LMFDB - Embedded newform 1134.2.l.f.269.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1134,2,Mod(215,1134)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1134, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("1134.215");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1134 = 2 \cdot 3^{4} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1134.l (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:	$9.05503558921$
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			269.2
Root			$-0.258819 + 0.965926i$ of defining polynomial
Character	$\chi$	$=$	1134.269
Dual form			1134.2.l.f.215.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000i q^{2} -1.00000 q^{4} +(0.358719 - 0.621320i) q^{5} +(-1.62132 + 2.09077i) q^{7} +1.00000i q^{8} +O(q^{10})$	\(q-1.00000i q^{2} -1.00000 q^{4} +(0.358719 - 0.621320i) q^{5} +(-1.62132 + 2.09077i) q^{7} +1.00000i q^{8} +(-0.621320 - 0.358719i) q^{10} +(-2.59808 + 1.50000i) q^{11} +(2.12132 - 1.22474i) q^{13} +(2.09077 + 1.62132i) q^{14} +1.00000 q^{16} +(2.95680 - 5.12132i) q^{17} +(-5.12132 + 2.95680i) q^{19} +(-0.358719 + 0.621320i) q^{20} +(1.50000 + 2.59808i) q^{22} +(3.67423 + 2.12132i) q^{23} +(2.24264 + 3.88437i) q^{25} +(-1.22474 - 2.12132i) q^{26} +(1.62132 - 2.09077i) q^{28} +(6.27231 + 3.62132i) q^{29} +9.08052i q^{31} -1.00000i q^{32} +(-5.12132 - 2.95680i) q^{34} +(0.717439 + 1.75736i) q^{35} +(0.121320 + 0.210133i) q^{37} +(2.95680 + 5.12132i) q^{38} +(0.621320 + 0.358719i) q^{40} +(5.91359 + 10.2426i) q^{41} +(0.121320 - 0.210133i) q^{43} +(2.59808 - 1.50000i) q^{44} +(2.12132 - 3.67423i) q^{46} -5.91359 q^{47} +(-1.74264 - 6.77962i) q^{49} +(3.88437 - 2.24264i) q^{50} +(-2.12132 + 1.22474i) q^{52} +(6.27231 + 3.62132i) q^{53} +2.15232i q^{55} +(-2.09077 - 1.62132i) q^{56} +(3.62132 - 6.27231i) q^{58} +8.06591 q^{59} +1.01461i q^{61} +9.08052 q^{62} -1.00000 q^{64} -1.75736i q^{65} -10.0000 q^{67} +(-2.95680 + 5.12132i) q^{68} +(1.75736 - 0.717439i) q^{70} +1.75736i q^{71} +(-1.24264 - 0.717439i) q^{73} +(0.210133 - 0.121320i) q^{74} +(5.12132 - 2.95680i) q^{76} +(1.07616 - 7.86396i) q^{77} -2.75736 q^{79} +(0.358719 - 0.621320i) q^{80} +(10.2426 - 5.91359i) q^{82} +(3.31552 - 5.74264i) q^{83} +(-2.12132 - 3.67423i) q^{85} +(-0.210133 - 0.121320i) q^{86} +(-1.50000 - 2.59808i) q^{88} +(-5.19615 - 9.00000i) q^{89} +(-0.878680 + 6.42090i) q^{91} +(-3.67423 - 2.12132i) q^{92} +5.91359i q^{94} +4.24264i q^{95} +(11.7426 + 6.77962i) q^{97} +(-6.77962 + 1.74264i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 8 q^{4} + 4 q^{7}+O(q^{10}) $ 8 * q - 8 * q^4 + 4 * q^7	$ 8 q - 8 q^{4} + 4 q^{7} + 12 q^{10} + 8 q^{16} - 24 q^{19} + 12 q^{22} - 16 q^{25} - 4 q^{28} - 24 q^{34} - 16 q^{37} - 12 q^{40} - 16 q^{43} + 20 q^{49} + 12 q^{58} - 8 q^{64} - 80 q^{67} + 48 q^{70} + 24 q^{73} + 24 q^{76} - 56 q^{79} + 48 q^{82} - 12 q^{88} - 24 q^{91} + 60 q^{97}+O(q^{100}) $ 8 * q - 8 * q^4 + 4 * q^7 + 12 * q^10 + 8 * q^16 - 24 * q^19 + 12 * q^22 - 16 * q^25 - 4 * q^28 - 24 * q^34 - 16 * q^37 - 12 * q^40 - 16 * q^43 + 20 * q^49 + 12 * q^58 - 8 * q^64 - 80 * q^67 + 48 * q^70 + 24 * q^73 + 24 * q^76 - 56 * q^79 + 48 * q^82 - 12 * q^88 - 24 * q^91 + 60 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1134\mathbb{Z}\right)^\times$.

$n$	$325$	$407$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

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

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

$2$		−	1.00000i		−	0.707107i
$2$		−	1.00000i		−	0.707107i
$3$		0			0
$3$		0			0
$4$	−1.00000			−0.500000
$5$	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
$7$	−1.62132	+	2.09077i	−0.612801	+	0.790237i
$7$	−1.62132	+	2.09077i	−0.612801	+	0.790237i
$8$			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	−0.837616	−	0.546259i	$-0.816051\pi$
$11$	−2.59808	+	1.50000i	−0.783349	+	0.452267i	0.0542666	+	0.998526i	$0.482718\pi$
$12$		0			0
$13$	2.12132	−	1.22474i	0.588348	−	0.339683i	−0.176096	−	0.984373i	$-0.556347\pi$
$13$	2.12132	−	1.22474i	0.588348	−	0.339683i	0.764444	+	0.644690i	$0.223014\pi$
$14$	2.09077	+	1.62132i	0.558782	+	0.433316i
$15$		0			0
$16$	1.00000			0.250000
$17$	2.95680	−	5.12132i	0.717128	−	1.24210i	−0.245005	−	0.969522i	$-0.578789\pi$
$17$	2.95680	−	5.12132i	0.717128	−	1.24210i	0.962133	−	0.272581i	$-0.0878772\pi$
$18$		0			0
$19$	−5.12132	+	2.95680i	−1.17491	+	0.678335i	−0.954832	−	0.297146i	$-0.903965\pi$
$19$	−5.12132	+	2.95680i	−1.17491	+	0.678335i	−0.220080	+	0.975482i	$0.570632\pi$
$20$	−0.358719	+	0.621320i	−0.0802121	+	0.138931i
$21$		0			0
$22$	1.50000	+	2.59808i	0.319801	+	0.553912i
$23$	3.67423	+	2.12132i	0.766131	+	0.442326i	0.831493	−	0.555536i	$-0.187487\pi$
$23$	3.67423	+	2.12132i	0.766131	+	0.442326i	−0.0653618	+	0.997862i	$0.520820\pi$
$24$		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
$29$	6.27231	+	3.62132i	1.16474	+	0.672462i	0.952435	−	0.304741i	$-0.0985700\pi$
$29$	6.27231	+	3.62132i	1.16474	+	0.672462i	0.212304	+	0.977204i	$0.431903\pi$
$30$		0			0
$31$			9.08052i			1.63091i	0.578821	+	0.815455i	$0.303513\pi$
$31$			9.08052i			1.63091i	−0.578821	+	0.815455i	$0.696487\pi$
$32$		−	1.00000i		−	0.176777i
$33$		0			0
$34$	−5.12132	−	2.95680i	−0.878299	−	0.507086i
$35$	0.717439	+	1.75736i	0.121269	+	0.297048i
$36$		0			0
$37$	0.121320	+	0.210133i	0.0199449	+	0.0345457i	0.875826	−	0.482628i	$-0.160318\pi$
$37$	0.121320	+	0.210133i	0.0199449	+	0.0345457i	−0.855881	+	0.517173i	$0.826984\pi$
$38$	2.95680	+	5.12132i	0.479656	+	0.830788i
$39$		0			0
$40$	0.621320	+	0.358719i	0.0982394	+	0.0567185i
$41$	5.91359	+	10.2426i	0.923548	+	1.59963i	0.793880	+	0.608074i	$0.208058\pi$
$41$	5.91359	+	10.2426i	0.923548	+	1.59963i	0.129668	+	0.991558i	$0.458609\pi$
$42$		0			0
$43$	0.121320	−	0.210133i	0.0185012	−	0.0320450i	−0.856627	−	0.515937i	$-0.827444\pi$
$43$	0.121320	−	0.210133i	0.0185012	−	0.0320450i	0.875128	+	0.483892i	$0.160777\pi$
$44$	2.59808	−	1.50000i	0.391675	−	0.226134i
$45$		0			0
$46$	2.12132	−	3.67423i	0.312772	−	0.541736i
$47$	−5.91359			−0.862586			−0.431293	−	0.902212i	$-0.641942\pi$
$47$	−5.91359			−0.862586			−0.431293	+	0.902212i	$0.641942\pi$
$48$		0			0
$49$	−1.74264	−	6.77962i	−0.248949	−	0.968517i
$50$	3.88437	−	2.24264i	0.549333	−	0.317157i
$51$		0			0
$52$	−2.12132	+	1.22474i	−0.294174	+	0.169842i
$53$	6.27231	+	3.62132i	0.861568	+	0.497427i	0.864537	−	0.502569i	$-0.167612\pi$
$53$	6.27231	+	3.62132i	0.861568	+	0.497427i	−0.00296896	+	0.999996i	$0.500945\pi$
