LMFDB - Embedded newform 770.2.n.i.421.2

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:	$12$
Relative dimension:	$3$ over $\Q(\zeta_{5})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 3 x^{11} + 11 x^{10} - 21 x^{9} + 61 x^{8} - 34 x^{7} + 141 x^{6} + 192 x^{5} + 289 x^{4} + \cdots + 1 $ x^12 - 3x^11 + 11x^10 - 21x^9 + 61x^8 - 34x^7 + 141x^6 + 192x^5 + 289x^4 - 55x^3 + 222x^2 - 24*x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			421.2
Root			$-0.748642 - 2.30408i$ of defining polynomial
Character	$\chi$	$=$	770.421
Dual form			770.2.n.i.631.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.809017 + 0.587785i) q^{2} +(0.361989 + 1.11409i) q^{3} +(0.309017 - 0.951057i) q^{4} +(-0.809017 - 0.587785i) q^{5} +(-0.947700 - 0.688544i) q^{6} +(0.309017 - 0.951057i) q^{7} +(0.309017 + 0.951057i) q^{8} +(1.31690 - 0.956780i) q^{9} +O(q^{10})$	\(q+(-0.809017 + 0.587785i) q^{2} +(0.361989 + 1.11409i) q^{3} +(0.309017 - 0.951057i) q^{4} +(-0.809017 - 0.587785i) q^{5} +(-0.947700 - 0.688544i) q^{6} +(0.309017 - 0.951057i) q^{7} +(0.309017 + 0.951057i) q^{8} +(1.31690 - 0.956780i) q^{9} +1.00000 q^{10} +(-3.15523 + 1.02203i) q^{11} +1.17142 q^{12} +(-2.19634 + 1.59574i) q^{13} +(0.309017 + 0.951057i) q^{14} +(0.361989 - 1.11409i) q^{15} +(-0.809017 - 0.587785i) q^{16} +(4.32225 + 3.14030i) q^{17} +(-0.503009 + 1.54810i) q^{18} +(1.22867 + 3.78144i) q^{19} +(-0.809017 + 0.587785i) q^{20} +1.17142 q^{21} +(1.95190 - 2.68144i) q^{22} +5.49704 q^{23} +(-0.947700 + 0.688544i) q^{24} +(0.309017 + 0.951057i) q^{25} +(0.838928 - 2.58196i) q^{26} +(4.38574 + 3.18643i) q^{27} +(-0.809017 - 0.587785i) q^{28} +(-1.54490 + 4.75471i) q^{29} +(0.361989 + 1.11409i) q^{30} +(2.32196 - 1.68700i) q^{31} +1.00000 q^{32} +(-2.28079 - 3.14524i) q^{33} -5.34260 q^{34} +(-0.809017 + 0.587785i) q^{35} +(-0.503009 - 1.54810i) q^{36} +(0.0125281 - 0.0385574i) q^{37} +(-3.21669 - 2.33706i) q^{38} +(-2.57284 - 1.86928i) q^{39} +(0.309017 - 0.951057i) q^{40} +(1.58530 + 4.87904i) q^{41} +(-0.947700 + 0.688544i) q^{42} +12.2705 q^{43} +(-0.00300917 + 3.31662i) q^{44} -1.62777 q^{45} +(-4.44720 + 3.23108i) q^{46} +(3.05922 + 9.41530i) q^{47} +(0.361989 - 1.11409i) q^{48} +(-0.809017 - 0.587785i) q^{49} +(-0.809017 - 0.587785i) q^{50} +(-1.93396 + 5.95213i) q^{51} +(0.838928 + 2.58196i) q^{52} +(-3.68815 + 2.67960i) q^{53} -5.42107 q^{54} +(3.15337 + 1.02775i) q^{55} +1.00000 q^{56} +(-3.76810 + 2.73768i) q^{57} +(-1.54490 - 4.75471i) q^{58} +(-0.180684 + 0.556087i) q^{59} +(-0.947700 - 0.688544i) q^{60} +(-5.87316 - 4.26710i) q^{61} +(-0.886910 + 2.72963i) q^{62} +(-0.503009 - 1.54810i) q^{63} +(-0.809017 + 0.587785i) q^{64} +2.71483 q^{65} +(3.69392 + 1.20393i) q^{66} -14.4148 q^{67} +(4.32225 - 3.14030i) q^{68} +(1.98987 + 6.12419i) q^{69} +(0.309017 - 0.951057i) q^{70} +(-6.64053 - 4.82463i) q^{71} +(1.31690 + 0.956780i) q^{72} +(4.50848 - 13.8757i) q^{73} +(0.0125281 + 0.0385574i) q^{74} +(-0.947700 + 0.688544i) q^{75} +3.97605 q^{76} +(-0.00300917 + 3.31662i) q^{77} +3.18021 q^{78} +(-5.46363 + 3.96956i) q^{79} +(0.309017 + 0.951057i) q^{80} +(-0.453341 + 1.39524i) q^{81} +(-4.15036 - 3.01541i) q^{82} +(12.6040 + 9.15735i) q^{83} +(0.361989 - 1.11409i) q^{84} +(-1.65095 - 5.08111i) q^{85} +(-9.92704 + 7.21242i) q^{86} -5.85640 q^{87} +(-1.94703 - 2.68497i) q^{88} +2.73408 q^{89} +(1.31690 - 0.956780i) q^{90} +(0.838928 + 2.58196i) q^{91} +(1.69868 - 5.22800i) q^{92} +(2.71999 + 1.97619i) q^{93} +(-8.00913 - 5.81897i) q^{94} +(1.22867 - 3.78144i) q^{95} +(0.361989 + 1.11409i) q^{96} +(1.07421 - 0.780461i) q^{97} +1.00000 q^{98} +(-3.17724 + 4.36477i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 3 q^{2} + 2 q^{3} - 3 q^{4} - 3 q^{5} - 3 q^{6} - 3 q^{7} - 3 q^{8} - 15 q^{9}+O(q^{10}) $ 12 * q - 3 * q^2 + 2 * q^3 - 3 * q^4 - 3 * q^5 - 3 * q^6 - 3 * q^7 - 3 * q^8 - 15 * q^9	\( 12 q - 3 q^{2} + 2 q^{3} - 3 q^{4} - 3 q^{5} - 3 q^{6} - 3 q^{7} - 3 q^{8} - 15 q^{9} + 12 q^{10} + q^{11} + 2 q^{12} - 6 q^{13} - 3 q^{14} + 2 q^{15} - 3 q^{16} - 6 q^{17} - 13 q^{19} - 3 q^{20} + 2 q^{21} + q^{22} - 12 q^{23} - 3 q^{24} - 3 q^{25} + 4 q^{26} - 7 q^{27} - 3 q^{28} - 26 q^{29} + 2 q^{30} + 12 q^{32} - 15 q^{33} + 14 q^{34} - 3 q^{35} - 18 q^{37} + 2 q^{38} - 40 q^{39} - 3 q^{40} + 16 q^{41} - 3 q^{42} + 38 q^{43} + 6 q^{44} + 30 q^{45} + 8 q^{46} - 26 q^{47} + 2 q^{48} - 3 q^{49} - 3 q^{50} - 13 q^{51} + 4 q^{52} + 8 q^{54} + 11 q^{55} + 12 q^{56} - 41 q^{57} - 26 q^{58} + 21 q^{59} - 3 q^{60} + 4 q^{61} - 3 q^{64} + 4 q^{65} - 30 q^{66} + 10 q^{67} - 6 q^{68} + 18 q^{69} - 3 q^{70} - 4 q^{71} - 15 q^{72} - 14 q^{73} - 18 q^{74} - 3 q^{75} + 22 q^{76} + 6 q^{77} + 40 q^{78} - 2 q^{79} - 3 q^{80} + 26 q^{81} - 29 q^{82} + 35 q^{83} + 2 q^{84} - q^{85} - 37 q^{86} + 28 q^{87} - 19 q^{88} + 2 q^{89} - 15 q^{90} + 4 q^{91} - 2 q^{92} + 6 q^{93} + 4 q^{94} - 13 q^{95} + 2 q^{96} + 19 q^{97} + 12 q^{98} - 81 q^{99}+O(q^{100}) \) 12 * q - 3 * q^2 + 2 * q^3 - 3 * q^4 - 3 * q^5 - 3 * q^6 - 3 * q^7 - 3 * q^8 - 15 * q^9 + 12 * q^10 + q^11 + 2 * q^12 - 6 * q^13 - 3 * q^14 + 2 * q^15 - 3 * q^16 - 6 * q^17 - 13 * q^19 - 3 * q^20 + 2 * q^21 + q^22 - 12 * q^23 - 3 * q^24 - 3 * q^25 + 4 * q^26 - 7 * q^27 - 3 * q^28 - 26 * q^29 + 2 * q^30 + 12 * q^32 - 15 * q^33 + 14 * q^34 - 3 * q^35 - 18 * q^37 + 2 * q^38 - 40 * q^39 - 3 * q^40 + 16 * q^41 - 3 * q^42 + 38 * q^43 + 6 * q^44 + 30 * q^45 + 8 * q^46 - 26 * q^47 + 2 * q^48 - 3 * q^49 - 3 * q^50 - 13 * q^51 + 4 * q^52 + 8 * q^54 + 11 * q^55 + 12 * q^56 - 41 * q^57 - 26 * q^58 + 21 * q^59 - 3 * q^60 + 4 * q^61 - 3 * q^64 + 4 * q^65 - 30 * q^66 + 10 * q^67 - 6 * q^68 + 18 * q^69 - 3 * q^70 - 4 * q^71 - 15 * q^72 - 14 * q^73 - 18 * q^74 - 3 * q^75 + 22 * q^76 + 6 * q^77 + 40 * q^78 - 2 * q^79 - 3 * q^80 + 26 * q^81 - 29 * q^82 + 35 * q^83 + 2 * q^84 - q^85 - 37 * q^86 + 28 * q^87 - 19 * q^88 + 2 * q^89 - 15 * q^90 + 4 * q^91 - 2 * q^92 + 6 * q^93 + 4 * q^94 - 13 * q^95 + 2 * q^96 + 19 * q^97 + 12 * q^98 - 81 * 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
$3$	0.361989	+	1.11409i	0.208995	+	0.643219i	0.999526	+	0.0307971i	$0.00980458\pi$
$3$	0.361989	+	1.11409i	0.208995	+	0.643219i	−0.790531	+	0.612422i	$0.790195\pi$
$4$	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
$6$	−0.947700	−	0.688544i	−0.386897	−	0.281097i
$7$	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
$9$	1.31690	−	0.956780i	0.438965	−	0.318927i
$10$	1.00000			0.316228
$11$	−3.15523	+	1.02203i	−0.951336	+	0.308154i
$11$	−3.15523	+	1.02203i	−0.951336	+	0.308154i
$12$	1.17142			0.338160
$13$	−2.19634	+	1.59574i	−0.609156	+	0.442578i	−0.849117	−	0.528205i	$-0.822865\pi$
$13$	−2.19634	+	1.59574i	−0.609156	+	0.442578i	0.239961	+	0.970782i	$0.422865\pi$
$14$	0.309017	+	0.951057i	0.0825883	+	0.254181i
$15$	0.361989	−	1.11409i	0.0934652	−	0.287656i
$16$	−0.809017	−	0.587785i	−0.202254	−	0.146946i
$17$	4.32225	+	3.14030i	1.04830	+	0.761635i	0.971889	−	0.235441i	$-0.0756535\pi$
$17$	4.32225	+	3.14030i	1.04830	+	0.761635i	0.0764121	+	0.997076i	$0.475654\pi$
$18$	−0.503009	+	1.54810i	−0.118560	+	0.364891i
$19$	1.22867	+	3.78144i	0.281875	+	0.867523i	0.987318	+	0.158756i	$0.0507482\pi$
$19$	1.22867	+	3.78144i	0.281875	+	0.867523i	−0.705443	+	0.708767i	$0.749252\pi$
$20$	−0.809017	+	0.587785i	−0.180902	+	0.131433i
$21$	1.17142			0.255625
$22$	1.95190	−	2.68144i	0.416146	−	0.571684i
$23$	5.49704			1.14621			0.573106	−	0.819481i	$-0.305738\pi$
$23$	5.49704			1.14621			0.573106	+	0.819481i	$0.305738\pi$
$24$	−0.947700	+	0.688544i	−0.193448	+	0.140549i
$25$	0.309017	+	0.951057i	0.0618034	+	0.190211i
$26$	0.838928	−	2.58196i	0.164527	−	0.506363i
$27$	4.38574	+	3.18643i	0.844036	+	0.613228i
$28$	−0.809017	−	0.587785i	−0.152890	−	0.111081i
$29$	−1.54490	+	4.75471i	−0.286880	+	0.882927i	0.698948	+	0.715172i	$0.253652\pi$
$29$	−1.54490	+	4.75471i	−0.286880	+	0.882927i	−0.985829	+	0.167755i	$0.946348\pi$
$30$	0.361989	+	1.11409i	0.0660899	+	0.203404i
$31$	2.32196	−	1.68700i	0.417036	−	0.302995i	−0.359408	−	0.933181i	$-0.617021\pi$
$31$	2.32196	−	1.68700i	0.417036	−	0.302995i	0.776444	+	0.630186i	$0.217021\pi$
$32$	1.00000			0.176777
$33$	−2.28079	−	3.14524i	−0.397035	−	0.547515i
$34$	−5.34260			−0.916248
$35$	−0.809017	+	0.587785i	−0.136749	+	0.0993538i
$36$	−0.503009	−	1.54810i	−0.0838349	−	0.258017i
$37$	0.0125281	−	0.0385574i	0.00205960	−	0.00633880i	−0.950021	−	0.312185i	$-0.898939\pi$
$37$	0.0125281	−	0.0385574i	0.00205960	−	0.00633880i	0.952081	+	0.305846i	$0.0989392\pi$
$38$	−3.21669	−	2.33706i	−0.521816	−	0.379121i
$39$	−2.57284	−	1.86928i	−0.411984	−	0.299324i
$40$	0.309017	−	0.951057i	0.0488599	−	0.150375i
$41$	1.58530	+	4.87904i	0.247582	+	0.761978i	0.995201	+	0.0978504i	$0.0311967\pi$
$41$	1.58530	+	4.87904i	0.247582	+	0.761978i	−0.747620	+	0.664127i	$0.768803\pi$
$42$	−0.947700	+	0.688544i	−0.146233	+	0.106245i
$43$	12.2705			1.87123			0.935617	−	0.353017i	$-0.114844\pi$
$43$	12.2705			1.87123			0.935617	+	0.353017i	$0.114844\pi$
$44$	−0.00300917	+	3.31662i	−0.000453649	+	0.500000i
$45$	−1.62777			−0.242654
$46$	−4.44720	+	3.23108i	−0.655704	+	0.476397i
$47$	3.05922	+	9.41530i	0.446233	+	1.37336i	0.881126	+	0.472881i	$0.156786\pi$
$47$	3.05922	+	9.41530i	0.446233	+	1.37336i	−0.434894	+	0.900482i	$0.643214\pi$
$48$	0.361989	−	1.11409i	0.0522486	−	0.160805i
$49$	−0.809017	−	0.587785i	−0.115574	−	0.0839693i
$50$	−0.809017	−	0.587785i	−0.114412	−	0.0831254i
