LMFDB - Embedded newform 403.2.r.a.218.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [403,2,Mod(218,403)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(403, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([5, 0]))

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

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

chi := DirichletCharacter("403.218");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 403 = 13 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	403.r (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.21797120146$
Analytic rank:	$0$
Dimension:	$68$
Relative dimension:	$34$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			218.12
Character	$\chi$	$=$	403.218
Dual form			403.2.r.a.342.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.624164 + 0.360361i) q^{2} +(-1.13079 - 1.95859i) q^{3} +(-0.740280 + 1.28220i) q^{4} -4.09116i q^{5} +(1.41160 + 0.814986i) q^{6} +(3.77469 + 2.17932i) q^{7} -2.50852i q^{8} +(-1.05738 + 1.83143i) q^{9} +O(q^{10})$	\(q+(-0.624164 + 0.360361i) q^{2} +(-1.13079 - 1.95859i) q^{3} +(-0.740280 + 1.28220i) q^{4} -4.09116i q^{5} +(1.41160 + 0.814986i) q^{6} +(3.77469 + 2.17932i) q^{7} -2.50852i q^{8} +(-1.05738 + 1.83143i) q^{9} +(1.47430 + 2.55356i) q^{10} +(2.01650 - 1.16423i) q^{11} +3.34841 q^{12} +(-3.58590 - 0.375943i) q^{13} -3.14137 q^{14} +(-8.01290 + 4.62625i) q^{15} +(-0.576587 - 0.998677i) q^{16} +(0.398795 - 0.690734i) q^{17} -1.52415i q^{18} +(1.19148 + 0.687900i) q^{19} +(5.24570 + 3.02861i) q^{20} -9.85742i q^{21} +(-0.839084 + 1.45334i) q^{22} +(-2.60205 - 4.50689i) q^{23} +(-4.91315 + 2.83661i) q^{24} -11.7376 q^{25} +(2.37366 - 1.05757i) q^{26} -2.00206 q^{27} +(-5.58866 + 3.22661i) q^{28} +(-3.63186 - 6.29057i) q^{29} +(3.33424 - 5.77508i) q^{30} +1.00000i q^{31} +(5.06465 + 2.92408i) q^{32} +(-4.56047 - 2.63299i) q^{33} +0.574842i q^{34} +(8.91596 - 15.4429i) q^{35} +(-1.56551 - 2.71154i) q^{36} +(4.61040 - 2.66182i) q^{37} -0.991570 q^{38} +(3.31858 + 7.44841i) q^{39} -10.2628 q^{40} +(-6.66980 + 3.85081i) q^{41} +(3.55223 + 6.15265i) q^{42} +(0.787186 - 1.36345i) q^{43} +3.44741i q^{44} +(7.49268 + 4.32590i) q^{45} +(3.24822 + 1.87536i) q^{46} +6.45999i q^{47} +(-1.30400 + 2.25859i) q^{48} +(5.99887 + 10.3904i) q^{49} +(7.32621 - 4.22979i) q^{50} -1.80382 q^{51} +(3.13660 - 4.31954i) q^{52} +7.57760 q^{53} +(1.24961 - 0.721465i) q^{54} +(-4.76304 - 8.24983i) q^{55} +(5.46686 - 9.46888i) q^{56} -3.11148i q^{57} +(4.53375 + 2.61756i) q^{58} +(-12.1182 - 6.99647i) q^{59} -13.6989i q^{60} +(-3.33187 + 5.77097i) q^{61} +(-0.360361 - 0.624164i) q^{62} +(-7.98254 + 4.60872i) q^{63} -1.90855 q^{64} +(-1.53804 + 14.6705i) q^{65} +3.79531 q^{66} +(13.2733 - 7.66334i) q^{67} +(0.590440 + 1.02267i) q^{68} +(-5.88476 + 10.1927i) q^{69} +12.8519i q^{70} +(-1.09326 - 0.631193i) q^{71} +(4.59417 + 2.65245i) q^{72} -3.91949i q^{73} +(-1.91843 + 3.32282i) q^{74} +(13.2728 + 22.9892i) q^{75} +(-1.76405 + 1.01848i) q^{76} +10.1489 q^{77} +(-4.75546 - 3.45314i) q^{78} +1.39666 q^{79} +(-4.08575 + 2.35891i) q^{80} +(5.43604 + 9.41550i) q^{81} +(2.77536 - 4.80707i) q^{82} -0.500360i q^{83} +(12.6392 + 7.29725i) q^{84} +(-2.82591 - 1.63154i) q^{85} +1.13469i q^{86} +(-8.21375 + 14.2266i) q^{87} +(-2.92048 - 5.05842i) q^{88} +(6.23317 - 3.59872i) q^{89} -6.23555 q^{90} +(-12.7164 - 9.23389i) q^{91} +7.70499 q^{92} +(1.95859 - 1.13079i) q^{93} +(-2.32793 - 4.03210i) q^{94} +(2.81431 - 4.87453i) q^{95} -13.2261i q^{96} +(1.66240 + 0.959786i) q^{97} +(-7.48856 - 4.32352i) q^{98} +4.92410i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 68 q + 32 q^{4} - 34 q^{9}+O(q^{10}) $ 68 * q + 32 * q^4 - 34 * q^9	$ 68 q + 32 q^{4} - 34 q^{9} + 8 q^{10} - 12 q^{11} - 16 q^{12} + 6 q^{13} - 8 q^{14} - 36 q^{16} - 6 q^{17} + 12 q^{19} - 12 q^{20} - 20 q^{22} - 8 q^{23} + 48 q^{24} - 72 q^{25} - 12 q^{27} - 6 q^{28} + 32 q^{30} + 6 q^{33} + 30 q^{35} + 40 q^{36} - 42 q^{37} - 36 q^{38} - 14 q^{39} + 8 q^{40} + 18 q^{41} - 16 q^{42} + 12 q^{43} + 60 q^{45} + 30 q^{46} - 46 q^{48} + 22 q^{49} + 56 q^{51} + 20 q^{53} - 114 q^{54} - 6 q^{55} - 2 q^{56} - 12 q^{58} + 6 q^{59} + 6 q^{61} - 8 q^{62} - 30 q^{63} + 24 q^{64} + 24 q^{65} + 8 q^{66} - 48 q^{67} + 58 q^{68} - 28 q^{69} - 30 q^{71} + 72 q^{72} + 8 q^{74} - 4 q^{75} - 12 q^{76} - 20 q^{77} + 26 q^{78} + 16 q^{79} + 42 q^{80} - 58 q^{81} - 42 q^{82} - 72 q^{84} + 30 q^{85} - 20 q^{87} + 64 q^{88} + 18 q^{89} + 52 q^{90} - 22 q^{91} + 48 q^{92} + 8 q^{94} - 32 q^{95} - 168 q^{98}+O(q^{100}) $ 68 * q + 32 * q^4 - 34 * q^9 + 8 * q^10 - 12 * q^11 - 16 * q^12 + 6 * q^13 - 8 * q^14 - 36 * q^16 - 6 * q^17 + 12 * q^19 - 12 * q^20 - 20 * q^22 - 8 * q^23 + 48 * q^24 - 72 * q^25 - 12 * q^27 - 6 * q^28 + 32 * q^30 + 6 * q^33 + 30 * q^35 + 40 * q^36 - 42 * q^37 - 36 * q^38 - 14 * q^39 + 8 * q^40 + 18 * q^41 - 16 * q^42 + 12 * q^43 + 60 * q^45 + 30 * q^46 - 46 * q^48 + 22 * q^49 + 56 * q^51 + 20 * q^53 - 114 * q^54 - 6 * q^55 - 2 * q^56 - 12 * q^58 + 6 * q^59 + 6 * q^61 - 8 * q^62 - 30 * q^63 + 24 * q^64 + 24 * q^65 + 8 * q^66 - 48 * q^67 + 58 * q^68 - 28 * q^69 - 30 * q^71 + 72 * q^72 + 8 * q^74 - 4 * q^75 - 12 * q^76 - 20 * q^77 + 26 * q^78 + 16 * q^79 + 42 * q^80 - 58 * q^81 - 42 * q^82 - 72 * q^84 + 30 * q^85 - 20 * q^87 + 64 * q^88 + 18 * q^89 + 52 * q^90 - 22 * q^91 + 48 * q^92 + 8 * q^94 - 32 * q^95 - 168 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/403\mathbb{Z}\right)^\times$.

$n$	$249$	$313$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$

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 $

$2$	−0.624164	+	0.360361i	−0.441351	+	0.254814i	−0.704170	−	0.710031i	$-0.748681\pi$
$2$	−0.624164	+	0.360361i	−0.441351	+	0.254814i	0.262820	+	0.964845i	$0.415348\pi$
$3$	−1.13079	−	1.95859i	−0.652862	−	1.13079i	−0.982425	−	0.186657i	$-0.940235\pi$
$3$	−1.13079	−	1.95859i	−0.652862	−	1.13079i	0.329563	−	0.944134i	$-0.393099\pi$
$4$	−0.740280	+	1.28220i	−0.370140	+	0.641101i
$5$		−	4.09116i		−	1.82962i	−0.403879	−	0.914812i	$-0.632338\pi$
$5$		−	4.09116i		−	1.82962i	0.403879	−	0.914812i	$-0.367662\pi$
$6$	1.41160	+	0.814986i	0.576282	+	0.332717i
$7$	3.77469	+	2.17932i	1.42670	+	0.823706i	0.996859	−	0.0791988i	$-0.0252362\pi$
$7$	3.77469	+	2.17932i	1.42670	+	0.823706i	0.429841	+	0.902904i	$0.358570\pi$
$8$		−	2.50852i		−	0.886895i
$9$	−1.05738	+	1.83143i	−0.352459	+	0.610476i
$10$	1.47430	+	2.55356i	0.466214	+	0.807506i
$11$	2.01650	−	1.16423i	0.607997	−	0.351027i	−0.164184	−	0.986430i	$-0.552499\pi$
$11$	2.01650	−	1.16423i	0.607997	−	0.351027i	0.772181	+	0.635402i	$0.219166\pi$
$12$	3.34841			0.966601
$13$	−3.58590	−	0.375943i	−0.994549	−	0.104268i
$13$	−3.58590	−	0.375943i	−0.994549	−	0.104268i
$14$	−3.14137			−0.839567
$15$	−8.01290	+	4.62625i	−2.06892	+	1.19449i
$16$	−0.576587	−	0.998677i	−0.144147	−	0.249669i
$17$	0.398795	−	0.690734i	0.0967221	−	0.167528i	−0.813604	−	0.581420i	$-0.802498\pi$
$17$	0.398795	−	0.690734i	0.0967221	−	0.167528i	0.910326	+	0.413892i	$0.135831\pi$
$18$		−	1.52415i		−	0.359245i
$19$	1.19148	+	0.687900i	0.273344	+	0.157815i	0.630406	−	0.776265i	$-0.282888\pi$
$19$	1.19148	+	0.687900i	0.273344	+	0.157815i	−0.357063	+	0.934080i	$0.616222\pi$
$20$	5.24570	+	3.02861i	1.17297	+	0.677217i
$21$		−	9.85742i		−	2.15107i
$22$	−0.839084	+	1.45334i	−0.178893	+	0.309852i
$23$	−2.60205	−	4.50689i	−0.542566	−	0.939751i	−0.998756	−	0.0498690i	$-0.984120\pi$
$23$	−2.60205	−	4.50689i	−0.542566	−	0.939751i	0.456190	−	0.889882i	$-0.349214\pi$
$24$	−4.91315	+	2.83661i	−1.00289	+	0.579020i
$25$	−11.7376			−2.34753
$26$	2.37366	−	1.05757i	0.465514	−	0.207406i
$27$	−2.00206			−0.385297
$28$	−5.58866	+	3.22661i	−1.05616	+	0.609772i
$29$	−3.63186	−	6.29057i	−0.674420	−	1.16813i	−0.976638	−	0.214891i	$-0.931060\pi$
$29$	−3.63186	−	6.29057i	−0.674420	−	1.16813i	0.302218	−	0.953239i	$-0.402273\pi$
$30$	3.33424	−	5.77508i	0.608747	−	1.05438i
$31$			1.00000i			0.179605i
$31$			1.00000i			0.179605i
$32$	5.06465	+	2.92408i	0.895312	+	0.516909i
$33$	−4.56047	−	2.63299i	−0.793877	−	0.458345i
$34$			0.574842i			0.0985845i
$35$	8.91596	−	15.4429i	1.50707	−	2.61033i
$36$	−1.56551	−	2.71154i	−0.260918	−	0.451923i
$37$	4.61040	−	2.66182i	0.757946	−	0.437600i	−0.0706120	−	0.997504i	$-0.522495\pi$
$37$	4.61040	−	2.66182i	0.757946	−	0.437600i	0.828558	+	0.559904i	$0.189162\pi$
$38$	−0.991570			−0.160854
$39$	3.31858	+	7.44841i	0.531399	+	1.19270i
$40$	−10.2628			−1.62268
$41$	−6.66980	+	3.85081i	−1.04165	+	0.601395i	−0.920299	−	0.391215i	$-0.872055\pi$
$41$	−6.66980	+	3.85081i	−1.04165	+	0.601395i	−0.121348	+	0.992610i	$0.538722\pi$
$42$	3.55223	+	6.15265i	0.548121	+	0.949374i
$43$	0.787186	−	1.36345i	0.120045	−	0.207924i	−0.799740	−	0.600346i	$-0.795030\pi$
$43$	0.787186	−	1.36345i	0.120045	−	0.207924i	0.919785	+	0.392422i	$0.128363\pi$
$44$			3.44741i			0.519717i
$45$	7.49268	+	4.32590i	1.11694	+	0.644867i
$46$	3.24822	+	1.87536i	0.478923	+	0.276507i
