LMFDB - Embedded newform 2645.2.a.y.1.25

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			1.25
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)

$f(q)$	$=$	$q+2.77870 q^{2} +1.69218 q^{3} +5.72115 q^{4} +1.00000 q^{5} +4.70206 q^{6} -3.35352 q^{7} +10.3399 q^{8} -0.136520 q^{9} +O(q^{10})$	\(q+2.77870 q^{2} +1.69218 q^{3} +5.72115 q^{4} +1.00000 q^{5} +4.70206 q^{6} -3.35352 q^{7} +10.3399 q^{8} -0.136520 q^{9} +2.77870 q^{10} +1.57904 q^{11} +9.68122 q^{12} -1.04899 q^{13} -9.31840 q^{14} +1.69218 q^{15} +17.2892 q^{16} +3.53895 q^{17} -0.379348 q^{18} +1.70838 q^{19} +5.72115 q^{20} -5.67476 q^{21} +4.38767 q^{22} +17.4971 q^{24} +1.00000 q^{25} -2.91482 q^{26} -5.30756 q^{27} -19.1860 q^{28} +0.0815466 q^{29} +4.70206 q^{30} -2.03266 q^{31} +27.3617 q^{32} +2.67202 q^{33} +9.83367 q^{34} -3.35352 q^{35} -0.781052 q^{36} -6.40783 q^{37} +4.74707 q^{38} -1.77508 q^{39} +10.3399 q^{40} -11.3200 q^{41} -15.7684 q^{42} -1.00073 q^{43} +9.03393 q^{44} -0.136520 q^{45} -4.57199 q^{47} +29.2565 q^{48} +4.24607 q^{49} +2.77870 q^{50} +5.98855 q^{51} -6.00141 q^{52} +9.25901 q^{53} -14.7481 q^{54} +1.57904 q^{55} -34.6752 q^{56} +2.89089 q^{57} +0.226593 q^{58} -0.510491 q^{59} +9.68122 q^{60} -7.95667 q^{61} -5.64815 q^{62} +0.457823 q^{63} +41.4512 q^{64} -1.04899 q^{65} +7.42474 q^{66} -4.71905 q^{67} +20.2469 q^{68} -9.31840 q^{70} +11.5525 q^{71} -1.41161 q^{72} +4.38733 q^{73} -17.8054 q^{74} +1.69218 q^{75} +9.77390 q^{76} -5.29534 q^{77} -4.93240 q^{78} -2.28723 q^{79} +17.2892 q^{80} -8.57180 q^{81} -31.4549 q^{82} -3.61133 q^{83} -32.4661 q^{84} +3.53895 q^{85} -2.78073 q^{86} +0.137992 q^{87} +16.3272 q^{88} +11.2643 q^{89} -0.379348 q^{90} +3.51780 q^{91} -3.43963 q^{93} -12.7042 q^{94} +1.70838 q^{95} +46.3009 q^{96} +6.99455 q^{97} +11.7985 q^{98} -0.215571 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	2.77870	1.96483	0.982417	−	0.186699i	$-0.0597788\pi$
$2$	2.77870	1.96483	0.982417	+	0.186699i	$0.0597788\pi$
$3$	1.69218	0.976982	0.488491	−	0.872569i	$-0.337548\pi$
$3$	1.69218	0.976982	0.488491	+	0.872569i	$0.337548\pi$
$4$	5.72115	2.86057
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	4.70206	1.91961
$7$	−3.35352	−1.26751	−0.633755	−	0.773534i	$-0.718487\pi$
$7$	−3.35352	−1.26751	−0.633755	+	0.773534i	$0.718487\pi$
$8$	10.3399	3.65572
$9$	−0.136520	−0.0455067
$10$	2.77870	0.878701
$11$	1.57904	0.476099	0.238049	−	0.971253i	$-0.423492\pi$
$11$	1.57904	0.476099	0.238049	+	0.971253i	$0.423492\pi$
$12$	9.68122	2.79473
$13$	−1.04899	−0.290937	−0.145468	−	0.989363i	$-0.546469\pi$
$13$	−1.04899	−0.290937	−0.145468	+	0.989363i	$0.546469\pi$
$14$	−9.31840	−2.49045
$15$	1.69218	0.436920
$16$	17.2892	4.32231
$17$	3.53895	0.858322	0.429161	−	0.903228i	$-0.358809\pi$
$17$	3.53895	0.858322	0.429161	+	0.903228i	$0.358809\pi$
$18$	−0.379348	−0.0894132
$19$	1.70838	0.391929	0.195965	−	0.980611i	$-0.437216\pi$
$19$	1.70838	0.391929	0.195965	+	0.980611i	$0.437216\pi$
$20$	5.72115	1.27929
$21$	−5.67476	−1.23833
$22$	4.38767	0.935455
$23$	0	0
$23$	0	0
$24$	17.4971	3.57157
$25$	1.00000	0.200000
$26$	−2.91482	−0.571643
$27$	−5.30756	−1.02144
$28$	−19.1860	−3.62581
$29$	0.0815466	0.0151428	0.00757141	−	0.999971i	$-0.497590\pi$
$29$	0.0815466	0.0151428	0.00757141	+	0.999971i	$0.497590\pi$
$30$	4.70206	0.858474
$31$	−2.03266	−0.365077	−0.182538	−	0.983199i	$-0.558431\pi$
$31$	−2.03266	−0.365077	−0.182538	+	0.983199i	$0.558431\pi$
$32$	27.3617	4.83690
$33$	2.67202	0.465140
$34$	9.83367	1.68646
$35$	−3.35352	−0.566848
$36$	−0.781052	−0.130175
$37$	−6.40783	−1.05344	−0.526721	−	0.850038i	$-0.676579\pi$
$37$	−6.40783	−1.05344	−0.526721	+	0.850038i	$0.676579\pi$
$38$	4.74707	0.770076
$39$	−1.77508	−0.284240
$40$	10.3399	1.63489
$41$	−11.3200	−1.76789	−0.883946	−	0.467590i	$-0.845122\pi$
$41$	−11.3200	−1.76789	−0.883946	+	0.467590i	$0.845122\pi$
$42$	−15.7684	−2.43312
$43$	−1.00073	−0.152610	−0.0763052	−	0.997085i	$-0.524312\pi$
$43$	−1.00073	−0.152610	−0.0763052	+	0.997085i	$0.524312\pi$
$44$	9.03393	1.36192
$45$	−0.136520	−0.0203512
$46$	0	0
$47$	−4.57199	−0.666893	−0.333447	−	0.942769i	$-0.608212\pi$
$47$	−4.57199	−0.666893	−0.333447	+	0.942769i	$0.608212\pi$
$48$	29.2565	4.22282
$49$	4.24607	0.606582
$50$	2.77870	0.392967
$51$	5.98855	0.838565
$52$	−6.00141	−0.832246
$53$	9.25901	1.27182	0.635912	−	0.771762i	$-0.280624\pi$
$53$	9.25901	1.27182	0.635912	+	0.771762i	$0.280624\pi$
$54$	−14.7481	−2.00696
$55$	1.57904	0.212918
$56$	−34.6752	−4.63366
$57$	2.89089	0.382908
$58$	0.226593	0.0297531
$59$	−0.510491	−0.0664602	−0.0332301	−	0.999448i	$-0.510579\pi$
$59$	−0.510491	−0.0664602	−0.0332301	+	0.999448i	$0.510579\pi$
$60$	9.68122	1.24984
$61$	−7.95667	−1.01875	−0.509374	−	0.860545i	$-0.670123\pi$
$61$	−7.95667	−1.01875	−0.509374	+	0.860545i	$0.670123\pi$
$62$	−5.64815	−0.717315
$63$	0.457823	0.0576802
$64$	41.4512	5.18141
$65$	−1.04899	−0.130111
$66$	7.42474	0.913923
$67$	−4.71905	−0.576524	−0.288262	−	0.957552i	$-0.593077\pi$
$67$	−4.71905	−0.576524	−0.288262	+	0.957552i	$0.593077\pi$
$68$	20.2469	2.45529
$69$	0	0
$70$	−9.31840	−1.11376
$71$	11.5525	1.37103	0.685517	−	0.728057i	$-0.259576\pi$
$71$	11.5525	1.37103	0.685517	+	0.728057i	$0.259576\pi$
$72$	−1.41161	−0.166360
$73$	4.38733	0.513498	0.256749	−	0.966478i	$-0.417349\pi$
$73$	4.38733	0.513498	0.256749	+	0.966478i	$0.417349\pi$
$74$	−17.8054	−2.06984
$75$	1.69218	0.195396
$76$	9.77390	1.12114
$77$	−5.29534	−0.603460
$78$	−4.93240	−0.558484
$79$	−2.28723	−0.257334	−0.128667	−	0.991688i	$-0.541070\pi$
