LMFDB - Embedded newform 1001.2.i.a.144.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1001,2,Mod(144,1001)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1001, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("1001.144");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1001 = 7 \cdot 11 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1001.i (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:	$7.99302524233$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{3})$
Coefficient field:	8.0.447703281.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{7} - 2x^{6} + 2x^{5} + 3x^{4} + 4x^{3} - 8x^{2} - 8x + 16 $ x^8 - x^7 - 2x^6 + 2x^5 + 3x^4 + 4x^3 - 8x^2 - 8x + 16
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			144.4
Root			$-1.38232 + 0.298668i$ of defining polynomial
Character	$\chi$	$=$	1001.144
Dual form			1001.2.i.a.716.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.949812 + 1.64512i) q^{2} +(-0.432504 + 0.749119i) q^{3} +(-0.804286 + 1.39306i) q^{4} +(0.432504 + 0.749119i) q^{5} -1.64319 q^{6} +(-2.00000 + 1.73205i) q^{7} +0.743565 q^{8} +(1.12588 + 1.95008i) q^{9} +O(q^{10})$	\(q+(0.949812 + 1.64512i) q^{2} +(-0.432504 + 0.749119i) q^{3} +(-0.804286 + 1.39306i) q^{4} +(0.432504 + 0.749119i) q^{5} -1.64319 q^{6} +(-2.00000 + 1.73205i) q^{7} +0.743565 q^{8} +(1.12588 + 1.95008i) q^{9} +(-0.821595 + 1.42304i) q^{10} +(0.500000 - 0.866025i) q^{11} +(-0.695714 - 1.20501i) q^{12} -1.00000 q^{13} +(-4.74906 - 1.64512i) q^{14} -0.748238 q^{15} +(2.31482 + 4.00939i) q^{16} +(-1.12822 + 1.95413i) q^{17} +(-2.13875 + 3.70443i) q^{18} +(1.70625 + 2.95531i) q^{19} -1.39143 q^{20} +(-0.432504 - 2.24736i) q^{21} +1.89962 q^{22} +(-1.64553 - 2.85013i) q^{23} +(-0.321595 + 0.557018i) q^{24} +(2.12588 - 3.68213i) q^{25} +(-0.949812 - 1.64512i) q^{26} -4.54281 q^{27} +(-0.804286 - 4.17919i) q^{28} -3.74357 q^{29} +(-0.710686 - 1.23094i) q^{30} +(-4.16426 + 7.21270i) q^{31} +(-3.65372 + 6.32843i) q^{32} +(0.432504 + 0.749119i) q^{33} -4.28638 q^{34} +(-2.16252 - 0.749119i) q^{35} -3.62212 q^{36} +(-4.44070 - 7.69152i) q^{37} +(-3.24123 + 5.61397i) q^{38} +(0.432504 - 0.749119i) q^{39} +(0.321595 + 0.557018i) q^{40} +1.15606 q^{41} +(3.28638 - 2.84609i) q^{42} +8.92957 q^{43} +(0.804286 + 1.39306i) q^{44} +(-0.973896 + 1.68684i) q^{45} +(3.12588 - 5.41418i) q^{46} +(1.75410 + 3.03819i) q^{47} -4.00467 q^{48} +(1.00000 - 6.92820i) q^{49} +8.07675 q^{50} +(-0.975917 - 1.69034i) q^{51} +(0.804286 - 1.39306i) q^{52} +(-2.03604 + 3.52652i) q^{53} +(-4.31482 - 7.47349i) q^{54} +0.865008 q^{55} +(-1.48713 + 1.28789i) q^{56} -2.95183 q^{57} +(-3.55568 - 6.15862i) q^{58} +(0.121442 - 0.210345i) q^{59} +(0.601798 - 1.04234i) q^{60} +(-1.78698 - 3.09514i) q^{61} -15.8210 q^{62} +(-5.62940 - 1.95008i) q^{63} -4.62212 q^{64} +(-0.432504 - 0.749119i) q^{65} +(-0.821595 + 1.42304i) q^{66} +(0.419634 - 0.726827i) q^{67} +(-1.81482 - 3.14336i) q^{68} +2.84678 q^{69} +(-0.821595 - 4.26913i) q^{70} -4.32504 q^{71} +(0.837166 + 1.45001i) q^{72} +(-0.524083 + 0.907739i) q^{73} +(8.43566 - 14.6110i) q^{74} +(1.83890 + 3.18507i) q^{75} -5.48924 q^{76} +(0.500000 + 2.59808i) q^{77} +1.64319 q^{78} +(5.81482 + 10.0716i) q^{79} +(-2.00234 + 3.46815i) q^{80} +(-1.41286 + 2.44714i) q^{81} +(1.09804 + 1.90186i) q^{82} +14.4195 q^{83} +(3.47857 + 1.20501i) q^{84} -1.95183 q^{85} +(8.48141 + 14.6902i) q^{86} +(1.61911 - 2.80437i) q^{87} +(0.371783 - 0.643946i) q^{88} +(3.06480 + 5.30838i) q^{89} -3.70007 q^{90} +(2.00000 - 1.73205i) q^{91} +5.29390 q^{92} +(-3.60211 - 6.23904i) q^{93} +(-3.33213 + 5.77142i) q^{94} +(-1.47592 + 2.55636i) q^{95} +(-3.16050 - 5.47414i) q^{96} -5.88140 q^{97} +(12.3476 - 4.93537i) q^{98} +2.25176 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 2 q^{2} - q^{3} - 4 q^{4} + q^{5} + 6 q^{6} - 16 q^{7} + 6 q^{8} - 3 q^{9}+O(q^{10}) $ 8 * q - 2 * q^2 - q^3 - 4 * q^4 + q^5 + 6 * q^6 - 16 * q^7 + 6 * q^8 - 3 * q^9	\( 8 q - 2 q^{2} - q^{3} - 4 q^{4} + q^{5} + 6 q^{6} - 16 q^{7} + 6 q^{8} - 3 q^{9} + 3 q^{10} + 4 q^{11} - 8 q^{12} - 8 q^{13} + 10 q^{14} - 30 q^{15} + 4 q^{16} - 9 q^{17} - 5 q^{18} + 4 q^{19} - 16 q^{20} - q^{21} - 4 q^{22} - 6 q^{23} + 7 q^{24} + 5 q^{25} + 2 q^{26} + 2 q^{27} - 4 q^{28} - 30 q^{29} + 11 q^{30} + 10 q^{31} + 2 q^{32} + q^{33} + 4 q^{34} - 5 q^{35} - 34 q^{36} - 9 q^{37} - 14 q^{38} + q^{39} - 7 q^{40} - 10 q^{41} - 12 q^{42} + 14 q^{43} + 4 q^{44} + 4 q^{45} + 13 q^{46} + 2 q^{47} - 56 q^{48} + 8 q^{49} + 2 q^{50} - 10 q^{51} + 4 q^{52} + 27 q^{53} - 20 q^{54} + 2 q^{55} - 12 q^{56} - 28 q^{57} + 10 q^{58} - 4 q^{59} - 5 q^{60} - 19 q^{61} - 88 q^{62} + 15 q^{63} - 42 q^{64} - q^{65} + 3 q^{66} + q^{67} - 16 q^{69} + 3 q^{70} - 10 q^{71} + 21 q^{72} - 2 q^{73} + 5 q^{74} - 2 q^{75} + 38 q^{76} + 4 q^{77} - 6 q^{78} + 32 q^{79} - 28 q^{80} - 4 q^{81} + 16 q^{82} + 40 q^{84} - 20 q^{85} + 22 q^{86} - 4 q^{87} + 3 q^{88} + 3 q^{89} - 58 q^{90} + 16 q^{91} - 30 q^{92} - 17 q^{93} - 5 q^{94} - 14 q^{95} + q^{96} + 6 q^{97} - 26 q^{98} - 6 q^{99}+O(q^{100}) \) 8 * q - 2 * q^2 - q^3 - 4 * q^4 + q^5 + 6 * q^6 - 16 * q^7 + 6 * q^8 - 3 * q^9 + 3 * q^10 + 4 * q^11 - 8 * q^12 - 8 * q^13 + 10 * q^14 - 30 * q^15 + 4 * q^16 - 9 * q^17 - 5 * q^18 + 4 * q^19 - 16 * q^20 - q^21 - 4 * q^22 - 6 * q^23 + 7 * q^24 + 5 * q^25 + 2 * q^26 + 2 * q^27 - 4 * q^28 - 30 * q^29 + 11 * q^30 + 10 * q^31 + 2 * q^32 + q^33 + 4 * q^34 - 5 * q^35 - 34 * q^36 - 9 * q^37 - 14 * q^38 + q^39 - 7 * q^40 - 10 * q^41 - 12 * q^42 + 14 * q^43 + 4 * q^44 + 4 * q^45 + 13 * q^46 + 2 * q^47 - 56 * q^48 + 8 * q^49 + 2 * q^50 - 10 * q^51 + 4 * q^52 + 27 * q^53 - 20 * q^54 + 2 * q^55 - 12 * q^56 - 28 * q^57 + 10 * q^58 - 4 * q^59 - 5 * q^60 - 19 * q^61 - 88 * q^62 + 15 * q^63 - 42 * q^64 - q^65 + 3 * q^66 + q^67 - 16 * q^69 + 3 * q^70 - 10 * q^71 + 21 * q^72 - 2 * q^73 + 5 * q^74 - 2 * q^75 + 38 * q^76 + 4 * q^77 - 6 * q^78 + 32 * q^79 - 28 * q^80 - 4 * q^81 + 16 * q^82 + 40 * q^84 - 20 * q^85 + 22 * q^86 - 4 * q^87 + 3 * q^88 + 3 * q^89 - 58 * q^90 + 16 * q^91 - 30 * q^92 - 17 * q^93 - 5 * q^94 - 14 * q^95 + q^96 + 6 * q^97 - 26 * q^98 - 6 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1001\mathbb{Z}\right)^\times$.

$n$	$365$	$430$	$925$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$1$

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 $

$2$	0.949812	+	1.64512i	0.671619	+	1.16328i	0.977445	+	0.211190i	$0.0677340\pi$
$2$	0.949812	+	1.64512i	0.671619	+	1.16328i	−0.305826	+	0.952087i	$0.598933\pi$
$3$	−0.432504	+	0.749119i	−0.249706	+	0.432504i	−0.963444	−	0.267909i	$-0.913667\pi$
$3$	−0.432504	+	0.749119i	−0.249706	+	0.432504i	0.713738	+	0.700413i	$0.247001\pi$
$4$	−0.804286	+	1.39306i	−0.402143	+	0.696532i
$5$	0.432504	+	0.749119i	0.193422	+	0.335016i	0.946382	−	0.323050i	$-0.104708\pi$
$5$	0.432504	+	0.749119i	0.193422	+	0.335016i	−0.752960	+	0.658066i	$0.771375\pi$
$6$	−1.64319			−0.670829
$7$	−2.00000	+	1.73205i	−0.755929	+	0.654654i
$7$	−2.00000	+	1.73205i	−0.755929	+	0.654654i
$8$	0.743565			0.262890
$9$	1.12588	+	1.95008i	0.375294	+	0.650028i
$10$	−0.821595	+	1.42304i	−0.259811	+	0.450006i
$11$	0.500000	−	0.866025i	0.150756	−	0.261116i
$11$	0.500000	−	0.866025i	0.150756	−	0.261116i
$12$	−0.695714	−	1.20501i	−0.200835	−	0.347857i
$13$	−1.00000			−0.277350
$13$	−1.00000			−0.277350
$14$	−4.74906	−	1.64512i	−1.26924	−	0.439678i
$15$	−0.748238			−0.193194
$16$	2.31482	+	4.00939i	0.578705	+	1.00235i
$17$	−1.12822	+	1.95413i	−0.273633	+	0.473946i	−0.969789	−	0.243944i	$-0.921559\pi$
$17$	−1.12822	+	1.95413i	−0.273633	+	0.473946i	0.696156	+	0.717890i	$0.254892\pi$
$18$	−2.13875	+	3.70443i	−0.504108	+	0.873141i
$19$	1.70625	+	2.95531i	0.391440	+	0.677994i	0.992640	−	0.121105i	$-0.0386437\pi$
$19$	1.70625	+	2.95531i	0.391440	+	0.677994i	−0.601200	+	0.799099i	$0.705310\pi$
$20$	−1.39143			−0.311133
$21$	−0.432504	−	2.24736i	−0.0943801	−	0.490413i
$22$	1.89962			0.405001
$23$	−1.64553	−	2.85013i	−0.343116	−	0.594294i	0.641894	−	0.766794i	$-0.278149\pi$
$23$	−1.64553	−	2.85013i	−0.343116	−	0.594294i	−0.985010	+	0.172499i	$0.944816\pi$
$24$	−0.321595	+	0.557018i	−0.0656452	+	0.113701i
$25$	2.12588	−	3.68213i	0.425176	−	0.736427i
$26$	−0.949812	−	1.64512i	−0.186273	−	0.322635i
$27$	−4.54281			−0.874265
$28$	−0.804286	−	4.17919i	−0.151996	−	0.789793i
$29$	−3.74357			−0.695163			−0.347581	−	0.937650i	$-0.612997\pi$
$29$	−3.74357			−0.695163			−0.347581	+	0.937650i	$0.612997\pi$
$30$	−0.710686	−	1.23094i	−0.129753	−	0.224739i
$31$	−4.16426	+	7.21270i	−0.747922	+	1.29544i	0.200894	+	0.979613i	$0.435615\pi$
$31$	−4.16426	+	7.21270i	−0.747922	+	1.29544i	−0.948817	+	0.315827i	$0.897718\pi$
$32$	−3.65372	+	6.32843i	−0.645893	+	1.11872i
$33$	0.432504	+	0.749119i	0.0752892	+	0.130405i
$34$	−4.28638			−0.735108
$35$	−2.16252	−	0.749119i	−0.365532	−	0.126624i
$36$	−3.62212			−0.603687
$37$	−4.44070	−	7.69152i	−0.730047	−	1.26448i	−0.956863	−	0.290540i	$-0.906165\pi$
$37$	−4.44070	−	7.69152i	−0.730047	−	1.26448i	0.226816	−	0.973938i	$-0.427168\pi$
$38$	−3.24123	+	5.61397i	−0.525797	+	0.910707i
$39$	0.432504	−	0.749119i	0.0692560	−	0.119955i
