LMFDB - Embedded newform 2548.2.bb.c.1733.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2548,2,Mod(569,2548)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2548, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 2, 5]))

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

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

chi := DirichletCharacter("2548.569");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2548 = 2^{2} \cdot 7^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2548.bb (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$20.3458824350$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 38x^{14} + 587x^{12} + 4762x^{10} + 21849x^{8} + 56552x^{6} + 76456x^{4} + 42624x^{2} + 2704 $ x^16 + 38x^14 + 587x^12 + 4762x^10 + 21849x^8 + 56552x^6 + 76456x^4 + 42624*x^2 + 2704
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	no (minimal twist has level 364)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			1733.4
Root			$-0.268953i$ of defining polynomial
Character	$\chi$	$=$	2548.1733
Dual form			2548.2.bb.c.569.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.134476 - 0.232920i) q^{3} +(1.17420 - 0.677925i) q^{5} +(1.46383 - 2.53543i) q^{9} +(-2.42763 + 1.40159i) q^{11} +(-0.303042 + 3.59279i) q^{13} +(-0.315805 - 0.182330i) q^{15} -5.81868 q^{17} +(2.75793 + 1.59229i) q^{19} -7.55347 q^{23} +(-1.58083 + 2.73809i) q^{25} -1.59426 q^{27} +(-3.60830 + 6.24977i) q^{29} +(6.96637 + 4.02203i) q^{31} +(0.652918 + 0.376962i) q^{33} +6.95744i q^{37} +(0.877586 - 0.412562i) q^{39} +(-4.38164 - 2.52974i) q^{41} +(3.13427 + 5.42872i) q^{43} -3.96948i q^{45} +(-2.28903 + 1.32157i) q^{47} +(0.782475 + 1.35529i) q^{51} +(5.54434 - 9.60308i) q^{53} +(-1.90035 + 3.29150i) q^{55} -0.856503i q^{57} +6.29558i q^{59} +(6.40404 - 11.0921i) q^{61} +(2.07981 + 4.42410i) q^{65} +(-4.29803 + 2.48147i) q^{67} +(1.01576 + 1.75936i) q^{69} +(-14.2993 + 8.25572i) q^{71} +(13.3672 + 7.71755i) q^{73} +0.850340 q^{75} +(-7.38303 - 12.7878i) q^{79} +(-4.17711 - 7.23496i) q^{81} +9.79310i q^{83} +(-6.83230 + 3.94463i) q^{85} +1.94093 q^{87} -8.36820i q^{89} -2.16348i q^{93} +4.31782 q^{95} +(10.5685 - 6.10170i) q^{97} +8.20678i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 14 q^{9} - 6 q^{11} - 10 q^{13} + 6 q^{15} + 4 q^{17} + 22 q^{25} + 12 q^{27} - 22 q^{29} - 30 q^{31} + 42 q^{33} - 18 q^{39} - 36 q^{41} + 6 q^{43} + 18 q^{47} + 2 q^{51} - 4 q^{53} - 2 q^{55} - 4 q^{61}+ \cdots + 42 q^{97}+O(q^{100}) $ 16 * q - 14 * q^9 - 6 * q^11 - 10 * q^13 + 6 * q^15 + 4 * q^17 + 22 * q^25 + 12 * q^27 - 22 * q^29 - 30 * q^31 + 42 * q^33 - 18 * q^39 - 36 * q^41 + 6 * q^43 + 18 * q^47 + 2 * q^51 - 4 * q^53 - 2 * q^55 - 4 * q^61 + 30 * q^65 - 24 * q^67 + 52 * q^69 + 36 * q^71 + 12 * q^73 - 20 * q^75 - 4 * q^79 + 42 * q^85 + 52 * q^87 + 60 * q^95 + 42 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2548\mathbb{Z}\right)^\times$.

$n$	$197$	$885$	$1275$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{2}{3}\right)$	$1$

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 $

$2$		0			0
$2$		0			0
$3$	−0.134476	−	0.232920i	−0.0776400	−	0.134476i	0.824591	−	0.565729i	$-0.191405\pi$
$3$	−0.134476	−	0.232920i	−0.0776400	−	0.134476i	−0.902231	+	0.431252i	$0.858072\pi$
$4$		0			0
$5$	1.17420	−	0.677925i	0.525119	−	0.303177i	−0.213908	−	0.976854i	$-0.568619\pi$
$5$	1.17420	−	0.677925i	0.525119	−	0.303177i	0.739026	+	0.673676i	$0.235286\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$		0			0
$9$	1.46383	−	2.53543i	0.487944	−	0.845144i
$10$		0			0
$11$	−2.42763	+	1.40159i	−0.731958	+	0.422596i	−0.819138	−	0.573597i	$-0.805548\pi$
$11$	−2.42763	+	1.40159i	−0.731958	+	0.422596i	0.0871803	+	0.996193i	$0.472214\pi$
$12$		0			0
$13$	−0.303042	+	3.59279i	−0.0840488	+	0.996462i
$13$	−0.303042	+	3.59279i	−0.0840488	+	0.996462i
$14$		0			0
$15$	−0.315805	−	0.182330i	−0.0815405	−	0.0470774i
$16$		0			0
$17$	−5.81868			−1.41124			−0.705618	−	0.708592i	$-0.749331\pi$
$17$	−5.81868			−1.41124			−0.705618	+	0.708592i	$0.749331\pi$
$18$		0			0
$19$	2.75793	+	1.59229i	0.632713	+	0.365297i	0.781802	−	0.623527i	$-0.214301\pi$
$19$	2.75793	+	1.59229i	0.632713	+	0.365297i	−0.149089	+	0.988824i	$0.547634\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−7.55347			−1.57501			−0.787504	−	0.616310i	$-0.788627\pi$
$23$	−7.55347			−1.57501			−0.787504	+	0.616310i	$0.788627\pi$
$24$		0			0
$25$	−1.58083	+	2.73809i	−0.316167	+	0.547617i
$26$		0			0
$27$	−1.59426			−0.306816
$28$		0			0
$29$	−3.60830	+	6.24977i	−0.670045	+	1.16055i	0.307845	+	0.951436i	$0.400392\pi$
$29$	−3.60830	+	6.24977i	−0.670045	+	1.16055i	−0.977891	+	0.209116i	$0.932941\pi$
$30$		0			0
$31$	6.96637	+	4.02203i	1.25120	+	0.722379i	0.971347	−	0.237665i	$-0.0763821\pi$
$31$	6.96637	+	4.02203i	1.25120	+	0.722379i	0.279849	+	0.960044i	$0.409715\pi$
$32$		0			0
$33$	0.652918	+	0.376962i	0.113658	+	0.0656207i
$34$		0			0
$35$		0			0
$36$		0			0
$37$			6.95744i			1.14380i	0.820325	+	0.571898i	$0.193793\pi$
$37$			6.95744i			1.14380i	−0.820325	+	0.571898i	$0.806207\pi$
$38$		0			0
$39$	0.877586	−	0.412562i	0.140526	−	0.0660627i
$40$		0			0
$41$	−4.38164	−	2.52974i	−0.684298	−	0.395079i	0.117175	−	0.993111i	$-0.462616\pi$
$41$	−4.38164	−	2.52974i	−0.684298	−	0.395079i	−0.801472	+	0.598032i	$0.795950\pi$
$42$		0			0
$43$	3.13427	+	5.42872i	0.477972	+	0.827872i	0.999681	−	0.0252518i	$-0.00803875\pi$
$43$	3.13427	+	5.42872i	0.477972	+	0.827872i	−0.521709	+	0.853123i	$0.674705\pi$
$44$		0			0
$45$		−	3.96948i		−	0.591734i
$46$		0			0
$47$	−2.28903	+	1.32157i	−0.333890	+	0.192771i	−0.657567	−	0.753396i	$-0.728414\pi$
$47$	−2.28903	+	1.32157i	−0.333890	+	0.192771i	0.323677	+	0.946168i	$0.395081\pi$
$48$		0			0
$49$		0			0
$50$		0			0
$51$	0.782475	+	1.35529i	0.109568	+	0.189778i
$52$		0			0
$53$	5.54434	−	9.60308i	0.761574	−	1.31908i	−0.180466	−	0.983581i	$-0.557760\pi$
$53$	5.54434	−	9.60308i	0.761574	−	1.31908i	0.942039	−	0.335503i	$-0.108906\pi$
$54$		0			0
$55$	−1.90035	+	3.29150i	−0.256243	+	0.443826i
$56$		0			0
$57$		−	0.856503i		−	0.113447i
$58$		0			0
$59$			6.29558i			0.819614i	0.912172	+	0.409807i	$0.134404\pi$
$59$			6.29558i			0.819614i	−0.912172	+	0.409807i	$0.865596\pi$
$60$		0			0
$61$	6.40404	−	11.0921i	0.819953	−	1.42020i	−0.0857630	−	0.996316i	$-0.527333\pi$
