LMFDB - Embedded newform 287.2.e.c.165.5

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			165.5
Root			$1.40131 + 2.42714i$ of defining polynomial
Character	$\chi$	$=$	287.165
Dual form			287.2.e.c.247.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.20443 + 2.08614i) q^{2} +(0.448226 - 0.776350i) q^{3} +(-1.90131 + 3.29316i) q^{4} +(-0.448226 - 0.776350i) q^{5} +2.15943 q^{6} +(0.117164 + 2.64316i) q^{7} -4.34226 q^{8} +(1.09819 + 1.90212i) q^{9} +O(q^{10})$	\(q+(1.20443 + 2.08614i) q^{2} +(0.448226 - 0.776350i) q^{3} +(-1.90131 + 3.29316i) q^{4} +(-0.448226 - 0.776350i) q^{5} +2.15943 q^{6} +(0.117164 + 2.64316i) q^{7} -4.34226 q^{8} +(1.09819 + 1.90212i) q^{9} +(1.07971 - 1.87012i) q^{10} +(-0.652657 + 1.13043i) q^{11} +(1.70443 + 2.95216i) q^{12} +0.896451 q^{13} +(-5.37287 + 3.42792i) q^{14} -0.803625 q^{15} +(-1.42734 - 2.47222i) q^{16} +(1.32837 - 2.30080i) q^{17} +(-2.64538 + 4.58194i) q^{18} +(-1.50486 - 2.60649i) q^{19} +3.40886 q^{20} +(2.10453 + 1.09377i) q^{21} -3.14432 q^{22} +(-2.67599 - 4.63495i) q^{23} +(-1.94631 + 3.37111i) q^{24} +(2.09819 - 3.63417i) q^{25} +(1.07971 + 1.87012i) q^{26} +4.65830 q^{27} +(-8.92711 - 4.63962i) q^{28} +0.155602 q^{29} +(-0.967911 - 1.67647i) q^{30} +(4.25648 - 7.37245i) q^{31} +(-0.904004 + 1.56578i) q^{32} +(0.585075 + 1.01338i) q^{33} +6.39970 q^{34} +(1.99950 - 1.27569i) q^{35} -8.35198 q^{36} +(1.03061 + 1.78506i) q^{37} +(3.62500 - 6.27868i) q^{38} +(0.401812 - 0.695960i) q^{39} +(1.94631 + 3.37111i) q^{40} -1.00000 q^{41} +(0.253008 + 5.70770i) q^{42} -4.43766 q^{43} +(-2.48181 - 4.29861i) q^{44} +(0.984472 - 1.70515i) q^{45} +(6.44609 - 11.1650i) q^{46} +(-1.12879 - 1.95513i) q^{47} -2.55907 q^{48} +(-6.97255 + 0.619366i) q^{49} +10.1085 q^{50} +(-1.19082 - 2.06255i) q^{51} +(-1.70443 + 2.95216i) q^{52} +(5.03723 - 8.72473i) q^{53} +(5.61060 + 9.71784i) q^{54} +1.17015 q^{55} +(-0.508757 - 11.4773i) q^{56} -2.69806 q^{57} +(0.187412 + 0.324607i) q^{58} +(-2.91928 + 5.05634i) q^{59} +(1.52794 - 2.64647i) q^{60} +(1.33103 + 2.30542i) q^{61} +20.5066 q^{62} +(-4.89892 + 3.12554i) q^{63} -10.0646 q^{64} +(-0.401812 - 0.695960i) q^{65} +(-1.40937 + 2.44109i) q^{66} +(-2.10869 + 3.65235i) q^{67} +(5.05127 + 8.74906i) q^{68} -4.79779 q^{69} +(5.06952 + 2.63474i) q^{70} +1.45793 q^{71} +(-4.76862 - 8.25949i) q^{72} +(-7.00169 + 12.1273i) q^{73} +(-2.48259 + 4.29997i) q^{74} +(-1.88092 - 3.25785i) q^{75} +11.4448 q^{76} +(-3.06438 - 1.59263i) q^{77} +1.93582 q^{78} +(7.12230 + 12.3362i) q^{79} +(-1.27954 + 2.21622i) q^{80} +(-1.20659 + 2.08988i) q^{81} +(-1.20443 - 2.08614i) q^{82} -4.73758 q^{83} +(-7.60332 + 4.85096i) q^{84} -2.38163 q^{85} +(-5.34485 - 9.25756i) q^{86} +(0.0697449 - 0.120802i) q^{87} +(2.83401 - 4.90864i) q^{88} +(-2.15873 - 3.73902i) q^{89} +4.74291 q^{90} +(0.105032 + 2.36946i) q^{91} +20.3515 q^{92} +(-3.81573 - 6.60904i) q^{93} +(2.71911 - 4.70963i) q^{94} +(-1.34903 + 2.33659i) q^{95} +(0.810396 + 1.40365i) q^{96} +14.5549 q^{97} +(-9.69003 - 13.7997i) q^{98} -2.86696 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 $\left(\mathbb{Z}/287\mathbb{Z}\right)^\times$.

$n$	$206$	$211$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$

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 $

$2$	1.20443	+	2.08614i	0.851662	+	1.47512i	0.879708	+	0.475514i	$0.157738\pi$
$2$	1.20443	+	2.08614i	0.851662	+	1.47512i	−0.0280464	+	0.999607i	$0.508929\pi$
$3$	0.448226	−	0.776350i	0.258783	−	0.448226i	−0.707133	−	0.707081i	$-0.750012\pi$
$3$	0.448226	−	0.776350i	0.258783	−	0.448226i	0.965916	+	0.258855i	$0.0833451\pi$
$4$	−1.90131	+	3.29316i	−0.950655	+	1.64658i
$5$	−0.448226	−	0.776350i	−0.200453	−	0.347194i	0.748222	−	0.663449i	$-0.230908\pi$
$5$	−0.448226	−	0.776350i	−0.200453	−	0.347194i	−0.948674	+	0.316255i	$0.897575\pi$
$6$	2.15943			0.881583
$7$	0.117164	+	2.64316i	0.0442839	+	0.999019i
$7$	0.117164	+	2.64316i	0.0442839	+	0.999019i
$8$	−4.34226			−1.53522
$9$	1.09819	+	1.90212i	0.366063	+	0.634039i
$10$	1.07971	−	1.87012i	0.341436	−	0.591384i
$11$	−0.652657	+	1.13043i	−0.196783	+	0.340839i	−0.947484	−	0.319804i	$-0.896383\pi$
$11$	−0.652657	+	1.13043i	−0.196783	+	0.340839i	0.750700	+	0.660643i	$0.229716\pi$
$12$	1.70443	+	2.95216i	0.492027	+	0.852216i
$13$	0.896451			0.248631			0.124315	−	0.992243i	$-0.460327\pi$
$13$	0.896451			0.248631			0.124315	+	0.992243i	$0.460327\pi$
$14$	−5.37287	+	3.42792i	−1.43596	+	0.916150i
$15$	−0.803625			−0.207495
$16$	−1.42734	−	2.47222i	−0.356834	−	0.618055i
$17$	1.32837	−	2.30080i	0.322176	−	0.558026i	−0.658761	−	0.752353i	$-0.728919\pi$
$17$	1.32837	−	2.30080i	0.322176	−	0.558026i	0.980937	+	0.194327i	$0.0622523\pi$
$18$	−2.64538	+	4.58194i	−0.623523	+	1.07997i
$19$	−1.50486	−	2.60649i	−0.345238	−	0.597970i	0.640159	−	0.768243i	$-0.278869\pi$
$19$	−1.50486	−	2.60649i	−0.345238	−	0.597970i	−0.985397	+	0.170273i	$0.945535\pi$
$20$	3.40886			0.762245
$21$	2.10453	+	1.09377i	0.459246	+	0.238680i
$22$	−3.14432			−0.670372
$23$	−2.67599	−	4.63495i	−0.557982	−	0.966454i	−0.997665	−	0.0683003i	$-0.978242\pi$
$23$	−2.67599	−	4.63495i	−0.557982	−	0.966454i	0.439683	−	0.898153i	$-0.355091\pi$
$24$	−1.94631	+	3.37111i	−0.397289	+	0.688125i
$25$	2.09819	−	3.63417i	0.419638	−	0.726833i
$26$	1.07971	+	1.87012i	0.211749	+	0.366761i
$27$	4.65830			0.896490
$28$	−8.92711	−	4.63962i	−1.68707	−	0.876805i
$29$	0.155602			0.0288946			0.0144473	−	0.999896i	$-0.495401\pi$
$29$	0.155602			0.0288946			0.0144473	+	0.999896i	$0.495401\pi$
$30$	−0.967911	−	1.67647i	−0.176716	−	0.306080i
$31$	4.25648	−	7.37245i	0.764487	−	1.32413i	−0.176030	−	0.984385i	$-0.556326\pi$
$31$	4.25648	−	7.37245i	0.764487	−	1.32413i	0.940517	−	0.339746i	$-0.110341\pi$
$32$	−0.904004	+	1.56578i	−0.159807	+	0.276794i
$33$	0.585075	+	1.01338i	0.101849	+	0.176407i
$34$	6.39970			1.09754
$35$	1.99950	−	1.27569i	0.337977	−	0.215631i
$36$	−8.35198			−1.39200
$37$	1.03061	+	1.78506i	0.169431	+	0.293462i	0.938220	−	0.346040i	$-0.112474\pi$
$37$	1.03061	+	1.78506i	0.169431	+	0.293462i	−0.768789	+	0.639502i	$0.779140\pi$
$38$	3.62500	−	6.27868i	0.588052	−	1.01854i
$39$	0.401812	−	0.695960i	0.0643415	−	0.111443i
$40$	1.94631	+	3.37111i	0.307739	+	0.533020i
$41$	−1.00000			−0.156174
$41$	−1.00000			−0.156174
$42$	0.253008	+	5.70770i	0.0390399	+	0.880718i
$43$	−4.43766			−0.676736			−0.338368	−	0.941014i	$-0.609875\pi$
$43$	−4.43766			−0.676736			−0.338368	+	0.941014i	$0.609875\pi$
$44$	−2.48181	−	4.29861i	−0.374146	−	0.648040i
$45$	0.984472	−	1.70515i	0.146756	−	0.254189i
$46$	6.44609	−	11.1650i	0.950424	−	1.64618i
$47$	−1.12879	−	1.95513i	−0.164651	−	0.285185i	0.771880	−	0.635768i	$-0.219317\pi$
$47$	−1.12879	−	1.95513i	−0.164651	−	0.285185i	−0.936531	+	0.350584i	$0.885983\pi$
$48$	−2.55907			−0.369371
$49$	−6.97255	+	0.619366i	−0.996078	+	0.0884809i
$50$	10.1085			1.42956
$51$	−1.19082	−	2.06255i	−0.166748	−	0.288815i
$52$	−1.70443	+	2.95216i	−0.236362	+	0.409391i
$53$	5.03723	−	8.72473i	0.691916	−	1.19843i	−0.279293	−	0.960206i	$-0.590100\pi$
$53$	5.03723	−	8.72473i	0.691916	−	1.19843i	0.971209	−	0.238228i	$-0.0765666\pi$
$54$	5.61060	+	9.71784i	0.763506	+	1.32243i
$55$	1.17015			0.157783
$56$	−0.508757	−	11.4773i	−0.0679856	−	1.53372i
$57$	−2.69806			−0.357367
$58$	0.187412	+	0.324607i	0.0246084	+	0.0426230i
$59$	−2.91928	+	5.05634i	−0.380058	+	0.658280i	−0.991070	−	0.133342i	$-0.957429\pi$
$59$	−2.91928	+	5.05634i	−0.380058	+	0.658280i	0.611012	+	0.791621i	$0.290763\pi$
$60$	1.52794	−	2.64647i	0.197256	−	0.341658i
$61$	1.33103	+	2.30542i	0.170421	+	0.295178i	0.938567	−	0.345097i	$-0.112154\pi$
$61$	1.33103	+	2.30542i	0.170421	+	0.295178i	−0.768146	+	0.640275i	$0.778820\pi$
$62$	20.5066			2.60434
$63$	−4.89892	+	3.12554i	−0.617206	+	0.393781i
$64$	−10.0646			−1.25807
$65$	−0.401812	−	0.695960i	−0.0498387	−	0.0863232i
$66$	−1.40937	+	2.44109i	−0.173481	+	0.300478i
$67$	−2.10869	+	3.65235i	−0.257617	+	0.446206i	−0.965603	−	0.260021i	$-0.916271\pi$
$67$	−2.10869	+	3.65235i	−0.257617	+	0.446206i	0.707986	+	0.706226i	$0.249604\pi$
$68$	5.05127	+	8.74906i	0.612557	+	1.06098i
$69$	−4.79779			−0.577586
$70$	5.06952	+	2.63474i	0.605924	+	0.314912i
$71$	1.45793			0.173025			0.0865125	−	0.996251i	$-0.472428\pi$
$71$	1.45793			0.173025			0.0865125	+	0.996251i	$0.472428\pi$
$72$	−4.76862	−	8.25949i	−0.561987	−	0.973390i
$73$	−7.00169	+	12.1273i	−0.819486	+	1.41939i	0.0865760	+	0.996245i	$0.472407\pi$
