LMFDB - Embedded newform 770.2.n.k.141.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [770,2,Mod(71,770)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(770, base_ring=CyclotomicField(10))

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

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

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

chi := DirichletCharacter("770.71");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 770 = 2 \cdot 5 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	770.n (of order $5$, degree $4$, 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:	$6.14848095564$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{5})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 5 x^{15} + 18 x^{14} - 35 x^{13} + 89 x^{12} - 185 x^{11} + 837 x^{10} - 1660 x^{9} + 4196 x^{8} + \cdots + 25 $ x^16 - 5x^15 + 18x^14 - 35x^13 + 89x^12 - 185x^11 + 837x^10 - 1660x^9 + 4196x^8 - 8420x^7 + 13485x^6 - 14630x^5 + 11615x^4 - 5200x^3 + 1425x^2 - 225*x + 25
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			141.4
Root			$-2.05435 - 1.49258i$ of defining polynomial
Character	$\chi$	$=$	770.141
Dual form			770.2.n.k.71.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.309017 - 0.951057i) q^{2} +(2.05435 - 1.49258i) q^{3} +(-0.809017 - 0.587785i) q^{4} +(-0.309017 - 0.951057i) q^{5} +(-0.784693 - 2.41504i) q^{6} +(0.809017 + 0.587785i) q^{7} +(-0.809017 + 0.587785i) q^{8} +(1.06554 - 3.27939i) q^{9} +O(q^{10})$	\(q+(0.309017 - 0.951057i) q^{2} +(2.05435 - 1.49258i) q^{3} +(-0.809017 - 0.587785i) q^{4} +(-0.309017 - 0.951057i) q^{5} +(-0.784693 - 2.41504i) q^{6} +(0.809017 + 0.587785i) q^{7} +(-0.809017 + 0.587785i) q^{8} +(1.06554 - 3.27939i) q^{9} -1.00000 q^{10} +(1.57392 - 2.91938i) q^{11} -2.53932 q^{12} +(-1.27148 + 3.91321i) q^{13} +(0.809017 - 0.587785i) q^{14} +(-2.05435 - 1.49258i) q^{15} +(0.309017 + 0.951057i) q^{16} +(-2.11624 - 6.51311i) q^{17} +(-2.78961 - 2.02677i) q^{18} +(5.35695 - 3.89205i) q^{19} +(-0.309017 + 0.951057i) q^{20} +2.53932 q^{21} +(-2.29013 - 2.39902i) q^{22} -3.13877 q^{23} +(-0.784693 + 2.41504i) q^{24} +(-0.809017 + 0.587785i) q^{25} +(3.32878 + 2.41850i) q^{26} +(-0.351660 - 1.08230i) q^{27} +(-0.309017 - 0.951057i) q^{28} +(-4.44605 - 3.23024i) q^{29} +(-2.05435 + 1.49258i) q^{30} +(-1.72249 + 5.30127i) q^{31} +1.00000 q^{32} +(-1.12402 - 8.34663i) q^{33} -6.84829 q^{34} +(0.309017 - 0.951057i) q^{35} +(-2.78961 + 2.02677i) q^{36} +(6.29838 + 4.57604i) q^{37} +(-2.04617 - 6.29747i) q^{38} +(3.22869 + 9.93689i) q^{39} +(0.809017 + 0.587785i) q^{40} +(-2.35226 + 1.70902i) q^{41} +(0.784693 - 2.41504i) q^{42} +3.23479 q^{43} +(-2.98929 + 1.43670i) q^{44} -3.44815 q^{45} +(-0.969934 + 2.98515i) q^{46} +(1.21343 - 0.881607i) q^{47} +(2.05435 + 1.49258i) q^{48} +(0.309017 + 0.951057i) q^{49} +(0.309017 + 0.951057i) q^{50} +(-14.0688 - 10.2216i) q^{51} +(3.32878 - 2.41850i) q^{52} +(-3.43975 + 10.5865i) q^{53} -1.13800 q^{54} +(-3.26286 - 0.594745i) q^{55} -1.00000 q^{56} +(5.19589 - 15.9913i) q^{57} +(-4.44605 + 3.23024i) q^{58} +(6.00637 + 4.36389i) q^{59} +(0.784693 + 2.41504i) q^{60} +(-0.705073 - 2.16999i) q^{61} +(4.50953 + 3.27637i) q^{62} +(2.78961 - 2.02677i) q^{63} +(0.309017 - 0.951057i) q^{64} +4.11459 q^{65} +(-8.28546 - 1.51025i) q^{66} +14.1969 q^{67} +(-2.11624 + 6.51311i) q^{68} +(-6.44815 + 4.68485i) q^{69} +(-0.809017 - 0.587785i) q^{70} +(0.0188133 + 0.0579014i) q^{71} +(1.06554 + 3.27939i) q^{72} +(3.16555 + 2.29991i) q^{73} +(6.29838 - 4.57604i) q^{74} +(-0.784693 + 2.41504i) q^{75} -6.62155 q^{76} +(2.98929 - 1.43670i) q^{77} +10.4483 q^{78} +(-1.31018 + 4.03232i) q^{79} +(0.809017 - 0.587785i) q^{80} +(6.03099 + 4.38177i) q^{81} +(0.898483 + 2.76525i) q^{82} +(3.16642 + 9.74525i) q^{83} +(-2.05435 - 1.49258i) q^{84} +(-5.54038 + 4.02533i) q^{85} +(0.999606 - 3.07647i) q^{86} -13.9551 q^{87} +(0.442644 + 3.28695i) q^{88} -6.54394 q^{89} +(-1.06554 + 3.27939i) q^{90} +(-3.32878 + 2.41850i) q^{91} +(2.53932 + 1.84492i) q^{92} +(4.37395 + 13.4616i) q^{93} +(-0.463488 - 1.42647i) q^{94} +(-5.35695 - 3.89205i) q^{95} +(2.05435 - 1.49258i) q^{96} +(-0.213537 + 0.657198i) q^{97} +1.00000 q^{98} +(-7.89671 - 8.27219i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 4 q^{2} - 5 q^{3} - 4 q^{4} + 4 q^{5} + 5 q^{6} + 4 q^{7} - 4 q^{8} + q^{9}+O(q^{10}) $ 16 * q - 4 * q^2 - 5 * q^3 - 4 * q^4 + 4 * q^5 + 5 * q^6 + 4 * q^7 - 4 * q^8 + q^9	\( 16 q - 4 q^{2} - 5 q^{3} - 4 q^{4} + 4 q^{5} + 5 q^{6} + 4 q^{7} - 4 q^{8} + q^{9} - 16 q^{10} - 2 q^{11} + 8 q^{13} + 4 q^{14} + 5 q^{15} - 4 q^{16} - 13 q^{17} - 9 q^{18} + 15 q^{19} + 4 q^{20} - 2 q^{22} + 20 q^{23} + 5 q^{24} - 4 q^{25} - 7 q^{26} + 10 q^{27} + 4 q^{28} - 14 q^{29} + 5 q^{30} - 6 q^{31} + 16 q^{32} - 25 q^{33} + 12 q^{34} - 4 q^{35} - 9 q^{36} + 28 q^{37} - 20 q^{38} + 15 q^{39} + 4 q^{40} + 2 q^{41} - 5 q^{42} - 10 q^{43} + 3 q^{44} - 16 q^{45} - 10 q^{46} - 10 q^{47} - 5 q^{48} - 4 q^{49} - 4 q^{50} - 42 q^{51} - 7 q^{52} - 2 q^{53} - 3 q^{55} - 16 q^{56} + 21 q^{57} - 14 q^{58} + 7 q^{59} - 5 q^{60} + 4 q^{61} + 14 q^{62} + 9 q^{63} - 4 q^{64} + 2 q^{65} - 10 q^{66} + 66 q^{67} - 13 q^{68} - 64 q^{69} - 4 q^{70} + 2 q^{71} + q^{72} + 12 q^{73} + 28 q^{74} + 5 q^{75} + 10 q^{76} - 3 q^{77} + 70 q^{78} + 2 q^{79} + 4 q^{80} - 30 q^{81} - 13 q^{82} - 5 q^{83} + 5 q^{84} - 7 q^{85} + 5 q^{86} - 24 q^{87} - 2 q^{88} + 2 q^{89} - q^{90} + 7 q^{91} - 38 q^{93} + 25 q^{94} - 15 q^{95} - 5 q^{96} + 22 q^{97} + 16 q^{98} - 18 q^{99}+O(q^{100}) \) 16 * q - 4 * q^2 - 5 * q^3 - 4 * q^4 + 4 * q^5 + 5 * q^6 + 4 * q^7 - 4 * q^8 + q^9 - 16 * q^10 - 2 * q^11 + 8 * q^13 + 4 * q^14 + 5 * q^15 - 4 * q^16 - 13 * q^17 - 9 * q^18 + 15 * q^19 + 4 * q^20 - 2 * q^22 + 20 * q^23 + 5 * q^24 - 4 * q^25 - 7 * q^26 + 10 * q^27 + 4 * q^28 - 14 * q^29 + 5 * q^30 - 6 * q^31 + 16 * q^32 - 25 * q^33 + 12 * q^34 - 4 * q^35 - 9 * q^36 + 28 * q^37 - 20 * q^38 + 15 * q^39 + 4 * q^40 + 2 * q^41 - 5 * q^42 - 10 * q^43 + 3 * q^44 - 16 * q^45 - 10 * q^46 - 10 * q^47 - 5 * q^48 - 4 * q^49 - 4 * q^50 - 42 * q^51 - 7 * q^52 - 2 * q^53 - 3 * q^55 - 16 * q^56 + 21 * q^57 - 14 * q^58 + 7 * q^59 - 5 * q^60 + 4 * q^61 + 14 * q^62 + 9 * q^63 - 4 * q^64 + 2 * q^65 - 10 * q^66 + 66 * q^67 - 13 * q^68 - 64 * q^69 - 4 * q^70 + 2 * q^71 + q^72 + 12 * q^73 + 28 * q^74 + 5 * q^75 + 10 * q^76 - 3 * q^77 + 70 * q^78 + 2 * q^79 + 4 * q^80 - 30 * q^81 - 13 * q^82 - 5 * q^83 + 5 * q^84 - 7 * q^85 + 5 * q^86 - 24 * q^87 - 2 * q^88 + 2 * q^89 - q^90 + 7 * q^91 - 38 * q^93 + 25 * q^94 - 15 * q^95 - 5 * q^96 + 22 * q^97 + 16 * q^98 - 18 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/770\mathbb{Z}\right)^\times$.

$n$	$211$	$617$	$661$
$\chi(n)$	$e\left(\frac{3}{5}\right)$	$1$	$1$

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 $

$2$	0.309017	−	0.951057i	0.218508	−	0.672499i
$2$	0.309017	−	0.951057i	0.218508	−	0.672499i
$3$	2.05435	−	1.49258i	1.18608	−	0.861739i	0.193237	−	0.981152i	$-0.438101\pi$
$3$	2.05435	−	1.49258i	1.18608	−	0.861739i	0.992845	+	0.119413i	$0.0381014\pi$
$4$	−0.809017	−	0.587785i	−0.404508	−	0.293893i
$5$	−0.309017	−	0.951057i	−0.138197	−	0.425325i
$5$	−0.309017	−	0.951057i	−0.138197	−	0.425325i
$6$	−0.784693	−	2.41504i	−0.320350	−	0.985935i
$7$	0.809017	+	0.587785i	0.305780	+	0.222162i
$7$	0.809017	+	0.587785i	0.305780	+	0.222162i
$8$	−0.809017	+	0.587785i	−0.286031	+	0.207813i
$9$	1.06554	−	3.27939i	0.355179	−	1.09313i
$10$	−1.00000			−0.316228
$11$	1.57392	−	2.91938i	0.474554	−	0.880227i
$11$	1.57392	−	2.91938i	0.474554	−	0.880227i
$12$	−2.53932			−0.733039
$13$	−1.27148	+	3.91321i	−0.352645	+	1.08533i	0.604718	+	0.796440i	$0.293286\pi$
$13$	−1.27148	+	3.91321i	−0.352645	+	1.08533i	−0.957363	+	0.288889i	$0.906714\pi$
$14$	0.809017	−	0.587785i	0.216219	−	0.157092i
$15$	−2.05435	−	1.49258i	−0.530432	−	0.385381i
$16$	0.309017	+	0.951057i	0.0772542	+	0.237764i
$17$	−2.11624	−	6.51311i	−0.513263	−	1.57966i	−0.786420	−	0.617692i	$-0.788068\pi$
$17$	−2.11624	−	6.51311i	−0.513263	−	1.57966i	0.273157	−	0.961970i	$-0.411932\pi$
$18$	−2.78961	−	2.02677i	−0.657518	−	0.477715i
$19$	5.35695	−	3.89205i	1.22897	−	0.892898i	0.232156	−	0.972679i	$-0.425422\pi$
$19$	5.35695	−	3.89205i	1.22897	−	0.892898i	0.996812	+	0.0797809i	$0.0254221\pi$
$20$	−0.309017	+	0.951057i	−0.0690983	+	0.212663i
$21$	2.53932			0.554125
$22$	−2.29013	−	2.39902i	−0.488257	−	0.511473i
$23$	−3.13877			−0.654479			−0.327240	−	0.944941i	$-0.606118\pi$
$23$	−3.13877			−0.654479			−0.327240	+	0.944941i	$0.606118\pi$
$24$	−0.784693	+	2.41504i	−0.160175	+	0.492967i
$25$	−0.809017	+	0.587785i	−0.161803	+	0.117557i
$26$	3.32878	+	2.41850i	0.652827	+	0.474306i
$27$	−0.351660	−	1.08230i	−0.0676770	−	0.208288i
$28$	−0.309017	−	0.951057i	−0.0583987	−	0.179733i
$29$	−4.44605	−	3.23024i	−0.825610	−	0.599841i	0.0927040	−	0.995694i	$-0.470449\pi$
$29$	−4.44605	−	3.23024i	−0.825610	−	0.599841i	−0.918314	+	0.395853i	$0.870449\pi$
$30$	−2.05435	+	1.49258i	−0.375072	+	0.272506i
$31$	−1.72249	+	5.30127i	−0.309368	+	0.952137i	0.668643	+	0.743583i	$0.266875\pi$
$31$	−1.72249	+	5.30127i	−0.309368	+	0.952137i	−0.978011	+	0.208553i	$0.933125\pi$
$32$	1.00000			0.176777
$33$	−1.12402	−	8.34663i	−0.195666	−	1.45296i
$34$	−6.84829			−1.17447
$35$	0.309017	−	0.951057i	0.0522334	−	0.160758i
$36$	−2.78961	+	2.02677i	−0.464935	+	0.337795i
$37$	6.29838	+	4.57604i	1.03545	+	0.752296i	0.969392	−	0.245519i	$-0.0789585\pi$
$37$	6.29838	+	4.57604i	1.03545	+	0.752296i	0.0660556	+	0.997816i	$0.478959\pi$
