LMFDB - Embedded newform 968.2.i.j.81.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [968,2,Mod(9,968)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(968, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 0, 6]))

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

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

chi := DirichletCharacter("968.9");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 968 = 2^{3} \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	968.i (of order $5$, 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:	$7.72951891566$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\zeta_{10})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + x^{2} - x + 1 $ x^4 - x^3 + x^2 - x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 88)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			81.1
Root			$0.809017 - 0.587785i$ of defining polynomial
Character	$\chi$	$=$	968.81
Dual form			968.2.i.j.729.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.927051 + 2.85317i) q^{3} +(2.42705 - 1.76336i) q^{5} +(-0.618034 - 1.90211i) q^{7} +(-4.85410 - 3.52671i) q^{9} +O(q^{10})$	\(q+(-0.927051 + 2.85317i) q^{3} +(2.42705 - 1.76336i) q^{5} +(-0.618034 - 1.90211i) q^{7} +(-4.85410 - 3.52671i) q^{9} +(2.78115 + 8.55951i) q^{15} +(4.85410 - 3.52671i) q^{17} +(1.23607 - 3.80423i) q^{19} +6.00000 q^{21} +1.00000 q^{23} +(1.23607 - 3.80423i) q^{25} +(7.28115 - 5.29007i) q^{27} +(-2.47214 - 7.60845i) q^{29} +(5.66312 + 4.11450i) q^{31} +(-4.85410 - 3.52671i) q^{35} +(-0.309017 - 0.951057i) q^{37} +(1.23607 - 3.80423i) q^{41} +6.00000 q^{43} -18.0000 q^{45} +(-2.47214 + 7.60845i) q^{47} +(2.42705 - 1.76336i) q^{49} +(5.56231 + 17.1190i) q^{51} +(-1.61803 - 1.17557i) q^{53} +(9.70820 + 7.05342i) q^{57} +(-0.309017 - 0.951057i) q^{59} +(-3.23607 + 2.35114i) q^{61} +(-3.70820 + 11.4127i) q^{63} -5.00000 q^{67} +(-0.927051 + 2.85317i) q^{69} +(-2.42705 + 1.76336i) q^{71} +(4.94427 + 15.2169i) q^{73} +(9.70820 + 7.05342i) q^{75} +(-1.61803 - 1.17557i) q^{79} +(2.78115 + 8.55951i) q^{81} +(1.61803 - 1.17557i) q^{83} +(5.56231 - 17.1190i) q^{85} +24.0000 q^{87} +15.0000 q^{89} +(-16.9894 + 12.3435i) q^{93} +(-3.70820 - 11.4127i) q^{95} +(5.66312 + 4.11450i) q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 3 q^{3} + 3 q^{5} + 2 q^{7} - 6 q^{9}+O(q^{10}) $ 4 * q + 3 * q^3 + 3 * q^5 + 2 * q^7 - 6 * q^9	$ 4 q + 3 q^{3} + 3 q^{5} + 2 q^{7} - 6 q^{9} - 9 q^{15} + 6 q^{17} - 4 q^{19} + 24 q^{21} + 4 q^{23} - 4 q^{25} + 9 q^{27} + 8 q^{29} + 7 q^{31} - 6 q^{35} + q^{37} - 4 q^{41} + 24 q^{43} - 72 q^{45} + 8 q^{47} + 3 q^{49} - 18 q^{51} - 2 q^{53} + 12 q^{57} + q^{59} - 4 q^{61} + 12 q^{63} - 20 q^{67} + 3 q^{69} - 3 q^{71} - 16 q^{73} + 12 q^{75} - 2 q^{79} - 9 q^{81} + 2 q^{83} - 18 q^{85} + 96 q^{87} + 60 q^{89} - 21 q^{93} + 12 q^{95} + 7 q^{97}+O(q^{100}) $ 4 * q + 3 * q^3 + 3 * q^5 + 2 * q^7 - 6 * q^9 - 9 * q^15 + 6 * q^17 - 4 * q^19 + 24 * q^21 + 4 * q^23 - 4 * q^25 + 9 * q^27 + 8 * q^29 + 7 * q^31 - 6 * q^35 + q^37 - 4 * q^41 + 24 * q^43 - 72 * q^45 + 8 * q^47 + 3 * q^49 - 18 * q^51 - 2 * q^53 + 12 * q^57 + q^59 - 4 * q^61 + 12 * q^63 - 20 * q^67 + 3 * q^69 - 3 * q^71 - 16 * q^73 + 12 * q^75 - 2 * q^79 - 9 * q^81 + 2 * q^83 - 18 * q^85 + 96 * q^87 + 60 * q^89 - 21 * q^93 + 12 * q^95 + 7 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/968\mathbb{Z}\right)^\times$.

$n$	$485$	$727$	$849$
$\chi(n)$	$1$	$1$	$e\left(\frac{1}{5}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−0.927051	+	2.85317i	−0.535233	+	1.64728i	0.207912	+	0.978148i	$0.433333\pi$
$3$	−0.927051	+	2.85317i	−0.535233	+	1.64728i	−0.743145	+	0.669131i	$0.766667\pi$
$4$		0			0
$5$	2.42705	−	1.76336i	1.08541	−	0.788597i	0.106792	−	0.994281i	$-0.465942\pi$
$5$	2.42705	−	1.76336i	1.08541	−	0.788597i	0.978618	+	0.205685i	$0.0659421\pi$
$6$		0			0
$7$	−0.618034	−	1.90211i	−0.233595	−	0.718931i	−0.997305	−	0.0733714i	$-0.976624\pi$
$7$	−0.618034	−	1.90211i	−0.233595	−	0.718931i	0.763710	−	0.645560i	$-0.223376\pi$
$8$		0			0
$9$	−4.85410	−	3.52671i	−1.61803	−	1.17557i
$10$		0			0
$11$		0			0
$11$		0			0
$12$		0			0
$13$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$13$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$14$		0			0
$15$	2.78115	+	8.55951i	0.718091	+	2.21006i
$16$		0			0
$17$	4.85410	−	3.52671i	1.17729	−	0.855353i	0.185429	−	0.982658i	$-0.440633\pi$
$17$	4.85410	−	3.52671i	1.17729	−	0.855353i	0.991864	+	0.127304i	$0.0406325\pi$
$18$		0			0
$19$	1.23607	−	3.80423i	0.283573	−	0.872749i	−0.703249	−	0.710943i	$-0.748268\pi$
$19$	1.23607	−	3.80423i	0.283573	−	0.872749i	0.986823	−	0.161806i	$-0.0517318\pi$
$20$		0			0
$21$	6.00000			1.30931
$22$		0			0
$23$	1.00000			0.208514			0.104257	−	0.994550i	$-0.466753\pi$
$23$	1.00000			0.208514			0.104257	+	0.994550i	$0.466753\pi$
$24$		0			0
$25$	1.23607	−	3.80423i	0.247214	−	0.760845i
$26$		0			0
$27$	7.28115	−	5.29007i	1.40126	−	1.01807i
$28$		0			0
$29$	−2.47214	−	7.60845i	−0.459064	−	1.41285i	−0.866297	−	0.499530i	$-0.833506\pi$
$29$	−2.47214	−	7.60845i	−0.459064	−	1.41285i	0.407233	−	0.913324i	$-0.366494\pi$
$30$		0			0
$31$	5.66312	+	4.11450i	1.01713	+	0.738985i	0.965692	−	0.259691i	$-0.0836207\pi$
$31$	5.66312	+	4.11450i	1.01713	+	0.738985i	0.0514344	+	0.998676i	$0.483621\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	−4.85410	−	3.52671i	−0.820493	−	0.596123i
$36$		0			0
$37$	−0.309017	−	0.951057i	−0.0508021	−	0.156353i	0.922437	−	0.386148i	$-0.126194\pi$
$37$	−0.309017	−	0.951057i	−0.0508021	−	0.156353i	−0.973239	+	0.229795i	$0.926194\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	1.23607	−	3.80423i	0.193041	−	0.594120i	−0.806952	−	0.590616i	$-0.798885\pi$
$41$	1.23607	−	3.80423i	0.193041	−	0.594120i	0.999994	−	0.00350392i	$-0.00111533\pi$
$42$		0			0
$43$	6.00000			0.914991			0.457496	−	0.889212i	$-0.348747\pi$
$43$	6.00000			0.914991			0.457496	+	0.889212i	$0.348747\pi$
$44$		0			0
$45$	−18.0000			−2.68328
$46$		0			0
$47$	−2.47214	+	7.60845i	−0.360598	+	1.10981i	0.592094	+	0.805869i	$0.298301\pi$
$47$	−2.47214	+	7.60845i	−0.360598	+	1.10981i	−0.952692	+	0.303938i	$0.901699\pi$
$48$		0			0
$49$	2.42705	−	1.76336i	0.346722	−	0.251908i
$50$		0			0
$51$	5.56231	+	17.1190i	0.778879	+	2.39714i
$52$		0			0
$53$	−1.61803	−	1.17557i	−0.222254	−	0.161477i	0.471087	−	0.882087i	$-0.343862\pi$
$53$	−1.61803	−	1.17557i	−0.222254	−	0.161477i	−0.693341	+	0.720610i	$0.743862\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$	9.70820	+	7.05342i	1.28588	+	0.934249i
$58$		0			0
$59$	−0.309017	−	0.951057i	−0.0402306	−	0.123817i	0.928924	−	0.370270i	$-0.120735\pi$
