LMFDB - Embedded newform 765.2.be.b.451.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [765,2,Mod(406,765)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(765, base_ring=CyclotomicField(8))

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

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

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

chi := DirichletCharacter("765.406");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 765 = 3^{2} \cdot 5 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	765.be (of order $8$, degree $4$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$6.10855575463$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$6$ over $\Q(\zeta_{8})$
Twist minimal:	no (minimal twist has level 85)
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			451.5
Character	$\chi$	$=$	765.451
Dual form			765.2.be.b.631.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.27691 - 1.27691i) q^{2} -1.26102i q^{4} +(0.382683 - 0.923880i) q^{5} +(1.66158 + 4.01142i) q^{7} +(0.943613 + 0.943613i) q^{8} +(-0.691061 - 1.66837i) q^{10} +(-0.0485041 + 0.0200910i) q^{11} +3.02508i q^{13} +(7.24394 + 3.00054i) q^{14} +4.93187 q^{16} +(-3.12202 + 2.69314i) q^{17} +(5.52988 - 5.52988i) q^{19} +(-1.16503 - 0.482572i) q^{20} +(-0.0362810 + 0.0875901i) q^{22} +(-0.962654 + 0.398744i) q^{23} +(-0.707107 - 0.707107i) q^{25} +(3.86277 + 3.86277i) q^{26} +(5.05848 - 2.09529i) q^{28} +(0.161016 - 0.388726i) q^{29} +(-1.27892 - 0.529745i) q^{31} +(4.41035 - 4.41035i) q^{32} +(-0.547638 + 7.42546i) q^{34} +4.34193 q^{35} +(0.311301 + 0.128945i) q^{37} -14.1224i q^{38} +(1.23289 - 0.510679i) q^{40} +(-2.52291 - 6.09084i) q^{41} +(-7.06729 - 7.06729i) q^{43} +(0.0253352 + 0.0611647i) q^{44} +(-0.720064 + 1.73839i) q^{46} +6.13168i q^{47} +(-8.38087 + 8.38087i) q^{49} -1.80583 q^{50} +3.81469 q^{52} +(8.52974 - 8.52974i) q^{53} +0.0525004i q^{55} +(-2.21733 + 5.35312i) q^{56} +(-0.290767 - 0.701974i) q^{58} +(-3.60468 - 3.60468i) q^{59} +(-2.28486 - 5.51614i) q^{61} +(-2.30951 + 0.956630i) q^{62} -1.39954i q^{64} +(2.79481 + 1.15765i) q^{65} +0.916040 q^{67} +(3.39611 + 3.93693i) q^{68} +(5.54427 - 5.54427i) q^{70} +(-3.86169 - 1.59956i) q^{71} +(2.06289 - 4.98025i) q^{73} +(0.562156 - 0.232853i) q^{74} +(-6.97330 - 6.97330i) q^{76} +(-0.161187 - 0.161187i) q^{77} +(9.22305 - 3.82031i) q^{79} +(1.88734 - 4.55645i) q^{80} +(-10.9990 - 4.55595i) q^{82} +(4.61746 - 4.61746i) q^{83} +(1.29339 + 3.91499i) q^{85} -18.0487 q^{86} +(-0.0647272 - 0.0268109i) q^{88} +10.2159i q^{89} +(-12.1349 + 5.02642i) q^{91} +(0.502825 + 1.21393i) q^{92} +(7.82963 + 7.82963i) q^{94} +(-2.99275 - 7.22514i) q^{95} +(-7.35663 + 17.7605i) q^{97} +21.4033i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 8 q^{11} - 24 q^{16} + 8 q^{17} - 8 q^{19} - 32 q^{22} + 16 q^{23} - 16 q^{26} + 48 q^{28} + 8 q^{29} + 16 q^{34} + 32 q^{35} + 24 q^{37} + 16 q^{40} - 16 q^{41} + 8 q^{43} - 16 q^{44} + 8 q^{46}+ \cdots - 40 q^{97}+O(q^{100}) $ 24 * q + 8 * q^11 - 24 * q^16 + 8 * q^17 - 8 * q^19 - 32 * q^22 + 16 * q^23 - 16 * q^26 + 48 * q^28 + 8 * q^29 + 16 * q^34 + 32 * q^35 + 24 * q^37 + 16 * q^40 - 16 * q^41 + 8 * q^43 - 16 * q^44 + 8 * q^46 - 8 * q^50 - 48 * q^52 - 24 * q^53 - 64 * q^56 - 64 * q^58 - 32 * q^59 + 32 * q^61 + 32 * q^62 - 8 * q^65 + 16 * q^67 + 40 * q^68 + 24 * q^71 + 64 * q^74 - 8 * q^76 - 24 * q^77 + 32 * q^80 - 80 * q^82 + 96 * q^83 + 16 * q^86 - 8 * q^88 - 24 * q^91 - 80 * q^92 + 56 * q^94 + 16 * q^95 - 40 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/765\mathbb{Z}\right)^\times$.

$n$	$307$	$496$	$596$
$\chi(n)$	$1$	$e\left(\frac{1}{8}\right)$	$1$

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 $

$2$	1.27691	−	1.27691i	0.902915	−	0.902915i	−0.0927724	−	0.995687i	$-0.529573\pi$
$2$	1.27691	−	1.27691i	0.902915	−	0.902915i	0.995687	+	0.0927724i	$0.0295729\pi$
$3$		0			0
$3$		0			0
$4$		−	1.26102i		−	0.630511i
$5$	0.382683	−	0.923880i	0.171141	−	0.413171i
$5$	0.382683	−	0.923880i	0.171141	−	0.413171i
$6$		0			0
$7$	1.66158	+	4.01142i	0.628020	+	1.51617i	0.842080	+	0.539353i	$0.181331\pi$
$7$	1.66158	+	4.01142i	0.628020	+	1.51617i	−0.214060	+	0.976821i	$0.568669\pi$
$8$	0.943613	+	0.943613i	0.333617	+	0.333617i
$9$		0			0
$10$	−0.691061	−	1.66837i	−0.218533	−	0.527585i
$11$	−0.0485041	+	0.0200910i	−0.0146245	+	0.00605768i	−0.389984	−	0.920822i	$-0.627519\pi$
$11$	−0.0485041	+	0.0200910i	−0.0146245	+	0.00605768i	0.375359	+	0.926879i	$0.377519\pi$
$12$		0			0
$13$			3.02508i			0.839006i	0.907754	+	0.419503i	$0.137796\pi$
$13$			3.02508i			0.839006i	−0.907754	+	0.419503i	$0.862204\pi$
$14$	7.24394	+	3.00054i	1.93602	+	0.801928i
$15$		0			0
$16$	4.93187			1.23297
$17$	−3.12202	+	2.69314i	−0.757200	+	0.653183i
$17$	−3.12202	+	2.69314i	−0.757200	+	0.653183i
$18$		0			0
$19$	5.52988	−	5.52988i	1.26864	−	1.26864i	0.321851	−	0.946790i	$-0.395695\pi$
$19$	5.52988	−	5.52988i	1.26864	−	1.26864i	0.946790	−	0.321851i	$-0.104305\pi$
$20$	−1.16503	−	0.482572i	−0.260509	−	0.107906i
$21$		0			0
$22$	−0.0362810	+	0.0875901i	−0.00773514	+	0.0186743i
$23$	−0.962654	+	0.398744i	−0.200727	+	0.0831439i	−0.480782	−	0.876840i	$-0.659647\pi$
$23$	−0.962654	+	0.398744i	−0.200727	+	0.0831439i	0.280055	+	0.959984i	$0.409647\pi$
$24$		0			0
$25$	−0.707107	−	0.707107i	−0.141421	−	0.141421i
$26$	3.86277	+	3.86277i	0.757551	+	0.757551i
$27$		0			0
$28$	5.05848	−	2.09529i	0.955964	−	0.395973i
$29$	0.161016	−	0.388726i	0.0298999	−	0.0721847i	−0.908224	−	0.418484i	$-0.862562\pi$
$29$	0.161016	−	0.388726i	0.0298999	−	0.0721847i	0.938124	+	0.346299i	$0.112562\pi$
$30$		0			0
$31$	−1.27892	−	0.529745i	−0.229701	−	0.0951451i	0.264865	−	0.964286i	$-0.414673\pi$
$31$	−1.27892	−	0.529745i	−0.229701	−	0.0951451i	−0.494565	+	0.869141i	$0.664673\pi$
$32$	4.41035	−	4.41035i	0.779647	−	0.779647i
$33$		0			0
$34$	−0.547638	+	7.42546i	−0.0939192	+	1.27346i
$35$	4.34193			0.733920
$36$		0			0
$37$	0.311301	+	0.128945i	0.0511775	+	0.0211984i	0.408125	−	0.912926i	$-0.366183\pi$
$37$	0.311301	+	0.128945i	0.0511775	+	0.0211984i	−0.356948	+	0.934124i	$0.616183\pi$
$38$		−	14.1224i		−	2.29095i
$39$		0			0
$40$	1.23289	−	0.510679i	0.194937	−	0.0807455i
$41$	−2.52291	−	6.09084i	−0.394012	−	0.951230i	−0.989057	−	0.147537i	$-0.952865\pi$
$41$	−2.52291	−	6.09084i	−0.394012	−	0.951230i	0.595044	−	0.803693i	$-0.297135\pi$
$42$		0			0
$43$	−7.06729	−	7.06729i	−1.07775	−	1.07775i	−0.996711	−	0.0810414i	$-0.974175\pi$
$43$	−7.06729	−	7.06729i	−1.07775	−	1.07775i	−0.0810414	−	0.996711i	$-0.525825\pi$
$44$	0.0253352	+	0.0611647i	0.00381943	+	0.00922092i
$45$		0			0
$46$	−0.720064	+	1.73839i	−0.106168	+	0.256311i
$47$			6.13168i			0.894398i	0.894435	+	0.447199i	$0.147578\pi$
$47$			6.13168i			0.894398i	−0.894435	+	0.447199i	$0.852422\pi$
$48$		0			0
$49$	−8.38087	+	8.38087i	−1.19727	+	1.19727i
$50$	−1.80583			−0.255383
$51$		0			0
$52$	3.81469			0.529002
$53$	8.52974	−	8.52974i	1.17165	−	1.17165i	0.189834	−	0.981816i	$-0.439205\pi$
$53$	8.52974	−	8.52974i	1.17165	−	1.17165i	0.981816	−	0.189834i	$-0.0607949\pi$
$54$		0			0
$55$			0.0525004i			0.00707916i
$56$	−2.21733	+	5.35312i	−0.296304	+	0.715340i
$57$		0			0
$58$	−0.290767	−	0.701974i	−0.0381796	−	0.0921737i
$59$	−3.60468	−	3.60468i	−0.469290	−	0.469290i	0.432395	−	0.901684i	$-0.357669\pi$
$59$	−3.60468	−	3.60468i	−0.469290	−	0.469290i	−0.901684	+	0.432395i	$0.857669\pi$
$60$		0			0
$61$	−2.28486	−	5.51614i	−0.292547	−	0.706270i	0.707453	−	0.706760i	$-0.249844\pi$
$61$	−2.28486	−	5.51614i	−0.292547	−	0.706270i	−1.00000		0.000490243i	$0.999844\pi$
