LMFDB - Embedded newform 225.2.p.b.32.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [225,2,Mod(32,225)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(225, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([10, 3]))

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

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

chi := DirichletCharacter("225.32");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 225 = 3^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	225.p (of order $12$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$1.79663404548$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{12})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 6 x^{15} + 18 x^{14} - 36 x^{13} + 34 x^{12} + 18 x^{11} - 72 x^{10} + 132 x^{9} - 93 x^{8} + \cdots + 1 $ x^16 - 6x^15 + 18x^14 - 36x^13 + 34x^12 + 18x^11 - 72x^10 + 132x^9 - 93x^8 - 102x^7 + 144x^6 - 432x^5 + 502x^4 + 288x^3 + 72x^2 + 12*x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 45)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			32.1
Root			$-1.29724 + 0.347596i$ of defining polynomial
Character	$\chi$	$=$	225.32
Dual form			225.2.p.b.218.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.29724 - 0.347596i) q^{2} +(1.25897 - 1.18953i) q^{3} +(-0.170031 - 0.0981673i) q^{4} +(-2.04667 + 1.10550i) q^{6} +(0.530190 - 1.97869i) q^{7} +(2.08575 + 2.08575i) q^{8} +(0.170031 - 2.99518i) q^{9} +O(q^{10})$	\(q+(-1.29724 - 0.347596i) q^{2} +(1.25897 - 1.18953i) q^{3} +(-0.170031 - 0.0981673i) q^{4} +(-2.04667 + 1.10550i) q^{6} +(0.530190 - 1.97869i) q^{7} +(2.08575 + 2.08575i) q^{8} +(0.170031 - 2.99518i) q^{9} +(-0.762281 + 0.440103i) q^{11} +(-0.330837 + 0.0786668i) q^{12} +(-1.43820 - 5.36743i) q^{13} +(-1.37557 + 2.38256i) q^{14} +(-1.78439 - 3.09066i) q^{16} +(-1.13610 + 1.13610i) q^{17} +(-1.26168 + 3.82638i) q^{18} +1.52456i q^{19} +(-1.68622 - 3.12180i) q^{21} +(1.14184 - 0.305956i) q^{22} +(-1.53331 + 0.410850i) q^{23} +(5.10696 + 0.144840i) q^{24} +7.46278i q^{26} +(-3.34879 - 3.97311i) q^{27} +(-0.284392 + 0.284392i) q^{28} +(-0.796583 - 1.37972i) q^{29} +(3.49518 - 6.05383i) q^{31} +(-0.286379 - 1.06878i) q^{32} +(-0.436175 + 1.46084i) q^{33} +(1.86870 - 1.07889i) q^{34} +(-0.322939 + 0.492581i) q^{36} +(4.25746 + 4.25746i) q^{37} +(0.529931 - 1.97773i) q^{38} +(-8.19538 - 5.04667i) q^{39} +(3.11546 + 1.79871i) q^{41} +(1.10232 + 4.63586i) q^{42} +(1.85841 + 0.497959i) q^{43} +0.172815 q^{44} +2.13189 q^{46} +(7.99942 + 2.14344i) q^{47} +(-5.92294 - 1.76847i) q^{48} +(2.42805 + 1.40183i) q^{49} +(-0.0788937 + 2.78174i) q^{51} +(-0.282368 + 1.05381i) q^{52} +(4.65601 + 4.65601i) q^{53} +(2.96317 + 6.31812i) q^{54} +(5.23290 - 3.02121i) q^{56} +(1.81351 + 1.91938i) q^{57} +(0.553777 + 2.06672i) q^{58} +(-3.81780 + 6.61262i) q^{59} +(6.64002 + 11.5008i) q^{61} +(-6.63838 + 6.63838i) q^{62} +(-5.83639 - 1.92445i) q^{63} +8.62358i q^{64} +(1.07361 - 1.74345i) q^{66} +(-3.20857 + 0.859733i) q^{67} +(0.304699 - 0.0816439i) q^{68} +(-1.44168 + 2.34117i) q^{69} -5.89798i q^{71} +(6.60182 - 5.89254i) q^{72} +(-1.58900 + 1.58900i) q^{73} +(-4.04309 - 7.00284i) q^{74} +(0.149662 - 0.259222i) q^{76} +(0.466676 + 1.74166i) q^{77} +(8.87721 + 9.39544i) q^{78} +(6.69401 - 3.86479i) q^{79} +(-8.94218 - 1.01854i) q^{81} +(-3.41628 - 3.41628i) q^{82} +(2.57170 - 9.59770i) q^{83} +(-0.0197489 + 0.696335i) q^{84} +(-2.23772 - 1.29195i) q^{86} +(-2.64410 - 0.789474i) q^{87} +(-2.50787 - 0.671981i) q^{88} +4.62765 q^{89} -11.3830 q^{91} +(0.301043 + 0.0806641i) q^{92} +(-2.80088 - 11.7792i) q^{93} +(-9.63215 - 5.56112i) q^{94} +(-1.63189 - 1.00491i) q^{96} +(1.02621 - 3.82988i) q^{97} +(-2.66250 - 2.66250i) q^{98} +(1.18858 + 2.35800i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 6 q^{2} + 6 q^{3} + 2 q^{7}+O(q^{10}) $ 16 * q + 6 * q^2 + 6 * q^3 + 2 * q^7	$ 16 q + 6 q^{2} + 6 q^{3} + 2 q^{7} + 6 q^{12} + 2 q^{13} - 8 q^{16} - 36 q^{18} - 12 q^{21} + 10 q^{22} - 18 q^{23} - 18 q^{27} + 16 q^{28} - 4 q^{31} - 30 q^{32} + 12 q^{33} - 48 q^{36} - 4 q^{37} + 30 q^{38} - 24 q^{41} - 6 q^{42} + 2 q^{43} + 32 q^{46} + 12 q^{47} + 30 q^{48} + 36 q^{51} + 14 q^{52} + 36 q^{56} + 6 q^{57} + 6 q^{58} + 8 q^{61} - 36 q^{63} + 36 q^{66} - 4 q^{67} - 42 q^{68} - 18 q^{72} + 8 q^{73} + 24 q^{76} + 6 q^{77} + 42 q^{78} - 48 q^{81} - 32 q^{82} + 66 q^{83} - 48 q^{86} + 18 q^{87} - 18 q^{88} - 40 q^{91} + 60 q^{92} + 18 q^{93} - 24 q^{96} - 28 q^{97}+O(q^{100}) $ 16 * q + 6 * q^2 + 6 * q^3 + 2 * q^7 + 6 * q^12 + 2 * q^13 - 8 * q^16 - 36 * q^18 - 12 * q^21 + 10 * q^22 - 18 * q^23 - 18 * q^27 + 16 * q^28 - 4 * q^31 - 30 * q^32 + 12 * q^33 - 48 * q^36 - 4 * q^37 + 30 * q^38 - 24 * q^41 - 6 * q^42 + 2 * q^43 + 32 * q^46 + 12 * q^47 + 30 * q^48 + 36 * q^51 + 14 * q^52 + 36 * q^56 + 6 * q^57 + 6 * q^58 + 8 * q^61 - 36 * q^63 + 36 * q^66 - 4 * q^67 - 42 * q^68 - 18 * q^72 + 8 * q^73 + 24 * q^76 + 6 * q^77 + 42 * q^78 - 48 * q^81 - 32 * q^82 + 66 * q^83 - 48 * q^86 + 18 * q^87 - 18 * q^88 - 40 * q^91 + 60 * q^92 + 18 * q^93 - 24 * q^96 - 28 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/225\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{4}\right)$

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 $

$2$	−1.29724	−	0.347596i	−0.917290	−	0.245787i	−0.230863	−	0.972986i	$-0.574155\pi$
$2$	−1.29724	−	0.347596i	−0.917290	−	0.245787i	−0.686427	+	0.727199i	$0.740822\pi$
$3$	1.25897	−	1.18953i	0.726869	−	0.686776i
$3$	1.25897	−	1.18953i	0.726869	−	0.686776i
$4$	−0.170031	−	0.0981673i	−0.0850154	−	0.0490837i
$5$		0			0
$5$		0			0
$6$	−2.04667	+	1.10550i	−0.835551	+	0.451318i
$7$	0.530190	−	1.97869i	0.200393	−	0.747876i	−0.790412	−	0.612576i	$-0.790133\pi$
$7$	0.530190	−	1.97869i	0.200393	−	0.747876i	0.990805	−	0.135300i	$-0.0432000\pi$
$8$	2.08575	+	2.08575i	0.737423	+	0.737423i
$9$	0.170031	−	2.99518i	0.0566769	−	0.998393i
$10$		0			0
$11$	−0.762281	+	0.440103i	−0.229836	+	0.132696i	−0.610497	−	0.792019i	$-0.709030\pi$
$11$	−0.762281	+	0.440103i	−0.229836	+	0.132696i	0.380660	+	0.924715i	$0.375697\pi$
$12$	−0.330837	+	0.0786668i	−0.0955045	+	0.0227092i
$13$	−1.43820	−	5.36743i	−0.398885	−	1.48866i	−0.815062	−	0.579374i	$-0.803297\pi$
$13$	−1.43820	−	5.36743i	−0.398885	−	1.48866i	0.416177	−	0.909283i	$-0.363370\pi$
$14$	−1.37557	+	2.38256i	−0.367637	+	0.636766i
$15$		0			0
$16$	−1.78439	−	3.09066i	−0.446098	−	0.772664i
$17$	−1.13610	+	1.13610i	−0.275544	+	0.275544i	−0.831327	−	0.555783i	$-0.812418\pi$
$17$	−1.13610	+	1.13610i	−0.275544	+	0.275544i	0.555783	+	0.831327i	$0.312418\pi$
$18$	−1.26168	+	3.82638i	−0.297381	+	0.901885i
$19$			1.52456i			0.349758i	0.984590	+	0.174879i	$0.0559535\pi$
$19$			1.52456i			0.349758i	−0.984590	+	0.174879i	$0.944047\pi$
$20$		0			0
$21$	−1.68622	−	3.12180i	−0.367964	−	0.681233i
$22$	1.14184	−	0.305956i	0.243442	−	0.0652300i
$23$	−1.53331	+	0.410850i	−0.319718	+	0.0856682i	−0.415109	−	0.909772i	$-0.636257\pi$
$23$	−1.53331	+	0.410850i	−0.319718	+	0.0856682i	0.0953909	+	0.995440i	$0.469590\pi$
$24$	5.10696	+	0.144840i	1.04245	+	0.0295653i
$25$		0			0
$26$			7.46278i			1.46357i
$27$	−3.34879	−	3.97311i	−0.644476	−	0.764625i
$28$	−0.284392	+	0.284392i	−0.0537450	+	0.0537450i
$29$	−0.796583	−	1.37972i	−0.147922	−	0.256208i	0.782537	−	0.622603i	$-0.213925\pi$
$29$	−0.796583	−	1.37972i	−0.147922	−	0.256208i	−0.930459	+	0.366396i	$0.880592\pi$
$30$		0			0
$31$	3.49518	−	6.05383i	0.627752	−	1.08730i	−0.360249	−	0.932856i	$-0.617308\pi$
$31$	3.49518	−	6.05383i	0.627752	−	1.08730i	0.988002	−	0.154443i	$-0.0493583\pi$
$32$	−0.286379	−	1.06878i	−0.0506251	−	0.188936i
$33$	−0.436175	+	1.46084i	−0.0759284	+	0.254299i
$34$	1.86870	−	1.07889i	0.320479	−	0.185029i
$35$		0			0
$36$	−0.322939	+	0.492581i	−0.0538232	+	0.0820968i
$37$	4.25746	+	4.25746i	0.699922	+	0.699922i	0.964393	−	0.264472i	$-0.0851975\pi$
$37$	4.25746	+	4.25746i	0.699922	+	0.699922i	−0.264472	+	0.964393i	$0.585198\pi$
$38$	0.529931	−	1.97773i	0.0859661	−	0.320830i
$39$	−8.19538	−	5.04667i	−1.31231	−	0.808114i
$40$		0			0
$41$	3.11546	+	1.79871i	0.486552	+	0.280911i	0.723143	−	0.690698i	$-0.242697\pi$
$41$	3.11546	+	1.79871i	0.486552	+	0.280911i	−0.236591	+	0.971609i	$0.576030\pi$
$42$	1.10232	+	4.63586i	0.170092	+	0.715329i
$43$	1.85841	+	0.497959i	0.283404	+	0.0759380i	0.397721	−	0.917506i	$-0.369801\pi$
$43$	1.85841	+	0.497959i	0.283404	+	0.0759380i	−0.114317	+	0.993444i	$0.536468\pi$
$44$	0.172815			0.0260528
$45$		0			0
$46$	2.13189			0.314330
$47$	7.99942	+	2.14344i	1.16683	+	0.312652i	0.789693	−	0.613503i	$-0.210240\pi$
$47$	7.99942	+	2.14344i	1.16683	+	0.312652i	0.377142	+	0.926155i	$0.376907\pi$
$48$	−5.92294	−	1.76847i	−0.854902	−	0.255256i
$49$	2.42805	+	1.40183i	0.346864	+	0.200262i
$50$		0			0
$51$	−0.0788937	+	2.78174i	−0.0110473	+	0.389522i