$38$	−2.04617	−	6.29747i	−0.331933	−	1.02158i
$39$	3.22869	+	9.93689i	0.517005	+	1.59118i
$40$	0.809017	+	0.587785i	0.127917	+	0.0929370i
$41$	−2.35226	+	1.70902i	−0.367361	+	0.266904i	−0.756116	−	0.654438i	$-0.772905\pi$
$41$	−2.35226	+	1.70902i	−0.367361	+	0.266904i	0.388755	+	0.921341i	$0.372905\pi$
$42$	0.784693	−	2.41504i	0.121081	−	0.372648i
$43$	3.23479			0.493301			0.246651	−	0.969104i	$-0.420670\pi$
$43$	3.23479			0.493301			0.246651	+	0.969104i	$0.420670\pi$
$44$	−2.98929	+	1.43670i	−0.450653	+	0.216591i
$45$	−3.44815			−0.514020
$46$	−0.969934	+	2.98515i	−0.143009	+	0.440136i
$47$	1.21343	−	0.881607i	0.176997	−	0.128596i	−0.495760	−	0.868460i	$-0.665110\pi$
$47$	1.21343	−	0.881607i	0.176997	−	0.128596i	0.672756	+	0.739864i	$0.265110\pi$
$48$	2.05435	+	1.49258i	0.296520	+	0.215435i
$49$	0.309017	+	0.951057i	0.0441453	+	0.135865i
$50$	0.309017	+	0.951057i	0.0437016	+	0.134500i
$51$	−14.0688	−	10.2216i	−1.97003	−	1.43131i
$52$	3.32878	−	2.41850i	0.461618	−	0.335385i
$53$	−3.43975	+	10.5865i	−0.472486	+	1.45416i	0.376832	+	0.926282i	$0.377013\pi$
$53$	−3.43975	+	10.5865i	−0.472486	+	1.45416i	−0.849318	+	0.527881i	$0.822987\pi$
$54$	−1.13800			−0.154862
$55$	−3.26286	−	0.594745i	−0.439964	−	0.0801954i
$56$	−1.00000			−0.133631
$57$	5.19589	−	15.9913i	0.688212	−	2.11810i
$58$	−4.44605	+	3.23024i	−0.583794	+	0.424151i
$59$	6.00637	+	4.36389i	0.781963	+	0.568129i	0.905568	−	0.424202i	$-0.139445\pi$
$59$	6.00637	+	4.36389i	0.781963	+	0.568129i	−0.123604	+	0.992332i	$0.539445\pi$
$60$	0.784693	+	2.41504i	0.101303	+	0.311780i
$61$	−0.705073	−	2.16999i	−0.0902753	−	0.277839i	0.895718	−	0.444622i	$-0.146662\pi$
$61$	−0.705073	−	2.16999i	−0.0902753	−	0.277839i	−0.985994	+	0.166783i	$0.946662\pi$
$62$	4.50953	+	3.27637i	0.572711	+	0.416099i
$63$	2.78961	−	2.02677i	0.351458	−	0.255349i
$64$	0.309017	−	0.951057i	0.0386271	−	0.118882i
$65$	4.11459			0.510352
$66$	−8.28546	−	1.51025i	−1.01987	−	0.185899i
$67$	14.1969			1.73442			0.867212	−	0.497939i	$-0.165910\pi$
$67$	14.1969			1.73442			0.867212	+	0.497939i	$0.165910\pi$
$68$	−2.11624	+	6.51311i	−0.256632	+	0.789831i
$69$	−6.44815	+	4.68485i	−0.776266	+	0.563990i
$70$	−0.809017	−	0.587785i	−0.0966960	−	0.0702538i
$71$	0.0188133	+	0.0579014i	0.00223273	+	0.00687163i	0.952167	−	0.305579i	$-0.0988501\pi$
$71$	0.0188133	+	0.0579014i	0.00223273	+	0.00687163i	−0.949934	+	0.312451i	$0.898850\pi$
$72$	1.06554	+	3.27939i	0.125575	+	0.386479i
$73$	3.16555	+	2.29991i	0.370500	+	0.269184i	0.757418	−	0.652930i	$-0.226460\pi$
$73$	3.16555	+	2.29991i	0.370500	+	0.269184i	−0.386918	+	0.922114i	$0.626460\pi$
$74$	6.29838	−	4.57604i	0.732172	−	0.531954i
$75$	−0.784693	+	2.41504i	−0.0906086	+	0.278865i
$76$	−6.62155			−0.759544
$77$	2.98929	−	1.43670i	0.340662	−	0.163728i
$78$	10.4483			1.18303
$79$	−1.31018	+	4.03232i	−0.147407	+	0.453671i	−0.997313	−	0.0732634i	$-0.976659\pi$
$79$	−1.31018	+	4.03232i	−0.147407	+	0.453671i	0.849906	+	0.526934i	$0.176659\pi$
$80$	0.809017	−	0.587785i	0.0904508	−	0.0657164i
$81$	6.03099	+	4.38177i	0.670110	+	0.486863i
$82$	0.898483	+	2.76525i	0.0992209	+	0.305371i
$83$	3.16642	+	9.74525i	0.347560	+	1.06968i	0.960199	+	0.279317i	$0.0901081\pi$
$83$	3.16642	+	9.74525i	0.347560	+	1.06968i	−0.612639	+	0.790363i	$0.709892\pi$
$84$	−2.05435	−	1.49258i	−0.224148	−	0.162853i
$85$	−5.54038	+	4.02533i	−0.600939	+	0.436608i
$86$	0.999606	−	3.07647i	0.107790	−	0.331744i
$87$	−13.9551			−1.49615
$88$	0.442644	+	3.28695i	0.0471861	+	0.350390i
$89$	−6.54394			−0.693656			−0.346828	−	0.937929i	$-0.612741\pi$
$89$	−6.54394			−0.693656			−0.346828	+	0.937929i	$0.612741\pi$
$90$	−1.06554	+	3.27939i	−0.112317	+	0.345678i
$91$	−3.32878	+	2.41850i	−0.348950	+	0.253527i
$92$	2.53932	+	1.84492i	0.264742	+	0.192347i
$93$	4.37395	+	13.4616i	0.453557	+	1.39591i
$94$	−0.463488	−	1.42647i	−0.0478052	−	0.147129i
$95$	−5.35695	−	3.89205i	−0.549611	−	0.399316i
$96$	2.05435	−	1.49258i	0.209672	−	0.152335i
$97$	−0.213537	+	0.657198i	−0.0216814	+	0.0667284i	−0.961312	−	0.275463i	$-0.911169\pi$
$97$	−0.213537	+	0.657198i	−0.0216814	+	0.0667284i	0.939630	+	0.342191i	$0.111169\pi$
$98$	1.00000			0.101015
$99$	−7.89671	−	8.27219i	−0.793649	−	0.831386i
$100$	1.00000			0.100000
$101$	4.51753	−	13.9035i	0.449511	−	1.38345i	−0.427949	−	0.903803i	$-0.640764\pi$
$101$	4.51753	−	13.9035i	0.449511	−	1.38345i	0.877460	−	0.479649i	$-0.159236\pi$
$102$	−14.0688	+	10.2216i	−1.39302	+	1.01209i
$103$	−0.868543	−	0.631033i	−0.0855800	−	0.0621775i	0.544172	−	0.838973i	$-0.316844\pi$
$103$	−0.868543	−	0.631033i	−0.0855800	−	0.0621775i	−0.629753	+	0.776796i	$0.716844\pi$
$104$	−1.27148	−	3.91321i	−0.124679	−	0.383722i
$105$	−0.784693	−	2.41504i	−0.0765782	−	0.235684i
$106$	9.00539	+	6.54280i	0.874680	+	0.635493i
$107$	15.2727	−	11.0963i	1.47647	−	1.07272i	0.497793	−	0.867296i	$-0.334144\pi$
$107$	15.2727	−	11.0963i	1.47647	−	1.07272i	0.978674	−	0.205420i	$-0.0658559\pi$
$108$	−0.351660	+	1.08230i	−0.0338385	+	0.104144i
$109$	4.22315			0.404504			0.202252	−	0.979333i	$-0.435174\pi$
$109$	4.22315			0.404504			0.202252	+	0.979333i	$0.435174\pi$
$110$	−1.57392	+	2.91938i	−0.150067	+	0.278352i
$111$	19.7692			1.87641
$112$	−0.309017	+	0.951057i	−0.0291994	+	0.0898664i
$113$	−5.95877	+	4.32930i	−0.560554	+	0.407267i	−0.831662	−	0.555283i	$-0.812610\pi$
$113$	−5.95877	+	4.32930i	−0.560554	+	0.407267i	0.271107	+	0.962549i	$0.412610\pi$
$114$	−13.6030	−	9.88317i	−1.27404	−	0.925643i
$115$	0.969934	+	2.98515i	0.0904468	+	0.278367i
$116$	1.69824	+	5.22664i	0.157677	+	0.485281i
$117$	11.4781	+	8.33934i	1.06115	+	0.770972i
$118$	6.00637	−	4.36389i	0.552931	−	0.401728i
$119$	2.11624	−	6.51311i	0.193995	−	0.597056i
$120$	2.53932			0.231807
$121$	−6.04558	−	9.18972i	−0.549598	−	0.835429i
$122$	−2.28166			−0.206572
$123$	−2.28154	+	7.02185i	−0.205719	+	0.633139i
$124$	4.50953	−	3.27637i	0.404968	−	0.294226i
$125$	0.809017	+	0.587785i	0.0723607	+	0.0525731i
$126$	−1.06554	−	3.27939i	−0.0949256	−	0.292151i
$127$	−4.63622	−	14.2688i	−0.411398	−	1.26615i	−0.915433	−	0.402470i	$-0.868152\pi$
$127$	−4.63622	−	14.2688i	−0.411398	−	1.26615i	0.504035	−	0.863683i	$-0.331848\pi$
$128$	−0.809017	−	0.587785i	−0.0715077	−	0.0519534i
$129$	6.64541	−	4.82817i	0.585096	−	0.425097i
$130$	1.27148	−	3.91321i	0.111516	−	0.343211i
$131$	−6.77296			−0.591757			−0.295878	−	0.955226i	$-0.595612\pi$
$131$	−6.77296			−0.591757			−0.295878	+	0.955226i	$0.595612\pi$
$132$	−3.99668	+	7.41325i	−0.347866	+	0.645240i
$133$	6.62155			0.574161
$134$	4.38707	−	13.5020i	0.378986	−	1.16640i
$135$	−0.920658	+	0.668897i	−0.0792376	+	0.0575695i
$136$	5.54038	+	4.02533i	0.475084	+	0.345169i
$137$	−2.82781	−	8.70311i	−0.241596	−	0.743557i	−0.996178	−	0.0873506i	$-0.972160\pi$
$137$	−2.82781	−	8.70311i	−0.241596	−	0.743557i	0.754581	−	0.656207i	$-0.227840\pi$
$138$	2.46297	+	7.58025i	0.209662	+	0.645274i
$139$	−12.8740	−	9.35348i	−1.09195	−	0.793352i	−0.112227	−	0.993683i	$-0.535798\pi$
$139$	−12.8740	−	9.35348i	−1.09195	−	0.793352i	−0.979728	+	0.200331i	$0.935798\pi$
$140$	−0.809017	+	0.587785i	−0.0683744	+	0.0496769i
$141$	1.17695	−	3.62227i	0.0991167	−	0.305050i
$142$	0.0608812			0.00510903
$143$	9.42295	+	9.87100i	0.787987	+	0.825454i
$144$	3.44815			0.287346
$145$	−1.69824	+	5.22664i	−0.141031	+	0.434049i
$146$	3.16555	−	2.29991i	0.261983	−	0.190342i
$147$	2.05435	+	1.49258i	0.169440	+	0.123106i
$148$	−2.40577	−	7.40419i	−0.197753	−	0.608621i
$149$	2.97604	+	9.15932i	0.243807	+	0.750361i	0.995830	+	0.0912245i	$0.0290781\pi$
$149$	2.97604	+	9.15932i	0.243807	+	0.750361i	−0.752023	+	0.659137i	$0.770922\pi$
$150$	2.05435	+	1.49258i	0.167737	+	0.121868i
$151$	−16.4670	+	11.9640i	−1.34006	+	0.973613i	−0.340622	+	0.940200i	$0.610638\pi$
$151$	−16.4670	+	11.9640i	−1.34006	+	0.973613i	−0.999442	+	0.0334132i	$0.989362\pi$
$152$	−2.04617	+	6.29747i	−0.165966	+	0.510792i
$153$	−23.6139			−1.90907
$154$	−0.442644	−	3.28695i	−0.0356693	−	0.264870i
$155$	5.57409			0.447721
$156$	3.22869	−	9.93689i	0.258502	−	0.795588i
$157$	4.86753	−	3.53647i	0.388472	−	0.282241i	−0.376357	−	0.926475i	$-0.622823\pi$
$157$	4.86753	−	3.53647i	0.388472	−	0.282241i	0.764829	+	0.644233i	$0.222823\pi$
$158$	3.43009	+	2.49211i	0.272884	+	0.198261i
$159$	8.73463	+	26.8824i	0.692701	+	2.13192i
$160$	−0.309017	−	0.951057i	−0.0244299	−	0.0751876i
$161$	−2.53932	−	1.84492i	−0.200127	−	0.145400i
$162$	6.03099	−	4.38177i	0.473839	−	0.344264i
$163$	−2.66203	+	8.19288i	−0.208506	+	0.641716i	0.791045	+	0.611758i	$0.209537\pi$
$163$	−2.66203	+	8.19288i	−0.208506	+	0.641716i	−0.999551	+	0.0299581i	$0.990463\pi$
$164$	2.90755			0.227042
$165$	−7.59078	+	3.64825i	−0.590941	+	0.284016i
$166$	10.2468			0.795303
$167$	−2.78607	+	8.57463i	−0.215592	+	0.663525i	0.783519	+	0.621368i	$0.213423\pi$
$167$	−2.78607	+	8.57463i	−0.215592	+	0.663525i	−0.999111	+	0.0421565i	$0.986577\pi$
$168$	−2.05435	+	1.49258i	−0.158497	+	0.115155i
$169$	−3.17933	−	2.30992i	−0.244564	−	0.177686i
$170$	2.11624	+	6.51311i	0.162308	+	0.499533i
$171$	−7.05551	−	21.7146i	−0.539548	−	1.66056i
$172$	−2.61700	−	1.90136i	−0.199545	−	0.144978i
$173$	10.4677	−	7.60521i	0.795842	−	0.578213i	−0.113849	−	0.993498i	$-0.536318\pi$
$173$	10.4677	−	7.60521i	0.795842	−	0.578213i	0.909691	+	0.415285i	$0.136318\pi$
$174$	−4.31237	+	13.2721i	−0.326920	+	1.00616i
$175$	−1.00000			−0.0755929
$176$	3.26286	+	0.594745i	0.245948	+	0.0448306i
$177$	18.8526			1.41705
$178$	−2.02219	+	6.22365i	−0.151569	+	0.466483i
$179$	−12.7503	+	9.26363i	−0.953002	+	0.692396i	−0.951515	−	0.307603i	$-0.900473\pi$
