LMFDB - Embedded newform 418.2.m.b.189.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [418,2,Mod(151,418)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(418, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([3, 5]))

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

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

chi := DirichletCharacter("418.151");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 418 = 2 \cdot 11 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	418.m (of order $10$, 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:	$3.33774680449$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$10$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			189.8
Character	$\chi$	$=$	418.189
Dual form			418.2.m.b.303.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.309017 + 0.951057i) q^{2} +(0.943373 + 1.29844i) q^{3} +(-0.809017 - 0.587785i) q^{4} +(-0.757060 - 2.32999i) q^{5} +(-1.52641 + 0.495961i) q^{6} +(-2.75444 + 3.79116i) q^{7} +(0.809017 - 0.587785i) q^{8} +(0.131053 - 0.403339i) q^{9} +O(q^{10})$	\(q+(-0.309017 + 0.951057i) q^{2} +(0.943373 + 1.29844i) q^{3} +(-0.809017 - 0.587785i) q^{4} +(-0.757060 - 2.32999i) q^{5} +(-1.52641 + 0.495961i) q^{6} +(-2.75444 + 3.79116i) q^{7} +(0.809017 - 0.587785i) q^{8} +(0.131053 - 0.403339i) q^{9} +2.44990 q^{10} +(-1.86579 + 2.74205i) q^{11} -1.60496i q^{12} +(-0.993792 + 3.05858i) q^{13} +(-2.75444 - 3.79116i) q^{14} +(2.31117 - 3.18105i) q^{15} +(0.309017 + 0.951057i) q^{16} +(-6.01824 + 1.95544i) q^{17} +(0.343101 + 0.249277i) q^{18} +(-1.66403 + 4.02877i) q^{19} +(-0.757060 + 2.32999i) q^{20} -7.52107 q^{21} +(-2.03128 - 2.62181i) q^{22} -0.141672 q^{23} +(1.52641 + 0.495961i) q^{24} +(-0.810634 + 0.588960i) q^{25} +(-2.60178 - 1.89030i) q^{26} +(5.22657 - 1.69822i) q^{27} +(4.45678 - 1.44810i) q^{28} +(-1.90294 - 1.38257i) q^{29} +(2.31117 + 3.18105i) q^{30} +(7.44405 + 2.41872i) q^{31} -1.00000 q^{32} +(-5.32053 + 0.164153i) q^{33} -6.32795i q^{34} +(10.9187 + 3.54769i) q^{35} +(-0.343101 + 0.249277i) q^{36} +(-2.80820 + 3.86516i) q^{37} +(-3.31737 - 2.82755i) q^{38} +(-4.90890 + 1.59500i) q^{39} +(-1.98201 - 1.44001i) q^{40} +(7.41151 - 5.38478i) q^{41} +(2.32414 - 7.15296i) q^{42} -6.62826i q^{43} +(3.12119 - 1.12168i) q^{44} -1.03899 q^{45} +(0.0437791 - 0.134738i) q^{46} +(-4.37990 + 3.18219i) q^{47} +(-0.943373 + 1.29844i) q^{48} +(-4.62285 - 14.2277i) q^{49} +(-0.309635 - 0.952958i) q^{50} +(-8.21648 - 5.96962i) q^{51} +(2.60178 - 1.89030i) q^{52} +(9.91555 + 3.22176i) q^{53} +5.49554i q^{54} +(7.80146 + 2.27138i) q^{55} +4.68613i q^{56} +(-6.80093 + 1.63998i) q^{57} +(1.90294 - 1.38257i) q^{58} +(6.81633 - 9.38187i) q^{59} +(-3.73955 + 1.21505i) q^{60} +(-5.30656 + 1.72421i) q^{61} +(-4.60068 + 6.33229i) q^{62} +(1.16815 + 1.60782i) q^{63} +(0.309017 - 0.951057i) q^{64} +7.87882 q^{65} +(1.48801 - 5.11085i) q^{66} +14.8066i q^{67} +(6.01824 + 1.95544i) q^{68} +(-0.133650 - 0.183953i) q^{69} +(-6.74810 + 9.28796i) q^{70} +(-13.3336 + 4.33236i) q^{71} +(-0.131053 - 0.403339i) q^{72} +(0.815469 - 1.12240i) q^{73} +(-2.80820 - 3.86516i) q^{74} +(-1.52946 - 0.496952i) q^{75} +(3.71428 - 2.28125i) q^{76} +(-5.25634 - 14.6263i) q^{77} -5.16152i q^{78} +(-2.69471 + 8.29347i) q^{79} +(1.98201 - 1.44001i) q^{80} +(6.10634 + 4.43652i) q^{81} +(2.83095 + 8.71275i) q^{82} +(3.80677 - 1.23690i) q^{83} +(6.08467 + 4.42077i) q^{84} +(9.11234 + 12.5421i) q^{85} +(6.30385 + 2.04825i) q^{86} -3.77513i q^{87} +(0.102278 + 3.31505i) q^{88} +3.81235i q^{89} +(0.321066 - 0.988139i) q^{90} +(-8.85822 - 12.1923i) q^{91} +(0.114615 + 0.0832728i) q^{92} +(3.88195 + 11.9474i) q^{93} +(-1.67297 - 5.14889i) q^{94} +(10.6468 + 0.827162i) q^{95} +(-0.943373 - 1.29844i) q^{96} +(0.0710011 + 0.0230697i) q^{97} +14.9599 q^{98} +(0.861457 + 1.11190i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q + 10 q^{2} - 10 q^{4} + 2 q^{5} + 5 q^{6} - 5 q^{7} + 10 q^{8} + 8 q^{9}+O(q^{10}) $ 40 * q + 10 * q^2 - 10 * q^4 + 2 * q^5 + 5 * q^6 - 5 * q^7 + 10 * q^8 + 8 * q^9	$ 40 q + 10 q^{2} - 10 q^{4} + 2 q^{5} + 5 q^{6} - 5 q^{7} + 10 q^{8} + 8 q^{9} - 2 q^{10} + 4 q^{11} - 8 q^{13} - 5 q^{14} - 30 q^{15} - 10 q^{16} - 15 q^{17} - 13 q^{18} + 11 q^{19} + 2 q^{20} - 4 q^{22} + 6 q^{23} - 5 q^{24} - 36 q^{25} - 2 q^{26} + 45 q^{27} + 2 q^{29} - 30 q^{30} - 40 q^{32} - 27 q^{33} - 5 q^{35} + 13 q^{36} + 14 q^{38} + 30 q^{39} + 3 q^{40} + 8 q^{41} + 20 q^{42} - 6 q^{44} + 18 q^{45} - q^{46} - 8 q^{47} + 31 q^{49} - 9 q^{50} - 41 q^{51} + 2 q^{52} + 40 q^{53} - 31 q^{55} - 10 q^{57} - 2 q^{58} - 35 q^{59} - 20 q^{60} + 5 q^{61} + 30 q^{62} - 25 q^{63} - 10 q^{64} - 8 q^{65} - 48 q^{66} + 15 q^{68} + 60 q^{69} + 10 q^{70} - 50 q^{71} - 8 q^{72} + 10 q^{73} + 35 q^{75} + 11 q^{76} - 64 q^{77} + 42 q^{79} - 3 q^{80} + 11 q^{81} + 7 q^{82} + 25 q^{83} + 20 q^{84} - 45 q^{85} + 40 q^{86} + 6 q^{88} + 22 q^{90} + 70 q^{91} - 4 q^{92} - 18 q^{93} - 7 q^{94} - 5 q^{95} + 15 q^{97} + 74 q^{98} + 50 q^{99}+O(q^{100}) $ 40 * q + 10 * q^2 - 10 * q^4 + 2 * q^5 + 5 * q^6 - 5 * q^7 + 10 * q^8 + 8 * q^9 - 2 * q^10 + 4 * q^11 - 8 * q^13 - 5 * q^14 - 30 * q^15 - 10 * q^16 - 15 * q^17 - 13 * q^18 + 11 * q^19 + 2 * q^20 - 4 * q^22 + 6 * q^23 - 5 * q^24 - 36 * q^25 - 2 * q^26 + 45 * q^27 + 2 * q^29 - 30 * q^30 - 40 * q^32 - 27 * q^33 - 5 * q^35 + 13 * q^36 + 14 * q^38 + 30 * q^39 + 3 * q^40 + 8 * q^41 + 20 * q^42 - 6 * q^44 + 18 * q^45 - q^46 - 8 * q^47 + 31 * q^49 - 9 * q^50 - 41 * q^51 + 2 * q^52 + 40 * q^53 - 31 * q^55 - 10 * q^57 - 2 * q^58 - 35 * q^59 - 20 * q^60 + 5 * q^61 + 30 * q^62 - 25 * q^63 - 10 * q^64 - 8 * q^65 - 48 * q^66 + 15 * q^68 + 60 * q^69 + 10 * q^70 - 50 * q^71 - 8 * q^72 + 10 * q^73 + 35 * q^75 + 11 * q^76 - 64 * q^77 + 42 * q^79 - 3 * q^80 + 11 * q^81 + 7 * q^82 + 25 * q^83 + 20 * q^84 - 45 * q^85 + 40 * q^86 + 6 * q^88 + 22 * q^90 + 70 * q^91 - 4 * q^92 - 18 * q^93 - 7 * q^94 - 5 * q^95 + 15 * q^97 + 74 * q^98 + 50 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/418\mathbb{Z}\right)^\times$.

$n$	$287$	$343$
$\chi(n)$	$-1$	$e\left(\frac{1}{10}\right)$

Coefficient data

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

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

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

$2$	−0.309017	+	0.951057i	−0.218508	+	0.672499i
$2$	−0.309017	+	0.951057i	−0.218508	+	0.672499i
$3$	0.943373	+	1.29844i	0.544657	+	0.749656i	0.989275	−	0.146064i	$-0.0466607\pi$
$3$	0.943373	+	1.29844i	0.544657	+	0.749656i	−0.444618	+	0.895720i	$0.646661\pi$
$4$	−0.809017	−	0.587785i	−0.404508	−	0.293893i
$5$	−0.757060	−	2.32999i	−0.338568	−	1.04200i	−0.964938	−	0.262478i	$-0.915460\pi$
$5$	−0.757060	−	2.32999i	−0.338568	−	1.04200i	0.626370	−	0.779526i	$-0.284540\pi$
$6$	−1.52641	+	0.495961i	−0.623154	+	0.202475i
$7$	−2.75444	+	3.79116i	−1.04108	+	1.43292i	−0.144787	+	0.989463i	$0.546250\pi$
$7$	−2.75444	+	3.79116i	−1.04108	+	1.43292i	−0.896293	+	0.443462i	$0.853750\pi$
$8$	0.809017	−	0.587785i	0.286031	−	0.207813i
