LMFDB - Embedded newform 900.2.k.n.343.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [900,2,Mod(307,900)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(900, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 0, 1]))

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

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

chi := DirichletCharacter("900.307");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 900 = 2^{2} \cdot 3^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	900.k (of order $4$, 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:	$7.18653618192$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(i)$
Coefficient field:	12.0.426337261060096.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 4x^{9} - 3x^{8} + 4x^{7} + 8x^{6} + 8x^{5} - 12x^{4} - 32x^{3} + 64 $ x^12 - 4x^9 - 3x^8 + 4x^7 + 8x^6 + 8x^5 - 12x^4 - 32*x^3 + 64
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{6} $
Twist minimal:	no (minimal twist has level 60)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			343.6
Root			$-0.394157 - 1.35818i$ of defining polynomial
Character	$\chi$	$=$	900.343
Dual form			900.2.k.n.307.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.35818 - 0.394157i) q^{2} +(1.68928 - 1.07067i) q^{4} +(2.47817 + 2.47817i) q^{7} +(1.87233 - 2.12000i) q^{8} +O(q^{10})$	\(q+(1.35818 - 0.394157i) q^{2} +(1.68928 - 1.07067i) q^{4} +(2.47817 + 2.47817i) q^{7} +(1.87233 - 2.12000i) q^{8} -3.02831i q^{11} +(-0.363328 - 0.363328i) q^{13} +(4.34258 + 2.38900i) q^{14} +(1.70734 - 3.61732i) q^{16} +(-2.36333 + 2.36333i) q^{17} +4.95634 q^{19} +(-1.19363 - 4.11297i) q^{22} +(0.900390 - 0.900390i) q^{23} +(-0.636672 - 0.350255i) q^{26} +(6.83963 + 1.53303i) q^{28} +3.50466i q^{29} +3.85607i q^{31} +(0.893077 - 5.58591i) q^{32} +(-2.27829 + 4.14134i) q^{34} +(0.363328 - 0.363328i) q^{37} +(6.73158 - 1.95358i) q^{38} -2.72666 q^{41} +(3.92870 - 3.92870i) q^{43} +(-3.24231 - 5.11566i) q^{44} +(0.867993 - 1.57778i) q^{46} +(-5.85673 - 5.85673i) q^{47} +5.28267i q^{49} +(-1.00277 - 0.224760i) q^{52} +(3.14134 + 3.14134i) q^{53} +(9.89367 - 0.613763i) q^{56} +(1.38139 + 4.75995i) q^{58} +8.68516 q^{59} -15.2920 q^{61} +(1.51990 + 5.23723i) q^{62} +(-0.988770 - 7.93866i) q^{64} +(-3.92870 - 3.92870i) q^{67} +(-1.46199 + 6.52267i) q^{68} +4.25583i q^{71} +(-9.28267 - 9.28267i) q^{73} +(0.350255 - 0.636672i) q^{74} +(8.37266 - 5.30660i) q^{76} +(7.50466 - 7.50466i) q^{77} -0.399759 q^{79} +(-3.70328 + 1.07473i) q^{82} +(0.199879 - 0.199879i) q^{83} +(3.78734 - 6.88438i) q^{86} +(-6.42000 - 5.66999i) q^{88} +4.28267i q^{89} -1.80078i q^{91} +(0.556993 - 2.48503i) q^{92} +(-10.2629 - 5.64600i) q^{94} +(-6.73599 + 6.73599i) q^{97} +(2.08220 + 7.17480i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 12 q^{8}+O(q^{10}) $ 12 * q - 12 * q^8	$ 12 q - 12 q^{8} + 4 q^{13} + 12 q^{16} - 20 q^{17} - 12 q^{22} - 16 q^{26} + 4 q^{28} + 20 q^{32} - 4 q^{37} + 16 q^{38} - 16 q^{41} - 40 q^{46} + 8 q^{52} + 4 q^{53} + 64 q^{56} + 20 q^{58} - 32 q^{61} - 56 q^{62} - 16 q^{68} - 44 q^{73} + 8 q^{76} + 48 q^{77} - 16 q^{82} - 64 q^{86} - 60 q^{88} + 56 q^{92} + 20 q^{97} + 24 q^{98}+O(q^{100}) $ 12 * q - 12 * q^8 + 4 * q^13 + 12 * q^16 - 20 * q^17 - 12 * q^22 - 16 * q^26 + 4 * q^28 + 20 * q^32 - 4 * q^37 + 16 * q^38 - 16 * q^41 - 40 * q^46 + 8 * q^52 + 4 * q^53 + 64 * q^56 + 20 * q^58 - 32 * q^61 - 56 * q^62 - 16 * q^68 - 44 * q^73 + 8 * q^76 + 48 * q^77 - 16 * q^82 - 64 * q^86 - 60 * q^88 + 56 * q^92 + 20 * q^97 + 24 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/900\mathbb{Z}\right)^\times$.

$n$	$101$	$451$	$577$
$\chi(n)$	$1$	$-1$	$e\left(\frac{3}{4}\right)$

Coefficient data

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

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

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

$2$	1.35818	−	0.394157i	0.960375	−	0.278711i
$2$	1.35818	−	0.394157i	0.960375	−	0.278711i
$3$		0			0
$3$		0			0
$4$	1.68928	−	1.07067i	0.844640	−	0.535334i
$5$		0			0
$5$		0			0
$6$		0			0
$7$	2.47817	+	2.47817i	0.936661	+	0.936661i	0.998110	−	0.0614493i	$-0.0195722\pi$
$7$	2.47817	+	2.47817i	0.936661	+	0.936661i	−0.0614493	+	0.998110i	$0.519572\pi$
$8$	1.87233	−	2.12000i	0.661968	−	0.749532i
$9$		0			0
$10$		0			0
$11$		−	3.02831i		−	0.913069i	−0.889706	−	0.456534i	$-0.849091\pi$
$11$		−	3.02831i		−	0.913069i	0.889706	−	0.456534i	$-0.150909\pi$
$12$		0			0
$13$	−0.363328	−	0.363328i	−0.100769	−	0.100769i	0.654925	−	0.755694i	$-0.272700\pi$
$13$	−0.363328	−	0.363328i	−0.100769	−	0.100769i	−0.755694	+	0.654925i	$0.772700\pi$
$14$	4.34258	+	2.38900i	1.16060	+	0.638488i
$15$		0			0
$16$	1.70734	−	3.61732i	0.426835	−	0.904330i
$17$	−2.36333	+	2.36333i	−0.573191	+	0.573191i	−0.933019	−	0.359828i	$-0.882836\pi$
$17$	−2.36333	+	2.36333i	−0.573191	+	0.573191i	0.359828	+	0.933019i	$0.382836\pi$
$18$		0			0
$19$	4.95634			1.13706			0.568532	−	0.822661i	$-0.307512\pi$
$19$	4.95634			1.13706			0.568532	+	0.822661i	$0.307512\pi$
$20$		0			0
$21$		0			0
$22$	−1.19363	−	4.11297i	−0.254482	−	0.876888i
$23$	0.900390	−	0.900390i	0.187744	−	0.187744i	−0.606976	−	0.794720i	$-0.707618\pi$
$23$	0.900390	−	0.900390i	0.187744	−	0.187744i	0.794720	+	0.606976i	$0.207618\pi$
$24$		0			0
$25$		0			0
$26$	−0.636672	−	0.350255i	−0.124862	−	0.0686907i
$27$		0			0
$28$	6.83963	+	1.53303i	1.29257	+	0.289715i
$29$			3.50466i			0.650800i	0.945576	+	0.325400i	$0.105499\pi$
$29$			3.50466i			0.650800i	−0.945576	+	0.325400i	$0.894501\pi$
$30$		0			0
$31$			3.85607i			0.692571i	0.938129	+	0.346286i	$0.112557\pi$
$31$			3.85607i			0.692571i	−0.938129	+	0.346286i	$0.887443\pi$
$32$	0.893077	−	5.58591i	0.157875	−	0.987459i
$33$		0			0
$34$	−2.27829	+	4.14134i	−0.390724	+	0.710233i
$35$		0			0
$36$		0			0
$37$	0.363328	−	0.363328i	0.0597308	−	0.0597308i	−0.676610	−	0.736341i	$-0.736552\pi$
$37$	0.363328	−	0.363328i	0.0597308	−	0.0597308i	0.736341	+	0.676610i	$0.236552\pi$
$38$	6.73158	−	1.95358i	1.09201	−	0.316912i
$39$		0			0
$40$		0			0
$41$	−2.72666			−0.425832			−0.212916	−	0.977070i	$-0.568296\pi$
$41$	−2.72666			−0.425832			−0.212916	+	0.977070i	$0.568296\pi$
$42$		0			0
$43$	3.92870	−	3.92870i	0.599121	−	0.599121i	−0.340958	−	0.940079i	$-0.610751\pi$
$43$	3.92870	−	3.92870i	0.599121	−	0.599121i	0.940079	+	0.340958i	$0.110751\pi$
$44$	−3.24231	−	5.11566i	−0.488797	−	0.771215i
$45$		0			0
$46$	0.867993	−	1.57778i	0.127979	−	0.232631i
$47$	−5.85673	−	5.85673i	−0.854292	−	0.854292i	0.136366	−	0.990659i	$-0.456458\pi$
$47$	−5.85673	−	5.85673i	−0.854292	−	0.854292i	−0.990659	+	0.136366i	$0.956458\pi$
$48$		0			0
$49$			5.28267i			0.754667i
$50$		0			0
$51$		0			0
$52$	−1.00277	−	0.224760i	−0.139059	−	0.0311685i
$53$	3.14134	+	3.14134i	0.431496	+	0.431496i	0.889137	−	0.457641i	$-0.151306\pi$
$53$	3.14134	+	3.14134i	0.431496	+	0.431496i	−0.457641	+	0.889137i	$0.651306\pi$
$54$		0			0
$55$		0			0
