LMFDB - Embedded newform 287.2.e.d.247.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [287,2,Mod(165,287)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(287, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4, 0]))

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

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

chi := DirichletCharacter("287.165");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 287 = 7 \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	287.e (of order $3$, 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:	$2.29170653801$
Analytic rank:	$0$
Dimension:	$34$
Relative dimension:	$17$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			247.1
Character	$\chi$	$=$	287.247
Dual form			287.2.e.d.165.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.36755 + 2.36867i) q^{2} +(-1.26123 - 2.18452i) q^{3} +(-2.74039 - 4.74650i) q^{4} +(0.813928 - 1.40976i) q^{5} +6.89919 q^{6} +(-1.98316 + 1.75131i) q^{7} +9.52032 q^{8} +(-1.68141 + 2.91228i) q^{9} +O(q^{10})$	\(q+(-1.36755 + 2.36867i) q^{2} +(-1.26123 - 2.18452i) q^{3} +(-2.74039 - 4.74650i) q^{4} +(0.813928 - 1.40976i) q^{5} +6.89919 q^{6} +(-1.98316 + 1.75131i) q^{7} +9.52032 q^{8} +(-1.68141 + 2.91228i) q^{9} +(2.22618 + 3.85585i) q^{10} +(0.608615 + 1.05415i) q^{11} +(-6.91254 + 11.9729i) q^{12} -3.49396 q^{13} +(-1.43619 - 7.09245i) q^{14} -4.10620 q^{15} +(-7.53874 + 13.0575i) q^{16} +(-1.79682 - 3.11219i) q^{17} +(-4.59882 - 7.96539i) q^{18} +(0.449133 - 0.777920i) q^{19} -8.92193 q^{20} +(6.32698 + 2.12345i) q^{21} -3.32925 q^{22} +(-4.23810 + 7.34060i) q^{23} +(-12.0073 - 20.7973i) q^{24} +(1.17504 + 2.03524i) q^{25} +(4.77817 - 8.27603i) q^{26} +0.915183 q^{27} +(13.7472 + 4.61381i) q^{28} -7.30066 q^{29} +(5.61544 - 9.72623i) q^{30} +(5.02488 + 8.70334i) q^{31} +(-11.0989 - 19.2239i) q^{32} +(1.53521 - 2.65906i) q^{33} +9.82898 q^{34} +(0.854777 + 4.22122i) q^{35} +18.4309 q^{36} +(-0.173053 + 0.299737i) q^{37} +(1.22842 + 2.12769i) q^{38} +(4.40669 + 7.63261i) q^{39} +(7.74885 - 13.4214i) q^{40} +1.00000 q^{41} +(-13.6822 + 12.0826i) q^{42} -6.77186 q^{43} +(3.33569 - 5.77759i) q^{44} +(2.73709 + 4.74077i) q^{45} +(-11.5916 - 20.0773i) q^{46} +(-0.0977234 + 0.169262i) q^{47} +38.0323 q^{48} +(0.865858 - 6.94624i) q^{49} -6.42773 q^{50} +(-4.53241 + 7.85037i) q^{51} +(9.57483 + 16.5841i) q^{52} +(-2.72120 - 4.71326i) q^{53} +(-1.25156 + 2.16777i) q^{54} +1.98147 q^{55} +(-18.8803 + 16.6730i) q^{56} -2.26584 q^{57} +(9.98403 - 17.2928i) q^{58} +(-4.31286 - 7.47010i) q^{59} +(11.2526 + 19.4901i) q^{60} +(-0.0722249 + 0.125097i) q^{61} -27.4871 q^{62} +(-1.76579 - 8.72018i) q^{63} +30.5583 q^{64} +(-2.84383 + 4.92566i) q^{65} +(4.19895 + 7.27280i) q^{66} +(1.29476 + 2.24259i) q^{67} +(-9.84800 + 17.0572i) q^{68} +21.3809 q^{69} +(-11.1676 - 3.74806i) q^{70} +7.50089 q^{71} +(-16.0075 + 27.7259i) q^{72} +(2.97807 + 5.15818i) q^{73} +(-0.473318 - 0.819811i) q^{74} +(2.96400 - 5.13380i) q^{75} -4.92320 q^{76} +(-3.05312 - 1.02468i) q^{77} -24.1055 q^{78} +(-6.71739 + 11.6349i) q^{79} +(12.2720 + 21.2557i) q^{80} +(3.88996 + 6.73761i) q^{81} +(-1.36755 + 2.36867i) q^{82} -10.6580 q^{83} +(-7.25947 - 35.8501i) q^{84} -5.84993 q^{85} +(9.26087 - 16.0403i) q^{86} +(9.20782 + 15.9484i) q^{87} +(5.79421 + 10.0359i) q^{88} +(2.88655 - 4.99965i) q^{89} -14.9724 q^{90} +(6.92909 - 6.11899i) q^{91} +46.4563 q^{92} +(12.6751 - 21.9538i) q^{93} +(-0.267284 - 0.462949i) q^{94} +(-0.731123 - 1.26634i) q^{95} +(-27.9966 + 48.4915i) q^{96} +3.67240 q^{97} +(15.2692 + 11.5503i) q^{98} -4.09332 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 34 q - 3 q^{2} - q^{3} - 25 q^{4} + q^{5} + 4 q^{6} - 2 q^{7} + 18 q^{8} - 26 q^{9}+O(q^{10}) $ 34 * q - 3 * q^2 - q^3 - 25 * q^4 + q^5 + 4 * q^6 - 2 * q^7 + 18 * q^8 - 26 * q^9	\( 34 q - 3 q^{2} - q^{3} - 25 q^{4} + q^{5} + 4 q^{6} - 2 q^{7} + 18 q^{8} - 26 q^{9} + 2 q^{10} - 15 q^{11} - 4 q^{12} - 10 q^{13} + 21 q^{14} + 48 q^{15} - 33 q^{16} - 4 q^{17} - 10 q^{18} - 5 q^{19} - 52 q^{20} + 12 q^{21} + 32 q^{22} - 12 q^{23} - 16 q^{24} - 24 q^{25} - 31 q^{26} - 22 q^{27} + 60 q^{28} + 28 q^{29} + 33 q^{30} + 3 q^{31} - 16 q^{32} - 4 q^{33} - 48 q^{34} + 45 q^{35} + 114 q^{36} - 24 q^{37} - 45 q^{39} - 36 q^{40} + 34 q^{41} + 65 q^{42} + 28 q^{43} + 9 q^{44} + 21 q^{45} - 44 q^{46} - 19 q^{47} - 120 q^{48} - 10 q^{49} - 8 q^{50} - 2 q^{51} + 25 q^{52} - 4 q^{53} - 68 q^{54} + 18 q^{55} + 25 q^{56} - 24 q^{57} + q^{58} + 27 q^{59} - 66 q^{60} + q^{61} - 46 q^{62} + 37 q^{63} + 150 q^{64} - 22 q^{65} + 16 q^{66} - 49 q^{67} - 45 q^{68} + 24 q^{69} + 73 q^{70} + 80 q^{71} + 23 q^{72} + 14 q^{73} - 33 q^{74} - 27 q^{75} - 18 q^{76} - 20 q^{77} - 24 q^{78} - 61 q^{79} + 82 q^{80} - 53 q^{81} - 3 q^{82} - 36 q^{83} + 188 q^{84} - 26 q^{85} + 4 q^{86} + 17 q^{87} - 74 q^{88} - 18 q^{89} - 40 q^{90} + 7 q^{91} + 56 q^{92} + 36 q^{93} + 5 q^{94} - 20 q^{95} - 148 q^{96} + 52 q^{97} + 142 q^{98} + 76 q^{99}+O(q^{100}) \) 34 * q - 3 * q^2 - q^3 - 25 * q^4 + q^5 + 4 * q^6 - 2 * q^7 + 18 * q^8 - 26 * q^9 + 2 * q^10 - 15 * q^11 - 4 * q^12 - 10 * q^13 + 21 * q^14 + 48 * q^15 - 33 * q^16 - 4 * q^17 - 10 * q^18 - 5 * q^19 - 52 * q^20 + 12 * q^21 + 32 * q^22 - 12 * q^23 - 16 * q^24 - 24 * q^25 - 31 * q^26 - 22 * q^27 + 60 * q^28 + 28 * q^29 + 33 * q^30 + 3 * q^31 - 16 * q^32 - 4 * q^33 - 48 * q^34 + 45 * q^35 + 114 * q^36 - 24 * q^37 - 45 * q^39 - 36 * q^40 + 34 * q^41 + 65 * q^42 + 28 * q^43 + 9 * q^44 + 21 * q^45 - 44 * q^46 - 19 * q^47 - 120 * q^48 - 10 * q^49 - 8 * q^50 - 2 * q^51 + 25 * q^52 - 4 * q^53 - 68 * q^54 + 18 * q^55 + 25 * q^56 - 24 * q^57 + q^58 + 27 * q^59 - 66 * q^60 + q^61 - 46 * q^62 + 37 * q^63 + 150 * q^64 - 22 * q^65 + 16 * q^66 - 49 * q^67 - 45 * q^68 + 24 * q^69 + 73 * q^70 + 80 * q^71 + 23 * q^72 + 14 * q^73 - 33 * q^74 - 27 * q^75 - 18 * q^76 - 20 * q^77 - 24 * q^78 - 61 * q^79 + 82 * q^80 - 53 * q^81 - 3 * q^82 - 36 * q^83 + 188 * q^84 - 26 * q^85 + 4 * q^86 + 17 * q^87 - 74 * q^88 - 18 * q^89 - 40 * q^90 + 7 * q^91 + 56 * q^92 + 36 * q^93 + 5 * q^94 - 20 * q^95 - 148 * q^96 + 52 * q^97 + 142 * q^98 + 76 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/287\mathbb{Z}\right)^\times$.

$n$	$206$	$211$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$

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 $

$2$	−1.36755	+	2.36867i	−0.967005	+	1.67490i	−0.262876	+	0.964830i	$0.584671\pi$
$2$	−1.36755	+	2.36867i	−0.967005	+	1.67490i	−0.704129	+	0.710072i	$0.748662\pi$
$3$	−1.26123	−	2.18452i	−0.728172	−	1.26123i	−0.957655	−	0.287918i	$-0.907037\pi$
$3$	−1.26123	−	2.18452i	−0.728172	−	1.26123i	0.229483	−	0.973313i	$-0.426296\pi$
$4$	−2.74039	−	4.74650i	−1.37020	−	2.37325i
$5$	0.813928	−	1.40976i	0.363999	−	0.630466i	−0.624616	−	0.780932i	$-0.714744\pi$
$5$	0.813928	−	1.40976i	0.363999	−	0.630466i	0.988615	+	0.150467i	$0.0480777\pi$
$6$	6.89919			2.81658
$7$	−1.98316	+	1.75131i	−0.749565	+	0.661931i
$7$	−1.98316	+	1.75131i	−0.749565	+	0.661931i
$8$	9.52032			3.36594
$9$	−1.68141	+	2.91228i	−0.560469	+	0.970761i
$10$	2.22618	+	3.85585i	0.703979	+	1.21933i
$11$	0.608615	+	1.05415i	0.183504	+	0.317839i	0.943072	−	0.332590i	$-0.107923\pi$
$11$	0.608615	+	1.05415i	0.183504	+	0.317839i	−0.759567	+	0.650429i	$0.774589\pi$
$12$	−6.91254	+	11.9729i	−1.99548	+	3.45627i
$13$	−3.49396			−0.969050			−0.484525	−	0.874777i	$-0.661008\pi$
$13$	−3.49396			−0.969050			−0.484525	+	0.874777i	$0.661008\pi$
$14$	−1.43619	−	7.09245i	−0.383837	−	1.89554i
$15$	−4.10620			−1.06022
$16$	−7.53874	+	13.0575i	−1.88468	+	3.26437i
$17$	−1.79682	−	3.11219i	−0.435793	−	0.754816i	0.561567	−	0.827431i	$-0.310199\pi$
$17$	−1.79682	−	3.11219i	−0.435793	−	0.754816i	−0.997360	+	0.0726154i	$0.976865\pi$
$18$	−4.59882	−	7.96539i	−1.08395	−	1.87746i
$19$	0.449133	−	0.777920i	0.103038	−	0.178467i	−0.809897	−	0.586572i	$-0.800477\pi$
$19$	0.449133	−	0.777920i	0.103038	−	0.178467i	0.912935	+	0.408105i	$0.133810\pi$
$20$	−8.92193			−1.99500
$21$	6.32698	+	2.12345i	1.38066	+	0.463374i
$22$	−3.32925			−0.709799
$23$	−4.23810	+	7.34060i	−0.883705	+	1.53062i	−0.0365139	+	0.999333i	$0.511625\pi$
$23$	−4.23810	+	7.34060i	−0.883705	+	1.53062i	−0.847191	+	0.531289i	$0.821708\pi$
$24$	−12.0073	−	20.7973i	−2.45098	−	4.24523i
$25$	1.17504	+	2.03524i	0.235009	+	0.407047i
$26$	4.77817	−	8.27603i	0.937076	−	1.62306i
$27$	0.915183			0.176127
$28$	13.7472	+	4.61381i	2.59798	+	0.871929i
$29$	−7.30066			−1.35570			−0.677849	−	0.735201i	$-0.737088\pi$
$29$	−7.30066			−1.35570			−0.677849	+	0.735201i	$0.737088\pi$
$30$	5.61544	−	9.72623i	1.02523	−	1.77576i
$31$	5.02488	+	8.70334i	0.902495	+	1.56317i	0.824245	+	0.566233i	$0.191600\pi$
$31$	5.02488	+	8.70334i	0.902495	+	1.56317i	0.0782491	+	0.996934i	$0.475067\pi$
$32$	−11.0989	−	19.2239i	−1.96203	−	3.39833i
$33$	1.53521	−	2.65906i	0.267245	−	0.462883i
$34$	9.82898			1.68566
$35$	0.854777	+	4.22122i	0.144484	+	0.713517i
$36$	18.4309			3.07181
$37$	−0.173053	+	0.299737i	−0.0284497	+	0.0492764i	−0.879900	−	0.475159i	$-0.842390\pi$
