LMFDB - Embedded newform 1575.2.bk.i.26.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1575,2,Mod(26,1575)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1575, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 0, 5]))

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

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

chi := DirichletCharacter("1575.26");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1575 = 3^{2} \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1575.bk (of order $6$, degree $2$, 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:	$12.5764383184$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 315)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			26.6
Character	$\chi$	$=$	1575.26
Dual form			1575.2.bk.i.1151.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.14177 - 0.659204i) q^{2} +(-0.130901 - 0.226727i) q^{4} +(1.57437 - 2.12635i) q^{7} +2.98198i q^{8} +(-2.08688 + 1.20486i) q^{11} +1.69332i q^{13} +(-3.19927 + 1.38998i) q^{14} +(1.70393 - 2.95129i) q^{16} +(0.480231 + 0.831785i) q^{17} +(-3.56633 - 2.05902i) q^{19} +3.17699 q^{22} +(4.99818 + 2.88570i) q^{23} +(1.11625 - 1.93339i) q^{26} +(-0.688188 - 0.0786111i) q^{28} +5.56553i q^{29} +(-7.58148 + 4.37717i) q^{31} +(1.27393 - 0.735506i) q^{32} -1.26628i q^{34} +(-1.98654 + 3.44079i) q^{37} +(2.71463 + 4.70187i) q^{38} -1.87474 q^{41} +10.2706 q^{43} +(0.546349 + 0.315435i) q^{44} +(-3.80453 - 6.58963i) q^{46} +(-5.05376 + 8.75337i) q^{47} +(-2.04272 - 6.69532i) q^{49} +(0.383923 - 0.221658i) q^{52} +(-11.0060 + 6.35430i) q^{53} +(6.34072 + 4.69473i) q^{56} +(3.66882 - 6.35458i) q^{58} +(-3.38686 - 5.86621i) q^{59} +(1.98485 + 1.14595i) q^{61} +11.5418 q^{62} -8.75510 q^{64} +(-2.39872 - 4.15470i) q^{67} +(0.125726 - 0.217763i) q^{68} +2.24602i q^{71} +(12.7295 - 7.34937i) q^{73} +(4.53637 - 2.61907i) q^{74} +1.07811i q^{76} +(-0.723564 + 6.33432i) q^{77} +(-0.892703 + 1.54621i) q^{79} +(2.14052 + 1.23583i) q^{82} +9.62086 q^{83} +(-11.7267 - 6.77039i) q^{86} +(-3.59286 - 6.22302i) q^{88} +(-0.220850 + 0.382523i) q^{89} +(3.60060 + 2.66592i) q^{91} -1.51096i q^{92} +(11.5405 - 6.66292i) q^{94} +12.4926i q^{97} +(-2.08125 + 8.99111i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 24 q^{4} + 36 q^{19} - 60 q^{31} - 24 q^{46} - 36 q^{49} + 48 q^{61} - 48 q^{64} + 60 q^{79} + 60 q^{91} - 48 q^{94}+O(q^{100}) $ 24 * q + 24 * q^4 + 36 * q^19 - 60 * q^31 - 24 * q^46 - 36 * q^49 + 48 * q^61 - 48 * q^64 + 60 * q^79 + 60 * q^91 - 48 * q^94

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1575\mathbb{Z}\right)^\times$.

$n$	$127$	$451$	$1226$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$	$-1$

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 $

$2$	−1.14177	−	0.659204i	−0.807356	−	0.466127i	0.0386807	−	0.999252i	$-0.487684\pi$
$2$	−1.14177	−	0.659204i	−0.807356	−	0.466127i	−0.846037	+	0.533124i	$0.821018\pi$
$3$		0			0
$3$		0			0
$4$	−0.130901	−	0.226727i	−0.0654506	−	0.113364i
$5$		0			0
$5$		0			0
$6$		0			0
$7$	1.57437	−	2.12635i	0.595056	−	0.803685i
$7$	1.57437	−	2.12635i	0.595056	−	0.803685i
$8$			2.98198i			1.05429i
$9$		0			0
$10$		0			0
$11$	−2.08688	+	1.20486i	−0.629217	+	0.363279i	−0.780449	−	0.625220i	$-0.785009\pi$
$11$	−2.08688	+	1.20486i	−0.629217	+	0.363279i	0.151232	+	0.988498i	$0.451676\pi$
$12$		0			0
$13$			1.69332i			0.469643i	0.972038	+	0.234822i	$0.0754506\pi$
$13$			1.69332i			0.469643i	−0.972038	+	0.234822i	$0.924549\pi$
$14$	−3.19927	+	1.38998i	−0.855041	+	0.371488i
$15$		0			0
$16$	1.70393	−	2.95129i	0.425982	−	0.737822i
$17$	0.480231	+	0.831785i	0.116473	+	0.201737i	0.918368	−	0.395728i	$-0.129508\pi$
$17$	0.480231	+	0.831785i	0.116473	+	0.201737i	−0.801895	+	0.597466i	$0.796174\pi$
$18$		0			0
$19$	−3.56633	−	2.05902i	−0.818172	−	0.472372i	0.0316139	−	0.999500i	$-0.489935\pi$
$19$	−3.56633	−	2.05902i	−0.818172	−	0.472372i	−0.849786	+	0.527129i	$0.823269\pi$
$20$		0			0
$21$		0			0
$22$	3.17699			0.677336
$23$	4.99818	+	2.88570i	1.04219	+	0.601710i	0.920453	−	0.390853i	$-0.127820\pi$
$23$	4.99818	+	2.88570i	1.04219	+	0.601710i	0.121738	+	0.992562i	$0.461153\pi$
$24$		0			0
$25$		0			0
$26$	1.11625	−	1.93339i	0.218914	−	0.379170i
$27$		0			0
$28$	−0.688188	−	0.0786111i	−0.130055	−	0.0148561i
$29$			5.56553i			1.03349i	0.856138	+	0.516747i	$0.172857\pi$
$29$			5.56553i			1.03349i	−0.856138	+	0.516747i	$0.827143\pi$
$30$		0			0
$31$	−7.58148	+	4.37717i	−1.36167	+	0.786163i	−0.989847	−	0.142139i	$-0.954602\pi$
$31$	−7.58148	+	4.37717i	−1.36167	+	0.786163i	−0.371827	+	0.928302i	$0.621269\pi$
$32$	1.27393	−	0.735506i	0.225202	−	0.130020i
$33$		0			0
$34$		−	1.26628i		−	0.217165i
$35$		0			0
$36$		0			0
$37$	−1.98654	+	3.44079i	−0.326586	+	0.565663i	−0.981832	−	0.189752i	$-0.939231\pi$
$37$	−1.98654	+	3.44079i	−0.326586	+	0.565663i	0.655246	+	0.755415i	$0.272565\pi$
$38$	2.71463	+	4.70187i	0.440371	+	0.762744i
$39$		0			0
$40$		0			0
$41$	−1.87474			−0.292784			−0.146392	−	0.989227i	$-0.546766\pi$
$41$	−1.87474			−0.292784			−0.146392	+	0.989227i	$0.546766\pi$
$42$		0			0
$43$	10.2706			1.56625			0.783123	−	0.621867i	$-0.213625\pi$
$43$	10.2706			1.56625			0.783123	+	0.621867i	$0.213625\pi$
$44$	0.546349	+	0.315435i	0.0823652	+	0.0475536i
$45$		0			0
$46$	−3.80453	−	6.58963i	−0.560947	−	0.971588i
$47$	−5.05376	+	8.75337i	−0.737167	+	1.27681i	0.216599	+	0.976261i	$0.430504\pi$
$47$	−5.05376	+	8.75337i	−0.737167	+	1.27681i	−0.953766	+	0.300550i	$0.902830\pi$
$48$		0			0
$49$	−2.04272	−	6.69532i	−0.291818	−	0.956474i
$50$		0			0
$51$		0			0
$52$	0.383923	−	0.221658i	0.0532405	−	0.0307384i
$53$	−11.0060	+	6.35430i	−1.51179	+	0.872830i	−0.511880	+	0.859057i	$0.671051\pi$
$53$	−11.0060	+	6.35430i	−1.51179	+	0.872830i	−0.999905	+	0.0137732i	$0.995616\pi$
$54$		0			0
$55$		0			0
$56$	6.34072	+	4.69473i	0.847315	+	0.627360i
$57$		0			0
$58$	3.66882	−	6.35458i	0.481740	−	0.834398i
$59$	−3.38686	−	5.86621i	−0.440931	−	0.763715i	0.556828	−	0.830628i	$-0.312018\pi$
$59$	−3.38686	−	5.86621i	−0.440931	−	0.763715i	−0.997759	+	0.0669127i	$0.978685\pi$
$60$		0			0
$61$	1.98485	+	1.14595i	0.254134	+	0.146724i	0.621656	−	0.783291i	$-0.286460\pi$
$61$	1.98485	+	1.14595i	0.254134	+	0.146724i	−0.367522	+	0.930015i	$0.619794\pi$
$62$	11.5418			1.46581
$63$		0			0
$64$	−8.75510			−1.09439
$65$		0			0
$66$		0			0
$67$	−2.39872	−	4.15470i	−0.293050	−	0.507577i	0.681480	−	0.731837i	$-0.261337\pi$
$67$	−2.39872	−	4.15470i	−0.293050	−	0.507577i	−0.974529	+	0.224260i	$0.928004\pi$
$68$	0.125726	−	0.217763i	0.0152465	−	0.0264077i
$69$		0			0
$70$		0			0
$71$			2.24602i			0.266554i	0.991079	+	0.133277i	$0.0425500\pi$
$71$			2.24602i			0.266554i	−0.991079	+	0.133277i	$0.957450\pi$
$72$		0			0
$73$	12.7295	−	7.34937i	1.48987	−	0.860178i	0.489940	−	0.871756i	$-0.337019\pi$
