LMFDB - Embedded newform 900.2.k.n.343.4

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			343.4
Root			$-1.35818 - 0.394157i$ of defining polynomial
Character	$\chi$	$=$	900.343
Dual form			900.2.k.n.307.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

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

$2$	0.394157	−	1.35818i	0.278711	−	0.960375i
$2$	0.394157	−	1.35818i	0.278711	−	0.960375i
$3$		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	0.0614493	−	0.998110i	$-0.480428\pi$
$7$	−2.47817	−	2.47817i	−0.936661	−	0.936661i	−0.998110	+	0.0614493i	$0.980428\pi$
$8$	−2.12000	+	1.87233i	−0.749532	+	0.661968i
$9$		0			0
$10$		0			0
$11$			3.02831i			0.913069i	0.889706	+	0.456534i	$0.150909\pi$
$11$			3.02831i			0.913069i	−0.889706	+	0.456534i	$0.849091\pi$
$12$		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	$-0.692488\pi$
$19$	−4.95634			−1.13706			−0.568532	+	0.822661i	$0.692488\pi$
$20$		0			0
$21$		0			0
$22$	4.11297	+	1.19363i	0.876888	+	0.254482i
$23$	−0.900390	+	0.900390i	−0.187744	+	0.187744i	−0.794720	−	0.606976i	$-0.792382\pi$
$23$	−0.900390	+	0.900390i	−0.187744	+	0.187744i	0.606976	+	0.794720i	$0.292382\pi$
$24$		0			0
$25$		0			0
$26$	−0.636672	+	0.350255i	−0.124862	+	0.0686907i
$27$		0			0
$28$	1.53303	+	6.83963i	0.289715	+	1.29257i
$29$			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	$-0.887443\pi$
$31$		−	3.85607i		−	0.692571i	0.938129	−	0.346286i	$-0.112557\pi$
$32$	5.58591	−	0.893077i	0.987459	−	0.157875i
$33$		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	$0.236552\pi$
$38$	−1.95358	+	6.73158i	−0.316912	+	1.09201i
$39$		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	−0.940079	−	0.340958i	$-0.889249\pi$
$43$	−3.92870	+	3.92870i	−0.599121	+	0.599121i	0.340958	+	0.940079i	$0.389249\pi$
$44$	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	0.990659	−	0.136366i	$-0.0435423\pi$
$47$	5.85673	+	5.85673i	0.854292	+	0.854292i	−0.136366	+	0.990659i	$0.543542\pi$
$48$		0			0
$49$			5.28267i			0.754667i
$50$		0			0
$51$		0			0
$52$	0.224760	+	1.00277i	0.0311685	+	0.139059i
$53$	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
$58$	4.75995	+	1.38139i	0.625012	+	0.181385i
$59$	−8.68516			−1.13071			−0.565356	−	0.824847i	$-0.691261\pi$
$59$	−8.68516			−1.13071			−0.565356	+	0.824847i	$0.691261\pi$
$60$		0			0
$61$	−15.2920			−1.95794			−0.978970	−	0.204004i	$-0.934604\pi$
$61$	−15.2920			−1.95794			−0.978970	+	0.204004i	$0.934604\pi$
$62$	−5.23723	−	1.51990i	−0.665128	−	0.193027i
$63$		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	0.905121	−	0.425154i	$-0.139780\pi$
$67$	3.92870	+	3.92870i	0.479967	+	0.479967i	−0.425154	+	0.905121i	$0.639780\pi$
$68$	6.52267	−	1.46199i	0.790989	−	0.177292i
$69$		0			0
$70$		0			0
$71$		−	4.25583i		−	0.505075i	−0.967587	−	0.252537i	$-0.918735\pi$
$71$		−	4.25583i		−	0.505075i	0.967587	−	0.252537i	$-0.0812650\pi$
$72$		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	$-0.492841\pi$
$79$	0.399759			0.0449764			0.0224882	+	0.999747i	$0.492841\pi$
$80$		0			0
$81$		0			0
$82$	−1.07473	+	3.70328i	−0.118684	+	0.408959i
$83$	−0.199879	+	0.199879i	−0.0219396	+	0.0219396i	−0.717991	−	0.696052i	$-0.754938\pi$
$83$	−0.199879	+	0.199879i	−0.0219396	+	0.0219396i	0.696052	+	0.717991i	$0.254938\pi$
$84$		0			0
$85$		0			0
$86$	3.78734	+	6.88438i	0.408399	+	0.742362i
$87$		0			0
$88$	−5.66999	−	6.42000i	−0.604422	−	0.684374i
$89$			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
$92$	2.48503	−	0.556993i	0.259082	−	0.0580705i
