LMFDB - Embedded newform 847.2.e.h.485.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [847,2,Mod(485,847)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(847, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([2, 0]))

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

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

chi := DirichletCharacter("847.485");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 847 = 7 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	847.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:	$6.76332905120$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - x^{19} + 15 x^{18} - 14 x^{17} + 149 x^{16} - 131 x^{15} + 825 x^{14} - 595 x^{13} + 3197 x^{12} + \cdots + 1 $ x^20 - x^19 + 15x^18 - 14x^17 + 149x^16 - 131x^15 + 825x^14 - 595x^13 + 3197x^12 - 1997x^11 + 6915x^10 - 2406x^9 + 9021x^8 - 3913x^7 + 4916x^6 - 1317x^5 + 1429x^4 - 426x^3 + 205x^2 - 15x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 77)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			485.1
Root			$1.22380 - 2.11968i$ of defining polynomial
Character	$\chi$	$=$	847.485
Dual form			847.2.e.h.606.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.22380 + 2.11968i) q^{2} +(-1.45751 - 2.52448i) q^{3} +(-1.99536 - 3.45607i) q^{4} +(0.165961 - 0.287453i) q^{5} +7.13479 q^{6} +(2.29605 + 1.31460i) q^{7} +4.87248 q^{8} +(-2.74868 + 4.76085i) q^{9} +O(q^{10})$	\(q+(-1.22380 + 2.11968i) q^{2} +(-1.45751 - 2.52448i) q^{3} +(-1.99536 - 3.45607i) q^{4} +(0.165961 - 0.287453i) q^{5} +7.13479 q^{6} +(2.29605 + 1.31460i) q^{7} +4.87248 q^{8} +(-2.74868 + 4.76085i) q^{9} +(0.406206 + 0.703570i) q^{10} +(-5.81652 + 10.0745i) q^{12} -1.74501 q^{13} +(-5.59643 + 3.25808i) q^{14} -0.967562 q^{15} +(-1.97221 + 3.41597i) q^{16} +(-0.580126 - 1.00481i) q^{17} +(-6.72765 - 11.6526i) q^{18} +(-3.17726 + 5.50317i) q^{19} -1.32461 q^{20} +(-0.0278291 - 7.71237i) q^{21} +(1.13826 - 1.97152i) q^{23} +(-7.10170 - 12.3005i) q^{24} +(2.44491 + 4.23471i) q^{25} +(2.13554 - 3.69886i) q^{26} +7.27984 q^{27} +(-0.0380986 - 10.5584i) q^{28} +4.23486 q^{29} +(1.18410 - 2.05092i) q^{30} +(-2.50494 - 4.33869i) q^{31} +(0.0453088 + 0.0784772i) q^{32} +2.83983 q^{34} +(0.758941 - 0.441834i) q^{35} +21.9384 q^{36} +(-1.16475 + 2.01741i) q^{37} +(-7.77664 - 13.4695i) q^{38} +(2.54337 + 4.40525i) q^{39} +(0.808644 - 1.40061i) q^{40} +4.00603 q^{41} +(16.3818 + 9.37940i) q^{42} +3.39882 q^{43} +(0.912348 + 1.58023i) q^{45} +(2.78599 + 4.82548i) q^{46} +(2.28169 - 3.95200i) q^{47} +11.4981 q^{48} +(3.54366 + 6.03676i) q^{49} -11.9683 q^{50} +(-1.69108 + 2.92904i) q^{51} +(3.48193 + 6.03087i) q^{52} +(2.47088 + 4.27969i) q^{53} +(-8.90906 + 15.4309i) q^{54} +(11.1874 + 6.40536i) q^{56} +18.5236 q^{57} +(-5.18261 + 8.97655i) q^{58} +(0.507637 + 0.879253i) q^{59} +(1.93064 + 3.34396i) q^{60} +(-2.76430 + 4.78790i) q^{61} +12.2622 q^{62} +(-12.5697 + 7.31772i) q^{63} -8.11064 q^{64} +(-0.289604 + 0.501609i) q^{65} +(5.34243 + 9.25335i) q^{67} +(-2.31512 + 4.00991i) q^{68} -6.63609 q^{69} +(0.00775593 + 2.14943i) q^{70} +5.76054 q^{71} +(-13.3929 + 23.1972i) q^{72} +(2.66384 + 4.61390i) q^{73} +(-2.85085 - 4.93781i) q^{74} +(7.12698 - 12.3443i) q^{75} +25.3591 q^{76} -12.4503 q^{78} +(1.95713 - 3.38985i) q^{79} +(0.654621 + 1.13384i) q^{80} +(-2.36442 - 4.09530i) q^{81} +(-4.90257 + 8.49151i) q^{82} +12.4007 q^{83} +(-26.5990 + 15.4852i) q^{84} -0.385114 q^{85} +(-4.15947 + 7.20441i) q^{86} +(-6.17236 - 10.6908i) q^{87} +(9.37654 - 16.2406i) q^{89} -4.46612 q^{90} +(-4.00662 - 2.29399i) q^{91} -9.08494 q^{92} +(-7.30197 + 12.6474i) q^{93} +(5.58465 + 9.67290i) q^{94} +(1.05460 + 1.82663i) q^{95} +(0.132076 - 0.228763i) q^{96} +8.38594 q^{97} +(-17.1327 + 0.123644i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - q^{2} + 3 q^{3} - 9 q^{4} + 2 q^{5} + 18 q^{6} + 11 q^{7} - 6 q^{8} - 9 q^{9}+O(q^{10}) $ 20 * q - q^2 + 3 * q^3 - 9 * q^4 + 2 * q^5 + 18 * q^6 + 11 * q^7 - 6 * q^8 - 9 * q^9	\( 20 q - q^{2} + 3 q^{3} - 9 q^{4} + 2 q^{5} + 18 q^{6} + 11 q^{7} - 6 q^{8} - 9 q^{9} - 7 q^{10} - 9 q^{12} + 2 q^{13} - 19 q^{14} - 2 q^{15} - 15 q^{16} - 19 q^{17} - 17 q^{18} - 28 q^{19} - 10 q^{20} + q^{21} - 7 q^{23} - 19 q^{24} + 8 q^{25} + 5 q^{26} + 12 q^{27} - 8 q^{28} - 30 q^{29} + 22 q^{30} + 14 q^{31} + 15 q^{32} + 24 q^{34} - 8 q^{35} + 32 q^{36} - 13 q^{37} - 24 q^{38} - 4 q^{39} - 10 q^{40} + 70 q^{41} + 25 q^{42} + 36 q^{43} - 8 q^{45} - 9 q^{46} - 16 q^{47} - 66 q^{48} - 25 q^{49} + 12 q^{50} + 21 q^{51} + 4 q^{52} + 9 q^{53} - 17 q^{54} + 12 q^{56} + 8 q^{57} + 9 q^{58} - 12 q^{59} + 21 q^{60} - 20 q^{61} + 76 q^{62} - 12 q^{63} - 58 q^{64} + 20 q^{65} - 19 q^{67} - 56 q^{68} + 18 q^{69} + 21 q^{70} + 30 q^{71} + 4 q^{72} - 3 q^{73} - 42 q^{74} + 27 q^{75} + 48 q^{76} - 50 q^{78} + 32 q^{79} + 6 q^{80} + 46 q^{81} + 18 q^{82} + 58 q^{83} - 73 q^{84} - 46 q^{85} - 9 q^{86} - 24 q^{87} - 5 q^{89} + 24 q^{90} + 28 q^{91} + 30 q^{92} + q^{93} + 19 q^{94} - q^{95} - 46 q^{96} + 8 q^{97} - 58 q^{98}+O(q^{100}) \) 20 * q - q^2 + 3 * q^3 - 9 * q^4 + 2 * q^5 + 18 * q^6 + 11 * q^7 - 6 * q^8 - 9 * q^9 - 7 * q^10 - 9 * q^12 + 2 * q^13 - 19 * q^14 - 2 * q^15 - 15 * q^16 - 19 * q^17 - 17 * q^18 - 28 * q^19 - 10 * q^20 + q^21 - 7 * q^23 - 19 * q^24 + 8 * q^25 + 5 * q^26 + 12 * q^27 - 8 * q^28 - 30 * q^29 + 22 * q^30 + 14 * q^31 + 15 * q^32 + 24 * q^34 - 8 * q^35 + 32 * q^36 - 13 * q^37 - 24 * q^38 - 4 * q^39 - 10 * q^40 + 70 * q^41 + 25 * q^42 + 36 * q^43 - 8 * q^45 - 9 * q^46 - 16 * q^47 - 66 * q^48 - 25 * q^49 + 12 * q^50 + 21 * q^51 + 4 * q^52 + 9 * q^53 - 17 * q^54 + 12 * q^56 + 8 * q^57 + 9 * q^58 - 12 * q^59 + 21 * q^60 - 20 * q^61 + 76 * q^62 - 12 * q^63 - 58 * q^64 + 20 * q^65 - 19 * q^67 - 56 * q^68 + 18 * q^69 + 21 * q^70 + 30 * q^71 + 4 * q^72 - 3 * q^73 - 42 * q^74 + 27 * q^75 + 48 * q^76 - 50 * q^78 + 32 * q^79 + 6 * q^80 + 46 * q^81 + 18 * q^82 + 58 * q^83 - 73 * q^84 - 46 * q^85 - 9 * q^86 - 24 * q^87 - 5 * q^89 + 24 * q^90 + 28 * q^91 + 30 * q^92 + q^93 + 19 * q^94 - q^95 - 46 * q^96 + 8 * q^97 - 58 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/847\mathbb{Z}\right)^\times$.

$n$	$122$	$365$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−1.22380	+	2.11968i	−0.865356	+	1.49884i	0.00133803	+	0.999999i	$0.499574\pi$
$2$	−1.22380	+	2.11968i	−0.865356	+	1.49884i	−0.866694	+	0.498841i	$0.833759\pi$
$3$	−1.45751	−	2.52448i	−0.841494	−	1.45751i	−0.888631	−	0.458623i	$-0.848343\pi$
$3$	−1.45751	−	2.52448i	−0.841494	−	1.45751i	0.0471367	−	0.998888i	$-0.484990\pi$
$4$	−1.99536	−	3.45607i	−0.997681	−	1.72803i
$5$	0.165961	−	0.287453i	0.0742202	−	0.128553i	−0.826527	−	0.562897i	$-0.809687\pi$
$5$	0.165961	−	0.287453i	0.0742202	−	0.128553i	0.900747	+	0.434344i	$0.143020\pi$
$6$	7.13479			2.91277
$7$	2.29605	+	1.31460i	0.867824	+	0.496872i
$7$	2.29605	+	1.31460i	0.867824	+	0.496872i
$8$	4.87248			1.72268
$9$	−2.74868	+	4.76085i	−0.916226	+	1.58695i
$10$	0.406206	+	0.703570i	0.128454	+	0.222488i
$11$		0			0
$11$		0			0
$12$	−5.81652	+	10.0745i	−1.67909	+	2.90826i
$13$	−1.74501			−0.483979			−0.241989	−	0.970279i	$-0.577800\pi$
$13$	−1.74501			−0.483979			−0.241989	+	0.970279i	$0.577800\pi$
$14$	−5.59643	+	3.25808i	−1.49571	+	0.870758i
$15$	−0.967562			−0.249823
$16$	−1.97221	+	3.41597i	−0.493053	+	0.853992i
$17$	−0.580126	−	1.00481i	−0.140701	−	0.243702i	0.787060	−	0.616877i	$-0.211602\pi$
$17$	−0.580126	−	1.00481i	−0.140701	−	0.243702i	−0.927761	+	0.373175i	$0.878269\pi$
$18$	−6.72765	−	11.6526i	−1.58572	−	2.74655i
$19$	−3.17726	+	5.50317i	−0.728913	+	1.26251i	0.228430	+	0.973560i	$0.426641\pi$
$19$	−3.17726	+	5.50317i	−0.728913	+	1.26251i	−0.957343	+	0.288954i	$0.906693\pi$
$20$	−1.32461			−0.296192
$21$	−0.0278291	−	7.71237i	−0.00607281	−	1.68298i
$22$		0			0
$23$	1.13826	−	1.97152i	0.237343	−	0.411090i	−0.722608	−	0.691258i	$-0.757057\pi$
$23$	1.13826	−	1.97152i	0.237343	−	0.411090i	0.959951	+	0.280168i	$0.0903901\pi$
$24$	−7.10170	−	12.3005i	−1.44963	−	2.51083i
$25$	2.44491	+	4.23471i	0.488983	+	0.846943i
$26$	2.13554	−	3.69886i	0.418814	−	0.725407i
$27$	7.27984			1.40101
$28$	−0.0380986	−	10.5584i	−0.00719996	−	1.99535i
$29$	4.23486			0.786394			0.393197	−	0.919454i	$-0.371369\pi$
$29$	4.23486			0.786394			0.393197	+	0.919454i	$0.371369\pi$
$30$	1.18410	−	2.05092i	0.216186	−	0.374445i
$31$	−2.50494	−	4.33869i	−0.449901	−	0.779252i	0.548478	−	0.836165i	$-0.315208\pi$
$31$	−2.50494	−	4.33869i	−0.449901	−	0.779252i	−0.998379	+	0.0569132i	$0.981874\pi$
$32$	0.0453088	+	0.0784772i	0.00800955	+	0.0138729i
$33$		0			0
$34$	2.83983			0.487026
$35$	0.758941	−	0.441834i	0.128284	−	0.0746835i
$36$	21.9384			3.65640
$37$	−1.16475	+	2.01741i	−0.191484	+	0.331661i	−0.945742	−	0.324917i	$-0.894663\pi$
$37$	−1.16475	+	2.01741i	−0.191484	+	0.331661i	0.754258	+	0.656578i	$0.227997\pi$
$38$	−7.77664	−	13.4695i	−1.26154	−	2.18505i
$39$	2.54337	+	4.40525i	0.407265	+	0.705404i
$40$	0.808644	−	1.40061i	0.127858	−	0.221456i
