LMFDB - Embedded newform 816.2.bq.f.49.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [816,2,Mod(49,816)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(816, base_ring=CyclotomicField(8))

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

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

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

chi := DirichletCharacter("816.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 816 = 2^{4} \cdot 3 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	816.bq (of order $8$, degree $4$, 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:	$6.51579280494$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{8})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 36x^{14} + 466x^{12} + 2956x^{10} + 10049x^{8} + 18032x^{6} + 14800x^{4} + 3200x^{2} + 64 $ x^16 + 36x^14 + 466x^12 + 2956x^10 + 10049x^8 + 18032x^6 + 14800x^4 + 3200*x^2 + 64
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 408)
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			49.3
Root			$-1.71472i$ of defining polynomial
Character	$\chi$	$=$	816.49
Dual form			816.2.bq.f.433.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.382683 + 0.923880i) q^{3} +(-2.50807 + 1.03888i) q^{5} +(-2.22010 - 0.919595i) q^{7} +(-0.707107 + 0.707107i) q^{9} +(1.87280 - 4.52134i) q^{11} -1.07051i q^{13} +(-1.91959 - 1.91959i) q^{15} +(3.25570 + 2.52991i) q^{17} +(-1.61272 - 1.61272i) q^{19} -2.40302i q^{21} +(2.41400 - 5.82790i) q^{23} +(1.67562 - 1.67562i) q^{25} +(-0.923880 - 0.382683i) q^{27} +(3.13555 - 1.29879i) q^{29} +(-2.67656 - 6.46178i) q^{31} +4.89386 q^{33} +6.52351 q^{35} +(-1.63047 - 3.93630i) q^{37} +(0.989020 - 0.409666i) q^{39} +(7.08028 + 2.93275i) q^{41} +(4.37197 - 4.37197i) q^{43} +(1.03888 - 2.50807i) q^{45} +8.19868i q^{47} +(-0.866566 - 0.866566i) q^{49} +(-1.09143 + 3.97603i) q^{51} +(-7.97888 - 7.97888i) q^{53} +13.2855i q^{55} +(0.872800 - 2.10713i) q^{57} +(8.89888 - 8.89888i) q^{59} +(-2.52414 - 1.04553i) q^{61} +(2.22010 - 0.919595i) q^{63} +(1.11213 + 2.68491i) q^{65} -12.8012 q^{67} +6.30808 q^{69} +(1.62627 + 3.92615i) q^{71} +(-9.47623 + 3.92518i) q^{73} +(2.18931 + 0.906841i) q^{75} +(-8.31560 + 8.31560i) q^{77} +(-0.464750 + 1.12200i) q^{79} -1.00000i q^{81} +(-2.92403 - 2.92403i) q^{83} +(-10.7938 - 2.96293i) q^{85} +(2.39984 + 2.39984i) q^{87} +2.96634i q^{89} +(-0.984434 + 2.37663i) q^{91} +(4.94563 - 4.94563i) q^{93} +(5.72025 + 2.36941i) q^{95} +(16.8658 - 6.98605i) q^{97} +(1.87280 + 4.52134i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 8 q^{11} - 8 q^{15} + 8 q^{19} + 8 q^{23} - 8 q^{25} + 32 q^{29} - 8 q^{31} - 8 q^{33} - 16 q^{35} + 8 q^{37} + 8 q^{39} + 40 q^{41} + 24 q^{43} + 8 q^{45} + 24 q^{49} - 8 q^{51} - 24 q^{53} - 8 q^{57}+ \cdots + 8 q^{99}+O(q^{100}) $ 16 * q + 8 * q^11 - 8 * q^15 + 8 * q^19 + 8 * q^23 - 8 * q^25 + 32 * q^29 - 8 * q^31 - 8 * q^33 - 16 * q^35 + 8 * q^37 + 8 * q^39 + 40 * q^41 + 24 * q^43 + 8 * q^45 + 24 * q^49 - 8 * q^51 - 24 * q^53 - 8 * q^57 + 16 * q^59 - 64 * q^65 - 8 * q^69 + 16 * q^71 + 24 * q^73 + 96 * q^79 - 32 * q^85 - 16 * q^87 + 24 * q^93 + 8 * q^95 + 56 * q^97 + 8 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/816\mathbb{Z}\right)^\times$.

$n$	$241$	$511$	$545$	$613$
$\chi(n)$	$e\left(\frac{3}{8}\right)$	$1$	$1$	$1$

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
$3$	0.382683	+	0.923880i	0.220942	+	0.533402i
$3$	0.382683	+	0.923880i	0.220942	+	0.533402i
$4$		0			0
$5$	−2.50807	+	1.03888i	−1.12164	+	0.464600i	−0.864933	−	0.501888i	$-0.832639\pi$
$5$	−2.50807	+	1.03888i	−1.12164	+	0.464600i	−0.256711	+	0.966488i	$0.582639\pi$
$6$		0			0
$7$	−2.22010	−	0.919595i	−0.839118	−	0.347574i	−0.0786124	−	0.996905i	$-0.525049\pi$
$7$	−2.22010	−	0.919595i	−0.839118	−	0.347574i	−0.760506	+	0.649331i	$0.775049\pi$
$8$		0			0
$9$	−0.707107	+	0.707107i	−0.235702	+	0.235702i
$10$		0			0
$11$	1.87280	−	4.52134i	0.564671	−	1.36324i	−0.341324	−	0.939946i	$-0.610875\pi$
$11$	1.87280	−	4.52134i	0.564671	−	1.36324i	0.905994	−	0.423290i	$-0.139125\pi$
$12$		0			0
$13$		−	1.07051i		−	0.296906i	−0.988920	−	0.148453i	$-0.952571\pi$
$13$		−	1.07051i		−	0.296906i	0.988920	−	0.148453i	$-0.0474293\pi$
$14$		0			0
$15$	−1.91959	−	1.91959i	−0.495637	−	0.495637i
$16$		0			0
$17$	3.25570	+	2.52991i	0.789622	+	0.613593i
$17$	3.25570	+	2.52991i	0.789622	+	0.613593i
$18$		0			0
$19$	−1.61272	−	1.61272i	−0.369984	−	0.369984i	0.497487	−	0.867471i	$-0.334256\pi$
$19$	−1.61272	−	1.61272i	−0.369984	−	0.369984i	−0.867471	+	0.497487i	$0.834256\pi$
$20$		0			0
$21$		−	2.40302i		−	0.524381i
$22$		0			0
$23$	2.41400	−	5.82790i	0.503353	−	1.21520i	−0.444294	−	0.895881i	$-0.646545\pi$
$23$	2.41400	−	5.82790i	0.503353	−	1.21520i	0.947647	−	0.319321i	$-0.103455\pi$
$24$		0			0
$25$	1.67562	−	1.67562i	0.335125	−	0.335125i
$26$		0			0
$27$	−0.923880	−	0.382683i	−0.177801	−	0.0736475i
$28$		0			0
$29$	3.13555	−	1.29879i	0.582257	−	0.241179i	−0.0720587	−	0.997400i	$-0.522957\pi$
$29$	3.13555	−	1.29879i	0.582257	−	0.241179i	0.654315	+	0.756222i	$0.272957\pi$
$30$		0			0
$31$	−2.67656	−	6.46178i	−0.480724	−	1.16057i	−0.959266	−	0.282506i	$-0.908834\pi$
$31$	−2.67656	−	6.46178i	−0.480724	−	1.16057i	0.478542	−	0.878065i	$-0.341166\pi$
$32$		0			0
$33$	4.89386			0.851912
$34$		0			0
$35$	6.52351			1.10267
$36$		0			0
$37$	−1.63047	−	3.93630i	−0.268047	−	0.647123i	0.731344	−	0.682009i	$-0.238893\pi$
$37$	−1.63047	−	3.93630i	−0.268047	−	0.647123i	−0.999391	+	0.0348855i	$0.988893\pi$
$38$		0			0
$39$	0.989020	−	0.409666i	0.158370	−	0.0655990i
$40$		0			0
$41$	7.08028	+	2.93275i	1.10575	+	0.458018i	0.859473	−	0.511180i	$-0.170792\pi$
$41$	7.08028	+	2.93275i	1.10575	+	0.458018i	0.246280	+	0.969199i	$0.420792\pi$
$42$		0			0
$43$	4.37197	−	4.37197i	0.666719	−	0.666719i	−0.290236	−	0.956955i	$-0.593734\pi$
$43$	4.37197	−	4.37197i	0.666719	−	0.666719i	0.956955	+	0.290236i	$0.0937339\pi$
$44$		0			0
$45$	1.03888	−	2.50807i	0.154867	−	0.373881i
$46$		0			0
$47$			8.19868i			1.19590i	0.801533	+	0.597950i	$0.204018\pi$
$47$			8.19868i			1.19590i	−0.801533	+	0.597950i	$0.795982\pi$
$48$		0			0
$49$	−0.866566	−	0.866566i	−0.123795	−	0.123795i
$50$		0			0
$51$	−1.09143	+	3.97603i	−0.152831	+	0.556755i
$52$		0			0
$53$	−7.97888	−	7.97888i	−1.09598	−	1.09598i	−0.994875	−	0.101108i	$-0.967761\pi$
$53$	−7.97888	−	7.97888i	−1.09598	−	1.09598i	−0.101108	−	0.994875i	$-0.532239\pi$
$54$		0			0
$55$			13.2855i			1.79141i
$56$		0			0
$57$	0.872800	−	2.10713i	0.115605	−	0.279096i
$58$		0			0
$59$	8.89888	−	8.89888i	1.15854	−	1.15854i	0.173745	−	0.984791i	$-0.444413\pi$
$59$	8.89888	−	8.89888i	1.15854	−	1.15854i	0.984791	−	0.173745i	$-0.0555869\pi$
$60$		0			0
