LMFDB - Embedded newform 287.2.e.c.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:	$10$
Relative dimension:	$5$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - x^{9} + 7x^{8} + 4x^{7} + 32x^{6} + 3x^{5} + 30x^{4} - 7x^{3} + 26x^{2} - 5x + 1 $ x^10 - x^9 + 7x^8 + 4x^7 + 32x^6 + 3x^5 + 30x^4 - 7x^3 + 26x^2 - 5x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			247.1
Root			$0.440981 - 0.763802i$ of defining polynomial
Character	$\chi$	$=$	287.247
Dual form			287.2.e.c.165.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.985135 + 1.70630i) q^{2} +(-0.257781 - 0.446490i) q^{3} +(-0.940981 - 1.62983i) q^{4} +(0.257781 - 0.446490i) q^{5} +1.01580 q^{6} +(1.91822 + 1.82221i) q^{7} -0.232565 q^{8} +(1.36710 - 2.36788i) q^{9} +O(q^{10})$	\(q+(-0.985135 + 1.70630i) q^{2} +(-0.257781 - 0.446490i) q^{3} +(-0.940981 - 1.62983i) q^{4} +(0.257781 - 0.446490i) q^{5} +1.01580 q^{6} +(1.91822 + 1.82221i) q^{7} -0.232565 q^{8} +(1.36710 - 2.36788i) q^{9} +(0.507899 + 0.879706i) q^{10} +(2.24292 + 3.88484i) q^{11} +(-0.485135 + 0.840278i) q^{12} -0.515563 q^{13} +(-4.99894 + 1.47794i) q^{14} -0.265805 q^{15} +(2.11107 - 3.65648i) q^{16} +(2.69180 + 4.66233i) q^{17} +(2.69355 + 4.66537i) q^{18} +(-1.95654 + 3.38883i) q^{19} -0.970270 q^{20} +(0.319118 - 1.32620i) q^{21} -8.83830 q^{22} +(-1.07283 + 1.85819i) q^{23} +(0.0599510 + 0.103838i) q^{24} +(2.36710 + 4.09993i) q^{25} +(0.507899 - 0.879706i) q^{26} -2.95634 q^{27} +(1.16488 - 4.84103i) q^{28} -3.58854 q^{29} +(0.261854 - 0.453544i) q^{30} +(-3.08924 - 5.35072i) q^{31} +(3.92681 + 6.80144i) q^{32} +(1.15636 - 2.00288i) q^{33} -10.6071 q^{34} +(1.30808 - 0.386734i) q^{35} -5.14565 q^{36} +(4.76638 - 8.25561i) q^{37} +(-3.85492 - 6.67692i) q^{38} +(0.132902 + 0.230194i) q^{39} +(-0.0599510 + 0.103838i) q^{40} -1.00000 q^{41} +(1.94852 + 1.85099i) q^{42} +9.50489 q^{43} +(4.22108 - 7.31113i) q^{44} +(-0.704824 - 1.22079i) q^{45} +(-2.11376 - 3.66114i) q^{46} +(-5.13348 + 8.89144i) q^{47} -2.17678 q^{48} +(0.359116 + 6.99078i) q^{49} -9.32764 q^{50} +(1.38779 - 2.40372i) q^{51} +(0.485135 + 0.840278i) q^{52} +(0.856512 + 1.48352i) q^{53} +(2.91239 - 5.04441i) q^{54} +2.31273 q^{55} +(-0.446111 - 0.423782i) q^{56} +2.01744 q^{57} +(3.53520 - 6.12314i) q^{58} +(-2.10826 - 3.65161i) q^{59} +(0.250117 + 0.433216i) q^{60} +(7.70806 - 13.3507i) q^{61} +12.1733 q^{62} +(6.93716 - 2.05098i) q^{63} -7.02948 q^{64} +(-0.132902 + 0.230194i) q^{65} +(2.27835 + 3.94622i) q^{66} +(1.88978 + 3.27319i) q^{67} +(5.06586 - 8.77433i) q^{68} +1.10622 q^{69} +(-0.628748 + 2.61297i) q^{70} +6.37594 q^{71} +(-0.317939 + 0.550687i) q^{72} +(-1.74836 - 3.02825i) q^{73} +(9.39105 + 16.2658i) q^{74} +(1.22039 - 2.11377i) q^{75} +7.36429 q^{76} +(-2.77659 + 11.5390i) q^{77} -0.523707 q^{78} +(3.51288 - 6.08448i) q^{79} +(-1.08839 - 1.88515i) q^{80} +(-3.33920 - 5.78367i) q^{81} +(0.985135 - 1.70630i) q^{82} +7.25513 q^{83} +(-2.46176 + 0.727820i) q^{84} +2.77558 q^{85} +(-9.36360 + 16.2182i) q^{86} +(0.925059 + 1.60225i) q^{87} +(-0.521624 - 0.903480i) q^{88} +(1.64964 - 2.85727i) q^{89} +2.77739 q^{90} +(-0.988961 - 0.939462i) q^{91} +4.03804 q^{92} +(-1.59270 + 2.75863i) q^{93} +(-10.1143 - 17.5185i) q^{94} +(1.00872 + 1.74716i) q^{95} +(2.02452 - 3.50657i) q^{96} -19.3033 q^{97} +(-12.2822 - 6.27410i) q^{98} +12.2651 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + 2 q^{2} + 2 q^{3} - 6 q^{4} - 2 q^{5} + 2 q^{6} + 8 q^{7} - 6 q^{8} - 5 q^{9}+O(q^{10}) $ 10 * q + 2 * q^2 + 2 * q^3 - 6 * q^4 - 2 * q^5 + 2 * q^6 + 8 * q^7 - 6 * q^8 - 5 * q^9	\( 10 q + 2 q^{2} + 2 q^{3} - 6 q^{4} - 2 q^{5} + 2 q^{6} + 8 q^{7} - 6 q^{8} - 5 q^{9} + q^{10} + 6 q^{11} + 7 q^{12} + 4 q^{13} - 24 q^{14} - 40 q^{15} + 12 q^{16} + 3 q^{17} + 8 q^{18} - 7 q^{19} + 14 q^{20} - 15 q^{21} - 26 q^{22} - 16 q^{24} + 5 q^{25} + q^{26} + 26 q^{27} - 5 q^{28} - 20 q^{29} - 14 q^{30} + 6 q^{31} + 3 q^{32} + 17 q^{33} + 2 q^{34} - 9 q^{35} - 30 q^{36} + 18 q^{37} + 7 q^{38} + 20 q^{39} + 16 q^{40} - 10 q^{41} - 35 q^{42} - 28 q^{43} - 2 q^{44} + 7 q^{45} + 3 q^{46} - 3 q^{47} + 18 q^{48} - 8 q^{49} - 8 q^{50} - 7 q^{52} + 9 q^{53} + 25 q^{54} + 34 q^{55} - 15 q^{56} + 62 q^{57} + 5 q^{58} + 19 q^{59} + 3 q^{60} + 23 q^{61} + 72 q^{62} + 13 q^{63} - 2 q^{64} - 20 q^{65} - 23 q^{66} + 11 q^{67} + 24 q^{68} + 38 q^{69} - 40 q^{70} - 25 q^{72} - 13 q^{73} - 2 q^{74} - 11 q^{75} + 24 q^{76} + 23 q^{77} + 28 q^{78} + 41 q^{79} + 9 q^{80} + 7 q^{81} - 2 q^{82} - 4 q^{83} - 23 q^{84} - 20 q^{86} - 32 q^{87} + 10 q^{88} - 14 q^{89} + 44 q^{90} - 6 q^{91} + 34 q^{92} + 15 q^{93} - 10 q^{94} + 31 q^{95} + 33 q^{96} - 54 q^{97} - 85 q^{98} - 18 q^{99}+O(q^{100}) \) 10 * q + 2 * q^2 + 2 * q^3 - 6 * q^4 - 2 * q^5 + 2 * q^6 + 8 * q^7 - 6 * q^8 - 5 * q^9 + q^10 + 6 * q^11 + 7 * q^12 + 4 * q^13 - 24 * q^14 - 40 * q^15 + 12 * q^16 + 3 * q^17 + 8 * q^18 - 7 * q^19 + 14 * q^20 - 15 * q^21 - 26 * q^22 - 16 * q^24 + 5 * q^25 + q^26 + 26 * q^27 - 5 * q^28 - 20 * q^29 - 14 * q^30 + 6 * q^31 + 3 * q^32 + 17 * q^33 + 2 * q^34 - 9 * q^35 - 30 * q^36 + 18 * q^37 + 7 * q^38 + 20 * q^39 + 16 * q^40 - 10 * q^41 - 35 * q^42 - 28 * q^43 - 2 * q^44 + 7 * q^45 + 3 * q^46 - 3 * q^47 + 18 * q^48 - 8 * q^49 - 8 * q^50 - 7 * q^52 + 9 * q^53 + 25 * q^54 + 34 * q^55 - 15 * q^56 + 62 * q^57 + 5 * q^58 + 19 * q^59 + 3 * q^60 + 23 * q^61 + 72 * q^62 + 13 * q^63 - 2 * q^64 - 20 * q^65 - 23 * q^66 + 11 * q^67 + 24 * q^68 + 38 * q^69 - 40 * q^70 - 25 * q^72 - 13 * q^73 - 2 * q^74 - 11 * q^75 + 24 * q^76 + 23 * q^77 + 28 * q^78 + 41 * q^79 + 9 * q^80 + 7 * q^81 - 2 * q^82 - 4 * q^83 - 23 * q^84 - 20 * q^86 - 32 * q^87 + 10 * q^88 - 14 * q^89 + 44 * q^90 - 6 * q^91 + 34 * q^92 + 15 * q^93 - 10 * q^94 + 31 * q^95 + 33 * q^96 - 54 * q^97 - 85 * q^98 - 18 * 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 $

$2$	−0.985135	+	1.70630i	−0.696596	+	1.20654i	0.273044	+	0.962001i	$0.411969\pi$
$2$	−0.985135	+	1.70630i	−0.696596	+	1.20654i	−0.969640	+	0.244537i	$0.921364\pi$
$3$	−0.257781	−	0.446490i	−0.148830	−	0.257781i	0.781965	−	0.623322i	$-0.214217\pi$
$3$	−0.257781	−	0.446490i	−0.148830	−	0.257781i	−0.930795	+	0.365541i	$0.880884\pi$
$4$	−0.940981	−	1.62983i	−0.470491	−	0.814914i
$5$	0.257781	−	0.446490i	0.115283	−	0.199677i	−0.802610	−	0.596505i	$-0.796556\pi$
$5$	0.257781	−	0.446490i	0.115283	−	0.199677i	0.917893	+	0.396828i	$0.129889\pi$
$6$	1.01580			0.414698
$7$	1.91822	+	1.82221i	0.725018	+	0.688730i
$7$	1.91822	+	1.82221i	0.725018	+	0.688730i
$8$	−0.232565			−0.0822242
$9$	1.36710	−	2.36788i	0.455699	−	0.789294i
$10$	0.507899	+	0.879706i	0.160612	+	0.278188i
$11$	2.24292	+	3.88484i	0.676265	+	1.17132i	0.976098	+	0.217333i	$0.0697358\pi$
$11$	2.24292	+	3.88484i	0.676265	+	1.17132i	−0.299833	+	0.953992i	$0.596931\pi$
$12$	−0.485135	+	0.840278i	−0.140046	+	0.242567i
$13$	−0.515563			−0.142991			−0.0714957	−	0.997441i	$-0.522777\pi$
$13$	−0.515563			−0.142991			−0.0714957	+	0.997441i	$0.522777\pi$
$14$	−4.99894	+	1.47794i	−1.33602	+	0.394996i
$15$	−0.265805			−0.0686305
$16$	2.11107	−	3.65648i	0.527768	−	0.914121i
$17$	2.69180	+	4.66233i	0.652856	+	1.13078i	0.982427	+	0.186650i	$0.0597629\pi$
$17$	2.69180	+	4.66233i	0.652856	+	1.13078i	−0.329570	+	0.944131i	$0.606904\pi$
$18$	2.69355	+	4.66537i	0.634876	+	1.09964i
$19$	−1.95654	+	3.38883i	−0.448862	+	0.777452i	−0.998312	−	0.0580747i	$-0.981504\pi$
$19$	−1.95654	+	3.38883i	−0.448862	+	0.777452i	0.549450	+	0.835526i	$0.314837\pi$
$20$	−0.970270			−0.216959
$21$	0.319118	−	1.32620i	0.0696372	−	0.289400i
$22$	−8.83830			−1.88433
$23$	−1.07283	+	1.85819i	−0.223700	+	0.387459i	−0.955929	−	0.293599i	$-0.905147\pi$
$23$	−1.07283	+	1.85819i	−0.223700	+	0.387459i	0.732229	+	0.681059i	$0.238480\pi$
$24$	0.0599510	+	0.103838i	0.0122374	+	0.0211959i
$25$	2.36710	+	4.09993i	0.473420	+	0.819987i
$26$	0.507899	−	0.879706i	0.0996071	−	0.172525i
$27$	−2.95634			−0.568947
$28$	1.16488	−	4.84103i	0.220141	−	0.914868i
$29$	−3.58854			−0.666375			−0.333188	−	0.942861i	$-0.608124\pi$
$29$	−3.58854			−0.666375			−0.333188	+	0.942861i	$0.608124\pi$
$30$	0.261854	−	0.453544i	0.0478077	−	0.0828054i
$31$	−3.08924	−	5.35072i	−0.554844	−	0.961018i	−0.997916	−	0.0645315i	$-0.979445\pi$
$31$	−3.08924	−	5.35072i	−0.554844	−	0.961018i	0.443072	−	0.896486i	$-0.353889\pi$
$32$	3.92681	+	6.80144i	0.694169	+	1.20234i
$33$	1.15636	−	2.00288i	0.201297	−	0.348657i
$34$	−10.6071			−1.81911
$35$	1.30808	−	0.386734i	0.221106	−	0.0653700i
$36$	−5.14565			−0.857609
$37$	4.76638	−	8.25561i	0.783588	−	1.35721i	−0.146252	−	0.989247i	$-0.546721\pi$
$37$	4.76638	−	8.25561i	0.783588	−	1.35721i	0.929839	−	0.367966i	$-0.119946\pi$
$38$	−3.85492	−	6.67692i	−0.625351	−	1.08314i
$39$	0.132902	+	0.230194i	0.0212814	+	0.0368605i
$40$	−0.0599510	+	0.103838i	−0.00947908	+	0.0164183i
$41$	−1.00000			−0.156174
$41$	−1.00000			−0.156174
$42$	1.94852	+	1.85099i	0.300663	+	0.285615i
$43$	9.50489			1.44948			0.724741	−	0.689021i	$-0.241959\pi$
$43$	9.50489			1.44948			0.724741	+	0.689021i	$0.241959\pi$
$44$	4.22108	−	7.31113i	0.636352	−	1.10219i
