LMFDB - Embedded newform 325.4.b.b.274.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [325,4,Mod(274,325)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(325, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 0]))

N = Newforms(chi, 4, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("325.274");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 325 = 5^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	325.b (of order $2$, degree $1$, not minimal)

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:	no
Analytic conductor:	$19.1756207519$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(i)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} + 1 $ x^2 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 13)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			274.1
Root			$-1.00000i$ of defining polynomial
Character	$\chi$	$=$	325.274
Dual form			325.4.b.b.274.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-5.00000i q^{2} +7.00000i q^{3} -17.0000 q^{4} +35.0000 q^{6} -13.0000i q^{7} +45.0000i q^{8} -22.0000 q^{9} +O(q^{10})$	\(q-5.00000i q^{2} +7.00000i q^{3} -17.0000 q^{4} +35.0000 q^{6} -13.0000i q^{7} +45.0000i q^{8} -22.0000 q^{9} -26.0000 q^{11} -119.000i q^{12} -13.0000i q^{13} -65.0000 q^{14} +89.0000 q^{16} +77.0000i q^{17} +110.000i q^{18} +126.000 q^{19} +91.0000 q^{21} +130.000i q^{22} +96.0000i q^{23} -315.000 q^{24} -65.0000 q^{26} +35.0000i q^{27} +221.000i q^{28} +82.0000 q^{29} +196.000 q^{31} -85.0000i q^{32} -182.000i q^{33} +385.000 q^{34} +374.000 q^{36} -131.000i q^{37} -630.000i q^{38} +91.0000 q^{39} +336.000 q^{41} -455.000i q^{42} +201.000i q^{43} +442.000 q^{44} +480.000 q^{46} -105.000i q^{47} +623.000i q^{48} +174.000 q^{49} -539.000 q^{51} +221.000i q^{52} +432.000i q^{53} +175.000 q^{54} +585.000 q^{56} +882.000i q^{57} -410.000i q^{58} +294.000 q^{59} -56.0000 q^{61} -980.000i q^{62} +286.000i q^{63} +287.000 q^{64} -910.000 q^{66} +478.000i q^{67} -1309.00i q^{68} -672.000 q^{69} +9.00000 q^{71} -990.000i q^{72} -98.0000i q^{73} -655.000 q^{74} -2142.00 q^{76} +338.000i q^{77} -455.000i q^{78} -1304.00 q^{79} -839.000 q^{81} -1680.00i q^{82} +308.000i q^{83} -1547.00 q^{84} +1005.00 q^{86} +574.000i q^{87} -1170.00i q^{88} +1190.00 q^{89} -169.000 q^{91} -1632.00i q^{92} +1372.00i q^{93} -525.000 q^{94} +595.000 q^{96} +70.0000i q^{97} -870.000i q^{98} +572.000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 34 q^{4} + 70 q^{6} - 44 q^{9}+O(q^{10}) $ 2 * q - 34 * q^4 + 70 * q^6 - 44 * q^9	$ 2 q - 34 q^{4} + 70 q^{6} - 44 q^{9} - 52 q^{11} - 130 q^{14} + 178 q^{16} + 252 q^{19} + 182 q^{21} - 630 q^{24} - 130 q^{26} + 164 q^{29} + 392 q^{31} + 770 q^{34} + 748 q^{36} + 182 q^{39} + 672 q^{41} + 884 q^{44} + 960 q^{46} + 348 q^{49} - 1078 q^{51} + 350 q^{54} + 1170 q^{56} + 588 q^{59} - 112 q^{61} + 574 q^{64} - 1820 q^{66} - 1344 q^{69} + 18 q^{71} - 1310 q^{74} - 4284 q^{76} - 2608 q^{79} - 1678 q^{81} - 3094 q^{84} + 2010 q^{86} + 2380 q^{89} - 338 q^{91} - 1050 q^{94} + 1190 q^{96} + 1144 q^{99}+O(q^{100}) $ 2 * q - 34 * q^4 + 70 * q^6 - 44 * q^9 - 52 * q^11 - 130 * q^14 + 178 * q^16 + 252 * q^19 + 182 * q^21 - 630 * q^24 - 130 * q^26 + 164 * q^29 + 392 * q^31 + 770 * q^34 + 748 * q^36 + 182 * q^39 + 672 * q^41 + 884 * q^44 + 960 * q^46 + 348 * q^49 - 1078 * q^51 + 350 * q^54 + 1170 * q^56 + 588 * q^59 - 112 * q^61 + 574 * q^64 - 1820 * q^66 - 1344 * q^69 + 18 * q^71 - 1310 * q^74 - 4284 * q^76 - 2608 * q^79 - 1678 * q^81 - 3094 * q^84 + 2010 * q^86 + 2380 * q^89 - 338 * q^91 - 1050 * q^94 + 1190 * q^96 + 1144 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/325\mathbb{Z}\right)^\times$.

$n$	$27$	$301$
$\chi(n)$	$-1$	$1$

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 $

$2$	− 5.00000i	− 1.76777i	−0.467707	−	0.883883i	$-0.654920\pi$
$2$	− 5.00000i	− 1.76777i	0.467707	−	0.883883i	$-0.345080\pi$
$3$	7.00000i	1.34715i	0.739119	+	0.673575i	$0.235242\pi$
$3$	7.00000i	1.34715i	−0.739119	+	0.673575i	$0.764758\pi$
$4$	−17.0000	−2.12500
$5$	0	0
$5$	0	0
$6$	35.0000	2.38145
$7$	− 13.0000i	− 0.701934i	−0.936388	−	0.350967i	$-0.885853\pi$
$7$	− 13.0000i	− 0.701934i	0.936388	−	0.350967i	$-0.114147\pi$
$8$	45.0000i	1.98874i
$9$	−22.0000	−0.814815
$10$	0	0
$11$	−26.0000	−0.712663	−0.356332	−	0.934360i	$-0.615973\pi$
$11$	−26.0000	−0.712663	−0.356332	+	0.934360i	$0.615973\pi$
$12$	− 119.000i	− 2.86270i
$13$	− 13.0000i	− 0.277350i
$13$	− 13.0000i	− 0.277350i
$14$	−65.0000	−1.24086
$15$	0	0
$16$	89.0000	1.39062
$17$	77.0000i	1.09854i	0.835644	+	0.549272i	$0.185095\pi$
$17$	77.0000i	1.09854i	−0.835644	+	0.549272i	$0.814905\pi$
$18$	110.000i	1.44040i
$19$	126.000	1.52139	0.760694	−	0.649110i	$-0.224859\pi$
$19$	126.000	1.52139	0.760694	+	0.649110i	$0.224859\pi$
$20$	0	0
$21$	91.0000	0.945611
$22$	130.000i	1.25982i
$23$	96.0000i	0.870321i	0.900353	+	0.435161i	$0.143308\pi$
$23$	96.0000i	0.870321i	−0.900353	+	0.435161i	$0.856692\pi$
$24$	−315.000	−2.67913
$25$	0	0
$26$	−65.0000	−0.490290
$27$	35.0000i	0.249472i
$28$	221.000i	1.49161i
$29$	82.0000	0.525070	0.262535	−	0.964923i	$-0.415442\pi$
$29$	82.0000	0.525070	0.262535	+	0.964923i	$0.415442\pi$
$30$	0	0
$31$	196.000	1.13557	0.567785	−	0.823177i	$-0.307801\pi$
$31$	196.000	1.13557	0.567785	+	0.823177i	$0.307801\pi$
$32$	− 85.0000i	− 0.469563i
$33$	− 182.000i	− 0.960065i
$34$	385.000	1.94197
$35$	0	0
$36$	374.000	1.73148
$37$	− 131.000i	− 0.582061i	−0.956714	−	0.291031i	$-0.906002\pi$
$37$	− 131.000i	− 0.582061i	0.956714	−	0.291031i	$-0.0939982\pi$
$38$	− 630.000i	− 2.68946i
$39$	91.0000	0.373632
$40$	0	0
$41$	336.000	1.27986	0.639932	−	0.768432i	$-0.278963\pi$
$41$	336.000	1.27986	0.639932	+	0.768432i	$0.278963\pi$
$42$	− 455.000i	− 1.67162i
$43$	201.000i	0.712842i	0.934325	+	0.356421i	$0.116003\pi$
$43$	201.000i	0.712842i	−0.934325	+	0.356421i	$0.883997\pi$
