	0.139029	−	0.990288i	$-0.455602\pi$
$977$	8.69125	0.278058	0.139029	+	0.990288i	$0.455602\pi$
$978$	8.72834	0.279102
$979$	6.14029	0.196245
$980$	−1.45305	−0.0464159
$981$	6.83133	0.218108
$982$	−0.438973	−0.0140082
$983$	36.9954	1.17997	0.589985	−	0.807414i	$-0.299134\pi$
$983$	36.9954	1.17997	0.589985	+	0.807414i	$0.299134\pi$
$984$	35.0827	1.11840
$985$	−5.71154	−0.181985
$986$	−31.7364	−1.01069
$987$	−8.29325	−0.263977
$988$	18.3012	0.582240
$989$	0	0
$990$	0.385204	0.0122426
$991$	35.1296	1.11593	0.557965	−	0.829865i	$-0.311582\pi$
$991$	35.1296	1.11593	0.557965	+	0.829865i	$0.311582\pi$
$992$	−39.4894	−1.25379
$993$	37.2826	1.18313
$994$	6.11888	0.194079
$995$	14.9011	0.472396
$996$	−8.25407	−0.261540
$997$	−7.40369	−0.234477	−0.117239	−	0.993104i	$-0.537404\pi$
$997$	−7.40369	−0.234477	−0.117239	+	0.993104i	$0.537404\pi$
$998$	−4.65925	−0.147486
$999$	−24.1469	−0.763975

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2645.2.a.y.1.10		25
23.4	even	11		115.2.g.c.16.4	✓	50
23.6	even	11		115.2.g.c.36.4	yes	50
23.22	odd	2		2645.2.a.x.1.10		25
115.4	even	22		575.2.k.d.476.2		50
115.27	odd	44		575.2.p.d.499.7		100
115.29	even	22		575.2.k.d.151.2		50
115.52	odd	44		575.2.p.d.174.4		100
115.73	odd	44		575.2.p.d.499.4		100
115.98	odd	44		575.2.p.d.174.7		100

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
115.2.g.c.16.4	✓	50	23.4	even	11
115.2.g.c.36.4	yes	50	23.6	even	11
575.2.k.d.151.2		50	115.29	even	22
575.2.k.d.476.2		50	115.4	even	22
575.2.p.d.174.4		100	115.52	odd	44
575.2.p.d.174.7		100	115.98	odd	44
575.2.p.d.499.4		100	115.73	odd	44
575.2.p.d.499.7		100	115.27	odd	44
2645.2.a.x.1.10		25	23.22	odd	2
2645.2.a.y.1.10		25	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:	\( N \)	\(=\)	\( 2645 = 5 \cdot 23^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2645.a (trivial)

