LMFDB - Embedded newform 1264.2.n.i.735.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1264,2,Mod(735,1264)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1264, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 0, 1]))

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

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

chi := DirichletCharacter("1264.735");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1264 = 2^{4} \cdot 79 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1264.n (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:	$10.0930908155$
Analytic rank:	$0$
Dimension:	$28$
Relative dimension:	$14$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			735.8
Character	$\chi$	$=$	1264.735
Dual form			1264.2.n.i.767.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.143444 - 0.248452i) q^{3} +(-1.31050 - 2.26985i) q^{5} +(0.522039 + 0.904199i) q^{7} +(1.45885 + 2.52680i) q^{9} +O(q^{10})$	\(q+(0.143444 - 0.248452i) q^{3} +(-1.31050 - 2.26985i) q^{5} +(0.522039 + 0.904199i) q^{7} +(1.45885 + 2.52680i) q^{9} +(3.34034 - 1.92855i) q^{11} +(0.0743559 - 0.128788i) q^{13} -0.751930 q^{15} -2.07112i q^{17} +(3.33400 - 1.92488i) q^{19} +0.299533 q^{21} +(-5.48230 + 3.16521i) q^{23} +(-0.934814 + 1.61915i) q^{25} +1.69771 q^{27} +(-4.48579 + 2.58987i) q^{29} +(7.96760 - 4.60010i) q^{31} -1.10655i q^{33} +(1.36826 - 2.36990i) q^{35} +(0.737560 + 0.425831i) q^{37} +(-0.0213317 - 0.0369477i) q^{39} +10.0287i q^{41} +(5.84945 - 10.1315i) q^{43} +(3.82364 - 6.62273i) q^{45} +(-1.36826 - 2.36990i) q^{47} +(2.95495 - 5.11812i) q^{49} +(-0.514574 - 0.297089i) q^{51} +(5.26082 - 3.03733i) q^{53} +(-8.75503 - 5.05472i) q^{55} -1.10445i q^{57} +(5.30608 - 9.19039i) q^{59} +6.39920i q^{61} +(-1.52315 + 2.63818i) q^{63} -0.389773 q^{65} -11.6644i q^{67} +1.81611i q^{69} -3.93147 q^{71} +(-8.04018 - 13.9260i) q^{73} +(0.268186 + 0.464512i) q^{75} +(3.48758 + 2.01356i) q^{77} +(5.46822 - 7.00704i) q^{79} +(-4.13302 + 7.15860i) q^{81} +(5.05759 - 2.92000i) q^{83} +(-4.70114 + 2.71421i) q^{85} +1.48600i q^{87} +0.247488 q^{89} +0.155267 q^{91} -2.63942i q^{93} +(-8.73840 - 5.04512i) q^{95} -8.68782 q^{97} +(9.74611 + 5.62692i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q - 20 q^{9}+O(q^{10}) $ 28 * q - 20 * q^9	$ 28 q - 20 q^{9} - 8 q^{13} + 32 q^{21} - 14 q^{25} + 30 q^{37} - 6 q^{45} - 12 q^{49} - 18 q^{53} - 48 q^{65} + 22 q^{73} - 66 q^{77} - 14 q^{81} + 60 q^{89} - 16 q^{97}+O(q^{100}) $ 28 * q - 20 * q^9 - 8 * q^13 + 32 * q^21 - 14 * q^25 + 30 * q^37 - 6 * q^45 - 12 * q^49 - 18 * q^53 - 48 * q^65 + 22 * q^73 - 66 * q^77 - 14 * q^81 + 60 * q^89 - 16 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1264\mathbb{Z}\right)^\times$.

$n$	$159$	$161$	$949$
$\chi(n)$	$-1$	$e\left(\frac{1}{6}\right)$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	0.143444	−	0.248452i	0.0828172	−	0.143444i	−0.821642	−	0.570004i	$-0.806942\pi$
$3$	0.143444	−	0.248452i	0.0828172	−	0.143444i	0.904459	+	0.426561i	$0.140275\pi$
$4$		0			0
$5$	−1.31050	−	2.26985i	−0.586073	−	1.01511i	−0.994741	−	0.102425i	$-0.967340\pi$
$5$	−1.31050	−	2.26985i	−0.586073	−	1.01511i	0.408668	−	0.912683i	$-0.365993\pi$
$6$		0			0
$7$	0.522039	+	0.904199i	0.197312	+	0.341755i	0.947656	−	0.319293i	$-0.103445\pi$
$7$	0.522039	+	0.904199i	0.197312	+	0.341755i	−0.750344	+	0.661048i	$0.770112\pi$
$8$		0			0
$9$	1.45885	+	2.52680i	0.486283	+	0.842266i
$10$		0			0
$11$	3.34034	−	1.92855i	1.00715	−	0.581479i	0.0967952	−	0.995304i	$-0.469141\pi$
$11$	3.34034	−	1.92855i	1.00715	−	0.581479i	0.910356	+	0.413825i	$0.135807\pi$
$12$		0			0
$13$	0.0743559	−	0.128788i	0.0206226	−	0.0357194i	−0.855530	−	0.517753i	$-0.826768\pi$
$13$	0.0743559	−	0.128788i	0.0206226	−	0.0357194i	0.876153	+	0.482034i	$0.160102\pi$
$14$		0			0
$15$	−0.751930			−0.194148
$16$		0			0
$17$		−	2.07112i		−	0.502321i	−0.967945	−	0.251161i	$-0.919188\pi$
$17$		−	2.07112i		−	0.502321i	0.967945	−	0.251161i	$-0.0808123\pi$
$18$		0			0
$19$	3.33400	−	1.92488i	0.764871	−	0.441599i	−0.0661707	−	0.997808i	$-0.521078\pi$
$19$	3.33400	−	1.92488i	0.764871	−	0.441599i	0.831042	+	0.556210i	$0.187745\pi$
$20$		0			0
$21$	0.299533			0.0653634
$22$		0			0
$23$	−5.48230	+	3.16521i	−1.14314	+	0.659991i	−0.947206	−	0.320626i	$-0.896107\pi$
$23$	−5.48230	+	3.16521i	−1.14314	+	0.659991i	−0.195932	+	0.980617i	$0.562773\pi$
$24$		0			0
$25$	−0.934814	+	1.61915i	−0.186963	+	0.323829i
$26$		0			0
$27$	1.69771			0.326725
$28$		0			0
$29$	−4.48579	+	2.58987i	−0.832990	+	0.480927i	−0.854875	−	0.518834i	$-0.826366\pi$
$29$	−4.48579	+	2.58987i	−0.832990	+	0.480927i	0.0218856	+	0.999760i	$0.493033\pi$
$30$		0			0
$31$	7.96760	−	4.60010i	1.43102	−	0.826202i	0.433825	−	0.900997i	$-0.357164\pi$
$31$	7.96760	−	4.60010i	1.43102	−	0.826202i	0.997199	+	0.0747955i	$0.0238304\pi$
$32$		0			0
$33$		−	1.10655i		−	0.192626i
$34$		0			0
$35$	1.36826	−	2.36990i	0.231279	−	0.400587i
$36$		0			0
$37$	0.737560	+	0.425831i	0.121254	+	0.0700061i	0.559400	−	0.828898i	$-0.311031\pi$
$37$	0.737560	+	0.425831i	0.121254	+	0.0700061i	−0.438146	+	0.898904i	$0.644365\pi$
$38$		0			0
$39$	−0.0213317	−	0.0369477i	−0.00341581	−	0.00591636i
$40$		0			0
$41$			10.0287i			1.56622i	0.621881	+	0.783112i	$0.286369\pi$
$41$			10.0287i			1.56622i	−0.621881	+	0.783112i	$0.713631\pi$
$42$		0			0
$43$	5.84945	−	10.1315i	0.892032	−	1.54505i	0.0545975	−	0.998508i	$-0.482612\pi$
$43$	5.84945	−	10.1315i	0.892032	−	1.54505i	0.837435	−	0.546537i	$-0.184054\pi$
$44$		0			0
$45$	3.82364	−	6.62273i	0.569994	−	0.987259i
$46$		0			0
$47$	−1.36826	−	2.36990i	−0.199582	−	0.345686i	0.748811	−	0.662784i	$-0.230625\pi$
$47$	−1.36826	−	2.36990i	−0.199582	−	0.345686i	−0.948393	+	0.317098i	$0.897292\pi$
$48$		0			0
$49$	2.95495	−	5.11812i	0.422136	−	0.731160i
$50$		0			0
$51$	−0.514574	−	0.297089i	−0.0720548	−	0.0416008i
$52$		0			0
$53$	5.26082	−	3.03733i	0.722629	−	0.417210i	−0.0930906	−	0.995658i	$-0.529675\pi$
$53$	5.26082	−	3.03733i	0.722629	−	0.417210i	0.815720	+	0.578448i	$0.196341\pi$
$54$		0			0
$55$	−8.75503	−	5.05472i	−1.18053	−	0.681578i
$56$		0			0
$57$		−	1.10445i		−	0.146288i
$58$		0			0
$59$	5.30608	−	9.19039i	0.690792	−	1.19649i	−0.280786	−	0.959770i	$-0.590595\pi$
$59$	5.30608	−	9.19039i	0.690792	−	1.19649i	0.971579	−	0.236717i	$-0.0760715\pi$
$60$		0			0
$61$			6.39920i			0.819334i	0.912235	+	0.409667i	$0.134355\pi$
$61$			6.39920i			0.819334i	−0.912235	+	0.409667i	$0.865645\pi$
$62$		0			0
$63$	−1.52315	+	2.63818i	−0.191899	+	0.332379i
