LMFDB - Embedded newform 272.2.l.c.205.9

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [272,2,Mod(69,272)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(272, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([0, 1, 0])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("272.69"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 272 = 2^{4} \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	272.l (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [32] 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:	$2.17193093498$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			205.9
Character	$\chi$	$=$	272.205
Dual form			272.2.l.c.69.9

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.120143 + 1.40910i) q^{2} +(-0.775950 - 0.775950i) q^{3} +(-1.97113 + 0.338586i) q^{4} +(2.17252 - 2.17252i) q^{5} +(1.00017 - 1.18662i) q^{6} +4.50381i q^{7} +(-0.713919 - 2.73684i) q^{8} -1.79580i q^{9} +(3.32232 + 2.80029i) q^{10} +(3.11241 - 3.11241i) q^{11} +(1.79223 + 1.26677i) q^{12} +(4.85895 + 4.85895i) q^{13} +(-6.34633 + 0.541100i) q^{14} -3.37154 q^{15} +(3.77072 - 1.33480i) q^{16} +1.00000 q^{17} +(2.53047 - 0.215753i) q^{18} +(1.00902 + 1.00902i) q^{19} +(-3.54674 + 5.01792i) q^{20} +(3.49473 - 3.49473i) q^{21} +(4.75964 + 4.01177i) q^{22} +0.939859i q^{23} +(-1.56969 + 2.67762i) q^{24} -4.43972i q^{25} +(-6.26298 + 7.43051i) q^{26} +(-3.72130 + 3.72130i) q^{27} +(-1.52493 - 8.87761i) q^{28} +(-4.70389 - 4.70389i) q^{29} +(-0.405066 - 4.75084i) q^{30} -1.02653 q^{31} +(2.33389 + 5.15296i) q^{32} -4.83015 q^{33} +(0.120143 + 1.40910i) q^{34} +(9.78464 + 9.78464i) q^{35} +(0.608035 + 3.53976i) q^{36} +(0.570494 - 0.570494i) q^{37} +(-1.30059 + 1.54304i) q^{38} -7.54060i q^{39} +(-7.49687 - 4.39485i) q^{40} -9.73348i q^{41} +(5.34430 + 4.50457i) q^{42} +(-2.00067 + 2.00067i) q^{43} +(-5.08116 + 7.18880i) q^{44} +(-3.90143 - 3.90143i) q^{45} +(-1.32436 + 0.112917i) q^{46} -2.08234 q^{47} +(-3.96162 - 1.89015i) q^{48} -13.2843 q^{49} +(6.25601 - 0.533399i) q^{50} +(-0.775950 - 0.775950i) q^{51} +(-11.2228 - 7.93245i) q^{52} +(0.661257 - 0.661257i) q^{53} +(-5.69078 - 4.79660i) q^{54} -13.5236i q^{55} +(12.3262 - 3.21536i) q^{56} -1.56590i q^{57} +(6.06312 - 7.19339i) q^{58} +(-1.91578 + 1.91578i) q^{59} +(6.64575 - 1.14156i) q^{60} +(3.22968 + 3.22968i) q^{61} +(-0.123330 - 1.44648i) q^{62} +8.08797 q^{63} +(-6.98064 + 3.90777i) q^{64} +21.1124 q^{65} +(-0.580308 - 6.80618i) q^{66} +(-1.82638 - 1.82638i) q^{67} +(-1.97113 + 0.338586i) q^{68} +(0.729283 - 0.729283i) q^{69} +(-12.6120 + 14.9631i) q^{70} +0.725017i q^{71} +(-4.91484 + 1.28206i) q^{72} +5.81707i q^{73} +(0.872425 + 0.735344i) q^{74} +(-3.44500 + 3.44500i) q^{75} +(-2.33055 - 1.64727i) q^{76} +(14.0177 + 14.0177i) q^{77} +(10.6255 - 0.905948i) q^{78} +3.09100 q^{79} +(5.29210 - 11.0919i) q^{80} +0.387679 q^{81} +(13.7155 - 1.16941i) q^{82} +(-11.0125 - 11.0125i) q^{83} +(-5.70531 + 8.07185i) q^{84} +(2.17252 - 2.17252i) q^{85} +(-3.05952 - 2.57878i) q^{86} +7.29996i q^{87} +(-10.7402 - 6.29618i) q^{88} +8.88407i q^{89} +(5.02877 - 5.96623i) q^{90} +(-21.8838 + 21.8838i) q^{91} +(-0.318223 - 1.85259i) q^{92} +(0.796534 + 0.796534i) q^{93} +(-0.250178 - 2.93422i) q^{94} +4.38424 q^{95} +(2.18746 - 5.80942i) q^{96} -8.48221 q^{97} +(-1.59602 - 18.7190i) q^{98} +(-5.58928 - 5.58928i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 2 q^{4} - 16 q^{6} - 18 q^{8} - 6 q^{10} - 4 q^{11} + 2 q^{12} + 14 q^{14} + 24 q^{15} + 26 q^{16} + 32 q^{17} + 10 q^{18} - 14 q^{20} - 8 q^{22} - 50 q^{24} - 6 q^{26} + 12 q^{27} - 8 q^{29} + 36 q^{30}+ \cdots - 24 q^{99}+O(q^{100}) $ 32 * q - 2 * q^4 - 16 * q^6 - 18 * q^8 - 6 * q^10 - 4 * q^11 + 2 * q^12 + 14 * q^14 + 24 * q^15 + 26 * q^16 + 32 * q^17 + 10 * q^18 - 14 * q^20 - 8 * q^22 - 50 * q^24 - 6 * q^26 + 12 * q^27 - 8 * q^29 + 36 * q^30 - 24 * q^31 + 10 * q^32 + 12 * q^35 + 16 * q^36 - 8 * q^37 - 34 * q^38 - 38 * q^40 - 12 * q^42 - 12 * q^43 + 38 * q^44 - 40 * q^45 + 26 * q^46 + 32 * q^47 + 30 * q^48 - 32 * q^49 - 2 * q^50 - 54 * q^52 + 8 * q^53 - 52 * q^54 - 36 * q^56 - 26 * q^58 - 12 * q^59 + 28 * q^60 + 6 * q^62 - 40 * q^63 + 10 * q^64 + 28 * q^66 + 8 * q^67 - 2 * q^68 - 32 * q^70 - 32 * q^72 - 14 * q^74 + 8 * q^75 + 30 * q^76 + 56 * q^77 + 108 * q^78 + 48 * q^79 + 90 * q^80 - 64 * q^81 + 32 * q^82 + 4 * q^83 - 8 * q^84 - 54 * q^86 - 66 * q^88 - 66 * q^90 - 28 * q^91 + 24 * q^92 - 24 * q^93 + 12 * q^94 - 40 * q^95 + 70 * q^96 + 12 * q^98 - 24 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/272\mathbb{Z}\right)^\times$.

$n$	$69$	$239$	$241$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$1$	$1$

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 $

$2$	0.120143	+	1.40910i	0.0849537	+	0.996385i
$2$	0.120143	+	1.40910i	0.0849537	+	0.996385i
$3$	−0.775950	−	0.775950i	−0.447995	−	0.447995i	0.446693	−	0.894687i	$-0.352602\pi$
$3$	−0.775950	−	0.775950i	−0.447995	−	0.447995i	−0.894687	+	0.446693i	$0.852602\pi$
$4$	−1.97113	+	0.338586i	−0.985566	+	0.169293i
$5$	2.17252	−	2.17252i	0.971582	−	0.971582i	−0.0280252	−	0.999607i	$-0.508922\pi$
$5$	2.17252	−	2.17252i	0.971582	−	0.971582i	0.999607	+	0.0280252i	$0.00892188\pi$
$6$	1.00017	−	1.18662i	0.408317	−	0.484434i
$7$			4.50381i			1.70228i	0.524937	+	0.851141i	$0.324089\pi$
$7$			4.50381i			1.70228i	−0.524937	+	0.851141i	$0.675911\pi$
$8$	−0.713919	−	2.73684i	−0.252409	−	0.967621i
$9$		−	1.79580i		−	0.598601i
$10$	3.32232	+	2.80029i	1.05061	+	0.885530i
$11$	3.11241	−	3.11241i	0.938428	−	0.938428i	−0.0597832	−	0.998211i	$-0.519041\pi$
$11$	3.11241	−	3.11241i	0.938428	−	0.938428i	0.998211	+	0.0597832i	$0.0190409\pi$
$12$	1.79223	+	1.26677i	0.517371	+	0.365686i
$13$	4.85895	+	4.85895i	1.34763	+	1.34763i	0.888230	+	0.459400i	$0.151935\pi$
$13$	4.85895	+	4.85895i	1.34763	+	1.34763i	0.459400	+	0.888230i	$0.348065\pi$
$14$	−6.34633	+	0.541100i	−1.69613	+	0.144615i
$15$	−3.37154			−0.870527
$16$	3.77072	−	1.33480i	0.942680	−	0.333699i
$17$	1.00000			0.242536
$17$	1.00000			0.242536
$18$	2.53047	−	0.215753i	0.596437	−	0.0508534i
$19$	1.00902	+	1.00902i	0.231485	+	0.231485i	0.813312	−	0.581827i	$-0.197662\pi$
$19$	1.00902	+	1.00902i	0.231485	+	0.231485i	−0.581827	+	0.813312i	$0.697662\pi$
$20$	−3.54674	+	5.01792i	−0.793076	+	1.12204i
$21$	3.49473	−	3.49473i	0.762614	−	0.762614i
$22$	4.75964	+	4.01177i	1.01476	+	0.855313i
$23$			0.939859i			0.195974i	0.995188	+	0.0979871i	$0.0312404\pi$
$23$			0.939859i			0.195974i	−0.995188	+	0.0979871i	$0.968760\pi$
$24$	−1.56969	+	2.67762i	−0.320411	+	0.546567i
$25$		−	4.43972i		−	0.887943i
$26$	−6.26298	+	7.43051i	−1.22827	+	1.45724i
$27$	−3.72130	+	3.72130i	−0.716165	+	0.716165i
$28$	−1.52493	−	8.87761i	−0.288185	−	1.67771i
$29$	−4.70389	−	4.70389i	−0.873490	−	0.873490i	0.119361	−	0.992851i	$-0.461915\pi$
$29$	−4.70389	−	4.70389i	−0.873490	−	0.873490i	−0.992851	+	0.119361i	$0.961915\pi$
$30$	−0.405066	−	4.75084i	−0.0739545	−	0.867380i
$31$	−1.02653			−0.184370			−0.0921849	−	0.995742i	$-0.529385\pi$
$31$	−1.02653			−0.184370			−0.0921849	+	0.995742i	$0.529385\pi$
$32$	2.33389	+	5.15296i	0.412577	+	0.910923i
$33$	−4.83015			−0.840822
$34$	0.120143	+	1.40910i	0.0206043	+	0.241659i
$35$	9.78464	+	9.78464i	1.65391	+	1.65391i
$36$	0.608035	+	3.53976i	0.101339	+	0.589961i
$37$	0.570494	−	0.570494i	0.0937887	−	0.0937887i	−0.658656	−	0.752444i	$-0.728875\pi$
$37$	0.570494	−	0.570494i	0.0937887	−	0.0937887i	0.752444	+	0.658656i	$0.228875\pi$
$38$	−1.30059	+	1.54304i	−0.210983	+	0.250314i
$39$		−	7.54060i		−	1.20746i
$40$	−7.49687	−	4.39485i	−1.18536	−	0.694887i
$41$		−	9.73348i		−	1.52011i	−0.649857	−	0.760057i	$-0.725171\pi$
$41$		−	9.73348i		−	1.52011i	0.649857	−	0.760057i	$-0.274829\pi$
$42$	5.34430	+	4.50457i	0.824643	+	0.695070i
$43$	−2.00067	+	2.00067i	−0.305100	+	0.305100i	−0.843005	−	0.537905i	$-0.819216\pi$
$43$	−2.00067	+	2.00067i	−0.305100	+	0.305100i	0.537905	+	0.843005i	$0.319216\pi$
$44$	−5.08116	+	7.18880i	−0.766013	+	1.08375i
$45$	−3.90143	−	3.90143i	−0.581590	−	0.581590i
$46$	−1.32436	+	0.112917i	−0.195266	+	0.0166487i
$47$	−2.08234			−0.303740			−0.151870	−	0.988400i	$-0.548530\pi$
$47$	−2.08234			−0.303740			−0.151870	+	0.988400i	$0.548530\pi$
$48$	−3.96162	−	1.89015i	−0.571811	−	0.272820i
$49$	−13.2843			−1.89776
$50$	6.25601	−	0.533399i	0.884733	−	0.0754340i
$51$	−0.775950	−	0.775950i	−0.108655	−	0.108655i
$52$	−11.2228	−	7.93245i	−1.55632	−	1.10003i
$53$	0.661257	−	0.661257i	0.0908306	−	0.0908306i	−0.660232	−	0.751062i	$-0.729542\pi$
$53$	0.661257	−	0.661257i	0.0908306	−	0.0908306i	0.751062	+	0.660232i	$0.229542\pi$
$54$	−5.69078	−	4.79660i	−0.774417	−	0.652735i
$55$		−	13.5236i		−	1.82352i
$56$	12.3262	−	3.21536i	1.64716	−	0.429671i
$57$		−	1.56590i		−	0.207408i
$58$	6.06312	−	7.19339i	0.796126	−	0.944539i