$52$	−0.282368	+	1.05381i	−0.0391574	+	0.146137i
$53$	4.65601	+	4.65601i	0.639552	+	0.639552i	0.950445	−	0.310893i	$-0.100628\pi$
$53$	4.65601	+	4.65601i	0.639552	+	0.639552i	−0.310893	+	0.950445i	$0.600628\pi$
$54$	2.96317	+	6.31812i	0.403236	+	0.859787i
$55$		0			0
$56$	5.23290	−	3.02121i	0.699275	−	0.403727i
$57$	1.81351	+	1.91938i	0.240206	+	0.254229i
$58$	0.553777	+	2.06672i	0.0727145	+	0.271374i
$59$	−3.81780	+	6.61262i	−0.497035	+	0.860890i	−0.999994	−	0.00342048i	$-0.998911\pi$
$59$	−3.81780	+	6.61262i	−0.497035	+	0.860890i	0.502959	+	0.864310i	$0.332245\pi$
$60$		0			0
$61$	6.64002	+	11.5008i	0.850167	+	1.47253i	0.881057	+	0.473010i	$0.156833\pi$
$61$	6.64002	+	11.5008i	0.850167	+	1.47253i	−0.0308900	+	0.999523i	$0.509834\pi$
$62$	−6.63838	+	6.63838i	−0.843075	+	0.843075i
$63$	−5.83639	−	1.92445i	−0.735317	−	0.242458i
$64$			8.62358i			1.07795i
$65$		0			0
$66$	1.07361	−	1.74345i	0.132152	−	0.214604i
$67$	−3.20857	+	0.859733i	−0.391989	+	0.105033i	−0.449429	−	0.893316i	$-0.648373\pi$
$67$	−3.20857	+	0.859733i	−0.391989	+	0.105033i	0.0574406	+	0.998349i	$0.481706\pi$
$68$	0.304699	−	0.0816439i	0.0369502	−	0.00990078i
$69$	−1.44168	+	2.34117i	−0.173558	+	0.281844i
$70$		0			0
$71$		−	5.89798i		−	0.699961i	−0.936757	−	0.349980i	$-0.886188\pi$
$71$		−	5.89798i		−	0.699961i	0.936757	−	0.349980i	$-0.113812\pi$
$72$	6.60182	−	5.89254i	0.778032	−	0.694442i
$73$	−1.58900	+	1.58900i	−0.185979	+	0.185979i	−0.793955	−	0.607976i	$-0.791982\pi$
$73$	−1.58900	+	1.58900i	−0.185979	+	0.185979i	0.607976	+	0.793955i	$0.291982\pi$
$74$	−4.04309	−	7.00284i	−0.470000	−	0.814063i
$75$		0			0
$76$	0.149662	−	0.259222i	0.0171674	−	0.0297348i
$77$	0.466676	+	1.74166i	0.0531827	+	0.198480i
$78$	8.87721	+	9.39544i	1.00515	+	1.06382i
$79$	6.69401	−	3.86479i	0.753135	−	0.434823i	−0.0736905	−	0.997281i	$-0.523478\pi$
$79$	6.69401	−	3.86479i	0.753135	−	0.434823i	0.826826	+	0.562458i	$0.190144\pi$
$80$		0			0
$81$	−8.94218	−	1.01854i	−0.993575	−	0.113172i
$82$	−3.41628	−	3.41628i	−0.377265	−	0.377265i
$83$	2.57170	−	9.59770i	0.282280	−	1.05348i	−0.668523	−	0.743691i	$-0.733073\pi$
$83$	2.57170	−	9.59770i	0.282280	−	1.05348i	0.950804	−	0.309794i	$-0.100260\pi$
$84$	−0.0197489	+	0.696335i	−0.00215478	+	0.0759763i
$85$		0			0
$86$	−2.23772	−	1.29195i	−0.241299	−	0.139314i
$87$	−2.64410	−	0.789474i	−0.283477	−	0.0846405i
$88$	−2.50787	−	0.671981i	−0.267340	−	0.0716334i
$89$	4.62765			0.490530			0.245265	−	0.969456i	$-0.421125\pi$
$89$	4.62765			0.490530			0.245265	+	0.969456i	$0.421125\pi$
$90$		0			0
$91$	−11.3830			−1.19327
$92$	0.301043	+	0.0806641i	0.0313859	+	0.00840982i
$93$	−2.80088	−	11.7792i	−0.290437	−	1.22145i
$94$	−9.63215	−	5.56112i	−0.993480	−	0.573586i
$95$		0			0
$96$	−1.63189	−	1.00491i	−0.166554	−	0.102563i
$97$	1.02621	−	3.82988i	0.104196	−	0.388865i	−0.894057	−	0.447954i	$-0.852153\pi$
$97$	1.02621	−	3.82988i	0.104196	−	0.388865i	0.998253	+	0.0590888i	$0.0188195\pi$
$98$	−2.66250	−	2.66250i	−0.268953	−	0.268953i
$99$	1.18858	+	2.35800i	0.119456	+	0.236988i
$100$		0			0
$101$	−2.23195	+	1.28862i	−0.222087	+	0.128222i	−0.606916	−	0.794766i	$-0.707594\pi$
$101$	−2.23195	+	1.28862i	−0.222087	+	0.128222i	0.384829	+	0.922988i	$0.374260\pi$
$102$	1.06927	−	3.58117i	0.105873	−	0.354589i
$103$	3.38106	+	12.6183i	0.333146	+	1.24332i	0.905865	+	0.423566i	$0.139222\pi$
$103$	3.38106	+	12.6183i	0.333146	+	1.24332i	−0.572719	+	0.819752i	$0.694111\pi$
$104$	8.19538	−	14.1948i	0.803623	−	1.39192i
$105$		0			0
$106$	−4.42157	−	7.65839i	−0.429461	−	0.743848i
$107$	9.23034	−	9.23034i	0.892331	−	0.892331i	−0.102411	−	0.994742i	$-0.532656\pi$
$107$	9.23034	−	9.23034i	0.892331	−	0.892331i	0.994742	+	0.102411i	$0.0326557\pi$
$108$	0.179369	+	1.00429i	0.0172598	+	0.0966381i
$109$		−	8.05480i		−	0.771510i	−0.922601	−	0.385755i	$-0.873941\pi$
$109$		−	8.05480i		−	0.771510i	0.922601	−	0.385755i	$-0.126059\pi$
$110$		0			0
$111$	10.4244	+	0.295649i	0.989441	+	0.0280618i
$112$	−7.06153	+	1.89213i	−0.667252	+	0.178790i
$113$	−11.5941	+	3.10662i	−1.09068	+	0.292246i	−0.758963	−	0.651134i	$-0.774294\pi$
$113$	−11.5941	+	3.10662i	−1.09068	+	0.292246i	−0.331714	+	0.943380i	$0.607627\pi$
$114$	−1.68540	−	3.12028i	−0.157852	−	0.292241i
$115$		0			0
$116$			0.312794i			0.0290422i
$117$	−16.3209	+	3.39503i	−1.50887	+	0.313871i
$118$	7.25113	−	7.25113i	0.667521	−	0.667521i
$119$	1.64564	+	2.85034i	0.150856	+	0.261290i
$120$		0			0
$121$	−5.11262	+	8.85532i	−0.464784	+	0.805029i
$122$	−4.61608	−	17.2274i	−0.417920	−	1.55970i
$123$	6.06190	−	1.44140i	0.546583	−	0.129967i
$124$	−1.18858	+	0.686224i	−0.106737	+	0.0616248i
$125$		0			0
$126$	6.90230	+	4.52519i	0.614906	+	0.403136i
$127$	−1.90230	−	1.90230i	−0.168802	−	0.168802i	0.617651	−	0.786452i	$-0.288085\pi$
$127$	−1.90230	−	1.90230i	−0.168802	−	0.168802i	−0.786452	+	0.617651i	$0.788085\pi$
$128$	2.42476	−	9.04933i	0.214321	−	0.799855i
$129$	2.93202	−	1.58372i	0.258150	−	0.139438i
$130$		0			0
$131$	−18.5109	−	10.6873i	−1.61731	−	0.933754i	−0.987613	−	0.156912i	$-0.949846\pi$
$131$	−18.5109	−	10.6873i	−1.61731	−	0.933754i	−0.629696	−	0.776841i	$-0.716821\pi$
$132$	0.217569	−	0.205569i	0.0189370	−	0.0178925i
$133$	3.01664	+	0.808307i	0.261576	+	0.0700891i
$134$	4.46113			0.385383
$135$		0			0
$136$	−4.73922			−0.406385
$137$	−6.62594	−	1.77541i	−0.566092	−	0.151684i	−0.0355883	−	0.999367i	$-0.511331\pi$
$137$	−6.62594	−	1.77541i	−0.566092	−	0.151684i	−0.530504	+	0.847683i	$0.677997\pi$
$138$	2.68400	−	2.53595i	0.228477	−	0.215875i
$139$	1.24863	+	0.720896i	0.105907	+	0.0611456i	0.552018	−	0.833832i	$-0.313858\pi$
$139$	1.24863	+	0.720896i	0.105907	+	0.0611456i	−0.446111	+	0.894978i	$0.647191\pi$
$140$		0			0
$141$	12.6207	−	6.81703i	1.06286	−	0.574097i
$142$	−2.05011	+	7.65111i	−0.172041	+	0.642067i
$143$	3.45853	+	3.45853i	0.289217	+	0.289217i
$144$	−9.56047	+	4.81906i	−0.796706	+	0.401589i
$145$		0			0
$146$	2.61366	−	1.50900i	0.216308	−	0.124885i
$147$	4.72437	−	1.12337i	0.389659	−	0.0926536i
$148$	−0.305956	−	1.14184i	−0.0251494	−	0.0938589i
$149$	−8.28457	+	14.3493i	−0.678699	+	1.17554i	0.296674	+	0.954979i	$0.404122\pi$
$149$	−8.28457	+	14.3493i	−0.678699	+	1.17554i	−0.975373	+	0.220562i	$0.929211\pi$
$150$		0			0
$151$	0.00283730	+	0.00491435i	0.000230896	+	0.000399924i	0.866141	−	0.499800i	$-0.166593\pi$
$151$	0.00283730	+	0.00491435i	0.000230896	+	0.000399924i	−0.865910	+	0.500200i	$0.833260\pi$
$152$	−3.17985	+	3.17985i	−0.257920	+	0.257920i
$153$	3.20964	+	3.59599i	0.259484	+	0.290718i
$154$		−	2.42157i		−	0.195136i
$155$		0			0
$156$	0.898049	+	1.66261i	0.0719014	+	0.133115i
$157$	8.17112	−	2.18944i	0.652126	−	0.174737i	0.0824362	−	0.996596i	$-0.473730\pi$
$157$	8.17112	−	2.18944i	0.652126	−	0.174737i	0.569690	+	0.821860i	$0.307063\pi$
$158$	−10.0272	+	2.68677i	−0.797717	+	0.213748i
$159$	11.4003	+	0.323326i	0.904099	+	0.0256414i
$160$		0			0
$161$			3.25179i			0.256277i
$162$	11.2461	+	4.42956i	0.883581	+	0.348019i
$163$	−4.19302	+	4.19302i	−0.328422	+	0.328422i	−0.851986	−	0.523564i	$-0.824602\pi$
$163$	−4.19302	+	4.19302i	−0.328422	+	0.328422i	0.523564	+	0.851986i	$0.324602\pi$
$164$	−0.353149	−	0.611672i	−0.0275763	−	0.0477635i
$165$		0			0
$166$	−6.67224	+	11.5567i	−0.517866	+	0.896970i
$167$	1.54428	+	5.76334i	0.119500	+	0.445980i	0.999584	−	0.0288375i	$-0.00918054\pi$
$167$	1.54428	+	5.76334i	0.119500	+	0.445980i	−0.880084	+	0.474818i	$0.842514\pi$
$168$	2.99425	−	10.0283i	0.231012	−	0.773702i
$169$	−15.4826	+	8.93886i	−1.19097	+	0.687605i
$170$		0			0
$171$	4.56633	+	0.259222i	0.349196	+	0.0198232i
$172$	−0.267103	−	0.267103i	−0.0203664	−	0.0203664i
$173$	−3.53677	+	13.1994i	−0.268896	+	1.00353i	0.690927	+	0.722925i	$0.257203\pi$
$173$	−3.53677	+	13.1994i	−0.268896	+	1.00353i	−0.959822	+	0.280608i	$0.909464\pi$
$174$	3.15562	+	1.94322i	0.239227	+	0.147315i
$175$		0			0
$176$	2.72042	+	1.57063i	0.205059	+	0.118391i
$177$	3.05941	+	12.8665i	0.229959	+	0.967106i
$178$	−6.00319	−	1.60855i	−0.449958	−	0.120566i
$179$	17.2370			1.28836			0.644178	−	0.764875i	$-0.277199\pi$
$179$	17.2370			1.28836			0.644178	+	0.764875i	$0.277199\pi$
$180$		0			0
$181$	14.7708			1.09790			0.548952	−	0.835854i	$-0.315027\pi$
$181$	14.7708			1.09790			0.548952	+	0.835854i	$0.315027\pi$
$182$	14.7666	+	3.95669i	1.09457	+	0.293289i
$183$	22.0402	+	6.58076i	1.62926	+	0.486464i
$184$	−4.05503	−	2.34117i	−0.298941	−	0.172594i
$185$		0			0
$186$	−0.460987	+	16.2541i	−0.0338012	+	1.19181i
$187$	0.366025	−	1.36603i	0.0267664	−	0.0998937i
$188$	−1.14973	−	1.14973i	−0.0838528	−	0.0838528i
$189$	−9.63706	+	4.51974i	−0.700993	+	0.328763i
$190$		0			0
$191$	4.56792	−	2.63729i	0.330523	−	0.190827i	−0.325550	−	0.945525i	$-0.605550\pi$
$191$	4.56792	−	2.63729i	0.330523	−	0.190827i	0.656073	+	0.754697i	$0.272216\pi$