$61$	−2.52414	−	1.04553i	−0.323183	−	0.133867i	0.215193	−	0.976572i	$-0.430962\pi$
$61$	−2.52414	−	1.04553i	−0.323183	−	0.133867i	−0.538376	+	0.842705i	$0.680962\pi$
$62$		0			0
$63$	2.22010	−	0.919595i	0.279706	−	0.115858i
$64$		0			0
$65$	1.11213	+	2.68491i	0.137942	+	0.333022i
$66$		0			0
$67$	−12.8012			−1.56392			−0.781958	−	0.623331i	$-0.785779\pi$
$67$	−12.8012			−1.56392			−0.781958	+	0.623331i	$0.785779\pi$
$68$		0			0
$69$	6.30808			0.759403
$70$		0			0
$71$	1.62627	+	3.92615i	0.193002	+	0.465948i	0.990524	−	0.137342i	$-0.0438559\pi$
$71$	1.62627	+	3.92615i	0.193002	+	0.465948i	−0.797521	+	0.603291i	$0.793856\pi$
$72$		0			0
$73$	−9.47623	+	3.92518i	−1.10911	+	0.459408i	−0.860631	−	0.509229i	$-0.829931\pi$
$73$	−9.47623	+	3.92518i	−1.10911	+	0.459408i	−0.248478	+	0.968637i	$0.579931\pi$
$74$		0			0
$75$	2.18931	+	0.906841i	0.252799	+	0.104713i
$76$		0			0
$77$	−8.31560	+	8.31560i	−0.947651	+	0.947651i
$78$		0			0
$79$	−0.464750	+	1.12200i	−0.0522884	+	0.126235i	−0.947865	−	0.318672i	$-0.896763\pi$
$79$	−0.464750	+	1.12200i	−0.0522884	+	0.126235i	0.895577	+	0.444907i	$0.146763\pi$
$80$		0			0
$81$		−	1.00000i		−	0.111111i
$82$		0			0
$83$	−2.92403	−	2.92403i	−0.320954	−	0.320954i	0.528179	−	0.849133i	$-0.322875\pi$
$83$	−2.92403	−	2.92403i	−0.320954	−	0.320954i	−0.849133	+	0.528179i	$0.822875\pi$
$84$		0			0
$85$	−10.7938	−	2.96293i	−1.17075	−	0.321374i
$86$		0			0
$87$	2.39984	+	2.39984i	0.257290	+	0.257290i
$88$		0			0
$89$			2.96634i			0.314431i	0.987564	+	0.157216i	$0.0502518\pi$
$89$			2.96634i			0.314431i	−0.987564	+	0.157216i	$0.949748\pi$
$90$		0			0
$91$	−0.984434	+	2.37663i	−0.103197	+	0.249139i
$92$		0			0
$93$	4.94563	−	4.94563i	0.512838	−	0.512838i
$94$		0			0
$95$	5.72025	+	2.36941i	0.586886	+	0.243096i
$96$		0			0
$97$	16.8658	−	6.98605i	1.71247	−	0.709326i	0.712495	−	0.701678i	$-0.247565\pi$
$97$	16.8658	−	6.98605i	1.71247	−	0.709326i	0.999971	−	0.00764885i	$-0.00243473\pi$
$98$		0			0
$99$	1.87280	+	4.52134i	0.188224	+	0.454412i
$100$		0			0
$101$	−9.04503			−0.900014			−0.450007	−	0.893025i	$-0.648579\pi$
$101$	−9.04503			−0.900014			−0.450007	+	0.893025i	$0.648579\pi$
$102$		0			0
$103$	2.23568			0.220288			0.110144	−	0.993916i	$-0.464869\pi$
$103$	2.23568			0.220288			0.110144	+	0.993916i	$0.464869\pi$
$104$		0			0
$105$	2.49644	+	6.02694i	0.243628	+	0.588169i
$106$		0			0
$107$	−5.04118	+	2.08813i	−0.487350	+	0.201867i	−0.612808	−	0.790232i	$-0.709960\pi$
$107$	−5.04118	+	2.08813i	−0.487350	+	0.201867i	0.125458	+	0.992099i	$0.459960\pi$
$108$		0			0
$109$	−2.44258	−	1.01175i	−0.233956	−	0.0969079i	0.262625	−	0.964898i	$-0.415412\pi$
$109$	−2.44258	−	1.01175i	−0.233956	−	0.0969079i	−0.496582	+	0.867990i	$0.665412\pi$
$110$		0			0
$111$	3.01271	−	3.01271i	0.285954	−	0.285954i
$112$		0			0
$113$	5.35434	−	12.9265i	0.503694	−	1.21602i	−0.443764	−	0.896144i	$-0.646357\pi$
$113$	5.35434	−	12.9265i	0.503694	−	1.21602i	0.947458	−	0.319880i	$-0.103643\pi$
$114$		0			0
$115$			17.1246i			1.59688i
$116$		0			0
$117$	0.756964	+	0.756964i	0.0699813	+	0.0699813i
$118$		0			0
$119$	−4.90147	−	8.61057i	−0.449317	−	0.789330i
$120$		0			0
$121$	−9.15696	−	9.15696i	−0.832451	−	0.832451i
$122$		0			0
$123$			7.66364i			0.691007i
$124$		0			0
$125$	2.73257	−	6.59701i	0.244409	−	0.590054i
$126$		0			0
$127$	−10.2828	+	10.2828i	−0.912449	+	0.912449i	−0.996464	−	0.0840159i	$-0.973225\pi$
$127$	−10.2828	+	10.2828i	−0.912449	+	0.912449i	0.0840159	+	0.996464i	$0.473225\pi$
$128$		0			0
$129$	5.71225	+	2.36609i	0.502936	+	0.208323i
$130$		0			0
$131$	2.23079	−	0.924024i	0.194905	−	0.0807323i	−0.283096	−	0.959092i	$-0.591361\pi$
$131$	2.23079	−	0.924024i	0.194905	−	0.0807323i	0.478001	+	0.878359i	$0.341361\pi$
$132$		0			0
$133$	2.09735	+	5.06346i	0.181864	+	0.439058i
$134$		0			0
$135$	2.71472			0.233646
$136$		0			0
$137$	−1.42184			−0.121476			−0.0607382	−	0.998154i	$-0.519345\pi$
$137$	−1.42184			−0.121476			−0.0607382	+	0.998154i	$0.519345\pi$
$138$		0			0
$139$	−5.94425	−	14.3507i	−0.504184	−	1.21721i	−0.947185	−	0.320687i	$-0.896086\pi$
$139$	−5.94425	−	14.3507i	−0.504184	−	1.21721i	0.443001	−	0.896521i	$-0.353914\pi$
$140$		0			0
$141$	−7.57460	+	3.13750i	−0.637896	+	0.264225i
$142$		0			0
$143$	−4.84013	−	2.00485i	−0.404752	−	0.167654i
$144$		0			0
$145$	−6.51490	+	6.51490i	−0.541033	+	0.541033i
$146$		0			0
$147$	0.468982	−	1.13222i	0.0386810	−	0.0933842i
$148$		0			0
$149$		−	16.2390i		−	1.33035i	−0.746687	−	0.665176i	$-0.768357\pi$
$149$		−	16.2390i		−	1.33035i	0.746687	−	0.665176i	$-0.231643\pi$
$150$		0			0
$151$	−2.48539	−	2.48539i	−0.202258	−	0.202258i	0.598709	−	0.800967i	$-0.295681\pi$
$151$	−2.48539	−	2.48539i	−0.202258	−	0.202258i	−0.800967	+	0.598709i	$0.795681\pi$
$152$		0			0
$153$	−4.09104	+	0.513208i	−0.330741	+	0.0414904i
$154$		0			0
$155$	13.4260	+	13.4260i	1.07840	+	1.07840i
$156$		0			0
$157$			21.3904i			1.70714i	0.520975	+	0.853572i	$0.325568\pi$
$157$			21.3904i			1.70714i	−0.520975	+	0.853572i	$0.674432\pi$
$158$		0			0
$159$	4.31814	−	10.4249i	0.342451	−	0.826749i
$160$		0			0
$161$	−10.7186	+	10.7186i	−0.844746	+	0.844746i
$162$		0			0
$163$	−18.3602	−	7.60506i	−1.43809	−	0.595675i	−0.478752	−	0.877950i	$-0.658911\pi$
$163$	−18.3602	−	7.60506i	−1.43809	−	0.595675i	−0.959333	+	0.282275i	$0.908911\pi$
$164$		0			0
$165$	−12.2742	+	5.08412i	−0.955542	+	0.395798i
$166$		0			0
$167$	−3.03768	−	7.33360i	−0.235063	−	0.567491i	0.761697	−	0.647934i	$-0.224367\pi$
$167$	−3.03768	−	7.33360i	−0.235063	−	0.567491i	−0.996759	+	0.0804426i	$0.974367\pi$
$168$		0			0
$169$	11.8540			0.911847
$170$		0			0
$171$	2.28074			0.174412
$172$		0			0
$173$	9.18012	+	22.1628i	0.697951	+	1.68500i	0.728112	+	0.685458i	$0.240398\pi$
$173$	9.18012	+	22.1628i	0.697951	+	1.68500i	−0.0301604	+	0.999545i	$0.509602\pi$
$174$		0			0
$175$	−5.26094	+	2.17915i	−0.397690	+	0.164728i
$176$		0			0
$177$	11.6269	+	4.81604i	0.873935	+	0.361996i
$178$		0			0
$179$	−17.0828	+	17.0828i	−1.27683	+	1.27683i	−0.334392	+	0.942434i	$0.608531\pi$
$179$	−17.0828	+	17.0828i	−1.27683	+	1.27683i	−0.942434	+	0.334392i	$0.891469\pi$
$180$		0			0
$181$	4.65785	−	11.2451i	0.346216	−	0.835838i	−0.650844	−	0.759211i	$-0.725585\pi$
$181$	4.65785	−	11.2451i	0.346216	−	0.835838i	0.997060	−	0.0766270i	$-0.0244151\pi$
$182$		0			0
$183$		−	2.73211i		−	0.201964i
$184$		0			0
$185$	8.17866	+	8.17866i	0.601307	+	0.601307i
$186$		0			0
$187$	17.5359	−	9.98209i	1.28235	−	0.729963i
$188$		0			0
$189$	1.69919	+	1.69919i	0.123598	+	0.123598i
$190$		0			0
$191$		−	3.27804i		−	0.237191i	−0.992943	−	0.118595i	$-0.962161\pi$
$191$		−	3.27804i		−	0.237191i	0.992943	−	0.118595i	$-0.0378392\pi$
$192$		0			0
$193$	−7.94091	+	19.1711i	−0.571599	+	1.37996i	0.328593	+	0.944472i	$0.393425\pi$
