LMFDB - Embedded newform 1575.2.bc.d.899.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1575,2,Mod(899,1575)]

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, 3, 1]))

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

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

chi := DirichletCharacter("1575.899");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1575 = 3^{2} \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1575.bc (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:	$12.5764383184$
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			899.6
Character	$\chi$	$=$	1575.899
Dual form			1575.2.bc.d.1349.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.199105 - 0.344861i) q^{2} +(0.920714 - 1.59472i) q^{4} +(1.30338 + 2.30243i) q^{7} -1.52970 q^{8} +O(q^{10})$	\(q+(-0.199105 - 0.344861i) q^{2} +(0.920714 - 1.59472i) q^{4} +(1.30338 + 2.30243i) q^{7} -1.52970 q^{8} +(4.44725 + 2.56762i) q^{11} -5.09545 q^{13} +(0.534507 - 0.907912i) q^{14} +(-1.53686 - 2.66191i) q^{16} +(3.88520 + 2.24312i) q^{17} +(3.29211 - 1.90070i) q^{19} -2.04491i q^{22} +(1.32238 + 2.29043i) q^{23} +(1.01453 + 1.75722i) q^{26} +(4.87179 + 0.0413461i) q^{28} +9.13574i q^{29} +(-4.11981 - 2.37857i) q^{31} +(-2.14169 + 3.70952i) q^{32} -1.78647i q^{34} +(8.14197 - 4.70077i) q^{37} +(-1.31095 - 0.756879i) q^{38} +7.51505 q^{41} +6.73246i q^{43} +(8.18929 - 4.72809i) q^{44} +(0.526586 - 0.912074i) q^{46} +(-6.77706 + 3.91274i) q^{47} +(-3.60239 + 6.00190i) q^{49} +(-4.69146 + 8.12584i) q^{52} +(-1.44597 + 2.50449i) q^{53} +(-1.99378 - 3.52202i) q^{56} +(3.15056 - 1.81897i) q^{58} +(2.46549 - 4.27036i) q^{59} +(10.2772 - 5.93354i) q^{61} +1.89434i q^{62} -4.44174 q^{64} +(6.06052 + 3.49905i) q^{67} +(7.15432 - 4.13055i) q^{68} -1.23868i q^{71} +(-0.289080 + 0.500701i) q^{73} +(-3.24222 - 1.87190i) q^{74} -7.00000i q^{76} +(-0.115303 + 13.5861i) q^{77} +(-2.46562 - 4.27058i) q^{79} +(-1.49629 - 2.59164i) q^{82} -9.75683i q^{83} +(2.32176 - 1.34047i) q^{86} +(-6.80294 - 3.92768i) q^{88} +(-3.63524 - 6.29642i) q^{89} +(-6.64133 - 11.7319i) q^{91} +4.87014 q^{92} +(2.69870 + 1.55809i) q^{94} +0.313935 q^{97} +(2.78707 + 0.0473103i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 16 q^{4}+O(q^{10}) $ 24 * q - 16 * q^4	$ 24 q - 16 q^{4} + 24 q^{11} + 24 q^{14} - 32 q^{16} - 12 q^{19} + 12 q^{31} + 48 q^{41} - 24 q^{44} - 8 q^{46} - 12 q^{49} - 120 q^{56} + 48 q^{59} + 112 q^{64} - 168 q^{74} - 36 q^{79} - 168 q^{86} - 24 q^{89} - 36 q^{91} - 24 q^{94}+O(q^{100}) $ 24 * q - 16 * q^4 + 24 * q^11 + 24 * q^14 - 32 * q^16 - 12 * q^19 + 12 * q^31 + 48 * q^41 - 24 * q^44 - 8 * q^46 - 12 * q^49 - 120 * q^56 + 48 * q^59 + 112 * q^64 - 168 * q^74 - 36 * q^79 - 168 * q^86 - 24 * q^89 - 36 * q^91 - 24 * q^94

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	−0.199105	−	0.344861i	−0.140789	−	0.243853i	0.787005	−	0.616946i	$-0.211630\pi$
$2$	−0.199105	−	0.344861i	−0.140789	−	0.243853i	−0.927794	+	0.373093i	$0.878297\pi$
$3$		0			0
$3$		0			0
$4$	0.920714	−	1.59472i	0.460357	−	0.797362i
$5$		0			0
$5$		0			0
$6$		0			0
$7$	1.30338	+	2.30243i	0.492632	+	0.870237i
$7$	1.30338	+	2.30243i	0.492632	+	0.870237i
$8$	−1.52970			−0.540830
$9$		0			0
$10$		0			0
$11$	4.44725	+	2.56762i	1.34090	+	0.774166i	0.986939	−	0.161096i	$-0.0515028\pi$
$11$	4.44725	+	2.56762i	1.34090	+	0.774166i	0.353956	+	0.935262i	$0.384836\pi$
$12$		0			0
$13$	−5.09545			−1.41322			−0.706612	−	0.707601i	$-0.749778\pi$
$13$	−5.09545			−1.41322			−0.706612	+	0.707601i	$0.749778\pi$
$14$	0.534507	−	0.907912i	0.142853	−	0.242650i
$15$		0			0
$16$	−1.53686	−	2.66191i	−0.384214	−	0.665479i
$17$	3.88520	+	2.24312i	0.942299	+	0.544037i	0.890680	−	0.454630i	$-0.150228\pi$
$17$	3.88520	+	2.24312i	0.942299	+	0.544037i	0.0516191	+	0.998667i	$0.483562\pi$
$18$		0			0
$19$	3.29211	−	1.90070i	0.755261	−	0.436050i	−0.0723306	−	0.997381i	$-0.523044\pi$
$19$	3.29211	−	1.90070i	0.755261	−	0.436050i	0.827592	+	0.561330i	$0.189710\pi$
$20$		0			0
$21$		0			0
$22$		−	2.04491i		−	0.435976i
$23$	1.32238	+	2.29043i	0.275736	+	0.477588i	0.970320	−	0.241823i	$-0.0777453\pi$
$23$	1.32238	+	2.29043i	0.275736	+	0.477588i	−0.694585	+	0.719411i	$0.744412\pi$
$24$		0			0
$25$		0			0
$26$	1.01453	+	1.75722i	0.198966	+	0.344619i
$27$		0			0
$28$	4.87179	+	0.0413461i	0.920681	+	0.00781368i
$29$			9.13574i			1.69646i	0.529624	+	0.848232i	$0.322333\pi$
$29$			9.13574i			1.69646i	−0.529624	+	0.848232i	$0.677667\pi$
$30$		0			0
$31$	−4.11981	−	2.37857i	−0.739939	−	0.427204i	0.0821082	−	0.996623i	$-0.473835\pi$
$31$	−4.11981	−	2.37857i	−0.739939	−	0.427204i	−0.822047	+	0.569419i	$0.807168\pi$
$32$	−2.14169	+	3.70952i	−0.378601	+	0.655756i
$33$		0			0
$34$		−	1.78647i		−	0.306377i
$35$		0			0
$36$		0			0
$37$	8.14197	−	4.70077i	1.33853	−	0.772801i	0.351942	−	0.936022i	$-0.385522\pi$
$37$	8.14197	−	4.70077i	1.33853	−	0.772801i	0.986590	+	0.163221i	$0.0521882\pi$
$38$	−1.31095	−	0.756879i	−0.212665	−	0.122782i
$39$		0			0
$40$		0			0
$41$	7.51505			1.17365			0.586827	−	0.809712i	$-0.300377\pi$
$41$	7.51505			1.17365			0.586827	+	0.809712i	$0.300377\pi$
$42$		0			0
$43$			6.73246i			1.02669i	0.858182	+	0.513345i	$0.171594\pi$
$43$			6.73246i			1.02669i	−0.858182	+	0.513345i	$0.828406\pi$
$44$	8.18929	−	4.72809i	1.23458	−	0.712786i
$45$		0			0
$46$	0.526586	−	0.912074i	0.0776409	−	0.134478i
$47$	−6.77706	+	3.91274i	−0.988536	+	0.570732i	−0.904836	−	0.425759i	$-0.860007\pi$
$47$	−6.77706	+	3.91274i	−0.988536	+	0.570732i	−0.0836998	+	0.996491i	$0.526674\pi$
$48$		0			0
$49$	−3.60239	+	6.00190i	−0.514627	+	0.857414i
$50$		0			0
$51$		0			0
$52$	−4.69146	+	8.12584i	−0.650588	+	1.12685i
$53$	−1.44597	+	2.50449i	−0.198619	+	0.344018i	−0.948081	−	0.318029i	$-0.896979\pi$
$53$	−1.44597	+	2.50449i	−0.198619	+	0.344018i	0.749462	+	0.662047i	$0.230312\pi$
$54$		0			0
$55$		0			0
$56$	−1.99378	−	3.52202i	−0.266430	−	0.470650i
$57$		0			0
$58$	3.15056	−	1.81897i	0.413688	−	0.238843i
$59$	2.46549	−	4.27036i	0.320980	−	0.555953i	−0.659711	−	0.751520i	$-0.729321\pi$
$59$	2.46549	−	4.27036i	0.320980	−	0.555953i	0.980690	+	0.195566i	$0.0626545\pi$
$60$		0			0
$61$	10.2772	−	5.93354i	1.31586	−	0.759712i	0.332800	−	0.942997i	$-0.392007\pi$
$61$	10.2772	−	5.93354i	1.31586	−	0.759712i	0.983060	+	0.183285i	$0.0586733\pi$
$62$			1.89434i			0.240582i
$63$		0			0
$64$	−4.44174			−0.555218
$65$		0			0
$66$		0			0
$67$	6.06052	+	3.49905i	0.740411	+	0.427476i	0.822219	−	0.569172i	$-0.192736\pi$
$67$	6.06052	+	3.49905i	0.740411	+	0.427476i	−0.0818078	+	0.996648i	$0.526069\pi$
$68$	7.15432	−	4.13055i	0.867588	−	0.500902i
$69$		0			0
$70$		0			0
$71$		−	1.23868i		−	0.147004i	−0.997295	−	0.0735022i	$-0.976582\pi$
$71$		−	1.23868i		−	0.147004i	0.997295	−	0.0735022i	$-0.0234176\pi$
$72$		0			0