$56$	9.89367	−	0.613763i	1.32210	−	0.0820176i
$57$		0			0
$58$	1.38139	+	4.75995i	0.181385	+	0.625012i
$59$	8.68516			1.13071			0.565356	−	0.824847i	$-0.308739\pi$
$59$	8.68516			1.13071			0.565356	+	0.824847i	$0.308739\pi$
$60$		0			0
$61$	−15.2920			−1.95794			−0.978970	−	0.204004i	$-0.934604\pi$
$61$	−15.2920			−1.95794			−0.978970	+	0.204004i	$0.934604\pi$
$62$	1.51990	+	5.23723i	0.193027	+	0.665128i
$63$		0			0
$64$	−0.988770	−	7.93866i	−0.123596	−	0.992333i
$65$		0			0
$66$		0			0
$67$	−3.92870	−	3.92870i	−0.479967	−	0.479967i	0.425154	−	0.905121i	$-0.360220\pi$
$67$	−3.92870	−	3.92870i	−0.479967	−	0.479967i	−0.905121	+	0.425154i	$0.860220\pi$
$68$	−1.46199	+	6.52267i	−0.177292	+	0.790989i
$69$		0			0
$70$		0			0
$71$			4.25583i			0.505075i	0.967587	+	0.252537i	$0.0812650\pi$
$71$			4.25583i			0.505075i	−0.967587	+	0.252537i	$0.918735\pi$
$72$		0			0
$73$	−9.28267	−	9.28267i	−1.08645	−	1.08645i	−0.995891	−	0.0905640i	$-0.971133\pi$
$73$	−9.28267	−	9.28267i	−1.08645	−	1.08645i	−0.0905640	−	0.995891i	$-0.528867\pi$
$74$	0.350255	−	0.636672i	0.0407163	−	0.0740116i
$75$		0			0
$76$	8.37266	−	5.30660i	0.960410	−	0.608709i
$77$	7.50466	−	7.50466i	0.855236	−	0.855236i
$78$		0			0
$79$	−0.399759			−0.0449764			−0.0224882	−	0.999747i	$-0.507159\pi$
$79$	−0.399759			−0.0449764			−0.0224882	+	0.999747i	$0.507159\pi$
$80$		0			0
$81$		0			0
$82$	−3.70328	+	1.07473i	−0.408959	+	0.118684i
$83$	0.199879	−	0.199879i	0.0219396	−	0.0219396i	−0.696052	−	0.717991i	$-0.745062\pi$
$83$	0.199879	−	0.199879i	0.0219396	−	0.0219396i	0.717991	+	0.696052i	$0.245062\pi$
$84$		0			0
$85$		0			0
$86$	3.78734	−	6.88438i	0.408399	−	0.742362i
$87$		0			0
$88$	−6.42000	−	5.66999i	−0.684374	−	0.604422i
$89$			4.28267i			0.453962i	0.973899	+	0.226981i	$0.0728856\pi$
$89$			4.28267i			0.453962i	−0.973899	+	0.226981i	$0.927114\pi$
$90$		0			0
$91$		−	1.80078i		−	0.188773i
$92$	0.556993	−	2.48503i	0.0580705	−	0.259082i
$93$		0			0
$94$	−10.2629	−	5.64600i	−1.05854	−	0.582340i
$95$		0			0
$96$		0			0
$97$	−6.73599	+	6.73599i	−0.683936	+	0.683936i	−0.960885	−	0.276949i	$-0.910677\pi$
$97$	−6.73599	+	6.73599i	−0.683936	+	0.683936i	0.276949	+	0.960885i	$0.410677\pi$
$98$	2.08220	+	7.17480i	0.210334	+	0.724764i
$99$		0			0
$100$		0			0
$101$	−5.78734			−0.575862			−0.287931	−	0.957651i	$-0.592967\pi$
$101$	−5.78734			−0.575862			−0.287931	+	0.957651i	$0.592967\pi$
$102$		0			0
$103$	−13.0914	+	13.0914i	−1.28993	+	1.28993i	−0.355104	+	0.934827i	$0.615555\pi$
$103$	−13.0914	+	13.0914i	−1.28993	+	1.28993i	−0.934827	+	0.355104i	$0.884445\pi$
$104$	−1.45052	+	0.0899847i	−0.142236	+	0.00882373i
$105$		0			0
$106$	5.50466	+	3.02831i	0.534660	+	0.294135i
$107$	9.71281	+	9.71281i	0.938973	+	0.938973i	0.998242	−	0.0592694i	$-0.0188771\pi$
$107$	9.71281	+	9.71281i	0.938973	+	0.938973i	−0.0592694	+	0.998242i	$0.518877\pi$
$108$		0			0
$109$			10.4626i			1.00214i	0.865407	+	0.501070i	$0.167060\pi$
$109$			10.4626i			1.00214i	−0.865407	+	0.501070i	$0.832940\pi$
$110$		0			0
$111$		0			0
$112$	13.1954	−	4.73325i	1.24685	−	0.447251i
$113$	−10.6460	−	10.6460i	−1.00149	−	1.00149i	−0.999999	−	0.00149259i	$-0.999525\pi$
$113$	−10.6460	−	10.6460i	−1.00149	−	1.00149i	−0.00149259	−	0.999999i	$-0.500475\pi$
$114$		0			0
$115$		0			0
$116$	3.75233	+	5.92036i	0.348395	+	0.549692i
$117$		0			0
$118$	11.7960	−	3.42331i	1.08591	−	0.315142i
$119$	−11.7135			−1.07377
$120$		0			0
$121$	1.82936			0.166305
$122$	−20.7692	+	6.02745i	−1.88036	+	0.545699i
$123$		0			0
$124$	4.12858	+	6.51399i	0.370757	+	0.584974i
$125$		0			0
$126$		0			0
$127$	−1.77766	−	1.77766i	−0.157742	−	0.157742i	0.623823	−	0.781565i	$-0.285578\pi$
$127$	−1.77766	−	1.77766i	−0.157742	−	0.157742i	−0.781565	+	0.623823i	$0.785578\pi$
$128$	−4.47200	−	10.3924i	−0.395273	−	0.918564i
$129$		0			0
$130$		0			0
$131$			18.1981i			1.58997i	0.606626	+	0.794987i	$0.292523\pi$
$131$			18.1981i			1.58997i	−0.606626	+	0.794987i	$0.707477\pi$
$132$		0			0
$133$	12.2827	+	12.2827i	1.06504	+	1.06504i
$134$	−6.88438	−	3.78734i	−0.594720	−	0.327176i
$135$		0			0
$136$	0.585320	+	9.43517i	0.0501908	+	0.809060i
$137$	−5.91934	+	5.91934i	−0.505724	+	0.505724i	−0.913211	−	0.407487i	$-0.866405\pi$
$137$	−5.91934	+	5.91934i	−0.505724	+	0.505724i	0.407487	+	0.913211i	$0.366405\pi$
$138$		0			0
$139$	−12.4140			−1.05294			−0.526470	−	0.850194i	$-0.676485\pi$
$139$	−12.4140			−1.05294			−0.526470	+	0.850194i	$0.676485\pi$
$140$		0			0
$141$		0			0
$142$	1.67747	+	5.78017i	0.140770	+	0.485061i
$143$	−1.10027	+	1.10027i	−0.0920091	+	0.0920091i
$144$		0			0
$145$		0			0
$146$	−16.2663	−	8.94867i	−1.34621	−	0.740597i
$147$		0			0
$148$	0.224760	−	1.00277i	0.0184751	−	0.0824270i
$149$		−	5.78734i		−	0.474117i	−0.971495	−	0.237059i	$-0.923817\pi$
$149$		−	5.78734i		−	0.474117i	0.971495	−	0.237059i	$-0.0761833\pi$
$150$		0			0
$151$			18.0708i			1.47058i	0.677751	+	0.735292i	$0.262955\pi$
$151$			18.0708i			1.47058i	−0.677751	+	0.735292i	$0.737045\pi$
$152$	9.27990	−	10.5074i	0.752700	−	0.852265i
$153$		0			0
$154$	7.23464	−	13.1507i	0.582984	−	1.05971i
$155$		0			0
$156$		0			0
$157$	3.91934	−	3.91934i	0.312798	−	0.312798i	−0.533195	−	0.845992i	$-0.679009\pi$
$157$	3.91934	−	3.91934i	0.312798	−	0.312798i	0.845992	+	0.533195i	$0.179009\pi$
$158$	−0.542943	+	0.157568i	−0.0431942	+	0.0125354i
$159$		0			0
$160$		0			0
$161$	4.46264			0.351705
$162$		0			0
$163$	−3.22819	+	3.22819i	−0.252851	+	0.252851i	−0.822139	−	0.569287i	$-0.807219\pi$
$163$	−3.22819	+	3.22819i	−0.252851	+	0.252851i	0.569287	+	0.822139i	$0.307219\pi$
$164$	−4.60609	+	2.91934i	−0.359675	+	0.227962i
$165$		0			0
$166$	0.192688	−	0.350255i	0.0149555	−	0.0271851i
$167$	6.95700	+	6.95700i	0.538349	+	0.538349i	0.923044	−	0.384695i	$-0.125693\pi$
$167$	6.95700	+	6.95700i	0.538349	+	0.538349i	−0.384695	+	0.923044i	$0.625693\pi$
$168$		0			0
$169$		−	12.7360i		−	0.979691i
$170$		0			0
$171$		0			0
$172$	2.43034	−	10.8430i	0.185312	−	0.826771i
$173$	0.627343	+	0.627343i	0.0476960	+	0.0476960i	0.730553	−	0.682857i	$-0.239263\pi$
$173$	0.627343	+	0.627343i	0.0476960	+	0.0476960i	−0.682857	+	0.730553i	$0.739263\pi$
$174$		0			0
$175$		0			0
$176$	−10.9543	−	5.17035i	−0.825715	−	0.389730i
$177$		0			0
$178$	1.68804	+	5.81662i	0.126524	+	0.435974i
$179$	8.93968			0.668183			0.334091	−	0.942541i	$-0.391571\pi$
$179$	8.93968			0.668183			0.334091	+	0.942541i	$0.391571\pi$
$180$		0			0
$181$	−1.00933			−0.0750228			−0.0375114	−	0.999296i	$-0.511943\pi$
$181$	−1.00933			−0.0750228			−0.0375114	+	0.999296i	$0.511943\pi$
$182$	−0.709789	−	2.44577i	−0.0526131	−	0.181293i
$183$		0			0
$184$	−0.222998	−	3.59465i	−0.0164396	−	0.265001i
$185$		0			0
$186$		0			0
$187$	7.15688	+	7.15688i	0.523363	+	0.523363i
$188$	−16.1643	−	3.62305i	−1.17890	−	0.264238i
$189$		0			0
$190$		0			0
$191$		−	21.6262i		−	1.56481i	−0.622768	−	0.782407i	$-0.713992\pi$
$191$		−	21.6262i		−	1.56481i	0.622768	−	0.782407i	$-0.286008\pi$
$192$		0			0