$193$	−7.94091	+	19.1711i	−0.571599	+	1.37996i	−0.900193	+	0.435492i	$0.856575\pi$
$194$		0			0
$195$	−2.05494	+	2.05494i	−0.147157	+	0.147157i
$196$		0			0
$197$	18.2135	+	7.54429i	1.29766	+	0.537508i	0.921259	−	0.388949i	$-0.127162\pi$
$197$	18.2135	+	7.54429i	1.29766	+	0.537508i	0.376401	+	0.926457i	$0.377162\pi$
$198$		0			0
$199$	14.0934	−	5.83768i	0.999055	−	0.413822i	0.177605	−	0.984102i	$-0.443165\pi$
$199$	14.0934	−	5.83768i	0.999055	−	0.413822i	0.821451	+	0.570280i	$0.193165\pi$
$200$		0			0
$201$	−4.89881	−	11.8268i	−0.345535	−	0.834196i
$202$		0			0
$203$	−8.15558			−0.572410
$204$		0			0
$205$	−20.8046			−1.45306
$206$		0			0
$207$	2.41400	+	5.82790i	0.167784	+	0.405067i
$208$		0			0
$209$	−10.3120	+	4.27137i	−0.713295	+	0.295457i
$210$		0			0
$211$	11.5631	+	4.78961i	0.796039	+	0.329730i	0.743369	−	0.668882i	$-0.233227\pi$
$211$	11.5631	+	4.78961i	0.796039	+	0.329730i	0.0526704	+	0.998612i	$0.483227\pi$
$212$		0			0
$213$	−3.00495	+	3.00495i	−0.205896	+	0.205896i
$214$		0			0
$215$	−6.42327	+	15.5071i	−0.438063	+	1.05758i
$216$		0			0
$217$			16.8071i			1.14094i
$218$		0			0
$219$	−7.25280	−	7.25280i	−0.490099	−	0.490099i
$220$		0			0
$221$	2.70829	−	3.48525i	0.182179	−	0.234443i
$222$		0			0
$223$	5.32288	+	5.32288i	0.356446	+	0.356446i	0.862501	−	0.506055i	$-0.168897\pi$
$223$	5.32288	+	5.32288i	0.356446	+	0.356446i	−0.506055	+	0.862501i	$0.668897\pi$
$224$		0			0
$225$			2.36969i			0.157979i
$226$		0			0
$227$	−1.83963	+	4.44126i	−0.122101	+	0.294777i	−0.973097	−	0.230394i	$-0.925999\pi$
$227$	−1.83963	+	4.44126i	−0.122101	+	0.294777i	0.850997	+	0.525171i	$0.175999\pi$
$228$		0			0
$229$	−9.47732	+	9.47732i	−0.626279	+	0.626279i	−0.947130	−	0.320851i	$-0.896031\pi$
$229$	−9.47732	+	9.47732i	−0.626279	+	0.626279i	0.320851	+	0.947130i	$0.396031\pi$
$230$		0			0
$231$	−10.8649	−	4.50037i	−0.714855	−	0.296103i
$232$		0			0
$233$	12.7306	−	5.27318i	0.834008	−	0.345457i	0.0755198	−	0.997144i	$-0.475938\pi$
$233$	12.7306	−	5.27318i	0.834008	−	0.345457i	0.758488	+	0.651687i	$0.225938\pi$
$234$		0			0
$235$	−8.51742	−	20.5629i	−0.555616	−	1.34137i
$236$		0			0
$237$	−1.21445			−0.0788870
$238$		0			0
$239$	17.0060			1.10003			0.550014	−	0.835155i	$-0.314622\pi$
$239$	17.0060			1.10003			0.550014	+	0.835155i	$0.314622\pi$
$240$		0			0
$241$	−7.42077	−	17.9153i	−0.478014	−	1.15403i	−0.960539	−	0.278145i	$-0.910280\pi$
$241$	−7.42077	−	17.9153i	−0.478014	−	1.15403i	0.482525	−	0.875882i	$-0.339720\pi$
$242$		0			0
$243$	0.923880	−	0.382683i	0.0592669	−	0.0245492i
$244$		0			0
$245$	3.07366	+	1.27315i	0.196369	+	0.0813388i
$246$		0			0
$247$	−1.72644	+	1.72644i	−0.109850	+	0.109850i
$248$		0			0
$249$	1.58247	−	3.82042i	0.100285	−	0.242110i
$250$		0			0
$251$			21.5316i			1.35906i	0.733646	+	0.679532i	$0.237817\pi$
$251$			21.5316i			1.35906i	−0.733646	+	0.679532i	$0.762183\pi$
$252$		0			0
$253$	−21.8290	−	21.8290i	−1.37238	−	1.37238i
$254$		0			0
$255$	−1.39322	−	11.1060i	−0.0872466	−	0.695486i
$256$		0			0
$257$	13.5195	+	13.5195i	0.843324	+	0.843324i	0.989290	−	0.145966i	$-0.0466290\pi$
$257$	13.5195	+	13.5195i	0.843324	+	0.843324i	−0.145966	+	0.989290i	$0.546629\pi$
$258$		0			0
$259$			10.2383i			0.636179i
$260$		0			0
$261$	−1.29879	+	3.13555i	−0.0803929	+	0.194086i
$262$		0			0
$263$	−7.83952	+	7.83952i	−0.483406	+	0.483406i	−0.906218	−	0.422812i	$-0.861043\pi$
$263$	−7.83952	+	7.83952i	−0.483406	+	0.483406i	0.422812	+	0.906218i	$0.361043\pi$
$264$		0			0
$265$	28.3007	+	11.7225i	1.73850	+	0.720109i
$266$		0			0
$267$	−2.74054	+	1.13517i	−0.167718	+	0.0694712i
$268$		0			0
$269$	1.69352	+	4.08852i	0.103256	+	0.249282i	0.967061	−	0.254544i	$-0.0819254\pi$
$269$	1.69352	+	4.08852i	0.103256	+	0.249282i	−0.863805	+	0.503826i	$0.831925\pi$
$270$		0			0
$271$	−16.2476			−0.986973			−0.493486	−	0.869753i	$-0.664278\pi$
$271$	−16.2476			−0.986973			−0.493486	+	0.869753i	$0.664278\pi$
$272$		0			0
$273$	−2.57245			−0.155692
$274$		0			0
$275$	−4.43795	−	10.7142i	−0.267619	−	0.646089i
$276$		0			0
$277$	−0.591916	+	0.245180i	−0.0355648	+	0.0147314i	−0.400395	−	0.916343i	$-0.631127\pi$
$277$	−0.591916	+	0.245180i	−0.0355648	+	0.0147314i	0.364830	+	0.931074i	$0.381127\pi$
$278$		0			0
$279$	6.46178	+	2.67656i	0.386857	+	0.160241i
$280$		0			0
$281$	0.0521155	−	0.0521155i	0.00310895	−	0.00310895i	−0.705551	−	0.708660i	$-0.749300\pi$
$281$	0.0521155	−	0.0521155i	0.00310895	−	0.00310895i	0.708660	+	0.705551i	$0.249300\pi$
$282$		0			0
$283$	7.82868	−	18.9001i	0.465367	−	1.12350i	−0.500797	−	0.865565i	$-0.666960\pi$
$283$	7.82868	−	18.9001i	0.465367	−	1.12350i	0.966164	−	0.257930i	$-0.0830404\pi$
$284$		0			0
$285$			6.19156i			0.366756i
$286$		0			0
$287$	−13.0220	−	13.0220i	−0.768663	−	0.768663i
$288$		0			0
$289$	4.19911	+	16.4732i	0.247007	+	0.969014i
$290$		0			0
$291$	12.9085	+	12.9085i	0.756712	+	0.756712i
$292$		0			0
$293$		−	7.88796i		−	0.460820i	−0.973094	−	0.230410i	$-0.925993\pi$
$293$		−	7.88796i		−	0.460820i	0.973094	−	0.230410i	$-0.0740067\pi$
$294$		0			0
$295$	−13.0742	+	31.5639i	−0.761209	+	1.83772i
$296$		0			0
$297$	−3.46048	+	3.46048i	−0.200798	+	0.200798i
$298$		0			0
$299$	−6.23882	−	2.58420i	−0.360800	−	0.149448i
$300$		0			0
$301$	−13.7266	+	5.68576i	−0.791190	+	0.327722i
$302$		0			0
$303$	−3.46138	−	8.35652i	−0.198851	−	0.480069i
$304$		0			0
$305$	7.41691			0.424691
$306$		0			0
$307$	4.63954			0.264793			0.132396	−	0.991197i	$-0.457733\pi$
$307$	4.63954			0.264793			0.132396	+	0.991197i	$0.457733\pi$
$308$		0			0
$309$	0.855556	+	2.06550i	0.0486709	+	0.117502i
$310$		0			0
$311$	5.16892	−	2.14104i	0.293103	−	0.121407i	−0.231287	−	0.972886i	$-0.574294\pi$
$311$	5.16892	−	2.14104i	0.293103	−	0.121407i	0.524389	+	0.851479i	$0.324294\pi$
$312$		0			0
$313$	0.810266	+	0.335623i	0.0457990	+	0.0189705i	0.405465	−	0.914110i	$-0.367109\pi$
$313$	0.810266	+	0.335623i	0.0457990	+	0.0189705i	−0.359666	+	0.933081i	$0.617109\pi$
$314$		0			0
$315$	−4.61282	+	4.61282i	−0.259903	+	0.259903i
$316$		0			0
$317$	11.3854	−	27.4867i	0.639467	−	1.54381i	−0.187925	−	0.982183i	$-0.560176\pi$
$317$	11.3854	−	27.4867i	0.639467	−	1.54381i	0.827392	−	0.561625i	$-0.189824\pi$
$318$		0			0
$319$		−	16.6092i		−	0.929939i
$320$		0			0
$321$	−3.85836	−	3.85836i	−0.215352	−	0.215352i
$322$		0			0
$323$	−1.17049	−	9.33059i	−0.0651280	−	0.519168i
$324$		0			0
$325$	−1.79377	−	1.79377i	−0.0995003	−	0.0995003i
$326$		0			0
$327$		−	2.64382i		−	0.146204i
$328$		0			0
$329$	7.53947	−	18.2019i	0.415664	−	1.00350i
$330$		0			0
$331$	8.18438	−	8.18438i	0.449854	−	0.449854i	−0.445452	−	0.895306i	$-0.646957\pi$
$331$	8.18438	−	8.18438i	0.449854	−	0.449854i	0.895306	+	0.445452i	$0.146957\pi$