$192$	10.2580	+	10.8569i	0.740309	+	0.783527i
$193$	−2.40873	−	8.98952i	−0.173384	−	0.647080i	−0.996821	−	0.0796715i	$-0.974613\pi$
$193$	−2.40873	−	8.98952i	−0.173384	−	0.647080i	0.823437	−	0.567408i	$-0.192054\pi$
$194$	−2.66250	+	4.61158i	−0.191156	+	0.331092i
$195$		0			0
$196$	−0.275228	−	0.476709i	−0.0196592	−	0.0340507i
$197$	−9.49539	+	9.49539i	−0.676519	+	0.676519i	−0.959211	−	0.282692i	$-0.908773\pi$
$197$	−9.49539	+	9.49539i	−0.676519	+	0.676519i	0.282692	+	0.959211i	$0.408773\pi$
$198$	−0.722243	−	3.47204i	−0.0513276	−	0.246747i
$199$		−	17.6342i		−	1.25005i	−0.780604	−	0.625026i	$-0.785088\pi$
$199$		−	17.6342i		−	1.25005i	0.780604	−	0.625026i	$-0.214912\pi$
$200$		0			0
$201$	−3.01682	+	4.89907i	−0.212790	+	0.345554i
$202$	3.34330	−	0.895835i	0.235234	−	0.0630307i
$203$	−3.15239	+	0.844680i	−0.221254	+	0.0592849i
$204$	0.286490	−	0.465237i	0.0200583	−	0.0325731i
$205$		0			0
$206$		−	17.5443i		−	1.22237i
$207$	0.969859	+	4.66240i	0.0674098	+	0.324060i
$208$	−14.0226	+	14.0226i	−0.972291	+	0.972291i
$209$	−0.670964	−	1.16214i	−0.0464116	−	0.0803872i
$210$		0			0
$211$	0.0616050	−	0.106703i	0.00424106	−	0.00734574i	−0.863897	−	0.503668i	$-0.831983\pi$
$211$	0.0616050	−	0.106703i	0.00424106	−	0.00734574i	0.868138	+	0.496323i	$0.165317\pi$
$212$	−0.334597	−	1.24873i	−0.0229802	−	0.0857633i
$213$	−7.01583	−	7.42540i	−0.480716	−	0.508780i
$214$	−15.1824	+	8.76558i	−1.03785	+	0.599203i
$215$		0			0
$216$	1.30216	−	15.2716i	0.0886009	−	1.03910i
$217$	−10.1256	−	10.1256i	−0.687368	−	0.687368i
$218$	−2.79981	+	10.4490i	−0.189627	+	0.707698i
$219$	−0.110345	+	3.89068i	−0.00745640	+	0.262908i
$220$		0			0
$221$	7.73186	+	4.46399i	0.520101	+	0.300281i
$222$	−13.4202	−	4.00701i	−0.900707	−	0.268933i
$223$	2.41842	+	0.648014i	0.161949	+	0.0433942i	0.338883	−	0.940829i	$-0.389951\pi$
$223$	2.41842	+	0.648014i	0.161949	+	0.0433942i	−0.176933	+	0.984223i	$0.556618\pi$
$224$	−2.26663			−0.151445
$225$		0			0
$226$	16.1202			1.07230
$227$	−14.7293	−	3.94671i	−0.977619	−	0.261952i	−0.265577	−	0.964090i	$-0.585563\pi$
$227$	−14.7293	−	3.94671i	−0.977619	−	0.261952i	−0.712042	+	0.702137i	$0.752229\pi$
$228$	−0.119932	−	0.504382i	−0.00794272	−	0.0334035i
$229$	19.1083	+	11.0322i	1.26271	+	0.729029i	0.973599	−	0.228265i	$-0.0733054\pi$
$229$	19.1083	+	11.0322i	1.26271	+	0.729029i	0.289116	+	0.957294i	$0.406639\pi$
$230$		0			0
$231$	2.65929	+	1.63758i	0.174969	+	0.107745i
$232$	1.21628	−	4.53922i	0.0798527	−	0.298014i
$233$	−4.22173	−	4.22173i	−0.276575	−	0.276575i	0.555165	−	0.831740i	$-0.312655\pi$
$233$	−4.22173	−	4.22173i	−0.276575	−	0.276575i	−0.831740	+	0.555165i	$0.812655\pi$
$234$	22.3524	+	1.26890i	1.46122	+	0.0829507i
$235$		0			0
$236$	1.29829	−	0.749566i	0.0845112	−	0.0487926i
$237$	3.83030	−	12.8284i	0.248805	−	0.833294i
$238$	−1.14404	−	4.26960i	−0.0741569	−	0.276757i
$239$	6.79199	−	11.7641i	0.439338	−	0.760955i	−0.558301	−	0.829639i	$-0.688547\pi$
$239$	6.79199	−	11.7641i	0.439338	−	0.760955i	0.997639	+	0.0686835i	$0.0218799\pi$
$240$		0			0
$241$	−2.56728	−	4.44666i	−0.165373	−	0.286434i	0.771415	−	0.636333i	$-0.219549\pi$
$241$	−2.56728	−	4.44666i	−0.165373	−	0.286434i	−0.936788	+	0.349898i	$0.886216\pi$
$242$	9.71038	−	9.71038i	0.624207	−	0.624207i
$243$	−12.4696	+	9.35468i	−0.799923	+	0.600103i
$244$		−	2.60733i		−	0.166917i
$245$		0			0
$246$	−8.36479	−	0.237236i	−0.533319	−	0.0151256i
$247$	8.18298	−	2.19262i	0.520670	−	0.139513i
$248$	19.9168	−	5.33669i	1.26472	−	0.338880i
$249$	−8.17907	−	15.1424i	−0.518327	−	0.959609i
$250$		0			0
$251$			2.60221i			0.164250i	0.996622	+	0.0821251i	$0.0261707\pi$
$251$			2.60221i			0.164250i	−0.996622	+	0.0821251i	$0.973829\pi$
$252$	0.803448	+	0.900159i	0.0506125	+	0.0567047i
$253$	0.987999	−	0.987999i	0.0621150	−	0.0621150i
$254$	1.80652	+	3.12898i	0.113351	+	0.196329i
$255$		0			0
$256$	2.33257	−	4.04013i	0.145786	−	0.252508i
$257$	2.73197	+	10.1958i	0.170415	+	0.635999i	0.997287	+	0.0736085i	$0.0234515\pi$
$257$	2.73197	+	10.1958i	0.170415	+	0.635999i	−0.826872	+	0.562390i	$0.809882\pi$
$258$	−4.35404	+	1.03531i	−0.271071	+	0.0644555i
$259$	10.6815	−	6.16695i	0.663714	−	0.383196i
$260$		0			0
$261$	−4.26796	+	2.15131i	−0.264180	+	0.133163i
$262$	20.2984	+	20.2984i	1.25404	+	1.25404i
$263$	2.17720	−	8.12541i	0.134252	−	0.501034i	−0.865748	−	0.500480i	$-0.833157\pi$
$263$	2.17720	−	8.12541i	0.134252	−	0.501034i	1.00000		0.000554412i	$-0.000176475\pi$
$264$	−3.95668	+	2.13718i	−0.243517	+	0.131534i
$265$		0			0
$266$	−3.63236	−	2.09714i	−0.222714	−	0.128584i
$267$	5.82609	−	5.50473i	0.356551	−	0.336884i
$268$	0.629953	+	0.168795i	0.0384805	+	0.0103108i
$269$	−26.7708			−1.63225			−0.816123	−	0.577878i	$-0.803881\pi$
$269$	−26.7708			−1.63225			−0.816123	+	0.577878i	$0.803881\pi$
$270$		0			0
$271$	−18.5850			−1.12896			−0.564480	−	0.825447i	$-0.690923\pi$
$271$	−18.5850			−1.12896			−0.564480	+	0.825447i	$0.690923\pi$
$272$	5.53853	+	1.48405i	0.335823	+	0.0899834i
$273$	−14.3309	+	13.5405i	−0.867347	+	0.819506i
$274$	7.97833	+	4.60629i	0.481989	+	0.278276i
$275$		0			0
$276$	0.474957	−	0.256546i	0.0285891	−	0.0154422i
$277$	−7.05259	+	26.3206i	−0.423749	+	1.58145i	0.342891	+	0.939375i	$0.388594\pi$
$277$	−7.05259	+	26.3206i	−0.423749	+	1.58145i	−0.766640	+	0.642078i	$0.778073\pi$
$278$	−1.36920	−	1.36920i	−0.0821189	−	0.0821189i
$279$	−17.5380	−	11.4980i	−1.04997	−	0.688368i
$280$		0			0
$281$	−22.7050	+	13.1087i	−1.35447	+	0.782002i	−0.988872	−	0.148772i	$-0.952468\pi$
$281$	−22.7050	+	13.1087i	−1.35447	+	0.782002i	−0.365595	+	0.930774i	$0.619135\pi$
$282$	−18.7418	+	4.45643i	−1.11606	+	0.265377i
$283$	0.921880	+	3.44050i	0.0548001	+	0.204517i	0.987898	−	0.155106i	$-0.0495720\pi$
$283$	0.921880	+	3.44050i	0.0548001	+	0.204517i	−0.933098	+	0.359623i	$0.882905\pi$
$284$	−0.578988	+	1.00284i	−0.0343566	+	0.0595074i
$285$		0			0
$286$	−3.28439	−	5.68873i	−0.194210	−	0.336382i
$287$	5.21088	−	5.21088i	0.307589	−	0.307589i
$288$	−3.24988	+	0.676030i	−0.191501	+	0.0398355i
$289$			14.4186i			0.848151i
$290$		0			0
$291$	−3.26378	−	6.04243i	−0.191326	−	0.354213i
$292$	0.426168	−	0.114191i	0.0249396	−	0.00668254i
$293$	−2.87816	+	0.771199i	−0.168144	+	0.0450539i	−0.341909	−	0.939733i	$-0.611073\pi$
$293$	−2.87816	+	0.771199i	−0.168144	+	0.0450539i	0.173765	+	0.984787i	$0.444407\pi$
$294$	−6.51914	−	0.184891i	−0.380204	−	0.0107831i
$295$		0			0
$296$			17.7600i			1.03228i
$297$	4.30130	+	1.55481i	0.249587	+	0.0902192i
$298$	15.7349	−	15.7349i	0.911496	−	0.911496i
$299$	4.41042	+	7.63907i	0.255061	+	0.441779i
$300$		0			0
$301$	1.97062	−	3.41321i	0.113584	−	0.196734i
$302$	−0.00197247	−	0.00736135i	−0.000113503	−	0.000423598i
$303$	−1.27712	+	4.27731i	−0.0733684	+	0.245725i
$304$	4.71190	−	2.72042i	0.270246	−	0.156027i
$305$		0			0
$306$	−2.91374	−	5.78053i	−0.166568	−	0.330451i
$307$	−21.8017	−	21.8017i	−1.24429	−	1.24429i	−0.958205	−	0.286081i	$-0.907647\pi$
$307$	−21.8017	−	21.8017i	−1.24429	−	1.24429i	−0.286081	−	0.958205i	$-0.592353\pi$
$308$	0.0916247	−	0.341948i	0.00522080	−	0.0194843i
$309$	19.2665	+	11.8642i	1.09603	+	0.674933i
$310$		0			0
$311$	29.3878	+	16.9671i	1.66643	+	0.962114i	0.969539	+	0.244939i	$0.0787679\pi$
$311$	29.3878	+	16.9671i	1.66643	+	0.962114i	0.696892	+	0.717176i	$0.254565\pi$
$312$	−6.56741	−	27.6196i	−0.371806	−	1.56365i
$313$	22.4027	+	6.00279i	1.26628	+	0.339298i	0.828603	−	0.559836i	$-0.189136\pi$
$313$	22.4027	+	6.00279i	1.26628	+	0.339298i	0.437673	+	0.899134i	$0.355803\pi$
$314$	−11.3610			−0.641137
$315$		0			0
$316$	−1.51758			−0.0853708
$317$	3.86401	+	1.03536i	0.217024	+	0.0581515i	0.365693	−	0.930736i	$-0.380832\pi$
$317$	3.86401	+	1.03536i	0.217024	+	0.0581515i	−0.148669	+	0.988887i	$0.547499\pi$
$318$	−14.6765	−	4.38211i	−0.823019	−	0.245737i
$319$	1.21444	+	0.701157i	0.0679956	+	0.0392573i
$320$		0			0
$321$	0.640980	−	22.6005i	0.0357760	−	1.26144i
$322$	1.13031	−	4.21836i	0.0629896	−	0.235080i
$323$	−1.73205	−	1.73205i	−0.0963739	−	0.0963739i
$324$	1.42046	+	1.05101i	0.0789143	+	0.0583896i
$325$		0			0
$326$	6.89684	−	3.98189i	0.381981	−	0.220537i
$327$	−9.58143	−	10.1408i	−0.529854	−	0.560786i
$328$	2.74640	+	10.2497i	0.151645	+	0.565945i
$329$	8.48242	−	14.6920i	0.467651	−	0.809995i
$330$		0			0
$331$	−2.98175	−	5.16454i	−0.163892	−	0.283869i	0.772369	−	0.635174i	$-0.219071\pi$
$331$	−2.98175	−	5.16454i	−0.163892	−	0.283869i	−0.936261	+	0.351305i	$0.885738\pi$
$332$	−1.37945	+	1.37945i	−0.0757071	+	0.0757071i
$333$	13.4757	−	12.0279i	0.738466	−	0.659127i
$334$		−	8.01324i		−	0.438465i
$335$		0			0
$336$	−6.63954	+	10.7821i	−0.362216	+	0.588210i
$337$	−9.56887	+	2.56397i	−0.521250	+	0.139668i	−0.509845	−	0.860267i	$-0.670297\pi$
$337$	−9.56887	+	2.56397i	−0.521250	+	0.139668i	−0.0114051	+	0.999935i	$0.503630\pi$