$73$	−0.289080	+	0.500701i	−0.0338342	+	0.0586026i	−0.882447	−	0.470412i	$-0.844105\pi$
$73$	−0.289080	+	0.500701i	−0.0338342	+	0.0586026i	0.848612	+	0.529015i	$0.177438\pi$
$74$	−3.24222	−	1.87190i	−0.376900	−	0.217603i
$75$		0			0
$76$		−	7.00000i		−	0.802955i
$77$	−0.115303	+	13.5861i	−0.0131400	+	1.54828i
$78$		0			0
$79$	−2.46562	−	4.27058i	−0.277404	−	0.480478i	0.693335	−	0.720616i	$-0.256141\pi$
$79$	−2.46562	−	4.27058i	−0.277404	−	0.480478i	−0.970739	+	0.240138i	$0.922807\pi$
$80$		0			0
$81$		0			0
$82$	−1.49629	−	2.59164i	−0.165237	−	0.286199i
$83$		−	9.75683i		−	1.07095i	−0.844551	−	0.535475i	$-0.820132\pi$
$83$		−	9.75683i		−	1.07095i	0.844551	−	0.535475i	$-0.179868\pi$
$84$		0			0
$85$		0			0
$86$	2.32176	−	1.34047i	0.250362	−	0.144547i
$87$		0			0
$88$	−6.80294	−	3.92768i	−0.725196	−	0.418692i
$89$	−3.63524	−	6.29642i	−0.385334	−	0.667419i	0.606481	−	0.795098i	$-0.292581\pi$
$89$	−3.63524	−	6.29642i	−0.385334	−	0.667419i	−0.991816	+	0.127679i	$0.959247\pi$
$90$		0			0
$91$	−6.64133	−	11.7319i	−0.696200	−	1.22984i
$92$	4.87014			0.507747
$93$		0			0
$94$	2.69870	+	1.55809i	0.278350	+	0.160705i
$95$		0			0
$96$		0			0
$97$	0.313935			0.0318752			0.0159376	−	0.999873i	$-0.494927\pi$
$97$	0.313935			0.0318752			0.0159376	+	0.999873i	$0.494927\pi$
$98$	2.78707	+	0.0473103i	0.281537	+	0.00477906i
$99$		0			0
$100$		0			0
$101$	4.92727	−	8.53428i	0.490282	−	0.849193i	−0.509656	−	0.860378i	$-0.670227\pi$
$101$	4.92727	−	8.53428i	0.490282	−	0.849193i	0.999937	+	0.0111855i	$0.00356052\pi$
$102$		0			0
$103$	−3.28738	−	5.69390i	−0.323915	−	0.561037i	0.657377	−	0.753562i	$-0.271666\pi$
$103$	−3.28738	−	5.69390i	−0.323915	−	0.561037i	−0.981292	+	0.192525i	$0.938332\pi$
$104$	7.79451			0.764314
$105$		0			0
$106$	1.15160			0.111853
$107$	2.40766	+	4.17019i	0.232757	+	0.403148i	0.958619	−	0.284694i	$-0.0918919\pi$
$107$	2.40766	+	4.17019i	0.232757	+	0.403148i	−0.725861	+	0.687841i	$0.758559\pi$
$108$		0			0
$109$	2.69220	−	4.66303i	0.257866	−	0.446637i	−0.707804	−	0.706409i	$-0.750314\pi$
$109$	2.69220	−	4.66303i	0.257866	−	0.446637i	0.965670	+	0.259772i	$0.0836474\pi$
$110$		0			0
$111$		0			0
$112$	4.12576	−	7.00800i	0.389848	−	0.662194i
$113$	9.47858			0.891669			0.445835	−	0.895115i	$-0.352907\pi$
$113$	9.47858			0.891669			0.445835	+	0.895115i	$0.352907\pi$
$114$		0			0
$115$		0			0
$116$	14.5690	+	8.41141i	1.35270	+	0.780980i
$117$		0			0
$118$	−1.96357			−0.180761
$119$	−0.100731	+	11.8691i	−0.00923398	+	1.08803i
$120$		0			0
$121$	7.68533	+	13.3114i	0.698667	+	1.21013i
$122$	−4.09249	−	2.36280i	−0.370516	−	0.213918i
$123$		0			0
$124$	−7.58633	+	4.37997i	−0.681272	+	0.393333i
$125$		0			0
$126$		0			0
$127$		−	8.62994i		−	0.765783i	−0.923793	−	0.382892i	$-0.874928\pi$
$127$		−	8.62994i		−	0.765783i	0.923793	−	0.382892i	$-0.125072\pi$
$128$	5.16776	+	8.95082i	0.456769	+	0.791148i
$129$		0			0
$130$		0			0
$131$	7.75657	+	13.4348i	0.677695	+	1.17380i	0.975673	+	0.219229i	$0.0703543\pi$
$131$	7.75657	+	13.4348i	0.677695	+	1.17380i	−0.297979	+	0.954573i	$0.596312\pi$
$132$		0			0
$133$	8.66711	+	5.10251i	0.751533	+	0.442444i
$134$		−	2.78671i		−	0.240735i
$135$		0			0
$136$	−5.94318	−	3.43130i	−0.509624	−	0.294231i
$137$	0.552096	−	0.956258i	0.0471687	−	0.0816986i	−0.841477	−	0.540293i	$-0.818313\pi$
$137$	0.552096	−	0.956258i	0.0471687	−	0.0816986i	0.888646	+	0.458594i	$0.151647\pi$
$138$		0			0
$139$		−	6.48061i		−	0.549678i	−0.961490	−	0.274839i	$-0.911375\pi$
$139$		−	6.48061i		−	0.549678i	0.961490	−	0.274839i	$-0.0886246\pi$
$140$		0			0
$141$		0			0
$142$	−0.427172	+	0.246628i	−0.0358475	+	0.0206966i
$143$	−22.6607	−	13.0832i	−1.89499	−	1.09407i
$144$		0			0
$145$		0			0
$146$	0.230229			0.0190539
$147$		0			0
$148$		−	17.3123i		−	1.42306i
$149$	−14.2091	+	8.20362i	−1.16405	+	0.672066i	−0.952272	−	0.305251i	$-0.901260\pi$
$149$	−14.2091	+	8.20362i	−1.16405	+	0.672066i	−0.211781	+	0.977317i	$0.567926\pi$
$150$		0			0
$151$	−4.67919	+	8.10460i	−0.380787	+	0.659543i	−0.991175	−	0.132560i	$-0.957680\pi$
$151$	−4.67919	+	8.10460i	−0.380787	+	0.659543i	0.610388	+	0.792103i	$0.291014\pi$
$152$	−5.03593	+	2.90749i	−0.408468	+	0.235829i
$153$		0			0
$154$	4.70826	−	2.66530i	0.379402	−	0.214776i
$155$		0			0
$156$		0			0
$157$	−4.43951	+	7.68946i	−0.354312	+	0.613686i	−0.987000	−	0.160721i	$-0.948618\pi$
$157$	−4.43951	+	7.68946i	−0.354312	+	0.613686i	0.632688	+	0.774407i	$0.281952\pi$
$158$	−0.981836	+	1.70059i	−0.0781107	+	0.135292i
$159$		0			0
$160$		0			0
$161$	−3.54999	+	6.03000i	−0.279779	+	0.475231i
$162$		0			0
$163$	−6.12185	+	3.53445i	−0.479501	+	0.276840i	−0.720208	−	0.693758i	$-0.755954\pi$
$163$	−6.12185	+	3.53445i	−0.479501	+	0.276840i	0.240708	+	0.970598i	$0.422620\pi$
$164$	6.91921	−	11.9844i	0.540300	−	0.935827i
$165$		0			0
$166$	−3.36474	+	1.94264i	−0.261155	+	0.150778i
$167$		−	25.0272i		−	1.93666i	−0.249669	−	0.968331i	$-0.580322\pi$
$167$		−	25.0272i		−	1.93666i	0.249669	−	0.968331i	$-0.419678\pi$
$168$		0			0
$169$	12.9637			0.997204
$170$		0			0
$171$		0			0
$172$	10.7364	+	6.19867i	0.818644	+	0.472644i
$173$	−0.631692	+	0.364708i	−0.0480267	+	0.0277282i	−0.523821	−	0.851828i	$-0.675494\pi$
$173$	−0.631692	+	0.364708i	−0.0480267	+	0.0277282i	0.475794	+	0.879557i	$0.342161\pi$
$174$		0			0
$175$		0			0
$176$		−	15.7843i		−	1.18978i
$177$		0			0
$178$	−1.44759	+	2.50730i	−0.108502	+	0.187930i
$179$	−2.25510	−	1.30198i	−0.168554	−	0.0973147i	0.413350	−	0.910572i	$-0.364359\pi$
$179$	−2.25510	−	1.30198i	−0.168554	−	0.0973147i	−0.581904	+	0.813258i	$0.697692\pi$
$180$		0			0
$181$		−	3.89250i		−	0.289327i	−0.989481	−	0.144663i	$-0.953790\pi$
$181$		−	3.89250i		−	0.289327i	0.989481	−	0.144663i	$-0.0462100\pi$
$182$	−2.72356	+	4.62622i	−0.201884	+	0.342918i
$183$		0			0
$184$	−2.02284	−	3.50367i	−0.149126	−	0.258294i
$185$		0			0
$186$		0			0
$187$	11.5190	+	19.9514i	0.842350	+	1.45899i
$188$			14.4101i			1.05096i
$189$		0			0
$190$		0			0
$191$	−6.64485	+	3.83640i	−0.480804	+	0.277592i	−0.720752	−	0.693193i	$-0.756203\pi$
$191$	−6.64485	+	3.83640i	−0.480804	+	0.277592i	0.239947	+	0.970786i	$0.422870\pi$
$192$		0			0
$193$	0.0524815	+	0.0303002i	0.00377770	+	0.00218106i	0.501888	−	0.864933i	$-0.332639\pi$
$193$	0.0524815	+	0.0303002i	0.00377770	+	0.00218106i	−0.498110	+	0.867114i	$0.665972\pi$
$194$	−0.0625061	−	0.108264i	−0.00448768	−	0.00777288i
$195$		0			0
$196$	6.25461	+	11.2708i	0.446758	+	0.805060i
$197$	12.3018			0.876464			0.438232	−	0.898862i	$-0.355605\pi$
$197$	12.3018			0.876464			0.438232	+	0.898862i	$0.355605\pi$
$198$		0			0
$199$	9.68559	+	5.59198i	0.686593	+	0.396405i	0.802335	−	0.596875i	$-0.203591\pi$
$199$	9.68559	+	5.59198i	0.686593	+	0.396405i	−0.115741	+	0.993279i	$0.536924\pi$
$200$		0			0
$201$		0			0
$202$	−3.92418			−0.276105