$332$		0			0
$333$	3.93630	+	1.63047i	0.215708	+	0.0893491i
$334$		0			0
$335$	32.1063	−	13.2989i	1.75416	−	0.726595i
$336$		0			0
$337$	6.47644	+	15.6355i	0.352794	+	0.851720i	0.996273	+	0.0862562i	$0.0274904\pi$
$337$	6.47644	+	15.6355i	0.352794	+	0.851720i	−0.643479	+	0.765464i	$0.722510\pi$
$338$		0			0
$339$	13.9916			0.759917
$340$		0			0
$341$	−34.2286			−1.85358
$342$		0			0
$343$	7.56414	+	18.2614i	0.408425	+	0.986025i
$344$		0			0
$345$	−15.8211	+	6.55332i	−0.851780	+	0.352819i
$346$		0			0
$347$	2.02695	+	0.839592i	0.108813	+	0.0450716i	0.436426	−	0.899740i	$-0.356244\pi$
$347$	2.02695	+	0.839592i	0.108813	+	0.0450716i	−0.327613	+	0.944812i	$0.606244\pi$
$348$		0			0
$349$	18.7192	−	18.7192i	1.00201	−	1.00201i	0.00201610	−	0.999998i	$-0.499358\pi$
$349$	18.7192	−	18.7192i	1.00201	−	1.00201i	0.999998	−	0.00201610i	$-0.000641744\pi$
$350$		0			0
$351$	−0.409666	+	0.989020i	−0.0218663	+	0.0527900i
$352$		0			0
$353$		−	24.9345i		−	1.32713i	−0.748120	−	0.663564i	$-0.769043\pi$
$353$		−	24.9345i		−	1.32713i	0.748120	−	0.663564i	$-0.230957\pi$
$354$		0			0
$355$	−8.15758	−	8.15758i	−0.432959	−	0.432959i
$356$		0			0
$357$	6.07942	−	7.82349i	0.321757	−	0.414063i
$358$		0			0
$359$	−2.09699	−	2.09699i	−0.110675	−	0.110675i	0.649601	−	0.760276i	$-0.274936\pi$
$359$	−2.09699	−	2.09699i	−0.110675	−	0.110675i	−0.760276	+	0.649601i	$0.774936\pi$
$360$		0			0
$361$		−	13.7982i		−	0.726223i
$362$		0			0
$363$	4.95571	−	11.9641i	0.260107	−	0.627955i
$364$		0			0
$365$	19.6893	−	19.6893i	1.03058	−	1.03058i
$366$		0			0
$367$	21.6341	+	8.96114i	1.12929	+	0.467768i	0.867540	−	0.497368i	$-0.165700\pi$
$367$	21.6341	+	8.96114i	1.12929	+	0.467768i	0.261751	+	0.965135i	$0.415700\pi$
$368$		0			0
$369$	−7.08028	+	2.93275i	−0.368585	+	0.152673i
$370$		0			0
$371$	10.3766	+	25.0512i	0.538724	+	1.30060i
$372$		0			0
$373$	30.4720			1.57778			0.788890	−	0.614534i	$-0.210656\pi$
$373$	30.4720			1.57778			0.788890	+	0.614534i	$0.210656\pi$
$374$		0			0
$375$	7.14055			0.368736
$376$		0			0
$377$	−1.39036	−	3.35663i	−0.0716073	−	0.172875i
$378$		0			0
$379$	2.43151	−	1.00717i	0.124898	−	0.0517346i	−0.319359	−	0.947634i	$-0.603468\pi$
$379$	2.43151	−	1.00717i	0.124898	−	0.0517346i	0.444257	+	0.895899i	$0.353468\pi$
$380$		0			0
$381$	−13.4351	−	5.56500i	−0.688301	−	0.285103i
$382$		0			0
$383$	−13.8259	+	13.8259i	−0.706473	+	0.706473i	−0.965792	−	0.259319i	$-0.916502\pi$
$383$	−13.8259	+	13.8259i	−0.706473	+	0.706473i	0.259319	+	0.965792i	$0.416502\pi$
$384$		0			0
$385$	12.2172	−	29.4950i	0.622648	−	1.50321i
$386$		0			0
$387$			6.18290i			0.314294i
$388$		0			0
$389$	−10.3694	−	10.3694i	−0.525748	−	0.525748i	0.393553	−	0.919302i	$-0.371246\pi$
$389$	−10.3694	−	10.3694i	−0.525748	−	0.525748i	−0.919302	+	0.393553i	$0.871246\pi$
$390$		0			0
$391$	22.6033	−	12.8667i	1.14310	−	0.650696i
$392$		0			0
$393$	1.70737	+	1.70737i	0.0861256	+	0.0861256i
$394$		0			0
$395$		−	3.29689i		−	0.165884i
$396$		0			0
$397$	5.12132	−	12.3639i	0.257031	−	0.620529i	−0.741708	−	0.670723i	$-0.765984\pi$
$397$	5.12132	−	12.3639i	0.257031	−	0.620529i	0.998739	+	0.0501941i	$0.0159840\pi$
$398$		0			0
$399$	−3.87541	+	3.87541i	−0.194013	+	0.194013i
$400$		0			0
$401$	−6.03313	−	2.49900i	−0.301280	−	0.124794i	0.226922	−	0.973913i	$-0.427134\pi$
$401$	−6.03313	−	2.49900i	−0.301280	−	0.124794i	−0.528202	+	0.849119i	$0.677134\pi$
$402$		0			0
$403$	−6.91739	+	2.86528i	−0.344580	+	0.142730i
$404$		0			0
$405$	1.03888	+	2.50807i	0.0516222	+	0.124627i
$406$		0			0
$407$	−20.8509			−1.03354
$408$		0			0
$409$	−6.45254			−0.319058			−0.159529	−	0.987193i	$-0.550997\pi$
$409$	−6.45254			−0.319058			−0.159529	+	0.987193i	$0.550997\pi$
$410$		0			0
$411$	−0.544116	−	1.31361i	−0.0268393	−	0.0647958i
$412$		0			0
$413$	−27.9398	+	11.5730i	−1.37483	+	0.569471i
$414$		0			0
$415$	10.3714	+	4.29596i	0.509111	+	0.210881i
$416$		0			0
$417$	10.9835	−	10.9835i	0.537866	−	0.537866i
$418$		0			0
$419$	−8.77323	+	21.1805i	−0.428600	+	1.03473i	0.551131	+	0.834419i	$0.314196\pi$
$419$	−8.77323	+	21.1805i	−0.428600	+	1.03473i	−0.979732	+	0.200314i	$0.935804\pi$
$420$		0			0
$421$		−	26.8644i		−	1.30929i	−0.755936	−	0.654645i	$-0.772818\pi$
$421$		−	26.8644i		−	1.30929i	0.755936	−	0.654645i	$-0.227182\pi$
$422$		0			0
$423$	−5.79734	−	5.79734i	−0.281877	−	0.281877i
$424$		0			0
$425$	9.69449	−	1.21614i	0.470252	−	0.0589917i
$426$		0			0
$427$	4.64238	+	4.64238i	0.224660	+	0.224660i
$428$		0			0
$429$		−	5.23892i		−	0.252937i
$430$		0			0
$431$	14.8232	−	35.7865i	0.714010	−	1.72377i	0.0242809	−	0.999705i	$-0.492270\pi$
$431$	14.8232	−	35.7865i	0.714010	−	1.72377i	0.689729	−	0.724068i	$-0.257730\pi$
$432$		0			0
$433$	−21.6205	+	21.6205i	−1.03901	+	1.03901i	−0.0398071	+	0.999207i	$0.512674\pi$
$433$	−21.6205	+	21.6205i	−1.03901	+	1.03901i	−0.999207	+	0.0398071i	$0.987326\pi$
$434$		0			0
$435$	−8.51213	−	3.52584i	−0.408125	−	0.169051i
$436$		0			0
$437$	−13.2919	+	5.50569i	−0.635839	+	0.263373i
$438$		0			0
$439$	0.602318	+	1.45412i	0.0287471	+	0.0694016i	0.937601	−	0.347713i	$-0.113042\pi$
$439$	0.602318	+	1.45412i	0.0287471	+	0.0694016i	−0.908854	+	0.417114i	$0.863042\pi$
$440$		0			0
$441$	1.22551			0.0583576
$442$		0			0
$443$	−14.7788			−0.702164			−0.351082	−	0.936345i	$-0.614186\pi$
$443$	−14.7788			−0.702164			−0.351082	+	0.936345i	$0.614186\pi$
$444$		0			0
$445$	−3.08166	−	7.43979i	−0.146085	−	0.352680i
$446$		0			0
$447$	15.0029	−	6.21440i	0.709612	−	0.293931i
$448$		0			0
$449$	−9.04315	−	3.74579i	−0.426773	−	0.176775i	0.158950	−	0.987287i	$-0.449189\pi$
$449$	−9.04315	−	3.74579i	−0.426773	−	0.176775i	−0.585722	+	0.810512i	$0.699189\pi$
$450$		0			0
$451$	26.5199	−	26.5199i	1.24877	−	1.24877i
$452$		0			0
$453$	1.34508	−	3.24731i	0.0631974	−	0.152572i
$454$		0			0
$455$		−	6.98347i		−	0.327390i
$456$		0			0
$457$	−17.3054	−	17.3054i	−0.809513	−	0.809513i	0.175047	−	0.984560i	$-0.443992\pi$
$457$	−17.3054	−	17.3054i	−0.809513	−	0.809513i	−0.984560	+	0.175047i	$0.943992\pi$
$458$		0			0
$459$	−2.03972	−	3.58323i	−0.0952058	−	0.167251i
$460$		0			0
$461$	9.62092	+	9.62092i	0.448091	+	0.448091i	0.894719	−	0.446629i	$-0.147375\pi$
$461$	9.62092	+	9.62092i	0.448091	+	0.448091i	−0.446629	+	0.894719i	$0.647375\pi$
$462$		0			0
$463$			10.8498i			0.504233i	0.967697	+	0.252117i	$0.0811267\pi$
$463$			10.8498i			0.504233i	−0.967697	+	0.252117i	$0.918873\pi$
$464$		0			0
$465$	−7.26610	+	17.5419i	−0.336957	+	0.813487i
$466$		0			0
$467$	−10.9692	+	10.9692i	−0.507594	+	0.507594i	−0.913787	−	0.406193i	$-0.866856\pi$
$467$	−10.9692	+	10.9692i	−0.507594	+	0.507594i	0.406193	+	0.913787i	$0.366856\pi$
$468$		0			0
$469$	28.4199	+	11.7719i	1.31231	+	0.543577i
$470$		0			0
