LMFDB - Embedded newform 126.2.k.a.89.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [126,2,Mod(17,126)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(126, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([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("126.17");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 126 = 2 \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	126.k (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$1.00611506547$
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:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{2}\cdot 3^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			89.2
Root			$0.258819 + 0.965926i$ of defining polynomial
Character	$\chi$	$=$	126.89
Dual form			126.2.k.a.17.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 - 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} +(0.358719 - 0.621320i) q^{5} +(2.62132 - 0.358719i) q^{7} -1.00000i q^{8} +O(q^{10})$	\(q+(-0.866025 - 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} +(0.358719 - 0.621320i) q^{5} +(2.62132 - 0.358719i) q^{7} -1.00000i q^{8} +(-0.621320 + 0.358719i) q^{10} +(2.59808 - 1.50000i) q^{11} -2.44949i q^{13} +(-2.44949 - 1.00000i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(2.95680 + 5.12132i) q^{17} +(-5.12132 - 2.95680i) q^{19} +0.717439 q^{20} -3.00000 q^{22} +(-3.67423 - 2.12132i) q^{23} +(2.24264 + 3.88437i) q^{25} +(-1.22474 + 2.12132i) q^{26} +(1.62132 + 2.09077i) q^{28} +7.24264i q^{29} +(-7.86396 + 4.54026i) q^{31} +(0.866025 - 0.500000i) q^{32} -5.91359i q^{34} +(0.717439 - 1.75736i) q^{35} +(0.121320 - 0.210133i) q^{37} +(2.95680 + 5.12132i) q^{38} +(-0.621320 - 0.358719i) q^{40} -11.8272 q^{41} -0.242641 q^{43} +(2.59808 + 1.50000i) q^{44} +(2.12132 + 3.67423i) q^{46} +(2.95680 - 5.12132i) q^{47} +(6.74264 - 1.88064i) q^{49} -4.48528i q^{50} +(2.12132 - 1.22474i) q^{52} +(6.27231 - 3.62132i) q^{53} -2.15232i q^{55} +(-0.358719 - 2.62132i) q^{56} +(3.62132 - 6.27231i) q^{58} +(-4.03295 - 6.98528i) q^{59} +(0.878680 + 0.507306i) q^{61} +9.08052 q^{62} -1.00000 q^{64} +(-1.52192 - 0.878680i) q^{65} +(5.00000 + 8.66025i) q^{67} +(-2.95680 + 5.12132i) q^{68} +(-1.50000 + 1.16320i) q^{70} -1.75736i q^{71} +(-1.24264 + 0.717439i) q^{73} +(-0.210133 + 0.121320i) q^{74} -5.91359i q^{76} +(6.27231 - 4.86396i) q^{77} +(1.37868 - 2.38794i) q^{79} +(0.358719 + 0.621320i) q^{80} +(10.2426 + 5.91359i) q^{82} -6.63103 q^{83} +4.24264 q^{85} +(0.210133 + 0.121320i) q^{86} +(-1.50000 - 2.59808i) q^{88} +(-5.19615 + 9.00000i) q^{89} +(-0.878680 - 6.42090i) q^{91} -4.24264i q^{92} +(-5.12132 + 2.95680i) q^{94} +(-3.67423 + 2.12132i) q^{95} +13.5592i q^{97} +(-6.77962 - 1.74264i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 4 q^{4} + 4 q^{7}+O(q^{10}) $ 8 * q + 4 * q^4 + 4 * q^7	$ 8 q + 4 q^{4} + 4 q^{7} + 12 q^{10} - 4 q^{16} - 24 q^{19} - 24 q^{22} - 16 q^{25} - 4 q^{28} - 12 q^{31} - 16 q^{37} + 12 q^{40} + 32 q^{43} + 20 q^{49} + 12 q^{58} + 24 q^{61} - 8 q^{64} + 40 q^{67} - 12 q^{70} + 24 q^{73} + 28 q^{79} + 48 q^{82} - 12 q^{88} - 24 q^{91} - 24 q^{94}+O(q^{100}) $ 8 * q + 4 * q^4 + 4 * q^7 + 12 * q^10 - 4 * q^16 - 24 * q^19 - 24 * q^22 - 16 * q^25 - 4 * q^28 - 12 * q^31 - 16 * q^37 + 12 * q^40 + 32 * q^43 + 20 * q^49 + 12 * q^58 + 24 * q^61 - 8 * q^64 + 40 * q^67 - 12 * q^70 + 24 * q^73 + 28 * q^79 + 48 * q^82 - 12 * q^88 - 24 * q^91 - 24 * q^94

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/126\mathbb{Z}\right)^\times$.

$n$	$29$	$73$
$\chi(n)$	$-1$	$e\left(\frac{5}{6}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.866025	−	0.500000i	−0.612372	−	0.353553i
$2$	−0.866025	−	0.500000i	−0.612372	−	0.353553i
$3$		0			0
$3$		0			0
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$	0.358719	−	0.621320i	0.160424	−	0.277863i	−0.774597	−	0.632456i	$-0.782047\pi$
$5$	0.358719	−	0.621320i	0.160424	−	0.277863i	0.935021	+	0.354593i	$0.115380\pi$
$6$		0			0
$7$	2.62132	−	0.358719i	0.990766	−	0.135583i
$7$	2.62132	−	0.358719i	0.990766	−	0.135583i
$8$		−	1.00000i		−	0.353553i
$9$		0			0
$10$	−0.621320	+	0.358719i	−0.196479	+	0.113437i
$11$	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
$13$		−	2.44949i		−	0.679366i	−0.940540	−	0.339683i	$-0.889680\pi$
$13$		−	2.44949i		−	0.679366i	0.940540	−	0.339683i	$-0.110320\pi$
$14$	−2.44949	−	1.00000i	−0.654654	−	0.267261i
$15$		0			0
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	2.95680	+	5.12132i	0.717128	+	1.24210i	0.962133	+	0.272581i	$0.0878772\pi$
$17$	2.95680	+	5.12132i	0.717128	+	1.24210i	−0.245005	+	0.969522i	$0.578789\pi$
$18$		0			0
$19$	−5.12132	−	2.95680i	−1.17491	−	0.678335i	−0.220080	−	0.975482i	$-0.570632\pi$
$19$	−5.12132	−	2.95680i	−1.17491	−	0.678335i	−0.954832	+	0.297146i	$0.903965\pi$
$20$	0.717439			0.160424
$21$		0			0
$22$	−3.00000			−0.639602
$23$	−3.67423	−	2.12132i	−0.766131	−	0.442326i	0.0653618	−	0.997862i	$-0.479180\pi$
$23$	−3.67423	−	2.12132i	−0.766131	−	0.442326i	−0.831493	+	0.555536i	$0.812513\pi$
$24$		0			0
$25$	2.24264	+	3.88437i	0.448528	+	0.776874i
$26$	−1.22474	+	2.12132i	−0.240192	+	0.416025i
$27$		0			0
$28$	1.62132	+	2.09077i	0.306401	+	0.395118i
$29$			7.24264i			1.34492i	0.740131	+	0.672462i	$0.234763\pi$
$29$			7.24264i			1.34492i	−0.740131	+	0.672462i	$0.765237\pi$
$30$		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	$0.636846\pi$
$32$	0.866025	−	0.500000i	0.153093	−	0.0883883i
$33$		0			0
$34$		−	5.91359i		−	1.01417i
$35$	0.717439	−	1.75736i	0.121269	−	0.297048i
$36$		0			0
$37$	0.121320	−	0.210133i	0.0199449	−	0.0345457i	−0.855881	−	0.517173i	$-0.826984\pi$
$37$	0.121320	−	0.210133i	0.0199449	−	0.0345457i	0.875826	+	0.482628i	$0.160318\pi$
$38$	2.95680	+	5.12132i	0.479656	+	0.830788i
$39$		0			0
$40$	−0.621320	−	0.358719i	−0.0982394	−	0.0567185i
$41$	−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
$43$	−0.242641			−0.0370024			−0.0185012	−	0.999829i	$-0.505889\pi$
$43$	−0.242641			−0.0370024			−0.0185012	+	0.999829i	$0.505889\pi$
$44$	2.59808	+	1.50000i	0.391675	+	0.226134i
$45$		0			0
$46$	2.12132	+	3.67423i	0.312772	+	0.541736i
$47$	2.95680	−	5.12132i	0.431293	−	0.747021i	−0.565692	−	0.824617i	$-0.691391\pi$
$47$	2.95680	−	5.12132i	0.431293	−	0.747021i	0.996985	+	0.0775953i	$0.0247242\pi$
$48$		0			0
$49$	6.74264	−	1.88064i	0.963234	−	0.268662i
$50$		−	4.48528i		−	0.634315i
$51$		0			0
$52$	2.12132	−	1.22474i	0.294174	−	0.169842i
$53$	6.27231	−	3.62132i	0.861568	−	0.497427i	−0.00296896	−	0.999996i	$-0.500945\pi$
$53$	6.27231	−	3.62132i	0.861568	−	0.497427i	0.864537	+	0.502569i	$0.167612\pi$
$54$		0			0
$55$		−	2.15232i		−	0.290218i
$56$	−0.358719	−	2.62132i	−0.0479359	−	0.350289i
$57$		0			0
$58$	3.62132	−	6.27231i	0.475503	−	0.823595i
$59$	−4.03295	−	6.98528i	−0.525046	−	0.909406i	−0.999575	−	0.0291661i	$-0.990715\pi$
$59$	−4.03295	−	6.98528i	−0.525046	−	0.909406i	0.474529	−	0.880240i	$-0.342619\pi$
$60$		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	$0.645977\pi$
$62$	9.08052			1.15323
$63$		0			0
$64$	−1.00000			−0.125000
$65$	−1.52192	−	0.878680i	−0.188771	−	0.108987i