$59$	−0.309017	−	0.951057i	−0.0402306	−	0.123817i	−0.969155	+	0.246453i	$0.920735\pi$
$60$		0			0
$61$	−3.23607	+	2.35114i	−0.414336	+	0.301033i	−0.775355	−	0.631526i	$-0.782429\pi$
$61$	−3.23607	+	2.35114i	−0.414336	+	0.301033i	0.361019	+	0.932559i	$0.382429\pi$
$62$		0			0
$63$	−3.70820	+	11.4127i	−0.467190	+	1.43786i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	−5.00000			−0.610847			−0.305424	−	0.952217i	$-0.598798\pi$
$67$	−5.00000			−0.610847			−0.305424	+	0.952217i	$0.598798\pi$
$68$		0			0
$69$	−0.927051	+	2.85317i	−0.111604	+	0.343481i
$70$		0			0
$71$	−2.42705	+	1.76336i	−0.288038	+	0.209272i	−0.722416	−	0.691459i	$-0.756968\pi$
$71$	−2.42705	+	1.76336i	−0.288038	+	0.209272i	0.434378	+	0.900731i	$0.356968\pi$
$72$		0			0
$73$	4.94427	+	15.2169i	0.578683	+	1.78100i	0.623280	+	0.781999i	$0.285800\pi$
$73$	4.94427	+	15.2169i	0.578683	+	1.78100i	−0.0445966	+	0.999005i	$0.514200\pi$
$74$		0			0
$75$	9.70820	+	7.05342i	1.12101	+	0.814459i
$76$		0			0
$77$		0			0
$78$		0			0
$79$	−1.61803	−	1.17557i	−0.182043	−	0.132262i	0.493032	−	0.870011i	$-0.335889\pi$
$79$	−1.61803	−	1.17557i	−0.182043	−	0.132262i	−0.675075	+	0.737749i	$0.735889\pi$
$80$		0			0
$81$	2.78115	+	8.55951i	0.309017	+	0.951057i
$82$		0			0
$83$	1.61803	−	1.17557i	0.177602	−	0.129036i	−0.495432	−	0.868646i	$-0.664990\pi$
$83$	1.61803	−	1.17557i	0.177602	−	0.129036i	0.673035	+	0.739611i	$0.264990\pi$
$84$		0			0
$85$	5.56231	−	17.1190i	0.603317	−	1.85682i
$86$		0			0
$87$	24.0000			2.57307
$88$		0			0
$89$	15.0000			1.59000			0.794998	−	0.606612i	$-0.207472\pi$
$89$	15.0000			1.59000			0.794998	+	0.606612i	$0.207472\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$	−16.9894	+	12.3435i	−1.76171	+	1.27996i
$94$		0			0
$95$	−3.70820	−	11.4127i	−0.380454	−	1.17092i
$96$		0			0
$97$	5.66312	+	4.11450i	0.575003	+	0.417764i	0.836919	−	0.547327i	$-0.184354\pi$
$97$	5.66312	+	4.11450i	0.575003	+	0.417764i	−0.261916	+	0.965091i	$0.584354\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	8.09017	+	5.87785i	0.805002	+	0.584868i	0.912377	−	0.409350i	$-0.134245\pi$
$101$	8.09017	+	5.87785i	0.805002	+	0.584868i	−0.107375	+	0.994219i	$0.534245\pi$
$102$		0			0
$103$	−4.94427	−	15.2169i	−0.487174	−	1.49937i	−0.828808	−	0.559533i	$-0.810980\pi$
$103$	−4.94427	−	15.2169i	−0.487174	−	1.49937i	0.341634	−	0.939833i	$-0.389020\pi$
$104$		0			0
$105$	14.5623	−	10.5801i	1.42114	−	1.03252i
$106$		0			0
$107$	0.618034	−	1.90211i	0.0597476	−	0.183884i	−0.916728	−	0.399512i	$-0.869180\pi$
$107$	0.618034	−	1.90211i	0.0597476	−	0.183884i	0.976476	+	0.215627i	$0.0691797\pi$
$108$		0			0
$109$	−14.0000			−1.34096			−0.670478	−	0.741929i	$-0.733911\pi$
$109$	−14.0000			−1.34096			−0.670478	+	0.741929i	$0.733911\pi$
$110$		0			0
$111$	3.00000			0.284747
$112$		0			0
$113$	−2.16312	+	6.65740i	−0.203489	+	0.626275i	0.796283	+	0.604924i	$0.206797\pi$
$113$	−2.16312	+	6.65740i	−0.203489	+	0.626275i	−0.999772	+	0.0213507i	$0.993203\pi$
$114$		0			0
$115$	2.42705	−	1.76336i	0.226324	−	0.164434i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	−9.70820	−	7.05342i	−0.889950	−	0.646586i
$120$		0			0
$121$		0			0
$122$		0			0
$123$	9.70820	+	7.05342i	0.875359	+	0.635986i
$124$		0			0
$125$	0.927051	+	2.85317i	0.0829180	+	0.255195i
$126$		0			0
$127$	−3.23607	+	2.35114i	−0.287155	+	0.208630i	−0.722032	−	0.691860i	$-0.756792\pi$
$127$	−3.23607	+	2.35114i	−0.287155	+	0.208630i	0.434877	+	0.900490i	$0.356792\pi$
$128$		0			0
$129$	−5.56231	+	17.1190i	−0.489734	+	1.50725i
$130$		0			0
$131$	−2.00000			−0.174741			−0.0873704	−	0.996176i	$-0.527846\pi$
$131$	−2.00000			−0.174741			−0.0873704	+	0.996176i	$0.527846\pi$
$132$		0			0
$133$	−8.00000			−0.693688
$134$		0			0
$135$	8.34346	−	25.6785i	0.718091	−	2.21006i
$136$		0			0
$137$	12.1353	−	8.81678i	1.03678	−	0.753268i	0.0671295	−	0.997744i	$-0.478616\pi$
$137$	12.1353	−	8.81678i	1.03678	−	0.753268i	0.969655	+	0.244476i	$0.0786159\pi$
$138$		0			0
$139$	−6.79837	−	20.9232i	−0.576631	−	1.77469i	−0.630559	−	0.776142i	$-0.717174\pi$
$139$	−6.79837	−	20.9232i	−0.576631	−	1.77469i	0.0539282	−	0.998545i	$-0.482826\pi$
$140$		0			0
$141$	−19.4164	−	14.1068i	−1.63516	−	1.18801i
$142$		0			0
$143$		0			0
$144$		0			0
$145$	−19.4164	−	14.1068i	−1.61244	−	1.17151i
$146$		0			0
$147$	2.78115	+	8.55951i	0.229386	+	0.705976i
$148$		0			0
$149$	−14.5623	+	10.5801i	−1.19299	+	0.866758i	−0.993577	−	0.113157i	$-0.963904\pi$
$149$	−14.5623	+	10.5801i	−1.19299	+	0.866758i	−0.199413	+	0.979915i	$0.563904\pi$
$150$		0			0
$151$	−5.56231	+	17.1190i	−0.452654	+	1.39313i	0.421213	+	0.906962i	$0.361604\pi$
$151$	−5.56231	+	17.1190i	−0.452654	+	1.39313i	−0.873867	+	0.486164i	$0.838396\pi$
$152$		0			0
$153$	−36.0000			−2.91043
$154$		0			0
$155$	21.0000			1.68676
$156$		0			0
$157$	−3.39919	+	10.4616i	−0.271285	+	0.834928i	0.718894	+	0.695120i	$0.244649\pi$
$157$	−3.39919	+	10.4616i	−0.271285	+	0.834928i	−0.990179	+	0.139808i	$0.955351\pi$
$158$		0			0
$159$	4.85410	−	3.52671i	0.384955	−	0.279686i
$160$		0			0
$161$	−0.618034	−	1.90211i	−0.0487079	−	0.149908i
$162$		0			0
$163$	3.23607	+	2.35114i	0.253468	+	0.184156i	0.707263	−	0.706951i	$-0.249930\pi$
$163$	3.23607	+	2.35114i	0.253468	+	0.184156i	−0.453794	+	0.891107i	$0.649930\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−12.9443	−	9.40456i	−1.00166	−	0.727747i	−0.0392148	−	0.999231i	$-0.512486\pi$
$167$	−12.9443	−	9.40456i	−1.00166	−	0.727747i	−0.962443	+	0.271484i	$0.912486\pi$
$168$		0			0
$169$	−4.01722	−	12.3637i	−0.309017	−	0.951057i
$170$		0			0
$171$	−19.4164	+	14.1068i	−1.48481	+	1.07878i
$172$		0			0
$173$	5.56231	−	17.1190i	0.422894	−	1.30153i	−0.482102	−	0.876115i	$-0.660127\pi$
$173$	5.56231	−	17.1190i	0.422894	−	1.30153i	0.904996	−	0.425420i	$-0.139873\pi$
$174$		0			0
$175$	−8.00000			−0.604743
$176$		0			0
$177$	3.00000			0.225494
$178$		0			0
$179$	−1.54508	+	4.75528i	−0.115485	+	0.355427i	−0.992048	−	0.125861i	$-0.959831\pi$
$179$	−1.54508	+	4.75528i	−0.115485	+	0.355427i	0.876563	+	0.481287i	$0.159831\pi$
$180$		0			0
$181$	4.04508	−	2.93893i	0.300669	−	0.218449i	−0.427213	−	0.904151i	$-0.640505\pi$
$181$	4.04508	−	2.93893i	0.300669	−	0.218449i	0.727882	+	0.685702i	$0.240505\pi$
$182$		0			0
$183$	−3.70820	−	11.4127i	−0.274118	−	0.843649i
$184$		0			0
$185$	−2.42705	−	1.76336i	−0.178440	−	0.129644i
$186$		0			0
$187$		0			0
$188$		0			0
$189$	−14.5623	−	10.5801i	−1.05925	−	0.769592i
$190$		0			0
$191$	−2.78115	−	8.55951i	−0.201237	−	0.619344i	−0.999847	−	0.0174951i	$-0.994431\pi$
$191$	−2.78115	−	8.55951i	−0.201237	−	0.619344i	0.798610	−	0.601849i	$-0.205569\pi$
$192$		0			0
$193$	−3.23607	+	2.35114i	−0.232937	+	0.169239i	−0.698131	−	0.715970i	$-0.745985\pi$