$193$	−11.5653	−	11.5653i	−0.832492	−	0.832492i	0.155365	−	0.987857i	$-0.450345\pi$
$193$	−11.5653	−	11.5653i	−0.832492	−	0.832492i	−0.987857	+	0.155365i	$0.950345\pi$
$194$	−6.49362	+	11.8037i	−0.466214	+	0.847455i
$195$		0			0
$196$	5.65599	+	8.92392i	0.403999	+	0.637423i
$197$	−9.42401	+	9.42401i	−0.671433	+	0.671433i	−0.958046	−	0.286614i	$-0.907470\pi$
$197$	−9.42401	+	9.42401i	−0.671433	+	0.671433i	0.286614	+	0.958046i	$0.407470\pi$
$198$		0			0
$199$	11.0130			0.780688			0.390344	−	0.920669i	$-0.372356\pi$
$199$	11.0130			0.780688			0.390344	+	0.920669i	$0.372356\pi$
$200$		0			0
$201$		0			0
$202$	−7.86022	+	2.28112i	−0.553043	+	0.160499i
$203$	−8.68516	+	8.68516i	−0.609579	+	0.609579i
$204$		0			0
$205$		0			0
$206$	−12.6203	+	22.9404i	−0.879300	+	1.59834i
$207$		0			0
$208$	−1.93460	+	0.693949i	−0.134140	+	0.0481167i
$209$		−	15.0093i		−	1.03822i
$210$		0			0
$211$		−	27.9835i		−	1.92646i	−0.268669	−	0.963232i	$-0.586584\pi$
$211$		−	27.9835i		−	1.92646i	0.268669	−	0.963232i	$-0.413416\pi$
$212$	8.66993	+	1.94327i	0.595453	+	0.133464i
$213$		0			0
$214$	17.0201	+	9.36333i	1.16347	+	0.640064i
$215$		0			0
$216$		0			0
$217$	−9.55602	+	9.55602i	−0.648705	+	0.648705i
$218$	4.12392	+	14.2101i	0.279307	+	0.962430i
$219$		0			0
$220$		0			0
$221$	1.71733			0.115520
$222$		0			0
$223$	8.53479	−	8.53479i	0.571531	−	0.571531i	−0.361025	−	0.932556i	$-0.617573\pi$
$223$	8.53479	−	8.53479i	0.571531	−	0.571531i	0.932556	+	0.361025i	$0.117573\pi$
$224$	16.0560	−	11.6297i	1.07279	−	0.777039i
$225$		0			0
$226$	−18.6553	−	10.2629i	−1.24093	−	0.682681i
$227$	−1.02765	−	1.02765i	−0.0682074	−	0.0682074i	0.672180	−	0.740388i	$-0.265358\pi$
$227$	−1.02765	−	1.02765i	−0.0682074	−	0.0682074i	−0.740388	+	0.672180i	$0.765358\pi$
$228$		0			0
$229$		−	8.84802i		−	0.584693i	−0.956312	−	0.292347i	$-0.905564\pi$
$229$		−	8.84802i		−	0.584693i	0.956312	−	0.292347i	$-0.0944361\pi$
$230$		0			0
$231$		0			0
$232$	7.42988	+	6.56188i	0.487795	+	0.430809i
$233$	−4.91002	−	4.91002i	−0.321666	−	0.321666i	0.527740	−	0.849406i	$-0.323040\pi$
$233$	−4.91002	−	4.91002i	−0.321666	−	0.321666i	−0.849406	+	0.527740i	$0.823040\pi$
$234$		0			0
$235$		0			0
$236$	14.6717	−	9.29892i	0.955045	−	0.605308i
$237$		0			0
$238$	−15.9089	+	4.61694i	−1.03122	+	0.299272i
$239$	−19.0259			−1.23068			−0.615340	−	0.788262i	$-0.710981\pi$
$239$	−19.0259			−1.23068			−0.615340	+	0.788262i	$0.710981\pi$
$240$		0			0
$241$	2.90663			0.187232			0.0936161	−	0.995608i	$-0.470157\pi$
$241$	2.90663			0.187232			0.0936161	+	0.995608i	$0.470157\pi$
$242$	2.48459	−	0.721054i	0.159716	−	0.0463511i
$243$		0			0
$244$	−25.8325	+	16.3727i	−1.65376	+	1.04815i
$245$		0			0
$246$		0			0
$247$	−1.80078	−	1.80078i	−0.114581	−	0.114581i
$248$	8.17486	+	7.21984i	0.519104	+	0.458460i
$249$		0			0
$250$		0			0
$251$			2.77379i			0.175080i	0.996161	+	0.0875401i	$0.0279006\pi$
$251$			2.77379i			0.175080i	−0.996161	+	0.0875401i	$0.972099\pi$
$252$		0			0
$253$	−2.72666	−	2.72666i	−0.171423	−	0.171423i
$254$	−3.11505	−	1.71370i	−0.195456	−	0.107527i
$255$		0			0
$256$	−10.1700	−	12.3520i	−0.635624	−	0.771999i
$257$	−2.08066	+	2.08066i	−0.129788	+	0.129788i	−0.769017	−	0.639229i	$-0.779254\pi$
$257$	−2.08066	+	2.08066i	−0.129788	+	0.129788i	0.639229	+	0.769017i	$0.279254\pi$
$258$		0			0
$259$	1.80078			0.111895
$260$		0			0
$261$		0			0
$262$	7.17290	+	24.7162i	0.443143	+	1.52697i
$263$	4.75646	−	4.75646i	0.293296	−	0.293296i	−0.545085	−	0.838381i	$-0.683503\pi$
$263$	4.75646	−	4.75646i	0.293296	−	0.293296i	0.838381	+	0.545085i	$0.183503\pi$
$264$		0			0
$265$		0			0
$266$	21.5233	+	11.8407i	1.31968	+	0.726001i
$267$		0			0
$268$	−10.8430	−	2.43034i	−0.662342	−	0.148457i
$269$			21.6846i			1.32214i	0.750326	+	0.661068i	$0.229896\pi$
$269$			21.6846i			1.32214i	−0.750326	+	0.661068i	$0.770104\pi$
$270$		0			0
$271$		−	3.15556i		−	0.191687i	−0.995396	−	0.0958434i	$-0.969445\pi$
$271$		−	3.15556i		−	0.191687i	0.995396	−	0.0958434i	$-0.0305548\pi$
$272$	4.51391	+	12.5839i	0.273696	+	0.763012i
$273$		0			0
$274$	−5.70636	+	10.3727i	−0.344734	+	0.626635i
$275$		0			0
$276$		0			0
$277$	3.53397	−	3.53397i	0.212336	−	0.212336i	−0.592923	−	0.805259i	$-0.702026\pi$
$277$	3.53397	−	3.53397i	0.212336	−	0.212336i	0.805259	+	0.592923i	$0.202026\pi$
$278$	−16.8604	+	4.89305i	−1.01122	+	0.293466i
$279$		0			0
$280$		0			0
$281$	−0.179969			−0.0107361			−0.00536804	−	0.999986i	$-0.501709\pi$
$281$	−0.179969			−0.0107361			−0.00536804	+	0.999986i	$0.501709\pi$
$282$		0			0
$283$	9.84007	−	9.84007i	0.584931	−	0.584931i	−0.351323	−	0.936254i	$-0.614268\pi$
$283$	9.84007	−	9.84007i	0.584931	−	0.584931i	0.936254	+	0.351323i	$0.114268\pi$
$284$	4.55658	+	7.18930i	0.270384	+	0.426606i
$285$		0			0
$286$	−1.06068	+	1.92804i	−0.0627193	+	0.114007i
$287$	−6.75712	−	6.75712i	−0.398860	−	0.398860i
$288$		0			0
$289$			5.82936i			0.342903i
$290$		0			0
$291$		0			0
$292$	−25.6197	−	5.74238i	−1.49928	−	0.336047i
$293$	15.8680	+	15.8680i	0.927018	+	0.927018i	0.997512	−	0.0704942i	$-0.0224576\pi$
$293$	15.8680	+	15.8680i	0.927018	+	0.927018i	−0.0704942	+	0.997512i	$0.522458\pi$
$294$		0			0
$295$		0			0
$296$	−0.0899847	−	1.45052i	−0.00523026	−	0.0843100i
$297$		0			0
$298$	−2.28112	−	7.86022i	−0.132142	−	0.455330i
$299$	−0.654274			−0.0378376
$300$		0			0
$301$	19.4720			1.12235
$302$	7.12274	+	24.5434i	0.409868	+	1.41231i
$303$		0			0
$304$	8.46216	−	17.9287i	0.485338	−	1.02828i
$305$		0			0
$306$		0			0
$307$	7.78477	+	7.78477i	0.444300	+	0.444300i	0.893454	−	0.449154i	$-0.148275\pi$
$307$	7.78477	+	7.78477i	0.444300	+	0.444300i	−0.449154	+	0.893454i	$0.648275\pi$
$308$	4.64248	−	20.7125i	0.264530	−	1.18020i
$309$		0			0
$310$		0			0
$311$		−	7.05788i		−	0.400215i	−0.979774	−	0.200108i	$-0.935871\pi$
$311$		−	7.05788i		−	0.400215i	0.979774	−	0.200108i	$-0.0641292\pi$
$312$		0			0
$313$	11.3013	+	11.3013i	0.638789	+	0.638789i	0.950257	−	0.311468i	$-0.100821\pi$
$313$	11.3013	+	11.3013i	0.638789	+	0.638789i	−0.311468	+	0.950257i	$0.600821\pi$
$314$	3.77832	−	6.86799i	0.213223	−	0.387583i
$315$		0			0
$316$	−0.675305	+	0.428009i	−0.0379889	+	0.0240774i
$317$	19.4754	−	19.4754i	1.09385	−	1.09385i	0.0987310	−	0.995114i	$-0.468522\pi$
$317$	19.4754	−	19.4754i	1.09385	−	1.09385i	0.995114	−	0.0987310i	$-0.0314783\pi$
$318$		0			0
$319$	10.6132			0.594225
$320$		0			0
$321$		0			0
$322$	6.06105	−	1.75898i	0.337769	−	0.0980241i
$323$	−11.7135	+	11.7135i	−0.651755	+	0.651755i
$324$		0			0
$325$		0			0
$326$	−3.11203	+	5.65685i	−0.172359	+	0.313304i
$327$		0			0
$328$	−5.10520	+	5.78050i	−0.281887	+	0.319175i
$329$		−	29.0280i		−	1.60036i
$330$		0			0
$331$			15.0143i			0.825259i	0.910899	+	0.412630i	$0.135390\pi$
$331$			15.0143i			0.825259i	−0.910899	+	0.412630i	$0.864610\pi$
$332$	0.123648	−	0.551657i	0.00678607	−	0.0302761i
$333$		0			0
$334$	12.1910	+	6.70668i	0.667061	+	0.366973i
$335$		0			0
$336$		0			0
