LMFDB - Embedded newform 585.2.c.b.469.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [585,2,Mod(469,585)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(585, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("585.469");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 585 = 3^{2} \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	585.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:	$4.67124851824$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	6.0.350464.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 2x^{5} + 2x^{4} + 2x^{3} + 4x^{2} - 4x + 2 $ x^6 - 2x^5 + 2x^4 + 2x^3 + 4x^2 - 4*x + 2
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2 $
Twist minimal:	no (minimal twist has level 65)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			469.1
Root			$0.403032 - 0.403032i$ of defining polynomial
Character	$\chi$	$=$	585.469
Dual form			585.2.c.b.469.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.67513i q^{2} -5.15633 q^{4} +(-1.67513 + 1.48119i) q^{5} +0.806063i q^{7} +8.44358i q^{8} +O(q^{10})$	\(q-2.67513i q^{2} -5.15633 q^{4} +(-1.67513 + 1.48119i) q^{5} +0.806063i q^{7} +8.44358i q^{8} +(3.96239 + 4.48119i) q^{10} +3.67513 q^{11} +1.00000i q^{13} +2.15633 q^{14} +12.2750 q^{16} +1.35026i q^{17} +1.67513 q^{19} +(8.63752 - 7.63752i) q^{20} -9.83146i q^{22} +6.48119i q^{23} +(0.612127 - 4.96239i) q^{25} +2.67513 q^{26} -4.15633i q^{28} +2.41819 q^{29} -5.28726 q^{31} -15.9502i q^{32} +3.61213 q^{34} +(-1.19394 - 1.35026i) q^{35} +3.76845i q^{37} -4.48119i q^{38} +(-12.5066 - 14.1441i) q^{40} +8.31265 q^{41} +6.79384i q^{43} -18.9502 q^{44} +17.3380 q^{46} -3.19394i q^{47} +6.35026 q^{49} +(-13.2750 - 1.63752i) q^{50} -5.15633i q^{52} +5.73813i q^{53} +(-6.15633 + 5.44358i) q^{55} -6.80606 q^{56} -6.46898i q^{58} +5.98778 q^{59} -1.76845 q^{61} +14.1441i q^{62} -18.1187 q^{64} +(-1.48119 - 1.67513i) q^{65} +9.89446i q^{67} -6.96239i q^{68} +(-3.61213 + 3.19394i) q^{70} -8.56230 q^{71} +11.7685i q^{73} +10.0811 q^{74} -8.63752 q^{76} +2.96239i q^{77} +2.26187 q^{79} +(-20.5623 + 18.1817i) q^{80} -22.2374i q^{82} +3.84367i q^{83} +(-2.00000 - 2.26187i) q^{85} +18.1744 q^{86} +31.0313i q^{88} +2.77575 q^{89} -0.806063 q^{91} -33.4191i q^{92} -8.54420 q^{94} +(-2.80606 + 2.48119i) q^{95} -1.87399i q^{97} -16.9878i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 10 q^{4}+O(q^{10}) $ 6 * q - 10 * q^4	$ 6 q - 10 q^{4} + 2 q^{10} + 12 q^{11} - 8 q^{14} + 10 q^{16} + 20 q^{20} + 2 q^{25} + 6 q^{26} + 12 q^{29} - 20 q^{31} + 20 q^{34} - 8 q^{35} - 34 q^{40} + 8 q^{41} - 40 q^{44} + 32 q^{46} + 18 q^{49} - 16 q^{50} - 16 q^{55} - 40 q^{56} - 16 q^{59} + 12 q^{61} - 66 q^{64} + 2 q^{65} - 20 q^{70} + 24 q^{71} - 4 q^{74} - 20 q^{76} + 32 q^{79} - 48 q^{80} - 12 q^{85} + 32 q^{86} + 20 q^{89} - 4 q^{91} - 32 q^{94} - 16 q^{95}+O(q^{100}) $ 6 * q - 10 * q^4 + 2 * q^10 + 12 * q^11 - 8 * q^14 + 10 * q^16 + 20 * q^20 + 2 * q^25 + 6 * q^26 + 12 * q^29 - 20 * q^31 + 20 * q^34 - 8 * q^35 - 34 * q^40 + 8 * q^41 - 40 * q^44 + 32 * q^46 + 18 * q^49 - 16 * q^50 - 16 * q^55 - 40 * q^56 - 16 * q^59 + 12 * q^61 - 66 * q^64 + 2 * q^65 - 20 * q^70 + 24 * q^71 - 4 * q^74 - 20 * q^76 + 32 * q^79 - 48 * q^80 - 12 * q^85 + 32 * q^86 + 20 * q^89 - 4 * q^91 - 32 * q^94 - 16 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/585\mathbb{Z}\right)^\times$.

$n$	$326$	$352$	$496$
$\chi(n)$	$1$	$-1$	$1$

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 $

$2$		−	2.67513i		−	1.89160i	−0.324745	−	0.945802i	$-0.605279\pi$
$2$		−	2.67513i		−	1.89160i	0.324745	−	0.945802i	$-0.394721\pi$
$3$		0			0
$3$		0			0
$4$	−5.15633			−2.57816
$5$	−1.67513	+	1.48119i	−0.749141	+	0.662410i
$5$	−1.67513	+	1.48119i	−0.749141	+	0.662410i
$6$		0			0
$7$			0.806063i			0.304663i	0.988329	+	0.152332i	$0.0486782\pi$
$7$			0.806063i			0.304663i	−0.988329	+	0.152332i	$0.951322\pi$
$8$			8.44358i			2.98526i
$9$		0			0
$10$	3.96239	+	4.48119i	1.25302	+	1.41708i
$11$	3.67513			1.10809			0.554047	−	0.832486i	$-0.313083\pi$
$11$	3.67513			1.10809			0.554047	+	0.832486i	$0.313083\pi$
$12$		0			0
$13$			1.00000i			0.277350i
$13$			1.00000i			0.277350i
$14$	2.15633			0.576302
$15$		0			0
$16$	12.2750			3.06876
$17$			1.35026i			0.327487i	0.986503	+	0.163743i	$0.0523569\pi$
$17$			1.35026i			0.327487i	−0.986503	+	0.163743i	$0.947643\pi$
$18$		0			0
$19$	1.67513			0.384301			0.192151	−	0.981365i	$-0.438454\pi$
$19$	1.67513			0.384301			0.192151	+	0.981365i	$0.438454\pi$
$20$	8.63752	−	7.63752i	1.93141	−	1.70780i
$21$		0			0
$22$		−	9.83146i		−	2.09607i
$23$			6.48119i			1.35142i	0.737166	+	0.675711i	$0.236163\pi$
$23$			6.48119i			1.35142i	−0.737166	+	0.675711i	$0.763837\pi$
$24$		0			0
$25$	0.612127	−	4.96239i	0.122425	−	0.992478i
$26$	2.67513			0.524636
$27$		0			0
$28$		−	4.15633i		−	0.785472i
$29$	2.41819			0.449047			0.224523	−	0.974469i	$-0.427917\pi$
$29$	2.41819			0.449047			0.224523	+	0.974469i	$0.427917\pi$
$30$		0			0
$31$	−5.28726			−0.949620			−0.474810	−	0.880088i	$-0.657483\pi$
$31$	−5.28726			−0.949620			−0.474810	+	0.880088i	$0.657483\pi$
$32$		−	15.9502i		−	2.81962i
$33$		0			0
$34$	3.61213			0.619475
$35$	−1.19394	−	1.35026i	−0.201812	−	0.228236i
$36$		0			0
$37$			3.76845i			0.619530i	0.950813	+	0.309765i	$0.100250\pi$
$37$			3.76845i			0.619530i	−0.950813	+	0.309765i	$0.899750\pi$
$38$		−	4.48119i		−	0.726946i
$39$		0			0
$40$	−12.5066	−	14.1441i	−1.97747	−	2.23638i
$41$	8.31265			1.29822			0.649109	−	0.760695i	$-0.275142\pi$
$41$	8.31265			1.29822			0.649109	+	0.760695i	$0.275142\pi$
$42$		0			0
$43$			6.79384i			1.03605i	0.855365	+	0.518026i	$0.173333\pi$
$43$			6.79384i			1.03605i	−0.855365	+	0.518026i	$0.826667\pi$
$44$	−18.9502			−2.85685
$45$		0			0
$46$	17.3380			2.55635
$47$		−	3.19394i		−	0.465884i	−0.972491	−	0.232942i	$-0.925165\pi$
$47$		−	3.19394i		−	0.465884i	0.972491	−	0.232942i	$-0.0748352\pi$
$48$		0			0
$49$	6.35026			0.907180
$50$	−13.2750	−	1.63752i	−1.87737	−	0.231580i
$51$		0			0
$52$		−	5.15633i		−	0.715054i
$53$			5.73813i			0.788193i	0.919069	+	0.394097i	$0.128943\pi$
$53$			5.73813i			0.788193i	−0.919069	+	0.394097i	$0.871057\pi$
$54$		0			0
$55$	−6.15633	+	5.44358i	−0.830119	+	0.734013i
$56$	−6.80606			−0.909498
$57$		0			0
$58$		−	6.46898i		−	0.849418i
$59$	5.98778			0.779543			0.389771	−	0.920912i	$-0.372554\pi$
$59$	5.98778			0.779543			0.389771	+	0.920912i	$0.372554\pi$
