LMFDB - Embedded newform 880.2.w.a.221.19

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [880,2,Mod(221,880)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("880.221"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(880, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([0, 3, 0, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 880 = 2^{4} \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	880.w (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [72] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$7.02683537787$
Analytic rank:	$0$
Dimension:	$72$
Relative dimension:	$36$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			221.19
Character	$\chi$	$=$	880.221
Dual form			880.2.w.a.661.19

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.107309 - 1.41014i) q^{2} +(-0.986180 - 0.986180i) q^{3} +(-1.97697 - 0.302640i) q^{4} +(-0.707107 + 0.707107i) q^{5} +(-1.49647 + 1.28482i) q^{6} +2.23618i q^{7} +(-0.638910 + 2.75532i) q^{8} -1.05490i q^{9} +(0.921238 + 1.07300i) q^{10} +(0.707107 - 0.707107i) q^{11} +(1.65119 + 2.24811i) q^{12} +(3.09627 + 3.09627i) q^{13} +(3.15332 + 0.239962i) q^{14} +1.39467 q^{15} +(3.81682 + 1.19662i) q^{16} +3.43520 q^{17} +(-1.48755 - 0.113200i) q^{18} +(1.53589 + 1.53589i) q^{19} +(1.61193 - 1.18393i) q^{20} +(2.20528 - 2.20528i) q^{21} +(-0.921238 - 1.07300i) q^{22} -5.65468i q^{23} +(3.34732 - 2.08716i) q^{24} -1.00000i q^{25} +(4.69841 - 4.03390i) q^{26} +(-3.99886 + 3.99886i) q^{27} +(0.676758 - 4.42087i) q^{28} +(-4.57244 - 4.57244i) q^{29} +(0.149660 - 1.96667i) q^{30} +0.331393 q^{31} +(2.09697 - 5.25383i) q^{32} -1.39467 q^{33} +(0.368627 - 4.84411i) q^{34} +(-1.58122 - 1.58122i) q^{35} +(-0.319254 + 2.08550i) q^{36} +(6.72218 - 6.72218i) q^{37} +(2.33062 - 2.00100i) q^{38} -6.10695i q^{39} +(-1.49653 - 2.40008i) q^{40} +8.37938i q^{41} +(-2.87310 - 3.34639i) q^{42} +(-3.88293 + 3.88293i) q^{43} +(-1.61193 + 1.18393i) q^{44} +(0.745924 + 0.745924i) q^{45} +(-7.97388 - 0.606797i) q^{46} +11.0815 q^{47} +(-2.58399 - 4.94415i) q^{48} +1.99948 q^{49} +(-1.41014 - 0.107309i) q^{50} +(-3.38773 - 3.38773i) q^{51} +(-5.18417 - 7.05828i) q^{52} +(7.42398 - 7.42398i) q^{53} +(5.20983 + 6.06805i) q^{54} +1.00000i q^{55} +(-6.16140 - 1.42872i) q^{56} -3.02932i q^{57} +(-6.93843 + 5.95710i) q^{58} +(-3.58002 + 3.58002i) q^{59} +(-2.75722 - 0.422083i) q^{60} +(10.6343 + 10.6343i) q^{61} +(0.0355613 - 0.467309i) q^{62} +2.35894 q^{63} +(-7.18359 - 3.52080i) q^{64} -4.37878 q^{65} +(-0.149660 + 1.96667i) q^{66} +(0.841057 + 0.841057i) q^{67} +(-6.79130 - 1.03963i) q^{68} +(-5.57654 + 5.57654i) q^{69} +(-2.39942 + 2.06006i) q^{70} -11.1058i q^{71} +(2.90658 + 0.673983i) q^{72} -8.47722i q^{73} +(-8.75784 - 10.2005i) q^{74} +(-0.986180 + 0.986180i) q^{75} +(-2.57158 - 3.50122i) q^{76} +(1.58122 + 1.58122i) q^{77} +(-8.61164 - 0.655329i) q^{78} -7.06343 q^{79} +(-3.54504 + 1.85276i) q^{80} +4.72250 q^{81} +(11.8161 + 0.899181i) q^{82} +(1.05612 + 1.05612i) q^{83} +(-5.02718 + 3.69237i) q^{84} +(-2.42906 + 2.42906i) q^{85} +(5.05879 + 5.89213i) q^{86} +9.01850i q^{87} +(1.49653 + 2.40008i) q^{88} -9.20046i q^{89} +(1.13190 - 0.971811i) q^{90} +(-6.92382 + 6.92382i) q^{91} +(-1.71133 + 11.1791i) q^{92} +(-0.326813 - 0.326813i) q^{93} +(1.18914 - 15.6265i) q^{94} -2.17207 q^{95} +(-7.24922 + 3.11323i) q^{96} +14.8636 q^{97} +(0.214562 - 2.81955i) q^{98} +(-0.745924 - 0.745924i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q + 12 q^{6} - 4 q^{10} + 12 q^{12} - 8 q^{14} + 8 q^{15} + 4 q^{16} + 56 q^{17} + 20 q^{18} + 8 q^{19} - 8 q^{20} + 4 q^{22} - 24 q^{24} - 24 q^{27} + 20 q^{28} - 20 q^{30} + 20 q^{32} - 8 q^{33} + 4 q^{34}+ \cdots - 60 q^{98}+O(q^{100}) $ 72 * q + 12 * q^6 - 4 * q^10 + 12 * q^12 - 8 * q^14 + 8 * q^15 + 4 * q^16 + 56 * q^17 + 20 * q^18 + 8 * q^19 - 8 * q^20 + 4 * q^22 - 24 * q^24 - 24 * q^27 + 20 * q^28 - 20 * q^30 + 20 * q^32 - 8 * q^33 + 4 * q^34 - 60 * q^36 + 12 * q^38 - 40 * q^42 + 8 * q^44 - 20 * q^46 + 40 * q^47 + 20 * q^48 - 24 * q^49 + 32 * q^51 - 84 * q^52 + 72 * q^54 + 8 * q^56 - 8 * q^58 + 32 * q^60 - 16 * q^61 - 96 * q^62 + 36 * q^64 - 40 * q^65 + 20 * q^66 - 76 * q^68 - 16 * q^69 + 24 * q^70 + 20 * q^72 + 56 * q^74 + 56 * q^76 - 132 * q^78 - 16 * q^79 + 56 * q^81 + 36 * q^82 - 40 * q^83 - 152 * q^84 + 16 * q^85 + 56 * q^86 - 36 * q^90 + 88 * q^91 + 80 * q^92 + 48 * q^93 - 76 * q^94 - 32 * q^96 - 64 * q^97 - 60 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/880\mathbb{Z}\right)^\times$.

$n$	$111$	$177$	$321$	$661$
$\chi(n)$	$1$	$1$	$1$	$e\left(\frac{3}{4}\right)$

Coefficient data

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

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

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

$2$	0.107309	−	1.41014i	0.0758787	−	0.997117i
$2$	0.107309	−	1.41014i	0.0758787	−	0.997117i
$3$	−0.986180	−	0.986180i	−0.569372	−	0.569372i	0.362581	−	0.931952i	$-0.381896\pi$
$3$	−0.986180	−	0.986180i	−0.569372	−	0.569372i	−0.931952	+	0.362581i	$0.881896\pi$
$4$	−1.97697	−	0.302640i	−0.988485	−	0.151320i
$5$	−0.707107	+	0.707107i	−0.316228	+	0.316228i
$5$	−0.707107	+	0.707107i	−0.316228	+	0.316228i
$6$	−1.49647	+	1.28482i	−0.610933	+	0.524527i
$7$			2.23618i			0.845198i	0.906317	+	0.422599i	$0.138882\pi$
$7$			2.23618i			0.845198i	−0.906317	+	0.422599i	$0.861118\pi$
$8$	−0.638910	+	2.75532i	−0.225889	+	0.974153i
$9$		−	1.05490i		−	0.351632i
$10$	0.921238	+	1.07300i	0.291321	+	0.339311i
$11$	0.707107	−	0.707107i	0.213201	−	0.213201i
$11$	0.707107	−	0.707107i	0.213201	−	0.213201i
$12$	1.65119	+	2.24811i	0.476658	+	0.648972i
$13$	3.09627	+	3.09627i	0.858750	+	0.858750i	0.991191	−	0.132441i	$-0.0422816\pi$
$13$	3.09627	+	3.09627i	0.858750	+	0.858750i	−0.132441	+	0.991191i	$0.542282\pi$
$14$	3.15332	+	0.239962i	0.842761	+	0.0641325i
$15$	1.39467			0.360102
$16$	3.81682	+	1.19662i	0.954205	+	0.299155i
$17$	3.43520			0.833160			0.416580	−	0.909099i	$-0.363229\pi$
$17$	3.43520			0.833160			0.416580	+	0.909099i	$0.363229\pi$
$18$	−1.48755	−	0.113200i	−0.350618	−	0.0266814i
$19$	1.53589	+	1.53589i	0.352356	+	0.352356i	0.860986	−	0.508629i	$-0.169848\pi$
$19$	1.53589	+	1.53589i	0.352356	+	0.352356i	−0.508629	+	0.860986i	$0.669848\pi$
$20$	1.61193	−	1.18393i	0.360438	−	0.264735i
$21$	2.20528	−	2.20528i	0.481232	−	0.481232i
$22$	−0.921238	−	1.07300i	−0.196409	−	0.228763i
$23$		−	5.65468i		−	1.17908i	−0.807738	−	0.589542i	$-0.799308\pi$
$23$		−	5.65468i		−	1.17908i	0.807738	−	0.589542i	$-0.200692\pi$
$24$	3.34732	−	2.08716i	0.683270	−	0.426041i
$25$		−	1.00000i		−	0.200000i
$26$	4.69841	−	4.03390i	0.921435	−	0.791113i
$27$	−3.99886	+	3.99886i	−0.769581	+	0.769581i
$28$	0.676758	−	4.42087i	0.127895	−	0.835465i
$29$	−4.57244	−	4.57244i	−0.849081	−	0.849081i	0.140938	−	0.990018i	$-0.454988\pi$
$29$	−4.57244	−	4.57244i	−0.849081	−	0.849081i	−0.990018	+	0.140938i	$0.954988\pi$
$30$	0.149660	−	1.96667i	0.0273241	−	0.359064i
$31$	0.331393			0.0595199			0.0297600	−	0.999557i	$-0.490526\pi$
$31$	0.331393			0.0595199			0.0297600	+	0.999557i	$0.490526\pi$
$32$	2.09697	−	5.25383i	0.370696	−	0.928754i
$33$	−1.39467			−0.242781
$34$	0.368627	−	4.84411i	0.0632191	−	0.830758i
$35$	−1.58122	−	1.58122i	−0.267275	−	0.267275i
$36$	−0.319254	+	2.08550i	−0.0532089	+	0.347583i
$37$	6.72218	−	6.72218i	1.10512	−	1.10512i	0.111337	−	0.993783i	$-0.464487\pi$
$37$	6.72218	−	6.72218i	1.10512	−	1.10512i	0.993783	−	0.111337i	$-0.0355133\pi$
$38$	2.33062	−	2.00100i	0.378077	−	0.324604i
$39$		−	6.10695i		−	0.977895i
$40$	−1.49653	−	2.40008i	−0.236622	−	0.379487i
$41$			8.37938i			1.30864i	0.756218	+	0.654320i	$0.227045\pi$
$41$			8.37938i			1.30864i	−0.756218	+	0.654320i	$0.772955\pi$
$42$	−2.87310	−	3.34639i	−0.443329	−	0.516359i
$43$	−3.88293	+	3.88293i	−0.592141	+	0.592141i	−0.938209	−	0.346068i	$-0.887517\pi$
$43$	−3.88293	+	3.88293i	−0.592141	+	0.592141i	0.346068	+	0.938209i	$0.387517\pi$
$44$	−1.61193	+	1.18393i	−0.243007	+	0.178484i
$45$	0.745924	+	0.745924i	0.111196	+	0.111196i
$46$	−7.97388	−	0.606797i	−1.17568	−	0.0894673i
$47$	11.0815			1.61641			0.808203	−	0.588904i	$-0.200440\pi$
$47$	11.0815			1.61641			0.808203	+	0.588904i	$0.200440\pi$
$48$	−2.58399	−	4.94415i	−0.372967	−	0.713627i
$49$	1.99948			0.285641
$50$	−1.41014	−	0.107309i	−0.199423	−	0.0151757i
$51$	−3.38773	−	3.38773i	−0.474377	−	0.474377i
$52$	−5.18417	−	7.05828i	−0.718915	−	0.978807i
$53$	7.42398	−	7.42398i	1.01976	−	1.01976i	0.0199619	−	0.999801i	$-0.493646\pi$
$53$	7.42398	−	7.42398i	1.01976	−	1.01976i	0.999801	−	0.0199619i	$-0.00635450\pi$
$54$	5.20983	+	6.06805i	0.708967	+	0.825757i
$55$			1.00000i			0.134840i
$56$	−6.16140	−	1.42872i	−0.823352	−	0.190921i
$57$		−	3.02932i		−	0.401243i
$58$	−6.93843	+	5.95710i	−0.911060	+	0.782206i
$59$	−3.58002	+	3.58002i	−0.466079	+	0.466079i	−0.900642	−	0.434562i	$-0.856903\pi$
