LMFDB - Embedded newform 187.2.g.e.137.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [187,2,Mod(69,187)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(187, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([8, 0]))

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

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

chi := DirichletCharacter("187.69");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 187 = 11 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	187.g (of order $5$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$1.49320251780$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{5})$
Coefficient field:	8.0.13140625.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 3x^{7} + 5x^{6} - 3x^{5} + 4x^{4} + 3x^{3} + 5x^{2} + 3x + 1 $ x^8 - 3x^7 + 5x^6 - 3x^5 + 4x^4 + 3x^3 + 5x^2 + 3*x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			137.2
Root			$1.69513 - 1.23158i$ of defining polynomial
Character	$\chi$	$=$	187.137
Dual form			187.2.g.e.86.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.400166 + 1.23158i) q^{2} +(-0.386111 - 0.280526i) q^{3} +(0.261370 - 0.189896i) q^{4} +(0.547647 - 1.68548i) q^{5} +(0.190983 - 0.587785i) q^{6} +(1.85666 - 1.34895i) q^{7} +(2.43376 + 1.76823i) q^{8} +(-0.856664 - 2.63654i) q^{9} +O(q^{10})$	\(q+(0.400166 + 1.23158i) q^{2} +(-0.386111 - 0.280526i) q^{3} +(0.261370 - 0.189896i) q^{4} +(0.547647 - 1.68548i) q^{5} +(0.190983 - 0.587785i) q^{6} +(1.85666 - 1.34895i) q^{7} +(2.43376 + 1.76823i) q^{8} +(-0.856664 - 2.63654i) q^{9} +2.29496 q^{10} +(-2.54508 + 2.12663i) q^{11} -0.154189 q^{12} +(1.04228 + 3.20780i) q^{13} +(2.40431 + 1.74683i) q^{14} +(-0.684276 + 0.497155i) q^{15} +(-1.00415 + 3.09044i) q^{16} +(-0.309017 + 0.951057i) q^{17} +(2.90431 - 2.11011i) q^{18} +(0.372057 + 0.270315i) q^{19} +(-0.176929 - 0.544531i) q^{20} -1.09529 q^{21} +(-3.63757 - 2.28348i) q^{22} -5.90904 q^{23} +(-0.443667 - 1.36547i) q^{24} +(1.50415 + 1.09283i) q^{25} +(-3.53359 + 2.56731i) q^{26} +(-0.851296 + 2.62002i) q^{27} +(0.229116 - 0.705148i) q^{28} +(-1.39026 + 1.01008i) q^{29} +(-0.886111 - 0.643798i) q^{30} +(-1.12755 - 3.47023i) q^{31} +1.80862 q^{32} +(1.57926 - 0.107152i) q^{33} -1.29496 q^{34} +(-1.25683 - 3.86812i) q^{35} +(-0.724576 - 0.526435i) q^{36} +(1.14965 - 0.835268i) q^{37} +(-0.184031 + 0.566390i) q^{38} +(0.497438 - 1.53096i) q^{39} +(4.31316 - 3.13370i) q^{40} +(-2.34581 - 1.70433i) q^{41} +(-0.438299 - 1.34895i) q^{42} -5.72162 q^{43} +(-0.261370 + 1.03914i) q^{44} -4.91300 q^{45} +(-2.36459 - 7.27747i) q^{46} +(7.98772 + 5.80342i) q^{47} +(1.25466 - 0.911566i) q^{48} +(-0.535571 + 1.64832i) q^{49} +(-0.743998 + 2.28979i) q^{50} +(0.386111 - 0.280526i) q^{51} +(0.881571 + 0.640499i) q^{52} +(-4.36337 - 13.4291i) q^{53} -3.56743 q^{54} +(2.19059 + 5.45434i) q^{55} +6.90392 q^{56} +(-0.0678250 - 0.208744i) q^{57} +(-1.80033 - 1.30802i) q^{58} +(-11.4670 + 8.33123i) q^{59} +(-0.0844411 + 0.259883i) q^{60} +(1.27503 - 3.92414i) q^{61} +(3.82268 - 2.77734i) q^{62} +(-5.14709 - 3.73958i) q^{63} +(2.73204 + 8.40835i) q^{64} +5.97750 q^{65} +(0.763932 + 1.90211i) q^{66} +3.30325 q^{67} +(0.0998345 + 0.307259i) q^{68} +(2.28155 + 1.65764i) q^{69} +(4.26097 - 3.09578i) q^{70} +(-2.96262 + 9.11801i) q^{71} +(2.57709 - 7.93148i) q^{72} +(7.46799 - 5.42581i) q^{73} +(1.48875 + 1.08164i) q^{74} +(-0.274201 - 0.843905i) q^{75} +0.148577 q^{76} +(-1.85666 + 7.38161i) q^{77} +2.08456 q^{78} +(-1.84395 - 5.67509i) q^{79} +(4.65897 + 3.38494i) q^{80} +(-5.66465 + 4.11561i) q^{81} +(1.16031 - 3.57108i) q^{82} +(-4.10639 + 12.6382i) q^{83} +(-0.286277 + 0.207992i) q^{84} +(1.43376 + 1.04169i) q^{85} +(-2.28959 - 7.04665i) q^{86} +0.820148 q^{87} +(-9.95449 + 0.675403i) q^{88} +5.59388 q^{89} +(-1.96601 - 6.05076i) q^{90} +(6.26231 + 4.54984i) q^{91} +(-1.54445 + 1.12211i) q^{92} +(-0.538133 + 1.65620i) q^{93} +(-3.95098 + 12.1599i) q^{94} +(0.659369 - 0.479059i) q^{95} +(-0.698330 - 0.507366i) q^{96} +(-1.35327 - 4.16495i) q^{97} -2.24436 q^{98} +(7.78722 + 4.88842i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - q^{2} + 3 q^{3} + 5 q^{4} - 3 q^{5} + 6 q^{6} + 3 q^{7} + 6 q^{8} + 5 q^{9}+O(q^{10}) $ 8 * q - q^2 + 3 * q^3 + 5 * q^4 - 3 * q^5 + 6 * q^6 + 3 * q^7 + 6 * q^8 + 5 * q^9	\( 8 q - q^{2} + 3 q^{3} + 5 q^{4} - 3 q^{5} + 6 q^{6} + 3 q^{7} + 6 q^{8} + 5 q^{9} + 12 q^{10} + 2 q^{11} + 2 q^{12} + 3 q^{13} - 10 q^{15} + 7 q^{16} + 2 q^{17} + 4 q^{18} - 5 q^{19} - 4 q^{20} + 6 q^{21} - 9 q^{22} - 24 q^{23} - 7 q^{24} - 3 q^{25} - 19 q^{26} + 3 q^{27} + 16 q^{28} + 10 q^{29} - q^{30} + 17 q^{31} - 24 q^{32} - 8 q^{33} - 4 q^{34} + 6 q^{35} - q^{36} - 13 q^{37} - 38 q^{38} - 11 q^{39} + 15 q^{40} - 22 q^{41} - 9 q^{42} + 8 q^{43} - 5 q^{44} - 24 q^{45} - 20 q^{46} + 9 q^{47} + 13 q^{48} + q^{49} - q^{50} - 3 q^{51} - 18 q^{52} - 23 q^{53} + 22 q^{54} - 12 q^{55} + 2 q^{56} + 16 q^{57} - 6 q^{58} - 35 q^{59} - q^{60} - 19 q^{61} - 6 q^{62} - 4 q^{63} + 8 q^{64} + 10 q^{65} + 24 q^{66} - 10 q^{67} + 5 q^{68} + 12 q^{69} + 3 q^{70} - 5 q^{71} + 19 q^{72} + 39 q^{73} - 7 q^{74} + 6 q^{75} + 32 q^{76} - 3 q^{77} + 6 q^{78} - 3 q^{79} + 21 q^{80} + 7 q^{81} - 5 q^{82} + 29 q^{83} + 8 q^{84} - 2 q^{85} - 14 q^{86} + 32 q^{87} + 9 q^{88} + 40 q^{89} + 9 q^{90} + 21 q^{91} + 12 q^{92} - 14 q^{93} + 40 q^{94} + 23 q^{95} - 12 q^{96} - 5 q^{97} + 30 q^{98} + 20 q^{99}+O(q^{100}) \) 8 * q - q^2 + 3 * q^3 + 5 * q^4 - 3 * q^5 + 6 * q^6 + 3 * q^7 + 6 * q^8 + 5 * q^9 + 12 * q^10 + 2 * q^11 + 2 * q^12 + 3 * q^13 - 10 * q^15 + 7 * q^16 + 2 * q^17 + 4 * q^18 - 5 * q^19 - 4 * q^20 + 6 * q^21 - 9 * q^22 - 24 * q^23 - 7 * q^24 - 3 * q^25 - 19 * q^26 + 3 * q^27 + 16 * q^28 + 10 * q^29 - q^30 + 17 * q^31 - 24 * q^32 - 8 * q^33 - 4 * q^34 + 6 * q^35 - q^36 - 13 * q^37 - 38 * q^38 - 11 * q^39 + 15 * q^40 - 22 * q^41 - 9 * q^42 + 8 * q^43 - 5 * q^44 - 24 * q^45 - 20 * q^46 + 9 * q^47 + 13 * q^48 + q^49 - q^50 - 3 * q^51 - 18 * q^52 - 23 * q^53 + 22 * q^54 - 12 * q^55 + 2 * q^56 + 16 * q^57 - 6 * q^58 - 35 * q^59 - q^60 - 19 * q^61 - 6 * q^62 - 4 * q^63 + 8 * q^64 + 10 * q^65 + 24 * q^66 - 10 * q^67 + 5 * q^68 + 12 * q^69 + 3 * q^70 - 5 * q^71 + 19 * q^72 + 39 * q^73 - 7 * q^74 + 6 * q^75 + 32 * q^76 - 3 * q^77 + 6 * q^78 - 3 * q^79 + 21 * q^80 + 7 * q^81 - 5 * q^82 + 29 * q^83 + 8 * q^84 - 2 * q^85 - 14 * q^86 + 32 * q^87 + 9 * q^88 + 40 * q^89 + 9 * q^90 + 21 * q^91 + 12 * q^92 - 14 * q^93 + 40 * q^94 + 23 * q^95 - 12 * q^96 - 5 * q^97 + 30 * q^98 + 20 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/187\mathbb{Z}\right)^\times$.

$n$	$35$	$122$
$\chi(n)$	$e\left(\frac{2}{5}\right)$	$1$

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 $

$2$	0.400166	+	1.23158i	0.282960	+	0.870861i	0.987003	+	0.160703i	$0.0513762\pi$
$2$	0.400166	+	1.23158i	0.282960	+	0.870861i	−0.704043	+	0.710157i	$0.748624\pi$
$3$	−0.386111	−	0.280526i	−0.222922	−	0.161962i	0.470719	−	0.882283i	$-0.343994\pi$
$3$	−0.386111	−	0.280526i	−0.222922	−	0.161962i	−0.693641	+	0.720321i	$0.743994\pi$
$4$	0.261370	−	0.189896i	0.130685	−	0.0949482i
$5$	0.547647	−	1.68548i	0.244915	−	0.753771i	−0.750735	−	0.660603i	$-0.770301\pi$
$5$	0.547647	−	1.68548i	0.244915	−	0.753771i	0.995650	−	0.0931682i	$-0.0296994\pi$
$6$	0.190983	−	0.587785i	0.0779685	−	0.239962i
$7$	1.85666	−	1.34895i	0.701753	−	0.509853i	−0.178750	−	0.983895i	$-0.557205\pi$
$7$	1.85666	−	1.34895i	0.701753	−	0.509853i	0.880503	+	0.474041i	$0.157205\pi$
$8$	2.43376	+	1.76823i	0.860464	+	0.625163i
$9$	−0.856664	−	2.63654i	−0.285555	−	0.878847i
$10$	2.29496			0.725731
$11$	−2.54508	+	2.12663i	−0.767372	+	0.641202i
$11$	−2.54508	+	2.12663i	−0.767372	+	0.641202i
$12$	−0.154189			−0.0445105
$13$	1.04228	+	3.20780i	0.289076	+	0.889685i	0.985147	+	0.171712i	$0.0549298\pi$
$13$	1.04228	+	3.20780i	0.289076	+	0.889685i	−0.696071	+	0.717973i	$0.745070\pi$
$14$	2.40431	+	1.74683i	0.642579	+	0.466861i
$15$	−0.684276	+	0.497155i	−0.176679	+	0.128365i
$16$	−1.00415	+	3.09044i	−0.251036	+	0.772610i
$17$	−0.309017	+	0.951057i	−0.0749476	+	0.230665i
$17$	−0.309017	+	0.951057i	−0.0749476	+	0.230665i
$18$	2.90431	−	2.11011i	0.684553	−	0.497357i
$19$	0.372057	+	0.270315i	0.0853558	+	0.0620146i	0.629645	−	0.776883i	$-0.283200\pi$
$19$	0.372057	+	0.270315i	0.0853558	+	0.0620146i	−0.544289	+	0.838898i	$0.683200\pi$
$20$	−0.176929	−	0.544531i	−0.0395625	−	0.121761i
$21$	−1.09529			−0.239013
$22$	−3.63757	−	2.28348i	−0.775533	−	0.486840i
$23$	−5.90904			−1.23212			−0.616060	−	0.787699i	$-0.711272\pi$
$23$	−5.90904			−1.23212			−0.616060	+	0.787699i	$0.711272\pi$
$24$	−0.443667	−	1.36547i	−0.0905632	−	0.278725i
$25$	1.50415	+	1.09283i	0.300829	+	0.218565i
$26$	−3.53359	+	2.56731i	−0.692995	+	0.503490i
$27$	−0.851296	+	2.62002i	−0.163832	+	0.504223i
$28$	0.229116	−	0.705148i	0.0432989	−	0.133260i
$29$	−1.39026	+	1.01008i	−0.258164	+	0.187567i	−0.709337	−	0.704869i	$-0.751006\pi$
$29$	−1.39026	+	1.01008i	−0.258164	+	0.187567i	0.451173	+	0.892436i	$0.351006\pi$
$30$	−0.886111	−	0.643798i	−0.161781	−	0.117541i
$31$	−1.12755	−	3.47023i	−0.202514	−	0.623273i	−0.999806	−	0.0196798i	$-0.993735\pi$
$31$	−1.12755	−	3.47023i	−0.202514	−	0.623273i	0.797293	−	0.603593i	$-0.206265\pi$
$32$	1.80862			0.319722
$33$	1.57926	−	0.107152i	0.274914	−	0.0186527i
$34$	−1.29496			−0.222084
$35$	−1.25683	−	3.86812i	−0.212443	−	0.653832i
$36$	−0.724576	−	0.526435i	−0.120763	−	0.0877392i
$37$	1.14965	−	0.835268i	0.189001	−	0.137317i	−0.489261	−	0.872137i	$-0.662733\pi$
$37$	1.14965	−	0.835268i	0.189001	−	0.137317i	0.678262	+	0.734820i	$0.262733\pi$