$61$	6.40404	−	11.0921i	0.819953	−	1.42020i	0.905716	−	0.423885i	$-0.139334\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	2.07981	+	4.42410i	0.257969	+	0.548742i
$66$		0			0
$67$	−4.29803	+	2.48147i	−0.525088	+	0.303160i	−0.739014	−	0.673690i	$-0.764708\pi$
$67$	−4.29803	+	2.48147i	−0.525088	+	0.303160i	0.213926	+	0.976850i	$0.431375\pi$
$68$		0			0
$69$	1.01576	+	1.75936i	0.122284	+	0.211801i
$70$		0			0
$71$	−14.2993	+	8.25572i	−1.69702	+	0.979773i	−0.748453	+	0.663188i	$0.769203\pi$
$71$	−14.2993	+	8.25572i	−1.69702	+	0.979773i	−0.948564	+	0.316586i	$0.897464\pi$
$72$		0			0
$73$	13.3672	+	7.71755i	1.56451	+	0.903271i	0.996791	+	0.0800494i	$0.0255078\pi$
$73$	13.3672	+	7.71755i	1.56451	+	0.903271i	0.567720	+	0.823222i	$0.307826\pi$
$74$		0			0
$75$	0.850340			0.0981888
$76$		0			0
$77$		0			0
$78$		0			0
$79$	−7.38303	−	12.7878i	−0.830656	−	1.43874i	−0.897519	−	0.440976i	$-0.854632\pi$
$79$	−7.38303	−	12.7878i	−0.830656	−	1.43874i	0.0668627	−	0.997762i	$-0.478701\pi$
$80$		0			0
$81$	−4.17711	−	7.23496i	−0.464123	−	0.803884i
$82$		0			0
$83$			9.79310i			1.07493i	0.843285	+	0.537466i	$0.180618\pi$
$83$			9.79310i			1.07493i	−0.843285	+	0.537466i	$0.819382\pi$
$84$		0			0
$85$	−6.83230	+	3.94463i	−0.741067	+	0.427855i
$86$		0			0
$87$	1.94093			0.208089
$88$		0			0
$89$		−	8.36820i		−	0.887027i	−0.896268	−	0.443513i	$-0.853732\pi$
$89$		−	8.36820i		−	0.887027i	0.896268	−	0.443513i	$-0.146268\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$		−	2.16348i		−	0.224342i
$94$		0			0
$95$	4.31782			0.442999
$96$		0			0
$97$	10.5685	−	6.10170i	1.07306	−	0.619534i	0.144047	−	0.989571i	$-0.453988\pi$
$97$	10.5685	−	6.10170i	1.07306	−	0.619534i	0.929017	+	0.370037i	$0.120655\pi$
$98$		0			0
$99$			8.20678i			0.824813i
$100$		0			0
$101$	1.21143	+	2.09825i	0.120541	+	0.208784i	0.919981	−	0.391962i	$-0.128204\pi$
$101$	1.21143	+	2.09825i	0.120541	+	0.208784i	−0.799440	+	0.600746i	$0.794870\pi$
$102$		0			0
$103$	7.24547	+	12.5495i	0.713917	+	1.23654i	0.963376	+	0.268155i	$0.0864141\pi$
$103$	7.24547	+	12.5495i	0.713917	+	1.23654i	−0.249458	+	0.968386i	$0.580253\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	6.48741			0.627161			0.313581	−	0.949562i	$-0.398471\pi$
$107$	6.48741			0.627161			0.313581	+	0.949562i	$0.398471\pi$
$108$		0			0
$109$	2.54304	+	1.46822i	0.243579	+	0.140630i	0.616820	−	0.787104i	$-0.288420\pi$
$109$	2.54304	+	1.46822i	0.243579	+	0.140630i	−0.373242	+	0.927734i	$0.621754\pi$
$110$		0			0
$111$	1.62053	−	0.935612i	0.153814	−	0.0888044i
$112$		0			0
$113$	1.66909	+	2.89095i	0.157015	+	0.271957i	0.933791	−	0.357819i	$-0.116480\pi$
$113$	1.66909	+	2.89095i	0.157015	+	0.271957i	−0.776776	+	0.629777i	$0.783146\pi$
$114$		0			0
$115$	−8.86929	+	5.12069i	−0.827066	+	0.477507i
$116$		0			0
$117$	8.66568	+	6.02759i	0.801142	+	0.557251i
$118$		0			0
$119$		0			0
$120$		0			0
$121$	−1.57108	+	2.72119i	−0.142825	+	0.247381i
$122$		0			0
$123$			1.36076i			0.122696i
$124$		0			0
$125$			11.0660i			0.989773i
$126$		0			0
$127$	−6.27512	+	10.8688i	−0.556827	+	0.964452i	0.440932	+	0.897540i	$0.354648\pi$
$127$	−6.27512	+	10.8688i	−0.556827	+	0.964452i	−0.997759	+	0.0669115i	$0.978685\pi$
$128$		0			0
$129$	0.842971	−	1.46007i	0.0742195	−	0.128552i
$130$		0			0
$131$	0.630004	+	1.09120i	0.0550437	+	0.0953385i	0.892234	−	0.451573i	$-0.149137\pi$
$131$	0.630004	+	1.09120i	0.0550437	+	0.0953385i	−0.837191	+	0.546911i	$0.815804\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$	−1.87199	+	1.08079i	−0.161115	+	0.0930197i
$136$		0			0
$137$		−	8.32302i		−	0.711083i	−0.934660	−	0.355542i	$-0.884296\pi$
$137$		−	8.32302i		−	0.711083i	0.934660	−	0.355542i	$-0.115704\pi$
$138$		0			0
$139$	−2.89438	−	5.01322i	−0.245498	−	0.425216i	0.716773	−	0.697306i	$-0.245618\pi$
$139$	−2.89438	−	5.01322i	−0.245498	−	0.425216i	−0.962272	+	0.272091i	$0.912285\pi$
$140$		0			0
$141$	0.615642	+	0.355441i	0.0518464	+	0.0299335i
$142$		0			0
$143$	−4.29996	−	9.14671i	−0.359580	−	0.764886i
$144$		0			0
$145$			9.78464i			0.812570i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−12.3009	−	7.10193i	−1.00773	−	0.581812i	−0.0972028	−	0.995265i	$-0.530990\pi$
$149$	−12.3009	−	7.10193i	−1.00773	−	0.581812i	−0.910526	+	0.413452i	$0.864323\pi$
$150$		0			0
$151$	−9.65700	−	5.57547i	−0.785875	−	0.453725i	0.0526332	−	0.998614i	$-0.483239\pi$
$151$	−9.65700	−	5.57547i	−0.785875	−	0.453725i	−0.838508	+	0.544889i	$0.816572\pi$
$152$		0			0
$153$	−8.51757	+	14.7529i	−0.688605	+	1.19270i
$154$		0			0
$155$	10.9066			0.876036
$156$		0			0
$157$	2.02375	−	3.50523i	0.161513	−	0.279748i	−0.773899	−	0.633309i	$-0.781696\pi$
$157$	2.02375	−	3.50523i	0.161513	−	0.279748i	0.935411	+	0.353561i	$0.115029\pi$
$158$		0			0
$159$	−2.98233			−0.236514
$160$		0			0
$161$		0			0
$162$		0			0
$163$	4.56675	+	2.63661i	0.357695	+	0.206515i	0.668069	−	0.744099i	$-0.267121\pi$
$163$	4.56675	+	2.63661i	0.357695	+	0.206515i	−0.310374	+	0.950615i	$0.600454\pi$
$164$		0			0
$165$	1.02221			0.0795789
$166$		0			0
$167$	4.63307	+	2.67491i	0.358518	+	0.206990i	0.668430	−	0.743775i	$-0.266966\pi$
$167$	4.63307	+	2.67491i	0.358518	+	0.206990i	−0.309912	+	0.950765i	$0.600300\pi$
$168$		0			0
$169$	−12.8163	−	2.17754i	−0.985872	−	0.167503i
$170$		0			0
$171$	8.07429	−	4.66170i	0.617457	−	0.356489i
$172$		0			0
$173$	4.87155	−	8.43777i	0.370377	−	0.641511i	−0.619247	−	0.785197i	$-0.712562\pi$
$173$	4.87155	−	8.43777i	0.370377	−	0.641511i	0.989623	+	0.143685i	$0.0458952\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	1.46637	−	0.846607i	0.110219	−	0.0636349i
$178$		0			0
$179$	5.70263	+	9.87724i	0.426234	+	0.738259i	0.996535	−	0.0831767i	$-0.0265066\pi$
$179$	5.70263	+	9.87724i	0.426234	+	0.738259i	−0.570301	+	0.821436i	$0.693173\pi$
$180$		0			0
$181$	−25.4727			−1.89337			−0.946685	−	0.322160i	$-0.895591\pi$
$181$	−25.4727			−1.89337			−0.946685	+	0.322160i	$0.895591\pi$
$182$		0			0
$183$	−3.44477			−0.254645
$184$		0			0
$185$	4.71663	+	8.16943i	0.346773	+	0.600629i
$186$		0			0
$187$	14.1256	−	8.15541i	1.03297	−	0.596383i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−8.18905	+	14.1838i	−0.592539	+	1.02631i	0.401351	+	0.915924i	$0.368541\pi$
$191$	−8.18905	+	14.1838i	−0.592539	+	1.02631i	−0.993889	+	0.110382i	$0.964792\pi$
$192$		0			0
$193$	−8.28132	+	4.78122i	−0.596103	+	0.344160i	−0.767507	−	0.641041i	$-0.778503\pi$
$193$	−8.28132	+	4.78122i	−0.596103	+	0.344160i	0.171404	+	0.985201i	$0.445170\pi$
$194$		0			0