$51$	−1.93396	+	5.95213i	−0.270809	+	0.833464i
$52$	0.838928	+	2.58196i	0.116338	+	0.358053i
$53$	−3.68815	+	2.67960i	−0.506606	+	0.368071i	−0.811535	−	0.584304i	$-0.801367\pi$
$53$	−3.68815	+	2.67960i	−0.506606	+	0.368071i	0.304929	+	0.952375i	$0.401367\pi$
$54$	−5.42107			−0.737714
$55$	3.15337	+	1.02775i	0.425200	+	0.138582i
$56$	1.00000			0.133631
$57$	−3.76810	+	2.73768i	−0.499097	+	0.362615i
$58$	−1.54490	−	4.75471i	−0.202855	−	0.624324i
$59$	−0.180684	+	0.556087i	−0.0235230	+	0.0723964i	−0.962129	−	0.272595i	$-0.912118\pi$
$59$	−0.180684	+	0.556087i	−0.0235230	+	0.0723964i	0.938606	+	0.344991i	$0.112118\pi$
$60$	−0.947700	−	0.688544i	−0.122348	−	0.0888907i
$61$	−5.87316	−	4.26710i	−0.751982	−	0.546347i	0.144459	−	0.989511i	$-0.453856\pi$
$61$	−5.87316	−	4.26710i	−0.751982	−	0.546347i	−0.896440	+	0.443164i	$0.853856\pi$
$62$	−0.886910	+	2.72963i	−0.112638	+	0.346663i
$63$	−0.503009	−	1.54810i	−0.0633732	−	0.195043i
$64$	−0.809017	+	0.587785i	−0.101127	+	0.0734732i
$65$	2.71483			0.336733
$66$	3.69392	+	1.20393i	0.454690	+	0.148194i
$67$	−14.4148			−1.76105			−0.880526	−	0.473998i	$-0.842811\pi$
$67$	−14.4148			−1.76105			−0.880526	+	0.473998i	$0.842811\pi$
$68$	4.32225	−	3.14030i	0.524150	−	0.380818i
$69$	1.98987	+	6.12419i	0.239552	+	0.737266i
$70$	0.309017	−	0.951057i	0.0369346	−	0.113673i
$71$	−6.64053	−	4.82463i	−0.788086	−	0.572578i	0.119309	−	0.992857i	$-0.461932\pi$
$71$	−6.64053	−	4.82463i	−0.788086	−	0.572578i	−0.907395	+	0.420279i	$0.861932\pi$
$72$	1.31690	+	0.956780i	0.155198	+	0.112758i
$73$	4.50848	−	13.8757i	0.527678	−	1.62403i	−0.231281	−	0.972887i	$-0.574292\pi$
$73$	4.50848	−	13.8757i	0.527678	−	1.62403i	0.758959	−	0.651138i	$-0.225708\pi$
$74$	0.0125281	+	0.0385574i	0.00145636	+	0.00448221i
$75$	−0.947700	+	0.688544i	−0.109431	+	0.0795062i
$76$	3.97605			0.456084
$77$	−0.00300917	+	3.31662i	−0.000342927	+	0.377964i
$78$	3.18021			0.360088
$79$	−5.46363	+	3.96956i	−0.614707	+	0.446610i	−0.851069	−	0.525055i	$-0.824045\pi$
$79$	−5.46363	+	3.96956i	−0.614707	+	0.446610i	0.236362	+	0.971665i	$0.424045\pi$
$80$	0.309017	+	0.951057i	0.0345492	+	0.106331i
$81$	−0.453341	+	1.39524i	−0.0503713	+	0.155027i
$82$	−4.15036	−	3.01541i	−0.458330	−	0.332996i
$83$	12.6040	+	9.15735i	1.38347	+	1.00515i	0.996546	+	0.0830371i	$0.0264620\pi$
$83$	12.6040	+	9.15735i	1.38347	+	1.00515i	0.386923	+	0.922112i	$0.373538\pi$
$84$	0.361989	−	1.11409i	0.0394963	−	0.121557i
$85$	−1.65095	−	5.08111i	−0.179071	−	0.551124i
$86$	−9.92704	+	7.21242i	−1.07046	+	0.777735i
$87$	−5.85640			−0.627872
$88$	−1.94703	−	2.68497i	−0.207554	−	0.286219i
$89$	2.73408			0.289812			0.144906	−	0.989445i	$-0.453712\pi$
$89$	2.73408			0.289812			0.144906	+	0.989445i	$0.453712\pi$
$90$	1.31690	−	0.956780i	0.138813	−	0.100853i
$91$	0.838928	+	2.58196i	0.0879436	+	0.270662i
$92$	1.69868	−	5.22800i	0.177100	−	0.545056i
$93$	2.71999	+	1.97619i	0.282050	+	0.204922i
$94$	−8.00913	−	5.81897i	−0.826079	−	0.600181i
$95$	1.22867	−	3.78144i	0.126058	−	0.387968i
$96$	0.361989	+	1.11409i	0.0369454	+	0.113706i
$97$	1.07421	−	0.780461i	0.109070	−	0.0792438i	−0.531913	−	0.846799i	$-0.678527\pi$
$97$	1.07421	−	0.780461i	0.109070	−	0.0792438i	0.640983	+	0.767555i	$0.278527\pi$
$98$	1.00000			0.101015
$99$	−3.17724	+	4.36477i	−0.319325	+	0.438675i
$100$	1.00000			0.100000
$101$	−10.4794	+	7.61374i	−1.04274	+	0.757596i	−0.970819	−	0.239815i	$-0.922913\pi$
$101$	−10.4794	+	7.61374i	−1.04274	+	0.757596i	−0.0719223	+	0.997410i	$0.522913\pi$
$102$	−1.93396	−	5.95213i	−0.191491	−	0.589348i
$103$	2.85536	−	8.78789i	0.281347	−	0.865897i	−0.706123	−	0.708089i	$-0.749557\pi$
$103$	2.85536	−	8.78789i	0.281347	−	0.865897i	0.987470	−	0.157808i	$-0.0504426\pi$
$104$	−2.19634	−	1.59574i	−0.215369	−	0.156475i
$105$	−0.947700	−	0.688544i	−0.0924860	−	0.0671950i
$106$	1.40875	−	4.33568i	0.136830	−	0.421118i
$107$	3.09084	+	9.51263i	0.298803	+	0.919621i	0.981917	+	0.189310i	$0.0606250\pi$
$107$	3.09084	+	9.51263i	0.298803	+	0.919621i	−0.683114	+	0.730311i	$0.739375\pi$
$108$	4.38574	−	3.18643i	0.422018	−	0.306614i
$109$	−0.535064			−0.0512498			−0.0256249	−	0.999672i	$-0.508158\pi$
$109$	−0.535064			−0.0512498			−0.0256249	+	0.999672i	$0.508158\pi$
$110$	−3.15523	+	1.02203i	−0.300839	+	0.0974468i
$111$	0.0474914			0.00450768
$112$	−0.809017	+	0.587785i	−0.0764449	+	0.0555405i
$113$	−0.479646	−	1.47620i	−0.0451213	−	0.138869i	0.925958	−	0.377627i	$-0.123260\pi$
$113$	−0.479646	−	1.47620i	−0.0451213	−	0.138869i	−0.971079	+	0.238758i	$0.923260\pi$
$114$	1.43929	−	4.42966i	0.134801	−	0.414876i
$115$	−4.44720	−	3.23108i	−0.414704	−	0.301300i
$116$	4.04459	+	2.93857i	0.375531	+	0.272839i
$117$	−1.36558	+	4.20283i	−0.126248	+	0.388552i
$118$	−0.180684	−	0.556087i	−0.0166333	−	0.0511920i
$119$	4.32225	−	3.14030i	0.396220	−	0.287871i
$120$	1.17142			0.106936
$121$	8.91090	−	6.44948i	0.810082	−	0.586316i
$122$	7.25963			0.657256
$123$	−4.86182	+	3.53232i	−0.438375	+	0.318498i
$124$	−0.886910	−	2.72963i	−0.0796469	−	0.245128i
$125$	0.309017	−	0.951057i	0.0276393	−	0.0850651i
$126$	1.31690	+	0.956780i	0.117318	+	0.0852368i
$127$	13.9780	+	10.1556i	1.24034	+	0.901163i	0.997621	−	0.0689330i	$-0.0219595\pi$
$127$	13.9780	+	10.1556i	1.24034	+	0.901163i	0.242723	+	0.970096i	$0.421959\pi$
$128$	0.309017	−	0.951057i	0.0273135	−	0.0840623i
$129$	4.44179	+	13.6704i	0.391078	+	1.20361i
$130$	−2.19634	+	1.59574i	−0.192632	+	0.139955i
$131$	11.0180			0.962651			0.481325	−	0.876542i	$-0.340156\pi$
$131$	11.0180			0.962651			0.481325	+	0.876542i	$0.340156\pi$
$132$	−3.69610	+	1.19723i	−0.321704	+	0.104205i
$133$	3.97605			0.344767
$134$	11.6618	−	8.47283i	1.00743	−	0.731941i
$135$	−1.67520	−	5.15574i	−0.144179	−	0.443736i
$136$	−1.65095	+	5.08111i	−0.141568	+	0.435702i
$137$	−7.67733	−	5.57791i	−0.655919	−	0.476553i	0.209363	−	0.977838i	$-0.432861\pi$
$137$	−7.67733	−	5.57791i	−0.655919	−	0.476553i	−0.865282	+	0.501285i	$0.832861\pi$
$138$	−5.20955	−	3.78496i	−0.443466	−	0.322197i
$139$	−3.35603	+	10.3288i	−0.284655	+	0.876078i	0.701847	+	0.712328i	$0.252359\pi$
$139$	−3.35603	+	10.3288i	−0.284655	+	0.876078i	−0.986502	+	0.163750i	$0.947641\pi$
$140$	0.309017	+	0.951057i	0.0261167	+	0.0803789i
$141$	−9.38207	+	6.81647i	−0.790113	+	0.574050i
$142$	8.20815			0.688813
$143$	5.29906	−	7.27964i	0.443130	−	0.608754i
$144$	−1.62777			−0.135648
$145$	4.04459	−	2.93857i	0.335885	−	0.244035i
$146$	4.50848	+	13.8757i	0.373125	+	1.14836i
$147$	0.361989	−	1.11409i	0.0298564	−	0.0918884i
$148$	−0.0327989	−	0.0238298i	−0.00269605	−	0.00195880i
$149$	−9.97639	−	7.24827i	−0.817298	−	0.593802i	0.0986394	−	0.995123i	$-0.468551\pi$
$149$	−9.97639	−	7.24827i	−0.817298	−	0.593802i	−0.915937	+	0.401322i	$0.868551\pi$
$150$	0.361989	−	1.11409i	0.0295563	−	0.0909649i
$151$	−2.69079	−	8.28141i	−0.218974	−	0.673931i	−0.998848	−	0.0479948i	$-0.984717\pi$
$151$	−2.69079	−	8.28141i	−0.218974	−	0.673931i	0.779874	−	0.625937i	$-0.215283\pi$
$152$	−3.21669	+	2.33706i	−0.260908	+	0.189561i
$153$	8.69653			0.703073
$154$	−1.94703	−	2.68497i	−0.156896	−	0.216361i
$155$	−2.87010			−0.230532
$156$	−2.57284	+	1.86928i	−0.205992	+	0.149662i
$157$	−5.91071	−	18.1913i	−0.471726	−	1.45182i	−0.850323	−	0.526261i	$-0.823593\pi$
$157$	−5.91071	−	18.1913i	−0.471726	−	1.45182i	0.378597	−	0.925562i	$-0.376407\pi$
$158$	2.08692	−	6.42288i	0.166027	−	0.510977i
$159$	−4.32037	−	3.13894i	−0.342628	−	0.248934i
$160$	−0.809017	−	0.587785i	−0.0639584	−	0.0464685i
$161$	1.69868	−	5.22800i	0.133875	−	0.412024i
$162$	−0.453341	−	1.39524i	−0.0356179	−	0.109620i
$163$	15.0675	−	10.9472i	1.18018	−	0.857448i	0.187984	−	0.982172i	$-0.439805\pi$
$163$	15.0675	−	10.9472i	1.18018	−	0.857448i	0.992191	+	0.124724i	$0.0398046\pi$
$164$	5.13012			0.400595
$165$	−0.00352500	+	3.88516i	−0.000274421	+	0.302460i
$166$	−15.5794			−1.20920
$167$	−1.34370	+	0.976256i	−0.103979	+	0.0755450i	−0.638560	−	0.769572i	$-0.720469\pi$
$167$	−1.34370	+	0.976256i	−0.103979	+	0.0755450i	0.534581	+	0.845117i	$0.320469\pi$
$168$	0.361989	+	1.11409i	0.0279281	+	0.0859538i
$169$	−1.73968	+	5.35417i	−0.133821	+	0.411859i
$170$	4.32225	+	3.14030i	0.331502	+	0.240850i
$171$	5.23603	+	3.80420i	0.400410	+	0.290915i
$172$	3.79179	−	11.6699i	0.289121	−	0.889824i
$173$	−3.21547	−	9.89621i	−0.244468	−	0.752395i	−0.995724	−	0.0923834i	$-0.970551\pi$
$173$	−3.21547	−	9.89621i	−0.244468	−	0.752395i	0.751256	−	0.660011i	$-0.229449\pi$
$174$	4.73792	−	3.44230i	0.359181	−	0.260960i
$175$	1.00000			0.0755929
$176$	3.15337	+	1.02775i	0.237694	+	0.0774699i
$177$	−0.684935			−0.0514829
$178$	−2.21192	+	1.60705i	−0.165790	+	0.120454i
$179$	−7.85569	−	24.1773i	−0.587162	−	1.80710i	−0.590410	−	0.807104i	$-0.701034\pi$
$179$	−7.85569	−	24.1773i	−0.587162	−	1.80710i	0.00324784	−	0.999995i	$-0.498966\pi$
$180$	−0.503009	+	1.54810i	−0.0374921	+	0.115389i
$181$	7.56141	+	5.49368i	0.562035	+	0.408342i	0.832203	−	0.554471i	$-0.187079\pi$
$181$	7.56141	+	5.49368i	0.562035	+	0.408342i	−0.270168	+	0.962813i	$0.587079\pi$
$182$	−2.19634	−	1.59574i	−0.162804	−	0.118284i
$183$	2.62791	−	8.08787i	0.194260	−	0.597872i
$184$	1.69868	+	5.22800i	0.125228	+	0.385413i
$185$	−0.0327989	+	0.0238298i	−0.00241142	+	0.00175200i
$186$	−3.36210			−0.246521
$187$	−16.8472	−	5.49088i	−1.23199	−	0.401533i
$188$	9.89983			0.722019
$189$	4.38574	−	3.18643i	0.319016	−	0.231778i
$190$	1.22867	+	3.78144i	0.0891368	+	0.274335i
$191$	1.40884	−	4.33598i	0.101940	−	0.313740i	−0.887060	−	0.461655i	$-0.847256\pi$
