LMFDB - Embedded newform 183.2.c.a.121.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [183,2,Mod(121,183)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(183, 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("183.121");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 183 = 3 \cdot 61 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	183.c (of order $2$, degree $1$, 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:	$1.46126235699$
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:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			121.2
Root			$1.00000i$ of defining polynomial
Character	$\chi$	$=$	183.121
Dual form			183.2.c.a.121.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000i q^{2} -1.00000 q^{3} +1.00000 q^{4} -3.00000 q^{5} -1.00000i q^{6} +3.00000i q^{7} +3.00000i q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000i q^{2} -1.00000 q^{3} +1.00000 q^{4} -3.00000 q^{5} -1.00000i q^{6} +3.00000i q^{7} +3.00000i q^{8} +1.00000 q^{9} -3.00000i q^{10} +5.00000i q^{11} -1.00000 q^{12} -3.00000 q^{13} -3.00000 q^{14} +3.00000 q^{15} -1.00000 q^{16} -4.00000i q^{17} +1.00000i q^{18} +6.00000 q^{19} -3.00000 q^{20} -3.00000i q^{21} -5.00000 q^{22} -5.00000i q^{23} -3.00000i q^{24} +4.00000 q^{25} -3.00000i q^{26} -1.00000 q^{27} +3.00000i q^{28} +4.00000i q^{29} +3.00000i q^{30} +5.00000i q^{32} -5.00000i q^{33} +4.00000 q^{34} -9.00000i q^{35} +1.00000 q^{36} +6.00000i q^{37} +6.00000i q^{38} +3.00000 q^{39} -9.00000i q^{40} +9.00000 q^{41} +3.00000 q^{42} -12.0000i q^{43} +5.00000i q^{44} -3.00000 q^{45} +5.00000 q^{46} +6.00000 q^{47} +1.00000 q^{48} -2.00000 q^{49} +4.00000i q^{50} +4.00000i q^{51} -3.00000 q^{52} +2.00000i q^{53} -1.00000i q^{54} -15.0000i q^{55} -9.00000 q^{56} -6.00000 q^{57} -4.00000 q^{58} -5.00000i q^{59} +3.00000 q^{60} +(5.00000 + 6.00000i) q^{61} +3.00000i q^{63} -7.00000 q^{64} +9.00000 q^{65} +5.00000 q^{66} +9.00000i q^{67} -4.00000i q^{68} +5.00000i q^{69} +9.00000 q^{70} +8.00000i q^{71} +3.00000i q^{72} -11.0000 q^{73} -6.00000 q^{74} -4.00000 q^{75} +6.00000 q^{76} -15.0000 q^{77} +3.00000i q^{78} -3.00000i q^{79} +3.00000 q^{80} +1.00000 q^{81} +9.00000i q^{82} -6.00000 q^{83} -3.00000i q^{84} +12.0000i q^{85} +12.0000 q^{86} -4.00000i q^{87} -15.0000 q^{88} -8.00000i q^{89} -3.00000i q^{90} -9.00000i q^{91} -5.00000i q^{92} +6.00000i q^{94} -18.0000 q^{95} -5.00000i q^{96} -6.00000 q^{97} -2.00000i q^{98} +5.00000i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 2 q^{3} + 2 q^{4} - 6 q^{5} + 2 q^{9}+O(q^{10}) $ 2 * q - 2 * q^3 + 2 * q^4 - 6 * q^5 + 2 * q^9	$ 2 q - 2 q^{3} + 2 q^{4} - 6 q^{5} + 2 q^{9} - 2 q^{12} - 6 q^{13} - 6 q^{14} + 6 q^{15} - 2 q^{16} + 12 q^{19} - 6 q^{20} - 10 q^{22} + 8 q^{25} - 2 q^{27} + 8 q^{34} + 2 q^{36} + 6 q^{39} + 18 q^{41} + 6 q^{42} - 6 q^{45} + 10 q^{46} + 12 q^{47} + 2 q^{48} - 4 q^{49} - 6 q^{52} - 18 q^{56} - 12 q^{57} - 8 q^{58} + 6 q^{60} + 10 q^{61} - 14 q^{64} + 18 q^{65} + 10 q^{66} + 18 q^{70} - 22 q^{73} - 12 q^{74} - 8 q^{75} + 12 q^{76} - 30 q^{77} + 6 q^{80} + 2 q^{81} - 12 q^{83} + 24 q^{86} - 30 q^{88} - 36 q^{95} - 12 q^{97}+O(q^{100}) $ 2 * q - 2 * q^3 + 2 * q^4 - 6 * q^5 + 2 * q^9 - 2 * q^12 - 6 * q^13 - 6 * q^14 + 6 * q^15 - 2 * q^16 + 12 * q^19 - 6 * q^20 - 10 * q^22 + 8 * q^25 - 2 * q^27 + 8 * q^34 + 2 * q^36 + 6 * q^39 + 18 * q^41 + 6 * q^42 - 6 * q^45 + 10 * q^46 + 12 * q^47 + 2 * q^48 - 4 * q^49 - 6 * q^52 - 18 * q^56 - 12 * q^57 - 8 * q^58 + 6 * q^60 + 10 * q^61 - 14 * q^64 + 18 * q^65 + 10 * q^66 + 18 * q^70 - 22 * q^73 - 12 * q^74 - 8 * q^75 + 12 * q^76 - 30 * q^77 + 6 * q^80 + 2 * q^81 - 12 * q^83 + 24 * q^86 - 30 * q^88 - 36 * q^95 - 12 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/183\mathbb{Z}\right)^\times$.

$n$	$62$	$124$
$\chi(n)$	$1$	$-1$

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	0.935414	+	0.353553i	$0.115027\pi$
$2$			1.00000i			0.707107i	−0.935414	+	0.353553i	$0.884973\pi$
$3$	−1.00000			−0.577350
$3$	−1.00000			−0.577350
$4$	1.00000			0.500000
$5$	−3.00000			−1.34164			−0.670820	−	0.741620i	$-0.734058\pi$
$5$	−3.00000			−1.34164			−0.670820	+	0.741620i	$0.734058\pi$
$6$		−	1.00000i		−	0.408248i
$7$			3.00000i			1.13389i	0.823754	+	0.566947i	$0.191875\pi$
$7$			3.00000i			1.13389i	−0.823754	+	0.566947i	$0.808125\pi$
$8$			3.00000i			1.06066i
$9$	1.00000			0.333333
$10$		−	3.00000i		−	0.948683i
$11$			5.00000i			1.50756i	0.657129	+	0.753778i	$0.271771\pi$
$11$			5.00000i			1.50756i	−0.657129	+	0.753778i	$0.728229\pi$
$12$	−1.00000			−0.288675
$13$	−3.00000			−0.832050			−0.416025	−	0.909353i	$-0.636577\pi$
$13$	−3.00000			−0.832050			−0.416025	+	0.909353i	$0.636577\pi$
$14$	−3.00000			−0.801784
$15$	3.00000			0.774597
$16$	−1.00000			−0.250000
$17$		−	4.00000i		−	0.970143i	−0.874475	−	0.485071i	$-0.838794\pi$
$17$		−	4.00000i		−	0.970143i	0.874475	−	0.485071i	$-0.161206\pi$
$18$			1.00000i			0.235702i
$19$	6.00000			1.37649			0.688247	−	0.725476i	$-0.258380\pi$
$19$	6.00000			1.37649			0.688247	+	0.725476i	$0.258380\pi$
$20$	−3.00000			−0.670820
$21$		−	3.00000i		−	0.654654i
$22$	−5.00000			−1.06600
$23$		−	5.00000i		−	1.04257i	−0.853382	−	0.521286i	$-0.825452\pi$
$23$		−	5.00000i		−	1.04257i	0.853382	−	0.521286i	$-0.174548\pi$
$24$		−	3.00000i		−	0.612372i
$25$	4.00000			0.800000
$26$		−	3.00000i		−	0.588348i
$27$	−1.00000			−0.192450
$28$			3.00000i			0.566947i
$29$			4.00000i			0.742781i	0.928477	+	0.371391i	$0.121119\pi$
$29$			4.00000i			0.742781i	−0.928477	+	0.371391i	$0.878881\pi$
$30$			3.00000i			0.547723i
$31$		0			0		1.00000			$0$
$31$		0			0		−1.00000			$\pi$
$32$			5.00000i			0.883883i
$33$		−	5.00000i		−	0.870388i
$34$	4.00000			0.685994
$35$		−	9.00000i		−	1.52128i
$36$	1.00000			0.166667
$37$			6.00000i			0.986394i	0.869918	+	0.493197i	$0.164172\pi$
$37$			6.00000i			0.986394i	−0.869918	+	0.493197i	$0.835828\pi$
$38$			6.00000i			0.973329i
$39$	3.00000			0.480384
$40$		−	9.00000i		−	1.42302i
$41$	9.00000			1.40556			0.702782	−	0.711405i	$-0.251941\pi$
$41$	9.00000			1.40556			0.702782	+	0.711405i	$0.251941\pi$
$42$	3.00000			0.462910
$43$		−	12.0000i		−	1.82998i	−0.403473	−	0.914991i	$-0.632197\pi$
$43$		−	12.0000i		−	1.82998i	0.403473	−	0.914991i	$-0.367803\pi$
$44$			5.00000i			0.753778i
$45$	−3.00000			−0.447214
$46$	5.00000			0.737210
$47$	6.00000			0.875190			0.437595	−	0.899172i	$-0.355830\pi$
$47$	6.00000			0.875190			0.437595	+	0.899172i	$0.355830\pi$
$48$	1.00000			0.144338
$49$	−2.00000			−0.285714