$73$	−7.00169	+	12.1273i	−0.819486	+	1.41939i	−0.906062	+	0.423146i	$0.860926\pi$
$74$	−2.48259	+	4.29997i	−0.288595	+	0.499861i
$75$	−1.88092	−	3.25785i	−0.217190	−	0.376185i
$76$	11.4448			1.31281
$77$	−3.06438	−	1.59263i	−0.349219	−	0.181497i
$78$	1.93582			0.219189
$79$	7.12230	+	12.3362i	0.801322	+	1.38793i	0.918747	+	0.394848i	$0.129203\pi$
$79$	7.12230	+	12.3362i	0.801322	+	1.38793i	−0.117425	+	0.993082i	$0.537464\pi$
$80$	−1.27954	+	2.21622i	−0.143057	+	0.247781i
$81$	−1.20659	+	2.08988i	−0.134066	+	0.232209i
$82$	−1.20443	−	2.08614i	−0.133007	−	0.230375i
$83$	−4.73758			−0.520017			−0.260009	−	0.965606i	$-0.583725\pi$
$83$	−4.73758			−0.520017			−0.260009	+	0.965606i	$0.583725\pi$
$84$	−7.60332	+	4.85096i	−0.829591	+	0.529284i
$85$	−2.38163			−0.258324
$86$	−5.34485	−	9.25756i	−0.576350	−	0.998268i
$87$	0.0697449	−	0.120802i	0.00747743	−	0.0129513i
$88$	2.83401	−	4.90864i	0.302106	−	0.523263i
$89$	−2.15873	−	3.73902i	−0.228825	−	0.396336i	0.728635	−	0.684902i	$-0.240155\pi$
$89$	−2.15873	−	3.73902i	−0.228825	−	0.396336i	−0.957460	+	0.288566i	$0.906822\pi$
$90$	4.74291			0.499947
$91$	0.105032	+	2.36946i	0.0110103	+	0.248387i
$92$	20.3515			2.12179
$93$	−3.81573	−	6.60904i	−0.395673	−	0.685326i
$94$	2.71911	−	4.70963i	0.280455	−	0.485762i
$95$	−1.34903	+	2.33659i	−0.138408	+	0.239729i
$96$	0.810396	+	1.40365i	0.0827107	+	0.143259i
$97$	14.5549			1.47782			0.738911	−	0.673803i	$-0.235340\pi$
$97$	14.5549			1.47782			0.738911	+	0.673803i	$0.235340\pi$
$98$	−9.69003	−	13.7997i	−0.978841	−	1.39398i
$99$	−2.86696			−0.288140
$100$	7.97861	+	13.8194i	0.797861	+	1.38194i
$101$	3.80318	−	6.58730i	0.378430	−	0.655460i	−0.612404	−	0.790545i	$-0.709797\pi$
$101$	3.80318	−	6.58730i	0.378430	−	0.655460i	0.990834	+	0.135085i	$0.0431307\pi$
$102$	2.86851	−	4.96841i	0.284025	−	0.491946i
$103$	2.52967	+	4.38152i	0.249256	+	0.431724i	0.963320	−	0.268357i	$-0.0864806\pi$
$103$	2.52967	+	4.38152i	0.249256	+	0.431724i	−0.714064	+	0.700081i	$0.753147\pi$
$104$	−3.89263			−0.381703
$105$	−0.0941560	−	2.12411i	−0.00918869	−	0.207292i
$106$	24.2680			2.35711
$107$	−7.32822	−	12.6928i	−0.708445	−	1.22706i	−0.965434	−	0.260649i	$-0.916064\pi$
$107$	−7.32822	−	12.6928i	−0.708445	−	1.22706i	0.256988	−	0.966415i	$-0.417270\pi$
$108$	−8.85686	+	15.3405i	−0.852252	+	1.47614i
$109$	6.12276	−	10.6049i	0.586454	−	1.01577i	−0.408238	−	0.912875i	$-0.633857\pi$
$109$	6.12276	−	10.6049i	0.586454	−	1.01577i	0.994692	−	0.102893i	$-0.0328099\pi$
$110$	1.40937	+	2.44109i	0.134378	+	0.232749i
$111$	1.84778			0.175383
$112$	6.36723	−	4.06233i	0.601646	−	0.383854i
$113$	6.07154			0.571163			0.285581	−	0.958354i	$-0.407813\pi$
$113$	6.07154			0.571163			0.285581	+	0.958354i	$0.407813\pi$
$114$	−3.24963	−	5.62853i	−0.304356	−	0.527160i
$115$	−2.39889	+	4.15501i	−0.223698	+	0.387456i
$116$	−0.295848	+	0.512423i	−0.0274688	+	0.0475773i
$117$	0.984472	+	1.70515i	0.0910144	+	0.157642i
$118$	−14.0643			−1.29472
$119$	6.23701	+	3.24151i	0.571745	+	0.297149i
$120$	3.48955			0.318551
$121$	4.64808	+	8.05071i	0.422553	+	0.731882i
$122$	−3.20627	+	5.55343i	−0.290282	+	0.502784i
$123$	−0.448226	+	0.776350i	−0.0404151	+	0.0700011i
$124$	16.1858	+	28.0346i	1.45353	+	2.51758i
$125$	−8.24410			−0.737375
$126$	−12.4207	−	6.45532i	−1.10653	−	0.575086i
$127$	−10.2213			−0.906998			−0.453499	−	0.891257i	$-0.649824\pi$
$127$	−10.2213			−0.906998			−0.453499	+	0.891257i	$0.649824\pi$
$128$	−10.3141	−	17.8645i	−0.911646	−	1.57902i
$129$	−1.98907	+	3.44517i	−0.175128	+	0.303331i
$130$	0.967911	−	1.67647i	0.0848914	−	0.147036i
$131$	−9.09633	−	15.7553i	−0.794750	−	1.37655i	−0.922998	−	0.384805i	$-0.874269\pi$
$131$	−9.09633	−	15.7553i	−0.794750	−	1.37655i	0.128248	−	0.991742i	$-0.459065\pi$
$132$	−4.44964			−0.387291
$133$	6.71305	−	4.28296i	0.582095	−	0.371380i
$134$	−10.1591			−0.877610
$135$	−2.08797	−	3.61647i	−0.179704	−	0.311256i
$136$	−5.76811	+	9.99067i	−0.494612	+	0.856693i
$137$	−3.67833	+	6.37106i	−0.314261	+	0.544316i	−0.979280	−	0.202510i	$-0.935090\pi$
$137$	−3.67833	+	6.37106i	−0.314261	+	0.544316i	0.665019	+	0.746826i	$0.268423\pi$
$138$	−5.77860	−	10.0088i	−0.491907	−	0.852009i
$139$	−21.3116			−1.80763			−0.903813	−	0.427927i	$-0.859244\pi$
$139$	−21.3116			−1.80763			−0.903813	+	0.427927i	$0.859244\pi$
$140$	0.399396	+	9.01015i	0.0337552	+	0.761497i
$141$	−2.02382			−0.170436
$142$	1.75598	+	3.04145i	0.147359	+	0.255233i
$143$	−0.585075	+	1.01338i	−0.0489264	+	0.0847431i
$144$	3.13497	−	5.42992i	0.261247	−	0.452493i
$145$	−0.0697449	−	0.120802i	−0.00579200	−	0.0100320i
$146$	−33.7322			−2.79170
$147$	−2.64443	+	5.69075i	−0.218109	+	0.469365i
$148$	−7.83800			−0.644280
$149$	2.85301	+	4.94156i	0.233728	+	0.404829i	0.958902	−	0.283737i	$-0.0915742\pi$
$149$	2.85301	+	4.94156i	0.233728	+	0.404829i	−0.725174	+	0.688565i	$0.758241\pi$
$150$	4.53088	−	7.84772i	0.369945	−	0.640764i
$151$	−3.22538	+	5.58651i	−0.262477	+	0.454624i	−0.966900	−	0.255157i	$-0.917873\pi$
$151$	−3.22538	+	5.58651i	−0.262477	+	0.454624i	0.704422	+	0.709781i	$0.251206\pi$
$152$	6.53449	+	11.3181i	0.530017	+	0.918016i
$153$	5.83518			0.471747
$154$	−0.368402	−	8.31093i	−0.0296867	−	0.669714i
$155$	−7.63146			−0.612974
$156$	1.52794	+	2.64647i	0.122333	+	0.211887i
$157$	1.70879	−	2.95970i	0.136376	−	0.236210i	−0.789746	−	0.613434i	$-0.789788\pi$
$157$	1.70879	−	2.95970i	0.136376	−	0.236210i	0.926122	+	0.377223i	$0.123121\pi$
$158$	−17.1566	+	29.7162i	−1.36491	+	2.36409i
$159$	−4.51563	−	7.82130i	−0.358113	−	0.620269i
$160$	1.62079			0.128135
$161$	11.9374	−	7.61610i	0.940796	−	0.600233i
$162$	−5.81304			−0.456716
$163$	10.6142	+	18.3843i	0.831368	+	1.43997i	0.896953	+	0.442125i	$0.145775\pi$
$163$	10.6142	+	18.3843i	0.831368	+	1.43997i	−0.0655850	+	0.997847i	$0.520891\pi$
$164$	1.90131	−	3.29316i	0.148467	−	0.257153i
$165$	0.524491	−	0.908446i	0.0408316	−	0.0707224i
$166$	−5.70609	−	9.88324i	−0.442879	−	0.767088i
$167$	−13.6306			−1.05477			−0.527384	−	0.849627i	$-0.676827\pi$
$167$	−13.6306			−1.05477			−0.527384	+	0.849627i	$0.676827\pi$
$168$	−9.13841	−	4.74943i	−0.705044	−	0.366427i
$169$	−12.1964			−0.938183
$170$	−2.86851	−	4.96841i	−0.220005	−	0.381059i
$171$	3.30523	−	5.72483i	0.252757	−	0.437789i
$172$	8.43736	−	14.6139i	0.643343	−	1.11430i
$173$	−5.38868	−	9.33347i	−0.409694	−	0.709611i	0.585161	−	0.810917i	$-0.301031\pi$
$173$	−5.38868	−	9.33347i	−0.409694	−	0.709611i	−0.994855	+	0.101306i	$0.967698\pi$
$174$	0.336012			0.0254730
$175$	9.85150	+	5.12004i	0.744704	+	0.387039i
$176$	3.72624			0.280876
$177$	2.61699	+	4.53276i	0.196705	+	0.340703i
$178$	5.20008	−	9.00680i	0.389762	−	0.675088i
$179$	3.28737	−	5.69389i	0.245710	−	0.425581i	−0.716621	−	0.697462i	$-0.754312\pi$
$179$	3.28737	−	5.69389i	0.245710	−	0.425581i	0.962331	+	0.271881i	$0.0876457\pi$
$180$	3.74357	+	6.48405i	0.279029	+	0.483293i
$181$	−0.346946			−0.0257883			−0.0128942	−	0.999917i	$-0.504104\pi$
$181$	−0.346946			−0.0257883			−0.0128942	+	0.999917i	$0.504104\pi$
$182$	−4.81651	+	3.07296i	−0.357024	+	0.227783i
$183$	2.38641			0.176409
$184$	11.6198	+	20.1262i	0.856626	+	1.48372i
$185$	0.923888	−	1.60022i	0.0679256	−	0.117651i
$186$	9.19157	−	15.9203i	0.673959	−	1.16733i
$187$	1.73394	+	3.00326i	0.126798	+	0.219620i
$188$	8.58474			0.626107
$189$	0.545785	+	12.3126i	0.0397000	+	0.895610i
$190$	−6.49927			−0.471506
$191$	8.15017	+	14.1165i	0.589725	+	1.02143i	0.994268	+	0.106915i	$0.0340974\pi$
$191$	8.15017	+	14.1165i	0.589725	+	1.02143i	−0.404543	+	0.914519i	$0.632569\pi$
$192$	−4.51121	+	7.81364i	−0.325568	+	0.563901i
$193$	9.06066	−	15.6935i	0.652201	−	1.12965i	−0.330387	−	0.943846i	$-0.607179\pi$
$193$	9.06066	−	15.6935i	0.652201	−	1.12965i	0.982588	−	0.185799i	$-0.0594875\pi$
$194$	17.5303	+	30.3634i	1.25860	+	2.17997i
$195$	−0.720411			−0.0515897
$196$	11.2173	−	24.1393i	0.801235	−	1.72424i
$197$	−2.71127			−0.193170			−0.0965849	−	0.995325i	$-0.530792\pi$
$197$	−2.71127			−0.193170			−0.0965849	+	0.995325i	$0.530792\pi$
$198$	−3.45305	−	5.98087i	−0.245398	−	0.425042i
$199$	−3.74900	+	6.49347i	−0.265760	+	0.460310i	−0.967762	−	0.251865i	$-0.918956\pi$
$199$	−3.74900	+	6.49347i	−0.265760	+	0.460310i	0.702003	+	0.712174i	$0.252290\pi$
$200$	−9.11088	+	15.7805i	−0.644236	+	1.11585i
$201$	1.89033	+	3.27415i	0.133334	+	0.230941i
$202$	18.3227			1.28918
$203$	0.0182310	+	0.411281i	0.00127956	+	0.0288662i
$204$	9.05644			0.634077