$191$	1.40884	−	4.33598i	0.101940	−	0.313740i	0.989000	+	0.147914i	$0.0472560\pi$
$192$	−0.947700	−	0.688544i	−0.0683943	−	0.0496914i
$193$	−12.7943	−	9.29561i	−0.920955	−	0.669113i	0.0228068	−	0.999740i	$-0.492740\pi$
$193$	−12.7943	−	9.29561i	−0.920955	−	0.669113i	−0.943761	+	0.330627i	$0.892740\pi$
$194$	−0.410312	+	1.26281i	−0.0294587	+	0.0906646i
$195$	0.982738	+	3.02456i	0.0703754	+	0.216593i
$196$	−0.809017	+	0.587785i	−0.0577869	+	0.0419847i
$197$	14.6162			1.04136			0.520679	−	0.853753i	$-0.325679\pi$
$197$	14.6162			1.04136			0.520679	+	0.853753i	$0.325679\pi$
$198$	0.00489824	−	5.39871i	0.000348103	−	0.383669i
$199$	16.4255			1.16438			0.582188	−	0.813054i	$-0.302197\pi$
$199$	16.4255			1.16438			0.582188	+	0.813054i	$0.302197\pi$
$200$	−0.809017	+	0.587785i	−0.0572061	+	0.0415627i
$201$	−5.21801	−	16.0594i	−0.368050	−	1.13274i
$202$	4.00278	−	12.3193i	0.281635	−	0.866782i
$203$	4.04459	+	2.93857i	0.283875	+	0.206247i
$204$	5.06318	+	3.67862i	0.354494	+	0.257555i
$205$	1.58530	−	4.87904i	0.110722	−	0.340767i
$206$	2.85536	+	8.78789i	0.198942	+	0.612281i
$207$	7.23903	−	5.25946i	0.503147	−	0.365558i
$208$	2.71483			0.188239
$209$	−7.74147	−	10.6756i	−0.535489	−	0.738445i
$210$	1.17142			0.0808358
$211$	3.87485	−	2.81524i	0.266756	−	0.193809i	−0.446364	−	0.894851i	$-0.647281\pi$
$211$	3.87485	−	2.81524i	0.266756	−	0.193809i	0.713120	+	0.701042i	$0.247281\pi$
$212$	1.40875	+	4.33568i	0.0967531	+	0.297775i
$213$	2.97126	−	9.14460i	0.203587	−	0.626578i
$214$	−8.09193	−	5.87913i	−0.553153	−	0.401889i
$215$	−9.92704	−	7.21242i	−0.677019	−	0.491883i
$216$	−1.67520	+	5.15574i	−0.113983	+	0.350804i
$217$	−0.886910	−	2.72963i	−0.0602074	−	0.185299i
$218$	0.432876	−	0.314503i	0.0293181	−	0.0213008i
$219$	17.0907			1.15489
$220$	1.95190	−	2.68144i	0.131597	−	0.180782i
$221$	−14.5042			−0.975661
$222$	−0.0384214	+	0.0279147i	−0.00257867	+	0.00187352i
$223$	−7.18426	−	22.1109i	−0.481094	−	1.48065i	−0.837560	−	0.546346i	$-0.816019\pi$
$223$	−7.18426	−	22.1109i	−0.481094	−	1.48065i	0.356466	−	0.934308i	$-0.383981\pi$
$224$	0.309017	−	0.951057i	0.0206471	−	0.0635451i
$225$	1.31690	+	0.956780i	0.0877930	+	0.0637854i
$226$	1.25573	+	0.912341i	0.0835299	+	0.0606880i
$227$	−5.26883	+	16.2158i	−0.349705	+	1.07628i	0.609312	+	0.792930i	$0.291446\pi$
$227$	−5.26883	+	16.2158i	−0.349705	+	1.07628i	−0.959017	+	0.283349i	$0.908554\pi$
$228$	1.43929	+	4.42966i	0.0953190	+	0.293362i
$229$	−8.49880	+	6.17474i	−0.561617	+	0.408038i	−0.832050	−	0.554700i	$-0.812833\pi$
$229$	−8.49880	+	6.17474i	−0.561617	+	0.408038i	0.270434	+	0.962739i	$0.412833\pi$
$230$	5.49704			0.362464
$231$	−3.69610	+	1.19723i	−0.243185	+	0.0787719i
$232$	−4.99939			−0.328226
$233$	−17.0492	+	12.3870i	−1.11693	+	0.811496i	−0.983741	−	0.179595i	$-0.942521\pi$
$233$	−17.0492	+	12.3870i	−1.11693	+	0.811496i	−0.133188	+	0.991091i	$0.542521\pi$
$234$	−1.36558	−	4.20283i	−0.0892710	−	0.274748i
$235$	3.05922	−	9.41530i	0.199561	−	0.614186i
$236$	0.473036	+	0.343681i	0.0307920	+	0.0223717i
$237$	−6.40022	−	4.65003i	−0.415739	−	0.302052i
$238$	−1.65095	+	5.08111i	−0.107015	+	0.329360i
$239$	0.376485	+	1.15870i	0.0243528	+	0.0749503i	0.962494	−	0.271302i	$-0.0874542\pi$
$239$	0.376485	+	1.15870i	0.0243528	+	0.0749503i	−0.938141	+	0.346252i	$0.887454\pi$
$240$	−0.947700	+	0.688544i	−0.0611738	+	0.0444453i
$241$	−1.70364			−0.109741			−0.0548706	−	0.998493i	$-0.517475\pi$
$241$	−1.70364			−0.109741			−0.0548706	+	0.998493i	$0.517475\pi$
$242$	−3.41816	+	10.4554i	−0.219728	+	0.672101i
$243$	14.5447			0.933042
$244$	−5.87316	+	4.26710i	−0.375991	+	0.273173i
$245$	0.309017	+	0.951057i	0.0197424	+	0.0607608i
$246$	1.85705	−	5.71541i	0.118401	−	0.364401i
$247$	−8.73276	−	6.34472i	−0.555652	−	0.403705i
$248$	2.32196	+	1.68700i	0.147445	+	0.107125i
$249$	−5.63958	+	17.3568i	−0.357394	+	1.09994i
$250$	0.309017	+	0.951057i	0.0195440	+	0.0601501i
$251$	15.5999	−	11.3340i	0.984656	−	0.715394i	0.0259115	−	0.999664i	$-0.491751\pi$
$251$	15.5999	−	11.3340i	0.984656	−	0.715394i	0.958744	+	0.284270i	$0.0917512\pi$
$252$	−1.62777			−0.102540
$253$	−17.3444	+	5.61815i	−1.09043	+	0.353210i
$254$	−17.2777			−1.08410
$255$	5.06318	−	3.67862i	0.317069	−	0.230364i
$256$	0.309017	+	0.951057i	0.0193136	+	0.0594410i
$257$	−3.08083	+	9.48182i	−0.192177	+	0.591460i	0.807821	+	0.589428i	$0.200647\pi$
$257$	−3.08083	+	9.48182i	−0.192177	+	0.591460i	−0.999998	+	0.00203201i	$0.999353\pi$
$258$	−11.6287	−	8.44878i	−0.723974	−	0.525998i
$259$	−0.0327989	−	0.0238298i	−0.00203803	−	0.00148071i
$260$	0.838928	−	2.58196i	0.0520281	−	0.160126i
$261$	2.51474	+	7.73958i	0.155659	+	0.479068i
$262$	−8.91378	+	6.47624i	−0.550695	+	0.400103i
$263$	15.3900			0.948985			0.474493	−	0.880260i	$-0.342632\pi$
$263$	15.3900			0.948985			0.474493	+	0.880260i	$0.342632\pi$
$264$	2.28649	−	3.14109i	0.140724	−	0.193321i
$265$	4.55880			0.280045
$266$	−3.21669	+	2.33706i	−0.197228	+	0.143294i
$267$	0.989707	+	3.04601i	0.0605691	+	0.186412i
$268$	−4.45443	+	13.7093i	−0.272098	+	0.837430i
$269$	13.4719	+	9.78787i	0.821393	+	0.596777i	0.917111	−	0.398631i	$-0.130515\pi$
$269$	13.4719	+	9.78787i	0.821393	+	0.596777i	−0.0957179	+	0.995409i	$0.530515\pi$
$270$	4.38574	+	3.18643i	0.266908	+	0.193920i
$271$	−0.882086	+	2.71478i	−0.0535829	+	0.164911i	−0.974267	−	0.225398i	$-0.927632\pi$
$271$	−0.882086	+	2.71478i	−0.0535829	+	0.164911i	0.920684	+	0.390309i	$0.127632\pi$
$272$	−1.65095	−	5.08111i	−0.100104	−	0.308088i
$273$	−2.57284	+	1.86928i	−0.155716	+	0.113134i
$274$	9.48971			0.573294
$275$	−1.94703	−	2.68497i	−0.117410	−	0.161910i
$276$	6.43935			0.387603
$277$	−20.2634	+	14.7222i	−1.21751	+	0.884572i	−0.995891	−	0.0905618i	$-0.971134\pi$
$277$	−20.2634	+	14.7222i	−1.21751	+	0.884572i	−0.221618	+	0.975134i	$0.571134\pi$
$278$	−3.35603	−	10.3288i	−0.201281	−	0.619480i
$279$	1.44369	−	4.44321i	0.0864313	−	0.266008i
$280$	−0.809017	−	0.587785i	−0.0483480	−	0.0351269i
$281$	−3.54208	−	2.57347i	−0.211303	−	0.153520i	0.477100	−	0.878849i	$-0.341688\pi$
$281$	−3.54208	−	2.57347i	−0.211303	−	0.153520i	−0.688403	+	0.725329i	$0.741688\pi$
$282$	3.58363	−	11.0293i	0.213402	−	0.656784i
$283$	−2.30590	−	7.09684i	−0.137072	−	0.421863i	0.858835	−	0.512253i	$-0.171189\pi$
$283$	−2.30590	−	7.09684i	−0.137072	−	0.421863i	−0.995907	+	0.0903894i	$0.971189\pi$
$284$	−6.64053	+	4.82463i	−0.394043	+	0.286289i
$285$	4.65762			0.275894
$286$	−0.00816937	+	9.00406i	−0.000483065	+	0.532421i
$287$	5.13012			0.302822
$288$	1.31690	−	0.956780i	0.0775988	−	0.0563788i
$289$	3.56710	+	10.9784i	0.209829	+	0.645788i
$290$	−1.54490	+	4.75471i	−0.0907195	+	0.279206i
$291$	1.25835	+	0.914248i	0.0737661	+	0.0535942i
$292$	−11.8034	−	8.57564i	−0.690739	−	0.501851i
$293$	1.80983	−	5.57007i	0.105731	−	0.325407i	−0.884170	−	0.467165i	$-0.845275\pi$
$293$	1.80983	−	5.57007i	0.105731	−	0.325407i	0.989901	+	0.141758i	$0.0452754\pi$
$294$	0.361989	+	1.11409i	0.0211116	+	0.0649749i
$295$	0.473036	−	0.343681i	0.0275412	−	0.0200099i
$296$	0.0405417			0.00235644
$297$	−17.0946	−	5.57153i	−0.991931	−	0.323293i
$298$	12.3315			0.714344
$299$	−12.0734	+	8.77183i	−0.698222	+	0.507288i
$300$	0.361989	+	1.11409i	0.0208995	+	0.0643219i
$301$	3.79179	−	11.6699i	0.218555	−	0.672644i
$302$	7.04459	+	5.11819i	0.405370	+	0.294519i
$303$	−12.2758	−	8.91890i	−0.705227	−	0.512377i
$304$	1.22867	−	3.78144i	0.0704688	−	0.216881i
$305$	2.24335	+	6.90432i	0.128454	+	0.395340i
$306$	−7.03564	+	5.11169i	−0.402201	+	0.292216i
$307$	34.7874			1.98542			0.992712	−	0.120513i	$-0.0384540\pi$
$307$	34.7874			1.98542			0.992712	+	0.120513i	$0.0384540\pi$
$308$	3.15337	+	1.02775i	0.179680	+	0.0585618i
$309$	10.8241			0.615761
$310$	2.32196	−	1.68700i	0.131878	−	0.0958153i
$311$	6.04992	+	18.6197i	0.343059	+	1.05583i	0.962615	+	0.270875i	$0.0873130\pi$
$311$	6.04992	+	18.6197i	0.343059	+	1.05583i	−0.619555	+	0.784953i	$0.712687\pi$
$312$	0.982738	−	3.02456i	0.0556366	−	0.171232i
$313$	10.0018	+	7.26677i	0.565338	+	0.410742i	0.833409	−	0.552657i	$-0.186386\pi$
$313$	10.0018	+	7.26677i	0.565338	+	0.410742i	−0.268071	+	0.963399i	$0.586386\pi$
$314$	15.4744	+	11.2428i	0.873273	+	0.634470i
$315$	−0.503009	+	1.54810i	−0.0283414	+	0.0872257i
$316$	2.08692	+	6.42288i	0.117399	+	0.361315i
$317$	−4.17097	+	3.03039i	−0.234265	+	0.170204i	−0.698724	−	0.715391i	$-0.746249\pi$
$317$	−4.17097	+	3.03039i	−0.234265	+	0.170204i	0.464459	+	0.885594i	$0.346249\pi$
$318$	5.34028			0.299468
$319$	0.0150440	−	16.5811i	0.000842303	−	0.928364i
$320$	1.00000			0.0559017
$321$	−9.47906	+	6.88694i	−0.529069	+	0.384391i
$322$	1.69868	+	5.22800i	0.0946637	+	0.291345i
$323$	−6.56427	+	20.2027i	−0.365246	+	1.12411i
$324$	1.18686	+	0.862306i	0.0659368	+	0.0479059i
$325$	−2.19634	−	1.59574i	−0.121831	−	0.0885155i
$326$	−5.75526	+	17.7129i	−0.318755	+	0.981026i
$327$	−0.193687	−	0.596108i	−0.0107109	−	0.0329649i
$328$	−4.15036	+	3.01541i	−0.229165	+	0.166498i
$329$	9.89983			0.545795
$330$	−2.28079	−	3.14524i	−0.125553	−	0.173140i
$331$	−32.5061			−1.78670			−0.893349	−	0.449364i	$-0.851651\pi$
$331$	−32.5061			−1.78670			−0.893349	+	0.449364i	$0.851651\pi$
$332$	12.6040	−	9.15735i	0.691735	−	0.502575i
$333$	−0.0203928	−	0.0627627i	−0.00111752	−	0.00343938i
$334$	0.513248	−	1.57962i	0.0280837	−	0.0864327i
$335$	11.6618	+	8.47283i	0.637155	+	0.462920i
$336$	−0.947700	−	0.688544i	−0.0517013	−	0.0375632i
$337$	−8.38292	+	25.8000i	−0.456647	+	1.40541i	0.412544	+	0.910938i	$0.364640\pi$