$37$	−0.173053	+	0.299737i	−0.0284497	+	0.0492764i	0.851450	+	0.524436i	$0.175724\pi$
$38$	1.22842	+	2.12769i	0.199277	+	0.345157i
$39$	4.40669	+	7.63261i	0.705635	+	1.22220i
$40$	7.74885	−	13.4214i	1.22520	−	2.12211i
$41$	1.00000			0.156174
$41$	1.00000			0.156174
$42$	−13.6822	+	12.0826i	−2.11121	+	1.86438i
$43$	−6.77186			−1.03270			−0.516350	−	0.856378i	$-0.672710\pi$
$43$	−6.77186			−1.03270			−0.516350	+	0.856378i	$0.672710\pi$
$44$	3.33569	−	5.77759i	0.502874	−	0.871004i
$45$	2.73709	+	4.74077i	0.408021	+	0.706713i
$46$	−11.5916	−	20.0773i	−1.70909	−	2.96024i
$47$	−0.0977234	+	0.169262i	−0.0142544	+	0.0246894i	−0.873065	−	0.487605i	$-0.837871\pi$
$47$	−0.0977234	+	0.169262i	−0.0142544	+	0.0246894i	0.858810	+	0.512294i	$0.171204\pi$
$48$	38.0323			5.48950
$49$	0.865858	−	6.94624i	0.123694	−	0.992320i
$50$	−6.42773			−0.909019
$51$	−4.53241	+	7.85037i	−0.634665	+	1.09927i
$52$	9.57483	+	16.5841i	1.32779	+	2.29980i
$53$	−2.72120	−	4.71326i	−0.373786	−	0.647416i	0.616359	−	0.787466i	$-0.288607\pi$
$53$	−2.72120	−	4.71326i	−0.373786	−	0.647416i	−0.990145	+	0.140049i	$0.955274\pi$
$54$	−1.25156	+	2.16777i	−0.170316	+	0.294996i
$55$	1.98147			0.267182
$56$	−18.8803	+	16.6730i	−2.52299	+	2.22802i
$57$	−2.26584			−0.300118
$58$	9.98403	−	17.2928i	1.31097	−	2.27066i
$59$	−4.31286	−	7.47010i	−0.561487	−	0.972524i	−0.997367	−	0.0725190i	$-0.976896\pi$
$59$	−4.31286	−	7.47010i	−0.561487	−	0.972524i	0.435880	−	0.900005i	$-0.356437\pi$
$60$	11.2526	+	19.4901i	1.45271	+	2.51616i
$61$	−0.0722249	+	0.125097i	−0.00924745	+	0.0160171i	−0.870612	−	0.491970i	$-0.836277\pi$
$61$	−0.0722249	+	0.125097i	−0.00924745	+	0.0160171i	0.861365	+	0.507987i	$0.169610\pi$
$62$	−27.4871			−3.49087
$63$	−1.76579	−	8.72018i	−0.222469	−	1.09864i
$64$	30.5583			3.81979
$65$	−2.84383	+	4.92566i	−0.352734	+	0.610953i
$66$	4.19895	+	7.27280i	0.516855	+	0.895220i
$67$	1.29476	+	2.24259i	0.158180	+	0.273976i	0.934212	−	0.356717i	$-0.116104\pi$
$67$	1.29476	+	2.24259i	0.158180	+	0.273976i	−0.776032	+	0.630693i	$0.782771\pi$
$68$	−9.84800	+	17.0572i	−1.19425	+	2.06849i
$69$	21.3809			2.57396
$70$	−11.1676	−	3.74806i	−1.33479	−	0.447979i
$71$	7.50089			0.890192			0.445096	−	0.895483i	$-0.353170\pi$
$71$	7.50089			0.890192			0.445096	+	0.895483i	$0.353170\pi$
$72$	−16.0075	+	27.7259i	−1.88651	+	3.26752i
$73$	2.97807	+	5.15818i	0.348557	+	0.603719i	0.985993	−	0.166784i	$-0.0533384\pi$
$73$	2.97807	+	5.15818i	0.348557	+	0.603719i	−0.637436	+	0.770503i	$0.720005\pi$
$74$	−0.473318	−	0.819811i	−0.0550221	−	0.0953011i
$75$	2.96400	−	5.13380i	0.342254	−	0.592801i
$76$	−4.92320			−0.564730
$77$	−3.05312	−	1.02468i	−0.347936	−	0.116773i
$78$	−24.1055			−2.72941
$79$	−6.71739	+	11.6349i	−0.755765	+	1.30902i	0.189228	+	0.981933i	$0.439402\pi$
$79$	−6.71739	+	11.6349i	−0.755765	+	1.30902i	−0.944993	+	0.327091i	$0.893932\pi$
$80$	12.2720	+	21.2557i	1.37205	+	2.37646i
$81$	3.88996	+	6.73761i	0.432218	+	0.748624i
$82$	−1.36755	+	2.36867i	−0.151021	+	0.261576i
$83$	−10.6580			−1.16987			−0.584934	−	0.811081i	$-0.698879\pi$
$83$	−10.6580			−1.16987			−0.584934	+	0.811081i	$0.698879\pi$
$84$	−7.25947	−	35.8501i	−0.792073	−	3.91157i
$85$	−5.84993			−0.634514
$86$	9.26087	−	16.0403i	0.998625	−	1.72967i
$87$	9.20782	+	15.9484i	0.987182	+	1.70985i
$88$	5.79421	+	10.0359i	0.617665	+	1.06983i
$89$	2.88655	−	4.99965i	0.305973	−	0.529961i	−0.671504	−	0.741001i	$-0.734351\pi$
$89$	2.88655	−	4.99965i	0.305973	−	0.529961i	0.977478	+	0.211039i	$0.0676848\pi$
$90$	−14.9724			−1.57823
$91$	6.92909	−	6.11899i	0.726366	−	0.641444i
$92$	46.4563			4.84340
$93$	12.6751	−	21.9538i	1.31434	−	2.27651i
$94$	−0.267284	−	0.462949i	−0.0275682	−	0.0477495i
$95$	−0.731123	−	1.26634i	−0.0750116	−	0.129924i
$96$	−27.9966	+	48.4915i	−2.85739	+	4.94914i
$97$	3.67240			0.372876			0.186438	−	0.982467i	$-0.440306\pi$
$97$	3.67240			0.372876			0.186438	+	0.982467i	$0.440306\pi$
$98$	15.2692	+	11.5503i	1.54243	+	1.16675i
$99$	−4.09332			−0.411394
$100$	6.44017	−	11.1547i	0.644017	−	1.11547i
$101$	−8.86869	−	15.3610i	−0.882468	−	1.52848i	−0.848589	−	0.529053i	$-0.822547\pi$
$101$	−8.86869	−	15.3610i	−0.882468	−	1.52848i	−0.0338788	−	0.999426i	$-0.510786\pi$
$102$	−12.3966	−	21.4716i	−1.22745	−	2.12600i
$103$	−2.92843	+	5.07218i	−0.288546	+	0.499777i	−0.973463	−	0.228844i	$-0.926505\pi$
$103$	−2.92843	+	5.07218i	−0.288546	+	0.499777i	0.684917	+	0.728621i	$0.259839\pi$
$104$	−33.2636			−3.26176
$105$	8.14326	−	7.19121i	0.794701	−	0.701791i
$106$	14.8855			1.44581
$107$	6.76618	−	11.7194i	0.654112	−	1.13295i	−0.328004	−	0.944676i	$-0.606376\pi$
$107$	6.76618	−	11.7194i	0.654112	−	1.13295i	0.982116	−	0.188278i	$-0.0602907\pi$
$108$	−2.50796	−	4.34392i	−0.241329	−	0.417994i
$109$	−3.68513	−	6.38283i	−0.352971	−	0.611364i	0.633797	−	0.773499i	$-0.281495\pi$
$109$	−3.68513	−	6.38283i	−0.352971	−	0.611364i	−0.986769	+	0.162135i	$0.948162\pi$
$110$	−2.70977	+	4.69346i	−0.258366	+	0.447503i
$111$	0.873039			0.0828652
$112$	−7.91710	−	39.0977i	−0.748095	−	3.69439i
$113$	−13.2842			−1.24967			−0.624837	−	0.780755i	$-0.714835\pi$
$113$	−13.2842			−1.24967			−0.624837	+	0.780755i	$0.714835\pi$
$114$	3.09865	−	5.36702i	0.290215	−	0.502668i
$115$	6.89901	+	11.9494i	0.643336	+	1.11429i
$116$	20.0067	+	34.6526i	1.85757	+	3.21741i
$117$	5.87477	−	10.1754i	0.543122	−	0.940716i
$118$	23.5922			2.17184
$119$	9.01377	+	3.02518i	0.826291	+	0.277318i
$120$	−39.0923			−3.56863
$121$	4.75918	−	8.24313i	0.432652	−	0.749376i
$122$	−0.197543	−	0.342154i	−0.0178847	−	0.0309772i
$123$	−1.26123	−	2.18452i	−0.113721	−	0.196971i
$124$	27.5403	−	47.7012i	2.47319	−	4.28369i
$125$	11.9649			1.07017
$126$	23.0700	+	7.74272i	2.05524	+	0.689776i
$127$	−11.8912			−1.05518			−0.527588	−	0.849501i	$-0.676903\pi$
$127$	−11.8912			−1.05518			−0.527588	+	0.849501i	$0.676903\pi$
$128$	−19.5923	+	33.9349i	−1.73173	+	2.99945i
$129$	8.54088	+	14.7932i	0.751983	+	1.30247i
$130$	−7.77817	−	13.4722i	−0.682190	−	1.18159i
$131$	0.610260	−	1.05700i	0.0533187	−	0.0923507i	−0.838134	−	0.545464i	$-0.816353\pi$
$131$	0.610260	−	1.05700i	0.0533187	−	0.0923507i	0.891453	+	0.453113i	$0.149687\pi$
$132$	−16.8283			−1.46472
$133$	0.471674	+	2.32931i	0.0408993	+	0.201977i
$134$	−7.08260			−0.611843
$135$	0.744893	−	1.29019i	0.0641102	−	0.111042i
$136$	−17.1063	−	29.6290i	−1.46685	−	2.54067i
$137$	−3.46538	−	6.00221i	−0.296067	−	0.512803i	0.679165	−	0.733985i	$-0.262342\pi$
$137$	−3.46538	−	6.00221i	−0.296067	−	0.512803i	−0.975233	+	0.221182i	$0.929009\pi$
$138$	−29.2395	+	50.6442i	−2.48903	+	4.31112i
$139$	−4.26449			−0.361709			−0.180855	−	0.983510i	$-0.557886\pi$
$139$	−4.26449			−0.361709			−0.180855	+	0.983510i	$0.557886\pi$
$140$	17.6936	−	15.6250i	1.49538	−	1.32056i
$141$	0.493007			0.0415187
$142$	−10.2579	+	17.7671i	−0.860820	+	1.49098i
$143$	−2.12648	−	3.68317i	−0.177825	−	0.308002i
$144$	−25.3514	−	43.9099i	−2.11261	−	3.65915i
$145$	−5.94221	+	10.2922i	−0.493474	+	0.854721i
$146$	−16.2907			−1.34823
$147$	−16.2662	+	6.86933i	−1.34162	+	0.566573i
$148$	1.89693			0.155927
$149$	0.375656	−	0.650655i	0.0307749	−	0.0533037i	−0.850228	−	0.526415i	$-0.823536\pi$
$149$	0.375656	−	0.650655i	0.0307749	−	0.0533037i	0.881003	+	0.473111i	$0.156869\pi$
$150$	8.10686	+	14.0415i	0.661922	+	1.14648i
$151$	−5.47007	−	9.47443i	−0.445148	−	0.771018i	0.552915	−	0.833238i	$-0.313515\pi$
$151$	−5.47007	−	9.47443i	−0.445148	−	0.771018i	−0.998062	+	0.0622195i	$0.980182\pi$
$152$	4.27588	−	7.40605i	0.346820	−	0.600710i
$153$	12.0848			0.976994
$154$	6.60244	−	5.83053i	0.532040	−	0.469838i
$155$	16.3595			1.31403
$156$	24.1521	−	41.8327i	1.93372	−	3.34930i
$157$	1.43371	+	2.48325i	0.114422	+	0.198185i	0.917549	−	0.397624i	$-0.130165\pi$
$157$	1.43371	+	2.48325i	0.114422	+	0.198185i	−0.803126	+	0.595809i	$0.796832\pi$
$158$	−18.3728	−	31.8225i	−1.46166	−	2.53167i
$159$	−6.86413	+	11.8890i	−0.544361	+	0.942861i
$160$	−36.1348			−2.85671
$161$	−4.45080	−	21.9798i	−0.350773	−	1.73225i
$162$	−21.2789			−1.67183
$163$	−7.41813	+	12.8486i	−0.581033	+	1.00638i	0.414325	+	0.910129i	$0.364018\pi$
$163$	−7.41813	+	12.8486i	−0.581033	+	1.00638i	−0.995357	+	0.0962490i	$0.969315\pi$
$164$	−2.74039	−	4.74650i	−0.213989	−	0.370640i
$165$	−2.49910	−	4.32856i	−0.194554	−	0.336978i
$166$	14.5754	−	25.2453i	1.13127	−	1.95941i
$167$	4.60491			0.356338			0.178169	−	0.984000i	$-0.442983\pi$
$167$	4.60491			0.356338			0.178169	+	0.984000i	$0.442983\pi$
$168$	60.2349	+	20.2159i	4.64722	+	1.55969i
$169$	−0.792248			−0.0609421
$170$	8.00008	−	13.8565i	0.613578	−	1.06275i
$171$	1.51035	+	2.61600i	0.115499	+	0.200051i
$172$	18.5576	+	32.1427i	1.41500	+	2.45086i
$173$	−4.17414	+	7.22982i	−0.317354	+	0.549673i	−0.979935	−	0.199317i	$-0.936128\pi$
$173$	−4.17414	+	7.22982i	−0.317354	+	0.549673i	0.662581	+	0.748990i	$0.269461\pi$
$174$	−50.3687			−3.81844
$175$	−5.89462	−	1.97834i	−0.445592	−	0.149548i
$176$	−18.3528			−1.38339
$177$	−10.8790	+	18.8430i	−0.817718	+	1.41633i
$178$	7.89500	+	13.6745i	0.591755	+	1.02495i
$179$	9.39080	+	16.2653i	0.701901	+	1.21573i	0.967798	+	0.251727i	$0.0809986\pi$
$179$	9.39080	+	16.2653i	0.701901	+	1.21573i	−0.265897	+	0.964001i	$0.585668\pi$