$40$	0.321595	+	0.557018i	0.0508486	+	0.0880723i
$41$	1.15606			0.180546			0.0902731	−	0.995917i	$-0.471226\pi$
$41$	1.15606			0.180546			0.0902731	+	0.995917i	$0.471226\pi$
$42$	3.28638	−	2.84609i	0.507099	−	0.439161i
$43$	8.92957			1.36175			0.680873	−	0.732401i	$-0.261600\pi$
$43$	8.92957			1.36175			0.680873	+	0.732401i	$0.261600\pi$
$44$	0.804286	+	1.39306i	0.121251	+	0.210012i
$45$	−0.973896	+	1.68684i	−0.145180	+	0.251459i
$46$	3.12588	−	5.41418i	0.460886	−	0.798278i
$47$	1.75410	+	3.03819i	0.255862	+	0.443165i	0.965129	−	0.261774i	$-0.0843075\pi$
$47$	1.75410	+	3.03819i	0.255862	+	0.443165i	−0.709268	+	0.704939i	$0.750974\pi$
$48$	−4.00467			−0.578025
$49$	1.00000	−	6.92820i	0.142857	−	0.989743i
$50$	8.07675			1.14223
$51$	−0.975917	−	1.69034i	−0.136656	−	0.236695i
$52$	0.804286	−	1.39306i	0.111534	−	0.193183i
$53$	−2.03604	+	3.52652i	−0.279671	+	0.484405i	−0.971303	−	0.237845i	$-0.923559\pi$
$53$	−2.03604	+	3.52652i	−0.279671	+	0.484405i	0.691632	+	0.722250i	$0.256892\pi$
$54$	−4.31482	−	7.47349i	−0.587173	−	1.01701i
$55$	0.865008			0.116638
$56$	−1.48713	+	1.28789i	−0.198726	+	0.172102i
$57$	−2.95183			−0.390980
$58$	−3.55568	−	6.15862i	−0.466884	−	0.808667i
$59$	0.121442	−	0.210345i	0.0158105	−	0.0273845i	−0.858012	−	0.513630i	$-0.828300\pi$
$59$	0.121442	−	0.210345i	0.0158105	−	0.0273845i	0.873822	+	0.486245i	$0.161634\pi$
$60$	0.601798	−	1.04234i	0.0776917	−	0.134566i
$61$	−1.78698	−	3.09514i	−0.228799	−	0.396292i	0.728653	−	0.684883i	$-0.240147\pi$
$61$	−1.78698	−	3.09514i	−0.228799	−	0.396292i	−0.957452	+	0.288591i	$0.906813\pi$
$62$	−15.8210			−2.00927
$63$	−5.62940	−	1.95008i	−0.709238	−	0.245687i
$64$	−4.62212			−0.577765
$65$	−0.432504	−	0.749119i	−0.0536455	−	0.0929167i
$66$	−0.821595	+	1.42304i	−0.101131	+	0.175165i
$67$	0.419634	−	0.726827i	0.0512664	−	0.0887961i	−0.839253	−	0.543741i	$-0.817008\pi$
$67$	0.419634	−	0.726827i	0.0512664	−	0.0887961i	0.890520	+	0.454944i	$0.150341\pi$
$68$	−1.81482	−	3.14336i	−0.220079	−	0.381188i
$69$	2.84678			0.342713
$70$	−0.821595	−	4.26913i	−0.0981993	−	0.510259i
$71$	−4.32504			−0.513288			−0.256644	−	0.966506i	$-0.582617\pi$
$71$	−4.32504			−0.513288			−0.256644	+	0.966506i	$0.582617\pi$
$72$	0.837166	+	1.45001i	0.0986609	+	0.170886i
$73$	−0.524083	+	0.907739i	−0.0613393	+	0.106243i	−0.895064	−	0.445937i	$-0.852871\pi$
$73$	−0.524083	+	0.907739i	−0.0613393	+	0.106243i	0.833725	+	0.552180i	$0.186204\pi$
$74$	8.43566	−	14.6110i	0.980626	−	1.69849i
$75$	1.83890	+	3.18507i	0.212338	+	0.367781i
$76$	−5.48924			−0.629660
$77$	0.500000	+	2.59808i	0.0569803	+	0.296078i
$78$	1.64319			0.186055
$79$	5.81482	+	10.0716i	0.654218	+	1.13314i	0.982089	+	0.188417i	$0.0603356\pi$
$79$	5.81482	+	10.0716i	0.654218	+	1.13314i	−0.327871	+	0.944723i	$0.606331\pi$
$80$	−2.00234	+	3.46815i	−0.223868	+	0.387751i
$81$	−1.41286	+	2.44714i	−0.156984	+	0.271905i
$82$	1.09804	+	1.90186i	0.121258	+	0.210025i
$83$	14.4195			1.58275			0.791375	−	0.611331i	$-0.209365\pi$
$83$	14.4195			1.58275			0.791375	+	0.611331i	$0.209365\pi$
$84$	3.47857	+	1.20501i	0.379543	+	0.131478i
$85$	−1.95183			−0.211706
$86$	8.48141	+	14.6902i	0.914574	+	1.58409i
$87$	1.61911	−	2.80437i	0.173586	−	0.300660i
$88$	0.371783	−	0.643946i	0.0396321	−	0.0686449i
$89$	3.06480	+	5.30838i	0.324868	+	0.562687i	0.981486	−	0.191536i	$-0.0613469\pi$
$89$	3.06480	+	5.30838i	0.324868	+	0.562687i	−0.656618	+	0.754223i	$0.728014\pi$
$90$	−3.70007			−0.390022
$91$	2.00000	−	1.73205i	0.209657	−	0.181568i
$92$	5.29390			0.551927
$93$	−3.60211	−	6.23904i	−0.373522	−	0.646959i
$94$	−3.33213	+	5.77142i	−0.343683	+	0.595276i
$95$	−1.47592	+	2.55636i	−0.151426	+	0.262277i
$96$	−3.16050	−	5.47414i	−0.322567	−	0.558702i
$97$	−5.88140			−0.597166			−0.298583	−	0.954384i	$-0.596514\pi$
$97$	−5.88140			−0.597166			−0.298583	+	0.954384i	$0.596514\pi$
$98$	12.3476	−	4.93537i	1.24729	−	0.498548i
$99$	2.25176			0.226311
$100$	3.41963	+	5.92298i	0.341963	+	0.592298i
$101$	4.97156	−	8.61099i	0.494689	−	0.856826i	−0.505293	−	0.862948i	$-0.668615\pi$
$101$	4.97156	−	8.61099i	0.494689	−	0.856826i	0.999981	+	0.00612224i	$0.00194878\pi$
$102$	1.85387	−	3.21101i	0.183561	−	0.317937i
$103$	1.60180	+	2.77439i	0.157830	+	0.273369i	0.934086	−	0.357049i	$-0.116217\pi$
$103$	1.60180	+	2.77439i	0.157830	+	0.273369i	−0.776256	+	0.630418i	$0.782884\pi$
$104$	−0.743565			−0.0729126
$105$	1.49648	−	1.29599i	0.146041	−	0.126475i
$106$	−7.73542			−0.751330
$107$	−0.986765	−	1.70913i	−0.0953942	−	0.165228i	0.814379	−	0.580334i	$-0.197078\pi$
$107$	−0.986765	−	1.70913i	−0.0953942	−	0.165228i	−0.909773	+	0.415106i	$0.863744\pi$
$108$	3.65372	−	6.32843i	0.351580	−	0.608954i
$109$	3.40196	−	5.89237i	0.325849	−	0.564387i	−0.655835	−	0.754904i	$-0.727683\pi$
$109$	3.40196	−	5.89237i	0.325849	−	0.564387i	0.981684	+	0.190518i	$0.0610166\pi$
$110$	0.821595	+	1.42304i	0.0783360	+	0.135682i
$111$	7.68248			0.729189
$112$	−11.5741	−	4.00939i	−1.09365	−	0.378851i
$113$	16.1202			1.51647			0.758233	−	0.651984i	$-0.226063\pi$
$113$	16.1202			1.51647			0.758233	+	0.651984i	$0.226063\pi$
$114$	−2.80369	−	4.85613i	−0.262589	−	0.454818i
$115$	1.42339	−	2.46539i	0.132732	−	0.229899i
$116$	3.01090	−	5.21503i	0.279555	−	0.484203i
$117$	−1.12588	−	1.95008i	−0.104088	−	0.180285i
$118$	0.461390			0.0424744
$119$	−1.12822	−	5.86239i	−0.103424	−	0.537404i
$120$	−0.556364			−0.0507888
$121$	−0.500000	−	0.866025i	−0.0454545	−	0.0787296i
$122$	3.39459	−	5.87960i	0.307331	−	0.532314i
$123$	−0.500000	+	0.866025i	−0.0450835	+	0.0780869i
$124$	−6.69851	−	11.6022i	−0.601544	−	1.04190i
$125$	8.00284			0.715796
$126$	−2.13875	−	11.1133i	−0.190535	−	0.990049i
$127$	7.70639			0.683832			0.341916	−	0.939731i	$-0.388924\pi$
$127$	7.70639			0.683832			0.341916	+	0.939731i	$0.388924\pi$
$128$	2.91730	+	5.05291i	0.257855	+	0.446618i
$129$	−3.86207	+	6.68930i	−0.340036	+	0.588960i
$130$	0.821595	−	1.42304i	0.0720586	−	0.124809i
$131$	5.85122	+	10.1346i	0.511224	+	0.885465i	0.999915	+	0.0130089i	$0.00414098\pi$
$131$	5.85122	+	10.1346i	0.511224	+	0.885465i	−0.488692	+	0.872457i	$0.662526\pi$
$132$	−1.39143			−0.121108
$133$	−8.53124	−	2.95531i	−0.739752	−	0.256258i
$134$	1.59429			0.137726
$135$	−1.96478	−	3.40311i	−0.169102	−	0.292893i
$136$	−0.838903	+	1.45302i	−0.0719353	+	0.124596i
$137$	3.36088	−	5.82122i	0.287140	−	0.497341i	−0.685986	−	0.727615i	$-0.740629\pi$
$137$	3.36088	−	5.82122i	0.287140	−	0.497341i	0.973126	+	0.230274i	$0.0739623\pi$
$138$	2.70391	+	4.68331i	0.230172	+	0.398670i
$139$	7.06923			0.599605			0.299802	−	0.954001i	$-0.403079\pi$
$139$	7.06923			0.599605			0.299802	+	0.954001i	$0.403079\pi$
$140$	2.78285	−	2.41002i	0.235194	−	0.203684i
$141$	−3.03462			−0.255561
$142$	−4.10797	−	7.11522i	−0.344733	−	0.597096i
$143$	−0.500000	+	0.866025i	−0.0418121	+	0.0724207i
$144$	−5.21242	+	9.02818i	−0.434369	+	0.752348i
$145$	−1.61911	−	2.80437i	−0.134459	−	0.232891i
$146$	−1.99112			−0.164787
$147$	4.75754	+	3.74559i	0.392395	+	0.308931i
$148$	14.2864			1.17433
$149$	5.42655	+	9.39906i	0.444560	+	0.770001i	0.998021	−	0.0628738i	$-0.0200266\pi$
$149$	5.42655	+	9.39906i	0.444560	+	0.770001i	−0.553461	+	0.832875i	$0.686693\pi$
$150$	−3.49323	+	6.05044i	−0.285221	+	0.494017i
$151$	6.58654	−	11.4082i	0.536005	−	0.928388i	−0.463109	−	0.886301i	$-0.653266\pi$
$151$	6.58654	−	11.4082i	0.536005	−	0.928388i	0.999114	−	0.0420868i	$-0.0134006\pi$
$152$	1.26871	+	2.19746i	0.102906	+	0.178238i
$153$	−5.08095			−0.410771
$154$	−3.79925	+	3.29025i	−0.306152	+	0.265136i
$155$	−7.20423			−0.578657
$156$	0.695714	+	1.20501i	0.0557017	+	0.0964781i
$157$	−1.88053	+	3.25717i	−0.150083	+	0.259951i	−0.931258	−	0.364361i	$-0.881287\pi$
$157$	−1.88053	+	3.25717i	−0.150083	+	0.259951i	0.781175	+	0.624312i	$0.214621\pi$
$158$	−11.0460	+	19.1322i	−0.878770	+	1.52208i
$159$	−1.76119	−	3.05047i	−0.139671	−	0.241918i
$160$	−6.32100			−0.499719
$161$	8.22763	+	2.85013i	0.648428	+	0.224622i
$162$	−5.36780			−0.421734
$163$	8.01731	+	13.8864i	0.627964	+	1.08767i	0.987960	+	0.154712i	$0.0494449\pi$
$163$	8.01731	+	13.8864i	0.627964	+	1.08767i	−0.359996	+	0.932954i	$0.617222\pi$
$164$	−0.929803	+	1.61047i	−0.0726054	+	0.125756i
$165$	−0.374119	+	0.647993i	−0.0291251	+	0.0504462i
$166$	13.6959	+	23.7219i	1.06300	+	1.84118i
$167$	−8.71647			−0.674500			−0.337250	−	0.941415i	$-0.609497\pi$
$167$	−8.71647			−0.674500			−0.337250	+	0.941415i	$0.609497\pi$
$168$	−0.321595	−	1.67105i	−0.0248116	−	0.128925i
$169$	1.00000			0.0769231
$170$	−1.85387	−	3.21101i	−0.142186	−	0.246273i
$171$	−3.84206	+	6.65465i	−0.293810	+	0.508894i
$172$	−7.18193	+	12.4395i	−0.547617	+	0.948500i
$173$	−1.70249	−	2.94880i	−0.129438	−	0.224193i	0.794021	−	0.607890i	$-0.207984\pi$
$173$	−1.70249	−	2.94880i	−0.129438	−	0.224193i	−0.923459	+	0.383697i	$0.874651\pi$
$174$	6.15139			0.466335
$175$	2.12588	+	11.0464i	0.160701	+	0.835029i
$176$	4.62964			0.348972
$177$	0.105049	+	0.181950i	0.00789594	+	0.0136762i
$178$	−5.82196	+	10.0839i	−0.436374	+	0.755822i
$179$	8.54831	−	14.8061i	0.638931	−	1.10666i	−0.346737	−	0.937962i	$-0.612710\pi$
$179$	8.54831	−	14.8061i	0.638931	−	1.10666i	0.985668	−	0.168698i	$-0.0539563\pi$