$9$	0.131053	−	0.403339i	0.0436843	−	0.134446i
$10$	2.44990			0.774726
$11$	−1.86579	+	2.74205i	−0.562557	+	0.826758i
$11$	−1.86579	+	2.74205i	−0.562557	+	0.826758i
$12$		−	1.60496i		−	0.463313i
$13$	−0.993792	+	3.05858i	−0.275628	+	0.848297i	0.713424	+	0.700732i	$0.247143\pi$
$13$	−0.993792	+	3.05858i	−0.275628	+	0.848297i	−0.989052	+	0.147564i	$0.952857\pi$
$14$	−2.75444	−	3.79116i	−0.736155	−	1.01323i
$15$	2.31117	−	3.18105i	0.596741	−	0.821344i
$16$	0.309017	+	0.951057i	0.0772542	+	0.237764i
$17$	−6.01824	+	1.95544i	−1.45964	+	0.474265i	−0.927959	−	0.372681i	$-0.878438\pi$
$17$	−6.01824	+	1.95544i	−1.45964	+	0.474265i	−0.531678	+	0.846946i	$0.678438\pi$
$18$	0.343101	+	0.249277i	0.0808696	+	0.0587552i
$19$	−1.66403	+	4.02877i	−0.381755	+	0.924263i
$19$	−1.66403	+	4.02877i	−0.381755	+	0.924263i
$20$	−0.757060	+	2.32999i	−0.169284	+	0.521002i
$21$	−7.52107			−1.64123
$22$	−2.03128	−	2.62181i	−0.433071	−	0.558972i
$23$	−0.141672			−0.0295407			−0.0147703	−	0.999891i	$-0.504702\pi$
$23$	−0.141672			−0.0295407			−0.0147703	+	0.999891i	$0.504702\pi$
$24$	1.52641	+	0.495961i	0.311577	+	0.101238i
$25$	−0.810634	+	0.588960i	−0.162127	+	0.117792i
$26$	−2.60178	−	1.89030i	−0.510251	−	0.370719i
$27$	5.22657	−	1.69822i	1.00585	−	0.326822i
$28$	4.45678	−	1.44810i	0.842252	−	0.273664i
$29$	−1.90294	−	1.38257i	−0.353367	−	0.256736i	0.396913	−	0.917856i	$-0.370081\pi$
$29$	−1.90294	−	1.38257i	−0.353367	−	0.256736i	−0.750280	+	0.661120i	$0.770081\pi$
$30$	2.31117	+	3.18105i	0.421960	+	0.580778i
$31$	7.44405	+	2.41872i	1.33699	+	0.434415i	0.888297	−	0.459270i	$-0.151889\pi$
$31$	7.44405	+	2.41872i	1.33699	+	0.434415i	0.448695	+	0.893685i	$0.351889\pi$
$32$	−1.00000			−0.176777
$33$	−5.32053	+	0.164153i	−0.926185	+	0.0285753i
$34$		−	6.32795i		−	1.08523i
$35$	10.9187	+	3.54769i	1.84559	+	0.599668i
$36$	−0.343101	+	0.249277i	−0.0571834	+	0.0415462i
$37$	−2.80820	+	3.86516i	−0.461665	+	0.635428i	−0.974853	−	0.222849i	$-0.928464\pi$
$37$	−2.80820	+	3.86516i	−0.461665	+	0.635428i	0.513188	+	0.858276i	$0.328464\pi$
$38$	−3.31737	−	2.82755i	−0.538149	−	0.458689i
$39$	−4.90890	+	1.59500i	−0.786053	+	0.255404i
$40$	−1.98201	−	1.44001i	−0.313383	−	0.227686i
$41$	7.41151	−	5.38478i	1.15748	−	0.840961i	0.168026	−	0.985783i	$-0.446261\pi$
$41$	7.41151	−	5.38478i	1.15748	−	0.840961i	0.989458	+	0.144822i	$0.0462608\pi$
$42$	2.32414	−	7.15296i	0.358622	−	1.10373i
$43$		−	6.62826i		−	1.01080i	−0.862885	−	0.505400i	$-0.831345\pi$
$43$		−	6.62826i		−	1.01080i	0.862885	−	0.505400i	$-0.168655\pi$
$44$	3.12119	−	1.12168i	0.470537	−	0.169099i
$45$	−1.03899			−0.154884
$46$	0.0437791	−	0.134738i	0.00645487	−	0.0198661i
$47$	−4.37990	+	3.18219i	−0.638875	+	0.464170i	−0.859463	−	0.511197i	$-0.829202\pi$
$47$	−4.37990	+	3.18219i	−0.638875	+	0.464170i	0.220589	+	0.975367i	$0.429202\pi$
$48$	−0.943373	+	1.29844i	−0.136164	+	0.187414i
$49$	−4.62285	−	14.2277i	−0.660407	−	2.03252i
$50$	−0.309635	−	0.952958i	−0.0437890	−	0.134769i
$51$	−8.21648	−	5.96962i	−1.15054	−	0.835914i
$52$	2.60178	−	1.89030i	0.360802	−	0.262138i
$53$	9.91555	+	3.22176i	1.36201	+	0.442543i	0.896712	−	0.442614i	$-0.145949\pi$
$53$	9.91555	+	3.22176i	1.36201	+	0.442543i	0.465294	+	0.885156i	$0.345949\pi$
$54$			5.49554i			0.747849i
$55$	7.80146	+	2.27138i	1.05195	+	0.306273i
$56$			4.68613i			0.626211i
$57$	−6.80093	+	1.63998i	−0.900805	+	0.217221i
$58$	1.90294	−	1.38257i	0.249868	−	0.181540i
$59$	6.81633	−	9.38187i	0.887410	−	1.22142i	−0.0869025	−	0.996217i	$-0.527697\pi$
