LMFDB - Embedded newform 496.2.n.b.97.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [496,2,Mod(33,496)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(496, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 0, 8]))

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

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

chi := DirichletCharacter("496.33");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$N$	$=$	$496 = 2^{4} \cdot 31$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	496.n (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:	$3.96057994026$
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:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$1$
Twist minimal:	no (minimal twist has level 31)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			97.1
Root			$-0.309017 - 0.951057i$ of defining polynomial
Character	$\chi$	$=$	496.97
Dual form			496.2.n.b.225.1

$q$ -expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.309017 - 0.951057i) q^{3} -2.61803 q^{5} +(2.42705 - 1.76336i) q^{7} +(1.61803 + 1.17557i) q^{9} +(-0.618034 + 0.449028i) q^{11} +(1.50000 - 4.61653i) q^{13} +(-0.809017 + 2.48990i) q^{15} +(-0.190983 - 0.138757i) q^{17} +(-1.54508 - 4.75528i) q^{19} +(-0.927051 - 2.85317i) q^{21} +(-4.42705 - 3.21644i) q^{23} +1.85410 q^{25} +(4.04508 - 2.93893i) q^{27} +(-2.66312 - 8.19624i) q^{29} +(5.54508 - 0.502029i) q^{31} +(0.236068 + 0.726543i) q^{33} +(-6.35410 + 4.61653i) q^{35} +0.236068 q^{37} +(-3.92705 - 2.85317i) q^{39} +(2.00000 + 6.15537i) q^{41} +(1.42705 + 4.39201i) q^{43} +(-4.23607 - 3.07768i) q^{45} +(1.04508 - 3.21644i) q^{47} +(0.618034 - 1.90211i) q^{49} +(-0.190983 + 0.138757i) q^{51} +(10.2812 + 7.46969i) q^{53} +(1.61803 - 1.17557i) q^{55} -5.00000 q^{57} +(-2.92705 + 9.00854i) q^{59} -6.94427 q^{61} +6.00000 q^{63} +(-3.92705 + 12.0862i) q^{65} +4.23607 q^{67} +(-4.42705 + 3.21644i) q^{69} +(0.0729490 + 0.0530006i) q^{71} +(6.92705 - 5.03280i) q^{73} +(0.572949 - 1.76336i) q^{75} +(-0.708204 + 2.17963i) q^{77} +(0.309017 + 0.951057i) q^{81} +(1.26393 + 3.88998i) q^{83} +(0.500000 + 0.363271i) q^{85} -8.61803 q^{87} +(5.16312 - 3.75123i) q^{89} +(-4.50000 - 13.8496i) q^{91} +(1.23607 - 5.42882i) q^{93} +(4.04508 + 12.4495i) q^{95} +(4.28115 - 3.11044i) q^{97} -1.52786 q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$4 q - q^{3} - 6 q^{5} + 3 q^{7} + 2 q^{9} + 2 q^{11} + 6 q^{13} - q^{15} - 3 q^{17} + 5 q^{19} + 3 q^{21} - 11 q^{23} - 6 q^{25} + 5 q^{27} + 5 q^{29} + 11 q^{31} - 8 q^{33} - 12 q^{35} - 8 q^{37} - 9 q^{39}+ \cdots - 24 q^{99}+O(q^{100})$ 4 * q - q^3 - 6 * q^5 + 3 * q^7 + 2 * q^9 + 2 * q^11 + 6 * q^13 - q^15 - 3 * q^17 + 5 * q^19 + 3 * q^21 - 11 * q^23 - 6 * q^25 + 5 * q^27 + 5 * q^29 + 11 * q^31 - 8 * q^33 - 12 * q^35 - 8 * q^37 - 9 * q^39 + 8 * q^41 - q^43 - 8 * q^45 - 7 * q^47 - 2 * q^49 - 3 * q^51 + 21 * q^53 + 2 * q^55 - 20 * q^57 - 5 * q^59 + 8 * q^61 + 24 * q^63 - 9 * q^65 + 8 * q^67 - 11 * q^69 + 7 * q^71 + 21 * q^73 + 9 * q^75 + 24 * q^77 - q^81 + 14 * q^83 + 2 * q^85 - 30 * q^87 + 5 * q^89 - 18 * q^91 - 4 * q^93 + 5 * q^95 - 3 * q^97 - 24 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/496\mathbb{Z}\right)^\times$ .

$n$	$63$	$65$	$373$
$\chi(n)$	$1$	$e\left(\frac{3}{5}\right)$	$1$

Coefficient data

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

Display

a_p

with

p

up to: 50 250 1000 (See

a_n

instead) (See

a_n

instead) (See

a_n

instead) Display

a_n

with

n

up to: 50 250 1000 (See only

a_p

) (See only

a_p

) (See only

a_p

)