$64$		0			0
$65$	−0.389773			−0.0483454
$66$		0			0
$67$		−	11.6644i		−	1.42503i	−0.701656	−	0.712516i	$-0.747555\pi$
$67$		−	11.6644i		−	1.42503i	0.701656	−	0.712516i	$-0.252445\pi$
$68$		0			0
$69$			1.81611i			0.218634i
$70$		0			0
$71$	−3.93147			−0.466579			−0.233290	−	0.972407i	$-0.574949\pi$
$71$	−3.93147			−0.466579			−0.233290	+	0.972407i	$0.574949\pi$
$72$		0			0
$73$	−8.04018	−	13.9260i	−0.941032	−	1.62992i	−0.763508	−	0.645799i	$-0.776525\pi$
$73$	−8.04018	−	13.9260i	−0.941032	−	1.62992i	−0.177524	−	0.984116i	$-0.556809\pi$
$74$		0			0
$75$	0.268186	+	0.464512i	0.0309675	+	0.0536372i
$76$		0			0
$77$	3.48758	+	2.01356i	0.397447	+	0.229466i
$78$		0			0
$79$	5.46822	−	7.00704i	0.615223	−	0.788353i
$79$	5.46822	−	7.00704i	0.615223	−	0.788353i
$80$		0			0
$81$	−4.13302	+	7.15860i	−0.459224	+	0.795400i
$82$		0			0
$83$	5.05759	−	2.92000i	0.555142	−	0.320512i	−0.196051	−	0.980594i	$-0.562812\pi$
$83$	5.05759	−	2.92000i	0.555142	−	0.320512i	0.751194	+	0.660082i	$0.229478\pi$
$84$		0			0
$85$	−4.70114	+	2.71421i	−0.509910	+	0.294397i
$86$		0			0
$87$			1.48600i			0.159316i
$88$		0			0
$89$	0.247488			0.0262337			0.0131169	−	0.999914i	$-0.495825\pi$
$89$	0.247488			0.0262337			0.0131169	+	0.999914i	$0.495825\pi$
$90$		0			0
$91$	0.155267			0.0162764
$92$		0			0
$93$		−	2.63942i		−	0.273695i
$94$		0			0
$95$	−8.73840	−	5.04512i	−0.896541	−	0.517618i
$96$		0			0
$97$	−8.68782			−0.882115			−0.441057	−	0.897479i	$-0.645396\pi$
$97$	−8.68782			−0.882115			−0.441057	+	0.897479i	$0.645396\pi$
$98$		0			0
$99$	9.74611	+	5.62692i	0.979521	+	0.565527i
$100$		0			0
$101$	7.60721			0.756946			0.378473	−	0.925612i	$-0.376449\pi$
$101$	7.60721			0.756946			0.378473	+	0.925612i	$0.376449\pi$
$102$		0			0
$103$	4.38442	−	7.59404i	0.432010	−	0.748263i	−0.565036	−	0.825066i	$-0.691138\pi$
$103$	4.38442	−	7.59404i	0.432010	−	0.748263i	0.997046	+	0.0768028i	$0.0244712\pi$
$104$		0			0
$105$	−0.392537	−	0.679895i	−0.0383077	−	0.0663509i
$106$		0			0
$107$	−7.72723	+	13.3840i	−0.747020	+	1.29388i	0.202225	+	0.979339i	$0.435183\pi$
$107$	−7.72723	+	13.3840i	−0.747020	+	1.29388i	−0.949245	+	0.314537i	$0.898151\pi$
$108$		0			0
$109$	−7.91549	−	4.57001i	−0.758166	−	0.437727i	0.0704708	−	0.997514i	$-0.477550\pi$
$109$	−7.91549	−	4.57001i	−0.758166	−	0.437727i	−0.828637	+	0.559786i	$0.810883\pi$
$110$		0			0
$111$	0.211596	−	0.122165i	0.0200838	−	0.0115954i
$112$		0			0
$113$	10.2401	+	5.91210i	0.963304	+	0.556164i	0.897188	−	0.441648i	$-0.145606\pi$
$113$	10.2401	+	5.91210i	0.963304	+	0.556164i	0.0661155	+	0.997812i	$0.478939\pi$
$114$		0			0
$115$	14.3691	+	8.29600i	1.33992	+	0.773606i
$116$		0			0
$117$	0.433896			0.0401137
$118$		0			0
$119$	1.87271	−	1.08121i	0.171671	−	0.0991142i
$120$		0			0
$121$	1.93860	−	3.35775i	0.176236	−	0.305250i
$122$		0			0
$123$	2.49165	+	1.43856i	0.224665	+	0.129710i
$124$		0			0
$125$	−8.20470			−0.733850
$126$		0			0
$127$	8.12979	+	14.0812i	0.721402	+	1.24951i	0.960438	+	0.278495i	$0.0898355\pi$
$127$	8.12979	+	14.0812i	0.721402	+	1.24951i	−0.239035	+	0.971011i	$0.576831\pi$
$128$		0			0
$129$	−1.67813	−	2.90661i	−0.147751	−	0.255913i
$130$		0			0
$131$			13.8554i			1.21056i	0.796014	+	0.605278i	$0.206938\pi$
$131$			13.8554i			1.21056i	−0.796014	+	0.605278i	$0.793062\pi$
$132$		0			0
$133$	3.48096	+	2.00973i	0.301837	+	0.174266i
$134$		0			0
$135$	−2.22485	−	3.85355i	−0.191484	−	0.331661i
$136$		0			0
$137$		−	0.134464i		−	0.0114880i	−0.999984	−	0.00574400i	$-0.998172\pi$
$137$		−	0.134464i		−	0.0114880i	0.999984	−	0.00574400i	$-0.00182838\pi$
$138$		0			0
$139$	5.19993	+	9.00655i	0.441052	+	0.763925i	0.997768	−	0.0667781i	$-0.0212720\pi$
$139$	5.19993	+	9.00655i	0.441052	+	0.763925i	−0.556715	+	0.830703i	$0.687939\pi$
$140$		0			0
$141$	−0.785075			−0.0661152
$142$		0			0
$143$		−	0.573596i		−	0.0479665i
$144$		0			0
$145$	11.7572	+	6.78804i	0.976385	+	0.563716i
$146$		0			0
$147$	−0.847737	−	1.46832i	−0.0699202	−	0.121105i
$148$		0			0
$149$	−12.7110	+	7.33868i	−1.04132	+	0.601208i	−0.920208	−	0.391431i	$-0.871980\pi$
$149$	−12.7110	+	7.33868i	−1.04132	+	0.601208i	−0.121115	+	0.992639i	$0.538647\pi$
$150$		0			0
$151$	−14.6546	+	8.46086i	−1.19258	+	0.688535i	−0.958890	−	0.283777i	$-0.908412\pi$
$151$	−14.6546	+	8.46086i	−1.19258	+	0.688535i	−0.233687	+	0.972312i	$0.575079\pi$
$152$		0			0
$153$	5.23331	−	3.02146i	0.423088	−	0.244270i
$154$		0			0
$155$	−20.8831	−	12.0568i	−1.67737	−	0.968429i
$156$		0			0
$157$		−	3.85502i		−	0.307664i	−0.988097	−	0.153832i	$-0.950839\pi$
$157$		−	3.85502i		−	0.307664i	0.988097	−	0.153832i	$-0.0491614\pi$
$158$		0			0
$159$		−	1.74274i		−	0.138209i
$160$		0			0
$161$	−5.72395	−	3.30472i	−0.451110	−	0.260449i
$162$		0			0
$163$	6.62216	−	3.82331i	0.518688	−	0.299465i	−0.217710	−	0.976014i	$-0.569859\pi$
$163$	6.62216	−	3.82331i	0.518688	−	0.299465i	0.736398	+	0.676549i	$0.236525\pi$
$164$		0			0
$165$	−2.51171	+	1.45013i	−0.195536	+	0.112893i
$166$		0			0
$167$	−0.182390	+	0.105303i	−0.0141137	+	0.00814858i	−0.507040	−	0.861922i	$-0.669260\pi$
$167$	−0.182390	+	0.105303i	−0.0141137	+	0.00814858i	0.492927	+	0.870071i	$0.335927\pi$
$168$		0			0
$169$	6.48894	+	11.2392i	0.499149	+	0.864552i
$170$		0			0
$171$	9.72759	+	5.61623i	0.743887	+	0.429484i
$172$		0			0
$173$		−	8.25740i		−	0.627798i	−0.949456	−	0.313899i	$-0.898365\pi$
$173$		−	8.25740i		−	0.627798i	0.949456	−	0.313899i	$-0.101635\pi$
$174$		0			0
$175$	−1.95204			−0.147560
$176$		0			0
$177$	−1.52224	−	2.63661i	−0.114419	−	0.198179i
$178$		0			0
$179$			17.0994i			1.27807i	0.769179	+	0.639034i	$0.220666\pi$
$179$			17.0994i			1.27807i	−0.769179	+	0.639034i	$0.779334\pi$
$180$		0			0
$181$	5.28591	+	9.15546i	0.392898	+	0.680520i	0.992830	−	0.119531i	$-0.0381391\pi$
$181$	5.28591	+	9.15546i	0.392898	+	0.680520i	−0.599932	+	0.800051i	$0.704806\pi$
$182$		0			0
$183$	1.58989	+	0.917924i	0.117528	+	0.0678549i
$184$		0			0
$185$		−	2.23220i		−	0.164115i
$186$		0			0
$187$	−3.99426	−	6.91827i	−0.292089	−	0.505914i
$188$		0			0
$189$	0.886272	+	1.53507i	0.0644668	+	0.111660i
$190$		0			0
$191$	5.18928			0.375483			0.187742	−	0.982218i	$-0.439883\pi$
$191$	5.18928			0.375483			0.187742	+	0.982218i	$0.439883\pi$
$192$		0			0
$193$	2.96781	+	1.71347i	0.213628	+	0.123338i	0.602996	−	0.797744i	$-0.293973\pi$
$193$	2.96781	+	1.71347i	0.213628	+	0.123338i	−0.389369	+	0.921082i	$0.627307\pi$
$194$		0			0
$195$	−0.0559105	+	0.0968397i	−0.00400383	+	0.00693484i
$196$		0			0
