LMFDB - Embedded newform 2352.2.bl.s.31.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2352,2,Mod(31,2352)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2352, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 0, 0, 1]))

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

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

chi := DirichletCharacter("2352.31");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2352 = 2^{4} \cdot 3 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2352.bl (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:	$18.7808145554$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	8.0.339738624.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 4x^{6} + 14x^{4} - 8x^{2} + 4 $ x^8 - 4x^6 + 14x^4 - 8*x^2 + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			31.2
Root			$-1.60021 - 0.923880i$ of defining polynomial
Character	$\chi$	$=$	2352.31
Dual form			2352.2.bl.s.607.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 - 0.866025i) q^{3} +(-0.662827 + 0.382683i) q^{5} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(0.500000 - 0.866025i) q^{3} +(-0.662827 + 0.382683i) q^{5} +(-0.500000 - 0.866025i) q^{9} +(-1.87476 - 1.08239i) q^{11} -0.317025i q^{13} +0.765367i q^{15} +(-2.92586 - 1.68925i) q^{17} +(2.82843 + 4.89898i) q^{19} +(-4.52607 + 2.61313i) q^{23} +(-2.20711 + 3.82282i) q^{25} -1.00000 q^{27} -2.58579 q^{29} +(0.828427 - 1.43488i) q^{31} +(-1.87476 + 1.08239i) q^{33} +(0.707107 + 1.22474i) q^{37} +(-0.274552 - 0.158513i) q^{39} -5.99162i q^{41} +7.39104i q^{43} +(0.662827 + 0.382683i) q^{45} +(4.82843 + 8.36308i) q^{47} +(-2.92586 + 1.68925i) q^{51} +(-0.828427 + 1.43488i) q^{53} +1.65685 q^{55} +5.65685 q^{57} +(2.82843 - 4.89898i) q^{59} +(-6.12627 + 3.53701i) q^{61} +(0.121320 + 0.210133i) q^{65} +(-10.1503 - 5.86030i) q^{67} +5.22625i q^{69} +15.6788i q^{71} +(5.73800 + 3.31283i) q^{73} +(2.20711 + 3.82282i) q^{75} +(-11.7034 + 6.75699i) q^{79} +(-0.500000 + 0.866025i) q^{81} -6.34315 q^{83} +2.58579 q^{85} +(-1.29289 + 2.23936i) q^{87} +(9.87579 - 5.70179i) q^{89} +(-0.828427 - 1.43488i) q^{93} +(-3.74952 - 2.16478i) q^{95} +3.82683i q^{97} +2.16478i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 4 q^{3} - 4 q^{9}+O(q^{10}) $ 8 * q + 4 * q^3 - 4 * q^9	$ 8 q + 4 q^{3} - 4 q^{9} - 12 q^{25} - 8 q^{27} - 32 q^{29} - 16 q^{31} + 16 q^{47} + 16 q^{53} - 32 q^{55} - 16 q^{65} + 12 q^{75} - 4 q^{81} - 96 q^{83} + 32 q^{85} - 16 q^{87} + 16 q^{93}+O(q^{100}) $ 8 * q + 4 * q^3 - 4 * q^9 - 12 * q^25 - 8 * q^27 - 32 * q^29 - 16 * q^31 + 16 * q^47 + 16 * q^53 - 32 * q^55 - 16 * q^65 + 12 * q^75 - 4 * q^81 - 96 * q^83 + 32 * q^85 - 16 * q^87 + 16 * q^93

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2352\mathbb{Z}\right)^\times$.

$n$	$785$	$1471$	$1765$	$2257$
$\chi(n)$	$1$	$-1$	$1$	$e\left(\frac{1}{6}\right)$

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
$3$	0.500000	−	0.866025i	0.288675	−	0.500000i
$3$	0.500000	−	0.866025i	0.288675	−	0.500000i
$4$		0			0
$5$	−0.662827	+	0.382683i	−0.296425	+	0.171141i	−0.640836	−	0.767678i	$-0.721412\pi$
$5$	−0.662827	+	0.382683i	−0.296425	+	0.171141i	0.344411	+	0.938819i	$0.388079\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$		0			0
$9$	−0.500000	−	0.866025i	−0.166667	−	0.288675i
$10$		0			0
$11$	−1.87476	−	1.08239i	−0.565261	−	0.326354i	0.189993	−	0.981785i	$-0.439153\pi$
$11$	−1.87476	−	1.08239i	−0.565261	−	0.326354i	−0.755254	+	0.655432i	$0.772487\pi$
$12$		0			0
$13$		−	0.317025i		−	0.0879270i	−0.999033	−	0.0439635i	$-0.986001\pi$
$13$		−	0.317025i		−	0.0879270i	0.999033	−	0.0439635i	$-0.0139985\pi$
$14$		0			0
$15$			0.765367i			0.197617i
$16$		0			0
$17$	−2.92586	−	1.68925i	−0.709625	−	0.409702i	0.101297	−	0.994856i	$-0.467701\pi$
$17$	−2.92586	−	1.68925i	−0.709625	−	0.409702i	−0.810922	+	0.585154i	$0.801034\pi$
$18$		0			0
$19$	2.82843	+	4.89898i	0.648886	+	1.12390i	0.983389	+	0.181509i	$0.0580980\pi$
$19$	2.82843	+	4.89898i	0.648886	+	1.12390i	−0.334504	+	0.942394i	$0.608569\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−4.52607	+	2.61313i	−0.943750	+	0.544874i	−0.891134	−	0.453740i	$-0.850089\pi$
$23$	−4.52607	+	2.61313i	−0.943750	+	0.544874i	−0.0526163	+	0.998615i	$0.516756\pi$
$24$		0			0
$25$	−2.20711	+	3.82282i	−0.441421	+	0.764564i
$26$		0			0
$27$	−1.00000			−0.192450
$28$		0			0
$29$	−2.58579			−0.480168			−0.240084	−	0.970752i	$-0.577175\pi$
$29$	−2.58579			−0.480168			−0.240084	+	0.970752i	$0.577175\pi$
$30$		0			0
$31$	0.828427	−	1.43488i	0.148790	−	0.257712i	−0.781991	−	0.623290i	$-0.785796\pi$
$31$	0.828427	−	1.43488i	0.148790	−	0.257712i	0.930780	+	0.365579i	$0.119129\pi$
$32$		0			0
$33$	−1.87476	+	1.08239i	−0.326354	+	0.188420i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	0.707107	+	1.22474i	0.116248	+	0.201347i	0.918278	−	0.395937i	$-0.129580\pi$
$37$	0.707107	+	1.22474i	0.116248	+	0.201347i	−0.802030	+	0.597284i	$0.796247\pi$
$38$		0			0
$39$	−0.274552	−	0.158513i	−0.0439635	−	0.0253823i
$40$		0			0
$41$		−	5.99162i		−	0.935734i	−0.883799	−	0.467867i	$-0.845023\pi$
$41$		−	5.99162i		−	0.935734i	0.883799	−	0.467867i	$-0.154977\pi$
$42$		0			0
$43$			7.39104i			1.12712i	0.826074	+	0.563561i	$0.190569\pi$
$43$			7.39104i			1.12712i	−0.826074	+	0.563561i	$0.809431\pi$
$44$		0			0
$45$	0.662827	+	0.382683i	0.0988084	+	0.0570471i
$46$		0			0
$47$	4.82843	+	8.36308i	0.704298	+	1.21988i	0.966944	+	0.254988i	$0.0820717\pi$
$47$	4.82843	+	8.36308i	0.704298	+	1.21988i	−0.262646	+	0.964892i	$0.584595\pi$
$48$		0			0
$49$		0			0
$50$		0			0
$51$	−2.92586	+	1.68925i	−0.409702	+	0.236542i
$52$		0			0
$53$	−0.828427	+	1.43488i	−0.113793	+	0.197096i	−0.917297	−	0.398204i	$-0.869633\pi$
$53$	−0.828427	+	1.43488i	−0.113793	+	0.197096i	0.803503	+	0.595300i	$0.202967\pi$
$54$		0			0
$55$	1.65685			0.223410
$56$		0			0
$57$	5.65685			0.749269
$58$		0			0
$59$	2.82843	−	4.89898i	0.368230	−	0.637793i	−0.621059	−	0.783764i	$-0.713297\pi$
$59$	2.82843	−	4.89898i	0.368230	−	0.637793i	0.989289	+	0.145971i	$0.0466306\pi$
$60$		0			0
$61$	−6.12627	+	3.53701i	−0.784389	+	0.452867i	−0.837983	−	0.545696i	$-0.816265\pi$
$61$	−6.12627	+	3.53701i	−0.784389	+	0.452867i	0.0535946	+	0.998563i	$0.482932\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	0.121320	+	0.210133i	0.0150479	+	0.0260638i