$41$	4.00603			0.625637			0.312819	−	0.949813i	$-0.398727\pi$
$41$	4.00603			0.625637			0.312819	+	0.949813i	$0.398727\pi$
$42$	16.3818	+	9.37940i	2.52777	+	1.44727i
$43$	3.39882			0.518315			0.259158	−	0.965835i	$-0.416555\pi$
$43$	3.39882			0.518315			0.259158	+	0.965835i	$0.416555\pi$
$44$		0			0
$45$	0.912348	+	1.58023i	0.136005	+	0.235567i
$46$	2.78599	+	4.82548i	0.410772	+	0.711478i
$47$	2.28169	−	3.95200i	0.332819	−	0.576459i	−0.650245	−	0.759725i	$-0.725334\pi$
$47$	2.28169	−	3.95200i	0.332819	−	0.576459i	0.983063	+	0.183266i	$0.0586670\pi$
$48$	11.4981			1.65960
$49$	3.54366	+	6.03676i	0.506237	+	0.862395i
$50$	−11.9683			−1.69258
$51$	−1.69108	+	2.92904i	−0.236798	+	0.410147i
$52$	3.48193	+	6.03087i	0.482856	+	0.836332i
$53$	2.47088	+	4.27969i	0.339402	+	0.587861i	0.984320	−	0.176390i	$-0.0564421\pi$
$53$	2.47088	+	4.27969i	0.339402	+	0.587861i	−0.644919	+	0.764251i	$0.723109\pi$
$54$	−8.90906	+	15.4309i	−1.21237	+	2.09988i
$55$		0			0
$56$	11.1874	+	6.40536i	1.49499	+	0.855953i
$57$	18.5236			2.45350
$58$	−5.18261	+	8.97655i	−0.680510	+	1.17868i
$59$	0.507637	+	0.879253i	0.0660887	+	0.114469i	0.897176	−	0.441672i	$-0.145615\pi$
$59$	0.507637	+	0.879253i	0.0660887	+	0.114469i	−0.831088	+	0.556141i	$0.812281\pi$
$60$	1.93064	+	3.34396i	0.249244	+	0.431703i
$61$	−2.76430	+	4.78790i	−0.353932	+	0.613028i	−0.986935	−	0.161122i	$-0.948489\pi$
$61$	−2.76430	+	4.78790i	−0.353932	+	0.613028i	0.633003	+	0.774150i	$0.281822\pi$
$62$	12.2622			1.55730
$63$	−12.5697	+	7.31772i	−1.58363	+	0.921946i
$64$	−8.11064			−1.01383
$65$	−0.289604	+	0.501609i	−0.0359210	+	0.0622170i
$66$		0			0
$67$	5.34243	+	9.25335i	0.652681	+	1.13048i	0.982470	+	0.186422i	$0.0596892\pi$
$67$	5.34243	+	9.25335i	0.652681	+	1.13048i	−0.329789	+	0.944055i	$0.606977\pi$
$68$	−2.31512	+	4.00991i	−0.280750	+	0.486273i
$69$	−6.63609			−0.798891
$70$	0.00775593	+	2.14943i	0.000927011	+	0.256906i
$71$	5.76054			0.683650			0.341825	−	0.939764i	$-0.388955\pi$
$71$	5.76054			0.683650			0.341825	+	0.939764i	$0.388955\pi$
$72$	−13.3929	+	23.1972i	−1.57837	+	2.73381i
$73$	2.66384	+	4.61390i	0.311779	+	0.540017i	0.978748	−	0.205069i	$-0.0657419\pi$
$73$	2.66384	+	4.61390i	0.311779	+	0.540017i	−0.666969	+	0.745086i	$0.732409\pi$
$74$	−2.85085	−	4.93781i	−0.331404	−	0.574009i
$75$	7.12698	−	12.3443i	0.822952	−	1.42540i
$76$	25.3591			2.90889
$77$		0			0
$78$	−12.4503			−1.40972
$79$	1.95713	−	3.38985i	0.220194	−	0.381388i	−0.734673	−	0.678422i	$-0.762664\pi$
$79$	1.95713	−	3.38985i	0.220194	−	0.381388i	0.954867	+	0.297034i	$0.0959975\pi$
$80$	0.654621	+	1.13384i	0.0731889	+	0.126767i
$81$	−2.36442	−	4.09530i	−0.262713	−	0.455033i
$82$	−4.90257	+	8.49151i	−0.541399	+	0.937730i
$83$	12.4007			1.36116			0.680578	−	0.732676i	$-0.261729\pi$
$83$	12.4007			1.36116			0.680578	+	0.732676i	$0.261729\pi$
$84$	−26.5990	+	15.4852i	−2.90218	+	1.68957i
$85$	−0.385114			−0.0417714
$86$	−4.15947	+	7.20441i	−0.448527	+	0.776872i
$87$	−6.17236	−	10.6908i	−0.661746	−	1.14618i
$88$		0			0
$89$	9.37654	−	16.2406i	0.993911	−	1.72150i	0.401534	−	0.915844i	$-0.368477\pi$
$89$	9.37654	−	16.2406i	0.993911	−	1.72150i	0.592377	−	0.805661i	$-0.298190\pi$
$90$	−4.46612			−0.470770
$91$	−4.00662	−	2.29399i	−0.420008	−	0.240475i
$92$	−9.08494			−0.947170
$93$	−7.30197	+	12.6474i	−0.757179	+	1.31147i
$94$	5.58465	+	9.67290i	0.576013	+	0.997684i
$95$	1.05460	+	1.82663i	0.108200	+	0.187408i
$96$	0.132076	−	0.228763i	0.0134800	−	0.0233480i
$97$	8.38594			0.851463			0.425732	−	0.904849i	$-0.360017\pi$
$97$	8.38594			0.851463			0.425732	+	0.904849i	$0.360017\pi$
$98$	−17.1327	+	0.123644i	−1.73067	+	0.0124899i
$99$		0			0
$100$	9.75697	−	16.8996i	0.975697	−	1.68996i
$101$	−1.42622	−	2.47029i	−0.141914	−	0.245803i	0.786303	−	0.617841i	$-0.211992\pi$
$101$	−1.42622	−	2.47029i	−0.141914	−	0.245803i	−0.928217	+	0.372038i	$0.878659\pi$
$102$	−4.13908	−	7.16909i	−0.409830	−	0.709846i
$103$	1.47852	−	2.56087i	0.145683	−	0.252330i	−0.783945	−	0.620831i	$-0.786795\pi$
$103$	1.47852	−	2.56087i	0.145683	−	0.252330i	0.929627	+	0.368501i	$0.120129\pi$
$104$	−8.50253			−0.833742
$105$	−2.22157	−	1.27196i	−0.216803	−	0.124130i
$106$	−12.0954			−1.17481
$107$	7.03678	−	12.1881i	0.680271	−	1.17826i	−0.294627	−	0.955612i	$-0.595195\pi$
$107$	7.03678	−	12.1881i	0.680271	−	1.17826i	0.974898	−	0.222652i	$-0.0714712\pi$
$108$	−14.5259	−	25.1596i	−1.39776	−	2.42099i
$109$	5.02348	+	8.70092i	0.481162	+	0.833397i	0.999766	−	0.0216175i	$-0.00688162\pi$
$109$	5.02348	+	8.70092i	0.481162	+	0.833397i	−0.518605	+	0.855014i	$0.673548\pi$
$110$		0			0
$111$	6.79057			0.644532
$112$	−9.01892	+	5.25056i	−0.852208	+	0.496131i
$113$	−6.32321			−0.594837			−0.297419	−	0.954747i	$-0.596126\pi$
$113$	−6.32321			−0.594837			−0.297419	+	0.954747i	$0.596126\pi$
$114$	−22.6691	+	39.2640i	−2.12315	+	3.67741i
$115$	−0.377813	−	0.654392i	−0.0352313	−	0.0610224i
$116$	−8.45008	−	14.6360i	−0.784570	−	1.35891i
$117$	4.79647	−	8.30773i	0.443434	−	0.768050i
$118$	−2.48498			−0.228761
$119$	−0.0110767	−	3.06972i	−0.00101540	−	0.281400i
$120$	−4.71443			−0.430367
$121$		0			0
$122$	−6.76588	−	11.7188i	−0.612554	−	1.06097i
$123$	−5.83884	−	10.1132i	−0.526470	−	0.911873i
$124$	−9.99654	+	17.3145i	−0.897716	+	1.55489i
$125$	3.28266			0.293610
$126$	−0.128455	−	35.5991i	−0.0114437	−	3.17142i
$127$	11.7186			1.03986			0.519929	−	0.854210i	$-0.325958\pi$
$127$	11.7186			1.03986			0.519929	+	0.854210i	$0.325958\pi$
$128$	9.83516	−	17.0350i	0.869314	−	1.50570i
$129$	−4.95382	−	8.58027i	−0.436160	−	0.755451i
$130$	−0.708834	−	1.22774i	−0.0621688	−	0.107680i
$131$	−0.485168	+	0.840336i	−0.0423894	+	0.0734205i	−0.886442	−	0.462840i	$-0.846830\pi$
$131$	−0.485168	+	0.840336i	−0.0423894	+	0.0734205i	0.844052	+	0.536261i	$0.180164\pi$
$132$		0			0
$133$	−14.5296	+	8.45872i	−1.25988	+	0.733464i
$134$	−26.1522			−2.25921
$135$	1.20817	−	2.09262i	0.103983	−	0.180104i
$136$	−2.82665	−	4.89591i	−0.242383	−	0.419821i
$137$	2.84726	+	4.93160i	0.243258	+	0.421335i	0.961640	−	0.274313i	$-0.0884505\pi$
$137$	2.84726	+	4.93160i	0.243258	+	0.421335i	−0.718382	+	0.695649i	$0.755117\pi$
$138$	8.12123	−	14.0664i	0.691325	−	1.19741i
$139$	−12.8825			−1.09268			−0.546341	−	0.837563i	$-0.683980\pi$
$139$	−12.8825			−1.09268			−0.546341	+	0.837563i	$0.683980\pi$
$140$	−3.04137	−	1.74133i	−0.257043	−	0.147169i
$141$	−13.3023			−1.12026
$142$	−7.04973	+	12.2105i	−0.591601	+	1.02468i
$143$		0			0
$144$	−10.8419	−	18.7788i	−0.903495	−	1.56490i
$145$	0.702823	−	1.21733i	0.0583663	−	0.101093i
$146$	−13.0400			−1.07920
$147$	10.0748	−	17.7446i	0.830954	−	1.46355i
$148$	9.29643			0.764161
$149$	−7.81192	+	13.5306i	−0.639977	+	1.10847i	0.345460	+	0.938433i	$0.387723\pi$
$149$	−7.81192	+	13.5306i	−0.639977	+	1.10847i	−0.985437	+	0.170040i	$0.945610\pi$
$150$	17.4440	+	30.2138i	1.42429	+	2.46695i
$151$	10.6373	+	18.4244i	0.865652	+	1.49935i	0.866398	+	0.499354i	$0.166429\pi$
$151$	10.6373	+	18.4244i	0.865652	+	1.49935i	−0.000745594		1.00000i	$0.500237\pi$
$152$	−15.4811	+	26.8141i	−1.25569	+	2.17491i
$153$	6.37831			0.515656
$154$		0			0
$155$	−1.66290			−0.133567
$156$	10.1499	−	17.5801i	0.812642	−	1.40754i
$157$	3.14883	+	5.45393i	0.251304	+	0.435271i	0.963885	−	0.266318i	$-0.0858073\pi$
$157$	3.14883	+	5.45393i	0.251304	+	0.435271i	−0.712581	+	0.701590i	$0.752474\pi$
$158$	4.79026	+	8.29698i	0.381093	+	0.660072i
$159$	7.20268	−	12.4754i	0.571209	−	0.989364i
$160$	0.0300781			0.00237788
$161$	5.20525	−	3.03035i	0.410231	−	0.238825i
$162$	11.5743			0.909362
$163$	4.03251	−	6.98451i	0.315850	−	0.547069i	−0.663768	−	0.747939i	$-0.731044\pi$
$163$	4.03251	−	6.98451i	0.315850	−	0.547069i	0.979618	+	0.200870i	$0.0643769\pi$
$164$	−7.99348	−	13.8451i	−0.624186	−	1.08112i
$165$		0			0
$166$	−15.1760	+	26.2856i	−1.17788	+	2.04015i
$167$	11.1242			0.860818			0.430409	−	0.902634i	$-0.358369\pi$
$167$	11.1242			0.860818			0.430409	+	0.902634i	$0.358369\pi$
$168$	−0.135597	−	37.5784i	−0.0104615	−	2.89924i
$169$	−9.95494			−0.765765
$170$	0.471301	−	0.816318i	0.0361472	−	0.0626087i
$171$	−17.4665	−	30.2529i	−1.33570	−	2.31350i
$172$	−6.78188	−	11.7466i	−0.517113	−	0.895667i
$173$	−0.0805336	+	0.139488i	−0.00612286	+	0.0106051i	−0.869071	−	0.494688i	$-0.835282\pi$
$173$	−0.0805336	+	0.139488i	−0.00612286	+	0.0106051i	0.862948	+	0.505293i	$0.168616\pi$
$174$	30.2149			2.29058
$175$	0.0466822	+	12.9372i	0.00352884	+	0.977959i
$176$		0			0
$177$	1.47977	−	2.56304i	0.111227	−	0.192650i
$178$	22.9500	+	39.7505i	1.72017	+	2.97943i
$179$	3.34113	+	5.78701i	0.249728	+	0.432542i	0.963450	−	0.267887i	$-0.0863255\pi$
$179$	3.34113	+	5.78701i	0.249728	+	0.432542i	−0.713722	+	0.700429i	$0.752992\pi$
$180$	3.64093	−	6.30627i	0.271379	−	0.470042i
$181$	−17.9801			−1.33645			−0.668224	−	0.743960i	$-0.732945\pi$
$181$	−17.9801			−1.33645			−0.668224	+	0.743960i	$0.732945\pi$
$182$	9.76582	−	5.68538i	0.723891	−	0.421429i
$183$	16.1160			1.19133
$184$	5.54614	−	9.60620i	0.408867	−	0.708178i
$185$	0.386608	+	0.669625i	0.0284240	+	0.0492318i