$79$	−2.28723	−0.257334	−0.128667	+	0.991688i	$0.541070\pi$
$80$	17.2892	1.93300
$81$	−8.57180	−0.952422
$82$	−31.4549	−3.47361
$83$	−3.61133	−0.396395	−0.198197	−	0.980162i	$-0.563509\pi$
$83$	−3.61133	−0.396395	−0.198197	+	0.980162i	$0.563509\pi$
$84$	−32.4661	−3.54235
$85$	3.53895	0.383853
$86$	−2.78073	−0.299854
$87$	0.137992	0.0147943
$88$	16.3272	1.74048
$89$	11.2643	1.19401	0.597006	−	0.802237i	$-0.296357\pi$
$89$	11.2643	1.19401	0.597006	+	0.802237i	$0.296357\pi$
$90$	−0.379348	−0.0399868
$91$	3.51780	0.368765
$92$	0	0
$93$	−3.43963	−0.356673
$94$	−12.7042	−1.31033
$95$	1.70838	0.175276
$96$	46.3009	4.72557
$97$	6.99455	0.710189	0.355094	−	0.934830i	$-0.384449\pi$
$97$	6.99455	0.710189	0.355094	+	0.934830i	$0.384449\pi$
$98$	11.7985	1.19183
$99$	−0.215571	−0.0216657
$100$	5.72115	0.572115
$101$	−3.96548	−0.394580	−0.197290	−	0.980345i	$-0.563214\pi$
$101$	−3.96548	−0.394580	−0.197290	+	0.980345i	$0.563214\pi$
$102$	16.6404	1.64764
$103$	−14.5623	−1.43487	−0.717435	−	0.696626i	$-0.754684\pi$
$103$	−14.5623	−1.43487	−0.717435	+	0.696626i	$0.754684\pi$
$104$	−10.8465	−1.06358
$105$	−5.67476	−0.553800
$106$	25.7280	2.49892
$107$	19.5335	1.88838	0.944188	−	0.329408i	$-0.106849\pi$
$107$	19.5335	1.88838	0.944188	+	0.329408i	$0.106849\pi$
$108$	−30.3654	−2.92191
$109$	−2.00614	−0.192153	−0.0960766	−	0.995374i	$-0.530629\pi$
$109$	−2.00614	−0.192153	−0.0960766	+	0.995374i	$0.530629\pi$
$110$	4.38767	0.418348
$111$	−10.8432	−1.02919
$112$	−57.9798	−5.47857
$113$	−3.05021	−0.286939	−0.143470	−	0.989655i	$-0.545826\pi$
$113$	−3.05021	−0.286939	−0.143470	+	0.989655i	$0.545826\pi$
$114$	8.03290	0.752350
$115$	0	0
$116$	0.466540	0.0433172
$117$	0.143208	0.0132396
$118$	−1.41850	−0.130583
$119$	−11.8679	−1.08793
$120$	17.4971	1.59726
$121$	−8.50663	−0.773330
$122$	−22.1092	−2.00167
$123$	−19.1555	−1.72720
$124$	−11.6292	−1.04433
$125$	1.00000	0.0894427
$126$	1.27215	0.113332
$127$	6.96235	0.617809	0.308904	−	0.951093i	$-0.400038\pi$
$127$	6.96235	0.617809	0.308904	+	0.951093i	$0.400038\pi$
$128$	60.4571	5.34370
$129$	−1.69342	−0.149098
$130$	−2.91482	−0.255646
$131$	5.45517	0.476621	0.238310	−	0.971189i	$-0.423406\pi$
$131$	5.45517	0.476621	0.238310	+	0.971189i	$0.423406\pi$
$132$	15.2871	1.33057
$133$	−5.72908	−0.496774
$134$	−13.1128	−1.13277
$135$	−5.30756	−0.456802
$136$	36.5926	3.13779
$137$	−10.6529	−0.910137	−0.455068	−	0.890456i	$-0.650385\pi$
$137$	−10.6529	−0.910137	−0.455068	+	0.890456i	$0.650385\pi$
$138$	0	0
$139$	10.2336	0.868000	0.434000	−	0.900913i	$-0.357102\pi$
$139$	10.2336	0.868000	0.434000	+	0.900913i	$0.357102\pi$
$140$	−19.1860	−1.62151
$141$	−7.73664	−0.651542
$142$	32.1010	2.69386
$143$	−1.65639	−0.138515
$144$	−2.36033	−0.196694
$145$	0.0815466	0.00677208
$146$	12.1911	1.00894
$147$	7.18513	0.592619
$148$	−36.6602	−3.01345
$149$	−15.8033	−1.29465	−0.647327	−	0.762212i	$-0.724113\pi$
$149$	−15.8033	−1.29465	−0.647327	+	0.762212i	$0.724113\pi$
$150$	4.70206	0.383921
$151$	−0.919085	−0.0747941	−0.0373970	−	0.999300i	$-0.511907\pi$
$151$	−0.919085	−0.0747941	−0.0373970	+	0.999300i	$0.511907\pi$
$152$	17.6645	1.43278
$153$	−0.483139	−0.0390594
$154$	−14.7141	−1.18570
$155$	−2.03266	−0.163267
$156$	−10.1555	−0.813090
$157$	−13.5566	−1.08194	−0.540968	−	0.841043i	$-0.681942\pi$
$157$	−13.5566	−1.08194	−0.540968	+	0.841043i	$0.681942\pi$
$158$	−6.35552	−0.505618
$159$	15.6679	1.24255
$160$	27.3617	2.16313
$161$	0	0
$162$	−23.8184	−1.87135
$163$	−7.80762	−0.611540	−0.305770	−	0.952105i	$-0.598914\pi$
$163$	−7.80762	−0.611540	−0.305770	+	0.952105i	$0.598914\pi$
$164$	−64.7636	−5.05718
$165$	2.67202	0.208017
$166$	−10.0348	−0.778850
$167$	−16.9187	−1.30921	−0.654605	−	0.755971i	$-0.727165\pi$
$167$	−16.9187	−1.30921	−0.654605	+	0.755971i	$0.727165\pi$
$168$	−58.6767	−4.52700
$169$	−11.8996	−0.915356
$170$	9.83367	0.754208
$171$	−0.233228	−0.0178354
$172$	−5.72534	−0.436553
$173$	5.55366	0.422237	0.211118	−	0.977460i	$-0.432289\pi$
$173$	5.55366	0.422237	0.211118	+	0.977460i	$0.432289\pi$
$174$	0.383437	0.0290683
$175$	−3.35352	−0.253502
$176$	27.3004	2.05785
$177$	−0.863843	−0.0649304
$178$	31.3000	2.34603
$179$	−7.57003	−0.565810	−0.282905	−	0.959148i	$-0.591298\pi$
$179$	−7.57003	−0.565810	−0.282905	+	0.959148i	$0.591298\pi$
$180$	−0.781052	−0.0582162
$181$	11.4137	0.848370	0.424185	−	0.905576i	$-0.360561\pi$
$181$	11.4137	0.848370	0.424185	+	0.905576i	$0.360561\pi$
$182$	9.77489	0.724563
$183$	−13.4641	−0.995298
$184$	0	0
$185$	−6.40783	−0.471113
$186$	−9.55769	−0.700804
$187$	5.58815	0.408646
$188$	−26.1570	−1.90770
$189$	17.7990	1.29469
$190$	4.74707	0.344389
$191$	−0.356495	−0.0257951	−0.0128975	−	0.999917i	$-0.504106\pi$
$191$	−0.356495	−0.0257951	−0.0128975	+	0.999917i	$0.504106\pi$
$192$	70.1431	5.06214
$193$	18.9479	1.36390	0.681949	−	0.731400i	$-0.261132\pi$
$193$	18.9479	1.36390	0.681949	+	0.731400i	$0.261132\pi$
$194$	19.4357	1.39540
$195$	−1.77508	−0.127116
$196$	24.2924	1.73517
$197$	20.0851	1.43101	0.715504	−	0.698609i	$-0.246197\pi$
$197$	20.0851	1.43101	0.715504	+	0.698609i	$0.246197\pi$
$198$	−0.599006	−0.0425695
$199$	8.91188	0.631747	0.315873	−	0.948801i	$-0.397703\pi$
$199$	8.91188	0.631747	0.315873	+	0.948801i	$0.397703\pi$
$200$	10.3399	0.731144
$201$	−7.98550	−0.563254
$202$	−11.0189	−0.775285
$203$	−0.273468	−0.0191937
$204$	34.2614	2.39878
$205$	−11.3200	−0.790625
$206$	−40.4643	−2.81928
$207$	0	0
$208$	−18.1362	−1.25752
$209$	2.69760	0.186597
$210$	−15.7684	−1.08813
$211$	−22.8740	−1.57471	−0.787356	−	0.616499i	$-0.788550\pi$
