LMFDB - Embedded newform 3150.2.bp.e.1349.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3150,2,Mod(899,3150)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3150, 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("3150.899");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 3150 = 2 \cdot 3^{2} \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	3150.bp (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:	$25.1528766367$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\zeta_{24})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{4} + 1 $ x^8 - x^4 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{2}\cdot 3^{2} $
Twist minimal:	no (minimal twist has level 126)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			1349.3
Root			$-0.258819 + 0.965926i$ of defining polynomial
Character	$\chi$	$=$	3150.1349
Dual form			3150.2.bp.e.899.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(0.358719 + 2.62132i) q^{7} -1.00000 q^{8} +O(q^{10})$	\(q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(0.358719 + 2.62132i) q^{7} -1.00000 q^{8} +(2.59808 - 1.50000i) q^{11} -2.44949 q^{13} +(2.44949 + 1.00000i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(-5.12132 + 2.95680i) q^{17} +(5.12132 + 2.95680i) q^{19} -3.00000i q^{22} +(-2.12132 + 3.67423i) q^{23} +(-1.22474 + 2.12132i) q^{26} +(2.09077 - 1.62132i) q^{28} -7.24264i q^{29} +(-7.86396 + 4.54026i) q^{31} +(0.500000 + 0.866025i) q^{32} +5.91359i q^{34} +(0.210133 + 0.121320i) q^{37} +(5.12132 - 2.95680i) q^{38} -11.8272 q^{41} +0.242641i q^{43} +(-2.59808 - 1.50000i) q^{44} +(2.12132 + 3.67423i) q^{46} +(5.12132 + 2.95680i) q^{47} +(-6.74264 + 1.88064i) q^{49} +(1.22474 + 2.12132i) q^{52} +(-3.62132 - 6.27231i) q^{53} +(-0.358719 - 2.62132i) q^{56} +(-6.27231 - 3.62132i) q^{58} +(4.03295 + 6.98528i) q^{59} +(0.878680 + 0.507306i) q^{61} +9.08052i q^{62} +1.00000 q^{64} +(-8.66025 + 5.00000i) q^{67} +(5.12132 + 2.95680i) q^{68} -1.75736i q^{71} +(0.717439 + 1.24264i) q^{73} +(0.210133 - 0.121320i) q^{74} -5.91359i q^{76} +(4.86396 + 6.27231i) q^{77} +(-1.37868 + 2.38794i) q^{79} +(-5.91359 + 10.2426i) q^{82} +6.63103i q^{83} +(0.210133 + 0.121320i) q^{86} +(-2.59808 + 1.50000i) q^{88} +(5.19615 - 9.00000i) q^{89} +(-0.878680 - 6.42090i) q^{91} +4.24264 q^{92} +(5.12132 - 2.95680i) q^{94} -13.5592 q^{97} +(-1.74264 + 6.77962i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 4 q^{2} - 4 q^{4} - 8 q^{8}+O(q^{10}) $ 8 * q + 4 * q^2 - 4 * q^4 - 8 * q^8	$ 8 q + 4 q^{2} - 4 q^{4} - 8 q^{8} - 4 q^{16} - 24 q^{17} + 24 q^{19} - 12 q^{31} + 4 q^{32} + 24 q^{38} + 24 q^{47} - 20 q^{49} - 12 q^{53} + 24 q^{61} + 8 q^{64} + 24 q^{68} - 12 q^{77} - 28 q^{79} - 24 q^{91} + 24 q^{94} + 20 q^{98}+O(q^{100}) $ 8 * q + 4 * q^2 - 4 * q^4 - 8 * q^8 - 4 * q^16 - 24 * q^17 + 24 * q^19 - 12 * q^31 + 4 * q^32 + 24 * q^38 + 24 * q^47 - 20 * q^49 - 12 * q^53 + 24 * q^61 + 8 * q^64 + 24 * q^68 - 12 * q^77 - 28 * q^79 - 24 * q^91 + 24 * q^94 + 20 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/3150\mathbb{Z}\right)^\times$.

$n$	$127$	$451$	$2801$
$\chi(n)$	$-1$	$e\left(\frac{5}{6}\right)$	$-1$

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 $

$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$3$		0			0
$3$		0			0
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$		0			0
$5$		0			0
$6$		0			0
$7$	0.358719	+	2.62132i	0.135583	+	0.990766i
$7$	0.358719	+	2.62132i	0.135583	+	0.990766i
$8$	−1.00000			−0.353553
$9$		0			0
$10$		0			0
$11$	2.59808	−	1.50000i	0.783349	−	0.452267i	−0.0542666	−	0.998526i	$-0.517282\pi$
$11$	2.59808	−	1.50000i	0.783349	−	0.452267i	0.837616	+	0.546259i	$0.183949\pi$
$12$		0			0
$13$	−2.44949			−0.679366			−0.339683	−	0.940540i	$-0.610320\pi$
$13$	−2.44949			−0.679366			−0.339683	+	0.940540i	$0.610320\pi$
$14$	2.44949	+	1.00000i	0.654654	+	0.267261i
$15$		0			0
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−5.12132	+	2.95680i	−1.24210	+	0.717128i	−0.969522	−	0.245005i	$-0.921211\pi$
$17$	−5.12132	+	2.95680i	−1.24210	+	0.717128i	−0.272581	+	0.962133i	$0.587877\pi$
$18$		0			0
$19$	5.12132	+	2.95680i	1.17491	+	0.678335i	0.954832	−	0.297146i	$-0.0960350\pi$
$19$	5.12132	+	2.95680i	1.17491	+	0.678335i	0.220080	+	0.975482i	$0.429368\pi$
$20$		0			0
$21$		0			0
$22$		−	3.00000i		−	0.639602i
$23$	−2.12132	+	3.67423i	−0.442326	+	0.766131i	−0.997862	−	0.0653618i	$-0.979180\pi$
$23$	−2.12132	+	3.67423i	−0.442326	+	0.766131i	0.555536	+	0.831493i	$0.312513\pi$
$24$		0			0
$25$		0			0
$26$	−1.22474	+	2.12132i	−0.240192	+	0.416025i
$27$		0			0
$28$	2.09077	−	1.62132i	0.395118	−	0.306401i
$29$		−	7.24264i		−	1.34492i	−0.740131	−	0.672462i	$-0.765237\pi$
$29$		−	7.24264i		−	1.34492i	0.740131	−	0.672462i	$-0.234763\pi$
$30$		0			0
$31$	−7.86396	+	4.54026i	−1.41241	+	0.815455i	−0.995615	−	0.0935461i	$-0.970180\pi$
$31$	−7.86396	+	4.54026i	−1.41241	+	0.815455i	−0.416794	+	0.909001i	$0.636846\pi$
$32$	0.500000	+	0.866025i	0.0883883	+	0.153093i
$33$		0			0
$34$			5.91359i			1.01417i
$35$		0			0
$36$		0			0
$37$	0.210133	+	0.121320i	0.0345457	+	0.0199449i	0.517173	−	0.855881i	$-0.326984\pi$
$37$	0.210133	+	0.121320i	0.0345457	+	0.0199449i	−0.482628	+	0.875826i	$0.660318\pi$
$38$	5.12132	−	2.95680i	0.830788	−	0.479656i
$39$		0			0
$40$		0			0
$41$	−11.8272			−1.84710			−0.923548	−	0.383483i	$-0.874724\pi$
$41$	−11.8272			−1.84710			−0.923548	+	0.383483i	$0.874724\pi$
$42$		0			0
$43$			0.242641i			0.0370024i	0.999829	+	0.0185012i	$0.00588944\pi$
$43$			0.242641i			0.0370024i	−0.999829	+	0.0185012i	$0.994111\pi$
$44$	−2.59808	−	1.50000i	−0.391675	−	0.226134i
$45$		0			0
$46$	2.12132	+	3.67423i	0.312772	+	0.541736i
$47$	5.12132	+	2.95680i	0.747021	+	0.431293i	0.824617	−	0.565692i	$-0.191391\pi$
$47$	5.12132	+	2.95680i	0.747021	+	0.431293i	−0.0775953	+	0.996985i	$0.524724\pi$
$48$		0			0
$49$	−6.74264	+	1.88064i	−0.963234	+	0.268662i
$50$		0			0
$51$		0			0
$52$	1.22474	+	2.12132i	0.169842	+	0.294174i
$53$	−3.62132	−	6.27231i	−0.497427	−	0.861568i	0.502569	−	0.864537i	$-0.332388\pi$
$53$	−3.62132	−	6.27231i	−0.497427	−	0.861568i	−0.999996	+	0.00296896i	$0.999055\pi$
$54$		0			0
$55$		0			0
$56$	−0.358719	−	2.62132i	−0.0479359	−	0.350289i
$57$		0			0
$58$	−6.27231	−	3.62132i	−0.823595	−	0.475503i
$59$	4.03295	+	6.98528i	0.525046	+	0.909406i	0.999575	+	0.0291661i	$0.00928518\pi$
$59$	4.03295	+	6.98528i	0.525046	+	0.909406i	−0.474529	+	0.880240i	$0.657381\pi$
$60$		0			0
$61$	0.878680	+	0.507306i	0.112503	+	0.0649539i	0.555196	−	0.831720i	$-0.312643\pi$
$61$	0.878680	+	0.507306i	0.112503	+	0.0649539i	−0.442692	+	0.896674i	$0.645977\pi$
$62$			9.08052i			1.15323i
$63$		0			0
$64$	1.00000			0.125000
$65$		0			0
$66$		0			0
$67$	−8.66025	+	5.00000i	−1.05802	+	0.610847i	−0.924883	−	0.380251i	$-0.875838\pi$
$67$	−8.66025	+	5.00000i	−1.05802	+	0.610847i	−0.133135	+	0.991098i	$0.542504\pi$
$68$	5.12132	+	2.95680i	0.621051	+	0.358564i
$69$		0			0
$70$		0			0