$62$	−2.30951	+	0.956630i	−0.293308	+	0.121492i
$63$		0			0
$64$		−	1.39954i		−	0.174943i
$65$	2.79481	+	1.15765i	0.346653	+	0.143588i
$66$		0			0
$67$	0.916040			0.111912			0.0559561	−	0.998433i	$-0.482179\pi$
$67$	0.916040			0.111912			0.0559561	+	0.998433i	$0.482179\pi$
$68$	3.39611	+	3.93693i	0.411839	+	0.477423i
$69$		0			0
$70$	5.54427	−	5.54427i	0.662667	−	0.662667i
$71$	−3.86169	−	1.59956i	−0.458298	−	0.189833i	0.141577	−	0.989927i	$-0.454783\pi$
$71$	−3.86169	−	1.59956i	−0.458298	−	0.189833i	−0.599875	+	0.800094i	$0.704783\pi$
$72$		0			0
$73$	2.06289	−	4.98025i	0.241443	−	0.582895i	−0.755984	−	0.654590i	$-0.772841\pi$
$73$	2.06289	−	4.98025i	0.241443	−	0.582895i	0.997427	+	0.0716959i	$0.0228411\pi$
$74$	0.562156	−	0.232853i	0.0653493	−	0.0270686i
$75$		0			0
$76$	−6.97330	−	6.97330i	−0.799892	−	0.799892i
$77$	−0.161187	−	0.161187i	−0.0183690	−	0.0183690i
$78$		0			0
$79$	9.22305	−	3.82031i	1.03767	−	0.429819i	0.202198	−	0.979345i	$-0.435192\pi$
$79$	9.22305	−	3.82031i	1.03767	−	0.429819i	0.835477	+	0.549526i	$0.185192\pi$
$80$	1.88734	−	4.55645i	0.211011	−	0.509427i
$81$		0			0
$82$	−10.9990	−	4.55595i	−1.21464	−	0.503120i
$83$	4.61746	−	4.61746i	0.506833	−	0.506833i	−0.406720	−	0.913553i	$-0.633328\pi$
$83$	4.61746	−	4.61746i	0.506833	−	0.506833i	0.913553	+	0.406720i	$0.133328\pi$
$84$		0			0
$85$	1.29339	+	3.91499i	0.140288	+	0.424640i
$86$	−18.0487			−1.94624
$87$		0			0
$88$	−0.0647272	−	0.0268109i	−0.00689994	−	0.00285805i
$89$			10.2159i			1.08289i	0.840738	+	0.541443i	$0.182122\pi$
$89$			10.2159i			1.08289i	−0.840738	+	0.541443i	$0.817878\pi$
$90$		0			0
$91$	−12.1349	+	5.02642i	−1.27208	+	0.526912i
$92$	0.502825	+	1.21393i	0.0524231	+	0.126561i
$93$		0			0
$94$	7.82963	+	7.82963i	0.807565	+	0.807565i
$95$	−2.99275	−	7.22514i	−0.307050	−	0.741283i
$96$		0			0
$97$	−7.35663	+	17.7605i	−0.746952	+	1.80330i	−0.172036	+	0.985091i	$0.555035\pi$
$97$	−7.35663	+	17.7605i	−0.746952	+	1.80330i	−0.574916	+	0.818212i	$0.694965\pi$
$98$			21.4033i			2.16206i
$99$		0			0
$100$	−0.891677	+	0.891677i	−0.0891677	+	0.0891677i
$101$	13.2926			1.32266			0.661331	−	0.750094i	$-0.269992\pi$
$101$	13.2926			1.32266			0.661331	+	0.750094i	$0.269992\pi$
$102$		0			0
$103$	−6.91299			−0.681157			−0.340579	−	0.940216i	$-0.610623\pi$
$103$	−6.91299			−0.681157			−0.340579	+	0.940216i	$0.610623\pi$
$104$	−2.85450	+	2.85450i	−0.279907	+	0.279907i
$105$		0			0
$106$		−	21.7835i		−	2.11580i
$107$	−5.64104	+	13.6187i	−0.545339	+	1.31657i	0.375572	+	0.926793i	$0.377446\pi$
$107$	−5.64104	+	13.6187i	−0.545339	+	1.31657i	−0.920911	+	0.389773i	$0.872554\pi$
$108$		0			0
$109$	−1.81709	−	4.38684i	−0.174046	−	0.420183i	0.812652	−	0.582749i	$-0.198023\pi$
$109$	−1.81709	−	4.38684i	−0.174046	−	0.420183i	−0.986698	+	0.162566i	$0.948023\pi$
$110$	0.0670386	+	0.0670386i	0.00639188	+	0.00639188i
$111$		0			0
$112$	8.19471	+	19.7838i	0.774328	+	1.86939i
$113$	−2.78393	+	1.15314i	−0.261890	+	0.108478i	−0.509765	−	0.860314i	$-0.670268\pi$
$113$	−2.78393	+	1.15314i	−0.261890	+	0.108478i	0.247875	+	0.968792i	$0.420268\pi$
$114$		0			0
$115$			1.04197i			0.0971641i
$116$	−0.490192	−	0.203044i	−0.0455132	−	0.0188522i
$117$		0			0
$118$	−9.20574			−0.847457
$119$	−15.9908	−	8.04884i	−1.46588	−	0.737836i
$120$		0			0
$121$	−7.77623	+	7.77623i	−0.706930	+	0.706930i
$122$	−9.96122	−	4.12607i	−0.901846	−	0.373557i
$123$		0			0
$124$	−0.668020	+	1.61274i	−0.0599900	+	0.144829i
$125$	−0.923880	+	0.382683i	−0.0826343	+	0.0342282i
$126$		0			0
$127$	0.00585984	+	0.00585984i	0.000519977	+	0.000519977i	0.707367	−	0.706847i	$-0.249883\pi$
$127$	0.00585984	+	0.00585984i	0.000519977	+	0.000519977i	−0.706847	+	0.707367i	$0.749883\pi$
$128$	7.03360	+	7.03360i	0.621689	+	0.621689i
$129$		0			0
$130$	5.04695	−	2.09051i	0.442647	−	0.183350i
$131$	−3.13210	+	7.56157i	−0.273653	+	0.660657i	−0.999634	−	0.0270577i	$-0.991386\pi$
$131$	−3.13210	+	7.56157i	−0.273653	+	0.660657i	0.725981	+	0.687715i	$0.241386\pi$
$132$		0			0
$133$	31.3710	+	12.9943i	2.72021	+	1.12675i
$134$	1.16971	−	1.16971i	0.101047	−	0.101047i
$135$		0			0
$136$	−5.48726	−	0.404693i	−0.470528	−	0.0347021i
$137$	2.23387			0.190852			0.0954260	−	0.995437i	$-0.469579\pi$
$137$	2.23387			0.190852			0.0954260	+	0.995437i	$0.469579\pi$
$138$		0			0
$139$	−18.2335	−	7.55257i	−1.54655	−	0.640601i	−0.563859	−	0.825871i	$-0.690684\pi$
$139$	−18.2335	−	7.55257i	−1.54655	−	0.640601i	−0.982688	+	0.185270i	$0.940684\pi$
$140$		−	5.47526i		−	0.462744i
$141$		0			0
$142$	−6.97355	+	2.88854i	−0.585207	+	0.242401i
$143$	−0.0607770	−	0.146729i	−0.00508243	−	0.0122701i
$144$		0			0
$145$	−0.297518	−	0.297518i	−0.0247076	−	0.0247076i
$146$	−3.72523	−	8.99349i	−0.308302	−	0.744306i
$147$		0			0
$148$	0.162602	−	0.392557i	0.0133658	−	0.0322680i
$149$		−	10.1835i		−	0.834263i	−0.908846	−	0.417132i	$-0.863035\pi$
$149$		−	10.1835i		−	0.834263i	0.908846	−	0.417132i	$-0.136965\pi$
$150$		0			0
$151$	10.8529	−	10.8529i	0.883200	−	0.883200i	−0.110659	−	0.993858i	$-0.535296\pi$
$151$	10.8529	−	10.8529i	0.883200	−	0.883200i	0.993858	+	0.110659i	$0.0352961\pi$
$152$	10.4361			0.846482
$153$		0			0
$154$	−0.411645			−0.0331713
$155$	−0.978842	+	0.978842i	−0.0786225	+	0.0786225i
$156$		0			0
$157$		−	9.41222i		−	0.751177i	−0.926787	−	0.375588i	$-0.877441\pi$
$157$		−	9.41222i		−	0.751177i	0.926787	−	0.375588i	$-0.122559\pi$
$158$	6.89884	−	16.6553i	0.548842	−	1.32502i
$159$		0			0
$160$	−2.38686	−	5.76240i	−0.188698	−	0.455558i
$161$	−3.19906	−	3.19906i	−0.252121	−	0.252121i
$162$		0			0
$163$	−4.76262	−	11.4980i	−0.373037	−	0.900592i	−0.993232	−	0.116144i	$-0.962947\pi$
$163$	−4.76262	−	11.4980i	−0.373037	−	0.900592i	0.620195	−	0.784448i	$-0.287053\pi$
$164$	−7.68068	+	3.18144i	−0.599761	+	0.248429i
$165$		0			0
$166$		−	11.7922i		−	0.915253i
$167$	−11.6432	−	4.82277i	−0.900977	−	0.373197i	−0.116382	−	0.993205i	$-0.537130\pi$
$167$	−11.6432	−	4.82277i	−0.900977	−	0.373197i	−0.784596	+	0.620008i	$0.787130\pi$
$168$		0			0
$169$	3.84890			0.296069
$170$	6.65066	+	3.34755i	0.510082	+	0.256746i
$171$		0			0
$172$	−8.91201	+	8.91201i	−0.679534	+	0.679534i
$173$	−11.2681	−	4.66741i	−0.856699	−	0.354856i	−0.0892832	−	0.996006i	$-0.528458\pi$
$173$	−11.2681	−	4.66741i	−0.856699	−	0.354856i	−0.767416	+	0.641150i	$0.778458\pi$
$174$		0			0
$175$	1.66158	−	4.01142i	0.125604	−	0.303235i
$176$	−0.239216	+	0.0990864i	−0.0180316	+	0.00746892i
$177$		0			0
$178$	13.0449	+	13.0449i	0.977754	+	0.977754i
$179$	−9.80106	−	9.80106i	−0.732566	−	0.732566i	0.238562	−	0.971127i	$-0.423324\pi$
$179$	−9.80106	−	9.80106i	−0.732566	−	0.732566i	−0.971127	+	0.238562i	$0.923324\pi$
$180$		0			0
$181$	1.88863	−	0.782297i	0.140381	−	0.0581476i	−0.311387	−	0.950283i	$-0.600794\pi$
$181$	1.88863	−	0.782297i	0.140381	−	0.0581476i	0.451768	+	0.892136i	$0.350794\pi$
$182$	−9.07686	+	21.9135i	−0.672822	+	1.62434i
$183$		0			0
$184$	−1.28463	−	0.532112i	−0.0947043	−	0.0392278i
$185$	0.238259	−	0.238259i	0.0175172	−	0.0175172i
$186$		0			0
$187$	0.0973225	−	0.193353i	0.00711693	−	0.0141394i
$188$	7.73218			0.563927
$189$		0			0
$190$	−13.0474	−	5.40440i	−0.946556	−	0.392076i
$191$		−	3.08056i		−	0.222902i	−0.993770	−	0.111451i	$-0.964450\pi$
$191$		−	3.08056i		−	0.222902i	0.993770	−	0.111451i	$-0.0355498\pi$
$192$		0			0
$193$	19.0706	−	7.89931i	1.37273	−	0.568605i	0.430205	−	0.902731i	$-0.358441\pi$
$193$	19.0706	−	7.89931i	1.37273	−	0.568605i	0.942528	+	0.334126i	$0.108441\pi$
$194$	13.2848	+	32.0724i	0.953794	+	2.30266i
$195$		0			0
$196$	10.5685	+	10.5685i	0.754890	+	0.754890i