$59$	−3.58002	+	3.58002i	−0.466079	+	0.466079i	0.434562	+	0.900642i	$0.356903\pi$
$60$	−2.75722	−	0.422083i	−0.355956	−	0.0544906i
$61$	10.6343	+	10.6343i	1.36158	+	1.36158i	0.871904	+	0.489678i	$0.162886\pi$
$61$	10.6343	+	10.6343i	1.36158	+	1.36158i	0.489678	+	0.871904i	$0.337114\pi$
$62$	0.0355613	−	0.467309i	0.00451629	−	0.0593483i
$63$	2.35894			0.297199
$64$	−7.18359	−	3.52080i	−0.897949	−	0.440100i
$65$	−4.37878			−0.543121
$66$	−0.149660	+	1.96667i	−0.0184219	+	0.242081i
$67$	0.841057	+	0.841057i	0.102751	+	0.102751i	0.756614	−	0.653862i	$-0.226852\pi$
$67$	0.841057	+	0.841057i	0.102751	+	0.102751i	−0.653862	+	0.756614i	$0.726852\pi$
$68$	−6.79130	−	1.03963i	−0.823566	−	0.126074i
$69$	−5.57654	+	5.57654i	−0.671336	+	0.671336i
$70$	−2.39942	+	2.06006i	−0.286785	+	0.246224i
$71$		−	11.1058i		−	1.31802i	−0.752133	−	0.659011i	$-0.770975\pi$
$71$		−	11.1058i		−	1.31802i	0.752133	−	0.659011i	$-0.229025\pi$
$72$	2.90658	+	0.673983i	0.342544	+	0.0794297i
$73$		−	8.47722i		−	0.992183i	−0.868270	−	0.496092i	$-0.834768\pi$
$73$		−	8.47722i		−	0.992183i	0.868270	−	0.496092i	$-0.165232\pi$
$74$	−8.75784	−	10.2005i	−1.01808	−	1.18579i
$75$	−0.986180	+	0.986180i	−0.113874	+	0.113874i
$76$	−2.57158	−	3.50122i	−0.294980	−	0.401618i
$77$	1.58122	+	1.58122i	0.180197	+	0.180197i
$78$	−8.61164	−	0.655329i	−0.975076	−	0.0742014i
$79$	−7.06343			−0.794698			−0.397349	−	0.917668i	$-0.630070\pi$
$79$	−7.06343			−0.794698			−0.397349	+	0.917668i	$0.630070\pi$
$80$	−3.54504	+	1.85276i	−0.396347	+	0.207145i
$81$	4.72250			0.524723
$82$	11.8161	+	0.899181i	1.30487	+	0.0992979i
$83$	1.05612	+	1.05612i	0.115924	+	0.115924i	0.762689	−	0.646765i	$-0.223879\pi$
$83$	1.05612	+	1.05612i	0.115924	+	0.115924i	−0.646765	+	0.762689i	$0.723879\pi$
$84$	−5.02718	+	3.69237i	−0.548510	+	0.402870i
$85$	−2.42906	+	2.42906i	−0.263468	+	0.263468i
$86$	5.05879	+	5.89213i	0.545503	+	0.635365i
$87$			9.01850i			0.966885i
$88$	1.49653	+	2.40008i	0.159531	+	0.255850i
$89$		−	9.20046i		−	0.975247i	−0.873054	−	0.487623i	$-0.837864\pi$
$89$		−	9.20046i		−	0.975247i	0.873054	−	0.487623i	$-0.162136\pi$
$90$	1.13190	−	0.971811i	0.119313	−	0.102438i
$91$	−6.92382	+	6.92382i	−0.725813	+	0.725813i
$92$	−1.71133	+	11.1791i	−0.178419	+	1.16551i
$93$	−0.326813	−	0.326813i	−0.0338889	−	0.0338889i
$94$	1.18914	−	15.6265i	0.122651	−	1.61175i
$95$	−2.17207			−0.222850
$96$	−7.24922	+	3.11323i	−0.739870	+	0.317742i
$97$	14.8636			1.50917			0.754586	−	0.656201i	$-0.227838\pi$
$97$	14.8636			1.50917			0.754586	+	0.656201i	$0.227838\pi$
$98$	0.214562	−	2.81955i	0.0216740	−	0.284817i
$99$	−0.745924	−	0.745924i	−0.0749682	−	0.0749682i
$100$	−0.302640	+	1.97697i	−0.0302640	+	0.197697i
$101$	−4.57952	+	4.57952i	−0.455679	+	0.455679i	−0.897234	−	0.441555i	$-0.854427\pi$
$101$	−4.57952	+	4.57952i	−0.455679	+	0.455679i	0.441555	+	0.897234i	$0.354427\pi$
$102$	−5.14070	+	4.41363i	−0.509005	+	0.437015i
$103$		−	16.9004i		−	1.66525i	−0.553839	−	0.832624i	$-0.686838\pi$
$103$		−	16.9004i		−	1.66525i	0.553839	−	0.832624i	$-0.313162\pi$
$104$	−10.5094	+	6.55297i	−1.03054	+	0.642572i
$105$			3.11874i			0.304358i
$106$	−9.67217	−	11.2655i	−0.939444	−	1.09420i
$107$	−11.1259	+	11.1259i	−1.07558	+	1.07558i	−0.0786831	+	0.996900i	$0.525072\pi$
$107$	−11.1259	+	11.1259i	−1.07558	+	1.07558i	−0.996900	+	0.0786831i	$0.974928\pi$
$108$	9.11584	−	6.69541i	0.877172	−	0.644266i
$109$	3.46060	+	3.46060i	0.331465	+	0.331465i	0.853143	−	0.521678i	$-0.174694\pi$
$109$	3.46060	+	3.46060i	0.331465	+	0.331465i	−0.521678	+	0.853143i	$0.674694\pi$
$110$	1.41014	+	0.107309i	0.134451	+	0.0102315i
$111$	−13.2586			−1.25845
$112$	−2.67586	+	8.53510i	−0.252845	+	0.806492i
$113$	20.3192			1.91147			0.955735	−	0.294229i	$-0.0950629\pi$
$113$	20.3192			1.91147			0.955735	+	0.294229i	$0.0950629\pi$
$114$	−4.27176	−	0.325073i	−0.400087	−	0.0304458i
$115$	3.99847	+	3.99847i	0.372859	+	0.372859i
$116$	7.65577	+	10.4234i	0.710821	+	0.967786i
$117$	3.26624	−	3.26624i	0.301964	−	0.301964i
$118$	4.66415	+	5.43249i	0.429370	+	0.500101i
$119$			7.68175i			0.704185i
$120$	−0.891068	+	3.84276i	−0.0813430	+	0.350795i
$121$		−	1.00000i		−	0.0909091i
$122$	16.1370	−	13.8546i	1.46097	−	1.25434i
$123$	8.26358	−	8.26358i	0.745102	−	0.745102i
$124$	−0.655154	−	0.100293i	−0.0588345	−	0.00900655i
$125$	0.707107	+	0.707107i	0.0632456	+	0.0632456i
$126$	0.253135	−	3.32643i	0.0225511	−	0.296342i
$127$	13.9419			1.23714			0.618570	−	0.785730i	$-0.287712\pi$
$127$	13.9419			1.23714			0.618570	+	0.785730i	$0.287712\pi$
$128$	−5.73567	+	9.75203i	−0.506967	+	0.861966i
$129$	7.65853			0.674296
$130$	−0.469881	+	6.17468i	−0.0412113	+	0.541555i
$131$	7.17465	+	7.17465i	0.626852	+	0.626852i	0.947275	−	0.320422i	$-0.103825\pi$
$131$	7.17465	+	7.17465i	0.626852	+	0.626852i	−0.320422	+	0.947275i	$0.603825\pi$
$132$	2.75722	+	0.422083i	0.239985	+	0.0367376i
$133$	−3.43452	+	3.43452i	−0.297811	+	0.297811i
$134$	1.27626	−	1.09575i	0.110252	−	0.0946586i
$135$		−	5.65524i		−	0.486726i
$136$	−2.19479	+	9.46509i	−0.188201	+	0.811625i
$137$			10.2896i			0.879096i	0.898219	+	0.439548i	$0.144861\pi$
$137$			10.2896i			0.879096i	−0.898219	+	0.439548i	$0.855139\pi$
$138$	7.26527	+	8.46209i	0.618461	+	0.720341i
$139$	−8.61334	+	8.61334i	−0.730574	+	0.730574i	−0.970733	−	0.240160i	$-0.922800\pi$
$139$	−8.61334	+	8.61334i	−0.730574	+	0.730574i	0.240160	+	0.970733i	$0.422800\pi$
$140$	2.64748	+	3.60456i	0.223753	+	0.304641i
$141$	−10.9284	−	10.9284i	−0.920336	−	0.920336i
$142$	−15.6608	−	1.19175i	−1.31422	−	0.100010i
$143$	4.37878			0.366172
$144$	1.26231	−	4.02635i	0.105192	−	0.335529i
$145$	6.46641			0.537006
$146$	−11.9540	−	0.909679i	−0.989323	−	0.0752856i
$147$	−1.97185	−	1.97185i	−0.162636	−	0.162636i
$148$	−15.3239	+	11.2551i	−1.25962	+	0.925167i
$149$	9.74192	−	9.74192i	0.798089	−	0.798089i	−0.184705	−	0.982794i	$-0.559133\pi$
$149$	9.74192	−	9.74192i	0.798089	−	0.798089i	0.982794	+	0.184705i	$0.0591329\pi$
$150$	1.28482	+	1.49647i	0.104905	+	0.122187i
$151$			16.2319i			1.32093i	0.750856	+	0.660466i	$0.229641\pi$
$151$			16.2319i			1.32093i	−0.750856	+	0.660466i	$0.770359\pi$
$152$	−5.21315	+	3.25057i	−0.422842	+	0.263656i
$153$		−	3.62379i		−	0.292966i
$154$	2.39942	−	2.06006i	0.193350	−	0.166004i
$155$	−0.234330	+	0.234330i	−0.0188218	+	0.0188218i
$156$	−1.84821	+	12.0733i	−0.147975	+	0.966634i
$157$	9.46793	+	9.46793i	0.755623	+	0.755623i	0.975523	−	0.219900i	$-0.0705730\pi$
$157$	9.46793	+	9.46793i	0.755623	+	0.755623i	−0.219900	+	0.975523i	$0.570573\pi$
$158$	−0.757968	+	9.96040i	−0.0603007	+	0.792407i
$159$	−14.6428			−1.16125
$160$	2.23223	+	5.19780i	0.176473	+	0.410922i
$161$	12.6449			0.996559
$162$	0.506766	−	6.65938i	0.0398153	−	0.523210i
$163$	0.357690	+	0.357690i	0.0280164	+	0.0280164i	0.720976	−	0.692960i	$-0.243694\pi$
$163$	0.357690	+	0.357690i	0.0280164	+	0.0280164i	−0.692960	+	0.720976i	$0.743694\pi$
$164$	2.53593	−	16.5658i	0.198023	−	1.29357i
$165$	0.986180	−	0.986180i	0.0767740	−	0.0767740i
$166$	1.60260	−	1.37594i	0.124386	−	0.106794i
$167$		−	11.5578i		−	0.894367i	−0.894442	−	0.447184i	$-0.852427\pi$
$167$		−	11.5578i		−	0.894367i	0.894442	−	0.447184i	$-0.147573\pi$
$168$	4.66728	+	7.48523i	0.360088	+	0.577498i
$169$			6.17372i			0.474901i
$170$	3.16464	+	3.68596i	0.242717	+	0.282700i
$171$	1.62020	−	1.62020i	0.123900	−	0.123900i
$172$	8.85156	−	6.50130i	0.674925	−	0.495720i
$173$	−0.604912	−	0.604912i	−0.0459906	−	0.0459906i	0.683737	−	0.729728i	$-0.260353\pi$
$173$	−0.604912	−	0.604912i	−0.0459906	−	0.0459906i	−0.729728	+	0.683737i	$0.760353\pi$
$174$	12.7173	+	0.967764i	0.964097	+	0.0733660i
$175$	2.23618			0.169040
$176$	3.54504	−	1.85276i	0.267217	−	0.139657i
$177$	7.06110			0.530745
$178$	−12.9739	−	0.987289i	−0.972435	−	0.0740005i
$179$	−14.4707	−	14.4707i	−1.08159	−	1.08159i	−0.996361	−	0.0852296i	$-0.972838\pi$
$179$	−14.4707	−	14.4707i	−1.08159	−	1.08159i	−0.0852296	−	0.996361i	$-0.527162\pi$
$180$	−1.24892	−	1.70042i	−0.0930893	−	0.126742i
$181$	−14.2256	+	14.2256i	−1.05738	+	1.05738i	−0.0591340	+	0.998250i	$0.518834\pi$
$181$	−14.2256	+	14.2256i	−1.05738	+	1.05738i	−0.998250	+	0.0591340i	$0.981166\pi$
$182$	9.02054	+	10.5065i	0.668647	+	0.778794i
$183$		−	20.9747i		−	1.55049i
$184$	15.5805	+	3.61283i	1.14861	+	0.266342i
$185$			9.50660i			0.698939i
$186$	−0.495921	+	0.425781i	−0.0363627	+	0.0312198i
$187$	2.42906	−	2.42906i	0.177630	−	0.177630i
$188$	−21.9078	−	3.35371i	−1.59779	−	0.244594i
$189$	−8.94218	−	8.94218i	−0.650448	−	0.650448i
$190$	−0.233082	+	3.06292i	−0.0169096	+	0.222207i
$191$	21.0761			1.52501			0.762507	−	0.646980i	$-0.223968\pi$
$191$	21.0761			1.52501			0.762507	+	0.646980i	$0.223968\pi$
$192$	3.61217	+	10.5565i	0.260686	+	0.761847i
$193$	−6.15135			−0.442784			−0.221392	−	0.975185i	$-0.571060\pi$