$66$		0			0
$67$	−10.1503	−	5.86030i	−1.24006	−	0.715950i	−0.270955	−	0.962592i	$-0.587339\pi$
$67$	−10.1503	−	5.86030i	−1.24006	−	0.715950i	−0.969107	+	0.246642i	$0.920673\pi$
$68$		0			0
$69$			5.22625i			0.629167i
$70$		0			0
$71$			15.6788i			1.86073i	0.366640	+	0.930363i	$0.380508\pi$
$71$			15.6788i			1.86073i	−0.366640	+	0.930363i	$0.619492\pi$
$72$		0			0
$73$	5.73800	+	3.31283i	0.671582	+	0.387738i	0.796676	−	0.604407i	$-0.206590\pi$
$73$	5.73800	+	3.31283i	0.671582	+	0.387738i	−0.125094	+	0.992145i	$0.539923\pi$
$74$		0			0
$75$	2.20711	+	3.82282i	0.254855	+	0.441421i
$76$		0			0
$77$		0			0
$78$		0			0
$79$	−11.7034	+	6.75699i	−1.31674	+	0.760220i	−0.983203	−	0.182517i	$-0.941576\pi$
$79$	−11.7034	+	6.75699i	−1.31674	+	0.760220i	−0.333537	+	0.942737i	$0.608242\pi$
$80$		0			0
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$		0			0
$83$	−6.34315			−0.696251			−0.348125	−	0.937448i	$-0.613182\pi$
$83$	−6.34315			−0.696251			−0.348125	+	0.937448i	$0.613182\pi$
$84$		0			0
$85$	2.58579			0.280468
$86$		0			0
$87$	−1.29289	+	2.23936i	−0.138613	+	0.240084i
$88$		0			0
$89$	9.87579	−	5.70179i	1.04683	−	0.604389i	0.125071	−	0.992148i	$-0.460084\pi$
$89$	9.87579	−	5.70179i	1.04683	−	0.604389i	0.921761	+	0.387759i	$0.126751\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$	−0.828427	−	1.43488i	−0.0859039	−	0.148790i
$94$		0			0
$95$	−3.74952	−	2.16478i	−0.384692	−	0.222102i
$96$		0			0
$97$			3.82683i			0.388556i	0.980946	+	0.194278i	$0.0622364\pi$
$97$			3.82683i			0.388556i	−0.980946	+	0.194278i	$0.937764\pi$
$98$		0			0
$99$			2.16478i			0.217569i
$100$		0			0
$101$	−14.4019	−	8.31492i	−1.43304	−	0.827365i	−0.435687	−	0.900098i	$-0.643494\pi$
$101$	−14.4019	−	8.31492i	−1.43304	−	0.827365i	−0.997351	+	0.0727333i	$0.976828\pi$
$102$		0			0
$103$	6.00000	+	10.3923i	0.591198	+	1.02398i	0.994071	+	0.108729i	$0.0346780\pi$
$103$	6.00000	+	10.3923i	0.591198	+	1.02398i	−0.402874	+	0.915255i	$0.631989\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−3.42786	+	1.97908i	−0.331384	+	0.191324i	−0.656455	−	0.754365i	$-0.727945\pi$
$107$	−3.42786	+	1.97908i	−0.331384	+	0.191324i	0.325072	+	0.945689i	$0.394612\pi$
$108$		0			0
$109$	2.36396	−	4.09450i	0.226426	−	0.392182i	−0.730320	−	0.683105i	$-0.760629\pi$
$109$	2.36396	−	4.09450i	0.226426	−	0.392182i	0.956746	+	0.290923i	$0.0939624\pi$
$110$		0			0
$111$	1.41421			0.134231
$112$		0			0
$113$	−16.9706			−1.59646			−0.798228	−	0.602355i	$-0.794229\pi$
$113$	−16.9706			−1.59646			−0.798228	+	0.602355i	$0.794229\pi$
$114$		0			0
$115$	2.00000	−	3.46410i	0.186501	−	0.323029i
$116$		0			0
$117$	−0.274552	+	0.158513i	−0.0253823	+	0.0146545i
$118$		0			0
$119$		0			0
$120$		0			0
$121$	−3.15685	−	5.46783i	−0.286987	−	0.497076i
$122$		0			0
$123$	−5.18889	−	2.99581i	−0.467867	−	0.270123i
$124$		0			0
$125$		−	7.20533i		−	0.644464i
$126$		0			0
$127$			13.5140i			1.19917i	0.800311	+	0.599586i	$0.204668\pi$
$127$			13.5140i			1.19917i	−0.800311	+	0.599586i	$0.795332\pi$
$128$		0			0
$129$	6.40083	+	3.69552i	0.563561	+	0.325372i
$130$		0			0
$131$	7.65685	+	13.2621i	0.668982	+	1.15871i	0.978189	+	0.207717i	$0.0666032\pi$
$131$	7.65685	+	13.2621i	0.668982	+	1.15871i	−0.309207	+	0.950995i	$0.600063\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$	0.662827	−	0.382683i	0.0570471	−	0.0329361i
$136$		0			0
$137$	6.70711	−	11.6170i	0.573027	−	0.992512i	−0.423226	−	0.906024i	$-0.639102\pi$
$137$	6.70711	−	11.6170i	0.573027	−	0.992512i	0.996253	−	0.0864875i	$-0.0275642\pi$
$138$		0			0
$139$	−17.6569			−1.49763			−0.748817	−	0.662776i	$-0.769378\pi$
$139$	−17.6569			−1.49763			−0.748817	+	0.662776i	$0.769378\pi$
$140$		0			0
$141$	9.65685			0.813254
$142$		0			0
$143$	−0.343146	+	0.594346i	−0.0286953	+	0.0497017i
$144$		0			0
$145$	1.71393	−	0.989538i	0.142334	−	0.0821766i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	6.48528	+	11.2328i	0.531295	+	0.920230i	0.999333	+	0.0365215i	$0.0116277\pi$
$149$	6.48528	+	11.2328i	0.531295	+	0.920230i	−0.468038	+	0.883708i	$0.655039\pi$
$150$		0			0
$151$	5.30262	+	3.06147i	0.431521	+	0.249139i	0.699994	−	0.714148i	$-0.253186\pi$
$151$	5.30262	+	3.06147i	0.431521	+	0.249139i	−0.268473	+	0.963287i	$0.586519\pi$
$152$		0			0
$153$			3.37849i			0.273135i
$154$		0			0
$155$			1.26810i			0.101856i
$156$		0			0
$157$	12.9154	+	7.45669i	1.03076	+	0.595109i	0.917202	−	0.398422i	$-0.130442\pi$
$157$	12.9154	+	7.45669i	1.03076	+	0.595109i	0.113557	+	0.993531i	$0.463776\pi$
$158$		0			0
$159$	0.828427	+	1.43488i	0.0656985	+	0.113793i
$160$		0			0
$161$		0			0
$162$		0			0
$163$	−5.30262	+	3.06147i	−0.415333	+	0.239793i	−0.693079	−	0.720862i	$-0.743746\pi$
$163$	−5.30262	+	3.06147i	−0.415333	+	0.239793i	0.277746	+	0.960655i	$0.410413\pi$
$164$		0			0
$165$	0.828427	−	1.43488i	0.0644930	−	0.111705i
$166$		0			0
$167$	9.65685			0.747270			0.373635	−	0.927576i	$-0.378111\pi$
$167$	9.65685			0.747270			0.373635	+	0.927576i	$0.378111\pi$
$168$		0			0
$169$	12.8995			0.992269
$170$		0			0
$171$	2.82843	−	4.89898i	0.216295	−	0.374634i
$172$		0			0
$173$	8.16186	−	4.71225i	0.620535	−	0.358266i	−0.156542	−	0.987671i	$-0.550035\pi$
$173$	8.16186	−	4.71225i	0.620535	−	0.358266i	0.777077	+	0.629405i	$0.216701\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	−2.82843	−	4.89898i	−0.212598	−	0.368230i
$178$		0			0
$179$	−17.3277	−	10.0042i	−1.29513	−	0.747746i	−0.315575	−	0.948901i	$-0.602197\pi$
$179$	−17.3277	−	10.0042i	−1.29513	−	0.747746i	−0.979560	+	0.201154i	$0.935531\pi$
$180$		0			0
$181$			16.1815i			1.20276i	0.798963	+	0.601380i	$0.205382\pi$
$181$			16.1815i			1.20276i	−0.798963	+	0.601380i	$0.794618\pi$
$182$		0			0
$183$			7.07401i			0.522926i
$184$		0			0
$185$	−0.937379	−	0.541196i	−0.0689175	−	0.0397895i
$186$		0			0
$187$	3.65685	+	6.33386i	0.267416	+	0.463178i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−12.0251	+	6.94269i	−0.870106	+	0.502356i	−0.867383	−	0.497641i	$-0.834200\pi$
$191$	−12.0251	+	6.94269i	−0.870106	+	0.502356i	−0.00272234	+	0.999996i	$0.500867\pi$
$192$		0			0
$193$	−1.65685	+	2.86976i	−0.119263	+	0.206570i	−0.919476	−	0.393147i	$-0.871386\pi$
$193$	−1.65685	+	2.86976i	−0.119263	+	0.206570i	0.800213	+	0.599716i	$0.204720\pi$
$194$		0			0
$195$	0.242641			0.0173759
$196$		0			0
$197$	−25.3137			−1.80353			−0.901764	−	0.432230i	$-0.857727\pi$