$73$	12.7295	−	7.34937i	1.48987	−	0.860178i	0.999933	+	0.0115780i	$0.00368547\pi$
$74$	4.53637	−	2.61907i	0.527342	−	0.304461i
$75$		0			0
$76$			1.07811i			0.123668i
$77$	−0.723564	+	6.33432i	−0.0824577	+	0.721863i
$78$		0			0
$79$	−0.892703	+	1.54621i	−0.100437	+	0.173962i	−0.911865	−	0.410491i	$-0.865357\pi$
$79$	−0.892703	+	1.54621i	−0.100437	+	0.173962i	0.811428	+	0.584453i	$0.198691\pi$
$80$		0			0
$81$		0			0
$82$	2.14052	+	1.23583i	0.236381	+	0.136475i
$83$	9.62086			1.05603			0.528013	−	0.849236i	$-0.322937\pi$
$83$	9.62086			1.05603			0.528013	+	0.849236i	$0.322937\pi$
$84$		0			0
$85$		0			0
$86$	−11.7267	−	6.77039i	−1.26452	−	0.730070i
$87$		0			0
$88$	−3.59286	−	6.22302i	−0.383000	−	0.663376i
$89$	−0.220850	+	0.382523i	−0.0234100	+	0.0405474i	−0.877493	−	0.479589i	$-0.840786\pi$
$89$	−0.220850	+	0.382523i	−0.0234100	+	0.0405474i	0.854083	+	0.520137i	$0.174119\pi$
$90$		0			0
$91$	3.60060	+	2.66592i	0.377445	+	0.279464i
$92$		−	1.51096i		−	0.157529i
$93$		0			0
$94$	11.5405	−	6.66292i	1.19031	−	0.687227i
$95$		0			0
$96$		0			0
$97$			12.4926i			1.26843i	0.773157	+	0.634215i	$0.218677\pi$
$97$			12.4926i			1.26843i	−0.773157	+	0.634215i	$0.781323\pi$
$98$	−2.08125	+	8.99111i	−0.210238	+	0.908239i
$99$		0			0
$100$		0			0
$101$	4.74466	+	8.21799i	0.472111	+	0.817720i	0.999491	−	0.0319094i	$-0.0101588\pi$
$101$	4.74466	+	8.21799i	0.472111	+	0.817720i	−0.527380	+	0.849630i	$0.676825\pi$
$102$		0			0
$103$	6.99979	+	4.04133i	0.689710	+	0.398204i	0.803503	−	0.595300i	$-0.202967\pi$
$103$	6.99979	+	4.04133i	0.689710	+	0.398204i	−0.113793	+	0.993504i	$0.536300\pi$
$104$	−5.04945			−0.495139
$105$		0			0
$106$	16.7551			1.62740
$107$	4.69926	+	2.71312i	0.454294	+	0.262287i	0.709642	−	0.704562i	$-0.248857\pi$
$107$	4.69926	+	2.71312i	0.454294	+	0.262287i	−0.255348	+	0.966849i	$0.582190\pi$
$108$		0			0
$109$	8.68208	+	15.0378i	0.831592	+	1.44036i	0.896775	+	0.442487i	$0.145904\pi$
$109$	8.68208	+	15.0378i	0.831592	+	1.44036i	−0.0651830	+	0.997873i	$0.520763\pi$
$110$		0			0
$111$		0			0
$112$	−3.59286	−	8.26956i	−0.339493	−	0.781400i
$113$			5.92400i			0.557283i	0.960395	+	0.278642i	$0.0898841\pi$
$113$			5.92400i			0.557283i	−0.960395	+	0.278642i	$0.910116\pi$
$114$		0			0
$115$		0			0
$116$	1.26186	−	0.728535i	0.117161	−	0.0676427i
$117$		0			0
$118$			8.93051i			0.822121i
$119$	2.52473	+	0.288397i	0.231441	+	0.0264373i
$120$		0			0
$121$	−2.59663	+	4.49750i	−0.236057	+	0.408863i
$122$	−1.51083	−	2.61684i	−0.136784	−	0.236917i
$123$		0			0
$124$	1.98485	+	1.14595i	0.178245	+	0.102910i
$125$		0			0
$126$		0			0
$127$	5.01325			0.444854			0.222427	−	0.974949i	$-0.428602\pi$
$127$	5.01325			0.444854			0.222427	+	0.974949i	$0.428602\pi$
$128$	7.44848	+	4.30038i	0.658359	+	0.380104i
$129$		0			0
$130$		0			0
$131$	8.52739	−	14.7699i	0.745042	−	1.29045i	−0.205134	−	0.978734i	$-0.565763\pi$
$131$	8.52739	−	14.7699i	0.745042	−	1.29045i	0.950175	−	0.311716i	$-0.100904\pi$
$132$		0			0
$133$	−9.99291	+	4.34160i	−0.866495	+	0.376464i
$134$			6.32497i			0.546394i
$135$		0			0
$136$	−2.48036	+	1.43204i	−0.212689	+	0.122796i
$137$	−8.59026	+	4.95959i	−0.733915	+	0.423726i	−0.819853	−	0.572574i	$-0.805945\pi$
$137$	−8.59026	+	4.95959i	−0.733915	+	0.423726i	0.0859376	+	0.996301i	$0.472611\pi$
$138$		0			0
$139$			15.1104i			1.28164i	0.767689	+	0.640822i	$0.221407\pi$
$139$			15.1104i			1.28164i	−0.767689	+	0.640822i	$0.778593\pi$
$140$		0			0
$141$		0			0
$142$	1.48059	−	2.56445i	0.124248	−	0.215204i
$143$	−2.04022	−	3.53376i	−0.170611	−	0.295508i
$144$		0			0
$145$		0			0
$146$	−19.3789			−1.60381
$147$		0			0
$148$	1.04016			0.0855008
$149$	2.02420	+	1.16867i	0.165829	+	0.0957413i	0.580618	−	0.814176i	$-0.302811\pi$
$149$	2.02420	+	1.16867i	0.165829	+	0.0957413i	−0.414789	+	0.909918i	$0.636144\pi$
$150$		0			0
$151$	−5.01515	−	8.68650i	−0.408127	−	0.706897i	0.586553	−	0.809911i	$-0.300485\pi$
$151$	−5.01515	−	8.68650i	−0.408127	−	0.706897i	−0.994680	+	0.103014i	$0.967151\pi$
$152$	6.13995	−	10.6347i	0.498016	−	0.862588i
$153$		0			0
$154$	5.00175	−	6.75539i	0.403053	−	0.544365i
$155$		0			0
$156$		0			0
$157$	17.9727	−	10.3765i	1.43437	−	0.828137i	0.436924	−	0.899498i	$-0.356068\pi$
$157$	17.9727	−	10.3765i	1.43437	−	0.828137i	0.997451	+	0.0713615i	$0.0227344\pi$
$158$	2.03853	−	1.17695i	0.162177	−	0.0936328i
$159$		0			0
$160$		0			0
$161$	14.0050	−	6.08471i	1.10375	−	0.479543i
$162$		0			0
$163$	−7.81001	+	13.5273i	−0.611727	+	1.05954i	0.379222	+	0.925306i	$0.376192\pi$
$163$	−7.81001	+	13.5273i	−0.611727	+	1.05954i	−0.990949	+	0.134237i	$0.957142\pi$
$164$	0.245405	+	0.425054i	0.0191629	+	0.0331911i
$165$		0			0
$166$	−10.9848	−	6.34211i	−0.852590	−	0.492243i
$167$	−14.7858			−1.14416			−0.572080	−	0.820198i	$-0.693863\pi$
$167$	−14.7858			−1.14416			−0.572080	+	0.820198i	$0.693863\pi$
$168$		0			0
$169$	10.1327			0.779435
$170$		0			0
$171$		0			0
$172$	−1.34443	−	2.32862i	−0.102512	−	0.177555i
$173$	−3.43176	+	5.94398i	−0.260912	+	0.451912i	−0.966484	−	0.256725i	$-0.917356\pi$
$173$	−3.43176	+	5.94398i	−0.260912	+	0.451912i	0.705573	+	0.708637i	$0.250690\pi$
$174$		0			0
$175$		0			0
$176$			8.21197i			0.619000i
$177$		0			0
$178$	0.504321	−	0.291170i	0.0378005	−	0.0218241i
$179$	10.1393	−	5.85393i	0.757847	−	0.437543i	−0.0706751	−	0.997499i	$-0.522515\pi$
$179$	10.1393	−	5.85393i	0.757847	−	0.437543i	0.828522	+	0.559956i	$0.189182\pi$
$180$		0			0
$181$			17.3498i			1.28960i	0.764351	+	0.644800i	$0.223059\pi$
$181$			17.3498i			1.28960i	−0.764351	+	0.644800i	$0.776941\pi$
$182$	−2.35369	−	5.41740i	−0.174467	−	0.401565i
$183$		0			0
$184$	−8.60508	+	14.9044i	−0.634375	+	1.09877i
$185$		0			0
$186$		0			0
$187$	−2.00437	−	1.15722i	−0.146574	−	0.0846244i
$188$	2.64617			0.192992
$189$		0			0
$190$		0			0
$191$	16.3677	+	9.44988i	1.18432	+	0.683770i	0.957011	−	0.290052i	$-0.0936727\pi$
$191$	16.3677	+	9.44988i	1.18432	+	0.683770i	0.227313	+	0.973822i	$0.427006\pi$
$192$		0			0
$193$	−11.6611	−	20.1976i	−0.839382	−	1.45385i	−0.890412	−	0.455155i	$-0.849584\pi$
$193$	−11.6611	−	20.1976i	−0.839382	−	1.45385i	0.0510306	−	0.998697i	$-0.483749\pi$
$194$	8.23516	−	14.2637i	0.591250	−	1.02407i
$195$		0			0
$196$	−1.25062	+	1.33957i	−0.0893298	+	0.0956833i
$197$			0.842929i			0.0600562i	0.999549	+	0.0300281i	$0.00955968\pi$
$197$			0.842929i			0.0600562i	−0.999549	+	0.0300281i	$0.990440\pi$
$198$		0			0
$199$	0.739952	−	0.427211i	0.0524538	−	0.0302842i	−0.473544	−	0.880770i	$-0.657025\pi$
$199$	0.739952	−	0.427211i	0.0524538	−	0.0302842i	0.525998	+	0.850486i	$0.323692\pi$
$200$		0			0
$201$		0			0
$202$		−	12.5108i		−	0.880255i
$203$	11.8343	+	8.76220i	0.830603	+	0.614986i
$204$		0			0
$205$		0			0
$206$	−5.32812	−	9.22857i	−0.371228	−	0.642985i
$207$		0			0