$45$	−0.704824	−	1.22079i	−0.105069	−	0.181985i
$46$	−2.11376	−	3.66114i	−0.311657	−	0.539805i
$47$	−5.13348	+	8.89144i	−0.748794	+	1.29695i	0.199607	+	0.979876i	$0.436034\pi$
$47$	−5.13348	+	8.89144i	−0.748794	+	1.29695i	−0.948401	+	0.317074i	$0.897300\pi$
$48$	−2.17678			−0.314191
$49$	0.359116	+	6.99078i	0.0513024	+	0.998683i
$50$	−9.32764			−1.31913
$51$	1.38779	−	2.40372i	0.194329	−	0.336588i
$52$	0.485135	+	0.840278i	0.0672761	+	0.116526i
$53$	0.856512	+	1.48352i	0.117651	+	0.203777i	0.918836	−	0.394639i	$-0.129130\pi$
$53$	0.856512	+	1.48352i	0.117651	+	0.203777i	−0.801185	+	0.598416i	$0.795797\pi$
$54$	2.91239	−	5.04441i	0.396326	−	0.686457i
$55$	2.31273			0.311848
$56$	−0.446111	−	0.423782i	−0.0596141	−	0.0566303i
$57$	2.01744			0.267217
$58$	3.53520	−	6.12314i	0.464194	−	0.804008i
$59$	−2.10826	−	3.65161i	−0.274472	−	0.475399i	0.695530	−	0.718497i	$-0.255170\pi$
$59$	−2.10826	−	3.65161i	−0.274472	−	0.475399i	−0.970002	+	0.243098i	$0.921836\pi$
$60$	0.250117	+	0.433216i	0.0322900	+	0.0559280i
$61$	7.70806	−	13.3507i	0.986916	−	1.70939i	0.353821	−	0.935313i	$-0.384882\pi$
$61$	7.70806	−	13.3507i	0.986916	−	1.70939i	0.633094	−	0.774075i	$-0.281785\pi$
$62$	12.1733			1.54601
$63$	6.93716	−	2.05098i	0.874001	−	0.258399i
$64$	−7.02948			−0.878685
$65$	−0.132902	+	0.230194i	−0.0164845	+	0.0285520i
$66$	2.27835	+	3.94622i	0.280445	+	0.485746i
$67$	1.88978	+	3.27319i	0.230873	+	0.399884i	0.958065	−	0.286550i	$-0.0925084\pi$
$67$	1.88978	+	3.27319i	0.230873	+	0.399884i	−0.727192	+	0.686434i	$0.759175\pi$
$68$	5.06586	−	8.77433i	0.614326	−	1.06404i
$69$	1.10622			0.133173
$70$	−0.628748	+	2.61297i	−0.0751497	+	0.312309i
$71$	6.37594			0.756685			0.378342	−	0.925666i	$-0.376494\pi$
$71$	6.37594			0.756685			0.378342	+	0.925666i	$0.376494\pi$
$72$	−0.317939	+	0.550687i	−0.0374695	+	0.0648991i
$73$	−1.74836	−	3.02825i	−0.204630	−	0.354430i	0.745385	−	0.666635i	$-0.232266\pi$
$73$	−1.74836	−	3.02825i	−0.204630	−	0.354430i	−0.950015	+	0.312205i	$0.898933\pi$
$74$	9.39105	+	16.2658i	1.09169	+	1.89086i
$75$	1.22039	−	2.11377i	0.140918	−	0.244077i
$76$	7.36429			0.844742
$77$	−2.77659	+	11.5390i	−0.316422	+	1.31500i
$78$	−0.523707			−0.0592982
$79$	3.51288	−	6.08448i	0.395229	−	0.684557i	−0.597901	−	0.801570i	$-0.703998\pi$
$79$	3.51288	−	6.08448i	0.395229	−	0.684557i	0.993130	+	0.117013i	$0.0373318\pi$
$80$	−1.08839	−	1.88515i	−0.121686	−	0.210766i
$81$	−3.33920	−	5.78367i	−0.371023	−	0.642630i
$82$	0.985135	−	1.70630i	0.108790	−	0.188430i
$83$	7.25513			0.796354			0.398177	−	0.917309i	$-0.369643\pi$
$83$	7.25513			0.796354			0.398177	+	0.917309i	$0.369643\pi$
$84$	−2.46176	+	0.727820i	−0.268600	+	0.0794116i
$85$	2.77558			0.301054
$86$	−9.36360	+	16.2182i	−1.00970	+	1.74886i
$87$	0.925059	+	1.60225i	0.0991767	+	0.171779i
$88$	−0.521624	−	0.903480i	−0.0556054	−	0.0963113i
$89$	1.64964	−	2.85727i	0.174862	−	0.302870i	−0.765252	−	0.643731i	$-0.777385\pi$
$89$	1.64964	−	2.85727i	0.174862	−	0.302870i	0.940113	+	0.340862i	$0.110719\pi$
$90$	2.77739			0.292762
$91$	−0.988961	−	0.939462i	−0.103671	−	0.0984824i
$92$	4.03804			0.420995
$93$	−1.59270	+	2.75863i	−0.165155	+	0.286057i
$94$	−10.1143	−	17.5185i	−1.04321	−	1.80690i
$95$	1.00872	+	1.74716i	0.103493	+	0.179254i
$96$	2.02452	−	3.50657i	0.206627	−	0.357888i
$97$	−19.3033			−1.95995			−0.979976	−	0.199117i	$-0.936193\pi$
$97$	−19.3033			−1.95995			−0.979976	+	0.199117i	$0.936193\pi$
$98$	−12.2822	−	6.27410i	−1.24069	−	0.633780i
$99$	12.2651			1.23269
$100$	4.45479	−	7.71592i	0.445479	−	0.771592i
$101$	−9.84181	−	17.0465i	−0.979297	−	1.69619i	−0.664958	−	0.746880i	$-0.731551\pi$
$101$	−9.84181	−	17.0465i	−0.979297	−	1.69619i	−0.314338	−	0.949311i	$-0.601783\pi$
$102$	2.73432	+	4.73598i	0.270738	+	0.468932i
$103$	1.76776	−	3.06186i	0.174183	−	0.301694i	−0.765695	−	0.643203i	$-0.777605\pi$
$103$	1.76776	−	3.06186i	0.174183	−	0.301694i	0.939878	+	0.341510i	$0.110938\pi$
$104$	0.119902			0.0117574
$105$	−0.509872	−	0.484352i	−0.0497584	−	0.0472679i
$106$	−3.37512			−0.327821
$107$	0.976783	−	1.69184i	0.0944292	−	0.163556i	−0.814941	−	0.579544i	$-0.803231\pi$
$107$	0.976783	−	1.69184i	0.0944292	−	0.163556i	0.909370	+	0.415988i	$0.136564\pi$
$108$	2.78186	+	4.81832i	0.267684	+	0.463643i
$109$	−2.56449	−	4.44182i	−0.245633	−	0.425449i	0.716676	−	0.697406i	$-0.245663\pi$
$109$	−2.56449	−	4.44182i	−0.245633	−	0.425449i	−0.962309	+	0.271957i	$0.912329\pi$
$110$	−2.27835	+	3.94622i	−0.217232	+	0.376257i
$111$	−4.91473			−0.466486
$112$	10.7124	−	3.16712i	1.01222	−	0.299264i
$113$	−15.0460			−1.41541			−0.707706	−	0.706507i	$-0.750270\pi$
$113$	−15.0460			−1.41541			−0.707706	+	0.706507i	$0.750270\pi$
$114$	−1.98745	+	3.44237i	−0.186142	+	0.322407i
$115$	0.553109	+	0.958014i	0.0515777	+	0.0893352i
$116$	3.37675	+	5.84870i	0.313523	+	0.543039i
$117$	−0.704824	+	1.22079i	−0.0651610	+	0.112862i
$118$	8.30768			0.764784
$119$	−3.33228	+	13.8484i	−0.305470	+	1.26948i
$120$	0.0618170			0.00564309
$121$	−4.56135	+	7.90048i	−0.414668	+	0.718226i
$122$	15.1870	+	26.3046i	1.37496	+	2.38150i
$123$	0.257781	+	0.446490i	0.0232434	+	0.0402587i
$124$	−5.81383	+	10.0699i	−0.522098	+	0.904300i
$125$	5.01859			0.448876
$126$	−3.33445	+	13.8574i	−0.297057	+	1.23452i
$127$	1.40476			0.124653			0.0623263	−	0.998056i	$-0.480148\pi$
$127$	1.40476			0.124653			0.0623263	+	0.998056i	$0.480148\pi$
$128$	−0.928641	+	1.60845i	−0.0820810	+	0.142169i
$129$	−2.45018	−	4.24384i	−0.215727	−	0.373649i
$130$	−0.261854	−	0.453544i	−0.0229661	−	0.0397784i
$131$	4.35076	−	7.53575i	0.380128	−	0.658401i	−0.610952	−	0.791668i	$-0.709213\pi$
$131$	4.35076	−	7.53575i	0.380128	−	0.658401i	0.991080	+	0.133266i	$0.0425466\pi$
$132$	−4.35247			−0.378834
$133$	−9.92824	+	2.93529i	−0.860887	+	0.254522i
$134$	−7.44675			−0.643301
$135$	−0.762088	+	1.31998i	−0.0655901	+	0.113605i
$136$	−0.626018	−	1.08430i	−0.0536806	−	0.0929776i
$137$	−7.18169	−	12.4391i	−0.613573	−	1.06274i	−0.990633	−	0.136551i	$-0.956398\pi$
$137$	−7.18169	−	12.4391i	−0.613573	−	1.06274i	0.377060	−	0.926189i	$-0.376935\pi$
$138$	−1.08977	+	1.88755i	−0.0927678	+	0.160679i
$139$	−17.7700			−1.50723			−0.753614	−	0.657317i	$-0.771691\pi$
$139$	−17.7700			−1.50723			−0.753614	+	0.657317i	$0.771691\pi$
$140$	−1.86119	−	1.76803i	−0.157299	−	0.149426i
$141$	5.29326			0.445773
$142$	−6.28116	+	10.8793i	−0.527103	+	0.912970i
$143$	−1.15636	−	2.00288i	−0.0967000	−	0.167489i
$144$	−5.77208	−	9.99754i	−0.481007	−	0.833128i
$145$	−0.925059	+	1.60225i	−0.0768220	+	0.133060i
$146$	6.88949			0.570178
$147$	3.02874	−	1.96244i	0.249807	−	0.161859i
$148$	−17.9403			−1.47468
$149$	−7.85456	+	13.6045i	−0.643471	+	1.11452i	0.341182	+	0.939997i	$0.389173\pi$
$149$	−7.85456	+	13.6045i	−0.643471	+	1.11452i	−0.984652	+	0.174526i	$0.944161\pi$
$150$	2.40449	+	4.16470i	0.196326	+	0.340046i
$151$	8.54754	+	14.8048i	0.695589	+	1.20480i	0.969982	+	0.243177i	$0.0781897\pi$
$151$	8.54754	+	14.8048i	0.695589	+	1.20480i	−0.274393	+	0.961618i	$0.588477\pi$
$152$	0.455024	−	0.788125i	0.0369073	−	0.0639254i
$153$	14.7198			1.19002
$154$	−16.9538	−	16.1052i	−1.36617	−	1.29780i
$155$	−3.18539			−0.255857
$156$	0.250117	−	0.433216i	0.0200254	−	0.0346850i
$157$	−0.720512	−	1.24796i	−0.0575031	−	0.0995983i	0.835841	−	0.548972i	$-0.184981\pi$
$157$	−0.720512	−	1.24796i	−0.0575031	−	0.0995983i	−0.893344	+	0.449374i	$0.851647\pi$
$158$	6.92131	+	11.9881i	0.550630	+	0.953719i
$159$	0.441586	−	0.764849i	0.0350200	−	0.0606564i
$160$	4.04904			0.320104
$161$	−5.44392	+	1.60950i	−0.429041	+	0.126846i
$162$	13.1583			1.03381
$163$	3.96292	−	6.86398i	0.310400	−	0.537629i	−0.668049	−	0.744117i	$-0.732870\pi$
$163$	3.96292	−	6.86398i	0.310400	−	0.537629i	0.978449	+	0.206489i	$0.0662037\pi$
$164$	0.940981	+	1.62983i	0.0734783	+	0.127268i
$165$	−0.596178	−	1.03261i	−0.0464124	−	0.0803886i
$166$	−7.14728	+	12.3795i	−0.554737	+	0.960832i
$167$	7.86926			0.608942			0.304471	−	0.952522i	$-0.401520\pi$
$167$	7.86926			0.608942			0.304471	+	0.952522i	$0.401520\pi$
$168$	−0.0742157	+	0.308427i	−0.00572586	+	0.0237957i
$169$	−12.7342			−0.979553
$170$	−2.73432	+	4.73598i	−0.209713	+	0.363233i
$171$	5.34957	+	9.26573i	0.409092	+	0.708568i
$172$	−8.94392	−	15.4913i	−0.681968	−	1.18120i
$173$	3.87875	−	6.71819i	0.294896	−	0.510775i	−0.680065	−	0.733152i	$-0.738048\pi$
$173$	3.87875	−	6.71819i	0.294896	−	0.510775i	0.974961	+	0.222377i	$0.0713817\pi$
$174$	−3.64523			−0.276344
$175$	−2.93032	+	12.1779i	−0.221512	+	0.920563i
$176$	18.9398			1.42764
$177$	−1.08694	+	1.88263i	−0.0816994	+	0.141507i
$178$	3.25024	+	5.62958i	0.243616	+	0.421955i
$179$	−6.18475	−	10.7123i	−0.462270	−	0.800675i	0.536804	−	0.843707i	$-0.319631\pi$
$179$	−6.18475	−	10.7123i	−0.462270	−	0.800675i	−0.999074	+	0.0430323i	$0.986298\pi$
$180$	−1.32645	+	2.29748i	−0.0988680	+	0.171244i
$181$	−6.45029			−0.479446			−0.239723	−	0.970841i	$-0.577057\pi$
$181$	−6.45029			−0.479446			−0.239723	+	0.970841i	$0.577057\pi$
$182$	2.57727	−	0.761971i	0.191040	−	0.0564811i
$183$	−7.94797			−0.587531
$184$	0.249502	−	0.432151i	0.0183935	−	0.0318586i
$185$	−2.45737	−	4.25628i	−0.180669	−	0.312928i