$471$	−19.7622	+	8.18577i	−0.910594	+	0.377180i
$472$		0			0
$473$	−11.5793	−	27.9550i	−0.532418	−	1.28537i
$474$		0			0
$475$	−5.40464			−0.247982
$476$		0			0
$477$	11.2838			0.516652
$478$		0			0
$479$	−16.4855	−	39.7996i	−0.753244	−	1.81849i	−0.540407	−	0.841403i	$-0.681730\pi$
$479$	−16.4855	−	39.7996i	−0.753244	−	1.81849i	−0.212836	−	0.977088i	$-0.568270\pi$
$480$		0			0
$481$	−4.21384	+	1.74543i	−0.192134	+	0.0795847i
$482$		0			0
$483$	−14.0046	−	5.80087i	−0.637229	−	0.263949i
$484$		0			0
$485$	−35.0430	+	35.0430i	−1.59122	+	1.59122i
$486$		0			0
$487$	−16.2097	+	39.1337i	−0.734531	+	1.77331i	−0.107666	+	0.994187i	$0.534338\pi$
$487$	−16.2097	+	39.1337i	−0.734531	+	1.77331i	−0.626865	+	0.779128i	$0.715662\pi$
$488$		0			0
$489$		−	19.8730i		−	0.898688i
$490$		0			0
$491$	−3.65738	−	3.65738i	−0.165055	−	0.165055i	0.619747	−	0.784802i	$-0.287235\pi$
$491$	−3.65738	−	3.65738i	−0.165055	−	0.165055i	−0.784802	+	0.619747i	$0.787235\pi$
$492$		0			0
$493$	13.4942	+	3.70420i	0.607748	+	0.166829i
$494$		0			0
$495$	−9.39423	−	9.39423i	−0.422239	−	0.422239i
$496$		0			0
$497$		−	10.2119i		−	0.458068i
$498$		0			0
$499$	8.48908	−	20.4945i	0.380023	−	0.917458i	−0.611937	−	0.790907i	$-0.709609\pi$
$499$	8.48908	−	20.4945i	0.380023	−	0.917458i	0.991960	−	0.126551i	$-0.0403907\pi$
$500$		0			0
$501$	5.61290	−	5.61290i	0.250766	−	0.250766i
$502$		0			0
$503$	25.0563	+	10.3786i	1.11720	+	0.462761i	0.863413	−	0.504498i	$-0.168322\pi$
$503$	25.0563	+	10.3786i	1.11720	+	0.462761i	0.253791	+	0.967259i	$0.418322\pi$
$504$		0			0
$505$	22.6856	−	9.39667i	1.00950	−	0.418147i
$506$		0			0
$507$	4.53633	+	10.9517i	0.201466	+	0.486381i
$508$		0			0
$509$	25.9336			1.14949			0.574743	−	0.818334i	$-0.305102\pi$
$509$	25.9336			1.14949			0.574743	+	0.818334i	$0.305102\pi$
$510$		0			0
$511$	24.6478			1.09035
$512$		0			0
$513$	0.872800	+	2.10713i	0.0385351	+	0.0930319i
$514$		0			0
$515$	−5.60724	+	2.32259i	−0.247084	+	0.102346i
$516$		0			0
$517$	37.0690	+	15.3545i	1.63029	+	0.675290i
$518$		0			0
$519$	−16.9626	+	16.9626i	−0.744577	+	0.744577i
$520$		0			0
$521$	−14.8942	+	35.9578i	−0.652527	+	1.57534i	0.156573	+	0.987666i	$0.449955\pi$
$521$	−14.8942	+	35.9578i	−0.652527	+	1.57534i	−0.809099	+	0.587672i	$0.800045\pi$
$522$		0			0
$523$		−	29.2087i		−	1.27721i	−0.769536	−	0.638603i	$-0.779512\pi$
$523$		−	29.2087i		−	1.27721i	0.769536	−	0.638603i	$-0.220488\pi$
$524$		0			0
$525$	−4.02655	−	4.02655i	−0.175733	−	0.175733i
$526$		0			0
$527$	7.63367	−	27.8091i	0.332528	−	1.21138i
$528$		0			0
$529$	−11.8736	−	11.8736i	−0.516244	−	0.516244i
$530$		0			0
$531$			12.5849i			0.546139i
$532$		0			0
$533$	3.13953	−	7.57950i	0.135988	−	0.328304i
$534$		0			0
$535$	10.4743	−	10.4743i	0.452845	−	0.452845i
$536$		0			0
$537$	−22.3197	−	9.24513i	−0.963166	−	0.398957i
$538$		0			0
$539$	−5.54094	+	2.29513i	−0.238665	+	0.0988584i
$540$		0			0
$541$	5.71438	+	13.7957i	0.245680	+	0.593125i	0.997828	−	0.0658697i	$-0.0209822\pi$
$541$	5.71438	+	13.7957i	0.245680	+	0.593125i	−0.752148	+	0.658994i	$0.770982\pi$
$542$		0			0
$543$	12.1716			0.522332
$544$		0			0
$545$	7.17724			0.307439
$546$		0			0
$547$	−8.00943	−	19.3365i	−0.342458	−	0.826767i	−0.997466	−	0.0711452i	$-0.977335\pi$
$547$	−8.00943	−	19.3365i	−0.342458	−	0.826767i	0.655008	−	0.755622i	$-0.272665\pi$
$548$		0			0
$549$	2.52414	−	1.04553i	0.107728	−	0.0446223i
$550$		0			0
$551$	−7.15136	−	2.96219i	−0.304658	−	0.126194i
$552$		0			0
$553$	2.06358	−	2.06358i	0.0877523	−	0.0877523i
$554$		0			0
$555$	−4.42626	+	10.6859i	−0.187884	+	0.453592i
$556$		0			0
$557$			11.4512i			0.485203i	0.970126	+	0.242602i	$0.0780008\pi$
$557$			11.4512i			0.485203i	−0.970126	+	0.242602i	$0.921999\pi$
$558$		0			0
$559$	−4.68023	−	4.68023i	−0.197952	−	0.197952i
$560$		0			0
$561$	15.9329	+	12.3810i	0.672689	+	0.522728i
$562$		0			0
$563$	16.1023	+	16.1023i	0.678629	+	0.678629i	0.959690	−	0.281061i	$-0.0906862\pi$
$563$	16.1023	+	16.1023i	0.678629	+	0.678629i	−0.281061	+	0.959690i	$0.590686\pi$
$564$		0			0
$565$			37.9831i			1.59796i
$566$		0			0
$567$	−0.919595	+	2.22010i	−0.0386194	+	0.0932354i
$568$		0			0
$569$	−22.4856	+	22.4856i	−0.942644	+	0.942644i	−0.998442	−	0.0557985i	$-0.982230\pi$
$569$	−22.4856	+	22.4856i	−0.942644	+	0.942644i	0.0557985	+	0.998442i	$0.482230\pi$
$570$		0			0
$571$	36.9087	+	15.2881i	1.54458	+	0.639787i	0.982326	−	0.187176i	$-0.0599335\pi$
$571$	36.9087	+	15.2881i	1.54458	+	0.639787i	0.562256	+	0.826963i	$0.309933\pi$
$572$		0			0
$573$	3.02852	−	1.25445i	0.126518	−	0.0524055i
$574$		0			0
$575$	−5.72042	−	13.8103i	−0.238558	−	0.575930i
$576$		0			0
$577$	28.3973			1.18219			0.591097	−	0.806600i	$-0.298695\pi$
$577$	28.3973			1.18219			0.591097	+	0.806600i	$0.298695\pi$
$578$		0			0
$579$	−20.7506			−0.862366
$580$		0			0
$581$	3.80271	+	9.18055i	0.157763	+	0.380873i
$582$		0			0
$583$	−51.0181	+	21.1324i	−2.11295	+	0.875214i
$584$		0			0
$585$	−2.68491	−	1.11213i	−0.111007	−	0.0459808i
$586$		0			0
$587$	7.76184	−	7.76184i	0.320365	−	0.320365i	−0.528542	−	0.848907i	$-0.677261\pi$
$587$	7.76184	−	7.76184i	0.320365	−	0.320365i	0.848907	+	0.528542i	$0.177261\pi$
$588$		0			0
$589$	−6.10453	+	14.7376i	−0.251533	+	0.607254i
$590$		0			0
$591$			19.7142i			0.810933i
$592$		0			0
$593$	−2.22864	−	2.22864i	−0.0915194	−	0.0915194i	0.659865	−	0.751384i	$-0.270613\pi$
$593$	−2.22864	−	2.22864i	−0.0915194	−	0.0915194i	−0.751384	+	0.659865i	$0.770613\pi$
$594$		0			0
$595$	21.2386	+	16.5039i	0.870696	+	0.676594i
$596$		0			0
$597$	10.7866	+	10.7866i	0.441467	+	0.441467i
$598$		0			0
$599$			15.4176i			0.629945i	0.949101	+	0.314972i	$0.101995\pi$
$599$			15.4176i			0.629945i	−0.949101	+	0.314972i	$0.898005\pi$
$600$		0			0
$601$	8.10132	−	19.5583i	0.330460	−	0.797801i	−0.668096	−	0.744075i	$-0.732890\pi$
$601$	8.10132	−	19.5583i	0.330460	−	0.797801i	0.998556	−	0.0537256i	$-0.0171096\pi$
$602$		0			0
$603$	9.05182	−	9.05182i	0.368618	−	0.368618i
$604$		0			0
$605$	32.4793	+	13.4534i	1.32047	+	0.546957i
$606$		0			0
$607$	14.0086	−	5.80253i	0.568590	−	0.235518i	−0.0798199	−	0.996809i	$-0.525435\pi$
$607$	14.0086	−	5.80253i	0.568590	−	0.235518i	0.648409	+	0.761292i	$0.275435\pi$
$608$		0			0
$609$	−3.12101	−	7.53478i	−0.126470	−	0.305325i
$610$		0			0
$611$	8.77676			0.355070
$612$		0			0
$613$	43.4543			1.75510			0.877551	−	0.479484i	$-0.159176\pi$
$613$	43.4543			1.75510			0.877551	+	0.479484i	$0.159176\pi$
$614$		0			0
$615$	−7.96158	−	19.2210i	−0.321042	−	0.775064i
$616$		0			0
$617$	−36.3420	+	15.0534i	−1.46307	+	0.606025i	−0.965268	−	0.261263i	$-0.915861\pi$
$617$	−36.3420	+	15.0534i	−1.46307	+	0.606025i	−0.497807	+	0.867288i	$0.665861\pi$
$618$		0			0