$50$			4.00000i			0.565685i
$51$			4.00000i			0.560112i
$52$	−3.00000			−0.416025
$53$			2.00000i			0.274721i	0.990521	+	0.137361i	$0.0438619\pi$
$53$			2.00000i			0.274721i	−0.990521	+	0.137361i	$0.956138\pi$
$54$		−	1.00000i		−	0.136083i
$55$		−	15.0000i		−	2.02260i
$56$	−9.00000			−1.20268
$57$	−6.00000			−0.794719
$58$	−4.00000			−0.525226
$59$		−	5.00000i		−	0.650945i	−0.945552	−	0.325472i	$-0.894477\pi$
$59$		−	5.00000i		−	0.650945i	0.945552	−	0.325472i	$-0.105523\pi$
$60$	3.00000			0.387298
$61$	5.00000	+	6.00000i	0.640184	+	0.768221i
$61$	5.00000	+	6.00000i	0.640184	+	0.768221i
$62$		0			0
$63$			3.00000i			0.377964i
$64$	−7.00000			−0.875000
$65$	9.00000			1.11631
$66$	5.00000			0.615457
$67$			9.00000i			1.09952i	0.835321	+	0.549762i	$0.185282\pi$
$67$			9.00000i			1.09952i	−0.835321	+	0.549762i	$0.814718\pi$
$68$		−	4.00000i		−	0.485071i
$69$			5.00000i			0.601929i
$70$	9.00000			1.07571
$71$			8.00000i			0.949425i	0.880141	+	0.474713i	$0.157448\pi$
$71$			8.00000i			0.949425i	−0.880141	+	0.474713i	$0.842552\pi$
$72$			3.00000i			0.353553i
$73$	−11.0000			−1.28745			−0.643726	−	0.765256i	$-0.722612\pi$
$73$	−11.0000			−1.28745			−0.643726	+	0.765256i	$0.722612\pi$
$74$	−6.00000			−0.697486
$75$	−4.00000			−0.461880
$76$	6.00000			0.688247
$77$	−15.0000			−1.70941
$78$			3.00000i			0.339683i
$79$		−	3.00000i		−	0.337526i	−0.985657	−	0.168763i	$-0.946023\pi$
$79$		−	3.00000i		−	0.337526i	0.985657	−	0.168763i	$-0.0539773\pi$
$80$	3.00000			0.335410
$81$	1.00000			0.111111
$82$			9.00000i			0.993884i
$83$	−6.00000			−0.658586			−0.329293	−	0.944228i	$-0.606810\pi$
$83$	−6.00000			−0.658586			−0.329293	+	0.944228i	$0.606810\pi$
$84$		−	3.00000i		−	0.327327i
$85$			12.0000i			1.30158i
$86$	12.0000			1.29399
$87$		−	4.00000i		−	0.428845i
$88$	−15.0000			−1.59901
$89$		−	8.00000i		−	0.847998i	−0.905663	−	0.423999i	$-0.860626\pi$
$89$		−	8.00000i		−	0.847998i	0.905663	−	0.423999i	$-0.139374\pi$
$90$		−	3.00000i		−	0.316228i
$91$		−	9.00000i		−	0.943456i
$92$		−	5.00000i		−	0.521286i
$93$		0			0
$94$			6.00000i			0.618853i
$95$	−18.0000			−1.84676
$96$		−	5.00000i		−	0.510310i
$97$	−6.00000			−0.609208			−0.304604	−	0.952479i	$-0.598524\pi$
$97$	−6.00000			−0.609208			−0.304604	+	0.952479i	$0.598524\pi$
$98$		−	2.00000i		−	0.202031i
$99$			5.00000i			0.502519i
$100$	4.00000			0.400000
$101$		−	2.00000i		−	0.199007i	−0.995037	−	0.0995037i	$-0.968274\pi$
$101$		−	2.00000i		−	0.199007i	0.995037	−	0.0995037i	$-0.0317255\pi$
$102$	−4.00000			−0.396059
$103$		0			0			−	1.00000i	$-0.5\pi$
$103$		0			0				1.00000i	$0.5\pi$
$104$		−	9.00000i		−	0.882523i
$105$			9.00000i			0.878310i
$106$	−2.00000			−0.194257
$107$	12.0000			1.16008			0.580042	−	0.814587i	$-0.303036\pi$
$107$	12.0000			1.16008			0.580042	+	0.814587i	$0.303036\pi$
$108$	−1.00000			−0.0962250
$109$	−11.0000			−1.05361			−0.526804	−	0.849987i	$-0.676610\pi$
$109$	−11.0000			−1.05361			−0.526804	+	0.849987i	$0.676610\pi$
$110$	15.0000			1.43019
$111$		−	6.00000i		−	0.569495i
$112$		−	3.00000i		−	0.283473i
$113$	21.0000			1.97551			0.987757	−	0.156001i	$-0.0498603\pi$
$113$	21.0000			1.97551			0.987757	+	0.156001i	$0.0498603\pi$
$114$		−	6.00000i		−	0.561951i
$115$			15.0000i			1.39876i
$116$			4.00000i			0.371391i
$117$	−3.00000			−0.277350
$118$	5.00000			0.460287
$119$	12.0000			1.10004
$120$			9.00000i			0.821584i
$121$	−14.0000			−1.27273
$122$	−6.00000	+	5.00000i	−0.543214	+	0.452679i
$123$	−9.00000			−0.811503
$124$		0			0
$125$	3.00000			0.268328
$126$	−3.00000			−0.267261
$127$	18.0000			1.59724			0.798621	−	0.601834i	$-0.205563\pi$
$127$	18.0000			1.59724			0.798621	+	0.601834i	$0.205563\pi$
$128$			3.00000i			0.265165i
$129$			12.0000i			1.05654i
$130$			9.00000i			0.789352i
$131$		0			0			−	1.00000i	$-0.5\pi$
$131$		0			0				1.00000i	$0.5\pi$
$132$		−	5.00000i		−	0.435194i
$133$			18.0000i			1.56080i
$134$	−9.00000			−0.777482
$135$	3.00000			0.258199
$136$	12.0000			1.02899
$137$	−9.00000			−0.768922			−0.384461	−	0.923141i	$-0.625613\pi$
$137$	−9.00000			−0.768922			−0.384461	+	0.923141i	$0.625613\pi$
$138$	−5.00000			−0.425628
$139$			9.00000i			0.763370i	0.924292	+	0.381685i	$0.124656\pi$
$139$			9.00000i			0.763370i	−0.924292	+	0.381685i	$0.875344\pi$
$140$		−	9.00000i		−	0.760639i
$141$	−6.00000			−0.505291
$142$	−8.00000			−0.671345
$143$		−	15.0000i		−	1.25436i
$144$	−1.00000			−0.0833333
$145$		−	12.0000i		−	0.996546i
$146$		−	11.0000i		−	0.910366i
$147$	2.00000			0.164957
$148$			6.00000i			0.493197i
$149$	−9.00000			−0.737309			−0.368654	−	0.929567i	$-0.620181\pi$
$149$	−9.00000			−0.737309			−0.368654	+	0.929567i	$0.620181\pi$
$150$		−	4.00000i		−	0.326599i
$151$		−	21.0000i		−	1.70896i	−0.519488	−	0.854478i	$-0.673877\pi$
$151$		−	21.0000i		−	1.70896i	0.519488	−	0.854478i	$-0.326123\pi$
$152$			18.0000i			1.45999i
$153$		−	4.00000i		−	0.323381i
$154$		−	15.0000i		−	1.20873i
$155$		0			0
$156$	3.00000			0.240192
$157$			24.0000i			1.91541i	0.287754	+	0.957704i	$0.407091\pi$
$157$			24.0000i			1.91541i	−0.287754	+	0.957704i	$0.592909\pi$
$158$	3.00000			0.238667
$159$		−	2.00000i		−	0.158610i
$160$		−	15.0000i		−	1.18585i
$161$	15.0000			1.18217
$162$			1.00000i			0.0785674i
$163$	24.0000			1.87983			0.939913	−	0.341415i	$-0.110906\pi$
$163$	24.0000			1.87983			0.939913	+	0.341415i	$0.110906\pi$
$164$	9.00000			0.702782
$165$			15.0000i			1.16775i
$166$		−	6.00000i		−	0.465690i
$167$	−12.0000			−0.928588			−0.464294	−	0.885681i	$-0.653692\pi$
$167$	−12.0000			−0.928588			−0.464294	+	0.885681i	$0.653692\pi$
$168$	9.00000			0.694365
$169$	−4.00000			−0.307692
$170$	−12.0000			−0.920358
$171$	6.00000			0.458831
$172$		−	12.0000i		−	0.914991i
$173$		−	16.0000i		−	1.21646i	−0.793762	−	0.608229i	$-0.791880\pi$
$173$		−	16.0000i		−	1.21646i	0.793762	−	0.608229i	$-0.208120\pi$
$174$	4.00000			0.303239
$175$			12.0000i			0.907115i
$176$		−	5.00000i		−	0.376889i
$177$			5.00000i			0.375823i
$178$	8.00000			0.599625
$179$	6.00000			0.448461			0.224231	−	0.974536i	$-0.428013\pi$
$179$	6.00000			0.448461			0.224231	+	0.974536i	$0.428013\pi$
$180$	−3.00000			−0.223607
$181$		−	6.00000i		−	0.445976i	−0.974821	−	0.222988i	$-0.928419\pi$
$181$		−	6.00000i		−	0.445976i	0.974821	−	0.222988i	$-0.0715812\pi$
$182$	9.00000			0.667124
$183$	−5.00000	−	6.00000i	−0.369611	−	0.443533i
$184$	15.0000			1.10581
$185$		−	18.0000i		−	1.32339i
$186$		0			0
$187$	20.0000			1.46254
$188$	6.00000			0.437595
$189$		−	3.00000i		−	0.218218i
