LMFDB - Embedded newform 225.2.p.b.182.1

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			182.1
Root			$-0.347596 + 1.29724i$ of defining polynomial
Character	$\chi$	$=$	225.182
Dual form			225.2.p.b.68.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.347596 - 1.29724i) q^{2} +(1.18953 - 1.25897i) q^{3} +(0.170031 - 0.0981673i) q^{4} +(-2.04667 - 1.10550i) q^{6} +(-1.97869 + 0.530190i) q^{7} +(-2.08575 - 2.08575i) q^{8} +(-0.170031 - 2.99518i) q^{9} +O(q^{10})$	\(q+(-0.347596 - 1.29724i) q^{2} +(1.18953 - 1.25897i) q^{3} +(0.170031 - 0.0981673i) q^{4} +(-2.04667 - 1.10550i) q^{6} +(-1.97869 + 0.530190i) q^{7} +(-2.08575 - 2.08575i) q^{8} +(-0.170031 - 2.99518i) q^{9} +(-0.762281 - 0.440103i) q^{11} +(0.0786668 - 0.330837i) q^{12} +(5.36743 + 1.43820i) q^{13} +(1.37557 + 2.38256i) q^{14} +(-1.78439 + 3.09066i) q^{16} +(1.13610 - 1.13610i) q^{17} +(-3.82638 + 1.26168i) q^{18} +1.52456i q^{19} +(-1.68622 + 3.12180i) q^{21} +(-0.305956 + 1.14184i) q^{22} +(-0.410850 + 1.53331i) q^{23} +(-5.10696 + 0.144840i) q^{24} -7.46278i q^{26} +(-3.97311 - 3.34879i) q^{27} +(-0.284392 + 0.284392i) q^{28} +(0.796583 - 1.37972i) q^{29} +(3.49518 + 6.05383i) q^{31} +(-1.06878 - 0.286379i) q^{32} +(-1.46084 + 0.436175i) q^{33} +(-1.86870 - 1.07889i) q^{34} +(-0.322939 - 0.492581i) q^{36} +(4.25746 + 4.25746i) q^{37} +(1.97773 - 0.529931i) q^{38} +(8.19538 - 5.04667i) q^{39} +(3.11546 - 1.79871i) q^{41} +(4.63586 + 1.10232i) q^{42} +(-0.497959 - 1.85841i) q^{43} -0.172815 q^{44} +2.13189 q^{46} +(2.14344 + 7.99942i) q^{47} +(1.76847 + 5.92294i) q^{48} +(-2.42805 + 1.40183i) q^{49} +(-0.0788937 - 2.78174i) q^{51} +(1.05381 - 0.282368i) q^{52} +(-4.65601 - 4.65601i) q^{53} +(-2.96317 + 6.31812i) q^{54} +(5.23290 + 3.02121i) q^{56} +(1.91938 + 1.81351i) q^{57} +(-2.06672 - 0.553777i) q^{58} +(3.81780 + 6.61262i) q^{59} +(6.64002 - 11.5008i) q^{61} +(6.63838 - 6.63838i) q^{62} +(1.92445 + 5.83639i) q^{63} +8.62358i q^{64} +(1.07361 + 1.74345i) q^{66} +(0.859733 - 3.20857i) q^{67} +(0.0816439 - 0.304699i) q^{68} +(1.44168 + 2.34117i) q^{69} +5.89798i q^{71} +(-5.89254 + 6.60182i) q^{72} +(-1.58900 + 1.58900i) q^{73} +(4.04309 - 7.00284i) q^{74} +(0.149662 + 0.259222i) q^{76} +(1.74166 + 0.466676i) q^{77} +(-9.39544 - 8.87721i) q^{78} +(-6.69401 - 3.86479i) q^{79} +(-8.94218 + 1.01854i) q^{81} +(-3.41628 - 3.41628i) q^{82} +(9.59770 - 2.57170i) q^{83} +(0.0197489 + 0.696335i) q^{84} +(-2.23772 + 1.29195i) q^{86} +(-0.789474 - 2.64410i) q^{87} +(0.671981 + 2.50787i) q^{88} -4.62765 q^{89} -11.3830 q^{91} +(0.0806641 + 0.301043i) q^{92} +(11.7792 + 2.80088i) q^{93} +(9.63215 - 5.56112i) q^{94} +(-1.63189 + 1.00491i) q^{96} +(-3.82988 + 1.02621i) 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 $\left(\mathbb{Z}/225\mathbb{Z}\right)^\times$.

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

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 $

$2$	−0.347596	−	1.29724i	−0.245787	−	0.917290i	−0.972986	−	0.230863i	$-0.925845\pi$
$2$	−0.347596	−	1.29724i	−0.245787	−	0.917290i	0.727199	−	0.686427i	$-0.240822\pi$
$3$	1.18953	−	1.25897i	0.686776	−	0.726869i
$3$	1.18953	−	1.25897i	0.686776	−	0.726869i
$4$	0.170031	−	0.0981673i	0.0850154	−	0.0490837i
$5$		0			0
$5$		0			0
$6$	−2.04667	−	1.10550i	−0.835551	−	0.451318i
$7$	−1.97869	+	0.530190i	−0.747876	+	0.200393i	−0.612576	−	0.790412i	$-0.709867\pi$
$7$	−1.97869	+	0.530190i	−0.747876	+	0.200393i	−0.135300	+	0.990805i	$0.543200\pi$
$8$	−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	0.380660	−	0.924715i	$-0.375697\pi$
$11$	−0.762281	−	0.440103i	−0.229836	−	0.132696i	−0.610497	+	0.792019i	$0.709030\pi$
$12$	0.0786668	−	0.330837i	0.0227092	−	0.0955045i
$13$	5.36743	+	1.43820i	1.48866	+	0.398885i	0.909283	−	0.416177i	$-0.136630\pi$
$13$	5.36743	+	1.43820i	1.48866	+	0.398885i	0.579374	+	0.815062i	$0.303297\pi$
$14$	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	−0.555783	−	0.831327i	$-0.687582\pi$
$17$	1.13610	−	1.13610i	0.275544	−	0.275544i	0.831327	+	0.555783i	$0.187582\pi$
$18$	−3.82638	+	1.26168i	−0.901885	+	0.297381i
$19$			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
$22$	−0.305956	+	1.14184i	−0.0652300	+	0.243442i
$23$	−0.410850	+	1.53331i	−0.0856682	+	0.319718i	−0.995440	−	0.0953909i	$-0.969590\pi$
$23$	−0.410850	+	1.53331i	−0.0856682	+	0.319718i	0.909772	+	0.415109i	$0.136257\pi$
$24$	−5.10696	+	0.144840i	−1.04245	+	0.0295653i
$25$		0			0
$26$		−	7.46278i		−	1.46357i
$27$	−3.97311	−	3.34879i	−0.764625	−	0.644476i
$28$	−0.284392	+	0.284392i	−0.0537450	+	0.0537450i
$29$	0.796583	−	1.37972i	0.147922	−	0.256208i	−0.782537	−	0.622603i	$-0.786075\pi$
$29$	0.796583	−	1.37972i	0.147922	−	0.256208i	0.930459	+	0.366396i	$0.119408\pi$
$30$		0			0
$31$	3.49518	+	6.05383i	0.627752	+	1.08730i	0.988002	+	0.154443i	$0.0493583\pi$
$31$	3.49518	+	6.05383i	0.627752	+	1.08730i	−0.360249	+	0.932856i	$0.617308\pi$
$32$	−1.06878	−	0.286379i	−0.188936	−	0.0506251i
$33$	−1.46084	+	0.436175i	−0.254299	+	0.0759284i
$34$	−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	$0.585198\pi$
$38$	1.97773	−	0.529931i	0.320830	−	0.0859661i
$39$	8.19538	−	5.04667i	1.31231	−	0.808114i
$40$		0			0
$41$	3.11546	−	1.79871i	0.486552	−	0.280911i	−0.236591	−	0.971609i	$-0.576030\pi$
$41$	3.11546	−	1.79871i	0.486552	−	0.280911i	0.723143	+	0.690698i	$0.242697\pi$
$42$	4.63586	+	1.10232i	0.715329	+	0.170092i
$43$	−0.497959	−	1.85841i	−0.0759380	−	0.283404i	0.917506	−	0.397721i	$-0.130199\pi$
$43$	−0.497959	−	1.85841i	−0.0759380	−	0.283404i	−0.993444	+	0.114317i	$0.963532\pi$
$44$	−0.172815			−0.0260528
$45$		0			0
$46$	2.13189			0.314330
$47$	2.14344	+	7.99942i	0.312652	+	1.16683i	0.926155	+	0.377142i	$0.123093\pi$
$47$	2.14344	+	7.99942i	0.312652	+	1.16683i	−0.613503	+	0.789693i	$0.710240\pi$
$48$	1.76847	+	5.92294i	0.255256	+	0.854902i
$49$	−2.42805	+	1.40183i	−0.346864	+	0.200262i
$50$		0			0
$51$	−0.0788937	−	2.78174i	−0.0110473	−	0.389522i
$52$	1.05381	−	0.282368i	0.146137	−	0.0391574i
$53$	−4.65601	−	4.65601i	−0.639552	−	0.639552i	0.310893	−	0.950445i	$-0.399372\pi$
$53$	−4.65601	−	4.65601i	−0.639552	−	0.639552i	−0.950445	+	0.310893i	$0.899372\pi$
$54$	−2.96317	+	6.31812i	−0.403236	+	0.859787i
$55$		0			0
$56$	5.23290	+	3.02121i	0.699275	+	0.403727i
$57$	1.91938	+	1.81351i	0.254229	+	0.240206i
$58$	−2.06672	−	0.553777i	−0.271374	−	0.0727145i
$59$	3.81780	+	6.61262i	0.497035	+	0.860890i	0.999994	−	0.00342048i	$-0.00108877\pi$
$59$	3.81780	+	6.61262i	0.497035	+	0.860890i	−0.502959	+	0.864310i	$0.667755\pi$
$60$		0			0
$61$	6.64002	−	11.5008i	0.850167	−	1.47253i	−0.0308900	−	0.999523i	$-0.509834\pi$
$61$	6.64002	−	11.5008i	0.850167	−	1.47253i	0.881057	−	0.473010i	$-0.156833\pi$
$62$	6.63838	−	6.63838i	0.843075	−	0.843075i
$63$	1.92445	+	5.83639i	0.242458	+	0.735317i
$64$			8.62358i			1.07795i
$65$		0			0
$66$	1.07361	+	1.74345i	0.132152	+	0.214604i