$93$		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	$0.410677\pi$
$98$	7.17480	+	2.08220i	0.724764	+	0.210334i
$99$		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	$-0.384445\pi$
$103$	13.0914	−	13.0914i	1.28993	−	1.28993i	0.934827	−	0.355104i	$-0.115555\pi$
$104$	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	0.0592694	−	0.998242i	$-0.481123\pi$
$107$	−9.71281	−	9.71281i	−0.938973	−	0.938973i	−0.998242	+	0.0592694i	$0.981123\pi$
$108$		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
$112$	4.73325	−	13.1954i	0.447251	−	1.24685i
$113$	−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
$118$	−3.42331	+	11.7960i	−0.315142	+	1.08591i
$119$	11.7135			1.07377
$120$		0			0
$121$	1.82936			0.166305
$122$	−6.02745	+	20.7692i	−0.545699	+	1.88036i
$123$		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	0.781565	−	0.623823i	$-0.214422\pi$
$127$	1.77766	+	1.77766i	0.157742	+	0.157742i	−0.623823	+	0.781565i	$0.714422\pi$
$128$	−10.3924	−	4.47200i	−0.918564	−	0.395273i
$129$		0			0
$130$		0			0
$131$		−	18.1981i		−	1.58997i	−0.606626	−	0.794987i	$-0.707477\pi$
$131$		−	18.1981i		−	1.58997i	0.606626	−	0.794987i	$-0.292523\pi$
$132$		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	$-0.323515\pi$
$139$	12.4140			1.05294			0.526470	+	0.850194i	$0.323515\pi$
$140$		0			0
$141$		0			0
$142$	−5.78017	−	1.67747i	−0.485061	−	0.140770i
$143$	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
$148$	−1.00277	+	0.224760i	−0.0824270	+	0.0184751i
$149$		−	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	$-0.737045\pi$
$151$		−	18.0708i		−	1.47058i	0.677751	−	0.735292i	$-0.262955\pi$
$152$	10.5074	−	9.27990i	0.852265	−	0.752700i
$153$		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	$0.179009\pi$
$158$	0.157568	−	0.542943i	0.0125354	−	0.0431942i
$159$		0			0
$160$		0			0
$161$	4.46264			0.351705
$162$		0			0
$163$	3.22819	−	3.22819i	0.252851	−	0.252851i	−0.569287	−	0.822139i	$-0.692781\pi$
$163$	3.22819	−	3.22819i	0.252851	−	0.252851i	0.822139	+	0.569287i	$0.192781\pi$
$164$	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	0.384695	−	0.923044i	$-0.374307\pi$
$167$	−6.95700	−	6.95700i	−0.538349	−	0.538349i	−0.923044	+	0.384695i	$0.874307\pi$
$168$		0			0
$169$		−	12.7360i		−	0.979691i
$170$		0			0
$171$		0			0
$172$	10.8430	−	2.43034i	0.826771	−	0.185312i
$173$	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
$178$	5.81662	+	1.68804i	0.435974	+	0.126524i
$179$	−8.93968			−0.668183			−0.334091	−	0.942541i	$-0.608429\pi$
$179$	−8.93968			−0.668183			−0.334091	+	0.942541i	$0.608429\pi$
$180$		0			0
$181$	−1.00933			−0.0750228			−0.0375114	−	0.999296i	$-0.511943\pi$
$181$	−1.00933			−0.0750228			−0.0375114	+	0.999296i	$0.511943\pi$
$182$	2.44577	+	0.709789i	0.181293	+	0.0526131i
$183$		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
$188$	−3.62305	−	16.1643i	−0.264238	−	1.17890i
$189$		0			0
$190$		0			0
$191$			21.6262i			1.56481i	0.622768	+	0.782407i	$0.286008\pi$
$191$			21.6262i			1.56481i	−0.622768	+	0.782407i	$0.713992\pi$
$192$		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	$-0.627644\pi$
$199$	−11.0130			−0.780688			−0.390344	+	0.920669i	$0.627644\pi$
$200$		0			0
$201$		0			0
$202$	−2.28112	+	7.86022i	−0.160499	+	0.553043i
$203$	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
$208$	0.693949	−	1.93460i	0.0481167	−	0.134140i
$209$		−	15.0093i		−	1.03822i
$210$		0			0
$211$			27.9835i			1.92646i	0.268669	+	0.963232i	$0.413416\pi$
$211$			27.9835i			1.92646i	−0.268669	+	0.963232i	$0.586584\pi$