$338$	23.1918	−	6.21422i	1.26147	−	0.338009i
$339$	−10.9012	+	17.7026i	−0.592072	+	0.961476i
$340$		0			0
$341$			6.15295i			0.333201i
$342$	−5.83354	−	1.92351i	−0.315442	−	0.104012i
$343$	14.2007	−	14.2007i	0.766764	−	0.766764i
$344$	2.83755	+	4.91478i	0.152990	+	0.264987i
$345$		0			0
$346$	9.17611	−	15.8935i	0.493311	−	0.854440i
$347$	2.74569	+	10.2471i	0.147396	+	0.550091i	0.999637	+	0.0269407i	$0.00857654\pi$
$347$	2.74569	+	10.2471i	0.147396	+	0.550091i	−0.852241	+	0.523150i	$0.824757\pi$
$348$	0.372078	+	0.393799i	0.0199455	+	0.0211098i
$349$	8.08831	−	4.66979i	0.432957	−	0.249968i	−0.267648	−	0.963517i	$-0.586247\pi$
$349$	8.08831	−	4.66979i	0.432957	−	0.249968i	0.700606	+	0.713549i	$0.252913\pi$
$350$		0			0
$351$	−16.5091	+	23.6885i	−0.881193	+	1.26440i
$352$	0.688675	+	0.688675i	0.0367065	+	0.0367065i
$353$	4.96965	−	18.5470i	0.264508	−	0.987156i	−0.698043	−	0.716055i	$-0.745946\pi$
$353$	4.96965	−	18.5470i	0.264508	−	0.987156i	0.962551	−	0.271100i	$-0.0873876\pi$
$354$	0.503538	−	17.7544i	0.0267627	−	0.943638i
$355$		0			0
$356$	−0.786842	−	0.454284i	−0.0417026	−	0.0240770i
$357$	5.46239	+	1.63096i	0.289100	+	0.0863194i
$358$	−22.3606	−	5.99152i	−1.18180	−	0.316662i
$359$	−12.5944			−0.664705			−0.332352	−	0.943155i	$-0.607842\pi$
$359$	−12.5944			−0.664705			−0.332352	+	0.943155i	$0.607842\pi$
$360$		0			0
$361$	16.6757			0.877669
$362$	−19.1613	−	5.13426i	−1.00710	−	0.269851i
$363$	4.09702	+	17.2302i	0.215038	+	0.904353i
$364$	1.93546	+	1.11744i	0.101446	+	0.0585698i
$365$		0			0
$366$	−26.3041	−	16.1979i	−1.37494	−	0.846680i
$367$	7.32206	−	27.3263i	0.382209	−	1.42642i	−0.460312	−	0.887757i	$-0.652262\pi$
$367$	7.32206	−	27.3263i	0.382209	−	1.42642i	0.842520	−	0.538665i	$-0.181071\pi$
$368$	4.00583	+	4.00583i	0.208818	+	0.208818i
$369$	5.91718	−	9.02551i	0.308036	−	0.469849i
$370$		0			0
$371$	11.6814	−	6.74425i	0.606467	−	0.350144i
$372$	−0.680100	+	2.27779i	−0.0352616	+	0.118098i
$373$	−0.604851	−	2.25734i	−0.0313180	−	0.116880i	0.948497	−	0.316785i	$-0.102603\pi$
$373$	−0.604851	−	2.25734i	−0.0313180	−	0.116880i	−0.979815	+	0.199905i	$0.935937\pi$
$374$	−0.949649	+	1.64484i	−0.0491052	+	0.0850526i
$375$		0			0
$376$	12.2141	+	21.1554i	0.629894	+	1.09101i
$377$	−6.25992	+	6.25992i	−0.322402	+	0.322402i
$378$	14.0727	−	2.51341i	0.723820	−	0.129276i
$379$			18.4618i			0.948320i	0.880439	+	0.474160i	$0.157248\pi$
$379$			18.4618i			0.948320i	−0.880439	+	0.474160i	$0.842752\pi$
$380$		0			0
$381$	−4.65779	−	0.132101i	−0.238626	−	0.00676772i
$382$	−6.84241	+	1.83342i	−0.350088	+	0.0938059i
$383$	23.3806	−	6.26481i	1.19469	−	0.320117i	0.393953	−	0.919131i	$-0.371107\pi$
$383$	23.3806	−	6.26481i	1.19469	−	0.320117i	0.800739	+	0.599014i	$0.204441\pi$
$384$	−7.71175	−	14.2772i	−0.393539	−	0.728580i
$385$		0			0
$386$			12.4989i			0.636176i
$387$	1.80746	−	5.48159i	0.0918784	−	0.278645i
$388$	−0.550457	+	0.550457i	−0.0279452	+	0.0279452i
$389$	−13.5444	−	23.4596i	−0.686729	−	1.18945i	−0.972890	−	0.231268i	$-0.925712\pi$
$389$	−13.5444	−	23.4596i	−0.686729	−	1.18945i	0.286161	−	0.958182i	$-0.407621\pi$
$390$		0			0
$391$	1.27523	−	2.20876i	0.0644911	−	0.111702i
$392$	2.14042	+	7.98815i	0.108108	+	0.403463i
$393$	−36.0177	+	8.56432i	−1.81685	+	0.432013i
$394$	15.6184	−	9.01729i	0.786844	−	0.454284i
$395$		0			0
$396$	0.0293839	−	0.517611i	0.00147659	−	0.0260110i
$397$	18.2252	+	18.2252i	0.914698	+	0.914698i	0.996637	−	0.0819389i	$-0.0261112\pi$
$397$	18.2252	+	18.2252i	0.914698	+	0.914698i	−0.0819389	+	0.996637i	$0.526111\pi$
$398$	−6.12955	+	22.8758i	−0.307247	+	1.14666i
$399$	4.75938	−	2.57075i	0.238267	−	0.128699i
$400$		0			0
$401$	−11.1294	−	6.42558i	−0.555777	−	0.320878i	0.195672	−	0.980669i	$-0.437311\pi$
$401$	−11.1294	−	6.42558i	−0.555777	−	0.320878i	−0.751449	+	0.659791i	$0.770645\pi$
$402$	5.61645	−	5.30666i	0.280123	−	0.264672i
$403$	−37.5202	−	10.0535i	−1.86902	−	0.500801i
$404$	0.506000			0.0251745
$405$		0			0
$406$	4.38302			0.217526
$407$	−5.11910	−	1.37166i	−0.253744	−	0.0679906i
$408$	−5.96656	+	5.63745i	−0.295389	+	0.279096i
$409$	−22.2450	−	12.8431i	−1.09994	−	0.635053i	−0.163737	−	0.986504i	$-0.552355\pi$
$409$	−22.2450	−	12.8431i	−1.09994	−	0.635053i	−0.936206	+	0.351451i	$0.885688\pi$
$410$		0			0
$411$	−10.4538	+	5.64656i	−0.515648	+	0.278524i
$412$	0.663820	−	2.47741i	0.0327041	−	0.122053i
$413$	11.0602	+	11.0602i	0.544237	+	0.544237i
$414$	0.362487	−	6.38540i	0.0178153	−	0.313825i
$415$		0			0
$416$	−5.32474	+	3.07424i	−0.261067	+	0.150727i
$417$	2.42952	−	0.577694i	0.118974	−	0.0282898i
$418$	0.466448	+	1.74081i	0.0228147	+	0.0851457i
$419$	−6.13243	+	10.6217i	−0.299589	+	0.518903i	−0.976042	−	0.217583i	$-0.930183\pi$
$419$	−6.13243	+	10.6217i	−0.299589	+	0.518903i	0.676453	+	0.736486i	$0.263516\pi$
$420$		0			0
$421$	−7.24056	−	12.5410i	−0.352883	−	0.611212i	0.633870	−	0.773439i	$-0.281465\pi$
$421$	−7.24056	−	12.5410i	−0.352883	−	0.611212i	−0.986753	+	0.162228i	$0.948132\pi$
$422$	−0.117006	+	0.117006i	−0.00569577	+	0.00569577i
$423$	7.78012	−	23.5952i	0.378283	−	1.14724i
$424$			19.4225i			0.943240i
$425$		0			0
$426$	6.52020	+	12.0712i	0.315905	+	0.584853i
$427$	26.2771	−	7.04094i	1.27164	−	0.340735i
$428$	−2.47556	+	0.663324i	−0.119661	+	0.0320630i
$429$	8.46824	+	0.240170i	0.408850	+	0.0115955i
$430$		0			0
$431$		−	35.9660i		−	1.73242i	−0.499678	−	0.866211i	$-0.666548\pi$
$431$		−	35.9660i		−	1.73242i	0.499678	−	0.866211i	$-0.333452\pi$
$432$	−6.30395	+	17.4396i	−0.303299	+	0.839061i
$433$	0.331545	−	0.331545i	0.0159331	−	0.0159331i	−0.699095	−	0.715028i	$-0.746414\pi$
$433$	0.331545	−	0.331545i	0.0159331	−	0.0159331i	0.715028	+	0.699095i	$0.246414\pi$
$434$	9.61573	+	16.6549i	0.461570	+	0.799462i
$435$		0			0
$436$	−0.790718	+	1.36956i	−0.0378685	+	0.0655902i
$437$	−0.626366	−	2.33763i	−0.0299632	−	0.111824i
$438$	1.49553	−	5.00881i	0.0714591	−	0.239330i
$439$	1.28953	−	0.744511i	0.0615459	−	0.0355336i	−0.468911	−	0.883245i	$-0.655354\pi$
$439$	1.28953	−	0.744511i	0.0615459	−	0.0355336i	0.530457	+	0.847712i	$0.322020\pi$
$440$		0			0
$441$	4.61158	−	7.03407i	0.219599	−	0.334956i
$442$	−8.47845	−	8.47845i	−0.403279	−	0.403279i
$443$	−8.29218	+	30.9468i	−0.393973	+	1.47033i	0.429548	+	0.903044i	$0.358673\pi$
$443$	−8.29218	+	30.9468i	−0.393973	+	1.47033i	−0.823522	+	0.567285i	$0.807994\pi$
$444$	−1.74345	−	1.07361i	−0.0827403	−	0.0509511i
$445$		0			0
$446$	−2.91203	−	1.68126i	−0.137889	−	0.0796101i
$447$	6.63888	+	27.9202i	0.314008	+	1.32058i
$448$	17.0634	+	4.57213i	0.806172	+	0.216013i
$449$	21.8283			1.03014			0.515071	−	0.857147i	$-0.327766\pi$
$449$	21.8283			1.03014			0.515071	+	0.857147i	$0.327766\pi$
$450$		0			0
$451$	−3.16647			−0.149103
$452$	2.27631	+	0.609937i	0.107069	+	0.0286890i
$453$	0.00941786	+	0.00281198i	0.000442490	+	0.000132118i
$454$	17.7357	+	10.2397i	0.832376	+	0.480572i
$455$		0			0
$456$	−0.220817	+	7.78588i	−0.0103407	+	0.364607i
$457$	0.235886	−	0.880339i	0.0110343	−	0.0411805i	−0.960189	−	0.279351i	$-0.909881\pi$
$457$	0.235886	−	0.880339i	0.0110343	−	0.0411805i	0.971223	+	0.238170i	$0.0765475\pi$
$458$	−20.9534	−	20.9534i	−0.979090	−	0.979090i
$459$	8.31839	+	0.709282i	0.388269	+	0.0331065i
$460$		0			0
$461$	−18.7320	+	10.8149i	−0.872434	+	0.503700i	−0.868156	−	0.496291i	$-0.834695\pi$
$461$	−18.7320	+	10.8149i	−0.872434	+	0.503700i	−0.00427761	+	0.999991i	$0.501362\pi$
$462$	−2.88054	−	3.04870i	−0.134015	−	0.141838i
$463$	−4.85644	−	18.1245i	−0.225698	−	0.842316i	−0.982124	−	0.188236i	$-0.939723\pi$
$463$	−4.85644	−	18.1245i	−0.225698	−	0.842316i	0.756426	−	0.654079i	$-0.226944\pi$
$464$	−2.84283	+	4.92393i	−0.131975	+	0.228588i
$465$		0			0
$466$	4.00916	+	6.94407i	0.185721	+	0.321678i
$467$	16.8295	−	16.8295i	0.778777	−	0.778777i	−0.200846	−	0.979623i	$-0.564369\pi$
$467$	16.8295	−	16.8295i	0.778777	−	0.778777i	0.979623	+	0.200846i	$0.0643691\pi$
$468$	3.10834	+	1.02492i	0.143683	+	0.0473771i
$469$			6.80460i			0.314207i
$470$		0			0
$471$	7.68281	−	12.4763i	0.354005	−	0.574875i
$472$	−21.7552	+	5.82929i	−1.00136	+	0.268315i
$473$	−1.63578	+	0.438306i	−0.0752133	+	0.0201533i
$474$	−9.42793	+	15.3102i	−0.433039	+	0.703220i
$475$		0			0
$476$		−	0.646194i		−	0.0296182i
$477$	14.7372	−	13.1539i	0.674772	−	0.602276i
$478$	−12.9000	+	12.9000i	−0.590033	+	0.590033i
$479$	8.91724	+	15.4451i	0.407439	+	0.705705i	0.994602	−	0.103764i	$-0.0330886\pi$
$479$	8.91724	+	15.4451i	0.407439	+	0.705705i	−0.587163	+	0.809469i	$0.699755\pi$
$480$		0			0
$481$	16.7285	−	28.9747i	0.762756	−	1.32113i
$482$	1.78475	+	6.66078i	0.0812931	+	0.303390i
$483$	3.86810	+	4.09392i	0.176005	+	0.186280i
$484$	1.73861	−	1.00378i	0.0790275	−	0.0456265i
$485$		0			0
$486$	19.4277	−	7.80094i	0.881259	−	0.353858i
$487$	21.8232	+	21.8232i	0.988904	+	0.988904i	0.999939	−	0.0110354i	$-0.00351274\pi$
