LMFDB - Embedded newform 770.2.n.f.421.1

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:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{5})$
Coefficient field:	8.0.484000000.9
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + x^{6} + 16x^{4} + 66x^{2} + 121 $ x^8 + x^6 + 16x^4 + 66x^2 + 121
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			421.1
Root			$-0.476925 + 1.46782i$ of defining polynomial
Character	$\chi$	$=$	770.421
Dual form			770.2.n.f.631.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.809017 - 0.587785i) q^{2} +(-0.785942 - 2.41888i) q^{3} +(0.309017 - 0.951057i) q^{4} +(-0.809017 - 0.587785i) q^{5} +(-2.05762 - 1.49495i) q^{6} +(-0.309017 + 0.951057i) q^{7} +(-0.309017 - 0.951057i) q^{8} +(-2.80623 + 2.03884i) q^{9} +O(q^{10})$	\(q+(0.809017 - 0.587785i) q^{2} +(-0.785942 - 2.41888i) q^{3} +(0.309017 - 0.951057i) q^{4} +(-0.809017 - 0.587785i) q^{5} +(-2.05762 - 1.49495i) q^{6} +(-0.309017 + 0.951057i) q^{7} +(-0.309017 - 0.951057i) q^{8} +(-2.80623 + 2.03884i) q^{9} -1.00000 q^{10} +(-2.31504 + 2.37499i) q^{11} -2.54336 q^{12} +(-5.19594 + 3.77507i) q^{13} +(0.309017 + 0.951057i) q^{14} +(-0.785942 + 2.41888i) q^{15} +(-0.809017 - 0.587785i) q^{16} +(-3.19873 - 2.32401i) q^{17} +(-1.07188 + 3.29892i) q^{18} +(-0.762867 - 2.34786i) q^{19} +(-0.809017 + 0.587785i) q^{20} +2.54336 q^{21} +(-0.476925 + 3.28216i) q^{22} +4.99442 q^{23} +(-2.05762 + 1.49495i) q^{24} +(0.309017 + 0.951057i) q^{25} +(-1.98467 + 6.10820i) q^{26} +(0.964387 + 0.700668i) q^{27} +(0.809017 + 0.587785i) q^{28} +(2.79476 - 8.60137i) q^{29} +(0.785942 + 2.41888i) q^{30} +(-6.38242 + 4.63710i) q^{31} -1.00000 q^{32} +(7.56431 + 3.73321i) q^{33} -3.95385 q^{34} +(0.809017 - 0.587785i) q^{35} +(1.07188 + 3.29892i) q^{36} +(3.41279 - 10.5035i) q^{37} +(-1.99721 - 1.45106i) q^{38} +(13.2152 + 9.60138i) q^{39} +(-0.309017 + 0.951057i) q^{40} +(2.14886 + 6.61350i) q^{41} +(2.05762 - 1.49495i) q^{42} -3.02295 q^{43} +(1.54336 + 2.93565i) q^{44} +3.46869 q^{45} +(4.04057 - 2.93565i) q^{46} +(-2.58951 - 7.96970i) q^{47} +(-0.785942 + 2.41888i) q^{48} +(-0.809017 - 0.587785i) q^{49} +(0.809017 + 0.587785i) q^{50} +(-3.10750 + 9.56389i) q^{51} +(1.98467 + 6.10820i) q^{52} +(-8.14004 + 5.91409i) q^{53} +1.19205 q^{54} +(3.26889 - 0.560659i) q^{55} +1.00000 q^{56} +(-5.07963 + 3.69057i) q^{57} +(-2.79476 - 8.60137i) q^{58} +(-1.26566 + 3.89529i) q^{59} +(2.05762 + 1.49495i) q^{60} +(-2.91000 - 2.11424i) q^{61} +(-2.43787 + 7.50298i) q^{62} +(-1.07188 - 3.29892i) q^{63} +(-0.809017 + 0.587785i) q^{64} +6.42254 q^{65} +(8.31398 - 1.42596i) q^{66} -1.28222 q^{67} +(-3.19873 + 2.32401i) q^{68} +(-3.92533 - 12.0809i) q^{69} +(0.309017 - 0.951057i) q^{70} +(4.77340 + 3.46808i) q^{71} +(2.80623 + 2.03884i) q^{72} +(3.16808 - 9.75035i) q^{73} +(-3.41279 - 10.5035i) q^{74} +(2.05762 - 1.49495i) q^{75} -2.46869 q^{76} +(-1.54336 - 2.93565i) q^{77} +16.3348 q^{78} +(-5.02480 + 3.65073i) q^{79} +(0.309017 + 0.951057i) q^{80} +(-2.27877 + 7.01334i) q^{81} +(5.62578 + 4.08737i) q^{82} +(-10.7909 - 7.84005i) q^{83} +(0.785942 - 2.41888i) q^{84} +(1.22181 + 3.76033i) q^{85} +(-2.44561 + 1.77684i) q^{86} -23.0022 q^{87} +(2.97414 + 1.46782i) q^{88} +14.7432 q^{89} +(2.80623 - 2.03884i) q^{90} +(-1.98467 - 6.10820i) q^{91} +(1.54336 - 4.74998i) q^{92} +(16.2328 + 11.7938i) q^{93} +(-6.77943 - 4.92554i) q^{94} +(-0.762867 + 2.34786i) q^{95} +(0.785942 + 2.41888i) q^{96} +(9.67611 - 7.03010i) q^{97} -1.00000 q^{98} +(1.65431 - 11.3848i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 2 q^{2} + 2 q^{3} - 2 q^{4} - 2 q^{5} - 2 q^{6} + 2 q^{7} + 2 q^{8} + 2 q^{9}+O(q^{10}) $ 8 * q + 2 * q^2 + 2 * q^3 - 2 * q^4 - 2 * q^5 - 2 * q^6 + 2 * q^7 + 2 * q^8 + 2 * q^9	$ 8 q + 2 q^{2} + 2 q^{3} - 2 q^{4} - 2 q^{5} - 2 q^{6} + 2 q^{7} + 2 q^{8} + 2 q^{9} - 8 q^{10} - 8 q^{12} - 2 q^{13} - 2 q^{14} + 2 q^{15} - 2 q^{16} - 6 q^{17} + 8 q^{18} + 6 q^{19} - 2 q^{20} + 8 q^{21} - 2 q^{24} - 2 q^{25} + 12 q^{26} - 4 q^{27} + 2 q^{28} + 20 q^{29} - 2 q^{30} - 6 q^{31} - 8 q^{32} - 8 q^{33} - 24 q^{34} + 2 q^{35} - 8 q^{36} + 16 q^{37} + 4 q^{38} + 20 q^{39} + 2 q^{40} - 12 q^{41} + 2 q^{42} + 20 q^{43} + 12 q^{45} - 16 q^{47} + 2 q^{48} - 2 q^{49} + 2 q^{50} - 20 q^{51} - 12 q^{52} - 30 q^{53} + 44 q^{54} + 8 q^{56} - 20 q^{58} - 18 q^{59} + 2 q^{60} + 8 q^{61} - 24 q^{62} + 8 q^{63} - 2 q^{64} + 28 q^{65} + 18 q^{66} - 6 q^{68} - 28 q^{69} - 2 q^{70} + 22 q^{71} - 2 q^{72} - 50 q^{73} - 16 q^{74} + 2 q^{75} - 4 q^{76} + 60 q^{78} - 34 q^{79} - 2 q^{80} - 28 q^{81} + 12 q^{82} - 34 q^{83} - 2 q^{84} - 6 q^{85} + 4 q^{87} - 8 q^{89} - 2 q^{90} + 12 q^{91} + 56 q^{93} - 24 q^{94} + 6 q^{95} - 2 q^{96} - 8 q^{98} - 24 q^{99}+O(q^{100}) $ 8 * q + 2 * q^2 + 2 * q^3 - 2 * q^4 - 2 * q^5 - 2 * q^6 + 2 * q^7 + 2 * q^8 + 2 * q^9 - 8 * q^10 - 8 * q^12 - 2 * q^13 - 2 * q^14 + 2 * q^15 - 2 * q^16 - 6 * q^17 + 8 * q^18 + 6 * q^19 - 2 * q^20 + 8 * q^21 - 2 * q^24 - 2 * q^25 + 12 * q^26 - 4 * q^27 + 2 * q^28 + 20 * q^29 - 2 * q^30 - 6 * q^31 - 8 * q^32 - 8 * q^33 - 24 * q^34 + 2 * q^35 - 8 * q^36 + 16 * q^37 + 4 * q^38 + 20 * q^39 + 2 * q^40 - 12 * q^41 + 2 * q^42 + 20 * q^43 + 12 * q^45 - 16 * q^47 + 2 * q^48 - 2 * q^49 + 2 * q^50 - 20 * q^51 - 12 * q^52 - 30 * q^53 + 44 * q^54 + 8 * q^56 - 20 * q^58 - 18 * q^59 + 2 * q^60 + 8 * q^61 - 24 * q^62 + 8 * q^63 - 2 * q^64 + 28 * q^65 + 18 * q^66 - 6 * q^68 - 28 * q^69 - 2 * q^70 + 22 * q^71 - 2 * q^72 - 50 * q^73 - 16 * q^74 + 2 * q^75 - 4 * q^76 + 60 * q^78 - 34 * q^79 - 2 * q^80 - 28 * q^81 + 12 * q^82 - 34 * q^83 - 2 * q^84 - 6 * q^85 + 4 * q^87 - 8 * q^89 - 2 * q^90 + 12 * q^91 + 56 * q^93 - 24 * q^94 + 6 * q^95 - 2 * q^96 - 8 * q^98 - 24 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$211$	$617$	$661$
$\chi(n)$	$e\left(\frac{4}{5}\right)$	$1$	$1$

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 $

$2$	0.809017	−	0.587785i	0.572061	−	0.415627i
$2$	0.809017	−	0.587785i	0.572061	−	0.415627i
$3$	−0.785942	−	2.41888i	−0.453764	−	1.39654i	−0.872580	−	0.488471i	$-0.837555\pi$
$3$	−0.785942	−	2.41888i	−0.453764	−	1.39654i	0.418816	−	0.908071i	$-0.362445\pi$
$4$	0.309017	−	0.951057i	0.154508	−	0.475528i
$5$	−0.809017	−	0.587785i	−0.361803	−	0.262866i
$5$	−0.809017	−	0.587785i	−0.361803	−	0.262866i
$6$	−2.05762	−	1.49495i	−0.840021	−	0.610311i
$7$	−0.309017	+	0.951057i	−0.116797	+	0.359466i
$7$	−0.309017	+	0.951057i	−0.116797	+	0.359466i
$8$	−0.309017	−	0.951057i	−0.109254	−	0.336249i
$9$	−2.80623	+	2.03884i	−0.935410	+	0.679615i
$10$	−1.00000			−0.316228
$11$	−2.31504	+	2.37499i	−0.698012	+	0.716086i
$11$	−2.31504	+	2.37499i	−0.698012	+	0.716086i
$12$	−2.54336			−0.734205
$13$	−5.19594	+	3.77507i	−1.44110	+	1.04702i	−0.453283	+	0.891366i	$0.649747\pi$
$13$	−5.19594	+	3.77507i	−1.44110	+	1.04702i	−0.987812	+	0.155651i	$0.950253\pi$
$14$	0.309017	+	0.951057i	0.0825883	+	0.254181i
$15$	−0.785942	+	2.41888i	−0.202929	+	0.624552i
$16$	−0.809017	−	0.587785i	−0.202254	−	0.146946i
$17$	−3.19873	−	2.32401i	−0.775806	−	0.563656i	0.127911	−	0.991786i	$-0.459173\pi$
$17$	−3.19873	−	2.32401i	−0.775806	−	0.563656i	−0.903718	+	0.428129i	$0.859173\pi$
$18$	−1.07188	+	3.29892i	−0.252646	+	0.777563i
$19$	−0.762867	−	2.34786i	−0.175014	−	0.538637i	0.824620	−	0.565687i	$-0.191389\pi$
$19$	−0.762867	−	2.34786i	−0.175014	−	0.538637i	−0.999634	+	0.0270497i	$0.991389\pi$
$20$	−0.809017	+	0.587785i	−0.180902	+	0.131433i
$21$	2.54336			0.555007
$22$	−0.476925	+	3.28216i	−0.101681	+	0.699758i
$23$	4.99442			1.04141			0.520705	−	0.853737i	$-0.325669\pi$
$23$	4.99442			1.04141			0.520705	+	0.853737i	$0.325669\pi$
$24$	−2.05762	+	1.49495i	−0.420011	+	0.305156i
$25$	0.309017	+	0.951057i	0.0618034	+	0.190211i
$26$	−1.98467	+	6.10820i	−0.389227	+	1.19792i
$27$	0.964387	+	0.700668i	0.185596	+	0.134844i
$28$	0.809017	+	0.587785i	0.152890	+	0.111081i
$29$	2.79476	−	8.60137i	0.518973	−	1.59724i	−0.256961	−	0.966422i	$-0.582721\pi$
$29$	2.79476	−	8.60137i	0.518973	−	1.59724i	0.775935	−	0.630813i	$-0.217279\pi$
$30$	0.785942	+	2.41888i	0.143493	+	0.441625i
$31$	−6.38242	+	4.63710i	−1.14632	+	0.832847i	−0.987987	−	0.154539i	$-0.950611\pi$
$31$	−6.38242	+	4.63710i	−1.14632	+	0.832847i	−0.158329	+	0.987386i	$0.550611\pi$
$32$	−1.00000			−0.176777
$33$	7.56431	+	3.73321i	1.31678	+	0.649868i
$34$	−3.95385			−0.678080
$35$	0.809017	−	0.587785i	0.136749	−	0.0993538i
$36$	1.07188	+	3.29892i	0.178647	+	0.549820i
$37$	3.41279	−	10.5035i	0.561059	−	1.72676i	−0.118320	−	0.992975i	$-0.537751\pi$
$37$	3.41279	−	10.5035i	0.561059	−	1.72676i	0.679379	−	0.733787i	$-0.262249\pi$
$38$	−1.99721	−	1.45106i	−0.323991	−	0.235393i
$39$	13.2152	+	9.60138i	2.11612	+	1.53745i
$40$	−0.309017	+	0.951057i	−0.0488599	+	0.150375i
$41$	2.14886	+	6.61350i	0.335595	+	1.03286i	0.966428	+	0.256937i	$0.0827133\pi$
$41$	2.14886	+	6.61350i	0.335595	+	1.03286i	−0.630833	+	0.775919i	$0.717287\pi$
$42$	2.05762	−	1.49495i	0.317498	−	0.230676i
$43$	−3.02295			−0.460995			−0.230497	−	0.973073i	$-0.574035\pi$
$43$	−3.02295			−0.460995			−0.230497	+	0.973073i	$0.574035\pi$
$44$	1.54336	+	2.93565i	0.232671	+	0.442566i
$45$	3.46869			0.517082
$46$	4.04057	−	2.93565i	0.595750	−	0.432838i
$47$	−2.58951	−	7.96970i	−0.377719	−	1.16250i	−0.941626	−	0.336661i	$-0.890702\pi$
$47$	−2.58951	−	7.96970i	−0.377719	−	1.16250i	0.563907	−	0.825839i	$-0.309298\pi$