$190$		−	18.0000i		−	1.30586i
$191$		−	19.0000i		−	1.37479i	−0.726283	−	0.687396i	$-0.758754\pi$
$191$		−	19.0000i		−	1.37479i	0.726283	−	0.687396i	$-0.241246\pi$
$192$	7.00000			0.505181
$193$		−	6.00000i		−	0.431889i	−0.976406	−	0.215945i	$-0.930717\pi$
$193$		−	6.00000i		−	0.431889i	0.976406	−	0.215945i	$-0.0692831\pi$
$194$		−	6.00000i		−	0.430775i
$195$	−9.00000			−0.644503
$196$	−2.00000			−0.142857
$197$	−3.00000			−0.213741			−0.106871	−	0.994273i	$-0.534083\pi$
$197$	−3.00000			−0.213741			−0.106871	+	0.994273i	$0.534083\pi$
$198$	−5.00000			−0.355335
$199$	−16.0000			−1.13421			−0.567105	−	0.823646i	$-0.691937\pi$
$199$	−16.0000			−1.13421			−0.567105	+	0.823646i	$0.691937\pi$
$200$			12.0000i			0.848528i
$201$		−	9.00000i		−	0.634811i
$202$	2.00000			0.140720
$203$	−12.0000			−0.842235
$204$			4.00000i			0.280056i
$205$	−27.0000			−1.88576
$206$		0			0
$207$		−	5.00000i		−	0.347524i
$208$	3.00000			0.208013
$209$			30.0000i			2.07514i
$210$	−9.00000			−0.621059
$211$		−	12.0000i		−	0.826114i	−0.910705	−	0.413057i	$-0.864461\pi$
$211$		−	12.0000i		−	0.826114i	0.910705	−	0.413057i	$-0.135539\pi$
$212$			2.00000i			0.137361i
$213$		−	8.00000i		−	0.548151i
$214$			12.0000i			0.820303i
$215$			36.0000i			2.45518i
$216$		−	3.00000i		−	0.204124i
$217$		0			0
$218$		−	11.0000i		−	0.745014i
$219$	11.0000			0.743311
$220$		−	15.0000i		−	1.01130i
$221$			12.0000i			0.807207i
$222$	6.00000			0.402694
$223$			9.00000i			0.602685i	0.953516	+	0.301342i	$0.0974347\pi$
$223$			9.00000i			0.602685i	−0.953516	+	0.301342i	$0.902565\pi$
$224$	−15.0000			−1.00223
$225$	4.00000			0.266667
$226$			21.0000i			1.39690i
$227$			13.0000i			0.862840i	0.902151	+	0.431420i	$0.141987\pi$
$227$			13.0000i			0.862840i	−0.902151	+	0.431420i	$0.858013\pi$
$228$	−6.00000			−0.397360
$229$	−9.00000			−0.594737			−0.297368	−	0.954763i	$-0.596109\pi$
$229$	−9.00000			−0.594737			−0.297368	+	0.954763i	$0.596109\pi$
$230$	−15.0000			−0.989071
$231$	15.0000			0.986928
$232$	−12.0000			−0.787839
$233$			4.00000i			0.262049i	0.991379	+	0.131024i	$0.0418266\pi$
$233$			4.00000i			0.262049i	−0.991379	+	0.131024i	$0.958173\pi$
$234$		−	3.00000i		−	0.196116i
$235$	−18.0000			−1.17419
$236$		−	5.00000i		−	0.325472i
$237$			3.00000i			0.194871i
$238$			12.0000i			0.777844i
$239$	12.0000			0.776215			0.388108	−	0.921614i	$-0.373129\pi$
$239$	12.0000			0.776215			0.388108	+	0.921614i	$0.373129\pi$
$240$	−3.00000			−0.193649
$241$	9.00000			0.579741			0.289870	−	0.957066i	$-0.406388\pi$
$241$	9.00000			0.579741			0.289870	+	0.957066i	$0.406388\pi$
$242$		−	14.0000i		−	0.899954i
$243$	−1.00000			−0.0641500
$244$	5.00000	+	6.00000i	0.320092	+	0.384111i
$245$	6.00000			0.383326
$246$		−	9.00000i		−	0.573819i
$247$	−18.0000			−1.14531
$248$		0			0
$249$	6.00000			0.380235
$250$			3.00000i			0.189737i
$251$			4.00000i			0.252478i	0.992000	+	0.126239i	$0.0402906\pi$
$251$			4.00000i			0.252478i	−0.992000	+	0.126239i	$0.959709\pi$
$252$			3.00000i			0.188982i
$253$	25.0000			1.57174
$254$			18.0000i			1.12942i
$255$		−	12.0000i		−	0.751469i
$256$	−17.0000			−1.06250
$257$	6.00000			0.374270			0.187135	−	0.982334i	$-0.440080\pi$
$257$	6.00000			0.374270			0.187135	+	0.982334i	$0.440080\pi$
$258$	−12.0000			−0.747087
$259$	−18.0000			−1.11847
$260$	9.00000			0.558156
$261$			4.00000i			0.247594i
$262$		0			0
$263$	6.00000			0.369976			0.184988	−	0.982741i	$-0.440775\pi$
$263$	6.00000			0.369976			0.184988	+	0.982741i	$0.440775\pi$
$264$	15.0000			0.923186
$265$		−	6.00000i		−	0.368577i
$266$	−18.0000			−1.10365
$267$			8.00000i			0.489592i
$268$			9.00000i			0.549762i
$269$	−6.00000			−0.365826			−0.182913	−	0.983129i	$-0.558553\pi$
$269$	−6.00000			−0.365826			−0.182913	+	0.983129i	$0.558553\pi$
$270$			3.00000i			0.182574i
$271$	16.0000			0.971931			0.485965	−	0.873978i	$-0.338468\pi$
$271$	16.0000			0.971931			0.485965	+	0.873978i	$0.338468\pi$
$272$			4.00000i			0.242536i
$273$			9.00000i			0.544705i
$274$		−	9.00000i		−	0.543710i
$275$			20.0000i			1.20605i
$276$			5.00000i			0.300965i
$277$		−	18.0000i		−	1.08152i	−0.841178	−	0.540758i	$-0.818138\pi$
$277$		−	18.0000i		−	1.08152i	0.841178	−	0.540758i	$-0.181862\pi$
$278$	−9.00000			−0.539784
$279$		0			0
$280$	27.0000			1.61356
$281$		−	28.0000i		−	1.67034i	−0.549992	−	0.835170i	$-0.685369\pi$
$281$		−	28.0000i		−	1.67034i	0.549992	−	0.835170i	$-0.314631\pi$
$282$		−	6.00000i		−	0.357295i
$283$	−22.0000			−1.30776			−0.653882	−	0.756596i	$-0.726861\pi$
$283$	−22.0000			−1.30776			−0.653882	+	0.756596i	$0.726861\pi$
$284$			8.00000i			0.474713i
$285$	18.0000			1.06623
$286$	15.0000			0.886969
$287$			27.0000i			1.59376i
$288$			5.00000i			0.294628i
$289$	1.00000			0.0588235
$290$	12.0000			0.704664
$291$	6.00000			0.351726
$292$	−11.0000			−0.643726
$293$	−6.00000			−0.350524			−0.175262	−	0.984522i	$-0.556077\pi$
$293$	−6.00000			−0.350524			−0.175262	+	0.984522i	$0.556077\pi$
$294$			2.00000i			0.116642i
$295$			15.0000i			0.873334i
$296$	−18.0000			−1.04623
$297$		−	5.00000i		−	0.290129i
$298$		−	9.00000i		−	0.521356i
$299$			15.0000i			0.867472i
$300$	−4.00000			−0.230940
$301$	36.0000			2.07501
$302$	21.0000			1.20841
$303$			2.00000i			0.114897i
$304$	−6.00000			−0.344124
$305$	−15.0000	−	18.0000i	−0.858898	−	1.03068i
$306$	4.00000			0.228665
$307$		−	33.0000i		−	1.88341i	−0.336440	−	0.941705i	$-0.609223\pi$
$307$		−	33.0000i		−	1.88341i	0.336440	−	0.941705i	$-0.390777\pi$
$308$	−15.0000			−0.854704
$309$		0			0
$310$		0			0
$311$			19.0000i			1.07739i	0.842500	+	0.538696i	$0.181083\pi$
$311$			19.0000i			1.07739i	−0.842500	+	0.538696i	$0.818917\pi$
$312$			9.00000i			0.509525i
$313$		−	6.00000i		−	0.339140i	−0.985518	−	0.169570i	$-0.945762\pi$
$313$		−	6.00000i		−	0.339140i	0.985518	−	0.169570i	$-0.0542379\pi$
$314$	−24.0000			−1.35440
$315$		−	9.00000i		−	0.507093i
$316$		−	3.00000i		−	0.168763i
$317$	−18.0000			−1.01098			−0.505490	−	0.862832i	$-0.668688\pi$
$317$	−18.0000			−1.01098			−0.505490	+	0.862832i	$0.668688\pi$
$318$	2.00000			0.112154
$319$	−20.0000			−1.11979
$320$	21.0000			1.17394
$321$	−12.0000			−0.669775
$322$			15.0000i			0.835917i
$323$		−	24.0000i		−	1.33540i
$324$	1.00000			0.0555556
$325$	−12.0000			−0.665640
$326$			24.0000i			1.32924i
$327$	11.0000			0.608301
$328$			27.0000i			1.49083i
$329$			18.0000i			0.992372i
$330$	−15.0000			−0.825723
$331$		−	15.0000i		−	0.824475i	−0.911077	−	0.412237i	$-0.864747\pi$
$331$		−	15.0000i		−	0.824475i	0.911077	−	0.412237i	$-0.135253\pi$