$197$	−25.3137			−1.80353			−0.901764	+	0.432230i	$0.857727\pi$
$198$		0			0
$199$	2.82843	−	4.89898i	0.200502	−	0.347279i	−0.748188	−	0.663486i	$-0.769076\pi$
$199$	2.82843	−	4.89898i	0.200502	−	0.347279i	0.948690	+	0.316207i	$0.102409\pi$
$200$		0			0
$201$	−10.1503	+	5.86030i	−0.715950	+	0.413354i
$202$		0			0
$203$		0			0
$204$		0			0
$205$	2.29289	+	3.97141i	0.160143	+	0.277375i
$206$		0			0
$207$	4.52607	+	2.61313i	0.314583	+	0.181625i
$208$		0			0
$209$		−	12.2459i		−	0.847065i
$210$		0			0
$211$		−	7.39104i		−	0.508820i	−0.967096	−	0.254410i	$-0.918119\pi$
$211$		−	7.39104i		−	0.508820i	0.967096	−	0.254410i	$-0.0818813\pi$
$212$		0			0
$213$	13.5782	+	7.83938i	0.930363	+	0.537145i
$214$		0			0
$215$	−2.82843	−	4.89898i	−0.192897	−	0.334108i
$216$		0			0
$217$		0			0
$218$		0			0
$219$	5.73800	−	3.31283i	0.387738	−	0.223861i
$220$		0			0
$221$	−0.535534	+	0.927572i	−0.0360239	+	0.0623952i
$222$		0			0
$223$	19.3137			1.29334			0.646671	−	0.762769i	$-0.276161\pi$
$223$	19.3137			1.29334			0.646671	+	0.762769i	$0.276161\pi$
$224$		0			0
$225$	4.41421			0.294281
$226$		0			0
$227$	−1.65685	+	2.86976i	−0.109969	+	0.190472i	−0.915758	−	0.401731i	$-0.868409\pi$
$227$	−1.65685	+	2.86976i	−0.109969	+	0.190472i	0.805788	+	0.592204i	$0.201742\pi$
$228$		0			0
$229$	4.09069	−	2.36176i	0.270320	−	0.156069i	−0.358713	−	0.933448i	$-0.616784\pi$
$229$	4.09069	−	2.36176i	0.270320	−	0.156069i	0.629033	+	0.777379i	$0.283451\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−0.121320	−	0.210133i	−0.00794796	−	0.0137663i	0.862024	−	0.506867i	$-0.169197\pi$
$233$	−0.121320	−	0.210133i	−0.00794796	−	0.0137663i	−0.869972	+	0.493101i	$0.835863\pi$
$234$		0			0
$235$	−6.40083	−	3.69552i	−0.417544	−	0.241069i
$236$		0			0
$237$			13.5140i			0.877827i
$238$		0			0
$239$			0.896683i			0.0580016i	0.999579	+	0.0290008i	$0.00923254\pi$
$239$			0.896683i			0.0580016i	−0.999579	+	0.0290008i	$0.990767\pi$
$240$		0			0
$241$	−2.69841	−	1.55793i	−0.173820	−	0.100355i	0.410566	−	0.911831i	$-0.365331\pi$
$241$	−2.69841	−	1.55793i	−0.173820	−	0.100355i	−0.584386	+	0.811476i	$0.698665\pi$
$242$		0			0
$243$	0.500000	+	0.866025i	0.0320750	+	0.0555556i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	1.55310	−	0.896683i	0.0988214	−	0.0570546i
$248$		0			0
$249$	−3.17157	+	5.49333i	−0.200990	+	0.348125i
$250$		0			0
$251$	−8.97056			−0.566217			−0.283108	−	0.959088i	$-0.591366\pi$
$251$	−8.97056			−0.566217			−0.283108	+	0.959088i	$0.591366\pi$
$252$		0			0
$253$	11.3137			0.711287
$254$		0			0
$255$	1.29289	−	2.23936i	0.0809641	−	0.140234i
$256$		0			0
$257$	16.4374	−	9.49016i	1.02534	−	0.591980i	0.109693	−	0.993965i	$-0.465013\pi$
$257$	16.4374	−	9.49016i	1.02534	−	0.591980i	0.915646	+	0.401985i	$0.131680\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$	1.29289	+	2.23936i	0.0800281	+	0.138613i
$262$		0			0
$263$	22.6303	+	13.0656i	1.39545	+	0.805661i	0.993911	−	0.110183i	$-0.0351435\pi$
$263$	22.6303	+	13.0656i	1.39545	+	0.805661i	0.401535	+	0.915844i	$0.368477\pi$
$264$		0			0
$265$		−	1.26810i		−	0.0778988i
$266$		0			0
$267$		−	11.4036i		−	0.697888i
$268$		0			0
$269$	−21.8067	−	12.5901i	−1.32958	−	0.767631i	−0.344343	−	0.938844i	$-0.611898\pi$
$269$	−21.8067	−	12.5901i	−1.32958	−	0.767631i	−0.985234	+	0.171213i	$0.945231\pi$
$270$		0			0
$271$	−4.82843	−	8.36308i	−0.293306	−	0.508021i	0.681283	−	0.732020i	$-0.261422\pi$
$271$	−4.82843	−	8.36308i	−0.293306	−	0.508021i	−0.974589	+	0.223999i	$0.928089\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	8.27558	−	4.77791i	0.499036	−	0.288119i
$276$		0			0
$277$	4.65685	−	8.06591i	0.279803	−	0.484633i	−0.691532	−	0.722345i	$-0.743064\pi$
$277$	4.65685	−	8.06591i	0.279803	−	0.484633i	0.971336	+	0.237712i	$0.0763974\pi$
$278$		0			0
$279$	−1.65685			−0.0991933
$280$		0			0
$281$	−22.3848			−1.33536			−0.667682	−	0.744447i	$-0.732713\pi$
$281$	−22.3848			−1.33536			−0.667682	+	0.744447i	$0.732713\pi$
$282$		0			0
$283$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$283$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$284$		0			0
$285$	−3.74952	+	2.16478i	−0.222102	+	0.128231i
$286$		0			0
$287$		0			0
$288$		0			0
$289$	−2.79289	−	4.83743i	−0.164288	−	0.284555i
$290$		0			0
$291$	3.31414	+	1.91342i	0.194278	+	0.112167i
$292$		0			0
$293$		−	31.4119i		−	1.83510i	−0.397617	−	0.917552i	$-0.630163\pi$
$293$		−	31.4119i		−	1.83510i	0.397617	−	0.917552i	$-0.369837\pi$
$294$		0			0
$295$			4.32957i			0.252077i
$296$		0			0
$297$	1.87476	+	1.08239i	0.108785	+	0.0628068i
$298$		0			0
$299$	0.828427	+	1.43488i	0.0479092	+	0.0829811i
$300$		0			0
$301$		0			0
$302$		0			0
$303$	−14.4019	+	8.31492i	−0.827365	+	0.477679i
$304$		0			0
$305$	2.70711	−	4.68885i	0.155008	−	0.268483i
$306$		0			0
$307$	−3.31371			−0.189123			−0.0945617	−	0.995519i	$-0.530145\pi$
$307$	−3.31371			−0.189123			−0.0945617	+	0.995519i	$0.530145\pi$
$308$		0			0
$309$	12.0000			0.682656
$310$		0			0
$311$	2.00000	−	3.46410i	0.113410	−	0.196431i	−0.803733	−	0.594990i	$-0.797156\pi$
$311$	2.00000	−	3.46410i	0.113410	−	0.196431i	0.917143	+	0.398559i	$0.130489\pi$
$312$		0			0
$313$	−17.2140	+	9.93850i	−0.972992	+	0.561757i	−0.900147	−	0.435586i	$-0.856541\pi$
$313$	−17.2140	+	9.93850i	−0.972992	+	0.561757i	−0.0728452	+	0.997343i	$0.523208\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	2.65685	+	4.60181i	0.149224	+	0.258463i	0.930941	−	0.365170i	$-0.118989\pi$
$317$	2.65685	+	4.60181i	0.149224	+	0.258463i	−0.781717	+	0.623633i	$0.785656\pi$
$318$		0			0
$319$	4.84772	+	2.79884i	0.271420	+	0.156705i
$320$		0			0
$321$			3.95815i			0.220922i
$322$		0			0
$323$		−	19.1116i		−	1.06340i
$324$		0			0
$325$	1.21193	+	0.699709i	0.0672258	+	0.0388129i
$326$		0			0
$327$	−2.36396	−	4.09450i	−0.130727	−	0.226426i
$328$		0			0
$329$		0			0
$330$		0			0
$331$	21.8538	−	12.6173i	1.20119	−	0.693509i	0.240372	−	0.970681i	$-0.422730\pi$
$331$	21.8538	−	12.6173i	1.20119	−	0.693509i	0.960820	+	0.277172i	$0.0893972\pi$
$332$		0			0
$333$	0.707107	−	1.22474i	0.0387492	−	0.0671156i
$334$		0			0
$335$	8.97056			0.490114
$336$		0			0
$337$	20.7279			1.12912			0.564561	−	0.825391i	$-0.309046\pi$
$337$	20.7279			1.12912			0.564561	+	0.825391i	$0.309046\pi$
$338$		0			0
$339$	−8.48528	+	14.6969i	−0.460857	+	0.798228i
$340$		0			0