$66$		0			0
$67$	5.00000	+	8.66025i	0.610847	+	1.05802i	0.991098	+	0.133135i	$0.0425044\pi$
$67$	5.00000	+	8.66025i	0.610847	+	1.05802i	−0.380251	+	0.924883i	$0.624162\pi$
$68$	−2.95680	+	5.12132i	−0.358564	+	0.621051i
$69$		0			0
$70$	−1.50000	+	1.16320i	−0.179284	+	0.139029i
$71$		−	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
$73$	−1.24264	+	0.717439i	−0.145440	+	0.0839699i	−0.570954	−	0.820982i	$-0.693427\pi$
$73$	−1.24264	+	0.717439i	−0.145440	+	0.0839699i	0.425514	+	0.904952i	$0.360093\pi$
$74$	−0.210133	+	0.121320i	−0.0244275	+	0.0141032i
$75$		0			0
$76$		−	5.91359i		−	0.678335i
$77$	6.27231	−	4.86396i	0.714796	−	0.554300i
$78$		0			0
$79$	1.37868	−	2.38794i	0.155114	−	0.268665i	−0.777987	−	0.628281i	$-0.783759\pi$
$79$	1.37868	−	2.38794i	0.155114	−	0.268665i	0.933100	+	0.359616i	$0.117092\pi$
$80$	0.358719	+	0.621320i	0.0401061	+	0.0694657i
$81$		0			0
$82$	10.2426	+	5.91359i	1.13111	+	0.653047i
$83$	−6.63103			−0.727850			−0.363925	−	0.931428i	$-0.618564\pi$
$83$	−6.63103			−0.727850			−0.363925	+	0.931428i	$0.618564\pi$
$84$		0			0
$85$	4.24264			0.460179
$86$	0.210133	+	0.121320i	0.0226592	+	0.0130823i
$87$		0			0
$88$	−1.50000	−	2.59808i	−0.159901	−	0.276956i
$89$	−5.19615	+	9.00000i	−0.550791	+	0.953998i	0.447427	+	0.894321i	$0.352341\pi$
$89$	−5.19615	+	9.00000i	−0.550791	+	0.953998i	−0.998218	+	0.0596775i	$0.980993\pi$
$90$		0			0
$91$	−0.878680	−	6.42090i	−0.0921107	−	0.673093i
$92$		−	4.24264i		−	0.442326i
$93$		0			0
$94$	−5.12132	+	2.95680i	−0.528224	+	0.304970i
$95$	−3.67423	+	2.12132i	−0.376969	+	0.217643i
$96$		0			0
$97$			13.5592i			1.37673i	0.725364	+	0.688366i	$0.241672\pi$
$97$			13.5592i			1.37673i	−0.725364	+	0.688366i	$0.758328\pi$
$98$	−6.77962	−	1.74264i	−0.684845	−	0.176033i
$99$		0			0
$100$	−2.24264	+	3.88437i	−0.224264	+	0.388437i
$101$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$101$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$102$		0			0
$103$	−4.75736	−	2.74666i	−0.468757	−	0.270637i	0.246963	−	0.969025i	$-0.420568\pi$
$103$	−4.75736	−	2.74666i	−0.468757	−	0.270637i	−0.715719	+	0.698388i	$0.753901\pi$
$104$	−2.44949			−0.240192
$105$		0			0
$106$	−7.24264			−0.703467
$107$	9.94655	+	5.74264i	0.961569	+	0.555162i	0.896656	−	0.442729i	$-0.145990\pi$
$107$	9.94655	+	5.74264i	0.961569	+	0.555162i	0.0649133	+	0.997891i	$0.479323\pi$
$108$		0			0
$109$	−9.24264	−	16.0087i	−0.885284	−	1.53336i	−0.845387	−	0.534154i	$-0.820630\pi$
$109$	−9.24264	−	16.0087i	−0.885284	−	1.53336i	−0.0398971	−	0.999204i	$-0.512703\pi$
$110$	−1.07616	+	1.86396i	−0.102608	+	0.177722i
$111$		0			0
$112$	−1.00000	+	2.44949i	−0.0944911	+	0.231455i
$113$			8.48528i			0.798228i	0.916901	+	0.399114i	$0.130682\pi$
$113$			8.48528i			0.798228i	−0.916901	+	0.399114i	$0.869318\pi$
$114$		0			0
$115$	−2.63604	+	1.52192i	−0.245812	+	0.141920i
$116$	−6.27231	+	3.62132i	−0.582369	+	0.336231i
$117$		0			0
$118$			8.06591i			0.742527i
$119$	9.58783	+	12.3640i	0.878915	+	1.13340i
$120$		0			0
$121$	−1.00000	+	1.73205i	−0.0909091	+	0.157459i
$122$	−0.507306	−	0.878680i	−0.0459293	−	0.0795519i
$123$		0			0
$124$	−7.86396	−	4.54026i	−0.706205	−	0.407727i
$125$	6.80511			0.608668
$126$		0			0
$127$	3.24264			0.287738			0.143869	−	0.989597i	$-0.454046\pi$
$127$	3.24264			0.287738			0.143869	+	0.989597i	$0.454046\pi$
$128$	0.866025	+	0.500000i	0.0765466	+	0.0441942i
$129$		0			0
$130$	0.878680	+	1.52192i	0.0770653	+	0.133481i
$131$	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
$133$	−14.4853	−	5.91359i	−1.25603	−	0.512773i
$134$		−	10.0000i		−	0.863868i
$135$		0			0
$136$	5.12132	−	2.95680i	0.439150	−	0.253543i
$137$	2.15232	−	1.24264i	0.183885	−	0.106166i	−0.405232	−	0.914214i	$-0.632809\pi$
$137$	2.15232	−	1.24264i	0.183885	−	0.106166i	0.589117	+	0.808048i	$0.299476\pi$
$138$		0			0
$139$		−	0.594346i		−	0.0504118i	−0.999682	−	0.0252059i	$-0.991976\pi$
$139$		−	0.594346i		−	0.0504118i	0.999682	−	0.0252059i	$-0.00802413\pi$
$140$	1.88064	−	0.257359i	0.158943	−	0.0217508i
$141$		0			0
$142$	−0.878680	+	1.52192i	−0.0737372	+	0.127717i
$143$	−3.67423	−	6.36396i	−0.307255	−	0.532181i
$144$		0			0
$145$	4.50000	+	2.59808i	0.373705	+	0.215758i
$146$	1.43488			0.118751
$147$		0			0
$148$	0.242641			0.0199449
$149$	3.04384	+	1.75736i	0.249361	+	0.143968i	0.619472	−	0.785019i	$-0.287347\pi$
$149$	3.04384	+	1.75736i	0.249361	+	0.143968i	−0.370111	+	0.928988i	$0.620680\pi$
$150$		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	$0.901761\pi$
$152$	−2.95680	+	5.12132i	−0.239828	+	0.415394i
$153$		0			0
$154$	−7.86396	+	1.07616i	−0.633696	+	0.0867193i
$155$			6.51472i			0.523275i
$156$		0			0
$157$	12.7279	−	7.34847i	1.01580	−	0.586472i	0.102915	−	0.994690i	$-0.467183\pi$
$157$	12.7279	−	7.34847i	1.01580	−	0.586472i	0.912884	+	0.408219i	$0.133850\pi$
$158$	−2.38794	+	1.37868i	−0.189975	+	0.109682i
$159$		0			0
$160$		−	0.717439i		−	0.0567185i
$161$	−10.3923	−	4.24264i	−0.819028	−	0.334367i
$162$		0			0
$163$	1.12132	−	1.94218i	0.0878286	−	0.152124i	−0.818764	−	0.574130i	$-0.805341\pi$
$163$	1.12132	−	1.94218i	0.0878286	−	0.152124i	0.906593	+	0.422006i	$0.138674\pi$
$164$	−5.91359	−	10.2426i	−0.461774	−	0.799816i
$165$		0			0
$166$	5.74264	+	3.31552i	0.445715	+	0.257334i
$167$	16.1318			1.24832			0.624159	−	0.781298i	$-0.285442\pi$
$167$	16.1318			1.24832			0.624159	+	0.781298i	$0.285442\pi$
$168$		0			0
$169$	7.00000			0.538462
$170$	−3.67423	−	2.12132i	−0.281801	−	0.162698i
$171$		0			0
$172$	−0.121320	−	0.210133i	−0.00925059	−	0.0160225i
$173$	10.3923	−	18.0000i	0.790112	−	1.36851i	−0.135785	−	0.990738i	$-0.543356\pi$
$173$	10.3923	−	18.0000i	0.790112	−	1.36851i	0.925897	−	0.377776i	$-0.123311\pi$
$174$		0			0
$175$	7.27208	+	9.37769i	0.549717	+	0.708887i
$176$			3.00000i			0.226134i
$177$		0			0
$178$	9.00000	−	5.19615i	0.674579	−	0.389468i
$179$	−22.9369	+	13.2426i	−1.71439	+	0.989801i	−0.785966	+	0.618269i	$0.787834\pi$
$179$	−22.9369	+	13.2426i	−1.71439	+	0.989801i	−0.928420	+	0.371532i	$0.878833\pi$
$180$		0			0
$181$			11.8272i			0.879108i	0.898216	+	0.439554i	$0.144863\pi$
$181$			11.8272i			0.879108i	−0.898216	+	0.439554i	$0.855137\pi$
$182$	−2.44949	+	6.00000i	−0.181568	+	0.444750i
$183$		0			0
$184$	−2.12132	+	3.67423i	−0.156386	+	0.270868i
$185$	−0.0870399	−	0.150758i	−0.00639930	−	0.0110839i
$186$		0			0
$187$	15.3640	+	8.87039i	1.12352	+	0.648667i
$188$	5.91359			0.431293
$189$		0			0
$190$	4.24264			0.307794
$191$	−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
$193$	−4.74264	−	8.21449i	−0.341383	−	0.591292i	0.643307	−	0.765608i	$-0.277562\pi$
$193$	−4.74264	−	8.21449i	−0.341383	−	0.591292i	−0.984690	+	0.174316i	$0.944229\pi$
$194$	6.77962	−	11.7426i	0.486748	−	0.843072i
$195$		0			0
$196$	5.00000	+	4.89898i	0.357143	+	0.349927i
$197$		−	26.4853i		−	1.88700i	−0.331375	−	0.943499i	$-0.607513\pi$
$197$		−	26.4853i		−	1.88700i	0.331375	−	0.943499i	$-0.392487\pi$
$198$		0			0
$199$	19.9706	−	11.5300i	1.41568	−	0.817341i	0.419761	−	0.907635i	$-0.362114\pi$
$199$	19.9706	−	11.5300i	1.41568	−	0.817341i	0.995915	+	0.0902942i	$0.0287807\pi$