$59$	−1.91578	+	1.91578i	−0.249413	+	0.249413i	−0.820730	−	0.571316i	$-0.806433\pi$
$59$	−1.91578	+	1.91578i	−0.249413	+	0.249413i	0.571316	+	0.820730i	$0.306433\pi$
$60$	6.64575	−	1.14156i	0.857962	−	0.147374i
$61$	3.22968	+	3.22968i	0.413518	+	0.413518i	0.882962	−	0.469444i	$-0.155546\pi$
$61$	3.22968	+	3.22968i	0.413518	+	0.413518i	−0.469444	+	0.882962i	$0.655546\pi$
$62$	−0.123330	−	1.44648i	−0.0156629	−	0.183703i
$63$	8.08797			1.01899
$64$	−6.98064	+	3.90777i	−0.872580	+	0.488472i
$65$	21.1124			2.61866
$66$	−0.580308	−	6.80618i	−0.0714309	−	0.837782i
$67$	−1.82638	−	1.82638i	−0.223128	−	0.223128i	0.586686	−	0.809814i	$-0.300432\pi$
$67$	−1.82638	−	1.82638i	−0.223128	−	0.223128i	−0.809814	+	0.586686i	$0.800432\pi$
$68$	−1.97113	+	0.338586i	−0.239035	+	0.0410596i
$69$	0.729283	−	0.729283i	0.0877954	−	0.0877954i
$70$	−12.6120	+	14.9631i	−1.50742	+	1.78843i
$71$			0.725017i			0.0860436i	0.999074	+	0.0430218i	$0.0136985\pi$
$71$			0.725017i			0.0860436i	−0.999074	+	0.0430218i	$0.986302\pi$
$72$	−4.91484	+	1.28206i	−0.579219	+	0.151092i
$73$			5.81707i			0.680836i	0.940274	+	0.340418i	$0.110569\pi$
$73$			5.81707i			0.680836i	−0.940274	+	0.340418i	$0.889431\pi$
$74$	0.872425	+	0.735344i	0.101417	+	0.0854820i
$75$	−3.44500	+	3.44500i	−0.397794	+	0.397794i
$76$	−2.33055	−	1.64727i	−0.267333	−	0.188955i
$77$	14.0177	+	14.0177i	1.59747	+	1.59747i
$78$	10.6255	−	0.905948i	1.20310	−	0.102578i
$79$	3.09100			0.347765			0.173882	−	0.984766i	$-0.444369\pi$
$79$	3.09100			0.347765			0.173882	+	0.984766i	$0.444369\pi$
$80$	5.29210	−	11.0919i	0.591675	−	1.24011i
$81$	0.387679			0.0430754
$82$	13.7155	−	1.16941i	1.51462	−	0.129139i
$83$	−11.0125	−	11.0125i	−1.20878	−	1.20878i	−0.971423	−	0.237355i	$-0.923720\pi$
$83$	−11.0125	−	11.0125i	−1.20878	−	1.20878i	−0.237355	−	0.971423i	$-0.576280\pi$
$84$	−5.70531	+	8.07185i	−0.622501	+	0.880711i
$85$	2.17252	−	2.17252i	0.235643	−	0.235643i
$86$	−3.05952	−	2.57878i	−0.329916	−	0.278077i
$87$			7.29996i			0.782638i
$88$	−10.7402	−	6.29618i	−1.14491	−	0.671175i
$89$			8.88407i			0.941710i	0.882211	+	0.470855i	$0.156054\pi$
$89$			8.88407i			0.941710i	−0.882211	+	0.470855i	$0.843946\pi$
$90$	5.02877	−	5.96623i	0.530079	−	0.628896i
$91$	−21.8838	+	21.8838i	−2.29404	+	2.29404i
$92$	−0.318223	−	1.85259i	−0.0331771	−	0.193145i
$93$	0.796534	+	0.796534i	0.0825967	+	0.0825967i
$94$	−0.250178	−	2.93422i	−0.0258038	−	0.302642i
$95$	4.38424			0.449814
$96$	2.18746	−	5.80942i	0.223256	−	0.592921i
$97$	−8.48221			−0.861238			−0.430619	−	0.902534i	$-0.641705\pi$
$97$	−8.48221			−0.861238			−0.430619	+	0.902534i	$0.641705\pi$
$98$	−1.59602	−	18.7190i	−0.161222	−	1.89090i
$99$	−5.58928	−	5.58928i	−0.561744	−	0.561744i
$100$	1.50323	+	8.75126i	0.150323	+	0.875126i
$101$	−10.5110	+	10.5110i	−1.04588	+	1.04588i	−0.0469840	+	0.998896i	$0.514961\pi$
$101$	−10.5110	+	10.5110i	−1.04588	+	1.04588i	−0.998896	+	0.0469840i	$0.985039\pi$
$102$	1.00017	−	1.18662i	0.0990313	−	0.117493i
$103$		−	7.03090i		−	0.692776i	−0.938091	−	0.346388i	$-0.887408\pi$
$103$		−	7.03090i		−	0.692776i	0.938091	−	0.346388i	$-0.112592\pi$
$104$	9.82929	−	16.7671i	0.963841	−	1.64415i
$105$		−	15.1848i		−	1.48188i
$106$	1.01122	+	0.852332i	0.0982186	+	0.0827858i
$107$	−3.92859	+	3.92859i	−0.379791	+	0.379791i	−0.871027	−	0.491236i	$-0.836545\pi$
$107$	−3.92859	+	3.92859i	−0.379791	+	0.379791i	0.491236	+	0.871027i	$0.336545\pi$
$108$	6.07520	−	8.59516i	0.584586	−	0.827070i
$109$	2.72340	+	2.72340i	0.260854	+	0.260854i	0.825401	−	0.564547i	$-0.190949\pi$
$109$	2.72340	+	2.72340i	0.260854	+	0.260854i	−0.564547	+	0.825401i	$0.690949\pi$
$110$	19.0561	−	1.62476i	1.81693	−	0.154915i
$111$	−0.885350			−0.0840337
$112$	6.01168	+	16.9826i	0.568050	+	1.60471i
$113$	−15.6610			−1.47327			−0.736634	−	0.676292i	$-0.763586\pi$
$113$	−15.6610			−1.47327			−0.736634	+	0.676292i	$0.763586\pi$
$114$	2.20651	−	0.188131i	0.206659	−	0.0176201i
$115$	2.04187	+	2.04187i	0.190405	+	0.190405i
$116$	10.8647	+	7.67931i	1.00876	+	0.713006i
$117$	8.72571	−	8.72571i	0.806693	−	0.806693i
$118$	−2.92969	−	2.46936i	−0.269700	−	0.227323i
$119$			4.50381i			0.412864i
$120$	2.40701	+	9.22738i	0.219729	+	0.842340i
$121$		−	8.37424i		−	0.761295i
$122$	−4.16292	+	4.93896i	−0.376893	+	0.447153i
$123$	−7.55269	+	7.55269i	−0.681003	+	0.681003i
$124$	2.02342	−	0.347568i	0.181709	−	0.0312125i
$125$	1.21723	+	1.21723i	0.108873	+	0.108873i
$126$	0.971710	+	11.3968i	0.0865668	+	1.01530i
$127$	−19.1546			−1.69970			−0.849850	−	0.527025i	$-0.823307\pi$
$127$	−19.1546			−1.69970			−0.849850	+	0.527025i	$0.823307\pi$
$128$	−6.34512	−	9.36693i	−0.560835	−	0.827928i
$129$	3.10484			0.273366
$130$	2.53649	+	29.7494i	0.222465	+	2.60920i
$131$	6.80811	+	6.80811i	0.594827	+	0.594827i	0.938931	−	0.344104i	$-0.111817\pi$
$131$	6.80811	+	6.80811i	0.594827	+	0.594827i	−0.344104	+	0.938931i	$0.611817\pi$
$132$	9.52087	−	1.63542i	0.828685	−	0.142345i
$133$	−4.54444	+	4.54444i	−0.394053	+	0.394053i
$134$	2.35413	−	2.79298i	0.203366	−	0.241277i
$135$			16.1692i			1.39163i
$136$	−0.713919	−	2.73684i	−0.0612181	−	0.234683i
$137$			1.88541i			0.161082i	0.996751	+	0.0805409i	$0.0256648\pi$
$137$			1.88541i			0.161082i	−0.996751	+	0.0805409i	$0.974335\pi$
$138$	1.11525	+	0.940016i	0.0949366	+	0.0800195i
$139$	13.2412	−	13.2412i	1.12310	−	1.12310i	0.131828	−	0.991273i	$-0.457915\pi$
$139$	13.2412	−	13.2412i	1.12310	−	1.12310i	0.991273	−	0.131828i	$-0.0420846\pi$
$140$	−22.5998	−	15.9739i	−1.91003	−	1.35004i
$141$	1.61579	+	1.61579i	0.136074	+	0.136074i
$142$	−1.02162	+	0.0871054i	−0.0857326	+	0.00730972i
$143$	30.2461			2.52931
$144$	−2.39703	−	6.77147i	−0.199753	−	0.564289i
$145$	−20.4386			−1.69733
$146$	−8.19684	+	0.698878i	−0.678375	+	0.0578396i
$147$	10.3080	+	10.3080i	0.850188	+	0.850188i
$148$	−0.931358	+	1.31768i	−0.0765571	+	0.108313i
$149$	−1.94257	+	1.94257i	−0.159142	+	0.159142i	−0.782186	−	0.623045i	$-0.785896\pi$
$149$	−1.94257	+	1.94257i	−0.159142	+	0.159142i	0.623045	+	0.782186i	$0.285896\pi$
$150$	−5.26824	−	4.44046i	−0.430150	−	0.362562i
$151$		−	1.56410i		−	0.127284i	−0.997973	−	0.0636422i	$-0.979728\pi$
$151$		−	1.56410i		−	0.127284i	0.997973	−	0.0636422i	$-0.0202716\pi$
$152$	2.04117	−	3.48189i	0.165561	−	0.282419i
$153$		−	1.79580i		−	0.145182i
$154$	−18.0683	+	21.4365i	−1.45598	+	1.72741i
$155$	−2.23016	+	2.23016i	−0.179130	+	0.179130i
$156$	2.55314	+	14.8635i	0.204415	+	1.19003i
$157$	11.6821	+	11.6821i	0.932334	+	0.932334i	0.997851	−	0.0655178i	$-0.0208699\pi$
$157$	11.6821	+	11.6821i	0.932334	+	0.932334i	−0.0655178	+	0.997851i	$0.520870\pi$
$158$	0.371361	+	4.35553i	0.0295439	+	0.346507i
$159$	−1.02620			−0.0813833
$160$	16.2653	+	6.12450i	1.28589	+	0.484184i
$161$	−4.23295			−0.333603
$162$	0.0465768	+	0.546279i	0.00365942	+	0.0429197i
$163$	4.63417	+	4.63417i	0.362977	+	0.362977i	0.864908	−	0.501931i	$-0.167377\pi$
$163$	4.63417	+	4.63417i	0.362977	+	0.362977i	−0.501931	+	0.864908i	$0.667377\pi$
$164$	3.29562	+	19.1860i	0.257345	+	1.49817i
$165$	−10.4936	+	10.4936i	−0.816928	+	0.816928i
$166$	14.1946	−	16.8408i	1.10172	−	1.30710i
$167$		−	18.7666i		−	1.45220i	−0.687587	−	0.726102i	$-0.741330\pi$
$167$		−	18.7666i		−	1.45220i	0.687587	−	0.726102i	$-0.258670\pi$
$168$	−12.0595	−	7.06959i	−0.930411	−	0.545430i
$169$			34.2187i			2.63221i
$170$	3.32232	+	2.80029i	0.254810	+	0.214773i
$171$	1.81200	−	1.81200i	0.138567	−	0.138567i
$172$	3.26619	−	4.62099i	0.249045	−	0.352347i
$173$	8.50653	+	8.50653i	0.646740	+	0.646740i	0.952204	−	0.305464i	$-0.0988115\pi$
$173$	8.50653	+	8.50653i	0.646740	+	0.646740i	−0.305464	+	0.952204i	$0.598812\pi$
$174$	−10.2864	+	0.877037i	−0.779809	+	0.0664880i
$175$	19.9957			1.51153
$176$	7.58160	−	15.8905i	0.571485	−	1.19779i
$177$	2.97310			0.223472
$178$	−12.5186	+	1.06736i	−0.938305	+	0.0800017i
$179$	12.2237	+	12.2237i	0.913639	+	0.913639i	0.996556	−	0.0829177i	$-0.0264239\pi$
$179$	12.2237	+	12.2237i	0.913639	+	0.913639i	−0.0829177	+	0.996556i	$0.526424\pi$
$180$	9.01119	+	6.36925i	0.671655	+	0.474736i
$181$	16.0857	−	16.0857i	1.19564	−	1.19564i	0.220182	−	0.975459i	$-0.429335\pi$
$181$	16.0857	−	16.0857i	1.19564	−	1.19564i	0.975459	−	0.220182i	$-0.0706650\pi$
$182$	−33.4657	−	28.2073i	−2.48064	−	2.09086i
$183$		−	5.01213i		−	0.370508i
$184$	2.57225	−	0.670983i	0.189629	−	0.0494656i
$185$		−	2.47882i		−	0.182247i
$186$	−1.02670	+	1.21809i	−0.0752812	+	0.0893150i
$187$	3.11241	−	3.11241i	0.227602	−	0.227602i
$188$	4.10456	−	0.705051i	0.299356	−	0.0514211i
$189$	−16.7601	−	16.7601i	−1.21911	−	1.21911i
$190$	0.526734	+	6.17784i	0.0382133	+	0.448188i
$191$	−18.3240			−1.32587			−0.662937	−	0.748675i	$-0.730690\pi$
$191$	−18.3240			−1.32587			−0.662937	+	0.748675i	$0.730690\pi$
$192$	8.44886	+	2.38439i	0.609744	+	0.172078i
$193$	6.38959			0.459933			0.229966	−	0.973199i	$-0.426138\pi$
$193$	6.38959			0.459933			0.229966	+	0.973199i	$0.426138\pi$