$332$	−6.00000			−0.329293
$333$			6.00000i			0.328798i
$334$		−	12.0000i		−	0.656611i
$335$		−	27.0000i		−	1.47517i
$336$			3.00000i			0.163663i
$337$		−	6.00000i		−	0.326841i	−0.986557	−	0.163420i	$-0.947747\pi$
$337$		−	6.00000i		−	0.326841i	0.986557	−	0.163420i	$-0.0522527\pi$
$338$		−	4.00000i		−	0.217571i
$339$	−21.0000			−1.14056
$340$			12.0000i			0.650791i
$341$		0			0
$342$			6.00000i			0.324443i
$343$			15.0000i			0.809924i
$344$	36.0000			1.94099
$345$		−	15.0000i		−	0.807573i
$346$	16.0000			0.860165
$347$	−18.0000			−0.966291			−0.483145	−	0.875540i	$-0.660506\pi$
$347$	−18.0000			−0.966291			−0.483145	+	0.875540i	$0.660506\pi$
$348$		−	4.00000i		−	0.214423i
$349$		−	12.0000i		−	0.642345i	−0.947021	−	0.321173i	$-0.895923\pi$
$349$		−	12.0000i		−	0.642345i	0.947021	−	0.321173i	$-0.104077\pi$
$350$	−12.0000			−0.641427
$351$	3.00000			0.160128
$352$	−25.0000			−1.33250
$353$	−9.00000			−0.479022			−0.239511	−	0.970894i	$-0.576987\pi$
$353$	−9.00000			−0.479022			−0.239511	+	0.970894i	$0.576987\pi$
$354$	−5.00000			−0.265747
$355$		−	24.0000i		−	1.27379i
$356$		−	8.00000i		−	0.423999i
$357$	−12.0000			−0.635107
$358$			6.00000i			0.317110i
$359$		−	8.00000i		−	0.422224i	−0.977462	−	0.211112i	$-0.932292\pi$
$359$		−	8.00000i		−	0.422224i	0.977462	−	0.211112i	$-0.0677085\pi$
$360$		−	9.00000i		−	0.474342i
$361$	17.0000			0.894737
$362$	6.00000			0.315353
$363$	14.0000			0.734809
$364$		−	9.00000i		−	0.471728i
$365$	33.0000			1.72730
$366$	6.00000	−	5.00000i	0.313625	−	0.261354i
$367$	6.00000			0.313197			0.156599	−	0.987662i	$-0.449947\pi$
$367$	6.00000			0.313197			0.156599	+	0.987662i	$0.449947\pi$
$368$			5.00000i			0.260643i
$369$	9.00000			0.468521
$370$	18.0000			0.935775
$371$	−6.00000			−0.311504
$372$		0			0
$373$			24.0000i			1.24267i	0.783544	+	0.621336i	$0.213410\pi$
$373$			24.0000i			1.24267i	−0.783544	+	0.621336i	$0.786590\pi$
$374$			20.0000i			1.03418i
$375$	−3.00000			−0.154919
$376$			18.0000i			0.928279i
$377$		−	12.0000i		−	0.618031i
$378$	3.00000			0.154303
$379$	20.0000			1.02733			0.513665	−	0.857991i	$-0.328287\pi$
$379$	20.0000			1.02733			0.513665	+	0.857991i	$0.328287\pi$
$380$	−18.0000			−0.923381
$381$	−18.0000			−0.922168
$382$	19.0000			0.972125
$383$		−	13.0000i		−	0.664269i	−0.943232	−	0.332134i	$-0.892231\pi$
$383$		−	13.0000i		−	0.664269i	0.943232	−	0.332134i	$-0.107769\pi$
$384$		−	3.00000i		−	0.153093i
$385$	45.0000			2.29341
$386$	6.00000			0.305392
$387$		−	12.0000i		−	0.609994i
$388$	−6.00000			−0.304604
$389$		−	4.00000i		−	0.202808i	−0.994845	−	0.101404i	$-0.967667\pi$
$389$		−	4.00000i		−	0.202808i	0.994845	−	0.101404i	$-0.0323335\pi$
$390$		−	9.00000i		−	0.455733i
$391$	−20.0000			−1.01144
$392$		−	6.00000i		−	0.303046i
$393$		0			0
$394$		−	3.00000i		−	0.151138i
$395$			9.00000i			0.452839i
$396$			5.00000i			0.251259i
$397$		−	36.0000i		−	1.80679i	−0.428811	−	0.903394i	$-0.641067\pi$
$397$		−	36.0000i		−	1.80679i	0.428811	−	0.903394i	$-0.358933\pi$
$398$		−	16.0000i		−	0.802008i
$399$		−	18.0000i		−	0.901127i
$400$	−4.00000			−0.200000
$401$			22.0000i			1.09863i	0.835616	+	0.549314i	$0.185111\pi$
$401$			22.0000i			1.09863i	−0.835616	+	0.549314i	$0.814889\pi$
$402$	9.00000			0.448879
$403$		0			0
$404$		−	2.00000i		−	0.0995037i
$405$	−3.00000			−0.149071
$406$		−	12.0000i		−	0.595550i
$407$	−30.0000			−1.48704
$408$	−12.0000			−0.594089
$409$		−	6.00000i		−	0.296681i	−0.988936	−	0.148340i	$-0.952607\pi$
$409$		−	6.00000i		−	0.296681i	0.988936	−	0.148340i	$-0.0473931\pi$
$410$		−	27.0000i		−	1.33343i
$411$	9.00000			0.443937
$412$		0			0
$413$	15.0000			0.738102
$414$	5.00000			0.245737
$415$	18.0000			0.883585
$416$		−	15.0000i		−	0.735436i
$417$		−	9.00000i		−	0.440732i
$418$	−30.0000			−1.46735
$419$			20.0000i			0.977064i	0.872546	+	0.488532i	$0.162467\pi$
$419$			20.0000i			0.977064i	−0.872546	+	0.488532i	$0.837533\pi$
$420$			9.00000i			0.439155i
$421$		0			0		1.00000			$0$
$421$		0			0		−1.00000			$\pi$
$422$	12.0000			0.584151
$423$	6.00000			0.291730
$424$	−6.00000			−0.291386
$425$		−	16.0000i		−	0.776114i
$426$	8.00000			0.387601
$427$	−18.0000	+	15.0000i	−0.871081	+	0.725901i
$428$	12.0000			0.580042
$429$			15.0000i			0.724207i
$430$	−36.0000			−1.73607
$431$	24.0000			1.15604			0.578020	−	0.816023i	$-0.303826\pi$
$431$	24.0000			1.15604			0.578020	+	0.816023i	$0.303826\pi$
$432$	1.00000			0.0481125
$433$		−	6.00000i		−	0.288342i	−0.989553	−	0.144171i	$-0.953949\pi$
$433$		−	6.00000i		−	0.288342i	0.989553	−	0.144171i	$-0.0460515\pi$
$434$		0			0
$435$			12.0000i			0.575356i
$436$	−11.0000			−0.526804
$437$		−	30.0000i		−	1.43509i
$438$			11.0000i			0.525600i
$439$	26.0000			1.24091			0.620456	−	0.784241i	$-0.286947\pi$
$439$	26.0000			1.24091			0.620456	+	0.784241i	$0.286947\pi$
$440$	45.0000			2.14529
$441$	−2.00000			−0.0952381
$442$	−12.0000			−0.570782
$443$	12.0000			0.570137			0.285069	−	0.958507i	$-0.407984\pi$
$443$	12.0000			0.570137			0.285069	+	0.958507i	$0.407984\pi$
$444$		−	6.00000i		−	0.284747i
$445$			24.0000i			1.13771i
$446$	−9.00000			−0.426162
$447$	9.00000			0.425685
$448$		−	21.0000i		−	0.992157i
$449$	−9.00000			−0.424736			−0.212368	−	0.977190i	$-0.568118\pi$
$449$	−9.00000			−0.424736			−0.212368	+	0.977190i	$0.568118\pi$
$450$			4.00000i			0.188562i
$451$			45.0000i			2.11897i
$452$	21.0000			0.987757
$453$			21.0000i			0.986666i
$454$	−13.0000			−0.610120
$455$			27.0000i			1.26578i
$456$		−	18.0000i		−	0.842927i
$457$			30.0000i			1.40334i	0.712502	+	0.701670i	$0.247562\pi$
$457$			30.0000i			1.40334i	−0.712502	+	0.701670i	$0.752438\pi$
$458$		−	9.00000i		−	0.420542i
$459$			4.00000i			0.186704i
$460$			15.0000i			0.699379i
$461$	−42.0000			−1.95614			−0.978068	−	0.208288i	$-0.933211\pi$
$461$	−42.0000			−1.95614			−0.978068	+	0.208288i	$0.933211\pi$
$462$			15.0000i			0.697863i
$463$	36.0000			1.67306			0.836531	−	0.547920i	$-0.184580\pi$
$463$	36.0000			1.67306			0.836531	+	0.547920i	$0.184580\pi$
$464$		−	4.00000i		−	0.185695i
$465$		0			0
$466$	−4.00000			−0.185296
$467$		−	13.0000i		−	0.601568i	−0.953692	−	0.300784i	$-0.902752\pi$
$467$		−	13.0000i		−	0.601568i	0.953692	−	0.300784i	$-0.0972484\pi$
$468$	−3.00000			−0.138675
$469$	−27.0000			−1.24674
$470$		−	18.0000i		−	0.830278i
$471$		−	24.0000i		−	1.10586i
$472$	15.0000			0.690431
$473$	60.0000			2.75880
$474$	−3.00000			−0.137795
$475$	24.0000			1.10120
$476$	12.0000			0.550019
$477$			2.00000i			0.0915737i
$478$			12.0000i			0.548867i