$67$	0.859733	−	3.20857i	0.105033	−	0.391989i	−0.893316	−	0.449429i	$-0.851627\pi$
$67$	0.859733	−	3.20857i	0.105033	−	0.391989i	0.998349	+	0.0574406i	$0.0182940\pi$
$68$	0.0816439	−	0.304699i	0.00990078	−	0.0369502i
$69$	1.44168	+	2.34117i	0.173558	+	0.281844i
$70$		0			0
$71$			5.89798i			0.699961i	0.936757	+	0.349980i	$0.113812\pi$
$71$			5.89798i			0.699961i	−0.936757	+	0.349980i	$0.886188\pi$
$72$	−5.89254	+	6.60182i	−0.694442	+	0.778032i
$73$	−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
$77$	1.74166	+	0.466676i	0.198480	+	0.0531827i
$78$	−9.39544	−	8.87721i	−1.06382	−	1.00515i
$79$	−6.69401	−	3.86479i	−0.753135	−	0.434823i	0.0736905	−	0.997281i	$-0.476522\pi$
$79$	−6.69401	−	3.86479i	−0.753135	−	0.434823i	−0.826826	+	0.562458i	$0.809856\pi$
$80$		0			0
$81$	−8.94218	+	1.01854i	−0.993575	+	0.113172i
$82$	−3.41628	−	3.41628i	−0.377265	−	0.377265i
$83$	9.59770	−	2.57170i	1.05348	−	0.282280i	0.309794	−	0.950804i	$-0.399740\pi$
$83$	9.59770	−	2.57170i	1.05348	−	0.282280i	0.743691	+	0.668523i	$0.233073\pi$
$84$	0.0197489	+	0.696335i	0.00215478	+	0.0759763i
$85$		0			0
$86$	−2.23772	+	1.29195i	−0.241299	+	0.139314i
$87$	−0.789474	−	2.64410i	−0.0846405	−	0.283477i
$88$	0.671981	+	2.50787i	0.0716334	+	0.267340i
$89$	−4.62765			−0.490530			−0.245265	−	0.969456i	$-0.578875\pi$
$89$	−4.62765			−0.490530			−0.245265	+	0.969456i	$0.578875\pi$
$90$		0			0
$91$	−11.3830			−1.19327
$92$	0.0806641	+	0.301043i	0.00840982	+	0.0313859i
$93$	11.7792	+	2.80088i	1.22145	+	0.290437i
$94$	9.63215	−	5.56112i	0.993480	−	0.573586i
$95$		0			0
$96$	−1.63189	+	1.00491i	−0.166554	+	0.102563i
$97$	−3.82988	+	1.02621i	−0.388865	+	0.104196i	−0.447954	−	0.894057i	$-0.647847\pi$
$97$	−3.82988	+	1.02621i	−0.388865	+	0.104196i	0.0590888	+	0.998253i	$0.481180\pi$
$98$	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	0.384829	−	0.922988i	$-0.374260\pi$
$101$	−2.23195	−	1.28862i	−0.222087	−	0.128222i	−0.606916	+	0.794766i	$0.707594\pi$
$102$	−3.58117	+	1.06927i	−0.354589	+	0.105873i
$103$	−12.6183	−	3.38106i	−1.24332	−	0.333146i	−0.423566	−	0.905865i	$-0.639222\pi$
$103$	−12.6183	−	3.38106i	−1.24332	−	0.333146i	−0.819752	+	0.572719i	$0.805889\pi$
$104$	−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	−0.994742	−	0.102411i	$-0.967344\pi$
$107$	−9.23034	+	9.23034i	−0.892331	+	0.892331i	0.102411	+	0.994742i	$0.467344\pi$
$108$	−1.00429	−	0.179369i	−0.0966381	−	0.0172598i
$109$		−	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
$112$	1.89213	−	7.06153i	0.178790	−	0.667252i
$113$	−3.10662	+	11.5941i	−0.292246	+	1.09068i	0.651134	+	0.758963i	$0.274294\pi$
$113$	−3.10662	+	11.5941i	−0.292246	+	1.09068i	−0.943380	+	0.331714i	$0.892373\pi$
$114$	1.68540	−	3.12028i	0.157852	−	0.292241i
$115$		0			0
$116$		−	0.312794i		−	0.0290422i
$117$	3.39503	−	16.3209i	0.313871	−	1.50887i
$118$	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
$122$	−17.2274	−	4.61608i	−1.55970	−	0.417920i
$123$	1.44140	−	6.06190i	0.129967	−	0.546583i
$124$	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	$0.788085\pi$
$128$	9.04933	−	2.42476i	0.799855	−	0.214321i
$129$	−2.93202	−	1.58372i	−0.258150	−	0.139438i
$130$		0			0
$131$	−18.5109	+	10.6873i	−1.61731	+	0.933754i	−0.629696	+	0.776841i	$0.716821\pi$
$131$	−18.5109	+	10.6873i	−1.61731	+	0.933754i	−0.987613	+	0.156912i	$0.949846\pi$
$132$	−0.205569	+	0.217569i	−0.0178925	+	0.0189370i
$133$	−0.808307	−	3.01664i	−0.0700891	−	0.261576i
$134$	−4.46113			−0.385383
$135$		0			0
$136$	−4.73922			−0.406385
$137$	−1.77541	−	6.62594i	−0.151684	−	0.566092i	−0.999367	−	0.0355883i	$-0.988669\pi$
$137$	−1.77541	−	6.62594i	−0.151684	−	0.566092i	0.847683	−	0.530504i	$-0.177997\pi$
$138$	2.53595	−	2.68400i	0.215875	−	0.228477i
$139$	−1.24863	+	0.720896i	−0.105907	+	0.0611456i	−0.552018	−	0.833832i	$-0.686142\pi$
$139$	−1.24863	+	0.720896i	−0.105907	+	0.0611456i	0.446111	+	0.894978i	$0.352809\pi$
$140$		0			0
$141$	12.6207	+	6.81703i	1.06286	+	0.574097i
$142$	7.65111	−	2.05011i	0.642067	−	0.172041i
$143$	−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
$147$	−1.12337	+	4.72437i	−0.0926536	+	0.389659i
$148$	1.14184	+	0.305956i	0.0938589	+	0.0251494i
$149$	8.28457	+	14.3493i	0.678699	+	1.17554i	0.975373	+	0.220562i	$0.0707891\pi$
$149$	8.28457	+	14.3493i	0.678699	+	1.17554i	−0.296674	+	0.954979i	$0.595878\pi$
$150$		0			0
$151$	0.00283730	−	0.00491435i	0.000230896	−	0.000399924i	−0.865910	−	0.500200i	$-0.833260\pi$
$151$	0.00283730	−	0.00491435i	0.000230896	−	0.000399924i	0.866141	+	0.499800i	$0.166593\pi$
$152$	3.17985	−	3.17985i	0.257920	−	0.257920i
$153$	−3.59599	−	3.20964i	−0.290718	−	0.259484i
$154$		−	2.42157i		−	0.195136i
$155$		0			0
$156$	0.898049	−	1.66261i	0.0719014	−	0.133115i
$157$	−2.18944	+	8.17112i	−0.174737	+	0.652126i	0.821860	+	0.569690i	$0.192937\pi$
$157$	−2.18944	+	8.17112i	−0.174737	+	0.652126i	−0.996596	+	0.0824362i	$0.973730\pi$
$158$	−2.68677	+	10.0272i	−0.213748	+	0.797717i
$159$	−11.4003	+	0.323326i	−0.904099	+	0.0256414i
$160$		0			0
$161$		−	3.25179i		−	0.256277i
$162$	4.42956	+	11.2461i	0.348019	+	0.883581i
$163$	−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
$167$	5.76334	+	1.54428i	0.445980	+	0.119500i	0.474818	−	0.880084i	$-0.342514\pi$
$167$	5.76334	+	1.54428i	0.445980	+	0.119500i	−0.0288375	+	0.999584i	$0.509181\pi$
$168$	10.0283	−	2.99425i	0.773702	−	0.231012i
$169$	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
$173$	−13.1994	+	3.53677i	−1.00353	+	0.268896i	−0.722925	−	0.690927i	$-0.757203\pi$
$173$	−13.1994	+	3.53677i	−1.00353	+	0.268896i	−0.280608	+	0.959822i	$0.590536\pi$
$174$	−3.15562	+	1.94322i	−0.239227	+	0.147315i
$175$		0			0
$176$	2.72042	−	1.57063i	0.205059	−	0.118391i
$177$	12.8665	+	3.05941i	0.967106	+	0.229959i
$178$	1.60855	+	6.00319i	0.120566	+	0.449958i
$179$	−17.2370			−1.28836			−0.644178	−	0.764875i	$-0.722801\pi$
$179$	−17.2370			−1.28836			−0.644178	+	0.764875i	$0.722801\pi$
$180$		0			0
$181$	14.7708			1.09790			0.548952	−	0.835854i	$-0.315027\pi$
$181$	14.7708			1.09790			0.548952	+	0.835854i	$0.315027\pi$
$182$	3.95669	+	14.7666i	0.293289	+	1.09457i
$183$	−6.58076	−	22.0402i	−0.486464	−	1.62926i
$184$	4.05503	−	2.34117i	0.298941	−	0.172594i
$185$		0			0
$186$	−0.460987	−	16.2541i	−0.0338012	−	1.19181i
$187$	−1.36603	+	0.366025i	−0.0998937	+	0.0267664i
$188$	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	0.656073	−	0.754697i	$-0.272216\pi$
$191$	4.56792	+	2.63729i	0.330523	+	0.190827i	−0.325550	+	0.945525i	$0.605550\pi$
$192$	10.8569	+	10.2580i	0.783527	+	0.740309i
$193$	8.98952	+	2.40873i	0.647080	+	0.173384i	0.567408	−	0.823437i	$-0.307946\pi$
$193$	8.98952	+	2.40873i	0.647080	+	0.173384i	0.0796715	+	0.996821i	$0.474613\pi$
$194$	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	−0.282692	−	0.959211i	$-0.591227\pi$
$197$	9.49539	−	9.49539i	0.676519	−	0.676519i	0.959211	+	0.282692i	$0.0912274\pi$