$208$	4.99749	+	2.88530i	0.346513	+	0.200060i
$209$	9.92331			0.686410
$210$		0			0
$211$	16.1933			1.11479			0.557395	−	0.830247i	$-0.311801\pi$
$211$	16.1933			1.11479			0.557395	+	0.830247i	$0.311801\pi$
$212$	2.88139	+	1.66357i	0.197894	+	0.114254i
$213$		0			0
$214$	−3.57699	−	6.19553i	−0.244518	−	0.423518i
$215$		0			0
$216$		0			0
$217$	−2.62866	+	23.0122i	−0.178445	+	1.56217i
$218$		−	22.8930i		−	1.55051i
$219$		0			0
$220$		0			0
$221$	−1.40848	+	0.813187i	−0.0947447	+	0.0547009i
$222$		0			0
$223$			10.0027i			0.669832i	0.942248	+	0.334916i	$0.108708\pi$
$223$			10.0027i			0.669832i	−0.942248	+	0.334916i	$0.891292\pi$
$224$	0.441699	−	3.86679i	0.0295123	−	0.258361i
$225$		0			0
$226$	3.90512	−	6.76387i	0.259765	−	0.449926i
$227$	−2.33913	−	4.05150i	−0.155254	−	0.268908i	0.777898	−	0.628391i	$-0.216286\pi$
$227$	−2.33913	−	4.05150i	−0.155254	−	0.268908i	−0.933151	+	0.359484i	$0.882953\pi$
$228$		0			0
$229$	−12.3460	−	7.12797i	−0.815848	−	0.471030i	0.0331349	−	0.999451i	$-0.489451\pi$
$229$	−12.3460	−	7.12797i	−0.815848	−	0.471030i	−0.848982	+	0.528421i	$0.822784\pi$
$230$		0			0
$231$		0			0
$232$	−16.5963			−1.08960
$233$	−19.3166	−	11.1524i	−1.26547	−	0.730621i	−0.291345	−	0.956618i	$-0.594103\pi$
$233$	−19.3166	−	11.1524i	−1.26547	−	0.730621i	−0.974128	+	0.225997i	$0.927436\pi$
$234$		0			0
$235$		0			0
$236$	−0.886687	+	1.53579i	−0.0577184	+	0.0999712i
$237$		0			0
$238$	−2.69255	−	1.99359i	−0.174532	−	0.129225i
$239$		−	6.39734i		−	0.413810i	−0.978361	−	0.206905i	$-0.933661\pi$
$239$		−	6.39734i		−	0.413810i	0.978361	−	0.206905i	$-0.0663391\pi$
$240$		0			0
$241$	−6.20841	+	3.58443i	−0.399919	+	0.230893i	−0.686449	−	0.727178i	$-0.740832\pi$
$241$	−6.20841	+	3.58443i	−0.399919	+	0.230893i	0.286530	+	0.958071i	$0.407498\pi$
$242$	5.92953	−	3.42342i	0.381165	−	0.220066i
$243$		0			0
$244$		−	0.600026i		−	0.0384127i
$245$		0			0
$246$		0			0
$247$	3.48659	−	6.03895i	0.221846	−	0.384249i
$248$	−13.0526	−	22.6078i	−0.828842	−	1.43560i
$249$		0			0
$250$		0			0
$251$	−16.3470			−1.03181			−0.515906	−	0.856645i	$-0.672545\pi$
$251$	−16.3470			−1.03181			−0.515906	+	0.856645i	$0.672545\pi$
$252$		0			0
$253$	−13.9074			−0.874353
$254$	−5.72400	−	3.30475i	−0.359156	−	0.207359i
$255$		0			0
$256$	3.08545	+	5.34415i	0.192840	+	0.334009i
$257$	6.11896	−	10.5984i	0.381690	−	0.661107i	−0.609614	−	0.792699i	$-0.708675\pi$
$257$	6.11896	−	10.5984i	0.381690	−	0.661107i	0.991304	+	0.131592i	$0.0420087\pi$
$258$		0			0
$259$	4.18878	+	9.64116i	0.260278	+	0.599073i
$260$		0			0
$261$		0			0
$262$	−19.4727	+	11.2426i	−1.20303	+	0.694569i
$263$	−8.15918	+	4.71070i	−0.503117	+	0.290474i	−0.730000	−	0.683448i	$-0.760480\pi$
$263$	−8.15918	+	4.71070i	−0.503117	+	0.290474i	0.226883	+	0.973922i	$0.427146\pi$
$264$		0			0
$265$		0			0
$266$	14.2716	+	1.63024i	0.875051	+	0.0999563i
$267$		0			0
$268$	−0.627989	+	1.08771i	−0.0383605	+	0.0664424i
$269$	−3.81600	−	6.60950i	−0.232666	−	0.402988i	0.725926	−	0.687773i	$-0.241411\pi$
$269$	−3.81600	−	6.60950i	−0.232666	−	0.402988i	−0.958592	+	0.284784i	$0.908078\pi$
$270$		0			0
$271$	−4.71908	−	2.72456i	−0.286664	−	0.165505i	0.349773	−	0.936835i	$-0.386259\pi$
$271$	−4.71908	−	2.72456i	−0.286664	−	0.165505i	−0.636436	+	0.771329i	$0.719592\pi$
$272$	3.27312			0.198462
$273$		0			0
$274$	13.0775			0.790041
$275$		0			0
$276$		0			0
$277$	8.52809	+	14.7711i	0.512403	+	0.887508i	0.999897	+	0.0143815i	$0.00457793\pi$
$277$	8.52809	+	14.7711i	0.512403	+	0.887508i	−0.487494	+	0.873127i	$0.662089\pi$
$278$	9.96081	−	17.2526i	0.597410	−	1.03474i
$279$		0			0
$280$		0			0
$281$			25.3828i			1.51421i	0.653292	+	0.757106i	$0.273387\pi$
$281$			25.3828i			1.51421i	−0.653292	+	0.757106i	$0.726613\pi$
$282$		0			0
$283$	8.29651	−	4.78999i	0.493176	−	0.284735i	−0.232715	−	0.972545i	$-0.574761\pi$
$283$	8.29651	−	4.78999i	0.493176	−	0.284735i	0.725891	+	0.687810i	$0.241428\pi$
$284$	0.509235	−	0.294007i	0.0302175	−	0.0174461i
$285$		0			0
$286$			5.37967i			0.318107i
$287$	−2.95153	+	3.98634i	−0.174223	+	0.235306i
$288$		0			0
$289$	8.03876	−	13.9235i	0.472868	−	0.819031i
$290$		0			0
$291$		0			0
$292$	−3.33261	−	1.92408i	−0.195026	−	0.112598i
$293$	−1.44713			−0.0845421			−0.0422710	−	0.999106i	$-0.513459\pi$
$293$	−1.44713			−0.0845421			−0.0422710	+	0.999106i	$0.513459\pi$
$294$		0			0
$295$		0			0
$296$	−10.2604	−	5.92382i	−0.596372	−	0.344315i
$297$		0			0
$298$	−1.54079	−	2.66872i	−0.0892553	−	0.154595i
$299$	−4.88642	+	8.46353i	−0.282589	+	0.489459i
$300$		0			0
$301$	16.1697	−	21.8388i	0.932004	−	1.25877i
$302$			13.2240i			0.760957i
$303$		0			0
$304$	−12.1535	+	7.01684i	−0.697053	+	0.402444i
$305$		0			0
$306$		0			0
$307$			7.69871i			0.439388i	0.975569	+	0.219694i	$0.0705059\pi$
$307$			7.69871i			0.439388i	−0.975569	+	0.219694i	$0.929494\pi$
$308$	1.53088	−	0.665118i	0.0872299	−	0.0378986i
$309$		0			0
$310$		0			0
$311$	−16.5875	−	28.7304i	−0.940592	−	1.62915i	−0.764345	−	0.644807i	$-0.776938\pi$
$311$	−16.5875	−	28.7304i	−0.940592	−	1.62915i	−0.176247	−	0.984346i	$-0.556396\pi$
$312$		0			0
$313$	7.32351	+	4.22823i	0.413950	+	0.238994i	0.692485	−	0.721432i	$-0.256516\pi$
$313$	7.32351	+	4.22823i	0.413950	+	0.238994i	−0.278536	+	0.960426i	$0.589849\pi$
$314$	−27.3610			−1.54407
$315$		0			0
$316$	0.467423			0.0262946
$317$	5.14563	+	2.97083i	0.289008	+	0.166859i	0.637494	−	0.770455i	$-0.279971\pi$
$317$	5.14563	+	2.97083i	0.289008	+	0.166859i	−0.348487	+	0.937314i	$0.613304\pi$
$318$		0			0
$319$	−6.70568	−	11.6146i	−0.375446	−	0.650292i
$320$		0			0
$321$		0			0
$322$	−20.0016	−	2.28476i	−1.11464	−	0.127325i
$323$		−	3.95522i		−	0.220074i
$324$		0			0
$325$		0			0
$326$	17.8345	−	10.2968i	0.987764	−	0.570286i
$327$		0			0
$328$		−	5.59042i		−	0.308679i
$329$	10.6562	+	24.5271i	0.587498	+	1.35222i
$330$		0			0
$331$	−13.2551	+	22.9585i	−0.728566	+	1.26191i	0.228923	+	0.973445i	$0.426480\pi$
$331$	−13.2551	+	22.9585i	−0.728566	+	1.26191i	−0.957489	+	0.288469i	$0.906854\pi$
$332$	−1.25938	−	2.18131i	−0.0691175	−	0.119715i
$333$		0			0
$334$	16.8820	+	9.74685i	0.923744	+	0.533324i
$335$		0			0
$336$		0			0
$337$	−3.42106			−0.186357			−0.0931784	−	0.995649i	$-0.529703\pi$
$337$	−3.42106			−0.186357			−0.0931784	+	0.995649i	$0.529703\pi$
$338$	−11.5692	−	6.67948i	−0.629282	−	0.363316i
$339$		0			0
$340$		0			0
$341$	10.5477	−	18.2692i	0.571192	−	0.989334i
$342$		0			0
$343$	−17.4526	−	6.19736i	−0.942351	−	0.334626i
$344$			30.6266i			1.65127i
$345$		0			0
$346$	7.83658	−	4.52445i	0.421297	−	0.243236i
$347$	−11.6038	+	6.69946i	−0.622925	+	0.359646i	−0.778007	−	0.628256i	$-0.783769\pi$
$347$	−11.6038	+	6.69946i	−0.622925	+	0.359646i	0.155082	+	0.987902i	$0.450436\pi$
$348$		0			0
$349$		−	15.2584i		−	0.816762i	−0.912812	−	0.408381i	$-0.866094\pi$