$179$	−12.7503	+	9.26363i	−0.953002	+	0.692396i	−0.00148685	+	0.999999i	$0.500473\pi$
$180$	2.78961	+	2.02677i	0.207925	+	0.151067i
$181$	−4.51455	−	13.8943i	−0.335564	−	1.03276i	−0.966444	−	0.256878i	$-0.917306\pi$
$181$	−4.51455	−	13.8943i	−0.335564	−	1.03276i	0.630880	−	0.775880i	$-0.282694\pi$
$182$	1.27148	+	3.91321i	0.0942483	+	0.290066i
$183$	−4.68734	−	3.40555i	−0.346498	−	0.251746i
$184$	2.53932	−	1.84492i	0.187201	−	0.136010i
$185$	2.40577	−	7.40419i	0.176876	−	0.544367i
$186$	14.1544			1.03785
$187$	−22.3450	−	4.07299i	−1.63403	−	0.297846i
$188$	−1.49988			−0.109390
$189$	0.351660	−	1.08230i	0.0255795	−	0.0787256i
$190$	−5.35695	+	3.89205i	−0.388634	+	0.282359i
$191$	14.5352	+	10.5604i	1.05173	+	0.764125i	0.972540	−	0.232734i	$-0.0747673\pi$
$191$	14.5352	+	10.5604i	1.05173	+	0.764125i	0.0791880	+	0.996860i	$0.474767\pi$
$192$	−0.784693	−	2.41504i	−0.0566304	−	0.174290i
$193$	7.36017	+	22.6523i	0.529797	+	1.63055i	0.754630	+	0.656150i	$0.227816\pi$
$193$	7.36017	+	22.6523i	0.529797	+	1.63055i	−0.224833	+	0.974397i	$0.572184\pi$
$194$	0.559046	+	0.406171i	0.0401372	+	0.0291614i
$195$	8.45283	−	6.14134i	0.605320	−	0.439790i
$196$	0.309017	−	0.951057i	0.0220726	−	0.0679326i
$197$	−1.85551			−0.132200			−0.0660998	−	0.997813i	$-0.521056\pi$
$197$	−1.85551			−0.132200			−0.0660998	+	0.997813i	$0.521056\pi$
$198$	−10.3075	+	4.95397i	−0.732525	+	0.352063i
$199$	21.8206			1.54682			0.773411	−	0.633905i	$-0.218549\pi$
$199$	21.8206			1.54682			0.773411	+	0.633905i	$0.218549\pi$
$200$	0.309017	−	0.951057i	0.0218508	−	0.0672499i
$201$	29.1654	−	21.1899i	2.05717	−	1.49462i
$202$	−11.8270	−	8.59285i	−0.832148	−	0.604591i
$203$	−1.69824	−	5.22664i	−0.119193	−	0.366838i
$204$	5.37381	+	16.5389i	0.376242	+	1.15795i
$205$	2.35226	+	1.70902i	0.164289	+	0.119363i
$206$	−0.868543	+	0.631033i	−0.0605142	+	0.0439662i
$207$	−3.34448	+	10.2932i	−0.232457	+	0.715430i
$208$	−4.11459			−0.285296
$209$	−2.93099	−	21.7647i	−0.202741	−	1.50550i
$210$	−2.53932			−0.175230
$211$	−8.21125	+	25.2716i	−0.565286	+	1.73977i	0.101816	+	0.994803i	$0.467535\pi$
$211$	−8.21125	+	25.2716i	−0.565286	+	1.73977i	−0.667102	+	0.744967i	$0.732465\pi$
$212$	9.00539	−	6.54280i	0.618492	−	0.449361i
$213$	0.125071	+	0.0908697i	0.00856975	+	0.00622629i
$214$	−5.83365	−	17.9541i	−0.398780	−	1.22732i
$215$	−0.999606	−	3.07647i	−0.0681726	−	0.209814i
$216$	0.920658	+	0.668897i	0.0626428	+	0.0455127i
$217$	−4.50953	+	3.27637i	−0.306127	+	0.222414i
$218$	1.30502	−	4.01645i	0.0883874	−	0.272029i
$219$	9.93595			0.671409
$220$	2.29013	+	2.39902i	0.154401	+	0.161742i
$221$	28.1779			1.89545
$222$	6.10901	−	18.8016i	0.410010	−	1.26188i
$223$	8.00306	−	5.81457i	0.535925	−	0.389372i	−0.286645	−	0.958037i	$-0.592540\pi$
$223$	8.00306	−	5.81457i	0.535925	−	0.389372i	0.822569	+	0.568665i	$0.192540\pi$
$224$	0.809017	+	0.587785i	0.0540547	+	0.0392731i
$225$	1.06554	+	3.27939i	0.0710358	+	0.218626i
$226$	2.27605	+	7.00496i	0.151401	+	0.465963i
$227$	−11.2696	−	8.18782i	−0.747987	−	0.543445i	0.147215	−	0.989105i	$-0.452969\pi$
$227$	−11.2696	−	8.18782i	−0.747987	−	0.543445i	−0.895202	+	0.445660i	$0.852969\pi$
$228$	−13.6030	+	9.88317i	−0.900881	+	0.654529i
$229$	−3.14980	+	9.69409i	−0.208145	+	0.640604i	0.791425	+	0.611266i	$0.209340\pi$
$229$	−3.14980	+	9.69409i	−0.208145	+	0.640604i	−0.999570	+	0.0293371i	$0.990660\pi$
$230$	3.13877			0.206965
$231$	3.99668	−	7.41325i	0.262962	−	0.487756i
$232$	5.49561			0.360805
$233$	−4.08277	+	12.5655i	−0.267471	+	0.823191i	0.723643	+	0.690175i	$0.242466\pi$
$233$	−4.08277	+	12.5655i	−0.267471	+	0.823191i	−0.991114	+	0.133016i	$0.957534\pi$
$234$	11.4781	−	8.33934i	0.750348	−	0.545160i
$235$	−1.21343	−	0.881607i	−0.0791553	−	0.0575097i
$236$	−2.29423	−	7.06091i	−0.149342	−	0.459626i
$237$	3.32696	+	10.2393i	0.216110	+	0.665117i
$238$	−5.54038	−	4.02533i	−0.359130	−	0.260923i
$239$	−4.12702	+	2.99846i	−0.266955	+	0.193954i	−0.713208	−	0.700953i	$-0.752758\pi$
$239$	−4.12702	+	2.99846i	−0.266955	+	0.193954i	0.446253	+	0.894907i	$0.352758\pi$
$240$	0.784693	−	2.41504i	0.0506517	−	0.155890i
$241$	24.0075			1.54646			0.773229	−	0.634127i	$-0.218640\pi$
$241$	24.0075			1.54646			0.773229	+	0.634127i	$0.218640\pi$
$242$	−10.6081	+	2.90990i	−0.681917	+	0.187056i
$243$	22.3439			1.43336
$244$	−0.705073	+	2.16999i	−0.0451377	+	0.138919i
$245$	0.809017	−	0.587785i	0.0516862	−	0.0375522i
$246$	5.97314	+	4.33974i	0.380834	+	0.276692i
$247$	8.41916	+	25.9115i	0.535699	+	1.64871i
$248$	−1.72249	−	5.30127i	−0.109378	−	0.336631i
$249$	21.0505	+	15.2941i	1.33402	+	0.969222i
$250$	0.809017	−	0.587785i	0.0511667	−	0.0371748i
$251$	4.78873	−	14.7382i	0.302262	−	0.930267i	−0.678423	−	0.734672i	$-0.737336\pi$
$251$	4.78873	−	14.7382i	0.302262	−	0.930267i	0.980685	−	0.195595i	$-0.0626638\pi$
$252$	−3.44815			−0.217213
$253$	−4.94017	+	9.16328i	−0.310586	+	0.576090i
$254$	−15.0031			−0.941380
$255$	−5.37381	+	16.5389i	−0.336521	+	1.03571i
$256$	−0.809017	+	0.587785i	−0.0505636	+	0.0367366i
$257$	3.33705	+	2.42451i	0.208159	+	0.151237i	0.686980	−	0.726676i	$-0.258936\pi$
$257$	3.33705	+	2.42451i	0.208159	+	0.151237i	−0.478821	+	0.877912i	$0.658936\pi$
$258$	−2.53832	−	7.81215i	−0.158029	−	0.486363i
$259$	2.40577	+	7.40419i	0.149487	+	0.460074i
$260$	−3.32878	−	2.41850i	−0.206442	−	0.149989i
$261$	−15.3306	+	11.1384i	−0.948942	+	0.689447i
$262$	−2.09296	+	6.44147i	−0.129304	+	0.397955i
$263$	0.308382			0.0190156			0.00950781	−	0.999955i	$-0.496974\pi$
$263$	0.308382			0.0190156			0.00950781	+	0.999955i	$0.496974\pi$
$264$	5.81537	+	6.09189i	0.357912	+	0.374930i
$265$	11.1313			0.683788
$266$	2.04617	−	6.29747i	0.125459	−	0.386123i
$267$	−13.4436	+	9.76732i	−0.822733	+	0.597750i
$268$	−11.4855	−	8.34471i	−0.701589	−	0.509734i
$269$	−5.29707	−	16.3027i	−0.322968	−	0.993993i	−0.972350	−	0.233530i	$-0.924972\pi$
$269$	−5.29707	−	16.3027i	−0.322968	−	0.993993i	0.649382	−	0.760463i	$-0.275028\pi$
$270$	0.351660	+	1.08230i	0.0214013	+	0.0658666i
$271$	−21.5407	−	15.6502i	−1.30850	−	0.950684i	−0.308505	−	0.951223i	$-0.599829\pi$
$271$	−21.5407	−	15.6502i	−1.30850	−	0.950684i	−1.00000		0.000538195i	$0.999829\pi$
$272$	5.54038	−	4.02533i	0.335935	−	0.244071i
$273$	−3.22869	+	9.93689i	−0.195409	+	0.601408i
$274$	−9.15100			−0.552832
$275$	0.442644	+	3.28695i	0.0266925	+	0.198211i
$276$	7.97035			0.479759
$277$	−4.85556	+	14.9439i	−0.291742	+	0.897891i	0.692554	+	0.721366i	$0.256485\pi$
$277$	−4.85556	+	14.9439i	−0.291742	+	0.897891i	−0.984296	+	0.176525i	$0.943515\pi$
$278$	−12.8740	+	9.35348i	−0.772129	+	0.560984i
$279$	15.5495	+	11.2974i	0.930927	+	0.676358i
$280$	0.309017	+	0.951057i	0.0184673	+	0.0568365i
$281$	−5.38747	−	16.5809i	−0.321390	−	0.989136i	−0.973044	−	0.230620i	$-0.925925\pi$
$281$	−5.38747	−	16.5809i	−0.321390	−	0.989136i	0.651654	−	0.758516i	$-0.274075\pi$
$282$	−3.08128	−	2.23868i	−0.183488	−	0.133312i
$283$	−12.1510	+	8.82821i	−0.722302	+	0.524783i	−0.887119	−	0.461541i	$-0.847297\pi$
$283$	−12.1510	+	8.82821i	−0.722302	+	0.524783i	0.164817	+	0.986324i	$0.447297\pi$
$284$	0.0188133	−	0.0579014i	0.00111636	−	0.00343582i
$285$	−16.8142			−0.995990
$286$	12.2997	−	5.91145i	0.727298	−	0.349552i
$287$	−2.90755			−0.171627
$288$	1.06554	−	3.27939i	0.0627874	−	0.193240i
$289$	−24.1889	+	17.5743i	−1.42288	+	1.03378i
$290$	4.44605	+	3.23024i	0.261081	+	0.189686i
$291$	0.542238	+	1.66884i	0.0317866	+	0.0978290i
$292$	−1.20913	−	3.72133i	−0.0707592	−	0.217774i
$293$	−6.07302	−	4.41231i	−0.354790	−	0.257770i	0.396086	−	0.918213i	$-0.370368\pi$
$293$	−6.07302	−	4.41231i	−0.354790	−	0.257770i	−0.750876	+	0.660444i	$0.770368\pi$
$294$	2.05435	−	1.49258i	0.119812	−	0.0870488i
$295$	2.29423	−	7.06091i	0.133575	−	0.411102i
$296$	−7.78523			−0.452507
$297$	−3.71312	−	0.676817i	−0.215457	−	0.0392729i
$298$	9.63068			0.557891
$299$	3.99088	−	12.2827i	0.230799	−	0.710326i
$300$	2.05435	−	1.49258i	0.118608	−	0.0861739i
$301$	2.61700	+	1.90136i	0.150842	+	0.109593i
$302$	6.28983	+	19.3581i	0.361939	+	1.11393i
$303$	−11.4715	−	35.3055i	−0.659018	−	2.02825i
$304$	5.35695	+	3.89205i	0.307242	+	0.223224i
$305$	−1.84590	+	1.34113i	−0.105696	+	0.0767928i
$306$	−7.29711	+	22.4582i	−0.417148	+	1.28385i
$307$	−5.08116			−0.289997			−0.144998	−	0.989432i	$-0.546318\pi$
$307$	−5.08116			−0.289997			−0.144998	+	0.989432i	$0.546318\pi$
$308$	−3.26286	−	0.594745i	−0.185919	−	0.0338887i
$309$	−2.72616			−0.155086
$310$	1.72249	−	5.30127i	0.0978307	−	0.301092i
$311$	−8.77265	+	6.37370i	−0.497451	+	0.361420i	−0.808043	−	0.589124i	$-0.799473\pi$
$311$	−8.77265	+	6.37370i	−0.497451	+	0.361420i	0.310591	+	0.950544i	$0.399473\pi$
$312$	−8.45283	−	6.14134i	−0.478547	−	0.347685i
$313$	10.3225	+	31.7695i	0.583463	+	1.79572i	0.605356	+	0.795955i	$0.293031\pi$
$313$	10.3225	+	31.7695i	0.583463	+	1.79572i	−0.0218922	+	0.999760i	$0.506969\pi$
$314$	−1.85923	−	5.72213i	−0.104923	−	0.322918i
$315$	−2.78961	−	2.02677i	−0.157177	−	0.114196i
$316$	3.43009	−	2.49211i	0.192958	−	0.140192i
$317$	−8.55999	+	26.3450i	−0.480777	+	1.47968i	0.357228	+	0.934017i	$0.383722\pi$
$317$	−8.55999	+	26.3450i	−0.480777	+	1.47968i	−0.838005	+	0.545663i	$0.816278\pi$
$318$	28.2659			1.58507
$319$	−16.4280	+	7.89557i	−0.919792	+	0.442067i
$320$	−1.00000			−0.0559017
$321$	14.8135	−	45.5913i	0.826809	−	2.54466i
$322$	−2.53932	+	1.84492i	−0.141511	+	0.102814i
$323$	−36.6860	−	26.6539i	−2.04126	−	1.48306i
$324$	−2.30363	−	7.08985i	−0.127980	−	0.393881i
$325$	−1.27148	−	3.91321i	−0.0705290	−	0.217066i
$326$	6.96928	+	5.06348i	0.385993	+	0.280440i