$212$	−1.94327	−	8.66993i	−0.133464	−	0.595453i
$213$		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
$218$	14.2101	+	4.12392i	0.962430	+	0.279307i
$219$		0			0
$220$		0			0
$221$	1.71733			0.115520
$222$		0			0
$223$	−8.53479	+	8.53479i	−0.571531	+	0.571531i	−0.932556	−	0.361025i	$-0.882427\pi$
$223$	−8.53479	+	8.53479i	−0.571531	+	0.571531i	0.361025	+	0.932556i	$0.382427\pi$
$224$	−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	0.740388	−	0.672180i	$-0.234642\pi$
$227$	1.02765	+	1.02765i	0.0682074	+	0.0682074i	−0.672180	+	0.740388i	$0.734642\pi$
$228$		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
$232$	−6.56188	−	7.42988i	−0.430809	−	0.487795i
$233$	−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
$238$	4.61694	−	15.9089i	0.299272	−	1.03122i
$239$	19.0259			1.23068			0.615340	−	0.788262i	$-0.289019\pi$
$239$	19.0259			1.23068			0.615340	+	0.788262i	$0.289019\pi$
$240$		0			0
$241$	2.90663			0.187232			0.0936161	−	0.995608i	$-0.470157\pi$
$241$	2.90663			0.187232			0.0936161	+	0.995608i	$0.470157\pi$
$242$	0.721054	−	2.48459i	0.0463511	−	0.159716i
$243$		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
$248$	7.21984	+	8.17486i	0.458460	+	0.519104i
$249$		0			0
$250$		0			0
$251$		−	2.77379i		−	0.175080i	−0.996161	−	0.0875401i	$-0.972099\pi$
$251$		−	2.77379i		−	0.175080i	0.996161	−	0.0875401i	$-0.0279006\pi$
$252$		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
$262$	−24.7162	−	7.17290i	−1.52697	−	0.443143i
$263$	−4.75646	+	4.75646i	−0.293296	+	0.293296i	−0.838381	−	0.545085i	$-0.816497\pi$
$263$	−4.75646	+	4.75646i	−0.293296	+	0.293296i	0.545085	+	0.838381i	$0.316497\pi$
$264$		0			0
$265$		0			0
$266$	21.5233	−	11.8407i	1.31968	−	0.726001i
$267$		0			0
$268$	−2.43034	−	10.8430i	−0.148457	−	0.662342i
$269$			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	$0.0305548\pi$
$271$			3.15556i			0.191687i	−0.995396	+	0.0958434i	$0.969445\pi$
$272$	−12.5839	−	4.51391i	−0.763012	−	0.273696i
$273$		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	$0.202026\pi$
$278$	4.89305	−	16.8604i	0.293466	−	1.01122i
$279$		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	−0.936254	−	0.351323i	$-0.885732\pi$
$283$	−9.84007	+	9.84007i	−0.584931	+	0.584931i	0.351323	+	0.936254i	$0.385732\pi$
$284$	−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
$292$	5.74238	+	25.6197i	0.336047	+	1.49928i
$293$	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
$298$	−7.86022	−	2.28112i	−0.455330	−	0.132142i
$299$	0.654274			0.0378376
$300$		0			0
$301$	19.4720			1.12235
$302$	−24.5434	−	7.12274i	−1.41231	−	0.409868i
$303$		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	0.449154	−	0.893454i	$-0.351725\pi$
$307$	−7.78477	−	7.78477i	−0.444300	−	0.444300i	−0.893454	+	0.449154i	$0.851725\pi$
$308$	−20.7125	+	4.64248i	−1.18020	+	0.264530i
$309$		0			0
$310$		0			0
$311$			7.05788i			0.400215i	0.979774	+	0.200108i	$0.0641292\pi$
$311$			7.05788i			0.400215i	−0.979774	+	0.200108i	$0.935871\pi$
$312$		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
$322$	1.75898	−	6.06105i	0.0980241	−	0.337769i
$323$	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
$328$	5.78050	−	5.10520i	0.319175	−	0.281887i
$329$		−	29.0280i		−	1.60036i
$330$		0			0
$331$		−	15.0143i		−	0.825259i	−0.910899	−	0.412630i	$-0.864610\pi$
$331$		−	15.0143i		−	0.825259i	0.910899	−	0.412630i	$-0.135390\pi$
$332$	0.551657	−	0.123648i	0.0302761	−	0.00678607i
$333$		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	$-0.0624513\pi$
$338$	−17.2977	−	5.01997i	−0.940871	−	0.273051i