$198$	3.47204	+	0.722243i	0.246747	+	0.0513276i
$199$		−	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
$202$	−0.895835	+	3.34330i	−0.0630307	+	0.235234i
$203$	−0.844680	+	3.15239i	−0.0592849	+	0.221254i
$204$	−0.286490	−	0.465237i	−0.0200583	−	0.0325731i
$205$		0			0
$206$			17.5443i			1.22237i
$207$	4.66240	+	0.969859i	0.324060	+	0.0674098i
$208$	−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	0.868138	−	0.496323i	$-0.165317\pi$
$211$	0.0616050	+	0.106703i	0.00424106	+	0.00734574i	−0.863897	+	0.503668i	$0.831983\pi$
$212$	−1.24873	−	0.334597i	−0.0857633	−	0.0229802i
$213$	7.42540	+	7.01583i	0.508780	+	0.480716i
$214$	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
$218$	−10.4490	+	2.79981i	−0.707698	+	0.189627i
$219$	0.110345	+	3.89068i	0.00745640	+	0.262908i
$220$		0			0
$221$	7.73186	−	4.46399i	0.520101	−	0.300281i
$222$	−4.00701	−	13.4202i	−0.268933	−	0.900707i
$223$	−0.648014	−	2.41842i	−0.0433942	−	0.161949i	0.940829	−	0.338883i	$-0.110049\pi$
$223$	−0.648014	−	2.41842i	−0.0433942	−	0.161949i	−0.984223	+	0.176933i	$0.943382\pi$
$224$	2.26663			0.151445
$225$		0			0
$226$	16.1202			1.07230
$227$	−3.94671	−	14.7293i	−0.261952	−	0.977619i	−0.964090	−	0.265577i	$-0.914437\pi$
$227$	−3.94671	−	14.7293i	−0.261952	−	0.977619i	0.702137	−	0.712042i	$-0.252229\pi$
$228$	0.504382	+	0.119932i	0.0334035	+	0.00794272i
$229$	−19.1083	+	11.0322i	−1.26271	+	0.729029i	−0.973599	−	0.228265i	$-0.926695\pi$
$229$	−19.1083	+	11.0322i	−1.26271	+	0.729029i	−0.289116	+	0.957294i	$0.593361\pi$
$230$		0			0
$231$	2.65929	−	1.63758i	0.174969	−	0.107745i
$232$	−4.53922	+	1.21628i	−0.298014	+	0.0798527i
$233$	4.22173	+	4.22173i	0.276575	+	0.276575i	0.831740	−	0.555165i	$-0.187345\pi$
$233$	4.22173	+	4.22173i	0.276575	+	0.276575i	−0.555165	+	0.831740i	$0.687345\pi$
$234$	−22.3524	+	1.26890i	−1.46122	+	0.0829507i
$235$		0			0
$236$	1.29829	+	0.749566i	0.0845112	+	0.0487926i
$237$	−12.8284	+	3.83030i	−0.833294	+	0.248805i
$238$	4.26960	+	1.14404i	0.276757	+	0.0741569i
$239$	−6.79199	−	11.7641i	−0.439338	−	0.760955i	0.558301	−	0.829639i	$-0.311453\pi$
$239$	−6.79199	−	11.7641i	−0.439338	−	0.760955i	−0.997639	+	0.0686835i	$0.978120\pi$
$240$		0			0
$241$	−2.56728	+	4.44666i	−0.165373	+	0.286434i	−0.936788	−	0.349898i	$-0.886216\pi$
$241$	−2.56728	+	4.44666i	−0.165373	+	0.286434i	0.771415	+	0.636333i	$0.219549\pi$
$242$	−9.71038	+	9.71038i	−0.624207	+	0.624207i
$243$	−9.35468	+	12.4696i	−0.600103	+	0.799923i
$244$		−	2.60733i		−	0.166917i
$245$		0			0
$246$	−8.36479	+	0.237236i	−0.533319	+	0.0151256i
$247$	−2.19262	+	8.18298i	−0.139513	+	0.520670i
$248$	5.33669	−	19.9168i	0.338880	−	1.26472i
$249$	8.17907	−	15.1424i	0.518327	−	0.959609i
$250$		0			0
$251$		−	2.60221i		−	0.164250i	−0.996622	−	0.0821251i	$-0.973829\pi$
$251$		−	2.60221i		−	0.164250i	0.996622	−	0.0821251i	$-0.0261707\pi$
$252$	0.900159	+	0.803448i	0.0567047	+	0.0506125i
$253$	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
$257$	10.1958	+	2.73197i	0.635999	+	0.170415i	0.562390	−	0.826872i	$-0.309882\pi$
$257$	10.1958	+	2.73197i	0.635999	+	0.170415i	0.0736085	+	0.997287i	$0.476548\pi$
$258$	−1.03531	+	4.35404i	−0.0644555	+	0.271071i
$259$	−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
$263$	8.12541	−	2.17720i	0.501034	−	0.134252i	0.000554412	−	1.00000i	$-0.499824\pi$
$263$	8.12541	−	2.17720i	0.501034	−	0.134252i	0.500480	+	0.865748i	$0.333157\pi$
$264$	3.95668	+	2.13718i	0.243517	+	0.131534i
$265$		0			0
$266$	−3.63236	+	2.09714i	−0.222714	+	0.128584i
$267$	−5.50473	+	5.82609i	−0.336884	+	0.356551i
$268$	−0.168795	−	0.629953i	−0.0103108	−	0.0384805i
$269$	26.7708			1.63225			0.816123	−	0.577878i	$-0.196119\pi$
$269$	26.7708			1.63225			0.816123	+	0.577878i	$0.196119\pi$
$270$		0			0
$271$	−18.5850			−1.12896			−0.564480	−	0.825447i	$-0.690923\pi$
$271$	−18.5850			−1.12896			−0.564480	+	0.825447i	$0.690923\pi$
$272$	1.48405	+	5.53853i	0.0899834	+	0.335823i
$273$	−13.5405	+	14.3309i	−0.819506	+	0.867347i
$274$	−7.97833	+	4.60629i	−0.481989	+	0.278276i
$275$		0			0
$276$	0.474957	+	0.256546i	0.0285891	+	0.0154422i
$277$	26.3206	−	7.05259i	1.58145	−	0.423749i	0.642078	−	0.766640i	$-0.278073\pi$
$277$	26.3206	−	7.05259i	1.58145	−	0.423749i	0.939375	+	0.342891i	$0.111406\pi$
$278$	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	−0.365595	−	0.930774i	$-0.619135\pi$
$281$	−22.7050	−	13.1087i	−1.35447	−	0.782002i	−0.988872	+	0.148772i	$0.952468\pi$
$282$	4.45643	−	18.7418i	0.265377	−	1.11606i
$283$	−3.44050	−	0.921880i	−0.204517	−	0.0548001i	0.155106	−	0.987898i	$-0.450428\pi$
$283$	−3.44050	−	0.921880i	−0.204517	−	0.0548001i	−0.359623	+	0.933098i	$0.617095\pi$
$284$	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
$288$	−0.676030	+	3.24988i	−0.0398355	+	0.191501i
$289$			14.4186i			0.848151i
$290$		0			0
$291$	−3.26378	+	6.04243i	−0.191326	+	0.354213i
$292$	−0.114191	+	0.426168i	−0.00668254	+	0.0249396i
$293$	−0.771199	+	2.87816i	−0.0450539	+	0.168144i	−0.984787	−	0.173765i	$-0.944407\pi$
$293$	−0.771199	+	2.87816i	−0.0450539	+	0.168144i	0.939733	+	0.341909i	$0.111073\pi$
$294$	6.51914	−	0.184891i	0.380204	−	0.0107831i
$295$		0			0
$296$		−	17.7600i		−	1.03228i
$297$	1.55481	+	4.30130i	0.0902192	+	0.249587i
$298$	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
$302$	−0.00736135	−	0.00197247i	−0.000423598	−	0.000113503i
$303$	−4.27731	+	1.27712i	−0.245725	+	0.0733684i
$304$	−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	$-0.592353\pi$
$308$	0.341948	−	0.0916247i	0.0194843	−	0.00522080i
$309$	−19.2665	+	11.8642i	−1.09603	+	0.674933i
$310$		0			0
$311$	29.3878	−	16.9671i	1.66643	−	0.962114i	0.696892	−	0.717176i	$-0.254565\pi$
$311$	29.3878	−	16.9671i	1.66643	−	0.962114i	0.969539	−	0.244939i	$-0.0787679\pi$
$312$	−27.6196	−	6.56741i	−1.56365	−	0.371806i
$313$	−6.00279	−	22.4027i	−0.339298	−	1.26628i	−0.899134	−	0.437673i	$-0.855803\pi$
$313$	−6.00279	−	22.4027i	−0.339298	−	1.26628i	0.559836	−	0.828603i	$-0.310864\pi$
$314$	11.3610			0.641137
$315$		0			0
$316$	−1.51758			−0.0853708
$317$	1.03536	+	3.86401i	0.0581515	+	0.217024i	0.988887	−	0.148669i	$-0.0474987\pi$
$317$	1.03536	+	3.86401i	0.0581515	+	0.217024i	−0.930736	+	0.365693i	$0.880832\pi$
$318$	4.38211	+	14.6765i	0.245737	+	0.823019i
$319$	−1.21444	+	0.701157i	−0.0679956	+	0.0392573i
$320$		0			0
$321$	0.640980	+	22.6005i	0.0357760	+	1.26144i
$322$	−4.21836	+	1.13031i	−0.235080	+	0.0629896i
$323$	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
$327$	−10.1408	−	9.58143i	−0.560786	−	0.529854i
$328$	−10.2497	−	2.74640i	−0.565945	−	0.151645i
$329$	−8.48242	−	14.6920i	−0.467651	−	0.809995i
$330$		0			0
$331$	−2.98175	+	5.16454i	−0.163892	+	0.283869i	−0.936261	−	0.351305i	$-0.885738\pi$
$331$	−2.98175	+	5.16454i	−0.163892	+	0.283869i	0.772369	+	0.635174i	$0.219071\pi$
$332$	1.37945	−	1.37945i	0.0757071	−	0.0757071i
$333$	12.0279	−	13.4757i	0.659127	−	0.738466i