$48$	−0.785942	+	2.41888i	−0.113441	+	0.349135i
$49$	−0.809017	−	0.587785i	−0.115574	−	0.0839693i
$50$	0.809017	+	0.587785i	0.114412	+	0.0831254i
$51$	−3.10750	+	9.56389i	−0.435137	+	1.33921i
$52$	1.98467	+	6.10820i	0.275225	+	0.847055i
$53$	−8.14004	+	5.91409i	−1.11812	+	0.812362i	−0.983923	−	0.178592i	$-0.942846\pi$
$53$	−8.14004	+	5.91409i	−1.11812	+	0.812362i	−0.134198	+	0.990955i	$0.542846\pi$
$54$	1.19205			0.162217
$55$	3.26889	−	0.560659i	0.440777	−	0.0755992i
$56$	1.00000			0.133631
$57$	−5.07963	+	3.69057i	−0.672814	+	0.488828i
$58$	−2.79476	−	8.60137i	−0.366969	−	1.12942i
$59$	−1.26566	+	3.89529i	−0.164774	+	0.507123i	−0.999020	−	0.0442704i	$-0.985904\pi$
$59$	−1.26566	+	3.89529i	−0.164774	+	0.507123i	0.834245	+	0.551393i	$0.185904\pi$
$60$	2.05762	+	1.49495i	0.265638	+	0.192997i
$61$	−2.91000	−	2.11424i	−0.372588	−	0.270701i	0.385696	−	0.922626i	$-0.373962\pi$
$61$	−2.91000	−	2.11424i	−0.372588	−	0.270701i	−0.758283	+	0.651925i	$0.773962\pi$
$62$	−2.43787	+	7.50298i	−0.309609	+	0.952879i
$63$	−1.07188	−	3.29892i	−0.135045	−	0.415625i
$64$	−0.809017	+	0.587785i	−0.101127	+	0.0734732i
$65$	6.42254			0.796618
$66$	8.31398	−	1.42596i	1.02338	−	0.175523i
$67$	−1.28222			−0.156648			−0.0783239	−	0.996928i	$-0.524957\pi$
$67$	−1.28222			−0.156648			−0.0783239	+	0.996928i	$0.524957\pi$
$68$	−3.19873	+	2.32401i	−0.387903	+	0.281828i
$69$	−3.92533	−	12.0809i	−0.472554	−	1.45437i
$70$	0.309017	−	0.951057i	0.0369346	−	0.113673i
$71$	4.77340	+	3.46808i	0.566499	+	0.411585i	0.833832	−	0.552019i	$-0.186142\pi$
$71$	4.77340	+	3.46808i	0.566499	+	0.411585i	−0.267333	+	0.963604i	$0.586142\pi$
$72$	2.80623	+	2.03884i	0.330717	+	0.240280i
$73$	3.16808	−	9.75035i	0.370796	−	1.14119i	−0.575476	−	0.817819i	$-0.695183\pi$
$73$	3.16808	−	9.75035i	0.370796	−	1.14119i	0.946272	−	0.323373i	$-0.104817\pi$
$74$	−3.41279	−	10.5035i	−0.396729	−	1.22101i
$75$	2.05762	−	1.49495i	0.237594	−	0.172622i
$76$	−2.46869			−0.283178
$77$	−1.54336	−	2.93565i	−0.175882	−	0.334548i
$78$	16.3348			1.84956
$79$	−5.02480	+	3.65073i	−0.565334	+	0.410739i	−0.833407	−	0.552659i	$-0.813613\pi$
$79$	−5.02480	+	3.65073i	−0.565334	+	0.410739i	0.268073	+	0.963399i	$0.413613\pi$
$80$	0.309017	+	0.951057i	0.0345492	+	0.106331i
$81$	−2.27877	+	7.01334i	−0.253197	+	0.779260i
$82$	5.62578	+	4.08737i	0.621264	+	0.451375i
$83$	−10.7909	−	7.84005i	−1.18446	−	0.860557i	−0.191788	−	0.981436i	$-0.561429\pi$
$83$	−10.7909	−	7.84005i	−1.18446	−	0.860557i	−0.992667	+	0.120879i	$0.961429\pi$
$84$	0.785942	−	2.41888i	0.0857533	−	0.263922i
$85$	1.22181	+	3.76033i	0.132524	+	0.407866i
$86$	−2.44561	+	1.77684i	−0.263717	+	0.191602i
$87$	−23.0022			−2.46610
$88$	2.97414	+	1.46782i	0.317044	+	0.156471i
$89$	14.7432			1.56278			0.781388	−	0.624045i	$-0.214512\pi$
$89$	14.7432			1.56278			0.781388	+	0.624045i	$0.214512\pi$
$90$	2.80623	−	2.03884i	0.295803	−	0.214913i
$91$	−1.98467	−	6.10820i	−0.208050	−	0.640313i
$92$	1.54336	−	4.74998i	0.160907	−	0.495220i
$93$	16.2328	+	11.7938i	1.68326	+	1.22296i
$94$	−6.77943	−	4.92554i	−0.699245	−	0.508031i
$95$	−0.762867	+	2.34786i	−0.0782685	+	0.240886i
$96$	0.785942	+	2.41888i	0.0802149	+	0.246876i
$97$	9.67611	−	7.03010i	0.982460	−	0.713799i	0.0242028	−	0.999707i	$-0.492295\pi$
$97$	9.67611	−	7.03010i	0.982460	−	0.713799i	0.958257	+	0.285908i	$0.0922953\pi$
$98$	−1.00000			−0.101015
$99$	1.65431	−	11.3848i	0.166264	−	1.14421i
$100$	1.00000			0.100000
$101$	1.82930	−	1.32907i	0.182023	−	0.132247i	−0.493043	−	0.870005i	$-0.664115\pi$
$101$	1.82930	−	1.32907i	0.182023	−	0.132247i	0.675065	+	0.737758i	$0.264115\pi$
$102$	3.10750	+	9.56389i	0.307688	+	0.946966i
$103$	4.15192	−	12.7783i	0.409101	−	1.25908i	−0.508321	−	0.861168i	$-0.669733\pi$
$103$	4.15192	−	12.7783i	0.409101	−	1.25908i	0.917422	−	0.397916i	$-0.130267\pi$
$104$	5.19594	+	3.77507i	0.509504	+	0.370176i
$105$	−2.05762	−	1.49495i	−0.200803	−	0.145892i
$106$	−3.10922	+	9.56920i	−0.301994	+	0.929442i
$107$	4.13708	+	12.7326i	0.399947	+	1.23091i	0.925041	+	0.379866i	$0.124030\pi$
$107$	4.13708	+	12.7326i	0.399947	+	1.23091i	−0.525094	+	0.851044i	$0.675970\pi$
$108$	0.964387	−	0.700668i	0.0927982	−	0.0674218i
$109$	−8.67624			−0.831033			−0.415516	−	0.909586i	$-0.636399\pi$
$109$	−8.67624			−0.831033			−0.415516	+	0.909586i	$0.636399\pi$
$110$	2.31504	−	2.37499i	0.220731	−	0.226446i
$111$	−28.0889			−2.66608
$112$	0.809017	−	0.587785i	0.0764449	−	0.0555405i
$113$	−2.83267	−	8.71806i	−0.266475	−	0.820126i	−0.991350	−	0.131246i	$-0.958102\pi$
$113$	−2.83267	−	8.71806i	−0.266475	−	0.820126i	0.724875	−	0.688881i	$-0.241898\pi$
$114$	−1.94025	+	5.97147i	−0.181721	+	0.559279i
$115$	−4.04057	−	2.93565i	−0.376785	−	0.273751i
$116$	−7.31677	−	5.31594i	−0.679345	−	0.493573i
$117$	6.88422	−	21.1874i	0.636446	−	1.95878i
$118$	1.26566	+	3.89529i	0.116513	+	0.358590i
$119$	3.19873	−	2.32401i	0.293227	−	0.213042i
$120$	2.54336			0.232176
$121$	−0.281153	−	10.9964i	−0.0255594	−	0.999673i
$122$	−3.59696			−0.325653
$123$	14.3084	−	10.3957i	1.29015	−	0.937345i
$124$	2.43787	+	7.50298i	0.218927	+	0.673787i
$125$	0.309017	−	0.951057i	0.0276393	−	0.0850651i
$126$	−2.80623	−	2.03884i	−0.249999	−	0.181635i
$127$	−12.3615	−	8.98117i	−1.09691	−	0.796950i	−0.116355	−	0.993208i	$-0.537121\pi$
$127$	−12.3615	−	8.98117i	−1.09691	−	0.796950i	−0.980552	+	0.196258i	$0.937121\pi$
$128$	−0.309017	+	0.951057i	−0.0273135	+	0.0840623i
$129$	2.37586	+	7.31215i	0.209183	+	0.643799i
$130$	5.19594	−	3.77507i	0.455714	−	0.331096i
$131$	−5.65461			−0.494045			−0.247023	−	0.969010i	$-0.579452\pi$
$131$	−5.65461			−0.494045			−0.247023	+	0.969010i	$0.579452\pi$
$132$	5.88799	−	6.04046i	0.512484	−	0.525754i
$133$	2.46869			0.214063
$134$	−1.03734	+	0.753669i	−0.0896122	+	0.0651071i
$135$	−0.368363	−	1.13370i	−0.0317036	−	0.0975738i
$136$	−1.22181	+	3.76033i	−0.104769	+	0.322446i
$137$	3.19795	+	2.32344i	0.273219	+	0.198505i	0.715954	−	0.698147i	$-0.245992\pi$
$137$	3.19795	+	2.32344i	0.273219	+	0.198505i	−0.442735	+	0.896652i	$0.645992\pi$
$138$	−10.2766	−	7.46642i	−0.874806	−	0.635584i
$139$	−6.49721	+	19.9964i	−0.551086	+	1.69607i	0.154975	+	0.987918i	$0.450470\pi$
$139$	−6.49721	+	19.9964i	−0.551086	+	1.69607i	−0.706061	+	0.708151i	$0.749530\pi$
$140$	−0.309017	−	0.951057i	−0.0261167	−	0.0803789i
$141$	−17.2425	+	12.5274i	−1.45208	+	1.05500i
$142$	5.90025			0.495138
$143$	3.06307	−	21.0798i	0.256147	−	1.76278i
$144$	3.46869			0.289057
$145$	−7.31677	+	5.31594i	−0.607624	+	0.441465i
$146$	−3.16808	−	9.75035i	−0.262192	−	0.806944i
$147$	−0.785942	+	2.41888i	−0.0648234	+	0.199506i
$148$	−8.93480	−	6.49151i	−0.734436	−	0.533599i
$149$	6.91975	+	5.02749i	0.566888	+	0.411868i	0.833973	−	0.551805i	$-0.186061\pi$
$149$	6.91975	+	5.02749i	0.566888	+	0.411868i	−0.267085	+	0.963673i	$0.586061\pi$
$150$	0.785942	−	2.41888i	0.0641719	−	0.197501i
$151$	−0.683406	−	2.10331i	−0.0556148	−	0.171165i	0.919391	−	0.393346i	$-0.128682\pi$
$151$	−0.683406	−	2.10331i	−0.0556148	−	0.171165i	−0.975005	+	0.222181i	$0.928682\pi$
$152$	−1.99721	+	1.45106i	−0.161995	+	0.117696i
$153$	13.7147			1.10877
$154$	−2.97414	−	1.46782i	−0.239663	−	0.118281i
$155$	7.88910			0.633668
$156$	13.2152	−	9.60138i	1.05806	−	0.768726i
$157$	−4.13660	−	12.7311i	−0.330136	−	1.01606i	−0.969068	−	0.246792i	$-0.920623\pi$
$157$	−4.13660	−	12.7311i	−0.330136	−	1.01606i	0.638932	−	0.769263i	$-0.279377\pi$
$158$	−1.91930	+	5.90700i	−0.152691	+	0.469936i
$159$	20.7031	+	15.0417i	1.64186	+	1.19288i
$160$	0.809017	+	0.587785i	0.0639584	+	0.0464685i
$161$	−1.54336	+	4.74998i	−0.121634	+	0.374351i
$162$	2.27877	+	7.01334i	0.179037	+	0.551020i
$163$	−1.66095	+	1.20675i	−0.130095	+	0.0945198i	−0.650930	−	0.759138i	$-0.725621\pi$
$163$	−1.66095	+	1.20675i	−0.130095	+	0.0945198i	0.520835	+	0.853658i	$0.325621\pi$
$164$	6.95385			0.543004
$165$	−3.92533	−	7.46642i	−0.305586	−	0.581260i
$166$	−13.3383			−1.03525
$167$	−17.1525	+	12.4621i	−1.32730	+	0.964343i	−0.327494	+	0.944853i	$0.606204\pi$
$167$	−17.1525	+	12.4621i	−1.32730	+	0.964343i	−0.999810	+	0.0194894i	$0.993796\pi$
$168$	−0.785942	−	2.41888i	−0.0606367	−	0.186621i
$169$	8.72943	−	26.8664i	0.671494	−	2.06665i
$170$	3.19873	+	2.32401i	0.245332	+	0.178244i
$171$	6.92771	+	5.03328i	0.529775	+	0.384904i
$172$	−0.934142	+	2.87499i	−0.0712276	+	0.219216i
$173$	−1.82700	−	5.62293i	−0.138904	−	0.427504i	0.857272	−	0.514863i	$-0.172157\pi$
$173$	−1.82700	−	5.62293i	−0.138904	−	0.427504i	−0.996177	+	0.0873592i	$0.972157\pi$
$174$	−18.6092	+	13.5204i	−1.41076	+	1.02498i
$175$	−1.00000			−0.0755929
$176$	3.26889	−	0.560659i	0.246402	−	0.0422613i
$177$	10.4170			0.782987
$178$	11.9275	−	8.66584i	0.894004	−	0.649532i
$179$	−5.52768	−	17.0124i	−0.413158	−	1.27157i	−0.913888	−	0.405966i	$-0.866935\pi$
$179$	−5.52768	−	17.0124i	−0.413158	−	1.27157i	0.500730	−	0.865604i	$-0.333065\pi$
$180$	1.07188	−	3.29892i	0.0798935	−	0.245887i
$181$	−8.95660	−	6.50735i	−0.665739	−	0.483688i	0.202857	−	0.979208i	$-0.434977\pi$
$181$	−8.95660	−	6.50735i	−0.665739	−	0.483688i	−0.868596	+	0.495521i	$0.834977\pi$
$182$	−5.19594	−	3.77507i	−0.385149	−	0.279827i
$183$	−2.82700	+	8.70062i	−0.208978	+	0.643168i
$184$	−1.54336	−	4.74998i	−0.113778	−	0.350173i
$185$	−8.93480	+	6.49151i	−0.656900	+	0.477265i
$186$	20.0648			1.47123
$187$	12.9247	−	2.21676i	0.945149	−	0.162106i
$188$	−8.37984			−0.611162
$189$	−0.964387	+	0.700668i	−0.0701488	+	0.0509661i