$205$	0.448226	+	0.776350i	0.0313054	+	0.0542226i
$206$	−6.09363	+	10.5545i	−0.424564	+	0.735366i
$207$	5.87747	−	10.1801i	0.408513	−	0.707565i
$208$	−1.27954	−	2.21622i	−0.0887199	−	0.153667i
$209$	3.92862			0.271749
$210$	4.31777	−	2.75476i	0.297954	−	0.190097i
$211$	−24.4598			−1.68388			−0.841940	−	0.539572i	$-0.818586\pi$
$211$	−24.4598			−1.68388			−0.841940	+	0.539572i	$0.818586\pi$
$212$	19.1547	+	33.1768i	1.31555	+	2.27859i
$213$	0.653484	−	1.13187i	0.0447760	−	0.0775542i
$214$	17.6527	−	30.5753i	1.20671	−	2.09009i
$215$	1.98907	+	3.44517i	0.135654	+	0.234959i
$216$	−20.2275			−1.37631
$217$	19.9852	+	10.3868i	1.35669	+	0.705100i
$218$	29.4978			1.99784
$219$	6.27667	+	10.8715i	0.424138	+	0.734629i
$220$	−2.22482	+	3.85350i	−0.149997	+	0.259803i
$221$	1.19082	−	2.06255i	0.0801029	−	0.138742i
$222$	2.22552	+	3.85471i	0.149367	+	0.258711i
$223$	9.17487			0.614395			0.307197	−	0.951646i	$-0.400609\pi$
$223$	9.17487			0.614395			0.307197	+	0.951646i	$0.400609\pi$
$224$	−4.24452	−	2.20597i	−0.283599	−	0.147393i
$225$	9.21681			0.614454
$226$	7.31276	+	12.6661i	0.486437	+	0.842534i
$227$	13.0951	−	22.6814i	0.869152	−	1.50542i	0.00628797	−	0.999980i	$-0.497998\pi$
$227$	13.0951	−	22.6814i	0.869152	−	1.50542i	0.862864	−	0.505436i	$-0.168668\pi$
$228$	5.12985	−	8.88517i	0.339733	−	0.588435i
$229$	−4.01871	−	6.96061i	−0.265564	−	0.459970i	0.702147	−	0.712032i	$-0.252225\pi$
$229$	−4.01871	−	6.96061i	−0.265564	−	0.459970i	−0.967711	+	0.252062i	$0.918891\pi$
$230$	−11.5572			−0.762060
$231$	−2.60997	+	1.66518i	−0.171723	+	0.109561i
$232$	−0.675665			−0.0443596
$233$	9.64654	+	16.7083i	0.631966	+	1.09460i	0.987149	+	0.159800i	$0.0510850\pi$
$233$	9.64654	+	16.7083i	0.631966	+	1.09460i	−0.355184	+	0.934797i	$0.615582\pi$
$234$	−2.37146	+	4.10748i	−0.155027	+	0.268515i
$235$	−1.01191	+	1.75268i	−0.0660096	+	0.114332i
$236$	−11.1009	−	19.2273i	−0.722608	−	1.25159i
$237$	12.7696			0.829474
$238$	0.749816	+	16.9154i	0.0486033	+	1.09646i
$239$	−18.7297			−1.21152			−0.605761	−	0.795647i	$-0.707131\pi$
$239$	−18.7297			−1.21152			−0.605761	+	0.795647i	$0.707131\pi$
$240$	1.14704	+	1.98674i	0.0740413	+	0.128243i
$241$	−8.77793	+	15.2038i	−0.565436	+	0.979364i	0.431573	+	0.902078i	$0.357959\pi$
$241$	−8.77793	+	15.2038i	−0.565436	+	0.979364i	−0.997009	+	0.0772863i	$0.975374\pi$
$242$	−11.1966	+	19.3930i	−0.719743	+	1.24663i
$243$	8.06910	+	13.9761i	0.517633	+	0.896567i
$244$	−10.1228			−0.648047
$245$	3.60612	+	5.13552i	0.230386	+	0.328096i
$246$	−2.15943			−0.137680
$247$	−1.34903	−	2.33659i	−0.0858369	−	0.148674i
$248$	−18.4828	+	32.0131i	−1.17366	+	2.03283i
$249$	−2.12351	+	3.67802i	−0.134572	+	0.233085i
$250$	−9.92945	−	17.1983i	−0.627994	−	1.08772i
$251$	−5.31684			−0.335596			−0.167798	−	0.985821i	$-0.553666\pi$
$251$	−5.31684			−0.335596			−0.167798	+	0.985821i	$0.553666\pi$
$252$	−0.978552	−	22.0756i	−0.0616430	−	1.39063i
$253$	6.98601			0.439207
$254$	−12.3109	−	21.3231i	−0.772455	−	1.33793i
$255$	−1.06751	+	1.84898i	−0.0668500	+	0.115788i
$256$	14.7807	−	25.6008i	0.923791	−	1.60005i
$257$	−0.875786	−	1.51691i	−0.0546300	−	0.0946220i	0.837417	−	0.546564i	$-0.184065\pi$
$257$	−0.875786	−	1.51691i	−0.0546300	−	0.0946220i	−0.892047	+	0.451942i	$0.850731\pi$
$258$	−9.58280			−0.596599
$259$	−4.59745	+	2.93320i	−0.285671	+	0.182260i
$260$	3.05588			0.189518
$261$	0.170880	+	0.295973i	0.0105772	+	0.0183203i
$262$	21.9118	−	37.9524i	1.35372	−	2.34470i
$263$	4.08047	−	7.06758i	0.251612	−	0.435805i	−0.712358	−	0.701817i	$-0.752373\pi$
$263$	4.08047	−	7.06758i	0.251612	−	0.435805i	0.963970	+	0.266011i	$0.0857059\pi$
$264$	−2.54055	−	4.40036i	−0.156360	−	0.270823i
$265$	−9.03126			−0.554786
$266$	17.0202	+	8.84579i	1.04358	+	0.542370i
$267$	−3.87039			−0.236864
$268$	−8.01853	−	13.8885i	−0.489810	−	0.848375i
$269$	14.3384	−	24.8348i	0.874226	−	1.51420i	0.0166410	−	0.999862i	$-0.494703\pi$
$269$	14.3384	−	24.8348i	0.874226	−	1.51420i	0.857585	−	0.514342i	$-0.171964\pi$
$270$	5.02963	−	8.71157i	0.306093	−	0.530169i
$271$	1.10957	+	1.92183i	0.0674014	+	0.116743i	0.897757	−	0.440492i	$-0.145196\pi$
$271$	1.10957	+	1.92183i	0.0674014	+	0.116743i	−0.830355	+	0.557234i	$0.811863\pi$
$272$	−7.58410			−0.459854
$273$	1.88661	+	0.980511i	0.114183	+	0.0593433i
$274$	−17.7212			−1.07058
$275$	2.73879	+	4.74373i	0.165155	+	0.286058i
$276$	9.12208	−	15.7999i	0.549085	−	0.951042i
$277$	−2.02985	+	3.51581i	−0.121962	+	0.211244i	−0.920541	−	0.390645i	$-0.872252\pi$
$277$	−2.02985	+	3.51581i	−0.121962	+	0.211244i	0.798579	+	0.601890i	$0.205585\pi$
$278$	−25.6684	−	44.4589i	−1.53949	−	2.66647i
$279$	18.6977			1.11940
$280$	−8.68234	+	5.53938i	−0.518869	+	0.331041i
$281$	−18.1101			−1.08036			−0.540179	−	0.841550i	$-0.681644\pi$
$281$	−18.1101			−1.08036			−0.540179	+	0.841550i	$0.681644\pi$
$282$	−2.43755	−	4.22196i	−0.145154	−	0.251414i
$283$	3.41910	−	5.92206i	0.203245	−	0.352030i	−0.746327	−	0.665579i	$-0.768185\pi$
$283$	3.41910	−	5.92206i	0.203245	−	0.352030i	0.949572	+	0.313549i	$0.101518\pi$
$284$	−2.77198	+	4.80122i	−0.164487	+	0.284900i
$285$	1.20934	+	2.09464i	0.0716352	+	0.124076i
$286$	−2.81873			−0.166675
$287$	−0.117164	−	2.64316i	−0.00691598	−	0.156021i
$288$	−3.97107			−0.233997
$289$	4.97089	+	8.60983i	0.292405	+	0.506460i
$290$	0.168006	−	0.290995i	0.00986564	−	0.0170878i
$291$	6.52386	−	11.2997i	0.382435	−	0.662398i
$292$	−26.6248	−	46.1154i	−1.55810	−	2.69870i
$293$	26.8765			1.57014			0.785072	−	0.619405i	$-0.212626\pi$
$293$	26.8765			1.57014			0.785072	+	0.619405i	$0.212626\pi$
$294$	−15.0567	+	1.33748i	−0.878125	+	0.0780032i
$295$	5.23398			0.304734
$296$	−4.47516	−	7.75120i	−0.260113	−	0.450530i
$297$	−3.04027	+	5.26590i	−0.176414	+	0.305559i
$298$	−6.87251	+	11.9035i	−0.398114	+	0.689554i
$299$	−2.39889	−	4.15501i	−0.138732	−	0.240290i
$300$	14.3049			0.825892
$301$	−0.519934	−	11.7294i	−0.0299685	−	0.676073i
$302$	−15.5390			−0.894167
$303$	−3.40936	−	5.90519i	−0.195863	−	0.339244i
$304$	−4.29588	+	7.44068i	−0.246385	+	0.426752i
$305$	1.19321	−	2.06669i	0.0683228	−	0.118339i
$306$	7.02808	+	12.1730i	0.401768	+	0.695883i
$307$	−23.5760			−1.34555			−0.672777	−	0.739846i	$-0.734898\pi$
$307$	−23.5760			−1.34555			−0.672777	+	0.739846i	$0.734898\pi$
$308$	11.0711	−	7.06344i	0.630836	−	0.402477i
$309$	4.53546			0.258013
$310$	−9.19157	−	15.9203i	−0.522046	−	0.904211i
$311$	−14.1055	+	24.4315i	−0.799852	+	1.38538i	0.119860	+	0.992791i	$0.461755\pi$
$311$	−14.1055	+	24.4315i	−0.799852	+	1.38538i	−0.919712	+	0.392593i	$0.871578\pi$
$312$	−1.74477	+	3.02204i	−0.0987784	+	0.171089i
$313$	5.79313	+	10.0340i	0.327447	+	0.567155i	0.982005	−	0.188857i	$-0.0604783\pi$
$313$	5.79313	+	10.0340i	0.327447	+	0.567155i	−0.654557	+	0.756012i	$0.727145\pi$
$314$	8.23246			0.464585
$315$	4.62233	+	2.40233i	0.260439	+	0.135356i
$316$	−54.1668			−3.04712
$317$	12.6753	+	21.9543i	0.711918	+	1.23308i	0.964136	+	0.265407i	$0.0855065\pi$
$317$	12.6753	+	21.9543i	0.711918	+	1.23308i	−0.252219	+	0.967670i	$0.581160\pi$
$318$	10.8775	−	18.8404i	0.609981	−	1.05652i
$319$	−0.101555	+	0.175898i	−0.00568598	+	0.00984840i
$320$	4.51121	+	7.81364i	0.252184	+	0.436796i
$321$	−13.1388			−0.733335
$322$	30.2660	+	15.7299i	1.68666	+	0.876592i
$323$	−7.99601			−0.444910
$324$	−4.58822	−	7.94703i	−0.254901	−	0.441502i
$325$	1.88092	−	3.25785i	0.104335	−	0.180713i
$326$	−25.5682	+	44.2853i	−1.41609	+	2.45274i
$327$	−5.48876	−	9.50680i	−0.303529	−	0.525727i
$328$	4.34226			0.239761
$329$	5.03545	−	3.21265i	0.277613	−	0.177119i
$330$	2.52686			0.139099
$331$	11.4551	+	19.8407i	0.629627	+	1.09055i	0.987627	+	0.156824i	$0.0501254\pi$
$331$	11.4551	+	19.8407i	0.629627	+	1.09055i	−0.358000	+	0.933722i	$0.616541\pi$
$332$	9.00761	−	15.6016i	0.494357	−	0.856251i
$333$	−2.26360	+	3.92066i	−0.124044	+	0.214851i
$334$	−16.4171	−	28.4353i	−0.898306	−	1.55591i
$335$	3.78067			0.206560
$336$	−0.299832	−	6.76403i	−0.0163572	−	0.369008i
$337$	30.4011			1.65605			0.828026	−	0.560690i	$-0.189464\pi$
$337$	30.4011			1.65605			0.828026	+	0.560690i	$0.189464\pi$
$338$	−14.6897	−	25.4433i	−0.799014	−	1.38393i
$339$	2.72142	−	4.71364i	0.147807	−	0.256010i
$340$	4.52822	−	7.84310i	0.245577	−	0.425352i
$341$	5.55605	+	9.62336i	0.300877	+	0.521134i
$342$	15.9237			0.861055
$343$	−2.45401	−	18.3570i	−0.132504	−	0.991182i
$344$	19.2695			1.03894
$345$	2.15049	+	3.72476i	0.115779	+	0.200534i
$346$	12.9806	−	22.4830i	0.697841	−	1.20870i