$180$	−1.56658	−	2.71340i	−0.116766	−	0.202245i
$181$	−8.20240			−0.609679			−0.304840	−	0.952404i	$-0.598603\pi$
$181$	−8.20240			−0.609679			−0.304840	+	0.952404i	$0.598603\pi$
$182$	4.74906	+	1.64512i	0.352024	+	0.121945i
$183$	3.09150			0.228530
$184$	−1.22356	−	2.11926i	−0.0902017	−	0.156234i
$185$	3.84124	−	6.65322i	0.282414	−	0.489155i
$186$	6.84266	−	11.8518i	0.501728	−	0.869019i
$187$	1.12822	+	1.95413i	0.0825034	+	0.142900i
$188$	−5.64319			−0.411572
$189$	9.08563	−	7.86838i	0.660882	−	0.572341i
$190$	−5.60737			−0.406802
$191$	1.26285	+	2.18731i	0.0913763	+	0.158268i	0.908090	−	0.418774i	$-0.137540\pi$
$191$	1.26285	+	2.18731i	0.0913763	+	0.158268i	−0.816714	+	0.577042i	$0.804207\pi$
$192$	1.99909	−	3.46252i	0.144272	−	0.249886i
$193$	2.92023	−	5.05799i	0.210203	−	0.364082i	−0.741575	−	0.670870i	$-0.765921\pi$
$193$	2.92023	−	5.05799i	0.210203	−	0.364082i	0.951778	+	0.306788i	$0.0992542\pi$
$194$	−5.58623	−	9.67563i	−0.401068	−	0.694670i
$195$	0.748238			0.0535824
$196$	8.84715	+	6.96532i	0.631939	+	0.497523i
$197$	0.869211			0.0619288			0.0309644	−	0.999520i	$-0.490142\pi$
$197$	0.869211			0.0619288			0.0309644	+	0.999520i	$0.490142\pi$
$198$	2.13875	+	3.70443i	0.151994	+	0.263262i
$199$	−11.2619	+	19.5062i	−0.798337	+	1.38276i	0.122361	+	0.992486i	$0.460953\pi$
$199$	−11.2619	+	19.5062i	−0.798337	+	1.38276i	−0.920698	+	0.390275i	$0.872380\pi$
$200$	1.58073	−	2.73791i	0.111775	−	0.193599i
$201$	0.362986	+	0.628711i	0.0256031	+	0.0443459i
$202$	18.8882			1.32897
$203$	7.48713	−	6.48404i	0.525494	−	0.455091i
$204$	3.13967			0.219821
$205$	0.500000	+	0.866025i	0.0349215	+	0.0604858i
$206$	−3.04281	+	5.27031i	−0.212003	+	0.367200i
$207$	3.70533	−	6.41782i	0.257538	−	0.446070i
$208$	−2.31482	−	4.00939i	−0.160504	−	0.278001i
$209$	3.41249			0.236047
$210$	3.55343	+	1.23094i	0.245210	+	0.0849432i
$211$	3.34856			0.230525			0.115262	−	0.993335i	$-0.463229\pi$
$211$	3.34856			0.230525			0.115262	+	0.993335i	$0.463229\pi$
$212$	−3.27512	−	5.67267i	−0.224936	−	0.389600i
$213$	1.87060	−	3.23997i	0.128171	−	0.221999i
$214$	1.87448	−	3.24670i	0.128137	−	0.221940i
$215$	3.86207	+	6.68930i	0.263391	+	0.456207i
$216$	−3.37788			−0.229835
$217$	−4.16426	−	21.6381i	−0.282688	−	1.46889i
$218$	12.9249			0.875384
$219$	−0.453336	−	0.785201i	−0.0306336	−	0.0530590i
$220$	−0.695714	+	1.20501i	−0.0469050	+	0.0812419i
$221$	1.12822	−	1.95413i	0.0758921	−	0.131449i
$222$	7.29691	+	12.6386i	0.489737	+	0.848249i
$223$	−16.6977			−1.11816			−0.559079	−	0.829114i	$-0.688845\pi$
$223$	−16.6977			−1.11816			−0.559079	+	0.829114i	$0.688845\pi$
$224$	−3.65372	−	18.9853i	−0.244125	−	1.26851i
$225$	9.57396			0.638264
$226$	15.3112	+	26.5198i	1.01849	+	1.76407i
$227$	−9.70730	+	16.8135i	−0.644296	+	1.11595i	0.340167	+	0.940365i	$0.389516\pi$
$227$	−9.70730	+	16.8135i	−0.644296	+	1.11595i	−0.984464	+	0.175589i	$0.943817\pi$
$228$	2.37412	−	4.11209i	0.157230	−	0.272330i
$229$	11.0483	+	19.1362i	0.730093	+	1.26456i	0.956843	+	0.290605i	$0.0938565\pi$
$229$	11.0483	+	19.1362i	0.730093	+	1.26456i	−0.226750	+	0.973953i	$0.572810\pi$
$230$	5.40782			0.356581
$231$	−2.16252	−	0.749119i	−0.142283	−	0.0492884i
$232$	−2.78358			−0.182751
$233$	−1.75002	−	3.03113i	−0.114648	−	0.198576i	0.802991	−	0.595991i	$-0.203241\pi$
$233$	−1.75002	−	3.03113i	−0.114648	−	0.198576i	−0.917639	+	0.397415i	$0.869907\pi$
$234$	2.13875	−	3.70443i	0.139815	−	0.242166i
$235$	−1.51731	+	2.62806i	−0.0989783	+	0.171435i
$236$	0.195349	+	0.338355i	0.0127161	+	0.0220250i
$237$	−10.0597			−0.653449
$238$	8.57276	−	7.42423i	0.555689	−	0.481241i
$239$	6.15470			0.398114			0.199057	−	0.979988i	$-0.436212\pi$
$239$	6.15470			0.398114			0.199057	+	0.979988i	$0.436212\pi$
$240$	−1.73204	−	2.99997i	−0.111802	−	0.193648i
$241$	8.85974	−	15.3455i	0.570706	−	0.988491i	−0.425788	−	0.904823i	$-0.640003\pi$
$241$	8.85974	−	15.3455i	0.570706	−	0.988491i	0.996494	−	0.0836683i	$-0.0266636\pi$
$242$	0.949812	−	1.64512i	0.0610562	−	0.105753i
$243$	−8.03635	−	13.9194i	−0.515532	−	0.892928i
$244$	5.74897			0.368040
$245$	5.62255	−	2.24736i	0.359211	−	0.143578i
$246$	−1.89962			−0.121116
$247$	−1.70625	−	2.95531i	−0.108566	−	0.188042i
$248$	−3.09640	+	5.36311i	−0.196621	+	0.340558i
$249$	−6.23651	+	10.8019i	−0.395223	+	0.684546i
$250$	7.60120	+	13.1657i	0.480742	+	0.832670i
$251$	−8.90787			−0.562260			−0.281130	−	0.959670i	$-0.590709\pi$
$251$	−8.90787			−0.562260			−0.281130	+	0.959670i	$0.590709\pi$
$252$	7.24425	−	6.27370i	0.456345	−	0.395206i
$253$	−3.29105			−0.206907
$254$	7.31962	+	12.6780i	0.459274	+	0.795486i
$255$	0.844175	−	1.46215i	0.0528643	−	0.0915637i
$256$	−10.1639	+	17.6044i	−0.635243	+	1.10027i
$257$	−11.7176	−	20.2955i	−0.730924	−	1.26600i	−0.956489	−	0.291769i	$-0.905756\pi$
$257$	−11.7176	−	20.2955i	−0.730924	−	1.26600i	0.225565	−	0.974228i	$-0.427577\pi$
$258$	−14.6730			−0.913499
$259$	22.2035	+	7.69152i	1.37966	+	0.477928i
$260$	1.39143			0.0862927
$261$	−4.21481	−	7.30026i	−0.260890	−	0.451875i
$262$	−11.1151	+	19.2520i	−0.686695	+	1.18939i
$263$	−7.62227	+	13.2022i	−0.470009	+	0.814079i	−0.999412	−	0.0342911i	$-0.989083\pi$
$263$	−7.62227	+	13.2022i	−0.470009	+	0.814079i	0.529403	+	0.848371i	$0.322416\pi$
$264$	0.321595	+	0.557018i	0.0197928	+	0.0342821i
$265$	−3.52238			−0.216378
$266$	−3.24123	−	16.8419i	−0.198732	−	1.03264i
$267$	−5.30214			−0.324486
$268$	0.675012	+	1.16915i	0.0412329	+	0.0714175i
$269$	8.22062	−	14.2385i	0.501220	−	0.868139i	−0.498779	−	0.866729i	$-0.666218\pi$
$269$	8.22062	−	14.2385i	0.501220	−	0.868139i	0.999999	−	0.00140935i	$-0.000448611\pi$
$270$	3.73235	−	6.46462i	0.227144	−	0.393424i
$271$	11.3658	+	19.6861i	0.690422	+	1.19585i	0.971700	+	0.236220i	$0.0759085\pi$
$271$	11.3658	+	19.6861i	0.690422	+	1.19585i	−0.281278	+	0.959626i	$0.590758\pi$
$272$	−10.4465			−0.633411
$273$	0.432504	+	2.24736i	0.0261763	+	0.136016i
$274$	12.7688			0.771394
$275$	−2.12588	−	3.68213i	−0.128195	−	0.222041i
$276$	−2.28963	+	3.96576i	−0.137820	+	0.238710i
$277$	0.0173084	−	0.0299790i	0.00103996	−	0.00180126i	−0.865505	−	0.500900i	$-0.833002\pi$
$277$	0.0173084	−	0.0299790i	0.00103996	−	0.00180126i	0.866545	+	0.499099i	$0.166336\pi$
$278$	6.71444	+	11.6298i	0.402706	+	0.697507i
$279$	−18.7538			−1.12276
$280$	−1.60797	−	0.557018i	−0.0960948	−	0.0332882i
$281$	12.2546			0.731048			0.365524	−	0.930802i	$-0.380890\pi$
$281$	12.2546			0.731048			0.365524	+	0.930802i	$0.380890\pi$
$282$	−2.88232	−	4.99232i	−0.171639	−	0.297288i
$283$	8.20336	−	14.2086i	0.487639	−	0.844616i	−0.512260	−	0.858831i	$-0.671192\pi$
$283$	8.20336	−	14.2086i	0.487639	−	0.844616i	0.999899	+	0.0142147i	$0.00452484\pi$
$284$	3.47857	−	6.02506i	0.206415	−	0.357521i
$285$	−1.27668	−	2.21127i	−0.0756239	−	0.130985i
$286$	−1.89962			−0.112327
$287$	−2.31212	+	2.00235i	−0.136480	+	0.118195i
$288$	−16.4546			−0.969598
$289$	5.95425	+	10.3131i	0.350250	+	0.606651i
$290$	3.07569	−	5.32726i	0.180611	−	0.312827i
$291$	2.54373	−	4.40587i	0.149116	−	0.258276i
$292$	−0.843026	−	1.46016i	−0.0493344	−	0.0854496i
$293$	17.3463			1.01338			0.506690	−	0.862128i	$-0.330869\pi$
$293$	17.3463			1.01338			0.506690	+	0.862128i	$0.330869\pi$
$294$	−1.64319	+	11.3843i	−0.0958328	+	0.663949i
$295$	0.210097			0.0122323
$296$	−3.30195	−	5.71914i	−0.191922	−	0.332419i
$297$	−2.27141	+	3.93419i	−0.131800	+	0.228285i
$298$	−10.3084	+	17.8547i	−0.597150	+	1.03429i
$299$	1.64553	+	2.85013i	0.0951632	+	0.164828i
$300$	−5.91602			−0.341561
$301$	−17.8591	+	15.4665i	−1.02938	+	0.891472i
$302$	25.0239			1.43996
$303$	4.30044	+	7.44857i	0.247054	+	0.427909i
$304$	−7.89931	+	13.6820i	−0.453056	+	0.784717i
$305$	1.54575	−	2.67732i	0.0885094	−	0.153303i
$306$	−4.82595	−	8.35879i	−0.275881	−	0.477840i
$307$	−16.2170			−0.925551			−0.462775	−	0.886476i	$-0.653146\pi$
$307$	−16.2170			−0.925551			−0.462775	+	0.886476i	$0.653146\pi$
$308$	−4.02143	−	1.39306i	−0.229142	−	0.0793772i
$309$	−2.77113			−0.157644
$310$	−6.84266	−	11.8518i	−0.388637	−	0.673139i
$311$	−0.260923	+	0.451931i	−0.0147956	+	0.0256267i	−0.873328	−	0.487132i	$-0.838043\pi$
$311$	−0.260923	+	0.451931i	−0.0147956	+	0.0256267i	0.858533	+	0.512759i	$0.171376\pi$
$312$	0.321595	−	0.557018i	0.0182067	−	0.0315350i
$313$	−5.34619	−	9.25986i	−0.302184	−	0.523399i	0.674446	−	0.738324i	$-0.264382\pi$
$313$	−5.34619	−	9.25986i	−0.302184	−	0.523399i	−0.976630	+	0.214926i	$0.931049\pi$
$314$	−7.14460			−0.403193
$315$	−0.973896	−	5.06051i	−0.0548728	−	0.285127i
$316$	−18.7071			−1.05236
$317$	−5.61031	−	9.71734i	−0.315106	−	0.545780i	0.664354	−	0.747418i	$-0.268707\pi$
$317$	−5.61031	−	9.71734i	−0.315106	−	0.545780i	−0.979460	+	0.201638i	$0.935374\pi$
$318$	3.34560	−	5.79474i	0.187612	−	0.324953i
$319$	−1.87178	+	3.24202i	−0.104800	+	0.181518i
$320$	−1.99909	−	3.46252i	−0.111752	−	0.193561i
$321$	1.70712			0.0952821
$322$	3.12588	+	16.2426i	0.174199	+	0.905162i
$323$	−7.70007			−0.428443
$324$	−2.27269	−	3.93641i	−0.126260	−	0.218689i
$325$	−2.12588	+	3.68213i	−0.117923	+	0.204248i
$326$	−15.2299	+	26.3789i	−0.843505	+	1.46099i
$327$	2.94272	+	5.09694i	0.162733	+	0.281862i
$328$	0.859605			0.0474638