$203$	−21.0344	+	11.9074i	−1.47633	+	0.835734i
$204$		0			0
$205$		0			0
$206$	−1.30907	+	2.26737i	−0.0912071	+	0.157975i
$207$		0			0
$208$	7.83099	+	13.5637i	0.542981	+	0.940471i
$209$	19.5211			1.35030
$210$		0			0
$211$	5.62551			0.387276			0.193638	−	0.981073i	$-0.437971\pi$
$211$	5.62551			0.387276			0.193638	+	0.981073i	$0.437971\pi$
$212$	2.66265	+	4.61184i	0.182871	+	0.316742i
$213$		0			0
$214$	0.958756	−	1.66061i	0.0655392	−	0.113517i
$215$		0			0
$216$		0			0
$217$	0.106813	−	12.5858i	0.00725097	−	0.854377i
$218$	−2.14412			−0.145218
$219$		0			0
$220$		0			0
$221$	−19.7969	−	11.4297i	−1.33168	−	0.768846i
$222$		0			0
$223$	3.16328			0.211829			0.105914	−	0.994375i	$-0.466223\pi$
$223$	3.16328			0.211829			0.105914	+	0.994375i	$0.466223\pi$
$224$	−11.3324	−	0.0961759i	−0.757175	−	0.00642603i
$225$		0			0
$226$	−1.88724	−	3.26879i	−0.125537	−	0.217436i
$227$	−9.73831	−	5.62242i	−0.646354	−	0.373173i	0.140704	−	0.990052i	$-0.455063\pi$
$227$	−9.73831	−	5.62242i	−0.646354	−	0.373173i	−0.787058	+	0.616879i	$0.788397\pi$
$228$		0			0
$229$	−19.7354	+	11.3942i	−1.30415	+	0.752952i	−0.981113	−	0.193434i	$-0.938037\pi$
$229$	−19.7354	+	11.3942i	−1.30415	+	0.752952i	−0.323038	+	0.946386i	$0.604704\pi$
$230$		0			0
$231$		0			0
$232$		−	13.9749i		−	0.917499i
$233$	−1.61347	−	2.79461i	−0.105702	−	0.183081i	0.808323	−	0.588740i	$-0.200376\pi$
$233$	−1.61347	−	2.79461i	−0.105702	−	0.183081i	−0.914025	+	0.405658i	$0.867042\pi$
$234$		0			0
$235$		0			0
$236$	−4.54003	−	7.86356i	−0.295531	−	0.511874i
$237$		0			0
$238$	4.11323	−	2.32845i	0.266621	−	0.150931i
$239$			23.1272i			1.49598i	0.663712	+	0.747988i	$0.268980\pi$
$239$			23.1272i			1.49598i	−0.663712	+	0.747988i	$0.731020\pi$
$240$		0			0
$241$	12.8600	+	7.42473i	0.828386	+	0.478269i	0.853300	−	0.521421i	$-0.174598\pi$
$241$	12.8600	+	7.42473i	0.828386	+	0.478269i	−0.0249139	+	0.999690i	$0.507931\pi$
$242$	3.06038	−	5.30074i	0.196729	−	0.340744i
$243$		0			0
$244$		−	21.8524i		−	1.39896i
$245$		0			0
$246$		0			0
$247$	−16.7748	+	9.68492i	−1.06735	+	0.616237i
$248$	6.30206	+	3.63849i	0.400181	+	0.231045i
$249$		0			0
$250$		0			0
$251$	−12.6710			−0.799789			−0.399895	−	0.916561i	$-0.630953\pi$
$251$	−12.6710			−0.799789			−0.399895	+	0.916561i	$0.630953\pi$
$252$		0			0
$253$			13.5815i			0.853861i
$254$	−2.97613	+	1.71827i	−0.186739	+	0.107814i
$255$		0			0
$256$	−2.38389	+	4.12901i	−0.148993	+	0.258063i
$257$	6.89937	−	3.98336i	0.430371	−	0.248475i	−0.269134	−	0.963103i	$-0.586737\pi$
$257$	6.89937	−	3.98336i	0.430371	−	0.248475i	0.699505	+	0.714628i	$0.253404\pi$
$258$		0			0
$259$	21.4353	+	12.6194i	1.33192	+	0.784133i
$260$		0			0
$261$		0			0
$262$	3.08875	−	5.34987i	0.190824	−	0.330516i
$263$	3.50162	−	6.06499i	0.215919	−	0.373983i	−0.737637	−	0.675197i	$-0.764058\pi$
$263$	3.50162	−	6.06499i	0.215919	−	0.373983i	0.953557	+	0.301214i	$0.0973918\pi$
$264$		0			0
$265$		0			0
$266$	0.0339888	−	4.00488i	0.00208399	−	0.245555i
$267$		0			0
$268$	11.1600	−	6.44324i	0.681707	−	0.393584i
$269$	−5.08855	+	8.81364i	−0.310255	+	0.537377i	−0.978417	−	0.206638i	$-0.933748\pi$
$269$	−5.08855	+	8.81364i	−0.310255	+	0.537377i	0.668163	+	0.744015i	$0.267081\pi$
$270$		0			0
$271$	2.60706	−	1.50519i	0.158367	−	0.0914335i	−0.418722	−	0.908115i	$-0.637522\pi$
$271$	2.60706	−	1.50519i	0.158367	−	0.0914335i	0.577089	+	0.816681i	$0.304188\pi$
$272$		−	13.7894i		−	0.836107i
$273$		0			0
$274$	−0.439701			−0.0265633
$275$		0			0
$276$		0			0
$277$	−28.7319	−	16.5884i	−1.72634	−	0.996700i	−0.903754	−	0.428053i	$-0.859200\pi$
$277$	−28.7319	−	16.5884i	−1.72634	−	0.996700i	−0.822581	−	0.568647i	$-0.807467\pi$
$278$	−2.23491	+	1.29032i	−0.134041	+	0.0773885i
$279$		0			0
$280$		0			0
$281$			6.12689i			0.365500i	0.983159	+	0.182750i	$0.0584998\pi$
$281$			6.12689i			0.365500i	−0.983159	+	0.182750i	$0.941500\pi$
$282$		0			0
$283$	4.11340	−	7.12461i	0.244516	−	0.423514i	−0.717479	−	0.696580i	$-0.754704\pi$
$283$	4.11340	−	7.12461i	0.244516	−	0.423514i	0.961995	+	0.273066i	$0.0880376\pi$
$284$	−1.97535	−	1.14047i	−0.117216	−	0.0676745i
$285$		0			0
$286$			10.4197i			0.616131i
$287$	9.79499	+	17.3029i	0.578180	+	1.02136i
$288$		0			0
$289$	1.56319	+	2.70752i	0.0919522	+	0.159266i
$290$		0			0
$291$		0			0
$292$	0.532320	+	0.922005i	0.0311516	+	0.0539562i
$293$		−	31.5059i		−	1.84059i	−0.391220	−	0.920297i	$-0.627947\pi$
$293$		−	31.5059i		−	1.84059i	0.391220	−	0.920297i	$-0.372053\pi$
$294$		0			0
$295$		0			0
$296$	−12.4547	+	7.19075i	−0.723918	+	0.417954i
$297$		0			0
$298$	5.65821	+	3.26677i	0.327771	+	0.189239i
$299$	−6.73813	−	11.6708i	−0.389676	−	0.674939i
$300$		0			0
$301$	−15.5010	+	8.77498i	−0.893465	+	0.505781i
$302$	3.72661			0.214442
$303$		0			0
$304$	−10.1190	−	5.84221i	−0.580364	−	0.335073i
$305$		0			0
$306$		0			0
$307$	−23.7716			−1.35672			−0.678360	−	0.734730i	$-0.737309\pi$
$307$	−23.7716			−1.35672			−0.678360	+	0.734730i	$0.737309\pi$
$308$	21.5599	+	12.6928i	1.22849	+	0.723237i
$309$		0			0
$310$		0			0
$311$	−9.29730	+	16.1034i	−0.527201	+	0.913139i	0.472296	+	0.881440i	$0.343425\pi$
$311$	−9.29730	+	16.1034i	−0.527201	+	0.913139i	−0.999497	+	0.0316995i	$0.989908\pi$
$312$		0			0
$313$	−4.07310	−	7.05481i	−0.230225	−	0.398762i	0.727649	−	0.685950i	$-0.240613\pi$
$313$	−4.07310	−	7.05481i	−0.230225	−	0.398762i	−0.957874	+	0.287188i	$0.907280\pi$
$314$	3.53572			0.199532
$315$		0			0
$316$	−9.08053			−0.510820
$317$	−15.7065	−	27.2045i	−0.882165	−	1.52795i	−0.848929	−	0.528507i	$-0.822752\pi$
$317$	−15.7065	−	27.2045i	−0.882165	−	1.52795i	−0.0332365	−	0.999448i	$-0.510581\pi$
$318$		0			0
$319$	−23.4571	+	40.6289i	−1.31335	+	2.27478i
$320$		0			0
$321$		0			0
$322$	2.78633	+	0.0236472i	0.155276	+	0.00131781i
$323$	17.0540			0.948910
$324$		0			0
$325$		0			0
$326$	2.43779	+	1.40746i	0.135017	+	0.0779518i
$327$		0			0
$328$	−11.4958			−0.634747
$329$	−17.8419	−	10.5039i	−0.983657	−	0.579100i
$330$		0			0
$331$	−2.76563	−	4.79021i	−0.152013	−	0.263294i	0.779955	−	0.625836i	$-0.215242\pi$
$331$	−2.76563	−	4.79021i	−0.152013	−	0.263294i	−0.931967	+	0.362542i	$0.881909\pi$
$332$	−15.5594	−	8.98325i	−0.853935	−	0.493020i
$333$		0			0
$334$	−8.63089	+	4.98305i	−0.472261	+	0.272660i
$335$		0			0
$336$		0			0
$337$		−	13.3563i		−	0.727566i	−0.931484	−	0.363783i	$-0.881485\pi$
$337$		−	13.3563i		−	0.727566i	0.931484	−	0.363783i	$-0.118515\pi$
$338$	−2.58113	−	4.47065i	−0.140395	−	0.243172i
$339$		0			0
$340$		0			0
$341$	−12.2145	−	21.1562i	−0.661454	−	1.14567i
$342$		0			0
$343$	−18.5143	−	0.471474i	−0.999676	−	0.0254572i
$344$		−	10.2986i		−	0.555265i
$345$		0			0
$346$	0.251547	+	0.145230i	0.0135232	+	0.00780764i
$347$	−16.2045	+	28.0670i	−0.869901	+	1.50671i	−0.00780492	+	0.999970i	$0.502484\pi$