$59$	6.81633	−	9.38187i	0.887410	−	1.22142i	0.974313	−	0.225199i	$-0.0723031\pi$
$60$	−3.73955	+	1.21505i	−0.482774	+	0.156863i
$61$	−5.30656	+	1.72421i	−0.679435	+	0.220762i	−0.628348	−	0.777932i	$-0.716269\pi$
$61$	−5.30656	+	1.72421i	−0.679435	+	0.220762i	−0.0510872	+	0.998694i	$0.516269\pi$
$62$	−4.60068	+	6.33229i	−0.584287	+	0.804202i
$63$	1.16815	+	1.60782i	0.147173	+	0.202566i
$64$	0.309017	−	0.951057i	0.0386271	−	0.118882i
$65$	7.87882			0.977247
$66$	1.48801	−	5.11085i	0.183162	−	0.629102i
$67$			14.8066i			1.80892i	0.426560	+	0.904459i	$0.359725\pi$
$67$			14.8066i			1.80892i	−0.426560	+	0.904459i	$0.640275\pi$
$68$	6.01824	+	1.95544i	0.729819	+	0.237133i
$69$	−0.133650	−	0.183953i	−0.0160895	−	0.0221453i
$70$	−6.74810	+	9.28796i	−0.806552	+	1.11012i
$71$	−13.3336	+	4.33236i	−1.58241	+	0.514157i	−0.962677	−	0.270654i	$-0.912760\pi$
$71$	−13.3336	+	4.33236i	−1.58241	+	0.514157i	−0.619736	+	0.784811i	$0.712760\pi$
$72$	−0.131053	−	0.403339i	−0.0154447	−	0.0475339i
$73$	0.815469	−	1.12240i	0.0954435	−	0.131367i	−0.758624	−	0.651528i	$-0.774128\pi$
$73$	0.815469	−	1.12240i	0.0954435	−	0.131367i	0.854068	+	0.520161i	$0.174128\pi$
$74$	−2.80820	−	3.86516i	−0.326447	−	0.449315i
$75$	−1.52946	−	0.496952i	−0.176607	−	0.0573831i
$76$	3.71428	−	2.28125i	0.426058	−	0.261677i
$77$	−5.25634	−	14.6263i	−0.599015	−	1.66682i
$78$		−	5.16152i		−	0.584427i
$79$	−2.69471	+	8.29347i	−0.303179	+	0.933088i	0.677172	+	0.735825i	$0.263205\pi$
$79$	−2.69471	+	8.29347i	−0.303179	+	0.933088i	−0.980351	+	0.197263i	$0.936795\pi$
$80$	1.98201	−	1.44001i	0.221595	−	0.160998i
$81$	6.10634	+	4.43652i	0.678483	+	0.492946i
$82$	2.83095	+	8.71275i	0.312626	+	0.962163i
$83$	3.80677	−	1.23690i	0.417848	−	0.135767i	−0.0925448	−	0.995709i	$-0.529500\pi$
$83$	3.80677	−	1.23690i	0.417848	−	0.135767i	0.510392	+	0.859942i	$0.329500\pi$
$84$	6.08467	+	4.42077i	0.663892	+	0.482346i
$85$	9.11234	+	12.5421i	0.988372	+	1.36038i
$86$	6.30385	+	2.04825i	0.679762	+	0.220868i
$87$		−	3.77513i		−	0.404737i
$88$	0.102278	+	3.31505i	0.0109029	+	0.353385i
$89$			3.81235i			0.404109i	0.979374	+	0.202054i	$0.0647618\pi$
$89$			3.81235i			0.404109i	−0.979374	+	0.202054i	$0.935238\pi$
$90$	0.321066	−	0.988139i	0.0338433	−	0.104159i
$91$	−8.85822	−	12.1923i	−0.928594	−	1.27810i
$92$	0.114615	+	0.0832728i	0.0119495	+	0.00868179i
$93$	3.88195	+	11.9474i	0.402540	+	1.23889i
$94$	−1.67297	−	5.14889i	−0.172554	−	0.531067i
$95$	10.6468	+	0.827162i	1.09234	+	0.0848650i
$96$	−0.943373	−	1.29844i	−0.0962826	−	0.132522i
$97$	0.0710011	+	0.0230697i	0.00720907	+	0.00234237i	0.312619	−	0.949879i	$-0.398794\pi$
$97$	0.0710011	+	0.0230697i	0.00720907	+	0.00234237i	−0.305410	+	0.952221i	$0.598794\pi$
$98$	14.9599			1.51117
$99$	0.861457	+	1.11190i	0.0865797	+	0.111750i
$100$	1.00200			0.100200
$101$	7.62412	+	2.47723i	0.758629	+	0.246493i	0.662690	−	0.748894i	$-0.269415\pi$
$101$	7.62412	+	2.47723i	0.758629	+	0.246493i	0.0959386	+	0.995387i	$0.469415\pi$
$102$	8.21648	−	5.96962i	0.813553	−	0.591081i
$103$	0.500148	−	0.688395i	0.0492811	−	0.0678296i	−0.783665	−	0.621183i	$-0.786652\pi$
$103$	0.500148	−	0.688395i	0.0492811	−	0.0678296i	0.832946	+	0.553354i	$0.186652\pi$
$104$	0.993792	+	3.05858i	0.0974493	+	0.299918i
$105$	5.69390	+	17.5240i	0.555668	+	1.71017i
$106$	−6.12815	+	8.43467i	−0.595218	+	0.819248i
$107$	7.08278	−	5.14594i	0.684718	−	0.497477i	−0.190201	−	0.981745i	$-0.560914\pi$
$107$	7.08278	−	5.14594i	0.684718	−	0.497477i	0.874920	+	0.484268i	$0.160914\pi$