$190$	0.762867	+	2.34786i	0.0553442	+	0.170332i
$191$	−2.95413	+	9.09187i	−0.213753	+	0.657865i	0.785487	+	0.618879i	$0.212413\pi$
$191$	−2.95413	+	9.09187i	−0.213753	+	0.657865i	−0.999240	+	0.0389860i	$0.987587\pi$
$192$	2.05762	+	1.49495i	0.148496	+	0.107889i
$193$	13.4981	+	9.80695i	0.971615	+	0.705920i	0.955819	−	0.293955i	$-0.0949717\pi$
$193$	13.4981	+	9.80695i	0.971615	+	0.705920i	0.0157962	+	0.999875i	$0.494972\pi$
$194$	3.69594	−	11.3749i	0.265353	−	0.816674i
$195$	−5.04774	−	15.5354i	−0.361476	−	1.11251i
$196$	−0.809017	+	0.587785i	−0.0577869	+	0.0419847i
$197$	0.533440			0.0380060			0.0190030	−	0.999819i	$-0.493951\pi$
$197$	0.533440			0.0380060			0.0190030	+	0.999819i	$0.493951\pi$
$198$	−5.35344	−	10.1829i	−0.380453	−	0.723664i
$199$	−2.81443			−0.199510			−0.0997548	−	0.995012i	$-0.531806\pi$
$199$	−2.81443			−0.199510			−0.0997548	+	0.995012i	$0.531806\pi$
$200$	0.809017	−	0.587785i	0.0572061	−	0.0415627i
$201$	1.00775	+	3.10153i	0.0710811	+	0.218765i
$202$	0.698732	−	2.15048i	0.0491626	−	0.151307i
$203$	7.31677	+	5.31594i	0.513536	+	0.373106i
$204$	8.13553	+	5.91081i	0.569601	+	0.413840i
$205$	2.14886	−	6.61350i	0.150083	−	0.461907i
$206$	−4.15192	−	12.7783i	−0.289278	−	0.890307i
$207$	−14.0155	+	10.1829i	−0.974144	+	0.707757i
$208$	6.42254			0.445323
$209$	7.34222	+	3.62360i	0.507872	+	0.250650i
$210$	−2.54336			−0.175509
$211$	2.59078	−	1.88232i	0.178357	−	0.129584i	−0.495025	−	0.868879i	$-0.664841\pi$
$211$	2.59078	−	1.88232i	0.178357	−	0.129584i	0.673382	+	0.739295i	$0.264841\pi$
$212$	3.10922	+	9.56920i	0.213542	+	0.657215i
$213$	4.63726	−	14.2720i	0.317740	−	0.977902i
$214$	10.8310	+	7.86920i	0.740394	+	0.537928i
$215$	2.44561	+	1.77684i	0.166790	+	0.121180i
$216$	0.368363	−	1.13370i	0.0250639	−	0.0771389i
$217$	−2.43787	−	7.50298i	−0.165493	−	0.509335i
$218$	−7.01922	+	5.09976i	−0.475402	+	0.345400i
$219$	−26.0749			−1.76198
$220$	0.476925	−	3.28216i	0.0321543	−	0.221283i
$221$	25.3938			1.70817
$222$	−22.7244	+	16.5103i	−1.52516	+	1.10810i
$223$	−0.237490	−	0.730921i	−0.0159035	−	0.0489461i	0.942790	−	0.333388i	$-0.108192\pi$
$223$	−0.237490	−	0.730921i	−0.0159035	−	0.0489461i	−0.958693	+	0.284442i	$0.908192\pi$
$224$	0.309017	−	0.951057i	0.0206471	−	0.0635451i
$225$	−2.80623	−	2.03884i	−0.187082	−	0.135923i
$226$	−7.41603	−	5.38806i	−0.493307	−	0.358408i
$227$	2.03561	−	6.26497i	0.135108	−	0.415821i	−0.860498	−	0.509453i	$-0.829848\pi$
$227$	2.03561	−	6.26497i	0.135108	−	0.415821i	0.995607	+	0.0936322i	$0.0298478\pi$
$228$	1.94025	+	5.97147i	0.128496	+	0.395470i
$229$	18.8362	−	13.6853i	1.24473	−	0.904352i	0.246829	−	0.969059i	$-0.420611\pi$
$229$	18.8362	−	13.6853i	1.24473	−	0.904352i	0.997904	+	0.0647076i	$0.0206115\pi$
$230$	−4.99442			−0.329323
$231$	−5.88799	+	6.04046i	−0.387401	+	0.397433i
$232$	−9.04402			−0.593769
$233$	1.39344	−	1.01239i	0.0912872	−	0.0663241i	−0.541205	−	0.840890i	$-0.682032\pi$
$233$	1.39344	−	1.01239i	0.0912872	−	0.0663241i	0.632493	+	0.774566i	$0.282032\pi$
$234$	−6.88422	−	21.1874i	−0.450035	−	1.38507i
$235$	−2.58951	+	7.96970i	−0.168921	+	0.519886i
$236$	3.31353	+	2.40742i	0.215692	+	0.156710i
$237$	12.7799	+	9.28513i	0.830142	+	0.603134i
$238$	1.22181	−	3.76033i	0.0791980	−	0.243746i
$239$	3.59810	+	11.0738i	0.232742	+	0.716306i	0.997413	+	0.0718853i	$0.0229016\pi$
$239$	3.59810	+	11.0738i	0.232742	+	0.716306i	−0.764671	+	0.644421i	$0.777098\pi$
$240$	2.05762	−	1.49495i	0.132819	−	0.0964986i
$241$	−9.58236			−0.617254			−0.308627	−	0.951183i	$-0.599870\pi$
$241$	−9.58236			−0.617254			−0.308627	+	0.951183i	$0.599870\pi$
$242$	−6.69098	−	8.73102i	−0.430113	−	0.561251i
$243$	22.3316			1.43257
$244$	−2.91000	+	2.11424i	−0.186294	+	0.135350i
$245$	0.309017	+	0.951057i	0.0197424	+	0.0607608i
$246$	5.46532	−	16.8205i	0.348456	−	1.07244i
$247$	12.8272	+	9.31949i	0.816174	+	0.592985i
$248$	6.38242	+	4.63710i	0.405284	+	0.294456i
$249$	−10.4831	+	32.2637i	−0.664341	+	2.04463i
$250$	−0.309017	−	0.951057i	−0.0195440	−	0.0601501i
$251$	6.83950	−	4.96919i	0.431706	−	0.313653i	−0.350625	−	0.936516i	$-0.614031\pi$
$251$	6.83950	−	4.96919i	0.431706	−	0.313653i	0.782331	+	0.622863i	$0.214031\pi$
$252$	−3.46869			−0.218507
$253$	−11.5623	+	11.8617i	−0.726916	+	0.745739i
$254$	−15.2797			−0.958732
$255$	8.13553	−	5.91081i	0.509467	−	0.370149i
$256$	0.309017	+	0.951057i	0.0193136	+	0.0594410i
$257$	−6.29635	+	19.3782i	−0.392756	+	1.20878i	0.537940	+	0.842983i	$0.319203\pi$
$257$	−6.29635	+	19.3782i	−0.392756	+	1.20878i	−0.930696	+	0.365794i	$0.880797\pi$
$258$	6.22008	+	4.51916i	0.387246	+	0.281350i
$259$	8.93480	+	6.49151i	0.555181	+	0.403363i
$260$	1.98467	−	6.10820i	0.123084	−	0.378814i
$261$	9.69414	+	29.8355i	0.600052	+	1.84677i
$262$	−4.57467	+	3.32369i	−0.282624	+	0.205338i
$263$	16.1920			0.998444			0.499222	−	0.866474i	$-0.333619\pi$
$263$	16.1920			0.998444			0.499222	+	0.866474i	$0.333619\pi$
$264$	1.21299	−	8.34771i	0.0746546	−	0.513766i
$265$	10.0616			0.618082
$266$	1.99721	−	1.45106i	0.122457	−	0.0889702i
$267$	−11.5873	−	35.6621i	−0.709131	−	2.18248i
$268$	−0.396227	+	1.21946i	−0.0242034	+	0.0744905i
$269$	21.6933	+	15.7611i	1.32267	+	0.960973i	0.999895	+	0.0144955i	$0.00461424\pi$
$269$	21.6933	+	15.7611i	1.32267	+	0.960973i	0.322771	+	0.946477i	$0.395386\pi$
$270$	−0.964387	−	0.700668i	−0.0586907	−	0.0426413i
$271$	−6.93163	+	21.3334i	−0.421067	+	1.29591i	0.485644	+	0.874157i	$0.338585\pi$
$271$	−6.93163	+	21.3334i	−0.421067	+	1.29591i	−0.906711	+	0.421753i	$0.861415\pi$
$272$	1.22181	+	3.76033i	0.0740829	+	0.228004i
$273$	−13.2152	+	9.60138i	−0.799818	+	0.581102i
$274$	3.95288			0.238802
$275$	−2.97414	−	1.46782i	−0.179347	−	0.0885131i
$276$	−12.7026			−0.764608
$277$	−17.8914	+	12.9989i	−1.07499	+	0.781026i	−0.976803	−	0.214142i	$-0.931305\pi$
$277$	−17.8914	+	12.9989i	−1.07499	+	0.781026i	−0.0981876	+	0.995168i	$0.531305\pi$
$278$	6.49721	+	19.9964i	0.389677	+	1.19930i
$279$	8.45620	−	26.0255i	0.506260	−	1.55811i
$280$	−0.809017	−	0.587785i	−0.0483480	−	0.0351269i
$281$	10.1696	+	7.38864i	0.606667	+	0.440769i	0.848239	−	0.529613i	$-0.177663\pi$
$281$	10.1696	+	7.38864i	0.606667	+	0.440769i	−0.241572	+	0.970383i	$0.577663\pi$
$282$	−6.58607	+	20.2698i	−0.392195	+	1.20705i
$283$	1.57746	+	4.85492i	0.0937703	+	0.288595i	0.986931	−	0.161142i	$-0.0515177\pi$
$283$	1.57746	+	4.85492i	0.0937703	+	0.288595i	−0.893161	+	0.449737i	$0.851518\pi$
$284$	4.77340	−	3.46808i	0.283249	−	0.205793i
$285$	6.27877			0.371922
$286$	−9.91230	−	18.8543i	−0.586127	−	1.11488i
$287$	−6.95385			−0.410473
$288$	2.80623	−	2.03884i	0.165359	−	0.120140i
$289$	−0.422448	−	1.30016i	−0.0248499	−	0.0764800i
$290$	−2.79476	+	8.60137i	−0.164114	+	0.505090i
$291$	−24.6098	−	17.8801i	−1.44265	−	1.04815i
$292$	−8.29414	−	6.02605i	−0.485378	−	0.352648i
$293$	5.33226	−	16.4110i	0.311514	−	0.958742i	−0.665651	−	0.746263i	$-0.731846\pi$
$293$	5.33226	−	16.4110i	0.311514	−	0.958742i	0.977166	−	0.212479i	$-0.0681538\pi$
$294$	0.785942	+	2.41888i	0.0458371	+	0.141072i
$295$	3.31353	−	2.40742i	0.192921	−	0.140165i
$296$	−11.0440			−0.641921
$297$	−3.89668	+	0.668332i	−0.226108	+	0.0387806i
$298$	8.55328			0.495478
$299$	−25.9507	+	18.8543i	−1.50077	+	1.09037i
$300$	−0.785942	−	2.41888i	−0.0453764	−	0.139654i
$301$	0.934142	−	2.87499i	0.0538430	−	0.165712i
$302$	−1.78918	−	1.29992i	−0.102956	−	0.0748017i
$303$	−4.65258	−	3.38030i	−0.267284	−	0.194193i
$304$	−0.762867	+	2.34786i	−0.0437534	+	0.134659i
$305$	1.11152	+	3.42091i	0.0636456	+	0.195881i
$306$	11.0954	−	8.06129i	0.634282	−	0.460833i
$307$	24.8048			1.41569			0.707844	−	0.706369i	$-0.249668\pi$
$307$	24.8048			1.41569			0.707844	+	0.706369i	$0.249668\pi$
$308$	−3.26889	+	0.560659i	−0.186262	+	0.0319465i
$309$	−34.1724			−1.94400
$310$	6.38242	−	4.63710i	0.362497	−	0.263369i
$311$	−4.65745	−	14.3342i	−0.264100	−	0.812816i	−0.991899	−	0.127026i	$-0.959457\pi$
$311$	−4.65745	−	14.3342i	−0.264100	−	0.812816i	0.727800	−	0.685790i	$-0.240543\pi$
$312$	5.04774	−	15.5354i	0.285772	−	0.879517i
$313$	11.8713	+	8.62498i	0.671004	+	0.487513i	0.870361	−	0.492414i	$-0.163885\pi$
$313$	11.8713	+	8.62498i	0.671004	+	0.487513i	−0.199357	+	0.979927i	$0.563885\pi$
$314$	−10.8298	−	7.86828i	−0.611158	−	0.444033i
$315$	−1.07188	+	3.29892i	−0.0603938	+	0.185873i
$316$	1.91930	+	5.90700i	0.107969	+	0.332295i
$317$	11.5438	−	8.38707i	0.648365	−	0.471065i	−0.214349	−	0.976757i	$-0.568763\pi$
$317$	11.5438	−	8.38707i	0.648365	−	0.471065i	0.862714	+	0.505692i	$0.168763\pi$
$318$	25.5904			1.43504
$319$	13.9582	+	26.5501i	0.781509	+	1.48652i
$320$	1.00000			0.0559017
$321$	27.5472	−	20.0142i	1.53754	−	1.11709i
$322$	1.54336	+	4.74998i	0.0860082	+	0.264706i
$323$	−3.01626	+	9.28310i	−0.167829	+	0.516526i
$324$	5.96590	+	4.33448i	0.331439	+	0.240805i
$325$	−5.19594	−	3.77507i	−0.288219	−	0.209403i
$326$	−0.634425	+	1.95256i	−0.0351375	+	0.108142i
$327$	6.81902	+	20.9868i	0.377093	+	1.16057i
$328$	5.62578	−	4.08737i	0.310632	−	0.225687i
$329$	8.37984			0.461995
$330$	−7.56431	−	3.73321i	−0.416401	−	0.205506i
$331$	−12.9209			−0.710197			−0.355099	−	0.934829i	$-0.615553\pi$
$331$	−12.9209			−0.710197			−0.355099	+	0.934829i	$0.615553\pi$
$332$	−10.7909	+	7.84005i	−0.592228	+	0.430279i
$333$	11.8379	+	36.4333i	0.648713	+	1.99653i
$334$	−6.55169	+	20.1640i	−0.358492	+	1.10333i
$335$	1.03734	+	0.753669i	0.0566757	+	0.0411773i