$334$		−	8.01324i		−	0.438465i
$335$		0			0
$336$	−6.63954	−	10.7821i	−0.362216	−	0.588210i
$337$	2.56397	−	9.56887i	0.139668	−	0.521250i	−0.860267	−	0.509845i	$-0.829703\pi$
$337$	2.56397	−	9.56887i	0.139668	−	0.521250i	0.999935	−	0.0114051i	$-0.00363044\pi$
$338$	6.21422	−	23.1918i	0.338009	−	1.26147i
$339$	10.9012	+	17.7026i	0.592072	+	0.961476i
$340$		0			0
$341$		−	6.15295i		−	0.333201i
$342$	−1.92351	−	5.83354i	−0.104012	−	0.315442i
$343$	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
$347$	10.2471	+	2.74569i	0.550091	+	0.147396i	0.523150	−	0.852241i	$-0.324757\pi$
$347$	10.2471	+	2.74569i	0.550091	+	0.147396i	0.0269407	+	0.999637i	$0.491423\pi$
$348$	−0.393799	−	0.372078i	−0.0211098	−	0.0199455i
$349$	−8.08831	−	4.66979i	−0.432957	−	0.249968i	0.267648	−	0.963517i	$-0.413753\pi$
$349$	−8.08831	−	4.66979i	−0.432957	−	0.249968i	−0.700606	+	0.713549i	$0.747087\pi$
$350$		0			0
$351$	−16.5091	−	23.6885i	−0.881193	−	1.26440i
$352$	0.688675	+	0.688675i	0.0367065	+	0.0367065i
$353$	18.5470	−	4.96965i	0.987156	−	0.264508i	0.271100	−	0.962551i	$-0.412612\pi$
$353$	18.5470	−	4.96965i	0.987156	−	0.264508i	0.716055	+	0.698043i	$0.245946\pi$
$354$	−0.503538	−	17.7544i	−0.0267627	−	0.943638i
$355$		0			0
$356$	−0.786842	+	0.454284i	−0.0417026	+	0.0240770i
$357$	1.63096	+	5.46239i	0.0863194	+	0.289100i
$358$	5.99152	+	22.3606i	0.316662	+	1.18180i
$359$	12.5944			0.664705			0.332352	−	0.943155i	$-0.392158\pi$
$359$	12.5944			0.664705			0.332352	+	0.943155i	$0.392158\pi$
$360$		0			0
$361$	16.6757			0.877669
$362$	−5.13426	−	19.1613i	−0.269851	−	1.00710i
$363$	−17.2302	−	4.09702i	−0.904353	−	0.215038i
$364$	−1.93546	+	1.11744i	−0.101446	+	0.0585698i
$365$		0			0
$366$	−26.3041	+	16.1979i	−1.37494	+	0.846680i
$367$	−27.3263	+	7.32206i	−1.42642	+	0.382209i	−0.887757	−	0.460312i	$-0.847738\pi$
$367$	−27.3263	+	7.32206i	−1.42642	+	0.382209i	−0.538665	+	0.842520i	$0.681071\pi$
$368$	−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
$372$	2.27779	−	0.680100i	0.118098	−	0.0352616i
$373$	2.25734	+	0.604851i	0.116880	+	0.0313180i	0.316785	−	0.948497i	$-0.397397\pi$
$373$	2.25734	+	0.604851i	0.116880	+	0.0313180i	−0.199905	+	0.979815i	$0.564063\pi$
$374$	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
$378$	2.51341	−	14.0727i	0.129276	−	0.723820i
$379$			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
$382$	1.83342	−	6.84241i	0.0938059	−	0.350088i
$383$	6.26481	−	23.3806i	0.320117	−	1.19469i	−0.599014	−	0.800739i	$-0.704441\pi$
$383$	6.26481	−	23.3806i	0.320117	−	1.19469i	0.919131	−	0.393953i	$-0.128893\pi$
$384$	7.71175	−	14.2772i	0.393539	−	0.728580i
$385$		0			0
$386$		−	12.4989i		−	0.636176i
$387$	−5.48159	+	1.80746i	−0.278645	+	0.0918784i
$388$	−0.550457	+	0.550457i	−0.0279452	+	0.0279452i
$389$	13.5444	−	23.4596i	0.686729	−	1.18945i	−0.286161	−	0.958182i	$-0.592379\pi$
$389$	13.5444	−	23.4596i	0.686729	−	1.18945i	0.972890	−	0.231268i	$-0.0742876\pi$
$390$		0			0
$391$	1.27523	+	2.20876i	0.0644911	+	0.111702i
$392$	7.98815	+	2.14042i	0.403463	+	0.108108i
$393$	−8.56432	+	36.0177i	−0.432013	+	1.81685i
$394$	−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	$0.526111\pi$
$398$	−22.8758	+	6.12955i	−1.14666	+	0.307247i
$399$	−4.75938	−	2.57075i	−0.238267	−	0.128699i
$400$		0			0
$401$	−11.1294	+	6.42558i	−0.555777	+	0.320878i	−0.751449	−	0.659791i	$-0.770645\pi$
$401$	−11.1294	+	6.42558i	−0.555777	+	0.320878i	0.195672	+	0.980669i	$0.437311\pi$
$402$	−5.30666	+	5.61645i	−0.264672	+	0.280123i
$403$	10.0535	+	37.5202i	0.500801	+	1.86902i
$404$	−0.506000			−0.0251745
$405$		0			0
$406$	4.38302			0.217526
$407$	−1.37166	−	5.11910i	−0.0679906	−	0.253744i
$408$	−5.63745	+	5.96656i	−0.279096	+	0.295389i
$409$	22.2450	−	12.8431i	1.09994	−	0.635053i	0.163737	−	0.986504i	$-0.447645\pi$
$409$	22.2450	−	12.8431i	1.09994	−	0.635053i	0.936206	+	0.351451i	$0.114312\pi$
$410$		0			0
$411$	−10.4538	−	5.64656i	−0.515648	−	0.278524i
$412$	−2.47741	+	0.663820i	−0.122053	+	0.0327041i
$413$	−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
$417$	−0.577694	+	2.42952i	−0.0282898	+	0.118974i
$418$	−1.74081	−	0.466448i	−0.0851457	−	0.0228147i
$419$	6.13243	+	10.6217i	0.299589	+	0.518903i	0.976042	−	0.217583i	$-0.0698172\pi$
$419$	6.13243	+	10.6217i	0.299589	+	0.518903i	−0.676453	+	0.736486i	$0.736484\pi$
$420$		0			0
$421$	−7.24056	+	12.5410i	−0.352883	+	0.611212i	−0.986753	−	0.162228i	$-0.948132\pi$
$421$	−7.24056	+	12.5410i	−0.352883	+	0.611212i	0.633870	+	0.773439i	$0.281465\pi$
$422$	0.117006	−	0.117006i	0.00569577	−	0.00569577i
$423$	23.5952	−	7.78012i	1.14724	−	0.378283i
$424$			19.4225i			0.943240i
$425$		0			0
$426$	6.52020	−	12.0712i	0.315905	−	0.584853i
$427$	−7.04094	+	26.2771i	−0.340735	+	1.27164i
$428$	−0.663324	+	2.47556i	−0.0320630	+	0.119661i
$429$	−8.46824	+	0.240170i	−0.408850	+	0.0115955i
$430$		0			0
$431$			35.9660i			1.73242i	0.499678	+	0.866211i	$0.333452\pi$
$431$			35.9660i			1.73242i	−0.499678	+	0.866211i	$0.666548\pi$
$432$	17.4396	−	6.30395i	0.839061	−	0.303299i
$433$	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
$437$	−2.33763	−	0.626366i	−0.111824	−	0.0299632i
$438$	5.00881	−	1.49553i	0.239330	−	0.0714591i
$439$	−1.28953	−	0.744511i	−0.0615459	−	0.0355336i	0.468911	−	0.883245i	$-0.344646\pi$
$439$	−1.28953	−	0.744511i	−0.0615459	−	0.0355336i	−0.530457	+	0.847712i	$0.677980\pi$
$440$		0			0
$441$	4.61158	+	7.03407i	0.219599	+	0.334956i
$442$	−8.47845	−	8.47845i	−0.403279	−	0.403279i
$443$	−30.9468	+	8.29218i	−1.47033	+	0.393973i	−0.903044	−	0.429548i	$-0.858673\pi$
$443$	−30.9468	+	8.29218i	−1.47033	+	0.393973i	−0.567285	+	0.823522i	$0.692006\pi$
$444$	1.74345	−	1.07361i	0.0827403	−	0.0509511i
$445$		0			0
$446$	−2.91203	+	1.68126i	−0.137889	+	0.0796101i
$447$	27.9202	+	6.63888i	1.32058	+	0.314008i
$448$	−4.57213	−	17.0634i	−0.216013	−	0.806172i
$449$	−21.8283			−1.03014			−0.515071	−	0.857147i	$-0.672234\pi$
$449$	−21.8283			−1.03014			−0.515071	+	0.857147i	$0.672234\pi$
$450$		0			0
$451$	−3.16647			−0.149103
$452$	0.609937	+	2.27631i	0.0286890	+	0.107069i
$453$	−0.00281198	−	0.00941786i	−0.000132118	−	0.000442490i
$454$	−17.7357	+	10.2397i	−0.832376	+	0.480572i
$455$		0			0
$456$	−0.220817	−	7.78588i	−0.0103407	−	0.364607i
$457$	−0.880339	+	0.235886i	−0.0411805	+	0.0110343i	−0.279351	−	0.960189i	$-0.590119\pi$
$457$	−0.880339	+	0.235886i	−0.0411805	+	0.0110343i	0.238170	+	0.971223i	$0.423452\pi$
$458$	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	−0.00427761	−	0.999991i	$-0.501362\pi$
$461$	−18.7320	−	10.8149i	−0.872434	−	0.503700i	−0.868156	+	0.496291i	$0.834695\pi$
$462$	−3.04870	−	2.88054i	−0.141838	−	0.134015i
$463$	18.1245	+	4.85644i	0.842316	+	0.225698i	0.654079	−	0.756426i	$-0.273056\pi$
$463$	18.1245	+	4.85644i	0.842316	+	0.225698i	0.188236	+	0.982124i	$0.439723\pi$
$464$	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	−0.979623	−	0.200846i	$-0.935631\pi$