$186$	−17.8723	−	30.9557i	−1.31046	−	2.26978i
$187$		0			0
$188$	−18.2112			−1.32819
$189$	16.7149	+	9.57008i	1.21583	+	0.696121i
$190$	−5.16249			−0.374526
$191$	7.37368	−	12.7716i	0.533541	−	0.924120i	−0.465692	−	0.884947i	$-0.654194\pi$
$191$	7.37368	−	12.7716i	0.533541	−	0.924120i	0.999232	−	0.0391727i	$-0.0124722\pi$
$192$	11.8213	+	20.4752i	0.853132	+	1.47767i
$193$	7.29387	+	12.6334i	0.525025	+	0.909369i	0.999575	+	0.0291411i	$0.00927722\pi$
$193$	7.29387	+	12.6334i	0.525025	+	0.909369i	−0.474551	+	0.880228i	$0.657389\pi$
$194$	−10.2627	+	17.7755i	−0.736819	+	1.27621i
$195$	1.68841			0.120909
$196$	13.7926	−	24.2926i	0.985184	−	1.73519i
$197$	5.99987			0.427473			0.213737	−	0.976891i	$-0.431437\pi$
$197$	5.99987			0.427473			0.213737	+	0.976891i	$0.431437\pi$
$198$		0			0
$199$	−9.97164	−	17.2714i	−0.706871	−	1.22434i	−0.966012	−	0.258497i	$-0.916773\pi$
$199$	−9.97164	−	17.2714i	−0.706871	−	1.22434i	0.259141	−	0.965839i	$-0.416560\pi$
$200$	11.9128	+	20.6336i	0.842362	+	1.45901i
$201$	15.5733	−	26.9737i	1.09846	−	1.90258i
$202$	6.98163			0.491226
$203$	9.72343	+	5.56714i	0.682451	+	0.390737i
$204$	13.4973			0.944997
$205$	0.664847	−	1.15155i	0.0464349	−	0.0804276i
$206$	3.61881	+	6.26797i	0.252135	+	0.436710i
$207$	6.25740	+	10.8381i	0.434920	+	0.753303i
$208$	3.44153	−	5.96090i	0.238627	−	0.413314i
$209$		0			0
$210$	5.41489	−	3.15239i	0.373663	−	0.217536i
$211$	−10.2194			−0.703529			−0.351765	−	0.936089i	$-0.614418\pi$
$211$	−10.2194			−0.703529			−0.351765	+	0.936089i	$0.614418\pi$
$212$	9.86060	−	17.0791i	0.677229	−	1.17300i
$213$	−8.39605	−	14.5424i	−0.575288	−	0.996428i
$214$	17.2232	+	29.8314i	1.17735	+	2.03923i
$215$	0.564073	−	0.977003i	0.0384695	−	0.0666310i
$216$	35.4709			2.41349
$217$	−0.0478284	−	13.2548i	−0.00324680	−	0.899797i
$218$	−24.5909			−1.66550
$219$	7.76515	−	13.4496i	0.524720	−	0.908842i
$220$		0			0
$221$	1.01233	+	1.75340i	0.0680964	+	0.117946i
$222$	−8.31028	+	14.3938i	−0.557750	+	0.966051i
$223$	27.1525			1.81826			0.909132	−	0.416507i	$-0.136746\pi$
$223$	27.1525			1.81826			0.909132	+	0.416507i	$0.136746\pi$
$224$	0.000865108		0.239750i	5.78025e−5		0.0160190i
$225$	−26.8811			−1.79207
$226$	7.73833	−	13.4032i	0.514746	−	0.891566i
$227$	0.515864	+	0.893503i	0.0342391	+	0.0593038i	0.882637	−	0.470055i	$-0.155766\pi$
$227$	0.515864	+	0.893503i	0.0342391	+	0.0593038i	−0.848398	+	0.529359i	$0.822433\pi$
$228$	−36.9612	−	64.0186i	−2.44781	−	4.23974i
$229$	−7.95473	+	13.7780i	−0.525663	+	0.910475i	0.473890	+	0.880584i	$0.342849\pi$
$229$	−7.95473	+	13.7780i	−0.525663	+	0.910475i	−0.999553	+	0.0298912i	$0.990484\pi$
$230$	1.84947			0.121950
$231$		0			0
$232$	20.6343			1.35471
$233$	−9.97486	+	17.2770i	−0.653475	+	1.13185i	0.328799	+	0.944400i	$0.393356\pi$
$233$	−9.97486	+	17.2770i	−0.653475	+	1.13185i	−0.982274	+	0.187452i	$0.939977\pi$
$234$	11.7398	+	20.3340i	0.767456	+	1.32927i
$235$	−0.757344	−	1.31176i	−0.0494037	−	0.0855697i
$236$	2.02584	−	3.50886i	0.131871	−	0.228407i
$237$	−11.4102			−0.741169
$238$	6.52037	+	3.73323i	0.422653	+	0.241990i
$239$	−24.2476			−1.56845			−0.784224	−	0.620478i	$-0.786939\pi$
$239$	−24.2476			−1.56845			−0.784224	+	0.620478i	$0.786939\pi$
$240$	1.90824	−	3.30516i	0.123176	−	0.213347i
$241$	0.563109	+	0.975333i	0.0362730	+	0.0628267i	0.883592	−	0.468258i	$-0.155118\pi$
$241$	0.563109	+	0.975333i	0.0362730	+	0.0628267i	−0.847319	+	0.531084i	$0.821785\pi$
$242$		0			0
$243$	4.02742	−	6.97570i	0.258359	−	0.447492i
$244$	22.0631			1.41244
$245$	2.32340	−	0.0167676i	0.148436	−	0.00107124i
$246$	28.5822			1.82234
$247$	5.54435	−	9.60309i	0.352778	−	0.611030i
$248$	−12.2053	−	21.1402i	−0.775037	−	1.34240i
$249$	−18.0742	−	31.3054i	−1.14541	−	1.98390i
$250$	−4.01731	+	6.95818i	−0.254077	+	0.440074i
$251$	−10.6887			−0.674668			−0.337334	−	0.941385i	$-0.609525\pi$
$251$	−10.6887			−0.674668			−0.337334	+	0.941385i	$0.609525\pi$
$252$	50.3716	+	28.8402i	3.17311	+	1.81676i
$253$		0			0
$254$	−14.3412	+	24.8397i	−0.899847	+	1.55858i
$255$	0.561307	+	0.972213i	0.0351504	+	0.0608823i
$256$	15.9619	+	27.6468i	0.997616	+	1.72792i
$257$	−13.1574	+	22.7893i	−0.820738	+	1.42156i	0.0843951	+	0.996432i	$0.473104\pi$
$257$	−13.1574	+	22.7893i	−0.820738	+	1.42156i	−0.905133	+	0.425128i	$0.860229\pi$
$258$	24.2499			1.50973
$259$	−5.32642	+	3.10089i	−0.330968	+	0.192680i
$260$	2.31146			0.143351
$261$	−11.6403	+	20.1615i	−0.720514	+	1.24797i
$262$	−1.18750	−	2.05680i	−0.0733637	−	0.127070i
$263$	−10.6048	−	18.3680i	−0.653918	−	1.13262i	−0.982164	−	0.188026i	$-0.939791\pi$
$263$	−10.6048	−	18.3680i	−0.653918	−	1.13262i	0.328246	−	0.944592i	$-0.393542\pi$
$264$		0			0
$265$	1.64028			0.100762
$266$	−0.148484	−	41.1498i	−0.00910413	−	2.52306i
$267$	−54.6656			−3.34548
$268$	21.3201	−	36.9276i	1.30233	−	2.25571i
$269$	−11.3190	−	19.6050i	−0.690130	−	1.19534i	−0.971795	−	0.235828i	$-0.924220\pi$
$269$	−11.3190	−	19.6050i	−0.690130	−	1.19534i	0.281664	−	0.959513i	$-0.409114\pi$
$270$	2.95712	+	5.12188i	0.179964	+	0.311708i
$271$	−8.03052	+	13.9093i	−0.487819	+	0.844927i	−0.999902	−	0.0140086i	$-0.995541\pi$
$271$	−8.03052	+	13.9093i	−0.487819	+	0.844927i	0.512083	+	0.858936i	$0.328874\pi$
$272$	4.57652			0.277492
$273$	0.0485621	+	13.4582i	0.00293911	+	0.814526i
$274$	−13.9379			−0.842019
$275$		0			0
$276$	13.2414	+	22.9348i	0.797038	+	1.38051i
$277$	−11.1698	−	19.3466i	−0.671127	−	1.16243i	−0.977585	−	0.210541i	$-0.932477\pi$
$277$	−11.1698	−	19.3466i	−0.671127	−	1.16243i	0.306458	−	0.951884i	$-0.400856\pi$
$278$	15.7656	−	27.3069i	0.945559	−	1.63776i
$279$	27.5411			1.64884
$280$	3.69793	−	2.15283i	0.220993	−	0.128656i
$281$	−0.985176			−0.0587706			−0.0293853	−	0.999568i	$-0.509355\pi$
$281$	−0.985176			−0.0587706			−0.0293853	+	0.999568i	$0.509355\pi$
$282$	16.2794	−	28.1967i	0.969423	−	1.67909i
$283$	9.56155	+	16.5611i	0.568375	+	0.984454i	0.996727	+	0.0808424i	$0.0257610\pi$
$283$	9.56155	+	16.5611i	0.568375	+	0.984454i	−0.428352	+	0.903612i	$0.640906\pi$
$284$	−11.4944	−	19.9088i	−0.682065	−	1.18137i
$285$	3.07419	−	5.32466i	0.182099	−	0.315406i
$286$		0			0
$287$	9.19804	+	5.26633i	0.542943	+	0.310862i
$288$	−0.498157			−0.0293542
$289$	7.82691	−	13.5566i	0.460406	−	0.797447i
$290$	1.72023	+	2.97952i	0.101015	+	0.174963i
$291$	−12.2226	−	21.1702i	−0.716502	−	1.24102i
$292$	10.6306	−	18.4128i	0.622111	−	1.07753i
$293$	−6.88397			−0.402166			−0.201083	−	0.979574i	$-0.564446\pi$
$293$	−6.88397			−0.402166			−0.201083	+	0.979574i	$0.564446\pi$
$294$	25.2833	+	43.0711i	1.47455	+	2.51195i
$295$	0.336992			0.0196205
$296$	−5.67525	+	9.82982i	−0.329867	+	0.571347i
$297$		0			0
$298$	−19.1204	−	33.1175i	−1.10762	−	1.91845i
$299$	−1.98627	+	3.44032i	−0.114869	+	0.198959i
$300$	−56.8836			−3.28418
$301$	7.80385	+	4.46809i	0.449807	+	0.257536i
$302$	−52.0717			−2.99639
$303$	−4.15747	+	7.20095i	−0.238840	+	0.413684i
$304$	−12.5324	−	21.7068i	−0.718785	−	1.24497i
$305$	0.917532	+	1.58921i	0.0525377	+	0.0909980i
$306$	−7.80577	+	13.5200i	−0.446226	+	0.772886i
$307$	10.2466			0.584802			0.292401	−	0.956296i	$-0.405546\pi$
$307$	10.2466			0.584802			0.292401	+	0.956296i	$0.405546\pi$
$308$		0			0
$309$	−8.61982			−0.490365
$310$	2.03505	−	3.52481i	0.115583	−	0.200196i
$311$	16.1033	+	27.8918i	0.913135	+	1.58160i	0.809608	+	0.586970i	$0.199679\pi$
$311$	16.1033	+	27.8918i	0.913135	+	1.58160i	0.103527	+	0.994627i	$0.466987\pi$
$312$	12.3925	+	21.4645i	0.701589	+	1.21519i
$313$	11.7330	−	20.3221i	0.663187	−	1.14867i	−0.316586	−	0.948564i	$-0.602537\pi$
$313$	11.7330	−	20.3221i	0.663187	−	1.14867i	0.979773	−	0.200110i	$-0.0641300\pi$
$314$	−15.4141			−0.869869
$315$	0.0174200	+	4.82766i	0.000981506	+	0.272008i
$316$	−15.6207			−0.878734
$317$	−3.14149	+	5.44122i	−0.176444	+	0.305609i	−0.940660	−	0.339351i	$-0.889793\pi$
$317$	−3.14149	+	5.44122i	−0.176444	+	0.305609i	0.764216	+	0.644960i	$0.223126\pi$
$318$	17.6292	+	30.5347i	0.988598	+	1.71230i
$319$		0			0
$320$	−1.34605	+	2.33143i	−0.0752466	+	0.130331i
$321$	−41.0247			−2.28978
$322$	0.0531946	+	14.7420i	0.00296442	+	0.821539i
$323$	7.37284			0.410236
$324$	−9.43575	+	16.3432i	−0.524208	+	0.907955i
$325$	−4.26640	−	7.38962i	−0.236657	−	0.409902i
$326$	9.86994	+	17.0952i	0.546646	+	0.946818i
$327$	14.6435	−	25.3634i	0.809790	−	1.40260i
$328$	19.5193			1.07777
$329$	10.4342	−	6.07447i	0.575254	−	0.334896i
$330$		0			0
$331$	8.01248	−	13.8780i	0.440405	−	0.762805i	−0.557314	−	0.830302i	$-0.688168\pi$
$331$	8.01248	−	13.8780i	0.440405	−	0.762805i	0.997719	+	0.0674972i	$0.0215014\pi$
$332$	−24.7439	−	42.8577i	−1.35800	−	2.35212i
$333$	−6.40307	−	11.0904i	−0.350886	−	0.607752i
$334$	−13.6138	+	23.5798i	−0.744913	+	1.29023i
$335$	3.54654			0.193768
$336$	26.4001	+	15.1154i	1.44024	+	0.824611i
$337$	−17.8618			−0.972993			−0.486496	−	0.873683i	$-0.661725\pi$
$337$	−17.8618			−0.972993			−0.486496	+	0.873683i	$0.661725\pi$
$338$	12.1828	−	21.1013i	0.662659	−	1.14776i
$339$	9.21615	+	15.9628i	0.500552	+	0.866982i