$336$	−2.05762	−	1.49495i	−0.112253	−	0.0815562i
$337$	6.36585	−	19.5921i	0.346770	−	1.06725i	−0.613859	−	0.789416i	$-0.710384\pi$
$337$	6.36585	−	19.5921i	0.346770	−	1.06725i	0.960629	−	0.277833i	$-0.0896162\pi$
$338$	−8.72943	−	26.8664i	−0.474818	−	1.46134i
$339$	−18.8616	+	13.7038i	−1.02442	+	0.744287i
$340$	3.95385			0.214428
$341$	3.76251	−	25.8933i	0.203751	−	1.40220i
$342$	8.56312			0.463040
$343$	0.809017	−	0.587785i	0.0436828	−	0.0317374i
$344$	0.934142	+	2.87499i	0.0503655	+	0.155009i
$345$	−3.92533	+	12.0809i	−0.211333	+	0.650415i
$346$	−4.78315	−	3.47516i	−0.257144	−	0.186826i
$347$	3.08349	+	2.24028i	0.165530	+	0.120265i	0.667466	−	0.744640i	$-0.267379\pi$
$347$	3.08349	+	2.24028i	0.165530	+	0.120265i	−0.501936	+	0.864905i	$0.667379\pi$
$348$	−7.10808	+	21.8764i	−0.381033	+	1.17270i
$349$	−6.11180	−	18.8102i	−0.327157	−	1.00689i	−0.970457	−	0.241272i	$-0.922435\pi$
$349$	−6.11180	−	18.8102i	−0.327157	−	1.00689i	0.643300	−	0.765614i	$-0.277565\pi$
$350$	−0.809017	+	0.587785i	−0.0432438	+	0.0314184i
$351$	−7.65598			−0.408646
$352$	2.31504	−	2.37499i	0.123392	−	0.126587i
$353$	−2.85223			−0.151809			−0.0759044	−	0.997115i	$-0.524184\pi$
$353$	−2.85223			−0.151809			−0.0759044	+	0.997115i	$0.524184\pi$
$354$	8.42750	−	6.12294i	0.447917	−	0.325430i
$355$	−1.82328	−	5.61147i	−0.0967696	−	0.297826i
$356$	4.55590	−	14.0216i	0.241462	−	0.743144i
$357$	−8.13553	−	5.91081i	−0.430578	−	0.312833i
$358$	−14.4716	−	10.5143i	−0.764850	−	0.555696i
$359$	5.23394	−	16.1084i	0.276237	−	0.850169i	−0.712653	−	0.701517i	$-0.752506\pi$
$359$	5.23394	−	16.1084i	0.276237	−	0.850169i	0.988890	−	0.148652i	$-0.0474935\pi$
$360$	−1.07188	−	3.29892i	−0.0564933	−	0.173868i
$361$	10.4408	−	7.58570i	0.549517	−	0.399248i
$362$	−11.0710			−0.581877
$363$	−26.3780	+	9.32261i	−1.38449	+	0.489310i
$364$	−6.42254			−0.336633
$365$	−8.29414	+	6.02605i	−0.434135	+	0.315418i
$366$	2.82700	+	8.70062i	0.147770	+	0.454789i
$367$	−6.18204	+	19.0264i	−0.322700	+	0.993168i	0.649768	+	0.760132i	$0.274866\pi$
$367$	−6.18204	+	19.0264i	−0.322700	+	0.993168i	−0.972468	+	0.233036i	$0.925134\pi$
$368$	−4.04057	−	2.93565i	−0.210629	−	0.153031i
$369$	−19.5141	−	14.1778i	−1.01586	−	0.738068i
$370$	−3.41279	+	10.5035i	−0.177422	+	0.546050i
$371$	−3.10922	−	9.56920i	−0.161423	−	0.496808i
$372$	16.2328	−	11.7938i	0.841631	−	0.611481i
$373$	−23.1627			−1.19932			−0.599660	−	0.800255i	$-0.704697\pi$
$373$	−23.1627			−1.19932			−0.599660	+	0.800255i	$0.704697\pi$
$374$	9.15333	−	9.39035i	0.473308	−	0.485564i
$375$	−2.54336			−0.131339
$376$	−6.77943	+	4.92554i	−0.349622	+	0.254016i
$377$	17.9494	+	55.2427i	0.924443	+	2.84514i
$378$	−0.368363	+	1.13370i	−0.0189466	+	0.0583115i
$379$	−26.3795	−	19.1658i	−1.35502	−	0.984481i	−0.998744	−	0.0501010i	$-0.984046\pi$
$379$	−26.3795	−	19.1658i	−1.35502	−	0.984481i	−0.356278	−	0.934380i	$-0.615954\pi$
$380$	1.99721	+	1.45106i	0.102455	+	0.0744378i
$381$	−12.0089	+	36.9597i	−0.615236	+	1.89350i
$382$	2.95413	+	9.09187i	0.151146	+	0.465181i
$383$	−4.18202	+	3.03842i	−0.213691	+	0.155256i	−0.689482	−	0.724303i	$-0.742162\pi$
$383$	−4.18202	+	3.03842i	−0.213691	+	0.155256i	0.475791	+	0.879558i	$0.342162\pi$
$384$	2.54336			0.129790
$385$	−0.476925	+	3.28216i	−0.0243064	+	0.167274i
$386$	16.6846			0.849223
$387$	8.48308	−	6.16332i	0.431219	−	0.313299i
$388$	−3.69594	−	11.3749i	−0.187633	−	0.577475i
$389$	−0.268314	+	0.825787i	−0.0136041	+	0.0418690i	−0.957628	−	0.288008i	$-0.907007\pi$
$389$	−0.268314	+	0.825787i	−0.0136041	+	0.0418690i	0.944024	+	0.329877i	$0.107007\pi$
$390$	−13.2152	−	9.60138i	−0.669176	−	0.486185i
$391$	−15.9758	−	11.6071i	−0.807932	−	0.586997i
$392$	−0.309017	+	0.951057i	−0.0156077	+	0.0480356i
$393$	4.44419	+	13.6778i	0.224180	+	0.689955i
$394$	0.431562	−	0.313548i	0.0217418	−	0.0157963i
$395$	6.21099			0.312509
$396$	−10.3164	−	5.09143i	−0.518417	−	0.255854i
$397$	−16.7823			−0.842280			−0.421140	−	0.906996i	$-0.638370\pi$
$397$	−16.7823			−0.842280			−0.421140	+	0.906996i	$0.638370\pi$
$398$	−2.27692	+	1.65428i	−0.114132	+	0.0829215i
$399$	−1.94025	−	5.97147i	−0.0971339	−	0.298947i
$400$	0.309017	−	0.951057i	0.0154508	−	0.0475528i
$401$	1.34614	+	0.978031i	0.0672233	+	0.0488406i	0.620889	−	0.783898i	$-0.286772\pi$
$401$	1.34614	+	0.978031i	0.0672233	+	0.0488406i	−0.553666	+	0.832739i	$0.686772\pi$
$402$	2.63832	+	1.91685i	0.131587	+	0.0956039i
$403$	15.6573	−	48.1882i	0.779945	−	2.40042i
$404$	−0.698732	−	2.15048i	−0.0347632	−	0.106990i
$405$	5.96590	−	4.33448i	0.296448	−	0.215382i
$406$	9.04402			0.448847
$407$	17.0449	+	32.4214i	0.844885	+	1.60707i
$408$	10.0561			0.497850
$409$	16.5468	−	12.0220i	0.818187	−	0.594448i	−0.0980056	−	0.995186i	$-0.531246\pi$
$409$	16.5468	−	12.0220i	0.818187	−	0.594448i	0.916193	+	0.400738i	$0.131246\pi$
$410$	−2.14886	−	6.61350i	−0.106125	−	0.326618i
$411$	3.10673	−	9.56154i	0.153244	−	0.471636i
$412$	−10.8699	−	7.89743i	−0.535520	−	0.389078i
$413$	−3.31353	−	2.40742i	−0.163048	−	0.118461i
$414$	−5.35344	+	16.4762i	−0.263107	+	0.809761i
$415$	4.12176	+	12.6855i	0.202329	+	0.622705i
$416$	5.19594	−	3.77507i	0.254752	−	0.185088i
$417$	53.4753			2.61869
$418$	8.06988	−	1.38409i	0.394711	−	0.0676982i
$419$	18.0870			0.883609			0.441804	−	0.897111i	$-0.354339\pi$
$419$	18.0870			0.883609			0.441804	+	0.897111i	$0.354339\pi$
$420$	−2.05762	+	1.49495i	−0.100402	+	0.0729461i
$421$	−4.52289	−	13.9200i	−0.220432	−	0.678420i	−0.998723	−	0.0505167i	$-0.983913\pi$
$421$	−4.52289	−	13.9200i	−0.220432	−	0.678420i	0.778291	−	0.627904i	$-0.216087\pi$
$422$	0.989592	−	3.04565i	0.0481726	−	0.148260i
$423$	23.5157	+	17.0852i	1.14337	+	0.830710i
$424$	8.14004	+	5.91409i	0.395315	+	0.287214i
$425$	1.22181	−	3.76033i	0.0592663	−	0.182403i
$426$	−4.63726	−	14.2720i	−0.224676	−	0.691481i
$427$	2.91000	−	2.11424i	0.140825	−	0.102315i
$428$	13.3879			0.647128
$429$	−53.3969	+	9.15828i	−2.57802	+	0.442166i
$430$	3.02295			0.145779
$431$	0.509264	−	0.370002i	0.0245304	−	0.0178224i	−0.575453	−	0.817835i	$-0.695174\pi$
$431$	0.509264	−	0.370002i	0.0245304	−	0.0178224i	0.599983	+	0.800013i	$0.295174\pi$
$432$	−0.368363	−	1.13370i	−0.0177229	−	0.0545454i
$433$	−4.69050	+	14.4359i	−0.225411	+	0.693743i	0.772839	+	0.634602i	$0.218836\pi$
$433$	−4.69050	+	14.4359i	−0.225411	+	0.693743i	−0.998250	+	0.0591409i	$0.981164\pi$
$434$	−6.38242	−	4.63710i	−0.306366	−	0.222588i
$435$	18.6092	+	13.5204i	0.892242	+	0.648252i
$436$	−2.68110	+	8.25159i	−0.128402	+	0.395180i
$437$	−3.81008	−	11.7262i	−0.182261	−	0.560941i
$438$	−21.0950	+	15.3264i	−1.00796	+	0.732324i
$439$	12.5690			0.599888			0.299944	−	0.953957i	$-0.403032\pi$
$439$	12.5690			0.599888			0.299944	+	0.953957i	$0.403032\pi$
$440$	−1.54336	−	2.93565i	−0.0735769	−	0.139952i
$441$	3.46869			0.165176
$442$	20.5440	−	14.9261i	0.977178	−	0.709961i
$443$	−0.883389	−	2.71879i	−0.0419711	−	0.129174i	0.927875	−	0.372890i	$-0.121633\pi$
$443$	−0.883389	−	2.71879i	−0.0419711	−	0.129174i	−0.969846	+	0.243717i	$0.921633\pi$
$444$	−8.67996	+	26.7142i	−0.411933	+	1.26780i
$445$	−11.9275	−	8.66584i	−0.565418	−	0.410800i
$446$	−0.621758	−	0.451734i	−0.0294411	−	0.0213902i
$447$	6.72239	−	20.6894i	0.317958	−	0.978574i
$448$	−0.309017	−	0.951057i	−0.0145997	−	0.0449332i
$449$	−23.0357	+	16.7364i	−1.08712	+	0.789839i	−0.978911	−	0.204289i	$-0.934512\pi$
$449$	−23.0357	+	16.7364i	−1.08712	+	0.789839i	−0.108209	+	0.994128i	$0.534512\pi$
$450$	−3.46869			−0.163516
$451$	−20.6817	−	10.2070i	−0.973863	−	0.480630i
$452$	−9.16671			−0.431166
$453$	−4.55053	+	3.30616i	−0.213803	+	0.155337i
$454$	−2.03561	−	6.26497i	−0.0955361	−	0.294030i
$455$	−1.98467	+	6.10820i	−0.0930430	+	0.286357i
$456$	5.07963	+	3.69057i	0.237876	+	0.172827i
$457$	−6.17590	−	4.48705i	−0.288896	−	0.209895i	0.433892	−	0.900965i	$-0.357140\pi$
$457$	−6.17590	−	4.48705i	−0.288896	−	0.209895i	−0.722788	+	0.691069i	$0.757140\pi$
$458$	7.19480	−	22.1433i	0.336191	−	1.03469i
$459$	−1.45645	−	4.48250i	−0.0679814	−	0.209225i
$460$	−4.04057	+	2.93565i	−0.188393	+	0.136875i
$461$	−4.72213			−0.219931			−0.109966	−	0.993935i	$-0.535074\pi$
$461$	−4.72213			−0.219931			−0.109966	+	0.993935i	$0.535074\pi$
$462$	−1.21299	+	8.34771i	−0.0564335	+	0.388371i
$463$	−19.4328			−0.903117			−0.451558	−	0.892242i	$-0.649132\pi$
$463$	−19.4328			−0.903117			−0.451558	+	0.892242i	$0.649132\pi$
$464$	−7.31677	+	5.31594i	−0.339672	+	0.246786i
$465$	−6.20038	−	19.0828i	−0.287536	−	0.884943i
$466$	0.532246	−	1.63809i	0.0246558	−	0.0758829i
$467$	10.9573	+	7.96094i	0.507043	+	0.368388i	0.811701	−	0.584073i	$-0.198542\pi$
$467$	10.9573	+	7.96094i	0.507043	+	0.368388i	−0.304658	+	0.952462i	$0.598542\pi$
$468$	−18.0231	−	13.0946i	−0.833119	−	0.605296i
$469$	0.396227	−	1.21946i	0.0182961	−	0.0563095i
$470$	2.58951	+	7.96970i	0.119445	+	0.367615i
$471$	−27.5440	+	20.0119i	−1.26916	+	0.922099i
$472$	4.09575			0.188522
$473$	6.99825	−	7.17947i	0.321780	−	0.330112i
$474$	15.7968			0.725571
$475$	1.99721	−	1.45106i	0.0916384	−	0.0665792i
$476$	−1.22181	−	3.76033i	−0.0560014	−	0.172355i
$477$	10.7849	−	33.1926i	0.493808	−	1.51978i
$478$	9.41996	+	6.84400i	0.430859	+	0.313037i
$479$	−3.50324	−	2.54525i	−0.160067	−	0.116296i	0.504868	−	0.863196i	$-0.331541\pi$
$479$	−3.50324	−	2.54525i	−0.160067	−	0.116296i	−0.664936	+	0.746901i	$0.731541\pi$
$480$	0.785942	−	2.41888i	0.0358732	−	0.110406i