$337$	21.5840	−	21.5840i	1.17576	−	1.17576i	0.194940	−	0.980815i	$-0.437549\pi$
$337$	21.5840	−	21.5840i	1.17576	−	1.17576i	0.980815	−	0.194940i	$-0.0624513\pi$
$338$	−5.01997	−	17.2977i	−0.273051	−	0.940871i
$339$		0			0
$340$		0			0
$341$	11.6774			0.632365
$342$		0			0
$343$	4.25583	−	4.25583i	0.229793	−	0.229793i
$344$	−0.973012	−	15.6846i	−0.0524613	−	0.845659i
$345$		0			0
$346$	1.09931	+	0.604770i	0.0590995	+	0.0325127i
$347$	−16.9969	−	16.9969i	−0.912444	−	0.912444i	0.0840201	−	0.996464i	$-0.473224\pi$
$347$	−16.9969	−	16.9969i	−0.912444	−	0.912444i	−0.996464	+	0.0840201i	$0.973224\pi$
$348$		0			0
$349$			4.38538i			0.234744i	0.993088	+	0.117372i	$0.0374469\pi$
$349$			4.38538i			0.234744i	−0.993088	+	0.117372i	$0.962553\pi$
$350$		0			0
$351$		0			0
$352$	−16.9159	−	2.70451i	−0.901618	−	0.144151i
$353$	−2.62734	−	2.62734i	−0.139839	−	0.139839i	0.633722	−	0.773561i	$-0.281526\pi$
$353$	−2.62734	−	2.62734i	−0.139839	−	0.139839i	−0.773561	+	0.633722i	$0.781526\pi$
$354$		0			0
$355$		0			0
$356$	4.58532	+	7.23464i	0.243021	+	0.383435i
$357$		0			0
$358$	12.1416	−	3.52363i	0.641706	−	0.186230i
$359$	34.9952			1.84697			0.923487	−	0.383630i	$-0.125326\pi$
$359$	34.9952			1.84697			0.923487	+	0.383630i	$0.125326\pi$
$360$		0			0
$361$	5.56534			0.292913
$362$	−1.37085	+	0.397834i	−0.0720500	+	0.0209097i
$363$		0			0
$364$	−1.92804	−	3.04202i	−0.101057	−	0.159445i
$365$		0			0
$366$		0			0
$367$	9.93581	+	9.93581i	0.518645	+	0.518645i	0.917161	−	0.398516i	$-0.130475\pi$
$367$	9.93581	+	9.93581i	0.518645	+	0.518645i	−0.398516	+	0.917161i	$0.630475\pi$
$368$	−1.71973	−	4.79427i	−0.0896469	−	0.249918i
$369$		0			0
$370$		0			0
$371$			15.5695i			0.808330i
$372$		0			0
$373$	7.08998	+	7.08998i	0.367105	+	0.367105i	0.866421	−	0.499315i	$-0.166415\pi$
$373$	7.08998	+	7.08998i	0.367105	+	0.367105i	−0.499315	+	0.866421i	$0.666415\pi$
$374$	12.5412	+	6.89937i	0.648492	+	0.356758i
$375$		0			0
$376$	−23.3820	+	1.45052i	−1.20583	+	0.0748051i
$377$	1.27334	−	1.27334i	0.0655805	−	0.0655805i
$378$		0			0
$379$	−30.0388			−1.54299			−0.771495	−	0.636235i	$-0.780491\pi$
$379$	−30.0388			−1.54299			−0.771495	+	0.636235i	$0.780491\pi$
$380$		0			0
$381$		0			0
$382$	−8.52410	−	29.3721i	−0.436131	−	1.50281i
$383$	11.9133	−	11.9133i	0.608744	−	0.608744i	−0.333874	−	0.942618i	$-0.608356\pi$
$383$	11.9133	−	11.9133i	0.608744	−	0.608744i	0.942618	+	0.333874i	$0.108356\pi$
$384$		0			0
$385$		0			0
$386$	−20.2663	−	11.1492i	−1.03153	−	0.567480i
$387$		0			0
$388$	−4.16697	+	18.5910i	−0.211546	+	0.943814i
$389$			16.3340i			0.828168i	0.910239	+	0.414084i	$0.135898\pi$
$389$			16.3340i			0.828168i	−0.910239	+	0.414084i	$0.864102\pi$
$390$		0			0
$391$			4.25583i			0.215227i
$392$	11.1992	+	9.89090i	0.565647	+	0.499566i
$393$		0			0
$394$	−9.08492	+	16.5140i	−0.457692	+	0.831963i
$395$		0			0
$396$		0			0
$397$	19.1927	−	19.1927i	0.963253	−	0.963253i	−0.0360950	−	0.999348i	$-0.511492\pi$
$397$	19.1927	−	19.1927i	0.963253	−	0.963253i	0.999348	+	0.0360950i	$0.0114919\pi$
$398$	14.9575	−	4.34083i	0.749753	−	0.217586i
$399$		0			0
$400$		0			0
$401$	−26.5653			−1.32661			−0.663305	−	0.748349i	$-0.730847\pi$
$401$	−26.5653			−1.32661			−0.663305	+	0.748349i	$0.730847\pi$
$402$		0			0
$403$	1.40102	−	1.40102i	0.0697898	−	0.0697898i
$404$	−9.77644	+	6.19632i	−0.486396	+	0.308278i
$405$		0			0
$406$	−8.37266	+	15.2193i	−0.415528	+	0.755321i
$407$	−1.10027	−	1.10027i	−0.0545383	−	0.0545383i
$408$		0			0
$409$		−	25.3947i		−	1.25569i	−0.778339	−	0.627844i	$-0.783938\pi$
$409$		−	25.3947i		−	1.25569i	0.778339	−	0.627844i	$-0.216062\pi$
$410$		0			0
$411$		0			0
$412$	−8.09849	+	36.1315i	−0.398984	+	1.78007i
$413$	21.5233	+	21.5233i	1.05909	+	1.05909i
$414$		0			0
$415$		0			0
$416$	−2.35400	+	1.70504i	−0.115414	+	0.0835964i
$417$		0			0
$418$	−5.91603	−	20.3853i	−0.289362	−	0.997078i
$419$	−40.0788			−1.95798			−0.978988	−	0.203919i	$-0.934632\pi$
$419$	−40.0788			−1.95798			−0.978988	+	0.203919i	$0.934632\pi$
$420$		0			0
$421$	19.3947			0.945240			0.472620	−	0.881266i	$-0.343308\pi$
$421$	19.3947			0.945240			0.472620	+	0.881266i	$0.343308\pi$
$422$	−11.0299	−	38.0065i	−0.536927	−	1.85013i
$423$		0			0
$424$	12.5412	−	0.778008i	0.609056	−	0.0377834i
$425$		0			0
$426$		0			0
$427$	−37.8962	−	37.8962i	−1.83393	−	1.83393i
$428$	26.8069	+	6.00847i	1.29576	+	0.290430i
$429$		0			0
$430$		0			0
$431$		−	15.8241i		−	0.762218i	−0.924530	−	0.381109i	$-0.875542\pi$
$431$		−	15.8241i		−	0.762218i	0.924530	−	0.381109i	$-0.124458\pi$
$432$		0			0
$433$	21.1214	+	21.1214i	1.01503	+	1.01503i	0.999885	+	0.0151424i	$0.00482018\pi$
$433$	21.1214	+	21.1214i	1.01503	+	1.01503i	0.0151424	+	0.999885i	$0.495180\pi$
$434$	−9.21218	+	16.7453i	−0.442199	+	0.803801i
$435$		0			0
$436$	11.2020	+	17.6743i	0.536479	+	0.846447i
$437$	4.46264	−	4.46264i	0.213477	−	0.213477i
$438$		0			0
$439$	−6.61188			−0.315568			−0.157784	−	0.987474i	$-0.550435\pi$
$439$	−6.61188			−0.315568			−0.157784	+	0.987474i	$0.550435\pi$
$440$		0			0
$441$		0			0
$442$	2.33243	−	0.676896i	0.110942	−	0.0321967i
$443$	14.5419	−	14.5419i	0.690906	−	0.690906i	−0.271525	−	0.962431i	$-0.587528\pi$
$443$	14.5419	−	14.5419i	0.690906	−	0.690906i	0.962431	+	0.271525i	$0.0875280\pi$
$444$		0			0
$445$		0			0
$446$	8.22769	−	14.9558i	0.389593	−	0.708177i
$447$		0			0
$448$	17.2230	−	22.1237i	0.813711	−	1.04525i
$449$			33.6120i			1.58625i	0.609060	+	0.793124i	$0.291547\pi$
$449$			33.6120i			1.58625i	−0.609060	+	0.793124i	$0.708453\pi$
$450$		0			0
$451$			8.25715i			0.388814i
$452$	−29.3824	−	6.58575i	−1.38203	−	0.309768i
$453$		0			0
$454$	−1.80078	−	0.990671i	−0.0845148	−	0.0464945i
$455$		0			0
$456$		0			0
$457$	−15.5653	+	15.5653i	−0.728116	+	0.728116i	−0.970244	−	0.242128i	$-0.922155\pi$
$457$	−15.5653	+	15.5653i	−0.728116	+	0.728116i	0.242128	+	0.970244i	$0.422155\pi$
$458$	−3.48751	−	12.0172i	−0.162960	−	0.561525i
$459$		0			0
$460$		0			0
$461$	26.1473			1.21780			0.608900	−	0.793247i	$-0.291611\pi$
$461$	26.1473			1.21780			0.608900	+	0.793247i	$0.291611\pi$
$462$		0			0
$463$	−5.77898	+	5.77898i	−0.268572	+	0.268572i	−0.828525	−	0.559953i	$-0.810819\pi$
$463$	−5.77898	+	5.77898i	−0.268572	+	0.268572i	0.559953	+	0.828525i	$0.310819\pi$
$464$	12.6775	+	5.98365i	0.588538	+	0.277784i
$465$		0			0
$466$	−8.60398	−	4.73335i	−0.398572	−	0.219268i
$467$	2.25517	+	2.25517i	0.104357	+	0.104357i	0.757357	−	0.653000i	$-0.226490\pi$
$467$	2.25517	+	2.25517i	0.104357	+	0.104357i	−0.653000	+	0.757357i	$0.726490\pi$
$468$		0			0
$469$		−	19.4720i		−	0.899132i
$470$		0			0
$471$		0			0
$472$	16.2615	−	18.4125i	0.748495	−	0.847505i
$473$	−11.8973	−	11.8973i	−0.547038	−	0.547038i
$474$		0			0
$475$		0			0
$476$	−19.7873	+	12.5412i	−0.906951	+	0.574827i
$477$		0			0
$478$	−25.8405	+	7.49917i	−1.18191	+	0.343004i
$479$	−1.40102			−0.0640143			−0.0320071	−	0.999488i	$-0.510190\pi$
$479$	−1.40102			−0.0640143			−0.0320071	+	0.999488i	$0.510190\pi$