$47$			6.45999i			0.942287i	0.882057	+	0.471143i	$0.156159\pi$
$47$			6.45999i			0.942287i	−0.882057	+	0.471143i	$0.843841\pi$
$48$	−1.30400	+	2.25859i	−0.188216	+	0.325999i
$49$	5.99887	+	10.3904i	0.856982	+	1.48434i
$50$	7.32621	−	4.22979i	1.03608	−	0.598182i
$51$	−1.80382			−0.252585
$52$	3.13660	−	4.31954i	0.434968	−	0.599013i
$53$	7.57760			1.04086			0.520432	−	0.853903i	$-0.325771\pi$
$53$	7.57760			1.04086			0.520432	+	0.853903i	$0.325771\pi$
$54$	1.24961	−	0.721465i	0.170051	−	0.0981790i
$55$	−4.76304	−	8.24983i	−0.642248	−	1.11241i
$56$	5.46686	−	9.46888i	0.730540	−	1.26533i
$57$		−	3.11148i		−	0.412126i
$58$	4.53375	+	2.61756i	0.595311	+	0.343703i
$59$	−12.1182	−	6.99647i	−1.57766	−	0.910862i	−0.995185	−	0.0980138i	$-0.968751\pi$
$59$	−12.1182	−	6.99647i	−1.57766	−	0.910862i	−0.582475	−	0.812849i	$-0.697916\pi$
$60$		−	13.6989i		−	1.76852i
$61$	−3.33187	+	5.77097i	−0.426603	+	0.738897i	−0.996569	−	0.0827709i	$-0.973623\pi$
$61$	−3.33187	+	5.77097i	−0.426603	+	0.738897i	0.569966	+	0.821668i	$0.306956\pi$
$62$	−0.360361	−	0.624164i	−0.0457659	−	0.0792689i
$63$	−7.98254	+	4.60872i	−1.00571	+	0.580644i
$64$	−1.90855			−0.238569
$65$	−1.53804	+	14.6705i	−0.190771	+	1.81965i
$66$	3.79531			0.467171
$67$	13.2733	−	7.66334i	1.62159	−	0.936226i	0.635096	−	0.772433i	$-0.280961\pi$
$67$	13.2733	−	7.66334i	1.62159	−	0.936226i	0.986495	−	0.163792i	$-0.0523727\pi$
$68$	0.590440	+	1.02267i	0.0716014	+	0.124017i
$69$	−5.88476	+	10.1927i	−0.708441	+	1.22706i
$70$			12.8519i			1.53609i
$71$	−1.09326	−	0.631193i	−0.129746	−	0.0749088i	0.433722	−	0.901047i	$-0.357200\pi$
$71$	−1.09326	−	0.631193i	−0.129746	−	0.0749088i	−0.563468	+	0.826138i	$0.690533\pi$
$72$	4.59417	+	2.65245i	0.541428	+	0.312594i
$73$		−	3.91949i		−	0.458742i	−0.973339	−	0.229371i	$-0.926333\pi$
$73$		−	3.91949i		−	0.458742i	0.973339	−	0.229371i	$-0.0736668\pi$
$74$	−1.91843	+	3.32282i	−0.223013	+	0.386270i
$75$	13.2728	+	22.9892i	1.53261	+	2.65456i
$76$	−1.76405	+	1.01848i	−0.202351	+	0.116827i
$77$	10.1489			1.15657
$78$	−4.75546	−	3.45314i	−0.538450	−	0.390991i
$79$	1.39666			0.157137			0.0785685	−	0.996909i	$-0.474965\pi$
$79$	1.39666			0.157137			0.0785685	+	0.996909i	$0.474965\pi$
$80$	−4.08575	+	2.35891i	−0.456801	+	0.263734i
$81$	5.43604	+	9.41550i	0.604004	+	1.04617i
$82$	2.77536	−	4.80707i	0.306488	−	0.530852i
$83$		−	0.500360i		−	0.0549216i	−0.999623	−	0.0274608i	$-0.991258\pi$
$83$		−	0.500360i		−	0.0549216i	0.999623	−	0.0274608i	$-0.00874215\pi$
$84$	12.6392	+	7.29725i	1.37905	+	0.796195i
$85$	−2.82591	−	1.63154i	−0.306513	−	0.176965i
$86$			1.13469i			0.122356i
$87$	−8.21375	+	14.2266i	−0.880607	+	1.52526i
$88$	−2.92048	−	5.05842i	−0.311324	−	0.539229i
$89$	6.23317	−	3.59872i	0.660715	−	0.381464i	−0.131834	−	0.991272i	$-0.542087\pi$
$89$	6.23317	−	3.59872i	0.660715	−	0.381464i	0.792549	+	0.609808i	$0.208753\pi$
$90$	−6.23555			−0.657284
$91$	−12.7164	−	9.23389i	−1.33304	−	0.967975i
$92$	7.70499			0.803301
$93$	1.95859	−	1.13079i	0.203096	−	0.117258i
$94$	−2.32793	−	4.03210i	−0.240108	−	0.415879i
$95$	2.81431	−	4.87453i	0.288742	−	0.500116i
$96$		−	13.2261i		−	1.34988i
$97$	1.66240	+	0.959786i	0.168791	+	0.0974515i	0.582016	−	0.813178i	$-0.302264\pi$
$97$	1.66240	+	0.959786i	0.168791	+	0.0974515i	−0.413225	+	0.910629i	$0.635598\pi$
$98$	−7.48856	−	4.32352i	−0.756459	−	0.436742i
$99$			4.92410i			0.494890i
$100$	8.68913	−	15.0500i	0.868913	−	1.50500i
$101$	5.68387	+	9.84475i	0.565566	+	0.979589i	0.996997	+	0.0774432i	$0.0246756\pi$
$101$	5.68387	+	9.84475i	0.565566	+	0.979589i	−0.431431	+	0.902146i	$0.641991\pi$
$102$	1.12588	−	0.650026i	0.111478	−	0.0643621i
$103$	16.4309			1.61898			0.809490	−	0.587133i	$-0.199743\pi$
$103$	16.4309			1.61898			0.809490	+	0.587133i	$0.199743\pi$
$104$	−0.943059	+	8.99529i	−0.0924746	+	0.882061i
$105$	−40.3283			−3.93564
$106$	−4.72966	+	2.73067i	−0.459386	+	0.265226i
$107$	0.718091	+	1.24377i	0.0694205	+	0.120240i	0.898646	−	0.438674i	$-0.144552\pi$
$107$	0.718091	+	1.24377i	0.0694205	+	0.120240i	−0.829226	+	0.558914i	$0.811218\pi$
$108$	1.48208	−	2.56705i	0.142614	−	0.247014i
$109$		−	17.3138i		−	1.65836i	−0.558978	−	0.829182i	$-0.688806\pi$
$109$		−	17.3138i		−	1.65836i	0.558978	−	0.829182i	$-0.311194\pi$
$110$	5.94584	+	3.43283i	0.566913	+	0.327307i
$111$	−10.4268	−	6.01992i	−0.989669	−	0.571385i
$112$		−	5.02627i		−	0.474938i
$113$	0.976197	−	1.69082i	0.0918329	−	0.159059i	−0.816450	−	0.577417i	$-0.804061\pi$
$113$	0.976197	−	1.69082i	0.0918329	−	0.159059i	0.908282	+	0.418358i	$0.137394\pi$
$114$	1.12126	+	1.94208i	0.105015	+	0.181892i
$115$	−18.4384	+	10.6454i	−1.71939	+	0.992691i
$116$	10.7544			0.998518
$117$	4.48016	−	6.16980i	0.414191	−	0.570399i
$118$	10.0850			0.928402
$119$	3.01066	−	1.73821i	0.275987	−	0.159341i
$120$	11.6050	+	20.1005i	1.05939	+	1.83492i
$121$	−2.78916	+	4.83096i	−0.253560	+	0.439178i
$122$		−	4.80271i		−	0.434817i
$123$	15.0843	+	8.70892i	1.36010	+	0.785257i
$124$	−1.28220	−	0.740280i	−0.115145	−	0.0664791i
$125$			27.5648i			2.46547i
$126$	3.32161	−	5.75320i	0.295912	−	0.512535i
$127$	−4.00908	−	6.94392i	−0.355748	−	0.616173i	0.631498	−	0.775378i	$-0.282441\pi$
$127$	−4.00908	−	6.94392i	−0.355748	−	0.616173i	−0.987246	+	0.159204i	$0.949107\pi$
$128$	−8.93805	+	5.16039i	−0.790019	+	0.456118i
$129$	−3.56057			−0.313491
$130$	−4.32669	−	9.71105i	−0.379476	−	0.851715i
$131$	−1.51116			−0.132031			−0.0660153	−	0.997819i	$-0.521029\pi$
$131$	−1.51116			−0.132031			−0.0660153	+	0.997819i	$0.521029\pi$
$132$	6.75205	−	3.89830i	0.587691	−	0.339303i
$133$	2.99831	+	5.19322i	0.259986	+	0.450309i
$134$	−5.52314	+	9.56636i	−0.477127	+	0.826408i
$135$			8.19076i			0.704949i
$136$	−1.73272	−	1.00039i	−0.148579	−	0.0857823i
$137$	11.1649	+	6.44604i	0.953880	+	0.550723i	0.894284	−	0.447500i	$-0.147686\pi$
$137$	11.1649	+	6.44604i	0.953880	+	0.550723i	0.0595956	+	0.998223i	$0.481019\pi$
$138$		−	8.48255i		−	0.722083i
$139$	1.92007	−	3.32566i	0.162858	−	0.282079i	−0.773034	−	0.634364i	$-0.781262\pi$
$139$	1.92007	−	3.32566i	0.162858	−	0.282079i	0.935893	+	0.352285i	$0.114595\pi$
$140$	13.2006	+	22.8641i	1.11565	+	1.93237i
$141$	12.6525	−	7.30490i	1.06553	−	0.615184i
$142$	0.909830			0.0763512
$143$	−7.66864	+	3.41671i	−0.641284	+	0.285719i
$144$	2.43868			0.203223
$145$	−25.7358	+	14.8585i	−2.13724	+	1.23394i
$146$	1.41243	+	2.44640i	0.116894	+	0.202466i
$147$	13.5669	−	23.4986i	1.11898	−	1.93814i
$148$			7.88196i			0.647893i
$149$	−2.21356	−	1.27800i	−0.181342	−	0.104698i	0.406581	−	0.913615i	$-0.366721\pi$
$149$	−2.21356	−	1.27800i	−0.181342	−	0.104698i	−0.587923	+	0.808917i	$0.700054\pi$
$150$	−16.5688	−	9.56601i	−1.35284	−	0.781061i
$151$			0.148968i			0.0121228i	0.999982	+	0.00606140i	$0.00192942\pi$
$151$			0.148968i			0.0121228i	−0.999982	+	0.00606140i	$0.998071\pi$
$152$	1.72561	−	2.98884i	0.139965	−	0.242427i
$153$	0.843353	+	1.46073i	0.0681811	+	0.118093i
$154$	−6.33457	+	3.65726i	−0.510454	+	0.294711i
$155$	4.09116			0.328610
$156$	−12.0070	−	1.25881i	−0.961333	−	0.100785i
$157$	−1.68608			−0.134564			−0.0672821	−	0.997734i	$-0.521433\pi$
$157$	−1.68608			−0.134564			−0.0672821	+	0.997734i	$0.521433\pi$
$158$	−0.871747	+	0.503303i	−0.0693525	+	0.0400407i
$159$	−8.56868	−	14.8414i	−0.679540	−	1.17700i
$160$	11.9629	−	20.7203i	0.945749	−	1.63808i
$161$		−	22.6828i		−	1.78766i
$162$	−6.78596	−	3.91788i	−0.533155	−	0.307817i
$163$	6.45159	+	3.72483i	0.505327	+	0.291751i	0.730911	−	0.682473i	$-0.239096\pi$
$163$	6.45159	+	3.72483i	0.505327	+	0.291751i	−0.225584	+	0.974224i	$0.572429\pi$
$164$		−	11.4027i		−	0.890401i
$165$	−10.7720	+	18.6577i	−0.838599	+	1.45250i
$166$	0.180310	+	0.312307i	0.0139948	+	0.0242397i
$167$	14.7620	−	8.52287i	1.14232	−	0.659519i	0.195317	−	0.980740i	$-0.437427\pi$
$167$	14.7620	−	8.52287i	1.14232	−	0.659519i	0.947004	+	0.321221i	$0.104093\pi$
$168$	−24.7275			−1.90777
$169$	12.7173	+	2.69619i	0.978256	+	0.207399i
$170$	2.35177			0.180373
$171$	−2.51968	+	1.45474i	−0.192685	+	0.111247i
$172$	1.16548	+	2.01866i	0.0888667	+	0.153922i
$173$	−7.66084	+	13.2690i	−0.582443	+	1.00882i	0.412746	+	0.910846i	$0.364570\pi$
$173$	−7.66084	+	13.2690i	−0.582443	+	1.00882i	−0.995189	+	0.0979740i	$0.968764\pi$
$174$		−	11.8397i		−	0.897563i
$175$	−44.3060	−	25.5801i	−3.34922	−	1.93367i
$176$	−2.32537	−	1.34255i	−0.175281	−	0.101199i
$177$			31.6462i			2.37867i
$178$	−2.59368	+	4.49239i	−0.194405	+	0.336719i
$179$	−3.27062	−	5.66488i	−0.244458	−	0.423413i	0.717521	−	0.696537i	$-0.245277\pi$
$179$	−3.27062	−	5.66488i	−0.244458	−	0.423413i	−0.961979	+	0.273123i	$0.911943\pi$
$180$	−11.0934	+	6.40475i	−0.826850	+	0.477382i
$181$	17.8179			1.32439			0.662197	−	0.749330i	$-0.269624\pi$
$181$	17.8179			1.32439			0.662197	+	0.749330i	$0.269624\pi$
$182$	11.2646	+	1.18098i	0.834990	+	0.0875398i
$183$	15.0706			1.11405
$184$	−11.3056	+	6.52730i	−0.833461	+	0.481199i
$185$	−10.8899	−	18.8619i	−0.800644	−	1.38676i
$186$	−0.814986	+	1.41160i	−0.0597577	+	0.103503i