$339$		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	0.996464	−	0.0840201i	$-0.0267760\pi$
$347$	16.9969	+	16.9969i	0.912444	+	0.912444i	−0.0840201	+	0.996464i	$0.526776\pi$
$348$		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
$352$	2.70451	+	16.9159i	0.144151	+	0.901618i
$353$	−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
$358$	−3.52363	+	12.1416i	−0.186230	+	0.641706i
$359$	−34.9952			−1.84697			−0.923487	−	0.383630i	$-0.874674\pi$
$359$	−34.9952			−1.84697			−0.923487	+	0.383630i	$0.874674\pi$
$360$		0			0
$361$	5.56534			0.292913
$362$	−0.397834	+	1.37085i	−0.0209097	+	0.0720500i
$363$		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	0.398516	−	0.917161i	$-0.369525\pi$
$367$	−9.93581	−	9.93581i	−0.518645	−	0.518645i	−0.917161	+	0.398516i	$0.869525\pi$
$368$	−4.79427	−	1.71973i	−0.249918	−	0.0896469i
$369$		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	$-0.219509\pi$
$379$	30.0388			1.54299			0.771495	+	0.636235i	$0.219509\pi$
$380$		0			0
$381$		0			0
$382$	29.3721	+	8.52410i	1.50281	+	0.436131i
$383$	−11.9133	+	11.9133i	−0.608744	+	0.608744i	−0.942618	−	0.333874i	$-0.891644\pi$
$383$	−11.9133	+	11.9133i	−0.608744	+	0.608744i	0.333874	+	0.942618i	$0.391644\pi$
$384$		0			0
$385$		0			0
$386$	−20.2663	+	11.1492i	−1.03153	+	0.567480i
$387$		0			0
$388$	18.5910	−	4.16697i	0.943814	−	0.211546i
$389$			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
$392$	−9.89090	−	11.1992i	−0.499566	−	0.565647i
$393$		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	$0.0114919\pi$
$398$	−4.34083	+	14.9575i	−0.217586	+	0.749753i
$399$		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
$412$	−36.1315	+	8.09849i	−1.78007	+	0.398984i
$413$	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
$418$	−20.3853	−	5.91603i	−0.997078	−	0.289362i
$419$	40.0788			1.95798			0.978988	−	0.203919i	$-0.0653679\pi$
$419$	40.0788			1.95798			0.978988	+	0.203919i	$0.0653679\pi$
$420$		0			0
$421$	19.3947			0.945240			0.472620	−	0.881266i	$-0.343308\pi$
$421$	19.3947			0.945240			0.472620	+	0.881266i	$0.343308\pi$
$422$	38.0065	+	11.0299i	1.85013	+	0.536927i
$423$		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
$428$	6.00847	+	26.8069i	0.290430	+	1.29576i
$429$		0			0
$430$		0			0
$431$			15.8241i			0.762218i	0.924530	+	0.381109i	$0.124458\pi$
$431$			15.8241i			0.762218i	−0.924530	+	0.381109i	$0.875542\pi$
$432$		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	$-0.449565\pi$
$439$	6.61188			0.315568			0.157784	+	0.987474i	$0.449565\pi$
$440$		0			0
$441$		0			0
$442$	0.676896	−	2.33243i	0.0321967	−	0.110942i
$443$	−14.5419	+	14.5419i	−0.690906	+	0.690906i	−0.962431	−	0.271525i	$-0.912472\pi$
$443$	−14.5419	+	14.5419i	−0.690906	+	0.690906i	0.271525	+	0.962431i	$0.412472\pi$
$444$		0			0
$445$		0			0
$446$	8.22769	+	14.9558i	0.389593	+	0.708177i
$447$		0			0
$448$	−22.1237	+	17.2230i	−1.04525	+	0.813711i
$449$			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
$452$	6.58575	+	29.3824i	0.309768	+	1.38203i
$453$		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	$0.422155\pi$
$458$	−12.0172	−	3.48751i	−0.561525	−	0.162960i
$459$		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	−0.559953	−	0.828525i	$-0.689181\pi$
$463$	5.77898	−	5.77898i	0.268572	−	0.268572i	0.828525	+	0.559953i	$0.189181\pi$
$464$	−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	0.653000	−	0.757357i	$-0.273510\pi$
$467$	−2.25517	−	2.25517i	−0.104357	−	0.104357i	−0.757357	+	0.653000i	$0.773510\pi$
$468$		0			0