$480$		0			0
$481$	−0.264015			−0.0120380
$482$	3.94771	−	1.14567i	0.179813	−	0.0521837i
$483$		0			0
$484$	3.09030	−	1.95864i	0.140468	−	0.0890289i
$485$		0			0
$486$		0			0
$487$	−0.978144	−	0.978144i	−0.0443239	−	0.0443239i	0.684597	−	0.728921i	$-0.259978\pi$
$487$	−0.978144	−	0.978144i	−0.0443239	−	0.0443239i	−0.728921	+	0.684597i	$0.759978\pi$
$488$	−28.6317	+	32.4190i	−1.29609	+	1.46754i
$489$		0			0
$490$		0			0
$491$		−	36.1134i		−	1.62978i	−0.579619	−	0.814888i	$-0.696799\pi$
$491$		−	36.1134i		−	1.62978i	0.579619	−	0.814888i	$-0.303201\pi$
$492$		0			0
$493$	−8.28267	−	8.28267i	−0.373033	−	0.373033i
$494$	−3.15556	−	1.73599i	−0.141976	−	0.0781057i
$495$		0			0
$496$	13.9486	+	6.58363i	0.626313	+	0.295614i
$497$	−10.5467	+	10.5467i	−0.473084	+	0.473084i
$498$		0			0
$499$	6.35736			0.284595			0.142297	−	0.989824i	$-0.454551\pi$
$499$	6.35736			0.284595			0.142297	+	0.989824i	$0.454551\pi$
$500$		0			0
$501$		0			0
$502$	1.09331	+	3.76730i	0.0487968	+	0.168143i
$503$	17.1704	−	17.1704i	0.765592	−	0.765592i	−0.211735	−	0.977327i	$-0.567911\pi$
$503$	17.1704	−	17.1704i	0.765592	−	0.765592i	0.977327	+	0.211735i	$0.0679114\pi$
$504$		0			0
$505$		0			0
$506$	−4.77801	−	2.62855i	−0.212408	−	0.116853i
$507$		0			0
$508$	−4.90626	−	1.09968i	−0.217680	−	0.0487906i
$509$		−	18.8739i		−	0.836572i	−0.908315	−	0.418286i	$-0.862631\pi$
$509$		−	18.8739i		−	0.836572i	0.908315	−	0.418286i	$-0.137369\pi$
$510$		0			0
$511$		−	46.0081i		−	2.03528i
$512$	−18.6812	−	12.7676i	−0.825602	−	0.564253i
$513$		0			0
$514$	−2.00579	+	3.64600i	−0.0884717	+	0.160818i
$515$		0			0
$516$		0			0
$517$	−17.7360	+	17.7360i	−0.780028	+	0.780028i
$518$	2.44577	−	0.709789i	0.107461	−	0.0311864i
$519$		0			0
$520$		0			0
$521$	33.9346			1.48670			0.743351	−	0.668901i	$-0.233235\pi$
$521$	33.9346			1.48670			0.743351	+	0.668901i	$0.233235\pi$
$522$		0			0
$523$	−3.78345	+	3.78345i	−0.165439	+	0.165439i	−0.784971	−	0.619532i	$-0.787322\pi$
$523$	−3.78345	+	3.78345i	−0.165439	+	0.165439i	0.619532	+	0.784971i	$0.287322\pi$
$524$	19.4841	+	30.7417i	0.851167	+	1.34296i
$525$		0			0
$526$	4.58532	−	8.33491i	0.199929	−	0.363419i
$527$	−9.11317	−	9.11317i	−0.396976	−	0.396976i
$528$		0			0
$529$			21.3786i			0.929504i
$530$		0			0
$531$		0			0
$532$	33.8995	+	7.59822i	1.46973	+	0.329425i
$533$	0.990671	+	0.990671i	0.0429107	+	0.0429107i
$534$		0			0
$535$		0			0
$536$	−15.6846	+	0.973012i	−0.677473	+	0.0420277i
$537$		0			0
$538$	8.54715	+	29.4515i	0.368494	+	1.26975i
$539$	15.9976			0.689063
$540$		0			0
$541$	28.4813			1.22451			0.612253	−	0.790662i	$-0.290263\pi$
$541$	28.4813			1.22451			0.612253	+	0.790662i	$0.290263\pi$
$542$	−1.24379	−	4.28581i	−0.0534252	−	0.184091i
$543$		0			0
$544$	11.0907	+	15.3120i	0.475510	+	0.656496i
$545$		0			0
$546$		0			0
$547$	−0.726896	−	0.726896i	−0.0310798	−	0.0310798i	0.691396	−	0.722476i	$-0.256996\pi$
$547$	−0.726896	−	0.726896i	−0.0310798	−	0.0310798i	−0.722476	+	0.691396i	$0.756996\pi$
$548$	−3.66178	+	16.3371i	−0.156424	+	0.697886i
$549$		0			0
$550$		0			0
$551$			17.3703i			0.740001i
$552$		0			0
$553$	−0.990671	−	0.990671i	−0.0421276	−	0.0421276i
$554$	3.40681	−	6.19269i	0.144742	−	0.263102i
$555$		0			0
$556$	−20.9707	+	13.2912i	−0.889356	+	0.563675i
$557$	−11.4427	+	11.4427i	−0.484841	+	0.484841i	−0.906674	−	0.421832i	$-0.861387\pi$
$557$	−11.4427	+	11.4427i	−0.484841	+	0.484841i	0.421832	+	0.906674i	$0.361387\pi$
$558$		0			0
$559$	−2.85481			−0.120746
$560$		0			0
$561$		0			0
$562$	−0.244430	+	0.0709362i	−0.0103107	+	0.00299226i
$563$	−7.08426	+	7.08426i	−0.298566	+	0.298566i	−0.840452	−	0.541886i	$-0.817710\pi$
$563$	−7.08426	+	7.08426i	−0.298566	+	0.298566i	0.541886	+	0.840452i	$0.317710\pi$
$564$		0			0
$565$		0			0
$566$	9.48601	−	17.2431i	0.398727	−	0.724780i
$567$		0			0
$568$	9.02235	+	7.96832i	0.378569	+	0.334343i
$569$		−	46.2427i		−	1.93860i	−0.245890	−	0.969298i	$-0.579080\pi$
$569$		−	46.2427i		−	1.93860i	0.245890	−	0.969298i	$-0.420920\pi$
$570$		0			0
$571$		−	31.2381i		−	1.30727i	−0.756808	−	0.653637i	$-0.773242\pi$
$571$		−	31.2381i		−	1.30727i	0.756808	−	0.653637i	$-0.226758\pi$
$572$	−0.680641	+	3.03669i	−0.0284590	+	0.126970i
$573$		0			0
$574$	−11.8407	−	6.51399i	−0.494222	−	0.271889i
$575$		0			0
$576$		0			0
$577$	−1.16131	+	1.16131i	−0.0483461	+	0.0483461i	−0.730866	−	0.682520i	$-0.760884\pi$
$577$	−1.16131	+	1.16131i	−0.0483461	+	0.0483461i	0.682520	+	0.730866i	$0.260884\pi$
$578$	2.29768	+	7.91729i	0.0955709	+	0.329316i
$579$		0			0
$580$		0			0
$581$	0.990671			0.0411000
$582$		0			0
$583$	9.51293	−	9.51293i	0.393985	−	0.393985i
$584$	−37.0594	+	2.29902i	−1.53353	+	0.0951341i
$585$		0			0
$586$	27.8060	+	15.2970i	1.14866	+	0.631915i
$587$	23.6268	+	23.6268i	0.975183	+	0.975183i	0.999699	−	0.0245164i	$-0.00780461\pi$
$587$	23.6268	+	23.6268i	0.975183	+	0.975183i	−0.0245164	+	0.999699i	$0.507805\pi$
$588$		0			0
$589$			19.1120i			0.787498i
$590$		0			0
$591$		0			0
$592$	−0.693949	−	1.93460i	−0.0285211	−	0.0795115i
$593$	−0.260625	−	0.260625i	−0.0107026	−	0.0107026i	0.701735	−	0.712438i	$-0.252409\pi$
$593$	−0.260625	−	0.260625i	−0.0107026	−	0.0107026i	−0.712438	+	0.701735i	$0.752409\pi$
$594$		0			0
$595$		0			0
$596$	−6.19632	−	9.77644i	−0.253811	−	0.400458i
$597$		0			0
$598$	−0.888619	+	0.257887i	−0.0363383	+	0.0105458i
$599$	33.0851			1.35182			0.675910	−	0.736984i	$-0.263751\pi$
$599$	33.0851			1.35182			0.675910	+	0.736984i	$0.263751\pi$
$600$		0			0
$601$	−24.3200			−0.992033			−0.496016	−	0.868313i	$-0.665204\pi$
$601$	−24.3200			−0.992033			−0.496016	+	0.868313i	$0.665204\pi$
$602$	26.4464	−	7.67501i	1.07787	−	0.312810i
$603$		0			0
$604$	19.3479	+	30.5267i	0.787253	+	1.24211i
$605$		0			0
$606$		0			0
$607$	4.53347	+	4.53347i	0.184008	+	0.184008i	0.793100	−	0.609092i	$-0.208466\pi$
$607$	4.53347	+	4.53347i	0.184008	+	0.184008i	−0.609092	+	0.793100i	$0.708466\pi$
$608$	4.42639	−	27.6857i	0.179514	−	1.12280i
$609$		0			0
$610$		0			0
$611$			4.25583i			0.172173i
$612$		0			0
$613$	20.2793	+	20.2793i	0.819073	+	0.819073i	0.985974	−	0.166901i	$-0.0533761\pi$
$613$	20.2793	+	20.2793i	0.819073	+	0.819073i	−0.166901	+	0.985974i	$0.553376\pi$
$614$	13.6415	+	7.50466i	0.550526	+	0.302864i
$615$		0			0
$616$	−1.85866	−	29.9611i	−0.0748877	−	1.20717i
$617$	17.1086	−	17.1086i	0.688768	−	0.688768i	−0.273192	−	0.961960i	$-0.588079\pi$
$617$	17.1086	−	17.1086i	0.688768	−	0.688768i	0.961960	+	0.273192i	$0.0880793\pi$
$618$		0			0
$619$	29.4373			1.18319			0.591593	−	0.806237i	$-0.298499\pi$
$619$	29.4373			1.18319			0.591593	+	0.806237i	$0.298499\pi$
$620$		0			0
$621$		0			0
$622$	−2.78191	−	9.58583i	−0.111544	−	0.384357i
$623$	−10.6132	+	10.6132i	−0.425209	+	0.425209i
$624$		0			0
$625$		0			0
$626$	19.8037	+	10.8947i	0.791514	+	0.435439i
$627$		0			0
$628$	2.42456	−	10.8172i	0.0967503	−	0.431653i
$629$			1.71733i			0.0684743i
$630$		0			0
$631$			5.25710i			0.209282i	0.994510	+	0.104641i	$0.0333693\pi$