$327$	8.67584	−	6.30337i	0.479775	−	0.348577i
$328$	0.898483	−	2.76525i	0.0496105	−	0.152685i
$329$	1.49988			0.0826911
$330$	1.12402	+	8.34663i	0.0618751	+	0.459467i
$331$	−28.8317			−1.58473			−0.792367	−	0.610045i	$-0.791152\pi$
$331$	−28.8317			−1.58473			−0.792367	+	0.610045i	$0.791152\pi$
$332$	3.16642	−	9.74525i	0.173780	−	0.534840i
$333$	21.7178	−	15.7789i	1.19013	−	0.864677i
$334$	7.29401	+	5.29941i	0.399111	+	0.289971i
$335$	−4.38707	−	13.5020i	−0.239691	−	0.737695i
$336$	0.784693	+	2.41504i	0.0428085	+	0.131751i
$337$	13.7314	+	9.97646i	0.747998	+	0.543453i	0.895206	−	0.445653i	$-0.147028\pi$
$337$	13.7314	+	9.97646i	0.747998	+	0.543453i	−0.147207	+	0.989106i	$0.547028\pi$
$338$	−3.17933	+	2.30992i	−0.172933	+	0.125643i
$339$	−5.77962	+	17.7878i	−0.313906	+	0.966103i
$340$	6.84829			0.371401
$341$	12.7654	+	13.3724i	0.691284	+	0.724154i
$342$	−22.8321			−1.23462
$343$	−0.309017	+	0.951057i	−0.0166853	+	0.0513522i
$344$	−2.61700	+	1.90136i	−0.141099	+	0.102515i
$345$	6.44815	+	4.68485i	0.347157	+	0.252224i
$346$	−3.99829	−	12.3055i	−0.214950	−	0.661547i
$347$	7.05990	+	21.7281i	0.378995	+	1.16643i	0.940744	+	0.339119i	$0.110129\pi$
$347$	7.05990	+	21.7281i	0.378995	+	1.16643i	−0.561749	+	0.827308i	$0.689871\pi$
$348$	11.2899	+	8.20262i	0.605204	+	0.439707i
$349$	12.2502	−	8.90032i	0.655741	−	0.476423i	−0.209481	−	0.977813i	$-0.567178\pi$
$349$	12.2502	−	8.90032i	0.655741	−	0.476423i	0.865222	+	0.501389i	$0.167178\pi$
$350$	−0.309017	+	0.951057i	−0.0165177	+	0.0508361i
$351$	4.68239			0.249927
$352$	1.57392	−	2.91938i	0.0838900	−	0.155604i
$353$	−9.01014			−0.479561			−0.239781	−	0.970827i	$-0.577076\pi$
$353$	−9.01014			−0.479561			−0.239781	+	0.970827i	$0.577076\pi$
$354$	5.82579	−	17.9299i	0.309637	−	0.952965i
$355$	0.0492539	−	0.0357850i	0.00261412	−	0.00189927i
$356$	5.29416	+	3.84643i	0.280590	+	0.203860i
$357$	−5.37381	−	16.5389i	−0.284412	−	0.875330i
$358$	4.87018	+	14.9889i	0.257397	+	0.792186i
$359$	−29.8470	−	21.6851i	−1.57526	−	1.14450i	−0.921886	−	0.387462i	$-0.873352\pi$
$359$	−29.8470	−	21.6851i	−1.57526	−	1.14450i	−0.653377	−	0.757033i	$-0.726648\pi$
$360$	2.78961	−	2.02677i	0.147025	−	0.106820i
$361$	7.67751	−	23.6290i	0.404080	−	1.24363i
$362$	−14.6094			−0.767852
$363$	−26.1361	−	9.85546i	−1.37179	−	0.517278i
$364$	4.11459			0.215663
$365$	1.20913	−	3.72133i	0.0632889	−	0.194783i
$366$	−4.68734	+	3.40555i	−0.245011	+	0.178011i
$367$	−27.9176	−	20.2834i	−1.45729	−	1.05878i	−0.984059	−	0.177844i	$-0.943088\pi$
$367$	−27.9176	−	20.2834i	−1.45729	−	1.05878i	−0.473230	−	0.880939i	$-0.656912\pi$
$368$	−0.969934	−	2.98515i	−0.0505613	−	0.155612i
$369$	3.09811	+	9.53499i	0.161281	+	0.496372i
$370$	−6.29838	−	4.57604i	−0.327437	−	0.237897i
$371$	−9.00539	+	6.54280i	−0.467536	+	0.339685i
$372$	4.37395	−	13.4616i	0.226779	−	0.697953i
$373$	2.31601			0.119918			0.0599592	−	0.998201i	$-0.480903\pi$
$373$	2.31601			0.119918			0.0599592	+	0.998201i	$0.480903\pi$
$374$	−10.7786	+	19.9928i	−0.557350	+	1.03380i
$375$	2.53932			0.131130
$376$	−0.463488	+	1.42647i	−0.0239026	+	0.0735646i
$377$	18.2937	−	13.2911i	0.942172	−	0.684528i
$378$	−0.920658	−	0.668897i	−0.0473535	−	0.0344043i
$379$	−2.44863	−	7.53611i	−0.125778	−	0.387104i	0.868264	−	0.496102i	$-0.165236\pi$
$379$	−2.44863	−	7.53611i	−0.125778	−	0.387104i	−0.994042	+	0.108998i	$0.965236\pi$
$380$	2.04617	+	6.29747i	0.104966	+	0.323053i
$381$	−30.8217	−	22.3933i	−1.57904	−	1.14724i
$382$	14.5352	−	10.5604i	0.743684	−	0.540318i
$383$	5.93452	−	18.2646i	0.303240	−	0.933275i	−0.677089	−	0.735901i	$-0.736759\pi$
$383$	5.93452	−	18.2646i	0.303240	−	0.933275i	0.980328	−	0.197374i	$-0.0632413\pi$
$384$	−2.53932			−0.129584
$385$	−2.29013	−	2.39902i	−0.116716	−	0.122265i
$386$	23.8180			1.21231
$387$	3.44679	−	10.6081i	0.175210	−	0.539242i
$388$	0.559046	−	0.406171i	0.0283813	−	0.0206202i
$389$	6.19652	+	4.50204i	0.314176	+	0.228262i	0.733686	−	0.679488i	$-0.237798\pi$
$389$	6.19652	+	4.50204i	0.314176	+	0.228262i	−0.419510	+	0.907751i	$0.637798\pi$
$390$	−3.22869	−	9.93689i	−0.163491	−	0.503174i
$391$	6.64239	+	20.4432i	0.335920	+	1.03386i
$392$	−0.809017	−	0.587785i	−0.0408615	−	0.0296876i
$393$	−13.9141	+	10.1092i	−0.701872	+	0.509940i
$394$	−0.573384	+	1.76470i	−0.0288867	+	0.0889041i
$395$	4.23983			0.213329
$396$	1.52630	+	11.3339i	0.0766997	+	0.569550i
$397$	−20.0239			−1.00497			−0.502486	−	0.864585i	$-0.667581\pi$
$397$	−20.0239			−1.00497			−0.502486	+	0.864585i	$0.667581\pi$
$398$	6.74294	−	20.7526i	0.337993	−	1.04024i
$399$	13.6030	−	9.88317i	0.681002	−	0.494777i
$400$	−0.809017	−	0.587785i	−0.0404508	−	0.0293893i
$401$	6.41401	+	19.7403i	0.320301	+	0.985784i	0.973517	+	0.228613i	$0.0734190\pi$
$401$	6.41401	+	19.7403i	0.320301	+	0.985784i	−0.653217	+	0.757171i	$0.726581\pi$
$402$	−11.1402	−	34.2860i	−0.555622	−	1.71003i
$403$	−18.5549	−	13.4809i	−0.924285	−	0.671532i
$404$	−11.8270	+	8.59285i	−0.588417	+	0.427510i
$405$	2.30363	−	7.08985i	0.114468	−	0.352298i
$406$	−5.49561			−0.272743
$407$	23.2723	−	11.1851i	1.15357	−	0.554423i
$408$	17.3900			0.860934
$409$	10.1528	−	31.2472i	0.502026	−	1.54508i	−0.303688	−	0.952772i	$-0.598218\pi$
$409$	10.1528	−	31.2472i	0.502026	−	1.54508i	0.805714	−	0.592305i	$-0.201782\pi$
$410$	2.35226	−	1.70902i	0.116170	−	0.0844023i
$411$	−18.7994	−	13.6586i	−0.927305	−	0.673727i
$412$	0.331754	+	1.02103i	0.0163443	+	0.0503027i
$413$	2.29423	+	7.06091i	0.112892	+	0.347445i
$414$	8.75596	+	6.36158i	0.430332	+	0.312654i
$415$	8.28981	−	6.02290i	0.406931	−	0.295652i
$416$	−1.27148	+	3.91321i	−0.0623394	+	0.191861i
$417$	−40.4084			−1.97881
$418$	−21.6052	−	3.93813i	−1.05675	−	0.192620i
$419$	−16.3625			−0.799361			−0.399680	−	0.916655i	$-0.630879\pi$
$419$	−16.3625			−0.799361			−0.399680	+	0.916655i	$0.630879\pi$
$420$	−0.784693	+	2.41504i	−0.0382891	+	0.117842i
$421$	−21.0726	+	15.3102i	−1.02702	+	0.746171i	−0.967709	−	0.252069i	$-0.918889\pi$
$421$	−21.0726	+	15.3102i	−1.02702	+	0.746171i	−0.0593072	+	0.998240i	$0.518889\pi$
$422$	21.4973	+	15.6187i	1.04647	+	0.760307i
$423$	−1.59818	−	4.91868i	−0.0777060	−	0.239155i
$424$	−3.43975	−	10.5865i	−0.167049	−	0.514124i
$425$	5.54038	+	4.02533i	0.268748	+	0.195257i
$426$	0.125071	−	0.0908697i	0.00605973	−	0.00440265i
$427$	0.705073	−	2.16999i	0.0341209	−	0.105013i
$428$	−18.8781			−0.912507
$429$	34.0913	+	6.21405i	1.64594	+	0.300017i
$430$	−3.23479			−0.155996
$431$	5.64188	−	17.3639i	0.271760	−	0.836390i	−0.718299	−	0.695735i	$-0.755079\pi$
$431$	5.64188	−	17.3639i	0.271760	−	0.836390i	0.990059	−	0.140656i	$-0.0449211\pi$
$432$	0.920658	−	0.668897i	0.0442952	−	0.0321823i
$433$	−26.3818	−	19.1675i	−1.26783	−	0.921130i	−0.268713	−	0.963220i	$-0.586598\pi$
$433$	−26.3818	−	19.1675i	−1.26783	−	0.921130i	−0.999114	+	0.0420905i	$0.986598\pi$
$434$	1.72249	+	5.30127i	0.0826821	+	0.254469i
$435$	4.31237	+	13.2721i	0.206762	+	0.636349i
$436$	−3.41660	−	2.48230i	−0.163625	−	0.118881i
$437$	−16.8142	+	12.2163i	−0.804334	+	0.584383i
$438$	3.07038	−	9.44965i	0.146708	−	0.451522i
$439$	−29.2540			−1.39622			−0.698108	−	0.715993i	$-0.745974\pi$
$439$	−29.2540			−1.39622			−0.698108	+	0.715993i	$0.745974\pi$
$440$	2.98929	−	1.43670i	0.142509	−	0.0684922i
$441$	3.44815			0.164198
$442$	8.70746	−	26.7988i	0.414172	−	1.27469i
$443$	−9.23016	+	6.70611i	−0.438538	+	0.318617i	−0.785054	−	0.619427i	$-0.787365\pi$
$443$	−9.23016	+	6.70611i	−0.438538	+	0.318617i	0.346516	+	0.938044i	$0.387365\pi$
$444$	−15.9936	−	11.6200i	−0.759023	−	0.551462i
$445$	2.02219	+	6.22365i	0.0958609	+	0.295029i
$446$	−3.05690	−	9.40817i	−0.144748	−	0.445490i
$447$	19.7848	+	14.3745i	0.935790	+	0.679891i
$448$	0.809017	−	0.587785i	0.0382225	−	0.0277702i
$449$	4.21238	−	12.9644i	0.198794	−	0.611826i	−0.801117	−	0.598508i	$-0.795760\pi$
$449$	4.21238	−	12.9644i	0.198794	−	0.611826i	0.999911	−	0.0133185i	$-0.00423952\pi$
$450$	3.44815			0.162547
$451$	1.28701	+	9.55699i	0.0606031	+	0.450021i
$452$	7.36545			0.346442
$453$	−15.9719	+	49.1564i	−0.750425	+	2.30957i
$454$	−11.2696	+	8.18782i	−0.528907	+	0.384273i
$455$	3.32878	+	2.41850i	0.156055	+	0.113381i
$456$	5.19589	+	15.9913i	0.243320	+	0.748861i
$457$	−2.05915	−	6.33743i	−0.0963232	−	0.296452i	0.891273	−	0.453467i	$-0.149813\pi$
$457$	−2.05915	−	6.33743i	−0.0963232	−	0.296452i	−0.987596	+	0.157015i	$0.949813\pi$
$458$	8.24629	+	5.99128i	0.385324	+	0.279954i
$459$	−6.30493	+	4.58080i	−0.294289	+	0.213814i
$460$	0.969934	−	2.98515i	0.0452234	−	0.139183i
$461$	18.1977			0.847553			0.423776	−	0.905767i	$-0.360704\pi$
$461$	18.1977			0.847553			0.423776	+	0.905767i	$0.360704\pi$
$462$	−5.81537	−	6.09189i	−0.270556	−	0.283420i
$463$	11.3971			0.529666			0.264833	−	0.964294i	$-0.414683\pi$
$463$	11.3971			0.529666			0.264833	+	0.964294i	$0.414683\pi$
$464$	1.69824	−	5.22664i	0.0788387	−	0.242641i
$465$	11.4511	−	8.31975i	0.531034	−	0.385819i
$466$	10.6888	+	7.76588i	0.495150	+	0.359748i
$467$	7.10101	+	21.8547i	0.328595	+	1.01131i	0.969791	+	0.243936i	$0.0784386\pi$
$467$	7.10101	+	21.8547i	0.328595	+	1.01131i	−0.641196	+	0.767377i	$0.721561\pi$
$468$	−4.38425	−	13.4933i	−0.202662	−	0.623730i
$469$	11.4855	+	8.34471i	0.530352	+	0.385323i
$470$	−1.21343	+	0.881607i	−0.0559713	+	0.0406655i
$471$	4.72119	−	14.5303i	0.217541	−	0.669522i
$472$	−7.42428			−0.341730
$473$	5.09129	−	9.44359i	0.234098	−	0.434217i
$474$	10.7663			0.494512
$475$	−2.04617	+	6.29747i	−0.0938848	+	0.288948i
$476$	−5.54038	+	4.02533i	−0.253943	+	0.184500i
$477$	31.0519	+	22.5605i	1.42177	+	1.03298i
$478$	1.57638	+	4.85161i	0.0721021	+	0.221907i