$337$	−8.38292	+	25.8000i	−0.456647	+	1.40541i	−0.869191	+	0.494477i	$0.835360\pi$
$338$	−1.73968	−	5.35417i	−0.0946259	−	0.291228i
$339$	1.47099	−	1.06874i	0.0798932	−	0.0580458i
$340$	−5.34260			−0.289743
$341$	−5.60214	+	7.69599i	−0.303373	+	0.416761i
$342$	−6.47209			−0.349971
$343$	−0.809017	+	0.587785i	−0.0436828	+	0.0317374i
$344$	3.79179	+	11.6699i	0.204440	+	0.629201i
$345$	1.98987	−	6.12419i	0.107131	−	0.329715i
$346$	8.41822	+	6.11619i	0.452566	+	0.328809i
$347$	−9.05767	−	6.58078i	−0.486241	−	0.353275i	0.317496	−	0.948260i	$-0.397158\pi$
$347$	−9.05767	−	6.58078i	−0.486241	−	0.353275i	−0.803737	+	0.594985i	$0.797158\pi$
$348$	−1.80973	+	5.56976i	−0.0970115	+	0.298571i
$349$	−8.83296	−	27.1851i	−0.472817	−	1.45518i	−0.848879	−	0.528588i	$-0.822722\pi$
$349$	−8.83296	−	27.1851i	−0.472817	−	1.45518i	0.376061	−	0.926595i	$-0.377278\pi$
$350$	−0.809017	+	0.587785i	−0.0432438	+	0.0314184i
$351$	−14.7173			−0.785550
$352$	−3.15523	+	1.02203i	−0.168174	+	0.0544744i
$353$	4.00343			0.213081			0.106541	−	0.994308i	$-0.466023\pi$
$353$	4.00343			0.213081			0.106541	+	0.994308i	$0.466023\pi$
$354$	0.554124	−	0.402595i	0.0294514	−	0.0213977i
$355$	2.53646	+	7.80642i	0.134621	+	0.414322i
$356$	0.844877	−	2.60026i	0.0447784	−	0.137814i
$357$	5.06318	+	3.67862i	0.267972	+	0.194693i
$358$	20.5665	+	14.9424i	1.08697	+	0.789731i
$359$	−3.02119	+	9.29826i	−0.159452	+	0.490743i	−0.998585	−	0.0531837i	$-0.983063\pi$
$359$	−3.02119	+	9.29826i	−0.159452	+	0.490743i	0.839133	+	0.543927i	$0.183063\pi$
$360$	−0.503009	−	1.54810i	−0.0265109	−	0.0815922i
$361$	2.58163	−	1.87566i	0.135875	−	0.0987190i
$362$	−9.34641			−0.491237
$363$	10.4109	+	7.59289i	0.546432	+	0.398523i
$364$	2.71483			0.142296
$365$	−11.8034	+	8.57564i	−0.617816	+	0.448870i
$366$	2.62791	+	8.08787i	0.137363	+	0.422760i
$367$	−4.05434	+	12.4780i	−0.211635	+	0.651345i	0.787741	+	0.616007i	$0.211251\pi$
$367$	−4.05434	+	12.4780i	−0.211635	+	0.651345i	−0.999375	+	0.0353378i	$0.988749\pi$
$368$	−4.44720	−	3.23108i	−0.231826	−	0.168432i
$369$	6.75583	+	4.90840i	0.351695	+	0.255521i
$370$	0.0125281	−	0.0385574i	0.000651303	−	0.00200451i
$371$	1.40875	+	4.33568i	0.0731385	+	0.225097i
$372$	2.71999	−	1.97619i	0.141025	−	0.102461i
$373$	−15.2552			−0.789886			−0.394943	−	0.918706i	$-0.629236\pi$
$373$	−15.2552			−0.789886			−0.394943	+	0.918706i	$0.629236\pi$
$374$	16.8571	−	5.46030i	0.871661	−	0.282346i
$375$	1.17142			0.0604919
$376$	−8.00913	+	5.81897i	−0.413039	+	0.300091i
$377$	−4.19413	−	12.9082i	−0.216009	−	0.664807i
$378$	−1.67520	+	5.15574i	−0.0861631	+	0.265183i
$379$	−21.5503	−	15.6572i	−1.10696	−	0.804256i	−0.124781	−	0.992184i	$-0.539823\pi$
$379$	−21.5503	−	15.6572i	−1.10696	−	0.804256i	−0.982183	+	0.187928i	$0.939823\pi$
$380$	−3.21669	−	2.33706i	−0.165013	−	0.119889i
$381$	−6.25435	+	19.2489i	−0.320420	+	0.986151i
$382$	1.40884	+	4.33598i	0.0720828	+	0.221848i
$383$	−5.51748	+	4.00869i	−0.281930	+	0.204834i	−0.719759	−	0.694224i	$-0.755748\pi$
$383$	−5.51748	+	4.00869i	−0.281930	+	0.204834i	0.437829	+	0.899058i	$0.355748\pi$
$384$	1.17142			0.0597788
$385$	1.95190	−	2.68144i	0.0994779	−	0.136659i
$386$	15.8146			0.804944
$387$	16.1590	−	11.7402i	0.821406	−	0.596786i
$388$	−0.410312	−	1.26281i	−0.0208305	−	0.0641096i
$389$	7.13231	−	21.9510i	0.361622	−	1.11296i	−0.590447	−	0.807077i	$-0.701048\pi$
$389$	7.13231	−	21.9510i	0.361622	−	1.11296i	0.952069	−	0.305883i	$-0.0989515\pi$
$390$	−2.57284	−	1.86928i	−0.130281	−	0.0946546i
$391$	23.7596	+	17.2624i	1.20158	+	0.872996i
$392$	0.309017	−	0.951057i	0.0156077	−	0.0480356i
$393$	3.98841	+	12.2751i	0.201189	+	0.619195i
$394$	−11.8247	+	8.59116i	−0.595721	+	0.432816i
$395$	6.75342			0.339801
$396$	3.16932	+	4.37052i	0.159264	+	0.219627i
$397$	−15.6435			−0.785123			−0.392561	−	0.919726i	$-0.628411\pi$
$397$	−15.6435			−0.785123			−0.392561	+	0.919726i	$0.628411\pi$
$398$	−13.2885	+	9.65469i	−0.666095	+	0.483946i
$399$	1.43929	+	4.42966i	0.0720544	+	0.221761i
$400$	0.309017	−	0.951057i	0.0154508	−	0.0475528i
$401$	1.22460	+	0.889724i	0.0611536	+	0.0444307i	0.617942	−	0.786224i	$-0.287967\pi$
$401$	1.22460	+	0.889724i	0.0611536	+	0.0444307i	−0.556788	+	0.830654i	$0.687967\pi$
$402$	13.6609	+	9.92525i	0.681346	+	0.495027i
$403$	−2.40781	+	7.41047i	−0.119941	+	0.369142i
$404$	4.00278	+	12.3193i	0.199146	+	0.612908i
$405$	1.18686	−	0.862306i	0.0589757	−	0.0428483i
$406$	−4.99939			−0.248116
$407$	−0.000121997		0.134462i	−6.04716e−6		0.00666501i
$408$	−6.25844			−0.309839
$409$	11.4969	−	8.35302i	0.568487	−	0.413030i	−0.266068	−	0.963954i	$-0.585725\pi$
$409$	11.4969	−	8.35302i	0.568487	−	0.413030i	0.834555	+	0.550924i	$0.185725\pi$
$410$	1.58530	+	4.87904i	0.0782922	+	0.240958i
$411$	3.43517	−	10.5724i	0.169444	−	0.521496i
$412$	−7.47543	−	5.43122i	−0.368288	−	0.267577i
$413$	0.473036	+	0.343681i	0.0232766	+	0.0169114i
$414$	−2.76506	+	8.50999i	−0.135895	+	0.418243i
$415$	−4.81430	−	14.8169i	−0.236325	−	0.727333i
$416$	−2.19634	+	1.59574i	−0.107685	+	0.0782374i
$417$	−12.7220			−0.623001
$418$	12.5379	+	4.08640i	0.613250	+	0.199872i
$419$	6.61451			0.323140			0.161570	−	0.986861i	$-0.448344\pi$
$419$	6.61451			0.323140			0.161570	+	0.986861i	$0.448344\pi$
$420$	−0.947700	+	0.688544i	−0.0462430	+	0.0335975i
$421$	−11.8327	−	36.4172i	−0.576688	−	1.77486i	−0.630357	−	0.776305i	$-0.717092\pi$
$421$	−11.8327	−	36.4172i	−0.576688	−	1.77486i	0.0536688	−	0.998559i	$-0.482908\pi$
$422$	−1.48006	+	4.55516i	−0.0720483	+	0.221742i
$423$	13.0370	+	9.47196i	0.633883	+	0.460543i
$424$	−3.68815	−	2.67960i	−0.179112	−	0.130133i
$425$	−1.65095	+	5.08111i	−0.0800830	+	0.246470i
$426$	2.97126	+	9.14460i	0.143958	+	0.443057i
$427$	−5.87316	+	4.26710i	−0.284222	+	0.206500i
$428$	10.0022			0.483473
$429$	10.0284	+	3.26847i	0.484174	+	0.157803i
$430$	12.2705			0.591736
$431$	−5.44568	+	3.95652i	−0.262309	+	0.190579i	−0.711164	−	0.703026i	$-0.751832\pi$
$431$	−5.44568	+	3.95652i	−0.262309	+	0.190579i	0.448855	+	0.893604i	$0.351832\pi$
$432$	−1.67520	−	5.15574i	−0.0805982	−	0.248056i
$433$	−7.96334	+	24.5086i	−0.382694	+	1.17781i	0.555446	+	0.831553i	$0.312548\pi$
$433$	−7.96334	+	24.5086i	−0.382694	+	1.17781i	−0.938139	+	0.346258i	$0.887452\pi$
$434$	2.32196	+	1.68700i	0.111458	+	0.0809787i
$435$	4.73792	+	3.44230i	0.227166	+	0.165046i
$436$	−0.165344	+	0.508876i	−0.00791854	+	0.0243707i
$437$	6.75403	+	20.7868i	0.323089	+	0.994365i
$438$	−13.8267	+	10.0457i	−0.660665	+	0.480002i
$439$	13.8131			0.659262			0.329631	−	0.944110i	$-0.393076\pi$
$439$	13.8131			0.659262			0.329631	+	0.944110i	$0.393076\pi$
$440$	−0.00300917	+	3.31662i	−0.000143456	+	0.158114i
$441$	−1.62777			−0.0775129
$442$	11.7342	−	8.52538i	0.558138	−	0.405511i
$443$	−8.68975	−	26.7443i	−0.412862	−	1.27066i	−0.914149	−	0.405378i	$-0.867140\pi$
$443$	−8.68975	−	26.7443i	−0.412862	−	1.27066i	0.501287	−	0.865281i	$-0.332860\pi$
$444$	0.0146757	−	0.0451670i	0.000696476	−	0.00214353i
$445$	−2.21192	−	1.60705i	−0.104855	−	0.0761816i
$446$	18.8086	+	13.6653i	0.890615	+	0.647069i
$447$	4.46387	−	13.7384i	0.211134	−	0.649803i
$448$	0.309017	+	0.951057i	0.0145997	+	0.0449332i
$449$	−22.5373	+	16.3743i	−1.06360	+	0.772751i	−0.974751	−	0.223294i	$-0.928319\pi$
$449$	−22.5373	+	16.3743i	−1.06360	+	0.772751i	−0.0888496	+	0.996045i	$0.528319\pi$
$450$	−1.62777			−0.0767339
$451$	−9.98849	−	13.7742i	−0.470340	−	0.648604i
$452$	−1.55217			−0.0730078
$453$	8.25218	−	5.99556i	0.387721	−	0.281696i
$454$	−5.26883	−	16.2158i	−0.247278	−	0.761045i
$455$	0.838928	−	2.58196i	0.0393296	−	0.121044i
$456$	−3.76810	−	2.73768i	−0.176457	−	0.128204i
$457$	30.8105	+	22.3852i	1.44126	+	1.04713i	0.987778	+	0.155865i	$0.0498165\pi$
$457$	30.8105	+	22.3852i	1.44126	+	1.04713i	0.453477	+	0.891268i	$0.350183\pi$
$458$	3.24625	−	9.99094i	0.151687	−	0.466846i
$459$	8.94994	+	27.5451i	0.417747	+	1.28569i
$460$	−4.44720	+	3.23108i	−0.207352	+	0.150650i
$461$	13.9251			0.648556			0.324278	−	0.945962i	$-0.394879\pi$
$461$	13.9251			0.648556			0.324278	+	0.945962i	$0.394879\pi$
$462$	2.28649	−	3.14109i	0.106377	−	0.146137i
$463$	−2.93872			−0.136574			−0.0682870	−	0.997666i	$-0.521753\pi$
$463$	−2.93872			−0.136574			−0.0682870	+	0.997666i	$0.521753\pi$
$464$	4.04459	−	2.93857i	0.187766	−	0.136420i
$465$	−1.03895	−	3.19754i	−0.0481799	−	0.148283i
$466$	6.51221	−	20.0425i	0.301672	−	0.928451i
$467$	25.7344	+	18.6972i	1.19085	+	0.865202i	0.993354	−	0.115102i	$-0.0367196\pi$
$467$	25.7344	+	18.6972i	1.19085	+	0.865202i	0.197494	+	0.980304i	$0.436720\pi$
$468$	3.57514	+	2.59749i	0.165261	+	0.120069i
$469$	−4.45443	+	13.7093i	−0.205686	+	0.633038i
$470$	3.05922	+	9.41530i	0.141111	+	0.434295i
$471$	18.1271	−	13.1701i	0.835252	−	0.606846i
$472$	−0.584705			−0.0269132
$473$	−38.7162	+	12.5408i	−1.78017	+	0.576628i
$474$	7.91110			0.363369
$475$	−3.21669	+	2.33706i	−0.147592	+	0.107232i
$476$	−1.65095	−	5.08111i	−0.0756714	−	0.232893i
$477$	−2.29312	+	7.05749i	−0.104995	+	0.323140i
$478$	−0.985652	−	0.716118i	−0.0450827	−	0.0327545i
$479$	−30.5586	−	22.2021i	−1.39626	−	1.01444i	−0.995146	−	0.0984135i	$-0.968623\pi$
$479$	−30.5586	−	22.2021i	−1.39626	−	1.01444i	−0.401114	−	0.916028i	$-0.631377\pi$
$480$	0.361989	−	1.11409i	0.0165225	−	0.0508509i
$481$	0.0340116	+	0.104677i	0.00155079	+	0.00477285i
$482$	1.37828	−	1.00138i	0.0627787	−	0.0456114i
$483$	6.43935			0.293001
$484$	−3.38020	−	10.4678i	−0.153645	−	0.475808i
$485$	−1.32780			−0.0602922