$631$			5.25710i			0.209282i	−0.994510	+	0.104641i	$0.966631\pi$
$632$	−0.748480	+	0.847487i	−0.0297729	+	0.0337112i
$633$		0			0
$634$	18.7746	−	34.1273i	0.745635	−	1.35537i
$635$		0			0
$636$		0			0
$637$	1.91934	−	1.91934i	0.0760472	−	0.0760472i
$638$	14.4146	−	4.18326i	0.570679	−	0.165617i
$639$		0			0
$640$		0			0
$641$	−20.0773			−0.793004			−0.396502	−	0.918034i	$-0.629776\pi$
$641$	−20.0773			−0.793004			−0.396502	+	0.918034i	$0.629776\pi$
$642$		0			0
$643$	9.28480	−	9.28480i	0.366157	−	0.366157i	−0.499917	−	0.866073i	$-0.666636\pi$
$643$	9.28480	−	9.28480i	0.366157	−	0.366157i	0.866073	+	0.499917i	$0.166636\pi$
$644$	7.53866	−	4.77801i	0.297065	−	0.188280i
$645$		0			0
$646$	−11.2920	+	20.5259i	−0.444278	+	0.807580i
$647$	28.7387	+	28.7387i	1.12983	+	1.12983i	0.990204	+	0.139630i	$0.0445912\pi$
$647$	28.7387	+	28.7387i	1.12983	+	1.12983i	0.139630	+	0.990204i	$0.455409\pi$
$648$		0			0
$649$		−	26.3013i		−	1.03242i
$650$		0			0
$651$		0			0
$652$	−1.99700	+	8.90963i	−0.0782084	+	0.348928i
$653$	−11.9380	−	11.9380i	−0.467170	−	0.467170i	0.433826	−	0.900996i	$-0.357163\pi$
$653$	−11.9380	−	11.9380i	−0.467170	−	0.467170i	−0.900996	+	0.433826i	$0.857163\pi$
$654$		0			0
$655$		0			0
$656$	−4.65533	+	9.86318i	−0.181760	+	0.385093i
$657$		0			0
$658$	−11.4416	−	39.4251i	−0.446039	−	1.53695i
$659$	17.9963			0.701038			0.350519	−	0.936556i	$-0.386005\pi$
$659$	17.9963			0.701038			0.350519	+	0.936556i	$0.386005\pi$
$660$		0			0
$661$	−9.06794			−0.352702			−0.176351	−	0.984327i	$-0.556429\pi$
$661$	−9.06794			−0.352702			−0.176351	+	0.984327i	$0.556429\pi$
$662$	5.91798	+	20.3920i	0.230009	+	0.792558i
$663$		0			0
$664$	−0.0495037	−	0.797984i	−0.00192112	−	0.0309678i
$665$		0			0
$666$		0			0
$667$	3.15556	+	3.15556i	0.122184	+	0.122184i
$668$	19.2010	+	4.30369i	0.742908	+	0.166515i
$669$		0			0
$670$		0			0
$671$			46.3089i			1.78773i
$672$		0			0
$673$	−35.7640	−	35.7640i	−1.37860	−	1.37860i	−0.846988	−	0.531611i	$-0.821587\pi$
$673$	−35.7640	−	35.7640i	−1.37860	−	1.37860i	−0.531611	−	0.846988i	$-0.678413\pi$
$674$	20.8074	−	37.8223i	0.801470	−	1.45686i
$675$		0			0
$676$	−13.6360	−	21.5147i	−0.524462	−	0.827487i
$677$	16.2020	−	16.2020i	0.622694	−	0.622694i	−0.323525	−	0.946219i	$-0.604868\pi$
$677$	16.2020	−	16.2020i	0.622694	−	0.622694i	0.946219	+	0.323525i	$0.104868\pi$
$678$		0			0
$679$	−33.3859			−1.28123
$680$		0			0
$681$		0			0
$682$	15.8599	−	4.60272i	0.607308	−	0.176247i
$683$	33.3943	−	33.3943i	1.27780	−	1.27780i	0.335897	−	0.941899i	$-0.390961\pi$
$683$	33.3943	−	33.3943i	1.27780	−	1.27780i	0.941899	−	0.335897i	$-0.109039\pi$
$684$		0			0
$685$		0			0
$686$	4.10270	−	7.45763i	0.156642	−	0.284734i
$687$		0			0
$688$	−7.50373	−	20.9190i	−0.286077	−	0.797528i
$689$		−	2.28267i		−	0.0869629i
$690$		0			0
$691$			24.6365i			0.937216i	0.883406	+	0.468608i	$0.155244\pi$
$691$			24.6365i			0.937216i	−0.883406	+	0.468608i	$0.844756\pi$
$692$	1.73143	+	0.388082i	0.0658193	+	0.0147527i
$693$		0			0
$694$	−29.7843	−	16.3854i	−1.13060	−	0.621980i
$695$		0			0
$696$		0			0
$697$	6.44398	−	6.44398i	0.244083	−	0.244083i
$698$	1.72853	+	5.95611i	0.0654256	+	0.225442i
$699$		0			0
$700$		0			0
$701$	23.0420			0.870285			0.435143	−	0.900362i	$-0.356698\pi$
$701$	23.0420			0.870285			0.435143	+	0.900362i	$0.356698\pi$
$702$		0			0
$703$	1.80078	−	1.80078i	0.0679177	−	0.0679177i
$704$	−24.0407	+	2.99430i	−0.906068	+	0.112852i
$705$		0			0
$706$	−4.60398	−	2.53281i	−0.173273	−	0.0953235i
$707$	−14.3420	−	14.3420i	−0.539387	−	0.539387i
$708$		0			0
$709$			37.7360i			1.41720i	0.705608	+	0.708602i	$0.250674\pi$
$709$			37.7360i			1.41720i	−0.705608	+	0.708602i	$0.749326\pi$
$710$		0			0
$711$		0			0
$712$	9.07925	+	8.01857i	0.340259	+	0.300509i
$713$	3.47197	+	3.47197i	0.130026	+	0.130026i
$714$		0			0
$715$		0			0
$716$	15.1016	−	9.57143i	0.564374	−	0.357701i
$717$		0			0
$718$	47.5296	−	13.7936i	1.77379	−	0.514772i
$719$	−41.3423			−1.54181			−0.770903	−	0.636953i	$-0.780195\pi$
$719$	−41.3423			−1.54181			−0.770903	+	0.636953i	$0.780195\pi$
$720$		0			0
$721$	−64.8853			−2.41646
$722$	7.55871	−	2.19362i	0.281306	−	0.0816380i
$723$		0			0
$724$	−1.70504	+	1.08066i	−0.0633673	+	0.0401623i
$725$		0			0
$726$		0			0
$727$	−9.48981	−	9.48981i	−0.351958	−	0.351958i	0.508880	−	0.860838i	$-0.330060\pi$
$727$	−9.48981	−	9.48981i	−0.351958	−	0.351958i	−0.860838	+	0.508880i	$0.830060\pi$
$728$	−3.81765	−	3.37165i	−0.141491	−	0.124962i
$729$		0			0
$730$		0			0
$731$			18.5696i			0.686821i
$732$		0			0
$733$	−3.21134	−	3.21134i	−0.118614	−	0.118614i	0.645308	−	0.763922i	$-0.276729\pi$
$733$	−3.21134	−	3.21134i	−0.118614	−	0.118614i	−0.763922	+	0.645308i	$0.776729\pi$
$734$	17.4108	+	9.57830i	0.642646	+	0.353542i
$735$		0			0
$736$	−4.22538	−	5.83362i	−0.155750	−	0.215030i
$737$	−11.8973	+	11.8973i	−0.438243	+	0.438243i
$738$		0			0
$739$	25.3832			0.933737			0.466868	−	0.884327i	$-0.345382\pi$
$739$	25.3832			0.933737			0.466868	+	0.884327i	$0.345382\pi$
$740$		0			0
$741$		0			0
$742$	6.13684	+	21.1462i	0.225290	+	0.776300i
$743$	−32.7400	+	32.7400i	−1.20111	+	1.20111i	−0.227285	+	0.973828i	$0.572985\pi$
$743$	−32.7400	+	32.7400i	−1.20111	+	1.20111i	−0.973828	+	0.227285i	$0.927015\pi$
$744$		0			0
$745$		0			0
$746$	12.4240	+	6.83488i	0.454875	+	0.250243i
$747$		0			0
$748$	19.7526	+	4.42734i	0.722228	+	0.161880i
$749$			48.1400i			1.75900i
$750$		0			0
$751$			24.4810i			0.893323i	0.894703	+	0.446662i	$0.147387\pi$
$751$			24.4810i			0.893323i	−0.894703	+	0.446662i	$0.852613\pi$
$752$	−31.1851	+	11.1862i	−1.13720	+	0.407920i
$753$		0			0
$754$	1.22753	−	2.23132i	0.0447039	−	0.0812599i
$755$		0			0
$756$		0			0
$757$	−22.9473	+	22.9473i	−0.834035	+	0.834035i	−0.988066	−	0.154031i	$-0.950774\pi$
$757$	−22.9473	+	22.9473i	−0.834035	+	0.834035i	0.154031	+	0.988066i	$0.450774\pi$
$758$	−40.7980	+	11.8400i	−1.48185	+	0.430048i
$759$		0			0
$760$		0			0
$761$	−37.0466			−1.34294			−0.671470	−	0.741032i	$-0.734337\pi$
$761$	−37.0466			−1.34294			−0.671470	+	0.741032i	$0.734337\pi$
$762$		0			0
$763$	−25.9282	+	25.9282i	−0.938665	+	0.938665i
$764$	−23.1544	−	36.5327i	−0.837698	−	1.32170i
$765$		0			0
$766$	11.4847	−	20.8761i	0.414959	−	0.754286i
$767$	−3.15556	−	3.15556i	−0.113941	−	0.113941i
$768$		0			0
$769$		−	6.62395i		−	0.238866i	−0.992842	−	0.119433i	$-0.961892\pi$
$769$		−	6.62395i		−	0.238866i	0.992842	−	0.119433i	$-0.0381077\pi$
$770$		0			0
$771$		0			0
$772$	−31.9198	−	7.15447i	−1.14882	−	0.257495i
$773$	16.2606	+	16.2606i	0.584854	+	0.584854i	0.936233	−	0.351379i	$-0.114287\pi$
$773$	16.2606	+	16.2606i	0.584854	+	0.584854i	−0.351379	+	0.936233i	$0.614287\pi$
$774$		0			0
$775$		0			0
$776$	1.66829	+	26.8922i	0.0598880	+	0.965375i
$777$		0			0
$778$	6.43817	+	22.1845i	0.230819	+	0.795352i
$779$	−13.5142			−0.484198
$780$		0			0
$781$	12.8880			0.461168
$782$	1.67747	+	5.78017i	0.0599860	+	0.206698i