$186$	−3.13804	−	5.43525i	−0.230092	−	0.398532i
$187$	−12.0749	+	20.9144i	−0.883008	+	1.52941i
$188$	19.3220			1.40920
$189$	−5.67090	−	5.38706i	−0.412497	−	0.391851i
$190$	−3.97491			−0.288370
$191$	6.37777	−	11.0466i	0.461479	−	0.799305i	−0.537556	−	0.843228i	$-0.680652\pi$
$191$	6.37777	−	11.0466i	0.461479	−	0.799305i	0.999035	+	0.0439231i	$0.0139857\pi$
$192$	1.81207	+	3.13860i	0.130775	+	0.226509i
$193$	10.0716	+	17.4444i	0.724966	+	1.25568i	0.958988	+	0.283447i	$0.0914779\pi$
$193$	10.0716	+	17.4444i	0.724966	+	1.25568i	−0.234022	+	0.972231i	$0.575189\pi$
$194$	19.0163	−	32.9373i	1.36529	−	2.36476i
$195$	0.137039			0.00981357
$196$	11.0558	−	7.16349i	0.789703	−	0.511678i
$197$	20.2152			1.44027			0.720135	−	0.693834i	$-0.244080\pi$
$197$	20.2152			1.44027			0.720135	+	0.693834i	$0.244080\pi$
$198$	−12.0828	+	20.9281i	−0.858688	+	1.48729i
$199$	3.29276	+	5.70323i	0.233418	+	0.404291i	0.958812	−	0.284043i	$-0.0916757\pi$
$199$	3.29276	+	5.70323i	0.233418	+	0.404291i	−0.725394	+	0.688334i	$0.758342\pi$
$200$	−0.550505	−	0.953502i	−0.0389266	−	0.0674228i
$201$	0.974300	−	1.68754i	0.0687218	−	0.119030i
$202$	38.7820			2.72869
$203$	−6.88360	−	6.53907i	−0.483134	−	0.458953i
$204$	−5.22354			−0.365721
$205$	−0.257781	+	0.446490i	−0.0180042	+	0.0311842i
$206$	3.48297	+	6.03268i	0.242670	+	0.420317i
$207$	2.93332	+	5.08065i	0.203880	+	0.353130i
$208$	−1.08839	+	1.88515i	−0.0754662	+	0.130711i
$209$	−17.5535			−1.21420
$210$	1.32874	−	0.392844i	0.0916920	−	0.0271088i
$211$	−19.7713			−1.36111			−0.680557	−	0.732695i	$-0.738262\pi$
$211$	−19.7713			−1.36111			−0.680557	+	0.732695i	$0.738262\pi$
$212$	1.61192	−	2.79193i	0.110707	−	0.191751i
$213$	−1.64360	−	2.84680i	−0.112617	−	0.195059i
$214$	1.92453	+	3.33338i	0.131558	+	0.227865i
$215$	2.45018	−	4.24384i	0.167101	−	0.289428i
$216$	0.687541			0.0467813
$217$	3.82429	−	15.8931i	0.259610	−	1.07889i
$218$	10.1055			0.684428
$219$	−0.901391	+	1.56125i	−0.0609103	+	0.105500i
$220$	−2.17623	−	3.76935i	−0.146722	−	0.254129i
$221$	−1.38779	−	2.40372i	−0.0933528	−	0.161692i
$222$	4.84167	−	8.38603i	0.324952	−	0.562833i
$223$	22.9084			1.53406			0.767031	−	0.641609i	$-0.221733\pi$
$223$	22.9084			1.53406			0.767031	+	0.641609i	$0.221733\pi$
$224$	−4.86116	+	20.2021i	−0.324800	+	1.34981i
$225$	12.9442			0.862948
$226$	14.8224	−	25.6731i	0.985970	−	1.70775i
$227$	−0.176489	−	0.305688i	−0.0117140	−	0.0202892i	0.860109	−	0.510110i	$-0.170395\pi$
$227$	−0.176489	−	0.305688i	−0.0117140	−	0.0202892i	−0.871823	+	0.489821i	$0.837062\pi$
$228$	−1.89838	−	3.28808i	−0.125723	−	0.217759i
$229$	6.77197	−	11.7294i	0.447504	−	0.775100i	−0.550719	−	0.834691i	$-0.685646\pi$
$229$	6.77197	−	11.7294i	0.447504	−	0.775100i	0.998223	+	0.0595907i	$0.0189796\pi$
$230$	−2.17955			−0.143715
$231$	5.86782	−	1.73483i	0.386074	−	0.114143i
$232$	0.834570			0.0547922
$233$	7.24695	−	12.5521i	0.474763	−	0.822314i	−0.524819	−	0.851214i	$-0.675867\pi$
$233$	7.24695	−	12.5521i	0.474763	−	0.822314i	0.999582	+	0.0288998i	$0.00920036\pi$
$234$	−1.38869	−	2.40529i	−0.0907818	−	0.157239i
$235$	2.64663	+	4.58409i	0.172647	+	0.299033i
$236$	−3.96767	+	6.87220i	−0.258273	+	0.447342i
$237$	−3.62222			−0.235288
$238$	−20.3468	−	19.3284i	−1.31889	−	1.25287i
$239$	−5.66844			−0.366661			−0.183330	−	0.983051i	$-0.558688\pi$
$239$	−5.66844			−0.366661			−0.183330	+	0.983051i	$0.558688\pi$
$240$	−0.561133	+	0.971911i	−0.0362210	+	0.0627366i
$241$	7.45972	+	12.9206i	0.480523	+	0.832290i	0.999750	−	0.0223461i	$-0.00711356\pi$
$241$	7.45972	+	12.9206i	0.480523	+	0.832290i	−0.519227	+	0.854636i	$0.673780\pi$
$242$	−8.98708	−	15.5661i	−0.577712	−	1.00063i
$243$	−6.15607	+	10.6626i	−0.394912	+	0.684008i
$244$	−29.0125			−1.85734
$245$	3.21389	+	1.64175i	0.205328	+	0.104888i
$246$	−1.01580			−0.0647649
$247$	1.00872	−	1.74716i	0.0641834	−	0.111169i
$248$	0.718450	+	1.24439i	0.0456216	+	0.0790189i
$249$	−1.87024	−	3.23935i	−0.118521	−	0.205285i
$250$	−4.94399	+	8.56323i	−0.312685	+	0.541586i
$251$	−0.263911			−0.0166579			−0.00832895	−	0.999965i	$-0.502651\pi$
$251$	−0.263911			−0.0166579			−0.00832895	+	0.999965i	$0.502651\pi$
$252$	−9.87048	−	9.37645i	−0.621782	−	0.590661i
$253$	−9.62504			−0.605121
$254$	−1.38388	+	2.39695i	−0.0868325	+	0.150398i
$255$	−0.715493	−	1.23927i	−0.0448059	−	0.0776061i
$256$	−8.85915	−	15.3445i	−0.553697	−	0.959032i
$257$	−3.18495	+	5.51650i	−0.198672	+	0.344110i	−0.948098	−	0.317978i	$-0.896996\pi$
$257$	−3.18495	+	5.51650i	−0.198672	+	0.344110i	0.749426	+	0.662088i	$0.230330\pi$
$258$	9.65504			0.601097
$259$	24.1864	−	7.15072i	1.50287	−	0.444324i
$260$	0.500235			0.0310232
$261$	−4.90589	+	8.49725i	−0.303667	+	0.525966i
$262$	8.57218	+	14.8475i	0.529591	+	0.917279i
$263$	7.22199	+	12.5089i	0.445327	+	0.771329i	0.998075	−	0.0620196i	$-0.0197541\pi$
$263$	7.22199	+	12.5089i	0.445327	+	0.771329i	−0.552748	+	0.833348i	$0.686421\pi$
$264$	−0.268930	+	0.465801i	−0.0165515	+	0.0286680i
$265$	0.883171			0.0542528
$266$	4.77216	−	19.8322i	0.292600	−	1.21599i
$267$	−1.70099			−0.104099
$268$	3.55649	−	6.16003i	0.217247	−	0.376284i
$269$	−7.44198	−	12.8899i	−0.453745	−	0.785910i	0.544870	−	0.838521i	$-0.316579\pi$
$269$	−7.44198	−	12.8899i	−0.453745	−	0.785910i	−0.998615	+	0.0526107i	$0.983246\pi$
$270$	−1.50152	−	2.60071i	−0.0913796	−	0.158274i
$271$	0.560186	−	0.970270i	0.0340289	−	0.0589397i	−0.848509	−	0.529180i	$-0.822500\pi$
$271$	0.560186	−	0.970270i	0.0340289	−	0.0589397i	0.882538	+	0.470241i	$0.155833\pi$
$272$	22.7303			1.37823
$273$	−0.164525	+	0.683738i	−0.00995751	+	0.0413817i
$274$	28.2997			1.70965
$275$	−10.6184	+	18.3916i	−0.640314	+	1.10906i
$276$	−1.04093	−	1.80295i	−0.0626567	−	0.108525i
$277$	−2.05229	−	3.55467i	−0.123310	−	0.213579i	0.797761	−	0.602974i	$-0.206018\pi$
$277$	−2.05229	−	3.55467i	−0.123310	−	0.213579i	−0.921071	+	0.389395i	$0.872684\pi$
$278$	17.5058	−	30.3209i	1.04993	−	1.81853i
$279$	−16.8932			−1.01137
$280$	−0.304214	+	0.0899410i	−0.0181802	+	0.00537500i
$281$	18.7308			1.11739			0.558694	−	0.829374i	$-0.311303\pi$
$281$	18.7308			1.11739			0.558694	+	0.829374i	$0.311303\pi$
$282$	−5.21457	+	9.03190i	−0.310523	+	0.537842i
$283$	−3.52868	−	6.11186i	−0.209758	−	0.363312i	0.741880	−	0.670533i	$-0.233934\pi$
$283$	−3.52868	−	6.11186i	−0.209758	−	0.363312i	−0.951638	+	0.307220i	$0.900601\pi$
$284$	−5.99964	−	10.3917i	−0.356013	−	0.616633i
$285$	0.520059	−	0.900768i	0.0308056	−	0.0533569i
$286$	4.55670			0.269443
$287$	−1.91822	−	1.82221i	−0.113229	−	0.107562i
$288$	21.4734			1.26533
$289$	−5.99153	+	10.3776i	−0.352443	+	0.610450i
$290$	−1.82262	−	3.15686i	−0.107028	−	0.185377i
$291$	4.97603	+	8.61873i	0.291700	+	0.505239i
$292$	−3.29035	+	5.69906i	−0.192553	+	0.333512i
$293$	−8.05119			−0.470356			−0.235178	−	0.971952i	$-0.575567\pi$
$293$	−8.05119			−0.470356			−0.235178	+	0.971952i	$0.575567\pi$
$294$	0.364790	+	7.10122i	0.0212750	+	0.414152i
$295$	−2.17388			−0.126568
$296$	−1.10849	+	1.91997i	−0.0644299	+	0.111596i
$297$	−6.63082	−	11.4849i	−0.384759	−	0.666422i
$298$	−15.4756	−	26.8045i	−0.896478	−	1.55274i
$299$	0.553109	−	0.958014i	0.0319871	−	0.0554034i
$300$	−4.59345			−0.265203
$301$	18.2324	+	17.3199i	1.05090	+	0.998302i
$302$	−33.6819			−1.93818
$303$	−5.07407	+	8.78855i	−0.291498	+	0.504889i
$304$	8.26081	+	14.3081i	0.473790	+	0.820628i
$305$	−3.97399	−	6.88315i	−0.227550	−	0.394128i
$306$	−14.5010	+	25.1164i	−0.828966	+	1.43581i
$307$	−16.1909			−0.924065			−0.462033	−	0.886863i	$-0.652880\pi$
$307$	−16.1909			−0.924065			−0.462033	+	0.886863i	$0.652880\pi$
$308$	21.4194	−	6.33265i	1.22048	−	0.360836i
$309$	−1.82279			−0.103695
$310$	3.13804	−	5.43525i	0.178229	−	0.308701i
$311$	−0.870402	−	1.50758i	−0.0493560	−	0.0854871i	0.840292	−	0.542134i	$-0.182384\pi$
$311$	−0.870402	−	1.50758i	−0.0493560	−	0.0854871i	−0.889648	+	0.456647i	$0.849050\pi$
$312$	−0.0309085	−	0.0535351i	−0.00174985	−	0.00303083i
$313$	−3.30988	+	5.73287i	−0.187085	+	0.324041i	−0.944277	−	0.329151i	$-0.893237\pi$
$313$	−3.30988	+	5.73287i	−0.187085	+	0.324041i	0.757192	+	0.653192i	$0.226571\pi$
$314$	2.83921			0.160226
$315$	0.872530	−	3.62608i	0.0491615	−	0.204307i
$316$	−13.2222			−0.743807
$317$	0.712326	−	1.23379i	0.0400082	−	0.0692963i	−0.845328	−	0.534248i	$-0.820595\pi$
$317$	0.712326	−	1.23379i	0.0400082	−	0.0692963i	0.885336	+	0.464952i	$0.153928\pi$
$318$	0.870043	+	1.50696i	0.0487896	+	0.0845060i
$319$	−8.04880	−	13.9409i	−0.450646	−	0.780542i
$320$	−1.81207	+	3.13860i	−0.101298	+	0.175453i
$321$	−1.00719			−0.0562156
$322$	2.61670	−	10.8746i	0.145823	−	0.606016i
$323$	−21.0665			−1.17217
$324$	−6.28426	+	10.8847i	−0.349125	+	0.604703i
$325$	−1.22039	−	2.11377i	−0.0676949	−	0.117251i
$326$	7.80803	+	13.5239i	0.432447	+	0.749020i
$327$	−1.32215	+	2.29004i	−0.0731152	+	0.126639i
$328$	0.232565			0.0128413
$329$	−26.0492	+	7.70146i	−1.43614	+	0.424595i
$330$	2.34926			0.129323
$331$	0.0852397	−	0.147639i	0.00468519	−	0.00811500i	−0.863673	−	0.504052i	$-0.831842\pi$
$331$	0.0852397	−	0.147639i	0.00468519	−	0.00811500i	0.868358	+	0.495937i	$0.165175\pi$