$193$	−3.23607	+	2.35114i	−0.232937	+	0.169239i	0.465194	+	0.885209i	$0.345985\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	6.00000			0.427482			0.213741	−	0.976890i	$-0.431435\pi$
$197$	6.00000			0.427482			0.213741	+	0.976890i	$0.431435\pi$
$198$		0			0
$199$	8.00000			0.567105			0.283552	−	0.958957i	$-0.408487\pi$
$199$	8.00000			0.567105			0.283552	+	0.958957i	$0.408487\pi$
$200$		0			0
$201$	4.63525	−	14.2658i	0.326946	−	1.00624i
$202$		0			0
$203$	−12.9443	+	9.40456i	−0.908510	+	0.660071i
$204$		0			0
$205$	−3.70820	−	11.4127i	−0.258992	−	0.797096i
$206$		0			0
$207$	−4.85410	−	3.52671i	−0.337383	−	0.245123i
$208$		0			0
$209$		0			0
$210$		0			0
$211$	−16.1803	−	11.7557i	−1.11390	−	0.809296i	−0.130627	−	0.991432i	$-0.541699\pi$
$211$	−16.1803	−	11.7557i	−1.11390	−	0.809296i	−0.983273	+	0.182135i	$0.941699\pi$
$212$		0			0
$213$	−2.78115	−	8.55951i	−0.190561	−	0.586488i
$214$		0			0
$215$	14.5623	−	10.5801i	0.993141	−	0.721559i
$216$		0			0
$217$	4.32624	−	13.3148i	0.293684	−	0.903867i
$218$		0			0
$219$	−48.0000			−3.24354
$220$		0			0
$221$		0			0
$222$		0			0
$223$	8.96149	−	27.5806i	0.600106	−	1.84694i	0.0726433	−	0.997358i	$-0.476857\pi$
$223$	8.96149	−	27.5806i	0.600106	−	1.84694i	0.527463	−	0.849578i	$-0.323143\pi$
$224$		0			0
$225$	−19.4164	+	14.1068i	−1.29443	+	0.940456i
$226$		0			0
$227$	5.56231	+	17.1190i	0.369183	+	1.13623i	0.947320	+	0.320289i	$0.103780\pi$
$227$	5.56231	+	17.1190i	0.369183	+	1.13623i	−0.578137	+	0.815940i	$0.696220\pi$
$228$		0			0
$229$	16.9894	+	12.3435i	1.12269	+	0.815681i	0.984614	−	0.174741i	$-0.0559089\pi$
$229$	16.9894	+	12.3435i	1.12269	+	0.815681i	0.138074	+	0.990422i	$0.455909\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	12.9443	+	9.40456i	0.848007	+	0.616113i	0.924596	−	0.380949i	$-0.124403\pi$
$233$	12.9443	+	9.40456i	0.848007	+	0.616113i	−0.0765885	+	0.997063i	$0.524403\pi$
$234$		0			0
$235$	7.41641	+	22.8254i	0.483793	+	1.48896i
$236$		0			0
$237$	4.85410	−	3.52671i	0.315308	−	0.229085i
$238$		0			0
$239$	−0.618034	+	1.90211i	−0.0399773	+	0.123037i	−0.969053	−	0.246851i	$-0.920604\pi$
$239$	−0.618034	+	1.90211i	−0.0399773	+	0.123037i	0.929076	+	0.369889i	$0.120604\pi$
$240$		0			0
$241$		0			0			−	1.00000i	$-0.5\pi$
$241$		0			0				1.00000i	$0.5\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	2.78115	−	8.55951i	0.177681	−	0.546847i
$246$		0			0
$247$		0			0
$248$		0			0
$249$	1.85410	+	5.70634i	0.117499	+	0.361625i
$250$		0			0
$251$	10.5172	+	7.64121i	0.663841	+	0.482309i	0.867958	−	0.496638i	$-0.165432\pi$
$251$	10.5172	+	7.64121i	0.663841	+	0.482309i	−0.204117	+	0.978947i	$0.565432\pi$
$252$		0			0
$253$		0			0
$254$		0			0
$255$	43.6869	+	31.7404i	2.73578	+	1.98766i
$256$		0			0
$257$	−3.09017	−	9.51057i	−0.192760	−	0.593253i	−0.999995	−	0.00302385i	$-0.999037\pi$
$257$	−3.09017	−	9.51057i	−0.192760	−	0.593253i	0.807236	−	0.590229i	$-0.200963\pi$
$258$		0			0
$259$	−1.61803	+	1.17557i	−0.100540	+	0.0730464i
$260$		0			0
$261$	−14.8328	+	45.6507i	−0.918128	+	2.82571i
$262$		0			0
$263$	14.0000			0.863277			0.431638	−	0.902047i	$-0.357936\pi$
$263$	14.0000			0.863277			0.431638	+	0.902047i	$0.357936\pi$
$264$		0			0
$265$	−6.00000			−0.368577
$266$		0			0
$267$	−13.9058	+	42.7975i	−0.851019	+	2.61917i
$268$		0			0
$269$	−21.0344	+	15.2824i	−1.28249	+	0.931785i	−0.999625	−	0.0273737i	$-0.991286\pi$
$269$	−21.0344	+	15.2824i	−1.28249	+	0.931785i	−0.282867	+	0.959159i	$0.591286\pi$
$270$		0			0
$271$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$271$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$		0			0
$276$		0			0
$277$	1.61803	+	1.17557i	0.0972182	+	0.0706332i	0.635332	−	0.772239i	$-0.280863\pi$
$277$	1.61803	+	1.17557i	0.0972182	+	0.0706332i	−0.538114	+	0.842872i	$0.680863\pi$
$278$		0			0
$279$	−12.9787	−	39.9444i	−0.777015	−	2.39141i
$280$		0			0
$281$	−4.85410	+	3.52671i	−0.289571	+	0.210386i	−0.723081	−	0.690763i	$-0.757275\pi$
$281$	−4.85410	+	3.52671i	−0.289571	+	0.210386i	0.433510	+	0.901149i	$0.357275\pi$
$282$		0			0
$283$	1.23607	−	3.80423i	0.0734766	−	0.226138i	−0.907573	−	0.419894i	$-0.862067\pi$
$283$	1.23607	−	3.80423i	0.0734766	−	0.226138i	0.981050	+	0.193756i	$0.0620672\pi$
$284$		0			0
$285$	36.0000			2.13246
$286$		0			0
$287$	−8.00000			−0.472225
$288$		0			0
$289$	5.87132	−	18.0701i	0.345372	−	1.06295i
$290$		0			0
$291$	−16.9894	+	12.3435i	−0.995934	+	0.723588i
$292$		0			0
$293$	3.70820	+	11.4127i	0.216636	+	0.666736i	0.999033	+	0.0439568i	$0.0139964\pi$
$293$	3.70820	+	11.4127i	0.216636	+	0.666736i	−0.782398	+	0.622779i	$0.786004\pi$
$294$		0			0
$295$	−2.42705	−	1.76336i	−0.141308	−	0.102667i
$296$		0			0
$297$		0			0
$298$		0			0
$299$		0			0
$300$		0			0
$301$	−3.70820	−	11.4127i	−0.213737	−	0.657816i
$302$		0			0
$303$	−24.2705	+	17.6336i	−1.39430	+	1.01302i
$304$		0			0
$305$	−3.70820	+	11.4127i	−0.212331	+	0.653488i
$306$		0			0
$307$	−4.00000			−0.228292			−0.114146	−	0.993464i	$-0.536413\pi$
$307$	−4.00000			−0.228292			−0.114146	+	0.993464i	$0.536413\pi$
$308$		0			0
$309$	48.0000			2.73062
$310$		0			0
$311$	−3.70820	+	11.4127i	−0.210273	+	0.647154i	0.789183	+	0.614159i	$0.210505\pi$
$311$	−3.70820	+	11.4127i	−0.210273	+	0.647154i	−0.999456	+	0.0329949i	$0.989495\pi$
$312$		0			0
$313$	7.28115	−	5.29007i	0.411555	−	0.299012i	−0.362676	−	0.931915i	$-0.618137\pi$
$313$	7.28115	−	5.29007i	0.411555	−	0.299012i	0.774231	+	0.632903i	$0.218137\pi$
$314$		0			0
$315$	11.1246	+	34.2380i	0.626801	+	1.92909i
$316$		0			0
$317$	12.1353	+	8.81678i	0.681584	+	0.495200i	0.873883	−	0.486137i	$-0.161594\pi$
$317$	12.1353	+	8.81678i	0.681584	+	0.495200i	−0.192299	+	0.981336i	$0.561594\pi$
$318$		0			0
$319$		0			0
$320$		0			0
$321$	4.85410	+	3.52671i	0.270930	+	0.196842i
$322$		0			0
$323$	−7.41641	−	22.8254i	−0.412660	−	1.27004i
$324$		0			0
$325$		0			0
$326$		0			0
$327$	12.9787	−	39.9444i	0.717725	−	2.20893i
$328$		0			0
$329$	16.0000			0.882109
$330$		0			0
$331$	−35.0000			−1.92377			−0.961887	−	0.273447i	$-0.911836\pi$
$331$	−35.0000			−1.92377			−0.961887	+	0.273447i	$0.911836\pi$
$332$		0			0
$333$	−1.85410	+	5.70634i	−0.101604	+	0.312705i
$334$		0			0
$335$	−12.1353	+	8.81678i	−0.663020	+	0.481712i
$336$		0			0
$337$	−3.09017	−	9.51057i	−0.168332	−	0.518073i	0.830934	−	0.556371i	$-0.187807\pi$
$337$	−3.09017	−	9.51057i	−0.168332	−	0.518073i	−0.999266	+	0.0382973i	$0.987807\pi$
$338$		0			0
$339$	−16.9894	−	12.3435i	−0.922735	−	0.670406i
$340$		0			0
$341$		0			0
$342$		0			0
$343$	−16.1803	−	11.7557i	−0.873656	−	0.634748i
$344$		0			0
$345$	2.78115	+	8.55951i	0.149732	+	0.460828i
$346$		0			0