$194$	−1.01908	−	11.9523i	−0.0731653	−	0.858124i
$195$	−16.3821	−	16.3821i	−1.17315	−	1.17315i
$196$	26.1852	−	4.49790i	1.87037	−	0.321278i
$197$	5.92635	−	5.92635i	0.422235	−	0.422235i	−0.463738	−	0.885973i	$-0.653492\pi$
$197$	5.92635	−	5.92635i	0.422235	−	0.422235i	0.885973	+	0.463738i	$0.153492\pi$
$198$	7.20436	−	8.54738i	0.511991	−	0.607436i
$199$		−	16.1748i		−	1.14660i	−0.819345	−	0.573301i	$-0.805663\pi$
$199$		−	16.1748i		−	1.14660i	0.819345	−	0.573301i	$-0.194337\pi$
$200$	−12.1508	+	3.16960i	−0.859192	+	0.224124i
$201$			2.83436i			0.199920i
$202$	−16.0738	−	13.5482i	−1.13095	−	0.953247i
$203$	21.1854	−	21.1854i	1.48693	−	1.48693i
$204$	1.79223	+	1.26677i	0.125481	+	0.0886919i
$205$	−21.1462	−	21.1462i	−1.47692	−	1.47692i
$206$	9.90726	−	0.844712i	0.690271	−	0.0588539i
$207$	1.68780			0.117310
$208$	24.8074	+	11.8360i	1.72009	+	0.820680i
$209$	6.28098			0.434464
$210$	21.3969	−	1.82434i	1.47653	−	0.125891i
$211$	−6.39257	−	6.39257i	−0.440083	−	0.440083i	0.451957	−	0.892040i	$-0.350726\pi$
$211$	−6.39257	−	6.39257i	−0.440083	−	0.440083i	−0.892040	+	0.451957i	$0.850726\pi$
$212$	−1.07953	+	1.52732i	−0.0741425	+	0.104897i
$213$	0.562576	−	0.562576i	0.0385471	−	0.0385471i
$214$	−6.00777	−	5.06379i	−0.410683	−	0.346153i
$215$			8.69302i			0.592859i
$216$	12.8413	+	7.52792i	0.873742	+	0.512210i
$217$		−	4.62329i		−	0.313849i
$218$	−3.51034	+	4.16474i	−0.237751	+	0.282072i
$219$	4.51375	−	4.51375i	0.305011	−	0.305011i
$220$	4.57890	+	26.6568i	0.308709	+	1.79720i
$221$	4.85895	+	4.85895i	0.326848	+	0.326848i
$222$	−0.106368	−	1.24755i	−0.00713898	−	0.0837299i
$223$	−12.4925			−0.836561			−0.418280	−	0.908318i	$-0.637367\pi$
$223$	−12.4925			−0.836561			−0.418280	+	0.908318i	$0.637367\pi$
$224$	−23.2080	+	10.5114i	−1.55065	+	0.702322i
$225$	−7.97286			−0.531524
$226$	−1.88156	−	22.0680i	−0.125159	−	1.46794i
$227$	−9.27733	−	9.27733i	−0.615758	−	0.615758i	0.328682	−	0.944441i	$-0.393395\pi$
$227$	−9.27733	−	9.27733i	−0.615758	−	0.615758i	−0.944441	+	0.328682i	$0.893395\pi$
$228$	0.530192	+	3.08659i	0.0351128	+	0.204415i
$229$	9.25164	−	9.25164i	0.611366	−	0.611366i	−0.331936	−	0.943302i	$-0.607702\pi$
$229$	9.25164	−	9.25164i	0.611366	−	0.611366i	0.943302	+	0.331936i	$0.107702\pi$
$230$	−2.63188	+	3.12251i	−0.173541	+	0.205892i
$231$		−	21.7541i		−	1.43132i
$232$	−9.51561	+	16.2320i	−0.624731	+	1.06568i
$233$		−	6.11785i		−	0.400794i	−0.979715	−	0.200397i	$-0.935777\pi$
$233$		−	6.11785i		−	0.400794i	0.979715	−	0.200397i	$-0.0642232\pi$
$234$	13.3437	+	11.2471i	0.872308	+	0.735245i
$235$	−4.52393	+	4.52393i	−0.295108	+	0.295108i
$236$	3.12760	−	4.42491i	0.203589	−	0.288037i
$237$	−2.39846	−	2.39846i	−0.155797	−	0.155797i
$238$	−6.34633	+	0.541100i	−0.411371	+	0.0350743i
$239$	−2.09725			−0.135660			−0.0678298	−	0.997697i	$-0.521607\pi$
$239$	−2.09725			−0.135660			−0.0678298	+	0.997697i	$0.521607\pi$
$240$	−12.7131	+	4.50032i	−0.820629	+	0.290494i
$241$	−12.2668			−0.790171			−0.395086	−	0.918644i	$-0.629285\pi$
$241$	−12.2668			−0.790171			−0.395086	+	0.918644i	$0.629285\pi$
$242$	11.8002	−	1.00610i	0.758543	−	0.0646748i
$243$	10.8631	+	10.8631i	0.696868	+	0.696868i
$244$	−7.45964	−	5.27259i	−0.477555	−	0.337543i
$245$	−28.8605	+	28.8605i	−1.84383	+	1.84383i
$246$	−11.5499	−	9.73510i	−0.736395	−	0.620687i
$247$			9.80555i			0.623912i
$248$	0.732858	+	2.80945i	0.0465365	+	0.178400i
$249$			17.0903i			1.08305i
$250$	−1.56896	+	1.86144i	−0.0992298	+	0.117728i
$251$	−5.62543	+	5.62543i	−0.355074	+	0.355074i	−0.861993	−	0.506920i	$-0.830784\pi$
$251$	−5.62543	+	5.62543i	−0.355074	+	0.355074i	0.506920	+	0.861993i	$0.330784\pi$
$252$	−15.9424	+	2.73847i	−1.00428	+	0.172508i
$253$	2.92523	+	2.92523i	0.183908	+	0.183908i
$254$	−2.30129	−	26.9908i	−0.144396	−	1.69355i
$255$	−3.37154			−0.211134
$256$	12.4366	−	10.0663i	0.777290	−	0.629143i
$257$	0.782280			0.0487973			0.0243986	−	0.999702i	$-0.492233\pi$
$257$	0.782280			0.0487973			0.0243986	+	0.999702i	$0.492233\pi$
$258$	0.373024	+	4.37504i	0.0232235	+	0.272378i
$259$	2.56940	+	2.56940i	0.159655	+	0.159655i
$260$	−41.6152	+	7.14835i	−2.58087	+	0.443322i
$261$	−8.44726	+	8.44726i	−0.522872	+	0.522872i
$262$	−8.77536	+	10.4113i	−0.542144	+	0.643209i
$263$			7.87124i			0.485362i	0.970106	+	0.242681i	$0.0780268\pi$
$263$			7.87124i			0.485362i	−0.970106	+	0.242681i	$0.921973\pi$
$264$	3.44834	+	13.2194i	0.212231	+	0.813597i
$265$		−	2.87319i		−	0.176499i
$266$	−6.94956	−	5.85760i	−0.426105	−	0.359152i
$267$	6.89359	−	6.89359i	0.421881	−	0.421881i
$268$	4.21842	+	2.98165i	0.257681	+	0.182133i
$269$	−10.5926	−	10.5926i	−0.645841	−	0.645841i	0.306144	−	0.951985i	$-0.400961\pi$
$269$	−10.5926	−	10.5926i	−0.645841	−	0.645841i	−0.951985	+	0.306144i	$0.900961\pi$
$270$	−22.7841	+	1.94262i	−1.38660	+	0.118224i
$271$	−13.0932			−0.795357			−0.397679	−	0.917525i	$-0.630184\pi$
$271$	−13.0932			−0.795357			−0.397679	+	0.917525i	$0.630184\pi$
$272$	3.77072	−	1.33480i	0.228633	−	0.0809339i
$273$	33.9615			2.05544
$274$	−2.65674	+	0.226519i	−0.160500	+	0.0136845i
$275$	−13.8182	−	13.8182i	−0.833271	−	0.833271i
$276$	−1.19059	+	1.68444i	−0.0716650	+	0.101391i
$277$	3.63859	−	3.63859i	0.218621	−	0.218621i	−0.589296	−	0.807917i	$-0.700595\pi$
$277$	3.63859	−	3.63859i	0.218621	−	0.218621i	0.807917	+	0.589296i	$0.200595\pi$
$278$	20.2490	+	17.0673i	1.21445	+	1.02363i
$279$			1.84344i			0.110364i
$280$	19.7936	−	33.7645i	1.18289	−	2.01781i
$281$		−	11.0862i		−	0.661350i	−0.943745	−	0.330675i	$-0.892724\pi$
$281$		−	11.0862i		−	0.661350i	0.943745	−	0.330675i	$-0.107276\pi$
$282$	−2.08269	+	2.47094i	−0.124022	+	0.147142i
$283$	16.9873	−	16.9873i	1.00979	−	1.00979i	0.00984067	−	0.999952i	$-0.496868\pi$
$283$	16.9873	−	16.9873i	1.00979	−	1.00979i	0.999952	−	0.00984067i	$-0.00313243\pi$
$284$	−0.245481	−	1.42910i	−0.0145666	−	0.0848017i
$285$	−3.40195	−	3.40195i	−0.201514	−	0.201514i
$286$	3.63385	+	42.6198i	0.214874	+	2.52016i
$287$	43.8378			2.58766
$288$	9.25370	−	4.19120i	0.545279	−	0.246969i
$289$	1.00000			0.0588235
$290$	−2.45555	−	28.8001i	−0.144195	−	1.69120i
$291$	6.58177	+	6.58177i	0.385830	+	0.385830i
$292$	−1.96958	−	11.4662i	−0.115261	−	0.671009i
$293$	−2.26510	+	2.26510i	−0.132328	+	0.132328i	−0.770169	−	0.637840i	$-0.779828\pi$
$293$	−2.26510	+	2.26510i	−0.132328	+	0.132328i	0.637840	+	0.770169i	$0.279828\pi$
$294$	−13.2866	+	15.7634i	−0.774888	+	0.919341i
$295$			8.32415i			0.484651i
$296$	−1.96864	−	1.15407i	−0.114425	−	0.0670788i
$297$			23.1645i			1.34414i
$298$	−2.97067	−	2.50390i	−0.172086	−	0.145047i
$299$	−4.56672	+	4.56672i	−0.264100	+	0.264100i
$300$	5.62411	−	7.95697i	0.324708	−	0.459396i
$301$	−9.01066	−	9.01066i	−0.519366	−	0.519366i
$302$	2.20397	−	0.187915i	0.126824	−	0.0108133i
$303$	16.3120			0.937097
$304$	5.15157	+	2.45790i	0.295463	+	0.140970i
$305$	14.0331			0.803533
$306$	2.53047	−	0.215753i	0.144657	−	0.0123338i
$307$	−15.6190	−	15.6190i	−0.891425	−	0.891425i	0.103232	−	0.994657i	$-0.467082\pi$
$307$	−15.6190	−	15.6190i	−0.891425	−	0.891425i	−0.994657	+	0.103232i	$0.967082\pi$
$308$	−32.3770	−	22.8846i	−1.84485	−	1.30397i
$309$	−5.45563	+	5.45563i	−0.310360	+	0.310360i
$310$	−3.41045	−	2.87458i	−0.193701	−	0.163265i
$311$		−	14.2111i		−	0.805840i	−0.915235	−	0.402920i	$-0.867995\pi$
$311$		−	14.2111i		−	0.805840i	0.915235	−	0.402920i	$-0.132005\pi$
$312$	−20.6374	+	5.38338i	−1.16837	+	0.304774i
$313$			31.7081i			1.79225i	0.443806	+	0.896123i	$0.353628\pi$
$313$			31.7081i			1.79225i	−0.443806	+	0.896123i	$0.646372\pi$
$314$	−15.0577	+	17.8648i	−0.849758	+	1.00817i
$315$	17.5713	−	17.5713i	0.990030	−	0.990030i
$316$	−6.09277	+	1.04657i	−0.342745	+	0.0588742i
$317$	−4.67464	−	4.67464i	−0.262554	−	0.262554i	0.563537	−	0.826091i	$-0.309440\pi$
$317$	−4.67464	−	4.67464i	−0.262554	−	0.262554i	−0.826091	+	0.563537i	$0.809440\pi$
$318$	−0.123291	−	1.44603i	−0.00691381	−	0.0810891i
$319$	−29.2809			−1.63942
$320$	−6.67587	+	23.6553i	−0.373193	+	1.32237i
$321$	6.09677			0.340289
$322$	−0.508558	−	5.96465i	−0.0283408	−	0.332397i
$323$	1.00902	+	1.00902i	0.0561434	+	0.0561434i
$324$	−0.764166	+	0.131263i	−0.0424537	+	0.00729238i
$325$	21.5723	−	21.5723i	1.19662	−	1.19662i
$326$	−5.97326	+	7.08678i	−0.330828	+	0.392501i
$327$		−	4.22644i		−	0.233723i
$328$	−26.6390	+	6.94892i	−1.47089	+	0.383690i
$329$		−	9.37846i		−	0.517051i
$330$	−16.0473	−	13.5258i	−0.883375	−	0.744573i
$331$	11.2617	−	11.2617i	0.618999	−	0.618999i	−0.326275	−	0.945275i	$-0.605794\pi$
$331$	11.2617	−	11.2617i	0.618999	−	0.618999i	0.945275	+	0.326275i	$0.105794\pi$
$332$	25.4357	+	17.9784i	1.39597	+	0.986692i
$333$	−1.02450	−	1.02450i	−0.0561420	−	0.0561420i
$334$	26.4440	−	2.25467i	1.44695	−	0.123370i
$335$	−7.93570			−0.433574
$336$	8.51290	−	17.8424i	0.464417	−	0.973384i
$337$	−2.09201			−0.113959			−0.0569795	−	0.998375i	$-0.518147\pi$