$193$	−6.15135			−0.442784			−0.221392	+	0.975185i	$0.571060\pi$
$194$	1.59500	−	20.9597i	0.114514	−	1.50482i
$195$	4.31827	+	4.31827i	0.309238	+	0.309238i
$196$	−3.95292	−	0.605124i	−0.282351	−	0.0432231i
$197$	−0.580553	+	0.580553i	−0.0413627	+	0.0413627i	−0.727486	−	0.686123i	$-0.759311\pi$
$197$	−0.580553	+	0.580553i	−0.0413627	+	0.0413627i	0.686123	+	0.727486i	$0.259311\pi$
$198$	−1.13190	+	0.971811i	−0.0804406	+	0.0690636i
$199$			5.96545i			0.422879i	0.977391	+	0.211440i	$0.0678152\pi$
$199$			5.96545i			0.422879i	−0.977391	+	0.211440i	$0.932185\pi$
$200$	2.75532	+	0.638910i	0.194831	+	0.0451777i
$201$		−	1.65887i		−	0.117008i
$202$	5.96632	+	6.94916i	0.419789	+	0.488941i
$203$	10.2248	−	10.2248i	0.717641	−	0.717641i
$204$	5.67218	+	7.72271i	0.397132	+	0.540698i
$205$	−5.92512	−	5.92512i	−0.413828	−	0.413828i
$206$	−23.8319	−	1.81356i	−1.66045	−	0.126357i
$207$	−5.96511			−0.414604
$208$	8.11283	+	15.5229i	0.562524	+	1.07632i
$209$	2.17207			0.150245
$210$	4.39784	+	0.334668i	0.303480	+	0.0230943i
$211$	−7.77379	−	7.77379i	−0.535170	−	0.535170i	0.386936	−	0.922106i	$-0.373533\pi$
$211$	−7.77379	−	7.77379i	−0.535170	−	0.535170i	−0.922106	+	0.386936i	$0.873533\pi$
$212$	−16.9238	+	12.4302i	−1.16233	+	0.853710i
$213$	−10.9524	+	10.9524i	−0.750444	+	0.750444i
$214$	14.4952	+	16.8830i	0.990868	+	1.15410i
$215$		−	5.49129i		−	0.374503i
$216$	−8.46323	−	13.5731i	−0.575850	−	0.923529i
$217$			0.741055i			0.0503061i
$218$	5.25127	−	4.50856i	0.355661	−	0.305358i
$219$	−8.36007	+	8.36007i	−0.564921	+	0.564921i
$220$	0.302640	−	1.97697i	0.0204040	−	0.133287i
$221$	10.6363	+	10.6363i	0.715475	+	0.715475i
$222$	−1.42276	+	18.6964i	−0.0954894	+	1.25482i
$223$	−16.9749			−1.13672			−0.568360	−	0.822780i	$-0.692422\pi$
$223$	−16.9749			−1.13672			−0.568360	+	0.822780i	$0.692422\pi$
$224$	11.7485	+	4.68922i	0.784981	+	0.313312i
$225$	−1.05490			−0.0703264
$226$	2.18043	−	28.6528i	0.145040	−	1.90596i
$227$	1.52135	+	1.52135i	0.100976	+	0.100976i	0.755790	−	0.654814i	$-0.227253\pi$
$227$	1.52135	+	1.52135i	0.100976	+	0.100976i	−0.654814	+	0.755790i	$0.727253\pi$
$228$	−0.916793	+	5.98888i	−0.0607161	+	0.396623i
$229$	−8.50834	+	8.50834i	−0.562247	+	0.562247i	−0.929945	−	0.367698i	$-0.880146\pi$
$229$	−8.50834	+	8.50834i	−0.562247	+	0.562247i	0.367698	+	0.929945i	$0.380146\pi$
$230$	6.06745	−	5.20931i	0.400076	−	0.343492i
$231$		−	3.11874i		−	0.205198i
$232$	15.5199	−	9.67716i	1.01893	−	0.635337i
$233$			12.3004i			0.805825i	0.915239	+	0.402912i	$0.132002\pi$
$233$			12.3004i			0.805825i	−0.915239	+	0.402912i	$0.867998\pi$
$234$	−4.25535	−	4.95634i	−0.278181	−	0.324006i
$235$	−7.83582	+	7.83582i	−0.511152	+	0.511152i
$236$	8.16106	−	5.99414i	0.531239	−	0.390185i
$237$	6.96582	+	6.96582i	0.452479	+	0.452479i
$238$	10.8323	+	0.824318i	0.702155	+	0.0534326i
$239$	12.7679			0.825889			0.412944	−	0.910756i	$-0.364500\pi$
$239$	12.7679			0.825889			0.412944	+	0.910756i	$0.364500\pi$
$240$	5.32320	+	1.66889i	0.343611	+	0.107726i
$241$	12.5944			0.811277			0.405638	−	0.914034i	$-0.367049\pi$
$241$	12.5944			0.811277			0.405638	+	0.914034i	$0.367049\pi$
$242$	−1.41014	−	0.107309i	−0.0906470	−	0.00689806i
$243$	7.33934	+	7.33934i	0.470819	+	0.470819i
$244$	−17.8053	−	24.2420i	−1.13987	−	1.55194i
$245$	−1.41385	+	1.41385i	−0.0903275	+	0.0903275i
$246$	−10.7660	−	12.5395i	−0.686417	−	0.799491i
$247$			9.51102i			0.605172i
$248$	−0.211730	+	0.913094i	−0.0134449	+	0.0579815i
$249$		−	2.08304i		−	0.132008i
$250$	1.07300	−	0.921238i	0.0678622	−	0.0582642i
$251$	−3.33089	+	3.33089i	−0.210244	+	0.210244i	−0.804371	−	0.594127i	$-0.797498\pi$
$251$	−3.33089	+	3.33089i	−0.210244	+	0.210244i	0.594127	+	0.804371i	$0.297498\pi$
$252$	−4.66356	−	0.713910i	−0.293776	−	0.0449721i
$253$	−3.99847	−	3.99847i	−0.251381	−	0.251381i
$254$	1.49608	−	19.6599i	0.0938725	−	1.23357i
$255$	4.79098			0.300023
$256$	13.1362	+	9.13456i	0.821013	+	0.570910i
$257$	−20.6703			−1.28938			−0.644690	−	0.764444i	$-0.723014\pi$
$257$	−20.6703			−1.28938			−0.644690	+	0.764444i	$0.723014\pi$
$258$	0.821827	−	10.7996i	0.0511647	−	0.672352i
$259$	15.0320	+	15.0320i	0.934045	+	0.934045i
$260$	8.65672	+	1.32519i	0.536867	+	0.0821850i
$261$	−4.82345	+	4.82345i	−0.298564	+	0.298564i
$262$	10.8871	−	9.34734i	0.672610	−	0.577480i
$263$		−	3.77384i		−	0.232705i	−0.993208	−	0.116352i	$-0.962880\pi$
$263$		−	3.77384i		−	0.232705i	0.993208	−	0.116352i	$-0.0371202\pi$
$264$	0.891068	−	3.84276i	0.0548414	−	0.236506i
$265$			10.4991i			0.644955i
$266$	4.47459	+	5.21170i	0.274355	+	0.319550i
$267$	−9.07331	+	9.07331i	−0.555278	+	0.555278i
$268$	−1.40821	−	1.91728i	−0.0860199	−	0.117117i
$269$	−5.66007	−	5.66007i	−0.345100	−	0.345100i	0.513180	−	0.858281i	$-0.328467\pi$
$269$	−5.66007	−	5.66007i	−0.345100	−	0.345100i	−0.858281	+	0.513180i	$0.828467\pi$
$270$	−7.97466	−	0.606857i	−0.485322	−	0.0369321i
$271$	−9.63263			−0.585141			−0.292570	−	0.956244i	$-0.594511\pi$
$271$	−9.63263			−0.585141			−0.292570	+	0.956244i	$0.594511\pi$
$272$	13.1116	+	4.11063i	0.795005	+	0.249244i
$273$	13.6563			0.826515
$274$	14.5097	+	1.10416i	0.876562	+	0.0667047i
$275$	−0.707107	−	0.707107i	−0.0426401	−	0.0426401i
$276$	12.7123	−	9.33697i	0.765193	−	0.562019i
$277$	1.80330	−	1.80330i	0.108350	−	0.108350i	−0.650854	−	0.759203i	$-0.725589\pi$
$277$	1.80330	−	1.80330i	0.108350	−	0.108350i	0.759203	+	0.650854i	$0.225589\pi$
$278$	11.2217	+	13.0703i	0.673033	+	0.783903i
$279$		−	0.349585i		−	0.0209291i
$280$	5.36703	−	3.34651i	0.320741	−	0.199992i
$281$		−	7.21935i		−	0.430670i	−0.976540	−	0.215335i	$-0.930916\pi$
$281$		−	7.21935i		−	0.430670i	0.976540	−	0.215335i	$-0.0690844\pi$
$282$	−16.5832	+	14.2378i	−0.987516	+	0.847848i
$283$	3.14046	−	3.14046i	0.186681	−	0.186681i	−0.607579	−	0.794259i	$-0.707859\pi$
$283$	3.14046	−	3.14046i	0.186681	−	0.186681i	0.794259	+	0.607579i	$0.207859\pi$
$284$	−3.36107	+	21.9559i	−0.199443	+	1.30284i
$285$	2.14205	+	2.14205i	0.126884	+	0.126884i
$286$	0.469881	−	6.17468i	0.0277847	−	0.365116i
$287$	−18.7378			−1.10606
$288$	−5.54224	−	2.21209i	−0.326580	−	0.130349i
$289$	−5.19937			−0.305845
$290$	0.693902	−	9.11852i	0.0407473	−	0.535458i
$291$	−14.6582	−	14.6582i	−0.859280	−	0.859280i
$292$	−2.56554	+	16.7592i	−0.150137	+	0.980758i
$293$	9.82084	−	9.82084i	0.573740	−	0.573740i	−0.359432	−	0.933171i	$-0.617029\pi$
$293$	9.82084	−	9.82084i	0.573740	−	0.573740i	0.933171	+	0.359432i	$0.117029\pi$
$294$	−2.99218	+	2.56898i	−0.174507	+	0.149826i
$295$		−	5.06292i		−	0.294774i
$296$	14.2269	+	22.8166i	0.826922	+	1.32619i
$297$			5.65524i			0.328150i
$298$	−12.6920	−	14.7828i	−0.735230	−	0.856346i
$299$	17.5084	−	17.5084i	1.01254	−	1.01254i
$300$	2.24811	−	1.65119i	0.129794	−	0.0953316i
$301$	−8.68294	−	8.68294i	−0.500476	−	0.500476i
$302$	22.8892	+	1.74182i	1.31712	+	0.100231i
$303$	9.03246			0.518901
$304$	4.02433	+	7.70007i	0.230811	+	0.441629i
$305$	−15.0392			−0.861140
$306$	−5.11003	−	0.388864i	−0.292121	−	0.0222299i
$307$	−9.97025	−	9.97025i	−0.569032	−	0.569032i	0.362825	−	0.931857i	$-0.381812\pi$
$307$	−9.97025	−	9.97025i	−0.569032	−	0.569032i	−0.931857	+	0.362825i	$0.881812\pi$
$308$	−2.64748	−	3.60456i	−0.150854	−	0.205389i
$309$	−16.6669	+	16.6669i	−0.948145	+	0.948145i
$310$	0.305292	+	0.355583i	0.0173394	+	0.0201958i
$311$		−	23.5008i		−	1.33261i	−0.745680	−	0.666304i	$-0.767875\pi$
$311$		−	23.5008i		−	1.33261i	0.745680	−	0.666304i	$-0.232125\pi$
$312$	16.8266	+	3.90179i	0.952620	+	0.220895i
$313$			25.2486i			1.42714i	0.700585	+	0.713569i	$0.252922\pi$
$313$			25.2486i			1.42714i	−0.700585	+	0.713569i	$0.747078\pi$
$314$	14.3671	−	12.3351i	0.810780	−	0.696109i
$315$	−1.66802	+	1.66802i	−0.0939825	+	0.0939825i
$316$	13.9642	+	2.13768i	0.785547	+	0.120254i
$317$	1.05870	+	1.05870i	0.0594626	+	0.0594626i	0.736213	−	0.676750i	$-0.236612\pi$
$317$	1.05870	+	1.05870i	0.0594626	+	0.0594626i	−0.676750	+	0.736213i	$0.736612\pi$
$318$	−1.57130	+	20.6483i	−0.0881140	+	1.15790i
$319$	−6.46641			−0.362049
$320$	7.56915	−	2.58998i	0.423128	−	0.144784i
$321$	21.9443			1.22481
$322$	1.35691	−	17.8311i	0.0756176	−	0.993686i
$323$	5.27608	+	5.27608i	0.293569	+	0.293569i
$324$	−9.33625	−	1.42922i	−0.518680	−	0.0794010i
$325$	3.09627	−	3.09627i	0.171750	−	0.171750i
$326$	0.542774	−	0.466008i	0.0300615	−	0.0258098i
$327$		−	6.82555i		−	0.377454i
$328$	−23.0879	−	5.35367i	−1.27482	−	0.295607i
$329$			24.7803i			1.36618i
$330$	−1.28482	−	1.49647i	−0.0707272	−	0.0823782i
$331$	−13.6960	+	13.6960i	−0.752802	+	0.752802i	−0.975001	−	0.222199i	$-0.928676\pi$
$331$	−13.6960	+	13.6960i	−0.752802	+	0.752802i	0.222199	+	0.975001i	$0.428676\pi$
$332$	−1.76829	−	2.40754i	−0.0970475	−	0.132131i
$333$	−7.09120	−	7.09120i	−0.388596	−	0.388596i
$334$	−16.2980	−	1.24025i	−0.891789	−	0.0678634i
$335$	−1.18943			−0.0649857
$336$	11.0560	−	5.77827i	0.603156	−	0.315231i