$54$		0			0
$55$			2.15232i			0.290218i
$56$	−2.09077	−	1.62132i	−0.279391	−	0.216658i
$57$		0			0
$58$	3.62132	−	6.27231i	0.475503	−	0.823595i
$59$	8.06591			1.05009			0.525046	−	0.851074i	$-0.324048\pi$
$59$	8.06591			1.05009			0.525046	+	0.851074i	$0.324048\pi$
$60$		0			0
$61$			1.01461i			0.129908i	0.997888	+	0.0649539i	$0.0206900\pi$
$61$			1.01461i			0.129908i	−0.997888	+	0.0649539i	$0.979310\pi$
$62$	9.08052			1.15323
$63$		0			0
$64$	−1.00000			−0.125000
$65$		−	1.75736i		−	0.217974i
$66$		0			0
$67$	−10.0000			−1.22169			−0.610847	−	0.791748i	$-0.709171\pi$
$67$	−10.0000			−1.22169			−0.610847	+	0.791748i	$0.709171\pi$
$68$	−2.95680	+	5.12132i	−0.358564	+	0.621051i
$69$		0			0
$70$	1.75736	−	0.717439i	0.210045	−	0.0857504i
$71$			1.75736i			0.208560i	0.994548	+	0.104280i	$0.0332538\pi$
$71$			1.75736i			0.208560i	−0.994548	+	0.104280i	$0.966746\pi$
$72$		0			0
$73$	−1.24264	−	0.717439i	−0.145440	−	0.0839699i	0.425514	−	0.904952i	$-0.360093\pi$
$73$	−1.24264	−	0.717439i	−0.145440	−	0.0839699i	−0.570954	+	0.820982i	$0.693427\pi$
$74$	0.210133	−	0.121320i	0.0244275	−	0.0141032i
$75$		0			0
$76$	5.12132	−	2.95680i	0.587456	−	0.339168i
$77$	1.07616	−	7.86396i	0.122640	−	0.896182i
$78$		0			0
$79$	−2.75736			−0.310227			−0.155114	−	0.987897i	$-0.549574\pi$
$79$	−2.75736			−0.310227			−0.155114	+	0.987897i	$0.549574\pi$
$80$	0.358719	−	0.621320i	0.0401061	−	0.0694657i
$81$		0			0
$82$	10.2426	−	5.91359i	1.13111	−	0.653047i
$83$	3.31552	−	5.74264i	0.363925	−	0.630337i	−0.624678	−	0.780882i	$-0.714770\pi$
$83$	3.31552	−	5.74264i	0.363925	−	0.630337i	0.988603	+	0.150546i	$0.0481031\pi$
$84$		0			0
$85$	−2.12132	−	3.67423i	−0.230089	−	0.398527i
$86$	−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	−0.998218	−	0.0596775i	$-0.980993\pi$
$89$	−5.19615	−	9.00000i	−0.550791	−	0.953998i	0.447427	−	0.894321i	$-0.352341\pi$
$90$		0			0
$91$	−0.878680	+	6.42090i	−0.0921107	+	0.673093i
$92$	−3.67423	−	2.12132i	−0.383065	−	0.221163i
$93$		0			0
$94$			5.91359i			0.609940i
$95$			4.24264i			0.435286i
$96$		0			0
$97$	11.7426	+	6.77962i	1.19228	+	0.688366i	0.958824	−	0.284001i	$-0.0916617\pi$
$97$	11.7426	+	6.77962i	1.19228	+	0.688366i	0.233460	+	0.972366i	$0.424995\pi$
$98$	−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	0.715719	−	0.698388i	$-0.246099\pi$
$103$	4.75736	+	2.74666i	0.468757	+	0.270637i	−0.246963	+	0.969025i	$0.579432\pi$
$104$	1.22474	+	2.12132i	0.120096	+	0.208013i
$105$		0			0
$106$	3.62132	−	6.27231i	0.351734	−	0.609221i
$107$	9.94655	−	5.74264i	0.961569	−	0.555162i	0.0649133	−	0.997891i	$-0.479323\pi$
$107$	9.94655	−	5.74264i	0.961569	−	0.555162i	0.896656	+	0.442729i	$0.145990\pi$
$108$		0			0
$109$	−9.24264	+	16.0087i	−0.885284	+	1.53336i	−0.0398971	+	0.999204i	$0.512703\pi$
$109$	−9.24264	+	16.0087i	−0.885284	+	1.53336i	−0.845387	+	0.534154i	$0.820630\pi$
$110$	2.15232			0.205215
$111$		0			0
$112$	−1.62132	+	2.09077i	−0.153200	+	0.197559i
$113$	−7.34847	+	4.24264i	−0.691286	+	0.399114i	−0.804094	−	0.594503i	$-0.797349\pi$
$113$	−7.34847	+	4.24264i	−0.691286	+	0.399114i	0.112808	+	0.993617i	$0.464016\pi$
$114$		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
$119$	5.91359	+	14.4853i	0.542098	+	1.32786i
$120$		0			0
$121$	−1.00000	+	1.73205i	−0.0909091	+	0.157459i
$122$	1.01461			0.0918586
$123$		0			0
$124$		−	9.08052i		−	0.815455i
$125$	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	$0.454046\pi$
$128$			1.00000i			0.0883883i
$129$		0			0
$130$	−1.75736			−0.154131
$131$	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
$133$	2.12132	−	15.5014i	0.183942	−	1.34414i
$134$			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	−0.589117	−	0.808048i	$-0.700524\pi$
$137$	−2.15232	+	1.24264i	−0.183885	+	0.106166i	0.405232	+	0.914214i	$0.367191\pi$
$138$		0			0
$139$	0.514719	−	0.297173i	0.0436579	−	0.0252059i	−0.478012	−	0.878353i	$-0.658643\pi$
$139$	0.514719	−	0.297173i	0.0436579	−	0.0252059i	0.521670	+	0.853147i	$0.325309\pi$
$140$	−0.717439	−	1.75736i	−0.0606347	−	0.148524i
$141$		0			0
$142$	1.75736			0.147474
$143$	−3.67423	+	6.36396i	−0.307255	+	0.532181i
$144$		0			0
$145$	4.50000	−	2.59808i	0.373705	−	0.215758i
$146$	−0.717439	+	1.24264i	−0.0593757	+	0.102842i
$147$		0			0
$148$	−0.121320	−	0.210133i	−0.00997247	−	0.0172728i
$149$	−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	$0.901761\pi$
$152$	−2.95680	−	5.12132i	−0.239828	−	0.415394i
$153$		0			0
$154$	−7.86396	−	1.07616i	−0.633696	−	0.0867193i
$155$	5.64191	+	3.25736i	0.453169	+	0.261637i
$156$		0			0
$157$		−	14.6969i		−	1.17294i	−0.809970	−	0.586472i	$-0.800517\pi$
$157$		−	14.6969i		−	1.17294i	0.809970	−	0.586472i	$-0.199483\pi$
$158$			2.75736i			0.219364i
$159$		0			0
$160$	−0.621320	−	0.358719i	−0.0491197	−	0.0283593i
$161$	−10.3923	+	4.24264i	−0.819028	+	0.334367i
$162$		0			0
$163$	1.12132	+	1.94218i	0.0878286	+	0.152124i	0.906593	−	0.422006i	$-0.138674\pi$
$163$	1.12132	+	1.94218i	0.0878286	+	0.152124i	−0.818764	+	0.574130i	$0.805341\pi$
$164$	−5.91359	−	10.2426i	−0.461774	−	0.799816i
$165$		0			0
$166$	−5.74264	−	3.31552i	−0.445715	−	0.257334i
$167$	−8.06591	−	13.9706i	−0.624159	−	1.08107i	−0.988703	−	0.149889i	$-0.952109\pi$
$167$	−8.06591	−	13.9706i	−0.624159	−	1.08107i	0.364544	−	0.931186i	$-0.381225\pi$
$168$		0			0
$169$	−3.50000	+	6.06218i	−0.269231	+	0.466321i
$170$	−3.67423	+	2.12132i	−0.281801	+	0.162698i
$171$		0			0
$172$	−0.121320	+	0.210133i	−0.00925059	+	0.0160225i
$173$	−20.7846			−1.58022			−0.790112	−	0.612962i	$-0.789978\pi$
$173$	−20.7846			−1.58022			−0.790112	+	0.612962i	$0.789978\pi$
$174$		0			0
$175$	−11.7574	−	1.60896i	−0.888773	−	0.121626i
$176$	−2.59808	+	1.50000i	−0.195837	+	0.113067i
$177$		0			0
$178$	−9.00000	+	5.19615i	−0.674579	+	0.389468i
$179$	−22.9369	−	13.2426i	−1.71439	−	0.989801i	−0.928420	−	0.371532i	$-0.878833\pi$
$179$	−22.9369	−	13.2426i	−1.71439	−	0.989801i	−0.785966	−	0.618269i	$-0.787834\pi$
$180$		0			0
$181$		−	11.8272i		−	0.879108i	−0.898216	−	0.439554i	$-0.855137\pi$
$181$		−	11.8272i		−	0.879108i	0.898216	−	0.439554i	$-0.144863\pi$
$182$	6.42090	+	0.878680i	0.475949	+	0.0651321i
$183$		0			0
$184$	−2.12132	+	3.67423i	−0.156386	+	0.270868i
$185$	0.174080			0.0127986
$186$		0			0
$187$			17.7408i			1.29733i
$188$	5.91359			0.431293
$189$		0			0
$190$	4.24264			0.307794
$191$		−	8.48528i		−	0.613973i	−0.951714	−	0.306987i	$-0.900679\pi$
$191$		−	8.48528i		−	0.613973i	0.951714	−	0.306987i	$-0.0993207\pi$