$487$	21.8232	+	21.8232i	0.988904	+	0.988904i	−0.0110354	+	0.999939i	$0.503513\pi$
$488$	−10.1385	+	37.8372i	−0.458946	+	1.71281i
$489$	−0.291174	+	10.2666i	−0.0131674	+	0.464273i
$490$		0			0
$491$	35.1670	+	20.3037i	1.58707	+	0.916292i	0.993787	+	0.111295i	$0.0354997\pi$
$491$	35.1670	+	20.3037i	1.58707	+	0.916292i	0.593278	+	0.804998i	$0.297834\pi$
$492$	−1.17221	−	0.349997i	−0.0528472	−	0.0157791i
$493$	2.47249	+	0.662503i	0.111356	+	0.0298376i
$494$	−11.3775			−0.511896
$495$		0			0
$496$	−24.9471			−1.12016
$497$	−11.6703	−	3.12705i	−0.523484	−	0.140267i
$498$	5.34683	+	22.4864i	0.239597	+	1.00764i
$499$	−37.3397	−	21.5581i	−1.67156	−	0.965073i	−0.966768	−	0.255655i	$-0.917709\pi$
$499$	−37.3397	−	21.5581i	−1.67156	−	0.965073i	−0.704788	−	0.709418i	$-0.748958\pi$
$500$		0			0
$501$	8.79988	+	5.41892i	0.393150	+	0.242100i
$502$	0.904518	−	3.37571i	0.0403706	−	0.150665i
$503$	−28.0936	−	28.0936i	−1.25263	−	1.25263i	−0.954537	−	0.298093i	$-0.903649\pi$
$503$	−28.0936	−	28.0936i	−1.25263	−	1.25263i	−0.298093	−	0.954537i	$-0.596351\pi$
$504$	−8.15932	−	16.1872i	−0.363445	−	0.721033i
$505$		0			0
$506$	−1.62510	+	0.938252i	−0.0722445	+	0.0417104i
$507$	−8.85909	+	29.6708i	−0.393446	+	1.31773i
$508$	0.136706	+	0.510193i	0.00606534	+	0.0226361i
$509$	−7.39188	+	12.8031i	−0.327639	+	0.567488i	−0.982043	−	0.188658i	$-0.939586\pi$
$509$	−7.39188	+	12.8031i	−0.327639	+	0.567488i	0.654404	+	0.756145i	$0.272920\pi$
$510$		0			0
$511$	2.30168	+	3.98663i	0.101820	+	0.176358i
$512$	−17.6794	+	17.6794i	−0.781325	+	0.781325i
$513$	6.05725	−	5.10544i	0.267434	−	0.225411i
$514$		−	14.1761i		−	0.625282i
$515$		0			0
$516$	−0.654003	−	0.0185484i	−0.0287909	−	0.000816546i
$517$	−7.04114	+	1.88667i	−0.309669	+	0.0829755i
$518$	−16.0001	+	4.28721i	−0.703003	+	0.188369i
$519$	11.2484	+	20.8248i	0.493750	+	0.914108i
$520$		0			0
$521$			28.4812i			1.24778i	0.781511	+	0.623892i	$0.214449\pi$
$521$			28.4812i			1.24778i	−0.781511	+	0.623892i	$0.785551\pi$
$522$	6.28437	−	1.30725i	0.275059	−	0.0572170i
$523$	−15.4076	+	15.4076i	−0.673726	+	0.673726i	−0.958573	−	0.284847i	$-0.908057\pi$
$523$	−15.4076	+	15.4076i	−0.673726	+	0.673726i	0.284847	+	0.958573i	$0.408057\pi$
$524$	2.09829	+	3.63434i	0.0916641	+	0.158767i
$525$		0			0
$526$	−5.64872	+	9.78386i	−0.246296	+	0.426597i
$527$	2.90687	+	10.8486i	0.126625	+	0.472572i
$528$	5.29325	−	1.25863i	0.230359	−	0.0547750i
$529$	−17.7363	+	10.2401i	−0.771145	+	0.445221i
$530$		0			0
$531$	19.1568	+	12.5593i	0.831335	+	0.545028i
$532$	−0.433573	−	0.433573i	−0.0187978	−	0.0187978i
$533$	5.17380	−	19.3089i	0.224102	−	0.836361i
$534$	−9.47128	+	5.11586i	−0.409862	+	0.221385i
$535$		0			0
$536$	−8.48544	−	4.89907i	−0.366515	−	0.211608i
$537$	21.7010	−	20.5040i	0.936466	−	0.884813i
$538$	34.7283	+	9.30542i	1.49724	+	0.401185i
$539$	−2.46780			−0.106296
$540$		0			0
$541$	−1.11754			−0.0480466			−0.0240233	−	0.999711i	$-0.507648\pi$
$541$	−1.11754			−0.0480466			−0.0240233	+	0.999711i	$0.507648\pi$
$542$	24.1093	+	6.46008i	1.03558	+	0.277484i
$543$	18.5960	−	17.5703i	0.798033	−	0.754015i
$544$	1.53959	+	0.888885i	0.0660096	+	0.0381106i
$545$		0			0
$546$	23.2973	−	12.5839i	0.997033	−	0.538542i
$547$	−8.33894	+	31.1213i	−0.356547	+	1.33065i	0.521979	+	0.852958i	$0.325194\pi$
$547$	−8.33894	+	31.1213i	−0.356547	+	1.33065i	−0.878526	+	0.477694i	$0.841473\pi$
$548$	0.952326	+	0.952326i	0.0406813	+	0.0406813i
$549$	35.5761	−	17.9325i	1.51835	−	0.765342i
$550$		0			0
$551$	2.10347	−	1.21444i	0.0896109	−	0.0517369i
$552$	−7.89008	+	1.87611i	−0.335824	+	0.0798526i
$553$	−4.09814	−	15.2945i	−0.174271	−	0.650387i
$554$	18.2979	−	31.6928i	0.777402	−	1.34650i
$555$		0			0
$556$	−0.141537	−	0.245149i	−0.00600250	−	0.0103966i
$557$	30.4033	−	30.4033i	1.28823	−	1.28823i	0.352366	−	0.935862i	$-0.385377\pi$
$557$	30.4033	−	30.4033i	1.28823	−	1.28823i	0.935862	−	0.352366i	$-0.114623\pi$
$558$	18.7544	+	21.0119i	0.793937	+	0.889503i
$559$		−	10.6910i		−	0.452182i
$560$		0			0
$561$	−1.16411	−	2.15519i	−0.0491489	−	0.0909922i
$562$	34.0105	−	9.11308i	1.43465	−	0.384412i
$563$	−1.12220	+	0.300692i	−0.0472950	+	0.0126727i	−0.282389	−	0.959300i	$-0.591127\pi$
$563$	−1.12220	+	0.300692i	−0.0472950	+	0.0126727i	0.235094	+	0.971973i	$0.424460\pi$
$564$	−2.81512	−	0.0798405i	−0.118538	−	0.00336189i
$565$		0			0
$566$		−	4.78361i		−	0.201070i
$567$	−6.75644	+	17.1538i	−0.283744	+	0.720393i
$568$	12.3017	−	12.3017i	0.516167	−	0.516167i
$569$	0.145367	+	0.251784i	0.00609412	+	0.0105553i	0.869056	−	0.494713i	$-0.164727\pi$
$569$	0.145367	+	0.251784i	0.00609412	+	0.0105553i	−0.862962	+	0.505268i	$0.831394\pi$
$570$		0			0
$571$	−13.0283	+	22.5656i	−0.545215	+	0.944341i	0.453378	+	0.891318i	$0.350219\pi$
$571$	−13.0283	+	22.5656i	−0.545215	+	0.944341i	−0.998593	+	0.0530223i	$0.983115\pi$
$572$	−0.248542	−	0.927572i	−0.0103921	−	0.0387837i
$573$	2.61375	−	8.75395i	0.109191	−	0.365702i
$574$	−8.57106	+	4.94851i	−0.357749	+	0.206547i
$575$		0			0
$576$	25.8292	+	1.46627i	1.07621	+	0.0610948i
$577$	2.52834	+	2.52834i	0.105256	+	0.105256i	0.757774	−	0.652517i	$-0.226287\pi$
$577$	2.52834	+	2.52834i	0.105256	+	0.105256i	−0.652517	+	0.757774i	$0.726287\pi$
$578$	5.01183	−	18.7044i	0.208465	−	0.778000i
$579$	−13.7258	−	8.45230i	−0.570427	−	0.351266i
$580$		0			0
$581$	−17.6274	−	10.1772i	−0.731309	−	0.422222i
$582$	2.13360	+	8.97298i	0.0884408	+	0.371942i
$583$	−5.59831	−	1.50006i	−0.231858	−	0.0621262i
$584$	−6.62852			−0.274290
$585$		0			0
$586$	4.00174			0.165310
$587$	−40.0121	−	10.7212i	−1.65147	−	0.442511i	−0.691449	−	0.722425i	$-0.743027\pi$
$587$	−40.0121	−	10.7212i	−1.65147	−	0.442511i	−0.960025	+	0.279914i	$0.909694\pi$
$588$	−0.913566	−	0.272772i	−0.0376748	−	0.0112489i
$589$	9.22943	+	5.32861i	0.380292	+	0.219562i
$590$		0			0
$591$	−0.659386	+	23.2495i	−0.0271235	+	0.956358i
$592$	5.56137	−	20.7553i	0.228571	−	0.853038i
$593$	26.6583	+	26.6583i	1.09473	+	1.09473i	0.995017	+	0.0997087i	$0.0317911\pi$
$593$	26.6583	+	26.6583i	1.09473	+	1.09473i	0.0997087	+	0.995017i	$0.468209\pi$
$594$	−5.03939	−	3.51208i	−0.206769	−	0.144102i
$595$		0			0
$596$	2.81726	−	1.62655i	0.115400	−	0.0666260i
$597$	−20.9764	−	22.2009i	−0.858506	−	0.908624i
$598$	−3.06608	−	11.4428i	−0.125382	−	0.467930i
$599$	13.2427	−	22.9370i	0.541080	−	0.937178i	−0.457762	−	0.889075i	$-0.651349\pi$
$599$	13.2427	−	22.9370i	0.541080	−	0.937178i	0.998842	−	0.0481037i	$-0.0153178\pi$
$600$		0			0
$601$	4.26710	+	7.39084i	0.174059	+	0.301479i	0.939835	−	0.341628i	$-0.110978\pi$
$601$	4.26710	+	7.39084i	0.174059	+	0.301479i	−0.765776	+	0.643107i	$0.777645\pi$
$602$	−3.74279	+	3.74279i	−0.152545	+	0.152545i
$603$	2.02950	+	9.75641i	0.0826475	+	0.397312i
$604$		−	0.00111412i		−	4.53329e-5i
$605$		0			0
$606$	3.14351	−	5.10480i	0.127696	−	0.207368i
$607$	−44.4113	+	11.9000i	−1.80260	+	0.483005i	−0.994379	−	0.105876i	$-0.966235\pi$
$607$	−44.4113	+	11.9000i	−1.80260	+	0.483005i	−0.808220	+	0.588881i	$0.799569\pi$
$608$	1.62942	−	0.436602i	0.0660818	−	0.0177066i
$609$	−2.96400	+	4.81329i	−0.120107	+	0.195045i
$610$		0			0
$611$		−	46.0190i		−	1.86173i
$612$	−0.192730	−	0.926510i	−0.00779064	−	0.0374520i
$613$	−17.3219	+	17.3219i	−0.699625	+	0.699625i	−0.964330	−	0.264705i	$-0.914726\pi$
$613$	−17.3219	+	17.3219i	−0.699625	+	0.699625i	0.264705	+	0.964330i	$0.414726\pi$
$614$	20.7039	+	35.8602i	0.835542	+	1.44720i
$615$		0			0
$616$	−2.65929	+	4.60603i	−0.107146	+	0.185582i
$617$	−9.74553	−	36.3708i	−0.392340	−	1.46423i	−0.826263	−	0.563284i	$-0.809538\pi$
$617$	−9.74553	−	36.3708i	−0.392340	−	1.46423i	0.433923	−	0.900950i	$-0.357129\pi$
$618$	−20.8694	−	22.0878i	−0.839492	−	0.888500i
$619$	−8.57434	+	4.95040i	−0.344632	+	0.198973i	−0.662318	−	0.749223i	$-0.730427\pi$
$619$	−8.57434	+	4.95040i	−0.344632	+	0.198973i	0.317687	+	0.948196i	$0.397094\pi$
$620$		0			0
$621$	6.76710	+	4.71617i	0.271554	+	0.189253i
$622$	−32.2255	−	32.2255i	−1.29213	−	1.29213i
$623$	2.45353	−	9.15670i	0.0982986	−	0.366855i
$624$	−0.973765	+	34.3344i	−0.0389818	+	1.37447i
$625$		0			0
$626$	−26.9753	−	15.5742i	−1.07815	−	0.622469i
$627$	−2.22713	−	0.664976i	−0.0889431	−	0.0265566i
$628$	−1.60427	−	0.429864i	−0.0640175	−	0.0171534i
$629$	−9.67378			−0.385719
$630$		0			0
$631$	−22.0279			−0.876918			−0.438459	−	0.898751i	$-0.644476\pi$
$631$	−22.0279			−0.876918			−0.438459	+	0.898751i	$0.644476\pi$
$632$	22.0230	+	5.90104i	0.876027	+	0.234731i
$633$	−0.0493675	−	0.207617i	−0.00196218	−	0.00825205i
$634$	−4.65268	−	2.68622i	−0.184781	−	0.106684i
$635$		0			0
$636$	−1.90665	−	1.17411i	−0.0756038	−	0.0465564i
$637$	4.03223	−	15.0485i	0.159763	−	0.596242i
$638$	−1.33171	−	1.33171i	−0.0527227	−	0.0527227i
$639$	−17.6655	−	1.00284i	−0.698836	−	0.0396716i
$640$		0			0
