LMFDB - Embedded newform 2366.2.d.p.337.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2366,2,Mod(337,2366)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2366, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("2366.337");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2366 = 2 \cdot 7 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2366.d (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:	$18.8926051182$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	6.0.153664.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} + 5x^{4} + 6x^{2} + 1 $ x^6 + 5x^4 + 6x^2 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			337.5
Root			$-0.445042i$ of defining polynomial
Character	$\chi$	$=$	2366.337
Dual form			2366.2.d.p.337.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000i q^{2} +0.554958 q^{3} -1.00000 q^{4} +1.35690i q^{5} +0.554958i q^{6} +1.00000i q^{7} -1.00000i q^{8} -2.69202 q^{9} +O(q^{10})$	\(q+1.00000i q^{2} +0.554958 q^{3} -1.00000 q^{4} +1.35690i q^{5} +0.554958i q^{6} +1.00000i q^{7} -1.00000i q^{8} -2.69202 q^{9} -1.35690 q^{10} -1.80194i q^{11} -0.554958 q^{12} -1.00000 q^{14} +0.753020i q^{15} +1.00000 q^{16} -5.29590 q^{17} -2.69202i q^{18} +1.95108i q^{19} -1.35690i q^{20} +0.554958i q^{21} +1.80194 q^{22} -4.85086 q^{23} -0.554958i q^{24} +3.15883 q^{25} -3.15883 q^{27} -1.00000i q^{28} +5.96077 q^{29} -0.753020 q^{30} -3.63102i q^{31} +1.00000i q^{32} -1.00000i q^{33} -5.29590i q^{34} -1.35690 q^{35} +2.69202 q^{36} -7.75302i q^{37} -1.95108 q^{38} +1.35690 q^{40} +0.0392287i q^{41} -0.554958 q^{42} -2.26875 q^{43} +1.80194i q^{44} -3.65279i q^{45} -4.85086i q^{46} -10.5700i q^{47} +0.554958 q^{48} -1.00000 q^{49} +3.15883i q^{50} -2.93900 q^{51} -3.66487 q^{53} -3.15883i q^{54} +2.44504 q^{55} +1.00000 q^{56} +1.08277i q^{57} +5.96077i q^{58} -4.07606i q^{59} -0.753020i q^{60} -11.5036 q^{61} +3.63102 q^{62} -2.69202i q^{63} -1.00000 q^{64} +1.00000 q^{66} -2.22521i q^{67} +5.29590 q^{68} -2.69202 q^{69} -1.35690i q^{70} +7.78986i q^{71} +2.69202i q^{72} -14.1032i q^{73} +7.75302 q^{74} +1.75302 q^{75} -1.95108i q^{76} +1.80194 q^{77} -12.0804 q^{79} +1.35690i q^{80} +6.32304 q^{81} -0.0392287 q^{82} +2.85086i q^{83} -0.554958i q^{84} -7.18598i q^{85} -2.26875i q^{86} +3.30798 q^{87} -1.80194 q^{88} +6.61894i q^{89} +3.65279 q^{90} +4.85086 q^{92} -2.01507i q^{93} +10.5700 q^{94} -2.64742 q^{95} +0.554958i q^{96} -3.64310i q^{97} -1.00000i q^{98} +4.85086i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 4 q^{3} - 6 q^{4} - 6 q^{9}+O(q^{10}) $ 6 * q + 4 * q^3 - 6 * q^4 - 6 * q^9	$ 6 q + 4 q^{3} - 6 q^{4} - 6 q^{9} - 4 q^{12} - 6 q^{14} + 6 q^{16} - 4 q^{17} + 2 q^{22} - 2 q^{23} + 2 q^{25} - 2 q^{27} + 10 q^{29} - 14 q^{30} + 6 q^{36} - 30 q^{38} - 4 q^{42} + 2 q^{43} + 4 q^{48} - 6 q^{49} + 2 q^{51} - 24 q^{53} + 14 q^{55} + 6 q^{56} - 6 q^{61} - 8 q^{62} - 6 q^{64} + 6 q^{66} + 4 q^{68} - 6 q^{69} + 56 q^{74} + 20 q^{75} + 2 q^{77} - 4 q^{79} - 2 q^{81} - 26 q^{82} + 30 q^{87} - 2 q^{88} - 14 q^{90} + 2 q^{92} + 14 q^{94} + 14 q^{95}+O(q^{100}) $ 6 * q + 4 * q^3 - 6 * q^4 - 6 * q^9 - 4 * q^12 - 6 * q^14 + 6 * q^16 - 4 * q^17 + 2 * q^22 - 2 * q^23 + 2 * q^25 - 2 * q^27 + 10 * q^29 - 14 * q^30 + 6 * q^36 - 30 * q^38 - 4 * q^42 + 2 * q^43 + 4 * q^48 - 6 * q^49 + 2 * q^51 - 24 * q^53 + 14 * q^55 + 6 * q^56 - 6 * q^61 - 8 * q^62 - 6 * q^64 + 6 * q^66 + 4 * q^68 - 6 * q^69 + 56 * q^74 + 20 * q^75 + 2 * q^77 - 4 * q^79 - 2 * q^81 - 26 * q^82 + 30 * q^87 - 2 * q^88 - 14 * q^90 + 2 * q^92 + 14 * q^94 + 14 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2366\mathbb{Z}\right)^\times$.

$n$	$339$	$2199$
$\chi(n)$	$1$	$-1$

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 $

$2$	1.00000i	0.707107i
$2$	1.00000i	0.707107i
$3$	0.554958	0.320405	0.160203	−	0.987084i	$-0.448785\pi$
$3$	0.554958	0.320405	0.160203	+	0.987084i	$0.448785\pi$
$4$	−1.00000	−0.500000
$5$	1.35690i	0.606822i	0.952860	+	0.303411i	$0.0981256\pi$
$5$	1.35690i	0.606822i	−0.952860	+	0.303411i	$0.901874\pi$
$6$	0.554958i	0.226561i
$7$	1.00000i	0.377964i
$7$	1.00000i	0.377964i
$8$	− 1.00000i	− 0.353553i
$9$	−2.69202	−0.897340
$10$	−1.35690	−0.429088
$11$	− 1.80194i	− 0.543305i	−0.962395	−	0.271652i	$-0.912430\pi$
$11$	− 1.80194i	− 0.543305i	0.962395	−	0.271652i	$-0.0875701\pi$
$12$	−0.554958	−0.160203
$13$	0	0
$13$	0	0
$14$	−1.00000	−0.267261
$15$	0.753020i	0.194429i
$16$	1.00000	0.250000
$17$	−5.29590	−1.28444	−0.642222	−	0.766519i	$-0.721987\pi$
$17$	−5.29590	−1.28444	−0.642222	+	0.766519i	$0.721987\pi$
$18$	− 2.69202i	− 0.634516i
$19$	1.95108i	0.447609i	0.974634	+	0.223805i	$0.0718477\pi$
$19$	1.95108i	0.447609i	−0.974634	+	0.223805i	$0.928152\pi$
$20$	− 1.35690i	− 0.303411i
$21$	0.554958i	0.121102i
$22$	1.80194	0.384174
$23$	−4.85086	−1.01147	−0.505737	−	0.862688i	$-0.668779\pi$
$23$	−4.85086	−1.01147	−0.505737	+	0.862688i	$0.668779\pi$
$24$	− 0.554958i	− 0.113280i
$25$	3.15883	0.631767
$26$	0	0
$27$	−3.15883	−0.607918
$28$	− 1.00000i	− 0.188982i
$29$	5.96077	1.10689	0.553444	−	0.832887i	$-0.313313\pi$
$29$	5.96077	1.10689	0.553444	+	0.832887i	$0.313313\pi$
$30$	−0.753020	−0.137482
$31$	− 3.63102i	− 0.652151i	−0.945344	−	0.326075i	$-0.894274\pi$
$31$	− 3.63102i	− 0.652151i	0.945344	−	0.326075i	$-0.105726\pi$
$32$	1.00000i	0.176777i
$33$	− 1.00000i	− 0.174078i
$34$	− 5.29590i	− 0.908239i
$35$	−1.35690	−0.229357
$36$	2.69202	0.448670
$37$	− 7.75302i	− 1.27459i	−0.770620	−	0.637294i	$-0.780054\pi$
$37$	− 7.75302i	− 1.27459i	0.770620	−	0.637294i	$-0.219946\pi$
$38$	−1.95108	−0.316507
$39$	0	0
$40$	1.35690	0.214544
$41$	0.0392287i	0.00612649i	0.999995	+	0.00306324i	$0.000975062\pi$
$41$	0.0392287i	0.00612649i	−0.999995	+	0.00306324i	$0.999025\pi$
$42$	−0.554958	−0.0856319
$43$	−2.26875	−0.345981	−0.172991	−	0.984923i	$-0.555343\pi$
$43$	−2.26875	−0.345981	−0.172991	+	0.984923i	$0.555343\pi$
$44$	1.80194i	0.271652i
$45$	− 3.65279i	− 0.544526i
$46$	− 4.85086i	− 0.715220i
$47$	− 10.5700i	− 1.54180i	−0.636958	−	0.770898i	$-0.719808\pi$