$200$	3.88437	−	2.24264i	0.274666	−	0.158579i
$201$		0			0
$202$		0			0
$203$	2.59808	+	18.9853i	0.182349	+	1.33251i
$204$		0			0
$205$	−4.24264	+	7.34847i	−0.296319	+	0.513239i
$206$	2.74666	+	4.75736i	0.191369	+	0.331461i
$207$		0			0
$208$	2.12132	+	1.22474i	0.147087	+	0.0849208i
$209$	−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	$0.502659\pi$
$212$	6.27231	+	3.62132i	0.430784	+	0.248713i
$213$		0			0
$214$	−5.74264	−	9.94655i	−0.392559	−	0.679932i
$215$	−0.0870399	+	0.150758i	−0.00593607	+	0.0102816i
$216$		0			0
$217$	−18.9853	+	14.7224i	−1.28880	+	0.999424i
$218$			18.4853i			1.25198i
$219$		0			0
$220$	1.86396	−	1.07616i	0.125668	−	0.0725546i
$221$	12.5446	−	7.24264i	0.843843	−	0.487193i
$222$		0			0
$223$			2.15232i			0.144130i	0.997400	+	0.0720649i	$0.0229589\pi$
$223$			2.15232i			0.144130i	−0.997400	+	0.0720649i	$0.977041\pi$
$224$	2.09077	−	1.62132i	0.139695	−	0.108329i
$225$		0			0
$226$	4.24264	−	7.34847i	0.282216	−	0.488813i
$227$	−7.79423	−	13.5000i	−0.517321	−	0.896026i	−0.999798	−	0.0201176i	$-0.993596\pi$
$227$	−7.79423	−	13.5000i	−0.517321	−	0.896026i	0.482476	−	0.875909i	$-0.339737\pi$
$228$		0			0
$229$	−12.0000	−	6.92820i	−0.792982	−	0.457829i	0.0480291	−	0.998846i	$-0.484706\pi$
$229$	−12.0000	−	6.92820i	−0.792982	−	0.457829i	−0.841011	+	0.541017i	$0.818039\pi$
$230$	3.04384			0.200705
$231$		0			0
$232$	7.24264			0.475503
$233$	−16.2189	−	9.36396i	−1.06253	−	0.613453i	−0.136401	−	0.990654i	$-0.543554\pi$
$233$	−16.2189	−	9.36396i	−1.06253	−	0.613453i	−0.926132	+	0.377200i	$0.876887\pi$
$234$		0			0
$235$	−2.12132	−	3.67423i	−0.138380	−	0.239681i
$236$	4.03295	−	6.98528i	0.262523	−	0.454703i
$237$		0			0
$238$	−2.12132	−	15.5014i	−0.137505	−	1.00481i
$239$			12.7279i			0.823301i	0.911342	+	0.411650i	$0.135048\pi$
$239$			12.7279i			0.823301i	−0.911342	+	0.411650i	$0.864952\pi$
$240$		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	$0.258573\pi$
$242$	1.73205	−	1.00000i	0.111340	−	0.0642824i
$243$		0			0
$244$			1.01461i			0.0649539i
$245$	1.25024	−	4.86396i	0.0798748	−	0.310747i
$246$		0			0
$247$	−7.24264	+	12.5446i	−0.460838	+	0.798195i
$248$	4.54026	+	7.86396i	0.288307	+	0.499362i
$249$		0			0
$250$	−5.89340	−	3.40256i	−0.372731	−	0.215196i
$251$	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
$253$	−12.7279			−0.800198
$254$	−2.80821	−	1.62132i	−0.176203	−	0.101731i
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−2.15232	+	3.72792i	−0.134258	+	0.232541i	−0.925314	−	0.379203i	$-0.876198\pi$
$257$	−2.15232	+	3.72792i	−0.134258	+	0.232541i	0.791056	+	0.611744i	$0.209532\pi$
$258$		0			0
$259$	0.242641	−	0.594346i	0.0150770	−	0.0369309i
$260$		−	1.75736i		−	0.108987i
$261$		0			0
$262$	−4.50000	+	2.59808i	−0.278011	+	0.160510i
$263$	−13.1750	+	7.60660i	−0.812407	+	0.469043i	−0.847791	−	0.530331i	$-0.822068\pi$
$263$	−13.1750	+	7.60660i	−0.812407	+	0.469043i	0.0353843	+	0.999374i	$0.488734\pi$
$264$		0			0
$265$		−	5.19615i		−	0.319197i
$266$	9.58783	+	12.3640i	0.587867	+	0.758083i
$267$		0			0
$268$	−5.00000	+	8.66025i	−0.305424	+	0.529009i
$269$	6.98975	+	12.1066i	0.426173	+	0.738153i	0.996529	−	0.0832447i	$-0.0265283\pi$
$269$	6.98975	+	12.1066i	0.426173	+	0.738153i	−0.570357	+	0.821397i	$0.693195\pi$
$270$		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	$0.727074\pi$
$272$	−5.91359			−0.358564
$273$		0			0
$274$	−2.48528			−0.150141
$275$	11.6531	+	6.72792i	0.702709	+	0.405709i
$276$		0			0
$277$	−6.48528	−	11.2328i	−0.389663	−	0.674916i	0.602741	−	0.797937i	$-0.294075\pi$
$277$	−6.48528	−	11.2328i	−0.389663	−	0.674916i	−0.992404	+	0.123021i	$0.960742\pi$
$278$	−0.297173	+	0.514719i	−0.0178232	+	0.0308708i
$279$		0			0
$280$	−1.75736	−	0.717439i	−0.105022	−	0.0428752i
$281$			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
$283$	−18.3640	+	10.6024i	−1.09162	+	0.630250i	−0.934008	−	0.357251i	$-0.883714\pi$
$283$	−18.3640	+	10.6024i	−1.09162	+	0.630250i	−0.157616	+	0.987501i	$0.550381\pi$
$284$	1.52192	−	0.878680i	0.0903092	−	0.0521400i
$285$		0			0
$286$			7.34847i			0.434524i
$287$	−31.0028	+	4.24264i	−1.83004	+	0.250435i
$288$		0			0
$289$	−8.98528	+	15.5630i	−0.528546	+	0.915468i
$290$	−2.59808	−	4.50000i	−0.152564	−	0.264249i
$291$		0			0
$292$	−1.24264	−	0.717439i	−0.0727200	−	0.0419849i
$293$	0.717439			0.0419132			0.0209566	−	0.999780i	$-0.493329\pi$
$293$	0.717439			0.0419132			0.0209566	+	0.999780i	$0.493329\pi$
$294$		0			0
$295$	−5.78680			−0.336920
$296$	−0.210133	−	0.121320i	−0.0122137	−	0.00705160i
$297$		0			0
$298$	−1.75736	−	3.04384i	−0.101801	−	0.176325i
$299$	−5.19615	+	9.00000i	−0.300501	+	0.520483i
$300$		0			0
$301$	−0.636039	+	0.0870399i	−0.0366607	+	0.00501690i
$302$			5.24264i			0.301680i
$303$		0			0
$304$	5.12132	−	2.95680i	0.293728	−	0.169584i
$305$	0.630399	−	0.363961i	0.0360965	−	0.0208403i
$306$		0			0
$307$		−	9.97204i		−	0.569134i	−0.958656	−	0.284567i	$-0.908150\pi$
$307$		−	9.97204i		−	0.569134i	0.958656	−	0.284567i	$-0.0918499\pi$
$308$	7.34847	+	3.00000i	0.418718	+	0.170941i
$309$		0			0
$310$	3.25736	−	5.64191i	0.185006	−	0.320439i
$311$	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
$313$	15.9853	+	9.22911i	0.903542	+	0.521660i	0.878348	−	0.478023i	$-0.158646\pi$
$313$	15.9853	+	9.22911i	0.903542	+	0.521660i	0.0251940	+	0.999683i	$0.491980\pi$
$314$	−14.6969			−0.829396
$315$		0			0
$316$	2.75736			0.155114
$317$	−1.07616	−	0.621320i	−0.0604431	−	0.0348968i	0.469474	−	0.882946i	$-0.344444\pi$
$317$	−1.07616	−	0.621320i	−0.0604431	−	0.0348968i	−0.529917	+	0.848050i	$0.677777\pi$
$318$		0			0
$319$	10.8640	+	18.8169i	0.608265	+	1.05355i
$320$	−0.358719	+	0.621320i	−0.0200530	+	0.0347329i
$321$		0			0
$322$	6.87868	+	8.87039i	0.383334	+	0.494327i
$323$		−	34.9706i		−	1.94581i
$324$		0			0
$325$	9.51472	−	5.49333i	0.527782	−	0.304715i
$326$	−1.94218	+	1.12132i	−0.107568	+	0.0621042i
$327$		0			0
$328$			11.8272i			0.653047i
$329$	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	$-0.204699\pi$
$332$	−3.31552	−	5.74264i	−0.181963	−	0.315168i
$333$		0			0
$334$	−13.9706	−	8.06591i	−0.764435	−	0.441347i
$335$	7.17439			0.391979
$336$		0			0
$337$	−5.00000			−0.272367			−0.136184	−	0.990684i	$-0.543484\pi$
$337$	−5.00000			−0.272367			−0.136184	+	0.990684i	$0.543484\pi$
$338$	−6.06218	−	3.50000i	−0.329739	−	0.190375i
$339$		0			0
$340$	2.12132	+	3.67423i	0.115045	+	0.199263i
$341$	−13.6208	+	23.5919i	−0.737607	+	1.27757i
$342$		0			0
$343$	17.0000	−	7.34847i	0.917914	−	0.396780i
$344$			0.242641i			0.0130823i
$345$		0			0
$346$	−18.0000	+	10.3923i	−0.967686	+	0.558694i
$347$	−2.15232	+	1.24264i	−0.115542	+	0.0667084i	−0.556657	−	0.830742i	$-0.687916\pi$
$347$	−2.15232	+	1.24264i	−0.115542	+	0.0667084i	0.441115	+	0.897451i	$0.354583\pi$
$348$		0			0
$349$		−	2.27541i		−	0.121800i	−0.998144	−	0.0608999i	$-0.980603\pi$
$349$		−	2.27541i		−	0.121800i	0.998144	−	0.0608999i	$-0.0193971\pi$
$350$	−1.60896	−	11.7574i	−0.0860024	−	0.628457i
$351$		0			0
$352$	1.50000	−	2.59808i	0.0799503	−	0.138478i
$353$	4.47871	+	7.75736i	0.238378	+	0.412883i	0.960249	−	0.279145i	$-0.0900510\pi$