$195$	0.750776	−	1.07937i	0.0537642	−	0.0772951i
$196$		0			0
$197$	2.60716	+	1.50525i	0.185753	+	0.107244i	0.589993	−	0.807409i	$-0.299131\pi$
$197$	2.60716	+	1.50525i	0.185753	+	0.107244i	−0.404240	+	0.914653i	$0.632464\pi$
$198$		0			0
$199$	−4.61969			−0.327481			−0.163741	−	0.986503i	$-0.552356\pi$
$199$	−4.61969			−0.327481			−0.163741	+	0.986503i	$0.552356\pi$
$200$		0			0
$201$	1.15597	+	0.667399i	0.0815357	+	0.0470747i
$202$		0			0
$203$		0			0
$204$		0			0
$205$	−6.85991			−0.479117
$206$		0			0
$207$	−11.0570	+	19.1513i	−0.768516	+	1.33111i
$208$		0			0
$209$	−8.92697			−0.617492
$210$		0			0
$211$	−1.16932	+	2.02533i	−0.0804995	+	0.139429i	−0.903465	−	0.428663i	$-0.858985\pi$
$211$	−1.16932	+	2.02533i	−0.0804995	+	0.139429i	0.822965	+	0.568092i	$0.192318\pi$
$212$		0			0
$213$	3.84584	+	2.22040i	0.263513	+	0.152139i
$214$		0			0
$215$	7.36053	+	4.24960i	0.501984	+	0.289821i
$216$		0			0
$217$		0			0
$218$		0			0
$219$		−	4.15132i		−	0.280520i
$220$		0			0
$221$	1.76331	−	20.9053i	0.118613	−	1.40624i
$222$		0			0
$223$	4.21429	+	2.43312i	0.282210	+	0.162934i	0.634423	−	0.772986i	$-0.281238\pi$
$223$	4.21429	+	2.43312i	0.282210	+	0.162934i	−0.352214	+	0.935920i	$0.614571\pi$
$224$		0			0
$225$	4.62815	+	8.01620i	0.308544	+	0.534413i
$226$		0			0
$227$			28.0796i			1.86371i	0.362832	+	0.931855i	$0.381810\pi$
$227$			28.0796i			1.86371i	−0.362832	+	0.931855i	$0.618190\pi$
$228$		0			0
$229$	0.155261	−	0.0896399i	0.0102599	−	0.00592357i	−0.494861	−	0.868972i	$-0.664781\pi$
$229$	0.155261	−	0.0896399i	0.0102599	−	0.00592357i	0.505121	+	0.863048i	$0.331448\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−7.56918	−	13.1102i	−0.495873	−	0.858878i	0.504115	−	0.863636i	$-0.331819\pi$
$233$	−7.56918	−	13.1102i	−0.495873	−	0.858878i	−0.999989	+	0.00475858i	$0.998485\pi$
$234$		0			0
$235$	−1.79186	+	3.10358i	−0.116888	+	0.202456i
$236$		0			0
$237$	−1.98569	+	3.43931i	−0.128984	+	0.223407i
$238$		0			0
$239$		−	12.8703i		−	0.832512i	−0.909247	−	0.416256i	$-0.863342\pi$
$239$		−	12.8703i		−	0.832512i	0.909247	−	0.416256i	$-0.136658\pi$
$240$		0			0
$241$		−	9.83172i		−	0.633317i	−0.948540	−	0.316659i	$-0.897439\pi$
$241$		−	9.83172i		−	0.633317i	0.948540	−	0.316659i	$-0.102561\pi$
$242$		0			0
$243$	−3.51484	+	6.08788i	−0.225477	+	0.390538i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	−6.55654	+	9.42614i	−0.417183	+	0.599771i
$248$		0			0
$249$	2.28101	−	1.31694i	0.144553	−	0.0834578i
$250$		0			0
$251$	8.66099	+	15.0013i	0.546677	+	0.946872i	0.998499	+	0.0547641i	$0.0174407\pi$
$251$	8.66099	+	15.0013i	0.546677	+	0.946872i	−0.451823	+	0.892108i	$0.649226\pi$
$252$		0			0
$253$	18.3370	−	10.5869i	1.15284	−	0.665592i
$254$		0			0
$255$	1.83757	+	1.06092i	0.115073	+	0.0664374i
$256$		0			0
$257$	−10.7060			−0.667824			−0.333912	−	0.942604i	$-0.608369\pi$
$257$	−10.7060			−0.667824			−0.333912	+	0.942604i	$0.608369\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$	10.5639	+	18.2972i	0.653889	+	1.13257i
$262$		0			0
$263$	7.03484	+	12.1847i	0.433787	+	0.751341i	0.997196	−	0.0748372i	$-0.0238437\pi$
$263$	7.03484	+	12.1847i	0.433787	+	0.751341i	−0.563409	+	0.826178i	$0.690510\pi$
$264$		0			0
$265$		−	15.0346i		−	0.923567i
$266$		0			0
$267$	−1.94912	+	1.12533i	−0.119284	+	0.0688688i
$268$		0			0
$269$	0.544023			0.0331697			0.0165848	−	0.999862i	$-0.494721\pi$
$269$	0.544023			0.0331697			0.0165848	+	0.999862i	$0.494721\pi$
$270$		0			0
$271$		−	0.741214i		−	0.0450256i	−0.999747	−	0.0225128i	$-0.992833\pi$
$271$		−	0.741214i		−	0.0450256i	0.999747	−	0.0225128i	$-0.00716665\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$		−	8.86274i		−	0.534443i
$276$		0			0
$277$	14.1335			0.849200			0.424600	−	0.905381i	$-0.360415\pi$
$277$	14.1335			0.849200			0.424600	+	0.905381i	$0.360415\pi$
$278$		0			0
$279$	20.3952	−	11.7752i	1.22103	−	0.704961i
$280$		0			0
$281$			25.8051i			1.53940i	0.638404	+	0.769702i	$0.279595\pi$
$281$			25.8051i			1.53940i	−0.638404	+	0.769702i	$0.720405\pi$
$282$		0			0
$283$	−13.6409	−	23.6267i	−0.810865	−	1.40446i	−0.912259	−	0.409613i	$-0.865664\pi$
$283$	−13.6409	−	23.6267i	−0.810865	−	1.40446i	0.101394	−	0.994846i	$-0.467670\pi$
$284$		0			0
$285$	−0.580645	−	1.00571i	−0.0343944	−	0.0595729i
$286$		0			0
$287$		0			0
$288$		0			0
$289$	16.8570			0.991589
$290$		0			0
$291$	−2.84242	−	1.64107i	−0.166625	−	0.0962013i
$292$		0			0
$293$	1.50010	−	0.866083i	0.0876367	−	0.0505971i	−0.455541	−	0.890215i	$-0.650554\pi$
$293$	1.50010	−	0.866083i	0.0876367	−	0.0505971i	0.543178	+	0.839618i	$0.317221\pi$
$294$		0			0
$295$	4.26793	+	7.39227i	0.248489	+	0.430395i
$296$		0			0
$297$	3.87028	−	2.23451i	0.224576	−	0.129659i
$298$		0			0
$299$	2.28902	−	27.1381i	0.132378	−	1.56943i
$300$		0			0
$301$		0			0
$302$		0			0
$303$	0.325817	−	0.564331i	0.0187177	−	0.0324200i
$304$		0			0
$305$		−	17.3658i		−	0.994365i
$306$		0			0
$307$		−	21.4365i		−	1.22345i	−0.791072	−	0.611723i	$-0.790477\pi$
$307$		−	21.4365i		−	1.22345i	0.791072	−	0.611723i	$-0.209523\pi$
$308$		0			0
$309$	1.94869	−	3.37523i	0.110857	−	0.192010i
$310$		0			0
$311$	−13.6362	+	23.6186i	−0.773237	+	1.33929i	0.162543	+	0.986701i	$0.448030\pi$
$311$	−13.6362	+	23.6186i	−0.773237	+	1.33929i	−0.935780	+	0.352584i	$0.885303\pi$
$312$		0			0
$313$	3.64110	+	6.30658i	0.205807	+	0.356469i	0.950390	−	0.311062i	$-0.100685\pi$
$313$	3.64110	+	6.30658i	0.205807	+	0.356469i	−0.744582	+	0.667531i	$0.767351\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−2.20695	+	1.27418i	−0.123954	+	0.0715651i	−0.560695	−	0.828022i	$-0.689466\pi$
$317$	−2.20695	+	1.27418i	−0.123954	+	0.0715651i	0.436741	+	0.899587i	$0.356133\pi$
$318$		0			0
$319$		−	20.2295i		−	1.13263i
$320$		0			0
$321$	−0.872404	−	1.51105i	−0.0486928	−	0.0843384i
$322$		0			0
$323$	−16.0475	−	9.26503i	−0.892907	−	0.515520i
$324$		0			0
$325$	−9.35832	−	6.50937i	−0.519106	−	0.361075i
$326$		0			0
$327$		−	0.789766i		−	0.0436741i
$328$		0			0
$329$		0			0
$330$		0			0
$331$	−0.169450	−	0.0978320i	−0.00931381	−	0.00537733i	0.495336	−	0.868702i	$-0.335045\pi$
$331$	−0.169450	−	0.0978320i	−0.00931381	−	0.00537733i	−0.504650	+	0.863324i	$0.668378\pi$
$332$		0			0
$333$	17.6401	+	10.1845i	0.966672	+	0.558109i
$334$		0			0
$335$	−3.36450	+	5.82749i	−0.183822	+	0.318390i
$336$		0			0
$337$	2.00900			0.109437			0.0547185	−	0.998502i	$-0.482574\pi$
$337$	2.00900			0.109437			0.0547185	+	0.998502i	$0.482574\pi$
