LMFDB - Embedded newform 525.2.n.c.316.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [525,2,Mod(106,525)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(525, base_ring=CyclotomicField(10))

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

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

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

chi := DirichletCharacter("525.106");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 525 = 3 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	525.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:	$4.19214610612$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$6$ over $\Q(\zeta_{5})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			316.1
Character	$\chi$	$=$	525.316
Dual form			525.2.n.c.211.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.66257 - 1.20793i) q^{2} +(0.309017 + 0.951057i) q^{3} +(0.687021 + 2.11443i) q^{4} +(2.21818 + 0.282242i) q^{5} +(0.635047 - 1.95447i) q^{6} +1.00000 q^{7} +(0.141773 - 0.436331i) q^{8} +(-0.809017 + 0.587785i) q^{9} +O(q^{10})$	\(q+(-1.66257 - 1.20793i) q^{2} +(0.309017 + 0.951057i) q^{3} +(0.687021 + 2.11443i) q^{4} +(2.21818 + 0.282242i) q^{5} +(0.635047 - 1.95447i) q^{6} +1.00000 q^{7} +(0.141773 - 0.436331i) q^{8} +(-0.809017 + 0.587785i) q^{9} +(-3.34697 - 3.14866i) q^{10} +(-1.63608 - 1.18868i) q^{11} +(-1.79865 + 1.30679i) q^{12} +(4.82750 - 3.50739i) q^{13} +(-1.66257 - 1.20793i) q^{14} +(0.417028 + 2.19684i) q^{15} +(2.83452 - 2.05940i) q^{16} +(-0.186089 + 0.572724i) q^{17} +2.05505 q^{18} +(-1.44167 + 4.43699i) q^{19} +(0.927157 + 4.88411i) q^{20} +(0.309017 + 0.951057i) q^{21} +(1.28426 + 3.95254i) q^{22} +(-0.298513 - 0.216883i) q^{23} +0.458786 q^{24} +(4.84068 + 1.25213i) q^{25} -12.2628 q^{26} +(-0.809017 - 0.587785i) q^{27} +(0.687021 + 2.11443i) q^{28} +(1.78251 + 5.48599i) q^{29} +(1.96028 - 4.15614i) q^{30} +(-2.18648 + 6.72930i) q^{31} -8.11779 q^{32} +(0.624927 - 1.92333i) q^{33} +(1.00120 - 0.727413i) q^{34} +(2.21818 + 0.282242i) q^{35} +(-1.79865 - 1.30679i) q^{36} +(8.38061 - 6.08887i) q^{37} +(7.75645 - 5.63539i) q^{38} +(4.82750 + 3.50739i) q^{39} +(0.437629 - 0.927848i) q^{40} +(1.90759 - 1.38595i) q^{41} +(0.635047 - 1.95447i) q^{42} +12.2210 q^{43} +(1.38937 - 4.27603i) q^{44} +(-1.96045 + 1.07548i) q^{45} +(0.234321 + 0.721167i) q^{46} +(-2.90011 - 8.92561i) q^{47} +(2.83452 + 2.05940i) q^{48} +1.00000 q^{49} +(-6.53550 - 7.92896i) q^{50} -0.602198 q^{51} +(10.7327 + 7.79779i) q^{52} +(0.449868 + 1.38455i) q^{53} +(0.635047 + 1.95447i) q^{54} +(-3.29363 - 3.09849i) q^{55} +(0.141773 - 0.436331i) q^{56} -4.66533 q^{57} +(3.66315 - 11.2740i) q^{58} +(1.23701 - 0.898737i) q^{59} +(-4.35856 + 2.39105i) q^{60} +(-2.65549 - 1.92933i) q^{61} +(11.7637 - 8.54684i) q^{62} +(-0.809017 + 0.587785i) q^{63} +(7.82738 + 5.68692i) q^{64} +(11.6982 - 6.41750i) q^{65} +(-3.36223 + 2.44281i) q^{66} +(-2.82717 + 8.70115i) q^{67} -1.33883 q^{68} +(0.114022 - 0.350923i) q^{69} +(-3.34697 - 3.14866i) q^{70} +(-2.33304 - 7.18037i) q^{71} +(0.141773 + 0.436331i) q^{72} +(-1.44101 - 1.04696i) q^{73} -21.2883 q^{74} +(0.305006 + 4.99069i) q^{75} -10.3722 q^{76} +(-1.63608 - 1.18868i) q^{77} +(-3.78940 - 11.6626i) q^{78} +(-0.352284 - 1.08422i) q^{79} +(6.86875 - 3.76811i) q^{80} +(0.309017 - 0.951057i) q^{81} -4.84565 q^{82} +(-0.538954 + 1.65873i) q^{83} +(-1.79865 + 1.30679i) q^{84} +(-0.574427 + 1.21788i) q^{85} +(-20.3184 - 14.7622i) q^{86} +(-4.66666 + 3.39053i) q^{87} +(-0.750610 + 0.545350i) q^{88} +(12.8598 + 9.34318i) q^{89} +(4.55849 + 0.580023i) q^{90} +(4.82750 - 3.50739i) q^{91} +(0.253499 - 0.780190i) q^{92} -7.07560 q^{93} +(-5.95988 + 18.3426i) q^{94} +(-4.45018 + 9.43516i) q^{95} +(-2.50854 - 7.72048i) q^{96} +(-1.40656 - 4.32896i) q^{97} +(-1.66257 - 1.20793i) q^{98} +2.02231 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + q^{2} - 6 q^{3} - 9 q^{4} - q^{5} + q^{6} + 24 q^{7} + 9 q^{8} - 6 q^{9}+O(q^{10}) $ 24 * q + q^2 - 6 * q^3 - 9 * q^4 - q^5 + q^6 + 24 * q^7 + 9 * q^8 - 6 * q^9	\( 24 q + q^{2} - 6 q^{3} - 9 q^{4} - q^{5} + q^{6} + 24 q^{7} + 9 q^{8} - 6 q^{9} - 16 q^{10} + 2 q^{11} + q^{12} + 8 q^{13} + q^{14} - 6 q^{15} + 13 q^{16} + 12 q^{17} - 4 q^{18} + 19 q^{19} + 11 q^{20} - 6 q^{21} - 19 q^{22} - 6 q^{24} + 9 q^{25} - 14 q^{26} - 6 q^{27} - 9 q^{28} + 5 q^{29} - 6 q^{30} + 17 q^{31} - 26 q^{32} + 7 q^{33} - 7 q^{34} - q^{35} + q^{36} + 22 q^{37} - 16 q^{38} + 8 q^{39} + 3 q^{40} + 37 q^{41} + q^{42} + 8 q^{43} + 13 q^{44} + 4 q^{45} + 24 q^{46} - 24 q^{47} + 13 q^{48} + 24 q^{49} - 21 q^{50} - 8 q^{51} + 23 q^{52} - 24 q^{53} + q^{54} - 55 q^{55} + 9 q^{56} - 26 q^{57} + 8 q^{58} - 39 q^{60} + 24 q^{62} - 6 q^{63} - q^{64} - 34 q^{65} + 16 q^{66} + 34 q^{67} + 22 q^{68} + 10 q^{69} - 16 q^{70} - 24 q^{71} + 9 q^{72} + 46 q^{73} + 10 q^{74} + 24 q^{75} - 20 q^{76} + 2 q^{77} - 14 q^{78} + 10 q^{79} + 6 q^{80} - 6 q^{81} - 78 q^{82} + 42 q^{83} + q^{84} - 22 q^{85} - 96 q^{86} - 10 q^{87} - 39 q^{88} + 29 q^{89} + 14 q^{90} + 8 q^{91} + 42 q^{92} - 58 q^{93} + 54 q^{94} - 42 q^{95} + 9 q^{96} - 32 q^{97} + q^{98} - 18 q^{99}+O(q^{100}) \) 24 * q + q^2 - 6 * q^3 - 9 * q^4 - q^5 + q^6 + 24 * q^7 + 9 * q^8 - 6 * q^9 - 16 * q^10 + 2 * q^11 + q^12 + 8 * q^13 + q^14 - 6 * q^15 + 13 * q^16 + 12 * q^17 - 4 * q^18 + 19 * q^19 + 11 * q^20 - 6 * q^21 - 19 * q^22 - 6 * q^24 + 9 * q^25 - 14 * q^26 - 6 * q^27 - 9 * q^28 + 5 * q^29 - 6 * q^30 + 17 * q^31 - 26 * q^32 + 7 * q^33 - 7 * q^34 - q^35 + q^36 + 22 * q^37 - 16 * q^38 + 8 * q^39 + 3 * q^40 + 37 * q^41 + q^42 + 8 * q^43 + 13 * q^44 + 4 * q^45 + 24 * q^46 - 24 * q^47 + 13 * q^48 + 24 * q^49 - 21 * q^50 - 8 * q^51 + 23 * q^52 - 24 * q^53 + q^54 - 55 * q^55 + 9 * q^56 - 26 * q^57 + 8 * q^58 - 39 * q^60 + 24 * q^62 - 6 * q^63 - q^64 - 34 * q^65 + 16 * q^66 + 34 * q^67 + 22 * q^68 + 10 * q^69 - 16 * q^70 - 24 * q^71 + 9 * q^72 + 46 * q^73 + 10 * q^74 + 24 * q^75 - 20 * q^76 + 2 * q^77 - 14 * q^78 + 10 * q^79 + 6 * q^80 - 6 * q^81 - 78 * q^82 + 42 * q^83 + q^84 - 22 * q^85 - 96 * q^86 - 10 * q^87 - 39 * q^88 + 29 * q^89 + 14 * q^90 + 8 * q^91 + 42 * q^92 - 58 * q^93 + 54 * q^94 - 42 * q^95 + 9 * q^96 - 32 * q^97 + q^98 - 18 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/525\mathbb{Z}\right)^\times$.

$n$	$127$	$176$	$451$
$\chi(n)$	$e\left(\frac{1}{5}\right)$	$1$	$1$

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 $

$2$	−1.66257	−	1.20793i	−1.17562	−	0.854136i	−0.183947	−	0.982936i	$-0.558887\pi$
$2$	−1.66257	−	1.20793i	−1.17562	−	0.854136i	−0.991671	+	0.128800i	$0.958887\pi$
$3$	0.309017	+	0.951057i	0.178411	+	0.549093i
$3$	0.309017	+	0.951057i	0.178411	+	0.549093i
$4$	0.687021	+	2.11443i	0.343511	+	1.05722i
$5$	2.21818	+	0.282242i	0.992002	+	0.126223i
$5$	2.21818	+	0.282242i	0.992002	+	0.126223i
$6$	0.635047	−	1.95447i	0.259257	−	0.797910i
$7$	1.00000			0.377964
$7$	1.00000			0.377964
$8$	0.141773	−	0.436331i	0.0501242	−	0.154266i
$9$	−0.809017	+	0.587785i	−0.269672	+	0.195928i
$10$	−3.34697	−	3.14866i	−1.05840	−	0.995694i
$11$	−1.63608	−	1.18868i	−0.493297	−	0.358401i	0.313154	−	0.949702i	$-0.398614\pi$
$11$	−1.63608	−	1.18868i	−0.493297	−	0.358401i	−0.806451	+	0.591301i	$0.798614\pi$
$12$	−1.79865	+	1.30679i	−0.519224	+	0.377238i
$13$	4.82750	−	3.50739i	1.33891	−	0.972774i	0.339425	−	0.940633i	$-0.389767\pi$
$13$	4.82750	−	3.50739i	1.33891	−	0.972774i	0.999483	−	0.0321412i	$-0.0102326\pi$
$14$	−1.66257	−	1.20793i	−0.444342	−	0.322833i
$15$	0.417028	+	2.19684i	0.107676	+	0.567221i
$16$	2.83452	−	2.05940i	0.708631	−	0.514851i
$17$	−0.186089	+	0.572724i	−0.0451333	+	0.138906i	−0.971084	−	0.238739i	$-0.923266\pi$
$17$	−0.186089	+	0.572724i	−0.0451333	+	0.138906i	0.925951	+	0.377645i	$0.123266\pi$
$18$	2.05505			0.484381
$19$	−1.44167	+	4.43699i	−0.330741	+	1.01792i	0.638041	+	0.770002i	$0.279745\pi$
$19$	−1.44167	+	4.43699i	−0.330741	+	1.01792i	−0.968782	+	0.247913i	$0.920255\pi$
$20$	0.927157	+	4.88411i	0.207319	+	1.09212i
$21$	0.309017	+	0.951057i	0.0674330	+	0.207538i
$22$	1.28426	+	3.95254i	0.273805	+	0.842685i
$23$	−0.298513	−	0.216883i	−0.0622443	−	0.0452232i	0.556228	−	0.831030i	$-0.312248\pi$
$23$	−0.298513	−	0.216883i	−0.0622443	−	0.0452232i	−0.618472	+	0.785807i	$0.712248\pi$
$24$	0.458786			0.0936492
$25$	4.84068	+	1.25213i	0.968136	+	0.250426i
$26$	−12.2628			−2.40493
$27$	−0.809017	−	0.587785i	−0.155695	−	0.113119i
$28$	0.687021	+	2.11443i	0.129835	+	0.399590i
$29$	1.78251	+	5.48599i	0.331003	+	1.01872i	0.968658	+	0.248400i	$0.0799048\pi$
$29$	1.78251	+	5.48599i	0.331003	+	1.01872i	−0.637654	+	0.770323i	$0.720095\pi$
$30$	1.96028	−	4.15614i	0.357897	−	0.758804i
$31$	−2.18648	+	6.72930i	−0.392704	+	1.20862i	0.538032	+	0.842925i	$0.319168\pi$
$31$	−2.18648	+	6.72930i	−0.392704	+	1.20862i	−0.930736	+	0.365693i	$0.880832\pi$
$32$	−8.11779			−1.43504
$33$	0.624927	−	1.92333i	0.108786	−	0.334808i
$34$	1.00120	−	0.727413i	0.171704	−	0.124750i
$35$	2.21818	+	0.282242i	0.374941	+	0.0477076i
$36$	−1.79865	−	1.30679i	−0.299774	−	0.217799i
$37$	8.38061	−	6.08887i	1.37776	−	1.00100i	0.380679	−	0.924707i	$-0.375690\pi$
$37$	8.38061	−	6.08887i	1.37776	−	1.00100i	0.997085	−	0.0762966i	$-0.0243096\pi$
$38$	7.75645	−	5.63539i	1.25826	−	0.914181i
$39$	4.82750	+	3.50739i	0.773019	+	0.561631i
$40$	0.437629	−	0.927848i	0.0691952	−	0.146706i
$41$	1.90759	−	1.38595i	0.297916	−	0.216449i	−0.428778	−	0.903410i	$-0.641056\pi$
$41$	1.90759	−	1.38595i	0.297916	−	0.216449i	0.726694	+	0.686961i	$0.241056\pi$
$42$	0.635047	−	1.95447i	0.0979898	−	0.301582i