$340$	0.768441	+	1.33098i	0.0416746	+	0.0721825i
$341$		0			0
$342$	85.5019			4.62341
$343$	0.200479	+	18.5192i	0.0108249	+	0.999941i
$344$	16.5607			0.892893
$345$	−1.10133	+	1.90757i	−0.0592938	+	0.102700i
$346$	−0.197114	−	0.341411i	−0.0105969	−	0.0183544i
$347$	9.23348	+	15.9929i	0.495679	+	0.858541i	0.999988	−	0.00498213i	$-0.00158587\pi$
$347$	9.23348	+	15.9929i	0.495679	+	0.858541i	−0.504308	+	0.863524i	$0.668253\pi$
$348$	−24.6322	+	42.6642i	−1.32042	+	2.28704i
$349$	−18.6829			−1.00007			−0.500037	−	0.866004i	$-0.666680\pi$
$349$	−18.6829			−1.00007			−0.500037	+	0.866004i	$0.666680\pi$
$350$	−27.4798	−	15.7335i	−1.46886	−	0.840993i
$351$	−12.7034			−0.678057
$352$		0			0
$353$	−4.51913	−	7.82736i	−0.240529	−	0.416608i	0.720336	−	0.693625i	$-0.243988\pi$
$353$	−4.51913	−	7.82736i	−0.240529	−	0.416608i	−0.960865	+	0.277017i	$0.910654\pi$
$354$	3.62189	+	6.27329i	0.192501	+	0.333422i
$355$	0.956027	−	1.65589i	0.0507406	−	0.0878853i
$356$	−74.8383			−3.96642
$357$	−7.73330	+	4.50211i	−0.409290	+	0.238277i
$358$	−16.3555			−0.864414
$359$	−6.55028	+	11.3454i	−0.345711	+	0.598788i	−0.985483	−	0.169776i	$-0.945695\pi$
$359$	−6.55028	+	11.3454i	−0.345711	+	0.598788i	0.639772	+	0.768565i	$0.279029\pi$
$360$	4.44540	+	7.69966i	0.234293	+	0.405808i
$361$	−10.6899	−	18.5155i	−0.562628	−	0.974500i
$362$	22.0040	−	38.1120i	1.15650	−	2.00312i
$363$		0			0
$364$	0.0664824	+	18.4245i	0.00348463	+	0.965706i
$365$	1.76838			0.0925611
$366$	−19.7227	+	34.1607i	−1.03092	+	1.78561i
$367$	3.86118	+	6.68776i	0.201552	+	0.349098i	0.949029	−	0.315190i	$-0.102068\pi$
$367$	3.86118	+	6.68776i	0.201552	+	0.349098i	−0.747477	+	0.664288i	$0.768735\pi$
$368$	4.48977	+	7.77650i	0.234045	+	0.405378i
$369$	−11.0113	+	19.0721i	−0.573225	+	0.992855i
$370$	−1.89252			−0.0983875
$371$	0.0471780	+	13.0746i	0.00244936	+	0.678799i
$372$	58.2803			3.02169
$373$	−11.4140	+	19.7696i	−0.590995	+	1.02363i	0.403104	+	0.915154i	$0.367931\pi$
$373$	−11.4140	+	19.7696i	−0.590995	+	1.02363i	−0.994099	+	0.108479i	$0.965402\pi$
$374$		0			0
$375$	−4.78451	−	8.28701i	−0.247071	−	0.427940i
$376$	11.1175	−	19.2561i	0.573341	−	0.993056i
$377$	−7.38987			−0.380598
$378$	−40.7411	+	23.7183i	−2.09550	+	1.21994i
$379$	25.7158			1.32093			0.660466	−	0.750856i	$-0.270359\pi$
$379$	25.7158			1.32093			0.660466	+	0.750856i	$0.270359\pi$
$380$	4.20863	−	7.28956i	0.215898	−	0.373947i
$381$	−17.0800	−	29.5834i	−0.875034	−	1.51560i
$382$	18.0478	+	31.2597i	0.923405	+	1.59938i
$383$	15.8001	−	27.3666i	0.807348	−	1.39837i	−0.107347	−	0.994222i	$-0.534236\pi$
$383$	15.8001	−	27.3666i	0.807348	−	1.39837i	0.914695	−	0.404146i	$-0.132431\pi$
$384$	−57.3394			−2.92609
$385$		0			0
$386$	−35.7049			−1.81733
$387$	−9.34226	+	16.1813i	−0.474894	+	0.822540i
$388$	−16.7330	−	28.9824i	−0.849489	−	1.47136i
$389$	−3.52923	−	6.11280i	−0.178939	−	0.309931i	0.762578	−	0.646896i	$-0.223933\pi$
$389$	−3.52923	−	6.11280i	−0.178939	−	0.309931i	−0.941517	+	0.336964i	$0.890600\pi$
$390$	−2.06627	+	3.57888i	−0.104629	+	0.181224i
$391$	−2.64133			−0.133578
$392$	17.2664	+	29.4140i	0.872086	+	1.48563i
$393$	2.82855			0.142682
$394$	−7.34263	+	12.7178i	−0.369916	+	0.640714i
$395$	−0.649616	−	1.12517i	−0.0326857	−	0.0566133i
$396$		0			0
$397$	−8.20738	+	14.2156i	−0.411917	+	0.713461i	−0.995099	−	0.0988805i	$-0.968474\pi$
$397$	−8.20738	+	14.2156i	−0.411917	+	0.713461i	0.583183	+	0.812341i	$0.301807\pi$
$398$	48.8131			2.44678
$399$	42.5309	+	24.3510i	2.12921	+	1.21908i
$400$	−19.2875			−0.964377
$401$	−17.5104	+	30.3290i	−0.874430	+	1.51456i	−0.0170613	+	0.999854i	$0.505431\pi$
$401$	−17.5104	+	30.3290i	−0.874430	+	1.51456i	−0.857369	+	0.514703i	$0.827902\pi$
$402$	38.1171	+	66.0208i	1.90111	+	3.29282i
$403$	4.37115	+	7.57106i	0.217743	+	0.377141i
$404$	−5.69166	+	9.85824i	−0.283170	+	0.490466i
$405$	−1.56961			−0.0779945
$406$	−23.7001	+	13.7975i	−1.17622	+	0.684759i
$407$		0			0
$408$	−8.23976	+	14.2717i	−0.407929	+	0.706553i
$409$	5.51322	+	9.54918i	0.272611	+	0.472176i	0.969530	−	0.244974i	$-0.0787794\pi$
$409$	5.51322	+	9.54918i	0.272611	+	0.472176i	−0.696919	+	0.717150i	$0.745446\pi$
$410$	1.62728	+	2.81852i	0.0803654	+	0.139197i
$411$	8.29984	−	14.3757i	0.409401	−	0.709103i
$412$	−11.8007			−0.581379
$413$	0.00969261	+	2.68614i	0.000476942	+	0.132177i
$414$	−30.6312			−1.50544
$415$	2.05804	−	3.56463i	0.101025	−	0.174981i
$416$	−0.0790644	−	0.136944i	−0.00387645	−	0.00671421i
$417$	18.7764	+	32.5218i	0.919487	+	1.59260i
$418$		0			0
$419$	3.17464			0.155091			0.0775457	−	0.996989i	$-0.475292\pi$
$419$	3.17464			0.155091			0.0775457	+	0.996989i	$0.475292\pi$
$420$	0.0368627	+	10.2159i	0.00179872	+	0.498485i
$421$	9.58948			0.467363			0.233681	−	0.972313i	$-0.424923\pi$
$421$	9.58948			0.467363			0.233681	+	0.972313i	$0.424923\pi$
$422$	12.5064	−	21.6618i	0.608803	−	1.05448i
$423$	12.5433	+	21.7256i	0.609874	+	1.05633i
$424$	12.0393	+	20.8527i	0.584682	+	1.01270i
$425$	2.83671	−	4.91333i	0.137601	−	0.238332i
$426$	41.1003			1.99131
$427$	−12.6411	+	7.35930i	−0.611747	+	0.356141i
$428$	−56.1637			−2.71477
$429$		0			0
$430$	1.38062	+	2.39131i	0.0665795	+	0.115319i
$431$	−3.71934	−	6.44209i	−0.179154	−	0.310305i	0.762437	−	0.647063i	$-0.224003\pi$
$431$	−3.71934	−	6.44209i	−0.179154	−	0.310305i	−0.941591	+	0.336758i	$0.890670\pi$
$432$	−14.3574	+	24.8677i	−0.690770	+	1.19645i
$433$	13.2615			0.637308			0.318654	−	0.947871i	$-0.396769\pi$
$433$	13.2615			0.637308			0.318654	+	0.947871i	$0.396769\pi$
$434$	28.1545	+	16.1199i	1.35146	+	0.773778i
$435$	−4.09749			−0.196460
$436$	20.0473	−	34.7229i	0.960092	−	1.66293i
$437$	7.23307	+	12.5280i	0.346005	+	0.599298i
$438$	19.0059	+	32.9193i	0.908139	+	1.57294i
$439$	−14.4061	+	24.9520i	−0.687563	+	1.19089i	0.285060	+	0.958510i	$0.407986\pi$
$439$	−14.4061	+	24.9520i	−0.687563	+	1.19089i	−0.972624	+	0.232385i	$0.925347\pi$
$440$		0			0
$441$	−38.4805	+	0.277707i	−1.83240	+	0.0132242i
$442$	−4.95553			−0.235710
$443$	−7.66270	+	13.2722i	−0.364066	+	0.630581i	−0.988626	−	0.150396i	$-0.951945\pi$
$443$	−7.66270	+	13.2722i	−0.364066	+	0.630581i	0.624560	+	0.780977i	$0.285278\pi$
$444$	−13.5496	−	23.4687i	−0.643038	−	1.11377i
$445$	−3.11229	−	5.39064i	−0.147537	−	0.255541i
$446$	−33.2291	+	57.5546i	−1.57345	+	2.72529i
$447$	45.5438			2.15415
$448$	−18.6224	−	10.6622i	−0.879826	−	0.503744i
$449$	20.6134			0.972808			0.486404	−	0.873734i	$-0.338308\pi$
$449$	20.6134			0.972808			0.486404	+	0.873734i	$0.338308\pi$
$450$	32.8970	−	56.9794i	1.55078	−	2.68603i
$451$		0			0
$452$	12.6171	+	21.8534i	0.593458	+	1.02790i
$453$	31.0080	−	53.7074i	1.45688	−	2.52340i
$454$	−2.52525			−0.118516
$455$	−1.32436	+	0.771004i	−0.0620869	+	0.0361452i
$456$	90.2557			4.22661
$457$	5.13196	−	8.88882i	0.240063	−	0.415801i	−0.720669	−	0.693279i	$-0.756165\pi$
$457$	5.13196	−	8.88882i	0.240063	−	0.415801i	0.960732	+	0.277478i	$0.0894986\pi$
$458$	−19.4700	−	33.7229i	−0.909771	−	1.57577i
$459$	−4.22322	−	7.31484i	−0.197123	−	0.341427i
$460$	−1.50775	+	2.61150i	−0.0702991	+	0.121762i
$461$	−3.11108			−0.144898			−0.0724488	−	0.997372i	$-0.523081\pi$
$461$	−3.11108			−0.144898			−0.0724488	+	0.997372i	$0.523081\pi$
$462$		0			0
$463$	26.0494			1.21062			0.605310	−	0.795990i	$-0.293049\pi$
$463$	26.0494			1.21062			0.605310	+	0.795990i	$0.293049\pi$
$464$	−8.35204	+	14.4662i	−0.387734	+	0.671574i
$465$	2.42369	+	4.19795i	0.112396	+	0.194675i
$466$	−24.4144	−	42.2870i	−1.13098	−	1.95891i
$467$	−14.4818	+	25.0832i	−0.670137	+	1.16071i	0.307728	+	0.951474i	$0.400431\pi$
$467$	−14.4818	+	25.0832i	−0.670137	+	1.16071i	−0.977865	+	0.209237i	$0.932902\pi$
$468$	−38.2828			−1.76962
$469$	0.102006	+	28.2693i	0.00471020	+	1.30535i
$470$	3.70734			0.171007
$471$	9.17891	−	15.8983i	0.422942	−	0.732557i
$472$	2.47345	+	4.28415i	0.113850	+	0.197194i
$473$		0			0
$474$	13.9637	−	24.1859i	0.641375	−	1.11089i
$475$	−31.0725			−1.42570
$476$	−10.5870	+	6.16348i	−0.485256	+	0.282502i
$477$	−27.1666			−1.24387
$478$	29.6742	−	51.3972i	1.35726	−	2.35085i
$479$	−15.7883	−	27.3461i	−0.721384	−	1.24947i	−0.960445	−	0.278469i	$-0.910173\pi$
$479$	−15.7883	−	27.3461i	−0.721384	−	1.24947i	0.239061	−	0.971005i	$-0.423160\pi$
$480$	−0.0438391	−	0.0759315i	−0.00200097	−	0.00346579i
$481$	2.03251	−	3.52041i	0.0926744	−	0.160517i
$482$	−2.75652			−0.125556
$483$	−15.2368	−	8.72380i	−0.693297	−	0.396947i
$484$		0			0
$485$	1.39174	−	2.41057i	0.0631957	−	0.109458i
$486$	9.85751	+	17.0737i	0.447146	+	0.774479i
$487$	−14.9993	−	25.9796i	−0.679683	−	1.17725i	−0.975076	−	0.221870i	$-0.928784\pi$
$487$	−14.9993	−	25.9796i	−0.679683	−	1.17725i	0.295393	−	0.955376i	$-0.404549\pi$
$488$	−13.4690	+	23.3290i	−0.609712	+	1.05605i
$489$	−23.5097			−1.06314
$490$	−2.80783	+	4.94538i	−0.126845	+	0.223409i
$491$	−15.5809			−0.703156			−0.351578	−	0.936159i	$-0.614355\pi$
$491$	−15.5809			−0.703156			−0.351578	+	0.936159i	$0.614355\pi$
$492$	−23.3012	+	40.3588i	−1.05050	+	1.81952i
$493$	−2.45675	−	4.25522i	−0.110647	−	0.191645i