$192$		0			0
$193$	9.48528			0.682765			0.341383	−	0.939924i	$-0.389105\pi$
$193$	9.48528			0.682765			0.341383	+	0.939924i	$0.389105\pi$
$194$	6.77962	−	11.7426i	0.486748	−	0.843072i
$195$		0			0
$196$	1.74264	+	6.77962i	0.124474	+	0.484258i
$197$			26.4853i			1.88700i	0.331375	+	0.943499i	$0.392487\pi$
$197$			26.4853i			1.88700i	−0.331375	+	0.943499i	$0.607513\pi$
$198$		0			0
$199$	19.9706	+	11.5300i	1.41568	+	0.817341i	0.995915	−	0.0902942i	$-0.0287807\pi$
$199$	19.9706	+	11.5300i	1.41568	+	0.817341i	0.419761	+	0.907635i	$0.362114\pi$
$200$	−3.88437	+	2.24264i	−0.274666	+	0.158579i
$201$		0			0
$202$		0			0
$203$	−17.7408	+	7.24264i	−1.24516	+	0.508334i
$204$		0			0
$205$	8.48528			0.592638
$206$	2.74666	−	4.75736i	0.191369	−	0.331461i
$207$		0			0
$208$	2.12132	−	1.22474i	0.147087	−	0.0849208i
$209$	8.87039	−	15.3640i	0.613578	−	1.06275i
$210$		0			0
$211$	0.121320	+	0.210133i	0.00835204	+	0.0144662i	0.870171	−	0.492749i	$-0.164008\pi$
$211$	0.121320	+	0.210133i	0.00835204	+	0.0144662i	−0.861819	+	0.507216i	$0.830675\pi$
$212$	−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
$218$	16.0087	+	9.24264i	1.08425	+	0.625991i
$219$		0			0
$220$		−	2.15232i		−	0.145109i
$221$		−	14.4853i		−	0.974385i
$222$		0			0
$223$	1.86396	+	1.07616i	0.124820	+	0.0720649i	0.561110	−	0.827741i	$-0.310374\pi$
$223$	1.86396	+	1.07616i	0.124820	+	0.0720649i	−0.436290	+	0.899806i	$0.643708\pi$
$224$	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	0.841011	−	0.541017i	$-0.181961\pi$
$229$	12.0000	+	6.92820i	0.792982	+	0.457829i	−0.0480291	+	0.998846i	$0.515294\pi$
$230$	−1.52192	−	2.63604i	−0.100352	−	0.173815i
$231$		0			0
$232$	−3.62132	+	6.27231i	−0.237751	+	0.411797i
$233$	−16.2189	+	9.36396i	−1.06253	+	0.613453i	−0.926132	−	0.377200i	$-0.876887\pi$
$233$	−16.2189	+	9.36396i	−1.06253	+	0.613453i	−0.136401	+	0.990654i	$0.543554\pi$
$234$		0			0
$235$	−2.12132	+	3.67423i	−0.138380	+	0.239681i
$236$	−8.06591			−0.525046
$237$		0			0
$238$	14.4853	−	5.91359i	0.938941	−	0.383321i
$239$	−11.0227	+	6.36396i	−0.712999	+	0.411650i	−0.812171	−	0.583420i	$-0.801714\pi$
$239$	−11.0227	+	6.36396i	−0.712999	+	0.411650i	0.0991712	+	0.995070i	$0.468381\pi$
$240$		0			0
$241$	−6.25736	+	3.61269i	−0.403072	+	0.232714i	−0.687809	−	0.725892i	$-0.741427\pi$
$241$	−6.25736	+	3.61269i	−0.403072	+	0.232714i	0.284737	+	0.958606i	$0.408094\pi$
$242$	1.73205	+	1.00000i	0.111340	+	0.0642824i
$243$		0			0
$244$		−	1.01461i		−	0.0649539i
$245$	−4.83743	−	1.34924i	−0.309052	−	0.0861999i
$246$		0			0
$247$	−7.24264	+	12.5446i	−0.460838	+	0.798195i
$248$	−9.08052			−0.576614
$249$		0			0
$250$		−	6.80511i		−	0.430393i
$251$	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
$254$		−	3.24264i		−	0.203461i
$255$		0			0
$256$	1.00000			0.0625000
$257$	−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
$259$	−0.636039	−	0.0870399i	−0.0395215	−	0.00540840i
$260$			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	−0.0353843	−	0.999374i	$-0.511266\pi$
$263$	13.1750	−	7.60660i	0.812407	−	0.469043i	0.847791	+	0.530331i	$0.177932\pi$
$264$		0			0
$265$	4.50000	−	2.59808i	0.276433	−	0.159599i
$266$	−15.5014	−	2.12132i	−0.950453	−	0.130066i
$267$		0			0
$268$	10.0000			0.610847
$269$	6.98975	−	12.1066i	0.426173	−	0.738153i	−0.570357	−	0.821397i	$-0.693195\pi$
$269$	6.98975	−	12.1066i	0.426173	−	0.738153i	0.996529	+	0.0832447i	$0.0265283\pi$
$270$		0			0
$271$	−5.37868	+	3.10538i	−0.326732	+	0.188639i	−0.654389	−	0.756158i	$-0.727074\pi$
$271$	−5.37868	+	3.10538i	−0.326732	+	0.188639i	0.327658	+	0.944797i	$0.393741\pi$
$272$	2.95680	−	5.12132i	0.179282	−	0.310526i
$273$		0			0
$274$	1.24264	+	2.15232i	0.0750707	+	0.130026i
$275$	−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
$281$	5.19615	+	3.00000i	0.309976	+	0.178965i	0.646916	−	0.762561i	$-0.276058\pi$
$281$	5.19615	+	3.00000i	0.309976	+	0.178965i	−0.336939	+	0.941526i	$0.609392\pi$
$282$		0			0
$283$			21.2049i			1.26050i	0.776393	+	0.630250i	$0.217047\pi$
$283$			21.2049i			1.26050i	−0.776393	+	0.630250i	$0.782953\pi$
$284$		−	1.75736i		−	0.104280i
$285$		0			0
$286$	6.36396	+	3.67423i	0.376309	+	0.217262i
$287$	−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
$293$	−0.358719	−	0.621320i	−0.0209566	−	0.0362979i	0.855357	−	0.518039i	$-0.173338\pi$
$293$	−0.358719	−	0.621320i	−0.0209566	−	0.0362979i	−0.876314	+	0.481741i	$0.840005\pi$
$294$		0			0
$295$	2.89340	−	5.01151i	0.168460	−	0.291782i
$296$	−0.210133	+	0.121320i	−0.0122137	+	0.00705160i
$297$		0			0
$298$	−1.75736	+	3.04384i	−0.101801	+	0.176325i
$299$	10.3923			0.601003
$300$		0			0
$301$	0.242641	+	0.594346i	0.0139856	+	0.0342575i
$302$	−4.54026	+	2.62132i	−0.261263	+	0.150840i
$303$		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	$0.0918499\pi$
$307$			9.97204i			0.569134i	−0.958656	+	0.284567i	$0.908150\pi$
$308$	−1.07616	+	7.86396i	−0.0613198	+	0.448091i
$309$		0			0
$310$	3.25736	−	5.64191i	0.185006	−	0.320439i
$311$	−8.95743			−0.507929			−0.253965	−	0.967214i	$-0.581735\pi$
$311$	−8.95743			−0.507929			−0.253965	+	0.967214i	$0.581735\pi$
$312$		0			0
$313$			18.4582i			1.04332i	0.853154	+	0.521660i	$0.174687\pi$
$313$			18.4582i			1.04332i	−0.853154	+	0.521660i	$0.825313\pi$
$314$	−14.6969			−0.829396
$315$		0			0
$316$	2.75736			0.155114
$317$		−	1.24264i		−	0.0697937i	−0.999391	−	0.0348968i	$-0.988890\pi$
$317$		−	1.24264i		−	0.0697937i	0.999391	−	0.0348968i	$-0.0111103\pi$
$318$		0			0
$319$	−21.7279			−1.21653
$320$	−0.358719	+	0.621320i	−0.0200530	+	0.0347329i
$321$		0			0
$322$	4.24264	+	10.3923i	0.236433	+	0.579141i
$323$			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
$328$	−10.2426	+	5.91359i	−0.565555	+	0.326523i
$329$	9.58783	−	12.3640i	0.528594	−	0.681647i
$330$		0			0
$331$	−33.4558			−1.83890			−0.919450	−	0.393208i	$-0.871365\pi$
$331$	−33.4558			−1.83890			−0.919450	+	0.393208i	$0.871365\pi$
$332$	−3.31552	+	5.74264i	−0.181963	+	0.315168i
$333$		0			0
$334$	−13.9706	+	8.06591i	−0.764435	+	0.441347i
$335$	−3.58719	+	6.21320i	−0.195989	+	0.339464i
$336$		0			0
$337$	2.50000	+	4.33013i	0.136184	+	0.235877i	0.926049	−	0.377403i	$-0.123183\pi$
$337$	2.50000	+	4.33013i	0.136184	+	0.235877i	−0.789865	+	0.613280i	$0.789850\pi$
$338$	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
$344$	0.210133	+	0.121320i	0.0113296	+	0.00654115i
$345$		0			0
$346$			20.7846i			1.11739i
$347$			2.48528i			0.133417i	0.997773	+	0.0667084i	$0.0212497\pi$