$337$	−2.09201			−0.113959			−0.0569795	+	0.998375i	$0.518147\pi$
$338$	−48.2176	+	4.11113i	−2.62269	+	0.223616i
$339$	12.1522	+	12.1522i	0.660016	+	0.660016i
$340$	−3.54674	+	5.01792i	−0.192349	+	0.272135i
$341$	−3.19498	+	3.19498i	−0.173018	+	0.173018i
$342$	2.77099	+	2.33560i	0.149838	+	0.126295i
$343$		−	28.3035i		−	1.52825i
$344$	6.90385	+	4.04721i	0.372231	+	0.218211i
$345$		−	3.16877i		−	0.170601i
$346$	−10.9646	+	13.0086i	−0.589459	+	0.699345i
$347$	−2.84506	+	2.84506i	−0.152731	+	0.152731i	−0.779337	−	0.626606i	$-0.784444\pi$
$347$	−2.84506	+	2.84506i	−0.152731	+	0.152731i	0.626606	+	0.779337i	$0.284444\pi$
$348$	−2.47167	−	14.3892i	−0.132495	−	0.771341i
$349$	21.8320	+	21.8320i	1.16864	+	1.16864i	0.982529	+	0.186110i	$0.0595880\pi$
$349$	21.8320	+	21.8320i	1.16864	+	1.16864i	0.186110	+	0.982529i	$0.440412\pi$
$350$	2.40233	+	28.1759i	0.128410	+	1.50607i
$351$	−36.1632			−1.93025
$352$	23.3022	+	8.77411i	1.24201	+	0.467662i
$353$	−23.5766			−1.25485			−0.627427	−	0.778675i	$-0.715892\pi$
$353$	−23.5766			−1.25485			−0.627427	+	0.778675i	$0.715892\pi$
$354$	0.357196	+	4.18940i	0.0189848	+	0.222664i
$355$	1.57512	+	1.57512i	0.0835984	+	0.0835984i
$356$	−3.00803	−	17.5117i	−0.159425	−	0.928117i
$357$	3.49473	−	3.49473i	0.184961	−	0.184961i
$358$	−15.7558	+	18.6929i	−0.832719	+	0.987953i
$359$			30.9516i			1.63356i	0.576947	+	0.816782i	$0.304244\pi$
$359$			30.9516i			1.63356i	−0.576947	+	0.816782i	$0.695756\pi$
$360$	−7.89229	+	13.4629i	−0.415960	+	0.709557i
$361$		−	16.9638i		−	0.892829i
$362$	24.5990	+	20.7338i	1.29289	+	1.08974i
$363$	−6.49799	+	6.49799i	−0.341056	+	0.341056i
$364$	35.7263	−	50.5454i	1.87257	−	2.64930i
$365$	12.6377	+	12.6377i	0.661488	+	0.661488i
$366$	7.06260	−	0.602171i	0.369168	−	0.0314760i
$367$	31.9582			1.66821			0.834103	−	0.551608i	$-0.185986\pi$
$367$	31.9582			1.66821			0.834103	+	0.551608i	$0.185986\pi$
$368$	1.25452	+	3.54394i	0.0653964	+	0.184741i
$369$	−17.4794			−0.909942
$370$	3.49291	−	0.297813i	0.181588	−	0.0154825i
$371$	2.97818	+	2.97818i	0.154619	+	0.154619i
$372$	−1.83977	−	1.30038i	−0.0953876	−	0.0674214i
$373$	11.5111	−	11.5111i	0.596023	−	0.596023i	−0.343229	−	0.939252i	$-0.611521\pi$
$373$	11.5111	−	11.5111i	0.596023	−	0.596023i	0.939252	+	0.343229i	$0.111521\pi$
$374$	4.75964	+	4.01177i	0.246115	+	0.207444i
$375$		−	1.88902i		−	0.0975487i
$376$	1.48662	+	5.69903i	0.0766666	+	0.293905i
$377$		−	45.7119i		−	2.35428i
$378$	21.6030	−	25.6302i	1.11114	−	1.31828i
$379$	−20.9191	+	20.9191i	−1.07454	+	1.07454i	−0.0775525	+	0.996988i	$0.524711\pi$
$379$	−20.9191	+	20.9191i	−1.07454	+	1.07454i	−0.996988	+	0.0775525i	$0.975289\pi$
$380$	−8.64192	+	1.48444i	−0.443321	+	0.0761504i
$381$	14.8630	+	14.8630i	0.761457	+	0.761457i
$382$	−2.20149	−	25.8203i	−0.112638	−	1.32108i
$383$	17.4399			0.891139			0.445569	−	0.895247i	$-0.353001\pi$
$383$	17.4399			0.891139			0.445569	+	0.895247i	$0.353001\pi$
$384$	−2.34478	+	12.1918i	−0.119656	+	0.622158i
$385$	60.9077			3.10414
$386$	0.767663	+	9.00358i	0.0390730	+	0.458270i
$387$	3.59282	+	3.59282i	0.182633	+	0.182633i
$388$	16.7196	−	2.87196i	0.848807	−	0.145802i
$389$	−19.1820	+	19.1820i	−0.972568	+	0.972568i	−0.999634	−	0.0270661i	$-0.991384\pi$
$389$	−19.1820	+	19.1820i	−0.972568	+	0.972568i	0.0270661	+	0.999634i	$0.491384\pi$
$390$	21.1159	−	25.0523i	1.06924	−	1.26857i
$391$			0.939859i			0.0475307i
$392$	9.48395	+	36.3572i	0.479012	+	1.83632i
$393$		−	10.5655i		−	0.532959i
$394$	9.06283	+	7.63882i	0.456579	+	0.384838i
$395$	6.71527	−	6.71527i	0.337882	−	0.337882i
$396$	12.9097	+	9.12476i	0.648735	+	0.458536i
$397$	−3.42843	−	3.42843i	−0.172068	−	0.172068i	0.615819	−	0.787887i	$-0.288825\pi$
$397$	−3.42843	−	3.42843i	−0.172068	−	0.172068i	−0.787887	+	0.615819i	$0.788825\pi$
$398$	22.7919	−	1.94328i	1.14246	−	0.0974081i
$399$	7.05252			0.353067
$400$	−5.92612	−	16.7409i	−0.296306	−	0.837046i
$401$	9.82099			0.490437			0.245219	−	0.969468i	$-0.421140\pi$
$401$	9.82099			0.490437			0.245219	+	0.969468i	$0.421140\pi$
$402$	−3.99389	+	0.340527i	−0.199197	+	0.0169840i
$403$	−4.98784	−	4.98784i	−0.248462	−	0.248462i
$404$	17.1596	−	24.2774i	0.853723	−	1.20784i
$405$	0.842241	−	0.842241i	0.0418513	−	0.0418513i
$406$	32.3977	+	27.3071i	1.60787	+	1.35523i
$407$		−	3.55123i		−	0.176028i
$408$	−1.56969	+	2.67762i	−0.0777112	+	0.132562i
$409$			2.99721i			0.148203i	0.997251	+	0.0741013i	$0.0236088\pi$
$409$			2.99721i			0.148203i	−0.997251	+	0.0741013i	$0.976391\pi$
$410$	27.2566	−	32.3377i	1.34611	−	1.59705i
$411$	1.46299	−	1.46299i	0.0721638	−	0.0721638i
$412$	2.38057	+	13.8588i	0.117282	+	0.682776i
$413$	−8.62832	−	8.62832i	−0.424572	−	0.424572i
$414$	0.202777	+	2.37828i	0.00996595	+	0.116886i
$415$	−47.8498			−2.34885
$416$	−13.6977	+	36.3782i	−0.671586	+	1.78359i
$417$	−20.5489			−1.00629
$418$	0.754614	+	8.85053i	0.0369094	+	0.432894i
$419$	−14.0747	−	14.0747i	−0.687593	−	0.687593i	0.274106	−	0.961699i	$-0.411618\pi$
$419$	−14.0747	−	14.0747i	−0.687593	−	0.687593i	−0.961699	+	0.274106i	$0.911618\pi$
$420$	5.14136	+	29.9312i	0.250873	+	1.46049i
$421$	−23.4032	+	23.4032i	−1.14060	+	1.14060i	−0.152263	+	0.988340i	$0.548656\pi$
$421$	−23.4032	+	23.4032i	−1.14060	+	1.14060i	−0.988340	+	0.152263i	$0.951344\pi$
$422$	8.23976	−	9.77580i	0.401105	−	0.475878i
$423$			3.73947i			0.181819i
$424$	−2.28184	−	1.33767i	−0.110816	−	0.0649631i
$425$		−	4.43972i		−	0.215358i
$426$	0.860317	+	0.725138i	0.0416825	+	0.0351330i
$427$	−14.5459	+	14.5459i	−0.703924	+	0.703924i
$428$	6.41360	−	9.07393i	0.310013	−	0.438605i
$429$	−23.4695	−	23.4695i	−1.13312	−	1.13312i
$430$	−12.2493	+	1.04440i	−0.590716	+	0.0503656i
$431$	13.9766			0.673228			0.336614	−	0.941643i	$-0.390718\pi$
$431$	13.9766			0.673228			0.336614	+	0.941643i	$0.390718\pi$
$432$	−9.06481	+	18.9992i	−0.436131	+	0.914098i
$433$	5.72126			0.274946			0.137473	−	0.990506i	$-0.456102\pi$
$433$	5.72126			0.274946			0.137473	+	0.990506i	$0.456102\pi$
$434$	6.51468	−	0.555454i	0.312715	−	0.0266627i
$435$	15.8593	+	15.8593i	0.760397	+	0.760397i
$436$	−6.29028	−	4.44607i	−0.301250	−	0.212928i
$437$	−0.948337	+	0.948337i	−0.0453651	+	0.0453651i
$438$	6.90263	+	5.81804i	0.329820	+	0.277997i
$439$		−	7.98444i		−	0.381077i	−0.981680	−	0.190538i	$-0.938977\pi$
$439$		−	7.98444i		−	0.381077i	0.981680	−	0.190538i	$-0.0610233\pi$
$440$	−37.0120	+	9.65475i	−1.76448	+	0.460272i
$441$			23.8561i			1.13600i
$442$	−6.26298	+	7.43051i	−0.297900	+	0.353433i
$443$	20.4846	−	20.4846i	0.973255	−	0.973255i	−0.0263969	−	0.999652i	$-0.508403\pi$
$443$	20.4846	−	20.4846i	0.973255	−	0.973255i	0.999652	+	0.0263969i	$0.00840337\pi$
$444$	1.74514	−	0.299767i	0.0828208	−	0.0142263i
$445$	19.3009	+	19.3009i	0.914948	+	0.914948i
$446$	−1.50088	−	17.6032i	−0.0710689	−	0.833537i
$447$	3.01468			0.142590
$448$	−17.5999	−	31.4395i	−0.831516	−	1.48538i
$449$	−13.6807			−0.645632			−0.322816	−	0.946462i	$-0.604629\pi$
$449$	−13.6807			−0.645632			−0.322816	+	0.946462i	$0.604629\pi$
$450$	−0.957880	−	11.2346i	−0.0451549	−	0.529602i
$451$	−30.2946	−	30.2946i	−1.42652	−	1.42652i
$452$	30.8700	−	5.30262i	1.45200	−	0.249414i
$453$	−1.21366	+	1.21366i	−0.0570227	+	0.0570227i
$454$	11.9581	−	14.1873i	0.561221	−	0.665843i
$455$			95.0861i			4.45771i
$456$	−4.28562	+	1.11793i	−0.200693	+	0.0523517i
$457$		−	11.4385i		−	0.535072i	−0.963548	−	0.267536i	$-0.913791\pi$
$457$		−	11.4385i		−	0.535072i	0.963548	−	0.267536i	$-0.0862095\pi$
$458$	14.1480	+	11.9250i	0.661093	+	0.557218i
$459$	−3.72130	+	3.72130i	−0.173696	+	0.173696i
$460$	−4.71613	−	3.33344i	−0.219891	−	0.155422i
$461$	7.61112	+	7.61112i	0.354485	+	0.354485i	0.861775	−	0.507290i	$-0.169353\pi$
$461$	7.61112	+	7.61112i	0.354485	+	0.354485i	−0.507290	+	0.861775i	$0.669353\pi$
$462$	30.6538	−	2.61360i	1.42614	−	0.121596i
$463$	−4.72113			−0.219410			−0.109705	−	0.993964i	$-0.534991\pi$
$463$	−4.72113			−0.219410			−0.109705	+	0.993964i	$0.534991\pi$
$464$	−24.0158	−	11.4583i	−1.11490	−	0.531938i
$465$	3.46098			0.160499
$466$	8.62068	−	0.735015i	0.399345	−	0.0340489i
$467$	5.96443	+	5.96443i	0.276001	+	0.276001i	0.831510	−	0.555509i	$-0.187477\pi$
$467$	5.96443	+	5.96443i	0.276001	+	0.276001i	−0.555509	+	0.831510i	$0.687477\pi$
$468$	−14.2451	+	20.1539i	−0.658481	+	0.931616i
$469$	8.22567	−	8.22567i	0.379826	−	0.379826i
$470$	−6.91819	−	5.83115i	−0.319112	−	0.268971i
$471$		−	18.1295i		−	0.835361i
$472$	6.61091	+	3.87548i	0.304292	+	0.178383i
$473$			12.4538i			0.572628i
$474$	3.09152	−	3.66783i	0.141998	−	0.168469i
$475$	4.47976	−	4.47976i	0.205546	−	0.205546i
$476$	−1.52493	−	8.87761i	−0.0698951	−	0.406905i
$477$	−1.18749	−	1.18749i	−0.0543713	−	0.0543713i
$478$	−0.251969	−	2.95523i	−0.0115248	−	0.135169i
$479$	22.6443			1.03465			0.517323	−	0.855790i	$-0.326929\pi$
$479$	22.6443			1.03465			0.517323	+	0.855790i	$0.326929\pi$