$494$	13.5703	+	23.5045i	0.610557	+	1.05752i
$495$		0			0
$496$	19.7611			0.887300
$497$	13.2265	+	7.57280i	0.593288	+	0.339687i
$498$	88.4766			3.96473
$499$	−2.62232	+	4.54199i	−0.117391	+	0.203327i	−0.918733	−	0.394879i	$-0.870786\pi$
$499$	−2.62232	+	4.54199i	−0.117391	+	0.203327i	0.801342	+	0.598207i	$0.204120\pi$
$500$	−6.55009	−	11.3451i	−0.292929	−	0.507368i
$501$	−16.2137	−	28.0829i	−0.724373	−	1.25465i
$502$	13.0809	−	22.6567i	0.583827	−	1.01122i
$503$	39.7996			1.77458			0.887289	−	0.461214i	$-0.152586\pi$
$503$	39.7996			1.77458			0.887289	+	0.461214i	$0.152586\pi$
$504$	−61.2456	+	35.6555i	−2.72810	+	1.58822i
$505$	−0.946791			−0.0421316
$506$		0			0
$507$	14.5094	+	25.1311i	0.644387	+	1.11611i
$508$	−23.3828	−	40.5003i	−1.03745	−	1.79691i
$509$	0.469637	−	0.813434i	0.0208163	−	0.0360548i	−0.855430	−	0.517919i	$-0.826707\pi$
$509$	0.469637	−	0.813434i	0.0208163	−	0.0360548i	0.876246	+	0.481864i	$0.160040\pi$
$510$	−2.74771			−0.121671
$511$	0.0508622	+	14.0956i	0.00225001	+	0.623553i
$512$	−38.7957			−1.71454
$513$	−23.1299	+	40.0622i	−1.02121	+	1.76879i
$514$	−32.2041	−	55.7791i	−1.42046	−	2.46031i
$515$	−0.490754	−	0.850010i	−0.0216252	−	0.0374559i
$516$	−19.7693	+	34.2415i	−0.870296	+	1.50740i
$517$		0			0
$518$	−0.0544329	−	15.0852i	−0.00239164	−	0.662804i
$519$	0.469514			0.0206094
$520$	−1.41109	+	2.44408i	−0.0618805	+	0.107180i
$521$	13.0273	+	22.5640i	0.570738	+	0.988547i	0.996490	+	0.0837074i	$0.0266761\pi$
$521$	13.0273	+	22.5640i	0.570738	+	0.988547i	−0.425752	+	0.904840i	$0.639991\pi$
$522$	−28.4907	−	49.3473i	−1.24700	−	2.15987i
$523$	2.26945	−	3.93080i	0.0992362	−	0.171882i	−0.812133	−	0.583473i	$-0.801693\pi$
$523$	2.26945	−	3.93080i	0.0992362	−	0.171882i	0.911369	+	0.411591i	$0.135027\pi$
$524$	3.87234			0.169164
$525$	32.5917	−	18.9739i	1.42242	−	0.828090i
$526$	51.9123			2.26348
$527$	−2.90637	+	5.03397i	−0.126603	+	0.219283i
$528$		0			0
$529$	8.90874	+	15.4304i	0.387337	+	0.670887i
$530$	−2.00737	+	3.47687i	−0.0871948	+	0.151026i
$531$	−5.58132			−0.242209
$532$	58.2257	+	33.3371i	2.52440	+	1.44535i
$533$	−6.99057			−0.302795
$534$	66.8997	−	115.874i	2.89503	−	5.01434i
$535$	−2.33567	−	4.04549i	−0.100980	−	0.174902i
$536$	26.0309	+	45.0868i	1.12436	+	1.94745i
$537$	9.73948	−	16.8693i	0.420289	−	0.727963i
$538$	55.4086			2.38883
$539$		0			0
$540$	−9.64296			−0.414967
$541$	−6.20051	+	10.7396i	−0.266581	+	0.461732i	−0.967977	−	0.251041i	$-0.919227\pi$
$541$	−6.20051	+	10.7396i	−0.266581	+	0.461732i	0.701396	+	0.712772i	$0.252561\pi$
$542$	−19.6555	−	34.0442i	−0.844274	−	1.46233i
$543$	26.2061	+	45.3904i	1.12461	+	1.94789i
$544$	0.0525696	−	0.0910533i	0.00225390	−	0.00390388i
$545$	3.33481			0.142848
$546$	−28.5864	−	16.3671i	−1.22339	−	0.700449i
$547$	−0.200859			−0.00858810			−0.00429405	−	0.999991i	$-0.501367\pi$
$547$	−0.200859			−0.00858810			−0.00429405	+	0.999991i	$0.501367\pi$
$548$	11.3626	−	19.6807i	0.485388	−	0.840716i
$549$	−15.1963	−	26.3208i	−0.648563	−	1.12334i
$550$		0			0
$551$	−13.4552	+	23.3052i	−0.573213	+	0.992833i
$552$	−32.3342			−1.37624
$553$	8.94995	−	5.21041i	0.380591	−	0.221569i
$554$	54.6782			2.32305
$555$	1.12697	−	1.95197i	0.0478373	−	0.0828566i
$556$	25.7053	+	44.5229i	1.09015	+	1.88819i
$557$	12.1790	+	21.0947i	0.516042	+	0.893812i	0.999827	+	0.0186243i	$0.00592866\pi$
$557$	12.1790	+	21.0947i	0.516042	+	0.893812i	−0.483784	+	0.875187i	$0.660738\pi$
$558$	−33.7048	+	58.3784i	−1.42684	+	2.47135i
$559$	−5.93098			−0.250854
$560$	0.0124991	+	3.46391i	0.000528182	+	0.146377i
$561$		0			0
$562$	1.20566	−	2.08826i	0.0508575	−	0.0880878i
$563$	−17.0797	−	29.5829i	−0.719824	−	1.24677i	−0.961069	−	0.276307i	$-0.910889\pi$
$563$	−17.0797	−	29.5829i	−0.719824	−	1.24677i	0.241246	−	0.970464i	$-0.422444\pi$
$564$	26.5430	+	45.9738i	1.11766	+	1.93585i
$565$	−1.04941	+	1.81763i	−0.0441489	+	0.0764682i
$566$	−46.8056			−1.96739
$567$	−0.0451453	−	12.5113i	−0.00189592	−	0.525424i
$568$	28.0681			1.17771
$569$	5.93802	−	10.2850i	0.248935	−	0.431168i	−0.714296	−	0.699844i	$-0.753253\pi$
$569$	5.93802	−	10.2850i	0.248935	−	0.431168i	0.963231	+	0.268676i	$0.0865862\pi$
$570$	7.52438	+	13.0326i	0.315162	+	0.545876i
$571$	−12.4734	−	21.6046i	−0.521998	−	0.904126i	−0.999673	−	0.0255896i	$-0.991854\pi$
$571$	−12.4734	−	21.6046i	−0.521998	−	0.904126i	0.477675	−	0.878537i	$-0.341480\pi$
$572$		0			0
$573$	−42.9889			−1.79589
$574$	−22.4195	+	13.0520i	−0.935770	+	0.544779i
$575$	11.1318			0.464227
$576$	22.2935	−	38.6135i	0.928897	−	1.60890i
$577$	−1.97473	−	3.42034i	−0.0822092	−	0.142391i	0.821989	−	0.569503i	$-0.192864\pi$
$577$	−1.97473	−	3.42034i	−0.0822092	−	0.142391i	−0.904199	+	0.427112i	$0.859531\pi$
$578$	19.1571	+	33.1811i	0.796830	+	1.38015i
$579$	21.2618	−	36.8265i	0.883611	−	1.53046i
$580$	−5.60954			−0.232924
$581$	28.4726	+	16.3020i	1.18124	+	0.676320i
$582$	59.8320			2.48011
$583$		0			0
$584$	12.9795	+	22.4812i	0.537096	+	0.930277i
$585$	−1.59206	−	2.75752i	−0.0658235	−	0.114010i
$586$	8.42458	−	14.5918i	0.348016	−	0.602782i
$587$	−39.7359			−1.64008			−0.820038	−	0.572309i	$-0.806048\pi$
$587$	−39.7359			−1.64008			−0.820038	+	0.572309i	$0.806048\pi$
$588$	−81.4292	+	0.587661i	−3.35808	+	0.0242347i
$589$	31.8354			1.31176
$590$	−0.412410	+	0.714316i	−0.0169787	+	0.0294079i
$591$	−8.74488	−	15.1466i	−0.359716	−	0.623047i
$592$	−4.59428	−	7.95753i	−0.188824	−	0.327053i
$593$	5.75165	−	9.96216i	0.236192	−	0.409097i	−0.723426	−	0.690402i	$-0.757434\pi$
$593$	5.75165	−	9.96216i	0.236192	−	0.409097i	0.959618	+	0.281305i	$0.0907672\pi$
$594$		0			0
$595$	−0.884239	−	0.506270i	−0.0362503	−	0.0207551i
$596$	62.3504			2.55397
$597$	−29.0675	+	50.3465i	−1.18966	+	2.06054i
$598$	−4.86159	−	8.42051i	−0.198805	−	0.344340i
$599$	8.49856	+	14.7199i	0.347242	+	0.601440i	0.985758	−	0.168168i	$-0.0537851\pi$
$599$	8.49856	+	14.7199i	0.347242	+	0.601440i	−0.638517	+	0.769608i	$0.720452\pi$
$600$	34.7261	−	60.1473i	1.41769	−	2.45550i
$601$	−19.2573			−0.785522			−0.392761	−	0.919641i	$-0.628480\pi$
$601$	−19.2573			−0.785522			−0.392761	+	0.919641i	$0.628480\pi$
$602$	−19.0213	+	11.0736i	−0.775248	+	0.451328i
$603$	−58.7384			−2.39201
$604$	42.4506	−	73.5265i	1.72729	−	2.99175i
$605$		0			0
$606$	−10.1758	−	17.6250i	−0.413364	−	0.715967i
$607$	18.3204	−	31.7318i	0.743601	−	1.28796i	−0.207244	−	0.978289i	$-0.566449\pi$
$607$	18.3204	−	31.7318i	0.743601	−	1.28796i	0.950845	−	0.309666i	$-0.100217\pi$
$608$	−0.575831			−0.0233530
$609$	−0.117852	−	32.6608i	−0.00477562	−	1.32348i
$610$	−4.49149			−0.181855
$611$	−3.98157	+	6.89628i	−0.161077	+	0.278994i
$612$	−12.7270	−	22.0439i	−0.514460	−	0.891071i
$613$	−13.9892	−	24.2300i	−0.565018	−	0.978640i	−0.997048	−	0.0767805i	$-0.975536\pi$
$613$	−13.9892	−	24.2300i	−0.565018	−	0.978640i	0.432030	−	0.901859i	$-0.357797\pi$
$614$	−12.5397	+	21.7194i	−0.506061	+	0.876524i
$615$	−3.87608			−0.156299
$616$		0			0
$617$	15.6773			0.631142			0.315571	−	0.948902i	$-0.397804\pi$
$617$	15.6773			0.631142			0.315571	+	0.948902i	$0.397804\pi$
$618$	10.5489	−	18.2713i	0.424340	−	0.734978i
$619$	−22.2212	−	38.4882i	−0.893144	−	1.54697i	−0.836085	−	0.548600i	$-0.815161\pi$
$619$	−22.2212	−	38.4882i	−0.893144	−	1.54697i	−0.0570594	−	0.998371i	$-0.518172\pi$
$620$	3.31808	+	5.74708i	0.133257	+	0.230808i
$621$	8.28633	−	14.3524i	0.332519	−	0.575940i
$622$	−78.8288			−3.16075
$623$	42.8789	−	24.9629i	1.71791	−	1.00012i
$624$	−20.0643			−0.803213
$625$	−11.6798	+	20.2300i	−0.467191	+	0.809199i
$626$	28.7176	+	49.7403i	1.14779	+	1.98802i
$627$		0			0
$628$	12.5661	−	21.7651i	0.501442	−	0.868524i
$629$	2.70282			0.107768
$630$	−10.2544	−	5.87116i	−0.408546	−	0.233912i
$631$	−9.71861			−0.386892			−0.193446	−	0.981111i	$-0.561966\pi$
$631$	−9.71861			−0.386892			−0.193446	+	0.981111i	$0.561966\pi$
$632$	9.53608	−	16.5170i	0.379325	−	0.657010i
$633$	14.8948	+	25.7986i	0.592016	+	1.02540i
$634$	−7.68909	−	13.3179i	−0.305373	−	0.528921i
$635$	1.94483	−	3.36855i	0.0771784	−	0.133677i
$636$	−57.4878			−2.27954
$637$	−6.18372	−	10.5342i	−0.245008	−	0.417381i
$638$		0			0
$639$	−15.8339	+	27.4251i	−0.626378	+	1.08492i
$640$	−3.26451	−	5.65430i	−0.129041	−	0.223506i
$641$	9.50996	+	16.4717i	0.375621	+	0.650594i	0.990420	−	0.138090i	$-0.0440962\pi$
$641$	9.50996	+	16.4717i	0.375621	+	0.650594i	−0.614799	+	0.788684i	$0.710763\pi$
$642$	50.2060	−	86.9593i	1.98147	−	3.43201i
$643$	−11.6174			−0.458144			−0.229072	−	0.973409i	$-0.573569\pi$
$643$	−11.6174			−0.458144			−0.229072	+	0.973409i	$0.573569\pi$
$644$	−20.8594	−	11.9431i	−0.821977	−	0.470622i
$645$	−3.28857			−0.129487
$646$	−9.02286	+	15.6280i	−0.355000	+	0.614877i
$647$	13.5243	+	23.4248i	0.531695	+	0.920923i	0.999315	+	0.0369937i	$0.0117782\pi$
$647$	13.5243	+	23.4248i	0.531695	+	0.920923i	−0.467620	+	0.883929i	$0.654889\pi$
$648$	−11.5206	−	19.9543i	−0.452572	−	0.783878i
$649$		0			0
$650$	20.8848			0.819171
$651$	−33.3919	+	19.4398i	−1.30873	+	0.761906i
$652$	−32.1852			−1.26047