$347$	25.8885	−	18.8091i	1.38977	−	1.00973i	0.393879	−	0.919162i	$-0.371133\pi$
$347$	25.8885	−	18.8091i	1.38977	−	1.00973i	0.995891	−	0.0905647i	$-0.0288672\pi$
$348$		0			0
$349$	−4.32624	+	13.3148i	−0.231578	+	0.712724i	0.765979	+	0.642866i	$0.222255\pi$
$349$	−4.32624	+	13.3148i	−0.231578	+	0.712724i	−0.997557	+	0.0698585i	$0.977745\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	3.00000			0.159674			0.0798369	−	0.996808i	$-0.474560\pi$
$353$	3.00000			0.159674			0.0798369	+	0.996808i	$0.474560\pi$
$354$		0			0
$355$	−2.78115	+	8.55951i	−0.147608	+	0.454292i
$356$		0			0
$357$	29.1246	−	21.1603i	1.54144	−	1.11992i
$358$		0			0
$359$	7.41641	+	22.8254i	0.391423	+	1.20468i	0.931712	+	0.363197i	$0.118315\pi$
$359$	7.41641	+	22.8254i	0.391423	+	1.20468i	−0.540289	+	0.841479i	$0.681685\pi$
$360$		0			0
$361$	2.42705	+	1.76336i	0.127740	+	0.0928082i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	38.8328	+	28.2137i	2.03260	+	1.47677i
$366$		0			0
$367$	10.1976	+	31.3849i	0.532308	+	1.63828i	0.749394	+	0.662124i	$0.230345\pi$
$367$	10.1976	+	31.3849i	0.532308	+	1.63828i	−0.217086	+	0.976153i	$0.569655\pi$
$368$		0			0
$369$	−19.4164	+	14.1068i	−1.01078	+	0.734373i
$370$		0			0
$371$	−1.23607	+	3.80423i	−0.0641735	+	0.197506i
$372$		0			0
$373$	−22.0000			−1.13912			−0.569558	−	0.821951i	$-0.692886\pi$
$373$	−22.0000			−1.13912			−0.569558	+	0.821951i	$0.692886\pi$
$374$		0			0
$375$	−9.00000			−0.464758
$376$		0			0
$377$		0			0
$378$		0			0
$379$	−20.2254	+	14.6946i	−1.03891	+	0.754813i	−0.970073	−	0.242815i	$-0.921929\pi$
$379$	−20.2254	+	14.6946i	−1.03891	+	0.754813i	−0.0688378	+	0.997628i	$0.521929\pi$
$380$		0			0
$381$	−3.70820	−	11.4127i	−0.189977	−	0.584689i
$382$		0			0
$383$	−0.809017	−	0.587785i	−0.0413388	−	0.0300344i	0.566924	−	0.823770i	$-0.308133\pi$
$383$	−0.809017	−	0.587785i	−0.0413388	−	0.0300344i	−0.608263	+	0.793736i	$0.708133\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	−29.1246	−	21.1603i	−1.48049	−	1.07564i
$388$		0			0
$389$	4.01722	+	12.3637i	0.203681	+	0.626866i	0.999765	+	0.0216798i	$0.00690144\pi$
$389$	4.01722	+	12.3637i	0.203681	+	0.626866i	−0.796084	+	0.605186i	$0.793099\pi$
$390$		0			0
$391$	4.85410	−	3.52671i	0.245482	−	0.178353i
$392$		0			0
$393$	1.85410	−	5.70634i	0.0935271	−	0.287847i
$394$		0			0
$395$	−6.00000			−0.301893
$396$		0			0
$397$	−26.0000			−1.30490			−0.652451	−	0.757831i	$-0.726259\pi$
$397$	−26.0000			−1.30490			−0.652451	+	0.757831i	$0.726259\pi$
$398$		0			0
$399$	7.41641	−	22.8254i	0.371285	−	1.14270i
$400$		0			0
$401$	4.85410	−	3.52671i	0.242402	−	0.176116i	−0.459951	−	0.887945i	$-0.652133\pi$
$401$	4.85410	−	3.52671i	0.242402	−	0.176116i	0.702353	+	0.711829i	$0.252133\pi$
$402$		0			0
$403$		0			0
$404$		0			0
$405$	21.8435	+	15.8702i	1.08541	+	0.788597i
$406$		0			0
$407$		0			0
$408$		0			0
$409$	−27.5066	−	19.9847i	−1.36011	−	0.988180i	−0.998438	−	0.0558755i	$-0.982205\pi$
$409$	−27.5066	−	19.9847i	−1.36011	−	0.988180i	−0.361675	−	0.932304i	$-0.617795\pi$
$410$		0			0
$411$	13.9058	+	42.7975i	0.685921	+	2.11105i
$412$		0			0
$413$	−1.61803	+	1.17557i	−0.0796182	+	0.0578460i
$414$		0			0
$415$	1.85410	−	5.70634i	0.0910143	−	0.280113i
$416$		0			0
$417$	66.0000			3.23203
$418$		0			0
$419$	−28.0000			−1.36789			−0.683945	−	0.729534i	$-0.739737\pi$
$419$	−28.0000			−1.36789			−0.683945	+	0.729534i	$0.739737\pi$
$420$		0			0
$421$	9.27051	−	28.5317i	0.451817	−	1.39055i	−0.423015	−	0.906123i	$-0.639028\pi$
$421$	9.27051	−	28.5317i	0.451817	−	1.39055i	0.874832	−	0.484427i	$-0.160972\pi$
$422$		0			0
$423$	38.8328	−	28.2137i	1.88812	−	1.37180i
$424$		0			0
$425$	−7.41641	−	22.8254i	−0.359749	−	1.10719i
$426$		0			0
$427$	6.47214	+	4.70228i	0.313209	+	0.227559i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	21.0344	+	15.2824i	1.01319	+	0.736128i	0.964876	−	0.262704i	$-0.0846143\pi$
$431$	21.0344	+	15.2824i	1.01319	+	0.736128i	0.0483169	+	0.998832i	$0.484614\pi$
$432$		0			0
$433$	4.01722	+	12.3637i	0.193055	+	0.594163i	0.999994	+	0.00352765i	$0.00112289\pi$
$433$	4.01722	+	12.3637i	0.193055	+	0.594163i	−0.806938	+	0.590636i	$0.798877\pi$
$434$		0			0
$435$	58.2492	−	42.3205i	2.79284	−	2.02911i
$436$		0			0
$437$	1.23607	−	3.80423i	0.0591292	−	0.181981i
$438$		0			0
$439$	−32.0000			−1.52728			−0.763638	−	0.645644i	$-0.776589\pi$
$439$	−32.0000			−1.52728			−0.763638	+	0.645644i	$0.776589\pi$
$440$		0			0
$441$	−18.0000			−0.857143
$442$		0			0
$443$	−2.78115	+	8.55951i	−0.132137	+	0.406675i	−0.995134	−	0.0985344i	$-0.968585\pi$
$443$	−2.78115	+	8.55951i	−0.132137	+	0.406675i	0.862997	+	0.505209i	$0.168585\pi$
$444$		0			0
$445$	36.4058	−	26.4503i	1.72580	−	1.25387i
$446$		0			0
$447$	−16.6869	−	51.3571i	−0.789264	−	2.42911i
$448$		0			0
$449$	16.9894	+	12.3435i	0.801777	+	0.582525i	0.911435	−	0.411444i	$-0.134975\pi$
$449$	16.9894	+	12.3435i	0.801777	+	0.582525i	−0.109658	+	0.993969i	$0.534975\pi$
$450$		0			0
$451$		0			0
$452$		0			0
$453$	−43.6869	−	31.7404i	−2.05259	−	1.49129i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−9.70820	+	7.05342i	−0.454131	+	0.329945i	−0.791224	−	0.611526i	$-0.790556\pi$
$457$	−9.70820	+	7.05342i	−0.454131	+	0.329945i	0.337094	+	0.941471i	$0.390556\pi$
$458$		0			0
$459$	16.6869	−	51.3571i	0.778879	−	2.39714i
$460$		0			0
$461$	−28.0000			−1.30409			−0.652045	−	0.758180i	$-0.726089\pi$
$461$	−28.0000			−1.30409			−0.652045	+	0.758180i	$0.726089\pi$
$462$		0			0
$463$	27.0000			1.25480			0.627398	−	0.778699i	$-0.284120\pi$
$463$	27.0000			1.25480			0.627398	+	0.778699i	$0.284120\pi$
$464$		0			0
$465$	−19.4681	+	59.9166i	−0.902810	+	2.77856i
$466$		0			0
$467$	26.6976	−	19.3969i	1.23542	−	0.897582i	0.238132	−	0.971233i	$-0.423465\pi$
$467$	26.6976	−	19.3969i	1.23542	−	0.897582i	0.997284	+	0.0736508i	$0.0234650\pi$
$468$		0			0
$469$	3.09017	+	9.51057i	0.142691	+	0.439157i
$470$		0			0
$471$	−26.6976	−	19.3969i	−1.23016	−	0.893763i
$472$		0			0
$473$		0			0
$474$		0			0
$475$	−12.9443	−	9.40456i	−0.593924	−	0.431511i
$476$		0			0
$477$	3.70820	+	11.4127i	0.169787	+	0.522551i
$478$		0			0
$479$	−6.47214	+	4.70228i	−0.295719	+	0.214853i	−0.725745	−	0.687964i	$-0.758505\pi$
$479$	−6.47214	+	4.70228i	−0.295719	+	0.214853i	0.430025	+	0.902817i	$0.358505\pi$
$480$		0			0
$481$		0			0
$482$		0			0
$483$	6.00000			0.273009
$484$		0			0
$485$	21.0000			0.953561
$486$		0			0
$487$	2.78115	−	8.55951i	0.126026	−	0.387868i	−0.868061	−	0.496458i	$-0.834634\pi$
$487$	2.78115	−	8.55951i	0.126026	−	0.387868i	0.994087	+	0.108590i	$0.0346336\pi$
$488$		0			0
$489$	−9.70820	+	7.05342i	−0.439020	+	0.318967i
$490$		0			0
$491$	2.47214	+	7.60845i	0.111566	+	0.343365i	0.991215	−	0.132258i	$-0.0422228\pi$