$38$	−0.184031	+	0.566390i	−0.0298538	+	0.0918807i
$39$	0.497438	−	1.53096i	0.0796538	−	0.245149i
$40$	4.31316	−	3.13370i	0.681971	−	0.495481i
$41$	−2.34581	−	1.70433i	−0.366354	−	0.266172i	0.389343	−	0.921093i	$-0.372702\pi$
$41$	−2.34581	−	1.70433i	−0.366354	−	0.266172i	−0.755697	+	0.654921i	$0.772702\pi$
$42$	−0.438299	−	1.34895i	−0.0676310	−	0.208147i
$43$	−5.72162			−0.872539			−0.436269	−	0.899816i	$-0.643701\pi$
$43$	−5.72162			−0.872539			−0.436269	+	0.899816i	$0.643701\pi$
$44$	−0.261370	+	1.03914i	−0.0394030	+	0.156656i
$45$	−4.91300			−0.732386
$46$	−2.36459	−	7.27747i	−0.348640	−	1.07300i
$47$	7.98772	+	5.80342i	1.16513	+	0.846515i	0.990418	−	0.138104i	$-0.0441010\pi$
$47$	7.98772	+	5.80342i	1.16513	+	0.846515i	0.174711	+	0.984620i	$0.444101\pi$
$48$	1.25466	−	0.911566i	0.181095	−	0.131573i
$49$	−0.535571	+	1.64832i	−0.0765102	+	0.235474i
$50$	−0.743998	+	2.28979i	−0.105217	+	0.323825i
$51$	0.386111	−	0.280526i	0.0540664	−	0.0392816i
$52$	0.881571	+	0.640499i	0.122252	+	0.0888212i
$53$	−4.36337	−	13.4291i	−0.599355	−	1.84463i	−0.531729	−	0.846915i	$-0.678457\pi$
$53$	−4.36337	−	13.4291i	−0.599355	−	1.84463i	−0.0676266	−	0.997711i	$-0.521543\pi$
$54$	−3.56743			−0.485466
$55$	2.19059	+	5.45434i	0.295379	+	0.735463i
$56$	6.90392			0.922575
$57$	−0.0678250	−	0.208744i	−0.00898364	−	0.0276488i
$58$	−1.80033	−	1.30802i	−0.236395	−	0.171751i
$59$	−11.4670	+	8.33123i	−1.49287	+	1.08463i	−0.519755	+	0.854315i	$0.673977\pi$
$59$	−11.4670	+	8.33123i	−1.49287	+	1.08463i	−0.973115	+	0.230319i	$0.926023\pi$
$60$	−0.0844411	+	0.259883i	−0.0109013	+	0.0335507i
$61$	1.27503	−	3.92414i	0.163251	−	0.502434i	−0.835652	−	0.549259i	$-0.814910\pi$
$61$	1.27503	−	3.92414i	0.163251	−	0.502434i	0.998903	+	0.0468245i	$0.0149102\pi$
$62$	3.82268	−	2.77734i	0.485480	−	0.352722i
$63$	−5.14709	−	3.73958i	−0.648472	−	0.471142i
$64$	2.73204	+	8.40835i	0.341505	+	1.05104i
$65$	5.97750			0.741418
$66$	0.763932	+	1.90211i	0.0940335	+	0.234134i
$67$	3.30325			0.403557			0.201778	−	0.979431i	$-0.435328\pi$
$67$	3.30325			0.403557			0.201778	+	0.979431i	$0.435328\pi$
$68$	0.0998345	+	0.307259i	0.0121067	+	0.0372606i
$69$	2.28155	+	1.65764i	0.274666	+	0.199557i
$70$	4.26097	−	3.09578i	0.509284	−	0.370016i
$71$	−2.96262	+	9.11801i	−0.351599	+	1.08211i	0.606357	+	0.795193i	$0.292630\pi$
$71$	−2.96262	+	9.11801i	−0.351599	+	1.08211i	−0.957956	+	0.286917i	$0.907370\pi$
$72$	2.57709	−	7.93148i	0.303713	−	0.934734i
$73$	7.46799	−	5.42581i	0.874062	−	0.635043i	−0.0576117	−	0.998339i	$-0.518349\pi$
$73$	7.46799	−	5.42581i	0.874062	−	0.635043i	0.931674	+	0.363296i	$0.118349\pi$
$74$	1.48875	+	1.08164i	0.173064	+	0.125738i
$75$	−0.274201	−	0.843905i	−0.0316620	−	0.0974458i
$76$	0.148577			0.0170429
$77$	−1.85666	+	7.38161i	−0.211586	+	0.841213i
$78$	2.08456			0.236030
$79$	−1.84395	−	5.67509i	−0.207460	−	0.638498i	−0.999603	−	0.0281620i	$-0.991035\pi$
$79$	−1.84395	−	5.67509i	−0.207460	−	0.638498i	0.792143	−	0.610336i	$-0.208965\pi$
$80$	4.65897	+	3.38494i	0.520889	+	0.378448i
$81$	−5.66465	+	4.11561i	−0.629405	+	0.457290i
$82$	1.16031	−	3.57108i	0.128135	−	0.394359i
$83$	−4.10639	+	12.6382i	−0.450735	+	1.38722i	0.425335	+	0.905036i	$0.360156\pi$
$83$	−4.10639	+	12.6382i	−0.450735	+	1.38722i	−0.876070	+	0.482184i	$0.839844\pi$
$84$	−0.286277	+	0.207992i	−0.0312354	+	0.0226938i
$85$	1.43376	+	1.04169i	0.155513	+	0.112987i
$86$	−2.28959	−	7.04665i	−0.246893	−	0.759860i
$87$	0.820148			0.0879291
$88$	−9.95449	+	0.675403i	−1.06115	+	0.0719982i
$89$	5.59388			0.592950			0.296475	−	0.955041i	$-0.404189\pi$
$89$	5.59388			0.592950			0.296475	+	0.955041i	$0.404189\pi$
$90$	−1.96601	−	6.05076i	−0.207236	−	0.637806i
$91$	6.26231	+	4.54984i	0.656469	+	0.476953i
$92$	−1.54445	+	1.12211i	−0.161020	+	0.116988i
$93$	−0.538133	+	1.65620i	−0.0558018	+	0.171740i
$94$	−3.95098	+	12.1599i	−0.407512	+	1.25419i
$95$	0.659369	−	0.479059i	0.0676498	−	0.0491504i
$96$	−0.698330	−	0.507366i	−0.0712730	−	0.0517828i
$97$	−1.35327	−	4.16495i	−0.137404	−	0.422887i	0.858552	−	0.512726i	$-0.171364\pi$
$97$	−1.35327	−	4.16495i	−0.137404	−	0.422887i	−0.995956	+	0.0898398i	$0.971364\pi$
$98$	−2.24436			−0.226714
$99$	7.78722	+	4.88842i	0.782645	+	0.491304i
$100$	0.600662			0.0600662
$101$	2.76710	+	8.51625i	0.275337	+	0.847399i	0.989130	+	0.147043i	$0.0469755\pi$
$101$	2.76710	+	8.51625i	0.275337	+	0.847399i	−0.713794	+	0.700356i	$0.753024\pi$
$102$	0.500000	+	0.363271i	0.0495074	+	0.0359692i
$103$	4.38355	−	3.18484i	0.431924	−	0.313811i	−0.350494	−	0.936565i	$-0.613986\pi$
$103$	4.38355	−	3.18484i	0.431924	−	0.313811i	0.782418	+	0.622754i	$0.213986\pi$
$104$	−3.13548	+	9.65001i	−0.307459	+	0.946261i
$105$	−0.599834	+	1.84610i	−0.0585378	+	0.180161i
$106$	14.7930	−	10.7477i	1.43682	−	1.04391i
$107$	1.46933	+	1.06753i	0.142045	+	0.103202i	0.656539	−	0.754292i	$-0.272020\pi$
$107$	1.46933	+	1.06753i	0.142045	+	0.103202i	−0.514493	+	0.857494i	$0.672020\pi$
$108$	0.275029	+	0.846452i	0.0264647	+	0.0814499i
$109$	12.8182			1.22776			0.613880	−	0.789399i	$-0.289608\pi$
$109$	12.8182			1.22776			0.613880	+	0.789399i	$0.289608\pi$
$110$	−5.84088	+	4.88053i	−0.556906	+	0.465340i
$111$	−0.678207			−0.0643726
$112$	2.30448	+	7.09245i	0.217753	+	0.670173i
$113$	−12.8354	−	9.32548i	−1.20745	−	0.877267i	−0.212457	−	0.977170i	$-0.568147\pi$
$113$	−12.8354	−	9.32548i	−1.20745	−	0.877267i	−0.994997	+	0.0999033i	$0.968147\pi$
$114$	0.229944	−	0.167064i	0.0215362	−	0.0156470i
$115$	−3.23607	+	9.95959i	−0.301765	+	0.928737i
$116$	−0.171561	+	0.528010i	−0.0159290	+	0.0490245i
$117$	7.56462	−	5.49602i	0.699350	−	0.508107i
$118$	−14.8493	−	10.7886i	−1.36699	−	0.993174i
$119$	0.709183	+	2.18264i	0.0650107	+	0.200082i
$120$	−2.54445			−0.232275
$121$	1.95492	−	10.8249i	0.177720	−	0.984081i
$122$	5.34312			0.483743
$123$	0.427635	+	1.31612i	0.0385585	+	0.118671i
$124$	−0.953692	−	0.692898i	−0.0856441	−	0.0622241i
$125$	9.83447	−	7.14516i	0.879622	−	0.639083i
$126$	2.54591	−	7.83551i	0.226808	−	0.698043i
$127$	3.03954	−	9.35476i	0.269716	−	0.830100i	−0.720853	−	0.693088i	$-0.756250\pi$
$127$	3.03954	−	9.35476i	0.269716	−	0.830100i	0.990569	−	0.137013i	$-0.0437501\pi$
$128$	−6.33590	+	4.60330i	−0.560020	+	0.406878i
$129$	2.20918	+	1.60507i	0.194508	+	0.141318i
$130$	2.39199	+	7.36179i	0.209792	+	0.645672i
$131$	19.0766			1.66673			0.833364	−	0.552724i	$-0.186412\pi$
$131$	19.0766			1.66673			0.833364	+	0.552724i	$0.186412\pi$
$132$	0.392424	−	0.327902i	0.0341561	−	0.0285402i
$133$	1.05543			0.0915171
$134$	1.32185	+	4.06823i	0.114190	+	0.351442i
$135$	3.94979	+	2.86969i	0.339944	+	0.246984i
$136$	−2.43376	+	1.76823i	−0.208693	+	0.151624i
$137$	4.69588	−	14.4524i	0.401196	−	1.23476i	−0.522833	−	0.852435i	$-0.675125\pi$
$137$	4.69588	−	14.4524i	0.401196	−	1.23476i	0.924030	−	0.382321i	$-0.124875\pi$
$138$	−1.12853	+	3.47325i	−0.0960665	+	0.295662i
$139$	−11.7879	+	8.56438i	−0.999833	+	0.726421i	−0.962052	−	0.272865i	$-0.912029\pi$
$139$	−11.7879	+	8.56438i	−0.999833	+	0.726421i	−0.0377808	+	0.999286i	$0.512029\pi$
$140$	−1.06304	−	0.772344i	−0.0898433	−	0.0652750i
$141$	−1.45614	−	4.48153i	−0.122629	−	0.377413i
$142$	−12.4151			−1.04185
$143$	−9.47449	−	5.94760i	−0.792297	−	0.497363i
$144$	9.00829			0.750691
$145$	0.941105	+	2.89642i	0.0781545	+	0.240535i
$146$	9.67077	+	7.02623i	0.800359	+	0.581495i
$147$	0.669187	−	0.486193i	0.0551936	−	0.0401005i
$148$	0.141869	−	0.436628i	0.0116616	−	0.0358906i
$149$	3.40367	−	10.4754i	0.278840	−	0.858180i	−0.709338	−	0.704868i	$-0.751006\pi$
$149$	3.40367	−	10.4754i	0.278840	−	0.858180i	0.988178	−	0.153312i	$-0.0489939\pi$
$150$	0.929613	−	0.675403i	0.0759026	−	0.0551465i
$151$	−8.74589	−	6.35426i	−0.711730	−	0.517102i	0.172001	−	0.985097i	$-0.444977\pi$
$151$	−8.74589	−	6.35426i	−0.711730	−	0.517102i	−0.883731	+	0.467995i	$0.844977\pi$
$152$	0.427518	+	1.31577i	0.0346763	+	0.106723i
$153$	2.77222			0.224121
$154$	−9.83404	+	0.667231i	−0.792450	+	0.0537670i
$155$	−6.46652			−0.519404
$156$	−0.160708	−	0.494608i	−0.0128669	−	0.0396003i
$157$	−0.0320095	−	0.0232562i	−0.00255463	−	0.00185605i	0.586507	−	0.809944i	$-0.300503\pi$
$157$	−0.0320095	−	0.0232562i	−0.00255463	−	0.00185605i	−0.589062	+	0.808088i	$0.700503\pi$
$158$	6.25146	−	4.54195i	0.497340	−	0.361338i
$159$	−2.08246	+	6.40916i	−0.165150	+	0.508280i
$160$	0.990486	−	3.04840i	0.0783048	−	0.240997i
$161$	−10.9711	+	7.97097i	−0.864644	+	0.628201i
$162$	−7.33551	−	5.32956i	−0.576332	−	0.418730i
$163$	−3.34996	−	10.3101i	−0.262389	−	0.807550i	−0.992283	−	0.123990i	$-0.960431\pi$
$163$	−3.34996	−	10.3101i	−0.262389	−	0.807550i	0.729895	−	0.683560i	$-0.239569\pi$
$164$	−0.936771			−0.0731495
$165$	0.684276	−	2.72050i	0.0532708	−	0.211791i
$166$	−17.2082			−1.33561
$167$	−3.59627	−	11.0682i	−0.278288	−	0.856482i	−0.988331	−	0.152324i	$-0.951324\pi$
$167$	−3.59627	−	11.0682i	−0.278288	−	0.856482i	0.710043	−	0.704159i	$-0.248676\pi$
$168$	−2.66568	−	1.93673i	−0.205662	−	0.149422i
$169$	1.31356	−	0.954355i	0.101043	−	0.0734120i
$170$	−0.709183	+	2.18264i	−0.0543918	+	0.167401i
$171$	0.393970	−	1.21251i	0.0301276	−	0.0927233i
$172$	−1.49546	+	1.08651i	−0.114028	+	0.0828460i
$173$	1.84414	+	1.33984i	0.140207	+	0.101866i	0.655678	−	0.755041i	$-0.272383\pi$
$173$	1.84414	+	1.33984i	0.140207	+	0.101866i	−0.515471	+	0.856907i	$0.672383\pi$
$174$	0.328195	+	1.01008i	0.0248804	+	0.0765740i
$175$	4.26685			0.322544
$176$	−4.01658	−	10.0009i	−0.302761	−	0.753845i
$177$	6.76465			0.508462
$178$	2.23848	+	6.88933i	0.167781	+	0.516377i
$179$	2.99960	+	2.17934i	0.224201	+	0.162892i	0.694216	−	0.719767i	$-0.255751\pi$