$467$	−16.8295	+	16.8295i	−0.778777	+	0.778777i	0.200846	+	0.979623i	$0.435631\pi$
$468$	−1.02492	−	3.10834i	−0.0473771	−	0.143683i
$469$			6.80460i			0.314207i
$470$		0			0
$471$	7.68281	+	12.4763i	0.354005	+	0.574875i
$472$	5.82929	−	21.7552i	0.268315	−	1.00136i
$473$	−0.438306	+	1.63578i	−0.0201533	+	0.0752133i
$474$	9.42793	+	15.3102i	0.433039	+	0.703220i
$475$		0			0
$476$			0.646194i			0.0296182i
$477$	−13.1539	+	14.7372i	−0.602276	+	0.674772i
$478$	−12.9000	+	12.9000i	−0.590033	+	0.590033i
$479$	−8.91724	+	15.4451i	−0.407439	+	0.705705i	−0.994602	−	0.103764i	$-0.966911\pi$
$479$	−8.91724	+	15.4451i	−0.407439	+	0.705705i	0.587163	+	0.809469i	$0.300245\pi$
$480$		0			0
$481$	16.7285	+	28.9747i	0.762756	+	1.32113i
$482$	6.66078	+	1.78475i	0.303390	+	0.0812931i
$483$	−4.09392	−	3.86810i	−0.186280	−	0.176005i
$484$	−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	$0.503513\pi$
$488$	−37.8372	+	10.1385i	−1.71281	+	0.458946i
$489$	0.291174	+	10.2666i	0.0131674	+	0.464273i
$490$		0			0
$491$	35.1670	−	20.3037i	1.58707	−	0.916292i	0.593278	−	0.804998i	$-0.297834\pi$
$491$	35.1670	−	20.3037i	1.58707	−	0.916292i	0.993787	−	0.111295i	$-0.0354997\pi$
$492$	−0.349997	−	1.17221i	−0.0157791	−	0.0528472i
$493$	−0.662503	−	2.47249i	−0.0298376	−	0.111356i
$494$	11.3775			0.511896
$495$		0			0
$496$	−24.9471			−1.12016
$497$	−3.12705	−	11.6703i	−0.140267	−	0.523484i
$498$	−22.4864	−	5.34683i	−1.00764	−	0.239597i
$499$	37.3397	−	21.5581i	1.67156	−	0.965073i	0.704788	−	0.709418i	$-0.251042\pi$
$499$	37.3397	−	21.5581i	1.67156	−	0.965073i	0.966768	−	0.255655i	$-0.0822910\pi$
$500$		0			0
$501$	8.79988	−	5.41892i	0.393150	−	0.242100i
$502$	−3.37571	+	0.904518i	−0.150665	+	0.0403706i
$503$	28.0936	+	28.0936i	1.25263	+	1.25263i	0.954537	+	0.298093i	$0.0963506\pi$
$503$	28.0936	+	28.0936i	1.25263	+	1.25263i	0.298093	+	0.954537i	$0.403649\pi$
$504$	8.15932	−	16.1872i	0.363445	−	0.721033i
$505$		0			0
$506$	−1.62510	−	0.938252i	−0.0722445	−	0.0417104i
$507$	29.6708	−	8.85909i	1.31773	−	0.393446i
$508$	−0.510193	−	0.136706i	−0.0226361	−	0.00606534i
$509$	7.39188	+	12.8031i	0.327639	+	0.567488i	0.982043	−	0.188658i	$-0.0604136\pi$
$509$	7.39188	+	12.8031i	0.327639	+	0.567488i	−0.654404	+	0.756145i	$0.727080\pi$
$510$		0			0
$511$	2.30168	−	3.98663i	0.101820	−	0.176358i
$512$	17.6794	−	17.6794i	0.781325	−	0.781325i
$513$	5.10544	−	6.05725i	0.225411	−	0.267434i
$514$		−	14.1761i		−	0.625282i
$515$		0			0
$516$	−0.654003	+	0.0185484i	−0.0287909	+	0.000816546i
$517$	1.88667	−	7.04114i	0.0829755	−	0.309669i
$518$	−4.28721	+	16.0001i	−0.188369	+	0.703003i
$519$	−11.2484	+	20.8248i	−0.493750	+	0.914108i
$520$		0			0
$521$		−	28.4812i		−	1.24778i	−0.781511	−	0.623892i	$-0.785551\pi$
$521$		−	28.4812i		−	1.24778i	0.781511	−	0.623892i	$-0.214449\pi$
$522$	−1.30725	+	6.28437i	−0.0572170	+	0.275059i
$523$	−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
$527$	10.8486	+	2.90687i	0.472572	+	0.126625i
$528$	1.25863	−	5.29325i	0.0547750	−	0.230359i
$529$	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
$533$	19.3089	−	5.17380i	0.836361	−	0.224102i
$534$	9.47128	+	5.11586i	0.409862	+	0.221385i
$535$		0			0
$536$	−8.48544	+	4.89907i	−0.366515	+	0.211608i
$537$	−20.5040	+	21.7010i	−0.884813	+	0.936466i
$538$	−9.30542	−	34.7283i	−0.401185	−	1.49724i
$539$	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	$0.507648\pi$
$542$	6.46008	+	24.1093i	0.277484	+	1.03558i
$543$	17.5703	−	18.5960i	0.754015	−	0.798033i
$544$	−1.53959	+	0.888885i	−0.0660096	+	0.0381106i
$545$		0			0
$546$	23.2973	+	12.5839i	0.997033	+	0.538542i
$547$	31.1213	−	8.33894i	1.33065	−	0.356547i	0.477694	−	0.878526i	$-0.341473\pi$
$547$	31.1213	−	8.33894i	1.33065	−	0.356547i	0.852958	+	0.521979i	$0.174806\pi$
$548$	−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
$552$	1.87611	−	7.89008i	0.0798526	−	0.335824i
$553$	15.2945	+	4.09814i	0.650387	+	0.174271i
$554$	−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	$0.614623\pi$
$557$	−30.4033	+	30.4033i	−1.28823	+	1.28823i	−0.935862	+	0.352366i	$0.885377\pi$
$558$	−21.0119	−	18.7544i	−0.889503	−	0.793937i
$559$		−	10.6910i		−	0.452182i
$560$		0			0
$561$	−1.16411	+	2.15519i	−0.0491489	+	0.0909922i
$562$	−9.11308	+	34.0105i	−0.384412	+	1.43465i
$563$	−0.300692	+	1.12220i	−0.0126727	+	0.0472950i	−0.971973	−	0.235094i	$-0.924460\pi$
$563$	−0.300692	+	1.12220i	−0.0126727	+	0.0472950i	0.959300	+	0.282389i	$0.0911269\pi$
$564$	2.81512	−	0.0798405i	0.118538	−	0.00336189i
$565$		0			0
$566$			4.78361i			0.201070i
$567$	17.1538	−	6.75644i	0.720393	−	0.283744i
$568$	12.3017	−	12.3017i	0.516167	−	0.516167i
$569$	−0.145367	+	0.251784i	−0.00609412	+	0.0105553i	−0.869056	−	0.494713i	$-0.835273\pi$
$569$	−0.145367	+	0.251784i	−0.00609412	+	0.0105553i	0.862962	+	0.505268i	$0.168606\pi$
$570$		0			0
$571$	−13.0283	−	22.5656i	−0.545215	−	0.944341i	−0.998593	−	0.0530223i	$-0.983115\pi$
$571$	−13.0283	−	22.5656i	−0.545215	−	0.944341i	0.453378	−	0.891318i	$-0.350219\pi$
$572$	−0.927572	−	0.248542i	−0.0387837	−	0.0103921i
$573$	8.75395	−	2.61375i	0.365702	−	0.109191i
$574$	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	$0.726287\pi$
$578$	18.7044	−	5.01183i	0.778000	−	0.208465i
$579$	13.7258	−	8.45230i	0.570427	−	0.351266i
$580$		0			0
$581$	−17.6274	+	10.1772i	−0.731309	+	0.422222i
$582$	8.97298	+	2.13360i	0.371942	+	0.0884408i
$583$	1.50006	+	5.59831i	0.0621262	+	0.231858i
$584$	6.62852			0.274290
$585$		0			0
$586$	4.00174			0.165310
$587$	−10.7212	−	40.0121i	−0.442511	−	1.65147i	−0.722425	−	0.691449i	$-0.756973\pi$
$587$	−10.7212	−	40.0121i	−0.442511	−	1.65147i	0.279914	−	0.960025i	$-0.409694\pi$
$588$	0.272772	+	0.913566i	0.0112489	+	0.0376748i
$589$	−9.22943	+	5.32861i	−0.380292	+	0.219562i
$590$		0			0
$591$	−0.659386	−	23.2495i	−0.0271235	−	0.956358i
$592$	−20.7553	+	5.56137i	−0.853038	+	0.228571i
$593$	−26.6583	−	26.6583i	−1.09473	−	1.09473i	−0.995017	−	0.0997087i	$-0.968209\pi$
$593$	−26.6583	−	26.6583i	−1.09473	−	1.09473i	−0.0997087	−	0.995017i	$-0.531791\pi$
$594$	5.03939	−	3.51208i	0.206769	−	0.144102i
$595$		0			0
$596$	2.81726	+	1.62655i	0.115400	+	0.0666260i
$597$	−22.2009	−	20.9764i	−0.908624	−	0.858506i
$598$	11.4428	+	3.06608i	0.467930	+	0.125382i
$599$	−13.2427	−	22.9370i	−0.541080	−	0.937178i	−0.998842	−	0.0481037i	$-0.984682\pi$
$599$	−13.2427	−	22.9370i	−0.541080	−	0.937178i	0.457762	−	0.889075i	$-0.348651\pi$
$600$		0			0
$601$	4.26710	−	7.39084i	0.174059	−	0.301479i	−0.765776	−	0.643107i	$-0.777645\pi$
$601$	4.26710	−	7.39084i	0.174059	−	0.301479i	0.939835	+	0.341628i	$0.110978\pi$
$602$	3.74279	−	3.74279i	0.152545	−	0.152545i
$603$	−9.75641	−	2.02950i	−0.397312	−	0.0826475i
$604$		−	0.00111412i		−	4.53329e-5i
$605$		0			0
$606$	3.14351	+	5.10480i	0.127696	+	0.207368i
$607$	11.9000	−	44.4113i	0.483005	−	1.80260i	−0.105876	−	0.994379i	$-0.533765\pi$