$469$		−	19.4720i		−	0.899132i
$470$		0			0
$471$		0			0
$472$	18.4125	−	16.2615i	0.847505	−	0.748495i
$473$	−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
$478$	7.49917	−	25.8405i	0.343004	−	1.18191i
$479$	1.40102			0.0640143			0.0320071	−	0.999488i	$-0.489810\pi$
$479$	1.40102			0.0640143			0.0320071	+	0.999488i	$0.489810\pi$
$480$		0			0
$481$	−0.264015			−0.0120380
$482$	1.14567	−	3.94771i	0.0521837	−	0.179813i
$483$		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	0.728921	−	0.684597i	$-0.240022\pi$
$487$	0.978144	+	0.978144i	0.0443239	+	0.0443239i	−0.684597	+	0.728921i	$0.740022\pi$
$488$	32.4190	−	28.6317i	1.46754	−	1.29609i
$489$		0			0
$490$		0			0
$491$			36.1134i			1.62978i	0.579619	+	0.814888i	$0.303201\pi$
$491$			36.1134i			1.62978i	−0.579619	+	0.814888i	$0.696799\pi$
$492$		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	$-0.545449\pi$
$499$	−6.35736			−0.284595			−0.142297	+	0.989824i	$0.545449\pi$
$500$		0			0
$501$		0			0
$502$	−3.76730	−	1.09331i	−0.168143	−	0.0487968i
$503$	−17.1704	+	17.1704i	−0.765592	+	0.765592i	−0.977327	−	0.211735i	$-0.932089\pi$
$503$	−17.1704	+	17.1704i	−0.765592	+	0.765592i	0.211735	+	0.977327i	$0.432089\pi$
$504$		0			0
$505$		0			0
$506$	−4.77801	+	2.62855i	−0.212408	+	0.116853i
$507$		0			0
$508$	−1.09968	−	4.90626i	−0.0487906	−	0.217680i
$509$		−	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
$512$	12.7676	+	18.6812i	0.564253	+	0.825602i
$513$		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
$518$	−0.709789	+	2.44577i	−0.0311864	+	0.107461i
$519$		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	−0.619532	−	0.784971i	$-0.712678\pi$
$523$	3.78345	−	3.78345i	0.165439	−	0.165439i	0.784971	+	0.619532i	$0.212678\pi$
$524$	−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
$532$	−7.59822	−	33.8995i	−0.329425	−	1.46973i
$533$	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
$538$	29.4515	+	8.54715i	1.26975	+	0.368494i
$539$	−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	$0.290263\pi$
$542$	4.28581	+	1.24379i	0.184091	+	0.0534252i
$543$		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	0.722476	−	0.691396i	$-0.243004\pi$
$547$	0.726896	+	0.726896i	0.0310798	+	0.0310798i	−0.691396	+	0.722476i	$0.743004\pi$
$548$	16.3371	−	3.66178i	0.697886	−	0.156424i
$549$		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
$562$	−0.0709362	+	0.244430i	−0.00299226	+	0.0103107i
$563$	7.08426	−	7.08426i	0.298566	−	0.298566i	−0.541886	−	0.840452i	$-0.682290\pi$
$563$	7.08426	−	7.08426i	0.298566	−	0.298566i	0.840452	+	0.541886i	$0.182290\pi$
$564$		0			0
$565$		0			0
$566$	9.48601	+	17.2431i	0.398727	+	0.724780i
$567$		0			0
$568$	7.96832	+	9.02235i	0.334343	+	0.378569i
$569$		−	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	$0.226758\pi$
$571$			31.2381i			1.30727i	−0.756808	+	0.653637i	$0.773242\pi$
$572$	−3.03669	+	0.680641i	−0.126970	+	0.0284590i
$573$		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	$0.260884\pi$
$578$	7.91729	+	2.29768i	0.329316	+	0.0955709i
$579$		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	0.0245164	−	0.999699i	$-0.492195\pi$
$587$	−23.6268	−	23.6268i	−0.975183	−	0.975183i	−0.999699	+	0.0245164i	$0.992195\pi$
$588$		0			0
$589$			19.1120i			0.787498i
$590$		0			0
$591$		0			0
$592$	1.93460	+	0.693949i	0.0795115	+	0.0285211i
$593$	−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
$598$	0.257887	−	0.888619i	0.0105458	−	0.0363383i
$599$	−33.0851			−1.35182			−0.675910	−	0.736984i	$-0.736249\pi$
$599$	−33.0851			−1.35182			−0.675910	+	0.736984i	$0.736249\pi$