$179$	2.99960	+	2.17934i	0.224201	+	0.162892i	−0.470015	+	0.882659i	$0.655751\pi$
$180$	−1.28411	+	0.932961i	−0.0957119	+	0.0695388i
$181$	−7.59880	+	23.3867i	−0.564814	+	1.73832i	0.103688	+	0.994610i	$0.466936\pi$
$181$	−7.59880	+	23.3867i	−0.564814	+	1.73832i	−0.668502	+	0.743710i	$0.733064\pi$
$182$	−3.09754	+	9.53325i	−0.229605	+	0.706651i
$183$	−1.59313	+	1.15747i	−0.117767	+	0.0855630i
$184$	−14.3812	−	10.4485i	−1.06019	−	0.770276i
$185$	−0.778230	−	2.39515i	−0.0572166	−	0.176095i
$186$	−2.25510			−0.165352
$187$	−1.23607	−	3.07768i	−0.0903902	−	0.225063i
$188$	3.18980			0.232640
$189$	1.95369	+	6.01285i	0.142110	+	0.437370i
$190$	0.853858	+	0.620364i	0.0619454	+	0.0450059i
$191$	−2.68364	+	1.94978i	−0.194181	+	0.141081i	−0.680628	−	0.732630i	$-0.738293\pi$
$191$	−2.68364	+	1.94978i	−0.194181	+	0.141081i	0.486447	+	0.873710i	$0.338293\pi$
$192$	1.30389	−	4.01297i	0.0941004	−	0.289611i
$193$	2.29935	−	7.07668i	0.165511	−	0.509391i	−0.833563	−	0.552425i	$-0.813703\pi$
$193$	2.29935	−	7.07668i	0.165511	−	0.509391i	0.999074	+	0.0430345i	$0.0137025\pi$
$194$	4.58795	−	3.33334i	0.329395	−	0.239320i
$195$	−2.30798	−	1.67685i	−0.165278	−	0.120082i
$196$	0.173028	+	0.532524i	0.0123591	+	0.0380374i
$197$	1.13810			0.0810859			0.0405430	−	0.999178i	$-0.487091\pi$
$197$	1.13810			0.0810859			0.0405430	+	0.999178i	$0.487091\pi$
$198$	−2.90431	+	11.5468i	−0.206400	+	0.820594i
$199$	1.30917			0.0928045			0.0464022	−	0.998923i	$-0.485224\pi$
$199$	1.30917			0.0928045			0.0464022	+	0.998923i	$0.485224\pi$
$200$	1.72836	+	5.31935i	0.122214	+	0.376135i
$201$	−1.27542	−	0.926650i	−0.0899615	−	0.0653608i
$202$	−9.38118	+	6.81582i	−0.660057	+	0.479560i
$203$	−1.21870	+	3.75076i	−0.0855357	+	0.263252i
$204$	0.0476470	−	0.146642i	0.00333596	−	0.0102670i
$205$	−4.15730	+	3.02046i	−0.290358	+	0.210958i
$206$	5.67653	+	4.12424i	0.395503	+	0.287350i
$207$	5.06206	+	15.5794i	0.351838	+	1.08284i
$208$	−10.9601			−0.759948
$209$	−1.52178	+	0.103251i	−0.105264	+	0.00714204i
$210$	−2.51366			−0.173459
$211$	−6.04532	−	18.6056i	−0.416177	−	1.28086i	−0.911194	−	0.411977i	$-0.864838\pi$
$211$	−6.04532	−	18.6056i	−0.416177	−	1.28086i	0.495017	−	0.868883i	$-0.335162\pi$
$212$	−3.69059	−	2.68137i	−0.253471	−	0.184157i
$213$	3.70175	−	2.68948i	0.253639	−	0.184280i
$214$	−0.726777	+	2.23679i	−0.0496815	+	0.152904i
$215$	−3.13343	+	9.64370i	−0.213698	+	0.657695i
$216$	−6.70464	+	4.87121i	−0.456193	+	0.331444i
$217$	−6.77463	−	4.92206i	−0.459892	−	0.334131i
$218$	5.12940	+	15.7867i	0.347407	+	1.06921i
$219$	−4.40556			−0.297700
$220$	1.60831	+	1.00962i	0.108432	+	0.0680683i
$221$	−3.37289			−0.226885
$222$	−0.271395	−	0.835268i	−0.0182149	−	0.0560595i
$223$	−3.84355	−	2.79251i	−0.257383	−	0.187000i	0.451609	−	0.892216i	$-0.350850\pi$
$223$	−3.84355	−	2.79251i	−0.257383	−	0.187000i	−0.708993	+	0.705216i	$0.750850\pi$
$224$	3.35800	−	2.43973i	0.224366	−	0.163011i
$225$	1.59273	−	4.90192i	0.106182	−	0.326795i
$226$	6.34881	−	19.5396i	0.422316	−	1.29976i
$227$	2.94141	−	2.13706i	0.195228	−	0.141842i	−0.485877	−	0.874027i	$-0.661500\pi$
$227$	2.94141	−	2.13706i	0.195228	−	0.141842i	0.681105	+	0.732186i	$0.261500\pi$
$228$	−0.0573671	−	0.0416796i	−0.00379923	−	0.00276030i
$229$	4.87462	+	15.0025i	0.322124	+	0.991395i	0.972722	+	0.231973i	$0.0745182\pi$
$229$	4.87462	+	15.0025i	0.322124	+	0.991395i	−0.650598	+	0.759422i	$0.725482\pi$
$230$	−13.5610			−0.894188
$231$	2.78762	−	2.32928i	0.183412	−	0.153255i
$232$	−5.16960			−0.339401
$233$	−5.79398	−	17.8321i	−0.379577	−	1.16822i	−0.940339	−	0.340240i	$-0.889492\pi$
$233$	−5.79398	−	17.8321i	−0.379577	−	1.16822i	0.560762	−	0.827977i	$-0.310508\pi$
$234$	9.79591	+	7.11714i	0.640378	+	0.465262i
$235$	14.1560	−	10.2849i	0.923437	−	0.670916i
$236$	−1.41505	+	4.35507i	−0.0921117	+	0.283491i
$237$	−0.880043	+	2.70849i	−0.0571649	+	0.175936i
$238$	−2.40431	+	1.74683i	−0.155848	+	0.113230i
$239$	10.6058	+	7.70553i	0.686029	+	0.498429i	0.875352	−	0.483486i	$-0.160629\pi$
$239$	10.6058	+	7.70553i	0.686029	+	0.498429i	−0.189323	+	0.981915i	$0.560629\pi$
$240$	−0.849317	−	2.61393i	−0.0548232	−	0.168728i
$241$	−2.37801			−0.153181			−0.0765905	−	0.997063i	$-0.524403\pi$
$241$	−2.37801			−0.153181			−0.0765905	+	0.997063i	$0.524403\pi$
$242$	14.1140	−	1.92411i	0.907285	−	0.123686i
$243$	11.6063			0.744543
$244$	−0.411925	−	1.26777i	−0.0263708	−	0.0811610i
$245$	2.48491	+	1.80539i	0.158755	+	0.115342i
$246$	−1.44979	+	1.05333i	−0.0924353	+	0.0671582i
$247$	−0.479332	+	1.47523i	−0.0304991	+	0.0938667i
$248$	3.39199	−	10.4395i	0.215392	−	0.662907i
$249$	5.13087	−	3.72779i	0.325155	−	0.236239i
$250$	12.7353	+	9.25272i	0.805450	+	0.585193i
$251$	−6.96281	−	21.4293i	−0.439489	−	1.35261i	−0.888416	−	0.459039i	$-0.848194\pi$
$251$	−6.96281	−	21.4293i	−0.439489	−	1.35261i	0.448927	−	0.893568i	$-0.351806\pi$
$252$	−2.05543			−0.129480
$253$	15.0390	−	12.5663i	0.945494	−	0.790038i
$254$	12.7375			0.799221
$255$	−0.261370	−	0.804414i	−0.0163676	−	0.0503744i
$256$	6.10038	+	4.43219i	0.381274	+	0.277012i
$257$	23.7644	−	17.2659i	1.48239	−	1.07702i	0.505607	−	0.862764i	$-0.331269\pi$
$257$	23.7644	−	17.2659i	1.48239	−	1.07702i	0.976778	−	0.214252i	$-0.0687315\pi$
$258$	−1.09273	+	3.36308i	−0.0680305	+	0.209376i
$259$	1.00778	−	3.10163i	0.0626204	−	0.192726i
$260$	1.56234	−	1.13511i	0.0968922	−	0.0703963i
$261$	3.85410	+	2.80017i	0.238563	+	0.173326i
$262$	7.63379	+	23.4944i	0.471617	+	1.45149i
$263$	9.57854			0.590638			0.295319	−	0.955399i	$-0.404574\pi$
$263$	9.57854			0.590638			0.295319	+	0.955399i	$0.404574\pi$
$264$	4.03301	+	2.53171i	0.248215	+	0.155816i
$265$	−25.0241			−1.53722
$266$	0.422345	+	1.29984i	0.0258956	+	0.0796986i
$267$	−2.15986	−	1.56923i	−0.132181	−	0.0960354i
$268$	0.863371	−	0.627276i	0.0527388	−	0.0383170i
$269$	−1.45149	+	4.46723i	−0.0884990	+	0.272372i	−0.985505	−	0.169647i	$-0.945737\pi$
$269$	−1.45149	+	4.46723i	−0.0884990	+	0.272372i	0.897006	+	0.442018i	$0.145737\pi$
$270$	−1.95369	+	6.01285i	−0.118898	+	0.365930i
$271$	−5.00509	+	3.63641i	−0.304038	+	0.220896i	−0.729334	−	0.684158i	$-0.760170\pi$
$271$	−5.00509	+	3.63641i	−0.304038	+	0.220896i	0.425296	+	0.905054i	$0.360170\pi$
$272$	−2.62889	−	1.91000i	−0.159400	−	0.115811i
$273$	−1.14160	−	3.51349i	−0.0690929	−	0.212646i
$274$	19.6785			1.18882
$275$	−6.15221	+	0.417422i	−0.370992	+	0.0251715i
$276$	0.911108			0.0548423
$277$	9.36922	+	28.8355i	0.562942	+	1.73256i	0.673989	+	0.738741i	$0.264579\pi$
$277$	9.36922	+	28.8355i	0.562942	+	1.73256i	−0.111047	+	0.993815i	$0.535421\pi$
$278$	−15.2648	−	11.0906i	−0.915524	−	0.665167i
$279$	−8.18349	+	5.94565i	−0.489932	+	0.355957i
$280$	3.78091	−	11.6364i	0.225953	−	0.695410i
$281$	−7.63524	+	23.4989i	−0.455480	+	1.40182i	0.415090	+	0.909780i	$0.363750\pi$
$281$	−7.63524	+	23.4989i	−0.455480	+	1.40182i	−0.870570	+	0.492044i	$0.836250\pi$
$282$	4.93668	−	3.58671i	0.293975	−	0.213585i
$283$	21.9501	+	15.9477i	1.30480	+	0.947993i	0.999990	−	0.00442055i	$-0.00140711\pi$
$283$	21.9501	+	15.9477i	1.30480	+	0.947993i	0.304810	+	0.952413i	$0.401407\pi$
$284$	0.957138	+	2.94577i	0.0567957	+	0.174799i
$285$	−0.388979			−0.0230411
$286$	3.53359	−	14.0486i	0.208946	−	0.830714i
$287$	−6.65443			−0.392799
$288$	−1.54938	−	4.76851i	−0.0912982	−	0.280987i
$289$	−0.809017	−	0.587785i	−0.0475892	−	0.0345756i
$290$	−3.19059	+	2.31810i	−0.187358	+	0.136123i
$291$	−0.645864	+	1.98776i	−0.0378612	+	0.116525i
$292$	0.921566	−	2.83629i	0.0539306	−	0.165981i
$293$	−2.79591	+	2.03135i	−0.163339	+	0.118672i	−0.666452	−	0.745548i	$-0.732188\pi$
$293$	−2.79591	+	2.03135i	−0.163339	+	0.118672i	0.503113	+	0.864220i	$0.332188\pi$
$294$	0.866573	+	0.629602i	0.0505395	+	0.0367191i
$295$	7.76231	+	23.8899i	0.451939	+	1.39093i
$296$	4.27491			0.248474
$297$	−3.40518	−	8.47856i	−0.197589	−	0.491976i
$298$	14.2634			0.826256
$299$	−6.15887	−	18.9550i	−0.356176	−	1.09620i
$300$	−0.231923	−	0.168502i	−0.0133901	−	0.00972844i
$301$	−10.6231	+	7.71815i	−0.612307	+	0.444867i
$302$	4.32599	−	13.3140i	0.248933	−	0.766137i
$303$	1.32063	−	4.06447i	0.0758680	−	0.233498i
$304$	−1.20899	+	0.878386i	−0.0693406	+	0.0503789i
$305$	−5.91580	−	4.29808i	−0.338738	−	0.246107i
$306$	1.10935	+	3.41422i	0.0634172	+	0.195178i
$307$	26.1611			1.49309			0.746547	−	0.665332i	$-0.231710\pi$
$307$	26.1611			1.49309			0.746547	+	0.665332i	$0.231710\pi$
$308$	0.916465	+	2.28191i	0.0522205	+	0.130024i
$309$	−2.58597			−0.147111
$310$	−2.58768	−	7.96406i	−0.146970	−	0.452328i
$311$	−6.50158	−	4.72368i	−0.368671	−	0.267855i	0.387989	−	0.921664i	$-0.373170\pi$
$311$	−6.50158	−	4.72368i	−0.368671	−	0.267855i	−0.756660	+	0.653809i	$0.773170\pi$
$312$	3.91773	−	2.84639i	0.221798	−	0.161145i
$313$	2.62911	−	8.09157i	0.148606	−	0.457362i	−0.848851	−	0.528632i	$-0.822705\pi$
$313$	2.62911	−	8.09157i	0.148606	−	0.457362i	0.997457	+	0.0712697i	$0.0227051\pi$
$314$	0.0158329	−	0.0487287i	0.000893503	−	0.00274992i
$315$	−9.12178	+	6.62736i	−0.513954	+	0.373410i
$316$	−1.55963	−	1.13314i	−0.0877362	−	0.0637441i
$317$	−2.52210	−	7.76223i	−0.141655	−	0.435970i	0.854910	−	0.518776i	$-0.173612\pi$
$317$	−2.52210	−	7.76223i	−0.141655	−	0.435970i	−0.996566	+	0.0828055i	$0.973612\pi$
$318$	−8.72674			−0.489371
$319$	1.39026	−	5.52730i	0.0778394	−	0.309469i
$320$	15.6683			0.875887
$321$	−0.267855	−	0.824372i	−0.0149502	−	0.0460119i
$322$	−14.2072	−	10.3221i	−0.791735	−	0.575229i
$323$	−0.372057	+	0.270315i	−0.0207018	+	0.0150408i
$324$	−0.699030	+	2.15139i	−0.0388350	+	0.119522i
$325$	−1.93783	+	5.96403i	−0.107492	+	0.330825i
$326$	11.3572	−	8.25150i	0.629018	−	0.457008i