$43$	12.2210			1.86369			0.931845	−	0.362856i	$-0.118198\pi$
$43$	12.2210			1.86369			0.931845	+	0.362856i	$0.118198\pi$
$44$	1.38937	−	4.27603i	0.209455	−	0.644636i
$45$	−1.96045	+	1.07548i	−0.292246	+	0.160323i
$46$	0.234321	+	0.721167i	0.0345488	+	0.106330i
$47$	−2.90011	−	8.92561i	−0.423024	−	1.30193i	−0.904874	−	0.425680i	$-0.860035\pi$
$47$	−2.90011	−	8.92561i	−0.423024	−	1.30193i	0.481849	−	0.876254i	$-0.339965\pi$
$48$	2.83452	+	2.05940i	0.409128	+	0.297249i
$49$	1.00000			0.142857
$50$	−6.53550	−	7.92896i	−0.924259	−	1.12132i
$51$	−0.602198			−0.0843245
$52$	10.7327	+	7.79779i	1.48836	+	1.08136i
$53$	0.449868	+	1.38455i	0.0617941	+	0.190183i	0.977188	−	0.212377i	$-0.0681205\pi$
$53$	0.449868	+	1.38455i	0.0617941	+	0.190183i	−0.915394	+	0.402560i	$0.868121\pi$
$54$	0.635047	+	1.95447i	0.0864189	+	0.265970i
$55$	−3.29363	−	3.09849i	−0.444113	−	0.417800i
$56$	0.141773	−	0.436331i	0.0189452	−	0.0583072i
$57$	−4.66533			−0.617938
$58$	3.66315	−	11.2740i	0.480995	−	1.48035i
$59$	1.23701	−	0.898737i	0.161044	−	0.117006i	−0.504344	−	0.863503i	$-0.668266\pi$
$59$	1.23701	−	0.898737i	0.161044	−	0.117006i	0.665389	+	0.746497i	$0.268266\pi$
$60$	−4.35856	+	2.39105i	−0.562687	+	0.308683i
$61$	−2.65549	−	1.92933i	−0.340001	−	0.247025i	0.404661	−	0.914467i	$-0.367389\pi$
$61$	−2.65549	−	1.92933i	−0.340001	−	0.247025i	−0.744662	+	0.667442i	$0.767389\pi$
$62$	11.7637	−	8.54684i	1.49399	−	1.08545i
$63$	−0.809017	+	0.587785i	−0.101927	+	0.0740540i
$64$	7.82738	+	5.68692i	0.978423	+	0.710866i
$65$	11.6982	−	6.41750i	1.45099	−	0.795993i
$66$	−3.36223	+	2.44281i	−0.413862	+	0.300689i
$67$	−2.82717	+	8.70115i	−0.345394	+	1.06301i	0.615978	+	0.787763i	$0.288761\pi$
$67$	−2.82717	+	8.70115i	−0.345394	+	1.06301i	−0.961372	+	0.275251i	$0.911239\pi$
$68$	−1.33883			−0.162358
$69$	0.114022	−	0.350923i	0.0137266	−	0.0422462i
$70$	−3.34697	−	3.14866i	−0.400039	−	0.376337i
$71$	−2.33304	−	7.18037i	−0.276881	−	0.852153i	−0.988716	−	0.149805i	$-0.952135\pi$
$71$	−2.33304	−	7.18037i	−0.276881	−	0.852153i	0.711834	−	0.702347i	$-0.247865\pi$
$72$	0.141773	+	0.436331i	0.0167081	+	0.0514221i
$73$	−1.44101	−	1.04696i	−0.168658	−	0.122537i	0.500254	−	0.865878i	$-0.333240\pi$
$73$	−1.44101	−	1.04696i	−0.168658	−	0.122537i	−0.668912	+	0.743341i	$0.733240\pi$
$74$	−21.2883			−2.47472
$75$	0.305006	+	4.99069i	0.0352190	+	0.576275i
$76$	−10.3722			−1.18977
$77$	−1.63608	−	1.18868i	−0.186449	−	0.135463i
$78$	−3.78940	−	11.6626i	−0.429065	−	1.32053i
$79$	−0.352284	−	1.08422i	−0.0396350	−	0.121984i	0.929281	−	0.369373i	$-0.120427\pi$
$79$	−0.352284	−	1.08422i	−0.0396350	−	0.121984i	−0.968916	+	0.247389i	$0.920427\pi$
$80$	6.86875	−	3.76811i	0.767949	−	0.421288i
$81$	0.309017	−	0.951057i	0.0343352	−	0.105673i
$82$	−4.84565			−0.535112
$83$	−0.538954	+	1.65873i	−0.0591578	+	0.182069i	−0.976269	−	0.216564i	$-0.930515\pi$
$83$	−0.538954	+	1.65873i	−0.0591578	+	0.182069i	0.917111	+	0.398633i	$0.130515\pi$
$84$	−1.79865	+	1.30679i	−0.196248	+	0.142583i
$85$	−0.574427	+	1.21788i	−0.0623054	+	0.132098i
$86$	−20.3184	−	14.7622i	−2.19099	−	1.59184i
$87$	−4.66666	+	3.39053i	−0.500319	+	0.363503i
$88$	−0.750610	+	0.545350i	−0.0800153	+	0.0581345i
$89$	12.8598	+	9.34318i	1.36313	+	0.990375i	0.998239	+	0.0593259i	$0.0188951\pi$
$89$	12.8598	+	9.34318i	1.36313	+	0.990375i	0.364895	+	0.931049i	$0.381105\pi$
$90$	4.55849	+	0.580023i	0.480507	+	0.0611398i
$91$	4.82750	−	3.50739i	0.506060	−	0.367674i
$92$	0.253499	−	0.780190i	0.0264291	−	0.0813404i
$93$	−7.07560			−0.733706
$94$	−5.95988	+	18.3426i	−0.614714	+	1.89190i
$95$	−4.45018	+	9.43516i	−0.456579	+	0.968027i
$96$	−2.50854	−	7.72048i	−0.256026	−	0.787968i
$97$	−1.40656	−	4.32896i	−0.142815	−	0.439539i	0.853909	−	0.520423i	$-0.174226\pi$
$97$	−1.40656	−	4.32896i	−0.142815	−	0.439539i	−0.996724	+	0.0808837i	$0.974226\pi$
$98$	−1.66257	−	1.20793i	−0.167945	−	0.122019i
$99$	2.02231			0.203249
$100$	0.678103	+	11.0955i	0.0678103	+	1.10955i
$101$	−7.91242			−0.787315			−0.393658	−	0.919257i	$-0.628790\pi$
$101$	−7.91242			−0.787315			−0.393658	+	0.919257i	$0.628790\pi$
$102$	1.00120	+	0.727413i	0.0991334	+	0.0720246i
$103$	−0.964839	−	2.96947i	−0.0950684	−	0.292590i	0.892203	−	0.451634i	$-0.149159\pi$
$103$	−0.964839	−	2.96947i	−0.0950684	−	0.292590i	−0.987271	+	0.159044i	$0.949159\pi$
$104$	−0.845974	−	2.60364i	−0.0829546	−	0.255308i
$105$	0.417028	+	2.19684i	0.0406978	+	0.214389i
$106$	0.924503	−	2.84533i	0.0897957	−	0.276363i
$107$	16.3107			1.57682			0.788408	−	0.615152i	$-0.210905\pi$
$107$	16.3107			1.57682			0.788408	+	0.615152i	$0.210905\pi$
$108$	0.687021	−	2.11443i	0.0661087	−	0.203462i
$109$	−5.92944	+	4.30799i	−0.567938	+	0.412631i	−0.834355	−	0.551227i	$-0.814160\pi$
$109$	−5.92944	+	4.30799i	−0.567938	+	0.412631i	0.266418	+	0.963858i	$0.414160\pi$
$110$	1.73315	+	9.12994i	0.165249	+	0.870505i
$111$	8.38061	+	6.08887i	0.795452	+	0.577930i
$112$	2.83452	−	2.05940i	0.267837	−	0.194595i
$113$	−12.1526	+	8.82939i	−1.14322	+	0.830599i	−0.987565	−	0.157212i	$-0.949749\pi$
$113$	−12.1526	+	8.82939i	−1.14322	+	0.830599i	−0.155657	+	0.987811i	$0.549749\pi$
$114$	7.75645	+	5.63539i	0.726458	+	0.527803i
$115$	−0.600944	−	0.565339i	−0.0560383	−	0.0527181i
$116$	−10.3751	+	7.53798i	−0.963308	+	0.699884i
$117$	−1.84394	+	5.67507i	−0.170473	+	0.524661i
$118$	−3.14223			−0.289265
$119$	−0.186089	+	0.572724i	−0.0170588	+	0.0525015i
$120$	1.01767	+	0.129489i	0.0929002	+	0.0118206i
$121$	−2.13539	−	6.57206i	−0.194127	−	0.597460i
$122$	2.08446	+	6.41529i	0.188718	+	0.580813i
$123$	1.90759	+	1.38595i	0.172002	+	0.124967i
$124$	−15.7308			−1.41267
$125$	10.3841	+	4.14370i	0.928783	+	0.370624i
$126$	2.05505			0.183079
$127$	−9.16714	−	6.66032i	−0.813452	−	0.591007i	0.101377	−	0.994848i	$-0.467675\pi$
$127$	−9.16714	−	6.66032i	−0.813452	−	0.591007i	−0.914829	+	0.403841i	$0.867675\pi$
$128$	−1.12711	−	3.46890i	−0.0996238	−	0.306611i
$129$	3.77651	+	11.6229i	0.332503	+	1.02334i
$130$	−27.2011	−	3.46107i	−2.38569	−	0.303556i
$131$	−6.38215	+	19.6423i	−0.557611	+	1.71615i	0.131334	+	0.991338i	$0.458074\pi$
$131$	−6.38215	+	19.6423i	−0.557611	+	1.71615i	−0.688945	+	0.724813i	$0.741926\pi$
$132$	4.49609			0.391334
$133$	−1.44167	+	4.43699i	−0.125008	+	0.384736i
$134$	15.2108	−	11.0513i	1.31401	−	0.954684i
$135$	−1.62865	−	1.53215i	−0.140172	−	0.131867i
$136$	0.223515	+	0.162393i	0.0191662	+	0.0139251i
$137$	8.42056	−	6.11790i	0.719417	−	0.522687i	−0.166781	−	0.985994i	$-0.553337\pi$
$137$	8.42056	−	6.11790i	0.719417	−	0.522687i	0.886198	+	0.463307i	$0.153337\pi$
$138$	−0.613461	+	0.445706i	−0.0522213	+	0.0379410i
$139$	−6.42809	−	4.67028i	−0.545223	−	0.396128i	0.280798	−	0.959767i	$-0.409401\pi$
$139$	−6.42809	−	4.67028i	−0.545223	−	0.396128i	−0.826021	+	0.563639i	$0.809401\pi$
$140$	0.927157	+	4.88411i	0.0783591	+	0.412783i
$141$	7.59258	−	5.51633i	0.639411	−	0.464559i
$142$	−4.79453	+	14.7560i	−0.402348	+	1.23830i
$143$	−12.0674			−1.00912
$144$	−1.08269	+	3.33218i	−0.0902244	+	0.277682i
$145$	2.40555	+	12.6720i	0.199770	+	1.05235i
$146$	1.13114	+	3.48129i	0.0936137	+	0.288113i
$147$	0.309017	+	0.951057i	0.0254873	+	0.0784418i
$148$	18.6322	+	13.5371i	1.53156	+	1.11274i
$149$	−22.6938			−1.85915			−0.929574	−	0.368636i	$-0.879825\pi$
$149$	−22.6938			−1.85915			−0.929574	+	0.368636i	$0.879825\pi$
$150$	5.52131	−	8.66581i	0.450813	−	0.707561i
$151$	−0.946018			−0.0769859			−0.0384929	−	0.999259i	$-0.512256\pi$
$151$	−0.946018			−0.0769859			−0.0384929	+	0.999259i	$0.512256\pi$
$152$	1.73161	+	1.25809i	0.140452	+	0.102044i
$153$	−0.186089	−	0.572724i	−0.0150444	−	0.0463020i
$154$	1.28426	+	3.95254i	0.103489	+	0.318505i
$155$	−6.74931	+	14.3097i	−0.542118	+	1.14938i
$156$	−4.09954	+	12.6171i	−0.328226	+	1.01018i
$157$	8.41466			0.671563			0.335782	−	0.941940i	$-0.391000\pi$
$157$	8.41466			0.671563			0.335782	+	0.941940i	$0.391000\pi$
$158$	−0.723962	+	2.22813i	−0.0575953	+	0.177260i
$159$	−1.17777	+	0.855700i	−0.0934032	+	0.0678614i
$160$	−18.0068	−	2.29118i	−1.42356	−	0.181134i
$161$	−0.298513	−	0.216883i	−0.0235261	−	0.0170927i
$162$	−1.66257	+	1.20793i	−0.130624	+	0.0949040i
$163$	−16.9438	+	12.3104i	−1.32714	+	0.964224i	−0.327327	+	0.944911i	$0.606148\pi$
$163$	−16.9438	+	12.3104i	−1.32714	+	0.964224i	−0.999813	+	0.0193131i	$0.993852\pi$
$164$	4.24105	+	3.08131i	0.331171	+	0.240610i
$165$	1.92905	−	4.08991i	0.150176	−	0.318399i
$166$	2.89968	−	2.10674i	0.225059	−	0.163515i
$167$	−1.27891	+	3.93609i	−0.0989653	+	0.304584i	−0.988267	−	0.152738i	$-0.951191\pi$
$167$	−1.27891	+	3.93609i	−0.0989653	+	0.304584i	0.889301	+	0.457321i	$0.151191\pi$
$168$	0.458786			0.0353961
$169$	6.98581	−	21.5001i	0.537370	−	1.65386i
$170$	2.42615	−	1.33096i	0.186077	−	0.102080i
$171$	−1.44167	−	4.43699i	−0.110247	−	0.339305i
$172$	8.39611	+	25.8406i	0.640197	+	1.97033i
$173$	−4.52356	−	3.28656i	−0.343920	−	0.249872i	0.402394	−	0.915467i	$-0.368178\pi$
$173$	−4.52356	−	3.28656i	−0.343920	−	0.249872i	−0.746314	+	0.665594i	$0.768178\pi$
$174$	11.8542			0.898664
$175$	4.84068	+	1.25213i	0.365921	+	0.0946521i
$176$	−7.08549			−0.534089
$177$	1.23701	+	0.898737i	0.0929791	+	0.0675532i
$178$	−10.0944	−	31.0674i	−0.756609	−	2.32860i
$179$	−6.01043	−	18.4982i	−0.449241	−	1.38262i	−0.877766	−	0.479090i	$-0.840967\pi$
$179$	−6.01043	−	18.4982i	−0.449241	−	1.38262i	0.428525	−	0.903530i	$-0.359033\pi$
$180$	−3.62089	−	3.40636i	−0.269885	−	0.253895i
$181$	5.89961	−	18.1571i	0.438514	−	1.34961i	−0.450928	−	0.892560i	$-0.648907\pi$