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

$2$		0			0
$2$		0			0
$3$	0.309017	−	0.951057i	0.178411	−	0.549093i	−0.821362	−	0.570408i	$-0.806785\pi$
$3$	0.309017	−	0.951057i	0.178411	−	0.549093i	0.999773	+	0.0213149i	$0.00678525\pi$
$4$		0			0
$5$	−2.61803			−1.17082			−0.585410	−	0.810737i	$-0.699067\pi$
$5$	−2.61803			−1.17082			−0.585410	+	0.810737i	$0.699067\pi$
$6$		0			0
$7$	2.42705	−	1.76336i	0.917339	−	0.666486i	−0.0255212	−	0.999674i	$-0.508125\pi$
$7$	2.42705	−	1.76336i	0.917339	−	0.666486i	0.942860	+	0.333188i	$0.108125\pi$
$8$		0			0
$9$	1.61803	+	1.17557i	0.539345	+	0.391857i
$10$		0			0
$11$	−0.618034	+	0.449028i	−0.186344	+	0.135387i	−0.677046	−	0.735940i	$-0.736740\pi$
$11$	−0.618034	+	0.449028i	−0.186344	+	0.135387i	0.490702	+	0.871327i	$0.336740\pi$
$12$		0			0
$13$	1.50000	−	4.61653i	0.416025	−	1.28039i	−0.495306	−	0.868719i	$-0.664944\pi$
$13$	1.50000	−	4.61653i	0.416025	−	1.28039i	0.911331	−	0.411675i	$-0.135056\pi$
$14$		0			0
$15$	−0.809017	+	2.48990i	−0.208887	+	0.642889i
$16$		0			0
$17$	−0.190983	−	0.138757i	−0.0463202	−	0.0336536i	0.564384	−	0.825512i	$-0.309114\pi$
$17$	−0.190983	−	0.138757i	−0.0463202	−	0.0336536i	−0.610704	+	0.791859i	$0.709114\pi$
$18$		0			0
$19$	−1.54508	−	4.75528i	−0.354467	−	1.09094i	−0.956318	−	0.292328i	$-0.905570\pi$
$19$	−1.54508	−	4.75528i	−0.354467	−	1.09094i	0.601851	−	0.798608i	$-0.294430\pi$
$20$		0			0
$21$	−0.927051	−	2.85317i	−0.202299	−	0.622613i
$22$		0			0
$23$	−4.42705	−	3.21644i	−0.923104	−	0.670674i	0.0211907	−	0.999775i	$-0.493254\pi$
$23$	−4.42705	−	3.21644i	−0.923104	−	0.670674i	−0.944295	+	0.329101i	$0.893254\pi$
$24$		0			0
$25$	1.85410			0.370820
$26$		0			0
$27$	4.04508	−	2.93893i	0.778477	−	0.565597i
$28$		0			0
$29$	−2.66312	−	8.19624i	−0.494529	−	1.52200i	−0.817690	−	0.575659i	$-0.804746\pi$
$29$	−2.66312	−	8.19624i	−0.494529	−	1.52200i	0.323161	−	0.946344i	$-0.395254\pi$
$30$		0			0
$31$	5.54508	−	0.502029i	0.995927	−	0.0901670i
$31$	5.54508	−	0.502029i	0.995927	−	0.0901670i
$32$		0			0
$33$	0.236068	+	0.726543i	0.0410942	+	0.126475i
$34$		0			0
$35$	−6.35410	+	4.61653i	−1.07404	+	0.780335i
$36$		0			0
$37$	0.236068			0.0388093			0.0194047	−	0.999812i	$-0.493823\pi$
$37$	0.236068			0.0388093			0.0194047	+	0.999812i	$0.493823\pi$
$38$		0			0
$39$	−3.92705	−	2.85317i	−0.628831	−	0.456873i
$40$		0			0
$41$	2.00000	+	6.15537i	0.312348	+	0.961307i	0.976833	+	0.214005i	$0.0686510\pi$
$41$	2.00000	+	6.15537i	0.312348	+	0.961307i	−0.664485	+	0.747302i	$0.731349\pi$
$42$		0			0
$43$	1.42705	+	4.39201i	0.217623	+	0.669775i	0.998957	+	0.0456620i	$0.0145397\pi$
$43$	1.42705	+	4.39201i	0.217623	+	0.669775i	−0.781334	+	0.624113i	$0.785460\pi$
$44$		0			0
$45$	−4.23607	−	3.07768i	−0.631476	−	0.458794i
$46$		0			0
$47$	1.04508	−	3.21644i	0.152441	−	0.469166i	−0.845451	−	0.534052i	$-0.820668\pi$
$47$	1.04508	−	3.21644i	0.152441	−	0.469166i	0.997893	+	0.0648863i	$0.0206685\pi$
$48$		0			0
$49$	0.618034	−	1.90211i	0.0882906	−	0.271730i
$50$		0			0
$51$	−0.190983	+	0.138757i	−0.0267430	+	0.0194299i
$52$		0			0
$53$	10.2812	+	7.46969i	1.41222	+	1.02604i	0.992994	+	0.118162i	$0.0377001\pi$
$53$	10.2812	+	7.46969i	1.41222	+	1.02604i	0.419231	+	0.907880i	$0.362300\pi$
$54$		0			0
$55$	1.61803	−	1.17557i	0.218176	−	0.158514i
$56$		0			0
$57$	−5.00000			−0.662266
$58$		0			0
$59$	−2.92705	+	9.00854i	−0.381070	+	1.17281i	0.558222	+	0.829692i	$0.311484\pi$
$59$	−2.92705	+	9.00854i	−0.381070	+	1.17281i	−0.939292	+	0.343120i	$0.888516\pi$
$60$		0			0
$61$	−6.94427			−0.889123			−0.444561	−	0.895748i	$-0.646640\pi$
$61$	−6.94427			−0.889123			−0.444561	+	0.895748i	$0.646640\pi$
$62$		0			0
$63$	6.00000			0.755929
$64$		0			0
$65$	−3.92705	+	12.0862i	−0.487091	+	1.49911i
$66$		0			0
$67$	4.23607			0.517518			0.258759	−	0.965942i	$-0.416686\pi$
$67$	4.23607			0.517518			0.258759	+	0.965942i	$0.416686\pi$
$68$		0			0
$69$	−4.42705	+	3.21644i	−0.532954	+	0.387214i
$70$		0			0
$71$	0.0729490	+	0.0530006i	0.00865746	+	0.00629001i	0.592106	−	0.805860i	$-0.298297\pi$
$71$	0.0729490	+	0.0530006i	0.00865746	+	0.00629001i	−0.583448	+	0.812150i	$0.698297\pi$
$72$		0			0
$73$	6.92705	−	5.03280i	0.810750	−	0.589044i	−0.103298	−	0.994650i	$-0.532940\pi$
$73$	6.92705	−	5.03280i	0.810750	−	0.589044i	0.914048	+	0.405606i	$0.132940\pi$
$74$		0			0
$75$	0.572949	−	1.76336i	0.0661585	−	0.203615i
$76$		0			0
$77$	−0.708204	+	2.17963i	−0.0807073	+	0.248392i
$78$		0			0
$79$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$79$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$80$		0			0
$81$	0.309017	+	0.951057i	0.0343352	+	0.105673i
$82$		0			0
$83$	1.26393	+	3.88998i	0.138735	+	0.426981i	0.996152	−	0.0876401i	$-0.0279326\pi$
$83$	1.26393	+	3.88998i	0.138735	+	0.426981i	−0.857418	+	0.514621i	$0.827933\pi$
$84$		0			0
$85$	0.500000	+	0.363271i	0.0542326	+	0.0394023i
$86$		0			0
$87$	−8.61803			−0.923950
$88$		0			0
$89$	5.16312	−	3.75123i	0.547290	−	0.397629i	−0.279496	−	0.960147i	$-0.590167\pi$
$89$	5.16312	−	3.75123i	0.547290	−	0.397629i	0.826785	+	0.562518i	$0.190167\pi$
$90$		0			0
$91$	−4.50000	−	13.8496i	−0.471728	−	1.45183i
$92$		0			0
$93$	1.23607	−	5.42882i	0.128174	−	0.562943i
$94$		0			0
$95$	4.04508	+	12.4495i	0.415017	+	1.27729i
$96$		0			0
$97$	4.28115	−	3.11044i	0.434685	−	0.315817i	−0.348834	−	0.937184i	$-0.613422\pi$
$97$	4.28115	−	3.11044i	0.434685	−	0.315817i	0.783520	+	0.621367i	$0.213422\pi$
$98$		0			0
$99$	−1.52786			−0.153556
$100$		0			0
$101$	−3.85410	−	2.80017i	−0.383497	−	0.278627i	0.379288	−	0.925279i	$-0.376169\pi$
$101$	−3.85410	−	2.80017i	−0.383497	−	0.278627i	−0.762786	+	0.646651i	$0.776169\pi$
$102$		0			0
$103$	0.0450850	+	0.138757i	0.00444235	+	0.0136722i	0.953253	−	0.302173i	$-0.0977120\pi$
$103$	0.0450850	+	0.138757i	0.00444235	+	0.0136722i	−0.948811	+	0.315845i	$0.897712\pi$
$104$		0			0
$105$	2.42705	+	7.46969i	0.236856	+	0.728968i
$106$		0			0
$107$	0.881966	+	0.640786i	0.0852629	+	0.0619471i	0.629600	−	0.776919i	$-0.283219\pi$
$107$	0.881966	+	0.640786i	0.0852629	+	0.0619471i	−0.544337	+	0.838867i	$0.683219\pi$
$108$		0			0
$109$	−2.60081	+	8.00448i	−0.249113	+	0.766690i	0.745820	+	0.666147i	$0.232058\pi$
$109$	−2.60081	+	8.00448i	−0.249113	+	0.766690i	−0.994933	+	0.100543i	$0.967942\pi$
$110$		0			0
$111$	0.0729490	−	0.224514i	0.00692401	−	0.0213099i
$112$		0			0
$113$	1.50000	−	1.08981i	0.141108	−	0.102521i	−0.514992	−	0.857195i	$-0.672205\pi$
$113$	1.50000	−	1.08981i	0.141108	−	0.102521i	0.656100	+	0.754674i	$0.272205\pi$
$114$		0			0
$115$	11.5902	+	8.42075i	1.08079	+	0.785239i
$116$		0			0
$117$	7.85410	−	5.70634i	0.726112	−	0.527551i
$118$		0			0
$119$	−0.708204			−0.0649209
$120$		0			0
$121$	−3.21885	+	9.90659i	−0.292622	+	0.900599i
$122$		0			0
$123$	6.47214			0.583573
$124$		0			0
$125$	8.23607			0.736656
$126$		0			0
$127$	−3.16312	+	9.73508i	−0.280681	+	0.863849i	0.706979	+	0.707235i	$0.250058\pi$
$127$	−3.16312	+	9.73508i	−0.280681	+	0.863849i	−0.987660	+	0.156614i	$0.949942\pi$
$128$		0			0
$129$	4.61803			0.406595
$130$		0			0
$131$	0.0729490	−	0.0530006i	0.00637359	−	0.00463068i	−0.584594	−	0.811326i	$-0.698746\pi$
$131$	0.0729490	−	0.0530006i	0.00637359	−	0.00463068i	0.590967	+	0.806695i	$0.298746\pi$
$132$		0			0
$133$	−12.1353	−	8.81678i	−1.05226	−	0.764512i
$134$		0			0
$135$	−10.5902	+	7.69421i	−0.911457	+	0.662212i
$136$		0			0
$137$	−2.00000	+	6.15537i	−0.170872	+	0.525888i	−0.999421	−	0.0340275i	$-0.989167\pi$
$137$	−2.00000	+	6.15537i	−0.170872	+	0.525888i	0.828549	+	0.559916i	$0.189167\pi$
$138$		0			0
$139$	−1.80902	+	5.56758i	−0.153439	+	0.472236i	−0.997999	−	0.0632239i	$-0.979862\pi$
$139$	−1.80902	+	5.56758i	−0.153439	+	0.472236i	0.844561	+	0.535460i	$0.179862\pi$
$140$		0			0
$141$	−2.73607	−	1.98787i	−0.230418	−	0.167409i
$142$		0			0
$143$	1.14590	+	3.52671i	0.0958248	+	0.294918i
$144$		0			0
$145$	6.97214	+	21.4580i	0.579004	+	1.78199i
$146$		0			0
$147$	−1.61803	−	1.17557i	−0.133453	−	0.0969594i
$148$		0			0