$347$			2.48528i			0.133417i	−0.997773	+	0.0667084i	$0.978750\pi$
$348$		0			0
$349$	−1.97056	−	1.13770i	−0.105482	−	0.0608999i	0.446331	−	0.894868i	$-0.352730\pi$
$349$	−1.97056	−	1.13770i	−0.105482	−	0.0608999i	−0.551813	+	0.833968i	$0.686064\pi$
$350$	−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
$356$	5.19615	+	9.00000i	0.275396	+	0.476999i
$357$		0			0
$358$	−13.2426	+	22.9369i	−0.699895	+	1.21225i
$359$	15.5885	−	9.00000i	0.822727	−	0.475002i	−0.0286287	−	0.999590i	$-0.509114\pi$
$359$	15.5885	−	9.00000i	0.822727	−	0.475002i	0.851356	+	0.524588i	$0.175781\pi$
$360$		0			0
$361$	7.98528	−	13.8309i	0.420278	−	0.727943i
$362$	−11.8272			−0.621623
$363$		0			0
$364$	0.878680	−	6.42090i	0.0460553	−	0.336546i
$365$	−0.891519	+	0.514719i	−0.0466642	+	0.0269416i
$366$		0			0
$367$	13.3492	−	7.70719i	0.696825	−	0.402312i	−0.109339	−	0.994005i	$-0.534873\pi$
$367$	13.3492	−	7.70719i	0.696825	−	0.402312i	0.806164	+	0.591693i	$0.201540\pi$
$368$	3.67423	+	2.12132i	0.191533	+	0.110581i
$369$		0			0
$370$		−	0.174080i		−	0.00904998i
$371$	−17.7408	+	7.24264i	−0.921055	+	0.376019i
$372$		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	$-0.109402\pi$
$374$	17.7408			0.917354
$375$		0			0
$376$		−	5.91359i		−	0.304970i
$377$	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	$0.396094\pi$
$380$		−	4.24264i		−	0.217643i
$381$		0			0
$382$	−8.48528			−0.434145
$383$	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
$385$	−4.50000	−	3.48960i	−0.229341	−	0.177846i
$386$		−	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	−0.992302	−	0.123843i	$-0.960478\pi$
$389$	−27.2416	+	15.7279i	−1.38120	+	0.797437i	−0.388900	+	0.921280i	$0.627145\pi$
$390$		0			0
$391$	21.7279	−	12.5446i	1.09883	−	0.634409i
$392$	6.77962	−	1.74264i	0.342422	−	0.0880166i
$393$		0			0
$394$	26.4853			1.33431
$395$	−0.989118	+	1.71320i	−0.0497680	+	0.0862006i
$396$		0			0
$397$	12.0000	−	6.92820i	0.602263	−	0.347717i	−0.167668	−	0.985843i	$-0.553624\pi$
$397$	12.0000	−	6.92820i	0.602263	−	0.347717i	0.769931	+	0.638127i	$0.220290\pi$
$398$	11.5300	−	19.9706i	0.577947	−	1.00103i
$399$		0			0
$400$	2.24264	+	3.88437i	0.112132	+	0.194218i
$401$		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
$407$	−0.630399	−	0.363961i	−0.0312477	−	0.0180409i
$408$		0			0
$409$		−	14.9941i		−	0.741411i	−0.928750	−	0.370706i	$-0.879116\pi$
$409$		−	14.9941i		−	0.741411i	0.928750	−	0.370706i	$-0.120884\pi$
$410$		−	8.48528i		−	0.419058i
$411$		0			0
$412$	−4.75736	−	2.74666i	−0.234378	−	0.135318i
$413$	−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
$419$	11.8272	+	20.4853i	0.577796	+	1.00077i	0.995732	+	0.0922950i	$0.0294203\pi$
$419$	11.8272	+	20.4853i	0.577796	+	1.00077i	−0.417936	+	0.908476i	$0.637246\pi$
$420$		0			0
$421$	7.12132	−	12.3345i	0.347072	−	0.601146i	−0.638656	−	0.769492i	$-0.720509\pi$
$421$	7.12132	−	12.3345i	0.347072	−	0.601146i	0.985728	+	0.168346i	$0.0538426\pi$
$422$	0.210133	−	0.121320i	0.0102291	−	0.00590578i
$423$		0			0
$424$	−3.62132	+	6.27231i	−0.175867	+	0.304610i
$425$	26.5241			1.28661
$426$		0			0
$427$	−2.12132	−	1.64501i	−0.102658	−	0.0796077i
$428$	−9.94655	+	5.74264i	−0.480784	+	0.277581i
$429$		0			0
$430$	−0.150758	+	0.0870399i	−0.00727018	+	0.00419744i
$431$	3.04384	+	1.75736i	0.146616	+	0.0846490i	0.571514	−	0.820593i	$-0.306356\pi$
$431$	3.04384	+	1.75736i	0.146616	+	0.0846490i	−0.424897	+	0.905242i	$0.639690\pi$
$432$		0			0
$433$			3.46410i			0.166474i	0.996530	+	0.0832370i	$0.0265259\pi$
$433$			3.46410i			0.166474i	−0.996530	+	0.0832370i	$0.973474\pi$
$434$	−14.7224	+	18.9853i	−0.706699	+	0.911323i
$435$		0			0
$436$	9.24264	−	16.0087i	0.442642	−	0.766679i
$437$	−25.0892			−1.20018
$438$		0			0
$439$		−	16.8493i		−	0.804171i	−0.915602	−	0.402086i	$-0.868285\pi$
$439$		−	16.8493i		−	0.804171i	0.915602	−	0.402086i	$-0.131715\pi$
$440$	−2.15232			−0.102608
$441$		0			0
$442$	−14.4853			−0.688995
$443$			16.4558i			0.781841i	0.920425	+	0.390920i	$0.127843\pi$
$443$			16.4558i			0.781841i	−0.920425	+	0.390920i	$0.872157\pi$
$444$		0			0
$445$	−7.45584			−0.353441
$446$	1.07616	−	1.86396i	0.0509576	−	0.0882611i
$447$		0			0
$448$	1.62132	−	2.09077i	0.0766002	−	0.0987796i
$449$			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
$452$	7.34847	−	4.24264i	0.345643	−	0.199557i
$453$		0			0
$454$	−13.5000	+	7.79423i	−0.633586	+	0.365801i
$455$	3.67423	+	2.84924i	0.172251	+	0.133575i
$456$		0			0
$457$	−23.0000			−1.07589			−0.537947	−	0.842978i	$-0.680800\pi$
$457$	−23.0000			−1.07589			−0.537947	+	0.842978i	$0.680800\pi$
$458$	6.92820	−	12.0000i	0.323734	−	0.560723i
$459$		0			0
$460$	−2.63604	+	1.52192i	−0.122906	+	0.0709598i
$461$	16.3059	−	28.2426i	0.759441	−	1.31539i	−0.183695	−	0.982983i	$-0.558806\pi$
$461$	16.3059	−	28.2426i	0.759441	−	1.31539i	0.943136	−	0.332408i	$-0.107861\pi$
$462$		0			0
$463$	14.7279	+	25.5095i	0.684465	+	1.18553i	0.973605	+	0.228241i	$0.0732973\pi$
$463$	14.7279	+	25.5095i	0.684465	+	1.18553i	−0.289140	+	0.957287i	$0.593369\pi$
$464$	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	−0.798578	−	0.601892i	$-0.794414\pi$
$467$	−19.8931	−	34.4558i	−0.920542	−	1.59443i	−0.121965	−	0.992534i	$-0.538920\pi$
$468$		0			0
$469$	16.2132	−	20.9077i	0.748656	−	0.965428i
$470$	3.67423	+	2.12132i	0.169480	+	0.0978492i
$471$		0			0
$472$			8.06591i			0.371264i
$473$			0.727922i			0.0334699i
$474$		0			0
$475$	−22.9706	−	13.2621i	−1.05396	−	0.608505i
$476$	−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
$482$	3.61269	+	6.25736i	0.164553	+	0.285015i
$483$		0			0
$484$	1.00000	−	1.73205i	0.0454545	−	0.0787296i
$485$	8.42463	−	4.86396i	0.382543	−	0.220861i
$486$		0			0
$487$	7.10660	−	12.3090i	0.322031	−	0.557774i	−0.658876	−	0.752251i	$-0.728968\pi$
$487$	7.10660	−	12.3090i	0.322031	−	0.557774i	0.980907	+	0.194478i	$0.0623012\pi$
$488$	−1.01461			−0.0459293
$489$		0			0
$490$	−1.34924	+	4.83743i	−0.0609526	+	0.218533i
$491$	12.0989	−	6.98528i	0.546014	−	0.315241i	−0.201499	−	0.979489i	$-0.564581\pi$
$491$	12.0989	−	6.98528i	0.546014	−	0.315241i	0.747513	+	0.664247i	$0.231248\pi$
$492$		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
$497$	−3.67423	−	2.84924i	−0.164812	−	0.127806i
$498$		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	$0.913120\pi$
$500$	−6.80511			−0.304334
$501$		0			0
$502$		−	27.4156i		−	1.22362i
$503$	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
$506$			12.7279i			0.565825i