$187$		−	1.85715i		−	0.135808i
$188$	−8.28301	−	4.78220i	−0.604101	−	0.348778i
$189$	−7.55717	−	4.36313i	−0.549703	−	0.317371i
$190$			4.05667i			0.294302i
$191$	11.8961	−	20.6046i	0.860771	−	1.49090i	−0.0104144	−	0.999946i	$-0.503315\pi$
$191$	11.8961	−	20.6046i	0.860771	−	1.49090i	0.871186	−	0.490954i	$-0.163352\pi$
$192$	2.15817	+	3.73806i	0.155752	+	0.269771i
$193$	10.6670	−	6.15859i	0.767826	−	0.443305i	−0.0642722	−	0.997932i	$-0.520473\pi$
$193$	10.6670	−	6.15859i	0.767826	−	0.443305i	0.832099	+	0.554628i	$0.187139\pi$
$194$	−1.38348			−0.0993279
$195$	30.4727	−	13.5769i	2.18219	−	0.972260i
$196$	−17.7634			−1.26881
$197$	−6.55490	+	3.78447i	−0.467017	+	0.269632i	−0.714990	−	0.699134i	$-0.753569\pi$
$197$	−6.55490	+	3.78447i	−0.467017	+	0.269632i	0.247973	+	0.968767i	$0.420236\pi$
$198$	−1.77445	−	3.07344i	−0.126105	−	0.218420i
$199$	7.65280	−	13.2550i	0.542493	−	0.939625i	−0.456268	−	0.889843i	$-0.650814\pi$
$199$	7.65280	−	13.2550i	0.542493	−	0.939625i	0.998760	−	0.0497821i	$-0.0158527\pi$
$200$			29.4440i			2.08201i
$201$	−30.0186	−	17.3313i	−2.11735	−	1.22245i
$202$	−7.09533	−	4.09649i	−0.499226	−	0.288228i
$203$		−	31.6600i		−	2.22209i
$204$	1.33533	−	2.31286i	0.0934917	−	0.161932i
$205$	15.7543	+	27.2872i	1.10033	+	1.90582i
$206$	−10.2556	+	5.92105i	−0.714538	+	0.412539i
$207$	11.0054			0.764928
$208$	1.69214	+	3.79792i	0.117328	+	0.263338i
$209$	3.20348			0.221589
$210$	25.1715	−	14.5328i	1.73700	−	1.00286i
$211$	−2.55504	−	4.42545i	−0.175896	−	0.304661i	0.764575	−	0.644535i	$-0.222949\pi$
$211$	−2.55504	−	4.42545i	−0.175896	−	0.304661i	−0.940471	+	0.339874i	$0.889616\pi$
$212$	−5.60954	+	9.71601i	−0.385265	+	0.667298i
$213$			2.85499i			0.195621i
$214$	−0.896413	−	0.517544i	−0.0612775	−	0.0353786i
$215$	−5.57809	−	3.22051i	−0.380422	−	0.219637i
$216$			5.02221i			0.341718i
$217$	−2.17932	+	3.77469i	−0.147942	+	0.256243i
$218$	6.23924	+	10.8067i	0.422574	+	0.731920i
$219$	−7.67666	+	4.43212i	−0.518741	+	0.299495i
$220$	14.1039			0.950886
$221$	−1.68972	+	2.32698i	−0.113663	+	0.156529i
$222$	8.67738			0.582388
$223$	−1.27362	+	0.735327i	−0.0852881	+	0.0492411i	−0.542038	−	0.840354i	$-0.682347\pi$
$223$	−1.27362	+	0.735327i	−0.0852881	+	0.0492411i	0.456749	+	0.889595i	$0.349014\pi$
$224$	12.7450	+	22.0750i	0.851561	+	1.47495i
$225$	12.4111	−	21.4966i	0.827406	−	1.43311i
$226$			1.40713i			0.0936012i
$227$	−12.1307	−	7.00364i	−0.805140	−	0.464848i	0.0401253	−	0.999195i	$-0.487224\pi$
$227$	−12.1307	−	7.00364i	−0.805140	−	0.464848i	−0.845265	+	0.534347i	$0.820558\pi$
$228$	3.98955	+	2.30337i	0.264214	+	0.152544i
$229$			20.0439i			1.32454i	0.749265	+	0.662270i	$0.230407\pi$
$229$			20.0439i			1.32454i	−0.749265	+	0.662270i	$0.769593\pi$
$230$	7.67240	−	13.2890i	0.505903	−	0.876250i
$231$	−11.4763	−	19.8775i	−0.755083	−	1.30784i
$232$	−15.7800	+	9.11059i	−1.03601	+	0.598139i
$233$	2.61846			0.171541			0.0857706	−	0.996315i	$-0.472665\pi$
$233$	2.61846			0.171541			0.0857706	+	0.996315i	$0.472665\pi$
$234$	−0.572993	+	5.46544i	−0.0374577	+	0.357287i
$235$	26.4289			1.72403
$236$	17.9418	−	10.3587i	1.16791	−	0.674293i
$237$	−1.57933	−	2.73549i	−0.102589	−	0.177689i
$238$	−1.25276	+	2.16985i	−0.0812046	+	0.140651i
$239$		−	4.88486i		−	0.315975i	−0.987441	−	0.157988i	$-0.949499\pi$
$239$		−	4.88486i		−	0.315975i	0.987441	−	0.157988i	$-0.0505006\pi$
$240$	9.24027	+	5.33487i	0.596457	+	0.344364i
$241$	−16.4576	−	9.50182i	−1.06013	−	0.612066i	−0.134661	−	0.990892i	$-0.542995\pi$
$241$	−16.4576	−	9.50182i	−1.06013	−	0.612066i	−0.925468	+	0.378826i	$0.876328\pi$
$242$		−	4.02042i		−	0.258442i
$243$	9.29096	−	16.0924i	0.596015	−	1.03233i
$244$	−4.93303	−	8.54427i	−0.315805	−	0.546991i
$245$	42.5087	−	24.5424i	2.71578	−	1.56796i
$246$	−12.5534			−0.800377
$247$	−4.01391	−	2.91467i	−0.255399	−	0.185456i
$248$	2.50852			0.159291
$249$	−0.979998	+	0.565802i	−0.0621049	+	0.0358563i
$250$	−9.93327	−	17.2049i	−0.628235	−	1.08814i
$251$	2.36237	−	4.09175i	0.149112	−	0.258269i	−0.781788	−	0.623545i	$-0.785692\pi$
$251$	2.36237	−	4.09175i	0.149112	−	0.258269i	0.930899	+	0.365276i	$0.119025\pi$
$252$		−	13.6470i		−	0.859678i
$253$	−10.4941	−	6.05876i	−0.659757	−	0.380911i
$254$	5.00464	+	2.88943i	0.314019	+	0.181299i
$255$			7.37971i			0.462135i
$256$	5.62775	−	9.74756i	0.351735	−	0.609222i
$257$	8.58930	+	14.8771i	0.535786	+	0.928008i	0.999125	+	0.0418270i	$0.0133178\pi$
$257$	8.58930	+	14.8771i	0.535786	+	0.928008i	−0.463339	+	0.886181i	$0.653349\pi$
$258$	2.22238	−	1.28309i	0.138359	−	0.0798819i
$259$	23.2038			1.44182
$260$	−17.6720	−	12.8324i	−1.09597	−	0.795829i
$261$	15.3610			0.950820
$262$	0.943212	−	0.544563i	0.0582718	−	0.0336432i
$263$	9.73524	+	16.8619i	0.600300	+	1.03975i	0.992775	+	0.119988i	$0.0382856\pi$
$263$	9.73524	+	16.8619i	0.600300	+	1.03975i	−0.392475	+	0.919763i	$0.628381\pi$
$264$	−6.60490	+	11.4400i	−0.406504	+	0.704085i
$265$		−	31.0012i		−	1.90439i
$266$	−3.74287	−	2.16095i	−0.229490	−	0.132496i
$267$	−14.0968	−	8.13881i	−0.862712	−	0.498087i
$268$			22.6920i			1.38614i
$269$	9.03524	−	15.6495i	0.550888	−	0.954167i	−0.447322	−	0.894373i	$-0.647622\pi$
$269$	9.03524	−	15.6495i	0.550888	−	0.954167i	0.998211	−	0.0597938i	$-0.0190443\pi$
$270$	−2.95163	−	5.11238i	−0.179631	−	0.311129i
$271$	−18.8522	+	10.8843i	−1.14519	+	0.661177i	−0.947711	−	0.319130i	$-0.896609\pi$
$271$	−18.8522	+	10.8843i	−1.14519	+	0.661177i	−0.197481	+	0.980307i	$0.563276\pi$
$272$	−0.919760			−0.0557687
$273$	−3.70583	+	35.3477i	−0.224287	+	2.13934i
$274$	−9.29162			−0.561327
$275$	−23.6689	+	13.6653i	−1.42729	+	0.824046i
$276$	−8.71273	−	15.0909i	−0.524445	−	0.908365i
$277$	−11.5573	+	20.0179i	−0.694413	+	1.20276i	0.275965	+	0.961168i	$0.411002\pi$
$277$	−11.5573	+	20.0179i	−0.694413	+	1.20276i	−0.970378	+	0.241591i	$0.922331\pi$
$278$			2.76768i			0.165994i
$279$	−1.83143	−	1.05738i	−0.109645	−	0.0633034i
$280$	−38.7388	−	22.3658i	−2.31508	−	1.33661i
$281$			24.7729i			1.47782i	0.673802	+	0.738912i	$0.264660\pi$
$281$			24.7729i			1.47782i	−0.673802	+	0.738912i	$0.735340\pi$
$282$	−5.26481	+	9.11891i	−0.313515	+	0.543023i
$283$	8.63763	+	14.9608i	0.513454	+	0.889328i	0.999878	+	0.0156054i	$0.00496756\pi$
$283$	8.63763	+	14.9608i	0.513454	+	0.889328i	−0.486424	+	0.873723i	$0.661699\pi$
$284$	1.61863	−	0.934518i	0.0960482	−	0.0554535i
$285$	−12.7296			−0.754036
$286$	3.55524	−	4.89607i	0.210226	−	0.289510i
$287$	−33.5686			−1.98149
$288$	−10.7105	+	6.18370i	−0.631121	+	0.364378i
$289$	8.18192	+	14.1715i	0.481290	+	0.833618i
$290$	10.7089	−	18.5483i	0.628848	−	1.08920i
$291$		−	4.34127i		−	0.254490i
$292$	5.02558	+	2.90152i	0.294100	+	0.169798i
$293$	16.1245	+	9.30948i	0.942003	+	0.543865i	0.890587	−	0.454812i	$-0.150294\pi$
$293$	16.1245	+	9.30948i	0.942003	+	0.543865i	0.0514150	+	0.998677i	$0.483627\pi$
$294$			19.5560i			1.14053i
$295$	−28.6237	+	49.5777i	−1.66654	+	2.88653i
$296$	−6.67722	−	11.5653i	−0.388105	−	0.672218i
$297$	−4.03715	+	2.33085i	−0.234259	+	0.135250i
$298$	1.84217			0.106714
$299$	7.63637	+	17.1395i	0.441622	+	0.991201i
$300$	−39.3023			−2.26912
$301$	5.94278	−	3.43106i	0.342536	−	0.197763i
$302$	−0.0536821	−	0.0929802i	−0.00308906	−	0.00535041i
$303$	12.8545	−	22.2647i	0.738474	−	1.27907i
$304$		−	1.58653i		−	0.0909940i
$305$	23.6100	+	13.6312i	1.35190	+	0.780523i
$306$	−1.05278	−	0.607824i	−0.0601835	−	0.0347470i
$307$			14.0972i			0.804569i	0.915515	+	0.402285i	$0.131784\pi$
$307$			14.0972i			0.804569i	−0.915515	+	0.402285i	$0.868216\pi$
$308$	−7.51301	+	13.0129i	−0.428093	+	0.741480i
$309$	−18.5799	−	32.1813i	−1.05697	−	1.83073i
$310$	−2.55356	+	1.47430i	−0.145032	+	0.0837345i
$311$	−6.88888			−0.390633			−0.195316	−	0.980740i	$-0.562573\pi$
$311$	−6.88888			−0.390633			−0.195316	+	0.980740i	$0.562573\pi$
$312$	18.6845	−	8.32473i	1.05780	−	0.471295i
$313$	−17.2706			−0.976190			−0.488095	−	0.872791i	$-0.662308\pi$
$313$	−17.2706			−0.976190			−0.488095	+	0.872791i	$0.662308\pi$
$314$	1.05239	−	0.607599i	0.0593899	−	0.0342888i
$315$	18.8550	+	32.6579i	1.06236	+	1.84006i
$316$	−1.03392	+	1.79080i	−0.0581626	+	0.100741i
$317$		−	8.82771i		−	0.495813i	−0.968784	−	0.247907i	$-0.920257\pi$
$317$		−	8.82771i		−	0.495813i	0.968784	−	0.247907i	$-0.0797426\pi$
$318$	10.6965	+	6.17564i	0.599831	+	0.346313i
$319$	−14.6473	−	8.45661i	−0.820090	−	0.473479i
$320$			7.80819i			0.436491i
$321$	1.62402	−	2.81289i	0.0906440	−	0.157000i
$322$	8.17401	+	14.1578i	0.455520	+	0.788984i
$323$	0.950311	−	0.548662i	0.0528767	−	0.0305284i
$324$	−16.0968			−0.894264
$325$	42.0899	+	4.41268i	2.33473	+	0.244771i
$326$	−5.36913			−0.297369
$327$	−33.9107	+	19.5783i	−1.87526	+	1.08268i
$328$	9.65982	+	16.7313i	0.533374	+	0.923831i
$329$	−14.0784	+	24.3845i	−0.776167	+	1.34436i
$330$		−	15.5272i		−	0.854747i
$331$	26.5013	+	15.3005i	1.45664	+	0.840992i	0.998844	−	0.0480649i	$-0.0153054\pi$
$331$	26.5013	+	15.3005i	1.45664	+	0.840992i	0.457797	+	0.889057i	$0.348639\pi$
$332$	0.641562	+	0.370406i	0.0352103	+	0.0203287i