$479$	−30.0000			−1.37073			−0.685367	−	0.728197i	$-0.740358\pi$
$479$	−30.0000			−1.37073			−0.685367	+	0.728197i	$0.740358\pi$
$480$			15.0000i			0.684653i
$481$		−	18.0000i		−	0.820729i
$482$			9.00000i			0.409939i
$483$	−15.0000			−0.682524
$484$	−14.0000			−0.636364
$485$	18.0000			0.817338
$486$		−	1.00000i		−	0.0453609i
$487$	−2.00000			−0.0906287			−0.0453143	−	0.998973i	$-0.514429\pi$
$487$	−2.00000			−0.0906287			−0.0453143	+	0.998973i	$0.514429\pi$
$488$	−18.0000	+	15.0000i	−0.814822	+	0.679018i
$489$	−24.0000			−1.08532
$490$			6.00000i			0.271052i
$491$	−18.0000			−0.812329			−0.406164	−	0.913800i	$-0.633134\pi$
$491$	−18.0000			−0.812329			−0.406164	+	0.913800i	$0.633134\pi$
$492$	−9.00000			−0.405751
$493$	16.0000			0.720604
$494$		−	18.0000i		−	0.809858i
$495$		−	15.0000i		−	0.674200i
$496$		0			0
$497$	−24.0000			−1.07655
$498$			6.00000i			0.268866i
$499$		−	3.00000i		−	0.134298i	−0.997743	−	0.0671492i	$-0.978610\pi$
$499$		−	3.00000i		−	0.134298i	0.997743	−	0.0671492i	$-0.0213904\pi$
$500$	3.00000			0.134164
$501$	12.0000			0.536120
$502$	−4.00000			−0.178529
$503$	−6.00000			−0.267527			−0.133763	−	0.991013i	$-0.542706\pi$
$503$	−6.00000			−0.267527			−0.133763	+	0.991013i	$0.542706\pi$
$504$	−9.00000			−0.400892
$505$			6.00000i			0.266996i
$506$			25.0000i			1.11139i
$507$	4.00000			0.177646
$508$	18.0000			0.798621
$509$		−	16.0000i		−	0.709188i	−0.935020	−	0.354594i	$-0.884619\pi$
$509$		−	16.0000i		−	0.709188i	0.935020	−	0.354594i	$-0.115381\pi$
$510$	12.0000			0.531369
$511$		−	33.0000i		−	1.45983i
$512$		−	11.0000i		−	0.486136i
$513$	−6.00000			−0.264906
$514$			6.00000i			0.264649i
$515$		0			0
$516$			12.0000i			0.528271i
$517$			30.0000i			1.31940i
$518$		−	18.0000i		−	0.790875i
$519$			16.0000i			0.702322i
$520$			27.0000i			1.18403i
$521$		−	4.00000i		−	0.175243i	−0.996154	−	0.0876216i	$-0.972073\pi$
$521$		−	4.00000i		−	0.175243i	0.996154	−	0.0876216i	$-0.0279266\pi$
$522$	−4.00000			−0.175075
$523$		−	33.0000i		−	1.44299i	−0.692420	−	0.721495i	$-0.743455\pi$
$523$		−	33.0000i		−	1.44299i	0.692420	−	0.721495i	$-0.256545\pi$
$524$		0			0
$525$		−	12.0000i		−	0.523723i
$526$			6.00000i			0.261612i
$527$		0			0
$528$			5.00000i			0.217597i
$529$	−2.00000			−0.0869565
$530$	6.00000			0.260623
$531$		−	5.00000i		−	0.216982i
$532$			18.0000i			0.780399i
$533$	−27.0000			−1.16950
$534$	−8.00000			−0.346194
$535$	−36.0000			−1.55642
$536$	−27.0000			−1.16622
$537$	−6.00000			−0.258919
$538$		−	6.00000i		−	0.258678i
$539$		−	10.0000i		−	0.430730i
$540$	3.00000			0.129099
$541$		−	24.0000i		−	1.03184i	−0.856637	−	0.515920i	$-0.827450\pi$
$541$		−	24.0000i		−	1.03184i	0.856637	−	0.515920i	$-0.172550\pi$
$542$			16.0000i			0.687259i
$543$			6.00000i			0.257485i
$544$	20.0000			0.857493
$545$	33.0000			1.41356
$546$	−9.00000			−0.385164
$547$		−	21.0000i		−	0.897895i	−0.893558	−	0.448948i	$-0.851799\pi$
$547$		−	21.0000i		−	0.897895i	0.893558	−	0.448948i	$-0.148201\pi$
$548$	−9.00000			−0.384461
$549$	5.00000	+	6.00000i	0.213395	+	0.256074i
$550$	−20.0000			−0.852803
$551$			24.0000i			1.02243i
$552$	−15.0000			−0.638442
$553$	9.00000			0.382719
$554$	18.0000			0.764747
$555$			18.0000i			0.764057i
$556$			9.00000i			0.381685i
$557$			40.0000i			1.69485i	0.530912	+	0.847427i	$0.321850\pi$
$557$			40.0000i			1.69485i	−0.530912	+	0.847427i	$0.678150\pi$
$558$		0			0
$559$			36.0000i			1.52264i
$560$			9.00000i			0.380319i
$561$	−20.0000			−0.844401
$562$	28.0000			1.18111
$563$	18.0000			0.758610			0.379305	−	0.925272i	$-0.376163\pi$
$563$	18.0000			0.758610			0.379305	+	0.925272i	$0.376163\pi$
$564$	−6.00000			−0.252646
$565$	−63.0000			−2.65043
$566$		−	22.0000i		−	0.924729i
$567$			3.00000i			0.125988i
$568$	−24.0000			−1.00702
$569$	3.00000			0.125767			0.0628833	−	0.998021i	$-0.479970\pi$
$569$	3.00000			0.125767			0.0628833	+	0.998021i	$0.479970\pi$
$570$			18.0000i			0.753937i
$571$		0			0			−	1.00000i	$-0.5\pi$
$571$		0			0				1.00000i	$0.5\pi$
$572$		−	15.0000i		−	0.627182i
$573$			19.0000i			0.793736i
$574$	−27.0000			−1.12696
$575$		−	20.0000i		−	0.834058i
$576$	−7.00000			−0.291667
$577$			6.00000i			0.249783i	0.992170	+	0.124892i	$0.0398583\pi$
$577$			6.00000i			0.249783i	−0.992170	+	0.124892i	$0.960142\pi$
$578$			1.00000i			0.0415945i
$579$			6.00000i			0.249351i
$580$		−	12.0000i		−	0.498273i
$581$		−	18.0000i		−	0.746766i
$582$			6.00000i			0.248708i
$583$	−10.0000			−0.414158
$584$		−	33.0000i		−	1.36555i
$585$	9.00000			0.372104
$586$		−	6.00000i		−	0.247858i
$587$		−	20.0000i		−	0.825488i	−0.910847	−	0.412744i	$-0.864570\pi$
$587$		−	20.0000i		−	0.825488i	0.910847	−	0.412744i	$-0.135430\pi$
$588$	2.00000			0.0824786
$589$		0			0
$590$	−15.0000			−0.617540
$591$	3.00000			0.123404
$592$		−	6.00000i		−	0.246598i
$593$			34.0000i			1.39621i	0.715994	+	0.698106i	$0.245974\pi$
$593$			34.0000i			1.39621i	−0.715994	+	0.698106i	$0.754026\pi$
$594$	5.00000			0.205152
$595$	−36.0000			−1.47586
$596$	−9.00000			−0.368654
$597$	16.0000			0.654836
$598$	−15.0000			−0.613396
$599$			17.0000i			0.694601i	0.937754	+	0.347301i	$0.112902\pi$
$599$			17.0000i			0.694601i	−0.937754	+	0.347301i	$0.887098\pi$
$600$		−	12.0000i		−	0.489898i
$601$	−9.00000			−0.367118			−0.183559	−	0.983009i	$-0.558762\pi$
$601$	−9.00000			−0.367118			−0.183559	+	0.983009i	$0.558762\pi$
$602$			36.0000i			1.46725i
$603$			9.00000i			0.366508i
$604$		−	21.0000i		−	0.854478i
$605$	42.0000			1.70754
$606$	−2.00000			−0.0812444
$607$	22.0000			0.892952			0.446476	−	0.894795i	$-0.352679\pi$
$607$	22.0000			0.892952			0.446476	+	0.894795i	$0.352679\pi$
$608$			30.0000i			1.21666i
$609$	12.0000			0.486265
$610$	18.0000	−	15.0000i	0.728799	−	0.607332i
$611$	−18.0000			−0.728202
$612$		−	4.00000i		−	0.161690i
$613$	−6.00000			−0.242338			−0.121169	−	0.992632i	$-0.538664\pi$
$613$	−6.00000			−0.242338			−0.121169	+	0.992632i	$0.538664\pi$
$614$	33.0000			1.33177
$615$	27.0000			1.08875
$616$		−	45.0000i		−	1.81310i
$617$		−	8.00000i		−	0.322068i	−0.986949	−	0.161034i	$-0.948517\pi$
$617$		−	8.00000i		−	0.322068i	0.986949	−	0.161034i	$-0.0514829\pi$
$618$		0			0
$619$	18.0000			0.723481			0.361741	−	0.932279i	$-0.382183\pi$
$619$	18.0000			0.723481			0.361741	+	0.932279i	$0.382183\pi$
$620$		0			0
$621$			5.00000i			0.200643i
$622$	−19.0000			−0.761831
$623$	24.0000			0.961540
$624$	−3.00000			−0.120096
$625$	−29.0000			−1.16000
$626$	6.00000			0.239808
$627$		−	30.0000i		−	1.19808i