$211$	−22.8740	−1.57471	−0.787356	+	0.616499i	$0.788550\pi$
$212$	52.9722	3.63815
$213$	19.5490	1.33948
$214$	54.2777	3.71035
$215$	−1.00073	−0.0682495
$216$	−54.8799	−3.73410
$217$	6.81656	0.462738
$218$	−5.57445	−0.377549
$219$	7.42416	0.501678
$220$	9.03393	0.609067
$221$	−3.71232	−0.249718
$222$	−30.1300	−2.02219
$223$	4.23290	0.283456	0.141728	−	0.989906i	$-0.454734\pi$
$223$	4.23290	0.283456	0.141728	+	0.989906i	$0.454734\pi$
$224$	−91.7578	−6.13083
$225$	−0.136520	−0.00910135
$226$	−8.47560	−0.563788
$227$	26.0456	1.72871	0.864354	−	0.502885i	$-0.167728\pi$
$227$	26.0456	1.72871	0.864354	+	0.502885i	$0.167728\pi$
$228$	16.5392	1.09534
$229$	−3.05308	−0.201753	−0.100876	−	0.994899i	$-0.532165\pi$
$229$	−3.05308	−0.201753	−0.100876	+	0.994899i	$0.532165\pi$
$230$	0	0
$231$	−8.96068	−0.589569
$232$	0.843187	0.0553579
$233$	23.6475	1.54920	0.774601	−	0.632451i	$-0.217951\pi$
$233$	23.6475	1.54920	0.774601	+	0.632451i	$0.217951\pi$
$234$	0.397931	0.0260136
$235$	−4.57199	−0.298244
$236$	−2.92059	−0.190114
$237$	−3.87041	−0.251410
$238$	−32.9774	−2.13761
$239$	4.98975	0.322760	0.161380	−	0.986892i	$-0.448406\pi$
$239$	4.98975	0.322760	0.161380	+	0.986892i	$0.448406\pi$
$240$	29.2565	1.88850
$241$	−21.6317	−1.39342	−0.696710	−	0.717353i	$-0.745354\pi$
$241$	−21.6317	−1.39342	−0.696710	+	0.717353i	$0.745354\pi$
$242$	−23.6373	−1.51947
$243$	1.41764	0.0909417
$244$	−45.5213	−2.91420
$245$	4.24607	0.271272
$246$	−53.2274	−3.39366
$247$	−1.79207	−0.114027
$248$	−21.0176	−1.33462
$249$	−6.11103	−0.387270
$250$	2.77870	0.175740
$251$	−7.39546	−0.466797	−0.233399	−	0.972381i	$-0.574985\pi$
$251$	−7.39546	−0.466797	−0.233399	+	0.972381i	$0.574985\pi$
$252$	2.61927	0.164999
$253$	0	0
$254$	19.3463	1.21389
$255$	5.98855	0.375018
$256$	85.0893	5.31808
$257$	−1.64782	−0.102788	−0.0513942	−	0.998678i	$-0.516366\pi$
$257$	−1.64782	−0.102788	−0.0513942	+	0.998678i	$0.516366\pi$
$258$	−4.70551	−0.292952
$259$	21.4888	1.33525
$260$	−6.00141	−0.372192
$261$	−0.0111328	−0.000689101 0
$262$	15.1583	0.936481
$263$	−27.3611	−1.68716	−0.843579	−	0.537005i	$-0.819556\pi$
$263$	−27.3611	−1.68716	−0.843579	+	0.537005i	$0.819556\pi$
$264$	27.6286	1.70042
$265$	9.25901	0.568777
$266$	−15.9194	−0.976079
$267$	19.0612	1.16653
$268$	−26.9984	−1.64919
$269$	5.01313	0.305656	0.152828	−	0.988253i	$-0.451162\pi$
$269$	5.01313	0.305656	0.152828	+	0.988253i	$0.451162\pi$
$270$	−14.7481	−0.897541
$271$	−16.3423	−0.992725	−0.496362	−	0.868115i	$-0.665331\pi$
$271$	−16.3423	−0.992725	−0.496362	+	0.868115i	$0.665331\pi$
$272$	61.1858	3.70994
$273$	5.95275	0.360277
$274$	−29.6011	−1.78827
$275$	1.57904	0.0952198
$276$	0	0
$277$	−21.5397	−1.29419	−0.647097	−	0.762408i	$-0.724017\pi$
$277$	−21.5397	−1.29419	−0.647097	+	0.762408i	$0.724017\pi$
$278$	28.4360	1.70548
$279$	0.277499	0.0166135
$280$	−34.6752	−2.07224
$281$	−7.92990	−0.473058	−0.236529	−	0.971624i	$-0.576010\pi$
$281$	−7.92990	−0.473058	−0.236529	+	0.971624i	$0.576010\pi$
$282$	−21.4978	−1.28017
$283$	22.2521	1.32275	0.661375	−	0.750056i	$-0.269973\pi$
$283$	22.2521	1.32275	0.661375	+	0.750056i	$0.269973\pi$
$284$	66.0938	3.92195
$285$	2.89089	0.171242
$286$	−4.60262	−0.272158
$287$	37.9619	2.24082
$288$	−3.73542	−0.220112
$289$	−4.47581	−0.263283
$290$	0.226593	0.0133060
$291$	11.8361	0.693842
$292$	25.1006	1.46890
$293$	−0.0999099	−0.00583680	−0.00291840	−	0.999996i	$-0.500929\pi$
$293$	−0.0999099	−0.00583680	−0.00291840	+	0.999996i	$0.500929\pi$
$294$	19.9653	1.16440
$295$	−0.510491	−0.0297219
$296$	−66.2566	−3.85109
$297$	−8.38086	−0.486307
$298$	−43.9125	−2.54378
$299$	0	0
$300$	9.68122	0.558946
$301$	3.35598	0.193435
$302$	−2.55386	−0.146958
$303$	−6.71031	−0.385498
$304$	29.5366	1.69404
$305$	−7.95667	−0.455598
$306$	−1.34250	−0.0767453
$307$	−1.62360	−0.0926640	−0.0463320	−	0.998926i	$-0.514753\pi$
$307$	−1.62360	−0.0926640	−0.0463320	+	0.998926i	$0.514753\pi$
$308$	−30.2954	−1.72624
$309$	−24.6421	−1.40184
$310$	−5.64815	−0.320793
$311$	24.2371	1.37436	0.687180	−	0.726487i	$-0.258848\pi$
$311$	24.2371	1.37436	0.687180	+	0.726487i	$0.258848\pi$
$312$	−18.3542	−1.03910
$313$	−20.8984	−1.18125	−0.590624	−	0.806947i	$-0.701118\pi$
$313$	−20.8984	−1.18125	−0.590624	+	0.806947i	$0.701118\pi$
$314$	−37.6697	−2.12583
$315$	0.457823	0.0257954
$316$	−13.0856	−0.736122
$317$	14.5114	0.815042	0.407521	−	0.913196i	$-0.366393\pi$
$317$	14.5114	0.815042	0.407521	+	0.913196i	$0.366393\pi$
$318$	43.5364	2.44140
$319$	0.128765	0.00720948
$320$	41.4512	2.31720
$321$	33.0543	1.84491
$322$	0	0
$323$	6.04588	0.336402
$324$	−49.0406	−2.72448
$325$	−1.04899	−0.0581874
$326$	−21.6950	−1.20157
$327$	−3.39475	−0.187730
$328$	−117.048	−6.46292
$329$	15.3322	0.845294
$330$	7.42474	0.408719
$331$	16.0210	0.880596	0.440298	−	0.897852i	$-0.354873\pi$
$331$	16.0210	0.880596	0.440298	+	0.897852i	$0.354873\pi$
$332$	−20.6609	−1.13392
$333$	0.874799	0.0479387
$334$	−47.0119	−2.57238
$335$	−4.71905	−0.257829
$336$	−98.1123	−5.35247
$337$	17.2790	0.941247	0.470624	−	0.882334i	$-0.344029\pi$
$337$	17.2790	0.941247	0.470624	+	0.882334i	$0.344029\pi$
$338$	−33.0654	−1.79852
$339$	−5.16151	−0.280335
$340$	20.2469	1.09804
$341$	−3.20966	−0.173813
$342$	−0.648071	−0.0350437
$343$	9.23534	0.498662
$344$	−10.3475	−0.557901
$345$	0	0
$346$	15.4319	0.829626
$347$	4.87529	0.261719	0.130860	−	0.991401i	$-0.458226\pi$
$347$	4.87529	0.261719	0.130860	+	0.991401i	$0.458226\pi$
$348$	0.789471	0.0423201
$349$	−24.6124	−1.31747	−0.658736	−	0.752374i	$-0.728909\pi$
$349$	−24.6124	−1.31747	−0.658736	+	0.752374i	$0.728909\pi$