$337$	−27.9177			−1.52077			−0.760387	−	0.649470i	$-0.774991\pi$
$337$	−27.9177			−1.52077			−0.760387	+	0.649470i	$0.774991\pi$
$338$	8.70579	+	0.662494i	0.473532	+	0.0360349i
$339$	−20.0384	−	20.0384i	−1.08834	−	1.08834i
$340$	5.53730	−	4.06704i	0.300302	−	0.220566i
$341$	0.234330	−	0.234330i	0.0126897	−	0.0126897i
$342$	−2.11084	−	2.45857i	−0.114141	−	0.132944i
$343$			20.1245i			1.08662i
$344$	−8.21787	−	13.1796i	−0.443078	−	0.710594i
$345$		−	7.88642i		−	0.424590i
$346$	−0.917921	+	0.788096i	−0.0493477	+	0.0423683i
$347$	−0.208947	+	0.208947i	−0.0112169	+	0.0112169i	−0.712693	−	0.701476i	$-0.752525\pi$
$347$	−0.208947	+	0.208947i	−0.0112169	+	0.0112169i	0.701476	+	0.712693i	$0.252525\pi$
$348$	2.72936	−	17.8293i	0.146309	−	0.955751i
$349$	−13.8166	−	13.8166i	−0.739588	−	0.739588i	0.232910	−	0.972498i	$-0.425175\pi$
$349$	−13.8166	−	13.8166i	−0.739588	−	0.739588i	−0.972498	+	0.232910i	$0.925175\pi$
$350$	0.239962	−	3.15332i	0.0128265	−	0.168552i
$351$	−24.7631			−1.32175
$352$	−2.23223	−	5.19780i	−0.118978	−	0.277044i
$353$	−30.1187			−1.60305			−0.801527	−	0.597958i	$-0.795979\pi$
$353$	−30.1187			−1.60305			−0.801527	+	0.597958i	$0.795979\pi$
$354$	0.757717	−	9.95711i	0.0402722	−	0.529215i
$355$	7.85302	+	7.85302i	0.416795	+	0.416795i
$356$	−2.78443	+	18.1890i	−0.147574	+	0.964016i
$357$	7.57559	−	7.57559i	0.400943	−	0.400943i
$358$	−21.9585	+	18.8528i	−1.16054	+	0.996403i
$359$			11.0904i			0.585330i	0.956215	+	0.292665i	$0.0945421\pi$
$359$			11.0904i			0.585330i	−0.956215	+	0.292665i	$0.905458\pi$
$360$	−2.53184	+	1.57868i	−0.133440	+	0.0832039i
$361$		−	14.2821i		−	0.751690i
$362$	18.5336	+	21.5866i	0.974103	+	1.13457i
$363$	−0.986180	+	0.986180i	−0.0517610	+	0.0517610i
$364$	15.7836	−	11.5928i	0.827285	−	0.607625i
$365$	5.99430	+	5.99430i	0.313756	+	0.313756i
$366$	−29.5771	−	2.25076i	−1.54602	−	0.117649i
$367$	10.4103			0.543414			0.271707	−	0.962380i	$-0.412412\pi$
$367$	10.4103			0.543414			0.271707	+	0.962380i	$0.412412\pi$
$368$	6.76651	−	21.5829i	0.352729	−	1.12509i
$369$	8.83938			0.460160
$370$	13.4056	+	1.02014i	0.696924	+	0.0530346i
$371$	16.6014	+	16.6014i	0.861901	+	0.861901i
$372$	0.547193	+	0.745006i	0.0283706	+	0.0386268i
$373$	−11.5618	+	11.5618i	−0.598649	+	0.598649i	−0.939953	−	0.341304i	$-0.889132\pi$
$373$	−11.5618	+	11.5618i	−0.598649	+	0.598649i	0.341304	+	0.939953i	$0.389132\pi$
$374$	−3.16464	−	3.68596i	−0.163640	−	0.190596i
$375$		−	1.39467i		−	0.0720204i
$376$	−7.08009	+	30.5332i	−0.365128	+	1.57463i
$377$		−	28.3150i		−	1.45830i
$378$	−13.5693	+	11.6501i	−0.697928	+	0.599218i
$379$	−19.6153	+	19.6153i	−1.00757	+	1.00757i	−0.00760104	+	0.999971i	$0.502420\pi$
$379$	−19.6153	+	19.6153i	−1.00757	+	1.00757i	−0.999971	+	0.00760104i	$0.997580\pi$
$380$	4.29412	+	0.657355i	0.220284	+	0.0337216i
$381$	−13.7492	−	13.7492i	−0.704392	−	0.704392i
$382$	2.26165	−	29.7202i	0.115716	−	1.52062i
$383$	29.8126			1.52335			0.761677	−	0.647956i	$-0.224376\pi$
$383$	29.8126			1.52335			0.761677	+	0.647956i	$0.224376\pi$
$384$	15.2737	−	3.96085i	0.779431	−	0.202126i
$385$	−2.23618			−0.113966
$386$	−0.660094	+	8.67425i	−0.0335979	+	0.441507i
$387$	4.09609	+	4.09609i	0.208216	+	0.208216i
$388$	−29.3849	−	4.49833i	−1.49179	−	0.228368i
$389$	−6.05902	+	6.05902i	−0.307204	+	0.307204i	−0.843824	−	0.536620i	$-0.819701\pi$
$389$	−6.05902	+	6.05902i	−0.307204	+	0.307204i	0.536620	+	0.843824i	$0.319701\pi$
$390$	6.55273	−	5.62596i	0.331811	−	0.284882i
$391$		−	19.4250i		−	0.982365i
$392$	−1.27749	+	5.50922i	−0.0645230	+	0.278258i
$393$		−	14.1510i		−	0.713824i
$394$	0.756361	+	0.880958i	0.0381049	+	0.0443820i
$395$	4.99460	−	4.99460i	0.251306	−	0.251306i
$396$	1.24892	+	1.70042i	0.0627608	+	0.0854491i
$397$	−12.0524	−	12.0524i	−0.604894	−	0.604894i	0.336713	−	0.941607i	$-0.390685\pi$
$397$	−12.0524	−	12.0524i	−0.604894	−	0.604894i	−0.941607	+	0.336713i	$0.890685\pi$
$398$	8.41210	+	0.640144i	0.421660	+	0.0320875i
$399$	6.77412			0.339130
$400$	1.19662	−	3.81682i	0.0598310	−	0.190841i
$401$	24.0022			1.19861			0.599307	−	0.800519i	$-0.295443\pi$
$401$	24.0022			1.19861			0.599307	+	0.800519i	$0.295443\pi$
$402$	−2.33923	−	0.178011i	−0.116670	−	0.00887838i
$403$	1.02608	+	1.02608i	0.0511127	+	0.0511127i
$404$	10.4395	−	7.66762i	0.519385	−	0.381478i
$405$	−3.33932	+	3.33932i	−0.165932	+	0.165932i
$406$	−13.3212	−	15.5156i	−0.661119	−	0.770026i
$407$		−	9.50660i		−	0.471225i
$408$	11.4987	−	7.16983i	0.569273	−	0.354960i
$409$			4.09821i			0.202644i	0.994854	+	0.101322i	$0.0323072\pi$
$409$			4.09821i			0.202644i	−0.994854	+	0.101322i	$0.967693\pi$
$410$	−8.99104	+	7.71941i	−0.444036	+	0.381234i
$411$	10.1474	−	10.1474i	0.500532	−	0.500532i
$412$	−5.11474	+	33.4116i	−0.251985	+	1.64607i
$413$	−8.00559	−	8.00559i	−0.393929	−	0.393929i
$414$	−0.640108	+	8.41161i	−0.0314596	+	0.413408i
$415$	−1.49358			−0.0733168
$416$	22.7600	−	9.77445i	1.11590	−	0.479232i
$417$	16.9886			0.831936
$418$	0.233082	−	3.06292i	0.0114004	−	0.149812i
$419$	−10.7926	−	10.7926i	−0.527254	−	0.527254i	0.392499	−	0.919753i	$-0.371611\pi$
$419$	−10.7926	−	10.7926i	−0.527254	−	0.527254i	−0.919753	+	0.392499i	$0.871611\pi$
$420$	0.943854	−	6.16565i	0.0460554	−	0.300853i
$421$	23.0821	−	23.0821i	1.12495	−	1.12495i	0.133969	−	0.990986i	$-0.457228\pi$
$421$	23.0821	−	23.0821i	1.12495	−	1.12495i	0.990986	−	0.133969i	$-0.0427723\pi$
$422$	−11.7963	+	10.1279i	−0.574235	+	0.493019i
$423$		−	11.6899i		−	0.568380i
$424$	15.7122	+	25.1987i	0.763052	+	1.22376i
$425$		−	3.43520i		−	0.166632i
$426$	14.2691	+	16.6196i	0.691338	+	0.805223i
$427$	−23.7802	+	23.7802i	−1.15081	+	1.15081i
$428$	25.3627	−	18.6285i	1.22595	−	0.900440i
$429$	−4.31827	−	4.31827i	−0.208488	−	0.208488i
$430$	−7.74347	−	0.589263i	−0.373423	−	0.0284168i
$431$	−26.5964			−1.28110			−0.640551	−	0.767916i	$-0.721294\pi$
$431$	−26.5964			−1.28110			−0.640551	+	0.767916i	$0.721294\pi$
$432$	−20.0480	+	10.4778i	−0.964561	+	0.504114i
$433$	−15.8732			−0.762818			−0.381409	−	0.924406i	$-0.624561\pi$
$433$	−15.8732			−0.762818			−0.381409	+	0.924406i	$0.624561\pi$
$434$	1.04499	+	0.0795217i	0.0501611	+	0.00381716i
$435$	−6.37704	−	6.37704i	−0.305756	−	0.305756i
$436$	−5.79418	−	7.88881i	−0.277491	−	0.377806i
$437$	8.68495	−	8.68495i	0.415458	−	0.415458i
$438$	10.8917	+	12.6859i	0.520427	+	0.606158i
$439$			19.3138i			0.921795i	0.887453	+	0.460898i	$0.152472\pi$
$439$			19.3138i			0.921795i	−0.887453	+	0.460898i	$0.847528\pi$
$440$	−2.75532	−	0.638910i	−0.131355	−	0.0304588i
$441$		−	2.10925i		−	0.100440i
$442$	16.1400	−	13.8573i	0.767702	−	0.659123i
$443$	4.78196	−	4.78196i	0.227198	−	0.227198i	−0.584323	−	0.811521i	$-0.698640\pi$
$443$	4.78196	−	4.78196i	0.227198	−	0.227198i	0.811521	+	0.584323i	$0.198640\pi$
$444$	26.2118	+	4.01257i	1.24396	+	0.190428i
$445$	6.50571	+	6.50571i	0.308400	+	0.308400i
$446$	−1.82155	+	23.9369i	−0.0862529	+	1.13344i
$447$	−19.2146			−0.908819
$448$	7.87316	−	16.0638i	0.371972	−	0.758944i
$449$	−2.78804			−0.131576			−0.0657880	−	0.997834i	$-0.520956\pi$
$449$	−2.78804			−0.131576			−0.0657880	+	0.997834i	$0.520956\pi$
$450$	−0.113200	+	1.48755i	−0.00533628	+	0.0701237i
$451$	5.92512	+	5.92512i	0.279003	+	0.279003i
$452$	−40.1704	−	6.14940i	−1.88946	−	0.289243i
$453$	16.0076	−	16.0076i	0.752101	−	0.752101i
$454$	2.30857	−	1.98206i	0.108347	−	0.0930227i
$455$		−	9.79176i		−	0.459045i
$456$	8.34675	+	1.93546i	0.390873	+	0.0906363i
$457$		−	11.1854i		−	0.523232i	−0.965172	−	0.261616i	$-0.915745\pi$
$457$		−	11.1854i		−	0.523232i	0.965172	−	0.261616i	$-0.0842554\pi$
$458$	11.0849	+	12.9109i	0.517963	+	0.603289i
$459$	−13.7369	+	13.7369i	−0.641184	+	0.641184i
$460$	−6.69475	−	9.11494i	−0.312144	−	0.424986i
$461$	−21.5677	−	21.5677i	−1.00451	−	1.00451i	−0.999990	−	0.00451978i	$-0.998561\pi$
$461$	−21.5677	−	21.5677i	−1.00451	−	1.00451i	−0.00451978	−	0.999990i	$-0.501439\pi$
$462$	−4.39784	−	0.334668i	−0.204606	−	0.0155701i
$463$	−11.4753			−0.533302			−0.266651	−	0.963793i	$-0.585917\pi$
$463$	−11.4753			−0.533302			−0.266651	+	0.963793i	$0.585917\pi$
$464$	−11.9807	−	22.9236i	−0.556190	−	1.06420i
$465$	0.462184			0.0214332
$466$	17.3452	+	1.31994i	0.803502	+	0.0611450i
$467$	22.6235	+	22.6235i	1.04689	+	1.04689i	0.998845	+	0.0480441i	$0.0152988\pi$
$467$	22.6235	+	22.6235i	1.04689	+	1.04689i	0.0480441	+	0.998845i	$0.484701\pi$
$468$	−7.44575	+	5.46876i	−0.344180	+	0.252794i
$469$	−1.88076	+	1.88076i	−0.0868453	+	0.0868453i
$470$	10.2087	+	11.8904i	0.470893	+	0.548464i
$471$		−	18.6742i		−	0.860460i
$472$	−7.57680	−	12.1514i	−0.348751	−	0.559315i
$473$			5.49129i			0.252490i
$474$	10.5702	−	9.07526i	0.485508	−	0.416841i
$475$	1.53589	−	1.53589i	0.0704713	−	0.0704713i
$476$	2.32480	−	15.1866i	0.106557	−	0.696076i
$477$	−7.83153	−	7.83153i	−0.358581	−	0.358581i
$478$	1.37011	−	18.0045i	0.0626674	−	0.823508i