$71$		−	1.75736i		−	0.208560i	−0.994548	−	0.104280i	$-0.966746\pi$
$71$		−	1.75736i		−	0.208560i	0.994548	−	0.104280i	$-0.0332538\pi$
$72$		0			0
$73$	0.717439	+	1.24264i	0.0839699	+	0.145440i	0.904952	−	0.425514i	$-0.139907\pi$
$73$	0.717439	+	1.24264i	0.0839699	+	0.145440i	−0.820982	+	0.570954i	$0.806573\pi$
$74$	0.210133	−	0.121320i	0.0244275	−	0.0141032i
$75$		0			0
$76$		−	5.91359i		−	0.678335i
$77$	4.86396	+	6.27231i	0.554300	+	0.714796i
$78$		0			0
$79$	−1.37868	+	2.38794i	−0.155114	+	0.268665i	−0.933100	−	0.359616i	$-0.882908\pi$
$79$	−1.37868	+	2.38794i	−0.155114	+	0.268665i	0.777987	+	0.628281i	$0.216241\pi$
$80$		0			0
$81$		0			0
$82$	−5.91359	+	10.2426i	−0.653047	+	1.13111i
$83$			6.63103i			0.727850i	0.931428	+	0.363925i	$0.118564\pi$
$83$			6.63103i			0.727850i	−0.931428	+	0.363925i	$0.881436\pi$
$84$		0			0
$85$		0			0
$86$	0.210133	+	0.121320i	0.0226592	+	0.0130823i
$87$		0			0
$88$	−2.59808	+	1.50000i	−0.276956	+	0.159901i
$89$	5.19615	−	9.00000i	0.550791	−	0.953998i	−0.447427	−	0.894321i	$-0.647659\pi$
$89$	5.19615	−	9.00000i	0.550791	−	0.953998i	0.998218	−	0.0596775i	$-0.0190072\pi$
$90$		0			0
$91$	−0.878680	−	6.42090i	−0.0921107	−	0.673093i
$92$	4.24264			0.442326
$93$		0			0
$94$	5.12132	−	2.95680i	0.528224	−	0.304970i
$95$		0			0
$96$		0			0
$97$	−13.5592			−1.37673			−0.688366	−	0.725364i	$-0.741672\pi$
$97$	−13.5592			−1.37673			−0.688366	+	0.725364i	$0.741672\pi$
$98$	−1.74264	+	6.77962i	−0.176033	+	0.684845i
$99$		0			0
$100$		0			0
$101$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$101$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$102$		0			0
$103$	−2.74666	+	4.75736i	−0.270637	+	0.468757i	−0.969025	−	0.246963i	$-0.920568\pi$
$103$	−2.74666	+	4.75736i	−0.270637	+	0.468757i	0.698388	+	0.715719i	$0.253901\pi$
$104$	2.44949			0.240192
$105$		0			0
$106$	−7.24264			−0.703467
$107$	−5.74264	+	9.94655i	−0.555162	+	0.961569i	0.442729	+	0.896656i	$0.354010\pi$
$107$	−5.74264	+	9.94655i	−0.555162	+	0.961569i	−0.997891	+	0.0649133i	$0.979323\pi$
$108$		0			0
$109$	9.24264	+	16.0087i	0.885284	+	1.53336i	0.845387	+	0.534154i	$0.179370\pi$
$109$	9.24264	+	16.0087i	0.885284	+	1.53336i	0.0398971	+	0.999204i	$0.487297\pi$
$110$		0			0
$111$		0			0
$112$	−2.44949	−	1.00000i	−0.231455	−	0.0944911i
$113$	8.48528			0.798228			0.399114	−	0.916901i	$-0.369318\pi$
$113$	8.48528			0.798228			0.399114	+	0.916901i	$0.369318\pi$
$114$		0			0
$115$		0			0
$116$	−6.27231	+	3.62132i	−0.582369	+	0.336231i
$117$		0			0
$118$	8.06591			0.742527
$119$	−9.58783	−	12.3640i	−0.878915	−	1.13340i
$120$		0			0
$121$	−1.00000	+	1.73205i	−0.0909091	+	0.157459i
$122$	0.878680	−	0.507306i	0.0795519	−	0.0459293i
$123$		0			0
$124$	7.86396	+	4.54026i	0.706205	+	0.407727i
$125$		0			0
$126$		0			0
$127$			3.24264i			0.287738i	0.989597	+	0.143869i	$0.0459544\pi$
$127$			3.24264i			0.287738i	−0.989597	+	0.143869i	$0.954046\pi$
$128$	0.500000	−	0.866025i	0.0441942	−	0.0765466i
$129$		0			0
$130$		0			0
$131$	2.59808	−	4.50000i	0.226995	−	0.393167i	−0.729921	−	0.683531i	$-0.760443\pi$
$131$	2.59808	−	4.50000i	0.226995	−	0.393167i	0.956916	+	0.290365i	$0.0937766\pi$
$132$		0			0
$133$	−5.91359	+	14.4853i	−0.512773	+	1.25603i
$134$			10.0000i			0.863868i
$135$		0			0
$136$	5.12132	−	2.95680i	0.439150	−	0.253543i
$137$	1.24264	+	2.15232i	0.106166	+	0.183885i	0.914214	−	0.405232i	$-0.132809\pi$
$137$	1.24264	+	2.15232i	0.106166	+	0.183885i	−0.808048	+	0.589117i	$0.799476\pi$
$138$		0			0
$139$			0.594346i			0.0504118i	0.999682	+	0.0252059i	$0.00802413\pi$
$139$			0.594346i			0.0504118i	−0.999682	+	0.0252059i	$0.991976\pi$
$140$		0			0
$141$		0			0
$142$	−1.52192	−	0.878680i	−0.127717	−	0.0737372i
$143$	−6.36396	+	3.67423i	−0.532181	+	0.307255i
$144$		0			0
$145$		0			0
$146$	1.43488			0.118751
$147$		0			0
$148$		−	0.242641i		−	0.0199449i
$149$	−3.04384	−	1.75736i	−0.249361	−	0.143968i	0.370111	−	0.928988i	$-0.379320\pi$
$149$	−3.04384	−	1.75736i	−0.249361	−	0.143968i	−0.619472	+	0.785019i	$0.712653\pi$
$150$		0			0
$151$	−2.62132	−	4.54026i	−0.213320	−	0.369481i	0.739432	−	0.673232i	$-0.235094\pi$
$151$	−2.62132	−	4.54026i	−0.213320	−	0.369481i	−0.952752	+	0.303751i	$0.901761\pi$
$152$	−5.12132	−	2.95680i	−0.415394	−	0.239828i
$153$		0			0
$154$	7.86396	−	1.07616i	0.633696	−	0.0867193i
$155$		0			0
$156$		0			0
$157$	7.34847	+	12.7279i	0.586472	+	1.01580i	0.994690	+	0.102915i	$0.0328168\pi$
$157$	7.34847	+	12.7279i	0.586472	+	1.01580i	−0.408219	+	0.912884i	$0.633850\pi$
$158$	1.37868	+	2.38794i	0.109682	+	0.189975i
$159$		0			0
$160$		0			0
$161$	−10.3923	−	4.24264i	−0.819028	−	0.334367i
$162$		0			0
$163$	−1.94218	−	1.12132i	−0.152124	−	0.0878286i	0.422006	−	0.906593i	$-0.361326\pi$
$163$	−1.94218	−	1.12132i	−0.152124	−	0.0878286i	−0.574130	+	0.818764i	$0.694659\pi$
$164$	5.91359	+	10.2426i	0.461774	+	0.799816i
$165$		0			0
$166$	5.74264	+	3.31552i	0.445715	+	0.257334i
$167$			16.1318i			1.24832i	0.781298	+	0.624159i	$0.214558\pi$
$167$			16.1318i			1.24832i	−0.781298	+	0.624159i	$0.785442\pi$
$168$		0			0
$169$	−7.00000			−0.538462
$170$		0			0
$171$		0			0
$172$	0.210133	−	0.121320i	0.0160225	−	0.00925059i
$173$	−18.0000	−	10.3923i	−1.36851	−	0.790112i	−0.377776	−	0.925897i	$-0.623311\pi$
$173$	−18.0000	−	10.3923i	−1.36851	−	0.790112i	−0.990738	+	0.135785i	$0.956644\pi$
$174$		0			0
$175$		0			0
$176$			3.00000i			0.226134i
$177$		0			0
$178$	−5.19615	−	9.00000i	−0.389468	−	0.674579i
$179$	22.9369	−	13.2426i	1.71439	−	0.989801i	0.785966	−	0.618269i	$-0.212166\pi$
$179$	22.9369	−	13.2426i	1.71439	−	0.989801i	0.928420	−	0.371532i	$-0.121167\pi$
$180$		0			0
$181$			11.8272i			0.879108i	0.898216	+	0.439554i	$0.144863\pi$
$181$			11.8272i			0.879108i	−0.898216	+	0.439554i	$0.855137\pi$
$182$	−6.00000	−	2.44949i	−0.444750	−	0.181568i
$183$		0			0
$184$	2.12132	−	3.67423i	0.156386	−	0.270868i
$185$		0			0
$186$		0			0
$187$	−8.87039	+	15.3640i	−0.648667	+	1.12352i
$188$		−	5.91359i		−	0.431293i
$189$		0			0
$190$		0			0
$191$	−7.34847	−	4.24264i	−0.531717	−	0.306987i	0.209999	−	0.977702i	$-0.432654\pi$
$191$	−7.34847	−	4.24264i	−0.531717	−	0.306987i	−0.741715	+	0.670715i	$0.765987\pi$
$192$		0			0
$193$	−8.21449	+	4.74264i	−0.591292	+	0.341383i	−0.765608	−	0.643307i	$-0.777562\pi$
$193$	−8.21449	+	4.74264i	−0.591292	+	0.341383i	0.174316	+	0.984690i	$0.444229\pi$
$194$	−6.77962	+	11.7426i	−0.486748	+	0.843072i
$195$		0			0
$196$	5.00000	+	4.89898i	0.357143	+	0.349927i
$197$	26.4853			1.88700			0.943499	−	0.331375i	$-0.107513\pi$
$197$	26.4853			1.88700			0.943499	+	0.331375i	$0.107513\pi$
$198$		0			0
$199$	−19.9706	+	11.5300i	−1.41568	+	0.817341i	−0.995915	−	0.0902942i	$-0.971219\pi$
$199$	−19.9706	+	11.5300i	−1.41568	+	0.817341i	−0.419761	+	0.907635i	$0.637886\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	18.9853	−	2.59808i	1.33251	−	0.182349i
$204$		0			0
$205$		0			0
$206$	2.74666	+	4.75736i	0.191369	+	0.331461i
$207$		0			0
$208$	1.22474	−	2.12132i	0.0849208	−	0.147087i