$349$		−	15.2584i		−	0.816762i	0.912812	−	0.408381i	$-0.133906\pi$
$350$		0			0
$351$		0			0
$352$	−1.77236	+	3.06982i	−0.0944672	+	0.163622i
$353$	−18.4609	−	31.9752i	−0.982574	−	1.70187i	−0.652258	−	0.757997i	$-0.726178\pi$
$353$	−18.4609	−	31.9752i	−0.982574	−	1.70187i	−0.330316	−	0.943871i	$-0.607155\pi$
$354$		0			0
$355$		0			0
$356$	0.115638			0.00612880
$357$		0			0
$358$	−15.4357			−0.815804
$359$	−7.71108	−	4.45200i	−0.406975	−	0.234967i	0.282514	−	0.959263i	$-0.408832\pi$
$359$	−7.71108	−	4.45200i	−0.406975	−	0.234967i	−0.689489	+	0.724296i	$0.742165\pi$
$360$		0			0
$361$	−1.02087	−	1.76820i	−0.0537301	−	0.0930633i
$362$	11.4370	−	19.8095i	0.601118	−	1.04117i
$363$		0			0
$364$	0.133114	−	1.16533i	0.00697707	−	0.0610797i
$365$		0			0
$366$		0			0
$367$	12.5174	−	7.22690i	0.653401	−	0.377241i	−0.136357	−	0.990660i	$-0.543539\pi$
$367$	12.5174	−	7.22690i	0.653401	−	0.377241i	0.789758	+	0.613419i	$0.210206\pi$
$368$	17.0331	−	9.83404i	0.887910	−	0.512635i
$369$		0			0
$370$		0			0
$371$	−3.81600	+	33.4065i	−0.198117	+	1.73438i
$372$		0			0
$373$	−10.5607	+	18.2917i	−0.546812	+	0.947107i	0.451678	+	0.892181i	$0.350826\pi$
$373$	−10.5607	+	18.2917i	−0.546812	+	0.947107i	−0.998490	+	0.0549259i	$0.982508\pi$
$374$	1.52569	+	2.64257i	0.0788915	+	0.136644i
$375$		0			0
$376$	−26.1024	−	15.0702i	−1.34613	−	0.777186i
$377$	−9.42425			−0.485374
$378$		0			0
$379$	0.0133979			0.000688205			0.000344103	−	1.00000i	$-0.499890\pi$
$379$	0.0133979			0.000688205			0.000344103		1.00000i	$0.499890\pi$
$380$		0			0
$381$		0			0
$382$	−12.4588	−	21.5793i	−0.637447	−	1.10409i
$383$	8.61124	−	14.9151i	0.440014	−	0.762127i	−0.557676	−	0.830059i	$-0.688307\pi$
$383$	8.61124	−	14.9151i	0.440014	−	0.762127i	0.997690	+	0.0679321i	$0.0216401\pi$
$384$		0			0
$385$		0			0
$386$			30.7481i			1.56504i
$387$		0			0
$388$	2.83241	−	1.63529i	0.143794	−	0.0830194i
$389$	−22.3077	+	12.8793i	−1.13104	+	0.653008i	−0.944197	−	0.329381i	$-0.893160\pi$
$389$	−22.3077	+	12.8793i	−1.13104	+	0.653008i	−0.186846	+	0.982389i	$0.559827\pi$
$390$		0			0
$391$			5.54321i			0.280332i
$392$	19.9653	−	6.09135i	1.00840	−	0.307660i
$393$		0			0
$394$	0.555662	−	0.962434i	0.0279938	−	0.0484867i
$395$		0			0
$396$		0			0
$397$	13.2051	+	7.62398i	0.662746	+	0.382637i	0.793322	−	0.608802i	$-0.208349\pi$
$397$	13.2051	+	7.62398i	0.662746	+	0.382637i	−0.130576	+	0.991438i	$0.541683\pi$
$398$	−1.12648			−0.0564652
$399$		0			0
$400$		0			0
$401$	−11.3640	−	6.56104i	−0.567494	−	0.327643i	0.188654	−	0.982044i	$-0.439588\pi$
$401$	−11.3640	−	6.56104i	−0.567494	−	0.327643i	−0.756148	+	0.654401i	$0.772921\pi$
$402$		0			0
$403$	−7.41196	−	12.8379i	−0.369216	−	0.639501i
$404$	1.24216	−	2.15149i	0.0617999	−	0.107041i
$405$		0			0
$406$	−7.73598	−	17.8057i	−0.383930	−	0.883680i
$407$		−	9.57401i		−	0.474566i
$408$		0			0
$409$	−28.4692	+	16.4367i	−1.40771	+	0.812744i	−0.995167	−	0.0981933i	$-0.968694\pi$
$409$	−28.4692	+	16.4367i	−1.40771	+	0.812744i	−0.412546	+	0.910937i	$0.635360\pi$
$410$		0			0
$411$		0			0
$412$		−	2.11606i		−	0.104251i
$413$	−17.8058	−	2.03394i	−0.876165	−	0.100084i
$414$		0			0
$415$		0			0
$416$	1.24545	+	2.15718i	0.0610632	+	0.105765i
$417$		0			0
$418$	−11.3302	−	6.54148i	−0.554177	−	0.319954i
$419$	−9.33114			−0.455856			−0.227928	−	0.973678i	$-0.573195\pi$
$419$	−9.33114			−0.455856			−0.227928	+	0.973678i	$0.573195\pi$
$420$		0			0
$421$	−13.0720			−0.637093			−0.318546	−	0.947907i	$-0.603195\pi$
$421$	−13.0720			−0.637093			−0.318546	+	0.947907i	$0.603195\pi$
$422$	−18.4890	−	10.6747i	−0.900033	−	0.519634i
$423$		0			0
$424$	−18.9484	−	32.8195i	−0.920214	−	1.59386i
$425$		0			0
$426$		0			0
$427$	5.56158	−	2.41633i	0.269144	−	0.116934i
$428$		−	1.42060i		−	0.0686673i
$429$		0			0
$430$		0			0
$431$	5.18251	−	2.99212i	0.249633	−	0.144125i	−0.369963	−	0.929046i	$-0.620630\pi$
$431$	5.18251	−	2.99212i	0.249633	−	0.144125i	0.619596	+	0.784921i	$0.287296\pi$
$432$		0			0
$433$			19.4335i			0.933916i	0.884280	+	0.466958i	$0.154650\pi$
$433$			19.4335i			0.933916i	−0.884280	+	0.466958i	$0.845350\pi$
$434$	18.1710	−	24.5419i	0.872237	−	1.17805i
$435$		0			0
$436$	2.27299	−	3.93693i	0.108856	−	0.188545i
$437$	−11.8834	−	20.5827i	−0.568461	−	0.984603i
$438$		0			0
$439$	−24.1175	−	13.9242i	−1.15107	−	0.664568i	−0.201919	−	0.979402i	$-0.564718\pi$
$439$	−24.1175	−	13.9242i	−1.15107	−	0.664568i	−0.949147	+	0.314834i	$0.898051\pi$
$440$		0			0
$441$		0			0
$442$	2.14422			0.101990
$443$	20.2916	+	11.7154i	0.964084	+	0.556614i	0.897428	−	0.441162i	$-0.145434\pi$
$443$	20.2916	+	11.7154i	0.964084	+	0.556614i	0.0666564	+	0.997776i	$0.478767\pi$
$444$		0			0
$445$		0			0
$446$	6.59383	−	11.4208i	0.312227	−	0.540793i
$447$		0			0
$448$	−13.7838	+	18.6164i	−0.651222	+	0.879543i
$449$		−	15.7868i		−	0.745025i	−0.928027	−	0.372513i	$-0.878496\pi$
$449$		−	15.7868i		−	0.745025i	0.928027	−	0.372513i	$-0.121504\pi$
$450$		0			0
$451$	3.91234	−	2.25879i	0.184225	−	0.106362i
$452$	1.34313	−	0.775458i	0.0631757	−	0.0364745i
$453$		0			0
$454$			6.16786i			0.289472i
$455$		0			0
$456$		0			0
$457$	−13.3575	+	23.1358i	−0.624836	+	1.08225i	0.363737	+	0.931502i	$0.381501\pi$
$457$	−13.3575	+	23.1358i	−0.624836	+	1.08225i	−0.988573	+	0.150746i	$0.951833\pi$
$458$	9.39757	+	16.2771i	0.439120	+	0.760578i
$459$		0			0
$460$		0			0
$461$	−33.1750			−1.54512			−0.772558	−	0.634944i	$-0.781023\pi$
$461$	−33.1750			−1.54512			−0.772558	+	0.634944i	$0.781023\pi$
$462$		0			0
$463$	9.01458			0.418943			0.209472	−	0.977815i	$-0.432826\pi$
$463$	9.01458			0.418943			0.209472	+	0.977815i	$0.432826\pi$
$464$	16.4255	+	9.48327i	0.762535	+	0.440250i
$465$		0			0
$466$	14.7035	+	25.4672i	0.681125	+	1.17974i
$467$	−16.2346	+	28.1192i	−0.751248	+	1.30120i	0.195970	+	0.980610i	$0.437214\pi$
$467$	−16.2346	+	28.1192i	−0.751248	+	1.30120i	−0.947218	+	0.320590i	$0.896119\pi$
$468$		0			0
$469$	−12.6108	−	1.44052i	−0.582313	−	0.0665171i
$470$		0			0
$471$		0			0
$472$	17.4929	−	10.0995i	0.805176	−	0.464869i
$473$	−21.4334	+	12.3746i	−0.985509	+	0.568984i
$474$		0			0
$475$		0			0
$476$	−0.265102	−	0.610176i	−0.0121509	−	0.0279674i
$477$		0			0
$478$	−4.21715	+	7.30432i	−0.192888	+	0.334092i
$479$	2.08303	+	3.60791i	0.0951759	+	0.164849i	0.909682	−	0.415305i	$-0.136325\pi$
$479$	2.08303	+	3.60791i	0.0951759	+	0.164849i	−0.814506	+	0.580155i	$0.802992\pi$
$480$		0			0
$481$	−5.82638	−	3.36386i	−0.265660	−	0.153379i
$482$	9.45148			0.430503
$483$		0			0
$484$	1.35961			0.0618003
$485$		0			0
$486$		0			0
$487$	−10.3166	−	17.8689i	−0.467491	−	0.809719i	0.531819	−	0.846858i	$-0.321509\pi$
$487$	−10.3166	−	17.8689i	−0.467491	−	0.809719i	−0.999310	+	0.0371394i	$0.988175\pi$
$488$	−3.41720	+	5.91877i	−0.154690	+	0.267930i
$489$		0			0
$490$		0			0