$486$	−11.7669	+	8.54915i	−0.533757	+	0.387797i
$487$	−2.94538	−	9.06495i	−0.133468	−	0.410772i	0.861881	−	0.507111i	$-0.169287\pi$
$487$	−2.94538	−	9.06495i	−0.133468	−	0.410772i	−0.995349	+	0.0963390i	$0.969287\pi$
$488$	2.24335	−	6.90432i	0.101552	−	0.312544i
$489$	17.6504	+	12.8237i	0.798177	+	0.579910i
$490$	−0.809017	−	0.587785i	−0.0365477	−	0.0265534i
$491$	−6.86614	+	21.1318i	−0.309864	+	0.953665i	0.667953	+	0.744204i	$0.267171\pi$
$491$	−6.86614	+	21.1318i	−0.309864	+	0.953665i	−0.977817	+	0.209461i	$0.932829\pi$
$492$	1.85705	+	5.71541i	0.0837222	+	0.257671i
$493$	−21.6087	+	15.6996i	−0.973205	+	0.707075i
$494$	10.7943			0.485658
$495$	5.13599	−	1.66363i	0.230846	−	0.0747748i
$496$	−2.87010			−0.128871
$497$	−6.64053	+	4.82463i	−0.297869	+	0.216414i
$498$	−5.63958	−	17.3568i	−0.252715	−	0.777778i
$499$	−3.34869	+	10.3062i	−0.149908	+	0.461369i	−0.997609	−	0.0691046i	$-0.977986\pi$
$499$	−3.34869	+	10.3062i	−0.149908	+	0.461369i	0.847702	+	0.530473i	$0.177986\pi$
$500$	−0.809017	−	0.587785i	−0.0361803	−	0.0262866i
$501$	−1.57404	−	1.14361i	−0.0703229	−	0.0510926i
$502$	−5.95862	+	18.3388i	−0.265946	+	0.818499i
$503$	−3.78527	−	11.6499i	−0.168777	−	0.519442i	0.830518	−	0.556992i	$-0.188045\pi$
$503$	−3.78527	−	11.6499i	−0.168777	−	0.519442i	−0.999295	+	0.0375503i	$0.988045\pi$
$504$	1.31690	−	0.956780i	0.0586592	−	0.0426184i
$505$	12.9533			0.576413
$506$	10.7297	−	14.7400i	0.476992	−	0.655271i
$507$	−6.59476			−0.292884
$508$	13.9780	−	10.1556i	0.620172	−	0.450581i
$509$	−0.0911819	−	0.280629i	−0.00404157	−	0.0124387i	0.949015	−	0.315230i	$-0.102082\pi$
$509$	−0.0911819	−	0.280629i	−0.00404157	−	0.0124387i	−0.953057	+	0.302791i	$0.902082\pi$
$510$	−1.93396	+	5.95213i	−0.0856373	+	0.263565i
$511$	−11.8034	−	8.57564i	−0.522150	−	0.379364i
$512$	−0.809017	−	0.587785i	−0.0357538	−	0.0259767i
$513$	−6.66068	+	20.4995i	−0.294076	+	0.905074i
$514$	−3.08083	−	9.48182i	−0.135890	−	0.418225i
$515$	−7.47543	+	5.43122i	−0.329407	+	0.239328i
$516$	14.3739			0.632777
$517$	−19.2752	−	26.5808i	−0.847724	−	1.16902i
$518$	0.0405417			0.00178130
$519$	9.86128	−	7.16464i	0.432862	−	0.314493i
$520$	0.838928	+	2.58196i	0.0367894	+	0.113226i
$521$	8.51950	−	26.2203i	0.373246	−	1.14873i	−0.571408	−	0.820666i	$-0.693603\pi$
$521$	8.51950	−	26.2203i	0.373246	−	1.14873i	0.944654	−	0.328067i	$-0.106397\pi$
$522$	−6.58368	−	4.78332i	−0.288160	−	0.209360i
$523$	−19.6182	−	14.2535i	−0.857845	−	0.623261i	0.0694527	−	0.997585i	$-0.477875\pi$
$523$	−19.6182	−	14.2535i	−0.857845	−	0.623261i	−0.927298	+	0.374324i	$0.877875\pi$
$524$	3.40476	−	10.4788i	0.148738	−	0.457768i
$525$	0.361989	+	1.11409i	0.0157985	+	0.0486228i
$526$	−12.4507	+	9.04599i	−0.542878	+	0.394424i
$527$	15.3338			0.667951
$528$	−0.00352500	+	3.88516i	−0.000153406	+	0.169080i
$529$	7.21747			0.313803
$530$	−3.68815	+	2.67960i	−0.160203	+	0.116394i
$531$	0.294112	+	0.905183i	0.0127634	+	0.0392816i
$532$	1.22867	−	3.78144i	0.0532694	−	0.163946i
$533$	−11.2675	−	8.18632i	−0.488050	−	0.354589i
$534$	−2.59109	−	1.88253i	−0.112127	−	0.0814652i
$535$	3.09084	−	9.51263i	0.133629	−	0.411267i
$536$	−4.45443	−	13.7093i	−0.192402	−	0.592152i
$537$	24.0920	−	17.5039i	1.03965	−	0.755347i
$538$	−16.6521			−0.717924
$539$	3.15337	+	1.02775i	0.135825	+	0.0442685i
$540$	−5.42107			−0.233286
$541$	−15.8876	+	11.5430i	−0.683062	+	0.496273i	−0.874372	−	0.485256i	$-0.838726\pi$
$541$	−15.8876	+	11.5430i	−0.683062	+	0.496273i	0.191310	+	0.981530i	$0.438726\pi$
$542$	−0.882086	−	2.71478i	−0.0378888	−	0.116610i
$543$	−3.38330	+	10.4127i	−0.145191	+	0.446853i
$544$	4.32225	+	3.14030i	0.185315	+	0.134639i
$545$	0.432876	+	0.314503i	0.0185424	+	0.0134718i
$546$	0.982738	−	3.02456i	0.0420573	−	0.129439i
$547$	−0.155163	−	0.477544i	−0.00663431	−	0.0204183i	0.947685	−	0.319208i	$-0.103417\pi$
$547$	−0.155163	−	0.477544i	−0.00663431	−	0.0204183i	−0.954319	+	0.298790i	$0.903417\pi$
$548$	−7.67733	+	5.57791i	−0.327959	+	0.238276i
$549$	−11.8170			−0.504338
$550$	3.15337	+	1.02775i	0.134460	+	0.0438236i
$551$	−19.8778			−0.846823
$552$	−5.20955	+	3.78496i	−0.221733	+	0.161098i
$553$	2.08692	+	6.42288i	0.0887449	+	0.273129i
$554$	7.73992	−	23.8210i	0.328838	−	1.01206i
$555$	−0.0384214	−	0.0279147i	−0.00163090	−	0.00118492i
$556$	8.78620	+	6.38355i	0.372618	+	0.270723i
$557$	0.775313	−	2.38617i	0.0328511	−	0.101105i	−0.933286	−	0.359133i	$-0.883073\pi$
$557$	0.775313	−	2.38617i	0.0328511	−	0.101105i	0.966138	+	0.258028i	$0.0830725\pi$
$558$	1.44369	+	4.44321i	0.0611161	+	0.188096i
$559$	−26.9502	+	19.5805i	−1.13987	+	0.828166i
$560$	1.00000			0.0422577
$561$	0.0188327	−	20.7569i	0.000795117	−	0.876356i
$562$	4.37825			0.184685
$563$	14.0532	−	10.2102i	0.592270	−	0.430309i	−0.250857	−	0.968024i	$-0.580712\pi$
$563$	14.0532	−	10.2102i	0.592270	−	0.430309i	0.843127	+	0.537715i	$0.180712\pi$
$564$	3.58363	+	11.0293i	0.150898	+	0.464417i
$565$	−0.479646	+	1.47620i	−0.0201789	+	0.0621042i
$566$	6.03693	+	4.38609i	0.253751	+	0.184361i
$567$	1.18686	+	0.862306i	0.0498436	+	0.0362135i
$568$	2.53646	−	7.80642i	0.106427	−	0.327550i
$569$	−9.81476	−	30.2067i	−0.411456	−	1.26633i	−0.915382	−	0.402585i	$-0.868112\pi$
$569$	−9.81476	−	30.2067i	−0.411456	−	1.26633i	0.503926	−	0.863747i	$-0.331888\pi$
$570$	−3.76810	+	2.73768i	−0.157828	+	0.114669i
$571$	7.43290			0.311057			0.155529	−	0.987831i	$-0.450292\pi$
$571$	7.43290			0.311057			0.155529	+	0.987831i	$0.450292\pi$
$572$	−5.28585	−	7.28924i	−0.221012	−	0.304779i
$573$	5.34065			0.223109
$574$	−4.15036	+	3.01541i	−0.173233	+	0.125861i
$575$	1.69868	+	5.22800i	0.0708398	+	0.218023i
$576$	−0.503009	+	1.54810i	−0.0209587	+	0.0645043i
$577$	14.9136	+	10.8354i	0.620861	+	0.451082i	0.853222	−	0.521548i	$-0.174645\pi$
$577$	14.9136	+	10.8354i	0.620861	+	0.451082i	−0.232361	+	0.972630i	$0.574645\pi$
$578$	−9.33879	−	6.78503i	−0.388442	−	0.282220i
$579$	5.72473	−	17.6189i	0.237912	−	0.732216i
$580$	−1.54490	−	4.75471i	−0.0641484	−	0.197428i
$581$	12.6040	−	9.15735i	0.522902	−	0.379911i
$582$	−1.55541			−0.0644739
$583$	8.89831	−	12.2241i	0.368530	−	0.506272i
$584$	14.5897			0.603728
$585$	3.57514	−	2.59749i	0.147814	−	0.107393i
$586$	1.80983	+	5.57007i	0.0747632	+	0.230098i
$587$	3.14010	−	9.66423i	0.129606	−	0.398886i	−0.865106	−	0.501589i	$-0.832749\pi$
$587$	3.14010	−	9.66423i	0.129606	−	0.398886i	0.994712	+	0.102703i	$0.0327491\pi$
$588$	−0.947700	−	0.688544i	−0.0390825	−	0.0283951i
$589$	9.23222	+	6.70760i	0.380407	+	0.276382i
$590$	−0.180684	+	0.556087i	−0.00743863	+	0.0228937i
$591$	5.29089	+	16.2837i	0.217638	+	0.669821i
$592$	−0.0327989	+	0.0238298i	−0.00134803	+	0.000979399i
$593$	−22.2216			−0.912532			−0.456266	−	0.889844i	$-0.650813\pi$
$593$	−22.2216			−0.912532			−0.456266	+	0.889844i	$0.650813\pi$
$594$	17.1047	−	5.54050i	0.701815	−	0.227330i
$595$	−5.34260			−0.219025
$596$	−9.97639	+	7.24827i	−0.408649	+	0.296901i
$597$	5.94587	+	18.2995i	0.243348	+	0.748949i
$598$	4.61162	−	14.1931i	0.188583	−	0.580400i
$599$	−7.64755	−	5.55627i	−0.312471	−	0.227023i	0.420485	−	0.907299i	$-0.361860\pi$
$599$	−7.64755	−	5.55627i	−0.312471	−	0.227023i	−0.732956	+	0.680276i	$0.761860\pi$
$600$	−0.947700	−	0.688544i	−0.0386897	−	0.0281097i
$601$	8.31376	−	25.5871i	0.339125	−	1.04372i	−0.625529	−	0.780201i	$-0.715117\pi$
$601$	8.31376	−	25.5871i	0.339125	−	1.04372i	0.964654	−	0.263519i	$-0.0848833\pi$
$602$	3.79179	+	11.6699i	0.154542	+	0.475631i
$603$	−18.9828	+	13.7918i	−0.773040	+	0.561647i
$604$	−8.70759			−0.354307
$605$	−11.0000	−	0.0199606i	−0.447213	−	0.000811512i
$606$	15.1737			0.616391
$607$	13.8774	−	10.0825i	0.563267	−	0.409238i	−0.269386	−	0.963032i	$-0.586821\pi$
$607$	13.8774	−	10.0825i	0.563267	−	0.409238i	0.832653	+	0.553795i	$0.186821\pi$
$608$	1.22867	+	3.78144i	0.0498290	+	0.153358i
$609$	−1.80973	+	5.56976i	−0.0733338	+	0.225698i
$610$	−5.87316	−	4.26710i	−0.237797	−	0.172770i
$611$	−21.7434	−	15.7975i	−0.879645	−	0.639099i
$612$	2.68738	−	8.27090i	0.108631	−	0.334331i
$613$	11.6339	+	35.8053i	0.469887	+	1.44616i	0.852731	+	0.522350i	$0.174945\pi$
$613$	11.6339	+	35.8053i	0.469887	+	1.44616i	−0.382844	+	0.923813i	$0.625055\pi$
$614$	−28.1436	+	20.4475i	−1.13578	+	0.825195i
$615$	6.00954			0.242328
$616$	−3.15523	+	1.02203i	−0.127128	+	0.0411788i
$617$	22.0199			0.886488			0.443244	−	0.896401i	$-0.353828\pi$
$617$	22.0199			0.886488			0.443244	+	0.896401i	$0.353828\pi$
$618$	−8.75688	+	6.36224i	−0.352253	+	0.255927i
$619$	9.38673	+	28.8894i	0.377285	+	1.16116i	0.941924	+	0.335825i	$0.109015\pi$
$619$	9.38673	+	28.8894i	0.377285	+	1.16116i	−0.564640	+	0.825338i	$0.690985\pi$
$620$	−0.886910	+	2.72963i	−0.0356192	+	0.109625i
$621$	24.1086	+	17.5159i	0.967444	+	0.702889i
$622$	−15.8389	−	11.5076i	−0.635081	−	0.461414i
$623$	0.844877	−	2.60026i	0.0338493	−	0.104177i
$624$	0.982738	+	3.02456i	0.0393410	+	0.121079i
$625$	−0.809017	+	0.587785i	−0.0323607	+	0.0235114i
$626$	−12.3630			−0.494123
$627$	9.09120	−	12.4891i	0.363068	−	0.498767i
$628$	−19.1275			−0.763269
$629$	0.175231	−	0.127313i	0.00698694	−	0.00507631i
$630$	−0.503009	−	1.54810i	−0.0200404	−	0.0616779i
$631$	14.4945	−	44.6095i	0.577017	−	1.77588i	−0.0521877	−	0.998637i	$-0.516619\pi$
$631$	14.4945	−	44.6095i	0.577017	−	1.77588i	0.629205	−	0.777239i	$-0.283381\pi$
$632$	−5.46363	−	3.96956i	−0.217332	−	0.157901i
$633$	4.53908	+	3.29784i	0.180412	+	0.131077i
$634$	1.59317	−	4.90327i	0.0632728	−	0.194734i
$635$	−5.33911	−	16.4321i	−0.211876	−	0.652087i