$341$	−3.10620	+	1.79337i	−0.168210	+	0.0971162i
$342$		0			0
$343$		0			0
$344$		0			0
$345$	−2.00000	−	3.46410i	−0.107676	−	0.186501i
$346$		0			0
$347$	2.97297	+	1.71644i	0.159597	+	0.0921435i	0.577671	−	0.816269i	$-0.303961\pi$
$347$	2.97297	+	1.71644i	0.159597	+	0.0921435i	−0.418074	+	0.908413i	$0.637295\pi$
$348$		0			0
$349$			20.7737i			1.11199i	0.831186	+	0.555995i	$0.187663\pi$
$349$			20.7737i			1.11199i	−0.831186	+	0.555995i	$0.812337\pi$
$350$		0			0
$351$			0.317025i			0.0169216i
$352$		0			0
$353$	−12.9154	−	7.45669i	−0.687416	−	0.396880i	0.115227	−	0.993339i	$-0.463240\pi$
$353$	−12.9154	−	7.45669i	−0.687416	−	0.396880i	−0.802643	+	0.596459i	$0.796574\pi$
$354$		0			0
$355$	−6.00000	−	10.3923i	−0.318447	−	0.551566i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	13.5782	−	7.83938i	0.716630	−	0.413747i	−0.0968810	−	0.995296i	$-0.530887\pi$
$359$	13.5782	−	7.83938i	0.716630	−	0.413747i	0.813511	+	0.581549i	$0.197553\pi$
$360$		0			0
$361$	−6.50000	+	11.2583i	−0.342105	+	0.592544i
$362$		0			0
$363$	−6.31371			−0.331384
$364$		0			0
$365$	−5.07107			−0.265432
$366$		0			0
$367$	−10.8284	+	18.7554i	−0.565239	+	0.979023i	0.431788	+	0.901975i	$0.357883\pi$
$367$	−10.8284	+	18.7554i	−0.565239	+	0.979023i	−0.997027	+	0.0770481i	$0.975450\pi$
$368$		0			0
$369$	−5.18889	+	2.99581i	−0.270123	+	0.155956i
$370$		0			0
$371$		0			0
$372$		0			0
$373$	−17.3137	−	29.9882i	−0.896470	−	1.55273i	−0.831975	−	0.554813i	$-0.812790\pi$
$373$	−17.3137	−	29.9882i	−0.896470	−	1.55273i	−0.0644950	−	0.997918i	$-0.520544\pi$
$374$		0			0
$375$	−6.24000	−	3.60266i	−0.322232	−	0.186041i
$376$		0			0
$377$			0.819760i			0.0422198i
$378$		0			0
$379$		−	33.1509i		−	1.70285i	−0.524479	−	0.851423i	$-0.675740\pi$
$379$		−	33.1509i		−	1.70285i	0.524479	−	0.851423i	$-0.324260\pi$
$380$		0			0
$381$	11.7034	+	6.75699i	0.599586	+	0.346171i
$382$		0			0
$383$	−18.1421	−	31.4231i	−0.927020	−	1.60565i	−0.788280	−	0.615317i	$-0.789028\pi$
$383$	−18.1421	−	31.4231i	−0.927020	−	1.60565i	−0.138740	−	0.990329i	$-0.544305\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	6.40083	−	3.69552i	0.325372	−	0.187854i
$388$		0			0
$389$	−10.0208	+	17.3566i	−0.508076	+	0.880013i	0.491881	+	0.870663i	$0.336310\pi$
$389$	−10.0208	+	17.3566i	−0.508076	+	0.880013i	−0.999956	+	0.00935003i	$0.997024\pi$
$390$		0			0
$391$	17.6569			0.892946
$392$		0			0
$393$	15.3137			0.772474
$394$		0			0
$395$	5.17157	−	8.95743i	0.260210	−	0.450697i
$396$		0			0
$397$	−16.8257	+	9.71433i	−0.844459	+	0.487548i	−0.858777	−	0.512349i	$-0.828775\pi$
$397$	−16.8257	+	9.71433i	−0.844459	+	0.487548i	0.0143187	+	0.999897i	$0.495442\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	11.4350	+	19.8061i	0.571038	+	0.989067i	0.996460	+	0.0840717i	$0.0267925\pi$
$401$	11.4350	+	19.8061i	0.571038	+	0.989067i	−0.425422	+	0.904995i	$0.639874\pi$
$402$		0			0
$403$	−0.454893	−	0.262632i	−0.0226598	−	0.0130827i
$404$		0			0
$405$		−	0.765367i		−	0.0380314i
$406$		0			0
$407$		−	3.06147i		−	0.151751i
$408$		0			0
$409$	6.83621	+	3.94689i	0.338029	+	0.195161i	0.659400	−	0.751792i	$-0.270810\pi$
$409$	6.83621	+	3.94689i	0.338029	+	0.195161i	−0.321371	+	0.946953i	$0.604144\pi$
$410$		0			0
$411$	−6.70711	−	11.6170i	−0.330837	−	0.573027i
$412$		0			0
$413$		0			0
$414$		0			0
$415$	4.20441	−	2.42742i	0.206386	−	0.119157i
$416$		0			0
$417$	−8.82843	+	15.2913i	−0.432330	+	0.748817i
$418$		0			0
$419$	−22.6274			−1.10542			−0.552711	−	0.833373i	$-0.686407\pi$
$419$	−22.6274			−1.10542			−0.552711	+	0.833373i	$0.686407\pi$
$420$		0			0
$421$	−6.68629			−0.325870			−0.162935	−	0.986637i	$-0.552096\pi$
$421$	−6.68629			−0.325870			−0.162935	+	0.986637i	$0.552096\pi$
$422$		0			0
$423$	4.82843	−	8.36308i	0.234766	−	0.406627i
$424$		0			0
$425$	12.9154	−	7.45669i	0.626488	−	0.361703i
$426$		0			0
$427$		0			0
$428$		0			0
$429$	0.343146	+	0.594346i	0.0165672	+	0.0286953i
$430$		0			0
$431$	13.1233	+	7.57675i	0.632128	+	0.364959i	0.781576	−	0.623811i	$-0.214416\pi$
$431$	13.1233	+	7.57675i	0.632128	+	0.364959i	−0.149448	+	0.988770i	$0.547750\pi$
$432$		0			0
$433$		−	9.87285i		−	0.474459i	−0.971454	−	0.237229i	$-0.923761\pi$
$433$		−	9.87285i		−	0.474459i	0.971454	−	0.237229i	$-0.0762393\pi$
$434$		0			0
$435$		−	1.97908i		−	0.0948894i
$436$		0			0
$437$	−25.6033	−	14.7821i	−1.22477	−	0.707122i
$438$		0			0
$439$	−11.3137	−	19.5959i	−0.539974	−	0.935262i	−0.998905	−	0.0467902i	$-0.985101\pi$
$439$	−11.3137	−	19.5959i	−0.539974	−	0.935262i	0.458931	−	0.888472i	$-0.348233\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	22.6303	−	13.0656i	1.07520	−	0.620767i	0.145602	−	0.989343i	$-0.453488\pi$
$443$	22.6303	−	13.0656i	1.07520	−	0.620767i	0.929597	+	0.368576i	$0.120155\pi$
$444$		0			0
$445$	−4.36396	+	7.55860i	−0.206872	+	0.358312i
$446$		0			0
$447$	12.9706			0.613487
$448$		0			0
$449$	−29.6569			−1.39959			−0.699797	−	0.714342i	$-0.746726\pi$
$449$	−29.6569			−1.39959			−0.699797	+	0.714342i	$0.746726\pi$
$450$		0			0
$451$	−6.48528	+	11.2328i	−0.305380	+	0.528934i
$452$		0			0
$453$	5.30262	−	3.06147i	0.249139	−	0.143840i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	9.65685	+	16.7262i	0.451729	+	0.782417i	0.998494	−	0.0548693i	$-0.0174742\pi$
$457$	9.65685	+	16.7262i	0.451729	+	0.782417i	−0.546765	+	0.837286i	$0.684141\pi$
$458$		0			0
$459$	2.92586	+	1.68925i	0.136567	+	0.0788473i
$460$		0			0
$461$		−	24.2066i		−	1.12741i	−0.825975	−	0.563706i	$-0.809375\pi$
$461$		−	24.2066i		−	1.12741i	0.825975	−	0.563706i	$-0.190625\pi$
$462$		0			0
$463$			1.79337i			0.0833448i	0.999131	+	0.0416724i	$0.0132686\pi$
$463$			1.79337i			0.0833448i	−0.999131	+	0.0416724i	$0.986731\pi$
$464$		0			0
$465$	1.09821	+	0.634051i	0.0509282	+	0.0294034i
$466$		0			0
$467$	−9.65685	−	16.7262i	−0.446866	−	0.773994i	0.551314	−	0.834298i	$-0.314127\pi$
$467$	−9.65685	−	16.7262i	−0.446866	−	0.773994i	−0.998180	+	0.0603032i	$0.980793\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$	12.9154	−	7.45669i	0.595109	−	0.343586i
$472$		0			0
$473$	8.00000	−	13.8564i	0.367840	−	0.637118i
$474$		0			0
$475$	−24.9706			−1.14573
$476$		0			0
$477$	1.65685			0.0758621
$478$		0			0
$479$	−13.3137	+	23.0600i	−0.608319	+	1.05364i	0.383199	+	0.923666i	$0.374822\pi$
$479$	−13.3137	+	23.0600i	−0.608319	+	1.05364i	−0.991518	+	0.129973i	$0.958511\pi$