$181$	5.89961	−	18.1571i	0.438514	−	1.34961i	0.889442	−	0.457048i	$-0.151093\pi$
$182$	−12.2628			−0.908976
$183$	1.01431	−	3.12172i	0.0749797	−	0.230764i
$184$	−0.136954	+	0.0995027i	−0.0100964	+	0.00733543i
$185$	20.3083	−	11.1409i	1.49309	−	0.819093i
$186$	11.7637	+	8.54684i	0.862557	+	0.626684i
$187$	0.985244	−	0.715821i	0.0720482	−	0.0523460i
$188$	16.8802	−	12.2642i	1.23111	−	0.894457i
$189$	−0.809017	−	0.587785i	−0.0588473	−	0.0427551i
$190$	18.7958	−	10.3111i	1.36359	−	0.748048i
$191$	7.05427	−	5.12523i	0.510429	−	0.370849i	−0.302557	−	0.953131i	$-0.597840\pi$
$191$	7.05427	−	5.12523i	0.510429	−	0.370849i	0.812986	+	0.582283i	$0.197840\pi$
$192$	−2.98979	+	9.20164i	−0.215770	+	0.664071i
$193$	−18.2348			−1.31257			−0.656283	−	0.754515i	$-0.727872\pi$
$193$	−18.2348			−1.31257			−0.656283	+	0.754515i	$0.727872\pi$
$194$	−2.89057	+	8.89625i	−0.207531	+	0.638714i
$195$	9.71836	+	9.14255i	0.695946	+	0.654712i
$196$	0.687021	+	2.11443i	0.0490729	+	0.151031i
$197$	−4.19509	−	12.9112i	−0.298888	−	0.919882i	−0.981888	−	0.189464i	$-0.939325\pi$
$197$	−4.19509	−	12.9112i	−0.298888	−	0.919882i	0.683000	−	0.730418i	$-0.260675\pi$
$198$	−3.36223	−	2.44281i	−0.238944	−	0.173603i
$199$	−24.7131			−1.75187			−0.875934	−	0.482431i	$-0.839754\pi$
$199$	−24.7131			−1.75187			−0.875934	+	0.482431i	$0.839754\pi$
$200$	1.23262	−	1.93462i	0.0871593	−	0.136798i
$201$	−9.14893			−0.645316
$202$	13.1550	+	9.55765i	0.925581	+	0.672474i
$203$	1.78251	+	5.48599i	0.125107	+	0.385041i
$204$	−0.413723	−	1.27331i	−0.0289664	−	0.0891493i
$205$	4.62257	−	2.53589i	0.322854	−	0.177114i
$206$	−1.98280	+	6.10242i	−0.138148	+	0.425176i
$207$	0.368983			0.0256461
$208$	6.46056	−	19.8836i	0.447959	−	1.37868i
$209$	7.63285	−	5.54559i	0.527975	−	0.383597i
$210$	1.96028	−	4.15614i	0.135272	−	0.286801i
$211$	−6.14364	−	4.46362i	−0.422946	−	0.307288i	0.355876	−	0.934533i	$-0.384182\pi$
$211$	−6.14364	−	4.46362i	−0.422946	−	0.307288i	−0.778822	+	0.627245i	$0.784182\pi$
$212$	−2.61847	+	1.90243i	−0.179838	+	0.130660i
$213$	6.10799	−	4.43771i	0.418512	−	0.304067i
$214$	−27.1178	−	19.7022i	−1.85373	−	1.34682i
$215$	27.1085	+	3.44929i	1.84878	+	0.235240i
$216$	−0.371165	+	0.269667i	−0.0252546	+	0.0183485i
$217$	−2.18648	+	6.72930i	−0.148428	+	0.456815i
$218$	15.0619			1.02012
$219$	0.550418	−	1.69401i	0.0371938	−	0.114471i
$220$	4.28875	−	9.09289i	0.289147	−	0.613043i
$221$	1.11042	+	3.41751i	0.0746948	+	0.229887i
$222$	−6.57845	−	20.2464i	−0.441517	−	1.35885i
$223$	−11.4705	−	8.33380i	−0.768121	−	0.558072i	0.133270	−	0.991080i	$-0.457452\pi$
$223$	−11.4705	−	8.33380i	−0.768121	−	0.558072i	−0.901390	+	0.433008i	$0.857452\pi$
$224$	−8.11779			−0.542393
$225$	−4.65217	+	1.83229i	−0.310145	+	0.122152i
$226$	30.8699			2.05344
$227$	9.99296	+	7.26031i	0.663256	+	0.481884i	0.867761	−	0.496982i	$-0.165558\pi$
$227$	9.99296	+	7.26031i	0.663256	+	0.481884i	−0.204505	+	0.978866i	$0.565558\pi$
$228$	−3.20518	−	9.86453i	−0.212268	−	0.653294i
$229$	8.24298	+	25.3693i	0.544712	+	1.67645i	0.721675	+	0.692233i	$0.243373\pi$
$229$	8.24298	+	25.3693i	0.544712	+	1.67645i	−0.176963	+	0.984218i	$0.556627\pi$
$230$	0.316224	+	1.66582i	0.0208512	+	0.109841i
$231$	0.624927	−	1.92333i	0.0411172	−	0.126546i
$232$	2.64642			0.173746
$233$	−2.63562	+	8.11159i	−0.172665	+	0.531408i	−0.999519	−	0.0310083i	$-0.990128\pi$
$233$	−2.63562	+	8.11159i	−0.172665	+	0.531408i	0.826854	+	0.562416i	$0.190128\pi$
$234$	9.92078	−	7.20787i	0.648542	−	0.471193i
$235$	−3.91379	−	20.6172i	−0.255307	−	1.34492i
$236$	2.75017	+	1.99812i	0.179021	+	0.130066i
$237$	0.922291	−	0.670083i	0.0599092	−	0.0435266i
$238$	1.00120	−	0.727413i	0.0648980	−	0.0471512i
$239$	−10.6022	−	7.70295i	−0.685799	−	0.498262i	0.189477	−	0.981885i	$-0.439321\pi$
$239$	−10.6022	−	7.70295i	−0.685799	−	0.498262i	−0.875277	+	0.483623i	$0.839321\pi$
$240$	5.70625	+	5.36816i	0.368337	+	0.346513i
$241$	−1.05837	+	0.768954i	−0.0681758	+	0.0495327i	−0.621351	−	0.783532i	$-0.713416\pi$
$241$	−1.05837	+	0.768954i	−0.0681758	+	0.0495327i	0.553175	+	0.833065i	$0.313416\pi$
$242$	−4.38835	+	13.5059i	−0.282094	+	0.868195i
$243$	1.00000			0.0641500
$244$	2.25506	−	6.94035i	0.144365	−	0.444310i
$245$	2.21818	+	0.282242i	0.141715	+	0.0180318i
$246$	−1.49739	−	4.60848i	−0.0954699	−	0.293826i
$247$	8.60260	+	26.4761i	0.547370	+	1.68463i
$248$	2.62622	+	1.90806i	0.166765	+	0.121162i
$249$	−1.74409			−0.110527
$250$	−12.2591	−	19.4325i	−0.775330	−	1.22902i
$251$	5.15699			0.325507			0.162753	−	0.986667i	$-0.447963\pi$
$251$	5.15699			0.325507			0.162753	+	0.986667i	$0.447963\pi$
$252$	−1.79865	−	1.30679i	−0.113304	−	0.0823202i
$253$	0.230587	+	0.709675i	0.0144969	+	0.0446169i
$254$	7.19584	+	22.1465i	0.451507	+	1.38960i
$255$	−1.33578	−	0.169966i	−0.0836501	−	0.0106437i
$256$	3.66330	−	11.2745i	0.228957	−	0.704656i
$257$	8.21520			0.512450			0.256225	−	0.966617i	$-0.417521\pi$
$257$	8.21520			0.512450			0.256225	+	0.966617i	$0.417521\pi$
$258$	7.76093	−	23.8857i	0.483174	−	1.48706i
$259$	8.38061	−	6.08887i	0.520746	−	0.378344i
$260$	21.6063	+	20.3262i	1.33997	+	1.26058i
$261$	−4.66666	−	3.39053i	−0.288859	−	0.209868i
$262$	34.3373	−	24.9475i	2.12136	−	1.54126i
$263$	−4.61060	+	3.34980i	−0.284302	+	0.206557i	−0.720791	−	0.693152i	$-0.756221\pi$
$263$	−4.61060	+	3.34980i	−0.284302	+	0.206557i	0.436490	+	0.899709i	$0.356221\pi$
$264$	−0.750610	−	0.545350i	−0.0461969	−	0.0335640i
$265$	0.607111	+	3.19816i	0.0372946	+	0.196462i
$266$	7.75645	−	5.63539i	0.475579	−	0.345528i
$267$	−4.91200	+	15.1176i	−0.300609	+	0.925181i
$268$	−20.3403			−1.24248
$269$	5.41149	−	16.6548i	0.329944	−	1.01546i	−0.639215	−	0.769028i	$-0.720741\pi$
$269$	5.41149	−	16.6548i	0.329944	−	1.01546i	0.969159	−	0.246436i	$-0.0792594\pi$
$270$	0.857016	+	4.51462i	0.0521563	+	0.274751i
$271$	−0.136622	−	0.420479i	−0.00829919	−	0.0255423i	0.946821	−	0.321760i	$-0.104275\pi$
$271$	−0.136622	−	0.420479i	−0.00829919	−	0.0255423i	−0.955120	+	0.296218i	$0.904275\pi$
$272$	0.651995	+	2.00663i	0.0395330	+	0.121670i
$273$	4.82750	+	3.50739i	0.292174	+	0.212277i
$274$	−21.3898			−1.29221
$275$	−6.43136	−	7.80261i	−0.387825	−	0.470515i
$276$	0.820340			0.0493787
$277$	−18.7797	−	13.6442i	−1.12836	−	0.819802i	−0.142906	−	0.989736i	$-0.545645\pi$
$277$	−18.7797	−	13.6442i	−1.12836	−	0.819802i	−0.985455	+	0.169934i	$0.945645\pi$
$278$	5.04580	+	15.5294i	0.302627	+	0.931389i
$279$	−2.18648	−	6.72930i	−0.130901	−	0.402873i
$280$	0.437629	−	0.927848i	0.0261533	−	0.0554495i
$281$	−1.69692	+	5.22259i	−0.101230	+	0.311553i	−0.988827	−	0.149067i	$-0.952373\pi$
$281$	−1.69692	+	5.22259i	−0.101230	+	0.311553i	0.887597	+	0.460620i	$0.152373\pi$
$282$	−19.2866			−1.14850
$283$	−7.94411	+	24.4495i	−0.472229	+	1.45337i	0.377431	+	0.926038i	$0.376808\pi$
$283$	−7.94411	+	24.4495i	−0.472229	+	1.45337i	−0.849659	+	0.527332i	$0.823192\pi$
$284$	13.5796	−	9.86613i	0.805799	−	0.585447i
$285$	−10.3486	−	1.31675i	−0.612995	−	0.0779977i
$286$	20.0629	+	14.5765i	1.18634	+	0.861928i
$287$	1.90759	−	1.38595i	0.112602	−	0.0818100i
$288$	6.56743	−	4.77152i	0.386990	−	0.281164i
$289$	13.4599	+	9.77919i	0.791759	+	0.575247i
$290$	11.3075	−	23.9739i	0.664001	−	1.40780i
$291$	3.68243	−	2.67545i	0.215868	−	0.156837i
$292$	1.22371	−	3.76621i	0.0716125	−	0.220401i
$293$	−1.80905			−0.105686			−0.0528429	−	0.998603i	$-0.516828\pi$
$293$	−1.80905			−0.105686			−0.0528429	+	0.998603i	$0.516828\pi$
$294$	0.635047	−	1.95447i	0.0370367	−	0.113987i
$295$	2.99757	−	1.64443i	0.174525	−	0.0957424i
$296$	−1.46862	−	4.51996i	−0.0853620	−	0.262717i
$297$	0.624927	+	1.92333i	0.0362619	+	0.111603i
$298$	37.7301	+	27.4125i	2.18565	+	1.58796i
$299$	−2.20177			−0.127331
$300$	−10.3429	+	4.07362i	−0.597150	+	0.235191i
$301$	12.2210			0.704409
$302$	1.57283	+	1.14272i	0.0905059	+	0.0657564i
$303$	−2.44507	−	7.52516i	−0.140466	−	0.432309i
$304$	5.05111	+	15.5457i	0.289701	+	0.891609i
$305$	−5.34583	−	5.02909i	−0.306101	−	0.287965i
$306$	−0.382424	+	1.17698i	−0.0218617	+	0.0672834i
$307$	−21.0192			−1.19963			−0.599815	−	0.800138i	$-0.704759\pi$
$307$	−21.0192			−1.19963			−0.599815	+	0.800138i	$0.704759\pi$
$308$	1.38937	−	4.27603i	0.0791666	−	0.243650i
$309$	2.52598	−	1.83523i	0.143698	−	0.104403i
$310$	28.5064	−	15.6382i	1.61905	−	0.888192i
$311$	−5.89911	−	4.28596i	−0.334508	−	0.243034i	0.407833	−	0.913057i	$-0.366285\pi$
$311$	−5.89911	−	4.28596i	−0.334508	−	0.243034i	−0.742341	+	0.670022i	$0.766285\pi$
$312$	2.21479	−	1.60914i	0.125388	−	0.0910996i
$313$	−3.38179	+	2.45701i	−0.191150	+	0.138878i	−0.679244	−	0.733912i	$-0.737692\pi$
$313$	−3.38179	+	2.45701i	−0.191150	+	0.138878i	0.488094	+	0.872791i	$0.337692\pi$
$314$	−13.9900	−	10.1643i	−0.789501	−	0.573606i
$315$	−1.96045	+	1.07548i	−0.110459	+	0.0605963i
$316$	2.05048	−	1.48976i	0.115349	−	0.0838056i
$317$	8.57198	−	26.3818i	0.481450	−	1.48175i	−0.355607	−	0.934636i	$-0.615726\pi$
$317$	8.57198	−	26.3818i	0.481450	−	1.48175i	0.837057	−	0.547115i	$-0.184274\pi$
$318$	2.99176			0.167769
$319$	3.60477	−	11.0944i	0.201829	−	0.621164i
$320$	15.7575	+	14.8239i	0.880870	+	0.828679i
$321$	5.04029	+	15.5124i	0.281321	+	0.865819i
$322$	0.234321	+	0.721167i	0.0130582	+	0.0401891i
$323$	−2.27289	−	1.65135i	−0.126467	−	0.0918837i
$324$	2.22325			0.123514
$325$	27.7601	−	10.9335i	1.53985	−	0.606480i
$326$	43.0404			2.38379
$327$	−5.92944	−	4.30799i	−0.327899	−	0.238232i
$328$	−0.334288	−	1.02883i	−0.0184580	−	0.0568078i
$329$	−2.90011	−	8.92561i	−0.159888	−	0.492085i
$330$	−8.14752	+	4.46963i	−0.448506	+	0.246045i
$331$	3.17249	−	9.76392i	0.174376	−	0.536673i	−0.825229	−	0.564799i	$-0.808954\pi$