$209$	17.7408			1.22716
$210$		0			0
$211$	−0.242641			−0.0167041			−0.00835204	−	0.999965i	$-0.502659\pi$
$211$	−0.242641			−0.0167041			−0.00835204	+	0.999965i	$0.502659\pi$
$212$	−3.62132	+	6.27231i	−0.248713	+	0.430784i
$213$		0			0
$214$	5.74264	+	9.94655i	0.392559	+	0.679932i
$215$		0			0
$216$		0			0
$217$	−14.7224	−	18.9853i	−0.999424	−	1.28880i
$218$	18.4853			1.25198
$219$		0			0
$220$		0			0
$221$	12.5446	−	7.24264i	0.843843	−	0.487193i
$222$		0			0
$223$	2.15232			0.144130			0.0720649	−	0.997400i	$-0.477041\pi$
$223$	2.15232			0.144130			0.0720649	+	0.997400i	$0.477041\pi$
$224$	−2.09077	+	1.62132i	−0.139695	+	0.108329i
$225$		0			0
$226$	4.24264	−	7.34847i	0.282216	−	0.488813i
$227$	13.5000	−	7.79423i	0.896026	−	0.517321i	0.0201176	−	0.999798i	$-0.493596\pi$
$227$	13.5000	−	7.79423i	0.896026	−	0.517321i	0.875909	+	0.482476i	$0.160263\pi$
$228$		0			0
$229$	12.0000	+	6.92820i	0.792982	+	0.457829i	0.841011	−	0.541017i	$-0.181961\pi$
$229$	12.0000	+	6.92820i	0.792982	+	0.457829i	−0.0480291	+	0.998846i	$0.515294\pi$
$230$		0			0
$231$		0			0
$232$			7.24264i			0.475503i
$233$	−9.36396	+	16.2189i	−0.613453	+	1.06253i	0.377200	+	0.926132i	$0.376887\pi$
$233$	−9.36396	+	16.2189i	−0.613453	+	1.06253i	−0.990654	+	0.136401i	$0.956446\pi$
$234$		0			0
$235$		0			0
$236$	4.03295	−	6.98528i	0.262523	−	0.454703i
$237$		0			0
$238$	−15.5014	+	2.12132i	−1.00481	+	0.137505i
$239$		−	12.7279i		−	0.823301i	−0.911342	−	0.411650i	$-0.864952\pi$
$239$		−	12.7279i		−	0.823301i	0.911342	−	0.411650i	$-0.135048\pi$
$240$		0			0
$241$	6.25736	−	3.61269i	0.403072	−	0.232714i	−0.284737	−	0.958606i	$-0.591906\pi$
$241$	6.25736	−	3.61269i	0.403072	−	0.232714i	0.687809	+	0.725892i	$0.258573\pi$
$242$	1.00000	+	1.73205i	0.0642824	+	0.111340i
$243$		0			0
$244$		−	1.01461i		−	0.0649539i
$245$		0			0
$246$		0			0
$247$	−12.5446	−	7.24264i	−0.798195	−	0.460838i
$248$	7.86396	−	4.54026i	0.499362	−	0.288307i
$249$		0			0
$250$		0			0
$251$	27.4156			1.73046			0.865230	−	0.501375i	$-0.167172\pi$
$251$	27.4156			1.73046			0.865230	+	0.501375i	$0.167172\pi$
$252$		0			0
$253$			12.7279i			0.800198i
$254$	2.80821	+	1.62132i	0.176203	+	0.101731i
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−3.72792	−	2.15232i	−0.232541	−	0.134258i	0.379203	−	0.925314i	$-0.376198\pi$
$257$	−3.72792	−	2.15232i	−0.232541	−	0.134258i	−0.611744	+	0.791056i	$0.709532\pi$
$258$		0			0
$259$	−0.242641	+	0.594346i	−0.0150770	+	0.0369309i
$260$		0			0
$261$		0			0
$262$	−2.59808	−	4.50000i	−0.160510	−	0.278011i
$263$	7.60660	+	13.1750i	0.469043	+	0.812407i	0.999374	−	0.0353843i	$-0.0112655\pi$
$263$	7.60660	+	13.1750i	0.469043	+	0.812407i	−0.530331	+	0.847791i	$0.677932\pi$
$264$		0			0
$265$		0			0
$266$	9.58783	+	12.3640i	0.587867	+	0.758083i
$267$		0			0
$268$	8.66025	+	5.00000i	0.529009	+	0.305424i
$269$	−6.98975	−	12.1066i	−0.426173	−	0.738153i	0.570357	−	0.821397i	$-0.306805\pi$
$269$	−6.98975	−	12.1066i	−0.426173	−	0.738153i	−0.996529	+	0.0832447i	$0.973472\pi$
$270$		0			0
$271$	−5.37868	−	3.10538i	−0.326732	−	0.188639i	0.327658	−	0.944797i	$-0.393741\pi$
$271$	−5.37868	−	3.10538i	−0.326732	−	0.188639i	−0.654389	+	0.756158i	$0.727074\pi$
$272$		−	5.91359i		−	0.358564i
$273$		0			0
$274$	2.48528			0.150141
$275$		0			0
$276$		0			0
$277$	11.2328	−	6.48528i	0.674916	−	0.389663i	−0.123021	−	0.992404i	$-0.539258\pi$
$277$	11.2328	−	6.48528i	0.674916	−	0.389663i	0.797937	+	0.602741i	$0.205925\pi$
$278$	0.514719	+	0.297173i	0.0308708	+	0.0178232i
$279$		0			0
$280$		0			0
$281$			6.00000i			0.357930i	0.983855	+	0.178965i	$0.0572749\pi$
$281$			6.00000i			0.357930i	−0.983855	+	0.178965i	$0.942725\pi$
$282$		0			0
$283$	10.6024	+	18.3640i	0.630250	+	1.09162i	0.987501	+	0.157616i	$0.0503807\pi$
$283$	10.6024	+	18.3640i	0.630250	+	1.09162i	−0.357251	+	0.934008i	$0.616286\pi$
$284$	−1.52192	+	0.878680i	−0.0903092	+	0.0521400i
$285$		0			0
$286$			7.34847i			0.434524i
$287$	−4.24264	−	31.0028i	−0.250435	−	1.83004i
$288$		0			0
$289$	8.98528	−	15.5630i	0.528546	−	0.915468i
$290$		0			0
$291$		0			0
$292$	0.717439	−	1.24264i	0.0419849	−	0.0727200i
$293$		−	0.717439i		−	0.0419132i	−0.999780	−	0.0209566i	$-0.993329\pi$
$293$		−	0.717439i		−	0.0419132i	0.999780	−	0.0209566i	$-0.00667119\pi$
$294$		0			0
$295$		0			0
$296$	−0.210133	−	0.121320i	−0.0122137	−	0.00705160i
$297$		0			0
$298$	−3.04384	+	1.75736i	−0.176325	+	0.101801i
$299$	5.19615	−	9.00000i	0.300501	−	0.520483i
$300$		0			0
$301$	−0.636039	+	0.0870399i	−0.0366607	+	0.00501690i
$302$	−5.24264			−0.301680
$303$		0			0
$304$	−5.12132	+	2.95680i	−0.293728	+	0.169584i
$305$		0			0
$306$		0			0
$307$	9.97204			0.569134			0.284567	−	0.958656i	$-0.408150\pi$
$307$	9.97204			0.569134			0.284567	+	0.958656i	$0.408150\pi$
$308$	3.00000	−	7.34847i	0.170941	−	0.418718i
$309$		0			0
$310$		0			0
$311$	4.47871	+	7.75736i	0.253965	+	0.439879i	0.964614	−	0.263667i	$-0.0849320\pi$
$311$	4.47871	+	7.75736i	0.253965	+	0.439879i	−0.710649	+	0.703547i	$0.751599\pi$
$312$		0			0
$313$	9.22911	−	15.9853i	0.521660	−	0.903542i	−0.478023	−	0.878348i	$-0.658646\pi$
$313$	9.22911	−	15.9853i	0.521660	−	0.903542i	0.999683	−	0.0251940i	$-0.00802035\pi$
$314$	14.6969			0.829396
$315$		0			0
$316$	2.75736			0.155114
$317$	0.621320	−	1.07616i	0.0348968	−	0.0604431i	−0.848050	−	0.529917i	$-0.822223\pi$
$317$	0.621320	−	1.07616i	0.0348968	−	0.0604431i	0.882946	+	0.469474i	$0.155556\pi$
$318$		0			0
$319$	−10.8640	−	18.8169i	−0.608265	−	1.05355i
$320$		0			0
$321$		0			0
$322$	−8.87039	+	6.87868i	−0.494327	+	0.383334i
$323$	−34.9706			−1.94581
$324$		0			0
$325$		0			0
$326$	−1.94218	+	1.12132i	−0.107568	+	0.0621042i
$327$		0			0
$328$	11.8272			0.653047
$329$	−5.91359	+	14.4853i	−0.326027	+	0.798599i
$330$		0			0
$331$	16.7279	−	28.9736i	0.919450	−	1.59253i	0.119197	−	0.992871i	$-0.461968\pi$
$331$	16.7279	−	28.9736i	0.919450	−	1.59253i	0.800253	−	0.599663i	$-0.204699\pi$
$332$	5.74264	−	3.31552i	0.315168	−	0.181963i
$333$		0			0
$334$	13.9706	+	8.06591i	0.764435	+	0.441347i
$335$		0			0
$336$		0			0
$337$		−	5.00000i		−	0.272367i	−0.990684	−	0.136184i	$-0.956516\pi$
$337$		−	5.00000i		−	0.272367i	0.990684	−	0.136184i	$-0.0434837\pi$
$338$	−3.50000	+	6.06218i	−0.190375	+	0.329739i
$339$		0			0
$340$		0			0
$341$	−13.6208	+	23.5919i	−0.737607	+	1.27757i
$342$		0			0
$343$	−7.34847	−	17.0000i	−0.396780	−	0.917914i
$344$		−	0.242641i		−	0.0130823i
$345$		0			0
$346$	−18.0000	+	10.3923i	−0.967686	+	0.558694i
$347$	−1.24264	−	2.15232i	−0.0667084	−	0.115542i	0.830742	−	0.556657i	$-0.187916\pi$
$347$	−1.24264	−	2.15232i	−0.0667084	−	0.115542i	−0.897451	+	0.441115i	$0.854583\pi$
$348$		0			0
$349$			2.27541i			0.121800i	0.998144	+	0.0608999i	$0.0193971\pi$
$349$			2.27541i			0.121800i	−0.998144	+	0.0608999i	$0.980603\pi$
$350$		0			0
$351$		0			0
$352$	2.59808	+	1.50000i	0.138478	+	0.0799503i
$353$	7.75736	−	4.47871i	0.412883	−	0.238378i	−0.279145	−	0.960249i	$-0.590051\pi$