$108$	−5.22657	−	1.69822i	−0.502927	−	0.163411i
$109$	−5.12419			−0.490808			−0.245404	−	0.969421i	$-0.578921\pi$
$109$	−5.12419			−0.490808			−0.245404	+	0.969421i	$0.578921\pi$
$110$	−4.57100	+	6.71774i	−0.435828	+	0.640511i
$111$	−7.66786			−0.727801
$112$	−4.45678	−	1.44810i	−0.421126	−	0.136832i
$113$	8.79244	+	12.1017i	0.827123	+	1.13844i	0.988452	+	0.151536i	$0.0484220\pi$
$113$	8.79244	+	12.1017i	0.827123	+	1.13844i	−0.161329	+	0.986901i	$0.551578\pi$
$114$	0.541885	−	6.97485i	0.0507522	−	0.653255i
$115$	0.107254	+	0.330095i	0.0100015	+	0.0307815i
$116$	0.726858	+	2.23704i	0.0674871	+	0.207704i
$117$	1.10340	+	0.801670i	0.102010	+	0.0741144i
$118$	6.81633	+	9.38187i	0.627494	+	0.863671i
$119$	9.16348	−	28.2023i	0.840015	−	2.58530i
$120$		−	3.93199i		−	0.358940i
$121$	−4.03765	−	10.2322i	−0.367059	−	0.930198i
$122$		−	5.57965i		−	0.505157i
$123$	13.9836	+	4.54356i	1.26086	+	0.409679i
$124$	−4.60068	−	6.33229i	−0.413153	−	0.568656i
$125$	−7.92407	−	5.75718i	−0.708751	−	0.514938i
$126$	−1.89010	+	0.614131i	−0.168384	+	0.0547111i
$127$	1.78759	+	5.50162i	0.158623	+	0.488190i	0.998510	−	0.0545707i	$-0.0173790\pi$
$127$	1.78759	+	5.50162i	0.158623	+	0.488190i	−0.839887	+	0.542761i	$0.817379\pi$
$128$	0.809017	+	0.587785i	0.0715077	+	0.0519534i
$129$	8.60641	−	6.25293i	0.757752	−	0.550539i
$130$	−2.43469	+	7.49320i	−0.213536	+	0.657197i
$131$		−	6.17097i		−	0.539160i	−0.962978	−	0.269580i	$-0.913115\pi$
$131$		−	6.17097i		−	0.539160i	0.962978	−	0.269580i	$-0.0868849\pi$
$132$	4.40088	+	2.99452i	0.383048	+	0.260640i
$133$	−10.6902	−	17.4056i	−0.926962	−	1.50926i
$134$	−14.0819	−	4.57550i	−1.21649	−	0.395263i
$135$	−7.91366	−	10.8922i	−0.681099	−	0.937453i
$136$	−3.71948	+	5.11942i	−0.318943	+	0.438987i
$137$	3.43690	+	10.5777i	0.293634	+	0.903714i	0.983677	+	0.179945i	$0.0575919\pi$
$137$	3.43690	+	10.5777i	0.293634	+	0.903714i	−0.690042	+	0.723769i	$0.742408\pi$
$138$	0.216250	−	0.0702638i	0.0184084	−	0.00598125i
$139$	−5.72644	+	7.88177i	−0.485710	+	0.668523i	−0.979590	−	0.201008i	$-0.935578\pi$
$139$	−5.72644	+	7.88177i	−0.485710	+	0.668523i	0.493880	+	0.869530i	$0.335578\pi$
$140$	−6.74810	−	9.28796i	−0.570318	−	0.784976i
$141$	−8.26377	−	2.68506i	−0.695935	−	0.226123i
$142$		−	14.0198i		−	1.17652i
$143$	−6.53255	−	8.43169i	−0.546280	−	0.705093i
$144$	0.424096			0.0353413
$145$	−1.78073	+	5.48052i	−0.147881	+	0.455132i
$146$	0.815469	+	1.12240i	0.0674887	+	0.0928903i
$147$	14.1127	−	19.4245i	1.16400	−	1.60211i
$148$	4.54376	−	1.47636i	0.373495	−	0.121356i
$149$	16.8811	−	5.48499i	1.38295	−	0.449348i	0.479312	−	0.877645i	$-0.340886\pi$
$149$	16.8811	−	5.48499i	1.38295	−	0.449348i	0.903638	+	0.428297i	$0.140886\pi$
$150$	0.945259	−	1.30104i	0.0771801	−	0.106229i
$151$	−3.39356	+	2.46557i	−0.276164	+	0.200645i	−0.717243	−	0.696824i	$-0.754596\pi$
$151$	−3.39356	+	2.46557i	−0.276164	+	0.200645i	0.441078	+	0.897469i	$0.354596\pi$
$152$	1.02182	+	4.23744i	0.0828806	+	0.343702i
$153$			2.68366i			0.216961i
$154$	15.5348	−	0.479289i	1.25183	−	0.0386222i
$155$		−	19.1757i		−	1.54023i
$156$	4.90890	+	1.59500i	0.393027	+	0.127702i
$157$	−6.07413	+	4.41311i	−0.484768	+	0.352205i	−0.803169	−	0.595751i	$-0.796854\pi$
$157$	−6.07413	+	4.41311i	−0.484768	+	0.352205i	0.318400	+	0.947956i	$0.396854\pi$
$158$	−7.05485	−	5.12565i	−0.561254	−	0.407775i
$159$	5.17080	+	15.9141i	0.410071	+	1.26207i
$160$	0.757060	+	2.32999i	0.0598509	+	0.184202i
$161$	0.390227	−	0.537102i	0.0307542	−	0.0423296i
$162$	−6.10634	+	4.43652i	−0.479760	+	0.348566i