$641$	21.8054	−	12.5894i	0.861263	−	0.497251i	−0.00317173	−	0.999995i	$-0.501010\pi$
$641$	21.8054	−	12.5894i	0.861263	−	0.497251i	0.864435	+	0.502744i	$0.167676\pi$
$642$	−8.68736	+	29.0956i	−0.342863	+	1.14831i
$643$	8.05166	+	30.0492i	0.317526	+	1.18502i	0.921614	+	0.388107i	$0.126871\pi$
$643$	8.05166	+	30.0492i	0.317526	+	1.18502i	−0.604088	+	0.796918i	$0.706462\pi$
$644$	0.319219	−	0.552904i	0.0125790	−	0.0217875i
$645$		0			0
$646$	1.64484	+	2.84895i	0.0647154	+	0.112090i
$647$	−7.86580	+	7.86580i	−0.309237	+	0.309237i	−0.844613	−	0.535377i	$-0.820170\pi$
$647$	−7.86580	+	7.86580i	−0.309237	+	0.309237i	0.535377	+	0.844613i	$0.320170\pi$
$648$	−16.5267	−	20.7755i	−0.649230	−	0.816140i
$649$		−	6.72090i		−	0.263818i
$650$		0			0
$651$	−24.7925	−	0.703147i	−0.971695	−	0.0275585i
$652$	1.12456	−	0.301325i	0.0440411	−	0.0118008i
$653$	−0.279676	+	0.0749391i	−0.0109446	+	0.00293259i	−0.264287	−	0.964444i	$-0.585137\pi$
$653$	−0.279676	+	0.0749391i	−0.0109446	+	0.00293259i	0.253343	+	0.967377i	$0.418470\pi$
$654$	8.90457	+	16.4855i	0.348196	+	0.644635i
$655$		0			0
$656$		−	12.8384i		−	0.501256i
$657$	4.48917	+	5.02953i	0.175139	+	0.196221i
$658$	−16.1106	+	16.1106i	−0.628058	+	0.628058i
$659$	−13.4009	−	23.2111i	−0.522026	−	0.904175i	−0.999672	−	0.0256228i	$-0.991843\pi$
$659$	−13.4009	−	23.2111i	−0.522026	−	0.904175i	0.477646	−	0.878552i	$-0.341490\pi$
$660$		0			0
$661$	−12.6438	+	21.8997i	−0.491787	+	0.851800i	−0.999955	−	0.00945786i	$-0.996989\pi$
$661$	−12.6438	+	21.8997i	−0.491787	+	0.851800i	0.508168	+	0.861258i	$0.330323\pi$
$662$	2.07289	+	7.73611i	0.0805650	+	0.300673i
$663$	15.0443	−	3.57724i	0.584271	−	0.138928i
$664$	25.3823	−	14.6545i	0.985024	−	0.568704i
$665$		0			0
$666$	−21.6622	+	10.9191i	−0.839393	+	0.423106i
$667$	1.78827	+	1.78827i	0.0692421	+	0.0692421i
$668$	0.303196	−	1.13154i	0.0117310	−	0.0437807i
$669$	3.81556	−	2.06095i	0.147518	−	0.0796811i
$670$		0			0
$671$	−10.1231	−	5.84458i	−0.390799	−	0.225628i
$672$	−2.85362	+	2.69622i	−0.110081	+	0.104009i
$673$	23.5227	+	6.30290i	0.906735	+	0.242959i	0.681906	−	0.731439i	$-0.261151\pi$
$673$	23.5227	+	6.30290i	0.906735	+	0.242959i	0.224829	+	0.974398i	$0.427818\pi$
$674$	13.3044			0.512466
$675$		0			0
$676$	3.51002			0.135001
$677$	0.896681	+	0.240265i	0.0344623	+	0.00923414i	0.276009	−	0.961155i	$-0.410988\pi$
$677$	0.896681	+	0.240265i	0.0344623	+	0.00923414i	−0.241547	+	0.970389i	$0.577655\pi$
$678$	20.2949	−	19.1754i	0.779420	−	0.736429i
$679$	−7.03407	−	4.06112i	−0.269943	−	0.155852i
$680$		0			0
$681$	−23.2386	+	12.5522i	−0.890503	+	0.481000i
$682$	2.13874	−	7.98188i	0.0818966	−	0.305642i
$683$	−22.2024	−	22.2024i	−0.849550	−	0.849550i	0.140526	−	0.990077i	$-0.455120\pi$
$683$	−22.2024	−	22.2024i	−0.849550	−	0.849550i	−0.990077	+	0.140526i	$0.955120\pi$
$684$	−0.750970	−	0.492340i	−0.0287141	−	0.0188251i
$685$		0			0
$686$	−23.3578	+	13.4856i	−0.891805	+	0.514884i
$687$	37.1801	−	8.84071i	1.41851	−	0.337294i
$688$	−1.77711	−	6.63225i	−0.0677515	−	0.252852i
$689$	18.2945	−	31.6871i	0.696966	−	1.20718i
$690$		0			0
$691$	−4.05877	−	7.02999i	−0.154403	−	0.267433i	0.778439	−	0.627721i	$-0.216012\pi$
$691$	−4.05877	−	7.02999i	−0.154403	−	0.267433i	−0.932841	+	0.360287i	$0.882679\pi$
$692$	1.89711	−	1.89711i	0.0721173	−	0.0721173i
$693$	5.29593	−	1.10164i	0.201176	−	0.0418479i
$694$		−	14.2473i		−	0.540821i
$695$		0			0
$696$	−3.86828	−	7.16156i	−0.146627	−	0.271458i
$697$	−5.58297	+	1.49595i	−0.211470	+	0.0566633i
$698$	−12.1157	+	3.24640i	−0.458586	+	0.122878i
$699$	−10.3369	−	0.293168i	−0.390979	−	0.0110887i
$700$		0			0
$701$		−	19.6359i		−	0.741637i	−0.928705	−	0.370819i	$-0.879077\pi$
$701$		−	19.6359i		−	0.741637i	0.928705	−	0.370819i	$-0.120923\pi$
$702$	29.6504	−	24.9913i	1.11908	−	0.943236i
$703$	−6.49076	+	6.49076i	−0.244804	+	0.244804i
$704$	−3.79526	−	6.57359i	−0.143039	−	0.247752i
$705$		0			0
$706$	−12.8937	+	22.3325i	−0.485260	+	0.840496i
$707$	1.36642	+	5.09956i	0.0513896	+	0.191789i
$708$	0.742876	−	2.48804i	0.0279190	−	0.0935061i
$709$	2.68383	−	1.54951i	0.100793	−	0.0581931i	−0.448756	−	0.893654i	$-0.648133\pi$
$709$	2.68383	−	1.54951i	0.100793	−	0.0581931i	0.549549	+	0.835461i	$0.314799\pi$
$710$		0			0
$711$	−10.4375	−	20.7069i	−0.391438	−	0.776569i
$712$	9.65210	+	9.65210i	0.361728	+	0.361728i
$713$	−2.87199	+	10.7184i	−0.107557	+	0.401408i
$714$	−6.51914	−	4.01445i	−0.243973	−	0.150237i
$715$		0			0
$716$	−2.93083	−	1.69211i	−0.109530	−	0.0632373i
$717$	−5.44280	−	22.8900i	−0.203265	−	0.854841i
$718$	16.3380	+	4.37774i	0.609727	+	0.163376i
$719$	20.3126			0.757533			0.378767	−	0.925492i	$-0.376348\pi$
$719$	20.3126			0.757533			0.378767	+	0.925492i	$0.376348\pi$
$720$		0			0
$721$	26.7604			0.996608
$722$	−21.6325	−	5.79640i	−0.805077	−	0.215720i
$723$	−8.52158	−	2.54437i	−0.316921	−	0.0946261i
$724$	−2.51149	−	1.45001i	−0.0933388	−	0.0538892i
$725$		0			0
$726$	0.674315	−	23.7759i	0.0250262	−	0.882407i
$727$	−4.57247	+	17.0647i	−0.169584	+	0.632895i	0.827827	+	0.560983i	$0.189577\pi$
$727$	−4.57247	+	17.0647i	−0.169584	+	0.632895i	−0.997411	+	0.0719119i	$0.977090\pi$
$728$	−23.7421	−	23.7421i	−0.879941	−	0.879941i
$729$	−4.57117	+	26.6102i	−0.169303	+	0.985564i
$730$		0			0
$731$	−2.67706	+	1.54560i	−0.0990147	+	0.0571662i
$732$	−3.10150	−	3.28256i	−0.114635	−	0.121327i
$733$	6.82693	+	25.4785i	0.252158	+	0.941068i	0.969649	+	0.244500i	$0.0786239\pi$
$733$	6.82693	+	25.4785i	0.252158	+	0.941068i	−0.717491	+	0.696568i	$0.754709\pi$
$734$	−18.9970	+	32.9038i	−0.701192	+	1.21450i
$735$		0			0
$736$	0.878218	+	1.52112i	0.0323715	+	0.0560692i
$737$	2.06746	−	2.06746i	0.0761558	−	0.0761558i
$738$	−10.8133	+	9.65150i	−0.398041	+	0.355277i
$739$			6.41459i			0.235965i	0.993016	+	0.117982i	$0.0376426\pi$
$739$			6.41459i			0.235965i	−0.993016	+	0.117982i	$0.962357\pi$
$740$		0			0
$741$	7.69396	−	12.4944i	0.282645	−	0.458992i
$742$	−17.4979	+	4.68854i	−0.642368	+	0.172122i
$743$	18.4970	−	4.95625i	0.678588	−	0.181827i	0.0969677	−	0.995288i	$-0.469086\pi$
$743$	18.4970	−	4.95625i	0.678588	−	0.181827i	0.581620	+	0.813460i	$0.302419\pi$
$744$	18.7266	−	30.4104i	0.686549	−	1.11490i
$745$		0			0
$746$			3.13856i			0.114911i
$747$	−28.3096	−	9.33459i	−1.03579	−	0.341535i
$748$	−0.196335	+	0.196335i	−0.00717870	+	0.00717870i
$749$	−13.3702	−	23.1579i	−0.488536	−	0.846170i
$750$		0			0
$751$	−1.96958	+	3.41141i	−0.0718709	+	0.124484i	−0.899721	−	0.436465i	$-0.856230\pi$
$751$	−1.96958	+	3.41141i	−0.0718709	+	0.124484i	0.827850	+	0.560949i	$0.189564\pi$
$752$	−7.64946	−	28.5482i	−0.278947	−	1.04105i
$753$	3.09541	+	3.27612i	0.112803	+	0.119388i
$754$	10.2966	−	5.94472i	0.374979	−	0.216494i
$755$		0			0
$756$	2.08229	+	0.177550i	0.0757321	+	0.00645743i
$757$	−17.3710	−	17.3710i	−0.631361	−	0.631361i	0.317049	−	0.948409i	$-0.397308\pi$
$757$	−17.3710	−	17.3710i	−0.631361	−	0.631361i	−0.948409	+	0.317049i	$0.897308\pi$
$758$	6.41725	−	23.9495i	0.233085	−	0.869885i
$759$	0.0686093	−	2.41912i	0.00249036	−	0.0878085i
$760$		0			0
$761$	7.11860	+	4.10993i	0.258049	+	0.148985i	0.623444	−	0.781868i	$-0.285733\pi$
$761$	7.11860	+	4.10993i	0.258049	+	0.148985i	−0.365395	+	0.930853i	$0.619066\pi$
$762$	5.99637	+	1.79039i	0.217226	+	0.0648591i
$763$	−15.9380	−	4.27057i	−0.576994	−	0.154605i
$764$	−1.03558			−0.0374660
$765$		0			0
$766$	−32.5079			−1.17456
$767$	40.9835	+	10.9815i	1.47983	+	0.396519i
$768$	−1.86921	−	7.86108i	−0.0674495	−	0.283662i
$769$	1.91615	+	1.10629i	0.0690983	+	0.0398939i	0.534151	−	0.845389i	$-0.320631\pi$
$769$	1.91615	+	1.10629i	0.0690983	+	0.0398939i	−0.465053	+	0.885283i	$0.653965\pi$
$770$		0			0
$771$	15.5677	+	9.58654i	0.560659	+	0.345251i
$772$	−0.472918	+	1.76495i	−0.0170207	+	0.0635221i
$773$	8.23173	+	8.23173i	0.296075	+	0.296075i	0.839474	−	0.543400i	$-0.182863\pi$
$773$	8.23173	+	8.23173i	0.296075	+	0.296075i	−0.543400	+	0.839474i	$0.682863\pi$
$774$	−4.25009	+	6.48270i	−0.152766	+	0.233016i
$775$		0			0
$776$	10.1286	−	5.84773i	0.363595	−	0.209921i
$777$	6.11191	−	20.4700i	0.219264	−	0.734356i
$778$	9.41596	+	35.1408i	0.337579	+	1.25986i
$779$	−2.74224	+	4.74970i	−0.0982511	+	0.170176i
$780$		0			0
$781$	2.59572	+	4.49591i	0.0928820	+	0.160876i
$782$	−2.42204	+	2.42204i	−0.0866119	+	0.0866119i
$783$	−2.81419	+	7.78531i	−0.100571	+	0.278224i
$784$		−	10.0057i		−	0.357346i
$785$		0			0
$786$	49.7006	+	1.40957i	1.77276	+	0.0502778i
$787$	−33.8541	+	9.07119i	−1.20677	+	0.323353i	−0.805494	−	0.592604i	$-0.798100\pi$
$787$	−33.8541	+	9.07119i	−1.20677	+	0.323353i	−0.401276	+	0.915957i	$0.631433\pi$
$788$	2.54665	−	0.682372i	0.0907205	−	0.0243085i
$789$	−6.92440	−	12.8195i	−0.246515	−	0.456387i
$790$		0			0
$791$			24.5882i			0.874256i
$792$	−2.43912	+	7.39725i	−0.0866703	+	0.262850i