$347$	−11.2940	+	19.5617i	−0.606292	+	1.05013i	0.385554	+	0.922685i	$0.374010\pi$
$347$	−11.2940	+	19.5617i	−0.606292	+	1.05013i	−0.991846	+	0.127443i	$0.959323\pi$
$348$	0.265213	+	0.459363i	0.0142169	+	0.0246244i
$349$	18.3169			0.980480			0.490240	−	0.871587i	$-0.336909\pi$
$349$	18.3169			0.980480			0.490240	+	0.871587i	$0.336909\pi$
$350$	1.18435	+	26.7183i	0.0633063	+	1.42815i
$351$	4.17594			0.222895
$352$	−1.18001	−	2.04384i	−0.0628947	−	0.108937i
$353$	−5.88921	+	10.2004i	−0.313451	+	0.542913i	−0.979107	−	0.203346i	$-0.934818\pi$
$353$	−5.88921	+	10.2004i	−0.313451	+	0.542913i	0.665656	+	0.746259i	$0.268152\pi$
$354$	−6.30397	+	10.9188i	−0.335052	+	0.580328i
$355$	−0.653484	−	1.13187i	−0.0346833	−	0.0600732i
$356$	16.4176			0.870133
$357$	5.31213	−	3.38917i	0.281148	−	0.179374i
$358$	15.8376			0.837045
$359$	3.93031	+	6.80750i	0.207434	+	0.359286i	0.950905	−	0.309482i	$-0.100155\pi$
$359$	3.93031	+	6.80750i	0.207434	+	0.359286i	−0.743472	+	0.668767i	$0.766822\pi$
$360$	−4.27483	+	7.40423i	−0.225303	+	0.390237i
$361$	4.97080	−	8.60969i	0.261621	−	0.453141i
$362$	−0.417873	−	0.723777i	−0.0219629	−	0.0380409i
$363$	8.33355			0.437398
$364$	−8.00272	−	4.15919i	−0.419457	−	0.218001i
$365$	12.5533			0.657072
$366$	2.87427	+	4.97838i	0.150240	+	0.260224i
$367$	14.8544	−	25.7285i	0.775392	−	1.34302i	−0.159182	−	0.987249i	$-0.550886\pi$
$367$	14.8544	−	25.7285i	0.775392	−	1.34302i	0.934574	−	0.355769i	$-0.115781\pi$
$368$	−7.63907	+	13.2313i	−0.398214	+	0.689727i
$369$	−1.09819	−	1.90212i	−0.0571694	−	0.0990202i
$370$	4.45104			0.231398
$371$	23.6510	+	12.2919i	1.22790	+	0.638166i
$372$	29.0195			1.50459
$373$	−14.9580	−	25.9081i	−0.774497	−	1.34147i	−0.935077	−	0.354446i	$-0.884670\pi$
$373$	−14.9580	−	25.9081i	−0.774497	−	1.34147i	0.160579	−	0.987023i	$-0.448664\pi$
$374$	−4.17681	+	7.23445i	−0.215978	+	0.374084i
$375$	−3.69522	+	6.40031i	−0.190820	+	0.330510i
$376$	4.90152	+	8.48967i	0.252776	+	0.437821i
$377$	0.139490			0.00718409
$378$	−25.0284	+	15.9683i	−1.28732	+	0.821319i
$379$	−12.7841			−0.656673			−0.328336	−	0.944561i	$-0.606488\pi$
$379$	−12.7841			−0.656673			−0.328336	+	0.944561i	$0.606488\pi$
$380$	−5.12985	−	8.88517i	−0.263156	−	0.455800i
$381$	−4.58147	+	7.93534i	−0.234716	+	0.406540i
$382$	−19.6326	+	34.0047i	−1.00449	+	1.73983i
$383$	−17.3166	−	29.9933i	−0.884839	−	1.53259i	−0.845898	−	0.533345i	$-0.820935\pi$
$383$	−17.3166	−	29.9933i	−0.884839	−	1.53259i	−0.0389415	−	0.999241i	$-0.512399\pi$
$384$	−18.4922			−0.943675
$385$	0.137100	+	3.09289i	0.00698725	+	0.157628i
$386$	43.6518			2.22182
$387$	−4.87338	−	8.44094i	−0.247728	−	0.429077i
$388$	−27.6733	+	47.9315i	−1.40490	+	2.43336i
$389$	6.34201	−	10.9847i	0.321553	−	0.556946i	−0.659256	−	0.751919i	$-0.729129\pi$
$389$	6.34201	−	10.9847i	0.321553	−	0.556946i	0.980809	+	0.194973i	$0.0624619\pi$
$390$	−0.867685	−	1.50287i	−0.0439369	−	0.0761010i
$391$	−14.2188			−0.719074
$392$	30.2766	−	2.68945i	1.52920	−	0.135838i
$393$	−16.3088			−0.822672
$394$	−3.26554	−	5.65607i	−0.164515	−	0.284949i
$395$	6.38480	−	11.0588i	0.321254	−	0.556428i
$396$	5.45098	−	9.44137i	0.273922	−	0.474447i
$397$	6.77570	+	11.7359i	0.340063	+	0.589006i	0.984444	−	0.175698i	$-0.0562183\pi$
$397$	6.77570	+	11.7359i	0.340063	+	0.589006i	−0.644381	+	0.764704i	$0.722885\pi$
$398$	−18.0617			−0.905350
$399$	−0.316116	−	7.13140i	−0.0158256	−	0.357017i
$400$	−11.9793			−0.598964
$401$	4.97918	+	8.62420i	0.248649	+	0.430672i	0.963151	−	0.268961i	$-0.0866802\pi$
$401$	4.97918	+	8.62420i	0.248649	+	0.430672i	−0.714503	+	0.699633i	$0.753347\pi$
$402$	−4.55356	+	7.88699i	−0.227111	+	0.393367i
$403$	3.81573	−	6.60904i	0.190075	−	0.329220i
$404$	14.4620	+	25.0490i	0.719513	+	1.24623i
$405$	2.16331			0.107496
$406$	−0.836029	+	0.533392i	−0.0414914	+	0.0264718i
$407$	−2.69053			−0.133365
$408$	5.17083	+	8.95615i	0.255994	+	0.443395i
$409$	−15.5389	+	26.9142i	−0.768351	+	1.33082i	0.170105	+	0.985426i	$0.445589\pi$
$409$	−15.5389	+	26.9142i	−0.768351	+	1.33082i	−0.938457	+	0.345397i	$0.887744\pi$
$410$	−1.07971	+	1.87012i	−0.0533233	+	0.0923586i
$411$	3.29744	+	5.71134i	0.162651	+	0.281720i
$412$	−19.2388			−0.947826
$413$	−13.7067	−	7.12369i	−0.674464	−	0.350534i
$414$	28.3161			1.39166
$415$	2.12351	+	3.67802i	0.104239	+	0.180547i
$416$	−0.810396	+	1.40365i	−0.0397329	+	0.0688195i
$417$	−9.55241	+	16.5453i	−0.467783	+	0.810224i
$418$	4.73176	+	8.19565i	0.231438	+	0.400862i
$419$	−8.89660			−0.434627			−0.217314	−	0.976102i	$-0.569729\pi$
$419$	−8.89660			−0.434627			−0.217314	+	0.976102i	$0.569729\pi$
$420$	7.17405	+	3.72851i	0.350058	+	0.181933i
$421$	14.3826			0.700964			0.350482	−	0.936569i	$-0.386018\pi$
$421$	14.3826			0.700964			0.350482	+	0.936569i	$0.386018\pi$
$422$	−29.4601	−	51.0264i	−1.43410	−	2.48393i
$423$	2.47925	−	4.29419i	0.120545	−	0.208791i
$424$	−21.8730	+	37.8851i	−1.06224	+	1.83986i
$425$	−5.57432	−	9.65501i	−0.270394	−	0.468337i
$426$	3.14830			0.152536
$427$	−5.93762	+	3.78824i	−0.287342	+	0.183326i
$428$	55.7328			2.69395
$429$	0.524491	+	0.908446i	0.0253227	+	0.0438602i
$430$	−4.79140	+	8.29895i	−0.231062	+	0.400211i
$431$	−11.6448	+	20.1694i	−0.560911	+	0.971526i	0.436506	+	0.899701i	$0.356216\pi$
$431$	−11.6448	+	20.1694i	−0.560911	+	0.971526i	−0.997417	+	0.0718251i	$0.977118\pi$
$432$	−6.64896	−	11.5163i	−0.319898	−	0.554080i
$433$	−38.2638			−1.83884			−0.919420	−	0.393277i	$-0.871341\pi$
$433$	−38.2638			−1.83884			−0.919420	+	0.393277i	$0.871341\pi$
$434$	2.40264	+	54.2021i	0.115330	+	2.60178i
$435$	−0.125046			−0.00599548
$436$	23.2825	+	40.3265i	1.11503	+	1.93129i
$437$	−8.05397	+	13.9499i	−0.385273	+	0.667313i
$438$	−15.1196	+	26.1880i	−0.722444	+	1.25131i
$439$	13.0493	+	22.6020i	0.622809	+	1.07874i	0.988960	+	0.148181i	$0.0473419\pi$
$439$	13.0493	+	22.6020i	0.622809	+	1.07874i	−0.366151	+	0.930555i	$0.619325\pi$
$440$	−5.08110			−0.242232
$441$	−8.83527	−	12.5824i	−0.420727	−	0.599163i
$442$	5.73702			0.272882
$443$	−10.4810	−	18.1535i	−0.497965	−	0.862501i	0.502032	−	0.864849i	$-0.332586\pi$
$443$	−10.4810	−	18.1535i	−0.497965	−	0.862501i	−0.999997	+	0.00234806i	$0.999253\pi$
$444$	−3.51319	+	6.08503i	−0.166729	+	0.288783i
$445$	−1.93519	+	3.35185i	−0.0917370	+	0.158893i
$446$	11.0505	+	19.1400i	0.523257	+	0.906307i
$447$	5.11517			0.241939
$448$	−1.17921	−	26.6023i	−0.0557124	−	1.25684i
$449$	12.4845			0.589181			0.294590	−	0.955624i	$-0.404817\pi$
$449$	12.4845			0.589181			0.294590	+	0.955624i	$0.404817\pi$
$450$	11.1010	+	19.2275i	0.523307	+	0.906394i
$451$	0.652657	−	1.13043i	0.0307324	−	0.0532301i
$452$	−11.5439	+	19.9946i	−0.542979	+	0.940467i
$453$	2.89139	+	5.00804i	0.135849	+	0.235298i
$454$	63.0886			2.96089
$455$	1.79245	−	1.14359i	0.0840314	−	0.0536125i
$456$	11.7157			0.548638
$457$	−12.9805	−	22.4829i	−0.607202	−	1.05170i	−0.991699	−	0.128579i	$-0.958958\pi$
$457$	−12.9805	−	22.4829i	−0.607202	−	1.05170i	0.384497	−	0.923126i	$-0.374375\pi$
$458$	9.68052	−	16.7671i	0.452341	−	0.783477i
$459$	6.18793	−	10.7178i	0.288828	−	0.500264i
$460$	−9.12208	−	15.7999i	−0.425319	−	0.736674i
$461$	−30.5008			−1.42056			−0.710282	−	0.703918i	$-0.751432\pi$
$461$	−30.5008			−1.42056			−0.710282	+	0.703918i	$0.751432\pi$
$462$	−6.61732	−	3.43916i	−0.307865	−	0.160004i
$463$	4.72338			0.219514			0.109757	−	0.993958i	$-0.464993\pi$
$463$	4.72338			0.219514			0.109757	+	0.993958i	$0.464993\pi$
$464$	−0.222097	−	0.384682i	−0.0103106	−	0.0178584i
$465$	−3.42062	+	5.92468i	−0.158627	+	0.274751i
$466$	−23.2372	+	40.2480i	−1.07644	+	1.86445i
$467$	0.146385	+	0.253547i	0.00677390	+	0.0117327i	0.869392	−	0.494122i	$-0.164510\pi$
$467$	0.146385	+	0.253547i	0.00677390	+	0.0117327i	−0.862619	+	0.505855i	$0.831177\pi$
$468$	−7.48714			−0.346093
$469$	−9.90080	−	5.14566i	−0.457176	−	0.237605i
$470$	−4.87510			−0.224871
$471$	−1.53184	−	2.65323i	−0.0705836	−	0.122254i
$472$	12.6763	−	21.9560i	0.583473	−	1.01060i
$473$	2.89627	−	5.01648i	0.133171	−	0.230658i
$474$	15.3801	+	26.6391i	0.706431	+	1.22357i
$475$	−12.6299			−0.579499
$476$	−22.5333	+	14.3764i	−1.03281	+	0.658940i
$477$	22.1273			1.01314
$478$	−22.5586	−	39.0727i	−1.03181	−	1.78714i
$479$	14.7911	−	25.6189i	0.675822	−	1.17056i	−0.300406	−	0.953811i	$-0.597122\pi$
$479$	14.7911	−	25.6189i	0.675822	−	1.17056i	0.976228	−	0.216746i	$-0.0695444\pi$
$480$	0.726480	−	1.25830i	0.0331591	−	0.0574333i
$481$	0.923888	+	1.60022i	0.0421257	+	0.0729638i