$619$	−9.69556	−	4.01603i	−0.389697	−	0.161418i	0.179227	−	0.983808i	$-0.442640\pi$
$619$	−9.69556	−	4.01603i	−0.389697	−	0.161418i	−0.568924	+	0.822390i	$0.692640\pi$
$620$		0			0
$621$	−4.46048	+	4.46048i	−0.178993	+	0.178993i
$622$		0			0
$623$	2.72783	−	6.58557i	0.109288	−	0.263845i
$624$		0			0
$625$			31.2330i			1.24932i
$626$		0			0
$627$	−7.89246	−	7.89246i	−0.315194	−	0.315194i
$628$		0			0
$629$	4.65017	−	16.9403i	0.185414	−	0.675455i
$630$		0			0
$631$	32.2236	+	32.2236i	1.28280	+	1.28280i	0.939067	+	0.343734i	$0.111692\pi$
$631$	32.2236	+	32.2236i	1.28280	+	1.28280i	0.343734	+	0.939067i	$0.388308\pi$
$632$		0			0
$633$			12.5159i			0.497460i
$634$		0			0
$635$	15.1074	−	36.4725i	0.599519	−	1.44737i
$636$		0			0
$637$	−0.927666	+	0.927666i	−0.0367555	+	0.0367555i
$638$		0			0
$639$	−3.92615	−	1.62627i	−0.155316	−	0.0643341i
$640$		0			0
$641$	13.8538	−	5.73842i	0.547191	−	0.226654i	−0.0919230	−	0.995766i	$-0.529301\pi$
$641$	13.8538	−	5.73842i	0.547191	−	0.226654i	0.639114	+	0.769112i	$0.279301\pi$
$642$		0			0
$643$	−7.89107	−	19.0507i	−0.311193	−	0.751287i	−0.999661	−	0.0260206i	$-0.991716\pi$
$643$	−7.89107	−	19.0507i	−0.311193	−	0.751287i	0.688468	−	0.725267i	$-0.258284\pi$
$644$		0			0
$645$	−16.7848			−0.660901
$646$		0			0
$647$	−26.8160			−1.05424			−0.527122	−	0.849790i	$-0.676729\pi$
$647$	−26.8160			−1.05424			−0.527122	+	0.849790i	$0.676729\pi$
$648$		0			0
$649$	−23.5690	−	56.9007i	−0.925166	−	2.23355i
$650$		0			0
$651$	−15.5278	+	6.43182i	−0.608582	+	0.252083i
$652$		0			0
$653$	−12.6601	−	5.24399i	−0.495428	−	0.205213i	0.120957	−	0.992658i	$-0.461404\pi$
$653$	−12.6601	−	5.24399i	−0.495428	−	0.205213i	−0.616385	+	0.787445i	$0.711404\pi$
$654$		0			0
$655$	−4.63504	+	4.63504i	−0.181106	+	0.181106i
$656$		0			0
$657$	3.92518	−	9.47623i	0.153136	−	0.369703i
$658$		0			0
$659$		−	20.2130i		−	0.787388i	−0.919241	−	0.393694i	$-0.871197\pi$
$659$		−	20.2130i		−	0.787388i	0.919241	−	0.393694i	$-0.128803\pi$
$660$		0			0
$661$	5.04254	+	5.04254i	0.196132	+	0.196132i	0.798340	−	0.602208i	$-0.205712\pi$
$661$	5.04254	+	5.04254i	0.196132	+	0.196132i	−0.602208	+	0.798340i	$0.705712\pi$
$662$		0			0
$663$	4.25637	+	1.16839i	0.165304	+	0.0453763i
$664$		0			0
$665$	−10.5206	−	10.5206i	−0.407972	−	0.407972i
$666$		0			0
$667$		−	21.4089i		−	0.828957i
$668$		0			0
$669$	−2.88072	+	6.95468i	−0.111375	+	0.268883i
$670$		0			0
$671$	−9.45443	+	9.45443i	−0.364984	+	0.364984i
$672$		0			0
$673$	−34.6300	−	14.3442i	−1.33489	−	0.552929i	−0.402844	−	0.915269i	$-0.631978\pi$
$673$	−34.6300	−	14.3442i	−1.33489	−	0.552929i	−0.932046	+	0.362339i	$0.881978\pi$
$674$		0			0
$675$	−2.18931	+	0.906841i	−0.0842665	+	0.0349043i
$676$		0			0
$677$	14.0912	+	34.0193i	0.541571	+	1.30747i	0.923614	+	0.383323i	$0.125220\pi$
$677$	14.0912	+	34.0193i	0.541571	+	1.30747i	−0.382044	+	0.924144i	$0.624780\pi$
$678$		0			0
$679$	−43.8681			−1.68350
$680$		0			0
$681$	−4.80718			−0.184212
$682$		0			0
$683$	−6.42199	−	15.5041i	−0.245731	−	0.593246i	0.752102	−	0.659047i	$-0.229040\pi$
$683$	−6.42199	−	15.5041i	−0.245731	−	0.593246i	−0.997833	+	0.0658003i	$0.979040\pi$
$684$		0			0
$685$	3.56609	−	1.47712i	0.136253	−	0.0564379i
$686$		0			0
$687$	−12.3827	−	5.12909i	−0.472430	−	0.195687i
$688$		0			0
$689$	−8.54146	+	8.54146i	−0.325404	+	0.325404i
$690$		0			0
$691$	−5.24785	+	12.6694i	−0.199638	+	0.481968i	−0.991716	−	0.128452i	$-0.958999\pi$
$691$	−5.24785	+	12.6694i	−0.199638	+	0.481968i	0.792078	+	0.610420i	$0.208999\pi$
$692$		0			0
$693$		−	11.7600i		−	0.446727i
$694$		0			0
$695$	29.8172	+	29.8172i	1.13103	+	1.13103i
$696$		0			0
$697$	15.6316	+	27.4606i	0.592091	+	1.04014i
$698$		0			0
$699$	9.74356	+	9.74356i	0.368535	+	0.368535i
$700$		0			0
$701$			11.5629i			0.436724i	0.975868	+	0.218362i	$0.0700713\pi$
$701$			11.5629i			0.436724i	−0.975868	+	0.218362i	$0.929929\pi$
$702$		0			0
$703$	−3.71867	+	8.97766i	−0.140252	+	0.338599i
$704$		0			0
$705$	15.7381	−	15.7381i	0.592733	−	0.592733i
$706$		0			0
$707$	20.0809	+	8.31776i	0.755218	+	0.312822i
$708$		0			0
$709$	−13.9142	+	5.76346i	−0.522560	+	0.216451i	−0.628341	−	0.777938i	$-0.716266\pi$
$709$	−13.9142	+	5.76346i	−0.522560	+	0.216451i	0.105781	+	0.994389i	$0.466266\pi$
$710$		0			0
$711$	−0.464750	−	1.12200i	−0.0174295	−	0.0420785i
$712$		0			0
$713$	−44.1199			−1.65230
$714$		0			0
$715$	14.2222			0.531880
$716$		0			0
$717$	6.50793	+	15.7115i	0.243043	+	0.586758i
$718$		0			0
$719$	−1.76251	+	0.730055i	−0.0657305	+	0.0272264i	−0.415306	−	0.909682i	$-0.636326\pi$
$719$	−1.76251	+	0.730055i	−0.0657305	+	0.0272264i	0.349576	+	0.936908i	$0.386326\pi$
$720$		0			0
$721$	−4.96342	−	2.05592i	−0.184847	−	0.0765663i
$722$		0			0
$723$	13.7118	−	13.7118i	0.509947	−	0.509947i
$724$		0			0
$725$	3.07772	−	7.43027i	0.114304	−	0.275953i
$726$		0			0
$727$			4.61649i			0.171216i	0.996329	+	0.0856082i	$0.0272833\pi$
$727$			4.61649i			0.171216i	−0.996329	+	0.0856082i	$0.972717\pi$
$728$		0			0
$729$	0.707107	+	0.707107i	0.0261891	+	0.0261891i
$730$		0			0
$731$	25.2945	−	3.17311i	0.935550	−	0.117362i
$732$		0			0
$733$	4.76113	+	4.76113i	0.175856	+	0.175856i	0.789547	−	0.613691i	$-0.210316\pi$
$733$	4.76113	+	4.76113i	0.175856	+	0.175856i	−0.613691	+	0.789547i	$0.710316\pi$
$734$		0			0
$735$			3.32691i			0.122715i
$736$		0			0
$737$	−23.9741	+	57.8786i	−0.883097	+	2.13199i
$738$		0			0
$739$	−6.49918	+	6.49918i	−0.239076	+	0.239076i	−0.816468	−	0.577391i	$-0.804071\pi$
$739$	−6.49918	+	6.49918i	−0.239076	+	0.239076i	0.577391	+	0.816468i	$0.304071\pi$
$740$		0			0
$741$	−2.25570	−	0.934340i	−0.0828651	−	0.0343238i
$742$		0			0
$743$	−7.90655	+	3.27500i	−0.290063	+	0.120148i	−0.522970	−	0.852351i	$-0.675176\pi$
$743$	−7.90655	+	3.27500i	−0.290063	+	0.120148i	0.232907	+	0.972499i	$0.425176\pi$
$744$		0			0
$745$	16.8703	+	40.7286i	0.618081	+	1.49218i
$746$		0			0
$747$	4.13520			0.151299
$748$		0			0
$749$	13.1122			0.479108
$750$		0			0
$751$	−3.59617	−	8.68192i	−0.131226	−	0.316808i	0.844586	−	0.535420i	$-0.179847\pi$
$751$	−3.59617	−	8.68192i	−0.131226	−	0.316808i	−0.975812	+	0.218613i	$0.929847\pi$
$752$		0			0
$753$	−19.8926	+	8.23980i	−0.724928	+	0.300275i
$754$		0			0
$755$	8.81554	+	3.65151i	0.320830	+	0.132892i
$756$		0			0
$757$	−30.9701	+	30.9701i	−1.12563	+	1.12563i	−0.134750	+	0.990880i	$0.543023\pi$
$757$	−30.9701	+	30.9701i	−1.12563	+	1.12563i	−0.990880	+	0.134750i	$0.956977\pi$
$758$		0			0
$759$	11.8138	−	28.5210i	0.428813	−	1.03525i
$760$		0			0
$761$		−	7.85599i		−	0.284779i	−0.989811	−	0.142390i	$-0.954521\pi$
$761$		−	7.85599i		−	0.284779i	0.989811	−	0.142390i	$-0.0454786\pi$
$762$		0			0
$763$	4.49236	+	4.49236i	0.162634	+	0.162634i
$764$		0			0
$765$	9.72746	−	5.53725i	0.351697	−	0.200200i