$180$	15.0014	−	25.9832i	1.11814	−	1.93667i
$181$	−7.46823			−0.555110			−0.277555	−	0.960710i	$-0.589524\pi$
$181$	−7.46823			−0.555110			−0.277555	+	0.960710i	$0.589524\pi$
$182$	5.01798	+	24.7807i	0.371957	+	1.83687i
$183$	0.364369			0.0269349
$184$	−40.3481	+	69.8849i	−2.97450	+	5.15198i
$185$	0.281705	+	0.487928i	0.0207114	+	0.0358732i
$186$	34.6676	+	60.0460i	2.54195	+	4.40279i
$187$	2.18715	−	3.78825i	0.159940	−	0.277024i
$188$	1.07120			0.0781255
$189$	−1.81496	+	1.60277i	−0.132019	+	0.116584i
$190$	3.99939			0.290146
$191$	3.94062	−	6.82535i	0.285133	−	0.493865i	−0.687508	−	0.726176i	$-0.741296\pi$
$191$	3.94062	−	6.82535i	0.285133	−	0.493865i	0.972641	+	0.232311i	$0.0746289\pi$
$192$	−38.5411	−	66.7552i	−2.78147	−	4.81764i
$193$	3.03496	+	5.25671i	0.218461	+	0.378386i	0.954338	−	0.298730i	$-0.0965629\pi$
$193$	3.03496	+	5.25671i	0.218461	+	0.378386i	−0.735876	+	0.677116i	$0.763230\pi$
$194$	−5.02220	+	8.69871i	−0.360573	+	0.624531i
$195$	14.3469			1.02740
$196$	−35.3432	+	14.9256i	−2.52451	+	1.06612i
$197$	3.69414			0.263197			0.131598	−	0.991303i	$-0.457989\pi$
$197$	3.69414			0.263197			0.131598	+	0.991303i	$0.457989\pi$
$198$	5.59782	−	9.69572i	0.397820	−	0.689044i
$199$	−5.62796	−	9.74792i	−0.398956	−	0.691012i	0.594642	−	0.803991i	$-0.297294\pi$
$199$	−5.62796	−	9.74792i	−0.398956	−	0.691012i	−0.993597	+	0.112979i	$0.963961\pi$
$200$	11.1868	+	19.3761i	0.791026	+	1.37010i
$201$	3.26598	−	5.65684i	0.230364	−	0.399003i
$202$	48.5136			3.41340
$203$	14.4784	−	12.7857i	1.01618	−	0.897379i
$204$	49.6824			3.47846
$205$	0.813928	−	1.40976i	0.0568472	−	0.0984622i
$206$	−8.00955	−	13.8729i	−0.558052	−	0.966574i
$207$	−14.2519	−	24.6851i	−0.990578	−	1.71573i
$208$	26.3400	−	45.6223i	1.82635	−	3.16334i
$209$	1.09340			0.0756317
$210$	5.89727	+	29.1230i	0.406951	+	2.00968i
$211$	3.60065			0.247879			0.123939	−	0.992290i	$-0.460447\pi$
$211$	3.60065			0.247879			0.123939	+	0.992290i	$0.460447\pi$
$212$	−14.9143	+	25.8324i	−1.02432	+	1.77418i
$213$	−9.46035	−	16.3858i	−0.648213	−	1.12274i
$214$	18.5062	+	32.0537i	1.26506	+	2.19115i
$215$	−5.51181	+	9.54673i	−0.375902	+	0.651081i
$216$	8.71284			0.592833
$217$	−25.2074	−	8.46004i	−1.71119	−	0.574305i
$218$	20.1584			1.36530
$219$	7.51208	−	13.0113i	0.507619	−	0.879222i
$220$	−5.43002	−	9.40507i	−0.366092	−	0.634090i
$221$	6.27802	+	10.8739i	0.422305	+	0.731454i
$222$	−1.19393	+	2.06794i	−0.0801311	+	0.138791i
$223$	8.26860			0.553706			0.276853	−	0.960912i	$-0.410708\pi$
$223$	8.26860			0.553706			0.276853	+	0.960912i	$0.410708\pi$
$224$	55.6778	+	18.6865i	3.72013	+	1.24854i
$225$	−7.90291			−0.526861
$226$	18.1669	−	31.4659i	1.20844	−	2.09308i
$227$	−7.11648	−	12.3261i	−0.472337	−	0.818112i	0.527162	−	0.849765i	$-0.323256\pi$
$227$	−7.11648	−	12.3261i	−0.472337	−	0.818112i	−0.999499	+	0.0316529i	$0.989923\pi$
$228$	6.20929	+	10.7548i	0.411221	+	0.712255i
$229$	−12.5774	+	21.7847i	−0.831139	+	1.43958i	0.0659958	+	0.997820i	$0.478978\pi$
$229$	−12.5774	+	21.7847i	−0.831139	+	1.43958i	−0.897135	+	0.441756i	$0.854356\pi$
$230$	−37.7390			−2.48844
$231$	1.61226	+	7.96196i	0.106079	+	0.523859i
$232$	−69.5046			−4.56320
$233$	4.02622	−	6.97361i	0.263766	−	0.456856i	−0.703473	−	0.710722i	$-0.748369\pi$
$233$	4.02622	−	6.97361i	0.263766	−	0.456856i	0.967240	+	0.253865i	$0.0817019\pi$
$234$	16.0681	+	27.8308i	1.05040	+	1.81935i
$235$	0.159080	+	0.275534i	0.0103772	+	0.0179739i
$236$	−23.6379	+	40.9420i	−1.53870	+	2.66510i
$237$	33.8887			2.20131
$238$	−19.4925	+	17.2136i	−1.26351	+	1.11579i
$239$	−20.0964			−1.29993			−0.649963	−	0.759966i	$-0.725216\pi$
$239$	−20.0964			−1.29993			−0.649963	+	0.759966i	$0.725216\pi$
$240$	30.9556	−	53.6166i	1.99817	−	3.46094i
$241$	−12.2586	−	21.2325i	−0.789647	−	1.36771i	−0.926183	−	0.377073i	$-0.876930\pi$
$241$	−12.2586	−	21.2325i	−0.789647	−	1.36771i	0.136537	−	0.990635i	$-0.456403\pi$
$242$	13.0168	+	22.5458i	0.836754	+	1.44930i
$243$	11.1851	−	19.3731i	0.717522	−	1.24278i
$244$	0.791699			0.0506833
$245$	−9.08782	−	6.87439i	−0.580599	−	0.439189i
$246$	6.89919			0.439876
$247$	−1.56925	+	2.71802i	−0.0998490	+	0.172944i
$248$	47.8384	+	82.8586i	3.03774	+	5.26153i
$249$	13.4422	+	23.2826i	0.851865	+	1.47547i
$250$	−16.3626	+	28.3408i	−1.03486	+	1.79243i
$251$	−1.96237			−0.123864			−0.0619318	−	0.998080i	$-0.519726\pi$
$251$	−1.96237			−0.123864			−0.0619318	+	0.998080i	$0.519726\pi$
$252$	−36.5514	+	32.2781i	−2.30252	+	2.03333i
$253$	−10.3175			−0.648655
$254$	16.2619	−	28.1664i	1.02036	−	1.76732i
$255$	7.37811	+	12.7793i	0.462035	+	0.800269i
$256$	−23.0286	−	39.8868i	−1.43929	−	2.49292i
$257$	−4.05923	+	7.03079i	−0.253208	+	0.438569i	−0.964407	−	0.264422i	$-0.914819\pi$
$257$	−4.05923	+	7.03079i	−0.253208	+	0.438569i	0.711199	+	0.702990i	$0.248152\pi$
$258$	−46.7204			−2.90868
$259$	−0.181738	−	0.897495i	−0.0112927	−	0.0557676i
$260$	31.1729			1.93326
$261$	12.2754	−	21.2616i	0.759827	−	1.31606i
$262$	1.66912	+	2.89101i	0.103119	+	0.178607i
$263$	−4.18574	−	7.24991i	−0.258103	−	0.447048i	0.707630	−	0.706583i	$-0.249764\pi$
$263$	−4.18574	−	7.24991i	−0.258103	−	0.447048i	−0.965734	+	0.259534i	$0.916431\pi$
$264$	14.6157	−	25.3151i	0.899532	−	1.55804i
$265$	−8.85945			−0.544231
$266$	−6.16240	−	2.06821i	−0.377841	−	0.126810i
$267$	−14.5624			−0.891205
$268$	7.09630	−	12.2912i	0.433476	−	0.750802i
$269$	2.43541	+	4.21825i	0.148489	+	0.257191i	0.930669	−	0.365861i	$-0.119226\pi$
$269$	2.43541	+	4.21825i	0.148489	+	0.257191i	−0.782180	+	0.623053i	$0.785892\pi$
$270$	2.03736	+	3.52881i	0.123990	+	0.214757i
$271$	−1.80834	+	3.13213i	−0.109849	+	0.190263i	−0.915709	−	0.401843i	$-0.868370\pi$
$271$	−1.80834	+	3.13213i	−0.109849	+	0.190263i	0.805860	+	0.592106i	$0.201703\pi$
$272$	54.1831			3.28533
$273$	−22.1062	−	7.41924i	−1.33793	−	0.449033i
$274$	18.9563			1.14519
$275$	−1.43030	+	2.47735i	−0.0862503	+	0.149390i
$276$	−58.5921	−	101.484i	−3.52683	−	6.10865i
$277$	9.41826	+	16.3129i	0.565888	+	0.980147i	0.996966	+	0.0778325i	$0.0247999\pi$
$277$	9.41826	+	16.3129i	0.565888	+	0.980147i	−0.431078	+	0.902315i	$0.641867\pi$
$278$	5.83191	−	10.1012i	0.349775	−	0.605827i
$279$	−33.7955			−2.02328
$280$	8.13775	+	40.1874i	0.486324	+	2.40166i
$281$	−1.20938			−0.0721456			−0.0360728	−	0.999349i	$-0.511485\pi$
$281$	−1.20938			−0.0721456			−0.0360728	+	0.999349i	$0.511485\pi$
$282$	−0.674213	+	1.16777i	−0.0401488	+	0.0695398i
$283$	3.65879	+	6.33720i	0.217492	+	0.376708i	0.954041	−	0.299677i	$-0.0968790\pi$
$283$	3.65879	+	6.33720i	0.217492	+	0.376708i	−0.736548	+	0.676385i	$0.763546\pi$
$284$	−20.5554	−	35.6030i	−1.21974	−	2.11265i
$285$	−1.84423	+	3.19430i	−0.109243	+	0.189214i
$286$	11.6323			0.687830
$287$	−1.98316	+	1.75131i	−0.117062	+	0.103376i
$288$	74.6471			4.39862
$289$	2.04287	−	3.53835i	0.120169	−	0.208138i
$290$	−16.2526	−	28.1503i	−0.954383	−	1.65304i
$291$	−4.63175	−	8.02242i	−0.271518	−	0.470283i
$292$	16.3222	−	28.2709i	0.955184	−	1.65443i
$293$	8.12874			0.474886			0.237443	−	0.971401i	$-0.423691\pi$
$293$	8.12874			0.474886			0.237443	+	0.971401i	$0.423691\pi$
$294$	5.97372	−	47.9235i	0.348395	−	2.79495i
$295$	−14.0414			−0.817524
$296$	−1.64752	+	2.85359i	−0.0957601	+	0.165861i
$297$	0.556994	+	0.964743i	0.0323201	+	0.0559800i
$298$	1.02746	+	1.77961i	0.0595190	+	0.103090i
$299$	14.8077	−	25.6478i	0.856354	−	1.48325i
$300$	−32.4902			−1.87582
$301$	13.4297	−	11.8596i	0.774075	−	0.683576i
$302$	29.9224			1.72184
$303$	−22.3709	+	38.7476i	−1.28518	+	2.22599i
$304$	6.77178	+	11.7291i	0.388388	+	0.672709i
$305$	0.117572	+	0.203640i	0.00673214	+	0.0116604i
$306$	−16.5265	+	28.6248i	−0.944758	+	1.63637i
$307$	−7.66920			−0.437704			−0.218852	−	0.975758i	$-0.570231\pi$
$307$	−7.66920			−0.437704			−0.218852	+	0.975758i	$0.570231\pi$
$308$	3.50310	+	17.2997i	0.199608	+	0.985742i
$309$	14.7737			0.840445
$310$	−22.3725	+	38.7503i	−1.27067	+	2.20087i
$311$	7.50387	+	12.9971i	0.425505	+	0.736997i	0.996467	−	0.0839797i	$-0.0267631\pi$
$311$	7.50387	+	12.9971i	0.425505	+	0.736997i	−0.570962	+	0.820976i	$0.693430\pi$
$312$	41.9531	+	72.6649i	2.37513	+	4.11384i
$313$	−4.11544	+	7.12815i	−0.232618	+	0.402907i	−0.958578	−	0.284831i	$-0.908063\pi$
$313$	−4.11544	+	7.12815i	−0.232618	+	0.402907i	0.725960	+	0.687737i	$0.241396\pi$
$314$	−7.84267			−0.442587
$315$	−13.7306	−	4.60824i	−0.773633	−	0.259645i
$316$	73.6332			4.14219
$317$	2.60239	−	4.50747i	0.146165	−	0.253165i	−0.783642	−	0.621213i	$-0.786640\pi$
$317$	2.60239	−	4.50747i	0.146165	−	0.253165i	0.929807	+	0.368048i	$0.119974\pi$
$318$	−18.7741	−	32.5177i	−1.05280	−	1.82350i
$319$	−4.44329	−	7.69601i	−0.248777	−	0.430894i
$320$	24.8723	−	43.0801i	1.39040	−	2.40825i
$321$	−34.1349			−1.90522
$322$	58.1496	+	19.5160i	3.24055	+	1.08759i
$323$	−3.22804			−0.179613
$324$	21.3201	−	36.9274i	1.18445	−	2.05152i
$325$	−4.10556	−	7.11103i	−0.227735	−	0.394449i
$326$	−20.2893	−	35.1422i	−1.12372	−	1.94635i
$327$	−9.29559	+	16.1004i	−0.514047	+	0.890356i
$328$	9.52032			0.525672
$329$	−0.102628	−	0.506817i	−0.00565807	−	0.0279417i