$600$		0			0
$601$	−24.3200			−0.992033			−0.496016	−	0.868313i	$-0.665204\pi$
$601$	−24.3200			−0.992033			−0.496016	+	0.868313i	$0.665204\pi$
$602$	7.67501	−	26.4464i	0.312810	−	1.07787i
$603$		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	0.609092	−	0.793100i	$-0.291534\pi$
$607$	−4.53347	−	4.53347i	−0.184008	−	0.184008i	−0.793100	+	0.609092i	$0.791534\pi$
$608$	−27.6857	+	4.42639i	−1.12280	+	0.179514i
$609$		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	$-0.701501\pi$
$619$	−29.4373			−1.18319			−0.591593	+	0.806237i	$0.701501\pi$
$620$		0			0
$621$		0			0
$622$	9.58583	+	2.78191i	0.384357	+	0.111544i
$623$	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
$628$	−10.8172	+	2.42456i	−0.431653	+	0.0967503i
$629$			1.71733i			0.0684743i
$630$		0			0
$631$		−	5.25710i		−	0.209282i	−0.994510	−	0.104641i	$-0.966631\pi$
$631$		−	5.25710i		−	0.209282i	0.994510	−	0.104641i	$-0.0333693\pi$
$632$	−0.847487	+	0.748480i	−0.0337112	+	0.0297729i
$633$		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
$638$	−4.18326	+	14.4146i	−0.165617	+	0.570679i
$639$		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	−0.866073	−	0.499917i	$-0.833364\pi$
$643$	−9.28480	+	9.28480i	−0.366157	+	0.366157i	0.499917	+	0.866073i	$0.333364\pi$
$644$	−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	$-0.955409\pi$
$647$	−28.7387	−	28.7387i	−1.12983	−	1.12983i	−0.139630	−	0.990204i	$-0.544591\pi$
$648$		0			0
$649$		−	26.3013i		−	1.03242i
$650$		0			0
$651$		0			0
$652$	−8.90963	+	1.99700i	−0.348928	+	0.0782084i
$653$	−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
$658$	−39.4251	−	11.4416i	−1.53695	−	0.446039i
$659$	−17.9963			−0.701038			−0.350519	−	0.936556i	$-0.613995\pi$
$659$	−17.9963			−0.701038			−0.350519	+	0.936556i	$0.613995\pi$
$660$		0			0
$661$	−9.06794			−0.352702			−0.176351	−	0.984327i	$-0.556429\pi$
$661$	−9.06794			−0.352702			−0.176351	+	0.984327i	$0.556429\pi$
$662$	−20.3920	−	5.91798i	−0.792558	−	0.230009i
$663$		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
$668$	4.30369	+	19.2010i	0.166515	+	0.742908i
$669$		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
$682$	4.60272	−	15.8599i	0.176247	−	0.607308i
$683$	−33.3943	+	33.3943i	−1.27780	+	1.27780i	−0.335897	+	0.941899i	$0.609039\pi$
$683$	−33.3943	+	33.3943i	−1.27780	+	1.27780i	−0.941899	+	0.335897i	$0.890961\pi$
$684$		0			0
$685$		0			0
$686$	4.10270	+	7.45763i	0.156642	+	0.284734i
$687$		0			0
$688$	−20.9190	−	7.50373i	−0.797528	−	0.286077i
$689$		−	2.28267i		−	0.0869629i
$690$		0			0
$691$		−	24.6365i		−	0.937216i	−0.883406	−	0.468608i	$-0.844756\pi$
$691$		−	24.6365i		−	0.937216i	0.883406	−	0.468608i	$-0.155244\pi$
$692$	−0.388082	−	1.73143i	−0.0147527	−	0.0658193i
$693$		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
$698$	5.95611	+	1.72853i	0.225442	+	0.0654256i
$699$		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
$712$	−8.01857	−	9.07925i	−0.300509	−	0.340259i
$713$	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
$718$	−13.7936	+	47.5296i	−0.514772	+	1.77379i
$719$	41.3423			1.54181			0.770903	−	0.636953i	$-0.219805\pi$
$719$	41.3423			1.54181			0.770903	+	0.636953i	$0.219805\pi$
$720$		0			0
$721$	−64.8853			−2.41646
$722$	2.19362	−	7.55871i	0.0816380	−	0.281306i
$723$		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	0.860838	−	0.508880i	$-0.169940\pi$
$727$	9.48981	+	9.48981i	0.351958	+	0.351958i	−0.508880	+	0.860838i	$0.669940\pi$
$728$	−3.37165	−	3.81765i	−0.124962	−	0.141491i