$347$	−16.2045	+	28.0670i	−0.869901	+	1.50671i	−0.862097	+	0.506744i	$0.830849\pi$
$348$		0			0
$349$			6.33160i			0.338923i	0.985537	+	0.169461i	$0.0542028\pi$
$349$			6.33160i			0.338923i	−0.985537	+	0.169461i	$0.945797\pi$
$350$		0			0
$351$		0			0
$352$	−19.0493	+	10.9981i	−1.01533	+	0.586200i
$353$	13.5012	+	7.79492i	0.718596	+	0.414882i	0.814236	−	0.580534i	$-0.197156\pi$
$353$	13.5012	+	7.79492i	0.718596	+	0.414882i	−0.0956395	+	0.995416i	$0.530490\pi$
$354$		0			0
$355$		0			0
$356$	−13.3881			−0.709566
$357$		0			0
$358$			1.03693i			0.0548032i
$359$	9.43467	−	5.44711i	0.497943	−	0.287487i	−0.229921	−	0.973209i	$-0.573847\pi$
$359$	9.43467	−	5.44711i	0.497943	−	0.287487i	0.727864	+	0.685722i	$0.240513\pi$
$360$		0			0
$361$	−2.27469	+	3.93987i	−0.119720	+	0.207362i
$362$	−1.34237	+	0.775017i	−0.0705533	+	0.0407340i
$363$		0			0
$364$	−24.8240	−	0.210677i	−1.30113	−	0.0110425i
$365$		0			0
$366$		0			0
$367$	−2.48714	+	4.30786i	−0.129828	+	0.224868i	−0.923610	−	0.383334i	$-0.874776\pi$
$367$	−2.48714	+	4.30786i	−0.129828	+	0.224868i	0.793782	+	0.608202i	$0.208109\pi$
$368$	4.06462	−	7.04013i	0.211883	−	0.366992i
$369$		0			0
$370$		0			0
$371$	−7.65106	−	0.0649334i	−0.397223	−	0.00337117i
$372$		0			0
$373$	−11.1371	+	6.43003i	−0.576659	+	0.332934i	−0.759805	−	0.650151i	$-0.774705\pi$
$373$	−11.1371	+	6.43003i	−0.576659	+	0.332934i	0.183145	+	0.983086i	$0.441372\pi$
$374$	4.58697	−	7.94487i	0.237187	−	0.410820i
$375$		0			0
$376$	10.3669	−	5.98531i	0.534630	−	0.308669i
$377$		−	46.5508i		−	2.39749i
$378$		0			0
$379$	37.8472			1.94408			0.972039	−	0.234818i	$-0.0754495\pi$
$379$	37.8472			1.94408			0.972039	+	0.234818i	$0.0754495\pi$
$380$		0			0
$381$		0			0
$382$	2.64605	+	1.52770i	0.135384	+	0.0781638i
$383$	−24.6317	+	14.2211i	−1.25862	+	0.726665i	−0.972806	−	0.231620i	$-0.925597\pi$
$383$	−24.6317	+	14.2211i	−1.25862	+	0.726665i	−0.285814	+	0.958285i	$0.592264\pi$
$384$		0			0
$385$		0			0
$386$		−	0.0241317i		−	0.00122827i
$387$		0			0
$388$	0.289044	−	0.500639i	0.0146740	−	0.0254161i
$389$	−8.24116	−	4.75803i	−0.417843	−	0.241242i	0.276311	−	0.961068i	$-0.410888\pi$
$389$	−8.24116	−	4.75803i	−0.417843	−	0.241242i	−0.694154	+	0.719826i	$0.744221\pi$
$390$		0			0
$391$			11.8650i			0.600041i
$392$	5.51056	−	9.18109i	0.278325	−	0.463715i
$393$		0			0
$394$	−2.44935	−	4.24239i	−0.123396	−	0.213729i
$395$		0			0
$396$		0			0
$397$	4.82809	+	8.36250i	0.242315	+	0.419702i	0.961373	−	0.275248i	$-0.0887599\pi$
$397$	4.82809	+	8.36250i	0.242315	+	0.419702i	−0.719058	+	0.694950i	$0.755427\pi$
$398$		−	4.45357i		−	0.223237i
$399$		0			0
$400$		0			0
$401$	−7.76875	+	4.48529i	−0.387953	+	0.223985i	−0.681273	−	0.732030i	$-0.738573\pi$
$401$	−7.76875	+	4.48529i	−0.387953	+	0.223985i	0.293320	+	0.956014i	$0.405240\pi$
$402$		0			0
$403$	20.9923	+	12.1199i	1.04570	+	0.603735i
$404$	−9.07322	−	15.7153i	−0.451409	−	0.781864i
$405$		0			0
$406$	8.29445	+	4.88312i	0.411647	+	0.242345i
$407$	48.2791			2.39311
$408$		0			0
$409$	−26.3659	−	15.2223i	−1.30371	−	0.752696i	−0.322670	−	0.946512i	$-0.604580\pi$
$409$	−26.3659	−	15.2223i	−1.30371	−	0.752696i	−0.981038	+	0.193815i	$0.937914\pi$
$410$		0			0
$411$		0			0
$412$	−12.1069			−0.596466
$413$	13.0457	+	0.110717i	0.641936	+	0.00544802i
$414$		0			0
$415$		0			0
$416$	10.9129	−	18.9017i	0.535048	−	0.926731i
$417$		0			0
$418$	−3.88675	−	6.73205i	−0.190107	−	0.329275i
$419$	−24.0920			−1.17697			−0.588485	−	0.808508i	$-0.700276\pi$
$419$	−24.0920			−1.17697			−0.588485	+	0.808508i	$0.700276\pi$
$420$		0			0
$421$	−22.3663			−1.09007			−0.545033	−	0.838415i	$-0.683483\pi$
$421$	−22.3663			−1.09007			−0.545033	+	0.838415i	$0.683483\pi$
$422$	−1.12007	−	1.94002i	−0.0545241	−	0.0944386i
$423$		0			0
$424$	2.21189	−	3.83111i	0.107419	−	0.186055i
$425$		0			0
$426$		0			0
$427$	27.0567	+	15.9289i	1.30937	+	0.770852i
$428$	8.86707			0.428606
$429$		0			0
$430$		0			0
$431$	−8.90954	−	5.14392i	−0.429157	−	0.247774i	0.269830	−	0.962908i	$-0.413032\pi$
$431$	−8.90954	−	5.14392i	−0.429157	−	0.247774i	−0.698988	+	0.715134i	$0.746366\pi$
$432$		0			0
$433$	4.91252			0.236080			0.118040	−	0.993009i	$-0.462339\pi$
$433$	4.91252			0.236080			0.118040	+	0.993009i	$0.462339\pi$
$434$	−4.36160	+	2.46906i	−0.209363	+	0.118519i
$435$		0			0
$436$	−4.95749	−	8.58663i	−0.237421	−	0.411225i
$437$	8.70684	+	5.02690i	0.416505	+	0.240469i
$438$		0			0
$439$	27.0138	−	15.5964i	1.28930	−	0.744378i	0.310771	−	0.950485i	$-0.399413\pi$
$439$	27.0138	−	15.5964i	1.28930	−	0.744378i	0.978529	+	0.206107i	$0.0660796\pi$
$440$		0			0
$441$		0			0
$442$			9.10288i			0.432980i
$443$	−5.27762	−	9.14111i	−0.250747	−	0.434307i	0.712984	−	0.701180i	$-0.247343\pi$
$443$	−5.27762	−	9.14111i	−0.250747	−	0.434307i	−0.963732	+	0.266873i	$0.914010\pi$
$444$		0			0
$445$		0			0
$446$	−0.629826	−	1.09089i	−0.0298231	−	0.0516552i
$447$		0			0
$448$	−5.78929	−	10.2268i	−0.273518	−	0.483171i
$449$			32.9402i			1.55454i	0.629166	+	0.777271i	$0.283397\pi$
$449$			32.9402i			1.55454i	−0.629166	+	0.777271i	$0.716603\pi$
$450$		0			0
$451$	33.4213	+	19.2958i	1.57375	+	0.908603i
$452$	8.72706	−	15.1157i	0.410486	−	0.710983i
$453$		0			0
$454$			4.47781i			0.210154i
$455$		0			0
$456$		0			0
$457$	27.8509	−	16.0797i	1.30281	−	0.752177i	0.321923	−	0.946766i	$-0.395671\pi$
$457$	27.8509	−	16.0797i	1.30281	−	0.752177i	0.980885	+	0.194589i	$0.0623374\pi$
$458$	7.85884	+	4.53730i	0.367220	+	0.212014i
$459$		0			0
$460$		0			0
$461$	−39.6617			−1.84723			−0.923615	−	0.383322i	$-0.874780\pi$
$461$	−39.6617			−1.84723			−0.923615	+	0.383322i	$0.874780\pi$
$462$		0			0
$463$		−	34.2241i		−	1.59053i	−0.606262	−	0.795265i	$-0.707332\pi$
$463$		−	34.2241i		−	1.59053i	0.606262	−	0.795265i	$-0.292668\pi$
$464$	24.3186	−	14.0403i	1.12896	−	0.651806i
$465$		0			0
$466$	−0.642501	+	1.11284i	−0.0297633	+	0.0515515i
$467$	−25.7197	+	14.8493i	−1.19017	+	0.687144i	−0.958345	−	0.285614i	$-0.907802\pi$
$467$	−25.7197	+	14.8493i	−1.19017	+	0.687144i	−0.231823	+	0.972758i	$0.574469\pi$
$468$		0			0
$469$	−0.157130	+	18.5145i	−0.00725559	+	0.854922i
$470$		0			0
$471$		0			0
$472$	−3.77146	+	6.53236i	−0.173595	+	0.300676i
$473$	−17.2864	+	29.9409i	−0.794829	+	1.37669i
$474$		0			0
$475$		0			0
$476$	18.8351	+	11.0886i	0.863306	+	0.508247i
$477$		0			0
$478$	7.97567	−	4.60476i	0.364799	−	0.210617i
$479$	−4.69594	+	8.13361i	−0.214563	+	0.371634i	−0.953137	−	0.302538i	$-0.902166\pi$
$479$	−4.69594	+	8.13361i	−0.214563	+	0.371634i	0.738574	+	0.674172i	$0.235499\pi$
$480$		0			0
$481$	−41.4870	+	23.9525i	−1.89165	+	1.09214i
$482$		−	5.91321i		−	0.269339i
$483$		0			0
$484$	28.3040			1.28654
$485$		0			0
$486$		0			0
$487$	6.87859	+	3.97135i	0.311699	+	0.179959i	0.647686	−	0.761907i	$-0.275737\pi$
$487$	6.87859	+	3.97135i	0.311699	+	0.179959i	−0.335988	+	0.941866i	$0.609070\pi$