$197$	8.83897	−	5.10318i	0.629750	−	0.363587i	−0.150905	−	0.988548i	$-0.548219\pi$
$197$	8.83897	−	5.10318i	0.629750	−	0.363587i	0.780655	+	0.624962i	$0.214885\pi$
$198$		0			0
$199$	2.74146			0.194337			0.0971685	−	0.995268i	$-0.469021\pi$
$199$	2.74146			0.194337			0.0971685	+	0.995268i	$0.469021\pi$
$200$		0			0
$201$	−2.89804	−	1.67318i	−0.204412	−	0.118017i
$202$		0			0
$203$	−4.68351	−	2.70403i	−0.328718	−	0.189786i
$204$		0			0
$205$	22.7637	−	13.1426i	1.58989	−	0.917921i
$206$		0			0
$207$	−15.9957	−	9.23511i	−1.11178	−	0.641884i
$208$		0			0
$209$	7.42446	−	12.8595i	0.513561	−	0.889514i
$210$		0			0
$211$	4.58922	+	7.94876i	0.315935	+	0.547215i	0.979636	−	0.200783i	$-0.0643485\pi$
$211$	4.58922	+	7.94876i	0.315935	+	0.547215i	−0.663701	+	0.747998i	$0.731015\pi$
$212$		0			0
$213$	−0.563943	+	0.976779i	−0.0386408	+	0.0669278i
$214$		0			0
$215$	−30.6628			−2.09118
$216$		0			0
$217$	8.31880	+	4.80286i	0.564717	+	0.326040i
$218$		0			0
$219$	−4.61325			−0.311734
$220$		0			0
$221$	−0.266736	−	0.154000i	−0.0179426	−	0.0103592i
$222$		0			0
$223$		−	4.54495i		−	0.304352i	−0.988353	−	0.152176i	$-0.951372\pi$
$223$		−	4.54495i		−	0.304352i	0.988353	−	0.152176i	$-0.0486281\pi$
$224$		0			0
$225$	−5.45501			−0.363667
$226$		0			0
$227$	−8.97620			−0.595772			−0.297886	−	0.954602i	$-0.596281\pi$
$227$	−8.97620			−0.595772			−0.297886	+	0.954602i	$0.596281\pi$
$228$		0			0
$229$			12.4381i			0.821934i	0.911650	+	0.410967i	$0.134809\pi$
$229$			12.4381i			0.821934i	−0.911650	+	0.410967i	$0.865191\pi$
$230$		0			0
$231$	1.00054	−	0.577663i	0.0658309	−	0.0380075i
$232$		0			0
$233$	−13.7408	+	7.93324i	−0.900188	+	0.519724i	−0.877261	−	0.480013i	$-0.840632\pi$
$233$	−13.7408	+	7.93324i	−0.900188	+	0.519724i	−0.0229269	+	0.999737i	$0.507298\pi$
$234$		0			0
$235$	−3.58622	+	6.21151i	−0.233939	+	0.405194i
$236$		0			0
$237$	−0.956528	−	2.36370i	−0.0621331	−	0.153539i
$238$		0			0
$239$	−13.3607	−	7.71378i	−0.864229	−	0.498963i	0.00119740	−	0.999999i	$-0.499619\pi$
$239$	−13.3607	−	7.71378i	−0.864229	−	0.498963i	−0.865426	+	0.501037i	$0.832952\pi$
$240$		0			0
$241$	−6.23424	−	10.7980i	−0.401583	−	0.695562i	0.592334	−	0.805692i	$-0.298206\pi$
$241$	−6.23424	−	10.7980i	−0.401583	−	0.695562i	−0.993917	+	0.110130i	$0.964873\pi$
$242$		0			0
$243$	3.73228	+	6.46449i	0.239426	+	0.414697i
$244$		0			0
$245$	−15.4898			−0.989609
$246$		0			0
$247$		−	0.572506i		−	0.0364277i
$248$		0			0
$249$		−	1.67542i		−	0.106175i
$250$		0			0
$251$	12.2210			0.771380			0.385690	−	0.922628i	$-0.373963\pi$
$251$	12.2210			0.771380			0.385690	+	0.922628i	$0.373963\pi$
$252$		0			0
$253$	−12.2085	+	21.1457i	−0.767542	+	1.32942i
$254$		0			0
$255$			1.55734i			0.0975245i
$256$		0			0
$257$	−13.8767	+	24.0352i	−0.865606	+	1.49927i	0.000838460		1.00000i	$0.499733\pi$
$257$	−13.8767	+	24.0352i	−0.865606	+	1.49927i	−0.866444	+	0.499274i	$0.833600\pi$
$258$		0			0
$259$			0.889201i			0.0552523i
$260$		0			0
$261$	−13.0882	−	7.55645i	−0.810137	−	0.467733i
$262$		0			0
$263$	−26.0931	+	15.0649i	−1.60897	+	0.928940i	−0.619370	+	0.785099i	$0.712612\pi$
$263$	−26.0931	+	15.0649i	−1.60897	+	0.928940i	−0.989601	+	0.143841i	$0.954055\pi$
$264$		0			0
$265$	−13.7886	−	7.96085i	−0.847026	−	0.489031i
$266$		0			0
$267$	0.0355006	−	0.0614888i	0.00217260	−	0.00376306i
$268$		0			0
$269$	−2.60650	−	4.51458i	−0.158921	−	0.275259i	0.775559	−	0.631275i	$-0.217468\pi$
$269$	−2.60650	−	4.51458i	−0.158921	−	0.275259i	−0.934480	+	0.356016i	$0.884135\pi$
$270$		0			0
$271$	6.19956	−	10.7380i	0.376596	−	0.652284i	−0.613968	−	0.789331i	$-0.710428\pi$
$271$	6.19956	−	10.7380i	0.376596	−	0.652284i	0.990565	+	0.137047i	$0.0437610\pi$
$272$		0			0
$273$	0.0222720	−	0.0385763i	0.00134796	−	0.00233474i
$274$		0			0
$275$			7.21134i			0.434860i
$276$		0			0
$277$	3.87674	+	6.71471i	0.232931	+	0.403448i	0.958669	−	0.284523i	$-0.0918351\pi$
$277$	3.87674	+	6.71471i	0.232931	+	0.403448i	−0.725739	+	0.687971i	$0.758502\pi$
$278$		0			0
$279$	23.2470	+	13.4217i	1.39176	+	0.803535i
$280$		0			0
$281$	8.06094	−	13.9620i	0.480875	−	0.832900i	−0.518884	−	0.854845i	$-0.673652\pi$
$281$	8.06094	−	13.9620i	0.480875	−	0.832900i	0.999759	+	0.0219443i	$0.00698565\pi$
$282$		0			0
$283$			1.25774i			0.0747647i	0.999301	+	0.0373823i	$0.0119019\pi$
$283$			1.25774i			0.0747647i	−0.999301	+	0.0373823i	$0.988098\pi$
$284$		0			0
$285$	−2.50693	+	1.44738i	−0.148498	+	0.0857353i
$286$		0			0
$287$	−9.06796	+	5.23539i	−0.535265	+	0.309035i
$288$		0			0
$289$	12.7104			0.747673
$290$		0			0
$291$	−1.24621	+	2.15850i	−0.0730542	+	0.126534i
$292$		0			0
$293$	13.2857	−	7.67048i	0.776157	−	0.448114i	−0.0589099	−	0.998263i	$-0.518762\pi$
$293$	13.2857	−	7.67048i	0.776157	−	0.448114i	0.835066	+	0.550149i	$0.185429\pi$
$294$		0			0
$295$	−27.8144			−1.61942
$296$		0			0
$297$	5.67094	−	3.27412i	0.329061	−	0.189984i
$298$		0			0
$299$			0.941407i			0.0544430i
$300$		0			0
$301$	12.2146			0.704036
$302$		0			0
$303$	1.09121	−	1.89002i	0.0626881	−	0.108579i
$304$		0			0
$305$	14.5252	−	8.38615i	0.831712	−	0.480189i
$306$		0			0
$307$	10.3818	+	17.9819i	0.592523	+	1.02628i	0.993891	+	0.110363i	$0.0352013\pi$
$307$	10.3818	+	17.9819i	0.592523	+	1.02628i	−0.401369	+	0.915917i	$0.631465\pi$
$308$		0			0
$309$	−1.25783	−	2.17863i	−0.0715557	−	0.123938i
$310$		0			0
$311$	13.7085	+	23.7438i	0.777339	+	1.34639i	0.933471	+	0.358654i	$0.116764\pi$
$311$	13.7085	+	23.7438i	0.777339	+	1.34639i	−0.156132	+	0.987736i	$0.549903\pi$
$312$		0			0
$313$	−5.38681	+	9.33023i	−0.304480	+	0.527376i	−0.977146	−	0.212572i	$-0.931816\pi$
$313$	−5.38681	+	9.33023i	−0.304480	+	0.527376i	0.672665	+	0.739947i	$0.265149\pi$
$314$		0			0
$315$	7.98436			0.449868
$316$		0			0
$317$	−4.86194			−0.273074			−0.136537	−	0.990635i	$-0.543597\pi$
$317$	−4.86194			−0.273074			−0.136537	+	0.990635i	$0.543597\pi$
$318$		0			0
$319$	−9.98938	+	17.3021i	−0.559298	+	0.968732i
$320$		0			0
$321$	2.21684	+	3.83969i	0.123732	+	0.214310i
$322$		0			0
$323$	−3.98667	−	6.90512i	−0.221824	−	0.384211i
$324$		0			0
$325$	0.139018	+	0.240786i	0.00771132	+	0.0133564i
$326$		0			0
$327$	−2.27085	+	1.31108i	−0.125578	+	0.0725027i
$328$		0			0
$329$	1.42858	−	2.47437i	0.0787599	−	0.136416i
$330$		0			0
$331$	−15.4317			−0.848201			−0.424101	−	0.905615i	$-0.639410\pi$
$331$	−15.4317			−0.848201			−0.424101	+	0.905615i	$0.639410\pi$
$332$		0			0
$333$			2.48489i			0.136171i
$334$		0			0
$335$	−26.4764	+	15.2862i	−1.44656	+	0.835173i
$336$		0			0