$327$	−4.94925	−	3.59584i	−0.273694	−	0.198850i
$328$	−2.69549	−	8.29586i	−0.148833	−	0.458062i
$329$	22.6590			1.24923
$330$	3.62435	−	0.245909i	0.199514	−	0.0135368i
$331$	−12.0088			−0.660066			−0.330033	−	0.943969i	$-0.607060\pi$
$331$	−12.0088			−0.660066			−0.330033	+	0.943969i	$0.607060\pi$
$332$	1.32666	+	4.08303i	0.0728097	+	0.224085i
$333$	−3.18708	−	2.31555i	−0.174651	−	0.126891i
$334$	12.1923	−	8.85822i	0.667132	−	0.484700i
$335$	1.80902	−	5.56758i	0.0988372	−	0.304189i
$336$	1.09983	−	3.38494i	0.0600009	−	0.184664i
$337$	−24.1941	+	17.5781i	−1.31794	+	0.957538i	−0.317982	+	0.948097i	$0.603005\pi$
$337$	−24.1941	+	17.5781i	−1.31794	+	0.957538i	−0.999955	+	0.00944086i	$0.996995\pi$
$338$	1.70101	+	1.23585i	0.0925226	+	0.0672216i
$339$	2.33986	+	7.20135i	0.127084	+	0.391123i
$340$	0.572554			0.0310511
$341$	10.2496	+	6.43417i	0.555047	+	0.348430i
$342$	1.65096			0.0892739
$343$	6.19339	+	19.0613i	0.334412	+	1.02921i
$344$	−13.9250	−	10.1171i	−0.750788	−	0.545479i
$345$	4.04341	−	2.93771i	0.217690	−	0.158161i
$346$	−0.912169	+	2.80737i	−0.0490385	+	0.150925i
$347$	−6.92072	+	21.2998i	−0.371524	+	1.14343i	0.574270	+	0.818666i	$0.305286\pi$
$347$	−6.92072	+	21.2998i	−0.371524	+	1.14343i	−0.945794	+	0.324767i	$0.894714\pi$
$348$	0.214362	−	0.155743i	0.0114910	−	0.00834871i
$349$	22.1402	+	16.0858i	1.18514	+	0.861051i	0.992742	−	0.120267i	$-0.0383749\pi$
$349$	22.1402	+	16.0858i	1.18514	+	0.861051i	0.192394	+	0.981318i	$0.438375\pi$
$350$	1.70745	+	5.25499i	0.0912669	+	0.280891i
$351$	−9.29180			−0.495959
$352$	−4.60310	+	3.84626i	−0.245346	+	0.205007i
$353$	−4.38269			−0.233267			−0.116633	−	0.993175i	$-0.537210\pi$
$353$	−4.38269			−0.233267			−0.116633	+	0.993175i	$0.537210\pi$
$354$	2.70698	+	8.33123i	0.143874	+	0.442800i
$355$	13.7458	+	9.98691i	0.729551	+	0.530050i
$356$	1.46207	−	1.06226i	0.0774897	−	0.0562996i
$357$	0.338464	−	1.04169i	0.0179134	−	0.0551319i
$358$	−1.48370	+	4.56636i	−0.0784160	+	0.241340i
$359$	−19.3078	+	14.0279i	−1.01902	+	0.740365i	−0.966083	−	0.258233i	$-0.916860\pi$
$359$	−19.3078	+	14.0279i	−1.01902	+	0.740365i	−0.0529419	+	0.998598i	$0.516860\pi$
$360$	−11.9570	−	8.68730i	−0.630192	−	0.457861i
$361$	−5.80597	−	17.8689i	−0.305577	−	0.940470i
$362$	−31.8434			−1.67365
$363$	−3.79148	+	3.63121i	−0.199001	+	0.190589i
$364$	2.50078			0.131076
$365$	−5.05530	−	15.5586i	−0.264606	−	0.814375i
$366$	−2.06304	−	1.49889i	−0.107837	−	0.0783481i
$367$	−27.8280	+	20.2183i	−1.45261	+	1.05538i	−0.467399	+	0.884046i	$0.654809\pi$
$367$	−27.8280	+	20.2183i	−1.45261	+	1.05538i	−0.985212	+	0.171338i	$0.945191\pi$
$368$	5.93354	−	18.2615i	0.309307	−	0.951949i
$369$	−2.48397	+	7.64487i	−0.129310	+	0.397976i
$370$	2.63840	−	1.91691i	0.137164	−	0.0996554i
$371$	−26.2164	−	19.0473i	−1.36109	−	0.988888i
$372$	0.173855	+	0.535072i	0.00901398	+	0.0277422i
$373$	3.32338			0.172078			0.0860390	−	0.996292i	$-0.472579\pi$
$373$	3.32338			0.172078			0.0860390	+	0.996292i	$0.472579\pi$
$374$	3.29579	−	2.75390i	0.170421	−	0.142401i
$375$	−5.80161			−0.299594
$376$	9.17841	+	28.2482i	0.473340	+	1.45679i
$377$	−4.68918	−	3.40689i	−0.241505	−	0.175464i
$378$	−6.62352	+	4.81227i	−0.340677	+	0.247516i
$379$	−1.20006	+	3.69342i	−0.0616431	+	0.189718i	−0.977136	−	0.212617i	$-0.931801\pi$
$379$	−1.20006	+	3.69342i	−0.0616431	+	0.189718i	0.915492	+	0.402335i	$0.131801\pi$
$380$	0.0813675	−	0.250423i	0.00417407	−	0.0128465i
$381$	−3.79786	+	2.75931i	−0.194570	+	0.141364i
$382$	−3.47521	−	2.52489i	−0.177807	−	0.129184i
$383$	−8.99693	−	27.6897i	−0.459721	−	1.41488i	−0.865501	−	0.500906i	$-0.833000\pi$
$383$	−8.99693	−	27.6897i	−0.459721	−	1.41488i	0.405780	−	0.913971i	$-0.367000\pi$
$384$	3.73771			0.190739
$385$	11.4248	+	7.17190i	0.582261	+	0.365514i
$386$	9.63564			0.490441
$387$	4.90150	+	15.0853i	0.249157	+	0.766828i
$388$	−1.14461	−	0.831611i	−0.0581090	−	0.0422187i
$389$	−8.67409	+	6.30209i	−0.439794	+	0.319529i	−0.785553	−	0.618794i	$-0.787621\pi$
$389$	−8.67409	+	6.30209i	−0.439794	+	0.319529i	0.345759	+	0.938323i	$0.387621\pi$
$390$	1.14160	−	3.51349i	0.0578072	−	0.177912i
$391$	1.82599	−	5.61983i	0.0923445	−	0.284207i
$392$	−4.21806	+	3.06460i	−0.213044	+	0.154786i
$393$	−7.36568	−	5.35148i	−0.371550	−	0.269947i
$394$	0.455427	+	1.40166i	0.0229441	+	0.0706146i
$395$	−10.5751			−0.532092
$396$	2.96364	−	0.201080i	0.148928	−	0.0101047i
$397$	−5.35321			−0.268670			−0.134335	−	0.990936i	$-0.542890\pi$
$397$	−5.35321			−0.268670			−0.134335	+	0.990936i	$0.542890\pi$
$398$	0.523884	+	1.61235i	0.0262599	+	0.0808197i
$399$	−0.407512	−	0.296075i	−0.0204011	−	0.0148223i
$400$	−4.88769	+	3.55112i	−0.244385	+	0.177556i
$401$	11.9613	−	36.8132i	0.597321	−	1.83837i	0.0545049	−	0.998514i	$-0.482642\pi$
$401$	11.9613	−	36.8132i	0.597321	−	1.83837i	0.542816	−	0.839852i	$-0.317358\pi$
$402$	0.630865	−	1.94160i	0.0314647	−	0.0968384i
$403$	9.95661	−	7.23390i	0.495974	−	0.360346i
$404$	2.34044	+	1.70043i	0.116441	+	0.0845996i
$405$	3.83456	+	11.8016i	0.190541	+	0.586425i
$406$	−5.10705			−0.253459
$407$	−1.14965	+	4.57070i	−0.0569860	+	0.226561i
$408$	1.43574			0.0710796
$409$	−0.797886	−	2.45564i	−0.0394529	−	0.121424i	0.929390	−	0.369098i	$-0.120333\pi$
$409$	−0.797886	−	2.45564i	−0.0394529	−	0.121424i	−0.968843	+	0.247675i	$0.920333\pi$
$410$	−5.38355	−	3.91138i	−0.265875	−	0.193169i
$411$	−5.86743	+	4.26294i	−0.289419	+	0.210275i
$412$	0.540940	−	1.66484i	0.0266502	−	0.0820208i
$413$	−10.0519	+	30.9366i	−0.494622	+	1.52229i
$414$	−17.1617	+	12.4687i	−0.843451	+	0.612803i
$415$	19.0526	+	13.8425i	0.935255	+	0.679502i
$416$	1.88509	+	5.80171i	0.0924241	+	0.284452i
$417$	6.95396			0.340537
$418$	−0.736126	−	1.83288i	−0.0360051	−	0.0896490i
$419$	4.72712			0.230935			0.115467	−	0.993311i	$-0.463163\pi$
$419$	4.72712			0.230935			0.115467	+	0.993311i	$0.463163\pi$
$420$	0.193789	+	0.596422i	0.00945594	+	0.0291024i
$421$	−18.8348	−	13.6843i	−0.917952	−	0.666931i	0.0250611	−	0.999686i	$-0.492022\pi$
$421$	−18.8348	−	13.6843i	−0.917952	−	0.666931i	−0.943013	+	0.332755i	$0.892022\pi$
$422$	20.4952	−	14.8906i	0.997690	−	0.724864i
$423$	8.45815	−	26.0315i	0.411250	−	1.26570i
$424$	13.1263	−	40.3986i	0.637469	−	1.96193i
$425$	−1.50415	+	1.09283i	−0.0729618	+	0.0530098i
$426$	4.79362	+	3.48277i	0.232252	+	0.168741i
$427$	−2.92614	−	9.00575i	−0.141606	−	0.435819i
$428$	0.586759			0.0283621
$429$	1.98975	+	4.95428i	0.0960661	+	0.239195i
$430$	−13.1309			−0.633228
$431$	−5.08819	−	15.6598i	−0.245090	−	0.754308i	−0.995622	−	0.0934742i	$-0.970203\pi$
$431$	−5.08819	−	15.6598i	−0.245090	−	0.754308i	0.750532	−	0.660834i	$-0.229797\pi$
$432$	−7.24219	−	5.26176i	−0.348440	−	0.253157i
$433$	−9.31524	+	6.76792i	−0.447662	+	0.325245i	−0.788672	−	0.614814i	$-0.789231\pi$
$433$	−9.31524	+	6.76792i	−0.447662	+	0.325245i	0.341010	+	0.940060i	$0.389231\pi$
$434$	3.35095	−	10.3132i	0.160851	−	0.495048i
$435$	0.449152	−	1.38235i	0.0215352	−	0.0662785i
$436$	3.35029	−	2.43413i	0.160450	−	0.116574i
$437$	−2.19850	−	1.59731i	−0.105169	−	0.0764095i
$438$	−1.76295	−	5.42581i	−0.0842372	−	0.259255i
$439$	−27.5823			−1.31643			−0.658216	−	0.752829i	$-0.728689\pi$
$439$	−27.5823			−1.31643			−0.658216	+	0.752829i	$0.728689\pi$
$440$	−4.31316	+	17.1480i	−0.205622	+	0.817499i
$441$	4.80467			0.228794
$442$	−1.34971	−	4.15399i	−0.0641993	−	0.197585i
$443$	−9.27692	−	6.74008i	−0.440760	−	0.320231i	0.345177	−	0.938538i	$-0.387819\pi$
$443$	−9.27692	−	6.74008i	−0.440760	−	0.320231i	−0.785937	+	0.618307i	$0.787819\pi$
$444$	−0.177263	+	0.128789i	−0.00841253	+	0.00611206i
$445$	3.06347	−	9.42840i	0.145223	−	0.446949i
$446$	1.90114	−	5.85112i	0.0900218	−	0.277059i
$447$	−4.25283	+	3.08986i	−0.201152	+	0.146145i
$448$	16.4149	+	11.9261i	0.775530	+	0.563456i
$449$	7.41047	+	22.8071i	0.349722	+	1.07633i	0.959007	+	0.283382i	$0.0914564\pi$
$449$	7.41047	+	22.8071i	0.349722	+	1.07633i	−0.609285	+	0.792951i	$0.708544\pi$
$450$	6.67448			0.314638
$451$	9.59477	−	0.650997i	0.451800	−	0.0306542i
$452$	−5.12567			−0.241091
$453$	1.59435	+	4.90690i	0.0749091	+	0.230546i
$454$	3.80902	+	2.76741i	0.178766	+	0.129881i
$455$	11.0982	−	8.06333i	0.520292	−	0.378015i
$456$	0.204037	−	0.627962i	0.00955492	−	0.0294070i
$457$	8.36727	−	25.7518i	0.391405	−	1.20462i	−0.540322	−	0.841458i	$-0.681698\pi$
$457$	8.36727	−	25.7518i	0.391405	−	1.20462i	0.931726	−	0.363161i	$-0.118302\pi$
$458$	−16.5262	+	12.0070i	−0.772219	+	0.561050i
$459$	−2.22872	−	1.61926i	−0.104028	−	0.0755806i
$460$	1.04548	+	3.21766i	0.0487458	+	0.150024i
$461$	−25.7781			−1.20061			−0.600304	−	0.799772i	$-0.704954\pi$
$461$	−25.7781			−1.20061			−0.600304	+	0.799772i	$0.704954\pi$
$462$	3.98421	+	2.50108i	0.185362	+	0.116361i
$463$	−22.5595			−1.04843			−0.524214	−	0.851587i	$-0.675641\pi$
$463$	−22.5595			−1.04843			−0.524214	+	0.851587i	$0.675641\pi$
$464$	−1.72558	−	5.31078i	−0.0801078	−	0.246547i
$465$	2.49680	+	1.81403i	0.115786	+	0.0841237i
$466$	19.6431	−	14.2715i	0.909949	−	0.661117i
$467$	7.33946	−	22.5885i	0.339630	−	1.04527i	−0.624766	−	0.780812i	$-0.714806\pi$
$467$	7.33946	−	22.5885i	0.339630	−	1.04527i	0.964396	−	0.264462i	$-0.0851942\pi$
$468$	0.933491	−	2.87299i	0.0431506	−	0.132804i
$469$	6.13303	−	4.45591i	0.283197	−	0.205755i
$470$	18.3315	+	13.3186i	0.845570	+	0.614342i
$471$	0.00583524	+	0.0179590i	0.000268873	+	0.000827507i
$472$	−42.6393			−1.96263
$473$	14.5620	−	12.1677i	0.669562	−	0.559474i
$474$	−3.68790			−0.169391
$475$	0.264221	+	0.813188i	0.0121233	+	0.0373116i
$476$	0.599834	+	0.435805i	0.0274934	+	0.0199751i
$477$	−31.6684	+	23.0084i	−1.44999	+	1.05348i