$331$	3.17249	−	9.76392i	0.174376	−	0.536673i	0.999604	+	0.0281253i	$0.00895376\pi$
$332$	−3.87754			−0.212808
$333$	−3.20111	+	9.85200i	−0.175420	+	0.539886i
$334$	6.88081	−	4.99920i	0.376501	−	0.273544i
$335$	−8.72702	+	18.5028i	−0.476808	+	1.01092i
$336$	2.83452	+	2.05940i	0.154636	+	0.112350i
$337$	3.32668	−	2.41698i	0.181216	−	0.131661i	−0.493479	−	0.869758i	$-0.664275\pi$
$337$	3.32668	−	2.41698i	0.181216	−	0.131661i	0.674695	+	0.738097i	$0.264275\pi$
$338$	−37.5851	+	27.3072i	−2.04436	+	1.48531i
$339$	−12.1526	−	8.82939i	−0.660039	−	0.479547i
$340$	−2.96978	−	0.377875i	−0.161059	−	0.0204932i
$341$	11.5763	−	8.41064i	0.626889	−	0.455462i
$342$	−2.96270	+	9.11825i	−0.160204	+	0.493059i
$343$	1.00000			0.0539949
$344$	1.73261	−	5.33242i	0.0934159	−	0.287505i
$345$	0.351967	−	0.746231i	0.0189493	−	0.0401757i
$346$	3.55082	+	10.9283i	0.190893	+	0.587508i
$347$	−5.42004	−	16.6812i	−0.290963	−	0.895492i	−0.984548	−	0.175117i	$-0.943970\pi$
$347$	−5.42004	−	16.6812i	−0.290963	−	0.895492i	0.693585	−	0.720375i	$-0.256030\pi$
$348$	−10.3751	−	7.53798i	−0.556166	−	0.404078i
$349$	−16.2936			−0.872178			−0.436089	−	0.899904i	$-0.643637\pi$
$349$	−16.2936			−0.872178			−0.436089	+	0.899904i	$0.643637\pi$
$350$	−6.53550	−	7.92896i	−0.349337	−	0.423821i
$351$	−5.96712			−0.318501
$352$	13.2814	+	9.64948i	0.707899	+	0.514319i
$353$	−8.18014	−	25.1759i	−0.435385	−	1.33998i	−0.892692	−	0.450668i	$-0.851186\pi$
$353$	−8.18014	−	25.1759i	−0.435385	−	1.33998i	0.457307	−	0.889309i	$-0.348814\pi$
$354$	−0.971001	−	2.98843i	−0.0516081	−	0.158834i
$355$	−3.14852	−	16.5859i	−0.167106	−	0.880286i
$356$	−10.9206	+	33.6101i	−0.578790	+	1.78133i
$357$	−0.602198			−0.0318717
$358$	−12.3518	+	38.0148i	−0.652811	+	2.00914i
$359$	−11.8404	+	8.60255i	−0.624912	+	0.454025i	−0.854634	−	0.519231i	$-0.826218\pi$
$359$	−11.8404	+	8.60255i	−0.624912	+	0.454025i	0.229722	+	0.973256i	$0.426218\pi$
$360$	0.191327	+	1.00788i	0.0100838	+	0.0531198i
$361$	−2.23716	−	1.62539i	−0.117745	−	0.0855469i
$362$	−31.7411	+	23.0612i	−1.66827	+	1.21207i
$363$	5.59053	−	4.06176i	0.293427	−	0.213187i
$364$	10.7327	+	7.79779i	0.562548	+	0.408715i
$365$	−2.90093	−	2.72906i	−0.151842	−	0.142845i
$366$	−5.45718	+	3.96487i	−0.285251	+	0.207247i
$367$	−1.17407	+	3.61341i	−0.0612859	+	0.188619i	−0.977012	−	0.213185i	$-0.931616\pi$
$367$	−1.17407	+	3.61341i	−0.0612859	+	0.188619i	0.915726	+	0.401803i	$0.131616\pi$
$368$	−1.29279			−0.0673915
$369$	−0.728636	+	2.24251i	−0.0379313	+	0.116741i
$370$	−47.2214	−	6.00846i	−2.45492	−	0.312365i
$371$	0.449868	+	1.38455i	0.0233560	+	0.0718823i
$372$	−4.86109	−	14.9609i	−0.252036	−	0.775686i
$373$	−4.78936	−	3.47967i	−0.247983	−	0.180171i	0.456849	−	0.889544i	$-0.348978\pi$
$373$	−4.78936	−	3.47967i	−0.247983	−	0.180171i	−0.704833	+	0.709374i	$0.748978\pi$
$374$	−2.50270			−0.129412
$375$	−0.732024	+	11.1563i	−0.0378016	+	0.576111i
$376$	−4.30568			−0.222048
$377$	27.8465	+	20.2317i	1.43417	+	1.04199i
$378$	0.635047	+	1.95447i	0.0326633	+	0.100527i
$379$	2.32791	+	7.16458i	0.119577	+	0.368020i	0.992874	−	0.119168i	$-0.0380227\pi$
$379$	2.32791	+	7.16458i	0.119577	+	0.368020i	−0.873297	+	0.487188i	$0.838023\pi$
$380$	−23.0074	−	2.92747i	−1.18025	−	0.150176i
$381$	3.50154	−	10.7766i	0.179389	−	0.552103i
$382$	−17.9192			−0.916824
$383$	10.4302	−	32.1010i	0.532960	−	1.64028i	−0.215055	−	0.976602i	$-0.568993\pi$
$383$	10.4302	−	32.1010i	0.532960	−	1.64028i	0.748015	−	0.663681i	$-0.231007\pi$
$384$	2.95082	−	2.14390i	0.150584	−	0.109405i
$385$	−3.29363	−	3.09849i	−0.167859	−	0.157913i
$386$	30.3166	+	22.0263i	1.54308	+	1.12111i
$387$	−9.88703	+	7.18334i	−0.502586	+	0.365150i
$388$	8.18696	−	5.94818i	0.415630	−	0.301973i
$389$	21.8623	+	15.8839i	1.10846	+	0.805346i	0.982421	−	0.186679i	$-0.0597723\pi$
$389$	21.8623	+	15.8839i	1.10846	+	0.805346i	0.126043	+	0.992025i	$0.459772\pi$
$390$	−5.11392	−	26.9393i	−0.258953	−	1.36412i
$391$	0.179764	−	0.130606i	0.00909106	−	0.00660504i
$392$	0.141773	−	0.436331i	0.00716060	−	0.0220380i
$393$	−20.6531			−1.04181
$394$	−8.62114	+	26.5331i	−0.434327	+	1.33672i
$395$	−0.475418	−	2.50442i	−0.0239209	−	0.126011i
$396$	1.38937	+	4.27603i	0.0698184	+	0.214879i
$397$	0.677999	+	2.08667i	0.0340278	+	0.104727i	0.966628	−	0.256185i	$-0.0824656\pi$
$397$	0.677999	+	2.08667i	0.0340278	+	0.104727i	−0.932600	+	0.360912i	$0.882466\pi$
$398$	41.0874	+	29.8518i	2.05953	+	1.49633i
$399$	−4.66533			−0.233558
$400$	16.2997	−	6.41971i	0.814983	−	0.320986i
$401$	−18.7855			−0.938102			−0.469051	−	0.883171i	$-0.655404\pi$
$401$	−18.7855			−0.938102			−0.469051	+	0.883171i	$0.655404\pi$
$402$	15.2108	+	11.0513i	0.758644	+	0.551187i
$403$	13.0470	+	40.1546i	0.649918	+	2.00024i
$404$	−5.43600	−	16.7303i	−0.270451	−	0.832363i
$405$	0.953885	−	2.02240i	0.0473989	−	0.100494i
$406$	3.66315	−	11.2740i	0.181799	−	0.559519i
$407$	−20.9491			−1.03841
$408$	−0.0853751	+	0.262758i	−0.00422670	+	0.0130084i
$409$	−12.1946	+	8.85993i	−0.602986	+	0.438095i	−0.846938	−	0.531692i	$-0.821556\pi$
$409$	−12.1946	+	8.85993i	−0.602986	+	0.438095i	0.243951	+	0.969787i	$0.421556\pi$
$410$	−10.7485	−	1.36765i	−0.530832	−	0.0675432i
$411$	8.42056	+	6.11790i	0.415356	+	0.301774i
$412$	5.61588	−	4.08017i	0.276674	−	0.201016i
$413$	1.23701	−	0.898737i	0.0608691	−	0.0442240i
$414$	−0.613461	−	0.445706i	−0.0301500	−	0.0219052i
$415$	−1.66366	+	3.52725i	−0.0816659	+	0.173146i
$416$	−39.1887	+	28.4722i	−1.92138	+	1.39597i
$417$	2.45531	−	7.55667i	0.120237	−	0.370052i
$418$	−19.3889			−0.948340
$419$	5.08879	−	15.6617i	0.248604	−	0.765123i	−0.746419	−	0.665476i	$-0.768229\pi$
$419$	5.08879	−	15.6617i	0.248604	−	0.765123i	0.995023	−	0.0996473i	$-0.0317715\pi$
$420$	−4.35856	+	2.39105i	−0.212676	+	0.116671i
$421$	2.27155	+	6.99112i	0.110709	+	0.340727i	0.991028	−	0.133655i	$-0.0426716\pi$
$421$	2.27155	+	6.99112i	0.110709	+	0.340727i	−0.880319	+	0.474382i	$0.842672\pi$
$422$	4.82252	+	14.8422i	0.234756	+	0.722506i
$423$	7.59258	+	5.51633i	0.369164	+	0.268213i
$424$	0.667902			0.0324362
$425$	−1.61792	+	2.53936i	−0.0784808	+	0.123177i
$426$	−15.5154			−0.751725
$427$	−2.65549	−	1.92933i	−0.128508	−	0.0933666i
$428$	11.2058	+	34.4879i	0.541653	+	1.66704i
$429$	−3.72902	−	11.4767i	−0.180039	−	0.554102i
$430$	−40.9034	−	38.4799i	−1.97254	−	1.85566i
$431$	−9.67256	+	29.7691i	−0.465911	+	1.43393i	0.391923	+	0.919998i	$0.371810\pi$
$431$	−9.67256	+	29.7691i	−0.465911	+	1.43393i	−0.857834	+	0.513927i	$0.828190\pi$
$432$	−3.50367			−0.168570
$433$	5.74354	−	17.6768i	0.276017	−	0.849493i	−0.712932	−	0.701234i	$-0.752633\pi$
$433$	5.74354	−	17.6768i	0.276017	−	0.849493i	0.988949	−	0.148259i	$-0.0473670\pi$
$434$	11.7637	−	8.54684i	0.564676	−	0.410261i
$435$	−11.3085	+	6.20369i	−0.542199	+	0.297444i
$436$	−13.1826	−	9.57773i	−0.631333	−	0.458690i
$437$	1.39266	−	1.01183i	0.0666201	−	0.0484023i
$438$	−2.96136	+	2.15155i	−0.141499	+	0.102805i
$439$	31.8421	+	23.1347i	1.51974	+	1.10416i	0.961615	+	0.274402i	$0.0884800\pi$
$439$	31.8421	+	23.1347i	1.51974	+	1.10416i	0.558128	+	0.829755i	$0.311520\pi$
$440$	−1.81891	+	0.997833i	−0.0867132	+	0.0475698i
$441$	−0.809017	+	0.587785i	−0.0385246	+	0.0279898i
$442$	2.28197	−	7.02318i	0.108542	−	0.334058i
$443$	−3.19609			−0.151851			−0.0759255	−	0.997113i	$-0.524191\pi$
$443$	−3.19609			−0.151851			−0.0759255	+	0.997113i	$0.524191\pi$
$444$	−7.11686	+	21.9034i	−0.337751	+	1.03949i
$445$	25.8883	+	24.3545i	1.22722	+	1.15451i
$446$	9.00388	+	27.7111i	0.426346	+	1.31216i
$447$	−7.01277	−	21.5831i	−0.331692	−	1.02084i
$448$	7.82738	+	5.68692i	0.369809	+	0.268682i
$449$	14.7334			0.695314			0.347657	−	0.937622i	$-0.386977\pi$
$449$	14.7334			0.695314			0.347657	+	0.937622i	$0.386977\pi$
$450$	9.94786	+	2.57319i	0.468946	+	0.121302i
$451$	−4.76843			−0.224537
$452$	−27.0183	−	19.6299i	−1.27083	−	0.923314i
$453$	−0.292336	−	0.899717i	−0.0137351	−	0.0422724i
$454$	−7.84408	−	24.1416i	−0.368141	−	1.13302i
$455$	11.6982	−	6.41750i	0.548421	−	0.300857i
$456$	−0.661415	+	2.03563i	−0.0309736	+	0.0953270i
$457$	−26.4245			−1.23608			−0.618042	−	0.786145i	$-0.712074\pi$
$457$	−26.4245			−1.23608			−0.618042	+	0.786145i	$0.712074\pi$
$458$	16.9398	−	52.1353i	0.791544	−	2.43612i
$459$	0.487188	−	0.353963i	0.0227400	−	0.0165216i
$460$	0.782510	−	1.65906i	0.0364847	−	0.0773539i
$461$	−18.8496	−	13.6950i	−0.877914	−	0.637842i	0.0547847	−	0.998498i	$-0.482553\pi$
$461$	−18.8496	−	13.6950i	−0.877914	−	0.637842i	−0.932699	+	0.360656i	$0.882553\pi$
$462$	−3.36223	+	2.44281i	−0.156425	+	0.113650i
$463$	−30.2922	+	22.0086i	−1.40780	+	1.02283i	−0.414161	+	0.910204i	$0.635925\pi$
$463$	−30.2922	+	22.0086i	−1.40780	+	1.02283i	−0.993638	+	0.112622i	$0.964075\pi$
$464$	16.3504	+	11.8793i	0.759049	+	0.551482i
$465$	−15.6950	−	1.99703i	−0.727838	−	0.0926102i
$466$	14.1801	−	10.3025i	0.656883	−	0.477253i
$467$	0.0689361	−	0.212164i	0.00318998	−	0.00981776i	−0.949449	−	0.313922i	$-0.898357\pi$
$467$	0.0689361	−	0.212164i	0.00318998	−	0.00981776i	0.952639	+	0.304104i	$0.0983570\pi$
$468$	−13.2664			−0.613239
$469$	−2.82717	+	8.70115i	−0.130547	+	0.401782i
$470$	−18.3972	+	39.0052i	−0.848598	+	1.79917i
$471$	2.60027	+	8.00282i	0.119814	+	0.368751i
$472$	−0.216774	−	0.667161i	−0.00997781	−	0.0307086i
$473$	−19.9946	−	14.5269i	−0.919353	−	0.667949i
$474$	−2.34279			−0.107608
$475$	−12.5343	+	19.6729i	−0.575114	+	0.902654i
$476$	−1.33883			−0.0613654
$477$	−1.17777	−	0.855700i	−0.0539264	−	0.0391798i
$478$	8.32231	+	25.6134i	0.380654	+	1.17153i