$329$	−8.77049	−	3.03819i	−0.483533	−	0.167501i
$330$	−1.42137			−0.0782439
$331$	9.44748	+	16.3635i	0.519280	+	0.899420i	0.999749	+	0.0224079i	$0.00713324\pi$
$331$	9.44748	+	16.3635i	0.519280	+	0.899420i	−0.480469	+	0.877012i	$0.659533\pi$
$332$	−11.5974	+	20.0874i	−0.636492	+	1.10244i
$333$	9.99940	−	17.3195i	0.547964	−	0.949101i
$334$	−8.27900	−	14.3397i	−0.453007	−	0.784631i
$335$	0.725973			0.0396641
$336$	8.00935	−	6.93630i	0.436946	−	0.378406i
$337$	−15.3350			−0.835351			−0.417676	−	0.908596i	$-0.637155\pi$
$337$	−15.3350			−0.835351			−0.417676	+	0.908596i	$0.637155\pi$
$338$	0.949812	+	1.64512i	0.0516630	+	0.0894829i
$339$	−6.97207	+	12.0760i	−0.378671	+	0.655877i
$340$	1.56983	−	2.71903i	0.0851361	−	0.147460i
$341$	4.16426	+	7.21270i	0.225507	+	0.390590i
$342$	−14.5970			−0.789313
$343$	10.0000	+	15.5885i	0.539949	+	0.841698i
$344$	6.63971			0.357989
$345$	1.23125	+	2.13258i	0.0662880	+	0.114814i
$346$	3.23409	−	5.60161i	0.173866	−	0.301144i
$347$	12.1592	−	21.0604i	0.652741	−	1.13058i	−0.329714	−	0.944081i	$-0.606952\pi$
$347$	12.1592	−	21.0604i	0.652741	−	1.13058i	0.982455	−	0.186500i	$-0.0597144\pi$
$348$	2.60445	+	4.51104i	0.139613	+	0.241817i
$349$	−3.24955			−0.173944			−0.0869722	−	0.996211i	$-0.527719\pi$
$349$	−3.24955			−0.173944			−0.0869722	+	0.996211i	$0.527719\pi$
$350$	−16.1535	+	13.9893i	−0.863441	+	0.747762i
$351$	4.54281			0.242477
$352$	3.65372	+	6.32843i	0.194744	+	0.337307i
$353$	11.5978	−	20.0880i	0.617290	−	1.06918i	−0.372689	−	0.927956i	$-0.621564\pi$
$353$	11.5978	−	20.0880i	0.617290	−	1.06918i	0.989978	−	0.141220i	$-0.0451026\pi$
$354$	−0.199553	+	0.345636i	−0.0106061	+	0.0183703i
$355$	−1.87060	−	3.23997i	−0.0992809	−	0.171960i
$356$	−9.85989			−0.522573
$357$	4.87958	+	1.69034i	0.258255	+	0.0894621i
$358$	32.4772			1.71647
$359$	−4.56824	−	7.91242i	−0.241102	−	0.417602i	0.719926	−	0.694051i	$-0.244176\pi$
$359$	−4.56824	−	7.91242i	−0.241102	−	0.417602i	−0.961029	+	0.276449i	$0.910842\pi$
$360$	−0.724155	+	1.25427i	−0.0381663	+	0.0661060i
$361$	3.67744	−	6.36952i	0.193550	−	0.335238i
$362$	−7.79074	−	13.4940i	−0.409472	−	0.709226i
$363$	0.865008			0.0454011
$364$	0.804286	+	4.17919i	0.0421561	+	0.219049i
$365$	−0.906672			−0.0474574
$366$	2.93634	+	5.08590i	0.153485	+	0.265844i
$367$	16.5661	−	28.6934i	0.864745	−	1.49778i	−0.00255576	−	0.999997i	$-0.500814\pi$
$367$	16.5661	−	28.6934i	0.864745	−	1.49778i	0.867300	−	0.497785i	$-0.165853\pi$
$368$	7.61819	−	13.1951i	0.397126	−	0.687842i
$369$	1.30159	+	2.25441i	0.0677578	+	0.117360i
$370$	14.5938			0.758697
$371$	−2.03604	−	10.5796i	−0.105706	−	0.549264i
$372$	11.5885			0.600837
$373$	−11.3110	−	19.5912i	−0.585660	−	1.01439i	−0.994793	−	0.101918i	$-0.967502\pi$
$373$	−11.3110	−	19.5912i	−0.585660	−	1.01439i	0.409133	−	0.912475i	$-0.365831\pi$
$374$	−2.14319	+	3.71211i	−0.110822	+	0.191949i
$375$	−3.46126	+	5.99508i	−0.178739	+	0.309585i
$376$	1.30429	+	2.25909i	0.0672634	+	0.116504i
$377$	3.74357			0.192803
$378$	21.5741	+	7.47349i	1.10965	+	0.384395i
$379$	−27.1610			−1.39517			−0.697584	−	0.716503i	$-0.745742\pi$
$379$	−27.1610			−1.39517			−0.697584	+	0.716503i	$0.745742\pi$
$380$	−2.37412	−	4.11209i	−0.121790	−	0.210946i
$381$	−3.33304	+	5.77300i	−0.170757	+	0.295760i
$382$	−2.39893	+	4.15507i	−0.122740	+	0.212592i
$383$	−1.05400	−	1.82557i	−0.0538567	−	0.0932825i	0.837840	−	0.545916i	$-0.183818\pi$
$383$	−1.05400	−	1.82557i	−0.0538567	−	0.0932825i	−0.891697	+	0.452633i	$0.850485\pi$
$384$	−5.04697			−0.257552
$385$	−1.73002	+	1.49824i	−0.0881697	+	0.0763572i
$386$	11.0947			0.564705
$387$	10.0536	+	17.4134i	0.511055	+	0.885173i
$388$	4.73033	−	8.19317i	0.240146	−	0.415945i
$389$	15.0527	−	26.0721i	0.763205	−	1.32191i	−0.177986	−	0.984033i	$-0.556958\pi$
$389$	15.0527	−	26.0721i	0.763205	−	1.32191i	0.941191	−	0.337876i	$-0.109709\pi$
$390$	0.710686	+	1.23094i	0.0359870	+	0.0623313i
$391$	7.42604			0.375551
$392$	0.743565	−	5.15157i	0.0375557	−	0.260194i
$393$	−10.1227			−0.510623
$394$	0.825588	+	1.42996i	0.0415925	+	0.0720403i
$395$	−5.02986	+	8.71198i	−0.253080	+	0.438347i
$396$	−1.81106	+	3.13685i	−0.0910093	+	0.157633i
$397$	−18.0067	−	31.1885i	−0.903730	−	1.56531i	−0.822614	−	0.568601i	$-0.807485\pi$
$397$	−18.0067	−	31.1885i	−0.903730	−	1.56531i	−0.0811159	−	0.996705i	$-0.525848\pi$
$398$	−42.7869			−2.14471
$399$	5.90367	−	5.11273i	0.295553	−	0.255956i
$400$	19.6841			0.984206
$401$	−3.85086	−	6.66988i	−0.192303	−	0.333078i	0.753710	−	0.657207i	$-0.228262\pi$
$401$	−3.85086	−	6.66988i	−0.192303	−	0.333078i	−0.946013	+	0.324129i	$0.894929\pi$
$402$	−0.689538	+	1.19431i	−0.0343910	+	0.0595670i
$403$	4.16426	−	7.21270i	0.207436	−	0.359290i
$404$	7.99711	+	13.8514i	0.397871	+	0.689133i
$405$	−2.44427			−0.121457
$406$	17.7784	+	6.15862i	0.882328	+	0.305647i
$407$	−8.88140			−0.440235
$408$	−0.725657	−	1.25688i	−0.0359254	−	0.0622246i
$409$	−6.15372	+	10.6586i	−0.304282	+	0.527032i	−0.977101	−	0.212775i	$-0.931750\pi$
$409$	−6.15372	+	10.6586i	−0.304282	+	0.527032i	0.672819	+	0.739807i	$0.265083\pi$
$410$	−0.949812	+	1.64512i	−0.0469079	+	0.0812468i
$411$	2.90719	+	5.03540i	0.143401	+	0.248378i
$412$	−5.15322			−0.253881
$413$	0.121442	+	0.631034i	0.00597579	+	0.0310511i
$414$	14.0775			0.691870
$415$	6.23651	+	10.8019i	0.306138	+	0.530247i
$416$	3.65372	−	6.32843i	0.179138	−	0.310277i
$417$	−3.05747	+	5.29569i	−0.149725	+	0.259331i
$418$	3.24123	+	5.61397i	0.158534	+	0.274588i
$419$	−11.5576			−0.564624			−0.282312	−	0.959323i	$-0.591101\pi$
$419$	−11.5576			−0.564624			−0.282312	+	0.959323i	$0.591101\pi$
$420$	0.601798	+	3.12703i	0.0293647	+	0.152584i
$421$	−35.4489			−1.72767			−0.863836	−	0.503774i	$-0.831945\pi$
$421$	−35.4489			−1.72767			−0.863836	+	0.503774i	$0.831945\pi$
$422$	3.18051	+	5.50880i	0.154825	+	0.268164i
$423$	−3.94981	+	6.84128i	−0.192046	+	0.332634i
$424$	−1.51393	+	2.62220i	−0.0735228	+	0.127345i
$425$	4.79691	+	8.30850i	0.232684	+	0.403021i
$426$	7.10686			0.344328
$427$	8.93489	+	3.09514i	0.432390	+	0.149784i
$428$	3.17457			0.153449
$429$	−0.432504	−	0.749119i	−0.0208815	−	0.0361678i
$430$	−7.33649	+	12.7072i	−0.353797	+	0.612794i
$431$	−9.60715	+	16.6401i	−0.462760	+	0.801524i	−0.999097	−	0.0424797i	$-0.986474\pi$
$431$	−9.60715	+	16.6401i	−0.462760	+	0.801524i	0.536337	+	0.844004i	$0.319808\pi$
$432$	−10.5158	−	18.2139i	−0.505941	−	0.876316i
$433$	11.4839			0.551883			0.275941	−	0.961174i	$-0.411010\pi$
$433$	11.4839			0.551883			0.275941	+	0.961174i	$0.411010\pi$
$434$	31.6421	−	27.4029i	1.51887	−	1.31538i
$435$	2.80108			0.134301
$436$	5.47230	+	9.47830i	0.262076	+	0.453928i
$437$	5.61535	−	9.72607i	0.268619	−	0.465261i
$438$	0.861168	−	1.49159i	0.0411482	−	0.0712708i
$439$	−13.6522	−	23.6462i	−0.651582	−	1.12857i	−0.982739	−	0.184998i	$-0.940772\pi$
$439$	−13.6522	−	23.6462i	−0.651582	−	1.12857i	0.331157	−	0.943576i	$-0.392561\pi$
$440$	0.643189			0.0306629
$441$	14.6365	−	5.85025i	0.696974	−	0.278583i
$442$	4.28638			0.203882
$443$	−3.22173	−	5.58019i	−0.153069	−	0.265123i	0.779285	−	0.626669i	$-0.215582\pi$
$443$	−3.22173	−	5.58019i	−0.153069	−	0.265123i	−0.932354	+	0.361546i	$0.882249\pi$
$444$	−6.17891	+	10.7022i	−0.293238	+	0.507903i
$445$	−2.65107	+	4.59179i	−0.125673	+	0.217672i
$446$	−15.8597	−	27.4697i	−0.750976	−	1.30073i
$447$	−9.38802			−0.444038
$448$	9.24425	−	8.00575i	0.436750	−	0.378236i
$449$	7.73842			0.365199			0.182599	−	0.983187i	$-0.441549\pi$
$449$	7.73842			0.365199			0.182599	+	0.983187i	$0.441549\pi$
$450$	9.09346	+	15.7503i	0.428670	+	0.742478i
$451$	0.578030	−	1.00118i	0.0272184	−	0.0471436i
$452$	−12.9653	+	22.4565i	−0.609836	+	1.05627i
$453$	5.69741	+	9.86820i	0.267688	+	0.463649i
$454$	−36.8805			−1.73089
$455$	2.16252	+	0.749119i	0.101380	+	0.0351192i
$456$	−2.19488			−0.102785
$457$	2.70986	+	4.69362i	0.126762	+	0.219558i	0.922420	−	0.386187i	$-0.126208\pi$
$457$	2.70986	+	4.69362i	0.126762	+	0.219558i	−0.795658	+	0.605746i	$0.792875\pi$
$458$	−20.9876	+	36.3517i	−0.980688	+	1.69860i
$459$	5.12528	−	8.87725i	0.239228	−	0.414354i
$460$	2.28963	+	3.96576i	0.106755	+	0.184904i
$461$	12.0310			0.560338			0.280169	−	0.959951i	$-0.409610\pi$
$461$	12.0310			0.560338			0.280169	+	0.959951i	$0.409610\pi$
$462$	−0.821595	−	4.26913i	−0.0382240	−	0.198618i
$463$	−9.47569			−0.440373			−0.220186	−	0.975458i	$-0.570667\pi$
$463$	−9.47569			−0.440373			−0.220186	+	0.975458i	$0.570667\pi$
$464$	−8.66568	−	15.0094i	−0.402294	−	0.696794i
$465$	3.11585	−	5.39682i	0.144494	−	0.250271i
$466$	3.32439	−	5.75801i	0.153999	−	0.266735i
$467$	−12.5964	−	21.8177i	−0.582894	−	1.00960i	−0.995134	−	0.0985268i	$-0.968587\pi$
$467$	−12.5964	−	21.8177i	−0.582894	−	1.00960i	0.412240	−	0.911075i	$-0.364746\pi$
$468$	3.62212			0.167433
$469$	0.419634	+	2.18048i	0.0193769	+	0.100685i
$470$	−5.76463			−0.265903
$471$	−1.62667	−	2.81748i	−0.0749531	−	0.129823i
$472$	0.0903004	−	0.156405i	0.00415641	−	0.00719912i
$473$	4.46478	−	7.73323i	0.205291	−	0.355574i
$474$	−9.55485	−	16.5495i	−0.438869	−	0.760143i
$475$	14.5091			0.665724
$476$	9.07410	+	3.14336i	0.415911	+	0.144076i
$477$	−9.16935			−0.419836
$478$	5.84581	+	10.1252i	0.267381	+	0.463118i