$338$		0			0
$339$	0.448906	−	0.777529i	0.0243813	−	0.0422296i
$340$		0			0
$341$	−22.5490			−1.22110
$342$		0			0
$343$		0			0
$344$		0			0
$345$	2.38542	+	1.37722i	0.128427	+	0.0741473i
$346$		0			0
$347$	4.54901			0.244204			0.122102	−	0.992518i	$-0.461037\pi$
$347$	4.54901			0.244204			0.122102	+	0.992518i	$0.461037\pi$
$348$		0			0
$349$	−4.65700	−	2.68872i	−0.249284	−	0.143924i	0.370153	−	0.928971i	$-0.379305\pi$
$349$	−4.65700	−	2.68872i	−0.249284	−	0.143924i	−0.619436	+	0.785047i	$0.712639\pi$
$350$		0			0
$351$	0.483129	−	5.72786i	0.0257875	−	0.305730i
$352$		0			0
$353$	7.10223	−	4.10047i	0.378013	−	0.218246i	−0.298940	−	0.954272i	$-0.596633\pi$
$353$	7.10223	−	4.10047i	0.378013	−	0.218246i	0.676954	+	0.736026i	$0.263300\pi$
$354$		0			0
$355$	−11.1935	+	19.3877i	−0.594090	+	1.02899i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	27.5105	−	15.8832i	1.45195	−	0.838284i	0.453359	−	0.891328i	$-0.350226\pi$
$359$	27.5105	−	15.8832i	1.45195	−	0.838284i	0.998592	+	0.0530438i	$0.0168923\pi$
$360$		0			0
$361$	−4.42921	−	7.67162i	−0.233117	−	0.403770i
$362$		0			0
$363$	0.845093			0.0443559
$364$		0			0
$365$	20.9277			1.09541
$366$		0			0
$367$	8.66870	+	15.0146i	0.452502	+	0.783757i	0.998541	−	0.0540031i	$-0.0171981\pi$
$367$	8.66870	+	15.0146i	0.452502	+	0.783757i	−0.546038	+	0.837760i	$0.683865\pi$
$368$		0			0
$369$	−12.8280	+	7.40624i	−0.667798	+	0.385553i
$370$		0			0
$371$		0			0
$372$		0			0
$373$	−8.04814	+	13.9398i	−0.416717	+	0.721775i	−0.995607	−	0.0936306i	$-0.970153\pi$
$373$	−8.04814	+	13.9398i	−0.416717	+	0.721775i	0.578890	+	0.815406i	$0.303486\pi$
$374$		0			0
$375$	2.57749	−	1.48812i	0.133101	−	0.0768460i
$376$		0			0
$377$	−21.3607	−	14.8578i	−1.10013	−	0.765218i
$378$		0			0
$379$	−15.2907	−	8.82811i	−0.785432	−	0.453470i	0.0529197	−	0.998599i	$-0.483147\pi$
$379$	−15.2907	−	8.82811i	−0.785432	−	0.453470i	−0.838352	+	0.545129i	$0.816481\pi$
$380$		0			0
$381$	3.37542			0.172928
$382$		0			0
$383$	7.12262	+	4.11225i	0.363949	+	0.210126i	0.670812	−	0.741628i	$-0.265946\pi$
$383$	7.12262	+	4.11225i	0.363949	+	0.210126i	−0.306863	+	0.951754i	$0.599279\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	18.3522			0.932894
$388$		0			0
$389$	−7.58442	+	13.1366i	−0.384545	+	0.666052i	−0.991706	−	0.128527i	$-0.958975\pi$
$389$	−7.58442	+	13.1366i	−0.384545	+	0.666052i	0.607161	+	0.794579i	$0.292308\pi$
$390$		0			0
$391$	43.9512			2.22271
$392$		0			0
$393$	0.169441	−	0.293481i	0.00854719	−	0.0148042i
$394$		0			0
$395$	−17.3383	−	10.0103i	−0.872386	−	0.503672i
$396$		0			0
$397$	−24.5139	−	14.1531i	−1.23032	−	0.710325i	−0.263223	−	0.964735i	$-0.584785\pi$
$397$	−24.5139	−	14.1531i	−1.23032	−	0.710325i	−0.967096	+	0.254410i	$0.918119\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$		−	17.1192i		−	0.854894i	−0.904040	−	0.427447i	$-0.859413\pi$
$401$		−	17.1192i		−	0.854894i	0.904040	−	0.427447i	$-0.140587\pi$
$402$		0			0
$403$	−16.5614	+	23.8099i	−0.824984	+	1.18605i
$404$		0			0
$405$	−9.80952	−	5.66353i	−0.487439	−	0.281423i
$406$		0			0
$407$	−9.75149	−	16.8901i	−0.483364	−	0.837210i
$408$		0			0
$409$		−	11.3400i		−	0.560726i	−0.959894	−	0.280363i	$-0.909545\pi$
$409$		−	11.3400i		−	0.560726i	0.959894	−	0.280363i	$-0.0904549\pi$
$410$		0			0
$411$	−1.93860	+	1.11925i	−0.0956240	+	0.0552085i
$412$		0			0
$413$		0			0
$414$		0			0
$415$	6.63899	+	11.4991i	0.325895	+	0.564467i
$416$		0			0
$417$	−0.778453	+	1.34832i	−0.0381210	+	0.0660275i
$418$		0			0
$419$	0.0694276	−	0.120252i	0.00339176	−	0.00587470i	−0.864325	−	0.502934i	$-0.832254\pi$
$419$	0.0694276	−	0.120252i	0.00339176	−	0.00587470i	0.867716	+	0.497060i	$0.165587\pi$
$420$		0			0
$421$		−	24.3258i		−	1.18557i	−0.805362	−	0.592783i	$-0.798029\pi$
$421$		−	24.3258i		−	1.18557i	0.805362	−	0.592783i	$-0.201971\pi$
$422$		0			0
$423$			7.73824i			0.376246i
$424$		0			0
$425$	9.19837	−	15.9320i	0.446186	−	0.772818i
$426$		0			0
$427$		0			0
$428$		0			0
$429$	−1.55221	+	2.23156i	−0.0749414	+	0.107741i
$430$		0			0
$431$	−24.9349	+	14.3962i	−1.20107	+	0.693440i	−0.960794	−	0.277263i	$-0.910573\pi$
$431$	−24.9349	+	14.3962i	−1.20107	+	0.693440i	−0.240280	+	0.970704i	$0.577239\pi$
$432$		0			0
$433$	12.6367	+	21.8873i	0.607279	+	1.05184i	0.991687	+	0.128675i	$0.0410723\pi$
$433$	12.6367	+	21.8873i	0.607279	+	1.05184i	−0.384408	+	0.923163i	$0.625594\pi$
$434$		0			0
$435$	2.27904	−	1.31580i	0.109272	−	0.0630880i
$436$		0			0
$437$	−20.8319	−	12.0273i	−0.996527	−	0.575345i
$438$		0			0
$439$	6.03023			0.287807			0.143904	−	0.989592i	$-0.454034\pi$
$439$	6.03023			0.287807			0.143904	+	0.989592i	$0.454034\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−11.7494	−	20.3505i	−0.558230	−	0.966883i	−0.997644	−	0.0685983i	$-0.978147\pi$
$443$	−11.7494	−	20.3505i	−0.558230	−	0.966883i	0.439414	−	0.898285i	$-0.355186\pi$
$444$		0			0
$445$	−5.67301	−	9.82594i	−0.268927	−	0.465794i
$446$		0			0
$447$			3.82017i			0.180688i
$448$		0			0
$449$	20.2543	−	11.6938i	0.955859	−	0.551865i	0.0609627	−	0.998140i	$-0.480583\pi$
$449$	20.2543	−	11.6938i	0.955859	−	0.551865i	0.894896	+	0.446275i	$0.147250\pi$
$450$		0			0
$451$	14.1827			0.667836
$452$		0			0
$453$			2.99908i			0.140909i
$454$		0			0
$455$		0			0
$456$		0			0
$457$			26.1674i			1.22406i	0.790835	+	0.612030i	$0.209647\pi$
$457$			26.1674i			1.22406i	−0.790835	+	0.612030i	$0.790353\pi$
$458$		0			0
$459$	9.27650			0.432990
$460$		0			0
$461$	21.8524	−	12.6165i	1.01777	−	0.587609i	0.104312	−	0.994545i	$-0.466736\pi$
$461$	21.8524	−	12.6165i	1.01777	−	0.587609i	0.913457	+	0.406936i	$0.133403\pi$
$462$		0			0
$463$		−	18.1600i		−	0.843968i	−0.906603	−	0.421984i	$-0.861334\pi$
$463$		−	18.1600i		−	0.843968i	0.906603	−	0.421984i	$-0.138666\pi$
$464$		0			0
$465$	−1.46668	−	2.54036i	−0.0680154	−	0.117806i
$466$		0			0
$467$	−6.31641	−	10.9403i	−0.292289	−	0.506259i	0.682062	−	0.731294i	$-0.261083\pi$
$467$	−6.31641	−	10.9403i	−0.292289	−	0.506259i	−0.974351	+	0.225036i	$0.927750\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$	−1.08859			−0.0501594
$472$		0			0
$473$	−15.2177	−	8.78594i	−0.699710	−	0.403978i
$474$		0			0
$475$	−8.71966	+	5.03430i	−0.400086	+	0.230990i
$476$		0			0
$477$	−16.2320	−	28.1146i	−0.743211	−	1.28728i
$478$		0			0
$479$	10.6585	−	6.15368i	0.486999	−	0.281169i	−0.236330	−	0.971673i	$-0.575945\pi$
$479$	10.6585	−	6.15368i	0.486999	−	0.281169i	0.723329	+	0.690504i	$0.242611\pi$