$653$	−5.50820	+	9.54049i	−0.215553	+	0.373348i	−0.953443	−	0.301572i	$-0.902489\pi$
$653$	−5.50820	+	9.54049i	−0.215553	+	0.373348i	0.737891	+	0.674920i	$0.235822\pi$
$654$	35.8415	+	62.0793i	1.40151	+	2.42749i
$655$	0.161038	+	0.278927i	0.00629229	+	0.0108986i
$656$	−7.90074	+	13.6845i	−0.308472	+	0.534290i
$657$	−29.2881			−1.14264
$658$	0.106631	+	29.5510i	0.00415691	+	1.15202i
$659$	27.0259			1.05278			0.526389	−	0.850244i	$-0.323545\pi$
$659$	27.0259			1.05278			0.526389	+	0.850244i	$0.323545\pi$
$660$		0			0
$661$	18.6904	+	32.3727i	0.726973	+	1.25915i	0.958157	+	0.286244i	$0.0924067\pi$
$661$	18.6904	+	32.3727i	0.726973	+	1.25915i	−0.231184	+	0.972910i	$0.574260\pi$
$662$	19.6113	+	33.9678i	0.762215	+	1.32019i
$663$	2.95095	−	5.11120i	0.114605	−	0.198502i
$664$	60.4223			2.34484
$665$	0.0201362	+	5.58040i	0.000780847	+	0.216399i
$666$	31.3442			1.21456
$667$	4.82036	−	8.34911i	0.186645	−	0.323279i
$668$	−22.1968	−	38.4460i	−0.858821	−	1.48752i
$669$	−39.5750	−	68.5460i	−1.53006	−	2.65014i
$670$	−4.34025	+	7.51754i	−0.167679	+	0.290428i
$671$		0			0
$672$	0.603985	−	0.351623i	0.0232992	−	0.0135641i
$673$	4.99951			0.192717			0.0963585	−	0.995347i	$-0.469280\pi$
$673$	4.99951			0.192717			0.0963585	+	0.995347i	$0.469280\pi$
$674$	21.8592	−	37.8612i	0.841985	−	1.45836i
$675$	17.7986	+	30.8281i	0.685068	+	1.18657i
$676$	19.8637	+	34.4049i	0.763988	+	1.32327i
$677$	10.3079	−	17.8538i	0.396165	−	0.686178i	−0.597084	−	0.802179i	$-0.703674\pi$
$677$	10.3079	−	17.8538i	0.396165	−	0.686178i	0.993249	+	0.116001i	$0.0370075\pi$
$678$	−45.1148			−1.73262
$679$	19.2545	+	11.0242i	0.738920	+	0.423068i
$680$	−1.87646			−0.0719590
$681$	1.50375	−	2.60458i	0.0576240	−	0.0998077i
$682$		0			0
$683$	−9.03901	−	15.6560i	−0.345868	−	0.599061i	0.639643	−	0.768672i	$-0.279082\pi$
$683$	−9.03901	−	15.6560i	−0.345868	−	0.599061i	−0.985511	+	0.169611i	$0.945749\pi$
$684$	−69.7040	+	120.731i	−2.66520	+	4.61626i
$685$	1.89014			0.0722186
$686$	−39.5001	−	22.2388i	−1.50812	−	0.849080i
$687$	46.3764			1.76937
$688$	−6.70319	+	11.6103i	−0.255557	+	0.442638i
$689$	−4.31171	−	7.46811i	−0.164263	−	0.284512i
$690$	−2.69562	−	4.66895i	−0.102621	−	0.177744i
$691$	6.38399	−	11.0574i	0.242859	−	0.420643i	−0.718669	−	0.695353i	$-0.755248\pi$
$691$	6.38399	−	11.0574i	0.242859	−	0.420643i	0.961527	+	0.274709i	$0.0885816\pi$
$692$	0.642775			0.0244346
$693$		0			0
$694$	−45.1996			−1.71575
$695$	−2.13800	+	3.70313i	−0.0810991	+	0.140468i
$696$	−30.0747	−	52.0909i	−1.13998	−	1.97450i
$697$	−2.32400	−	4.02529i	−0.0880279	−	0.152469i
$698$	22.8641	−	39.6018i	0.865419	−	1.49895i
$699$	58.1539			2.19958
$700$	44.6186	−	25.9757i	1.68643	−	0.981789i
$701$	16.1963			0.611726			0.305863	−	0.952075i	$-0.401055\pi$
$701$	16.1963			0.611726			0.305863	+	0.952075i	$0.401055\pi$
$702$	15.5464	−	26.9271i	0.586761	−	1.01630i
$703$	−7.40145	−	12.8197i	−0.279151	−	0.483504i
$704$		0			0
$705$	−2.20768	+	3.82381i	−0.0831459	+	0.144013i
$706$	22.1220			0.832573
$707$	−0.0272317	−	7.54681i	−0.00102415	−	0.283827i
$708$	−11.8107			−0.443874
$709$	6.48885	−	11.2390i	0.243694	−	0.422090i	−0.718070	−	0.695971i	$-0.754974\pi$
$709$	6.48885	−	11.2390i	0.243694	−	0.422090i	0.961764	+	0.273881i	$0.0883074\pi$
$710$	2.33997	+	4.05294i	0.0878174	+	0.152104i
$711$	10.7590	+	18.6352i	0.403495	+	0.698875i
$712$	45.6870	−	79.1323i	1.71219	−	2.96561i
$713$	−11.4051			−0.427124
$714$	−0.0790298	−	21.9018i	−0.00295762	−	0.819654i
$715$		0			0
$716$	13.3335	−	23.0944i	0.498298	−	0.863077i
$717$	35.3412	+	61.2127i	1.31984	+	2.28603i
$718$	−16.0324	−	27.7690i	−0.598325	−	1.03633i
$719$	19.7779	−	34.2563i	0.737590	−	1.27754i	−0.215987	−	0.976396i	$-0.569297\pi$
$719$	19.7779	−	34.2563i	0.737590	−	1.27754i	0.953577	−	0.301148i	$-0.0973698\pi$
$720$	−7.19737			−0.268230
$721$	6.76126	−	3.93621i	0.251803	−	0.146592i
$722$	52.3292			1.94749
$723$	1.64147	−	2.84312i	0.0610471	−	0.105737i
$724$	35.8767	+	62.1403i	1.33335	+	2.30943i
$725$	10.3539	+	17.9334i	0.384533	+	0.666031i
$726$		0			0
$727$	−24.9474			−0.925250			−0.462625	−	0.886554i	$-0.653092\pi$
$727$	−24.9474			−0.925250			−0.462625	+	0.886554i	$0.653092\pi$
$728$	−19.5222	−	11.1774i	−0.723541	−	0.414263i
$729$	−37.6666			−1.39506
$730$	−2.16414	+	3.74839i	−0.0800982	+	0.138734i
$731$	−1.97174	−	3.41516i	−0.0729276	−	0.126314i
$732$	−32.1572	−	55.6979i	−1.18856	−	2.05865i
$733$	−20.9682	+	36.3180i	−0.774479	+	1.34144i	0.160608	+	0.987018i	$0.448655\pi$
$733$	−20.9682	+	36.3180i	−0.774479	+	1.34144i	−0.935087	+	0.354419i	$0.884679\pi$
$734$	−18.9012			−0.697656
$735$	−3.42871	−	5.84094i	−0.126470	−	0.215446i
$736$	0.206292			0.00760404
$737$		0			0
$738$	−26.9512	−	46.6808i	−0.992087	−	1.71834i
$739$	11.7375	+	20.3299i	0.431770	+	0.747847i	0.997026	−	0.0770683i	$-0.0245560\pi$
$739$	11.7375	+	20.3299i	0.431770	+	0.747847i	−0.565256	+	0.824916i	$0.691223\pi$
$740$	1.54285	−	2.67229i	0.0567162	−	0.0982353i
$741$	−32.3238			−1.18744
$742$	−27.7717	−	15.9007i	−1.01953	−	0.583731i
$743$	1.48560			0.0545012			0.0272506	−	0.999629i	$-0.491325\pi$
$743$	1.48560			0.0545012			0.0272506	+	0.999629i	$0.491325\pi$
$744$	−35.5787	+	61.6242i	−1.30438	+	2.25925i
$745$	2.59295	+	4.49113i	0.0949984	+	0.164542i
$746$	−27.9369	−	48.3881i	−1.02284	−	1.77161i
$747$	−34.0856	+	59.0380i	−1.24713	+	2.16009i
$748$		0			0
$749$	32.1792	−	18.7338i	1.17580	−	0.684518i
$750$	23.4211			0.855217
$751$	10.0324	−	17.3766i	0.366087	−	0.634082i	−0.622863	−	0.782331i	$-0.714030\pi$
$751$	10.0324	−	17.3766i	0.366087	−	0.634082i	0.988950	+	0.148249i	$0.0473638\pi$
$752$	8.99995	+	15.5884i	0.328194	+	0.568449i
$753$	15.5790	+	26.9836i	0.567729	+	0.983336i
$754$	9.04371	−	15.6642i	0.329353	−	0.570455i
$755$	7.06153			0.256995
$756$	−0.277352	−	76.8634i	−0.0100872	−	2.79550i
$757$	29.2144			1.06182			0.530908	−	0.847429i	$-0.321851\pi$
$757$	29.2144			1.06182			0.530908	+	0.847429i	$0.321851\pi$
$758$	−31.4710	+	54.5093i	−1.14308	+	1.97987i
$759$		0			0
$760$	5.13854	+	8.90021i	0.186394	+	0.322845i
$761$	−7.65559	+	13.2599i	−0.277515	+	0.480670i	−0.970767	−	0.240026i	$-0.922844\pi$
$761$	−7.65559	+	13.2599i	−0.277515	+	0.480670i	0.693252	+	0.720696i	$0.256178\pi$
$762$	83.6098			3.02886
$763$	0.0959162	+	26.5816i	0.00347240	+	0.962317i
$764$	−58.8526			−2.12921
$765$	1.05855	−	1.83347i	0.0382721	−	0.0662892i
$766$	38.6723	+	66.9823i	1.39729	+	2.42017i
$767$	−0.885832	−	1.53431i	−0.0319855	−	0.0554006i
$768$	46.5292	−	80.5909i	1.67898	−	2.90807i
$769$	−5.33355			−0.192333			−0.0961664	−	0.995365i	$-0.530658\pi$
$769$	−5.33355			−0.192333			−0.0961664	+	0.995365i	$0.530658\pi$
$770$		0			0
$771$	76.7084			2.76259
$772$	29.1078	−	50.4162i	1.04761	−	1.81452i
$773$	23.6508	+	40.9644i	0.850660	+	1.47339i	0.880614	+	0.473834i	$0.157130\pi$
$773$	23.6508	+	40.9644i	0.850660	+	1.47339i	−0.0299544	+	0.999551i	$0.509536\pi$
$774$	−22.8661	−	39.6052i	−0.821904	−	1.42358i
$775$	12.2487	−	21.2155i	0.439988	−	0.762081i
$776$	40.8604			1.46680
$777$	15.5915	+	8.92688i	0.559341	+	0.320250i
$778$	17.2762			0.619383
$779$	−12.7282	+	22.0459i	−0.456035	+	0.789876i
$780$	−3.36898	−	5.83524i	−0.120629	−	0.208935i
$781$		0			0
$782$	3.23245	−	5.59877i	0.115592	−	0.200212i
$783$	30.8291			1.10174
$784$	−27.6102	+	0.199259i	−0.986080	+	0.00711638i
$785$	2.09034			0.0746073
$786$	−3.46158	+	5.99563i	−0.123470	+	0.213857i
$787$	−4.85445	−	8.40816i	−0.173042	−	0.299718i	0.766440	−	0.642316i	$-0.222026\pi$
$787$	−4.85445	−	8.40816i	−0.173042	−	0.299718i	−0.939482	+	0.342598i	$0.888693\pi$
$788$	−11.9719	−	20.7360i	−0.426482	−	0.738688i
$789$	−30.9131	+	53.5431i	−1.10054	+	1.90618i
$790$	3.17999			0.113139
$791$	−14.5184	−	8.31249i	−0.516214	−	0.295558i
$792$		0			0
$793$	4.82372	−	8.35494i	0.171295	−	0.296692i
$794$	−20.0883	−	34.7940i	−0.712909	−	1.23479i
$795$	−2.39073	−	4.14087i	−0.0847905	−	0.146861i
$796$	−39.7940	+	68.9253i	−1.41046	+	2.44299i
$797$	49.9570			1.76957			0.884783	−	0.466003i	$-0.154306\pi$
$797$	49.9570			1.76957			0.884783	+	0.466003i	$0.154306\pi$
$798$	−103.666	+	60.3512i	−3.66973	+	2.13641i
$799$	−5.29467			−0.187312
$800$	−0.221552	+	0.383740i	−0.00783306	+	0.0135673i
$801$	51.5462	+	89.2806i	1.82129	+	3.15457i
$802$	−42.8585	−	74.2331i	−1.51339	−	2.62126i
$803$		0			0
$804$	−124.297			−4.38363
$805$	−0.00721381	−	1.99919i	−0.000254253	−	0.0704621i
$806$	−21.3976			−0.753699
$807$	−32.9951	+	57.1492i	−1.16148	+	2.01175i
$808$	−6.94924	−	12.0364i	−0.244474	−	0.423441i
$809$	−15.5651	−	26.9595i	−0.547240	−	0.947847i	−0.998462	−	0.0554354i	$-0.982345\pi$
$809$	−15.5651	−	26.9595i	−0.547240	−	0.947847i	0.451223	−	0.892411i	$-0.350988\pi$
$810$	1.92088	−	3.32707i	0.0674930	−	0.116901i
$811$	−7.16571			−0.251622			−0.125811	−	0.992054i	$-0.540153\pi$
$811$	−7.16571			−0.251622			−0.125811	+	0.992054i	$0.540153\pi$
$812$	−0.161342	−	44.7133i	−0.00566200	−	1.56913i
$813$	46.8183			1.64199
$814$		0			0
$815$	−1.33848	−	2.31832i	−0.0468849	−	0.0812070i
$816$	−6.67033	−	11.5534i	−0.233508	−	0.404448i