$491$			33.6376i			1.51805i	0.651064	+	0.759023i	$0.274323\pi$
$491$			33.6376i			1.51805i	−0.651064	+	0.759023i	$0.725677\pi$
$492$		0			0
$493$	−4.62933	+	2.67274i	−0.208494	+	0.120374i
$494$	−7.96179	+	4.59674i	−0.358218	+	0.206817i
$495$		0			0
$496$			29.8335i			1.33956i
$497$	4.77583	+	3.53607i	0.214225	+	0.158614i
$498$		0			0
$499$	13.4181	−	23.2408i	0.600675	−	1.04040i	−0.392044	−	0.919946i	$-0.628232\pi$
$499$	13.4181	−	23.2408i	0.600675	−	1.04040i	0.992719	−	0.120453i	$-0.0384347\pi$
$500$		0			0
$501$		0			0
$502$	18.6646	+	10.7760i	0.833040	+	0.480956i
$503$	22.8321			1.01803			0.509017	−	0.860757i	$-0.330009\pi$
$503$	22.8321			1.01803			0.509017	+	0.860757i	$0.330009\pi$
$504$		0			0
$505$		0			0
$506$	15.8791	+	9.16783i	0.705914	+	0.407560i
$507$		0			0
$508$	−0.656240	−	1.13664i	−0.0291159	−	0.0504303i
$509$	7.67782	−	13.2984i	0.340313	−	0.589440i	−0.644177	−	0.764876i	$-0.722800\pi$
$509$	7.67782	−	13.2984i	0.340313	−	0.589440i	0.984491	+	0.175436i	$0.0561335\pi$
$510$		0			0
$511$	4.41358	−	38.6379i	0.195245	−	1.70924i
$512$		−	25.3373i		−	1.11976i
$513$		0			0
$514$	−13.9729	+	8.06729i	−0.616320	+	0.355833i
$515$		0			0
$516$		0			0
$517$		−	24.3563i		−	1.07119i
$518$	1.57285	−	13.7693i	0.0691072	−	0.604988i
$519$		0			0
$520$		0			0
$521$	−9.31915	−	16.1412i	−0.408279	−	0.707160i	0.586418	−	0.810009i	$-0.300538\pi$
$521$	−9.31915	−	16.1412i	−0.408279	−	0.707160i	−0.994697	+	0.102848i	$0.967204\pi$
$522$		0			0
$523$	−7.96399	−	4.59801i	−0.348241	−	0.201057i	0.315669	−	0.948869i	$-0.397771\pi$
$523$	−7.96399	−	4.59801i	−0.348241	−	0.201057i	−0.663910	+	0.747812i	$0.731104\pi$
$524$	−4.46498			−0.195054
$525$		0			0
$526$	12.4213			0.541592
$527$	−7.28172	−	4.20411i	−0.317197	−	0.183134i
$528$		0			0
$529$	5.15451	+	8.92787i	0.224109	+	0.388168i
$530$		0			0
$531$		0			0
$532$	2.29244	+	1.69735i	0.0993900	+	0.0735893i
$533$		−	3.17453i		−	0.137504i
$534$		0			0
$535$		0			0
$536$	12.3892	−	7.15291i	0.535132	−	0.308959i
$537$		0			0
$538$			10.0621i			0.433807i
$539$	12.3298	+	11.5111i	0.531083	+	0.495819i
$540$		0			0
$541$	4.49603	−	7.78736i	0.193300	−	0.334805i	−0.753042	−	0.657972i	$-0.771414\pi$
$541$	4.49603	−	7.78736i	0.193300	−	0.334805i	0.946342	+	0.323168i	$0.104748\pi$
$542$	3.59208	+	6.22167i	0.154293	+	0.267244i
$543$		0			0
$544$	1.22357	+	0.706426i	0.0524599	+	0.0302878i
$545$		0			0
$546$		0			0
$547$	12.8673			0.550165			0.275082	−	0.961421i	$-0.411295\pi$
$547$	12.8673			0.550165			0.275082	+	0.961421i	$0.411295\pi$
$548$	2.24895	+	1.29843i	0.0960703	+	0.0554662i
$549$		0			0
$550$		0			0
$551$	11.4595	−	19.8485i	0.488193	−	0.845575i
$552$		0			0
$553$	1.88233	+	4.33250i	0.0800449	+	0.184237i
$554$		−	22.4870i		−	0.955380i
$555$		0			0
$556$	3.42594	−	1.97796i	0.145292	−	0.0838844i
$557$	−5.91023	+	3.41227i	−0.250424	+	0.144583i	−0.619959	−	0.784635i	$-0.712851\pi$
$557$	−5.91023	+	3.41227i	−0.250424	+	0.144583i	0.369534	+	0.929217i	$0.379517\pi$
$558$		0			0
$559$			17.3914i			0.735577i
$560$		0			0
$561$		0			0
$562$	16.7324	−	28.9815i	0.705816	−	1.22251i
$563$	4.34307	+	7.52241i	0.183038	+	0.317032i	0.942914	−	0.333037i	$-0.108073\pi$
$563$	4.34307	+	7.52241i	0.183038	+	0.317032i	−0.759875	+	0.650069i	$0.774740\pi$
$564$		0			0
$565$		0			0
$566$	−12.6303			−0.530892
$567$		0			0
$568$	−6.69759			−0.281025
$569$	−28.5427	−	16.4792i	−1.19657	−	0.690842i	−0.236784	−	0.971562i	$-0.576093\pi$
$569$	−28.5427	−	16.4792i	−1.19657	−	0.690842i	−0.959790	+	0.280720i	$0.909427\pi$
$570$		0			0
$571$	−4.38204	−	7.58991i	−0.183383	−	0.317628i	0.759648	−	0.650335i	$-0.225371\pi$
$571$	−4.38204	−	7.58991i	−0.183383	−	0.317628i	−0.943030	+	0.332707i	$0.892038\pi$
$572$	−0.534133	+	0.925146i	−0.0223332	+	0.0386823i
$573$		0			0
$574$	5.99779	−	2.60585i	0.250343	−	0.108766i
$575$		0			0
$576$		0			0
$577$	−30.7939	+	17.7788i	−1.28197	+	0.740143i	−0.977207	−	0.212287i	$-0.931909\pi$
$577$	−30.7939	+	17.7788i	−1.28197	+	0.740143i	−0.304758	+	0.952430i	$0.598576\pi$
$578$	−18.3569	+	10.5984i	−0.763546	+	0.440833i
$579$		0			0
$580$		0			0
$581$	15.1468	−	20.4573i	0.628394	−	0.848712i
$582$		0			0
$583$	15.3121	−	26.5213i	0.634161	−	1.09840i
$584$	21.9156	+	37.9590i	0.906876	+	1.57075i
$585$		0			0
$586$	1.65229	+	0.953952i	0.0682556	+	0.0394074i
$587$	31.4362			1.29751			0.648755	−	0.760997i	$-0.275290\pi$
$587$	31.4362			1.29751			0.648755	+	0.760997i	$0.275290\pi$
$588$		0			0
$589$	36.0507			1.48544
$590$		0			0
$591$		0			0
$592$	6.76985	+	11.7257i	0.278239	+	0.481924i
$593$	6.49446	−	11.2487i	0.266695	−	0.461930i	−0.701311	−	0.712855i	$-0.747402\pi$
$593$	6.49446	−	11.2487i	0.266695	−	0.461930i	0.968006	+	0.250926i	$0.0807349\pi$
$594$		0			0
$595$		0			0
$596$		−	0.611922i		−	0.0250653i
$597$		0			0
$598$	11.1584	−	6.44229i	0.456300	−	0.263445i
$599$	−12.7099	+	7.33804i	−0.519311	+	0.299824i	−0.736653	−	0.676271i	$-0.763595\pi$
$599$	−12.7099	+	7.33804i	−0.519311	+	0.299824i	0.217342	+	0.976096i	$0.430261\pi$
$600$		0			0
$601$			9.55020i			0.389561i	0.980847	+	0.194780i	$0.0623994\pi$
$601$			9.55020i			0.389561i	−0.980847	+	0.194780i	$0.937601\pi$
$602$	−32.8583	+	14.2759i	−1.33920	+	0.581842i
$603$		0			0
$604$	−1.31298	+	2.27414i	−0.0534243	+	0.0925336i
$605$		0			0
$606$		0			0
$607$	−23.5998	−	13.6253i	−0.957885	−	0.553035i	−0.0623639	−	0.998053i	$-0.519864\pi$
$607$	−23.5998	−	13.6253i	−0.957885	−	0.553035i	−0.895522	+	0.445018i	$0.853197\pi$
$608$	−6.05769			−0.245672
$609$		0			0
$610$		0			0
$611$	−14.8223	−	8.55765i	−0.599646	−	0.346206i
$612$		0			0
$613$	24.2382	+	41.9818i	0.978971	+	1.69563i	0.666152	+	0.745816i	$0.267940\pi$
$613$	24.2382	+	41.9818i	0.978971	+	1.69563i	0.312819	+	0.949813i	$0.398727\pi$
$614$	5.07501	−	8.79018i	0.204811	−	0.354743i
$615$		0			0
$616$	−18.8888	−	2.15765i	−0.761051	−	0.0869342i
$617$			8.42587i			0.339213i	0.985512	+	0.169606i	$0.0542497\pi$
$617$			8.42587i			0.339213i	−0.985512	+	0.169606i	$0.945750\pi$
$618$		0			0
$619$	14.9893	−	8.65410i	0.602472	−	0.347837i	−0.167541	−	0.985865i	$-0.553583\pi$
$619$	14.9893	−	8.65410i	0.602472	−	0.347837i	0.770014	+	0.638028i	$0.220249\pi$
$620$		0			0
$621$		0			0
$622$			43.7382i			1.75374i
$623$	0.465678	+	1.07184i	0.0186570	+	0.0429422i
$624$		0			0
$625$		0			0
$626$	−5.57453	−	9.65537i	−0.222803	−	0.385906i
$627$		0			0
$628$	−4.70528	−	2.71660i	−0.187761	−	0.108404i
$629$	−3.81600			−0.152154
$630$		0			0
$631$	16.3945			0.652653			0.326327	−	0.945257i	$-0.394189\pi$
$631$	16.3945			0.652653			0.326327	+	0.945257i	$0.394189\pi$
$632$	−4.61075	−	2.66202i	−0.183406	−	0.105889i
$633$		0			0
$634$	−3.91677	−	6.78404i	−0.155555	−	0.269429i
$635$		0			0
$636$		0			0
$637$	11.3373	−	3.45899i	0.449202	−	0.137050i
$638$			17.6816i			0.700023i
$639$		0			0