$337$	9.71194			0.529043			0.264522	−	0.964380i	$-0.414786\pi$
$337$	9.71194			0.529043			0.264522	+	0.964380i	$0.414786\pi$
$338$		0			0
$339$	2.93774	−	1.69611i	0.159556	−	0.0921198i
$340$		0			0
$341$	17.7430	−	30.7318i	0.960838	−	1.66422i
$342$		0			0
$343$	13.4790			0.727795
$344$		0			0
$345$	4.12231	−	2.38001i	0.221937	−	0.128136i
$346$		0			0
$347$	7.56059	−	4.36511i	0.405874	−	0.234331i	−0.283141	−	0.959078i	$-0.591377\pi$
$347$	7.56059	−	4.36511i	0.405874	−	0.234331i	0.689015	+	0.724747i	$0.258043\pi$
$348$		0			0
$349$		−	16.8346i		−	0.901135i	−0.892742	−	0.450567i	$-0.851222\pi$
$349$		−	16.8346i		−	0.901135i	0.892742	−	0.450567i	$-0.148778\pi$
$350$		0			0
$351$	0.126235	−	0.218645i	0.00673791	−	0.0116704i
$352$		0			0
$353$	11.3640	+	6.56099i	0.604843	+	0.349206i	0.770944	−	0.636902i	$-0.219785\pi$
$353$	11.3640	+	6.56099i	0.604843	+	0.349206i	−0.166101	+	0.986109i	$0.553118\pi$
$354$		0			0
$355$	5.15218	+	8.92384i	0.273449	+	0.473628i
$356$		0			0
$357$		−	0.620370i		−	0.0328334i
$358$		0			0
$359$	−3.14249	+	5.44295i	−0.165854	+	0.287268i	−0.936958	−	0.349441i	$-0.886371\pi$
$359$	−3.14249	+	5.44295i	−0.165854	+	0.287268i	0.771104	+	0.636709i	$0.219705\pi$
$360$		0			0
$361$	−2.08964	+	3.61937i	−0.109981	+	0.190493i
$362$		0			0
$363$	−0.556159	−	0.963295i	−0.0291908	−	0.0505599i
$364$		0			0
$365$	−21.0733	+	36.5000i	−1.10303	+	1.91050i
$366$		0			0
$367$	19.3513	+	11.1725i	1.01013	+	0.583199i	0.911230	−	0.411898i	$-0.135134\pi$
$367$	19.3513	+	11.1725i	1.01013	+	0.583199i	0.0989004	+	0.995097i	$0.468467\pi$
$368$		0			0
$369$	−25.3406	+	14.6304i	−1.31918	+	0.761628i
$370$		0			0
$371$	5.49271	+	3.17122i	0.285167	+	0.164641i
$372$		0			0
$373$		−	24.8708i		−	1.28776i	−0.765125	−	0.643881i	$-0.777323\pi$
$373$		−	24.8708i		−	1.28776i	0.765125	−	0.643881i	$-0.222677\pi$
$374$		0			0
$375$	−1.17691	+	2.03847i	−0.0607754	+	0.105266i
$376$		0			0
$377$			0.770288i			0.0396719i
$378$		0			0
$379$	−7.87089	+	13.6328i	−0.404300	+	0.700269i	−0.994240	−	0.107179i	$-0.965818\pi$
$379$	−7.87089	+	13.6328i	−0.404300	+	0.700269i	0.589939	+	0.807447i	$0.299152\pi$
$380$		0			0
$381$	4.66466			0.238978
$382$		0			0
$383$		−	2.01323i		−	0.102871i	−0.998676	−	0.0514355i	$-0.983620\pi$
$383$		−	2.01323i		−	0.102871i	0.998676	−	0.0514355i	$-0.0163797\pi$
$384$		0			0
$385$		−	10.5551i		−	0.537935i
$386$		0			0
$387$	34.1338			1.73512
$388$		0			0
$389$	−2.29928	−	3.98248i	−0.116578	−	0.201920i	0.801831	−	0.597551i	$-0.203859\pi$
$389$	−2.29928	−	3.98248i	−0.116578	−	0.201920i	−0.918410	+	0.395631i	$0.870526\pi$
$390$		0			0
$391$	6.55553	+	11.3545i	0.331528	+	0.574223i
$392$		0			0
$393$	3.44241	+	1.98747i	0.173646	+	0.100255i
$394$		0			0
$395$	−23.0710	−	3.22933i	−1.16083	−	0.162485i
$396$		0			0
$397$	−19.2267	+	33.3015i	−0.964958	+	1.67136i	−0.255230	+	0.966880i	$0.582151\pi$
$397$	−19.2267	+	33.3015i	−0.964958	+	1.67136i	−0.709728	+	0.704476i	$0.751182\pi$
$398$		0			0
$399$	0.998641	−	0.576566i	0.0499946	−	0.0288644i
$400$		0			0
$401$	−6.12521	+	3.53639i	−0.305878	+	0.176599i	−0.645081	−	0.764115i	$-0.723176\pi$
$401$	−6.12521	+	3.53639i	−0.305878	+	0.176599i	0.339202	+	0.940713i	$0.389843\pi$
$402$		0			0
$403$		−	1.36818i		−	0.0681538i
$404$		0			0
$405$	21.6653			1.07656
$406$		0			0
$407$	3.28494			0.162828
$408$		0			0
$409$			26.5919i			1.31489i	0.753504	+	0.657444i	$0.228362\pi$
$409$			26.5919i			1.31489i	−0.753504	+	0.657444i	$0.771638\pi$
$410$		0			0
$411$	−0.0334077	−	0.0192879i	−0.00164788	−	0.000951403i
$412$		0			0
$413$	11.0799			0.545207
$414$		0			0
$415$	−13.2559	−	7.65331i	−0.650708	−	0.375686i
$416$		0			0
$417$	2.98359			0.146107
$418$		0			0
$419$	7.93143	−	13.7376i	0.387476	−	0.671128i	−0.604633	−	0.796504i	$-0.706680\pi$
$419$	7.93143	−	13.7376i	0.387476	−	0.671128i	0.992109	+	0.125376i	$0.0400137\pi$
$420$		0			0
$421$	−14.0224	−	24.2875i	−0.683409	−	1.18370i	−0.973934	−	0.226831i	$-0.927163\pi$
$421$	−14.0224	−	24.2875i	−0.683409	−	1.18370i	0.290526	−	0.956867i	$-0.406170\pi$
$422$		0			0
$423$	3.99218	−	6.91466i	0.194106	−	0.336202i
$424$		0			0
$425$	3.35345	+	1.93612i	0.162666	+	0.0939154i
$426$		0			0
$427$	−5.78615	+	3.34064i	−0.280012	+	0.161665i
$428$		0			0
$429$	−0.142511	−	0.0822786i	−0.00688048	−	0.00397245i
$430$		0			0
$431$	−33.3303	−	19.2433i	−1.60546	−	0.926915i	−0.990368	−	0.138462i	$-0.955784\pi$
$431$	−33.3303	−	19.2433i	−1.60546	−	0.926915i	−0.615096	−	0.788452i	$-0.710883\pi$
$432$		0			0
$433$	−23.4070			−1.12487			−0.562435	−	0.826842i	$-0.690135\pi$
$433$	−23.4070			−1.12487			−0.562435	+	0.826842i	$0.690135\pi$
$434$		0			0
$435$	3.37300	−	1.94740i	0.161723	−	0.0933708i
$436$		0			0
$437$	−12.1853	+	21.1056i	−0.582902	+	1.00962i
$438$		0			0
$439$	0.366674	+	0.211699i	0.0175004	+	0.0101038i	0.508725	−	0.860929i	$-0.330117\pi$
$439$	0.366674	+	0.211699i	0.0175004	+	0.0101038i	−0.491224	+	0.871033i	$0.663450\pi$
$440$		0			0
$441$	17.2433			0.821109
$442$		0			0
$443$	−17.4892	−	30.2922i	−0.830938	−	1.43923i	−0.897295	−	0.441431i	$-0.854471\pi$
$443$	−17.4892	−	30.2922i	−0.830938	−	1.43923i	0.0663577	−	0.997796i	$-0.478862\pi$
$444$		0			0
$445$	−0.324333	−	0.561761i	−0.0153749	−	0.0266300i
$446$		0			0
$447$			4.21074i			0.199161i
$448$		0			0
$449$	−31.4024	−	18.1302i	−1.48197	−	0.855615i	−0.482178	−	0.876073i	$-0.660154\pi$
$449$	−31.4024	−	18.1302i	−1.48197	−	0.855615i	−0.999791	+	0.0204579i	$0.993488\pi$
$450$		0			0
$451$	19.3409	+	33.4994i	0.910727	+	1.57743i
$452$		0			0
$453$			4.85462i			0.228090i
$454$		0			0
$455$	−0.203477	−	0.352432i	−0.00953915	−	0.0165223i
$456$		0			0
$457$	−18.9743			−0.887580			−0.443790	−	0.896131i	$-0.646366\pi$
$457$	−18.9743			−0.887580			−0.443790	+	0.896131i	$0.646366\pi$
$458$		0			0
$459$		−	3.51617i		−	0.164121i
$460$		0			0
$461$	5.40097	+	3.11825i	0.251548	+	0.145232i	0.620473	−	0.784228i	$-0.286941\pi$
$461$	5.40097	+	3.11825i	0.251548	+	0.145232i	−0.368925	+	0.929459i	$0.620274\pi$
$462$		0			0
$463$	−10.3933	−	18.0018i	−0.483019	−	0.836614i	0.516790	−	0.856112i	$-0.327127\pi$
$463$	−10.3933	−	18.0018i	−0.483019	−	0.836614i	−0.999810	+	0.0194977i	$0.993793\pi$
$464$		0			0
$465$	−5.99108	+	3.45895i	−0.277830	+	0.160405i
$466$		0			0
$467$	13.5119	−	7.80111i	0.625257	−	0.360992i	−0.153656	−	0.988124i	$-0.549105\pi$
$467$	13.5119	−	7.80111i	0.625257	−	0.360992i	0.778913	+	0.627132i	$0.215771\pi$
$468$		0			0
$469$	10.5469	−	6.08927i	0.487012	−	0.281177i
$470$		0			0
$471$	−0.957785	−	0.552977i	−0.0441324	−	0.0254798i