$60$		0			0
$61$	−1.76845			−0.226427			−0.113214	−	0.993571i	$-0.536114\pi$
$61$	−1.76845			−0.226427			−0.113214	+	0.993571i	$0.536114\pi$
$62$			14.1441i			1.79630i
$63$		0			0
$64$	−18.1187			−2.26484
$65$	−1.48119	−	1.67513i	−0.183720	−	0.207774i
$66$		0			0
$67$			9.89446i			1.20880i	0.796681	+	0.604400i	$0.206587\pi$
$67$			9.89446i			1.20880i	−0.796681	+	0.604400i	$0.793413\pi$
$68$		−	6.96239i		−	0.844314i
$69$		0			0
$70$	−3.61213	+	3.19394i	−0.431732	+	0.381748i
$71$	−8.56230			−1.01616			−0.508079	−	0.861311i	$-0.669644\pi$
$71$	−8.56230			−1.01616			−0.508079	+	0.861311i	$0.669644\pi$
$72$		0			0
$73$			11.7685i			1.37739i	0.725050	+	0.688697i	$0.241817\pi$
$73$			11.7685i			1.37739i	−0.725050	+	0.688697i	$0.758183\pi$
$74$	10.0811			1.17190
$75$		0			0
$76$	−8.63752			−0.990791
$77$			2.96239i			0.337596i
$78$		0			0
$79$	2.26187			0.254480			0.127240	−	0.991872i	$-0.459388\pi$
$79$	2.26187			0.254480			0.127240	+	0.991872i	$0.459388\pi$
$80$	−20.5623	+	18.1817i	−2.29893	+	2.03278i
$81$		0			0
$82$		−	22.2374i		−	2.45571i
$83$			3.84367i			0.421898i	0.977497	+	0.210949i	$0.0676554\pi$
$83$			3.84367i			0.421898i	−0.977497	+	0.210949i	$0.932345\pi$
$84$		0			0
$85$	−2.00000	−	2.26187i	−0.216930	−	0.245334i
$86$	18.1744			1.95980
$87$		0			0
$88$			31.0313i			3.30794i
$89$	2.77575			0.294229			0.147114	−	0.989120i	$-0.453001\pi$
$89$	2.77575			0.294229			0.147114	+	0.989120i	$0.453001\pi$
$90$		0			0
$91$	−0.806063			−0.0844984
$92$		−	33.4191i		−	3.48419i
$93$		0			0
$94$	−8.54420			−0.881267
$95$	−2.80606	+	2.48119i	−0.287896	+	0.254565i
$96$		0			0
$97$		−	1.87399i		−	0.190275i	−0.995464	−	0.0951375i	$-0.969671\pi$
$97$		−	1.87399i		−	0.190275i	0.995464	−	0.0951375i	$-0.0303291\pi$
$98$		−	16.9878i		−	1.71603i
$99$		0			0
$100$	−3.15633	+	25.5877i	−0.315633	+	2.55877i
$101$	−10.4993			−1.04472			−0.522359	−	0.852725i	$-0.674948\pi$
$101$	−10.4993			−1.04472			−0.522359	+	0.852725i	$0.674948\pi$
$102$		0			0
$103$		−	15.3684i		−	1.51429i	−0.653247	−	0.757145i	$-0.726594\pi$
$103$		−	15.3684i		−	1.51429i	0.653247	−	0.757145i	$-0.273406\pi$
$104$	−8.44358			−0.827961
$105$		0			0
$106$	15.3503			1.49095
$107$		−	11.1309i		−	1.07607i	−0.842923	−	0.538034i	$-0.819167\pi$
$107$		−	11.1309i		−	1.07607i	0.842923	−	0.538034i	$-0.180833\pi$
$108$		0			0
$109$	−9.58769			−0.918334			−0.459167	−	0.888350i	$-0.651852\pi$
$109$	−9.58769			−0.918334			−0.459167	+	0.888350i	$0.651852\pi$
$110$	14.5623	+	16.4690i	1.38846	+	1.57026i
$111$		0			0
$112$			9.89446i			0.934939i
$113$			0.574515i			0.0540459i	0.999635	+	0.0270229i	$0.00860271\pi$
$113$			0.574515i			0.0540459i	−0.999635	+	0.0270229i	$0.991397\pi$
$114$		0			0
$115$	−9.59991	−	10.8568i	−0.895196	−	1.01241i
$116$	−12.4690			−1.15772
$117$		0			0
$118$		−	16.0181i		−	1.47459i
$119$	−1.08840			−0.0997732
$120$		0			0
$121$	2.50659			0.227872
$122$			4.73084i			0.428310i
$123$		0			0
$124$	27.2628			2.44827
$125$	6.32487	+	9.21933i	0.565713	+	0.824602i
$126$		0			0
$127$		−	4.29455i		−	0.381080i	−0.981679	−	0.190540i	$-0.938976\pi$
$127$		−	4.29455i		−	0.381080i	0.981679	−	0.190540i	$-0.0610239\pi$
$128$			16.5696i			1.46456i
$129$		0			0
$130$	−4.48119	+	3.96239i	−0.393027	+	0.347524i
$131$	0.836381			0.0730749			0.0365375	−	0.999332i	$-0.488367\pi$
$131$	0.836381			0.0730749			0.0365375	+	0.999332i	$0.488367\pi$
$132$		0			0
$133$			1.35026i			0.117083i
$134$	26.4690			2.28657
$135$		0			0
$136$	−11.4010			−0.977632
$137$			14.9380i			1.27624i	0.769939	+	0.638118i	$0.220287\pi$
$137$			14.9380i			1.27624i	−0.769939	+	0.638118i	$0.779713\pi$
$138$		0			0
$139$	8.43866			0.715758			0.357879	−	0.933768i	$-0.383500\pi$
$139$	8.43866			0.715758			0.357879	+	0.933768i	$0.383500\pi$
$140$	6.15633	+	6.96239i	0.520304	+	0.588429i
$141$		0			0
$142$			22.9053i			1.92217i
$143$			3.67513i			0.307330i
$144$		0			0
$145$	−4.05079	+	3.58181i	−0.336399	+	0.297453i
$146$	31.4821			2.60548
$147$		0			0
$148$		−	19.4314i		−	1.59725i
$149$	−11.3503			−0.929850			−0.464925	−	0.885350i	$-0.653919\pi$
$149$	−11.3503			−0.929850			−0.464925	+	0.885350i	$0.653919\pi$
$150$		0			0
$151$	13.9878			1.13831			0.569155	−	0.822230i	$-0.307271\pi$
$151$	13.9878			1.13831			0.569155	+	0.822230i	$0.307271\pi$
$152$			14.1441i			1.14724i
$153$		0			0
$154$	7.92478			0.638597
$155$	8.85685	−	7.83146i	0.711399	−	0.629038i
$156$		0			0
$157$			2.77575i			0.221529i	0.993847	+	0.110764i	$0.0353299\pi$
$157$			2.77575i			0.221529i	−0.993847	+	0.110764i	$0.964670\pi$
$158$		−	6.05079i		−	0.481375i
$159$		0			0
$160$	23.6253	+	26.7186i	1.86774	+	2.11229i
$161$	−5.22425			−0.411729
$162$		0			0
$163$		−	2.23155i		−	0.174788i	−0.996174	−	0.0873942i	$-0.972146\pi$
$163$		−	2.23155i		−	0.174788i	0.996174	−	0.0873942i	$-0.0278540\pi$
$164$	−42.8627			−3.34702
$165$		0			0
$166$	10.2823			0.798064
$167$			15.6932i			1.21438i	0.794557	+	0.607189i	$0.207703\pi$
$167$			15.6932i			1.21438i	−0.794557	+	0.607189i	$0.792297\pi$
$168$		0			0
$169$	−1.00000			−0.0769231
$170$	−6.05079	+	5.35026i	−0.464074	+	0.410346i
$171$		0			0
$172$		−	35.0313i		−	2.67111i
$173$		−	25.5877i		−	1.94540i	−0.232075	−	0.972698i	$-0.574551\pi$
$173$		−	25.5877i		−	1.94540i	0.232075	−	0.972698i	$-0.425449\pi$
$174$		0			0
$175$	4.00000	+	0.493413i	0.302372	+	0.0372985i
$176$	45.1124			3.40047
$177$		0			0
$178$		−	7.42548i		−	0.556564i
$179$	12.1260			0.906340			0.453170	−	0.891424i	$-0.350293\pi$
$179$	12.1260			0.906340			0.453170	+	0.891424i	$0.350293\pi$
$180$		0			0
$181$	−2.73084			−0.202982			−0.101491	−	0.994836i	$-0.532361\pi$
$181$	−2.73084			−0.202982			−0.101491	+	0.994836i	$0.532361\pi$
$182$			2.15633i			0.159837i
$183$		0			0
$184$	−54.7245			−4.03434
$185$	−5.58181	−	6.31265i	−0.410383	−	0.464115i
$186$		0			0
$187$			4.96239i			0.362886i
$188$			16.4690i			1.20112i
$189$		0			0
$190$	6.63752	+	7.50659i	0.481536	+	0.544585i
$191$	−20.6253			−1.49239			−0.746197	−	0.665725i	$-0.768122\pi$
$191$	−20.6253			−1.49239			−0.746197	+	0.665725i	$0.768122\pi$
$192$		0			0
$193$			21.7889i			1.56840i	0.620508	+	0.784200i	$0.286927\pi$
$193$			21.7889i			1.56840i	−0.620508	+	0.784200i	$0.713073\pi$
$194$	−5.01317			−0.359925
$195$		0			0
$196$	−32.7440			−2.33886
$197$		−	2.00000i		−	0.142494i	−0.997459	−	0.0712470i	$-0.977302\pi$
$197$		−	2.00000i		−	0.142494i	0.997459	−	0.0712470i	$-0.0226979\pi$