$353$	7.75736	−	4.47871i	0.412883	−	0.238378i	0.692028	+	0.721871i	$0.256718\pi$
$354$		0			0
$355$		0			0
$356$	−10.3923			−0.550791
$357$		0			0
$358$		−	26.4853i		−	1.39979i
$359$	−15.5885	−	9.00000i	−0.822727	−	0.475002i	0.0286287	−	0.999590i	$-0.490886\pi$
$359$	−15.5885	−	9.00000i	−0.822727	−	0.475002i	−0.851356	+	0.524588i	$0.824219\pi$
$360$		0			0
$361$	7.98528	+	13.8309i	0.420278	+	0.727943i
$362$	10.2426	+	5.91359i	0.538341	+	0.310811i
$363$		0			0
$364$	−5.12132	+	3.97141i	−0.268430	+	0.208158i
$365$		0			0
$366$		0			0
$367$	−7.70719	−	13.3492i	−0.402312	−	0.696825i	0.591693	−	0.806164i	$-0.298460\pi$
$367$	−7.70719	−	13.3492i	−0.402312	−	0.696825i	−0.994005	+	0.109339i	$0.965127\pi$
$368$	−2.12132	−	3.67423i	−0.110581	−	0.191533i
$369$		0			0
$370$		0			0
$371$	15.1427	−	11.7426i	0.786170	−	0.609648i
$372$		0			0
$373$	−25.5095	−	14.7279i	−1.32083	−	0.762583i	−0.336971	−	0.941515i	$-0.609402\pi$
$373$	−25.5095	−	14.7279i	−1.32083	−	0.762583i	−0.983861	+	0.178932i	$0.942736\pi$
$374$	8.87039	+	15.3640i	0.458677	+	0.794452i
$375$		0			0
$376$	−5.12132	−	2.95680i	−0.264112	−	0.152485i
$377$			17.7408i			0.913696i
$378$		0			0
$379$	−12.4853			−0.641326			−0.320663	−	0.947193i	$-0.603906\pi$
$379$	−12.4853			−0.641326			−0.320663	+	0.947193i	$0.603906\pi$
$380$		0			0
$381$		0			0
$382$	−7.34847	+	4.24264i	−0.375980	+	0.217072i
$383$	−19.2426	−	11.1097i	−0.983253	−	0.567681i	−0.0800023	−	0.996795i	$-0.525493\pi$
$383$	−19.2426	−	11.1097i	−0.983253	−	0.567681i	−0.903251	+	0.429113i	$0.858826\pi$
$384$		0			0
$385$		0			0
$386$			9.48528i			0.482788i
$387$		0			0
$388$	6.77962	+	11.7426i	0.344183	+	0.596142i
$389$	−27.2416	+	15.7279i	−1.38120	+	0.797437i	−0.992302	−	0.123843i	$-0.960478\pi$
$389$	−27.2416	+	15.7279i	−1.38120	+	0.797437i	−0.388900	+	0.921280i	$0.627145\pi$
$390$		0			0
$391$		−	25.0892i		−	1.26882i
$392$	6.74264	−	1.88064i	0.340555	−	0.0949865i
$393$		0			0
$394$	13.2426	−	22.9369i	0.667155	−	1.15555i
$395$		0			0
$396$		0			0
$397$	−6.92820	+	12.0000i	−0.347717	+	0.602263i	−0.985843	−	0.167668i	$-0.946376\pi$
$397$	−6.92820	+	12.0000i	−0.347717	+	0.602263i	0.638127	+	0.769931i	$0.279710\pi$
$398$			23.0600i			1.15589i
$399$		0			0
$400$		0			0
$401$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$401$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$402$		0			0
$403$	19.2627	−	11.1213i	0.959543	−	0.553992i
$404$		0			0
$405$		0			0
$406$	7.24264	−	17.7408i	0.359446	−	0.880460i
$407$	0.727922			0.0360818
$408$		0			0
$409$	−12.9853	+	7.49706i	−0.642081	+	0.370706i	−0.785416	−	0.618969i	$-0.787551\pi$
$409$	−12.9853	+	7.49706i	−0.642081	+	0.370706i	0.143335	+	0.989674i	$0.454217\pi$
$410$		0			0
$411$		0			0
$412$	5.49333			0.270637
$413$	−16.8640	+	13.0774i	−0.829821	+	0.643498i
$414$		0			0
$415$		0			0
$416$	−1.22474	−	2.12132i	−0.0600481	−	0.104006i
$417$		0			0
$418$	8.87039	−	15.3640i	0.433865	−	0.751476i
$419$	23.6544			1.15559			0.577796	−	0.816181i	$-0.303913\pi$
$419$	23.6544			1.15559			0.577796	+	0.816181i	$0.303913\pi$
$420$		0			0
$421$	−14.2426			−0.694144			−0.347072	−	0.937839i	$-0.612824\pi$
$421$	−14.2426			−0.694144			−0.347072	+	0.937839i	$0.612824\pi$
$422$	−0.121320	+	0.210133i	−0.00590578	+	0.0102291i
$423$		0			0
$424$	3.62132	+	6.27231i	0.175867	+	0.304610i
$425$		0			0
$426$		0			0
$427$	−1.01461	+	2.48528i	−0.0491005	+	0.120271i
$428$	11.4853			0.555162
$429$		0			0
$430$		0			0
$431$	3.04384	−	1.75736i	0.146616	−	0.0846490i	−0.424897	−	0.905242i	$-0.639690\pi$
$431$	3.04384	−	1.75736i	0.146616	−	0.0846490i	0.571514	+	0.820593i	$0.306356\pi$
$432$		0			0
$433$	−3.46410			−0.166474			−0.0832370	−	0.996530i	$-0.526526\pi$
$433$	−3.46410			−0.166474			−0.0832370	+	0.996530i	$0.526526\pi$
$434$	−23.8030	+	3.25736i	−1.14258	+	0.156358i
$435$		0			0
$436$	9.24264	−	16.0087i	0.442642	−	0.766679i
$437$	−21.7279	+	12.5446i	−1.03939	+	0.600091i
$438$		0			0
$439$	14.5919	+	8.42463i	0.696433	+	0.402086i	0.806017	−	0.591892i	$-0.201619\pi$
$439$	14.5919	+	8.42463i	0.696433	+	0.402086i	−0.109585	+	0.993977i	$0.534952\pi$
$440$		0			0
$441$		0			0
$442$		−	14.4853i		−	0.688995i
$443$	8.22792	−	14.2512i	0.390920	−	0.677094i	−0.601651	−	0.798759i	$-0.705490\pi$
$443$	8.22792	−	14.2512i	0.390920	−	0.677094i	0.992571	+	0.121665i	$0.0388234\pi$
$444$		0			0
$445$		0			0
$446$	1.07616	−	1.86396i	0.0509576	−	0.0882611i
$447$		0			0
$448$	0.358719	+	2.62132i	0.0169479	+	0.123846i
$449$			1.75736i			0.0829349i	0.999140	+	0.0414675i	$0.0132033\pi$
$449$			1.75736i			0.0829349i	−0.999140	+	0.0414675i	$0.986797\pi$
$450$		0			0
$451$	−30.7279	+	17.7408i	−1.44692	+	0.835380i
$452$	−4.24264	−	7.34847i	−0.199557	−	0.345643i
$453$		0			0
$454$		−	15.5885i		−	0.731603i
$455$		0			0
$456$		0			0
$457$	19.9186	+	11.5000i	0.931752	+	0.537947i	0.887365	−	0.461067i	$-0.152533\pi$
$457$	19.9186	+	11.5000i	0.931752	+	0.537947i	0.0443868	+	0.999014i	$0.485867\pi$
$458$	12.0000	−	6.92820i	0.560723	−	0.323734i
$459$		0			0
$460$		0			0
$461$	−32.6118			−1.51888			−0.759441	−	0.650576i	$-0.774528\pi$
$461$	−32.6118			−1.51888			−0.759441	+	0.650576i	$0.774528\pi$
$462$		0			0
$463$			29.4558i			1.36893i	0.729046	+	0.684465i	$0.239964\pi$
$463$			29.4558i			1.36893i	−0.729046	+	0.684465i	$0.760036\pi$
$464$	6.27231	+	3.62132i	0.291185	+	0.168116i
$465$		0			0
$466$	9.36396	+	16.2189i	0.433777	+	0.751324i
$467$	−34.4558	−	19.8931i	−1.59443	−	0.920542i	−0.992534	−	0.121965i	$-0.961080\pi$
$467$	−34.4558	−	19.8931i	−1.59443	−	0.920542i	−0.601892	−	0.798578i	$-0.705586\pi$
$468$		0			0
$469$	−16.2132	−	20.9077i	−0.748656	−	0.965428i
$470$		0			0
$471$		0			0
$472$	−4.03295	−	6.98528i	−0.185632	−	0.321524i
$473$	0.363961	+	0.630399i	0.0167349	+	0.0289858i
$474$		0			0
$475$		0			0
$476$	−5.91359	+	14.4853i	−0.271049	+	0.663932i
$477$		0			0
$478$	−11.0227	−	6.36396i	−0.504167	−	0.291081i
$479$	6.00063	+	10.3934i	0.274176	+	0.474886i	0.969927	−	0.243397i	$-0.0782616\pi$
$479$	6.00063	+	10.3934i	0.274176	+	0.474886i	−0.695751	+	0.718283i	$0.744928\pi$
$480$		0			0
$481$	−0.514719	−	0.297173i	−0.0234691	−	0.0135499i
$482$		−	7.22538i		−	0.329107i
$483$		0			0
$484$	2.00000			0.0909091
$485$		0			0
$486$		0			0
$487$	−12.3090	+	7.10660i	−0.557774	+	0.322031i	−0.752251	−	0.658876i	$-0.771032\pi$
$487$	−12.3090	+	7.10660i	−0.557774	+	0.322031i	0.194478	+	0.980907i	$0.437699\pi$
$488$	−0.878680	−	0.507306i	−0.0397760	−	0.0229647i
$489$		0			0
$490$		0			0
$491$		−	13.9706i		−	0.630483i	−0.949012	−	0.315241i	$-0.897915\pi$
$491$		−	13.9706i		−	0.630483i	0.949012	−	0.315241i	$-0.102085\pi$
$492$		0			0
$493$	21.4150	+	37.0919i	0.964483	+	1.67053i
$494$	−12.5446	+	7.24264i	−0.564409	+	0.325862i
$495$		0			0
$496$		−	9.08052i		−	0.407727i
$497$	4.60660	−	0.630399i	0.206634	−	0.0282773i
$498$		0			0
$499$	15.9706	−	27.6618i	0.714941	−	1.23831i	−0.248042	−	0.968749i	$-0.579787\pi$
$499$	15.9706	−	27.6618i	0.714941	−	1.23831i	0.962982	−	0.269564i	$-0.0868796\pi$