$44$	442.000	1.51441
$45$	0	0
$46$	480.000	1.53852
$47$	− 105.000i	− 0.325869i	−0.986637	−	0.162934i	$-0.947904\pi$
$47$	− 105.000i	− 0.325869i	0.986637	−	0.162934i	$-0.0520959\pi$
$48$	623.000i	1.87338i
$49$	174.000	0.507289
$50$	0	0
$51$	−539.000	−1.47990
$52$	221.000i	0.589369i
$53$	432.000i	1.11962i	0.828622	+	0.559809i	$0.189126\pi$
$53$	432.000i	1.11962i	−0.828622	+	0.559809i	$0.810874\pi$
$54$	175.000	0.441009
$55$	0	0
$56$	585.000	1.39596
$57$	882.000i	2.04954i
$58$	− 410.000i	− 0.928201i
$59$	294.000	0.648738	0.324369	−	0.945931i	$-0.394848\pi$
$59$	294.000	0.648738	0.324369	+	0.945931i	$0.394848\pi$
$60$	0	0
$61$	−56.0000	−0.117542	−0.0587710	−	0.998271i	$-0.518718\pi$
$61$	−56.0000	−0.117542	−0.0587710	+	0.998271i	$0.518718\pi$
$62$	− 980.000i	− 2.00742i
$63$	286.000i	0.571946i
$64$	287.000	0.560547
$65$	0	0
$66$	−910.000	−1.69717
$67$	478.000i	0.871597i	0.900044	+	0.435798i	$0.143534\pi$
$67$	478.000i	0.871597i	−0.900044	+	0.435798i	$0.856466\pi$
$68$	− 1309.00i	− 2.33441i
$69$	−672.000	−1.17245
$70$	0	0
$71$	9.00000	0.0150437	0.00752186	−	0.999972i	$-0.497606\pi$
$71$	9.00000	0.0150437	0.00752186	+	0.999972i	$0.497606\pi$
$72$	− 990.000i	− 1.62045i
$73$	− 98.0000i	− 0.157124i	−0.996909	−	0.0785619i	$-0.974967\pi$
$73$	− 98.0000i	− 0.157124i	0.996909	−	0.0785619i	$-0.0250328\pi$
$74$	−655.000	−1.02895
$75$	0	0
$76$	−2142.00	−3.23295
$77$	338.000i	0.500243i
$78$	− 455.000i	− 0.660495i
$79$	−1304.00	−1.85711	−0.928554	−	0.371198i	$-0.878947\pi$
$79$	−1304.00	−1.85711	−0.928554	+	0.371198i	$0.878947\pi$
$80$	0	0
$81$	−839.000	−1.15089
$82$	− 1680.00i	− 2.26250i
$83$	308.000i	0.407318i	0.979042	+	0.203659i	$0.0652834\pi$
$83$	308.000i	0.407318i	−0.979042	+	0.203659i	$0.934717\pi$
$84$	−1547.00	−2.00942
$85$	0	0
$86$	1005.00	1.26014
$87$	574.000i	0.707348i
$88$	− 1170.00i	− 1.41730i
$89$	1190.00	1.41730	0.708650	−	0.705560i	$-0.249304\pi$
$89$	1190.00	1.41730	0.708650	+	0.705560i	$0.249304\pi$
$90$	0	0
$91$	−169.000	−0.194681
$92$	− 1632.00i	− 1.84943i
$93$	1372.00i	1.52978i
$94$	−525.000	−0.576060
$95$	0	0
$96$	595.000	0.632572
$97$	70.0000i	0.0732724i	0.999329	+	0.0366362i	$0.0116643\pi$
$97$	70.0000i	0.0732724i	−0.999329	+	0.0366362i	$0.988336\pi$
$98$	− 870.000i	− 0.896768i
$99$	572.000	0.580689
$100$	0	0
$101$	420.000	0.413778	0.206889	−	0.978364i	$-0.433666\pi$
$101$	420.000	0.413778	0.206889	+	0.978364i	$0.433666\pi$
$102$	2695.00i	2.61613i
$103$	− 588.000i	− 0.562499i	−0.959635	−	0.281249i	$-0.909251\pi$
$103$	− 588.000i	− 0.562499i	0.959635	−	0.281249i	$-0.0907488\pi$
$104$	585.000	0.551577
$105$	0	0
$106$	2160.00	1.97922
$107$	− 684.000i	− 0.617989i	−0.951064	−	0.308994i	$-0.900008\pi$
$107$	− 684.000i	− 0.617989i	0.951064	−	0.308994i	$-0.0999924\pi$
$108$	− 595.000i	− 0.530129i
$109$	−373.000	−0.327770	−0.163885	−	0.986479i	$-0.552403\pi$
$109$	−373.000	−0.327770	−0.163885	+	0.986479i	$0.552403\pi$
$110$	0	0
$111$	917.000	0.784124
$112$	− 1157.00i	− 0.976127i
$113$	1734.00i	1.44355i	0.692128	+	0.721774i	$0.256673\pi$
$113$	1734.00i	1.44355i	−0.692128	+	0.721774i	$0.743327\pi$
$114$	4410.00	3.62311
$115$	0	0
$116$	−1394.00	−1.11577
$117$	286.000i	0.225989i
$118$	− 1470.00i	− 1.14682i
$119$	1001.00	0.771105
$120$	0	0
$121$	−655.000	−0.492111
$122$	280.000i	0.207787i
$123$	2352.00i	1.72417i
$124$	−3332.00	−2.41308
$125$	0	0
$126$	1430.00	1.01107
$127$	1892.00i	1.32195i	0.750407	+	0.660976i	$0.229857\pi$
$127$	1892.00i	1.32195i	−0.750407	+	0.660976i	$0.770143\pi$
$128$	− 2115.00i	− 1.46048i
$129$	−1407.00	−0.960306
$130$	0	0
$131$	1435.00	0.957073	0.478536	−	0.878068i	$-0.341167\pi$
$131$	1435.00	0.957073	0.478536	+	0.878068i	$0.341167\pi$
$132$	3094.00i	2.04014i
$133$	− 1638.00i	− 1.06791i
$134$	2390.00	1.54078
$135$	0	0
$136$	−3465.00	−2.18472
$137$	− 1776.00i	− 1.10755i	−0.832667	−	0.553773i	$-0.813187\pi$
$137$	− 1776.00i	− 1.10755i	0.832667	−	0.553773i	$-0.186813\pi$
$138$	3360.00i	2.07262i
$139$	1869.00	1.14048	0.570239	−	0.821479i	$-0.306850\pi$
$139$	1869.00	1.14048	0.570239	+	0.821479i	$0.306850\pi$
$140$	0	0
$141$	735.000	0.438994
$142$	− 45.0000i	− 0.0265938i
$143$	338.000i	0.197657i
$144$	−1958.00	−1.13310
$145$	0	0
$146$	−490.000	−0.277758
$147$	1218.00i	0.683394i
$148$	2227.00i	1.23688i
$149$	−2466.00	−1.35586	−0.677928	−	0.735128i	$-0.737122\pi$
$149$	−2466.00	−1.35586	−0.677928	+	0.735128i	$0.737122\pi$
$150$	0	0
$151$	−3323.00	−1.79087	−0.895437	−	0.445189i	$-0.853137\pi$
$151$	−3323.00	−1.79087	−0.895437	+	0.445189i	$0.853137\pi$
$152$	5670.00i	3.02564i
$153$	− 1694.00i	− 0.895110i
$154$	1690.00	0.884312
$155$	0	0
$156$	−1547.00	−0.793969
$157$	− 2730.00i	− 1.38776i	−0.720092	−	0.693878i	$-0.755901\pi$
$157$	− 2730.00i	− 1.38776i	0.720092	−	0.693878i	$-0.244099\pi$
$158$	6520.00i	3.28293i
$159$	−3024.00	−1.50829
$160$	0	0
$161$	1248.00	0.610908
$162$	4195.00i	2.03451i
$163$	544.000i	0.261407i	0.991421	+	0.130704i	$0.0417236\pi$
$163$	544.000i	0.261407i	−0.991421	+	0.130704i	$0.958276\pi$
$164$	−5712.00	−2.71971
$165$	0	0
$166$	1540.00	0.720043
$167$	1624.00i	0.752508i	0.926516	+	0.376254i	$0.122788\pi$
$167$	1624.00i	0.752508i	−0.926516	+	0.376254i	$0.877212\pi$
$168$	4095.00i	1.88057i
$169$	−169.000	−0.0769231
$170$	0	0
$171$	−2772.00	−1.23965
$172$	− 3417.00i	− 1.51479i
$173$	336.000i	0.147662i	0.997271	+	0.0738312i	$0.0235226\pi$
$173$	336.000i	0.147662i	−0.997271	+	0.0738312i	$0.976477\pi$
$174$	2870.00	1.25043
$175$	0	0
$176$	−2314.00	−0.991047
$177$	2058.00i	0.873948i
$178$	− 5950.00i	− 2.50546i
$179$	3029.00	1.26479	0.632397	−	0.774645i	$-0.282071\pi$
$179$	3029.00	1.26479	0.632397	+	0.774645i	$0.282071\pi$
$180$	0	0
$181$	−28.0000	−0.0114985	−0.00574924	−	0.999983i	$-0.501830\pi$
$181$	−28.0000	−0.0114985	−0.00574924	+	0.999983i	$0.501830\pi$
$182$	845.000i	0.344151i
$183$	− 392.000i	− 0.158347i
$184$	−4320.00	−1.73084
$185$	0	0