$353$	4.47871	+	7.75736i	0.238378	+	0.412883i	−0.721871	+	0.692028i	$0.756718\pi$
$354$		0			0
$355$	−1.09188	−	0.630399i	−0.0579511	−	0.0334581i
$356$	−10.3923			−0.550791
$357$		0			0
$358$	26.4853			1.39979
$359$	15.5885	+	9.00000i	0.822727	+	0.475002i	0.851356	−	0.524588i	$-0.175781\pi$
$359$	15.5885	+	9.00000i	0.822727	+	0.475002i	−0.0286287	+	0.999590i	$0.509114\pi$
$360$		0			0
$361$	7.98528	+	13.8309i	0.420278	+	0.727943i
$362$	5.91359	−	10.2426i	0.310811	−	0.538341i
$363$		0			0
$364$	5.12132	−	3.97141i	0.268430	−	0.208158i
$365$			1.02944i			0.0538832i
$366$		0			0
$367$	−13.3492	+	7.70719i	−0.696825	+	0.402312i	−0.806164	−	0.591693i	$-0.798460\pi$
$367$	−13.3492	+	7.70719i	−0.696825	+	0.402312i	0.109339	+	0.994005i	$0.465127\pi$
$368$	3.67423	−	2.12132i	0.191533	−	0.110581i
$369$		0			0
$370$			0.174080i			0.00904998i
$371$	15.1427	−	11.7426i	0.786170	−	0.609648i
$372$		0			0
$373$	14.7279	−	25.5095i	0.762583	−	1.32083i	−0.178932	−	0.983861i	$-0.557264\pi$
$373$	14.7279	−	25.5095i	0.762583	−	1.32083i	0.941515	−	0.336971i	$-0.109402\pi$
$374$	−8.87039	−	15.3640i	−0.458677	−	0.794452i
$375$		0			0
$376$	−5.12132	−	2.95680i	−0.264112	−	0.152485i
$377$	17.7408			0.913696
$378$		0			0
$379$	12.4853			0.641326			0.320663	−	0.947193i	$-0.396094\pi$
$379$	12.4853			0.641326			0.320663	+	0.947193i	$0.396094\pi$
$380$	−3.67423	−	2.12132i	−0.188484	−	0.108821i
$381$		0			0
$382$	4.24264	+	7.34847i	0.217072	+	0.375980i
$383$	11.1097	−	19.2426i	0.567681	−	0.983253i	−0.429113	−	0.903251i	$-0.641174\pi$
$383$	11.1097	−	19.2426i	0.567681	−	0.983253i	0.996795	−	0.0800023i	$-0.0254928\pi$
$384$		0			0
$385$	−0.772078	−	5.64191i	−0.0393487	−	0.287538i
$386$			9.48528i			0.482788i
$387$		0			0
$388$	−11.7426	+	6.77962i	−0.596142	+	0.344183i
$389$	27.2416	−	15.7279i	1.38120	−	0.797437i	0.388900	−	0.921280i	$-0.372855\pi$
$389$	27.2416	−	15.7279i	1.38120	−	0.797437i	0.992302	+	0.123843i	$0.0395218\pi$
$390$		0			0
$391$		−	25.0892i		−	1.26882i
$392$	−1.88064	−	6.74264i	−0.0949865	−	0.340555i
$393$		0			0
$394$	−13.2426	+	22.9369i	−0.667155	+	1.15555i
$395$	−0.989118	−	1.71320i	−0.0497680	−	0.0862006i
$396$		0			0
$397$	12.0000	+	6.92820i	0.602263	+	0.347717i	0.769931	−	0.638127i	$-0.220290\pi$
$397$	12.0000	+	6.92820i	0.602263	+	0.347717i	−0.167668	+	0.985843i	$0.553624\pi$
$398$	−23.0600			−1.15589
$399$		0			0
$400$	−4.48528			−0.224264
$401$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$401$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$402$		0			0
$403$	11.1213	+	19.2627i	0.553992	+	0.959543i
$404$		0			0
$405$		0			0
$406$	7.24264	−	17.7408i	0.359446	−	0.880460i
$407$		−	0.727922i		−	0.0360818i
$408$		0			0
$409$	12.9853	−	7.49706i	0.642081	−	0.370706i	−0.143335	−	0.989674i	$-0.545783\pi$
$409$	12.9853	−	7.49706i	0.642081	−	0.370706i	0.785416	+	0.618969i	$0.212449\pi$
$410$	7.34847	−	4.24264i	0.362915	−	0.209529i
$411$		0			0
$412$		−	5.49333i		−	0.270637i
$413$	−13.0774	−	16.8640i	−0.643498	−	0.829821i
$414$		0			0
$415$	−2.37868	+	4.11999i	−0.116765	+	0.202243i
$416$	−1.22474	−	2.12132i	−0.0600481	−	0.104006i
$417$		0			0
$418$	15.3640	+	8.87039i	0.751476	+	0.433865i
$419$	−23.6544			−1.15559			−0.577796	−	0.816181i	$-0.696087\pi$
$419$	−23.6544			−1.15559			−0.577796	+	0.816181i	$0.696087\pi$
$420$		0			0
$421$	−14.2426			−0.694144			−0.347072	−	0.937839i	$-0.612824\pi$
$421$	−14.2426			−0.694144			−0.347072	+	0.937839i	$0.612824\pi$
$422$	0.210133	+	0.121320i	0.0102291	+	0.00590578i
$423$		0			0
$424$	−3.62132	−	6.27231i	−0.175867	−	0.304610i
$425$	−13.2621	+	22.9706i	−0.643304	+	1.11424i
$426$		0			0
$427$	2.48528	+	1.01461i	0.120271	+	0.0491005i
$428$			11.4853i			0.555162i
$429$		0			0
$430$	0.150758	−	0.0870399i	0.00727018	−	0.00419744i
$431$	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
$433$		−	3.46410i		−	0.166474i	−0.996530	−	0.0832370i	$-0.973474\pi$
$433$		−	3.46410i		−	0.166474i	0.996530	−	0.0832370i	$-0.0265259\pi$
$434$	23.8030	−	3.25736i	1.14258	−	0.156358i
$435$		0			0
$436$	9.24264	−	16.0087i	0.442642	−	0.766679i
$437$	12.5446	+	21.7279i	0.600091	+	1.03939i
$438$		0			0
$439$	−14.5919	−	8.42463i	−0.696433	−	0.402086i	0.109585	−	0.993977i	$-0.465048\pi$
$439$	−14.5919	−	8.42463i	−0.696433	−	0.402086i	−0.806017	+	0.591892i	$0.798381\pi$
$440$	−2.15232			−0.102608
$441$		0			0
$442$	−14.4853			−0.688995
$443$	14.2512	+	8.22792i	0.677094	+	0.390920i	0.798759	−	0.601651i	$-0.205490\pi$
$443$	14.2512	+	8.22792i	0.677094	+	0.390920i	−0.121665	+	0.992571i	$0.538823\pi$
$444$		0			0
$445$	3.72792	+	6.45695i	0.176720	+	0.306089i
$446$	1.07616	−	1.86396i	0.0509576	−	0.0882611i
$447$		0			0
$448$	−2.62132	+	0.358719i	−0.123846	+	0.0169479i
$449$		−	1.75736i		−	0.0829349i	−0.999140	−	0.0414675i	$-0.986797\pi$
$449$		−	1.75736i		−	0.0829349i	0.999140	−	0.0414675i	$-0.0132033\pi$
$450$		0			0
$451$	−30.7279	+	17.7408i	−1.44692	+	0.835380i
$452$	−7.34847	+	4.24264i	−0.345643	+	0.199557i
$453$		0			0
$454$			15.5885i			0.731603i
$455$	−4.30463	−	1.75736i	−0.201804	−	0.0823863i
$456$		0			0
$457$	11.5000	−	19.9186i	0.537947	−	0.931752i	−0.461067	−	0.887365i	$-0.652533\pi$
$457$	11.5000	−	19.9186i	0.537947	−	0.931752i	0.999014	−	0.0443868i	$-0.0141334\pi$
$458$	6.92820	+	12.0000i	0.323734	+	0.560723i
$459$		0			0
$460$	−2.63604	−	1.52192i	−0.122906	−	0.0709598i
$461$	−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
$463$	−29.4558			−1.36893			−0.684465	−	0.729046i	$-0.739964\pi$
$463$	−29.4558			−1.36893			−0.684465	+	0.729046i	$0.739964\pi$
$464$	−6.27231	−	3.62132i	−0.291185	−	0.168116i
$465$		0			0
$466$	9.36396	+	16.2189i	0.433777	+	0.751324i
$467$	−19.8931	+	34.4558i	−0.920542	+	1.59443i	−0.121965	+	0.992534i	$0.538920\pi$
$467$	−19.8931	+	34.4558i	−0.920542	+	1.59443i	−0.798578	+	0.601892i	$0.794414\pi$
$468$		0			0
$469$	16.2132	+	20.9077i	0.748656	+	0.965428i
$470$			4.24264i			0.195698i
$471$		0			0
$472$	−6.98528	+	4.03295i	−0.321524	+	0.185632i
$473$	−0.630399	+	0.363961i	−0.0289858	+	0.0167349i
$474$		0			0
$475$		−	26.5241i		−	1.21701i
$476$	−5.91359	+	14.4853i	−0.271049	+	0.663932i
$477$		0			0
$478$	6.36396	−	11.0227i	0.291081	−	0.504167i
$479$	−6.00063	−	10.3934i	−0.274176	−	0.474886i	0.695751	−	0.718283i	$-0.255072\pi$
$479$	−6.00063	−	10.3934i	−0.274176	−	0.474886i	−0.969927	+	0.243397i	$0.921738\pi$
$480$		0			0
$481$	−0.514719	−	0.297173i	−0.0234691	−	0.0135499i
$482$	−7.22538			−0.329107
$483$		0			0
$484$	−2.00000			−0.0909091
$485$	8.42463	+	4.86396i	0.382543	+	0.220861i
$486$		0			0
$487$	7.10660	+	12.3090i	0.322031	+	0.557774i	0.980907	−	0.194478i	$-0.0623012\pi$
$487$	7.10660	+	12.3090i	0.322031	+	0.557774i	−0.658876	+	0.752251i	$0.728968\pi$
$488$	0.507306	−	0.878680i	0.0229647	−	0.0397760i
$489$		0			0
$490$	−3.51472	+	3.58719i	−0.158779	+	0.162053i
$491$		−	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
$493$	−37.0919	+	21.4150i	−1.67053	+	0.964483i
$494$	12.5446	−	7.24264i	0.564409	−	0.325862i
$495$		0			0
$496$		−	9.08052i		−	0.407727i
$497$	−0.630399	−	4.60660i	−0.0282773	−	0.206634i