$163$	−6.91309	+	21.2763i	−0.541475	+	1.66649i	0.187752	+	0.982217i	$0.439880\pi$
$163$	−6.91309	+	21.2763i	−0.541475	+	1.66649i	−0.729227	+	0.684272i	$0.760120\pi$
$164$	−9.16113			−0.715364
$165$	4.41043	+	12.2725i	0.343352	+	0.955413i
$166$			4.00268i			0.310668i
$167$	0.0720420	−	0.221722i	0.00557478	−	0.0171574i	−0.948230	−	0.317583i	$-0.897129\pi$
$167$	0.0720420	−	0.221722i	0.00557478	−	0.0171574i	0.953805	+	0.300426i	$0.0971287\pi$
$168$	−6.08467	+	4.42077i	−0.469443	+	0.341070i
$169$	2.14995	+	1.56203i	0.165381	+	0.120156i
$170$	−14.7441	+	4.79064i	−1.13082	+	0.367425i
$171$	1.40688	+	1.19915i	0.107587	+	0.0917014i
$172$	−3.89600	+	5.36238i	−0.297067	+	0.408877i
$173$	−8.71052	+	6.32856i	−0.662248	+	0.481152i	−0.867421	−	0.497574i	$-0.834224\pi$
$173$	−8.71052	+	6.32856i	−0.662248	+	0.481152i	0.205173	+	0.978726i	$0.434224\pi$
$174$	3.59037	+	1.16658i	0.272185	+	0.0884382i
$175$		−	4.69550i		−	0.354947i
$176$	−3.18440	−	0.927134i	−0.240033	−	0.0698853i
$177$	18.6122			1.39898
$178$	−3.62576	−	1.17808i	−0.271762	−	0.0883010i
$179$	−1.72678	−	2.37670i	−0.129065	−	0.177643i	0.739594	−	0.673054i	$-0.235018\pi$
$179$	−1.72678	−	2.37670i	−0.129065	−	0.177643i	−0.868659	+	0.495410i	$0.835018\pi$
$180$	0.840561	+	0.610704i	0.0626517	+	0.0455192i
$181$	−13.2297	+	4.29857i	−0.983352	+	0.319511i	−0.756194	−	0.654347i	$-0.772943\pi$
$181$	−13.2297	+	4.29857i	−0.983352	+	0.319511i	−0.227158	+	0.973858i	$0.572943\pi$
$182$	14.3329	−	4.65704i	1.06243	−	0.345203i
$183$	−7.24485	−	5.26369i	−0.535554	−	0.389103i
$184$	−0.114615	+	0.0832728i	−0.00844954	+	0.00613895i
$185$	11.1318	+	3.61693i	0.818423	+	0.265922i
$186$	−12.5623			−0.921110
$187$	5.86686	−	20.1508i	0.429027	−	1.47357i
$188$	5.41386			0.394846
$189$	−7.95807	+	24.4924i	−0.578865	+	1.78156i
$190$	−4.07671	+	9.87008i	−0.295756	+	0.716051i
$191$	3.69265	+	2.68287i	0.267191	+	0.194125i	0.713311	−	0.700848i	$-0.247195\pi$
$191$	3.69265	+	2.68287i	0.267191	+	0.194125i	−0.446120	+	0.894973i	$0.647195\pi$
$192$	1.52641	−	0.495961i	0.110159	−	0.0357929i
$193$	−3.52328	−	10.8435i	−0.253611	−	0.780536i	−0.994100	−	0.108467i	$-0.965406\pi$
$193$	−3.52328	−	10.8435i	−0.253611	−	0.780536i	0.740489	−	0.672069i	$-0.234594\pi$
$194$	−0.0438811	+	0.0603972i	−0.00315048	+	0.00433626i
$195$	7.43267	+	10.2302i	0.532264	+	0.732599i
$196$	−4.62285	+	14.2277i	−0.330204	+	1.01626i
$197$			0.452252i			0.0322216i	0.999870	+	0.0161108i	$0.00512846\pi$
$197$			0.452252i			0.0322216i	−0.999870	+	0.0161108i	$0.994872\pi$
$198$	−1.32368	+	0.475699i	−0.0940701	+	0.0338065i
$199$	9.71665			0.688795			0.344397	−	0.938824i	$-0.388083\pi$
$199$	9.71665			0.688795			0.344397	+	0.938824i	$0.388083\pi$
$200$	−0.309635	+	0.952958i	−0.0218945	+	0.0673843i
$201$	−19.2256	+	13.9682i	−1.35607	+	0.985240i
$202$	−4.71197	+	6.48547i	−0.331533	+	0.456316i
$203$	10.4831	−	3.40616i	0.735767	−	0.239065i
$204$	3.13842	+	9.65905i	0.219733	+	0.676269i
$205$	−18.1574	−	13.1922i	−1.26817	−	0.921380i
$206$	0.500148	+	0.688395i	0.0348470	+	0.0479628i
$207$	−0.0185665	+	0.0571419i	−0.00129046	+	0.00397163i
$208$	−3.21598			−0.222988
$209$	−7.94234	−	12.0797i	−0.549383	−	0.835570i
$210$	−18.4259			−1.27150
$211$	7.17003	−	22.0671i	0.493605	−	1.51916i	−0.325513	−	0.945537i	$-0.605537\pi$
$211$	7.17003	−	22.0671i	0.493605	−	1.51916i	0.819119	−	0.573624i	$-0.194463\pi$
$212$	−6.12815	−	8.43467i	−0.420883	−	0.579296i
$213$	−18.2039	−	13.2259i	−1.24731	−	0.906225i
$214$	2.70538	+	8.32631i	0.184936	+	0.569175i