$333$			11.2582i			0.616944i
$334$	−6.14262	+	10.6393i	−0.336109	+	0.582159i
$335$	−31.3520	−	54.3032i	−1.71294	−	2.96690i
$336$	−9.84438	+	5.68366i	−0.537055	+	0.310069i
$337$	20.1248			1.09627			0.548134	−	0.836390i	$-0.315338\pi$
$337$	20.1248			1.09627			0.548134	+	0.836390i	$0.315338\pi$
$338$	−8.90930	+	2.89997i	−0.484602	+	0.157738i
$339$	−4.41550			−0.239817
$340$	4.18392	−	2.41559i	0.226905	−	0.131004i
$341$	1.16423	+	2.01650i	0.0630464	+	0.109199i
$342$	1.04846	−	1.81599i	0.0566943	−	0.0981974i
$343$			21.7834i			1.17619i
$344$	−3.42023	−	1.97467i	−0.184406	−	0.106467i
$345$	41.7000	+	24.0755i	2.24505	+	1.29618i
$346$		−	11.0427i		−	0.593658i
$347$	11.4376	−	19.8105i	0.614003	−	1.06349i	−0.376555	−	0.926394i	$-0.622891\pi$
$347$	11.4376	−	19.8105i	0.614003	−	1.06349i	0.990558	−	0.137091i	$-0.0437752\pi$
$348$	−12.1609	−	21.0634i	−0.651895	−	1.12912i
$349$	−26.1172	+	15.0787i	−1.39802	+	0.807147i	−0.994185	−	0.107685i	$-0.965656\pi$
$349$	−26.1172	+	15.0787i	−1.39802	+	0.807147i	−0.403834	+	0.914832i	$0.632323\pi$
$350$	36.8722			1.97090
$351$	7.17919	+	0.752661i	0.383197	+	0.0401741i
$352$	13.6171			0.725796
$353$	23.8835	−	13.7892i	1.27119	−	0.733923i	0.295980	−	0.955194i	$-0.404354\pi$
$353$	23.8835	−	13.7892i	1.27119	−	0.733923i	0.975212	+	0.221271i	$0.0710204\pi$
$354$	−11.4041	−	19.7524i	−0.606119	−	1.04983i
$355$	−2.58231	+	4.47270i	−0.137055	+	0.237386i
$356$			10.6562i			0.564780i
$357$	−6.80886	−	3.93109i	−0.360363	−	0.208056i
$358$	4.08281	+	2.35721i	0.215783	+	0.124582i
$359$			3.40955i			0.179949i	0.995944	+	0.0899746i	$0.0286786\pi$
$359$			3.40955i			0.179949i	−0.995944	+	0.0899746i	$0.971321\pi$
$360$	10.8516	−	18.7955i	0.571929	−	0.990610i
$361$	−8.55359	−	14.8152i	−0.450189	−	0.779750i
$362$	−11.1213	+	6.42088i	−0.584522	+	0.337474i
$363$	12.6158			0.662159
$364$	21.2534	−	9.46929i	1.11398	−	0.496326i
$365$	−16.0353			−0.839325
$366$	−9.40653	+	5.43086i	−0.491687	+	0.283876i
$367$	−9.82275	−	17.0135i	−0.512743	−	0.888098i	−0.999891	−	0.0147779i	$-0.995296\pi$
$367$	−9.82275	−	17.0135i	−0.512743	−	0.888098i	0.487147	−	0.873320i	$-0.338037\pi$
$368$	−3.00062	+	5.19722i	−0.156418	+	0.270924i
$369$		−	16.2870i		−	0.847868i
$370$	13.5942	+	7.84862i	0.706729	+	0.408030i
$371$	28.6031	+	16.5140i	1.48500	+	0.857365i
$372$			3.34841i			0.173607i
$373$	−1.02497	+	1.77530i	−0.0530710	+	0.0919217i	−0.891340	−	0.453335i	$-0.850234\pi$
$373$	−1.02497	+	1.77530i	−0.0530710	+	0.0919217i	0.838269	+	0.545256i	$0.183568\pi$
$374$	0.669245	+	1.15917i	0.0346059	+	0.0599391i
$375$	53.9880	−	31.1700i	2.78793	−	1.60961i
$376$	16.2050			0.835709
$377$	10.6586	+	23.9227i	0.548945	+	1.23208i
$378$	6.28922			0.323482
$379$	7.44523	−	4.29850i	0.382436	−	0.220799i	−0.296442	−	0.955051i	$-0.595800\pi$
$379$	7.44523	−	4.29850i	0.382436	−	0.220799i	0.678877	+	0.734252i	$0.262467\pi$
$380$	4.16675	+	7.21703i	0.213750	+	0.370226i
$381$	−9.06685	+	15.7042i	−0.464509	+	0.804553i
$382$			17.1476i			0.877346i
$383$	13.9106	+	8.03128i	0.710797	+	0.410379i	0.811356	−	0.584552i	$-0.198730\pi$
$383$	13.9106	+	8.03128i	0.710797	+	0.410379i	−0.100559	+	0.994931i	$0.532063\pi$
$384$	20.2141	+	11.6706i	1.03155	+	0.595565i
$385$		−	41.5208i		−	2.11609i
$386$	−4.43863	+	7.68794i	−0.225920	+	0.391306i
$387$	1.66470	+	2.88335i	0.0846217	+	0.146569i
$388$	−2.46128	+	1.42102i	−0.124952	+	0.0721413i
$389$	14.9513			0.758062			0.379031	−	0.925384i	$-0.376257\pi$
$389$	14.9513			0.758062			0.379031	+	0.925384i	$0.376257\pi$
$390$	−14.1274	+	19.4554i	−0.715367	+	0.985161i
$391$	−4.15075			−0.209912
$392$	26.0644	−	15.0483i	1.31645	−	0.760053i
$393$	1.70881	+	2.95974i	0.0861978	+	0.149299i
$394$	2.72755	−	4.72426i	0.137412	−	0.238005i
$395$		−	5.71398i		−	0.287502i
$396$	−6.31369	−	3.64521i	−0.317275	−	0.183179i
$397$	19.1868	+	11.0775i	0.962960	+	0.555965i	0.897083	−	0.441863i	$-0.145682\pi$
$397$	19.1868	+	11.0775i	0.962960	+	0.555965i	0.0658771	+	0.997828i	$0.479015\pi$
$398$			11.0311i			0.552939i
$399$	6.78092	−	11.7449i	0.339470	−	0.587980i
$400$	6.76776	+	11.7221i	0.338388	+	0.586105i
$401$	−22.9086	+	13.2263i	−1.14400	+	0.660488i	−0.947418	−	0.320000i	$-0.896317\pi$
$401$	−22.9086	+	13.2263i	−1.14400	+	0.660488i	−0.196581	+	0.980488i	$0.562984\pi$
$402$	24.9821			1.24599
$403$	0.375943	−	3.58590i	0.0187271	−	0.178626i
$404$	−16.8306			−0.837354
$405$	38.5204	−	22.2397i	1.91409	−	1.10510i
$406$	11.4090	+	19.7610i	0.566220	+	0.980722i
$407$	6.19791	−	10.7351i	0.307219	−	0.532119i
$408$			4.52491i			0.224016i
$409$	0.748535	+	0.432167i	0.0370127	+	0.0213693i	0.518392	−	0.855143i	$-0.326531\pi$
$409$	0.748535	+	0.432167i	0.0370127	+	0.0213693i	−0.481379	+	0.876512i	$0.659864\pi$
$410$	−19.6665	−	11.3545i	−0.971260	−	0.560757i
$411$		−	29.1565i		−	1.43818i
$412$	−12.1634	+	21.0677i	−0.599249	+	1.03793i
$413$	−30.4951	−	52.8190i	−1.50057	−	2.59906i
$414$	−6.86917	+	3.96592i	−0.337601	+	0.194914i
$415$	−2.04705			−0.100486
$416$	−17.0620	−	12.3895i	−0.836535	−	0.607443i
$417$	−8.68480			−0.425296
$418$	−1.99950	+	1.15441i	−0.0977987	+	0.0564641i
$419$	9.37015	+	16.2296i	0.457762	+	0.792867i	0.998842	−	0.0481040i	$-0.0153179\pi$
$419$	9.37015	+	16.2296i	0.457762	+	0.792867i	−0.541080	+	0.840971i	$0.681985\pi$
$420$	29.8542	−	51.7091i	1.45674	−	2.52314i
$421$		−	11.9429i		−	0.582064i	−0.956713	−	0.291032i	$-0.906001\pi$
$421$		−	11.9429i		−	0.582064i	0.956713	−	0.291032i	$-0.0939985\pi$
$422$	3.18952	+	1.84147i	0.155264	+	0.0896415i
$423$	−11.8310	−	6.83064i	−0.575244	−	0.332117i
$424$		−	19.0085i		−	0.923136i
$425$	−4.68091	+	8.10758i	−0.227058	+	0.393275i
$426$	−1.02883	−	1.78198i	−0.0498468	−	0.0863373i
$427$	−25.1536	+	14.5224i	−1.21727	+	0.702790i
$428$	−2.12635			−0.102781
$429$	15.3635	+	11.1561i	0.741759	+	0.538622i
$430$	4.64219			0.223866
$431$	−3.48620	+	2.01276i	−0.167925	+	0.0969513i	−0.581607	−	0.813470i	$-0.697576\pi$
$431$	−3.48620	+	2.01276i	−0.167925	+	0.0969513i	0.413682	+	0.910421i	$0.364242\pi$
$432$	1.15436	+	1.99941i	0.0555392	+	0.0961968i
$433$	12.0902	−	20.9409i	0.581020	−	1.00636i	−0.414339	−	0.910123i	$-0.635987\pi$
$433$	12.0902	−	20.9409i	0.581020	−	1.00636i	0.995359	−	0.0962330i	$-0.0306794\pi$
$434$		−	3.14137i		−	0.150791i
$435$	58.2035	+	33.6038i	2.79064	+	1.61118i
$436$	22.1998	+	12.8171i	1.06318	+	0.613827i
$437$		−	7.15981i		−	0.342500i
$438$	3.19433	−	5.53274i	0.152631	−	0.264365i
$439$	13.4851	+	23.3568i	0.643607	+	1.11476i	0.984621	+	0.174702i	$0.0558962\pi$
$439$	13.4851	+	23.3568i	0.643607	+	1.11476i	−0.341014	+	0.940058i	$0.610770\pi$
$440$	−20.6948	+	11.9482i	−0.986587	+	0.569606i
$441$	−25.3723			−1.20820
$442$	0.216108	−	2.06132i	0.0102792	−	0.0980472i
$443$	−9.32536			−0.443061			−0.221531	−	0.975153i	$-0.571105\pi$
$443$	−9.32536			−0.443061			−0.221531	+	0.975153i	$0.571105\pi$
$444$	15.4375	−	8.91285i	0.732631	−	0.422985i
$445$	−14.7230	−	25.5009i	−0.697936	−	1.20886i
$446$	0.529967	−	0.917929i	0.0250947	−	0.0434652i
$447$			5.78061i			0.273413i
$448$	−7.20419	−	4.15934i	−0.340366	−	0.196510i
$449$	−24.5073	−	14.1493i	−1.15657	−	0.667746i	−0.206091	−	0.978533i	$-0.566074\pi$
$449$	−24.5073	−	14.1493i	−1.15657	−	0.667746i	−0.950480	+	0.310787i	$0.899408\pi$
$450$			17.8899i			0.843338i
$451$	−8.96642	+	15.5303i	−0.422212	+	0.731293i
$452$	1.44532	+	2.50336i	0.0679820	+	0.117748i
$453$	0.291766	−	0.168451i	0.0137084	−	0.00791452i
$454$	10.0954			0.473799
$455$	−37.7774	+	52.0248i	−1.77103	+	2.43896i
$456$	−7.80521			−0.365512
$457$	−11.1153	+	6.41741i	−0.519951	+	0.300194i	−0.736915	−	0.675986i	$-0.763718\pi$
$457$	−11.1153	+	6.41741i	−0.519951	+	0.300194i	0.216963	+	0.976180i	$0.430385\pi$
$458$	−7.22306	−	12.5107i	−0.337511	−	0.584587i
$459$	−0.798413	+	1.38289i	−0.0372667	+	0.0645478i
$460$		−	31.5224i		−	1.46974i
$461$	−29.7757	−	17.1910i	−1.38679	−	0.800665i	−0.393839	−	0.919179i	$-0.628853\pi$
$461$	−29.7757	−	17.1910i	−1.38679	−	0.800665i	−0.992952	+	0.118515i	$0.962187\pi$
$462$	14.3261	+	8.27120i	0.666512	+	0.384811i
$463$			6.26836i			0.291316i	0.989335	+	0.145658i	$0.0465298\pi$
$463$			6.26836i			0.291316i	−0.989335	+	0.145658i	$0.953470\pi$
$464$	−4.18817	+	7.25412i	−0.194431	+	0.336764i
$465$	−4.62625	−	8.01290i	−0.214537	−	0.371589i
$466$	−1.63435	+	0.943592i	−0.0757098	+	0.0437111i
$467$	1.05747			0.0489337			0.0244669	−	0.999701i	$-0.492211\pi$
$467$	1.05747			0.0489337			0.0244669	+	0.999701i	$0.492211\pi$
$468$	4.59437	+	10.3118i	0.212375	+	0.476665i
$469$	66.8035			3.08470
$470$	−16.4960	+	9.52395i	−0.760902	+	0.439307i
$471$	1.90661	+	3.30234i	0.0878518	+	0.152164i
$472$	−17.5508	+	30.3988i	−0.807839	+	1.39922i
$473$		−	3.66585i		−	0.168556i
$474$	1.97153	+	1.13826i	0.0905552	+	0.0522821i
$475$	−13.9851	−	8.07431i	−0.641681	−	0.370475i
$476$			5.14703i			0.235914i
$477$	−8.01237	+	13.8778i	−0.366861	+	0.635422i
$478$	1.76031	+	3.04895i	0.0805149	+	0.139456i
$479$	−10.3206	+	5.95861i	−0.471561	+	0.272256i	−0.716893	−	0.697183i	$-0.754436\pi$