$472$		0			0
$473$		−	45.1238i		−	2.07479i
$474$		0			0
$475$			7.19763i			0.330250i
$476$		0			0
$477$	15.3495	+	8.86202i	0.702804	+	0.405764i
$478$		0			0
$479$	2.91564	−	1.68334i	0.133219	−	0.0769139i	−0.431909	−	0.901917i	$-0.642160\pi$
$479$	2.91564	−	1.68334i	0.133219	−	0.0769139i	0.565128	+	0.825003i	$0.308827\pi$
$480$		0			0
$481$	0.109684	−	0.0633260i	0.00500115	−	0.00288742i
$482$		0			0
$483$	−1.64213	+	0.948083i	−0.0747194	+	0.0431393i
$484$		0			0
$485$	11.3854	+	19.7201i	0.516983	+	0.895442i
$486$		0			0
$487$	16.1944	+	9.34985i	0.733839	+	0.423682i	0.819825	−	0.572614i	$-0.194071\pi$
$487$	16.1944	+	9.34985i	0.733839	+	0.423682i	−0.0859861	+	0.996296i	$0.527404\pi$
$488$		0			0
$489$		−	2.19371i		−	0.0992032i
$490$		0			0
$491$	27.0613			1.22126			0.610630	−	0.791916i	$-0.290916\pi$
$491$	27.0613			1.22126			0.610630	+	0.791916i	$0.290916\pi$
$492$		0			0
$493$	5.36394	+	9.29062i	0.241580	+	0.418429i
$494$		0			0
$495$		−	29.4963i		−	1.32576i
$496$		0			0
$497$	−2.05238	−	3.55483i	−0.0920618	−	0.159456i
$498$		0			0
$499$	−10.4927	−	6.05797i	−0.469718	−	0.271192i	0.246404	−	0.969167i	$-0.420751\pi$
$499$	−10.4927	−	6.05797i	−0.469718	−	0.271192i	−0.716122	+	0.697975i	$0.754084\pi$
$500$		0			0
$501$			0.0604200i			0.00269937i
$502$		0			0
$503$	2.65090	+	4.59149i	0.118198	+	0.204724i	0.919053	−	0.394133i	$-0.128955\pi$
$503$	2.65090	+	4.59149i	0.118198	+	0.204724i	−0.800856	+	0.598857i	$0.795622\pi$
$504$		0			0
$505$	−9.96924	−	17.2672i	−0.443625	−	0.768382i
$506$		0			0
$507$	3.72319			0.165353
$508$		0			0
$509$	33.8558	+	19.5466i	1.50063	+	0.866390i	1.00000		0.000729200i	$0.000232111\pi$
$509$	33.8558	+	19.5466i	1.50063	+	0.866390i	0.500631	+	0.865661i	$0.333101\pi$
$510$		0			0
$511$	8.39458	−	14.5398i	0.371354	−	0.643205i
$512$		0			0
$513$	5.66016	−	3.26790i	0.249902	−	0.144281i
$514$		0			0
$515$	−22.9831			−1.01276
$516$		0			0
$517$	−9.14094	−	5.27753i	−0.402018	−	0.232105i
$518$		0			0
$519$	−2.05156	−	1.18447i	−0.0900536	−	0.0519925i
$520$		0			0
$521$	13.2815	−	7.66809i	0.581874	−	0.335945i	−0.180004	−	0.983666i	$-0.557611\pi$
$521$	13.2815	−	7.66809i	0.581874	−	0.335945i	0.761878	+	0.647721i	$0.224278\pi$
$522$		0			0
$523$	−18.6932	−	10.7925i	−0.817397	−	0.471924i	0.0321209	−	0.999484i	$-0.489774\pi$
$523$	−18.6932	−	10.7925i	−0.817397	−	0.471924i	−0.849518	+	0.527560i	$0.823107\pi$
$524$		0			0
$525$	−0.280007	+	0.484987i	−0.0122205	+	0.0211666i
$526$		0			0
$527$	−9.52737	−	16.5019i	−0.415019	−	0.718834i
$528$		0			0
$529$	8.53705	−	14.7866i	0.371176	−	0.642896i
$530$		0			0
$531$	30.9630			1.34368
$532$		0			0
$533$	1.29158	+	0.745695i	0.0559446	+	0.0322996i
$534$		0			0
$535$	40.5061			1.75123
$536$		0			0
$537$	4.24837	+	2.45280i	0.183331	+	0.105846i
$538$		0			0
$539$		−	22.7951i		−	0.981853i
$540$		0			0
$541$	−0.189401			−0.00814298			−0.00407149	−	0.999992i	$-0.501296\pi$
$541$	−0.189401			−0.00814298			−0.00407149	+	0.999992i	$0.501296\pi$
$542$		0			0
$543$	3.03292			0.130155
$544$		0			0
$545$			23.9560i			1.02616i
$546$		0			0
$547$	1.13519	−	0.655400i	0.0485371	−	0.0280229i	−0.475535	−	0.879697i	$-0.657746\pi$
$547$	1.13519	−	0.655400i	0.0485371	−	0.0280229i	0.524072	+	0.851674i	$0.324412\pi$
$548$		0			0
$549$	−16.1695	+	9.33546i	−0.690097	+	0.398428i
$550$		0			0
$551$	−9.97040	+	17.2692i	−0.424753	+	0.735694i
$552$		0			0
$553$	9.19038	+	1.28641i	0.390815	+	0.0547037i
$554$		0			0
$555$	−0.554594	−	0.320195i	−0.0235412	−	0.0135915i
$556$		0			0
$557$	−20.5233	−	35.5473i	−0.869598	−	1.50619i	−0.862408	−	0.506214i	$-0.831045\pi$
$557$	−20.5233	−	35.5473i	−0.869598	−	1.50619i	−0.00719035	−	0.999974i	$-0.502289\pi$
$558$		0			0
$559$	−0.869882	−	1.50668i	−0.0367921	−	0.0637258i
$560$		0			0
$561$	−2.29181			−0.0967601
$562$		0			0
$563$		−	32.9162i		−	1.38725i	−0.720335	−	0.693627i	$-0.756012\pi$
$563$		−	32.9162i		−	1.38725i	0.720335	−	0.693627i	$-0.243988\pi$
$564$		0			0
$565$		−	30.9912i		−	1.30381i
$566$		0			0
$567$	−8.63039			−0.362442
$568$		0			0
$569$	−3.39794	+	5.88540i	−0.142449	+	0.246729i	−0.928418	−	0.371537i	$-0.878831\pi$
$569$	−3.39794	+	5.88540i	−0.142449	+	0.246729i	0.785969	+	0.618266i	$0.212164\pi$
$570$		0			0
$571$		−	8.46019i		−	0.354048i	−0.984207	−	0.177024i	$-0.943353\pi$
$571$		−	8.46019i		−	0.354048i	0.984207	−	0.177024i	$-0.0566470\pi$
$572$		0			0
$573$	0.744369	−	1.28929i	0.0310965	−	0.0538607i
$574$		0			0
$575$		−	11.8355i		−	0.493575i
$576$		0			0
$577$	−3.23698	−	1.86887i	−0.134757	−	0.0778020i	0.431106	−	0.902301i	$-0.358124\pi$
$577$	−3.23698	−	1.86887i	−0.134757	−	0.0778020i	−0.565863	+	0.824499i	$0.691457\pi$
$578$		0			0
$579$	0.851426	−	0.491571i	0.0353841	−	0.0204290i
$580$		0			0
$581$	5.28052	+	3.04871i	0.219073	+	0.126482i
$582$		0			0
$583$	11.7153	−	20.2915i	0.485198	−	0.840387i
$584$		0			0
$585$	−0.568620	−	0.984878i	−0.0235095	−	0.0407197i
$586$		0			0
$587$	−10.7362	+	18.5956i	−0.443130	+	0.767524i	−0.997920	−	0.0644666i	$-0.979465\pi$
$587$	−10.7362	+	18.5956i	−0.443130	+	0.767524i	0.554790	+	0.831991i	$0.312799\pi$
$588$		0			0
$589$	17.7093	−	30.6734i	0.729699	−	1.26388i
$590$		0			0
$591$		−	2.92807i		−	0.120445i
$592$		0			0
$593$	16.6239	+	28.7935i	0.682664	+	1.18241i	0.974165	+	0.225838i	$0.0725119\pi$
$593$	16.6239	+	28.7935i	0.682664	+	1.18241i	−0.291501	+	0.956570i	$0.594155\pi$
$594$		0			0
$595$	−4.90836	−	2.83384i	−0.201223	−	0.116176i
$596$		0			0
$597$	0.393245	−	0.681120i	0.0160944	−	0.0278764i
$598$		0			0
$599$			20.2184i			0.826103i	0.910708	+	0.413051i	$0.135537\pi$
$599$			20.2184i			0.826103i	−0.910708	+	0.413051i	$0.864463\pi$
$600$		0			0
$601$	−38.1708	+	22.0379i	−1.55702	+	0.898946i	−0.559479	+	0.828844i	$0.688999\pi$
$601$	−38.1708	+	22.0379i	−1.55702	+	0.898946i	−0.997540	+	0.0701013i	$0.977668\pi$
$602$		0			0
$603$	29.4736	−	17.0166i	1.20026	−	0.692969i
$604$		0			0
$605$	−10.1621			−0.413149
$606$		0			0
$607$	−14.7616	+	25.5679i	−0.599156	+	1.03777i	0.393789	+	0.919201i	$0.371164\pi$
$607$	−14.7616	+	25.5679i	−0.599156	+	1.03777i	−0.992946	+	0.118569i	$0.962169\pi$
$608$		0			0
$609$	−1.34364	+	0.775751i	−0.0544470	+	0.0314350i
$610$		0			0
$611$	−0.406954			−0.0164636
$612$		0			0
$613$	−24.3742	+	14.0725i	−0.984466	+	0.568382i	−0.903616	−	0.428344i	$-0.859097\pi$
$613$	−24.3742	+	14.0725i	−0.984466	+	0.568382i	−0.0808509	+	0.996726i	$0.525764\pi$
$614$		0			0
$615$		−	7.54090i		−	0.304079i
$616$		0			0
$617$	44.1730			1.77834			0.889170	−	0.457577i	$-0.151283\pi$