$607$	11.9000	−	44.4113i	0.483005	−	1.80260i	0.588881	−	0.808220i	$-0.299569\pi$
$608$	0.436602	−	1.62942i	0.0177066	−	0.0660818i
$609$	2.96400	+	4.81329i	0.120107	+	0.195045i
$610$		0			0
$611$			46.0190i			1.86173i
$612$	−0.926510	−	0.192730i	−0.0374520	−	0.00779064i
$613$	−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
$617$	−36.3708	−	9.74553i	−1.46423	−	0.392340i	−0.563284	−	0.826263i	$-0.690462\pi$
$617$	−36.3708	−	9.74553i	−1.46423	−	0.392340i	−0.900950	+	0.433923i	$0.857129\pi$
$618$	22.0878	+	20.8694i	0.888500	+	0.839492i
$619$	8.57434	+	4.95040i	0.344632	+	0.198973i	0.662318	−	0.749223i	$-0.269573\pi$
$619$	8.57434	+	4.95040i	0.344632	+	0.198973i	−0.317687	+	0.948196i	$0.602906\pi$
$620$		0			0
$621$	6.76710	−	4.71617i	0.271554	−	0.189253i
$622$	−32.2255	−	32.2255i	−1.29213	−	1.29213i
$623$	9.15670	−	2.45353i	0.366855	−	0.0982986i
$624$	0.973765	+	34.3344i	0.0389818	+	1.37447i
$625$		0			0
$626$	−26.9753	+	15.5742i	−1.07815	+	0.622469i
$627$	−0.664976	−	2.22713i	−0.0265566	−	0.0889431i
$628$	0.429864	+	1.60427i	0.0171534	+	0.0640175i
$629$	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	$0.644476\pi$
$632$	5.90104	+	22.0230i	0.234731	+	0.876027i
$633$	0.207617	+	0.0493675i	0.00825205	+	0.00196218i
$634$	4.65268	−	2.68622i	0.184781	−	0.106684i
$635$		0			0
$636$	−1.90665	+	1.17411i	−0.0756038	+	0.0465564i
$637$	−15.0485	+	4.03223i	−0.596242	+	0.159763i
$638$	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	0.864435	−	0.502744i	$-0.167676\pi$
$641$	21.8054	+	12.5894i	0.861263	+	0.497251i	−0.00317173	+	0.999995i	$0.501010\pi$
$642$	29.0956	−	8.68736i	1.14831	−	0.342863i
$643$	−30.0492	−	8.05166i	−1.18502	−	0.317526i	−0.388107	−	0.921614i	$-0.626871\pi$
$643$	−30.0492	−	8.05166i	−1.18502	−	0.317526i	−0.796918	+	0.604088i	$0.793538\pi$
$644$	−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	−0.535377	−	0.844613i	$-0.679830\pi$
$647$	7.86580	−	7.86580i	0.309237	−	0.309237i	0.844613	+	0.535377i	$0.179830\pi$
$648$	20.7755	+	16.5267i	0.816140	+	0.649230i
$649$		−	6.72090i		−	0.263818i
$650$		0			0
$651$	−24.7925	+	0.703147i	−0.971695	+	0.0275585i
$652$	−0.301325	+	1.12456i	−0.0118008	+	0.0440411i
$653$	−0.0749391	+	0.279676i	−0.00293259	+	0.0109446i	−0.967377	−	0.253343i	$-0.918470\pi$
$653$	−0.0749391	+	0.279676i	−0.00293259	+	0.0109446i	0.964444	+	0.264287i	$0.0851367\pi$
$654$	−8.90457	+	16.4855i	−0.348196	+	0.644635i
$655$		0			0
$656$			12.8384i			0.501256i
$657$	5.02953	+	4.48917i	0.196221	+	0.175139i
$658$	−16.1106	+	16.1106i	−0.628058	+	0.628058i
$659$	13.4009	−	23.2111i	0.522026	−	0.904175i	−0.477646	−	0.878552i	$-0.658510\pi$
$659$	13.4009	−	23.2111i	0.522026	−	0.904175i	0.999672	−	0.0256228i	$-0.00815688\pi$
$660$		0			0
$661$	−12.6438	−	21.8997i	−0.491787	−	0.851800i	0.508168	−	0.861258i	$-0.330323\pi$
$661$	−12.6438	−	21.8997i	−0.491787	−	0.851800i	−0.999955	+	0.00945786i	$0.996989\pi$
$662$	7.73611	+	2.07289i	0.300673	+	0.0805650i
$663$	3.57724	−	15.0443i	0.138928	−	0.584271i
$664$	−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
$668$	1.13154	−	0.303196i	0.0437807	−	0.0117310i
$669$	−3.81556	−	2.06095i	−0.147518	−	0.0796811i
$670$		0			0
$671$	−10.1231	+	5.84458i	−0.390799	+	0.225628i
$672$	2.69622	−	2.85362i	0.104009	−	0.110081i
$673$	−6.30290	−	23.5227i	−0.242959	−	0.906735i	−0.974398	−	0.224829i	$-0.927818\pi$
$673$	−6.30290	−	23.5227i	−0.242959	−	0.906735i	0.731439	−	0.681906i	$-0.238849\pi$
$674$	−13.3044			−0.512466
$675$		0			0
$676$	3.51002			0.135001
$677$	0.240265	+	0.896681i	0.00923414	+	0.0344623i	0.970389	−	0.241547i	$-0.0776547\pi$
$677$	0.240265	+	0.896681i	0.00923414	+	0.0344623i	−0.961155	+	0.276009i	$0.910988\pi$
$678$	19.1754	−	20.2949i	0.736429	−	0.779420i
$679$	7.03407	−	4.06112i	0.269943	−	0.155852i
$680$		0			0
$681$	−23.2386	−	12.5522i	−0.890503	−	0.481000i
$682$	−7.98188	+	2.13874i	−0.305642	+	0.0818966i
$683$	22.2024	+	22.2024i	0.849550	+	0.849550i	0.990077	−	0.140526i	$-0.0448795\pi$
$683$	22.2024	+	22.2024i	0.849550	+	0.849550i	−0.140526	+	0.990077i	$0.544880\pi$
$684$	0.750970	−	0.492340i	0.0287141	−	0.0188251i
$685$		0			0
$686$	−23.3578	−	13.4856i	−0.891805	−	0.514884i
$687$	−8.84071	+	37.1801i	−0.337294	+	1.41851i
$688$	6.63225	+	1.77711i	0.252852	+	0.0677515i
$689$	−18.2945	−	31.6871i	−0.696966	−	1.20718i
$690$		0			0
$691$	−4.05877	+	7.02999i	−0.154403	+	0.267433i	−0.932841	−	0.360287i	$-0.882679\pi$
$691$	−4.05877	+	7.02999i	−0.154403	+	0.267433i	0.778439	+	0.627721i	$0.216012\pi$
$692$	−1.89711	+	1.89711i	−0.0721173	+	0.0721173i
$693$	1.10164	−	5.29593i	0.0418479	−	0.201176i
$694$		−	14.2473i		−	0.540821i
$695$		0			0
$696$	−3.86828	+	7.16156i	−0.146627	+	0.271458i
$697$	1.49595	−	5.58297i	0.0566633	−	0.211470i
$698$	−3.24640	+	12.1157i	−0.122878	+	0.458586i
$699$	10.3369	−	0.293168i	0.390979	−	0.0110887i
$700$		0			0
$701$			19.6359i			0.741637i	0.928705	+	0.370819i	$0.120923\pi$
$701$			19.6359i			0.741637i	−0.928705	+	0.370819i	$0.879077\pi$
$702$	−24.9913	+	29.6504i	−0.943236	+	1.11908i
$703$	−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
$707$	5.09956	+	1.36642i	0.191789	+	0.0513896i
$708$	2.48804	−	0.742876i	0.0935061	−	0.0279190i
$709$	−2.68383	−	1.54951i	−0.100793	−	0.0581931i	0.448756	−	0.893654i	$-0.351867\pi$
$709$	−2.68383	−	1.54951i	−0.100793	−	0.0581931i	−0.549549	+	0.835461i	$0.685201\pi$
$710$		0			0
$711$	−10.4375	+	20.7069i	−0.391438	+	0.776569i
$712$	9.65210	+	9.65210i	0.361728	+	0.361728i
$713$	−10.7184	+	2.87199i	−0.401408	+	0.107557i
$714$	6.51914	−	4.01445i	0.243973	−	0.150237i
$715$		0			0
$716$	−2.93083	+	1.69211i	−0.109530	+	0.0632373i
$717$	−22.8900	−	5.44280i	−0.854841	−	0.203265i
$718$	−4.37774	−	16.3380i	−0.163376	−	0.609727i
$719$	−20.3126			−0.757533			−0.378767	−	0.925492i	$-0.623652\pi$
$719$	−20.3126			−0.757533			−0.378767	+	0.925492i	$0.623652\pi$
$720$		0			0
$721$	26.7604			0.996608
$722$	−5.79640	−	21.6325i	−0.215720	−	0.805077i
$723$	2.54437	+	8.52158i	0.0946261	+	0.316921i
$724$	2.51149	−	1.45001i	0.0933388	−	0.0538892i
$725$		0			0
$726$	0.674315	+	23.7759i	0.0250262	+	0.882407i
$727$	17.0647	−	4.57247i	0.632895	−	0.169584i	0.0719119	−	0.997411i	$-0.477090\pi$
$727$	17.0647	−	4.57247i	0.632895	−	0.169584i	0.560983	+	0.827827i	$0.310423\pi$
$728$	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
$732$	−3.28256	−	3.10150i	−0.121327	−	0.114635i
$733$	−25.4785	−	6.82693i	−0.941068	−	0.252158i	−0.244500	−	0.969649i	$-0.578624\pi$
$733$	−25.4785	−	6.82693i	−0.941068	−	0.252158i	−0.696568	+	0.717491i	$0.745291\pi$
$734$	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
$738$	−9.65150	+	10.8133i	−0.355277	+	0.398041i
$739$			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
$742$	4.68854	−	17.4979i	0.172122	−	0.642368i
$743$	4.95625	−	18.4970i	0.181827	−	0.678588i	−0.813460	−	0.581620i	$-0.802419\pi$
$743$	4.95625	−	18.4970i	0.181827	−	0.678588i	0.995288	−	0.0969677i	$-0.0309144\pi$