$149$	−17.0344			−1.39552			−0.697758	−	0.716334i	$-0.745819\pi$
$149$	−17.0344			−1.39552			−0.697758	+	0.716334i	$0.745819\pi$
$150$		0			0
$151$	−15.7812	+	11.4657i	−1.28425	+	0.933064i	−0.999673	−	0.0255888i	$-0.991854\pi$
$151$	−15.7812	+	11.4657i	−1.28425	+	0.933064i	−0.284579	+	0.958652i	$0.591854\pi$
$152$		0			0
$153$	−0.145898	−	0.449028i	−0.0117952	−	0.0363018i
$154$		0			0
$155$	−14.5172	+	1.31433i	−1.16605	+	0.105569i
$156$		0			0
$157$	3.00000	+	9.23305i	0.239426	+	0.736878i	0.996503	+	0.0835524i	$0.0266266\pi$
$157$	3.00000	+	9.23305i	0.239426	+	0.736878i	−0.757077	+	0.653325i	$0.773373\pi$
$158$		0			0
$159$	10.2812	−	7.46969i	0.815348	−	0.592385i
$160$		0			0
$161$	−16.4164			−1.29379
$162$		0			0
$163$	−10.2812	−	7.46969i	−0.805282	−	0.585072i	0.107177	−	0.994240i	$-0.465819\pi$
$163$	−10.2812	−	7.46969i	−0.805282	−	0.585072i	−0.912459	+	0.409168i	$0.865819\pi$
$164$		0			0
$165$	−0.618034	−	1.90211i	−0.0481139	−	0.148079i
$166$		0			0
$167$	2.85410	+	8.78402i	0.220857	+	0.679728i	0.998686	+	0.0512518i	$0.0163211\pi$
$167$	2.85410	+	8.78402i	0.220857	+	0.679728i	−0.777829	+	0.628476i	$0.783679\pi$
$168$		0			0
$169$	−8.54508	−	6.20837i	−0.657314	−	0.477567i
$170$		0			0
$171$	3.09017	−	9.51057i	0.236311	−	0.727291i
$172$		0			0
$173$	0.281153	−	0.865300i	0.0213757	−	0.0657875i	−0.939800	−	0.341726i	$-0.888989\pi$
$173$	0.281153	−	0.865300i	0.0213757	−	0.0657875i	0.961175	+	0.275938i	$0.0889886\pi$
$174$		0			0
$175$	4.50000	−	3.26944i	0.340168	−	0.247147i
$176$		0			0
$177$	7.66312	+	5.56758i	0.575995	+	0.418485i
$178$		0			0
$179$	16.0172	−	11.6372i	1.19718	−	0.869805i	0.203179	−	0.979142i	$-0.434873\pi$
$179$	16.0172	−	11.6372i	1.19718	−	0.869805i	0.994005	+	0.109337i	$0.0348728\pi$
$180$		0			0
$181$	17.0000			1.26360			0.631800	−	0.775131i	$-0.282316\pi$
$181$	17.0000			1.26360			0.631800	+	0.775131i	$0.282316\pi$
$182$		0			0
$183$	−2.14590	+	6.60440i	−0.158629	+	0.488211i
$184$		0			0
$185$	−0.618034			−0.0454388
$186$		0			0
$187$	0.180340			0.0131878
$188$		0			0
$189$	4.63525	−	14.2658i	0.337165	−	1.03769i
$190$		0			0
$191$	16.0902			1.16424			0.582122	−	0.813102i	$-0.302223\pi$
$191$	16.0902			1.16424			0.582122	+	0.813102i	$0.302223\pi$
$192$		0			0
$193$	1.92705	−	1.40008i	0.138712	−	0.100780i	−0.516265	−	0.856429i	$-0.672678\pi$
$193$	1.92705	−	1.40008i	0.138712	−	0.100780i	0.654977	+	0.755648i	$0.272678\pi$
$194$		0			0
$195$	10.2812	+	7.46969i	0.736249	+	0.534916i
$196$		0			0
$197$	−13.2812	+	9.64932i	−0.946243	+	0.687486i	−0.949915	−	0.312507i	$-0.898831\pi$
$197$	−13.2812	+	9.64932i	−0.946243	+	0.687486i	0.00367232	+	0.999993i	$0.498831\pi$
$198$		0			0
$199$	8.25329	−	25.4010i	0.585060	−	1.80063i	−0.0139686	−	0.999902i	$-0.504446\pi$
$199$	8.25329	−	25.4010i	0.585060	−	1.80063i	0.599029	−	0.800728i	$-0.295554\pi$
$200$		0			0
$201$	1.30902	−	4.02874i	0.0923309	−	0.284165i
$202$		0			0
$203$	−20.9164	−	15.1967i	−1.46804	−	1.06660i
$204$		0			0
$205$	−5.23607	−	16.1150i	−0.365703	−	1.12552i
$206$		0			0
$207$	−3.38197	−	10.4086i	−0.235063	−	0.723449i
$208$		0			0
$209$	3.09017	+	2.24514i	0.213752	+	0.155300i
$210$		0			0
$211$	8.00000			0.550743			0.275371	−	0.961338i	$-0.411199\pi$
$211$	8.00000			0.550743			0.275371	+	0.961338i	$0.411199\pi$
$212$		0			0
$213$	0.0729490	−	0.0530006i	0.00499838	−	0.00363154i
$214$		0			0
$215$	−3.73607	−	11.4984i	−0.254798	−	0.784187i
$216$		0			0
$217$	12.5729	−	10.9964i	0.853507	−	0.746485i
$218$		0			0
$219$	−2.64590	−	8.14324i	−0.178793	−	0.550269i
$220$		0			0
$221$	−0.927051	+	0.673542i	−0.0623602	+	0.0453073i
$222$		0			0
$223$	−0.708204			−0.0474248			−0.0237124	−	0.999719i	$-0.507549\pi$
$223$	−0.708204			−0.0474248			−0.0237124	+	0.999719i	$0.507549\pi$
$224$		0			0
$225$	3.00000	+	2.17963i	0.200000	+	0.145309i
$226$		0			0
$227$	6.40983	+	19.7274i	0.425435	+	1.30936i	0.902577	+	0.430529i	$0.141673\pi$
$227$	6.40983	+	19.7274i	0.425435	+	1.30936i	−0.477141	+	0.878827i	$0.658327\pi$
$228$		0			0
$229$	−2.23607	−	6.88191i	−0.147764	−	0.454769i	0.849592	−	0.527440i	$-0.176848\pi$
$229$	−2.23607	−	6.88191i	−0.147764	−	0.454769i	−0.997356	+	0.0726703i	$0.976848\pi$
$230$		0			0
$231$	1.85410	+	1.34708i	0.121991	+	0.0886316i
$232$		0			0
$233$	5.80902	−	17.8783i	0.380561	−	1.17125i	−0.559088	−	0.829108i	$-0.688849\pi$
$233$	5.80902	−	17.8783i	0.380561	−	1.17125i	0.939649	−	0.342139i	$-0.111151\pi$
$234$		0			0
$235$	−2.73607	+	8.42075i	−0.178481	+	0.549309i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	−10.8541	−	7.88597i	−0.702093	−	0.510101i	0.178520	−	0.983936i	$-0.442869\pi$
$239$	−10.8541	−	7.88597i	−0.702093	−	0.510101i	−0.880613	+	0.473836i	$0.842869\pi$
$240$		0			0
$241$	6.89919	−	5.01255i	0.444416	−	0.322887i	−0.342971	−	0.939346i	$-0.611433\pi$
$241$	6.89919	−	5.01255i	0.444416	−	0.322887i	0.787387	+	0.616459i	$0.211433\pi$
$242$		0			0
$243$	16.0000			1.02640
$244$		0			0
$245$	−1.61803	+	4.97980i	−0.103372	+	0.318148i
$246$		0			0
$247$	−24.2705			−1.54430
$248$		0			0
$249$	4.09017			0.259204
$250$		0			0
$251$	−0.291796	+	0.898056i	−0.0184180	+	0.0566848i	−0.959843	−	0.280537i	$-0.909487\pi$
$251$	−0.291796	+	0.898056i	−0.0184180	+	0.0566848i	0.941425	+	0.337222i	$0.109487\pi$
$252$		0			0
$253$	4.18034			0.262816
$254$		0			0
$255$	0.500000	−	0.363271i	0.0313112	−	0.0227489i
$256$		0			0
$257$	−1.14590	−	0.832544i	−0.0714792	−	0.0519326i	0.551472	−	0.834194i	$-0.314066\pi$
$257$	−1.14590	−	0.832544i	−0.0714792	−	0.0519326i	−0.622951	+	0.782261i	$0.714066\pi$
$258$		0			0
$259$	0.572949	−	0.416272i	0.0356013	−	0.0258659i
$260$		0			0
$261$	5.32624	−	16.3925i	0.329686	−	1.01467i
$262$		0			0
$263$	3.33688	−	10.2699i	0.205761	−	0.633267i	−0.793920	−	0.608022i	$-0.791963\pi$
$263$	3.33688	−	10.2699i	0.205761	−	0.633267i	0.999681	−	0.0252452i	$-0.00803665\pi$
$264$		0			0
$265$	−26.9164	−	19.5559i	−1.65346	−	1.20131i
$266$		0			0
$267$	−1.97214	−	6.06961i	−0.120693	−	0.371454i
$268$		0			0
$269$	−0.427051	−	1.31433i	−0.0260378	−	0.0801360i	0.937193	−	0.348811i	$-0.113414\pi$
$269$	−0.427051	−	1.31433i	−0.0260378	−	0.0801360i	−0.963231	+	0.268675i	$0.913414\pi$
$270$		0			0
$271$	7.73607	+	5.62058i	0.469933	+	0.341426i	0.797415	−	0.603431i	$-0.206200\pi$
$271$	7.73607	+	5.62058i	0.469933	+	0.341426i	−0.327482	+	0.944857i	$0.606200\pi$
$272$		0			0
$273$	−14.5623			−0.881351
$274$		0			0
$275$	−1.14590	+	0.832544i	−0.0691003	+	0.0502043i
$276$		0			0
$277$	4.11803	+	12.6740i	0.247429	+	0.761507i	0.995228	+	0.0975818i	$0.0311108\pi$
$277$	4.11803	+	12.6740i	0.247429	+	0.761507i	−0.747799	+	0.663925i	$0.768889\pi$
$278$		0			0
$279$	9.56231	+	5.70634i	0.572480	+	0.341630i
$280$		0			0
$281$	5.88197	+	18.1028i	0.350889	+	1.07992i	0.958355	+	0.285579i	$0.0921859\pi$
$281$	5.88197	+	18.1028i	0.350889	+	1.07992i	−0.607466	+	0.794345i	$0.707814\pi$
$282$		0			0
$283$	5.30902	−	3.85723i	0.315588	−	0.229288i	−0.418702	−	0.908124i	$-0.637515\pi$
$283$	5.30902	−	3.85723i	0.315588	−	0.229288i	0.734291	+	0.678835i	$0.237515\pi$
$284$		0			0
$285$	13.0902			0.775395
$286$		0			0
$287$	15.7082	+	11.4127i	0.927226	+	0.673669i
$288$		0			0
$289$	−5.23607	−	16.1150i	−0.308004	−	0.947939i
$290$		0			0
$291$	−1.63525	−	5.03280i	−0.0958603	−	0.295028i
$292$		0			0
$293$	6.66312	+	4.84104i	0.389264	+	0.282817i	0.765154	−	0.643848i	$-0.222663\pi$
$293$	6.66312	+	4.84104i	0.389264	+	0.282817i	−0.375890	+	0.926664i	$0.622663\pi$
$294$		0			0
$295$	7.66312	−	23.5847i	0.446164	−	1.37315i
$296$		0			0
$297$	−1.18034	+	3.63271i	−0.0684903	+	0.210791i
$298$		0			0
$299$	−21.4894	+	15.6129i	−1.24276	+	0.902919i
$300$		0			0
$301$	11.2082	+	8.14324i	0.646030	+	0.469368i
$302$		0			0
$303$	−3.85410	+	2.80017i	−0.221412	+	0.160866i
$304$		0			0
$305$	18.1803			1.04100
$306$		0			0
$307$	−1.88197	+	5.79210i	−0.107409	+	0.330572i	−0.990288	−	0.139028i	$-0.955602\pi$
$307$	−1.88197	+	5.79210i	−0.107409	+	0.330572i	0.882879	+	0.469601i	$0.155602\pi$
$308$		0			0
$309$	0.145898			0.00829985