$491$	2.47214	+	7.60845i	0.111566	+	0.343365i	−0.879649	+	0.475623i	$0.842223\pi$
$492$		0			0
$493$	−38.8328	−	28.2137i	−1.74894	−	1.27068i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	4.85410	+	3.52671i	0.217736	+	0.158195i
$498$		0			0
$499$	−6.18034	−	19.0211i	−0.276670	−	0.851503i	−0.988773	−	0.149427i	$-0.952257\pi$
$499$	−6.18034	−	19.0211i	−0.276670	−	0.851503i	0.712103	−	0.702075i	$-0.247743\pi$
$500$		0			0
$501$	38.8328	−	28.2137i	1.73492	−	1.26049i
$502$		0			0
$503$	−9.27051	+	28.5317i	−0.413352	+	1.27217i	0.500365	+	0.865814i	$0.333199\pi$
$503$	−9.27051	+	28.5317i	−0.413352	+	1.27217i	−0.913717	+	0.406351i	$0.866801\pi$
$504$		0			0
$505$	30.0000			1.33498
$506$		0			0
$507$	39.0000			1.73205
$508$		0			0
$509$	−4.01722	+	12.3637i	−0.178060	+	0.548013i	−0.999760	−	0.0219076i	$-0.993026\pi$
$509$	−4.01722	+	12.3637i	−0.178060	+	0.548013i	0.821700	+	0.569921i	$0.193026\pi$
$510$		0			0
$511$	25.8885	−	18.8091i	1.14524	−	0.832067i
$512$		0			0
$513$	−11.1246	−	34.2380i	−0.491164	−	1.51165i
$514$		0			0
$515$	−38.8328	−	28.2137i	−1.71118	−	1.24324i
$516$		0			0
$517$		0			0
$518$		0			0
$519$	43.6869	+	31.7404i	1.91764	+	1.39325i
$520$		0			0
$521$	11.4336	+	35.1891i	0.500916	+	1.54166i	0.807529	+	0.589828i	$0.200804\pi$
$521$	11.4336	+	35.1891i	0.500916	+	1.54166i	−0.306613	+	0.951834i	$0.599196\pi$
$522$		0			0
$523$	−35.5967	+	25.8626i	−1.55654	+	1.13089i	−0.617759	+	0.786367i	$0.711959\pi$
$523$	−35.5967	+	25.8626i	−1.55654	+	1.13089i	−0.938778	+	0.344523i	$0.888041\pi$
$524$		0			0
$525$	7.41641	−	22.8254i	0.323679	−	0.996180i
$526$		0			0
$527$	42.0000			1.82955
$528$		0			0
$529$	−22.0000			−0.956522
$530$		0			0
$531$	−1.85410	+	5.70634i	−0.0804612	+	0.247634i
$532$		0			0
$533$		0			0
$534$		0			0
$535$	−1.85410	−	5.70634i	−0.0801598	−	0.246707i
$536$		0			0
$537$	−12.1353	−	8.81678i	−0.523675	−	0.380472i
$538$		0			0
$539$		0			0
$540$		0			0
$541$	−9.70820	−	7.05342i	−0.417388	−	0.303250i	0.359198	−	0.933261i	$-0.383050\pi$
$541$	−9.70820	−	7.05342i	−0.417388	−	0.303250i	−0.776586	+	0.630011i	$0.783050\pi$
$542$		0			0
$543$	4.63525	+	14.2658i	0.198918	+	0.612206i
$544$		0			0
$545$	−33.9787	+	24.6870i	−1.45549	+	1.05747i
$546$		0			0
$547$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$547$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$548$		0			0
$549$	24.0000			1.02430
$550$		0			0
$551$	−32.0000			−1.36325
$552$		0			0
$553$	−1.23607	+	3.80423i	−0.0525630	+	0.161772i
$554$		0			0
$555$	7.28115	−	5.29007i	0.309068	−	0.224551i
$556$		0			0
$557$	12.9787	+	39.9444i	0.549926	+	1.69250i	0.708981	+	0.705228i	$0.249155\pi$
$557$	12.9787	+	39.9444i	0.549926	+	1.69250i	−0.159055	+	0.987270i	$0.550845\pi$
$558$		0			0
$559$		0			0
$560$		0			0
$561$		0			0
$562$		0			0
$563$	9.70820	+	7.05342i	0.409152	+	0.297266i	0.773258	−	0.634091i	$-0.218626\pi$
$563$	9.70820	+	7.05342i	0.409152	+	0.297266i	−0.364106	+	0.931357i	$0.618626\pi$
$564$		0			0
$565$	6.48936	+	19.9722i	0.273009	+	0.840236i
$566$		0			0
$567$	14.5623	−	10.5801i	0.611559	−	0.444324i
$568$		0			0
$569$	−7.41641	+	22.8254i	−0.310912	+	0.956889i	0.666493	+	0.745512i	$0.267795\pi$
$569$	−7.41641	+	22.8254i	−0.310912	+	0.956889i	−0.977405	+	0.211377i	$0.932205\pi$
$570$		0			0
$571$	−4.00000			−0.167395			−0.0836974	−	0.996491i	$-0.526673\pi$
$571$	−4.00000			−0.167395			−0.0836974	+	0.996491i	$0.526673\pi$
$572$		0			0
$573$	27.0000			1.12794
$574$		0			0
$575$	1.23607	−	3.80423i	0.0515476	−	0.158647i
$576$		0			0
$577$	18.6074	−	13.5191i	0.774636	−	0.562806i	−0.128728	−	0.991680i	$-0.541090\pi$
$577$	18.6074	−	13.5191i	0.774636	−	0.562806i	0.903364	+	0.428874i	$0.141090\pi$
$578$		0			0
$579$	−3.70820	−	11.4127i	−0.154108	−	0.474295i
$580$		0			0
$581$	−3.23607	−	2.35114i	−0.134255	−	0.0975418i
$582$		0			0
$583$		0			0
$584$		0			0
$585$		0			0
$586$		0			0
$587$	3.70820	+	11.4127i	0.153054	+	0.471052i	0.997959	−	0.0638654i	$-0.0203428\pi$
$587$	3.70820	+	11.4127i	0.153054	+	0.471052i	−0.844905	+	0.534917i	$0.820343\pi$
$588$		0			0
$589$	22.6525	−	16.4580i	0.933379	−	0.678140i
$590$		0			0
$591$	−5.56231	+	17.1190i	−0.228803	+	0.704182i
$592$		0			0
$593$	−4.00000			−0.164260			−0.0821302	−	0.996622i	$-0.526172\pi$
$593$	−4.00000			−0.164260			−0.0821302	+	0.996622i	$0.526172\pi$
$594$		0			0
$595$	−36.0000			−1.47586
$596$		0			0
$597$	−7.41641	+	22.8254i	−0.303533	+	0.934180i
$598$		0			0
$599$	−38.8328	+	28.2137i	−1.58667	+	1.15278i	−0.678155	+	0.734919i	$0.737220\pi$
$599$	−38.8328	+	28.2137i	−1.58667	+	1.15278i	−0.908511	+	0.417861i	$0.862780\pi$
$600$		0			0
$601$	11.7426	+	36.1401i	0.478993	+	1.47419i	0.840497	+	0.541817i	$0.182263\pi$
$601$	11.7426	+	36.1401i	0.478993	+	1.47419i	−0.361504	+	0.932371i	$0.617737\pi$
$602$		0			0
$603$	24.2705	+	17.6336i	0.988372	+	0.718094i
$604$		0			0
$605$		0			0
$606$		0			0
$607$	14.5623	+	10.5801i	0.591066	+	0.429434i	0.842696	−	0.538389i	$-0.180967\pi$
$607$	14.5623	+	10.5801i	0.591066	+	0.429434i	−0.251631	+	0.967823i	$0.580967\pi$
$608$		0			0
$609$	−14.8328	−	45.6507i	−0.601056	−	1.84986i
$610$		0			0
$611$		0			0
$612$		0			0
$613$	−4.94427	+	15.2169i	−0.199697	+	0.614605i	0.800192	+	0.599744i	$0.204731\pi$
$613$	−4.94427	+	15.2169i	−0.199697	+	0.614605i	−0.999890	+	0.0148615i	$0.995269\pi$
$614$		0			0
$615$	36.0000			1.45166
$616$		0			0
$617$	18.0000			0.724653			0.362326	−	0.932051i	$-0.381983\pi$
$617$	18.0000			0.724653			0.362326	+	0.932051i	$0.381983\pi$
$618$		0			0
$619$	−0.927051	+	2.85317i	−0.0372613	+	0.114679i	−0.967957	−	0.251116i	$-0.919203\pi$
$619$	−0.927051	+	2.85317i	−0.0372613	+	0.114679i	0.930696	+	0.365794i	$0.119203\pi$
$620$		0			0
$621$	7.28115	−	5.29007i	0.292183	−	0.212283i
$622$		0			0
$623$	−9.27051	−	28.5317i	−0.371415	−	1.14310i
$624$		0			0
$625$	23.4615	+	17.0458i	0.938460	+	0.681831i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	−4.85410	−	3.52671i	−0.193546	−	0.140619i
$630$		0			0
$631$	2.78115	+	8.55951i	0.110716	+	0.340749i	0.991029	−	0.133644i	$-0.0426678\pi$
$631$	2.78115	+	8.55951i	0.110716	+	0.340749i	−0.880313	+	0.474392i	$0.842668\pi$
$632$		0			0
$633$	48.5410	−	35.2671i	1.92933	−	1.40174i
$634$		0			0
$635$	−3.70820	+	11.4127i	−0.147156	+	0.452898i
$636$		0			0
$637$		0			0
$638$		0			0
$639$	18.0000			0.712069
$640$		0			0
$641$	−2.78115	+	8.55951i	−0.109849	+	0.338080i	−0.990838	−	0.135057i	$-0.956878\pi$
$641$	−2.78115	+	8.55951i	−0.109849	+	0.338080i	0.880989	+	0.473137i	$0.156878\pi$
$642$		0			0
$643$	−5.66312	+	4.11450i	−0.223332	+	0.162260i	−0.693825	−	0.720144i	$-0.744076\pi$
$643$	−5.66312	+	4.11450i	−0.223332	+	0.162260i	0.470493	+	0.882403i	$0.344076\pi$