$186$	6860.00	2.70430
$187$	− 2002.00i	− 0.782892i
$188$	1785.00i	0.692471i
$189$	455.000	0.175113
$190$	0	0
$191$	422.000	0.159868	0.0799342	−	0.996800i	$-0.474529\pi$
$191$	422.000	0.159868	0.0799342	+	0.996800i	$0.474529\pi$
$192$	2009.00i	0.755141i
$193$	− 492.000i	− 0.183497i	−0.995782	−	0.0917485i	$-0.970754\pi$
$193$	− 492.000i	− 0.183497i	0.995782	−	0.0917485i	$-0.0292456\pi$
$194$	350.000	0.129529
$195$	0	0
$196$	−2958.00	−1.07799
$197$	2991.00i	1.08173i	0.841111	+	0.540863i	$0.181902\pi$
$197$	2991.00i	1.08173i	−0.841111	+	0.540863i	$0.818098\pi$
$198$	− 2860.00i	− 1.02652i
$199$	70.0000	0.0249355	0.0124678	−	0.999922i	$-0.496031\pi$
$199$	70.0000	0.0249355	0.0124678	+	0.999922i	$0.496031\pi$
$200$	0	0
$201$	−3346.00	−1.17417
$202$	− 2100.00i	− 0.731463i
$203$	− 1066.00i	− 0.368564i
$204$	9163.00	3.14480
$205$	0	0
$206$	−2940.00	−0.994367
$207$	− 2112.00i	− 0.709150i
$208$	− 1157.00i	− 0.385690i
$209$	−3276.00	−1.08424
$210$	0	0
$211$	2851.00	0.930194	0.465097	−	0.885260i	$-0.346019\pi$
$211$	2851.00	0.930194	0.465097	+	0.885260i	$0.346019\pi$
$212$	− 7344.00i	− 2.37919i
$213$	63.0000i	0.0202661i
$214$	−3420.00	−1.09246
$215$	0	0
$216$	−1575.00	−0.496135
$217$	− 2548.00i	− 0.797095i
$218$	1865.00i	0.579421i
$219$	686.000	0.211669
$220$	0	0
$221$	1001.00	0.304681
$222$	− 4585.00i	− 1.38615i
$223$	− 217.000i	− 0.0651632i	−0.999469	−	0.0325816i	$-0.989627\pi$
$223$	− 217.000i	− 0.0651632i	0.999469	−	0.0325816i	$-0.0103729\pi$
$224$	−1105.00	−0.329602
$225$	0	0
$226$	8670.00	2.55186
$227$	− 2576.00i	− 0.753194i	−0.926377	−	0.376597i	$-0.877094\pi$
$227$	− 2576.00i	− 0.753194i	0.926377	−	0.376597i	$-0.122906\pi$
$228$	− 14994.0i	− 4.35527i
$229$	−455.000	−0.131298	−0.0656490	−	0.997843i	$-0.520912\pi$
$229$	−455.000	−0.131298	−0.0656490	+	0.997843i	$0.520912\pi$
$230$	0	0
$231$	−2366.00	−0.673902
$232$	3690.00i	1.04423i
$233$	− 3061.00i	− 0.860656i	−0.902673	−	0.430328i	$-0.858398\pi$
$233$	− 3061.00i	− 0.860656i	0.902673	−	0.430328i	$-0.141602\pi$
$234$	1430.00	0.399496
$235$	0	0
$236$	−4998.00	−1.37857
$237$	− 9128.00i	− 2.50180i
$238$	− 5005.00i	− 1.36313i
$239$	3477.00	0.941039	0.470520	−	0.882389i	$-0.344066\pi$
$239$	3477.00	0.941039	0.470520	+	0.882389i	$0.344066\pi$
$240$	0	0
$241$	−1610.00	−0.430329	−0.215164	−	0.976578i	$-0.569029\pi$
$241$	−1610.00	−0.430329	−0.215164	+	0.976578i	$0.569029\pi$
$242$	3275.00i	0.869938i
$243$	− 4928.00i	− 1.30095i
$244$	952.000	0.249777
$245$	0	0
$246$	11760.0	3.04793
$247$	− 1638.00i	− 0.421957i
$248$	8820.00i	2.25835i
$249$	−2156.00	−0.548719
$250$	0	0
$251$	1008.00	0.253484	0.126742	−	0.991936i	$-0.459548\pi$
$251$	1008.00	0.253484	0.126742	+	0.991936i	$0.459548\pi$
$252$	− 4862.00i	− 1.21539i
$253$	− 2496.00i	− 0.620246i
$254$	9460.00	2.33690
$255$	0	0
$256$	−8279.00	−2.02124
$257$	6041.00i	1.46625i	0.680092	+	0.733127i	$0.261940\pi$
$257$	6041.00i	1.46625i	−0.680092	+	0.733127i	$0.738060\pi$
$258$	7035.00i	1.69760i
$259$	−1703.00	−0.408569
$260$	0	0
$261$	−1804.00	−0.427834
$262$	− 7175.00i	− 1.69188i
$263$	3708.00i	0.869373i	0.900582	+	0.434686i	$0.143141\pi$
$263$	3708.00i	0.869373i	−0.900582	+	0.434686i	$0.856859\pi$
$264$	8190.00	1.90932
$265$	0	0
$266$	−8190.00	−1.88782
$267$	8330.00i	1.90932i
$268$	− 8126.00i	− 1.85214i
$269$	−8344.00	−1.89124	−0.945618	−	0.325278i	$-0.894542\pi$
$269$	−8344.00	−1.89124	−0.945618	+	0.325278i	$0.894542\pi$
$270$	0	0
$271$	−1617.00	−0.362457	−0.181228	−	0.983441i	$-0.558007\pi$
$271$	−1617.00	−0.362457	−0.181228	+	0.983441i	$0.558007\pi$
$272$	6853.00i	1.52766i
$273$	− 1183.00i	− 0.262265i
$274$	−8880.00	−1.95788
$275$	0	0
$276$	11424.0	2.49146
$277$	− 3820.00i	− 0.828598i	−0.910141	−	0.414299i	$-0.864027\pi$
$277$	− 3820.00i	− 0.828598i	0.910141	−	0.414299i	$-0.135973\pi$
$278$	− 9345.00i	− 2.01610i
$279$	−4312.00	−0.925278
$280$	0	0
$281$	−6214.00	−1.31920	−0.659602	−	0.751615i	$-0.729275\pi$
$281$	−6214.00	−1.31920	−0.659602	+	0.751615i	$0.729275\pi$
$282$	− 3675.00i	− 0.776039i
$283$	5292.00i	1.11158i	0.831323	+	0.555789i	$0.187584\pi$
$283$	5292.00i	1.11158i	−0.831323	+	0.555789i	$0.812416\pi$
$284$	−153.000	−0.0319679
$285$	0	0
$286$	1690.00	0.349412
$287$	− 4368.00i	− 0.898379i
$288$	1870.00i	0.382607i
$289$	−1016.00	−0.206798
$290$	0	0
$291$	−490.000	−0.0987090
$292$	1666.00i	0.333888i
$293$	903.000i	0.180047i	0.995940	+	0.0900236i	$0.0286942\pi$
$293$	903.000i	0.180047i	−0.995940	+	0.0900236i	$0.971306\pi$
$294$	6090.00	1.20808
$295$	0	0
$296$	5895.00	1.15757
$297$	− 910.000i	− 0.177790i
$298$	12330.0i	2.39684i
$299$	1248.00	0.241384
$300$	0	0
$301$	2613.00	0.500368
$302$	16615.0i	3.16585i
$303$	2940.00i	0.557421i
$304$	11214.0	2.11568
$305$	0	0
$306$	−8470.00	−1.58235
$307$	2114.00i	0.393004i	0.980503	+	0.196502i	$0.0629583\pi$
$307$	2114.00i	0.393004i	−0.980503	+	0.196502i	$0.937042\pi$
$308$	− 5746.00i	− 1.06302i
$309$	4116.00	0.757770
$310$	0	0
$311$	3402.00	0.620288	0.310144	−	0.950690i	$-0.399623\pi$
$311$	3402.00	0.620288	0.310144	+	0.950690i	$0.399623\pi$
$312$	4095.00i	0.743057i
$313$	10689.0i	1.93028i	0.261732	+	0.965141i	$0.415706\pi$
$313$	10689.0i	1.93028i	−0.261732	+	0.965141i	$0.584294\pi$
$314$	−13650.0	−2.45323
$315$	0	0
$316$	22168.0	3.94635
$317$	− 7054.00i	− 1.24982i	−0.780698	−	0.624909i	$-0.785136\pi$
$317$	− 7054.00i	− 1.24982i	0.780698	−	0.624909i	$-0.214864\pi$
$318$	15120.0i	2.66631i
$319$	−2132.00	−0.374198
$320$	0	0
$321$	4788.00	0.832524
$322$	− 6240.00i	− 1.07994i
$323$	9702.00i	1.67131i
$324$	14263.0	2.44564
$325$	0	0
$326$	2720.00	0.462107
$327$	− 2611.00i	− 0.441555i
$328$	15120.0i	2.54531i
$329$	−1365.00	−0.228738
$330$	0	0
$331$	9704.00	1.61142	0.805710	−	0.592310i	$-0.201784\pi$
$331$	9704.00	1.61142	0.805710	+	0.592310i	$0.201784\pi$
$332$	− 5236.00i	− 0.865551i
$333$	2882.00i	0.474272i
$334$	8120.00	1.33026
$335$	0	0
$336$	8099.00	1.31499