$480$	−7.86879	−	17.3734i	−0.359159	−	0.792983i
$481$	5.54400			0.252785
$482$	−1.47376	−	17.2851i	−0.0671280	−	0.787315i
$483$	3.28456	+	3.28456i	0.149453	+	0.149453i
$484$	2.83540	+	16.5067i	0.128882	+	0.750306i
$485$	−18.4278	+	18.4278i	−0.836763	+	0.836763i
$486$	−14.0021	+	16.6123i	−0.635147	+	0.753550i
$487$			37.6490i			1.70604i	0.521879	+	0.853020i	$0.325231\pi$
$487$			37.6490i			1.70604i	−0.521879	+	0.853020i	$0.674769\pi$
$488$	6.53340	−	11.1449i	0.295753	−	0.504504i
$489$		−	7.19177i		−	0.325223i
$490$	−44.1348	−	37.2000i	−1.99381	−	1.68053i
$491$	22.5336	−	22.5336i	1.01692	−	1.01692i	0.0170706	−	0.999854i	$-0.494566\pi$
$491$	22.5336	−	22.5336i	1.01692	−	1.01692i	0.999854	−	0.0170706i	$-0.00543402\pi$
$492$	12.3301	−	17.4446i	0.555884	−	0.786463i
$493$	−4.70389	−	4.70389i	−0.211852	−	0.211852i
$494$	−13.8170	+	1.17807i	−0.621657	+	0.0530037i
$495$	−24.2857			−1.09156
$496$	−3.87075	+	1.37021i	−0.173802	+	0.0615240i
$497$	−3.26534			−0.146471
$498$	−24.0819	+	2.05327i	−1.07914	+	0.0920093i
$499$	17.4136	+	17.4136i	0.779541	+	0.779541i	0.979753	−	0.200212i	$-0.0641631\pi$
$499$	17.4136	+	17.4136i	0.779541	+	0.779541i	−0.200212	+	0.979753i	$0.564163\pi$
$500$	−2.81146	−	1.98719i	−0.125732	−	0.0888696i
$501$	−14.5619	+	14.5619i	−0.650580	+	0.650580i
$502$	−8.60265	−	7.25094i	−0.383955	−	0.323625i
$503$			44.7961i			1.99736i	0.0513857	+	0.998679i	$0.483636\pi$
$503$			44.7961i			1.99736i	−0.0513857	+	0.998679i	$0.516364\pi$
$504$	−5.77416	−	22.1355i	−0.257201	−	0.985994i
$505$			45.6706i			2.03232i
$506$	−3.77050	+	4.47339i	−0.167619	+	0.198866i
$507$	26.5520	−	26.5520i	1.17922	−	1.17922i
$508$	37.7563	−	6.48550i	1.67517	−	0.287748i
$509$	−18.4796	−	18.4796i	−0.819093	−	0.819093i	0.166883	−	0.985977i	$-0.446630\pi$
$509$	−18.4796	−	18.4796i	−0.819093	−	0.819093i	−0.985977	+	0.166883i	$0.946630\pi$
$510$	−0.405066	−	4.75084i	−0.0179366	−	0.210371i
$511$	−26.1990			−1.15898
$512$	15.6786	+	16.3151i	0.692902	+	0.721032i
$513$	−7.50974			−0.331563
$514$	0.0939852	+	1.10231i	0.00414551	+	0.0486209i
$515$	−15.2748	−	15.2748i	−0.673088	−	0.673088i
$516$	−6.12006	+	1.05126i	−0.269420	+	0.0462790i
$517$	−6.48110	+	6.48110i	−0.285038	+	0.285038i
$518$	−3.31185	+	3.92924i	−0.145514	+	0.172641i
$519$		−	13.2013i		−	0.579472i
$520$	−15.0725	−	57.7812i	−0.660974	−	2.53387i
$521$		−	20.5699i		−	0.901186i	−0.892730	−	0.450593i	$-0.851213\pi$
$521$		−	20.5699i		−	0.901186i	0.892730	−	0.450593i	$-0.148787\pi$
$522$	−12.9179	−	10.8882i	−0.565402	−	0.476562i
$523$	1.75837	−	1.75837i	0.0768880	−	0.0768880i	−0.667617	−	0.744505i	$-0.732686\pi$
$523$	1.75837	−	1.75837i	0.0768880	−	0.0768880i	0.744505	+	0.667617i	$0.232686\pi$
$524$	−15.7248	−	11.1145i	−0.686941	−	0.485541i
$525$	−15.5156	−	15.5156i	−0.677157	−	0.677157i
$526$	−11.0914	+	0.945672i	−0.483607	+	0.0412333i
$527$	−1.02653			−0.0447162
$528$	−18.2132	+	6.44727i	−0.792626	+	0.280582i
$529$	22.1167			0.961594
$530$	4.04862	−	0.345193i	0.175861	−	0.0149942i
$531$	3.44037	+	3.44037i	0.149299	+	0.149299i
$532$	7.41901	−	10.4964i	0.321655	−	0.455076i
$533$	47.2944	−	47.2944i	2.04855	−	2.04855i
$534$	10.5420	+	8.88556i	0.456196	+	0.384516i
$535$			17.0699i			0.737996i
$536$	−3.69463	+	6.30240i	−0.159584	+	0.272222i
$537$		−	18.9699i		−	0.818611i
$538$	13.6534	−	16.1986i	0.588640	−	0.698373i
$539$	−41.3464	+	41.3464i	−1.78091	+	1.78091i
$540$	−5.47468	−	31.8717i	−0.235593	−	1.37154i
$541$	6.98297	+	6.98297i	0.300221	+	0.300221i	0.841100	−	0.540879i	$-0.181908\pi$
$541$	6.98297	+	6.98297i	0.300221	+	0.300221i	−0.540879	+	0.841100i	$0.681908\pi$
$542$	−1.57306	−	18.4497i	−0.0675686	−	0.792482i
$543$	−24.9634			−1.07128
$544$	2.33389	+	5.15296i	0.100065	+	0.220931i
$545$	11.8333			0.506882
$546$	4.08022	+	47.8551i	0.174617	+	2.04801i
$547$	−1.92849	−	1.92849i	−0.0824563	−	0.0824563i	0.664676	−	0.747132i	$-0.268570\pi$
$547$	−1.92849	−	1.92849i	−0.0824563	−	0.0824563i	−0.747132	+	0.664676i	$0.768570\pi$
$548$	−0.638376	−	3.71640i	−0.0272701	−	0.158757i
$549$	5.79987	−	5.79987i	0.247532	−	0.247532i
$550$	17.8111	−	21.1314i	0.759469	−	0.901048i
$551$		−	9.49264i		−	0.404400i
$552$	−2.51659	−	1.47529i	−0.107113	−	0.0627923i
$553$			13.9213i			0.591993i
$554$	5.56428	+	4.68999i	0.236404	+	0.199258i
$555$	−1.92344	+	1.92344i	−0.0816456	+	0.0816456i
$556$	−21.6168	+	30.5833i	−0.916756	+	1.29702i
$557$	−22.8329	−	22.8329i	−0.967462	−	0.967462i	0.0320253	−	0.999487i	$-0.489804\pi$
$557$	−22.8329	−	22.8329i	−0.967462	−	0.967462i	−0.999487	+	0.0320253i	$0.989804\pi$
$558$	−2.59760	+	0.221476i	−0.109965	+	0.00937583i
$559$	−19.4423			−0.822323
$560$	49.9556	+	23.8346i	2.11101	+	1.00720i
$561$	−4.83015			−0.203929
$562$	15.6216	−	1.33193i	0.658959	−	0.0561841i
$563$	18.1431	+	18.1431i	0.764639	+	0.764639i	0.977157	−	0.212518i	$-0.0681666\pi$
$563$	18.1431	+	18.1431i	0.764639	+	0.764639i	−0.212518	+	0.977157i	$0.568167\pi$
$564$	−3.73202	−	2.63785i	−0.157146	−	0.111073i
$565$	−34.0240	+	34.0240i	−1.43140	+	1.43140i
$566$	25.9778	+	21.8960i	1.09193	+	0.920356i
$567$			1.74603i			0.0733265i
$568$	1.98426	−	0.517603i	0.0832576	−	0.0217182i
$569$			28.7669i			1.20597i	0.797752	+	0.602986i	$0.206022\pi$
$569$			28.7669i			1.20597i	−0.797752	+	0.602986i	$0.793978\pi$
$570$	4.38497	−	5.20241i	0.183666	−	0.217905i
$571$	−1.10068	+	1.10068i	−0.0460622	+	0.0460622i	−0.729763	−	0.683701i	$-0.760369\pi$
$571$	−1.10068	+	1.10068i	−0.0460622	+	0.0460622i	0.683701	+	0.729763i	$0.260369\pi$
$572$	−59.6191	+	10.2409i	−2.49280	+	0.428194i
$573$	14.2185	+	14.2185i	0.593985	+	0.593985i
$574$	5.26679	+	61.7718i	0.219831	+	2.57831i
$575$	4.17271			0.174014
$576$	7.01759	+	12.5359i	0.292400	+	0.522327i
$577$	−6.73319			−0.280306			−0.140153	−	0.990130i	$-0.544759\pi$
$577$	−6.73319			−0.280306			−0.140153	+	0.990130i	$0.544759\pi$
$578$	0.120143	+	1.40910i	0.00499728	+	0.0586109i
$579$	−4.95800	−	4.95800i	−0.206048	−	0.206048i
$580$	40.2872	−	6.92023i	1.67283	−	0.287347i
$581$	49.5982	−	49.5982i	2.05768	−	2.05768i
$582$	−8.48363	+	10.0651i	−0.351658	+	0.417213i
$583$		−	4.11621i		−	0.170476i
$584$	15.9204	−	4.15292i	0.658791	−	0.171849i
$585$		−	37.9136i		−	1.56754i
$586$	−3.46389	−	2.91962i	−0.143092	−	0.120608i
$587$	−15.1946	+	15.1946i	−0.627150	+	0.627150i	−0.947350	−	0.320200i	$-0.896250\pi$
$587$	−15.1946	+	15.1946i	−0.627150	+	0.627150i	0.320200	+	0.947350i	$0.396250\pi$
$588$	−23.8085	−	16.8283i	−0.981848	−	0.693985i
$589$	−1.03579	−	1.03579i	−0.0426789	−	0.0426789i
$590$	−11.7296	+	1.00009i	−0.482899	+	0.0411729i
$591$	−9.19710			−0.378318
$592$	1.38968	−	2.91267i	0.0571155	−	0.119710i
$593$	18.5640			0.762330			0.381165	−	0.924507i	$-0.375523\pi$
$593$	18.5640			0.762330			0.381165	+	0.924507i	$0.375523\pi$
$594$	−32.6411	+	2.78304i	−1.33928	+	0.114190i
$595$	9.78464	+	9.78464i	0.401131	+	0.401131i
$596$	3.17134	−	4.48680i	0.129903	−	0.183786i
$597$	−12.5508	+	12.5508i	−0.513672	+	0.513672i
$598$	−6.98363	−	5.88632i	−0.285582	−	0.240709i
$599$			5.26185i			0.214994i	0.994205	+	0.107497i	$0.0342835\pi$
$599$			5.26185i			0.214994i	−0.994205	+	0.107497i	$0.965716\pi$
$600$	11.8879	+	6.96897i	0.485320	+	0.284507i
$601$		−	22.9232i		−	0.935057i	−0.883978	−	0.467529i	$-0.845145\pi$
$601$		−	22.9232i		−	0.935057i	0.883978	−	0.467529i	$-0.154855\pi$
$602$	11.6144	−	13.7795i	0.473366	−	0.561610i
$603$	−3.27982	+	3.27982i	−0.133564	+	0.133564i
$604$	0.529581	+	3.08304i	0.0215484	+	0.125447i
$605$	−18.1932	−	18.1932i	−0.739660	−	0.739660i
$606$	1.95976	+	22.9852i	0.0796099	+	0.933710i
$607$	12.4839			0.506707			0.253354	−	0.967374i	$-0.418466\pi$
$607$	12.4839			0.506707			0.253354	+	0.967374i	$0.418466\pi$
$608$	−2.84450	+	7.55438i	−0.115360	+	0.306371i
$609$	−32.8777			−1.33227
$610$	1.68597	+	19.7741i	0.0682631	+	0.800628i
$611$	−10.1180	−	10.1180i	−0.409329	−	0.409329i
$612$	0.608035	+	3.53976i	0.0245783	+	0.143087i
$613$	14.0507	−	14.0507i	0.567504	−	0.567504i	−0.363925	−	0.931428i	$-0.618563\pi$
$613$	14.0507	−	14.0507i	0.567504	−	0.567504i	0.931428	+	0.363925i	$0.118563\pi$
$614$	20.1323	−	23.8853i	0.812473	−	0.963933i
$615$			32.8168i			1.32330i
$616$	28.3568	−	48.3719i	1.14253	−	1.94896i
$617$			18.9661i			0.763547i	0.924256	+	0.381774i	$0.124687\pi$
$617$			18.9661i			0.763547i	−0.924256	+	0.381774i	$0.875313\pi$
$618$	−8.34299	−	7.03208i	−0.335604	−	0.282872i
$619$	8.53200	−	8.53200i	0.342930	−	0.342930i	−0.514538	−	0.857468i	$-0.672036\pi$
$619$	8.53200	−	8.53200i	0.342930	−	0.342930i	0.857468	+	0.514538i	$0.172036\pi$
$620$	3.64083	−	5.15103i	0.146219	−	0.206870i
$621$	−3.49750	−	3.49750i	−0.140350	−	0.140350i
$622$	20.0249	−	1.70736i	0.802927	−	0.0684591i
$623$	−40.0122			−1.60306
$624$	−10.0652	−	28.4335i	−0.402929	−	1.13825i
$625$	27.4875			1.09950
$626$	−44.6799	+	3.80949i	−1.78577	+	0.152258i
$627$	−4.87373	−	4.87373i	−0.194638	−	0.194638i