$332$	−6.82694	−	11.8246i	−0.374677	−	0.648960i
$333$	−13.0322	−	22.5724i	−0.714161	−	1.23696i
$334$	−7.75228	+	13.4273i	−0.424186	+	0.734712i
$335$	1.94860			0.106463
$336$	−4.17553	−	3.96654i	−0.227794	−	0.216393i
$337$	0.121912			0.00664096			0.00332048	−	0.999994i	$-0.498943\pi$
$337$	0.121912			0.00664096			0.00332048	+	0.999994i	$0.498943\pi$
$338$	12.5449	−	21.7284i	0.682353	−	1.18187i
$339$	3.87859	+	6.71791i	0.210656	+	0.364867i
$340$	−2.61177	−	4.52372i	−0.141643	−	0.245333i
$341$	13.8578	−	24.0024i	0.750442	−	1.29980i
$342$	−21.0802			−1.13989
$343$	−12.0498	+	14.0642i	−0.650628	+	0.759397i
$344$	−2.21051			−0.119183
$345$	0.285163	−	0.493916i	0.0153526	−	0.0265915i
$346$	7.64219	+	13.2367i	0.410846	+	0.711607i
$347$	2.56298	+	4.43920i	0.137588	+	0.238309i	0.926583	−	0.376090i	$-0.122732\pi$
$347$	2.56298	+	4.43920i	0.137588	+	0.238309i	−0.788995	+	0.614399i	$0.789398\pi$
$348$	1.74093	−	3.01537i	0.0933235	−	0.161641i
$349$	31.8658			1.70573			0.852867	−	0.522128i	$-0.174862\pi$
$349$	31.8658			1.70573			0.852867	+	0.522128i	$0.174862\pi$
$350$	−17.8924	−	16.9969i	−0.956391	−	0.908523i
$351$	1.52418			0.0813545
$352$	−17.6150	+	30.5101i	−0.938884	+	1.62620i
$353$	6.85025	+	11.8650i	0.364602	+	0.631509i	0.988712	−	0.149827i	$-0.0478717\pi$
$353$	6.85025	+	11.8650i	0.364602	+	0.631509i	−0.624110	+	0.781336i	$0.714538\pi$
$354$	−2.14156	−	3.70930i	−0.113823	−	0.197147i
$355$	1.64360	−	2.84680i	0.0872331	−	0.151092i
$356$	−6.20913			−0.329083
$357$	7.04216	−	2.08202i	0.372711	−	0.110192i
$358$	24.3712			1.28806
$359$	−9.34075	+	16.1787i	−0.492986	+	0.853877i	−0.999967	−	0.00808019i	$-0.997428\pi$
$359$	−9.34075	+	16.1787i	−0.492986	+	0.853877i	0.506981	+	0.861957i	$0.330761\pi$
$360$	0.163918	+	0.283914i	0.00863922	+	0.0149636i
$361$	1.84387	+	3.19368i	0.0970458	+	0.168088i
$362$	6.35441	−	11.0062i	0.333980	−	0.578471i
$363$	4.70332			0.246860
$364$	−0.600567	+	2.49585i	−0.0314783	+	0.130818i
$365$	−1.80278			−0.0943619
$366$	7.82982	−	13.5617i	0.409271	−	0.708879i
$367$	9.05946	+	15.6914i	0.472900	+	0.819086i	0.999519	−	0.0310149i	$-0.00987392\pi$
$367$	9.05946	+	15.6914i	0.472900	+	0.819086i	−0.526619	+	0.850101i	$0.676541\pi$
$368$	4.52963	+	7.84554i	0.236123	+	0.408977i
$369$	−1.36710	+	2.36788i	−0.0711683	+	0.123267i
$370$	9.68335			0.503413
$371$	−1.06031	+	4.40646i	−0.0550485	+	0.228772i
$372$	5.99479			0.310815
$373$	6.14444	−	10.6425i	0.318147	−	0.551047i	−0.661954	−	0.749544i	$-0.730273\pi$
$373$	6.14444	−	10.6425i	0.318147	−	0.551047i	0.980101	+	0.198497i	$0.0636061\pi$
$374$	−23.7909	−	41.2071i	−1.23020	−	2.13077i
$375$	−1.29370	−	2.24075i	−0.0668063	−	0.115712i
$376$	1.19387	−	2.06784i	0.0615690	−	0.106641i
$377$	1.85012			0.0952859
$378$	14.7786	−	4.36929i	0.760127	−	0.224732i
$379$	24.5683			1.26199			0.630995	−	0.775787i	$-0.282647\pi$
$379$	24.5683			1.26199			0.630995	+	0.775787i	$0.282647\pi$
$380$	1.89838	−	3.28808i	0.0973846	−	0.168675i
$381$	−0.362122	−	0.627214i	−0.0185521	−	0.0321331i
$382$	12.5659	+	21.7648i	0.642928	+	1.11358i
$383$	−10.2904	+	17.8235i	−0.525814	+	0.910737i	0.473733	+	0.880668i	$0.342906\pi$
$383$	−10.2904	+	17.8235i	−0.525814	+	0.910737i	−0.999548	+	0.0300690i	$0.990427\pi$
$384$	0.957545			0.0488645
$385$	4.43631	+	4.21427i	0.226096	+	0.214779i
$386$	−39.6873			−2.02003
$387$	12.9941	−	22.5065i	0.660528	−	1.14407i
$388$	18.1640	+	31.4610i	0.922139	+	1.59719i
$389$	−0.789604	−	1.36763i	−0.0400345	−	0.0693418i	0.845314	−	0.534270i	$-0.179413\pi$
$389$	−0.789604	−	1.36763i	−0.0400345	−	0.0693418i	−0.885348	+	0.464928i	$0.846080\pi$
$390$	−0.135002	+	0.233830i	−0.00683609	+	0.0118405i
$391$	−11.5513			−0.584176
$392$	−0.0835180	−	1.62581i	−0.00421830	−	0.0821160i
$393$	−4.48618			−0.226298
$394$	−19.9147	+	34.4932i	−1.00329	+	1.73774i
$395$	−1.81111	−	3.13693i	−0.0911267	−	0.157836i
$396$	−11.5413	−	19.9901i	−0.579971	−	1.00454i
$397$	−15.3899	+	26.6561i	−0.772398	+	1.33783i	0.163847	+	0.986486i	$0.447610\pi$
$397$	−15.3899	+	26.6561i	−0.772398	+	1.33783i	−0.936245	+	0.351347i	$0.885724\pi$
$398$	−12.9753			−0.650391
$399$	3.86989	+	3.67620i	0.193737	+	0.184040i
$400$	19.9884			0.999422
$401$	−0.968062	+	1.67673i	−0.0483427	+	0.0837320i	−0.889184	−	0.457549i	$-0.848727\pi$
$401$	−0.968062	+	1.67673i	−0.0483427	+	0.0837320i	0.840841	+	0.541281i	$0.182061\pi$
$402$	1.91963	+	3.32490i	0.0957426	+	0.165831i
$403$	1.59270	+	2.75863i	0.0793379	+	0.137417i
$404$	−18.5219	+	32.0809i	−0.921500	+	1.59608i
$405$	−3.44314			−0.171091
$406$	17.9389	−	5.30365i	0.890293	−	0.263216i
$407$	42.7623			2.11965
$408$	−0.322752	+	0.559022i	−0.0159786	+	0.0276757i
$409$	−2.57324	−	4.45698i	−0.127238	−	0.220383i	0.795367	−	0.606128i	$-0.207278\pi$
$409$	−2.57324	−	4.45698i	−0.127238	−	0.220383i	−0.922606	+	0.385744i	$0.873945\pi$
$410$	−0.507899	−	0.879706i	−0.0250833	−	0.0434456i
$411$	−3.70261	+	6.41311i	−0.182636	+	0.316335i
$412$	−6.65373			−0.327806
$413$	2.60990	−	10.8463i	0.128425	−	0.533710i
$414$	−11.5589			−0.568087
$415$	1.87024	−	3.23935i	0.0918063	−	0.159013i
$416$	−2.02452	−	3.50657i	−0.0992602	−	0.171924i
$417$	4.58076	+	7.93411i	0.224321	+	0.388535i
$418$	17.2925	−	29.9515i	0.845805	−	1.46498i
$419$	−1.25489			−0.0613055			−0.0306527	−	0.999530i	$-0.509759\pi$
$419$	−1.25489			−0.0613055			−0.0306527	+	0.999530i	$0.509759\pi$
$420$	−0.309630	+	1.28677i	−0.0151084	+	0.0627879i
$421$	1.44769			0.0705560			0.0352780	−	0.999378i	$-0.488768\pi$
$421$	1.44769			0.0705560			0.0352780	+	0.999378i	$0.488768\pi$
$422$	19.4774	−	33.7359i	0.948146	−	1.64224i
$423$	14.0359	+	24.3109i	0.682450	+	1.18204i
$424$	−0.199195	−	0.345016i	−0.00967376	−	0.0167554i
$425$	−12.7435	+	22.0724i	−0.618150	+	1.07067i
$426$	6.47666			0.313795
$427$	39.1136	−	11.5640i	1.89284	−	0.559619i
$428$	−3.67654			−0.177712
$429$	−0.596178	+	1.03261i	−0.0287837	+	0.0498549i
$430$	4.82752	+	8.36151i	0.232804	+	0.403228i
$431$	−4.00867	−	6.94322i	−0.193091	−	0.334443i	0.753182	−	0.657812i	$-0.228518\pi$
$431$	−4.00867	−	6.94322i	−0.193091	−	0.334443i	−0.946273	+	0.323369i	$0.895185\pi$
$432$	−6.24104	+	10.8098i	−0.300272	+	0.520086i
$433$	−36.9842			−1.77735			−0.888673	−	0.458542i	$-0.848372\pi$
$433$	−36.9842			−1.77735			−0.888673	+	0.458542i	$0.848372\pi$
$434$	23.3510	+	22.1822i	1.12088	+	1.06478i
$435$	0.953852			0.0457337
$436$	−4.82627	+	8.35934i	−0.231136	+	0.400340i
$437$	−4.19807	−	7.27126i	−0.200821	−	0.347832i
$438$	−1.77598	−	3.07609i	−0.0848597	−	0.146981i
$439$	−3.30651	+	5.72705i	−0.157811	+	0.273337i	−0.934079	−	0.357066i	$-0.883777\pi$
$439$	−3.30651	+	5.72705i	−0.157811	+	0.273337i	0.776268	+	0.630403i	$0.217110\pi$
$440$	−0.537860			−0.0256415
$441$	17.0443	+	8.70674i	0.811633	+	0.414606i
$442$	5.46864			0.260117
$443$	8.55510	−	14.8179i	0.406465	−	0.704019i	−0.588026	−	0.808842i	$-0.700095\pi$
$443$	8.55510	−	14.8179i	0.406465	−	0.704019i	0.994491	+	0.104824i	$0.0334279\pi$
$444$	4.62467	+	8.01017i	0.219477	+	0.380146i
$445$	−0.850494	−	1.47310i	−0.0403173	−	0.0698316i
$446$	−22.5679	+	39.0888i	−1.06862	+	1.85091i
$447$	8.09904			0.383071
$448$	−13.4841	−	12.8092i	−0.637063	−	0.605177i
$449$	29.0713			1.37196			0.685980	−	0.727621i	$-0.259374\pi$
$449$	29.0713			1.37196			0.685980	+	0.727621i	$0.259374\pi$
$450$	−12.7518	+	22.0868i	−0.601125	+	1.04118i
$451$	−2.24292	−	3.88484i	−0.105615	−	0.182930i
$452$	14.1580	+	24.5224i	0.665938	+	1.15344i
$453$	4.40679	−	7.63279i	0.207049	−	0.358620i
$454$	0.695463			0.0326397
$455$	−0.674397	+	0.199386i	−0.0316162	+	0.00934735i
$456$	−0.469187			−0.0219717
$457$	14.4421	−	25.0144i	0.675572	−	1.17013i	−0.300729	−	0.953710i	$-0.597230\pi$
$457$	14.4421	−	25.0144i	0.675572	−	1.17013i	0.976301	−	0.216416i	$-0.0694367\pi$
$458$	13.3426	+	23.1101i	0.623459	+	1.07986i
$459$	−7.95786	−	13.7834i	−0.371441	−	0.643355i
$460$	1.04093	−	1.80295i	0.0485337	−	0.0840628i
$461$	−40.2707			−1.87559			−0.937796	−	0.347188i	$-0.887137\pi$
$461$	−40.2707			−1.87559			−0.937796	+	0.347188i	$0.887137\pi$
$462$	−2.82046	+	11.7213i	−0.131220	+	0.545325i
$463$	−1.14609			−0.0532632			−0.0266316	−	0.999645i	$-0.508478\pi$
$463$	−1.14609			−0.0532632			−0.0266316	+	0.999645i	$0.508478\pi$
$464$	−7.57567	+	13.1214i	−0.351691	+	0.609147i
$465$	0.821135	+	1.42225i	0.0380792	+	0.0659551i
$466$	14.2784	+	24.7310i	0.661436	+	1.14564i
$467$	16.8090	−	29.1141i	0.777830	−	1.34724i	−0.155360	−	0.987858i	$-0.549654\pi$
$467$	16.8090	−	29.1141i	0.777830	−	1.34724i	0.933190	−	0.359383i	$-0.117013\pi$
$468$	2.65291			0.122631
$469$	−2.33943	+	9.72227i	−0.108025	+	0.448933i
$470$	−10.4291			−0.481060
$471$	−0.371469	+	0.643403i	−0.0171164	+	0.0296465i
$472$	0.490308	+	0.849238i	0.0225682	+	0.0390894i
$473$	21.3187	+	36.9250i	0.980234	+	1.69781i
$474$	3.56837	−	6.18060i	0.163901	−	0.283884i
$475$	−18.5253			−0.850000
$476$	25.7061	−	7.60002i	1.17824	−	0.348346i
$477$	4.68374			0.214454
$478$	5.58417	−	9.67207i	0.255414	−	0.442390i
$479$	−15.3537	−	26.5933i	−0.701527	−	1.21508i	−0.967930	−	0.251219i	$-0.919168\pi$
$479$	−15.3537	−	26.5933i	−0.701527	−	1.21508i	0.266403	−	0.963862i	$-0.414165\pi$