$498$		0			0
$499$	−15.9706	+	27.6618i	−0.714941	+	1.23831i	0.248042	+	0.968749i	$0.420213\pi$
$499$	−15.9706	+	27.6618i	−0.714941	+	1.23831i	−0.962982	+	0.269564i	$0.913120\pi$
$500$	3.40256	+	5.89340i	0.152167	+	0.263561i
$501$		0			0
$502$	−23.7426	−	13.7078i	−1.05969	−	0.611810i
$503$	31.0028			1.38235			0.691174	−	0.722688i	$-0.257094\pi$
$503$	31.0028			1.38235			0.691174	+	0.722688i	$0.257094\pi$
$504$		0			0
$505$		0			0
$506$	11.0227	+	6.36396i	0.490019	+	0.282913i
$507$		0			0
$508$	1.62132	+	2.80821i	0.0719345	+	0.124594i
$509$	−8.59871	+	14.8934i	−0.381131	+	0.660138i	−0.991224	−	0.132191i	$-0.957799\pi$
$509$	−8.59871	+	14.8934i	−0.381131	+	0.660138i	0.610093	+	0.792330i	$0.291132\pi$
$510$		0			0
$511$	−3.00000	+	2.32640i	−0.132712	+	0.102914i
$512$			1.00000i			0.0441942i
$513$		0			0
$514$	3.72792	−	2.15232i	0.164432	−	0.0949346i
$515$	−3.41311	+	1.97056i	−0.150400	+	0.0868334i
$516$		0			0
$517$		−	17.7408i		−	0.780238i
$518$	−0.507306	+	0.393398i	−0.0222897	+	0.0172849i
$519$		0			0
$520$	−0.878680	+	1.52192i	−0.0385327	+	0.0667405i
$521$	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
$523$	5.84924	+	3.37706i	0.255770	+	0.147669i	0.622403	−	0.782697i	$-0.286156\pi$
$523$	5.84924	+	3.37706i	0.255770	+	0.147669i	−0.366634	+	0.930365i	$0.619490\pi$
$524$	5.19615			0.226995
$525$		0			0
$526$	15.2132			0.663327
$527$	−46.5043	−	26.8492i	−2.02576	−	1.16957i
$528$		0			0
$529$	−2.50000	−	4.33013i	−0.108696	−	0.188266i
$530$	−2.59808	+	4.50000i	−0.112853	+	0.195468i
$531$		0			0
$532$	−2.12132	−	15.5014i	−0.0919709	−	0.672072i
$533$			28.9706i			1.25485i
$534$		0			0
$535$	7.13604	−	4.11999i	0.308518	−	0.178123i
$536$	8.66025	−	5.00000i	0.374066	−	0.215967i
$537$		0			0
$538$		−	13.9795i		−	0.602699i
$539$	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	$0.269208\pi$
$542$	3.10538	+	5.37868i	0.133388	+	0.231034i
$543$		0			0
$544$	5.12132	+	2.95680i	0.219575	+	0.126772i
$545$	−13.2621			−0.568084
$546$		0			0
$547$	−39.6985			−1.69738			−0.848692	−	0.528887i	$-0.822610\pi$
$547$	−39.6985			−1.69738			−0.848692	+	0.528887i	$0.822610\pi$
$548$	2.15232	+	1.24264i	0.0919424	+	0.0530830i
$549$		0			0
$550$	−6.72792	−	11.6531i	−0.286880	−	0.496890i
$551$	21.4150	−	37.0919i	0.912310	−	1.58017i
$552$		0			0
$553$	2.75736	−	6.75412i	0.117255	−	0.287215i
$554$			12.9706i			0.551066i
$555$		0			0
$556$	0.514719	−	0.297173i	0.0218289	−	0.0126029i
$557$	−8.42463	+	4.86396i	−0.356963	+	0.206093i	−0.667748	−	0.744388i	$-0.732741\pi$
$557$	−8.42463	+	4.86396i	−0.356963	+	0.206093i	0.310785	+	0.950480i	$0.399408\pi$
$558$		0			0
$559$			0.594346i			0.0251382i
$560$	1.16320	+	1.50000i	0.0491541	+	0.0633866i
$561$		0			0
$562$	3.00000	−	5.19615i	0.126547	−	0.219186i
$563$	−17.2950	−	29.9558i	−0.728898	−	1.26249i	−0.957349	−	0.288933i	$-0.906700\pi$
$563$	−17.2950	−	29.9558i	−0.728898	−	1.26249i	0.228451	−	0.973555i	$-0.426634\pi$
$564$		0			0
$565$	5.27208	+	3.04384i	0.221798	+	0.128055i
$566$	21.2049			0.891307
$567$		0			0
$568$	−1.75736			−0.0737372
$569$	8.87039	+	5.12132i	0.371866	+	0.214697i	0.674273	−	0.738482i	$-0.264457\pi$
$569$	8.87039	+	5.12132i	0.371866	+	0.214697i	−0.302407	+	0.953179i	$0.597790\pi$
$570$		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	$0.891793\pi$
$572$	3.67423	−	6.36396i	0.153627	−	0.266091i
$573$		0			0
$574$	28.9706	+	11.8272i	1.20921	+	0.493657i
$575$		−	19.0294i		−	0.793582i
$576$		0			0
$577$	9.25736	−	5.34474i	0.385389	−	0.222504i	−0.294771	−	0.955568i	$-0.595243\pi$
$577$	9.25736	−	5.34474i	0.385389	−	0.222504i	0.680160	+	0.733063i	$0.261910\pi$
$578$	15.5630	−	8.98528i	0.647334	−	0.373738i
$579$		0			0
$580$			5.19615i			0.215758i
$581$	−17.3821	+	2.37868i	−0.721129	+	0.0986843i
$582$		0			0
$583$	10.8640	−	18.8169i	0.449939	−	0.779318i
$584$	0.717439	+	1.24264i	0.0296878	+	0.0514208i
$585$		0			0
$586$	−0.621320	−	0.358719i	−0.0256665	−	0.0148186i
$587$	−5.19615			−0.214468			−0.107234	−	0.994234i	$-0.534199\pi$
$587$	−5.19615			−0.214468			−0.107234	+	0.994234i	$0.534199\pi$
$588$		0			0
$589$	53.6985			2.21261
$590$	5.01151	+	2.89340i	0.206321	+	0.119119i
$591$		0			0
$592$	0.121320	+	0.210133i	0.00498624	+	0.00863641i
$593$	11.7401	−	20.3345i	0.482110	−	0.835039i	−0.517679	−	0.855575i	$-0.673204\pi$
$593$	11.7401	−	20.3345i	0.482110	−	0.835039i	0.999789	+	0.0205360i	$0.00653726\pi$
$594$		0			0
$595$	11.1213	−	1.52192i	0.455930	−	0.0623925i
$596$			3.51472i			0.143968i
$597$		0			0
$598$	9.00000	−	5.19615i	0.368037	−	0.212486i
$599$	6.45695	−	3.72792i	0.263824	−	0.152319i	−0.362254	−	0.932079i	$-0.617993\pi$
$599$	6.45695	−	3.72792i	0.263824	−	0.152319i	0.626078	+	0.779761i	$0.284659\pi$
$600$		0			0
$601$			23.3572i			0.952760i	0.879240	+	0.476380i	$0.158051\pi$
$601$			23.3572i			0.952760i	−0.879240	+	0.476380i	$0.841949\pi$
$602$	0.594346	+	0.242641i	0.0242237	+	0.00988930i
$603$		0			0
$604$	2.62132	−	4.54026i	0.106660	−	0.184741i
$605$	0.717439	+	1.24264i	0.0291680	+	0.0505205i
$606$		0			0
$607$	−17.3787	−	10.0336i	−0.705379	−	0.407251i	0.103969	−	0.994581i	$-0.466846\pi$
$607$	−17.3787	−	10.0336i	−0.705379	−	0.407251i	−0.809348	+	0.587330i	$0.800179\pi$
$608$	−5.91359			−0.239828
$609$		0			0
$610$	−0.727922			−0.0294727
$611$	−12.5446	−	7.24264i	−0.507501	−	0.293006i
$612$		0			0
$613$	18.6066	+	32.2276i	0.751514	+	1.30166i	0.947089	+	0.320971i	$0.104009\pi$
$613$	18.6066	+	32.2276i	0.751514	+	1.30166i	−0.195575	+	0.980689i	$0.562657\pi$
$614$	−4.98602	+	8.63604i	−0.201219	+	0.348522i
$615$		0			0
$616$	−4.86396	−	6.27231i	−0.195975	−	0.252719i
$617$		−	17.6985i		−	0.712514i	−0.934388	−	0.356257i	$-0.884053\pi$
$617$		−	17.6985i		−	0.712514i	0.934388	−	0.356257i	$-0.115947\pi$
$618$		0			0
$619$	5.33452	−	3.07989i	0.214413	−	0.123791i	−0.388948	−	0.921260i	$-0.627161\pi$
$619$	5.33452	−	3.07989i	0.214413	−	0.123791i	0.603360	+	0.797469i	$0.293828\pi$
$620$	−5.64191	+	3.25736i	−0.226585	+	0.130819i
$621$		0			0
$622$		−	8.95743i		−	0.359160i
$623$	−10.3923	+	25.4558i	−0.416359	+	1.01987i
$624$		0			0
$625$	−8.77208	+	15.1937i	−0.350883	+	0.607747i
$626$	−9.22911	−	15.9853i	−0.368869	−	0.638900i
$627$		0			0
$628$	12.7279	+	7.34847i	0.507899	+	0.293236i
$629$	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	$0.335978\pi$
$632$	−2.38794	−	1.37868i	−0.0949873	−	0.0548409i
$633$		0			0
$634$	0.621320	+	1.07616i	0.0246758	+	0.0427397i
$635$	1.16320	−	2.01472i	0.0461601	−	0.0799517i
$636$		0			0
$637$	−4.60660	−	16.5160i	−0.182520	−	0.654389i
$638$		−	21.7279i		−	0.860217i
$639$		0			0
$640$	0.621320	−	0.358719i	0.0245598	−	0.0141796i
$641$	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
$643$			32.0174i			1.26264i	0.775520	+	0.631322i	$0.217488\pi$
$643$			32.0174i			1.26264i	−0.775520	+	0.631322i	$0.782512\pi$
$644$	−1.52192	−	11.1213i	−0.0599720	−	0.438241i
$645$		0			0
$646$	−17.4853	+	30.2854i	−0.687949	+	1.19156i
$647$	16.2189	+	28.0919i	0.637629	+	1.10441i	0.985952	+	0.167031i	$0.0534180\pi$
$647$	16.2189	+	28.0919i	0.637629	+	1.10441i	−0.348323	+	0.937375i	$0.613249\pi$
$648$		0			0