$198$		0			0
$199$	16.7513			1.18747			0.593734	−	0.804661i	$-0.297653\pi$
$199$	16.7513			1.18747			0.593734	+	0.804661i	$0.297653\pi$
$200$	41.9003	+	5.16854i	2.96280	+	0.365471i
$201$		0			0
$202$			28.0870i			1.97619i
$203$			1.94921i			0.136808i
$204$		0			0
$205$	−13.9248	+	12.3127i	−0.972549	+	0.859953i
$206$	−41.1124			−2.86443
$207$		0			0
$208$			12.2750i			0.851121i
$209$	6.15633			0.425842
$210$		0			0
$211$	−4.90175			−0.337451			−0.168725	−	0.985663i	$-0.553965\pi$
$211$	−4.90175			−0.337451			−0.168725	+	0.985663i	$0.553965\pi$
$212$		−	29.5877i		−	2.03209i
$213$		0			0
$214$	−29.7767			−2.03549
$215$	−10.0630	−	11.3806i	−0.686291	−	0.776149i
$216$		0			0
$217$		−	4.26187i		−	0.289314i
$218$			25.6483i			1.73712i
$219$		0			0
$220$	31.7440	−	28.0689i	2.14018	−	1.89240i
$221$	−1.35026			−0.0908284
$222$		0			0
$223$		−	24.9076i		−	1.66794i	−0.551811	−	0.833969i	$-0.686063\pi$
$223$		−	24.9076i		−	1.66794i	0.551811	−	0.833969i	$-0.313937\pi$
$224$	12.8568			0.859034
$225$		0			0
$226$	1.53690			0.102233
$227$		−	9.95509i		−	0.660743i	−0.943851	−	0.330371i	$-0.892826\pi$
$227$		−	9.95509i		−	0.660743i	0.943851	−	0.330371i	$-0.107174\pi$
$228$		0			0
$229$	−5.35026			−0.353555			−0.176778	−	0.984251i	$-0.556567\pi$
$229$	−5.35026			−0.353555			−0.176778	+	0.984251i	$0.556567\pi$
$230$	−29.0435	+	25.6810i	−1.91507	+	1.69336i
$231$		0			0
$232$			20.4182i			1.34052i
$233$		−	10.7612i		−	0.704987i	−0.935814	−	0.352493i	$-0.885334\pi$
$233$		−	10.7612i		−	0.704987i	0.935814	−	0.352493i	$-0.114666\pi$
$234$		0			0
$235$	4.73084	+	5.35026i	0.308606	+	0.349013i
$236$	−30.8749			−2.00979
$237$		0			0
$238$			2.91160i			0.188731i
$239$	−11.8618			−0.767274			−0.383637	−	0.923484i	$-0.625329\pi$
$239$	−11.8618			−0.767274			−0.383637	+	0.923484i	$0.625329\pi$
$240$		0			0
$241$	−28.6253			−1.84392			−0.921959	−	0.387288i	$-0.873412\pi$
$241$	−28.6253			−1.84392			−0.921959	+	0.387288i	$0.873412\pi$
$242$		−	6.70545i		−	0.431043i
$243$		0			0
$244$	9.11871			0.583766
$245$	−10.6375	+	9.40597i	−0.679606	+	0.600925i
$246$		0			0
$247$			1.67513i			0.106586i
$248$		−	44.6434i		−	2.83486i
$249$		0			0
$250$	24.6629	−	16.9199i	1.55982	−	1.07011i
$251$	19.3865			1.22366			0.611831	−	0.790988i	$-0.290433\pi$
$251$	19.3865			1.22366			0.611831	+	0.790988i	$0.290433\pi$
$252$		0			0
$253$			23.8192i			1.49750i
$254$	−11.4885			−0.720852
$255$		0			0
$256$	8.08840			0.505525
$257$		−	22.8627i		−	1.42614i	−0.701094	−	0.713069i	$-0.747305\pi$
$257$		−	22.8627i		−	1.42614i	0.701094	−	0.713069i	$-0.252695\pi$
$258$		0			0
$259$	−3.03761			−0.188748
$260$	7.63752	+	8.63752i	0.473659	+	0.535676i
$261$		0			0
$262$		−	2.23743i		−	0.138229i
$263$			21.8822i			1.34932i	0.738130	+	0.674658i	$0.235709\pi$
$263$			21.8822i			1.34932i	−0.738130	+	0.674658i	$0.764291\pi$
$264$		0			0
$265$	−8.49929	−	9.61213i	−0.522107	−	0.590468i
$266$	3.61213			0.221474
$267$		0			0
$268$		−	51.0191i		−	3.11648i
$269$	22.7513			1.38717			0.693586	−	0.720374i	$-0.256030\pi$
$269$	22.7513			1.38717			0.693586	+	0.720374i	$0.256030\pi$
$270$		0			0
$271$	0.123638			0.00751049			0.00375525	−	0.999993i	$-0.498805\pi$
$271$	0.123638			0.00751049			0.00375525	+	0.999993i	$0.498805\pi$
$272$			16.5745i			1.00498i
$273$		0			0
$274$	39.9610			2.41413
$275$	2.24965	−	18.2374i	0.135659	−	1.09976i
$276$		0			0
$277$		−	15.3503i		−	0.922308i	−0.887320	−	0.461154i	$-0.847436\pi$
$277$		−	15.3503i		−	0.922308i	0.887320	−	0.461154i	$-0.152564\pi$
$278$		−	22.5745i		−	1.35393i
$279$		0			0
$280$	11.4010	−	10.0811i	0.681343	−	0.602461i
$281$	−13.9248			−0.830683			−0.415341	−	0.909666i	$-0.636338\pi$
$281$	−13.9248			−0.830683			−0.415341	+	0.909666i	$0.636338\pi$
$282$		0			0
$283$		−	20.3815i		−	1.21156i	−0.795634	−	0.605778i	$-0.792862\pi$
$283$		−	20.3815i		−	1.21156i	0.795634	−	0.605778i	$-0.207138\pi$
$284$	44.1500			2.61982
$285$		0			0
$286$	9.83146			0.581346
$287$			6.70052i			0.395519i
$288$		0			0
$289$	15.1768			0.892753
$290$	9.58181	+	10.8364i	0.562663	+	0.636334i
$291$		0			0
$292$		−	60.6820i		−	3.55114i
$293$			5.38058i			0.314337i	0.987572	+	0.157168i	$0.0502365\pi$
$293$			5.38058i			0.314337i	−0.987572	+	0.157168i	$0.949763\pi$
$294$		0			0
$295$	−10.0303	+	8.86907i	−0.583988	+	0.516377i
$296$	−31.8192			−1.84946
$297$		0			0
$298$			30.3634i			1.75891i
$299$	−6.48119			−0.374817
$300$		0			0
$301$	−5.47627			−0.315647
$302$		−	37.4191i		−	2.15323i
$303$		0			0
$304$	20.5623			1.17933
$305$	2.96239	−	2.61942i	0.169626	−	0.149988i
$306$		0			0
$307$		−	19.1695i		−	1.09406i	−0.837113	−	0.547031i	$-0.815758\pi$
$307$		−	19.1695i		−	1.09406i	0.837113	−	0.547031i	$-0.184242\pi$
$308$		−	15.2750i		−	0.870376i
$309$		0			0
$310$	−20.9502	−	23.6932i	−1.18989	−	1.34568i
$311$	25.2506			1.43183			0.715915	−	0.698187i	$-0.246010\pi$
$311$	25.2506			1.43183			0.715915	+	0.698187i	$0.246010\pi$
$312$		0			0
$313$		−	2.81194i		−	0.158940i	−0.996837	−	0.0794702i	$-0.974677\pi$
$313$		−	2.81194i		−	0.158940i	0.996837	−	0.0794702i	$-0.0253229\pi$
$314$	7.42548			0.419044
$315$		0			0
$316$	−11.6629			−0.656090
$317$			23.7685i			1.33497i	0.744624	+	0.667485i	$0.232629\pi$
$317$			23.7685i			1.33497i	−0.744624	+	0.667485i	$0.767371\pi$
$318$		0			0
$319$	8.88717			0.497586
$320$	30.3512	−	26.8373i	1.69668	−	1.50025i
$321$		0			0
$322$			13.9756i			0.778828i
$323$			2.26187i			0.125854i
$324$		0			0
$325$	4.96239	+	0.612127i	0.275264	+	0.0339547i
$326$	−5.96968			−0.330630
$327$		0			0
$328$			70.1886i			3.87551i
$329$	2.57452			0.141938
$330$		0			0
$331$	−11.8011			−0.648649			−0.324325	−	0.945946i	$-0.605137\pi$
$331$	−11.8011			−0.648649			−0.324325	+	0.945946i	$0.605137\pi$
$332$		−	19.8192i		−	1.08772i
$333$		0			0
$334$	41.9814			2.29712
$335$	−14.6556	−	16.5745i	−0.800722	−	0.905563i
$336$		0			0
$337$			16.1114i			0.877645i	0.898574	+	0.438822i	$0.144604\pi$
$337$			16.1114i			0.877645i	−0.898574	+	0.438822i	$0.855396\pi$
$338$			2.67513i			0.145508i
$339$		0			0
$340$	10.3127	+	11.6629i	0.559282	+	0.632510i
$341$	−19.4314			−1.05227
$342$		0			0
$343$			10.7612i			0.581048i
$344$	−57.3644			−3.09288
$345$		0			0
$346$	−68.4504			−3.67992
$347$		−	27.4944i		−	1.47598i	−0.674814	−	0.737988i	$-0.735776\pi$
$347$		−	27.4944i		−	1.47598i	0.674814	−	0.737988i	$-0.264224\pi$
$348$		0			0
$349$	17.6023			0.942228			0.471114	−	0.882072i	$-0.343852\pi$