$480$	−1.04377	−	1.80786i	−0.0476412	−	0.0825170i
$481$	−2.45737	+	4.25628i	−0.112046	+	0.194070i
$482$	−29.3953			−1.33892
$483$	2.12197	+	2.01576i	0.0965529	+	0.0917203i
$484$	17.1686			0.780389
$485$	−4.97603	+	8.61873i	−0.225950	+	0.391356i
$486$	−12.1291	−	21.0083i	−0.550188	−	0.952954i
$487$	−16.2676	−	28.1763i	−0.737154	−	1.27679i	−0.953772	−	0.300532i	$-0.902836\pi$
$487$	−16.2676	−	28.1763i	−0.737154	−	1.27679i	0.216617	−	0.976257i	$-0.430498\pi$
$488$	−1.79263	+	3.10492i	−0.0811484	+	0.140553i
$489$	−4.08627			−0.184788
$490$	−5.96744	+	3.86653i	−0.269582	+	0.174672i
$491$	−12.9510			−0.584470			−0.292235	−	0.956347i	$-0.594399\pi$
$491$	−12.9510			−0.584470			−0.292235	+	0.956347i	$0.594399\pi$
$492$	0.485135	−	0.840278i	0.0218716	−	0.0378827i
$493$	−9.65962	−	16.7310i	−0.435048	−	0.753524i
$494$	1.98745	+	3.44237i	0.0894197	+	0.154879i
$495$	3.16172	−	5.47627i	0.142109	−	0.246140i
$496$	−26.0864			−1.17131
$497$	12.2304	+	11.6183i	0.548610	+	0.521151i
$498$	7.36974			0.330246
$499$	1.97776	−	3.42558i	0.0885367	−	0.153350i	−0.818356	−	0.574712i	$-0.805114\pi$
$499$	1.97776	−	3.42558i	0.0885367	−	0.153350i	0.906893	+	0.421361i	$0.138448\pi$
$500$	−4.72240	−	8.17943i	−0.211192	−	0.365795i
$501$	−2.02855	−	3.51355i	−0.0906289	−	0.156974i
$502$	0.259988	−	0.450312i	0.0116038	−	0.0200984i
$503$	10.4604			0.466408			0.233204	−	0.972428i	$-0.425079\pi$
$503$	10.4604			0.466408			0.233204	+	0.972428i	$0.425079\pi$
$504$	−1.61334	+	0.476986i	−0.0718640	+	0.0212467i
$505$	−10.1481			−0.451586
$506$	9.48196	−	16.4232i	0.421525	−	0.730102i
$507$	3.28264	+	5.68570i	0.145787	+	0.252511i
$508$	−1.32186	−	2.28952i	−0.0586479	−	0.101581i
$509$	11.6531	−	20.1838i	0.516516	−	0.894631i	−0.483301	−	0.875454i	$-0.660562\pi$
$509$	11.6531	−	20.1838i	0.516516	−	0.894631i	0.999816	−	0.0191766i	$-0.00610449\pi$
$510$	2.81943			0.124846
$511$	2.16437	−	8.99473i	0.0957460	−	0.397903i
$512$	31.1953			1.37865
$513$	5.78420	−	10.0185i	0.255379	−	0.442329i
$514$	−6.27522	−	10.8690i	−0.276788	−	0.479411i
$515$	−0.911393	−	1.57858i	−0.0401608	−	0.0695605i
$516$	−4.61115	+	7.98675i	−0.202995	+	0.351597i
$517$	−46.0558			−2.02553
$518$	−11.6255	+	48.3137i	−0.510797	+	2.12278i
$519$	−3.99948			−0.175558
$520$	0.0309085	−	0.0535351i	0.00135543	−	0.00234767i
$521$	−0.0327177	−	0.0566688i	−0.00143339	−	0.00248271i	0.865308	−	0.501241i	$-0.167123\pi$
$521$	−0.0327177	−	0.0566688i	−0.00143339	−	0.00248271i	−0.866741	+	0.498758i	$0.833790\pi$
$522$	−9.66592	−	16.7419i	−0.423066	−	0.732772i
$523$	−12.5293	+	21.7014i	−0.547868	+	0.948935i	0.450553	+	0.892750i	$0.351227\pi$
$523$	−12.5293	+	21.7014i	−0.547868	+	0.948935i	−0.998420	+	0.0561850i	$0.982106\pi$
$524$	−16.3760			−0.715387
$525$	6.19270	−	1.83088i	0.270272	−	0.0799060i
$526$	−28.4585			−1.24085
$527$	16.6312	−	28.8061i	0.724467	−	1.25481i
$528$	−4.88233	−	8.45645i	−0.212476	−	0.368020i
$529$	9.19809	+	15.9316i	0.399917	+	0.692676i
$530$	−0.870043	+	1.50696i	−0.0377922	+	0.0654581i
$531$	−11.5288			−0.500307
$532$	14.1263	+	13.4193i	0.612453	+	0.581799i
$533$	0.515563			0.0223315
$534$	1.67570	−	2.90240i	0.0725148	−	0.125599i
$535$	−0.503593	−	0.872249i	−0.0217722	−	0.0377106i
$536$	−0.439497	−	0.761231i	−0.0189834	−	0.0328802i
$537$	−3.18862	+	5.52286i	−0.137599	+	0.238329i
$538$	29.3254			1.26431
$539$	−26.3526	+	17.0749i	−1.13509	+	0.735466i
$540$	2.86844			0.123438
$541$	14.4534	−	25.0340i	0.621399	−	1.07629i	−0.367827	−	0.929894i	$-0.619898\pi$
$541$	14.4534	−	25.0340i	0.621399	−	1.07629i	0.989226	−	0.146400i	$-0.0467685\pi$
$542$	1.10372	+	1.91169i	0.0474087	+	0.0821143i
$543$	1.66276	+	2.87999i	0.0713561	+	0.123592i
$544$	−21.1404	+	36.6162i	−0.906386	+	1.56991i
$545$	−2.64431			−0.113270
$546$	−1.00458	−	0.954304i	−0.0429922	−	0.0408404i
$547$	−6.28935			−0.268913			−0.134457	−	0.990919i	$-0.542929\pi$
$547$	−6.28935			−0.268913			−0.134457	+	0.990919i	$0.542929\pi$
$548$	−13.5157	+	23.4098i	−0.577361	+	1.00002i
$549$	−21.0753	−	36.5035i	−0.899473	−	1.55793i
$550$	−20.9211	−	36.2364i	−0.892079	−	1.54513i
$551$	7.02114	−	12.1610i	0.299111	−	0.518075i
$552$	−0.257268			−0.0109501
$553$	17.8256	−	5.27016i	0.758024	−	0.224110i
$554$	8.08712			0.343589
$555$	−1.26693	+	2.19438i	−0.0537780	+	0.0931463i
$556$	16.7212	+	28.9620i	0.709137	+	1.22826i
$557$	−9.19562	−	15.9273i	−0.389631	−	0.674860i	0.602769	−	0.797916i	$-0.294064\pi$
$557$	−9.19562	−	15.9273i	−0.389631	−	0.674860i	−0.992400	+	0.123055i	$0.960731\pi$
$558$	16.6420	−	28.8249i	0.704514	−	1.22025i
$559$	−4.90037			−0.207263
$560$	1.34736	−	5.59939i	0.0569363	−	0.236617i
$561$	12.4508			0.525672
$562$	−18.4524	+	31.9605i	−0.778368	+	1.34817i
$563$	−3.71660	−	6.43734i	−0.156636	−	0.271302i	0.777017	−	0.629479i	$-0.216732\pi$
$563$	−3.71660	−	6.43734i	−0.156636	−	0.271302i	−0.933654	+	0.358177i	$0.883398\pi$
$564$	−4.98086	−	8.62709i	−0.209732	−	0.363266i
$565$	−3.87859	+	6.71791i	−0.163173	+	0.282625i
$566$	13.9049			0.584467
$567$	4.13373	−	17.1791i	0.173600	−	0.721453i
$568$	−1.48282			−0.0622178
$569$	4.61510	−	7.99359i	0.193475	−	0.335109i	−0.752924	−	0.658107i	$-0.771357\pi$
$569$	4.61510	−	7.99359i	0.193475	−	0.335109i	0.946400	+	0.322998i	$0.104691\pi$
$570$	1.02466	+	1.77476i	0.0429181	+	0.0743364i
$571$	8.06880	+	13.9756i	0.337669	+	0.584860i	0.983994	−	0.178203i	$-0.0570283\pi$
$571$	8.06880	+	13.9756i	0.337669	+	0.584860i	−0.646325	+	0.763062i	$0.723695\pi$
$572$	−2.17623	+	3.76935i	−0.0909929	+	0.157604i
$573$	−6.57628			−0.274728
$574$	4.99894	−	1.47794i	0.208652	−	0.0616881i
$575$	−10.1579			−0.423615
$576$	−9.60999	+	16.6450i	−0.400416	+	0.693541i
$577$	−9.25155	−	16.0242i	−0.385147	−	0.667094i	0.606643	−	0.794975i	$-0.292516\pi$
$577$	−9.25155	−	16.0242i	−0.385147	−	0.667094i	−0.991790	+	0.127880i	$0.959183\pi$
$578$	−11.8049	−	20.4468i	−0.491021	−	0.850473i
$579$	5.19252	−	8.99370i	0.215794	−	0.373765i
$580$	3.48185			0.144576
$581$	13.9169	+	13.2204i	0.577371	+	0.548473i
$582$	−19.6082			−0.812787
$583$	−3.84217	+	6.65483i	−0.159126	+	0.275615i
$584$	0.406608	+	0.704267i	0.0168256	+	0.0291428i
$585$	0.363381	+	0.629395i	0.0150240	+	0.0260223i
$586$	7.93151	−	13.7378i	0.327648	−	0.567502i
$587$	−28.8110			−1.18916			−0.594579	−	0.804037i	$-0.702681\pi$
$587$	−28.8110			−1.18916			−0.594579	+	0.804037i	$0.702681\pi$
$588$	−6.04842	−	3.08971i	−0.249433	−	0.127418i
$589$	24.1769			0.996193
$590$	2.14156	−	3.70930i	0.0881668	−	0.152709i
$591$	−5.21109	−	9.02588i	−0.214356	−	0.371275i
$592$	−20.1243	−	34.8563i	−0.827105	−	1.43259i
$593$	−21.8076	+	37.7718i	−0.895529	+	1.55110i	−0.0623811	+	0.998052i	$0.519869\pi$
$593$	−21.8076	+	37.7718i	−0.895529	+	1.55110i	−0.833148	+	0.553050i	$0.813464\pi$
$594$	26.1290			1.07209
$595$	5.32416	+	5.05768i	0.218269	+	0.207345i
$596$	29.5640			1.21099
$597$	1.69762	−	2.94037i	0.0694791	−	0.120341i
$598$	1.08977	+	1.88755i	0.0445642	+	0.0771875i
$599$	15.7335	+	27.2512i	0.642853	+	1.11345i	0.984793	+	0.173732i	$0.0555826\pi$
$599$	15.7335	+	27.2512i	0.642853	+	1.11345i	−0.341940	+	0.939722i	$0.611084\pi$
$600$	−0.283820	+	0.491590i	−0.0115869	+	0.0200691i
$601$	43.0423			1.75573			0.877866	−	0.478906i	$-0.158966\pi$
$601$	43.0423			1.75573			0.877866	+	0.478906i	$0.158966\pi$
$602$	−47.5144	+	14.0477i	−1.93654	+	0.572540i
$603$	10.3340			0.420835
$604$	16.0861	−	27.8620i	0.654536	−	1.13369i
$605$	2.35166	+	4.07319i	0.0956086	+	0.165599i
$606$	−9.99728	−	17.3158i	−0.406112	−	0.703407i
$607$	−15.5268	+	26.8932i	−0.630212	+	1.09156i	0.357296	+	0.933991i	$0.383699\pi$
$607$	−15.5268	+	26.8932i	−0.630212	+	1.09156i	−0.987508	+	0.157568i	$0.949635\pi$
$608$	−30.7319			−1.24634
$609$	−1.14517	+	4.75911i	−0.0464045	+	0.192849i
$610$	15.6596			0.634041
$611$	2.64663	−	4.58409i	0.107071	−	0.185453i
$612$	−13.8511	−	23.9907i	−0.559896	−	0.969768i
$613$	15.7543	+	27.2872i	0.636309	+	1.10212i	0.986236	+	0.165342i	$0.0528730\pi$
$613$	15.7543	+	27.2872i	0.636309	+	1.10212i	−0.349927	+	0.936777i	$0.613794\pi$
$614$	15.9503	−	27.6266i	0.643700	−	1.11492i
$615$	0.265805			0.0107183
$616$	0.645739	−	2.68358i	0.0260176	−	0.108124i
$617$	−47.8573			−1.92666			−0.963331	−	0.268315i	$-0.913533\pi$
$617$	−47.8573			−1.92666			−0.963331	+	0.268315i	$0.913533\pi$
$618$	1.79569	−	3.11022i	0.0722332	−	0.125112i
$619$	9.06760	+	15.7055i	0.364458	+	0.631259i	0.988689	−	0.149980i	$-0.0479210\pi$
$619$	9.06760	+	15.7055i	0.364458	+	0.631259i	−0.624231	+	0.781240i	$0.714588\pi$
$620$	2.99740	+	5.19164i	0.120378	+	0.208501i
$621$	3.17164	−	5.49344i	0.127273	−	0.220444i
$622$	3.42985			0.137525
$623$	8.37091	−	2.47486i	0.335373	−	0.0991533i
$624$	1.12227			0.0449266
$625$	−10.5418	+	18.2589i	−0.421672	+	0.730357i
$626$	−6.52135	−	11.2953i	−0.260646	−	0.451451i
$627$	4.52495	+	7.83745i	0.180709	+	0.312998i
$628$	−1.35598	+	2.34862i	−0.0541094	+	0.0937202i
$629$	51.3205			2.04628
$630$	5.32764	+	5.06098i	0.212258	+	0.201634i
$631$	−33.0495			−1.31568			−0.657839	−	0.753158i	$-0.728529\pi$
$631$	−33.0495			−1.31568			−0.657839	+	0.753158i	$0.728529\pi$
$632$	−0.816973	+	1.41504i	−0.0324974	+	0.0562872i