$47$	− 10.5700i	− 1.54180i	0.636958	−	0.770898i	$-0.280192\pi$
$48$	0.554958	0.0801013
$49$	−1.00000	−0.142857
$50$	3.15883i	0.446727i
$51$	−2.93900	−0.411542
$52$	0	0
$53$	−3.66487	−0.503409	−0.251705	−	0.967804i	$-0.580991\pi$
$53$	−3.66487	−0.503409	−0.251705	+	0.967804i	$0.580991\pi$
$54$	− 3.15883i	− 0.429863i
$55$	2.44504	0.329689
$56$	1.00000	0.133631
$57$	1.08277i	0.143416i
$58$	5.96077i	0.782688i
$59$	− 4.07606i	− 0.530658i	−0.964158	−	0.265329i	$-0.914519\pi$
$59$	− 4.07606i	− 0.530658i	0.964158	−	0.265329i	$-0.0854806\pi$
$60$	− 0.753020i	− 0.0972145i
$61$	−11.5036	−1.47289	−0.736446	−	0.676497i	$-0.763497\pi$
$61$	−11.5036	−1.47289	−0.736446	+	0.676497i	$0.763497\pi$
$62$	3.63102	0.461140
$63$	− 2.69202i	− 0.339163i
$64$	−1.00000	−0.125000
$65$	0	0
$66$	1.00000	0.123091
$67$	− 2.22521i	− 0.271853i	−0.990719	−	0.135926i	$-0.956599\pi$
$67$	− 2.22521i	− 0.271853i	0.990719	−	0.135926i	$-0.0434010\pi$
$68$	5.29590	0.642222
$69$	−2.69202	−0.324081
$70$	− 1.35690i	− 0.162180i
$71$	7.78986i	0.924486i	0.886753	+	0.462243i	$0.152955\pi$
$71$	7.78986i	0.924486i	−0.886753	+	0.462243i	$0.847045\pi$
$72$	2.69202i	0.317258i
$73$	− 14.1032i	− 1.65066i	−0.564654	−	0.825328i	$-0.690990\pi$
$73$	− 14.1032i	− 1.65066i	0.564654	−	0.825328i	$-0.309010\pi$
$74$	7.75302	0.901270
$75$	1.75302	0.202421
$76$	− 1.95108i	− 0.223805i
$77$	1.80194	0.205350
$78$	0	0
$79$	−12.0804	−1.35915	−0.679574	−	0.733607i	$-0.737835\pi$
$79$	−12.0804	−1.35915	−0.679574	+	0.733607i	$0.737835\pi$
$80$	1.35690i	0.151706i
$81$	6.32304	0.702560
$82$	−0.0392287	−0.00433208
$83$	2.85086i	0.312922i	0.987684	+	0.156461i	$0.0500086\pi$
$83$	2.85086i	0.312922i	−0.987684	+	0.156461i	$0.949991\pi$
$84$	− 0.554958i	− 0.0605509i
$85$	− 7.18598i	− 0.779429i
$86$	− 2.26875i	− 0.244646i
$87$	3.30798	0.354653
$88$	−1.80194	−0.192087
$89$	6.61894i	0.701606i	0.936449	+	0.350803i	$0.114091\pi$
$89$	6.61894i	0.701606i	−0.936449	+	0.350803i	$0.885909\pi$
$90$	3.65279	0.385038
$91$	0	0
$92$	4.85086	0.505737
$93$	− 2.01507i	− 0.208953i
$94$	10.5700	1.09021
$95$	−2.64742	−0.271619
$96$	0.554958i	0.0566402i
$97$	− 3.64310i	− 0.369901i	−0.982748	−	0.184951i	$-0.940787\pi$
$97$	− 3.64310i	− 0.369901i	0.982748	−	0.184951i	$-0.0592125\pi$
$98$	− 1.00000i	− 0.101015i
$99$	4.85086i	0.487529i
$100$	−3.15883	−0.315883
$101$	−7.85086	−0.781189	−0.390595	−	0.920563i	$-0.627731\pi$
$101$	−7.85086	−0.781189	−0.390595	+	0.920563i	$0.627731\pi$
$102$	− 2.93900i	− 0.291004i
$103$	17.0804	1.68298	0.841490	−	0.540273i	$-0.181679\pi$
$103$	17.0804	1.68298	0.841490	+	0.540273i	$0.181679\pi$
$104$	0	0
$105$	−0.753020	−0.0734873
$106$	− 3.66487i	− 0.355964i
$107$	13.8562	1.33953	0.669766	−	0.742572i	$-0.266394\pi$
$107$	13.8562	1.33953	0.669766	+	0.742572i	$0.266394\pi$
$108$	3.15883	0.303959
$109$	− 2.18060i	− 0.208864i	−0.994532	−	0.104432i	$-0.966698\pi$
$109$	− 2.18060i	− 0.208864i	0.994532	−	0.104432i	$-0.0333025\pi$
$110$	2.44504i	0.233126i
$111$	− 4.30260i	− 0.408385i
$112$	1.00000i	0.0944911i
$113$	−17.5090	−1.64711	−0.823555	−	0.567236i	$-0.808013\pi$
$113$	−17.5090	−1.64711	−0.823555	+	0.567236i	$0.808013\pi$
$114$	−1.08277	−0.101411
$115$	− 6.58211i	− 0.613784i
$116$	−5.96077	−0.553444
$117$	0	0
$118$	4.07606	0.375232
$119$	− 5.29590i	− 0.485474i
$120$	0.753020	0.0687410
$121$	7.75302	0.704820
$122$	− 11.5036i	− 1.04149i
$123$	0.0217703i	0.00196296i
$124$	3.63102i	0.326075i
$125$	11.0707i	0.990192i
$126$	2.69202	0.239824
$127$	4.96316	0.440410	0.220205	−	0.975454i	$-0.429327\pi$
$127$	4.96316	0.440410	0.220205	+	0.975454i	$0.429327\pi$
$128$	− 1.00000i	− 0.0883883i
$129$	−1.25906	−0.110854
$130$	0	0
$131$	−11.0761	−0.967720	−0.483860	−	0.875145i	$-0.660766\pi$
$131$	−11.0761	−0.967720	−0.483860	+	0.875145i	$0.660766\pi$
$132$	1.00000i	0.0870388i
$133$	−1.95108	−0.169180
$134$	2.22521	0.192229
$135$	− 4.28621i	− 0.368898i
$136$	5.29590i	0.454119i
$137$	− 10.3056i	− 0.880466i	−0.897884	−	0.440233i	$-0.854896\pi$
$137$	− 10.3056i	− 0.880466i	0.897884	−	0.440233i	$-0.145104\pi$
$138$	− 2.69202i	− 0.229160i
$139$	0.987918	0.0837941	0.0418971	−	0.999122i	$-0.486660\pi$
$139$	0.987918	0.0837941	0.0418971	+	0.999122i	$0.486660\pi$
$140$	1.35690	0.114679
$141$	− 5.86592i	− 0.494000i
$142$	−7.78986	−0.653710
$143$	0	0
$144$	−2.69202	−0.224335
$145$	8.08815i	0.671684i
$146$	14.1032	1.16719
$147$	−0.554958	−0.0457722
$148$	7.75302i	0.637294i
$149$	− 5.60627i	− 0.459283i	−0.973275	−	0.229642i	$-0.926245\pi$
$149$	− 5.60627i	− 0.459283i	0.973275	−	0.229642i	$-0.0737554\pi$
$150$	1.75302i	0.143134i
$151$	15.5894i	1.26865i	0.773068	+	0.634324i	$0.218721\pi$
$151$	15.5894i	1.26865i	−0.773068	+	0.634324i	$0.781279\pi$
$152$	1.95108	0.158254
$153$	14.2567	1.15258
$154$	1.80194i	0.145204i
$155$	4.92692	0.395740
$156$	0	0
$157$	−8.49827	−0.678236	−0.339118	−	0.940744i	$-0.610129\pi$
$157$	−8.49827	−0.678236	−0.339118	+	0.940744i	$0.610129\pi$
$158$	− 12.0804i	− 0.961063i
$159$	−2.03385	−0.161295
$160$	−1.35690	−0.107272
$161$	− 4.85086i	− 0.382301i
$162$	6.32304i	0.496785i
$163$	− 5.25906i	− 0.411921i	−0.978560	−	0.205961i	$-0.933968\pi$
$163$	− 5.25906i	− 0.411921i	0.978560	−	0.205961i	$-0.0660319\pi$
$164$	− 0.0392287i	− 0.00306324i
$165$	1.35690	0.105634
$166$	−2.85086	−0.221269
$167$	− 14.0954i	− 1.09074i	−0.838196	−	0.545369i	$-0.816390\pi$
$167$	− 14.0954i	− 1.09074i	0.838196	−	0.545369i	$-0.183610\pi$
$168$	0.554958	0.0428159
$169$	0	0
$170$	7.18598	0.551140
$171$	− 5.25236i	− 0.401658i
$172$	2.26875	0.172991
$173$	−17.8877	−1.35998	−0.679988	−	0.733223i	$-0.738015\pi$
$173$	−17.8877	−1.35998	−0.679988	+	0.733223i	$0.738015\pi$
$174$	3.30798i	0.250777i
$175$	3.15883i	0.238785i
$176$	− 1.80194i	− 0.135826i
$177$	− 2.26205i	− 0.170026i
$178$	−6.61894	−0.496111
$179$	0.0556221	0.00415739	0.00207870	−	0.999998i	$-0.499338\pi$
$179$	0.0556221	0.00415739	0.00207870	+	0.999998i	$0.499338\pi$
$180$	3.65279i	0.272263i
$181$	8.45042	0.628115	0.314057	−	0.949404i	$-0.398312\pi$