$783$		0			0
$784$	19.1091	+	9.01932i	0.682468	+	0.322118i
$785$		0			0
$786$		0			0
$787$	31.2117	+	31.2117i	1.11258	+	1.11258i	0.992801	+	0.119776i	$0.0382177\pi$
$787$	31.2117	+	31.2117i	1.11258	+	1.11258i	0.119776	+	0.992801i	$0.461782\pi$
$788$	−5.82981	+	26.0098i	−0.207678	+	0.926560i
$789$		0			0
$790$		0			0
$791$		−	52.7652i		−	1.87612i
$792$		0			0
$793$	5.55602	+	5.55602i	0.197300	+	0.197300i
$794$	18.5021	−	33.6320i	0.656615	−	1.19355i
$795$		0			0
$796$	18.6040	−	11.7912i	0.659401	−	0.417929i
$797$	17.3540	−	17.3540i	0.614710	−	0.614710i	−0.329460	−	0.944170i	$-0.606867\pi$
$797$	17.3540	−	17.3540i	0.614710	−	0.614710i	0.944170	+	0.329460i	$0.106867\pi$
$798$		0			0
$799$	27.6828			0.979346
$800$		0			0
$801$		0			0
$802$	−36.0804	+	10.4709i	−1.27404	+	0.369741i
$803$	−28.1108	+	28.1108i	−0.992008	+	0.992008i
$804$		0			0
$805$		0			0
$806$	1.35061	−	2.45505i	0.0475732	−	0.0864756i
$807$		0			0
$808$	−10.8358	+	12.2691i	−0.381202	+	0.431627i
$809$			27.4320i			0.964458i	0.876045	+	0.482229i	$0.160173\pi$
$809$			27.4320i			0.964458i	−0.876045	+	0.482229i	$0.839827\pi$
$810$		0			0
$811$			27.1840i			0.954559i	0.878751	+	0.477280i	$0.158377\pi$
$811$			27.1840i			0.954559i	−0.878751	+	0.477280i	$0.841623\pi$
$812$	−5.37275	+	23.9706i	−0.188547	+	0.841203i
$813$		0			0
$814$	−1.92804	−	1.06068i	−0.0675777	−	0.0371768i
$815$		0			0
$816$		0			0
$817$	19.4720	−	19.4720i	0.681238	−	0.681238i
$818$	−10.0095	−	34.4905i	−0.349974	−	1.20593i
$819$		0			0
$820$		0			0
$821$	−23.6074			−0.823903			−0.411951	−	0.911206i	$-0.635153\pi$
$821$	−23.6074			−0.823903			−0.411951	+	0.911206i	$0.635153\pi$
$822$		0			0
$823$	−24.6596	+	24.6596i	−0.859579	+	0.859579i	−0.991288	−	0.131709i	$-0.957954\pi$
$823$	−24.6596	+	24.6596i	−0.859579	+	0.859579i	0.131709	+	0.991288i	$0.457954\pi$
$824$	3.24231	+	52.2650i	0.112951	+	1.82074i
$825$		0			0
$826$	37.7160	+	20.7489i	1.31231	+	0.721946i
$827$	−13.5406	−	13.5406i	−0.470854	−	0.470854i	0.431337	−	0.902191i	$-0.358042\pi$
$827$	−13.5406	−	13.5406i	−0.470854	−	0.470854i	−0.902191	+	0.431337i	$0.858042\pi$
$828$		0			0
$829$			9.00933i			0.312907i	0.987685	+	0.156453i	$0.0500061\pi$
$829$			9.00933i			0.312907i	−0.987685	+	0.156453i	$0.949994\pi$
$830$		0			0
$831$		0			0
$832$	−2.52509	+	3.24359i	−0.0875418	+	0.112451i
$833$	−12.4847	−	12.4847i	−0.432569	−	0.432569i
$834$		0			0
$835$		0			0
$836$	−16.0700	−	25.3550i	−0.555793	−	0.876920i
$837$		0			0
$838$	−54.4340	+	15.7973i	−1.88039	+	0.545709i
$839$	10.2597			0.354203			0.177102	−	0.984193i	$-0.443328\pi$
$839$	10.2597			0.354203			0.177102	+	0.984193i	$0.443328\pi$
$840$		0			0
$841$	16.7173			0.576460
$842$	26.3414	−	7.64455i	0.907785	−	0.263449i
$843$		0			0
$844$	−29.9611	−	47.2720i	−1.03130	−	1.62717i
$845$		0			0
$846$		0			0
$847$	4.53347	+	4.53347i	0.155772	+	0.155772i
$848$	16.7265	−	5.99988i	0.574392	−	0.206037i
$849$		0			0
$850$		0			0
$851$		−	0.654274i		−	0.0224282i
$852$		0			0
$853$	−17.1086	−	17.1086i	−0.585789	−	0.585789i	0.350699	−	0.936488i	$-0.385944\pi$
$853$	−17.1086	−	17.1086i	−0.585789	−	0.585789i	−0.936488	+	0.350699i	$0.885944\pi$
$854$	−66.4067	−	36.5327i	−2.27239	−	1.25012i
$855$		0			0
$856$	38.7767	−	2.40555i	1.32536	−	0.0822200i
$857$	−26.7674	+	26.7674i	−0.914356	+	0.914356i	−0.996611	−	0.0822556i	$-0.973788\pi$
$857$	−26.7674	+	26.7674i	−0.914356	+	0.914356i	0.0822556	+	0.996611i	$0.473788\pi$
$858$		0			0
$859$	−28.6378			−0.977109			−0.488554	−	0.872533i	$-0.662476\pi$
$859$	−28.6378			−0.977109			−0.488554	+	0.872533i	$0.662476\pi$
$860$		0			0
$861$		0			0
$862$	−6.23716	−	21.4918i	−0.212438	−	0.732015i
$863$	−15.8157	+	15.8157i	−0.538371	+	0.538371i	−0.923050	−	0.384679i	$-0.874312\pi$
$863$	−15.8157	+	15.8157i	−0.538371	+	0.538371i	0.384679	+	0.923050i	$0.374312\pi$
$864$		0			0
$865$		0			0
$866$	37.0116	+	20.3614i	1.25771	+	0.691908i
$867$		0			0
$868$	−5.91147	+	26.3741i	−0.200648	+	0.895196i
$869$			1.21059i			0.0410665i
$870$		0			0
$871$			2.85481i			0.0967316i
$872$	22.1808	+	19.5895i	0.751135	+	0.663384i
$873$		0			0
$874$	4.30207	−	7.82003i	0.145520	−	0.264516i
$875$		0			0
$876$		0			0
$877$	17.3727	−	17.3727i	0.586633	−	0.586633i	−0.350085	−	0.936718i	$-0.613847\pi$
$877$	17.3727	−	17.3727i	0.586633	−	0.586633i	0.936718	+	0.350085i	$0.113847\pi$
$878$	−8.98009	+	2.60612i	−0.303063	+	0.0879522i
$879$		0			0
$880$		0			0
$881$	−56.5254			−1.90439			−0.952194	−	0.305493i	$-0.901179\pi$
$881$	−56.5254			−1.90439			−0.952194	+	0.305493i	$0.901179\pi$
$882$		0			0
$883$	15.1962	−	15.1962i	0.511392	−	0.511392i	−0.403561	−	0.914953i	$-0.632228\pi$
$883$	15.1962	−	15.1962i	0.511392	−	0.511392i	0.914953	+	0.403561i	$0.132228\pi$
$884$	2.90105	−	1.83869i	0.0975728	−	0.0618418i
$885$		0			0
$886$	14.0187	−	25.4822i	0.470966	−	0.856092i
$887$	−11.0676	−	11.0676i	−0.371613	−	0.371613i	0.496451	−	0.868065i	$-0.334636\pi$
$887$	−11.0676	−	11.0676i	−0.371613	−	0.371613i	−0.868065	+	0.496451i	$0.834636\pi$
$888$		0			0
$889$		−	8.81070i		−	0.295501i
$890$		0			0
$891$		0			0
$892$	5.27973	−	23.5556i	0.176778	−	0.788699i
$893$	−29.0280	−	29.0280i	−0.971385	−	0.971385i
$894$		0			0
$895$		0			0
$896$	14.6717	−	36.8364i	0.490146	−	1.23062i
$897$		0			0
$898$	13.2484	+	45.6510i	0.442105	+	1.52339i
$899$	−13.5142			−0.450725
$900$		0			0
$901$	−14.8480			−0.494659
$902$	3.25461	+	11.2147i	0.108367	+	0.373407i
$903$		0			0
$904$	−42.5023	+	2.63667i	−1.41361	+	0.0876944i
$905$		0			0
$906$		0			0
$907$	28.1654	+	28.1654i	0.935217	+	0.935217i	0.998026	−	0.0628084i	$-0.0200057\pi$
$907$	28.1654	+	28.1654i	0.935217	+	0.935217i	−0.0628084	+	0.998026i	$0.520006\pi$
$908$	−2.83625	−	0.635716i	−0.0941244	−	0.0210970i
$909$		0			0
$910$		0			0
$911$			34.8499i			1.15463i	0.816522	+	0.577315i	$0.195899\pi$
$911$			34.8499i			1.15463i	−0.816522	+	0.577315i	$0.804101\pi$
$912$		0			0
$913$	−0.605296	−	0.605296i	−0.0200324	−	0.0200324i
$914$	−15.0053	+	27.2757i	−0.496331	+	0.902198i
$915$		0			0
$916$	−9.47329	−	14.9468i	−0.313006	−	0.493856i
$917$	−45.0980	+	45.0980i	−1.48927	+	1.48927i
$918$		0			0
$919$	−21.1171			−0.696590			−0.348295	−	0.937385i	$-0.613239\pi$
$919$	−21.1171			−0.696590			−0.348295	+	0.937385i	$0.613239\pi$
$920$		0			0
$921$		0			0
$922$	35.5126	−	10.3061i	1.16954	−	0.339414i
$923$	1.54626	−	1.54626i	0.0508959	−	0.0508959i
$924$		0			0
$925$		0			0
$926$	−5.57104	+	10.1267i	−0.183076	+	0.332784i
$927$		0			0
$928$	19.5767	+	3.12993i	0.642638	+	0.102745i
$929$		−	39.0653i		−	1.28169i	−0.767670	−	0.640845i	$-0.778584\pi$
$929$		−	39.0653i		−	1.28169i	0.767670	−	0.640845i	$-0.221416\pi$
$930$		0			0
$931$			26.1827i			0.858105i
$932$	−13.5514	−	3.03740i	−0.443891	−	0.0994933i
$933$		0			0
$934$	3.95181	+	2.17403i	0.129307	+	0.0711364i
$935$		0			0
$936$		0			0
$937$	−1.82936	+	1.82936i	−0.0597626	+	0.0597626i	−0.736356	−	0.676594i	$-0.763455\pi$
$937$	−1.82936	+	1.82936i	−0.0597626	+	0.0597626i	0.676594	+	0.736356i	$0.263455\pi$