$481$	21.9188	+	67.4591i	0.999410	+	3.07587i
$482$	−7.75229	+	5.63237i	−0.353107	+	0.256547i
$483$	12.7026			0.577990
$484$	−10.5451	−	3.13068i	−0.479322	−	0.142304i
$485$	−11.9603			−0.543090
$486$	18.0666	−	13.1262i	0.819518	−	0.595415i
$487$	−11.3026	−	34.7858i	−0.512170	−	1.57630i	−0.788374	−	0.615197i	$-0.789077\pi$
$487$	−11.3026	−	34.7858i	−0.512170	−	1.57630i	0.276204	−	0.961099i	$-0.410923\pi$
$488$	−1.11152	+	3.42091i	−0.0503162	+	0.154857i
$489$	4.22439	+	3.06920i	0.191033	+	0.138794i
$490$	0.809017	+	0.587785i	0.0365477	+	0.0265534i
$491$	−9.80286	+	30.1701i	−0.442397	+	1.36156i	0.442916	+	0.896563i	$0.353944\pi$
$491$	−9.80286	+	30.1701i	−0.442397	+	1.36156i	−0.885313	+	0.464995i	$0.846056\pi$
$492$	−5.46532	−	16.8205i	−0.246396	−	0.758328i
$493$	−28.9294	+	21.0184i	−1.30291	+	0.946623i
$494$	15.8553			0.713362
$495$	−8.03017	+	8.23810i	−0.360929	+	0.370275i
$496$	7.88910			0.354231
$497$	−4.77340	+	3.46808i	−0.214116	+	0.155565i
$498$	10.4831	+	32.2637i	0.469760	+	1.44577i
$499$	11.3713	−	34.9973i	0.509049	−	1.56669i	−0.284805	−	0.958585i	$-0.591929\pi$
$499$	11.3713	−	34.9973i	0.509049	−	1.56669i	0.793855	−	0.608107i	$-0.208071\pi$
$500$	−0.809017	−	0.587785i	−0.0361803	−	0.0262866i
$501$	43.6251	+	31.6955i	1.94903	+	1.41605i
$502$	2.61246	−	8.04032i	0.116600	−	0.358857i
$503$	2.83090	+	8.71261i	0.126224	+	0.388476i	0.994122	−	0.108266i	$-0.0345297\pi$
$503$	2.83090	+	8.71261i	0.126224	+	0.388476i	−0.867898	+	0.496742i	$0.834530\pi$
$504$	−2.80623	+	2.03884i	−0.124999	+	0.0908174i
$505$	−2.26114			−0.100620
$506$	−2.38197	+	16.3925i	−0.105891	+	0.728734i
$507$	−71.8475			−3.19086
$508$	−12.3615	+	8.98117i	−0.548453	+	0.398475i
$509$	4.63523	+	14.2658i	0.205453	+	0.632320i	0.999694	+	0.0247172i	$0.00786853\pi$
$509$	4.63523	+	14.2658i	0.205453	+	0.632320i	−0.794241	+	0.607602i	$0.792131\pi$
$510$	3.10750	−	9.56389i	0.137602	−	0.423496i
$511$	8.29414	+	6.02605i	0.366911	+	0.266577i
$512$	0.809017	+	0.587785i	0.0357538	+	0.0259767i
$513$	0.909374	−	2.79877i	0.0401498	−	0.123569i
$514$	6.29635	+	19.3782i	0.277720	+	0.854735i
$515$	−10.8699	+	7.89743i	−0.478984	+	0.348002i
$516$	7.68845			0.338465
$517$	24.9228	+	12.3001i	1.09610	+	0.540959i
$518$	11.0440			0.485246
$519$	−12.1653	+	8.83860i	−0.533997	+	0.387972i
$520$	−1.98467	−	6.10820i	−0.0870337	−	0.267862i
$521$	−5.19586	+	15.9912i	−0.227635	+	0.700588i	0.770378	+	0.637587i	$0.220067\pi$
$521$	−5.19586	+	15.9912i	−0.227635	+	0.700588i	−0.998013	+	0.0630015i	$0.979933\pi$
$522$	25.3796	+	18.4394i	1.11083	+	0.807069i
$523$	−0.977990	−	0.710551i	−0.0427645	−	0.0310702i	0.566198	−	0.824269i	$-0.308414\pi$
$523$	−0.977990	−	0.710551i	−0.0427645	−	0.0310702i	−0.608962	+	0.793199i	$0.708414\pi$
$524$	−1.74737	+	5.37785i	−0.0763342	+	0.234932i
$525$	0.785942	+	2.41888i	0.0343013	+	0.105569i
$526$	13.0996	−	9.51745i	0.571172	−	0.414980i
$527$	31.1923			1.35876
$528$	−3.92533	−	7.46642i	−0.170828	−	0.324934i
$529$	1.94427			0.0845336
$530$	8.14004	−	5.91409i	0.353581	−	0.256892i
$531$	−4.39016	−	13.5115i	−0.190517	−	0.586351i
$532$	0.762867	−	2.34786i	0.0330745	−	0.101793i
$533$	−36.1318	−	26.2513i	−1.56504	−	1.13707i
$534$	−30.3360	−	22.0404i	−1.31277	−	0.953780i
$535$	4.13708	−	12.7326i	0.178862	−	0.550480i
$536$	0.396227	+	1.21946i	0.0171144	+	0.0526727i
$537$	−36.8066	+	26.7416i	−1.58832	+	1.15398i
$538$	26.8144			1.15605
$539$	3.26889	−	0.560659i	0.140801	−	0.0241493i
$540$	−1.19205			−0.0512976
$541$	3.77643	−	2.74374i	0.162362	−	0.117963i	−0.503638	−	0.863915i	$-0.668005\pi$
$541$	3.77643	−	2.74374i	0.162362	−	0.117963i	0.665999	+	0.745952i	$0.268005\pi$
$542$	6.93163	+	21.3334i	0.297739	+	0.916347i
$543$	−8.70114	+	26.7794i	−0.373402	+	1.14921i
$544$	3.19873	+	2.32401i	0.137145	+	0.0996413i
$545$	7.01922	+	5.09976i	0.300670	+	0.218450i
$546$	−5.04774	+	15.5354i	−0.216024	+	0.664852i
$547$	6.84613	+	21.0702i	0.292719	+	0.900898i	0.983978	+	0.178290i	$0.0570566\pi$
$547$	6.84613	+	21.0702i	0.292719	+	0.900898i	−0.691258	+	0.722608i	$0.742943\pi$
$548$	3.19795	−	2.32344i	0.136609	−	0.0992526i
$549$	12.4767			0.532494
$550$	−3.26889	+	0.560659i	−0.139386	+	0.0239066i
$551$	−22.3269			−0.951157
$552$	−10.2766	+	7.46642i	−0.437403	+	0.317792i
$553$	−1.91930	−	5.90700i	−0.0816170	−	0.251191i
$554$	−6.83391	+	21.0326i	−0.290345	+	0.893590i
$555$	22.7244	+	16.5103i	0.964598	+	0.700822i
$556$	17.0099	+	12.3584i	0.721381	+	0.524114i
$557$	−11.6817	+	35.9525i	−0.494968	+	1.52335i	0.322039	+	0.946726i	$0.395632\pi$
$557$	−11.6817	+	35.9525i	−0.494968	+	1.52335i	−0.817007	+	0.576628i	$0.804368\pi$
$558$	−8.45620	−	26.0255i	−0.357980	−	1.10175i
$559$	15.7071	−	11.4118i	0.664338	−	0.482670i
$560$	−1.00000			−0.0422577
$561$	−15.5202	−	29.5211i	−0.655262	−	1.24638i
$562$	12.5703			0.530247
$563$	8.00803	−	5.81817i	0.337498	−	0.245207i	−0.406107	−	0.913825i	$-0.633114\pi$
$563$	8.00803	−	5.81817i	0.337498	−	0.245207i	0.743605	+	0.668619i	$0.233114\pi$
$564$	6.58607	+	20.2698i	0.277323	+	0.853514i
$565$	−2.83267	+	8.71806i	−0.119171	+	0.366772i
$566$	4.12984	+	3.00051i	0.173590	+	0.126121i
$567$	−5.96590	−	4.33448i	−0.250544	−	0.182031i
$568$	1.82328	−	5.61147i	0.0765030	−	0.235452i
$569$	1.53025	+	4.70961i	0.0641512	+	0.197437i	0.977995	−	0.208629i	$-0.0669002\pi$
$569$	1.53025	+	4.70961i	0.0641512	+	0.197437i	−0.913844	+	0.406066i	$0.866900\pi$
$570$	5.07963	−	3.69057i	0.212762	−	0.154581i
$571$	8.53293			0.357092			0.178546	−	0.983932i	$-0.442861\pi$
$571$	8.53293			0.357092			0.178546	+	0.983932i	$0.442861\pi$
$572$	−19.1015	−	9.42716i	−0.798674	−	0.394169i
$573$	24.3139			1.01573
$574$	−5.62578	+	4.08737i	−0.234816	+	0.170604i
$575$	1.54336	+	4.74998i	0.0643626	+	0.198088i
$576$	1.07188	−	3.29892i	0.0446618	−	0.137455i
$577$	7.95151	+	5.77711i	0.331026	+	0.240504i	0.740866	−	0.671653i	$-0.234415\pi$
$577$	7.95151	+	5.77711i	0.331026	+	0.240504i	−0.409840	+	0.912157i	$0.634415\pi$
$578$	−1.10598	−	0.803543i	−0.0460028	−	0.0334230i
$579$	13.1131	−	40.3580i	0.544963	−	1.67722i
$580$	2.79476	+	8.60137i	0.116046	+	0.357153i
$581$	10.7909	−	7.84005i	0.447682	−	0.325260i
$582$	−30.4194			−1.26093
$583$	4.79865	−	33.0239i	0.198740	−	1.36771i
$584$	−10.2521			−0.424236
$585$	−18.0231	+	13.0946i	−0.745164	+	0.541393i
$586$	−5.33226	−	16.4110i	−0.220274	−	0.677933i
$587$	6.20045	−	19.0830i	0.255920	−	0.787641i	−0.737727	−	0.675099i	$-0.764101\pi$
$587$	6.20045	−	19.0830i	0.255920	−	0.787641i	0.993647	−	0.112542i	$-0.0358993\pi$
$588$	2.05762	+	1.49495i	0.0848549	+	0.0616507i
$589$	15.7562	+	11.4476i	0.649223	+	0.471688i
$590$	1.26566	−	3.89529i	0.0521062	−	0.160366i
$591$	−0.419253	−	1.29033i	−0.0172458	−	0.0530770i
$592$	−8.93480	+	6.49151i	−0.367218	+	0.266800i
$593$	3.85286			0.158218			0.0791090	−	0.996866i	$-0.474792\pi$
$593$	3.85286			0.158218			0.0791090	+	0.996866i	$0.474792\pi$
$594$	−2.75964	+	2.83110i	−0.113229	+	0.116162i
$595$	−3.95385			−0.162092
$596$	6.91975	−	5.02749i	0.283444	−	0.205934i
$597$	2.21198	+	6.80777i	0.0905302	+	0.278623i
$598$	−9.91230	+	30.5069i	−0.405344	+	1.24752i
$599$	−5.97520	−	4.34124i	−0.244140	−	0.177378i	0.458986	−	0.888444i	$-0.348213\pi$
$599$	−5.97520	−	4.34124i	−0.244140	−	0.177378i	−0.703126	+	0.711065i	$0.748213\pi$
$600$	−2.05762	−	1.49495i	−0.0840021	−	0.0610311i
$601$	7.94779	−	24.4608i	0.324197	−	0.997776i	−0.647605	−	0.761976i	$-0.724229\pi$
$601$	7.94779	−	24.4608i	0.324197	−	0.997776i	0.971802	−	0.235799i	$-0.0757708\pi$
$602$	−0.934142	−	2.87499i	−0.0380728	−	0.117176i
$603$	3.59820	−	2.61424i	0.146530	−	0.106460i
$604$	−2.21155			−0.0899866
$605$	−6.23607	+	9.06154i	−0.253532	+	0.368404i
$606$	−5.75091			−0.233615
$607$	−2.44661	+	1.77757i	−0.0993048	+	0.0721492i	−0.636330	−	0.771417i	$-0.719548\pi$
$607$	−2.44661	+	1.77757i	−0.0993048	+	0.0721492i	0.537025	+	0.843566i	$0.319548\pi$
$608$	0.762867	+	2.34786i	0.0309383	+	0.0952184i
$609$	7.10808	−	21.8764i	0.288034	−	0.886477i
$610$	2.91000	+	2.11424i	0.117823	+	0.0856031i
$611$	43.5412	+	31.6345i	1.76149	+	1.27980i
$612$	4.23807	−	13.0434i	0.171314	−	0.527250i
$613$	−6.39757	−	19.6897i	−0.258395	−	0.795259i	−0.993142	−	0.116917i	$-0.962699\pi$
$613$	−6.39757	−	19.6897i	−0.258395	−	0.795259i	0.734746	−	0.678342i	$-0.237301\pi$
$614$	20.0675	−	14.5799i	0.809860	−	0.588398i
$615$	−17.6862			−0.713175
$616$	−2.31504	+	2.37499i	−0.0932757	+	0.0956911i
$617$	16.2405			0.653817			0.326909	−	0.945056i	$-0.393993\pi$
$617$	16.2405			0.653817			0.326909	+	0.945056i	$0.393993\pi$
$618$	−27.6460	+	20.0860i	−1.11209	+	0.807978i
$619$	−11.1089	−	34.1896i	−0.446503	−	1.37419i	−0.880827	−	0.473438i	$-0.843013\pi$
$619$	−11.1089	−	34.1896i	−0.446503	−	1.37419i	0.434324	−	0.900757i	$-0.356987\pi$
$620$	2.43787	−	7.50298i	0.0979071	−	0.301327i
$621$	4.81656	+	3.49943i	0.193282	+	0.140427i
$622$	−12.1934	−	8.85900i	−0.488909	−	0.355213i
$623$	−4.55590	+	14.0216i	−0.182528	+	0.561764i
$624$	−5.04774	−	15.5354i	−0.202071	−	0.621912i
$625$	−0.809017	+	0.587785i	−0.0323607	+	0.0235114i
$626$	14.6737			0.586479
$627$	2.99450	−	20.6079i	0.119589	−	0.823000i
$628$	−13.3863			−0.534172
$629$	−35.3269	+	25.6665i	−1.40857	+	1.02339i
$630$	1.07188	+	3.29892i	0.0427049	+	0.131432i
$631$	−12.8157	+	39.4428i	−0.510187	+	1.57019i	0.281686	+	0.959507i	$0.409106\pi$
$631$	−12.8157	+	39.4428i	−0.510187	+	1.57019i	−0.791872	+	0.610687i	$0.790894\pi$