$500$		0			0
$501$		0			0
$502$	13.7078	−	23.7426i	0.611810	−	1.05969i
$503$		−	31.0028i		−	1.38235i	−0.722688	−	0.691174i	$-0.757094\pi$
$503$		−	31.0028i		−	1.38235i	0.722688	−	0.691174i	$-0.242906\pi$
$504$		0			0
$505$		0			0
$506$	11.0227	+	6.36396i	0.490019	+	0.282913i
$507$		0			0
$508$	2.80821	−	1.62132i	0.124594	−	0.0719345i
$509$	8.59871	−	14.8934i	0.381131	−	0.660138i	−0.610093	−	0.792330i	$-0.708868\pi$
$509$	8.59871	−	14.8934i	0.381131	−	0.660138i	0.991224	+	0.132191i	$0.0422013\pi$
$510$		0			0
$511$	−3.00000	+	2.32640i	−0.132712	+	0.102914i
$512$	−1.00000			−0.0441942
$513$		0			0
$514$	−3.72792	+	2.15232i	−0.164432	+	0.0949346i
$515$		0			0
$516$		0			0
$517$	17.7408			0.780238
$518$	0.393398	+	0.507306i	0.0172849	+	0.0222897i
$519$		0			0
$520$		0			0
$521$	16.9363	+	29.3345i	0.741993	+	1.28517i	0.951587	+	0.307380i	$0.0994524\pi$
$521$	16.9363	+	29.3345i	0.741993	+	1.28517i	−0.209594	+	0.977788i	$0.567214\pi$
$522$		0			0
$523$	3.37706	−	5.84924i	0.147669	−	0.255770i	−0.782697	−	0.622403i	$-0.786156\pi$
$523$	3.37706	−	5.84924i	0.147669	−	0.255770i	0.930365	+	0.366634i	$0.119490\pi$
$524$	−5.19615			−0.226995
$525$		0			0
$526$	15.2132			0.663327
$527$	26.8492	−	46.5043i	1.16957	−	2.02576i
$528$		0			0
$529$	2.50000	+	4.33013i	0.108696	+	0.188266i
$530$		0			0
$531$		0			0
$532$	15.5014	−	2.12132i	0.672072	−	0.0919709i
$533$	28.9706			1.25485
$534$		0			0
$535$		0			0
$536$	8.66025	−	5.00000i	0.374066	−	0.215967i
$537$		0			0
$538$	−13.9795			−0.602699
$539$	−14.6969	+	15.0000i	−0.633042	+	0.646096i
$540$		0			0
$541$	−7.36396	+	12.7548i	−0.316601	+	0.548370i	−0.979777	−	0.200094i	$-0.935875\pi$
$541$	−7.36396	+	12.7548i	−0.316601	+	0.548370i	0.663175	+	0.748464i	$0.269208\pi$
$542$	−5.37868	+	3.10538i	−0.231034	+	0.133388i
$543$		0			0
$544$	−5.12132	−	2.95680i	−0.219575	−	0.126772i
$545$		0			0
$546$		0			0
$547$		−	39.6985i		−	1.69738i	−0.528887	−	0.848692i	$-0.677390\pi$
$547$		−	39.6985i		−	1.69738i	0.528887	−	0.848692i	$-0.322610\pi$
$548$	1.24264	−	2.15232i	0.0530830	−	0.0919424i
$549$		0			0
$550$		0			0
$551$	21.4150	−	37.0919i	0.912310	−	1.58017i
$552$		0			0
$553$	−6.75412	−	2.75736i	−0.287215	−	0.117255i
$554$		−	12.9706i		−	0.551066i
$555$		0			0
$556$	0.514719	−	0.297173i	0.0218289	−	0.0126029i
$557$	−4.86396	−	8.42463i	−0.206093	−	0.356963i	0.744388	−	0.667748i	$-0.232741\pi$
$557$	−4.86396	−	8.42463i	−0.206093	−	0.356963i	−0.950480	+	0.310785i	$0.899408\pi$
$558$		0			0
$559$		−	0.594346i		−	0.0251382i
$560$		0			0
$561$		0			0
$562$	5.19615	+	3.00000i	0.219186	+	0.126547i
$563$	−29.9558	+	17.2950i	−1.26249	+	0.728898i	−0.973555	−	0.228451i	$-0.926634\pi$
$563$	−29.9558	+	17.2950i	−1.26249	+	0.728898i	−0.288933	+	0.957349i	$0.593300\pi$
$564$		0			0
$565$		0			0
$566$	21.2049			0.891307
$567$		0			0
$568$			1.75736i			0.0737372i
$569$	−8.87039	−	5.12132i	−0.371866	−	0.214697i	0.302407	−	0.953179i	$-0.402210\pi$
$569$	−8.87039	−	5.12132i	−0.371866	−	0.214697i	−0.674273	+	0.738482i	$0.735543\pi$
$570$		0			0
$571$	−4.36396	−	7.55860i	−0.182626	−	0.316318i	0.760148	−	0.649750i	$-0.225126\pi$
$571$	−4.36396	−	7.55860i	−0.182626	−	0.316318i	−0.942774	+	0.333432i	$0.891793\pi$
$572$	6.36396	+	3.67423i	0.266091	+	0.153627i
$573$		0			0
$574$	−28.9706	−	11.8272i	−1.20921	−	0.493657i
$575$		0			0
$576$		0			0
$577$	5.34474	+	9.25736i	0.222504	+	0.385389i	0.955568	−	0.294771i	$-0.0952435\pi$
$577$	5.34474	+	9.25736i	0.222504	+	0.385389i	−0.733063	+	0.680160i	$0.761910\pi$
$578$	−8.98528	−	15.5630i	−0.373738	−	0.647334i
$579$		0			0
$580$		0			0
$581$	−17.3821	+	2.37868i	−0.721129	+	0.0986843i
$582$		0			0
$583$	−18.8169	−	10.8640i	−0.779318	−	0.449939i
$584$	−0.717439	−	1.24264i	−0.0296878	−	0.0514208i
$585$		0			0
$586$	−0.621320	−	0.358719i	−0.0256665	−	0.0148186i
$587$		−	5.19615i		−	0.214468i	−0.994234	−	0.107234i	$-0.965801\pi$
$587$		−	5.19615i		−	0.214468i	0.994234	−	0.107234i	$-0.0341994\pi$
$588$		0			0
$589$	−53.6985			−2.21261
$590$		0			0
$591$		0			0
$592$	−0.210133	+	0.121320i	−0.00863641	+	0.00498624i
$593$	−20.3345	−	11.7401i	−0.835039	−	0.482110i	0.0205360	−	0.999789i	$-0.493463\pi$
$593$	−20.3345	−	11.7401i	−0.835039	−	0.482110i	−0.855575	+	0.517679i	$0.826796\pi$
$594$		0			0
$595$		0			0
$596$			3.51472i			0.143968i
$597$		0			0
$598$	−5.19615	−	9.00000i	−0.212486	−	0.368037i
$599$	−6.45695	+	3.72792i	−0.263824	+	0.152319i	−0.626078	−	0.779761i	$-0.715341\pi$
$599$	−6.45695	+	3.72792i	−0.263824	+	0.152319i	0.362254	+	0.932079i	$0.382007\pi$
$600$		0			0
$601$			23.3572i			0.952760i	0.879240	+	0.476380i	$0.158051\pi$
$601$			23.3572i			0.952760i	−0.879240	+	0.476380i	$0.841949\pi$
$602$	−0.242641	+	0.594346i	−0.00988930	+	0.0242237i
$603$		0			0
$604$	−2.62132	+	4.54026i	−0.106660	+	0.184741i
$605$		0			0
$606$		0			0
$607$	10.0336	−	17.3787i	0.407251	−	0.705379i	−0.587330	−	0.809348i	$-0.699821\pi$
$607$	10.0336	−	17.3787i	0.407251	−	0.705379i	0.994581	+	0.103969i	$0.0331542\pi$
$608$			5.91359i			0.239828i
$609$		0			0
$610$		0			0
$611$	−12.5446	−	7.24264i	−0.507501	−	0.293006i
$612$		0			0
$613$	32.2276	−	18.6066i	1.30166	−	0.751514i	0.320971	−	0.947089i	$-0.395991\pi$
$613$	32.2276	−	18.6066i	1.30166	−	0.751514i	0.980689	+	0.195575i	$0.0626575\pi$
$614$	4.98602	−	8.63604i	0.201219	−	0.348522i
$615$		0			0
$616$	−4.86396	−	6.27231i	−0.195975	−	0.252719i
$617$	17.6985			0.712514			0.356257	−	0.934388i	$-0.384053\pi$
$617$	17.6985			0.712514			0.356257	+	0.934388i	$0.384053\pi$
$618$		0			0
$619$	−5.33452	+	3.07989i	−0.214413	+	0.123791i	−0.603360	−	0.797469i	$-0.706172\pi$
$619$	−5.33452	+	3.07989i	−0.214413	+	0.123791i	0.388948	+	0.921260i	$0.372839\pi$
$620$		0			0
$621$		0			0
$622$	8.95743			0.359160
$623$	25.4558	+	10.3923i	1.01987	+	0.416359i
$624$		0			0
$625$		0			0
$626$	−9.22911	−	15.9853i	−0.368869	−	0.638900i
$627$		0			0
$628$	7.34847	−	12.7279i	0.293236	−	0.507899i
$629$	−1.43488			−0.0572123
$630$		0			0
$631$	24.7574			0.985575			0.492787	−	0.870150i	$-0.335978\pi$
$631$	24.7574			0.985575			0.492787	+	0.870150i	$0.335978\pi$
$632$	1.37868	−	2.38794i	0.0548409	−	0.0949873i
$633$		0			0
$634$	−0.621320	−	1.07616i	−0.0246758	−	0.0427397i
$635$		0			0
$636$		0			0
$637$	16.5160	−	4.60660i	0.654389	−	0.182520i
$638$	−21.7279			−0.860217
$639$		0			0
$640$		0			0
$641$	15.3273	−	8.84924i	0.605393	−	0.349524i	−0.165767	−	0.986165i	$-0.553010\pi$
$641$	15.3273	−	8.84924i	0.605393	−	0.349524i	0.771160	+	0.636641i	$0.219677\pi$
$642$		0			0
$643$	32.0174			1.26264			0.631322	−	0.775520i	$-0.282512\pi$
$643$	32.0174			1.26264			0.631322	+	0.775520i	$0.282512\pi$
$644$	1.52192	+	11.1213i	0.0599720	+	0.438241i
$645$		0			0
$646$	−17.4853	+	30.2854i	−0.687949	+	1.19156i
$647$	−28.0919	+	16.2189i	−1.10441	+	0.637629i	−0.937375	−	0.348323i	$-0.886751\pi$
$647$	−28.0919	+	16.2189i	−1.10441	+	0.637629i	−0.167031	+	0.985952i	$0.553418\pi$
$648$		0			0
$649$	20.9558	+	12.0989i	0.822589	+	0.474922i
$650$		0			0