$337$	− 10449.0i	− 1.68900i	−0.535555	−	0.844500i	$-0.679897\pi$
$337$	− 10449.0i	− 1.68900i	0.535555	−	0.844500i	$-0.320103\pi$
$338$	845.000i	0.135982i
$339$	−12138.0	−1.94468
$340$	0	0
$341$	−5096.00	−0.809278
$342$	13860.0i	2.19141i
$343$	− 6721.00i	− 1.05802i
$344$	−9045.00	−1.41766
$345$	0	0
$346$	1680.00	0.261033
$347$	− 621.000i	− 0.0960721i	−0.998846	−	0.0480361i	$-0.984704\pi$
$347$	− 621.000i	− 0.0960721i	0.998846	−	0.0480361i	$-0.0152962\pi$
$348$	− 9758.00i	− 1.50311i
$349$	−12481.0	−1.91431	−0.957153	−	0.289584i	$-0.906483\pi$
$349$	−12481.0	−1.91431	−0.957153	+	0.289584i	$0.906483\pi$
$350$	0	0
$351$	455.000	0.0691912
$352$	2210.00i	0.334640i
$353$	1400.00i	0.211089i	0.994415	+	0.105545i	$0.0336586\pi$
$353$	1400.00i	0.211089i	−0.994415	+	0.105545i	$0.966341\pi$
$354$	10290.0	1.54494
$355$	0	0
$356$	−20230.0	−3.01176
$357$	7007.00i	1.03879i
$358$	− 15145.0i	− 2.23586i
$359$	4968.00	0.730365	0.365182	−	0.930936i	$-0.381007\pi$
$359$	4968.00	0.730365	0.365182	+	0.930936i	$0.381007\pi$
$360$	0	0
$361$	9017.00	1.31462
$362$	140.000i	0.0203266i
$363$	− 4585.00i	− 0.662948i
$364$	2873.00	0.413698
$365$	0	0
$366$	−1960.00	−0.279920
$367$	8722.00i	1.24056i	0.784381	+	0.620279i	$0.212981\pi$
$367$	8722.00i	1.24056i	−0.784381	+	0.620279i	$0.787019\pi$
$368$	8544.00i	1.21029i
$369$	−7392.00	−1.04285
$370$	0	0
$371$	5616.00	0.785898
$372$	− 23324.0i	− 3.25079i
$373$	− 10012.0i	− 1.38982i	−0.719098	−	0.694908i	$-0.755445\pi$
$373$	− 10012.0i	− 1.38982i	0.719098	−	0.694908i	$-0.244555\pi$
$374$	−10010.0	−1.38397
$375$	0	0
$376$	4725.00	0.648067
$377$	− 1066.00i	− 0.145628i
$378$	− 2275.00i	− 0.309559i
$379$	3372.00	0.457013	0.228507	−	0.973542i	$-0.426616\pi$
$379$	3372.00	0.457013	0.228507	+	0.973542i	$0.426616\pi$
$380$	0	0
$381$	−13244.0	−1.78087
$382$	− 2110.00i	− 0.282610i
$383$	847.000i	0.113002i	0.998403	+	0.0565009i	$0.0179944\pi$
$383$	847.000i	0.113002i	−0.998403	+	0.0565009i	$0.982006\pi$
$384$	14805.0	1.96749
$385$	0	0
$386$	−2460.00	−0.324380
$387$	− 4422.00i	− 0.580834i
$388$	− 1190.00i	− 0.155704i
$389$	−11314.0	−1.47466	−0.737330	−	0.675533i	$-0.763914\pi$
$389$	−11314.0	−1.47466	−0.737330	+	0.675533i	$0.763914\pi$
$390$	0	0
$391$	−7392.00	−0.956086
$392$	7830.00i	1.00886i
$393$	10045.0i	1.28932i
$394$	14955.0	1.91224
$395$	0	0
$396$	−9724.00	−1.23396
$397$	1862.00i	0.235393i	0.993050	+	0.117697i	$0.0375510\pi$
$397$	1862.00i	0.235393i	−0.993050	+	0.117697i	$0.962449\pi$
$398$	− 350.000i	− 0.0440802i
$399$	11466.0	1.43864
$400$	0	0
$401$	6820.00	0.849313	0.424657	−	0.905355i	$-0.360395\pi$
$401$	6820.00	0.849313	0.424657	+	0.905355i	$0.360395\pi$
$402$	16730.0i	2.07566i
$403$	− 2548.00i	− 0.314950i
$404$	−7140.00	−0.879278
$405$	0	0
$406$	−5330.00	−0.651536
$407$	3406.00i	0.414814i
$408$	− 24255.0i	− 2.94314i
$409$	12992.0	1.57069	0.785346	−	0.619057i	$-0.212485\pi$
$409$	12992.0	1.57069	0.785346	+	0.619057i	$0.212485\pi$
$410$	0	0
$411$	12432.0	1.49203
$412$	9996.00i	1.19531i
$413$	− 3822.00i	− 0.455371i
$414$	−10560.0	−1.25361
$415$	0	0
$416$	−1105.00	−0.130233
$417$	13083.0i	1.53640i
$418$	16380.0i	1.91668i
$419$	7343.00	0.856155	0.428078	−	0.903742i	$-0.359191\pi$
$419$	7343.00	0.856155	0.428078	+	0.903742i	$0.359191\pi$
$420$	0	0
$421$	−5059.00	−0.585655	−0.292827	−	0.956165i	$-0.594596\pi$
$421$	−5059.00	−0.585655	−0.292827	+	0.956165i	$0.594596\pi$
$422$	− 14255.0i	− 1.64437i
$423$	2310.00i	0.265523i
$424$	−19440.0	−2.22663
$425$	0	0
$426$	315.000	0.0358258
$427$	728.000i	0.0825068i
$428$	11628.0i	1.31323i
$429$	−2366.00	−0.266274
$430$	0	0
$431$	3243.00	0.362436	0.181218	−	0.983443i	$-0.441996\pi$
$431$	3243.00	0.362436	0.181218	+	0.983443i	$0.441996\pi$
$432$	3115.00i	0.346922i
$433$	− 11599.0i	− 1.28733i	−0.765309	−	0.643663i	$-0.777414\pi$
$433$	− 11599.0i	− 1.28733i	0.765309	−	0.643663i	$-0.222586\pi$
$434$	−12740.0	−1.40908
$435$	0	0
$436$	6341.00	0.696511
$437$	12096.0i	1.32410i
$438$	− 3430.00i	− 0.374182i
$439$	17374.0	1.88887	0.944437	−	0.328692i	$-0.106608\pi$
$439$	17374.0	1.88887	0.944437	+	0.328692i	$0.106608\pi$
$440$	0	0
$441$	−3828.00	−0.413346
$442$	− 5005.00i	− 0.538605i
$443$	− 989.000i	− 0.106070i	−0.998593	−	0.0530348i	$-0.983111\pi$
$443$	− 989.000i	− 0.106070i	0.998593	−	0.0530348i	$-0.0168894\pi$
$444$	−15589.0	−1.66626
$445$	0	0
$446$	−1085.00	−0.115193
$447$	− 17262.0i	− 1.82654i
$448$	− 3731.00i	− 0.393467i
$449$	14474.0	1.52131	0.760657	−	0.649154i	$-0.224877\pi$
$449$	14474.0	1.52131	0.760657	+	0.649154i	$0.224877\pi$
$450$	0	0
$451$	−8736.00	−0.912111
$452$	− 29478.0i	− 3.06754i
$453$	− 23261.0i	− 2.41258i
$454$	−12880.0	−1.33147
$455$	0	0
$456$	−39690.0	−4.07600
$457$	− 1594.00i	− 0.163160i	−0.996667	−	0.0815801i	$-0.974003\pi$
$457$	− 1594.00i	− 0.163160i	0.996667	−	0.0815801i	$-0.0259966\pi$
$458$	2275.00i	0.232104i
$459$	−2695.00	−0.274056
$460$	0	0
$461$	−5915.00	−0.597590	−0.298795	−	0.954317i	$-0.596585\pi$
$461$	−5915.00	−0.597590	−0.298795	+	0.954317i	$0.596585\pi$
$462$	11830.0i	1.19130i
$463$	11072.0i	1.11136i	0.831396	+	0.555680i	$0.187542\pi$
$463$	11072.0i	1.11136i	−0.831396	+	0.555680i	$0.812458\pi$
$464$	7298.00	0.730175
$465$	0	0
$466$	−15305.0	−1.52144
$467$	1260.00i	0.124852i	0.998050	+	0.0624260i	$0.0198837\pi$
$467$	1260.00i	0.124852i	−0.998050	+	0.0624260i	$0.980116\pi$
$468$	− 4862.00i	− 0.480227i
$469$	6214.00	0.611804
$470$	0	0
$471$	19110.0	1.86952
$472$	13230.0i	1.29017i
$473$	− 5226.00i	− 0.508016i
$474$	−45640.0	−4.42260
$475$	0	0
$476$	−17017.0	−1.63860
$477$	− 9504.00i	− 0.912281i
$478$	− 17385.0i	− 1.66354i
$479$	12033.0	1.14781	0.573906	−	0.818921i	$-0.305428\pi$
$479$	12033.0	1.14781	0.573906	+	0.818921i	$0.305428\pi$
$480$	0	0
$481$	−1703.00	−0.161435
$482$	8050.00i	0.760721i
$483$	8736.00i	0.822985i
$484$	11135.0	1.04574
$485$	0	0
$486$	−24640.0	−2.29978
$487$	− 2280.00i	− 0.212149i	−0.994358	−	0.106075i	$-0.966172\pi$