$482$	−42.2897			−1.92624
$483$	−0.562129	−	12.6813i	−0.0255777	−	0.577019i
$484$	−35.3497			−1.60681
$485$	−6.52386	−	11.2997i	−0.296233	−	0.513091i
$486$	−19.4374	+	33.6665i	−0.881696	+	1.52714i
$487$	6.00928	−	10.4084i	0.272306	−	0.471649i	−0.697146	−	0.716930i	$-0.745547\pi$
$487$	6.00928	−	10.4084i	0.272306	−	0.471649i	0.969452	+	0.245281i	$0.0788802\pi$
$488$	−5.77969	−	10.0107i	−0.261634	−	0.453164i
$489$	19.0302			0.860577
$490$	−6.37007	+	13.7082i	−0.287770	+	0.619275i
$491$	−7.02928			−0.317227			−0.158613	−	0.987341i	$-0.550702\pi$
$491$	−7.02928			−0.317227			−0.158613	+	0.987341i	$0.550702\pi$
$492$	−1.70443	−	2.95216i	−0.0768417	−	0.133094i
$493$	0.206697	−	0.358009i	0.00930915	−	0.0161239i
$494$	3.24963	−	5.62853i	0.146208	−	0.253239i
$495$	1.28504	+	2.22576i	0.0577585	+	0.100041i
$496$	−24.3017			−1.09118
$497$	0.170818	+	3.85355i	0.00766222	+	0.172855i
$498$	−10.2305			−0.458438
$499$	15.4259	+	26.7185i	0.690558	+	1.19608i	0.971655	+	0.236403i	$0.0759685\pi$
$499$	15.4259	+	26.7185i	0.690558	+	1.19608i	−0.281097	+	0.959679i	$0.590698\pi$
$500$	15.6746	−	27.1492i	0.700989	−	1.21415i
$501$	−6.10959	+	10.5821i	−0.272956	+	0.472774i
$502$	−6.40377	−	11.0917i	−0.285814	−	0.495045i
$503$	15.0642			0.671681			0.335840	−	0.941919i	$-0.390980\pi$
$503$	15.0642			0.671681			0.335840	+	0.941919i	$0.390980\pi$
$504$	21.2724	−	13.5719i	0.947548	−	0.604541i
$505$	−6.81873			−0.303429
$506$	8.41417	+	14.5738i	0.374055	+	0.647883i
$507$	−5.46673	+	9.46865i	−0.242786	+	0.420518i
$508$	19.4339	−	33.6606i	0.862242	−	1.49345i
$509$	1.53769	+	2.66336i	0.0681570	+	0.118051i	0.898090	−	0.439812i	$-0.144955\pi$
$509$	1.53769	+	2.66336i	0.0681570	+	0.118051i	−0.829933	+	0.557863i	$0.811621\pi$
$510$	−5.14296			−0.227734
$511$	−32.8746	−	17.0857i	−1.45429	−	0.755826i
$512$	29.9527			1.32374
$513$	−7.01008	−	12.1418i	−0.309502	−	0.536074i
$514$	2.10965	−	3.65402i	0.0930526	−	0.161172i
$515$	2.26773	−	3.92782i	0.0999281	−	0.173080i
$516$	−7.56368	−	13.1007i	−0.332973	−	0.576725i
$517$	2.94686			0.129603
$518$	−11.6564	−	6.05806i	−0.512151	−	0.266176i
$519$	−9.66138			−0.424088
$520$	1.74477	+	3.02204i	0.0765134	+	0.132525i
$521$	−8.86932	+	15.3621i	−0.388572	+	0.673026i	−0.992258	−	0.124196i	$-0.960365\pi$
$521$	−8.86932	+	15.3621i	−0.388572	+	0.673026i	0.603686	+	0.797222i	$0.293698\pi$
$522$	−0.411627	+	0.712959i	−0.0180164	+	0.0312054i
$523$	7.47436	+	12.9460i	0.326831	+	0.566088i	0.981881	−	0.189497i	$-0.0606859\pi$
$523$	7.47436	+	12.9460i	0.326831	+	0.566088i	−0.655050	+	0.755585i	$0.727353\pi$
$524$	69.1797			3.02213
$525$	8.39064	−	5.35328i	0.366198	−	0.233636i
$526$	19.6586			0.857154
$527$	−11.3083	−	19.5866i	−0.492599	−	0.853207i
$528$	1.67020	−	2.89287i	0.0726860	−	0.125896i
$529$	−2.82183	+	4.88755i	−0.122688	+	0.212502i
$530$	−10.8775	−	18.8404i	−0.472490	−	0.818376i
$531$	−12.8237			−0.556500
$532$	1.34092	+	30.2504i	0.0581363	+	1.31152i
$533$	−0.896451			−0.0388296
$534$	−4.66162	−	8.07415i	−0.201728	−	0.349403i
$535$	−6.56939	+	11.3785i	−0.284019	+	0.491936i
$536$	9.15646	−	15.8595i	0.395499	−	0.685024i
$537$	−2.94697	−	5.10430i	−0.127171	−	0.220267i
$538$	69.0783			2.97818
$539$	3.85053	−	8.28624i	0.165854	−	0.356914i
$540$	15.8795			0.683345
$541$	−1.79372	−	3.10681i	−0.0771180	−	0.133572i	0.824887	−	0.565297i	$-0.191238\pi$
$541$	−1.79372	−	3.10681i	−0.0771180	−	0.133572i	−0.902005	+	0.431725i	$0.857905\pi$
$542$	−2.67279	+	4.62941i	−0.114806	+	0.198850i
$543$	−0.155510	+	0.269351i	−0.00667358	+	0.0115590i
$544$	2.40170	+	4.15986i	0.102972	+	0.178353i
$545$	−10.9775			−0.470225
$546$	0.226809	+	5.11668i	0.00970653	+	0.218974i
$547$	15.7526			0.673531			0.336765	−	0.941589i	$-0.390667\pi$
$547$	15.7526			0.673531			0.336765	+	0.941589i	$0.390667\pi$
$548$	−13.9873	−	24.2267i	−0.597507	−	1.03491i
$549$	−2.92345	+	5.06356i	−0.124770	+	0.216107i
$550$	−6.59738	+	11.4270i	−0.281313	+	0.487249i
$551$	−0.234159	−	0.405575i	−0.00997551	−	0.0172781i
$552$	20.8332			0.886722
$553$	−31.7720	+	20.2707i	−1.35108	+	0.861998i
$554$	−9.77927			−0.415481
$555$	−0.828220	−	1.43452i	−0.0351560	−	0.0608920i
$556$	40.5199	−	70.1826i	1.71843	−	2.97641i
$557$	−5.96441	+	10.3307i	−0.252720	+	0.437724i	−0.964274	−	0.264908i	$-0.914659\pi$
$557$	−5.96441	+	10.3307i	−0.252720	+	0.437724i	0.711554	+	0.702632i	$0.247992\pi$
$558$	22.5201	+	39.0059i	0.953350	+	1.65125i
$559$	−3.97814			−0.168258
$560$	−6.00774	−	3.12235i	−0.253873	−	0.131944i
$561$	3.10878			0.131253
$562$	−21.8124	−	37.7802i	−0.920100	−	1.59366i
$563$	13.8251	−	23.9457i	0.582657	−	1.00919i	−0.412506	−	0.910955i	$-0.635346\pi$
$563$	13.8251	−	23.9457i	0.582657	−	1.00919i	0.995163	−	0.0982371i	$-0.0313204\pi$
$564$	3.84790	−	6.66476i	0.162026	−	0.280637i
$565$	−2.72142	−	4.71364i	−0.114491	−	0.198304i
$566$	16.4723			0.692382
$567$	−5.66526	−	2.94436i	−0.237918	−	0.123651i
$568$	−6.33073			−0.265632
$569$	6.37186	+	11.0364i	0.267122	+	0.462669i	0.968117	−	0.250497i	$-0.0805939\pi$
$569$	6.37186	+	11.0364i	0.267122	+	0.462669i	−0.700995	+	0.713166i	$0.747261\pi$
$570$	−2.91314	+	5.04570i	−0.122018	+	0.211341i
$571$	−10.2874	+	17.8183i	−0.430514	+	0.745673i	−0.996918	−	0.0784556i	$-0.975001\pi$
$571$	−10.2874	+	17.8183i	−0.430514	+	0.745673i	0.566403	+	0.824128i	$0.308334\pi$
$572$	−2.22482	−	3.85350i	−0.0930243	−	0.161123i
$573$	14.6125			0.610444
$574$	5.37287	−	3.42792i	0.224259	−	0.143079i
$575$	−22.4589			−0.936601
$576$	−11.0528	−	19.1440i	−0.460534	−	0.797668i
$577$	12.9819	−	22.4854i	0.540445	−	0.936078i	−0.458433	−	0.888729i	$-0.651589\pi$
$577$	12.9819	−	22.4854i	0.540445	−	0.936078i	0.998878	−	0.0473494i	$-0.0150774\pi$
$578$	−11.9742	+	20.7399i	−0.498060	+	0.862666i
$579$	−8.12244	−	14.0685i	−0.337557	−	0.584666i
$580$	0.530426			0.0220248
$581$	−0.555075	−	12.5222i	−0.0230284	−	0.519507i
$582$	31.4302			1.30282
$583$	6.57516	+	11.3885i	0.272315	+	0.471664i
$584$	30.4032	−	52.6598i	1.25809	−	2.17908i
$585$	0.882531	−	1.52859i	0.0364882	−	0.0631993i
$586$	32.3709	+	56.0681i	1.33723	+	2.31615i
$587$	−38.0271			−1.56955			−0.784773	−	0.619783i	$-0.787220\pi$
$587$	−38.0271			−1.56955			−0.784773	+	0.619783i	$0.787220\pi$
$588$	−13.7127	−	19.5284i	−0.565502	−	0.805338i
$589$	−25.6216			−1.05572
$590$	6.30397	+	10.9188i	0.259531	+	0.449520i
$591$	−1.21526	+	2.10489i	−0.0499891	+	0.0865837i
$592$	2.94204	−	5.09577i	0.120917	−	0.209435i
$593$	−20.2433	−	35.0624i	−0.831291	−	1.43984i	−0.897015	−	0.442001i	$-0.854269\pi$
$593$	−20.2433	−	35.0624i	−0.831291	−	1.43984i	0.0657236	−	0.997838i	$-0.479064\pi$
$594$	−14.6472			−0.600981
$595$	−0.279042	−	6.29502i	−0.0114396	−	0.258071i
$596$	−21.6978			−0.888778
$597$	3.36080	+	5.82108i	0.137548	+	0.238241i
$598$	5.77860	−	10.0088i	0.236305	−	0.409292i
$599$	20.0089	−	34.6564i	0.817540	−	1.41602i	−0.0899496	−	0.995946i	$-0.528671\pi$
$599$	20.0089	−	34.6564i	0.817540	−	1.41602i	0.907490	−	0.420075i	$-0.137996\pi$
$600$	8.16746	+	14.1465i	0.333435	+	0.577527i
$601$	−18.2716			−0.745316			−0.372658	−	0.927969i	$-0.621554\pi$
$601$	−18.2716			−0.745316			−0.372658	+	0.927969i	$0.621554\pi$
$602$	23.8429	−	15.2119i	0.971766	−	0.619992i
$603$	−9.26293			−0.377216
$604$	−12.2649	−	21.2434i	−0.499051	−	0.864381i
$605$	4.16678	−	7.21707i	0.169404	−	0.293415i
$606$	8.21269	−	14.2248i	0.333618	−	0.577843i
$607$	15.0916	+	26.1394i	0.612548	+	1.06096i	0.990809	+	0.135266i	$0.0431889\pi$
$607$	15.0916	+	26.1394i	0.612548	+	1.06096i	−0.378261	+	0.925699i	$0.623478\pi$
$608$	5.44159			0.220686
$609$	0.327469	+	0.170193i	0.0132697	+	0.00689657i
$610$	5.74854			0.232751
$611$	−1.01191	−	1.75268i	−0.0409374	−	0.0709057i
$612$	−11.0945	+	19.2162i	−0.448468	+	0.776769i
$613$	20.0359	−	34.7032i	0.809243	−	1.40165i	−0.104146	−	0.994562i	$-0.533211\pi$
$613$	20.0359	−	34.7032i	0.809243	−	1.40165i	0.913389	−	0.407088i	$-0.133456\pi$
$614$	−28.3957	−	49.1827i	−1.14596	−	1.98485i
$615$	0.803625			0.0324053
$616$	13.3064	+	6.91560i	0.536128	+	0.278638i
$617$	43.3379			1.74472			0.872358	−	0.488867i	$-0.162590\pi$
$617$	43.3379			1.74472			0.872358	+	0.488867i	$0.162590\pi$
$618$	5.46265	+	9.46158i	0.219740	+	0.380601i
$619$	−11.8397	+	20.5069i	−0.475876	+	0.824241i	−0.999618	−	0.0276356i	$-0.991202\pi$
$619$	−11.8397	+	20.5069i	−0.475876	+	0.824241i	0.523742	+	0.851877i	$0.324536\pi$
$620$	14.5098	−	25.1317i	0.582726	−	1.00931i
$621$	−12.4656	−	21.5910i	−0.500225	−	0.866416i
$622$	−67.9566			−2.72481