$651$		0			0
$652$			2.24264i			0.0878286i
$653$	−9.62132	+	16.6646i	−0.376511	+	0.652137i	−0.990552	−	0.137138i	$-0.956210\pi$
$653$	−9.62132	+	16.6646i	−0.376511	+	0.652137i	0.614041	+	0.789274i	$0.289543\pi$
$654$		0			0
$655$		0			0
$656$	5.91359	−	10.2426i	0.230887	−	0.399908i
$657$		0			0
$658$	9.58783	+	12.3640i	0.373772	+	0.481997i
$659$		−	6.00000i		−	0.233727i	−0.993148	−	0.116863i	$-0.962716\pi$
$659$		−	6.00000i		−	0.233727i	0.993148	−	0.116863i	$-0.0372840\pi$
$660$		0			0
$661$	30.8787	−	17.8278i	1.20104	−	0.693422i	0.240255	−	0.970710i	$-0.422769\pi$
$661$	30.8787	−	17.8278i	1.20104	−	0.693422i	0.960787	+	0.277288i	$0.0894357\pi$
$662$	−16.7279	−	28.9736i	−0.650149	−	1.12609i
$663$		0			0
$664$		−	6.63103i		−	0.257334i
$665$		0			0
$666$		0			0
$667$	26.6112	+	15.3640i	1.03039	+	0.594895i
$668$	13.9706	−	8.06591i	0.540537	−	0.312079i
$669$		0			0
$670$		0			0
$671$	3.04384			0.117506
$672$		0			0
$673$		−	17.9706i		−	0.692714i	−0.938103	−	0.346357i	$-0.887419\pi$
$673$		−	17.9706i		−	0.692714i	0.938103	−	0.346357i	$-0.112581\pi$
$674$	−4.33013	−	2.50000i	−0.166790	−	0.0962964i
$675$		0			0
$676$	3.50000	+	6.06218i	0.134615	+	0.233161i
$677$	−1.86396	−	1.07616i	−0.0716378	−	0.0413601i	0.463753	−	0.885964i	$-0.346502\pi$
$677$	−1.86396	−	1.07616i	−0.0716378	−	0.0413601i	−0.535391	+	0.844604i	$0.679836\pi$
$678$		0			0
$679$	−4.86396	−	35.5431i	−0.186662	−	1.36402i
$680$		0			0
$681$		0			0
$682$	13.6208	+	23.5919i	0.521567	+	0.903380i
$683$	−3.98528	−	6.90271i	−0.152493	−	0.264125i	0.779651	−	0.626215i	$-0.215397\pi$
$683$	−3.98528	−	6.90271i	−0.152493	−	0.264125i	−0.932143	+	0.362090i	$0.882063\pi$
$684$		0			0
$685$		0			0
$686$	−18.3967	−	2.13604i	−0.702388	−	0.0815543i
$687$		0			0
$688$	−0.210133	−	0.121320i	−0.00801125	−	0.00462529i
$689$	8.87039	+	15.3640i	0.337935	+	0.585320i
$690$		0			0
$691$	24.7279	+	14.2767i	0.940694	+	0.543110i	0.890178	−	0.455613i	$-0.150580\pi$
$691$	24.7279	+	14.2767i	0.940694	+	0.543110i	0.0505165	+	0.998723i	$0.483913\pi$
$692$			20.7846i			0.790112i
$693$		0			0
$694$	−2.48528			−0.0943400
$695$		0			0
$696$		0			0
$697$	60.5708	−	34.9706i	2.29428	−	1.32460i
$698$	1.97056	+	1.13770i	0.0745869	+	0.0430628i
$699$		0			0
$700$		0			0
$701$			20.6985i			0.781771i	0.920439	+	0.390885i	$0.127831\pi$
$701$			20.6985i			0.781771i	−0.920439	+	0.390885i	$0.872169\pi$
$702$		0			0
$703$	0.717439	+	1.24264i	0.0270587	+	0.0468671i
$704$	2.59808	−	1.50000i	0.0979187	−	0.0565334i
$705$		0			0
$706$		−	8.95743i		−	0.337117i
$707$		0			0
$708$		0			0
$709$	13.4853	−	23.3572i	0.506450	−	0.877198i	−0.493522	−	0.869733i	$-0.664291\pi$
$709$	13.4853	−	23.3572i	0.506450	−	0.877198i	0.999972	−	0.00746433i	$-0.00237599\pi$
$710$		0			0
$711$		0			0
$712$	−5.19615	+	9.00000i	−0.194734	+	0.337289i
$713$		−	38.5254i		−	1.44279i
$714$		0			0
$715$		0			0
$716$	−22.9369	−	13.2426i	−0.857193	−	0.494901i
$717$		0			0
$718$	−15.5885	+	9.00000i	−0.581756	+	0.335877i
$719$	−8.06591	+	13.9706i	−0.300808	+	0.521014i	−0.976319	−	0.216335i	$-0.930590\pi$
$719$	−8.06591	+	13.9706i	−0.300808	+	0.521014i	0.675511	+	0.737349i	$0.263923\pi$
$720$		0			0
$721$	−13.4558	−	5.49333i	−0.501122	−	0.204582i
$722$	15.9706			0.594363
$723$		0			0
$724$	10.2426	−	5.91359i	0.380665	−	0.219777i
$725$		0			0
$726$		0			0
$727$	11.7041			0.434081			0.217040	−	0.976163i	$-0.430360\pi$
$727$	11.7041			0.434081			0.217040	+	0.976163i	$0.430360\pi$
$728$	0.878680	+	6.42090i	0.0325660	+	0.237974i
$729$		0			0
$730$		0			0
$731$	−0.717439	−	1.24264i	−0.0265354	−	0.0459607i
$732$		0			0
$733$	2.36245	−	4.09188i	0.0872591	−	0.151137i	−0.819093	−	0.573661i	$-0.805523\pi$
$733$	2.36245	−	4.09188i	0.0872591	−	0.151137i	0.906352	+	0.422524i	$0.138856\pi$
$734$	−15.4144			−0.568955
$735$		0			0
$736$	−4.24264			−0.156386
$737$	−15.0000	+	25.9808i	−0.552532	+	0.957014i
$738$		0			0
$739$	7.72792	+	13.3852i	0.284276	+	0.492381i	0.972433	−	0.233181i	$-0.0749134\pi$
$739$	7.72792	+	13.3852i	0.284276	+	0.492381i	−0.688157	+	0.725562i	$0.741580\pi$
$740$		0			0
$741$		0			0
$742$	−2.59808	−	18.9853i	−0.0953784	−	0.696972i
$743$	38.4853			1.41189			0.705944	−	0.708268i	$-0.250523\pi$
$743$	38.4853			1.41189			0.705944	+	0.708268i	$0.250523\pi$
$744$		0			0
$745$		0			0
$746$	−25.5095	+	14.7279i	−0.933969	+	0.539228i
$747$		0			0
$748$	17.7408			0.648667
$749$	−28.1331	−	11.4853i	−1.02796	−	0.419663i
$750$		0			0
$751$	−17.6213	+	30.5210i	−0.643011	+	1.11373i	0.341746	+	0.939792i	$0.388982\pi$
$751$	−17.6213	+	30.5210i	−0.643011	+	1.11373i	−0.984757	+	0.173936i	$0.944352\pi$
$752$	−5.12132	+	2.95680i	−0.186755	+	0.107823i
$753$		0			0
$754$	15.3640	+	8.87039i	0.559522	+	0.323040i
$755$		0			0
$756$		0			0
$757$		−	33.7574i		−	1.22693i	−0.789721	−	0.613466i	$-0.789775\pi$
$757$		−	33.7574i		−	1.22693i	0.789721	−	0.613466i	$-0.210225\pi$
$758$	−6.24264	+	10.8126i	−0.226743	+	0.392730i
$759$		0			0
$760$		0			0
$761$	14.7840	−	25.6066i	0.535919	−	0.928239i	−0.463199	−	0.886254i	$-0.653299\pi$
$761$	14.7840	−	25.6066i	0.535919	−	0.928239i	0.999118	−	0.0419845i	$-0.0133680\pi$
$762$		0			0
$763$	−38.6485	+	29.9706i	−1.39917	+	1.08501i
$764$			8.48528i			0.306987i
$765$		0			0
$766$	−19.2426	+	11.1097i	−0.695265	+	0.401411i
$767$	−9.87868	−	17.1104i	−0.356698	−	0.617820i
$768$		0			0
$769$		−	9.84895i		−	0.355162i	−0.984106	−	0.177581i	$-0.943173\pi$
$769$		−	9.84895i		−	0.355162i	0.984106	−	0.177581i	$-0.0568272\pi$
$770$		0			0
$771$		0			0
$772$	8.21449	+	4.74264i	0.295646	+	0.170691i
$773$	−13.9706	+	8.06591i	−0.502486	+	0.290111i	−0.729740	−	0.683725i	$-0.760359\pi$
$773$	−13.9706	+	8.06591i	−0.502486	+	0.290111i	0.227253	+	0.973836i	$0.427025\pi$
$774$		0			0
$775$		0			0
$776$	13.5592			0.486748
$777$		0			0
$778$			31.4558i			1.12775i
$779$	−60.5708	−	34.9706i	−2.17017	−	1.25295i
$780$		0			0
$781$	−2.63604	−	4.56575i	−0.0943249	−	0.163376i
$782$	−21.7279	−	12.5446i	−0.776989	−	0.448595i
$783$		0			0
$784$	1.74264	−	6.77962i	0.0622372	−	0.242129i
$785$		0			0
$786$		0			0
$787$	16.0958	+	27.8787i	0.573752	+	0.993768i	0.996176	+	0.0873693i	$0.0278460\pi$
$787$	16.0958	+	27.8787i	0.573752	+	0.993768i	−0.422424	+	0.906398i	$0.638821\pi$
$788$	−13.2426	−	22.9369i	−0.471750	−	0.817094i
$789$		0			0
$790$		0			0
$791$	3.04384	+	22.2426i	0.108226	+	0.790857i
$792$		0			0
$793$	−2.15232	−	1.24264i	−0.0764310	−	0.0441275i
$794$	6.92820	+	12.0000i	0.245873	+	0.425864i
$795$		0			0
$796$	19.9706	+	11.5300i	0.707838	+	0.408670i
$797$		−	6.45695i		−	0.228717i	−0.993440	−	0.114358i	$-0.963519\pi$
$797$		−	6.45695i		−	0.228717i	0.993440	−	0.114358i	$-0.0364812\pi$
$798$		0			0
$799$	−34.9706			−1.23717
$800$		0			0
$801$		0			0
$802$		0			0
$803$	3.72792	+	2.15232i	0.131556	+	0.0759536i
$804$		0			0
$805$		0			0
$806$		−	22.2426i		−	0.783464i
$807$		0			0
$808$		0			0
$809$	−6.08767	+	3.51472i	−0.214031	+	0.123571i	−0.603183	−	0.797602i	$-0.706101\pi$