$480$		0			0
$481$	−24.9966	−	2.10840i	−1.13975	−	0.0961347i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	8.27299	−	14.3292i	0.375657	−	0.650658i
$486$		0			0
$487$			15.6339i			0.708438i	0.935163	+	0.354219i	$0.115253\pi$
$487$			15.6339i			0.708438i	−0.935163	+	0.354219i	$0.884747\pi$
$488$		0			0
$489$		−	1.41825i		−	0.0641355i
$490$		0			0
$491$	5.10543	−	8.84286i	0.230405	−	0.399073i	−0.727523	−	0.686084i	$-0.759328\pi$
$491$	5.10543	−	8.84286i	0.230405	−	0.399073i	0.957927	+	0.287011i	$0.0926617\pi$
$492$		0			0
$493$	20.9956	−	36.3654i	0.945593	−	1.63781i
$494$		0			0
$495$	5.56358	+	9.63641i	0.250065	+	0.433124i
$496$		0			0
$497$		0			0
$498$		0			0
$499$	−0.589766	+	0.340502i	−0.0264016	+	0.0152430i	−0.513143	−	0.858303i	$-0.671519\pi$
$499$	−0.589766	+	0.340502i	−0.0264016	+	0.0152430i	0.486741	+	0.873546i	$0.338186\pi$
$500$		0			0
$501$		−	1.43885i		−	0.0642830i
$502$		0			0
$503$	−17.6701	−	30.6056i	−0.787873	−	1.36464i	−0.927268	−	0.374399i	$-0.877849\pi$
$503$	−17.6701	−	30.6056i	−0.787873	−	1.36464i	0.139395	−	0.990237i	$-0.455484\pi$
$504$		0			0
$505$	2.84492	+	1.64251i	0.126597	+	0.0730909i
$506$		0			0
$507$	1.21630	+	3.27801i	0.0540179	+	0.145581i
$508$		0			0
$509$			16.8260i			0.745800i	0.927872	+	0.372900i	$0.121636\pi$
$509$			16.8260i			0.745800i	−0.927872	+	0.372900i	$0.878364\pi$
$510$		0			0
$511$		0			0
$512$		0			0
$513$	−4.39687	−	2.53853i	−0.194126	−	0.112079i
$514$		0			0
$515$	17.0153	+	9.82377i	0.749783	+	0.432887i
$516$		0			0
$517$	3.70461	−	6.41658i	0.162929	−	0.282201i
$518$		0			0
$519$	−2.62043			−0.115024
$520$		0			0
$521$	2.38310	−	4.12764i	0.104405	−	0.180835i	−0.809090	−	0.587685i	$-0.800039\pi$
$521$	2.38310	−	4.12764i	0.104405	−	0.180835i	0.913495	+	0.406850i	$0.133373\pi$
$522$		0			0
$523$	0.638159			0.0279048			0.0139524	−	0.999903i	$-0.495559\pi$
$523$	0.638159			0.0279048			0.0139524	+	0.999903i	$0.495559\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−40.5351	−	23.4029i	−1.76573	−	1.01945i
$528$		0			0
$529$	34.0549			1.48065
$530$		0			0
$531$	15.9620	+	9.21567i	0.692692	+	0.399926i
$532$		0			0
$533$	10.4167	−	14.9757i	0.451196	−	0.648670i
$534$		0			0
$535$	7.61752	−	4.39798i	0.329334	−	0.190141i
$536$		0			0
$537$	1.53374	−	2.65651i	0.0661857	−	0.114637i
$538$		0			0
$539$		0			0
$540$		0			0
$541$	19.2301	−	11.1025i	0.826767	−	0.477334i	−0.0259776	−	0.999663i	$-0.508270\pi$
$541$	19.2301	−	11.1025i	0.826767	−	0.477334i	0.852744	+	0.522328i	$0.174937\pi$
$542$		0			0
$543$	3.42548	+	5.93310i	0.147001	+	0.254614i
$544$		0			0
$545$	3.98138			0.170544
$546$		0			0
$547$	16.2608			0.695263			0.347631	−	0.937631i	$-0.386986\pi$
$547$	16.2608			0.695263			0.347631	+	0.937631i	$0.386986\pi$
$548$		0			0
$549$	−18.7489	−	32.4740i	−0.800182	−	1.38596i
$550$		0			0
$551$	−19.9029	+	11.4909i	−0.847892	+	0.489531i
$552$		0			0
$553$		0			0
$554$		0			0
$555$	1.26855	−	2.19719i	0.0538470	−	0.0932657i
$556$		0			0
$557$	18.5915	−	10.7338i	0.787747	−	0.454806i	−0.0514219	−	0.998677i	$-0.516375\pi$
$557$	18.5915	−	10.7338i	0.787747	−	0.454806i	0.839169	+	0.543871i	$0.183042\pi$
$558$		0			0
$559$	−20.4541	+	9.61566i	−0.865115	+	0.406699i
$560$		0			0
$561$	−3.79912	−	2.19342i	−0.160399	−	0.0926064i
$562$		0			0
$563$	−11.1821			−0.471268			−0.235634	−	0.971842i	$-0.575717\pi$
$563$	−11.1821			−0.471268			−0.235634	+	0.971842i	$0.575717\pi$
$564$		0			0
$565$	3.91969	+	2.26304i	0.164903	+	0.0952066i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	13.1633			0.551835			0.275917	−	0.961181i	$-0.411018\pi$
$569$	13.1633			0.551835			0.275917	+	0.961181i	$0.411018\pi$
$570$		0			0
$571$	8.70996	−	15.0861i	0.364501	−	0.631334i	−0.624195	−	0.781268i	$-0.714573\pi$
$571$	8.70996	−	15.0861i	0.364501	−	0.631334i	0.988696	+	0.149935i	$0.0479064\pi$
$572$		0			0
$573$	4.40494			0.184019
$574$		0			0
$575$	11.9408	−	20.6821i	0.497965	−	0.862501i
$576$		0			0
$577$	−7.33543	−	4.23511i	−0.305378	−	0.176310i	0.339478	−	0.940614i	$-0.389749\pi$
$577$	−7.33543	−	4.23511i	−0.305378	−	0.176310i	−0.644856	+	0.764304i	$0.723083\pi$
$578$		0			0
$579$	2.22729	+	1.28592i	0.0925629	+	0.0534412i
$580$		0			0
$581$		0			0
$582$		0			0
$583$			31.0836i			1.28735i
$584$		0			0
$585$	14.2615	+	1.20292i	0.589641	+	0.0497346i
$586$		0			0
$587$	−18.2459	−	10.5342i	−0.753087	−	0.434795i	0.0737213	−	0.997279i	$-0.476512\pi$
$587$	−18.2459	−	10.5342i	−0.753087	−	0.434795i	−0.826808	+	0.562484i	$0.809846\pi$
$588$		0			0
$589$	12.8085	+	22.1850i	0.527765	+	0.914116i
$590$		0			0
$591$		−	0.809681i		−	0.0333058i
$592$		0			0
$593$	−11.4975	+	6.63806i	−0.472144	+	0.272593i	−0.717137	−	0.696932i	$-0.754548\pi$
$593$	−11.4975	+	6.63806i	−0.472144	+	0.272593i	0.244993	+	0.969525i	$0.421214\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	0.621240	+	1.07602i	0.0254257	+	0.0440385i
$598$		0			0
$599$	−2.69542	+	4.66860i	−0.110132	+	0.190754i	−0.915823	−	0.401582i	$-0.868461\pi$
$599$	−2.69542	+	4.66860i	−0.110132	+	0.190754i	0.805691	+	0.592335i	$0.201794\pi$
$600$		0			0
$601$	−12.2204	+	21.1663i	−0.498480	+	0.863392i	−0.999998	−	0.00175467i	$-0.999441\pi$
$601$	−12.2204	+	21.1663i	−0.498480	+	0.863392i	0.501519	+	0.865147i	$0.332775\pi$
$602$		0			0
$603$			14.5298i			0.591700i
$604$		0			0
$605$			4.26030i			0.173206i
$606$		0			0
$607$	−12.9291	+	22.3939i	−0.524776	+	0.908939i	0.474808	+	0.880090i	$0.342518\pi$
$607$	−12.9291	+	22.3939i	−0.524776	+	0.908939i	−0.999584	+	0.0288492i	$0.990816\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−4.05446	−	8.62451i	−0.164026	−	0.348910i
$612$		0			0
$613$	−12.2706	+	7.08441i	−0.495603	+	0.286136i	−0.726896	−	0.686748i	$-0.759038\pi$
$613$	−12.2706	+	7.08441i	−0.495603	+	0.286136i	0.231293	+	0.972884i	$0.425704\pi$
$614$		0			0
$615$	0.922496	+	1.59781i	0.0371986	+	0.0644299i
$616$		0			0
$617$	39.8763	−	23.0226i	1.60536	−	0.926855i	0.614970	−	0.788550i	$-0.289168\pi$
$617$	39.8763	−	23.0226i	1.60536	−	0.926855i	0.990390	−	0.138305i	$-0.0441654\pi$
$618$		0			0
$619$	−10.4169	−	6.01422i	−0.418692	−	0.241732i	0.275825	−	0.961208i	$-0.411049\pi$
$619$	−10.4169	−	6.01422i	−0.418692	−	0.241732i	−0.694518	+	0.719476i	$0.744382\pi$
$620$		0			0
$621$	12.0422			0.483238
$622$		0			0
$623$		0			0
$624$		0			0
$625$	−0.402250	−	0.696717i	−0.0160900	−	0.0278687i
$626$		0			0
$627$	1.20047	+	2.07927i	0.0479421	+	0.0830381i