$766$		0			0
$767$	−9.52632	−	9.52632i	−0.343976	−	0.343976i
$768$		0			0
$769$		−	33.7233i		−	1.21609i	−0.793901	−	0.608047i	$-0.791953\pi$
$769$		−	33.7233i		−	1.21609i	0.793901	−	0.608047i	$-0.208047\pi$
$770$		0			0
$771$	−7.31670	+	17.6641i	−0.263505	+	0.636156i
$772$		0			0
$773$	19.9064	−	19.9064i	0.715983	−	0.715983i	−0.251797	−	0.967780i	$-0.581022\pi$
$773$	19.9064	−	19.9064i	0.715983	−	0.715983i	0.967780	+	0.251797i	$0.0810215\pi$
$774$		0			0
$775$	−15.3124	−	6.34261i	−0.550038	−	0.227833i
$776$		0			0
$777$	−9.45899	+	3.91804i	−0.339339	+	0.140559i
$778$		0			0
$779$	−6.68883	−	16.1483i	−0.239652	−	0.578571i
$780$		0			0
$781$	20.7971			0.744180
$782$		0			0
$783$	−3.39389			−0.121288
$784$		0			0
$785$	−22.2220	−	53.6488i	−0.793139	−	1.91481i
$786$		0			0
$787$	−31.9518	+	13.2349i	−1.13896	+	0.471772i	−0.870817	−	0.491608i	$-0.836409\pi$
$787$	−31.9518	+	13.2349i	−1.13896	+	0.471772i	−0.268141	+	0.963380i	$0.586409\pi$
$788$		0			0
$789$	−10.2428	−	4.24272i	−0.364654	−	0.151045i
$790$		0			0
$791$	−23.7743	+	23.7743i	−0.845317	+	0.845317i
$792$		0			0
$793$	−1.11925	+	2.70211i	−0.0397458	+	0.0959549i
$794$		0			0
$795$			30.6324i			1.08642i
$796$		0			0
$797$	31.8112	+	31.8112i	1.12681	+	1.12681i	0.990692	+	0.136119i	$0.0434630\pi$
$797$	31.8112	+	31.8112i	1.12681	+	1.12681i	0.136119	+	0.990692i	$0.456537\pi$
$798$		0			0
$799$	−20.7419	+	26.6924i	−0.733797	+	0.944310i
$800$		0			0
$801$	−2.09752	−	2.09752i	−0.0741122	−	0.0741122i
$802$		0			0
$803$			50.1964i			1.77139i
$804$		0			0
$805$	15.7477	−	38.0184i	0.555035	−	1.33997i
$806$		0			0
$807$	−3.12922	+	3.12922i	−0.110154	+	0.110154i
$808$		0			0
$809$	28.7452	+	11.9066i	1.01063	+	0.418615i	0.825683	−	0.564134i	$-0.190790\pi$
$809$	28.7452	+	11.9066i	1.01063	+	0.418615i	0.184943	+	0.982749i	$0.440790\pi$
$810$		0			0
$811$	−44.6958	+	18.5136i	−1.56948	+	0.650101i	−0.986704	−	0.162529i	$-0.948035\pi$
$811$	−44.6958	+	18.5136i	−1.56948	+	0.650101i	−0.582779	+	0.812631i	$0.698035\pi$
$812$		0			0
$813$	−6.21770	−	15.0108i	−0.218064	−	0.526453i
$814$		0			0
$815$	53.9495			1.88977
$816$		0			0
$817$	−14.1016			−0.493351
$818$		0			0
$819$	−0.984434	−	2.37663i	−0.0343989	−	0.0830463i
$820$		0			0
$821$	−21.2625	+	8.80722i	−0.742067	+	0.307374i	−0.721500	−	0.692414i	$-0.756547\pi$
$821$	−21.2625	+	8.80722i	−0.742067	+	0.307374i	−0.0205669	+	0.999788i	$0.506547\pi$
$822$		0			0
$823$	−10.0413	−	4.15925i	−0.350018	−	0.144982i	0.200746	−	0.979643i	$-0.435664\pi$
$823$	−10.0413	−	4.15925i	−0.350018	−	0.144982i	−0.550764	+	0.834661i	$0.685664\pi$
$824$		0			0
$825$	8.20027	−	8.20027i	0.285497	−	0.285497i
$826$		0			0
$827$	−12.2934	+	29.6790i	−0.427485	+	1.03204i	0.552598	+	0.833448i	$0.313637\pi$
$827$	−12.2934	+	29.6790i	−0.427485	+	1.03204i	−0.980082	+	0.198591i	$0.936363\pi$
$828$		0			0
$829$			21.0657i			0.731642i	0.930685	+	0.365821i	$0.119212\pi$
$829$			21.0657i			0.731642i	−0.930685	+	0.365821i	$0.880788\pi$
$830$		0			0
$831$	−0.453033	−	0.453033i	−0.0157155	−	0.0157155i
$832$		0			0
$833$	−0.628942	−	5.01361i	−0.0217915	−	0.173711i
$834$		0			0
$835$	15.2374	+	15.2374i	0.527313	+	0.527313i
$836$		0			0
$837$			6.99418i			0.241754i
$838$		0			0
$839$	16.3781	−	39.5402i	0.565435	−	1.36508i	−0.339932	−	0.940450i	$-0.610404\pi$
$839$	16.3781	−	39.5402i	0.565435	−	1.36508i	0.905367	−	0.424631i	$-0.139596\pi$
$840$		0			0
$841$	−12.3613	+	12.3613i	−0.426251	+	0.426251i
$842$		0			0
$843$	0.0680922	+	0.0282047i	0.00234522	+	0.000971422i
$844$		0			0
$845$	−29.7307	+	12.3149i	−1.02277	+	0.423644i
$846$		0			0
$847$	11.9087	+	28.7500i	0.409186	+	0.987863i
$848$		0			0
$849$	20.4573			0.702094
$850$		0			0
$851$	−26.8763			−0.921307
$852$		0			0
$853$	5.75449	+	13.8926i	0.197030	+	0.475673i	0.991256	−	0.131949i	$-0.0421236\pi$
$853$	5.75449	+	13.8926i	0.197030	+	0.475673i	−0.794226	+	0.607622i	$0.792124\pi$
$854$		0			0
$855$	−5.72025	+	2.36941i	−0.195629	+	0.0810320i
$856$		0			0
$857$	11.2462	+	4.65833i	0.384163	+	0.159126i	0.566403	−	0.824129i	$-0.308335\pi$
$857$	11.2462	+	4.65833i	0.384163	+	0.159126i	−0.182240	+	0.983254i	$0.558335\pi$
$858$		0			0
$859$	−9.12775	+	9.12775i	−0.311435	+	0.311435i	−0.845465	−	0.534030i	$-0.820677\pi$
$859$	−9.12775	+	9.12775i	−0.311435	+	0.311435i	0.534030	+	0.845465i	$0.320677\pi$
$860$		0			0
$861$	7.04744	−	17.0140i	0.240176	−	0.579837i
$862$		0			0
$863$			21.4811i			0.731226i	0.930767	+	0.365613i	$0.119141\pi$
$863$			21.4811i			0.731226i	−0.930767	+	0.365613i	$0.880859\pi$
$864$		0			0
$865$	−46.0488	−	46.0488i	−1.56571	−	1.56571i
$866$		0			0
$867$	−13.6124	+	10.1835i	−0.462300	+	0.345850i
$868$		0			0
$869$	4.20258	+	4.20258i	0.142563	+	0.142563i
$870$		0			0
$871$			13.7038i			0.464335i
$872$		0			0
$873$	−6.98605	+	16.8658i	−0.236442	+	0.570822i
$874$		0			0
$875$	−12.1332	+	12.1332i	−0.410175	+	0.410175i
$876$		0			0
$877$	−47.3960	−	19.6321i	−1.60045	−	0.662928i	−0.608971	−	0.793192i	$-0.708417\pi$
$877$	−47.3960	−	19.6321i	−1.60045	−	0.662928i	−0.991479	+	0.130264i	$0.958417\pi$
$878$		0			0
$879$	7.28753	−	3.01859i	0.245802	−	0.101815i
$880$		0			0
$881$	−15.5491	−	37.5388i	−0.523861	−	1.26471i	−0.935487	−	0.353361i	$-0.885039\pi$
$881$	−15.5491	−	37.5388i	−0.523861	−	1.26471i	0.411626	−	0.911353i	$-0.364961\pi$
$882$		0			0
$883$	−3.59541			−0.120995			−0.0604975	−	0.998168i	$-0.519269\pi$
$883$	−3.59541			−0.120995			−0.0604975	+	0.998168i	$0.519269\pi$
$884$		0			0
$885$	−34.1645			−1.14843
$886$		0			0
$887$	15.3637	+	37.0913i	0.515864	+	1.24540i	0.940424	+	0.340005i	$0.110429\pi$
$887$	15.3637	+	37.0913i	0.515864	+	1.24540i	−0.424560	+	0.905400i	$0.639571\pi$
$888$		0			0
$889$	32.2848	−	13.3728i	1.08280	−	0.448509i
$890$		0			0
$891$	−4.52134	−	1.87280i	−0.151471	−	0.0627412i
$892$		0			0
$893$	13.2222	−	13.2222i	0.442465	−	0.442465i
$894$		0			0
$895$	25.0979	−	60.5917i	0.838930	−	2.02536i
$896$		0			0
$897$		−	6.75285i		−	0.225471i
$898$		0			0
$899$	−16.7850	−	16.7850i	−0.559810	−	0.559810i
$900$		0			0
$901$	−5.79096	−	46.1627i	−0.192925	−	1.53790i
$902$		0			0
$903$	−10.5059	−	10.5059i	−0.349615	−	0.349615i
$904$		0			0
$905$			33.0423i			1.09836i
$906$		0			0
$907$	−16.9424	+	40.9026i	−0.562563	+	1.35815i	0.345147	+	0.938549i	$0.387829\pi$
$907$	−16.9424	+	40.9026i	−0.562563	+	1.35815i	−0.907710	+	0.419599i	$0.862171\pi$
$908$		0			0
$909$	6.39580	−	6.39580i	0.212135	−	0.212135i
$910$		0			0
$911$	−8.08964	−	3.35084i	−0.268022	−	0.111018i	0.244625	−	0.969618i	$-0.421335\pi$
$911$	−8.08964	−	3.35084i	−0.268022	−	0.111018i	−0.512647	+	0.858599i	$0.671335\pi$
$912$		0			0
$913$	−18.6966	+	7.74440i	−0.618768	+	0.256302i
$914$		0			0
$915$	2.83833	+	6.85233i	0.0938323	+	0.226531i