$181$	8.45042	0.628115	0.314057	+	0.949404i	$0.398312\pi$
$182$	0	0
$183$	−6.38404	−0.471922
$184$	4.85086i	0.357610i
$185$	10.5200	0.773449
$186$	2.01507	0.147752
$187$	9.54288i	0.697844i
$188$	10.5700i	0.770898i
$189$	− 3.15883i	− 0.229771i
$190$	− 2.64742i	− 0.192064i
$191$	−4.33273	−0.313506	−0.156753	−	0.987638i	$-0.550103\pi$
$191$	−4.33273	−0.313506	−0.156753	+	0.987638i	$0.550103\pi$
$192$	−0.554958	−0.0400507
$193$	1.70410i	0.122664i	0.998117	+	0.0613320i	$0.0195348\pi$
$193$	1.70410i	0.122664i	−0.998117	+	0.0613320i	$0.980465\pi$
$194$	3.64310	0.261560
$195$	0	0
$196$	1.00000	0.0714286
$197$	− 25.7700i	− 1.83604i	−0.396538	−	0.918018i	$-0.629788\pi$
$197$	− 25.7700i	− 1.83604i	0.396538	−	0.918018i	$-0.370212\pi$
$198$	−4.85086	−0.344735
$199$	−6.72587	−0.476785	−0.238392	−	0.971169i	$-0.576620\pi$
$199$	−6.72587	−0.476785	−0.238392	+	0.971169i	$0.576620\pi$
$200$	− 3.15883i	− 0.223363i
$201$	− 1.23490i	− 0.0871030i
$202$	− 7.85086i	− 0.552384i
$203$	5.96077i	0.418364i
$204$	2.93900	0.205771
$205$	−0.0532292	−0.00371769
$206$	17.0804i	1.19005i
$207$	13.0586	0.907636
$208$	0	0
$209$	3.51573	0.243188
$210$	− 0.753020i	− 0.0519633i
$211$	−26.7536	−1.84179	−0.920897	−	0.389805i	$-0.872542\pi$
$211$	−26.7536	−1.84179	−0.920897	+	0.389805i	$0.872542\pi$
$212$	3.66487	0.251705
$213$	4.32304i	0.296210i
$214$	13.8562i	0.947193i
$215$	− 3.07846i	− 0.209949i
$216$	3.15883i	0.214931i
$217$	3.63102	0.246490
$218$	2.18060	0.147689
$219$	− 7.82669i	− 0.528879i
$220$	−2.44504	−0.164845
$221$	0	0
$222$	4.30260	0.288772
$223$	20.5851i	1.37848i	0.724533	+	0.689240i	$0.242055\pi$
$223$	20.5851i	1.37848i	−0.724533	+	0.689240i	$0.757945\pi$
$224$	−1.00000	−0.0668153
$225$	−8.50365	−0.566910
$226$	− 17.5090i	− 1.16468i
$227$	− 22.2543i	− 1.47707i	−0.674216	−	0.738534i	$-0.735518\pi$
$227$	− 22.2543i	− 1.47707i	0.674216	−	0.738534i	$-0.264482\pi$
$228$	− 1.08277i	− 0.0717081i
$229$	− 16.3230i	− 1.07866i	−0.842095	−	0.539329i	$-0.818678\pi$
$229$	− 16.3230i	− 1.07866i	0.842095	−	0.539329i	$-0.181322\pi$
$230$	6.58211	0.434011
$231$	1.00000	0.0657952
$232$	− 5.96077i	− 0.391344i
$233$	−6.88769	−0.451228	−0.225614	−	0.974217i	$-0.572439\pi$
$233$	−6.88769	−0.451228	−0.225614	+	0.974217i	$0.572439\pi$
$234$	0	0
$235$	14.3424	0.935596
$236$	4.07606i	0.265329i
$237$	−6.70410	−0.435478
$238$	5.29590	0.343282
$239$	14.1709i	0.916640i	0.888787	+	0.458320i	$0.151549\pi$
$239$	14.1709i	0.916640i	−0.888787	+	0.458320i	$0.848451\pi$
$240$	0.753020i	0.0486073i
$241$	− 3.91484i	− 0.252177i	−0.992019	−	0.126088i	$-0.959758\pi$
$241$	− 3.91484i	− 0.252177i	0.992019	−	0.126088i	$-0.0402423\pi$
$242$	7.75302i	0.498383i
$243$	12.9855	0.833022
$244$	11.5036	0.736446
$245$	− 1.35690i	− 0.0866889i
$246$	−0.0217703	−0.00138802
$247$	0	0
$248$	−3.63102	−0.230570
$249$	1.58211i	0.100262i
$250$	−11.0707	−0.700172
$251$	−10.3327	−0.652196	−0.326098	−	0.945336i	$-0.605734\pi$
$251$	−10.3327	−0.652196	−0.326098	+	0.945336i	$0.605734\pi$
$252$	2.69202i	0.169581i
$253$	8.74094i	0.549538i
$254$	4.96316i	0.311417i
$255$	− 3.98792i	− 0.249733i
$256$	1.00000	0.0625000
$257$	14.3884	0.897521	0.448760	−	0.893652i	$-0.351866\pi$
$257$	14.3884	0.897521	0.448760	+	0.893652i	$0.351866\pi$
$258$	− 1.25906i	− 0.0783857i
$259$	7.75302	0.481749
$260$	0	0
$261$	−16.0465	−0.993255
$262$	− 11.0761i	− 0.684282i
$263$	−17.6069	−1.08569	−0.542843	−	0.839834i	$-0.682652\pi$
$263$	−17.6069	−1.08569	−0.542843	+	0.839834i	$0.682652\pi$
$264$	−1.00000	−0.0615457
$265$	− 4.97285i	− 0.305480i
$266$	− 1.95108i	− 0.119629i
$267$	3.67324i	0.224798i
$268$	2.22521i	0.135926i
$269$	−4.15213	−0.253160	−0.126580	−	0.991956i	$-0.540400\pi$
$269$	−4.15213	−0.253160	−0.126580	+	0.991956i	$0.540400\pi$
$270$	4.28621	0.260850
$271$	− 17.5278i	− 1.06474i	−0.846512	−	0.532369i	$-0.821302\pi$
$271$	− 17.5278i	− 1.06474i	0.846512	−	0.532369i	$-0.178698\pi$
$272$	−5.29590	−0.321111
$273$	0	0
$274$	10.3056	0.622583
$275$	− 5.69202i	− 0.343242i
$276$	2.69202	0.162041
$277$	29.9855	1.80166	0.900828	−	0.434177i	$-0.142961\pi$
$277$	29.9855	1.80166	0.900828	+	0.434177i	$0.142961\pi$
$278$	0.987918i	0.0592514i
$279$	9.77479i	0.585201i
$280$	1.35690i	0.0810900i
$281$	9.24027i	0.551229i	0.961268	+	0.275614i	$0.0888813\pi$
$281$	9.24027i	0.551229i	−0.961268	+	0.275614i	$0.911119\pi$
$282$	5.86592	0.349310
$283$	−32.0291	−1.90393	−0.951965	−	0.306206i	$-0.900940\pi$
$283$	−32.0291	−1.90393	−0.951965	+	0.306206i	$0.900940\pi$
$284$	− 7.78986i	− 0.462243i
$285$	−1.46921	−0.0870282
$286$	0	0
$287$	−0.0392287	−0.00231559
$288$	− 2.69202i	− 0.158629i
$289$	11.0465	0.649796
$290$	−8.08815	−0.474952
$291$	− 2.02177i	− 0.118518i
$292$	14.1032i	0.825328i
$293$	22.1933i	1.29655i	0.761408	+	0.648273i	$0.224508\pi$
$293$	22.1933i	1.29655i	−0.761408	+	0.648273i	$0.775492\pi$
$294$	− 0.554958i	− 0.0323658i
$295$	5.53079	0.322015
$296$	−7.75302	−0.450635
$297$	5.69202i	0.330285i
$298$	5.60627	0.324762
$299$	0	0
$300$	−1.75302	−0.101211
$301$	− 2.26875i	− 0.130769i
$302$	−15.5894	−0.897069
$303$	−4.35690	−0.250297
$304$	1.95108i	0.111902i
$305$	− 15.6093i	− 0.893783i
$306$	14.2567i	0.814999i
$307$	20.8170i	1.18809i	0.804432	+	0.594045i	$0.202470\pi$
$307$	20.8170i	1.18809i	−0.804432	+	0.594045i	$0.797530\pi$
$308$	−1.80194	−0.102675
$309$	9.47889	0.539235
$310$	4.92692i	0.279830i
$311$	−28.1836	−1.59814	−0.799072	−	0.601235i	$-0.794676\pi$
$311$	−28.1836	−1.59814	−0.799072	+	0.601235i	$0.794676\pi$
$312$	0	0
$313$	16.0248	0.905773	0.452886	−	0.891568i	$-0.350394\pi$
$313$	16.0248	0.905773	0.452886	+	0.891568i	$0.350394\pi$
$314$	− 8.49827i	− 0.479585i
$315$	3.65279	0.205812
$316$	12.0804	0.679574
$317$	29.0834i	1.63348i	0.577003	+	0.816742i	$0.304222\pi$
$317$	29.0834i	1.63348i	−0.577003	+	0.816742i	$0.695778\pi$
$318$	− 2.03385i	− 0.114053i
$319$	− 10.7409i	− 0.601377i
$320$	− 1.35690i	− 0.0758528i
$321$	7.68963	0.429193
$322$	4.85086	0.270328
$323$	− 10.3327i	− 0.574929i
$324$	−6.32304	−0.351280
$325$	0	0
$326$	5.25906	0.291272
$327$	− 1.21014i	− 0.0669211i