$636$	−4.32037	+	3.13894i	−0.171314	+	0.124467i
$637$	2.71483			0.107565
$638$	9.73396	+	13.4232i	0.385371	+	0.531431i
$639$	−13.3610			−0.528553
$640$	−0.809017	+	0.587785i	−0.0319792	+	0.0232343i
$641$	−7.76410	−	23.8955i	−0.306664	−	0.943814i	−0.979051	−	0.203614i	$-0.934731\pi$
$641$	−7.76410	−	23.8955i	−0.306664	−	0.943814i	0.672387	−	0.740199i	$-0.265269\pi$
$642$	3.62068	−	11.1433i	0.142897	−	0.439791i
$643$	20.1373	+	14.6306i	0.794138	+	0.576975i	0.909189	−	0.416385i	$-0.136703\pi$
$643$	20.1373	+	14.6306i	0.794138	+	0.576975i	−0.115051	+	0.993360i	$0.536703\pi$
$644$	−4.44720	−	3.23108i	−0.175244	−	0.127322i
$645$	4.44179	−	13.6704i	0.174895	−	0.538272i
$646$	−6.56427	−	20.2027i	−0.258268	−	0.794866i
$647$	−32.9273	+	23.9231i	−1.29451	+	0.940514i	−0.999886	−	0.0150997i	$-0.995193\pi$
$647$	−32.9273	+	23.9231i	−1.29451	+	0.940514i	−0.294621	+	0.955614i	$0.595193\pi$
$648$	−1.46704			−0.0576309
$649$	0.00175947	−	1.93924i	6.90654e−5	−	0.0761220i
$650$	2.71483			0.106484
$651$	2.71999	−	1.97619i	0.106605	−	0.0774530i
$652$	−5.75526	−	17.7129i	−0.225394	−	0.693690i
$653$	−4.11216	+	12.6559i	−0.160921	+	0.495265i	−0.998713	−	0.0507259i	$-0.983847\pi$
$653$	−4.11216	+	12.6559i	−0.160921	+	0.495265i	0.837791	+	0.545990i	$0.183847\pi$
$654$	0.507080	+	0.368415i	0.0198284	+	0.0144062i
$655$	−8.91378	−	6.47624i	−0.348290	−	0.253048i
$656$	1.58530	−	4.87904i	0.0618954	−	0.190494i
$657$	−7.33878	−	22.5864i	−0.286313	−	0.881181i
$658$	−8.00913	+	5.81897i	−0.312228	+	0.226847i
$659$	−17.1669			−0.668726			−0.334363	−	0.942444i	$-0.608521\pi$
$659$	−17.1669			−0.668726			−0.334363	+	0.942444i	$0.608521\pi$
$660$	3.69392	+	1.20393i	0.143786	+	0.0468631i
$661$	1.82979			0.0711705			0.0355853	−	0.999367i	$-0.488670\pi$
$661$	1.82979			0.0711705			0.0355853	+	0.999367i	$0.488670\pi$
$662$	26.2980	−	19.1066i	1.02210	−	0.742600i
$663$	−5.25038	−	16.1590i	−0.203908	−	0.627564i
$664$	−4.81430	+	14.8169i	−0.186831	+	0.575007i
$665$	−3.21669	−	2.33706i	−0.124738	−	0.0906273i
$666$	0.0533892	+	0.0387895i	0.00206879	+	0.00150306i
$667$	−8.49237	+	26.1368i	−0.328826	+	1.01202i
$668$	0.513248	+	1.57962i	0.0198582	+	0.0611172i
$669$	22.0328	−	16.0078i	0.851839	−	0.618897i
$670$	−14.4148			−0.556894
$671$	22.8923	+	7.46112i	0.883746	+	0.288033i
$672$	1.17142			0.0451886
$673$	16.0640	−	11.6712i	0.619224	−	0.449892i	−0.233427	−	0.972374i	$-0.574994\pi$
$673$	16.0640	−	11.6712i	0.619224	−	0.449892i	0.852650	+	0.522482i	$0.174994\pi$
$674$	−8.38292	−	25.8000i	−0.322898	−	0.993778i
$675$	−1.67520	+	5.15574i	−0.0644786	+	0.198445i
$676$	4.55453	+	3.30906i	0.175174	+	0.127271i
$677$	20.0782	+	14.5877i	0.771669	+	0.560650i	0.902467	−	0.430759i	$-0.141754\pi$
$677$	20.0782	+	14.5877i	0.771669	+	0.560650i	−0.130798	+	0.991409i	$0.541754\pi$
$678$	−0.561868	+	1.72925i	−0.0215784	+	0.0664115i
$679$	−0.410312	−	1.26281i	−0.0157463	−	0.0484623i
$680$	4.32225	−	3.14030i	0.165751	−	0.120425i
$681$	−19.9731			−0.765370
$682$	0.00863662	−	9.51904i	0.000330713	−	0.364503i
$683$	7.25911			0.277762			0.138881	−	0.990309i	$-0.455649\pi$
$683$	7.25911			0.277762			0.138881	+	0.990309i	$0.455649\pi$
$684$	5.23603	−	3.80420i	0.200205	−	0.145457i
$685$	2.93248	+	9.02525i	0.112044	+	0.344837i
$686$	0.309017	−	0.951057i	0.0117983	−	0.0363115i
$687$	−9.95568	−	7.23322i	−0.379833	−	0.275965i
$688$	−9.92704	−	7.21242i	−0.378465	−	0.274971i
$689$	3.82451	−	11.7706i	0.145702	−	0.448425i
$690$	1.98987	+	6.12419i	0.0757530	+	0.233144i
$691$	16.1945	−	11.7660i	0.616066	−	0.447598i	−0.235479	−	0.971879i	$-0.575666\pi$
$691$	16.1945	−	11.7660i	0.616066	−	0.447598i	0.851545	+	0.524281i	$0.175666\pi$
$692$	−10.4055			−0.395557
$693$	3.16932	+	4.37052i	0.120392	+	0.166022i
$694$	11.1959			0.424990
$695$	8.78620	−	6.38355i	0.333280	−	0.242142i
$696$	−1.80973	−	5.56976i	−0.0685975	−	0.211121i
$697$	−8.46960	+	26.0667i	−0.320809	+	0.987348i
$698$	23.1250	+	16.8013i	0.875294	+	0.635938i
$699$	−19.9718	−	14.5103i	−0.755402	−	0.548831i
$700$	0.309017	−	0.951057i	0.0116797	−	0.0359466i
$701$	−12.6966	−	39.0762i	−0.479545	−	1.47589i	−0.839729	−	0.543006i	$-0.817286\pi$
$701$	−12.6966	−	39.0762i	−0.479545	−	1.47589i	0.360184	−	0.932881i	$-0.382714\pi$
$702$	11.9065	−	8.65060i	0.449383	−	0.326496i
$703$	0.161196			0.00607961
$704$	1.95190	−	2.68144i	0.0735649	−	0.101060i
$705$	11.5969			0.436764
$706$	−3.23884	+	2.35316i	−0.121895	+	0.0885622i
$707$	4.00278	+	12.3193i	0.150540	+	0.463315i
$708$	−0.211657	+	0.651412i	−0.00795455	+	0.0244816i
$709$	12.0528	+	8.75689i	0.452653	+	0.328872i	0.790642	−	0.612278i	$-0.209747\pi$
$709$	12.0528	+	8.75689i	0.452653	+	0.328872i	−0.337989	+	0.941150i	$0.609747\pi$
$710$	−6.64053	−	4.82463i	−0.249215	−	0.181065i
$711$	−3.39703	+	10.4550i	−0.127399	+	0.392093i
$712$	0.844877	+	2.60026i	0.0316631	+	0.0974490i
$713$	12.7639	−	9.27353i	0.478012	−	0.347296i
$714$	−6.25844			−0.234216
$715$	−8.56590	+	2.77464i	−0.320346	+	0.103766i
$716$	−25.4215			−0.950048
$717$	−1.15461	+	0.838876i	−0.0431198	+	0.0313284i
$718$	−3.02119	−	9.29826i	−0.112750	−	0.347008i
$719$	10.9301	−	33.6393i	0.407623	−	1.25454i	−0.511061	−	0.859544i	$-0.670748\pi$
$719$	10.9301	−	33.6393i	0.407623	−	1.25454i	0.918685	−	0.394991i	$-0.129252\pi$
$720$	1.31690	+	0.956780i	0.0490778	+	0.0356571i
$721$	−7.47543	−	5.43122i	−0.278399	−	0.202269i
$722$	−0.986093	+	3.03488i	−0.0366986	+	0.112947i
$723$	−0.616700	−	1.89801i	−0.0229353	−	0.0705877i
$724$	7.56141	−	5.49368i	0.281017	−	0.204171i
$725$	−4.99939			−0.185673
$726$	−12.8856	−	0.0233822i	−0.478230	−	0.000867796i
$727$	1.10139			0.0408482			0.0204241	−	0.999791i	$-0.493498\pi$
$727$	1.10139			0.0408482			0.0204241	+	0.999791i	$0.493498\pi$
$728$	−2.19634	+	1.59574i	−0.0814019	+	0.0591419i
$729$	6.62504	+	20.3898i	0.245372	+	0.755177i
$730$	4.50848	−	13.8757i	0.166866	−	0.513562i
$731$	53.0362	+	38.5331i	1.96162	+	1.42520i
$732$	−6.87995	−	4.99858i	−0.254290	−	0.184753i
$733$	3.99467	−	12.2943i	0.147547	−	0.454102i	−0.849783	−	0.527133i	$-0.823267\pi$
$733$	3.99467	−	12.2943i	0.147547	−	0.454102i	0.997330	+	0.0730307i	$0.0232671\pi$
$734$	−4.05434	−	12.4780i	−0.149648	−	0.460570i
$735$	−0.947700	+	0.688544i	−0.0349564	+	0.0253973i
$736$	5.49704			0.202624
$737$	45.4821	−	14.7324i	1.67535	−	0.542675i
$738$	−8.35067			−0.307392
$739$	26.0471	−	18.9243i	0.958157	−	0.696142i	0.00543489	−	0.999985i	$-0.498270\pi$
$739$	26.0471	−	18.9243i	0.958157	−	0.696142i	0.952722	+	0.303844i	$0.0982700\pi$
$740$	0.0125281	+	0.0385574i	0.000460541	+	0.00141740i
$741$	3.90741	−	12.0258i	0.143542	−	0.441778i
$742$	−3.68815	−	2.67960i	−0.135396	−	0.0983710i
$743$	−21.4254	−	15.5665i	−0.786022	−	0.571078i	0.120758	−	0.992682i	$-0.461467\pi$
$743$	−21.4254	−	15.5665i	−0.786022	−	0.571078i	−0.906780	+	0.421604i	$0.861467\pi$
$744$	−1.03895	+	3.19754i	−0.0380896	+	0.117228i
$745$	3.81064	+	11.7280i	0.139611	+	0.429679i
$746$	12.3417	−	8.96680i	0.451863	−	0.328298i
$747$	25.3597			0.927864
$748$	−10.4282	+	14.3258i	−0.381293	+	0.523805i
$749$	10.0022			0.365472
$750$	−0.947700	+	0.688544i	−0.0346051	+	0.0251421i
$751$	−11.9305	−	36.7182i	−0.435348	−	1.33986i	−0.892729	−	0.450594i	$-0.851212\pi$
$751$	−11.9305	−	36.7182i	−0.435348	−	1.33986i	0.457381	−	0.889271i	$-0.348788\pi$
$752$	3.05922	−	9.41530i	0.111558	−	0.343341i
$753$	18.2740	+	13.2769i	0.665943	+	0.483836i
$754$	10.9804	+	7.97771i	0.399882	+	0.290531i
$755$	−2.69079	+	8.28141i	−0.0979280	+	0.301391i
$756$	−1.67520	−	5.15574i	−0.0609265	−	0.187513i
$757$	31.4772	−	22.8695i	1.14406	−	0.831208i	0.156379	−	0.987697i	$-0.450018\pi$
$757$	31.4772	−	22.8695i	1.14406	−	0.831208i	0.987680	+	0.156490i	$0.0500177\pi$
$758$	26.6376			0.967522
$759$	−12.5376	−	17.2895i	−0.455086	−	0.627569i
$760$	3.97605			0.144226
$761$	−7.99350	+	5.80762i	−0.289764	+	0.210526i	−0.723165	−	0.690675i	$-0.757313\pi$
$761$	−7.99350	+	5.80762i	−0.289764	+	0.210526i	0.433401	+	0.901201i	$0.357313\pi$
$762$	−6.25435	−	19.2489i	−0.226571	−	0.697314i
$763$	−0.165344	+	0.508876i	−0.00598585	+	0.0184226i
$764$	−3.68840	−	2.67978i	−0.133442	−	0.0969511i
$765$	−7.03564	−	5.11169i	−0.254374	−	0.184814i
$766$	2.10749	−	6.48619i	0.0761467	−	0.234356i
$767$	−0.490525	−	1.50968i	−0.0177118	−	0.0545114i
$768$	−0.947700	+	0.688544i	−0.0341972	+	0.0248457i
$769$	−20.8801			−0.752955			−0.376478	−	0.926426i	$-0.622865\pi$
$769$	−20.8801			−0.752955			−0.376478	+	0.926426i	$0.622865\pi$
$770$	−0.00300917	+	3.31662i	−0.000108443	+	0.119523i
$771$	−11.6788			−0.420602
$772$	−12.7943	+	9.29561i	−0.460477	+	0.334556i
$773$	−11.5521	−	35.5537i	−0.415500	−	1.27878i	−0.911803	−	0.410627i	$-0.865310\pi$
$773$	−11.5521	−	35.5537i	−0.415500	−	1.27878i	0.496304	−	0.868149i	$-0.334690\pi$
$774$	−6.17217	+	18.9960i	−0.221854	+	0.682797i
$775$	2.32196	+	1.68700i	0.0834073	+	0.0605989i
$776$	1.07421	+	0.780461i	0.0385620	+	0.0280169i
$777$	0.0146757	−	0.0451670i	0.000526486	−	0.00162036i
$778$	7.13231	+	21.9510i	0.255706	+	0.786981i
$779$	−16.5020	+	11.9894i	−0.591246	+	0.429565i
$780$	3.18021			0.113870
$781$	25.8833	+	8.43597i	0.926178	+	0.301863i
$782$	−29.3685			−1.05022
$783$	−21.9260	+	15.9302i	−0.783573	+	0.569299i
$784$	0.309017	+	0.951057i	0.0110363	+	0.0339663i
$785$	−5.91071	+	18.1913i	−0.210962	+	0.649275i
$786$	−10.4418	−	7.58641i	−0.372446	−	0.270598i
$787$	13.2879	+	9.65419i	0.473661	+	0.344135i	0.798866	−	0.601509i	$-0.205433\pi$