$330$	13.6706			0.752540
$331$	0.581620	−	1.00740i	0.0319687	−	0.0553715i	−0.849598	−	0.527430i	$-0.823156\pi$
$331$	0.581620	−	1.00740i	0.0319687	−	0.0553715i	0.881567	+	0.472059i	$0.156489\pi$
$332$	29.2071	+	50.5882i	1.60295	+	2.77639i
$333$	−0.581945	−	1.00796i	−0.0318904	−	0.0552358i
$334$	−6.29745	+	10.9075i	−0.344581	+	0.596832i
$335$	4.21536			0.230310
$336$	−75.4243	+	66.6063i	−4.11473	+	3.63367i
$337$	22.7841			1.24113			0.620565	−	0.784155i	$-0.286903\pi$
$337$	22.7841			1.24113			0.620565	+	0.784155i	$0.286903\pi$
$338$	1.08344	−	1.87657i	0.0589313	−	0.102072i
$339$	16.7545	+	29.0196i	0.909978	+	1.57613i
$340$	16.0311	+	27.7667i	0.869409	+	1.50586i
$341$	−6.11643	+	10.5940i	−0.331223	+	0.573696i
$342$	−8.26192			−0.446754
$343$	10.4479	+	15.2919i	0.564131	+	0.825685i
$344$	−64.4703			−3.47600
$345$	17.4025	−	30.1420i	0.936919	−	1.62279i
$346$	−11.4167	−	19.7743i	−0.613766	−	1.06307i
$347$	−9.63349	−	16.6857i	−0.517153	−	0.895735i	−0.999802	−	0.0199207i	$-0.993659\pi$
$347$	−9.63349	−	16.6857i	−0.517153	−	0.895735i	0.482649	−	0.875814i	$-0.339675\pi$
$348$	50.4661	−	87.4099i	2.70527	−	4.68566i
$349$	20.9660			1.12228			0.561141	−	0.827720i	$-0.310363\pi$
$349$	20.9660			1.12228			0.561141	+	0.827720i	$0.310363\pi$
$350$	12.7472	−	11.2569i	0.681368	−	0.601708i
$351$	−3.19761			−0.170676
$352$	13.5099	−	23.3999i	0.720081	−	1.24722i
$353$	−6.82906	−	11.8283i	−0.363474	−	0.629556i	0.625056	−	0.780580i	$-0.285076\pi$
$353$	−6.82906	−	11.8283i	−0.363474	−	0.629556i	−0.988530	+	0.151024i	$0.951743\pi$
$354$	−29.7553	−	51.5376i	−1.58147	−	2.73919i
$355$	6.10518	−	10.5745i	0.324029	−	0.561235i
$356$	−31.6411			−1.67698
$357$	−4.75989	−	23.5062i	−0.251920	−	1.24408i
$358$	−51.3696			−2.71497
$359$	−15.9211	+	27.5761i	−0.840282	+	1.45541i	0.0493751	+	0.998780i	$0.484277\pi$
$359$	−15.9211	+	27.5761i	−0.840282	+	1.45541i	−0.889657	+	0.456630i	$0.849056\pi$
$360$	26.0579	+	45.1337i	1.37337	+	2.37875i
$361$	9.09656	+	15.7557i	0.478766	+	0.829248i
$362$	10.2132	−	17.6898i	0.536794	−	0.929754i
$363$	−24.0097			−1.26018
$364$	−48.0322	−	16.1205i	−2.51757	−	0.844942i
$365$	9.69575			0.507498
$366$	−0.498294	+	0.863070i	−0.0260462	+	0.0451134i
$367$	−16.5766	−	28.7115i	−0.865292	−	1.49873i	−0.866757	−	0.498731i	$-0.833800\pi$
$367$	−16.5766	−	28.7115i	−0.865292	−	1.49873i	0.00146454	−	0.999999i	$-0.499534\pi$
$368$	−63.8998	−	110.678i	−3.33101	−	5.76948i
$369$	−1.68141	+	2.91228i	−0.0875305	+	0.151607i
$370$	−1.54099			−0.0801120
$371$	13.6509	+	4.58150i	0.708722	+	0.237860i
$372$	−138.939			−7.20363
$373$	−9.63907	+	16.6954i	−0.499092	+	0.864453i	−0.999999	−	0.00104781i	$-0.999666\pi$
$373$	−9.63907	+	16.6954i	−0.499092	+	0.864453i	0.500907	+	0.865501i	$0.333000\pi$
$374$	5.98207	+	10.3612i	0.309325	+	0.535767i
$375$	−15.0905	−	26.1375i	−0.779269	−	1.34973i
$376$	−0.930358	+	1.61143i	−0.0479796	+	0.0831030i
$377$	25.5082			1.31374
$378$	−1.31437	−	6.49090i	−0.0676041	−	0.333856i
$379$	15.0064			0.770825			0.385413	−	0.922744i	$-0.374059\pi$
$379$	15.0064			0.770825			0.385413	+	0.922744i	$0.374059\pi$
$380$	−4.00713	+	6.94055i	−0.205561	+	0.356043i
$381$	14.9976	+	25.9766i	0.768349	+	1.33082i
$382$	10.7780	+	18.6680i	0.551450	+	0.955140i
$383$	−8.39071	+	14.5331i	−0.428745	+	0.742609i	−0.996762	−	0.0804082i	$-0.974378\pi$
$383$	−8.39071	+	14.5331i	−0.428745	+	0.742609i	0.568017	+	0.823017i	$0.307711\pi$
$384$	98.8417			5.04399
$385$	−3.92958	+	3.47017i	−0.200270	+	0.176856i
$386$	−16.6019			−0.845013
$387$	11.3863	−	19.7216i	0.578796	−	1.00250i
$388$	−10.0638	−	17.4311i	−0.510914	−	0.884929i
$389$	1.93609	+	3.35340i	0.0981635	+	0.170024i	0.910924	−	0.412573i	$-0.135370\pi$
$389$	1.93609	+	3.35340i	0.0981635	+	0.170024i	−0.812761	+	0.582597i	$0.802037\pi$
$390$	−19.6201	+	33.9831i	−0.993504	+	1.72080i
$391$	30.4604			1.54045
$392$	8.24325	−	66.1304i	0.416347	−	3.34009i
$393$	−3.07872			−0.155301
$394$	−5.05193	+	8.75020i	−0.254513	+	0.440829i
$395$	10.9349	+	18.9399i	0.550196	+	0.952968i
$396$	11.2173	+	19.4289i	0.563691	+	0.976341i
$397$	−16.5570	+	28.6775i	−0.830972	+	1.43928i	0.0662972	+	0.997800i	$0.478881\pi$
$397$	−16.5570	+	28.6775i	−0.830972	+	1.43928i	−0.897269	+	0.441485i	$0.854452\pi$
$398$	30.7861			1.54317
$399$	4.49353	−	3.96818i	0.224958	−	0.198657i
$400$	−35.4334			−1.77167
$401$	−6.76381	+	11.7153i	−0.337769	+	0.585033i	−0.984013	−	0.178098i	$-0.943005\pi$
$401$	−6.76381	+	11.7153i	−0.337769	+	0.585033i	0.646244	+	0.763131i	$0.276339\pi$
$402$	8.93279	+	15.4721i	0.445527	+	0.771676i
$403$	−17.5567	−	30.4091i	−0.874562	−	1.51479i
$404$	−48.6074	+	84.1905i	−2.41831	+	4.18864i
$405$	12.6646			0.629309
$406$	10.4851	+	51.7796i	0.520368	+	2.56978i
$407$	−0.421291			−0.0208826
$408$	−43.1500	+	74.7380i	−2.13624	+	3.70008i
$409$	13.2647	+	22.9752i	0.655899	+	1.13605i	0.981668	+	0.190601i	$0.0610437\pi$
$409$	13.2647	+	22.9752i	0.655899	+	1.13605i	−0.325768	+	0.945450i	$0.605623\pi$
$410$	2.22618	+	3.85585i	0.109943	+	0.190427i
$411$	−8.74128	+	15.1403i	−0.431176	+	0.746818i
$412$	32.1002			1.58146
$413$	21.6355	+	7.26127i	1.06461	+	0.357304i
$414$	77.9610			3.83158
$415$	−8.67484	+	15.0253i	−0.425831	+	0.737561i
$416$	38.7791	+	67.1674i	1.90130	+	3.29315i
$417$	5.37850	+	9.31584i	0.263386	+	0.456199i
$418$	−1.49527	+	2.58989i	−0.0731363	+	0.126676i
$419$	−24.0510			−1.17497			−0.587483	−	0.809237i	$-0.699881\pi$
$419$	−24.0510			−1.17497			−0.587483	+	0.809237i	$0.699881\pi$
$420$	−56.4489	−	18.9452i	−2.75442	−	0.924433i
$421$	18.3099			0.892370			0.446185	−	0.894941i	$-0.352782\pi$
$421$	18.3099			0.892370			0.446185	+	0.894941i	$0.352782\pi$
$422$	−4.92407	+	8.52874i	−0.239700	+	0.415173i
$423$	−0.328626	−	0.569196i	−0.0159783	−	0.0276753i
$424$	−25.9067	−	44.8717i	−1.25814	−	2.17916i
$425$	4.22269	−	7.31391i	0.204830	−	0.354777i
$426$	51.7501			2.50730
$427$	−0.0758498	−	0.374576i	−0.00367063	−	0.0181270i
$428$	−74.1681			−3.58505
$429$	−5.36396	+	9.29064i	−0.258974	+	0.448556i
$430$	−15.0754	−	26.1113i	−0.726998	−	1.25920i
$431$	11.4487	+	19.8298i	0.551465	+	0.955166i	0.998169	+	0.0604840i	$0.0192644\pi$
$431$	11.4487	+	19.8298i	0.551465	+	0.955166i	−0.446704	+	0.894682i	$0.647402\pi$
$432$	−6.89933	+	11.9500i	−0.331944	+	0.574944i
$433$	22.2473			1.06914			0.534570	−	0.845124i	$-0.320474\pi$
$433$	22.2473			1.06914			0.534570	+	0.845124i	$0.320474\pi$
$434$	54.5114	−	48.1383i	2.61663	−	2.31071i
$435$	29.9780			1.43733
$436$	−20.1974	+	34.9829i	−0.967280	+	1.67538i
$437$	3.80694	+	6.59381i	0.182110	+	0.315425i
$438$	20.5463	+	35.5872i	0.981741	+	1.70042i
$439$	15.5557	−	26.9433i	0.742434	−	1.28593i	−0.208951	−	0.977926i	$-0.567005\pi$
$439$	15.5557	−	26.9433i	0.742434	−	1.28593i	0.951384	−	0.308007i	$-0.0996619\pi$
$440$	18.8643			0.899319
$441$	18.7736	+	14.2011i	0.893979	+	0.676242i
$442$	−34.3421			−1.63349
$443$	15.5579	−	26.9470i	0.739176	−	1.28029i	−0.213691	−	0.976901i	$-0.568549\pi$
$443$	15.5579	−	26.9470i	0.739176	−	1.28029i	0.952867	−	0.303389i	$-0.0981182\pi$
$444$	−2.39247	−	4.14388i	−0.113542	−	0.196660i
$445$	−4.69888	−	8.13870i	−0.222748	−	0.385811i
$446$	−11.3077	+	19.5856i	−0.535437	+	0.927403i
$447$	−1.89515			−0.0896377
$448$	−60.6021	+	53.5170i	−2.86318	+	2.52844i
$449$	13.8683			0.654485			0.327242	−	0.944940i	$-0.393881\pi$
$449$	13.8683			0.654485			0.327242	+	0.944940i	$0.393881\pi$
$450$	10.8076	−	18.7194i	0.509477	−	0.882440i
$451$	0.608615	+	1.05415i	0.0286586	+	0.0496381i
$452$	36.4040	+	63.0536i	1.71230	+	2.96579i
$453$	−13.7980	+	23.8989i	−0.648288	+	1.12287i
$454$	38.9286			1.82701
$455$	−2.98656	−	14.7488i	−0.140012	−	0.691434i
$456$	−21.5715			−1.01018
$457$	−10.6517	+	18.4493i	−0.498267	+	0.863024i	−0.999998	−	0.00199975i	$-0.999363\pi$
$457$	−10.6517	+	18.4493i	−0.498267	+	0.863024i	0.501731	+	0.865024i	$0.332697\pi$
$458$	−34.4005	−	59.5835i	−1.60743	−	2.78415i
$459$	−1.64442	−	2.84822i	−0.0767550	−	0.132944i
$460$	37.8120	−	65.4924i	1.76299	−	3.05360i
$461$	−26.9224			−1.25390			−0.626951	−	0.779059i	$-0.715697\pi$
$461$	−26.9224			−1.25390			−0.626951	+	0.779059i	$0.715697\pi$
$462$	−21.0641	−	7.06949i	−0.979990	−	0.328902i
$463$	34.1462			1.58691			0.793455	−	0.608628i	$-0.208280\pi$
$463$	34.1462			1.58691			0.793455	+	0.608628i	$0.208280\pi$
$464$	55.0378	−	95.3282i	2.55506	−	4.42550i
$465$	−20.6332	−	35.7377i	−0.956840	−	1.65730i
$466$	11.0121	+	19.0735i	0.510126	+	0.883565i
$467$	4.95825	−	8.58794i	0.229441	−	0.397403i	−0.728202	−	0.685363i	$-0.759644\pi$
$467$	4.95825	−	8.58794i	0.229441	−	0.397403i	0.957642	+	0.287960i	$0.0929770\pi$
$468$	−64.3967			−2.97674
$469$	−6.49517	−	2.17990i	−0.299919	−	0.100658i
$470$	−0.870198			−0.0401393
$471$	3.61647	−	6.26391i	0.166638	−	0.288626i
$472$	−41.0598	−	71.1177i	−1.88993	−	3.27346i
$473$	−4.12146	−	7.13857i	−0.189505	−	0.328232i
$474$	−46.3446	+	80.2711i	−2.12868	+	3.68698i
$475$	2.11100			0.0968594
$476$	−10.3423	−	51.0741i	−0.474037	−	2.34098i
$477$	18.3018			0.837982
$478$	27.4828	−	47.6017i	1.25704	−	2.17725i
$479$	0.959713	+	1.66227i	0.0438504	+	0.0759511i	0.887118	−	0.461543i	$-0.152704\pi$