$349$	17.6023			0.942228			0.471114	+	0.882072i	$0.343852\pi$
$350$	1.31994	−	10.7005i	0.0705540	−	0.571967i
$351$		0			0
$352$		−	58.6190i		−	3.12440i
$353$			15.7685i			0.839270i	0.907693	+	0.419635i	$0.137842\pi$
$353$			15.7685i			0.839270i	−0.907693	+	0.419635i	$0.862158\pi$
$354$		0			0
$355$	14.3430	−	12.6824i	0.761246	−	0.673113i
$356$	−14.3127			−0.758569
$357$		0			0
$358$		−	32.4387i		−	1.71444i
$359$	−14.8242			−0.782389			−0.391195	−	0.920308i	$-0.627938\pi$
$359$	−14.8242			−0.782389			−0.391195	+	0.920308i	$0.627938\pi$
$360$		0			0
$361$	−16.1939			−0.852312
$362$			7.30536i			0.383961i
$363$		0			0
$364$	4.15633			0.217851
$365$	−17.4314	−	19.7137i	−0.912399	−	1.03186i
$366$		0			0
$367$		−	27.0313i		−	1.41102i	−0.708700	−	0.705510i	$-0.750718\pi$
$367$		−	27.0313i		−	1.41102i	0.708700	−	0.705510i	$-0.249282\pi$
$368$			79.5569i			4.14719i
$369$		0			0
$370$	−16.8872	+	14.9321i	−0.877922	+	0.776281i
$371$	−4.62530			−0.240134
$372$		0			0
$373$		−	12.9525i		−	0.670657i	−0.942101	−	0.335329i	$-0.891153\pi$
$373$		−	12.9525i		−	0.670657i	0.942101	−	0.335329i	$-0.108847\pi$
$374$	13.2750			0.686436
$375$		0			0
$376$	26.9683			1.39078
$377$			2.41819i			0.124543i
$378$		0			0
$379$	30.2858			1.55568			0.777840	−	0.628463i	$-0.216316\pi$
$379$	30.2858			1.55568			0.777840	+	0.628463i	$0.216316\pi$
$380$	14.4690	−	12.7938i	0.742243	−	0.656310i
$381$		0			0
$382$			55.1754i			2.82302i
$383$		−	21.0943i		−	1.07787i	−0.842348	−	0.538934i	$-0.818827\pi$
$383$		−	21.0943i		−	1.07787i	0.842348	−	0.538934i	$-0.181173\pi$
$384$		0			0
$385$	−4.38787	−	4.96239i	−0.223627	−	0.252907i
$386$	58.2882			2.96679
$387$		0			0
$388$			9.66291i			0.490560i
$389$	−6.77575			−0.343544			−0.171772	−	0.985137i	$-0.554949\pi$
$389$	−6.77575			−0.343544			−0.171772	+	0.985137i	$0.554949\pi$
$390$		0			0
$391$	−8.75131			−0.442573
$392$			53.6190i			2.70817i
$393$		0			0
$394$	−5.35026			−0.269542
$395$	−3.78892	+	3.35026i	−0.190641	+	0.168570i
$396$		0			0
$397$			10.4690i			0.525423i	0.964874	+	0.262711i	$0.0846167\pi$
$397$			10.4690i			0.525423i	−0.964874	+	0.262711i	$0.915383\pi$
$398$		−	44.8119i		−	2.24622i
$399$		0			0
$400$	7.51388	−	60.9135i	0.375694	−	3.04568i
$401$	−5.01317			−0.250346			−0.125173	−	0.992135i	$-0.539949\pi$
$401$	−5.01317			−0.250346			−0.125173	+	0.992135i	$0.539949\pi$
$402$		0			0
$403$		−	5.28726i		−	0.263377i
$404$	54.1378			2.69345
$405$		0			0
$406$	5.21440			0.258787
$407$			13.8496i			0.686497i
$408$		0			0
$409$	14.3879			0.711435			0.355717	−	0.934594i	$-0.384237\pi$
$409$	14.3879			0.711435			0.355717	+	0.934594i	$0.384237\pi$
$410$	32.9380	+	37.2506i	1.62669	+	1.83968i
$411$		0			0
$412$			79.2443i			3.90408i
$413$			4.82653i			0.237498i
$414$		0			0
$415$	−5.69323	−	6.43866i	−0.279470	−	0.316061i
$416$	15.9502			0.782021
$417$		0			0
$418$		−	16.4690i		−	0.805524i
$419$	17.4617			0.853059			0.426529	−	0.904474i	$-0.359736\pi$
$419$	17.4617			0.853059			0.426529	+	0.904474i	$0.359736\pi$
$420$		0			0
$421$	2.88717			0.140712			0.0703559	−	0.997522i	$-0.477586\pi$
$421$	2.88717			0.140712			0.0703559	+	0.997522i	$0.477586\pi$
$422$			13.1128i			0.638323i
$423$		0			0
$424$	−48.4504			−2.35296
$425$	6.70052	+	0.826531i	0.325023	+	0.0400927i
$426$		0			0
$427$		−	1.42548i		−	0.0689840i
$428$			57.3947i			2.77428i
$429$		0			0
$430$	−30.4445	+	26.9199i	−1.46817	+	1.29819i
$431$	−0.889535			−0.0428474			−0.0214237	−	0.999770i	$-0.506820\pi$
$431$	−0.889535			−0.0428474			−0.0214237	+	0.999770i	$0.506820\pi$
$432$		0			0
$433$			25.2506i			1.21347i	0.794906	+	0.606733i	$0.207520\pi$
$433$			25.2506i			1.21347i	−0.794906	+	0.606733i	$0.792480\pi$
$434$	−11.4010			−0.547268
$435$		0			0
$436$	49.4372			2.36761
$437$			10.8568i			0.519354i
$438$		0			0
$439$	−28.8119			−1.37512			−0.687560	−	0.726128i	$-0.741318\pi$
$439$	−28.8119			−1.37512			−0.687560	+	0.726128i	$0.741318\pi$
$440$	−45.9633	−	51.9814i	−2.19122	−	2.47812i
$441$		0			0
$442$			3.61213i			0.171811i
$443$			36.9805i			1.75700i	0.477746	+	0.878498i	$0.341454\pi$
$443$			36.9805i			1.75700i	−0.477746	+	0.878498i	$0.658546\pi$
$444$		0			0
$445$	−4.64974	+	4.11142i	−0.220419	+	0.194900i
$446$	−66.6312			−3.15508
$447$		0			0
$448$		−	14.6048i		−	0.690013i
$449$	−12.6859			−0.598686			−0.299343	−	0.954146i	$-0.596768\pi$
$449$	−12.6859			−0.598686			−0.299343	+	0.954146i	$0.596768\pi$
$450$		0			0
$451$	30.5501			1.43855
$452$		−	2.96239i		−	0.139339i
$453$		0			0
$454$	−26.6312			−1.24986
$455$	1.35026	−	1.19394i	0.0633012	−	0.0559726i
$456$		0			0
$457$		−	25.0494i		−	1.17176i	−0.810398	−	0.585880i	$-0.800749\pi$
$457$		−	25.0494i		−	1.17176i	0.810398	−	0.585880i	$-0.199251\pi$
$458$			14.3127i			0.668786i
$459$		0			0
$460$	49.5002	+	55.9814i	2.30796	+	2.61015i
$461$	36.8872			1.71801			0.859003	−	0.511970i	$-0.171084\pi$
$461$	36.8872			1.71801			0.859003	+	0.511970i	$0.171084\pi$
$462$		0			0
$463$			39.0191i			1.81337i	0.421809	+	0.906685i	$0.361395\pi$
$463$			39.0191i			1.81337i	−0.421809	+	0.906685i	$0.638605\pi$
$464$	29.6834			1.37802
$465$		0			0
$466$	−28.7875			−1.33356
$467$		−	32.7694i		−	1.51639i	−0.652029	−	0.758194i	$-0.726082\pi$
$467$		−	32.7694i		−	1.51639i	0.652029	−	0.758194i	$-0.273918\pi$
$468$		0			0
$469$	−7.97556			−0.368277
$470$	14.3127	−	12.6556i	0.660193	−	0.583760i
$471$		0			0
$472$			50.5583i			2.32714i
$473$			24.9683i			1.14804i
$474$		0			0
$475$	1.02539	−	8.31265i	0.0470482	−	0.381411i
$476$	5.61213			0.257231
$477$		0			0
$478$			31.7318i			1.45138i
$479$	16.8749			0.771036			0.385518	−	0.922700i	$-0.374023\pi$
$479$	16.8749			0.771036			0.385518	+	0.922700i	$0.374023\pi$
$480$		0			0
$481$	−3.76845			−0.171827
$482$			76.5764i			3.48796i
$483$		0			0
$484$	−12.9248			−0.587490
$485$	2.77575	+	3.13918i	0.126040	+	0.142543i
$486$		0			0
$487$		−	9.24472i		−	0.418918i	−0.977817	−	0.209459i	$-0.932830\pi$
$487$		−	9.24472i		−	0.418918i	0.977817	−	0.209459i	$-0.0671703\pi$
$488$		−	14.9321i		−	0.675943i
$489$		0			0
$490$	25.1622	+	28.4568i	1.13671	+	1.28555i
$491$	25.7499			1.16208			0.581038	−	0.813876i	$-0.302647\pi$
$491$	25.7499			1.16208			0.581038	+	0.813876i	$0.302647\pi$
$492$		0			0
$493$			3.26519i			0.147057i
$494$	4.48119			0.201618
$495$		0			0
$496$	−64.9013			−2.91415
$497$		−	6.90175i		−	0.309586i
$498$		0			0