$633$	5.09668	+	8.82771i	0.202575	+	0.350870i
$634$	1.40347	+	2.43089i	0.0557391	+	0.0965430i
$635$	0.362122	−	0.627214i	0.0143704	−	0.0248902i
$636$	−1.66209			−0.0659064
$637$	−0.185147	−	3.60419i	−0.00733579	−	0.142803i
$638$	31.7166			1.25567
$639$	8.71653	−	15.0975i	0.344821	−	0.597247i
$640$	0.478773	+	0.829258i	0.0189251	+	0.0327793i
$641$	−6.60223	−	11.4354i	−0.260772	−	0.451671i	0.705675	−	0.708536i	$-0.250644\pi$
$641$	−6.60223	−	11.4354i	−0.260772	−	0.451671i	−0.966447	+	0.256865i	$0.917310\pi$
$642$	0.992214	−	1.71856i	0.0391596	−	0.0678263i
$643$	24.0434			0.948177			0.474089	−	0.880477i	$-0.342778\pi$
$643$	24.0434			0.948177			0.474089	+	0.880477i	$0.342778\pi$
$644$	7.74584	+	7.35815i	0.305229	+	0.289952i
$645$	−2.52645			−0.0994787
$646$	20.7533	−	35.9458i	0.816528	−	1.41427i
$647$	−10.7234	−	18.5735i	−0.421580	−	0.730199i	0.574514	−	0.818495i	$-0.305191\pi$
$647$	−10.7234	−	18.5735i	−0.421580	−	0.730199i	−0.996094	+	0.0882961i	$0.971858\pi$
$648$	0.776583	+	1.34508i	0.0305071	+	0.0528398i
$649$	9.45730	−	16.3805i	0.371231	−	0.642992i
$650$	4.80898			0.188624
$651$	−8.08194	+	2.38943i	−0.316756	+	0.0936492i
$652$	−14.9161			−0.584161
$653$	6.24621	−	10.8187i	0.244433	−	0.423370i	−0.717539	−	0.696518i	$-0.754732\pi$
$653$	6.24621	−	10.8187i	0.244433	−	0.423370i	0.961972	+	0.273148i	$0.0880648\pi$
$654$	−2.60500	−	4.51199i	−0.101863	−	0.176433i
$655$	−2.24309	−	3.88515i	−0.0876449	−	0.151805i
$656$	−2.11107	+	3.65648i	−0.0824235	+	0.142762i
$657$	−9.56073			−0.373000
$658$	12.5209	−	52.0348i	0.488117	−	2.02853i
$659$	−12.4259			−0.484046			−0.242023	−	0.970271i	$-0.577811\pi$
$659$	−12.4259			−0.484046			−0.242023	+	0.970271i	$0.577811\pi$
$660$	−1.12198	+	1.94333i	−0.0436732	+	0.0756442i
$661$	10.5969	+	18.3544i	0.412173	+	0.713905i	0.995127	−	0.0986002i	$-0.0314365\pi$
$661$	10.5969	+	18.3544i	0.412173	+	0.713905i	−0.582954	+	0.812505i	$0.698103\pi$
$662$	0.167945	+	0.290889i	0.00652737	+	0.0113057i
$663$	−0.715493	+	1.23927i	−0.0277874	+	0.0481292i
$664$	−1.68729			−0.0654796
$665$	−1.24874	+	5.18952i	−0.0484239	+	0.201241i
$666$	51.3539			1.98992
$667$	3.84988	−	6.66819i	0.149068	−	0.258193i
$668$	−7.40483	−	12.8255i	−0.286501	−	0.496235i
$669$	−5.90537	−	10.2284i	−0.228315	−	0.395453i
$670$	−1.91963	+	3.32490i	−0.0741619	+	0.128452i
$671$	69.1541			2.66966
$672$	10.2732	−	3.03727i	0.396296	−	0.117165i
$673$	−7.84607			−0.302444			−0.151222	−	0.988500i	$-0.548321\pi$
$673$	−7.84607			−0.302444			−0.151222	+	0.988500i	$0.548321\pi$
$674$	−0.120100	+	0.208019i	−0.00462607	+	0.00801258i
$675$	−6.99794	−	12.1208i	−0.269351	−	0.466529i
$676$	11.9826	+	20.7545i	0.460871	+	0.798252i
$677$	12.2380	−	21.1968i	0.470344	−	0.814660i	−0.529080	−	0.848572i	$-0.677463\pi$
$677$	12.2380	−	21.1968i	0.470344	−	0.814660i	0.999425	+	0.0339112i	$0.0107963\pi$
$678$	−15.2837			−0.586968
$679$	−37.0279	−	35.1746i	−1.42100	−	1.34988i
$680$	−0.645503			−0.0247539
$681$	−0.0909912	+	0.157601i	−0.00348679	+	0.00603930i
$682$	27.3036	+	47.2913i	1.04551	+	1.81088i
$683$	22.6464	+	39.2247i	0.866539	+	1.50089i	0.865510	+	0.500891i	$0.166994\pi$
$683$	22.6464	+	39.2247i	0.866539	+	1.50089i	0.00102891	+	0.999999i	$0.499672\pi$
$684$	10.0677	−	17.4378i	0.384948	−	0.666750i
$685$	−7.40522			−0.282939
$686$	−12.1272	−	34.4158i	−0.463017	−	1.31400i
$687$	−6.98275			−0.266409
$688$	20.0655	−	34.7545i	0.764990	−	1.32500i
$689$	−0.441586	−	0.764849i	−0.0168231	−	0.0291384i
$690$	0.561847	+	0.973148i	0.0213892	+	0.0370471i
$691$	−25.4275	+	44.0417i	−0.967308	+	1.67543i	−0.264026	+	0.964516i	$0.585050\pi$
$691$	−25.4275	+	44.0417i	−0.967308	+	1.67543i	−0.703282	+	0.710911i	$0.748283\pi$
$692$	−14.5993			−0.554983
$693$	23.5272	+	22.3496i	0.893725	+	0.848993i
$694$	−10.0995			−0.383372
$695$	−4.58076	+	7.93411i	−0.173758	+	0.300958i
$696$	−0.215137	−	0.372628i	−0.00815473	−	0.0141244i
$697$	−2.69180	−	4.66233i	−0.101959	−	0.176598i
$698$	−31.3921	+	54.3726i	−1.18821	+	2.05804i
$699$	−7.47251			−0.282636
$700$	22.6053	−	6.68326i	0.854399	−	0.252604i
$701$	22.8323			0.862366			0.431183	−	0.902265i	$-0.358096\pi$
$701$	22.8323			0.862366			0.431183	+	0.902265i	$0.358096\pi$
$702$	−1.50152	+	2.60071i	−0.0566712	+	0.0981574i
$703$	18.6513	+	32.3049i	0.703445	+	1.21840i
$704$	−15.7665	−	27.3084i	−0.594224	−	1.02923i
$705$	1.36450	−	2.36339i	0.0513901	−	0.0890103i
$706$	−26.9937			−1.01592
$707$	12.1836	−	50.6327i	0.458210	−	1.90424i
$708$	4.09116			0.153755
$709$	5.21503	−	9.03270i	0.195855	−	0.339230i	−0.751326	−	0.659932i	$-0.770585\pi$
$709$	5.21503	−	9.03270i	0.195855	−	0.339230i	0.947180	+	0.320701i	$0.103919\pi$
$710$	3.23833	+	5.60896i	0.121532	+	0.210500i
$711$	−9.60489	−	16.6362i	−0.360211	−	0.623904i
$712$	−0.383650	+	0.664501i	−0.0143779	+	0.0249032i
$713$	13.2569			0.496474
$714$	−3.38492	+	14.0671i	−0.126678	+	0.526450i
$715$	−1.19236			−0.0445916
$716$	−11.6395	+	20.1601i	−0.434987	+	0.753420i
$717$	1.46122	+	2.53090i	0.0545701	+	0.0945183i
$718$	−18.4038	−	31.8763i	−0.686824	−	1.18961i
$719$	19.2010	−	33.2572i	0.716078	−	1.24028i	−0.246464	−	0.969152i	$-0.579269\pi$
$719$	19.2010	−	33.2572i	0.716078	−	1.24028i	0.962542	−	0.271132i	$-0.0873980\pi$
$720$	−5.95174			−0.221808
$721$	8.97029	−	2.65207i	0.334071	−	0.0987683i
$722$	−7.26585			−0.270407
$723$	3.84595	−	6.66139i	0.143033	−	0.247740i
$724$	6.06960	+	10.5129i	0.225575	+	0.390707i
$725$	−8.49443	−	14.7128i	−0.315475	−	0.546419i
$726$	−4.63340	+	8.02529i	−0.171962	+	0.297846i
$727$	3.22664			0.119669			0.0598347	−	0.998208i	$-0.480943\pi$
$727$	3.22664			0.119669			0.0598347	+	0.998208i	$0.480943\pi$
$728$	0.229998	+	0.218486i	0.00852430	+	0.00809764i
$729$	−13.6875			−0.506946
$730$	1.77598	−	3.07609i	0.0657321	−	0.113851i
$731$	25.5852	+	44.3149i	0.946304	+	1.63905i
$732$	7.47889	+	12.9538i	0.276428	+	0.478787i
$733$	10.3062	−	17.8509i	0.380668	−	0.659337i	−0.610490	−	0.792024i	$-0.709027\pi$
$733$	10.3062	−	17.8509i	0.380668	−	0.659337i	0.991158	+	0.132688i	$0.0423607\pi$
$734$	−35.6991			−1.31768
$735$	−0.0954549	−	1.85818i	−0.00352091	−	0.0685401i
$736$	−16.8512			−0.621142
$737$	−8.47723	+	14.6830i	−0.312263	+	0.540855i
$738$	−2.69355	−	4.66537i	−0.0991510	−	0.171735i
$739$	15.8841	+	27.5121i	0.584307	+	1.01205i	0.994961	+	0.100258i	$0.0319669\pi$
$739$	15.8841	+	27.5121i	0.584307	+	1.01205i	−0.410655	+	0.911791i	$0.634700\pi$
$740$	−4.62467	+	8.01017i	−0.170006	+	0.294460i
$741$	−1.04012			−0.0382097
$742$	−6.47421	−	6.15017i	−0.237676	−	0.225780i
$743$	−38.9143			−1.42763			−0.713813	−	0.700337i	$-0.753033\pi$
$743$	−38.9143			−1.42763			−0.713813	+	0.700337i	$0.753033\pi$
$744$	0.370406	−	0.641562i	0.0135797	−	0.0235208i
$745$	4.04952	+	7.01397i	0.148363	+	0.256972i
$746$	12.1062	+	20.9686i	0.443240	+	0.767714i
$747$	9.91847	−	17.1793i	0.362898	−	0.628558i
$748$	45.4492			1.66179
$749$	4.95656	−	1.46541i	0.181109	−	0.0535450i
$750$	5.09787			0.186148
$751$	9.36426	−	16.2194i	0.341707	−	0.591853i	−0.643043	−	0.765830i	$-0.722328\pi$
$751$	9.36426	−	16.2194i	0.341707	−	0.591853i	0.984750	+	0.173977i	$0.0556618\pi$
$752$	21.6743	+	37.5409i	0.790379	+	1.36898i
$753$	0.0680313	+	0.117834i	0.00247920	+	0.00429409i
$754$	−1.82262	+	3.15686i	−0.0663758	+	0.114966i
$755$	8.81358			0.320759
$756$	−3.44377	+	14.3117i	−0.125249	+	0.520512i
$757$	−7.02375			−0.255282			−0.127641	−	0.991820i	$-0.540741\pi$
$757$	−7.02375			−0.255282			−0.127641	+	0.991820i	$0.540741\pi$
$758$	−24.2031	+	41.9210i	−0.879097	+	1.52264i
$759$	2.48116	+	4.29749i	0.0900603	+	0.155989i
$760$	−0.234593	−	0.406328i	−0.00850960	−	0.0147391i
$761$	6.48763	−	11.2369i	0.235176	−	0.407338i	−0.724147	−	0.689645i	$-0.757767\pi$
$761$	6.48763	−	11.2369i	0.235176	−	0.407338i	0.959324	+	0.282308i	$0.0910999\pi$
$762$	1.42696			0.0516932
$763$	3.17468	−	13.1934i	0.114931	−	0.477633i
$764$	−24.0054			−0.868486
$765$	3.79449	−	6.57225i	0.137190	−	0.237620i
$766$	−20.2748	−	35.1171i	−0.732560	−	1.26883i
$767$	1.08694	+	1.88263i	0.0392471	+	0.0679780i
$768$	−4.56745	+	7.91105i	−0.164814	+	0.285466i
$769$	39.1892			1.41320			0.706599	−	0.707615i	$-0.250229\pi$
$769$	39.1892			1.41320			0.706599	+	0.707615i	$0.250229\pi$
$770$	−11.5612	+	3.41807i	−0.416636	+	0.123179i
$771$	3.28409			0.118274
$772$	18.9543	−	32.8298i	0.682180	−	1.18157i
$773$	−8.23834	−	14.2692i	−0.296312	−	0.513228i	0.678977	−	0.734160i	$-0.262424\pi$
$773$	−8.23834	−	14.2692i	−0.296312	−	0.513228i	−0.975289	+	0.220931i	$0.929090\pi$
$774$	25.6019	+	44.3438i	0.920241	+	1.59390i
$775$	14.6251	−	25.3314i	0.525348	−	0.909929i
$776$	4.48927			0.161156
$777$	−9.42753	−	8.95566i	−0.338211	−	0.321283i
$778$	3.11147			0.111551
$779$	1.95654	−	3.38883i	0.0701005	−	0.121418i
$780$	−0.128951	−	0.223350i	−0.00461719	−	0.00799721i
$781$	14.3007	+	24.7695i	0.511719	+	0.886324i
$782$	11.3796	−	19.7101i	0.406934	−	0.704830i
$783$	10.6089			0.379133
$784$	26.3198	+	13.4449i	0.939992	+	0.480176i
$785$	−0.742938			−0.0265166
$786$	4.41950	−	7.65479i	0.157638	−	0.273037i
$787$	−3.47810	−	6.02424i	−0.123981	−	0.214741i	0.797353	−	0.603513i	$-0.206233\pi$