$479$	−19.5647			−0.893932			−0.446966	−	0.894551i	$-0.647496\pi$
$479$	−19.5647			−0.893932			−0.446966	+	0.894551i	$0.647496\pi$
$480$	2.92459	−	7.32735i	0.133489	−	0.334446i
$481$	41.6273			1.89804
$482$	1.35149	−	17.7598i	0.0615587	−	0.808938i
$483$	−12.4702	−	12.4702i	−0.567412	−	0.567412i
$484$	−0.302640	+	1.97697i	−0.0137564	+	0.0898623i
$485$	−10.5102	+	10.5102i	−0.477242	+	0.477242i
$486$	11.1370	−	9.56189i	0.505186	−	0.433736i
$487$			17.9657i			0.814103i	0.913405	+	0.407051i	$0.133443\pi$
$487$			17.9657i			0.814103i	−0.913405	+	0.407051i	$0.866557\pi$
$488$	−36.0952	+	22.5065i	−1.63395	+	1.01882i
$489$		−	0.705493i		−	0.0319035i
$490$	1.84200	+	2.14544i	0.0832132	+	0.0969210i
$491$	12.4064	−	12.4064i	0.559894	−	0.559894i	−0.369383	−	0.929277i	$-0.620431\pi$
$491$	12.4064	−	12.4064i	0.559894	−	0.559894i	0.929277	+	0.369383i	$0.120431\pi$
$492$	−18.8377	+	13.8360i	−0.849271	+	0.623773i
$493$	−15.7073	−	15.7073i	−0.707420	−	0.707420i
$494$	13.4118	+	1.02062i	0.603427	+	0.0459197i
$495$	1.05490			0.0474141
$496$	1.26487	+	0.396551i	0.0567942	+	0.0178057i
$497$	24.8347			1.11399
$498$	−2.93738	−	0.223529i	−0.131627	−	0.0100166i
$499$	−3.33359	−	3.33359i	−0.149232	−	0.149232i	0.628543	−	0.777775i	$-0.283652\pi$
$499$	−3.33359	−	3.33359i	−0.149232	−	0.149232i	−0.777775	+	0.628543i	$0.783652\pi$
$500$	−1.18393	−	1.61193i	−0.0529470	−	0.0720876i
$501$	−11.3980	+	11.3980i	−0.509227	+	0.509227i
$502$	4.33957	+	5.05444i	0.193685	+	0.225591i
$503$			18.0100i			0.803027i	0.915853	+	0.401513i	$0.131516\pi$
$503$			18.0100i			0.803027i	−0.915853	+	0.401513i	$0.868484\pi$
$504$	−1.50715	+	6.49964i	−0.0671338	+	0.289517i
$505$		−	6.47641i		−	0.288197i
$506$	−6.06745	+	5.20931i	−0.269731	+	0.231582i
$507$	6.08840	−	6.08840i	0.270395	−	0.270395i
$508$	−27.5626	−	4.21936i	−1.22289	−	0.187204i
$509$	−11.0953	−	11.0953i	−0.491788	−	0.491788i	0.417081	−	0.908869i	$-0.363053\pi$
$509$	−11.0953	−	11.0953i	−0.491788	−	0.491788i	−0.908869	+	0.417081i	$0.863053\pi$
$510$	0.514113	−	6.75593i	0.0227653	−	0.299158i
$511$	18.9566			0.838591
$512$	14.2906	−	17.5436i	0.631561	−	0.775326i
$513$	−12.2836			−0.542334
$514$	−2.21811	+	29.1480i	−0.0978365	+	1.28566i
$515$	11.9504	+	11.9504i	0.526598	+	0.526598i
$516$	−15.1407	−	2.31778i	−0.666532	−	0.102034i
$517$	7.83582	−	7.83582i	0.344619	−	0.344619i
$518$	22.8103	−	19.5841i	1.00223	−	0.860478i
$519$			1.19311i			0.0523715i
$520$	2.79764	−	12.0649i	0.122685	−	0.529083i
$521$		−	20.2350i		−	0.886511i	−0.896395	−	0.443256i	$-0.853823\pi$
$521$		−	20.2350i		−	0.886511i	0.896395	−	0.443256i	$-0.146177\pi$
$522$	6.28412	+	7.31932i	0.275049	+	0.320358i
$523$	20.1980	−	20.1980i	0.883197	−	0.883197i	−0.110661	−	0.993858i	$-0.535297\pi$
$523$	20.1980	−	20.1980i	0.883197	−	0.883197i	0.993858	+	0.110661i	$0.0352968\pi$
$524$	−12.0127	−	16.3554i	−0.524779	−	0.714489i
$525$	−2.20528	−	2.20528i	−0.0962463	−	0.0962463i
$526$	−5.32162	−	0.404965i	−0.232034	−	0.0176573i
$527$	1.13840			0.0495896
$528$	−5.32320	−	1.66889i	−0.231663	−	0.0726291i
$529$	−8.97546			−0.390237
$530$	14.8052	+	1.12664i	0.643095	+	0.0489383i
$531$	3.77655	+	3.77655i	0.163888	+	0.163888i
$532$	7.82937	−	5.75052i	0.339446	−	0.249317i
$533$	−25.9448	+	25.9448i	−1.12379	+	1.12379i
$534$	11.8210	+	13.7683i	0.511543	+	0.595811i
$535$		−	15.7344i		−	0.680258i
$536$	−2.85474	+	1.78002i	−0.123306	+	0.0768853i
$537$			28.5414i			1.23165i
$538$	−8.58884	+	7.37409i	−0.370291	+	0.317920i
$539$	1.41385	−	1.41385i	0.0608988	−	0.0608988i
$540$	−1.71150	+	11.1802i	−0.0736513	+	0.481121i
$541$	−2.14298	−	2.14298i	−0.0921338	−	0.0921338i	0.659538	−	0.751671i	$-0.270752\pi$
$541$	−2.14298	−	2.14298i	−0.0921338	−	0.0921338i	−0.751671	+	0.659538i	$0.770752\pi$
$542$	−1.03367	+	13.5833i	−0.0443997	+	0.583454i
$543$	28.0581			1.20409
$544$	7.20354	−	18.0480i	0.308849	−	0.773800i
$545$	−4.89403			−0.209637
$546$	1.46544	−	19.2572i	0.0627149	−	0.824132i
$547$	−8.20061	−	8.20061i	−0.350633	−	0.350633i	0.509712	−	0.860345i	$-0.329752\pi$
$547$	−8.20061	−	8.20061i	−0.350633	−	0.350633i	−0.860345	+	0.509712i	$0.829752\pi$
$548$	3.11403	−	20.3421i	0.133025	−	0.868973i
$549$	11.2181	−	11.2181i	0.478776	−	0.478776i
$550$	−1.07300	+	0.921238i	−0.0457527	+	0.0392817i
$551$		−	14.0455i		−	0.598358i
$552$	−11.8023	−	18.9281i	−0.502337	−	0.805632i
$553$		−	15.7951i		−	0.671677i
$554$	−2.34938	−	2.73640i	−0.0998158	−	0.116259i
$555$	9.37522	−	9.37522i	0.397956	−	0.397956i
$556$	19.6350	−	14.4216i	0.832712	−	0.611611i
$557$	13.9332	+	13.9332i	0.590367	+	0.590367i	0.937731	−	0.347363i	$-0.112923\pi$
$557$	13.9332	+	13.9332i	0.590367	+	0.590367i	−0.347363	+	0.937731i	$0.612923\pi$
$558$	−0.492963	−	0.0375135i	−0.0208688	−	0.00158807i
$559$	−24.0451			−1.01700
$560$	−4.14311	−	7.92735i	−0.175078	−	0.334992i
$561$	−4.79098			−0.202275
$562$	−10.1803	−	0.774699i	−0.429429	−	0.0326787i
$563$	14.0641	+	14.0641i	0.592731	+	0.592731i	0.938368	−	0.345637i	$-0.112337\pi$
$563$	14.0641	+	14.0641i	0.592731	+	0.592731i	−0.345637	+	0.938368i	$0.612337\pi$
$564$	18.2977	+	24.9124i	0.770473	+	1.04900i
$565$	−14.3678	+	14.3678i	−0.604460	+	0.604460i
$566$	−4.09147	−	4.76547i	−0.171977	−	0.200308i
$567$			10.5604i			0.443495i
$568$	30.6002	+	7.09563i	1.28396	+	0.297726i
$569$			36.4387i			1.52759i	0.645459	+	0.763795i	$0.276666\pi$
$569$			36.4387i			1.52759i	−0.645459	+	0.763795i	$0.723334\pi$
$570$	3.25045	−	2.79073i	0.136146	−	0.116891i
$571$	−22.8527	+	22.8527i	−0.956358	+	0.956358i	−0.999087	−	0.0427291i	$-0.986395\pi$
$571$	−22.8527	+	22.8527i	−0.956358	+	0.956358i	0.0427291	+	0.999087i	$0.486395\pi$
$572$	−8.65672	−	1.32519i	−0.361955	−	0.0554091i
$573$	−20.7848	−	20.7848i	−0.868299	−	0.868299i
$574$	−2.01073	+	26.4229i	−0.0839264	+	1.10287i
$575$	−5.65468			−0.235817
$576$	−3.71408	+	7.57794i	−0.154753	+	0.315748i
$577$	−26.4192			−1.09985			−0.549923	−	0.835215i	$-0.685343\pi$
$577$	−26.4192			−1.09985			−0.549923	+	0.835215i	$0.685343\pi$
$578$	−0.557937	+	7.33182i	−0.0232071	+	0.304963i
$579$	6.06634	+	6.06634i	0.252109	+	0.252109i
$580$	−12.7839	−	1.95699i	−0.530822	−	0.0812597i
$581$	−2.36167	+	2.36167i	−0.0979787	+	0.0979787i
$582$	−22.2430	+	19.0971i	−0.922004	+	0.791602i
$583$		−	10.4991i		−	0.434828i
$584$	23.3575	+	5.41618i	0.966539	+	0.224123i
$585$			4.61916i			0.190979i
$586$	−12.7949	−	14.9026i	−0.528551	−	0.615620i
$587$	9.06913	−	9.06913i	0.374323	−	0.374323i	−0.494726	−	0.869049i	$-0.664732\pi$
$587$	9.06913	−	9.06913i	0.374323	−	0.374323i	0.869049	+	0.494726i	$0.164732\pi$
$588$	3.30153	+	4.49505i	0.136153	+	0.185373i
$589$	0.508982	+	0.508982i	0.0209722	+	0.0209722i
$590$	−7.13941	−	0.543295i	−0.293925	−	0.0223671i
$591$	1.14506			0.0471015
$592$	33.7012	−	17.6134i	1.38511	−	0.723908i
$593$	−3.12919			−0.128501			−0.0642503	−	0.997934i	$-0.520466\pi$
$593$	−3.12919			−0.128501			−0.0642503	+	0.997934i	$0.520466\pi$
$594$	7.97466	+	0.606857i	0.327204	+	0.0248996i
$595$	−5.43182	−	5.43182i	−0.222683	−	0.222683i
$596$	−22.2078	+	16.3112i	−0.909666	+	0.668132i
$597$	5.88301	−	5.88301i	0.240775	−	0.240775i
$598$	−22.8104	−	26.5680i	−0.932788	−	1.08645i
$599$		−	19.9260i		−	0.814154i	−0.913394	−	0.407077i	$-0.866548\pi$
$599$		−	19.9260i		−	0.814154i	0.913394	−	0.407077i	$-0.133452\pi$
$600$	−2.08716	−	3.34732i	−0.0852081	−	0.136654i
$601$		−	5.83784i		−	0.238131i	−0.992886	−	0.119065i	$-0.962010\pi$
$601$		−	5.83784i		−	0.238131i	0.992886	−	0.119065i	$-0.0379898\pi$
$602$	−13.1759	+	11.3124i	−0.537009	+	0.461058i
$603$	0.887228	−	0.887228i	0.0361307	−	0.0361307i
$604$	4.91241	−	32.0899i	0.199883	−	1.30572i
$605$	0.707107	+	0.707107i	0.0287480	+	0.0287480i
$606$	0.969261	−	12.7370i	0.0393736	−	0.517405i
$607$	14.4832			0.587855			0.293927	−	0.955828i	$-0.405038\pi$
$607$	14.4832			0.587855			0.293927	+	0.955828i	$0.405038\pi$
$608$	11.2900	−	4.84857i	0.457870	−	0.196635i
$609$	−20.1670			−0.817209
$610$	−1.61383	+	21.2073i	−0.0653422	+	0.858657i
$611$	34.3113	+	34.3113i	1.38809	+	1.38809i
$612$	−1.09670	+	7.16411i	−0.0443315	+	0.289592i
$613$	29.9476	−	29.9476i	1.20957	−	1.20957i	0.238406	−	0.971166i	$-0.423375\pi$
$613$	29.9476	−	29.9476i	1.20957	−	1.20957i	0.971166	−	0.238406i	$-0.0766249\pi$
$614$	−15.1293	+	12.9895i	−0.610569	+	0.524214i
$615$			11.6865i			0.471244i
$616$	−5.36703	+	3.34651i	−0.216244	+	0.134835i
$617$		−	13.1466i		−	0.529261i	−0.964350	−	0.264630i	$-0.914750\pi$
$617$		−	13.1466i		−	0.529261i	0.964350	−	0.264630i	$-0.0852499\pi$
$618$	21.7140	+	25.2910i	0.873467	+	1.01736i
$619$	11.1863	−	11.1863i	0.449617	−	0.449617i	−0.445610	−	0.895227i	$-0.647013\pi$
$619$	11.1863	−	11.1863i	0.449617	−	0.449617i	0.895227	+	0.445610i	$0.147013\pi$
$620$	0.534181	−	0.392346i	0.0214532	−	0.0157570i
$621$	22.6123	+	22.6123i	0.907400	+	0.907400i
$622$	−33.1394	−	2.52184i	−1.32877	−	0.101117i
$623$	20.5739			0.824276