$478$	−5.24594	+	16.1454i	−0.239944	+	0.738471i
$479$	6.85663	−	21.1025i	0.313287	−	0.964199i	−0.663166	−	0.748472i	$-0.730788\pi$
$479$	6.85663	−	21.1025i	0.313287	−	0.964199i	0.976454	−	0.215727i	$-0.0692122\pi$
$480$	−1.23760	+	0.899166i	−0.0564883	+	0.0410411i
$481$	3.87763	+	2.81726i	0.176805	+	0.128456i
$482$	−0.951597	−	2.92872i	−0.0433441	−	0.133399i
$483$	6.47214			0.294492
$484$	−1.54465	−	3.20053i	−0.0702115	−	0.145479i
$485$	−7.76107			−0.352412
$486$	4.64443	+	14.2941i	0.210676	+	0.648393i
$487$	13.6976	+	9.95189i	0.620697	+	0.450963i	0.853165	−	0.521641i	$-0.174680\pi$
$487$	13.6976	+	9.95189i	0.620697	+	0.450963i	−0.232468	+	0.972604i	$0.574680\pi$
$488$	10.0419	−	7.29586i	0.454575	−	0.330268i
$489$	−1.59880	+	4.92060i	−0.0723002	+	0.222517i
$490$	−1.22912	+	3.78283i	−0.0555258	+	0.170891i
$491$	2.18541	−	1.58779i	0.0986261	−	0.0716561i	−0.537379	−	0.843341i	$-0.680586\pi$
$491$	2.18541	−	1.58779i	0.0986261	−	0.0716561i	0.636005	+	0.771685i	$0.280586\pi$
$492$	0.361698	+	0.262789i	0.0163066	+	0.0118474i
$493$	−0.531031	−	1.63434i	−0.0239164	−	0.0736072i
$494$	−2.00868			−0.0903749
$495$	12.5040	−	10.4481i	0.562013	−	0.469608i
$496$	11.8568			0.532385
$497$	6.79911	+	20.9255i	0.304982	+	0.938637i
$498$	6.64428	+	4.82735i	0.297737	+	0.216319i
$499$	−9.51530	+	6.91327i	−0.425963	+	0.309481i	−0.780033	−	0.625739i	$-0.784798\pi$
$499$	−9.51530	+	6.91327i	−0.425963	+	0.309481i	0.354069	+	0.935219i	$0.384798\pi$
$500$	1.21360	−	3.73506i	0.0542736	−	0.167037i
$501$	−1.71636	+	5.28240i	−0.0766812	+	0.236000i
$502$	23.6057	−	17.1506i	1.05357	−	0.765467i
$503$	26.2029	+	19.0375i	1.16833	+	0.848840i	0.990808	−	0.135277i	$-0.0431924\pi$
$503$	26.2029	+	19.0375i	1.16833	+	0.848840i	0.177521	+	0.984117i	$0.443192\pi$
$504$	−5.91434	−	18.2025i	−0.263445	−	0.810802i
$505$	15.8694			0.706179
$506$	21.4946	+	13.4932i	0.955550	+	0.599845i
$507$	−0.774901			−0.0344146
$508$	−0.981989	−	3.02225i	−0.0435687	−	0.134091i
$509$	−9.30853	−	6.76304i	−0.412593	−	0.299767i	0.362057	−	0.932156i	$-0.382074\pi$
$509$	−9.30853	−	6.76304i	−0.412593	−	0.299767i	−0.774651	+	0.632389i	$0.782074\pi$
$510$	0.886111	−	0.643798i	0.0392377	−	0.0285078i
$511$	6.54642	−	20.1478i	0.289597	−	0.891287i
$512$	−7.85764	+	24.1833i	−0.347262	+	1.06876i
$513$	−1.02496	+	0.744679i	−0.0452532	+	0.0328784i
$514$	30.7741	+	22.3587i	1.35739	+	0.986199i
$515$	−2.96735	−	9.13257i	−0.130757	−	0.402429i
$516$	0.882210			0.0388371
$517$	−32.6711	+	2.21671i	−1.43687	+	0.0974907i
$518$	4.22319			0.185556
$519$	−0.336181	−	1.03466i	−0.0147567	−	0.0454165i
$520$	14.5478	+	10.5696i	0.637963	+	0.463507i
$521$	−9.89184	+	7.18684i	−0.433369	+	0.314861i	−0.782995	−	0.622028i	$-0.786309\pi$
$521$	−9.89184	+	7.18684i	−0.433369	+	0.314861i	0.349625	+	0.936890i	$0.386309\pi$
$522$	−1.90636	+	5.86718i	−0.0834392	+	0.256799i
$523$	1.40290	−	4.31768i	0.0613445	−	0.188799i	−0.915688	−	0.401891i	$-0.868353\pi$
$523$	1.40290	−	4.31768i	0.0613445	−	0.188799i	0.977032	+	0.213091i	$0.0683532\pi$
$524$	4.98604	−	3.62257i	0.217816	−	0.158253i
$525$	−1.64748	−	1.19697i	−0.0719020	−	0.0522399i
$526$	3.83300	+	11.7968i	0.167127	+	0.514364i
$527$	3.64882			0.158945
$528$	−1.25466	+	4.98821i	−0.0546022	+	0.217084i
$529$	11.9168			0.518120
$530$	−10.0138	−	30.8192i	−0.434971	−	1.33870i
$531$	31.7890	+	23.0960i	1.37952	+	1.00228i
$532$	0.275857	−	0.200422i	0.0119599	−	0.00868938i
$533$	3.02217	−	9.30129i	0.130905	−	0.402884i
$534$	1.06834	−	3.28800i	0.0462314	−	0.142286i
$535$	2.60398	−	1.89190i	0.112580	−	0.0817941i
$536$	8.03932	+	5.84091i	0.347246	+	0.252289i
$537$	−0.546819	−	1.68294i	−0.0235970	−	0.0726241i
$538$	−6.08260			−0.262240
$539$	−2.14229	−	5.33407i	−0.0922748	−	0.229755i
$540$	1.57730			0.0678762
$541$	12.5398	+	38.5935i	0.539128	+	1.65927i	0.734556	+	0.678548i	$0.237390\pi$
$541$	12.5398	+	38.5935i	0.539128	+	1.65927i	−0.195428	+	0.980718i	$0.562610\pi$
$542$	−6.48141	−	4.70902i	−0.278400	−	0.202270i
$543$	9.49457	−	6.89821i	0.407451	−	0.296031i
$544$	−0.558895	+	1.72010i	−0.0239624	+	0.0737488i
$545$	7.01984	−	21.6049i	0.300697	−	0.925450i
$546$	3.87032	−	2.81195i	0.165635	−	0.120341i
$547$	10.9012	+	7.92016i	0.466100	+	0.338642i	0.795919	−	0.605402i	$-0.206988\pi$
$547$	10.9012	+	7.92016i	0.466100	+	0.338642i	−0.329819	+	0.944044i	$0.606988\pi$
$548$	−1.51710	−	4.66917i	−0.0648075	−	0.199457i
$549$	−11.4384			−0.488180
$550$	−2.97599	−	7.40992i	−0.126897	−	0.315960i
$551$	−0.790296			−0.0336677
$552$	2.62165	+	8.06860i	0.111585	+	0.343422i
$553$	−11.0790	−	8.04935i	−0.471126	−	0.342293i
$554$	−31.7641	+	23.0779i	−1.34953	+	0.980487i
$555$	−0.371418	+	1.14311i	−0.0157658	+	0.0485222i
$556$	−1.45465	+	4.47695i	−0.0616908	+	0.189865i
$557$	20.7252	−	15.0577i	0.878154	−	0.638016i	−0.0546084	−	0.998508i	$-0.517391\pi$
$557$	20.7252	−	15.0577i	0.878154	−	0.638016i	0.932762	+	0.360492i	$0.117391\pi$
$558$	−10.5973	−	7.69940i	−0.448620	−	0.325941i
$559$	−5.96352	−	18.3538i	−0.252230	−	0.776284i
$560$	13.2163			0.558489
$561$	−0.386111	+	1.53508i	−0.0163016	+	0.0648111i
$562$	−31.9962			−1.34968
$563$	−8.40189	−	25.8584i	−0.354098	−	1.08980i	−0.956531	−	0.291631i	$-0.905802\pi$
$563$	−8.40189	−	25.8584i	−0.354098	−	1.08980i	0.602433	−	0.798169i	$-0.294198\pi$
$564$	−1.23162	−	0.894822i	−0.0518605	−	0.0376788i
$565$	−22.7472	+	16.5268i	−0.956983	+	0.695289i
$566$	−10.8572	+	33.4151i	−0.456364	+	1.40454i
$567$	−4.96562	+	15.2826i	−0.208536	+	0.641809i
$568$	−23.3330	+	16.9524i	−0.979033	+	0.711309i
$569$	33.1365	+	24.0751i	1.38916	+	1.00928i	0.995957	+	0.0898275i	$0.0286316\pi$
$569$	33.1365	+	24.0751i	1.38916	+	1.00928i	0.393199	+	0.919453i	$0.371368\pi$
$570$	−0.155656	−	0.479059i	−0.00651970	−	0.0200656i
$571$	−17.3757			−0.727149			−0.363575	−	0.931565i	$-0.618444\pi$
$571$	−17.3757			−0.727149			−0.363575	+	0.931565i	$0.618444\pi$
$572$	−3.60578	+	0.244649i	−0.150765	+	0.0102293i
$573$	1.58315			0.0661369
$574$	−2.66287	−	8.19549i	−0.111146	−	0.342073i
$575$	−8.88806	−	6.45755i	−0.370658	−	0.269298i
$576$	19.8285	−	14.4063i	0.826188	−	0.600261i
$577$	−8.64681	+	26.6121i	−0.359971	+	1.10788i	0.593099	+	0.805129i	$0.297904\pi$
$577$	−8.64681	+	26.6121i	−0.359971	+	1.10788i	−0.953071	+	0.302748i	$0.902096\pi$
$578$	0.400166	−	1.23158i	0.0166447	−	0.0512271i
$579$	−2.87300	+	2.08736i	−0.119398	+	0.0867476i
$580$	0.795997	+	0.578326i	0.0330520	+	0.0240137i
$581$	9.42402	+	29.0041i	0.390974	+	1.20329i
$582$	−2.70655			−0.112190
$583$	39.6638	+	24.8989i	1.64271	+	1.03121i
$584$	27.7694			1.14910
$585$	−5.12071	−	15.7599i	−0.211715	−	0.651593i
$586$	−3.62060	−	2.63052i	−0.149565	−	0.108666i
$587$	36.1329	−	26.2521i	1.49137	−	1.08354i	0.517700	−	0.855562i	$-0.326788\pi$
$587$	36.1329	−	26.2521i	1.49137	−	1.08354i	0.973666	−	0.227979i	$-0.0732117\pi$
$588$	0.0825792	−	0.254153i	0.00340551	−	0.0104811i
$589$	0.518546	−	1.59592i	0.0213663	−	0.0657587i
$590$	−26.3162	+	19.1199i	−1.08342	+	0.787152i
$591$	−0.439432	−	0.319266i	−0.0180758	−	0.0131328i
$592$	1.42693	+	4.39165i	0.0586466	+	0.180496i
$593$	−4.74883			−0.195011			−0.0975055	−	0.995235i	$-0.531086\pi$
$593$	−4.74883			−0.195011			−0.0975055	+	0.995235i	$0.531086\pi$
$594$	9.07941	−	7.58659i	0.372533	−	0.311282i
$595$	4.06719			0.166738
$596$	−1.09963	−	3.38431i	−0.0450425	−	0.138627i
$597$	−0.505485	−	0.367256i	−0.0206881	−	0.0150308i
$598$	20.8801	−	15.1703i	0.853852	−	0.620360i
$599$	3.09598	−	9.52844i	0.126498	−	0.389321i	−0.867673	−	0.497136i	$-0.834385\pi$
$599$	3.09598	−	9.52844i	0.126498	−	0.389321i	0.994171	+	0.107814i	$0.0343851\pi$
$600$	0.824877	−	2.53871i	0.0336755	−	0.103642i
$601$	−1.59288	+	1.15729i	−0.0649748	+	0.0472070i	−0.619799	−	0.784761i	$-0.712786\pi$
$601$	−1.59288	+	1.15729i	−0.0649748	+	0.0472070i	0.554824	+	0.831968i	$0.312786\pi$
$602$	−13.7566	−	9.99472i	−0.560675	−	0.407354i
$603$	−2.82978	−	8.70916i	−0.115237	−	0.354665i
$604$	−3.49256			−0.142110
$605$	−17.1746	−	9.22320i	−0.698246	−	0.374976i
$606$	5.53420			0.224811
$607$	6.79508	+	20.9131i	0.275804	+	0.848837i	0.989006	+	0.147878i	$0.0472443\pi$
$607$	6.79508	+	20.9131i	0.275804	+	0.848837i	−0.713202	+	0.700959i	$0.752756\pi$
$608$	0.672911	+	0.488899i	0.0272901	+	0.0198275i
$609$	1.52274	−	1.10634i	0.0617045	−	0.0448310i
$610$	2.92614	−	9.00575i	0.118476	−	0.364632i
$611$	−10.2908	+	31.6718i	−0.416321	+	1.28130i
$612$	0.724576	−	0.526435i	0.0292892	−	0.0212799i
$613$	21.5488	+	15.6561i	0.870349	+	0.632346i	0.930681	−	0.365833i	$-0.119216\pi$
$613$	21.5488	+	15.6561i	0.870349	+	0.632346i	−0.0603314	+	0.998178i	$0.519216\pi$
$614$	10.4688	+	32.2196i	0.422486	+	1.30028i
$615$	2.45250			0.0988943
$616$	−17.5711	+	14.6821i	−0.707958	+	0.591557i
$617$	−14.9625			−0.602368			−0.301184	−	0.953566i	$-0.597382\pi$
$617$	−14.9625			−0.602368			−0.301184	+	0.953566i	$0.597382\pi$
$618$	−1.03482	−	3.18484i	−0.0416264	−	0.128113i
$619$	6.76213	+	4.91297i	0.271793	+	0.197469i	0.715330	−	0.698787i	$-0.246277\pi$
$619$	6.76213	+	4.91297i	0.271793	+	0.197469i	−0.443537	+	0.896256i	$0.646277\pi$
$620$	−1.69016	+	1.22797i	−0.0678783	+	0.0493164i
$621$	5.03034	−	15.4818i	0.201861	−	0.621263i
$622$	3.21589	−	9.89749i	0.128945	−	0.396853i
$623$	10.3860	−	7.54584i	0.416105	−	0.302318i
$624$	4.23183	+	3.07461i	0.169409	+	0.123083i
$625$	−3.78458	−	11.6477i	−0.151383	−	0.465909i
$626$	11.0175			0.440348
$627$	0.616541	+	0.387032i	0.0246223	+	0.0154566i
$628$	−0.0127826			−0.000510081
$629$	0.439127	+	1.35149i	0.0175091	+	0.0538875i
$630$	−11.8124	−	8.58219i	−0.470616	−	0.341923i
$631$	36.0038	−	26.1583i	1.43329	−	1.04134i	0.443895	−	0.896079i	$-0.353596\pi$