$310$		0			0
$311$	−16.4721			−0.934049			−0.467025	−	0.884244i	$-0.654674\pi$
$311$	−16.4721			−0.934049			−0.467025	+	0.884244i	$0.654674\pi$
$312$		0			0
$313$	0.381966	−	1.17557i	0.0215900	−	0.0664472i	−0.939681	−	0.342052i	$-0.888878\pi$
$313$	0.381966	−	1.17557i	0.0215900	−	0.0664472i	0.961271	+	0.275605i	$0.0888781\pi$
$314$		0			0
$315$	−15.7082			−0.885057
$316$		0			0
$317$	−20.9443	+	15.2169i	−1.17635	+	0.854666i	−0.991755	−	0.128149i	$-0.959097\pi$
$317$	−20.9443	+	15.2169i	−1.17635	+	0.854666i	−0.184593	+	0.982815i	$0.559097\pi$
$318$		0			0
$319$	5.32624	+	3.86974i	0.298212	+	0.216664i
$320$		0			0
$321$	0.881966	−	0.640786i	0.0492265	−	0.0357652i
$322$		0			0
$323$	−0.364745	+	1.12257i	−0.0202950	+	0.0624615i
$324$		0			0
$325$	2.78115	−	8.55951i	0.154271	−	0.474796i
$326$		0			0
$327$	6.80902	+	4.94704i	0.376540	+	0.273572i
$328$		0			0
$329$	−3.13525	−	9.64932i	−0.172852	−	0.531984i
$330$		0			0
$331$	−3.48278	−	10.7189i	−0.191431	−	0.589164i	−1.00000		0.000762014i	$-0.999757\pi$
$331$	−3.48278	−	10.7189i	−0.191431	−	0.589164i	0.808569	−	0.588402i	$-0.200243\pi$
$332$		0			0
$333$	0.381966	+	0.277515i	0.0209316	+	0.0152077i
$334$		0			0
$335$	−11.0902			−0.605921
$336$		0			0
$337$	−15.3541	+	11.1554i	−0.836391	+	0.607674i	−0.921360	−	0.388710i	$-0.872921\pi$
$337$	−15.3541	+	11.1554i	−0.836391	+	0.607674i	0.0849690	+	0.996384i	$0.472921\pi$
$338$		0			0
$339$	−0.572949	−	1.76336i	−0.0311183	−	0.0957723i
$340$		0			0
$341$	−3.20163	+	2.80017i	−0.173378	+	0.151638i
$342$		0			0
$343$	4.63525	+	14.2658i	0.250280	+	0.770283i
$344$		0			0
$345$	11.5902	−	8.42075i	0.623994	−	0.453358i
$346$		0			0
$347$	−8.12461			−0.436152			−0.218076	−	0.975932i	$-0.569978\pi$
$347$	−8.12461			−0.436152			−0.218076	+	0.975932i	$0.569978\pi$
$348$		0			0
$349$	13.5172	+	9.82084i	0.723560	+	0.525697i	0.887520	−	0.460770i	$-0.152427\pi$
$349$	13.5172	+	9.82084i	0.723560	+	0.525697i	−0.163959	+	0.986467i	$0.552427\pi$
$350$		0			0
$351$	−7.50000	−	23.0826i	−0.400320	−	1.23206i
$352$		0			0
$353$	−10.0066	−	30.7971i	−0.532596	−	1.63916i	−0.748786	−	0.662812i	$-0.769363\pi$
$353$	−10.0066	−	30.7971i	−0.532596	−	1.63916i	0.216190	−	0.976351i	$-0.430637\pi$
$354$		0			0
$355$	−0.190983	−	0.138757i	−0.0101363	−	0.00736447i
$356$		0			0
$357$	−0.218847	+	0.673542i	−0.0115826	+	0.0356476i
$358$		0			0
$359$	7.82624	−	24.0867i	0.413053	−	1.27125i	−0.500928	−	0.865489i	$-0.667008\pi$
$359$	7.82624	−	24.0867i	0.413053	−	1.27125i	0.913981	−	0.405757i	$-0.132992\pi$
$360$		0			0
$361$	−4.85410	+	3.52671i	−0.255479	+	0.185616i
$362$		0			0
$363$	8.42705	+	6.12261i	0.442305	+	0.321354i
$364$		0			0
$365$	−18.1353	+	13.1760i	−0.949243	+	0.689665i
$366$		0			0
$367$	36.2705			1.89331			0.946653	−	0.322256i	$-0.104441\pi$
$367$	36.2705			1.89331			0.946653	+	0.322256i	$0.104441\pi$
$368$		0			0
$369$	−4.00000	+	12.3107i	−0.208232	+	0.640871i
$370$		0			0
$371$	38.1246			1.97933
$372$		0			0
$373$	−0.347524			−0.0179941			−0.00899706	−	0.999960i	$-0.502864\pi$
$373$	−0.347524			−0.0179941			−0.00899706	+	0.999960i	$0.502864\pi$
$374$		0			0
$375$	2.54508	−	7.83297i	0.131428	−	0.404493i
$376$		0			0
$377$	−41.8328			−2.15450
$378$		0			0
$379$	−14.8992	+	10.8249i	−0.765320	+	0.556037i	−0.900537	−	0.434779i	$-0.856827\pi$
$379$	−14.8992	+	10.8249i	−0.765320	+	0.556037i	0.135218	+	0.990816i	$0.456827\pi$
$380$		0			0
$381$	8.28115	+	6.01661i	0.424256	+	0.308240i
$382$		0			0
$383$	−13.6353	+	9.90659i	−0.696729	+	0.506203i	−0.878865	−	0.477070i	$-0.841699\pi$
$383$	−13.6353	+	9.90659i	−0.696729	+	0.506203i	0.182136	+	0.983273i	$0.441699\pi$
$384$		0			0
$385$	1.85410	−	5.70634i	0.0944938	−	0.290822i
$386$		0			0
$387$	−2.85410	+	8.78402i	−0.145082	+	0.446517i
$388$		0			0
$389$	23.5172	+	17.0863i	1.19237	+	0.866308i	0.993513	−	0.113721i	$-0.0362769\pi$
$389$	23.5172	+	17.0863i	1.19237	+	0.866308i	0.198858	+	0.980028i	$0.436277\pi$
$390$		0			0
$391$	0.399187	+	1.22857i	0.0201878	+	0.0621315i
$392$		0			0
$393$	−0.0278640	−	0.0857567i	−0.00140556	−	0.00432585i
$394$		0			0
$395$		0			0
$396$		0			0
$397$	16.2918			0.817662			0.408831	−	0.912610i	$-0.365937\pi$
$397$	16.2918			0.817662			0.408831	+	0.912610i	$0.365937\pi$
$398$		0			0
$399$	−12.1353	+	8.81678i	−0.607523	+	0.441391i
$400$		0			0
$401$	−9.21885	−	28.3727i	−0.460367	−	1.41686i	−0.864717	−	0.502260i	$-0.832502\pi$
$401$	−9.21885	−	28.3727i	−0.460367	−	1.41686i	0.404349	−	0.914605i	$-0.367498\pi$
$402$		0			0
$403$	6.00000	−	26.3521i	0.298881	−	1.31269i
$404$		0			0
$405$	−0.809017	−	2.48990i	−0.0402004	−	0.123724i
$406$		0			0
$407$	−0.145898	+	0.106001i	−0.00723190	+	0.00525428i
$408$		0			0
$409$	−6.18034			−0.305598			−0.152799	−	0.988257i	$-0.548829\pi$
$409$	−6.18034			−0.305598			−0.152799	+	0.988257i	$0.548829\pi$
$410$		0			0
$411$	5.23607	+	3.80423i	0.258276	+	0.187649i
$412$		0			0
$413$	8.78115	+	27.0256i	0.432092	+	1.32984i
$414$		0			0
$415$	−3.30902	−	10.1841i	−0.162433	−	0.499918i
$416$		0			0
$417$	4.73607	+	3.44095i	0.231926	+	0.168504i
$418$		0			0
$419$	−1.38197	+	4.25325i	−0.0675135	+	0.207785i	−0.979122	−	0.203275i	$-0.934841\pi$
$419$	−1.38197	+	4.25325i	−0.0675135	+	0.207785i	0.911608	+	0.411060i	$0.134841\pi$
$420$		0			0
$421$	4.56231	−	14.0413i	0.222353	−	0.684333i	−0.776196	−	0.630491i	$-0.782853\pi$
$421$	4.56231	−	14.0413i	0.222353	−	0.684333i	0.998549	−	0.0538414i	$-0.0171466\pi$
$422$		0			0
$423$	5.47214	−	3.97574i	0.266064	−	0.193307i
$424$		0			0
$425$	−0.354102	−	0.257270i	−0.0171765	−	0.0124794i
$426$		0			0
$427$	−16.8541	+	12.2452i	−0.815627	+	0.592588i
$428$		0			0
$429$	3.70820			0.179034
$430$		0			0
$431$	−9.03444	+	27.8052i	−0.435174	+	1.33933i	0.457735	+	0.889089i	$0.348661\pi$
$431$	−9.03444	+	27.8052i	−0.435174	+	1.33933i	−0.892908	+	0.450238i	$0.851339\pi$
$432$		0			0
$433$	0.583592			0.0280456			0.0140228	−	0.999902i	$-0.495536\pi$
$433$	0.583592			0.0280456			0.0140228	+	0.999902i	$0.495536\pi$
$434$		0			0
$435$	22.5623			1.08178
$436$		0			0
$437$	−8.45492	+	26.0216i	−0.404453	+	1.24478i
$438$		0			0
$439$	−41.8328			−1.99657			−0.998286	−	0.0585295i	$-0.981359\pi$
$439$	−41.8328			−1.99657			−0.998286	+	0.0585295i	$0.981359\pi$
$440$		0			0
$441$	3.23607	−	2.35114i	0.154098	−	0.111959i
$442$		0			0
$443$	−33.2705	−	24.1724i	−1.58073	−	1.14847i	−0.915853	−	0.401514i	$-0.868484\pi$
$443$	−33.2705	−	24.1724i	−1.58073	−	1.14847i	−0.664877	−	0.746953i	$-0.731516\pi$
$444$		0			0
$445$	−13.5172	+	9.82084i	−0.640778	+	0.465552i
$446$		0			0
$447$	−5.26393	+	16.2007i	−0.248975	+	0.766268i
$448$		0			0
$449$	7.43769	−	22.8909i	0.351006	−	1.08029i	−0.607283	−	0.794486i	$-0.707740\pi$
$449$	7.43769	−	22.8909i	0.351006	−	1.08029i	0.958289	−	0.285801i	$-0.0922596\pi$
$450$		0			0
$451$	−4.00000	−	2.90617i	−0.188353	−	0.136846i
$452$		0			0
$453$	6.02786	+	18.5519i	0.283214	+	0.871642i
$454$		0			0
$455$	11.7812	+	36.2587i	0.552309	+	1.69983i
$456$		0			0
$457$	12.7361	+	9.25330i	0.595768	+	0.432851i	0.844374	−	0.535754i	$-0.179972\pi$
$457$	12.7361	+	9.25330i	0.595768	+	0.432851i	−0.248606	+	0.968605i	$0.579972\pi$
$458$		0			0
$459$	−1.18034			−0.0550935
$460$		0			0
$461$	−8.69098	+	6.31437i	−0.404779	+	0.294089i	−0.771485	−	0.636248i	$-0.780486\pi$
$461$	−8.69098	+	6.31437i	−0.404779	+	0.294089i	0.366705	+	0.930337i	$0.380486\pi$
$462$		0			0
$463$	9.61803	+	29.6013i	0.446988	+	1.37569i	0.880289	+	0.474438i	$0.157349\pi$
$463$	9.61803	+	29.6013i	0.446988	+	1.37569i	−0.433301	+	0.901249i	$0.642651\pi$
$464$		0			0
$465$	−3.23607	+	14.2128i	−0.150069	+	0.659105i
$466$		0			0
$467$	10.1287	+	31.1729i	0.468699	+	1.44251i	0.854270	+	0.519830i	$0.174005\pi$
$467$	10.1287	+	31.1729i	0.468699	+	1.44251i	−0.385571	+	0.922678i	$0.625995\pi$
$468$		0			0
$469$	10.2812	−	7.46969i	0.474740	−	0.344918i
$470$		0			0
$471$	9.70820			0.447330
$472$		0			0
$473$	−2.85410	−	2.07363i	−0.131232	−	0.0953454i
$474$		0			0
$475$	−2.86475	−	8.81678i	−0.131444	−	0.404542i