$350$	−9.31840	−0.498089
$351$	5.56757	0.297175
$352$	43.2052	2.30284
$353$	34.4873	1.83557	0.917787	−	0.397073i	$-0.129974\pi$
$353$	34.4873	1.83557	0.917787	+	0.397073i	$0.129974\pi$
$354$	−2.40036	−0.127578
$355$	11.5525	0.613145
$356$	64.4446	3.41556
$357$	−20.0827	−1.06289
$358$	−21.0348	−1.11172
$359$	35.3557	1.86600	0.933000	−	0.359876i	$-0.117181\pi$
$359$	35.3557	1.86600	0.933000	+	0.359876i	$0.117181\pi$
$360$	−1.41161	−0.0743984
$361$	−16.0814	−0.846391
$362$	31.7151	1.66691
$363$	−14.3948	−0.755529
$364$	20.1258	1.05488
$365$	4.38733	0.229643
$366$	−37.4127	−1.95559
$367$	−28.9736	−1.51241	−0.756206	−	0.654334i	$-0.772949\pi$
$367$	−28.9736	−1.51241	−0.756206	+	0.654334i	$0.772949\pi$
$368$	0	0
$369$	1.54541	0.0804510
$370$	−17.8054	−0.925660
$371$	−31.0503	−1.61205
$372$	−19.6786	−1.02029
$373$	6.50371	0.336749	0.168375	−	0.985723i	$-0.446148\pi$
$373$	6.50371	0.336749	0.168375	+	0.985723i	$0.446148\pi$
$374$	15.5278	0.802922
$375$	1.69218	0.0873839
$376$	−47.2741	−2.43797
$377$	−0.0855414	−0.00440561
$378$	49.4580	2.54385
$379$	32.3573	1.66209	0.831043	−	0.556209i	$-0.187744\pi$
$379$	32.3573	1.66209	0.831043	+	0.556209i	$0.187744\pi$
$380$	9.77390	0.501390
$381$	11.7816	0.603588
$382$	−0.990592	−0.0506831
$383$	34.7860	1.77748	0.888741	−	0.458410i	$-0.151581\pi$
$383$	34.7860	1.77748	0.888741	+	0.458410i	$0.151581\pi$
$384$	102.304	5.22070
$385$	−5.29534	−0.269876
$386$	52.6504	2.67983
$387$	0.136620	0.00694480
$388$	40.0169	2.03155
$389$	17.6623	0.895516	0.447758	−	0.894155i	$-0.352223\pi$
$389$	17.6623	0.895516	0.447758	+	0.894155i	$0.352223\pi$
$390$	−4.93240	−0.249762
$391$	0	0
$392$	43.9041	2.21749
$393$	9.23115	0.465650
$394$	55.8105	2.81169
$395$	−2.28723	−0.115083
$396$	−1.23331	−0.0619763
$397$	33.5208	1.68236	0.841179	−	0.540756i	$-0.181862\pi$
$397$	33.5208	1.68236	0.841179	+	0.540756i	$0.181862\pi$
$398$	24.7634	1.24128
$399$	−9.69465	−0.485339
$400$	17.2892	0.864462
$401$	14.7408	0.736122	0.368061	−	0.929802i	$-0.380022\pi$
$401$	14.7408	0.736122	0.368061	+	0.929802i	$0.380022\pi$
$402$	−22.1893	−1.10670
$403$	2.13224	0.106214
$404$	−22.6871	−1.12873
$405$	−8.57180	−0.425936
$406$	−0.759884	−0.0377124
$407$	−10.1182	−0.501542
$408$	61.9213	3.06556
$409$	−8.55952	−0.423241	−0.211621	−	0.977352i	$-0.567874\pi$
$409$	−8.55952	−0.423241	−0.211621	+	0.977352i	$0.567874\pi$
$410$	−31.4549	−1.55345
$411$	−18.0266	−0.889187
$412$	−83.3133	−4.10455
$413$	1.71194	0.0842390
$414$	0	0
$415$	−3.61133	−0.177273
$416$	−28.7021	−1.40723
$417$	17.3171	0.848020
$418$	7.49582	0.366632
$419$	4.84326	0.236609	0.118304	−	0.992977i	$-0.462254\pi$
$419$	4.84326	0.236609	0.118304	+	0.992977i	$0.462254\pi$
$420$	−32.4661	−1.58419
$421$	−8.27742	−0.403417	−0.201708	−	0.979446i	$-0.564649\pi$
$421$	−8.27742	−0.403417	−0.201708	+	0.979446i	$0.564649\pi$
$422$	−63.5599	−3.09405
$423$	0.624169	0.0303481
$424$	95.7376	4.64943
$425$	3.53895	0.171664
$426$	54.3207	2.63185
$427$	26.6828	1.29127
$428$	111.754	5.40184
$429$	−2.80292	−0.135326
$430$	−2.78073	−0.134099
$431$	−7.23215	−0.348360	−0.174180	−	0.984714i	$-0.555728\pi$
$431$	−7.23215	−0.348360	−0.174180	+	0.984714i	$0.555728\pi$
$432$	−91.7637	−4.41499
$433$	−19.0370	−0.914862	−0.457431	−	0.889245i	$-0.651230\pi$
$433$	−19.0370	−0.914862	−0.457431	+	0.889245i	$0.651230\pi$
$434$	18.9412	0.909204
$435$	0.137992	0.00661620
$436$	−11.4774	−0.549668
$437$	0	0
$438$	20.6295	0.985715
$439$	1.75608	0.0838129	0.0419064	−	0.999122i	$-0.486657\pi$
$439$	1.75608	0.0838129	0.0419064	+	0.999122i	$0.486657\pi$
$440$	16.3272	0.778368
$441$	−0.579675	−0.0276036
$442$	−10.3154	−0.490654
$443$	−0.406374	−0.0193074	−0.00965371	−	0.999953i	$-0.503073\pi$
$443$	−0.406374	−0.0193074	−0.00965371	+	0.999953i	$0.503073\pi$
$444$	−62.0357	−2.94408
$445$	11.2643	0.533978
$446$	11.7619	0.556944
$447$	−26.7420	−1.26485
$448$	−139.007	−6.56748
$449$	24.2465	1.14426	0.572132	−	0.820161i	$-0.306116\pi$
$449$	24.2465	1.14426	0.572132	+	0.820161i	$0.306116\pi$
$450$	−0.379348	−0.0178826
$451$	−17.8748	−0.841691
$452$	−17.4507	−0.820811
$453$	−1.55526	−0.0730725
$454$	72.3728	3.39662
$455$	3.51780	0.164917
$456$	29.8916	1.39980
$457$	30.6443	1.43348	0.716741	−	0.697340i	$-0.245633\pi$
$457$	30.6443	1.43348	0.716741	+	0.697340i	$0.245633\pi$
$458$	−8.48357	−0.396411
$459$	−18.7832	−0.876725
$460$	0	0
$461$	−14.9961	−0.698440	−0.349220	−	0.937041i	$-0.613553\pi$
$461$	−14.9961	−0.698440	−0.349220	+	0.937041i	$0.613553\pi$
$462$	−24.8990	−1.15841
$463$	−18.9961	−0.882826	−0.441413	−	0.897304i	$-0.645523\pi$
$463$	−18.9961	−0.882826	−0.441413	+	0.897304i	$0.645523\pi$
$464$	1.40988	0.0654520
$465$	−3.43963	−0.159509
$466$	65.7093	3.04392
$467$	6.96249	0.322186	0.161093	−	0.986939i	$-0.448498\pi$
$467$	6.96249	0.322186	0.161093	+	0.986939i	$0.448498\pi$
$468$	0.819314	0.0378728
$469$	15.8254	0.730750
$470$	−12.7042	−0.585999
$471$	−22.9403	−1.05703
$472$	−5.27844	−0.242960
$473$	−1.58020	−0.0726576
$474$	−10.7547	−0.493979
$475$	1.70838	0.0783859
$476$	−67.8982	−3.11211
$477$	−1.26404	−0.0578765
$478$	13.8650	0.634170
$479$	27.4026	1.25205	0.626027	−	0.779801i	$-0.284680\pi$
$479$	27.4026	1.25205	0.626027	+	0.779801i	$0.284680\pi$
$480$	46.3009	2.11334
$481$	6.72174	0.306485
$482$	−60.1079	−2.73784
$483$	0	0
$484$	−48.6677	−2.21217
$485$	6.99455	0.317606
$486$	3.93919	0.178685
$487$	16.6109	0.752713	0.376357	−	0.926475i	$-0.377177\pi$
$487$	16.6109	0.752713	0.376357	+	0.926475i	$0.377177\pi$
$488$	−82.2715	−3.72426