$628$		0			0
$629$		−	40.4831i		−	1.61417i
$630$		0			0
$631$	21.0476	−	12.1518i	0.837890	−	0.483756i	−0.0186564	−	0.999826i	$-0.505939\pi$
$631$	21.0476	−	12.1518i	0.837890	−	0.483756i	0.856546	+	0.516070i	$0.172606\pi$
$632$		0			0
$633$	0.628986			0.0249999
$634$		0			0
$635$			17.0162i			0.675269i
$636$		0			0
$637$		0			0
$638$		0			0
$639$			48.3399i			1.91230i
$640$		0			0
$641$	17.7655			0.701696			0.350848	−	0.936432i	$-0.385893\pi$
$641$	17.7655			0.701696			0.350848	+	0.936432i	$0.385893\pi$
$642$		0			0
$643$	37.3742	−	21.5780i	1.47389	−	0.850953i	0.474326	−	0.880349i	$-0.342692\pi$
$643$	37.3742	−	21.5780i	1.47389	−	0.850953i	0.999568	+	0.0293964i	$0.00935852\pi$
$644$		0			0
$645$		−	2.28589i		−	0.0900067i
$646$		0			0
$647$	5.39974	+	9.35262i	0.212286	+	0.367689i	0.952429	−	0.304759i	$-0.0985760\pi$
$647$	5.39974	+	9.35262i	0.212286	+	0.367689i	−0.740144	+	0.672449i	$0.765243\pi$
$648$		0			0
$649$	−8.82383	−	15.2833i	−0.346366	−	0.599923i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−3.06560			−0.119966			−0.0599831	−	0.998199i	$-0.519105\pi$
$653$	−3.06560			−0.119966			−0.0599831	+	0.998199i	$0.519105\pi$
$654$		0			0
$655$	1.47950	+	0.854191i	0.0578089	+	0.0333760i
$656$		0			0
$657$	39.1346	−	22.5944i	1.52679	−	0.881491i
$658$		0			0
$659$	1.82436	+	3.15988i	0.0710670	+	0.123092i	0.899369	−	0.437190i	$-0.144026\pi$
$659$	1.82436	+	3.15988i	0.0710670	+	0.123092i	−0.828302	+	0.560282i	$0.810693\pi$
$660$		0			0
$661$	−23.5777	+	13.6126i	−0.917068	+	0.529469i	−0.882698	−	0.469940i	$-0.844276\pi$
$661$	−23.5777	+	13.6126i	−0.917068	+	0.529469i	−0.0343693	+	0.999409i	$0.510942\pi$
$662$		0			0
$663$	−5.10639	+	2.40056i	−0.198316	+	0.0932301i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	27.2552	−	47.2074i	1.05533	−	1.82788i
$668$		0			0
$669$		−	1.30879i		−	0.0506008i
$670$		0			0
$671$			35.9034i			1.38604i
$672$		0			0
$673$	14.1485	−	24.5059i	0.545384	−	0.944633i	−0.453199	−	0.891410i	$-0.649717\pi$
$673$	14.1485	−	24.5059i	0.545384	−	0.944633i	0.998583	−	0.0532233i	$-0.0169495\pi$
$674$		0			0
$675$	2.52027	−	4.36523i	0.0970051	−	0.168018i
$676$		0			0
$677$	−14.4181	−	24.9728i	−0.554131	−	0.959783i	−0.997971	−	0.0636769i	$-0.979717\pi$
$677$	−14.4181	−	24.9728i	−0.554131	−	0.959783i	0.443840	−	0.896106i	$-0.353616\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$	6.54031	−	3.77605i	0.250625	−	0.144698i
$682$		0			0
$683$			40.9045i			1.56517i	0.622546	+	0.782583i	$0.286098\pi$
$683$			40.9045i			1.56517i	−0.622546	+	0.782583i	$0.713902\pi$
$684$		0			0
$685$	−5.64238	−	9.77290i	−0.215584	−	0.373403i
$686$		0			0
$687$	−0.0417579	−	0.0241089i	−0.00159316	−	0.000919813i
$688$		0			0
$689$	32.8217	+	22.8298i	1.25041	+	0.869746i
$690$		0			0
$691$		−	42.2544i		−	1.60743i	−0.595011	−	0.803717i	$-0.702852\pi$
$691$		−	42.2544i		−	1.60743i	0.595011	−	0.803717i	$-0.297148\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−6.79717	−	3.92435i	−0.257831	−	0.148859i
$696$		0			0
$697$	25.4954	+	14.7198i	0.965706	+	0.557551i
$698$		0			0
$699$	−2.03575	+	3.52603i	−0.0769992	+	0.133367i
$700$		0			0
$701$	−30.3734			−1.14719			−0.573594	−	0.819140i	$-0.694451\pi$
$701$	−30.3734			−1.14719			−0.573594	+	0.819140i	$0.694451\pi$
$702$		0			0
$703$	−11.0783	+	19.1881i	−0.417825	+	0.723694i
$704$		0			0
$705$	0.963850			0.0363007
$706$		0			0
$707$		0			0
$708$		0			0
$709$	20.2907	+	11.7148i	0.762033	+	0.439960i	0.830025	−	0.557726i	$-0.188326\pi$
$709$	20.2907	+	11.7148i	0.762033	+	0.439960i	−0.0679919	+	0.997686i	$0.521659\pi$
$710$		0			0
$711$	−43.2301			−1.62125
$712$		0			0
$713$	−52.6203	−	30.3803i	−1.97064	−	1.13775i
$714$		0			0
$715$	−11.2498	−	7.82503i	−0.420719	−	0.292639i
$716$		0			0
$717$	−2.99776	+	1.73076i	−0.111953	+	0.0646363i
$718$		0			0
$719$	3.51491	−	6.08800i	0.131084	−	0.227044i	−0.793011	−	0.609208i	$-0.791488\pi$
$719$	3.51491	−	6.08800i	0.131084	−	0.227044i	0.924095	+	0.382164i	$0.124821\pi$
$720$		0			0
$721$		0			0
$722$		0			0
$723$	−2.29001	+	1.32214i	−0.0851662	+	0.0491708i
$724$		0			0
$725$	−11.4083	−	19.7597i	−0.423692	−	0.733857i
$726$		0			0
$727$	20.6810			0.767015			0.383507	−	0.923538i	$-0.374716\pi$
$727$	20.6810			0.767015			0.383507	+	0.923538i	$0.374716\pi$
$728$		0			0
$729$	−23.1720			−0.858222
$730$		0			0
$731$	−18.2373	−	31.5880i	−0.674531	−	1.16832i
$732$		0			0
$733$	33.7780	−	19.5018i	1.24762	−	0.720314i	0.276986	−	0.960874i	$-0.410664\pi$
$733$	33.7780	−	19.5018i	1.24762	−	0.720314i	0.970634	+	0.240560i	$0.0773311\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	6.95602	−	12.0482i	0.256228	−	0.443800i
$738$		0			0
$739$	−24.8910	+	14.3708i	−0.915629	+	0.528639i	−0.882238	−	0.470803i	$-0.843964\pi$
$739$	−24.8910	+	14.3708i	−0.915629	+	0.528639i	−0.0333913	+	0.999442i	$0.510631\pi$
$740$		0			0
$741$	3.07724	+	0.259557i	0.113045	+	0.00953505i
$742$		0			0
$743$	−5.48059	−	3.16422i	−0.201063	−	0.116084i	0.396088	−	0.918213i	$-0.370367\pi$
$743$	−5.48059	−	3.16422i	−0.201063	−	0.116084i	−0.597151	+	0.802129i	$0.703701\pi$
$744$		0			0
$745$	−19.2583			−0.705569
$746$		0			0
$747$	24.8297	+	14.3355i	0.908473	+	0.524507i
$748$		0			0
$749$		0			0
$750$		0			0
$751$	31.4405			1.14728			0.573641	−	0.819107i	$-0.305531\pi$
$751$	31.4405			1.14728			0.573641	+	0.819107i	$0.305531\pi$
$752$		0			0
$753$	2.32940	−	4.03464i	0.0848880	−	0.147030i
$754$		0			0
$755$	−15.1190			−0.550237
$756$		0			0
$757$	−12.7212	+	22.0337i	−0.462358	+	0.800828i	−0.999078	−	0.0429328i	$-0.986330\pi$
$757$	−12.7212	+	22.0337i	−0.462358	+	0.800828i	0.536720	+	0.843760i	$0.319663\pi$
$758$		0			0
$759$	−4.93180	−	2.84737i	−0.179013	−	0.103353i
$760$		0			0
$761$	−17.8492	−	10.3053i	−0.647034	−	0.373565i	0.140285	−	0.990111i	$-0.455198\pi$
$761$	−17.8492	−	10.3053i	−0.647034	−	0.373565i	−0.787319	+	0.616546i	$0.788531\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$			23.0971i			0.835077i
$766$		0			0
$767$	−22.6187	−	1.90783i	−0.816714	−	0.0688876i
$768$		0			0
$769$	−7.95173	−	4.59093i	−0.286747	−	0.165553i	0.349727	−	0.936852i	$-0.386274\pi$
$769$	−7.95173	−	4.59093i	−0.286747	−	0.165553i	−0.636474	+	0.771298i	$0.719608\pi$
$770$		0			0
$771$	1.43971	+	2.49365i	0.0518499	+	0.0898066i
$772$		0			0
$773$			8.49555i			0.305564i	0.988260	+	0.152782i	$0.0488232\pi$
$773$			8.49555i			0.305564i	−0.988260	+	0.152782i	$0.951177\pi$
$774$		0			0