$617$	44.1730			1.77834			0.889170	+	0.457577i	$0.151283\pi$
$618$		0			0
$619$	21.8865	−	37.9085i	0.879691	−	1.52367i	0.0280118	−	0.999608i	$-0.491082\pi$
$619$	21.8865	−	37.9085i	0.879691	−	1.52367i	0.851680	−	0.524063i	$-0.175584\pi$
$620$		0			0
$621$	−9.30735	+	5.37360i	−0.373491	+	0.215635i
$622$		0			0
$623$	0.129199	+	0.223779i	0.00517623	+	0.00896550i
$624$		0			0
$625$	15.4263	+	26.7192i	0.617053	+	1.06877i
$626$		0			0
$627$	−2.12998	−	3.68924i	−0.0850633	−	0.147334i
$628$		0			0
$629$	0.881948	−	1.52758i	0.0351656	−	0.0609085i
$630$		0			0
$631$	16.4255			0.653888			0.326944	−	0.945044i	$-0.393981\pi$
$631$	16.4255			0.653888			0.326944	+	0.945044i	$0.393981\pi$
$632$		0			0
$633$	2.63318			0.104659
$634$		0			0
$635$	21.3082	−	36.9068i	0.845589	−	1.46460i
$636$		0			0
$637$	−0.439436	−	0.761125i	−0.0174111	−	0.0301569i
$638$		0			0
$639$	−5.73541	−	9.93402i	−0.226889	−	0.392984i
$640$		0			0
$641$	16.2264	+	28.1050i	0.640906	+	1.11008i	0.985231	+	0.171231i	$0.0547744\pi$
$641$	16.2264	+	28.1050i	0.640906	+	1.11008i	−0.344325	+	0.938850i	$0.611892\pi$
$642$		0			0
$643$	−9.96359	+	5.75248i	−0.392925	+	0.226856i	−0.683427	−	0.730019i	$-0.739511\pi$
$643$	−9.96359	+	5.75248i	−0.392925	+	0.226856i	0.290501	+	0.956875i	$0.406178\pi$
$644$		0			0
$645$	−4.39838	+	7.61821i	−0.173186	+	0.299967i
$646$		0			0
$647$	4.26667			0.167740			0.0838701	−	0.996477i	$-0.473272\pi$
$647$	4.26667			0.167740			0.0838701	+	0.996477i	$0.473272\pi$
$648$		0			0
$649$		−	40.9321i		−	1.60673i
$650$		0			0
$651$	2.38656	−	1.37788i	0.0935366	−	0.0540034i
$652$		0			0
$653$	−14.8468			−0.581000			−0.290500	−	0.956875i	$-0.593822\pi$
$653$	−14.8468			−0.581000			−0.290500	+	0.956875i	$0.593822\pi$
$654$		0			0
$655$	31.4498	−	18.1575i	1.22884	−	0.709474i
$656$		0			0
$657$	23.4588	−	40.6318i	0.915215	−	1.58520i
$658$		0			0
$659$	−35.6690			−1.38947			−0.694734	−	0.719267i	$-0.744478\pi$
$659$	−35.6690			−1.38947			−0.694734	+	0.719267i	$0.744478\pi$
$660$		0			0
$661$	−16.7966	+	9.69753i	−0.653312	+	0.377190i	−0.789724	−	0.613462i	$-0.789776\pi$
$661$	−16.7966	+	9.69753i	−0.653312	+	0.377190i	0.136412	+	0.990652i	$0.456443\pi$
$662$		0			0
$663$	−0.0765232	+	0.0441807i	−0.00297192	+	0.00171584i
$664$		0			0
$665$		−	10.5350i		−	0.408530i
$666$		0			0
$667$	16.3949	−	28.3969i	0.634815	−	1.09953i
$668$		0			0
$669$	−1.12920	−	0.651943i	−0.0436574	−	0.0252056i
$670$		0			0
$671$	12.3412	+	21.3755i	0.476426	+	0.825194i
$672$		0			0
$673$			2.61221i			0.100693i	0.998732	+	0.0503467i	$0.0160326\pi$
$673$			2.61221i			0.100693i	−0.998732	+	0.0503467i	$0.983967\pi$
$674$		0			0
$675$	−1.58704	+	2.74884i	−0.0610853	+	0.105803i
$676$		0			0
$677$	3.08332	−	5.34046i	0.118502	−	0.205251i	−0.800673	−	0.599102i	$-0.795524\pi$
$677$	3.08332	−	5.34046i	0.118502	−	0.205251i	0.919174	+	0.393852i	$0.128858\pi$
$678$		0			0
$679$	−4.53539	−	7.85552i	−0.174052	−	0.301467i
$680$		0			0
$681$	−1.28758	+	2.23015i	−0.0493401	+	0.0854596i
$682$		0			0
$683$	−33.8278	−	19.5305i	−1.29439	−	0.747314i	−0.314957	−	0.949106i	$-0.601990\pi$
$683$	−33.8278	−	19.5305i	−1.29439	−	0.747314i	−0.979428	+	0.201792i	$0.935323\pi$
$684$		0			0
$685$	−0.305212	+	0.176214i	−0.0116616	+	0.00673280i
$686$		0			0
$687$	3.09027	+	1.78417i	0.117901	+	0.0680703i
$688$		0			0
$689$		−	0.903375i		−	0.0344158i
$690$		0			0
$691$	−18.3895	+	31.8516i	−0.699571	+	1.21169i	0.269044	+	0.963128i	$0.413292\pi$
$691$	−18.3895	+	31.8516i	−0.699571	+	1.21169i	−0.968615	+	0.248565i	$0.920041\pi$
$692$		0			0
$693$			11.7499i			0.446341i
$694$		0			0
$695$	13.6290	−	23.6061i	0.516978	−	0.895432i
$696$		0			0
$697$	20.7707			0.786748
$698$		0			0
$699$			4.55189i			0.172168i
$700$		0			0
$701$		−	8.47104i		−	0.319947i	−0.987121	−	0.159973i	$-0.948859\pi$
$701$		−	8.47104i		−	0.319947i	0.987121	−	0.159973i	$-0.0511409\pi$
$702$		0			0
$703$	3.27870			0.123658
$704$		0			0
$705$	1.02884	+	1.78200i	0.0387483	+	0.0671141i
$706$		0			0
$707$	3.97126	+	6.87843i	0.149355	+	0.258690i
$708$		0			0
$709$	25.1034	+	14.4935i	0.942778	+	0.544313i	0.890830	−	0.454337i	$-0.150124\pi$
$709$	25.1034	+	14.4935i	0.942778	+	0.544313i	0.0519481	+	0.998650i	$0.483457\pi$
$710$		0			0
$711$	25.6827	+	3.59489i	0.963175	+	0.134819i
$712$		0			0
$713$	−29.1205	+	50.4382i	−1.09057	+	1.88893i
$714$		0			0
$715$	−1.30198	+	0.751697i	−0.0486912	+	0.0281119i
$716$		0			0
$717$	−3.83300	+	2.21298i	−0.143146	+	0.0826454i
$718$		0			0
$719$		−	41.5467i		−	1.54943i	−0.632311	−	0.774714i	$-0.717894\pi$
$719$		−	41.5467i		−	1.54943i	0.632311	−	0.774714i	$-0.282106\pi$
$720$		0			0
$721$	9.15537			0.340964
$722$		0			0
$723$	−3.57705			−0.133032
$724$		0			0
$725$		−	9.68419i		−	0.359662i
$726$		0			0
$727$	14.3262	+	8.27126i	0.531331	+	0.306764i	0.741558	−	0.670889i	$-0.234087\pi$
$727$	14.3262	+	8.27126i	0.531331	+	0.306764i	−0.210227	+	0.977653i	$0.567420\pi$
$728$		0			0
$729$	−22.6566			−0.839134
$730$		0			0
$731$	−20.9837	−	12.1149i	−0.776109	−	0.448087i
$732$		0			0
$733$	18.8192			0.695105			0.347552	−	0.937661i	$-0.387013\pi$
$733$	18.8192			0.695105			0.347552	+	0.937661i	$0.387013\pi$
$734$		0			0
$735$	−2.22192	+	3.84847i	−0.0819566	+	0.141953i
$736$		0			0
$737$	−22.4954	−	38.9631i	−0.828627	−	1.43522i
$738$		0			0
$739$	−3.37826	+	5.85131i	−0.124271	+	0.215244i	−0.921448	−	0.388502i	$-0.872993\pi$
$739$	−3.37826	+	5.85131i	−0.124271	+	0.215244i	0.797177	+	0.603746i	$0.206326\pi$
$740$		0			0
$741$	−0.142240	−	0.0821223i	−0.00522532	−	0.00301684i
$742$		0			0
$743$	34.9054	−	20.1527i	1.28056	−	0.739329i	0.303606	−	0.952798i	$-0.401809\pi$
$743$	34.9054	−	20.1527i	1.28056	−	0.739329i	0.976950	+	0.213468i	$0.0684761\pi$
$744$		0			0
$745$	33.3154	+	19.2347i	1.22058	+	0.704703i
$746$		0			0
$747$	14.7565	+	8.51967i	0.539912	+	0.311719i
$748$		0			0
$749$	−16.1357			−0.589585
$750$		0			0
$751$	−6.89270	+	3.97950i	−0.251518	+	0.145214i	−0.620459	−	0.784239i	$-0.713054\pi$
$751$	−6.89270	+	3.97950i	−0.251518	+	0.145214i	0.368941	+	0.929453i	$0.379720\pi$
$752$		0			0
$753$	1.75302	−	3.03632i	0.0638835	−	0.110650i
$754$		0			0
$755$	38.4098	+	22.1759i	1.39787	+	0.807063i
$756$		0			0
$757$	−16.1997			−0.588787			−0.294393	−	0.955684i	$-0.595118\pi$
$757$	−16.1997			−0.588787			−0.294393	+	0.955684i	$0.595118\pi$
$758$		0			0
$759$	3.50246	+	6.06644i	0.127131	+	0.220198i
$760$		0			0
$761$	−9.40363	−	16.2876i	−0.340881	−	0.590424i	0.643715	−	0.765265i	$-0.277392\pi$
$761$	−9.40363	−	16.2876i	−0.340881	−	0.590424i	−0.984597	+	0.174841i	$0.944059\pi$