$488$	−15.7210	+	9.07652i	−0.711656	+	0.410875i
$489$		0			0
$490$		0			0
$491$			10.6921i			0.482526i	0.970460	+	0.241263i	$0.0775616\pi$
$491$			10.6921i			0.482526i	−0.970460	+	0.241263i	$0.922438\pi$
$492$		0			0
$493$	−20.4926	+	35.4942i	−0.922939	+	1.59858i
$494$	6.67990	+	3.85664i	0.300543	+	0.173518i
$495$		0			0
$496$			14.6221i			0.656552i
$497$	2.85198	−	1.61447i	0.127929	−	0.0724191i
$498$		0			0
$499$	3.61851	+	6.26745i	0.161987	+	0.280570i	0.935581	−	0.353112i	$-0.114876\pi$
$499$	3.61851	+	6.26745i	0.161987	+	0.280570i	−0.773594	+	0.633681i	$0.781543\pi$
$500$		0			0
$501$		0			0
$502$	2.52287	+	4.36974i	0.112601	+	0.195031i
$503$			2.22842i			0.0993603i	0.998765	+	0.0496802i	$0.0158202\pi$
$503$			2.22842i			0.0993603i	−0.998765	+	0.0496802i	$0.984180\pi$
$504$		0			0
$505$		0			0
$506$	4.68372	−	2.70415i	0.208217	−	0.120214i
$507$		0			0
$508$	−13.7624	−	7.94571i	−0.610606	−	0.352534i
$509$	−14.2749	−	24.7248i	−0.632724	−	1.09591i	−0.986993	−	0.160766i	$-0.948604\pi$
$509$	−14.2749	−	24.7248i	−0.632724	−	1.09591i	0.354269	−	0.935144i	$-0.384730\pi$
$510$		0			0
$511$	−1.52961	−	0.0129816i	−0.0676660	−	0.000574271i
$512$	22.5696			0.997445
$513$		0			0
$514$	−2.74740	−	1.58621i	−0.121183	−	0.0699649i
$515$		0			0
$516$		0			0
$517$	−40.1857			−1.76736
$518$	0.0840604	−	9.90478i	0.00369340	−	0.435191i
$519$		0			0
$520$		0			0
$521$	−0.909280	+	1.57492i	−0.0398363	+	0.0689985i	−0.885256	−	0.465104i	$-0.846017\pi$
$521$	−0.909280	+	1.57492i	−0.0398363	+	0.0689985i	0.845420	+	0.534102i	$0.179350\pi$
$522$		0			0
$523$	14.7067	+	25.4727i	0.643077	+	1.11384i	0.984742	+	0.174021i	$0.0556759\pi$
$523$	14.7067	+	25.4727i	0.643077	+	1.11384i	−0.341665	+	0.939822i	$0.610991\pi$
$524$	28.5663			1.24793
$525$		0			0
$526$	−2.78877			−0.121596
$527$	−10.6708	−	18.4824i	−0.464829	−	0.805108i
$528$		0			0
$529$	8.00261	−	13.8609i	0.347940	−	0.602649i
$530$		0			0
$531$		0			0
$532$	16.1170	−	9.12368i	0.698762	−	0.395562i
$533$	−38.2926			−1.65864
$534$		0			0
$535$		0			0
$536$	−9.27077	−	5.35248i	−0.400436	−	0.231192i
$537$		0			0
$538$	4.05263			0.174721
$539$	−31.4313	+	17.4424i	−1.35384	+	0.751296i
$540$		0			0
$541$	0.530113	+	0.918183i	0.0227913	+	0.0394758i	0.877196	−	0.480132i	$-0.159411\pi$
$541$	0.530113	+	0.918183i	0.0227913	+	0.0394758i	−0.854405	+	0.519608i	$0.826078\pi$
$542$	−1.03816	−	0.599381i	−0.0445927	−	0.0257456i
$543$		0			0
$544$	−16.6418	+	9.60814i	−0.713511	+	0.411946i
$545$		0			0
$546$		0			0
$547$		−	12.4665i		−	0.533030i	−0.963831	−	0.266515i	$-0.914128\pi$
$547$		−	12.4665i		−	0.533030i	0.963831	−	0.266515i	$-0.0858722\pi$
$548$	−1.01664	−	1.76088i	−0.0434289	−	0.0752211i
$549$		0			0
$550$		0			0
$551$	17.3643	+	30.0758i	0.739744	+	1.28127i
$552$		0			0
$553$	6.61907	−	11.2431i	0.281472	−	0.478106i
$554$			13.2114i			0.561297i
$555$		0			0
$556$	−10.3348	−	5.96679i	−0.438292	−	0.253048i
$557$	−10.1441	+	17.5701i	−0.429820	+	0.744470i	−0.996857	−	0.0792222i	$-0.974756\pi$
$557$	−10.1441	+	17.5701i	−0.429820	+	0.744470i	0.567037	+	0.823692i	$0.308090\pi$
$558$		0			0
$559$		−	34.3050i		−	1.45095i
$560$		0			0
$561$		0			0
$562$	2.11292	−	1.21990i	0.0891283	−	0.0514582i
$563$	30.9658	+	17.8781i	1.30505	+	0.753472i	0.981266	−	0.192658i	$-0.0617108\pi$
$563$	30.9658	+	17.8781i	1.30505	+	0.753472i	0.323786	+	0.946130i	$0.395044\pi$
$564$		0			0
$565$		0			0
$566$	−3.27600			−0.137700
$567$		0			0
$568$			1.89481i			0.0795043i
$569$	−4.01368	+	2.31730i	−0.168262	+	0.0971463i	−0.581766	−	0.813356i	$-0.697638\pi$
$569$	−4.01368	+	2.31730i	−0.168262	+	0.0971463i	0.413504	+	0.910502i	$0.364305\pi$
$570$		0			0
$571$	9.64058	−	16.6980i	0.403446	−	0.698788i	−0.590694	−	0.806896i	$-0.701146\pi$
$571$	9.64058	−	16.6980i	0.403446	−	0.698788i	0.994139	+	0.108108i	$0.0344791\pi$
$572$	−41.7281	+	24.0917i	−1.74474	+	1.00733i
$573$		0			0
$574$	4.01685	−	6.82300i	0.167660	−	0.284787i
$575$		0			0
$576$		0			0
$577$	−3.54796	+	6.14525i	−0.147703	+	0.255830i	−0.930378	−	0.366601i	$-0.880521\pi$
$577$	−3.54796	+	6.14525i	−0.147703	+	0.255830i	0.782675	+	0.622431i	$0.213855\pi$
$578$	0.622478	−	1.07816i	0.0258917	−	0.0448457i
$579$		0			0
$580$		0			0
$581$	22.4644	−	12.7169i	0.931982	−	0.527585i
$582$		0			0
$583$	−12.8611	+	7.42539i	−0.532654	+	0.307528i
$584$	0.442205	−	0.765921i	0.0182986	−	0.0316940i
$585$		0			0
$586$	−10.8651	+	6.27299i	−0.448835	+	0.259135i
$587$			28.1728i			1.16281i	0.813613	+	0.581407i	$0.197498\pi$
$587$			28.1728i			1.16281i	−0.813613	+	0.581407i	$0.802502\pi$
$588$		0			0
$589$	−18.0838			−0.745130
$590$		0			0
$591$		0			0
$592$	−25.0261	−	14.4488i	−1.02857	−	0.593843i
$593$	−8.08794	+	4.66958i	−0.332132	+	0.191757i	−0.656787	−	0.754076i	$-0.728085\pi$
$593$	−8.08794	+	4.66958i	−0.332132	+	0.191757i	0.324655	+	0.945832i	$0.394752\pi$
$594$		0			0
$595$		0			0
$596$			30.2127i			1.23756i
$597$		0			0
$598$	−2.68320	+	4.64743i	−0.109724	+	0.190048i
$599$	18.4745	+	10.6662i	0.754846	+	0.435811i	0.827442	−	0.561551i	$-0.189795\pi$
$599$	18.4745	+	10.6662i	0.754846	+	0.435811i	−0.0725959	+	0.997361i	$0.523128\pi$
$600$		0			0
$601$		−	35.7597i		−	1.45867i	−0.684157	−	0.729335i	$-0.739830\pi$
$601$		−	35.7597i		−	1.45867i	0.684157	−	0.729335i	$-0.260170\pi$
$602$	6.11248	+	3.59855i	0.249126	+	0.146666i
$603$		0			0
$604$	8.61640	+	14.9240i	0.350596	+	0.607251i
$605$		0			0
$606$		0			0
$607$	1.67301	+	2.89774i	0.0679055	+	0.117616i	0.897979	−	0.440038i	$-0.145035\pi$
$607$	1.67301	+	2.89774i	0.0679055	+	0.117616i	−0.830074	+	0.557654i	$0.811702\pi$
$608$			16.2828i			0.660356i
$609$		0			0
$610$		0			0
$611$	34.5322	−	19.9372i	1.39702	−	0.806572i
$612$		0			0
$613$	34.4079	+	19.8654i	1.38972	+	0.802357i	0.993284	−	0.115704i	$-0.0369123\pi$
$613$	34.4079	+	19.8654i	1.38972	+	0.802357i	0.396440	+	0.918061i	$0.370246\pi$
$614$	4.73306	+	8.19790i	0.191011	+	0.330840i
$615$		0			0
$616$	0.176379	−	20.7826i	0.00710650	−	0.837354i
$617$	33.2529			1.33871			0.669355	−	0.742942i	$-0.266570\pi$
$617$	33.2529			1.33871			0.669355	+	0.742942i	$0.266570\pi$
$618$		0			0
$619$	−15.8564	−	9.15472i	−0.637324	−	0.367959i	0.146259	−	0.989246i	$-0.453277\pi$
$619$	−15.8564	−	9.15472i	−0.637324	−	0.367959i	−0.783583	+	0.621287i	$0.786610\pi$
$620$		0			0
$621$		0			0
$622$	7.40457			0.296896
$623$	9.75897	−	16.5765i	0.390985	−	0.664125i
$624$		0			0
$625$		0			0
$626$	−1.62195	+	2.80930i	−0.0648262	+	0.112282i
$627$		0			0
$628$	8.17505	+	14.1596i	0.326220	+	0.565029i
$629$	42.1776			1.68173
$630$		0			0
$631$	44.2729			1.76248			0.881238	−	0.472673i	$-0.156711\pi$
$631$	44.2729			1.76248			0.881238	+	0.472673i	$0.156711\pi$
$632$	3.77165	+	6.53270i	0.150028	+	0.259857i
$633$		0			0
$634$	−6.25450	+	10.8331i	−0.248398	+	0.430238i
$635$		0			0