$479$	16.3135	−	28.2558i	0.745382	−	1.29104i	−0.204633	−	0.978839i	$-0.565600\pi$
$479$	16.3135	−	28.2558i	0.745382	−	1.29104i	0.950016	−	0.312202i	$-0.101066\pi$
$480$	2.73385	−	4.73517i	0.124783	−	0.216130i
$481$	4.44070	+	7.69152i	0.202479	+	0.350703i
$482$	33.6603			1.53319
$483$	−5.69357	+	4.93078i	−0.259066	+	0.224358i
$484$	1.60857			0.0731169
$485$	−2.54373	−	4.40587i	−0.115505	−	0.200060i
$486$	15.2661	−	26.4416i	0.692482	−	1.19941i
$487$	4.52748	−	7.84182i	0.205160	−	0.355347i	−0.745024	−	0.667038i	$-0.767562\pi$
$487$	4.52748	−	7.84182i	0.205160	−	0.355347i	0.950184	+	0.311691i	$0.100895\pi$
$488$	−1.32873	−	2.30144i	−0.0601490	−	0.104181i
$489$	−13.8701			−0.627226
$490$	9.03754	+	7.11522i	0.408275	+	0.321433i
$491$	36.4177			1.64351			0.821754	−	0.569842i	$-0.192996\pi$
$491$	36.4177			1.64351			0.821754	+	0.569842i	$0.192996\pi$
$492$	−0.804286	−	1.39306i	−0.0362600	−	0.0628042i
$493$	4.22356	−	7.31541i	0.190219	−	0.329470i
$494$	3.24123	−	5.61397i	0.145830	−	0.252585i
$495$	0.973896	+	1.68684i	0.0437733	+	0.0758177i
$496$	−38.5580			−1.73131
$497$	8.65008	−	7.49119i	0.388009	−	0.336026i
$498$	−23.6940			−1.06176
$499$	13.6768	+	23.6890i	0.612260	+	1.06046i	0.990859	+	0.134904i	$0.0430726\pi$
$499$	13.6768	+	23.6890i	0.612260	+	1.06046i	−0.378599	+	0.925561i	$0.623594\pi$
$500$	−6.43658	+	11.1485i	−0.287853	+	0.498575i
$501$	3.76990	−	6.52967i	0.168427	−	0.291724i
$502$	−8.46080	−	14.6545i	−0.377624	−	0.654064i
$503$	27.8549			1.24199			0.620995	−	0.783815i	$-0.286729\pi$
$503$	27.8549			1.24199			0.620995	+	0.783815i	$0.286729\pi$
$504$	−4.18583	−	1.45001i	−0.186452	−	0.0645887i
$505$	8.60087			0.382734
$506$	−3.12588	−	5.41418i	−0.138962	−	0.240690i
$507$	−0.432504	+	0.749119i	−0.0192082	+	0.0332695i
$508$	−6.19814	+	10.7355i	−0.274998	+	0.476311i
$509$	2.67269	+	4.62923i	0.118465	+	0.205187i	0.919159	−	0.393886i	$-0.128869\pi$
$509$	2.67269	+	4.62923i	0.118465	+	0.205187i	−0.800695	+	0.599073i	$0.795536\pi$
$510$	3.20723			0.142019
$511$	−0.524083	−	2.72322i	−0.0231841	−	0.120468i
$512$	−26.9460			−1.19085
$513$	−7.75116	−	13.4254i	−0.342222	−	0.592746i
$514$	22.2590	−	38.5538i	0.981804	−	1.70054i
$515$	−1.38557	+	2.39987i	−0.0610554	+	0.105751i
$516$	−6.21242	−	10.7602i	−0.273487	−	0.473693i
$517$	3.50820			0.154290
$518$	8.43566	+	43.8330i	0.370642	+	1.92591i
$519$	2.94533			0.129286
$520$	−0.321595	−	0.557018i	−0.0141029	−	0.0244269i
$521$	−10.0301	+	17.3726i	−0.439426	+	0.761108i	−0.997645	−	0.0685852i	$-0.978151\pi$
$521$	−10.0301	+	17.3726i	−0.439426	+	0.761108i	0.558219	+	0.829694i	$0.311485\pi$
$522$	8.00655	−	13.8678i	0.350437	−	0.606975i
$523$	−17.8819	−	30.9724i	−0.781921	−	1.35433i	−0.930821	−	0.365475i	$-0.880907\pi$
$523$	−17.8819	−	30.9724i	−0.781921	−	1.35433i	0.148900	−	0.988852i	$-0.452427\pi$
$524$	−18.8242			−0.822340
$525$	−9.19452	−	3.18507i	−0.401282	−	0.139008i
$526$	−28.9589			−1.26267
$527$	−9.39637	−	16.2750i	−0.409312	−	0.708950i
$528$	−2.00234	+	3.46815i	−0.0871405	+	0.150932i
$529$	6.08449	−	10.5386i	0.264543	−	0.458202i
$530$	−3.34560	−	5.79474i	−0.145323	−	0.251708i
$531$	0.546919			0.0237343
$532$	10.9785	−	9.50765i	0.475978	−	0.412209i
$533$	−1.15606			−0.0500745
$534$	−5.03604	−	8.72267i	−0.217931	−	0.377467i
$535$	0.853560	−	1.47841i	0.0369026	−	0.0639172i
$536$	0.312025	−	0.540443i	0.0134774	−	0.0233436i
$537$	7.39435	+	12.8074i	0.319090	+	0.552680i
$538$	31.2322			1.34651
$539$	−5.50000	−	4.33013i	−0.236902	−	0.186512i
$540$	6.32100			0.272012
$541$	21.2660	+	36.8337i	0.914295	+	1.58361i	0.807930	+	0.589278i	$0.200588\pi$
$541$	21.2660	+	36.8337i	0.914295	+	1.58361i	0.106365	+	0.994327i	$0.466079\pi$
$542$	−21.5907	+	37.3962i	−0.927401	+	1.60630i
$543$	3.54757	−	6.14457i	0.152241	−	0.263689i
$544$	−8.24439	−	14.2797i	−0.353475	−	0.612237i
$545$	5.88544			0.252105
$546$	−3.28638	+	2.84609i	−0.140644	+	0.121801i
$547$	−42.4002			−1.81290			−0.906452	−	0.422309i	$-0.861220\pi$
$547$	−42.4002			−1.81290			−0.906452	+	0.422309i	$0.861220\pi$
$548$	5.40623	+	9.36386i	0.230943	+	0.400004i
$549$	4.02385	−	6.96951i	0.171734	−	0.297451i
$550$	4.03838	−	6.99467i	0.172197	−	0.298254i
$551$	−6.38745	−	11.0634i	−0.272114	−	0.471316i
$552$	2.11677			0.0900957
$553$	−29.0741	−	10.0716i	−1.23636	−	0.428286i
$554$	0.0657589			0.00279383
$555$	3.32270	+	5.75509i	0.141041	+	0.244290i
$556$	−5.68569	+	9.84790i	−0.241127	+	0.417644i
$557$	−1.77621	+	3.07649i	−0.0752604	+	0.130355i	−0.901199	−	0.433405i	$-0.857312\pi$
$557$	−1.77621	+	3.07649i	−0.0752604	+	0.130355i	0.825939	+	0.563759i	$0.190645\pi$
$558$	−17.8126	−	30.8524i	−0.754068	−	1.30608i
$559$	−8.92957			−0.377680
$560$	−2.00234	−	10.4044i	−0.0846142	−	0.439668i
$561$	−1.95183			−0.0824065
$562$	11.6396	+	20.1603i	0.490986	+	0.850412i
$563$	11.7342	−	20.3242i	0.494536	−	0.856562i	−0.505444	−	0.862859i	$-0.668671\pi$
$563$	11.7342	−	20.3242i	0.494536	−	0.856562i	0.999980	+	0.00629749i	$0.00200457\pi$
$564$	2.44070	−	4.22742i	0.102772	−	0.178006i
$565$	6.97207	+	12.0760i	0.293317	+	0.508040i
$566$	31.1666			1.31003
$567$	−1.41286	−	7.34143i	−0.0593345	−	0.308311i
$568$	−3.21595			−0.134938
$569$	2.52647	+	4.37597i	0.105915	+	0.183450i	0.914112	−	0.405462i	$-0.132889\pi$
$569$	2.52647	+	4.37597i	0.105915	+	0.183450i	−0.808197	+	0.588913i	$0.799556\pi$
$570$	2.42521	−	4.20059i	0.101581	−	0.175943i
$571$	−19.5952	+	33.9398i	−0.820032	+	1.42034i	0.0856254	+	0.996327i	$0.472711\pi$
$571$	−19.5952	+	33.9398i	−0.820032	+	1.42034i	−0.905658	+	0.424010i	$0.860622\pi$
$572$	−0.804286	−	1.39306i	−0.0336289	−	0.0582470i
$573$	−2.18474			−0.0912689
$574$	−5.49020	−	1.90186i	−0.229156	−	0.0793821i
$575$	−13.9928			−0.583539
$576$	−5.20396	−	9.01352i	−0.216832	−	0.375563i
$577$	−10.9510	+	18.9677i	−0.455896	+	0.789635i	−0.998739	−	0.0501989i	$-0.984014\pi$
$577$	−10.9510	+	18.9677i	−0.455896	+	0.789635i	0.542843	+	0.839834i	$0.317348\pi$
$578$	−11.3108	+	19.5909i	−0.470469	+	0.814876i
$579$	2.52602	+	4.37520i	0.104978	+	0.181827i
$580$	5.20890			0.216288
$581$	−28.8391	+	24.9754i	−1.19645	+	1.03615i
$582$	9.66426			0.400596
$583$	2.03604	+	3.52652i	0.0843241	+	0.146054i
$584$	−0.389690	+	0.674963i	−0.0161255	+	0.0279302i
$585$	0.973896	−	1.68684i	0.0402656	−	0.0697421i
$586$	16.4757	+	28.5367i	0.680605	+	1.17884i
$587$	−1.74887			−0.0721835			−0.0360918	−	0.999348i	$-0.511491\pi$
$587$	−1.74887			−0.0721835			−0.0360918	+	0.999348i	$0.511491\pi$
$588$	−9.04428	+	3.61503i	−0.372980	+	0.149082i
$589$	−28.4210			−1.17107
$590$	0.199553	+	0.345636i	0.00821547	+	0.0142296i
$591$	−0.375937	+	0.651142i	−0.0154640	+	0.0267844i
$592$	20.5588	−	35.6090i	0.844963	−	1.46352i
$593$	11.1059	+	19.2359i	0.456063	+	0.789925i	0.998749	−	0.0500111i	$-0.0159257\pi$
$593$	11.1059	+	19.2359i	0.456063	+	0.789925i	−0.542685	+	0.839936i	$0.682592\pi$
$594$	−8.62964			−0.354078
$595$	3.90367	−	3.38067i	0.160035	−	0.138594i
$596$	−17.4580			−0.715108
$597$	−9.74166	−	16.8730i	−0.398699	−	0.690568i
$598$	−3.12588	+	5.41418i	−0.127827	+	0.221402i
$599$	19.2563	−	33.3530i	0.786793	−	1.36277i	−0.141129	−	0.989991i	$-0.545073\pi$
$599$	19.2563	−	33.3530i	0.786793	−	1.36277i	0.927922	−	0.372774i	$-0.121593\pi$
$600$	1.36734	+	2.36831i	0.0558216	+	0.0966858i
$601$	21.4530			0.875085			0.437542	−	0.899198i	$-0.355849\pi$
$601$	21.4530			0.875085			0.437542	+	0.899198i	$0.355849\pi$
$602$	−42.4071	−	14.6902i	−1.72838	−	0.598729i
$603$	1.88983			0.0769599
$604$	10.5949	+	18.3510i	0.431102	+	0.746690i
$605$	0.432504	−	0.749119i	0.0175838	−	0.0304560i
$606$	−8.16921	+	14.1495i	−0.331852	+	0.574784i
$607$	12.5667	+	21.7662i	0.510068	+	0.883463i	0.999932	+	0.0116644i	$0.00371296\pi$
$607$	12.5667	+	21.7662i	0.510068	+	0.883463i	−0.489864	+	0.871799i	$0.662954\pi$
$608$	−24.9366			−1.01131
$609$	1.61911	+	8.41312i	0.0656095	+	0.340917i
$610$	5.87269			0.237778
$611$	−1.75410	−	3.03819i	−0.0709632	−	0.122912i
$612$	4.08654	−	7.07810i	0.165189	−	0.286115i
$613$	16.6606	−	28.8571i	0.672917	−	1.16553i	−0.304156	−	0.952622i	$-0.598374\pi$
$613$	16.6606	−	28.8571i	0.672917	−	1.16553i	0.977073	−	0.212904i	$-0.0682922\pi$
$614$	−15.4031	−	26.6789i	−0.621617	−	1.07667i
$615$	−0.865008			−0.0348805
$616$	0.371783	+	1.93184i	0.0149795	+	0.0778360i
$617$	−33.2194			−1.33736			−0.668682	−	0.743549i	$-0.733141\pi$
$617$	−33.2194			−1.33736			−0.668682	+	0.743549i	$0.733141\pi$
$618$	−2.63206	−	4.55886i	−0.105877	−	0.183384i
$619$	0.703452	−	1.21842i	0.0282741	−	0.0489723i	−0.851542	−	0.524286i	$-0.824332\pi$
$619$	0.703452	−	1.21842i	0.0282741	−	0.0489723i	0.879816	+	0.475314i	$0.157666\pi$
$620$	5.79426	−	10.0360i	0.232703	−	0.403054i
$621$	7.47532	+	12.9476i	0.299974	+	0.519570i
$622$	−0.991310			−0.0397479
$623$	−15.3240	−	5.30838i	−0.613942	−	0.212676i
$624$	4.00467			0.160315
$625$	−7.16814	−	12.4156i	−0.286726	−	0.496624i
$626$	10.1557	−	17.5903i	0.405905	−	0.703048i
$627$	−1.47592	+	2.55636i	−0.0589424	+	0.102091i
$628$	−3.02497	−	5.23940i	−0.120709	−	0.209075i
$629$	20.0403			0.799059
$630$	7.40014	−	6.40871i	0.294829	−	0.255329i
$631$	−44.2320			−1.76085			−0.880424	−	0.474187i	$-0.842742\pi$