$328$	0.0392287	0.00216604
$329$	10.5700	0.582744
$330$	1.35690i	0.0746947i
$331$	− 7.32304i	− 0.402511i	−0.979539	−	0.201255i	$-0.935498\pi$
$331$	− 7.32304i	− 0.402511i	0.979539	−	0.201255i	$-0.0645021\pi$
$332$	− 2.85086i	− 0.156461i
$333$	20.8713i	1.14374i
$334$	14.0954	0.771268
$335$	3.01938	0.164966
$336$	0.554958i	0.0302754i
$337$	27.1618	1.47960	0.739799	−	0.672828i	$-0.234920\pi$
$337$	27.1618	1.47960	0.739799	+	0.672828i	$0.234920\pi$
$338$	0	0
$339$	−9.71678	−0.527743
$340$	7.18598i	0.389715i
$341$	−6.54288	−0.354317
$342$	5.25236	0.284015
$343$	− 1.00000i	− 0.0539949i
$344$	2.26875i	0.122323i
$345$	− 3.65279i	− 0.196660i
$346$	− 17.8877i	− 0.961648i
$347$	−12.8890	−0.691919	−0.345959	−	0.938249i	$-0.612447\pi$
$347$	−12.8890	−0.691919	−0.345959	+	0.938249i	$0.612447\pi$
$348$	−3.30798	−0.177326
$349$	19.6732i	1.05308i	0.850149	+	0.526542i	$0.176512\pi$
$349$	19.6732i	1.05308i	−0.850149	+	0.526542i	$0.823488\pi$
$350$	−3.15883	−0.168847
$351$	0	0
$352$	1.80194	0.0960436
$353$	30.3980i	1.61792i	0.587861	+	0.808962i	$0.299970\pi$
$353$	30.3980i	1.61792i	−0.587861	+	0.808962i	$0.700030\pi$
$354$	2.26205	0.120226
$355$	−10.5700	−0.560999
$356$	− 6.61894i	− 0.350803i
$357$	− 2.93900i	− 0.155548i
$358$	0.0556221i	0.00293972i
$359$	− 2.64310i	− 0.139498i	−0.997565	−	0.0697489i	$-0.977780\pi$
$359$	− 2.64310i	− 0.139498i	0.997565	−	0.0697489i	$-0.0222198\pi$
$360$	−3.65279	−0.192519
$361$	15.1933	0.799646
$362$	8.45042i	0.444144i
$363$	4.30260	0.225828
$364$	0	0
$365$	19.1366	1.00165
$366$	− 6.38404i	− 0.333699i
$367$	2.46921	0.128891	0.0644457	−	0.997921i	$-0.479472\pi$
$367$	2.46921	0.128891	0.0644457	+	0.997921i	$0.479472\pi$
$368$	−4.85086	−0.252868
$369$	− 0.105604i	− 0.00549755i
$370$	10.5200i	0.546911i
$371$	− 3.66487i	− 0.190271i
$372$	2.01507i	0.104476i
$373$	−5.96615	−0.308915	−0.154458	−	0.987999i	$-0.549363\pi$
$373$	−5.96615	−0.308915	−0.154458	+	0.987999i	$0.549363\pi$
$374$	−9.54288	−0.493450
$375$	6.14377i	0.317263i
$376$	−10.5700	−0.545107
$377$	0	0
$378$	3.15883	0.162473
$379$	22.0519i	1.13273i	0.824155	+	0.566365i	$0.191651\pi$
$379$	22.0519i	1.13273i	−0.824155	+	0.566365i	$0.808349\pi$
$380$	2.64742	0.135810
$381$	2.75435	0.141110
$382$	− 4.33273i	− 0.221682i
$383$	26.1758i	1.33752i	0.743478	+	0.668761i	$0.233175\pi$
$383$	26.1758i	1.33752i	−0.743478	+	0.668761i	$0.766825\pi$
$384$	− 0.554958i	− 0.0283201i
$385$	2.44504i	0.124611i
$386$	−1.70410	−0.0867366
$387$	6.10752	0.310463
$388$	3.64310i	0.184951i
$389$	15.4655	0.784131	0.392066	−	0.919937i	$-0.371761\pi$
$389$	15.4655	0.784131	0.392066	+	0.919937i	$0.371761\pi$
$390$	0	0
$391$	25.6896	1.29918
$392$	1.00000i	0.0505076i
$393$	−6.14675	−0.310063
$394$	25.7700	1.29827
$395$	− 16.3918i	− 0.824762i
$396$	− 4.85086i	− 0.243765i
$397$	34.9778i	1.75548i	0.479134	+	0.877742i	$0.340951\pi$
$397$	34.9778i	1.75548i	−0.479134	+	0.877742i	$0.659049\pi$
$398$	− 6.72587i	− 0.337138i
$399$	−1.08277	−0.0542063
$400$	3.15883	0.157942
$401$	27.3739i	1.36699i	0.729957	+	0.683493i	$0.239540\pi$
$401$	27.3739i	1.36699i	−0.729957	+	0.683493i	$0.760460\pi$
$402$	1.23490	0.0615911
$403$	0	0
$404$	7.85086	0.390595
$405$	8.57971i	0.426329i
$406$	−5.96077	−0.295828
$407$	−13.9705	−0.692490
$408$	2.93900i	0.145502i
$409$	− 29.0810i	− 1.43796i	−0.695030	−	0.718981i	$-0.744609\pi$
$409$	− 29.0810i	− 1.43796i	0.695030	−	0.718981i	$-0.255391\pi$
$410$	− 0.0532292i	− 0.00262880i
$411$	− 5.71917i	− 0.282106i
$412$	−17.0804	−0.841490
$413$	4.07606	0.200570
$414$	13.0586i	0.641795i
$415$	−3.86831	−0.189888
$416$	0	0
$417$	0.548253	0.0268481
$418$	3.51573i	0.171960i
$419$	−40.3086	−1.96920	−0.984601	−	0.174815i	$-0.944067\pi$
$419$	−40.3086	−1.96920	−0.984601	+	0.174815i	$0.944067\pi$
$420$	0.753020	0.0367436
$421$	4.26981i	0.208098i	0.994572	+	0.104049i	$0.0331799\pi$
$421$	4.26981i	0.208098i	−0.994572	+	0.104049i	$0.966820\pi$
$422$	− 26.7536i	− 1.30235i
$423$	28.4547i	1.38352i
$424$	3.66487i	0.177982i
$425$	−16.7289	−0.811469
$426$	−4.32304	−0.209452
$427$	− 11.5036i	− 0.556701i
$428$	−13.8562	−0.669766
$429$	0	0
$430$	3.07846	0.148456
$431$	− 6.25475i	− 0.301281i	−0.988589	−	0.150640i	$-0.951866\pi$
$431$	− 6.25475i	− 0.301281i	0.988589	−	0.150640i	$-0.0481335\pi$
$432$	−3.15883	−0.151979
$433$	15.9705	0.767491	0.383746	−	0.923439i	$-0.374634\pi$
$433$	15.9705	0.767491	0.383746	+	0.923439i	$0.374634\pi$
$434$	3.63102i	0.174295i
$435$	4.48858i	0.215211i
$436$	2.18060i	0.104432i
$437$	− 9.46442i	− 0.452745i
$438$	7.82669	0.373974
$439$	−30.4058	−1.45119	−0.725595	−	0.688122i	$-0.758435\pi$
$439$	−30.4058	−1.45119	−0.725595	+	0.688122i	$0.758435\pi$
$440$	− 2.44504i	− 0.116563i
$441$	2.69202	0.128191
$442$	0	0
$443$	−13.0291	−0.619030	−0.309515	−	0.950895i	$-0.600167\pi$
$443$	−13.0291	−0.619030	−0.309515	+	0.950895i	$0.600167\pi$
$444$	4.30260i	0.204192i
$445$	−8.98121	−0.425750
$446$	−20.5851	−0.974732
$447$	− 3.11124i	− 0.147157i
$448$	− 1.00000i	− 0.0472456i
$449$	− 20.2258i	− 0.954515i	−0.878764	−	0.477257i	$-0.841631\pi$
$449$	− 20.2258i	− 0.954515i	0.878764	−	0.477257i	$-0.158369\pi$
$450$	− 8.50365i	− 0.400866i
$451$	0.0706876	0.00332855
$452$	17.5090	0.823555
$453$	8.65146i	0.406481i
$454$	22.2543	1.04444
$455$	0	0
$456$	1.08277	0.0507053
$457$	20.5569i	0.961610i	0.876828	+	0.480805i	$0.159656\pi$
$457$	20.5569i	0.961610i	−0.876828	+	0.480805i	$0.840344\pi$
$458$	16.3230	0.762726
$459$	16.7289	0.780836
$460$	6.58211i	0.306892i
$461$	− 15.2513i	− 0.710323i	−0.934805	−	0.355162i	$-0.884426\pi$
$461$	− 15.2513i	− 0.710323i	0.934805	−	0.355162i	$-0.115574\pi$
$462$	1.00000i	0.0465242i
$463$	25.3207i	1.17675i	0.808588	+	0.588375i	$0.200232\pi$
$463$	25.3207i	1.17675i	−0.808588	+	0.588375i	$0.799768\pi$
$464$	5.96077	0.276722
$465$	2.73423	0.126797
$466$	− 6.88769i	− 0.319066i
$467$	−16.8019	−0.777501	−0.388750	−	0.921343i	$-0.627093\pi$
$467$	−16.8019	−0.777501	−0.388750	+	0.921343i	$0.627093\pi$
$468$	0	0
$469$	2.22521	0.102751
$470$	14.3424i	0.661567i
$471$	−4.71618	−0.217310