$479$	8.40555	+	25.8696i	0.384059	+	1.18201i	0.937160	+	0.348899i	$0.113444\pi$
$479$	8.40555	+	25.8696i	0.384059	+	1.18201i	−0.553101	+	0.833114i	$0.686556\pi$
$480$	−3.38535	−	17.8335i	−0.154519	−	0.813982i
$481$	19.1014	−	58.7881i	0.870949	−	2.68051i
$482$	2.68847			0.122456
$483$	0.114022	−	0.350923i	0.00518818	−	0.0159676i
$484$	12.4291	−	9.03029i	0.564961	−	0.410468i
$485$	−1.89820	−	9.99942i	−0.0861930	−	0.454050i
$486$	−1.66257	−	1.20793i	−0.0754159	−	0.0547928i
$487$	4.90963	−	3.56706i	0.222477	−	0.161639i	−0.470964	−	0.882152i	$-0.656094\pi$
$487$	4.90963	−	3.56706i	0.222477	−	0.161639i	0.693441	+	0.720514i	$0.256094\pi$
$488$	−1.21830	+	0.885147i	−0.0551499	+	0.0400687i
$489$	−16.9438	−	12.3104i	−0.766225	−	0.556695i
$490$	−3.34697	−	3.14866i	−0.151200	−	0.142242i
$491$	23.9721	−	17.4168i	1.08185	−	0.786007i	0.103843	−	0.994594i	$-0.466886\pi$
$491$	23.9721	−	17.4168i	1.08185	−	0.786007i	0.978004	+	0.208586i	$0.0668862\pi$
$492$	−1.61994	+	4.98566i	−0.0730325	+	0.224771i
$493$	−3.47366			−0.156446
$494$	17.6788	−	54.4098i	0.795407	−	2.44801i
$495$	4.48585	+	0.570780i	0.201624	+	0.0256547i
$496$	7.66070	+	23.5772i	0.343976	+	1.05865i
$497$	−2.33304	−	7.18037i	−0.104651	−	0.322083i
$498$	2.89968	+	2.10674i	0.129938	+	0.0944053i
$499$	12.2646			0.549039			0.274519	−	0.961582i	$-0.411481\pi$
$499$	12.2646			0.549039			0.274519	+	0.961582i	$0.411481\pi$
$500$	−1.62747	+	24.8033i	−0.0727827	+	1.10924i
$501$	−4.13865			−0.184901
$502$	−8.57388	−	6.22929i	−0.382671	−	0.278027i
$503$	8.93945	+	27.5128i	0.398590	+	1.22673i	0.926130	+	0.377204i	$0.123115\pi$
$503$	8.93945	+	27.5128i	0.398590	+	1.22673i	−0.527540	+	0.849530i	$0.676885\pi$
$504$	0.141773	+	0.436331i	0.00631505	+	0.0194357i
$505$	−17.5512	−	2.23322i	−0.781018	−	0.0993769i
$506$	0.473869	−	1.45842i	0.0210661	−	0.0648347i
$507$	22.6066			1.00399
$508$	7.78478	−	23.9591i	0.345394	−	1.06301i
$509$	6.22623	−	4.52362i	0.275973	−	0.200506i	−0.441186	−	0.897416i	$-0.645442\pi$
$509$	6.22623	−	4.52362i	0.275973	−	0.200506i	0.717159	+	0.696910i	$0.245442\pi$
$510$	2.01553	+	1.89612i	0.0892494	+	0.0839614i
$511$	−1.44101	−	1.04696i	−0.0637466	−	0.0463146i
$512$	−25.6110	+	18.6075i	−1.13186	+	0.822341i
$513$	3.77433	−	2.74221i	0.166641	−	0.121072i
$514$	−13.6584	−	9.92339i	−0.602445	−	0.437702i
$515$	−1.30208	−	6.85914i	−0.0573765	−	0.302250i
$516$	−21.9813	+	15.9704i	−0.967673	+	0.703056i
$517$	−5.86491	+	18.0503i	−0.257938	+	0.793852i
$518$	−21.2883			−0.935355
$519$	1.72785	−	5.31776i	0.0758440	−	0.233424i
$520$	−1.14167	−	6.01413i	−0.0500655	−	0.263737i
$521$	5.45944	+	16.8024i	0.239182	+	0.736127i	0.996539	+	0.0831260i	$0.0264904\pi$
$521$	5.45944	+	16.8024i	0.239182	+	0.736127i	−0.757357	+	0.653001i	$0.773510\pi$
$522$	3.66315	+	11.2740i	0.160332	+	0.493450i
$523$	15.3563	+	11.1570i	0.671485	+	0.487862i	0.870522	−	0.492130i	$-0.163781\pi$
$523$	15.3563	+	11.1570i	0.671485	+	0.487862i	−0.199037	+	0.979992i	$0.563781\pi$
$524$	−45.9169			−2.00589
$525$	0.305006	+	4.99069i	0.0133115	+	0.217812i
$526$	11.7118			0.510658
$527$	−3.44715	−	2.50450i	−0.150160	−	0.109098i
$528$	−2.18954	−	6.73870i	−0.0952873	−	0.293264i
$529$	−7.06532	−	21.7448i	−0.307188	−	0.945427i
$530$	2.85379	−	6.05053i	0.123961	−	0.262818i
$531$	−0.472494	+	1.45419i	−0.0205045	+	0.0631064i
$532$	−10.3722			−0.449691
$533$	4.34786	−	13.3813i	0.188327	−	0.579610i
$534$	26.4275	−	19.2007i	1.14363	−	0.830897i
$535$	36.1802	+	4.60357i	1.56421	+	0.199030i
$536$	3.39577	+	2.46717i	0.146675	+	0.106565i
$537$	15.7355	−	11.4325i	0.679037	−	0.493349i
$538$	−29.1149	+	21.1532i	−1.25523	+	0.911980i
$539$	−1.63608	−	1.18868i	−0.0704710	−	0.0512002i
$540$	2.12072	−	4.49630i	0.0912613	−	0.193490i
$541$	−22.1027	+	16.0585i	−0.950268	+	0.690410i	−0.950870	−	0.309590i	$-0.899808\pi$
$541$	−22.1027	+	16.0585i	−0.950268	+	0.690410i	0.000602254		1.00000i	$0.499808\pi$
$542$	−0.280765	+	0.864107i	−0.0120599	+	0.0371166i
$543$	19.0915			0.819296
$544$	1.51063	−	4.64925i	0.0647679	−	0.199335i
$545$	−14.3685	+	7.88238i	−0.615478	+	0.337644i
$546$	−3.78940	−	11.6626i	−0.162171	−	0.499112i
$547$	−13.8982	−	42.7744i	−0.594245	−	1.82890i	−0.558447	−	0.829540i	$-0.688603\pi$
$547$	−13.8982	−	42.7744i	−0.594245	−	1.82890i	−0.0357983	−	0.999359i	$-0.511397\pi$
$548$	18.7210	+	13.6016i	0.799721	+	0.581032i
$549$	3.28237			0.140088
$550$	1.26759	+	20.7410i	0.0540501	+	0.884401i
$551$	−26.9111			−1.14645
$552$	−0.136954	−	0.0995027i	−0.00582913	−	0.00423511i
$553$	−0.352284	−	1.08422i	−0.0149806	−	0.0461056i
$554$	14.7413	+	45.3691i	0.626298	+	1.92755i
$555$	16.8712	+	15.8716i	0.716142	+	0.673712i
$556$	5.45876	−	16.8003i	0.231503	−	0.712493i
$557$	36.7783			1.55835			0.779173	−	0.626809i	$-0.215639\pi$
$557$	36.7783			1.55835			0.779173	+	0.626809i	$0.215639\pi$
$558$	−4.49334	+	13.8291i	−0.190218	+	0.585431i
$559$	58.9971	−	42.8639i	2.49531	−	1.81295i
$560$	6.86875	−	3.76811i	0.290258	−	0.159232i
$561$	0.985244	+	0.715821i	0.0415970	+	0.0302220i
$562$	9.12978	−	6.63317i	0.385117	−	0.279804i
$563$	−36.5985	+	26.5903i	−1.54244	+	1.12065i	−0.593659	+	0.804716i	$0.702317\pi$
$563$	−36.5985	+	26.5903i	−1.54244	+	1.12065i	−0.948782	+	0.315933i	$0.897683\pi$
$564$	16.8802	+	12.2642i	0.710784	+	0.516415i
$565$	−29.4488	+	16.1552i	−1.23892	+	0.679656i
$566$	42.7409	−	31.0531i	1.79654	−	1.30526i
$567$	0.309017	−	0.951057i	0.0129775	−	0.0399406i
$568$	−3.46378			−0.145337
$569$	−2.81066	+	8.65032i	−0.117829	+	0.362640i	−0.992527	−	0.122029i	$-0.961060\pi$
$569$	−2.81066	+	8.65032i	−0.117829	+	0.362640i	0.874698	+	0.484669i	$0.161060\pi$
$570$	15.6147	+	14.6895i	0.654027	+	0.615277i
$571$	−6.30294	−	19.3985i	−0.263770	−	0.811801i	−0.991974	−	0.126440i	$-0.959645\pi$
$571$	−6.30294	−	19.3985i	−0.263770	−	0.811801i	0.728204	−	0.685360i	$-0.240355\pi$
$572$	−8.29053	−	25.5156i	−0.346644	−	1.06686i
$573$	7.05427	+	5.12523i	0.294696	+	0.214110i
$574$	−4.84565			−0.202253
$575$	−1.17344	−	1.42364i	−0.0489359	−	0.0593698i
$576$	−9.67517			−0.403132
$577$	29.0595	+	21.1130i	1.20976	+	0.878944i	0.995209	−	0.0977677i	$-0.0311702\pi$
$577$	29.0595	+	21.1130i	1.20976	+	0.878944i	0.214554	+	0.976712i	$0.431170\pi$
$578$	−10.5655	−	32.5173i	−0.439467	−	1.35254i
$579$	−5.63485	−	17.3423i	−0.234176	−	0.720721i
$580$	−25.1415	+	13.7923i	−1.04394	+	0.572695i
$581$	−0.538954	+	1.65873i	−0.0223596	+	0.0688157i
$582$	−9.35407			−0.387739
$583$	0.909771	−	2.79999i	0.0376789	−	0.115964i
$584$	−0.661116	+	0.480329i	−0.0273572	+	0.0198761i
$585$	−5.69195	+	12.0679i	−0.235333	+	0.498947i
$586$	3.00768	+	2.18521i	0.124246	+	0.0902701i
$587$	7.15994	−	5.20200i	0.295522	−	0.214710i	−0.430137	−	0.902764i	$-0.641535\pi$
$587$	7.15994	−	5.20200i	0.295522	−	0.214710i	0.725660	+	0.688054i	$0.241535\pi$
$588$	−1.79865	+	1.30679i	−0.0741749	+	0.0538912i
$589$	−26.7057	−	19.4028i	−1.10039	−	0.799478i
$590$	−6.97003	−	0.886869i	−0.286952	−	0.0365118i
$591$	10.9829	−	7.97954i	0.451776	−	0.328234i
$592$	11.2156	−	34.5181i	0.460959	−	1.41869i
$593$	−1.91229			−0.0785281			−0.0392641	−	0.999229i	$-0.512501\pi$
$593$	−1.91229			−0.0785281			−0.0392641	+	0.999229i	$0.512501\pi$
$594$	1.28426	−	3.95254i	0.0526938	−	0.162175i
$595$	−0.574427	+	1.21788i	−0.0235492	+	0.0499284i
$596$	−15.5911	−	47.9845i	−0.638637	−	1.96552i
$597$	−7.63678	−	23.5036i	−0.312553	−	0.961938i
$598$	3.66060	+	2.65958i	0.149693	+	0.108758i
$599$	19.0910			0.780039			0.390019	−	0.920807i	$-0.372468\pi$
$599$	19.0910			0.780039			0.390019	+	0.920807i	$0.372468\pi$
$600$	2.22083	+	0.574459i	0.0906652	+	0.0234522i
$601$	3.20576			0.130765			0.0653827	−	0.997860i	$-0.479173\pi$
$601$	3.20576			0.130765			0.0653827	+	0.997860i	$0.479173\pi$
$602$	−20.3184	−	14.7622i	−0.828115	−	0.601661i
$603$	−2.82717	−	8.70115i	−0.115131	−	0.354338i
$604$	−0.649935	−	2.00029i	−0.0264455	−	0.0813908i
$605$	−2.88178	−	15.1807i	−0.117161	−	0.617185i
$606$	−5.02476	+	15.4646i	−0.204117	+	0.628207i
$607$	32.4152			1.31569			0.657847	−	0.753152i	$-0.271467\pi$
$607$	32.4152			1.31569			0.657847	+	0.753152i	$0.271467\pi$
$608$	11.7031	−	36.0186i	0.474625	−	1.46075i
$609$	−4.66666	+	3.39053i	−0.189103	+	0.137391i
$610$	2.81304	+	14.8186i	0.113897	+	0.599989i
$611$	−45.3059	−	32.9166i	−1.83288	−	1.33166i
$612$	1.08314	−	0.786947i	0.0437833	−	0.0318104i
$613$	23.7030	−	17.2213i	0.957356	−	0.695560i	0.00482092	−	0.999988i	$-0.498465\pi$
$613$	23.7030	−	17.2213i	0.957356	−	0.695560i	0.952535	+	0.304428i	$0.0984654\pi$
$614$	34.9460	+	25.3898i	1.41031	+	1.02465i
$615$	3.84022	+	3.61269i	0.154853	+	0.145678i
$616$	−0.750610	+	0.545350i	−0.0302430	+	0.0219728i
$617$	4.24042	−	13.0507i	0.170713	−	0.525400i	−0.828699	−	0.559695i	$-0.810918\pi$
$617$	4.24042	−	13.0507i	0.170713	−	0.525400i	0.999412	+	0.0342946i	$0.0109184\pi$
$618$	−6.41646			−0.258108
$619$	−5.71826	+	17.5990i	−0.229836	+	0.707363i	0.767928	+	0.640536i	$0.221288\pi$
$619$	−5.71826	+	17.5990i	−0.229836	+	0.707363i	−0.997765	+	0.0668273i	$0.978712\pi$
$620$	−34.8938	−	4.43990i	−1.40137	−	0.178311i
$621$	0.114022	+	0.350923i	0.00457554	+	0.0140821i
$622$	4.63057	+	14.2514i	0.185669	+	0.571431i
$623$	12.8598	+	9.34318i	0.515216	+	0.374326i
$624$	20.9068			0.836942
$625$	21.8643	+	12.1223i	0.874574	+	0.484893i
$626$	8.59037			0.343340
$627$	7.63285	+	5.54559i	0.304827	+	0.221470i
$628$	5.78105	+	17.7923i	0.230689	+	0.709988i
$629$	1.92770	+	5.93285i	0.0768624	+	0.236558i
$630$	4.55849	+	0.580023i	0.181615	+	0.0231087i
$631$	3.64160	−	11.2077i	0.144970	−	0.446171i	−0.852037	−	0.523481i	$-0.824633\pi$