$649$	−20.9558	−	12.0989i	−0.822589	−	0.474922i
$650$	−10.9867			−0.430932
$651$		0			0
$652$	2.24264			0.0878286
$653$	−16.6646	−	9.62132i	−0.652137	−	0.376511i	0.137138	−	0.990552i	$-0.456210\pi$
$653$	−16.6646	−	9.62132i	−0.652137	−	0.376511i	−0.789274	+	0.614041i	$0.789543\pi$
$654$		0			0
$655$	−1.86396	−	3.22848i	−0.0728310	−	0.126147i
$656$	5.91359	−	10.2426i	0.230887	−	0.399908i
$657$		0			0
$658$	−12.3640	+	9.58783i	−0.481997	+	0.373772i
$659$			6.00000i			0.233727i	0.993148	+	0.116863i	$0.0372840\pi$
$659$			6.00000i			0.233727i	−0.993148	+	0.116863i	$0.962716\pi$
$660$		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	$0.0894357\pi$
$662$	−28.9736	+	16.7279i	−1.12609	+	0.650149i
$663$		0			0
$664$			6.63103i			0.257334i
$665$	−8.87039	+	6.87868i	−0.343979	+	0.266744i
$666$		0			0
$667$	15.3640	−	26.6112i	0.594895	−	1.03039i
$668$	8.06591	+	13.9706i	0.312079	+	0.540537i
$669$		0			0
$670$	−6.21320	−	3.58719i	−0.240037	−	0.138585i
$671$	3.04384			0.117506
$672$		0			0
$673$	17.9706			0.692714			0.346357	−	0.938103i	$-0.387419\pi$
$673$	17.9706			0.692714			0.346357	+	0.938103i	$0.387419\pi$
$674$	4.33013	+	2.50000i	0.166790	+	0.0962964i
$675$		0			0
$676$	3.50000	+	6.06218i	0.134615	+	0.233161i
$677$	−1.07616	+	1.86396i	−0.0413601	+	0.0716378i	−0.885964	−	0.463753i	$-0.846502\pi$
$677$	−1.07616	+	1.86396i	−0.0413601	+	0.0716378i	0.844604	+	0.535391i	$0.179836\pi$
$678$		0			0
$679$	4.86396	+	35.5431i	0.186662	+	1.36402i
$680$		−	4.24264i		−	0.162698i
$681$		0			0
$682$	23.5919	−	13.6208i	0.903380	−	0.521567i
$683$	6.90271	−	3.98528i	0.264125	−	0.152493i	−0.362090	−	0.932143i	$-0.617937\pi$
$683$	6.90271	−	3.98528i	0.264125	−	0.152493i	0.626215	+	0.779651i	$0.284603\pi$
$684$		0			0
$685$		−	1.78304i		−	0.0681264i
$686$	−18.3967	−	2.13604i	−0.702388	−	0.0815543i
$687$		0			0
$688$	0.121320	−	0.210133i	0.00462529	−	0.00801125i
$689$	−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	$0.483913\pi$
$692$	20.7846			0.790112
$693$		0			0
$694$	2.48528			0.0943400
$695$	−0.369279	−	0.213203i	−0.0140076	−	0.00808727i
$696$		0			0
$697$	−34.9706	−	60.5708i	−1.32460	−	2.29428i
$698$	−1.13770	+	1.97056i	−0.0430628	+	0.0745869i
$699$		0			0
$700$	−4.48528	+	10.9867i	−0.169528	+	0.415256i
$701$			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
$703$	−1.24264	+	0.717439i	−0.0468671	+	0.0270587i
$704$	−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	$0.335709\pi$
$709$	−13.4853	+	23.3572i	−0.506450	+	0.877198i	−0.999972	+	0.00746433i	$0.997624\pi$
$710$	0.630399	+	1.09188i	0.0236585	+	0.0409776i
$711$		0			0
$712$	9.00000	+	5.19615i	0.337289	+	0.194734i
$713$	38.5254			1.44279
$714$		0			0
$715$	−5.27208			−0.197165
$716$	−22.9369	−	13.2426i	−0.857193	−	0.494901i
$717$		0			0
$718$	−9.00000	−	15.5885i	−0.335877	−	0.581756i
$719$	8.06591	−	13.9706i	0.300808	−	0.521014i	−0.675511	−	0.737349i	$-0.736077\pi$
$719$	8.06591	−	13.9706i	0.300808	−	0.521014i	0.976319	+	0.216335i	$0.0694105\pi$
$720$		0			0
$721$	−13.4558	−	5.49333i	−0.501122	−	0.204582i
$722$		−	15.9706i		−	0.594363i
$723$		0			0
$724$	−10.2426	+	5.91359i	−0.380665	+	0.219777i
$725$	−28.1331	+	16.2426i	−1.04484	+	0.603237i
$726$		0			0
$727$		−	11.7041i		−	0.434081i	−0.976163	−	0.217040i	$-0.930360\pi$
$727$		−	11.7041i		−	0.434081i	0.976163	−	0.217040i	$-0.0696403\pi$
$728$	−6.42090	+	0.878680i	−0.237974	+	0.0325660i
$729$		0			0
$730$	0.514719	−	0.891519i	0.0190506	−	0.0329966i
$731$	−0.717439	−	1.24264i	−0.0265354	−	0.0459607i
$732$		0			0
$733$	4.09188	+	2.36245i	0.151137	+	0.0872591i	0.573661	−	0.819093i	$-0.305523\pi$
$733$	4.09188	+	2.36245i	0.151137	+	0.0872591i	−0.422524	+	0.906352i	$0.638856\pi$
$734$	15.4144			0.568955
$735$		0			0
$736$	−4.24264			−0.156386
$737$	25.9808	+	15.0000i	0.957014	+	0.552532i
$738$		0			0
$739$	−7.72792	−	13.3852i	−0.284276	−	0.492381i	0.688157	−	0.725562i	$-0.258420\pi$
$739$	−7.72792	−	13.3852i	−0.284276	−	0.492381i	−0.972433	+	0.233181i	$0.925087\pi$
$740$	0.0870399	−	0.150758i	0.00319965	−	0.00554196i
$741$		0			0
$742$	−18.9853	+	2.59808i	−0.696972	+	0.0953784i
$743$			38.4853i			1.41189i	0.708268	+	0.705944i	$0.249477\pi$
$743$			38.4853i			1.41189i	−0.708268	+	0.705944i	$0.750523\pi$
$744$		0			0
$745$	2.18377	−	1.26080i	0.0800070	−	0.0461921i
$746$	−25.5095	+	14.7279i	−0.933969	+	0.539228i
$747$		0			0
$748$			17.7408i			0.648667i
$749$	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	$0.944352\pi$
$752$	2.95680	+	5.12132i	0.107823	+	0.186755i
$753$		0			0
$754$	−15.3640	−	8.87039i	−0.559522	−	0.323040i
$755$	−3.76127			−0.136887
$756$		0			0
$757$	−33.7574			−1.22693			−0.613466	−	0.789721i	$-0.710225\pi$
$757$	−33.7574			−1.22693			−0.613466	+	0.789721i	$0.710225\pi$
$758$	−10.8126	−	6.24264i	−0.392730	−	0.226743i
$759$		0			0
$760$	2.12132	+	3.67423i	0.0769484	+	0.133278i
$761$	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
$763$	−29.9706	−	38.6485i	−1.08501	−	1.39917i
$764$		−	8.48528i		−	0.306987i
$765$		0			0
$766$	−19.2426	+	11.1097i	−0.695265	+	0.401411i
$767$	−17.1104	+	9.87868i	−0.617820	+	0.356698i
$768$		0			0
$769$			9.84895i			0.355162i	0.984106	+	0.177581i	$0.0568272\pi$
$769$			9.84895i			0.355162i	−0.984106	+	0.177581i	$0.943173\pi$
$770$	−2.15232	+	5.27208i	−0.0775641	+	0.189993i
$771$		0			0
$772$	4.74264	−	8.21449i	0.170691	−	0.295646i
$773$	−8.06591	−	13.9706i	−0.290111	−	0.502486i	0.683725	−	0.729740i	$-0.260359\pi$
$773$	−8.06591	−	13.9706i	−0.290111	−	0.502486i	−0.973836	+	0.227253i	$0.927025\pi$
$774$		0			0
$775$	−35.2721	−	20.3643i	−1.26701	−	0.731509i
$776$	13.5592			0.486748
$777$		0			0
$778$	−31.4558			−1.12775
$779$	60.5708	+	34.9706i	2.17017	+	1.25295i
$780$		0			0
$781$	−2.63604	−	4.56575i	−0.0943249	−	0.163376i
$782$	−12.5446	+	21.7279i	−0.448595	+	0.776989i
$783$		0			0
$784$	−1.74264	+	6.77962i	−0.0622372	+	0.242129i
$785$		−	10.5442i		−	0.376337i
$786$		0			0
$787$	27.8787	−	16.0958i	0.993768	−	0.573752i	0.0873693	−	0.996176i	$-0.472154\pi$
$787$	27.8787	−	16.0958i	0.993768	−	0.573752i	0.906398	+	0.422424i	$0.138821\pi$
$788$	22.9369	−	13.2426i	0.817094	−	0.471750i
$789$		0			0
$790$			1.97824i			0.0703825i
$791$	3.04384	+	22.2426i	0.108226	+	0.790857i
$792$		0			0
$793$	1.24264	−	2.15232i	0.0441275	−	0.0764310i
$794$	−6.92820	−	12.0000i	−0.245873	−	0.425864i
$795$		0			0
$796$	19.9706	+	11.5300i	0.707838	+	0.408670i
$797$	−6.45695			−0.228717			−0.114358	−	0.993440i	$-0.536481\pi$
$797$	−6.45695			−0.228717			−0.114358	+	0.993440i	$0.536481\pi$
$798$		0			0
$799$	34.9706			1.23717
$800$	3.88437	+	2.24264i	0.137333	+	0.0792893i
$801$		0			0
$802$		0			0
$803$	−2.15232	+	3.72792i	−0.0759536	+	0.131556i
$804$		0			0
$805$	−6.36396	+	4.93503i	−0.224300	+	0.173937i
$806$		−	22.2426i		−	0.783464i
$807$		0			0
$808$		0			0
$809$	6.08767	−	3.51472i	0.214031	−	0.123571i	−0.389152	−	0.921173i	$-0.627232\pi$
$809$	6.08767	−	3.51472i	0.214031	−	0.123571i	0.603183	+	0.797602i	$0.293899\pi$
$810$		0			0
$811$			31.1769i			1.09477i	0.836881	+	0.547385i	$0.184377\pi$
$811$			31.1769i			1.09477i	−0.836881	+	0.547385i	$0.815623\pi$