$628$	−26.9824	−	19.0716i	−1.07671	−	0.761038i
$629$	0.570494	−	0.570494i	0.0227471	−	0.0227471i
$630$	26.8708	+	22.6487i	1.07056	+	0.902345i
$631$		−	16.5467i		−	0.658712i	−0.944206	−	0.329356i	$-0.893168\pi$
$631$		−	16.5467i		−	0.658712i	0.944206	−	0.329356i	$-0.106832\pi$
$632$	−2.20672	−	8.45958i	−0.0877788	−	0.336504i
$633$			9.92063i			0.394310i
$634$	6.02542	−	7.14866i	0.239300	−	0.283910i
$635$	−41.6139	+	41.6139i	−1.65140	+	1.65140i
$636$	2.02278	−	0.347459i	0.0802086	−	0.0137776i
$637$	−64.5479	−	64.5479i	−2.55748	−	2.55748i
$638$	−3.51789	−	41.2597i	−0.139274	−	1.63349i
$639$	1.30199			0.0515058
$640$	−34.1348	−	6.56496i	−1.34930	−	0.259503i
$641$	−1.30042			−0.0513633			−0.0256817	−	0.999670i	$-0.508176\pi$
$641$	−1.30042			−0.0513633			−0.0256817	+	0.999670i	$0.508176\pi$
$642$	0.732483	+	8.59097i	0.0289088	+	0.339059i
$643$	12.9608	+	12.9608i	0.511124	+	0.511124i	0.914871	−	0.403747i	$-0.132292\pi$
$643$	12.9608	+	12.9608i	0.511124	+	0.511124i	−0.403747	+	0.914871i	$0.632292\pi$
$644$	8.34370	−	1.43322i	0.328788	−	0.0564767i
$645$	6.74535	−	6.74535i	0.265598	−	0.265598i
$646$	−1.30059	+	1.54304i	−0.0511708	+	0.0607100i
$647$			35.6317i			1.40083i	0.713737	+	0.700414i	$0.247001\pi$
$647$			35.6317i			1.40083i	−0.713737	+	0.700414i	$0.752999\pi$
$648$	−0.276771	−	1.06102i	−0.0108726	−	0.0416807i
$649$			11.9254i			0.468113i
$650$	32.9894	+	27.8058i	1.29395	+	1.09064i
$651$	−3.58744	+	3.58744i	−0.140603	+	0.140603i
$652$	−10.7036	−	7.56550i	−0.419187	−	0.296288i
$653$	−14.2647	−	14.2647i	−0.558221	−	0.558221i	0.370580	−	0.928801i	$-0.379159\pi$
$653$	−14.2647	−	14.2647i	−0.558221	−	0.558221i	−0.928801	+	0.370580i	$0.879159\pi$
$654$	5.95548	−	0.507776i	0.232878	−	0.0198556i
$655$	29.5815			1.15585
$656$	−12.9922	−	36.7022i	−0.507261	−	1.43298i
$657$	10.4463			0.407550
$658$	13.2152	−	1.12675i	0.515182	−	0.0439254i
$659$	−2.41615	−	2.41615i	−0.0941197	−	0.0941197i	0.658479	−	0.752599i	$-0.271200\pi$
$659$	−2.41615	−	2.41615i	−0.0941197	−	0.0941197i	−0.752599	+	0.658479i	$0.771200\pi$
$660$	17.1313	−	24.2373i	0.666836	−	0.943436i
$661$	−1.45974	+	1.45974i	−0.0567773	+	0.0567773i	−0.734925	−	0.678148i	$-0.762783\pi$
$661$	−1.45974	+	1.45974i	−0.0567773	+	0.0567773i	0.678148	+	0.734925i	$0.262783\pi$
$662$	17.2219	+	14.5159i	0.669348	+	0.564175i
$663$		−	7.54060i		−	0.292853i
$664$	−22.2774	+	38.0015i	−0.864532	+	1.47474i
$665$			19.7458i			0.765710i
$666$	1.32053	−	1.56670i	0.0511696	−	0.0607085i
$667$	4.42099	−	4.42099i	0.171181	−	0.171181i
$668$	6.35412	+	36.9914i	0.245848	+	1.43124i
$669$	9.69357	+	9.69357i	0.374775	+	0.374775i
$670$	−0.953416	−	11.1822i	−0.0368337	−	0.432006i
$671$	20.1042			0.776113
$672$	26.1645	+	9.85190i	1.00932	+	0.380045i
$673$	26.9635			1.03937			0.519684	−	0.854359i	$-0.326050\pi$
$673$	26.9635			1.03937			0.519684	+	0.854359i	$0.326050\pi$
$674$	−0.251339	−	2.94785i	−0.00968124	−	0.113547i
$675$	16.5215	+	16.5215i	0.635914	+	0.635914i
$676$	−11.5860	−	67.4496i	−0.445615	−	2.59422i
$677$	4.91878	−	4.91878i	0.189044	−	0.189044i	−0.606239	−	0.795283i	$-0.707322\pi$
$677$	4.91878	−	4.91878i	0.189044	−	0.189044i	0.795283	+	0.606239i	$0.207322\pi$
$678$	−15.6637	+	18.5837i	−0.601559	+	0.713701i
$679$		−	38.2023i		−	1.46607i
$680$	−7.49687	−	4.39485i	−0.287492	−	0.168535i
$681$			14.3975i			0.551713i
$682$	−4.88590	−	4.11819i	−0.187091	−	0.157694i
$683$	−13.2286	+	13.2286i	−0.506177	+	0.506177i	−0.913351	−	0.407174i	$-0.866514\pi$
$683$	−13.2286	+	13.2286i	−0.506177	+	0.506177i	0.407174	+	0.913351i	$0.366514\pi$
$684$	−2.95818	+	4.18521i	−0.113109	+	0.160026i
$685$	4.09611	+	4.09611i	0.156504	+	0.156504i
$686$	39.8825	−	3.40046i	1.52272	−	0.129830i
$687$	−14.3576			−0.547777
$688$	−4.87348	+	10.2145i	−0.185800	+	0.389423i
$689$	6.42602			0.244812
$690$	4.46512	−	0.380705i	0.169984	−	0.0144932i
$691$	−18.6252	−	18.6252i	−0.708536	−	0.708536i	0.257691	−	0.966227i	$-0.417038\pi$
$691$	−18.6252	−	18.6252i	−0.708536	−	0.708536i	−0.966227	+	0.257691i	$0.917038\pi$
$692$	−19.6477	−	13.8873i	−0.746893	−	0.527916i
$693$	25.1731	−	25.1731i	0.956247	−	0.956247i
$694$	−4.35080	−	3.66717i	−0.165154	−	0.139204i
$695$		−	57.5334i		−	2.18237i
$696$	19.9789	−	5.21158i	0.757297	−	0.197545i
$697$		−	9.73348i		−	0.368682i
$698$	−28.1405	+	33.3864i	−1.06513	+	1.26369i
$699$	−4.74715	+	4.74715i	−0.179554	+	0.179554i
$700$	−39.4141	+	6.77026i	−1.48971	+	0.255892i
$701$	29.3078	+	29.3078i	1.10694	+	1.10694i	0.993551	+	0.113388i	$0.0361704\pi$
$701$	29.3078	+	29.3078i	1.10694	+	1.10694i	0.113388	+	0.993551i	$0.463830\pi$
$702$	−4.34475	−	50.9576i	−0.163982	−	1.92327i
$703$	1.15128			0.0434214
$704$	−9.56403	+	33.8892i	−0.360458	+	1.27725i
$705$	7.02068			0.264414
$706$	−2.83255	−	33.2218i	−0.106605	−	1.25032i
$707$	−47.3394	−	47.3394i	−1.78038	−	1.78038i
$708$	−5.86037	+	1.00665i	−0.220246	+	0.0378322i
$709$	32.1946	−	32.1946i	1.20909	−	1.20909i	0.237771	−	0.971321i	$-0.423583\pi$
$709$	32.1946	−	32.1946i	1.20909	−	1.20909i	0.971321	−	0.237771i	$-0.0764169\pi$
$710$	−2.03026	+	2.40874i	−0.0761942	+	0.0903982i
$711$		−	5.55083i		−	0.208172i
$712$	24.3143	−	6.34251i	0.911218	−	0.237696i
$713$		−	0.964791i		−	0.0361317i
$714$	5.34430	+	4.50457i	0.200005	+	0.168579i
$715$	65.7104	−	65.7104i	2.45743	−	2.45743i
$716$	−28.2332	−	19.9557i	−1.05512	−	0.745778i
$717$	1.62736	+	1.62736i	0.0607748	+	0.0607748i
$718$	−43.6139	+	3.71861i	−1.62766	+	0.138777i
$719$	1.73697			0.0647780			0.0323890	−	0.999475i	$-0.489688\pi$
$719$	1.73697			0.0647780			0.0323890	+	0.999475i	$0.489688\pi$
$720$	−19.9188	−	9.50357i	−0.742329	−	0.354177i
$721$	31.6659			1.17930
$722$	23.9036	−	2.03807i	0.889602	−	0.0758491i
$723$	9.51839	+	9.51839i	0.353993	+	0.353993i
$724$	−26.2606	+	37.1534i	−0.975968	+	1.38080i
$725$	−20.8839	+	20.8839i	−0.775609	+	0.775609i
$726$	−9.93702	−	8.37564i	−0.368797	−	0.310849i
$727$		−	18.2447i		−	0.676660i	−0.941028	−	0.338330i	$-0.890138\pi$
$727$		−	18.2447i		−	0.676660i	0.941028	−	0.338330i	$-0.109862\pi$
$728$	75.5158	+	44.2693i	2.79880	+	1.64073i
$729$		−	18.0215i		−	0.667462i
$730$	−16.2895	+	19.3262i	−0.602901	+	0.715293i
$731$	−2.00067	+	2.00067i	−0.0739976	+	0.0739976i
$732$	1.69704	+	9.87958i	0.0627244	+	0.365160i
$733$	6.22628	+	6.22628i	0.229973	+	0.229973i	0.812681	−	0.582709i	$-0.198007\pi$
$733$	6.22628	+	6.22628i	0.229973	+	0.229973i	−0.582709	+	0.812681i	$0.698007\pi$
$734$	3.83955	+	45.0324i	0.141720	+	1.66218i
$735$	44.7887			1.65206
$736$	−4.84305	+	2.19352i	−0.178517	+	0.0808544i
$737$	−11.3689			−0.418779
$738$	−2.10002	−	24.6303i	−0.0773029	−	0.906652i
$739$	26.5750	+	26.5750i	0.977577	+	0.977577i	0.999754	−	0.0221771i	$-0.00705978\pi$
$739$	26.5750	+	26.5750i	0.977577	+	0.977577i	−0.0221771	+	0.999754i	$0.507060\pi$
$740$	0.839296	+	4.88609i	0.0308531	+	0.179616i
$741$	7.60862	−	7.60862i	0.279510	−	0.279510i
$742$	−3.83875	+	4.55436i	−0.140925	+	0.167196i
$743$			22.9297i			0.841210i	0.907244	+	0.420605i	$0.138182\pi$
$743$			22.9297i			0.841210i	−0.907244	+	0.420605i	$0.861818\pi$
$744$	1.61133	−	2.74865i	0.0590742	−	0.100770i
$745$			8.44058i			0.309239i
$746$	17.6033	+	14.8374i	0.644503	+	0.543234i
$747$	−19.7763	+	19.7763i	−0.723576	+	0.723576i
$748$	−5.08116	+	7.18880i	−0.185785	+	0.262849i
$749$	−17.6936	−	17.6936i	−0.646511	−	0.646511i
$750$	2.66182	−	0.226952i	0.0971960	−	0.00828712i
$751$	−41.1238			−1.50063			−0.750314	−	0.661081i	$-0.770098\pi$
$751$	−41.1238			−1.50063			−0.750314	+	0.661081i	$0.770098\pi$
$752$	−7.85191	+	2.77950i	−0.286330	+	0.101358i
$753$	8.73010			0.318142
$754$	64.4127	−	5.49195i	2.34577	−	0.200005i
$755$	−3.39803	−	3.39803i	−0.123667	−	0.123667i
$756$	38.7110	+	27.3616i	1.40791	+	0.995130i
$757$	−24.0665	+	24.0665i	−0.874711	+	0.874711i	−0.992981	−	0.118271i	$-0.962265\pi$
$757$	−24.0665	+	24.0665i	−0.874711	+	0.874711i	0.118271	+	0.992981i	$0.462265\pi$
$758$	−31.9904	−	26.9638i	−1.16194	−	0.979370i
$759$		−	4.53966i		−	0.164779i
$760$	−3.12999	−	11.9990i	−0.113537	−	0.435249i
$761$			8.82688i			0.319974i	0.987119	+	0.159987i	$0.0511453\pi$
$761$			8.82688i			0.319974i	−0.987119	+	0.159987i	$0.948855\pi$
$762$	−19.1578	+	22.7292i	−0.694015	+	0.823393i
$763$	−12.2657	+	12.2657i	−0.444047	+	0.444047i
$764$	36.1189	−	6.20424i	1.30674	−	0.224462i
$765$	−3.90143	−	3.90143i	−0.141056	−	0.141056i
$766$	2.09528	+	24.5746i	0.0757055	+	0.887917i
$767$	−18.6173			−0.672233
$768$	−17.4611	−	1.83928i	−0.630075	−	0.0663692i
$769$	−29.0883			−1.04895			−0.524476	−	0.851425i	$-0.675739\pi$
$769$	−29.0883			−1.04895			−0.524476	+	0.851425i	$0.675739\pi$
$770$	7.31762	+	85.8251i	0.263709	+	3.09292i
$771$	−0.607010	−	0.607010i	−0.0218609	−	0.0218609i
$772$	−12.5947	+	2.16343i	−0.453294	+	0.0778635i
$773$	−33.2345	+	33.2345i	−1.19536	+	1.19536i	−0.219821	+	0.975540i	$0.570547\pi$