$729$		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	$-0.654618\pi$
$739$	−25.3832			−0.933737			−0.466868	+	0.884327i	$0.654618\pi$
$740$		0			0
$741$		0			0
$742$	−21.1462	−	6.13684i	−0.776300	−	0.225290i
$743$	32.7400	−	32.7400i	1.20111	−	1.20111i	0.227285	−	0.973828i	$-0.427015\pi$
$743$	32.7400	−	32.7400i	1.20111	−	1.20111i	0.973828	−	0.227285i	$-0.0729850\pi$
$744$		0			0
$745$		0			0
$746$	12.4240	−	6.83488i	0.454875	−	0.250243i
$747$		0			0
$748$	4.42734	+	19.7526i	0.161880	+	0.722228i
$749$			48.1400i			1.75900i
$750$		0			0
$751$		−	24.4810i		−	0.893323i	−0.894703	−	0.446662i	$-0.852613\pi$
$751$		−	24.4810i		−	0.893323i	0.894703	−	0.446662i	$-0.147387\pi$
$752$	−11.1862	+	31.1851i	−0.407920	+	1.13720i
$753$		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	$0.450774\pi$
$758$	11.8400	−	40.7980i	0.430048	−	1.48185i
$759$		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
$772$	7.15447	+	31.9198i	0.257495	+	1.14882i
$773$	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
$778$	22.1845	+	6.43817i	0.795352	+	0.230819i
$779$	13.5142			0.484198
$780$		0			0
$781$	12.8880			0.461168
$782$	−5.78017	−	1.67747i	−0.206698	−	0.0599860i
$783$		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	$-0.961782\pi$
$787$	−31.2117	−	31.2117i	−1.11258	−	1.11258i	−0.119776	−	0.992801i	$-0.538218\pi$
$788$	26.0098	−	5.82981i	0.926560	−	0.207678i
$789$		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
$802$	−10.4709	+	36.0804i	−0.369741	+	1.27404i
$803$	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
$808$	12.2691	−	10.8358i	0.431627	−	0.381202i
$809$			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	$-0.841623\pi$
$811$		−	27.1840i		−	0.954559i	0.878751	−	0.477280i	$-0.158377\pi$
$812$	−23.9706	+	5.37275i	−0.841203	+	0.188547i
$813$		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
$818$	−34.4905	−	10.0095i	−1.20593	−	0.349974i
$819$		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	−0.131709	−	0.991288i	$-0.542046\pi$
$823$	24.6596	−	24.6596i	0.859579	−	0.859579i	0.991288	+	0.131709i	$0.0420465\pi$
$824$	−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	0.902191	−	0.431337i	$-0.141958\pi$
$827$	13.5406	+	13.5406i	0.470854	+	0.470854i	−0.431337	+	0.902191i	$0.641958\pi$
$828$		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
$832$	−3.24359	+	2.52509i	−0.112451	+	0.0875418i
$833$	−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
$838$	15.7973	−	54.4340i	0.545709	−	1.88039i
$839$	−10.2597			−0.354203			−0.177102	−	0.984193i	$-0.556672\pi$
$839$	−10.2597			−0.354203			−0.177102	+	0.984193i	$0.556672\pi$
$840$		0			0
$841$	16.7173			0.576460
$842$	7.64455	−	26.3414i	0.263449	−	0.907785i
$843$		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
$848$	−5.99988	+	16.7265i	−0.206037	+	0.574392i
$849$		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	$-0.337524\pi$
$859$	28.6378			0.977109			0.488554	+	0.872533i	$0.337524\pi$
$860$		0			0
$861$		0			0
$862$	21.4918	+	6.23716i	0.732015	+	0.212438i
$863$	15.8157	−	15.8157i	0.538371	−	0.538371i	−0.384679	−	0.923050i	$-0.625688\pi$
$863$	15.8157	−	15.8157i	0.538371	−	0.538371i	0.923050	+	0.384679i	$0.125688\pi$
$864$		0			0
$865$		0			0
$866$	37.0116	−	20.3614i	1.25771	−	0.691908i
$867$		0			0
$868$	26.3741	−	5.91147i	0.895196	−	0.200648i
$869$			1.21059i			0.0410665i
$870$		0			0
$871$		−	2.85481i		−	0.0967316i
$872$	−19.5895	−	22.1808i	−0.663384	−	0.751135i
$873$		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	$0.113847\pi$
$878$	2.60612	−	8.98009i	0.0879522	−	0.303063i