$479$	0.959713	+	1.66227i	0.0438504	+	0.0759511i	−0.843267	+	0.537495i	$0.819371\pi$
$480$	45.5743	+	78.9371i	2.08017	+	3.60297i
$481$	0.604640	−	1.04727i	0.0275692	−	0.0477513i
$482$	67.0572			3.05437
$483$	−42.4018	+	37.4445i	−1.92935	+	1.70378i
$484$	−52.1681			−2.37128
$485$	2.98907	−	5.17722i	0.135727	−	0.235085i
$486$	30.5923	+	52.9874i	1.38769	+	2.40356i
$487$	−10.3929	−	18.0010i	−0.470948	−	0.815705i	0.528500	−	0.848933i	$-0.322755\pi$
$487$	−10.3929	−	18.0010i	−0.470948	−	0.815705i	−0.999448	+	0.0332279i	$0.989421\pi$
$488$	−0.687604	+	1.19097i	−0.0311264	+	0.0539125i
$489$	37.4239			1.69237
$490$	28.7112	−	12.1249i	1.29704	−	0.547749i
$491$	−25.6725			−1.15858			−0.579292	−	0.815120i	$-0.696671\pi$
$491$	−25.6725			−1.15858			−0.579292	+	0.815120i	$0.696671\pi$
$492$	−6.91254	+	11.9729i	−0.311641	+	0.539779i
$493$	13.1180	+	22.7210i	0.590804	+	1.02330i
$494$	−4.29206	−	7.43407i	−0.193109	−	0.334475i
$495$	−3.33166	+	5.77061i	−0.149747	+	0.259370i
$496$	−151.525			−6.80367
$497$	−14.8755	+	13.1363i	−0.667256	+	0.589246i
$498$	−73.5316			−3.29503
$499$	−17.8510	+	30.9189i	−0.799121	+	1.38412i	0.121068	+	0.992644i	$0.461368\pi$
$499$	−17.8510	+	30.9189i	−0.799121	+	1.38412i	−0.920189	+	0.391474i	$0.871965\pi$
$500$	−32.7885	−	56.7913i	−1.46635	−	2.53979i
$501$	−5.80785	−	10.0595i	−0.259476	−	0.449425i
$502$	2.68364	−	4.64820i	0.119777	−	0.207459i
$503$	−13.9272			−0.620984			−0.310492	−	0.950576i	$-0.600494\pi$
$503$	−13.9272			−0.620984			−0.310492	+	0.950576i	$0.600494\pi$
$504$	−16.8109	−	83.0189i	−0.748818	−	3.69796i
$505$	−28.8739			−1.28487
$506$	14.1097	−	24.4387i	0.627252	−	1.08643i
$507$	0.999207	+	1.73068i	0.0443764	+	0.0768621i
$508$	32.5866	+	56.4417i	1.44580	+	2.50420i
$509$	18.9165	−	32.7644i	0.838460	−	1.45226i	−0.0527216	−	0.998609i	$-0.516790\pi$
$509$	18.9165	−	32.7644i	0.838460	−	1.45226i	0.891182	−	0.453646i	$-0.149877\pi$
$510$	−40.3598			−1.78716
$511$	−14.9395	−	5.01398i	−0.660886	−	0.221805i
$512$	47.6022			2.10374
$513$	0.411039	−	0.711940i	0.0181478	−	0.0314329i
$514$	−11.1024	−	19.2299i	−0.489706	−	0.848196i
$515$	4.76705	+	8.25678i	0.210061	+	0.363837i
$516$	46.8108	−	81.0786i	2.06073	−	3.56929i
$517$	−0.237904			−0.0104630
$518$	2.37440	+	0.796893i	0.104325	+	0.0350135i
$519$	21.0582			0.924353
$520$	−27.0742	+	46.8938i	−1.18728	+	2.05643i
$521$	5.54455	+	9.60345i	0.242911	+	0.420735i	0.961542	−	0.274657i	$-0.0885643\pi$
$521$	5.54455	+	9.60345i	0.242911	+	0.420735i	−0.718631	+	0.695392i	$0.755231\pi$
$522$	33.5744	+	58.1526i	1.46951	+	2.54527i
$523$	19.1635	−	33.1921i	0.837961	−	1.45139i	−0.0536356	−	0.998561i	$-0.517081\pi$
$523$	19.1635	−	33.1921i	0.837961	−	1.45139i	0.891597	−	0.452831i	$-0.149586\pi$
$524$	−6.68942			−0.292228
$525$	3.11276	+	15.3720i	0.135852	+	0.670891i
$526$	22.8968			0.998349
$527$	18.0576	−	31.2767i	0.786602	−	1.36243i
$528$	23.1471	+	40.0919i	1.00735	+	1.74478i
$529$	−24.4230	−	42.3018i	−1.06187	−	1.83921i
$530$	12.1158	−	20.9851i	0.526275	−	0.911534i
$531$	29.0067			1.25878
$532$	9.76350	−	8.62203i	0.423302	−	0.373812i
$533$	−3.49396			−0.151340
$534$	19.9148	−	34.4935i	0.861800	−	1.49268i
$535$	−11.0144	−	19.0774i	−0.476193	−	0.824790i
$536$	12.3265	+	21.3502i	0.532424	+	0.922186i
$537$	23.6879	−	41.0287i	1.02221	−	1.77052i
$538$	−13.3222			−0.574360
$539$	7.84937	−	3.31484i	0.338096	−	0.142780i
$540$	−8.16520			−0.351374
$541$	7.87557	−	13.6409i	0.338597	−	0.586468i	−0.645572	−	0.763699i	$-0.723381\pi$
$541$	7.87557	−	13.6409i	0.338597	−	0.586468i	0.984169	+	0.177232i	$0.0567143\pi$
$542$	−4.94599	−	8.56670i	−0.212448	−	0.367971i
$543$	9.41917	+	16.3145i	0.404215	+	0.700121i
$544$	−39.8855	+	69.0837i	−1.71008	+	2.96194i
$545$	−11.9977			−0.513925
$546$	47.8051	−	42.2161i	2.04587	−	1.80668i
$547$	−11.1033			−0.474741			−0.237371	−	0.971419i	$-0.576286\pi$
$547$	−11.1033			−0.474741			−0.237371	+	0.971419i	$0.576286\pi$
$548$	−18.9930	+	32.8968i	−0.811341	+	1.40528i
$549$	−0.242879	−	0.420679i	−0.0103658	−	0.0179541i
$550$	−3.91202	−	6.77581i	−0.166809	−	0.288921i
$551$	−3.27896	+	5.67933i	−0.139689	+	0.241948i
$552$	203.553			8.66378
$553$	−7.05453	−	34.8380i	−0.299989	−	1.48146i
$554$	−51.5198			−2.18887
$555$	0.710591	−	1.23078i	0.0301629	−	0.0522437i
$556$	11.6864	+	20.2414i	0.495613	+	0.858427i
$557$	10.9810	+	19.0196i	0.465278	+	0.805885i	0.999214	−	0.0396397i	$-0.0126210\pi$
$557$	10.9810	+	19.0196i	0.465278	+	0.805885i	−0.533936	+	0.845525i	$0.679288\pi$
$558$	46.2170	−	80.0502i	1.95652	−	3.38880i
$559$	23.6606			1.00074
$560$	−61.5625	−	20.6615i	−2.60149	−	0.873106i
$561$	−11.0340			−0.465855
$562$	1.65389	−	2.86462i	0.0697651	−	0.120837i
$563$	6.62512	+	11.4750i	0.279216	+	0.483616i	0.971190	−	0.238306i	$-0.0765922\pi$
$563$	6.62512	+	11.4750i	0.279216	+	0.483616i	−0.691974	+	0.721922i	$0.743259\pi$
$564$	−1.35103	−	2.34006i	−0.0568888	−	0.0985343i
$565$	−10.8124	+	18.7276i	−0.454881	+	0.787876i
$566$	−20.0143			−0.841264
$567$	−19.5140	−	6.54926i	−0.819513	−	0.275043i
$568$	71.4109			2.99633
$569$	−15.6895	+	27.1750i	−0.657738	+	1.13924i	0.323462	+	0.946241i	$0.395153\pi$
$569$	−15.6895	+	27.1750i	−0.657738	+	1.13924i	−0.981200	+	0.192995i	$0.938180\pi$
$570$	−5.04416	−	8.73674i	−0.211276	−	0.365942i
$571$	−0.789021	−	1.36663i	−0.0330195	−	0.0571915i	0.849043	−	0.528323i	$-0.177179\pi$
$571$	−0.789021	−	1.36663i	−0.0330195	−	0.0571915i	−0.882063	+	0.471132i	$0.843846\pi$
$572$	−11.6548	+	20.1867i	−0.487310	+	0.844046i
$573$	−19.8801			−0.830504
$574$	−1.43619	−	7.09245i	−0.0599453	−	0.296033i
$575$	−19.9198			−0.830714
$576$	−51.3810	+	88.9945i	−2.14088	+	3.70811i
$577$	−8.32726	−	14.4232i	−0.346668	−	0.600447i	0.638987	−	0.769217i	$-0.279354\pi$
$577$	−8.32726	−	14.4232i	−0.346668	−	0.600447i	−0.985655	+	0.168770i	$0.946020\pi$
$578$	5.58745	+	9.67775i	0.232407	+	0.402541i
$579$	7.65558	−	13.2599i	0.318155	−	0.551061i
$580$	65.1360			2.70462
$581$	21.1365	−	18.6654i	0.876891	−	0.774372i
$582$	25.3366			1.05024
$583$	3.31233	−	5.73712i	0.137183	−	0.237607i
$584$	28.3522	+	49.1075i	1.17322	+	2.03208i
$585$	−9.56327	−	16.5641i	−0.395393	−	0.684840i
$586$	−11.1165	+	19.2543i	−0.459217	+	0.795387i
$587$	23.2574			0.959936			0.479968	−	0.877286i	$-0.340648\pi$
$587$	23.2574			0.959936			0.479968	+	0.877286i	$0.340648\pi$
$588$	77.1812	+	58.3830i	3.18290	+	2.40767i
$589$	9.02734			0.371965
$590$	19.2024	−	33.2595i	0.790549	−	1.36927i
$591$	−4.65917	−	8.06991i	−0.191653	−	0.331952i
$592$	−2.60920	−	4.51927i	−0.107238	−	0.185741i
$593$	−0.980516	+	1.69830i	−0.0402650	+	0.0697410i	−0.885456	−	0.464724i	$-0.846154\pi$
$593$	−0.980516	+	1.69830i	−0.0402650	+	0.0697410i	0.845191	+	0.534465i	$0.179487\pi$
$594$	−3.04687			−0.125015
$595$	11.6014	−	10.2450i	0.475609	−	0.420005i
$596$	−4.11778			−0.168671
$597$	−14.1963	+	24.5888i	−0.581017	+	1.00635i
$598$	40.5007	+	70.1493i	1.65620	+	2.86862i
$599$	7.49406	+	12.9801i	0.306199	+	0.530352i	0.977528	−	0.210808i	$-0.0676093\pi$
$599$	7.49406	+	12.9801i	0.306199	+	0.530352i	−0.671329	+	0.741160i	$0.734276\pi$
$600$	28.2183	−	48.8755i	1.15201	−	1.99533i
$601$	−2.56199			−0.104506			−0.0522530	−	0.998634i	$-0.516640\pi$
$601$	−2.56199			−0.104506			−0.0522530	+	0.998634i	$0.516640\pi$
$602$	9.72566	+	48.0291i	0.396388	+	1.95752i
$603$	−8.70807			−0.354620
$604$	−29.9803	+	51.9274i	−1.21988	+	2.11289i
$605$	−7.74725	−	13.4186i	−0.314970	−	0.545545i
$606$	−61.1868	−	105.979i	−2.48554	−	4.30509i
$607$	3.54694	−	6.14349i	0.143966	−	0.249356i	−0.785021	−	0.619470i	$-0.787348\pi$
$607$	3.54694	−	6.14349i	0.143966	−	0.249356i	0.928987	+	0.370113i	$0.120681\pi$
$608$	−19.9395			−0.808654
$609$	−46.1911	−	15.5026i	−1.87176	−	0.628196i
$610$	−0.643141			−0.0260400
$611$	0.341442	−	0.591394i	0.0138133	−	0.0239253i
$612$	−33.1170	−	57.3603i	−1.33867	−	2.31865i
$613$	0.490667	+	0.849860i	0.0198179	+	0.0343255i	0.875764	−	0.482739i	$-0.160358\pi$
$613$	0.490667	+	0.849860i	0.0198179	+	0.0343255i	−0.855946	+	0.517065i	$0.827025\pi$
$614$	10.4880	−	18.1658i	0.423262	−	0.733112i
$615$	−4.10620			−0.165578
$616$	−29.0667	−	9.75531i	−1.17113	−	0.393053i
$617$	25.6319			1.03190			0.515950	−	0.856619i	$-0.327439\pi$
$617$	25.6319			1.03190			0.515950	+	0.856619i	$0.327439\pi$
$618$	−20.2038	+	34.9940i	−0.812715	+	1.40766i
$619$	−7.59848	−	13.1610i	−0.305409	−	0.528983i	0.671944	−	0.740602i	$-0.265460\pi$
$619$	−7.59848	−	13.1610i	−0.305409	−	0.528983i	−0.977352	+	0.211619i	$0.932126\pi$
$620$	−44.8316	−	77.6506i	−1.80048	−	3.11852i
$621$	−3.87864	+	6.71800i	−0.155644	+	0.269584i
$622$	−41.0477			−1.64586
$623$	3.03142	+	14.9703i	0.121451	+	0.599774i
$624$	−132.883			−5.31960
$625$	3.86332	−	6.69147i	0.154533	−	0.267659i
$626$	−11.2561	−	19.4962i	−0.449886	−	0.779225i
$627$	−1.37902	−	2.38854i	−0.0550729	−	0.0953891i
$628$	7.85784	−	13.6102i	0.313562	−	0.543105i
$629$	1.24378			0.0495928
$630$	29.6927	−	26.2213i	1.18299	−	1.04468i
$631$	−31.5571			−1.25627			−0.628134	−	0.778105i	$-0.716181\pi$
$631$	−31.5571			−1.25627			−0.628134	+	0.778105i	$0.716181\pi$
$632$	−63.9517	+	110.768i	−2.54386	+	4.40610i
