LMFDB - Embedded newform 756.2.be.d.107.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [756,2,Mod(107,756)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(756, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 3, 2]))

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

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

chi := DirichletCharacter("756.107");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 756 = 2^{2} \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	756.be (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$6.03669039281$
Analytic rank:	$0$
Dimension:	$28$
Relative dimension:	$14$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			107.10
Character	$\chi$	$=$	756.107
Dual form			756.2.be.d.431.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.498187 + 1.32356i) q^{2} +(-1.50362 + 1.31876i) q^{4} +(0.936239 + 0.540538i) q^{5} +(0.749282 + 2.53743i) q^{7} +(-2.49454 - 1.33314i) q^{8} +O(q^{10})$	\(q+(0.498187 + 1.32356i) q^{2} +(-1.50362 + 1.31876i) q^{4} +(0.936239 + 0.540538i) q^{5} +(0.749282 + 2.53743i) q^{7} +(-2.49454 - 1.33314i) q^{8} +(-0.249012 + 1.50846i) q^{10} +(2.43972 + 4.22571i) q^{11} +0.815997 q^{13} +(-2.98516 + 2.25584i) q^{14} +(0.521749 - 3.96583i) q^{16} +(1.47016 - 0.848796i) q^{17} +(-3.58740 - 2.07119i) q^{19} +(-2.12059 + 0.421910i) q^{20} +(-4.37755 + 5.33430i) q^{22} +(1.75645 - 3.04226i) q^{23} +(-1.91564 - 3.31798i) q^{25} +(0.406519 + 1.08002i) q^{26} +(-4.47290 - 2.82722i) q^{28} +9.61003i q^{29} +(-7.73929 + 4.46828i) q^{31} +(5.50894 - 1.28516i) q^{32} +(1.85585 + 1.52298i) q^{34} +(-0.670072 + 2.78066i) q^{35} +(-3.37978 + 5.85395i) q^{37} +(0.954144 - 5.77997i) q^{38} +(-1.61487 - 2.59653i) q^{40} +6.96667i q^{41} +0.510241i q^{43} +(-9.24111 - 3.13647i) q^{44} +(4.90165 + 0.809152i) q^{46} +(3.40777 - 5.90243i) q^{47} +(-5.87715 + 3.80251i) q^{49} +(3.43720 - 4.18843i) q^{50} +(-1.22695 + 1.07610i) q^{52} +(2.99884 - 1.73138i) q^{53} +5.27504i q^{55} +(1.51365 - 7.32863i) q^{56} +(-12.7195 + 4.78759i) q^{58} +(-2.50722 - 4.34263i) q^{59} +(6.85713 - 11.8769i) q^{61} +(-9.76964 - 8.01737i) q^{62} +(4.44546 + 6.65116i) q^{64} +(0.763968 + 0.441077i) q^{65} +(3.66826 - 2.11787i) q^{67} +(-1.09120 + 3.21505i) q^{68} +(-4.01419 + 0.498407i) q^{70} +11.8557 q^{71} +(-1.49777 - 2.59421i) q^{73} +(-9.43181 - 1.55698i) q^{74} +(8.12548 - 1.61664i) q^{76} +(-8.89444 + 9.35688i) q^{77} +(-3.41517 - 1.97175i) q^{79} +(2.63216 - 3.43094i) q^{80} +(-9.22080 + 3.47070i) q^{82} +11.3326 q^{83} +1.83523 q^{85} +(-0.675334 + 0.254195i) q^{86} +(-0.452489 - 13.7937i) q^{88} +(-0.313438 - 0.180963i) q^{89} +(0.611412 + 2.07054i) q^{91} +(1.37097 + 6.89073i) q^{92} +(9.50992 + 1.56987i) q^{94} +(-2.23911 - 3.87825i) q^{95} +8.12677 q^{97} +(-7.96077 - 5.88440i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q - 4 q^{4} + 2 q^{7}+O(q^{10}) $ 28 * q - 4 * q^4 + 2 * q^7	$ 28 q - 4 q^{4} + 2 q^{7} + 4 q^{10} + 8 q^{13} + 12 q^{16} - 42 q^{19} + 4 q^{22} + 6 q^{25} + 24 q^{28} + 30 q^{31} + 24 q^{34} + 12 q^{37} + 24 q^{46} - 14 q^{49} - 24 q^{52} - 44 q^{58} + 6 q^{61} + 8 q^{64} + 24 q^{67} - 32 q^{70} - 22 q^{73} + 48 q^{79} + 36 q^{82} - 24 q^{85} - 4 q^{88} + 16 q^{91} + 60 q^{94} - 4 q^{97}+O(q^{100}) $ 28 * q - 4 * q^4 + 2 * q^7 + 4 * q^10 + 8 * q^13 + 12 * q^16 - 42 * q^19 + 4 * q^22 + 6 * q^25 + 24 * q^28 + 30 * q^31 + 24 * q^34 + 12 * q^37 + 24 * q^46 - 14 * q^49 - 24 * q^52 - 44 * q^58 + 6 * q^61 + 8 * q^64 + 24 * q^67 - 32 * q^70 - 22 * q^73 + 48 * q^79 + 36 * q^82 - 24 * q^85 - 4 * q^88 + 16 * q^91 + 60 * q^94 - 4 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/756\mathbb{Z}\right)^\times$.

$n$	$29$	$325$	$379$
$\chi(n)$	$-1$	$e\left(\frac{1}{3}\right)$	$-1$

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 $

$2$	0.498187	+	1.32356i	0.352271	+	0.935898i
$2$	0.498187	+	1.32356i	0.352271	+	0.935898i
$3$		0			0
$3$		0			0
$4$	−1.50362	+	1.31876i	−0.751810	+	0.659380i
$5$	0.936239	+	0.540538i	0.418699	+	0.241736i	0.694520	−	0.719473i	$-0.255617\pi$
$5$	0.936239	+	0.540538i	0.418699	+	0.241736i	−0.275822	+	0.961209i	$0.588950\pi$
$6$		0			0
$7$	0.749282	+	2.53743i	0.283202	+	0.959060i
$7$	0.749282	+	2.53743i	0.283202	+	0.959060i
$8$	−2.49454	−	1.33314i	−0.881953	−	0.471337i
$9$		0			0
$10$	−0.249012	+	1.50846i	−0.0787446	+	0.477016i
$11$	2.43972	+	4.22571i	0.735602	+	1.27410i	0.954459	+	0.298343i	$0.0964341\pi$
$11$	2.43972	+	4.22571i	0.735602	+	1.27410i	−0.218856	+	0.975757i	$0.570233\pi$
$12$		0			0
$13$	0.815997			0.226317			0.113158	−	0.993577i	$-0.463903\pi$
$13$	0.815997			0.226317			0.113158	+	0.993577i	$0.463903\pi$
$14$	−2.98516	+	2.25584i	−0.797819	+	0.602897i
$15$		0			0
$16$	0.521749	−	3.96583i	0.130437	−	0.991457i
$17$	1.47016	−	0.848796i	0.356566	−	0.205863i	−0.311007	−	0.950407i	$-0.600666\pi$
$17$	1.47016	−	0.848796i	0.356566	−	0.205863i	0.667573	+	0.744544i	$0.267333\pi$
$18$		0			0
$19$	−3.58740	−	2.07119i	−0.823006	−	0.475163i	0.0284462	−	0.999595i	$-0.490944\pi$
$19$	−3.58740	−	2.07119i	−0.823006	−	0.475163i	−0.851452	+	0.524433i	$0.824277\pi$
$20$	−2.12059	+	0.421910i	−0.474178	+	0.0943419i
$21$		0			0
$22$	−4.37755	+	5.33430i	−0.933297	+	1.13728i
$23$	1.75645	−	3.04226i	0.366245	−	0.634354i	−0.622730	−	0.782436i	$-0.713977\pi$
$23$	1.75645	−	3.04226i	0.366245	−	0.634354i	0.988975	+	0.148082i	$0.0473100\pi$
$24$		0			0
$25$	−1.91564	−	3.31798i	−0.383128	−	0.663596i
$26$	0.406519	+	1.08002i	0.0797249	+	0.211810i
$27$		0			0
$28$	−4.47290	−	2.82722i	−0.845299	−	0.534294i
$29$			9.61003i			1.78454i	0.451504	+	0.892269i	$0.350888\pi$
$29$			9.61003i			1.78454i	−0.451504	+	0.892269i	$0.649112\pi$
$30$		0			0
$31$	−7.73929	+	4.46828i	−1.39002	+	0.802527i	−0.993317	−	0.115422i	$-0.963178\pi$
$31$	−7.73929	+	4.46828i	−1.39002	+	0.802527i	−0.396700	+	0.917948i	$0.629845\pi$
$32$	5.50894	−	1.28516i	0.973851	−	0.227186i
$33$		0			0
$34$	1.85585	+	1.52298i	0.318275	+	0.261190i
$35$	−0.670072	+	2.78066i	−0.113263	+	0.470017i
$36$		0			0
$37$	−3.37978	+	5.85395i	−0.555632	+	0.962383i	0.442222	+	0.896906i	$0.354190\pi$
$37$	−3.37978	+	5.85395i	−0.555632	+	0.962383i	−0.997854	+	0.0654777i	$0.979143\pi$
$38$	0.954144	−	5.77997i	0.154783	−	0.937635i
$39$		0			0
$40$	−1.61487	−	2.59653i	−0.255334	−	0.410548i
$41$			6.96667i			1.08801i	0.839082	+	0.544005i	$0.183093\pi$
$41$			6.96667i			1.08801i	−0.839082	+	0.544005i	$0.816907\pi$
$42$		0			0
$43$			0.510241i			0.0778110i	0.999243	+	0.0389055i	$0.0123871\pi$
$43$			0.510241i			0.0778110i	−0.999243	+	0.0389055i	$0.987613\pi$
$44$	−9.24111	−	3.13647i	−1.39315	−	0.472841i
$45$		0			0
$46$	4.90165	+	0.809152i	0.722708	+	0.119303i
$47$	3.40777	−	5.90243i	0.497074	−	0.860958i	−0.502920	−	0.864333i	$-0.667741\pi$
$47$	3.40777	−	5.90243i	0.497074	−	0.860958i	0.999994	+	0.00337527i	$0.00107438\pi$
$48$		0			0
$49$	−5.87715	+	3.80251i	−0.839593	+	0.543216i
$50$	3.43720	−	4.18843i	0.486094	−	0.592334i
$51$		0			0
$52$	−1.22695	+	1.07610i	−0.170147	+	0.149229i
$53$	2.99884	−	1.73138i	0.411922	−	0.237824i	−0.279693	−	0.960090i	$-0.590233\pi$
$53$	2.99884	−	1.73138i	0.411922	−	0.237824i	0.691615	+	0.722266i	$0.256899\pi$
$54$		0			0
$55$			5.27504i			0.711286i
$56$	1.51365	−	7.32863i	0.202270	−	0.979330i
$57$		0			0
$58$	−12.7195	+	4.78759i	−1.67015	+	0.628641i
$59$	−2.50722	−	4.34263i	−0.326412	−	0.565362i	0.655385	−	0.755295i	$-0.272506\pi$
$59$	−2.50722	−	4.34263i	−0.326412	−	0.565362i	−0.981797	+	0.189933i	$0.939173\pi$
$60$		0			0
$61$	6.85713	−	11.8769i	0.877966	−	1.52068i	0.0243965	−	0.999702i	$-0.492234\pi$