$879$		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	−0.914953	−	0.403561i	$-0.867772\pi$
$883$	−15.1962	+	15.1962i	−0.511392	+	0.511392i	0.403561	+	0.914953i	$0.367772\pi$
$884$	−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	0.868065	−	0.496451i	$-0.165364\pi$
$887$	11.0676	+	11.0676i	0.371613	+	0.371613i	−0.496451	+	0.868065i	$0.665364\pi$
$888$		0			0
$889$		−	8.81070i		−	0.295501i
$890$		0			0
$891$		0			0
$892$	23.5556	−	5.27973i	0.788699	−	0.176778i
$893$	−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
$898$	45.6510	+	13.2484i	1.52339	+	0.442105i
$899$	13.5142			0.450725
$900$		0			0
$901$	−14.8480			−0.494659
$902$	−11.2147	−	3.25461i	−0.373407	−	0.108367i
$903$		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	0.0628084	−	0.998026i	$-0.479994\pi$
$907$	−28.1654	−	28.1654i	−0.935217	−	0.935217i	−0.998026	+	0.0628084i	$0.979994\pi$
$908$	−0.635716	−	2.83625i	−0.0210970	−	0.0941244i
$909$		0			0
$910$		0			0
$911$		−	34.8499i		−	1.15463i	−0.816522	−	0.577315i	$-0.804101\pi$
$911$		−	34.8499i		−	1.15463i	0.816522	−	0.577315i	$-0.195899\pi$
$912$		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	$-0.386761\pi$
$919$	21.1171			0.696590			0.348295	+	0.937385i	$0.386761\pi$
$920$		0			0
$921$		0			0
$922$	10.3061	−	35.5126i	0.339414	−	1.16954i
$923$	−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
$928$	3.12993	+	19.5767i	0.102745	+	0.642638i
$929$		−	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
$932$	3.03740	+	13.5514i	0.0994933	+	0.443891i
$933$		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	$0.263455\pi$
$938$	−26.4464	−	7.67501i	−0.863504	−	0.250598i
$939$		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	0.916989	−	0.398913i	$-0.130613\pi$
$947$	15.9429	+	15.9429i	0.518075	+	0.518075i	−0.398913	+	0.916989i	$0.630613\pi$
$948$		0			0
$949$			6.74531i			0.218962i
$950$		0			0
$951$		0			0
$952$	−24.8325	+	21.9315i	−0.804826	+	0.710803i
$953$	−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
$958$	0.552222	−	1.90283i	0.0178415	−	0.0614777i
$959$	29.3383			0.947383
$960$		0			0
$961$	16.1307			0.520345
$962$	−0.104063	+	0.358578i	−0.00335513	+	0.0115610i
$963$		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	0.904780	−	0.425880i	$-0.140036\pi$
$967$	14.8921	+	14.8921i	0.478899	+	0.478899i	−0.425880	+	0.904780i	$0.640036\pi$
$968$	−3.87824	+	3.42516i	−0.124651	+	0.110089i
$969$		0			0
$970$		0			0
$971$			41.6250i			1.33581i	0.744246	+	0.667905i	$0.232809\pi$
$971$			41.6250i			1.33581i	−0.744246	+	0.667905i	$0.767191\pi$
$972$		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
$982$	49.0484	+	14.2343i	1.56520	+	0.454236i
$983$	22.2258	−	22.2258i	0.708893	−	0.708893i	−0.257410	−	0.966302i	$-0.582869\pi$
$983$	22.2258	−	22.2258i	0.708893	−	0.708893i	0.966302	+	0.257410i	$0.0828690\pi$
$984$		0			0
$985$		0			0
$986$	−14.5140	+	7.98465i	−0.462220	+	0.254283i
$987$		0			0
$988$	−1.11399	−	4.97006i	−0.0354406	−	0.158119i
$989$		−	7.07472i		−	0.224963i
$990$		0			0
$991$		−	0.353523i		−	0.0112300i	−0.999984	−	0.00561501i	$-0.998213\pi$
$991$		−	0.353523i		−	0.0112300i	0.999984	−	0.00561501i	$-0.00178732\pi$
$992$	−3.44377	−	21.5397i	−0.109340	−	0.683886i
$993$		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	$0.465167\pi$
$998$	−2.50580	+	8.63442i	−0.0793197	+	0.273318i
$999$		0			0

Twists

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

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

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