$499$	27.7015			1.24009			0.620044	−	0.784567i	$-0.287115\pi$
$499$	27.7015			1.24009			0.620044	+	0.784567i	$0.287115\pi$
$500$	−32.6131	−	47.5379i	−1.45850	−	2.12596i
$501$		0			0
$502$		−	51.8613i		−	2.31468i
$503$			2.35519i			0.105013i	0.998621	+	0.0525063i	$0.0167210\pi$
$503$			2.35519i			0.105013i	−0.998621	+	0.0525063i	$0.983279\pi$
$504$		0			0
$505$	17.5877	−	15.5515i	0.782642	−	0.692032i
$506$	63.7196			2.83268
$507$		0			0
$508$			22.1441i			0.982486i
$509$	21.5125			0.953523			0.476762	−	0.879033i	$-0.341810\pi$
$509$	21.5125			0.953523			0.476762	+	0.879033i	$0.341810\pi$
$510$		0			0
$511$	−9.48612			−0.419641
$512$			11.5017i			0.508306i
$513$		0			0
$514$	−61.1608			−2.69769
$515$	22.7635	+	25.7440i	1.00308	+	1.13442i
$516$		0			0
$517$		−	11.7381i		−	0.516243i
$518$			8.12601i			0.357036i
$519$		0			0
$520$	14.1441	−	12.5066i	0.620260	−	0.548450i
$521$	−37.7440			−1.65360			−0.826798	−	0.562499i	$-0.809840\pi$
$521$	−37.7440			−1.65360			−0.826798	+	0.562499i	$0.809840\pi$
$522$		0			0
$523$		−	23.7416i		−	1.03815i	−0.854729	−	0.519075i	$-0.826277\pi$
$523$		−	23.7416i		−	1.03815i	0.854729	−	0.519075i	$-0.173723\pi$
$524$	−4.31265			−0.188399
$525$		0			0
$526$	58.5379			2.55237
$527$		−	7.13918i		−	0.310988i
$528$		0			0
$529$	−19.0059			−0.826343
$530$	−25.7137	+	22.7367i	−1.11693	+	0.987620i
$531$		0			0
$532$		−	6.96239i		−	0.301858i
$533$			8.31265i			0.360061i
$534$		0			0
$535$	16.4871	+	18.6458i	0.712798	+	0.806127i
$536$	−83.5447			−3.60858
$537$		0			0
$538$		−	60.8627i		−	2.62398i
$539$	23.3380			1.00524
$540$		0			0
$541$	13.0376			0.560531			0.280265	−	0.959923i	$-0.409578\pi$
$541$	13.0376			0.560531			0.280265	+	0.959923i	$0.409578\pi$
$542$		−	0.330749i		−	0.0142069i
$543$		0			0
$544$	21.5369			0.923387
$545$	16.0606	−	14.2012i	0.687962	−	0.608314i
$546$		0			0
$547$			8.43041i			0.360458i	0.983625	+	0.180229i	$0.0576839\pi$
$547$			8.43041i			0.360458i	−0.983625	+	0.180229i	$0.942316\pi$
$548$		−	77.0249i		−	3.29034i
$549$		0			0
$550$	−48.7875	−	6.01810i	−2.08031	−	0.256613i
$551$	4.05079			0.172569
$552$		0			0
$553$			1.82321i			0.0775306i
$554$	−41.0640			−1.74464
$555$		0			0
$556$	−43.5125			−1.84534
$557$		−	13.6932i		−	0.580201i	−0.956996	−	0.290100i	$-0.906311\pi$
$557$		−	13.6932i		−	0.580201i	0.956996	−	0.290100i	$-0.0936887\pi$
$558$		0			0
$559$	−6.79384			−0.287349
$560$	−14.6556	−	16.5745i	−0.619313	−	0.700401i
$561$		0			0
$562$			37.2506i			1.57132i
$563$		−	8.86907i		−	0.373787i	−0.982380	−	0.186893i	$-0.940158\pi$
$563$		−	8.86907i		−	0.373787i	0.982380	−	0.186893i	$-0.0598419\pi$
$564$		0			0
$565$	−0.850969	−	0.962389i	−0.0358005	−	0.0404880i
$566$	−54.5233			−2.29178
$567$		0			0
$568$		−	72.2965i		−	3.03349i
$569$	−32.7816			−1.37428			−0.687139	−	0.726526i	$-0.741134\pi$
$569$	−32.7816			−1.37428			−0.687139	+	0.726526i	$0.741134\pi$
$570$		0			0
$571$	40.2882			1.68601			0.843005	−	0.537906i	$-0.180785\pi$
$571$	40.2882			1.68601			0.843005	+	0.537906i	$0.180785\pi$
$572$		−	18.9502i		−	0.792346i
$573$		0			0
$574$	17.9248			0.748166
$575$	32.1622	+	3.96731i	1.34126	+	0.165448i
$576$		0			0
$577$			28.8568i			1.20133i	0.799502	+	0.600663i	$0.205097\pi$
$577$			28.8568i			1.20133i	−0.799502	+	0.600663i	$0.794903\pi$
$578$		−	40.5999i		−	1.68873i
$579$		0			0
$580$	20.8872	−	18.4690i	0.867292	−	0.766882i
$581$	−3.09825			−0.128537
$582$		0			0
$583$			21.0884i			0.873392i
$584$	−99.3679			−4.11187
$585$		0			0
$586$	14.3938			0.594600
$587$		−	41.6786i		−	1.72026i	−0.510074	−	0.860131i	$-0.670382\pi$
$587$		−	41.6786i		−	1.72026i	0.510074	−	0.860131i	$-0.329618\pi$
$588$		0			0
$589$	−8.85685			−0.364940
$590$	23.7259	+	26.8324i	0.976781	+	1.10467i
$591$		0			0
$592$			46.2579i			1.90119i
$593$			22.4993i			0.923935i	0.886897	+	0.461968i	$0.152856\pi$
$593$			22.4993i			0.923935i	−0.886897	+	0.461968i	$0.847144\pi$
$594$		0			0
$595$	1.82321	−	1.61213i	0.0747442	−	0.0660908i
$596$	58.5256			2.39730
$597$		0			0
$598$			17.3380i			0.709005i
$599$	4.15045			0.169583			0.0847913	−	0.996399i	$-0.472978\pi$
$599$	4.15045			0.169583			0.0847913	+	0.996399i	$0.472978\pi$
$600$		0			0
$601$	27.9248			1.13908			0.569538	−	0.821965i	$-0.307122\pi$
$601$	27.9248			1.13908			0.569538	+	0.821965i	$0.307122\pi$
$602$			14.6497i			0.597079i
$603$		0			0
$604$	−72.1255			−2.93475
$605$	−4.19886	+	3.71274i	−0.170708	+	0.150944i
$606$		0			0
$607$			8.19489i			0.332620i	0.986073	+	0.166310i	$0.0531853\pi$
$607$			8.19489i			0.332620i	−0.986073	+	0.166310i	$0.946815\pi$
$608$		−	26.7186i		−	1.08358i
$609$		0			0
$610$	−7.00729	−	7.92478i	−0.283717	−	0.320865i
$611$	3.19394			0.129213
$612$		0			0
$613$		−	33.1392i		−	1.33848i	−0.743047	−	0.669239i	$-0.766620\pi$
$613$		−	33.1392i		−	1.33848i	0.743047	−	0.669239i	$-0.233380\pi$
$614$	−51.2809			−2.06953
$615$		0			0
$616$	−25.0132			−1.00781
$617$			29.0132i			1.16803i	0.811744	+	0.584013i	$0.198518\pi$
$617$			29.0132i			1.16803i	−0.811744	+	0.584013i	$0.801482\pi$
$618$		0			0
$619$	−12.2134			−0.490900			−0.245450	−	0.969409i	$-0.578936\pi$
$619$	−12.2134			−0.490900			−0.245450	+	0.969409i	$0.578936\pi$
$620$	−45.6688	+	40.3815i	−1.83410	+	1.62176i
$621$		0			0
$622$		−	67.5487i		−	2.70845i
$623$			2.23743i			0.0896406i
$624$		0			0
$625$	−24.2506	−	6.07522i	−0.970024	−	0.243009i
$626$	−7.52232			−0.300652
$627$		0			0
$628$		−	14.3127i		−	0.571137i
$629$	−5.08840			−0.202888
$630$		0			0
$631$	−1.22188			−0.0486424			−0.0243212	−	0.999704i	$-0.507742\pi$
$631$	−1.22188			−0.0486424			−0.0243212	+	0.999704i	$0.507742\pi$
$632$			19.0982i			0.759687i
$633$		0			0
$634$	63.5837			2.52523
$635$	6.36107	+	7.19394i	0.252431	+	0.285483i
$636$		0			0
$637$			6.35026i			0.251607i
$638$		−	23.7743i		−	0.941235i
$639$		0			0
$640$	−24.5428	−	27.7562i	−0.970139	−	1.09716i
$641$	22.1016			0.872960			0.436480	−	0.899714i	$-0.356225\pi$
$641$	22.1016			0.872960			0.436480	+	0.899714i	$0.356225\pi$
$642$		0			0
$643$		−	11.6688i		−	0.460172i	−0.973170	−	0.230086i	$-0.926099\pi$
$643$		−	11.6688i		−	0.460172i	0.973170	−	0.230086i	$-0.0739008\pi$
$644$	26.9380			1.06150
$645$		0			0
$646$	6.05079			0.238065
$647$		−	11.9575i		−	0.470096i	−0.971984	−	0.235048i	$-0.924475\pi$
$647$		−	11.9575i		−	0.470096i	0.971984	−	0.235048i	$-0.0755248\pi$
$648$		0			0
$649$	22.0059			0.863806
$650$	1.63752	−	13.2750i	0.0642288	−	0.520690i
$651$		0			0