$61$	6.85713	−	11.8769i	0.877966	−	1.52068i	0.853569	−	0.520979i	$-0.174433\pi$
$62$	−9.76964	−	8.01737i	−1.24075	−	1.01821i
$63$		0			0
$64$	4.44546	+	6.65116i	0.555682	+	0.831395i
$65$	0.763968	+	0.441077i	0.0947586	+	0.0547089i
$66$		0			0
$67$	3.66826	−	2.11787i	0.448150	−	0.258739i	−0.258899	−	0.965904i	$-0.583360\pi$
$67$	3.66826	−	2.11787i	0.448150	−	0.258739i	0.707048	+	0.707165i	$0.250026\pi$
$68$	−1.09120	+	3.21505i	−0.132328	+	0.389882i
$69$		0			0
$70$	−4.01419	+	0.498407i	−0.479788	+	0.0595711i
$71$	11.8557			1.40701			0.703503	−	0.710692i	$-0.251618\pi$
$71$	11.8557			1.40701			0.703503	+	0.710692i	$0.251618\pi$
$72$		0			0
$73$	−1.49777	−	2.59421i	−0.175301	−	0.303630i	0.764965	−	0.644072i	$-0.222756\pi$
$73$	−1.49777	−	2.59421i	−0.175301	−	0.303630i	−0.940265	+	0.340443i	$0.889423\pi$
$74$	−9.43181	−	1.55698i	−1.09643	−	0.180995i
$75$		0			0
$76$	8.12548	−	1.61664i	0.932056	−	0.185441i
$77$	−8.89444	+	9.35688i	−1.01362	+	1.06631i
$78$		0			0
$79$	−3.41517	−	1.97175i	−0.384237	−	0.221839i	0.295423	−	0.955366i	$-0.404539\pi$
$79$	−3.41517	−	1.97175i	−0.384237	−	0.221839i	−0.679660	+	0.733527i	$0.737873\pi$
$80$	2.63216	−	3.43094i	0.294284	−	0.383590i
$81$		0			0
$82$	−9.22080	+	3.47070i	−1.01827	+	0.383275i
$83$	11.3326			1.24392			0.621960	−	0.783049i	$-0.286337\pi$
$83$	11.3326			1.24392			0.621960	+	0.783049i	$0.286337\pi$
$84$		0			0
$85$	1.83523			0.199058
$86$	−0.675334	+	0.254195i	−0.0728232	+	0.0274106i
$87$		0			0
$88$	−0.452489	−	13.7937i	−0.0482355	−	1.47041i
$89$	−0.313438	−	0.180963i	−0.0332243	−	0.0191821i	0.483296	−	0.875457i	$-0.339440\pi$
$89$	−0.313438	−	0.180963i	−0.0332243	−	0.0191821i	−0.516520	+	0.856275i	$0.672773\pi$
$90$		0			0
$91$	0.611412	+	2.07054i	0.0640934	+	0.217052i
$92$	1.37097	+	6.89073i	0.142934	+	0.718408i
$93$		0			0
$94$	9.50992	+	1.56987i	0.980873	+	0.161920i
$95$	−2.23911	−	3.87825i	−0.229728	−	0.397900i
$96$		0			0
$97$	8.12677			0.825148			0.412574	−	0.910924i	$-0.364630\pi$
$97$	8.12677			0.825148			0.412574	+	0.910924i	$0.364630\pi$
$98$	−7.96077	−	5.88440i	−0.804159	−	0.594414i
$99$		0			0
$100$	7.25601	+	2.46272i	0.725601	+	0.246272i
$101$	1.32037	−	0.762317i	0.131382	−	0.0758534i	−0.432869	−	0.901457i	$-0.642499\pi$
$101$	1.32037	−	0.762317i	0.131382	−	0.0758534i	0.564250	+	0.825604i	$0.309165\pi$
$102$		0			0
$103$	6.69999	+	3.86824i	0.660170	+	0.381149i	0.792342	−	0.610078i	$-0.208862\pi$
$103$	6.69999	+	3.86824i	0.660170	+	0.381149i	−0.132172	+	0.991227i	$0.542195\pi$
$104$	−2.03554	−	1.08784i	−0.199601	−	0.106672i
$105$		0			0
$106$	3.78557	+	3.10659i	0.367687	+	0.301739i
$107$	−0.602928	+	1.04430i	−0.0582873	+	0.100957i	−0.893697	−	0.448672i	$-0.851897\pi$
$107$	−0.602928	+	1.04430i	−0.0582873	+	0.100957i	0.835409	+	0.549628i	$0.185231\pi$
$108$		0			0
$109$	0.314166	+	0.544151i	0.0300916	+	0.0521202i	0.880679	−	0.473713i	$-0.157087\pi$
$109$	0.314166	+	0.544151i	0.0300916	+	0.0521202i	−0.850587	+	0.525834i	$0.823753\pi$
$110$	−6.98183	+	2.62795i	−0.665691	+	0.250565i
$111$		0			0
$112$	10.4540	−	1.64762i	0.987807	−	0.155686i
$113$			11.7870i			1.10882i	0.832242	+	0.554412i	$0.187057\pi$
$113$			11.7870i			1.10882i	−0.832242	+	0.554412i	$0.812943\pi$
$114$		0			0
$115$	3.28891	−	1.89885i	0.306692	−	0.177069i
$116$	−12.6733	−	14.4498i	−1.17669	−	1.34163i
$117$		0			0
$118$	4.49867	−	5.48189i	0.414136	−	0.504649i
$119$	3.25533	+	3.09444i	0.298416	+	0.283667i
$120$		0			0
$121$	−6.40444	+	11.0928i	−0.582222	+	1.00844i
$122$	19.1359	+	3.15891i	1.73248	+	0.285994i
$123$		0			0
$124$	5.74436	−	16.9248i	0.515859	−	1.51990i
$125$		−	9.54728i		−	0.853934i
$126$		0			0
$127$		−	5.46528i		−	0.484966i	−0.970156	−	0.242483i	$-0.922038\pi$
$127$		−	5.46528i		−	0.484966i	0.970156	−	0.242483i	$-0.0779618\pi$
$128$	−6.58854	+	9.19735i	−0.582350	+	0.812938i
$129$		0			0
$130$	−0.203193	+	1.23090i	−0.0178212	+	0.107957i
$131$	7.94069	−	13.7537i	0.693782	−	1.20167i	−0.276808	−	0.960925i	$-0.589277\pi$
$131$	7.94069	−	13.7537i	0.693782	−	1.20167i	0.970590	−	0.240740i	$-0.0773901\pi$
$132$		0			0
$133$	2.56752	−	10.6547i	0.222633	−	0.923879i
$134$	4.63061	+	3.80007i	0.400024	+	0.328276i
$135$		0			0
$136$	−4.79894	+	0.157424i	−0.411505	+	0.0134990i
$137$	10.7072	−	6.18180i	0.914777	−	0.528147i	0.0328121	−	0.999462i	$-0.489554\pi$
$137$	10.7072	−	6.18180i	0.914777	−	0.528147i	0.881965	+	0.471315i	$0.156220\pi$
$138$		0			0
$139$		−	17.2243i		−	1.46095i	−0.682941	−	0.730473i	$-0.739299\pi$
$139$		−	17.2243i		−	1.46095i	0.682941	−	0.730473i	$-0.260701\pi$
$140$	−2.65949	−	5.06472i	−0.224768	−	0.428047i
$141$		0			0
$142$	5.90633	+	15.6917i	0.495648	+	1.31682i
$143$	1.99080	+	3.44817i	0.166479	+	0.288350i
$144$		0			0
$145$	−5.19459	+	8.99729i	−0.431387	+	0.747184i
$146$	2.68743	−	3.27479i	0.222413	−	0.271024i
$147$		0			0
$148$	−2.63804	−	13.2592i	−0.216846	−	1.08990i
$149$	−9.97002	−	5.75619i	−0.816776	−	0.471566i	0.0325274	−	0.999471i	$-0.489644\pi$
$149$	−9.97002	−	5.75619i	−0.816776	−	0.471566i	−0.849303	+	0.527905i	$0.822978\pi$
$150$		0			0
$151$	9.30760	−	5.37375i	0.757442	−	0.437309i	−0.0709346	−	0.997481i	$-0.522598\pi$
$151$	9.30760	−	5.37375i	0.757442	−	0.437309i	0.828377	+	0.560172i	$0.189265\pi$
$152$	6.18772	+	9.94917i	0.501890	+	0.806984i
$153$		0			0
$154$	−16.8155	−	7.11085i	−1.35503	−	0.573008i
$155$	−9.66109			−0.775998
$156$		0			0
$157$	11.7042	+	20.2723i	0.934099	+	1.61791i	0.776233	+	0.630446i	$0.217128\pi$
$157$	11.7042	+	20.2723i	0.934099	+	1.61791i	0.157865	+	0.987461i	$0.449539\pi$
$158$	0.908337	−	5.50248i	0.0722634	−	0.437754i
$159$		0			0
$160$	5.85236	+	1.77458i	0.462669	+	0.140292i
$161$	9.03560	+	2.17736i	0.712105	+	0.171600i
$162$		0			0
$163$	−2.35163	−	1.35771i	−0.184193	−	0.106344i	0.405068	−	0.914287i	$-0.367248\pi$
$163$	−2.35163	−	1.35771i	−0.184193	−	0.106344i	−0.589261	+	0.807942i	$0.700581\pi$
$164$	−9.18736	−	10.4752i	−0.717412	−	0.817978i
$165$		0			0
$166$	5.64577	+	14.9994i	0.438197	+	1.16418i
$167$	−6.84595			−0.529756			−0.264878	−	0.964282i	$-0.585332\pi$
$167$	−6.84595			−0.529756			−0.264878	+	0.964282i	$0.585332\pi$
$168$		0			0
$169$	−12.3341			−0.948781
$170$	0.914285	+	2.42903i	0.0701224	+	0.186298i
$171$		0			0
$172$	−0.672885	−	0.767209i	−0.0513070	−	0.0584991i
$173$	7.19348	+	4.15316i	0.546910	+	0.315759i	0.747875	−	0.663840i	$-0.231074\pi$
$173$	7.19348	+	4.15316i	0.546910	+	0.315759i	−0.200965	+	0.979599i	$0.564408\pi$
$174$		0			0
$175$	6.98381	−	7.34691i	0.527926	−	0.555374i
$176$	18.0314	−	7.47073i	1.35917	−	0.563128i
$177$		0			0
$178$	0.0833654	−	0.505007i	0.00624850	−	0.0378519i
$179$	10.4832	+	18.1575i	0.783554	+	1.35716i	0.929859	+	0.367917i	$0.119929\pi$
$179$	10.4832	+	18.1575i	0.783554	+	1.35716i	−0.146304	+	0.989240i	$0.546738\pi$
$180$		0			0
$181$	17.8558			1.32721			0.663605	−	0.748083i	$-0.269026\pi$
$181$	17.8558			1.32721			0.663605	+	0.748083i	$0.269026\pi$
$182$	−2.43589	+	1.84076i	−0.180560	+	0.136446i
$183$		0			0
$184$	−8.43729	+	5.24743i	−0.622005	+	0.386846i
$185$	−6.32856	+	3.65380i	−0.465285	+	0.268633i
$186$		0			0
$187$	7.17354	+	4.14165i	0.524581	+	0.302867i
$188$	2.65989	+	13.3690i	0.193992	+	0.975037i
$189$		0			0
$190$	4.01760	−	4.89568i	0.291467	−	0.355170i
$191$	−9.10942	+	15.7780i	−0.659135	+	1.14165i	0.321705	+	0.946840i	$0.395744\pi$
$191$	−9.10942	+	15.7780i	−0.659135	+	1.14165i	−0.980840	+	0.194815i	$0.937589\pi$
$192$		0			0
$193$	−9.35386	−	16.2014i	−0.673306	−	1.16620i	−0.976961	−	0.213418i	$-0.931540\pi$
$193$	−9.35386	−	16.2014i	−0.673306	−	1.16620i	0.303655	−	0.952782i	$-0.401793\pi$
$194$	4.04865	+	10.7563i	0.290676	+	0.772255i
$195$		0			0