$215$	−15.4438	+	5.01799i	−1.05326	+	0.342224i
$216$	3.23020	−	4.44599i	0.219787	−	0.302511i
$217$	−29.6740	+	21.5594i	−2.01440	+	1.46355i
$218$	1.58346	−	4.87339i	0.107246	−	0.330068i
$219$	2.22666			0.150464
$220$	−4.97643	−	6.42317i	−0.335511	−	0.433050i
$221$		−	20.3506i		−	1.36893i
$222$	2.36950	−	7.29257i	0.159030	−	0.489445i
$223$	0.160398	+	0.220769i	0.0107410	+	0.0147838i	0.814354	−	0.580369i	$-0.197092\pi$
$223$	0.160398	+	0.220769i	0.0107410	+	0.0147838i	−0.803613	+	0.595153i	$0.797092\pi$
$224$	2.75444	−	3.79116i	0.184039	−	0.253308i
$225$	0.131315	+	0.404145i	0.00875432	+	0.0269430i
$226$	−14.2265	+	4.62246i	−0.946330	+	0.307481i
$227$	9.00572	+	6.54304i	0.597730	+	0.434276i	0.845073	−	0.534652i	$-0.179557\pi$
$227$	9.00572	+	6.54304i	0.597730	+	0.434276i	−0.247342	+	0.968928i	$0.579557\pi$
$228$	6.46603	+	2.67071i	0.428223	+	0.176872i
$229$	4.29929	−	13.2319i	0.284105	−	0.874386i	−0.702560	−	0.711624i	$-0.747960\pi$
$229$	4.29929	−	13.2319i	0.284105	−	0.874386i	0.986665	−	0.162761i	$-0.0520401\pi$
$230$	−0.347082			−0.0228859
$231$	14.0327	−	20.6231i	0.923287	−	1.35690i
$232$	−2.35216			−0.154427
$233$	−9.80268	−	3.18508i	−0.642195	−	0.208662i	−0.0302253	−	0.999543i	$-0.509622\pi$
$233$	−9.80268	−	3.18508i	−0.642195	−	0.208662i	−0.611970	+	0.790881i	$0.709622\pi$
$234$	−1.10340	+	0.801670i	−0.0721318	+	0.0524068i
$235$	10.7303	+	7.79603i	0.699969	+	0.508557i
$236$	−11.0291	+	3.58356i	−0.717930	+	0.233270i
$237$	−13.3107	+	4.32491i	−0.864624	+	0.280933i
$238$	23.9903	+	17.4300i	1.55506	+	1.12982i
$239$	−13.7620	−	18.9417i	−0.890188	−	1.22524i	−0.973493	−	0.228715i	$-0.926548\pi$
$239$	−13.7620	−	18.9417i	−0.890188	−	1.22524i	0.0833053	−	0.996524i	$-0.473452\pi$
$240$	3.73955	+	1.21505i	0.241387	+	0.0784313i
$241$	0.383085			0.0246766			0.0123383	−	0.999924i	$-0.496072\pi$
$241$	0.383085			0.0246766			0.0123383	+	0.999924i	$0.496072\pi$
$242$	10.9791	−	0.678114i	0.705762	−	0.0435908i
$243$		−	4.37261i		−	0.280503i
$244$	5.30656	+	1.72421i	0.339718	+	0.110381i
$245$	−29.6506	+	21.5424i	−1.89431	+	1.37629i
$246$	−8.64237	+	11.8952i	−0.551017	+	0.758410i
$247$	−10.6686	−	9.09333i	−0.678827	−	0.578595i
$248$	7.44405	−	2.41872i	0.472698	−	0.153589i
$249$	5.19725	+	3.77602i	0.329362	+	0.239296i
$250$	7.92407	−	5.75718i	0.501162	−	0.364116i
$251$	1.59977	−	4.92357i	0.100976	−	0.310773i	−0.887789	−	0.460251i	$-0.847759\pi$
$251$	1.59977	−	4.92357i	0.100976	−	0.310773i	0.988765	+	0.149478i	$0.0477593\pi$
$252$		−	1.98737i		−	0.125192i
$253$	0.264331	−	0.388472i	0.0166183	−	0.0244230i
$254$	−5.78475			−0.362967
$255$	−7.68880	+	23.6637i	−0.481491	+	1.48188i
$256$	−0.809017	+	0.587785i	−0.0505636	+	0.0367366i
$257$	−1.36990	+	1.88550i	−0.0854519	+	0.117614i	−0.849603	−	0.527423i	$-0.823158\pi$
$257$	−1.36990	+	1.88550i	−0.0854519	+	0.117614i	0.764151	+	0.645038i	$0.223158\pi$
$258$	3.28736	+	10.1174i	0.204662	+	0.629885i
$259$	−6.91841	−	21.2927i	−0.429889	−	1.32306i
$260$	−6.37410	−	4.63105i	−0.395305	−	0.287206i
$261$	−0.807029	+	0.586341i	−0.0499538	+	0.0362936i
$262$	5.86894	+	1.90693i	0.362584	+	0.117811i
$263$			16.1835i			0.997918i	0.866626	+	0.498959i	$0.166284\pi$
$263$			16.1835i			0.997918i	−0.866626	+	0.498959i	$0.833716\pi$
$264$	−4.20791	+	3.26013i	−0.258979	+	0.200647i
$265$		−	25.5422i		−	1.56905i
$266$	19.8572	−	4.78839i	1.21752	−	0.293595i
$267$	−4.95012	+	3.59647i	−0.302942	+	0.220101i
$268$	8.70312	−	11.9788i	0.531628	−	0.731723i
$269$	−8.31984	+	2.70328i	−0.507269	+	0.164822i	−0.551460	−	0.834201i	$-0.685929\pi$