$640$		0			0
$641$	12.9885	−	7.49893i	0.513016	−	0.296190i	−0.221057	−	0.975261i	$-0.570951\pi$
$641$	12.9885	−	7.49893i	0.513016	−	0.296190i	0.734072	+	0.679071i	$0.237617\pi$
$642$		0			0
$643$		−	26.5806i		−	1.04824i	−0.851645	−	0.524119i	$-0.824395\pi$
$643$		−	26.5806i		−	1.04824i	0.851645	−	0.524119i	$-0.175605\pi$
$644$	−3.21284	−	2.37882i	−0.126604	−	0.0937385i
$645$		0			0
$646$	−2.60730	+	4.51597i	−0.102583	+	0.177678i
$647$	11.5482	+	20.0021i	0.454007	+	0.786364i	0.998631	−	0.0523172i	$-0.0166607\pi$
$647$	11.5482	+	20.0021i	0.454007	+	0.786364i	−0.544623	+	0.838681i	$0.683327\pi$
$648$		0			0
$649$	14.1359	+	8.16137i	0.554883	+	0.320362i
$650$		0			0
$651$		0			0
$652$	4.08936			0.160152
$653$	18.3223	+	10.5784i	0.717007	+	0.413964i	0.813650	−	0.581355i	$-0.197477\pi$
$653$	18.3223	+	10.5784i	0.717007	+	0.413964i	−0.0966433	+	0.995319i	$0.530811\pi$
$654$		0			0
$655$		0			0
$656$	−3.19441	+	5.53289i	−0.124721	+	0.216023i
$657$		0			0
$658$	4.00134	−	35.0290i	0.155988	−	1.36557i
$659$			34.2144i			1.33281i	0.745592	+	0.666403i	$0.232167\pi$
$659$			34.2144i			1.33281i	−0.745592	+	0.666403i	$0.767833\pi$
$660$		0			0
$661$	0.188317	−	0.108725i	0.00732467	−	0.00422890i	−0.496333	−	0.868132i	$-0.665321\pi$
$661$	0.188317	−	0.108725i	0.00732467	−	0.00422890i	0.503658	+	0.863903i	$0.331987\pi$
$662$	30.2687	−	17.4756i	1.17643	−	0.679209i
$663$		0			0
$664$			28.6892i			1.11336i
$665$		0			0
$666$		0			0
$667$	−16.0604	+	27.8175i	−0.621863	+	1.07710i
$668$	1.93548	+	3.35234i	0.0748859	+	0.129706i
$669$		0			0
$670$		0			0
$671$	−5.52284			−0.213207
$672$		0			0
$673$	29.8280			1.14979			0.574893	−	0.818229i	$-0.305044\pi$
$673$	29.8280			1.14979			0.574893	+	0.818229i	$0.305044\pi$
$674$	3.90607	+	2.25517i	0.150456	+	0.0868660i
$675$		0			0
$676$	−1.32638	−	2.29735i	−0.0510145	−	0.0883596i
$677$	−21.0579	+	36.4734i	−0.809321	+	1.40179i	0.104014	+	0.994576i	$0.466831\pi$
$677$	−21.0579	+	36.4734i	−0.809321	+	1.40179i	−0.913335	+	0.407209i	$0.866502\pi$
$678$		0			0
$679$	26.5636	+	19.6679i	1.01942	+	0.754786i
$680$		0			0
$681$		0			0
$682$	−24.0863	+	13.9062i	−0.922311	+	0.532497i
$683$	20.1941	−	11.6590i	0.772704	−	0.446121i	−0.0611342	−	0.998130i	$-0.519472\pi$
$683$	20.1941	−	11.6590i	0.772704	−	0.446121i	0.833838	+	0.552009i	$0.186138\pi$
$684$		0			0
$685$		0			0
$686$	15.8416	+	18.5808i	0.604835	+	0.709418i
$687$		0			0
$688$	17.5003	−	30.3114i	0.667192	−	1.15561i
$689$	−10.7599	−	18.6367i	−0.409919	−	0.710000i
$690$		0			0
$691$	4.66296	+	2.69216i	0.177387	+	0.102415i	0.586065	−	0.810264i	$-0.300676\pi$
$691$	4.66296	+	2.69216i	0.177387	+	0.102415i	−0.408677	+	0.912679i	$0.634010\pi$
$692$	1.79688			0.0683073
$693$		0			0
$694$	17.6652			0.670563
$695$		0			0
$696$		0			0
$697$	−0.900306	−	1.55938i	−0.0341015	−	0.0590656i
$698$	−10.0584	+	17.4216i	−0.380715	+	0.659418i
$699$		0			0
$700$		0			0
$701$			21.9593i			0.829391i	0.909960	+	0.414696i	$0.136112\pi$
$701$			21.9593i			0.829391i	−0.909960	+	0.414696i	$0.863888\pi$
$702$		0			0
$703$	14.1693	−	8.18066i	0.534406	−	0.308540i
$704$	18.2708	−	10.5487i	0.688607	−	0.397568i
$705$		0			0
$706$			48.6779i			1.83202i
$707$	24.9442	+	2.84935i	0.938121	+	0.107161i
$708$		0			0
$709$	−13.6505	+	23.6434i	−0.512657	+	0.887948i	0.487236	+	0.873271i	$0.338005\pi$
$709$	−13.6505	+	23.6434i	−0.512657	+	0.887948i	−0.999892	+	0.0146769i	$0.995328\pi$
$710$		0			0
$711$		0			0
$712$	−1.14067	−	0.658569i	−0.0427486	−	0.0246809i
$713$	−50.5248			−1.89217
$714$		0			0
$715$		0			0
$716$	−2.65449	−	1.53257i	−0.0992031	−	0.0572749i
$717$		0			0
$718$	5.86954	+	10.1663i	0.219049	+	0.379405i
$719$	16.3001	−	28.2327i	0.607893	−	1.05290i	−0.383694	−	0.923460i	$-0.625348\pi$
$719$	16.3001	−	28.2327i	0.607893	−	1.05290i	0.991587	−	0.129441i	$-0.0413183\pi$
$720$		0			0
$721$	19.6135	−	8.52145i	0.730446	−	0.317355i
$722$			2.69185i			0.100180i
$723$		0			0
$724$	3.93367	−	2.27111i	0.146194	−	0.0844050i
$725$		0			0
$726$		0			0
$727$			4.18319i			0.155146i	0.996987	+	0.0775729i	$0.0247171\pi$
$727$			4.18319i			0.155146i	−0.996987	+	0.0775729i	$0.975283\pi$
$728$	−7.94970	+	10.7369i	−0.294636	+	0.397936i
$729$		0			0
$730$		0			0
$731$	4.93224	+	8.54290i	0.182426	+	0.315970i
$732$		0			0
$733$	−0.562457	−	0.324735i	−0.0207748	−	0.0119944i	0.489577	−	0.871960i	$-0.337151\pi$
$733$	−0.562457	−	0.324735i	−0.0207748	−	0.0119944i	−0.510351	+	0.859966i	$0.670485\pi$
$734$	−19.0560			−0.703370
$735$		0			0
$736$	8.48979			0.312938
$737$	10.0116	+	5.78023i	0.368784	+	0.212917i
$738$		0			0
$739$	11.5360	+	19.9810i	0.424360	+	0.735012i	0.996360	−	0.0852408i	$-0.0271660\pi$
$739$	11.5360	+	19.9810i	0.424360	+	0.735012i	−0.572001	+	0.820253i	$0.693833\pi$
$740$		0			0
$741$		0			0
$742$	26.3787	−	35.6272i	0.968393	−	1.30792i
$743$			18.5599i			0.680897i	0.940263	+	0.340448i	$0.110579\pi$
$743$			18.5599i			0.680897i	−0.940263	+	0.340448i	$0.889421\pi$
$744$		0			0
$745$		0			0
$746$	24.1159	−	13.9233i	0.882945	−	0.509768i
$747$		0			0
$748$			0.605926i			0.0221549i
$749$	13.1674	−	5.72081i	0.481126	−	0.209034i
$750$		0			0
$751$	−11.0882	+	19.2053i	−0.404613	+	0.700811i	−0.994276	−	0.106838i	$-0.965927\pi$
$751$	−11.0882	+	19.2053i	−0.404613	+	0.700811i	0.589663	+	0.807649i	$0.299261\pi$
$752$	17.2225	+	29.8302i	0.628040	+	1.08780i
$753$		0			0
$754$	10.7604	+	6.21250i	0.391869	+	0.226246i
$755$		0			0
$756$		0			0
$757$	22.4056			0.814347			0.407173	−	0.913351i	$-0.366515\pi$
$757$	22.4056			0.814347			0.407173	+	0.913351i	$0.366515\pi$
$758$	−0.0152974	−	0.00883196i	−0.000555627	−	0.000320791i
$759$		0			0
$760$		0			0
$761$	−7.01527	+	12.1508i	−0.254303	+	0.440466i	−0.964706	−	0.263329i	$-0.915179\pi$
$761$	−7.01527	+	12.1508i	−0.254303	+	0.440466i	0.710403	+	0.703795i	$0.248513\pi$
$762$		0			0
$763$	45.6444	+	5.21392i	1.65244	+	0.188757i
$764$		−	4.94800i		−	0.179012i
$765$		0			0
$766$	−19.6642	+	11.3531i	−0.710496	+	0.410205i
$767$	9.93339	−	5.73505i	0.358674	−	0.207081i
$768$		0			0
$769$		−	40.4788i		−	1.45970i	−0.683606	−	0.729851i	$-0.739589\pi$
$769$		−	40.4788i		−	1.45970i	0.683606	−	0.729851i	$-0.260411\pi$
$770$		0			0
$771$		0			0
$772$	−3.05289	+	5.28777i	−0.109876	+	0.190311i
$773$	15.6561	+	27.1171i	0.563110	+	0.975335i	0.997223	+	0.0744762i	$0.0237285\pi$
$773$	15.6561	+	27.1171i	0.563110	+	0.975335i	−0.434113	+	0.900858i	$0.642938\pi$
$774$		0			0
$775$		0			0
$776$	−37.2526			−1.33729
$777$		0			0
$778$	33.9604			1.21754
$779$	6.68592	+	3.86012i	0.239548	+	0.138303i
$780$		0			0
$781$	−2.70614	−	4.68717i	−0.0968333	−	0.167720i
$782$	3.65410	−	6.32909i	0.130670	−	0.226328i
$783$		0			0
$784$	−23.2405	−	5.37967i	−0.830017	−	0.192131i
$785$		0			0
$786$		0			0
$787$	21.0932	−	12.1781i	0.751890	−	0.434104i	−0.0744866	−	0.997222i	$-0.523732\pi$