$632$	5.02480	+	3.65073i	0.199876	+	0.145218i
$633$	−6.58930	−	4.78741i	−0.261901	−	0.190282i
$634$	4.40934	−	13.5706i	0.175117	−	0.538956i
$635$	4.72168	+	14.5318i	0.187374	+	0.576678i
$636$	20.7031	−	15.0417i	0.820930	−	0.596441i
$637$	6.42254			0.254470
$638$	26.8982	+	13.2750i	1.06491	+	0.525564i
$639$	−20.4661			−0.809628
$640$	0.809017	−	0.587785i	0.0319792	−	0.0232343i
$641$	0.982315	+	3.02326i	0.0387991	+	0.119411i	0.968580	−	0.248702i	$-0.0800039\pi$
$641$	0.982315	+	3.02326i	0.0387991	+	0.119411i	−0.929781	+	0.368113i	$0.880004\pi$
$642$	10.5221	−	32.3837i	0.415274	−	1.27808i
$643$	−16.2410	−	11.7998i	−0.640482	−	0.465338i	0.219534	−	0.975605i	$-0.429546\pi$
$643$	−16.2410	−	11.7998i	−0.640482	−	0.465338i	−0.860016	+	0.510267i	$0.829546\pi$
$644$	4.04057	+	2.93565i	0.159221	+	0.115681i
$645$	2.37586	−	7.31215i	0.0935494	−	0.287916i
$646$	3.01626	+	9.28310i	0.118673	+	0.365239i
$647$	30.8832	−	22.4380i	1.21415	−	0.882128i	0.218545	−	0.975827i	$-0.429869\pi$
$647$	30.8832	−	22.4380i	1.21415	−	0.882128i	0.995601	+	0.0936984i	$0.0298689\pi$
$648$	7.37426			0.289688
$649$	−6.32122	−	12.0237i	−0.248130	−	0.471970i
$650$	−6.42254			−0.251913
$651$	−16.2328	+	11.7938i	−0.636213	+	0.462236i
$652$	0.634425	+	1.95256i	0.0248460	+	0.0764681i
$653$	13.6863	−	42.1219i	0.535584	−	1.64836i	−0.206799	−	0.978384i	$-0.566304\pi$
$653$	13.6863	−	42.1219i	0.535584	−	1.64836i	0.742383	−	0.669976i	$-0.233696\pi$
$654$	17.8524	+	12.9705i	0.698085	+	0.507188i
$655$	4.57467	+	3.32369i	0.178747	+	0.129867i
$656$	2.14886	−	6.61350i	0.0838988	−	0.258214i
$657$	10.9891	+	33.8209i	0.428725	+	1.31948i
$658$	6.77943	−	4.92554i	0.264290	−	0.192018i
$659$	30.2781			1.17947			0.589734	−	0.807598i	$-0.299233\pi$
$659$	30.2781			1.17947			0.589734	+	0.807598i	$0.299233\pi$
$660$	−8.31398	+	1.42596i	−0.323621	+	0.0555054i
$661$	7.16382			0.278640			0.139320	−	0.990247i	$-0.455508\pi$
$661$	7.16382			0.278640			0.139320	+	0.990247i	$0.455508\pi$
$662$	−10.4532	+	7.59472i	−0.406277	+	0.295177i
$663$	−19.9580	−	61.4245i	−0.775105	−	2.38553i
$664$	−4.12176	+	12.6855i	−0.159955	+	0.492292i
$665$	−1.99721	−	1.45106i	−0.0774486	−	0.0562697i
$666$	30.9920	+	22.5170i	1.20092	+	0.872518i
$667$	13.9582	−	42.9589i	0.540464	−	1.66338i
$668$	6.55169	+	20.1640i	0.253492	+	0.780170i
$669$	−1.58136	+	1.14892i	−0.0611388	+	0.0444199i
$670$	1.28222			0.0495364
$671$	11.7581	−	2.01667i	0.453916	−	0.0778526i
$672$	−2.54336			−0.0981123
$673$	−17.8339	+	12.9571i	−0.687446	+	0.499459i	−0.875820	−	0.482639i	$-0.839678\pi$
$673$	−17.8339	+	12.9571i	−0.687446	+	0.499459i	0.188374	+	0.982097i	$0.439678\pi$
$674$	−6.36585	−	19.5921i	−0.245204	−	0.754659i
$675$	−0.368363	+	1.13370i	−0.0141783	+	0.0436363i
$676$	−22.8539	−	16.6044i	−0.878998	−	0.638629i
$677$	−28.1578	−	20.4579i	−1.08219	−	0.786260i	−0.104130	−	0.994564i	$-0.533206\pi$
$677$	−28.1578	−	20.4579i	−1.08219	−	0.786260i	−0.978064	+	0.208304i	$0.933206\pi$
$678$	−7.20451	+	22.1732i	−0.276687	+	0.851556i
$679$	3.69594	+	11.3749i	0.141837	+	0.436530i
$680$	3.19873	−	2.32401i	0.122666	−	0.0891219i
$681$	−16.7541			−0.642018
$682$	−12.1757	−	23.1596i	−0.466233	−	0.886828i
$683$	35.0185			1.33995			0.669973	−	0.742385i	$-0.266306\pi$
$683$	35.0185			1.33995			0.669973	+	0.742385i	$0.266306\pi$
$684$	6.92771	−	5.03328i	0.264888	−	0.192452i
$685$	−1.22151	−	3.75941i	−0.0466714	−	0.143640i
$686$	0.309017	−	0.951057i	0.0117983	−	0.0363115i
$687$	−47.9073	−	34.8067i	−1.82778	−	1.32796i
$688$	2.44561	+	1.77684i	0.0932382	+	0.0677415i
$689$	19.9691	−	61.4585i	0.760762	−	2.34138i
$690$	3.92533	+	12.0809i	0.149435	+	0.459913i
$691$	15.8191	−	11.4932i	0.601786	−	0.437223i	−0.244726	−	0.969592i	$-0.578698\pi$
$691$	15.8191	−	11.4932i	0.601786	−	0.437223i	0.846513	+	0.532369i	$0.178698\pi$
$692$	−5.91230			−0.224752
$693$	10.3164	+	5.09143i	0.391886	+	0.193407i
$694$	3.81140			0.144679
$695$	17.0099	−	12.3584i	0.645223	−	0.468782i
$696$	7.10808	+	21.8764i	0.269431	+	0.829223i
$697$	8.49626	−	26.1488i	0.321819	−	0.990457i
$698$	−16.0009	−	11.6253i	−0.605643	−	0.440025i
$699$	−3.54402	−	2.57488i	−0.134047	−	0.0973910i
$700$	−0.309017	+	0.951057i	−0.0116797	+	0.0359466i
$701$	−4.30949	−	13.2632i	−0.162767	−	0.500946i	0.836098	−	0.548581i	$-0.184832\pi$
$701$	−4.30949	−	13.2632i	−0.162767	−	0.500946i	−0.998865	+	0.0476348i	$0.984832\pi$
$702$	−6.19381	+	4.50007i	−0.233770	+	0.169844i
$703$	−27.2643			−1.02829
$704$	0.476925	−	3.28216i	0.0179748	−	0.123701i
$705$	21.3130			0.802692
$706$	−2.30750	+	1.67650i	−0.0868440	+	0.0630959i
$707$	0.698732	+	2.15048i	0.0262785	+	0.0808770i
$708$	3.21902	−	9.90712i	0.120978	−	0.372332i
$709$	0.444308	+	0.322809i	0.0166863	+	0.0121233i	0.596097	−	0.802912i	$-0.296717\pi$
$709$	0.444308	+	0.322809i	0.0166863	+	0.0121233i	−0.579411	+	0.815036i	$0.696717\pi$
$710$	−4.77340	−	3.46808i	−0.179143	−	0.130155i
$711$	6.65746	−	20.4896i	0.249674	−	0.768419i
$712$	−4.55590	−	14.0216i	−0.170740	−	0.525482i
$713$	−31.8765	+	23.1596i	−1.19378	+	0.867335i
$714$	−10.0561			−0.376339
$715$	−14.8685	+	15.2535i	−0.556049	+	0.570447i
$716$	−17.8879			−0.668504
$717$	23.9584	−	17.4068i	0.894742	−	0.650068i
$718$	−5.23394	−	16.1084i	−0.195329	−	0.601160i
$719$	−8.00088	+	24.6242i	−0.298382	+	0.918327i	0.683682	+	0.729780i	$0.260378\pi$
$719$	−8.00088	+	24.6242i	−0.298382	+	0.918327i	−0.982064	+	0.188547i	$0.939622\pi$
$720$	−2.80623	−	2.03884i	−0.104582	−	0.0759833i
$721$	10.8699	+	7.89743i	0.404815	+	0.294116i
$722$	3.98804	−	12.2739i	0.148420	−	0.456788i
$723$	7.53118	+	23.1786i	0.280088	+	0.862021i
$724$	−8.95660	+	6.50735i	−0.332869	+	0.241844i
$725$	9.04402			0.335886
$726$	−15.8606	+	23.0468i	−0.588641	+	0.855346i
$727$	−41.6185			−1.54355			−0.771773	−	0.635898i	$-0.780630\pi$
$727$	−41.6185			−1.54355			−0.771773	+	0.635898i	$0.780630\pi$
$728$	−5.19594	+	3.77507i	−0.192574	+	0.139914i
$729$	−10.7150	−	32.9774i	−0.396852	−	1.22138i
$730$	−3.16808	+	9.75035i	−0.117256	+	0.360877i
$731$	9.66959	+	7.02537i	0.357643	+	0.259843i
$732$	7.40119	+	5.37728i	0.273556	+	0.198750i
$733$	−0.670104	+	2.06237i	−0.0247508	+	0.0761752i	−0.962669	−	0.270681i	$-0.912751\pi$
$733$	−0.670104	+	2.06237i	−0.0247508	+	0.0761752i	0.937918	+	0.346857i	$0.112751\pi$
$734$	6.18204	+	19.0264i	0.228183	+	0.702276i
$735$	2.05762	−	1.49495i	0.0758966	−	0.0551421i
$736$	−4.99442			−0.184097
$737$	2.96839	−	3.04525i	0.109342	−	0.112173i
$738$	−24.1207			−0.887897
$739$	−2.48164	+	1.80302i	−0.0912888	+	0.0663252i	−0.632493	−	0.774566i	$-0.717968\pi$
$739$	−2.48164	+	1.80302i	−0.0912888	+	0.0663252i	0.541205	+	0.840891i	$0.317968\pi$
$740$	3.41279	+	10.5035i	0.125457	+	0.386116i
$741$	12.4613	−	38.3520i	0.457778	−	1.40890i
$742$	−8.14004	−	5.91409i	−0.298830	−	0.217113i
$743$	−31.5381	−	22.9138i	−1.15702	−	0.840626i	−0.167623	−	0.985851i	$-0.553609\pi$
$743$	−31.5381	−	22.9138i	−1.15702	−	0.840626i	−0.989399	+	0.145226i	$0.953609\pi$
$744$	6.20038	−	19.0828i	0.227317	−	0.699609i
$745$	−2.64311	−	8.13466i	−0.0968361	−	0.298031i
$746$	−18.7390	+	13.6147i	−0.686085	+	0.498470i
$747$	46.2664			1.69280
$748$	1.88569	−	12.9771i	0.0689477	−	0.474492i
$749$	−13.3879			−0.489183
$750$	−2.05762	+	1.49495i	−0.0751338	+	0.0545879i
$751$	7.48994	+	23.0517i	0.273312	+	0.841167i	0.989661	+	0.143425i	$0.0458116\pi$
$751$	7.48994	+	23.0517i	0.273312	+	0.841167i	−0.716350	+	0.697742i	$0.754188\pi$
$752$	−2.58951	+	7.96970i	−0.0944298	+	0.290625i
$753$	−17.3953	−	12.6384i	−0.633921	−	0.460571i
$754$	46.9922	+	34.1418i	1.71136	+	1.24337i
$755$	−0.683406	+	2.10331i	−0.0248717	+	0.0765472i
$756$	0.368363	+	1.13370i	0.0133972	+	0.0412324i
$757$	19.5909	−	14.2336i	0.712042	−	0.517329i	−0.171790	−	0.985134i	$-0.554955\pi$
$757$	19.5909	−	14.2336i	0.712042	−	0.517329i	0.883832	+	0.467805i	$0.154955\pi$
$758$	−32.6068			−1.18433
$759$	37.7794	+	18.6452i	1.37130	+	0.676779i
$760$	2.46869			0.0895488
$761$	1.68162	−	1.22177i	0.0609588	−	0.0442892i	−0.556889	−	0.830587i	$-0.688005\pi$
$761$	1.68162	−	1.22177i	0.0609588	−	0.0442892i	0.617847	+	0.786298i	$0.288005\pi$
$762$	12.0089	+	36.9597i	0.435038	+	1.33891i
$763$	2.68110	−	8.25159i	0.0970625	−	0.298728i
$764$	7.73401	+	5.61909i	0.279807	+	0.203291i
$765$	−11.0954	−	8.06129i	−0.401155	−	0.291456i
$766$	−1.59739	+	4.91626i	−0.0577160	+	0.177632i
$767$	−8.12872	−	25.0176i	−0.293511	−	0.903334i
$768$	2.05762	−	1.49495i	0.0742481	−	0.0539444i
$769$	14.7508			0.531929			0.265964	−	0.963983i	$-0.414310\pi$
$769$	14.7508			0.531929			0.265964	+	0.963983i	$0.414310\pi$
$770$	1.54336	+	2.93565i	0.0556189	+	0.105793i
$771$	51.8221			1.86633
$772$	13.4981	−	9.80695i	0.485808	−	0.352960i
$773$	15.3140	+	47.1318i	0.550808	+	1.69521i	0.706766	+	0.707448i	$0.250153\pi$
$773$	15.3140	+	47.1318i	0.550808	+	1.69521i	−0.155958	+	0.987764i	$0.549847\pi$
$774$	3.24025	−	9.97246i	0.116468	−	0.358453i
$775$	−6.38242	−	4.63710i	−0.229263	−	0.166569i
$776$	−9.67611	−	7.03010i	−0.347352	−	0.252366i
$777$	8.67996	−	26.7142i	0.311392	−	0.958365i
$778$	0.268314	+	0.825787i	0.00961954	+	0.0296059i
$779$	13.8883	−	10.0905i	0.497600	−	0.361528i
$780$	−16.3348			−0.584881
$781$	−19.2873	+	3.30803i	−0.690154	+	0.118371i
$782$	−19.7472			−0.706159
$783$	8.72194	−	6.33686i	0.311697	−	0.226461i
$784$	0.309017	+	0.951057i	0.0110363	+	0.0339663i
$785$	−4.13660	+	12.7311i	−0.147642	+	0.454394i
$786$	11.6350	+	8.45336i	0.415008	+	0.301521i