$196$	3.82241	−	13.4681i	0.273029	−	0.962006i
$197$			22.2223i			1.58327i	0.610994	+	0.791635i	$0.290770\pi$
$197$			22.2223i			1.58327i	−0.610994	+	0.791635i	$0.709230\pi$
$198$		0			0
$199$	13.8519	−	7.99738i	0.981934	−	0.566920i	0.0790802	−	0.996868i	$-0.474802\pi$
$199$	13.8519	−	7.99738i	0.981934	−	0.566920i	0.902853	+	0.429949i	$0.141468\pi$
$200$	0.355289	+	10.8307i	0.0251227	+	0.765843i
$201$		0			0
$202$	1.66676	+	1.36781i	0.117273	+	0.0962391i
$203$	−24.3848	+	7.20063i	−1.71148	+	0.505385i
$204$		0			0
$205$	−3.76575	+	6.52247i	−0.263011	+	0.455549i
$206$	−1.78200	+	10.7949i	−0.124158	+	0.752120i
$207$		0			0
$208$	0.425745	−	3.23610i	0.0295201	−	0.224383i
$209$		−	20.2124i		−	1.39812i
$210$		0			0
$211$			8.32079i			0.572827i	0.958106	+	0.286414i	$0.0924631\pi$
$211$			8.32079i			0.572827i	−0.958106	+	0.286414i	$0.907537\pi$
$212$	−2.22584	+	6.55809i	−0.152872	+	0.450411i
$213$		0			0
$214$	−1.68257	−	0.277754i	−0.115018	−	0.0189869i
$215$	−0.275804	+	0.477707i	−0.0188097	+	0.0325794i
$216$		0			0
$217$	−17.1369	−	16.2899i	−1.16333	−	1.10583i
$218$	−0.563704	+	0.686906i	−0.0381788	+	0.0465232i
$219$		0			0
$220$	−6.95650	−	7.93165i	−0.469007	−	0.534752i
$221$	1.19965	−	0.692615i	0.0806969	−	0.0465904i
$222$		0			0
$223$			8.91285i			0.596848i	0.954433	+	0.298424i	$0.0964610\pi$
$223$			8.91285i			0.596848i	−0.954433	+	0.298424i	$0.903539\pi$
$224$	7.38875	+	13.0156i	0.493681	+	0.869643i
$225$		0			0
$226$	−15.6007	+	5.87210i	−1.03775	+	0.390607i
$227$	−10.2145	−	17.6920i	−0.677957	−	1.17426i	−0.975595	−	0.219578i	$-0.929532\pi$
$227$	−10.2145	−	17.6920i	−0.677957	−	1.17426i	0.297638	−	0.954679i	$-0.403801\pi$
$228$		0			0
$229$	6.21367	−	10.7624i	0.410611	−	0.711199i	−0.584346	−	0.811505i	$-0.698649\pi$
$229$	6.21367	−	10.7624i	0.410611	−	0.711199i	0.994957	+	0.100306i	$0.0319821\pi$
$230$	4.15173	+	3.40708i	0.273757	+	0.224657i
$231$		0			0
$232$	12.8116	−	23.9726i	0.841120	−	1.57388i
$233$	−2.18246	−	1.26005i	−0.142978	−	0.0825484i	0.426805	−	0.904344i	$-0.359639\pi$
$233$	−2.18246	−	1.26005i	−0.142978	−	0.0825484i	−0.569783	+	0.821796i	$0.692973\pi$
$234$		0			0
$235$	6.38097	−	3.68405i	0.416249	−	0.240321i
$236$	9.49679	+	3.22325i	0.618188	+	0.209816i
$237$		0			0
$238$	−2.47392	+	5.85023i	−0.160360	+	0.379214i
$239$	−25.2624			−1.63409			−0.817045	−	0.576574i	$-0.804389\pi$
$239$	−25.2624			−1.63409			−0.817045	+	0.576574i	$0.804389\pi$
$240$		0			0
$241$	7.31705	+	12.6735i	0.471333	+	0.816372i	0.999462	−	0.0327917i	$-0.0104398\pi$
$241$	7.31705	+	12.6735i	0.471333	+	0.816372i	−0.528130	+	0.849164i	$0.677106\pi$
$242$	−17.8726	−	2.95037i	−1.14889	−	0.189657i
$243$		0			0
$244$	5.35225	+	26.9013i	0.342643	+	1.72218i
$245$	−7.55782	+	0.383236i	−0.482851	+	0.0244841i
$246$		0			0
$247$	−2.92731	−	1.69008i	−0.186260	−	0.107537i
$248$	25.2628	−	0.828722i	1.60419	−	0.0526239i
$249$		0			0
$250$	12.6364	−	4.75632i	0.799195	−	0.300816i
$251$	11.3947			0.719227			0.359613	−	0.933101i	$-0.382909\pi$
$251$	11.3947			0.719227			0.359613	+	0.933101i	$0.382909\pi$
$252$		0			0
$253$	17.1409			1.07764
$254$	7.23363	−	2.72273i	0.453878	−	0.170839i
$255$		0			0
$256$	−15.4556	−	4.13833i	−0.965972	−	0.258646i
$257$	−19.8884	−	11.4826i	−1.24060	−	0.716263i	−0.271386	−	0.962471i	$-0.587482\pi$
$257$	−19.8884	−	11.4826i	−1.24060	−	0.716263i	−0.969217	+	0.246208i	$0.920815\pi$
$258$		0			0
$259$	−17.3864	−	4.18971i	−1.08034	−	0.260336i
$260$	−1.73039	+	0.344277i	−0.107314	+	0.0213512i
$261$		0			0
$262$	22.1598	+	3.65808i	1.36904	+	0.225997i
$263$	11.6566	+	20.1898i	0.718775	+	1.24495i	0.961485	+	0.274856i	$0.0886301\pi$
$263$	11.6566	+	20.1898i	0.718775	+	1.24495i	−0.242711	+	0.970099i	$0.578037\pi$
$264$		0			0
$265$	3.74351			0.229962
$266$	15.3812	−	1.90975i	0.943084	−	0.117094i
$267$		0			0
$268$	−2.72271	+	8.02203i	−0.166316	+	0.490024i
$269$	25.3140	−	14.6150i	1.54342	−	0.891094i	0.544801	−	0.838565i	$-0.316605\pi$
$269$	25.3140	−	14.6150i	1.54342	−	0.891094i	0.998619	−	0.0525290i	$-0.0167282\pi$
$270$		0			0
$271$	−0.829286	−	0.478788i	−0.0503755	−	0.0290843i	0.474601	−	0.880201i	$-0.342592\pi$
$271$	−0.829286	−	0.478788i	−0.0503755	−	0.0290843i	−0.524976	+	0.851117i	$0.675926\pi$
$272$	−2.59913	−	6.27325i	−0.157595	−	0.380372i
$273$		0			0
$274$	13.5162	+	11.0919i	0.816541	+	0.670087i
$275$	9.34723	−	16.1899i	0.563659	−	0.976286i
$276$		0			0
$277$	−6.06856	−	10.5111i	−0.364624	−	0.631548i	0.624091	−	0.781351i	$-0.285469\pi$
$277$	−6.06856	−	10.5111i	−0.364624	−	0.631548i	−0.988716	+	0.149803i	$0.952136\pi$
$278$	22.7974	−	8.58092i	1.36730	−	0.514649i
$279$		0			0
$280$	5.37854	−	6.04317i	0.321429	−	0.361148i
$281$		−	23.7714i		−	1.41808i	−0.705168	−	0.709041i	$-0.749128\pi$
$281$		−	23.7714i		−	1.41808i	0.705168	−	0.709041i	$-0.250872\pi$
$282$		0			0
$283$	−2.93570	+	1.69493i	−0.174509	+	0.100753i	−0.584710	−	0.811242i	$-0.698792\pi$
$283$	−2.93570	+	1.69493i	−0.174509	+	0.100753i	0.410201	+	0.911995i	$0.365458\pi$
$284$	−17.8264	+	15.6347i	−1.05780	+	0.927752i
$285$		0			0
$286$	−3.57207	+	4.35278i	−0.211221	+	0.257385i
$287$	−17.6775	+	5.22000i	−1.04347	+	0.308127i
$288$		0			0
$289$	−7.05909	+	12.2267i	−0.415241	+	0.719218i
$290$	−14.4963	−	2.39302i	−0.851253	−	0.140523i
$291$		0			0
$292$	5.67322	+	1.92552i	0.332000	+	0.112682i
$293$		−	14.2017i		−	0.829673i	−0.909896	−	0.414837i	$-0.863839\pi$
$293$		−	14.2017i		−	0.829673i	0.909896	−	0.414837i	$-0.136161\pi$
$294$		0			0
$295$		−	5.42099i		−	0.315622i
$296$	16.2351	−	10.0972i	0.943649	−	0.586887i
$297$		0			0
$298$	2.65174	−	16.0636i	0.153611	−	0.930538i
$299$	1.43326	−	2.48247i	0.0828873	−	0.143565i
$300$		0			0
$301$	−1.29470	+	0.382315i	−0.0746254	+	0.0220362i
$302$	11.7494	+	9.64204i	0.676102	+	0.554837i
$303$		0			0
$304$	−10.0857	+	13.1464i	−0.578454	+	0.753995i
$305$	12.8398	−	7.41308i	0.735206	−	0.424472i
$306$		0			0
$307$			25.7078i			1.46722i	0.679571	+	0.733610i	$0.262166\pi$
$307$			25.7078i			1.46722i	−0.679571	+	0.733610i	$0.737834\pi$
$308$	1.03439	−	25.7988i	0.0589399	−	1.47002i
$309$		0			0
$310$	−4.81303	−	12.7870i	−0.273362	−	0.726255i
$311$	−4.39864	−	7.61867i	−0.249424	−	0.432015i	0.713942	−	0.700205i	$-0.246908\pi$
$311$	−4.39864	−	7.61867i	−0.249424	−	0.432015i	−0.963366	+	0.268190i	$0.913575\pi$
$312$		0			0
$313$	−6.87877	+	11.9144i	−0.388811	+	0.673440i	−0.992290	−	0.123939i	$-0.960447\pi$
$313$	−6.87877	+	11.9144i	−0.388811	+	0.673440i	0.603479	+	0.797379i	$0.293781\pi$
$314$	−21.0007	+	25.5906i	−1.18514	+	1.44416i
$315$		0			0
$316$	7.73539	−	1.53902i	0.435149	−	0.0865769i
$317$	−9.53960	−	5.50769i	−0.535797	−	0.309343i	0.207577	−	0.978219i	$-0.433442\pi$
$317$	−9.53960	−	5.50769i	−0.535797	−	0.309343i	−0.743374	+	0.668876i	$0.766776\pi$
$318$		0			0
$319$	−40.6092	+	23.4458i	−2.27368	+	1.31271i
$320$	0.566808	+	8.63001i	0.0316855	+	0.482432i
$321$		0			0
$322$	1.61955	+	13.0439i	0.0902538	+	0.726908i
$323$	−7.03206			−0.391274
$324$		0			0
$325$	−1.56316	−	2.70746i	−0.0867082	−	0.150183i
$326$	0.625464	−	3.78891i	0.0346413	−	0.209848i
$327$		0			0
$328$	9.28757	−	17.3786i	0.512820	−	0.959574i
$329$	17.5304	+	4.22440i	0.966483	+	0.232899i
$330$		0			0
$331$	−2.42290	−	1.39886i	−0.133175	−	0.0768884i	0.431933	−	0.901906i	$-0.357832\pi$
$331$	−2.42290	−	1.39886i	−0.133175	−	0.0768884i	−0.565107	+	0.825017i	$0.691165\pi$
$332$	−17.0400	+	14.9450i	−0.935191	+	0.820215i
$333$		0			0
$334$	−3.41056	−	9.06103i	−0.186618	−	0.495797i
$335$	4.57916			0.250186
$336$		0			0
$337$	−3.38341			−0.184306			−0.0921530	−	0.995745i	$-0.529375\pi$
$337$	−3.38341			−0.184306			−0.0921530	+	0.995745i	$0.529375\pi$