$633$	−4.54125	−	7.86567i	−0.180498	−	0.312632i
$634$	7.11780	+	12.3284i	0.282684	+	0.489623i
$635$	−9.67859	+	16.7638i	−0.384083	+	0.665252i
$636$	75.2417			2.98353
$637$	−3.02527	+	24.2699i	−0.119866	+	0.961608i
$638$	24.3057			0.962273
$639$	−12.6120	+	21.8447i	−0.498925	+	0.864163i
$640$	31.8934	+	55.2411i	1.26070	+	2.18359i
$641$	−0.914988	−	1.58481i	−0.0361398	−	0.0625960i	0.847390	−	0.530971i	$-0.178173\pi$
$641$	−0.914988	−	1.58481i	−0.0361398	−	0.0625960i	−0.883530	+	0.468375i	$0.844840\pi$
$642$	46.6812	−	80.8542i	1.84236	−	3.19106i
$643$	1.13071			0.0445908			0.0222954	−	0.999751i	$-0.492903\pi$
$643$	1.13071			0.0445908			0.0222954	+	0.999751i	$0.492903\pi$
$644$	−92.1303	+	81.3591i	−3.63044	+	3.20600i
$645$	27.8066			1.09489
$646$	4.41452	−	7.64617i	0.173687	−	0.300834i
$647$	9.50582	+	16.4646i	0.373712	+	0.647289i	0.990133	−	0.140128i	$-0.0447513\pi$
$647$	9.50582	+	16.4646i	0.373712	+	0.647289i	−0.616421	+	0.787417i	$0.711418\pi$
$648$	37.0337	+	64.1442i	1.45482	+	2.51982i
$649$	5.24975	−	9.09283i	0.206071	−	0.356925i
$650$	22.4582			0.880885
$651$	13.3112	+	65.7359i	0.521707	+	2.57639i
$652$	81.3144			3.18452
$653$	−0.996447	+	1.72590i	−0.0389940	+	0.0675396i	−0.884864	−	0.465850i	$-0.845749\pi$
$653$	−0.996447	+	1.72590i	−0.0389940	+	0.0675396i	0.845870	+	0.533390i	$0.179082\pi$
$654$	−25.4244	−	44.0364i	−0.994173	−	1.72196i
$655$	−0.993415	−	1.72065i	−0.0388159	−	0.0672312i
$656$	−7.53874	+	13.0575i	−0.294338	+	0.509809i
$657$	−20.0294			−0.781422
$658$	1.34083	+	0.450007i	0.0522711	+	0.0175431i
$659$	−35.2999			−1.37509			−0.687544	−	0.726143i	$-0.741311\pi$
$659$	−35.2999			−1.37509			−0.687544	+	0.726143i	$0.741311\pi$
$660$	−13.6970	+	23.7239i	−0.533156	+	0.923453i
$661$	22.7259	+	39.3624i	0.883934	+	1.53102i	0.846930	+	0.531704i	$0.178448\pi$
$661$	22.7259	+	39.3624i	0.883934	+	1.53102i	0.0370040	+	0.999315i	$0.488219\pi$
$662$	1.59079	+	2.75533i	0.0618279	+	0.107089i
$663$	15.8361	−	27.4289i	0.615022	−	1.06525i
$664$	−101.468			−3.93770
$665$	3.66769	+	1.23094i	0.142227	+	0.0477338i
$666$	3.18336			0.123353
$667$	30.9409	−	53.5913i	1.19804	−	2.07506i
$668$	−12.6193	−	21.8572i	−0.488254	−	0.845680i
$669$	−10.4286	−	18.0629i	−0.403193	−	0.698351i
$670$	−5.76472	+	9.98479i	−0.222711	+	0.385746i
$671$	−0.175829			−0.00678779
$672$	−29.4017	−	145.197i	−1.13419	−	5.60109i
$673$	37.3426			1.43945			0.719726	−	0.694258i	$-0.244267\pi$
$673$	37.3426			1.43945			0.719726	+	0.694258i	$0.244267\pi$
$674$	−31.1584	+	53.9680i	−1.20018	+	2.07877i
$675$	1.07538	+	1.86261i	0.0413914	+	0.0716921i
$676$	2.17107	+	3.76041i	0.0835028	+	0.144631i
$677$	1.44862	−	2.50909i	0.0556751	−	0.0964322i	−0.836845	−	0.547441i	$-0.815602\pi$
$677$	1.44862	−	2.50909i	0.0556751	−	0.0964322i	0.892520	+	0.451008i	$0.148936\pi$
$678$	−91.6504			−3.51981
$679$	−7.28297	+	6.43150i	−0.279495	+	0.246818i
$680$	−55.6932			−2.13574
$681$	−17.9510	+	31.0921i	−0.687885	+	1.19145i
$682$	−16.7291	−	28.9756i	−0.640589	−	1.10953i
$683$	10.3744	+	17.9690i	0.396965	+	0.687563i	0.993350	−	0.115136i	$-0.0367302\pi$
$683$	10.3744	+	17.9690i	0.396965	+	0.687563i	−0.596385	+	0.802698i	$0.703397\pi$
$684$	8.27790	−	14.3378i	0.316514	−	0.548218i
$685$	−11.2823			−0.431073
$686$	−50.5094	+	3.83505i	−1.92846	+	0.146423i
$687$	63.4521			2.42085
$688$	51.0513	−	88.4234i	1.94631	−	3.37111i
$689$	9.50777	+	16.4679i	0.362217	+	0.627379i
$690$	47.5976	+	82.4415i	1.81201	+	3.13849i
$691$	−4.21742	+	7.30478i	−0.160438	+	0.277887i	−0.935026	−	0.354579i	$-0.884624\pi$
$691$	−4.21742	+	7.30478i	−0.160438	+	0.277887i	0.774588	+	0.632466i	$0.217957\pi$
$692$	45.7552			1.73935
$693$	8.11771	−	7.16865i	0.308366	−	0.272315i
$694$	52.6972			2.00036
$695$	−3.47098	+	6.01192i	−0.131662	+	0.228045i
$696$	87.6614	+	151.834i	3.32280	+	5.75525i
$697$	−1.79682	−	3.11219i	−0.0680595	−	0.117882i
$698$	−28.6720	+	49.6614i	−1.08525	+	1.87971i
$699$	−20.3119			−0.768268
$700$	6.76339	+	33.4003i	0.255632	+	1.26241i
$701$	−0.932485			−0.0352195			−0.0176097	−	0.999845i	$-0.505606\pi$
$701$	−0.932485			−0.0352195			−0.0176097	+	0.999845i	$0.505606\pi$
$702$	4.37290	−	7.57409i	0.165045	−	0.285866i
$703$	0.155448	+	0.269243i	0.00586281	+	0.0101547i
$704$	18.5983	+	32.2132i	0.700949	+	1.21408i
$705$	0.401272	−	0.695024i	0.0151128	−	0.0261761i
$706$	37.3564			1.40592
$707$	44.4899	+	14.9316i	1.67321	+	0.561561i
$708$	119.251			4.48174
$709$	−8.87711	+	15.3756i	−0.333387	+	0.577443i	−0.983174	−	0.182673i	$-0.941525\pi$
$709$	−8.87711	+	15.3756i	−0.333387	+	0.577443i	0.649787	+	0.760117i	$0.274858\pi$
$710$	16.6983	+	28.9223i	0.626676	+	1.08543i
$711$	−22.5893	−	39.1259i	−0.847166	−	1.46733i
$712$	27.4808	−	47.5982i	1.02989	−	1.78382i
$713$	−85.1837			−3.19016
$714$	62.1878	+	20.8713i	2.32732	+	0.781090i
$715$	−6.92319			−0.258913
$716$	51.4690	−	89.1469i	1.92349	−	3.33158i
$717$	25.3462	+	43.9008i	0.946570	+	1.63951i
$718$	−43.5458	−	75.4235i	−1.62511	−	2.81478i
$719$	22.6781	−	39.2796i	0.845751	−	1.46488i	−0.0392168	−	0.999231i	$-0.512486\pi$
$719$	22.6781	−	39.2796i	0.845751	−	1.46488i	0.884968	−	0.465653i	$-0.154180\pi$
$720$	−82.5367			−3.07596
$721$	−3.07540	−	15.1875i	−0.114534	−	0.565613i
$722$	−49.7601			−1.85188
$723$	−30.9219	+	53.5583i	−1.15000	+	1.99185i
$724$	20.4659	+	35.4480i	0.760610	+	1.31741i
$725$	−8.57860	−	14.8586i	−0.318601	−	0.551833i
$726$	32.8345	−	56.8710i	1.21860	−	2.11068i
$727$	−0.626513			−0.0232361			−0.0116180	−	0.999933i	$-0.503698\pi$
$727$	−0.626513			−0.0232361			−0.0116180	+	0.999933i	$0.503698\pi$
$728$	65.9671	−	58.2547i	2.44490	−	2.15906i
$729$	−33.0880			−1.22548
$730$	−13.2594	+	22.9660i	−0.490754	+	0.850010i
$731$	12.1678	+	21.0753i	0.450043	+	0.779498i
$732$	−0.998515	−	1.72948i	−0.0369062	−	0.0639234i
$733$	0.705228	−	1.22149i	0.0260482	−	0.0451168i	−0.852707	−	0.522389i	$-0.825041\pi$
$733$	0.705228	−	1.22149i	0.0260482	−	0.0451168i	0.878756	+	0.477272i	$0.158374\pi$
$734$	90.6775			3.34697
$735$	−3.55539	+	28.5227i	−0.131142	+	1.05207i
$736$	188.153			6.93541
$737$	−1.57602	+	2.72975i	−0.0580534	+	0.100552i
$738$	−4.59882	−	7.96539i	−0.169285	−	0.293210i
$739$	13.1464	+	22.7703i	0.483599	+	0.837619i	0.999823	−	0.0188353i	$-0.00599582\pi$
$739$	13.1464	+	22.7703i	0.483599	+	0.837619i	−0.516223	+	0.856454i	$0.672662\pi$
$740$	1.54397	−	2.67423i	0.0567574	−	0.0983066i
$741$	7.91675			0.290829
$742$	−29.5204	+	26.0691i	−1.08373	+	0.957028i
$743$	21.7068			0.796345			0.398173	−	0.917310i	$-0.369644\pi$
$743$	21.7068			0.796345			0.398173	+	0.917310i	$0.369644\pi$
$744$	120.671	−	209.008i	4.42400	−	7.66259i
$745$	−0.611513	−	1.05917i	−0.0224041	−	0.0388050i
$746$	−26.3639	−	45.6635i	−0.965249	−	1.67186i
$747$	17.9204	−	31.0391i	0.655674	−	1.13566i
$748$	−23.9746			−0.876597
$749$	7.10577	+	35.0911i	0.259639	+	1.28220i
$750$	82.5480			3.01423
$751$	−11.3638	+	19.6827i	−0.414671	+	0.718231i	−0.995394	−	0.0958703i	$-0.969437\pi$
$751$	−11.3638	+	19.6827i	−0.414671	+	0.718231i	0.580723	+	0.814101i	$0.302770\pi$
$752$	−1.47342	−	2.55204i	−0.0537302	−	0.0930634i
$753$	2.47500	+	4.28683i	0.0901940	+	0.156221i
$754$	−34.8838	+	60.4205i	−1.27039	+	2.20039i
$755$	−17.8089			−0.648134
$756$	12.5812	+	4.22249i	0.457575	+	0.153570i
$757$	−31.6788			−1.15139			−0.575693	−	0.817666i	$-0.695267\pi$
$757$	−31.6788			−1.15139			−0.575693	+	0.817666i	$0.695267\pi$
$758$	−20.5220	+	35.5451i	−0.745392	+	1.29106i
$759$	13.0127	+	22.5387i	0.472332	+	0.818103i
$760$	−6.96052	−	12.0560i	−0.252485	−	0.437316i
$761$	−10.9808	+	19.0193i	−0.398053	+	0.689448i	−0.993486	−	0.113957i	$-0.963647\pi$
$761$	−10.9808	+	19.0193i	−0.398053	+	0.689448i	0.595433	+	0.803405i	$0.296981\pi$
$762$	−82.0398			−2.97199
$763$	18.4865	+	6.20439i	0.669256	+	0.224614i
$764$	−43.1954			−1.56275
$765$	9.83611	−	17.0366i	0.355625	−	0.615961i
$766$	−22.9495	−	39.7496i	−0.829198	−	1.43621i
$767$	15.0690	+	26.1002i	0.544109	+	0.942424i
$768$	−58.0889	+	100.613i	−2.09610	+	3.63055i
$769$	−46.3364			−1.67093			−0.835466	−	0.549542i	$-0.814802\pi$
$769$	−46.3364			−1.67093			−0.835466	+	0.549542i	$0.814802\pi$
$770$	−2.84577	−	14.0535i	−0.102554	−	0.506453i
$771$	20.4785			0.737515
$772$	16.6340	−	28.8109i	0.598671	−	1.03693i
$773$	−20.3157	−	35.1878i	−0.730704	−	1.26562i	−0.956583	−	0.291461i	$-0.905859\pi$
$773$	−20.3157	−	35.1878i	−0.730704	−	1.26562i	0.225879	−	0.974155i	$-0.427475\pi$
$774$	31.1426	+	53.9405i	1.11940	+	1.93885i
$775$	−11.8089	+	20.4536i	−0.424188	+	0.734716i
$776$	34.9624			1.25508
$777$	−1.73138	+	1.52896i	−0.0621128	+	0.0548511i
$778$	−10.5908			−0.379698
$779$	0.449133	−	0.777920i	0.0160918	−	0.0278719i
$780$	−39.3162	−	68.0976i	−1.40774	−	2.43829i
$781$	4.56515	+	7.90708i	0.163354	+	0.282938i
$782$	−41.6562	+	72.1507i	−1.48962	+	2.58010i
$783$	−6.68144			−0.238775
$784$	84.1729	+	63.6718i	3.00618	+	2.27399i
$785$	4.66773			0.166599
$786$	4.21030	−	7.29246i	0.150177	−	0.260113i
$787$	5.65335	+	9.79190i	0.201520	+	0.349043i	0.949018	−	0.315220i	$-0.102078\pi$
$787$	5.65335	+	9.79190i	0.201520	+	0.349043i	−0.747498	+	0.664264i	$0.768745\pi$
$788$	−10.1234	−	17.5343i	−0.360632	−	0.624632i