$623$	9.62990	−	6.14393i	0.385814	−	0.246151i
$624$	−2.29409			−0.0918369
$625$	−6.79572	−	11.7705i	−0.271829	−	0.470821i
$626$	−13.9549	+	24.1705i	−0.557749	+	0.966049i
$627$	1.76091	−	3.04999i	0.0703240	−	0.121805i
$628$	6.49786	+	11.2546i	0.259293	+	0.449109i
$629$	5.47609			0.218346
$630$	0.555699	+	12.5363i	0.0221396	+	0.499457i
$631$	−15.6187			−0.621772			−0.310886	−	0.950447i	$-0.600626\pi$
$631$	−15.6187			−0.621772			−0.310886	+	0.950447i	$0.600626\pi$
$632$	−30.9269	−	53.5669i	−1.23021	−	2.13078i
$633$	−10.9635	+	18.9893i	−0.435760	+	0.754758i
$634$	−30.5331	+	52.8849i	−1.21263	+	2.10033i
$635$	4.58147	+	7.93534i	0.181810	+	0.314904i
$636$	34.3424			1.36177
$637$	−6.25055	+	0.555232i	−0.247656	+	0.0219991i
$638$	−0.489263			−0.0193701
$639$	1.60109	+	2.77316i	0.0633380	+	0.109705i
$640$	−9.24609	+	16.0147i	−0.365484	+	0.633036i
$641$	−4.74956	+	8.22648i	−0.187596	+	0.324926i	−0.944448	−	0.328660i	$-0.893403\pi$
$641$	−4.74956	+	8.22648i	−0.187596	+	0.324926i	0.756852	+	0.653586i	$0.226736\pi$
$642$	−15.8248	−	27.4093i	−0.624553	−	1.08176i
$643$	33.6019			1.32513			0.662564	−	0.749005i	$-0.269468\pi$
$643$	33.6019			1.32513			0.662564	+	0.749005i	$0.269468\pi$
$644$	2.38447	+	53.7923i	0.0939613	+	2.11971i
$645$	3.56621			0.140419
$646$	−9.63065	−	16.6808i	−0.378913	−	0.656296i
$647$	−7.47226	+	12.9423i	−0.293765	+	0.508816i	−0.974697	−	0.223531i	$-0.928242\pi$
$647$	−7.47226	+	12.9423i	−0.293765	+	0.508816i	0.680932	+	0.732347i	$0.261575\pi$
$648$	5.23935	−	9.07482i	0.205821	−	0.356492i
$649$	−3.81058	−	6.60011i	−0.149578	−	0.259077i
$650$	9.06177			0.355432
$651$	17.0217	−	10.8599i	0.667131	−	0.425634i
$652$	−80.7235			−3.16138
$653$	−7.58835	−	13.1434i	−0.296955	−	0.514341i	0.678483	−	0.734616i	$-0.262638\pi$
$653$	−7.58835	−	13.1434i	−0.296955	−	0.514341i	−0.975438	+	0.220275i	$0.929304\pi$
$654$	13.2217	−	22.9006i	0.517008	−	0.895484i
$655$	−8.15442	+	14.1239i	−0.318619	+	0.551865i
$656$	1.42734	+	2.47222i	0.0557281	+	0.0965239i
$657$	−30.7567			−1.19993
$658$	12.7669	+	6.63523i	0.497705	+	0.258668i
$659$	8.09942			0.315509			0.157754	−	0.987478i	$-0.449575\pi$
$659$	8.09942			0.315509			0.157754	+	0.987478i	$0.449575\pi$
$660$	1.99444	+	3.45447i	0.0776335	+	0.134465i
$661$	−7.51489	+	13.0162i	−0.292295	+	0.506270i	−0.974352	−	0.225029i	$-0.927752\pi$
$661$	−7.51489	+	13.0162i	−0.292295	+	0.506270i	0.682057	+	0.731299i	$0.261086\pi$
$662$	−27.5936	+	47.7936i	−1.07246	+	1.85755i
$663$	−1.06751	−	1.84898i	−0.0414586	−	0.0718084i
$664$	20.5718			0.798341
$665$	−6.33403	−	3.29194i	−0.245623	−	0.127656i
$666$	−10.9054			−0.422575
$667$	−0.416390	−	0.721208i	−0.0161227	−	0.0279253i
$668$	25.9160	−	44.8879i	1.00272	−	1.73676i
$669$	4.11241	−	7.12291i	0.158995	−	0.275388i
$670$	4.55356	+	7.88699i	0.175919	+	0.304701i
$671$	−3.47483			−0.134144
$672$	−3.61511	+	2.30646i	−0.139456	+	0.0889736i
$673$	44.9730			1.73358			0.866790	−	0.498673i	$-0.166179\pi$
$673$	44.9730			1.73358			0.866790	+	0.498673i	$0.166179\pi$
$674$	36.6160	+	63.4208i	1.41040	+	2.44288i
$675$	9.77398	−	16.9290i	0.376201	−	0.651599i
$676$	23.1891	−	40.1647i	0.891888	−	1.54479i
$677$	−25.8791	−	44.8240i	−0.994616	−	1.72273i	−0.587050	−	0.809551i	$-0.699711\pi$
$677$	−25.8791	−	44.8240i	−0.994616	−	1.72273i	−0.407567	−	0.913175i	$-0.633623\pi$
$678$	13.1111			0.503527
$679$	1.70531	+	38.4708i	0.0654437	+	1.47637i
$680$	10.3417			0.396585
$681$	−11.7391	−	20.3328i	−0.449844	−	0.779153i
$682$	−13.3838	+	23.1813i	−0.512491	+	0.887660i
$683$	7.15459	−	12.3921i	0.273763	−	0.474171i	−0.696059	−	0.717984i	$-0.745065\pi$
$683$	7.15459	−	12.3921i	0.273763	−	0.474171i	0.969822	+	0.243813i	$0.0783983\pi$
$684$	12.5685	+	21.7694i	0.480570	+	0.832372i
$685$	6.59489			0.251978
$686$	35.3394	−	27.2291i	1.34927	−	1.03961i
$687$	−7.20515			−0.274894
$688$	6.33403	+	10.9709i	0.241483	+	0.418260i
$689$	4.51563	−	7.82130i	0.172032	−	0.297968i
$690$	−5.18024	+	8.97243i	−0.197208	+	0.341575i
$691$	−14.0318	−	24.3037i	−0.533793	−	0.924557i	−0.999221	−	0.0394709i	$-0.987433\pi$
$691$	−14.0318	−	24.3037i	−0.533793	−	0.924557i	0.465428	−	0.885086i	$-0.345901\pi$
$692$	40.9822			1.55791
$693$	−0.335905	−	7.57782i	−0.0127600	−	0.287858i
$694$	−54.4112			−2.06542
$695$	9.55241	+	16.5453i	0.362343	+	0.627597i
$696$	−0.302850	+	0.524552i	−0.0114795	+	0.0198831i
$697$	−1.32837	+	2.30080i	−0.0503155	+	0.0871489i
$698$	22.0614	+	38.2115i	0.835037	+	1.44633i
$699$	17.2953			0.654169
$700$	−35.5919	+	22.7078i	−1.34525	+	0.858275i
$701$	42.0578			1.58850			0.794250	−	0.607591i	$-0.207864\pi$
$701$	42.0578			1.58850			0.794250	+	0.607591i	$0.207864\pi$
$702$	5.02963	+	8.71157i	0.189831	+	0.328797i
$703$	3.10183	−	5.37253i	0.116988	−	0.202629i
$704$	6.56872	−	11.3774i	0.247568	−	0.428801i
$705$	0.907126	+	1.57119i	0.0341644	+	0.0591744i
$706$	−28.3726			−1.06782
$707$	17.8568	+	9.28059i	0.671576	+	0.349033i
$708$	−19.9028			−0.747995
$709$	−3.71921	−	6.44187i	−0.139678	−	0.241929i	0.787697	−	0.616063i	$-0.211273\pi$
$709$	−3.71921	−	6.44187i	−0.139678	−	0.241929i	−0.927375	+	0.374134i	$0.877940\pi$
$710$	1.57415	−	2.72651i	0.0590769	−	0.102324i
$711$	−15.6432	+	27.0949i	−0.586668	+	1.01614i
$712$	9.37376	+	16.2358i	0.351296	+	0.608463i
$713$	−45.5612			−1.70628
$714$	13.4684	+	6.99980i	0.504041	+	0.261961i
$715$	1.04898			0.0392297
$716$	12.5006	+	21.6517i	0.467170	+	0.809162i
$717$	−8.39512	+	14.5408i	−0.313522	+	0.543035i
$718$	−9.46758	+	16.3983i	−0.353327	+	0.611980i
$719$	17.0252	+	29.4885i	0.634933	+	1.09974i	0.986529	+	0.163584i	$0.0523055\pi$
$719$	17.0252	+	29.4885i	0.634933	+	1.09974i	−0.351597	+	0.936152i	$0.614361\pi$
$720$	−5.62069			−0.209471
$721$	−11.2847	+	7.19968i	−0.420263	+	0.268130i
$722$	23.9480			0.891251
$723$	7.86899	+	13.6295i	0.292651	+	0.506886i
$724$	0.659652	−	1.14255i	0.0245158	−	0.0424626i
$725$	0.326482	−	0.565484i	0.0121253	−	0.0210016i
$726$	10.0372	+	17.3849i	0.372515	+	0.645215i
$727$	23.9058			0.886616			0.443308	−	0.896369i	$-0.353805\pi$
$727$	23.9058			0.886616			0.443308	+	0.896369i	$0.353805\pi$
$728$	−0.456076	−	10.2888i	−0.0169033	−	0.381329i
$729$	7.22754			0.267687
$730$	15.1196	+	26.1880i	0.559603	+	0.969261i
$731$	−5.89484	+	10.2102i	−0.218028	+	0.377636i
$732$	−4.53731	+	7.85885i	−0.167704	+	0.290471i
$733$	14.3011	+	24.7702i	0.528224	+	0.914910i	0.999459	+	0.0329023i	$0.0104750\pi$
$733$	14.3011	+	24.7702i	0.528224	+	0.914910i	−0.471235	+	0.882008i	$0.656192\pi$
$734$	71.5643			2.64148
$735$	5.60331	−	0.497738i	0.206681	−	0.0183593i
$736$	9.67642			0.356678
$737$	−2.75250	−	4.76746i	−0.101390	−	0.175612i
$738$	2.64538	−	4.58194i	0.0973779	−	0.168663i
$739$	−13.9154	+	24.1022i	−0.511887	+	0.886614i	0.488018	+	0.872833i	$0.337720\pi$
$739$	−13.9154	+	24.1022i	−0.511887	+	0.886614i	−0.999905	+	0.0137805i	$0.995613\pi$
$740$	3.51319	+	6.08503i	0.129148	+	0.223690i
$741$	−2.41868			−0.0888525
$742$	2.84334	+	64.1440i	0.104382	+	2.35480i
$743$	36.1223			1.32520			0.662599	−	0.748975i	$-0.269453\pi$
$743$	36.1223			1.32520			0.662599	+	0.748975i	$0.269453\pi$
$744$	16.5689	+	28.6982i	0.607445	+	1.05213i
$745$	2.55759	−	4.42987i	0.0937027	−	0.162298i
$746$	36.0318	−	62.4090i	1.31922	−	2.28495i
$747$	−5.20275	−	9.01143i	−0.190359	−	0.329711i
$748$	−13.1870			−0.482164
$749$	32.6906	−	20.8568i	1.19449	−	0.762090i
$750$	−17.8025			−0.650057
$751$	−10.5659	−	18.3007i	−0.385556	−	0.667803i	0.606290	−	0.795244i	$-0.292657\pi$
$751$	−10.5659	−	18.3007i	−0.385556	−	0.667803i	−0.991846	+	0.127441i	$0.959324\pi$
$752$	−3.22233	+	5.58125i	−0.117506	+	0.203527i
$753$	−2.38315	+	4.12773i	−0.0868467	+	0.150423i
$754$	0.168006	+	0.290995i	0.00611841	+	0.0105974i
$755$	5.78278			0.210457
$756$	−41.5851	−	21.6127i	−1.51244	−	0.786047i
$757$	−37.1869			−1.35158			−0.675791	−	0.737093i	$-0.736198\pi$
$757$	−37.1869			−1.35158			−0.675791	+	0.737093i	$0.736198\pi$
$758$	−15.3975	−	26.6693i	−0.559263	−	0.968672i
$759$	3.13131	−	5.42359i	0.113659	−	0.196864i
$760$	5.85785	−	10.1461i	0.212487	−	0.368037i
$761$	19.5201	+	33.8097i	0.707602	+	1.22560i	0.965744	+	0.259495i	$0.0835562\pi$
$761$	19.5201	+	33.8097i	0.707602	+	1.22560i	−0.258143	+	0.966107i	$0.583110\pi$
$762$	−22.0723			−0.799593
$763$	28.7479	+	14.9409i	1.04074	+	0.540897i
$764$	−61.9840			−2.24250
$765$	−2.61548	−	4.53014i	−0.0945628	−	0.163788i
$766$	41.7134	−	72.2498i	1.50717	−	2.61049i
$767$	−2.61699	+	4.53276i	−0.0944941	+	0.163669i