$489$	−13.2119	−0.597463
$490$	11.7985	0.533004
$491$	30.9553	1.39699	0.698496	−	0.715614i	$-0.253853\pi$
$491$	30.9553	1.39699	0.698496	+	0.715614i	$0.253853\pi$
$492$	−109.592	−4.94078
$493$	0.288590	0.0129974
$494$	−4.97962	−0.224044
$495$	−0.215571	−0.00968920
$496$	−35.1432	−1.57798
$497$	−38.7416	−1.73780
$498$	−16.9807	−0.760922
$499$	−2.66034	−0.119093	−0.0595466	−	0.998226i	$-0.518965\pi$
$499$	−2.66034	−0.119093	−0.0595466	+	0.998226i	$0.518965\pi$
$500$	5.72115	0.255858
$501$	−28.6295	−1.27907
$502$	−20.5497	−0.917180
$503$	7.90481	0.352458	0.176229	−	0.984349i	$-0.443610\pi$
$503$	7.90481	0.352458	0.176229	+	0.984349i	$0.443610\pi$
$504$	4.73386	0.210863
$505$	−3.96548	−0.176462
$506$	0	0
$507$	−20.1363	−0.894286
$508$	39.8327	1.76729
$509$	−21.7388	−0.963557	−0.481779	−	0.876293i	$-0.660009\pi$
$509$	−21.7388	−0.963557	−0.481779	+	0.876293i	$0.660009\pi$
$510$	16.6404	0.736848
$511$	−14.7130	−0.650864
$512$	115.523	5.10545
$513$	−9.06734	−0.400333
$514$	−4.57880	−0.201962
$515$	−14.5623	−0.641693
$516$	−9.68832	−0.426505
$517$	−7.21936	−0.317507
$518$	59.7108	2.62354
$519$	9.39780	0.412518
$520$	−10.8465	−0.475649
$521$	−20.8386	−0.912956	−0.456478	−	0.889735i	$-0.650889\pi$
$521$	−20.8386	−0.912956	−0.456478	+	0.889735i	$0.650889\pi$
$522$	−0.0309346	−0.00135397
$523$	−19.0568	−0.833294	−0.416647	−	0.909068i	$-0.636795\pi$
$523$	−19.0568	−0.833294	−0.416647	+	0.909068i	$0.636795\pi$
$524$	31.2099	1.36341
$525$	−5.67476	−0.247667
$526$	−76.0282	−3.31499
$527$	−7.19349	−0.313353
$528$	46.1973	2.01048
$529$	0	0
$530$	25.7280	1.11755
$531$	0.0696923	0.00302439
$532$	−32.7769	−1.42106
$533$	11.8746	0.514345
$534$	52.9653	2.29203
$535$	19.5335	0.844507
$536$	−48.7947	−2.10761
$537$	−12.8099	−0.552786
$538$	13.9300	0.600563
$539$	6.70472	0.288793
$540$	−30.3654	−1.30672
$541$	4.10097	0.176314	0.0881572	−	0.996107i	$-0.471902\pi$
$541$	4.10097	0.176314	0.0881572	+	0.996107i	$0.471902\pi$
$542$	−45.4103	−1.95054
$543$	19.3140	0.828842
$544$	96.8317	4.15162
$545$	−2.00614	−0.0859335
$546$	16.5409	0.707885
$547$	37.7979	1.61612	0.808061	−	0.589099i	$-0.200517\pi$
$547$	37.7979	1.61612	0.808061	+	0.589099i	$0.200517\pi$
$548$	−60.9467	−2.60351
$549$	1.08625	0.0463599
$550$	4.38767	0.187091
$551$	0.139313	0.00593492
$552$	0	0
$553$	7.67027	0.326173
$554$	−59.8522	−2.54288
$555$	−10.8432	−0.460269
$556$	58.5478	2.48298
$557$	5.73855	0.243150	0.121575	−	0.992582i	$-0.461205\pi$
$557$	5.73855	0.243150	0.121575	+	0.992582i	$0.461205\pi$
$558$	0.771086	0.0326427
$559$	1.04976	0.0444000
$560$	−57.9798	−2.45009
$561$	9.45617	0.399240
$562$	−22.0348	−0.929481
$563$	10.3876	0.437784	0.218892	−	0.975749i	$-0.429756\pi$
$563$	10.3876	0.437784	0.218892	+	0.975749i	$0.429756\pi$
$564$	−44.2624	−1.86379
$565$	−3.05021	−0.128323
$566$	61.8318	2.59898
$567$	28.7457	1.20720
$568$	119.453	5.01212
$569$	13.6777	0.573398	0.286699	−	0.958021i	$-0.407442\pi$
$569$	13.6777	0.573398	0.286699	+	0.958021i	$0.407442\pi$
$570$	8.03290	0.336461
$571$	−26.7476	−1.11935	−0.559676	−	0.828712i	$-0.689074\pi$
$571$	−26.7476	−1.11935	−0.559676	+	0.828712i	$0.689074\pi$
$572$	−9.47648	−0.396232
$573$	−0.603255	−0.0252013
$574$	105.485	4.40284
$575$	0	0
$576$	−5.65893	−0.235789
$577$	16.7230	0.696188	0.348094	−	0.937460i	$-0.386829\pi$
$577$	16.7230	0.696188	0.348094	+	0.937460i	$0.386829\pi$
$578$	−12.4369	−0.517307
$579$	32.0633	1.33250
$580$	0.466540	0.0193720
$581$	12.1106	0.502434
$582$	32.8888	1.36328
$583$	14.6204	0.605514
$584$	45.3647	1.87721
$585$	0.143208	0.00592092
$586$	−0.277619	−0.0114683
$587$	−30.4349	−1.25618	−0.628091	−	0.778140i	$-0.716164\pi$
$587$	−30.4349	−1.25618	−0.628091	+	0.778140i	$0.716164\pi$
$588$	41.1072	1.69523
$589$	−3.47256	−0.143084
$590$	−1.41850	−0.0583986
$591$	33.9877	1.39807
$592$	−110.787	−4.55330
$593$	−15.6669	−0.643364	−0.321682	−	0.946848i	$-0.604248\pi$
$593$	−15.6669	−0.643364	−0.321682	+	0.946848i	$0.604248\pi$
$594$	−23.2879	−0.955512
$595$	−11.8679	−0.486538
$596$	−90.4129	−3.70346
$597$	15.0805	0.617205
$598$	0	0
$599$	29.8484	1.21957	0.609786	−	0.792566i	$-0.291255\pi$
$599$	29.8484	1.21957	0.609786	+	0.792566i	$0.291255\pi$
$600$	17.4971	0.714314
$601$	31.5531	1.28708	0.643538	−	0.765414i	$-0.277466\pi$
$601$	31.5531	1.28708	0.643538	+	0.765414i	$0.277466\pi$
$602$	9.32524	0.380068
$603$	0.644246	0.0262357
$604$	−5.25822	−0.213954
$605$	−8.50663	−0.345844
$606$	−18.6459	−0.757439
$607$	8.65912	0.351463	0.175731	−	0.984438i	$-0.443771\pi$
$607$	8.65912	0.351463	0.175731	+	0.984438i	$0.443771\pi$
$608$	46.7441	1.89572
$609$	−0.462758	−0.0187519
$610$	−22.1092	−0.895174
$611$	4.79596	0.194024
$612$	−2.76411	−0.111732
$613$	−40.3867	−1.63120	−0.815601	−	0.578615i	$-0.803593\pi$
$613$	−40.3867	−1.63120	−0.815601	+	0.578615i	$0.803593\pi$
$614$	−4.51150	−0.182069
$615$	−19.1555	−0.772426
$616$	−54.7535	−2.20608
$617$	27.5692	1.10989	0.554946	−	0.831886i	$-0.312739\pi$
$617$	27.5692	1.10989	0.554946	+	0.831886i	$0.312739\pi$
$618$	−68.4729	−2.75439
$619$	38.5011	1.54749	0.773744	−	0.633498i	$-0.218381\pi$
$619$	38.5011	1.54749	0.773744	+	0.633498i	$0.218381\pi$
$620$	−11.6292	−0.467038
$621$	0	0
$622$	67.3476	2.70039
$623$	−37.7750	−1.51342
$624$	−30.6898	−1.22857
$625$	1.00000	0.0400000
$626$	−58.0703	−2.32096
$627$	4.56483	0.182302
$628$	−77.5595	−3.09496
$629$	−22.6770	−0.904192
$630$	1.27215	0.0506837
$631$	−6.92094	−0.275518	−0.137759	−	0.990466i	$-0.543990\pi$
$631$	−6.92094	−0.275518	−0.137759	+	0.990466i	$0.543990\pi$
$632$	−23.6498	−0.940740