$762$		0			0
$763$		−	9.54290i		−	0.345476i
$764$		0			0
$765$	−13.7165	−	7.91923i	−0.495921	−	0.286320i
$766$		0			0
$767$	−0.789076	−	1.36672i	−0.0284919	−	0.0493494i
$768$		0			0
$769$			42.4637i			1.53128i	0.643269	+	0.765640i	$0.277578\pi$
$769$			42.4637i			1.53128i	−0.643269	+	0.765640i	$0.722422\pi$
$770$		0			0
$771$	3.98105	+	6.89538i	0.143374	+	0.248331i
$772$		0			0
$773$	−27.1939			−0.978098			−0.489049	−	0.872256i	$-0.662656\pi$
$773$	−27.1939			−0.978098			−0.489049	+	0.872256i	$0.662656\pi$
$774$		0			0
$775$			17.2009i			0.617876i
$776$		0			0
$777$	0.220923	+	0.127550i	0.00792558	+	0.00457584i
$778$		0			0
$779$	19.3041	+	33.4357i	0.691642	+	1.19796i
$780$		0			0
$781$	−13.1324	+	7.58202i	−0.469916	+	0.271306i
$782$		0			0
$783$	−7.61557	+	4.39685i	−0.272158	+	0.157131i
$784$		0			0
$785$	−8.75031	+	5.05199i	−0.312312	+	0.180313i
$786$		0			0
$787$	42.2502	+	24.3932i	1.50606	+	0.869522i	0.999975	+	0.00703669i	$0.00223987\pi$
$787$	42.2502	+	24.3932i	1.50606	+	0.869522i	0.506082	+	0.862486i	$0.331093\pi$
$788$		0			0
$789$			8.64383i			0.307729i
$790$		0			0
$791$			12.3454i			0.438952i
$792$		0			0
$793$	0.824142	+	0.475818i	0.0292661	+	0.0168968i
$794$		0			0
$795$	−3.95577	+	2.28386i	−0.140297	+	0.0810003i
$796$		0			0
$797$	14.4351	−	8.33409i	0.511317	−	0.295209i	−0.222058	−	0.975033i	$-0.571277\pi$
$797$	14.4351	−	8.33409i	0.511317	−	0.295209i	0.733375	+	0.679825i	$0.237944\pi$
$798$		0			0
$799$	−4.90836	+	2.83384i	−0.173645	+	0.100254i
$800$		0			0
$801$	0.361048	+	0.625353i	0.0127570	+	0.0220958i
$802$		0			0
$803$	−53.7139	−	31.0118i	−1.89552	−	1.09438i
$804$		0			0
$805$			17.3233i			0.610568i
$806$		0			0
$807$	−1.49554			−0.0526455
$808$		0			0
$809$	0.0642072	+	0.111210i	0.00225741	+	0.00390994i	0.867152	−	0.498044i	$-0.165948\pi$
$809$	0.0642072	+	0.111210i	0.00225741	+	0.00390994i	−0.864894	+	0.501954i	$0.832615\pi$
$810$		0			0
$811$			4.32647i			0.151923i	0.997111	+	0.0759614i	$0.0242026\pi$
$811$			4.32647i			0.151923i	−0.997111	+	0.0759614i	$0.975797\pi$
$812$		0			0
$813$	−1.77857	−	3.08058i	−0.0623773	−	0.108041i
$814$		0			0
$815$	−17.3567	−	10.0209i	−0.607978	−	0.351016i
$816$		0			0
$817$		−	45.0380i		−	1.57568i
$818$		0			0
$819$	0.226511	+	0.392328i	0.00791492	+	0.0137091i
$820$		0			0
$821$	10.2204	+	17.7022i	0.356693	+	0.617810i	0.987406	−	0.158206i	$-0.0505709\pi$
$821$	10.2204	+	17.7022i	0.356693	+	0.617810i	−0.630713	+	0.776016i	$0.717238\pi$
$822$		0			0
$823$	10.2987			0.358991			0.179495	−	0.983759i	$-0.442553\pi$
$823$	10.2987			0.358991			0.179495	+	0.983759i	$0.442553\pi$
$824$		0			0
$825$	1.79167	+	1.03442i	0.0623778	+	0.0360139i
$826$		0			0
$827$	11.9104	−	20.6294i	0.414166	−	0.717356i	−0.581175	−	0.813779i	$-0.697407\pi$
$827$	11.9104	−	20.6294i	0.414166	−	0.717356i	0.995340	+	0.0964228i	$0.0307401\pi$
$828$		0			0
$829$	39.8812	−	23.0254i	1.38513	−	0.799707i	0.392371	−	0.919807i	$-0.371655\pi$
$829$	39.8812	−	23.0254i	1.38513	−	0.799707i	0.992762	+	0.120100i	$0.0383216\pi$
$830$		0			0
$831$	2.22437			0.0771626
$832$		0			0
$833$	−10.6003	−	6.12007i	−0.367278	−	0.212048i
$834$		0			0
$835$	0.478043	+	0.275998i	0.0165434	+	0.00955132i
$836$		0			0
$837$	13.5267	−	7.80963i	0.467551	−	0.269940i
$838$		0			0
$839$	37.7797	+	21.8121i	1.30430	+	0.753037i	0.981138	−	0.193307i	$-0.0619212\pi$
$839$	37.7797	+	21.8121i	1.30430	+	0.753037i	0.323161	+	0.946344i	$0.395255\pi$
$840$		0			0
$841$	−1.08515	+	1.87953i	−0.0374189	+	0.0648114i
$842$		0			0
$843$	−2.31258	−	4.00550i	−0.0796495	−	0.137957i
$844$		0			0
$845$	17.0075	−	29.4579i	0.585076	−	1.01338i
$846$		0			0
$847$	4.04810			0.139094
$848$		0			0
$849$	0.312487	+	0.180414i	0.0107245	+	0.00619180i
$850$		0			0
$851$	−5.39136			−0.184814
$852$		0			0
$853$	39.9886	+	23.0874i	1.36918	+	0.790498i	0.990824	−	0.135161i	$-0.0431550\pi$
$853$	39.9886	+	23.0874i	1.36918	+	0.790498i	0.378359	+	0.925659i	$0.376488\pi$
$854$		0			0
$855$		−	29.4402i		−	1.00683i
$856$		0			0
$857$	5.19449			0.177440			0.0887202	−	0.996057i	$-0.471722\pi$
$857$	5.19449			0.177440			0.0887202	+	0.996057i	$0.471722\pi$
$858$		0			0
$859$	−32.9763			−1.12514			−0.562569	−	0.826751i	$-0.690187\pi$
$859$	−32.9763			−1.12514			−0.562569	+	0.826751i	$0.690187\pi$
$860$		0			0
$861$			3.00393i			0.102374i
$862$		0			0
$863$	−9.78297	+	5.64820i	−0.333016	+	0.192267i	−0.657179	−	0.753734i	$-0.728251\pi$
$863$	−9.78297	+	5.64820i	−0.333016	+	0.192267i	0.324163	+	0.946001i	$0.394917\pi$
$864$		0			0
$865$	−18.7431	+	10.8213i	−0.637283	+	0.367935i
$866$		0			0
$867$	1.82323	−	3.15793i	0.0619202	−	0.107249i
$868$		0			0
$869$	4.75233	−	33.9516i	0.161212	−	1.15173i
$870$		0			0
$871$	−1.50224	−	0.867317i	−0.0509013	−	0.0293879i
$872$		0			0
$873$	−12.6742	−	21.9524i	−0.428957	−	0.742975i
$874$		0			0
$875$	−4.28318	−	7.41868i	−0.144798	−	0.250797i
$876$		0			0
$877$	−25.9467			−0.876156			−0.438078	−	0.898937i	$-0.644341\pi$
$877$	−25.9467			−0.876156			−0.438078	+	0.898937i	$0.644341\pi$
$878$		0			0
$879$		−	4.40112i		−	0.148446i
$880$		0			0
$881$			23.6966i			0.798360i	0.916873	+	0.399180i	$0.130705\pi$
$881$			23.6966i			0.798360i	−0.916873	+	0.399180i	$0.869295\pi$
$882$		0			0
$883$	−0.635140			−0.0213742			−0.0106871	−	0.999943i	$-0.503402\pi$
$883$	−0.635140			−0.0213742			−0.0106871	+	0.999943i	$0.503402\pi$
$884$		0			0
$885$	−3.98980	+	6.91054i	−0.134116	+	0.232295i
$886$		0			0
$887$			53.7876i			1.80601i	0.429630	+	0.903005i	$0.358644\pi$
$887$			53.7876i			1.80601i	−0.429630	+	0.903005i	$0.641356\pi$
$888$		0			0
$889$	−8.48814	+	14.7019i	−0.284683	+	0.493086i
$890$		0			0
$891$			31.8829i			1.06812i
$892$		0			0
$893$	−9.12358	−	5.26750i	−0.305309	−	0.176270i
$894$		0			0
$895$	38.8130	−	22.4087i	1.29738	−	0.749041i
$896$		0			0
$897$	0.233894	+	0.135039i	0.00780949	+	0.00450881i
$898$		0			0
$899$	−23.8273	+	41.2701i	−0.794685	+	1.37644i
$900$		0			0
$901$	−6.29070	−	10.8958i	−0.209574	−	0.362992i
$902$		0			0
$903$	1.75210	−	3.03473i	0.0583063	−	0.100989i
$904$		0			0
$905$	13.8543	−	23.9964i	0.460534	−	0.797668i
$906$		0			0
$907$		−	16.0116i		−	0.531657i	−0.964020	−	0.265828i	$-0.914355\pi$
$907$		−	16.0116i		−	0.531657i	0.964020	−	0.265828i	$-0.0856455\pi$
$908$		0			0
$909$	11.0978	+	19.2219i	0.368090	+	0.637550i
$910$		0			0
$911$	−10.0598	−	5.80801i	−0.333295	−	0.192428i	0.324008	−	0.946054i	$-0.394970\pi$
$911$	−10.0598	−	5.80801i	−0.333295	−	0.192428i	−0.657303	+	0.753626i	$0.728303\pi$