$480$		0			0
$481$	0.388275	−	0.224171i	0.0177038	−	0.0102213i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−1.46447	−	2.53653i	−0.0664980	−	0.115178i
$486$		0			0
$487$	30.9059	+	17.8435i	1.40048	+	0.808568i	0.994442	−	0.105288i	$-0.0335764\pi$
$487$	30.9059	+	17.8435i	1.40048	+	0.808568i	0.406039	+	0.913856i	$0.366910\pi$
$488$		0			0
$489$			6.12293i			0.276889i
$490$		0			0
$491$		−	14.4107i		−	0.650344i	−0.945655	−	0.325172i	$-0.894578\pi$
$491$		−	14.4107i		−	0.650344i	0.945655	−	0.325172i	$-0.105422\pi$
$492$		0			0
$493$	7.56565	+	4.36803i	0.340740	+	0.196726i
$494$		0			0
$495$	−0.828427	−	1.43488i	−0.0372350	−	0.0644930i
$496$		0			0
$497$		0			0
$498$		0			0
$499$	14.9981	−	8.65914i	0.671406	−	0.387636i	−0.125203	−	0.992131i	$-0.539958\pi$
$499$	14.9981	−	8.65914i	0.671406	−	0.387636i	0.796609	+	0.604495i	$0.206625\pi$
$500$		0			0
$501$	4.82843	−	8.36308i	0.215718	−	0.373635i
$502$		0			0
$503$	37.6569			1.67904			0.839518	−	0.543332i	$-0.182837\pi$
$503$	37.6569			1.67904			0.839518	+	0.543332i	$0.182837\pi$
$504$		0			0
$505$	12.7279			0.566385
$506$		0			0
$507$	6.44975	−	11.1713i	0.286443	−	0.496134i
$508$		0			0
$509$	−9.09924	+	5.25345i	−0.403317	+	0.232855i	−0.687914	−	0.725792i	$-0.741473\pi$
$509$	−9.09924	+	5.25345i	−0.403317	+	0.232855i	0.284597	+	0.958647i	$0.408140\pi$
$510$		0			0
$511$		0			0
$512$		0			0
$513$	−2.82843	−	4.89898i	−0.124878	−	0.216295i
$514$		0			0
$515$	−7.95393	−	4.59220i	−0.350492	−	0.202357i
$516$		0			0
$517$		−	20.9050i		−	0.919401i
$518$		0			0
$519$		−	9.42450i		−	0.413690i
$520$		0			0
$521$	1.43938	+	0.831025i	0.0630603	+	0.0364079i	0.531199	−	0.847247i	$-0.321742\pi$
$521$	1.43938	+	0.831025i	0.0630603	+	0.0364079i	−0.468138	+	0.883655i	$0.655075\pi$
$522$		0			0
$523$	−5.31371	−	9.20361i	−0.232352	−	0.402446i	0.726148	−	0.687539i	$-0.241309\pi$
$523$	−5.31371	−	9.20361i	−0.232352	−	0.402446i	−0.958500	+	0.285093i	$0.907976\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−4.84772	+	2.79884i	−0.211170	+	0.121919i
$528$		0			0
$529$	2.15685	−	3.73578i	0.0937763	−	0.162425i
$530$		0			0
$531$	−5.65685			−0.245487
$532$		0			0
$533$	−1.89949			−0.0822763
$534$		0			0
$535$	1.51472	−	2.62357i	0.0654870	−	0.113427i
$536$		0			0
$537$	−17.3277	+	10.0042i	−0.747746	+	0.431711i
$538$		0			0
$539$		0			0
$540$		0			0
$541$	6.00000	+	10.3923i	0.257960	+	0.446800i	0.965695	−	0.259678i	$-0.0836163\pi$
$541$	6.00000	+	10.3923i	0.257960	+	0.446800i	−0.707735	+	0.706478i	$0.750283\pi$
$542$		0			0
$543$	14.0136	+	8.09075i	0.601380	+	0.347207i
$544$		0			0
$545$			3.61859i			0.155004i
$546$		0			0
$547$		−	30.8322i		−	1.31829i	−0.752015	−	0.659146i	$-0.770918\pi$
$547$		−	30.8322i		−	1.31829i	0.752015	−	0.659146i	$-0.229082\pi$
$548$		0			0
$549$	6.12627	+	3.53701i	0.261463	+	0.150956i
$550$		0			0
$551$	−7.31371	−	12.6677i	−0.311574	−	0.539663i
$552$		0			0
$553$		0			0
$554$		0			0
$555$	−0.937379	+	0.541196i	−0.0397895	+	0.0229725i
$556$		0			0
$557$	−10.6569	+	18.4582i	−0.451545	+	0.782100i	−0.998482	−	0.0550743i	$-0.982460\pi$
$557$	−10.6569	+	18.4582i	−0.451545	+	0.782100i	0.546937	+	0.837174i	$0.315794\pi$
$558$		0			0
$559$	2.34315			0.0991045
$560$		0			0
$561$	7.31371			0.308785
$562$		0			0
$563$	−16.4853	+	28.5533i	−0.694772	+	1.20338i	0.275486	+	0.961305i	$0.411161\pi$
$563$	−16.4853	+	28.5533i	−0.694772	+	1.20338i	−0.970258	+	0.242075i	$0.922172\pi$
$564$		0			0
$565$	11.2485	−	6.49435i	0.473230	−	0.273219i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−1.29289	−	2.23936i	−0.0542009	−	0.0938787i	0.837652	−	0.546204i	$-0.183928\pi$
$569$	−1.29289	−	2.23936i	−0.0542009	−	0.0938787i	−0.891853	+	0.452326i	$0.850594\pi$
$570$		0			0
$571$	19.2025	+	11.0866i	0.803599	+	0.463958i	0.844728	−	0.535196i	$-0.179762\pi$
$571$	19.2025	+	11.0866i	0.803599	+	0.463958i	−0.0411293	+	0.999154i	$0.513096\pi$
$572$		0			0
$573$			13.8854i			0.580070i
$574$		0			0
$575$		−	23.0698i		−	0.962077i
$576$		0			0
$577$	−11.2014	−	6.46716i	−0.466322	−	0.269231i	0.248377	−	0.968664i	$-0.420103\pi$
$577$	−11.2014	−	6.46716i	−0.466322	−	0.269231i	−0.714699	+	0.699432i	$0.753436\pi$
$578$		0			0
$579$	1.65685	+	2.86976i	0.0688565	+	0.119263i
$580$		0			0
$581$		0			0
$582$		0			0
$583$	3.10620	−	1.79337i	0.128646	−	0.0742736i
$584$		0			0
$585$	0.121320	−	0.210133i	0.00501598	−	0.00868793i
$586$		0			0
$587$	−8.97056			−0.370255			−0.185127	−	0.982715i	$-0.559270\pi$
$587$	−8.97056			−0.370255			−0.185127	+	0.982715i	$0.559270\pi$
$588$		0			0
$589$	9.37258			0.386191
$590$		0			0
$591$	−12.6569	+	21.9223i	−0.520633	+	0.901764i
$592$		0			0
$593$	20.0261	−	11.5621i	0.822375	−	0.474798i	−0.0288600	−	0.999583i	$-0.509188\pi$
$593$	20.0261	−	11.5621i	0.822375	−	0.474798i	0.851235	+	0.524785i	$0.175854\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	−2.82843	−	4.89898i	−0.115760	−	0.200502i
$598$		0			0
$599$	8.27558	+	4.77791i	0.338131	+	0.195220i	0.659445	−	0.751753i	$-0.270791\pi$
$599$	8.27558	+	4.77791i	0.338131	+	0.195220i	−0.321314	+	0.946973i	$0.604125\pi$
$600$		0			0
$601$			44.1061i			1.79913i	0.436791	+	0.899563i	$0.356115\pi$
$601$			44.1061i			1.79913i	−0.436791	+	0.899563i	$0.643885\pi$
$602$		0			0
$603$			11.7206i			0.477300i
$604$		0			0
$605$	4.18490	+	2.41615i	0.170140	+	0.0982305i
$606$		0			0
$607$	−21.6569	−	37.5108i	−0.879025	−	1.52252i	−0.852413	−	0.522869i	$-0.824862\pi$
$607$	−21.6569	−	37.5108i	−0.879025	−	1.52252i	−0.0266118	−	0.999646i	$-0.508472\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	2.65131	−	1.53073i	0.107260	−	0.0619269i
$612$		0			0
$613$	2.12132	−	3.67423i	0.0856793	−	0.148401i	−0.820001	−	0.572362i	$-0.806027\pi$
$613$	2.12132	−	3.67423i	0.0856793	−	0.148401i	0.905680	+	0.423961i	$0.139361\pi$
$614$		0			0
$615$	4.58579			0.184917
$616$		0			0
$617$	−3.55635			−0.143173			−0.0715866	−	0.997434i	$-0.522806\pi$
$617$	−3.55635			−0.143173			−0.0715866	+	0.997434i	$0.522806\pi$
$618$		0			0
$619$	15.1716	−	26.2779i	0.609797	−	1.05620i	−0.381477	−	0.924379i	$-0.624584\pi$
$619$	15.1716	−	26.2779i	0.609797	−	1.05620i	0.991274	−	0.131821i	$-0.0420824\pi$
$620$		0			0
$621$	4.52607	−	2.61313i	0.181625	−	0.104861i
$622$		0			0
$623$		0			0
$624$		0			0
$625$	−8.27817	−	14.3382i	−0.331127	−	0.573529i
$626$		0			0