$633$	−38.7070	−1.53846
$634$	40.3228	1.60142
$635$	6.96235	0.276293
$636$	89.6386	3.55440
$637$	−4.45408	−0.176477
$638$	0.357800	0.0141654
$639$	−1.57716	−0.0623913
$640$	60.4571	2.38978
$641$	1.70697	0.0674213	0.0337107	−	0.999432i	$-0.489268\pi$
$641$	1.70697	0.0674213	0.0337107	+	0.999432i	$0.489268\pi$
$642$	91.8477	3.62494
$643$	3.03046	0.119510	0.0597548	−	0.998213i	$-0.480968\pi$
$643$	3.03046	0.119510	0.0597548	+	0.998213i	$0.480968\pi$
$644$	0	0
$645$	−1.69342	−0.0666785
$646$	16.7997	0.660973
$647$	−1.28622	−0.0505667	−0.0252833	−	0.999680i	$-0.508049\pi$
$647$	−1.28622	−0.0505667	−0.0252833	+	0.999680i	$0.508049\pi$
$648$	−88.6319	−3.48179
$649$	−0.806086	−0.0316416
$650$	−2.91482	−0.114329
$651$	11.5349	0.452087
$652$	−44.6685	−1.74936
$653$	−9.90387	−0.387568	−0.193784	−	0.981044i	$-0.562076\pi$
$653$	−9.90387	−0.387568	−0.193784	+	0.981044i	$0.562076\pi$
$654$	−9.43298	−0.368859
$655$	5.45517	0.213151
$656$	−195.715	−7.64138
$657$	−0.598959	−0.0233676
$658$	42.6036	1.66086
$659$	26.3008	1.02454	0.512268	−	0.858826i	$-0.328806\pi$
$659$	26.3008	1.02454	0.512268	+	0.858826i	$0.328806\pi$
$660$	15.2871	0.595048
$661$	−33.7266	−1.31181	−0.655907	−	0.754842i	$-0.727714\pi$
$661$	−33.7266	−1.31181	−0.655907	+	0.754842i	$0.727714\pi$
$662$	44.5176	1.73022
$663$	−6.28192	−0.243969
$664$	−37.3409	−1.44911
$665$	−5.72908	−0.222164
$666$	2.43080	0.0941916
$667$	0	0
$668$	−96.7945	−3.74509
$669$	7.16284	0.276932
$670$	−13.1128	−0.506592
$671$	−12.5639	−0.485024
$672$	−155.271	−5.98970
$673$	−27.2558	−1.05064	−0.525318	−	0.850906i	$-0.676054\pi$
$673$	−27.2558	−1.05064	−0.525318	+	0.850906i	$0.676054\pi$
$674$	48.0131	1.84939
$675$	−5.30756	−0.204288
$676$	−68.0795	−2.61844
$677$	−15.0977	−0.580250	−0.290125	−	0.956989i	$-0.593697\pi$
$677$	−15.0977	−0.580250	−0.290125	+	0.956989i	$0.593697\pi$
$678$	−14.3423	−0.550811
$679$	−23.4563	−0.900172
$680$	36.5926	1.40326
$681$	44.0739	1.68892
$682$	−8.91866	−0.341513
$683$	0.00681169	0.000260642 0	0.000130321	−	1.00000i	$-0.499959\pi$
$683$	0.00681169	0.000260642 0	0.000130321		1.00000i	$0.499959\pi$
$684$	−1.33433	−0.0510195
$685$	−10.6529	−0.407026
$686$	25.6622	0.979787
$687$	−5.16636	−0.197109
$688$	−17.3019	−0.659630
$689$	−9.71259	−0.370020
$690$	0	0
$691$	6.89679	0.262366	0.131183	−	0.991358i	$-0.458122\pi$
$691$	6.89679	0.262366	0.131183	+	0.991358i	$0.458122\pi$
$692$	31.7733	1.20784
$693$	0.722921	0.0274615
$694$	13.5469	0.514235
$695$	10.2336	0.388181
$696$	1.42683	0.0540837
$697$	−40.0610	−1.51742
$698$	−68.3904	−2.58862
$699$	40.0159	1.51354
$700$	−19.1860	−0.725161
$701$	−46.5476	−1.75808	−0.879039	−	0.476749i	$-0.841815\pi$
$701$	−46.5476	−1.75808	−0.879039	+	0.476749i	$0.841815\pi$
$702$	15.4706	0.583899
$703$	−10.9470	−0.412875
$704$	65.4532	2.46686
$705$	−7.73664	−0.291379
$706$	95.8297	3.60660
$707$	13.2983	0.500134
$708$	−4.94218	−0.185738
$709$	37.1775	1.39623	0.698115	−	0.715985i	$-0.254022\pi$
$709$	37.1775	1.39623	0.698115	+	0.715985i	$0.254022\pi$
$710$	32.1010	1.20473
$711$	0.312253	0.0117104
$712$	116.472	4.36497
$713$	0	0
$714$	−55.8037	−2.08840
$715$	−1.65639	−0.0619456
$716$	−43.3092	−1.61854
$717$	8.44356	0.315331
$718$	98.2426	3.66638
$719$	−32.8243	−1.22414	−0.612069	−	0.790804i	$-0.709663\pi$
$719$	−32.8243	−1.22414	−0.612069	+	0.790804i	$0.709663\pi$
$720$	−2.36033	−0.0879643
$721$	48.8350	1.81871
$722$	−44.6854	−1.66302
$723$	−36.6048	−1.36135
$724$	65.2992	2.42683
$725$	0.0815466	0.00302857
$726$	−39.9987	−1.48449
$727$	−39.6752	−1.47147	−0.735736	−	0.677268i	$-0.763164\pi$
$727$	−39.6752	−1.47147	−0.735736	+	0.677268i	$0.763164\pi$
$728$	36.3738	1.34810
$729$	28.1143	1.04127
$730$	12.1911	0.451211
$731$	−3.54155	−0.130989
$732$	−77.0303	−2.84712
$733$	−28.8999	−1.06744	−0.533722	−	0.845660i	$-0.679207\pi$
$733$	−28.8999	−1.06744	−0.533722	+	0.845660i	$0.679207\pi$
$734$	−80.5089	−2.97164
$735$	7.18513	0.265027
$736$	0	0
$737$	−7.45158	−0.274482
$738$	4.29423	0.158073
$739$	31.9339	1.17471	0.587354	−	0.809330i	$-0.300170\pi$
$739$	31.9339	1.17471	0.587354	+	0.809330i	$0.300170\pi$
$740$	−36.6602	−1.34765
$741$	−3.03251	−0.111402
$742$	−86.2792	−3.16741
$743$	−25.6268	−0.940157	−0.470078	−	0.882625i	$-0.655774\pi$
$743$	−25.6268	−0.940157	−0.470078	+	0.882625i	$0.655774\pi$
$744$	−35.5656	−1.30390
$745$	−15.8033	−0.578987
$746$	18.0718	0.661657
$747$	0.493019	0.0180386
$748$	31.9706	1.16896
$749$	−65.5059	−2.39354
$750$	4.70206	0.171695
$751$	−8.79112	−0.320793	−0.160396	−	0.987053i	$-0.551277\pi$
$751$	−8.79112	−0.320793	−0.160396	+	0.987053i	$0.551277\pi$
$752$	−79.0462	−2.88252
$753$	−12.5145	−0.456053
$754$	−0.237694	−0.00865629
$755$	−0.919085	−0.0334489
$756$	101.831	3.70355
$757$	30.7830	1.11883	0.559414	−	0.828889i	$-0.311026\pi$
$757$	30.7830	1.11883	0.559414	+	0.828889i	$0.311026\pi$
$758$	89.9112	3.26572
$759$	0	0
$760$	17.6645	0.640760
$761$	19.9404	0.722839	0.361419	−	0.932403i	$-0.382292\pi$
$761$	19.9404	0.722839	0.361419	+	0.932403i	$0.382292\pi$
$762$	32.7374	1.18595
$763$	6.72762	0.243556
$764$	−2.03956	−0.0737888
$765$	−0.483139	−0.0174679
$766$	96.6597	3.49246
$767$	0.535498	0.0193357
$768$	143.987	5.19567
$769$	7.06884	0.254909	0.127454	−	0.991844i	$-0.459319\pi$
$769$	7.06884	0.254909	0.127454	+	0.991844i	$0.459319\pi$
$770$	−14.7141	−0.530261
$771$	−2.78842	−0.100422
$772$	108.404	3.90153
$773$	−28.1460	−1.01234	−0.506172	−	0.862433i	$-0.668940\pi$
$773$	−28.1460	−1.01234	−0.506172	+	0.862433i	$0.668940\pi$
$774$	0.379626	0.0136454
$775$	−2.03266	−0.0730153
$776$	72.3232	2.59625