$812$	−15.1427	+	11.7426i	−0.531405	+	0.412086i
$813$		0			0
$814$	−0.363961	+	0.630399i	−0.0127568	+	0.0220955i
$815$	−0.804479	−	1.39340i	−0.0281797	−	0.0488086i
$816$		0			0
$817$	1.24264	+	0.717439i	0.0434745	+	0.0251000i
$818$	−14.9941			−0.524257
$819$		0			0
$820$	−8.48528			−0.296319
$821$	−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
$823$	−14.9706	−	25.9298i	−0.521841	−	0.903855i	−0.999677	−	0.0254062i	$-0.991912\pi$
$823$	−14.9706	−	25.9298i	−0.521841	−	0.903855i	0.477836	−	0.878449i	$-0.341421\pi$
$824$	−2.74666	+	4.75736i	−0.0956845	+	0.165730i
$825$		0			0
$826$	2.89340	+	21.1433i	0.100674	+	0.735671i
$827$			37.9706i			1.32037i	0.751105	+	0.660183i	$0.229521\pi$
$827$			37.9706i			1.32037i	−0.751105	+	0.660183i	$0.770479\pi$
$828$		0			0
$829$	11.3345	−	6.54399i	0.393664	−	0.227282i	−0.290082	−	0.957002i	$-0.593683\pi$
$829$	11.3345	−	6.54399i	0.393664	−	0.227282i	0.683747	+	0.729720i	$0.260349\pi$
$830$	4.11999	−	2.37868i	0.143007	−	0.0825652i
$831$		0			0
$832$			2.44949i			0.0849208i
$833$	29.5680	+	28.9706i	1.02447	+	1.00377i
$834$		0			0
$835$	5.78680	−	10.0230i	0.200260	−	0.346861i
$836$	−8.87039	−	15.3640i	−0.306789	−	0.531374i
$837$		0			0
$838$	20.4853	+	11.8272i	0.707652	+	0.408563i
$839$	−10.2182			−0.352772			−0.176386	−	0.984321i	$-0.556441\pi$
$839$	−10.2182			−0.352772			−0.176386	+	0.984321i	$0.556441\pi$
$840$		0			0
$841$	−23.4558			−0.808822
$842$	12.3345	+	7.12132i	0.425075	+	0.245417i
$843$		0			0
$844$	−0.121320	−	0.210133i	−0.00417602	−	0.00723308i
$845$	2.51104	−	4.34924i	0.0863823	−	0.149618i
$846$		0			0
$847$	−2.00000	+	4.89898i	−0.0687208	+	0.168331i
$848$			7.24264i			0.248713i
$849$		0			0
$850$	22.9706	−	13.2621i	0.787884	−	0.454885i
$851$	−0.891519	+	0.514719i	−0.0305609	+	0.0176443i
$852$		0			0
$853$			36.9164i			1.26399i	0.774971	+	0.631997i	$0.217765\pi$
$853$			36.9164i			1.26399i	−0.774971	+	0.631997i	$0.782235\pi$
$854$	−1.64501	−	2.12132i	−0.0562911	−	0.0725901i
$855$		0			0
$856$	5.74264	−	9.94655i	0.196279	−	0.339966i
$857$	−16.9363	−	29.3345i	−0.578533	−	1.00205i	−0.995648	−	0.0931946i	$-0.970292\pi$
$857$	−16.9363	−	29.3345i	−0.578533	−	1.00205i	0.417115	−	0.908854i	$-0.363041\pi$
$858$		0			0
$859$	8.12132	+	4.68885i	0.277096	+	0.159981i	0.632108	−	0.774880i	$-0.282190\pi$
$859$	8.12132	+	4.68885i	0.277096	+	0.159981i	−0.355012	+	0.934862i	$0.615523\pi$
$860$	−0.174080			−0.00593607
$861$		0			0
$862$	−3.51472			−0.119712
$863$	−29.0246	−	16.7574i	−0.988009	−	0.570427i	−0.0833303	−	0.996522i	$-0.526556\pi$
$863$	−29.0246	−	16.7574i	−0.988009	−	0.570427i	−0.904679	+	0.426095i	$0.859889\pi$
$864$		0			0
$865$	−7.45584	−	12.9139i	−0.253506	−	0.439086i
$866$	−1.73205	+	3.00000i	−0.0588575	+	0.101944i
$867$		0			0
$868$	−22.2426	−	9.08052i	−0.754964	−	0.308213i
$869$		−	8.27208i		−	0.280611i
$870$		0			0
$871$	21.2132	−	12.2474i	0.718782	−	0.414989i
$872$	−16.0087	+	9.24264i	−0.542124	+	0.312995i
$873$		0			0
$874$		−	25.0892i		−	0.848656i
$875$	17.8384	−	2.44113i	0.603047	−	0.0825251i
$876$		0			0
$877$	−2.24264	+	3.88437i	−0.0757286	+	0.131166i	−0.901403	−	0.432981i	$-0.857462\pi$
$877$	−2.24264	+	3.88437i	−0.0757286	+	0.131166i	0.825674	+	0.564147i	$0.190795\pi$
$878$	8.42463	+	14.5919i	0.284317	+	0.492452i
$879$		0			0
$880$	1.86396	+	1.07616i	0.0628341	+	0.0362773i
$881$	−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
$883$	41.4558			1.39510			0.697550	−	0.716536i	$-0.254273\pi$
$883$	41.4558			1.39510			0.697550	+	0.716536i	$0.254273\pi$
$884$	12.5446	+	7.24264i	0.421921	+	0.243596i
$885$		0			0
$886$	−8.22792	−	14.2512i	−0.276422	−	0.478778i
$887$	−5.28319	+	9.15076i	−0.177392	+	0.307252i	−0.940987	−	0.338444i	$-0.890099\pi$
$887$	−5.28319	+	9.15076i	−0.177392	+	0.307252i	0.763594	+	0.645696i	$0.223433\pi$
$888$		0			0
$889$	8.50000	−	1.16320i	0.285081	−	0.0390124i
$890$		−	7.45584i		−	0.249920i
$891$		0			0
$892$	−1.86396	+	1.07616i	−0.0624100	+	0.0360324i
$893$	−30.2854	+	17.4853i	−1.01346	+	0.585123i
$894$		0			0
$895$			19.0016i			0.635153i
$896$	2.44949	+	1.00000i	0.0818317	+	0.0334077i
$897$		0			0
$898$	−0.878680	+	1.52192i	−0.0293219	+	0.0507871i
$899$	−32.8835	−	56.9558i	−1.09673	−	1.89958i
$900$		0			0
$901$	37.0919	+	21.4150i	1.23571	+	0.713437i
$902$	35.4815			1.18141
$903$		0			0
$904$	8.48528			0.282216
$905$	7.34847	+	4.24264i	0.244271	+	0.141030i
$906$		0			0
$907$	15.8492	+	27.4517i	0.526265	+	0.911519i	0.999532	+	0.0305991i	$0.00974151\pi$
$907$	15.8492	+	27.4517i	0.526265	+	0.911519i	−0.473266	+	0.880919i	$0.656925\pi$
$908$	7.79423	−	13.5000i	0.258661	−	0.448013i
$909$		0			0
$910$	2.84924	+	3.67423i	0.0944515	+	0.121800i
$911$		−	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
$913$	−17.2279	+	9.94655i	−0.570161	+	0.329183i
$914$	−19.9186	+	11.5000i	−0.658848	+	0.380386i
$915$		0			0
$916$		−	13.8564i		−	0.457829i
$917$	5.19615	−	12.7279i	0.171592	−	0.420313i
$918$		0			0
$919$	−18.2426	+	31.5972i	−0.601769	+	1.04229i	0.390784	+	0.920482i	$0.372204\pi$
$919$	−18.2426	+	31.5972i	−0.601769	+	1.04229i	−0.992553	+	0.121812i	$0.961129\pi$
$920$	1.52192	+	2.63604i	0.0501761	+	0.0869076i
$921$		0			0
$922$	28.2426	+	16.3059i	0.930122	+	0.537006i
$923$	−4.30463			−0.141689
$924$		0			0
$925$	1.08831			0.0357835
$926$	25.5095	+	14.7279i	0.838294	+	0.483990i
$927$		0			0
$928$	3.62132	+	6.27231i	0.118876	+	0.205899i
$929$	15.5014	−	26.8492i	0.508585	−	0.880895i	−0.491366	−	0.870953i	$-0.663502\pi$
$929$	15.5014	−	26.8492i	0.508585	−	0.880895i	0.999951	−	0.00994164i	$-0.00316458\pi$
$930$		0			0
$931$	−40.0919	−	10.3053i	−1.31396	−	0.337741i
$932$		−	18.7279i		−	0.613453i
$933$		0			0
$934$	34.4558	−	19.8931i	1.12743	−	0.650922i
$935$	11.0227	−	6.36396i	0.360481	−	0.208124i
$936$		0			0
$937$		−	35.1844i		−	1.14942i	−0.818356	−	0.574712i	$-0.805114\pi$
$937$		−	35.1844i		−	1.14942i	0.818356	−	0.574712i	$-0.194886\pi$
$938$	−3.58719	−	26.2132i	−0.117126	−	0.855891i
$939$		0			0
$940$	2.12132	−	3.67423i	0.0691898	−	0.119840i
$941$	−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
$943$	43.4558	+	25.0892i	1.41512	+	0.817018i
$944$	8.06591			0.262523
$945$		0			0
$946$	0.727922			0.0236668
$947$	9.50079	+	5.48528i	0.308734	+	0.178248i	0.646360	−	0.763033i	$-0.276291\pi$
$947$	9.50079	+	5.48528i	0.308734	+	0.178248i	−0.337626	+	0.941280i	$0.609624\pi$
$948$		0			0
$949$	1.75736	+	3.04384i	0.0570463	+	0.0988071i
$950$	−13.2621	+	22.9706i	−0.430278	+	0.745263i
$951$		0			0
$952$	12.3640	−	9.58783i	0.400718	−	0.310743i
$953$		−	17.6985i		−	0.573310i	−0.958034	−	0.286655i	$-0.907457\pi$
$953$		−	17.6985i		−	0.573310i	0.958034	−	0.286655i	$-0.0925434\pi$
$954$		0			0
$955$	−5.27208	+	3.04384i	−0.170600	+	0.0984962i
$956$	−11.0227	+	6.36396i	−0.356500	+	0.205825i
$957$		0			0
$958$			12.0013i			0.387743i
$959$	5.19615	−	4.02944i	0.167793	−	0.130117i
$960$		0			0
$961$	25.7279	−	44.5621i	0.829933	−	1.43749i
$962$	0.297173	+	0.514719i	0.00958124	+	0.0165952i
$963$		0			0
$964$	6.25736	+	3.61269i	0.201536	+	0.116357i
$965$	−6.80511			−0.219064
$966$		0			0