$916$		0			0
$917$	−5.80230			−0.191609
$918$		0			0
$919$	32.6562			1.07723			0.538615	−	0.842552i	$-0.318948\pi$
$919$	32.6562			1.07723			0.538615	+	0.842552i	$0.318948\pi$
$920$		0			0
$921$	1.77548	+	4.28638i	0.0585039	+	0.141241i
$922$		0			0
$923$	4.20298	−	1.74093i	0.138343	−	0.0573034i
$924$		0			0
$925$	−9.32780	−	3.86370i	−0.306696	−	0.127038i
$926$		0			0
$927$	−1.58086	+	1.58086i	−0.0519223	+	0.0519223i
$928$		0			0
$929$	−18.8006	+	45.3888i	−0.616829	+	1.48916i	0.238537	+	0.971133i	$0.423332\pi$
$929$	−18.8006	+	45.3888i	−0.616829	+	1.48916i	−0.855366	+	0.518024i	$0.826668\pi$
$930$		0			0
$931$			2.79506i			0.0916045i
$932$		0			0
$933$	3.95612	+	3.95612i	0.129518	+	0.129518i
$934$		0			0
$935$	−33.6110	+	43.2534i	−1.09920	+	1.41454i
$936$		0			0
$937$	28.6009	+	28.6009i	0.934352	+	0.934352i	0.997974	−	0.0636224i	$-0.0202653\pi$
$937$	28.6009	+	28.6009i	0.934352	+	0.934352i	−0.0636224	+	0.997974i	$0.520265\pi$
$938$		0			0
$939$			0.877026i			0.0286207i
$940$		0			0
$941$	1.10983	−	2.67938i	0.0361796	−	0.0873452i	−0.904757	−	0.425928i	$-0.859948\pi$
$941$	1.10983	−	2.67938i	0.0361796	−	0.0873452i	0.940937	+	0.338583i	$0.109948\pi$
$942$		0			0
$943$	34.1835	−	34.1835i	1.11317	−	1.11317i
$944$		0			0
$945$	−6.02694	−	2.49644i	−0.196056	−	0.0812092i
$946$		0			0
$947$	41.7742	−	17.3034i	1.35748	−	0.562286i	0.419114	−	0.907934i	$-0.362341\pi$
$947$	41.7742	−	17.3034i	1.35748	−	0.562286i	0.938364	+	0.345648i	$0.112341\pi$
$948$		0			0
$949$	4.20194	+	10.1444i	0.136401	+	0.329301i
$950$		0			0
$951$	29.7514			0.964756
$952$		0			0
$953$	17.8145			0.577069			0.288534	−	0.957470i	$-0.406832\pi$
$953$	17.8145			0.577069			0.288534	+	0.957470i	$0.406832\pi$
$954$		0			0
$955$	3.40549	+	8.22157i	0.110199	+	0.266044i
$956$		0			0
$957$	15.3449	−	6.35608i	0.496032	−	0.205463i
$958$		0			0
$959$	3.15663	+	1.30752i	0.101933	+	0.0422221i
$960$		0			0
$961$	−12.6704	+	12.6704i	−0.408722	+	0.408722i
$962$		0			0
$963$	2.08813	−	5.04118i	0.0672889	−	0.162450i
$964$		0			0
$965$		−	56.3320i		−	1.81339i
$966$		0			0
$967$	−19.1664	−	19.1664i	−0.616349	−	0.616349i	0.328244	−	0.944593i	$-0.393543\pi$
$967$	−19.1664	−	19.1664i	−0.616349	−	0.616349i	−0.944593	+	0.328244i	$0.893543\pi$
$968$		0			0
$969$	8.17241	−	4.65206i	0.262536	−	0.149446i
$970$		0			0
$971$	−1.02700	−	1.02700i	−0.0329582	−	0.0329582i	0.690436	−	0.723394i	$-0.257419\pi$
$971$	−1.02700	−	1.02700i	−0.0329582	−	0.0329582i	−0.723394	+	0.690436i	$0.757419\pi$
$972$		0			0
$973$			37.3262i			1.19662i
$974$		0			0
$975$	0.970780	−	2.34367i	0.0310898	−	0.0750575i
$976$		0			0
$977$	34.2951	−	34.2951i	1.09720	−	1.09720i	0.102462	−	0.994737i	$-0.467328\pi$
$977$	34.2951	−	34.2951i	1.09720	−	1.09720i	0.994737	−	0.102462i	$-0.0326720\pi$
$978$		0			0
$979$	13.4118	+	5.55536i	0.428644	+	0.177550i
$980$		0			0
$981$	2.44258	−	1.01175i	0.0779854	−	0.0323026i
$982$		0			0
$983$	−6.76821	−	16.3399i	−0.215872	−	0.521162i	0.778433	−	0.627727i	$-0.216015\pi$
$983$	−6.76821	−	16.3399i	−0.215872	−	0.521162i	−0.994306	+	0.106565i	$0.966015\pi$
$984$		0			0
$985$	−53.5184			−1.70524
$986$		0			0
$987$	19.7016			0.627108
$988$		0			0
$989$	−14.9255	−	36.0333i	−0.474603	−	1.14579i
$990$		0			0
$991$	26.3051	−	10.8959i	0.835610	−	0.346121i	0.0764888	−	0.997070i	$-0.475629\pi$
$991$	26.3051	−	10.8959i	0.835610	−	0.346121i	0.759121	+	0.650950i	$0.225629\pi$
$992$		0			0
$993$	10.6934	+	4.42935i	0.339345	+	0.140561i
$994$		0			0
$995$	−29.2826	+	29.2826i	−0.928322	+	0.928322i
$996$		0			0
$997$	−4.92753	+	11.8961i	−0.156056	+	0.376753i	−0.982499	−	0.186267i	$-0.940361\pi$
$997$	−4.92753	+	11.8961i	−0.156056	+	0.376753i	0.826443	+	0.563021i	$0.190361\pi$
$998$		0			0
$999$			4.26062i			0.134800i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	816.2.bq.f.49.3		16
4.3	odd	2		408.2.ba.a.49.1	yes	16
12.11	even	2		1224.2.bq.e.865.4		16
17.8	even	8	inner	816.2.bq.f.433.3		16
68.39	even	16		6936.2.a.bo.1.7		8
68.59	odd	8		408.2.ba.a.25.1	✓	16
68.63	even	16		6936.2.a.bl.1.2		8
204.59	even	8		1224.2.bq.e.433.4		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
408.2.ba.a.25.1	✓	16	68.59	odd	8
408.2.ba.a.49.1	yes	16	4.3	odd	2
816.2.bq.f.49.3		16	1.1	even	1	trivial
816.2.bq.f.433.3		16	17.8	even	8	inner
1224.2.bq.e.433.4		16	204.59	even	8
1224.2.bq.e.865.4		16	12.11	even	2
6936.2.a.bl.1.2		8	68.63	even	16
6936.2.a.bo.1.7		8	68.39	even	16

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:	\( N \)	\(=\)	\( 816 = 2^{4} \cdot 3 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	816.bq (of order \(8\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.382683 + 0.923880i) q^{3} +(-2.50807 + 1.03888i) q^{5} +(-2.22010 - 0.919595i) q^{7} +(-0.707107 + 0.707107i) q^{9} +(1.87280 - 4.52134i) q^{11} -1.07051i q^{13} +(-1.91959 - 1.91959i) q^{15} +(3.25570 + 2.52991i) q^{17} +(-1.61272 - 1.61272i) q^{19} -2.40302i q^{21} +(2.41400 - 5.82790i) q^{23} +(1.67562 - 1.67562i) q^{25} +(-0.923880 - 0.382683i) q^{27} +(3.13555 - 1.29879i) q^{29} +(-2.67656 - 6.46178i) q^{31} +4.89386 q^{33} +6.52351 q^{35} +(-1.63047 - 3.93630i) q^{37} +(0.989020 - 0.409666i) q^{39} +(7.08028 + 2.93275i) q^{41} +(4.37197 - 4.37197i) q^{43} +(1.03888 - 2.50807i) q^{45} +8.19868i q^{47} +(-0.866566 - 0.866566i) q^{49} +(-1.09143 + 3.97603i) q^{51} +(-7.97888 - 7.97888i) q^{53} +13.2855i q^{55} +(0.872800 - 2.10713i) q^{57} +(8.89888 - 8.89888i) q^{59} +(-2.52414 - 1.04553i) q^{61} +(2.22010 - 0.919595i) q^{63} +(1.11213 + 2.68491i) q^{65} -12.8012 q^{67} +6.30808 q^{69} +(1.62627 + 3.92615i) q^{71} +(-9.47623 + 3.92518i) q^{73} +(2.18931 + 0.906841i) q^{75} +(-8.31560 + 8.31560i) q^{77} +(-0.464750 + 1.12200i) q^{79} -1.00000i q^{81} +(-2.92403 - 2.92403i) q^{83} +(-10.7938 - 2.96293i) q^{85} +(2.39984 + 2.39984i) q^{87} +2.96634i q^{89} +(-0.984434 + 2.37663i) q^{91} +(4.94563 - 4.94563i) q^{93} +(5.72025 + 2.36941i) q^{95} +(16.8658 - 6.98605i) q^{97} +(1.87280 + 4.52134i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 8 q^{11} - 8 q^{15} + 8 q^{19} + 8 q^{23} - 8 q^{25} + 32 q^{29} - 8 q^{31} - 8 q^{33} - 16 q^{35} + 8 q^{37} + 8 q^{39} + 40 q^{41} + 24 q^{43} + 8 q^{45} + 24 q^{49} - 8 q^{51} - 24 q^{53} - 8 q^{57}+ \cdots + 8 q^{99}+O(q^{100}) \) 16 * q + 8 * q^11 - 8 * q^15 + 8 * q^19 + 8 * q^23 - 8 * q^25 + 32 * q^29 - 8 * q^31 - 8 * q^33 - 16 * q^35 + 8 * q^37 + 8 * q^39 + 40 * q^41 + 24 * q^43 + 8 * q^45 + 24 * q^49 - 8 * q^51 - 24 * q^53 - 8 * q^57 + 16 * q^59 - 64 * q^65 - 8 * q^69 + 16 * q^71 + 24 * q^73 + 96 * q^79 - 32 * q^85 - 16 * q^87 + 24 * q^93 + 8 * q^95 + 56 * q^97 + 8 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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