$793$	52.1803	−	52.1803i	1.85298	−	1.85298i
$794$	−17.3076	−	29.9776i	−0.614223	−	1.06387i
$795$		0			0
$796$	−1.73110	+	2.99835i	−0.0613571	+	0.106274i
$797$	6.77343	+	25.2788i	0.239927	+	0.895421i	0.975866	+	0.218372i	$0.0700747\pi$
$797$	6.77343	+	25.2788i	0.239927	+	0.895421i	−0.735938	+	0.677049i	$0.763259\pi$
$798$	−7.06766	+	1.68056i	−0.250192	+	0.0594910i
$799$	−11.5233	+	6.65297i	−0.407664	+	0.235365i
$800$		0			0
$801$	0.786842	−	13.8606i	0.0278017	−	0.489741i
$802$	12.2041	+	12.2041i	0.430941	+	0.430941i
$803$	0.511942	−	1.91059i	0.0180660	−	0.0674233i
$804$	0.993882	−	0.536840i	0.0350515	−	0.0189329i
$805$		0			0
$806$	45.1784	+	26.0837i	1.59134	+	0.918761i
$807$	−33.7038	+	31.8447i	−1.18643	+	1.12099i
$808$	−7.34301	−	1.96755i	−0.258326	−	0.0692183i
$809$	40.3389			1.41824			0.709120	−	0.705088i	$-0.249092\pi$
$809$	40.3389			1.41824			0.709120	+	0.705088i	$0.249092\pi$
$810$		0			0
$811$	−4.50040			−0.158030			−0.0790152	−	0.996873i	$-0.525178\pi$
$811$	−4.50040			−0.158030			−0.0790152	+	0.996873i	$0.525178\pi$
$812$	0.618923	+	0.165840i	0.0217199	+	0.00581984i
$813$	−23.3981	+	22.1075i	−0.820606	+	0.775343i
$814$	6.16394	+	3.55875i	0.216046	+	0.124734i
$815$		0			0
$816$	8.73818	−	4.71988i	0.305898	−	0.165229i
$817$	−0.759168	+	2.83326i	−0.0265599	+	0.0991231i
$818$	24.3930	+	24.3930i	0.852880	+	0.852880i
$819$	−1.93546	+	34.0942i	−0.0676306	+	1.19135i
$820$		0			0
$821$	13.3109	−	7.68503i	0.464552	−	0.268209i	−0.249404	−	0.968399i	$-0.580235\pi$
$821$	13.3109	−	7.68503i	0.464552	−	0.268209i	0.713956	+	0.700190i	$0.246901\pi$
$822$	15.5238	−	3.69127i	0.541456	−	0.128748i
$823$	−3.77065	−	14.0723i	−0.131437	−	0.490528i	0.868551	−	0.495601i	$-0.165052\pi$
$823$	−3.77065	−	14.0723i	−0.131437	−	0.490528i	−0.999987	+	0.00507263i	$0.998385\pi$
$824$	−19.2665	+	33.3706i	−0.671182	+	1.16252i
$825$		0			0
$826$	−10.5033	−	18.1923i	−0.365457	−	0.632989i
$827$	3.31824	−	3.31824i	0.115387	−	0.115387i	−0.647056	−	0.762443i	$-0.724000\pi$
$827$	3.31824	−	3.31824i	0.115387	−	0.115387i	0.762443	+	0.647056i	$0.224000\pi$
$828$	0.292790	−	0.887961i	0.0101752	−	0.0308588i
$829$			33.9539i			1.17927i	0.807671	+	0.589633i	$0.200728\pi$
$829$			33.9539i			1.17927i	−0.807671	+	0.589633i	$0.799272\pi$
$830$		0			0
$831$	22.4302	+	41.5263i	0.778094	+	1.44053i
$832$	46.2865	−	12.4024i	1.60469	−	0.429977i
$833$	−4.35112	+	1.16588i	−0.150757	+	0.0403953i
$834$	−3.35248	−	0.0950807i	−0.116087	−	0.00329237i
$835$		0			0
$836$			0.263467i			0.00911220i
$837$	−35.7571	+	6.38629i	−1.23595	+	0.220743i
$838$	11.6473	−	11.6473i	0.402349	−	0.402349i
$839$	5.71824	+	9.90428i	0.197416	+	0.341934i	0.947690	−	0.319193i	$-0.103412\pi$
$839$	5.71824	+	9.90428i	0.197416	+	0.341934i	−0.750274	+	0.661127i	$0.770079\pi$
$840$		0			0
$841$	13.2309	−	22.9166i	0.456238	−	0.790228i
$842$	5.03357	+	18.7855i	0.173468	+	0.647392i
$843$	−12.9918	+	43.5119i	−0.447460	+	1.49863i
$844$	−0.0209495	+	0.0120952i	−0.000721111	+	0.000416334i
$845$		0			0
$846$	−18.2943	+	27.9044i	−0.628972	+	0.959374i
$847$	14.8113	+	14.8113i	0.508923	+	0.508923i
$848$	6.08198	−	22.6983i	0.208856	−	0.779462i
$849$	5.25321	+	3.23490i	0.180290	+	0.111021i
$850$		0			0
$851$	−8.27720	−	4.77884i	−0.283739	−	0.163817i
$852$	0.463975	+	1.95127i	0.0158955	+	0.0668494i
$853$	−23.0994	−	6.18947i	−0.790909	−	0.211923i	−0.159320	−	0.987227i	$-0.550930\pi$
$853$	−23.0994	−	6.18947i	−0.790909	−	0.211923i	−0.631589	+	0.775304i	$0.717597\pi$
$854$	−36.5353			−1.25021
$855$		0			0
$856$	38.5043			1.31605
$857$	14.4874	+	3.88189i	0.494881	+	0.132603i	0.497623	−	0.867393i	$-0.334206\pi$
$857$	14.4874	+	3.88189i	0.494881	+	0.132603i	−0.00274224	+	0.999996i	$0.500873\pi$
$858$	−10.9019	−	3.25508i	−0.372184	−	0.111127i
$859$	37.5983	+	21.7074i	1.28284	+	0.740646i	0.977366	−	0.211555i	$-0.0678529\pi$
$859$	37.5983	+	21.7074i	1.28284	+	0.740646i	0.305471	+	0.952201i	$0.401186\pi$
$860$		0			0
$861$	0.361857	−	12.7589i	0.0123321	−	0.434821i
$862$	−12.5016	+	46.6567i	−0.425807	+	1.58913i
$863$	2.78648	+	2.78648i	0.0948527	+	0.0948527i	0.752941	−	0.658088i	$-0.228635\pi$
$863$	2.78648	+	2.78648i	0.0948527	+	0.0948527i	−0.658088	+	0.752941i	$0.728635\pi$
$864$	−3.28736	+	4.71694i	−0.111838	+	0.160474i
$865$		0			0
$866$	−0.545339	+	0.314852i	−0.0185314	+	0.0106991i
$867$	17.1513	+	18.1526i	0.582490	+	0.616495i
$868$	0.727658	+	2.71566i	0.0246983	+	0.0921754i
$869$	−3.40181	+	5.89211i	−0.115399	+	0.199876i
$870$		0			0
$871$	9.22911	+	15.9853i	0.312717	+	0.541641i
$872$	16.8003	−	16.8003i	0.568929	−	0.568929i
$873$	−11.2967	−	3.72489i	−0.382335	−	0.126068i
$874$			3.25020i			0.109940i
$875$		0			0
$876$	0.400700	−	0.650704i	0.0135384	−	0.0219852i
$877$	41.5598	−	11.1359i	1.40338	−	0.376033i	0.523820	−	0.851829i	$-0.324507\pi$
$877$	41.5598	−	11.1359i	1.40338	−	0.376033i	0.879556	+	0.475796i	$0.157840\pi$
$878$	−1.93163	+	0.517577i	−0.0651892	+	0.0174674i
$879$	−2.70616	+	4.39458i	−0.0912764	+	0.148225i
$880$		0			0
$881$			47.0487i			1.58511i	0.609801	+	0.792555i	$0.291249\pi$
$881$			47.0487i			1.58511i	−0.609801	+	0.792555i	$0.708751\pi$
$882$	−8.42736	+	7.52195i	−0.283764	+	0.253277i
$883$	−21.0669	+	21.0669i	−0.708957	+	0.708957i	−0.966316	−	0.257359i	$-0.917148\pi$
$883$	−21.0669	+	21.0669i	−0.708957	+	0.708957i	0.257359	+	0.966316i	$0.417148\pi$
$884$	−0.876436	−	1.51803i	−0.0294777	−	0.0510569i
$885$		0			0
$886$	21.5140	−	37.2633i	0.722776	−	1.25188i
$887$	−0.939801	−	3.50739i	−0.0315554	−	0.117766i	0.948352	−	0.317221i	$-0.102750\pi$
$887$	−0.939801	−	3.50739i	−0.0315554	−	0.117766i	−0.979907	+	0.199454i	$0.936083\pi$
$888$	21.1260	+	22.3593i	0.708943	+	0.750330i
$889$	−4.77265	+	2.75549i	−0.160069	+	0.0924161i
$890$		0			0
$891$	7.26472	−	3.15906i	0.243377	−	0.105833i
$892$	−0.347592	−	0.347592i	−0.0116382	−	0.0116382i
$893$	−3.26780	+	12.1956i	−0.109353	+	0.408110i
$894$	1.09267	−	38.5269i	0.0365444	−	1.28853i
$895$		0			0
$896$	−16.6203	−	9.59572i	−0.555245	−	0.320571i
$897$	14.6395	+	4.37106i	0.488799	+	0.145945i
$898$	−28.3167	−	7.58743i	−0.944939	−	0.253196i
$899$	−11.1368			−0.371433
$900$		0			0
$901$	−10.5794			−0.352450
$902$	4.10768	+	1.10065i	0.136771	+	0.0366477i
$903$	−1.57916	−	6.64125i	−0.0525512	−	0.221007i
$904$	−30.6619	−	17.7026i	−1.01980	−	0.588781i
$905$		0			0
$906$	−0.0112398	−	0.00692143i	−0.000373419	−	0.000229949i
$907$	2.71600	−	10.1363i	0.0901833	−	0.336569i	−0.906062	−	0.423145i	$-0.860926\pi$
$907$	2.71600	−	10.1363i	0.0901833	−	0.336569i	0.996245	+	0.0865764i	$0.0275927\pi$
$908$	2.11700	+	2.11700i	0.0702551	+	0.0702551i
$909$	3.48014	+	6.90419i	0.115429	+	0.228998i
$910$		0			0
$911$	6.77512	−	3.91162i	0.224470	−	0.129598i	−0.383548	−	0.923521i	$-0.625298\pi$
$911$	6.77512	−	3.91162i	0.224470	−	0.129598i	0.608018	+	0.793923i	$0.291965\pi$
$912$	2.69614	−	9.02988i	0.0892780	−	0.299009i
$913$	2.26362	+	8.44796i	0.0749150	+	0.279587i
$914$	−0.612004	+	1.06002i	−0.0202433	+	0.0350624i
$915$		0			0
$916$	−2.16600	−	3.75163i	−0.0715668	−	0.123957i
$917$	−30.9612	+	30.9612i	−1.02243	+	1.02243i
$918$	−10.5444	−	3.81155i	−0.348019	−	0.125800i
$919$		−	4.61000i		−	0.152070i	−0.997105	−	0.0760349i	$-0.975774\pi$
$919$		−	4.61000i		−	0.152070i	0.997105	−	0.0760349i	$-0.0242260\pi$
$920$		0			0
$921$	−53.3815	−	1.51397i	−1.75898	−	0.0498869i
$922$	28.0591	−	7.51842i	0.924078	−	0.247606i
$923$	−31.6570	+	8.48246i	−1.04200	+	0.279204i
$924$	−0.291405	−	0.539494i	−0.00958651	−	0.0177481i
$925$		0			0
$926$			25.1999i			0.828122i
$927$	38.3689	−	7.98139i	1.26020	−	0.262143i
$928$	−1.24650	+	1.24650i	−0.0409182	+	0.0409182i
$929$	15.7062	+	27.2039i	0.515302	+	0.892530i	0.999842	+	0.0177609i	$0.00565375\pi$
$929$	15.7062	+	27.2039i	0.515302	+	0.892530i	−0.484540	+	0.874769i	$0.661013\pi$
$930$		0			0
$931$	−2.13718	+	3.70170i	−0.0700433	+	0.121318i
$932$	0.303388	+	1.13226i	0.00993782	+	0.0370884i
$933$	57.1814	−	13.5966i	1.87203	−	0.445134i
$934$	−27.6818	+	15.9821i	−0.905778	+	0.522951i
$935$		0			0
$936$	−41.1225	−	26.9602i	−1.34413	−	0.881221i
$937$	21.3617	+	21.3617i	0.697856	+	0.697856i	0.963948	−	0.266092i	$-0.0857324\pi$
$937$	21.3617	+	21.3617i	0.697856	+	0.697856i	−0.266092	+	0.963948i	$0.585732\pi$
$938$	2.36525	−	8.82722i	0.0772281	−	0.288219i
$939$	35.3449	−	19.0914i	1.15344	−	0.623023i
$940$		0			0
$941$	−5.77035	−	3.33151i	−0.188108	−	0.108604i	0.402989	−	0.915205i	$-0.367971\pi$
$941$	−5.77035	−	3.33151i	−0.188108	−	0.108604i	−0.591096	+	0.806601i	$0.701305\pi$
$942$	−14.3032	+	13.5142i	−0.466023	+	0.440318i
$943$	−5.51597	−	1.47800i	−0.179625	−	0.0481303i
$944$	27.2498			0.886905
$945$		0			0
$946$	2.27436			0.0739458
$947$	−3.23873	−	0.867814i	−0.105245	−	0.0282002i	0.205812	−	0.978591i	$-0.434016\pi$
$947$	−3.23873	−	0.867814i	−0.105245	−	0.0282002i	−0.311057	+	0.950391i	$0.600683\pi$