$652$			11.5066i			0.450633i
$653$		−	10.9986i		−	0.430408i	−0.976569	−	0.215204i	$-0.930958\pi$
$653$		−	10.9986i		−	0.430408i	0.976569	−	0.215204i	$-0.0690416\pi$
$654$		0			0
$655$	−1.40105	+	1.23884i	−0.0547434	+	0.0484056i
$656$	102.038			3.98392
$657$		0			0
$658$		−	6.88717i		−	0.268490i
$659$	−2.63989			−0.102835			−0.0514177	−	0.998677i	$-0.516374\pi$
$659$	−2.63989			−0.102835			−0.0514177	+	0.998677i	$0.516374\pi$
$660$		0			0
$661$	18.3028			0.711896			0.355948	−	0.934506i	$-0.384158\pi$
$661$	18.3028			0.711896			0.355948	+	0.934506i	$0.384158\pi$
$662$			31.5696i			1.22699i
$663$		0			0
$664$	−32.4544			−1.25947
$665$	−2.00000	−	2.26187i	−0.0775567	−	0.0877114i
$666$		0			0
$667$			15.6728i			0.606852i
$668$		−	80.9194i		−	3.13087i
$669$		0			0
$670$	−44.3390	+	39.2057i	−1.71296	+	1.51465i
$671$	−6.49929			−0.250902
$672$		0			0
$673$		−	6.71037i		−	0.258666i	−0.991601	−	0.129333i	$-0.958716\pi$
$673$		−	6.71037i		−	0.258666i	0.991601	−	0.129333i	$-0.0412836\pi$
$674$	43.1002			1.66016
$675$		0			0
$676$	5.15633			0.198320
$677$			1.57593i			0.0605679i	0.999541	+	0.0302840i	$0.00964116\pi$
$677$			1.57593i			0.0605679i	−0.999541	+	0.0302840i	$0.990359\pi$
$678$		0			0
$679$	1.51056			0.0579698
$680$	19.0982	−	16.8872i	0.732384	−	0.647593i
$681$		0			0
$682$			51.9814i			1.99047i
$683$			15.1939i			0.581380i	0.956817	+	0.290690i	$0.0938848\pi$
$683$			15.1939i			0.581380i	−0.956817	+	0.290690i	$0.906115\pi$
$684$		0			0
$685$	−22.1260	−	25.0230i	−0.845391	−	0.956081i
$686$	28.7875			1.09911
$687$		0			0
$688$			83.3947i			3.17939i
$689$	−5.73813			−0.218606
$690$		0			0
$691$	−18.7127			−0.711866			−0.355933	−	0.934511i	$-0.615837\pi$
$691$	−18.7127			−0.711866			−0.355933	+	0.934511i	$0.615837\pi$
$692$			131.938i			5.01555i
$693$		0			0
$694$	−73.5510			−2.79196
$695$	−14.1359	+	12.4993i	−0.536204	+	0.474125i
$696$		0			0
$697$			11.2243i			0.425149i
$698$		−	47.0884i		−	1.78232i
$699$		0			0
$700$	−20.6253	−	2.54420i	−0.779563	−	0.0961617i
$701$	−24.3028			−0.917904			−0.458952	−	0.888461i	$-0.651775\pi$
$701$	−24.3028			−0.917904			−0.458952	+	0.888461i	$0.651775\pi$
$702$		0			0
$703$			6.31265i			0.238086i
$704$	−66.5886			−2.50965
$705$		0			0
$706$	42.1827			1.58757
$707$		−	8.46310i		−	0.318287i
$708$		0			0
$709$	9.66291			0.362898			0.181449	−	0.983400i	$-0.441921\pi$
$709$	9.66291			0.362898			0.181449	+	0.983400i	$0.441921\pi$
$710$	−33.9271	−	38.3693i	−1.27326	−	1.43997i
$711$		0			0
$712$			23.4372i			0.878348i
$713$		−	34.2677i		−	1.28334i
$714$		0			0
$715$	−5.44358	−	6.15633i	−0.203578	−	0.230234i
$716$	−62.5256			−2.33669
$717$		0			0
$718$			39.6566i			1.47997i
$719$	28.4142			1.05967			0.529836	−	0.848100i	$-0.322254\pi$
$719$	28.4142			1.05967			0.529836	+	0.848100i	$0.322254\pi$
$720$		0			0
$721$	12.3879			0.461349
$722$			43.3209i			1.61224i
$723$		0			0
$724$	14.0811			0.523320
$725$	1.48024	−	12.0000i	0.0549747	−	0.445669i
$726$		0			0
$727$		−	34.8545i		−	1.29268i	−0.763049	−	0.646341i	$-0.776299\pi$
$727$		−	34.8545i		−	1.29268i	0.763049	−	0.646341i	$-0.223701\pi$
$728$		−	6.80606i		−	0.252249i
$729$		0			0
$730$	−52.7367	+	46.6312i	−1.95187	+	1.72590i
$731$	−9.17347			−0.339293
$732$		0			0
$733$		−	6.25202i		−	0.230923i	−0.993312	−	0.115462i	$-0.963165\pi$
$733$		−	6.25202i		−	0.230923i	0.993312	−	0.115462i	$-0.0368348\pi$
$734$	−72.3122			−2.66909
$735$		0			0
$736$	103.376			3.81050
$737$			36.3634i			1.33946i
$738$		0			0
$739$	32.0846			1.18025			0.590126	−	0.807311i	$-0.299078\pi$
$739$	32.0846			1.18025			0.590126	+	0.807311i	$0.299078\pi$
$740$	28.7816	+	32.5501i	1.05803	+	1.19656i
$741$		0			0
$742$			12.3733i			0.454238i
$743$		−	30.5442i		−	1.12056i	−0.828304	−	0.560279i	$-0.810694\pi$
$743$		−	30.5442i		−	1.12056i	0.828304	−	0.560279i	$-0.189306\pi$
$744$		0			0
$745$	19.0132	−	16.8119i	0.696589	−	0.615942i
$746$	−34.6497			−1.26862
$747$		0			0
$748$		−	25.5877i		−	0.935579i
$749$	8.97224			0.327838
$750$		0			0
$751$	28.1622			1.02765			0.513827	−	0.857894i	$-0.328227\pi$
$751$	28.1622			1.02765			0.513827	+	0.857894i	$0.328227\pi$
$752$		−	39.2057i		−	1.42968i
$753$		0			0
$754$	6.46898			0.235586
$755$	−23.4314	+	20.7186i	−0.852755	+	0.754028i
$756$		0			0
$757$			35.4109i			1.28703i	0.765433	+	0.643515i	$0.222525\pi$
$757$			35.4109i			1.28703i	−0.765433	+	0.643515i	$0.777475\pi$
$758$		−	81.0186i		−	2.94273i
$759$		0			0
$760$	−20.9502	−	23.6932i	−0.759943	−	0.859444i
$761$	19.2388			0.697407			0.348704	−	0.937233i	$-0.386622\pi$
$761$	19.2388			0.697407			0.348704	+	0.937233i	$0.386622\pi$
$762$		0			0
$763$		−	7.72829i		−	0.279783i
$764$	106.351			3.84764
$765$		0			0
$766$	−56.4299			−2.03890
$767$			5.98778i			0.216206i
$768$		0			0
$769$	−48.9643			−1.76570			−0.882849	−	0.469657i	$-0.844378\pi$
$769$	−48.9643			−1.76570			−0.882849	+	0.469657i	$0.844378\pi$
$770$	−13.2750	+	11.7381i	−0.478399	+	0.423013i
$771$		0			0
$772$		−	112.351i		−	4.04359i
$773$			46.1681i			1.66055i	0.557354	+	0.830275i	$0.311817\pi$
$773$			46.1681i			1.66055i	−0.557354	+	0.830275i	$0.688183\pi$
$774$		0			0
$775$	−3.23647	+	26.2374i	−0.116258	+	0.942476i
$776$	15.8232			0.568020
$777$		0			0
$778$			18.1260i			0.649849i
$779$	13.9248			0.498907
$780$		0			0
$781$	−31.4676			−1.12600
$782$			23.4109i			0.837172i
$783$		0			0
$784$	77.9497			2.78392
$785$	−4.11142	−	4.64974i	−0.146743	−	0.165956i
$786$		0			0
$787$		−	22.6458i		−	0.807234i	−0.914928	−	0.403617i	$-0.867753\pi$
$787$		−	22.6458i		−	0.807234i	0.914928	−	0.403617i	$-0.132247\pi$
$788$			10.3127i			0.367373i
$789$		0			0
$790$	8.96239	+	10.1359i	0.318867	+	0.360618i
$791$	−0.463096			−0.0164658
$792$		0			0
$793$		−	1.76845i		−	0.0627996i
$794$	28.0059			0.993891
$795$		0			0
$796$	−86.3752			−3.06149
$797$		−	8.23743i		−	0.291785i	−0.989300	−	0.145892i	$-0.953395\pi$
$797$		−	8.23743i		−	0.291785i	0.989300	−	0.145892i	$-0.0466053\pi$
$798$		0			0
$799$	4.31265			0.152571
$800$	−79.1509	−	9.76353i	−2.79841	−	0.345193i
$801$		0			0
$802$			13.4109i			0.473555i
$803$			43.2506i			1.52628i
$804$		0			0
$805$	8.75131	−	7.73813i	0.308443	−	0.272733i
$806$	−14.1441			−0.498205
$807$		0			0
$808$		−	88.6516i		−	3.11875i
$809$	44.1319			1.55159			0.775797	−	0.630982i	$-0.217348\pi$
$809$	44.1319			1.55159			0.775797	+	0.630982i	$0.217348\pi$
$810$		0			0
$811$	22.6883			0.796694			0.398347	−	0.917235i	$-0.369584\pi$