$197$	6.97881	+	16.8483i	0.497219	+	1.20039i	0.950975	+	0.309268i	$0.100084\pi$
$197$	6.97881	+	16.8483i	0.497219	+	1.20039i	−0.453756	+	0.891126i	$0.649916\pi$
$198$		0			0
$199$	−10.2053	+	24.6377i	−0.723432	+	1.74652i	−0.0601040	+	0.998192i	$0.519143\pi$
$199$	−10.2053	+	24.6377i	−0.723432	+	1.74652i	−0.663328	+	0.748328i	$0.730857\pi$
$200$		−	1.33447i		−	0.0943613i
$201$		0			0
$202$	16.9735	−	16.9735i	1.19425	−	1.19425i
$203$	1.82689			0.128222
$204$		0			0
$205$	−6.59268			−0.460453
$206$	−8.82730	+	8.82730i	−0.615027	+	0.615027i
$207$		0			0
$208$			14.9193i			1.03447i
$209$	−0.157121	+	0.379323i	−0.0108683	+	0.0262383i
$210$		0			0
$211$	2.98710	+	7.21149i	0.205640	+	0.496460i	0.992728	−	0.120382i	$-0.0384119\pi$
$211$	2.98710	+	7.21149i	0.205640	+	0.496460i	−0.787087	+	0.616842i	$0.788412\pi$
$212$	−10.7562	−	10.7562i	−0.738738	−	0.738738i
$213$		0			0
$214$	10.1868	+	24.5930i	0.696352	+	1.68114i
$215$	−9.23386	+	3.82479i	−0.629744	+	0.260849i
$216$		0			0
$217$		−	6.01049i		−	0.408019i
$218$	−7.92189	−	3.28135i	−0.536538	−	0.222241i
$219$		0			0
$220$	0.0662042			0.00446348
$221$	−8.14696	−	9.44435i	−0.548024	−	0.635295i
$222$		0			0
$223$	3.37213	−	3.37213i	0.225815	−	0.225815i	−0.585127	−	0.810942i	$-0.698955\pi$
$223$	3.37213	−	3.37213i	0.225815	−	0.225815i	0.810942	+	0.585127i	$0.198955\pi$
$224$	25.0199	+	10.3636i	1.67171	+	0.692447i
$225$		0			0
$226$	−2.08238	+	5.02731i	−0.138518	+	0.334411i
$227$	10.3577	−	4.29029i	0.687464	−	0.284757i	−0.0114793	−	0.999934i	$-0.503654\pi$
$227$	10.3577	−	4.29029i	0.687464	−	0.284757i	0.698943	+	0.715177i	$0.253654\pi$
$228$		0			0
$229$	−14.6007	−	14.6007i	−0.964838	−	0.964838i	0.0345640	−	0.999402i	$-0.488996\pi$
$229$	−14.6007	−	14.6007i	−0.964838	−	0.964838i	−0.999402	+	0.0345640i	$0.988996\pi$
$230$	1.33051	+	1.33051i	0.0877309	+	0.0877309i
$231$		0			0
$232$	0.518744	−	0.214871i	0.0340572	−	0.0141069i
$233$	1.17044	−	2.82569i	0.0766781	−	0.185117i	−0.880892	−	0.473317i	$-0.843057\pi$
$233$	1.17044	−	2.82569i	0.0766781	−	0.185117i	0.957570	+	0.288199i	$0.0930566\pi$
$234$		0			0
$235$	5.66494	+	2.34649i	0.369540	+	0.153068i
$236$	−4.54558	+	4.54558i	−0.295892	+	0.295892i
$237$		0			0
$238$	−30.6966	+	10.1412i	−1.98976	+	0.657358i
$239$	−4.94072			−0.319588			−0.159794	−	0.987150i	$-0.551083\pi$
$239$	−4.94072			−0.319588			−0.159794	+	0.987150i	$0.551083\pi$
$240$		0			0
$241$	1.53527	+	0.635928i	0.0988952	+	0.0409637i	0.431583	−	0.902073i	$-0.357955\pi$
$241$	1.53527	+	0.635928i	0.0988952	+	0.0409637i	−0.332687	+	0.943037i	$0.607955\pi$
$242$			19.8592i			1.27659i
$243$		0			0
$244$	−6.95597	+	2.88126i	−0.445311	+	0.184454i
$245$	4.53570	+	10.9501i	0.289775	+	0.699579i
$246$		0			0
$247$	16.7283	+	16.7283i	1.06440	+	1.06440i
$248$	−0.706929	−	1.70668i	−0.0448900	−	0.108374i
$249$		0			0
$250$	−0.691061	+	1.66837i	−0.0437065	+	0.105517i
$251$		−	9.14240i		−	0.577063i	−0.957470	−	0.288531i	$-0.906833\pi$
$251$		−	9.14240i		−	0.577063i	0.957470	−	0.288531i	$-0.0931670\pi$
$252$		0			0
$253$	0.0386814	−	0.0386814i	0.00243188	−	0.00243188i
$254$	0.0149650			0.000938989
$255$		0			0
$256$	20.7617			1.29761
$257$	11.7749	−	11.7749i	0.734498	−	0.734498i	−0.237009	−	0.971507i	$-0.576167\pi$
$257$	11.7749	−	11.7749i	0.734498	−	0.734498i	0.971507	+	0.237009i	$0.0761671\pi$
$258$		0			0
$259$			1.46301i			0.0909070i
$260$	1.45982	−	3.52431i	0.0905341	−	0.218569i
$261$		0			0
$262$	5.65605	+	13.6549i	0.349432	+	0.843603i
$263$	−15.3640	−	15.3640i	−0.947387	−	0.947387i	0.0512969	−	0.998683i	$-0.483665\pi$
$263$	−15.3640	−	15.3640i	−0.947387	−	0.947387i	−0.998683	+	0.0512969i	$0.983665\pi$
$264$		0			0
$265$	−4.61626	−	11.1446i	−0.283575	−	0.684610i
$266$	56.6507	−	23.4655i	3.47348	−	1.43876i
$267$		0			0
$268$		−	1.15515i		−	0.0705618i
$269$	21.4082	+	8.86758i	1.30528	+	0.540666i	0.923504	−	0.383588i	$-0.125312\pi$
$269$	21.4082	+	8.86758i	1.30528	+	0.540666i	0.381779	+	0.924254i	$0.375312\pi$
$270$		0			0
$271$	−3.95595			−0.240307			−0.120153	−	0.992755i	$-0.538339\pi$
$271$	−3.95595			−0.240307			−0.120153	+	0.992755i	$0.538339\pi$
$272$	−15.3974	+	13.2822i	−0.933603	+	0.805353i
$273$		0			0
$274$	2.85246	−	2.85246i	0.172323	−	0.172323i
$275$	0.0485041	+	0.0200910i	0.00292491	+	0.00121154i
$276$		0			0
$277$	−6.47115	+	15.6227i	−0.388814	+	0.938679i	0.601378	+	0.798964i	$0.294618\pi$
$277$	−6.47115	+	15.6227i	−0.388814	+	0.938679i	−0.990192	+	0.139714i	$0.955382\pi$
$278$	−32.9266	+	13.6387i	−1.97481	+	0.817992i
$279$		0			0
$280$	4.09710	+	4.09710i	0.244848	+	0.244848i
$281$	−3.30210	−	3.30210i	−0.196987	−	0.196987i	0.601720	−	0.798707i	$-0.294482\pi$
$281$	−3.30210	−	3.30210i	−0.196987	−	0.196987i	−0.798707	+	0.601720i	$0.794482\pi$
$282$		0			0
$283$	−8.03809	+	3.32949i	−0.477815	+	0.197917i	−0.608575	−	0.793497i	$-0.708258\pi$
$283$	−8.03809	+	3.32949i	−0.477815	+	0.197917i	0.130760	+	0.991414i	$0.458258\pi$
$284$	−2.01708	+	4.86967i	−0.119692	+	0.288962i
$285$		0			0
$286$	−0.264967	−	0.109753i	−0.0156678	−	0.00648982i
$287$	20.2409	−	20.2409i	1.19478	−	1.19478i
$288$		0			0
$289$	2.49398	−	16.8161i	0.146705	−	0.989180i
$290$	−0.759811			−0.0446176
$291$		0			0
$292$	−6.28021	−	2.60135i	−0.367521	−	0.152232i
$293$			0.739100i			0.0431787i	0.999767	+	0.0215893i	$0.00687263\pi$
$293$			0.739100i			0.0431787i	−0.999767	+	0.0215893i	$0.993127\pi$
$294$		0			0
$295$	−4.70974	+	1.95084i	−0.274212	+	0.113582i
$296$	0.172073	+	0.415421i	0.0100015	+	0.0241459i
$297$		0			0
$298$	−13.0034	−	13.0034i	−0.753269	−	0.753269i
$299$	−1.20623	−	2.91210i	−0.0697582	−	0.168411i
$300$		0			0
$301$	16.6070	−	40.0928i	0.957210	−	2.31091i
$302$		−	27.7165i		−	1.59491i
$303$		0			0
$304$	27.2726	−	27.2726i	1.56419	−	1.56419i
$305$	−5.97063			−0.341877
$306$		0			0
$307$	−2.86108			−0.163290			−0.0816451	−	0.996661i	$-0.526017\pi$
$307$	−2.86108			−0.163290			−0.0816451	+	0.996661i	$0.526017\pi$
$308$	−0.203261	+	0.203261i	−0.0115818	+	0.0115818i
$309$		0			0
$310$			2.49979i			0.141979i
$311$	−7.84424	+	18.9377i	−0.444806	+	1.07386i	0.529435	+	0.848350i	$0.322404\pi$
$311$	−7.84424	+	18.9377i	−0.444806	+	1.07386i	−0.974242	+	0.225507i	$0.927596\pi$
$312$		0			0
$313$	3.23958	+	7.82103i	0.183112	+	0.442071i	0.988605	−	0.150534i	$-0.0480994\pi$
$313$	3.23958	+	7.82103i	0.183112	+	0.442071i	−0.805493	+	0.592605i	$0.798099\pi$
$314$	−12.0186	−	12.0186i	−0.678249	−	0.678249i
$315$		0			0
$316$	−4.81750	−	11.6305i	−0.271005	−	0.654265i
$317$	19.4863	−	8.07149i	1.09446	−	0.453340i	0.238900	−	0.971044i	$-0.423213\pi$
$317$	19.4863	−	8.07149i	1.09446	−	0.453340i	0.855560	+	0.517704i	$0.173213\pi$
$318$		0			0
$319$			0.0220898i			0.00123679i
$320$	−1.29301	−	0.535581i	−0.0722813	−	0.0299399i
$321$		0			0
$322$	−8.16985			−0.455288
$323$	−2.37163	+	32.1571i	−0.131961	+	1.78927i
$324$		0			0
$325$	2.13905	−	2.13905i	0.118653	−	0.118653i
$326$	−20.7634	−	8.60048i	−1.14998	−	0.476337i
$327$		0			0
$328$	3.36675	−	8.12805i	0.185897	−	0.448796i
$329$	−24.5967	+	10.1883i	−1.35606	+	0.561699i
$330$		0			0
$331$	10.7665	+	10.7665i	0.591780	+	0.591780i	0.938112	−	0.346332i	$-0.112573\pi$
$331$	10.7665	+	10.7665i	0.591780	+	0.591780i	−0.346332	+	0.938112i	$0.612573\pi$
$332$	−5.82272	−	5.82272i	−0.319563	−	0.319563i
$333$		0			0
$334$	−21.0256	+	8.70910i	−1.15047	+	0.476541i
$335$	0.350554	−	0.846311i	0.0191528	−	0.0462389i
$336$		0			0
$337$	10.6003	+	4.39079i	0.577435	+	0.239182i	0.652235	−	0.758017i	$-0.273832\pi$
$337$	10.6003	+	4.39079i	0.577435	+	0.239182i	−0.0747994	+	0.997199i	$0.523832\pi$
$338$	4.91472	−	4.91472i	0.267326	−	0.267326i