$472$	−4.07606	−0.187616
$473$	4.08815i	0.187973i
$474$	− 6.70410i	− 0.307930i
$475$	6.16315i	0.282785i
$476$	5.29590i	0.242737i
$477$	9.86592	0.451729
$478$	−14.1709	−0.648163
$479$	27.5870i	1.26048i	0.776399	+	0.630241i	$0.217044\pi$
$479$	27.5870i	1.26048i	−0.776399	+	0.630241i	$0.782956\pi$
$480$	−0.753020	−0.0343705
$481$	0	0
$482$	3.91484	0.178316
$483$	− 2.69202i	− 0.122491i
$484$	−7.75302	−0.352410
$485$	4.94331	0.224464
$486$	12.9855i	0.589035i
$487$	− 29.4698i	− 1.33540i	−0.744429	−	0.667702i	$-0.767278\pi$
$487$	− 29.4698i	− 1.33540i	0.744429	−	0.667702i	$-0.232722\pi$
$488$	11.5036i	0.520746i
$489$	− 2.91856i	− 0.131982i
$490$	1.35690	0.0612983
$491$	8.30691	0.374886	0.187443	−	0.982276i	$-0.439980\pi$
$491$	8.30691	0.374886	0.187443	+	0.982276i	$0.439980\pi$
$492$	− 0.0217703i	0 0.000981479i
$493$	−31.5676	−1.42173
$494$	0	0
$495$	−6.58211	−0.295844
$496$	− 3.63102i	− 0.163038i
$497$	−7.78986	−0.349423
$498$	−1.58211	−0.0708958
$499$	− 42.2043i	− 1.88932i	−0.328046	−	0.944662i	$-0.606390\pi$
$499$	− 42.2043i	− 1.88932i	0.328046	−	0.944662i	$-0.393610\pi$
$500$	− 11.0707i	− 0.495096i
$501$	− 7.82238i	− 0.349478i
$502$	− 10.3327i	− 0.461172i
$503$	17.5133	0.780881	0.390441	−	0.920628i	$-0.372323\pi$
$503$	17.5133	0.780881	0.390441	+	0.920628i	$0.372323\pi$
$504$	−2.69202	−0.119912
$505$	− 10.6528i	− 0.474043i
$506$	−8.74094	−0.388582
$507$	0	0
$508$	−4.96316	−0.220205
$509$	6.94869i	0.307995i	0.988071	+	0.153998i	$0.0492148\pi$
$509$	6.94869i	0.307995i	−0.988071	+	0.153998i	$0.950785\pi$
$510$	3.98792	0.176588
$511$	14.1032	0.623889
$512$	1.00000i	0.0441942i
$513$	− 6.16315i	− 0.272110i
$514$	14.3884i	0.634643i
$515$	23.1763i	1.02127i
$516$	1.25906	0.0554271
$517$	−19.0465	−0.837665
$518$	7.75302i	0.340648i
$519$	−9.92692	−0.435743
$520$	0	0
$521$	−33.3889	−1.46280	−0.731398	−	0.681951i	$-0.761132\pi$
$521$	−33.3889	−1.46280	−0.731398	+	0.681951i	$0.761132\pi$
$522$	− 16.0465i	− 0.702337i
$523$	−0.281422	−0.0123057	−0.00615287	−	0.999981i	$-0.501959\pi$
$523$	−0.281422	−0.0123057	−0.00615287	+	0.999981i	$0.501959\pi$
$524$	11.0761	0.483860
$525$	1.75302i	0.0765081i
$526$	− 17.6069i	− 0.767696i
$527$	19.2295i	0.837651i
$528$	− 1.00000i	− 0.0435194i
$529$	0.530795	0.0230780
$530$	4.97285	0.216007
$531$	10.9729i	0.476181i
$532$	1.95108	0.0845902
$533$	0	0
$534$	−3.67324	−0.158956
$535$	18.8015i	0.812858i
$536$	−2.22521	−0.0961144
$537$	0.0308679	0.00133205
$538$	− 4.15213i	− 0.179011i
$539$	1.80194i	0.0776150i
$540$	4.28621i	0.184449i
$541$	− 33.4655i	− 1.43879i	−0.694599	−	0.719397i	$-0.744418\pi$
$541$	− 33.4655i	− 1.43879i	0.694599	−	0.719397i	$-0.255582\pi$
$542$	17.5278	0.752884
$543$	4.68963	0.201251
$544$	− 5.29590i	− 0.227060i
$545$	2.95885	0.126743
$546$	0	0
$547$	25.9148	1.10804	0.554019	−	0.832504i	$-0.313093\pi$
$547$	25.9148	1.10804	0.554019	+	0.832504i	$0.313093\pi$
$548$	10.3056i	0.440233i
$549$	30.9681	1.32168
$550$	5.69202	0.242709
$551$	11.6300i	0.495453i
$552$	2.69202i	0.114580i
$553$	− 12.0804i	− 0.513710i
$554$	29.9855i	1.27396i
$555$	5.83818	0.247817
$556$	−0.987918	−0.0418971
$557$	24.1588i	1.02364i	0.859092	+	0.511821i	$0.171029\pi$
$557$	24.1588i	1.02364i	−0.859092	+	0.511821i	$0.828971\pi$
$558$	−9.77479	−0.413800
$559$	0	0
$560$	−1.35690	−0.0573393
$561$	5.29590i	0.223593i
$562$	−9.24027	−0.389777
$563$	−5.58987	−0.235585	−0.117793	−	0.993038i	$-0.537582\pi$
$563$	−5.58987	−0.235585	−0.117793	+	0.993038i	$0.537582\pi$
$564$	5.86592i	0.247000i
$565$	− 23.7579i	− 0.999503i
$566$	− 32.0291i	− 1.34628i
$567$	6.32304i	0.265543i
$568$	7.78986	0.326855
$569$	−40.5217	−1.69876	−0.849379	−	0.527783i	$-0.823023\pi$
$569$	−40.5217	−1.69876	−0.849379	+	0.527783i	$0.823023\pi$
$570$	− 1.46921i	− 0.0615382i
$571$	−33.2180	−1.39013	−0.695066	−	0.718946i	$-0.744625\pi$
$571$	−33.2180	−1.39013	−0.695066	+	0.718946i	$0.744625\pi$
$572$	0	0
$573$	−2.40449	−0.100449
$574$	− 0.0392287i	− 0.00163737i
$575$	−15.3230	−0.639015
$576$	2.69202	0.112168
$577$	− 17.4896i	− 0.728104i	−0.931379	−	0.364052i	$-0.881393\pi$
$577$	− 17.4896i	− 0.728104i	0.931379	−	0.364052i	$-0.118607\pi$
$578$	11.0465i	0.459475i
$579$	0.945706i	0.0393022i
$580$	− 8.08815i	− 0.335842i
$581$	−2.85086	−0.118273
$582$	2.02177	0.0838051
$583$	6.60388i	0.273505i
$584$	−14.1032	−0.583595
$585$	0	0
$586$	−22.1933	−0.916796
$587$	− 35.8224i	− 1.47855i	−0.673405	−	0.739274i	$-0.735169\pi$
$587$	− 35.8224i	− 1.47855i	0.673405	−	0.739274i	$-0.264831\pi$
$588$	0.554958	0.0228861
$589$	7.08443	0.291909
$590$	5.53079i	0.227699i
$591$	− 14.3013i	− 0.588276i
$592$	− 7.75302i	− 0.318647i
$593$	− 12.0750i	− 0.495861i	−0.968778	−	0.247930i	$-0.920250\pi$
$593$	− 12.0750i	− 0.495861i	0.968778	−	0.247930i	$-0.0797504\pi$
$594$	−5.69202	−0.233546
$595$	7.18598	0.294596
$596$	5.60627i	0.229642i
$597$	−3.73258	−0.152764
$598$	0	0
$599$	20.6256	0.842741	0.421371	−	0.906889i	$-0.361549\pi$
$599$	20.6256	0.842741	0.421371	+	0.906889i	$0.361549\pi$
$600$	− 1.75302i	− 0.0715668i
$601$	−38.8025	−1.58279	−0.791394	−	0.611306i	$-0.790644\pi$
$601$	−38.8025	−1.58279	−0.791394	+	0.611306i	$0.790644\pi$
$602$	2.26875	0.0924673
$603$	5.99031i	0.243944i
$604$	− 15.5894i	− 0.634324i
$605$	10.5200i	0.427701i
$606$	− 4.35690i	− 0.176987i
$607$	2.24459	0.0911050	0.0455525	−	0.998962i	$-0.485495\pi$
$607$	2.24459	0.0911050	0.0455525	+	0.998962i	$0.485495\pi$
$608$	−1.95108	−0.0791269
$609$	3.30798i	0.134046i
$610$	15.6093	0.632000
$611$	0	0
$612$	−14.2567	−0.576292
$613$	4.24267i	0.171360i	0.996323	+	0.0856799i	$0.0273062\pi$
$613$	4.24267i	0.171360i	−0.996323	+	0.0856799i	$0.972694\pi$
$614$	−20.8170	−0.840106
$615$	−0.0295400	−0.00119117
$616$	− 1.80194i	− 0.0726021i
$617$	0.147817i	0.00595089i	0.999996	+	0.00297544i	$0.000947114\pi$
$617$	0.147817i	0.00595089i	−0.999996	+	0.00297544i	$0.999053\pi$
$618$	9.47889i	0.381297i
$619$	− 35.3575i	− 1.42114i	−0.703628	−	0.710569i	$-0.748438\pi$
$619$	− 35.3575i	− 1.42114i	0.703628	−	0.710569i	$-0.251562\pi$
$620$	−4.92692	−0.197870
$621$	15.3230	0.614893