$789$	−10.5584	+	18.2876i	−0.375887	+	0.651056i
$790$	−59.8163			−2.12817
$791$	26.3447	−	23.2647i	0.936711	−	0.827198i
$792$	−38.9697			−1.38473
$793$	0.252351	−	0.437085i	0.00896125	−	0.0155213i
$794$	−45.2851	−	78.4361i	−1.60711	−	2.78359i
$795$	11.1738	+	19.3536i	0.396294	+	0.686402i
$796$	−30.8457	+	53.4263i	−1.09330	+	1.89364i
$797$	34.0456			1.20596			0.602978	−	0.797758i	$-0.293981\pi$
$797$	34.0456			1.20596			0.602978	+	0.797758i	$0.293981\pi$
$798$	3.25417	+	16.0704i	0.115196	+	0.568885i
$799$	0.702366			0.0248479
$800$	26.0834	−	45.1778i	0.922187	−	1.59728i
$801$	9.70692	+	16.8129i	0.342977	+	0.594054i
$802$	−18.4997	−	32.0425i	−0.653248	−	1.13146i
$803$	−3.62500	+	6.27869i	−0.127924	+	0.221570i
$804$	−35.8003			−1.26258
$805$	−34.6090	−	11.6154i	−1.21981	−	0.409389i
$806$	96.0389			3.38282
$807$	6.14322	−	10.6404i	0.216252	−	0.374559i
$808$	−84.4328	−	146.242i	−2.97033	−	5.14477i
$809$	−14.7187	−	25.4936i	−0.517483	−	0.896307i	−0.999794	−	0.0203070i	$-0.993536\pi$
$809$	−14.7187	−	25.4936i	−0.517483	−	0.896307i	0.482311	−	0.876000i	$-0.339798\pi$
$810$	−17.3195	+	29.9982i	−0.608545	+	1.05403i
$811$	−4.02613			−0.141377			−0.0706883	−	0.997498i	$-0.522520\pi$
$811$	−4.02613			−0.141377			−0.0706883	+	0.997498i	$0.522520\pi$
$812$	−100.364	−	33.6839i	−3.52208	−	1.18207i
$813$	9.12292			0.319955
$814$	0.576137	−	0.997898i	0.0201936	−	0.0349763i
$815$	12.0756	+	20.9156i	0.422991	+	0.732642i
$816$	−68.3373	−	118.364i	−2.39229	−	4.14356i
$817$	−3.04146	+	5.26797i	−0.106407	+	0.184303i
$818$	−72.5609			−2.53703
$819$	6.16961	+	30.4680i	0.215584	+	1.06464i
$820$	−8.92193			−0.311567
$821$	2.47325	−	4.28380i	0.0863171	−	0.149506i	−0.819635	−	0.572887i	$-0.805824\pi$
$821$	2.47325	−	4.28380i	0.0863171	−	0.149506i	0.905952	+	0.423381i	$0.139157\pi$
$822$	−23.9083	−	41.4104i	−0.833898	−	1.44435i
$823$	3.86971	+	6.70254i	0.134890	+	0.233636i	0.925555	−	0.378612i	$-0.123599\pi$
$823$	3.86971	+	6.70254i	0.134890	+	0.233636i	−0.790666	+	0.612248i	$0.790265\pi$
$824$	−27.8795	+	48.2888i	−0.971230	+	1.68222i
$825$	7.21575			0.251220
$826$	−46.7872	+	41.3172i	−1.62794	+	1.43761i
$827$	37.0887			1.28970			0.644851	−	0.764309i	$-0.276920\pi$
$827$	37.0887			1.28970			0.644851	+	0.764309i	$0.276920\pi$
$828$	−78.1119	+	135.294i	−2.71458	+	4.70178i
$829$	−6.56188	−	11.3655i	−0.227903	−	0.394740i	0.729283	−	0.684212i	$-0.239854\pi$
$829$	−6.56188	−	11.3655i	−0.227903	−	0.394740i	−0.957187	+	0.289472i	$0.906520\pi$
$830$	−23.7266	−	41.0956i	−0.823562	−	1.42645i
$831$	23.7572	−	41.1487i	0.824128	−	1.42743i
$832$	−106.770			−3.70157
$833$	−23.1738	+	9.78645i	−0.802924	+	0.339080i
$834$	−29.4215			−1.01878
$835$	3.74806	−	6.49183i	0.129707	−	0.224659i
$836$	−2.99633	−	5.18980i	−0.103630	−	0.179493i
$837$	4.59868	+	7.96515i	0.158954	+	0.275316i
$838$	32.8909	−	56.9687i	1.13620	−	1.96795i
$839$	6.55476			0.226295			0.113148	−	0.993578i	$-0.463907\pi$
$839$	6.55476			0.226295			0.113148	+	0.993578i	$0.463907\pi$
$840$	77.5264	−	68.4626i	2.67492	−	2.36219i
$841$	24.2997			0.837919
$842$	−25.0397	+	43.3701i	−0.862926	+	1.49463i
$843$	1.52531	+	2.64191i	0.0525344	+	0.0909922i
$844$	−9.86720	−	17.0905i	−0.339643	−	0.588279i
$845$	−0.644832	+	1.11688i	−0.0221829	+	0.0384219i
$846$	1.79765			0.0618045
$847$	4.99803	+	24.6822i	0.171734	+	0.848092i
$848$	82.0577			2.81787
$849$	9.22915	−	15.9854i	0.316744	−	0.548616i
$850$	11.5495	+	20.0043i	0.396144	+	0.686142i
$851$	−1.46683	−	2.54063i	−0.0502824	−	0.0870916i
$852$	−51.8502	+	89.8072i	−1.77636	+	3.07674i
$853$	1.88559			0.0645612			0.0322806	−	0.999479i	$-0.489723\pi$
$853$	1.88559			0.0645612			0.0322806	+	0.999479i	$0.489723\pi$
$854$	0.990975	+	0.332589i	0.0339105	+	0.0113810i
$855$	4.91726			0.168167
$856$	64.4162	−	111.572i	2.20170	−	3.81346i
$857$	−27.4311	−	47.5120i	−0.937028	−	1.62298i	−0.770976	−	0.636864i	$-0.780231\pi$
$857$	−27.4311	−	47.5120i	−0.937028	−	1.62298i	−0.166052	−	0.986117i	$-0.553102\pi$
$858$	−14.6710	−	25.4109i	−0.500859	−	0.867513i
$859$	9.91177	−	17.1677i	0.338185	−	0.585754i	−0.645906	−	0.763417i	$-0.723520\pi$
$859$	9.91177	−	17.1677i	0.338185	−	0.585754i	0.984091	+	0.177663i	$0.0568536\pi$
$860$	60.4181			2.06024
$861$	6.32698	+	2.12345i	0.215623	+	0.0723669i
$862$	−62.6268			−2.13308
$863$	0.449928	−	0.779298i	0.0153157	−	0.0265276i	−0.858266	−	0.513205i	$-0.828458\pi$
$863$	0.449928	−	0.779298i	0.0153157	−	0.0265276i	0.873582	+	0.486678i	$0.161791\pi$
$864$	−10.1575	−	17.5934i	−0.345566	−	0.598538i
$865$	6.79489	+	11.7691i	0.231033	+	0.400162i
$866$	−30.4244	+	52.6966i	−1.03386	+	1.79070i
$867$	−10.3061			−0.350014
$868$	28.9225	+	142.831i	0.981694	+	4.84799i
$869$	−16.3532			−0.554745
$870$	−40.9965	+	71.0079i	−1.38991	+	2.40739i
$871$	−4.52384	−	7.83551i	−0.153284	−	0.265496i
$872$	−35.0836	−	60.7665i	−1.18808	−	2.05781i
$873$	−6.17480	+	10.6951i	−0.208985	+	0.361973i
$874$	−20.8247			−0.704407
$875$	−23.7283	+	20.9542i	−0.802162	+	0.708380i
$876$	−82.3442			−2.78215
$877$	28.7253	−	49.7536i	0.969983	−	1.68006i	0.274398	−	0.961616i	$-0.411521\pi$
$877$	28.7253	−	49.7536i	0.969983	−	1.68006i	0.695585	−	0.718444i	$-0.255145\pi$
$878$	42.5465	+	73.6927i	1.43587	+	2.48701i
$879$	−10.2522	−	17.7574i	−0.345799	−	0.598941i
$880$	−14.9378	+	25.8730i	−0.503554	+	0.872180i
$881$	−21.2587			−0.716225			−0.358112	−	0.933678i	$-0.616580\pi$
$881$	−21.2587			−0.716225			−0.358112	+	0.933678i	$0.616580\pi$
$882$	−59.3115	+	25.0476i	−1.99712	+	0.843397i
$883$	−20.0439			−0.674531			−0.337266	−	0.941410i	$-0.609502\pi$
$883$	−20.0439			−0.674531			−0.337266	+	0.941410i	$0.609502\pi$
$884$	34.4085	−	59.5973i	1.15728	−	2.00447i
$885$	17.7095	+	30.6737i	0.595298	+	1.03109i
$886$	42.5523	+	73.7028i	1.42957	+	2.47609i
$887$	25.3648	−	43.9331i	0.851665	−	1.47513i	−0.0280393	−	0.999607i	$-0.508926\pi$
$887$	25.3648	−	43.9331i	0.851665	−	1.47513i	0.879705	−	0.475521i	$-0.157740\pi$
$888$	8.31161			0.278919
$889$	23.5822	−	20.8252i	0.790922	−	0.698454i
$890$	25.7038			0.861595
$891$	−4.73498	+	8.20123i	−0.158628	+	0.274751i
$892$	−22.6592	−	39.2469i	−0.758687	−	1.31408i
$893$	0.0877816	+	0.152042i	0.00293750	+	0.00508790i
$894$	2.59172	−	4.48899i	0.0866801	−	0.150134i
$895$	30.5737			1.02197
$896$	−20.5756	−	101.610i	−0.687383	−	3.39457i
$897$	−74.7040			−2.49429
$898$	−18.9656	+	32.8494i	−0.632890	+	1.09620i
$899$	−36.6849	−	63.5402i	−1.22351	−	2.11918i
$900$	21.6571	+	37.5112i	0.721903	+	1.25037i
$901$	−9.77903	+	16.9378i	−0.325787	+	0.564279i
$902$	−3.32925			−0.110852
$903$	−42.8454	−	14.3797i	−1.42581	−	0.478526i
$904$	−126.470			−4.20633
$905$	−6.07860	+	10.5284i	−0.202060	+	0.349977i
$906$	−37.7390	−	65.3659i	−1.25380	−	2.17164i
$907$	−1.79752	−	3.11340i	−0.0596858	−	0.103379i	0.834639	−	0.550798i	$-0.185677\pi$
$907$	−1.79752	−	3.11340i	−0.0596858	−	0.103379i	−0.894324	+	0.447419i	$0.852343\pi$
$908$	−39.0039	+	67.5568i	−1.29439	+	2.24195i
$909$	59.6475			1.97838
$910$	39.0193	+	13.0956i	1.29348	+	0.434114i
$911$	39.2388			1.30004			0.650020	−	0.759917i	$-0.274760\pi$
$911$	39.2388			1.30004			0.650020	+	0.759917i	$0.274760\pi$
$912$	17.0816	−	29.5861i	0.565627	−	0.979695i
$913$	−6.48662	−	11.2352i	−0.214676	−	0.371829i
$914$	−29.1336	−	50.4609i	−0.963654	−	1.66910i
$915$	0.296570	−	0.513675i	0.00980431	−	0.0169816i
$916$	137.868			4.55530
$917$	0.640888	+	3.16496i	0.0211640	+	0.104516i
$918$	8.99532			0.296890
$919$	3.25731	−	5.64182i	0.107449	−	0.186106i	−0.807287	−	0.590159i	$-0.799065\pi$
$919$	3.25731	−	5.64182i	0.107449	−	0.186106i	0.914736	+	0.404052i	$0.132399\pi$
$920$	65.6808	+	113.762i	2.16543	+	3.75064i
$921$	9.67263	+	16.7535i	0.318724	+	0.552046i
$922$	36.8178	−	63.7703i	1.21253	−	2.10016i
$923$	−26.2078			−0.862640
$924$	33.3732	−	29.4715i	1.09790	−	0.969541i
$925$	−0.813380			−0.0267438
$926$	−46.6968	+	80.8812i	−1.53455	+	2.65792i
$927$	−9.84775	−	17.0568i	−0.323443	−	0.560219i
$928$	81.0293	+	140.347i	2.65992	+	4.60711i
$929$	1.54554	−	2.67696i	0.0507077	−	0.0878283i	−0.839557	−	0.543271i	$-0.817186\pi$
$929$	1.54554	−	2.67696i	0.0507077	−	0.0878283i	0.890265	+	0.455443i	$0.150519\pi$
$930$	112.868			3.70108
$931$	−5.01474	−	3.79335i	−0.164351	−	0.124322i
$932$	−44.1337			−1.44565
$933$	18.9282	−	32.7846i	0.619682	−	1.07332i
$934$	13.5613	+	23.4889i	0.443740	+	0.768581i
$935$	−3.56036	−	6.16672i	−0.116436	−	0.201673i
$936$	55.9296	−	96.8730i	1.82812	−	3.16639i
$937$	−27.4063			−0.895326			−0.447663	−	0.894202i	$-0.647744\pi$
$937$	−27.4063			−0.895326			−0.447663	+	0.894202i	$0.647744\pi$
$938$	14.0459	−	12.4038i	0.458616	−	0.404998i
$939$	20.7621			0.677544
$940$	0.871882	−	1.51014i	0.0284376	−	0.0492555i
$941$	9.02161	+	15.6259i	0.294096	+	0.509389i	0.974774	−	0.223193i	$-0.0716481\pi$
$941$	9.02161	+	15.6259i	0.294096	+	0.509389i	−0.680678	+	0.732583i	$0.738315\pi$
$942$	9.89142	+	17.1324i	0.322280	+	0.558205i
$943$	−4.23810	+	7.34060i	−0.138012	+	0.239043i
$944$	130.054			4.23290
$945$	0.782278	+	3.86320i	0.0254475	+	0.125670i
$946$	22.5452			0.733008
$947$	−4.71787	+	8.17160i	−0.153310	+	0.265541i	−0.932442	−	0.361318i	$-0.882327\pi$