$338$	−6.14471	−	16.3250i	−0.334228	−	0.887962i
$339$		0			0
$340$	−2.75948	+	2.42022i	−0.149654	+	0.131255i
$341$	−37.7633	−	21.8027i	−2.04500	−	1.18068i
$342$		0			0
$343$	−14.0523	−	12.0637i	−0.758751	−	0.651380i
$344$	0.680224	−	1.27282i	0.0366752	−	0.0686257i
$345$		0			0
$346$	−1.91326	+	11.5901i	−0.102857	+	0.623085i
$347$	−1.96566	−	3.40462i	−0.105522	−	0.182770i	0.808429	−	0.588593i	$-0.200318\pi$
$347$	−1.96566	−	3.40462i	−0.105522	−	0.182770i	−0.913951	+	0.405824i	$0.866985\pi$
$348$		0			0
$349$	16.1233			0.863058			0.431529	−	0.902099i	$-0.357974\pi$
$349$	16.1233			0.863058			0.431529	+	0.902099i	$0.357974\pi$
$350$	13.2033	+	5.58336i	0.705747	+	0.298443i
$351$		0			0
$352$	18.8709	+	20.1438i	1.00582	+	1.07367i
$353$	−32.2263	+	18.6059i	−1.71523	+	0.990290i	−0.788106	+	0.615539i	$0.788938\pi$
$353$	−32.2263	+	18.6059i	−1.71523	+	0.990290i	−0.927126	+	0.374750i	$0.877728\pi$
$354$		0			0
$355$	11.0997	+	6.40843i	0.589112	+	0.340124i
$356$	0.709939	−	0.141249i	0.0376267	−	0.00748617i
$357$		0			0
$358$	−18.8099	+	22.9210i	−0.994136	+	1.21141i
$359$	10.7770	−	18.6664i	0.568790	−	0.985173i	−0.427896	−	0.903828i	$-0.640745\pi$
$359$	10.7770	−	18.6664i	0.568790	−	0.985173i	0.996686	−	0.0813452i	$-0.0259216\pi$
$360$		0			0
$361$	−0.920383	−	1.59415i	−0.0484412	−	0.0839026i
$362$	8.89551	+	23.6332i	0.467538	+	1.24213i
$363$		0			0
$364$	−3.64988	−	2.30700i	−0.191305	−	0.120920i
$365$		−	3.23841i		−	0.169506i
$366$		0			0
$367$	1.45961	−	0.842704i	0.0761908	−	0.0439888i	−0.461421	−	0.887182i	$-0.652660\pi$
$367$	1.45961	−	0.842704i	0.0761908	−	0.0439888i	0.537611	+	0.843193i	$0.319327\pi$
$368$	−11.1486	−	8.55306i	−0.581163	−	0.445859i
$369$		0			0
$370$	−7.98882	−	6.55596i	−0.415319	−	0.340828i
$371$	6.64025	+	6.31207i	0.344744	+	0.327706i
$372$		0			0
$373$	2.14560	−	3.71630i	0.111095	−	0.192422i	−0.805117	−	0.593116i	$-0.797897\pi$
$373$	2.14560	−	3.71630i	0.111095	−	0.192422i	0.916212	+	0.400694i	$0.131231\pi$
$374$	−1.90795	+	11.5579i	−0.0986579	+	0.597646i
$375$		0			0
$376$	−16.3696	+	10.1808i	−0.844197	+	0.525035i
$377$			7.84176i			0.403871i
$378$		0			0
$379$			3.00059i			0.154130i	0.997026	+	0.0770650i	$0.0245549\pi$
$379$			3.00059i			0.154130i	−0.997026	+	0.0770650i	$0.975445\pi$
$380$	8.48124	+	2.87857i	0.435079	+	0.147668i
$381$		0			0
$382$	−25.4213	−	4.19649i	−1.30067	−	0.214711i
$383$	10.5636	−	18.2967i	0.539774	−	0.934916i	−0.459142	−	0.888363i	$-0.651843\pi$
$383$	10.5636	−	18.2967i	0.539774	−	0.934916i	0.998916	−	0.0465530i	$-0.0148236\pi$
$384$		0			0
$385$	−13.3851	+	3.95249i	−0.682166	+	0.201438i
$386$	16.7835	−	20.4517i	0.854258	−	1.04096i
$387$		0			0
$388$	−12.2196	+	10.7172i	−0.620355	+	0.544086i
$389$	29.5830	−	17.0798i	1.49992	−	0.865979i	0.499920	−	0.866072i	$-0.333363\pi$
$389$	29.5830	−	17.0798i	1.49992	−	0.865979i	1.00000		9.28896e-5i	$2.95677e-5\pi$
$390$		0			0
$391$		−	5.96347i		−	0.301585i
$392$	19.7301	−	1.65043i	0.996520	−	0.0833593i
$393$		0			0
$394$	−29.4125	+	11.0708i	−1.48178	+	0.557740i
$395$	−2.13161	−	3.69206i	−0.107253	−	0.185768i
$396$		0			0
$397$	8.42503	−	14.5926i	0.422840	−	0.732380i	−0.573376	−	0.819292i	$-0.694367\pi$
$397$	8.42503	−	14.5926i	0.422840	−	0.732380i	0.996216	+	0.0869120i	$0.0276999\pi$
$398$	17.4858	+	14.3496i	0.876486	+	0.719280i
$399$		0			0
$400$	−14.1580	+	5.86593i	−0.707901	+	0.293297i
$401$	−8.58950	−	4.95915i	−0.428939	−	0.247648i	0.269956	−	0.962873i	$-0.412991\pi$
$401$	−8.58950	−	4.95915i	−0.428939	−	0.247648i	−0.698894	+	0.715225i	$0.746324\pi$
$402$		0			0
$403$	−6.31524	+	3.64610i	−0.314584	+	0.181625i
$404$	−0.980025	+	2.88749i	−0.0487581	+	0.143658i
$405$		0			0
$406$	−21.6787	−	28.6875i	−1.07589	−	1.42374i
$407$	−32.9828			−1.63490
$408$		0			0
$409$	−18.0859	−	31.3257i	−0.894291	−	1.54896i	−0.834680	−	0.550736i	$-0.814347\pi$
$409$	−18.0859	−	31.3257i	−0.894291	−	1.54896i	−0.0596111	−	0.998222i	$-0.518986\pi$
$410$	−10.5089	−	1.73479i	−0.518998	−	0.0856750i
$411$		0			0
$412$	−15.1755	+	3.01931i	−0.747645	+	0.148751i
$413$	9.14053	−	9.61576i	0.449776	−	0.473161i
$414$		0			0
$415$	10.6101	+	6.12572i	0.520828	+	0.300700i
$416$	4.49528	−	1.04868i	0.220399	−	0.0514159i
$417$		0			0
$418$	26.7523	−	10.0696i	1.30850	−	0.492518i
$419$	−30.7098			−1.50027			−0.750137	−	0.661283i	$-0.770012\pi$
$419$	−30.7098			−1.50027			−0.750137	+	0.661283i	$0.770012\pi$
$420$		0			0
$421$	10.9036			0.531411			0.265706	−	0.964054i	$-0.414395\pi$
$421$	10.9036			0.531411			0.265706	+	0.964054i	$0.414395\pi$
$422$	−11.0131	+	4.14531i	−0.536108	+	0.201790i
$423$		0			0
$424$	−9.78891	+	0.321116i	−0.475391	+	0.0155947i
$425$	−5.63258	−	3.25197i	−0.273220	−	0.157744i
$426$		0			0
$427$	35.2748	+	8.50037i	1.70707	+	0.411362i
$428$	−0.470608	−	2.36535i	−0.0227477	−	0.114334i
$429$		0			0
$430$	−0.769676	−	0.127056i	−0.0371171	−	0.00612720i
$431$	7.83169	+	13.5649i	0.377239	+	0.653398i	0.990659	−	0.136359i	$-0.0435401\pi$
$431$	7.83169	+	13.5649i	0.377239	+	0.653398i	−0.613420	+	0.789757i	$0.710207\pi$
$432$		0			0
$433$	−22.8956			−1.10029			−0.550145	−	0.835069i	$-0.685428\pi$
$433$	−22.8956			−1.10029			−0.550145	+	0.835069i	$0.685428\pi$
$434$	13.0233	−	30.7971i	0.625140	−	1.47831i
$435$		0			0
$436$	−1.18999	−	0.403888i	−0.0569902	−	0.0193427i
$437$	−12.6022	+	7.27586i	−0.602843	+	0.348051i
$438$		0			0
$439$	−14.9901	−	8.65454i	−0.715438	−	0.413059i	0.0976331	−	0.995222i	$-0.468873\pi$
$439$	−14.9901	−	8.65454i	−0.715438	−	0.413059i	−0.813071	+	0.582164i	$0.802206\pi$
$440$	7.03238	−	13.1588i	0.335256	−	0.627321i
$441$		0			0
$442$	1.51436	+	1.24275i	0.0720310	+	0.0591116i
$443$	−5.69268	+	9.86000i	−0.270467	+	0.468463i	−0.968982	−	0.247133i	$-0.920512\pi$
$443$	−5.69268	+	9.86000i	−0.270467	+	0.468463i	0.698514	+	0.715596i	$0.253845\pi$
$444$		0			0
$445$	−0.195635	−	0.338850i	−0.00927400	−	0.0160630i
$446$	−11.7967	+	4.44026i	−0.558589	+	0.210252i
$447$		0			0
$448$	−13.5460	+	16.2637i	−0.639987	+	0.768386i
$449$		−	11.1088i		−	0.524258i	−0.965033	−	0.262129i	$-0.915575\pi$
$449$		−	11.1088i		−	0.524258i	0.965033	−	0.262129i	$-0.0844245\pi$
$450$		0			0
$451$	−29.4391	+	16.9967i	−1.38624	+	0.800343i
$452$	−15.5442	−	17.7231i	−0.731136	−	0.833625i
$453$		0			0
$454$	18.3277	−	22.3333i	0.860160	−	1.04816i
$455$	−0.546777	+	2.26901i	−0.0256333	+	0.106373i
$456$		0			0
$457$	−13.5658	+	23.4967i	−0.634582	+	1.09913i	0.352022	+	0.935992i	$0.385494\pi$
$457$	−13.5658	+	23.4967i	−0.634582	+	1.09913i	−0.986604	+	0.163136i	$0.947839\pi$
$458$	17.3402	+	2.86248i	0.810256	+	0.133755i
$459$		0			0
$460$	−2.44114	+	7.19243i	−0.113819	+	0.335349i
$461$		−	13.2528i		−	0.617246i	−0.951184	−	0.308623i	$-0.900132\pi$
$461$		−	13.2528i		−	0.617246i	0.951184	−	0.308623i	$-0.0998682\pi$
$462$		0			0
$463$		−	4.07186i		−	0.189235i	−0.995514	−	0.0946176i	$-0.969837\pi$
$463$		−	4.07186i		−	0.189235i	0.995514	−	0.0946176i	$-0.0301629\pi$
$464$	38.1117	+	5.01402i	1.76929	+	0.232770i
$465$		0			0
$466$	0.580472	−	3.51636i	0.0268899	−	0.162892i
$467$	−11.7529	+	20.3565i	−0.543857	+	0.941988i	0.454821	+	0.890583i	$0.349703\pi$
$467$	−11.7529	+	20.3565i	−0.543857	+	0.941988i	−0.998678	+	0.0514053i	$0.983630\pi$
$468$		0			0
$469$	8.12253	+	7.72109i	0.375064	+	0.356527i
$470$	8.05498	+	6.61025i	0.371549	+	0.304908i
$471$		0			0
$472$	0.465008	+	14.1753i	0.0214037	+	0.652473i
$473$	−2.15613	+	1.24484i	−0.0991390	+	0.0572380i
$474$		0			0
$475$			15.8706i			0.728191i
$476$	−8.97560	−	0.359872i	−0.411396	−	0.0164947i
$477$		0			0
$478$	−12.5854	−	33.4363i	−0.575643	−	1.52934i
$479$	−1.86090	−	3.22317i	−0.0850266	−	0.147270i	0.820376	−	0.571825i	$-0.193764\pi$