$622$	− 28.1836i	− 1.13006i
$623$	−6.61894	−0.265182
$624$	0	0
$625$	0.772398	0.0308959
$626$	16.0248i	0.640478i
$627$	1.95108	0.0779187
$628$	8.49827	0.339118
$629$	41.0592i	1.63714i
$630$	3.65279i	0.145531i
$631$	− 2.33214i	− 0.0928411i	−0.998922	−	0.0464205i	$-0.985219\pi$
$631$	− 2.33214i	− 0.0928411i	0.998922	−	0.0464205i	$-0.0147814\pi$
$632$	12.0804i	0.480532i
$633$	−14.8471	−0.590121
$634$	−29.0834	−1.15505
$635$	6.73450i	0.267250i
$636$	2.03385	0.0806475
$637$	0	0
$638$	10.7409	0.425238
$639$	− 20.9705i	− 0.829579i
$640$	1.35690	0.0536360
$641$	17.5767	0.694239	0.347120	−	0.937821i	$-0.387160\pi$
$641$	17.5767	0.694239	0.347120	+	0.937821i	$0.387160\pi$
$642$	7.68963i	0.303485i
$643$	− 3.70410i	− 0.146076i	−0.997329	−	0.0730378i	$-0.976731\pi$
$643$	− 3.70410i	− 0.146076i	0.997329	−	0.0730378i	$-0.0232694\pi$
$644$	4.85086i	0.191150i
$645$	− 1.70841i	− 0.0672688i
$646$	10.3327	0.406536
$647$	−50.4935	−1.98510	−0.992552	−	0.121823i	$-0.961126\pi$
$647$	−50.4935	−1.98510	−0.992552	+	0.121823i	$0.961126\pi$
$648$	− 6.32304i	− 0.248393i
$649$	−7.34481	−0.288309
$650$	0	0
$651$	2.01507	0.0789766
$652$	5.25906i	0.205961i
$653$	33.5109	1.31138	0.655692	−	0.755028i	$-0.272377\pi$
$653$	33.5109	1.31138	0.655692	+	0.755028i	$0.272377\pi$
$654$	1.21014	0.0473204
$655$	− 15.0291i	− 0.587234i
$656$	0.0392287i	0.00153162i
$657$	37.9661i	1.48120i
$658$	10.5700i	0.412062i
$659$	12.8194	0.499373	0.249686	−	0.968327i	$-0.419672\pi$
$659$	12.8194	0.499373	0.249686	+	0.968327i	$0.419672\pi$
$660$	−1.35690	−0.0528171
$661$	24.3163i	0.945796i	0.881117	+	0.472898i	$0.156792\pi$
$661$	24.3163i	0.945796i	−0.881117	+	0.472898i	$0.843208\pi$
$662$	7.32304	0.284618
$663$	0	0
$664$	2.85086	0.110635
$665$	− 2.64742i	− 0.102662i
$666$	−20.8713	−0.808746
$667$	−28.9148	−1.11959
$668$	14.0954i	0.545369i
$669$	11.4239i	0.441672i
$670$	3.01938i	0.116649i
$671$	20.7289i	0.800229i
$672$	−0.554958	−0.0214080
$673$	17.9812	0.693125	0.346562	−	0.938027i	$-0.387349\pi$
$673$	17.9812	0.693125	0.346562	+	0.938027i	$0.387349\pi$
$674$	27.1618i	1.04623i
$675$	−9.97823	−0.384062
$676$	0	0
$677$	−1.81461	−0.0697411	−0.0348706	−	0.999392i	$-0.511102\pi$
$677$	−1.81461	−0.0697411	−0.0348706	+	0.999392i	$0.511102\pi$
$678$	− 9.71678i	− 0.373171i
$679$	3.64310	0.139810
$680$	−7.18598	−0.275570
$681$	− 12.3502i	− 0.473260i
$682$	− 6.54288i	− 0.250540i
$683$	37.9081i	1.45051i	0.688478	+	0.725257i	$0.258279\pi$
$683$	37.9081i	1.45051i	−0.688478	+	0.725257i	$0.741721\pi$
$684$	5.25236i	0.200829i
$685$	13.9836	0.534286
$686$	1.00000	0.0381802
$687$	− 9.05861i	− 0.345607i
$688$	−2.26875	−0.0864953
$689$	0	0
$690$	3.65279	0.139059
$691$	30.0881i	1.14461i	0.820042	+	0.572304i	$0.193950\pi$
$691$	30.0881i	1.14461i	−0.820042	+	0.572304i	$0.806050\pi$
$692$	17.8877	0.679988
$693$	−4.85086	−0.184269
$694$	− 12.8890i	− 0.489260i
$695$	1.34050i	0.0508482i
$696$	− 3.30798i	− 0.125389i
$697$	− 0.207751i	− 0.00786913i
$698$	−19.6732	−0.744643
$699$	−3.82238	−0.144576
$700$	− 3.15883i	− 0.119393i
$701$	18.4625	0.697319	0.348660	−	0.937249i	$-0.386637\pi$
$701$	18.4625	0.697319	0.348660	+	0.937249i	$0.386637\pi$
$702$	0	0
$703$	15.1268	0.570517
$704$	1.80194i	0.0679131i
$705$	7.95944	0.299770
$706$	−30.3980	−1.14405
$707$	− 7.85086i	− 0.295262i
$708$	2.26205i	0.0850129i
$709$	3.07308i	0.115412i	0.998334	+	0.0577060i	$0.0183786\pi$
$709$	3.07308i	0.115412i	−0.998334	+	0.0577060i	$0.981621\pi$
$710$	− 10.5700i	− 0.396686i
$711$	32.5206	1.21962
$712$	6.61894	0.248055
$713$	17.6136i	0.659633i
$714$	2.93900	0.109989
$715$	0	0
$716$	−0.0556221	−0.00207870
$717$	7.86426i	0.293696i
$718$	2.64310	0.0986398
$719$	−28.6213	−1.06740	−0.533698	−	0.845675i	$-0.679198\pi$
$719$	−28.6213	−1.06740	−0.533698	+	0.845675i	$0.679198\pi$
$720$	− 3.65279i	− 0.136132i
$721$	17.0804i	0.636106i
$722$	15.1933i	0.565435i
$723$	− 2.17257i	− 0.0807988i
$724$	−8.45042	−0.314057
$725$	18.8291	0.699295
$726$	4.30260i	0.159685i
$727$	−35.8799	−1.33071	−0.665356	−	0.746526i	$-0.731720\pi$
$727$	−35.8799	−1.33071	−0.665356	+	0.746526i	$0.731720\pi$
$728$	0	0
$729$	−11.7627	−0.435656
$730$	19.1366i	0.708277i
$731$	12.0151	0.444393
$732$	6.38404	0.235961
$733$	13.8291i	0.510789i	0.966837	+	0.255394i	$0.0822053\pi$
$733$	13.8291i	0.510789i	−0.966837	+	0.255394i	$0.917795\pi$
$734$	2.46921i	0.0911400i
$735$	− 0.753020i	− 0.0277756i
$736$	− 4.85086i	− 0.178805i
$737$	−4.00969	−0.147699
$738$	0.105604	0.00388735
$739$	− 50.6262i	− 1.86232i	−0.364616	−	0.931158i	$-0.618800\pi$
$739$	− 50.6262i	− 1.86232i	0.364616	−	0.931158i	$-0.381200\pi$
$740$	−10.5200	−0.386724
$741$	0	0
$742$	3.66487	0.134542
$743$	− 36.8866i	− 1.35324i	−0.736333	−	0.676620i	$-0.763444\pi$
$743$	− 36.8866i	− 1.35324i	0.736333	−	0.676620i	$-0.236556\pi$
$744$	−2.01507	−0.0738759
$745$	7.60712	0.278703
$746$	− 5.96615i	− 0.218436i
$747$	− 7.67456i	− 0.280798i
$748$	− 9.54288i	− 0.348922i
$749$	13.8562i	0.506296i
$750$	−6.14377	−0.224339
$751$	10.3556	0.377880	0.188940	−	0.981989i	$-0.439495\pi$
$751$	10.3556	0.377880	0.188940	+	0.981989i	$0.439495\pi$
$752$	− 10.5700i	− 0.385449i
$753$	−5.73423	−0.208967
$754$	0	0
$755$	−21.1532	−0.769844
$756$	3.15883i	0.114886i
$757$	20.0234	0.727764	0.363882	−	0.931445i	$-0.381451\pi$
$757$	20.0234	0.727764	0.363882	+	0.931445i	$0.381451\pi$
$758$	−22.0519	−0.800961
$759$	4.85086i	0.176075i
$760$	2.64742i	0.0960319i
$761$	− 14.9694i	− 0.542640i	−0.962489	−	0.271320i	$-0.912540\pi$
$761$	− 14.9694i	− 0.542640i	0.962489	−	0.271320i	$-0.0874602\pi$
$762$	2.75435i	0.0997795i
$763$	2.18060	0.0789432
$764$	4.33273	0.156753
$765$	19.3448i	0.699413i
$766$	−26.1758	−0.945771
$767$	0	0
$768$	0.554958	0.0200253
$769$	6.11290i	0.220437i	0.993907	+	0.110218i	$0.0351550\pi$
$769$	6.11290i	0.220437i	−0.993907	+	0.110218i	$0.964845\pi$
$770$	−2.44504	−0.0881132
$771$	7.98493	0.287570
$772$	− 1.70410i	− 0.0613320i
$773$	21.3870i	0.769238i	0.923075	+	0.384619i	$0.125667\pi$
$773$	21.3870i	0.769238i	−0.923075	+	0.384619i	$0.874333\pi$