$744$	−18.7266	−	30.4104i	−0.686549	−	1.11490i
$745$		0			0
$746$		−	3.13856i		−	0.114911i
$747$	−9.33459	−	28.3096i	−0.341535	−	1.03579i
$748$	−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	0.827850	−	0.560949i	$-0.189564\pi$
$751$	−1.96958	−	3.41141i	−0.0718709	−	0.124484i	−0.899721	+	0.436465i	$0.856230\pi$
$752$	−28.5482	−	7.64946i	−1.04105	−	0.278947i
$753$	−3.27612	−	3.09541i	−0.119388	−	0.112803i
$754$	−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	$0.897308\pi$
$758$	23.9495	−	6.41725i	0.869885	−	0.233085i
$759$	−0.0686093	−	2.41912i	−0.00249036	−	0.0878085i
$760$		0			0
$761$	7.11860	−	4.10993i	0.258049	−	0.148985i	−0.365395	−	0.930853i	$-0.619066\pi$
$761$	7.11860	−	4.10993i	0.258049	−	0.148985i	0.623444	+	0.781868i	$0.285733\pi$
$762$	1.79039	+	5.99637i	0.0648591	+	0.217226i
$763$	4.27057	+	15.9380i	0.154605	+	0.576994i
$764$	1.03558			0.0374660
$765$		0			0
$766$	−32.5079			−1.17456
$767$	10.9815	+	40.9835i	0.396519	+	1.47983i
$768$	7.86108	+	1.86921i	0.283662	+	0.0674495i
$769$	−1.91615	+	1.10629i	−0.0690983	+	0.0398939i	−0.534151	−	0.845389i	$-0.679369\pi$
$769$	−1.91615	+	1.10629i	−0.0690983	+	0.0398939i	0.465053	+	0.885283i	$0.346035\pi$
$770$		0			0
$771$	15.5677	−	9.58654i	0.560659	−	0.345251i
$772$	1.76495	−	0.472918i	0.0635221	−	0.0170207i
$773$	−8.23173	−	8.23173i	−0.296075	−	0.296075i	0.543400	−	0.839474i	$-0.317137\pi$
$773$	−8.23173	−	8.23173i	−0.296075	−	0.296075i	−0.839474	+	0.543400i	$0.817137\pi$
$774$	4.25009	+	6.48270i	0.152766	+	0.233016i
$775$		0			0
$776$	10.1286	+	5.84773i	0.363595	+	0.209921i
$777$	−20.4700	+	6.11191i	−0.734356	+	0.219264i
$778$	−35.1408	−	9.41596i	−1.25986	−	0.337579i
$779$	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
$783$	−7.78531	+	2.81419i	−0.278224	+	0.100571i
$784$		−	10.0057i		−	0.357346i
$785$		0			0
$786$	49.7006	−	1.40957i	1.77276	−	0.0502778i
$787$	9.07119	−	33.8541i	0.323353	−	1.20677i	−0.592604	−	0.805494i	$-0.701900\pi$
$787$	9.07119	−	33.8541i	0.323353	−	1.20677i	0.915957	−	0.401276i	$-0.131433\pi$
$788$	0.682372	−	2.54665i	0.0243085	−	0.0907205i
$789$	6.92440	−	12.8195i	0.246515	−	0.456387i
$790$		0			0
$791$		−	24.5882i		−	0.874256i
$792$	7.39725	−	2.43912i	0.262850	−	0.0866703i
$793$	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
$797$	25.2788	+	6.77343i	0.895421	+	0.239927i	0.677049	−	0.735938i	$-0.263259\pi$
$797$	25.2788	+	6.77343i	0.895421	+	0.239927i	0.218372	+	0.975866i	$0.429925\pi$
$798$	−1.68056	+	7.06766i	−0.0594910	+	0.250192i
$799$	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
$803$	1.91059	−	0.511942i	0.0674233	−	0.0180660i
$804$	−0.993882	−	0.536840i	−0.0350515	−	0.0189329i
$805$		0			0
$806$	45.1784	−	26.0837i	1.59134	−	0.918761i
$807$	31.8447	−	33.7038i	1.12099	−	1.18643i
$808$	1.96755	+	7.34301i	0.0692183	+	0.258326i
$809$	−40.3389			−1.41824			−0.709120	−	0.705088i	$-0.750908\pi$
$809$	−40.3389			−1.41824			−0.709120	+	0.705088i	$0.750908\pi$
$810$		0			0
$811$	−4.50040			−0.158030			−0.0790152	−	0.996873i	$-0.525178\pi$
$811$	−4.50040			−0.158030			−0.0790152	+	0.996873i	$0.525178\pi$
$812$	0.165840	+	0.618923i	0.00581984	+	0.0217199i
$813$	−22.1075	+	23.3981i	−0.775343	+	0.820606i
$814$	−6.16394	+	3.55875i	−0.216046	+	0.124734i
$815$		0			0
$816$	8.73818	+	4.71988i	0.305898	+	0.165229i
$817$	2.83326	−	0.759168i	0.0991231	−	0.0265599i
$818$	−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	0.713956	−	0.700190i	$-0.246901\pi$
$821$	13.3109	+	7.68503i	0.464552	+	0.268209i	−0.249404	+	0.968399i	$0.580235\pi$
$822$	−3.69127	+	15.5238i	−0.128748	+	0.541456i
$823$	14.0723	+	3.77065i	0.490528	+	0.131437i	0.495601	−	0.868551i	$-0.334948\pi$
$823$	14.0723	+	3.77065i	0.490528	+	0.131437i	−0.00507263	+	0.999987i	$0.501615\pi$
$824$	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	−0.762443	−	0.647056i	$-0.776000\pi$
$827$	−3.31824	+	3.31824i	−0.115387	+	0.115387i	0.647056	+	0.762443i	$0.276000\pi$
$828$	0.887961	−	0.292790i	0.0308588	−	0.0101752i
$829$			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
$832$	−12.4024	+	46.2865i	−0.429977	+	1.60469i
$833$	−1.16588	+	4.35112i	−0.0403953	+	0.150757i
$834$	3.35248	−	0.0950807i	0.116087	−	0.00329237i
$835$		0			0
$836$		−	0.263467i		−	0.00911220i
$837$	6.38629	−	35.7571i	0.220743	−	1.23595i
$838$	11.6473	−	11.6473i	0.402349	−	0.402349i
$839$	−5.71824	+	9.90428i	−0.197416	+	0.341934i	−0.947690	−	0.319193i	$-0.896588\pi$
$839$	−5.71824	+	9.90428i	−0.197416	+	0.341934i	0.750274	+	0.661127i	$0.229921\pi$
$840$		0			0
$841$	13.2309	+	22.9166i	0.456238	+	0.790228i
$842$	18.7855	+	5.03357i	0.647392	+	0.173468i
$843$	−43.5119	+	12.9918i	−1.49863	+	0.447460i
$844$	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
$848$	22.6983	−	6.08198i	0.779462	−	0.208856i
$849$	−5.25321	+	3.23490i	−0.180290	+	0.111021i
$850$		0			0
$851$	−8.27720	+	4.77884i	−0.283739	+	0.163817i
$852$	1.95127	+	0.463975i	0.0668494	+	0.0158955i
$853$	6.18947	+	23.0994i	0.211923	+	0.790909i	0.987227	+	0.159320i	$0.0509302\pi$
$853$	6.18947	+	23.0994i	0.211923	+	0.790909i	−0.775304	+	0.631589i	$0.782403\pi$
$854$	36.5353			1.25021
$855$		0			0
$856$	38.5043			1.31605
$857$	3.88189	+	14.4874i	0.132603	+	0.494881i	0.999996	−	0.00274224i	$-0.000872884\pi$
$857$	3.88189	+	14.4874i	0.132603	+	0.494881i	−0.867393	+	0.497623i	$0.834206\pi$
$858$	3.25508	+	10.9019i	0.111127	+	0.372184i
$859$	−37.5983	+	21.7074i	−1.28284	+	0.740646i	−0.977366	−	0.211555i	$-0.932147\pi$
$859$	−37.5983	+	21.7074i	−1.28284	+	0.740646i	−0.305471	+	0.952201i	$0.598814\pi$
$860$		0			0
$861$	0.361857	+	12.7589i	0.0123321	+	0.434821i
$862$	46.6567	−	12.5016i	1.58913	−	0.425807i
$863$	−2.78648	−	2.78648i	−0.0948527	−	0.0948527i	0.658088	−	0.752941i	$-0.271365\pi$
$863$	−2.78648	−	2.78648i	−0.0948527	−	0.0948527i	−0.752941	+	0.658088i	$0.771365\pi$
$864$	3.28736	+	4.71694i	0.111838	+	0.160474i
$865$		0			0
$866$	−0.545339	−	0.314852i	−0.0185314	−	0.0106991i
$867$	18.1526	+	17.1513i	0.616495	+	0.582490i
$868$	−2.71566	−	0.727658i	−0.0921754	−	0.0246983i
$869$	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
$873$	3.72489	+	11.2967i	0.126068	+	0.382335i
$874$			3.25020i			0.109940i
$875$		0			0
$876$	0.400700	+	0.650704i	0.0135384	+	0.0219852i
$877$	−11.1359	+	41.5598i	−0.376033	+	1.40338i	0.475796	+	0.879556i	$0.342160\pi$
$877$	−11.1359	+	41.5598i	−0.376033	+	1.40338i	−0.851829	+	0.523820i	$0.824507\pi$
$878$	−0.517577	+	1.93163i	−0.0174674	+	0.0651892i
$879$	2.70616	+	4.39458i	0.0912764	+	0.148225i
$880$		0			0
$881$		−	47.0487i		−	1.58511i	−0.609801	−	0.792555i	$-0.708751\pi$
$881$		−	47.0487i		−	1.58511i	0.609801	−	0.792555i	$-0.291249\pi$
$882$	7.52195	−	8.42736i	0.253277	−	0.283764i
$883$	−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
$887$	−3.50739	−	0.939801i	−0.117766	−	0.0315554i	0.199454	−	0.979907i	$-0.436083\pi$