$817$	−10.7989	+	18.7043i	−0.377807	+	0.654381i
$818$	−26.9883			−0.943622
$819$	21.9343	−	12.7695i	0.766445	−	0.446202i
$820$	−5.30644			−0.185309
$821$	4.76893	−	8.26002i	0.166437	−	0.288277i	−0.770728	−	0.637164i	$-0.780107\pi$
$821$	4.76893	−	8.26002i	0.166437	−	0.288277i	0.937165	+	0.348888i	$0.113441\pi$
$822$	20.3146	+	35.1860i	0.708554	+	1.22725i
$823$	7.60897	+	13.1791i	0.265232	+	0.459395i	0.967624	−	0.252395i	$-0.0812181\pi$
$823$	7.60897	+	13.1791i	0.265232	+	0.459395i	−0.702392	+	0.711790i	$0.747885\pi$
$824$	7.20405	−	12.4778i	0.250965	−	0.434684i
$825$		0			0
$826$	−5.70563	−	3.26675i	−0.198524	−	0.113665i
$827$	−19.3465			−0.672745			−0.336373	−	0.941729i	$-0.609200\pi$
$827$	−19.3465			−0.672745			−0.336373	+	0.941729i	$0.609200\pi$
$828$	24.9716	−	43.2520i	0.867822	−	1.50311i
$829$	−12.0052	−	20.7937i	−0.416959	−	0.722195i	0.578673	−	0.815560i	$-0.303571\pi$
$829$	−12.0052	−	20.7937i	−0.416959	−	0.722195i	−0.995632	+	0.0933653i	$0.970238\pi$
$830$	5.03725	+	8.72477i	0.174845	+	0.302841i
$831$	−32.5601	+	56.3958i	−1.12950	+	1.95635i
$832$	14.1532			0.490672
$833$	4.01001	−	7.06277i	0.138939	−	0.244711i
$834$	−91.9143			−3.18273
$835$	1.84619	−	3.19769i	0.0638900	−	0.110661i
$836$		0			0
$837$	−18.2356	−	31.5850i	−0.630315	−	1.09174i
$838$	−3.88512	+	6.72922i	−0.134209	+	0.232457i
$839$	−10.5718			−0.364979			−0.182489	−	0.983208i	$-0.558416\pi$
$839$	−10.5718			−0.364979			−0.182489	+	0.983208i	$0.558416\pi$
$840$	−10.8245	−	6.19758i	−0.373482	−	0.213837i
$841$	−11.0660			−0.381585
$842$	−11.7356	+	20.3266i	−0.404435	+	0.700502i
$843$	1.43590	+	2.48706i	0.0494552	+	0.0856589i
$844$	20.3913	+	35.3188i	0.701897	+	1.21572i
$845$	−1.65213	+	2.86158i	−0.0568352	+	0.0984414i
$846$	−61.4016			−2.11103
$847$		0			0
$848$	−19.4924			−0.669372
$849$	27.8721	−	48.2759i	0.956569	−	1.65683i
$850$	6.94313	+	12.0259i	0.238147	+	0.412483i
$851$	2.65158	+	4.59267i	0.0908950	+	0.157435i
$852$	−33.5063	+	58.0346i	−1.14791	+	1.98823i
$853$	−2.78836			−0.0954716			−0.0477358	−	0.998860i	$-0.515201\pi$
$853$	−2.78836			−0.0954716			−0.0477358	+	0.998860i	$0.515201\pi$
$854$	−0.129185	−	35.8014i	−0.00442061	−	1.22510i
$855$	−11.5951			−0.396543
$856$	34.2866	−	59.3861i	1.17189	−	2.02978i
$857$	−9.23548	−	15.9963i	−0.315478	−	0.546424i	0.664061	−	0.747678i	$-0.268831\pi$
$857$	−9.23548	−	15.9963i	−0.315478	−	0.546424i	−0.979539	+	0.201255i	$0.935498\pi$
$858$		0			0
$859$	−20.6055	+	35.6897i	−0.703050	+	1.21772i	0.264341	+	0.964429i	$0.414846\pi$
$859$	−20.6055	+	35.6897i	−0.703050	+	1.21772i	−0.967391	+	0.253289i	$0.918488\pi$
$860$	−4.50212			−0.153521
$861$	−0.111484	−	30.8960i	−0.00379938	−	1.05293i
$862$	18.2069			0.620129
$863$	7.86758	−	13.6270i	0.267816	−	0.463870i	−0.700482	−	0.713670i	$-0.747032\pi$
$863$	7.86758	−	13.6270i	0.267816	−	0.463870i	0.968297	+	0.249800i	$0.0803649\pi$
$864$	0.329841	+	0.571302i	0.0112214	+	0.0194361i
$865$	0.0267309	+	0.0462993i	0.000908879	+	0.00157422i
$866$	−16.2294	+	28.1102i	−0.551498	+	0.955223i
$867$	−45.6312			−1.54972
$868$	−45.7142	+	26.6135i	−1.55164	+	0.903320i
$869$		0			0
$870$	5.01450	−	8.68536i	0.170007	−	0.294461i
$871$	−9.32259	−	16.1472i	−0.315884	−	0.547127i
$872$	24.4768	+	42.3951i	0.828889	+	1.43568i
$873$	−23.0502	+	39.9242i	−0.780133	+	1.35123i
$874$	−35.4073			−1.19767
$875$	7.53713	+	4.31538i	0.254802	+	0.145886i
$876$	−61.9771			−2.09401
$877$	−13.0679	+	22.6343i	−0.441271	+	0.764304i	−0.997784	−	0.0665346i	$-0.978806\pi$
$877$	−13.0679	+	22.6343i	−0.441271	+	0.764304i	0.556513	+	0.830839i	$0.312139\pi$
$878$	−35.2602	−	61.0724i	−1.18997	−	2.06110i
$879$	10.0335	+	17.3785i	0.338420	+	0.586161i
$880$		0			0
$881$	−3.85153			−0.129761			−0.0648806	−	0.997893i	$-0.520667\pi$
$881$	−3.85153			−0.129761			−0.0648806	+	0.997893i	$0.520667\pi$
$882$	46.5037	−	81.9061i	1.56586	−	2.75792i
$883$	−19.4825			−0.655638			−0.327819	−	0.944741i	$-0.606314\pi$
$883$	−19.4825			−0.655638			−0.327819	+	0.944741i	$0.606314\pi$
$884$	4.03991	−	6.99733i	0.135877	−	0.235346i
$885$	−0.491170	−	0.850732i	−0.0165105	−	0.0285970i
$886$	−18.7552	−	32.4849i	−0.630093	−	1.09135i
$887$	15.8617	−	27.4733i	0.532585	−	0.922464i	−0.466691	−	0.884420i	$-0.654554\pi$
$887$	15.8617	−	27.4733i	0.532585	−	0.922464i	0.999276	−	0.0380436i	$-0.0121126\pi$
$888$	33.0869			1.11033
$889$	26.9065	+	15.4053i	0.902413	+	0.516676i
$890$	15.2352			0.510686
$891$		0			0
$892$	−54.1790	−	93.8408i	−1.81405	−	3.14202i
$893$	14.4990	+	25.1131i	0.485191	+	0.840376i
$894$	−55.7364	+	96.5383i	−1.86411	+	3.22872i
$895$	2.21800			0.0741394
$896$	44.9762	−	26.1839i	1.50255	−	0.874741i
$897$	11.5800			0.386646
$898$	−25.2267	+	43.6939i	−0.841825	+	1.45808i
$899$	−10.6081	−	18.3738i	−0.353800	−	0.612799i
$900$	53.6375	+	92.9029i	1.78792	+	3.09676i
$901$	2.86684	−	4.96552i	0.0955084	−	0.165425i
$902$		0			0
$903$	−0.0945862	−	26.2130i	−0.00314763	−	0.872313i
$904$	−30.8097			−1.02472
$905$	−2.98399	+	5.16843i	−0.0991913	+	0.171804i
$906$	75.8951	+	131.454i	2.52144	+	4.36727i
$907$	−22.2209	−	38.4878i	−0.737833	−	1.27797i	−0.953469	−	0.301491i	$-0.902516\pi$
$907$	−22.2209	−	38.4878i	−0.737833	−	1.27797i	0.215636	−	0.976474i	$-0.430818\pi$
$908$	2.05867	−	3.56572i	0.0683194	−	0.118333i
$909$	15.6809			0.520102
$910$	−0.0135342	−	3.75077i	−0.000448654	−	0.124337i
$911$	20.0300			0.663624			0.331812	−	0.943346i	$-0.392340\pi$
$911$	20.0300			0.663624			0.331812	+	0.943346i	$0.392340\pi$
$912$	−36.5324	+	63.2759i	−1.20971	+	2.09527i
$913$		0			0
$914$	12.5610	+	21.7562i	0.415480	+	0.719632i
$915$	2.67463	−	4.63259i	0.0884204	−	0.153149i
$916$	63.4902			2.09778
$917$	−2.21867	+	1.29165i	−0.0732671	+	0.0426540i
$918$	20.6735			0.682327
$919$	−10.2459	+	17.7464i	−0.337980	+	0.585398i	−0.984053	−	0.177877i	$-0.943077\pi$
$919$	−10.2459	+	17.7464i	−0.337980	+	0.585398i	0.646073	+	0.763276i	$0.276410\pi$
$920$	−1.84089	−	3.18851i	−0.0606923	−	0.105122i
$921$	−14.9345	−	25.8673i	−0.492107	−	0.852355i
$922$	3.80734	−	6.59450i	0.125388	−	0.217178i
$923$	−10.0522			−0.330872
$924$		0			0
$925$	−11.3909			−0.374530
$926$	−31.8793	+	55.2165i	−1.04762	+	1.81453i
$927$	8.12794	+	14.0780i	0.266956	+	0.462382i
$928$	0.191877	+	0.332340i	0.00629866	+	0.0109096i
$929$	7.30406	−	12.6510i	0.239638	−	0.415066i	−0.720972	−	0.692964i	$-0.756304\pi$
$929$	7.30406	−	12.6510i	0.239638	−	0.415066i	0.960611	+	0.277898i	$0.0896378\pi$
$930$	−11.8644			−0.389050
$931$	−44.4804	+	0.321008i	−1.45779	+	0.0105206i
$932$	79.6138			2.60784
$933$	46.9415	−	81.3051i	1.53680	−	2.66181i
$934$	−35.4455	−	61.3935i	−1.15981	−	2.00886i
$935$		0			0
$936$	23.3707	−	40.4793i	0.763896	−	1.32311i
$937$	42.6433			1.39310			0.696549	−	0.717510i	$-0.254718\pi$
$937$	42.6433			1.39310			0.696549	+	0.717510i	$0.254718\pi$
$938$	−60.0466	−	34.3797i	−1.96059	−	1.12254i
$939$	−68.4038			−2.23227
$940$	−3.02235	+	5.23487i	−0.0985782	+	0.170742i
$941$	−28.5729	−	49.4896i	−0.931449	−	1.61332i	−0.780848	−	0.624721i	$-0.785213\pi$
$941$	−28.5729	−	49.4896i	−0.931449	−	1.61332i	−0.150601	−	0.988595i	$-0.548121\pi$
$942$	22.4663	+	38.9127i	0.731990	+	1.26784i
$943$	4.55990	−	7.89797i	0.148491	−	0.257193i
$944$	−4.00467			−0.130341
$945$	5.52497	−	3.21648i	0.179727	−	0.104632i
$946$		0			0
$947$	12.3832	−	21.4483i	0.402399	−	0.696975i	−0.591616	−	0.806220i	$-0.701510\pi$
$947$	12.3832	−	21.4483i	0.402399	−	0.696975i	0.994015	+	0.109245i	$0.0348433\pi$
$948$	22.7674	+	39.4343i	0.739450	+	1.28077i
$949$	−4.64843	−	8.05131i	−0.150894	−	0.261357i
$950$	38.0264	−	65.8637i	1.23374	−	2.13690i
$951$	18.3150			0.593905
$952$	−0.0539709	−	14.9571i	−0.00174921	−	0.484764i
$953$	−48.6290			−1.57525			−0.787624	−	0.616156i	$-0.788689\pi$
$953$	−48.6290			−1.57525			−0.787624	+	0.616156i	$0.788689\pi$
$954$	33.2465	−	57.5845i	1.07639	−	1.86437i
$955$	−2.44749	−	4.23918i	−0.0791990	−	0.137177i
$956$	48.3827	+	83.8014i	1.56481	+	2.71033i
$957$		0			0
$958$	77.2865			2.49702
$959$	0.0543645	+	15.0662i	0.00175552	+	0.486513i
$960$	7.84755			0.253278
$961$	2.95051	−	5.11043i	0.0951776	−	0.164852i
$962$	4.97476	+	8.61654i	0.160393	+	0.277808i
$963$	38.6837	+	67.0021i	1.24656	+	2.15911i
$964$	2.24721	−	3.89228i	0.0723778	−	0.125362i
$965$	4.84200			0.155870
$966$	37.1384	−	21.6209i	1.19491	−	0.695641i
$967$	−42.6054			−1.37010			−0.685049	−	0.728497i	$-0.740219\pi$
$967$	−42.6054			−1.37010			−0.685049	+	0.728497i	$0.740219\pi$
$968$		0			0
$969$	−10.7460	−	18.6126i	−0.345211	−	0.597923i
$970$	3.40642	+	5.90009i	0.109374	+	0.189441i
$971$	−7.21841	+	12.5027i	−0.231650	+	0.401229i	−0.958294	−	0.285785i	$-0.907746\pi$
$971$	−7.21841	+	12.5027i	−0.231650	+	0.401229i	0.726644	+	0.687014i	$0.241079\pi$
$972$	−32.1447			−1.03104
$973$	−29.5789	−	16.9354i	−0.948256	−	0.542923i
$974$	73.4244			2.35267
$975$	−12.4366	+	21.5409i	−0.398292	+	0.689861i
$976$	−10.9035	−	18.8855i	−0.349014	−	0.604510i
$977$	−1.71748	−	2.97476i	−0.0549470	−	0.0951709i	0.837244	−	0.546830i	$-0.184166\pi$