$811$	22.6883			0.796694			0.398347	+	0.917235i	$0.369584\pi$
$812$		−	10.0508i		−	0.352713i
$813$		0			0
$814$	37.0494			1.29858
$815$	3.30536	+	3.73813i	0.115782	+	0.130941i
$816$		0			0
$817$			11.3806i			0.398156i
$818$		−	38.4894i		−	1.34575i
$819$		0			0
$820$	71.8007	−	63.4880i	2.50739	−	2.21710i
$821$	50.2736			1.75456			0.877281	−	0.479978i	$-0.159355\pi$
$821$	50.2736			1.75456			0.877281	+	0.479978i	$0.159355\pi$
$822$		0			0
$823$		−	5.13093i		−	0.178853i	−0.995993	−	0.0894265i	$-0.971497\pi$
$823$		−	5.13093i		−	0.178853i	0.995993	−	0.0894265i	$-0.0285034\pi$
$824$	129.764			4.52054
$825$		0			0
$826$	12.9116			0.449252
$827$		−	18.6946i		−	0.650076i	−0.945701	−	0.325038i	$-0.894623\pi$
$827$		−	18.6946i		−	0.650076i	0.945701	−	0.325038i	$-0.105377\pi$
$828$		0			0
$829$	3.44121			0.119518			0.0597591	−	0.998213i	$-0.480967\pi$
$829$	3.44121			0.119518			0.0597591	+	0.998213i	$0.480967\pi$
$830$	−17.2243	+	15.2301i	−0.597863	+	0.528646i
$831$		0			0
$832$		−	18.1187i		−	0.628153i
$833$			8.57452i			0.297089i
$834$		0			0
$835$	−23.2447	−	26.2882i	−0.804417	−	0.909741i
$836$	−31.7440			−1.09789
$837$		0			0
$838$		−	46.7123i		−	1.61365i
$839$	−52.6248			−1.81681			−0.908406	−	0.418090i	$-0.862700\pi$
$839$	−52.6248			−1.81681			−0.908406	+	0.418090i	$0.862700\pi$
$840$		0			0
$841$	−23.1524			−0.798357
$842$		−	7.72355i		−	0.266171i
$843$		0			0
$844$	25.2750			0.870003
$845$	1.67513	−	1.48119i	0.0576263	−	0.0509546i
$846$		0			0
$847$			2.02047i			0.0694241i
$848$			70.4358i			2.41878i
$849$		0			0
$850$	2.21108	−	17.9248i	0.0758394	−	0.614815i
$851$	−24.4241			−0.837246
$852$		0			0
$853$			6.31853i			0.216342i	0.994132	+	0.108171i	$0.0344995\pi$
$853$			6.31853i			0.216342i	−0.994132	+	0.108171i	$0.965501\pi$
$854$	−3.81336			−0.130490
$855$		0			0
$856$	93.9850			3.21234
$857$			0.775746i			0.0264990i	0.999912	+	0.0132495i	$0.00421757\pi$
$857$			0.775746i			0.0264990i	−0.999912	+	0.0132495i	$0.995782\pi$
$858$		0			0
$859$	−3.24869			−0.110844			−0.0554220	−	0.998463i	$-0.517650\pi$
$859$	−3.24869			−0.110844			−0.0554220	+	0.998463i	$0.517650\pi$
$860$	51.8881	+	58.6820i	1.76937	+	2.00104i
$861$		0			0
$862$			2.37962i			0.0810503i
$863$		−	19.9208i		−	0.678112i	−0.940766	−	0.339056i	$-0.889892\pi$
$863$		−	19.9208i		−	0.678112i	0.940766	−	0.339056i	$-0.110108\pi$
$864$		0			0
$865$	37.9003	+	42.8627i	1.28865	+	1.45738i
$866$	67.5487			2.29540
$867$		0			0
$868$			21.9756i			0.745899i
$869$	8.31265			0.281987
$870$		0			0
$871$	−9.89446			−0.335261
$872$		−	80.9544i		−	2.74146i
$873$		0			0
$874$	29.0435			0.982411
$875$	−7.43136	+	5.09825i	−0.251226	+	0.172352i
$876$		0			0
$877$			22.1378i			0.747539i	0.927522	+	0.373770i	$0.121935\pi$
$877$			22.1378i			0.747539i	−0.927522	+	0.373770i	$0.878065\pi$
$878$			77.0757i			2.60118i
$879$		0			0
$880$	−75.5691	+	66.8202i	−2.54743	+	2.25251i
$881$	−2.23155			−0.0751828			−0.0375914	−	0.999293i	$-0.511969\pi$
$881$	−2.23155			−0.0751828			−0.0375914	+	0.999293i	$0.511969\pi$
$882$		0			0
$883$			4.30440i			0.144855i	0.997374	+	0.0724273i	$0.0230745\pi$
$883$			4.30440i			0.144855i	−0.997374	+	0.0724273i	$0.976925\pi$
$884$	6.96239			0.234170
$885$		0			0
$886$	98.9276			3.32354
$887$		−	15.9330i		−	0.534979i	−0.963561	−	0.267489i	$-0.913806\pi$
$887$		−	15.9330i		−	0.534979i	0.963561	−	0.267489i	$-0.0861940\pi$
$888$		0			0
$889$	3.46168			0.116101
$890$	10.9986	+	12.4387i	0.368673	+	0.416945i
$891$		0			0
$892$			128.432i			4.30022i
$893$		−	5.35026i		−	0.179040i
$894$		0			0
$895$	−20.3127	+	17.9610i	−0.678977	+	0.600369i
$896$	−13.3561			−0.446197
$897$		0			0
$898$			33.9365i			1.13248i
$899$	−12.7856			−0.426423
$900$		0			0
$901$	−7.74798			−0.258123
$902$		−	81.7255i		−	2.72116i
$903$		0			0
$904$	−4.85097			−0.161341
$905$	4.57452	−	4.04491i	0.152062	−	0.134457i
$906$		0			0
$907$		−	51.9086i		−	1.72360i	−0.507251	−	0.861798i	$-0.669338\pi$
$907$		−	51.9086i		−	1.72360i	0.507251	−	0.861798i	$-0.330662\pi$
$908$			51.3317i			1.70350i
$909$		0			0
$910$	−3.19394	−	3.61213i	−0.105878	−	0.119741i
$911$	9.67750			0.320630			0.160315	−	0.987066i	$-0.448749\pi$
$911$	9.67750			0.320630			0.160315	+	0.987066i	$0.448749\pi$
$912$		0			0
$913$			14.1260i			0.467503i
$914$	−67.0103			−2.21651
$915$		0			0
$916$	27.5877			0.911523
$917$			0.674176i			0.0222632i
$918$		0			0
$919$	−13.5515			−0.447022			−0.223511	−	0.974701i	$-0.571752\pi$
$919$	−13.5515			−0.447022			−0.223511	+	0.974701i	$0.571752\pi$
$920$	91.6707	−	81.0576i	3.02229	−	2.67239i
$921$		0			0
$922$		−	98.6780i		−	3.24979i
$923$		−	8.56230i		−	0.281831i
$924$		0			0
$925$	18.7005	+	2.30677i	0.614869	+	0.0758462i
$926$	104.381			3.43017
$927$		0			0
$928$		−	38.5705i		−	1.26614i
$929$	−9.44992			−0.310042			−0.155021	−	0.987911i	$-0.549545\pi$
$929$	−9.44992			−0.310042			−0.155021	+	0.987911i	$0.549545\pi$
$930$		0			0
$931$	10.6375			0.348631
$932$			55.4880i			1.81757i
$933$		0			0
$934$	−87.6625			−2.86840
$935$	−7.35026	−	8.31265i	−0.240379	−	0.271853i
$936$		0			0
$937$			16.0409i			0.524035i	0.965063	+	0.262017i	$0.0843877\pi$
$937$			16.0409i			0.524035i	−0.965063	+	0.262017i	$0.915612\pi$
$938$			21.3357i			0.696634i
$939$		0			0
$940$	−24.3938	−	27.5877i	−0.795636	−	0.899811i
$941$	21.6747			0.706574			0.353287	−	0.935515i	$-0.385064\pi$
$941$	21.6747			0.706574			0.353287	+	0.935515i	$0.385064\pi$
$942$		0			0
$943$			53.8759i			1.75444i
$944$	73.5002			2.39223
$945$		0			0
$946$	66.7934			2.17164
$947$			4.63118i			0.150493i	0.997165	+	0.0752466i	$0.0239744\pi$
$947$			4.63118i			0.150493i	−0.997165	+	0.0752466i	$0.976026\pi$
$948$		0			0
$949$	−11.7685			−0.382020
$950$	−22.2374	−	2.74306i	−0.721477	−	0.0889966i
$951$		0			0
$952$		−	9.18997i		−	0.297849i
$953$			26.2981i			0.851878i	0.904752	+	0.425939i	$0.140056\pi$
$953$			26.2981i			0.851878i	−0.904752	+	0.425939i	$0.859944\pi$
$954$		0			0
$955$	34.5501	−	30.5501i	1.11801	−	0.988577i
$956$	61.1632			1.97816
$957$		0			0
$958$		−	45.1427i		−	1.45849i
$959$	−12.0409			−0.388822
$960$		0			0
$961$	−3.04491			−0.0982228
$962$			10.0811i			0.325028i
$963$		0			0
$964$	147.601			4.75392
$965$	−32.2736	−	36.4993i	−1.03892	−	1.17495i
$966$		0			0
$967$		−	11.9405i		−	0.383981i	−0.981397	−	0.191990i	$-0.938506\pi$
$967$		−	11.9405i		−	0.383981i	0.981397	−	0.191990i	$-0.0614942\pi$