$624$	7.30770	−	23.3091i	0.292542	−	0.933112i
$625$	−1.00000			−0.0400000
$626$	35.6040	+	2.70940i	1.42302	+	0.108289i
$627$	−2.14205	−	2.14205i	−0.0855454	−	0.0855454i
$628$	−15.8524	−	21.5832i	−0.632581	−	0.861263i
$629$	23.0921	−	23.0921i	0.920741	−	0.920741i
$630$	2.17315	+	2.53113i	0.0865803	+	0.100843i
$631$		−	17.9248i		−	0.713576i	−0.934185	−	0.356788i	$-0.883872\pi$
$631$		−	17.9248i		−	0.713576i	0.934185	−	0.356788i	$-0.116128\pi$
$632$	4.51289	−	19.4620i	0.179513	−	0.774158i
$633$			15.3327i			0.609421i
$634$	1.60652	−	1.37931i	0.0638032	−	0.0547793i
$635$	−9.85838	+	9.85838i	−0.391218	+	0.391218i
$636$	28.9483	+	4.43149i	1.14788	+	0.175720i
$637$	6.19094	+	6.19094i	0.245294	+	0.245294i
$638$	−0.693902	+	9.11852i	−0.0274718	+	0.361005i
$639$	−11.7155			−0.463459
$640$	−2.83999	−	10.9515i	−0.112261	−	0.432894i
$641$	5.52762			0.218328			0.109164	−	0.994024i	$-0.465183\pi$
$641$	5.52762			0.218328			0.109164	+	0.994024i	$0.465183\pi$
$642$	2.35482	−	30.9445i	0.0929372	−	1.22128i
$643$	1.20994	+	1.20994i	0.0477154	+	0.0477154i	0.730562	−	0.682846i	$-0.239258\pi$
$643$	1.20994	+	1.20994i	0.0477154	+	0.0477154i	−0.682846	+	0.730562i	$0.739258\pi$
$644$	−24.9986	−	3.82685i	−0.985083	−	0.150799i
$645$	−5.41540	+	5.41540i	−0.213231	+	0.213231i
$646$	8.00617	−	6.87383i	0.314998	−	0.270447i
$647$		−	42.0228i		−	1.65209i	−0.563606	−	0.826044i	$-0.690586\pi$
$647$		−	42.0228i		−	1.65209i	0.563606	−	0.826044i	$-0.309414\pi$
$648$	−3.01725	+	13.0120i	−0.118529	+	0.511160i
$649$			5.06292i			0.198737i
$650$	−4.03390	−	4.69841i	−0.158223	−	0.184287i
$651$	0.730814	−	0.730814i	0.0286429	−	0.0286429i
$652$	−0.598890	−	0.815393i	−0.0234544	−	0.0319332i
$653$	15.3922	+	15.3922i	0.602344	+	0.602344i	0.940934	−	0.338590i	$-0.109950\pi$
$653$	15.3922	+	15.3922i	0.602344	+	0.602344i	−0.338590	+	0.940934i	$0.609950\pi$
$654$	−9.62496	−	0.732441i	−0.376366	−	0.0286407i
$655$	−10.1465			−0.396456
$656$	−10.0269	+	31.9826i	−0.391486	+	1.24871i
$657$	−8.94259			−0.348884
$658$	34.9436	+	2.65914i	1.36224	+	0.103664i
$659$	0.784582	+	0.784582i	0.0305630	+	0.0305630i	0.722223	−	0.691660i	$-0.243120\pi$
$659$	0.784582	+	0.784582i	0.0305630	+	0.0305630i	−0.691660	+	0.722223i	$0.743120\pi$
$660$	−2.24811	+	1.65119i	−0.0875074	+	0.0642725i
$661$	−17.0391	+	17.0391i	−0.662744	+	0.662744i	−0.956026	−	0.293282i	$-0.905252\pi$
$661$	−17.0391	+	17.0391i	−0.662744	+	0.662744i	0.293282	+	0.956026i	$0.405252\pi$
$662$	17.8436	+	20.7830i	0.693510	+	0.807753i
$663$		−	20.9786i		−	0.814743i
$664$	−3.58471	+	2.23518i	−0.139114	+	0.0867418i
$665$		−	4.85715i		−	0.188352i
$666$	−10.7605	+	9.23862i	−0.416961	+	0.357989i
$667$	−25.8557	+	25.8557i	−1.00114	+	1.00114i
$668$	−3.49784	+	22.8494i	−0.135336	+	0.884068i
$669$	16.7403	+	16.7403i	0.647216	+	0.647216i
$670$	−0.127637	+	1.67726i	−0.00493103	+	0.0647984i
$671$	15.0392			0.580580
$672$	−6.96174	−	16.2106i	−0.268555	−	0.625337i
$673$	20.0970			0.774682			0.387341	−	0.921936i	$-0.373394\pi$
$673$	20.0970			0.774682			0.387341	+	0.921936i	$0.373394\pi$
$674$	−2.99581	+	39.3678i	−0.115394	+	1.51639i
$675$	3.99886	+	3.99886i	0.153916	+	0.153916i
$676$	1.86841	−	12.2053i	0.0718620	−	0.469433i
$677$	−6.65953	+	6.65953i	−0.255947	+	0.255947i	−0.823403	−	0.567457i	$-0.807927\pi$
$677$	−6.65953	+	6.65953i	−0.255947	+	0.255947i	0.567457	+	0.823403i	$0.307927\pi$
$678$	−30.4072	+	26.1066i	−1.16778	+	1.00262i
$679$			33.2378i			1.27555i
$680$	−5.14088	−	8.24478i	−0.197144	−	0.316173i
$681$		−	3.00066i		−	0.114985i
$682$	−0.305292	−	0.355583i	−0.0116902	−	0.0136160i
$683$	15.9406	−	15.9406i	0.609950	−	0.609950i	−0.332983	−	0.942933i	$-0.608055\pi$
$683$	15.9406	−	15.9406i	0.609950	−	0.609950i	0.942933	+	0.332983i	$0.108055\pi$
$684$	−3.69343	+	2.71275i	−0.141222	+	0.103725i
$685$	−7.27582	−	7.27582i	−0.277995	−	0.277995i
$686$	28.3783	+	2.15953i	1.08349	+	0.0824514i
$687$	16.7815			0.640255
$688$	−19.4668	+	10.1740i	−0.742165	+	0.387882i
$689$	45.9733			1.75144
$690$	−11.1209	−	0.846281i	−0.423366	−	0.0322174i
$691$	2.45694	+	2.45694i	0.0934666	+	0.0934666i	0.752294	−	0.658827i	$-0.228947\pi$
$691$	2.45694	+	2.45694i	0.0934666	+	0.0934666i	−0.658827	+	0.752294i	$0.728947\pi$
$692$	1.01282	+	1.37896i	0.0385017	+	0.0524203i
$693$	1.66802	−	1.66802i	0.0633630	−	0.0633630i
$694$	0.272222	+	0.317066i	0.0103334	+	0.0120357i
$695$		−	12.1811i		−	0.462055i
$696$	−24.8489	−	5.76201i	−0.941894	−	0.218408i
$697$			28.7849i			1.09031i
$698$	−20.9660	+	18.0007i	−0.793574	+	0.681337i
$699$	12.1304	−	12.1304i	0.458814	−	0.458814i
$700$	−4.42087	−	0.676758i	−0.167093	−	0.0255791i
$701$	−18.2180	−	18.2180i	−0.688084	−	0.688084i	0.273724	−	0.961808i	$-0.411744\pi$
$701$	−18.2180	−	18.2180i	−0.688084	−	0.688084i	−0.961808	+	0.273724i	$0.911744\pi$
$702$	−2.65729	+	34.9193i	−0.100293	+	1.31794i
$703$	20.6490			0.778792
$704$	−7.56915	+	2.58998i	−0.285273	+	0.0976136i
$705$	15.4551			0.582071
$706$	−3.23200	+	42.4714i	−0.121638	+	1.59843i
$707$	−10.2406	−	10.2406i	−0.385139	−	0.385139i
$708$	−13.9596	−	2.13697i	−0.524633	−	0.0803122i
$709$	−26.4420	+	26.4420i	−0.993051	+	0.993051i	−0.999976	−	0.00692551i	$-0.997796\pi$
$709$	−26.4420	+	26.4420i	−0.993051	+	0.993051i	0.00692551	+	0.999976i	$0.497796\pi$
$710$	11.9165	−	10.2311i	0.447219	−	0.383968i
$711$			7.45119i			0.279441i
$712$	25.3502	+	5.87826i	0.950040	+	0.220297i
$713$		−	1.87392i		−	0.0701789i
$714$	−9.86969	−	11.4955i	−0.369364	−	0.430210i
$715$	−3.09627	+	3.09627i	−0.115794	+	0.115794i
$716$	24.2287	+	32.9875i	0.905470	+	1.23280i
$717$	−12.5915	−	12.5915i	−0.470238	−	0.470238i
$718$	15.6390	+	1.19010i	0.583643	+	0.0444141i
$719$	25.5603			0.953238			0.476619	−	0.879110i	$-0.341862\pi$
$719$	25.5603			0.953238			0.476619	+	0.879110i	$0.341862\pi$
$720$	1.95447	+	3.73965i	0.0728388	+	0.139368i
$721$	37.7924			1.40746
$722$	−20.1397	−	1.53259i	−0.749523	−	0.0570373i
$723$	−12.4204	−	12.4204i	−0.461918	−	0.461918i
$724$	32.4289	−	23.8184i	1.20521	−	0.885205i
$725$	−4.57244	+	4.57244i	−0.169816	+	0.169816i
$726$	1.28482	+	1.49647i	0.0476843	+	0.0555394i
$727$			3.43739i			0.127486i	0.997966	+	0.0637429i	$0.0203038\pi$
$727$			3.43739i			0.127486i	−0.997966	+	0.0637429i	$0.979696\pi$
$728$	−14.6536	−	23.5010i	−0.543100	−	0.871006i
$729$		−	28.6433i		−	1.06086i
$730$	9.09602	−	7.80954i	0.336659	−	0.289044i
$731$	−13.3387	+	13.3387i	−0.493348	+	0.493348i
$732$	−6.34777	+	41.4663i	−0.234620	+	1.53264i
$733$	−9.09599	−	9.09599i	−0.335968	−	0.335968i	0.518879	−	0.854847i	$-0.326349\pi$
$733$	−9.09599	−	9.09599i	−0.335968	−	0.335968i	−0.854847	+	0.518879i	$0.826349\pi$
$734$	1.11712	−	14.6800i	0.0412335	−	0.541847i
$735$	2.78862			0.102860
$736$	−29.7087	−	11.8577i	−1.09508	−	0.437082i
$737$	1.18943			0.0438134
$738$	0.948542	−	12.4647i	0.0349163	−	0.458833i
$739$	1.20931	+	1.20931i	0.0444853	+	0.0444853i	0.729000	−	0.684514i	$-0.239986\pi$
$739$	1.20931	+	1.20931i	0.0444853	+	0.0444853i	−0.684514	+	0.729000i	$0.739986\pi$
$740$	2.87708	−	18.7943i	0.105763	−	0.690891i
$741$	9.37958	−	9.37958i	0.344568	−	0.344568i
$742$	25.1917	−	21.6287i	0.924816	−	0.794016i
$743$			22.9148i			0.840664i	0.907370	+	0.420332i	$0.138086\pi$
$743$			22.9148i			0.840664i	−0.907370	+	0.420332i	$0.861914\pi$
$744$	1.10928	−	0.691671i	0.0406681	−	0.0253579i
$745$			13.7772i			0.504756i
$746$	15.0631	+	17.5445i	0.551499	+	0.642348i
$747$	1.11409	−	1.11409i	0.0407626	−	0.0407626i
$748$	−5.53730	+	4.06704i	−0.202464	+	0.148706i
$749$	−24.8796	−	24.8796i	−0.909080	−	0.909080i
$750$	−1.96667	−	0.149660i	−0.0718128	−	0.00546482i
$751$	21.2611			0.775830			0.387915	−	0.921695i	$-0.373195\pi$
$751$	21.2611			0.775830			0.387915	+	0.921695i	$0.373195\pi$
$752$	42.2962	+	13.2604i	1.54238	+	0.483556i
$753$	6.56971			0.239414
$754$	−39.9280	−	3.03844i	−1.45409	−	0.110654i
$755$	−11.4777	−	11.4777i	−0.417715	−	0.417715i
$756$	14.9722	+	20.3847i	0.544532	+	0.741384i
$757$	30.6333	−	30.6333i	1.11339	−	1.11339i	0.120696	−	0.992690i	$-0.461487\pi$
$757$	30.6333	−	30.6333i	1.11339	−	1.11339i	0.992690	−	0.120696i	$-0.0385125\pi$
$758$	25.5554	+	29.7652i	0.928214	+	1.08112i
$759$			7.88642i			0.286259i
$760$	1.38776	−	5.98475i	0.0503392	−	0.217090i
$761$		−	18.4765i		−	0.669773i	−0.942258	−	0.334887i	$-0.891302\pi$
$761$		−	18.4765i		−	0.669773i	0.942258	−	0.334887i	$-0.108698\pi$
$762$	−20.8636	+	17.9128i	−0.755809	+	0.648913i
$763$	−7.73853	+	7.73853i	−0.280154	+	0.280154i
$764$	−41.6668	−	6.37847i	−1.50745	−	0.230765i
$765$	2.56240	+	2.56240i	0.0926439	+	0.0926439i
$766$	3.19916	−	42.0399i	0.115590	−	1.51896i
$767$	−22.1694			−0.800491
$768$	−3.94634	−	21.9630i	−0.142401	−	0.792521i
$769$	−38.7300			−1.39664			−0.698320	−	0.715786i	$-0.746069\pi$
$769$	−38.7300			−1.39664			−0.698320	+	0.715786i	$0.746069\pi$
$770$	−0.239962	+	3.15332i	−0.00864763	+	0.113638i