$339$		0			0
$340$	4.93688	−	1.63100i	0.267740	−	0.0884532i
$341$	0.0726759			0.00393562
$342$		0			0
$343$	−19.4648	−	8.06258i	−1.05100	−	0.435338i
$344$		−	13.3376i		−	0.719114i
$345$		0			0
$346$	−20.3483	+	8.42854i	−1.09393	+	0.453121i
$347$	5.73424	+	13.8437i	0.307830	+	0.743168i	0.999775	+	0.0212172i	$0.00675416\pi$
$347$	5.73424	+	13.8437i	0.307830	+	0.743168i	−0.691945	+	0.721950i	$0.743246\pi$
$348$		0			0
$349$	−3.20791	−	3.20791i	−0.171715	−	0.171715i	0.616017	−	0.787733i	$-0.288745\pi$
$349$	−3.20791	−	3.20791i	−0.171715	−	0.171715i	−0.787733	+	0.616017i	$0.788745\pi$
$350$	−3.00054	−	7.24394i	−0.160386	−	0.387205i
$351$		0			0
$352$	−0.125311	+	0.302528i	−0.00667912	+	0.0161248i
$353$			7.71469i			0.410612i	0.978698	+	0.205306i	$0.0658189\pi$
$353$			7.71469i			0.410612i	−0.978698	+	0.205306i	$0.934181\pi$
$354$		0			0
$355$	−2.95561	+	2.95561i	−0.156867	+	0.156867i
$356$	12.8825			0.682771
$357$		0			0
$358$	−25.0302			−1.32289
$359$	7.79826	−	7.79826i	0.411577	−	0.411577i	−0.470711	−	0.882287i	$-0.656003\pi$
$359$	7.79826	−	7.79826i	0.411577	−	0.411577i	0.882287	+	0.470711i	$0.156003\pi$
$360$		0			0
$361$		−	42.1592i		−	2.21890i
$362$	1.41269	−	3.41055i	0.0742496	−	0.179254i
$363$		0			0
$364$	6.33843	+	15.3023i	0.332224	+	0.802059i
$365$	−3.81172	−	3.81172i	−0.199515	−	0.199515i
$366$		0			0
$367$	−6.13386	−	14.8084i	−0.320185	−	0.772995i	−0.999243	−	0.0389098i	$-0.987611\pi$
$367$	−6.13386	−	14.8084i	−0.320185	−	0.772995i	0.679058	−	0.734085i	$-0.262389\pi$
$368$	−4.74768	+	1.96655i	−0.247490	+	0.102514i
$369$		0			0
$370$		−	0.608473i		−	0.0316330i
$371$	48.3892	+	20.0435i	2.51224	+	1.04061i
$372$		0			0
$373$	−10.2501			−0.530732			−0.265366	−	0.964148i	$-0.585493\pi$
$373$	−10.2501			−0.530732			−0.265366	+	0.964148i	$0.585493\pi$
$374$	−0.122623	−	0.371168i	−0.00634066	−	0.0191926i
$375$		0			0
$376$	−5.78593	+	5.78593i	−0.298387	+	0.298387i
$377$	1.17593	+	0.487085i	0.0605634	+	0.0250862i
$378$		0			0
$379$	−5.33919	+	12.8899i	−0.274256	+	0.662112i	−0.999656	−	0.0262152i	$-0.991654\pi$
$379$	−5.33919	+	12.8899i	−0.274256	+	0.662112i	0.725401	+	0.688327i	$0.241654\pi$
$380$	−9.11105	+	3.77392i	−0.467387	+	0.193598i
$381$		0			0
$382$	−3.93362	−	3.93362i	−0.201261	−	0.201261i
$383$	3.97525	+	3.97525i	0.203126	+	0.203126i	0.801338	−	0.598212i	$-0.204122\pi$
$383$	3.97525	+	3.97525i	0.203126	+	0.203126i	−0.598212	+	0.801338i	$0.704122\pi$
$384$		0			0
$385$	−0.210601	+	0.0872339i	−0.0107332	+	0.00444585i
$386$	14.2648	−	34.4383i	0.726060	−	1.75286i
$387$		0			0
$388$	22.3963	+	9.27687i	1.13700	+	0.470962i
$389$	25.3255	−	25.3255i	1.28406	−	1.28406i	0.345717	−	0.938339i	$-0.387636\pi$
$389$	25.3255	−	25.3255i	1.28406	−	1.28406i	0.938339	−	0.345717i	$-0.112364\pi$
$390$		0			0
$391$	1.93155	−	3.83745i	0.0976825	−	0.194068i
$392$	−15.8166			−0.798858
$393$		0			0
$394$	30.4252	+	12.6025i	1.53280	+	0.634907i
$395$		−	9.98296i		−	0.502297i
$396$		0			0
$397$	3.59405	−	1.48870i	0.180380	−	0.0747159i	−0.290665	−	0.956825i	$-0.593877\pi$
$397$	3.59405	−	1.48870i	0.180380	−	0.0747159i	0.471046	+	0.882109i	$0.343877\pi$
$398$	18.4290	+	44.4915i	0.923761	+	2.23016i
$399$		0			0
$400$	−3.48736	−	3.48736i	−0.174368	−	0.174368i
$401$	−14.0592	−	33.9420i	−0.702085	−	1.69498i	−0.718890	−	0.695124i	$-0.755350\pi$
$401$	−14.0592	−	33.9420i	−0.702085	−	1.69498i	0.0168056	−	0.999859i	$-0.494650\pi$
$402$		0			0
$403$	1.60252	−	3.86883i	0.0798273	−	0.192720i
$404$		−	16.7622i		−	0.833952i
$405$		0			0
$406$	2.33278	−	2.33278i	0.115774	−	0.115774i
$407$	−0.0176900			−0.000876860
$408$		0			0
$409$	−22.3529			−1.10528			−0.552641	−	0.833419i	$-0.686380\pi$
$409$	−22.3529			−1.10528			−0.552641	+	0.833419i	$0.686380\pi$
$410$	−8.41829	+	8.41829i	−0.415750	+	0.415750i
$411$		0			0
$412$			8.71743i			0.429477i
$413$	8.47041	−	20.4494i	0.416802	−	1.00625i
$414$		0			0
$415$	−2.49895	−	6.03301i	−0.122669	−	0.296149i
$416$	13.3416	+	13.3416i	0.654128	+	0.654128i
$417$		0			0
$418$	0.283733	+	0.684993i	0.0138778	+	0.0335041i
$419$	−20.2014	+	8.36768i	−0.986901	+	0.408788i	−0.816978	−	0.576669i	$-0.804352\pi$
$419$	−20.2014	+	8.36768i	−0.986901	+	0.408788i	−0.169924	+	0.985457i	$0.554352\pi$
$420$		0			0
$421$			20.6111i			1.00453i	0.864715	+	0.502263i	$0.167499\pi$
$421$			20.6111i			1.00453i	−0.864715	+	0.502263i	$0.832501\pi$
$422$	13.0227	+	5.39419i	0.633937	+	0.262585i
$423$		0			0
$424$	16.0975			0.781766
$425$	4.11194	+	0.303261i	0.199458	+	0.0147103i
$426$		0			0
$427$	18.3311	−	18.3311i	0.887103	−	0.887103i
$428$	17.1734	+	7.11347i	0.830109	+	0.343842i
$429$		0			0
$430$	−6.90692	+	16.6748i	−0.333081	+	0.804130i
$431$	−20.6074	+	8.53585i	−0.992621	+	0.411157i	−0.819086	−	0.573670i	$-0.805519\pi$
$431$	−20.6074	+	8.53585i	−0.992621	+	0.411157i	−0.173535	+	0.984828i	$0.555519\pi$
$432$		0			0
$433$	−6.31536	−	6.31536i	−0.303497	−	0.303497i	0.538883	−	0.842380i	$-0.318846\pi$
$433$	−6.31536	−	6.31536i	−0.303497	−	0.303497i	−0.842380	+	0.538883i	$0.818846\pi$
$434$	−7.67489	−	7.67489i	−0.368406	−	0.368406i
$435$		0			0
$436$	−5.53190	+	2.29139i	−0.264930	+	0.109738i
$437$	−3.11835	+	7.52837i	−0.149171	+	0.360131i
$438$		0			0
$439$	20.5695	+	8.52016i	0.981728	+	0.406645i	0.815066	−	0.579369i	$-0.196701\pi$
$439$	20.5695	+	8.52016i	0.981728	+	0.406645i	0.166663	+	0.986014i	$0.446701\pi$
$440$	−0.0495401	+	0.0495401i	−0.00236173	+	0.00236173i
$441$		0			0
$442$	−22.4626	−	1.65665i	−1.06844	−	0.0787987i
$443$	6.17421			0.293346			0.146673	−	0.989185i	$-0.453144\pi$
$443$	6.17421			0.293346			0.146673	+	0.989185i	$0.453144\pi$
$444$		0			0
$445$	9.43828	+	3.90946i	0.447418	+	0.185326i
$446$		−	8.61184i		−	0.407783i
$447$		0			0
$448$	5.61414	−	2.32545i	0.265243	−	0.109867i
$449$	−11.5947	−	27.9922i	−0.547189	−	1.32103i	−0.919561	−	0.392948i	$-0.871455\pi$
$449$	−11.5947	−	27.9922i	−0.547189	−	1.32103i	0.372371	−	0.928084i	$-0.378545\pi$
$450$		0			0
$451$	0.244743	+	0.244743i	0.0115245	+	0.0115245i
$452$	1.45414	+	3.51060i	0.0683968	+	0.165125i
$453$		0			0
$454$	7.74754	−	18.7042i	0.363610	−	0.877833i
$455$			13.1347i			0.615763i
$456$		0			0
$457$	18.0847	−	18.0847i	0.845965	−	0.845965i	−0.143662	−	0.989627i	$-0.545888\pi$
$457$	18.0847	−	18.0847i	0.845965	−	0.845965i	0.989627	+	0.143662i	$0.0458877\pi$
$458$	−37.2876			−1.74233
$459$		0			0
$460$	1.31395			0.0612630
$461$	9.93945	−	9.93945i	0.462926	−	0.462926i	−0.436687	−	0.899613i	$-0.643848\pi$
$461$	9.93945	−	9.93945i	0.462926	−	0.462926i	0.899613	+	0.436687i	$0.143848\pi$
$462$		0			0
$463$			25.1233i			1.16758i	0.811905	+	0.583789i	$0.198431\pi$
$463$			25.1233i			1.16758i	−0.811905	+	0.583789i	$0.801569\pi$
$464$	0.794108	−	1.91715i	0.0368656	−	0.0890013i
$465$		0			0
$466$	−2.11362	−	5.10272i	−0.0979114	−	0.236379i
$467$	15.7614	+	15.7614i	0.729352	+	0.729352i	0.970491	−	0.241139i	$-0.0775209\pi$
$467$	15.7614	+	15.7614i	0.729352	+	0.729352i	−0.241139	+	0.970491i	$0.577521\pi$
$468$		0			0
$469$	1.52208	+	3.67462i	0.0702830	+	0.169678i
$470$	10.2299	−	4.23737i	0.471871	−	0.195455i
$471$		0			0
$472$		−	6.80285i		−	0.313126i
$473$	0.484782	+	0.200803i	0.0222903	+	0.00923294i
$474$		0			0
$475$	−7.82043			−0.358826
$476$	−10.1498	+	20.1648i	−0.465213	+	0.924250i
$477$		0			0
$478$	−6.30887	+	6.30887i	−0.288561	+	0.288561i
$479$	−24.7134	−	10.2366i	−1.12919	−	0.467724i	−0.261681	−	0.965154i	$-0.584277\pi$
$479$	−24.7134	−	10.2366i	−1.12919	−	0.467724i	−0.867504	+	0.497430i	$0.834277\pi$
$480$		0			0
$481$	−0.390068	+	0.941709i	−0.0177856	+	0.0429382i