$476$		0			0
$477$	7.85410	+	24.1724i	0.359615	+	1.10678i
$478$		0			0
$479$	−7.23607	−	5.25731i	−0.330624	−	0.240213i	0.410071	−	0.912054i	$-0.365504\pi$
$479$	−7.23607	−	5.25731i	−0.330624	−	0.240213i	−0.740696	+	0.671841i	$0.765504\pi$
$480$		0			0
$481$	0.354102	−	1.08981i	0.0161457	−	0.0496912i
$482$		0			0
$483$	−5.07295	+	15.6129i	−0.230827	+	0.710413i
$484$		0			0
$485$	−11.2082	+	8.14324i	−0.508938	+	0.369765i
$486$		0			0
$487$	18.5451	+	13.4738i	0.840358	+	0.610556i	0.922471	−	0.386067i	$-0.126167\pi$
$487$	18.5451	+	13.4738i	0.840358	+	0.610556i	−0.0821126	+	0.996623i	$0.526167\pi$
$488$		0			0
$489$	−10.2812	+	7.46969i	−0.464930	+	0.337791i
$490$		0			0
$491$	27.5967			1.24542			0.622712	−	0.782451i	$-0.286031\pi$
$491$	27.5967			1.24542			0.622712	+	0.782451i	$0.286031\pi$
$492$		0			0
$493$	−0.628677	+	1.93487i	−0.0283142	+	0.0871421i
$494$		0			0
$495$	4.00000			0.179787
$496$		0			0
$497$	0.270510			0.0121340
$498$		0			0
$499$	−1.28115	+	3.94298i	−0.0573523	+	0.176512i	−0.975629	−	0.219427i	$-0.929581\pi$
$499$	−1.28115	+	3.94298i	−0.0573523	+	0.176512i	0.918277	+	0.395940i	$0.129581\pi$
$500$		0			0
$501$	9.23607			0.412637
$502$		0			0
$503$	10.6353	−	7.72696i	0.474203	−	0.344528i	−0.324874	−	0.945757i	$-0.605322\pi$
$503$	10.6353	−	7.72696i	0.474203	−	0.344528i	0.799077	+	0.601229i	$0.205322\pi$
$504$		0			0
$505$	10.0902	+	7.33094i	0.449007	+	0.326222i
$506$		0			0
$507$	−8.54508	+	6.20837i	−0.379501	+	0.275723i
$508$		0			0
$509$	−0.590170	+	1.81636i	−0.0261588	+	0.0805086i	−0.963284	−	0.268486i	$-0.913477\pi$
$509$	−0.590170	+	1.81636i	−0.0261588	+	0.0805086i	0.937125	+	0.348994i	$0.113477\pi$
$510$		0			0
$511$	7.93769	−	24.4297i	0.351143	−	1.08071i
$512$		0			0
$513$	−20.2254	−	14.6946i	−0.892974	−	0.648784i
$514$		0			0
$515$	−0.118034	−	0.363271i	−0.00520120	−	0.0160076i
$516$		0			0
$517$	0.798374	+	2.45714i	0.0351124	+	0.108065i
$518$		0			0
$519$	−0.736068	−	0.534785i	−0.0323098	−	0.0234744i
$520$		0			0
$521$	31.0689			1.36115			0.680576	−	0.732677i	$-0.261729\pi$
$521$	31.0689			1.36115			0.680576	+	0.732677i	$0.261729\pi$
$522$		0			0
$523$	27.6074	−	20.0579i	1.20719	−	0.877073i	0.212215	−	0.977223i	$-0.431932\pi$
$523$	27.6074	−	20.0579i	1.20719	−	0.877073i	0.994972	+	0.100150i	$0.0319324\pi$
$524$		0			0
$525$	−1.71885	−	5.29007i	−0.0750166	−	0.230877i
$526$		0			0
$527$	−1.12868	−	0.673542i	−0.0491659	−	0.0293399i
$528$		0			0
$529$	2.14590	+	6.60440i	0.0932999	+	0.287148i
$530$		0			0
$531$	−15.3262	+	11.1352i	−0.665102	+	0.483225i
$532$		0			0
$533$	31.4164			1.36080
$534$		0			0
$535$	−2.30902	−	1.67760i	−0.0998275	−	0.0725289i
$536$		0			0
$537$	−6.11803	−	18.8294i	−0.264013	−	0.812547i
$538$		0			0
$539$	0.472136	+	1.45309i	0.0203363	+	0.0625888i
$540$		0			0
$541$	−17.7984	−	12.9313i	−0.765212	−	0.555959i	0.135293	−	0.990806i	$-0.456803\pi$
$541$	−17.7984	−	12.9313i	−0.765212	−	0.555959i	−0.900504	+	0.434847i	$0.856803\pi$
$542$		0			0
$543$	5.25329	−	16.1680i	0.225440	−	0.693834i
$544$		0			0
$545$	6.80902	−	20.9560i	0.291666	−	0.897656i
$546$		0			0
$547$	−19.1803	+	13.9353i	−0.820092	+	0.595832i	−0.916739	−	0.399487i	$-0.869188\pi$
$547$	−19.1803	+	13.9353i	−0.820092	+	0.595832i	0.0966468	+	0.995319i	$0.469188\pi$
$548$		0			0
$549$	−11.2361	−	8.16348i	−0.479544	−	0.348409i
$550$		0			0
$551$	−34.8607	+	25.3278i	−1.48511	+	1.07900i
$552$		0			0
$553$		0			0
$554$		0			0
$555$	−0.190983	+	0.587785i	−0.00810678	+	0.0249501i
$556$		0			0
$557$	35.8885			1.52065			0.760323	−	0.649545i	$-0.225041\pi$
$557$	35.8885			1.52065			0.760323	+	0.649545i	$0.225041\pi$
$558$		0			0
$559$	22.4164			0.948113
$560$		0			0
$561$	0.0557281	−	0.171513i	0.00235284	−	0.00724130i
$562$		0			0
$563$	8.56231			0.360858			0.180429	−	0.983588i	$-0.442251\pi$
$563$	8.56231			0.360858			0.180429	+	0.983588i	$0.442251\pi$
$564$		0			0
$565$	−3.92705	+	2.85317i	−0.165212	+	0.120034i
$566$		0			0
$567$	2.42705	+	1.76336i	0.101927	+	0.0740540i
$568$		0			0
$569$	−12.5623	+	9.12705i	−0.526639	+	0.382626i	−0.819099	−	0.573652i	$-0.805526\pi$
$569$	−12.5623	+	9.12705i	−0.526639	+	0.382626i	0.292460	+	0.956278i	$0.405526\pi$
$570$		0			0
$571$	−2.16312	+	6.65740i	−0.0905237	+	0.278603i	−0.986061	−	0.166383i	$-0.946791\pi$
$571$	−2.16312	+	6.65740i	−0.0905237	+	0.278603i	0.895538	+	0.444986i	$0.146791\pi$
$572$		0			0
$573$	4.97214	−	15.3027i	0.207714	−	0.639278i
$574$		0			0
$575$	−8.20820	−	5.96361i	−0.342306	−	0.248700i
$576$		0			0
$577$	12.0451	+	37.0710i	0.501443	+	1.54328i	0.806669	+	0.591004i	$0.201268\pi$
$577$	12.0451	+	37.0710i	0.501443	+	1.54328i	−0.305225	+	0.952280i	$0.598732\pi$
$578$		0			0
$579$	−0.736068	−	2.26538i	−0.0305899	−	0.0941462i
$580$		0			0
$581$	9.92705	+	7.21242i	0.411843	+	0.299222i
$582$		0			0
$583$	−9.70820			−0.402073
$584$		0			0
$585$	−20.5623	+	14.9394i	−0.850147	+	0.617668i
$586$		0			0
$587$	−11.1287	−	34.2505i	−0.459330	−	1.41367i	−0.865976	−	0.500086i	$-0.833302\pi$
$587$	−11.1287	−	34.2505i	−0.459330	−	1.41367i	0.406646	−	0.913586i	$-0.366698\pi$
$588$		0			0
$589$	−10.9549	−	25.5928i	−0.451389	−	1.05453i
$590$		0			0
$591$	5.07295	+	15.6129i	0.208673	+	0.642230i
$592$		0			0
$593$	−4.94427	+	3.59222i	−0.203037	+	0.147515i	−0.684658	−	0.728865i	$-0.740048\pi$
$593$	−4.94427	+	3.59222i	−0.203037	+	0.147515i	0.481621	+	0.876380i	$0.340048\pi$
$594$		0			0
$595$	1.85410			0.0760108
$596$		0			0
$597$	−21.6074	−	15.6987i	−0.884332	−	0.642505i
$598$		0			0
$599$	−9.20820	−	28.3399i	−0.376237	−	1.15794i	−0.942640	−	0.333810i	$-0.891666\pi$
$599$	−9.20820	−	28.3399i	−0.376237	−	1.15794i	0.566403	−	0.824128i	$-0.308334\pi$
$600$		0			0
$601$	6.79837	+	20.9232i	0.277311	+	0.853477i	0.988599	+	0.150575i	$0.0481126\pi$
$601$	6.79837	+	20.9232i	0.277311	+	0.853477i	−0.711287	+	0.702902i	$0.751887\pi$
$602$		0			0
$603$	6.85410	+	4.97980i	0.279121	+	0.202793i
$604$		0			0
$605$	8.42705	−	25.9358i	0.342608	−	1.05444i
$606$		0			0
$607$	7.85410	−	24.1724i	0.318788	−	0.981129i	−0.655379	−	0.755300i	$-0.727491\pi$
$607$	7.85410	−	24.1724i	0.318788	−	0.981129i	0.974167	−	0.225829i	$-0.0725090\pi$
$608$		0			0
$609$	−20.9164	+	15.1967i	−0.847576	+	0.615800i
$610$		0			0
$611$	−13.2812	−	9.64932i	−0.537298	−	0.390370i
$612$		0			0
$613$	−20.2705	+	14.7274i	−0.818718	+	0.594834i	−0.916345	−	0.400390i	$-0.868875\pi$
$613$	−20.2705	+	14.7274i	−0.818718	+	0.594834i	0.0976269	+	0.995223i	$0.468875\pi$
$614$		0			0
$615$	−16.9443			−0.683259
$616$		0			0
$617$	−4.39919	+	13.5393i	−0.177105	+	0.545072i	−0.999723	−	0.0235215i	$-0.992512\pi$
$617$	−4.39919	+	13.5393i	−0.177105	+	0.545072i	0.822619	+	0.568593i	$0.192512\pi$
$618$		0			0
$619$	40.0000			1.60774			0.803868	−	0.594808i	$-0.202772\pi$
$619$	40.0000			1.60774			0.803868	+	0.594808i	$0.202772\pi$
$620$		0			0
$621$	−27.3607			−1.09795
$622$		0			0
$623$	5.91641	−	18.2088i	0.237036	−	0.729521i
$624$		0			0
$625$	−30.8328			−1.23331
$626$		0			0
$627$	3.09017	−	2.24514i	0.123410	−	0.0896623i
$628$		0			0
$629$	−0.0450850	−	0.0327561i	−0.00179766	−	0.00130607i
$630$		0			0
$631$	−7.06231	+	5.13107i	−0.281146	+	0.204264i	−0.719417	−	0.694578i	$-0.755591\pi$
$631$	−7.06231	+	5.13107i	−0.281146	+	0.204264i	0.438271	+	0.898843i	$0.355591\pi$
$632$		0			0
$633$	2.47214	−	7.60845i	0.0982586	−	0.302409i
$634$		0			0
$635$	8.28115	−	25.4868i	0.328628	−	1.01141i
$636$		0			0
$637$	−7.85410	−	5.70634i	−0.311191	−	0.226093i
$638$		0			0
$639$	0.0557281	+	0.171513i	0.00220457	+	0.00678497i
$640$		0			0
$641$	−12.6976	−	39.0791i	−0.501523	−	1.54353i	−0.806538	−	0.591183i	$-0.798661\pi$
$641$	−12.6976	−	39.0791i	−0.501523	−	1.54353i	0.305014	−	0.952348i	$-0.401339\pi$
$642$		0			0
$643$	6.59017	+	4.78804i	0.259891	+	0.188822i	0.710099	−	0.704102i	$-0.248650\pi$
$643$	6.59017	+	4.78804i	0.259891	+	0.188822i	−0.450208	+	0.892924i	$0.648650\pi$
$644$		0			0
$645$	−12.0902			−0.476050
$646$		0			0
$647$	−24.1803	+	17.5680i	−0.950627	+	0.690671i	−0.950955	−	0.309329i	$-0.899896\pi$