$768$	−13.2501	−	22.9499i	−0.478123	−	0.828134i
$769$	7.69986			0.277664			0.138832	−	0.990316i	$-0.455665\pi$
$769$	7.69986			0.277664			0.138832	+	0.990316i	$0.455665\pi$
$770$	−6.28706	+	4.01118i	−0.226570	+	0.144553i
$771$	−1.57020			−0.0565493
$772$	34.4543	+	59.6765i	1.24004	+	2.14780i
$773$	3.24947	−	5.62824i	0.116875	−	0.202434i	−0.801653	−	0.597790i	$-0.796046\pi$
$773$	3.24947	−	5.62824i	0.116875	−	0.202434i	0.918528	+	0.395356i	$0.129379\pi$
$774$	11.7393	−	20.3331i	0.421961	−	0.730857i
$775$	−17.8618	−	30.9376i	−0.641615	−	1.11131i
$776$	−63.2010			−2.26878
$777$	0.216493	+	4.88396i	0.00776665	+	0.175211i
$778$	30.5541			1.09542
$779$	1.50486	+	2.60649i	0.0539171	+	0.0933872i
$780$	1.36972	−	2.37243i	0.0490440	−	0.0849466i
$781$	−0.951531	+	1.64810i	−0.0340485	+	0.0589737i
$782$	−17.1255	−	29.6623i	−0.612408	−	1.06072i
$783$	0.724841			0.0259037
$784$	11.4834	+	16.3536i	0.410121	+	0.584058i
$785$	−3.06369			−0.109348
$786$	−19.6429	−	34.0224i	−0.700638	−	1.21354i
$787$	−10.0970	+	17.4885i	−0.359920	+	0.623399i	−0.987947	−	0.154792i	$-0.950529\pi$
$787$	−10.0970	+	17.4885i	−0.359920	+	0.623399i	0.628028	+	0.778191i	$0.283863\pi$
$788$	5.15496	−	8.92865i	0.183638	−	0.318070i
$789$	−3.65794	−	6.33574i	−0.130226	−	0.225558i
$790$	30.7602			1.09440
$791$	0.711367	+	16.0480i	0.0252933	+	0.570602i
$792$	12.4491			0.442359
$793$	1.19321	+	2.06669i	0.0423720	+	0.0733904i
$794$	−16.3217	+	28.2701i	−0.579237	+	1.00327i
$795$	−4.04804	+	7.01141i	−0.143569	+	0.248669i
$796$	−14.2560	−	24.6922i	−0.505292	−	0.875191i
$797$	−0.786646			−0.0278644			−0.0139322	−	0.999903i	$-0.504435\pi$
$797$	−0.786646			−0.0278644			−0.0139322	+	0.999903i	$0.504435\pi$
$798$	14.4963	−	9.24875i	0.513165	−	0.327402i
$799$	−5.99780			−0.212187
$800$	3.79354	+	6.57061i	0.134122	+	0.232306i
$801$	4.74137	−	8.21230i	0.167528	−	0.290167i
$802$	−11.9942	+	20.7745i	−0.423529	+	0.733573i
$803$	−9.13940	−	15.8299i	−0.322522	−	0.558625i
$804$	−14.3764			−0.507018
$805$	−11.2634	−	5.85383i	−0.396982	−	0.206320i
$806$	18.3831			0.647519
$807$	−12.8537	−	22.2632i	−0.452470	−	0.783701i
$808$	−16.5144	+	28.6038i	−0.580974	+	1.00628i
$809$	−0.374126	+	0.648005i	−0.0131536	+	0.0227827i	−0.872527	−	0.488565i	$-0.837520\pi$
$809$	−0.374126	+	0.648005i	−0.0131536	+	0.0227827i	0.859374	+	0.511348i	$0.170854\pi$
$810$	2.60555	+	4.51295i	0.0915498	+	0.158569i
$811$	37.4757			1.31595			0.657975	−	0.753039i	$-0.271413\pi$
$811$	37.4757			1.31595			0.657975	+	0.753039i	$0.271413\pi$
$812$	−1.38908	−	0.721934i	−0.0487471	−	0.0253349i
$813$	1.98934			0.0697694
$814$	−3.24056	−	5.61281i	−0.113581	−	0.196729i
$815$	9.51511	−	16.4807i	0.333300	−	0.577292i
$816$	−3.39939	+	5.88791i	−0.119002	+	0.206118i
$817$	6.67805	+	11.5667i	0.233635	+	0.404668i
$818$	−74.8623			−2.61750
$819$	−4.39165	+	2.80189i	−0.153457	+	0.0979061i
$820$	−3.40886			−0.119043
$821$	−1.15072	−	1.99310i	−0.0401602	−	0.0695596i	0.845247	−	0.534376i	$-0.179454\pi$
$821$	−1.15072	−	1.99310i	−0.0401602	−	0.0695596i	−0.885407	+	0.464817i	$0.846120\pi$
$822$	−7.94309	+	13.7578i	−0.277047	+	0.479860i
$823$	16.2397	−	28.1280i	0.566082	−	0.980482i	−0.430867	−	0.902416i	$-0.641792\pi$
$823$	16.2397	−	28.1280i	0.566082	−	0.980482i	0.996948	−	0.0780664i	$-0.0248746\pi$
$824$	−10.9845	−	19.0257i	−0.382663	−	0.662792i
$825$	4.91039			0.170958
$826$	−1.64783	−	37.1741i	−0.0573354	−	1.29345i
$827$	19.7762			0.687685			0.343842	−	0.939027i	$-0.388271\pi$
$827$	19.7762			0.687685			0.343842	+	0.939027i	$0.388271\pi$
$828$	22.3498	+	38.7110i	0.776709	+	1.34530i
$829$	4.99964	−	8.65963i	0.173645	−	0.300761i	−0.766047	−	0.642785i	$-0.777779\pi$
$829$	4.99964	−	8.65963i	0.173645	−	0.300761i	0.939691	+	0.342024i	$0.111112\pi$
$830$	−5.11523	+	8.85984i	−0.177552	+	0.307530i
$831$	1.81966	+	3.15175i	0.0631234	+	0.109333i
$832$	−9.02241			−0.312796
$833$	−7.83706	+	16.8652i	−0.271538	+	0.584343i
$834$	−46.0209			−1.59357
$835$	6.10959	+	10.5821i	0.211431	+	0.366210i
$836$	−7.46953	+	12.9376i	−0.258339	+	0.447456i
$837$	19.8280	−	34.3431i	0.685355	−	1.18707i
$838$	−10.7153	−	18.5595i	−0.370155	−	0.641128i
$839$	9.04091			0.312127			0.156063	−	0.987747i	$-0.450120\pi$
$839$	9.04091			0.312127			0.156063	+	0.987747i	$0.450120\pi$
$840$	0.408850	+	9.22342i	0.0141067	+	0.318238i
$841$	−28.9758			−0.999165
$842$	17.3228	+	30.0040i	0.596984	+	1.03401i
$843$	−8.11741	+	14.0598i	−0.279579	+	0.484244i
$844$	46.5056	−	80.5500i	1.60079	−	2.77265i
$845$	5.46673	+	9.46865i	0.188061	+	0.325731i
$846$	11.9444			0.410656
$847$	−20.7347	+	13.2288i	−0.712452	+	0.454549i
$848$	−28.7593			−0.987597
$849$	−3.06506	−	5.30884i	−0.105193	−	0.182199i
$850$	13.4278	−	23.2576i	0.460569	−	0.797729i
$851$	5.51578	−	9.55361i	0.189078	−	0.327493i
$852$	2.48495	+	4.30406i	0.0851329	+	0.147455i
$853$	−43.3121			−1.48298			−0.741490	−	0.670964i	$-0.765880\pi$
$853$	−43.3121			−1.48298			−0.741490	+	0.670964i	$0.765880\pi$
$854$	−15.0542	−	7.82402i	−0.515146	−	0.267732i
$855$	−5.92596			−0.202664
$856$	31.8210	+	55.1156i	1.08762	+	1.88381i
$857$	−26.0011	+	45.0353i	−0.888182	+	1.53838i	−0.0461585	+	0.998934i	$0.514698\pi$
$857$	−26.0011	+	45.0353i	−0.888182	+	1.53838i	−0.842023	+	0.539441i	$0.818635\pi$
$858$	−1.26343	+	2.18832i	−0.0431327	+	0.0747080i
$859$	11.7071	+	20.2773i	0.399441	+	0.691853i	0.993657	−	0.112453i	$-0.0358708\pi$
$859$	11.7071	+	20.2773i	0.399441	+	0.691853i	−0.594216	+	0.804306i	$0.702537\pi$
$860$	−15.1274			−0.515839
$861$	−2.10453	−	1.09377i	−0.0717222	−	0.0372756i
$862$	−56.1015			−1.91083
$863$	10.7560	+	18.6300i	0.366139	+	0.634172i	0.988958	−	0.148194i	$-0.0473461\pi$
$863$	10.7560	+	18.6300i	0.366139	+	0.634172i	−0.622819	+	0.782366i	$0.714013\pi$
$864$	−4.21112	+	7.29388i	−0.143265	+	0.248143i
$865$	−4.83069	+	8.36700i	−0.164248	+	0.284487i
$866$	−46.0861	−	79.8235i	−1.56607	−	2.71251i
$867$	8.91231			0.302678
$868$	−72.2034	+	46.0662i	−2.45074	+	1.56359i
$869$	−18.5937			−0.630747
$870$	−0.150609	−	0.260862i	−0.00510612	−	0.00884407i
$871$	−1.89033	+	3.27415i	−0.0640515	+	0.110941i
$872$	−26.5866	+	46.0494i	−0.900337	+	1.55943i
$873$	15.9840	+	27.6850i	0.540975	+	0.936997i
$874$	−38.8018			−1.31249
$875$	−0.965913	−	21.7904i	−0.0326538	−	0.736652i
$876$	−47.7356			−1.61284
$877$	7.73987	+	13.4058i	0.261357	+	0.452683i	0.966603	−	0.256279i	$-0.0824967\pi$
$877$	7.73987	+	13.4058i	0.261357	+	0.452683i	−0.705246	+	0.708963i	$0.749163\pi$
$878$	−31.4340	+	54.4452i	−1.06084	+	1.83744i
$879$	12.0468	−	20.8656i	0.406327	−	0.703779i
$880$	−1.67020	−	2.89287i	−0.0563024	−	0.0975185i
$881$	−20.7757			−0.699951			−0.349975	−	0.936759i	$-0.613810\pi$
$881$	−20.7757			−0.699951			−0.349975	+	0.936759i	$0.613810\pi$
$882$	15.6072	−	33.5862i	0.525520	−	1.13091i
$883$	20.0013			0.673096			0.336548	−	0.941666i	$-0.390741\pi$
$883$	20.0013			0.673096			0.336548	+	0.941666i	$0.390741\pi$
$884$	4.52822	+	7.84310i	0.152300	+	0.263792i
$885$	2.34601	−	4.06340i	0.0788601	−	0.136590i
$886$	25.2472	−	43.7294i	0.848196	−	1.46912i
$887$	−7.70267	−	13.3414i	−0.258630	−	0.447961i	0.707245	−	0.706969i	$-0.249938\pi$
$887$	−7.70267	−	13.3414i	−0.258630	−	0.447961i	−0.965875	+	0.259008i	$0.916605\pi$
$888$	−8.02352			−0.269252
$889$	−1.19758	−	27.0166i	−0.0401654	−	0.906108i
$890$	−9.32323			−0.312515
$891$	−1.57498	−	2.72795i	−0.0527640	−	0.0913899i
$892$	−17.4443	+	30.2144i	−0.584077	+	1.01165i
$893$	−3.39735	+	5.88438i	−0.113688	+	0.196913i
$894$	6.16087	+	10.6709i	0.206050	+	0.356890i
$895$	−5.89393			−0.197012
$896$	46.0103	−	29.3549i	1.53710	−	0.980677i
$897$	−4.30098			−0.143606
$898$	15.0367	+	26.0444i	0.501782	+	0.869113i
$899$	0.662318	−	1.14717i	0.0220895	−	0.0382602i
$900$	−17.5240	+	30.3525i	−0.584134	+	1.01175i
$901$	−13.3826	−	23.1793i	−0.445838	−	0.772214i
$902$	3.14432			0.104694
$903$	−9.33918	−	4.85378i	−0.310788	−	0.161524i
$904$	−26.3642			−0.876861
$905$	0.155510	+	0.269351i	0.00516933	+	0.00895355i
$906$	−6.96497	+	12.0637i	−0.231396	+	0.400789i
$907$	9.50308	−	16.4598i	0.315545	−	0.546540i	−0.664008	−	0.747725i	$-0.731146\pi$
$907$	9.50308	−	16.4598i	0.315545	−	0.546540i	0.979553	+	0.201186i	$0.0644794\pi$
$908$	49.7957	+	86.2486i	1.65253	+	2.86226i
$909$	16.7064			0.554117
$910$	4.54458	+	2.36192i	0.150651	+	0.0782968i
$911$	5.36492			0.177748			0.0888739	−	0.996043i	$-0.471673\pi$
$911$	5.36492			0.177748			0.0888739	+	0.996043i	$0.471673\pi$