$631$	36.0038	−	26.1583i	1.43329	−	1.04134i	0.989393	−	0.145265i	$-0.0464036\pi$
$632$	5.54714	−	17.0723i	0.220653	−	0.679101i
$633$	−2.88519	+	8.87970i	−0.114676	+	0.352936i
$634$	8.55057	−	6.21235i	0.339587	−	0.246724i
$635$	−14.1027	−	10.2462i	−0.559648	−	0.406608i
$636$	0.672783	+	2.07061i	0.0266776	+	0.0821052i
$637$	−5.84570			−0.231615
$638$	7.36366	−	0.499618i	0.291530	−	0.0197801i
$639$	26.5780			1.05141
$640$	4.28896	+	13.2000i	0.169536	+	0.521778i
$641$	−26.1287	−	18.9836i	−1.03202	−	0.749808i	−0.0633094	−	0.997994i	$-0.520165\pi$
$641$	−26.1287	−	18.9836i	−1.03202	−	0.749808i	−0.968712	+	0.248186i	$0.920165\pi$
$642$	0.908096	−	0.659770i	0.0358397	−	0.0260391i
$643$	−10.0764	+	31.0118i	−0.397373	+	1.22299i	0.529725	+	0.848169i	$0.322295\pi$
$643$	−10.0764	+	31.0118i	−0.397373	+	1.22299i	−0.927098	+	0.374819i	$0.877705\pi$
$644$	−1.35386	+	4.16675i	−0.0533495	+	0.164193i
$645$	3.91516	−	2.84453i	0.154159	−	0.112003i
$646$	−0.481800	−	0.350049i	−0.0189562	−	0.0137725i
$647$	1.09156	+	3.35948i	0.0429137	+	0.132075i	0.970218	−	0.242234i	$-0.0778801\pi$
$647$	1.09156	+	3.35948i	0.0429137	+	0.132075i	−0.927304	+	0.374308i	$0.877880\pi$
$648$	−21.0637			−0.827461
$649$	11.4670	−	45.5896i	0.450117	−	1.78955i
$650$	−8.12065			−0.318518
$651$	1.23500	+	3.80093i	0.0484033	+	0.148970i
$652$	−2.83343	−	2.05861i	−0.110966	−	0.0806213i
$653$	−35.3764	+	25.7024i	−1.38438	+	1.00581i	−0.387929	+	0.921689i	$0.626810\pi$
$653$	−35.3764	+	25.7024i	−1.38438	+	1.00581i	−0.996455	+	0.0841253i	$0.973190\pi$
$654$	2.44806	−	7.53434i	0.0957266	−	0.294616i
$655$	10.4472	−	32.1533i	0.408207	−	1.25633i
$656$	7.62267	−	5.53820i	0.297615	−	0.216230i
$657$	−20.7029	−	15.0416i	−0.807698	−	0.586827i
$658$	9.06735	+	27.9064i	0.353482	+	1.08791i
$659$	21.1050			0.822134			0.411067	−	0.911605i	$-0.365156\pi$
$659$	21.1050			0.822134			0.411067	+	0.911605i	$0.365156\pi$
$660$	−0.337764	−	0.840999i	−0.0131475	−	0.0327358i
$661$	−30.1979			−1.17456			−0.587282	−	0.809382i	$-0.699802\pi$
$661$	−30.1979			−1.17456			−0.587282	+	0.809382i	$0.699802\pi$
$662$	−4.80553	−	14.7899i	−0.186772	−	0.574825i
$663$	1.30231	+	0.946183i	0.0505775	+	0.0367467i
$664$	−32.3411	+	23.4972i	−1.25508	+	0.911869i
$665$	0.578001	−	1.77890i	0.0224139	−	0.0689829i
$666$	1.57643	−	4.85176i	0.0610855	−	0.188002i
$667$	8.21508	−	5.96861i	0.318089	−	0.231105i
$668$	−3.04177	−	2.20997i	−0.117690	−	0.0855064i
$669$	0.700669	+	2.15644i	0.0270894	+	0.0833727i
$670$	7.58084			0.292874
$671$	5.10012	+	12.6988i	0.196888	+	0.490231i
$672$	−1.98097			−0.0764177
$673$	−5.49909	−	16.9245i	−0.211974	−	0.652390i	−0.999355	−	0.0359225i	$-0.988563\pi$
$673$	−5.49909	−	16.9245i	−0.211974	−	0.652390i	0.787380	−	0.616468i	$-0.211437\pi$
$674$	−31.3305	−	22.7629i	−1.20681	−	0.876795i
$675$	−4.14370	+	3.01057i	−0.159491	+	0.115877i
$676$	0.162096	−	0.498880i	0.00623446	−	0.0191877i
$677$	−5.07031	+	15.6048i	−0.194868	+	0.599742i	0.805110	+	0.593125i	$0.202106\pi$
$677$	−5.07031	+	15.6048i	−0.194868	+	0.599742i	−0.999978	+	0.00661672i	$0.997894\pi$
$678$	−7.93272	+	5.76346i	−0.304654	+	0.221344i
$679$	−8.13087	−	5.90742i	−0.312034	−	0.226706i
$680$	1.64748	+	5.07043i	0.0631780	+	0.194442i
$681$	−1.73521			−0.0664935
$682$	−3.82268	+	15.1980i	−0.146378	+	0.581960i
$683$	6.05498			0.231687			0.115844	−	0.993267i	$-0.463043\pi$
$683$	6.05498			0.231687			0.115844	+	0.993267i	$0.463043\pi$
$684$	−0.127280	−	0.391728i	−0.00486668	−	0.0149781i
$685$	−21.7877	−	15.8297i	−0.832464	−	0.604821i
$686$	−20.9972	+	15.2554i	−0.801677	+	0.582452i
$687$	2.32646	−	7.16011i	0.0887600	−	0.273175i
$688$	5.74534	−	17.6823i	0.219039	−	0.674133i
$689$	38.5300	−	27.9937i	1.46788	−	1.06647i
$690$	5.23607	+	3.80423i	0.199334	+	0.144824i
$691$	−14.1743	−	43.6240i	−0.539216	−	1.65954i	−0.734360	−	0.678761i	$-0.762517\pi$
$691$	−14.1743	−	43.6240i	−0.539216	−	1.65954i	0.195144	−	0.980775i	$-0.437483\pi$
$692$	0.736434			0.0279950
$693$	21.0525	−	1.42839i	0.799717	−	0.0542601i
$694$	−29.0019			−1.10090
$695$	7.97954	+	24.5585i	0.302681	+	0.931557i
$696$	1.99604	+	1.45021i	0.0756598	+	0.0549701i
$697$	2.34581	−	1.70433i	0.0888539	−	0.0645562i
$698$	−10.9512	+	33.7044i	−0.414510	+	1.27573i
$699$	−2.76524	+	8.51052i	−0.104591	+	0.321898i
$700$	1.11523	−	0.810260i	0.0421516	−	0.0306250i
$701$	30.1616	+	21.9137i	1.13919	+	0.827669i	0.987006	−	0.160683i	$-0.0513697\pi$
$701$	30.1616	+	21.9137i	1.13919	+	0.827669i	0.152183	+	0.988352i	$0.451370\pi$
$702$	−3.71826	−	11.4436i	−0.140337	−	0.431911i
$703$	0.653521			0.0246480
$704$	−24.8347	−	15.5899i	−0.935993	−	0.587568i
$705$	−8.35100			−0.314517
$706$	−1.75380	−	5.39764i	−0.0660052	−	0.203143i
$707$	16.6255	+	12.0792i	0.625268	+	0.454283i
$708$	1.76808	−	1.28458i	0.0664484	−	0.0482776i
$709$	−3.98706	+	12.2709i	−0.149737	+	0.460844i	−0.997590	−	0.0693883i	$-0.977895\pi$
$709$	−3.98706	+	12.2709i	−0.149737	+	0.460844i	0.847852	+	0.530232i	$0.177895\pi$
$710$	−6.79911	+	20.9255i	−0.255166	+	0.785320i
$711$	−13.3830	+	9.72329i	−0.501900	+	0.364652i
$712$	13.6142	+	9.89127i	0.510212	+	0.370691i
$713$	6.66272	+	20.5058i	0.249521	+	0.767947i
$714$	1.41837			0.0530810
$715$	−15.2133	+	12.7119i	−0.568944	+	0.475399i
$716$	1.19786			0.0447660
$717$	−1.93340	−	5.95039i	−0.0722041	−	0.222221i
$718$	−25.0028	−	18.1656i	−0.933097	−	0.677935i
$719$	11.8942	−	8.64166i	0.443580	−	0.322279i	−0.343476	−	0.939161i	$-0.611604\pi$
$719$	11.8942	−	8.64166i	0.443580	−	0.322279i	0.787056	+	0.616882i	$0.211604\pi$
$720$	4.93336	−	15.1833i	0.183856	−	0.565849i
$721$	3.84261	−	11.8263i	0.143106	−	0.440436i
$722$	19.6837	−	14.3011i	0.732552	−	0.532230i
$723$	0.918177	+	0.667094i	0.0341474	+	0.0248095i
$724$	2.45495	+	7.55557i	0.0912376	+	0.280800i
$725$	−3.19499			−0.118659
$726$	−5.98936	−	3.21644i	−0.222286	−	0.119373i
$727$	18.2856			0.678177			0.339088	−	0.940755i	$-0.389881\pi$
$727$	18.2856			0.678177			0.339088	+	0.940755i	$0.389881\pi$
$728$	7.19581	+	22.1464i	0.266694	+	0.820801i
$729$	12.5126	+	9.09095i	0.463431	+	0.336702i
$730$	17.1388	−	12.4520i	0.634334	−	0.460871i
$731$	1.76808	−	5.44158i	0.0653947	−	0.201264i
$732$	−0.196595	+	0.605058i	−0.00726637	+	0.0223636i
$733$	7.09899	−	5.15772i	0.262207	−	0.190505i	−0.448912	−	0.893576i	$-0.648188\pi$
$733$	7.09899	−	5.15772i	0.262207	−	0.190505i	0.711120	+	0.703071i	$0.248188\pi$
$734$	−36.0363	−	26.1819i	−1.33012	−	0.966391i
$735$	−0.452992	−	1.39417i	−0.0167089	−	0.0514246i
$736$	−10.6872			−0.393936
$737$	−8.40706	+	7.02479i	−0.309678	+	0.258761i
$738$	−10.4093			−0.383171
$739$	−14.2729	−	43.9276i	−0.525039	−	1.61590i	−0.764239	−	0.644933i	$-0.776885\pi$
$739$	−14.2729	−	43.9276i	−0.525039	−	1.61590i	0.239200	−	0.970970i	$-0.423115\pi$
$740$	−0.658236	−	0.478236i	−0.0241972	−	0.0175803i
$741$	0.598917	−	0.435138i	0.0220018	−	0.0159852i
$742$	12.9675	−	39.9098i	0.476051	−	1.46513i
$743$	11.5658	−	35.5958i	0.424307	−	1.30588i	−0.479349	−	0.877624i	$-0.659127\pi$
$743$	11.5658	−	35.5958i	0.424307	−	1.30588i	0.903656	−	0.428259i	$-0.140873\pi$
$744$	−4.23823	+	3.07926i	−0.155381	+	0.112891i
$745$	−15.7922	−	11.4737i	−0.578580	−	0.420363i
$746$	1.32990	+	4.09302i	0.0486912	+	0.149856i
$747$	36.8389			1.34786
$748$	−0.907512	−	0.569689i	−0.0331819	−	0.0208299i
$749$	4.16809			0.152299
$750$	−2.32160	−	7.14516i	−0.0847730	−	0.260904i
$751$	16.1315	+	11.7202i	0.588646	+	0.427676i	0.841831	−	0.539742i	$-0.181478\pi$
$751$	16.1315	+	11.7202i	0.588646	+	0.427676i	−0.253185	+	0.967418i	$0.581478\pi$
$752$	−25.9560	+	18.8581i	−0.946516	+	0.687684i
$753$	−3.32307	+	10.2274i	−0.121099	+	0.372706i
$754$	2.31942	−	7.13843i	0.0844681	−	0.259966i
$755$	−15.4997	+	11.2612i	−0.564090	+	0.409836i
$756$	1.65245	+	1.20058i	0.0600992	+	0.0436646i
$757$	−5.10935	−	15.7250i	−0.185702	−	0.571533i	0.814257	−	0.580504i	$-0.197144\pi$
$757$	−5.10935	−	15.7250i	−0.185702	−	0.571533i	−0.999960	+	0.00897080i	$0.997144\pi$
$758$	−5.02897			−0.182661
$759$	−9.33192	+	0.633163i	−0.338727	+	0.0229824i
$760$	2.45183			0.0889372
$761$	11.2678	+	34.6786i	0.408456	+	1.25710i	0.917975	+	0.396639i	$0.129824\pi$
$761$	11.2678	+	34.6786i	0.408456	+	1.25710i	−0.509519	+	0.860460i	$0.670176\pi$
$762$	−4.91809	−	3.57320i	−0.178163	−	0.129443i
$763$	23.7991	−	17.2910i	0.861584	−	0.625978i
$764$	−0.331167	+	1.01923i	−0.0119812	+	0.0368743i
$765$	1.51820	−	4.67254i	0.0548906	−	0.168936i
$766$	30.5019	−	22.1609i	1.10208	−	0.800707i
$767$	−38.6767	−	28.1003i	−1.39654	−	1.01464i
$768$	−1.11208	−	3.42264i	−0.0401288	−	0.123504i
$769$	−25.1338			−0.906349			−0.453175	−	0.891422i	$-0.649709\pi$
$769$	−25.1338			−0.906349			−0.453175	+	0.891422i	$0.649709\pi$
$770$	−4.26097	+	16.9405i	−0.153555	+	0.610494i
$771$	−14.0193			−0.504891
$772$	−0.742854	−	2.28627i	−0.0267359	−	0.0822847i
$773$	21.3440	+	15.5073i	0.767689	+	0.557759i	0.901259	−	0.433281i	$-0.142644\pi$
$773$	21.3440	+	15.5073i	0.767689	+	0.557759i	−0.133570	+	0.991039i	$0.542644\pi$
$774$	−16.6174	+	12.0732i	−0.597299	+	0.433963i
$775$	2.09637	−	6.45195i	0.0753037	−	0.231761i
$776$	4.07104	−	12.5294i	0.146142	−	0.449779i
$777$	−1.25920	+	0.914865i	−0.0451737	+	0.0328206i
$778$	−11.2326	−	8.16098i	−0.402709	−	0.292585i
$779$	−0.412069	−	1.26822i	−0.0147639	−	0.0454386i
$780$	−0.921665			−0.0330009
$781$	−11.8505	−	29.5065i	−0.424044	−	1.05583i
$782$	7.65199			0.273635
$783$	−1.46291	−	4.50238i	−0.0522802	−	0.160902i
$784$	−4.55624	−	3.31030i	−0.162723	−	0.118225i
$785$	−0.0567279	+	0.0412153i	−0.00202471	+	0.00147104i
$786$	3.64330	−	11.2129i	0.129952	−	0.399952i