$887$	−3.50739	−	0.939801i	−0.117766	−	0.0315554i	−0.317221	+	0.948352i	$0.602750\pi$
$888$	−22.3593	−	21.1260i	−0.750330	−	0.708943i
$889$	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
$893$	−12.1956	+	3.26780i	−0.408110	+	0.109353i
$894$	−1.09267	−	38.5269i	−0.0365444	−	1.28853i
$895$		0			0
$896$	−16.6203	+	9.59572i	−0.555245	+	0.320571i
$897$	4.37106	+	14.6395i	0.145945	+	0.488799i
$898$	7.58743	+	28.3167i	0.253196	+	0.944939i
$899$	11.1368			0.371433
$900$		0			0
$901$	−10.5794			−0.352450
$902$	1.10065	+	4.10768i	0.0366477	+	0.136771i
$903$	6.64125	+	1.57916i	0.221007	+	0.0525512i
$904$	30.6619	−	17.7026i	1.01980	−	0.588781i
$905$		0			0
$906$	−0.0112398	+	0.00692143i	−0.000373419	+	0.000229949i
$907$	−10.1363	+	2.71600i	−0.336569	+	0.0901833i	−0.423145	−	0.906062i	$-0.639074\pi$
$907$	−10.1363	+	2.71600i	−0.336569	+	0.0901833i	0.0865764	+	0.996245i	$0.472407\pi$
$908$	−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	0.608018	−	0.793923i	$-0.291965\pi$
$911$	6.77512	+	3.91162i	0.224470	+	0.129598i	−0.383548	+	0.923521i	$0.625298\pi$
$912$	−9.02988	+	2.69614i	−0.299009	+	0.0892780i
$913$	−8.44796	−	2.26362i	−0.279587	−	0.0749150i
$914$	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
$918$	3.81155	+	10.5444i	0.125800	+	0.348019i
$919$		−	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
$922$	−7.51842	+	28.0591i	−0.247606	+	0.924078i
$923$	−8.48246	+	31.6570i	−0.279204	+	1.04200i
$924$	0.291405	−	0.539494i	0.00958651	−	0.0177481i
$925$		0			0
$926$		−	25.1999i		−	0.828122i
$927$	−7.98139	+	38.3689i	−0.262143	+	1.26020i
$928$	−1.24650	+	1.24650i	−0.0409182	+	0.0409182i
$929$	−15.7062	+	27.2039i	−0.515302	+	0.892530i	0.484540	+	0.874769i	$0.338987\pi$
$929$	−15.7062	+	27.2039i	−0.515302	+	0.892530i	−0.999842	+	0.0177609i	$0.994346\pi$
$930$		0			0
$931$	−2.13718	−	3.70170i	−0.0700433	−	0.121318i
$932$	1.13226	+	0.303388i	0.0370884	+	0.00993782i
$933$	13.5966	−	57.1814i	0.445134	−	1.87203i
$934$	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	$0.585732\pi$
$938$	8.82722	−	2.36525i	0.288219	−	0.0772281i
$939$	−35.3449	−	19.0914i	−1.15344	−	0.623023i
$940$		0			0
$941$	−5.77035	+	3.33151i	−0.188108	+	0.108604i	−0.591096	−	0.806601i	$-0.701305\pi$
$941$	−5.77035	+	3.33151i	−0.188108	+	0.108604i	0.402989	+	0.915205i	$0.367971\pi$
$942$	13.5142	−	14.3032i	0.440318	−	0.466023i
$943$	1.47800	+	5.51597i	0.0481303	+	0.179625i
$944$	−27.2498			−0.886905
$945$		0			0
$946$	2.27436			0.0739458
$947$	−0.867814	−	3.23873i	−0.0282002	−	0.105245i	0.950391	−	0.311057i	$-0.100683\pi$
$947$	−0.867814	−	3.23873i	−0.0282002	−	0.105245i	−0.978591	+	0.205812i	$0.934016\pi$
$948$	−1.80521	+	1.91060i	−0.0586306	+	0.0620534i
$949$	−10.8142	+	6.24356i	−0.351043	+	0.202675i
$950$		0			0
$951$	6.09628	+	3.29287i	0.197685	+	0.106779i
$952$	9.37748	−	2.51269i	0.303926	−	0.0814367i
$953$	−30.7161	−	30.7161i	−0.994992	−	0.994992i	0.00499525	−	0.999988i	$-0.498410\pi$
$953$	−30.7161	−	30.7161i	−0.994992	−	0.994992i	−0.999988	+	0.00499525i	$0.998410\pi$
$954$	23.6900	+	11.9412i	0.766993	+	0.386612i
$955$		0			0
$956$	−2.30970	−	1.33350i	−0.0747009	−	0.0431286i
$957$	−0.561875	+	2.36300i	−0.0181629	+	0.0763848i
$958$	23.1357	+	6.19919i	0.747480	+	0.200287i
$959$	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
$963$	29.2160	+	26.0771i	0.941471	+	0.840322i
$964$			1.00809i			0.0324684i
$965$		0			0
$966$	−3.59485	+	6.65535i	−0.115662	+	0.214132i
$967$	1.48419	−	5.53906i	0.0477282	−	0.178124i	−0.937947	−	0.346779i	$-0.887276\pi$
$967$	1.48419	−	5.53906i	0.0477282	−	0.178124i	0.985675	+	0.168654i	$0.0539422\pi$
$968$	−7.80632	+	29.1336i	−0.250904	+	0.936388i
$969$	4.24094	−	0.120278i	0.136238	−	0.00386389i
$970$		0			0
$971$		−	14.2248i		−	0.456496i	−0.973603	−	0.228248i	$-0.926700\pi$
$971$		−	14.2248i		−	0.456496i	0.973603	−	0.228248i	$-0.0732998\pi$
$972$	−0.366480	+	3.03853i	−0.0117549	+	0.0974610i
$973$	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
$977$	−30.1529	−	8.07944i	−0.964676	−	0.258484i	−0.258097	−	0.966119i	$-0.583096\pi$
$977$	−30.1529	−	8.07944i	−0.964676	−	0.258484i	−0.706578	+	0.707635i	$0.749762\pi$
$978$	13.2171	−	3.94636i	0.422636	−	0.126191i
$979$	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
$983$	−9.94750	+	2.66543i	−0.317276	+	0.0850139i	−0.413943	−	0.910303i	$-0.635849\pi$
$983$	−9.94750	+	2.66543i	−0.317276	+	0.0850139i	0.0966666	+	0.995317i	$0.469182\pi$
$984$	−15.6500	+	9.63718i	−0.498903	+	0.307222i
$985$		0			0
$986$	−2.97715	+	1.71886i	−0.0948116	+	0.0547395i
$987$	−28.5869	−	6.79742i	−0.909932	−	0.216364i
$988$	0.430488	+	1.60660i	0.0136956	+	0.0511128i
$989$	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	$0.294270\pi$
$992$	−2.00189	−	7.47116i	−0.0635601	−	0.237210i
$993$	2.95514	+	9.89733i	0.0937785	+	0.314082i
$994$	−14.0523	+	8.11308i	−0.445711	+	0.257331i
$995$		0			0
$996$	−0.0957926	−	3.37759i	−0.00303530	−	0.107023i
$997$	−30.1153	+	8.06937i	−0.953761	+	0.255559i	−0.701957	−	0.712219i	$-0.747690\pi$
$997$	−30.1153	+	8.06937i	−0.953761	+	0.255559i	−0.251804	+	0.967778i	$0.581024\pi$
$998$	−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.182.1		16
3.2	odd	2		675.2.q.a.332.4		16
5.2	odd	4		45.2.l.a.38.4	yes	16
5.3	odd	4	inner	225.2.p.b.218.1		16
5.4	even	2		45.2.l.a.2.4	✓	16
9.4	even	3		675.2.q.a.557.4		16
9.5	odd	6	inner	225.2.p.b.32.1		16
15.2	even	4		135.2.m.a.8.1		16
15.8	even	4		675.2.q.a.143.4		16
15.14	odd	2		135.2.m.a.62.1		16
20.7	even	4		720.2.cu.c.353.4		16
20.19	odd	2		720.2.cu.c.497.3		16
45.2	even	12		405.2.f.a.323.6		16
45.4	even	6		135.2.m.a.17.1		16
45.7	odd	12		405.2.f.a.323.3		16
45.13	odd	12		675.2.q.a.368.4		16
45.14	odd	6		45.2.l.a.32.4	yes	16
45.22	odd	12		135.2.m.a.98.1		16
45.23	even	12	inner	225.2.p.b.68.1		16
45.29	odd	6		405.2.f.a.242.3		16
45.32	even	12		45.2.l.a.23.4	yes	16
45.34	even	6		405.2.f.a.242.6		16
180.59	even	6		720.2.cu.c.257.4		16
180.167	odd	12		720.2.cu.c.113.3		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
45.2.l.a.2.4	✓	16	5.4	even	2
45.2.l.a.23.4	yes	16	45.32	even	12
45.2.l.a.32.4	yes	16	45.14	odd	6
45.2.l.a.38.4	yes	16	5.2	odd	4
135.2.m.a.8.1		16	15.2	even	4
135.2.m.a.17.1		16	45.4	even	6
135.2.m.a.62.1		16	15.14	odd	2
135.2.m.a.98.1		16	45.22	odd	12
225.2.p.b.32.1		16	9.5	odd	6	inner
225.2.p.b.68.1		16	45.23	even	12	inner
225.2.p.b.182.1		16	1.1	even	1	trivial
225.2.p.b.218.1		16	5.3	odd	4	inner
405.2.f.a.242.3		16	45.29	odd	6
405.2.f.a.242.6		16	45.34	even	6
405.2.f.a.323.3		16	45.7	odd	12
405.2.f.a.323.6		16	45.2	even	12
675.2.q.a.143.4		16	15.8	even	4
675.2.q.a.332.4		16	3.2	odd	2
675.2.q.a.368.4		16	45.13	odd	12
675.2.q.a.557.4		16	9.4	even	3
720.2.cu.c.113.3		16	180.167	odd	12
720.2.cu.c.257.4		16	180.59	even	6
720.2.cu.c.353.4		16	20.7	even	4
720.2.cu.c.497.3		16	20.19	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

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