$912$		0			0
$913$	11.2627	−	19.5076i	0.372742	−	0.645608i
$914$		0			0
$915$		−	4.81176i		−	0.159072i
$916$		0			0
$917$	−12.5281	+	7.23309i	−0.413713	+	0.238858i
$918$		0			0
$919$	12.5658	−	7.25486i	0.414507	−	0.239316i	−0.278217	−	0.960518i	$-0.589744\pi$
$919$	12.5658	−	7.25486i	0.414507	−	0.239316i	0.692725	+	0.721202i	$0.256410\pi$
$920$		0			0
$921$	5.95683			0.196284
$922$		0			0
$923$	−0.292328	+	0.506326i	−0.00962208	+	0.0166659i
$924$		0			0
$925$	−1.37896	+	0.796145i	−0.0453400	+	0.0261771i
$926$		0			0
$927$	25.5848			0.840316
$928$		0			0
$929$	−14.2264	+	8.21361i	−0.466753	+	0.269480i	−0.714879	−	0.699248i	$-0.753518\pi$
$929$	−14.2264	+	8.21361i	−0.466753	+	0.269480i	0.248127	+	0.968728i	$0.420185\pi$
$930$		0			0
$931$		−	22.7517i		−	0.745658i
$932$		0			0
$933$	7.86559			0.257508
$934$		0			0
$935$	−10.4690	+	18.1328i	−0.342371	+	0.593005i
$936$		0			0
$937$	19.8188	−	11.4424i	0.647451	−	0.373806i	−0.140028	−	0.990148i	$-0.544719\pi$
$937$	19.8188	−	11.4424i	0.647451	−	0.373806i	0.787479	+	0.616341i	$0.211386\pi$
$938$		0			0
$939$	1.54541	+	2.67672i	0.0504324	+	0.0873515i
$940$		0			0
$941$	−13.3415	−	23.1081i	−0.434920	−	0.753304i	0.562369	−	0.826886i	$-0.309890\pi$
$941$	−13.3415	−	23.1081i	−0.434920	−	0.753304i	−0.997289	+	0.0735825i	$0.976557\pi$
$942$		0			0
$943$	−31.7430	−	54.9805i	−1.03369	−	1.79041i
$944$		0			0
$945$	2.32292	−	4.02341i	0.0755645	−	0.130882i
$946$		0			0
$947$	−38.5018			−1.25114			−0.625570	−	0.780168i	$-0.715133\pi$
$947$	−38.5018			−1.25114			−0.625570	+	0.780168i	$0.715133\pi$
$948$		0			0
$949$	−2.39134			−0.0776262
$950$		0			0
$951$	−0.697415	+	1.20796i	−0.0226152	+	0.0391707i
$952$		0			0
$953$	21.6779	+	37.5473i	0.702217	+	1.21628i	0.967686	+	0.252157i	$0.0811398\pi$
$953$	21.6779	+	37.5473i	0.702217	+	1.21628i	−0.265469	+	0.964119i	$0.585527\pi$
$954$		0			0
$955$	−6.80055	−	11.7789i	−0.220061	−	0.381156i
$956$		0			0
$957$	2.86582	+	4.96375i	0.0926389	+	0.160455i
$958$		0			0
$959$	0.121582	−	0.0701952i	0.00392608	−	0.00226672i
$960$		0			0
$961$	26.8218	−	46.4567i	0.865219	−	1.49860i
$962$		0			0
$963$	−45.0914			−1.45305
$964$		0			0
$965$		−	8.98198i		−	0.289140i
$966$		0			0
$967$	29.7752	−	17.1907i	0.957507	−	0.552817i	0.0621023	−	0.998070i	$-0.480219\pi$
$967$	29.7752	−	17.1907i	0.957507	−	0.552817i	0.895405	+	0.445253i	$0.146886\pi$
$968$		0			0
$969$	−2.28745			−0.0734835
$970$		0			0
$971$	−26.7681	+	15.4546i	−0.859029	+	0.495961i	−0.863687	−	0.504029i	$-0.831851\pi$
$971$	−26.7681	+	15.4546i	−0.859029	+	0.495961i	0.00465805	+	0.999989i	$0.498517\pi$
$972$		0			0
$973$	−5.42914	+	9.40354i	−0.174050	+	0.301464i
$974$		0			0
$975$	0.0797649			0.00255452
$976$		0			0
$977$	−28.3148	+	16.3475i	−0.905870	+	0.523004i	−0.879100	−	0.476637i	$-0.841856\pi$
$977$	−28.3148	+	16.3475i	−0.905870	+	0.523004i	−0.0267700	+	0.999642i	$0.508522\pi$
$978$		0			0
$979$	0.826696	−	0.477293i	0.0264213	−	0.0152544i
$980$		0			0
$981$		−	26.6678i		−	0.851437i
$982$		0			0
$983$	−0.0359291	+	0.0622311i	−0.00114596	+	0.00198486i	−0.866598	−	0.499007i	$-0.833698\pi$
$983$	−0.0359291	+	0.0622311i	−0.00114596	+	0.00198486i	0.865452	+	0.500992i	$0.167031\pi$
$984$		0			0
$985$	−23.1669	−	13.3754i	−0.738159	−	0.426176i
$986$		0			0
$987$	−0.409840	−	0.709864i	−0.0130453	−	0.0225952i
$988$		0			0
$989$			74.0588i			2.35493i
$990$		0			0
$991$	−27.6008	+	47.8059i	−0.876767	+	1.51860i	−0.0218982	+	0.999760i	$0.506971\pi$
$991$	−27.6008	+	47.8059i	−0.876767	+	1.51860i	−0.854869	+	0.518844i	$0.826362\pi$
$992$		0			0
$993$	−2.21357	+	3.83402i	−0.0702456	+	0.121669i
$994$		0			0
$995$	−3.59268	−	6.22271i	−0.113896	−	0.197273i
$996$		0			0
$997$	−17.9425	+	31.0774i	−0.568245	+	0.984230i	0.428494	+	0.903545i	$0.359044\pi$
$997$	−17.9425	+	31.0774i	−0.568245	+	0.984230i	−0.996740	+	0.0806854i	$0.974289\pi$
$998$		0			0
$999$	1.25216	+	0.722937i	0.0396167	+	0.0228727i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1264.2.n.i.735.8	yes	28
4.3	odd	2	inner	1264.2.n.i.735.7	✓	28
79.56	odd	6	inner	1264.2.n.i.767.7	yes	28
316.135	even	6	inner	1264.2.n.i.767.8	yes	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1264.2.n.i.735.7	✓	28	4.3	odd	2	inner
1264.2.n.i.735.8	yes	28	1.1	even	1	trivial
1264.2.n.i.767.7	yes	28	79.56	odd	6	inner
1264.2.n.i.767.8	yes	28	316.135	even	6	inner

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:	\( N \)	\(=\)	\( 1264 = 2^{4} \cdot 79 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1264.n (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.143444 - 0.248452i) q^{3} +(-1.31050 - 2.26985i) q^{5} +(0.522039 + 0.904199i) q^{7} +(1.45885 + 2.52680i) q^{9} +O(q^{10})\)	\(q+(0.143444 - 0.248452i) q^{3} +(-1.31050 - 2.26985i) q^{5} +(0.522039 + 0.904199i) q^{7} +(1.45885 + 2.52680i) q^{9} +(3.34034 - 1.92855i) q^{11} +(0.0743559 - 0.128788i) q^{13} -0.751930 q^{15} -2.07112i q^{17} +(3.33400 - 1.92488i) q^{19} +0.299533 q^{21} +(-5.48230 + 3.16521i) q^{23} +(-0.934814 + 1.61915i) q^{25} +1.69771 q^{27} +(-4.48579 + 2.58987i) q^{29} +(7.96760 - 4.60010i) q^{31} -1.10655i q^{33} +(1.36826 - 2.36990i) q^{35} +(0.737560 + 0.425831i) q^{37} +(-0.0213317 - 0.0369477i) q^{39} +10.0287i q^{41} +(5.84945 - 10.1315i) q^{43} +(3.82364 - 6.62273i) q^{45} +(-1.36826 - 2.36990i) q^{47} +(2.95495 - 5.11812i) q^{49} +(-0.514574 - 0.297089i) q^{51} +(5.26082 - 3.03733i) q^{53} +(-8.75503 - 5.05472i) q^{55} -1.10445i q^{57} +(5.30608 - 9.19039i) q^{59} +6.39920i q^{61} +(-1.52315 + 2.63818i) q^{63} -0.389773 q^{65} -11.6644i q^{67} +1.81611i q^{69} -3.93147 q^{71} +(-8.04018 - 13.9260i) q^{73} +(0.268186 + 0.464512i) q^{75} +(3.48758 + 2.01356i) q^{77} +(5.46822 - 7.00704i) q^{79} +(-4.13302 + 7.15860i) q^{81} +(5.05759 - 2.92000i) q^{83} +(-4.70114 + 2.71421i) q^{85} +1.48600i q^{87} +0.247488 q^{89} +0.155267 q^{91} -2.63942i q^{93} +(-8.73840 - 5.04512i) q^{95} -8.68782 q^{97} +(9.74611 + 5.62692i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q - 20 q^{9}+O(q^{10}) \) 28 * q - 20 * q^9	\( 28 q - 20 q^{9} - 8 q^{13} + 32 q^{21} - 14 q^{25} + 30 q^{37} - 6 q^{45} - 12 q^{49} - 18 q^{53} - 48 q^{65} + 22 q^{73} - 66 q^{77} - 14 q^{81} + 60 q^{89} - 16 q^{97}+O(q^{100}) \) 28 * q - 20 * q^9 - 8 * q^13 + 32 * q^21 - 14 * q^25 + 30 * q^37 - 6 * q^45 - 12 * q^49 - 18 * q^53 - 48 * q^65 + 22 * q^73 - 66 * q^77 - 14 * q^81 + 60 * q^89 - 16 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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