$636$		0			0
$637$	18.3558	−	30.5824i	0.727283	−	1.21172i
$638$	18.6817			0.739617
$639$		0			0
$640$		0			0
$641$	2.80892	+	1.62173i	0.110946	+	0.0640546i	0.554446	−	0.832220i	$-0.312930\pi$
$641$	2.80892	+	1.62173i	0.110946	+	0.0640546i	−0.443500	+	0.896274i	$0.646263\pi$
$642$		0			0
$643$	−38.7849			−1.52953			−0.764763	−	0.644311i	$-0.777144\pi$
$643$	−38.7849			−1.52953			−0.764763	+	0.644311i	$0.777144\pi$
$644$	6.34766	+	11.2132i	0.250133	+	0.441861i
$645$		0			0
$646$	−3.39554	−	5.88125i	−0.133596	−	0.231395i
$647$	−35.0104	−	20.2133i	−1.37640	−	0.794665i	−0.384677	−	0.923051i	$-0.625687\pi$
$647$	−35.0104	−	20.2133i	−1.37640	−	0.794665i	−0.991724	+	0.128386i	$0.959020\pi$
$648$		0			0
$649$	21.9293	−	12.6609i	0.860801	−	0.496983i
$650$		0			0
$651$		0			0
$652$			13.0169i			0.509781i
$653$	−19.1097	−	33.0989i	−0.747819	−	1.29526i	−0.948866	−	0.315679i	$-0.897768\pi$
$653$	−19.1097	−	33.0989i	−0.747819	−	1.29526i	0.201047	−	0.979582i	$-0.435566\pi$
$654$		0			0
$655$		0			0
$656$	−11.5496	−	20.0044i	−0.450935	−	0.781042i
$657$		0			0
$658$	−0.0699686	+	8.24436i	−0.00272766	+	0.321399i
$659$			3.10400i			0.120915i	0.998171	+	0.0604574i	$0.0192559\pi$
$659$			3.10400i			0.120915i	−0.998171	+	0.0604574i	$0.980744\pi$
$660$		0			0
$661$	12.5985	+	7.27377i	0.490026	+	0.282917i	0.724585	−	0.689185i	$-0.242031\pi$
$661$	12.5985	+	7.27377i	0.490026	+	0.282917i	−0.234559	+	0.972102i	$0.575365\pi$
$662$	−1.10130	+	1.90751i	−0.0428034	+	0.0741376i
$663$		0			0
$664$			14.9250i			0.579202i
$665$		0			0
$666$		0			0
$667$	−20.9248	+	12.0809i	−0.810211	+	0.467776i
$668$	−39.9115	−	23.0429i	−1.54422	−	0.891556i
$669$		0			0
$670$		0			0
$671$	60.9403			2.35257
$672$		0			0
$673$		−	32.6424i		−	1.25827i	−0.777295	−	0.629137i	$-0.783409\pi$
$673$		−	32.6424i		−	1.25827i	0.777295	−	0.629137i	$-0.216591\pi$
$674$	−4.60607	+	2.65932i	−0.177419	+	0.102433i
$675$		0			0
$676$	11.9358	−	20.6734i	0.459070	−	0.795133i
$677$	−14.3780	+	8.30114i	−0.552591	+	0.319039i	−0.750167	−	0.661249i	$-0.770027\pi$
$677$	−14.3780	+	8.30114i	−0.552591	+	0.319039i	0.197575	+	0.980288i	$0.436693\pi$
$678$		0			0
$679$	0.409177	+	0.722813i	0.0157028	+	0.0277390i
$680$		0			0
$681$		0			0
$682$	−4.86396	+	8.42462i	−0.186250	+	0.322595i
$683$	12.2391	−	21.1988i	0.468317	−	0.811149i	−0.531027	−	0.847355i	$-0.678194\pi$
$683$	12.2391	−	21.1988i	0.468317	−	0.811149i	0.999344	+	0.0362057i	$0.0115271\pi$
$684$		0			0
$685$		0			0
$686$	3.52369	+	6.47871i	0.134535	+	0.247358i
$687$		0			0
$688$	17.9212	−	10.3468i	0.683241	−	0.394469i
$689$	7.36786	−	12.7615i	0.280693	−	0.486175i
$690$		0			0
$691$	26.8707	−	15.5138i	1.02221	−	0.590174i	0.107467	−	0.994209i	$-0.465726\pi$
$691$	26.8707	−	15.5138i	1.02221	−	0.590174i	0.914744	+	0.404035i	$0.132393\pi$
$692$			1.34317i			0.0510595i
$693$		0			0
$694$	12.9056			0.489889
$695$		0			0
$696$		0			0
$697$	29.1975	+	16.8572i	1.10593	+	0.638511i
$698$	2.18352	−	1.26066i	0.0826474	−	0.0477165i
$699$		0			0
$700$		0			0
$701$		−	30.5243i		−	1.15289i	−0.817137	−	0.576443i	$-0.804440\pi$
$701$		−	30.5243i		−	1.15289i	0.817137	−	0.576443i	$-0.195560\pi$
$702$		0			0
$703$	17.8695	−	30.9509i	0.673960	−	1.16733i
$704$	−19.7535	−	11.4047i	−0.744489	−	0.429831i
$705$		0			0
$706$		−	6.20804i		−	0.233643i
$707$	26.0717	+	0.221267i	0.980528	+	0.00832159i
$708$		0			0
$709$	5.70901	+	9.88830i	0.214406	+	0.371363i	0.953089	−	0.302691i	$-0.0978850\pi$
$709$	5.70901	+	9.88830i	0.214406	+	0.371363i	−0.738682	+	0.674054i	$0.764552\pi$
$710$		0			0
$711$		0			0
$712$	5.56082	+	9.63162i	0.208400	+	0.360960i
$713$		−	12.5815i		−	0.471181i
$714$		0			0
$715$		0			0
$716$	−4.15260	+	2.39751i	−0.155190	+	0.0895990i
$717$		0			0
$718$	−3.75699	−	2.16910i	−0.140209	−	0.0809500i
$719$	0.0976746	+	0.169177i	0.00364265	+	0.00630925i	0.867841	−	0.496842i	$-0.165507\pi$
$719$	0.0976746	+	0.169177i	0.00364265	+	0.00630925i	−0.864198	+	0.503151i	$0.832174\pi$
$720$		0			0
$721$	8.82511	−	14.9903i	0.328664	−	0.558268i
$722$	1.81161			0.0674211
$723$		0			0
$724$	−6.20745	−	3.58388i	−0.230698	−	0.133194i
$725$		0			0
$726$		0			0
$727$	22.6268			0.839181			0.419590	−	0.907714i	$-0.362174\pi$
$727$	22.6268			0.839181			0.419590	+	0.907714i	$0.362174\pi$
$728$	10.1592	+	17.9463i	0.376526	+	0.665135i
$729$		0			0
$730$		0			0
$731$	−15.1017	+	26.1570i	−0.558558	+	0.967450i
$732$		0			0
$733$	−8.30708	−	14.3883i	−0.306829	−	0.531443i	0.670838	−	0.741604i	$-0.265935\pi$
$733$	−8.30708	−	14.3883i	−0.306829	−	0.531443i	−0.977667	+	0.210161i	$0.932601\pi$
$734$	1.98081			0.0731131
$735$		0			0
$736$	−11.3285			−0.417575
$737$	17.9684	+	31.1222i	0.661876	+	1.14640i
$738$		0			0
$739$	−0.165328	+	0.286356i	−0.00608168	+	0.0105338i	−0.869050	−	0.494724i	$-0.835269\pi$
$739$	−0.165328	+	0.286356i	−0.00608168	+	0.0105338i	0.862969	+	0.505258i	$0.168603\pi$
$740$		0			0
$741$		0			0
$742$	1.50097	+	2.65148i	0.0551025	+	0.0973389i
$743$	42.3387			1.55325			0.776627	−	0.629960i	$-0.216929\pi$
$743$	42.3387			1.55325			0.776627	+	0.629960i	$0.216929\pi$
$744$		0			0
$745$		0			0
$746$	4.43493	+	2.56051i	0.162374	+	0.0937468i
$747$		0			0
$748$	42.4227			1.55113
$749$	−6.46348	+	10.9788i	−0.236170	+	0.401158i
$750$		0			0
$751$	−4.52350	−	7.83494i	−0.165065	−	0.285901i	0.771613	−	0.636092i	$-0.219450\pi$
$751$	−4.52350	−	7.83494i	−0.165065	−	0.285901i	−0.936678	+	0.350191i	$0.886117\pi$
$752$	20.8308	+	12.0266i	0.759620	+	0.438567i
$753$		0			0
$754$	−16.0535	+	9.26850i	−0.584635	+	0.337539i
$755$		0			0
$756$		0			0
$757$		−	37.8499i		−	1.37568i	−0.725863	−	0.687839i	$-0.758559\pi$
$757$		−	37.8499i		−	1.37568i	0.725863	−	0.687839i	$-0.241441\pi$
$758$	−7.53557	−	13.0520i	−0.273704	−	0.474070i
$759$		0			0
$760$		0			0
$761$	−5.87367	−	10.1735i	−0.212920	−	0.368789i	0.739707	−	0.672929i	$-0.234964\pi$
$761$	−5.87367	−	10.1735i	−0.212920	−	0.368789i	−0.952627	+	0.304140i	$0.901631\pi$
$762$		0			0
$763$	14.2453	+	0.120897i	0.515713	+	0.00437678i
$764$			14.1289i			0.511167i
$765$		0			0
$766$	9.80860	+	5.66300i	0.354399	+	0.204612i
$767$	−12.5628	+	21.7594i	−0.453617	+	0.785687i
$768$		0			0
$769$		−	13.1169i		−	0.473007i	−0.971631	−	0.236504i	$-0.923998\pi$
$769$		−	13.1169i		−	0.473007i	0.971631	−	0.236504i	$-0.0760015\pi$
$770$		0			0
$771$		0			0
$772$	0.0966409	−	0.0557956i	0.00347818	−	0.00200813i
$773$	10.8882	+	6.28630i	0.391621	+	0.226102i	0.682862	−	0.730547i	$-0.260735\pi$
$773$	10.8882	+	6.28630i	0.391621	+	0.226102i	−0.291241	+	0.956650i	$0.594068\pi$
$774$		0			0
$775$		0			0
$776$	−0.480225			−0.0172391
$777$		0			0
$778$			3.78940i			0.135857i
$779$	24.7404	−	14.2838i	0.886415	−	0.511772i
$780$		0			0
$781$	3.18046	−	5.50872i	0.113806	−	0.197117i
$782$	4.09179	−	2.36239i	0.146322	−	0.0844790i
$783$		0			0