$644$		0			0
$645$	16.6869	+	51.3571i	0.657047	+	2.02218i
$646$		0			0
$647$	−12.1353	−	8.81678i	−0.477086	−	0.346623i	0.323110	−	0.946361i	$-0.395271\pi$
$647$	−12.1353	−	8.81678i	−0.477086	−	0.346623i	−0.800196	+	0.599738i	$0.795271\pi$
$648$		0			0
$649$		0			0
$650$		0			0
$651$	33.9787	+	24.6870i	1.33173	+	0.967559i
$652$		0			0
$653$	3.39919	+	10.4616i	0.133020	+	0.409395i	0.995277	−	0.0970771i	$-0.0309494\pi$
$653$	3.39919	+	10.4616i	0.133020	+	0.409395i	−0.862256	+	0.506472i	$0.830949\pi$
$654$		0			0
$655$	−4.85410	+	3.52671i	−0.189665	+	0.137800i
$656$		0			0
$657$	29.6656	−	91.3014i	1.15737	−	3.56201i
$658$		0			0
$659$	22.0000			0.856998			0.428499	−	0.903542i	$-0.359042\pi$
$659$	22.0000			0.856998			0.428499	+	0.903542i	$0.359042\pi$
$660$		0			0
$661$	−7.00000			−0.272268			−0.136134	−	0.990690i	$-0.543468\pi$
$661$	−7.00000			−0.272268			−0.136134	+	0.990690i	$0.543468\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	−19.4164	+	14.1068i	−0.752936	+	0.547040i
$666$		0			0
$667$	−2.47214	−	7.60845i	−0.0957215	−	0.294600i
$668$		0			0
$669$	70.3845	+	51.1373i	2.72122	+	1.97708i
$670$		0			0
$671$		0			0
$672$		0			0
$673$	27.5066	+	19.9847i	1.06030	+	0.770354i	0.974144	−	0.225928i	$-0.0725414\pi$
$673$	27.5066	+	19.9847i	1.06030	+	0.770354i	0.0861567	+	0.996282i	$0.472541\pi$
$674$		0			0
$675$	−11.1246	−	34.2380i	−0.428187	−	1.31782i
$676$		0			0
$677$	24.2705	−	17.6336i	0.932791	−	0.677713i	−0.0138832	−	0.999904i	$-0.504419\pi$
$677$	24.2705	−	17.6336i	0.932791	−	0.677713i	0.946675	+	0.322191i	$0.104419\pi$
$678$		0			0
$679$	4.32624	−	13.3148i	0.166026	−	0.510975i
$680$		0			0
$681$	−54.0000			−2.06928
$682$		0			0
$683$	8.00000			0.306111			0.153056	−	0.988218i	$-0.451089\pi$
$683$	8.00000			0.306111			0.153056	+	0.988218i	$0.451089\pi$
$684$		0			0
$685$	13.9058	−	42.7975i	0.531312	−	1.63521i
$686$		0			0
$687$	−50.9681	+	37.0305i	−1.94455	+	1.41280i
$688$		0			0
$689$		0			0
$690$		0			0
$691$	23.4615	+	17.0458i	0.892517	+	0.648452i	0.936533	−	0.350579i	$-0.114015\pi$
$691$	23.4615	+	17.0458i	0.892517	+	0.648452i	−0.0440159	+	0.999031i	$0.514015\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−53.3951	−	38.7938i	−2.02539	−	1.47153i
$696$		0			0
$697$	−7.41641	−	22.8254i	−0.280916	−	0.864572i
$698$		0			0
$699$	−38.8328	+	28.2137i	−1.46879	+	1.06714i
$700$		0			0
$701$	−3.09017	+	9.51057i	−0.116714	+	0.359209i	−0.992301	−	0.123852i	$-0.960475\pi$
$701$	−3.09017	+	9.51057i	−0.116714	+	0.359209i	0.875587	+	0.483061i	$0.160475\pi$
$702$		0			0
$703$	−4.00000			−0.150863
$704$		0			0
$705$	−72.0000			−2.71168
$706$		0			0
$707$	6.18034	−	19.0211i	0.232436	−	0.715363i
$708$		0			0
$709$	−15.3713	+	11.1679i	−0.577282	+	0.419420i	−0.837743	−	0.546064i	$-0.816125\pi$
$709$	−15.3713	+	11.1679i	−0.577282	+	0.419420i	0.260461	+	0.965484i	$0.416125\pi$
$710$		0			0
$711$	3.70820	+	11.4127i	0.139069	+	0.428009i
$712$		0			0
$713$	5.66312	+	4.11450i	0.212085	+	0.154089i
$714$		0			0
$715$		0			0
$716$		0			0
$717$	−4.85410	−	3.52671i	−0.181280	−	0.131707i
$718$		0			0
$719$	−7.10739	−	21.8743i	−0.265061	−	0.815774i	−0.991679	−	0.128732i	$-0.958909\pi$
$719$	−7.10739	−	21.8743i	−0.265061	−	0.815774i	0.726618	−	0.687041i	$-0.241091\pi$
$720$		0			0
$721$	−25.8885	+	18.8091i	−0.964140	+	0.700489i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	−32.0000			−1.18845
$726$		0			0
$727$	−35.0000			−1.29808			−0.649039	−	0.760755i	$-0.724829\pi$
$727$	−35.0000			−1.29808			−0.649039	+	0.760755i	$0.724829\pi$
$728$		0			0
$729$	−8.34346	+	25.6785i	−0.309017	+	0.951057i
$730$		0			0
$731$	29.1246	−	21.1603i	1.07721	−	0.782641i
$732$		0			0
$733$	1.23607	+	3.80423i	0.0456552	+	0.140512i	0.971286	−	0.237917i	$-0.0764645\pi$
$733$	1.23607	+	3.80423i	0.0456552	+	0.140512i	−0.925630	+	0.378429i	$0.876464\pi$
$734$		0			0
$735$	21.8435	+	15.8702i	0.805708	+	0.585381i
$736$		0			0
$737$		0			0
$738$		0			0
$739$	21.0344	+	15.2824i	0.773764	+	0.562173i	0.903101	−	0.429428i	$-0.141285\pi$
$739$	21.0344	+	15.2824i	0.773764	+	0.562173i	−0.129337	+	0.991601i	$0.541285\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	29.1246	−	21.1603i	1.06848	−	0.776295i	0.0928402	−	0.995681i	$-0.470405\pi$
$743$	29.1246	−	21.1603i	1.06848	−	0.776295i	0.975638	+	0.219386i	$0.0704054\pi$
$744$		0			0
$745$	−16.6869	+	51.3571i	−0.611361	+	1.88158i
$746$		0			0
$747$	−12.0000			−0.439057
$748$		0			0
$749$	−4.00000			−0.146157
$750$		0			0
$751$	7.10739	−	21.8743i	0.259352	−	0.798205i	−0.733588	−	0.679594i	$-0.762156\pi$
$751$	7.10739	−	21.8743i	0.259352	−	0.798205i	0.992941	−	0.118611i	$-0.0378440\pi$
$752$		0			0
$753$	−31.5517	+	22.9236i	−1.14981	+	0.835383i
$754$		0			0
$755$	16.6869	+	51.3571i	0.607299	+	1.86907i
$756$		0			0
$757$	−8.09017	−	5.87785i	−0.294042	−	0.213634i	0.430977	−	0.902363i	$-0.358169\pi$
$757$	−8.09017	−	5.87785i	−0.294042	−	0.213634i	−0.725019	+	0.688729i	$0.758169\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$761$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$762$		0			0
$763$	8.65248	+	26.6296i	0.313241	+	0.964056i
$764$		0			0
$765$	−87.3738	+	63.4808i	−3.15901	+	2.29515i
$766$		0			0
$767$		0			0
$768$		0			0
$769$	16.0000			0.576975			0.288487	−	0.957484i	$-0.406848\pi$
$769$	16.0000			0.576975			0.288487	+	0.957484i	$0.406848\pi$
$770$		0			0
$771$	30.0000			1.08042
$772$		0			0
$773$	−1.85410	+	5.70634i	−0.0666874	+	0.205243i	−0.978847	−	0.204591i	$-0.934413\pi$
$773$	−1.85410	+	5.70634i	−0.0666874	+	0.205243i	0.912160	+	0.409834i	$0.134413\pi$
$774$		0			0
$775$	22.6525	−	16.4580i	0.813701	−	0.591188i
$776$		0			0
$777$	−1.85410	−	5.70634i	−0.0665155	−	0.204714i
$778$		0			0
$779$	−12.9443	−	9.40456i	−0.463777	−	0.336953i
$780$		0			0
$781$		0			0
$782$		0			0
$783$	−58.2492	−	42.3205i	−2.08166	−	1.51241i
$784$		0			0
$785$	10.1976	+	31.3849i	0.363967	+	1.12017i
$786$		0			0
$787$	−19.4164	+	14.1068i	−0.692120	+	0.502855i	−0.877356	−	0.479839i	$-0.840695\pi$
$787$	−19.4164	+	14.1068i	−0.692120	+	0.502855i	0.185236	+	0.982694i	$0.440695\pi$
$788$		0			0
$789$	−12.9787	+	39.9444i	−0.462054	+	1.42206i
$790$		0			0
$791$	14.0000			0.497783
$792$		0			0
$793$		0			0
$794$		0			0
$795$	5.56231	−	17.1190i	0.197275	−	0.607149i
$796$		0			0
$797$	−0.809017	+	0.587785i	−0.0286569	+	0.0208204i	−0.602021	−	0.798480i	$-0.705638\pi$
$797$	−0.809017	+	0.587785i	−0.0286569	+	0.0208204i	0.573365	+	0.819300i	$0.305638\pi$
$798$		0			0
$799$	14.8328	+	45.6507i	0.524747	+	1.61501i
$800$		0			0
$801$	−72.8115	−	52.9007i	−2.57267	−	1.86915i
$802$		0			0
$803$		0			0
$804$		0			0
$805$	−4.85410	−	3.52671i	−0.171085	−	0.124300i
$806$		0			0