$479$	−10.3206	+	5.95861i	−0.471561	+	0.272256i	0.245332	+	0.969439i	$0.421103\pi$
$480$	−54.1101			−2.46977
$481$	−17.5331	+	7.81176i	−0.799442	+	0.356186i
$482$	13.6963			0.623851
$483$	−44.4263	+	25.6495i	−2.02147	+	1.16709i
$484$	−4.12951	−	7.15252i	−0.187705	−	0.325115i
$485$	3.92664	−	6.80114i	0.178300	−	0.308824i
$486$			13.3924i			0.607492i
$487$	3.04916	+	1.76043i	0.138171	+	0.0797729i	0.567492	−	0.823379i	$-0.307914\pi$
$487$	3.04916	+	1.76043i	0.138171	+	0.0797729i	−0.429321	+	0.903152i	$0.641247\pi$
$488$	14.4766	+	8.35806i	0.655324	+	0.378352i
$489$		−	16.8480i		−	0.761893i
$490$	−17.6883	+	30.6369i	−0.799074	+	1.38404i
$491$	14.8198	+	25.6686i	0.668806	+	1.15841i	0.978238	+	0.207485i	$0.0665277\pi$
$491$	14.8198	+	25.6686i	0.668806	+	1.15841i	−0.309432	+	0.950921i	$0.600139\pi$
$492$	−22.3332	+	12.8941i	−1.00686	+	0.581309i
$493$	−5.79348			−0.260925
$494$	3.55567	+	0.372774i	0.159977	+	0.0167719i
$495$	20.1453			0.905464
$496$	0.998677	−	0.576587i	0.0448419	−	0.0258895i
$497$	−2.75114	−	4.76512i	−0.123406	−	0.213745i
$498$	0.407786	−	0.706307i	0.0182733	−	0.0316504i
$499$		−	14.1978i		−	0.635582i	−0.948161	−	0.317791i	$-0.897059\pi$
$499$		−	14.1978i		−	0.635582i	0.948161	−	0.317791i	$-0.102941\pi$
$500$	−35.3436	−	20.4056i	−1.58061	−	0.912567i
$501$	−33.3856	−	19.2752i	−1.49156	−	0.861151i
$502$			3.40523i			0.151983i
$503$	11.5755	−	20.0494i	0.516126	−	0.893957i	−0.483698	−	0.875235i	$-0.660707\pi$
$503$	11.5755	−	20.0494i	0.516126	−	0.893957i	0.999825	−	0.0187222i	$-0.00595982\pi$
$504$	11.5611	+	20.0243i	0.514970	+	0.891955i
$505$	40.2765	−	23.2536i	1.79228	−	1.03477i
$506$	8.73336			0.388245
$507$	−9.09993	−	27.9568i	−0.404142	−	1.24161i
$508$	11.8713			0.526706
$509$	−17.2398	+	9.95339i	−0.764140	+	0.441176i	−0.830780	−	0.556601i	$-0.812105\pi$
$509$	−17.2398	+	9.95339i	−0.764140	+	0.441176i	0.0666402	+	0.997777i	$0.478772\pi$
$510$	−2.65936	−	4.60615i	−0.117759	−	0.203964i
$511$	8.54182	−	14.7949i	0.377868	−	0.654487i
$512$		−	12.5294i		−	0.553728i
$513$	−2.38541	−	1.37722i	−0.105318	−	0.0608056i
$514$	−10.7223	−	6.19050i	−0.472939	−	0.273051i
$515$		−	67.2214i		−	2.96213i
$516$	2.63582	−	4.56537i	0.116035	−	0.200979i
$517$	7.52089	+	13.0266i	0.330768	+	0.572908i
$518$	−14.4830	+	8.36176i	−0.636346	+	0.367395i
$519$	34.6512			1.52102
$520$	36.8012	+	3.85821i	1.61384	+	0.169194i
$521$	0.274785			0.0120385			0.00601927	−	0.999982i	$-0.498084\pi$
$521$	0.274785			0.0120385			0.00601927	+	0.999982i	$0.498084\pi$
$522$	−9.58777	+	5.53550i	−0.419645	+	0.242282i
$523$	−8.96971	−	15.5360i	−0.392218	−	0.679342i	0.600524	−	0.799607i	$-0.294959\pi$
$523$	−8.96971	−	15.5360i	−0.392218	−	0.679342i	−0.992742	+	0.120265i	$0.961625\pi$
$524$	1.11868	−	1.93761i	0.0488698	−	0.0846450i
$525$			115.703i			5.04968i
$526$	−12.1528	−	7.01640i	−0.529886	−	0.305930i
$527$	0.690734	+	0.398795i	0.0300888	+	0.0173718i
$528$			6.07259i			0.264276i
$529$	−2.04137	+	3.53575i	−0.0887550	+	0.153728i
$530$	11.1716	+	19.3498i	0.485265	+	0.840503i
$531$	25.6271	−	14.7958i	1.11212	−	0.642083i
$532$	−8.87834			−0.384925
$533$	25.3649	−	11.3011i	1.09868	−	0.489507i
$534$	11.7316			0.507678
$535$	5.08847	−	2.93783i	0.219994	−	0.127013i
$536$	−19.2236	−	33.2963i	−0.830334	−	1.43818i
$537$	−7.39678	+	12.8116i	−0.319194	+	0.552861i
$538$			13.0238i			0.561496i
$539$	24.1934	+	13.9681i	1.04209	+	0.601648i
$540$	−10.5022	−	6.06345i	−0.451943	−	0.260929i
$541$		−	14.7609i		−	0.634619i	−0.948322	−	0.317310i	$-0.897221\pi$
$541$		−	14.7609i		−	0.634619i	0.948322	−	0.317310i	$-0.102779\pi$
$542$	7.84460	−	13.5872i	0.336954	−	0.583622i
$543$	−20.1483	−	34.8979i	−0.864647	−	1.49761i
$544$	4.03952	−	2.33222i	0.173193	−	0.0999930i
$545$	−70.8338			−3.03418
$546$	−10.4249	−	23.3982i	−0.446145	−	1.00135i
$547$	6.58901			0.281726			0.140863	−	0.990029i	$-0.455012\pi$
$547$	6.58901			0.281726			0.140863	+	0.990029i	$0.455012\pi$
$548$	−16.5303	+	9.54375i	−0.706137	+	0.407689i
$549$	−7.04608	−	12.2042i	−0.300720	−	0.520861i
$550$	9.84885	−	17.0587i	0.419957	−	0.727386i
$551$		−	9.99343i		−	0.425734i
$552$	25.5686	+	14.7620i	1.08827	+	0.628313i
$553$	5.27198	+	3.04378i	0.224187	+	0.129435i
$554$		−	16.6593i		−	0.707784i
$555$	−24.6285	+	42.6578i	−1.04542	+	1.81072i
$556$	2.84278	+	4.92384i	0.120561	+	0.208817i
$557$	1.58873	−	0.917252i	0.0673165	−	0.0388652i	−0.465964	−	0.884804i	$-0.654292\pi$
$557$	1.58873	−	0.917252i	0.0673165	−	0.0388652i	0.533281	+	0.845938i	$0.320959\pi$
$558$	1.52415			0.0645224
$559$	−3.33535	+	4.59324i	−0.141070	+	0.194274i
$560$	−20.5633			−0.868958
$561$	−3.63739	+	2.10005i	−0.153571	+	0.0886642i
$562$	−8.92718	−	15.4623i	−0.376570	−	0.652239i
$563$	−5.61762	+	9.73000i	−0.236754	+	0.410070i	−0.959781	−	0.280750i	$-0.909417\pi$
$563$	−5.61762	+	9.73000i	−0.236754	+	0.410070i	0.723027	+	0.690820i	$0.242750\pi$
$564$			21.6307i			0.910816i
$565$	−6.91743	−	3.99378i	−0.291019	−	0.168020i
$566$	−10.7826	−	6.22533i	−0.453226	−	0.261670i
$567$			47.3875i			1.99009i
$568$	−1.58336	+	2.74246i	−0.0664362	+	0.115071i
$569$	−9.24916	−	16.0200i	−0.387745	−	0.671594i	0.604401	−	0.796680i	$-0.293413\pi$
$569$	−9.24916	−	16.0200i	−0.387745	−	0.671594i	−0.992146	+	0.125086i	$0.960079\pi$
$570$	7.94535	−	4.58725i	0.332794	−	0.192139i
$571$	9.25853			0.387457			0.193729	−	0.981055i	$-0.437942\pi$
$571$	9.25853			0.387457			0.193729	+	0.981055i	$0.437942\pi$
$572$	1.29603	−	12.3621i	0.0541897	−	0.516884i
$573$	−53.8080			−2.24786
$574$	20.9523	−	12.0968i	0.874532	−	0.504911i
$575$	30.5419	+	52.9002i	1.27369	+	2.20609i
$576$	2.01805	−	3.49537i	0.0840856	−	0.145640i
$577$		−	13.6985i		−	0.570277i	−0.958486	−	0.285139i	$-0.907960\pi$
$577$		−	13.6985i		−	0.570277i	0.958486	−	0.285139i	$-0.0920396\pi$
$578$	−10.2137	−	5.89690i	−0.424835	−	0.245279i
$579$	−24.1243	−	13.9281i	−1.00257	−	0.578834i
$580$		−	43.9979i		−	1.82691i
$581$	1.09044	−	1.88870i	0.0452392	−	0.0783567i
$582$	1.56442	+	2.70966i	0.0648475	+	0.112319i
$583$	15.2802	−	8.82203i	0.632842	−	0.365371i
$584$	−9.83211			−0.406856
$585$	−25.2417	−	18.3291i	−1.04362	−	0.757813i
$586$	−13.4191			−0.554338
$587$	13.3491	−	7.70713i	0.550978	−	0.318107i	−0.198538	−	0.980093i	$-0.563619\pi$
$587$	13.3491	−	7.70713i	0.550978	−	0.318107i	0.749516	+	0.661986i	$0.230286\pi$
$588$	20.0867	+	34.7911i	0.828360	+	1.43476i
$589$	−0.687900	+	1.19148i	−0.0283444	+	0.0490940i
$590$		−	41.2595i		−	1.69863i
$591$	14.8244	+	8.55889i	0.609796	+	0.352066i
$592$	−5.31659	−	3.06954i	−0.218511	−	0.126157i
$593$			0.490921i			0.0201597i	0.999949	+	0.0100799i	$0.00320857\pi$
$593$			0.490921i			0.0201597i	−0.999949	+	0.0100799i	$0.996791\pi$
$594$	1.67990	−	2.90967i	0.0689270	−	0.119385i
$595$	−7.11129	−	12.3171i	−0.291534	−	0.504952i
$596$	3.27731	−	1.89216i	0.134244	−	0.0775057i
$597$	−34.6149			−1.41669
$598$	−10.9427	−	7.94599i	−0.447482	−	0.324936i
$599$	37.2971			1.52392			0.761959	−	0.647625i	$-0.224238\pi$
$599$	37.2971			1.52392			0.761959	+	0.647625i	$0.224238\pi$
$600$	57.6687	−	33.2951i	2.35432	−	1.35927i
$601$	−16.7136	−	28.9487i	−0.681761	−	1.18084i	−0.974443	−	0.224634i	$-0.927881\pi$
$601$	−16.7136	−	28.9487i	−0.681761	−	1.18084i	0.292683	−	0.956210i	$-0.405452\pi$
$602$	−2.47284	+	4.28309i	−0.100786	+	0.174566i
$603$			32.4121i			1.31992i
$604$	−0.191006	−	0.110278i	−0.00777194	−	0.00448713i
$605$	19.7643	+	11.4109i	0.803532	+	0.463919i
$606$			18.5291i			0.752694i
$607$	−0.443511	+	0.768184i	−0.0180016	+	0.0311796i	−0.874886	−	0.484329i	$-0.839064\pi$
$607$	−0.443511	+	0.768184i	−0.0180016	+	0.0311796i	0.856884	+	0.515509i	$0.172397\pi$
$608$	4.02294	+	6.96794i	0.163152	+	0.282587i
$609$	−62.0088	+	35.8008i	−2.51272	+	1.45072i
$610$	−19.6487			−0.795552
$611$	2.42859	−	23.1649i	0.0982502	−	0.937151i
$612$	−2.49727			−0.100946
$613$	−4.94751	+	2.85645i	−0.199828	+	0.115371i	−0.596575	−	0.802557i	$-0.703472\pi$
$613$	−4.94751	+	2.85645i	−0.199828	+	0.115371i	0.396747	+	0.917928i	$0.370139\pi$
$614$	−5.08008	−	8.79896i	−0.205015	−	0.355097i
$615$	35.6296	−	61.7123i	1.43672	−	2.48848i
$616$		−	25.4586i		−	1.02576i
$617$	23.0513	+	13.3087i	0.928010	+	0.535787i	0.886182	−	0.463338i	$-0.153348\pi$
$617$	23.0513	+	13.3087i	0.928010	+	0.535787i	0.0418285	+	0.999125i	$0.486682\pi$
$618$	23.1938	+	13.3909i	0.932990	+	0.538662i
$619$			5.69633i			0.228955i	0.993426	+	0.114478i	$0.0365194\pi$
$619$			5.69633i			0.228955i	−0.993426	+	0.114478i	$0.963481\pi$
$620$	−3.02861	+	5.24570i	−0.121632	+	0.210672i
$621$	5.20947	+	9.02307i	0.209049	+	0.362083i
$622$	4.29979	−	2.48249i	0.172406	−	0.0995386i
$623$	31.3711			1.25686
$624$	5.52510	−	7.60885i	0.221181	−	0.304598i
$625$	54.0838			2.16335
$626$	10.7797	−	6.22364i	0.430842	−	0.248747i
$627$	−3.62247	−	6.27430i	−0.144667	−	0.250571i
$628$	1.24817	−	2.16190i	0.0498075	−	0.0862692i
$629$		−	4.24608i		−	0.169302i
$630$	−23.5373	−	13.5893i	−0.937748	−	0.541409i
$631$	−28.4768	−	16.4411i	−1.13364	−	0.654509i	−0.188794	−	0.982017i	$-0.560458\pi$