$631$	−44.2320			−1.76085			−0.880424	+	0.474187i	$0.842742\pi$
$632$	4.32370	+	7.48886i	0.171987	+	0.297891i
$633$	−1.44827	+	2.50847i	−0.0575634	+	0.0997028i
$634$	10.6575	−	18.4593i	0.423263	−	0.733112i
$635$	3.33304	+	5.77300i	0.132268	+	0.229094i
$636$	5.66600			0.224672
$637$	−1.00000	+	6.92820i	−0.0396214	+	0.274505i
$638$	−7.11137			−0.281542
$639$	−4.86948	−	8.43418i	−0.192634	−	0.333651i
$640$	−2.52348	+	4.37080i	−0.0997495	+	0.172771i
$641$	−4.37843	+	7.58366i	−0.172937	+	0.299537i	−0.939446	−	0.342698i	$-0.888659\pi$
$641$	−4.37843	+	7.58366i	−0.172937	+	0.299537i	0.766508	+	0.642235i	$0.221993\pi$
$642$	1.62144	+	2.80842i	0.0639932	+	0.110840i
$643$	−13.3910			−0.528088			−0.264044	−	0.964511i	$-0.585056\pi$
$643$	−13.3910			−0.528088			−0.264044	+	0.964511i	$0.585056\pi$
$644$	−10.5878	+	9.16930i	−0.417217	+	0.361321i
$645$	−6.68144			−0.263082
$646$	−7.31362	−	12.6676i	−0.287751	−	0.498399i
$647$	−2.26733	+	3.92714i	−0.0891381	+	0.154392i	−0.907147	−	0.420814i	$-0.861745\pi$
$647$	−2.26733	+	3.92714i	−0.0891381	+	0.154392i	0.818009	+	0.575205i	$0.195078\pi$
$648$	−1.05055	+	1.81961i	−0.0412696	+	0.0714810i
$649$	−0.121442	−	0.210345i	−0.00476704	−	0.00825675i
$650$	−8.07675			−0.316796
$651$	18.0106	+	6.23904i	0.705890	+	0.244527i
$652$	−25.7928			−1.01013
$653$	−9.54452	−	16.5316i	−0.373506	−	0.646931i	0.616596	−	0.787280i	$-0.288511\pi$
$653$	−9.54452	−	16.5316i	−0.373506	−	0.646931i	−0.990102	+	0.140348i	$0.955178\pi$
$654$	−5.59007	+	9.68228i	−0.218589	+	0.378607i
$655$	−5.06135	+	8.76652i	−0.197763	+	0.342536i
$656$	2.67607	+	4.63509i	0.104483	+	0.180970i
$657$	−2.36022			−0.0920810
$658$	−3.33213	−	17.3142i	−0.129900	−	0.674980i
$659$	11.1572			0.434621			0.217311	−	0.976103i	$-0.430272\pi$
$659$	11.1572			0.434621			0.217311	+	0.976103i	$0.430272\pi$
$660$	−0.601798	−	1.04234i	−0.0234249	−	0.0405732i
$661$	−16.6275	+	28.7996i	−0.646734	+	1.12018i	0.337164	+	0.941446i	$0.390532\pi$
$661$	−16.6275	+	28.7996i	−0.646734	+	1.12018i	−0.983898	+	0.178730i	$0.942801\pi$
$662$	−17.9467	+	31.0845i	−0.697517	+	1.20813i
$663$	0.975917	+	1.69034i	0.0379015	+	0.0656473i
$664$	10.7219			0.416089
$665$	−1.47592	−	7.66909i	−0.0572336	−	0.297394i
$666$	37.9902			1.47209
$667$	6.16013	+	10.6697i	0.238521	+	0.413131i
$668$	7.01053	−	12.1426i	0.271246	−	0.469811i
$669$	7.22181	−	12.5085i	0.279211	−	0.483608i
$670$	0.689538	+	1.19431i	0.0266392	+	0.0461404i
$671$	−3.57396			−0.137971
$672$	15.8025	+	5.47414i	0.609594	+	0.211170i
$673$	−19.1327			−0.737511			−0.368756	−	0.929526i	$-0.620216\pi$
$673$	−19.1327			−0.737511			−0.368756	+	0.929526i	$0.620216\pi$
$674$	−14.5654	−	25.2280i	−0.561038	−	0.971746i
$675$	−9.65748	+	16.7272i	−0.371717	+	0.643832i
$676$	−0.804286	+	1.39306i	−0.0309341	+	0.0535794i
$677$	−21.1089	−	36.5618i	−0.811282	−	1.40518i	−0.911967	−	0.410264i	$-0.865437\pi$
$677$	−21.1089	−	36.5618i	−0.811282	−	1.40518i	0.100684	−	0.994918i	$-0.467897\pi$
$678$	−26.4886			−1.01729
$679$	11.7628	−	10.1869i	0.451415	−	0.390937i
$680$	−1.45131			−0.0556554
$681$	−8.39689	−	14.5438i	−0.321770	−	0.557321i
$682$	−7.91052	+	13.7014i	−0.302910	+	0.524655i
$683$	−15.6399	+	27.0891i	−0.598444	+	1.03653i	0.394607	+	0.918850i	$0.370881\pi$
$683$	−15.6399	+	27.0891i	−0.598444	+	1.03653i	−0.993051	+	0.117685i	$0.962453\pi$
$684$	−6.18024	−	10.7045i	−0.236307	−	0.409296i
$685$	5.81438			0.222156
$686$	−16.1468	+	31.2573i	−0.616488	+	1.19341i
$687$	−19.1137			−0.729235
$688$	20.6703	+	35.8021i	0.788049	+	1.36494i
$689$	2.03604	−	3.52652i	0.0775669	−	0.134350i
$690$	−2.33890	+	4.05110i	−0.0890405	+	0.154223i
$691$	−0.492118	−	0.852374i	−0.0187211	−	0.0324258i	0.856513	−	0.516125i	$-0.172626\pi$
$691$	−0.492118	−	0.852374i	−0.0187211	−	0.0324258i	−0.875234	+	0.483699i	$0.839293\pi$
$692$	5.47715			0.208210
$693$	−4.50352	+	3.90017i	−0.171075	+	0.148155i
$694$	46.1959			1.75357
$695$	3.05747	+	5.29569i	0.115976	+	0.200877i
$696$	1.20391	−	2.08523i	0.0456341	−	0.0790406i
$697$	−1.30429	+	2.25909i	−0.0494034	+	0.0855691i
$698$	−3.08646	−	5.34591i	−0.116824	−	0.202346i
$699$	3.02757			0.114513
$700$	−17.0982	−	5.92298i	−0.646250	−	0.223868i
$701$	−23.3730			−0.882787			−0.441393	−	0.897314i	$-0.645516\pi$
$701$	−23.3730			−0.882787			−0.441393	+	0.897314i	$0.645516\pi$
$702$	4.31482	+	7.47349i	0.162852	+	0.282069i
$703$	15.1539	−	26.2473i	0.571539	−	0.989934i
$704$	−2.31106	+	4.00288i	−0.0871014	+	0.150864i
$705$	−1.31248	−	2.27329i	−0.0494310	−	0.0856170i
$706$	44.0630			1.65833
$707$	4.97156	+	25.8330i	0.186975	+	0.971549i
$708$	−0.337957			−0.0127012
$709$	18.9899	+	32.8914i	0.713180	+	1.23526i	0.963657	+	0.267142i	$0.0860791\pi$
$709$	18.9899	+	32.8914i	0.713180	+	1.23526i	−0.250477	+	0.968122i	$0.580588\pi$
$710$	3.55343	−	6.15472i	0.133358	−	0.230982i
$711$	−13.0936	+	22.6788i	−0.491048	+	0.850520i
$712$	2.27887	+	3.94713i	0.0854044	+	0.147925i
$713$	27.4096			1.02650
$714$	1.85387	+	9.63302i	0.0693795	+	0.360507i
$715$	−0.865008			−0.0323494
$716$	13.7506	+	23.8167i	0.513883	+	0.890072i
$717$	−2.66193	+	4.61060i	−0.0994116	+	0.172186i
$718$	8.67794	−	15.0306i	0.323858	−	0.560938i
$719$	12.0728	+	20.9106i	0.450238	+	0.779835i	0.998401	−	0.0565369i	$-0.0180058\pi$
$719$	12.0728	+	20.9106i	0.450238	+	0.779835i	−0.548163	+	0.836372i	$0.684673\pi$
$720$	−9.01757			−0.336065
$721$	−8.00899	−	2.77439i	−0.298270	−	0.103324i
$722$	13.9715			0.519966
$723$	7.66374	+	13.2740i	0.285017	+	0.493665i
$724$	6.59708	−	11.4265i	0.245178	−	0.424661i
$725$	−7.95837	+	13.7843i	−0.295567	+	0.511936i
$726$	0.821595	+	1.42304i	0.0304922	+	0.0528141i
$727$	−33.1492			−1.22944			−0.614718	−	0.788747i	$-0.710730\pi$
$727$	−33.1492			−1.22944			−0.614718	+	0.788747i	$0.710730\pi$
$728$	1.48713	−	1.28789i	0.0551167	−	0.0477325i
$729$	5.42586			0.200958
$730$	−0.861168	−	1.49159i	−0.0318733	−	0.0552061i
$731$	−10.0745	+	17.4495i	−0.372619	+	0.645394i
$732$	−2.48645	+	4.30666i	−0.0919018	+	0.159179i
$733$	4.03447	+	6.98791i	0.149017	+	0.258104i	0.930864	−	0.365365i	$-0.119056\pi$
$733$	4.03447	+	6.98791i	0.149017	+	0.258104i	−0.781848	+	0.623470i	$0.785723\pi$
$734$	62.9388			2.32311
$735$	−0.748238	+	5.18395i	−0.0275992	+	0.191213i
$736$	24.0492			0.886465
$737$	−0.419634	−	0.726827i	−0.0154574	−	0.0267730i
$738$	−2.47252	+	4.28254i	−0.0910148	+	0.157642i
$739$	9.00618	−	15.5992i	0.331298	−	0.573824i	−0.651469	−	0.758675i	$-0.725847\pi$
$739$	9.00618	−	15.5992i	0.331298	−	0.573824i	0.982767	+	0.184851i	$0.0591803\pi$
$740$	6.17891	+	10.7022i	0.227141	+	0.393420i
$741$	2.95183			0.108438
$742$	15.4708	−	13.3981i	0.567952	−	0.491861i
$743$	−4.56333			−0.167413			−0.0837063	−	0.996490i	$-0.526676\pi$
$743$	−4.56333			−0.167413			−0.0837063	+	0.996490i	$0.526676\pi$
$744$	−2.67841	−	4.63913i	−0.0981951	−	0.170079i
$745$	−4.69401	+	8.13026i	−0.171975	+	0.297870i
$746$	21.4866	−	37.2159i	0.786680	−	1.36257i
$747$	16.2347	+	28.1193i	0.593996	+	1.02883i
$748$	−3.62964			−0.132713
$749$	4.93383	+	1.70913i	0.180278	+	0.0624502i
$750$	−13.1502			−0.480177
$751$	23.1777	+	40.1450i	0.845767	+	1.46491i	0.884954	+	0.465679i	$0.154190\pi$
$751$	23.1777	+	40.1450i	0.845767	+	1.46491i	−0.0391868	+	0.999232i	$0.512477\pi$
$752$	−8.12084	+	14.0657i	−0.296137	+	0.512924i
$753$	3.85269	−	6.67305i	0.140400	−	0.243179i
$754$	3.55568	+	6.15862i	0.129490	+	0.224284i
$755$	11.3948			0.414700
$756$	3.65372	+	18.9853i	0.132885	+	0.690489i
$757$	−51.5926			−1.87517			−0.937583	−	0.347762i	$-0.886942\pi$
$757$	−51.5926			−1.87517			−0.937583	+	0.347762i	$0.886942\pi$
$758$	−25.7979	−	44.6832i	−0.937021	−	1.62297i
$759$	1.42339	−	2.46539i	0.0516659	−	0.0894879i
$760$	−1.09744	+	1.90082i	−0.0398083	+	0.0689501i
$761$	−23.9335	−	41.4540i	−0.867588	−	1.50271i	−0.864455	−	0.502711i	$-0.832336\pi$
$761$	−23.9335	−	41.4540i	−0.867588	−	1.50271i	−0.00313286	−	0.999995i	$-0.500997\pi$
$762$	−12.6631			−0.458734
$763$	3.40196	+	17.6771i	0.123159	+	0.639954i
$764$	−4.06276			−0.146985
$765$	−2.19753	−	3.80624i	−0.0794519	−	0.137615i
$766$	2.00220	−	3.46790i	0.0723423	−	0.125300i
$767$	−0.121442	+	0.210345i	−0.00438503	+	0.00759510i
$768$	−8.79184	−	15.2279i	−0.317248	−	0.549490i
$769$	−32.5219			−1.17277			−0.586385	−	0.810032i	$-0.699450\pi$
$769$	−32.5219			−1.17277			−0.586385	+	0.810032i	$0.699450\pi$
$770$	−4.10797	−	1.42304i	−0.148041	−	0.0512829i
$771$	20.2716			0.730065
$772$	4.69741	+	8.13615i	0.169063	+	0.292826i
$773$	5.41221	−	9.37422i	0.194664	−	0.337167i	−0.752127	−	0.659019i	$-0.770972\pi$
$773$	5.41221	−	9.37422i	0.194664	−	0.337167i	0.946790	+	0.321851i	$0.104305\pi$
$774$	−19.0981	+	33.0789i	−0.686468	+	1.18900i
$775$	17.7054	+	30.6667i	0.635998	+	1.10158i
$776$	−4.37320			−0.156989
$777$	−15.3650	+	13.3064i	−0.551215	+	0.477366i
$778$	57.1891			2.05033
$779$	1.97252	+	3.41651i	0.0706730	+	0.122409i
$780$	−0.601798	+	1.04234i	−0.0215478	+	0.0373219i
$781$	−2.16252	+	3.74559i	−0.0773810	+	0.134028i
$782$	7.05335	+	12.2168i	0.252227	+	0.436870i
$783$	17.0063			0.607756
$784$	30.0927	−	12.0282i	1.07474	−	0.429577i
$785$	−3.25334			−0.116117
$786$	−9.61467	−	16.6531i	−0.342944	−	0.593996i