$487$	− 2280.00i	− 0.212149i	0.994358	−	0.106075i	$-0.0338282\pi$
$488$	− 2520.00i	− 0.233760i
$489$	−3808.00	−0.352155
$490$	0	0
$491$	16767.0	1.54111	0.770554	−	0.637375i	$-0.219980\pi$
$491$	16767.0	1.54111	0.770554	+	0.637375i	$0.219980\pi$
$492$	− 39984.0i	− 3.66386i
$493$	6314.00i	0.576812i
$494$	−8190.00	−0.745922
$495$	0	0
$496$	17444.0	1.57915
$497$	− 117.000i	− 0.0105597i
$498$	10780.0i	0.970007i
$499$	−12840.0	−1.15190	−0.575949	−	0.817485i	$-0.695367\pi$
$499$	−12840.0	−1.15190	−0.575949	+	0.817485i	$0.695367\pi$
$500$	0	0
$501$	−11368.0	−1.01374
$502$	− 5040.00i	− 0.448100i
$503$	2198.00i	0.194839i	0.995243	+	0.0974195i	$0.0310588\pi$
$503$	2198.00i	0.194839i	−0.995243	+	0.0974195i	$0.968941\pi$
$504$	−12870.0	−1.13745
$505$	0	0
$506$	−12480.0	−1.09645
$507$	− 1183.00i	− 0.103627i
$508$	− 32164.0i	− 2.80915i
$509$	17066.0	1.48612	0.743062	−	0.669223i	$-0.233373\pi$
$509$	17066.0	1.48612	0.743062	+	0.669223i	$0.233373\pi$
$510$	0	0
$511$	−1274.00	−0.110290
$512$	24475.0i	2.11260i
$513$	4410.00i	0.379544i
$514$	30205.0	2.59200
$515$	0	0
$516$	23919.0	2.04065
$517$	2730.00i	0.232235i
$518$	8515.00i	0.722254i
$519$	−2352.00	−0.198924
$520$	0	0
$521$	2583.00	0.217204	0.108602	−	0.994085i	$-0.465363\pi$
$521$	2583.00	0.217204	0.108602	+	0.994085i	$0.465363\pi$
$522$	9020.00i	0.756312i
$523$	− 18620.0i	− 1.55678i	−0.627781	−	0.778390i	$-0.716037\pi$
$523$	− 18620.0i	− 1.55678i	0.627781	−	0.778390i	$-0.283963\pi$
$524$	−24395.0	−2.03378
$525$	0	0
$526$	18540.0	1.53685
$527$	15092.0i	1.24747i
$528$	− 16198.0i	− 1.33509i
$529$	2951.00	0.242541
$530$	0	0
$531$	−6468.00	−0.528601
$532$	27846.0i	2.26932i
$533$	− 4368.00i	− 0.354970i
$534$	41650.0	3.37523
$535$	0	0
$536$	−21510.0	−1.73338
$537$	21203.0i	1.70387i
$538$	41720.0i	3.34327i
$539$	−4524.00	−0.361526
$540$	0	0
$541$	−16833.0	−1.33772	−0.668861	−	0.743388i	$-0.733218\pi$
$541$	−16833.0	−1.33772	−0.668861	+	0.743388i	$0.733218\pi$
$542$	8085.00i	0.640739i
$543$	− 196.000i	− 0.0154902i
$544$	6545.00	0.515836
$545$	0	0
$546$	−5915.00	−0.463624
$547$	− 8615.00i	− 0.673402i	−0.941612	−	0.336701i	$-0.890689\pi$
$547$	− 8615.00i	− 0.673402i	0.941612	−	0.336701i	$-0.109311\pi$
$548$	30192.0i	2.35354i
$549$	1232.00	0.0957750
$550$	0	0
$551$	10332.0	0.798835
$552$	− 30240.0i	− 2.33170i
$553$	16952.0i	1.30357i
$554$	−19100.0	−1.46477
$555$	0	0
$556$	−31773.0	−2.42352
$557$	8535.00i	0.649263i	0.945841	+	0.324632i	$0.105240\pi$
$557$	8535.00i	0.649263i	−0.945841	+	0.324632i	$0.894760\pi$
$558$	21560.0i	1.63568i
$559$	2613.00	0.197707
$560$	0	0
$561$	14014.0	1.05467
$562$	31070.0i	2.33204i
$563$	4641.00i	0.347415i	0.984797	+	0.173708i	$0.0555748\pi$
$563$	4641.00i	0.347415i	−0.984797	+	0.173708i	$0.944425\pi$
$564$	−12495.0	−0.932862
$565$	0	0
$566$	26460.0	1.96501
$567$	10907.0i	0.807850i
$568$	405.000i	0.0299180i
$569$	4793.00	0.353134	0.176567	−	0.984289i	$-0.443501\pi$
$569$	4793.00	0.353134	0.176567	+	0.984289i	$0.443501\pi$
$570$	0	0
$571$	−5563.00	−0.407713	−0.203857	−	0.979001i	$-0.565348\pi$
$571$	−5563.00	−0.407713	−0.203857	+	0.979001i	$0.565348\pi$
$572$	− 5746.00i	− 0.420022i
$573$	2954.00i	0.215367i
$574$	−21840.0	−1.58813
$575$	0	0
$576$	−6314.00	−0.456742
$577$	24038.0i	1.73434i	0.498011	+	0.867171i	$0.334064\pi$
$577$	24038.0i	1.73434i	−0.498011	+	0.867171i	$0.665936\pi$
$578$	5080.00i	0.365571i
$579$	3444.00	0.247198
$580$	0	0
$581$	4004.00	0.285910
$582$	2450.00i	0.174494i
$583$	− 11232.0i	− 0.797911i
$584$	4410.00	0.312478
$585$	0	0
$586$	4515.00	0.318281
$587$	− 21224.0i	− 1.49235i	−0.665751	−	0.746174i	$-0.731889\pi$
$587$	− 21224.0i	− 1.49235i	0.665751	−	0.746174i	$-0.268111\pi$
$588$	− 20706.0i	− 1.45221i
$589$	24696.0	1.72764
$590$	0	0
$591$	−20937.0	−1.45725
$592$	− 11659.0i	− 0.809429i
$593$	− 4354.00i	− 0.301513i	−0.988571	−	0.150757i	$-0.951829\pi$
$593$	− 4354.00i	− 0.301513i	0.988571	−	0.150757i	$-0.0481710\pi$
$594$	−4550.00	−0.314291
$595$	0	0
$596$	41922.0	2.88119
$597$	490.000i	0.0335919i
$598$	− 6240.00i	− 0.426710i
$599$	−7310.00	−0.498629	−0.249314	−	0.968423i	$-0.580205\pi$
$599$	−7310.00	−0.498629	−0.249314	+	0.968423i	$0.580205\pi$
$600$	0	0
$601$	−7595.00	−0.515485	−0.257743	−	0.966214i	$-0.582979\pi$
$601$	−7595.00	−0.515485	−0.257743	+	0.966214i	$0.582979\pi$
$602$	− 13065.0i	− 0.884534i
$603$	− 10516.0i	− 0.710190i
$604$	56491.0	3.80561
$605$	0	0
$606$	14700.0	0.985391
$607$	− 826.000i	− 0.0552328i	−0.999619	−	0.0276164i	$-0.991208\pi$
$607$	− 826.000i	− 0.0552328i	0.999619	−	0.0276164i	$-0.00879169\pi$
$608$	− 10710.0i	− 0.714388i
$609$	7462.00	0.496511
$610$	0	0
$611$	−1365.00	−0.0903797
$612$	28798.0i	1.90211i
$613$	− 14590.0i	− 0.961312i	−0.876909	−	0.480656i	$-0.840398\pi$
$613$	− 14590.0i	− 0.961312i	0.876909	−	0.480656i	$-0.159602\pi$
$614$	10570.0	0.694740
$615$	0	0
$616$	−15210.0	−0.994851
$617$	4888.00i	0.318936i	0.987203	+	0.159468i	$0.0509779\pi$
$617$	4888.00i	0.318936i	−0.987203	+	0.159468i	$0.949022\pi$
$618$	− 20580.0i	− 1.33956i
$619$	11004.0	0.714520	0.357260	−	0.934005i	$-0.383711\pi$
$619$	11004.0	0.714520	0.357260	+	0.934005i	$0.383711\pi$
$620$	0	0
$621$	−3360.00	−0.217121
$622$	− 17010.0i	− 1.09653i
$623$	− 15470.0i	− 0.994851i
$624$	8099.00	0.519582
$625$	0	0
$626$	53445.0	3.41229
$627$	− 22932.0i	− 1.46063i
$628$	46410.0i	2.94898i
$629$	10087.0	0.639420
$630$	0	0
$631$	−4975.00	−0.313869	−0.156935	−	0.987609i	$-0.550161\pi$
$631$	−4975.00	−0.313869	−0.156935	+	0.987609i	$0.550161\pi$
$632$	− 58680.0i	− 3.69330i
$633$	19957.0i	1.25311i
$634$	−35270.0	−2.20939
$635$	0	0
$636$	51408.0	3.20513
$637$	− 2262.00i	− 0.140697i
$638$	10660.0i	0.661494i
$639$	−198.000	−0.0122578
$640$	0	0
$641$	3950.00	0.243394	0.121697	−	0.992567i	$-0.461166\pi$
$641$	3950.00	0.243394	0.121697	+	0.992567i	$0.461166\pi$
$642$	− 23940.0i	− 1.47171i