$627$	−10.6052	−	6.12293i	−0.423532	−	0.244526i
$628$		0			0
$629$		−	4.77791i		−	0.190508i
$630$		0			0
$631$			6.12293i			0.243750i	0.992545	+	0.121875i	$0.0388907\pi$
$631$			6.12293i			0.243750i	−0.992545	+	0.121875i	$0.961109\pi$
$632$		0			0
$633$	−6.40083	−	3.69552i	−0.254410	−	0.146884i
$634$		0			0
$635$	−5.17157	−	8.95743i	−0.205228	−	0.355465i
$636$		0			0
$637$		0			0
$638$		0			0
$639$	13.5782	−	7.83938i	0.537145	−	0.310121i
$640$		0			0
$641$	19.4350	−	33.6625i	0.767637	−	1.32959i	−0.171203	−	0.985236i	$-0.554766\pi$
$641$	19.4350	−	33.6625i	0.767637	−	1.32959i	0.938841	−	0.344351i	$-0.111901\pi$
$642$		0			0
$643$	21.6569			0.854063			0.427031	−	0.904237i	$-0.359559\pi$
$643$	21.6569			0.854063			0.427031	+	0.904237i	$0.359559\pi$
$644$		0			0
$645$	−5.65685			−0.222738
$646$		0			0
$647$	6.48528	−	11.2328i	0.254963	−	0.441608i	−0.709923	−	0.704280i	$-0.751270\pi$
$647$	6.48528	−	11.2328i	0.254963	−	0.441608i	0.964885	+	0.262671i	$0.0846035\pi$
$648$		0			0
$649$	−10.6052	+	6.12293i	−0.416292	+	0.240346i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−17.5355	−	30.3724i	−0.686218	−	1.18857i	−0.973052	−	0.230585i	$-0.925936\pi$
$653$	−17.5355	−	30.3724i	−0.686218	−	1.18857i	0.286834	−	0.957980i	$-0.407397\pi$
$654$		0			0
$655$	−10.1503	−	5.86030i	−0.396607	−	0.228981i
$656$		0			0
$657$		−	6.62567i		−	0.258492i
$658$		0			0
$659$		−	33.5223i		−	1.30584i	−0.757425	−	0.652922i	$-0.773543\pi$
$659$		−	33.5223i		−	1.30584i	0.757425	−	0.652922i	$-0.226457\pi$
$660$		0			0
$661$	29.2391	+	16.8812i	1.13727	+	0.656603i	0.945753	−	0.324887i	$-0.105326\pi$
$661$	29.2391	+	16.8812i	1.13727	+	0.656603i	0.191516	+	0.981489i	$0.438660\pi$
$662$		0			0
$663$	0.535534	+	0.927572i	0.0207984	+	0.0360239i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	11.7034	−	6.75699i	0.453159	−	0.261632i
$668$		0			0
$669$	9.65685	−	16.7262i	0.373356	−	0.646671i
$670$		0			0
$671$	15.3137			0.591179
$672$		0			0
$673$	−7.07107			−0.272570			−0.136285	−	0.990670i	$-0.543516\pi$
$673$	−7.07107			−0.272570			−0.136285	+	0.990670i	$0.543516\pi$
$674$		0			0
$675$	2.20711	−	3.82282i	0.0849516	−	0.147140i
$676$		0			0
$677$	−3.31414	+	1.91342i	−0.127373	+	0.0735386i	−0.562332	−	0.826911i	$-0.690096\pi$
$677$	−3.31414	+	1.91342i	−0.127373	+	0.0735386i	0.434960	+	0.900450i	$0.356763\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$	1.65685	+	2.86976i	0.0634908	+	0.109969i
$682$		0			0
$683$	18.8808	+	10.9008i	0.722454	+	0.417109i	0.815655	−	0.578538i	$-0.196377\pi$
$683$	18.8808	+	10.9008i	0.722454	+	0.417109i	−0.0932010	+	0.995647i	$0.529710\pi$
$684$		0			0
$685$			10.2668i			0.392274i
$686$		0			0
$687$		−	4.72352i		−	0.180213i
$688$		0			0
$689$	0.454893	+	0.262632i	0.0173300	+	0.0100055i
$690$		0			0
$691$	−0.828427	−	1.43488i	−0.0315149	−	0.0545853i	0.849838	−	0.527044i	$-0.176700\pi$
$691$	−0.828427	−	1.43488i	−0.0315149	−	0.0545853i	−0.881353	+	0.472459i	$0.843366\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	11.7034	−	6.75699i	0.443937	−	0.256307i
$696$		0			0
$697$	−10.1213	+	17.5306i	−0.383372	+	0.664020i
$698$		0			0
$699$	−0.242641			−0.00917751
$700$		0			0
$701$	6.38478			0.241150			0.120575	−	0.992704i	$-0.461526\pi$
$701$	6.38478			0.241150			0.120575	+	0.992704i	$0.461526\pi$
$702$		0			0
$703$	−4.00000	+	6.92820i	−0.150863	+	0.261302i
$704$		0			0
$705$	−6.40083	+	3.69552i	−0.241069	+	0.139181i
$706$		0			0
$707$		0			0
$708$		0			0
$709$	16.9497	+	29.3578i	0.636561	+	1.10256i	0.986182	+	0.165665i	$0.0529770\pi$
$709$	16.9497	+	29.3578i	0.636561	+	1.10256i	−0.349621	+	0.936891i	$0.613690\pi$
$710$		0			0
$711$	11.7034	+	6.75699i	0.438913	+	0.253407i
$712$		0			0
$713$			8.65914i			0.324287i
$714$		0			0
$715$		−	0.525265i		−	0.0196438i
$716$		0			0
$717$	0.776550	+	0.448342i	0.0290008	+	0.0167436i
$718$		0			0
$719$	10.1421	+	17.5667i	0.378238	+	0.655127i	0.990806	−	0.135291i	$-0.0431968\pi$
$719$	10.1421	+	17.5667i	0.378238	+	0.655127i	−0.612568	+	0.790418i	$0.709863\pi$
$720$		0			0
$721$		0			0
$722$		0			0
$723$	−2.69841	+	1.55793i	−0.100355	+	0.0579400i
$724$		0			0
$725$	5.70711	−	9.88500i	0.211957	−	0.367120i
$726$		0			0
$727$	−12.9706			−0.481052			−0.240526	−	0.970643i	$-0.577320\pi$
$727$	−12.9706			−0.481052			−0.240526	+	0.970643i	$0.577320\pi$
$728$		0			0
$729$	1.00000			0.0370370
$730$		0			0
$731$	12.4853	−	21.6251i	0.461785	−	0.799835i
$732$		0			0
$733$	44.2762	−	25.5629i	1.63538	−	0.944186i	0.652983	−	0.757373i	$-0.273517\pi$
$733$	44.2762	−	25.5629i	1.63538	−	0.944186i	0.982395	−	0.186813i	$-0.0598159\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	12.6863	+	21.9733i	0.467306	+	0.809397i
$738$		0			0
$739$	−36.2085	−	20.9050i	−1.33195	−	0.769003i	−0.346354	−	0.938104i	$-0.612580\pi$
$739$	−36.2085	−	20.9050i	−1.33195	−	0.769003i	−0.985599	+	0.169101i	$0.945914\pi$
$740$		0			0
$741$		−	1.79337i		−	0.0658810i
$742$		0			0
$743$			29.1927i			1.07098i	0.844542	+	0.535489i	$0.179873\pi$
$743$			29.1927i			1.07098i	−0.844542	+	0.535489i	$0.820127\pi$
$744$		0			0
$745$	−8.59724	−	4.96362i	−0.314979	−	0.181853i
$746$		0			0
$747$	3.17157	+	5.49333i	0.116042	+	0.200990i
$748$		0			0
$749$		0			0
$750$		0			0
$751$	−24.5051	+	14.1480i	−0.894204	+	0.516269i	−0.875315	−	0.483553i	$-0.839346\pi$
$751$	−24.5051	+	14.1480i	−0.894204	+	0.516269i	−0.0188884	+	0.999822i	$0.506013\pi$
$752$		0			0
$753$	−4.48528	+	7.76874i	−0.163453	+	0.283108i
$754$		0			0
$755$	−4.68629			−0.170552
$756$		0			0
$757$	−10.3848			−0.377441			−0.188721	−	0.982031i	$-0.560434\pi$
$757$	−10.3848			−0.377441			−0.188721	+	0.982031i	$0.560434\pi$
$758$		0			0
$759$	5.65685	−	9.79796i	0.205331	−	0.355643i
$760$		0			0
$761$	10.8798	−	6.28145i	0.394392	−	0.227702i	−0.289669	−	0.957127i	$-0.593545\pi$
$761$	10.8798	−	6.28145i	0.394392	−	0.227702i	0.684061	+	0.729424i	$0.260212\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$	−1.29289	−	2.23936i	−0.0467447	−	0.0809641i
$766$		0			0
$767$	−1.55310	−	0.896683i	−0.0560792	−	0.0323773i
$768$		0			0
$769$		−	40.5963i		−	1.46394i	−0.681337	−	0.731970i	$-0.738601\pi$
$769$		−	40.5963i		−	1.46394i	0.681337	−	0.731970i	$-0.261399\pi$
$770$		0			0
$771$		−	18.9803i		−	0.683560i
$772$		0			0
$773$	−7.51854	−	4.34083i	−0.270423	−	0.156129i	0.358657	−	0.933470i	$-0.383235\pi$