$787$	−3.47810	−	6.02424i	−0.123981	−	0.214741i	−0.921334	+	0.388772i	$0.872899\pi$
$788$	−19.0221	−	32.9472i	−0.677634	−	1.17370i
$789$	3.72339	−	6.44910i	0.132556	−	0.229594i
$790$	7.13674			0.253914
$791$	−28.8616	−	27.4170i	−1.02620	−	0.974837i
$792$	−2.85245			−0.101357
$793$	−3.97399	+	6.88315i	−0.141120	+	0.244428i
$794$	−30.3223	−	52.5198i	−1.07610	−	1.86386i
$795$	−0.227665	−	0.394327i	−0.00807445	−	0.0139854i
$796$	6.19685	−	10.7333i	0.219642	−	0.380430i
$797$	−39.3286			−1.39309			−0.696545	−	0.717513i	$-0.745280\pi$
$797$	−39.3286			−1.39309			−0.696545	+	0.717513i	$0.745280\pi$
$798$	−10.0851	+	2.98166i	−0.357008	+	0.105550i
$799$	−55.2731			−1.95542
$800$	−18.5903	+	32.1993i	−0.657266	+	1.13842i
$801$	−4.51045	−	7.81232i	−0.159369	−	0.276035i
$802$	−1.90734	−	3.30362i	−0.0673506	−	0.116655i
$803$	7.84286	−	13.5842i	0.276769	−	0.479377i
$804$	−3.66719			−0.129332
$805$	−0.684716	+	2.84556i	−0.0241331	+	0.100293i
$806$	−6.27608			−0.221066
$807$	−3.83681	+	6.64554i	−0.135062	+	0.233934i
$808$	2.28886	+	3.96443i	0.0805219	+	0.139468i
$809$	9.05939	+	15.6913i	0.318511	+	0.551677i	0.980178	−	0.198121i	$-0.0634838\pi$
$809$	9.05939	+	15.6913i	0.318511	+	0.551677i	−0.661666	+	0.749798i	$0.730151\pi$
$810$	3.39196	−	5.87504i	0.119181	−	0.206428i
$811$	33.5622			1.17853			0.589264	−	0.807940i	$-0.299418\pi$
$811$	33.5622			1.17853			0.589264	+	0.807940i	$0.299418\pi$
$812$	−4.18021	+	17.3722i	−0.146697	+	0.609646i
$813$	−0.577622			−0.0202581
$814$	−42.1267	+	72.9655i	−1.47654	+	2.55744i
$815$	−2.04314	−	3.53881i	−0.0715679	−	0.123959i
$816$	−5.85944	−	10.1489i	−0.205122	−	0.355281i
$817$	−18.5967	+	32.2105i	−0.650617	+	1.12690i
$818$	10.1399			0.354535
$819$	−3.57654	+	1.05741i	−0.124975	+	0.0369488i
$820$	0.970270			0.0338833
$821$	−5.83897	+	10.1134i	−0.203781	+	0.352960i	−0.949744	−	0.313028i	$-0.898657\pi$
$821$	−5.83897	+	10.1134i	−0.203781	+	0.352960i	0.745962	+	0.665988i	$0.231990\pi$
$822$	−7.29514	−	12.6356i	−0.254447	−	0.440716i
$823$	−5.45235	−	9.44374i	−0.190057	−	0.329188i	0.755212	−	0.655481i	$-0.227534\pi$
$823$	−5.45235	−	9.44374i	−0.190057	−	0.329188i	−0.945269	+	0.326293i	$0.894201\pi$
$824$	−0.411120	+	0.712081i	−0.0143221	+	0.0248065i
$825$	10.9489			0.381192
$826$	15.9359	+	15.1383i	0.554482	+	0.526729i
$827$	−28.0860			−0.976647			−0.488324	−	0.872663i	$-0.662391\pi$
$827$	−28.0860			−0.976647			−0.488324	+	0.872663i	$0.662391\pi$
$828$	5.52039	−	9.56160i	0.191847	−	0.332289i
$829$	24.0497	+	41.6553i	0.835281	+	1.44675i	0.893801	+	0.448463i	$0.148028\pi$
$829$	24.0497	+	41.6553i	0.835281	+	1.44675i	−0.0585206	+	0.998286i	$0.518638\pi$
$830$	3.68487	+	6.38239i	0.127904	+	0.221536i
$831$	−1.05808	+	1.83265i	−0.0367045	+	0.0635740i
$832$	3.62414			0.125644
$833$	−31.6267	+	20.4921i	−1.09580	+	0.710009i
$834$	−18.0507			−0.625044
$835$	2.02855	−	3.51355i	0.0702008	−	0.121591i
$836$	16.5175	+	28.6091i	0.571269	+	0.989467i
$837$	9.13283	+	15.8185i	0.315677	+	0.546768i
$838$	1.23624	−	2.14123i	0.0427051	−	0.0739675i
$839$	48.3307			1.66856			0.834281	−	0.551340i	$-0.185883\pi$
$839$	48.3307			1.66856			0.834281	+	0.551340i	$0.185883\pi$
$840$	0.118578	+	0.112643i	0.00409134	+	0.00388657i
$841$	−16.1224			−0.555944
$842$	−1.42617	+	2.47020i	−0.0491490	+	0.0851286i
$843$	−4.82846	−	8.36314i	−0.166301	−	0.288042i
$844$	18.6045	+	32.2239i	0.640392	+	1.10919i
$845$	−3.28264	+	5.68570i	−0.112926	+	0.195594i
$846$	−55.3091			−1.90157
$847$	−23.1460	+	6.84312i	−0.795305	+	0.235133i
$848$	7.23263			0.248369
$849$	−1.81926	+	3.15105i	−0.0624367	+	0.108144i
$850$	−25.1081	−	43.4885i	−0.861201	−	1.49164i
$851$	10.2270	+	17.7137i	0.350577	+	0.607217i
$852$	−3.09319	+	5.35756i	−0.105971	+	0.183547i
$853$	−0.00307791			−0.000105386			−5.26929e−5	−	1.00000i	$-0.500017\pi$
$853$	−0.00307791			−0.000105386			−5.26929e−5		1.00000i	$0.500017\pi$
$854$	−18.8005	+	78.1317i	−0.643341	+	2.67361i
$855$	5.51608			0.188646
$856$	−0.227166	+	0.393463i	−0.00776437	+	0.0134483i
$857$	15.6325	+	27.0763i	0.533997	+	0.924909i	0.999211	+	0.0397114i	$0.0126439\pi$
$857$	15.6325	+	27.0763i	0.533997	+	0.924909i	−0.465215	+	0.885198i	$0.654023\pi$
$858$	−1.17463	−	2.03452i	−0.0401013	−	0.0694574i
$859$	−19.5520	+	33.8650i	−0.667105	+	1.15546i	0.311605	+	0.950212i	$0.399133\pi$
$859$	−19.5520	+	33.8650i	−0.667105	+	1.15546i	−0.978710	+	0.205248i	$0.934200\pi$
$860$	−9.22231			−0.314478
$861$	−0.319118	+	1.32620i	−0.0108755	+	0.0451967i
$862$	15.7963			0.538025
$863$	−18.9978	+	32.9051i	−0.646692	+	1.12010i	0.337216	+	0.941427i	$0.390515\pi$
$863$	−18.9978	+	32.9051i	−0.646692	+	1.12010i	−0.983908	+	0.178676i	$0.942819\pi$
$864$	−11.6090	−	20.1074i	−0.394946	−	0.684066i
$865$	−1.99974	−	3.46365i	−0.0679932	−	0.117768i
$866$	36.4344	−	63.1062i	1.23809	−	2.14444i
$867$	6.17802			0.209817
$868$	−29.5016	+	8.72216i	−1.00135	+	0.296049i
$869$	31.5163			1.06912
$870$	−0.939673	+	1.62756i	−0.0318579	+	0.0551795i
$871$	−0.974300	−	1.68754i	−0.0330129	−	0.0571800i
$872$	0.596410	+	1.03301i	0.0201970	+	0.0349822i
$873$	−26.3895	+	45.7079i	−0.893148	+	1.54698i
$874$	16.5426			0.559563
$875$	9.62674	+	9.14491i	0.325443	+	0.309154i
$876$	3.39277			0.114631
$877$	5.15750	−	8.93305i	0.174156	−	0.301648i	−0.765713	−	0.643183i	$-0.777614\pi$
$877$	5.15750	−	8.93305i	0.174156	−	0.301648i	0.939869	+	0.341535i	$0.110947\pi$
$878$	−6.51472	−	11.2838i	−0.219861	−	0.380811i
$879$	2.07545	+	3.59478i	0.0700031	+	0.121249i
$880$	4.88233	−	8.45645i	0.164583	−	0.285067i
$881$	−37.4138			−1.26050			−0.630252	−	0.776391i	$-0.717048\pi$
$881$	−37.4138			−1.26050			−0.630252	+	0.776391i	$0.717048\pi$
$882$	−31.6473	+	20.5054i	−1.06562	+	0.690454i
$883$	32.8240			1.10462			0.552308	−	0.833640i	$-0.313747\pi$
$883$	32.8240			1.10462			0.552308	+	0.833640i	$0.313747\pi$
$884$	−2.61177	+	4.52372i	−0.0878433	+	0.152149i
$885$	0.560386	+	0.970616i	0.0188372	+	0.0326269i
$886$	16.8559	+	29.1952i	0.566284	+	0.980832i
$887$	−0.416932	+	0.722148i	−0.0139992	+	0.0242474i	−0.872940	−	0.487827i	$-0.837790\pi$
$887$	−0.416932	+	0.722148i	−0.0139992	+	0.0242474i	0.858941	+	0.512075i	$0.171123\pi$
$888$	1.14300			0.0383564
$889$	2.69464	+	2.55977i	0.0903754	+	0.0858520i
$890$	3.35141			0.112339
$891$	14.9791	−	25.9446i	0.501819	−	0.869176i
$892$	−21.5564	−	37.3368i	−0.721762	−	1.25013i
$893$	−20.0877	−	34.7930i	−0.672211	−	1.16430i
$894$	−7.97864	+	13.8194i	−0.266846	+	0.462190i
$895$	−6.37725			−0.213168
$896$	−4.71227	+	1.39319i	−0.157426	+	0.0465431i
$897$	−0.570325			−0.0190426
$898$	−28.6391	+	49.6044i	−0.955701	+	1.65532i
$899$	11.0859	+	19.2013i	0.369734	+	0.640399i
$900$	−12.1803	−	21.0968i	−0.406009	−	0.703228i
$901$	−4.61111	+	7.98668i	−0.153618	+	0.266075i
$902$	8.83830			0.294283
$903$	3.03318	−	12.6054i	0.100938	−	0.419480i
$904$	3.49919			0.116381
$905$	−1.66276	+	2.87999i	−0.0552722	+	0.0957342i
$906$	8.68257	+	15.0386i	0.288459	+	0.499626i
$907$	−25.0611	−	43.4070i	−0.832139	−	1.44131i	−0.896339	−	0.443370i	$-0.853783\pi$
$907$	−25.0611	−	43.4070i	−0.832139	−	1.44131i	0.0641996	−	0.997937i	$-0.479551\pi$
$908$	−0.332146	+	0.575294i	−0.0110227	+	0.0190918i
$909$	−53.8189			−1.78506
$910$	0.324159	−	1.34715i	0.0107458	−	0.0446575i
$911$	15.0089			0.497266			0.248633	−	0.968598i	$-0.420019\pi$
$911$	15.0089			0.497266			0.248633	+	0.968598i	$0.420019\pi$
$912$	4.25896	−	7.37674i	0.141028	−	0.244268i
$913$	16.2727	+	28.1851i	0.538546	+	0.932789i
$914$	28.4548	+	49.2852i	0.941201	+	1.63021i
$915$	−2.04884	+	3.54869i	−0.0677325	+	0.117316i
$916$	−25.4892			−0.842187
$917$	22.0774	−	6.52720i	0.729060	−	0.215547i
$918$	31.3582			1.03498
$919$	−20.8279	+	36.0749i	−0.687048	+	1.19000i	0.285741	+	0.958307i	$0.407760\pi$
$919$	−20.8279	+	36.0749i	−0.687048	+	1.19000i	−0.972789	+	0.231694i	$0.925573\pi$
$920$	−0.128634	−	0.222801i	−0.00424094	−	0.00734552i
$921$	4.17372	+	7.22909i	0.137529	+	0.238207i
$922$	39.6720	−	68.7140i	1.30653	−	2.26297i
$923$	−3.28720			−0.108199
$924$	−8.34898	−	7.93110i	−0.274661	−	0.260914i
$925$	45.1299			1.48386
$926$	1.12905	−	1.95557i	0.0371029	−	0.0642641i
$927$	−4.83341	−	8.37171i	−0.158750	−	0.274963i
$928$	−14.0915	−	24.4073i	−0.462577	−	0.801207i
$929$	−9.37244	+	16.2335i	−0.307500	+	0.532605i	−0.977815	−	0.209471i	$-0.932826\pi$
$929$	−9.37244	+	16.2335i	−0.307500	+	0.532605i	0.670315	+	0.742077i	$0.266159\pi$
$930$	−3.23571			−0.106103
$931$	−24.3932	−	12.4608i	−0.799456	−	0.408386i
$932$	−27.2770			−0.893487
$933$	−0.448747	+	0.777252i	−0.0146913	+	0.0254461i
$934$	33.1184	+	57.3627i	1.08367	+	1.87696i
$935$	6.22539	+	10.7827i	0.203592	+	0.352632i
$936$	0.163918	−	0.283914i	0.00535782	−	0.00928001i
$937$	31.6122			1.03272			0.516362	−	0.856370i	$-0.327286\pi$
$937$	31.6122			1.03272			0.516362	+	0.856370i	$0.327286\pi$
$938$	−14.2845	−	13.5695i	−0.466405	−	0.443061i
$939$	3.41290			0.111376
$940$	4.98086	−	8.62709i	0.162458	−	0.281385i
$941$	6.64299	+	11.5060i	0.216555	+	0.375085i	0.953753	−	0.300593i	$-0.0971845\pi$
$941$	6.64299	+	11.5060i	0.216555	+	0.375085i	−0.737197	+	0.675678i	$0.763851\pi$
$942$	−0.731894	−	1.26768i	−0.0238464	−	0.0413032i