$479$	−1.86090	−	3.22317i	−0.0850266	−	0.147270i	−0.905403	+	0.424554i	$0.860431\pi$
$480$		0			0
$481$	−2.75789	+	4.77681i	−0.125749	+	0.217804i
$482$	−13.1289	+	15.9983i	−0.598004	+	0.728704i
$483$		0			0
$484$	−4.99890	−	25.1253i	−0.227223	−	1.14206i
$485$	7.60860	+	4.39283i	0.345489	+	0.199468i
$486$		0			0
$487$	14.5697	−	8.41182i	0.660216	−	0.381176i	−0.132143	−	0.991231i	$-0.542186\pi$
$487$	14.5697	−	8.41182i	0.660216	−	0.381176i	0.792359	+	0.610055i	$0.208853\pi$
$488$	−32.9390	+	20.4859i	−1.49108	+	0.927352i
$489$		0			0
$490$	−4.27244	−	9.81230i	−0.193009	−	0.443275i
$491$	6.75735			0.304955			0.152477	−	0.988307i	$-0.451275\pi$
$491$	6.75735			0.304955			0.152477	+	0.988307i	$0.451275\pi$
$492$		0			0
$493$	8.15696	+	14.1283i	0.367371	+	0.636305i
$494$	0.778579	−	4.71644i	0.0350299	−	0.212203i
$495$		0			0
$496$	13.6825	+	33.0240i	0.614360	+	1.48282i
$497$	8.88323	+	30.0829i	0.398467	+	1.34940i
$498$		0			0
$499$	−14.9780	−	8.64752i	−0.670505	−	0.387116i	0.125763	−	0.992060i	$-0.459862\pi$
$499$	−14.9780	−	8.64752i	−0.670505	−	0.387116i	−0.796268	+	0.604944i	$0.793195\pi$
$500$	12.5906	+	14.3555i	0.563067	+	0.641997i
$501$		0			0
$502$	5.67668	+	15.0816i	0.253363	+	0.673123i
$503$	6.05186			0.269839			0.134920	−	0.990857i	$-0.456922\pi$
$503$	6.05186			0.269839			0.134920	+	0.990857i	$0.456922\pi$
$504$		0			0
$505$	1.64824			0.0733459
$506$	8.53938	+	22.6871i	0.379622	+	1.00856i
$507$		0			0
$508$	7.20739	+	8.21771i	0.319776	+	0.364602i
$509$	15.4989	+	8.94831i	0.686978	+	0.396627i	0.802479	−	0.596681i	$-0.203514\pi$
$509$	15.4989	+	8.94831i	0.686978	+	0.396627i	−0.115501	+	0.993307i	$0.536847\pi$
$510$		0			0
$511$	5.46040	−	5.74429i	0.241554	−	0.254113i
$512$	−2.22242	−	22.5180i	−0.0982182	−	0.995165i
$513$		0			0
$514$	5.28973	−	32.0439i	0.233320	−	1.41340i
$515$	4.18186	+	7.24320i	0.184275	+	0.319173i
$516$		0			0
$517$	33.2560			1.46260
$518$	−3.11635	−	25.0992i	−0.136925	−	1.10280i
$519$		0			0
$520$	−1.31773	−	2.11876i	−0.0577863	−	0.0929140i
$521$	−6.17964	+	3.56782i	−0.270735	+	0.156309i	−0.629222	−	0.777226i	$-0.716626\pi$
$521$	−6.17964	+	3.56782i	−0.270735	+	0.156309i	0.358487	+	0.933535i	$0.383293\pi$
$522$		0			0
$523$	−37.1480	−	21.4474i	−1.62437	−	0.937830i	−0.985732	−	0.168323i	$-0.946165\pi$
$523$	−37.1480	−	21.4474i	−1.62437	−	0.937830i	−0.638638	−	0.769507i	$-0.720502\pi$
$524$	6.19801	+	31.1522i	0.270761	+	1.36089i
$525$		0			0
$526$	−20.9152	+	25.4864i	−0.911947	+	1.11126i
$527$	−7.58532	+	13.1382i	−0.330422	+	0.572307i
$528$		0			0
$529$	5.32978	+	9.23146i	0.231730	+	0.401368i
$530$	1.86497	+	4.95476i	0.0810089	+	0.215221i
$531$		0			0
$532$	10.1904	+	19.4066i	0.441810	+	0.841381i
$533$			5.68478i			0.246235i
$534$		0			0
$535$	−1.12897	+	0.651811i	−0.0488096	+	0.0281803i
$536$	−11.9741	+	0.392797i	−0.517200	+	0.0169663i
$537$		0			0
$538$	31.9550	+	26.2235i	1.37768	+	1.13058i
$539$	−30.4069	−	15.5581i	−1.30972	−	0.670135i
$540$		0			0
$541$	6.68983	−	11.5871i	0.287618	−	0.498170i	−0.685622	−	0.727957i	$-0.740470\pi$
$541$	6.68983	−	11.5871i	0.287618	−	0.498170i	0.973241	+	0.229788i	$0.0738032\pi$
$542$	0.220566	−	1.33614i	0.00947412	−	0.0573919i
$543$		0			0
$544$	7.00817	−	6.56535i	0.300473	−	0.281487i
$545$			0.679274i			0.0290969i
$546$		0			0
$547$			16.1576i			0.690849i	0.938447	+	0.345424i	$0.112265\pi$
$547$			16.1576i			0.690849i	−0.938447	+	0.345424i	$0.887735\pi$
$548$	−7.94725	+	23.4153i	−0.339490	+	1.00025i
$549$		0			0
$550$	26.0849	+	4.30604i	1.11226	+	0.183610i
$551$	19.9042	−	34.4750i	0.847946	−	1.46869i
$552$		0			0
$553$	2.44426	−	10.1432i	0.103940	−	0.431332i
$554$	10.8887	−	13.2686i	0.462618	−	0.563727i
$555$		0			0
$556$	22.7147	+	25.8988i	0.963318	+	1.09835i
$557$	4.80203	−	2.77245i	0.203469	−	0.117473i	−0.394804	−	0.918765i	$-0.629187\pi$
$557$	4.80203	−	2.77245i	0.203469	−	0.117473i	0.598272	+	0.801293i	$0.295854\pi$
$558$		0			0
$559$			0.416355i			0.0176099i
$560$	10.6780	+	4.10820i	0.451228	+	0.173603i
$561$		0			0
$562$	31.4628	−	11.8426i	1.32718	−	0.499549i
$563$	21.7530	+	37.6772i	0.916778	+	1.58791i	0.804277	+	0.594255i	$0.202553\pi$
$563$	21.7530	+	37.6772i	0.916778	+	1.58791i	0.112501	+	0.993652i	$0.464114\pi$
$564$		0			0
$565$	−6.37130	+	11.0354i	−0.268042	+	0.464263i
$566$	−3.70586	−	3.04118i	−0.155769	−	0.127830i
$567$		0			0
$568$	−29.5744	−	15.8053i	−1.24091	−	0.663175i
$569$	31.6927	+	18.2978i	1.32863	+	0.767083i	0.985087	−	0.172056i	$-0.0550409\pi$
$569$	31.6927	+	18.2978i	1.32863	+	0.767083i	0.343539	+	0.939138i	$0.388374\pi$
$570$		0			0
$571$	17.5668	−	10.1422i	0.735148	−	0.424438i	−0.0851545	−	0.996368i	$-0.527138\pi$
$571$	17.5668	−	10.1422i	0.735148	−	0.424438i	0.820303	+	0.571930i	$0.193805\pi$
$572$	−7.54072	−	2.55935i	−0.315293	−	0.107012i
$573$		0			0
$574$	−15.7157	−	20.7966i	−0.655959	−	0.868035i
$575$	−13.4589			−0.561274
$576$		0			0
$577$	4.86675	+	8.42945i	0.202605	+	0.350923i	0.949367	−	0.314169i	$-0.101726\pi$
$577$	4.86675	+	8.42945i	0.202605	+	0.350923i	−0.746762	+	0.665092i	$0.768392\pi$
$578$	−19.6995	−	3.25195i	−0.819392	−	0.135263i
$579$		0			0
$580$	−4.05457	−	20.3789i	−0.168357	−	0.846188i
$581$	8.49135	+	28.7559i	0.352281	+	1.19299i
$582$		0			0
$583$	14.6326	+	8.44816i	0.606022	+	0.349887i
$584$	0.277788	+	8.46811i	0.0114950	+	0.350413i
$585$		0			0
$586$	18.7968	−	7.07510i	0.776489	−	0.292270i
$587$	32.9781			1.36115			0.680576	−	0.732678i	$-0.261730\pi$
$587$	32.9781			1.36115			0.680576	+	0.732678i	$0.261730\pi$
$588$		0			0
$589$	37.0185			1.52532
$590$	7.17500	−	2.70066i	0.295390	−	0.111184i
$591$		0			0
$592$	21.4524	+	16.4579i	0.881686	+	0.676416i
$593$	−30.7424	−	17.7491i	−1.26244	−	0.728869i	−0.288892	−	0.957362i	$-0.593287\pi$
$593$	−30.7424	−	17.7491i	−1.26244	−	0.728869i	−0.973546	+	0.228493i	$0.926620\pi$
$594$		0			0
$595$	1.37510	+	4.65677i	0.0563737	+	0.190909i
$596$	22.5822	−	4.49293i	0.925001	−	0.184037i
$597$		0			0
$598$	3.99973	+	0.660266i	0.163561	+	0.0270003i
$599$	14.8924	+	25.7944i	0.608488	+	1.05393i	0.991490	+	0.130185i	$0.0415570\pi$
$599$	14.8924	+	25.7944i	0.608488	+	1.05393i	−0.383002	+	0.923748i	$0.625110\pi$
$600$		0			0
$601$	−46.8743			−1.91204			−0.956021	−	0.293298i	$-0.905247\pi$
$601$	−46.8743			−1.91204			−0.956021	+	0.293298i	$0.905247\pi$
$602$	−1.15102	−	1.52315i	−0.0469121	−	0.0620791i
$603$		0			0
$604$	−6.90842	+	20.3546i	−0.281100	+	0.828215i
$605$	−11.9922	+	6.92368i	−0.487551	+	0.281488i
$606$		0			0
$607$	19.2150	+	11.0938i	0.779912	+	0.450283i	0.836399	−	0.548121i	$-0.184657\pi$
$607$	19.2150	+	11.0938i	0.779912	+	0.450283i	−0.0564869	+	0.998403i	$0.517990\pi$
$608$	−22.4245	−	6.79966i	−0.909435	−	0.275763i
$609$		0			0
$610$	16.2083	+	13.3012i	0.656254	+	0.538549i
$611$	2.78073	−	4.81636i	0.112496	−	0.194849i
$612$		0			0
$613$	−6.05599	−	10.4893i	−0.244599	−	0.423658i	0.717420	−	0.696641i	$-0.245323\pi$
$613$	−6.05599	−	10.4893i	−0.244599	−	0.423658i	−0.962019	+	0.272983i	$0.911990\pi$
$614$	−34.0258	+	12.8073i	−1.37317	+	0.516859i
$615$		0			0
$616$	34.6616	−	11.4835i	1.39655	−	0.462685i
$617$		−	19.5363i		−	0.786501i	−0.919431	−	0.393250i	$-0.871351\pi$
$617$		−	19.5363i		−	0.786501i	0.919431	−	0.393250i	$-0.128649\pi$
$618$		0			0
$619$	0.819203	−	0.472967i	0.0329265	−	0.0190102i	−0.483446	−	0.875374i	$-0.660615\pi$
$619$	0.819203	−	0.472967i	0.0329265	−	0.0190102i	0.516373	+	0.856364i	$0.327282\pi$
$620$	14.5266	−	12.7407i	0.583403	−	0.511677i
$621$		0			0
$622$	7.89242	−	9.61738i	0.316457	−	0.385622i
$623$	0.224329	−	0.930921i	0.00898757	−	0.0372966i
$624$		0			0