$647$	−24.1803	+	17.5680i	−0.950627	+	0.690671i	0.000327889		1.00000i	$0.499896\pi$
$648$		0			0
$649$	−2.23607	−	6.88191i	−0.0877733	−	0.270139i
$650$		0			0
$651$	−6.57295	−	15.3557i	−0.257614	−	0.601836i
$652$		0			0
$653$	12.2533	+	37.7117i	0.479508	+	1.47577i	0.839780	+	0.542927i	$0.182684\pi$
$653$	12.2533	+	37.7117i	0.479508	+	1.47577i	−0.360272	+	0.932847i	$0.617316\pi$
$654$		0			0
$655$	−0.190983	+	0.138757i	−0.00746232	+	0.00542170i
$656$		0			0
$657$	17.1246			0.668095
$658$		0			0
$659$	18.3541	+	13.3350i	0.714974	+	0.519459i	0.884775	−	0.466019i	$-0.154312\pi$
$659$	18.3541	+	13.3350i	0.714974	+	0.519459i	−0.169800	+	0.985478i	$0.554312\pi$
$660$		0			0
$661$	−5.13525	−	15.8047i	−0.199738	−	0.614731i	−0.999889	−	0.0149316i	$-0.995247\pi$
$661$	−5.13525	−	15.8047i	−0.199738	−	0.614731i	0.800150	−	0.599800i	$-0.204753\pi$
$662$		0			0
$663$	0.354102	+	1.08981i	0.0137522	+	0.0423249i
$664$		0			0
$665$	31.7705	+	23.0826i	1.23201	+	0.895106i
$666$		0			0
$667$	−14.5729	+	44.8509i	−0.564267	+	1.73663i
$668$		0			0
$669$	−0.218847	+	0.673542i	−0.00846112	+	0.0260406i
$670$		0			0
$671$	4.29180	−	3.11817i	0.165683	−	0.120376i
$672$		0			0
$673$	3.57295	+	2.59590i	0.137727	+	0.100065i	0.654516	−	0.756049i	$-0.272873\pi$
$673$	3.57295	+	2.59590i	0.137727	+	0.100065i	−0.516788	+	0.856113i	$0.672873\pi$
$674$		0			0
$675$	7.50000	−	5.44907i	0.288675	−	0.209735i
$676$		0			0
$677$	28.6525			1.10120			0.550602	−	0.834768i	$-0.314398\pi$
$677$	28.6525			1.10120			0.550602	+	0.834768i	$0.314398\pi$
$678$		0			0
$679$	4.90576	−	15.0984i	0.188266	−	0.579423i
$680$		0			0
$681$	20.7426			0.794860
$682$		0			0
$683$	−10.0557			−0.384772			−0.192386	−	0.981319i	$-0.561623\pi$
$683$	−10.0557			−0.384772			−0.192386	+	0.981319i	$0.561623\pi$
$684$		0			0
$685$	5.23607	−	16.1150i	0.200060	−	0.615721i
$686$		0			0
$687$	−7.23607			−0.276073
$688$		0			0
$689$	49.9058	−	36.2587i	1.90126	−	1.38134i
$690$		0			0
$691$	3.10081	+	2.25287i	0.117960	+	0.0857033i	0.645201	−	0.764013i	$-0.276773\pi$
$691$	3.10081	+	2.25287i	0.117960	+	0.0857033i	−0.527241	+	0.849716i	$0.676773\pi$
$692$		0			0
$693$	−3.70820	+	2.69417i	−0.140863	+	0.102343i
$694$		0			0
$695$	4.73607	−	14.5761i	0.179649	−	0.552904i
$696$		0			0
$697$	0.472136	−	1.45309i	0.0178834	−	0.0550395i
$698$		0			0
$699$	−15.2082	−	11.0494i	−0.575227	−	0.417927i
$700$		0			0
$701$	−9.28115	−	28.5645i	−0.350544	−	1.07886i	−0.958548	−	0.284930i	$-0.908030\pi$
$701$	−9.28115	−	28.5645i	−0.350544	−	1.07886i	0.608004	−	0.793934i	$-0.291970\pi$
$702$		0			0
$703$	−0.364745	−	1.12257i	−0.0137566	−	0.0423385i
$704$		0			0
$705$	7.16312	+	5.20431i	0.269779	+	0.196006i
$706$		0			0
$707$	−14.2918			−0.537498
$708$		0			0
$709$	−3.35410	+	2.43690i	−0.125966	+	0.0915196i	−0.648984	−	0.760802i	$-0.724806\pi$
$709$	−3.35410	+	2.43690i	−0.125966	+	0.0915196i	0.523018	+	0.852321i	$0.324806\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	−26.1631	−	15.6129i	−0.979817	−	0.584709i
$714$		0			0
$715$	−3.00000	−	9.23305i	−0.112194	−	0.345297i
$716$		0			0
$717$	−10.8541	+	7.88597i	−0.405354	+	0.294507i
$718$		0			0
$719$	41.3820			1.54329			0.771643	−	0.636055i	$-0.219435\pi$
$719$	41.3820			1.54329			0.771643	+	0.636055i	$0.219435\pi$
$720$		0			0
$721$	0.354102	+	0.257270i	0.0131874	+	0.00958124i
$722$		0			0
$723$	−2.63525	−	8.11048i	−0.0980062	−	0.301632i
$724$		0			0
$725$	−4.93769	−	15.1967i	−0.183381	−	0.564390i
$726$		0			0
$727$	−19.2812	−	14.0086i	−0.715098	−	0.519549i	0.169716	−	0.985493i	$-0.445715\pi$
$727$	−19.2812	−	14.0086i	−0.715098	−	0.519549i	−0.884814	+	0.465944i	$0.845715\pi$
$728$		0			0
$729$	4.01722	−	12.3637i	0.148786	−	0.457916i
$730$		0			0
$731$	0.336881	−	1.03681i	0.0124600	−	0.0383479i
$732$		0			0
$733$	−22.6074	+	16.4252i	−0.835023	+	0.606680i	−0.920976	−	0.389619i	$-0.872607\pi$
$733$	−22.6074	+	16.4252i	−0.835023	+	0.606680i	0.0859529	+	0.996299i	$0.472607\pi$
$734$		0			0
$735$	4.23607	+	3.07768i	0.156250	+	0.113522i
$736$		0			0
$737$	−2.61803	+	1.90211i	−0.0964365	+	0.0700652i
$738$		0			0
$739$	−21.7082			−0.798549			−0.399275	−	0.916831i	$-0.630738\pi$
$739$	−21.7082			−0.798549			−0.399275	+	0.916831i	$0.630738\pi$
$740$		0			0
$741$	−7.50000	+	23.0826i	−0.275519	+	0.847961i
$742$		0			0
$743$	3.43769			0.126117			0.0630584	−	0.998010i	$-0.479915\pi$
$743$	3.43769			0.126117			0.0630584	+	0.998010i	$0.479915\pi$
$744$		0			0
$745$	44.5967			1.63390
$746$		0			0
$747$	−2.52786	+	7.77997i	−0.0924897	+	0.284654i
$748$		0			0
$749$	3.27051			0.119502
$750$		0			0
$751$	−32.2254	+	23.4131i	−1.17592	+	0.854358i	−0.991706	−	0.128528i	$-0.958975\pi$
$751$	−32.2254	+	23.4131i	−1.17592	+	0.854358i	−0.184217	+	0.982886i	$0.558975\pi$
$752$		0			0
$753$	0.763932	+	0.555029i	0.0278392	+	0.0202264i
$754$		0			0
$755$	41.3156	−	30.0175i	1.50363	−	1.09245i
$756$		0			0
$757$	13.3262	−	41.0139i	0.484350	−	1.49068i	−0.348569	−	0.937283i	$-0.613332\pi$
$757$	13.3262	−	41.0139i	0.484350	−	1.49068i	0.832920	−	0.553394i	$-0.186668\pi$
$758$		0			0
$759$	1.29180	−	3.97574i	0.0468892	−	0.144310i
$760$		0			0
$761$	−2.83688	−	2.06111i	−0.102837	−	0.0747154i	0.535178	−	0.844739i	$-0.320244\pi$
$761$	−2.83688	−	2.06111i	−0.102837	−	0.0747154i	−0.638015	+	0.770024i	$0.720244\pi$
$762$		0			0
$763$	7.80244	+	24.0134i	0.282467	+	0.869345i
$764$		0			0
$765$	0.381966	+	1.17557i	0.0138100	+	0.0425028i
$766$		0			0
$767$	37.1976	+	27.0256i	1.34313	+	0.975838i
$768$		0			0
$769$	−53.7426			−1.93801			−0.969005	−	0.247042i	$-0.920541\pi$
$769$	−53.7426			−1.93801			−0.969005	+	0.247042i	$0.920541\pi$
$770$		0			0
$771$	−1.14590	+	0.832544i	−0.0412685	+	0.0299833i
$772$		0			0
$773$	−5.89919	−	18.1558i	−0.212179	−	0.653020i	−0.999342	−	0.0362746i	$-0.988451\pi$
$773$	−5.89919	−	18.1558i	−0.212179	−	0.653020i	0.787163	−	0.616745i	$-0.211549\pi$
$774$		0			0
$775$	10.2812	−	0.930812i	0.369310	−	0.0334358i
$776$		0			0
$777$	−0.218847	−	0.673542i	−0.00785109	−	0.0241632i
$778$		0			0
$779$	26.1803	−	19.0211i	0.938008	−	0.681503i
$780$		0			0
$781$	−0.0688837			−0.00246485
$782$		0			0
$783$	−34.8607	−	25.3278i	−1.24582	−	0.905141i
$784$		0			0
$785$	−7.85410	−	24.1724i	−0.280325	−	0.862751i
$786$		0			0
$787$	−9.66970	−	29.7603i	−0.344687	−	1.06084i	−0.961751	−	0.273926i	$-0.911678\pi$
$787$	−9.66970	−	29.7603i	−0.344687	−	1.06084i	0.617063	−	0.786913i	$-0.288322\pi$
$788$		0			0
$789$	−8.73607	−	6.34712i	−0.311012	−	0.225964i
$790$		0			0
$791$	1.71885	−	5.29007i	0.0611152	−	0.188093i
$792$		0			0
$793$	−10.4164	+	32.0584i	−0.369897	+	1.13843i
$794$		0			0
$795$	−26.9164	+	19.5559i	−0.954627	+	0.693577i
$796$		0			0
$797$	−7.32624	−	5.32282i	−0.259509	−	0.188544i	0.450422	−	0.892816i	$-0.351274\pi$
$797$	−7.32624	−	5.32282i	−0.259509	−	0.188544i	−0.709930	+	0.704272i	$0.751274\pi$
$798$		0			0
$799$	−0.645898	+	0.469272i	−0.0228502	+	0.0166017i
$800$		0			0
$801$	12.7639			0.450991
$802$		0			0
$803$	−2.02129	+	6.22088i	−0.0713296	+	0.219530i
$804$		0			0
$805$	42.9787			1.51480
$806$		0			0
$807$	−1.38197			−0.0486475
$808$		0			0
$809$	16.9336	−	52.1164i	0.595355	−	1.83231i	0.0424020	−	0.999101i	$-0.486499\pi$
$809$	16.9336	−	52.1164i	0.595355	−	1.83231i	0.552953	−	0.833213i	$-0.313501\pi$
$810$		0			0
$811$	−42.7771			−1.50211			−0.751053	−	0.660242i	$-0.770454\pi$
$811$	−42.7771			−1.50211			−0.751053	+	0.660242i	$0.770454\pi$
$812$		0			0
$813$	7.73607	−	5.62058i	0.271316	−	0.197122i
$814$		0			0
$815$	26.9164	+	19.5559i	0.942841	+	0.685014i
$816$		0			0
$817$	18.6803	−	13.5721i	0.653542	−	0.474826i
$818$		0			0
$819$	9.00000	−	27.6992i	0.314485	−	0.967887i
$820$		0			0
$821$	−10.0344	+	30.8828i	−0.350204	+	1.07782i	0.608534	+	0.793528i	$0.291758\pi$
$821$	−10.0344	+	30.8828i	−0.350204	+	1.07782i	−0.958738	+	0.284290i	$0.908242\pi$
$822$		0			0
$823$	−4.95492	−	3.59996i	−0.172717	−	0.125487i	0.498068	−	0.867138i	$-0.334043\pi$
$823$	−4.95492	−	3.59996i	−0.172717	−	0.125487i	−0.670786	+	0.741651i	$0.734043\pi$