$479$	0.422409	+	1.30004i	0.0193004	+	0.0594004i	0.960243	−	0.279166i	$-0.0900580\pi$
$479$	0.422409	+	1.30004i	0.0193004	+	0.0594004i	−0.940942	+	0.338566i	$0.890058\pi$
$480$	−2.05435	−	1.49258i	−0.0937680	−	0.0681264i
$481$	−25.9153	+	18.8285i	−1.18163	+	0.858508i
$482$	7.41872	−	22.8325i	0.337913	−	1.03999i
$483$	−7.97035			−0.362664
$484$	−0.510610	+	10.9881i	−0.0232095	+	0.499461i
$485$	0.691019			0.0313776
$486$	6.90464	−	21.2503i	0.313201	−	0.963933i
$487$	9.87790	−	7.17671i	0.447610	−	0.325208i	−0.341041	−	0.940048i	$-0.610780\pi$
$487$	9.87790	−	7.17671i	0.447610	−	0.325208i	0.788651	+	0.614840i	$0.210780\pi$
$488$	1.84590	+	1.34113i	0.0835602	+	0.0607100i
$489$	6.75975	+	20.8044i	0.305686	+	0.940806i
$490$	−0.309017	−	0.951057i	−0.0139600	−	0.0429644i
$491$	−32.2431	−	23.4260i	−1.45511	−	1.05720i	−0.984604	−	0.174802i	$-0.944072\pi$
$491$	−32.2431	−	23.4260i	−1.45511	−	1.05720i	−0.470506	−	0.882397i	$-0.655928\pi$
$492$	5.97314	−	4.33974i	0.269290	−	0.195651i
$493$	−11.6300	+	35.7936i	−0.523790	+	1.61206i
$494$	27.2450			1.22581
$495$	−5.42710	+	10.0665i	−0.243930	+	0.452454i
$496$	−5.57409			−0.250284
$497$	−0.0188133	+	0.0579014i	−0.000843892	+	0.00259723i
$498$	21.0505	−	15.2941i	0.943294	−	0.685343i
$499$	−29.7318	−	21.6014i	−1.33098	−	0.967011i	−0.999725	−	0.0234691i	$-0.992529\pi$
$499$	−29.7318	−	21.6014i	−1.33098	−	0.967011i	−0.331252	−	0.943542i	$-0.607471\pi$
$500$	−0.309017	−	0.951057i	−0.0138197	−	0.0425325i
$501$	7.07471	+	21.7737i	0.316075	+	0.972778i
$502$	−12.5371	−	9.10870i	−0.559556	−	0.406541i
$503$	−9.69056	+	7.04060i	−0.432081	+	0.313925i	−0.782480	−	0.622675i	$-0.786046\pi$
$503$	−9.69056	+	7.04060i	−0.432081	+	0.313925i	0.350400	+	0.936600i	$0.386046\pi$
$504$	−1.06554	+	3.27939i	−0.0474628	+	0.146075i
$505$	−14.6190			−0.650538
$506$	7.18820	+	7.52998i	0.319554	+	0.334749i
$507$	−9.97920			−0.443192
$508$	−4.63622	+	14.2688i	−0.205699	+	0.633077i
$509$	19.1420	−	13.9075i	0.848455	−	0.616438i	−0.0762649	−	0.997088i	$-0.524299\pi$
$509$	19.1420	−	13.9075i	0.848455	−	0.616438i	0.924720	+	0.380649i	$0.124299\pi$
$510$	14.0688	+	10.2216i	0.622978	+	0.452620i
$511$	1.20913	+	3.72133i	0.0534889	+	0.164622i
$512$	0.309017	+	0.951057i	0.0136568	+	0.0420312i
$513$	−6.09618	−	4.42914i	−0.269153	−	0.195551i
$514$	3.33705	−	2.42451i	0.147191	−	0.106940i
$515$	−0.331754	+	1.02103i	−0.0146188	+	0.0449921i
$516$	−8.21418			−0.361609
$517$	−0.663914	−	4.93004i	−0.0291989	−	0.216823i
$518$	7.78523			0.342063
$519$	10.1530	−	31.2476i	0.445665	−	1.37162i
$520$	−3.32878	+	2.41850i	−0.145976	+	0.106058i
$521$	7.60910	+	5.52834i	0.333361	+	0.242201i	0.741855	−	0.670560i	$-0.233946\pi$
$521$	7.60910	+	5.52834i	0.333361	+	0.242201i	−0.408494	+	0.912761i	$0.633946\pi$
$522$	5.85578	+	18.0222i	0.256301	+	0.788812i
$523$	−8.80500	−	27.0990i	−0.385016	−	1.18496i	−0.936469	−	0.350751i	$-0.885926\pi$
$523$	−8.80500	−	27.0990i	−0.385016	−	1.18496i	0.551453	−	0.834206i	$-0.314074\pi$
$524$	5.47944	+	3.98105i	0.239371	+	0.173913i
$525$	−2.05435	+	1.49258i	−0.0896593	+	0.0651413i
$526$	0.0952951	−	0.293288i	0.00415507	−	0.0127880i
$527$	38.1730			1.66284
$528$	7.59078	−	3.64825i	0.330346	−	0.158770i
$529$	−13.1481			−0.571657
$530$	3.43975	−	10.5865i	0.149413	−	0.459847i
$531$	20.7109	−	15.0473i	0.898775	−	0.652998i
$532$	−5.35695	−	3.89205i	−0.232253	−	0.168742i
$533$	−3.69689	−	11.3779i	−0.160130	−	0.492830i
$534$	5.13498	+	15.8039i	0.222212	+	0.683900i
$535$	−15.2727	−	11.0963i	−0.660296	−	0.479733i
$536$	−11.4855	+	8.34471i	−0.496098	+	0.360437i
$537$	−12.3669	+	38.0615i	−0.533673	+	1.64248i
$538$	−17.1417			−0.739030
$539$	3.26286	+	0.594745i	0.140541	+	0.0256175i
$540$	1.13800			0.0489715
$541$	−0.740741	+	2.27977i	−0.0318469	+	0.0980148i	−0.965716	−	0.259599i	$-0.916410\pi$
$541$	−0.740741	+	2.27977i	−0.0318469	+	0.0980148i	0.933870	+	0.357614i	$0.116410\pi$
$542$	−21.5407	+	15.6502i	−0.925253	+	0.672235i
$543$	−30.0128	−	21.8056i	−1.28797	−	0.935768i
$544$	−2.11624	−	6.51311i	−0.0907330	−	0.279247i
$545$	−1.30502	−	4.01645i	−0.0559011	−	0.172046i
$546$	8.45283	+	6.14134i	0.361748	+	0.262825i
$547$	−10.5441	+	7.66073i	−0.450832	+	0.327549i	−0.789924	−	0.613204i	$-0.789880\pi$
$547$	−10.5441	+	7.66073i	−0.450832	+	0.327549i	0.339092	+	0.940753i	$0.389880\pi$
$548$	−2.82781	+	8.70311i	−0.120798	+	0.371779i
$549$	−7.86752			−0.335777
$550$	3.26286	+	0.594745i	0.139129	+	0.0253600i
$551$	−36.3895			−1.55024
$552$	2.46297	−	7.58025i	0.104831	−	0.322637i
$553$	−3.43009	+	2.49211i	−0.145862	+	0.105975i
$554$	12.7120	+	9.23583i	0.540082	+	0.392393i
$555$	−6.10901	−	18.8016i	−0.259313	−	0.798084i
$556$	4.91741	+	15.1342i	0.208545	+	0.641835i
$557$	−16.2894	−	11.8349i	−0.690203	−	0.501462i	0.186524	−	0.982450i	$-0.440278\pi$
$557$	−16.2894	−	11.8349i	−0.690203	−	0.501462i	−0.876727	+	0.480988i	$0.840278\pi$
$558$	15.5495	−	11.2974i	0.658264	−	0.478257i
$559$	−4.11297	+	12.6584i	−0.173960	+	0.535394i
$560$	1.00000			0.0422577
$561$	−51.9839	+	24.9843i	−2.19476	+	1.05484i
$562$	−17.4342			−0.735419
$563$	3.36541	−	10.3577i	0.141835	−	0.436524i	−0.854755	−	0.519031i	$-0.826293\pi$
$563$	3.36541	−	10.3577i	0.141835	−	0.436524i	0.996590	+	0.0825073i	$0.0262928\pi$
$564$	−3.08128	+	2.23868i	−0.129745	+	0.0942656i
$565$	5.95877	+	4.32930i	0.250688	+	0.182135i
$566$	4.64127	+	14.2843i	0.195087	+	0.600416i
$567$	2.30363	+	7.08985i	0.0967435	+	0.297746i
$568$	−0.0492539	−	0.0357850i	−0.00206665	−	0.00150151i
$569$	18.2179	−	13.2361i	0.763734	−	0.554885i	−0.136319	−	0.990665i	$-0.543527\pi$
$569$	18.2179	−	13.2361i	0.763734	−	0.554885i	0.900053	+	0.435780i	$0.143527\pi$
$570$	−5.19589	+	15.9913i	−0.217632	+	0.669802i
$571$	14.1198			0.590893			0.295447	−	0.955359i	$-0.404532\pi$
$571$	14.1198			0.590893			0.295447	+	0.955359i	$0.404532\pi$
$572$	−1.82130	−	13.5245i	−0.0761524	−	0.565487i
$573$	45.6226			1.90591
$574$	−0.898483	+	2.76525i	−0.0375020	+	0.115419i
$575$	2.53932	−	1.84492i	0.105897	−	0.0769387i
$576$	−2.78961	−	2.02677i	−0.116234	−	0.0844488i
$577$	−3.89212	−	11.9787i	−0.162031	−	0.498681i	0.836774	−	0.547548i	$-0.184439\pi$
$577$	−3.89212	−	11.9787i	−0.162031	−	0.498681i	−0.998805	+	0.0488675i	$0.984439\pi$
$578$	9.23933	+	28.4357i	0.384306	+	1.18277i
$579$	48.9306	+	35.5502i	2.03349	+	1.47742i
$580$	4.44605	−	3.23024i	0.184612	−	0.134128i
$581$	−3.16642	+	9.74525i	−0.131365	+	0.404301i
$582$	1.75472			0.0727355
$583$	25.4921	+	26.7042i	1.05577	+	1.10597i
$584$	−3.91284			−0.161914
$585$	4.38425	−	13.4933i	0.181266	−	0.557881i
$586$	−6.07302	+	4.41231i	−0.250874	+	0.182271i
$587$	12.4603	+	9.05296i	0.514293	+	0.373656i	0.814450	−	0.580234i	$-0.197039\pi$
$587$	12.4603	+	9.05296i	0.514293	+	0.373656i	−0.300157	+	0.953890i	$0.597039\pi$
$588$	−0.784693	−	2.41504i	−0.0323602	−	0.0995945i
$589$	11.4055	+	35.1027i	0.469957	+	1.44638i
$590$	−6.00637	−	4.36389i	−0.247278	−	0.179658i
$591$	−3.81187	+	2.76949i	−0.156800	+	0.113922i
$592$	−2.40577	+	7.40419i	−0.0988764	+	0.304310i
$593$	27.0005			1.10878			0.554389	−	0.832258i	$-0.312952\pi$
$593$	27.0005			1.10878			0.554389	+	0.832258i	$0.312952\pi$
$594$	−1.79111	+	3.32224i	−0.0734901	+	0.136313i
$595$	−6.84829			−0.280753
$596$	2.97604	−	9.15932i	0.121904	−	0.375181i
$597$	44.8273	−	32.5689i	1.83466	−	1.33296i
$598$	−10.4483	−	7.59111i	−0.427262	−	0.310424i
$599$	11.9064	+	36.6441i	0.486482	+	1.49724i	0.829822	+	0.558028i	$0.188442\pi$
$599$	11.9064	+	36.6441i	0.486482	+	1.49724i	−0.343340	+	0.939211i	$0.611558\pi$
$600$	−0.784693	−	2.41504i	−0.0320350	−	0.0985935i
$601$	−12.8792	−	9.35726i	−0.525352	−	0.381691i	0.293264	−	0.956031i	$-0.405258\pi$
$601$	−12.8792	−	9.35726i	−0.525352	−	0.381691i	−0.818616	+	0.574341i	$0.805258\pi$
$602$	2.61700	−	1.90136i	0.106661	−	0.0774938i
$603$	15.1273	−	46.5570i	0.616031	−	1.89595i
$604$	20.3543			0.828205
$605$	−6.87176	+	8.58947i	−0.279377	+	0.349211i
$606$	−37.1224			−1.50799
$607$	6.26206	−	19.2726i	0.254169	−	0.782252i	−0.739823	−	0.672801i	$-0.765091\pi$
$607$	6.26206	−	19.2726i	0.254169	−	0.782252i	0.993992	−	0.109451i	$-0.0349092\pi$
$608$	5.35695	−	3.89205i	0.217253	−	0.157844i
$609$	−11.2899	−	8.20262i	−0.457491	−	0.332387i
$610$	0.705073	+	2.16999i	0.0285476	+	0.0878604i
$611$	1.90707	+	5.86934i	0.0771516	+	0.237448i
$612$	19.1041	+	13.8799i	0.772236	+	0.561063i
$613$	22.7035	−	16.4950i	0.916985	−	0.666229i	−0.0257866	−	0.999667i	$-0.508209\pi$
$613$	22.7035	−	16.4950i	0.916985	−	0.666229i	0.942772	+	0.333439i	$0.108209\pi$
$614$	−1.57016	+	4.83247i	−0.0633667	+	0.195023i
$615$	7.38321			0.297720
$616$	−1.57392	+	2.91938i	−0.0634149	+	0.117625i
$617$	38.0285			1.53097			0.765484	−	0.643455i	$-0.222500\pi$
$617$	38.0285			1.53097			0.765484	+	0.643455i	$0.222500\pi$
$618$	−0.842429	+	2.59273i	−0.0338875	+	0.104295i
$619$	28.1504	−	20.4525i	1.13146	−	0.822054i	0.145553	−	0.989350i	$-0.453504\pi$
$619$	28.1504	−	20.4525i	1.13146	−	0.822054i	0.985907	+	0.167297i	$0.0535037\pi$
$620$	−4.50953	−	3.27637i	−0.181107	−	0.131582i
$621$	1.10378	+	3.39709i	0.0442932	+	0.136320i
$622$	3.35085	+	10.3129i	0.134357	+	0.413508i
$623$	−5.29416	−	3.84643i	−0.212106	−	0.154104i
$624$	−8.45283	+	6.14134i	−0.338384	+	0.245850i
$625$	0.309017	−	0.951057i	0.0123607	−	0.0380423i
$626$	33.4044			1.33511
$627$	−38.5068	−	40.3377i	−1.53781	−	1.61093i
$628$	−6.01660			−0.240089
$629$	16.4754	−	50.7061i	0.656917	−	2.02178i
$630$	−2.78961	+	2.02677i	−0.111141	+	0.0807485i
$631$	24.0948	+	17.5059i	0.959199	+	0.696899i	0.952965	−	0.303082i	$-0.0980155\pi$