$628$			24.0000i			0.957704i
$629$	24.0000			0.956943
$630$	9.00000			0.358569
$631$			33.0000i			1.31371i	0.754017	+	0.656855i	$0.228113\pi$
$631$			33.0000i			1.31371i	−0.754017	+	0.656855i	$0.771887\pi$
$632$	9.00000			0.358001
$633$			12.0000i			0.476957i
$634$		−	18.0000i		−	0.714871i
$635$	−54.0000			−2.14292
$636$		−	2.00000i		−	0.0793052i
$637$	6.00000			0.237729
$638$		−	20.0000i		−	0.791808i
$639$			8.00000i			0.316475i
$640$		−	9.00000i		−	0.355756i
$641$			22.0000i			0.868948i	0.900684	+	0.434474i	$0.143066\pi$
$641$			22.0000i			0.868948i	−0.900684	+	0.434474i	$0.856934\pi$
$642$		−	12.0000i		−	0.473602i
$643$			24.0000i			0.946468i	0.880937	+	0.473234i	$0.156913\pi$
$643$			24.0000i			0.946468i	−0.880937	+	0.473234i	$0.843087\pi$
$644$	15.0000			0.591083
$645$		−	36.0000i		−	1.41750i
$646$	24.0000			0.944267
$647$			29.0000i			1.14011i	0.821607	+	0.570054i	$0.193078\pi$
$647$			29.0000i			1.14011i	−0.821607	+	0.570054i	$0.806922\pi$
$648$			3.00000i			0.117851i
$649$	25.0000			0.981336
$650$		−	12.0000i		−	0.470679i
$651$		0			0
$652$	24.0000			0.939913
$653$		−	32.0000i		−	1.25226i	−0.779720	−	0.626128i	$-0.784639\pi$
$653$		−	32.0000i		−	1.25226i	0.779720	−	0.626128i	$-0.215361\pi$
$654$			11.0000i			0.430134i
$655$		0			0
$656$	−9.00000			−0.351391
$657$	−11.0000			−0.429151
$658$	−18.0000			−0.701713
$659$	18.0000			0.701180			0.350590	−	0.936529i	$-0.385981\pi$
$659$	18.0000			0.701180			0.350590	+	0.936529i	$0.385981\pi$
$660$			15.0000i			0.583874i
$661$			12.0000i			0.466746i	0.972387	+	0.233373i	$0.0749763\pi$
$661$			12.0000i			0.466746i	−0.972387	+	0.233373i	$0.925024\pi$
$662$	15.0000			0.582992
$663$		−	12.0000i		−	0.466041i
$664$		−	18.0000i		−	0.698535i
$665$		−	54.0000i		−	2.09403i
$666$	−6.00000			−0.232495
$667$	20.0000			0.774403
$668$	−12.0000			−0.464294
$669$		−	9.00000i		−	0.347960i
$670$	27.0000			1.04310
$671$	−30.0000	+	25.0000i	−1.15814	+	0.965114i
$672$	15.0000			0.578638
$673$			12.0000i			0.462566i	0.972887	+	0.231283i	$0.0742923\pi$
$673$			12.0000i			0.462566i	−0.972887	+	0.231283i	$0.925708\pi$
$674$	6.00000			0.231111
$675$	−4.00000			−0.153960
$676$	−4.00000			−0.153846
$677$			22.0000i			0.845529i	0.906240	+	0.422764i	$0.138940\pi$
$677$			22.0000i			0.845529i	−0.906240	+	0.422764i	$0.861060\pi$
$678$		−	21.0000i		−	0.806500i
$679$		−	18.0000i		−	0.690777i
$680$	−36.0000			−1.38054
$681$		−	13.0000i		−	0.498161i
$682$		0			0
$683$	36.0000			1.37750			0.688751	−	0.724998i	$-0.258159\pi$
$683$	36.0000			1.37750			0.688751	+	0.724998i	$0.258159\pi$
$684$	6.00000			0.229416
$685$	27.0000			1.03162
$686$	−15.0000			−0.572703
$687$	9.00000			0.343371
$688$			12.0000i			0.457496i
$689$		−	6.00000i		−	0.228582i
$690$	15.0000			0.571040
$691$	−36.0000			−1.36950			−0.684752	−	0.728776i	$-0.740090\pi$
$691$	−36.0000			−1.36950			−0.684752	+	0.728776i	$0.740090\pi$
$692$		−	16.0000i		−	0.608229i
$693$	−15.0000			−0.569803
$694$		−	18.0000i		−	0.683271i
$695$		−	27.0000i		−	1.02417i
$696$	12.0000			0.454859
$697$		−	36.0000i		−	1.36360i
$698$	12.0000			0.454207
$699$		−	4.00000i		−	0.151294i
$700$			12.0000i			0.453557i
$701$			20.0000i			0.755390i	0.925930	+	0.377695i	$0.123283\pi$
$701$			20.0000i			0.755390i	−0.925930	+	0.377695i	$0.876717\pi$
$702$			3.00000i			0.113228i
$703$			36.0000i			1.35777i
$704$		−	35.0000i		−	1.31911i
$705$	18.0000			0.677919
$706$		−	9.00000i		−	0.338719i
$707$	6.00000			0.225653
$708$			5.00000i			0.187912i
$709$		−	30.0000i		−	1.12667i	−0.826227	−	0.563337i	$-0.809517\pi$
$709$		−	30.0000i		−	1.12667i	0.826227	−	0.563337i	$-0.190483\pi$
$710$	24.0000			0.900704
$711$		−	3.00000i		−	0.112509i
$712$	24.0000			0.899438
$713$		0			0
$714$		−	12.0000i		−	0.449089i
$715$			45.0000i			1.68290i
$716$	6.00000			0.224231
$717$	−12.0000			−0.448148
$718$	8.00000			0.298557
$719$	−36.0000			−1.34257			−0.671287	−	0.741198i	$-0.734258\pi$
$719$	−36.0000			−1.34257			−0.671287	+	0.741198i	$0.734258\pi$
$720$	3.00000			0.111803
$721$		0			0
$722$			17.0000i			0.632674i
$723$	−9.00000			−0.334714
$724$		−	6.00000i		−	0.222988i
$725$			16.0000i			0.594225i
$726$			14.0000i			0.519589i
$727$	−6.00000			−0.222528			−0.111264	−	0.993791i	$-0.535490\pi$
$727$	−6.00000			−0.222528			−0.111264	+	0.993791i	$0.535490\pi$
$728$	27.0000			1.00069
$729$	1.00000			0.0370370
$730$			33.0000i			1.22138i
$731$	−48.0000			−1.77534
$732$	−5.00000	−	6.00000i	−0.184805	−	0.221766i
$733$	5.00000			0.184679			0.0923396	−	0.995728i	$-0.470565\pi$
$733$	5.00000			0.184679			0.0923396	+	0.995728i	$0.470565\pi$
$734$			6.00000i			0.221464i
$735$	−6.00000			−0.221313
$736$	25.0000			0.921512
$737$	−45.0000			−1.65760
$738$			9.00000i			0.331295i
$739$			27.0000i			0.993211i	0.867976	+	0.496606i	$0.165420\pi$
$739$			27.0000i			0.993211i	−0.867976	+	0.496606i	$0.834580\pi$
$740$		−	18.0000i		−	0.661693i
$741$	18.0000			0.661247
$742$		−	6.00000i		−	0.220267i
$743$		−	11.0000i		−	0.403551i	−0.979432	−	0.201775i	$-0.935329\pi$
$743$		−	11.0000i		−	0.403551i	0.979432	−	0.201775i	$-0.0646711\pi$
$744$		0			0
$745$	27.0000			0.989203
$746$	−24.0000			−0.878702
$747$	−6.00000			−0.219529
$748$	20.0000			0.731272
$749$			36.0000i			1.31541i
$750$		−	3.00000i		−	0.109545i
$751$	22.0000			0.802791			0.401396	−	0.915905i	$-0.368525\pi$
$751$	22.0000			0.802791			0.401396	+	0.915905i	$0.368525\pi$
$752$	−6.00000			−0.218797
$753$		−	4.00000i		−	0.145768i
$754$	12.0000			0.437014
$755$			63.0000i			2.29280i
$756$		−	3.00000i		−	0.109109i
$757$	11.0000			0.399802			0.199901	−	0.979816i	$-0.435938\pi$
$757$	11.0000			0.399802			0.199901	+	0.979816i	$0.435938\pi$
$758$			20.0000i			0.726433i
$759$	−25.0000			−0.907443
$760$		−	54.0000i		−	1.95879i
$761$		−	46.0000i		−	1.66750i	−0.552143	−	0.833749i	$-0.686190\pi$
$761$		−	46.0000i		−	1.66750i	0.552143	−	0.833749i	$-0.313810\pi$
$762$		−	18.0000i		−	0.652071i
$763$		−	33.0000i		−	1.19468i
$764$		−	19.0000i		−	0.687396i
$765$			12.0000i			0.433861i
$766$	13.0000			0.469709
$767$			15.0000i			0.541619i
$768$	17.0000			0.613435
$769$			36.0000i			1.29819i	0.760706	+	0.649097i	$0.224853\pi$
$769$			36.0000i			1.29819i	−0.760706	+	0.649097i	$0.775147\pi$
$770$			45.0000i			1.62169i
$771$	−6.00000			−0.216085
$772$		−	6.00000i		−	0.215945i
$773$	6.00000			0.215805			0.107903	−	0.994161i	$-0.465587\pi$
$773$	6.00000			0.215805			0.107903	+	0.994161i	$0.465587\pi$
$774$	12.0000			0.431331
$775$		0			0
$776$		−	18.0000i		−	0.646162i
$777$	18.0000			0.645746