$807$	−24.1033	−	74.1824i	−0.848477	−	2.61134i
$808$		0			0
$809$	−9.70820	+	7.05342i	−0.341322	+	0.247985i	−0.745220	−	0.666819i	$-0.767655\pi$
$809$	−9.70820	+	7.05342i	−0.341322	+	0.247985i	0.403897	+	0.914804i	$0.367655\pi$
$810$		0			0
$811$	−8.03444	+	24.7275i	−0.282127	+	0.868299i	0.705118	+	0.709090i	$0.250894\pi$
$811$	−8.03444	+	24.7275i	−0.282127	+	0.868299i	−0.987245	+	0.159208i	$0.949106\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	12.0000			0.420342
$816$		0			0
$817$	7.41641	−	22.8254i	0.259467	−	0.798558i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−10.5066	−	32.3359i	−0.366682	−	1.12853i	−0.948921	−	0.315514i	$-0.897823\pi$
$821$	−10.5066	−	32.3359i	−0.366682	−	1.12853i	0.582239	−	0.813018i	$-0.302177\pi$
$822$		0			0
$823$	25.0795	+	18.2213i	0.874217	+	0.635156i	0.931715	−	0.363190i	$-0.118312\pi$
$823$	25.0795	+	18.2213i	0.874217	+	0.635156i	−0.0574979	+	0.998346i	$0.518312\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	12.9443	+	9.40456i	0.450116	+	0.327029i	0.789642	−	0.613568i	$-0.210266\pi$
$827$	12.9443	+	9.40456i	0.450116	+	0.327029i	−0.339525	+	0.940597i	$0.610266\pi$
$828$		0			0
$829$	−10.8156	−	33.2870i	−0.375641	−	1.15610i	−0.943045	−	0.332665i	$-0.892052\pi$
$829$	−10.8156	−	33.2870i	−0.375641	−	1.15610i	0.567404	−	0.823440i	$-0.307948\pi$
$830$		0			0
$831$	−4.85410	+	3.52671i	−0.168387	+	0.122340i
$832$		0			0
$833$	5.56231	−	17.1190i	0.192722	−	0.593139i
$834$		0			0
$835$	−48.0000			−1.66111
$836$		0			0
$837$	63.0000			2.17760
$838$		0			0
$839$	6.48936	−	19.9722i	0.224037	−	0.689516i	−0.774350	−	0.632757i	$-0.781923\pi$
$839$	6.48936	−	19.9722i	0.224037	−	0.689516i	0.998388	−	0.0567594i	$-0.0180768\pi$
$840$		0			0
$841$	−28.3156	+	20.5725i	−0.976400	+	0.709396i
$842$		0			0
$843$	−5.56231	−	17.1190i	−0.191576	−	0.589610i
$844$		0			0
$845$	−31.5517	−	22.9236i	−1.08541	−	0.788597i
$846$		0			0
$847$		0			0
$848$		0			0
$849$	9.70820	+	7.05342i	0.333185	+	0.242073i
$850$		0			0
$851$	−0.309017	−	0.951057i	−0.0105930	−	0.0326018i
$852$		0			0
$853$	21.0344	−	15.2824i	0.720206	−	0.523260i	−0.166244	−	0.986085i	$-0.553164\pi$
$853$	21.0344	−	15.2824i	0.720206	−	0.523260i	0.886450	+	0.462825i	$0.153164\pi$
$854$		0			0
$855$	−22.2492	+	68.4761i	−0.760907	+	2.34183i
$856$		0			0
$857$	−24.0000			−0.819824			−0.409912	−	0.912125i	$-0.634441\pi$
$857$	−24.0000			−0.819824			−0.409912	+	0.912125i	$0.634441\pi$
$858$		0			0
$859$	11.0000			0.375315			0.187658	−	0.982235i	$-0.439910\pi$
$859$	11.0000			0.375315			0.187658	+	0.982235i	$0.439910\pi$
$860$		0			0
$861$	7.41641	−	22.8254i	0.252751	−	0.777886i
$862$		0			0
$863$	12.9443	−	9.40456i	0.440628	−	0.320135i	−0.345256	−	0.938508i	$-0.612208\pi$
$863$	12.9443	−	9.40456i	0.440628	−	0.320135i	0.785884	+	0.618373i	$0.212208\pi$
$864$		0			0
$865$	−16.6869	−	51.3571i	−0.567372	−	1.74619i
$866$		0			0
$867$	46.1140	+	33.5038i	1.56611	+	1.13785i
$868$		0			0
$869$		0			0
$870$		0			0
$871$		0			0
$872$		0			0
$873$	−12.9787	−	39.9444i	−0.439263	−	1.35191i
$874$		0			0
$875$	4.85410	−	3.52671i	0.164099	−	0.119225i
$876$		0			0
$877$	17.3050	−	53.2592i	0.584347	−	1.79843i	−0.0175315	−	0.999846i	$-0.505581\pi$
$877$	17.3050	−	53.2592i	0.584347	−	1.79843i	0.601878	−	0.798588i	$-0.294419\pi$
$878$		0			0
$879$	−36.0000			−1.21425
$880$		0			0
$881$	−19.0000			−0.640126			−0.320063	−	0.947396i	$-0.603704\pi$
$881$	−19.0000			−0.640126			−0.320063	+	0.947396i	$0.603704\pi$
$882$		0			0
$883$	−8.65248	+	26.6296i	−0.291179	+	0.896157i	0.693299	+	0.720650i	$0.256156\pi$
$883$	−8.65248	+	26.6296i	−0.291179	+	0.896157i	−0.984478	+	0.175507i	$0.943844\pi$
$884$		0			0
$885$	7.28115	−	5.29007i	0.244753	−	0.177824i
$886$		0			0
$887$	−10.5066	−	32.3359i	−0.352776	−	1.08573i	−0.957288	−	0.289137i	$-0.906632\pi$
$887$	−10.5066	−	32.3359i	−0.352776	−	1.08573i	0.604511	−	0.796597i	$-0.293368\pi$
$888$		0			0
$889$	6.47214	+	4.70228i	0.217068	+	0.157709i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	25.8885	+	18.8091i	0.866327	+	0.629423i
$894$		0			0
$895$	4.63525	+	14.2658i	0.154939	+	0.476855i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	17.3050	−	53.2592i	0.577152	−	1.77629i
$900$		0			0
$901$	−12.0000			−0.399778
$902$		0			0
$903$	36.0000			1.19800
$904$		0			0
$905$	4.63525	−	14.2658i	0.154081	−	0.474213i
$906$		0			0
$907$	−22.6525	+	16.4580i	−0.752163	+	0.546478i	−0.896497	−	0.443051i	$-0.853896\pi$
$907$	−22.6525	+	16.4580i	−0.752163	+	0.546478i	0.144333	+	0.989529i	$0.453896\pi$
$908$		0			0
$909$	−18.5410	−	57.0634i	−0.614967	−	1.89267i
$910$		0			0
$911$	−29.1246	−	21.1603i	−0.964941	−	0.701071i	−0.0106483	−	0.999943i	$-0.503390\pi$
$911$	−29.1246	−	21.1603i	−0.964941	−	0.701071i	−0.954293	+	0.298872i	$0.903390\pi$
$912$		0			0
$913$		0			0
$914$		0			0
$915$	−29.1246	−	21.1603i	−0.962830	−	0.699537i
$916$		0			0
$917$	1.23607	+	3.80423i	0.0408186	+	0.125627i
$918$		0			0
$919$	40.4508	−	29.3893i	1.33435	−	0.969462i	0.334719	−	0.942318i	$-0.391359\pi$
$919$	40.4508	−	29.3893i	1.33435	−	0.969462i	0.999632	−	0.0271443i	$-0.00864136\pi$
$920$		0			0
$921$	3.70820	−	11.4127i	0.122189	−	0.376061i
$922$		0			0
$923$		0			0
$924$		0			0
$925$	−4.00000			−0.131519
$926$		0			0
$927$	−29.6656	+	91.3014i	−0.974347	+	2.99873i
$928$		0			0
$929$	17.7984	−	12.9313i	0.583946	−	0.424261i	−0.256199	−	0.966624i	$-0.582470\pi$
$929$	17.7984	−	12.9313i	0.583946	−	0.424261i	0.840144	+	0.542363i	$0.182470\pi$
$930$		0			0
$931$	−3.70820	−	11.4127i	−0.121531	−	0.374035i
$932$		0			0
$933$	−29.1246	−	21.1603i	−0.953497	−	0.692756i
$934$		0			0
$935$		0			0
$936$		0			0
$937$	−3.23607	−	2.35114i	−0.105718	−	0.0768084i	0.533670	−	0.845693i	$-0.320812\pi$
$937$	−3.23607	−	2.35114i	−0.105718	−	0.0768084i	−0.639388	+	0.768884i	$0.720812\pi$
$938$		0			0
$939$	8.34346	+	25.6785i	0.272278	+	0.837987i
$940$		0			0
$941$	−8.09017	+	5.87785i	−0.263732	+	0.191613i	−0.711791	−	0.702392i	$-0.752116\pi$
$941$	−8.09017	+	5.87785i	−0.263732	+	0.191613i	0.448059	+	0.894004i	$0.352116\pi$
$942$		0			0
$943$	1.23607	−	3.80423i	0.0402519	−	0.123883i
$944$		0			0
$945$	−54.0000			−1.75662
$946$		0			0
$947$	47.0000			1.52729			0.763647	−	0.645634i	$-0.223407\pi$
$947$	47.0000			1.52729			0.763647	+	0.645634i	$0.223407\pi$
$948$		0			0
$949$		0			0
$950$		0			0
$951$	−36.4058	+	26.4503i	−1.18054	+	0.857711i
$952$		0			0
$953$	−10.5066	−	32.3359i	−0.340341	−	1.04746i	−0.964031	−	0.265791i	$-0.914367\pi$
$953$	−10.5066	−	32.3359i	−0.340341	−	1.04746i	0.623689	−	0.781672i	$-0.285633\pi$
$954$		0			0
$955$	−21.8435	−	15.8702i	−0.706838	−	0.513548i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	−24.2705	−	17.6336i	−0.783736	−	0.569417i