$947$	−4.71787	+	8.17160i	−0.153310	+	0.265541i	0.779132	+	0.626860i	$0.215660\pi$
$948$	−92.8684	−	160.853i	−3.01623	−	5.22426i
$949$	−10.4053	−	18.0225i	−0.337769	−	0.585034i
$950$	−2.88690	+	5.00026i	−0.0936635	+	0.162230i
$951$	−13.1289			−0.425732
$952$	85.8140	+	28.8007i	2.78125	+	0.933436i
$953$	6.07115			0.196664			0.0983320	−	0.995154i	$-0.468649\pi$
$953$	6.07115			0.196664			0.0983320	+	0.995154i	$0.468649\pi$
$954$	−25.0286	+	43.3509i	−0.810332	+	1.40354i
$955$	−6.41476	−	11.1107i	−0.207577	−	0.359533i
$956$	55.0720	+	95.3875i	1.78116	+	3.08505i
$957$	−11.2080	+	19.4129i	−0.362304	+	0.627530i
$958$	−5.24983			−0.169614
$959$	17.3841	+	5.83441i	0.561362	+	0.188403i
$960$	−125.479			−4.04981
$961$	−34.9988	+	60.6197i	−1.12899	+	1.95547i
$962$	1.65375	+	2.86439i	0.0533192	+	0.0923515i
$963$	22.7534	+	39.4101i	0.733219	+	1.26997i
$964$	−67.1869	+	116.371i	−2.16394	+	3.74806i
$965$	9.88096			0.318079
$966$	−30.7070	−	151.643i	−0.987980	−	4.87903i
$967$	−39.5315			−1.27125			−0.635624	−	0.771999i	$-0.719257\pi$
$967$	−39.5315			−1.27125			−0.635624	+	0.771999i	$0.719257\pi$
$968$	45.3089	−	78.4773i	1.45628	−	2.52235i
$969$	4.07131	+	7.05171i	0.130789	+	0.226534i
$970$	8.17541	+	14.1602i	0.262497	+	0.454658i
$971$	−19.4266	+	33.6479i	−0.623431	+	1.07981i	0.365411	+	0.930846i	$0.380928\pi$
$971$	−19.4266	+	33.6479i	−0.623431	+	1.07981i	−0.988842	+	0.148967i	$0.952405\pi$
$972$	−122.606			−3.93259
$973$	8.45717	−	7.46842i	0.271124	−	0.239427i
$974$	56.8514			1.82164
$975$	−10.3561	+	17.9373i	−0.331661	+	0.574454i
$976$	−1.08897	−	1.88615i	−0.0348571	−	0.0603742i
$977$	−20.7163	−	35.8816i	−0.662772	−	1.14795i	−0.979884	−	0.199567i	$-0.936046\pi$
$977$	−20.7163	−	35.8816i	−0.662772	−	1.14795i	0.317112	−	0.948388i	$-0.397287\pi$
$978$	−51.1791	+	88.6448i	−1.63653	+	2.83455i
$979$	7.02718			0.224590
$980$	−7.72513	+	61.9739i	−0.246770	+	1.97968i
$981$	24.7848			0.791317
$982$	35.1085	−	60.8096i	1.12036	−	1.94051i
$983$	−25.0484	−	43.3852i	−0.798921	−	1.38377i	−0.920319	−	0.391168i	$-0.872071\pi$
$983$	−25.0484	−	43.3852i	−0.798921	−	1.38377i	0.121398	−	0.992604i	$-0.461262\pi$
$984$	−12.0073	−	20.7973i	−0.382779	−	0.662993i
$985$	3.00676	−	5.20787i	0.0958035	−	0.165937i
$986$	−71.7581			−2.28524
$987$	−0.977713	+	0.863406i	−0.0311210	+	0.0274825i
$988$	17.2015			0.547252
$989$	28.6998	−	49.7096i	0.912601	−	1.58067i
$990$	−9.11245	−	15.7832i	−0.289613	−	0.501624i
$991$	16.7744	+	29.0542i	0.532857	+	0.922936i	0.999264	+	0.0383652i	$0.0122150\pi$
$991$	16.7744	+	29.0542i	0.532857	+	0.922936i	−0.466407	+	0.884570i	$0.654452\pi$
$992$	111.541	−	193.195i	3.54144	−	6.13395i
$993$	−2.93423			−0.0931150
$994$	−10.7727	−	53.1997i	−0.341689	−	1.68739i
$995$	−18.3230			−0.580879
$996$	73.6738	−	127.607i	2.33445	−	4.04338i
$997$	14.2715	+	24.7189i	0.451982	+	0.782855i	0.998509	−	0.0545860i	$-0.0173839\pi$
$997$	14.2715	+	24.7189i	0.451982	+	0.782855i	−0.546527	+	0.837441i	$0.684051\pi$
$998$	−48.8244	−	84.5663i	−1.54551	−	2.67690i
$999$	−0.158375	+	0.274314i	−0.00501077	+	0.00867891i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	287.2.e.d.247.1	yes	34
7.2	even	3		2009.2.a.s.1.17		17
7.4	even	3	inner	287.2.e.d.165.1	✓	34
7.5	odd	6		2009.2.a.r.1.17		17

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
287.2.e.d.165.1	✓	34	7.4	even	3	inner
287.2.e.d.247.1	yes	34	1.1	even	1	trivial
2009.2.a.r.1.17		17	7.5	odd	6
2009.2.a.s.1.17		17	7.2	even	3

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:	\( N \)	\(=\)	\( 287 = 7 \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	287.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.36755 + 2.36867i) q^{2} +(-1.26123 - 2.18452i) q^{3} +(-2.74039 - 4.74650i) q^{4} +(0.813928 - 1.40976i) q^{5} +6.89919 q^{6} +(-1.98316 + 1.75131i) q^{7} +9.52032 q^{8} +(-1.68141 + 2.91228i) q^{9} +O(q^{10})\)	\(q+(-1.36755 + 2.36867i) q^{2} +(-1.26123 - 2.18452i) q^{3} +(-2.74039 - 4.74650i) q^{4} +(0.813928 - 1.40976i) q^{5} +6.89919 q^{6} +(-1.98316 + 1.75131i) q^{7} +9.52032 q^{8} +(-1.68141 + 2.91228i) q^{9} +(2.22618 + 3.85585i) q^{10} +(0.608615 + 1.05415i) q^{11} +(-6.91254 + 11.9729i) q^{12} -3.49396 q^{13} +(-1.43619 - 7.09245i) q^{14} -4.10620 q^{15} +(-7.53874 + 13.0575i) q^{16} +(-1.79682 - 3.11219i) q^{17} +(-4.59882 - 7.96539i) q^{18} +(0.449133 - 0.777920i) q^{19} -8.92193 q^{20} +(6.32698 + 2.12345i) q^{21} -3.32925 q^{22} +(-4.23810 + 7.34060i) q^{23} +(-12.0073 - 20.7973i) q^{24} +(1.17504 + 2.03524i) q^{25} +(4.77817 - 8.27603i) q^{26} +0.915183 q^{27} +(13.7472 + 4.61381i) q^{28} -7.30066 q^{29} +(5.61544 - 9.72623i) q^{30} +(5.02488 + 8.70334i) q^{31} +(-11.0989 - 19.2239i) q^{32} +(1.53521 - 2.65906i) q^{33} +9.82898 q^{34} +(0.854777 + 4.22122i) q^{35} +18.4309 q^{36} +(-0.173053 + 0.299737i) q^{37} +(1.22842 + 2.12769i) q^{38} +(4.40669 + 7.63261i) q^{39} +(7.74885 - 13.4214i) q^{40} +1.00000 q^{41} +(-13.6822 + 12.0826i) q^{42} -6.77186 q^{43} +(3.33569 - 5.77759i) q^{44} +(2.73709 + 4.74077i) q^{45} +(-11.5916 - 20.0773i) q^{46} +(-0.0977234 + 0.169262i) q^{47} +38.0323 q^{48} +(0.865858 - 6.94624i) q^{49} -6.42773 q^{50} +(-4.53241 + 7.85037i) q^{51} +(9.57483 + 16.5841i) q^{52} +(-2.72120 - 4.71326i) q^{53} +(-1.25156 + 2.16777i) q^{54} +1.98147 q^{55} +(-18.8803 + 16.6730i) q^{56} -2.26584 q^{57} +(9.98403 - 17.2928i) q^{58} +(-4.31286 - 7.47010i) q^{59} +(11.2526 + 19.4901i) q^{60} +(-0.0722249 + 0.125097i) q^{61} -27.4871 q^{62} +(-1.76579 - 8.72018i) q^{63} +30.5583 q^{64} +(-2.84383 + 4.92566i) q^{65} +(4.19895 + 7.27280i) q^{66} +(1.29476 + 2.24259i) q^{67} +(-9.84800 + 17.0572i) q^{68} +21.3809 q^{69} +(-11.1676 - 3.74806i) q^{70} +7.50089 q^{71} +(-16.0075 + 27.7259i) q^{72} +(2.97807 + 5.15818i) q^{73} +(-0.473318 - 0.819811i) q^{74} +(2.96400 - 5.13380i) q^{75} -4.92320 q^{76} +(-3.05312 - 1.02468i) q^{77} -24.1055 q^{78} +(-6.71739 + 11.6349i) q^{79} +(12.2720 + 21.2557i) q^{80} +(3.88996 + 6.73761i) q^{81} +(-1.36755 + 2.36867i) q^{82} -10.6580 q^{83} +(-7.25947 - 35.8501i) q^{84} -5.84993 q^{85} +(9.26087 - 16.0403i) q^{86} +(9.20782 + 15.9484i) q^{87} +(5.79421 + 10.0359i) q^{88} +(2.88655 - 4.99965i) q^{89} -14.9724 q^{90} +(6.92909 - 6.11899i) q^{91} +46.4563 q^{92} +(12.6751 - 21.9538i) q^{93} +(-0.267284 - 0.462949i) q^{94} +(-0.731123 - 1.26634i) q^{95} +(-27.9966 + 48.4915i) q^{96} +3.67240 q^{97} +(15.2692 + 11.5503i) q^{98} -4.09332 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 34 q - 3 q^{2} - q^{3} - 25 q^{4} + q^{5} + 4 q^{6} - 2 q^{7} + 18 q^{8} - 26 q^{9}+O(q^{10}) \) 34 * q - 3 * q^2 - q^3 - 25 * q^4 + q^5 + 4 * q^6 - 2 * q^7 + 18 * q^8 - 26 * q^9	\( 34 q - 3 q^{2} - q^{3} - 25 q^{4} + q^{5} + 4 q^{6} - 2 q^{7} + 18 q^{8} - 26 q^{9} + 2 q^{10} - 15 q^{11} - 4 q^{12} - 10 q^{13} + 21 q^{14} + 48 q^{15} - 33 q^{16} - 4 q^{17} - 10 q^{18} - 5 q^{19} - 52 q^{20} + 12 q^{21} + 32 q^{22} - 12 q^{23} - 16 q^{24} - 24 q^{25} - 31 q^{26} - 22 q^{27} + 60 q^{28} + 28 q^{29} + 33 q^{30} + 3 q^{31} - 16 q^{32} - 4 q^{33} - 48 q^{34} + 45 q^{35} + 114 q^{36} - 24 q^{37} - 45 q^{39} - 36 q^{40} + 34 q^{41} + 65 q^{42} + 28 q^{43} + 9 q^{44} + 21 q^{45} - 44 q^{46} - 19 q^{47} - 120 q^{48} - 10 q^{49} - 8 q^{50} - 2 q^{51} + 25 q^{52} - 4 q^{53} - 68 q^{54} + 18 q^{55} + 25 q^{56} - 24 q^{57} + q^{58} + 27 q^{59} - 66 q^{60} + q^{61} - 46 q^{62} + 37 q^{63} + 150 q^{64} - 22 q^{65} + 16 q^{66} - 49 q^{67} - 45 q^{68} + 24 q^{69} + 73 q^{70} + 80 q^{71} + 23 q^{72} + 14 q^{73} - 33 q^{74} - 27 q^{75} - 18 q^{76} - 20 q^{77} - 24 q^{78} - 61 q^{79} + 82 q^{80} - 53 q^{81} - 3 q^{82} - 36 q^{83} + 188 q^{84} - 26 q^{85} + 4 q^{86} + 17 q^{87} - 74 q^{88} - 18 q^{89} - 40 q^{90} + 7 q^{91} + 56 q^{92} + 36 q^{93} + 5 q^{94} - 20 q^{95} - 148 q^{96} + 52 q^{97} + 142 q^{98} + 76 q^{99}+O(q^{100}) \) 34 * q - 3 * q^2 - q^3 - 25 * q^4 + q^5 + 4 * q^6 - 2 * q^7 + 18 * q^8 - 26 * q^9 + 2 * q^10 - 15 * q^11 - 4 * q^12 - 10 * q^13 + 21 * q^14 + 48 * q^15 - 33 * q^16 - 4 * q^17 - 10 * q^18 - 5 * q^19 - 52 * q^20 + 12 * q^21 + 32 * q^22 - 12 * q^23 - 16 * q^24 - 24 * q^25 - 31 * q^26 - 22 * q^27 + 60 * q^28 + 28 * q^29 + 33 * q^30 + 3 * q^31 - 16 * q^32 - 4 * q^33 - 48 * q^34 + 45 * q^35 + 114 * q^36 - 24 * q^37 - 45 * q^39 - 36 * q^40 + 34 * q^41 + 65 * q^42 + 28 * q^43 + 9 * q^44 + 21 * q^45 - 44 * q^46 - 19 * q^47 - 120 * q^48 - 10 * q^49 - 8 * q^50 - 2 * q^51 + 25 * q^52 - 4 * q^53 - 68 * q^54 + 18 * q^55 + 25 * q^56 - 24 * q^57 + q^58 + 27 * q^59 - 66 * q^60 + q^61 - 46 * q^62 + 37 * q^63 + 150 * q^64 - 22 * q^65 + 16 * q^66 - 49 * q^67 - 45 * q^68 + 24 * q^69 + 73 * q^70 + 80 * q^71 + 23 * q^72 + 14 * q^73 - 33 * q^74 - 27 * q^75 - 18 * q^76 - 20 * q^77 - 24 * q^78 - 61 * q^79 + 82 * q^80 - 53 * q^81 - 3 * q^82 - 36 * q^83 + 188 * q^84 - 26 * q^85 + 4 * q^86 + 17 * q^87 - 74 * q^88 - 18 * q^89 - 40 * q^90 + 7 * q^91 + 56 * q^92 + 36 * q^93 + 5 * q^94 - 20 * q^95 - 148 * q^96 + 52 * q^97 + 142 * q^98 + 76 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

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