$778$	4.00000			0.143407
$779$	54.0000			1.93475
$780$	−9.00000			−0.322252
$781$	−40.0000			−1.43131
$782$		−	20.0000i		−	0.715199i
$783$		−	4.00000i		−	0.142948i
$784$	2.00000			0.0714286
$785$		−	72.0000i		−	2.56979i
$786$		0			0
$787$		0			0		1.00000			$0$
$787$		0			0		−1.00000			$\pi$
$788$	−3.00000			−0.106871
$789$	−6.00000			−0.213606
$790$	−9.00000			−0.320206
$791$			63.0000i			2.24002i
$792$	−15.0000			−0.533002
$793$	−15.0000	−	18.0000i	−0.532666	−	0.639199i
$794$	36.0000			1.27759
$795$			6.00000i			0.212798i
$796$	−16.0000			−0.567105
$797$	−3.00000			−0.106265			−0.0531327	−	0.998587i	$-0.516921\pi$
$797$	−3.00000			−0.106265			−0.0531327	+	0.998587i	$0.516921\pi$
$798$	18.0000			0.637193
$799$		−	24.0000i		−	0.849059i
$800$			20.0000i			0.707107i
$801$		−	8.00000i		−	0.282666i
$802$	−22.0000			−0.776847
$803$		−	55.0000i		−	1.94091i
$804$		−	9.00000i		−	0.317406i
$805$	−45.0000			−1.58604
$806$		0			0
$807$	6.00000			0.211210
$808$	6.00000			0.211079
$809$	−33.0000			−1.16022			−0.580109	−	0.814539i	$-0.696990\pi$
$809$	−33.0000			−1.16022			−0.580109	+	0.814539i	$0.696990\pi$
$810$		−	3.00000i		−	0.105409i
$811$		−	15.0000i		−	0.526721i	−0.964697	−	0.263361i	$-0.915169\pi$
$811$		−	15.0000i		−	0.526721i	0.964697	−	0.263361i	$-0.0848309\pi$
$812$	−12.0000			−0.421117
$813$	−16.0000			−0.561144
$814$		−	30.0000i		−	1.05150i
$815$	−72.0000			−2.52205
$816$		−	4.00000i		−	0.140028i
$817$		−	72.0000i		−	2.51896i
$818$	6.00000			0.209785
$819$		−	9.00000i		−	0.314485i
$820$	−27.0000			−0.942881
$821$			38.0000i			1.32621i	0.748527	+	0.663105i	$0.230762\pi$
$821$			38.0000i			1.32621i	−0.748527	+	0.663105i	$0.769238\pi$
$822$			9.00000i			0.313911i
$823$			24.0000i			0.836587i	0.908312	+	0.418294i	$0.137372\pi$
$823$			24.0000i			0.836587i	−0.908312	+	0.418294i	$0.862628\pi$
$824$		0			0
$825$		−	20.0000i		−	0.696311i
$826$			15.0000i			0.521917i
$827$	−42.0000			−1.46048			−0.730242	−	0.683189i	$-0.760592\pi$
$827$	−42.0000			−1.46048			−0.730242	+	0.683189i	$0.760592\pi$
$828$		−	5.00000i		−	0.173762i
$829$	−11.0000			−0.382046			−0.191023	−	0.981586i	$-0.561180\pi$
$829$	−11.0000			−0.382046			−0.191023	+	0.981586i	$0.561180\pi$
$830$			18.0000i			0.624789i
$831$			18.0000i			0.624413i
$832$	21.0000			0.728044
$833$			8.00000i			0.277184i
$834$	9.00000			0.311645
$835$	36.0000			1.24583
$836$			30.0000i			1.03757i
$837$		0			0
$838$	−20.0000			−0.690889
$839$	−30.0000			−1.03572			−0.517858	−	0.855467i	$-0.673270\pi$
$839$	−30.0000			−1.03572			−0.517858	+	0.855467i	$0.673270\pi$
$840$	−27.0000			−0.931589
$841$	13.0000			0.448276
$842$		0			0
$843$			28.0000i			0.964371i
$844$		−	12.0000i		−	0.413057i
$845$	12.0000			0.412813
$846$			6.00000i			0.206284i
$847$		−	42.0000i		−	1.44314i
$848$		−	2.00000i		−	0.0686803i
$849$	22.0000			0.755038
$850$	16.0000			0.548795
$851$	30.0000			1.02839
$852$		−	8.00000i		−	0.274075i
$853$	35.0000			1.19838			0.599189	−	0.800608i	$-0.295490\pi$
$853$	35.0000			1.19838			0.599189	+	0.800608i	$0.295490\pi$
$854$	−15.0000	−	18.0000i	−0.513289	−	0.615947i
$855$	−18.0000			−0.615587
$856$			36.0000i			1.23045i
$857$	45.0000			1.53717			0.768585	−	0.639747i	$-0.220961\pi$
$857$	45.0000			1.53717			0.768585	+	0.639747i	$0.220961\pi$
$858$	−15.0000			−0.512092
$859$	50.0000			1.70598			0.852989	−	0.521929i	$-0.174787\pi$
$859$	50.0000			1.70598			0.852989	+	0.521929i	$0.174787\pi$
$860$			36.0000i			1.22759i
$861$		−	27.0000i		−	0.920158i
$862$			24.0000i			0.817443i
$863$		0			0			−	1.00000i	$-0.5\pi$
$863$		0			0				1.00000i	$0.5\pi$
$864$		−	5.00000i		−	0.170103i
$865$			48.0000i			1.63205i
$866$	6.00000			0.203888
$867$	−1.00000			−0.0339618
$868$		0			0
$869$	15.0000			0.508840
$870$	−12.0000			−0.406838
$871$		−	27.0000i		−	0.914860i
$872$		−	33.0000i		−	1.11752i
$873$	−6.00000			−0.203069
$874$	30.0000			1.01477
$875$			9.00000i			0.304256i
$876$	11.0000			0.371656
$877$		−	24.0000i		−	0.810422i	−0.914223	−	0.405211i	$-0.867198\pi$
$877$		−	24.0000i		−	0.810422i	0.914223	−	0.405211i	$-0.132802\pi$
$878$			26.0000i			0.877457i
$879$	6.00000			0.202375
$880$			15.0000i			0.505650i
$881$	3.00000			0.101073			0.0505363	−	0.998722i	$-0.483907\pi$
$881$	3.00000			0.101073			0.0505363	+	0.998722i	$0.483907\pi$
$882$		−	2.00000i		−	0.0673435i
$883$			9.00000i			0.302874i	0.988467	+	0.151437i	$0.0483901\pi$
$883$			9.00000i			0.302874i	−0.988467	+	0.151437i	$0.951610\pi$
$884$			12.0000i			0.403604i
$885$		−	15.0000i		−	0.504219i
$886$			12.0000i			0.403148i
$887$			44.0000i			1.47738i	0.674048	+	0.738688i	$0.264554\pi$
$887$			44.0000i			1.47738i	−0.674048	+	0.738688i	$0.735446\pi$
$888$	18.0000			0.604040
$889$			54.0000i			1.81110i
$890$	−24.0000			−0.804482
$891$			5.00000i			0.167506i
$892$			9.00000i			0.301342i
$893$	36.0000			1.20469
$894$			9.00000i			0.301005i
$895$	−18.0000			−0.601674
$896$	−9.00000			−0.300669
$897$		−	15.0000i		−	0.500835i
$898$		−	9.00000i		−	0.300334i
$899$		0			0
$900$	4.00000			0.133333
$901$	8.00000			0.266519
$902$	−45.0000			−1.49834
$903$	−36.0000			−1.19800
$904$			63.0000i			2.09535i
$905$			18.0000i			0.598340i
$906$	−21.0000			−0.697678
$907$			12.0000i			0.398453i	0.979953	+	0.199227i	$0.0638430\pi$
$907$			12.0000i			0.398453i	−0.979953	+	0.199227i	$0.936157\pi$
$908$			13.0000i			0.431420i
$909$		−	2.00000i		−	0.0663358i
$910$	−27.0000			−0.895041
$911$	24.0000			0.795155			0.397578	−	0.917568i	$-0.369851\pi$
$911$	24.0000			0.795155			0.397578	+	0.917568i	$0.369851\pi$
$912$	6.00000			0.198680
$913$		−	30.0000i		−	0.992855i
$914$	−30.0000			−0.992312
$915$	15.0000	+	18.0000i	0.495885	+	0.595062i
$916$	−9.00000			−0.297368
$917$		0			0
$918$	−4.00000			−0.132020
$919$	−56.0000			−1.84727			−0.923635	−	0.383274i	$-0.874797\pi$
$919$	−56.0000			−1.84727			−0.923635	+	0.383274i	$0.874797\pi$
$920$	−45.0000			−1.48361
$921$			33.0000i			1.08739i
$922$		−	42.0000i		−	1.38320i
$923$		−	24.0000i		−	0.789970i
$924$	15.0000			0.493464
$925$			24.0000i			0.789115i
$926$			36.0000i			1.18303i
$927$		0			0
$928$	−20.0000			−0.656532
$929$	−3.00000			−0.0984268			−0.0492134	−	0.998788i	$-0.515671\pi$
$929$	−3.00000			−0.0984268			−0.0492134	+	0.998788i	$0.515671\pi$
$930$		0			0
$931$	−12.0000			−0.393284
$932$			4.00000i			0.131024i
$933$		−	19.0000i		−	0.622032i
$934$	13.0000			0.425373
$935$	−60.0000			−1.96221
$936$		−	9.00000i		−	0.294174i
$937$	3.00000			0.0980057			0.0490029	−	0.998799i	$-0.484396\pi$