$631$	−28.4768	−	16.4411i	−1.13364	−	0.654509i	−0.944848	+	0.327508i	$0.893791\pi$
$632$		−	3.50355i		−	0.139364i
$633$	−5.77843	+	10.0085i	−0.229672	+	0.397803i
$634$	3.18116	+	5.50994i	0.126340	+	0.218828i
$635$	−28.4087	+	16.4018i	−1.12737	+	0.650885i
$636$	25.3729			1.00610
$637$	−17.6052	−	39.5140i	−0.697542	−	1.56560i
$638$	12.1897			0.482597
$639$	2.31197	−	1.33482i	0.0914601	−	0.0528045i
$640$	21.1120	+	36.5670i	0.834525	+	1.44544i
$641$	6.66152	−	11.5381i	0.263114	−	0.455727i	−0.703954	−	0.710246i	$-0.748584\pi$
$641$	6.66152	−	11.5381i	0.263114	−	0.455727i	0.967068	+	0.254519i	$0.0819171\pi$
$642$			2.34094i			0.0923894i
$643$	7.13349	+	4.11852i	0.281317	+	0.162419i	0.634020	−	0.773317i	$-0.281404\pi$
$643$	7.13349	+	4.11852i	0.281317	+	0.162419i	−0.352702	+	0.935736i	$0.614737\pi$
$644$	29.0840	+	16.7916i	1.14607	+	0.661683i
$645$			14.5669i			0.573571i
$646$	−0.395433	+	0.684911i	−0.0155581	+	0.0269475i
$647$	5.33308	+	9.23717i	0.209665	+	0.363151i	0.951609	−	0.307311i	$-0.0994293\pi$
$647$	5.33308	+	9.23717i	0.209665	+	0.363151i	−0.741944	+	0.670462i	$0.766096\pi$
$648$	23.6189	−	13.6364i	0.927840	−	0.535688i
$649$	−32.5819			−1.27895
$650$	−27.8612	+	12.4134i	−1.09281	+	0.486892i
$651$	9.85742			0.386343
$652$	−9.55196	+	5.51482i	−0.374083	+	0.215977i
$653$	−4.66100	−	8.07308i	−0.182399	−	0.315924i	0.760298	−	0.649574i	$-0.225053\pi$
$653$	−4.66100	−	8.07308i	−0.182399	−	0.315924i	−0.942697	+	0.333650i	$0.891720\pi$
$654$	14.1105	−	24.4402i	0.551766	−	0.955686i
$655$			6.18240i			0.241567i
$656$	7.69143	+	4.44065i	0.300300	+	0.173378i
$657$	7.17827	+	4.14437i	0.280051	+	0.161687i
$658$		−	20.2932i		−	0.791113i
$659$	−0.0577387	+	0.100006i	−0.00224918	+	0.00389570i	−0.867148	−	0.498051i	$-0.834049\pi$
$659$	−0.0577387	+	0.100006i	−0.00224918	+	0.00389570i	0.864899	+	0.501947i	$0.167383\pi$
$660$	−15.9486	−	27.6238i	−0.620798	−	1.07525i
$661$	−28.9732	+	16.7277i	−1.12693	+	0.650631i	−0.943160	−	0.332339i	$-0.892162\pi$
$661$	−28.9732	+	16.7277i	−1.12693	+	0.650631i	−0.183766	+	0.982970i	$0.558829\pi$
$662$	−22.0548			−0.857186
$663$	6.46830	+	0.678132i	0.251208	+	0.0263365i
$664$	−1.25516			−0.0487097
$665$	21.2463	−	12.2666i	0.823897	−	0.475677i
$666$	−4.05701	−	7.02694i	−0.157206	−	0.272289i
$667$	−18.9006	+	32.7368i	−0.731834	+	1.26757i
$668$			25.2372i			0.976457i
$669$	2.88040	+	1.66300i	0.111363	+	0.0642954i
$670$	39.1376	+	22.5961i	1.51202	+	0.872963i
$671$			15.5162i			0.598996i
$672$	28.8239	−	49.9244i	1.11190	−	1.92587i
$673$	−15.9158	−	27.5670i	−0.613509	−	1.06263i	−0.990644	−	0.136470i	$-0.956424\pi$
$673$	−15.9158	−	27.5670i	−0.613509	−	1.06263i	0.377135	−	0.926158i	$-0.376909\pi$
$674$	−12.5612	+	7.25220i	−0.483839	+	0.279344i
$675$	23.4995			0.904494
$676$	−12.8714	+	14.3103i	−0.495055	+	0.550394i
$677$	−0.965599			−0.0371110			−0.0185555	−	0.999828i	$-0.505907\pi$
$677$	−0.965599			−0.0371110			−0.0185555	+	0.999828i	$0.505907\pi$
$678$	2.75599	−	1.59117i	0.105843	−	0.0611087i
$679$	4.18336	+	7.24579i	0.160543	+	0.278068i
$680$	−4.09274	+	7.08883i	−0.156949	+	0.271844i
$681$			31.6786i			1.21393i
$682$	−1.45334	−	0.839084i	−0.0556511	−	0.0321302i
$683$	−36.4502	−	21.0446i	−1.39473	−	0.805247i	−0.400895	−	0.916124i	$-0.631301\pi$
$683$	−36.4502	−	21.0446i	−1.39473	−	0.805247i	−0.993834	+	0.110877i	$0.964634\pi$
$684$		−	4.30765i		−	0.164707i
$685$	26.3718	−	45.6773i	1.00762	−	1.74524i
$686$	−7.84989	−	13.5964i	−0.299710	−	0.519113i
$687$	39.2578	−	22.6655i	1.49778	−	0.864743i
$688$	−1.81552			−0.0692162
$689$	−27.1725	−	2.84874i	−1.03519	−	0.108529i
$690$	−34.7035			−1.32114
$691$	16.7062	−	9.64533i	0.635534	−	0.366926i	−0.147358	−	0.989083i	$-0.547077\pi$
$691$	16.7062	−	9.64533i	0.635534	−	0.366926i	0.782892	+	0.622157i	$0.213744\pi$
$692$	−11.3423	−	19.6455i	−0.431170	−	0.746809i
$693$	−10.7312	+	18.5870i	−0.407644	+	0.706060i
$694$			16.4867i			0.625826i
$695$	−13.6058	−	7.85533i	−0.516099	−	0.297970i
$696$	35.6878	+	20.6043i	1.35274	+	0.781005i
$697$			6.14274i			0.232673i
$698$	10.8676	−	18.8232i	0.411344	−	0.712469i
$699$	−2.96093	−	5.12848i	−0.111993	−	0.193977i
$700$	65.5976	−	37.8728i	2.47936	−	1.43146i
$701$	−17.1449			−0.647554			−0.323777	−	0.946133i	$-0.604953\pi$
$701$	−17.1449			−0.647554			−0.323777	+	0.946133i	$0.604953\pi$
$702$	−4.75222	+	2.11732i	−0.179361	+	0.0799130i
$703$	7.32426			0.276240
$704$	−3.84858	+	2.22198i	−0.145049	+	0.0837441i
$705$	−29.8856	−	51.7633i	−1.12556	−	1.94952i
$706$	−9.93816	+	17.2134i	−0.374028	+	0.647835i
$707$			49.5479i			1.86344i
$708$	−40.5768	−	23.4270i	−1.52497	−	0.880441i
$709$	32.0493	+	18.5037i	1.20364	+	0.694920i	0.961362	−	0.275288i	$-0.0887732\pi$
$709$	32.0493	+	18.5037i	1.20364	+	0.694920i	0.242275	+	0.970208i	$0.422107\pi$
$710$		−	3.72226i		−	0.139694i
$711$	−1.47680	+	2.55789i	−0.0553843	+	0.0959283i
$712$	−9.02746	−	15.6360i	−0.338318	−	0.585985i
$713$	4.50689	−	2.60205i	0.168784	−	0.0974477i
$714$	5.66646			0.212062
$715$	13.9783	+	31.3737i	0.522759	+	1.17331i
$716$	9.68469			0.361934
$717$	−9.56742	+	5.52375i	−0.357302	+	0.206288i
$718$	−1.22867	−	2.12812i	−0.0458536	−	0.0794207i
$719$	−14.3803	+	24.9075i	−0.536296	+	0.928893i	0.462803	+	0.886461i	$0.346844\pi$
$719$	−14.3803	+	24.9075i	−0.536296	+	0.928893i	−0.999099	+	0.0424316i	$0.986490\pi$
$720$		−	9.97702i		−	0.371822i
$721$	62.0215	+	35.8081i	2.30980	+	1.33356i
$722$	10.6777	+	6.16476i	0.397382	+	0.229429i
$723$			42.9783i			1.59838i
$724$	−13.1902	+	22.8461i	−0.490211	+	0.849070i
$725$	42.6295	+	73.8364i	1.58322	+	2.74221i
$726$	−7.87434	+	4.54625i	−0.292244	+	0.168727i
$727$	−18.2293			−0.676088			−0.338044	−	0.941130i	$-0.609765\pi$
$727$	−18.2293			−0.676088			−0.338044	+	0.941130i	$0.609765\pi$
$728$	−23.1634	+	31.8992i	−0.858492	+	1.18226i
$729$	−9.40828			−0.348455
$730$	10.0086	−	5.77849i	0.370437	−	0.213872i
$731$	−0.627853	−	1.08747i	−0.0232220	−	0.0402216i
$732$	−11.1565	+	19.3236i	−0.412355	+	0.714219i
$733$			16.3094i			0.602403i	0.953561	+	0.301201i	$0.0973876\pi$
$733$			16.3094i			0.602403i	−0.953561	+	0.301201i	$0.902612\pi$
$734$	12.2620	+	7.07948i	0.452599	+	0.261308i
$735$	−96.1368	−	55.5046i	−3.54606	−	2.04732i
$736$		−	30.4344i		−	1.12183i
$737$	17.8437	−	30.9062i	0.657281	−	1.13844i
$738$	5.86921	+	10.1658i	0.216048	+	0.374207i
$739$	−40.3724	+	23.3090i	−1.48512	+	0.857435i	−0.999857	−	0.0169316i	$-0.994610\pi$
$739$	−40.3724	+	23.3090i	−1.48512	+	0.857435i	−0.485265	+	0.874367i	$0.661277\pi$
$740$	32.2464			1.18540
$741$	−1.16974	+	11.1575i	−0.0429715	+	0.409880i
$742$	−23.8040			−0.873874
$743$	34.6672	−	20.0151i	1.27181	−	0.734282i	0.296485	−	0.955037i	$-0.404185\pi$
$743$	34.6672	−	20.0151i	1.27181	−	0.734282i	0.975329	+	0.220755i	$0.0708521\pi$
$744$	−2.83661	−	4.91315i	−0.103995	−	0.180125i
$745$	−5.22851	+	9.05605i	−0.191558	+	0.331788i
$746$		−	1.47744i		−	0.0540929i
$747$	0.916373	+	0.529068i	0.0335283	+	0.0193576i
$748$	2.38124	+	1.37481i	0.0870669	+	0.0502681i
$749$			6.25980i			0.228728i
$750$	−22.4649	+	38.9104i	−0.820302	+	1.42081i
$751$	−1.31337	−	2.27483i	−0.0479256	−	0.0830096i	0.841067	−	0.540930i	$-0.181928\pi$
$751$	−1.31337	−	2.27483i	−0.0479256	−	0.0830096i	−0.888993	+	0.457921i	$0.848594\pi$
$752$	6.45145	−	3.72475i	0.235260	−	0.135827i
$753$	−10.6854			−0.389398
$754$	−15.2735	−	11.0908i	−0.556229	−	0.403901i
$755$	0.609451			0.0221802
$756$	11.1888	−	6.45988i	0.406934	−	0.234943i
$757$	5.98467	+	10.3657i	0.217516	+	0.376750i	0.954048	−	0.299654i	$-0.0968711\pi$
$757$	5.98467	+	10.3657i	0.217516	+	0.376750i	−0.736532	+	0.676403i	$0.763538\pi$
$758$	−3.09803	+	5.36594i	−0.112525	+	0.194900i
$759$			27.4047i			0.994729i
$760$	−12.2278	−	7.05975i	−0.443550	−	0.256084i
$761$	−34.9225	−	20.1625i	−1.26594	−	0.730890i	−0.291722	−	0.956503i	$-0.594228\pi$
$761$	−34.9225	−	20.1625i	−1.26594	−	0.730890i	−0.974217	+	0.225613i	$0.927561\pi$
$762$		−	13.0694i		−	0.473453i
$763$	37.7324	−	65.3544i	1.36600	−	2.36599i
$764$	17.6129	+	30.5064i	0.637211	+	1.10368i
$765$	5.97609	−	3.45030i	0.216066	−	0.124746i
$766$	−11.5766			−0.418281
$767$	40.8245	+	29.6444i	1.47409	+	1.07040i
$768$	−25.4553			−0.918537
$769$	−10.2371	+	5.91038i	−0.369159	+	0.213134i	−0.673091	−	0.739560i	$-0.735034\pi$
$769$	−10.2371	+	5.91038i	−0.369159	+	0.213134i	0.303932	+	0.952694i	$0.401700\pi$
$770$	14.9625	+	25.9158i	0.539210	+	0.933939i
$771$	19.4254	−	33.6458i	0.699589	−	1.21172i
$772$			18.2363i			0.656339i
$773$	−48.0707	−	27.7536i	−1.72898	−	0.998229i	−0.894236	−	0.447596i	$-0.852280\pi$
$773$	−48.0707	−	27.7536i	−1.72898	−	0.998229i	−0.834748	−	0.550633i	$-0.814386\pi$
$774$	−2.07810	−	1.19979i	−0.0746956	−	0.0431255i
$775$		−	11.7376i		−	0.421628i
$776$	2.40764	−	4.17015i	0.0864292	−	0.149700i
$777$	−26.2387	−	45.4467i	−0.941307	−	1.63039i
$778$	−9.33207	+	5.38788i	−0.334571	+	0.193165i
$779$	−10.5959			−0.379637
$780$	−5.15000	+	49.1228i	−0.184399	+	1.75888i
$781$	−2.93940			−0.105180