$787$	25.1397	+	18.2651i	0.896135	+	0.651080i	0.937470	−	0.348065i	$-0.113161\pi$
$787$	25.1397	+	18.2651i	0.896135	+	0.651080i	−0.0413357	+	0.999145i	$0.513161\pi$
$788$	0.164842	−	0.507332i	0.00587225	−	0.0180729i
$789$	−12.7260	−	39.1666i	−0.453058	−	1.39437i
$790$	5.02480	−	3.65073i	0.178774	−	0.129887i
$791$	9.16671			0.325931
$792$	−11.3388	+	1.94475i	−0.402906	+	0.0691038i
$793$	23.1016			0.820363
$794$	−13.5772	+	9.86440i	−0.481836	+	0.350074i
$795$	−7.90787	−	24.3379i	−0.280463	−	0.863177i
$796$	−0.869706	+	2.67668i	−0.0308259	+	0.0948724i
$797$	−14.8729	−	10.8058i	−0.526824	−	0.382760i	0.292344	−	0.956313i	$-0.405565\pi$
$797$	−14.8729	−	10.8058i	−0.526824	−	0.382760i	−0.819168	+	0.573553i	$0.805565\pi$
$798$	−5.07963	−	3.69057i	−0.179817	−	0.130645i
$799$	−10.2385	+	31.5110i	−0.362214	+	1.11478i
$800$	−0.309017	−	0.951057i	−0.0109254	−	0.0336249i
$801$	−41.3728	+	30.0591i	−1.46184	+	1.06209i
$802$	1.66393			0.0587553
$803$	15.8227	+	30.0966i	0.558372	+	1.06209i
$804$	3.26114			0.115012
$805$	4.04057	−	2.93565i	0.142412	−	0.103468i
$806$	−15.6573	−	48.1882i	−0.551505	−	1.69736i
$807$	21.0746	−	64.8609i	0.741861	−	2.28321i
$808$	−1.82930	−	1.32907i	−0.0643547	−	0.0467564i
$809$	−33.5303	−	24.3612i	−1.17886	−	0.856494i	−0.186820	−	0.982394i	$-0.559818\pi$
$809$	−33.5303	−	24.3612i	−1.17886	−	0.856494i	−0.992043	+	0.125900i	$0.959818\pi$
$810$	2.27877	−	7.01334i	0.0800679	−	0.246424i
$811$	−2.37989	−	7.32456i	−0.0835694	−	0.257200i	0.900537	−	0.434779i	$-0.143173\pi$
$811$	−2.37989	−	7.32456i	−0.0835694	−	0.257200i	−0.984107	+	0.177579i	$0.943173\pi$
$812$	7.31677	−	5.31594i	0.256768	−	0.186553i
$813$	57.0507			2.00086
$814$	32.8464	+	16.2107i	1.15127	+	0.568184i
$815$	2.05304			0.0719149
$816$	8.13553	−	5.91081i	0.284801	−	0.206920i
$817$	2.30611	+	7.09747i	0.0806804	+	0.248309i
$818$	6.32032	−	19.4519i	0.220985	−	0.680121i
$819$	18.0231	+	13.0946i	0.629779	+	0.457561i
$820$	−5.62578	−	4.08737i	−0.196461	−	0.142737i
$821$	14.9242	−	45.9321i	0.520860	−	1.60304i	−0.251500	−	0.967857i	$-0.580924\pi$
$821$	14.9242	−	45.9321i	0.520860	−	1.60304i	0.772360	−	0.635185i	$-0.219076\pi$
$822$	−3.10673	−	9.56154i	−0.108360	−	0.333497i
$823$	−29.7402	+	21.6075i	−1.03668	+	0.753191i	−0.969634	−	0.244559i	$-0.921357\pi$
$823$	−29.7402	+	21.6075i	−1.03668	+	0.753191i	−0.0670440	+	0.997750i	$0.521357\pi$
$824$	−13.4359			−0.468062
$825$	−1.21299	+	8.34771i	−0.0422310	+	0.290630i
$826$	−4.09575			−0.142509
$827$	−24.1910	+	17.5758i	−0.841204	+	0.611171i	−0.922707	−	0.385502i	$-0.874028\pi$
$827$	−24.1910	+	17.5758i	−0.841204	+	0.611171i	0.0815024	+	0.996673i	$0.474028\pi$
$828$	5.35344	+	16.4762i	0.186045	+	0.572588i
$829$	5.81983	−	17.9116i	0.202131	−	0.622096i	−0.797688	−	0.603071i	$-0.793944\pi$
$829$	5.81983	−	17.9116i	0.202131	−	0.622096i	0.999819	−	0.0190251i	$-0.00605625\pi$
$830$	10.7909	+	7.84005i	0.374558	+	0.272132i
$831$	45.5043	+	33.0608i	1.57853	+	1.14687i
$832$	1.98467	−	6.10820i	0.0688062	−	0.211764i
$833$	1.22181	+	3.76033i	0.0423331	+	0.130288i
$834$	43.2624	−	31.4320i	1.49805	−	1.08840i
$835$	21.2017			0.733716
$836$	5.71512	−	5.86311i	0.197662	−	0.202780i
$837$	−9.40419			−0.325056
$838$	14.6327	−	10.6313i	0.505479	−	0.367252i
$839$	2.40048	+	7.38792i	0.0828738	+	0.255059i	0.983904	−	0.178697i	$-0.0571880\pi$
$839$	2.40048	+	7.38792i	0.0828738	+	0.255059i	−0.901030	+	0.433756i	$0.857188\pi$
$840$	−0.785942	+	2.41888i	−0.0271176	+	0.0834593i
$841$	−42.7115	−	31.0317i	−1.47281	−	1.07006i
$842$	−11.8411	−	8.60305i	−0.408070	−	0.296481i
$843$	9.87954	−	30.4061i	0.340269	−	1.04724i
$844$	−0.989592	−	3.04565i	−0.0340632	−	0.104836i
$845$	−22.8539	+	16.6044i	−0.786199	+	0.571207i
$846$	29.0671			0.999346
$847$	10.5451	+	3.13068i	0.362333	+	0.107572i
$848$	10.0616			0.345518
$849$	10.5037	−	7.63138i	0.360486	−	0.261908i
$850$	−1.22181	−	3.76033i	−0.0419076	−	0.128978i
$851$	17.0449	−	52.4589i	0.584292	−	1.79827i
$852$	−12.1405	−	8.82059i	−0.415926	−	0.302188i
$853$	−19.5194	−	14.1817i	−0.668333	−	0.485572i	0.201134	−	0.979564i	$-0.435537\pi$
$853$	−19.5194	−	14.1817i	−0.668333	−	0.485572i	−0.869467	+	0.493992i	$0.835537\pi$
$854$	1.11152	−	3.42091i	0.0380355	−	0.117061i
$855$	−2.64615	−	8.14401i	−0.0904964	−	0.278519i
$856$	10.8310	−	7.86920i	0.370197	−	0.268964i
$857$	−22.2559			−0.760246			−0.380123	−	0.924936i	$-0.624118\pi$
$857$	−22.2559			−0.760246			−0.380123	+	0.924936i	$0.624118\pi$
$858$	−37.8159	+	38.7951i	−1.29101	+	1.32444i
$859$	5.09623			0.173881			0.0869406	−	0.996214i	$-0.472291\pi$
$859$	5.09623			0.173881			0.0869406	+	0.996214i	$0.472291\pi$
$860$	2.44561	−	1.77684i	0.0833948	−	0.0605899i
$861$	5.46532	+	16.8205i	0.186258	+	0.573242i
$862$	0.194521	−	0.598676i	0.00662543	−	0.0203910i
$863$	−11.9162	−	8.65763i	−0.405632	−	0.294709i	0.366199	−	0.930537i	$-0.380659\pi$
$863$	−11.9162	−	8.65763i	−0.405632	−	0.294709i	−0.771831	+	0.635828i	$0.780659\pi$
$864$	−0.964387	−	0.700668i	−0.0328091	−	0.0238372i
$865$	−1.82700	+	5.62293i	−0.0621199	+	0.191186i
$866$	4.69050	+	14.4359i	0.159390	+	0.490551i
$867$	−2.81291	+	2.04370i	−0.0955315	+	0.0694077i
$868$	−7.88910			−0.267774
$869$	2.96218	−	20.3854i	0.100485	−	0.691529i
$870$	23.0022			0.779848
$871$	6.66233	−	4.84047i	0.225745	−	0.164013i
$872$	2.68110	+	8.25159i	0.0907936	+	0.279434i
$873$	−12.8201	+	39.4562i	−0.433894	+	1.33539i
$874$	−9.97492	−	7.24721i	−0.337407	−	0.245140i
$875$	0.809017	+	0.587785i	0.0273498	+	0.0198708i
$876$	−8.05757	+	24.7987i	−0.272240	+	0.837869i
$877$	−15.5169	−	47.7561i	−0.523968	−	1.61261i	−0.766348	−	0.642426i	$-0.777928\pi$
$877$	−15.5169	−	47.7561i	−0.523968	−	1.61261i	0.242380	−	0.970181i	$-0.422072\pi$
$878$	10.1686	−	7.38790i	0.343172	−	0.249329i
$879$	−43.8872			−1.48028
$880$	−2.97414	−	1.46782i	−0.100258	−	0.0494804i
$881$	11.6181			0.391423			0.195711	−	0.980662i	$-0.437298\pi$
$881$	11.6181			0.391423			0.195711	+	0.980662i	$0.437298\pi$
$882$	2.80623	−	2.03884i	0.0944906	−	0.0686515i
$883$	0.852737	+	2.62445i	0.0286969	+	0.0883199i	0.964379	−	0.264524i	$-0.0852148\pi$
$883$	0.852737	+	2.62445i	0.0286969	+	0.0883199i	−0.935682	+	0.352844i	$0.885215\pi$
$884$	7.84710	−	24.1509i	0.263927	−	0.812283i
$885$	−8.42750	−	6.12294i	−0.283287	−	0.205820i
$886$	−2.31274	−	1.68030i	−0.0776981	−	0.0564509i
$887$	−10.7701	+	33.1471i	−0.361626	+	1.11297i	0.590442	+	0.807080i	$0.298954\pi$
$887$	−10.7701	+	33.1471i	−0.361626	+	1.11297i	−0.952067	+	0.305889i	$0.901046\pi$
$888$	8.67996	+	26.7142i	0.291280	+	0.896469i
$889$	12.3615	−	8.98117i	0.414592	−	0.301219i
$890$	−14.7432			−0.494193
$891$	−11.3812	−	21.6482i	−0.381283	−	0.725243i
$892$	−0.768535			−0.0257325
$893$	−16.7363	+	12.1596i	−0.560059	+	0.406907i
$894$	−6.72239	−	20.6894i	−0.224830	−	0.691956i
$895$	−5.52768	+	17.0124i	−0.184770	+	0.568663i
$896$	−0.809017	−	0.587785i	−0.0270274	−	0.0196365i
$897$	66.0021	+	47.9534i	2.20375	+	1.60112i
$898$	−8.79884	+	27.0800i	−0.293621	+	0.903673i
$899$	22.0481	+	67.8571i	0.735346	+	2.26316i
$900$	−2.80623	+	2.03884i	−0.0935410	+	0.0679615i
$901$	39.7822			1.32534
$902$	−22.7314	+	3.89874i	−0.756873	+	0.129814i
$903$	−7.68845			−0.255855
$904$	−7.41603	+	5.38806i	−0.246653	+	0.179204i
$905$	3.42112	+	10.5291i	0.113722	+	0.350000i
$906$	−1.73815	+	5.34947i	−0.0577461	+	0.177724i
$907$	4.25136	+	3.08879i	0.141164	+	0.102562i	0.656126	−	0.754651i	$-0.272194\pi$
$907$	4.25136	+	3.08879i	0.141164	+	0.102562i	−0.514962	+	0.857213i	$0.672194\pi$
$908$	−5.32930	−	3.87197i	−0.176859	−	0.128496i
$909$	−2.42368	+	7.45933i	−0.0803885	+	0.247410i
$910$	1.98467	+	6.10820i	0.0657913	+	0.202485i
$911$	9.04475	−	6.57139i	0.299666	−	0.217720i	−0.427784	−	0.903881i	$-0.640706\pi$
$911$	9.04475	−	6.57139i	0.299666	−	0.217720i	0.727450	+	0.686161i	$0.240706\pi$
$912$	6.27877			0.207911
$913$	43.6014	−	7.47823i	1.44300	−	0.247493i
$914$	−7.63383			−0.252505
$915$	7.40119	−	5.37728i	0.244676	−	0.177767i
$916$	−7.19480	−	22.1433i	−0.237723	−	0.731636i
$917$	1.74737	−	5.37785i	0.0577032	−	0.177592i
$918$	−3.81304	−	2.77034i	−0.125849	−	0.0914347i
$919$	19.7289	+	14.3339i	0.650796	+	0.472831i	0.863542	−	0.504277i	$-0.168241\pi$
$919$	19.7289	+	14.3339i	0.650796	+	0.472831i	−0.212746	+	0.977107i	$0.568241\pi$
$920$	−1.54336	+	4.74998i	−0.0508831	+	0.156602i
$921$	−19.4952	−	60.0000i	−0.642388	−	1.97707i
$922$	−3.82028	+	2.77560i	−0.125814	+	0.0914094i
$923$	−37.8946			−1.24732
$924$	3.92533	+	7.46642i	0.129134	+	0.245627i
$925$	11.0440			0.363125
$926$	−15.7214	+	11.4223i	−0.516638	+	0.375360i
$927$	14.4017	+	44.3240i	0.473015	+	1.45579i
$928$	−2.79476	+	8.60137i	−0.0917424	+	0.282354i
$929$	−16.1197	−	11.7116i	−0.528869	−	0.384246i	0.291066	−	0.956703i	$-0.405990\pi$
$929$	−16.1197	−	11.7116i	−0.528869	−	0.384246i	−0.819935	+	0.572457i	$0.805990\pi$
$930$	−16.2328	−	11.7938i	−0.532294	−	0.386734i
$931$	−0.762867	+	2.34786i	−0.0250020	+	0.0769481i
$932$	−0.532246	−	1.63809i	−0.0174343	−	0.0536573i
$933$	−31.0121	+	22.5316i	−1.01529	+	0.737653i
$934$	13.5440			0.443172
$935$	−11.7593	−	5.80356i	−0.384570	−	0.189797i
$936$	−22.2778			−0.728173
$937$	38.8069	−	28.1949i	1.26777	−	0.921087i	0.268656	−	0.963236i	$-0.413421\pi$
$937$	38.8069	−	28.1949i	1.26777	−	0.921087i	0.999111	+	0.0421495i	$0.0134206\pi$
$938$	−0.396227	−	1.21946i	−0.0129373	−	0.0398168i
$939$	11.5327	−	35.4939i	0.376354	−	1.15830i