$787$	−1.27548	+	2.20920i	−0.0454660	+	0.0787494i	−0.887863	−	0.460108i	$-0.847811\pi$
$787$	−1.27548	+	2.20920i	−0.0454660	+	0.0787494i	0.842397	+	0.538858i	$0.181144\pi$
$788$	−0.699095	+	1.21087i	−0.0249042	+	0.0431354i
$789$	−6.59332	−	11.4200i	−0.234728	−	0.406561i
$790$	−19.1097			−0.679893
$791$	−32.2405	+	27.9211i	−1.14634	+	0.992759i
$792$	1.67433			0.0594948
$793$	1.78698	+	3.09514i	0.0634574	+	0.109912i
$794$	34.2059	−	59.2464i	1.21392	−	2.10258i
$795$	1.52344	−	2.63868i	0.0540309	−	0.0935843i
$796$	−18.1156	−	31.3772i	−0.642092	−	1.11214i
$797$	23.9899			0.849767			0.424883	−	0.905248i	$-0.360315\pi$
$797$	23.9899			0.849767			0.424883	+	0.905248i	$0.360315\pi$
$798$	14.0184	+	4.85613i	0.496247	+	0.171905i
$799$	−7.91602			−0.280049
$800$	15.5348	+	26.9070i	0.549237	+	0.951306i
$801$	−6.90119	+	11.9532i	−0.243842	+	0.422346i
$802$	7.31518	−	12.6703i	0.258308	−	0.447403i
$803$	0.524083	+	0.907739i	0.0184945	+	0.0320334i
$804$	−1.16778			−0.0411844
$805$	1.42339	+	7.39616i	0.0501680	+	0.260681i
$806$	15.8210			0.557273
$807$	7.11090	+	12.3164i	0.250315	+	0.433559i
$808$	3.69668	−	6.40283i	0.130049	−	0.225251i
$809$	0.457866	−	0.793048i	0.0160977	−	0.0278821i	−0.857864	−	0.513876i	$-0.828209\pi$
$809$	0.457866	−	0.793048i	0.0160977	−	0.0278821i	0.873962	+	0.485994i	$0.161542\pi$
$810$	−2.32159	−	4.02112i	−0.0815725	−	0.141288i
$811$	16.1199			0.566045			0.283023	−	0.959113i	$-0.408663\pi$
$811$	16.1199			0.566045			0.283023	+	0.959113i	$0.408663\pi$
$812$	3.01090	+	15.6451i	0.105662	+	0.549035i
$813$	−19.6630			−0.689611
$814$	−8.43566	−	14.6110i	−0.295670	−	0.512115i
$815$	−6.93503	+	12.0118i	−0.242924	+	0.420756i
$816$	4.51814	−	7.82565i	0.158167	−	0.273953i
$817$	15.2360	+	26.3896i	0.533042	+	0.923256i
$818$	−23.3795			−0.817446
$819$	5.62940	+	1.95008i	0.196707	+	0.0681414i
$820$	−1.60857			−0.0561738
$821$	18.4477	+	31.9523i	0.643828	+	1.11514i	0.984571	+	0.174986i	$0.0559881\pi$
$821$	18.4477	+	31.9523i	0.643828	+	1.11514i	−0.340743	+	0.940157i	$0.610679\pi$
$822$	−5.52257	+	9.56537i	−0.192622	+	0.333631i
$823$	−3.92966	+	6.80637i	−0.136979	+	0.237255i	−0.926352	−	0.376659i	$-0.877073\pi$
$823$	−3.92966	+	6.80637i	−0.136979	+	0.237255i	0.789372	+	0.613915i	$0.210406\pi$
$824$	1.19104	+	2.06294i	0.0414919	+	0.0718660i
$825$	3.67781			0.128045
$826$	−0.922781	+	0.799151i	−0.0321076	+	0.0278060i
$827$	37.6321			1.30860			0.654299	−	0.756236i	$-0.272964\pi$
$827$	37.6321			1.30860			0.654299	+	0.756236i	$0.272964\pi$
$828$	5.96030	+	10.3235i	0.207135	+	0.358768i
$829$	13.5554	−	23.4787i	0.470800	−	0.815450i	−0.528642	−	0.848845i	$-0.677299\pi$
$829$	13.5554	−	23.4787i	0.470800	−	0.815450i	0.999442	+	0.0333950i	$0.0106319\pi$
$830$	−11.8470	+	20.5196i	−0.411216	+	0.712247i
$831$	0.0149719	+	0.0259321i	0.000519369	+	0.000899574i
$832$	4.62212			0.160243
$833$	12.4104	+	9.77065i	0.429995	+	0.338533i
$834$	−11.6161			−0.402232
$835$	−3.76990	−	6.52967i	−0.130463	−	0.225968i
$836$	−2.74462	+	4.75383i	−0.0949247	+	0.164414i
$837$	18.9174	−	32.7660i	0.653882	−	1.13256i
$838$	−10.9775	−	19.0136i	−0.379212	−	0.656814i
$839$	22.7743			0.786257			0.393129	−	0.919484i	$-0.371393\pi$
$839$	22.7743			0.786257			0.393129	+	0.919484i	$0.371393\pi$
$840$	1.11273	−	0.963650i	0.0383927	−	0.0332491i
$841$	−14.9857			−0.516749
$842$	−33.6698	−	58.3177i	−1.16034	−	2.00976i
$843$	−5.30016	+	9.18015i	−0.182547	+	0.316181i
$844$	−2.69320	+	4.66477i	−0.0927039	+	0.160568i
$845$	0.432504	+	0.749119i	0.0148786	+	0.0257705i
$846$	−15.0063			−0.515928
$847$	2.50000	+	0.866025i	0.0859010	+	0.0297570i
$848$	−18.8523			−0.647389
$849$	7.09597	+	12.2906i	0.243533	+	0.421812i
$850$	−9.11233	+	15.7830i	−0.312550	+	0.541353i
$851$	−14.6146	+	25.3132i	−0.500981	+	0.867725i
$852$	3.00899	+	5.21172i	0.103086	+	0.178551i
$853$	33.7807			1.15663			0.578315	−	0.815813i	$-0.303710\pi$
$853$	33.7807			1.15663			0.578315	+	0.815813i	$0.303710\pi$
$854$	3.39459	+	17.6388i	0.116160	+	0.603587i
$855$	−6.64683			−0.227317
$856$	−0.733724	−	1.27085i	−0.0250782	−	0.0434367i
$857$	−9.00114	+	15.5904i	−0.307473	+	0.532559i	−0.977809	−	0.209499i	$-0.932817\pi$
$857$	−9.00114	+	15.5904i	−0.307473	+	0.532559i	0.670336	+	0.742058i	$0.266150\pi$
$858$	0.821595	−	1.42304i	0.0280488	−	0.0485819i
$859$	1.92494	+	3.33409i	0.0656780	+	0.113758i	0.896995	−	0.442042i	$-0.145746\pi$
$859$	1.92494	+	3.33409i	0.0656780	+	0.113758i	−0.831317	+	0.555799i	$0.812412\pi$
$860$	−12.4248			−0.423684
$861$	−0.500000	−	2.59808i	−0.0170400	−	0.0885422i
$862$	−36.5000			−1.24319
$863$	0.241859	+	0.418913i	0.00823299	+	0.0142600i	0.870113	−	0.492853i	$-0.164046\pi$
$863$	0.241859	+	0.418913i	0.00823299	+	0.0142600i	−0.861880	+	0.507113i	$0.830713\pi$
$864$	16.5982	−	28.7489i	0.564682	−	0.978057i
$865$	1.47267	−	2.55073i	0.0500721	−	0.0867275i
$866$	10.9076	+	18.8925i	0.370655	+	0.641993i
$867$	−10.3009			−0.349838
$868$	33.4925	+	11.6022i	1.13681	+	0.393803i
$869$	11.6296			0.394508
$870$	2.66050	+	4.60812i	0.0901993	+	0.156230i
$871$	−0.419634	+	0.726827i	−0.0142188	+	0.0246276i
$872$	2.52958	−	4.38136i	0.0856624	−	0.148372i
$873$	−6.62176	−	11.4692i	−0.224113	−	0.388174i
$874$	21.3341			0.721637
$875$	−16.0057	+	13.8613i	−0.541091	+	0.468599i
$876$	1.45845			0.0492764
$877$	23.7797	+	41.1876i	0.802982	+	1.39081i	0.917645	+	0.397401i	$0.130088\pi$
$877$	23.7797	+	41.1876i	0.802982	+	1.39081i	−0.114663	+	0.993404i	$0.536579\pi$
$878$	25.9340	−	44.9190i	0.875229	−	1.51594i
$879$	−7.50233	+	12.9944i	−0.253047	+	0.438291i
$880$	2.00234	+	3.46815i	0.0674987	+	0.116911i
$881$	−41.0227			−1.38209			−0.691045	−	0.722812i	$-0.742849\pi$
$881$	−41.0227			−1.38209			−0.691045	+	0.722812i	$0.742849\pi$
$882$	23.5263	+	18.5221i	0.792170	+	0.623672i
$883$	−37.1143			−1.24900			−0.624498	−	0.781026i	$-0.714696\pi$
$883$	−37.1143			−1.24900			−0.624498	+	0.781026i	$0.714696\pi$
$884$	1.81482	+	3.14336i	0.0610390	+	0.105723i
$885$	−0.0908679	+	0.157388i	−0.00305449	+	0.00529053i
$886$	6.12007	−	10.6003i	0.205608	−	0.356123i
$887$	−18.1319	−	31.4053i	−0.608809	−	1.05449i	−0.991437	−	0.130586i	$-0.958314\pi$
$887$	−18.1319	−	31.4053i	−0.608809	−	1.05449i	0.382628	−	0.923903i	$-0.375019\pi$
$888$	5.71242			0.191696
$889$	−15.4128	+	13.3479i	−0.516928	+	0.447673i
$890$	−10.0721			−0.337617
$891$	1.41286	+	2.44714i	0.0473326	+	0.0819824i
$892$	13.4297	−	23.2609i	0.449660	−	0.778834i
$893$	−5.98585	+	10.3678i	−0.200309	+	0.346945i
$894$	−8.91685	−	15.4444i	−0.298224	−	0.516539i
$895$	14.7887			0.494332
$896$	−14.5865	−	5.05291i	−0.487300	−	0.168806i
$897$	−2.84678			−0.0950514
$898$	7.35005	+	12.7307i	0.245274	+	0.424828i
$899$	15.5892	−	27.0012i	0.519928	−	0.900541i
$900$	−7.70020	+	13.3371i	−0.256673	+	0.444571i
$901$	−4.59419	−	7.95737i	−0.153055	−	0.265098i
$902$	2.19608			0.0731214
$903$	−3.86207	−	20.0679i	−0.128522	−	0.667818i
$904$	11.9865			0.398663
$905$	−3.54757	−	6.14457i	−0.117925	−	0.204252i
$906$	−10.8229	+	18.7459i	−0.359568	+	0.622790i
$907$	13.5557	−	23.4791i	0.450109	−	0.779612i	−0.548283	−	0.836293i	$-0.684718\pi$
$907$	13.5557	−	23.4791i	0.450109	−	0.779612i	0.998392	+	0.0566809i	$0.0180518\pi$
$908$	−15.6149	−	27.0458i	−0.518199	−	0.897547i
$909$	22.3895			0.742614
$910$	0.821595	+	4.26913i	0.0272356	+	0.141520i
$911$	−46.4651			−1.53946			−0.769728	−	0.638372i	$-0.779608\pi$
$911$	−46.4651			−1.53946			−0.769728	+	0.638372i	$0.779608\pi$
$912$	−6.83296	−	11.8350i	−0.226262	−	0.391897i
$913$	7.20977	−	12.4877i	0.238609	−	0.413282i
$914$	−5.14772	+	8.91611i	−0.170271	+	0.294919i
$915$	1.33708	+	2.31590i	0.0442027	+	0.0765613i
$916$	−35.5440			−1.17441
$917$	−29.2561	−	10.1346i	−0.966122	−	0.334674i
$918$	19.4722			0.642679
$919$	−24.5060	−	42.4456i	−0.808377	−	1.40015i	−0.913988	−	0.405742i	$-0.867013\pi$
$919$	−24.5060	−	42.4456i	−0.808377	−	1.40015i	0.105611	−	0.994408i	$-0.466320\pi$
$920$	1.05838	−	1.83318i	0.0348939	−	0.0604380i
$921$	7.01390	−	12.1484i	0.231116	−	0.400304i
$922$	11.4272	+	19.7924i	0.376333	+	0.651828i
$923$	4.32504			0.142360
$924$	2.78285	−	2.41002i	0.0915492	−	0.0792839i
$925$	−37.7616			−1.24159
$926$	−9.00013	−	15.5887i	−0.295763	−	0.512276i
$927$	−3.60687	+	6.24728i	−0.118465	+	0.205187i
$928$	13.6779	−	23.6909i	0.449001	−	0.777692i
$929$	14.7393	+	25.5292i	0.483580	+	0.837585i	0.999822	−	0.0188578i	$-0.00600299\pi$
$929$	14.7393	+	25.5292i	0.483580	+	0.837585i	−0.516242	+	0.856442i	$0.672670\pi$
$930$	11.8379			0.388180
$931$	22.1812	−	8.86592i	0.726960	−	0.290569i
$932$	5.63008			0.184420
$933$	−0.225700	−	0.390924i	−0.00738909	−	0.0127983i
$934$	23.9285	−	41.4454i	0.782965	−	1.35613i
$935$	−0.975917	+	1.69034i	−0.0319159	+	0.0552799i
$936$	−0.837166	−	1.45001i	−0.0273636	−	0.0473952i
$937$	14.3326			0.468226			0.234113	−	0.972209i	$-0.424781\pi$
$937$	14.3326			0.468226			0.234113	+	0.972209i	$0.424781\pi$
$938$	−3.18859	+	2.76140i	−0.104111	+	0.0901628i
$939$	9.24898			0.301829
$940$	−2.44070	−	4.22742i	−0.0796069	−	0.137883i
$941$	19.3265	−	33.4745i	0.630026	−	1.09124i	−0.357520	−	0.933905i	$-0.616378\pi$
$941$	19.3265	−	33.4745i	0.630026	−	1.09124i	0.987546	−	0.157331i	$-0.0502890\pi$
$942$	3.09007	−	5.35215i	0.100680	−	0.174383i