$943$	1.07283	−	1.85819i	0.0349360	−	0.0605110i
$944$	−17.8027			−0.579430
$945$	−3.86712	+	1.14332i	−0.125797	+	0.0371921i
$946$	−84.0071			−2.73131
$947$	−5.86372	+	10.1563i	−0.190545	+	0.330034i	−0.945431	−	0.325822i	$-0.894359\pi$
$947$	−5.86372	+	10.1563i	−0.190545	+	0.330034i	0.754886	+	0.655856i	$0.227692\pi$
$948$	3.40844	+	5.90359i	0.110701	+	0.191740i
$949$	0.901391	+	1.56125i	0.0292604	+	0.0506805i
$950$	18.2499	−	31.6098i	0.592106	−	1.02556i
$951$	−0.734498			−0.0238177
$952$	0.774973	−	3.22065i	0.0251170	−	0.104382i
$953$	−26.4827			−0.857858			−0.428929	−	0.903338i	$-0.641109\pi$
$953$	−26.4827			−0.857858			−0.428929	+	0.903338i	$0.641109\pi$
$954$	−4.61412	+	7.99188i	−0.149388	+	0.258747i
$955$	−3.28814	−	5.69522i	−0.106402	−	0.184293i
$956$	5.33389	+	9.23857i	0.172510	+	0.298797i
$957$	−4.14966	+	7.18742i	−0.134139	+	0.232336i
$958$	60.5018			1.95472
$959$	8.89050	−	36.9473i	0.287089	−	1.19309i
$960$	1.86847			0.0603046
$961$	−3.58680	+	6.21252i	−0.115703	+	0.200404i
$962$	−4.84167	−	8.38603i	−0.156102	−	0.270376i
$963$	−2.67072	−	4.62582i	−0.0860626	−	0.149065i
$964$	14.0389	−	24.3161i	0.452163	−	0.783169i
$965$	10.3850			0.334306
$966$	−5.52992	+	1.63493i	−0.177922	+	0.0526029i
$967$	−56.8542			−1.82831			−0.914154	−	0.405367i	$-0.867144\pi$
$967$	−56.8542			−1.82831			−0.914154	+	0.405367i	$0.867144\pi$
$968$	1.06081	−	1.83738i	0.0340957	−	0.0590556i
$969$	5.43054	+	9.40598i	0.174454	+	0.302164i
$970$	−9.80411	−	16.9812i	−0.314791	−	0.545234i
$971$	−14.4468	+	25.0225i	−0.463619	+	0.803011i	−0.999138	−	0.0415118i	$-0.986783\pi$
$971$	−14.4468	+	25.0225i	−0.463619	+	0.803011i	0.535519	+	0.844523i	$0.320116\pi$
$972$	23.1710			0.743210
$973$	−34.0866	−	32.3806i	−1.09277	−	1.03807i
$974$	64.1030			2.05399
$975$	−0.629186	+	1.08978i	−0.0201501	+	0.0349010i
$976$	−32.5445	−	56.3687i	−1.04172	−	1.80432i
$977$	−17.2480	−	29.8745i	−0.551813	−	0.955769i	−0.998144	−	0.0609007i	$-0.980603\pi$
$977$	−17.2480	−	29.8745i	−0.551813	−	0.955769i	0.446330	−	0.894868i	$-0.352731\pi$
$978$	4.02553	−	6.97242i	0.128722	−	0.222953i
$979$	14.8000			0.473012
$980$	−0.348440	−	6.78294i	−0.0111305	−	0.216673i
$981$	−14.0236			−0.447739
$982$	12.7585	−	22.0983i	0.407139	−	0.705185i
$983$	20.5448	+	35.5847i	0.655279	+	1.13498i	0.981824	+	0.189794i	$0.0607821\pi$
$983$	20.5448	+	35.5847i	0.655279	+	1.13498i	−0.326545	+	0.945182i	$0.605885\pi$
$984$	−0.0599510	−	0.103838i	−0.00191117	−	0.00331024i
$985$	5.21109	−	9.02588i	0.166039	−	0.287588i
$986$	38.0641			1.21221
$987$	10.1536	+	9.64541i	0.323193	+	0.307017i
$988$	−3.79675			−0.120791
$989$	−10.1971	+	17.6619i	−0.324249	+	0.561616i
$990$	6.22945	+	10.7897i	0.197985	+	0.342920i
$991$	−15.8597	−	27.4697i	−0.503799	−	0.872605i	−0.999990	−	0.00439180i	$-0.998602\pi$
$991$	−15.8597	−	27.4697i	−0.503799	−	0.872605i	0.496192	−	0.868213i	$-0.334731\pi$
$992$	24.2617	−	42.0226i	0.770311	−	1.33422i
$993$	−0.0878928			−0.00278919
$994$	−31.8730	+	9.42326i	−1.01095	+	0.298888i
$995$	3.39525			0.107637
$996$	−3.51972	+	6.09633i	−0.111527	+	0.193170i
$997$	1.46607	+	2.53931i	0.0464310	+	0.0804208i	0.888307	−	0.459250i	$-0.151882\pi$
$997$	1.46607	+	2.53931i	0.0464310	+	0.0804208i	−0.841876	+	0.539671i	$0.818549\pi$
$998$	3.89672	+	6.74932i	0.123349	+	0.213646i
$999$	−14.0910	+	24.4064i	−0.445820	+	0.772183i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	287.2.e.c.247.1	yes	10
7.2	even	3		2009.2.a.l.1.5		5
7.4	even	3	inner	287.2.e.c.165.1	✓	10
7.5	odd	6		2009.2.a.m.1.5		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
287.2.e.c.165.1	✓	10	7.4	even	3	inner
287.2.e.c.247.1	yes	10	1.1	even	1	trivial
2009.2.a.l.1.5		5	7.2	even	3
2009.2.a.m.1.5		5	7.5	odd	6

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)

\(f(q)\)	\(=\)	\(q+(-0.985135 + 1.70630i) q^{2} +(-0.257781 - 0.446490i) q^{3} +(-0.940981 - 1.62983i) q^{4} +(0.257781 - 0.446490i) q^{5} +1.01580 q^{6} +(1.91822 + 1.82221i) q^{7} -0.232565 q^{8} +(1.36710 - 2.36788i) q^{9} +O(q^{10})\)	\(q+(-0.985135 + 1.70630i) q^{2} +(-0.257781 - 0.446490i) q^{3} +(-0.940981 - 1.62983i) q^{4} +(0.257781 - 0.446490i) q^{5} +1.01580 q^{6} +(1.91822 + 1.82221i) q^{7} -0.232565 q^{8} +(1.36710 - 2.36788i) q^{9} +(0.507899 + 0.879706i) q^{10} +(2.24292 + 3.88484i) q^{11} +(-0.485135 + 0.840278i) q^{12} -0.515563 q^{13} +(-4.99894 + 1.47794i) q^{14} -0.265805 q^{15} +(2.11107 - 3.65648i) q^{16} +(2.69180 + 4.66233i) q^{17} +(2.69355 + 4.66537i) q^{18} +(-1.95654 + 3.38883i) q^{19} -0.970270 q^{20} +(0.319118 - 1.32620i) q^{21} -8.83830 q^{22} +(-1.07283 + 1.85819i) q^{23} +(0.0599510 + 0.103838i) q^{24} +(2.36710 + 4.09993i) q^{25} +(0.507899 - 0.879706i) q^{26} -2.95634 q^{27} +(1.16488 - 4.84103i) q^{28} -3.58854 q^{29} +(0.261854 - 0.453544i) q^{30} +(-3.08924 - 5.35072i) q^{31} +(3.92681 + 6.80144i) q^{32} +(1.15636 - 2.00288i) q^{33} -10.6071 q^{34} +(1.30808 - 0.386734i) q^{35} -5.14565 q^{36} +(4.76638 - 8.25561i) q^{37} +(-3.85492 - 6.67692i) q^{38} +(0.132902 + 0.230194i) q^{39} +(-0.0599510 + 0.103838i) q^{40} -1.00000 q^{41} +(1.94852 + 1.85099i) q^{42} +9.50489 q^{43} +(4.22108 - 7.31113i) q^{44} +(-0.704824 - 1.22079i) q^{45} +(-2.11376 - 3.66114i) q^{46} +(-5.13348 + 8.89144i) q^{47} -2.17678 q^{48} +(0.359116 + 6.99078i) q^{49} -9.32764 q^{50} +(1.38779 - 2.40372i) q^{51} +(0.485135 + 0.840278i) q^{52} +(0.856512 + 1.48352i) q^{53} +(2.91239 - 5.04441i) q^{54} +2.31273 q^{55} +(-0.446111 - 0.423782i) q^{56} +2.01744 q^{57} +(3.53520 - 6.12314i) q^{58} +(-2.10826 - 3.65161i) q^{59} +(0.250117 + 0.433216i) q^{60} +(7.70806 - 13.3507i) q^{61} +12.1733 q^{62} +(6.93716 - 2.05098i) q^{63} -7.02948 q^{64} +(-0.132902 + 0.230194i) q^{65} +(2.27835 + 3.94622i) q^{66} +(1.88978 + 3.27319i) q^{67} +(5.06586 - 8.77433i) q^{68} +1.10622 q^{69} +(-0.628748 + 2.61297i) q^{70} +6.37594 q^{71} +(-0.317939 + 0.550687i) q^{72} +(-1.74836 - 3.02825i) q^{73} +(9.39105 + 16.2658i) q^{74} +(1.22039 - 2.11377i) q^{75} +7.36429 q^{76} +(-2.77659 + 11.5390i) q^{77} -0.523707 q^{78} +(3.51288 - 6.08448i) q^{79} +(-1.08839 - 1.88515i) q^{80} +(-3.33920 - 5.78367i) q^{81} +(0.985135 - 1.70630i) q^{82} +7.25513 q^{83} +(-2.46176 + 0.727820i) q^{84} +2.77558 q^{85} +(-9.36360 + 16.2182i) q^{86} +(0.925059 + 1.60225i) q^{87} +(-0.521624 - 0.903480i) q^{88} +(1.64964 - 2.85727i) q^{89} +2.77739 q^{90} +(-0.988961 - 0.939462i) q^{91} +4.03804 q^{92} +(-1.59270 + 2.75863i) q^{93} +(-10.1143 - 17.5185i) q^{94} +(1.00872 + 1.74716i) q^{95} +(2.02452 - 3.50657i) q^{96} -19.3033 q^{97} +(-12.2822 - 6.27410i) q^{98} +12.2651 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 2 q^{2} + 2 q^{3} - 6 q^{4} - 2 q^{5} + 2 q^{6} + 8 q^{7} - 6 q^{8} - 5 q^{9}+O(q^{10}) \) 10 * q + 2 * q^2 + 2 * q^3 - 6 * q^4 - 2 * q^5 + 2 * q^6 + 8 * q^7 - 6 * q^8 - 5 * q^9	\( 10 q + 2 q^{2} + 2 q^{3} - 6 q^{4} - 2 q^{5} + 2 q^{6} + 8 q^{7} - 6 q^{8} - 5 q^{9} + q^{10} + 6 q^{11} + 7 q^{12} + 4 q^{13} - 24 q^{14} - 40 q^{15} + 12 q^{16} + 3 q^{17} + 8 q^{18} - 7 q^{19} + 14 q^{20} - 15 q^{21} - 26 q^{22} - 16 q^{24} + 5 q^{25} + q^{26} + 26 q^{27} - 5 q^{28} - 20 q^{29} - 14 q^{30} + 6 q^{31} + 3 q^{32} + 17 q^{33} + 2 q^{34} - 9 q^{35} - 30 q^{36} + 18 q^{37} + 7 q^{38} + 20 q^{39} + 16 q^{40} - 10 q^{41} - 35 q^{42} - 28 q^{43} - 2 q^{44} + 7 q^{45} + 3 q^{46} - 3 q^{47} + 18 q^{48} - 8 q^{49} - 8 q^{50} - 7 q^{52} + 9 q^{53} + 25 q^{54} + 34 q^{55} - 15 q^{56} + 62 q^{57} + 5 q^{58} + 19 q^{59} + 3 q^{60} + 23 q^{61} + 72 q^{62} + 13 q^{63} - 2 q^{64} - 20 q^{65} - 23 q^{66} + 11 q^{67} + 24 q^{68} + 38 q^{69} - 40 q^{70} - 25 q^{72} - 13 q^{73} - 2 q^{74} - 11 q^{75} + 24 q^{76} + 23 q^{77} + 28 q^{78} + 41 q^{79} + 9 q^{80} + 7 q^{81} - 2 q^{82} - 4 q^{83} - 23 q^{84} - 20 q^{86} - 32 q^{87} + 10 q^{88} - 14 q^{89} + 44 q^{90} - 6 q^{91} + 34 q^{92} + 15 q^{93} - 10 q^{94} + 31 q^{95} + 33 q^{96} - 54 q^{97} - 85 q^{98} - 18 q^{99}+O(q^{100}) \) 10 * q + 2 * q^2 + 2 * q^3 - 6 * q^4 - 2 * q^5 + 2 * q^6 + 8 * q^7 - 6 * q^8 - 5 * q^9 + q^10 + 6 * q^11 + 7 * q^12 + 4 * q^13 - 24 * q^14 - 40 * q^15 + 12 * q^16 + 3 * q^17 + 8 * q^18 - 7 * q^19 + 14 * q^20 - 15 * q^21 - 26 * q^22 - 16 * q^24 + 5 * q^25 + q^26 + 26 * q^27 - 5 * q^28 - 20 * q^29 - 14 * q^30 + 6 * q^31 + 3 * q^32 + 17 * q^33 + 2 * q^34 - 9 * q^35 - 30 * q^36 + 18 * q^37 + 7 * q^38 + 20 * q^39 + 16 * q^40 - 10 * q^41 - 35 * q^42 - 28 * q^43 - 2 * q^44 + 7 * q^45 + 3 * q^46 - 3 * q^47 + 18 * q^48 - 8 * q^49 - 8 * q^50 - 7 * q^52 + 9 * q^53 + 25 * q^54 + 34 * q^55 - 15 * q^56 + 62 * q^57 + 5 * q^58 + 19 * q^59 + 3 * q^60 + 23 * q^61 + 72 * q^62 + 13 * q^63 - 2 * q^64 - 20 * q^65 - 23 * q^66 + 11 * q^67 + 24 * q^68 + 38 * q^69 - 40 * q^70 - 25 * q^72 - 13 * q^73 - 2 * q^74 - 11 * q^75 + 24 * q^76 + 23 * q^77 + 28 * q^78 + 41 * q^79 + 9 * q^80 + 7 * q^81 - 2 * q^82 - 4 * q^83 - 23 * q^84 - 20 * q^86 - 32 * q^87 + 10 * q^88 - 14 * q^89 + 44 * q^90 - 6 * q^91 + 34 * q^92 + 15 * q^93 - 10 * q^94 + 31 * q^95 + 33 * q^96 - 54 * q^97 - 85 * q^98 - 18 * q^99

Introduction

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