$507$		0			0
$508$	−3.24264			−0.143869
$509$	−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
$511$	3.51472	−	1.43488i	0.155482	−	0.0634753i
$512$		−	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
$517$	15.3640	−	8.87039i	0.675706	−	0.390119i
$518$	−0.0870399	+	0.636039i	−0.00382432	+	0.0279459i
$519$		0			0
$520$	1.75736			0.0770653
$521$	16.9363	−	29.3345i	0.741993	−	1.28517i	−0.209594	−	0.977788i	$-0.567214\pi$
$521$	16.9363	−	29.3345i	0.741993	−	1.28517i	0.951587	−	0.307380i	$-0.0994524\pi$
$522$		0			0
$523$	5.84924	−	3.37706i	0.255770	−	0.147669i	−0.366634	−	0.930365i	$-0.619490\pi$
$523$	5.84924	−	3.37706i	0.255770	−	0.147669i	0.622403	+	0.782697i	$0.286156\pi$
$524$	−2.59808	+	4.50000i	−0.113497	+	0.196583i
$525$		0			0
$526$	−7.60660	−	13.1750i	−0.331664	−	0.574458i
$527$	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
$533$	25.0892	+	14.4853i	1.08674	+	0.627427i
$534$		0			0
$535$		−	8.23999i		−	0.356246i
$536$		−	10.0000i		−	0.431934i
$537$		0			0
$538$	−12.1066	−	6.98975i	−0.521953	−	0.301350i
$539$	14.6969	+	15.0000i	0.633042	+	0.646096i
$540$		0			0
$541$	−7.36396	−	12.7548i	−0.316601	−	0.548370i	0.663175	−	0.748464i	$-0.269208\pi$
$541$	−7.36396	−	12.7548i	−0.316601	−	0.548370i	−0.979777	+	0.200094i	$0.935875\pi$
$542$	3.10538	+	5.37868i	0.133388	+	0.231034i
$543$		0			0
$544$	−5.12132	−	2.95680i	−0.219575	−	0.126772i
$545$	6.63103	+	11.4853i	0.284042	+	0.491975i
$546$		0			0
$547$	19.8492	−	34.3799i	0.848692	−	1.46998i	−0.0336833	−	0.999433i	$-0.510724\pi$
$547$	19.8492	−	34.3799i	0.848692	−	1.46998i	0.882376	−	0.470546i	$-0.155943\pi$
$548$	2.15232	−	1.24264i	0.0919424	−	0.0530830i
$549$		0			0
$550$	−6.72792	+	11.6531i	−0.286880	+	0.496890i
$551$	−42.8300			−1.82462
$552$		0			0
$553$	4.47056	−	5.76500i	0.190108	−	0.245153i
$554$	−11.2328	+	6.48528i	−0.477238	+	0.275533i
$555$		0			0
$556$	−0.514719	+	0.297173i	−0.0218289	+	0.0126029i
$557$	−8.42463	−	4.86396i	−0.356963	−	0.206093i	0.310785	−	0.950480i	$-0.399408\pi$
$557$	−8.42463	−	4.86396i	−0.356963	−	0.206093i	−0.667748	+	0.744388i	$0.732741\pi$
$558$		0			0
$559$		−	0.594346i		−	0.0251382i
$560$	0.717439	+	1.75736i	0.0303173	+	0.0742620i
$561$		0			0
$562$	3.00000	−	5.19615i	0.126547	−	0.219186i
$563$	34.5900			1.45780			0.728898	−	0.684622i	$-0.240033\pi$
$563$	34.5900			1.45780			0.728898	+	0.684622i	$0.240033\pi$
$564$		0			0
$565$			6.08767i			0.256110i
$566$	21.2049			0.891307
$567$		0			0
$568$	−1.75736			−0.0737372
$569$			10.2426i			0.429394i	0.976681	+	0.214697i	$0.0688764\pi$
$569$			10.2426i			0.429394i	−0.976681	+	0.214697i	$0.931124\pi$
$570$		0			0
$571$	8.72792			0.365252			0.182626	−	0.983182i	$-0.441540\pi$
$571$	8.72792			0.365252			0.182626	+	0.983182i	$0.441540\pi$
$572$	3.67423	−	6.36396i	0.153627	−	0.266091i
$573$		0			0
$574$	−4.24264	+	31.0028i	−0.177084	+	1.29403i
$575$			19.0294i			0.793582i
$576$		0			0
$577$	9.25736	+	5.34474i	0.385389	+	0.222504i	0.680160	−	0.733063i	$-0.261910\pi$
$577$	9.25736	+	5.34474i	0.385389	+	0.222504i	−0.294771	+	0.955568i	$0.595243\pi$
$578$	−15.5630	+	8.98528i	−0.647334	+	0.373738i
$579$		0			0
$580$	−4.50000	+	2.59808i	−0.186852	+	0.107879i
$581$	6.63103	+	16.2426i	0.275101	+	0.673858i
$582$		0			0
$583$	−21.7279			−0.899879
$584$	0.717439	−	1.24264i	0.0296878	−	0.0514208i
$585$		0			0
$586$	−0.621320	+	0.358719i	−0.0256665	+	0.0148186i
$587$	2.59808	−	4.50000i	0.107234	−	0.185735i	−0.807415	−	0.589984i	$-0.799134\pi$
$587$	2.59808	−	4.50000i	0.107234	−	0.185735i	0.914649	+	0.404249i	$0.132467\pi$
$588$		0			0
$589$	−26.8492	−	46.5043i	−1.10630	−	1.91617i
$590$	−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	0.999789	−	0.0205360i	$-0.00653726\pi$
$593$	11.7401	+	20.3345i	0.482110	+	0.835039i	−0.517679	+	0.855575i	$0.673204\pi$
$594$		0			0
$595$	11.1213	+	1.52192i	0.455930	+	0.0623925i
$596$	3.04384	+	1.75736i	0.124680	+	0.0719842i
$597$		0			0
$598$		−	10.3923i		−	0.424973i
$599$		−	7.45584i		−	0.304638i	−0.988331	−	0.152319i	$-0.951326\pi$
$599$		−	7.45584i		−	0.304638i	0.988331	−	0.152319i	$-0.0486740\pi$
$600$		0			0
$601$	20.2279	+	11.6786i	0.825114	+	0.476380i	0.852177	−	0.523254i	$-0.175282\pi$
$601$	20.2279	+	11.6786i	0.825114	+	0.476380i	−0.0270627	+	0.999634i	$0.508615\pi$
$602$	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	0.809348	−	0.587330i	$-0.199821\pi$
$607$	17.3787	+	10.0336i	0.705379	+	0.407251i	−0.103969	+	0.994581i	$0.533154\pi$
$608$	2.95680	+	5.12132i	0.119914	+	0.207697i
$609$		0			0
$610$	0.363961	−	0.630399i	0.0147364	−	0.0255241i
$611$	−12.5446	+	7.24264i	−0.507501	+	0.293006i
$612$		0			0
$613$	18.6066	−	32.2276i	0.751514	−	1.30166i	−0.195575	−	0.980689i	$-0.562657\pi$
$613$	18.6066	−	32.2276i	0.751514	−	1.30166i	0.947089	−	0.320971i	$-0.104009\pi$
$614$	9.97204			0.402439
$615$		0			0
$616$	7.86396	+	1.07616i	0.316848	+	0.0433597i
$617$	15.3273	−	8.84924i	0.617055	−	0.356257i	−0.158666	−	0.987332i	$-0.550719\pi$
$617$	15.3273	−	8.84924i	0.617055	−	0.356257i	0.775722	+	0.631075i	$0.217386\pi$
$618$		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	$0.372839\pi$
$620$	−5.64191	−	3.25736i	−0.226585	−	0.130819i
$621$		0			0
$622$			8.95743i			0.359160i
$623$	27.2416	+	3.72792i	1.09141	+	0.149356i
$624$		0			0
$625$	−8.77208	+	15.1937i	−0.350883	+	0.607747i
$626$	18.4582			0.737739
$627$		0			0
$628$			14.6969i			0.586472i
$629$	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	$0.335978\pi$
$632$		−	2.75736i		−	0.109682i
$633$		0			0
$634$	−1.24264			−0.0493516
$635$	1.16320	−	2.01472i	0.0461601	−	0.0799517i
$636$		0			0
$637$	−12.0000	−	12.2474i	−0.475457	−	0.485262i
$638$			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	−0.771160	−	0.636641i	$-0.780323\pi$
$641$	−15.3273	+	8.84924i	−0.605393	+	0.349524i	0.165767	+	0.986165i	$0.446990\pi$
$642$		0			0
$643$	−27.7279	+	16.0087i	−1.09348	+	0.631322i	−0.934501	−	0.355959i	$-0.884154\pi$
$643$	−27.7279	+	16.0087i	−1.09348	+	0.631322i	−0.158981	+	0.987282i	$0.550821\pi$
$644$	10.3923	−	4.24264i	0.409514	−	0.167183i
$645$		0			0
$646$	34.9706			1.37590
$647$	16.2189	−	28.0919i	0.637629	−	1.10441i	−0.348323	−	0.937375i	$-0.613249\pi$
$647$	16.2189	−	28.0919i	0.637629	−	1.10441i	0.985952	−	0.167031i	$-0.0534180\pi$
$648$		0			0
$649$	−20.9558	+	12.0989i	−0.822589	+	0.474922i
$650$	5.49333	−	9.51472i	0.215466	−	0.373198i
$651$		0			0
$652$	−1.12132	−	1.94218i	−0.0439143	−	0.0760618i
$653$	16.6646	+	9.62132i	0.652137	+	0.376511i	0.789274	−	0.614041i	$-0.210457\pi$