$482$	2.77243	−	1.14838i	0.126281	−	0.0523072i
$483$		0			0
$484$	9.80599	+	9.80599i	0.445727	+	0.445727i
$485$	13.5933	+	13.5933i	0.617239	+	0.617239i
$486$		0			0
$487$	−21.3841	+	8.85760i	−0.969008	+	0.401376i	−0.810343	−	0.585956i	$-0.800719\pi$
$487$	−21.3841	+	8.85760i	−0.969008	+	0.401376i	−0.158665	+	0.987332i	$0.550719\pi$
$488$	3.04908	−	7.36113i	0.138025	−	0.333223i
$489$		0			0
$490$	19.7741	+	8.19069i	0.893302	+	0.370018i
$491$	5.50823	−	5.50823i	0.248583	−	0.248583i	−0.571806	−	0.820389i	$-0.693757\pi$
$491$	5.50823	−	5.50823i	0.248583	−	0.248583i	0.820389	+	0.571806i	$0.193757\pi$
$492$		0			0
$493$	0.544201	+	1.64725i	0.0245096	+	0.0741883i
$494$	42.7213			1.92212
$495$		0			0
$496$	−6.30746	−	2.61263i	−0.283213	−	0.117311i
$497$		−	18.1487i		−	0.814079i
$498$		0			0
$499$	−8.12796	+	3.36671i	−0.363858	+	0.150715i	−0.557119	−	0.830432i	$-0.688093\pi$
$499$	−8.12796	+	3.36671i	−0.363858	+	0.150715i	0.193262	+	0.981147i	$0.438093\pi$
$500$	0.482572	+	1.16503i	0.0215813	+	0.0521018i
$501$		0			0
$502$	−11.6741	−	11.6741i	−0.521039	−	0.521039i
$503$	3.00003	+	7.24271i	0.133765	+	0.322937i	0.976542	−	0.215325i	$-0.0690812\pi$
$503$	3.00003	+	7.24271i	0.133765	+	0.322937i	−0.842778	+	0.538262i	$0.819081\pi$
$504$		0			0
$505$	5.08685	−	12.2807i	0.226362	−	0.546486i
$506$		−	0.0987858i		−	0.00439156i
$507$		0			0
$508$	0.00738938	−	0.00738938i	0.000327851	−	0.000327851i
$509$	−2.52868			−0.112082			−0.0560409	−	0.998428i	$-0.517848\pi$
$509$	−2.52868			−0.112082			−0.0560409	+	0.998428i	$0.517848\pi$
$510$		0			0
$511$	23.4055			1.03540
$512$	12.4437	−	12.4437i	0.549940	−	0.549940i
$513$		0			0
$514$		−	30.0711i		−	1.32638i
$515$	−2.64549	+	6.38677i	−0.116574	+	0.281435i
$516$		0			0
$517$	−0.123192	−	0.297412i	−0.00541797	−	0.0130801i
$518$	1.86814	+	1.86814i	0.0820813	+	0.0820813i
$519$		0			0
$520$	1.54485	+	3.72959i	0.0677459	+	0.163553i
$521$	−9.33885	+	3.86828i	−0.409142	+	0.169472i	−0.577755	−	0.816210i	$-0.696071\pi$
$521$	−9.33885	+	3.86828i	−0.409142	+	0.169472i	0.168613	+	0.985682i	$0.446071\pi$
$522$		0			0
$523$		−	5.80494i		−	0.253833i	−0.991913	−	0.126916i	$-0.959492\pi$
$523$		−	5.80494i		−	0.253833i	0.991913	−	0.126916i	$-0.0405079\pi$
$524$	9.53530	+	3.94965i	0.416552	+	0.172541i
$525$		0			0
$526$	−39.2371			−1.71082
$527$	5.41948	−	1.79043i	0.236076	−	0.0779925i
$528$		0			0
$529$	−15.4958	+	15.4958i	−0.673728	+	0.673728i
$530$	−20.1253	−	8.33618i	−0.874188	−	0.362101i
$531$		0			0
$532$	16.3861	−	39.5595i	0.710427	−	1.71512i
$533$	18.4253	−	7.63200i	0.798087	−	0.330579i
$534$		0			0
$535$	10.4233	+	10.4233i	0.450637	+	0.450637i
$536$	0.864387	+	0.864387i	0.0373358	+	0.0373358i
$537$		0			0
$538$	38.6596	−	16.0133i	1.66674	−	0.690384i
$539$	0.238126	−	0.574887i	0.0102568	−	0.0247621i
$540$		0			0
$541$	39.1174	+	16.2030i	1.68179	+	0.696620i	0.999409	−	0.0343783i	$-0.0109451\pi$
$541$	39.1174	+	16.2030i	1.68179	+	0.696620i	0.682380	+	0.730998i	$0.260945\pi$
$542$	−5.05141	+	5.05141i	−0.216976	+	0.216976i
$543$		0			0
$544$	−1.89149	+	25.6469i	−0.0810971	+	1.09960i
$545$	−4.74828			−0.203394
$546$		0			0
$547$	18.4832	+	7.65599i	0.790285	+	0.327347i	0.741058	−	0.671441i	$-0.234324\pi$
$547$	18.4832	+	7.65599i	0.790285	+	0.327347i	0.0492266	+	0.998788i	$0.484324\pi$
$548$		−	2.81695i		−	0.120334i
$549$		0			0
$550$	0.0875901	−	0.0362810i	0.00373485	−	0.00154703i
$551$	−1.25921	−	3.04001i	−0.0536443	−	0.129509i
$552$		0			0
$553$	30.6498	+	30.6498i	1.30336	+	1.30336i
$554$	11.6858	+	28.2120i	0.496482	+	1.19861i
$555$		0			0
$556$	−9.52395	+	22.9929i	−0.403906	+	0.975114i
$557$			25.8965i			1.09727i	0.836062	+	0.548636i	$0.184853\pi$
$557$			25.8965i			1.09727i	−0.836062	+	0.548636i	$0.815147\pi$
$558$		0			0
$559$	21.3791	−	21.3791i	0.904240	−	0.904240i
$560$	21.4138			0.904899
$561$		0			0
$562$	−8.43299			−0.355724
$563$	−19.8208	+	19.8208i	−0.835349	+	0.835349i	−0.988243	−	0.152894i	$-0.951141\pi$
$563$	−19.8208	+	19.8208i	−0.835349	+	0.835349i	0.152894	+	0.988243i	$0.451141\pi$
$564$		0			0
$565$			3.01331i			0.126771i
$566$	−6.01248	+	14.5154i	−0.252724	+	0.610129i
$567$		0			0
$568$	−2.13457	−	5.15331i	−0.0895645	−	0.216228i
$569$	27.7130	+	27.7130i	1.16179	+	1.16179i	0.984084	+	0.177706i	$0.0568675\pi$
$569$	27.7130	+	27.7130i	1.16179	+	1.16179i	0.177706	+	0.984084i	$0.443132\pi$
$570$		0			0
$571$	1.48008	+	3.57322i	0.0619392	+	0.149535i	0.951819	−	0.306661i	$-0.0992118\pi$
$571$	1.48008	+	3.57322i	0.0619392	+	0.149535i	−0.889880	+	0.456196i	$0.849212\pi$
$572$	−0.185028	+	0.0766411i	−0.00773641	+	0.00320452i
$573$		0			0
$574$		−	51.6918i		−	2.15757i
$575$	0.962654	+	0.398744i	0.0401454	+	0.0166288i
$576$		0			0
$577$	14.4808			0.602845			0.301423	−	0.953491i	$-0.402539\pi$
$577$	14.4808			0.602845			0.301423	+	0.953491i	$0.402539\pi$
$578$	−18.2881	−	24.6573i	−0.760684	−	1.02561i
$579$		0			0
$580$	−0.375177	+	0.375177i	−0.0155784	+	0.0155784i
$581$	26.1949	+	10.8503i	1.08675	+	0.450145i
$582$		0			0
$583$	−0.242356	+	0.585099i	−0.0100374	+	0.0242323i
$584$	6.64600	−	2.75286i	0.275013	−	0.113914i
$585$		0			0
$586$	0.943767	+	0.943767i	0.0389867	+	0.0389867i
$587$	−22.0937	−	22.0937i	−0.911905	−	0.911905i	0.0845171	−	0.996422i	$-0.473065\pi$
$587$	−22.0937	−	22.0937i	−0.911905	−	0.911905i	−0.996422	+	0.0845171i	$0.973065\pi$
$588$		0			0
$589$	−10.0017	+	4.14284i	−0.412113	+	0.170703i
$590$	−3.52289	+	8.50500i	−0.145035	+	0.350145i
$591$		0			0
$592$	1.53529	+	0.635939i	0.0631002	+	0.0261369i
$593$	−1.41805	+	1.41805i	−0.0582323	+	0.0582323i	−0.735623	−	0.677391i	$-0.763111\pi$
$593$	−1.41805	+	1.41805i	−0.0582323	+	0.0582323i	0.677391	+	0.735623i	$0.263111\pi$
$594$		0			0
$595$	−13.5556	+	11.6934i	−0.555724	+	0.479384i
$596$	−12.8416			−0.526012
$597$		0			0
$598$	−5.25876	−	2.17825i	−0.215047	−	0.0890753i
$599$			36.0451i			1.47276i	0.676567	+	0.736381i	$0.263467\pi$
$599$			36.0451i			1.47276i	−0.676567	+	0.736381i	$0.736533\pi$
$600$		0			0
$601$	−35.8417	+	14.8461i	−1.46201	+	0.605586i	−0.965022	−	0.262168i	$-0.915562\pi$
$601$	−35.8417	+	14.8461i	−1.46201	+	0.605586i	−0.496993	+	0.867755i	$0.665562\pi$
$602$	−29.9894	−	72.4007i	−1.22228	−	2.95083i
$603$		0			0
$604$	−13.6858	−	13.6858i	−0.556867	−	0.556867i
$605$	4.20846	+	10.1601i	0.171098	+	0.413068i
$606$		0			0
$607$	−11.0800	+	26.7496i	−0.449725	+	1.08573i	0.522701	+	0.852516i	$0.324925\pi$
$607$	−11.0800	+	26.7496i	−0.449725	+	1.08573i	−0.972425	+	0.233215i	$0.925075\pi$
$608$		−	48.7774i		−	1.97818i
$609$		0			0
$610$	−7.62399	+	7.62399i	−0.308686	+	0.308686i
$611$	−18.5488			−0.750405
$612$		0			0
$613$	9.10707			0.367831			0.183915	−	0.982942i	$-0.441123\pi$
$613$	9.10707			0.367831			0.183915	+	0.982942i	$0.441123\pi$
$614$	−3.65335	+	3.65335i	−0.147437	+	0.147437i
$615$		0			0
$616$		−	0.304197i		−	0.0122564i
$617$	1.93466	−	4.67068i	0.0778864	−	0.188035i	−0.880140	−	0.474714i	$-0.842551\pi$
$617$	1.93466	−	4.67068i	0.0778864	−	0.188035i	0.958027	+	0.286680i	$0.0925515\pi$
$618$		0			0
$619$	6.45177	+	15.5760i	0.259319	+	0.626051i	0.998894	−	0.0470233i	$-0.0149735\pi$
$619$	6.45177	+	15.5760i	0.259319	+	0.626051i	−0.739575	+	0.673074i	$0.764974\pi$
$620$	1.23434	+	1.23434i	0.0495723	+	0.0495723i
$621$		0			0
$622$	14.1654	+	34.1982i	0.567979	+	1.37122i
$623$	−40.9803	+	16.9746i	−1.64184	+	0.680074i
$624$		0			0
$625$			1.00000i			0.0400000i
$626$	14.1235	+	5.85013i	0.564487	+	0.233818i
$627$		0			0
$628$	−11.8690			−0.473625
$629$	−1.31915	+	0.435808i	−0.0525981	+	0.0173768i
$630$		0			0
$631$	1.91845	−	1.91845i	0.0763722	−	0.0763722i	−0.667889	−	0.744261i	$-0.732802\pi$