$787$	13.2879	+	9.65419i	0.473661	+	0.344135i	−0.325205	+	0.945643i	$0.605433\pi$
$788$	4.51664	−	13.9008i	0.160899	−	0.495195i
$789$	5.57100	+	17.1458i	0.198333	+	0.610405i
$790$	−5.46363	+	3.96956i	−0.194387	+	0.141231i
$791$	−1.55217			−0.0551887
$792$	−5.13296	−	1.67295i	−0.182392	−	0.0594457i
$793$	19.7086			0.699875
$794$	12.6558	−	9.19499i	0.449138	−	0.326318i
$795$	1.65024	+	5.07890i	0.0585278	+	0.180130i
$796$	5.07577	−	15.6216i	0.179906	−	0.553694i
$797$	−25.5353	−	18.5525i	−0.904507	−	0.657163i	0.0351125	−	0.999383i	$-0.488821\pi$
$797$	−25.5353	−	18.5525i	−0.904507	−	0.657163i	−0.939620	+	0.342220i	$0.888821\pi$
$798$	−3.76810	−	2.73768i	−0.133389	−	0.0969129i
$799$	−16.3442	+	50.3022i	−0.578215	+	1.77956i
$800$	0.309017	+	0.951057i	0.0109254	+	0.0336249i
$801$	3.60050	−	2.61591i	0.127217	−	0.0924288i
$802$	−1.51369			−0.0534502
$803$	−0.0439030	+	48.3887i	−0.00154930	+	1.70760i
$804$	−16.8858			−0.595518
$805$	−4.44720	+	3.23108i	−0.156743	+	0.113881i
$806$	−2.40781	−	7.41047i	−0.0848114	−	0.261023i
$807$	−6.02789	+	18.5519i	−0.212192	+	0.653059i
$808$	−10.4794	−	7.61374i	−0.368665	−	0.267851i
$809$	5.10080	+	3.70595i	0.179335	+	0.130294i	0.673831	−	0.738885i	$-0.264647\pi$
$809$	5.10080	+	3.70595i	0.179335	+	0.130294i	−0.494496	+	0.869180i	$0.664647\pi$
$810$	−0.453341	+	1.39524i	−0.0159288	+	0.0490238i
$811$	8.88095	+	27.3327i	0.311852	+	0.959783i	0.977031	+	0.213098i	$0.0683554\pi$
$811$	8.88095	+	27.3327i	0.311852	+	0.959783i	−0.665179	+	0.746684i	$0.731645\pi$
$812$	4.04459	−	2.93857i	0.141937	−	0.103124i
$813$	−3.34381			−0.117273
$814$	−0.0789358	−	0.108853i	−0.00276670	−	0.00381531i
$815$	−18.6244			−0.652385
$816$	5.06318	−	3.67862i	0.177247	−	0.128777i
$817$	15.0763	+	46.4002i	0.527454	+	1.62334i
$818$	−4.39144	+	13.5155i	−0.153543	+	0.472557i
$819$	3.57514	+	2.59749i	0.124926	+	0.0907638i
$820$	−4.15036	−	3.01541i	−0.144937	−	0.105303i
$821$	12.3956	−	38.1498i	0.432610	−	1.33144i	−0.462906	−	0.886407i	$-0.653193\pi$
$821$	12.3956	−	38.1498i	0.432610	−	1.33144i	0.895516	−	0.445029i	$-0.146807\pi$
$822$	3.43517	+	10.5724i	0.119815	+	0.368754i
$823$	13.5712	−	9.86009i	0.473064	−	0.343701i	−0.325570	−	0.945518i	$-0.605556\pi$
$823$	13.5712	−	9.86009i	0.473064	−	0.343701i	0.798634	+	0.601817i	$0.205556\pi$
$824$	9.24014			0.321895
$825$	2.28649	−	3.14109i	0.0796055	−	0.109359i
$826$	−0.584705			−0.0203445
$827$	−5.72837	+	4.16190i	−0.199195	+	0.144724i	−0.682912	−	0.730501i	$-0.739287\pi$
$827$	−5.72837	+	4.16190i	−0.199195	+	0.144724i	0.483717	+	0.875225i	$0.339287\pi$
$828$	−2.76506	−	8.50999i	−0.0960926	−	0.295743i
$829$	−5.49397	+	16.9087i	−0.190814	+	0.587264i	−1.00000		0.000288358i	$-0.999908\pi$
$829$	−5.49397	+	16.9087i	−0.190814	+	0.587264i	0.809186	+	0.587552i	$0.199908\pi$
$830$	12.6040	+	9.15735i	0.437491	+	0.317856i
$831$	−23.7370	−	17.2459i	−0.823426	−	0.598254i
$832$	0.838928	−	2.58196i	0.0290846	−	0.0895132i
$833$	−1.65095	−	5.08111i	−0.0572022	−	0.176050i
$834$	10.2923	−	7.47783i	0.356395	−	0.258936i
$835$	1.66091			0.0574780
$836$	−12.5453	+	4.06364i	−0.433889	+	0.140544i
$837$	15.5590			0.537798
$838$	−5.35125	+	3.88791i	−0.184856	+	0.134306i
$839$	−2.17268	−	6.68682i	−0.0750093	−	0.230855i	0.906521	−	0.422160i	$-0.138728\pi$
$839$	−2.17268	−	6.68682i	−0.0750093	−	0.230855i	−0.981531	+	0.191305i	$0.938728\pi$
$840$	0.361989	−	1.11409i	0.0124898	−	0.0384397i
$841$	3.24097	+	2.35470i	0.111758	+	0.0811967i
$842$	30.9783	+	22.5070i	1.06758	+	0.775644i
$843$	1.58488	−	4.87775i	0.0545861	−	0.167999i
$844$	−1.48006	−	4.55516i	−0.0509458	−	0.156795i
$845$	4.55453	−	3.30906i	0.156681	−	0.113835i
$846$	−16.1147			−0.554034
$847$	−3.38020	−	10.4678i	−0.116145	−	0.359677i
$848$	4.55880			0.156550
$849$	7.07179	−	5.13796i	0.242703	−	0.176334i
$850$	−1.65095	−	5.08111i	−0.0566273	−	0.174281i
$851$	0.0688673	−	0.211952i	0.00236074	−	0.00726562i
$852$	−7.77886	−	5.65167i	−0.266499	−	0.193623i
$853$	−39.0646	−	28.3821i	−1.33755	−	0.971783i	−0.999530	−	0.0306426i	$-0.990245\pi$
$853$	−39.0646	−	28.3821i	−1.33755	−	0.971783i	−0.338015	−	0.941141i	$-0.609755\pi$
$854$	2.24335	−	6.90432i	0.0767658	−	0.236261i
$855$	−1.99999	−	6.15533i	−0.0683981	−	0.210508i
$856$	−8.09193	+	5.87913i	−0.276576	+	0.200945i
$857$	−30.6816			−1.04806			−0.524032	−	0.851699i	$-0.675573\pi$
$857$	−30.6816			−1.04806			−0.524032	+	0.851699i	$0.675573\pi$
$858$	−10.0343	+	3.25027i	−0.342565	+	0.110962i
$859$	12.1328			0.413965			0.206983	−	0.978345i	$-0.433636\pi$
$859$	12.1328			0.413965			0.206983	+	0.978345i	$0.433636\pi$
$860$	−9.92704	+	7.21242i	−0.338509	+	0.245941i
$861$	1.85705	+	5.71541i	0.0632881	+	0.194781i
$862$	2.08007	−	6.40178i	0.0708473	−	0.218046i
$863$	34.0459	+	24.7358i	1.15894	+	0.842016i	0.989643	−	0.143550i	$-0.0458518\pi$
$863$	34.0459	+	24.7358i	1.15894	+	0.842016i	0.169292	+	0.985566i	$0.445852\pi$
$864$	4.38574	+	3.18643i	0.149206	+	0.108404i
$865$	−3.21547	+	9.89621i	−0.109329	+	0.336481i
$866$	−7.96334	−	24.5086i	−0.270605	−	0.832838i
$867$	−10.9397	+	7.94813i	−0.371530	+	0.269932i
$868$	−2.87010			−0.0974176
$869$	13.1820	−	18.1089i	0.447168	−	0.614301i
$870$	−5.85640			−0.198550
$871$	31.6599	−	23.0023i	1.07276	−	0.779402i
$872$	−0.165344	−	0.508876i	−0.00559925	−	0.0172327i
$873$	0.667895	−	2.05557i	0.0226048	−	0.0695705i
$874$	−17.6823	−	12.8469i	−0.598112	−	0.434554i
$875$	−0.809017	−	0.587785i	−0.0273498	−	0.0198708i
$876$	5.28133	−	16.2543i	0.178440	−	0.549181i
$877$	−10.6007	−	32.6255i	−0.357959	−	1.10168i	−0.954274	−	0.298934i	$-0.903369\pi$
$877$	−10.6007	−	32.6255i	−0.357959	−	1.10168i	0.596315	−	0.802751i	$-0.296631\pi$
$878$	−11.1750	+	8.11912i	−0.377138	+	0.274007i
$879$	6.86069			0.231405
$880$	−1.94703	−	2.68497i	−0.0656343	−	0.0905104i
$881$	0.874683			0.0294688			0.0147344	−	0.999891i	$-0.495310\pi$
$881$	0.874683			0.0294688			0.0147344	+	0.999891i	$0.495310\pi$
$882$	1.31690	−	0.956780i	0.0443422	−	0.0322165i
$883$	15.2410	+	46.9068i	0.512899	+	1.57854i	0.787073	+	0.616860i	$0.211596\pi$
$883$	15.2410	+	46.9068i	0.512899	+	1.57854i	−0.274174	+	0.961680i	$0.588404\pi$
$884$	−4.48206	+	13.7944i	−0.150748	+	0.463954i
$885$	0.554124	+	0.402595i	0.0186267	+	0.0135331i
$886$	22.7500	+	16.5289i	0.764303	+	0.555299i
$887$	3.16795	−	9.74994i	0.106369	−	0.327371i	−0.883680	−	0.468091i	$-0.844942\pi$
$887$	3.16795	−	9.74994i	0.106369	−	0.327371i	0.990049	+	0.140720i	$0.0449418\pi$
$888$	0.0146757	+	0.0451670i	0.000492483	+	0.00151571i
$889$	13.9780	−	10.1556i	0.468806	−	0.340607i
$890$	2.73408			0.0916466
$891$	0.00441458	−	4.86563i	0.000147894	−	0.163005i
$892$	−23.2488			−0.778426
$893$	−31.8447	+	23.1365i	−1.06564	+	0.774234i
$894$	4.46387	+	13.7384i	0.149294	+	0.459480i
$895$	−7.85569	+	24.1773i	−0.262587	+	0.808159i
$896$	−0.809017	−	0.587785i	−0.0270274	−	0.0196365i
$897$	−14.1430	−	10.2755i	−0.472222	−	0.343089i
$898$	8.60848	−	26.4942i	0.287269	−	0.884122i
$899$	4.43401	+	13.6465i	0.147883	+	0.455136i
$900$	1.31690	−	0.956780i	0.0438965	−	0.0318927i
$901$	−24.3558			−0.811411
$902$	16.1772	+	5.27251i	0.538641	+	0.175555i
$903$	14.3739			0.478334
$904$	1.25573	−	0.912341i	0.0417650	−	0.0303440i
$905$	−2.88820	−	8.88897i	−0.0960070	−	0.295479i
$906$	−3.15205	+	9.70102i	−0.104720	+	0.322295i
$907$	−43.6928	−	31.7447i	−1.45080	−	1.05407i	−0.985644	−	0.168835i	$-0.946000\pi$
$907$	−43.6928	−	31.7447i	−1.45080	−	1.05407i	−0.465152	−	0.885231i	$-0.654000\pi$
$908$	13.7940	+	10.0219i	0.457769	+	0.332589i
$909$	−6.51561	+	20.0530i	−0.216109	+	0.665116i
$910$	0.838928	+	2.58196i	0.0278102	+	0.0855910i
$911$	17.7468	−	12.8938i	0.587977	−	0.427190i	−0.253614	−	0.967305i	$-0.581619\pi$
$911$	17.7468	−	12.8938i	0.587977	−	0.427190i	0.841591	+	0.540115i	$0.181619\pi$
$912$	4.65762			0.154229
$913$	−49.1276	−	16.0118i	−1.62589	−	0.529914i
$914$	−38.0839			−1.25970
$915$	−6.87995	+	4.99858i	−0.227444	+	0.165248i
$916$	3.24625	+	9.99094i	0.107259	+	0.330110i
$917$	3.40476	−	10.4788i	0.112435	−	0.346040i
$918$	−23.4312	−	17.0238i	−0.773346	−	0.561869i
$919$	26.3236	+	19.1252i	0.868337	+	0.630884i	0.930140	−	0.367205i	$-0.119685\pi$
$919$	26.3236	+	19.1252i	0.868337	+	0.630884i	−0.0618033	+	0.998088i	$0.519685\pi$
$920$	1.69868	−	5.22800i	0.0560038	−	0.172362i
$921$	12.5927	+	38.7563i	0.414943	+	1.27706i
$922$	−11.2656	+	8.18496i	−0.371014	+	0.269557i
$923$	22.2837			0.733478
$924$	−0.00352500	+	3.88516i	−0.000115964	+	0.127813i
$925$	0.0405417			0.00133300
$926$	2.37748	−	1.72734i	0.0781288	−	0.0567639i
$927$	−4.64787	−	14.3047i	−0.152656	−	0.469827i
$928$	−1.54490	+	4.75471i	−0.0507138	+	0.156081i
$929$	−1.23054	−	0.894040i	−0.0403727	−	0.0293325i	0.567416	−	0.823431i	$-0.307943\pi$
$929$	−1.23054	−	0.894040i	−0.0403727	−	0.0293325i	−0.607789	+	0.794099i	$0.707943\pi$
$930$	2.71999	+	1.97619i	0.0891921	+	0.0648019i
$931$	1.22867	−	3.78144i	0.0402679	−	0.123932i
$932$	6.51221	+	20.0425i	0.213314	+	0.656514i
$933$	−18.5540	+	13.4803i	−0.607431	+	0.441324i
$934$	−31.8095			−1.04084
$935$	10.4022	+	14.3447i	0.340188	+	0.469123i
$936$	−4.41912			−0.144443
$937$	−28.5701	+	20.7574i	−0.933344	+	0.678114i	−0.946809	−	0.321795i	$-0.895714\pi$
$937$	−28.5701	+	20.7574i	−0.933344	+	0.678114i	0.0134649	+	0.999909i	$0.495714\pi$
$938$	−4.45443	−	13.7093i	−0.145442	−	0.447625i
$939$	−4.47526	+	13.7734i	−0.146045	+	0.449479i
$940$	−8.00913	−	5.81897i	−0.261229	−	0.189794i
$941$	−14.4266	−	10.4815i	−0.470294	−	0.341689i	0.327262	−	0.944934i	$-0.393874\pi$