$775$	−22.0254	+	12.7163i	−0.791174	+	0.456785i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−8.05618	−	13.9537i	−0.288642	−	0.499943i
$780$		0			0
$781$	23.1423	−	40.0836i	0.828096	−	1.43430i
$782$		0			0
$783$	5.75259	−	9.96377i	0.205581	−	0.356076i
$784$		0			0
$785$		−	5.48780i		−	0.195868i
$786$		0			0
$787$		−	1.96835i		−	0.0701640i	−0.999384	−	0.0350820i	$-0.988831\pi$
$787$		−	1.96835i		−	0.0701640i	0.999384	−	0.0350820i	$-0.0111692\pi$
$788$		0			0
$789$	1.89204	−	3.27711i	0.0673585	−	0.116668i
$790$		0			0
$791$		0			0
$792$		0			0
$793$	37.9110	+	26.3698i	1.34626	+	0.936418i
$794$		0			0
$795$	−3.50186	+	2.02180i	−0.124198	+	0.0717058i
$796$		0			0
$797$	19.2449	+	33.3332i	0.681690	+	1.18072i	0.974465	+	0.224540i	$0.0720879\pi$
$797$	19.2449	+	33.3332i	0.681690	+	1.18072i	−0.292775	+	0.956181i	$0.594579\pi$
$798$		0			0
$799$	13.3191	−	7.68981i	0.471197	−	0.272046i
$800$		0			0
$801$	−21.2170	−	12.2496i	−0.749665	−	0.432820i
$802$		0			0
$803$	−43.2674			−1.52687
$804$		0			0
$805$		0			0
$806$		0			0
$807$	−0.0731583	−	0.126714i	−0.00257529	−	0.00446054i
$808$		0			0
$809$	−0.899878	−	1.55863i	−0.0316380	−	0.0547987i	0.849773	−	0.527149i	$-0.176739\pi$
$809$	−0.899878	−	1.55863i	−0.0316380	−	0.0547987i	−0.881411	+	0.472350i	$0.843406\pi$
$810$		0			0
$811$		−	49.9235i		−	1.75305i	−0.481357	−	0.876525i	$-0.659856\pi$
$811$		−	49.9235i		−	1.75305i	0.481357	−	0.876525i	$-0.340144\pi$
$812$		0			0
$813$	−0.172644	+	0.0996759i	−0.00605488	+	0.00349579i
$814$		0			0
$815$	7.14970			0.250443
$816$		0			0
$817$			19.9627i			0.698406i
$818$		0			0
$819$		0			0
$820$		0			0
$821$		−	4.21824i		−	0.147217i	−0.997287	−	0.0736087i	$-0.976548\pi$
$821$		−	4.21824i		−	0.147217i	0.997287	−	0.0736087i	$-0.0234516\pi$
$822$		0			0
$823$	−14.4982			−0.505377			−0.252688	−	0.967548i	$-0.581315\pi$
$823$	−14.4982			−0.505377			−0.252688	+	0.967548i	$0.581315\pi$
$824$		0			0
$825$	−2.06431	+	1.19183i	−0.0718701	+	0.0414942i
$826$		0			0
$827$			26.2618i			0.913213i	0.889669	+	0.456607i	$0.150935\pi$
$827$			26.2618i			0.913213i	−0.889669	+	0.456607i	$0.849065\pi$
$828$		0			0
$829$	27.5790	+	47.7682i	0.957858	+	1.65906i	0.727688	+	0.685909i	$0.240595\pi$
$829$	27.5790	+	47.7682i	0.957858	+	1.65906i	0.230170	+	0.973150i	$0.426072\pi$
$830$		0			0
$831$	−1.90062	−	3.29198i	−0.0659319	−	0.114197i
$832$		0			0
$833$		0			0
$834$		0			0
$835$	7.25355			0.251019
$836$		0			0
$837$	−11.1062	−	6.41218i	−0.383887	−	0.221637i
$838$		0			0
$839$	6.07974	−	3.51014i	0.209896	−	0.121184i	−0.391367	−	0.920235i	$-0.627998\pi$
$839$	6.07974	−	3.51014i	0.209896	−	0.121184i	0.601263	+	0.799051i	$0.294664\pi$
$840$		0			0
$841$	−11.5397	−	19.9874i	−0.397922	−	0.689221i
$842$		0			0
$843$	6.01053	−	3.47018i	0.207014	−	0.119519i
$844$		0			0
$845$	−16.5252	+	6.13165i	−0.568483	+	0.210935i
$846$		0			0
$847$		0			0
$848$		0			0
$849$	−3.66875	+	6.35446i	−0.125911	+	0.218085i
$850$		0			0
$851$		−	52.5528i		−	1.80149i
$852$		0			0
$853$			57.6508i			1.97393i	0.160945	+	0.986963i	$0.448546\pi$
$853$			57.6508i			1.97393i	−0.160945	+	0.986963i	$0.551454\pi$
$854$		0			0
$855$	6.32056	−	10.9475i	0.216159	−	0.374398i
$856$		0			0
$857$	−1.25327	+	2.17073i	−0.0428109	+	0.0741506i	−0.886637	−	0.462466i	$-0.846965\pi$
$857$	−1.25327	+	2.17073i	−0.0428109	+	0.0741506i	0.843826	+	0.536617i	$0.180298\pi$
$858$		0			0
$859$	8.56526	+	14.8355i	0.292243	+	0.506180i	0.974340	−	0.225082i	$-0.0722650\pi$
$859$	8.56526	+	14.8355i	0.292243	+	0.506180i	−0.682097	+	0.731262i	$0.738932\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−48.1881	+	27.8214i	−1.64034	+	0.947053i	−0.659632	+	0.751589i	$0.729288\pi$
$863$	−48.1881	+	27.8214i	−1.64034	+	0.947053i	−0.980711	+	0.195464i	$0.937379\pi$
$864$		0			0
$865$		−	13.2102i		−	0.449159i
$866$		0			0
$867$	−2.26687	−	3.92634i	−0.0769870	−	0.133345i
$868$		0			0
$869$	35.8465	+	20.6960i	1.21601	+	0.702064i
$870$		0			0
$871$	−7.61292	−	16.1939i	−0.257954	−	0.548710i
$872$		0			0
$873$		−	35.7275i		−	1.20919i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−34.7751	−	20.0774i	−1.17427	−	0.677967i	−0.219590	−	0.975592i	$-0.570472\pi$
$877$	−34.7751	−	20.0774i	−1.17427	−	0.677967i	−0.954683	+	0.297626i	$0.903805\pi$
$878$		0			0
$879$	−0.403456	−	0.232936i	−0.0136082	−	0.00785672i
$880$		0			0
$881$	−25.3837	+	43.9658i	−0.855197	+	1.48124i	0.0212650	+	0.999774i	$0.493231\pi$
$881$	−25.3837	+	43.9658i	−0.855197	+	1.48124i	−0.876462	+	0.481471i	$0.840103\pi$
$882$		0			0
$883$	−46.3312			−1.55917			−0.779585	−	0.626297i	$-0.784570\pi$
$883$	−46.3312			−1.55917			−0.779585	+	0.626297i	$0.784570\pi$
$884$		0			0
$885$	1.14787	−	1.98817i	0.0385853	−	0.0668317i
$886$		0			0
$887$	10.2550			0.344331			0.172165	−	0.985068i	$-0.444924\pi$
$887$	10.2550			0.344331			0.172165	+	0.985068i	$0.444924\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	20.2809	+	11.7092i	0.679436	+	0.392273i
$892$		0			0
$893$	−8.41732			−0.281675
$894$		0			0
$895$	13.3921	+	7.73191i	0.447647	+	0.258449i
$896$		0			0
$897$	−6.62882	+	3.11627i	−0.221330	+	0.104049i
$898$		0			0
$899$	−50.2736	+	29.0255i	−1.67672	+	0.968053i
$900$		0			0
$901$	−32.2607	+	55.8772i	−1.07476	+	1.86154i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−29.9101	+	17.2686i	−0.994244	+	0.574027i
$906$		0			0
$907$	26.1472	+	45.2883i	0.868205	+	1.50377i	0.863830	+	0.503784i	$0.168059\pi$
$907$	26.1472	+	45.2883i	0.868205	+	1.50377i	0.00437495	+	0.999990i	$0.498607\pi$
$908$		0			0
$909$	7.09330			0.235270
$910$		0			0
$911$	50.9172			1.68696			0.843481	−	0.537159i	$-0.180502\pi$
$911$	50.9172			1.68696			0.843481	+	0.537159i	$0.180502\pi$
$912$		0			0
$913$	−13.7259	−	23.7740i	−0.454262	−	0.786805i
$914$		0			0
$915$	−4.04485	+	2.33530i	−0.133719	+	0.0772025i
$916$		0			0
$917$		0			0
$918$		0			0
$919$	−11.4323	+	19.8013i	−0.377117	+	0.653186i	−0.990641	−	0.136490i	$-0.956418\pi$
$919$	−11.4323	+	19.8013i	−0.377117	+	0.653186i	0.613524	+	0.789676i	$0.289751\pi$
$920$		0			0
$921$	−4.99299	+	2.88270i	−0.164525	+	0.0949884i
$922$		0			0
$923$	−25.3278	−	53.8763i	−0.833674	−	1.77336i
$924$		0			0
$925$	−19.0501	−	10.9986i	−0.626363	−	0.361631i
$926$		0			0
$927$	42.4246			1.39341
$928$		0			0
$929$	28.8090	+	16.6329i	0.945193	+	0.545708i	0.891584	−	0.452854i	$-0.149594\pi$
$929$	28.8090	+	16.6329i	0.945193	+	0.545708i	0.0536089	+	0.998562i	$0.482928\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$	7.33498			0.240137