$643$	3682.00i	0.225823i	0.993605	+	0.112911i	$0.0360176\pi$
$643$	3682.00i	0.225823i	−0.993605	+	0.112911i	$0.963982\pi$
$644$	−21216.0	−1.29818
$645$	0	0
$646$	48510.0	2.95449
$647$	10402.0i	0.632063i	0.948749	+	0.316032i	$0.102351\pi$
$647$	10402.0i	0.632063i	−0.948749	+	0.316032i	$0.897649\pi$
$648$	− 37755.0i	− 2.28882i
$649$	−7644.00	−0.462332
$650$	0	0
$651$	17836.0	1.07381
$652$	− 9248.00i	− 0.555490i
$653$	31680.0i	1.89852i	0.314491	+	0.949260i	$0.398166\pi$
$653$	31680.0i	1.89852i	−0.314491	+	0.949260i	$0.601834\pi$
$654$	−13055.0	−0.780567
$655$	0	0
$656$	29904.0	1.77981
$657$	2156.00i	0.128027i
$658$	6825.00i	0.404356i
$659$	−21940.0	−1.29691	−0.648453	−	0.761255i	$-0.724584\pi$
$659$	−21940.0	−1.29691	−0.648453	+	0.761255i	$0.724584\pi$
$660$	0	0
$661$	−31374.0	−1.84615	−0.923077	−	0.384616i	$-0.874334\pi$
$661$	−31374.0	−1.84615	−0.923077	+	0.384616i	$0.874334\pi$
$662$	− 48520.0i	− 2.84862i
$663$	7007.00i	0.410451i
$664$	−13860.0	−0.810049
$665$	0	0
$666$	14410.0	0.838403
$667$	7872.00i	0.456979i
$668$	− 27608.0i	− 1.59908i
$669$	1519.00	0.0877847
$670$	0	0
$671$	1456.00	0.0837679
$672$	− 7735.00i	− 0.444024i
$673$	− 18013.0i	− 1.03172i	−0.856672	−	0.515862i	$-0.827472\pi$
$673$	− 18013.0i	− 1.03172i	0.856672	−	0.515862i	$-0.172528\pi$
$674$	−52245.0	−2.98576
$675$	0	0
$676$	2873.00	0.163462
$677$	− 10640.0i	− 0.604030i	−0.953303	−	0.302015i	$-0.902341\pi$
$677$	− 10640.0i	− 0.604030i	0.953303	−	0.302015i	$-0.0976593\pi$
$678$	60690.0i	3.43774i
$679$	910.000	0.0514324
$680$	0	0
$681$	18032.0	1.01467
$682$	25480.0i	1.43062i
$683$	9336.00i	0.523034i	0.965199	+	0.261517i	$0.0842227\pi$
$683$	9336.00i	0.523034i	−0.965199	+	0.261517i	$0.915777\pi$
$684$	47124.0	2.63426
$685$	0	0
$686$	−33605.0	−1.87033
$687$	− 3185.00i	− 0.176878i
$688$	17889.0i	0.991296i
$689$	5616.00	0.310526
$690$	0	0
$691$	4200.00	0.231224	0.115612	−	0.993294i	$-0.463117\pi$
$691$	4200.00	0.231224	0.115612	+	0.993294i	$0.463117\pi$
$692$	− 5712.00i	− 0.313783i
$693$	− 7436.00i	− 0.407605i
$694$	−3105.00	−0.169833
$695$	0	0
$696$	−25830.0	−1.40673
$697$	25872.0i	1.40599i
$698$	62405.0i	3.38405i
$699$	21427.0	1.15943
$700$	0	0
$701$	9872.00	0.531898	0.265949	−	0.963987i	$-0.414315\pi$
$701$	9872.00	0.531898	0.265949	+	0.963987i	$0.414315\pi$
$702$	− 2275.00i	− 0.122314i
$703$	− 16506.0i	− 0.885541i
$704$	−7462.00	−0.399481
$705$	0	0
$706$	7000.00	0.373156
$707$	− 5460.00i	− 0.290445i
$708$	− 34986.0i	− 1.85714i
$709$	−28450.0	−1.50700	−0.753499	−	0.657449i	$-0.771636\pi$
$709$	−28450.0	−1.50700	−0.753499	+	0.657449i	$0.771636\pi$
$710$	0	0
$711$	28688.0	1.51320
$712$	53550.0i	2.81864i
$713$	18816.0i	0.988310i
$714$	35035.0	1.83635
$715$	0	0
$716$	−51493.0	−2.68769
$717$	24339.0i	1.26772i
$718$	− 24840.0i	− 1.29111i
$719$	−32718.0	−1.69705	−0.848523	−	0.529159i	$-0.822507\pi$
$719$	−32718.0	−1.69705	−0.848523	+	0.529159i	$0.822507\pi$
$720$	0	0
$721$	−7644.00	−0.394837
$722$	− 45085.0i	− 2.32395i
$723$	− 11270.0i	− 0.579718i
$724$	476.000	0.0244343
$725$	0	0
$726$	−22925.0	−1.17194
$727$	− 22834.0i	− 1.16488i	−0.812874	−	0.582439i	$-0.802099\pi$
$727$	− 22834.0i	− 1.16488i	0.812874	−	0.582439i	$-0.197901\pi$
$728$	− 7605.00i	− 0.387170i
$729$	11843.0	0.601687
$730$	0	0
$731$	−15477.0	−0.783088
$732$	6664.00i	0.336487i
$733$	− 7875.00i	− 0.396821i	−0.980119	−	0.198410i	$-0.936422\pi$
$733$	− 7875.00i	− 0.396821i	0.980119	−	0.198410i	$-0.0635779\pi$
$734$	43610.0	2.19302
$735$	0	0
$736$	8160.00	0.408671
$737$	− 12428.0i	− 0.621155i
$738$	36960.0i	1.84352i
$739$	2140.00	0.106524	0.0532620	−	0.998581i	$-0.483038\pi$
$739$	2140.00	0.106524	0.0532620	+	0.998581i	$0.483038\pi$
$740$	0	0
$741$	11466.0	0.568440
$742$	− 28080.0i	− 1.38928i
$743$	− 31971.0i	− 1.57860i	−0.614006	−	0.789302i	$-0.710443\pi$
$743$	− 31971.0i	− 1.57860i	0.614006	−	0.789302i	$-0.289557\pi$
$744$	−61740.0	−3.04234
$745$	0	0
$746$	−50060.0	−2.45687
$747$	− 6776.00i	− 0.331889i
$748$	34034.0i	1.66364i
$749$	−8892.00	−0.433787
$750$	0	0
$751$	−7432.00	−0.361115	−0.180558	−	0.983564i	$-0.557790\pi$
$751$	−7432.00	−0.361115	−0.180558	+	0.983564i	$0.557790\pi$
$752$	− 9345.00i	− 0.453161i
$753$	7056.00i	0.341481i
$754$	−5330.00	−0.257437
$755$	0	0
$756$	−7735.00	−0.372115
$757$	20176.0i	0.968704i	0.874873	+	0.484352i	$0.160945\pi$
$757$	20176.0i	0.968704i	−0.874873	+	0.484352i	$0.839055\pi$
$758$	− 16860.0i	− 0.807893i
$759$	17472.0	0.835564
$760$	0	0
$761$	−9478.00	−0.451481	−0.225741	−	0.974187i	$-0.572480\pi$
$761$	−9478.00	−0.451481	−0.225741	+	0.974187i	$0.572480\pi$
$762$	66220.0i	3.14816i
$763$	4849.00i	0.230073i
$764$	−7174.00	−0.339720
$765$	0	0
$766$	4235.00	0.199761
$767$	− 3822.00i	− 0.179928i
$768$	− 57953.0i	− 2.72292i
$769$	12096.0	0.567221	0.283610	−	0.958940i	$-0.408468\pi$
$769$	12096.0	0.567221	0.283610	+	0.958940i	$0.408468\pi$
$770$	0	0
$771$	−42287.0	−1.97526
$772$	8364.00i	0.389931i
$773$	− 17941.0i	− 0.834790i	−0.908725	−	0.417395i	$-0.862943\pi$
$773$	− 17941.0i	− 0.834790i	0.908725	−	0.417395i	$-0.137057\pi$
$774$	−22110.0	−1.02678
$775$	0	0
$776$	−3150.00	−0.145720
$777$	− 11921.0i	− 0.550403i
$778$	56570.0i	2.60685i
$779$	42336.0	1.94717
$780$	0	0
$781$	−234.000	−0.0107211
$782$	36960.0i	1.69014i
$783$	2870.00i	0.130990i
$784$	15486.0	0.705448
$785$	0	0
$786$	50225.0	2.27922
$787$	6664.00i	0.301837i	0.988546	+	0.150919i	$0.0482232\pi$
$787$	6664.00i	0.301837i	−0.988546	+	0.150919i	$0.951777\pi$
$788$	− 50847.0i	− 2.29867i
$789$	−25956.0	−1.17118
$790$	0	0
$791$	22542.0	1.01328
$792$	25740.0i	1.15484i
$793$	728.000i	0.0326003i
$794$	9310.00	0.416120
$795$	0	0
$796$	−1190.00	−0.0529880
$797$	− 1442.00i	− 0.0640882i	−0.999486	−	0.0320441i	$-0.989798\pi$
$797$	− 1442.00i	− 0.0640882i	0.999486	−	0.0320441i	$-0.0102017\pi$
$798$	− 57330.0i	− 2.54318i
$799$	8085.00	0.357981
$800$	0	0
$801$	−26180.0	−1.15484
$802$	− 34100.0i	− 1.50139i