$977$	−1.71748	−	2.97476i	−0.0549470	−	0.0951709i	−0.892191	+	0.451659i	$0.850832\pi$
$978$	28.7711	−	49.8330i	0.919998	−	1.59348i
$979$		0			0
$980$	−4.69397	−	7.99636i	−0.149943	−	0.255434i
$981$	−55.2317			−1.76341
$982$	19.0679	−	33.0265i	0.608480	−	1.05392i
$983$	−25.1403	−	43.5442i	−0.801850	−	1.38885i	−0.918397	−	0.395660i	$-0.870516\pi$
$983$	−25.1403	−	43.5442i	−0.801850	−	1.38885i	0.116547	−	0.993185i	$-0.462817\pi$
$984$	−28.4496	−	49.2762i	−0.906941	−	1.57087i
$985$	0.995746	−	1.72468i	0.0317271	−	0.0549530i
$986$	12.0263			0.382994
$987$	−30.5428	−	17.4873i	−0.972188	−	0.556626i
$988$	−44.2519			−1.40784
$989$	3.86873	−	6.70084i	0.123019	−	0.213074i
$990$		0			0
$991$	−11.9319	−	20.6667i	−0.379030	−	0.656500i	0.611891	−	0.790942i	$-0.290409\pi$
$991$	−11.9319	−	20.6667i	−0.379030	−	0.656500i	−0.990921	+	0.134442i	$0.957076\pi$
$992$	0.226992	−	0.393162i	0.00720701	−	0.0124829i
$993$	−46.7131			−1.48240
$994$	−32.2384	+	18.7683i	−1.02254	+	0.595294i
$995$	−6.61963			−0.209856
$996$	−72.1291	+	124.931i	−2.28550	+	3.95860i
$997$	6.21805	+	10.7700i	0.196928	+	0.341089i	0.947531	−	0.319665i	$-0.103570\pi$
$997$	6.21805	+	10.7700i	0.196928	+	0.341089i	−0.750603	+	0.660753i	$0.770237\pi$
$998$	−6.41837	−	11.1169i	−0.203170	−	0.351901i
$999$	−8.47923	+	14.6865i	−0.268271	+	0.464659i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	847.2.e.h.485.1		20
7.2	even	3		5929.2.a.by.1.10		10
7.4	even	3	inner	847.2.e.h.606.1		20
7.5	odd	6		5929.2.a.bz.1.10		10
11.2	odd	10		77.2.m.b.37.1	yes	40
11.3	even	5		847.2.n.h.9.5		40
11.4	even	5		847.2.n.h.632.1		40
11.5	even	5		847.2.n.j.366.1		40
11.6	odd	10		77.2.m.b.58.5	yes	40
11.7	odd	10		847.2.n.i.632.5		40
11.8	odd	10		847.2.n.i.9.1		40
11.9	even	5		847.2.n.j.807.5		40
11.10	odd	2		847.2.e.i.485.10		20
33.2	even	10		693.2.by.b.37.5		40
33.17	even	10		693.2.by.b.289.1		40
77.2	odd	30		539.2.f.h.246.5		20
77.4	even	15		847.2.n.h.753.5		40
77.6	even	10		539.2.q.h.520.5		40
77.13	even	10		539.2.q.h.422.1		40
77.17	even	30		539.2.q.h.410.1		40
77.18	odd	30		847.2.n.i.753.1		40
77.24	even	30		539.2.q.h.312.5		40
77.25	even	15		847.2.n.h.130.1		40
77.32	odd	6		847.2.e.i.606.10		20
77.39	odd	30		77.2.m.b.25.1	yes	40
77.46	odd	30		77.2.m.b.4.5	✓	40
77.53	even	15		847.2.n.j.81.1		40
77.54	even	6		5929.2.a.bx.1.1		10
77.60	even	15		847.2.n.j.487.5		40
77.61	even	30		539.2.f.g.344.5		20
77.65	odd	6		5929.2.a.bw.1.1		10
77.68	even	30		539.2.f.g.246.5		20
77.72	odd	30		539.2.f.h.344.5		20
77.74	odd	30		847.2.n.i.130.5		40
231.116	even	30		693.2.by.b.487.5		40
231.200	even	30		693.2.by.b.235.1		40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
77.2.m.b.4.5	✓	40	77.46	odd	30
77.2.m.b.25.1	yes	40	77.39	odd	30
77.2.m.b.37.1	yes	40	11.2	odd	10
77.2.m.b.58.5	yes	40	11.6	odd	10
539.2.f.g.246.5		20	77.68	even	30
539.2.f.g.344.5		20	77.61	even	30
539.2.f.h.246.5		20	77.2	odd	30
539.2.f.h.344.5		20	77.72	odd	30
539.2.q.h.312.5		40	77.24	even	30
539.2.q.h.410.1		40	77.17	even	30
539.2.q.h.422.1		40	77.13	even	10
539.2.q.h.520.5		40	77.6	even	10
693.2.by.b.37.5		40	33.2	even	10
693.2.by.b.235.1		40	231.200	even	30
693.2.by.b.289.1		40	33.17	even	10
693.2.by.b.487.5		40	231.116	even	30
847.2.e.h.485.1		20	1.1	even	1	trivial
847.2.e.h.606.1		20	7.4	even	3	inner
847.2.e.i.485.10		20	11.10	odd	2
847.2.e.i.606.10		20	77.32	odd	6
847.2.n.h.9.5		40	11.3	even	5
847.2.n.h.130.1		40	77.25	even	15
847.2.n.h.632.1		40	11.4	even	5
847.2.n.h.753.5		40	77.4	even	15
847.2.n.i.9.1		40	11.8	odd	10
847.2.n.i.130.5		40	77.74	odd	30
847.2.n.i.632.5		40	11.7	odd	10
847.2.n.i.753.1		40	77.18	odd	30
847.2.n.j.81.1		40	77.53	even	15
847.2.n.j.366.1		40	11.5	even	5
847.2.n.j.487.5		40	77.60	even	15
847.2.n.j.807.5		40	11.9	even	5
5929.2.a.bw.1.1		10	77.65	odd	6
5929.2.a.bx.1.1		10	77.54	even	6
5929.2.a.by.1.10		10	7.2	even	3
5929.2.a.bz.1.10		10	7.5	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 847 = 7 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	847.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.22380 + 2.11968i) q^{2} +(-1.45751 - 2.52448i) q^{3} +(-1.99536 - 3.45607i) q^{4} +(0.165961 - 0.287453i) q^{5} +7.13479 q^{6} +(2.29605 + 1.31460i) q^{7} +4.87248 q^{8} +(-2.74868 + 4.76085i) q^{9} +O(q^{10})\)	\(q+(-1.22380 + 2.11968i) q^{2} +(-1.45751 - 2.52448i) q^{3} +(-1.99536 - 3.45607i) q^{4} +(0.165961 - 0.287453i) q^{5} +7.13479 q^{6} +(2.29605 + 1.31460i) q^{7} +4.87248 q^{8} +(-2.74868 + 4.76085i) q^{9} +(0.406206 + 0.703570i) q^{10} +(-5.81652 + 10.0745i) q^{12} -1.74501 q^{13} +(-5.59643 + 3.25808i) q^{14} -0.967562 q^{15} +(-1.97221 + 3.41597i) q^{16} +(-0.580126 - 1.00481i) q^{17} +(-6.72765 - 11.6526i) q^{18} +(-3.17726 + 5.50317i) q^{19} -1.32461 q^{20} +(-0.0278291 - 7.71237i) q^{21} +(1.13826 - 1.97152i) q^{23} +(-7.10170 - 12.3005i) q^{24} +(2.44491 + 4.23471i) q^{25} +(2.13554 - 3.69886i) q^{26} +7.27984 q^{27} +(-0.0380986 - 10.5584i) q^{28} +4.23486 q^{29} +(1.18410 - 2.05092i) q^{30} +(-2.50494 - 4.33869i) q^{31} +(0.0453088 + 0.0784772i) q^{32} +2.83983 q^{34} +(0.758941 - 0.441834i) q^{35} +21.9384 q^{36} +(-1.16475 + 2.01741i) q^{37} +(-7.77664 - 13.4695i) q^{38} +(2.54337 + 4.40525i) q^{39} +(0.808644 - 1.40061i) q^{40} +4.00603 q^{41} +(16.3818 + 9.37940i) q^{42} +3.39882 q^{43} +(0.912348 + 1.58023i) q^{45} +(2.78599 + 4.82548i) q^{46} +(2.28169 - 3.95200i) q^{47} +11.4981 q^{48} +(3.54366 + 6.03676i) q^{49} -11.9683 q^{50} +(-1.69108 + 2.92904i) q^{51} +(3.48193 + 6.03087i) q^{52} +(2.47088 + 4.27969i) q^{53} +(-8.90906 + 15.4309i) q^{54} +(11.1874 + 6.40536i) q^{56} +18.5236 q^{57} +(-5.18261 + 8.97655i) q^{58} +(0.507637 + 0.879253i) q^{59} +(1.93064 + 3.34396i) q^{60} +(-2.76430 + 4.78790i) q^{61} +12.2622 q^{62} +(-12.5697 + 7.31772i) q^{63} -8.11064 q^{64} +(-0.289604 + 0.501609i) q^{65} +(5.34243 + 9.25335i) q^{67} +(-2.31512 + 4.00991i) q^{68} -6.63609 q^{69} +(0.00775593 + 2.14943i) q^{70} +5.76054 q^{71} +(-13.3929 + 23.1972i) q^{72} +(2.66384 + 4.61390i) q^{73} +(-2.85085 - 4.93781i) q^{74} +(7.12698 - 12.3443i) q^{75} +25.3591 q^{76} -12.4503 q^{78} +(1.95713 - 3.38985i) q^{79} +(0.654621 + 1.13384i) q^{80} +(-2.36442 - 4.09530i) q^{81} +(-4.90257 + 8.49151i) q^{82} +12.4007 q^{83} +(-26.5990 + 15.4852i) q^{84} -0.385114 q^{85} +(-4.15947 + 7.20441i) q^{86} +(-6.17236 - 10.6908i) q^{87} +(9.37654 - 16.2406i) q^{89} -4.46612 q^{90} +(-4.00662 - 2.29399i) q^{91} -9.08494 q^{92} +(-7.30197 + 12.6474i) q^{93} +(5.58465 + 9.67290i) q^{94} +(1.05460 + 1.82663i) q^{95} +(0.132076 - 0.228763i) q^{96} +8.38594 q^{97} +(-17.1327 + 0.123644i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - q^{2} + 3 q^{3} - 9 q^{4} + 2 q^{5} + 18 q^{6} + 11 q^{7} - 6 q^{8} - 9 q^{9}+O(q^{10}) \) 20 * q - q^2 + 3 * q^3 - 9 * q^4 + 2 * q^5 + 18 * q^6 + 11 * q^7 - 6 * q^8 - 9 * q^9	\( 20 q - q^{2} + 3 q^{3} - 9 q^{4} + 2 q^{5} + 18 q^{6} + 11 q^{7} - 6 q^{8} - 9 q^{9} - 7 q^{10} - 9 q^{12} + 2 q^{13} - 19 q^{14} - 2 q^{15} - 15 q^{16} - 19 q^{17} - 17 q^{18} - 28 q^{19} - 10 q^{20} + q^{21} - 7 q^{23} - 19 q^{24} + 8 q^{25} + 5 q^{26} + 12 q^{27} - 8 q^{28} - 30 q^{29} + 22 q^{30} + 14 q^{31} + 15 q^{32} + 24 q^{34} - 8 q^{35} + 32 q^{36} - 13 q^{37} - 24 q^{38} - 4 q^{39} - 10 q^{40} + 70 q^{41} + 25 q^{42} + 36 q^{43} - 8 q^{45} - 9 q^{46} - 16 q^{47} - 66 q^{48} - 25 q^{49} + 12 q^{50} + 21 q^{51} + 4 q^{52} + 9 q^{53} - 17 q^{54} + 12 q^{56} + 8 q^{57} + 9 q^{58} - 12 q^{59} + 21 q^{60} - 20 q^{61} + 76 q^{62} - 12 q^{63} - 58 q^{64} + 20 q^{65} - 19 q^{67} - 56 q^{68} + 18 q^{69} + 21 q^{70} + 30 q^{71} + 4 q^{72} - 3 q^{73} - 42 q^{74} + 27 q^{75} + 48 q^{76} - 50 q^{78} + 32 q^{79} + 6 q^{80} + 46 q^{81} + 18 q^{82} + 58 q^{83} - 73 q^{84} - 46 q^{85} - 9 q^{86} - 24 q^{87} - 5 q^{89} + 24 q^{90} + 28 q^{91} + 30 q^{92} + q^{93} + 19 q^{94} - q^{95} - 46 q^{96} + 8 q^{97} - 58 q^{98}+O(q^{100}) \) 20 * q - q^2 + 3 * q^3 - 9 * q^4 + 2 * q^5 + 18 * q^6 + 11 * q^7 - 6 * q^8 - 9 * q^9 - 7 * q^10 - 9 * q^12 + 2 * q^13 - 19 * q^14 - 2 * q^15 - 15 * q^16 - 19 * q^17 - 17 * q^18 - 28 * q^19 - 10 * q^20 + q^21 - 7 * q^23 - 19 * q^24 + 8 * q^25 + 5 * q^26 + 12 * q^27 - 8 * q^28 - 30 * q^29 + 22 * q^30 + 14 * q^31 + 15 * q^32 + 24 * q^34 - 8 * q^35 + 32 * q^36 - 13 * q^37 - 24 * q^38 - 4 * q^39 - 10 * q^40 + 70 * q^41 + 25 * q^42 + 36 * q^43 - 8 * q^45 - 9 * q^46 - 16 * q^47 - 66 * q^48 - 25 * q^49 + 12 * q^50 + 21 * q^51 + 4 * q^52 + 9 * q^53 - 17 * q^54 + 12 * q^56 + 8 * q^57 + 9 * q^58 - 12 * q^59 + 21 * q^60 - 20 * q^61 + 76 * q^62 - 12 * q^63 - 58 * q^64 + 20 * q^65 - 19 * q^67 - 56 * q^68 + 18 * q^69 + 21 * q^70 + 30 * q^71 + 4 * q^72 - 3 * q^73 - 42 * q^74 + 27 * q^75 + 48 * q^76 - 50 * q^78 + 32 * q^79 + 6 * q^80 + 46 * q^81 + 18 * q^82 + 58 * q^83 - 73 * q^84 - 46 * q^85 - 9 * q^86 - 24 * q^87 - 5 * q^89 + 24 * q^90 + 28 * q^91 + 30 * q^92 + q^93 + 19 * q^94 - q^95 - 46 * q^96 + 8 * q^97 - 58 * q^98

Introduction

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