$787$	−7.37037	+	22.6837i	−0.262725	+	0.808585i	0.729483	+	0.683998i	$0.239760\pi$
$787$	−7.37037	+	22.6837i	−0.262725	+	0.808585i	−0.992209	+	0.124587i	$0.960240\pi$
$788$	0.297464	−	0.216120i	0.0105967	−	0.00769897i
$789$	−3.69839	−	2.68703i	−0.131666	−	0.0956609i
$790$	−4.23179	−	13.0241i	−0.150561	−	0.463378i
$791$	−36.4106			−1.29461
$792$	10.3084	+	25.6668i	0.366292	+	0.912030i
$793$	13.9168			0.494200
$794$	−2.14217	−	6.59292i	−0.0760228	−	0.233974i
$795$	9.66208	+	7.01992i	0.342679	+	0.248971i
$796$	0.342177	−	0.248606i	0.0121281	−	0.00881162i
$797$	−8.81126	+	27.1183i	−0.312111	+	0.960578i	0.664817	+	0.747006i	$0.268510\pi$
$797$	−8.81126	+	27.1183i	−0.312111	+	0.960578i	−0.976927	+	0.213571i	$0.931490\pi$
$798$	0.201568	−	0.620364i	0.00713545	−	0.0219606i
$799$	−7.98772	+	5.80342i	−0.282585	+	0.205310i
$800$	2.72043	+	1.97651i	0.0961817	+	0.0698801i
$801$	−4.79208	−	14.7485i	−0.169320	−	0.521113i
$802$	50.1251			1.76998
$803$	−7.46799	+	29.6908i	−0.263540	+	1.04777i
$804$	−0.509325			−0.0179625
$805$	7.42666	+	22.8569i	0.261755	+	0.805600i
$806$	12.8934	+	9.36764i	0.454152	+	0.329961i
$807$	1.81361	−	1.31767i	0.0638422	−	0.0463841i
$808$	−8.32424	+	25.6194i	−0.292846	+	0.901286i
$809$	−7.78804	+	23.9691i	−0.273813	+	0.842709i	0.715718	+	0.698389i	$0.246099\pi$
$809$	−7.78804	+	23.9691i	−0.273813	+	0.842709i	−0.989531	+	0.144320i	$0.953901\pi$
$810$	−13.0002	+	9.44516i	−0.456779	+	0.331869i
$811$	−20.8160	−	15.1237i	−0.730948	−	0.531065i	0.158915	−	0.987292i	$-0.449200\pi$
$811$	−20.8160	−	15.1237i	−0.730948	−	0.531065i	−0.889863	+	0.456228i	$0.849200\pi$
$812$	0.393725	+	1.21176i	0.0138171	+	0.0425245i
$813$	2.95263			0.103553
$814$	−6.08925	+	0.413150i	−0.213428	+	0.0144809i
$815$	−19.2121			−0.672971
$816$	0.479238	+	1.47494i	0.0167767	+	0.0516334i
$817$	−2.12877	−	1.54664i	−0.0744762	−	0.0541102i
$818$	2.70504	−	1.96532i	0.0945794	−	0.0687160i
$819$	6.63113	−	20.4085i	0.231711	−	0.713132i
$820$	−0.513020	+	1.57891i	−0.0179154	+	0.0551380i
$821$	−32.7167	+	23.7701i	−1.14182	+	0.829582i	−0.987372	−	0.158419i	$-0.949360\pi$
$821$	−32.7167	+	23.7701i	−1.14182	+	0.829582i	−0.154449	+	0.988001i	$0.549360\pi$
$822$	−7.59810	−	5.52034i	−0.265014	−	0.192544i
$823$	10.2794	+	31.6367i	0.358317	+	1.10279i	0.954061	+	0.299613i	$0.0968574\pi$
$823$	10.2794	+	31.6367i	0.358317	+	1.10279i	−0.595744	+	0.803175i	$0.703143\pi$
$824$	16.3000			0.567838
$825$	2.49254	+	1.56469i	0.0867790	+	0.0544754i
$826$	−42.1234			−1.46566
$827$	5.06296	+	15.5822i	0.176056	+	0.541846i	0.999680	−	0.0252907i	$-0.00805114\pi$
$827$	5.06296	+	15.5822i	0.176056	+	0.541846i	−0.823624	+	0.567137i	$0.808051\pi$
$828$	4.28155	+	3.11073i	0.148794	+	0.108105i
$829$	0.682324	−	0.495737i	0.0236981	−	0.0172177i	−0.575873	−	0.817539i	$-0.695338\pi$
$829$	0.682324	−	0.495737i	0.0236981	−	0.0172177i	0.599571	+	0.800321i	$0.295338\pi$
$830$	−9.42402	+	29.0041i	−0.327112	+	1.00675i
$831$	4.47155	−	13.7620i	0.155116	−	0.477399i
$832$	−24.1248	+	17.5277i	−0.836377	+	0.607663i
$833$	−1.40214	−	1.01872i	−0.0485814	−	0.0352965i
$834$	2.78274	+	8.56438i	0.0963583	+	0.296560i
$835$	−20.6247			−0.713749
$836$	−0.378140	+	0.315967i	−0.0130782	+	0.0109279i
$837$	10.0520			0.347446
$838$	1.89163	+	5.82184i	0.0653453	+	0.201112i
$839$	14.8562	+	10.7937i	0.512894	+	0.372639i	0.813920	−	0.580976i	$-0.197329\pi$
$839$	14.8562	+	10.7937i	0.512894	+	0.372639i	−0.301026	+	0.953616i	$0.597329\pi$
$840$	−4.72418	+	3.43232i	−0.163000	+	0.118426i
$841$	−8.04894	+	24.7721i	−0.277550	+	0.854210i
$842$	9.31629	−	28.6726i	0.321061	−	0.988123i
$843$	9.54011	−	6.93129i	0.328579	−	0.238726i
$844$	−5.11320	−	3.71496i	−0.176004	−	0.127874i
$845$	−0.889185	−	2.73663i	−0.0305889	−	0.0941429i
$846$	35.4446			1.21861
$847$	−10.9726	−	22.7353i	−0.377022	−	0.781193i
$848$	45.8832			1.57564
$849$	−4.00145	−	12.3152i	−0.137329	−	0.422656i
$850$	−1.94781	−	1.41517i	−0.0668094	−	0.0485399i
$851$	−6.79332	+	4.93563i	−0.232872	+	0.169191i
$852$	0.456803	−	1.40590i	0.0156498	−	0.0481652i
$853$	−17.5164	+	53.9101i	−0.599752	+	1.84585i	−0.0702640	+	0.997528i	$0.522384\pi$
$853$	−17.5164	+	53.9101i	−0.599752	+	1.84585i	−0.529488	+	0.848318i	$0.677616\pi$
$854$	9.92038	−	7.20758i	0.339468	−	0.246638i
$855$	−1.82792	−	1.32806i	−0.0625134	−	0.0454187i
$856$	1.68836	+	5.19622i	0.0577068	+	0.177603i
$857$	30.5707			1.04427			0.522137	−	0.852862i	$-0.325135\pi$
$857$	30.5707			1.04427			0.522137	+	0.852862i	$0.325135\pi$
$858$	−5.30538	+	4.43308i	−0.181123	+	0.151343i
$859$	−7.81432			−0.266621			−0.133311	−	0.991074i	$-0.542561\pi$
$859$	−7.81432			−0.266621			−0.133311	+	0.991074i	$0.542561\pi$
$860$	1.01232	+	3.11560i	0.0345198	+	0.106241i
$861$	2.56935	+	1.86674i	0.0875633	+	0.0636185i
$862$	17.2503	−	12.5331i	0.587547	−	0.426878i
$863$	−4.39958	+	13.5405i	−0.149764	+	0.460925i	−0.997593	−	0.0693446i	$-0.977909\pi$
$863$	−4.39958	+	13.5405i	−0.149764	+	0.460925i	0.847829	+	0.530269i	$0.177909\pi$
$864$	−1.53967	+	4.73862i	−0.0523807	+	0.161211i
$865$	3.26822	−	2.37450i	0.111123	−	0.0807355i
$866$	−12.0629	−	8.76420i	−0.409914	−	0.297820i
$867$	0.147481	+	0.453901i	0.00500873	+	0.0154153i
$868$	−2.70537			−0.0918262
$869$	16.7618	+	10.5222i	0.568606	+	0.356941i
$870$	1.88221			0.0638129
$871$	3.44291	+	10.5962i	0.116659	+	0.359038i
$872$	31.1964	+	22.6655i	1.05644	+	0.767551i
$873$	−9.82176	+	7.13593i	−0.332416	+	0.241514i
$874$	1.08745	−	3.34682i	0.0367835	−	0.113208i
$875$	8.62088	−	26.5323i	0.291439	−	0.896957i
$876$	−1.15148	+	0.836600i	−0.0389049	+	0.0282661i
$877$	5.74455	+	4.17366i	0.193980	+	0.140934i	0.680536	−	0.732715i	$-0.261747\pi$
$877$	5.74455	+	4.17366i	0.193980	+	0.140934i	−0.486556	+	0.873649i	$0.661747\pi$
$878$	−11.0375	−	33.9699i	−0.372497	−	1.14643i
$879$	1.64938			0.0556321
$880$	−19.0560	+	1.29293i	−0.642377	+	0.0435848i
$881$	56.0676			1.88896			0.944482	−	0.328563i	$-0.106564\pi$
$881$	56.0676			1.88896			0.944482	+	0.328563i	$0.106564\pi$
$882$	1.92266	+	5.91734i	0.0647394	+	0.199247i
$883$	18.2677	+	13.2722i	0.614756	+	0.446647i	0.851086	−	0.525026i	$-0.175945\pi$
$883$	18.2677	+	13.2722i	0.614756	+	0.446647i	−0.236330	+	0.971673i	$0.575945\pi$
$884$	−0.881571	+	0.640499i	−0.0296504	+	0.0215423i
$885$	3.70464	−	11.4017i	0.124530	−	0.383264i
$886$	4.58866	−	14.1224i	0.154159	−	0.474453i
$887$	−24.8394	+	18.0469i	−0.834026	+	0.605955i	−0.920695	−	0.390282i	$-0.872378\pi$
$887$	−24.8394	+	18.0469i	−0.834026	+	0.605955i	0.0866696	+	0.996237i	$0.472378\pi$
$888$	−1.65059	−	1.19923i	−0.0553903	−	0.0402434i
$889$	−6.97564	−	21.4688i	−0.233956	−	0.720041i
$890$	12.8378			0.430322
$891$	5.66465	−	22.5212i	0.189773	−	0.754487i
$892$	−1.53488			−0.0513915
$893$	1.40314	+	4.31841i	0.0469541	+	0.144510i
$894$	−5.50726	−	4.00126i	−0.184190	−	0.133822i
$895$	5.31597	−	3.86228i	0.177693	−	0.129102i
$896$	−5.55404	+	17.0936i	−0.185547	+	0.571056i
$897$	−2.93938	+	9.04648i	−0.0981431	+	0.302053i
$898$	−25.1234	+	18.2532i	−0.838379	+	0.609118i
$899$	5.07280	+	3.68560i	0.169187	+	0.122922i
$900$	−0.514566	−	1.58367i	−0.0171522	−	0.0527890i
$901$	14.1202			0.470411
$902$	4.64125	+	11.5562i	0.154537	+	0.384781i
$903$	6.26685			0.208548
$904$	−14.7487	−	45.3919i	−0.490535	−	1.50971i
$905$	35.2565	+	25.6153i	1.17196	+	0.851482i
$906$	−5.40526	+	3.92715i	−0.179578	+	0.130471i
$907$	8.55835	−	26.3399i	0.284175	−	0.874602i	−0.702469	−	0.711714i	$-0.747919\pi$
$907$	8.55835	−	26.3399i	0.284175	−	0.874602i	0.986645	−	0.162888i	$-0.0520808\pi$
$908$	0.362976	−	1.11713i	0.0120458	−	0.0370731i
$909$	20.0830	−	14.5911i	0.666110	−	0.483957i
$910$	14.3718	+	10.4417i	0.476420	+	0.346139i
$911$	12.4604	+	38.3491i	0.412830	+	1.27056i	0.914177	+	0.405315i	$0.132838\pi$
$911$	12.4604	+	38.3491i	0.412830	+	1.27056i	−0.501347	+	0.865246i	$0.667162\pi$
$912$	0.713217			0.0236170
$913$	−16.4256	−	40.8980i	−0.543607	−	1.35353i
$914$	35.0638			1.15981
$915$	1.07843	+	3.31908i	0.0356519	+	0.109725i
$916$	4.12301	+	2.99554i	0.136228	+	0.0989754i
$917$	35.4188	−	25.7333i	1.16963	−	0.849787i
$918$	1.10240	−	3.39283i	0.0363845	−	0.111980i
$919$	−4.35982	+	13.4181i	−0.143817	+	0.442624i	−0.996857	−	0.0792221i	$-0.974756\pi$
$919$	−4.35982	+	13.4181i	−0.143817	+	0.442624i	0.853040	+	0.521846i	$0.174756\pi$
$920$	−25.4866	+	18.5171i	−0.840270	+	0.610492i
$921$	−10.1011	−	7.33889i	−0.332843	−	0.241825i
$922$	−10.3155	−	31.7479i	−0.339724	−	1.04556i
$923$	−32.3367			−1.06437
$924$	0.286277	−	1.13816i	0.00941782	−	0.0374428i
$925$	2.64204			0.0868698
$926$	−9.02753	−	27.7839i	−0.296663	−	0.913035i
$927$	−12.1522	−	8.82907i	−0.399130	−	0.289985i
$928$	−2.51445	+	1.82685i	−0.0825408	+	0.0599694i
$929$	3.43836	−	10.5822i	0.112809	−	0.347191i	−0.878675	−	0.477421i	$-0.841572\pi$
$929$	3.43836	−	10.5822i	0.112809	−	0.347191i	0.991484	+	0.130230i	$0.0415717\pi$
$930$	−1.23500	+	3.80093i	−0.0404971	+	0.124637i
$931$	−0.644829	+	0.468496i	−0.0211334	+	0.0153543i
$932$	−4.90062	−	3.56051i	−0.160525	−	0.116628i
$933$	1.18522	+	3.64773i	0.0388024	+	0.119421i
$934$	30.7567			1.00639
$935$	−5.86432	+	0.397889i	−0.191784	+	0.0130124i
$936$	28.1287			0.919415
$937$	6.29801	+	19.3833i	0.205747	+	0.633225i	0.999682	+	0.0252216i	$0.00802913\pi$
$937$	6.29801	+	19.3833i	0.205747	+	0.633225i	−0.793935	+	0.608003i	$0.791971\pi$
$938$	7.94205	+	5.77024i	0.259317	+	0.188405i
$939$	−3.28503	+	2.38671i	−0.107203	+	0.0778874i
$940$	1.74688	−	5.37635i	0.0569770	−	0.175357i
$941$	−10.8081	+	33.2639i	−0.352333	+	1.08437i	0.605206	+	0.796069i	$0.293091\pi$
$941$	−10.8081	+	33.2639i	−0.352333	+	1.08437i	−0.957540	+	0.288302i	$0.906909\pi$