$625$	−4.41753	+	7.65138i	−0.176701	+	0.306055i
$626$	−19.1963	−	3.16888i	−0.767238	−	0.126654i
$627$		0			0
$628$	−44.3330	−	15.0468i	−1.76908	−	0.600433i
$629$			11.4750i			0.457537i
$630$		0			0
$631$		−	6.23847i		−	0.248350i	−0.992260	−	0.124175i	$-0.960372\pi$
$631$		−	6.23847i		−	0.248350i	0.992260	−	0.124175i	$-0.0396284\pi$
$632$	5.89066	+	9.47152i	0.234318	+	0.376757i
$633$		0			0
$634$	2.53726	−	15.3701i	0.100767	−	0.610424i
$635$	2.95419	−	5.11681i	0.117234	−	0.203054i
$636$		0			0
$637$	−4.79574	+	3.10284i	−0.190014	+	0.122939i
$638$	−51.2628	−	42.0684i	−2.02952	−	1.66550i
$639$		0			0
$640$	−11.1400	+	5.04956i	−0.440346	+	0.199601i
$641$	6.36278	−	3.67355i	0.251315	−	0.145097i	−0.369051	−	0.929409i	$-0.620317\pi$
$641$	6.36278	−	3.67355i	0.251315	−	0.145097i	0.620366	+	0.784312i	$0.286984\pi$
$642$		0			0
$643$		−	44.8033i		−	1.76687i	−0.468553	−	0.883436i	$-0.655224\pi$
$643$		−	44.8033i		−	1.76687i	0.468553	−	0.883436i	$-0.344776\pi$
$644$	−16.4575	+	8.64186i	−0.648518	+	0.340537i
$645$		0			0
$646$	−3.50328	−	9.30735i	−0.137835	−	0.366193i
$647$	−4.89449	−	8.47750i	−0.192422	−	0.333285i	0.753630	−	0.657299i	$-0.228301\pi$
$647$	−4.89449	−	8.47750i	−0.192422	−	0.333285i	−0.946052	+	0.324014i	$0.894968\pi$
$648$		0			0
$649$	12.2338	−	21.1896i	0.480219	−	0.831764i
$650$	2.80475	−	3.41775i	0.110011	−	0.134055i
$651$		0			0
$652$	5.32645	−	1.05974i	0.208600	−	0.0415028i
$653$	0.378115	+	0.218305i	0.0147968	+	0.00854292i	0.507380	−	0.861722i	$-0.330614\pi$
$653$	0.378115	+	0.218305i	0.0147968	+	0.00854292i	−0.492583	+	0.870265i	$0.663947\pi$
$654$		0			0
$655$	14.8688	−	8.58449i	0.580971	−	0.335424i
$656$	27.6286	+	3.63485i	1.07872	+	0.141917i
$657$		0			0
$658$	3.14216	+	25.3071i	0.122494	+	0.986573i
$659$	−26.0531			−1.01489			−0.507443	−	0.861685i	$-0.669409\pi$
$659$	−26.0531			−1.01489			−0.507443	+	0.861685i	$0.669409\pi$
$660$		0			0
$661$	−19.9044	−	34.4754i	−0.774191	−	1.34094i	−0.935248	−	0.353993i	$-0.884824\pi$
$661$	−19.9044	−	34.4754i	−0.774191	−	1.34094i	0.161057	−	0.986945i	$-0.448510\pi$
$662$	0.644421	−	3.90375i	0.0250461	−	0.151723i
$663$		0			0
$664$	−28.2697	−	15.1080i	−1.09708	−	0.586306i
$665$	8.16308	−	8.58749i	0.316551	−	0.333009i
$666$		0			0
$667$	29.2362	+	16.8795i	1.13203	+	0.653578i
$668$	10.2937	−	9.02816i	0.398276	−	0.349310i
$669$		0			0
$670$	2.28128	+	6.06079i	0.0881334	+	0.234149i
$671$	66.9179			2.58333
$672$		0			0
$673$	−8.26652			−0.318651			−0.159326	−	0.987226i	$-0.550932\pi$
$673$	−8.26652			−0.318651			−0.159326	+	0.987226i	$0.550932\pi$
$674$	−1.68557	−	4.47814i	−0.0649257	−	0.172492i
$675$		0			0
$676$	18.5459	−	16.2658i	0.713303	−	0.625607i
$677$	−3.77905	−	2.18184i	−0.145241	−	0.0838548i	0.425619	−	0.904903i	$-0.360057\pi$
$677$	−3.77905	−	2.18184i	−0.145241	−	0.0838548i	−0.570859	+	0.821048i	$0.693390\pi$
$678$		0			0
$679$	6.08924	+	20.6211i	0.233684	+	0.791367i
$680$	−4.57804	−	2.44662i	−0.175560	−	0.0938236i
$681$		0			0
$682$	10.0440	−	60.8438i	0.384603	−	2.32983i
$683$	11.8552	+	20.5339i	0.453628	+	0.785706i	0.998608	−	0.0527426i	$-0.0167963\pi$
$683$	11.8552	+	20.5339i	0.453628	+	0.785706i	−0.544981	+	0.838449i	$0.683463\pi$
$684$		0			0
$685$	13.3660			0.510688
$686$	8.96642	−	24.6090i	0.342340	−	0.939576i
$687$		0			0
$688$	2.02353	+	0.266218i	0.0771462	+	0.0101494i
$689$	2.44705	−	1.41280i	0.0932250	−	0.0538235i
$690$		0			0
$691$	−19.8985	−	11.4884i	−0.756974	−	0.437039i	0.0712345	−	0.997460i	$-0.477306\pi$
$691$	−19.8985	−	11.4884i	−0.756974	−	0.437039i	−0.828208	+	0.560421i	$0.810639\pi$
$692$	−16.2933	+	3.24170i	−0.619378	+	0.123231i
$693$		0			0
$694$	3.52695	−	4.29780i	0.133881	−	0.163142i
$695$	9.31039	−	16.1261i	0.353163	−	0.611697i
$696$		0			0
$697$	5.91328	+	10.2421i	0.223982	+	0.387947i
$698$	8.03239	+	21.3401i	0.304030	+	0.807735i
$699$		0			0
$700$	−0.812191	+	20.2569i	−0.0306979	+	0.765640i
$701$			37.9118i			1.43191i	0.698146	+	0.715955i	$0.254009\pi$
$701$			37.9118i			1.43191i	−0.698146	+	0.715955i	$0.745991\pi$
$702$		0			0
$703$	24.2492	−	14.0003i	0.914577	−	0.528031i
$704$	−17.2602	+	35.0122i	−0.650519	+	1.31957i
$705$		0			0
$706$	−40.6807	−	33.3842i	−1.53104	−	1.25643i
$707$	2.92366	+	2.77917i	0.109956	+	0.104521i
$708$		0			0
$709$	14.4546	−	25.0361i	0.542855	−	0.940252i	−0.455884	−	0.890039i	$-0.650677\pi$
$709$	14.4546	−	25.0361i	0.542855	−	0.940252i	0.998739	−	0.0502127i	$-0.0159899\pi$
$710$	−2.95220	+	17.8837i	−0.110794	+	0.671165i
$711$		0			0
$712$	0.540633	+	0.869278i	0.0202611	+	0.0325776i
$713$			31.3932i			1.17568i
$714$		0			0
$715$			4.30441i			0.160976i
$716$	−39.7082	−	13.4771i	−1.48397	−	0.503664i
$717$		0			0
$718$	30.0750	+	4.96471i	1.12239	+	0.185281i
$719$	15.2533	−	26.4195i	0.568852	−	0.985280i	−0.427828	−	0.903860i	$-0.640721\pi$
$719$	15.2533	−	26.4195i	0.568852	−	0.985280i	0.996680	−	0.0814198i	$-0.0259454\pi$
$720$		0			0
$721$	−4.79523	+	19.8992i	−0.178584	+	0.741085i
$722$	1.65143	−	2.01237i	0.0614599	−	0.0748925i
$723$		0			0
$724$	−26.8483	+	23.5475i	−0.997810	+	0.875135i
$725$	31.8859	−	18.4093i	1.18421	−	0.683706i
$726$		0			0
$727$		−	19.4515i		−	0.721415i	−0.932679	−	0.360708i	$-0.882535\pi$
$727$		−	19.4515i		−	0.721415i	0.932679	−	0.360708i	$-0.117465\pi$
$728$	1.23513	−	5.98014i	0.0457771	−	0.221639i
$729$		0			0
$730$	4.28622	−	1.61333i	0.158640	−	0.0597120i
$731$	0.433091	+	0.750135i	0.0160184	+	0.0277447i
$732$		0			0
$733$	−9.52314	+	16.4946i	−0.351745	+	0.609241i	−0.986555	−	0.163428i	$-0.947745\pi$
$733$	−9.52314	+	16.4946i	−0.351745	+	0.609241i	0.634810	+	0.772668i	$0.281078\pi$
$734$	1.84253	+	1.51205i	0.0680089	+	0.0558109i
$735$		0			0
$736$	5.76638	−	19.0169i	0.212552	−	0.700972i
$737$	17.8990	+	10.3340i	0.659320	+	0.380658i
$738$		0			0
$739$	26.3030	−	15.1860i	0.967571	−	0.558628i	0.0690765	−	0.997611i	$-0.477995\pi$
$739$	26.3030	−	15.1860i	0.967571	−	0.558628i	0.898495	+	0.438984i	$0.144661\pi$
$740$	4.69728	−	13.8398i	0.172675	−	0.508760i
$741$		0			0
$742$	−5.04632	+	11.9334i	−0.185256	+	0.438087i
$743$	−13.1841			−0.483676			−0.241838	−	0.970317i	$-0.577750\pi$
$743$	−13.1841			−0.483676			−0.241838	+	0.970317i	$0.577750\pi$
$744$		0			0
$745$	−6.22288	−	10.7783i	−0.227989	−	0.394888i
$746$	5.98765	+	0.988427i	0.219223	+	0.0361889i
$747$		0			0
$748$	−16.2481	+	3.23271i	−0.594090	+	0.118200i
$749$	−3.10161	−	0.747414i	−0.113331	−	0.0273099i
$750$		0			0
$751$	−28.5934	−	16.5084i	−1.04339	−	0.602400i	−0.122596	−	0.992457i	$-0.539122\pi$
$751$	−28.5934	−	16.5084i	−1.04339	−	0.602400i	−0.920791	+	0.390057i	$0.872455\pi$
$752$	−21.6300	−	16.5942i	−0.788765	−	0.605128i
$753$		0			0
$754$	−10.3790	+	3.90666i	−0.377982	+	0.142272i
$755$	11.6189			0.422853
$756$		0			0
$757$	−31.2886			−1.13720			−0.568601	−	0.822613i	$-0.692515\pi$
$757$	−31.2886			−1.13720			−0.568601	+	0.822613i	$0.692515\pi$
$758$	−3.97146	+	1.49485i	−0.144250	+	0.0542956i
$759$		0			0
$760$	0.415282	+	12.6595i	0.0150639	+	0.459208i
$761$	4.37627	+	2.52664i	0.158640	+	0.0915906i	0.577218	−	0.816590i	$-0.304138\pi$
$761$	4.37627	+	2.52664i	0.158640	+	0.0915906i	−0.418579	+	0.908181i	$0.637472\pi$
$762$		0			0
$763$	−1.14535	+	1.20490i	−0.0414644	+	0.0436203i
$764$	−7.11024	−	35.7372i	−0.257240	−	1.29293i
$765$		0			0
$766$	29.4794	+	4.86638i	1.06513	+	0.175830i
$767$	−2.04588	−	3.54357i	−0.0738726	−	0.127951i
$768$		0			0
$769$	−5.29930			−0.191098			−0.0955489	−	0.995425i	$-0.530461\pi$
$769$	−5.29930			−0.191098			−0.0955489	+	0.995425i	$0.530461\pi$
$770$	−11.8996	−	15.7468i	−0.428832	−	0.567477i
$771$		0			0
$772$	35.4304	+	12.0252i	1.27517	+	0.432797i