$938$	−7.67501	−	26.4464i	−0.250598	−	0.863504i
$939$		0			0
$940$		0			0
$941$	−1.58193			−0.0515695			−0.0257847	−	0.999668i	$-0.508208\pi$
$941$	−1.58193			−0.0515695			−0.0257847	+	0.999668i	$0.508208\pi$
$942$		0			0
$943$	−2.45505	+	2.45505i	−0.0799476	+	0.0799476i
$944$	14.8285	−	31.4170i	0.482627	−	1.02254i
$945$		0			0
$946$	−20.8480	−	11.4692i	−0.677827	−	0.372896i
$947$	−15.9429	−	15.9429i	−0.518075	−	0.518075i	0.398913	−	0.916989i	$-0.369387\pi$
$947$	−15.9429	−	15.9429i	−0.518075	−	0.518075i	−0.916989	+	0.398913i	$0.869387\pi$
$948$		0			0
$949$			6.74531i			0.218962i
$950$		0			0
$951$		0			0
$952$	−21.9315	+	24.8325i	−0.710803	+	0.804826i
$953$	−27.2113	−	27.2113i	−0.881462	−	0.881462i	0.112221	−	0.993683i	$-0.464203\pi$
$953$	−27.2113	−	27.2113i	−0.881462	−	0.881462i	−0.993683	+	0.112221i	$0.964203\pi$
$954$		0			0
$955$		0			0
$956$	−32.1400	+	20.3704i	−1.03948	+	0.658825i
$957$		0			0
$958$	−1.90283	+	0.552222i	−0.0614777	+	0.0178415i
$959$	−29.3383			−0.947383
$960$		0			0
$961$	16.1307			0.520345
$962$	−0.358578	+	0.104063i	−0.0115610	+	0.00335513i
$963$		0			0
$964$	4.91011	−	3.11203i	0.158144	−	0.100232i
$965$		0			0
$966$		0			0
$967$	−14.8921	−	14.8921i	−0.478899	−	0.478899i	0.425880	−	0.904780i	$-0.359964\pi$
$967$	−14.8921	−	14.8921i	−0.478899	−	0.478899i	−0.904780	+	0.425880i	$0.859964\pi$
$968$	3.42516	−	3.87824i	0.110089	−	0.124651i
$969$		0			0
$970$		0			0
$971$		−	41.6250i		−	1.33581i	−0.744246	−	0.667905i	$-0.767191\pi$
$971$		−	41.6250i		−	1.33581i	0.744246	−	0.667905i	$-0.232809\pi$
$972$		0			0
$973$	−30.7640	−	30.7640i	−0.986248	−	0.986248i
$974$	−1.71403	−	0.942949i	−0.0549212	−	0.0302140i
$975$		0			0
$976$	−26.1086	+	55.3160i	−0.835717	+	1.77062i
$977$	−12.0807	+	12.0807i	−0.386494	+	0.386494i	−0.873435	−	0.486941i	$-0.838113\pi$
$977$	−12.0807	+	12.0807i	−0.386494	+	0.386494i	0.486941	+	0.873435i	$0.338113\pi$
$978$		0			0
$979$	12.9692			0.414499
$980$		0			0
$981$		0			0
$982$	−14.2343	−	49.0484i	−0.454236	−	1.56520i
$983$	−22.2258	+	22.2258i	−0.708893	+	0.708893i	−0.966302	−	0.257410i	$-0.917131\pi$
$983$	−22.2258	+	22.2258i	−0.708893	+	0.708893i	0.257410	+	0.966302i	$0.417131\pi$
$984$		0			0
$985$		0			0
$986$	−14.5140	−	7.98465i	−0.462220	−	0.254283i
$987$		0			0
$988$	−4.97006	−	1.11399i	−0.158119	−	0.0354406i
$989$		−	7.07472i		−	0.224963i
$990$		0			0
$991$			0.353523i			0.0112300i	0.999984	+	0.00561501i	$0.00178732\pi$
$991$			0.353523i			0.0112300i	−0.999984	+	0.00561501i	$0.998213\pi$
$992$	21.5397	+	3.44377i	0.683886	+	0.109340i
$993$		0			0
$994$	−10.1672	+	18.4813i	−0.322484	+	0.586191i
$995$		0			0
$996$		0			0
$997$	−27.9380	+	27.9380i	−0.884805	+	0.884805i	−0.994018	−	0.109213i	$-0.965167\pi$
$997$	−27.9380	+	27.9380i	−0.884805	+	0.884805i	0.109213	+	0.994018i	$0.465167\pi$
$998$	8.63442	−	2.50580i	0.273318	−	0.0793197i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	900.2.k.n.343.6		12
3.2	odd	2		300.2.j.d.43.1		12
4.3	odd	2	inner	900.2.k.n.343.4		12
5.2	odd	4	inner	900.2.k.n.307.4		12
5.3	odd	4		180.2.k.e.127.3		12
5.4	even	2		180.2.k.e.163.1		12
12.11	even	2		300.2.j.d.43.3		12
15.2	even	4		300.2.j.d.7.3		12
15.8	even	4		60.2.j.a.7.4	✓	12
15.14	odd	2		60.2.j.a.43.6	yes	12
20.3	even	4		180.2.k.e.127.1		12
20.7	even	4	inner	900.2.k.n.307.6		12
20.19	odd	2		180.2.k.e.163.3		12
60.23	odd	4		60.2.j.a.7.6	yes	12
60.47	odd	4		300.2.j.d.7.1		12
60.59	even	2		60.2.j.a.43.4	yes	12
120.29	odd	2		960.2.w.g.703.6		12
120.53	even	4		960.2.w.g.127.3		12
120.59	even	2		960.2.w.g.703.3		12
120.83	odd	4		960.2.w.g.127.6		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
60.2.j.a.7.4	✓	12	15.8	even	4
60.2.j.a.7.6	yes	12	60.23	odd	4
60.2.j.a.43.4	yes	12	60.59	even	2
60.2.j.a.43.6	yes	12	15.14	odd	2
180.2.k.e.127.1		12	20.3	even	4
180.2.k.e.127.3		12	5.3	odd	4
180.2.k.e.163.1		12	5.4	even	2
180.2.k.e.163.3		12	20.19	odd	2
300.2.j.d.7.1		12	60.47	odd	4
300.2.j.d.7.3		12	15.2	even	4
300.2.j.d.43.1		12	3.2	odd	2
300.2.j.d.43.3		12	12.11	even	2
900.2.k.n.307.4		12	5.2	odd	4	inner
900.2.k.n.307.6		12	20.7	even	4	inner
900.2.k.n.343.4		12	4.3	odd	2	inner
900.2.k.n.343.6		12	1.1	even	1	trivial
960.2.w.g.127.3		12	120.53	even	4
960.2.w.g.127.6		12	120.83	odd	4
960.2.w.g.703.3		12	120.59	even	2
960.2.w.g.703.6		12	120.29	odd	2

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:	\( N \)	\(=\)	\( 900 = 2^{2} \cdot 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	900.k (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.35818 - 0.394157i) q^{2} +(1.68928 - 1.07067i) q^{4} +(2.47817 + 2.47817i) q^{7} +(1.87233 - 2.12000i) q^{8} +O(q^{10})\)	\(q+(1.35818 - 0.394157i) q^{2} +(1.68928 - 1.07067i) q^{4} +(2.47817 + 2.47817i) q^{7} +(1.87233 - 2.12000i) q^{8} -3.02831i q^{11} +(-0.363328 - 0.363328i) q^{13} +(4.34258 + 2.38900i) q^{14} +(1.70734 - 3.61732i) q^{16} +(-2.36333 + 2.36333i) q^{17} +4.95634 q^{19} +(-1.19363 - 4.11297i) q^{22} +(0.900390 - 0.900390i) q^{23} +(-0.636672 - 0.350255i) q^{26} +(6.83963 + 1.53303i) q^{28} +3.50466i q^{29} +3.85607i q^{31} +(0.893077 - 5.58591i) q^{32} +(-2.27829 + 4.14134i) q^{34} +(0.363328 - 0.363328i) q^{37} +(6.73158 - 1.95358i) q^{38} -2.72666 q^{41} +(3.92870 - 3.92870i) q^{43} +(-3.24231 - 5.11566i) q^{44} +(0.867993 - 1.57778i) q^{46} +(-5.85673 - 5.85673i) q^{47} +5.28267i q^{49} +(-1.00277 - 0.224760i) q^{52} +(3.14134 + 3.14134i) q^{53} +(9.89367 - 0.613763i) q^{56} +(1.38139 + 4.75995i) q^{58} +8.68516 q^{59} -15.2920 q^{61} +(1.51990 + 5.23723i) q^{62} +(-0.988770 - 7.93866i) q^{64} +(-3.92870 - 3.92870i) q^{67} +(-1.46199 + 6.52267i) q^{68} +4.25583i q^{71} +(-9.28267 - 9.28267i) q^{73} +(0.350255 - 0.636672i) q^{74} +(8.37266 - 5.30660i) q^{76} +(7.50466 - 7.50466i) q^{77} -0.399759 q^{79} +(-3.70328 + 1.07473i) q^{82} +(0.199879 - 0.199879i) q^{83} +(3.78734 - 6.88438i) q^{86} +(-6.42000 - 5.66999i) q^{88} +4.28267i q^{89} -1.80078i q^{91} +(0.556993 - 2.48503i) q^{92} +(-10.2629 - 5.64600i) q^{94} +(-6.73599 + 6.73599i) q^{97} +(2.08220 + 7.17480i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 12 q^{8}+O(q^{10}) \) 12 * q - 12 * q^8	\( 12 q - 12 q^{8} + 4 q^{13} + 12 q^{16} - 20 q^{17} - 12 q^{22} - 16 q^{26} + 4 q^{28} + 20 q^{32} - 4 q^{37} + 16 q^{38} - 16 q^{41} - 40 q^{46} + 8 q^{52} + 4 q^{53} + 64 q^{56} + 20 q^{58} - 32 q^{61} - 56 q^{62} - 16 q^{68} - 44 q^{73} + 8 q^{76} + 48 q^{77} - 16 q^{82} - 64 q^{86} - 60 q^{88} + 56 q^{92} + 20 q^{97} + 24 q^{98}+O(q^{100}) \) 12 * q - 12 * q^8 + 4 * q^13 + 12 * q^16 - 20 * q^17 - 12 * q^22 - 16 * q^26 + 4 * q^28 + 20 * q^32 - 4 * q^37 + 16 * q^38 - 16 * q^41 - 40 * q^46 + 8 * q^52 + 4 * q^53 + 64 * q^56 + 20 * q^58 - 32 * q^61 - 56 * q^62 - 16 * q^68 - 44 * q^73 + 8 * q^76 + 48 * q^77 - 16 * q^82 - 64 * q^86 - 60 * q^88 + 56 * q^92 + 20 * q^97 + 24 * q^98

Introduction

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