$940$	6.77943	+	4.92554i	0.221121	+	0.160654i
$941$	35.4739	+	25.7733i	1.15642	+	0.840186i	0.989321	−	0.145755i	$-0.0465612\pi$
$941$	35.4739	+	25.7733i	1.15642	+	0.840186i	0.167095	+	0.985941i	$0.446561\pi$
$942$	−10.5209	+	32.3799i	−0.342788	+	1.05499i
$943$	10.7323	+	33.0306i	0.349492	+	1.07563i
$944$	3.31353	−	2.40742i	0.107846	−	0.0783548i
$945$	1.19205			0.0387773
$946$	1.44172	−	9.92178i	0.0468743	−	0.322585i
$947$	−27.0791			−0.879951			−0.439976	−	0.898010i	$-0.645013\pi$
$947$	−27.0791			−0.879951			−0.439976	+	0.898010i	$0.645013\pi$
$948$	12.7799	−	9.28513i	0.415071	−	0.301567i
$949$	20.3471	+	62.6220i	0.660495	+	2.03280i
$950$	0.762867	−	2.34786i	0.0247507	−	0.0761748i
$951$	−29.3601	−	21.3314i	−0.952066	−	0.691717i
$952$	−3.19873	−	2.32401i	−0.103671	−	0.0753218i
$953$	−9.54793	+	29.3855i	−0.309288	+	0.951890i	0.668755	+	0.743483i	$0.266828\pi$
$953$	−9.54793	+	29.3855i	−0.309288	+	0.951890i	−0.978042	+	0.208407i	$0.933172\pi$
$954$	−10.7849	−	33.1926i	−0.349175	−	1.07465i
$955$	7.73401	−	5.61909i	0.250267	−	0.181829i
$956$	11.6437			0.376585
$957$	53.2511	−	54.6300i	1.72136	−	1.76594i
$958$	−4.33024			−0.139904
$959$	−3.19795	+	2.32344i	−0.103267	+	0.0750279i
$960$	−0.785942	−	2.41888i	−0.0253662	−	0.0780690i
$961$	9.65304	−	29.7090i	0.311388	−	0.958355i
$962$	57.3841	+	41.6920i	1.85014	+	1.34420i
$963$	−37.5695	−	27.2958i	−1.21066	−	0.879596i
$964$	−2.96111	+	9.11337i	−0.0953710	+	0.293522i
$965$	−5.15582	−	15.8680i	−0.165972	−	0.510808i
$966$	10.2766	−	7.46642i	0.330646	−	0.240228i
$967$	33.0146			1.06168			0.530839	−	0.847473i	$-0.321877\pi$
$967$	33.0146			1.06168			0.530839	+	0.847473i	$0.321877\pi$
$968$	−10.3713	+	3.66547i	−0.333347	+	0.117813i
$969$	24.8253			0.797504
$970$	−9.67611	+	7.03010i	−0.310681	+	0.225723i
$971$	5.47214	+	16.8415i	0.175609	+	0.540470i	0.999661	−	0.0260453i	$-0.00829140\pi$
$971$	5.47214	+	16.8415i	0.175609	+	0.540470i	−0.824052	+	0.566515i	$0.808291\pi$
$972$	6.90083	−	21.2386i	0.221344	−	0.681228i
$973$	−17.0099	−	12.3584i	−0.545313	−	0.396193i
$974$	−29.5906	−	21.4988i	−0.948143	−	0.688867i
$975$	−5.04774	+	15.5354i	−0.161657	+	0.497530i
$976$	1.11152	+	3.42091i	0.0355789	+	0.109501i
$977$	−11.7011	+	8.50131i	−0.374350	+	0.271981i	−0.759012	−	0.651076i	$-0.774318\pi$
$977$	−11.7011	+	8.50131i	−0.374350	+	0.271981i	0.384663	+	0.923057i	$0.374318\pi$
$978$	5.22163			0.166969
$979$	−34.1311	+	35.0150i	−1.09084	+	1.11908i
$980$	1.00000			0.0319438
$981$	24.3475	−	17.6895i	0.777356	−	0.564782i
$982$	9.80286	+	30.1701i	0.312822	+	0.962767i
$983$	−3.82743	+	11.7796i	−0.122076	+	0.375712i	−0.993357	−	0.115073i	$-0.963290\pi$
$983$	−3.82743	+	11.7796i	−0.122076	+	0.375712i	0.871281	+	0.490785i	$0.163290\pi$
$984$	−14.3084	−	10.3957i	−0.456135	−	0.331402i
$985$	−0.431562	−	0.313548i	−0.0137507	−	0.00999047i
$986$	−11.0500	+	34.0085i	−0.351905	+	1.08305i
$987$	−6.58607	−	20.2698i	−0.209637	−	0.645196i
$988$	12.8272	−	9.31949i	0.408087	−	0.296492i
$989$	−15.0979			−0.480085
$990$	−1.65431	+	11.3848i	−0.0525773	+	0.361832i
$991$	−48.6112			−1.54419			−0.772093	−	0.635509i	$-0.780790\pi$
$991$	−48.6112			−1.54419			−0.772093	+	0.635509i	$0.780790\pi$
$992$	6.38242	−	4.63710i	0.202642	−	0.147228i
$993$	10.1551	+	31.2541i	0.322262	+	0.991820i
$994$	−1.82328	+	5.61147i	−0.0578309	+	0.177985i
$995$	2.27692	+	1.65428i	0.0721832	+	0.0524442i
$996$	27.4452	+	19.9401i	0.869634	+	0.631826i
$997$	−10.9005	+	33.5484i	−0.345223	+	1.06249i	0.616241	+	0.787558i	$0.288655\pi$
$997$	−10.9005	+	33.5484i	−0.345223	+	1.06249i	−0.961464	+	0.274930i	$0.911345\pi$
$998$	−11.3713	−	34.9973i	−0.359952	−	1.10782i
$999$	10.6507	−	7.73819i	0.336974	−	0.244826i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	770.2.n.f.421.1	✓	8
11.2	odd	10		8470.2.a.cs.1.2		4
11.4	even	5	inner	770.2.n.f.631.1	yes	8
11.9	even	5		8470.2.a.co.1.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
770.2.n.f.421.1	✓	8	1.1	even	1	trivial
770.2.n.f.631.1	yes	8	11.4	even	5	inner
8470.2.a.co.1.2		4	11.9	even	5
8470.2.a.cs.1.2		4	11.2	odd	10

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)

\(f(q)\)	\(=\)	\(q+(0.809017 - 0.587785i) q^{2} +(-0.785942 - 2.41888i) q^{3} +(0.309017 - 0.951057i) q^{4} +(-0.809017 - 0.587785i) q^{5} +(-2.05762 - 1.49495i) q^{6} +(-0.309017 + 0.951057i) q^{7} +(-0.309017 - 0.951057i) q^{8} +(-2.80623 + 2.03884i) q^{9} +O(q^{10})\)	\(q+(0.809017 - 0.587785i) q^{2} +(-0.785942 - 2.41888i) q^{3} +(0.309017 - 0.951057i) q^{4} +(-0.809017 - 0.587785i) q^{5} +(-2.05762 - 1.49495i) q^{6} +(-0.309017 + 0.951057i) q^{7} +(-0.309017 - 0.951057i) q^{8} +(-2.80623 + 2.03884i) q^{9} -1.00000 q^{10} +(-2.31504 + 2.37499i) q^{11} -2.54336 q^{12} +(-5.19594 + 3.77507i) q^{13} +(0.309017 + 0.951057i) q^{14} +(-0.785942 + 2.41888i) q^{15} +(-0.809017 - 0.587785i) q^{16} +(-3.19873 - 2.32401i) q^{17} +(-1.07188 + 3.29892i) q^{18} +(-0.762867 - 2.34786i) q^{19} +(-0.809017 + 0.587785i) q^{20} +2.54336 q^{21} +(-0.476925 + 3.28216i) q^{22} +4.99442 q^{23} +(-2.05762 + 1.49495i) q^{24} +(0.309017 + 0.951057i) q^{25} +(-1.98467 + 6.10820i) q^{26} +(0.964387 + 0.700668i) q^{27} +(0.809017 + 0.587785i) q^{28} +(2.79476 - 8.60137i) q^{29} +(0.785942 + 2.41888i) q^{30} +(-6.38242 + 4.63710i) q^{31} -1.00000 q^{32} +(7.56431 + 3.73321i) q^{33} -3.95385 q^{34} +(0.809017 - 0.587785i) q^{35} +(1.07188 + 3.29892i) q^{36} +(3.41279 - 10.5035i) q^{37} +(-1.99721 - 1.45106i) q^{38} +(13.2152 + 9.60138i) q^{39} +(-0.309017 + 0.951057i) q^{40} +(2.14886 + 6.61350i) q^{41} +(2.05762 - 1.49495i) q^{42} -3.02295 q^{43} +(1.54336 + 2.93565i) q^{44} +3.46869 q^{45} +(4.04057 - 2.93565i) q^{46} +(-2.58951 - 7.96970i) q^{47} +(-0.785942 + 2.41888i) q^{48} +(-0.809017 - 0.587785i) q^{49} +(0.809017 + 0.587785i) q^{50} +(-3.10750 + 9.56389i) q^{51} +(1.98467 + 6.10820i) q^{52} +(-8.14004 + 5.91409i) q^{53} +1.19205 q^{54} +(3.26889 - 0.560659i) q^{55} +1.00000 q^{56} +(-5.07963 + 3.69057i) q^{57} +(-2.79476 - 8.60137i) q^{58} +(-1.26566 + 3.89529i) q^{59} +(2.05762 + 1.49495i) q^{60} +(-2.91000 - 2.11424i) q^{61} +(-2.43787 + 7.50298i) q^{62} +(-1.07188 - 3.29892i) q^{63} +(-0.809017 + 0.587785i) q^{64} +6.42254 q^{65} +(8.31398 - 1.42596i) q^{66} -1.28222 q^{67} +(-3.19873 + 2.32401i) q^{68} +(-3.92533 - 12.0809i) q^{69} +(0.309017 - 0.951057i) q^{70} +(4.77340 + 3.46808i) q^{71} +(2.80623 + 2.03884i) q^{72} +(3.16808 - 9.75035i) q^{73} +(-3.41279 - 10.5035i) q^{74} +(2.05762 - 1.49495i) q^{75} -2.46869 q^{76} +(-1.54336 - 2.93565i) q^{77} +16.3348 q^{78} +(-5.02480 + 3.65073i) q^{79} +(0.309017 + 0.951057i) q^{80} +(-2.27877 + 7.01334i) q^{81} +(5.62578 + 4.08737i) q^{82} +(-10.7909 - 7.84005i) q^{83} +(0.785942 - 2.41888i) q^{84} +(1.22181 + 3.76033i) q^{85} +(-2.44561 + 1.77684i) q^{86} -23.0022 q^{87} +(2.97414 + 1.46782i) q^{88} +14.7432 q^{89} +(2.80623 - 2.03884i) q^{90} +(-1.98467 - 6.10820i) q^{91} +(1.54336 - 4.74998i) q^{92} +(16.2328 + 11.7938i) q^{93} +(-6.77943 - 4.92554i) q^{94} +(-0.762867 + 2.34786i) q^{95} +(0.785942 + 2.41888i) q^{96} +(9.67611 - 7.03010i) q^{97} -1.00000 q^{98} +(1.65431 - 11.3848i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 2 q^{2} + 2 q^{3} - 2 q^{4} - 2 q^{5} - 2 q^{6} + 2 q^{7} + 2 q^{8} + 2 q^{9}+O(q^{10}) \) 8 * q + 2 * q^2 + 2 * q^3 - 2 * q^4 - 2 * q^5 - 2 * q^6 + 2 * q^7 + 2 * q^8 + 2 * q^9	\( 8 q + 2 q^{2} + 2 q^{3} - 2 q^{4} - 2 q^{5} - 2 q^{6} + 2 q^{7} + 2 q^{8} + 2 q^{9} - 8 q^{10} - 8 q^{12} - 2 q^{13} - 2 q^{14} + 2 q^{15} - 2 q^{16} - 6 q^{17} + 8 q^{18} + 6 q^{19} - 2 q^{20} + 8 q^{21} - 2 q^{24} - 2 q^{25} + 12 q^{26} - 4 q^{27} + 2 q^{28} + 20 q^{29} - 2 q^{30} - 6 q^{31} - 8 q^{32} - 8 q^{33} - 24 q^{34} + 2 q^{35} - 8 q^{36} + 16 q^{37} + 4 q^{38} + 20 q^{39} + 2 q^{40} - 12 q^{41} + 2 q^{42} + 20 q^{43} + 12 q^{45} - 16 q^{47} + 2 q^{48} - 2 q^{49} + 2 q^{50} - 20 q^{51} - 12 q^{52} - 30 q^{53} + 44 q^{54} + 8 q^{56} - 20 q^{58} - 18 q^{59} + 2 q^{60} + 8 q^{61} - 24 q^{62} + 8 q^{63} - 2 q^{64} + 28 q^{65} + 18 q^{66} - 6 q^{68} - 28 q^{69} - 2 q^{70} + 22 q^{71} - 2 q^{72} - 50 q^{73} - 16 q^{74} + 2 q^{75} - 4 q^{76} + 60 q^{78} - 34 q^{79} - 2 q^{80} - 28 q^{81} + 12 q^{82} - 34 q^{83} - 2 q^{84} - 6 q^{85} + 4 q^{87} - 8 q^{89} - 2 q^{90} + 12 q^{91} + 56 q^{93} - 24 q^{94} + 6 q^{95} - 2 q^{96} - 8 q^{98} - 24 q^{99}+O(q^{100}) \) 8 * q + 2 * q^2 + 2 * q^3 - 2 * q^4 - 2 * q^5 - 2 * q^6 + 2 * q^7 + 2 * q^8 + 2 * q^9 - 8 * q^10 - 8 * q^12 - 2 * q^13 - 2 * q^14 + 2 * q^15 - 2 * q^16 - 6 * q^17 + 8 * q^18 + 6 * q^19 - 2 * q^20 + 8 * q^21 - 2 * q^24 - 2 * q^25 + 12 * q^26 - 4 * q^27 + 2 * q^28 + 20 * q^29 - 2 * q^30 - 6 * q^31 - 8 * q^32 - 8 * q^33 - 24 * q^34 + 2 * q^35 - 8 * q^36 + 16 * q^37 + 4 * q^38 + 20 * q^39 + 2 * q^40 - 12 * q^41 + 2 * q^42 + 20 * q^43 + 12 * q^45 - 16 * q^47 + 2 * q^48 - 2 * q^49 + 2 * q^50 - 20 * q^51 - 12 * q^52 - 30 * q^53 + 44 * q^54 + 8 * q^56 - 20 * q^58 - 18 * q^59 + 2 * q^60 + 8 * q^61 - 24 * q^62 + 8 * q^63 - 2 * q^64 + 28 * q^65 + 18 * q^66 - 6 * q^68 - 28 * q^69 - 2 * q^70 + 22 * q^71 - 2 * q^72 - 50 * q^73 - 16 * q^74 + 2 * q^75 - 4 * q^76 + 60 * q^78 - 34 * q^79 - 2 * q^80 - 28 * q^81 + 12 * q^82 - 34 * q^83 - 2 * q^84 - 6 * q^85 + 4 * q^87 - 8 * q^89 - 2 * q^90 + 12 * q^91 + 56 * q^93 - 24 * q^94 + 6 * q^95 - 2 * q^96 - 8 * q^98 - 24 * q^99

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