$774$	6.10752i	0.219530i
$775$	− 11.4698i	− 0.412007i
$776$	−3.64310	−0.130780
$777$	4.30260	0.154355
$778$	15.4655i	0.554464i
$779$	−0.0765384	−0.00274227
$780$	0	0
$781$	14.0368	0.502277
$782$	25.6896i	0.918659i
$783$	−18.8291	−0.672897
$784$	−1.00000	−0.0357143
$785$	− 11.5313i	− 0.411569i
$786$	− 6.14675i	− 0.219247i
$787$	40.5623i	1.44589i	0.690907	+	0.722944i	$0.257212\pi$
$787$	40.5623i	1.44589i	−0.690907	+	0.722944i	$0.742788\pi$
$788$	25.7700i	0.918018i
$789$	−9.77107	−0.347859
$790$	16.3918	0.583195
$791$	− 17.5090i	− 0.622549i
$792$	4.85086	0.172368
$793$	0	0
$794$	−34.9778	−1.24131
$795$	− 2.75973i	− 0.0978774i
$796$	6.72587	0.238392
$797$	40.6698	1.44060	0.720299	−	0.693664i	$-0.244005\pi$
$797$	40.6698	1.44060	0.720299	+	0.693664i	$0.244005\pi$
$798$	− 1.08277i	− 0.0383296i
$799$	55.9778i	1.98035i
$800$	3.15883i	0.111682i
$801$	− 17.8183i	− 0.629580i
$802$	−27.3739	−0.966605
$803$	−25.4131	−0.896809
$804$	1.23490i	0.0435515i
$805$	6.58211	0.231989
$806$	0	0
$807$	−2.30426	−0.0811137
$808$	7.85086i	0.276192i
$809$	−56.3666	−1.98174	−0.990872	−	0.134808i	$-0.956958\pi$
$809$	−56.3666	−1.98174	−0.990872	+	0.134808i	$0.956958\pi$
$810$	−8.57971	−0.301460
$811$	10.2397i	0.359564i	0.983706	+	0.179782i	$0.0575392\pi$
$811$	10.2397i	0.359564i	−0.983706	+	0.179782i	$0.942461\pi$
$812$	− 5.96077i	− 0.209182i
$813$	− 9.72720i	− 0.341148i
$814$	− 13.9705i	− 0.489664i
$815$	7.13600	0.249963
$816$	−2.93900	−0.102886
$817$	− 4.42652i	− 0.154864i
$818$	29.0810	1.01679
$819$	0	0
$820$	0.0532292	0.00185884
$821$	− 29.6219i	− 1.03381i	−0.856042	−	0.516906i	$-0.827084\pi$
$821$	− 29.6219i	− 1.03381i	0.856042	−	0.516906i	$-0.172916\pi$
$822$	5.71917	0.199479
$823$	17.0804	0.595384	0.297692	−	0.954662i	$-0.403783\pi$
$823$	17.0804	0.595384	0.297692	+	0.954662i	$0.403783\pi$
$824$	− 17.0804i	− 0.595023i
$825$	− 3.15883i	− 0.109976i
$826$	4.07606i	0.141824i
$827$	5.46575i	0.190063i	0.995474	+	0.0950313i	$0.0302951\pi$
$827$	5.46575i	0.190063i	−0.995474	+	0.0950313i	$0.969705\pi$
$828$	−13.0586	−0.453818
$829$	−41.7942	−1.45157	−0.725786	−	0.687921i	$-0.758524\pi$
$829$	−41.7942	−1.45157	−0.725786	+	0.687921i	$0.758524\pi$
$830$	− 3.86831i	− 0.134271i
$831$	16.6407	0.577260
$832$	0	0
$833$	5.29590	0.183492
$834$	0.548253i	0.0189845i
$835$	19.1260	0.661884
$836$	−3.51573	−0.121594
$837$	11.4698i	0.396454i
$838$	− 40.3086i	− 1.39244i
$839$	− 9.38511i	− 0.324010i	−0.986790	−	0.162005i	$-0.948204\pi$
$839$	− 9.38511i	− 0.324010i	0.986790	−	0.162005i	$-0.0517961\pi$
$840$	0.753020i	0.0259817i
$841$	6.53079	0.225200
$842$	−4.26981	−0.147148
$843$	5.12797i	0.176617i
$844$	26.7536	0.920897
$845$	0	0
$846$	−28.4547	−0.978294
$847$	7.75302i	0.266397i
$848$	−3.66487	−0.125852
$849$	−17.7748	−0.610029
$850$	− 16.7289i	− 0.573795i
$851$	37.6088i	1.28921i
$852$	− 4.32304i	− 0.148105i
$853$	− 6.23623i	− 0.213524i	−0.994285	−	0.106762i	$-0.965952\pi$
$853$	− 6.23623i	− 0.213524i	0.994285	−	0.106762i	$-0.0340483\pi$
$854$	11.5036	0.393647
$855$	7.12690	0.243735
$856$	− 13.8562i	− 0.473596i
$857$	−50.7426	−1.73333	−0.866667	−	0.498887i	$-0.833742\pi$
$857$	−50.7426	−1.73333	−0.866667	+	0.498887i	$0.833742\pi$
$858$	0	0
$859$	28.7681	0.981554	0.490777	−	0.871285i	$-0.336713\pi$
$859$	28.7681	0.981554	0.490777	+	0.871285i	$0.336713\pi$
$860$	3.07846i	0.104975i
$861$	−0.0217703	−0.000741929 0
$862$	6.25475	0.213038
$863$	− 32.1473i	− 1.09431i	−0.837032	−	0.547154i	$-0.815711\pi$
$863$	− 32.1473i	− 1.09431i	0.837032	−	0.547154i	$-0.184289\pi$
$864$	− 3.15883i	− 0.107466i
$865$	− 24.2717i	− 0.825264i
$866$	15.9705i	0.542698i
$867$	6.13036	0.208198
$868$	−3.63102	−0.123245
$869$	21.7681i	0.738432i
$870$	−4.48858	−0.152177
$871$	0	0
$872$	−2.18060	−0.0738446
$873$	9.80731i	0.331927i
$874$	9.46442	0.320139
$875$	−11.0707	−0.374258
$876$	7.82669i	0.264439i
$877$	− 24.5123i	− 0.827721i	−0.910340	−	0.413860i	$-0.864180\pi$
$877$	− 24.5123i	− 0.827721i	0.910340	−	0.413860i	$-0.135820\pi$
$878$	− 30.4058i	− 1.02615i
$879$	12.3163i	0.415420i
$880$	2.44504	0.0824223
$881$	48.2653	1.62610	0.813050	−	0.582195i	$-0.197806\pi$
$881$	48.2653	1.62610	0.813050	+	0.582195i	$0.197806\pi$
$882$	2.69202i	0.0906451i
$883$	44.9342	1.51216	0.756078	−	0.654481i	$-0.227113\pi$
$883$	44.9342	1.51216	0.756078	+	0.654481i	$0.227113\pi$
$884$	0	0
$885$	3.06936	0.103175
$886$	− 13.0291i	− 0.437720i
$887$	41.2610	1.38541	0.692704	−	0.721222i	$-0.256419\pi$
$887$	41.2610	1.38541	0.692704	+	0.721222i	$0.256419\pi$
$888$	−4.30260	−0.144386
$889$	4.96316i	0.166459i
$890$	− 8.98121i	− 0.301051i
$891$	− 11.3937i	− 0.381704i
$892$	− 20.5851i	− 0.689240i
$893$	20.6230	0.690122
$894$	3.11124	0.104056
$895$	0.0754734i	0.00252280i
$896$	1.00000	0.0334077
$897$	0	0
$898$	20.2258	0.674944
$899$	− 21.6437i	− 0.721858i
$900$	8.50365	0.283455
$901$	19.4088	0.646601
$902$	0.0706876i	0.00235364i
$903$	− 1.25906i	− 0.0418989i
$904$	17.5090i	0.582341i
$905$	11.4663i	0.381154i
$906$	−8.65146	−0.287426
$907$	30.0344	0.997277	0.498639	−	0.866810i	$-0.333833\pi$
$907$	30.0344	0.997277	0.498639	+	0.866810i	$0.333833\pi$
$908$	22.2543i	0.738534i
$909$	21.1347	0.700993
$910$	0	0
$911$	−15.4069	−0.510453	−0.255226	−	0.966881i	$-0.582150\pi$
$911$	−15.4069	−0.510453	−0.255226	+	0.966881i	$0.582150\pi$
$912$	1.08277i	0.0358541i
$913$	5.13706	0.170012
$914$	−20.5569	−0.679961
$915$	− 8.66248i	− 0.286373i
$916$	16.3230i	0.539329i
$917$	− 11.0761i	− 0.365764i
$918$	16.7289i	0.552135i
$919$	21.8073	0.719357	0.359678	−	0.933076i	$-0.382886\pi$
$919$	21.8073	0.719357	0.359678	+	0.933076i	$0.382886\pi$
$920$	−6.58211	−0.217006
$921$	11.5526i	0.380670i
$922$	15.2513	0.502275
$923$	0	0
$924$	−1.00000	−0.0328976
$925$	− 24.4905i	− 0.805243i
$926$	−25.3207	−0.832088
$927$	−45.9807	−1.51021
$928$	5.96077i	0.195672i
$929$	38.4523i	1.26158i	0.775953	+	0.630790i	$0.217269\pi$
$929$	38.4523i	1.26158i	−0.775953	+	0.630790i	$0.782731\pi$
$930$	2.73423i	0.0896591i
$931$	− 1.95108i	− 0.0639442i
$932$	6.88769	0.225614
$933$	−15.6407	−0.512054