$653$	16.6646	+	9.62132i	0.652137	+	0.376511i	−0.137138	+	0.990552i	$0.543790\pi$
$654$		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
$659$	5.19615	+	3.00000i	0.202413	+	0.116863i	0.597781	−	0.801660i	$-0.296049\pi$
$659$	5.19615	+	3.00000i	0.202413	+	0.116863i	−0.395367	+	0.918523i	$0.629383\pi$
$660$		0			0
$661$		−	35.6556i		−	1.38684i	−0.720532	−	0.693422i	$-0.756102\pi$
$661$		−	35.6556i		−	1.38684i	0.720532	−	0.693422i	$-0.243898\pi$
$662$			33.4558i			1.30030i
$663$		0			0
$664$	5.74264	+	3.31552i	0.222858	+	0.128667i
$665$	−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
$671$	−1.52192	−	2.63604i	−0.0587530	−	0.101763i
$672$		0			0
$673$	−8.98528	+	15.5630i	−0.346357	+	0.599908i	−0.985599	−	0.169097i	$-0.945915\pi$
$673$	−8.98528	+	15.5630i	−0.346357	+	0.599908i	0.639242	+	0.769005i	$0.279248\pi$
$674$	4.33013	−	2.50000i	0.166790	−	0.0962964i
$675$		0			0
$676$	3.50000	−	6.06218i	0.134615	−	0.233161i
$677$	2.15232			0.0827203			0.0413601	−	0.999144i	$-0.486831\pi$
$677$	2.15232			0.0827203			0.0413601	+	0.999144i	$0.486831\pi$
$678$		0			0
$679$	−33.2132	+	13.5592i	−1.27461	+	0.520356i
$680$	3.67423	−	2.12132i	0.140900	−	0.0813489i
$681$		0			0
$682$	−23.5919	+	13.6208i	−0.903380	+	0.521567i
$683$	6.90271	+	3.98528i	0.264125	+	0.152493i	0.626215	−	0.779651i	$-0.284603\pi$
$683$	6.90271	+	3.98528i	0.264125	+	0.152493i	−0.362090	+	0.932143i	$0.617937\pi$
$684$		0			0
$685$			1.78304i			0.0681264i
$686$	7.34847	−	17.0000i	0.280566	−	0.649063i
$687$		0			0
$688$	0.121320	−	0.210133i	0.00462529	−	0.00801125i
$689$	17.7408			0.675870
$690$		0			0
$691$			28.5533i			1.08622i	0.839661	+	0.543110i	$0.182753\pi$
$691$			28.5533i			1.08622i	−0.839661	+	0.543110i	$0.817247\pi$
$692$	20.7846			0.790112
$693$		0			0
$694$	2.48528			0.0943400
$695$		−	0.426407i		−	0.0161745i
$696$		0			0
$697$	69.9411			2.64921
$698$	−1.13770	+	1.97056i	−0.0430628	+	0.0745869i
$699$		0			0
$700$	11.7574	+	1.60896i	0.444386	+	0.0608129i
$701$		−	20.6985i		−	0.781771i	−0.920439	−	0.390885i	$-0.872169\pi$
$701$		−	20.6985i		−	0.781771i	0.920439	−	0.390885i	$-0.127831\pi$
$702$		0			0
$703$	−1.24264	−	0.717439i	−0.0468671	−	0.0270587i
$704$	2.59808	−	1.50000i	0.0979187	−	0.0565334i
$705$		0			0
$706$	7.75736	−	4.47871i	0.291952	−	0.168559i
$707$		0			0
$708$		0			0
$709$	26.9706			1.01290			0.506450	−	0.862269i	$-0.330957\pi$
$709$	26.9706			1.01290			0.506450	+	0.862269i	$0.330957\pi$
$710$	0.630399	−	1.09188i	0.0236585	−	0.0409776i
$711$		0			0
$712$	9.00000	−	5.19615i	0.337289	−	0.194734i
$713$	−19.2627	+	33.3640i	−0.721393	+	1.24949i
$714$		0			0
$715$	2.63604	+	4.56575i	0.0985823	+	0.170749i
$716$	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	0.976319	−	0.216335i	$-0.0694105\pi$
$719$	8.06591	+	13.9706i	0.300808	+	0.521014i	−0.675511	+	0.737349i	$0.736077\pi$
$720$		0			0
$721$	−13.4558	+	5.49333i	−0.501122	+	0.204582i
$722$	−13.8309	−	7.98528i	−0.514733	−	0.297181i
$723$		0			0
$724$			11.8272i			0.439554i
$725$			32.4853i			1.20647i
$726$		0			0
$727$	−10.1360	−	5.85204i	−0.375925	−	0.217040i	0.300119	−	0.953902i	$-0.402974\pi$
$727$	−10.1360	−	5.85204i	−0.375925	−	0.217040i	−0.676044	+	0.736861i	$0.736307\pi$
$728$	−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	0.422524	−	0.906352i	$-0.361144\pi$
$733$	−4.09188	−	2.36245i	−0.151137	−	0.0872591i	−0.573661	+	0.819093i	$0.694477\pi$
$734$	−7.70719	−	13.3492i	−0.284478	−	0.492730i
$735$		0			0
$736$	2.12132	−	3.67423i	0.0781929	−	0.135434i
$737$	25.9808	−	15.0000i	0.957014	−	0.552532i
$738$		0			0
$739$	−7.72792	+	13.3852i	−0.284276	+	0.492381i	−0.972433	−	0.233181i	$-0.925087\pi$
$739$	−7.72792	+	13.3852i	−0.284276	+	0.492381i	0.688157	+	0.725562i	$0.258420\pi$
$740$	−0.174080			−0.00639930
$741$		0			0
$742$	7.24264	+	17.7408i	0.265886	+	0.651284i
$743$	−33.3292	+	19.2426i	−1.22273	+	0.705944i	−0.965499	−	0.260406i	$-0.916144\pi$
$743$	−33.3292	+	19.2426i	−1.22273	+	0.705944i	−0.257232	+	0.966350i	$0.582810\pi$
$744$		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
$749$	−4.11999	+	30.1066i	−0.150541	+	1.10007i
$750$		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	$0.944352\pi$
$752$	−5.91359			−0.215646
$753$		0			0
$754$		−	17.7408i		−	0.646081i
$755$	−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	$0.710225\pi$
$758$		−	12.4853i		−	0.453486i
$759$		0			0
$760$	−4.24264			−0.153897
$761$	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
$763$	−18.4853	−	45.2795i	−0.669212	−	1.63923i
$764$			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
$769$	−8.52944	+	4.92447i	−0.307579	+	0.177581i	−0.645843	−	0.763470i	$-0.723494\pi$
$769$	−8.52944	+	4.92447i	−0.307579	+	0.177581i	0.338263	+	0.941051i	$0.390161\pi$
$770$	−3.48960	+	4.50000i	−0.125756	+	0.162169i
$771$		0			0
$772$	−9.48528			−0.341383
$773$	−8.06591	+	13.9706i	−0.290111	+	0.502486i	−0.973836	−	0.227253i	$-0.927025\pi$
$773$	−8.06591	+	13.9706i	−0.290111	+	0.502486i	0.683725	+	0.729740i	$0.260359\pi$
$774$		0			0
$775$	−35.2721	+	20.3643i	−1.26701	+	0.731509i
$776$	−6.77962	+	11.7426i	−0.243374	+	0.421536i
$777$		0			0
$778$	15.7279	+	27.2416i	0.563873	+	0.976657i
$779$	−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
$785$	−9.13151	−	5.27208i	−0.325917	−	0.188169i
$786$		0			0
$787$		−	32.1915i		−	1.14750i	−0.819029	−	0.573752i	$-0.805487\pi$
$787$		−	32.1915i		−	1.14750i	0.819029	−	0.573752i	$-0.194513\pi$
$788$		−	26.4853i		−	0.943499i
$789$		0			0
$790$	1.71320	+	0.989118i	0.0609530	+	0.0351913i
$791$	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
$797$	3.22848	+	5.59188i	0.114358	+	0.198075i	0.917523	−	0.397682i	$-0.130185\pi$
$797$	3.22848	+	5.59188i	0.114358	+	0.198075i	−0.803165	+	0.595757i	$0.796852\pi$
$798$		0			0
$799$	−17.4853	+	30.2854i	−0.618585	+	1.07142i
$800$	3.88437	−	2.24264i	0.137333	−	0.0792893i
$801$		0			0
$802$		0			0
$803$	4.30463			0.151907
$804$		0			0
$805$	−1.09188	+	7.97887i	−0.0384838	+	0.281218i
$806$	19.2627	−	11.1213i	0.678499	−	0.391732i
$807$		0			0
$808$		0			0
$809$	6.08767	+	3.51472i	0.214031	+	0.123571i	0.603183	−	0.797602i	$-0.293899\pi$
$809$	6.08767	+	3.51472i	0.214031	+	0.123571i	−0.389152	+	0.921173i	$0.627232\pi$
$810$		0			0
$811$		−	31.1769i		−	1.09477i	−0.836881	−	0.547385i	$-0.815623\pi$
$811$		−	31.1769i		−	1.09477i	0.836881	−	0.547385i	$-0.184377\pi$
$812$	17.7408	−	7.24264i	0.622579	−	0.254167i
$813$		0			0