$942$	−0.0197829	+	0.0143732i	−0.000644563	+	0.000468303i
$943$	13.8615	+	10.0710i	0.451392	+	0.327956i
$944$	−14.2327	−	43.8037i	−0.463235	−	1.42569i
$945$	11.2045			0.364482
$946$	20.8128	+	13.0652i	0.676683	+	0.424786i
$947$	−13.7832			−0.447892			−0.223946	−	0.974602i	$-0.571894\pi$
$947$	−13.7832			−0.447892			−0.223946	+	0.974602i	$0.571894\pi$
$948$	0.284317	+	0.875036i	0.00923417	+	0.0284199i
$949$	25.1887	+	18.3006i	0.817659	+	0.594064i
$950$	−0.895776	+	0.650819i	−0.0290628	+	0.0211154i
$951$	−1.20370	+	3.70460i	−0.0390326	+	0.120130i
$952$	−2.13343	+	6.56601i	−0.0691448	+	0.212806i
$953$	20.9888	−	15.2493i	0.679895	−	0.493973i	−0.193428	−	0.981115i	$-0.561961\pi$
$953$	20.9888	−	15.2493i	0.679895	−	0.493973i	0.873323	+	0.487142i	$0.161961\pi$
$954$	−41.0094	−	29.7950i	−1.32773	−	0.964650i
$955$	1.81663	+	5.59102i	0.0587848	+	0.180921i
$956$	4.23528			0.136979
$957$	−2.08735	+	1.74415i	−0.0674744	+	0.0563804i
$958$	28.7333			0.928331
$959$	−10.7769	−	33.1678i	−0.348004	−	1.07104i
$960$	−6.04972	−	4.39538i	−0.195254	−	0.141860i
$961$	14.3084	−	10.3956i	0.461560	−	0.335343i
$962$	−1.91800	+	5.90300i	−0.0618388	+	0.190320i
$963$	1.55587	−	4.78846i	0.0501371	−	0.154306i
$964$	−0.621540	+	0.451575i	−0.0200185	+	0.0145443i
$965$	−10.6684	−	7.75104i	−0.343428	−	0.249515i
$966$	2.58993	+	7.97097i	0.0833295	+	0.256462i
$967$	−0.401216			−0.0129022			−0.00645111	−	0.999979i	$-0.502053\pi$
$967$	−0.401216			−0.0129022			−0.00645111	+	0.999979i	$0.502053\pi$
$968$	23.8987	−	22.8884i	0.768133	−	0.735662i
$969$	0.219486			0.00705091
$970$	−3.10571	−	9.55841i	−0.0997185	−	0.306902i
$971$	−4.01609	−	2.91786i	−0.128882	−	0.0936385i	0.521476	−	0.853266i	$-0.325381\pi$
$971$	−4.01609	−	2.91786i	−0.128882	−	0.0936385i	−0.650359	+	0.759627i	$0.725381\pi$
$972$	3.03353	−	2.20399i	0.0973006	−	0.0706930i
$973$	−10.3332	+	31.8024i	−0.331268	+	1.01954i
$974$	−6.77527	+	20.8521i	−0.217094	+	0.668145i
$975$	2.42129	−	1.75917i	0.0775433	−	0.0563385i
$976$	10.8470	+	7.88081i	0.347204	+	0.252258i
$977$	16.3138	+	50.2086i	0.521923	+	1.60632i	0.770320	+	0.637657i	$0.220096\pi$
$977$	16.3138	+	50.2086i	0.521923	+	1.60632i	−0.248397	+	0.968658i	$0.579904\pi$
$978$	−6.69991			−0.214240
$979$	−14.2369	+	11.8961i	−0.455014	+	0.380201i
$980$	0.992319			0.0316985
$981$	−10.9809	−	33.7957i	−0.350593	−	1.07901i
$982$	2.83002	+	2.05613i	0.0903097	+	0.0656138i
$983$	48.4625	−	35.2100i	1.54571	−	1.12303i	0.599091	−	0.800681i	$-0.295529\pi$
$983$	48.4625	−	35.2100i	1.54571	−	1.12303i	0.946622	−	0.322345i	$-0.104471\pi$
$984$	−1.28645	+	3.95928i	−0.0410105	+	0.126217i
$985$	0.623275	−	1.91824i	0.0198592	−	0.0611203i
$986$	1.80033	−	1.30802i	0.0573342	−	0.0416558i
$987$	−8.74890	−	6.35645i	−0.278481	−	0.202328i
$988$	0.154858	+	0.476605i	0.00492670	+	0.0151628i
$989$	33.8093			1.07507
$990$	17.8714	+	11.2187i	0.567990	+	0.356555i
$991$	−18.9888			−0.603200			−0.301600	−	0.953435i	$-0.597521\pi$
$991$	−18.9888			−0.603200			−0.301600	+	0.953435i	$0.597521\pi$
$992$	−2.03931	−	6.27634i	−0.0647481	−	0.199274i
$993$	4.63675	+	3.36880i	0.147143	+	0.106906i
$994$	−23.0507	+	16.7473i	−0.731125	+	0.531193i
$995$	0.716962	−	2.20658i	0.0227292	−	0.0699533i
$996$	0.633160	−	1.94867i	0.0200624	−	0.0617458i
$997$	24.9358	−	18.1169i	0.789726	−	0.573769i	−0.118156	−	0.992995i	$-0.537698\pi$
$997$	24.9358	−	18.1169i	0.789726	−	0.573769i	0.907882	+	0.419226i	$0.137698\pi$
$998$	−12.3220	−	8.95243i	−0.390045	−	0.283384i
$999$	1.20973	+	3.72316i	0.0382741	+	0.117796i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	187.2.g.e.137.2	yes	8
11.3	even	5		2057.2.a.u.1.3		4
11.8	odd	10		2057.2.a.r.1.2		4
11.9	even	5	inner	187.2.g.e.86.2	✓	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
187.2.g.e.86.2	✓	8	11.9	even	5	inner
187.2.g.e.137.2	yes	8	1.1	even	1	trivial
2057.2.a.r.1.2		4	11.8	odd	10
2057.2.a.u.1.3		4	11.3	even	5

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:	\( N \)	\(=\)	\( 187 = 11 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	187.g (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.400166 + 1.23158i) q^{2} +(-0.386111 - 0.280526i) q^{3} +(0.261370 - 0.189896i) q^{4} +(0.547647 - 1.68548i) q^{5} +(0.190983 - 0.587785i) q^{6} +(1.85666 - 1.34895i) q^{7} +(2.43376 + 1.76823i) q^{8} +(-0.856664 - 2.63654i) q^{9} +O(q^{10})\)	\(q+(0.400166 + 1.23158i) q^{2} +(-0.386111 - 0.280526i) q^{3} +(0.261370 - 0.189896i) q^{4} +(0.547647 - 1.68548i) q^{5} +(0.190983 - 0.587785i) q^{6} +(1.85666 - 1.34895i) q^{7} +(2.43376 + 1.76823i) q^{8} +(-0.856664 - 2.63654i) q^{9} +2.29496 q^{10} +(-2.54508 + 2.12663i) q^{11} -0.154189 q^{12} +(1.04228 + 3.20780i) q^{13} +(2.40431 + 1.74683i) q^{14} +(-0.684276 + 0.497155i) q^{15} +(-1.00415 + 3.09044i) q^{16} +(-0.309017 + 0.951057i) q^{17} +(2.90431 - 2.11011i) q^{18} +(0.372057 + 0.270315i) q^{19} +(-0.176929 - 0.544531i) q^{20} -1.09529 q^{21} +(-3.63757 - 2.28348i) q^{22} -5.90904 q^{23} +(-0.443667 - 1.36547i) q^{24} +(1.50415 + 1.09283i) q^{25} +(-3.53359 + 2.56731i) q^{26} +(-0.851296 + 2.62002i) q^{27} +(0.229116 - 0.705148i) q^{28} +(-1.39026 + 1.01008i) q^{29} +(-0.886111 - 0.643798i) q^{30} +(-1.12755 - 3.47023i) q^{31} +1.80862 q^{32} +(1.57926 - 0.107152i) q^{33} -1.29496 q^{34} +(-1.25683 - 3.86812i) q^{35} +(-0.724576 - 0.526435i) q^{36} +(1.14965 - 0.835268i) q^{37} +(-0.184031 + 0.566390i) q^{38} +(0.497438 - 1.53096i) q^{39} +(4.31316 - 3.13370i) q^{40} +(-2.34581 - 1.70433i) q^{41} +(-0.438299 - 1.34895i) q^{42} -5.72162 q^{43} +(-0.261370 + 1.03914i) q^{44} -4.91300 q^{45} +(-2.36459 - 7.27747i) q^{46} +(7.98772 + 5.80342i) q^{47} +(1.25466 - 0.911566i) q^{48} +(-0.535571 + 1.64832i) q^{49} +(-0.743998 + 2.28979i) q^{50} +(0.386111 - 0.280526i) q^{51} +(0.881571 + 0.640499i) q^{52} +(-4.36337 - 13.4291i) q^{53} -3.56743 q^{54} +(2.19059 + 5.45434i) q^{55} +6.90392 q^{56} +(-0.0678250 - 0.208744i) q^{57} +(-1.80033 - 1.30802i) q^{58} +(-11.4670 + 8.33123i) q^{59} +(-0.0844411 + 0.259883i) q^{60} +(1.27503 - 3.92414i) q^{61} +(3.82268 - 2.77734i) q^{62} +(-5.14709 - 3.73958i) q^{63} +(2.73204 + 8.40835i) q^{64} +5.97750 q^{65} +(0.763932 + 1.90211i) q^{66} +3.30325 q^{67} +(0.0998345 + 0.307259i) q^{68} +(2.28155 + 1.65764i) q^{69} +(4.26097 - 3.09578i) q^{70} +(-2.96262 + 9.11801i) q^{71} +(2.57709 - 7.93148i) q^{72} +(7.46799 - 5.42581i) q^{73} +(1.48875 + 1.08164i) q^{74} +(-0.274201 - 0.843905i) q^{75} +0.148577 q^{76} +(-1.85666 + 7.38161i) q^{77} +2.08456 q^{78} +(-1.84395 - 5.67509i) q^{79} +(4.65897 + 3.38494i) q^{80} +(-5.66465 + 4.11561i) q^{81} +(1.16031 - 3.57108i) q^{82} +(-4.10639 + 12.6382i) q^{83} +(-0.286277 + 0.207992i) q^{84} +(1.43376 + 1.04169i) q^{85} +(-2.28959 - 7.04665i) q^{86} +0.820148 q^{87} +(-9.95449 + 0.675403i) q^{88} +5.59388 q^{89} +(-1.96601 - 6.05076i) q^{90} +(6.26231 + 4.54984i) q^{91} +(-1.54445 + 1.12211i) q^{92} +(-0.538133 + 1.65620i) q^{93} +(-3.95098 + 12.1599i) q^{94} +(0.659369 - 0.479059i) q^{95} +(-0.698330 - 0.507366i) q^{96} +(-1.35327 - 4.16495i) q^{97} -2.24436 q^{98} +(7.78722 + 4.88842i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - q^{2} + 3 q^{3} + 5 q^{4} - 3 q^{5} + 6 q^{6} + 3 q^{7} + 6 q^{8} + 5 q^{9}+O(q^{10}) \) 8 * q - q^2 + 3 * q^3 + 5 * q^4 - 3 * q^5 + 6 * q^6 + 3 * q^7 + 6 * q^8 + 5 * q^9	\( 8 q - q^{2} + 3 q^{3} + 5 q^{4} - 3 q^{5} + 6 q^{6} + 3 q^{7} + 6 q^{8} + 5 q^{9} + 12 q^{10} + 2 q^{11} + 2 q^{12} + 3 q^{13} - 10 q^{15} + 7 q^{16} + 2 q^{17} + 4 q^{18} - 5 q^{19} - 4 q^{20} + 6 q^{21} - 9 q^{22} - 24 q^{23} - 7 q^{24} - 3 q^{25} - 19 q^{26} + 3 q^{27} + 16 q^{28} + 10 q^{29} - q^{30} + 17 q^{31} - 24 q^{32} - 8 q^{33} - 4 q^{34} + 6 q^{35} - q^{36} - 13 q^{37} - 38 q^{38} - 11 q^{39} + 15 q^{40} - 22 q^{41} - 9 q^{42} + 8 q^{43} - 5 q^{44} - 24 q^{45} - 20 q^{46} + 9 q^{47} + 13 q^{48} + q^{49} - q^{50} - 3 q^{51} - 18 q^{52} - 23 q^{53} + 22 q^{54} - 12 q^{55} + 2 q^{56} + 16 q^{57} - 6 q^{58} - 35 q^{59} - q^{60} - 19 q^{61} - 6 q^{62} - 4 q^{63} + 8 q^{64} + 10 q^{65} + 24 q^{66} - 10 q^{67} + 5 q^{68} + 12 q^{69} + 3 q^{70} - 5 q^{71} + 19 q^{72} + 39 q^{73} - 7 q^{74} + 6 q^{75} + 32 q^{76} - 3 q^{77} + 6 q^{78} - 3 q^{79} + 21 q^{80} + 7 q^{81} - 5 q^{82} + 29 q^{83} + 8 q^{84} - 2 q^{85} - 14 q^{86} + 32 q^{87} + 9 q^{88} + 40 q^{89} + 9 q^{90} + 21 q^{91} + 12 q^{92} - 14 q^{93} + 40 q^{94} + 23 q^{95} - 12 q^{96} - 5 q^{97} + 30 q^{98} + 20 q^{99}+O(q^{100}) \) 8 * q - q^2 + 3 * q^3 + 5 * q^4 - 3 * q^5 + 6 * q^6 + 3 * q^7 + 6 * q^8 + 5 * q^9 + 12 * q^10 + 2 * q^11 + 2 * q^12 + 3 * q^13 - 10 * q^15 + 7 * q^16 + 2 * q^17 + 4 * q^18 - 5 * q^19 - 4 * q^20 + 6 * q^21 - 9 * q^22 - 24 * q^23 - 7 * q^24 - 3 * q^25 - 19 * q^26 + 3 * q^27 + 16 * q^28 + 10 * q^29 - q^30 + 17 * q^31 - 24 * q^32 - 8 * q^33 - 4 * q^34 + 6 * q^35 - q^36 - 13 * q^37 - 38 * q^38 - 11 * q^39 + 15 * q^40 - 22 * q^41 - 9 * q^42 + 8 * q^43 - 5 * q^44 - 24 * q^45 - 20 * q^46 + 9 * q^47 + 13 * q^48 + q^49 - q^50 - 3 * q^51 - 18 * q^52 - 23 * q^53 + 22 * q^54 - 12 * q^55 + 2 * q^56 + 16 * q^57 - 6 * q^58 - 35 * q^59 - q^60 - 19 * q^61 - 6 * q^62 - 4 * q^63 + 8 * q^64 + 10 * q^65 + 24 * q^66 - 10 * q^67 + 5 * q^68 + 12 * q^69 + 3 * q^70 - 5 * q^71 + 19 * q^72 + 39 * q^73 - 7 * q^74 + 6 * q^75 + 32 * q^76 - 3 * q^77 + 6 * q^78 - 3 * q^79 + 21 * q^80 + 7 * q^81 - 5 * q^82 + 29 * q^83 + 8 * q^84 - 2 * q^85 - 14 * q^86 + 32 * q^87 + 9 * q^88 + 40 * q^89 + 9 * q^90 + 21 * q^91 + 12 * q^92 - 14 * q^93 + 40 * q^94 + 23 * q^95 - 12 * q^96 - 5 * q^97 + 30 * q^98 + 20 * q^99

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