$968$			21.1646i			0.680255i
$969$		0			0
$970$	8.39772	−	7.42548i	0.269635	−	0.238418i
$971$	−30.1524			−0.967635			−0.483818	−	0.875169i	$-0.660750\pi$
$971$	−30.1524			−0.967635			−0.483818	+	0.875169i	$0.660750\pi$
$972$		0			0
$973$			6.80209i			0.218065i
$974$	−24.7308			−0.792427
$975$		0			0
$976$	−21.7078			−0.694850
$977$		−	26.9321i		−	0.861633i	−0.902439	−	0.430817i	$-0.858226\pi$
$977$		−	26.9321i		−	0.861633i	0.902439	−	0.430817i	$-0.141774\pi$
$978$		0			0
$979$	10.2012			0.326033
$980$	54.8505	−	48.5002i	1.75214	−	1.54928i
$981$		0			0
$982$		−	68.8843i		−	2.19819i
$983$		−	20.5902i		−	0.656727i	−0.944551	−	0.328363i	$-0.893503\pi$
$983$		−	20.5902i		−	0.656727i	0.944551	−	0.328363i	$-0.106497\pi$
$984$		0			0
$985$	2.96239	+	3.35026i	0.0943895	+	0.106748i
$986$	8.73481			0.278173
$987$		0			0
$988$		−	8.63752i		−	0.274796i
$989$	−44.0322			−1.40014
$990$		0			0
$991$	−48.1378			−1.52915			−0.764573	−	0.644537i	$-0.777050\pi$
$991$	−48.1378			−1.52915			−0.764573	+	0.644537i	$0.777050\pi$
$992$			84.3327i			2.67756i
$993$		0			0
$994$	−18.4631			−0.585614
$995$	−28.0606	+	24.8119i	−0.889582	+	0.786591i
$996$		0			0
$997$			33.4255i			1.05860i	0.848436	+	0.529298i	$0.177545\pi$
$997$			33.4255i			1.05860i	−0.848436	+	0.529298i	$0.822455\pi$
$998$		−	74.1051i		−	2.34576i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	585.2.c.b.469.1		6
3.2	odd	2		65.2.b.a.14.6	yes	6
5.2	odd	4		2925.2.a.bj.1.3		3
5.3	odd	4		2925.2.a.bf.1.1		3
5.4	even	2	inner	585.2.c.b.469.6		6
12.11	even	2		1040.2.d.c.209.3		6
15.2	even	4		325.2.a.j.1.1		3
15.8	even	4		325.2.a.k.1.3		3
15.14	odd	2		65.2.b.a.14.1	✓	6
39.2	even	12		845.2.l.d.654.1		12
39.5	even	4		845.2.d.b.844.6		6
39.8	even	4		845.2.d.a.844.2		6
39.11	even	12		845.2.l.e.654.5		12
39.17	odd	6		845.2.n.g.484.1		12
39.20	even	12		845.2.l.e.699.6		12
39.23	odd	6		845.2.n.g.529.6		12
39.29	odd	6		845.2.n.f.529.1		12
39.32	even	12		845.2.l.d.699.2		12
39.35	odd	6		845.2.n.f.484.6		12
39.38	odd	2		845.2.b.c.339.1		6
60.23	odd	4		5200.2.a.cb.1.3		3
60.47	odd	4		5200.2.a.cj.1.1		3
60.59	even	2		1040.2.d.c.209.4		6
195.29	odd	6		845.2.n.f.529.6		12
195.38	even	4		4225.2.a.ba.1.1		3
195.44	even	4		845.2.d.a.844.1		6
195.59	even	12		845.2.l.d.699.1		12
195.74	odd	6		845.2.n.f.484.1		12
195.77	even	4		4225.2.a.bh.1.3		3
195.89	even	12		845.2.l.d.654.2		12
195.119	even	12		845.2.l.e.654.6		12
195.134	odd	6		845.2.n.g.484.6		12
195.149	even	12		845.2.l.e.699.5		12
195.164	even	4		845.2.d.b.844.5		6
195.179	odd	6		845.2.n.g.529.1		12
195.194	odd	2		845.2.b.c.339.6		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
65.2.b.a.14.1	✓	6	15.14	odd	2
65.2.b.a.14.6	yes	6	3.2	odd	2
325.2.a.j.1.1		3	15.2	even	4
325.2.a.k.1.3		3	15.8	even	4
585.2.c.b.469.1		6	1.1	even	1	trivial
585.2.c.b.469.6		6	5.4	even	2	inner
845.2.b.c.339.1		6	39.38	odd	2
845.2.b.c.339.6		6	195.194	odd	2
845.2.d.a.844.1		6	195.44	even	4
845.2.d.a.844.2		6	39.8	even	4
845.2.d.b.844.5		6	195.164	even	4
845.2.d.b.844.6		6	39.5	even	4
845.2.l.d.654.1		12	39.2	even	12
845.2.l.d.654.2		12	195.89	even	12
845.2.l.d.699.1		12	195.59	even	12
845.2.l.d.699.2		12	39.32	even	12
845.2.l.e.654.5		12	39.11	even	12
845.2.l.e.654.6		12	195.119	even	12
845.2.l.e.699.5		12	195.149	even	12
845.2.l.e.699.6		12	39.20	even	12
845.2.n.f.484.1		12	195.74	odd	6
845.2.n.f.484.6		12	39.35	odd	6
845.2.n.f.529.1		12	39.29	odd	6
845.2.n.f.529.6		12	195.29	odd	6
845.2.n.g.484.1		12	39.17	odd	6
845.2.n.g.484.6		12	195.134	odd	6
845.2.n.g.529.1		12	195.179	odd	6
845.2.n.g.529.6		12	39.23	odd	6
1040.2.d.c.209.3		6	12.11	even	2
1040.2.d.c.209.4		6	60.59	even	2
2925.2.a.bf.1.1		3	5.3	odd	4
2925.2.a.bj.1.3		3	5.2	odd	4
4225.2.a.ba.1.1		3	195.38	even	4
4225.2.a.bh.1.3		3	195.77	even	4
5200.2.a.cb.1.3		3	60.23	odd	4
5200.2.a.cj.1.1		3	60.47	odd	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 585 = 3^{2} \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	585.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-2.67513i q^{2} -5.15633 q^{4} +(-1.67513 + 1.48119i) q^{5} +0.806063i q^{7} +8.44358i q^{8} +O(q^{10})\)	\(q-2.67513i q^{2} -5.15633 q^{4} +(-1.67513 + 1.48119i) q^{5} +0.806063i q^{7} +8.44358i q^{8} +(3.96239 + 4.48119i) q^{10} +3.67513 q^{11} +1.00000i q^{13} +2.15633 q^{14} +12.2750 q^{16} +1.35026i q^{17} +1.67513 q^{19} +(8.63752 - 7.63752i) q^{20} -9.83146i q^{22} +6.48119i q^{23} +(0.612127 - 4.96239i) q^{25} +2.67513 q^{26} -4.15633i q^{28} +2.41819 q^{29} -5.28726 q^{31} -15.9502i q^{32} +3.61213 q^{34} +(-1.19394 - 1.35026i) q^{35} +3.76845i q^{37} -4.48119i q^{38} +(-12.5066 - 14.1441i) q^{40} +8.31265 q^{41} +6.79384i q^{43} -18.9502 q^{44} +17.3380 q^{46} -3.19394i q^{47} +6.35026 q^{49} +(-13.2750 - 1.63752i) q^{50} -5.15633i q^{52} +5.73813i q^{53} +(-6.15633 + 5.44358i) q^{55} -6.80606 q^{56} -6.46898i q^{58} +5.98778 q^{59} -1.76845 q^{61} +14.1441i q^{62} -18.1187 q^{64} +(-1.48119 - 1.67513i) q^{65} +9.89446i q^{67} -6.96239i q^{68} +(-3.61213 + 3.19394i) q^{70} -8.56230 q^{71} +11.7685i q^{73} +10.0811 q^{74} -8.63752 q^{76} +2.96239i q^{77} +2.26187 q^{79} +(-20.5623 + 18.1817i) q^{80} -22.2374i q^{82} +3.84367i q^{83} +(-2.00000 - 2.26187i) q^{85} +18.1744 q^{86} +31.0313i q^{88} +2.77575 q^{89} -0.806063 q^{91} -33.4191i q^{92} -8.54420 q^{94} +(-2.80606 + 2.48119i) q^{95} -1.87399i q^{97} -16.9878i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 10 q^{4}+O(q^{10}) \) 6 * q - 10 * q^4	\( 6 q - 10 q^{4} + 2 q^{10} + 12 q^{11} - 8 q^{14} + 10 q^{16} + 20 q^{20} + 2 q^{25} + 6 q^{26} + 12 q^{29} - 20 q^{31} + 20 q^{34} - 8 q^{35} - 34 q^{40} + 8 q^{41} - 40 q^{44} + 32 q^{46} + 18 q^{49} - 16 q^{50} - 16 q^{55} - 40 q^{56} - 16 q^{59} + 12 q^{61} - 66 q^{64} + 2 q^{65} - 20 q^{70} + 24 q^{71} - 4 q^{74} - 20 q^{76} + 32 q^{79} - 48 q^{80} - 12 q^{85} + 32 q^{86} + 20 q^{89} - 4 q^{91} - 32 q^{94} - 16 q^{95}+O(q^{100}) \) 6 * q - 10 * q^4 + 2 * q^10 + 12 * q^11 - 8 * q^14 + 10 * q^16 + 20 * q^20 + 2 * q^25 + 6 * q^26 + 12 * q^29 - 20 * q^31 + 20 * q^34 - 8 * q^35 - 34 * q^40 + 8 * q^41 - 40 * q^44 + 32 * q^46 + 18 * q^49 - 16 * q^50 - 16 * q^55 - 40 * q^56 - 16 * q^59 + 12 * q^61 - 66 * q^64 + 2 * q^65 - 20 * q^70 + 24 * q^71 - 4 * q^74 - 20 * q^76 + 32 * q^79 - 48 * q^80 - 12 * q^85 + 32 * q^86 + 20 * q^89 - 4 * q^91 - 32 * q^94 - 16 * q^95

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