$824$		0			0
$825$	0.437694	+	1.34708i	0.0152386	+	0.0468994i
$826$		0			0
$827$	−0.826238	−	2.54290i	−0.0287311	−	0.0884253i	0.935663	−	0.352896i	$-0.114803\pi$
$827$	−0.826238	−	2.54290i	−0.0287311	−	0.0884253i	−0.964394	+	0.264470i	$0.914803\pi$
$828$		0			0
$829$	17.5623	+	12.7598i	0.609964	+	0.443165i	0.849402	−	0.527747i	$-0.176963\pi$
$829$	17.5623	+	12.7598i	0.609964	+	0.443165i	−0.239438	+	0.970912i	$0.576963\pi$
$830$		0			0
$831$	13.3262			0.462282
$832$		0			0
$833$	−0.381966	+	0.277515i	−0.0132343	+	0.00961531i
$834$		0			0
$835$	−7.47214	−	22.9969i	−0.258584	−	0.795839i
$836$		0			0
$837$	20.9549	−	18.3273i	0.724308	−	0.633486i
$838$		0			0
$839$	−3.45492	−	10.6331i	−0.119277	−	0.367097i	0.873538	−	0.486756i	$-0.161820\pi$
$839$	−3.45492	−	10.6331i	−0.119277	−	0.367097i	−0.992815	+	0.119659i	$0.961820\pi$
$840$		0			0
$841$	−36.6246	+	26.6093i	−1.26292	+	0.917563i
$842$		0			0
$843$	19.0344			0.655581
$844$		0			0
$845$	22.3713	+	16.2537i	0.769597	+	0.559145i
$846$		0			0
$847$	9.65654	+	29.7198i	0.331803	+	1.02118i
$848$		0			0
$849$	−2.02786	−	6.24112i	−0.0695961	−	0.214195i
$850$		0			0
$851$	−1.04508	−	0.759299i	−0.0358251	−	0.0260284i
$852$		0			0
$853$	1.23607	−	3.80423i	0.0423222	−	0.130254i	−0.927663	−	0.373419i	$-0.878185\pi$
$853$	1.23607	−	3.80423i	0.0423222	−	0.130254i	0.969985	+	0.243164i	$0.0781855\pi$
$854$		0			0
$855$	−8.09017	+	24.8990i	−0.276678	+	0.851527i
$856$		0			0
$857$	6.61803	−	4.80828i	0.226068	−	0.164248i	−0.468986	−	0.883206i	$-0.655381\pi$
$857$	6.61803	−	4.80828i	0.226068	−	0.164248i	0.695054	+	0.718958i	$0.255381\pi$
$858$		0			0
$859$	35.0238	+	25.4463i	1.19500	+	0.868216i	0.993783	−	0.111332i	$-0.0355116\pi$
$859$	35.0238	+	25.4463i	1.19500	+	0.868216i	0.201213	+	0.979547i	$0.435512\pi$
$860$		0			0
$861$	15.7082	−	11.4127i	0.535334	−	0.388943i
$862$		0			0
$863$	−2.49342			−0.0848771			−0.0424385	−	0.999099i	$-0.513513\pi$
$863$	−2.49342			−0.0848771			−0.0424385	+	0.999099i	$0.513513\pi$
$864$		0			0
$865$	−0.736068	+	2.26538i	−0.0250271	+	0.0770254i
$866$		0			0
$867$	−16.9443			−0.575458
$868$		0			0
$869$		0			0
$870$		0			0
$871$	6.35410	−	19.5559i	0.215301	−	0.662627i
$872$		0			0
$873$	10.5836			0.358200
$874$		0			0
$875$	19.9894	−	14.5231i	0.675764	−	0.490971i
$876$		0			0
$877$	−13.1803	−	9.57608i	−0.445068	−	0.323361i	0.342577	−	0.939490i	$-0.388700\pi$
$877$	−13.1803	−	9.57608i	−0.445068	−	0.323361i	−0.787646	+	0.616129i	$0.788700\pi$
$878$		0			0
$879$	6.66312	−	4.84104i	0.224741	−	0.163284i
$880$		0			0
$881$	−4.74671	+	14.6089i	−0.159921	+	0.492185i	−0.998626	−	0.0523999i	$-0.983313\pi$
$881$	−4.74671	+	14.6089i	−0.159921	+	0.492185i	0.838705	+	0.544585i	$0.183313\pi$
$882$		0			0
$883$	0.309017	−	0.951057i	0.0103992	−	0.0320056i	−0.945722	−	0.324976i	$-0.894644\pi$
$883$	0.309017	−	0.951057i	0.0103992	−	0.0320056i	0.956121	+	0.292970i	$0.0946438\pi$
$884$		0			0
$885$	−20.0623	−	14.5761i	−0.674387	−	0.489971i
$886$		0			0
$887$	−12.0836	−	37.1895i	−0.405727	−	1.24870i	−0.920286	−	0.391245i	$-0.872044\pi$
$887$	−12.0836	−	37.1895i	−0.405727	−	1.24870i	0.514559	−	0.857455i	$-0.327956\pi$
$888$		0			0
$889$	9.48936	+	29.2052i	0.318263	+	0.979512i
$890$		0			0
$891$	−0.618034	−	0.449028i	−0.0207049	−	0.0150430i
$892$		0			0
$893$	−16.9098			−0.565866
$894$		0			0
$895$	−41.9336	+	30.4666i	−1.40169	+	1.01838i
$896$		0			0
$897$	8.20820	+	25.2623i	0.274064	+	0.843482i
$898$		0			0
$899$	−18.8820	−	44.1119i	−0.629749	−	1.47121i
$900$		0			0
$901$	−0.927051	−	2.85317i	−0.0308845	−	0.0950529i
$902$		0			0
$903$	11.2082	−	8.14324i	0.372986	−	0.270990i
$904$		0			0
$905$	−44.5066			−1.47945
$906$		0			0
$907$	42.8156	+	31.1074i	1.42167	+	1.03290i	0.991493	+	0.130157i	$0.0415482\pi$
$907$	42.8156	+	31.1074i	1.42167	+	1.03290i	0.430175	+	0.902745i	$0.358452\pi$
$908$		0			0
$909$	−2.94427	−	9.06154i	−0.0976553	−	0.300552i
$910$		0			0
$911$	−2.52786	−	7.77997i	−0.0837519	−	0.257762i	0.900408	−	0.435047i	$-0.143268\pi$
$911$	−2.52786	−	7.77997i	−0.0837519	−	0.257762i	−0.984159	+	0.177286i	$0.943268\pi$
$912$		0			0
$913$	−2.52786	−	1.83660i	−0.0836601	−	0.0607826i
$914$		0			0
$915$	5.61803	−	17.2905i	0.185726	−	0.571607i
$916$		0			0
$917$	0.0835921	−	0.257270i	0.00276046	−	0.00849581i
$918$		0			0
$919$	7.98936	−	5.80461i	0.263545	−	0.191476i	−0.448164	−	0.893952i	$-0.647922\pi$
$919$	7.98936	−	5.80461i	0.263545	−	0.191476i	0.711708	+	0.702475i	$0.247922\pi$
$920$		0			0
$921$	4.92705	+	3.57971i	0.162352	+	0.117956i
$922$		0			0
$923$	0.354102	−	0.257270i	0.0116554	−	0.00846815i
$924$		0			0
$925$	0.437694			0.0143913
$926$		0			0
$927$	−0.0901699	+	0.277515i	−0.00296157	+	0.00911477i
$928$		0			0
$929$	33.5410			1.10045			0.550223	−	0.835018i	$-0.314543\pi$
$929$	33.5410			1.10045			0.550223	+	0.835018i	$0.314543\pi$
$930$		0			0
$931$	−10.0000			−0.327737
$932$		0			0
$933$	−5.09017	+	15.6659i	−0.166645	+	0.512880i
$934$		0			0
$935$	−0.472136			−0.0154405
$936$		0			0
$937$	−32.7533	+	23.7967i	−1.07000	+	0.777403i	−0.975913	−	0.218161i	$-0.929994\pi$
$937$	−32.7533	+	23.7967i	−1.07000	+	0.777403i	−0.0940905	+	0.995564i	$0.529994\pi$
$938$		0			0
$939$	−1.00000	−	0.726543i	−0.0326338	−	0.0237098i
$940$		0			0
$941$	−23.1246	+	16.8010i	−0.753841	+	0.547697i	−0.897015	−	0.442000i	$-0.854269\pi$
$941$	−23.1246	+	16.8010i	−0.753841	+	0.547697i	0.143174	+	0.989698i	$0.454269\pi$
$942$		0			0
$943$	10.9443	−	33.6830i	0.356395	−	1.09687i
$944$		0			0
$945$	−12.1353	+	37.3485i	−0.394760	+	1.21495i
$946$		0			0
$947$	17.8541	+	12.9718i	0.580180	+	0.421526i	0.838789	−	0.544456i	$-0.183264\pi$
$947$	17.8541	+	12.9718i	0.580180	+	0.421526i	−0.258609	+	0.965982i	$0.583264\pi$
$948$		0			0
$949$	−12.8435	−	39.5281i	−0.416916	−	1.28314i
$950$		0			0
$951$	8.00000	+	24.6215i	0.259418	+	0.798406i
$952$		0			0
$953$	−34.1525	−	24.8132i	−1.10631	−	0.803779i	−0.124229	−	0.992254i	$-0.539646\pi$
$953$	−34.1525	−	24.8132i	−1.10631	−	0.803779i	−0.982078	+	0.188474i	$0.939646\pi$
$954$		0			0
$955$	−42.1246			−1.36312
$956$		0			0
$957$	5.32624	−	3.86974i	0.172173	−	0.125091i
$958$		0			0
$959$	6.00000	+	18.4661i	0.193750	+	0.596302i
$960$		0			0
$961$	30.4959	−	5.56758i	0.983740	−	0.179599i
$962$		0			0
$963$	0.673762	+	2.07363i	0.0217117	+	0.0668217i
$964$		0			0
$965$	−5.04508	+	3.66547i	−0.162407	+	0.117996i
$966$		0			0
$967$	−43.6525			−1.40377			−0.701884	−	0.712291i	$-0.747658\pi$
$967$	−43.6525			−1.40377			−0.701884	+	0.712291i	$0.747658\pi$
$968$		0			0
$969$	0.954915	+	0.693786i	0.0306763	+	0.0222876i
$970$		0			0
$971$	6.35410	+	19.5559i	0.203913	+	0.627579i	0.999756	+	0.0220767i	$0.00702781\pi$
$971$	6.35410	+	19.5559i	0.203913	+	0.627579i	−0.795843	+	0.605502i	$0.792972\pi$
$972$		0			0
$973$	5.42705	+	16.7027i	0.173983	+	0.535465i
$974$		0			0
$975$	−7.28115	−	5.29007i	−0.233184	−	0.169418i
$976$		0			0
$977$	−1.87539	+	5.77185i	−0.0599990	+	0.184658i	−0.976564	−	0.215228i	$-0.930950\pi$
$977$	−1.87539	+	5.77185i	−0.0599990	+	0.184658i	0.916565	+	0.399886i	$0.130950\pi$
$978$		0			0
$979$	−1.50658	+	4.63677i	−0.0481504	+	0.148192i
$980$		0			0
$981$	−13.6180	+	9.89408i	−0.434790	+	0.315894i
$982$		0			0
$983$	17.0172	+	12.3637i	0.542765	+	0.394342i	0.825111	−	0.564971i	$-0.191113\pi$
$983$	17.0172	+	12.3637i	0.542765	+	0.394342i	−0.282346	+	0.959313i	$0.591113\pi$
$984$		0			0
$985$	34.7705	−	25.2623i	1.10788	−	0.804922i
$986$		0			0
$987$	−10.1459			−0.322947
$988$		0			0
$989$	7.80902	−	24.0337i	0.248312	−	0.764227i
$990$		0			0
$991$	17.2705			0.548616			0.274308	−	0.961642i	$-0.411551\pi$
$991$	17.2705			0.548616			0.274308	+	0.961642i	$0.411551\pi$
$992$		0			0
$993$	−11.2705			−0.357659
$994$		0			0
$995$	−21.6074	+	66.5007i	−0.685000	+	2.10821i
$996$		0			0
$997$	−27.2492			−0.862992			−0.431496	−	0.902115i	$-0.642014\pi$
$997$	−27.2492			−0.862992			−0.431496	+	0.902115i	$0.642014\pi$
$998$		0			0
$999$	0.954915	−	0.693786i	0.0302122	−	0.0219504i