$773$	−7.51854	−	4.34083i	−0.270423	−	0.156129i	−0.629080	+	0.777341i	$0.716568\pi$
$774$		0			0
$775$	3.65685	+	6.33386i	0.131358	+	0.227519i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	29.3528	−	16.9469i	1.05167	−	0.607184i
$780$		0			0
$781$	16.9706	−	29.3939i	0.607254	−	1.05180i
$782$		0			0
$783$	2.58579			0.0924085
$784$		0			0
$785$	−11.4142			−0.407391
$786$		0			0
$787$	−11.6569	+	20.1903i	−0.415522	+	0.719705i	−0.995483	−	0.0949390i	$-0.969734\pi$
$787$	−11.6569	+	20.1903i	−0.415522	+	0.719705i	0.579961	+	0.814644i	$0.303068\pi$
$788$		0			0
$789$	22.6303	−	13.0656i	0.805661	−	0.465149i
$790$		0			0
$791$		0			0
$792$		0			0
$793$	1.12132	+	1.94218i	0.0398193	+	0.0689690i
$794$		0			0
$795$	−1.09821	−	0.634051i	−0.0389494	−	0.0224875i
$796$		0			0
$797$			2.48181i			0.0879102i	0.999034	+	0.0439551i	$0.0139959\pi$
$797$			2.48181i			0.0879102i	−0.999034	+	0.0439551i	$0.986004\pi$
$798$		0			0
$799$		−	32.6256i		−	1.15421i
$800$		0			0
$801$	−9.87579	−	5.70179i	−0.348944	−	0.201463i
$802$		0			0
$803$	−7.17157	−	12.4215i	−0.253079	−	0.438346i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	−21.8067	+	12.5901i	−0.767631	+	0.443192i
$808$		0			0
$809$	5.00000	−	8.66025i	0.175791	−	0.304478i	−0.764644	−	0.644453i	$-0.777085\pi$
$809$	5.00000	−	8.66025i	0.175791	−	0.304478i	0.940435	+	0.339975i	$0.110418\pi$
$810$		0			0
$811$	1.65685			0.0581800			0.0290900	−	0.999577i	$-0.490739\pi$
$811$	1.65685			0.0581800			0.0290900	+	0.999577i	$0.490739\pi$
$812$		0			0
$813$	−9.65685			−0.338681
$814$		0			0
$815$	2.34315	−	4.05845i	0.0820768	−	0.142161i
$816$		0			0
$817$	−36.2085	+	20.9050i	−1.26678	+	0.731374i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	12.6569	+	21.9223i	0.441727	+	0.765094i	0.997818	−	0.0660277i	$-0.0210326\pi$
$821$	12.6569	+	21.9223i	0.441727	+	0.765094i	−0.556091	+	0.831122i	$0.687699\pi$
$822$		0			0
$823$	29.8077	+	17.2095i	1.03903	+	0.599885i	0.919559	−	0.392952i	$-0.128546\pi$
$823$	29.8077	+	17.2095i	1.03903	+	0.599885i	0.119473	+	0.992837i	$0.461880\pi$
$824$		0			0
$825$		−	9.55582i		−	0.332691i
$826$		0			0
$827$			12.6173i			0.438746i	0.975641	+	0.219373i	$0.0704012\pi$
$827$			12.6173i			0.438746i	−0.975641	+	0.219373i	$0.929599\pi$
$828$		0			0
$829$	18.8337	+	10.8736i	0.654122	+	0.377657i	0.790034	−	0.613064i	$-0.210063\pi$
$829$	18.8337	+	10.8736i	0.654122	+	0.377657i	−0.135912	+	0.990721i	$0.543396\pi$
$830$		0			0
$831$	−4.65685	−	8.06591i	−0.161544	−	0.279803i
$832$		0			0
$833$		0			0
$834$		0			0
$835$	−6.40083	+	3.69552i	−0.221510	+	0.127889i
$836$		0			0
$837$	−0.828427	+	1.43488i	−0.0286346	+	0.0495966i
$838$		0			0
$839$	−29.9411			−1.03368			−0.516841	−	0.856081i	$-0.672892\pi$
$839$	−29.9411			−1.03368			−0.516841	+	0.856081i	$0.672892\pi$
$840$		0			0
$841$	−22.3137			−0.769438
$842$		0			0
$843$	−11.1924	+	19.3858i	−0.385486	+	0.667682i
$844$		0			0
$845$	−8.55014	+	4.93642i	−0.294134	+	0.169818i
$846$		0			0
$847$		0			0
$848$		0			0
$849$		0			0
$850$		0			0
$851$	−6.40083	−	3.69552i	−0.219417	−	0.126681i
$852$		0			0
$853$			5.46635i			0.187164i	0.995612	+	0.0935822i	$0.0298318\pi$
$853$			5.46635i			0.187164i	−0.995612	+	0.0935822i	$0.970168\pi$
$854$		0			0
$855$			4.32957i			0.148068i
$856$		0			0
$857$	41.2366	+	23.8080i	1.40862	+	0.813264i	0.995255	−	0.0973029i	$-0.0310216\pi$
$857$	41.2366	+	23.8080i	1.40862	+	0.813264i	0.413361	+	0.910567i	$0.364355\pi$
$858$		0			0
$859$	19.3137	+	33.4523i	0.658975	+	1.14138i	0.980881	+	0.194607i	$0.0623431\pi$
$859$	19.3137	+	33.4523i	0.658975	+	1.14138i	−0.321906	+	0.946772i	$0.604324\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−27.4781	+	15.8645i	−0.935364	+	0.540033i	−0.888504	−	0.458869i	$-0.848255\pi$
$863$	−27.4781	+	15.8645i	−0.935364	+	0.540033i	−0.0468600	+	0.998901i	$0.514921\pi$
$864$		0			0
$865$	−3.60660	+	6.24682i	−0.122628	+	0.212398i
$866$		0			0
$867$	−5.58579			−0.189703
$868$		0			0
$869$	29.2548			0.992402
$870$		0			0
$871$	−1.85786	+	3.21792i	−0.0629513	+	0.109035i
$872$		0			0
$873$	3.31414	−	1.91342i	0.112167	−	0.0647594i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−18.1213	−	31.3870i	−0.611914	−	1.05987i	−0.990918	−	0.134470i	$-0.957067\pi$
$877$	−18.1213	−	31.3870i	−0.611914	−	1.05987i	0.379004	−	0.925395i	$-0.376267\pi$
$878$		0			0
$879$	−27.2035	−	15.7060i	−0.917552	−	0.529749i
$880$		0			0
$881$			50.7862i			1.71103i	0.517778	+	0.855515i	$0.326759\pi$
$881$			50.7862i			1.71103i	−0.517778	+	0.855515i	$0.673241\pi$
$882$		0			0
$883$			16.5754i			0.557808i	0.960319	+	0.278904i	$0.0899711\pi$
$883$			16.5754i			0.557808i	−0.960319	+	0.278904i	$0.910029\pi$
$884$		0			0
$885$	3.74952	+	2.16478i	0.126039	+	0.0727684i
$886$		0			0
$887$	12.3431	+	21.3790i	0.414442	+	0.717835i	0.995370	−	0.0961203i	$-0.0306433\pi$
$887$	12.3431	+	21.3790i	0.414442	+	0.717835i	−0.580927	+	0.813955i	$0.697310\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	1.87476	−	1.08239i	0.0628068	−	0.0362615i
$892$		0			0
$893$	−27.3137	+	47.3087i	−0.914018	+	1.58313i
$894$		0			0
$895$	15.3137			0.511881
$896$		0			0
$897$	1.65685			0.0553208
$898$		0			0
$899$	−2.14214	+	3.71029i	−0.0714442	+	0.123745i
$900$		0			0
$901$	4.84772	−	2.79884i	0.161501	−	0.0932427i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−6.19239	−	10.7255i	−0.205842	−	0.356529i
$906$		0			0
$907$	1.55310	+	0.896683i	0.0515699	+	0.0297739i	0.525563	−	0.850755i	$-0.323855\pi$
$907$	1.55310	+	0.896683i	0.0515699	+	0.0297739i	−0.473993	+	0.880528i	$0.657188\pi$
$908$		0			0
$909$			16.6298i			0.551577i
$910$		0			0
$911$			26.6565i			0.883170i	0.897219	+	0.441585i	$0.145584\pi$
$911$			26.6565i			0.883170i	−0.897219	+	0.441585i	$0.854416\pi$
$912$		0			0
$913$	11.8919	+	6.86577i	0.393563	+	0.227224i
$914$		0			0
$915$	−2.70711	−	4.68885i	−0.0894942	−	0.155008i
$916$		0			0
$917$		0			0
$918$		0			0
$919$	25.1484	−	14.5194i	0.829569	−	0.478952i	−0.0241358	−	0.999709i	$-0.507683\pi$
$919$	25.1484	−	14.5194i	0.829569	−	0.478952i	0.853705	+	0.520757i	$0.174350\pi$
$920$		0			0
$921$	−1.65685	+	2.86976i	−0.0545952	+	0.0945617i
$922$		0			0
$923$	4.97056			0.163608
$924$		0			0
$925$	−6.24264			−0.205257
$926$		0			0
$927$	6.00000	−	10.3923i	0.197066	−	0.341328i
$928$		0			0
$929$	−11.9780	+	6.91550i	−0.392985	+	0.226890i	−0.683453	−	0.729995i	$-0.739523\pi$