\(f(q)\)	\(=\)	\(q-0.898902 q^{2} -1.87885 q^{3} -1.19197 q^{4} +1.00000 q^{5} +1.68890 q^{6} -2.86688 q^{7} +2.86927 q^{8} +0.530083 q^{9} +O(q^{10})\)	\(q-0.898902 q^{2} -1.87885 q^{3} -1.19197 q^{4} +1.00000 q^{5} +1.68890 q^{6} -2.86688 q^{7} +2.86927 q^{8} +0.530083 q^{9} -0.898902 q^{10} -0.808414 q^{11} +2.23954 q^{12} +5.52848 q^{13} +2.57705 q^{14} -1.87885 q^{15} -0.195247 q^{16} -6.64696 q^{17} -0.476493 q^{18} -2.77720 q^{19} -1.19197 q^{20} +5.38645 q^{21} +0.726686 q^{22} -5.39094 q^{24} +1.00000 q^{25} -4.96957 q^{26} +4.64061 q^{27} +3.41725 q^{28} -5.31155 q^{29} +1.68890 q^{30} +7.09853 q^{31} -5.56304 q^{32} +1.51889 q^{33} +5.97497 q^{34} -2.86688 q^{35} -0.631846 q^{36} -5.20340 q^{37} +2.49643 q^{38} -10.3872 q^{39} +2.86927 q^{40} -6.50772 q^{41} -4.84189 q^{42} +1.99472 q^{43} +0.963609 q^{44} +0.530083 q^{45} -1.53965 q^{47} +0.366841 q^{48} +1.21903 q^{49} -0.898902 q^{50} +12.4887 q^{51} -6.58981 q^{52} -4.05029 q^{53} -4.17145 q^{54} -0.808414 q^{55} -8.22588 q^{56} +5.21795 q^{57} +4.77457 q^{58} -2.09263 q^{59} +2.23954 q^{60} -12.2909 q^{61} -6.38088 q^{62} -1.51969 q^{63} +5.39112 q^{64} +5.52848 q^{65} -1.36533 q^{66} +9.84478 q^{67} +7.92301 q^{68} +2.57705 q^{70} +2.37438 q^{71} +1.52095 q^{72} -7.47700 q^{73} +4.67735 q^{74} -1.87885 q^{75} +3.31036 q^{76} +2.31763 q^{77} +9.33708 q^{78} -10.1256 q^{79} -0.195247 q^{80} -10.3093 q^{81} +5.84981 q^{82} -3.68561 q^{83} -6.42051 q^{84} -6.64696 q^{85} -1.79306 q^{86} +9.97962 q^{87} -2.31956 q^{88} -7.59548 q^{89} -0.476493 q^{90} -15.8495 q^{91} -13.3371 q^{93} +1.38399 q^{94} -2.77720 q^{95} +10.4521 q^{96} -5.45755 q^{97} -1.09579 q^{98} -0.428527 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 25 q + 3 q^{2} + 10 q^{3} + 33 q^{4} + 25 q^{5} + 22 q^{6} + 14 q^{7} + 21 q^{8} + 29 q^{9}+O(q^{10}) \) 25 * q + 3 * q^2 + 10 * q^3 + 33 * q^4 + 25 * q^5 + 22 * q^6 + 14 * q^7 + 21 * q^8 + 29 * q^9	\( 25 q + 3 q^{2} + 10 q^{3} + 33 q^{4} + 25 q^{5} + 22 q^{6} + 14 q^{7} + 21 q^{8} + 29 q^{9} + 3 q^{10} - 8 q^{11} + 34 q^{12} + 15 q^{13} - 6 q^{14} + 10 q^{15} + 41 q^{16} + 19 q^{17} + 23 q^{18} - 8 q^{19} + 33 q^{20} - 21 q^{21} + 3 q^{22} + 51 q^{24} + 25 q^{25} + 7 q^{26} + 64 q^{27} + 27 q^{28} + 3 q^{29} + 22 q^{30} + 34 q^{31} + 30 q^{32} - q^{33} - 21 q^{34} + 14 q^{35} + 31 q^{36} - q^{37} - 7 q^{38} + 49 q^{39} + 21 q^{40} - 29 q^{42} + 25 q^{43} - 33 q^{44} + 29 q^{45} - 5 q^{47} + 42 q^{48} + 33 q^{49} + 3 q^{50} + 23 q^{51} + 67 q^{52} + 24 q^{53} + 37 q^{54} - 8 q^{55} - 55 q^{56} - 19 q^{57} + 49 q^{58} + 41 q^{59} + 34 q^{60} - 31 q^{61} - 3 q^{62} + 37 q^{63} + 77 q^{64} + 15 q^{65} - 39 q^{66} - 5 q^{67} + 27 q^{68} - 6 q^{70} + 15 q^{71} + 48 q^{72} + 34 q^{73} - 29 q^{74} + 10 q^{75} - 24 q^{76} - 35 q^{77} - 45 q^{78} - 41 q^{79} + 41 q^{80} + 25 q^{81} + 33 q^{82} + 62 q^{83} - 126 q^{84} + 19 q^{85} - 10 q^{86} + 26 q^{87} - 50 q^{88} - 23 q^{89} + 23 q^{90} + 19 q^{91} + 50 q^{93} + 9 q^{94} - 8 q^{95} + 64 q^{96} + 37 q^{97} - 55 q^{98} - 48 q^{99}+O(q^{100}) \) 25 * q + 3 * q^2 + 10 * q^3 + 33 * q^4 + 25 * q^5 + 22 * q^6 + 14 * q^7 + 21 * q^8 + 29 * q^9 + 3 * q^10 - 8 * q^11 + 34 * q^12 + 15 * q^13 - 6 * q^14 + 10 * q^15 + 41 * q^16 + 19 * q^17 + 23 * q^18 - 8 * q^19 + 33 * q^20 - 21 * q^21 + 3 * q^22 + 51 * q^24 + 25 * q^25 + 7 * q^26 + 64 * q^27 + 27 * q^28 + 3 * q^29 + 22 * q^30 + 34 * q^31 + 30 * q^32 - q^33 - 21 * q^34 + 14 * q^35 + 31 * q^36 - q^37 - 7 * q^38 + 49 * q^39 + 21 * q^40 - 29 * q^42 + 25 * q^43 - 33 * q^44 + 29 * q^45 - 5 * q^47 + 42 * q^48 + 33 * q^49 + 3 * q^50 + 23 * q^51 + 67 * q^52 + 24 * q^53 + 37 * q^54 - 8 * q^55 - 55 * q^56 - 19 * q^57 + 49 * q^58 + 41 * q^59 + 34 * q^60 - 31 * q^61 - 3 * q^62 + 37 * q^63 + 77 * q^64 + 15 * q^65 - 39 * q^66 - 5 * q^67 + 27 * q^68 - 6 * q^70 + 15 * q^71 + 48 * q^72 + 34 * q^73 - 29 * q^74 + 10 * q^75 - 24 * q^76 - 35 * q^77 - 45 * q^78 - 41 * q^79 + 41 * q^80 + 25 * q^81 + 33 * q^82 + 62 * q^83 - 126 * q^84 + 19 * q^85 - 10 * q^86 + 26 * q^87 - 50 * q^88 - 23 * q^89 + 23 * q^90 + 19 * q^91 + 50 * q^93 + 9 * q^94 - 8 * q^95 + 64 * q^96 + 37 * q^97 - 55 * q^98 - 48 * q^99

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