$631$	24.0948	+	17.5059i	0.959199	+	0.696899i	0.00623454	+	0.999981i	$0.498015\pi$
$632$	−1.31018	−	4.03232i	−0.0521161	−	0.160397i
$633$	20.8510	+	64.1727i	0.828752	+	2.55064i
$634$	22.4104	+	16.2821i	0.890029	+	0.646644i
$635$	−12.1378	+	8.81862i	−0.481673	+	0.349956i
$636$	8.73463	−	26.8824i	0.346351	−	1.06596i
$637$	−4.11459			−0.163026
$638$	2.43260	+	18.0638i	0.0963077	+	0.715154i
$639$	0.209927			0.00830460
$640$	−0.309017	+	0.951057i	−0.0122150	+	0.0375938i
$641$	−0.469101	+	0.340822i	−0.0185284	+	0.0134617i	−0.597011	−	0.802233i	$-0.703645\pi$
$641$	−0.469101	+	0.340822i	−0.0185284	+	0.0134617i	0.578483	+	0.815695i	$0.303645\pi$
$642$	−38.7823	−	28.1770i	−1.53061	−	1.11206i
$643$	14.6711	+	45.1529i	0.578571	+	1.78066i	0.623685	+	0.781676i	$0.285635\pi$
$643$	14.6711	+	45.1529i	0.578571	+	1.78066i	−0.0451146	+	0.998982i	$0.514365\pi$
$644$	0.969934	+	2.98515i	0.0382208	+	0.117631i
$645$	−6.64541	−	4.82817i	−0.261663	−	0.190109i
$646$	−36.6860	+	26.6539i	−1.44339	+	1.04868i
$647$	−12.8364	+	39.5064i	−0.504651	+	1.55316i	0.296704	+	0.954969i	$0.404112\pi$
$647$	−12.8364	+	39.5064i	−0.504651	+	1.55316i	−0.801356	+	0.598188i	$0.795888\pi$
$648$	−7.45471			−0.292849
$649$	22.1934	−	10.6665i	0.871166	−	0.418697i
$650$	−4.11459			−0.161388
$651$	−4.37395	+	13.4616i	−0.171429	+	0.527603i
$652$	6.96928	−	5.06348i	0.272938	−	0.198301i
$653$	21.4334	+	15.5723i	0.838753	+	0.609390i	0.922022	−	0.387137i	$-0.126536\pi$
$653$	21.4334	+	15.5723i	0.838753	+	0.609390i	−0.0832688	+	0.996527i	$0.526536\pi$
$654$	−3.31388	−	10.1991i	−0.129583	−	0.398815i
$655$	2.09296	+	6.44147i	0.0817788	+	0.251689i
$656$	−2.35226	−	1.70902i	−0.0918403	−	0.0667259i
$657$	10.9153	−	7.93043i	0.425846	−	0.309395i
$658$	0.463488	−	1.42647i	0.0180687	−	0.0556096i
$659$	−46.8092			−1.82343			−0.911713	−	0.410827i	$-0.865240\pi$
$659$	−46.8092			−1.82343			−0.911713	+	0.410827i	$0.865240\pi$
$660$	8.28546	+	1.51025i	0.322511	+	0.0587863i
$661$	−35.7060			−1.38880			−0.694401	−	0.719588i	$-0.744331\pi$
$661$	−35.7060			−1.38880			−0.694401	+	0.719588i	$0.744331\pi$
$662$	−8.90949	+	27.4206i	−0.346277	+	1.06573i
$663$	57.8874	−	42.0577i	2.24816	−	1.63339i
$664$	−8.28981	−	6.02290i	−0.321707	−	0.233734i
$665$	−2.04617	−	6.29747i	−0.0793472	−	0.244205i
$666$	−8.29544	−	25.5308i	−0.321442	−	0.989297i
$667$	13.9551	+	10.1390i	0.540345	+	0.392583i
$668$	7.29401	−	5.29941i	0.282214	−	0.205040i
$669$	7.76244	−	23.8903i	0.300113	−	0.923654i
$670$	−14.1969			−0.548473
$671$	−7.44476	−	1.35701i	−0.287402	−	0.0523867i
$672$	2.53932			0.0979564
$673$	4.82817	−	14.8596i	0.186112	−	0.572794i	−0.813854	−	0.581070i	$-0.802634\pi$
$673$	4.82817	−	14.8596i	0.186112	−	0.572794i	0.999966	+	0.00827564i	$0.00263425\pi$
$674$	13.7314	−	9.97646i	0.528915	−	0.384279i
$675$	0.920658	+	0.668897i	0.0354361	+	0.0257459i
$676$	1.21440	+	3.73753i	0.0467076	+	0.143751i
$677$	3.50218	+	10.7786i	0.134600	+	0.414255i	0.995528	−	0.0944718i	$-0.0301162\pi$
$677$	3.50218	+	10.7786i	0.134600	+	0.414255i	−0.860928	+	0.508727i	$0.830116\pi$
$678$	15.1312	+	10.9935i	0.581112	+	0.422202i
$679$	−0.559046	+	0.406171i	−0.0214542	+	0.0155874i
$680$	2.11624	−	6.51311i	0.0811541	−	0.249766i
$681$	−35.3726			−1.35548
$682$	16.6626	−	8.00832i	0.638043	−	0.306654i
$683$	−12.5315			−0.479504			−0.239752	−	0.970834i	$-0.577066\pi$
$683$	−12.5315			−0.479504			−0.239752	+	0.970834i	$0.577066\pi$
$684$	−7.05551	+	21.7146i	−0.269774	+	0.830279i
$685$	−7.40331	+	5.37882i	−0.282866	+	0.205514i
$686$	0.809017	+	0.587785i	0.0308884	+	0.0224417i
$687$	7.99835	+	24.6164i	0.305156	+	0.939174i
$688$	0.999606	+	3.07647i	0.0381096	+	0.117289i
$689$	−37.0535	−	26.9209i	−1.41163	−	1.02561i
$690$	6.44815	−	4.68485i	0.245477	−	0.178349i
$691$	1.05531	−	3.24791i	0.0401459	−	0.123556i	−0.928975	−	0.370143i	$-0.879309\pi$
$691$	1.05531	−	3.24791i	0.0401459	−	0.123556i	0.969121	+	0.246586i	$0.0793088\pi$
$692$	−12.9388			−0.491858
$693$	−1.52630	−	11.3339i	−0.0579795	−	0.430540i
$694$	22.8463			0.867234
$695$	−4.91741	+	15.1342i	−0.186528	+	0.574075i
$696$	11.2899	−	8.20262i	0.427944	−	0.310919i
$697$	16.1090	+	11.7038i	0.610171	+	0.443315i
$698$	−4.67918	−	14.4010i	−0.177109	−	0.545087i
$699$	10.3675	+	31.9077i	0.392133	+	1.20686i
$700$	0.809017	+	0.587785i	0.0305780	+	0.0222162i
$701$	−28.4015	+	20.6349i	−1.07271	+	0.779369i	−0.976397	−	0.215982i	$-0.930705\pi$
$701$	−28.4015	+	20.6349i	−1.07271	+	0.779369i	−0.0963122	+	0.995351i	$0.530705\pi$
$702$	1.44694	−	4.45322i	0.0546111	−	0.168076i
$703$	51.5503			1.94426
$704$	−2.29013	−	2.39902i	−0.0863125	−	0.0904165i
$705$	−3.80868			−0.143443
$706$	−2.78429	+	8.56915i	−0.104788	+	0.322504i
$707$	11.8270	−	8.59285i	0.444802	−	0.323167i
$708$	−15.2521	−	11.0813i	−0.573209	−	0.416461i
$709$	−8.94067	−	27.5165i	−0.335774	−	1.03341i	−0.966340	−	0.257270i	$-0.917177\pi$
$709$	−8.94067	−	27.5165i	−0.335774	−	1.03341i	0.630566	−	0.776136i	$-0.282823\pi$
$710$	−0.0188133	−	0.0579014i	−0.000706051	−	0.00217300i
$711$	11.8275	+	8.59316i	0.443565	+	0.322269i
$712$	5.29416	−	3.84643i	0.198407	−	0.144151i
$713$	5.40650	−	16.6395i	0.202475	−	0.623154i
$714$	−17.3900			−0.650805
$715$	6.47602	−	12.0121i	0.242190	−	0.449226i
$716$	15.7602			0.588987
$717$	−4.00294	+	12.3198i	−0.149493	+	0.460091i
$718$	−29.8470	+	21.6851i	−1.11388	+	0.809280i
$719$	5.71953	+	4.15548i	0.213303	+	0.154973i	0.689307	−	0.724470i	$-0.257915\pi$
$719$	5.71953	+	4.15548i	0.213303	+	0.154973i	−0.476004	+	0.879443i	$0.657915\pi$
$720$	−1.06554	−	3.27939i	−0.0397102	−	0.122215i
$721$	−0.331754	−	1.02103i	−0.0123552	−	0.0380253i
$722$	−20.1000	−	14.6035i	−0.748044	−	0.543486i
$723$	49.3198	−	35.8330i	1.83422	−	1.33264i
$724$	−4.51455	+	13.8943i	−0.167782	+	0.516379i
$725$	5.49561			0.204102
$726$	−17.4496	+	21.8114i	−0.647615	+	0.809497i
$727$	−28.5131			−1.05749			−0.528747	−	0.848779i	$-0.677338\pi$
$727$	−28.5131			−1.05749			−0.528747	+	0.848779i	$0.677338\pi$
$728$	1.27148	−	3.91321i	0.0471241	−	0.145033i
$729$	27.8093	−	20.2046i	1.02997	−	0.748320i
$730$	−3.16555	−	2.29991i	−0.117162	−	0.0851234i
$731$	−6.84559	−	21.0686i	−0.253193	−	0.779249i
$732$	1.79041	+	5.51030i	0.0661753	+	0.203667i
$733$	−32.4592	−	23.5830i	−1.19891	−	0.871059i	−0.204733	−	0.978818i	$-0.565632\pi$
$733$	−32.4592	−	23.5830i	−1.19891	−	0.871059i	−0.994177	+	0.107759i	$0.965632\pi$
$734$	−27.9176	+	20.2834i	−1.03046	+	0.748672i
$735$	0.784693	−	2.41504i	0.0289438	−	0.0890800i
$736$	−3.13877			−0.115697
$737$	22.3447	−	41.4461i	0.823077	−	1.52669i
$738$	10.0257			0.369050
$739$	−11.3005	+	34.7794i	−0.415696	+	1.27938i	0.495932	+	0.868362i	$0.334827\pi$
$739$	−11.3005	+	34.7794i	−0.415696	+	1.27938i	−0.911627	+	0.411018i	$0.865173\pi$
$740$	−6.29838	+	4.57604i	−0.231533	+	0.168219i
$741$	55.9708	+	40.6652i	2.05614	+	1.49387i
$742$	3.43975	+	10.5865i	0.126277	+	0.388641i
$743$	−0.0151877	−	0.0467431i	−0.000557184	−	0.00171484i	0.950778	−	0.309874i	$-0.100287\pi$
$743$	−0.0151877	−	0.0467431i	−0.000557184	−	0.00171484i	−0.951335	+	0.308159i	$0.900287\pi$
$744$	−11.4511	−	8.31975i	−0.419819	−	0.305017i
$745$	7.79139	−	5.66077i	0.285454	−	0.207395i
$746$	0.715686	−	2.20265i	0.0262031	−	0.0806449i
$747$	35.3324			1.29274
$748$	15.6835	+	16.4292i	0.573445	+	0.600711i
$749$	18.8781			0.689790
$750$	0.784693	−	2.41504i	0.0286529	−	0.0881847i
$751$	−5.17702	+	3.76132i	−0.188912	+	0.137253i	−0.678221	−	0.734858i	$-0.737249\pi$
$751$	−5.17702	+	3.76132i	−0.188912	+	0.137253i	0.489309	+	0.872110i	$0.337249\pi$
$752$	1.21343	+	0.881607i	0.0442492	+	0.0321489i
$753$	−12.1601	−	37.4250i	−0.443139	−	1.36384i
$754$	−6.98756	−	21.5055i	−0.254472	−	0.783184i
$755$	16.4670	+	11.9640i	0.599295	+	0.435413i
$756$	−0.920658	+	0.668897i	−0.0334840	+	0.0243275i
$757$	−5.93494	+	18.2659i	−0.215709	+	0.663885i	0.783393	+	0.621526i	$0.213487\pi$
$757$	−5.93494	+	18.2659i	−0.215709	+	0.663885i	−0.999102	+	0.0423583i	$0.986513\pi$
$758$	−7.92393			−0.287810
$759$	3.52803	+	26.1982i	0.128059	+	0.950934i
$760$	6.62155			0.240189
$761$	−0.888309	+	2.73394i	−0.0322012	+	0.0991051i	−0.965865	−	0.259045i	$-0.916592\pi$
$761$	−0.888309	+	2.73394i	−0.0322012	+	0.0991051i	0.933664	+	0.358150i	$0.116592\pi$
$762$	−30.8217	+	22.3933i	−1.11655	+	0.811223i
$763$	3.41660	+	2.48230i	0.123689	+	0.0898655i
$764$	−5.55194	−	17.0871i	−0.200862	−	0.618190i
$765$	7.29711	+	22.4582i	0.263827	+	0.811978i
$766$	−15.5368	−	11.2881i	−0.561366	−	0.407856i
$767$	−24.7138	+	17.9556i	−0.892363	+	0.648339i
$768$	−0.784693	+	2.41504i	−0.0283152	+	0.0871452i
$769$	−35.4758			−1.27929			−0.639646	−	0.768670i	$-0.720919\pi$
$769$	−35.4758			−1.27929			−0.639646	+	0.768670i	$0.720919\pi$
$770$	−2.98929	+	1.43670i	−0.107727	+	0.0517752i
$771$	10.4742			0.377220
$772$	7.36017	−	22.6523i	0.264898	−	0.815274i
$773$	25.2909	−	18.3749i	0.909650	−	0.660900i	−0.0312760	−	0.999511i	$-0.509957\pi$
$773$	25.2909	−	18.3749i	0.909650	−	0.660900i	0.940926	+	0.338611i	$0.109957\pi$
$774$	−9.02382	−	6.55619i	−0.324354	−	0.235657i
$775$	−1.72249	−	5.30127i	−0.0618736	−	0.190427i
$776$	−0.213537	−	0.657198i	−0.00766552	−	0.0235921i
$777$	15.9936	+	11.6200i	0.573767	+	0.416866i
$778$	6.19652	−	4.50204i	0.222156	−	0.161406i
$779$	−5.94936	+	18.3102i	−0.213158	+	0.656032i
$780$	−10.4483			−0.374108
$781$	0.198647	+	0.0362087i	0.00710814	+	0.00129565i
$782$	21.4952			0.768668
$783$	−1.93259	+	5.94789i	−0.0690650	+	0.212560i
$784$	−0.809017	+	0.587785i	−0.0288935	+	0.0209923i
$785$	−4.86753	−	3.53647i	−0.173730	−	0.126222i
$786$	5.31470	+	16.3570i	0.189569	+	0.583434i