$631$	3.64160	−	11.2077i	0.144970	−	0.446171i	0.997007	+	0.0773097i	$0.0246330\pi$
$632$	−0.523022			−0.0208047
$633$	2.34666	−	7.22228i	0.0932714	−	0.287060i
$634$	−46.1190	+	33.5074i	−1.83162	+	1.33075i
$635$	−18.4546	−	17.3612i	−0.732347	−	0.688956i
$636$	−2.61847	−	1.90243i	−0.103829	−	0.0754364i
$637$	4.82750	−	3.50739i	0.191273	−	0.138968i
$638$	−19.3944	+	14.0909i	−0.767832	+	0.557863i
$639$	6.10799	+	4.43771i	0.241628	+	0.175553i
$640$	−1.52108	−	8.01278i	−0.0601259	−	0.316733i
$641$	−10.4834	+	7.61661i	−0.414068	+	0.300838i	−0.775247	−	0.631659i	$-0.782374\pi$
$641$	−10.4834	+	7.61661i	−0.414068	+	0.300838i	0.361179	+	0.932497i	$0.382374\pi$
$642$	10.3581	−	31.8789i	0.408800	−	1.25816i
$643$	−7.88162			−0.310821			−0.155410	−	0.987850i	$-0.549670\pi$
$643$	−7.88162			−0.310821			−0.155410	+	0.987850i	$0.549670\pi$
$644$	0.253499	−	0.780190i	0.00998926	−	0.0307438i
$645$	5.09652	+	26.8476i	0.200675	+	1.05712i
$646$	1.78413	+	5.49099i	0.0701957	+	0.216040i
$647$	1.37898	+	4.24406i	0.0542132	+	0.166851i	0.974497	−	0.224400i	$-0.0720423\pi$
$647$	1.37898	+	4.24406i	0.0542132	+	0.166851i	−0.920284	+	0.391251i	$0.872042\pi$
$648$	−0.371165	−	0.269667i	−0.0145808	−	0.0105935i
$649$	−3.09215			−0.121378
$650$	−59.3601	−	15.3546i	−2.32829	−	0.602256i
$651$	−7.07560			−0.277315
$652$	−37.6703	−	27.3690i	−1.47528	−	1.07185i
$653$	2.12663	+	6.54508i	0.0832213	+	0.256129i	0.984005	−	0.178138i	$-0.0570074\pi$
$653$	2.12663	+	6.54508i	0.0832213	+	0.256129i	−0.900784	+	0.434267i	$0.857007\pi$
$654$	4.65438	+	14.3247i	0.182001	+	0.560140i
$655$	−19.7007	+	41.7688i	−0.769769	+	1.63204i
$656$	2.55290	−	7.85701i	0.0996739	−	0.306765i
$657$	1.78119			0.0694908
$658$	−5.95988	+	18.3426i	−0.232340	+	0.715070i
$659$	0.615047	−	0.446858i	0.0239588	−	0.0174071i	−0.575741	−	0.817632i	$-0.695286\pi$
$659$	0.615047	−	0.446858i	0.0239588	−	0.0174071i	0.599700	+	0.800225i	$0.295286\pi$
$660$	9.97315	+	1.26899i	0.388204	+	0.0493952i
$661$	−24.6429	−	17.9041i	−0.958499	−	0.696390i	−0.00569729	−	0.999984i	$-0.501814\pi$
$661$	−24.6429	−	17.9041i	−0.958499	−	0.696390i	−0.952802	+	0.303594i	$0.901814\pi$
$662$	−17.0686	+	12.4011i	−0.663391	+	0.481982i
$663$	−2.90711	+	2.11214i	−0.112903	+	0.0820287i
$664$	0.647346	+	0.470324i	0.0251219	+	0.0182521i
$665$	−4.45018	+	9.43516i	−0.172571	+	0.365880i
$666$	17.2226	−	12.5130i	0.667362	−	0.484867i
$667$	0.657714	−	2.02424i	0.0254668	−	0.0783787i
$668$	−9.20125			−0.356007
$669$	4.38134	−	13.4844i	0.169392	−	0.521336i
$670$	36.8594	−	20.2206i	1.42400	−	0.781191i
$671$	2.05124	+	6.31307i	0.0791872	+	0.243713i
$672$	−2.50854	−	7.72048i	−0.0967689	−	0.297824i
$673$	10.5855	+	7.69081i	0.408041	+	0.296459i	0.772808	−	0.634640i	$-0.218852\pi$
$673$	10.5855	+	7.69081i	0.408041	+	0.296459i	−0.364767	+	0.931099i	$0.618852\pi$
$674$	−8.45039			−0.325497
$675$	−3.18021	−	3.85827i	−0.122406	−	0.148505i
$676$	50.2600			1.93308
$677$	18.7465	+	13.6201i	0.720485	+	0.523463i	0.886539	−	0.462653i	$-0.153103\pi$
$677$	18.7465	+	13.6201i	0.720485	+	0.523463i	−0.166054	+	0.986117i	$0.553103\pi$
$678$	9.53933	+	29.3590i	0.366356	+	1.12753i
$679$	−1.40656	−	4.32896i	−0.0539790	−	0.166130i
$680$	0.449963	+	0.423303i	0.0172553	+	0.0162329i
$681$	−3.81697	+	11.7474i	−0.146267	+	0.450162i
$682$	−29.4058			−1.12601
$683$	2.46661	−	7.59143i	0.0943821	−	0.290478i	−0.892710	−	0.450631i	$-0.851199\pi$
$683$	2.46661	−	7.59143i	0.0943821	−	0.290478i	0.987092	+	0.160153i	$0.0511989\pi$
$684$	8.39127	−	6.09661i	0.320848	−	0.233110i
$685$	20.4051	−	11.1940i	0.779638	−	0.427700i
$686$	−1.66257	−	1.20793i	−0.0634774	−	0.0461190i
$687$	−21.5804	+	15.6791i	−0.823344	+	0.598194i
$688$	34.6408	−	25.1680i	1.32067	−	0.959522i
$689$	7.02790	+	5.10607i	0.267742	+	0.194526i
$690$	−1.48657	+	0.815512i	−0.0565926	+	0.0310460i
$691$	7.39633	−	5.37375i	0.281369	−	0.204427i	−0.438145	−	0.898904i	$-0.644364\pi$
$691$	7.39633	−	5.37375i	0.281369	−	0.204427i	0.719515	+	0.694477i	$0.244364\pi$
$692$	3.84143	−	11.8227i	0.146029	−	0.449432i
$693$	2.02231			0.0768211
$694$	−11.1385	+	34.2807i	−0.422811	+	1.30128i
$695$	−12.9405	−	12.1738i	−0.490862	−	0.461779i
$696$	0.817788	+	2.51689i	0.0309982	+	0.0954026i
$697$	0.438783	+	1.35044i	0.0166201	+	0.0511514i
$698$	27.0894	+	19.6816i	1.02535	+	0.744958i
$699$	−8.52903			−0.322598
$700$	0.678103	+	11.0955i	0.0256299	+	0.419372i
$701$	30.6365			1.15712			0.578562	−	0.815638i	$-0.303614\pi$
$701$	30.6365			1.15712			0.578562	+	0.815638i	$0.303614\pi$
$702$	9.92078	+	7.20787i	0.374436	+	0.272044i
$703$	14.9342	+	45.9628i	0.563255	+	1.73352i
$704$	−6.04628	−	18.6085i	−0.227878	−	0.701335i
$705$	18.3987	−	10.0933i	0.692934	−	0.380135i
$706$	−16.8106	+	51.7378i	−0.632676	+	1.94718i
$707$	−7.91242			−0.297577
$708$	−1.05047	+	3.23302i	−0.0394791	+	0.121504i
$709$	19.7387	−	14.3410i	0.741302	−	0.538588i	−0.151816	−	0.988409i	$-0.548512\pi$
$709$	19.7387	−	14.3410i	0.741302	−	0.538588i	0.893119	+	0.449821i	$0.148512\pi$
$710$	−14.7999	+	31.3784i	−0.555431	+	1.17761i
$711$	0.922291	+	0.670083i	0.0345886	+	0.0251301i
$712$	5.89988	−	4.28652i	0.221107	−	0.160644i
$713$	2.11216	−	1.53458i	0.0791011	−	0.0574703i
$714$	1.00120	+	0.727413i	0.0374689	+	0.0272227i
$715$	−26.7676	−	3.40592i	−1.00105	−	0.127374i
$716$	34.9839	−	25.4173i	1.30741	−	0.949890i
$717$	4.04968	−	12.4636i	0.151238	−	0.465463i
$718$	30.0768			1.12246
$719$	4.62177	−	14.2244i	0.172363	−	0.530479i	−0.827140	−	0.561996i	$-0.810034\pi$
$719$	4.62177	−	14.2244i	0.172363	−	0.530479i	0.999503	+	0.0315168i	$0.0100338\pi$
$720$	−3.34209	+	7.08582i	−0.124552	+	0.264073i
$721$	−0.964839	−	2.96947i	−0.0359325	−	0.110589i
$722$	1.75608	+	5.40466i	0.0653546	+	0.201141i
$723$	−1.05837	−	0.768954i	−0.0393613	−	0.0285977i
$724$	42.4452			1.57746
$725$	1.75937	+	28.7878i	0.0653413	+	1.06915i
$726$	−14.2010			−0.527048
$727$	1.65832	+	1.20484i	0.0615038	+	0.0446852i	0.618112	−	0.786090i	$-0.287898\pi$
$727$	1.65832	+	1.20484i	0.0615038	+	0.0446852i	−0.556609	+	0.830775i	$0.687898\pi$
$728$	−0.845974	−	2.60364i	−0.0313539	−	0.0964974i
$729$	0.309017	+	0.951057i	0.0114451	+	0.0352243i
$730$	1.52651	+	8.04139i	0.0564986	+	0.297625i
$731$	−2.27420	+	6.99928i	−0.0841145	+	0.258878i
$732$	7.29751			0.269724
$733$	1.70924	−	5.26050i	0.0631323	−	0.194301i	−0.914515	−	0.404551i	$-0.867428\pi$
$733$	1.70924	−	5.26050i	0.0631323	−	0.194301i	0.977648	+	0.210250i	$0.0674278\pi$
$734$	6.31673	−	4.58937i	0.233155	−	0.169397i
$735$	0.417028	+	2.19684i	0.0153823	+	0.0810315i
$736$	2.42327	+	1.76061i	0.0893229	+	0.0648969i
$737$	14.9684	−	10.8752i	0.551367	−	0.400592i
$738$	3.92021	−	2.84820i	0.144305	−	0.104844i
$739$	−14.8856	−	10.8150i	−0.547575	−	0.397837i	0.279315	−	0.960199i	$-0.409893\pi$
$739$	−14.8856	−	10.8150i	−0.547575	−	0.397837i	−0.826891	+	0.562363i	$0.809893\pi$
$740$	37.5088	+	35.2865i	1.37885	+	1.29716i
$741$	−22.5219	+	16.3631i	−0.827362	+	0.601114i
$742$	0.924503	−	2.84533i	0.0339396	−	0.104455i
$743$	26.0028			0.953951			0.476976	−	0.878917i	$-0.341733\pi$
$743$	26.0028			0.953951			0.476976	+	0.878917i	$0.341733\pi$
$744$	−1.00313	+	3.08731i	−0.0367764	+	0.113186i
$745$	−50.3390	−	6.40514i	−1.84428	−	0.234666i
$746$	3.75946	+	11.5704i	0.137643	+	0.423623i
$747$	−0.538954	−	1.65873i	−0.0197193	−	0.0606897i
$748$	2.19044	+	1.59145i	0.0800904	+	0.0581891i
$749$	16.3107			0.595981
$750$	14.6931	−	17.6640i	0.536518	−	0.644999i
$751$	−8.89838			−0.324706			−0.162353	−	0.986733i	$-0.551908\pi$
$751$	−8.89838			−0.324706			−0.162353	+	0.986733i	$0.551908\pi$
$752$	−26.6019	−	19.3274i	−0.970070	−	0.704797i
$753$	1.59360	+	4.90459i	0.0580740	+	0.178733i
$754$	−21.8584	−	67.2734i	−0.796038	−	2.44995i
$755$	−2.09844	−	0.267006i	−0.0763701	−	0.00971735i
$756$	0.687021	−	2.11443i	0.0249867	−	0.0769012i
$757$	−35.6722			−1.29653			−0.648265	−	0.761415i	$-0.724505\pi$
$757$	−35.6722			−1.29653			−0.648265	+	0.761415i	$0.724505\pi$
$758$	4.78399	−	14.7236i	0.173762	−	0.534785i
$759$	−0.603685	+	0.438603i	−0.0219124	+	0.0159203i
$760$	3.48594	+	3.27940i	0.126448	+	0.118956i
$761$	36.1159	+	26.2397i	1.30920	+	0.951189i	1.00000		0.000191298i	$6.08921e-5\pi$
$761$	36.1159	+	26.2397i	1.30920	+	0.951189i	0.309199	+	0.950997i	$0.399939\pi$
$762$	−18.8390	+	13.6873i	−0.682464	+	0.495839i
$763$	−5.92944	+	4.30799i	−0.214660	+	0.155960i
$764$	15.6834	+	11.3947i	0.567405	+	0.412244i
$765$	−0.251133	−	1.32293i	−0.00907975	−	0.0478306i
$766$	−56.1168	+	40.7712i	−2.02758	+	1.47312i
$767$	2.81943	−	8.67732i	0.101804	−	0.313320i
$768$	11.8547			0.427770
$769$	−13.2097	+	40.6553i	−0.476354	+	1.46607i	0.367769	+	0.929917i	$0.380122\pi$
$769$	−13.2097	+	40.6553i	−0.476354	+	1.46607i	−0.844123	+	0.536150i	$0.819878\pi$
$770$	1.73315	+	9.12994i	0.0624583	+	0.329020i
$771$	2.53864	+	7.81312i	0.0914267	+	0.281383i
$772$	−12.5277	−	38.5562i	−0.450880	−	1.38767i
$773$	−24.8032	−	18.0206i	−0.892108	−	0.648154i	0.0443190	−	0.999017i	$-0.485888\pi$
$773$	−24.8032	−	18.0206i	−0.892108	−	0.648154i	−0.936427	+	0.350863i	$0.885888\pi$
$774$	25.1149			0.902736
$775$	−19.0100	+	29.8366i	−0.682860	+	1.07176i
$776$	−2.08827			−0.0749646
$777$	8.38061	+	6.08887i	0.300653	+	0.218437i
$778$	−17.1611	−	52.8163i	−0.615254	−	1.89356i
$779$	3.39933	+	10.4621i	0.121794	+	0.374842i
$780$	−12.6546	+	26.8300i	−0.453108	+	0.960667i
$781$	−4.71813	+	14.5209i	−0.168828	+	0.519599i
$782$	−0.456634			−0.0163292
$783$	1.78251	−	5.48599i	0.0637016	−	0.196053i
$784$	2.83452	−	2.05940i	0.101233	−	0.0735501i
$785$	18.6653	+	2.37497i	0.666192	+	0.0847664i