$943$	−1.90233	−	3.29492i	−0.0619482	−	0.107297i
$944$	1.12447			0.0365984
$945$	9.82392	+	3.40311i	0.319572	+	0.110703i
$946$	16.9628			0.551509
$947$	26.5477	+	45.9819i	0.862684	+	1.49421i	0.869329	+	0.494234i	$0.164551\pi$
$947$	26.5477	+	45.9819i	0.862684	+	1.49421i	−0.00664528	+	0.999978i	$0.502115\pi$
$948$	8.09090	−	14.0138i	0.262780	−	0.455149i
$949$	0.524083	−	0.907739i	0.0170125	−	0.0294665i
$950$	13.7809	+	23.8693i	0.447112	+	0.774422i
$951$	9.70592			0.314736
$952$	−0.838903	−	4.35907i	−0.0271890	−	0.141278i
$953$	−56.1060			−1.81745			−0.908726	−	0.417392i	$-0.862944\pi$
$953$	−56.1060			−1.81745			−0.908726	+	0.417392i	$0.862944\pi$
$954$	−8.70916	−	15.0847i	−0.281969	−	0.488385i
$955$	−1.09237	+	1.89204i	−0.0353483	+	0.0612250i
$956$	−4.95014	+	8.57389i	−0.160099	+	0.277300i
$957$	−1.61911	−	2.80437i	−0.0523383	−	0.0906525i
$958$	61.9790			2.00245
$959$	3.36088	+	17.4637i	0.108529	+	0.563931i
$960$	3.45845			0.111621
$961$	−19.1821	−	33.2243i	−0.618776	−	1.07175i
$962$	−8.43566	+	14.6110i	−0.271977	+	0.471077i
$963$	2.22196	−	3.84855i	0.0716017	−	0.124018i
$964$	14.2515	+	24.6844i	0.459011	+	0.795030i
$965$	5.05205			0.162631
$966$	−13.5196	−	4.68331i	−0.434984	−	0.150683i
$967$	48.7958			1.56917			0.784583	−	0.620024i	$-0.212877\pi$
$967$	48.7958			1.56917			0.784583	+	0.620024i	$0.212877\pi$
$968$	−0.371783	−	0.643946i	−0.0119495	−	0.0206972i
$969$	3.33031	−	5.76827i	0.106985	−	0.185303i
$970$	4.83213	−	8.36949i	0.155150	−	0.268728i
$971$	29.2770	+	50.7093i	0.939544	+	1.62734i	0.766324	+	0.642454i	$0.222084\pi$
$971$	29.2770	+	50.7093i	0.939544	+	1.62734i	0.173220	+	0.984883i	$0.444583\pi$
$972$	25.8541			0.829271
$973$	−14.1385	+	12.2443i	−0.453258	+	0.392533i
$974$	17.2010			0.551156
$975$	−1.83890	−	3.18507i	−0.0588920	−	0.102004i
$976$	8.27306	−	14.3294i	0.264814	−	0.458672i
$977$	18.7568	−	32.4877i	0.600083	−	1.03937i	−0.392725	−	0.919656i	$-0.628467\pi$
$977$	18.7568	−	32.4877i	0.600083	−	1.03937i	0.992808	−	0.119719i	$-0.0381992\pi$
$978$	−13.1740	−	22.8180i	−0.421257	−	0.729638i
$979$	6.12959			0.195903
$980$	−1.39143	+	9.64009i	−0.0444475	+	0.307941i
$981$	15.3208			0.489156
$982$	34.5900	+	59.9116i	1.10381	+	1.91186i
$983$	27.2596	−	47.2151i	0.869447	−	1.50593i	0.00688474	−	0.999976i	$-0.497809\pi$
$983$	27.2596	−	47.2151i	0.869447	−	1.50593i	0.862563	−	0.505951i	$-0.168858\pi$
$984$	−0.371783	+	0.643946i	−0.0118520	+	0.0205283i
$985$	0.375937	+	0.651142i	0.0119784	+	0.0207471i
$986$	16.0463			0.511019
$987$	6.06923	−	5.25611i	0.193186	−	0.167304i
$988$	5.48924			0.174636
$989$	−14.6938	−	25.4505i	−0.467237	−	0.809278i
$990$	−1.85004	+	3.20436i	−0.0587980	+	0.101841i
$991$	−8.95705	+	15.5141i	−0.284530	+	0.492820i	−0.972495	−	0.232923i	$-0.925171\pi$
$991$	−8.95705	+	15.5141i	−0.284530	+	0.492820i	0.687965	+	0.725744i	$0.258504\pi$
$992$	−30.4301	−	52.7064i	−0.966156	−	1.67343i
$993$	−16.3443			−0.518670
$994$	20.5399	+	7.11522i	0.651485	+	0.225681i
$995$	−19.4833			−0.617662
$996$	−10.0319	−	17.3757i	−0.317872	−	0.550571i
$997$	−14.1911	+	24.5798i	−0.449438	+	0.778449i	−0.998349	−	0.0574313i	$-0.981709\pi$
$997$	−14.1911	+	24.5798i	−0.449438	+	0.778449i	0.548912	+	0.835880i	$0.315042\pi$
$998$	−25.9809	+	45.0002i	−0.822410	+	1.42446i
$999$	20.1733	+	34.9411i	0.638254	+	1.10549i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1001.2.i.a.144.4	✓	8
7.2	even	3	inner	1001.2.i.a.716.4	yes	8
7.3	odd	6		7007.2.a.l.1.1		4
7.4	even	3		7007.2.a.m.1.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1001.2.i.a.144.4	✓	8	1.1	even	1	trivial
1001.2.i.a.716.4	yes	8	7.2	even	3	inner
7007.2.a.l.1.1		4	7.3	odd	6
7007.2.a.m.1.1		4	7.4	even	3

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1001 = 7 \cdot 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1001.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.949812 + 1.64512i) q^{2} +(-0.432504 + 0.749119i) q^{3} +(-0.804286 + 1.39306i) q^{4} +(0.432504 + 0.749119i) q^{5} -1.64319 q^{6} +(-2.00000 + 1.73205i) q^{7} +0.743565 q^{8} +(1.12588 + 1.95008i) q^{9} +O(q^{10})\)	\(q+(0.949812 + 1.64512i) q^{2} +(-0.432504 + 0.749119i) q^{3} +(-0.804286 + 1.39306i) q^{4} +(0.432504 + 0.749119i) q^{5} -1.64319 q^{6} +(-2.00000 + 1.73205i) q^{7} +0.743565 q^{8} +(1.12588 + 1.95008i) q^{9} +(-0.821595 + 1.42304i) q^{10} +(0.500000 - 0.866025i) q^{11} +(-0.695714 - 1.20501i) q^{12} -1.00000 q^{13} +(-4.74906 - 1.64512i) q^{14} -0.748238 q^{15} +(2.31482 + 4.00939i) q^{16} +(-1.12822 + 1.95413i) q^{17} +(-2.13875 + 3.70443i) q^{18} +(1.70625 + 2.95531i) q^{19} -1.39143 q^{20} +(-0.432504 - 2.24736i) q^{21} +1.89962 q^{22} +(-1.64553 - 2.85013i) q^{23} +(-0.321595 + 0.557018i) q^{24} +(2.12588 - 3.68213i) q^{25} +(-0.949812 - 1.64512i) q^{26} -4.54281 q^{27} +(-0.804286 - 4.17919i) q^{28} -3.74357 q^{29} +(-0.710686 - 1.23094i) q^{30} +(-4.16426 + 7.21270i) q^{31} +(-3.65372 + 6.32843i) q^{32} +(0.432504 + 0.749119i) q^{33} -4.28638 q^{34} +(-2.16252 - 0.749119i) q^{35} -3.62212 q^{36} +(-4.44070 - 7.69152i) q^{37} +(-3.24123 + 5.61397i) q^{38} +(0.432504 - 0.749119i) q^{39} +(0.321595 + 0.557018i) q^{40} +1.15606 q^{41} +(3.28638 - 2.84609i) q^{42} +8.92957 q^{43} +(0.804286 + 1.39306i) q^{44} +(-0.973896 + 1.68684i) q^{45} +(3.12588 - 5.41418i) q^{46} +(1.75410 + 3.03819i) q^{47} -4.00467 q^{48} +(1.00000 - 6.92820i) q^{49} +8.07675 q^{50} +(-0.975917 - 1.69034i) q^{51} +(0.804286 - 1.39306i) q^{52} +(-2.03604 + 3.52652i) q^{53} +(-4.31482 - 7.47349i) q^{54} +0.865008 q^{55} +(-1.48713 + 1.28789i) q^{56} -2.95183 q^{57} +(-3.55568 - 6.15862i) q^{58} +(0.121442 - 0.210345i) q^{59} +(0.601798 - 1.04234i) q^{60} +(-1.78698 - 3.09514i) q^{61} -15.8210 q^{62} +(-5.62940 - 1.95008i) q^{63} -4.62212 q^{64} +(-0.432504 - 0.749119i) q^{65} +(-0.821595 + 1.42304i) q^{66} +(0.419634 - 0.726827i) q^{67} +(-1.81482 - 3.14336i) q^{68} +2.84678 q^{69} +(-0.821595 - 4.26913i) q^{70} -4.32504 q^{71} +(0.837166 + 1.45001i) q^{72} +(-0.524083 + 0.907739i) q^{73} +(8.43566 - 14.6110i) q^{74} +(1.83890 + 3.18507i) q^{75} -5.48924 q^{76} +(0.500000 + 2.59808i) q^{77} +1.64319 q^{78} +(5.81482 + 10.0716i) q^{79} +(-2.00234 + 3.46815i) q^{80} +(-1.41286 + 2.44714i) q^{81} +(1.09804 + 1.90186i) q^{82} +14.4195 q^{83} +(3.47857 + 1.20501i) q^{84} -1.95183 q^{85} +(8.48141 + 14.6902i) q^{86} +(1.61911 - 2.80437i) q^{87} +(0.371783 - 0.643946i) q^{88} +(3.06480 + 5.30838i) q^{89} -3.70007 q^{90} +(2.00000 - 1.73205i) q^{91} +5.29390 q^{92} +(-3.60211 - 6.23904i) q^{93} +(-3.33213 + 5.77142i) q^{94} +(-1.47592 + 2.55636i) q^{95} +(-3.16050 - 5.47414i) q^{96} -5.88140 q^{97} +(12.3476 - 4.93537i) q^{98} +2.25176 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 2 q^{2} - q^{3} - 4 q^{4} + q^{5} + 6 q^{6} - 16 q^{7} + 6 q^{8} - 3 q^{9}+O(q^{10}) \) 8 * q - 2 * q^2 - q^3 - 4 * q^4 + q^5 + 6 * q^6 - 16 * q^7 + 6 * q^8 - 3 * q^9	\( 8 q - 2 q^{2} - q^{3} - 4 q^{4} + q^{5} + 6 q^{6} - 16 q^{7} + 6 q^{8} - 3 q^{9} + 3 q^{10} + 4 q^{11} - 8 q^{12} - 8 q^{13} + 10 q^{14} - 30 q^{15} + 4 q^{16} - 9 q^{17} - 5 q^{18} + 4 q^{19} - 16 q^{20} - q^{21} - 4 q^{22} - 6 q^{23} + 7 q^{24} + 5 q^{25} + 2 q^{26} + 2 q^{27} - 4 q^{28} - 30 q^{29} + 11 q^{30} + 10 q^{31} + 2 q^{32} + q^{33} + 4 q^{34} - 5 q^{35} - 34 q^{36} - 9 q^{37} - 14 q^{38} + q^{39} - 7 q^{40} - 10 q^{41} - 12 q^{42} + 14 q^{43} + 4 q^{44} + 4 q^{45} + 13 q^{46} + 2 q^{47} - 56 q^{48} + 8 q^{49} + 2 q^{50} - 10 q^{51} + 4 q^{52} + 27 q^{53} - 20 q^{54} + 2 q^{55} - 12 q^{56} - 28 q^{57} + 10 q^{58} - 4 q^{59} - 5 q^{60} - 19 q^{61} - 88 q^{62} + 15 q^{63} - 42 q^{64} - q^{65} + 3 q^{66} + q^{67} - 16 q^{69} + 3 q^{70} - 10 q^{71} + 21 q^{72} - 2 q^{73} + 5 q^{74} - 2 q^{75} + 38 q^{76} + 4 q^{77} - 6 q^{78} + 32 q^{79} - 28 q^{80} - 4 q^{81} + 16 q^{82} + 40 q^{84} - 20 q^{85} + 22 q^{86} - 4 q^{87} + 3 q^{88} + 3 q^{89} - 58 q^{90} + 16 q^{91} - 30 q^{92} - 17 q^{93} - 5 q^{94} - 14 q^{95} + q^{96} + 6 q^{97} - 26 q^{98} - 6 q^{99}+O(q^{100}) \) 8 * q - 2 * q^2 - q^3 - 4 * q^4 + q^5 + 6 * q^6 - 16 * q^7 + 6 * q^8 - 3 * q^9 + 3 * q^10 + 4 * q^11 - 8 * q^12 - 8 * q^13 + 10 * q^14 - 30 * q^15 + 4 * q^16 - 9 * q^17 - 5 * q^18 + 4 * q^19 - 16 * q^20 - q^21 - 4 * q^22 - 6 * q^23 + 7 * q^24 + 5 * q^25 + 2 * q^26 + 2 * q^27 - 4 * q^28 - 30 * q^29 + 11 * q^30 + 10 * q^31 + 2 * q^32 + q^33 + 4 * q^34 - 5 * q^35 - 34 * q^36 - 9 * q^37 - 14 * q^38 + q^39 - 7 * q^40 - 10 * q^41 - 12 * q^42 + 14 * q^43 + 4 * q^44 + 4 * q^45 + 13 * q^46 + 2 * q^47 - 56 * q^48 + 8 * q^49 + 2 * q^50 - 10 * q^51 + 4 * q^52 + 27 * q^53 - 20 * q^54 + 2 * q^55 - 12 * q^56 - 28 * q^57 + 10 * q^58 - 4 * q^59 - 5 * q^60 - 19 * q^61 - 88 * q^62 + 15 * q^63 - 42 * q^64 - q^65 + 3 * q^66 + q^67 - 16 * q^69 + 3 * q^70 - 10 * q^71 + 21 * q^72 - 2 * q^73 + 5 * q^74 - 2 * q^75 + 38 * q^76 + 4 * q^77 - 6 * q^78 + 32 * q^79 - 28 * q^80 - 4 * q^81 + 16 * q^82 + 40 * q^84 - 20 * q^85 + 22 * q^86 - 4 * q^87 + 3 * q^88 + 3 * q^89 - 58 * q^90 + 16 * q^91 - 30 * q^92 - 17 * q^93 - 5 * q^94 - 14 * q^95 + q^96 + 6 * q^97 - 26 * q^98 - 6 * q^99

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