$814$	−0.363961	+	0.630399i	−0.0127568	+	0.0220955i
$815$	1.60896			0.0563593
$816$		0			0
$817$			1.43488i			0.0502000i
$818$	−14.9941			−0.524257
$819$		0			0
$820$	−8.48528			−0.296319
$821$		−	40.7574i		−	1.42244i	−0.702969	−	0.711221i	$-0.748143\pi$
$821$		−	40.7574i		−	1.42244i	0.702969	−	0.711221i	$-0.251857\pi$
$822$		0			0
$823$	29.9411			1.04368			0.521841	−	0.853043i	$-0.325245\pi$
$823$	29.9411			1.04368			0.521841	+	0.853043i	$0.325245\pi$
$824$	−2.74666	+	4.75736i	−0.0956845	+	0.165730i
$825$		0			0
$826$	16.8640	+	13.0774i	0.586772	+	0.455022i
$827$		−	37.9706i		−	1.32037i	−0.751105	−	0.660183i	$-0.770479\pi$
$827$		−	37.9706i		−	1.32037i	0.751105	−	0.660183i	$-0.229521\pi$
$828$		0			0
$829$	11.3345	+	6.54399i	0.393664	+	0.227282i	0.683747	−	0.729720i	$-0.260349\pi$
$829$	11.3345	+	6.54399i	0.393664	+	0.227282i	−0.290082	+	0.957002i	$0.593683\pi$
$830$	−4.11999	+	2.37868i	−0.143007	+	0.0825652i
$831$		0			0
$832$	−2.12132	+	1.22474i	−0.0735436	+	0.0424604i
$833$	−39.8732	−	11.1213i	−1.38153	−	0.385331i
$834$		0			0
$835$	−11.5736			−0.400521
$836$	−8.87039	+	15.3640i	−0.306789	+	0.531374i
$837$		0			0
$838$	20.4853	−	11.8272i	0.707652	−	0.408563i
$839$	5.10911	−	8.84924i	0.176386	−	0.305510i	−0.764254	−	0.644915i	$-0.776893\pi$
$839$	5.10911	−	8.84924i	0.176386	−	0.305510i	0.940640	+	0.339406i	$0.110226\pi$
$840$		0			0
$841$	11.7279	+	20.3134i	0.404411	+	0.700461i
$842$	−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
$848$	6.27231	+	3.62132i	0.215392	+	0.124357i
$849$		0			0
$850$		−	26.5241i		−	0.909770i
$851$			1.02944i			0.0352887i
$852$		0			0
$853$	31.9706	+	18.4582i	1.09465	+	0.631997i	0.934811	−	0.355146i	$-0.115569\pi$
$853$	31.9706	+	18.4582i	1.09465	+	0.631997i	0.159840	+	0.987143i	$0.448902\pi$
$854$	−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	0.355012	−	0.934862i	$-0.384477\pi$
$859$	−8.12132	−	4.68885i	−0.277096	−	0.159981i	−0.632108	+	0.774880i	$0.717810\pi$
$860$	0.0870399	+	0.150758i	0.00296804	+	0.00514079i
$861$		0			0
$862$	1.75736	−	3.04384i	0.0598559	−	0.103673i
$863$	−29.0246	+	16.7574i	−0.988009	+	0.570427i	−0.904679	−	0.426095i	$-0.859889\pi$
$863$	−29.0246	+	16.7574i	−0.988009	+	0.570427i	−0.0833303	+	0.996522i	$0.526556\pi$
$864$		0			0
$865$	−7.45584	+	12.9139i	−0.253506	+	0.439086i
$866$	3.46410			0.117715
$867$		0			0
$868$	18.9853	+	14.7224i	0.644402	+	0.499712i
$869$	7.16383	−	4.13604i	0.243016	−	0.140306i
$870$		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
$875$	−11.0333	+	14.2279i	−0.372992	+	0.480992i
$876$		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	$0.190795\pi$
$878$	−16.8493			−0.568635
$879$		0			0
$880$			2.15232i			0.0725546i
$881$	−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	$0.254273\pi$
$884$			14.4853i			0.487193i
$885$		0			0
$886$	16.4558			0.552845
$887$	−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
$889$	−5.25736	+	6.77962i	−0.176326	+	0.227381i
$890$			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
$895$	−16.4558	+	9.50079i	−0.550058	+	0.317576i
$896$	−2.09077	−	1.62132i	−0.0698477	−	0.0541645i
$897$		0			0
$898$	1.75736			0.0586438
$899$	−32.8835	+	56.9558i	−1.09673	+	1.89958i
$900$		0			0
$901$	37.0919	−	21.4150i	1.23571	−	0.713437i
$902$	−17.7408	+	30.7279i	−0.590703	+	1.02313i
$903$		0			0
$904$	−4.24264	−	7.34847i	−0.141108	−	0.244406i
$905$	−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
$911$	−5.82655	−	3.36396i	−0.193042	−	0.111453i	0.400364	−	0.916356i	$-0.368884\pi$
$911$	−5.82655	−	3.36396i	−0.193042	−	0.111453i	−0.593406	+	0.804903i	$0.702217\pi$
$912$		0			0
$913$			19.8931i			0.658365i
$914$			23.0000i			0.760772i
$915$		0			0
$916$	−12.0000	−	6.92820i	−0.396491	−	0.228914i
$917$	5.19615	+	12.7279i	0.171592	+	0.420313i
$918$		0			0
$919$	−18.2426	−	31.5972i	−0.601769	−	1.04229i	−0.992553	−	0.121812i	$-0.961129\pi$
$919$	−18.2426	−	31.5972i	−0.601769	−	1.04229i	0.390784	−	0.920482i	$-0.372204\pi$
$920$	1.52192	+	2.63604i	0.0501761	+	0.0869076i
$921$		0			0
$922$	−28.2426	−	16.3059i	−0.930122	−	0.537006i
$923$	2.15232	+	3.72792i	0.0708444	+	0.122706i
$924$		0			0
$925$	−0.544156	+	0.942506i	−0.0178917	+	0.0309894i
$926$	25.5095	−	14.7279i	0.838294	−	0.483990i
$927$		0			0
$928$	3.62132	−	6.27231i	0.118876	−	0.205899i
$929$	−31.0028			−1.01717			−0.508585	−	0.861012i	$-0.669831\pi$
$929$	−31.0028			−1.01717			−0.508585	+	0.861012i	$0.669831\pi$
$930$		0			0
$931$	28.9706	+	29.5680i	0.949472	+	0.969051i
$932$	16.2189	−	9.36396i	0.531266	−	0.306727i
$933$		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	$0.194886\pi$
$937$			35.1844i			1.14942i	−0.818356	+	0.574712i	$0.805114\pi$
$938$	−20.9077	−	16.2132i	−0.682661	−	0.529380i
$939$		0			0
$940$	2.12132	−	3.67423i	0.0691898	−	0.119840i
$941$	27.5897			0.899399			0.449700	−	0.893180i	$-0.351531\pi$
$941$	27.5897			0.899399			0.449700	+	0.893180i	$0.351531\pi$
$942$		0			0
$943$			50.1785i			1.63404i
$944$	8.06591			0.262523
$945$		0			0
$946$	0.727922			0.0236668
$947$			10.9706i			0.356495i	0.983986	+	0.178248i	$0.0570428\pi$
$947$			10.9706i			0.356495i	−0.983986	+	0.178248i	$0.942957\pi$
$948$		0			0
$949$	−3.51472			−0.114093
$950$	−13.2621	+	22.9706i	−0.430278	+	0.745263i
$951$		0			0
$952$	−14.4853	+	5.91359i	−0.469471	+	0.191661i
$953$			17.6985i			0.573310i	0.958034	+	0.286655i	$0.0925434\pi$
$953$			17.6985i			0.573310i	−0.958034	+	0.286655i	$0.907457\pi$
$954$		0			0
$955$	−5.27208	−	3.04384i	−0.170600	−	0.0984962i
$956$	11.0227	−	6.36396i	0.356500	−	0.205825i
$957$		0			0
$958$	−10.3934	+	6.00063i	−0.335795	+	0.193872i
$959$	0.891519	−	6.51472i	0.0287886	−	0.210371i
$960$		0			0
$961$	−51.4558			−1.65987
$962$	0.297173	−	0.514719i	0.00958124	−	0.0165952i
$963$		0			0
$964$	6.25736	−	3.61269i	0.201536	−	0.116357i
$965$	3.40256	−	5.89340i	0.109532	−	0.189715i
$966$		0			0
$967$	−23.8640	−	41.3336i	−0.767413	−	1.32920i	−0.938961	−	0.344023i	$-0.888210\pi$
$967$	−23.8640	−	41.3336i	−0.767413	−	1.32920i	0.171548	−	0.985176i	$-0.445123\pi$
$968$	−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	0.562921	−	0.826510i	$-0.309677\pi$
$971$	−13.5337	−	23.4411i	−0.434318	−	0.752262i	−0.997240	+	0.0742490i	$0.976344\pi$
$972$		0			0
$973$	−0.213203	+	1.55797i	−0.00683499	+	0.0499463i
$974$	−12.3090	−	7.10660i	−0.394406	−	0.227710i
$975$		0			0
$976$			1.01461i			0.0324769i
$977$		−	40.2426i		−	1.28748i	−0.765246	−	0.643738i	$-0.777383\pi$
$977$		−	40.2426i		−	1.28748i	0.765246	−	0.643738i	$-0.222617\pi$