$784$	21.5129	+	0.365180i	0.768318	+	0.0130421i
$785$		0			0
$786$		0			0
$787$	26.2556	−	45.4761i	0.935912	−	1.62105i	0.162912	−	0.986641i	$-0.447911\pi$
$787$	26.2556	−	45.4761i	0.935912	−	1.62105i	0.773000	−	0.634406i	$-0.218755\pi$
$788$	11.3264	−	19.6179i	0.403486	−	0.698859i
$789$		0			0
$790$		0			0
$791$	12.3542	+	21.8238i	0.439265	+	0.775964i
$792$		0			0
$793$	−52.3670	+	30.2341i	−1.85961	+	1.07364i
$794$	1.92260	−	3.33004i	0.0682304	−	0.118179i
$795$		0			0
$796$	17.8353	−	10.2972i	0.632156	−	0.364976i
$797$		−	24.2213i		−	0.857964i	−0.903313	−	0.428982i	$-0.858872\pi$
$797$		−	24.2213i		−	0.857964i	0.903313	−	0.428982i	$-0.141128\pi$
$798$		0			0
$799$	−35.1070			−1.24200
$800$		0			0
$801$		0			0
$802$	3.09360	+	1.78609i	0.109239	+	0.0630690i
$803$	−2.57122	+	1.48449i	−0.0907363	+	0.0523866i
$804$		0			0
$805$		0			0
$806$		−	9.65255i		−	0.339996i
$807$		0			0
$808$	−7.53724	+	13.0549i	−0.265159	+	0.459269i
$809$	−9.52648	−	5.50012i	−0.334933	−	0.193374i	0.323096	−	0.946366i	$-0.395276\pi$
$809$	−9.52648	−	5.50012i	−0.334933	−	0.193374i	−0.658029	+	0.752992i	$0.728610\pi$
$810$		0			0
$811$			7.18512i			0.252304i	0.992011	+	0.126152i	$0.0402626\pi$
$811$			7.18512i			0.252304i	−0.992011	+	0.126152i	$0.959737\pi$
$812$	−0.377727	+	44.5074i	−0.0132556	+	1.56190i
$813$		0			0
$814$	−9.61263	−	16.6496i	−0.336922	−	0.583567i
$815$		0			0
$816$		0			0
$817$	12.7964	+	22.1640i	0.447689	+	0.775420i
$818$			12.1234i			0.423885i
$819$		0			0
$820$		0			0
$821$	39.4307	−	22.7653i	1.37614	−	0.794515i	0.384448	−	0.923146i	$-0.374392\pi$
$821$	39.4307	−	22.7653i	1.37614	−	0.794515i	0.991693	+	0.128631i	$0.0410583\pi$
$822$		0			0
$823$	−10.9142	−	6.30134i	−0.380447	−	0.219651i	0.297566	−	0.954701i	$-0.403825\pi$
$823$	−10.9142	−	6.30134i	−0.380447	−	0.219651i	−0.678013	+	0.735050i	$0.737159\pi$
$824$	5.02869	+	8.70995i	0.175183	+	0.303425i
$825$		0			0
$826$	−2.55928	−	4.52099i	−0.0890489	−	0.157305i
$827$	−50.5644			−1.75830			−0.879148	−	0.476549i	$-0.841887\pi$
$827$	−50.5644			−1.75830			−0.879148	+	0.476549i	$0.841887\pi$
$828$		0			0
$829$	13.3885	+	7.72987i	0.465003	+	0.268470i	0.714146	−	0.699997i	$-0.246815\pi$
$829$	13.3885	+	7.72987i	0.465003	+	0.268470i	−0.249143	+	0.968467i	$0.580149\pi$
$830$		0			0
$831$		0			0
$832$	22.6327			0.784647
$833$	−27.4590	+	15.2380i	−0.951397	+	0.527965i
$834$		0			0
$835$		0			0
$836$	17.9733	−	31.1307i	0.621621	−	1.07668i
$837$		0			0
$838$	4.79684	+	8.30838i	0.165704	+	0.287008i
$839$	48.2725			1.66655			0.833276	−	0.552858i	$-0.186463\pi$
$839$	48.2725			1.66655			0.833276	+	0.552858i	$0.186463\pi$
$840$		0			0
$841$	−54.4618			−1.87799
$842$	4.45325	+	7.71325i	0.153469	+	0.265816i
$843$		0			0
$844$	5.17949	−	8.97114i	0.178285	−	0.308799i
$845$		0			0
$846$		0			0
$847$	−20.6316	+	35.0448i	−0.708911	+	1.20415i
$848$	8.88898			0.305249
$849$		0			0
$850$		0			0
$851$	21.5336	+	12.4324i	0.738161	+	0.426178i
$852$		0			0
$853$	−7.57394			−0.259327			−0.129663	−	0.991558i	$-0.541390\pi$
$853$	−7.57394			−0.259327			−0.129663	+	0.991558i	$0.541390\pi$
$854$	0.106105	−	12.5023i	0.00363084	−	0.427820i
$855$		0			0
$856$	−3.68299	−	6.37913i	−0.125882	−	0.218034i
$857$	0.451909	+	0.260910i	0.0154369	+	0.00891251i	0.507699	−	0.861535i	$-0.330496\pi$
$857$	0.451909	+	0.260910i	0.0154369	+	0.00891251i	−0.492262	+	0.870447i	$0.663830\pi$
$858$		0			0
$859$	−39.1327	+	22.5933i	−1.33519	+	0.770872i	−0.986090	−	0.166213i	$-0.946846\pi$
$859$	−39.1327	+	22.5933i	−1.33519	+	0.770872i	−0.349100	+	0.937085i	$0.613513\pi$
$860$		0			0
$861$		0			0
$862$			4.09673i			0.139535i
$863$	4.30717	+	7.46024i	0.146618	+	0.253950i	0.929975	−	0.367622i	$-0.119828\pi$
$863$	4.30717	+	7.46024i	0.146618	+	0.253950i	−0.783358	+	0.621571i	$0.786495\pi$
$864$		0			0
$865$		0			0
$866$	−0.978108	−	1.69413i	−0.0332375	−	0.0575690i
$867$		0			0
$868$	−19.9725	−	11.7582i	−0.677910	−	0.399100i
$869$		−	25.3231i		−	0.859027i
$870$		0			0
$871$	−30.8811	−	17.8292i	−1.04637	−	0.604120i
$872$	−4.11825	+	7.13302i	−0.139462	+	0.241555i
$873$		0			0
$874$		−	4.00353i		−	0.135421i
$875$		0			0
$876$		0			0
$877$	−1.28082	+	0.739482i	−0.0432502	+	0.0249705i	−0.521469	−	0.853270i	$-0.674616\pi$
$877$	−1.28082	+	0.739482i	−0.0432502	+	0.0249705i	0.478219	+	0.878241i	$0.341283\pi$
$878$	−10.7572	−	6.21067i	−0.363038	−	0.209600i
$879$		0			0
$880$		0			0
$881$	28.6082			0.963835			0.481918	−	0.876217i	$-0.339940\pi$
$881$	28.6082			0.963835			0.481918	+	0.876217i	$0.339940\pi$
$882$		0			0
$883$		−	2.70408i		−	0.0909996i	−0.998964	−	0.0454998i	$-0.985512\pi$
$883$		−	2.70408i		−	0.0909996i	0.998964	−	0.0454998i	$-0.0144880\pi$
$884$	−36.4545	+	21.0470i	−1.22610	+	0.707888i
$885$		0			0
$886$	−2.10161	+	3.64009i	−0.0706048	+	0.122291i
$887$	−15.3996	+	8.89098i	−0.517069	+	0.298530i	−0.735735	−	0.677270i	$-0.763163\pi$
$887$	−15.3996	+	8.89098i	−0.517069	+	0.298530i	0.218666	+	0.975800i	$0.429830\pi$
$888$		0			0
$889$	19.8698	−	11.2481i	0.666413	−	0.377250i
$890$		0			0
$891$		0			0
$892$	2.91248	−	5.04456i	0.0975170	−	0.168904i
$893$	−14.8739	+	25.7623i	−0.497735	+	0.862103i
$894$		0			0
$895$		0			0
$896$	−13.8731	+	23.5647i	−0.463467	+	0.787243i
$897$		0			0
$898$	11.3598	−	6.55856i	0.379080	−	0.218862i
$899$	21.7300	−	37.6375i	0.724736	−	1.25528i
$900$		0			0
$901$	−11.2357	+	6.48696i	−0.374317	+	0.216112i
$902$		−	15.3676i		−	0.511684i
$903$		0			0
$904$	−14.4994			−0.482241
$905$		0			0
$906$		0			0
$907$	38.2086	+	22.0597i	1.26869	+	0.732481i	0.974741	−	0.223338i	$-0.0716954\pi$
$907$	38.2086	+	22.0597i	1.26869	+	0.732481i	0.293954	+	0.955820i	$0.405029\pi$
$908$	−17.9324	+	10.3533i	−0.595108	+	0.343585i
$909$		0			0
$910$		0			0
$911$		−	2.01773i		−	0.0668505i	−0.999441	−	0.0334253i	$-0.989358\pi$
$911$		−	2.01773i		−	0.0668505i	0.999441	−	0.0334253i	$-0.0106416\pi$
$912$		0			0
$913$	25.0518	−	43.3910i	0.829094	−	1.43603i
$914$	−11.0905	−	6.40311i	−0.366841	−	0.211796i
$915$		0			0
$916$			41.9633i			1.38651i
$917$	−20.8229	+	35.3696i	−0.687632	+	1.16801i
$918$		0			0
$919$	−18.8068	−	32.5743i	−0.620379	−	1.07453i	−0.989415	−	0.145113i	$-0.953645\pi$
$919$	−18.8068	−	32.5743i	−0.620379	−	1.07453i	0.369036	−	0.929415i	$-0.379688\pi$
$920$		0			0
$921$		0			0
$922$	7.89686	+	13.6778i	0.260069	+	0.450453i
$923$			6.31164i			0.207750i
$924$		0			0
$925$		0			0
$926$	−11.8026	+	6.81421i	−0.387856	+	0.223929i
$927$		0			0
$928$	−33.8892	−	19.5659i	−1.11247	−	0.642283i
$929$	−19.6901	−	34.1042i	−0.646010	−	1.11892i	−0.984067	−	0.177797i	$-0.943103\pi$
$929$	−19.6901	−	34.1042i	−0.646010	−	1.11892i	0.338057	−	0.941126i	$-0.390230\pi$
$930$		0			0
$931$	−0.451634	+	26.6060i	−0.0148017	+	0.871975i
$932$	−5.94218			−0.194643
$933$		0			0
$934$	10.2419	+	5.91315i	0.335124	+	0.193484i