$787$	−3.99175	−	12.2853i	−0.142291	−	0.437925i	0.854362	−	0.519678i	$-0.173948\pi$
$787$	−3.99175	−	12.2853i	−0.142291	−	0.437925i	−0.996653	+	0.0817529i	$0.973948\pi$
$788$	1.50114	+	1.09064i	0.0534759	+	0.0388525i
$789$	0.633525	−	0.460283i	0.0225541	−	0.0163865i
$790$	1.31018	−	4.03232i	0.0466141	−	0.143463i
$791$	−7.36545			−0.261885
$792$	11.2508	+	2.05077i	0.399781	+	0.0728709i
$793$	9.38812			0.333382
$794$	−6.18773	+	19.0439i	−0.219594	+	0.675842i
$795$	22.8676	−	16.6143i	0.811029	−	0.589247i
$796$	−17.6533	−	12.8258i	−0.625703	−	0.454600i
$797$	3.12420	+	9.61531i	0.110665	+	0.340592i	0.991018	−	0.133727i	$-0.0426945\pi$
$797$	3.12420	+	9.61531i	0.110665	+	0.340592i	−0.880353	+	0.474319i	$0.842694\pi$
$798$	−5.19589	−	15.9913i	−0.183932	−	0.566086i
$799$	−8.30991	−	6.03750i	−0.293984	−	0.213592i
$800$	−0.809017	+	0.587785i	−0.0286031	+	0.0207813i
$801$	−6.97281	+	21.4601i	−0.246372	+	0.758255i
$802$	20.7562			0.732926
$803$	11.6966	−	5.62159i	0.412765	−	0.198382i
$804$	−36.0504			−1.27140
$805$	−0.969934	+	2.98515i	−0.0341857	+	0.105213i
$806$	−18.5549	+	13.4809i	−0.653568	+	0.474845i
$807$	−35.2151	−	25.5852i	−1.23963	−	0.900643i
$808$	4.51753	+	13.9035i	0.158926	+	0.489124i
$809$	1.56498	+	4.81652i	0.0550218	+	0.169340i	0.974791	−	0.223120i	$-0.0716242\pi$
$809$	1.56498	+	4.81652i	0.0550218	+	0.169340i	−0.919769	+	0.392460i	$0.871624\pi$
$810$	−6.03099	−	4.38177i	−0.211907	−	0.153960i
$811$	7.70306	−	5.59660i	0.270491	−	0.196523i	−0.444268	−	0.895894i	$-0.646536\pi$
$811$	7.70306	−	5.59660i	0.270491	−	0.196523i	0.714759	+	0.699371i	$0.246536\pi$
$812$	−1.69824	+	5.22664i	−0.0595965	+	0.183419i
$813$	−67.6114			−2.37124
$814$	−3.44609	−	25.5897i	−0.120785	−	0.896918i
$815$	8.61451			0.301753
$816$	5.37381	−	16.5389i	0.188121	−	0.578977i
$817$	17.3286	−	12.5900i	0.606252	−	0.440468i
$818$	−26.5805	−	19.3119i	−0.929365	−	0.675223i
$819$	4.38425	+	13.4933i	0.153198	+	0.471495i
$820$	−0.898483	−	2.76525i	−0.0313764	−	0.0965666i
$821$	−14.0774	−	10.2278i	−0.491305	−	0.356954i	0.314381	−	0.949297i	$-0.398203\pi$
$821$	−14.0774	−	10.2278i	−0.491305	−	0.356954i	−0.805686	+	0.592343i	$0.798203\pi$
$822$	−18.7994	+	13.6586i	−0.655704	+	0.476397i
$823$	5.71246	−	17.5812i	0.199124	−	0.612840i	−0.800780	−	0.598959i	$-0.795581\pi$
$823$	5.71246	−	17.5812i	0.199124	−	0.612840i	0.999904	−	0.0138814i	$-0.00441874\pi$
$824$	1.07358			0.0373998
$825$	5.81537	+	6.09189i	0.202465	+	0.212092i
$826$	7.42428			0.258324
$827$	−17.0795	+	52.5652i	−0.593911	+	1.82787i	−0.0338362	+	0.999427i	$0.510772\pi$
$827$	−17.0795	+	52.5652i	−0.593911	+	1.82787i	−0.560075	+	0.828442i	$0.689228\pi$
$828$	8.75596	−	6.36158i	0.304291	−	0.221080i
$829$	16.2367	+	11.7966i	0.563922	+	0.409714i	0.832892	−	0.553435i	$-0.186683\pi$
$829$	16.2367	+	11.7966i	0.563922	+	0.409714i	−0.268970	+	0.963149i	$0.586683\pi$
$830$	−3.16642	−	9.74525i	−0.109908	−	0.338263i
$831$	12.3298	+	37.9473i	0.427717	+	1.31638i
$832$	3.32878	+	2.41850i	0.115405	+	0.0838463i
$833$	5.54038	−	4.02533i	0.191963	−	0.139469i
$834$	−12.4869	+	38.4307i	−0.432386	+	1.33075i
$835$	9.01590			0.312008
$836$	−10.4218	+	19.3308i	−0.360444	+	0.668571i
$837$	6.34329			0.219256
$838$	−5.05629	+	15.5617i	−0.174667	+	0.537569i
$839$	8.70689	−	6.32593i	0.300595	−	0.218395i	−0.427255	−	0.904131i	$-0.640519\pi$
$839$	8.70689	−	6.32593i	0.300595	−	0.218395i	0.727851	+	0.685736i	$0.240519\pi$
$840$	2.05435	+	1.49258i	0.0708819	+	0.0514987i
$841$	0.371371	+	1.14296i	0.0128059	+	0.0394124i
$842$	8.04902	+	24.7723i	0.277388	+	0.853712i
$843$	−35.8161	−	26.0219i	−1.23357	−	0.896242i
$844$	21.4973	−	15.6187i	0.739968	−	0.537619i
$845$	−1.21440	+	3.73753i	−0.0417765	+	0.128575i
$846$	−5.17181			−0.177811
$847$	0.510610	−	10.9881i	0.0175448	−	0.377557i
$848$	−11.1313			−0.382249
$849$	−11.7857	+	36.2725i	−0.404483	+	1.24487i
$850$	5.54038	−	4.02533i	0.190034	−	0.138068i
$851$	−19.7692	−	14.3632i	−0.677679	−	0.492363i
$852$	−0.0477730	−	0.147030i	−0.00163668	−	0.00503717i
$853$	−4.52996	−	13.9418i	−0.155103	−	0.477358i	0.843068	−	0.537806i	$-0.180747\pi$
$853$	−4.52996	−	13.9418i	−0.155103	−	0.477358i	−0.998171	+	0.0604487i	$0.980747\pi$
$854$	−1.84590	−	1.34113i	−0.0631656	−	0.0458925i
$855$	−18.4716	+	13.4204i	−0.631714	+	0.458967i
$856$	−5.83365	+	17.9541i	−0.199390	+	0.613659i
$857$	34.6532			1.18373			0.591865	−	0.806037i	$-0.298392\pi$
$857$	34.6532			1.18373			0.591865	+	0.806037i	$0.298392\pi$
$858$	16.4447	−	30.5025i	0.561413	−	1.04134i
$859$	9.13441			0.311662			0.155831	−	0.987784i	$-0.450194\pi$
$859$	9.13441			0.311662			0.155831	+	0.987784i	$0.450194\pi$
$860$	−0.999606	+	3.07647i	−0.0340863	+	0.104907i
$861$	−5.97314	+	4.33974i	−0.203564	+	0.147898i
$862$	−14.7706	−	10.7315i	−0.503090	−	0.365516i
$863$	7.24276	+	22.2909i	0.246546	+	0.758792i	0.995378	+	0.0960319i	$0.0306151\pi$
$863$	7.24276	+	22.2909i	0.246546	+	0.758792i	−0.748832	+	0.662760i	$0.769385\pi$
$864$	−0.351660	−	1.08230i	−0.0119637	−	0.0368205i
$865$	−10.4677	−	7.60521i	−0.355911	−	0.258585i
$866$	−26.3818	+	19.1675i	−0.896489	+	0.651337i
$867$	−23.4616	+	72.2075i	−0.796799	+	2.45229i
$868$	5.57409			0.189197
$869$	9.70976	+	10.1714i	0.329381	+	0.345042i
$870$	13.9551			0.473123
$871$	−18.0510	+	55.5553i	−0.611636	+	1.88242i
$872$	−3.41660	+	2.48230i	−0.115701	+	0.0840614i
$873$	1.92768	+	1.40054i	0.0652419	+	0.0474010i
$874$	6.42247	+	19.7663i	0.217243	+	0.668606i
$875$	0.309017	+	0.951057i	0.0104467	+	0.0321516i
$876$	−8.03835	−	5.84020i	−0.271591	−	0.197322i
$877$	41.2568	−	29.9748i	1.39314	−	1.01218i	0.397631	−	0.917546i	$-0.369833\pi$
$877$	41.2568	−	29.9748i	1.39314	−	1.01218i	0.995512	−	0.0946320i	$-0.0301675\pi$
$878$	−9.03997	+	27.8222i	−0.305084	+	0.938953i
$879$	−19.0618			−0.642940
$880$	−0.442644	−	3.28695i	−0.0149215	−	0.110803i
$881$	−1.75183			−0.0590207			−0.0295103	−	0.999564i	$-0.509395\pi$
$881$	−1.75183			−0.0590207			−0.0295103	+	0.999564i	$0.509395\pi$
$882$	1.06554	−	3.27939i	0.0358785	−	0.110423i
$883$	33.0611	−	24.0203i	1.11259	−	0.808347i	0.129524	−	0.991576i	$-0.458655\pi$
$883$	33.0611	−	24.0203i	1.11259	−	0.808347i	0.983070	+	0.183229i	$0.0586551\pi$
$884$	−22.7964	−	16.5626i	−0.766727	−	0.557060i
$885$	−5.82579	−	17.9299i	−0.195832	−	0.602708i
$886$	3.52561	+	10.8507i	0.118445	+	0.364537i
$887$	19.0565	+	13.8454i	0.639856	+	0.464883i	0.859801	−	0.510630i	$-0.170588\pi$
$887$	19.0565	+	13.8454i	0.639856	+	0.464883i	−0.219945	+	0.975512i	$0.570588\pi$
$888$	−15.9936	+	11.6200i	−0.536710	+	0.389943i
$889$	4.63622	−	14.2688i	0.155494	−	0.478561i
$890$	6.54394			0.219353
$891$	22.2843	−	10.7102i	0.746553	−	0.358806i
$892$	−9.89233			−0.331220
$893$	3.06901	−	9.44545i	0.102701	−	0.316080i
$894$	19.7848	−	14.3745i	0.661704	−	0.480756i
$895$	12.7503	+	9.26363i	0.426195	+	0.309649i
$896$	−0.309017	−	0.951057i	−0.0103235	−	0.0317726i
$897$	−10.1341	−	31.1897i	−0.338369	−	1.04139i
$898$	−11.0282	−	8.01242i	−0.368014	−	0.267378i
$899$	24.7826	−	18.0056i	0.826548	−	0.600522i
$900$	1.06554	−	3.27939i	0.0355179	−	0.109313i
$901$	76.2302			2.53960
$902$	9.48695	+	1.72925i	0.315881	+	0.0575778i
$903$	8.21418			0.273351
$904$	2.27605	−	7.00496i	0.0757003	−	0.232981i
$905$	−11.8192	+	8.58718i	−0.392885	+	0.285448i
$906$	41.8149	+	30.3803i	1.38921	+	1.00932i
$907$	−12.8016	−	39.3992i	−0.425069	−	1.30823i	−0.902928	−	0.429791i	$-0.858587\pi$
$907$	−12.8016	−	39.3992i	−0.425069	−	1.30823i	0.477859	−	0.878436i	$-0.341413\pi$
$908$	4.30459	+	13.2482i	0.142853	+	0.439656i
$909$	−40.7814	−	29.6294i	−1.35263	−	0.982746i
$910$	3.32878	−	2.41850i	0.110348	−	0.0801724i
$911$	13.9409	−	42.9058i	0.461884	−	1.42153i	−0.400976	−	0.916089i	$-0.631329\pi$
$911$	13.9409	−	42.9058i	0.461884	−	1.42153i	0.862860	−	0.505444i	$-0.168671\pi$
$912$	16.8142			0.556775
$913$	33.4338	+	6.09421i	1.10650	+	0.201689i
$914$	−6.66357			−0.220411
$915$	−1.79041	+	5.51030i	−0.0591890	+	0.182165i
$916$	8.24629	−	5.99128i	0.272465	−	0.197957i
$917$	−5.47944	−	3.98105i	−0.180947	−	0.131466i
$918$	2.40827	+	7.41189i	0.0794848	+	0.244629i
$919$	1.82902	+	5.62913i	0.0603336	+	0.185688i	0.976681	−	0.214697i	$-0.0688764\pi$
$919$	1.82902	+	5.62913i	0.0603336	+	0.185688i	−0.916347	+	0.400385i	$0.868876\pi$
$920$	−2.53932	−	1.84492i	−0.0837189	−	0.0608254i
$921$	−10.4385	+	7.58401i	−0.343960	+	0.249902i
$922$	5.62341	−	17.3071i	0.185197	−	0.569978i
$923$	−0.250501			−0.00824535
$924$	−7.59078	+	3.64825i	−0.249718	+	0.120019i
$925$	−7.78523			−0.255977
$926$	3.52189	−	10.8393i	0.115736	−	0.356200i
$927$	−2.99486	+	2.17590i	−0.0983643	+	0.0714658i
$928$	−4.44605	−	3.23024i	−0.145949	−	0.106038i
$929$	−17.0796	−	52.5657i	−0.560365	−	1.72463i	−0.681337	−	0.731970i	$-0.738601\pi$
$929$	−17.0796	−	52.5657i	−0.560365	−	1.72463i	0.120972	−	0.992656i	$-0.461399\pi$
$930$	−4.37395	−	13.4616i	−0.143427	−	0.441424i
$931$	5.35695	+	3.89205i	0.175567	+	0.127557i
$932$	10.6888	−	7.76588i	0.350124	−	0.254380i
$933$	−8.50889	+	26.1877i	−0.278569	+	0.857346i
$934$	22.9793			0.751907
$935$	3.03136	+	22.5100i	0.0991360	+	0.736156i
$936$	−14.1877			−0.463740
$937$	−4.97418	+	15.3090i	−0.162499	+	0.500122i	−0.998843	−	0.0480833i	$-0.984689\pi$
$937$	−4.97418	+	15.3090i	−0.162499	+	0.500122i	0.836344	+	0.548205i	$0.184689\pi$
$938$	11.4855	−	8.34471i	0.375015	−	0.272464i
$939$	68.6244	+	49.8585i	2.23947	+	1.62707i
$940$	0.463488	+	1.42647i	0.0151173	+	0.0465263i
$941$	−15.4034	−	47.4068i	−0.502136	−	1.54542i	−0.805532	−	0.592552i	$-0.798120\pi$
$941$	−15.4034	−	47.4068i	−0.502136	−	1.54542i	0.303396	−	0.952865i	$-0.401880\pi$