$978$		0			0
$979$	27.0000	+	15.5885i	0.862924	+	0.498209i
$980$	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
$986$	−21.4150	−	37.0919i	−0.681993	−	1.18125i
$987$		0			0
$988$	7.24264	−	12.5446i	0.230419	−	0.399098i
$989$	0.891519	−	0.514719i	0.0283486	−	0.0163671i
$990$		0			0
$991$	−26.1066	+	45.2180i	−0.829304	+	1.43640i	0.0692818	+	0.997597i	$0.477929\pi$
$991$	−26.1066	+	45.2180i	−0.829304	+	1.43640i	−0.898585	+	0.438799i	$0.855404\pi$
$992$	9.08052			0.288307
$993$		0			0
$994$	−2.84924	+	3.67423i	−0.0903725	+	0.116540i
$995$	14.3277	−	8.27208i	0.454217	−	0.262243i
$996$		0			0
$997$	33.7279	−	19.4728i	1.06817	−	0.616711i	0.140492	−	0.990082i	$-0.455132\pi$
$997$	33.7279	−	19.4728i	1.06817	−	0.616711i	0.927682	+	0.373371i	$0.121798\pi$
$998$	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	1134.2.l.f.269.2		8
3.2	odd	2	inner	1134.2.l.f.269.3		8
7.5	odd	6		1134.2.t.e.593.2		8
9.2	odd	6		126.2.k.a.17.3	yes	8
9.4	even	3		1134.2.t.e.1025.3		8
9.5	odd	6		1134.2.t.e.1025.2		8
9.7	even	3		126.2.k.a.17.2	✓	8
21.5	even	6		1134.2.t.e.593.3		8
36.7	odd	6		1008.2.bt.c.17.3		8
36.11	even	6		1008.2.bt.c.17.2		8
45.2	even	12		3150.2.bp.e.899.2		8
45.7	odd	12		3150.2.bp.b.899.2		8
45.29	odd	6		3150.2.bf.a.1151.1		8
45.34	even	6		3150.2.bf.a.1151.3		8
45.38	even	12		3150.2.bp.b.899.3		8
45.43	odd	12		3150.2.bp.e.899.3		8
63.2	odd	6		882.2.k.a.215.1		8
63.5	even	6	inner	1134.2.l.f.215.4		8
63.11	odd	6		882.2.d.a.881.7		8
63.16	even	3		882.2.k.a.215.4		8
63.20	even	6		882.2.k.a.521.4		8
63.25	even	3		882.2.d.a.881.2		8
63.34	odd	6		882.2.k.a.521.1		8
63.38	even	6		882.2.d.a.881.6		8
63.40	odd	6	inner	1134.2.l.f.215.1		8
63.47	even	6		126.2.k.a.89.2	yes	8
63.52	odd	6		882.2.d.a.881.3		8
63.61	odd	6		126.2.k.a.89.3	yes	8
252.11	even	6		7056.2.k.f.881.5		8
252.47	odd	6		1008.2.bt.c.593.3		8
252.115	even	6		7056.2.k.f.881.6		8
252.151	odd	6		7056.2.k.f.881.4		8
252.187	even	6		1008.2.bt.c.593.2		8
252.227	odd	6		7056.2.k.f.881.3		8
315.47	odd	12		3150.2.bp.e.1349.3		8
315.124	odd	6		3150.2.bf.a.1601.1		8
315.173	odd	12		3150.2.bp.b.1349.2		8
315.187	even	12		3150.2.bp.b.1349.3		8
315.299	even	6		3150.2.bf.a.1601.3		8
315.313	even	12		3150.2.bp.e.1349.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
126.2.k.a.17.2	✓	8	9.7	even	3
126.2.k.a.17.3	yes	8	9.2	odd	6
126.2.k.a.89.2	yes	8	63.47	even	6
126.2.k.a.89.3	yes	8	63.61	odd	6
882.2.d.a.881.2		8	63.25	even	3
882.2.d.a.881.3		8	63.52	odd	6
882.2.d.a.881.6		8	63.38	even	6
882.2.d.a.881.7		8	63.11	odd	6
882.2.k.a.215.1		8	63.2	odd	6
882.2.k.a.215.4		8	63.16	even	3
882.2.k.a.521.1		8	63.34	odd	6
882.2.k.a.521.4		8	63.20	even	6
1008.2.bt.c.17.2		8	36.11	even	6
1008.2.bt.c.17.3		8	36.7	odd	6
1008.2.bt.c.593.2		8	252.187	even	6
1008.2.bt.c.593.3		8	252.47	odd	6
1134.2.l.f.215.1		8	63.40	odd	6	inner
1134.2.l.f.215.4		8	63.5	even	6	inner
1134.2.l.f.269.2		8	1.1	even	1	trivial
1134.2.l.f.269.3		8	3.2	odd	2	inner
1134.2.t.e.593.2		8	7.5	odd	6
1134.2.t.e.593.3		8	21.5	even	6
1134.2.t.e.1025.2		8	9.5	odd	6
1134.2.t.e.1025.3		8	9.4	even	3
3150.2.bf.a.1151.1		8	45.29	odd	6
3150.2.bf.a.1151.3		8	45.34	even	6
3150.2.bf.a.1601.1		8	315.124	odd	6
3150.2.bf.a.1601.3		8	315.299	even	6
3150.2.bp.b.899.2		8	45.7	odd	12
3150.2.bp.b.899.3		8	45.38	even	12
3150.2.bp.b.1349.2		8	315.173	odd	12
3150.2.bp.b.1349.3		8	315.187	even	12
3150.2.bp.e.899.2		8	45.2	even	12
3150.2.bp.e.899.3		8	45.43	odd	12
3150.2.bp.e.1349.2		8	315.313	even	12
3150.2.bp.e.1349.3		8	315.47	odd	12
7056.2.k.f.881.3		8	252.227	odd	6
7056.2.k.f.881.4		8	252.151	odd	6
7056.2.k.f.881.5		8	252.11	even	6
7056.2.k.f.881.6		8	252.115	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:	\( N \)	\(=\)	\( 1134 = 2 \cdot 3^{4} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1134.l (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q-1.00000i q^{2} -1.00000 q^{4} +(0.358719 - 0.621320i) q^{5} +(-1.62132 + 2.09077i) q^{7} +1.00000i q^{8} +O(q^{10})\)	\(q-1.00000i q^{2} -1.00000 q^{4} +(0.358719 - 0.621320i) q^{5} +(-1.62132 + 2.09077i) q^{7} +1.00000i q^{8} +(-0.621320 - 0.358719i) q^{10} +(-2.59808 + 1.50000i) q^{11} +(2.12132 - 1.22474i) q^{13} +(2.09077 + 1.62132i) q^{14} +1.00000 q^{16} +(2.95680 - 5.12132i) q^{17} +(-5.12132 + 2.95680i) q^{19} +(-0.358719 + 0.621320i) q^{20} +(1.50000 + 2.59808i) q^{22} +(3.67423 + 2.12132i) q^{23} +(2.24264 + 3.88437i) q^{25} +(-1.22474 - 2.12132i) q^{26} +(1.62132 - 2.09077i) q^{28} +(6.27231 + 3.62132i) q^{29} +9.08052i q^{31} -1.00000i q^{32} +(-5.12132 - 2.95680i) q^{34} +(0.717439 + 1.75736i) q^{35} +(0.121320 + 0.210133i) q^{37} +(2.95680 + 5.12132i) q^{38} +(0.621320 + 0.358719i) q^{40} +(5.91359 + 10.2426i) q^{41} +(0.121320 - 0.210133i) q^{43} +(2.59808 - 1.50000i) q^{44} +(2.12132 - 3.67423i) q^{46} -5.91359 q^{47} +(-1.74264 - 6.77962i) q^{49} +(3.88437 - 2.24264i) q^{50} +(-2.12132 + 1.22474i) q^{52} +(6.27231 + 3.62132i) q^{53} +2.15232i q^{55} +(-2.09077 - 1.62132i) q^{56} +(3.62132 - 6.27231i) q^{58} +8.06591 q^{59} +1.01461i q^{61} +9.08052 q^{62} -1.00000 q^{64} -1.75736i q^{65} -10.0000 q^{67} +(-2.95680 + 5.12132i) q^{68} +(1.75736 - 0.717439i) q^{70} +1.75736i q^{71} +(-1.24264 - 0.717439i) q^{73} +(0.210133 - 0.121320i) q^{74} +(5.12132 - 2.95680i) q^{76} +(1.07616 - 7.86396i) q^{77} -2.75736 q^{79} +(0.358719 - 0.621320i) q^{80} +(10.2426 - 5.91359i) q^{82} +(3.31552 - 5.74264i) q^{83} +(-2.12132 - 3.67423i) q^{85} +(-0.210133 - 0.121320i) q^{86} +(-1.50000 - 2.59808i) q^{88} +(-5.19615 - 9.00000i) q^{89} +(-0.878680 + 6.42090i) q^{91} +(-3.67423 - 2.12132i) q^{92} +5.91359i q^{94} +4.24264i q^{95} +(11.7426 + 6.77962i) q^{97} +(-6.77962 + 1.74264i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 8 q^{4} + 4 q^{7}+O(q^{10}) \) 8 * q - 8 * q^4 + 4 * q^7	\( 8 q - 8 q^{4} + 4 q^{7} + 12 q^{10} + 8 q^{16} - 24 q^{19} + 12 q^{22} - 16 q^{25} - 4 q^{28} - 24 q^{34} - 16 q^{37} - 12 q^{40} - 16 q^{43} + 20 q^{49} + 12 q^{58} - 8 q^{64} - 80 q^{67} + 48 q^{70} + 24 q^{73} + 24 q^{76} - 56 q^{79} + 48 q^{82} - 12 q^{88} - 24 q^{91} + 60 q^{97}+O(q^{100}) \) 8 * q - 8 * q^4 + 4 * q^7 + 12 * q^10 + 8 * q^16 - 24 * q^19 + 12 * q^22 - 16 * q^25 - 4 * q^28 - 24 * q^34 - 16 * q^37 - 12 * q^40 - 16 * q^43 + 20 * q^49 + 12 * q^58 - 8 * q^64 - 80 * q^67 + 48 * q^70 + 24 * q^73 + 24 * q^76 - 56 * q^79 + 48 * q^82 - 12 * q^88 - 24 * q^91 + 60 * q^97

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