$912$	3.85104	+	6.67020i	0.127521	+	0.220873i
$913$	3.09202	−	5.35553i	0.102331	−	0.177242i
$914$	31.2682	−	54.1582i	1.03426	−	1.79139i
$915$	−1.06965	−	1.85269i	−0.0353616	−	0.0612480i
$916$	30.5632			1.00984
$917$	40.5780	−	25.8890i	1.34000	−	0.854929i
$918$	29.8117			0.983934
$919$	−1.41634	−	2.45318i	−0.0467208	−	0.0809229i	0.841719	−	0.539915i	$-0.181544\pi$
$919$	−1.41634	−	2.45318i	−0.0467208	−	0.0809229i	−0.888440	+	0.458993i	$0.848210\pi$
$920$	10.4166	−	18.0421i	0.343426	−	0.594831i
$921$	−10.5674	+	18.3032i	−0.348207	+	0.603111i
$922$	−36.7361	−	63.6288i	−1.20984	−	2.09550i
$923$	1.30697			0.0430193
$924$	−0.521338	−	11.7611i	−0.0171508	−	0.386911i
$925$	8.64962			0.284398
$926$	5.68898	+	9.85361i	0.186952	+	0.323810i
$927$	−5.55611	+	9.62347i	−0.182487	+	0.316076i
$928$	−0.140665	+	0.243639i	−0.00461756	+	0.00799784i
$929$	24.9501	+	43.2148i	0.818585	+	1.41783i	0.906725	+	0.421722i	$0.138574\pi$
$929$	24.9501	+	43.2148i	0.818585	+	1.41783i	−0.0881405	+	0.996108i	$0.528092\pi$
$930$	−16.4796			−0.540387
$931$	12.1071	+	17.2418i	0.396793	+	0.565078i
$932$	−73.3642			−2.40313
$933$	12.6449	+	21.9017i	0.413976	+	0.717028i
$934$	−0.352622	+	0.610759i	−0.0115381	+	0.0199846i
$935$	1.55439	−	2.69228i	0.0508339	−	0.0880470i
$936$	−4.27483	−	7.40423i	−0.139727	−	0.242015i
$937$	−7.68076			−0.250919			−0.125460	−	0.992099i	$-0.540041\pi$
$937$	−7.68076			−0.250919			−0.125460	+	0.992099i	$0.540041\pi$
$938$	−1.19028	−	26.8520i	−0.0388640	−	0.876749i
$939$	10.3865			0.338951
$940$	−3.84790	−	6.66476i	−0.125505	−	0.217381i
$941$	−18.3546	+	31.7910i	−0.598341	+	1.03636i	0.394725	+	0.918799i	$0.370840\pi$
$941$	−18.3546	+	31.7910i	−0.598341	+	1.03636i	−0.993066	+	0.117558i	$0.962493\pi$
$942$	3.69000	−	6.39127i	0.120227	−	0.208239i
$943$	2.67599	+	4.63495i	0.0871422	+	0.150935i
$944$	16.6672			0.542470
$945$	9.31425	−	5.94255i	0.302993	−	0.193311i
$946$	13.9534			0.453665
$947$	18.5752	+	32.1731i	0.603611	+	1.04549i	0.992269	+	0.124103i	$0.0396054\pi$
$947$	18.5752	+	32.1731i	0.603611	+	1.04549i	−0.388658	+	0.921382i	$0.627061\pi$
$948$	−24.2789	+	42.0524i	−0.788544	+	1.36580i
$949$	−6.27667	+	10.8715i	−0.203749	+	0.352904i
$950$	−15.2118	−	26.3477i	−0.493537	−	0.854832i
$951$	22.7256			0.736929
$952$	−27.0827	−	14.0755i	−0.877755	−	0.456189i
$953$	−25.2779			−0.818831			−0.409415	−	0.912348i	$-0.634267\pi$
$953$	−25.2779			−0.818831			−0.409415	+	0.912348i	$0.634267\pi$
$954$	26.6508	+	46.1605i	0.862851	+	1.49450i
$955$	7.30623	−	12.6548i	0.236424	−	0.409498i
$956$	35.6109	−	61.6799i	1.15174	−	1.99487i
$957$	0.0910389	+	0.157684i	0.00294287	+	0.00509720i
$958$	71.2594			2.30229
$959$	−17.2707	−	8.97594i	−0.557699	−	0.289848i
$960$	8.08815			0.261044
$961$	−20.7353	−	35.9146i	−0.668881	−	1.15854i
$962$	−2.22552	+	3.85471i	−0.0717536	+	0.124281i
$963$	16.0955	−	27.8782i	0.518671	−	0.898364i
$964$	−33.3791	−	57.8144i	−1.07507	−	1.86207i
$965$	−16.2449			−0.522941
$966$	25.7779	−	16.4464i	0.829389	−	0.529155i
$967$	−2.98768			−0.0960772			−0.0480386	−	0.998845i	$-0.515297\pi$
$967$	−2.98768			−0.0960772			−0.0480386	+	0.998845i	$0.515297\pi$
$968$	−20.1832	−	34.9583i	−0.648712	−	1.12360i
$969$	−3.58402	+	6.20770i	−0.115135	+	0.199420i
$970$	15.7151	−	27.2193i	0.504581	−	0.873960i
$971$	11.8913	+	20.5963i	0.381608	+	0.660965i	0.991292	−	0.131679i	$-0.0420369\pi$
$971$	11.8913	+	20.5963i	0.381608	+	0.660965i	−0.609684	+	0.792645i	$0.708704\pi$
$972$	−61.3674			−1.96836
$973$	−2.49696	−	56.3299i	−0.0800487	−	1.80585i
$974$	28.9511			0.927652
$975$	−1.68616	−	2.92051i	−0.0540002	−	0.0935311i
$976$	3.79966	−	6.58121i	0.121624	−	0.210659i
$977$	8.30296	−	14.3811i	0.265635	−	0.460093i	−0.702095	−	0.712084i	$-0.747752\pi$
$977$	8.30296	−	14.3811i	0.265635	−	0.460093i	0.967730	+	0.251990i	$0.0810850\pi$
$978$	22.9206	+	39.6996i	0.732920	+	1.26945i
$979$	5.63563			0.180116
$980$	−23.7684	+	2.11133i	−0.759255	+	0.0674441i
$981$	26.8958			0.858715
$982$	−8.46629	−	14.6640i	−0.270170	−	0.467948i
$983$	−7.96437	+	13.7947i	−0.254024	+	0.439982i	−0.964630	−	0.263608i	$-0.915088\pi$
$983$	−7.96437	+	13.7947i	−0.254024	+	0.439982i	0.710606	+	0.703590i	$0.248421\pi$
$984$	1.94631	−	3.37111i	0.0620462	−	0.107467i
$985$	1.21526	+	2.10489i	0.0387214	+	0.0670674i
$986$	0.995808			0.0317130
$987$	−0.237119	−	5.34926i	−0.00754757	−	0.170269i
$988$	10.2597			0.326405
$989$	11.8751	+	20.5683i	0.377607	+	0.654034i
$990$	−3.09550	+	5.36156i	−0.0983813	+	0.170401i
$991$	1.62751	−	2.81894i	0.0516997	−	0.0895465i	−0.839017	−	0.544105i	$-0.816869\pi$
$991$	1.62751	−	2.81894i	0.0516997	−	0.0895465i	0.890717	+	0.454558i	$0.150203\pi$
$992$	7.69576	+	13.3295i	0.244341	+	0.423210i
$993$	20.5378			0.651747
$994$	−7.83329	+	4.99768i	−0.248457	+	0.158517i
$995$	6.72160			0.213089
$996$	−8.07488	−	13.9861i	−0.255862	−	0.443167i
$997$	−3.06131	+	5.30235i	−0.0969528	+	0.167927i	−0.910422	−	0.413681i	$-0.864243\pi$
$997$	−3.06131	+	5.30235i	−0.0969528	+	0.167927i	0.813469	+	0.581608i	$0.197576\pi$
$998$	−37.1589	+	64.3611i	−1.17624	+	2.03731i
$999$	4.80087	+	8.31535i	0.151893	+	0.263086i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	287.2.e.c.165.5	✓	10
7.2	even	3	inner	287.2.e.c.247.5	yes	10
7.3	odd	6		2009.2.a.m.1.1		5
7.4	even	3		2009.2.a.l.1.1		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
287.2.e.c.165.5	✓	10	1.1	even	1	trivial
287.2.e.c.247.5	yes	10	7.2	even	3	inner
2009.2.a.l.1.1		5	7.4	even	3
2009.2.a.m.1.1		5	7.3	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)

\(f(q)\)	\(=\)	\(q+(1.20443 + 2.08614i) q^{2} +(0.448226 - 0.776350i) q^{3} +(-1.90131 + 3.29316i) q^{4} +(-0.448226 - 0.776350i) q^{5} +2.15943 q^{6} +(0.117164 + 2.64316i) q^{7} -4.34226 q^{8} +(1.09819 + 1.90212i) q^{9} +O(q^{10})\)	\(q+(1.20443 + 2.08614i) q^{2} +(0.448226 - 0.776350i) q^{3} +(-1.90131 + 3.29316i) q^{4} +(-0.448226 - 0.776350i) q^{5} +2.15943 q^{6} +(0.117164 + 2.64316i) q^{7} -4.34226 q^{8} +(1.09819 + 1.90212i) q^{9} +(1.07971 - 1.87012i) q^{10} +(-0.652657 + 1.13043i) q^{11} +(1.70443 + 2.95216i) q^{12} +0.896451 q^{13} +(-5.37287 + 3.42792i) q^{14} -0.803625 q^{15} +(-1.42734 - 2.47222i) q^{16} +(1.32837 - 2.30080i) q^{17} +(-2.64538 + 4.58194i) q^{18} +(-1.50486 - 2.60649i) q^{19} +3.40886 q^{20} +(2.10453 + 1.09377i) q^{21} -3.14432 q^{22} +(-2.67599 - 4.63495i) q^{23} +(-1.94631 + 3.37111i) q^{24} +(2.09819 - 3.63417i) q^{25} +(1.07971 + 1.87012i) q^{26} +4.65830 q^{27} +(-8.92711 - 4.63962i) q^{28} +0.155602 q^{29} +(-0.967911 - 1.67647i) q^{30} +(4.25648 - 7.37245i) q^{31} +(-0.904004 + 1.56578i) q^{32} +(0.585075 + 1.01338i) q^{33} +6.39970 q^{34} +(1.99950 - 1.27569i) q^{35} -8.35198 q^{36} +(1.03061 + 1.78506i) q^{37} +(3.62500 - 6.27868i) q^{38} +(0.401812 - 0.695960i) q^{39} +(1.94631 + 3.37111i) q^{40} -1.00000 q^{41} +(0.253008 + 5.70770i) q^{42} -4.43766 q^{43} +(-2.48181 - 4.29861i) q^{44} +(0.984472 - 1.70515i) q^{45} +(6.44609 - 11.1650i) q^{46} +(-1.12879 - 1.95513i) q^{47} -2.55907 q^{48} +(-6.97255 + 0.619366i) q^{49} +10.1085 q^{50} +(-1.19082 - 2.06255i) q^{51} +(-1.70443 + 2.95216i) q^{52} +(5.03723 - 8.72473i) q^{53} +(5.61060 + 9.71784i) q^{54} +1.17015 q^{55} +(-0.508757 - 11.4773i) q^{56} -2.69806 q^{57} +(0.187412 + 0.324607i) q^{58} +(-2.91928 + 5.05634i) q^{59} +(1.52794 - 2.64647i) q^{60} +(1.33103 + 2.30542i) q^{61} +20.5066 q^{62} +(-4.89892 + 3.12554i) q^{63} -10.0646 q^{64} +(-0.401812 - 0.695960i) q^{65} +(-1.40937 + 2.44109i) q^{66} +(-2.10869 + 3.65235i) q^{67} +(5.05127 + 8.74906i) q^{68} -4.79779 q^{69} +(5.06952 + 2.63474i) q^{70} +1.45793 q^{71} +(-4.76862 - 8.25949i) q^{72} +(-7.00169 + 12.1273i) q^{73} +(-2.48259 + 4.29997i) q^{74} +(-1.88092 - 3.25785i) q^{75} +11.4448 q^{76} +(-3.06438 - 1.59263i) q^{77} +1.93582 q^{78} +(7.12230 + 12.3362i) q^{79} +(-1.27954 + 2.21622i) q^{80} +(-1.20659 + 2.08988i) q^{81} +(-1.20443 - 2.08614i) q^{82} -4.73758 q^{83} +(-7.60332 + 4.85096i) q^{84} -2.38163 q^{85} +(-5.34485 - 9.25756i) q^{86} +(0.0697449 - 0.120802i) q^{87} +(2.83401 - 4.90864i) q^{88} +(-2.15873 - 3.73902i) q^{89} +4.74291 q^{90} +(0.105032 + 2.36946i) q^{91} +20.3515 q^{92} +(-3.81573 - 6.60904i) q^{93} +(2.71911 - 4.70963i) q^{94} +(-1.34903 + 2.33659i) q^{95} +(0.810396 + 1.40365i) q^{96} +14.5549 q^{97} +(-9.69003 - 13.7997i) q^{98} -2.86696 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

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