$787$	21.0932	−	12.1781i	0.751890	−	0.434104i	0.826376	+	0.563118i	$0.190398\pi$
$788$	0.191115	−	0.110340i	0.00680819	−	0.00393071i
$789$		0			0
$790$		0			0
$791$	12.5965	+	9.32656i	0.447880	+	0.331614i
$792$		0			0
$793$	−1.94047	+	3.36099i	−0.0689081	+	0.119352i
$794$	−10.0515	−	17.4097i	−0.356715	−	0.617848i
$795$		0			0
$796$	−0.193721	−	0.111845i	−0.00686626	−	0.00396424i
$797$	−42.7862			−1.51557			−0.757783	−	0.652507i	$-0.773717\pi$
$797$	−42.7862			−1.51557			−0.757783	+	0.652507i	$0.773717\pi$
$798$		0			0
$799$	−9.70789			−0.343441
$800$		0			0
$801$		0			0
$802$	8.65012	+	14.9824i	0.305446	+	0.529049i
$803$	−17.7099	+	30.6744i	−0.624969	+	1.08248i
$804$		0			0
$805$		0			0
$806$			19.5440i			0.688407i
$807$		0			0
$808$	−24.5058	+	14.1485i	−0.862113	+	0.497741i
$809$	33.0092	−	19.0579i	1.16054	−	0.670038i	0.209107	−	0.977893i	$-0.432944\pi$
$809$	33.0092	−	19.0579i	1.16054	−	0.670038i	0.951433	+	0.307854i	$0.0996110\pi$
$810$		0			0
$811$		−	43.0019i		−	1.51000i	−0.655725	−	0.755000i	$-0.727637\pi$
$811$		−	43.0019i		−	1.51000i	0.655725	−	0.755000i	$-0.272363\pi$
$812$	0.437513	−	3.83014i	0.0153537	−	0.134411i
$813$		0			0
$814$	−6.31122	+	10.9314i	−0.221208	+	0.383144i
$815$		0			0
$816$		0			0
$817$	−36.6282	−	21.1473i	−1.28146	−	0.739850i
$818$	43.3406			1.51537
$819$		0			0
$820$		0			0
$821$	6.74916	+	3.89663i	0.235547	+	0.135993i	0.613129	−	0.789983i	$-0.289911\pi$
$821$	6.74916	+	3.89663i	0.235547	+	0.135993i	−0.377581	+	0.925976i	$0.623244\pi$
$822$		0			0
$823$	−11.5228	−	19.9581i	−0.401661	−	0.695697i	0.592265	−	0.805743i	$-0.298234\pi$
$823$	−11.5228	−	19.9581i	−0.401661	−	0.695697i	−0.993927	+	0.110046i	$0.964900\pi$
$824$	−12.0512	+	20.8732i	−0.419822	+	0.727153i
$825$		0			0
$826$	18.9894	+	14.0599i	0.660726	+	0.489207i
$827$		−	0.555383i		−	0.0193126i	−0.999953	−	0.00965628i	$-0.996926\pi$
$827$		−	0.555383i		−	0.0193126i	0.999953	−	0.00965628i	$-0.00307374\pi$
$828$		0			0
$829$	−20.8718	+	12.0504i	−0.724909	+	0.418526i	−0.816557	−	0.577265i	$-0.804120\pi$
$829$	−20.8718	+	12.0504i	−0.724909	+	0.418526i	0.0916480	+	0.995791i	$0.470787\pi$
$830$		0			0
$831$		0			0
$832$		−	14.8252i		−	0.513972i
$833$	4.58808	−	4.91441i	0.158968	−	0.170274i
$834$		0			0
$835$		0			0
$836$	−1.29897	−	2.24989i	−0.0449259	−	0.0778140i
$837$		0			0
$838$	10.6541	+	6.15112i	0.368038	+	0.212487i
$839$	45.5904			1.57395			0.786977	−	0.616982i	$-0.211645\pi$
$839$	45.5904			1.57395			0.786977	+	0.616982i	$0.211645\pi$
$840$		0			0
$841$	−1.97516			−0.0681090
$842$	14.9253	+	8.61714i	0.514361	+	0.296966i
$843$		0			0
$844$	−2.11972	−	3.67146i	−0.0729636	−	0.126377i
$845$		0			0
$846$		0			0
$847$	5.47519	+	12.6021i	0.188130	+	0.433012i
$848$			43.3090i			1.48724i
$849$		0			0
$850$		0			0
$851$	−19.8582	+	11.4651i	−0.680730	+	0.393019i
$852$		0			0
$853$			0.440934i			0.0150973i	0.999972	+	0.00754864i	$0.00240283\pi$
$853$			0.440934i			0.0150973i	−0.999972	+	0.00754864i	$0.997597\pi$
$854$	−7.94292	−	0.907313i	−0.271801	−	0.0310476i
$855$		0			0
$856$	−8.09045	+	14.0131i	−0.276526	+	0.478957i
$857$	−4.17631	−	7.23358i	−0.142660	−	0.247094i	0.785838	−	0.618433i	$-0.212232\pi$
$857$	−4.17631	−	7.23358i	−0.142660	−	0.247094i	−0.928497	+	0.371339i	$0.878899\pi$
$858$		0			0
$859$	−2.09709	−	1.21076i	−0.0715518	−	0.0413104i	0.463797	−	0.885941i	$-0.346487\pi$
$859$	−2.09709	−	1.21076i	−0.0715518	−	0.0413104i	−0.535349	+	0.844631i	$0.679820\pi$
$860$		0			0
$861$		0			0
$862$	−7.88967			−0.268723
$863$	13.2203	+	7.63275i	0.450025	+	0.259822i	0.707841	−	0.706372i	$-0.249669\pi$
$863$	13.2203	+	7.63275i	0.450025	+	0.259822i	−0.257816	+	0.966194i	$0.583003\pi$
$864$		0			0
$865$		0			0
$866$	12.8107	−	22.1887i	0.435324	−	0.754003i
$867$		0			0
$868$	5.56158	−	2.41633i	0.188772	−	0.0820155i
$869$		−	4.30233i		−	0.145946i
$870$		0			0
$871$	7.03525	−	4.06180i	0.238380	−	0.137629i
$872$	−44.8424	+	25.8897i	−1.51855	+	0.876738i
$873$		0			0
$874$			31.3344i			1.05990i
$875$		0			0
$876$		0			0
$877$	17.3127	−	29.9865i	0.584609	−	1.01257i	−0.410315	−	0.911944i	$-0.634581\pi$
$877$	17.3127	−	29.9865i	0.584609	−	1.01257i	0.994924	−	0.100629i	$-0.0320855\pi$
$878$	18.3578	+	31.7967i	0.619547	+	1.07309i
$879$		0			0
$880$		0			0
$881$	18.2805			0.615887			0.307943	−	0.951405i	$-0.400359\pi$
$881$	18.2805			0.615887			0.307943	+	0.951405i	$0.400359\pi$
$882$		0			0
$883$	−15.7048			−0.528508			−0.264254	−	0.964453i	$-0.585126\pi$
$883$	−15.7048			−0.528508			−0.264254	+	0.964453i	$0.585126\pi$
$884$	0.368743	+	0.212894i	0.0124022	+	0.00716040i
$885$		0			0
$886$	−15.4456	−	26.7526i	−0.518906	−	0.898772i
$887$	15.8438	−	27.4423i	0.531983	−	0.921422i	−0.467320	−	0.884088i	$-0.654780\pi$
$887$	15.8438	−	27.4423i	0.531983	−	0.921422i	0.999303	−	0.0373336i	$-0.0118864\pi$
$888$		0			0
$889$	7.89270	−	10.6599i	0.264713	−	0.357522i
$890$		0			0
$891$		0			0
$892$	2.26789	−	1.30937i	0.0759346	−	0.0438409i
$893$	36.0467	−	20.8116i	1.20626	−	0.696433i
$894$		0			0
$895$		0			0
$896$	20.8708	−	9.06769i	0.697244	−	0.302930i
$897$		0			0
$898$	−10.4067	+	18.0250i	−0.347277	+	0.601501i
$899$	−24.3613	−	42.1950i	−0.812494	−	1.40728i
$900$		0			0
$901$	−10.5708	−	6.10306i	−0.352165	−	0.203322i
$902$	−5.95601			−0.198314
$903$		0			0
$904$	−17.6652			−0.587537
$905$		0			0
$906$		0			0
$907$	1.60632	+	2.78222i	0.0533369	+	0.0923822i	0.891461	−	0.453097i	$-0.149681\pi$
$907$	1.60632	+	2.78222i	0.0533369	+	0.0923822i	−0.838124	+	0.545479i	$0.816348\pi$
$908$	−0.612391	+	1.06069i	−0.0203229	+	0.0352003i
$909$		0			0
$910$		0			0
$911$		−	43.0454i		−	1.42616i	−0.701084	−	0.713079i	$-0.747300\pi$
$911$		−	43.0454i		−	1.42616i	0.701084	−	0.713079i	$-0.252700\pi$
$912$		0			0
$913$	−20.0775	+	11.5918i	−0.664470	+	0.383632i
$914$	30.5024	−	17.6106i	1.00893	−	0.582506i
$915$		0			0
$916$			3.73224i			0.123317i
$917$	−17.9807	−	41.3855i	−0.593773	−	1.36667i
$918$		0			0
$919$	17.9287	−	31.0535i	0.591414	−	1.02436i	−0.402628	−	0.915364i	$-0.631903\pi$
$919$	17.9287	−	31.0535i	0.591414	−	1.02436i	0.994042	−	0.108996i	$-0.0347635\pi$
$920$		0			0
$921$		0			0
$922$	37.8784	+	21.8691i	1.24746	+	0.720221i
$923$	−3.80324			−0.125185
$924$		0			0
$925$		0			0
$926$	−10.2926	−	5.94245i	−0.338236	−	0.195281i
$927$		0			0
$928$	4.09348	+	7.09012i	0.134375	+	0.232745i
$929$	−3.44568	+	5.96810i	−0.113049	+	0.195807i	−0.916998	−	0.398891i	$-0.869395\pi$
$929$	−3.44568	+	5.96810i	−0.113049	+	0.195807i	0.803949	+	0.594698i	$0.202728\pi$
$930$		0			0
$931$	−6.50078	+	28.0837i	−0.213054	+	0.920406i
$932$			5.83947i			0.191278i
$933$		0			0
$934$	37.0725	−	21.4038i	1.21305	−	0.700354i
$935$		0			0
$936$		0			0
$937$		−	13.8533i		−	0.452566i	−0.974062	−	0.226283i	$-0.927343\pi$