$773$	−33.2345	+	33.2345i	−1.19536	+	1.19536i	−0.975540	+	0.219821i	$0.929453\pi$
$774$	−4.63099	+	5.49429i	−0.166458	+	0.197488i
$775$			4.55749i			0.163710i
$776$	6.05561	+	23.2145i	0.217384	+	0.833352i
$777$		−	3.98745i		−	0.143049i
$778$	−29.3340	−	24.7248i	−1.05167	−	0.886428i
$779$	9.82128	−	9.82128i	0.351884	−	0.351884i
$780$	37.8381	+	26.7446i	1.35482	+	0.957609i
$781$	2.25655	+	2.25655i	0.0807458	+	0.0807458i
$782$	−1.32436	+	0.112917i	−0.0473589	+	0.00403791i
$783$	35.0092			1.25113
$784$	−50.0915	+	17.7319i	−1.78898	+	0.633282i
$785$	50.7593			1.81168
$786$	14.8879	−	1.26937i	0.531032	−	0.0452768i
$787$	−15.8835	−	15.8835i	−0.566185	−	0.566185i	0.364872	−	0.931058i	$-0.381113\pi$
$787$	−15.8835	−	15.8835i	−0.566185	−	0.566185i	−0.931058	+	0.364872i	$0.881113\pi$
$788$	−9.67503	+	13.6882i	−0.344659	+	0.487622i
$789$	6.10769	−	6.10769i	0.217439	−	0.217439i
$790$	10.2693	+	8.65570i	0.365365	+	0.307956i
$791$		−	70.5344i		−	2.50792i
$792$	−11.3067	+	19.2873i	−0.401766	+	0.685344i
$793$			31.3857i			1.11454i
$794$	4.41911	−	5.24291i	0.156828	−	0.186064i
$795$	−2.22945	+	2.22945i	−0.0790705	+	0.0790705i
$796$	5.47657	+	31.8827i	0.194112	+	1.13005i
$797$	−20.9498	−	20.9498i	−0.742081	−	0.742081i	0.230897	−	0.972978i	$-0.425834\pi$
$797$	−20.9498	−	20.9498i	−0.742081	−	0.742081i	−0.972978	+	0.230897i	$0.925834\pi$
$798$	0.847308	+	9.93771i	0.0299944	+	0.351791i
$799$	−2.08234			−0.0736678
$800$	22.8777	−	10.3618i	0.808848	−	0.366345i
$801$	15.9540			0.563709
$802$	1.17992	+	13.8388i	0.0416644	+	0.488664i
$803$	18.1051	+	18.1051i	0.638916	+	0.638916i
$804$	−0.959674	−	5.58689i	−0.0338451	−	0.197034i
$805$	−9.19618	+	9.19618i	−0.324123	+	0.324123i
$806$	6.42912	−	7.62763i	0.226456	−	0.268672i
$807$			16.4386i			0.578667i
$808$	36.2708	+	21.2629i	1.27600	+	0.748026i
$809$		−	12.3832i		−	0.435372i	−0.976019	−	0.217686i	$-0.930149\pi$
$809$		−	12.3832i		−	0.435372i	0.976019	−	0.217686i	$-0.0698508\pi$
$810$	1.28799	+	1.08561i	0.0452554	+	0.0381446i
$811$	24.0529	−	24.0529i	0.844611	−	0.844611i	−0.144843	−	0.989455i	$-0.546268\pi$
$811$	24.0529	−	24.0529i	0.844611	−	0.844611i	0.989455	+	0.144843i	$0.0462678\pi$
$812$	−34.5862	+	48.9324i	−1.21374	+	1.71719i
$813$	10.1597	+	10.1597i	0.356316	+	0.356316i
$814$	5.00404	−	0.426654i	0.175392	−	0.0149542i
$815$	20.1357			0.705323
$816$	−3.96162	−	1.89015i	−0.138685	−	0.0661686i
$817$	−4.03744			−0.141252
$818$	−4.22338	+	0.360093i	−0.147667	+	0.0125904i
$819$	39.2990	+	39.2990i	1.37322	+	1.37322i
$820$	48.8418	+	34.5221i	1.70563	+	1.20557i
$821$	−12.9271	+	12.9271i	−0.451160	+	0.451160i	−0.895739	−	0.444579i	$-0.853353\pi$
$821$	−12.9271	+	12.9271i	−0.451160	+	0.451160i	0.444579	+	0.895739i	$0.353353\pi$
$822$	2.23726	+	1.88573i	0.0780335	+	0.0657724i
$823$			39.5959i			1.38023i	0.723701	+	0.690113i	$0.242439\pi$
$823$			39.5959i			1.38023i	−0.723701	+	0.690113i	$0.757561\pi$
$824$	−19.2425	+	5.01950i	−0.670344	+	0.174863i
$825$			21.4445i			0.746602i
$826$	11.1215	−	13.1948i	0.386968	−	0.459106i
$827$	12.8593	−	12.8593i	0.447161	−	0.447161i	−0.447249	−	0.894410i	$-0.647596\pi$
$827$	12.8593	−	12.8593i	0.447161	−	0.447161i	0.894410	+	0.447249i	$0.147596\pi$
$828$	−3.32688	+	0.571467i	−0.115617	+	0.0198598i
$829$	30.4311	+	30.4311i	1.05691	+	1.05691i	0.998279	+	0.0586351i	$0.0186748\pi$
$829$	30.4311	+	30.4311i	1.05691	+	1.05691i	0.0586351	+	0.998279i	$0.481325\pi$
$830$	−5.74880	−	67.4252i	−0.199544	−	2.34036i
$831$	−5.64672			−0.195883
$832$	−52.9062	−	14.9309i	−1.83419	−	0.517635i
$833$	−13.2843			−0.460275
$834$	−2.46881	−	28.9555i	−0.0854878	−	1.00265i
$835$	−40.7709	−	40.7709i	−1.41093	−	1.41093i
$836$	−12.3806	+	2.12665i	−0.428193	+	0.0735519i
$837$	3.82002	−	3.82002i	0.132039	−	0.132039i
$838$	18.1417	−	21.5236i	0.626694	−	0.743521i
$839$		−	8.66535i		−	0.299161i	−0.988750	−	0.149580i	$-0.952208\pi$
$839$		−	8.66535i		−	0.299161i	0.988750	−	0.149580i	$-0.0477923\pi$
$840$	−41.5584	+	10.8407i	−1.43390	+	0.374040i
$841$			15.2531i			0.525970i
$842$	−35.7892	−	30.1658i	−1.23338	−	1.03958i
$843$	−8.60237	+	8.60237i	−0.296282	+	0.296282i
$844$	14.7650	+	10.4362i	0.508233	+	0.359227i
$845$	74.3410	+	74.3410i	2.55741	+	2.55741i
$846$	−5.26929	+	0.449270i	−0.181162	+	0.0154462i
$847$	37.7160			1.29594
$848$	1.61077	−	3.37606i	0.0553141	−	0.115934i
$849$	−26.3626			−0.904764
$850$	6.25601	−	0.533399i	0.214579	−	0.0182954i
$851$	0.536184	+	0.536184i	0.0183802	+	0.0183802i
$852$	−0.918431	+	1.29939i	−0.0314649	+	0.0445165i
$853$	9.76761	−	9.76761i	0.334437	−	0.334437i	−0.519832	−	0.854269i	$-0.674005\pi$
$853$	9.76761	−	9.76761i	0.334437	−	0.334437i	0.854269	+	0.519832i	$0.174005\pi$
$854$	−22.2442	−	18.7490i	−0.761180	−	0.641578i
$855$		−	7.87324i		−	0.269259i
$856$	13.5566	+	7.94724i	0.463356	+	0.271631i
$857$			2.56197i			0.0875151i	0.999042	+	0.0437575i	$0.0139329\pi$
$857$			2.56197i			0.0875151i	−0.999042	+	0.0437575i	$0.986067\pi$
$858$	30.2512	−	35.8905i	1.03276	−	1.22528i
$859$	21.1030	−	21.1030i	0.720024	−	0.720024i	−0.248586	−	0.968610i	$-0.579966\pi$
$859$	21.1030	−	21.1030i	0.720024	−	0.720024i	0.968610	+	0.248586i	$0.0799657\pi$
$860$	−2.94334	−	17.1351i	−0.100367	−	0.584301i
$861$	−34.0159	−	34.0159i	−1.15926	−	1.15926i
$862$	1.67918	+	19.6944i	0.0571932	+	0.670794i
$863$	25.2613			0.859903			0.429952	−	0.902852i	$-0.358531\pi$
$863$	25.2613			0.859903			0.429952	+	0.902852i	$0.358531\pi$
$864$	−27.8608	−	10.4906i	−0.947844	−	0.356898i
$865$	36.9613			1.25672
$866$	0.687367	+	8.06183i	0.0233577	+	0.273952i
$867$	−0.775950	−	0.775950i	−0.0263526	−	0.0263526i
$868$	1.56538	+	9.11311i	0.0531325	+	0.309319i
$869$	9.62047	−	9.62047i	0.326352	−	0.326352i
$870$	−20.4420	+	24.2528i	−0.693050	+	0.822247i
$871$		−	17.7486i		−	0.601387i
$872$	5.50923	−	9.39780i	0.186566	−	0.318250i
$873$			15.2324i			0.515538i
$874$	−1.45024	−	1.22237i	−0.0490550	−	0.0413472i
$875$	−5.48219	+	5.48219i	−0.185332	+	0.185332i
$876$	−7.36891	+	10.4255i	−0.248972	+	0.352245i
$877$	7.82839	+	7.82839i	0.264346	+	0.264346i	0.826817	−	0.562471i	$-0.190149\pi$
$877$	7.82839	+	7.82839i	0.264346	+	0.264346i	−0.562471	+	0.826817i	$0.690149\pi$
$878$	11.2509	−	0.959272i	0.379699	−	0.0323739i
$879$	3.51521			0.118565
$880$	−18.0512	−	50.9936i	−0.608507	−	1.71900i
$881$	−39.8812			−1.34363			−0.671817	−	0.740718i	$-0.734486\pi$
$881$	−39.8812			−1.34363			−0.671817	+	0.740718i	$0.734486\pi$
$882$	−33.6156	+	2.86613i	−1.13190	+	0.0965077i
$883$	15.6339	+	15.6339i	0.526123	+	0.526123i	0.919414	−	0.393291i	$-0.128664\pi$
$883$	15.6339	+	15.6339i	0.526123	+	0.526123i	−0.393291	+	0.919414i	$0.628664\pi$
$884$	−11.2228	−	7.93245i	−0.377463	−	0.266797i
$885$	6.45913	−	6.45913i	0.217121	−	0.217121i
$886$	31.3260	+	26.4038i	1.05242	+	0.887055i
$887$		−	35.9022i		−	1.20548i	−0.797938	−	0.602739i	$-0.794076\pi$
$887$		−	35.9022i		−	1.20548i	0.797938	−	0.602739i	$-0.205924\pi$
$888$	0.632069	+	2.42307i	0.0212108	+	0.0813128i
$889$		−	86.2689i		−	2.89337i
$890$	−24.8780	+	29.5157i	−0.833912	+	0.989369i
$891$	1.20662	−	1.20662i	0.0404232	−	0.0404232i
$892$	24.6244	−	4.22980i	0.824486	−	0.141624i
$893$	−2.10112	−	2.10112i	−0.0703113	−	0.0703113i
$894$	0.362192	+	4.24799i	0.0121135	+	0.142074i
$895$	53.1123			1.77535
$896$	42.1869	−	28.5772i	1.40937	−	0.954699i
$897$	7.08710			0.236631
$898$	−1.64364	−	19.2775i	−0.0548488	−	0.643298i
$899$	4.82867	+	4.82867i	0.161045	+	0.161045i
$900$	15.7155	−	2.69950i	0.523852	−	0.0899833i
$901$	0.661257	−	0.661257i	0.0220297	−	0.0220297i
$902$	39.0485	−	46.3278i	1.30017	−	1.54255i
$903$			13.9836i			0.465346i
$904$	11.1807	+	42.8618i	0.371865	+	1.42556i
$905$		−	69.8931i		−	2.32333i
$906$	−1.85598	−	1.56436i	−0.0616609	−	0.0519723i
$907$	−22.9493	+	22.9493i	−0.762018	+	0.762018i	−0.976687	−	0.214669i	$-0.931133\pi$
$907$	−22.9493	+	22.9493i	−0.762018	+	0.762018i	0.214669	+	0.976687i	$0.431133\pi$
$908$	21.4280	+	15.1457i	0.711114	+	0.502627i
$909$	18.8756	+	18.8756i	0.626065	+	0.626065i
$910$	−133.986	+	11.4239i	−4.44159	+	0.378699i
$911$	7.92545			0.262582			0.131291	−	0.991344i	$-0.458088\pi$
$911$	7.92545			0.262582			0.131291	+	0.991344i	$0.458088\pi$
$912$	−2.09016	−	5.90456i	−0.0692120	−	0.195520i
$913$	−68.5509			−2.26870
$914$	16.1181	−	1.37426i	0.533138	−	0.0454564i
$915$	−10.8890	−	10.8890i	−0.359979	−	0.359979i
$916$	−15.1037	+	21.3687i	−0.499041	+	0.706041i
$917$	−30.6624	+	30.6624i	−1.01256	+	1.01256i
$918$	−5.69078	−	4.79660i	−0.187824	−	0.158312i
$919$			25.9928i			0.857424i	0.903441	+	0.428712i	$0.141032\pi$
$919$			25.9928i			0.857424i	−0.903441	+	0.428712i	$0.858968\pi$
$920$	4.13054	−	7.04600i	0.136180	−	0.232300i
$921$			24.2392i			0.798708i
$922$	−9.81042	+	11.6393i	−0.323089	+	0.383319i
$923$	−3.52282	+	3.52282i	−0.115955	+	0.115955i
$924$	7.36565	+	42.8802i	0.242312	+	1.41066i
$925$	−2.53283	−	2.53283i	−0.0832790	−	0.0832790i