$929$	−11.9780	+	6.91550i	−0.392985	+	0.226890i	0.290468	+	0.956885i	$0.406189\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$	−2.00000	−	3.46410i	−0.0654771	−	0.113410i
$934$		0			0
$935$	−4.84772	−	2.79884i	−0.158538	−	0.0915317i
$936$		0			0
$937$			3.82683i			0.125017i	0.998044	+	0.0625086i	$0.0199101\pi$
$937$			3.82683i			0.125017i	−0.998044	+	0.0625086i	$0.980090\pi$
$938$		0			0
$939$			19.8770i			0.648662i
$940$		0			0
$941$	−9.55413	−	5.51608i	−0.311456	−	0.179819i	0.336122	−	0.941818i	$-0.390885\pi$
$941$	−9.55413	−	5.51608i	−0.311456	−	0.179819i	−0.647578	+	0.761999i	$0.724218\pi$
$942$		0			0
$943$	15.6569	+	27.1185i	0.509857	+	0.883099i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−33.2356	+	19.1886i	−1.08001	+	0.623545i	−0.930899	−	0.365276i	$-0.880975\pi$
$947$	−33.2356	+	19.1886i	−1.08001	+	0.623545i	−0.149112	+	0.988820i	$0.547641\pi$
$948$		0			0
$949$	1.05025	−	1.81909i	0.0340926	−	0.0590502i
$950$		0			0
$951$	5.31371			0.172309
$952$		0			0
$953$	38.0000			1.23094			0.615470	−	0.788160i	$-0.288966\pi$
$953$	38.0000			1.23094			0.615470	+	0.788160i	$0.288966\pi$
$954$		0			0
$955$	5.31371	−	9.20361i	0.171948	−	0.297822i
$956$		0			0
$957$	4.84772	−	2.79884i	0.156705	−	0.0904735i
$958$		0			0
$959$		0			0
$960$		0			0
$961$	14.1274	+	24.4694i	0.455723	+	0.789336i
$962$		0			0
$963$	3.42786	+	1.97908i	0.110461	+	0.0637748i
$964$		0			0
$965$		−	2.53620i		−	0.0816433i
$966$		0			0
$967$			49.9439i			1.60609i	0.595920	+	0.803044i	$0.296787\pi$
$967$			49.9439i			1.60609i	−0.595920	+	0.803044i	$0.703213\pi$
$968$		0			0
$969$	−16.5512	−	9.55582i	−0.531700	−	0.306977i
$970$		0			0
$971$	5.51472	+	9.55177i	0.176976	+	0.306531i	0.940843	−	0.338842i	$-0.110035\pi$
$971$	5.51472	+	9.55177i	0.176976	+	0.306531i	−0.763868	+	0.645373i	$0.776702\pi$
$972$		0			0
$973$		0			0
$974$		0			0
$975$	1.21193	−	0.699709i	0.0388129	−	0.0224086i
$976$		0			0
$977$	21.0919	−	36.5322i	0.674789	−	1.16877i	−0.301741	−	0.953390i	$-0.597568\pi$
$977$	21.0919	−	36.5322i	0.674789	−	1.16877i	0.976530	−	0.215379i	$-0.0690988\pi$
$978$		0			0
$979$	−24.6863			−0.788977
$980$		0			0
$981$	−4.72792			−0.150951
$982$		0			0
$983$	11.7990	−	20.4364i	0.376329	−	0.651822i	−0.614196	−	0.789154i	$-0.710519\pi$
$983$	11.7990	−	20.4364i	0.376329	−	0.651822i	0.990525	+	0.137332i	$0.0438528\pi$
$984$		0			0
$985$	16.7786	−	9.68714i	0.534611	−	0.308658i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−19.3137	−	33.4523i	−0.614140	−	1.06372i
$990$		0			0
$991$	−13.2565	−	7.65367i	−0.421108	−	0.243127i	0.274443	−	0.961603i	$-0.411506\pi$
$991$	−13.2565	−	7.65367i	−0.421108	−	0.243127i	−0.695551	+	0.718476i	$0.744840\pi$
$992$		0			0
$993$		−	25.2346i		−	0.800795i
$994$		0			0
$995$			4.32957i			0.137257i
$996$		0			0
$997$	−42.2682	−	24.4036i	−1.33865	−	0.772868i	−0.352040	−	0.935985i	$-0.614512\pi$
$997$	−42.2682	−	24.4036i	−1.33865	−	0.772868i	−0.986607	+	0.163117i	$0.947845\pi$
$998$		0			0
$999$	−0.707107	−	1.22474i	−0.0223719	−	0.0387492i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2352.2.bl.s.31.2		8
4.3	odd	2		2352.2.bl.p.31.2		8
7.2	even	3	inner	2352.2.bl.s.607.3		8
7.3	odd	6		2352.2.b.j.1567.3	yes	4
7.4	even	3		2352.2.b.i.1567.2	✓	4
7.5	odd	6		2352.2.bl.p.607.2		8
7.6	odd	2		2352.2.bl.p.31.3		8
21.11	odd	6		7056.2.b.u.1567.3		4
21.17	even	6		7056.2.b.t.1567.2		4
28.3	even	6		2352.2.b.i.1567.3	yes	4
28.11	odd	6		2352.2.b.j.1567.2	yes	4
28.19	even	6	inner	2352.2.bl.s.607.2		8
28.23	odd	6		2352.2.bl.p.607.3		8
28.27	even	2	inner	2352.2.bl.s.31.3		8
84.11	even	6		7056.2.b.t.1567.3		4
84.59	odd	6		7056.2.b.u.1567.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2352.2.b.i.1567.2	✓	4	7.4	even	3
2352.2.b.i.1567.3	yes	4	28.3	even	6
2352.2.b.j.1567.2	yes	4	28.11	odd	6
2352.2.b.j.1567.3	yes	4	7.3	odd	6
2352.2.bl.p.31.2		8	4.3	odd	2
2352.2.bl.p.31.3		8	7.6	odd	2
2352.2.bl.p.607.2		8	7.5	odd	6
2352.2.bl.p.607.3		8	28.23	odd	6
2352.2.bl.s.31.2		8	1.1	even	1	trivial
2352.2.bl.s.31.3		8	28.27	even	2	inner
2352.2.bl.s.607.2		8	28.19	even	6	inner
2352.2.bl.s.607.3		8	7.2	even	3	inner
7056.2.b.t.1567.2		4	21.17	even	6
7056.2.b.t.1567.3		4	84.11	even	6
7056.2.b.u.1567.2		4	84.59	odd	6
7056.2.b.u.1567.3		4	21.11	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:	\( N \)	\(=\)	\( 2352 = 2^{4} \cdot 3 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2352.bl (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 - 0.866025i) q^{3} +(-0.662827 + 0.382683i) q^{5} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(0.500000 - 0.866025i) q^{3} +(-0.662827 + 0.382683i) q^{5} +(-0.500000 - 0.866025i) q^{9} +(-1.87476 - 1.08239i) q^{11} -0.317025i q^{13} +0.765367i q^{15} +(-2.92586 - 1.68925i) q^{17} +(2.82843 + 4.89898i) q^{19} +(-4.52607 + 2.61313i) q^{23} +(-2.20711 + 3.82282i) q^{25} -1.00000 q^{27} -2.58579 q^{29} +(0.828427 - 1.43488i) q^{31} +(-1.87476 + 1.08239i) q^{33} +(0.707107 + 1.22474i) q^{37} +(-0.274552 - 0.158513i) q^{39} -5.99162i q^{41} +7.39104i q^{43} +(0.662827 + 0.382683i) q^{45} +(4.82843 + 8.36308i) q^{47} +(-2.92586 + 1.68925i) q^{51} +(-0.828427 + 1.43488i) q^{53} +1.65685 q^{55} +5.65685 q^{57} +(2.82843 - 4.89898i) q^{59} +(-6.12627 + 3.53701i) q^{61} +(0.121320 + 0.210133i) q^{65} +(-10.1503 - 5.86030i) q^{67} +5.22625i q^{69} +15.6788i q^{71} +(5.73800 + 3.31283i) q^{73} +(2.20711 + 3.82282i) q^{75} +(-11.7034 + 6.75699i) q^{79} +(-0.500000 + 0.866025i) q^{81} -6.34315 q^{83} +2.58579 q^{85} +(-1.29289 + 2.23936i) q^{87} +(9.87579 - 5.70179i) q^{89} +(-0.828427 - 1.43488i) q^{93} +(-3.74952 - 2.16478i) q^{95} +3.82683i q^{97} +2.16478i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 4 q^{3} - 4 q^{9}+O(q^{10}) \) 8 * q + 4 * q^3 - 4 * q^9	\( 8 q + 4 q^{3} - 4 q^{9} - 12 q^{25} - 8 q^{27} - 32 q^{29} - 16 q^{31} + 16 q^{47} + 16 q^{53} - 32 q^{55} - 16 q^{65} + 12 q^{75} - 4 q^{81} - 96 q^{83} + 32 q^{85} - 16 q^{87} + 16 q^{93}+O(q^{100}) \) 8 * q + 4 * q^3 - 4 * q^9 - 12 * q^25 - 8 * q^27 - 32 * q^29 - 16 * q^31 + 16 * q^47 + 16 * q^53 - 32 * q^55 - 16 * q^65 + 12 * q^75 - 4 * q^81 - 96 * q^83 + 32 * q^85 - 16 * q^87 + 16 * q^93

Introduction

L-functions

Modular forms

Varieties

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Database

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