$967$	47.7279			1.53483			0.767413	−	0.641153i	$-0.221544\pi$
$967$	47.7279			1.53483			0.767413	+	0.641153i	$0.221544\pi$
$968$	1.73205	+	1.00000i	0.0556702	+	0.0321412i
$969$		0			0
$970$	−4.86396	−	8.42463i	−0.156172	−	0.270498i
$971$	−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
$973$	−0.213203	−	1.55797i	−0.00683499	−	0.0499463i
$974$		−	14.2132i		−	0.455420i
$975$		0			0
$976$	−0.878680	+	0.507306i	−0.0281259	+	0.0162385i
$977$	34.8511	−	20.1213i	1.11499	−	0.643738i	0.174871	−	0.984591i	$-0.444049\pi$
$977$	34.8511	−	20.1213i	1.11499	−	0.643738i	0.940116	+	0.340853i	$0.110716\pi$
$978$		0			0
$979$			31.1769i			0.996419i
$980$	4.83743	−	1.34924i	0.154526	−	0.0431000i
$981$		0			0
$982$	−6.98528	+	12.0989i	−0.222909	+	0.386090i
$983$	23.6544	+	40.9706i	0.754457	+	1.30676i	0.945644	+	0.325204i	$0.105433\pi$
$983$	23.6544	+	40.9706i	0.754457	+	1.30676i	−0.191187	+	0.981554i	$0.561234\pi$
$984$		0			0
$985$	−16.4558	−	9.50079i	−0.524327	−	0.302720i
$986$	42.8300			1.36399
$987$		0			0
$988$	−14.4853			−0.460838
$989$	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	$-0.477929\pi$
$992$	−4.54026	+	7.86396i	−0.144153	+	0.249681i
$993$		0			0
$994$	−1.75736	+	4.30463i	−0.0557401	+	0.136535i
$995$		−	16.5442i		−	0.524485i
$996$		0			0
$997$	−33.7279	+	19.4728i	−1.06817	+	0.616711i	−0.927682	−	0.373371i	$-0.878202\pi$
$997$	−33.7279	+	19.4728i	−1.06817	+	0.616711i	−0.140492	+	0.990082i	$0.544868\pi$
$998$	27.6618	−	15.9706i	0.875620	−	0.505539i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	126.2.k.a.89.2	yes	8
3.2	odd	2	inner	126.2.k.a.89.3	yes	8
4.3	odd	2		1008.2.bt.c.593.3		8
5.2	odd	4		3150.2.bp.e.1349.3		8
5.3	odd	4		3150.2.bp.b.1349.2		8
5.4	even	2		3150.2.bf.a.1601.3		8
7.2	even	3		882.2.d.a.881.6		8
7.3	odd	6	inner	126.2.k.a.17.3	yes	8
7.4	even	3		882.2.k.a.521.4		8
7.5	odd	6		882.2.d.a.881.7		8
7.6	odd	2		882.2.k.a.215.1		8
9.2	odd	6		1134.2.l.f.215.1		8
9.4	even	3		1134.2.t.e.593.3		8
9.5	odd	6		1134.2.t.e.593.2		8
9.7	even	3		1134.2.l.f.215.4		8
12.11	even	2		1008.2.bt.c.593.2		8
15.2	even	4		3150.2.bp.b.1349.3		8
15.8	even	4		3150.2.bp.e.1349.2		8
15.14	odd	2		3150.2.bf.a.1601.1		8
21.2	odd	6		882.2.d.a.881.3		8
21.5	even	6		882.2.d.a.881.2		8
21.11	odd	6		882.2.k.a.521.1		8
21.17	even	6	inner	126.2.k.a.17.2	✓	8
21.20	even	2		882.2.k.a.215.4		8
28.3	even	6		1008.2.bt.c.17.2		8
28.19	even	6		7056.2.k.f.881.5		8
28.23	odd	6		7056.2.k.f.881.3		8
35.3	even	12		3150.2.bp.b.899.3		8
35.17	even	12		3150.2.bp.e.899.2		8
35.24	odd	6		3150.2.bf.a.1151.1		8
63.31	odd	6		1134.2.l.f.269.3		8
63.38	even	6		1134.2.t.e.1025.3		8
63.52	odd	6		1134.2.t.e.1025.2		8
63.59	even	6		1134.2.l.f.269.2		8
84.23	even	6		7056.2.k.f.881.6		8
84.47	odd	6		7056.2.k.f.881.4		8
84.59	odd	6		1008.2.bt.c.17.3		8
105.17	odd	12		3150.2.bp.b.899.2		8
105.38	odd	12		3150.2.bp.e.899.3		8
105.59	even	6		3150.2.bf.a.1151.3		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
126.2.k.a.17.2	✓	8	21.17	even	6	inner
126.2.k.a.17.3	yes	8	7.3	odd	6	inner
126.2.k.a.89.2	yes	8	1.1	even	1	trivial
126.2.k.a.89.3	yes	8	3.2	odd	2	inner
882.2.d.a.881.2		8	21.5	even	6
882.2.d.a.881.3		8	21.2	odd	6
882.2.d.a.881.6		8	7.2	even	3
882.2.d.a.881.7		8	7.5	odd	6
882.2.k.a.215.1		8	7.6	odd	2
882.2.k.a.215.4		8	21.20	even	2
882.2.k.a.521.1		8	21.11	odd	6
882.2.k.a.521.4		8	7.4	even	3
1008.2.bt.c.17.2		8	28.3	even	6
1008.2.bt.c.17.3		8	84.59	odd	6
1008.2.bt.c.593.2		8	12.11	even	2
1008.2.bt.c.593.3		8	4.3	odd	2
1134.2.l.f.215.1		8	9.2	odd	6
1134.2.l.f.215.4		8	9.7	even	3
1134.2.l.f.269.2		8	63.59	even	6
1134.2.l.f.269.3		8	63.31	odd	6
1134.2.t.e.593.2		8	9.5	odd	6
1134.2.t.e.593.3		8	9.4	even	3
1134.2.t.e.1025.2		8	63.52	odd	6
1134.2.t.e.1025.3		8	63.38	even	6
3150.2.bf.a.1151.1		8	35.24	odd	6
3150.2.bf.a.1151.3		8	105.59	even	6
3150.2.bf.a.1601.1		8	15.14	odd	2
3150.2.bf.a.1601.3		8	5.4	even	2
3150.2.bp.b.899.2		8	105.17	odd	12
3150.2.bp.b.899.3		8	35.3	even	12
3150.2.bp.b.1349.2		8	5.3	odd	4
3150.2.bp.b.1349.3		8	15.2	even	4
3150.2.bp.e.899.2		8	35.17	even	12
3150.2.bp.e.899.3		8	105.38	odd	12
3150.2.bp.e.1349.2		8	15.8	even	4
3150.2.bp.e.1349.3		8	5.2	odd	4
7056.2.k.f.881.3		8	28.23	odd	6
7056.2.k.f.881.4		8	84.47	odd	6
7056.2.k.f.881.5		8	28.19	even	6
7056.2.k.f.881.6		8	84.23	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 126 = 2 \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	126.k (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 - 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} +(0.358719 - 0.621320i) q^{5} +(2.62132 - 0.358719i) q^{7} -1.00000i q^{8} +O(q^{10})\)	\(q+(-0.866025 - 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} +(0.358719 - 0.621320i) q^{5} +(2.62132 - 0.358719i) q^{7} -1.00000i q^{8} +(-0.621320 + 0.358719i) q^{10} +(2.59808 - 1.50000i) q^{11} -2.44949i q^{13} +(-2.44949 - 1.00000i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(2.95680 + 5.12132i) q^{17} +(-5.12132 - 2.95680i) q^{19} +0.717439 q^{20} -3.00000 q^{22} +(-3.67423 - 2.12132i) q^{23} +(2.24264 + 3.88437i) q^{25} +(-1.22474 + 2.12132i) q^{26} +(1.62132 + 2.09077i) q^{28} +7.24264i q^{29} +(-7.86396 + 4.54026i) q^{31} +(0.866025 - 0.500000i) q^{32} -5.91359i q^{34} +(0.717439 - 1.75736i) q^{35} +(0.121320 - 0.210133i) q^{37} +(2.95680 + 5.12132i) q^{38} +(-0.621320 - 0.358719i) q^{40} -11.8272 q^{41} -0.242641 q^{43} +(2.59808 + 1.50000i) q^{44} +(2.12132 + 3.67423i) q^{46} +(2.95680 - 5.12132i) q^{47} +(6.74264 - 1.88064i) q^{49} -4.48528i q^{50} +(2.12132 - 1.22474i) q^{52} +(6.27231 - 3.62132i) q^{53} -2.15232i q^{55} +(-0.358719 - 2.62132i) q^{56} +(3.62132 - 6.27231i) q^{58} +(-4.03295 - 6.98528i) q^{59} +(0.878680 + 0.507306i) q^{61} +9.08052 q^{62} -1.00000 q^{64} +(-1.52192 - 0.878680i) q^{65} +(5.00000 + 8.66025i) q^{67} +(-2.95680 + 5.12132i) q^{68} +(-1.50000 + 1.16320i) q^{70} -1.75736i q^{71} +(-1.24264 + 0.717439i) q^{73} +(-0.210133 + 0.121320i) q^{74} -5.91359i q^{76} +(6.27231 - 4.86396i) q^{77} +(1.37868 - 2.38794i) q^{79} +(0.358719 + 0.621320i) q^{80} +(10.2426 + 5.91359i) q^{82} -6.63103 q^{83} +4.24264 q^{85} +(0.210133 + 0.121320i) q^{86} +(-1.50000 - 2.59808i) q^{88} +(-5.19615 + 9.00000i) q^{89} +(-0.878680 - 6.42090i) q^{91} -4.24264i q^{92} +(-5.12132 + 2.95680i) q^{94} +(-3.67423 + 2.12132i) q^{95} +13.5592i q^{97} +(-6.77962 - 1.74264i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 4 q^{4} + 4 q^{7}+O(q^{10}) \) 8 * q + 4 * q^4 + 4 * q^7	\( 8 q + 4 q^{4} + 4 q^{7} + 12 q^{10} - 4 q^{16} - 24 q^{19} - 24 q^{22} - 16 q^{25} - 4 q^{28} - 12 q^{31} - 16 q^{37} + 12 q^{40} + 32 q^{43} + 20 q^{49} + 12 q^{58} + 24 q^{61} - 8 q^{64} + 40 q^{67} - 12 q^{70} + 24 q^{73} + 28 q^{79} + 48 q^{82} - 12 q^{88} - 24 q^{91} - 24 q^{94}+O(q^{100}) \) 8 * q + 4 * q^4 + 4 * q^7 + 12 * q^10 - 4 * q^16 - 24 * q^19 - 24 * q^22 - 16 * q^25 - 4 * q^28 - 12 * q^31 - 16 * q^37 + 12 * q^40 + 32 * q^43 + 20 * q^49 + 12 * q^58 + 24 * q^61 - 8 * q^64 + 40 * q^67 - 12 * q^70 + 24 * q^73 + 28 * q^79 + 48 * q^82 - 12 * q^88 - 24 * q^91 - 24 * q^94

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