$809$	−6.08767	+	3.51472i	−0.214031	+	0.123571i	0.389152	+	0.921173i	$0.372768\pi$
$810$		0			0
$811$			31.1769i			1.09477i	0.836881	+	0.547385i	$0.184377\pi$
$811$			31.1769i			1.09477i	−0.836881	+	0.547385i	$0.815623\pi$
$812$	−11.7426	−	15.1427i	−0.412086	−	0.531405i
$813$		0			0
$814$	0.363961	−	0.630399i	0.0127568	−	0.0220955i
$815$		0			0
$816$		0			0
$817$	−0.717439	+	1.24264i	−0.0251000	+	0.0434745i
$818$			14.9941i			0.524257i
$819$		0			0
$820$		0			0
$821$	−35.2969	−	20.3787i	−1.23187	−	0.711221i	−0.264451	−	0.964399i	$-0.585191\pi$
$821$	−35.2969	−	20.3787i	−1.23187	−	0.711221i	−0.967420	+	0.253178i	$0.918524\pi$
$822$		0			0
$823$	−25.9298	+	14.9706i	−0.903855	+	0.521841i	−0.878449	−	0.477836i	$-0.841421\pi$
$823$	−25.9298	+	14.9706i	−0.903855	+	0.521841i	−0.0254062	+	0.999677i	$0.508088\pi$
$824$	2.74666	−	4.75736i	0.0956845	−	0.165730i
$825$		0			0
$826$	2.89340	+	21.1433i	0.100674	+	0.735671i
$827$	−37.9706			−1.32037			−0.660183	−	0.751105i	$-0.729521\pi$
$827$	−37.9706			−1.32037			−0.660183	+	0.751105i	$0.729521\pi$
$828$		0			0
$829$	−11.3345	+	6.54399i	−0.393664	+	0.227282i	−0.683747	−	0.729720i	$-0.739651\pi$
$829$	−11.3345	+	6.54399i	−0.393664	+	0.227282i	0.290082	+	0.957002i	$0.406317\pi$
$830$		0			0
$831$		0			0
$832$	−2.44949			−0.0849208
$833$	28.9706	−	29.5680i	1.00377	−	1.02447i
$834$		0			0
$835$		0			0
$836$	−8.87039	−	15.3640i	−0.306789	−	0.531374i
$837$		0			0
$838$	11.8272	−	20.4853i	0.408563	−	0.707652i
$839$	10.2182			0.352772			0.176386	−	0.984321i	$-0.443559\pi$
$839$	10.2182			0.352772			0.176386	+	0.984321i	$0.443559\pi$
$840$		0			0
$841$	−23.4558			−0.808822
$842$	−7.12132	+	12.3345i	−0.245417	+	0.425075i
$843$		0			0
$844$	0.121320	+	0.210133i	0.00417602	+	0.00723308i
$845$		0			0
$846$		0			0
$847$	−4.89898	−	2.00000i	−0.168331	−	0.0687208i
$848$	7.24264			0.248713
$849$		0			0
$850$		0			0
$851$	−0.891519	+	0.514719i	−0.0305609	+	0.0176443i
$852$		0			0
$853$	36.9164			1.26399			0.631997	−	0.774971i	$-0.282235\pi$
$853$	36.9164			1.26399			0.631997	+	0.774971i	$0.282235\pi$
$854$	1.64501	+	2.12132i	0.0562911	+	0.0725901i
$855$		0			0
$856$	5.74264	−	9.94655i	0.196279	−	0.339966i
$857$	29.3345	−	16.9363i	1.00205	−	0.578533i	0.0931946	−	0.995648i	$-0.470292\pi$
$857$	29.3345	−	16.9363i	1.00205	−	0.578533i	0.908854	+	0.417115i	$0.136959\pi$
$858$		0			0
$859$	−8.12132	−	4.68885i	−0.277096	−	0.159981i	0.355012	−	0.934862i	$-0.384477\pi$
$859$	−8.12132	−	4.68885i	−0.277096	−	0.159981i	−0.632108	+	0.774880i	$0.717810\pi$
$860$		0			0
$861$		0			0
$862$		−	3.51472i		−	0.119712i
$863$	−16.7574	+	29.0246i	−0.570427	+	0.988009i	0.426095	+	0.904679i	$0.359889\pi$
$863$	−16.7574	+	29.0246i	−0.570427	+	0.988009i	−0.996522	+	0.0833303i	$0.973444\pi$
$864$		0			0
$865$		0			0
$866$	−1.73205	+	3.00000i	−0.0588575	+	0.101944i
$867$		0			0
$868$	−9.08052	+	22.2426i	−0.308213	+	0.754964i
$869$			8.27208i			0.280611i
$870$		0			0
$871$	21.2132	−	12.2474i	0.718782	−	0.414989i
$872$	−9.24264	−	16.0087i	−0.312995	−	0.542124i
$873$		0			0
$874$			25.0892i			0.848656i
$875$		0			0
$876$		0			0
$877$	−3.88437	−	2.24264i	−0.131166	−	0.0757286i	0.432981	−	0.901403i	$-0.357462\pi$
$877$	−3.88437	−	2.24264i	−0.131166	−	0.0757286i	−0.564147	+	0.825674i	$0.690795\pi$
$878$	14.5919	−	8.42463i	0.492452	−	0.284317i
$879$		0			0
$880$		0			0
$881$	−19.0016			−0.640179			−0.320090	−	0.947387i	$-0.603713\pi$
$881$	−19.0016			−0.640179			−0.320090	+	0.947387i	$0.603713\pi$
$882$		0			0
$883$		−	41.4558i		−	1.39510i	−0.716536	−	0.697550i	$-0.754273\pi$
$883$		−	41.4558i		−	1.39510i	0.716536	−	0.697550i	$-0.245727\pi$
$884$	−12.5446	−	7.24264i	−0.421921	−	0.243596i
$885$		0			0
$886$	−8.22792	−	14.2512i	−0.276422	−	0.478778i
$887$	−9.15076	−	5.28319i	−0.307252	−	0.177392i	0.338444	−	0.940987i	$-0.390099\pi$
$887$	−9.15076	−	5.28319i	−0.307252	−	0.177392i	−0.645696	+	0.763594i	$0.723433\pi$
$888$		0			0
$889$	−8.50000	+	1.16320i	−0.285081	+	0.0390124i
$890$		0			0
$891$		0			0
$892$	−1.07616	−	1.86396i	−0.0360324	−	0.0624100i
$893$	17.4853	+	30.2854i	0.585123	+	1.01346i
$894$		0			0
$895$		0			0
$896$	2.44949	+	1.00000i	0.0818317	+	0.0334077i
$897$		0			0
$898$	1.52192	+	0.878680i	0.0507871	+	0.0293219i
$899$	32.8835	+	56.9558i	1.09673	+	1.89958i
$900$		0			0
$901$	37.0919	+	21.4150i	1.23571	+	0.713437i
$902$			35.4815i			1.18141i
$903$		0			0
$904$	−8.48528			−0.282216
$905$		0			0
$906$		0			0
$907$	−27.4517	+	15.8492i	−0.911519	+	0.526265i	−0.880919	−	0.473266i	$-0.843075\pi$
$907$	−27.4517	+	15.8492i	−0.911519	+	0.526265i	−0.0305991	+	0.999532i	$0.509742\pi$
$908$	−13.5000	−	7.79423i	−0.448013	−	0.258661i
$909$		0			0
$910$		0			0
$911$		−	6.72792i		−	0.222906i	−0.993770	−	0.111453i	$-0.964450\pi$
$911$		−	6.72792i		−	0.222906i	0.993770	−	0.111453i	$-0.0355505\pi$
$912$		0			0
$913$	9.94655	+	17.2279i	0.329183	+	0.570161i
$914$	19.9186	−	11.5000i	0.658848	−	0.380386i
$915$		0			0
$916$		−	13.8564i		−	0.457829i
$917$	12.7279	+	5.19615i	0.420313	+	0.171592i
$918$		0			0
$919$	18.2426	−	31.5972i	0.601769	−	1.04229i	−0.390784	−	0.920482i	$-0.627796\pi$
$919$	18.2426	−	31.5972i	0.601769	−	1.04229i	0.992553	−	0.121812i	$-0.0388706\pi$
$920$		0			0
$921$		0			0
$922$	−16.3059	+	28.2426i	−0.537006	+	0.930122i
$923$			4.30463i			0.141689i
$924$		0			0
$925$		0			0
$926$	25.5095	+	14.7279i	0.838294	+	0.483990i
$927$		0			0
$928$	6.27231	−	3.62132i	0.205899	−	0.118876i
$929$	−15.5014	+	26.8492i	−0.508585	+	0.880895i	0.491366	+	0.870953i	$0.336498\pi$
$929$	−15.5014	+	26.8492i	−0.508585	+	0.880895i	−0.999951	+	0.00994164i	$0.996835\pi$
$930$		0			0
$931$	−40.0919	−	10.3053i	−1.31396	−	0.337741i
$932$	18.7279			0.613453
$933$		0			0
$934$	−34.4558	+	19.8931i	−1.12743	+	0.650922i
$935$		0			0
$936$		0			0
$937$	35.1844			1.14942			0.574712	−	0.818356i	$-0.305114\pi$
$937$	35.1844			1.14942			0.574712	+	0.818356i	$0.305114\pi$
$938$	−26.2132	+	3.58719i	−0.855891	+	0.117126i
$939$		0			0
$940$		0			0
$941$	−13.7949	−	23.8934i	−0.449700	−	0.778903i	0.548667	−	0.836041i	$-0.315136\pi$
$941$	−13.7949	−	23.8934i	−0.449700	−	0.778903i	−0.998366	+	0.0571387i	$0.981802\pi$
$942$		0			0
$943$	25.0892	−	43.4558i	0.817018	−	1.41512i
$944$	−8.06591			−0.262523
$945$		0			0
$946$	0.727922			0.0236668
$947$	−5.48528	+	9.50079i	−0.178248	+	0.308734i	−0.941280	−	0.337626i	$-0.890376\pi$
$947$	−5.48528	+	9.50079i	−0.178248	+	0.308734i	0.763033	+	0.646360i	$0.223709\pi$
$948$		0			0
$949$	−1.75736	−	3.04384i	−0.0570463	−	0.0988071i
$950$		0			0
$951$		0			0
$952$	9.58783	+	12.3640i	0.310743	+	0.400718i
$953$	−17.6985			−0.573310			−0.286655	−	0.958034i	$-0.592543\pi$
$953$	−17.6985			−0.573310			−0.286655	+	0.958034i	$0.592543\pi$
$954$		0			0
$955$		0			0
$956$	−11.0227	+	6.36396i	−0.356500	+	0.205825i
$957$		0			0
$958$	12.0013			0.387743
$959$	−5.19615	+	4.02944i	−0.167793	+	0.130117i
$960$		0			0
$961$	25.7279	−	44.5621i	0.829933	−	1.43749i
$962$	−0.514719	+	0.297173i	−0.0165952	+	0.00958124i
$963$		0			0