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

)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	496.2.n.b.97.1		4
4.3	odd	2		31.2.d.a.4.1	✓	4
12.11	even	2		279.2.i.a.190.1		4
20.3	even	4		775.2.bf.a.624.1		8
20.7	even	4		775.2.bf.a.624.2		8
20.19	odd	2		775.2.k.c.376.1		4
31.8	even	5	inner	496.2.n.b.225.1		4
124.3	even	30		961.2.c.d.439.1		4
124.7	odd	30		961.2.g.f.816.1		8
124.11	even	30		961.2.g.g.732.1		8
124.15	even	10		961.2.a.e.1.1		2
124.19	odd	30		961.2.g.f.235.1		8
124.23	even	10		961.2.d.b.628.1		4
124.27	even	10		961.2.d.e.374.1		4
124.35	odd	10		961.2.d.f.374.1		4
124.39	odd	10		31.2.d.a.8.1	yes	4
124.43	even	30		961.2.g.g.235.1		8
124.47	odd	10		961.2.a.d.1.1		2
124.51	odd	30		961.2.g.f.732.1		8
124.55	even	30		961.2.g.g.816.1		8
124.59	odd	30		961.2.c.f.439.1		4
124.67	odd	6		961.2.g.b.844.1		8
124.71	odd	30		961.2.g.b.448.1		8
124.75	even	30		961.2.c.d.521.1		4
124.79	even	30		961.2.g.c.846.1		8
124.83	even	30		961.2.g.g.338.1		8
124.87	odd	6		961.2.g.b.547.1		8
124.91	even	10		961.2.d.e.388.1		4
124.95	odd	10		961.2.d.f.388.1		4
124.99	even	6		961.2.g.c.547.1		8
124.103	odd	30		961.2.g.f.338.1		8
124.107	odd	30		961.2.g.b.846.1		8
124.111	odd	30		961.2.c.f.521.1		4
124.115	even	30		961.2.g.c.448.1		8
124.119	even	6		961.2.g.c.844.1		8
124.123	even	2		961.2.d.b.531.1		4
372.47	even	10		8649.2.a.g.1.2		2
372.263	odd	10		8649.2.a.f.1.2		2
372.287	even	10		279.2.i.a.163.1		4
620.39	odd	10		775.2.k.c.101.1		4
620.163	even	20		775.2.bf.a.349.2		8
620.287	even	20		775.2.bf.a.349.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
31.2.d.a.4.1	✓	4	4.3	odd	2
31.2.d.a.8.1	yes	4	124.39	odd	10
279.2.i.a.163.1		4	372.287	even	10
279.2.i.a.190.1		4	12.11	even	2
496.2.n.b.97.1		4	1.1	even	1	trivial
496.2.n.b.225.1		4	31.8	even	5	inner
775.2.k.c.101.1		4	620.39	odd	10
775.2.k.c.376.1		4	20.19	odd	2
775.2.bf.a.349.1		8	620.287	even	20
775.2.bf.a.349.2		8	620.163	even	20
775.2.bf.a.624.1		8	20.3	even	4
775.2.bf.a.624.2		8	20.7	even	4
961.2.a.d.1.1		2	124.47	odd	10
961.2.a.e.1.1		2	124.15	even	10
961.2.c.d.439.1		4	124.3	even	30
961.2.c.d.521.1		4	124.75	even	30
961.2.c.f.439.1		4	124.59	odd	30
961.2.c.f.521.1		4	124.111	odd	30
961.2.d.b.531.1		4	124.123	even	2
961.2.d.b.628.1		4	124.23	even	10
961.2.d.e.374.1		4	124.27	even	10
961.2.d.e.388.1		4	124.91	even	10
961.2.d.f.374.1		4	124.35	odd	10
961.2.d.f.388.1		4	124.95	odd	10
961.2.g.b.448.1		8	124.71	odd	30
961.2.g.b.547.1		8	124.87	odd	6
961.2.g.b.844.1		8	124.67	odd	6
961.2.g.b.846.1		8	124.107	odd	30
961.2.g.c.448.1		8	124.115	even	30
961.2.g.c.547.1		8	124.99	even	6
961.2.g.c.844.1		8	124.119	even	6
961.2.g.c.846.1		8	124.79	even	30
961.2.g.f.235.1		8	124.19	odd	30
961.2.g.f.338.1		8	124.103	odd	30
961.2.g.f.732.1		8	124.51	odd	30
961.2.g.f.816.1		8	124.7	odd	30
961.2.g.g.235.1		8	124.43	even	30
961.2.g.g.338.1		8	124.83	even	30
961.2.g.g.732.1		8	124.11	even	30
961.2.g.g.816.1		8	124.55	even	30
8649.2.a.f.1.2		2	372.263	odd	10
8649.2.a.g.1.2		2	372.47	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 $\F_{q}$

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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Newspace parameters

Newform invariants

Embedding invariants

$q$ -expansion

Character values

Coefficient data

Twists

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	496.2.n.b.97.1

Level	$496$
Weight	$2$
Character	496.97
Analytic conductor	$3.961$
Analytic rank	$0$
Dimension	$4$
Inner twists	$2$