$935$		0			0
$936$		0			0
$937$	−10.4952			−0.342864			−0.171432	−	0.985196i	$-0.554839\pi$
$937$	−10.4952			−0.342864			−0.171432	+	0.985196i	$0.554839\pi$
$938$	6.41622	−	3.63216i	0.209497	−	0.118594i
$939$		0			0
$940$		0			0
$941$	−11.1934	+	19.3875i	−0.364895	+	0.632016i	−0.988759	−	0.149516i	$-0.952228\pi$
$941$	−11.1934	+	19.3875i	−0.364895	+	0.632016i	0.623865	+	0.781532i	$0.285562\pi$
$942$		0			0
$943$	9.93776	+	17.2127i	0.323618	+	0.560523i
$944$	−15.1564			−0.493300
$945$		0			0
$946$	13.7673			0.447612
$947$	−7.67919	−	13.3007i	−0.249540	−	0.432216i	0.713858	−	0.700290i	$-0.246946\pi$
$947$	−7.67919	−	13.3007i	−0.249540	−	0.432216i	−0.963398	+	0.268074i	$0.913613\pi$
$948$		0			0
$949$	1.47299	−	2.55130i	0.0478154	−	0.0828186i
$950$		0			0
$951$		0			0
$952$	0.154088	−	18.1561i	0.00499401	−	0.588442i
$953$	−7.83975			−0.253955			−0.126977	−	0.991906i	$-0.540528\pi$
$953$	−7.83975			−0.253955			−0.126977	+	0.991906i	$0.540528\pi$
$954$		0			0
$955$		0			0
$956$	36.8815	+	21.2936i	1.19283	+	0.688683i
$957$		0			0
$958$	3.73995			0.120832
$959$	2.92131	+	0.0247927i	0.0943341	+	0.000800599i
$960$		0			0
$961$	−4.18480	−	7.24829i	−0.134994	−	0.233816i
$962$	16.5206	+	9.53816i	0.532645	+	0.307523i
$963$		0			0
$964$	23.6808	−	13.6721i	0.762707	−	0.440349i
$965$		0			0
$966$		0			0
$967$		−	31.3647i		−	1.00862i	−0.863523	−	0.504310i	$-0.831747\pi$
$967$		−	31.3647i		−	1.00862i	0.863523	−	0.504310i	$-0.168253\pi$
$968$	−11.7562	−	20.3624i	−0.377860	−	0.654472i
$969$		0			0
$970$		0			0
$971$	11.3560	+	19.6691i	0.364431	+	0.631213i	0.988685	−	0.150009i	$-0.0479302\pi$
$971$	11.3560	+	19.6691i	0.364431	+	0.631213i	−0.624254	+	0.781222i	$0.714597\pi$
$972$		0			0
$973$	14.9212	−	8.44671i	0.478350	−	0.270789i
$974$		−	3.16287i		−	0.101345i
$975$		0			0
$976$	−31.5892	−	18.2380i	−1.01114	−	0.583784i
$977$	5.41629	−	9.38128i	0.173282	−	0.300134i	−0.766283	−	0.642503i	$-0.777896\pi$
$977$	5.41629	−	9.38128i	0.173282	−	0.300134i	0.939566	+	0.342369i	$0.111229\pi$
$978$		0			0
$979$		−	37.3356i		−	1.19325i
$980$		0			0
$981$		0			0
$982$	3.68727	−	2.12885i	0.117665	−	0.0679342i
$983$	24.3551	+	14.0614i	0.776808	+	0.448490i	0.835298	−	0.549798i	$-0.185295\pi$
$983$	24.3551	+	14.0614i	0.776808	+	0.448490i	−0.0584896	+	0.998288i	$0.518628\pi$
$984$		0			0
$985$		0			0
$986$	16.3207			0.519758
$987$		0			0
$988$			35.6682i			1.13476i
$989$	−15.4202	+	8.90288i	−0.490335	+	0.283095i
$990$		0			0
$991$	1.02979	−	1.78365i	0.0327123	−	0.0566594i	−0.849206	−	0.528062i	$-0.822919\pi$
$991$	1.02979	−	1.78365i	0.0327123	−	0.0566594i	0.881918	+	0.471403i	$0.156252\pi$
$992$	17.6467	−	10.1883i	0.560283	−	0.323480i
$993$		0			0
$994$	−1.12461	−	0.662084i	−0.0356705	−	0.0210000i
$995$		0			0
$996$		0			0
$997$	−21.2589	+	36.8214i	−0.673275	+	1.16615i	0.303695	+	0.952769i	$0.401780\pi$
$997$	−21.2589	+	36.8214i	−0.673275	+	1.16615i	−0.976970	+	0.213378i	$0.931554\pi$
$998$	1.44093	−	2.49576i	0.0456119	−	0.0790021i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1575.2.bc.d.899.6		24
3.2	odd	2		1575.2.bc.c.899.7		24
5.2	odd	4		315.2.bj.a.206.4	yes	12
5.3	odd	4		1575.2.bk.f.1151.3		12
5.4	even	2	inner	1575.2.bc.d.899.7		24
7.5	odd	6		1575.2.bc.c.1349.6		24
15.2	even	4		315.2.bj.b.206.3	yes	12
15.8	even	4		1575.2.bk.e.1151.4		12
15.14	odd	2		1575.2.bc.c.899.6		24
21.5	even	6	inner	1575.2.bc.d.1349.7		24
35.12	even	12		315.2.bj.b.26.3	yes	12
35.17	even	12		2205.2.b.a.881.7		12
35.19	odd	6		1575.2.bc.c.1349.7		24
35.32	odd	12		2205.2.b.b.881.7		12
35.33	even	12		1575.2.bk.e.26.4		12
105.17	odd	12		2205.2.b.b.881.6		12
105.32	even	12		2205.2.b.a.881.6		12
105.47	odd	12		315.2.bj.a.26.4	✓	12
105.68	odd	12		1575.2.bk.f.26.3		12
105.89	even	6	inner	1575.2.bc.d.1349.6		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
315.2.bj.a.26.4	✓	12	105.47	odd	12
315.2.bj.a.206.4	yes	12	5.2	odd	4
315.2.bj.b.26.3	yes	12	35.12	even	12
315.2.bj.b.206.3	yes	12	15.2	even	4
1575.2.bc.c.899.6		24	15.14	odd	2
1575.2.bc.c.899.7		24	3.2	odd	2
1575.2.bc.c.1349.6		24	7.5	odd	6
1575.2.bc.c.1349.7		24	35.19	odd	6
1575.2.bc.d.899.6		24	1.1	even	1	trivial
1575.2.bc.d.899.7		24	5.4	even	2	inner
1575.2.bc.d.1349.6		24	105.89	even	6	inner
1575.2.bc.d.1349.7		24	21.5	even	6	inner
1575.2.bk.e.26.4		12	35.33	even	12
1575.2.bk.e.1151.4		12	15.8	even	4
1575.2.bk.f.26.3		12	105.68	odd	12
1575.2.bk.f.1151.3		12	5.3	odd	4
2205.2.b.a.881.6		12	105.32	even	12
2205.2.b.a.881.7		12	35.17	even	12
2205.2.b.b.881.6		12	105.17	odd	12
2205.2.b.b.881.7		12	35.32	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.bc (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.199105 - 0.344861i) q^{2} +(0.920714 - 1.59472i) q^{4} +(1.30338 + 2.30243i) q^{7} -1.52970 q^{8} +O(q^{10})\)	\(q+(-0.199105 - 0.344861i) q^{2} +(0.920714 - 1.59472i) q^{4} +(1.30338 + 2.30243i) q^{7} -1.52970 q^{8} +(4.44725 + 2.56762i) q^{11} -5.09545 q^{13} +(0.534507 - 0.907912i) q^{14} +(-1.53686 - 2.66191i) q^{16} +(3.88520 + 2.24312i) q^{17} +(3.29211 - 1.90070i) q^{19} -2.04491i q^{22} +(1.32238 + 2.29043i) q^{23} +(1.01453 + 1.75722i) q^{26} +(4.87179 + 0.0413461i) q^{28} +9.13574i q^{29} +(-4.11981 - 2.37857i) q^{31} +(-2.14169 + 3.70952i) q^{32} -1.78647i q^{34} +(8.14197 - 4.70077i) q^{37} +(-1.31095 - 0.756879i) q^{38} +7.51505 q^{41} +6.73246i q^{43} +(8.18929 - 4.72809i) q^{44} +(0.526586 - 0.912074i) q^{46} +(-6.77706 + 3.91274i) q^{47} +(-3.60239 + 6.00190i) q^{49} +(-4.69146 + 8.12584i) q^{52} +(-1.44597 + 2.50449i) q^{53} +(-1.99378 - 3.52202i) q^{56} +(3.15056 - 1.81897i) q^{58} +(2.46549 - 4.27036i) q^{59} +(10.2772 - 5.93354i) q^{61} +1.89434i q^{62} -4.44174 q^{64} +(6.06052 + 3.49905i) q^{67} +(7.15432 - 4.13055i) q^{68} -1.23868i q^{71} +(-0.289080 + 0.500701i) q^{73} +(-3.24222 - 1.87190i) q^{74} -7.00000i q^{76} +(-0.115303 + 13.5861i) q^{77} +(-2.46562 - 4.27058i) q^{79} +(-1.49629 - 2.59164i) q^{82} -9.75683i q^{83} +(2.32176 - 1.34047i) q^{86} +(-6.80294 - 3.92768i) q^{88} +(-3.63524 - 6.29642i) q^{89} +(-6.64133 - 11.7319i) q^{91} +4.87014 q^{92} +(2.69870 + 1.55809i) q^{94} +0.313935 q^{97} +(2.78707 + 0.0473103i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 16 q^{4}+O(q^{10}) \) 24 * q - 16 * q^4	\( 24 q - 16 q^{4} + 24 q^{11} + 24 q^{14} - 32 q^{16} - 12 q^{19} + 12 q^{31} + 48 q^{41} - 24 q^{44} - 8 q^{46} - 12 q^{49} - 120 q^{56} + 48 q^{59} + 112 q^{64} - 168 q^{74} - 36 q^{79} - 168 q^{86} - 24 q^{89} - 36 q^{91} - 24 q^{94}+O(q^{100}) \) 24 * q - 16 * q^4 + 24 * q^11 + 24 * q^14 - 32 * q^16 - 12 * q^19 + 12 * q^31 + 48 * q^41 - 24 * q^44 - 8 * q^46 - 12 * q^49 - 120 * q^56 + 48 * q^59 + 112 * q^64 - 168 * q^74 - 36 * q^79 - 168 * q^86 - 24 * q^89 - 36 * q^91 - 24 * q^94

Introduction

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