$803$	2548.00i	0.111976i
$804$	56882.0	2.49512
$805$	0	0
$806$	−12740.0	−0.556759
$807$	− 58408.0i	− 2.54778i
$808$	18900.0i	0.822896i
$809$	−30207.0	−1.31276	−0.656379	−	0.754431i	$-0.727913\pi$
$809$	−30207.0	−1.31276	−0.656379	+	0.754431i	$0.727913\pi$
$810$	0	0
$811$	21140.0	0.915322	0.457661	−	0.889127i	$-0.348687\pi$
$811$	21140.0	0.915322	0.457661	+	0.889127i	$0.348687\pi$
$812$	18122.0i	0.783199i
$813$	− 11319.0i	− 0.488284i
$814$	17030.0	0.733294
$815$	0	0
$816$	−47971.0	−2.05799
$817$	25326.0i	1.08451i
$818$	− 64960.0i	− 2.77662i
$819$	3718.00	0.158629
$820$	0	0
$821$	569.000	0.0241879	0.0120939	−	0.999927i	$-0.496150\pi$
$821$	569.000	0.0241879	0.0120939	+	0.999927i	$0.496150\pi$
$822$	− 62160.0i	− 2.63757i
$823$	8538.00i	0.361623i	0.983518	+	0.180812i	$0.0578724\pi$
$823$	8538.00i	0.361623i	−0.983518	+	0.180812i	$0.942128\pi$
$824$	26460.0	1.11866
$825$	0	0
$826$	−19110.0	−0.804990
$827$	− 32702.0i	− 1.37504i	−0.726164	−	0.687521i	$-0.758699\pi$
$827$	− 32702.0i	− 1.37504i	0.726164	−	0.687521i	$-0.241301\pi$
$828$	35904.0i	1.50694i
$829$	21154.0	0.886259	0.443130	−	0.896458i	$-0.353868\pi$
$829$	21154.0	0.886259	0.443130	+	0.896458i	$0.353868\pi$
$830$	0	0
$831$	26740.0	1.11625
$832$	− 3731.00i	− 0.155468i
$833$	13398.0i	0.557279i
$834$	65415.0	2.71599
$835$	0	0
$836$	55692.0	2.30400
$837$	6860.00i	0.283293i
$838$	− 36715.0i	− 1.51348i
$839$	2184.00	0.0898690	0.0449345	−	0.998990i	$-0.485692\pi$
$839$	2184.00	0.0898690	0.0449345	+	0.998990i	$0.485692\pi$
$840$	0	0
$841$	−17665.0	−0.724302
$842$	25295.0i	1.03530i
$843$	− 43498.0i	− 1.77717i
$844$	−48467.0	−1.97666
$845$	0	0
$846$	11550.0	0.469382
$847$	8515.00i	0.345430i
$848$	38448.0i	1.55697i
$849$	−37044.0	−1.49746
$850$	0	0
$851$	12576.0	0.506580
$852$	− 1071.00i	− 0.0430656i
$853$	− 36687.0i	− 1.47261i	−0.676648	−	0.736307i	$-0.736568\pi$
$853$	− 36687.0i	− 1.47261i	0.676648	−	0.736307i	$-0.263432\pi$
$854$	3640.00	0.145853
$855$	0	0
$856$	30780.0	1.22902
$857$	36806.0i	1.46706i	0.679658	+	0.733529i	$0.262128\pi$
$857$	36806.0i	1.46706i	−0.679658	+	0.733529i	$0.737872\pi$
$858$	11830.0i	0.470710i
$859$	−4900.00	−0.194628	−0.0973142	−	0.995254i	$-0.531025\pi$
$859$	−4900.00	−0.194628	−0.0973142	+	0.995254i	$0.531025\pi$
$860$	0	0
$861$	30576.0	1.21025
$862$	− 16215.0i	− 0.640702i
$863$	13697.0i	0.540268i	0.962823	+	0.270134i	$0.0870680\pi$
$863$	13697.0i	0.540268i	−0.962823	+	0.270134i	$0.912932\pi$
$864$	2975.00	0.117143
$865$	0	0
$866$	−57995.0	−2.27569
$867$	− 7112.00i	− 0.278588i
$868$	43316.0i	1.69383i
$869$	33904.0	1.32349
$870$	0	0
$871$	6214.00	0.241737
$872$	− 16785.0i	− 0.651848i
$873$	− 1540.00i	− 0.0597034i
$874$	60480.0	2.34069
$875$	0	0
$876$	−11662.0	−0.449797
$877$	6239.00i	0.240224i	0.992760	+	0.120112i	$0.0383253\pi$
$877$	6239.00i	0.240224i	−0.992760	+	0.120112i	$0.961675\pi$
$878$	− 86870.0i	− 3.33909i
$879$	−6321.00	−0.242551
$880$	0	0
$881$	133.000	0.00508613	0.00254307	−	0.999997i	$-0.499191\pi$
$881$	133.000	0.00508613	0.00254307	+	0.999997i	$0.499191\pi$
$882$	19140.0i	0.730700i
$883$	26003.0i	0.991020i	0.868602	+	0.495510i	$0.165019\pi$
$883$	26003.0i	0.991020i	−0.868602	+	0.495510i	$0.834981\pi$
$884$	−17017.0	−0.647448
$885$	0	0
$886$	−4945.00	−0.187506
$887$	− 31248.0i	− 1.18287i	−0.806353	−	0.591435i	$-0.798562\pi$
$887$	− 31248.0i	− 1.18287i	0.806353	−	0.591435i	$-0.201438\pi$
$888$	41265.0i	1.55942i
$889$	24596.0	0.927923
$890$	0	0
$891$	21814.0	0.820198
$892$	3689.00i	0.138472i
$893$	− 13230.0i	− 0.495773i
$894$	−86310.0	−3.22890
$895$	0	0
$896$	−27495.0	−1.02516
$897$	8736.00i	0.325180i
$898$	− 72370.0i	− 2.68933i
$899$	16072.0	0.596253
$900$	0	0
$901$	−33264.0	−1.22995
$902$	43680.0i	1.61240i
$903$	18291.0i	0.674071i
$904$	−78030.0	−2.87084
$905$	0	0
$906$	−116305.	−4.26487
$907$	− 38253.0i	− 1.40041i	−0.713943	−	0.700204i	$-0.753092\pi$
$907$	− 38253.0i	− 1.40041i	0.713943	−	0.700204i	$-0.246908\pi$
$908$	43792.0i	1.60054i
$909$	−9240.00	−0.337152
$910$	0	0
$911$	36374.0	1.32286	0.661429	−	0.750007i	$-0.269950\pi$
$911$	36374.0	1.32286	0.661429	+	0.750007i	$0.269950\pi$
$912$	78498.0i	2.85014i
$913$	− 8008.00i	− 0.290281i
$914$	−7970.00	−0.288429
$915$	0	0
$916$	7735.00	0.279008
$917$	− 18655.0i	− 0.671802i
$918$	13475.0i	0.484468i
$919$	27648.0	0.992408	0.496204	−	0.868206i	$-0.334727\pi$
$919$	27648.0	0.992408	0.496204	+	0.868206i	$0.334727\pi$
$920$	0	0
$921$	−14798.0	−0.529436
$922$	29575.0i	1.05640i
$923$	− 117.000i	− 0.00417237i
$924$	40222.0	1.43204
$925$	0	0
$926$	55360.0	1.96462
$927$	12936.0i	0.458332i
$928$	− 6970.00i	− 0.246553i
$929$	−756.000	−0.0266992	−0.0133496	−	0.999911i	$-0.504249\pi$
$929$	−756.000	−0.0266992	−0.0133496	+	0.999911i	$0.504249\pi$
$930$	0	0
$931$	21924.0	0.771783
$932$	52037.0i	1.82889i
$933$	23814.0i	0.835622i
$934$	6300.00	0.220709
$935$	0	0
$936$	−12870.0	−0.449433
$937$	20846.0i	0.726797i	0.931634	+	0.363399i	$0.118384\pi$
$937$	20846.0i	0.726797i	−0.931634	+	0.363399i	$0.881616\pi$
$938$	− 31070.0i	− 1.08153i
$939$	−74823.0	−2.60038
$940$	0	0
$941$	−41321.0	−1.43148	−0.715742	−	0.698365i	$-0.753911\pi$
$941$	−41321.0	−1.43148	−0.715742	+	0.698365i	$0.753911\pi$
$942$	− 95550.0i	− 3.30487i
$943$	32256.0i	1.11389i
$944$	26166.0	0.902151
$945$	0	0
$946$	−26130.0	−0.898055
$947$	54966.0i	1.88612i	0.332624	+	0.943060i	$0.392066\pi$
$947$	54966.0i	1.88612i	−0.332624	+	0.943060i	$0.607934\pi$
$948$	155176.i	5.31633i
$949$	−1274.00	−0.0435783
$950$	0	0
$951$	49378.0	1.68369
$952$	45045.0i	1.53353i
$953$	44553.0i	1.51439i	0.653189	+	0.757195i	$0.273431\pi$
$953$	44553.0i	1.51439i	−0.653189	+	0.757195i	$0.726569\pi$
$954$	−47520.0	−1.61270
$955$	0	0
$956$	−59109.0	−1.99971
$957$	− 14924.0i	− 0.504101i
$958$	− 60165.0i	− 2.02906i
$959$	−23088.0	−0.777425
$960$	0	0
$961$	8625.00	0.289517
$962$	8515.00i	0.285379i
$963$	15048.0i	0.503546i
$964$	27370.0	0.914448