$631$	1.91845	−	1.91845i	0.0763722	−	0.0763722i	0.744261	+	0.667889i	$0.232802\pi$
$632$	12.3079	+	5.09809i	0.489581	+	0.202791i
$633$		0			0
$634$	14.5757	−	35.1889i	0.578876	−	1.39753i
$635$	0.00765625	−	0.00317132i	0.000303829	−	0.000125850i
$636$		0			0
$637$	−25.3528	−	25.3528i	−1.00451	−	1.00451i
$638$	0.0282068	+	0.0282068i	0.00111672	+	0.00111672i
$639$		0			0
$640$	9.18985	−	3.80656i	0.363261	−	0.150467i
$641$	8.72988	−	21.0758i	0.344809	−	0.832443i	−0.652406	−	0.757870i	$-0.726240\pi$
$641$	8.72988	−	21.0758i	0.344809	−	0.832443i	0.997215	−	0.0745739i	$-0.0237597\pi$
$642$		0			0
$643$	−17.8097	−	7.37702i	−0.702346	−	0.290921i	0.00278691	−	0.999996i	$-0.499113\pi$
$643$	−17.8097	−	7.37702i	−0.702346	−	0.290921i	−0.705133	+	0.709075i	$0.749113\pi$
$644$	−4.03408	+	4.03408i	−0.158965	+	0.158965i
$645$		0			0
$646$	38.0335	+	44.0903i	1.49641	+	1.73471i
$647$	−12.8098			−0.503606			−0.251803	−	0.967778i	$-0.581024\pi$
$647$	−12.8098			−0.503606			−0.251803	+	0.967778i	$0.581024\pi$
$648$		0			0
$649$	0.247264	+	0.102420i	0.00970595	+	0.00402033i
$650$		−	5.46278i		−	0.214268i
$651$		0			0
$652$	−14.4992	+	6.00577i	−0.567833	+	0.235204i
$653$	15.9656	+	38.5442i	0.624780	+	1.50835i	0.846030	+	0.533136i	$0.178987\pi$
$653$	15.9656	+	38.5442i	0.624780	+	1.50835i	−0.221249	+	0.975217i	$0.571013\pi$
$654$		0			0
$655$	5.78738	+	5.78738i	0.226131	+	0.226131i
$656$	−12.4427	−	30.0392i	−0.485804	−	1.17284i
$657$		0			0
$658$	−18.3983	+	44.4175i	−0.717242	+	1.73158i
$659$			34.3290i			1.33727i	0.743592	+	0.668633i	$0.233120\pi$
$659$			34.3290i			1.33727i	−0.743592	+	0.668633i	$0.766880\pi$
$660$		0			0
$661$	−19.5875	+	19.5875i	−0.761865	+	0.761865i	−0.976659	−	0.214794i	$-0.931092\pi$
$661$	−19.5875	+	19.5875i	−0.761865	+	0.761865i	0.214794	+	0.976659i	$0.431092\pi$
$662$	27.4958			1.06865
$663$		0			0
$664$	8.71419			0.338176
$665$	24.0103	−	24.0103i	0.931081	−	0.931081i
$666$		0			0
$667$			0.438413i			0.0169754i
$668$	−6.08161	+	14.6823i	−0.235305	+	0.568076i
$669$		0			0
$670$	−0.633040	−	1.52829i	−0.0244565	−	0.0590431i
$671$	0.221650	+	0.221650i	0.00855671	+	0.00855671i
$672$		0			0
$673$	13.8561	+	33.4517i	0.534115	+	1.28947i	0.928777	+	0.370640i	$0.120862\pi$
$673$	13.8561	+	33.4517i	0.534115	+	1.28947i	−0.394662	+	0.918826i	$0.629138\pi$
$674$	19.1423	−	7.92902i	0.737336	−	0.305414i
$675$		0			0
$676$		−	4.85355i		−	0.186675i
$677$	−15.8129	−	6.54992i	−0.607739	−	0.251734i	0.0575224	−	0.998344i	$-0.481680\pi$
$677$	−15.8129	−	6.54992i	−0.607739	−	0.251734i	−0.665262	+	0.746610i	$0.731680\pi$
$678$		0			0
$679$	−83.4684			−3.20322
$680$	−2.47377	+	4.91469i	−0.0948647	+	0.188470i
$681$		0			0
$682$	0.0928009	−	0.0928009i	0.00355353	−	0.00355353i
$683$	−8.17654	−	3.38683i	−0.312866	−	0.129594i	0.220725	−	0.975336i	$-0.429158\pi$
$683$	−8.17654	−	3.38683i	−0.312866	−	0.129594i	−0.533591	+	0.845743i	$0.679158\pi$
$684$		0			0
$685$	0.854864	−	2.06382i	0.0326627	−	0.0788546i
$686$	−35.1501	+	14.5596i	−1.34204	+	0.555890i
$687$		0			0
$688$	−34.8550	−	34.8550i	−1.32883	−	1.32883i
$689$	25.8031	+	25.8031i	0.983021	+	0.983021i
$690$		0			0
$691$	1.29190	−	0.535121i	0.0491461	−	0.0203570i	−0.357975	−	0.933731i	$-0.616533\pi$
$691$	1.29190	−	0.535121i	0.0491461	−	0.0203570i	0.407121	+	0.913374i	$0.366533\pi$
$692$	−5.88570	+	14.2093i	−0.223741	+	0.540158i
$693$		0			0
$694$	24.9993	+	10.3551i	0.948962	+	0.393073i
$695$	−13.9553	+	13.9553i	−0.529356	+	0.529356i
$696$		0			0
$697$	24.2801	+	12.2212i	0.919673	+	0.462910i
$698$	−8.19245			−0.310089
$699$		0			0
$700$	−5.05848	−	2.09529i	−0.191193	−	0.0791946i
$701$			2.36331i			0.0892608i	0.999004	+	0.0446304i	$0.0142110\pi$
$701$			2.36331i			0.0892608i	−0.999004	+	0.0446304i	$0.985789\pi$
$702$		0			0
$703$	2.43451	−	1.00841i	0.0918191	−	0.0380327i
$704$	0.0281182	+	0.0678834i	0.00105975	+	0.00255845i
$705$		0			0
$706$	9.85100	+	9.85100i	0.370747	+	0.370747i
$707$	22.0867	+	53.3221i	0.830657	+	2.00538i
$708$		0			0
$709$	12.4474	−	30.0507i	0.467472	−	1.12858i	−0.497791	−	0.867297i	$-0.665855\pi$
$709$	12.4474	−	30.0507i	0.467472	−	1.12858i	0.965263	−	0.261280i	$-0.0841447\pi$
$710$			7.54812i			0.283276i
$711$		0			0
$712$	−9.63987	+	9.63987i	−0.361270	+	0.361270i
$713$	1.44239			0.0540179
$714$		0			0
$715$	−0.158818			−0.00593945
$716$	−12.3594	+	12.3594i	−0.461891	+	0.461891i
$717$		0			0
$718$		−	19.9154i		−	0.743237i
$719$	6.28758	−	15.1796i	0.234487	−	0.566102i	−0.762208	−	0.647332i	$-0.775885\pi$
$719$	6.28758	−	15.1796i	0.234487	−	0.566102i	0.996695	+	0.0812299i	$0.0258848\pi$
$720$		0			0
$721$	−11.4865	−	27.7309i	−0.427780	−	1.03275i
$722$	−53.8336	−	53.8336i	−2.00348	−	2.00348i
$723$		0			0
$724$	−0.986493	−	2.38160i	−0.0366627	−	0.0885116i
$725$	−0.388726	+	0.161016i	−0.0144369	+	0.00597997i
$726$		0			0
$727$		−	32.4709i		−	1.20428i	−0.798391	−	0.602139i	$-0.794315\pi$
$727$		−	32.4709i		−	1.20428i	0.798391	−	0.602139i	$-0.205685\pi$
$728$	−16.1936	−	6.70761i	−0.600175	−	0.248600i
$729$		0			0
$730$	−9.73448			−0.360289
$731$	41.0974	+	3.03099i	1.52004	+	0.112105i
$732$		0			0
$733$	−6.10533	+	6.10533i	−0.225506	+	0.225506i	−0.810812	−	0.585307i	$-0.800974\pi$
$733$	−6.10533	+	6.10533i	−0.225506	+	0.225506i	0.585307	+	0.810812i	$0.300974\pi$
$734$	−26.7415	−	11.0767i	−0.987048	−	0.408849i
$735$		0			0
$736$	−2.48704	+	6.00424i	−0.0916734	+	0.221319i
$737$	−0.0444317	+	0.0184042i	−0.00163666	+	0.000677928i
$738$		0			0
$739$	−7.49715	−	7.49715i	−0.275787	−	0.275787i	0.555637	−	0.831425i	$-0.312474\pi$
$739$	−7.49715	−	7.49715i	−0.275787	−	0.275787i	−0.831425	+	0.555637i	$0.812474\pi$
$740$	−0.300450	−	0.300450i	−0.0110448	−	0.0110448i
$741$		0			0
$742$	87.3827	−	36.1951i	3.20792	−	1.32876i
$743$	8.55008	−	20.6417i	0.313672	−	0.757272i	−0.685891	−	0.727705i	$-0.740587\pi$
$743$	8.55008	−	20.6417i	0.313672	−	0.757272i	0.999563	−	0.0295670i	$-0.00941283\pi$
$744$		0			0
$745$	−9.40831	−	3.89705i	−0.344694	−	0.142777i
$746$	−13.0886	+	13.0886i	−0.479206	+	0.479206i
$747$		0			0
$748$	−0.243822	−	0.122726i	−0.00891502	−	0.00448730i
$749$	−64.0032			−2.33863
$750$		0			0
$751$	6.59640	+	2.73232i	0.240706	+	0.0997037i	0.499775	−	0.866155i	$-0.333416\pi$
$751$	6.59640	+	2.73232i	0.240706	+	0.0997037i	−0.259069	+	0.965859i	$0.583416\pi$
$752$			30.2406i			1.10276i
$753$		0			0
$754$	2.12353	−	0.879593i	0.0773342	−	0.0320329i
$755$	−5.87357	−	14.1800i	−0.213761	−	0.516065i
$756$		0			0
$757$	12.7467	+	12.7467i	0.463287	+	0.463287i	0.899731	−	0.436444i	$-0.143762\pi$
$757$	12.7467	+	12.7467i	0.463287	+	0.463287i	−0.436444	+	0.899731i	$0.643762\pi$
$758$	9.64166	+	23.2770i	0.350201	+	0.845460i
$759$		0			0
$760$	3.99373	−	9.64173i	0.144868	−	0.349742i
$761$			49.9437i			1.81046i	0.424923	+	0.905230i	$0.360301\pi$
$761$			49.9437i			1.81046i	−0.424923	+	0.905230i	$0.639699\pi$
$762$		0			0
$763$	14.5782	−	14.5782i	0.527767	−	0.527767i
$764$	−3.88466			−0.140542
$765$		0			0
$766$	10.1521			0.366811
$767$	10.9044	−	10.9044i	0.393737	−	0.393737i
$768$		0			0
$769$			43.9115i			1.58349i	0.610852	+	0.791745i	$0.290827\pi$
$769$			43.9115i			1.58349i	−0.610852	+	0.791745i	$0.709173\pi$
$770$	−0.157530	+	0.380310i	−0.00567697	+	0.0137054i
$771$		0			0
$772$	−9.96120	−	24.0485i	−0.358511	−	0.865523i
$773$	−6.84309	−	6.84309i	−0.246129	−	0.246129i	0.573251	−	0.819380i	$-0.305682\pi$
$773$	−6.84309	−	6.84309i	−0.246129	−	0.246129i	−0.819380	+	0.573251i	$0.805682\pi$
$774$		0			0
$775$	0.529745	+	1.27892i	0.0190290	+	0.0459401i
$776$	−23.7008	+	9.81720i	−0.850810	+	0.352417i