$782$	2.59075	−	1.49577i	0.0926449	−	0.0534886i
$783$	7.27121	+	12.5941i	0.259852	+	0.450077i
$784$	6.91774	−	11.9819i	0.247062	−	0.427924i
$785$			6.89805i			0.246202i
$786$	−2.13315	−	1.23157i	−0.0760869	−	0.0439288i
$787$	−36.7237	−	21.2024i	−1.30906	−	0.755785i	−0.327119	−	0.944983i	$-0.606078\pi$
$787$	−36.7237	−	21.2024i	−1.30906	−	0.755785i	−0.981939	+	0.189198i	$0.939411\pi$
$788$		−	11.2063i		−	0.399207i
$789$	22.0170	−	38.1346i	0.783827	−	1.35763i
$790$	2.05910	+	3.56646i	0.0732594	+	0.126889i
$791$	7.36969	−	4.25489i	0.262036	−	0.151287i
$792$	12.3522			0.438916
$793$	14.1173	−	19.4415i	0.501320	−	0.690389i
$794$	−15.9676			−0.566671
$795$	−60.7186	+	35.0559i	−2.15347	+	1.24330i
$796$	11.3304	+	19.6249i	0.401596	+	0.695585i
$797$	−8.77434	+	15.1976i	−0.310803	+	0.538327i	−0.978536	−	0.206074i	$-0.933931\pi$
$797$	−8.77434	+	15.1976i	−0.310803	+	0.538327i	0.667733	+	0.744401i	$0.267265\pi$
$798$			9.77432i			0.346007i
$799$	4.46214	+	2.57622i	0.157859	+	0.0911400i
$800$	−59.4470	−	34.3217i	−2.10177	−	1.21346i
$801$			15.2208i			0.537801i
$802$	9.53246	−	16.5107i	0.336603	−	0.583013i
$803$	−4.56317	−	7.90364i	−0.161031	−	0.278914i
$804$	44.4444	−	25.6600i	1.56743	−	0.904957i
$805$	−92.7992			−3.27074
$806$	1.05757	+	2.37366i	0.0372513	+	0.0836087i
$807$	−40.8679			−1.43862
$808$	24.6957	−	14.2581i	0.868793	−	0.501598i
$809$	−13.3927	−	23.1968i	−0.470861	−	0.815555i	0.528583	−	0.848881i	$-0.322723\pi$
$809$	−13.3927	−	23.1968i	−0.470861	−	0.815555i	−0.999445	+	0.0333261i	$0.989390\pi$
$810$	−16.0287	+	27.7625i	−0.563190	+	0.975474i
$811$		−	50.2634i		−	1.76499i	−0.470323	−	0.882494i	$-0.655863\pi$
$811$		−	50.2634i		−	1.76499i	0.470323	−	0.882494i	$-0.344137\pi$
$812$	40.5945	+	23.4372i	1.42459	+	0.822485i
$813$	42.6359	+	24.6158i	1.49531	+	0.863315i
$814$			8.93395i			0.313135i
$815$	15.2389	−	26.3945i	0.533795	−	0.924559i
$816$	1.04006	+	1.80143i	0.0364093	+	0.0630627i
$817$	1.87583	−	1.08301i	0.0656270	−	0.0378897i
$818$	−0.622945			−0.0217808
$819$	30.3572	−	13.5254i	1.06077	−	0.472617i
$820$	−46.6503			−1.62910
$821$	25.5420	−	14.7467i	0.891423	−	0.514663i	0.0170151	−	0.999855i	$-0.494584\pi$
$821$	25.5420	−	14.7467i	0.891423	−	0.514663i	0.874408	+	0.485192i	$0.161250\pi$
$822$	10.5069	+	18.1984i	0.366469	+	0.634744i
$823$	−9.66731	+	16.7443i	−0.336981	+	0.583668i	−0.983863	−	0.178921i	$-0.942739\pi$
$823$	−9.66731	+	16.7443i	−0.336981	+	0.583668i	0.646882	+	0.762590i	$0.276073\pi$
$824$		−	41.2171i		−	1.43587i
$825$	53.5292	+	30.9051i	1.86365	+	1.07598i
$826$	38.0679	+	21.9785i	1.32455	+	0.764730i
$827$			23.1251i			0.804137i	0.915610	+	0.402068i	$0.131709\pi$
$827$			23.1251i			0.804137i	−0.915610	+	0.402068i	$0.868291\pi$
$828$	−8.14707	+	14.1111i	−0.283130	+	0.490396i
$829$	14.7887	+	25.6148i	0.513634	+	0.889640i	0.999875	+	0.0158151i	$0.00503431\pi$
$829$	14.7887	+	25.6148i	0.513634	+	0.889640i	−0.486241	+	0.873825i	$0.661632\pi$
$830$	1.27770	−	0.737679i	0.0443495	−	0.0256052i
$831$	52.2757			1.81342
$832$	6.84386	+	0.717506i	0.237268	+	0.0248750i
$833$	9.56929			0.331556
$834$	5.42074	−	3.12967i	0.187705	−	0.108371i
$835$	−34.8685	−	60.3939i	−1.20667	−	2.09002i
$836$	−2.37147	+	4.10751i	−0.0820191	+	0.142061i
$837$		−	2.00206i		−	0.0692014i
$838$	−11.6970	−	6.75328i	−0.404067	−	0.233288i
$839$	43.8041	+	25.2903i	1.51228	+	0.873118i	0.999897	+	0.0143633i	$0.00457214\pi$
$839$	43.8041	+	25.2903i	1.51228	+	0.873118i	0.512387	+	0.858754i	$0.328761\pi$
$840$			101.164i			3.49050i
$841$	−11.8808	+	20.5782i	−0.409684	+	0.709594i
$842$	4.30378	+	7.45436i	0.148318	+	0.256894i
$843$	48.5198	−	28.0129i	1.67111	−	0.964816i
$844$	7.56577			0.260424
$845$	11.0305	−	52.0287i	0.379462	−	1.78984i
$846$	9.84599			0.338512
$847$	−21.0564	+	12.1569i	−0.723507	+	0.417717i
$848$	−4.36914	−	7.56757i	−0.150037	−	0.259872i
$849$	19.5347	−	33.8351i	0.670429	−	1.16122i
$850$		−	6.74728i		−	0.231430i
$851$	−23.9930	−	13.8524i	−0.822471	−	0.474854i
$852$	−3.66067	−	2.11349i	−0.125413	−	0.0724070i
$853$		−	13.3613i		−	0.457482i	−0.973487	−	0.228741i	$-0.926539\pi$
$853$		−	13.3613i		−	0.457482i	0.973487	−	0.228741i	$-0.0734609\pi$
$854$	10.4666	−	18.1288i	0.358161	−	0.620354i
$855$	5.95157	+	10.3084i	0.203539	+	0.352541i
$856$	3.12002	−	1.80134i	0.106640	−	0.0615686i
$857$	−15.5837			−0.532329			−0.266164	−	0.963928i	$-0.585756\pi$
$857$	−15.5837			−0.532329			−0.266164	+	0.963928i	$0.585756\pi$
$858$	−13.6096	−	1.42682i	−0.464624	−	0.0487109i
$859$	35.2676			1.20331			0.601657	−	0.798754i	$-0.294507\pi$
$859$	35.2676			1.20331			0.601657	+	0.798754i	$0.294507\pi$
$860$	8.25869	−	4.76815i	0.281619	−	0.162593i
$861$	37.9590	+	65.7470i	1.29364	+	2.24065i
$862$	1.45064	−	2.51259i	0.0494091	−	0.0855790i
$863$			52.6130i			1.79097i	0.445096	+	0.895483i	$0.353170\pi$
$863$			52.6130i			1.79097i	−0.445096	+	0.895483i	$0.646830\pi$
$864$	−10.1397	−	5.85418i	−0.344961	−	0.199163i
$865$	54.2855	+	31.3417i	1.84576	+	1.06565i
$866$			17.4274i			0.592208i
$867$	18.5041	−	32.0500i	0.628432	−	1.08848i
$868$	−3.22661	−	5.58866i	−0.109518	−	0.189691i
$869$	2.81637	−	1.62603i	0.0955388	−	0.0551593i
$870$	−48.4381			−1.64220
$871$	−50.4776	+	22.4899i	−1.71037	+	0.762043i
$872$	−43.4321			−1.47079
$873$	−3.51556	+	2.02971i	−0.118984	+	0.0686952i
$874$	2.58012	+	4.46889i	0.0872738	+	0.151163i
$875$	−60.0724	+	104.049i	−2.03082	+	3.51748i
$876$		−	13.1240i		−	0.443420i
$877$	0.830503	+	0.479491i	0.0280441	+	0.0161913i	0.513956	−	0.857816i	$-0.328179\pi$
$877$	0.830503	+	0.479491i	0.0280441	+	0.0161913i	−0.485912	+	0.874008i	$0.661513\pi$
$878$	−16.8338	−	9.71899i	−0.568113	−	0.328000i
$879$		−	42.1083i		−	1.42028i
$880$	−5.49261	+	9.51348i	−0.185156	+	0.320699i
$881$	−8.42222	−	14.5877i	−0.283752	−	0.491473i	0.688554	−	0.725185i	$-0.258246\pi$
$881$	−8.42222	−	14.5877i	−0.283752	−	0.491473i	−0.972306	+	0.233712i	$0.924913\pi$
$882$	15.8365	−	9.14318i	0.533241	−	0.307867i
$883$	49.3520			1.66083			0.830413	−	0.557149i	$-0.188105\pi$
$883$	49.3520			1.66083			0.830413	+	0.557149i	$0.188105\pi$
$884$	−1.73279	−	3.88917i	−0.0582801	−	0.130807i
$885$	129.470			4.35208
$886$	5.82056	−	3.36050i	0.195545	−	0.112898i
$887$	−1.90837	−	3.30540i	−0.0640769	−	0.110984i	0.832207	−	0.554465i	$-0.187077\pi$
$887$	−1.90837	−	3.30540i	−0.0640769	−	0.110984i	−0.896284	+	0.443480i	$0.853744\pi$
$888$	−15.1011	+	26.1558i	−0.506759	+	0.877732i
$889$		−	34.9482i		−	1.17213i
$890$	18.3791	+	10.6112i	0.616069	+	0.355688i
$891$	21.9235	+	12.6576i	0.734466	+	0.424044i
$892$		−	2.17739i		−	0.0729044i
$893$	−4.44383	+	7.69693i	−0.148707	+	0.257568i
$894$	−2.08311	−	3.60805i	−0.0696695	−	0.120671i
$895$	−23.1760	+	13.3806i	−0.774687	+	0.447266i
$896$	−44.9845			−1.50283
$897$	24.9340	−	34.3376i	0.832522	−	1.14650i
$898$	20.3954			0.680604
$899$	6.29057	−	3.63186i	0.209802	−	0.121129i
$900$	18.3753	+	31.8270i	0.612512	+	1.06090i
$901$	3.02191	−	5.23410i	0.100674	−	0.174373i
$902$		−	12.9246i		−	0.430342i
$903$	−13.4401	−	7.75963i	−0.447258	−	0.258224i
$904$	−4.24146	−	2.44881i	−0.141069	−	0.0814461i
$905$		−	72.8960i		−	2.42314i
$906$	−0.121407	+	0.210282i	−0.00403346	+	0.00698616i
$907$	−17.2542	−	29.8852i	−0.572917	−	0.992322i	−0.996264	−	0.0863544i	$-0.972478\pi$
$907$	−17.2542	−	29.8852i	−0.572917	−	0.992322i	0.423347	−	0.905968i	$-0.360855\pi$
$908$	17.9602	−	10.3693i	0.596029	−	0.344117i
$909$	−24.0399			−0.797355
$910$	4.83157	−	46.0855i	0.160165	−	1.52772i
$911$	−17.0514			−0.564937			−0.282468	−	0.959277i	$-0.591153\pi$
$911$	−17.0514			−0.564937			−0.282468	+	0.959277i	$0.591153\pi$
$912$	−3.10737	+	1.79404i	−0.102895	+	0.0594066i
$913$	−0.582532	−	1.00897i	−0.0192790	−	0.0333922i
$914$	4.62518	−	8.01104i	0.152987	−	0.264982i
$915$		−	61.6563i		−	2.03830i
$916$	−25.7004	−	14.8381i	−0.849164	−	0.490265i
$917$	−5.70417	−	3.29330i	−0.188368	−	0.108754i
$918$		−	1.15087i		−	0.0379843i
$919$	−20.4215	+	35.3711i	−0.673644	+	1.16678i	0.303220	+	0.952921i	$0.401938\pi$
$919$	−20.4215	+	35.3711i	−0.673644	+	1.16678i	−0.976863	+	0.213864i	$0.931395\pi$
$920$	26.7042	+	46.2531i	0.880413	+	1.52492i
$921$	27.6106	−	15.9410i	0.909799	−	0.525273i
$922$	24.7799			0.816082
$923$	3.68302	+	2.67440i	0.121228	+	0.0880288i
$924$	33.9826			1.11794
$925$	−54.1152	+	31.2434i	−1.77930	+	1.02728i
$926$	−2.25888	−	3.91249i	−0.0742312	−	0.128572i
$927$	−17.3736	+	30.0920i	−0.570624	+	0.988349i
$928$		−	42.4794i		−	1.39445i
$929$	12.3770	+	7.14589i	0.406077	+	0.234449i	0.689103	−	0.724663i	$-0.258005\pi$
$929$	12.3770	+	7.14589i	0.406077	+	0.234449i	−0.283025	+	0.959112i	$0.591338\pi$
$930$	5.77508	+	3.33424i	0.189372	+	0.109334i
$931$			16.5065i			0.540979i
$932$	−1.93839	+	3.35740i	−0.0634942	+	0.109975i
$933$	7.78989	+	13.4925i	0.255029	+	0.441724i
$934$	−0.660033	+	0.381070i	−0.0215969	+	0.0124690i
$935$	−7.59791			−0.248478
$936$	−15.4771	−	11.2385i	−0.505884	−	0.367343i
$937$	37.0243			1.20953			0.604766	−	0.796403i	$-0.293267\pi$