$937$	3.00000			0.0980057			0.0490029	+	0.998799i	$0.484396\pi$
$938$		−	27.0000i		−	0.881581i
$939$			6.00000i			0.195803i
$940$	−18.0000			−0.587095
$941$		−	16.0000i		−	0.521585i	−0.965395	−	0.260793i	$-0.916016\pi$
$941$		−	16.0000i		−	0.521585i	0.965395	−	0.260793i	$-0.0839839\pi$
$942$	24.0000			0.781962
$943$		−	45.0000i		−	1.46540i
$944$			5.00000i			0.162736i
$945$			9.00000i			0.292770i
$946$			60.0000i			1.95077i
$947$		−	29.0000i		−	0.942373i	−0.882034	−	0.471187i	$-0.843826\pi$
$947$		−	29.0000i		−	0.942373i	0.882034	−	0.471187i	$-0.156174\pi$
$948$			3.00000i			0.0974355i
$949$	33.0000			1.07123
$950$			24.0000i			0.778663i
$951$	18.0000			0.583690
$952$			36.0000i			1.16677i
$953$		−	34.0000i		−	1.10137i	−0.834714	−	0.550684i	$-0.814367\pi$
$953$		−	34.0000i		−	1.10137i	0.834714	−	0.550684i	$-0.185633\pi$
$954$	−2.00000			−0.0647524
$955$			57.0000i			1.84448i
$956$	12.0000			0.388108
$957$	20.0000			0.646508
$958$		−	30.0000i		−	0.969256i
$959$		−	27.0000i		−	0.871875i
$960$	−21.0000			−0.677772
$961$	31.0000			1.00000
$962$	18.0000			0.580343
$963$	12.0000			0.386695
$964$	9.00000			0.289870
$965$			18.0000i			0.579441i
$966$		−	15.0000i		−	0.482617i
$967$	−22.0000			−0.707472			−0.353736	−	0.935345i	$-0.615089\pi$
$967$	−22.0000			−0.707472			−0.353736	+	0.935345i	$0.615089\pi$
$968$		−	42.0000i		−	1.34993i
$969$			24.0000i			0.770991i
$970$			18.0000i			0.577945i
$971$	36.0000			1.15529			0.577647	−	0.816286i	$-0.303971\pi$
$971$	36.0000			1.15529			0.577647	+	0.816286i	$0.303971\pi$
$972$	−1.00000			−0.0320750
$973$	−27.0000			−0.865580
$974$		−	2.00000i		−	0.0640841i
$975$	12.0000			0.384308
$976$	−5.00000	−	6.00000i	−0.160046	−	0.192055i
$977$	−30.0000			−0.959785			−0.479893	−	0.877327i	$-0.659324\pi$
$977$	−30.0000			−0.959785			−0.479893	+	0.877327i	$0.659324\pi$
$978$		−	24.0000i		−	0.767435i
$979$	40.0000			1.27841
$980$	6.00000			0.191663
$981$	−11.0000			−0.351203
$982$		−	18.0000i		−	0.574403i
$983$		−	16.0000i		−	0.510321i	−0.966899	−	0.255160i	$-0.917872\pi$
$983$		−	16.0000i		−	0.510321i	0.966899	−	0.255160i	$-0.0821283\pi$
$984$		−	27.0000i		−	0.860729i
$985$	9.00000			0.286764
$986$			16.0000i			0.509544i
$987$		−	18.0000i		−	0.572946i
$988$	−18.0000			−0.572656
$989$	−60.0000			−1.90789
$990$	15.0000			0.476731
$991$	−24.0000			−0.762385			−0.381193	−	0.924496i	$-0.624487\pi$
$991$	−24.0000			−0.762385			−0.381193	+	0.924496i	$0.624487\pi$
$992$		0			0
$993$			15.0000i			0.476011i
$994$		−	24.0000i		−	0.761234i
$995$	48.0000			1.52170
$996$	6.00000			0.190117
$997$			48.0000i			1.52018i	0.649821	+	0.760088i	$0.274844\pi$
$997$			48.0000i			1.52018i	−0.649821	+	0.760088i	$0.725156\pi$
$998$	3.00000			0.0949633
$999$		−	6.00000i		−	0.189832i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	183.2.c.a.121.2	yes	2
3.2	odd	2		549.2.c.b.487.1		2
4.3	odd	2		2928.2.l.b.1585.1		2
61.60	even	2	inner	183.2.c.a.121.1	✓	2
183.182	odd	2		549.2.c.b.487.2		2
244.243	odd	2		2928.2.l.b.1585.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
183.2.c.a.121.1	✓	2	61.60	even	2	inner
183.2.c.a.121.2	yes	2	1.1	even	1	trivial
549.2.c.b.487.1		2	3.2	odd	2
549.2.c.b.487.2		2	183.182	odd	2
2928.2.l.b.1585.1		2	4.3	odd	2
2928.2.l.b.1585.2		2	244.243	odd	2

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:	\( N \)	\(=\)	\( 183 = 3 \cdot 61 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	183.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+1.00000i q^{2} -1.00000 q^{3} +1.00000 q^{4} -3.00000 q^{5} -1.00000i q^{6} +3.00000i q^{7} +3.00000i q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000i q^{2} -1.00000 q^{3} +1.00000 q^{4} -3.00000 q^{5} -1.00000i q^{6} +3.00000i q^{7} +3.00000i q^{8} +1.00000 q^{9} -3.00000i q^{10} +5.00000i q^{11} -1.00000 q^{12} -3.00000 q^{13} -3.00000 q^{14} +3.00000 q^{15} -1.00000 q^{16} -4.00000i q^{17} +1.00000i q^{18} +6.00000 q^{19} -3.00000 q^{20} -3.00000i q^{21} -5.00000 q^{22} -5.00000i q^{23} -3.00000i q^{24} +4.00000 q^{25} -3.00000i q^{26} -1.00000 q^{27} +3.00000i q^{28} +4.00000i q^{29} +3.00000i q^{30} +5.00000i q^{32} -5.00000i q^{33} +4.00000 q^{34} -9.00000i q^{35} +1.00000 q^{36} +6.00000i q^{37} +6.00000i q^{38} +3.00000 q^{39} -9.00000i q^{40} +9.00000 q^{41} +3.00000 q^{42} -12.0000i q^{43} +5.00000i q^{44} -3.00000 q^{45} +5.00000 q^{46} +6.00000 q^{47} +1.00000 q^{48} -2.00000 q^{49} +4.00000i q^{50} +4.00000i q^{51} -3.00000 q^{52} +2.00000i q^{53} -1.00000i q^{54} -15.0000i q^{55} -9.00000 q^{56} -6.00000 q^{57} -4.00000 q^{58} -5.00000i q^{59} +3.00000 q^{60} +(5.00000 + 6.00000i) q^{61} +3.00000i q^{63} -7.00000 q^{64} +9.00000 q^{65} +5.00000 q^{66} +9.00000i q^{67} -4.00000i q^{68} +5.00000i q^{69} +9.00000 q^{70} +8.00000i q^{71} +3.00000i q^{72} -11.0000 q^{73} -6.00000 q^{74} -4.00000 q^{75} +6.00000 q^{76} -15.0000 q^{77} +3.00000i q^{78} -3.00000i q^{79} +3.00000 q^{80} +1.00000 q^{81} +9.00000i q^{82} -6.00000 q^{83} -3.00000i q^{84} +12.0000i q^{85} +12.0000 q^{86} -4.00000i q^{87} -15.0000 q^{88} -8.00000i q^{89} -3.00000i q^{90} -9.00000i q^{91} -5.00000i q^{92} +6.00000i q^{94} -18.0000 q^{95} -5.00000i q^{96} -6.00000 q^{97} -2.00000i q^{98} +5.00000i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 2 q^{3} + 2 q^{4} - 6 q^{5} + 2 q^{9}+O(q^{10}) \) 2 * q - 2 * q^3 + 2 * q^4 - 6 * q^5 + 2 * q^9	\( 2 q - 2 q^{3} + 2 q^{4} - 6 q^{5} + 2 q^{9} - 2 q^{12} - 6 q^{13} - 6 q^{14} + 6 q^{15} - 2 q^{16} + 12 q^{19} - 6 q^{20} - 10 q^{22} + 8 q^{25} - 2 q^{27} + 8 q^{34} + 2 q^{36} + 6 q^{39} + 18 q^{41} + 6 q^{42} - 6 q^{45} + 10 q^{46} + 12 q^{47} + 2 q^{48} - 4 q^{49} - 6 q^{52} - 18 q^{56} - 12 q^{57} - 8 q^{58} + 6 q^{60} + 10 q^{61} - 14 q^{64} + 18 q^{65} + 10 q^{66} + 18 q^{70} - 22 q^{73} - 12 q^{74} - 8 q^{75} + 12 q^{76} - 30 q^{77} + 6 q^{80} + 2 q^{81} - 12 q^{83} + 24 q^{86} - 30 q^{88} - 36 q^{95} - 12 q^{97}+O(q^{100}) \) 2 * q - 2 * q^3 + 2 * q^4 - 6 * q^5 + 2 * q^9 - 2 * q^12 - 6 * q^13 - 6 * q^14 + 6 * q^15 - 2 * q^16 + 12 * q^19 - 6 * q^20 - 10 * q^22 + 8 * q^25 - 2 * q^27 + 8 * q^34 + 2 * q^36 + 6 * q^39 + 18 * q^41 + 6 * q^42 - 6 * q^45 + 10 * q^46 + 12 * q^47 + 2 * q^48 - 4 * q^49 - 6 * q^52 - 18 * q^56 - 12 * q^57 - 8 * q^58 + 6 * q^60 + 10 * q^61 - 14 * q^64 + 18 * q^65 + 10 * q^66 + 18 * q^70 - 22 * q^73 - 12 * q^74 - 8 * q^75 + 12 * q^76 - 30 * q^77 + 6 * q^80 + 2 * q^81 - 12 * q^83 + 24 * q^86 - 30 * q^88 - 36 * q^95 - 12 * q^97

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