$777$		0			0
$778$		−	64.6771i		−	2.31879i
$779$	−47.6330	−	19.7302i	−1.70663	−	0.706909i
$780$		0			0
$781$	0.219445			0.00785234
$782$	−2.43367	−	7.36651i	−0.0870280	−	0.263426i
$783$		0			0
$784$	−41.3334	+	41.3334i	−1.47619	+	1.47619i
$785$	−8.69576	−	3.60190i	−0.310365	−	0.128557i
$786$		0			0
$787$	7.59181	−	18.3283i	0.270619	−	0.653332i	−0.728891	−	0.684630i	$-0.759964\pi$
$787$	7.59181	−	18.3283i	0.270619	−	0.653332i	0.999510	+	0.0312976i	$0.00996398\pi$
$788$	21.2461	−	8.80043i	0.756861	−	0.313502i
$789$		0			0
$790$	−12.7474	−	12.7474i	−0.453532	−	0.453532i
$791$	−9.25147	−	9.25147i	−0.328944	−	0.328944i
$792$		0			0
$793$	16.6868	−	6.91188i	0.592564	−	0.245448i
$794$	2.68835	−	6.49024i	0.0954059	−	0.230330i
$795$		0			0
$796$	31.0687	+	12.8691i	1.10120	+	0.456132i
$797$	3.93230	−	3.93230i	0.139289	−	0.139289i	−0.634024	−	0.773313i	$-0.718598\pi$
$797$	3.93230	−	3.93230i	0.139289	−	0.139289i	0.773313	+	0.634024i	$0.218598\pi$
$798$		0			0
$799$	−16.5135	−	19.1432i	−0.584205	−	0.677238i
$800$	−6.23717			−0.220517
$801$		0			0
$802$	−61.2935	−	25.3886i	−2.16435	−	0.896502i
$803$			0.283008i			0.00998714i
$804$		0			0
$805$	−4.17977	+	1.73132i	−0.147318	+	0.0610210i
$806$	−2.89388	−	6.98644i	−0.101933	−	0.246087i
$807$		0			0
$808$	12.5430	+	12.5430i	0.441263	+	0.441263i
$809$	−11.8801	−	28.6811i	−0.417683	−	1.00838i	−0.983017	−	0.183513i	$-0.941253\pi$
$809$	−11.8801	−	28.6811i	−0.417683	−	1.00838i	0.565335	−	0.824862i	$-0.308747\pi$
$810$		0			0
$811$	−17.9749	+	43.3953i	−0.631185	+	1.52382i	0.206949	+	0.978352i	$0.433647\pi$
$811$	−17.9749	+	43.3953i	−0.631185	+	1.52382i	−0.838134	+	0.545464i	$0.816353\pi$
$812$		−	2.30374i		−	0.0808455i
$813$		0			0
$814$	−0.0225886	+	0.0225886i	−0.000791730	+	0.000791730i
$815$	−12.4453			−0.435941
$816$		0			0
$817$	−78.1626			−2.73456
$818$	−28.5428	+	28.5428i	−0.997976	+	0.997976i
$819$		0			0
$820$			8.31351i			0.290320i
$821$	−6.40739	+	15.4688i	−0.223619	+	0.539865i	−0.995376	−	0.0960527i	$-0.969378\pi$
$821$	−6.40739	+	15.4688i	−0.223619	+	0.539865i	0.771757	+	0.635918i	$0.219378\pi$
$822$		0			0
$823$	−10.1792	−	24.5749i	−0.354826	−	0.856626i	−0.996010	−	0.0892387i	$-0.971557\pi$
$823$	−10.1792	−	24.5749i	−0.354826	−	0.856626i	0.641184	−	0.767387i	$-0.278443\pi$
$824$	−6.52318	−	6.52318i	−0.227246	−	0.227246i
$825$		0			0
$826$	−15.2961	−	36.9281i	−0.532220	−	1.28489i
$827$	−31.8605	+	13.1970i	−1.10790	+	0.458906i	−0.860213	−	0.509934i	$-0.829670\pi$
$827$	−31.8605	+	13.1970i	−1.10790	+	0.458906i	−0.247684	+	0.968841i	$0.579670\pi$
$828$		0			0
$829$		−	7.29346i		−	0.253312i	−0.991947	−	0.126656i	$-0.959576\pi$
$829$		−	7.29346i		−	0.253312i	0.991947	−	0.126656i	$-0.0404245\pi$
$830$	−10.8946	−	4.51269i	−0.378157	−	0.156638i
$831$		0			0
$832$	4.23372			0.146778
$833$	3.59436	−	48.7361i	0.124537	−	1.68861i
$834$		0			0
$835$	−8.91131	+	8.91131i	−0.308389	+	0.308389i
$836$	0.478334	+	0.198133i	0.0165435	+	0.00685256i
$837$		0			0
$838$	−15.1106	+	36.4802i	−0.521987	+	1.26019i
$839$	32.8053	−	13.5884i	1.13257	−	0.469124i	0.263913	−	0.964546i	$-0.414987\pi$
$839$	32.8053	−	13.5884i	1.13257	−	0.469124i	0.868652	+	0.495422i	$0.164987\pi$
$840$		0			0
$841$	20.3809	+	20.3809i	0.702790	+	0.702790i
$842$	26.3187	+	26.3187i	0.907001	+	0.907001i
$843$		0			0
$844$	9.09385	−	3.76680i	0.313023	−	0.129658i
$845$	1.47291	−	3.55592i	0.0506697	−	0.122327i
$846$		0			0
$847$	−44.1146	−	18.2728i	−1.51579	−	0.627862i
$848$	42.0676	−	42.0676i	1.44461	−	1.44461i
$849$		0			0
$850$	5.63783	−	4.86335i	0.193376	−	0.166812i
$851$	−0.351091			−0.0120352
$852$		0			0
$853$	0.220643	+	0.0913933i	0.00755467	+	0.00312925i	0.386458	−	0.922307i	$-0.373699\pi$
$853$	0.220643	+	0.0913933i	0.00755467	+	0.00312925i	−0.378903	+	0.925436i	$0.623699\pi$
$854$		−	46.8144i		−	1.60196i
$855$		0			0
$856$	−18.1737	+	7.52779i	−0.621164	+	0.257295i
$857$	6.96291	+	16.8099i	0.237848	+	0.574217i	0.997060	−	0.0766273i	$-0.0244152\pi$
$857$	6.96291	+	16.8099i	0.237848	+	0.574217i	−0.759211	+	0.650844i	$0.774415\pi$
$858$		0			0
$859$	−14.2525	−	14.2525i	−0.486288	−	0.486288i	0.420845	−	0.907133i	$-0.361734\pi$
$859$	−14.2525	−	14.2525i	−0.486288	−	0.486288i	−0.907133	+	0.420845i	$0.861734\pi$
$860$	4.82314	+	11.6441i	0.164468	+	0.397061i
$861$		0			0
$862$	−15.4143	+	37.2134i	−0.525013	+	1.26749i
$863$		−	14.7597i		−	0.502424i	−0.967932	−	0.251212i	$-0.919171\pi$
$863$		−	14.7597i		−	0.502424i	0.967932	−	0.251212i	$-0.0808292\pi$
$864$		0			0
$865$	−8.62424	+	8.62424i	−0.293233	+	0.293233i
$866$	−16.1284			−0.548064
$867$		0			0
$868$	−7.57936			−0.257260
$869$	−0.370602	+	0.370602i	−0.0125718	+	0.0125718i
$870$		0			0
$871$			2.77109i			0.0938949i
$872$	2.42485	−	5.85411i	0.0821158	−	0.198245i
$873$		0			0
$874$	5.63121	+	13.5950i	0.190479	+	0.459856i
$875$	−3.07021	−	3.07021i	−0.103792	−	0.103792i
$876$		0			0
$877$	16.3627	+	39.5030i	0.552528	+	1.33392i	0.915574	+	0.402149i	$0.131737\pi$
$877$	16.3627	+	39.5030i	0.552528	+	1.33392i	−0.363046	+	0.931771i	$0.618263\pi$
$878$	37.1450	−	15.3860i	1.25358	−	0.519251i
$879$		0			0
$880$			0.258925i			0.00872837i
$881$	40.3580	+	16.7168i	1.35970	+	0.563205i	0.938975	−	0.343985i	$-0.111777\pi$
$881$	40.3580	+	16.7168i	1.35970	+	0.563205i	0.420721	+	0.907190i	$0.361777\pi$
$882$		0			0
$883$	41.4824			1.39599			0.697997	−	0.716101i	$-0.254075\pi$
$883$	41.4824			1.39599			0.697997	+	0.716101i	$0.254075\pi$
$884$	−11.9095	+	10.2735i	−0.400561	+	0.345535i
$885$		0			0
$886$	7.88394	−	7.88394i	0.264866	−	0.264866i
$887$	−30.3770	−	12.5826i	−1.01996	−	0.422481i	−0.190881	−	0.981613i	$-0.561134\pi$
$887$	−30.3770	−	12.5826i	−1.01996	−	0.422481i	−0.829078	+	0.559132i	$0.811134\pi$
$888$		0			0
$889$	−0.0137697	+	0.0332429i	−0.000461819	+	0.00111493i
$890$	17.0439	−	7.05983i	0.571314	−	0.236646i
$891$		0			0
$892$	−4.25233	−	4.25233i	−0.142378	−	0.142378i
$893$	33.9075	+	33.9075i	1.13467	+	1.13467i
$894$		0			0
$895$	−12.8057	+	5.30430i	−0.428048	+	0.177303i
$896$	−16.5278	+	39.9017i	−0.552155	+	1.33302i
$897$		0			0
$898$	−50.5491	−	20.9381i	−1.68685	−	0.698714i
$899$	−0.411852	+	0.411852i	−0.0137360	+	0.0137360i
$900$		0			0
$901$	−3.65820	+	49.6018i	−0.121872	+	1.65248i
$902$	0.625031			0.0208113
$903$		0			0
$904$	−3.71507	−	1.53883i	−0.123561	−	0.0511808i
$905$		−	2.04424i		−	0.0679528i
$906$		0			0
$907$	33.6731	−	13.9479i	1.11810	−	0.463131i	0.254379	−	0.967105i	$-0.418129\pi$
$907$	33.6731	−	13.9479i	1.11810	−	0.463131i	0.863719	+	0.503973i	$0.168129\pi$
$908$	−5.41015	−	13.0613i	−0.179542	−	0.433453i
$909$		0			0
$910$	16.7719	+	16.7719i	0.555982	+	0.555982i
$911$	11.4322	+	27.5999i	0.378767	+	0.914425i	0.992197	+	0.124676i	$0.0397892\pi$
$911$	11.4322	+	27.5999i	0.378767	+	0.914425i	−0.613430	+	0.789749i	$0.710211\pi$
$912$		0			0
$913$	−0.131196	+	0.316736i	−0.00434196	+	0.0104824i
$914$		−	46.1852i		−	1.52767i
$915$		0			0
$916$	−18.4117	+	18.4117i	−0.608341	+	0.608341i
$917$	−35.5369			−1.17353
$918$		0			0
$919$	11.6218			0.383368			0.191684	−	0.981457i	$-0.438605\pi$
$919$	11.6218			0.383368			0.191684	+	0.981457i	$0.438605\pi$
$920$	−0.983215	+	0.983215i	−0.0324156	+	0.0324156i
$921$		0			0
$922$		−	25.3837i		−	0.835966i
$923$	4.83880	−	11.6819i	0.159271	−	0.384515i
$924$		0			0
$925$	−0.128945	−	0.311301i	−0.00423968	−	0.0102355i
$926$	32.0803	+	32.0803i	1.05422	+	1.05422i
$927$		0			0
$928$	−1.00428	−	2.42455i	−0.0329672	−	0.0795899i
$929$	4.65849	−	1.92961i	0.152840	−	0.0633085i	−0.304952	−	0.952368i	$-0.598640\pi$
$929$	4.65849	−	1.92961i	0.152840	−	0.0633085i	0.457792	+	0.889059i	$0.348640\pi$