$777$	36.3629	1.30451
$778$	49.0783	1.75954
$779$	−19.3389	−0.692888
$780$	−10.1555	−0.363625
$781$	18.2419	0.652748
$782$	0	0
$783$	−0.432814	−0.0154675
$784$	73.4114	2.62184
$785$	−13.5566	−0.483857
$786$	25.6505	0.914925
$787$	−35.1098	−1.25153	−0.625765	−	0.780012i	$-0.715213\pi$
$787$	−35.1098	−1.25153	−0.625765	+	0.780012i	$0.715213\pi$
$788$	114.910	4.09350
$789$	−46.3000	−1.64832
$790$	−6.35552	−0.226119
$791$	10.2289	0.363699
$792$	−2.22899	−0.0792037
$793$	8.34645	0.296391
$794$	93.1440	3.30556
$795$	15.6679	0.555684
$796$	50.9862	1.80716
$797$	−30.3907	−1.07649	−0.538247	−	0.842787i	$-0.680913\pi$
$797$	−30.3907	−1.07649	−0.538247	+	0.842787i	$0.680913\pi$
$798$	−26.9385	−0.953612
$799$	−16.1801	−0.572409
$800$	27.3617	0.967381
$801$	−1.53780	−0.0543356
$802$	40.9603	1.44636
$803$	6.92777	0.244476
$804$	−45.6862	−1.61123
$805$	0	0
$806$	5.92484	0.208693
$807$	8.48313	0.298620
$808$	−41.0028	−1.44247
$809$	10.2005	0.358631	0.179315	−	0.983792i	$-0.442612\pi$
$809$	10.2005	0.358631	0.179315	+	0.983792i	$0.442612\pi$
$810$	−23.8184	−0.836894
$811$	−1.34102	−0.0470895	−0.0235448	−	0.999723i	$-0.507495\pi$
$811$	−1.34102	−0.0470895	−0.0235448	+	0.999723i	$0.507495\pi$
$812$	−1.56455	−0.0549050
$813$	−27.6542	−0.969874
$814$	−28.1155	−0.985447
$815$	−7.80762	−0.273489
$816$	103.538	3.62454
$817$	−1.70963	−0.0598125
$818$	−23.7843	−0.831599
$819$	−0.480250	−0.0167813
$820$	−64.7636	−2.26164
$821$	33.5203	1.16987	0.584933	−	0.811081i	$-0.301121\pi$
$821$	33.5203	1.16987	0.584933	+	0.811081i	$0.301121\pi$
$822$	−50.0905	−1.74711
$823$	−15.9636	−0.556456	−0.278228	−	0.960515i	$-0.589747\pi$
$823$	−15.9636	−0.556456	−0.278228	+	0.960515i	$0.589747\pi$
$824$	−150.574	−5.24548
$825$	2.67202	0.0930280
$826$	4.75696	0.165516
$827$	1.15419	0.0401353	0.0200676	−	0.999799i	$-0.493612\pi$
$827$	1.15419	0.0401353	0.0200676	+	0.999799i	$0.493612\pi$
$828$	0	0
$829$	−26.9875	−0.937313	−0.468657	−	0.883380i	$-0.655262\pi$
$829$	−26.9875	−0.937313	−0.468657	+	0.883380i	$0.655262\pi$
$830$	−10.0348	−0.348312
$831$	−36.4491	−1.26440
$832$	−43.4819	−1.50746
$833$	15.0267	0.520643
$834$	48.1189	1.66622
$835$	−16.9187	−0.585496
$836$	15.4334	0.533775
$837$	10.7885	0.372904
$838$	13.4579	0.464897
$839$	−11.9940	−0.414079	−0.207039	−	0.978333i	$-0.566383\pi$
$839$	−11.9940	−0.414079	−0.207039	+	0.978333i	$0.566383\pi$
$840$	−58.6767	−2.02454
$841$	−28.9934	−0.999771
$842$	−23.0004	−0.792647
$843$	−13.4188	−0.462169
$844$	−130.866	−4.50458
$845$	−11.8996	−0.409360
$846$	1.73438	0.0596290
$847$	28.5271	0.980204
$848$	160.081	5.49722
$849$	37.6546	1.29230
$850$	9.83367	0.337292
$851$	0	0
$852$	111.843	3.83167
$853$	22.5566	0.772322	0.386161	−	0.922431i	$-0.373801\pi$
$853$	22.5566	0.772322	0.386161	+	0.922431i	$0.373801\pi$
$854$	74.1435	2.53714
$855$	−0.233228	−0.00797624
$856$	201.975	6.90337
$857$	−22.7303	−0.776453	−0.388226	−	0.921564i	$-0.626912\pi$
$857$	−22.7303	−0.776453	−0.388226	+	0.921564i	$0.626912\pi$
$858$	−7.78846	−0.265894
$859$	31.7762	1.08419	0.542095	−	0.840317i	$-0.317631\pi$
$859$	31.7762	1.08419	0.542095	+	0.840317i	$0.317631\pi$
$860$	−5.72534	−0.195233
$861$	64.2384	2.18924
$862$	−20.0959	−0.684471
$863$	11.0034	0.374559	0.187280	−	0.982307i	$-0.440033\pi$
$863$	11.0034	0.374559	0.187280	+	0.982307i	$0.440033\pi$
$864$	−145.224	−4.94061
$865$	5.55366	0.188830
$866$	−52.8982	−1.79755
$867$	−7.57389	−0.257223
$868$	38.9986	1.32370
$869$	−3.61163	−0.122516
$870$	0.383437	0.0129997
$871$	4.95023	0.167732
$872$	−20.7433	−0.702458
$873$	−0.954897	−0.0323184
$874$	0	0
$875$	−3.35352	−0.113370
$876$	42.4747	1.43509
$877$	42.9981	1.45194	0.725972	−	0.687724i	$-0.241390\pi$
$877$	42.9981	1.45194	0.725972	+	0.687724i	$0.241390\pi$
$878$	4.87960	0.164678
$879$	−0.169066	−0.00570245
$880$	27.3004	0.920297
$881$	46.2114	1.55690	0.778451	−	0.627705i	$-0.216006\pi$
$881$	46.2114	1.55690	0.778451	+	0.627705i	$0.216006\pi$
$882$	−1.61074	−0.0542364
$883$	7.33900	0.246977	0.123488	−	0.992346i	$-0.460592\pi$
$883$	7.33900	0.246977	0.123488	+	0.992346i	$0.460592\pi$
$884$	−21.2387	−0.714336
$885$	−0.863843	−0.0290378
$886$	−1.12919	−0.0379359
$887$	19.3202	0.648708	0.324354	−	0.945936i	$-0.394853\pi$
$887$	19.3202	0.648708	0.324354	+	0.945936i	$0.394853\pi$
$888$	−112.118	−3.76244
$889$	−23.3484	−0.783079
$890$	31.3000	1.04918
$891$	−13.5352	−0.453447
$892$	24.2171	0.810847
$893$	−7.81069	−0.261375
$894$	−74.3079	−2.48523
$895$	−7.57003	−0.253038
$896$	−202.744	−6.77319
$897$	0	0
$898$	67.3737	2.24829
$899$	−0.165757	−0.00552829
$900$	−0.781052	−0.0260351
$901$	32.7672	1.09163
$902$	−49.6686	−1.65378
$903$	5.67892	0.188983
$904$	−31.5390	−1.04897
$905$	11.4137	0.379403
$906$	−4.32159	−0.143575
$907$	54.6702	1.81529	0.907646	−	0.419736i	$-0.137877\pi$
$907$	54.6702	1.81529	0.907646	+	0.419736i	$0.137877\pi$
$908$	149.011	4.94509
$909$	0.541368	0.0179561
$910$	9.77489	0.324034
$911$	−44.0710	−1.46014	−0.730069	−	0.683373i	$-0.760512\pi$
$911$	−44.0710	−1.46014	−0.730069	+	0.683373i	$0.760512\pi$
$912$	49.9813	1.65505
$913$	−5.70244	−0.188723
$914$	85.1513	2.81655
$915$	−13.4641	−0.445111
$916$	−17.4671	−0.577129
$917$	−18.2940	−0.604122
$918$	−52.1928	−1.72262
$919$	−4.75833	−0.156963	−0.0784814	−	0.996916i	$-0.525007\pi$
$919$	−4.75833	−0.156963	−0.0784814	+	0.996916i	$0.525007\pi$
$920$	0	0
$921$	−2.74743	−0.0905310
$922$	−41.6697	−1.37232
$923$	−12.1185	−0.398884
$924$	−51.2654	−1.68651
$925$	−6.40783	−0.210688
$926$	−52.7845	−1.73461
$927$	1.98805	0.0652962
$928$	2.23125	0.0732444