$937$	37.0243			1.20953			0.604766	+	0.796403i	$0.293267\pi$
$938$	−41.6963	+	24.0734i	−1.36143	+	0.786024i
$939$	19.5294	+	33.8259i	0.637318	+	1.10387i
$940$	−19.5648	+	33.8872i	−0.638132	+	1.10528i
$941$			56.2582i			1.83397i	0.398926	+	0.916983i	$0.369383\pi$
$941$			56.2582i			1.83397i	−0.398926	+	0.916983i	$0.630617\pi$
$942$	−2.38007	−	1.37414i	−0.0775469	−	0.0447717i
$943$	34.7103	+	20.0400i	1.13032	+	0.652593i
$944$			16.1363i			0.525191i
$945$	−17.8503	+	30.9176i	−0.580670	+	1.00575i
$946$	1.32103	+	2.28809i	0.0429504	+	0.0743923i
$947$	0.830579	−	0.479535i	0.0269902	−	0.0155828i	−0.486444	−	0.873712i	$-0.661706\pi$
$947$	0.830579	−	0.479535i	0.0269902	−	0.0155828i	0.513434	+	0.858129i	$0.328373\pi$
$948$	4.67659			0.151889
$949$	−1.47350	+	14.0549i	−0.0478320	+	0.456241i
$950$	11.6387			0.377609
$951$	−17.2898	+	9.98229i	−0.560661	+	0.323698i
$952$	−4.36032	−	7.55230i	−0.141319	−	0.244771i
$953$	−1.83641	+	3.18075i	−0.0594871	+	0.103035i	−0.894235	−	0.447597i	$-0.852280\pi$
$953$	−1.83641	+	3.18075i	−0.0594871	+	0.103035i	0.834748	+	0.550632i	$0.185613\pi$
$954$		−	11.5494i		−	0.373925i
$955$	−84.2970	−	48.6689i	−2.72779	−	1.57489i
$956$	6.26337	+	3.61616i	0.202572	+	0.116955i
$957$			38.2506i			1.23647i
$958$	4.29450	−	7.43830i	0.138749	−	0.240320i
$959$	28.0960	+	48.6637i	0.907267	+	1.57143i
$960$	15.2930	−	8.82943i	0.493580	−	0.284969i
$961$	−1.00000			−0.0322581
$962$	8.12849	−	11.1941i	0.262073	−	0.360912i
$963$	−3.03717			−0.0978714
$964$	24.3665	−	14.0680i	0.784792	−	0.453100i
$965$	−25.1958	−	43.6404i	−0.811081	−	1.40483i
$966$	18.4862	−	32.0190i	0.594784	−	1.03020i
$967$			29.6305i			0.952851i	0.879215	+	0.476426i	$0.158068\pi$
$967$			29.6305i			0.952851i	−0.879215	+	0.476426i	$0.841932\pi$
$968$	12.1186	+	6.99665i	0.389505	+	0.224881i
$969$	−2.14921	−	1.24085i	−0.0690425	−	0.0398617i
$970$			5.66004i			0.181733i
$971$	−3.75069	+	6.49639i	−0.120365	+	0.208479i	−0.919912	−	0.392125i	$-0.871740\pi$
$971$	−3.75069	+	6.49639i	−0.120365	+	0.208479i	0.799546	+	0.600604i	$0.205073\pi$
$972$	13.7558	+	23.8258i	0.441218	+	0.764212i
$973$	14.4954	−	8.36890i	0.464700	−	0.268295i
$974$	−2.53757			−0.0813090
$975$	−38.9523	−	87.4267i	−1.24747	−	2.79989i
$976$	7.68445			0.245973
$977$	−18.1525	+	10.4803i	−0.580749	+	0.335296i	−0.761431	−	0.648246i	$-0.775503\pi$
$977$	−18.1525	+	10.4803i	−0.580749	+	0.335296i	0.180682	+	0.983542i	$0.442170\pi$
$978$	6.07136	+	10.5159i	0.194141	+	0.336262i
$979$	8.37945	−	14.5136i	0.267809	−	0.463858i
$980$			72.6729i			2.32145i
$981$	31.7091	+	18.3072i	1.01239	+	0.584505i
$982$	−18.4999	−	10.6809i	−0.590356	−	0.340842i
$983$		−	11.1548i		−	0.355784i	−0.984050	−	0.177892i	$-0.943072\pi$
$983$		−	11.1548i		−	0.355784i	0.984050	−	0.177892i	$-0.0569278\pi$
$984$	21.8465	−	37.8392i	0.696440	−	1.20627i
$985$	15.4829	+	26.8172i	0.493326	+	0.854466i
$986$	3.61608	−	2.08775i	0.115159	−	0.0664874i
$987$	63.6789			2.02692
$988$	6.70860	−	2.98897i	0.213429	−	0.0950918i
$989$	−8.19321			−0.260529
$990$	−12.5740	+	7.25958i	−0.399627	+	0.230725i
$991$	9.53498	+	16.5151i	0.302889	+	0.524619i	0.976789	−	0.214204i	$-0.0687156\pi$
$991$	9.53498	+	16.5151i	0.302889	+	0.524619i	−0.673900	+	0.738822i	$0.735382\pi$
$992$	−2.92408	+	5.06465i	−0.0928395	+	0.160803i
$993$		−	69.2067i		−	2.19621i
$994$	3.43433	+	1.98281i	0.108930	+	0.0628909i
$995$	−54.2285	−	31.3089i	−1.71916	−	0.992558i
$996$		−	1.67541i		−	0.0530873i
$997$	−15.3144	+	26.5253i	−0.485012	+	0.840066i	−0.999852	−	0.0172208i	$-0.994518\pi$
$997$	−15.3144	+	26.5253i	−0.485012	+	0.840066i	0.514840	+	0.857287i	$0.327851\pi$
$998$	5.11634	+	8.86177i	0.161955	+	0.280514i
$999$	−9.23031	+	5.32912i	−0.292034	+	0.168606i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	403.2.r.a.218.12	✓	68
13.2	odd	12		5239.2.a.q.1.14		34
13.4	even	6	inner	403.2.r.a.342.12	yes	68
13.11	odd	12		5239.2.a.r.1.21		34

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
403.2.r.a.218.12	✓	68	1.1	even	1	trivial
403.2.r.a.342.12	yes	68	13.4	even	6	inner
5239.2.a.q.1.14		34	13.2	odd	12
5239.2.a.r.1.21		34	13.11	odd	12

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 403 = 13 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	403.r (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.624164 + 0.360361i) q^{2} +(-1.13079 - 1.95859i) q^{3} +(-0.740280 + 1.28220i) q^{4} -4.09116i q^{5} +(1.41160 + 0.814986i) q^{6} +(3.77469 + 2.17932i) q^{7} -2.50852i q^{8} +(-1.05738 + 1.83143i) q^{9} +O(q^{10})\)	\(q+(-0.624164 + 0.360361i) q^{2} +(-1.13079 - 1.95859i) q^{3} +(-0.740280 + 1.28220i) q^{4} -4.09116i q^{5} +(1.41160 + 0.814986i) q^{6} +(3.77469 + 2.17932i) q^{7} -2.50852i q^{8} +(-1.05738 + 1.83143i) q^{9} +(1.47430 + 2.55356i) q^{10} +(2.01650 - 1.16423i) q^{11} +3.34841 q^{12} +(-3.58590 - 0.375943i) q^{13} -3.14137 q^{14} +(-8.01290 + 4.62625i) q^{15} +(-0.576587 - 0.998677i) q^{16} +(0.398795 - 0.690734i) q^{17} -1.52415i q^{18} +(1.19148 + 0.687900i) q^{19} +(5.24570 + 3.02861i) q^{20} -9.85742i q^{21} +(-0.839084 + 1.45334i) q^{22} +(-2.60205 - 4.50689i) q^{23} +(-4.91315 + 2.83661i) q^{24} -11.7376 q^{25} +(2.37366 - 1.05757i) q^{26} -2.00206 q^{27} +(-5.58866 + 3.22661i) q^{28} +(-3.63186 - 6.29057i) q^{29} +(3.33424 - 5.77508i) q^{30} +1.00000i q^{31} +(5.06465 + 2.92408i) q^{32} +(-4.56047 - 2.63299i) q^{33} +0.574842i q^{34} +(8.91596 - 15.4429i) q^{35} +(-1.56551 - 2.71154i) q^{36} +(4.61040 - 2.66182i) q^{37} -0.991570 q^{38} +(3.31858 + 7.44841i) q^{39} -10.2628 q^{40} +(-6.66980 + 3.85081i) q^{41} +(3.55223 + 6.15265i) q^{42} +(0.787186 - 1.36345i) q^{43} +3.44741i q^{44} +(7.49268 + 4.32590i) q^{45} +(3.24822 + 1.87536i) q^{46} +6.45999i q^{47} +(-1.30400 + 2.25859i) q^{48} +(5.99887 + 10.3904i) q^{49} +(7.32621 - 4.22979i) q^{50} -1.80382 q^{51} +(3.13660 - 4.31954i) q^{52} +7.57760 q^{53} +(1.24961 - 0.721465i) q^{54} +(-4.76304 - 8.24983i) q^{55} +(5.46686 - 9.46888i) q^{56} -3.11148i q^{57} +(4.53375 + 2.61756i) q^{58} +(-12.1182 - 6.99647i) q^{59} -13.6989i q^{60} +(-3.33187 + 5.77097i) q^{61} +(-0.360361 - 0.624164i) q^{62} +(-7.98254 + 4.60872i) q^{63} -1.90855 q^{64} +(-1.53804 + 14.6705i) q^{65} +3.79531 q^{66} +(13.2733 - 7.66334i) q^{67} +(0.590440 + 1.02267i) q^{68} +(-5.88476 + 10.1927i) q^{69} +12.8519i q^{70} +(-1.09326 - 0.631193i) q^{71} +(4.59417 + 2.65245i) q^{72} -3.91949i q^{73} +(-1.91843 + 3.32282i) q^{74} +(13.2728 + 22.9892i) q^{75} +(-1.76405 + 1.01848i) q^{76} +10.1489 q^{77} +(-4.75546 - 3.45314i) q^{78} +1.39666 q^{79} +(-4.08575 + 2.35891i) q^{80} +(5.43604 + 9.41550i) q^{81} +(2.77536 - 4.80707i) q^{82} -0.500360i q^{83} +(12.6392 + 7.29725i) q^{84} +(-2.82591 - 1.63154i) q^{85} +1.13469i q^{86} +(-8.21375 + 14.2266i) q^{87} +(-2.92048 - 5.05842i) q^{88} +(6.23317 - 3.59872i) q^{89} -6.23555 q^{90} +(-12.7164 - 9.23389i) q^{91} +7.70499 q^{92} +(1.95859 - 1.13079i) q^{93} +(-2.32793 - 4.03210i) q^{94} +(2.81431 - 4.87453i) q^{95} -13.2261i q^{96} +(1.66240 + 0.959786i) q^{97} +(-7.48856 - 4.32352i) q^{98} +4.92410i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 68 q + 32 q^{4} - 34 q^{9}+O(q^{10}) \) 68 * q + 32 * q^4 - 34 * q^9	\( 68 q + 32 q^{4} - 34 q^{9} + 8 q^{10} - 12 q^{11} - 16 q^{12} + 6 q^{13} - 8 q^{14} - 36 q^{16} - 6 q^{17} + 12 q^{19} - 12 q^{20} - 20 q^{22} - 8 q^{23} + 48 q^{24} - 72 q^{25} - 12 q^{27} - 6 q^{28} + 32 q^{30} + 6 q^{33} + 30 q^{35} + 40 q^{36} - 42 q^{37} - 36 q^{38} - 14 q^{39} + 8 q^{40} + 18 q^{41} - 16 q^{42} + 12 q^{43} + 60 q^{45} + 30 q^{46} - 46 q^{48} + 22 q^{49} + 56 q^{51} + 20 q^{53} - 114 q^{54} - 6 q^{55} - 2 q^{56} - 12 q^{58} + 6 q^{59} + 6 q^{61} - 8 q^{62} - 30 q^{63} + 24 q^{64} + 24 q^{65} + 8 q^{66} - 48 q^{67} + 58 q^{68} - 28 q^{69} - 30 q^{71} + 72 q^{72} + 8 q^{74} - 4 q^{75} - 12 q^{76} - 20 q^{77} + 26 q^{78} + 16 q^{79} + 42 q^{80} - 58 q^{81} - 42 q^{82} - 72 q^{84} + 30 q^{85} - 20 q^{87} + 64 q^{88} + 18 q^{89} + 52 q^{90} - 22 q^{91} + 48 q^{92} + 8 q^{94} - 32 q^{95} - 168 q^{98}+O(q^{100}) \) 68 * q + 32 * q^4 - 34 * q^9 + 8 * q^10 - 12 * q^11 - 16 * q^12 + 6 * q^13 - 8 * q^14 - 36 * q^16 - 6 * q^17 + 12 * q^19 - 12 * q^20 - 20 * q^22 - 8 * q^23 + 48 * q^24 - 72 * q^25 - 12 * q^27 - 6 * q^28 + 32 * q^30 + 6 * q^33 + 30 * q^35 + 40 * q^36 - 42 * q^37 - 36 * q^38 - 14 * q^39 + 8 * q^40 + 18 * q^41 - 16 * q^42 + 12 * q^43 + 60 * q^45 + 30 * q^46 - 46 * q^48 + 22 * q^49 + 56 * q^51 + 20 * q^53 - 114 * q^54 - 6 * q^55 - 2 * q^56 - 12 * q^58 + 6 * q^59 + 6 * q^61 - 8 * q^62 - 30 * q^63 + 24 * q^64 + 24 * q^65 + 8 * q^66 - 48 * q^67 + 58 * q^68 - 28 * q^69 - 30 * q^71 + 72 * q^72 + 8 * q^74 - 4 * q^75 - 12 * q^76 - 20 * q^77 + 26 * q^78 + 16 * q^79 + 42 * q^80 - 58 * q^81 - 42 * q^82 - 72 * q^84 + 30 * q^85 - 20 * q^87 + 64 * q^88 + 18 * q^89 + 52 * q^90 - 22 * q^91 + 48 * q^92 + 8 * q^94 - 32 * q^95 - 168 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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