$930$		0			0
$931$			92.6904i			3.03781i
$932$	−3.56326	−	1.47595i	−0.116718	−	0.0483464i
$933$		0			0
$934$	40.2520			1.31709
$935$	−0.141391	−	0.163907i	−0.00462398	−	0.00536034i
$936$		0			0
$937$	24.6863	−	24.6863i	0.806465	−	0.806465i	−0.177632	−	0.984097i	$-0.556844\pi$
$937$	24.6863	−	24.6863i	0.806465	−	0.806465i	0.984097	+	0.177632i	$0.0568437\pi$
$938$	6.63574	+	2.74861i	0.216665	+	0.0897454i
$939$		0			0
$940$	2.95898	−	7.14360i	0.0965112	−	0.232999i
$941$	−10.2169	+	4.23196i	−0.333060	+	0.137958i	−0.542945	−	0.839768i	$-0.682691\pi$
$941$	−10.2169	+	4.23196i	−0.333060	+	0.137958i	0.209885	+	0.977726i	$0.432691\pi$
$942$		0			0
$943$	4.85738	+	4.85738i	0.158178	+	0.158178i
$944$	−17.7778	−	17.7778i	−0.578619	−	0.578619i
$945$		0			0
$946$	0.875434	−	0.362616i	0.0284628	−	0.0117897i
$947$	−4.39774	+	10.6171i	−0.142907	+	0.345008i	−0.979086	−	0.203449i	$-0.934785\pi$
$947$	−4.39774	+	10.6171i	−0.142907	+	0.345008i	0.836178	+	0.548458i	$0.184785\pi$
$948$		0			0
$949$	15.0657	+	6.24040i	0.489052	+	0.202572i
$950$	−9.98602	+	9.98602i	−0.323989	+	0.323989i
$951$		0			0
$952$	−7.49414	−	22.6841i	−0.242887	−	0.735196i
$953$	0.704896			0.0228338			0.0114169	−	0.999935i	$-0.496366\pi$
$953$	0.704896			0.0228338			0.0114169	+	0.999935i	$0.496366\pi$
$954$		0			0
$955$	−2.84607	−	1.17888i	−0.0920966	−	0.0381477i
$956$			6.23035i			0.201504i
$957$		0			0
$958$	−44.6282	+	18.4856i	−1.44187	+	0.597243i
$959$	3.71176	+	8.96097i	0.119859	+	0.289365i
$960$		0			0
$961$	−20.5653	−	20.5653i	−0.663397	−	0.663397i
$962$	0.704397	+	1.70057i	0.0227107	+	0.0548284i
$963$		0			0
$964$	0.801919	−	1.93600i	0.0258281	−	0.0623545i
$965$		−	20.6419i		−	0.664486i
$966$		0			0
$967$	28.2521	−	28.2521i	0.908527	−	0.908527i	−0.0876267	−	0.996153i	$-0.527928\pi$
$967$	28.2521	−	28.2521i	0.908527	−	0.908527i	0.996153	+	0.0876267i	$0.0279283\pi$
$968$	−14.6755			−0.471688
$969$		0			0
$970$	34.7149			1.11463
$971$	−30.5851	+	30.5851i	−0.981521	+	0.981521i	−0.999832	−	0.0183111i	$-0.994171\pi$
$971$	−30.5851	+	30.5851i	−0.981521	+	0.981521i	0.0183111	+	0.999832i	$0.494171\pi$
$972$		0			0
$973$		−	85.6915i		−	2.74714i
$974$	−15.9953	+	38.6161i	−0.512523	+	1.23734i
$975$		0			0
$976$	−11.2686	−	27.2049i	−0.360700	−	0.870807i
$977$	34.5543	+	34.5543i	1.10549	+	1.10549i	0.993736	+	0.111753i	$0.0356467\pi$
$977$	34.5543	+	34.5543i	1.10549	+	1.10549i	0.111753	+	0.993736i	$0.464353\pi$
$978$		0			0
$979$	−0.205249	−	0.495514i	−0.00655977	−	0.0158367i
$980$	13.8084	−	5.71961i	0.441092	−	0.182706i
$981$		0			0
$982$		−	14.0671i		−	0.448898i
$983$	45.1621	+	18.7068i	1.44045	+	0.596653i	0.959907	−	0.280318i	$-0.0904401\pi$
$983$	45.1621	+	18.7068i	1.44045	+	0.596653i	0.480542	+	0.876972i	$0.340440\pi$
$984$		0			0
$985$	18.2365			0.581063
$986$	2.79829	+	1.40850i	0.0891158	+	0.0448557i
$987$		0			0
$988$	21.0948	−	21.0948i	0.671114	−	0.671114i
$989$	9.62140	+	3.98531i	0.305943	+	0.126726i
$990$		0			0
$991$	5.56191	−	13.4276i	0.176680	−	0.426543i	−0.810586	−	0.585619i	$-0.800851\pi$
$991$	5.56191	−	13.4276i	0.176680	−	0.426543i	0.987266	+	0.159076i	$0.0508515\pi$
$992$	−7.97684	+	3.30411i	−0.253265	+	0.104906i
$993$		0			0
$994$	−23.1743	−	23.1743i	−0.735044	−	0.735044i
$995$	18.8569	+	18.8569i	0.597803	+	0.597803i
$996$		0			0
$997$	−40.8392	+	16.9161i	−1.29339	+	0.535740i	−0.919994	−	0.391933i	$-0.871807\pi$
$997$	−40.8392	+	16.9161i	−1.29339	+	0.535740i	−0.373396	+	0.927672i	$0.621807\pi$
$998$	−6.07971	+	14.6777i	−0.192450	+	0.464615i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	765.2.be.b.451.5		24
3.2	odd	2		85.2.l.a.26.2	✓	24
15.2	even	4		425.2.n.f.349.2		24
15.8	even	4		425.2.n.c.349.5		24
15.14	odd	2		425.2.m.b.26.5		24
17.2	even	8	inner	765.2.be.b.631.5		24
51.2	odd	8		85.2.l.a.36.2	yes	24
51.11	even	16		1445.2.a.q.1.3		12
51.23	even	16		1445.2.a.p.1.3		12
51.41	even	16		1445.2.d.j.866.20		24
51.44	even	16		1445.2.d.j.866.19		24
255.2	even	8		425.2.n.c.274.5		24
255.53	even	8		425.2.n.f.274.2		24
255.74	even	16		7225.2.a.bs.1.10		12
255.104	odd	8		425.2.m.b.376.5		24
255.164	even	16		7225.2.a.bq.1.10		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
85.2.l.a.26.2	✓	24	3.2	odd	2
85.2.l.a.36.2	yes	24	51.2	odd	8
425.2.m.b.26.5		24	15.14	odd	2
425.2.m.b.376.5		24	255.104	odd	8
425.2.n.c.274.5		24	255.2	even	8
425.2.n.c.349.5		24	15.8	even	4
425.2.n.f.274.2		24	255.53	even	8
425.2.n.f.349.2		24	15.2	even	4
765.2.be.b.451.5		24	1.1	even	1	trivial
765.2.be.b.631.5		24	17.2	even	8	inner
1445.2.a.p.1.3		12	51.23	even	16
1445.2.a.q.1.3		12	51.11	even	16
1445.2.d.j.866.19		24	51.44	even	16
1445.2.d.j.866.20		24	51.41	even	16
7225.2.a.bq.1.10		12	255.164	even	16
7225.2.a.bs.1.10		12	255.74	even	16

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 765 = 3^{2} \cdot 5 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	765.be (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(1.27691 - 1.27691i) q^{2} -1.26102i q^{4} +(0.382683 - 0.923880i) q^{5} +(1.66158 + 4.01142i) q^{7} +(0.943613 + 0.943613i) q^{8} +(-0.691061 - 1.66837i) q^{10} +(-0.0485041 + 0.0200910i) q^{11} +3.02508i q^{13} +(7.24394 + 3.00054i) q^{14} +4.93187 q^{16} +(-3.12202 + 2.69314i) q^{17} +(5.52988 - 5.52988i) q^{19} +(-1.16503 - 0.482572i) q^{20} +(-0.0362810 + 0.0875901i) q^{22} +(-0.962654 + 0.398744i) q^{23} +(-0.707107 - 0.707107i) q^{25} +(3.86277 + 3.86277i) q^{26} +(5.05848 - 2.09529i) q^{28} +(0.161016 - 0.388726i) q^{29} +(-1.27892 - 0.529745i) q^{31} +(4.41035 - 4.41035i) q^{32} +(-0.547638 + 7.42546i) q^{34} +4.34193 q^{35} +(0.311301 + 0.128945i) q^{37} -14.1224i q^{38} +(1.23289 - 0.510679i) q^{40} +(-2.52291 - 6.09084i) q^{41} +(-7.06729 - 7.06729i) q^{43} +(0.0253352 + 0.0611647i) q^{44} +(-0.720064 + 1.73839i) q^{46} +6.13168i q^{47} +(-8.38087 + 8.38087i) q^{49} -1.80583 q^{50} +3.81469 q^{52} +(8.52974 - 8.52974i) q^{53} +0.0525004i q^{55} +(-2.21733 + 5.35312i) q^{56} +(-0.290767 - 0.701974i) q^{58} +(-3.60468 - 3.60468i) q^{59} +(-2.28486 - 5.51614i) q^{61} +(-2.30951 + 0.956630i) q^{62} -1.39954i q^{64} +(2.79481 + 1.15765i) q^{65} +0.916040 q^{67} +(3.39611 + 3.93693i) q^{68} +(5.54427 - 5.54427i) q^{70} +(-3.86169 - 1.59956i) q^{71} +(2.06289 - 4.98025i) q^{73} +(0.562156 - 0.232853i) q^{74} +(-6.97330 - 6.97330i) q^{76} +(-0.161187 - 0.161187i) q^{77} +(9.22305 - 3.82031i) q^{79} +(1.88734 - 4.55645i) q^{80} +(-10.9990 - 4.55595i) q^{82} +(4.61746 - 4.61746i) q^{83} +(1.29339 + 3.91499i) q^{85} -18.0487 q^{86} +(-0.0647272 - 0.0268109i) q^{88} +10.2159i q^{89} +(-12.1349 + 5.02642i) q^{91} +(0.502825 + 1.21393i) q^{92} +(7.82963 + 7.82963i) q^{94} +(-2.99275 - 7.22514i) q^{95} +(-7.35663 + 17.7605i) q^{97} +21.4033i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 8 q^{11} - 24 q^{16} + 8 q^{17} - 8 q^{19} - 32 q^{22} + 16 q^{23} - 16 q^{26} + 48 q^{28} + 8 q^{29} + 16 q^{34} + 32 q^{35} + 24 q^{37} + 16 q^{40} - 16 q^{41} + 8 q^{43} - 16 q^{44} + 8 q^{46}+ \cdots - 40 q^{97}+O(q^{100}) \) 24 * q + 8 * q^11 - 24 * q^16 + 8 * q^17 - 8 * q^19 - 32 * q^22 + 16 * q^23 - 16 * q^26 + 48 * q^28 + 8 * q^29 + 16 * q^34 + 32 * q^35 + 24 * q^37 + 16 * q^40 - 16 * q^41 + 8 * q^43 - 16 * q^44 + 8 * q^46 - 8 * q^50 - 48 * q^52 - 24 * q^53 - 64 * q^56 - 64 * q^58 - 32 * q^59 + 32 * q^61 + 32 * q^62 - 8 * q^65 + 16 * q^67 + 40 * q^68 + 24 * q^71 + 64 * q^74 - 8 * q^76 - 24 * q^77 + 32 * q^80 - 80 * q^82 + 96 * q^83 + 16 * q^86 - 8 * q^88 - 24 * q^91 - 80 * q^92 + 56 * q^94 + 16 * q^95 - 40 * q^97

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