$934$	− 16.8019i	− 0.549776i
$935$	−12.9487	−0.423467
$936$	0	0
$937$	57.4669	1.87736	0.938681	−	0.344786i	$-0.112048\pi$
$937$	57.4669	1.87736	0.938681	+	0.344786i	$0.112048\pi$
$938$	2.22521i	0.0726557i
$939$	8.89307	0.290214
$940$	−14.3424	−0.467798
$941$	14.1347i	0.460777i	0.973099	+	0.230389i	$0.0739997\pi$
$941$	14.1347i	0.460777i	−0.973099	+	0.230389i	$0.926000\pi$
$942$	− 4.71618i	− 0.153662i
$943$	− 0.190293i	− 0.00619678i
$944$	− 4.07606i	− 0.132665i
$945$	4.28621	0.139430
$946$	−4.08815	−0.132917
$947$	− 19.0858i	− 0.620204i	−0.950703	−	0.310102i	$-0.899637\pi$
$947$	− 19.0858i	− 0.620204i	0.950703	−	0.310102i	$-0.100363\pi$
$948$	6.70410	0.217739
$949$	0	0
$950$	−6.16315	−0.199959
$951$	16.1400i	0.523377i
$952$	−5.29590	−0.171641
$953$	31.9571	1.03519	0.517595	−	0.855626i	$-0.326827\pi$
$953$	31.9571	1.03519	0.517595	+	0.855626i	$0.326827\pi$
$954$	9.86592i	0.319421i
$955$	− 5.87907i	− 0.190242i
$956$	− 14.1709i	− 0.458320i
$957$	− 5.96077i	− 0.192684i
$958$	−27.5870	−0.891296
$959$	10.3056	0.332785
$960$	− 0.753020i	− 0.0243036i
$961$	17.8157	0.574699
$962$	0	0
$963$	−37.3013	−1.20202
$964$	3.91484i	0.126088i
$965$	−2.31229	−0.0744353
$966$	2.69202	0.0866144
$967$	1.42268i	0.0457503i	0.999738	+	0.0228752i	$0.00728203\pi$
$967$	1.42268i	0.0457503i	−0.999738	+	0.0228752i	$0.992718\pi$
$968$	− 7.75302i	− 0.249192i
$969$	− 5.73423i	− 0.184210i
$970$	4.94331i	0.158720i
$971$	−4.26742	−0.136948	−0.0684740	−	0.997653i	$-0.521813\pi$
$971$	−4.26742	−0.136948	−0.0684740	+	0.997653i	$0.521813\pi$
$972$	−12.9855	−0.416511
$973$	0.987918i	0.0316712i
$974$	29.4698	0.944273
$975$	0	0
$976$	−11.5036	−0.368223
$977$	− 23.5375i	− 0.753031i	−0.926410	−	0.376516i	$-0.877122\pi$
$977$	− 23.5375i	− 0.753031i	0.926410	−	0.376516i	$-0.122878\pi$
$978$	2.91856	0.0933252
$979$	11.9269	0.381186
$980$	1.35690i	0.0433444i
$981$	5.87023i	0.187422i
$982$	8.30691i	0.265084i
$983$	− 51.9734i	− 1.65770i	−0.559474	−	0.828848i	$-0.688997\pi$
$983$	− 51.9734i	− 1.65770i	0.559474	−	0.828848i	$-0.311003\pi$
$984$	0.0217703	0.000694011 0
$985$	34.9672	1.11415
$986$	− 31.5676i	− 1.00532i
$987$	5.86592	0.186714
$988$	0	0
$989$	11.0054	0.349951
$990$	− 6.58211i	− 0.209193i
$991$	−39.9332	−1.26852	−0.634259	−	0.773121i	$-0.718695\pi$
$991$	−39.9332	−1.26852	−0.634259	+	0.773121i	$0.718695\pi$
$992$	3.63102	0.115285
$993$	− 4.06398i	− 0.128967i
$994$	− 7.78986i	− 0.247079i
$995$	− 9.12631i	− 0.289323i
$996$	− 1.58211i	− 0.0501309i
$997$	−41.4827	−1.31377	−0.656886	−	0.753990i	$-0.728127\pi$
$997$	−41.4827	−1.31377	−0.656886	+	0.753990i	$0.728127\pi$
$998$	42.2043	1.33595
$999$	24.4905i	0.774845i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2366.2.d.p.337.5		6
13.5	odd	4		2366.2.a.bd.1.2	yes	3
13.8	odd	4		2366.2.a.y.1.2	✓	3
13.12	even	2	inner	2366.2.d.p.337.2		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2366.2.a.y.1.2	✓	3	13.8	odd	4
2366.2.a.bd.1.2	yes	3	13.5	odd	4
2366.2.d.p.337.2		6	13.12	even	2	inner
2366.2.d.p.337.5		6	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:	\( N \)	\(=\)	\( 2366 = 2 \cdot 7 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2366.d (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q+1.00000i q^{2} +0.554958 q^{3} -1.00000 q^{4} +1.35690i q^{5} +0.554958i q^{6} +1.00000i q^{7} -1.00000i q^{8} -2.69202 q^{9} +O(q^{10})\)	\(q+1.00000i q^{2} +0.554958 q^{3} -1.00000 q^{4} +1.35690i q^{5} +0.554958i q^{6} +1.00000i q^{7} -1.00000i q^{8} -2.69202 q^{9} -1.35690 q^{10} -1.80194i q^{11} -0.554958 q^{12} -1.00000 q^{14} +0.753020i q^{15} +1.00000 q^{16} -5.29590 q^{17} -2.69202i q^{18} +1.95108i q^{19} -1.35690i q^{20} +0.554958i q^{21} +1.80194 q^{22} -4.85086 q^{23} -0.554958i q^{24} +3.15883 q^{25} -3.15883 q^{27} -1.00000i q^{28} +5.96077 q^{29} -0.753020 q^{30} -3.63102i q^{31} +1.00000i q^{32} -1.00000i q^{33} -5.29590i q^{34} -1.35690 q^{35} +2.69202 q^{36} -7.75302i q^{37} -1.95108 q^{38} +1.35690 q^{40} +0.0392287i q^{41} -0.554958 q^{42} -2.26875 q^{43} +1.80194i q^{44} -3.65279i q^{45} -4.85086i q^{46} -10.5700i q^{47} +0.554958 q^{48} -1.00000 q^{49} +3.15883i q^{50} -2.93900 q^{51} -3.66487 q^{53} -3.15883i q^{54} +2.44504 q^{55} +1.00000 q^{56} +1.08277i q^{57} +5.96077i q^{58} -4.07606i q^{59} -0.753020i q^{60} -11.5036 q^{61} +3.63102 q^{62} -2.69202i q^{63} -1.00000 q^{64} +1.00000 q^{66} -2.22521i q^{67} +5.29590 q^{68} -2.69202 q^{69} -1.35690i q^{70} +7.78986i q^{71} +2.69202i q^{72} -14.1032i q^{73} +7.75302 q^{74} +1.75302 q^{75} -1.95108i q^{76} +1.80194 q^{77} -12.0804 q^{79} +1.35690i q^{80} +6.32304 q^{81} -0.0392287 q^{82} +2.85086i q^{83} -0.554958i q^{84} -7.18598i q^{85} -2.26875i q^{86} +3.30798 q^{87} -1.80194 q^{88} +6.61894i q^{89} +3.65279 q^{90} +4.85086 q^{92} -2.01507i q^{93} +10.5700 q^{94} -2.64742 q^{95} +0.554958i q^{96} -3.64310i q^{97} -1.00000i q^{98} +4.85086i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 4 q^{3} - 6 q^{4} - 6 q^{9}+O(q^{10}) \) 6 * q + 4 * q^3 - 6 * q^4 - 6 * q^9	\( 6 q + 4 q^{3} - 6 q^{4} - 6 q^{9} - 4 q^{12} - 6 q^{14} + 6 q^{16} - 4 q^{17} + 2 q^{22} - 2 q^{23} + 2 q^{25} - 2 q^{27} + 10 q^{29} - 14 q^{30} + 6 q^{36} - 30 q^{38} - 4 q^{42} + 2 q^{43} + 4 q^{48} - 6 q^{49} + 2 q^{51} - 24 q^{53} + 14 q^{55} + 6 q^{56} - 6 q^{61} - 8 q^{62} - 6 q^{64} + 6 q^{66} + 4 q^{68} - 6 q^{69} + 56 q^{74} + 20 q^{75} + 2 q^{77} - 4 q^{79} - 2 q^{81} - 26 q^{82} + 30 q^{87} - 2 q^{88} - 14 q^{90} + 2 q^{92} + 14 q^{94} + 14 q^{95}+O(q^{100}) \) 6 * q + 4 * q^3 - 6 * q^4 - 6 * q^9 - 4 * q^12 - 6 * q^14 + 6 * q^16 - 4 * q^17 + 2 * q^22 - 2 * q^23 + 2 * q^25 - 2 * q^27 + 10 * q^29 - 14 * q^30 + 6 * q^36 - 30 * q^38 - 4 * q^42 + 2 * q^43 + 4 * q^48 - 6 * q^49 + 2 * q^51 - 24 * q^53 + 14 * q^55 + 6 * q^56 - 6 * q^61 - 8 * q^62 - 6 * q^64 + 6 * q^66 + 4 * q^68 - 6 * q^69 + 56 * q^74 + 20 * q^75 + 2 * q^77 - 4 * q^79 - 2 * q^81 - 26 * q^82 + 30 * q^87 - 2 * q^88 - 14 * q^90 + 2 * q^92 + 14 * q^94 + 14 * q^95

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