$942$	−12.3602	−	8.98023i	−0.402718	−	0.292592i
$943$	7.38321	−	5.36422i	0.240430	−	0.174683i
$944$	−2.29423	+	7.06091i	−0.0746708	+	0.229813i
$945$	−1.13800			−0.0370190
$946$	−7.40810	−	7.76034i	−0.240858	−	0.252310i
$947$	−31.1447			−1.01207			−0.506033	−	0.862514i	$-0.668889\pi$
$947$	−31.1447			−1.01207			−0.506033	+	0.862514i	$0.668889\pi$
$948$	3.32696	−	10.2393i	0.108055	−	0.332558i
$949$	−13.0250	+	9.46319i	−0.422808	+	0.307188i
$950$	5.35695	+	3.89205i	0.173802	+	0.126275i
$951$	21.7366	+	66.8983i	0.704857	+	2.16933i
$952$	2.11624	+	6.51311i	0.0685877	+	0.211091i
$953$	31.4130	+	22.8229i	1.01757	+	0.739305i	0.965783	−	0.259353i	$-0.0835092\pi$
$953$	31.4130	+	22.8229i	1.01757	+	0.739305i	0.0517841	+	0.998658i	$0.483509\pi$
$954$	31.0519	−	22.5605i	1.00534	−	0.730424i
$955$	5.55194	−	17.0871i	0.179657	−	0.552926i
$956$	5.10128			0.164987
$957$	−21.9642	+	40.7403i	−0.710002	+	1.31695i
$958$	1.36694			0.0441640
$959$	2.82781	−	8.70311i	0.0913149	−	0.281038i
$960$	−2.05435	+	1.49258i	−0.0663040	+	0.0481727i
$961$	−0.0569969	−	0.0414107i	−0.00183861	−	0.00133583i
$962$	9.89875	+	30.4652i	0.319149	+	0.982238i
$963$	−20.1153	−	61.9085i	−0.648206	−	1.99497i
$964$	−19.4225	−	14.1112i	−0.625555	−	0.454492i
$965$	19.2692	−	13.9999i	0.620297	−	0.450672i
$966$	−2.46297	+	7.58025i	−0.0792449	+	0.243891i
$967$	18.4412			0.593030			0.296515	−	0.955028i	$-0.404176\pi$
$967$	18.4412			0.593030			0.296515	+	0.955028i	$0.404176\pi$
$968$	10.2926	+	3.88114i	0.330815	+	0.124745i
$969$	−115.149			−3.69911
$970$	0.213537	−	0.657198i	0.00685625	−	0.0211014i
$971$	−5.24451	+	3.81036i	−0.168304	+	0.122280i	−0.668749	−	0.743488i	$-0.733170\pi$
$971$	−5.24451	+	3.81036i	−0.168304	+	0.122280i	0.500445	+	0.865769i	$0.333170\pi$
$972$	−18.0766	−	13.1334i	−0.579807	−	0.421254i
$973$	−4.91741	−	15.1342i	−0.157645	−	0.485182i
$974$	−3.77302	−	11.6122i	−0.120895	−	0.372078i
$975$	−8.45283	−	6.14134i	−0.270707	−	0.196680i
$976$	1.84590	−	1.34113i	0.0590860	−	0.0429285i
$977$	−8.38820	+	25.8162i	−0.268362	+	0.825934i	0.722537	+	0.691332i	$0.242976\pi$
$977$	−8.38820	+	25.8162i	−0.268362	+	0.825934i	−0.990900	+	0.134602i	$0.957024\pi$
$978$	21.8750			0.699485
$979$	−10.2996	+	19.1042i	−0.329177	+	0.610574i
$980$	−1.00000			−0.0319438
$981$	4.49992	−	13.8493i	0.143671	−	0.442175i
$982$	−32.2431	+	23.4260i	−1.02892	+	0.747552i
$983$	8.01801	+	5.82543i	0.255735	+	0.185802i	0.708265	−	0.705947i	$-0.249478\pi$
$983$	8.01801	+	5.82543i	0.255735	+	0.185802i	−0.452530	+	0.891749i	$0.649478\pi$
$984$	−2.28154	−	7.02185i	−0.0727328	−	0.223848i
$985$	0.573384	+	1.76470i	0.0182695	+	0.0562279i
$986$	30.4478	+	22.1216i	0.969656	+	0.704496i
$987$	3.08128	−	2.23868i	0.0980783	−	0.0712581i
$988$	8.41916	−	25.9115i	0.267849	−	0.824355i
$989$	−10.1533			−0.322856
$990$	7.89671	+	8.27219i	0.250974	+	0.262907i
$991$	23.8739			0.758380			0.379190	−	0.925319i	$-0.376203\pi$
$991$	23.8739			0.758380			0.379190	+	0.925319i	$0.376203\pi$
$992$	−1.72249	+	5.30127i	−0.0546890	+	0.168316i
$993$	−59.2305	+	43.0335i	−1.87962	+	1.36563i
$994$	0.0492539	+	0.0357850i	0.00156224	+	0.00113503i
$995$	−6.74294	−	20.7526i	−0.213766	−	0.657903i
$996$	−8.04057	−	24.7463i	−0.254775	−	0.784117i
$997$	14.5272	+	10.5546i	0.460080	+	0.334268i	0.793563	−	0.608488i	$-0.208224\pi$
$997$	14.5272	+	10.5546i	0.460080	+	0.334268i	−0.333482	+	0.942756i	$0.608224\pi$
$998$	−29.7318	+	21.6014i	−0.941143	+	0.683780i
$999$	2.73775	−	8.42593i	0.0866186	−	0.266585i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	770.2.n.k.141.4	yes	16
11.4	even	5		8470.2.a.dh.1.2		8
11.5	even	5	inner	770.2.n.k.71.4	✓	16
11.7	odd	10		8470.2.a.dg.1.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
770.2.n.k.71.4	✓	16	11.5	even	5	inner
770.2.n.k.141.4	yes	16	1.1	even	1	trivial
8470.2.a.dg.1.2		8	11.7	odd	10
8470.2.a.dh.1.2		8	11.4	even	5

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:	\( N \)	\(=\)	\( 770 = 2 \cdot 5 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	770.n (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.309017 - 0.951057i) q^{2} +(2.05435 - 1.49258i) q^{3} +(-0.809017 - 0.587785i) q^{4} +(-0.309017 - 0.951057i) q^{5} +(-0.784693 - 2.41504i) q^{6} +(0.809017 + 0.587785i) q^{7} +(-0.809017 + 0.587785i) q^{8} +(1.06554 - 3.27939i) q^{9} +O(q^{10})\)	\(q+(0.309017 - 0.951057i) q^{2} +(2.05435 - 1.49258i) q^{3} +(-0.809017 - 0.587785i) q^{4} +(-0.309017 - 0.951057i) q^{5} +(-0.784693 - 2.41504i) q^{6} +(0.809017 + 0.587785i) q^{7} +(-0.809017 + 0.587785i) q^{8} +(1.06554 - 3.27939i) q^{9} -1.00000 q^{10} +(1.57392 - 2.91938i) q^{11} -2.53932 q^{12} +(-1.27148 + 3.91321i) q^{13} +(0.809017 - 0.587785i) q^{14} +(-2.05435 - 1.49258i) q^{15} +(0.309017 + 0.951057i) q^{16} +(-2.11624 - 6.51311i) q^{17} +(-2.78961 - 2.02677i) q^{18} +(5.35695 - 3.89205i) q^{19} +(-0.309017 + 0.951057i) q^{20} +2.53932 q^{21} +(-2.29013 - 2.39902i) q^{22} -3.13877 q^{23} +(-0.784693 + 2.41504i) q^{24} +(-0.809017 + 0.587785i) q^{25} +(3.32878 + 2.41850i) q^{26} +(-0.351660 - 1.08230i) q^{27} +(-0.309017 - 0.951057i) q^{28} +(-4.44605 - 3.23024i) q^{29} +(-2.05435 + 1.49258i) q^{30} +(-1.72249 + 5.30127i) q^{31} +1.00000 q^{32} +(-1.12402 - 8.34663i) q^{33} -6.84829 q^{34} +(0.309017 - 0.951057i) q^{35} +(-2.78961 + 2.02677i) q^{36} +(6.29838 + 4.57604i) q^{37} +(-2.04617 - 6.29747i) q^{38} +(3.22869 + 9.93689i) q^{39} +(0.809017 + 0.587785i) q^{40} +(-2.35226 + 1.70902i) q^{41} +(0.784693 - 2.41504i) q^{42} +3.23479 q^{43} +(-2.98929 + 1.43670i) q^{44} -3.44815 q^{45} +(-0.969934 + 2.98515i) q^{46} +(1.21343 - 0.881607i) q^{47} +(2.05435 + 1.49258i) q^{48} +(0.309017 + 0.951057i) q^{49} +(0.309017 + 0.951057i) q^{50} +(-14.0688 - 10.2216i) q^{51} +(3.32878 - 2.41850i) q^{52} +(-3.43975 + 10.5865i) q^{53} -1.13800 q^{54} +(-3.26286 - 0.594745i) q^{55} -1.00000 q^{56} +(5.19589 - 15.9913i) q^{57} +(-4.44605 + 3.23024i) q^{58} +(6.00637 + 4.36389i) q^{59} +(0.784693 + 2.41504i) q^{60} +(-0.705073 - 2.16999i) q^{61} +(4.50953 + 3.27637i) q^{62} +(2.78961 - 2.02677i) q^{63} +(0.309017 - 0.951057i) q^{64} +4.11459 q^{65} +(-8.28546 - 1.51025i) q^{66} +14.1969 q^{67} +(-2.11624 + 6.51311i) q^{68} +(-6.44815 + 4.68485i) q^{69} +(-0.809017 - 0.587785i) q^{70} +(0.0188133 + 0.0579014i) q^{71} +(1.06554 + 3.27939i) q^{72} +(3.16555 + 2.29991i) q^{73} +(6.29838 - 4.57604i) q^{74} +(-0.784693 + 2.41504i) q^{75} -6.62155 q^{76} +(2.98929 - 1.43670i) q^{77} +10.4483 q^{78} +(-1.31018 + 4.03232i) q^{79} +(0.809017 - 0.587785i) q^{80} +(6.03099 + 4.38177i) q^{81} +(0.898483 + 2.76525i) q^{82} +(3.16642 + 9.74525i) q^{83} +(-2.05435 - 1.49258i) q^{84} +(-5.54038 + 4.02533i) q^{85} +(0.999606 - 3.07647i) q^{86} -13.9551 q^{87} +(0.442644 + 3.28695i) q^{88} -6.54394 q^{89} +(-1.06554 + 3.27939i) q^{90} +(-3.32878 + 2.41850i) q^{91} +(2.53932 + 1.84492i) q^{92} +(4.37395 + 13.4616i) q^{93} +(-0.463488 - 1.42647i) q^{94} +(-5.35695 - 3.89205i) q^{95} +(2.05435 - 1.49258i) q^{96} +(-0.213537 + 0.657198i) q^{97} +1.00000 q^{98} +(-7.89671 - 8.27219i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 4 q^{2} - 5 q^{3} - 4 q^{4} + 4 q^{5} + 5 q^{6} + 4 q^{7} - 4 q^{8} + q^{9}+O(q^{10}) \) 16 * q - 4 * q^2 - 5 * q^3 - 4 * q^4 + 4 * q^5 + 5 * q^6 + 4 * q^7 - 4 * q^8 + q^9	\( 16 q - 4 q^{2} - 5 q^{3} - 4 q^{4} + 4 q^{5} + 5 q^{6} + 4 q^{7} - 4 q^{8} + q^{9} - 16 q^{10} - 2 q^{11} + 8 q^{13} + 4 q^{14} + 5 q^{15} - 4 q^{16} - 13 q^{17} - 9 q^{18} + 15 q^{19} + 4 q^{20} - 2 q^{22} + 20 q^{23} + 5 q^{24} - 4 q^{25} - 7 q^{26} + 10 q^{27} + 4 q^{28} - 14 q^{29} + 5 q^{30} - 6 q^{31} + 16 q^{32} - 25 q^{33} + 12 q^{34} - 4 q^{35} - 9 q^{36} + 28 q^{37} - 20 q^{38} + 15 q^{39} + 4 q^{40} + 2 q^{41} - 5 q^{42} - 10 q^{43} + 3 q^{44} - 16 q^{45} - 10 q^{46} - 10 q^{47} - 5 q^{48} - 4 q^{49} - 4 q^{50} - 42 q^{51} - 7 q^{52} - 2 q^{53} - 3 q^{55} - 16 q^{56} + 21 q^{57} - 14 q^{58} + 7 q^{59} - 5 q^{60} + 4 q^{61} + 14 q^{62} + 9 q^{63} - 4 q^{64} + 2 q^{65} - 10 q^{66} + 66 q^{67} - 13 q^{68} - 64 q^{69} - 4 q^{70} + 2 q^{71} + q^{72} + 12 q^{73} + 28 q^{74} + 5 q^{75} + 10 q^{76} - 3 q^{77} + 70 q^{78} + 2 q^{79} + 4 q^{80} - 30 q^{81} - 13 q^{82} - 5 q^{83} + 5 q^{84} - 7 q^{85} + 5 q^{86} - 24 q^{87} - 2 q^{88} + 2 q^{89} - q^{90} + 7 q^{91} - 38 q^{93} + 25 q^{94} - 15 q^{95} - 5 q^{96} + 22 q^{97} + 16 q^{98} - 18 q^{99}+O(q^{100}) \) 16 * q - 4 * q^2 - 5 * q^3 - 4 * q^4 + 4 * q^5 + 5 * q^6 + 4 * q^7 - 4 * q^8 + q^9 - 16 * q^10 - 2 * q^11 + 8 * q^13 + 4 * q^14 + 5 * q^15 - 4 * q^16 - 13 * q^17 - 9 * q^18 + 15 * q^19 + 4 * q^20 - 2 * q^22 + 20 * q^23 + 5 * q^24 - 4 * q^25 - 7 * q^26 + 10 * q^27 + 4 * q^28 - 14 * q^29 + 5 * q^30 - 6 * q^31 + 16 * q^32 - 25 * q^33 + 12 * q^34 - 4 * q^35 - 9 * q^36 + 28 * q^37 - 20 * q^38 + 15 * q^39 + 4 * q^40 + 2 * q^41 - 5 * q^42 - 10 * q^43 + 3 * q^44 - 16 * q^45 - 10 * q^46 - 10 * q^47 - 5 * q^48 - 4 * q^49 - 4 * q^50 - 42 * q^51 - 7 * q^52 - 2 * q^53 - 3 * q^55 - 16 * q^56 + 21 * q^57 - 14 * q^58 + 7 * q^59 - 5 * q^60 + 4 * q^61 + 14 * q^62 + 9 * q^63 - 4 * q^64 + 2 * q^65 - 10 * q^66 + 66 * q^67 - 13 * q^68 - 64 * q^69 - 4 * q^70 + 2 * q^71 + q^72 + 12 * q^73 + 28 * q^74 + 5 * q^75 + 10 * q^76 - 3 * q^77 + 70 * q^78 + 2 * q^79 + 4 * q^80 - 30 * q^81 - 13 * q^82 - 5 * q^83 + 5 * q^84 - 7 * q^85 + 5 * q^86 - 24 * q^87 - 2 * q^88 + 2 * q^89 - q^90 + 7 * q^91 - 38 * q^93 + 25 * q^94 - 15 * q^95 - 5 * q^96 + 22 * q^97 + 16 * q^98 - 18 * q^99

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