$929$	−21.8918	−0.718246	−0.359123	−	0.933290i	$-0.616924\pi$
$929$	−21.8918	−0.718246	−0.359123	+	0.933290i	$0.616924\pi$
$930$	−9.55769	−0.313409
$931$	7.25391	0.237737
$932$	135.291	4.43161
$933$	41.0136	1.34273
$934$	19.3466	0.633041
$935$	5.58815	0.182752
$936$	1.48076	0.0484002
$937$	54.1373	1.76859	0.884294	−	0.466931i	$-0.154640\pi$
$937$	54.1373	1.76859	0.884294	+	0.466931i	$0.154640\pi$
$938$	43.9740	1.43580
$939$	−35.3639	−1.15406
$940$	−26.1570	−0.853148
$941$	−17.6212	−0.574436	−0.287218	−	0.957865i	$-0.592730\pi$
$941$	−17.6212	−0.574436	−0.287218	+	0.957865i	$0.592730\pi$
$942$	−63.7440	−2.07689
$943$	0	0
$944$	−8.82600	−0.287262
$945$	17.7990	0.579001
$946$	−4.39089	−0.142760
$947$	−14.0000	−0.454939	−0.227470	−	0.973785i	$-0.573045\pi$
$947$	−14.0000	−0.454939	−0.227470	+	0.973785i	$0.573045\pi$
$948$	−22.1432	−0.719178
$949$	−4.60225	−0.149395
$950$	4.74707	0.154015
$951$	24.5560	0.796281
$952$	−122.714	−3.97718
$953$	16.6776	0.540239	0.270120	−	0.962827i	$-0.412937\pi$
$953$	16.6776	0.540239	0.270120	+	0.962827i	$0.412937\pi$
$954$	−3.51239	−0.113718
$955$	−0.356495	−0.0115359
$956$	28.5471	0.923279
$957$	0.217895	0.00704353
$958$	76.1434	2.46008
$959$	35.7246	1.15361
$960$	70.1431	2.26386
$961$	−26.8683	−0.866719
$962$	18.6777	0.602192
$963$	−2.66672	−0.0859338
$964$	−123.758	−3.98598
$965$	18.9479	0.609954
$966$	0	0
$967$	35.4674	1.14055	0.570277	−	0.821453i	$-0.306836\pi$
$967$	35.4674	1.14055	0.570277	+	0.821453i	$0.306836\pi$
$968$	−87.9580	−2.82708
$969$	10.2307	0.328658
$970$	19.4357	0.624044
$971$	−35.5074	−1.13949	−0.569743	−	0.821823i	$-0.692957\pi$
$971$	−35.5074	−1.13949	−0.569743	+	0.821823i	$0.692957\pi$
$972$	8.11053	0.260145
$973$	−34.3185	−1.10020
$974$	46.1567	1.47896
$975$	−1.77508	−0.0568480
$976$	−137.565	−4.40334
$977$	18.7951	0.601309	0.300654	−	0.953733i	$-0.402795\pi$
$977$	18.7951	0.601309	0.300654	+	0.953733i	$0.402795\pi$
$978$	−36.7119	−1.17392
$979$	17.7868	0.568467
$980$	24.2924	0.775993
$981$	0.273878	0.00874426
$982$	86.0153	2.74486
$983$	48.0392	1.53221	0.766106	−	0.642714i	$-0.222192\pi$
$983$	48.0392	1.53221	0.766106	+	0.642714i	$0.222192\pi$
$984$	−198.067	−6.31415
$985$	20.0851	0.639966
$986$	0.801903	0.0255378
$987$	25.9449	0.825836
$988$	−10.2527	−0.326182
$989$	0	0
$990$	−0.599006	−0.0190377
$991$	−28.8641	−0.916898	−0.458449	−	0.888721i	$-0.651595\pi$
$991$	−28.8641	−0.916898	−0.458449	+	0.888721i	$0.651595\pi$
$992$	−55.6170	−1.76584
$993$	27.1105	0.860326
$994$	−107.651	−3.41449
$995$	8.91188	0.282526
$996$	−34.9621	−1.10782
$997$	−46.2033	−1.46327	−0.731637	−	0.681694i	$-0.761243\pi$
$997$	−46.2033	−1.46327	−0.731637	+	0.681694i	$0.761243\pi$
$998$	−7.39227	−0.233998
$999$	34.0100	1.07603

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2645.2.a.y.1.25		25
23.4	even	11		115.2.g.c.16.1	✓	50
23.6	even	11		115.2.g.c.36.1	yes	50
23.22	odd	2		2645.2.a.x.1.25		25
115.4	even	22		575.2.k.d.476.5		50
115.27	odd	44		575.2.p.d.499.1		100
115.29	even	22		575.2.k.d.151.5		50
115.52	odd	44		575.2.p.d.174.10		100
115.73	odd	44		575.2.p.d.499.10		100
115.98	odd	44		575.2.p.d.174.1		100

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
115.2.g.c.16.1	✓	50	23.4	even	11
115.2.g.c.36.1	yes	50	23.6	even	11
575.2.k.d.151.5		50	115.29	even	22
575.2.k.d.476.5		50	115.4	even	22
575.2.p.d.174.1		100	115.98	odd	44
575.2.p.d.174.10		100	115.52	odd	44
575.2.p.d.499.1		100	115.27	odd	44
575.2.p.d.499.10		100	115.73	odd	44
2645.2.a.x.1.25		25	23.22	odd	2
2645.2.a.y.1.25		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)

\(f(q)\)	\(=\)	\(q+2.77870 q^{2} +1.69218 q^{3} +5.72115 q^{4} +1.00000 q^{5} +4.70206 q^{6} -3.35352 q^{7} +10.3399 q^{8} -0.136520 q^{9} +O(q^{10})\)	\(q+2.77870 q^{2} +1.69218 q^{3} +5.72115 q^{4} +1.00000 q^{5} +4.70206 q^{6} -3.35352 q^{7} +10.3399 q^{8} -0.136520 q^{9} +2.77870 q^{10} +1.57904 q^{11} +9.68122 q^{12} -1.04899 q^{13} -9.31840 q^{14} +1.69218 q^{15} +17.2892 q^{16} +3.53895 q^{17} -0.379348 q^{18} +1.70838 q^{19} +5.72115 q^{20} -5.67476 q^{21} +4.38767 q^{22} +17.4971 q^{24} +1.00000 q^{25} -2.91482 q^{26} -5.30756 q^{27} -19.1860 q^{28} +0.0815466 q^{29} +4.70206 q^{30} -2.03266 q^{31} +27.3617 q^{32} +2.67202 q^{33} +9.83367 q^{34} -3.35352 q^{35} -0.781052 q^{36} -6.40783 q^{37} +4.74707 q^{38} -1.77508 q^{39} +10.3399 q^{40} -11.3200 q^{41} -15.7684 q^{42} -1.00073 q^{43} +9.03393 q^{44} -0.136520 q^{45} -4.57199 q^{47} +29.2565 q^{48} +4.24607 q^{49} +2.77870 q^{50} +5.98855 q^{51} -6.00141 q^{52} +9.25901 q^{53} -14.7481 q^{54} +1.57904 q^{55} -34.6752 q^{56} +2.89089 q^{57} +0.226593 q^{58} -0.510491 q^{59} +9.68122 q^{60} -7.95667 q^{61} -5.64815 q^{62} +0.457823 q^{63} +41.4512 q^{64} -1.04899 q^{65} +7.42474 q^{66} -4.71905 q^{67} +20.2469 q^{68} -9.31840 q^{70} +11.5525 q^{71} -1.41161 q^{72} +4.38733 q^{73} -17.8054 q^{74} +1.69218 q^{75} +9.77390 q^{76} -5.29534 q^{77} -4.93240 q^{78} -2.28723 q^{79} +17.2892 q^{80} -8.57180 q^{81} -31.4549 q^{82} -3.61133 q^{83} -32.4661 q^{84} +3.53895 q^{85} -2.78073 q^{86} +0.137992 q^{87} +16.3272 q^{88} +11.2643 q^{89} -0.379348 q^{90} +3.51780 q^{91} -3.43963 q^{93} -12.7042 q^{94} +1.70838 q^{95} +46.3009 q^{96} +6.99455 q^{97} +11.7985 q^{98} -0.215571 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 25 q + 3 q^{2} + 10 q^{3} + 33 q^{4} + 25 q^{5} + 22 q^{6} + 14 q^{7} + 21 q^{8} + 29 q^{9}+O(q^{10}) \) 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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