$964$	−6.25736	−	3.61269i	−0.201536	−	0.116357i
$965$		0			0
$966$		0			0
$967$			47.7279i			1.53483i	0.641153	+	0.767413i	$0.278456\pi$
$967$			47.7279i			1.53483i	−0.641153	+	0.767413i	$0.721544\pi$
$968$	1.00000	−	1.73205i	0.0321412	−	0.0556702i
$969$		0			0
$970$		0			0
$971$	−13.5337	+	23.4411i	−0.434318	+	0.752262i	−0.997240	−	0.0742490i	$-0.976344\pi$
$971$	−13.5337	+	23.4411i	−0.434318	+	0.752262i	0.562921	+	0.826510i	$0.309677\pi$
$972$		0			0
$973$	−1.55797	+	0.213203i	−0.0499463	+	0.00683499i
$974$			14.2132i			0.455420i
$975$		0			0
$976$	−0.878680	+	0.507306i	−0.0281259	+	0.0162385i
$977$	20.1213	+	34.8511i	0.643738	+	1.11499i	0.984591	+	0.174871i	$0.0559507\pi$
$977$	20.1213	+	34.8511i	0.643738	+	1.11499i	−0.340853	+	0.940116i	$0.610716\pi$
$978$		0			0
$979$		−	31.1769i		−	0.996419i
$980$		0			0
$981$		0			0
$982$	−12.0989	−	6.98528i	−0.386090	−	0.222909i
$983$	40.9706	−	23.6544i	1.30676	−	0.754457i	0.325204	−	0.945644i	$-0.394567\pi$
$983$	40.9706	−	23.6544i	1.30676	−	0.754457i	0.981554	+	0.191187i	$0.0612336\pi$
$984$		0			0
$985$		0			0
$986$	42.8300			1.36399
$987$		0			0
$988$			14.4853i			0.460838i
$989$	−0.891519	−	0.514719i	−0.0283486	−	0.0163671i
$990$		0			0
$991$	−26.1066	−	45.2180i	−0.829304	−	1.43640i	−0.898585	−	0.438799i	$-0.855404\pi$
$991$	−26.1066	−	45.2180i	−0.829304	−	1.43640i	0.0692818	−	0.997597i	$-0.477929\pi$
$992$	−7.86396	−	4.54026i	−0.249681	−	0.144153i
$993$		0			0
$994$	1.75736	−	4.30463i	0.0557401	−	0.136535i
$995$		0			0
$996$		0			0
$997$	−19.4728	−	33.7279i	−0.616711	−	1.06817i	−0.990082	−	0.140492i	$-0.955132\pi$
$997$	−19.4728	−	33.7279i	−0.616711	−	1.06817i	0.373371	−	0.927682i	$-0.378202\pi$
$998$	−15.9706	−	27.6618i	−0.505539	−	0.875620i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3150.2.bp.e.1349.3		8
3.2	odd	2		3150.2.bp.b.1349.3		8
5.2	odd	4		3150.2.bf.a.1601.3		8
5.3	odd	4		126.2.k.a.89.2	yes	8
5.4	even	2		3150.2.bp.b.1349.2		8
7.3	odd	6	inner	3150.2.bp.e.899.2		8
15.2	even	4		3150.2.bf.a.1601.1		8
15.8	even	4		126.2.k.a.89.3	yes	8
15.14	odd	2	inner	3150.2.bp.e.1349.2		8
20.3	even	4		1008.2.bt.c.593.3		8
21.17	even	6		3150.2.bp.b.899.2		8
35.3	even	12		126.2.k.a.17.3	yes	8
35.13	even	4		882.2.k.a.215.1		8
35.17	even	12		3150.2.bf.a.1151.1		8
35.18	odd	12		882.2.k.a.521.4		8
35.23	odd	12		882.2.d.a.881.6		8
35.24	odd	6		3150.2.bp.b.899.3		8
35.33	even	12		882.2.d.a.881.7		8
45.13	odd	12		1134.2.t.e.593.3		8
45.23	even	12		1134.2.t.e.593.2		8
45.38	even	12		1134.2.l.f.215.1		8
45.43	odd	12		1134.2.l.f.215.4		8
60.23	odd	4		1008.2.bt.c.593.2		8
105.17	odd	12		3150.2.bf.a.1151.3		8
105.23	even	12		882.2.d.a.881.3		8
105.38	odd	12		126.2.k.a.17.2	✓	8
105.53	even	12		882.2.k.a.521.1		8
105.59	even	6	inner	3150.2.bp.e.899.3		8
105.68	odd	12		882.2.d.a.881.2		8
105.83	odd	4		882.2.k.a.215.4		8
140.3	odd	12		1008.2.bt.c.17.2		8
140.23	even	12		7056.2.k.f.881.3		8
140.103	odd	12		7056.2.k.f.881.5		8
315.38	odd	12		1134.2.t.e.1025.3		8
315.178	even	12		1134.2.t.e.1025.2		8
315.248	odd	12		1134.2.l.f.269.2		8
315.283	even	12		1134.2.l.f.269.3		8
420.23	odd	12		7056.2.k.f.881.6		8
420.143	even	12		1008.2.bt.c.17.3		8
420.383	even	12		7056.2.k.f.881.4		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
126.2.k.a.17.2	✓	8	105.38	odd	12
126.2.k.a.17.3	yes	8	35.3	even	12
126.2.k.a.89.2	yes	8	5.3	odd	4
126.2.k.a.89.3	yes	8	15.8	even	4
882.2.d.a.881.2		8	105.68	odd	12
882.2.d.a.881.3		8	105.23	even	12
882.2.d.a.881.6		8	35.23	odd	12
882.2.d.a.881.7		8	35.33	even	12
882.2.k.a.215.1		8	35.13	even	4
882.2.k.a.215.4		8	105.83	odd	4
882.2.k.a.521.1		8	105.53	even	12
882.2.k.a.521.4		8	35.18	odd	12
1008.2.bt.c.17.2		8	140.3	odd	12
1008.2.bt.c.17.3		8	420.143	even	12
1008.2.bt.c.593.2		8	60.23	odd	4
1008.2.bt.c.593.3		8	20.3	even	4
1134.2.l.f.215.1		8	45.38	even	12
1134.2.l.f.215.4		8	45.43	odd	12
1134.2.l.f.269.2		8	315.248	odd	12
1134.2.l.f.269.3		8	315.283	even	12
1134.2.t.e.593.2		8	45.23	even	12
1134.2.t.e.593.3		8	45.13	odd	12
1134.2.t.e.1025.2		8	315.178	even	12
1134.2.t.e.1025.3		8	315.38	odd	12
3150.2.bf.a.1151.1		8	35.17	even	12
3150.2.bf.a.1151.3		8	105.17	odd	12
3150.2.bf.a.1601.1		8	15.2	even	4
3150.2.bf.a.1601.3		8	5.2	odd	4
3150.2.bp.b.899.2		8	21.17	even	6
3150.2.bp.b.899.3		8	35.24	odd	6
3150.2.bp.b.1349.2		8	5.4	even	2
3150.2.bp.b.1349.3		8	3.2	odd	2
3150.2.bp.e.899.2		8	7.3	odd	6	inner
3150.2.bp.e.899.3		8	105.59	even	6	inner
3150.2.bp.e.1349.2		8	15.14	odd	2	inner
3150.2.bp.e.1349.3		8	1.1	even	1	trivial
7056.2.k.f.881.3		8	140.23	even	12
7056.2.k.f.881.4		8	420.383	even	12
7056.2.k.f.881.5		8	140.103	odd	12
7056.2.k.f.881.6		8	420.23	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:	\( N \)	\(=\)	\( 3150 = 2 \cdot 3^{2} \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3150.bp (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(0.358719 + 2.62132i) q^{7} -1.00000 q^{8} +O(q^{10})\)	\(q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(0.358719 + 2.62132i) q^{7} -1.00000 q^{8} +(2.59808 - 1.50000i) q^{11} -2.44949 q^{13} +(2.44949 + 1.00000i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(-5.12132 + 2.95680i) q^{17} +(5.12132 + 2.95680i) q^{19} -3.00000i q^{22} +(-2.12132 + 3.67423i) q^{23} +(-1.22474 + 2.12132i) q^{26} +(2.09077 - 1.62132i) q^{28} -7.24264i q^{29} +(-7.86396 + 4.54026i) q^{31} +(0.500000 + 0.866025i) q^{32} +5.91359i q^{34} +(0.210133 + 0.121320i) q^{37} +(5.12132 - 2.95680i) q^{38} -11.8272 q^{41} +0.242641i q^{43} +(-2.59808 - 1.50000i) q^{44} +(2.12132 + 3.67423i) q^{46} +(5.12132 + 2.95680i) q^{47} +(-6.74264 + 1.88064i) q^{49} +(1.22474 + 2.12132i) q^{52} +(-3.62132 - 6.27231i) q^{53} +(-0.358719 - 2.62132i) q^{56} +(-6.27231 - 3.62132i) q^{58} +(4.03295 + 6.98528i) q^{59} +(0.878680 + 0.507306i) q^{61} +9.08052i q^{62} +1.00000 q^{64} +(-8.66025 + 5.00000i) q^{67} +(5.12132 + 2.95680i) q^{68} -1.75736i q^{71} +(0.717439 + 1.24264i) q^{73} +(0.210133 - 0.121320i) q^{74} -5.91359i q^{76} +(4.86396 + 6.27231i) q^{77} +(-1.37868 + 2.38794i) q^{79} +(-5.91359 + 10.2426i) q^{82} +6.63103i q^{83} +(0.210133 + 0.121320i) q^{86} +(-2.59808 + 1.50000i) q^{88} +(5.19615 - 9.00000i) q^{89} +(-0.878680 - 6.42090i) q^{91} +4.24264 q^{92} +(5.12132 - 2.95680i) q^{94} -13.5592 q^{97} +(-1.74264 + 6.77962i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 4 q^{2} - 4 q^{4} - 8 q^{8}+O(q^{10}) \) 8 * q + 4 * q^2 - 4 * q^4 - 8 * q^8	\( 8 q + 4 q^{2} - 4 q^{4} - 8 q^{8} - 4 q^{16} - 24 q^{17} + 24 q^{19} - 12 q^{31} + 4 q^{32} + 24 q^{38} + 24 q^{47} - 20 q^{49} - 12 q^{53} + 24 q^{61} + 8 q^{64} + 24 q^{68} - 12 q^{77} - 28 q^{79} - 24 q^{91} + 24 q^{94} + 20 q^{98}+O(q^{100}) \) 8 * q + 4 * q^2 - 4 * q^4 - 8 * q^8 - 4 * q^16 - 24 * q^17 + 24 * q^19 - 12 * q^31 + 4 * q^32 + 24 * q^38 + 24 * q^47 - 20 * q^49 - 12 * q^53 + 24 * q^61 + 8 * q^64 + 24 * q^68 - 12 * q^77 - 28 * q^79 - 24 * q^91 + 24 * q^94 + 20 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more