$786$	34.3373	+	24.9475i	1.22477	+	0.889848i
$787$	22.7932	−	16.5602i	0.812490	−	0.590309i	−0.102061	−	0.994778i	$-0.532544\pi$
$787$	22.7932	−	16.5602i	0.812490	−	0.590309i	0.914552	+	0.404469i	$0.132544\pi$
$788$	24.4177	−	17.7405i	0.869844	−	0.631979i
$789$	−4.61060	−	3.34980i	−0.164142	−	0.119256i
$790$	−2.23475	+	4.73806i	−0.0795089	+	0.168573i
$791$	−12.1526	+	8.82939i	−0.432097	+	0.313937i
$792$	0.286708	−	0.882395i	0.0101877	−	0.0313546i
$793$	−19.5863			−0.695529
$794$	1.39332	−	4.28821i	0.0494472	−	0.152183i
$795$	−2.85402	+	1.56568i	−0.101222	+	0.0555291i
$796$	−16.9784	−	52.2543i	−0.601785	−	1.85210i
$797$	−6.26031	−	19.2673i	−0.221752	−	0.682481i	−0.998605	−	0.0527998i	$-0.983185\pi$
$797$	−6.26031	−	19.2673i	−0.221752	−	0.682481i	0.776854	−	0.629681i	$-0.216815\pi$
$798$	7.75645	+	5.63539i	0.274575	+	0.199491i
$799$	5.65159			0.199939
$800$	−39.2956	−	10.1645i	−1.38931	−	0.359370i
$801$	−15.8956			−0.561642
$802$	31.2323	+	22.6916i	1.10285	+	0.801267i
$803$	1.11311	+	3.42581i	0.0392809	+	0.120894i
$804$	−6.28551	−	19.3448i	−0.221673	−	0.682239i
$805$	−0.600944	−	0.565339i	−0.0211805	−	0.0199256i
$806$	26.8123	−	82.5198i	0.944423	−	2.90664i
$807$	17.5119			0.616450
$808$	−1.12176	+	3.45244i	−0.0394635	+	0.121456i
$809$	−10.9623	+	7.96454i	−0.385412	+	0.280018i	−0.763573	−	0.645722i	$-0.776557\pi$
$809$	−10.9623	+	7.96454i	−0.385412	+	0.280018i	0.378161	+	0.925740i	$0.376557\pi$
$810$	−4.02882	+	2.21016i	−0.141558	+	0.0776572i
$811$	−10.5576	−	7.67058i	−0.370729	−	0.269350i	0.386784	−	0.922170i	$-0.373586\pi$
$811$	−10.5576	−	7.67058i	−0.370729	−	0.269350i	−0.757513	+	0.652820i	$0.773586\pi$
$812$	−10.3751	+	7.53798i	−0.364096	+	0.264531i
$813$	0.357681	−	0.259870i	0.0125444	−	0.00911405i
$814$	34.8294	+	25.3050i	1.22077	+	0.886941i
$815$	−41.0590	+	22.5245i	−1.43823	+	0.788997i
$816$	−1.70694	+	1.24017i	−0.0597550	+	0.0434145i
$817$	−17.6186	+	54.2246i	−0.616398	+	1.89708i
$818$	30.9767			1.08307
$819$	−1.84394	+	5.67507i	−0.0644326	+	0.198303i
$820$	8.53776	+	8.03191i	0.298152	+	0.280486i
$821$	−10.6144	−	32.6677i	−0.370445	−	1.14011i	−0.946501	−	0.322701i	$-0.895409\pi$
$821$	−10.6144	−	32.6677i	−0.370445	−	1.14011i	0.576056	−	0.817410i	$-0.304591\pi$
$822$	−6.60981	−	20.3429i	−0.230544	−	0.709541i
$823$	35.4082	+	25.7256i	1.23425	+	0.896737i	0.997202	−	0.0747602i	$-0.0238191\pi$
$823$	35.4082	+	25.7256i	1.23425	+	0.896737i	0.237051	+	0.971497i	$0.423819\pi$
$824$	−1.43246			−0.0499021
$825$	5.43333	−	8.52772i	0.189164	−	0.296897i
$826$	−3.14223			−0.109332
$827$	13.4966	+	9.80586i	0.469323	+	0.340983i	0.797177	−	0.603745i	$-0.206326\pi$
$827$	13.4966	+	9.80586i	0.469323	+	0.340983i	−0.327854	+	0.944728i	$0.606326\pi$
$828$	0.253499	+	0.780190i	0.00880970	+	0.0271135i
$829$	−4.29016	−	13.2038i	−0.149004	−	0.458586i	0.848501	−	0.529195i	$-0.177506\pi$
$829$	−4.29016	−	13.2038i	−0.149004	−	0.458586i	−0.997504	+	0.0706087i	$0.977506\pi$
$830$	7.02663	−	3.85473i	0.243898	−	0.133799i
$831$	7.17320	−	22.0768i	0.248835	−	0.765837i
$832$	57.7330			2.00153
$833$	−0.186089	+	0.572724i	−0.00644761	+	0.0198437i
$834$	−13.2101	+	9.59767i	−0.457427	+	0.332340i
$835$	−3.94780	+	8.37001i	−0.136619	+	0.289656i
$836$	16.9697	+	12.3292i	0.586910	+	0.426415i
$837$	5.72428	−	4.15893i	0.197860	−	0.143754i
$838$	−27.3787	+	19.8918i	−0.945782	+	0.687151i
$839$	9.39609	+	6.82666i	0.324389	+	0.235682i	0.738046	−	0.674750i	$-0.235749\pi$
$839$	9.39609	+	6.82666i	0.324389	+	0.235682i	−0.413657	+	0.910433i	$0.635749\pi$
$840$	1.01767	+	0.129489i	0.0351130	+	0.00446778i
$841$	−3.45726	+	2.51185i	−0.119216	+	0.0866154i
$842$	4.66817	−	14.3671i	0.160876	−	0.495124i
$843$	−5.49135			−0.189132
$844$	5.21721	−	16.0569i	0.179584	−	0.552702i
$845$	21.5641	−	45.7195i	0.741826	−	1.57280i
$846$	−5.95988	−	18.3426i	−0.204905	−	0.630632i
$847$	−2.13539	−	6.57206i	−0.0733730	−	0.225819i
$848$	4.12651	+	2.99809i	0.141705	+	0.102955i
$849$	−25.7077			−0.882286
$850$	5.75729	−	2.26754i	0.197474	−	0.0777761i
$851$	−3.82229			−0.131027
$852$	13.5796	+	9.86613i	0.465228	+	0.338008i
$853$	3.36230	+	10.3481i	0.115123	+	0.354312i	0.991973	−	0.126453i	$-0.0403591\pi$
$853$	3.36230	+	10.3481i	0.115123	+	0.354312i	−0.876850	+	0.480765i	$0.840359\pi$
$854$	2.08446	+	6.41529i	0.0713286	+	0.219527i
$855$	−1.94557	−	10.2490i	−0.0665372	−	0.350507i
$856$	2.31241	−	7.11687i	0.0790366	−	0.243250i
$857$	26.3298			0.899410			0.449705	−	0.893177i	$-0.351529\pi$
$857$	26.3298			0.899410			0.449705	+	0.893177i	$0.351529\pi$
$858$	−7.66333	+	23.5853i	−0.261622	+	0.805189i
$859$	−39.0174	+	28.3478i	−1.33126	+	0.967215i	−0.331539	+	0.943441i	$0.607568\pi$
$859$	−39.0174	+	28.3478i	−1.33126	+	0.967215i	−0.999717	+	0.0237733i	$0.992432\pi$
$860$	11.3308	+	59.6889i	0.386378	+	2.03537i
$861$	1.90759	+	1.38595i	0.0650107	+	0.0472330i
$862$	52.0403	−	37.8095i	1.77250	−	1.28780i
$863$	14.6680	−	10.6569i	0.499305	−	0.362766i	−0.309447	−	0.950917i	$-0.600144\pi$
$863$	14.6680	−	10.6569i	0.499305	−	0.362766i	0.808751	+	0.588151i	$0.200144\pi$
$864$	6.56743	+	4.77152i	0.223429	+	0.162330i
$865$	−9.10648	−	8.56693i	−0.309630	−	0.291284i
$866$	−30.9014	+	22.4512i	−1.05007	+	0.762922i
$867$	−5.14123	+	15.8231i	−0.174605	+	0.537380i
$868$	−15.7308			−0.533939
$869$	−0.712426	+	2.19262i	−0.0241674	+	0.0743795i
$870$	26.2948	+	3.34575i	0.891476	+	0.113432i
$871$	16.8701	+	51.9208i	0.571621	+	1.75927i
$872$	1.03908	+	3.19796i	0.0351876	+	0.108296i
$873$	3.68243	+	2.67545i	0.124632	+	0.0905501i
$874$	−3.53762			−0.119662
$875$	10.3841	+	4.14370i	0.351047	+	0.140083i
$876$	3.96002			0.133797
$877$	−6.41499	−	4.66077i	−0.216619	−	0.157383i	0.474184	−	0.880426i	$-0.342743\pi$
$877$	−6.41499	−	4.66077i	−0.216619	−	0.157383i	−0.690803	+	0.723043i	$0.742743\pi$
$878$	−24.9948	−	76.9262i	−0.843535	−	2.59613i
$879$	−0.559027	−	1.72051i	−0.0188555	−	0.0580313i
$880$	−15.7169	−	1.99982i	−0.529817	−	0.0674140i
$881$	−15.2403	+	46.9049i	−0.513460	+	1.58027i	0.272608	+	0.962125i	$0.412114\pi$
$881$	−15.2403	+	46.9049i	−0.513460	+	1.58027i	−0.786067	+	0.618141i	$0.787886\pi$
$882$	2.05505			0.0691973
$883$	−10.3049	+	31.7153i	−0.346789	+	1.06731i	0.613831	+	0.789438i	$0.289628\pi$
$883$	−10.3049	+	31.7153i	−0.346789	+	1.06731i	−0.960619	+	0.277868i	$0.910372\pi$
$884$	−6.46323	+	4.69581i	−0.217382	+	0.157937i
$885$	2.49024	+	2.34270i	0.0837087	+	0.0787490i
$886$	5.31374	+	3.86066i	0.178519	+	0.129701i
$887$	−44.7303	+	32.4984i	−1.50190	+	1.09119i	−0.532277	+	0.846570i	$0.678663\pi$
$887$	−44.7303	+	32.4984i	−1.50190	+	1.09119i	−0.969619	+	0.244621i	$0.921337\pi$
$888$	3.84490	−	2.79349i	0.129027	−	0.0937433i
$889$	−9.16714	−	6.66032i	−0.307456	−	0.223380i
$890$	−13.6227	−	71.7624i	−0.456635	−	2.40548i
$891$	−1.63608	+	1.18868i	−0.0548108	+	0.0398223i
$892$	9.74079	−	29.9791i	0.326146	−	1.00377i
$893$	43.7838			1.46517
$894$	−14.4116	+	44.3544i	−0.481996	+	1.48343i
$895$	−8.11127	−	42.7288i	−0.271130	−	1.42827i
$896$	−1.12711	−	3.46890i	−0.0376543	−	0.115888i
$897$	−0.680383	−	2.09400i	−0.0227173	−	0.0699167i
$898$	−24.4954	−	17.7970i	−0.817423	−	0.593893i
$899$	−40.8143			−1.36123
$900$	−7.07039	−	8.57790i	−0.235680	−	0.285930i
$901$	−0.876682			−0.0292065
$902$	7.92787	+	5.75993i	0.263969	+	0.191785i
$903$	3.77651	+	11.6229i	0.125674	+	0.386786i
$904$	2.12963	+	6.55433i	0.0708305	+	0.217994i
$905$	18.2111	−	38.6107i	0.605358	−	1.28346i
$906$	−0.600766	+	1.84897i	−0.0199591	+	0.0614278i
$907$	12.1451			0.403272			0.201636	−	0.979461i	$-0.435374\pi$
$907$	12.1451			0.403272			0.201636	+	0.979461i	$0.435374\pi$
$908$	−8.48607	+	26.1174i	−0.281620	+	0.866738i
$909$	6.40128	−	4.65080i	0.212317	−	0.154257i
$910$	−27.2011	−	3.46107i	−0.901706	−	0.114733i
$911$	18.2897	+	13.2882i	0.605964	+	0.440259i	0.847991	−	0.530011i	$-0.177812\pi$
$911$	18.2897	+	13.2882i	0.605964	+	0.440259i	−0.242027	+	0.970270i	$0.577812\pi$
$912$	−13.2240	+	9.60779i	−0.437890	+	0.318146i
$913$	2.85347	−	2.07317i	0.0944361	−	0.0686119i
$914$	43.9326	+	31.9189i	1.45316	+	1.05578i
$915$	3.13100	−	6.63826i	0.103508	−	0.219454i
$916$	−47.9786	+	34.8585i	−1.58526	+	1.15176i
$917$	−6.38215	+	19.6423i	−0.210757	+	0.648644i
$918$	−1.23755			−0.0408452
$919$	4.62728	−	14.2413i	0.152640	−	0.469777i	−0.845274	−	0.534333i	$-0.820563\pi$
$919$	4.62728	−	14.2413i	0.152640	−	0.469777i	0.997914	+	0.0645554i	$0.0205629\pi$
$920$	−0.331872	+	0.182061i	−0.0109415	+	0.00600238i
$921$	−6.49530	−	19.9905i	−0.214027	−	0.658709i
$922$	14.7962	+	45.5381i	0.487287	+	1.49972i
$923$	−36.4471	−	26.4804i	−1.19967	−	0.871612i
$924$	4.49609			0.147910
$925$	48.1919	−	18.9806i	1.58454	−	0.624080i
$926$	76.9479			2.52866
$927$	2.52598	+	1.83523i	0.0829641	+	0.0602769i
$928$	−14.4700	−	44.5341i	−0.475002	−	1.46190i
$929$	13.4479	+	41.3882i	0.441210	+	1.35790i	0.886587	+	0.462561i	$0.153070\pi$
$929$	13.4479	+	41.3882i	0.441210	+	1.35790i	−0.445377	+	0.895343i	$0.646930\pi$
$930$	23.6818	+	22.2787i	0.776557	+	0.730546i
$931$	−1.44167	+	4.43699i	−0.0472487	+	0.145416i
$932$	−18.9622			−0.621126
$933$	2.25326	−	6.93482i	0.0737684	−	0.227036i
$934$	−0.370890	+	0.269468i	−0.0121359	+	0.00881725i
$935$	2.38749	−	1.30975i	0.0780792	−	0.0428333i
$936$	2.21479	+	1.60914i	0.0723927	+	0.0525964i
$937$	41.0368	−	29.8149i	1.34061	−	0.974012i	0.341191	−	0.939994i	$-0.389170\pi$
$937$	41.0368	−	29.8149i	1.34061	−	0.974012i	0.999421	−	0.0340180i	$-0.0108304\pi$
$938$	15.2108	−	11.0513i	0.496649	−	0.360837i
$939$	−3.38179	−	2.45701i	−0.110360	−	0.0801815i
$940$	40.9048	−	22.4399i	1.33417	−	0.731908i