$771$	20.3847	+	20.3847i	0.734137	+	0.734137i
$772$	12.1610	+	1.86164i	0.437685	+	0.0670020i
$773$	−14.7627	+	14.7627i	−0.530978	+	0.530978i	−0.920863	−	0.389885i	$-0.872515\pi$
$773$	−14.7627	+	14.7627i	−0.530978	+	0.530978i	0.389885	+	0.920863i	$0.372515\pi$
$774$	6.21559	−	5.33649i	0.223415	−	0.191816i
$775$		−	0.331393i		−	0.0119040i
$776$	−9.49651	+	40.9541i	−0.340905	+	1.47017i
$777$		−	29.6486i		−	1.06364i
$778$	7.89386	+	9.19423i	0.283009	+	0.329629i
$779$	−12.8698	+	12.8698i	−0.461108	+	0.461108i
$780$	−7.23020	−	9.84396i	−0.258883	−	0.352470i
$781$	−7.85302	−	7.85302i	−0.281003	−	0.281003i
$782$	−27.3919	−	2.08447i	−0.979532	−	0.0745406i
$783$	36.5691			1.30687
$784$	7.63167	+	2.39262i	0.272560	+	0.0854508i
$785$	−13.3897			−0.477898
$786$	−19.9548	−	1.51853i	−0.711766	−	0.0541640i
$787$	20.3777	+	20.3777i	0.726386	+	0.726386i	0.969898	−	0.243512i	$-0.0782996\pi$
$787$	20.3777	+	20.3777i	0.726386	+	0.726386i	−0.243512	+	0.969898i	$0.578300\pi$
$788$	1.32343	−	0.972038i	0.0471454	−	0.0346274i
$789$	−3.72168	+	3.72168i	−0.132495	+	0.132495i
$790$	−6.50710	−	7.57903i	−0.231512	−	0.269650i
$791$			45.4375i			1.61557i
$792$	2.53184	−	1.57868i	0.0899650	−	0.0560961i
$793$			65.8532i			2.33851i
$794$	−18.2889	+	15.7022i	−0.649049	+	0.557252i
$795$	10.3540	−	10.3540i	0.367219	−	0.367219i
$796$	1.80538	−	11.7935i	0.0639901	−	0.418010i
$797$	36.2995	+	36.2995i	1.28579	+	1.28579i	0.937318	+	0.348474i	$0.113300\pi$
$797$	36.2995	+	36.2995i	1.28579	+	1.28579i	0.348474	+	0.937318i	$0.386700\pi$
$798$	0.726922	−	9.55243i	0.0257328	−	0.338152i
$799$	38.0673			1.34672
$800$	−5.25383	−	2.09697i	−0.185751	−	0.0741393i
$801$	−9.70553			−0.342928
$802$	2.57565	−	33.8464i	0.0909493	−	1.19516i
$803$	−5.99430	−	5.99430i	−0.211534	−	0.211534i
$804$	−0.502039	+	3.27953i	−0.0177056	+	0.115660i
$805$	−8.94130	+	8.94130i	−0.315140	+	0.315140i
$806$	1.55702	−	1.33681i	0.0548437	−	0.0470870i
$807$			11.1637i			0.392981i
$808$	−9.69214	−	15.5439i	−0.340968	−	0.546834i
$809$			0.706108i			0.0248254i	0.999923	+	0.0124127i	$0.00395119\pi$
$809$			0.706108i			0.0248254i	−0.999923	+	0.0124127i	$0.996049\pi$
$810$	4.35055	+	5.06723i	0.152863	+	0.178044i
$811$	−1.23858	+	1.23858i	−0.0434925	+	0.0434925i	−0.728519	−	0.685026i	$-0.759791\pi$
$811$	−1.23858	+	1.23858i	−0.0434925	+	0.0434925i	0.685026	+	0.728519i	$0.259791\pi$
$812$	−23.3086	+	17.1197i	−0.817971	+	0.600784i
$813$	9.49951	+	9.49951i	0.333162	+	0.333162i
$814$	−13.4056	−	1.02014i	−0.469866	−	0.0357559i
$815$	−0.505849			−0.0177191
$816$	−8.87653	−	16.9842i	−0.310741	−	0.594565i
$817$	−11.9275			−0.417289
$818$	5.77904	+	0.439774i	0.202059	+	0.0153763i
$819$	7.30391	+	7.30391i	0.255219	+	0.255219i
$820$	9.92060	+	13.5070i	0.346442	+	0.471683i
$821$	16.3244	−	16.3244i	0.569726	−	0.569726i	−0.362325	−	0.932052i	$-0.618017\pi$
$821$	16.3244	−	16.3244i	0.569726	−	0.569726i	0.932052	+	0.362325i	$0.118017\pi$
$822$	−13.2203	−	15.3981i	−0.461110	−	0.537069i
$823$			44.5314i			1.55227i	0.630569	+	0.776133i	$0.282821\pi$
$823$			44.5314i			1.55227i	−0.630569	+	0.776133i	$0.717179\pi$
$824$	46.5661	+	10.7978i	1.62221	+	0.376160i
$825$			1.39467i			0.0485562i
$826$	−12.1480	+	10.4299i	−0.422684	+	0.362903i
$827$	−0.102717	+	0.102717i	−0.00357182	+	0.00357182i	−0.708890	−	0.705319i	$-0.750804\pi$
$827$	−0.102717	+	0.102717i	−0.00357182	+	0.00357182i	0.705319	+	0.708890i	$0.250804\pi$
$828$	11.7928	+	1.80528i	0.409829	+	0.0627378i
$829$	15.9431	+	15.9431i	0.553728	+	0.553728i	0.927515	−	0.373787i	$-0.121941\pi$
$829$	15.9431	+	15.9431i	0.553728	+	0.553728i	−0.373787	+	0.927515i	$0.621941\pi$
$830$	−0.160274	+	2.10615i	−0.00556318	+	0.0731054i
$831$	−3.55675			−0.123382
$832$	−11.3410	−	33.1436i	−0.393177	−	1.14905i
$833$	6.86864			0.237984
$834$	1.82303	−	23.9563i	0.0631262	−	0.829537i
$835$	8.17258	+	8.17258i	0.282824	+	0.282824i
$836$	−4.29412	−	0.657355i	−0.148515	−	0.0227351i
$837$	−1.32519	+	1.32519i	−0.0458054	+	0.0458054i
$838$	−16.3772	+	14.0609i	−0.565741	+	0.485726i
$839$			7.07344i			0.244202i	0.992518	+	0.122101i	$0.0389632\pi$
$839$			7.07344i			0.244202i	−0.992518	+	0.122101i	$0.961037\pi$
$840$	−8.59312	−	1.99259i	−0.296491	−	0.0687509i
$841$			12.8144i			0.441876i
$842$	−30.0721	−	35.0259i	−1.03635	−	1.20707i
$843$	−7.11958	+	7.11958i	−0.245211	+	0.245211i
$844$	13.0159	+	17.7212i	0.448026	+	0.609989i
$845$	−4.36548	−	4.36548i	−0.150177	−	0.150177i
$846$	−16.4843	−	1.25442i	−0.566742	−	0.0431280i
$847$	2.23618			0.0768362
$848$	37.2197	−	19.4523i	1.27813	−	0.667995i
$849$	−6.19411			−0.212581
$850$	−4.84411	−	0.368627i	−0.166152	−	0.0126438i
$851$	−38.0118	−	38.0118i	−1.30303	−	1.30303i
$852$	24.9671	−	18.3379i	0.855360	−	0.628246i
$853$	−34.1065	+	34.1065i	−1.16779	+	1.16779i	−0.185058	+	0.982728i	$0.559247\pi$
$853$	−34.1065	+	34.1065i	−1.16779	+	1.16779i	−0.982728	+	0.185058i	$0.940753\pi$
$854$	30.9815	+	36.0852i	1.06017	+	1.23481i
$855$			2.29131i			0.0783611i
$856$	−23.5470	−	37.7639i	−0.804820	−	1.29074i
$857$			17.1625i			0.586260i	0.956073	+	0.293130i	$0.0946968\pi$
$857$			17.1625i			0.586260i	−0.956073	+	0.293130i	$0.905303\pi$
$858$	−6.55273	+	5.62596i	−0.223707	+	0.192067i
$859$	25.5949	−	25.5949i	0.873288	−	0.873288i	−0.119541	−	0.992829i	$-0.538142\pi$
$859$	25.5949	−	25.5949i	0.873288	−	0.873288i	0.992829	+	0.119541i	$0.0381423\pi$
$860$	−1.66188	+	10.8561i	−0.0566697	+	0.370190i
$861$	18.4789	+	18.4789i	0.629759	+	0.629759i
$862$	−2.85402	+	37.5045i	−0.0972084	+	1.27741i
$863$	−25.7707			−0.877244			−0.438622	−	0.898672i	$-0.644533\pi$
$863$	−25.7707			−0.877244			−0.438622	+	0.898672i	$0.644533\pi$
$864$	12.6238	+	29.3948i	0.429471	+	1.00003i
$865$	0.855475			0.0290870
$866$	−1.70333	+	22.3834i	−0.0578816	+	0.760619i
$867$	5.12751	+	5.12751i	0.174140	+	0.174140i
$868$	0.224273	−	1.46504i	0.00761231	−	0.0497268i
$869$	−4.99460	+	4.99460i	−0.169430	+	0.169430i
$870$	−9.67681	+	8.30819i	−0.328075	+	0.281674i
$871$			5.20827i			0.176476i
$872$	−11.7461	+	7.32405i	−0.397772	+	0.248024i
$873$		−	15.6796i		−	0.530674i
$874$	−11.3150	−	13.1789i	−0.382735	−	0.445784i
$875$	−1.58122	+	1.58122i	−0.0534550	+	0.0534550i
$876$	19.0577	−	13.9975i	0.643900	−	0.472932i
$877$	−37.1063	−	37.1063i	−1.25299	−	1.25299i	−0.954373	−	0.298618i	$-0.903474\pi$
$877$	−37.1063	−	37.1063i	−1.25299	−	1.25299i	−0.298618	−	0.954373i	$-0.596526\pi$
$878$	27.2350	+	2.07253i	0.919138	+	0.0699446i
$879$	−19.3702			−0.653342
$880$	−1.19662	+	3.81682i	−0.0403380	+	0.128665i
$881$	−13.9209			−0.469007			−0.234503	−	0.972115i	$-0.575346\pi$
$881$	−13.9209			−0.469007			−0.234503	+	0.972115i	$0.575346\pi$
$882$	−2.97433	−	0.226341i	−0.100151	−	0.00762129i
$883$	12.2346	+	12.2346i	0.411727	+	0.411727i	0.882340	−	0.470613i	$-0.155967\pi$
$883$	12.2346	+	12.2346i	0.411727	+	0.411727i	−0.470613	+	0.882340i	$0.655967\pi$
$884$	−17.8087	−	24.2466i	−0.598971	−	0.815502i
$885$	−4.99295	+	4.99295i	−0.167836	+	0.167836i
$886$	−6.23006	−	7.25636i	−0.209303	−	0.243782i
$887$			50.4679i			1.69455i	0.531157	+	0.847274i	$0.321758\pi$
$887$			50.4679i			1.69455i	−0.531157	+	0.847274i	$0.678242\pi$
$888$	8.47102	−	36.5316i	0.284269	−	1.22592i
$889$			31.1765i			1.04563i
$890$	9.87205	−	8.47581i	0.330912	−	0.284110i
$891$	3.33932	−	3.33932i	0.111871	−	0.111871i
$892$	33.5588	+	5.13727i	1.12363	+	0.172008i
$893$	17.0200	+	17.0200i	0.569551	+	0.569551i
$894$	−2.06189	+	27.0952i	−0.0689600	+	0.906199i
$895$	20.4647			0.684058
$896$	−21.8073	−	12.8260i	−0.728531	−	0.428487i
$897$	−34.5329			−1.15302
$898$	−0.299181	+	3.93152i	−0.00998381	+	0.131197i
$899$	−1.51527	−	1.51527i	−0.0505372	−	0.0505372i
$900$	2.08550	+	0.319254i	0.0695166	+	0.0106418i
$901$	25.5029	−	25.5029i	0.849625	−	0.849625i
$902$	8.99104	−	7.71941i	0.299369	−	0.257028i
$903$			17.1259i			0.569914i
$904$	−12.9821	+	55.9859i	−0.431779	+	1.86206i
$905$		−	20.1181i		−	0.668748i
$906$	−20.8551	−	24.2906i	−0.692864	−	0.807001i
$907$	33.8169	−	33.8169i	1.12287	−	1.12287i	0.131565	−	0.991308i	$-0.458000\pi$
$907$	33.8169	−	33.8169i	1.12287	−	1.12287i	0.991308	−	0.131565i	$-0.0420003\pi$
$908$	−2.54725	−	3.46809i	−0.0845334	−	0.115093i
$909$	4.83091	+	4.83091i	0.160231	+	0.160231i
$910$	−13.8077	−	1.05074i	−0.457721	−	0.0348317i
$911$	−27.2981			−0.904426			−0.452213	−	0.891910i	$-0.649365\pi$
$911$	−27.2981			−0.904426			−0.452213	+	0.891910i	$0.649365\pi$
$912$	3.62495	−	11.5624i	0.120034	−	0.382868i
$913$	1.49358			0.0494301
$914$	−15.7730	−	1.20029i	−0.521724	−	0.0397022i
$915$	14.8313	+	14.8313i	0.490308	+	0.490308i
$916$	19.3957	−	14.2458i	0.640852	−	0.470693i
$917$	−16.0438	+	16.0438i	−0.529814	+	0.529814i
$918$	17.8968	+	20.8450i	0.590683	+	0.687987i
$919$		−	14.5011i		−	0.478347i	−0.970977	−	0.239174i	$-0.923124\pi$
$919$		−	14.5011i		−	0.478347i	0.970977	−	0.239174i	$-0.0768765\pi$