$941$	−14.4266	−	10.4815i	−0.470294	−	0.341689i	−0.797556	+	0.603245i	$0.793874\pi$
$942$	−6.92393	+	21.3097i	−0.225594	+	0.694307i
$943$	8.71444	+	26.8203i	0.283781	+	0.873388i
$944$	0.473036	−	0.343681i	0.0153960	−	0.0111859i
$945$	−5.42107			−0.176347
$946$	23.9507	−	32.9026i	0.778706	−	1.06975i
$947$	−26.5867			−0.863953			−0.431977	−	0.901885i	$-0.642184\pi$
$947$	−26.5867			−0.863953			−0.431977	+	0.901885i	$0.642184\pi$
$948$	−6.40022	+	4.65003i	−0.207869	+	0.151026i
$949$	12.2398	+	37.6701i	0.397319	+	1.22282i
$950$	1.22867	−	3.78144i	0.0398632	−	0.122686i
$951$	−4.88597	−	3.54986i	−0.158438	−	0.115112i
$952$	4.32225	+	3.14030i	0.140085	+	0.101778i
$953$	3.99509	−	12.2956i	0.129414	−	0.398294i	−0.865266	−	0.501314i	$-0.832850\pi$
$953$	3.99509	−	12.2956i	0.129414	−	0.398294i	0.994679	+	0.103019i	$0.0328503\pi$
$954$	−2.29312	−	7.05749i	−0.0742424	−	0.228495i
$955$	−3.68840	+	2.67978i	−0.119354	+	0.0867157i
$956$	1.21833			0.0394037
$957$	18.4783	−	5.98542i	0.597317	−	0.193481i
$958$	37.7725			1.22038
$959$	−7.67733	+	5.57791i	−0.247914	+	0.180120i
$960$	0.361989	+	1.11409i	0.0116831	+	0.0359570i
$961$	−7.03401	+	21.6484i	−0.226903	+	0.698337i
$962$	−0.0890434	−	0.0646938i	−0.00287088	−	0.00208581i
$963$	13.1718	+	9.56988i	0.424456	+	0.308385i
$964$	−0.526455	+	1.62026i	−0.0169560	+	0.0521851i
$965$	4.88699	+	15.0406i	0.157318	+	0.484174i
$966$	−5.20955	+	3.78496i	−0.167614	+	0.121779i
$967$	6.45564			0.207599			0.103800	−	0.994598i	$-0.466900\pi$
$967$	6.45564			0.207599			0.103800	+	0.994598i	$0.466900\pi$
$968$	8.88744	+	6.48178i	0.285653	+	0.208332i
$969$	−24.8838			−0.799384
$970$	1.07421	−	0.780461i	0.0344909	−	0.0250591i
$971$	5.11223	+	15.7338i	0.164059	+	0.504923i	0.998966	−	0.0454691i	$-0.0144783\pi$
$971$	5.11223	+	15.7338i	0.164059	+	0.504923i	−0.834906	+	0.550392i	$0.814478\pi$
$972$	4.49456	−	13.8328i	0.144163	−	0.443688i
$973$	8.78620	+	6.38355i	0.281673	+	0.204647i
$974$	7.71111	+	5.60245i	0.247080	+	0.179514i
$975$	0.982738	−	3.02456i	0.0314728	−	0.0968634i
$976$	2.24335	+	6.90432i	0.0718079	+	0.221002i
$977$	20.0469	−	14.5649i	0.641358	−	0.465974i	−0.218959	−	0.975734i	$-0.570266\pi$
$977$	20.0469	−	14.5649i	0.641358	−	0.465974i	0.860316	+	0.509761i	$0.170266\pi$
$978$	−21.8170			−0.697632
$979$	−8.62664	+	2.79431i	−0.275709	+	0.0893067i
$980$	1.00000			0.0319438
$981$	−0.704623	+	0.511939i	−0.0224969	+	0.0163449i
$982$	−6.86614	−	21.1318i	−0.219107	−	0.674343i
$983$	−14.3681	+	44.2206i	−0.458273	+	1.41042i	0.408977	+	0.912545i	$0.365886\pi$
$983$	−14.3681	+	44.2206i	−0.458273	+	1.41042i	−0.867250	+	0.497873i	$0.834114\pi$
$984$	−4.86182	−	3.53232i	−0.154989	−	0.112606i
$985$	−11.8247	−	8.59116i	−0.376767	−	0.273737i
$986$	8.25377	−	25.4025i	0.262854	−	0.808980i
$987$	3.58363	+	11.0293i	0.114068	+	0.351066i
$988$	−8.73276	+	6.34472i	−0.277826	+	0.201852i
$989$	67.4514			2.14483
$990$	−3.17724	+	4.36477i	−0.100979	+	0.138721i
$991$	47.0722			1.49530			0.747649	−	0.664094i	$-0.231182\pi$
$991$	47.0722			1.49530			0.747649	+	0.664094i	$0.231182\pi$
$992$	2.32196	−	1.68700i	0.0737223	−	0.0535624i
$993$	−11.7669	−	36.2147i	−0.373410	−	1.14924i
$994$	2.53646	−	7.80642i	0.0804516	−	0.247604i
$995$	−13.2885	−	9.65469i	−0.421275	−	0.306074i
$996$	14.7646	+	10.7271i	0.467834	+	0.339901i
$997$	17.3832	−	53.4998i	0.550530	−	1.69436i	−0.156935	−	0.987609i	$-0.550161\pi$
$997$	17.3832	−	53.4998i	0.550530	−	1.69436i	0.707465	−	0.706748i	$-0.249839\pi$
$998$	−3.34869	−	10.3062i	−0.106001	−	0.326237i
$999$	0.177805	−	0.129183i	0.00562551	−	0.00408717i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	770.2.n.i.421.2	✓	12
11.2	odd	10		8470.2.a.cy.1.4		6
11.4	even	5	inner	770.2.n.i.631.2	yes	12
11.9	even	5		8470.2.a.de.1.4		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
770.2.n.i.421.2	✓	12	1.1	even	1	trivial
770.2.n.i.631.2	yes	12	11.4	even	5	inner
8470.2.a.cy.1.4		6	11.2	odd	10
8470.2.a.de.1.4		6	11.9	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)

\(f(q)\)	\(=\)	\(q+(-0.809017 + 0.587785i) q^{2} +(0.361989 + 1.11409i) q^{3} +(0.309017 - 0.951057i) q^{4} +(-0.809017 - 0.587785i) q^{5} +(-0.947700 - 0.688544i) q^{6} +(0.309017 - 0.951057i) q^{7} +(0.309017 + 0.951057i) q^{8} +(1.31690 - 0.956780i) q^{9} +O(q^{10})\)	\(q+(-0.809017 + 0.587785i) q^{2} +(0.361989 + 1.11409i) q^{3} +(0.309017 - 0.951057i) q^{4} +(-0.809017 - 0.587785i) q^{5} +(-0.947700 - 0.688544i) q^{6} +(0.309017 - 0.951057i) q^{7} +(0.309017 + 0.951057i) q^{8} +(1.31690 - 0.956780i) q^{9} +1.00000 q^{10} +(-3.15523 + 1.02203i) q^{11} +1.17142 q^{12} +(-2.19634 + 1.59574i) q^{13} +(0.309017 + 0.951057i) q^{14} +(0.361989 - 1.11409i) q^{15} +(-0.809017 - 0.587785i) q^{16} +(4.32225 + 3.14030i) q^{17} +(-0.503009 + 1.54810i) q^{18} +(1.22867 + 3.78144i) q^{19} +(-0.809017 + 0.587785i) q^{20} +1.17142 q^{21} +(1.95190 - 2.68144i) q^{22} +5.49704 q^{23} +(-0.947700 + 0.688544i) q^{24} +(0.309017 + 0.951057i) q^{25} +(0.838928 - 2.58196i) q^{26} +(4.38574 + 3.18643i) q^{27} +(-0.809017 - 0.587785i) q^{28} +(-1.54490 + 4.75471i) q^{29} +(0.361989 + 1.11409i) q^{30} +(2.32196 - 1.68700i) q^{31} +1.00000 q^{32} +(-2.28079 - 3.14524i) q^{33} -5.34260 q^{34} +(-0.809017 + 0.587785i) q^{35} +(-0.503009 - 1.54810i) q^{36} +(0.0125281 - 0.0385574i) q^{37} +(-3.21669 - 2.33706i) q^{38} +(-2.57284 - 1.86928i) q^{39} +(0.309017 - 0.951057i) q^{40} +(1.58530 + 4.87904i) q^{41} +(-0.947700 + 0.688544i) q^{42} +12.2705 q^{43} +(-0.00300917 + 3.31662i) q^{44} -1.62777 q^{45} +(-4.44720 + 3.23108i) q^{46} +(3.05922 + 9.41530i) q^{47} +(0.361989 - 1.11409i) q^{48} +(-0.809017 - 0.587785i) q^{49} +(-0.809017 - 0.587785i) q^{50} +(-1.93396 + 5.95213i) q^{51} +(0.838928 + 2.58196i) q^{52} +(-3.68815 + 2.67960i) q^{53} -5.42107 q^{54} +(3.15337 + 1.02775i) q^{55} +1.00000 q^{56} +(-3.76810 + 2.73768i) q^{57} +(-1.54490 - 4.75471i) q^{58} +(-0.180684 + 0.556087i) q^{59} +(-0.947700 - 0.688544i) q^{60} +(-5.87316 - 4.26710i) q^{61} +(-0.886910 + 2.72963i) q^{62} +(-0.503009 - 1.54810i) q^{63} +(-0.809017 + 0.587785i) q^{64} +2.71483 q^{65} +(3.69392 + 1.20393i) q^{66} -14.4148 q^{67} +(4.32225 - 3.14030i) q^{68} +(1.98987 + 6.12419i) q^{69} +(0.309017 - 0.951057i) q^{70} +(-6.64053 - 4.82463i) q^{71} +(1.31690 + 0.956780i) q^{72} +(4.50848 - 13.8757i) q^{73} +(0.0125281 + 0.0385574i) q^{74} +(-0.947700 + 0.688544i) q^{75} +3.97605 q^{76} +(-0.00300917 + 3.31662i) q^{77} +3.18021 q^{78} +(-5.46363 + 3.96956i) q^{79} +(0.309017 + 0.951057i) q^{80} +(-0.453341 + 1.39524i) q^{81} +(-4.15036 - 3.01541i) q^{82} +(12.6040 + 9.15735i) q^{83} +(0.361989 - 1.11409i) q^{84} +(-1.65095 - 5.08111i) q^{85} +(-9.92704 + 7.21242i) q^{86} -5.85640 q^{87} +(-1.94703 - 2.68497i) q^{88} +2.73408 q^{89} +(1.31690 - 0.956780i) q^{90} +(0.838928 + 2.58196i) q^{91} +(1.69868 - 5.22800i) q^{92} +(2.71999 + 1.97619i) q^{93} +(-8.00913 - 5.81897i) q^{94} +(1.22867 - 3.78144i) q^{95} +(0.361989 + 1.11409i) q^{96} +(1.07421 - 0.780461i) q^{97} +1.00000 q^{98} +(-3.17724 + 4.36477i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 3 q^{2} + 2 q^{3} - 3 q^{4} - 3 q^{5} - 3 q^{6} - 3 q^{7} - 3 q^{8} - 15 q^{9}+O(q^{10}) \) 12 * q - 3 * q^2 + 2 * q^3 - 3 * q^4 - 3 * q^5 - 3 * q^6 - 3 * q^7 - 3 * q^8 - 15 * q^9	\( 12 q - 3 q^{2} + 2 q^{3} - 3 q^{4} - 3 q^{5} - 3 q^{6} - 3 q^{7} - 3 q^{8} - 15 q^{9} + 12 q^{10} + q^{11} + 2 q^{12} - 6 q^{13} - 3 q^{14} + 2 q^{15} - 3 q^{16} - 6 q^{17} - 13 q^{19} - 3 q^{20} + 2 q^{21} + q^{22} - 12 q^{23} - 3 q^{24} - 3 q^{25} + 4 q^{26} - 7 q^{27} - 3 q^{28} - 26 q^{29} + 2 q^{30} + 12 q^{32} - 15 q^{33} + 14 q^{34} - 3 q^{35} - 18 q^{37} + 2 q^{38} - 40 q^{39} - 3 q^{40} + 16 q^{41} - 3 q^{42} + 38 q^{43} + 6 q^{44} + 30 q^{45} + 8 q^{46} - 26 q^{47} + 2 q^{48} - 3 q^{49} - 3 q^{50} - 13 q^{51} + 4 q^{52} + 8 q^{54} + 11 q^{55} + 12 q^{56} - 41 q^{57} - 26 q^{58} + 21 q^{59} - 3 q^{60} + 4 q^{61} - 3 q^{64} + 4 q^{65} - 30 q^{66} + 10 q^{67} - 6 q^{68} + 18 q^{69} - 3 q^{70} - 4 q^{71} - 15 q^{72} - 14 q^{73} - 18 q^{74} - 3 q^{75} + 22 q^{76} + 6 q^{77} + 40 q^{78} - 2 q^{79} - 3 q^{80} + 26 q^{81} - 29 q^{82} + 35 q^{83} + 2 q^{84} - q^{85} - 37 q^{86} + 28 q^{87} - 19 q^{88} + 2 q^{89} - 15 q^{90} + 4 q^{91} - 2 q^{92} + 6 q^{93} + 4 q^{94} - 13 q^{95} + 2 q^{96} + 19 q^{97} + 12 q^{98} - 81 q^{99}+O(q^{100}) \) 12 * q - 3 * q^2 + 2 * q^3 - 3 * q^4 - 3 * q^5 - 3 * q^6 - 3 * q^7 - 3 * q^8 - 15 * q^9 + 12 * q^10 + q^11 + 2 * q^12 - 6 * q^13 - 3 * q^14 + 2 * q^15 - 3 * q^16 - 6 * q^17 - 13 * q^19 - 3 * q^20 + 2 * q^21 + q^22 - 12 * q^23 - 3 * q^24 - 3 * q^25 + 4 * q^26 - 7 * q^27 - 3 * q^28 - 26 * q^29 + 2 * q^30 + 12 * q^32 - 15 * q^33 + 14 * q^34 - 3 * q^35 - 18 * q^37 + 2 * q^38 - 40 * q^39 - 3 * q^40 + 16 * q^41 - 3 * q^42 + 38 * q^43 + 6 * q^44 + 30 * q^45 + 8 * q^46 - 26 * q^47 + 2 * q^48 - 3 * q^49 - 3 * q^50 - 13 * q^51 + 4 * q^52 + 8 * q^54 + 11 * q^55 + 12 * q^56 - 41 * q^57 - 26 * q^58 + 21 * q^59 - 3 * q^60 + 4 * q^61 - 3 * q^64 + 4 * q^65 - 30 * q^66 + 10 * q^67 - 6 * q^68 + 18 * q^69 - 3 * q^70 - 4 * q^71 - 15 * q^72 - 14 * q^73 - 18 * q^74 - 3 * q^75 + 22 * q^76 + 6 * q^77 + 40 * q^78 - 2 * q^79 - 3 * q^80 + 26 * q^81 - 29 * q^82 + 35 * q^83 + 2 * q^84 - q^85 - 37 * q^86 + 28 * q^87 - 19 * q^88 + 2 * q^89 - 15 * q^90 + 4 * q^91 - 2 * q^92 + 6 * q^93 + 4 * q^94 - 13 * q^95 + 2 * q^96 + 19 * q^97 + 12 * q^98 - 81 * q^99

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