$948$	−1.91060	+	1.80521i	−0.0620534	+	0.0586306i
$949$	10.8142	+	6.24356i	0.351043	+	0.202675i
$950$		0			0
$951$	6.09628	−	3.29287i	0.197685	−	0.106779i
$952$	−2.51269	+	9.37748i	−0.0814367	+	0.303926i
$953$	30.7161	+	30.7161i	0.994992	+	0.994992i	0.999988	−	0.00499525i	$-0.00159004\pi$
$953$	30.7161	+	30.7161i	0.994992	+	0.994992i	−0.00499525	+	0.999988i	$0.501590\pi$
$954$	−23.6900	+	11.9412i	−0.766993	+	0.386612i
$955$		0			0
$956$	−2.30970	+	1.33350i	−0.0747009	+	0.0431286i
$957$	2.36300	−	0.561875i	0.0763848	−	0.0181629i
$958$	−6.19919	−	23.1357i	−0.200287	−	0.747480i
$959$	−7.02601	+	12.1694i	−0.226882	+	0.392970i
$960$		0			0
$961$	−8.93253	−	15.4716i	−0.288146	−	0.499084i
$962$	−31.7725	+	31.7725i	−1.02439	+	1.02439i
$963$	−26.0771	−	29.2160i	−0.840322	−	0.941471i
$964$			1.00809i			0.0324684i
$965$		0			0
$966$	−3.59485	−	6.65535i	−0.115662	−	0.214132i
$967$	−5.53906	+	1.48419i	−0.178124	+	0.0477282i	−0.346779	−	0.937947i	$-0.612724\pi$
$967$	−5.53906	+	1.48419i	−0.178124	+	0.0477282i	0.168654	+	0.985675i	$0.446058\pi$
$968$	−29.1336	+	7.80632i	−0.936388	+	0.250904i
$969$	−4.24094	−	0.120278i	−0.136238	−	0.00386389i
$970$		0			0
$971$			14.2248i			0.456496i	0.973603	+	0.228248i	$0.0732998\pi$
$971$			14.2248i			0.456496i	−0.973603	+	0.228248i	$0.926700\pi$
$972$	3.03853	−	0.366480i	0.0974610	−	0.0117549i
$973$	2.08844	−	2.08844i	0.0669524	−	0.0669524i
$974$	−20.7244	−	35.8957i	−0.664052	−	1.15017i
$975$		0			0
$976$	23.6968	−	41.0440i	0.758516	−	1.31379i
$977$	−8.07944	−	30.1529i	−0.258484	−	0.964676i	−0.966119	−	0.258097i	$-0.916904\pi$
$977$	−8.07944	−	30.1529i	−0.258484	−	0.964676i	0.707635	−	0.706578i	$-0.249762\pi$
$978$	3.94636	−	13.2171i	0.126191	−	0.422636i
$979$	−3.52757	+	2.03664i	−0.112742	+	0.0650913i
$980$		0			0
$981$	−24.1256	−	1.36956i	−0.770270	−	0.0437268i
$982$	−38.5627	−	38.5627i	−1.23059	−	1.23059i
$983$	−2.66543	+	9.94750i	−0.0850139	+	0.317276i	−0.995317	−	0.0966666i	$-0.969182\pi$
$983$	−2.66543	+	9.94750i	−0.0850139	+	0.317276i	0.910303	+	0.413943i	$0.135849\pi$
$984$	15.6500	+	9.63718i	0.498903	+	0.307222i
$985$		0			0
$986$	−2.97715	−	1.71886i	−0.0948116	−	0.0547395i
$987$	−6.79742	−	28.5869i	−0.216364	−	0.909932i
$988$	−1.60660	−	0.430488i	−0.0511128	−	0.0136956i
$989$	−3.05411			−0.0971150
$990$		0			0
$991$	37.9180			1.20450			0.602252	−	0.798306i	$-0.294270\pi$
$991$	37.9180			1.20450			0.602252	+	0.798306i	$0.294270\pi$
$992$	−7.47116	−	2.00189i	−0.237210	−	0.0635601i
$993$	−9.89733	−	2.95514i	−0.314082	−	0.0937785i
$994$	14.0523	+	8.11308i	0.445711	+	0.257331i
$995$		0			0
$996$	−0.0957926	+	3.37759i	−0.00303530	+	0.107023i
$997$	8.06937	−	30.1153i	0.255559	−	0.953761i	−0.712219	−	0.701957i	$-0.752310\pi$
$997$	8.06937	−	30.1153i	0.255559	−	0.953761i	0.967778	−	0.251804i	$-0.0810237\pi$
$998$	40.9452	+	40.9452i	1.29610	+	1.29610i
$999$	2.65799	−	31.1727i	0.0840952	−	0.986260i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	225.2.p.b.32.1		16
3.2	odd	2		675.2.q.a.557.4		16
5.2	odd	4		45.2.l.a.23.4	yes	16
5.3	odd	4	inner	225.2.p.b.68.1		16
5.4	even	2		45.2.l.a.32.4	yes	16
9.2	odd	6	inner	225.2.p.b.182.1		16
9.7	even	3		675.2.q.a.332.4		16
15.2	even	4		135.2.m.a.98.1		16
15.8	even	4		675.2.q.a.368.4		16
15.14	odd	2		135.2.m.a.17.1		16
20.7	even	4		720.2.cu.c.113.3		16
20.19	odd	2		720.2.cu.c.257.4		16
45.2	even	12		45.2.l.a.38.4	yes	16
45.4	even	6		405.2.f.a.242.3		16
45.7	odd	12		135.2.m.a.8.1		16
45.14	odd	6		405.2.f.a.242.6		16
45.22	odd	12		405.2.f.a.323.6		16
45.29	odd	6		45.2.l.a.2.4	✓	16
45.32	even	12		405.2.f.a.323.3		16
45.34	even	6		135.2.m.a.62.1		16
45.38	even	12	inner	225.2.p.b.218.1		16
45.43	odd	12		675.2.q.a.143.4		16
180.47	odd	12		720.2.cu.c.353.4		16
180.119	even	6		720.2.cu.c.497.3		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
45.2.l.a.2.4	✓	16	45.29	odd	6
45.2.l.a.23.4	yes	16	5.2	odd	4
45.2.l.a.32.4	yes	16	5.4	even	2
45.2.l.a.38.4	yes	16	45.2	even	12
135.2.m.a.8.1		16	45.7	odd	12
135.2.m.a.17.1		16	15.14	odd	2
135.2.m.a.62.1		16	45.34	even	6
135.2.m.a.98.1		16	15.2	even	4
225.2.p.b.32.1		16	1.1	even	1	trivial
225.2.p.b.68.1		16	5.3	odd	4	inner
225.2.p.b.182.1		16	9.2	odd	6	inner
225.2.p.b.218.1		16	45.38	even	12	inner
405.2.f.a.242.3		16	45.4	even	6
405.2.f.a.242.6		16	45.14	odd	6
405.2.f.a.323.3		16	45.32	even	12
405.2.f.a.323.6		16	45.22	odd	12
675.2.q.a.143.4		16	45.43	odd	12
675.2.q.a.332.4		16	9.7	even	3
675.2.q.a.368.4		16	15.8	even	4
675.2.q.a.557.4		16	3.2	odd	2
720.2.cu.c.113.3		16	20.7	even	4
720.2.cu.c.257.4		16	20.19	odd	2
720.2.cu.c.353.4		16	180.47	odd	12
720.2.cu.c.497.3		16	180.119	even	6

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:	\( N \)	\(=\)	\( 225 = 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	225.p (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.29724 - 0.347596i) q^{2} +(1.25897 - 1.18953i) q^{3} +(-0.170031 - 0.0981673i) q^{4} +(-2.04667 + 1.10550i) q^{6} +(0.530190 - 1.97869i) q^{7} +(2.08575 + 2.08575i) q^{8} +(0.170031 - 2.99518i) q^{9} +O(q^{10})\)	\(q+(-1.29724 - 0.347596i) q^{2} +(1.25897 - 1.18953i) q^{3} +(-0.170031 - 0.0981673i) q^{4} +(-2.04667 + 1.10550i) q^{6} +(0.530190 - 1.97869i) q^{7} +(2.08575 + 2.08575i) q^{8} +(0.170031 - 2.99518i) q^{9} +(-0.762281 + 0.440103i) q^{11} +(-0.330837 + 0.0786668i) q^{12} +(-1.43820 - 5.36743i) q^{13} +(-1.37557 + 2.38256i) q^{14} +(-1.78439 - 3.09066i) q^{16} +(-1.13610 + 1.13610i) q^{17} +(-1.26168 + 3.82638i) q^{18} +1.52456i q^{19} +(-1.68622 - 3.12180i) q^{21} +(1.14184 - 0.305956i) q^{22} +(-1.53331 + 0.410850i) q^{23} +(5.10696 + 0.144840i) q^{24} +7.46278i q^{26} +(-3.34879 - 3.97311i) q^{27} +(-0.284392 + 0.284392i) q^{28} +(-0.796583 - 1.37972i) q^{29} +(3.49518 - 6.05383i) q^{31} +(-0.286379 - 1.06878i) q^{32} +(-0.436175 + 1.46084i) q^{33} +(1.86870 - 1.07889i) q^{34} +(-0.322939 + 0.492581i) q^{36} +(4.25746 + 4.25746i) q^{37} +(0.529931 - 1.97773i) q^{38} +(-8.19538 - 5.04667i) q^{39} +(3.11546 + 1.79871i) q^{41} +(1.10232 + 4.63586i) q^{42} +(1.85841 + 0.497959i) q^{43} +0.172815 q^{44} +2.13189 q^{46} +(7.99942 + 2.14344i) q^{47} +(-5.92294 - 1.76847i) q^{48} +(2.42805 + 1.40183i) q^{49} +(-0.0788937 + 2.78174i) q^{51} +(-0.282368 + 1.05381i) q^{52} +(4.65601 + 4.65601i) q^{53} +(2.96317 + 6.31812i) q^{54} +(5.23290 - 3.02121i) q^{56} +(1.81351 + 1.91938i) q^{57} +(0.553777 + 2.06672i) q^{58} +(-3.81780 + 6.61262i) q^{59} +(6.64002 + 11.5008i) q^{61} +(-6.63838 + 6.63838i) q^{62} +(-5.83639 - 1.92445i) q^{63} +8.62358i q^{64} +(1.07361 - 1.74345i) q^{66} +(-3.20857 + 0.859733i) q^{67} +(0.304699 - 0.0816439i) q^{68} +(-1.44168 + 2.34117i) q^{69} -5.89798i q^{71} +(6.60182 - 5.89254i) q^{72} +(-1.58900 + 1.58900i) q^{73} +(-4.04309 - 7.00284i) q^{74} +(0.149662 - 0.259222i) q^{76} +(0.466676 + 1.74166i) q^{77} +(8.87721 + 9.39544i) q^{78} +(6.69401 - 3.86479i) q^{79} +(-8.94218 - 1.01854i) q^{81} +(-3.41628 - 3.41628i) q^{82} +(2.57170 - 9.59770i) q^{83} +(-0.0197489 + 0.696335i) q^{84} +(-2.23772 - 1.29195i) q^{86} +(-2.64410 - 0.789474i) q^{87} +(-2.50787 - 0.671981i) q^{88} +4.62765 q^{89} -11.3830 q^{91} +(0.301043 + 0.0806641i) q^{92} +(-2.80088 - 11.7792i) q^{93} +(-9.63215 - 5.56112i) q^{94} +(-1.63189 - 1.00491i) q^{96} +(1.02621 - 3.82988i) q^{97} +(-2.66250 - 2.66250i) q^{98} +(1.18858 + 2.35800i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 6 q^{2} + 6 q^{3} + 2 q^{7}+O(q^{10}) \) 16 * q + 6 * q^2 + 6 * q^3 + 2 * q^7	\( 16 q + 6 q^{2} + 6 q^{3} + 2 q^{7} + 6 q^{12} + 2 q^{13} - 8 q^{16} - 36 q^{18} - 12 q^{21} + 10 q^{22} - 18 q^{23} - 18 q^{27} + 16 q^{28} - 4 q^{31} - 30 q^{32} + 12 q^{33} - 48 q^{36} - 4 q^{37} + 30 q^{38} - 24 q^{41} - 6 q^{42} + 2 q^{43} + 32 q^{46} + 12 q^{47} + 30 q^{48} + 36 q^{51} + 14 q^{52} + 36 q^{56} + 6 q^{57} + 6 q^{58} + 8 q^{61} - 36 q^{63} + 36 q^{66} - 4 q^{67} - 42 q^{68} - 18 q^{72} + 8 q^{73} + 24 q^{76} + 6 q^{77} + 42 q^{78} - 48 q^{81} - 32 q^{82} + 66 q^{83} - 48 q^{86} + 18 q^{87} - 18 q^{88} - 40 q^{91} + 60 q^{92} + 18 q^{93} - 24 q^{96} - 28 q^{97}+O(q^{100}) \) 16 * q + 6 * q^2 + 6 * q^3 + 2 * q^7 + 6 * q^12 + 2 * q^13 - 8 * q^16 - 36 * q^18 - 12 * q^21 + 10 * q^22 - 18 * q^23 - 18 * q^27 + 16 * q^28 - 4 * q^31 - 30 * q^32 + 12 * q^33 - 48 * q^36 - 4 * q^37 + 30 * q^38 - 24 * q^41 - 6 * q^42 + 2 * q^43 + 32 * q^46 + 12 * q^47 + 30 * q^48 + 36 * q^51 + 14 * q^52 + 36 * q^56 + 6 * q^57 + 6 * q^58 + 8 * q^61 - 36 * q^63 + 36 * q^66 - 4 * q^67 - 42 * q^68 - 18 * q^72 + 8 * q^73 + 24 * q^76 + 6 * q^77 + 42 * q^78 - 48 * q^81 - 32 * q^82 + 66 * q^83 - 48 * q^86 + 18 * q^87 - 18 * q^88 - 40 * q^91 + 60 * q^92 + 18 * q^93 - 24 * q^96 - 28 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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