$920$	−13.5717	+	8.46240i	−0.447446	+	0.278997i
$921$			19.6649i			0.647981i
$922$	−32.7279	+	28.0990i	−1.07783	+	0.925393i
$923$	34.3867	−	34.3867i	1.13185	−	1.13185i
$924$	−0.943854	+	6.16565i	−0.0310505	+	0.202835i
$925$	−6.72218	−	6.72218i	−0.221024	−	0.221024i
$926$	−1.23140	+	16.1817i	−0.0404663	+	0.531764i
$927$	−17.8282			−0.585555
$928$	−33.6111	+	14.4345i	−1.10334	+	0.473836i
$929$	−35.2040			−1.15501			−0.577504	−	0.816388i	$-0.695973\pi$
$929$	−35.2040			−1.15501			−0.577504	+	0.816388i	$0.695973\pi$
$930$	0.0495963	−	0.651742i	0.00162633	−	0.0213715i
$931$	3.07098	+	3.07098i	0.100647	+	0.100647i
$932$	3.72259	−	24.3175i	0.121937	−	0.796546i
$933$	−23.1760	+	23.1760i	−0.758750	+	0.758750i
$934$	34.3299	−	29.4745i	1.12331	−	0.964435i
$935$			3.43520i			0.112343i
$936$	6.91271	+	11.0864i	0.225949	+	0.362369i
$937$		−	48.0707i		−	1.57040i	−0.619241	−	0.785201i	$-0.712560\pi$
$937$		−	48.0707i		−	1.57040i	0.619241	−	0.785201i	$-0.287440\pi$
$938$	2.45030	+	2.85395i	0.0800052	+	0.0931846i
$939$	24.8997	−	24.8997i	0.812571	−	0.812571i
$940$	17.8626	−	13.1197i	0.582614	−	0.427919i
$941$	−15.1547	−	15.1547i	−0.494029	−	0.494029i	0.415544	−	0.909573i	$-0.363591\pi$
$941$	−15.1547	−	15.1547i	−0.494029	−	0.494029i	−0.909573	+	0.415544i	$0.863591\pi$
$942$	−26.3331	−	2.00390i	−0.857980	−	0.0652906i
$943$	47.3828			1.54299
$944$	−17.9482	+	9.38037i	−0.584165	+	0.305305i
$945$	12.6462			0.411379
$946$	7.74347	+	0.589263i	0.251762	+	0.0191586i
$947$	−22.7684	−	22.7684i	−0.739874	−	0.739874i	0.232679	−	0.972554i	$-0.425251\pi$
$947$	−22.7684	−	22.7684i	−0.739874	−	0.739874i	−0.972554	+	0.232679i	$0.925251\pi$
$948$	−11.6631	−	15.8793i	−0.378799	−	0.515737i
$949$	26.2477	−	26.2477i	0.852037	−	0.852037i
$950$	−2.00100	−	2.33062i	−0.0649209	−	0.0756154i
$951$		−	2.08814i		−	0.0677127i
$952$	−21.1657	−	4.90794i	−0.685984	−	0.159067i
$953$			3.99510i			0.129414i	0.997904	+	0.0647070i	$0.0206113\pi$
$953$			3.99510i			0.129414i	−0.997904	+	0.0647070i	$0.979389\pi$
$954$	−11.8839	+	10.2031i	−0.384756	+	0.330339i
$955$	−14.9031	+	14.9031i	−0.482252	+	0.482252i
$956$	−25.2418	−	3.86409i	−0.816379	−	0.124973i
$957$	6.37704	+	6.37704i	0.206141	+	0.206141i
$958$	−2.09946	+	27.5888i	−0.0678304	+	0.891355i
$959$	−23.0093			−0.743010
$960$	−10.0187	−	4.91036i	−0.323353	−	0.158481i
$961$	−30.8902			−0.996457
$962$	4.46697	−	58.7002i	0.144021	−	1.89257i
$963$	11.7367	+	11.7367i	0.378209	+	0.378209i
$964$	−24.8988	−	3.81157i	−0.801935	−	0.122762i
$965$	4.34966	−	4.34966i	0.140021	−	0.140021i
$966$	−18.9228	+	16.2465i	−0.608831	+	0.522722i
$967$		−	10.4838i		−	0.337136i	−0.985690	−	0.168568i	$-0.946086\pi$
$967$		−	10.4838i		−	0.337136i	0.985690	−	0.168568i	$-0.0539143\pi$
$968$	2.75532	+	0.638910i	0.0885594	+	0.0205353i
$969$		−	10.4063i		−	0.334300i
$970$	13.6929	+	15.9486i	0.439654	+	0.512079i
$971$	5.16271	−	5.16271i	0.165679	−	0.165679i	−0.619398	−	0.785077i	$-0.712623\pi$
$971$	5.16271	−	5.16271i	0.165679	−	0.165679i	0.785077	+	0.619398i	$0.212623\pi$
$972$	−12.2885	−	16.7308i	−0.394153	−	0.536641i
$973$	−19.2610	−	19.2610i	−0.617479	−	0.617479i
$974$	25.3341	+	1.92787i	0.811756	+	0.0617731i
$975$	−6.10695			−0.195579
$976$	27.8639	+	53.3143i	0.891903	+	1.70655i
$977$	−44.2236			−1.41484			−0.707419	−	0.706794i	$-0.750141\pi$
$977$	−44.2236			−1.41484			−0.707419	+	0.706794i	$0.750141\pi$
$978$	−0.994841	−	0.0757055i	−0.0318115	−	0.00242080i
$979$	−6.50571	−	6.50571i	−0.207923	−	0.207923i
$980$	3.22302	−	2.36725i	0.102956	−	0.0756190i
$981$	3.65057	−	3.65057i	0.116554	−	0.116554i
$982$	−16.1634	−	18.8261i	−0.515796	−	0.600764i
$983$		−	10.4981i		−	0.334837i	−0.985886	−	0.167418i	$-0.946457\pi$
$983$		−	10.4981i		−	0.334837i	0.985886	−	0.167418i	$-0.0535431\pi$
$984$	17.4891	+	28.0485i	0.557533	+	0.894154i
$985$		−	0.821026i		−	0.0261601i
$986$	−23.8349	+	20.4639i	−0.759058	+	0.651702i
$987$	24.4379	−	24.4379i	0.777866	−	0.777866i
$988$	2.87841	−	18.8030i	0.0915746	−	0.598203i
$989$	21.9567	+	21.9567i	0.698183	+	0.698183i
$990$	0.113200	−	1.48755i	0.00359772	−	0.0472774i
$991$	−40.6060			−1.28989			−0.644946	−	0.764228i	$-0.723120\pi$
$991$	−40.6060			−1.28989			−0.644946	+	0.764228i	$0.723120\pi$
$992$	0.694922	−	1.74108i	0.0220638	−	0.0552794i
$993$	27.0135			0.857248
$994$	2.66498	−	35.0203i	0.0845281	−	1.11078i
$995$	−4.21821	−	4.21821i	−0.133726	−	0.133726i
$996$	−0.630412	+	4.11812i	−0.0199754	+	0.130488i
$997$	16.1946	−	16.1946i	0.512889	−	0.512889i	−0.402521	−	0.915411i	$-0.631866\pi$
$997$	16.1946	−	16.1946i	0.512889	−	0.512889i	0.915411	+	0.402521i	$0.131866\pi$
$998$	−5.05855	+	4.34310i	−0.160125	+	0.137478i
$999$			53.7621i			1.70096i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	880.2.w.a.221.19	✓	72
16.5	even	4	inner	880.2.w.a.661.19	yes	72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
880.2.w.a.221.19	✓	72	1.1	even	1	trivial
880.2.w.a.661.19	yes	72	16.5	even	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 880 = 2^{4} \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	880.w (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.107309 - 1.41014i) q^{2} +(-0.986180 - 0.986180i) q^{3} +(-1.97697 - 0.302640i) q^{4} +(-0.707107 + 0.707107i) q^{5} +(-1.49647 + 1.28482i) q^{6} +2.23618i q^{7} +(-0.638910 + 2.75532i) q^{8} -1.05490i q^{9} +(0.921238 + 1.07300i) q^{10} +(0.707107 - 0.707107i) q^{11} +(1.65119 + 2.24811i) q^{12} +(3.09627 + 3.09627i) q^{13} +(3.15332 + 0.239962i) q^{14} +1.39467 q^{15} +(3.81682 + 1.19662i) q^{16} +3.43520 q^{17} +(-1.48755 - 0.113200i) q^{18} +(1.53589 + 1.53589i) q^{19} +(1.61193 - 1.18393i) q^{20} +(2.20528 - 2.20528i) q^{21} +(-0.921238 - 1.07300i) q^{22} -5.65468i q^{23} +(3.34732 - 2.08716i) q^{24} -1.00000i q^{25} +(4.69841 - 4.03390i) q^{26} +(-3.99886 + 3.99886i) q^{27} +(0.676758 - 4.42087i) q^{28} +(-4.57244 - 4.57244i) q^{29} +(0.149660 - 1.96667i) q^{30} +0.331393 q^{31} +(2.09697 - 5.25383i) q^{32} -1.39467 q^{33} +(0.368627 - 4.84411i) q^{34} +(-1.58122 - 1.58122i) q^{35} +(-0.319254 + 2.08550i) q^{36} +(6.72218 - 6.72218i) q^{37} +(2.33062 - 2.00100i) q^{38} -6.10695i q^{39} +(-1.49653 - 2.40008i) q^{40} +8.37938i q^{41} +(-2.87310 - 3.34639i) q^{42} +(-3.88293 + 3.88293i) q^{43} +(-1.61193 + 1.18393i) q^{44} +(0.745924 + 0.745924i) q^{45} +(-7.97388 - 0.606797i) q^{46} +11.0815 q^{47} +(-2.58399 - 4.94415i) q^{48} +1.99948 q^{49} +(-1.41014 - 0.107309i) q^{50} +(-3.38773 - 3.38773i) q^{51} +(-5.18417 - 7.05828i) q^{52} +(7.42398 - 7.42398i) q^{53} +(5.20983 + 6.06805i) q^{54} +1.00000i q^{55} +(-6.16140 - 1.42872i) q^{56} -3.02932i q^{57} +(-6.93843 + 5.95710i) q^{58} +(-3.58002 + 3.58002i) q^{59} +(-2.75722 - 0.422083i) q^{60} +(10.6343 + 10.6343i) q^{61} +(0.0355613 - 0.467309i) q^{62} +2.35894 q^{63} +(-7.18359 - 3.52080i) q^{64} -4.37878 q^{65} +(-0.149660 + 1.96667i) q^{66} +(0.841057 + 0.841057i) q^{67} +(-6.79130 - 1.03963i) q^{68} +(-5.57654 + 5.57654i) q^{69} +(-2.39942 + 2.06006i) q^{70} -11.1058i q^{71} +(2.90658 + 0.673983i) q^{72} -8.47722i q^{73} +(-8.75784 - 10.2005i) q^{74} +(-0.986180 + 0.986180i) q^{75} +(-2.57158 - 3.50122i) q^{76} +(1.58122 + 1.58122i) q^{77} +(-8.61164 - 0.655329i) q^{78} -7.06343 q^{79} +(-3.54504 + 1.85276i) q^{80} +4.72250 q^{81} +(11.8161 + 0.899181i) q^{82} +(1.05612 + 1.05612i) q^{83} +(-5.02718 + 3.69237i) q^{84} +(-2.42906 + 2.42906i) q^{85} +(5.05879 + 5.89213i) q^{86} +9.01850i q^{87} +(1.49653 + 2.40008i) q^{88} -9.20046i q^{89} +(1.13190 - 0.971811i) q^{90} +(-6.92382 + 6.92382i) q^{91} +(-1.71133 + 11.1791i) q^{92} +(-0.326813 - 0.326813i) q^{93} +(1.18914 - 15.6265i) q^{94} -2.17207 q^{95} +(-7.24922 + 3.11323i) q^{96} +14.8636 q^{97} +(0.214562 - 2.81955i) q^{98} +(-0.745924 - 0.745924i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q + 12 q^{6} - 4 q^{10} + 12 q^{12} - 8 q^{14} + 8 q^{15} + 4 q^{16} + 56 q^{17} + 20 q^{18} + 8 q^{19} - 8 q^{20} + 4 q^{22} - 24 q^{24} - 24 q^{27} + 20 q^{28} - 20 q^{30} + 20 q^{32} - 8 q^{33} + 4 q^{34}+ \cdots - 60 q^{98}+O(q^{100}) \) 72 * q + 12 * q^6 - 4 * q^10 + 12 * q^12 - 8 * q^14 + 8 * q^15 + 4 * q^16 + 56 * q^17 + 20 * q^18 + 8 * q^19 - 8 * q^20 + 4 * q^22 - 24 * q^24 - 24 * q^27 + 20 * q^28 - 20 * q^30 + 20 * q^32 - 8 * q^33 + 4 * q^34 - 60 * q^36 + 12 * q^38 - 40 * q^42 + 8 * q^44 - 20 * q^46 + 40 * q^47 + 20 * q^48 - 24 * q^49 + 32 * q^51 - 84 * q^52 + 72 * q^54 + 8 * q^56 - 8 * q^58 + 32 * q^60 - 16 * q^61 - 96 * q^62 + 36 * q^64 - 40 * q^65 + 20 * q^66 - 76 * q^68 - 16 * q^69 + 24 * q^70 + 20 * q^72 + 56 * q^74 + 56 * q^76 - 132 * q^78 - 16 * q^79 + 56 * q^81 + 36 * q^82 - 40 * q^83 - 152 * q^84 + 16 * q^85 + 56 * q^86 - 36 * q^90 + 88 * q^91 + 80 * q^92 + 48 * q^93 - 76 * q^94 - 32 * q^96 - 64 * q^97 - 60 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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