$937$		−	13.8533i		−	0.452566i	0.974062	−	0.226283i	$-0.0726575\pi$
$938$	13.4491	+	9.95784i	0.439129	+	0.325135i
$939$		0			0
$940$		0			0
$941$	−15.2003	−	26.3277i	−0.495516	−	0.858259i	0.504471	−	0.863429i	$-0.331688\pi$
$941$	−15.2003	−	26.3277i	−0.495516	−	0.858259i	−0.999987	+	0.00517013i	$0.998354\pi$
$942$		0			0
$943$	−9.37026	−	5.40992i	−0.305138	−	0.176171i
$944$	−23.0838			−0.751315
$945$		0			0
$946$	32.6295			1.06088
$947$	23.1883	+	13.3878i	0.753519	+	0.435044i	0.826964	−	0.562255i	$-0.190066\pi$
$947$	23.1883	+	13.3878i	0.753519	+	0.435044i	−0.0734452	+	0.997299i	$0.523399\pi$
$948$		0			0
$949$	12.4449	+	21.5551i	0.403977	+	0.699709i
$950$		0			0
$951$		0			0
$952$	−0.859993	+	7.52867i	−0.0278725	+	0.244006i
$953$		−	23.9462i		−	0.775693i	−0.921724	−	0.387846i	$-0.873219\pi$
$953$		−	23.9462i		−	0.775693i	0.921724	−	0.387846i	$-0.126781\pi$
$954$		0			0
$955$		0			0
$956$	−1.45045	+	0.837419i	−0.0469110	+	0.0270841i
$957$		0			0
$958$		−	5.49255i		−	0.177456i
$959$	−2.97842	+	26.0741i	−0.0961783	+	0.841977i
$960$		0			0
$961$	22.8192	−	39.5240i	0.736104	−	1.27497i
$962$	4.43494	+	7.68154i	0.142988	+	0.247663i
$963$		0			0
$964$	1.62538	+	0.938412i	0.0523499	+	0.0302242i
$965$		0			0
$966$		0			0
$967$	12.8640			0.413678			0.206839	−	0.978375i	$-0.433682\pi$
$967$	12.8640			0.413678			0.206839	+	0.978375i	$0.433682\pi$
$968$	−13.4114	−	7.74309i	−0.431060	−	0.248872i
$969$		0			0
$970$		0			0
$971$	17.4878	−	30.2897i	0.561209	−	0.972043i	−0.436182	−	0.899859i	$-0.643670\pi$
$971$	17.4878	−	30.2897i	0.561209	−	0.972043i	0.997391	−	0.0721846i	$-0.0229971\pi$
$972$		0			0
$973$	32.1299	+	23.7893i	1.03004	+	0.762650i
$974$			27.2031i			0.871642i
$975$		0			0
$976$	6.76408	−	3.90524i	0.216513	−	0.125004i
$977$	7.64984	−	4.41664i	0.244740	−	0.141301i	−0.372613	−	0.927987i	$-0.621538\pi$
$977$	7.64984	−	4.41664i	0.244740	−	0.141301i	0.617353	+	0.786686i	$0.288205\pi$
$978$		0			0
$979$		−	1.06437i		−	0.0340174i
$980$		0			0
$981$		0			0
$982$	22.1741	−	38.4066i	0.707603	−	1.22560i
$983$	25.6596	+	44.4437i	0.818414	+	1.41753i	0.906850	+	0.421453i	$0.138480\pi$
$983$	25.6596	+	44.4437i	0.818414	+	1.41753i	−0.0884361	+	0.996082i	$0.528187\pi$
$984$		0			0
$985$		0			0
$986$	7.04753			0.224439
$987$		0			0
$988$	−1.82559			−0.0580798
$989$	51.3341	+	29.6377i	1.63233	+	0.942425i
$990$		0			0
$991$	9.04272	+	15.6625i	0.287252	+	0.497534i	0.973153	−	0.230160i	$-0.0739251\pi$
$991$	9.04272	+	15.6625i	0.287252	+	0.497534i	−0.685901	+	0.727695i	$0.740592\pi$
$992$	−6.43887	+	11.1524i	−0.204434	+	0.354091i
$993$		0			0
$994$	−3.12193	−	7.18564i	−0.0990216	−	0.227915i
$995$		0			0
$996$		0			0
$997$	28.7737	−	16.6125i	0.911273	−	0.526124i	0.0304328	−	0.999537i	$-0.490311\pi$
$997$	28.7737	−	16.6125i	0.911273	−	0.526124i	0.880841	+	0.473413i	$0.156978\pi$
$998$	−30.6408	+	17.6905i	−0.969917	+	0.559982i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1575.2.bk.i.26.6		24
3.2	odd	2	inner	1575.2.bk.i.26.7		24
5.2	odd	4		315.2.bb.b.89.7	yes	24
5.3	odd	4		315.2.bb.b.89.5	✓	24
5.4	even	2	inner	1575.2.bk.i.26.8		24
7.3	odd	6	inner	1575.2.bk.i.1151.7		24
15.2	even	4		315.2.bb.b.89.6	yes	24
15.8	even	4		315.2.bb.b.89.8	yes	24
15.14	odd	2	inner	1575.2.bk.i.26.5		24
21.17	even	6	inner	1575.2.bk.i.1151.6		24
35.2	odd	12		2205.2.g.b.2204.12		24
35.3	even	12		315.2.bb.b.269.6	yes	24
35.12	even	12		2205.2.g.b.2204.11		24
35.17	even	12		315.2.bb.b.269.8	yes	24
35.23	odd	12		2205.2.g.b.2204.16		24
35.24	odd	6	inner	1575.2.bk.i.1151.5		24
35.33	even	12		2205.2.g.b.2204.15		24
105.2	even	12		2205.2.g.b.2204.14		24
105.17	odd	12		315.2.bb.b.269.5	yes	24
105.23	even	12		2205.2.g.b.2204.10		24
105.38	odd	12		315.2.bb.b.269.7	yes	24
105.47	odd	12		2205.2.g.b.2204.13		24
105.59	even	6	inner	1575.2.bk.i.1151.8		24
105.68	odd	12		2205.2.g.b.2204.9		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
315.2.bb.b.89.5	✓	24	5.3	odd	4
315.2.bb.b.89.6	yes	24	15.2	even	4
315.2.bb.b.89.7	yes	24	5.2	odd	4
315.2.bb.b.89.8	yes	24	15.8	even	4
315.2.bb.b.269.5	yes	24	105.17	odd	12
315.2.bb.b.269.6	yes	24	35.3	even	12
315.2.bb.b.269.7	yes	24	105.38	odd	12
315.2.bb.b.269.8	yes	24	35.17	even	12
1575.2.bk.i.26.5		24	15.14	odd	2	inner
1575.2.bk.i.26.6		24	1.1	even	1	trivial
1575.2.bk.i.26.7		24	3.2	odd	2	inner
1575.2.bk.i.26.8		24	5.4	even	2	inner
1575.2.bk.i.1151.5		24	35.24	odd	6	inner
1575.2.bk.i.1151.6		24	21.17	even	6	inner
1575.2.bk.i.1151.7		24	7.3	odd	6	inner
1575.2.bk.i.1151.8		24	105.59	even	6	inner
2205.2.g.b.2204.9		24	105.68	odd	12
2205.2.g.b.2204.10		24	105.23	even	12
2205.2.g.b.2204.11		24	35.12	even	12
2205.2.g.b.2204.12		24	35.2	odd	12
2205.2.g.b.2204.13		24	105.47	odd	12
2205.2.g.b.2204.14		24	105.2	even	12
2205.2.g.b.2204.15		24	35.33	even	12
2205.2.g.b.2204.16		24	35.23	odd	12

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:	\( N \)	\(=\)	\( 1575 = 3^{2} \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1575.bk (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.14177 - 0.659204i) q^{2} +(-0.130901 - 0.226727i) q^{4} +(1.57437 - 2.12635i) q^{7} +2.98198i q^{8} +(-2.08688 + 1.20486i) q^{11} +1.69332i q^{13} +(-3.19927 + 1.38998i) q^{14} +(1.70393 - 2.95129i) q^{16} +(0.480231 + 0.831785i) q^{17} +(-3.56633 - 2.05902i) q^{19} +3.17699 q^{22} +(4.99818 + 2.88570i) q^{23} +(1.11625 - 1.93339i) q^{26} +(-0.688188 - 0.0786111i) q^{28} +5.56553i q^{29} +(-7.58148 + 4.37717i) q^{31} +(1.27393 - 0.735506i) q^{32} -1.26628i q^{34} +(-1.98654 + 3.44079i) q^{37} +(2.71463 + 4.70187i) q^{38} -1.87474 q^{41} +10.2706 q^{43} +(0.546349 + 0.315435i) q^{44} +(-3.80453 - 6.58963i) q^{46} +(-5.05376 + 8.75337i) q^{47} +(-2.04272 - 6.69532i) q^{49} +(0.383923 - 0.221658i) q^{52} +(-11.0060 + 6.35430i) q^{53} +(6.34072 + 4.69473i) q^{56} +(3.66882 - 6.35458i) q^{58} +(-3.38686 - 5.86621i) q^{59} +(1.98485 + 1.14595i) q^{61} +11.5418 q^{62} -8.75510 q^{64} +(-2.39872 - 4.15470i) q^{67} +(0.125726 - 0.217763i) q^{68} +2.24602i q^{71} +(12.7295 - 7.34937i) q^{73} +(4.53637 - 2.61907i) q^{74} +1.07811i q^{76} +(-0.723564 + 6.33432i) q^{77} +(-0.892703 + 1.54621i) q^{79} +(2.14052 + 1.23583i) q^{82} +9.62086 q^{83} +(-11.7267 - 6.77039i) q^{86} +(-3.59286 - 6.22302i) q^{88} +(-0.220850 + 0.382523i) q^{89} +(3.60060 + 2.66592i) q^{91} -1.51096i q^{92} +(11.5405 - 6.66292i) q^{94} +12.4926i q^{97} +(-2.08125 + 8.99111i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 24 q^{4} + 36 q^{19} - 60 q^{31} - 24 q^{46} - 36 q^{49} + 48 q^{61} - 48 q^{64} + 60 q^{79} + 60 q^{91} - 48 q^{94}+O(q^{100}) \) 24 * q + 24 * q^4 + 36 * q^19 - 60 * q^31 - 24 * q^46 - 36 * q^49 + 48 * q^61 - 48 * q^64 + 60 * q^79 + 60 * q^91 - 48 * q^94

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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