$773$	−20.1963	+	11.6604i	−0.726411	+	0.419394i	−0.817108	−	0.576485i	$-0.804424\pi$
$773$	−20.1963	+	11.6604i	−0.726411	+	0.419394i	0.0906965	+	0.995879i	$0.471091\pi$
$774$		0			0
$775$	29.6513	+	17.1192i	1.06511	+	0.614940i
$776$	−20.2725	−	10.8341i	−0.727742	−	0.388923i
$777$		0			0
$778$	37.3440	+	30.6460i	1.33885	+	1.09871i
$779$	14.4293	−	24.9922i	0.516982	−	0.895439i
$780$		0			0
$781$	28.9244	+	50.0986i	1.03500	+	1.79267i
$782$	7.89300	−	2.97092i	0.282253	−	0.106240i
$783$		0			0
$784$	12.0137	+	25.2917i	0.429061	+	0.903276i
$785$			25.3063i			0.903220i
$786$		0			0
$787$	36.4126	−	21.0228i	1.29797	−	0.749383i	0.317917	−	0.948119i	$-0.397017\pi$
$787$	36.4126	−	21.0228i	1.29797	−	0.749383i	0.980053	+	0.198735i	$0.0636834\pi$
$788$	−29.3058	−	33.4138i	−1.04398	−	1.19032i
$789$		0			0
$790$	3.82472	−	4.66065i	0.136077	−	0.165818i
$791$	−29.9086	+	8.83176i	−1.06343	+	0.314021i
$792$		0			0
$793$	5.59540	−	9.69152i	0.198699	−	0.344156i
$794$	23.5114	+	3.88120i	0.834388	+	0.137739i
$795$		0			0
$796$	−10.2813	+	30.2923i	−0.364412	+	1.07368i
$797$			21.9503i			0.777519i	0.921339	+	0.388760i	$0.127096\pi$
$797$			21.9503i			0.777519i	−0.921339	+	0.388760i	$0.872904\pi$
$798$		0			0
$799$		−	11.5700i		−	0.409317i
$800$	−14.8172	−	15.8167i	−0.523869	−	0.559203i
$801$		0			0
$802$	2.28456	−	13.8393i	0.0806705	−	0.488682i
$803$	7.30827	−	12.6583i	0.257903	−	0.446702i
$804$		0			0
$805$	7.28254	+	6.92262i	0.256676	+	0.243990i
$806$	−7.97200	−	6.54215i	−0.280802	−	0.230437i
$807$		0			0
$808$	−4.31000	+	0.141385i	−0.151625	+	0.00497392i
$809$	−42.1387	+	24.3288i	−1.48152	+	0.855355i	−0.999780	−	0.0209595i	$-0.993328\pi$
$809$	−42.1387	+	24.3288i	−1.48152	+	0.855355i	−0.481739	+	0.876315i	$0.659995\pi$
$810$		0			0
$811$		−	2.14916i		−	0.0754672i	−0.999288	−	0.0377336i	$-0.987986\pi$
$811$		−	2.14916i		−	0.0754672i	0.999288	−	0.0377336i	$-0.0120138\pi$
$812$	27.1696	−	42.9847i	0.953467	−	1.50847i
$813$		0			0
$814$	−16.4316	−	43.6547i	−0.575927	−	1.53010i
$815$	−1.46779	−	2.54228i	−0.0514144	−	0.0890523i
$816$		0			0
$817$	1.05680	−	1.83044i	0.0369729	−	0.0640389i
$818$	32.4513	−	39.5438i	1.13463	−	1.38262i
$819$		0			0
$820$	−2.93931	−	14.7734i	−0.102645	−	0.515910i
$821$	−11.4656	−	6.61966i	−0.400152	−	0.231028i	0.286398	−	0.958111i	$-0.407542\pi$
$821$	−11.4656	−	6.61966i	−0.400152	−	0.231028i	−0.686549	+	0.727083i	$0.740875\pi$
$822$		0			0
$823$	−48.8020	+	28.1759i	−1.70113	+	0.982149i	−0.756514	+	0.653977i	$0.773099\pi$
$823$	−48.8020	+	28.1759i	−1.70113	+	0.982149i	−0.944618	+	0.328172i	$0.893568\pi$
$824$	−11.5565	−	18.5815i	−0.402589	−	0.647319i
$825$		0			0
$826$	17.2807	+	7.30759i	0.601273	+	0.254264i
$827$	44.4024			1.54402			0.772011	−	0.635609i	$-0.219251\pi$
$827$	44.4024			1.54402			0.772011	+	0.635609i	$0.219251\pi$
$828$		0			0
$829$	16.2282	+	28.1080i	0.563627	+	0.976231i	0.997176	+	0.0751011i	$0.0239279\pi$
$829$	16.2282	+	28.1080i	0.563627	+	0.976231i	−0.433549	+	0.901130i	$0.642739\pi$
$830$	−2.82197	+	17.0948i	−0.0979520	+	0.593369i
$831$		0			0
$832$	3.62748	+	5.42733i	0.125760	+	0.188159i
$833$	−5.41279	+	10.5788i	−0.187542	+	0.366534i
$834$		0			0
$835$	−6.40945	−	3.70050i	−0.221808	−	0.128061i
$836$	26.6553	+	30.3918i	0.921893	+	1.05112i
$837$		0			0
$838$	−15.2992	−	40.6463i	−0.528503	−	1.40410i
$839$	−25.8761			−0.893342			−0.446671	−	0.894698i	$-0.647391\pi$
$839$	−25.8761			−0.893342			−0.446671	+	0.894698i	$0.647391\pi$
$840$		0			0
$841$	−63.3527			−2.18458
$842$	5.43205	+	14.4316i	0.187201	+	0.497347i
$843$		0			0
$844$	−10.9731	−	12.5113i	−0.377710	−	0.430657i
$845$	−11.5477	−	6.66707i	−0.397253	−	0.229354i
$846$		0			0
$847$	−32.9460	−	7.93919i	−1.13204	−	0.272794i
$848$	−5.30172	−	12.7962i	−0.182062	−	0.439424i
$849$		0			0
$850$	1.49810	−	9.07515i	0.0513845	−	0.311275i
$851$	11.8728	+	20.5643i	0.406995	+	0.704936i
$852$		0			0
$853$	14.9017			0.510225			0.255113	−	0.966911i	$-0.417887\pi$
$853$	14.9017			0.510225			0.255113	+	0.966911i	$0.417887\pi$
$854$	6.32268	+	50.9231i	0.216358	+	1.74255i
$855$		0			0
$856$	2.89623	−	1.80126i	0.0989912	−	0.0615660i
$857$	−17.4299	+	10.0632i	−0.595395	+	0.343751i	−0.767228	−	0.641375i	$-0.778364\pi$
$857$	−17.4299	+	10.0632i	−0.595395	+	0.343751i	0.171833	+	0.985126i	$0.445031\pi$
$858$		0			0
$859$	−9.71584	−	5.60944i	−0.331500	−	0.191392i	0.325007	−	0.945712i	$-0.394633\pi$
$859$	−9.71584	−	5.60944i	−0.331500	−	0.191392i	−0.656507	+	0.754320i	$0.727967\pi$
$860$	−0.215276	−	1.08201i	−0.00734084	−	0.0368962i
$861$		0			0
$862$	−14.0523	+	17.1236i	−0.478623	+	0.583231i
$863$	16.4955	−	28.5711i	0.561514	−	0.972571i	−0.435850	−	0.900019i	$-0.643552\pi$
$863$	16.4955	−	28.5711i	0.561514	−	0.972571i	0.997365	−	0.0725520i	$-0.0231143\pi$
$864$		0			0
$865$	4.48988	+	7.77670i	0.152660	+	0.264416i
$866$	−11.4063	−	30.3036i	−0.387600	−	1.02976i
$867$		0			0
$868$	47.2499	+	1.89446i	1.60376	+	0.0643021i
$869$		−	19.2420i		−	0.652742i
$870$		0			0
$871$	2.99329	−	1.72818i	0.101424	−	0.0585571i
$872$	−0.0582677	−	1.77624i	−0.00197319	−	0.0601509i
$873$		0			0
$874$	−15.9083	−	13.0550i	−0.538105	−	0.441591i
$875$	24.2256	−	7.15361i	0.818974	−	0.241836i
$876$		0			0
$877$	17.8909	−	30.9880i	0.604134	−	1.04639i	−0.388054	−	0.921637i	$-0.626852\pi$
$877$	17.8909	−	30.9880i	0.604134	−	1.04639i	0.992188	−	0.124754i	$-0.0398142\pi$
$878$	3.98693	−	24.1519i	0.134552	−	0.815086i
$879$		0			0
$880$	20.9199	+	2.75224i	0.705209	+	0.0927781i
$881$		−	3.68853i		−	0.124270i	−0.998068	−	0.0621348i	$-0.980209\pi$
$881$		−	3.68853i		−	0.124270i	0.998068	−	0.0621348i	$-0.0197909\pi$
$882$		0			0
$883$		−	12.4938i		−	0.420449i	−0.977653	−	0.210224i	$-0.932581\pi$
$883$		−	12.4938i		−	0.420449i	0.977653	−	0.210224i	$-0.0674195\pi$
$884$	−0.890418	+	2.62347i	−0.0299480	+	0.0882370i
$885$		0			0
$886$	−15.8863	−	2.62248i	−0.533711	−	0.0881038i
$887$	−0.427511	+	0.740471i	−0.0143544	+	0.0248626i	−0.873113	−	0.487517i	$-0.837903\pi$
$887$	−0.427511	+	0.740471i	−0.0143544	+	0.0248626i	0.858759	+	0.512380i	$0.171236\pi$
$888$		0			0
$889$	13.8678	−	4.09504i	0.465111	−	0.137343i
$890$	0.351025	−	0.427745i	0.0117664	−	0.0143381i
$891$		0			0
$892$	−11.7539	−	13.4015i	−0.393550	−	0.448717i
$893$	−24.4500	+	14.1162i	−0.818190	+	0.472382i
$894$		0			0
$895$			22.6664i			0.757653i
$896$	−28.2743	−	9.82658i	−0.944579	−	0.328283i
$897$		0			0
$898$	14.7032	−	5.53426i	0.490652	−	0.184681i
$899$	−42.9403	−	74.3748i	−1.43214	−	2.48054i
$900$		0			0
$901$	2.93918	−	5.09081i	0.0979183	−	0.169599i
$902$	−37.1623	−	30.4969i	−1.23737	−	1.01544i
$903$		0			0
$904$	15.7137	−	29.4030i	0.522630	−	0.977930i
$905$	16.7173	+	9.65172i	0.555701	+	0.320834i
$906$		0			0
$907$	25.5068	−	14.7264i	0.846939	−	0.488981i	−0.0126776	−	0.999920i	$-0.504036\pi$
$907$	25.5068	−	14.7264i	0.846939	−	0.488981i	0.859617	+	0.510939i	$0.170702\pi$
$908$	38.6901	+	13.1316i	1.28398	+	0.435787i
$909$		0			0
$910$	−3.27557	+	0.406699i	−0.108584	+	0.0134819i
$911$	9.62988			0.319052			0.159526	−	0.987194i	$-0.449003\pi$
$911$	9.62988			0.319052			0.159526	+	0.987194i	$0.449003\pi$
$912$		0			0
$913$	27.6484	+	47.8885i	0.915030	+	1.58488i
$914$	−37.8575	−	6.24943i	−1.25222	−	0.206713i
$915$		0			0
$916$	4.85000	+	24.3769i	0.160249	+	0.805435i
$917$	40.8489	+	9.84360i	1.34895	+	0.325064i
$918$		0			0
$919$	−5.68583	−	3.28272i	−0.187558	−	0.108287i	0.403281	−	0.915076i	$-0.367870\pi$
$919$	−5.68583	−	3.28272i	−0.187558	−	0.108287i	−0.590839	+	0.806790i	$0.701203\pi$
$920$	−10.7358	+	0.352176i	−0.353947	+	0.0116109i
$921$		0			0
$922$	17.5409	−	6.60239i	0.577680	−	0.217438i
$923$	9.67418			0.318429