$960$		0			0
$961$	5.56231	+	17.1190i	0.179429	+	0.552226i
$962$		0			0
$963$	−9.70820	+	7.05342i	−0.312842	+	0.227293i
$964$		0			0
$965$	−3.70820	+	11.4127i	−0.119371	+	0.367387i
$966$		0			0
$967$	−8.00000			−0.257263			−0.128631	−	0.991692i	$-0.541058\pi$
$967$	−8.00000			−0.257263			−0.128631	+	0.991692i	$0.541058\pi$
$968$		0			0
$969$	72.0000			2.31297
$970$		0			0
$971$	16.3779	−	50.4060i	0.525592	−	1.61761i	−0.237551	−	0.971375i	$-0.576345\pi$
$971$	16.3779	−	50.4060i	0.525592	−	1.61761i	0.763143	−	0.646230i	$-0.223655\pi$
$972$		0			0
$973$	−35.5967	+	25.8626i	−1.14118	+	0.829115i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	8.89919	+	6.46564i	0.284710	+	0.206854i	0.720969	−	0.692967i	$-0.243697\pi$
$977$	8.89919	+	6.46564i	0.284710	+	0.206854i	−0.436259	+	0.899821i	$0.643697\pi$
$978$		0			0
$979$		0			0
$980$		0			0
$981$	67.9574	+	49.3740i	2.16971	+	1.57639i
$982$		0			0
$983$	7.72542	+	23.7764i	0.246403	+	0.758350i	0.995403	+	0.0957796i	$0.0305344\pi$
$983$	7.72542	+	23.7764i	0.246403	+	0.758350i	−0.749000	+	0.662570i	$0.769466\pi$
$984$		0			0
$985$	14.5623	−	10.5801i	0.463994	−	0.337111i
$986$		0			0
$987$	−14.8328	+	45.6507i	−0.472134	+	1.45308i
$988$		0			0
$989$	6.00000			0.190789
$990$		0			0
$991$	16.0000			0.508257			0.254128	−	0.967170i	$-0.418211\pi$
$991$	16.0000			0.508257			0.254128	+	0.967170i	$0.418211\pi$
$992$		0			0
$993$	32.4468	−	99.8609i	1.02967	−	3.16899i
$994$		0			0
$995$	19.4164	−	14.1068i	0.615542	−	0.447217i
$996$		0			0
$997$	0.618034	+	1.90211i	0.0195733	+	0.0602405i	0.960366	−	0.278742i	$-0.0899173\pi$
$997$	0.618034	+	1.90211i	0.0195733	+	0.0602405i	−0.940793	+	0.338982i	$0.889917\pi$
$998$		0			0
$999$	−7.28115	−	5.29007i	−0.230365	−	0.167370i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	968.2.i.j.81.1		4
11.2	odd	10		968.2.i.i.753.1		4
11.3	even	5	inner	968.2.i.j.729.1		4
11.4	even	5	inner	968.2.i.j.9.1		4
11.5	even	5		88.2.a.a.1.1	✓	1
11.6	odd	10		968.2.a.a.1.1		1
11.7	odd	10		968.2.i.i.9.1		4
11.8	odd	10		968.2.i.i.729.1		4
11.9	even	5	inner	968.2.i.j.753.1		4
11.10	odd	2		968.2.i.i.81.1		4
33.5	odd	10		792.2.a.g.1.1		1
33.17	even	10		8712.2.a.x.1.1		1
44.27	odd	10		176.2.a.c.1.1		1
44.39	even	10		1936.2.a.l.1.1		1
55.27	odd	20		2200.2.b.a.1849.2		2
55.38	odd	20		2200.2.b.a.1849.1		2
55.49	even	10		2200.2.a.k.1.1		1
77.27	odd	10		4312.2.a.l.1.1		1
88.5	even	10		704.2.a.l.1.1		1
88.27	odd	10		704.2.a.b.1.1		1
88.61	odd	10		7744.2.a.bk.1.1		1
88.83	even	10		7744.2.a.b.1.1		1
132.71	even	10		1584.2.a.q.1.1		1
176.5	even	20		2816.2.c.i.1409.2		2
176.27	odd	20		2816.2.c.d.1409.1		2
176.93	even	20		2816.2.c.i.1409.1		2
176.115	odd	20		2816.2.c.d.1409.2		2
220.27	even	20		4400.2.b.b.4049.1		2
220.159	odd	10		4400.2.a.a.1.1		1
220.203	even	20		4400.2.b.b.4049.2		2
264.5	odd	10		6336.2.a.h.1.1		1
264.203	even	10		6336.2.a.k.1.1		1
308.27	even	10		8624.2.a.c.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
88.2.a.a.1.1	✓	1	11.5	even	5
176.2.a.c.1.1		1	44.27	odd	10
704.2.a.b.1.1		1	88.27	odd	10
704.2.a.l.1.1		1	88.5	even	10
792.2.a.g.1.1		1	33.5	odd	10
968.2.a.a.1.1		1	11.6	odd	10
968.2.i.i.9.1		4	11.7	odd	10
968.2.i.i.81.1		4	11.10	odd	2
968.2.i.i.729.1		4	11.8	odd	10
968.2.i.i.753.1		4	11.2	odd	10
968.2.i.j.9.1		4	11.4	even	5	inner
968.2.i.j.81.1		4	1.1	even	1	trivial
968.2.i.j.729.1		4	11.3	even	5	inner
968.2.i.j.753.1		4	11.9	even	5	inner
1584.2.a.q.1.1		1	132.71	even	10
1936.2.a.l.1.1		1	44.39	even	10
2200.2.a.k.1.1		1	55.49	even	10
2200.2.b.a.1849.1		2	55.38	odd	20
2200.2.b.a.1849.2		2	55.27	odd	20
2816.2.c.d.1409.1		2	176.27	odd	20
2816.2.c.d.1409.2		2	176.115	odd	20
2816.2.c.i.1409.1		2	176.93	even	20
2816.2.c.i.1409.2		2	176.5	even	20
4312.2.a.l.1.1		1	77.27	odd	10
4400.2.a.a.1.1		1	220.159	odd	10
4400.2.b.b.4049.1		2	220.27	even	20
4400.2.b.b.4049.2		2	220.203	even	20
6336.2.a.h.1.1		1	264.5	odd	10
6336.2.a.k.1.1		1	264.203	even	10
7744.2.a.b.1.1		1	88.83	even	10
7744.2.a.bk.1.1		1	88.61	odd	10
8624.2.a.c.1.1		1	308.27	even	10
8712.2.a.x.1.1		1	33.17	even	10

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:	\( N \)	\(=\)	\( 968 = 2^{3} \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	968.i (of order \(5\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.927051 + 2.85317i) q^{3} +(2.42705 - 1.76336i) q^{5} +(-0.618034 - 1.90211i) q^{7} +(-4.85410 - 3.52671i) q^{9} +O(q^{10})\)	\(q+(-0.927051 + 2.85317i) q^{3} +(2.42705 - 1.76336i) q^{5} +(-0.618034 - 1.90211i) q^{7} +(-4.85410 - 3.52671i) q^{9} +(2.78115 + 8.55951i) q^{15} +(4.85410 - 3.52671i) q^{17} +(1.23607 - 3.80423i) q^{19} +6.00000 q^{21} +1.00000 q^{23} +(1.23607 - 3.80423i) q^{25} +(7.28115 - 5.29007i) q^{27} +(-2.47214 - 7.60845i) q^{29} +(5.66312 + 4.11450i) q^{31} +(-4.85410 - 3.52671i) q^{35} +(-0.309017 - 0.951057i) q^{37} +(1.23607 - 3.80423i) q^{41} +6.00000 q^{43} -18.0000 q^{45} +(-2.47214 + 7.60845i) q^{47} +(2.42705 - 1.76336i) q^{49} +(5.56231 + 17.1190i) q^{51} +(-1.61803 - 1.17557i) q^{53} +(9.70820 + 7.05342i) q^{57} +(-0.309017 - 0.951057i) q^{59} +(-3.23607 + 2.35114i) q^{61} +(-3.70820 + 11.4127i) q^{63} -5.00000 q^{67} +(-0.927051 + 2.85317i) q^{69} +(-2.42705 + 1.76336i) q^{71} +(4.94427 + 15.2169i) q^{73} +(9.70820 + 7.05342i) q^{75} +(-1.61803 - 1.17557i) q^{79} +(2.78115 + 8.55951i) q^{81} +(1.61803 - 1.17557i) q^{83} +(5.56231 - 17.1190i) q^{85} +24.0000 q^{87} +15.0000 q^{89} +(-16.9894 + 12.3435i) q^{93} +(-3.70820 - 11.4127i) q^{95} +(5.66312 + 4.11450i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 3 q^{3} + 3 q^{5} + 2 q^{7} - 6 q^{9}+O(q^{10}) \) 4 * q + 3 * q^3 + 3 * q^5 + 2 * q^7 - 6 * q^9	\( 4 q + 3 q^{3} + 3 q^{5} + 2 q^{7} - 6 q^{9} - 9 q^{15} + 6 q^{17} - 4 q^{19} + 24 q^{21} + 4 q^{23} - 4 q^{25} + 9 q^{27} + 8 q^{29} + 7 q^{31} - 6 q^{35} + q^{37} - 4 q^{41} + 24 q^{43} - 72 q^{45} + 8 q^{47} + 3 q^{49} - 18 q^{51} - 2 q^{53} + 12 q^{57} + q^{59} - 4 q^{61} + 12 q^{63} - 20 q^{67} + 3 q^{69} - 3 q^{71} - 16 q^{73} + 12 q^{75} - 2 q^{79} - 9 q^{81} + 2 q^{83} - 18 q^{85} + 96 q^{87} + 60 q^{89} - 21 q^{93} + 12 q^{95} + 7 q^{97}+O(q^{100}) \) 4 * q + 3 * q^3 + 3 * q^5 + 2 * q^7 - 6 * q^9 - 9 * q^15 + 6 * q^17 - 4 * q^19 + 24 * q^21 + 4 * q^23 - 4 * q^25 + 9 * q^27 + 8 * q^29 + 7 * q^31 - 6 * q^35 + q^37 - 4 * q^41 + 24 * q^43 - 72 * q^45 + 8 * q^47 + 3 * q^49 - 18 * q^51 - 2 * q^53 + 12 * q^57 + q^59 - 4 * q^61 + 12 * q^63 - 20 * q^67 + 3 * q^69 - 3 * q^71 - 16 * q^73 + 12 * q^75 - 2 * q^79 - 9 * q^81 + 2 * q^83 - 18 * q^85 + 96 * q^87 + 60 * q^89 - 21 * q^93 + 12 * q^95 + 7 * q^97

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