$934$		0			0
$935$	11.0575	−	19.1522i	0.361620	−	0.626344i
$936$		0			0
$937$	51.2179			1.67322			0.836608	−	0.547802i	$-0.184535\pi$
$937$	51.2179			1.67322			0.836608	+	0.547802i	$0.184535\pi$
$938$		0			0
$939$	0.979286	−	1.69617i	0.0319578	−	0.0553525i
$940$		0			0
$941$	8.91293	+	5.14588i	0.290553	+	0.167751i	0.638191	−	0.769878i	$-0.279683\pi$
$941$	8.91293	+	5.14588i	0.290553	+	0.167751i	−0.347638	+	0.937629i	$0.613016\pi$
$942$		0			0
$943$	33.0966	+	19.1083i	1.07777	+	0.622253i
$944$		0			0
$945$		0			0
$946$		0			0
$947$		−	35.4887i		−	1.15323i	−0.817017	−	0.576614i	$-0.804374\pi$
$947$		−	35.4887i		−	1.15323i	0.817017	−	0.576614i	$-0.195626\pi$
$948$		0			0
$949$	−31.7784	+	45.6868i	−1.03157	+	1.48306i
$950$		0			0
$951$	0.593565	+	0.342695i	0.0192477	+	0.0111126i
$952$		0			0
$953$	16.6676	+	28.8691i	0.539916	+	0.935163i	0.998908	+	0.0467220i	$0.0148775\pi$
$953$	16.6676	+	28.8691i	0.539916	+	0.935163i	−0.458992	+	0.888441i	$0.651789\pi$
$954$		0			0
$955$			22.2062i			0.718577i
$956$		0			0
$957$	−4.71185	+	2.72039i	−0.152313	+	0.0879377i
$958$		0			0
$959$		0			0
$960$		0			0
$961$	16.8535	+	29.1912i	0.543662	+	0.941650i
$962$		0			0
$963$	9.49647	−	16.4484i	0.306020	−	0.530041i
$964$		0			0
$965$	−6.48263	+	11.2282i	−0.208683	+	0.361450i
$966$		0			0
$967$			29.7131i			0.955509i	0.878494	+	0.477754i	$0.158549\pi$
$967$			29.7131i			0.955509i	−0.878494	+	0.477754i	$0.841451\pi$
$968$		0			0
$969$			4.98372i			0.160100i
$970$		0			0
$971$	−4.41851	+	7.65308i	−0.141797	+	0.245599i	−0.928173	−	0.372148i	$-0.878621\pi$
$971$	−4.41851	+	7.65308i	−0.141797	+	0.245599i	0.786377	+	0.617747i	$0.211955\pi$
$972$		0			0
$973$		0			0
$974$		0			0
$975$	−0.257689	+	3.05510i	−0.00825266	+	0.0978414i
$976$		0			0
$977$	12.8437	−	7.41533i	0.410907	−	0.237237i	−0.280272	−	0.959921i	$-0.590425\pi$
$977$	12.8437	−	7.41533i	0.410907	−	0.237237i	0.691180	+	0.722683i	$0.257091\pi$
$978$		0			0
$979$	11.7288	+	20.3149i	0.374854	+	0.649266i
$980$		0			0
$981$	7.44516	−	4.29846i	0.237706	−	0.137239i
$982$		0			0
$983$	17.6141	+	10.1695i	0.561803	+	0.324357i	0.753869	−	0.657025i	$-0.228185\pi$
$983$	17.6141	+	10.1695i	0.561803	+	0.324357i	−0.192066	+	0.981382i	$0.561519\pi$
$984$		0			0
$985$	4.08178			0.130056
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−23.6746	−	41.0057i	−0.752809	−	1.30390i
$990$		0			0
$991$	25.4453	+	44.0726i	0.808297	+	1.40001i	0.914042	+	0.405619i	$0.132944\pi$
$991$	25.4453	+	44.0726i	0.808297	+	1.40001i	−0.105745	+	0.994393i	$0.533723\pi$
$992$		0			0
$993$			0.0526244i			0.00166999i
$994$		0			0
$995$	−5.42445	+	3.13181i	−0.171967	+	0.0992849i
$996$		0			0
$997$	7.39394			0.234168			0.117084	−	0.993122i	$-0.462645\pi$
$997$	7.39394			0.234168			0.117084	+	0.993122i	$0.462645\pi$
$998$		0			0
$999$		−	11.0920i		−	0.350935i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2548.2.bb.c.1733.4		16
7.2	even	3		2548.2.bq.c.1941.5		16
7.3	odd	6		364.2.u.a.225.5	✓	16
7.4	even	3		2548.2.u.c.589.4		16
7.5	odd	6		2548.2.bq.e.1941.4		16
7.6	odd	2		2548.2.bb.d.1733.5		16
13.10	even	6		2548.2.bq.c.361.5		16
21.17	even	6		3276.2.cf.c.2773.5		16
28.3	even	6		1456.2.cc.f.225.4		16
91.10	odd	6		364.2.u.a.309.5	yes	16
91.17	odd	6		4732.2.g.k.337.8		16
91.23	even	6	inner	2548.2.bb.c.569.4		16
91.45	even	12		4732.2.a.s.1.4		8
91.59	even	12		4732.2.a.t.1.4		8
91.62	odd	6		2548.2.bq.e.361.4		16
91.75	odd	6		2548.2.bb.d.569.5		16
91.87	odd	6		4732.2.g.k.337.7		16
91.88	even	6		2548.2.u.c.1765.4		16
273.101	even	6		3276.2.cf.c.1765.4		16
364.283	even	6		1456.2.cc.f.673.4		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
364.2.u.a.225.5	✓	16	7.3	odd	6
364.2.u.a.309.5	yes	16	91.10	odd	6
1456.2.cc.f.225.4		16	28.3	even	6
1456.2.cc.f.673.4		16	364.283	even	6
2548.2.u.c.589.4		16	7.4	even	3
2548.2.u.c.1765.4		16	91.88	even	6
2548.2.bb.c.569.4		16	91.23	even	6	inner
2548.2.bb.c.1733.4		16	1.1	even	1	trivial
2548.2.bb.d.569.5		16	91.75	odd	6
2548.2.bb.d.1733.5		16	7.6	odd	2
2548.2.bq.c.361.5		16	13.10	even	6
2548.2.bq.c.1941.5		16	7.2	even	3
2548.2.bq.e.361.4		16	91.62	odd	6
2548.2.bq.e.1941.4		16	7.5	odd	6
3276.2.cf.c.1765.4		16	273.101	even	6
3276.2.cf.c.2773.5		16	21.17	even	6
4732.2.a.s.1.4		8	91.45	even	12
4732.2.a.t.1.4		8	91.59	even	12
4732.2.g.k.337.7		16	91.87	odd	6
4732.2.g.k.337.8		16	91.17	odd	6

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:	\( N \)	\(=\)	\( 2548 = 2^{2} \cdot 7^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2548.bb (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.134476 - 0.232920i) q^{3} +(1.17420 - 0.677925i) q^{5} +(1.46383 - 2.53543i) q^{9} +(-2.42763 + 1.40159i) q^{11} +(-0.303042 + 3.59279i) q^{13} +(-0.315805 - 0.182330i) q^{15} -5.81868 q^{17} +(2.75793 + 1.59229i) q^{19} -7.55347 q^{23} +(-1.58083 + 2.73809i) q^{25} -1.59426 q^{27} +(-3.60830 + 6.24977i) q^{29} +(6.96637 + 4.02203i) q^{31} +(0.652918 + 0.376962i) q^{33} +6.95744i q^{37} +(0.877586 - 0.412562i) q^{39} +(-4.38164 - 2.52974i) q^{41} +(3.13427 + 5.42872i) q^{43} -3.96948i q^{45} +(-2.28903 + 1.32157i) q^{47} +(0.782475 + 1.35529i) q^{51} +(5.54434 - 9.60308i) q^{53} +(-1.90035 + 3.29150i) q^{55} -0.856503i q^{57} +6.29558i q^{59} +(6.40404 - 11.0921i) q^{61} +(2.07981 + 4.42410i) q^{65} +(-4.29803 + 2.48147i) q^{67} +(1.01576 + 1.75936i) q^{69} +(-14.2993 + 8.25572i) q^{71} +(13.3672 + 7.71755i) q^{73} +0.850340 q^{75} +(-7.38303 - 12.7878i) q^{79} +(-4.17711 - 7.23496i) q^{81} +9.79310i q^{83} +(-6.83230 + 3.94463i) q^{85} +1.94093 q^{87} -8.36820i q^{89} -2.16348i q^{93} +4.31782 q^{95} +(10.5685 - 6.10170i) q^{97} +8.20678i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 14 q^{9} - 6 q^{11} - 10 q^{13} + 6 q^{15} + 4 q^{17} + 22 q^{25} + 12 q^{27} - 22 q^{29} - 30 q^{31} + 42 q^{33} - 18 q^{39} - 36 q^{41} + 6 q^{43} + 18 q^{47} + 2 q^{51} - 4 q^{53} - 2 q^{55} - 4 q^{61}+ \cdots + 42 q^{97}+O(q^{100}) \) 16 * q - 14 * q^9 - 6 * q^11 - 10 * q^13 + 6 * q^15 + 4 * q^17 + 22 * q^25 + 12 * q^27 - 22 * q^29 - 30 * q^31 + 42 * q^33 - 18 * q^39 - 36 * q^41 + 6 * q^43 + 18 * q^47 + 2 * q^51 - 4 * q^53 - 2 * q^55 - 4 * q^61 + 30 * q^65 - 24 * q^67 + 52 * q^69 + 36 * q^71 + 12 * q^73 - 20 * q^75 - 4 * q^79 + 42 * q^85 + 52 * q^87 + 60 * q^95 + 42 * q^97

Introduction

L-functions

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