$924$		0			0
$925$	25.8977			0.851512
$926$	5.38935	−	2.02854i	0.177105	−	0.0666621i
$927$		0			0
$928$	12.3504	+	52.9411i	0.405421	+	1.73788i
$929$	18.6881	+	10.7896i	0.613137	+	0.353995i	0.774192	−	0.632951i	$-0.218156\pi$
$929$	18.6881	+	10.7896i	0.613137	+	0.353995i	−0.161055	+	0.986945i	$0.551490\pi$
$930$		0			0
$931$	28.9594	−	1.46845i	0.949106	−	0.0481265i
$932$	4.94330	−	0.983513i	0.161923	−	0.0322161i
$933$		0			0
$934$	−32.7982	−	5.41425i	−1.07319	−	0.177160i
$935$	4.47743	+	7.75514i	0.146428	+	0.253620i
$936$		0			0
$937$	−38.5055			−1.25792			−0.628960	−	0.777437i	$-0.716519\pi$
$937$	−38.5055			−1.25792			−0.628960	+	0.777437i	$0.716519\pi$
$938$	−6.17279	+	14.5972i	−0.201549	+	0.476615i
$939$		0			0
$940$	−4.73618	+	13.9544i	−0.154477	+	0.455142i
$941$	−1.30779	+	0.755052i	−0.0426327	+	0.0246140i	−0.521165	−	0.853456i	$-0.674502\pi$
$941$	−1.30779	+	0.755052i	−0.0426327	+	0.0246140i	0.478532	+	0.878070i	$0.341169\pi$
$942$		0			0
$943$	21.1944	+	12.2366i	0.690184	+	0.398478i
$944$	−18.5303	+	7.67743i	−0.603108	+	0.249879i
$945$		0			0
$946$	−2.72178	−	2.23361i	−0.0884927	−	0.0726208i
$947$	−2.64972	+	4.58945i	−0.0861044	+	0.149137i	−0.905861	−	0.423574i	$-0.860775\pi$
$947$	−2.64972	+	4.58945i	−0.0861044	+	0.149137i	0.819757	+	0.572712i	$0.194109\pi$
$948$		0			0
$949$	−1.22218	−	2.11687i	−0.0396735	−	0.0687166i
$950$	−21.0056	+	7.90650i	−0.681513	+	0.256521i
$951$		0			0
$952$	−3.99521	−	12.0590i	−0.129486	−	0.390835i
$953$			60.6268i			1.96390i	0.189151	+	0.981948i	$0.439426\pi$
$953$			60.6268i			1.96390i	−0.189151	+	0.981948i	$0.560574\pi$
$954$		0			0
$955$	−17.0572	+	9.84797i	−0.551958	+	0.318673i
$956$	37.9851	−	33.3150i	1.22853	−	1.07749i
$957$		0			0
$958$	3.33899	−	4.06875i	0.107878	−	0.131455i
$959$	23.7086	+	22.5369i	0.765592	+	0.727754i
$960$		0			0
$961$	24.4310	−	42.3158i	0.788098	−	1.36503i
$962$	−7.69633	−	1.27049i	−0.248140	−	0.0409623i
$963$		0			0
$964$	−27.7154	−	9.40671i	−0.892652	−	0.302970i
$965$		−	20.2245i		−	0.651049i
$966$		0			0
$967$			43.5917i			1.40181i	0.713253	+	0.700907i	$0.247221\pi$
$967$			43.5917i			1.40181i	−0.713253	+	0.700907i	$0.752779\pi$
$968$	30.7644	−	19.1334i	0.988806	−	0.614972i
$969$		0			0
$970$	−2.02367	+	12.2589i	−0.0649760	+	0.393609i
$971$	−9.75149	+	16.8901i	−0.312940	+	0.542028i	−0.978997	−	0.203872i	$-0.934647\pi$
$971$	−9.75149	+	16.8901i	−0.312940	+	0.542028i	0.666057	+	0.745901i	$0.267981\pi$
$972$		0			0
$973$	43.7056	−	12.9059i	1.40114	−	0.413743i
$974$	18.3920	+	15.0932i	0.589317	+	0.483618i
$975$		0			0
$976$	−43.5240	−	33.3910i	−1.39317	−	1.06882i
$977$	51.2227	−	29.5734i	1.63876	−	0.946137i	0.657496	−	0.753458i	$-0.271616\pi$
$977$	51.2227	−	29.5734i	1.63876	−	0.946137i	0.981262	−	0.192679i	$-0.0617177\pi$
$978$		0			0
$979$		−	1.76600i		−	0.0564416i
$980$	10.8587	−	10.5432i	0.346868	−	0.336790i
$981$		0			0
$982$	3.36642	+	8.94376i	0.107427	+	0.285407i
$983$	21.1885	+	36.6996i	0.675809	+	1.17054i	0.976232	+	0.216729i	$0.0695389\pi$
$983$	21.1885	+	36.6996i	0.675809	+	1.17054i	−0.300423	+	0.953806i	$0.597128\pi$
$984$		0			0
$985$	−12.0120	+	20.8053i	−0.382733	+	0.662913i
$986$	−14.6359	+	17.8347i	−0.466103	+	0.567974i
$987$		0			0
$988$	6.63037	−	1.31917i	0.210940	−	0.0419684i
$989$	1.55228	+	0.896211i	0.0493597	+	0.0284979i
$990$		0			0
$991$	17.1417	−	9.89678i	0.544525	−	0.314381i	−0.202386	−	0.979306i	$-0.564870\pi$
$991$	17.1417	−	9.89678i	0.544525	−	0.314381i	0.746911	+	0.664924i	$0.231536\pi$
$992$	−36.8928	+	34.5616i	−1.17135	+	1.09733i
$993$		0			0
$994$	−35.3911	+	26.7444i	−1.12254	+	0.848281i
$995$	17.2916			0.548179
$996$		0			0
$997$	−20.1621	−	34.9217i	−0.638539	−	1.10598i	−0.985753	−	0.168197i	$-0.946206\pi$
$997$	−20.1621	−	34.9217i	−0.638539	−	1.10598i	0.347214	−	0.937786i	$-0.387128\pi$
$998$	3.98370	−	24.1323i	0.126102	−	0.763894i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	756.2.be.d.107.10	yes	28
3.2	odd	2	inner	756.2.be.d.107.5	yes	28
4.3	odd	2		756.2.be.c.107.14	yes	28
7.4	even	3		756.2.be.c.431.1	yes	28
12.11	even	2		756.2.be.c.107.1	✓	28
21.11	odd	6		756.2.be.c.431.14	yes	28
28.11	odd	6	inner	756.2.be.d.431.5	yes	28
84.11	even	6	inner	756.2.be.d.431.10	yes	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
756.2.be.c.107.1	✓	28	12.11	even	2
756.2.be.c.107.14	yes	28	4.3	odd	2
756.2.be.c.431.1	yes	28	7.4	even	3
756.2.be.c.431.14	yes	28	21.11	odd	6
756.2.be.d.107.5	yes	28	3.2	odd	2	inner
756.2.be.d.107.10	yes	28	1.1	even	1	trivial
756.2.be.d.431.5	yes	28	28.11	odd	6	inner
756.2.be.d.431.10	yes	28	84.11	even	6	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 756 = 2^{2} \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	756.be (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.498187 + 1.32356i) q^{2} +(-1.50362 + 1.31876i) q^{4} +(0.936239 + 0.540538i) q^{5} +(0.749282 + 2.53743i) q^{7} +(-2.49454 - 1.33314i) q^{8} +O(q^{10})\)	\(q+(0.498187 + 1.32356i) q^{2} +(-1.50362 + 1.31876i) q^{4} +(0.936239 + 0.540538i) q^{5} +(0.749282 + 2.53743i) q^{7} +(-2.49454 - 1.33314i) q^{8} +(-0.249012 + 1.50846i) q^{10} +(2.43972 + 4.22571i) q^{11} +0.815997 q^{13} +(-2.98516 + 2.25584i) q^{14} +(0.521749 - 3.96583i) q^{16} +(1.47016 - 0.848796i) q^{17} +(-3.58740 - 2.07119i) q^{19} +(-2.12059 + 0.421910i) q^{20} +(-4.37755 + 5.33430i) q^{22} +(1.75645 - 3.04226i) q^{23} +(-1.91564 - 3.31798i) q^{25} +(0.406519 + 1.08002i) q^{26} +(-4.47290 - 2.82722i) q^{28} +9.61003i q^{29} +(-7.73929 + 4.46828i) q^{31} +(5.50894 - 1.28516i) q^{32} +(1.85585 + 1.52298i) q^{34} +(-0.670072 + 2.78066i) q^{35} +(-3.37978 + 5.85395i) q^{37} +(0.954144 - 5.77997i) q^{38} +(-1.61487 - 2.59653i) q^{40} +6.96667i q^{41} +0.510241i q^{43} +(-9.24111 - 3.13647i) q^{44} +(4.90165 + 0.809152i) q^{46} +(3.40777 - 5.90243i) q^{47} +(-5.87715 + 3.80251i) q^{49} +(3.43720 - 4.18843i) q^{50} +(-1.22695 + 1.07610i) q^{52} +(2.99884 - 1.73138i) q^{53} +5.27504i q^{55} +(1.51365 - 7.32863i) q^{56} +(-12.7195 + 4.78759i) q^{58} +(-2.50722 - 4.34263i) q^{59} +(6.85713 - 11.8769i) q^{61} +(-9.76964 - 8.01737i) q^{62} +(4.44546 + 6.65116i) q^{64} +(0.763968 + 0.441077i) q^{65} +(3.66826 - 2.11787i) q^{67} +(-1.09120 + 3.21505i) q^{68} +(-4.01419 + 0.498407i) q^{70} +11.8557 q^{71} +(-1.49777 - 2.59421i) q^{73} +(-9.43181 - 1.55698i) q^{74} +(8.12548 - 1.61664i) q^{76} +(-8.89444 + 9.35688i) q^{77} +(-3.41517 - 1.97175i) q^{79} +(2.63216 - 3.43094i) q^{80} +(-9.22080 + 3.47070i) q^{82} +11.3326 q^{83} +1.83523 q^{85} +(-0.675334 + 0.254195i) q^{86} +(-0.452489 - 13.7937i) q^{88} +(-0.313438 - 0.180963i) q^{89} +(0.611412 + 2.07054i) q^{91} +(1.37097 + 6.89073i) q^{92} +(9.50992 + 1.56987i) q^{94} +(-2.23911 - 3.87825i) q^{95} +8.12677 q^{97} +(-7.96077 - 5.88440i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q - 4 q^{4} + 2 q^{7}+O(q^{10}) \) 28 * q - 4 * q^4 + 2 * q^7	\( 28 q - 4 q^{4} + 2 q^{7} + 4 q^{10} + 8 q^{13} + 12 q^{16} - 42 q^{19} + 4 q^{22} + 6 q^{25} + 24 q^{28} + 30 q^{31} + 24 q^{34} + 12 q^{37} + 24 q^{46} - 14 q^{49} - 24 q^{52} - 44 q^{58} + 6 q^{61} + 8 q^{64} + 24 q^{67} - 32 q^{70} - 22 q^{73} + 48 q^{79} + 36 q^{82} - 24 q^{85} - 4 q^{88} + 16 q^{91} + 60 q^{94} - 4 q^{97}+O(q^{100}) \) 28 * q - 4 * q^4 + 2 * q^7 + 4 * q^10 + 8 * q^13 + 12 * q^16 - 42 * q^19 + 4 * q^22 + 6 * q^25 + 24 * q^28 + 30 * q^31 + 24 * q^34 + 12 * q^37 + 24 * q^46 - 14 * q^49 - 24 * q^52 - 44 * q^58 + 6 * q^61 + 8 * q^64 + 24 * q^67 - 32 * q^70 - 22 * q^73 + 48 * q^79 + 36 * q^82 - 24 * q^85 - 4 * q^88 + 16 * q^91 + 60 * q^94 - 4 * q^97

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