$941$	7.36762	−	5.35289i	0.240178	−	0.174499i	−0.461185	−	0.887304i	$-0.652575\pi$
$941$	7.36762	−	5.35289i	0.240178	−	0.174499i	0.701362	+	0.712805i	$0.252575\pi$
$942$	5.34370	−	16.4462i	0.174107	−	0.535847i
$943$	−0.870031			−0.0283321
$944$	1.65546	−	5.09499i	0.0538807	−	0.165828i
$945$	−1.62865	−	1.53215i	−0.0529800	−	0.0498410i
$946$	15.6950	+	48.3042i	0.510288	+	1.57050i
$947$	−16.9431	−	52.1454i	−0.550576	−	1.69450i	−0.707350	−	0.706864i	$-0.750109\pi$
$947$	−16.9431	−	52.1454i	−0.550576	−	1.69450i	0.156774	−	0.987635i	$-0.449891\pi$
$948$	2.05048	+	1.48976i	0.0665965	+	0.0483852i
$949$	−10.6286			−0.345018
$950$	44.6027	−	17.5670i	1.44710	−	0.569950i
$951$	27.7395			0.899515
$952$	0.223515	+	0.162393i	0.00724416	+	0.00526319i
$953$	−16.5276	−	50.8666i	−0.535380	−	1.64773i	−0.742826	−	0.669484i	$-0.766515\pi$
$953$	−16.5276	−	50.8666i	−0.535380	−	1.64773i	0.207446	−	0.978246i	$-0.433485\pi$
$954$	0.924503	+	2.84533i	0.0299319	+	0.0921209i
$955$	17.0942	−	9.37769i	0.553156	−	0.303455i
$956$	9.00344	−	27.7097i	0.291192	−	0.896197i
$957$	11.6653			0.377085
$958$	17.2739	−	53.1635i	0.558093	−	1.71763i
$959$	8.42056	−	6.11790i	0.271914	−	0.197557i
$960$	−9.22900	+	19.5671i	−0.297865	+	0.631525i
$961$	−15.4232	−	11.2056i	−0.497523	−	0.361472i
$962$	−102.769	+	74.6664i	−3.31342	+	2.40734i
$963$	−13.1956	+	9.58720i	−0.425224	+	0.308943i
$964$	−2.35303	−	1.70957i	−0.0757859	−	0.0550617i
$965$	−40.4480	−	5.14662i	−1.30207	−	0.165675i
$966$	−0.613461	+	0.445706i	−0.0197378	+	0.0143403i
$967$	0.753107	−	2.31783i	0.0242183	−	0.0745362i	−0.938217	−	0.346048i	$-0.887524\pi$
$967$	0.753107	−	2.31783i	0.0242183	−	0.0745362i	0.962435	+	0.271512i	$0.0875235\pi$
$968$	−3.17034			−0.101898
$969$	0.868167	−	2.67194i	0.0278896	−	0.0858352i
$970$	−8.92271	+	18.9177i	−0.286491	+	0.607410i
$971$	7.57501	+	23.3135i	0.243094	+	0.748166i	0.995944	+	0.0899739i	$0.0286784\pi$
$971$	7.57501	+	23.3135i	0.243094	+	0.748166i	−0.752850	+	0.658192i	$0.771322\pi$
$972$	0.687021	+	2.11443i	0.0220362	+	0.0678205i
$973$	−6.42809	−	4.67028i	−0.206075	−	0.149722i
$974$	−12.4714			−0.399609
$975$	18.9767	+	23.0228i	0.607741	+	0.737320i
$976$	−11.5003			−0.368116
$977$	−33.8314	−	24.5800i	−1.08236	−	0.786383i	−0.104270	−	0.994549i	$-0.533251\pi$
$977$	−33.8314	−	24.5800i	−1.08236	−	0.786383i	−0.978093	+	0.208166i	$0.933251\pi$
$978$	13.3002	+	40.9339i	0.425294	+	1.30892i
$979$	−9.93357	−	30.5724i	−0.317478	−	0.977097i
$980$	0.927157	+	4.88411i	0.0296169	+	0.156017i
$981$	2.26485	−	6.97048i	0.0723109	−	0.222550i
$982$	−60.8937			−1.94319
$983$	10.8821	−	33.4917i	0.347086	−	1.06822i	−0.613372	−	0.789794i	$-0.710187\pi$
$983$	10.8821	−	33.4917i	0.347086	−	1.06822i	0.960458	−	0.278426i	$-0.0898126\pi$
$984$	0.875177	−	0.635853i	0.0278996	−	0.0202703i
$985$	−5.66141	−	29.8234i	−0.180387	−	0.950251i
$986$	5.77522	+	4.19594i	0.183920	+	0.133626i
$987$	7.59258	−	5.51633i	0.241674	−	0.175587i
$988$	−50.0717	+	36.3792i	−1.59299	+	1.15738i
$989$	−3.64814	−	2.65053i	−0.116004	−	0.0842820i
$990$	−6.76859	−	6.36756i	−0.215120	−	0.202374i
$991$	6.00878	−	4.36563i	0.190875	−	0.138679i	−0.488243	−	0.872707i	$-0.662362\pi$
$991$	6.00878	−	4.36563i	0.190875	−	0.138679i	0.679119	+	0.734029i	$0.262362\pi$
$992$	17.7494	−	54.6271i	0.563544	−	1.73441i
$993$	10.2664			0.325794
$994$	−4.79453	+	14.7560i	−0.152073	+	0.468033i
$995$	−54.8183	−	6.97509i	−1.73786	−	0.221125i
$996$	−1.19823	−	3.68776i	−0.0379673	−	0.116851i
$997$	−4.87954	−	15.0177i	−0.154536	−	0.475614i	0.843577	−	0.537008i	$-0.180446\pi$
$997$	−4.87954	−	15.0177i	−0.154536	−	0.475614i	−0.998114	+	0.0613936i	$0.980446\pi$
$998$	−20.3908	−	14.8148i	−0.645460	−	0.468954i
$999$	−10.3590			−0.327744

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	525.2.n.c.316.1	yes	24
25.11	even	5	inner	525.2.n.c.211.1	✓	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
525.2.n.c.211.1	✓	24	25.11	even	5	inner
525.2.n.c.316.1	yes	24	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 525 = 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	525.n (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.66257 - 1.20793i) q^{2} +(0.309017 + 0.951057i) q^{3} +(0.687021 + 2.11443i) q^{4} +(2.21818 + 0.282242i) q^{5} +(0.635047 - 1.95447i) q^{6} +1.00000 q^{7} +(0.141773 - 0.436331i) q^{8} +(-0.809017 + 0.587785i) q^{9} +O(q^{10})\)	\(q+(-1.66257 - 1.20793i) q^{2} +(0.309017 + 0.951057i) q^{3} +(0.687021 + 2.11443i) q^{4} +(2.21818 + 0.282242i) q^{5} +(0.635047 - 1.95447i) q^{6} +1.00000 q^{7} +(0.141773 - 0.436331i) q^{8} +(-0.809017 + 0.587785i) q^{9} +(-3.34697 - 3.14866i) q^{10} +(-1.63608 - 1.18868i) q^{11} +(-1.79865 + 1.30679i) q^{12} +(4.82750 - 3.50739i) q^{13} +(-1.66257 - 1.20793i) q^{14} +(0.417028 + 2.19684i) q^{15} +(2.83452 - 2.05940i) q^{16} +(-0.186089 + 0.572724i) q^{17} +2.05505 q^{18} +(-1.44167 + 4.43699i) q^{19} +(0.927157 + 4.88411i) q^{20} +(0.309017 + 0.951057i) q^{21} +(1.28426 + 3.95254i) q^{22} +(-0.298513 - 0.216883i) q^{23} +0.458786 q^{24} +(4.84068 + 1.25213i) q^{25} -12.2628 q^{26} +(-0.809017 - 0.587785i) q^{27} +(0.687021 + 2.11443i) q^{28} +(1.78251 + 5.48599i) q^{29} +(1.96028 - 4.15614i) q^{30} +(-2.18648 + 6.72930i) q^{31} -8.11779 q^{32} +(0.624927 - 1.92333i) q^{33} +(1.00120 - 0.727413i) q^{34} +(2.21818 + 0.282242i) q^{35} +(-1.79865 - 1.30679i) q^{36} +(8.38061 - 6.08887i) q^{37} +(7.75645 - 5.63539i) q^{38} +(4.82750 + 3.50739i) q^{39} +(0.437629 - 0.927848i) q^{40} +(1.90759 - 1.38595i) q^{41} +(0.635047 - 1.95447i) q^{42} +12.2210 q^{43} +(1.38937 - 4.27603i) q^{44} +(-1.96045 + 1.07548i) q^{45} +(0.234321 + 0.721167i) q^{46} +(-2.90011 - 8.92561i) q^{47} +(2.83452 + 2.05940i) q^{48} +1.00000 q^{49} +(-6.53550 - 7.92896i) q^{50} -0.602198 q^{51} +(10.7327 + 7.79779i) q^{52} +(0.449868 + 1.38455i) q^{53} +(0.635047 + 1.95447i) q^{54} +(-3.29363 - 3.09849i) q^{55} +(0.141773 - 0.436331i) q^{56} -4.66533 q^{57} +(3.66315 - 11.2740i) q^{58} +(1.23701 - 0.898737i) q^{59} +(-4.35856 + 2.39105i) q^{60} +(-2.65549 - 1.92933i) q^{61} +(11.7637 - 8.54684i) q^{62} +(-0.809017 + 0.587785i) q^{63} +(7.82738 + 5.68692i) q^{64} +(11.6982 - 6.41750i) q^{65} +(-3.36223 + 2.44281i) q^{66} +(-2.82717 + 8.70115i) q^{67} -1.33883 q^{68} +(0.114022 - 0.350923i) q^{69} +(-3.34697 - 3.14866i) q^{70} +(-2.33304 - 7.18037i) q^{71} +(0.141773 + 0.436331i) q^{72} +(-1.44101 - 1.04696i) q^{73} -21.2883 q^{74} +(0.305006 + 4.99069i) q^{75} -10.3722 q^{76} +(-1.63608 - 1.18868i) q^{77} +(-3.78940 - 11.6626i) q^{78} +(-0.352284 - 1.08422i) q^{79} +(6.86875 - 3.76811i) q^{80} +(0.309017 - 0.951057i) q^{81} -4.84565 q^{82} +(-0.538954 + 1.65873i) q^{83} +(-1.79865 + 1.30679i) q^{84} +(-0.574427 + 1.21788i) q^{85} +(-20.3184 - 14.7622i) q^{86} +(-4.66666 + 3.39053i) q^{87} +(-0.750610 + 0.545350i) q^{88} +(12.8598 + 9.34318i) q^{89} +(4.55849 + 0.580023i) q^{90} +(4.82750 - 3.50739i) q^{91} +(0.253499 - 0.780190i) q^{92} -7.07560 q^{93} +(-5.95988 + 18.3426i) q^{94} +(-4.45018 + 9.43516i) q^{95} +(-2.50854 - 7.72048i) q^{96} +(-1.40656 - 4.32896i) q^{97} +(-1.66257 - 1.20793i) q^{98} +2.02231 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + q^{2} - 6 q^{3} - 9 q^{4} - q^{5} + q^{6} + 24 q^{7} + 9 q^{8} - 6 q^{9}+O(q^{10}) \) 24 * q + q^2 - 6 * q^3 - 9 * q^4 - q^5 + q^6 + 24 * q^7 + 9 * q^8 - 6 * q^9	\( 24 q + q^{2} - 6 q^{3} - 9 q^{4} - q^{5} + q^{6} + 24 q^{7} + 9 q^{8} - 6 q^{9} - 16 q^{10} + 2 q^{11} + q^{12} + 8 q^{13} + q^{14} - 6 q^{15} + 13 q^{16} + 12 q^{17} - 4 q^{18} + 19 q^{19} + 11 q^{20} - 6 q^{21} - 19 q^{22} - 6 q^{24} + 9 q^{25} - 14 q^{26} - 6 q^{27} - 9 q^{28} + 5 q^{29} - 6 q^{30} + 17 q^{31} - 26 q^{32} + 7 q^{33} - 7 q^{34} - q^{35} + q^{36} + 22 q^{37} - 16 q^{38} + 8 q^{39} + 3 q^{40} + 37 q^{41} + q^{42} + 8 q^{43} + 13 q^{44} + 4 q^{45} + 24 q^{46} - 24 q^{47} + 13 q^{48} + 24 q^{49} - 21 q^{50} - 8 q^{51} + 23 q^{52} - 24 q^{53} + q^{54} - 55 q^{55} + 9 q^{56} - 26 q^{57} + 8 q^{58} - 39 q^{60} + 24 q^{62} - 6 q^{63} - q^{64} - 34 q^{65} + 16 q^{66} + 34 q^{67} + 22 q^{68} + 10 q^{69} - 16 q^{70} - 24 q^{71} + 9 q^{72} + 46 q^{73} + 10 q^{74} + 24 q^{75} - 20 q^{76} + 2 q^{77} - 14 q^{78} + 10 q^{79} + 6 q^{80} - 6 q^{81} - 78 q^{82} + 42 q^{83} + q^{84} - 22 q^{85} - 96 q^{86} - 10 q^{87} - 39 q^{88} + 29 q^{89} + 14 q^{90} + 8 q^{91} + 42 q^{92} - 58 q^{93} + 54 q^{94} - 42 q^{95} + 9 q^{96} - 32 q^{97} + q^{98} - 18 q^{99}+O(q^{100}) \) 24 * q + q^2 - 6 * q^3 - 9 * q^4 - q^5 + q^6 + 24 * q^7 + 9 * q^8 - 6 * q^9 - 16 * q^10 + 2 * q^11 + q^12 + 8 * q^13 + q^14 - 6 * q^15 + 13 * q^16 + 12 * q^17 - 4 * q^18 + 19 * q^19 + 11 * q^20 - 6 * q^21 - 19 * q^22 - 6 * q^24 + 9 * q^25 - 14 * q^26 - 6 * q^27 - 9 * q^28 + 5 * q^29 - 6 * q^30 + 17 * q^31 - 26 * q^32 + 7 * q^33 - 7 * q^34 - q^35 + q^36 + 22 * q^37 - 16 * q^38 + 8 * q^39 + 3 * q^40 + 37 * q^41 + q^42 + 8 * q^43 + 13 * q^44 + 4 * q^45 + 24 * q^46 - 24 * q^47 + 13 * q^48 + 24 * q^49 - 21 * q^50 - 8 * q^51 + 23 * q^52 - 24 * q^53 + q^54 - 55 * q^55 + 9 * q^56 - 26 * q^57 + 8 * q^58 - 39 * q^60 + 24 * q^62 - 6 * q^63 - q^64 - 34 * q^65 + 16 * q^66 + 34 * q^67 + 22 * q^68 + 10 * q^69 - 16 * q^70 - 24 * q^71 + 9 * q^72 + 46 * q^73 + 10 * q^74 + 24 * q^75 - 20 * q^76 + 2 * q^77 - 14 * q^78 + 10 * q^79 + 6 * q^80 - 6 * q^81 - 78 * q^82 + 42 * q^83 + q^84 - 22 * q^85 - 96 * q^86 - 10 * q^87 - 39 * q^88 + 29 * q^89 + 14 * q^90 + 8 * q^91 + 42 * q^92 - 58 * q^93 + 54 * q^94 - 42 * q^95 + 9 * q^96 - 32 * q^97 + q^98 - 18 * q^99

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