$965$	0	0
$966$	43680.0	1.45485
$967$	− 27907.0i	− 0.928054i	−0.885821	−	0.464027i	$-0.846404\pi$
$967$	− 27907.0i	− 0.928054i	0.885821	−	0.464027i	$-0.153596\pi$
$968$	− 29475.0i	− 0.978680i
$969$	−67914.0	−2.25151
$970$	0	0
$971$	−16443.0	−0.543441	−0.271720	−	0.962376i	$-0.587593\pi$
$971$	−16443.0	−0.543441	−0.271720	+	0.962376i	$0.587593\pi$
$972$	83776.0i	2.76452i
$973$	− 24297.0i	− 0.800541i
$974$	−11400.0	−0.375030
$975$	0	0
$976$	−4984.00	−0.163457
$977$	− 45414.0i	− 1.48713i	−0.668666	−	0.743563i	$-0.733134\pi$
$977$	− 45414.0i	− 1.48713i	0.668666	−	0.743563i	$-0.266866\pi$
$978$	19040.0i	0.622528i
$979$	−30940.0	−1.01006
$980$	0	0
$981$	8206.00	0.267072
$982$	− 83835.0i	− 2.72432i
$983$	8981.00i	0.291403i	0.989329	+	0.145702i	$0.0465440\pi$
$983$	8981.00i	0.291403i	−0.989329	+	0.145702i	$0.953456\pi$
$984$	−105840.	−3.42892
$985$	0	0
$986$	31570.0	1.01967
$987$	− 9555.00i	− 0.308145i
$988$	27846.0i	0.896659i
$989$	−19296.0	−0.620402
$990$	0	0
$991$	−17414.0	−0.558198	−0.279099	−	0.960262i	$-0.590036\pi$
$991$	−17414.0	−0.558198	−0.279099	+	0.960262i	$0.590036\pi$
$992$	− 16660.0i	− 0.533221i
$993$	67928.0i	2.17083i
$994$	−585.000	−0.0186671
$995$	0	0
$996$	36652.0	1.16603
$997$	− 23702.0i	− 0.752909i	−0.926435	−	0.376454i	$-0.877143\pi$
$997$	− 23702.0i	− 0.752909i	0.926435	−	0.376454i	$-0.122857\pi$
$998$	64200.0i	2.03629i
$999$	4585.00	0.145208

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	325.4.b.b.274.1		2
5.2	odd	4		325.4.a.d.1.1		1
5.3	odd	4		13.4.a.a.1.1	✓	1
5.4	even	2	inner	325.4.b.b.274.2		2
15.8	even	4		117.4.a.b.1.1		1
20.3	even	4		208.4.a.g.1.1		1
35.13	even	4		637.4.a.a.1.1		1
40.3	even	4		832.4.a.a.1.1		1
40.13	odd	4		832.4.a.r.1.1		1
55.43	even	4		1573.4.a.a.1.1		1
60.23	odd	4		1872.4.a.k.1.1		1
65.3	odd	12		169.4.c.e.22.1		2
65.8	even	4		169.4.b.a.168.1		2
65.18	even	4		169.4.b.a.168.2		2
65.23	odd	12		169.4.c.a.22.1		2
65.28	even	12		169.4.e.e.147.1		4
65.33	even	12		169.4.e.e.23.1		4
65.38	odd	4		169.4.a.e.1.1		1
65.43	odd	12		169.4.c.a.146.1		2
65.48	odd	12		169.4.c.e.146.1		2
65.58	even	12		169.4.e.e.23.2		4
65.63	even	12		169.4.e.e.147.2		4
195.38	even	4		1521.4.a.a.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
13.4.a.a.1.1	✓	1	5.3	odd	4
117.4.a.b.1.1		1	15.8	even	4
169.4.a.e.1.1		1	65.38	odd	4
169.4.b.a.168.1		2	65.8	even	4
169.4.b.a.168.2		2	65.18	even	4
169.4.c.a.22.1		2	65.23	odd	12
169.4.c.a.146.1		2	65.43	odd	12
169.4.c.e.22.1		2	65.3	odd	12
169.4.c.e.146.1		2	65.48	odd	12
169.4.e.e.23.1		4	65.33	even	12
169.4.e.e.23.2		4	65.58	even	12
169.4.e.e.147.1		4	65.28	even	12
169.4.e.e.147.2		4	65.63	even	12
208.4.a.g.1.1		1	20.3	even	4
325.4.a.d.1.1		1	5.2	odd	4
325.4.b.b.274.1		2	1.1	even	1	trivial
325.4.b.b.274.2		2	5.4	even	2	inner
637.4.a.a.1.1		1	35.13	even	4
832.4.a.a.1.1		1	40.3	even	4
832.4.a.r.1.1		1	40.13	odd	4
1521.4.a.a.1.1		1	195.38	even	4
1573.4.a.a.1.1		1	55.43	even	4
1872.4.a.k.1.1		1	60.23	odd	4

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:	\( N \)	\(=\)	\( 325 = 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	325.b (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q-5.00000i q^{2} +7.00000i q^{3} -17.0000 q^{4} +35.0000 q^{6} -13.0000i q^{7} +45.0000i q^{8} -22.0000 q^{9} +O(q^{10})\)	\(q-5.00000i q^{2} +7.00000i q^{3} -17.0000 q^{4} +35.0000 q^{6} -13.0000i q^{7} +45.0000i q^{8} -22.0000 q^{9} -26.0000 q^{11} -119.000i q^{12} -13.0000i q^{13} -65.0000 q^{14} +89.0000 q^{16} +77.0000i q^{17} +110.000i q^{18} +126.000 q^{19} +91.0000 q^{21} +130.000i q^{22} +96.0000i q^{23} -315.000 q^{24} -65.0000 q^{26} +35.0000i q^{27} +221.000i q^{28} +82.0000 q^{29} +196.000 q^{31} -85.0000i q^{32} -182.000i q^{33} +385.000 q^{34} +374.000 q^{36} -131.000i q^{37} -630.000i q^{38} +91.0000 q^{39} +336.000 q^{41} -455.000i q^{42} +201.000i q^{43} +442.000 q^{44} +480.000 q^{46} -105.000i q^{47} +623.000i q^{48} +174.000 q^{49} -539.000 q^{51} +221.000i q^{52} +432.000i q^{53} +175.000 q^{54} +585.000 q^{56} +882.000i q^{57} -410.000i q^{58} +294.000 q^{59} -56.0000 q^{61} -980.000i q^{62} +286.000i q^{63} +287.000 q^{64} -910.000 q^{66} +478.000i q^{67} -1309.00i q^{68} -672.000 q^{69} +9.00000 q^{71} -990.000i q^{72} -98.0000i q^{73} -655.000 q^{74} -2142.00 q^{76} +338.000i q^{77} -455.000i q^{78} -1304.00 q^{79} -839.000 q^{81} -1680.00i q^{82} +308.000i q^{83} -1547.00 q^{84} +1005.00 q^{86} +574.000i q^{87} -1170.00i q^{88} +1190.00 q^{89} -169.000 q^{91} -1632.00i q^{92} +1372.00i q^{93} -525.000 q^{94} +595.000 q^{96} +70.0000i q^{97} -870.000i q^{98} +572.000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 34 q^{4} + 70 q^{6} - 44 q^{9}+O(q^{10}) \) 2 * q - 34 * q^4 + 70 * q^6 - 44 * q^9	\( 2 q - 34 q^{4} + 70 q^{6} - 44 q^{9} - 52 q^{11} - 130 q^{14} + 178 q^{16} + 252 q^{19} + 182 q^{21} - 630 q^{24} - 130 q^{26} + 164 q^{29} + 392 q^{31} + 770 q^{34} + 748 q^{36} + 182 q^{39} + 672 q^{41} + 884 q^{44} + 960 q^{46} + 348 q^{49} - 1078 q^{51} + 350 q^{54} + 1170 q^{56} + 588 q^{59} - 112 q^{61} + 574 q^{64} - 1820 q^{66} - 1344 q^{69} + 18 q^{71} - 1310 q^{74} - 4284 q^{76} - 2608 q^{79} - 1678 q^{81} - 3094 q^{84} + 2010 q^{86} + 2380 q^{89} - 338 q^{91} - 1050 q^{94} + 1190 q^{96} + 1144 q^{99}+O(q^{100}) \) 2 * q - 34 * q^4 + 70 * q^6 - 44 * q^9 - 52 * q^11 - 130 * q^14 + 178 * q^16 + 252 * q^19 + 182 * q^21 - 630 * q^24 - 130 * q^26 + 164 * q^29 + 392 * q^31 + 770 * q^34 + 748 * q^36 + 182 * q^39 + 672 * q^41 + 884 * q^44 + 960 * q^46 + 348 * q^49 - 1078 * q^51 + 350 * q^54 + 1170 * q^56 + 588 * q^59 - 112 * q^61 + 574 * q^64 - 1820 * q^66 - 1344 * q^69 + 18 * q^71 - 1310 * q^74 - 4284 * q^76 - 2608 * q^79 - 1678 * q^81 - 3094 * q^84 + 2010 * q^86 + 2380 * q^89 - 338 * q^91 - 1050 * q^94 + 1190 * q^96 + 1144 * q^99

Introduction

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