$926$	−0.567209	−	6.65255i	−0.0186397	−	0.218616i
$927$	−12.6261			−0.414696
$928$	13.2606	−	35.2173i	0.435300	−	1.15606i
$929$	28.5846			0.937832			0.468916	−	0.883243i	$-0.344645\pi$
$929$	28.5846			0.937832			0.468916	+	0.883243i	$0.344645\pi$
$930$	0.415811	+	4.87687i	0.0136350	+	0.159919i
$931$	−13.4042	−	13.4042i	−0.439304	−	0.439304i
$932$	2.07142	+	12.0591i	0.0678517	+	0.395009i
$933$	−11.0271	+	11.0271i	−0.361012	+	0.361012i
$934$	−7.68791	+	9.12107i	−0.251556	+	0.298451i
$935$		−	13.5236i		−	0.442269i
$936$	−30.1104	−	17.6515i	−0.984189	−	0.576956i
$937$		−	52.5562i		−	1.71694i	−0.512867	−	0.858468i	$-0.671417\pi$
$937$		−	52.5562i		−	1.71694i	0.512867	−	0.858468i	$-0.328583\pi$
$938$	12.5791	+	10.6025i	0.410721	+	0.346185i
$939$	24.6039	−	24.6039i	0.802917	−	0.802917i
$940$	7.38551	−	10.4490i	0.240889	−	0.340809i
$941$	2.90024	+	2.90024i	0.0945451	+	0.0945451i	0.752797	−	0.658252i	$-0.228704\pi$
$941$	2.90024	+	2.90024i	0.0945451	+	0.0945451i	−0.658252	+	0.752797i	$0.728704\pi$
$942$	25.5462	−	2.17812i	0.832341	−	0.0709670i
$943$	9.14809			0.297903
$944$	−4.66669	+	9.78104i	−0.151888	+	0.318346i
$945$	−72.8232			−2.36894
$946$	−17.5487	+	1.49624i	−0.570558	+	0.0486469i
$947$	−15.6265	−	15.6265i	−0.507793	−	0.507793i	0.406056	−	0.913848i	$-0.366904\pi$
$947$	−15.6265	−	15.6265i	−0.507793	−	0.507793i	−0.913848	+	0.406056i	$0.866904\pi$
$948$	5.53977	+	3.91559i	0.179923	+	0.127173i
$949$	−28.2648	+	28.2648i	−0.917515	+	0.917515i
$950$	6.85065	+	5.77423i	0.222264	+	0.187341i
$951$			7.25457i			0.235246i
$952$	12.3262	−	3.21536i	0.399496	−	0.104210i
$953$		−	18.4048i		−	0.596188i	−0.954536	−	0.298094i	$-0.903649\pi$
$953$		−	18.4048i		−	0.596188i	0.954536	−	0.298094i	$-0.0963510\pi$
$954$	1.53062	−	1.81596i	0.0495557	−	0.0587938i
$955$	−39.8092	+	39.8092i	−1.28820	+	1.28820i
$956$	4.13395	−	0.710099i	0.133701	−	0.0229663i
$957$	22.7205	+	22.7205i	0.734450	+	0.734450i
$958$	2.72055	+	31.9081i	0.0878970	+	1.03091i
$959$	−8.49156			−0.274207
$960$	23.5355	−	13.1752i	0.759605	−	0.425228i
$961$	−29.9462			−0.966008
$962$	0.666071	+	7.81206i	0.0214750	+	0.251871i
$963$	7.05497	+	7.05497i	0.227343	+	0.227343i
$964$	24.1794	−	4.15336i	0.778766	−	0.133771i
$965$	13.8815	−	13.8815i	0.446863	−	0.446863i
$966$	−4.23366	+	5.02289i	−0.136216	+	0.161609i
$967$			38.5107i			1.23842i	0.785225	+	0.619210i	$0.212547\pi$
$967$			38.5107i			1.23842i	−0.785225	+	0.619210i	$0.787453\pi$
$968$	−22.9190	+	5.97854i	−0.736645	+	0.192157i
$969$		−	1.56590i		−	0.0503039i
$970$	−28.1806	−	23.7527i	−0.904824	−	0.762652i
$971$	30.3399	−	30.3399i	0.973654	−	0.973654i	−0.0260075	−	0.999662i	$-0.508279\pi$
$971$	30.3399	−	30.3399i	0.973654	−	0.973654i	0.999662	+	0.0260075i	$0.00827936\pi$
$972$	−25.0907	−	17.7345i	−0.804784	−	0.568834i
$973$	59.6357	+	59.6357i	1.91183	+	1.91183i
$974$	−53.0513	+	4.52325i	−1.69987	+	0.144934i
$975$	−33.4781			−1.07216
$976$	16.4892	+	7.86724i	0.527805	+	0.251824i
$977$	−62.1132			−1.98718			−0.993588	−	0.113062i	$-0.963934\pi$
$977$	−62.1132			−1.98718			−0.993588	+	0.113062i	$0.963934\pi$
$978$	10.1339	−	0.864039i	0.324048	−	0.0276289i
$979$	27.6509	+	27.6509i	0.883727	+	0.883727i
$980$	47.1161	−	66.6597i	1.50507	−	2.12937i
$981$	4.89069	−	4.89069i	0.156148	−	0.156148i
$982$	34.4593	+	29.0448i	1.09964	+	0.926857i
$983$			14.0676i			0.448688i	0.974510	+	0.224344i	$0.0720239\pi$
$983$			14.0676i			0.448688i	−0.974510	+	0.224344i	$0.927976\pi$
$984$	26.0626	+	15.2785i	0.830844	+	0.487062i
$985$		−	25.7503i		−	0.820472i
$986$	6.06312	−	7.19339i	0.193089	−	0.229084i
$987$	−7.27722	+	7.27722i	−0.231636	+	0.231636i
$988$	−3.32003	−	19.3280i	−0.105624	−	0.614907i
$989$	−1.88035	−	1.88035i	−0.0597917	−	0.0597917i
$990$	−2.91775	−	34.2210i	−0.0927322	−	1.08762i
$991$	−33.3616			−1.05977			−0.529884	−	0.848070i	$-0.677764\pi$
$991$	−33.3616			−1.05977			−0.529884	+	0.848070i	$0.677764\pi$
$992$	−2.39580	−	5.28965i	−0.0760667	−	0.167947i
$993$	−17.4770			−0.554617
$994$	−0.392307	−	4.60119i	−0.0124432	−	0.145941i
$995$	−35.1401	−	35.1401i	−1.11402	−	1.11402i
$996$	−5.78654	−	33.6872i	−0.183353	−	1.06742i
$997$	25.6464	−	25.6464i	0.812231	−	0.812231i	−0.172737	−	0.984968i	$-0.555261\pi$
$997$	25.6464	−	25.6464i	0.812231	−	0.812231i	0.984968	+	0.172737i	$0.0552610\pi$
$998$	−22.4454	+	26.6297i	−0.710498	+	0.842947i
$999$			4.24597i			0.134336i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	272.2.l.c.205.9	yes	32
4.3	odd	2		1088.2.l.c.273.11		32
16.5	even	4	inner	272.2.l.c.69.9	✓	32
16.11	odd	4		1088.2.l.c.817.11		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
272.2.l.c.69.9	✓	32	16.5	even	4	inner
272.2.l.c.205.9	yes	32	1.1	even	1	trivial
1088.2.l.c.273.11		32	4.3	odd	2
1088.2.l.c.817.11		32	16.11	odd	4

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:	\( N \)	\(=\)	\( 272 = 2^{4} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	272.l (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.120143 + 1.40910i) q^{2} +(-0.775950 - 0.775950i) q^{3} +(-1.97113 + 0.338586i) q^{4} +(2.17252 - 2.17252i) q^{5} +(1.00017 - 1.18662i) q^{6} +4.50381i q^{7} +(-0.713919 - 2.73684i) q^{8} -1.79580i q^{9} +(3.32232 + 2.80029i) q^{10} +(3.11241 - 3.11241i) q^{11} +(1.79223 + 1.26677i) q^{12} +(4.85895 + 4.85895i) q^{13} +(-6.34633 + 0.541100i) q^{14} -3.37154 q^{15} +(3.77072 - 1.33480i) q^{16} +1.00000 q^{17} +(2.53047 - 0.215753i) q^{18} +(1.00902 + 1.00902i) q^{19} +(-3.54674 + 5.01792i) q^{20} +(3.49473 - 3.49473i) q^{21} +(4.75964 + 4.01177i) q^{22} +0.939859i q^{23} +(-1.56969 + 2.67762i) q^{24} -4.43972i q^{25} +(-6.26298 + 7.43051i) q^{26} +(-3.72130 + 3.72130i) q^{27} +(-1.52493 - 8.87761i) q^{28} +(-4.70389 - 4.70389i) q^{29} +(-0.405066 - 4.75084i) q^{30} -1.02653 q^{31} +(2.33389 + 5.15296i) q^{32} -4.83015 q^{33} +(0.120143 + 1.40910i) q^{34} +(9.78464 + 9.78464i) q^{35} +(0.608035 + 3.53976i) q^{36} +(0.570494 - 0.570494i) q^{37} +(-1.30059 + 1.54304i) q^{38} -7.54060i q^{39} +(-7.49687 - 4.39485i) q^{40} -9.73348i q^{41} +(5.34430 + 4.50457i) q^{42} +(-2.00067 + 2.00067i) q^{43} +(-5.08116 + 7.18880i) q^{44} +(-3.90143 - 3.90143i) q^{45} +(-1.32436 + 0.112917i) q^{46} -2.08234 q^{47} +(-3.96162 - 1.89015i) q^{48} -13.2843 q^{49} +(6.25601 - 0.533399i) q^{50} +(-0.775950 - 0.775950i) q^{51} +(-11.2228 - 7.93245i) q^{52} +(0.661257 - 0.661257i) q^{53} +(-5.69078 - 4.79660i) q^{54} -13.5236i q^{55} +(12.3262 - 3.21536i) q^{56} -1.56590i q^{57} +(6.06312 - 7.19339i) q^{58} +(-1.91578 + 1.91578i) q^{59} +(6.64575 - 1.14156i) q^{60} +(3.22968 + 3.22968i) q^{61} +(-0.123330 - 1.44648i) q^{62} +8.08797 q^{63} +(-6.98064 + 3.90777i) q^{64} +21.1124 q^{65} +(-0.580308 - 6.80618i) q^{66} +(-1.82638 - 1.82638i) q^{67} +(-1.97113 + 0.338586i) q^{68} +(0.729283 - 0.729283i) q^{69} +(-12.6120 + 14.9631i) q^{70} +0.725017i q^{71} +(-4.91484 + 1.28206i) q^{72} +5.81707i q^{73} +(0.872425 + 0.735344i) q^{74} +(-3.44500 + 3.44500i) q^{75} +(-2.33055 - 1.64727i) q^{76} +(14.0177 + 14.0177i) q^{77} +(10.6255 - 0.905948i) q^{78} +3.09100 q^{79} +(5.29210 - 11.0919i) q^{80} +0.387679 q^{81} +(13.7155 - 1.16941i) q^{82} +(-11.0125 - 11.0125i) q^{83} +(-5.70531 + 8.07185i) q^{84} +(2.17252 - 2.17252i) q^{85} +(-3.05952 - 2.57878i) q^{86} +7.29996i q^{87} +(-10.7402 - 6.29618i) q^{88} +8.88407i q^{89} +(5.02877 - 5.96623i) q^{90} +(-21.8838 + 21.8838i) q^{91} +(-0.318223 - 1.85259i) q^{92} +(0.796534 + 0.796534i) q^{93} +(-0.250178 - 2.93422i) q^{94} +4.38424 q^{95} +(2.18746 - 5.80942i) q^{96} -8.48221 q^{97} +(-1.59602 - 18.7190i) q^{98} +(-5.58928 - 5.58928i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 2 q^{4} - 16 q^{6} - 18 q^{8} - 6 q^{10} - 4 q^{11} + 2 q^{12} + 14 q^{14} + 24 q^{15} + 26 q^{16} + 32 q^{17} + 10 q^{18} - 14 q^{20} - 8 q^{22} - 50 q^{24} - 6 q^{26} + 12 q^{27} - 8 q^{29} + 36 q^{30}+ \cdots - 24 q^{99}+O(q^{100}) \) 32 * q - 2 * q^4 - 16 * q^6 - 18 * q^8 - 6 * q^10 - 4 * q^11 + 2 * q^12 + 14 * q^14 + 24 * q^15 + 26 * q^16 + 32 * q^17 + 10 * q^18 - 14 * q^20 - 8 * q^22 - 50 * q^24 - 6 * q^26 + 12 * q^27 - 8 * q^29 + 36 * q^30 - 24 * q^31 + 10 * q^32 + 12 * q^35 + 16 * q^36 - 8 * q^37 - 34 * q^38 - 38 * q^40 - 12 * q^42 - 12 * q^43 + 38 * q^44 - 40 * q^45 + 26 * q^46 + 32 * q^47 + 30 * q^48 - 32 * q^49 - 2 * q^50 - 54 * q^52 + 8 * q^53 - 52 * q^54 - 36 * q^56 - 26 * q^58 - 12 * q^59 + 28 * q^60 + 6 * q^62 - 40 * q^63 + 10 * q^64 + 28 * q^66 + 8 * q^67 - 2 * q^68 - 32 * q^70 - 32 * q^72 - 14 * q^74 + 8 * q^75 + 30 * q^76 + 56 * q^77 + 108 * q^78 + 48 * q^79 + 90 * q^80 - 64 * q^81 + 32 * q^82 + 4 * q^83 - 8 * q^84 - 54 * q^86 - 66 * q^88 - 66 * q^90 - 28 * q^91 + 24 * q^92 - 24 * q^93 + 12 * q^94 - 40 * q^95 + 70 * q^96 + 12 * q^98 - 24 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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