$269$	−8.31984	+	2.70328i	−0.507269	+	0.164822i	0.0441907	+	0.999023i	$0.485929\pi$
$270$	12.8046	−	4.16046i	0.779261	−	0.253197i
$271$	−3.65072	+	5.02479i	−0.221766	+	0.305234i	−0.905374	−	0.424615i	$-0.860410\pi$
$271$	−3.65072	+	5.02479i	−0.221766	+	0.305234i	0.683608	+	0.729849i	$0.260410\pi$
$272$	−3.71948	−	5.11942i	−0.225526	−	0.310410i
$273$	7.47438	−	23.0038i	0.452370	−	1.39225i
$274$	−11.1220			−0.671908
$275$	−0.102483	−	3.32167i	−0.00617994	−	0.200305i
$276$			0.227378i			0.0136866i
$277$	13.3532	+	4.33872i	0.802317	+	0.260689i	0.681340	−	0.731967i	$-0.261397\pi$
$277$	13.3532	+	4.33872i	0.802317	+	0.260689i	0.120976	+	0.992655i	$0.461397\pi$
$278$	−5.72644	−	7.88177i	−0.343449	−	0.472717i
$279$	1.95113	−	2.68550i	0.116811	−	0.160776i
$280$	10.9187	−	3.54769i	0.652514	−	0.212015i
$281$	−2.05889	−	6.33661i	−0.122823	−	0.378010i	0.870675	−	0.491859i	$-0.163682\pi$
$281$	−2.05889	−	6.33661i	−0.122823	−	0.378010i	−0.993498	+	0.113848i	$0.963682\pi$
$282$	5.10729	−	7.02958i	0.304135	−	0.418606i
$283$	−9.90063	−	13.6271i	−0.588532	−	0.810044i	0.406067	−	0.913843i	$-0.366900\pi$
$283$	−9.90063	−	13.6271i	−0.588532	−	0.810044i	−0.994598	+	0.103799i	$0.966900\pi$
$284$	13.3336	+	4.33236i	0.791206	+	0.257078i
$285$	8.96986	+	14.6045i	0.531329	+	0.865098i
$286$	10.0377	−	3.60729i	0.593541	−	0.213304i
$287$			42.9303i			2.53409i
$288$	−0.131053	+	0.403339i	−0.00772236	+	0.0237670i
$289$	18.6422	−	13.5443i	1.09660	−	0.796725i
$290$	−4.66201	−	3.38715i	−0.273763	−	0.198900i
$291$	0.0370259	+	0.113954i	0.00217050	+	0.00668011i
$292$	−1.31946	+	0.428718i	−0.0772154	+	0.0250888i
$293$	−7.26667	−	5.27955i	−0.424524	−	0.308434i	0.354932	−	0.934892i	$-0.384504\pi$
$293$	−7.26667	−	5.27955i	−0.424524	−	0.308434i	−0.779455	+	0.626458i	$0.784504\pi$
$294$	14.1127	+	19.4245i	0.823071	+	1.13286i
$295$	−27.0200	−	8.77935i	−1.57317	−	0.511153i
$296$			4.77760i			0.277692i
$297$	−5.09510	+	17.5000i	−0.295648	+	1.01545i
$298$			17.7498i			1.02822i
$299$	0.140793	−	0.433315i	0.00814224	−	0.0250593i
$300$	0.945259	+	1.30104i	0.0545746	+	0.0751154i
$301$	25.1288	+	18.2572i	1.44840	+	1.05232i
$302$	−1.29623	−	3.98937i	−0.0745894	−	0.229562i
$303$	3.97586	+	12.2364i	0.228407	+	0.702965i
$304$	−4.34580	−	0.337631i	−0.249249	−	0.0193645i
$305$	8.03477	+	11.0589i	0.460069	+	0.633231i
$306$	−2.55231	−	0.829296i	−0.145906	−	0.0474077i
$307$	24.8626			1.41898			0.709491	−	0.704714i	$-0.248925\pi$
$307$	24.8626			1.41898			0.709491	+	0.704714i	$0.248925\pi$
$308$	−4.34467	+	14.9225i	−0.247561	+	0.850291i
$309$	1.36567			0.0776901
$310$	18.2372	+	5.92562i	1.03580	+	0.336552i
$311$	−25.2036	+	18.3115i	−1.42917	+	1.03835i	−0.438996	+	0.898489i	$0.644666\pi$
$311$	−25.2036	+	18.3115i	−1.42917	+	1.03835i	−0.990171	+	0.139861i	$0.955334\pi$
$312$	−3.03387	+	4.17576i	−0.171759	+	0.236406i
$313$	−3.90296	−	12.0121i	−0.220608	−	0.678963i	−0.998708	−	0.0508217i	$-0.983816\pi$
$313$	−3.90296	−	12.0121i	−0.220608	−	0.678963i	0.778099	−	0.628141i	$-0.216184\pi$
$314$	−2.32011	−	7.14057i	−0.130931	−	0.402966i
$315$	2.86184	−	3.93898i	0.161246	−	0.221937i
$316$	7.05485	−	5.12565i	0.396866	−	0.288340i
$317$	20.2667	+	6.58504i	1.13829	+	0.369853i	0.816721	−	0.577033i	$-0.195790\pi$
$317$	20.2667	+	6.58504i	1.13829	+	0.369853i	0.321569	+	0.946886i	$0.395790\pi$
$318$	−16.7331			−0.938344
$319$	7.34155	−	2.63837i	0.411048	−	0.147720i
$320$	−2.44990			−0.136953
$321$	13.3634	+	4.34203i	0.745873	+	0.242349i
$322$	0.390227	+	0.537102i	0.0217465	+	0.0299315i
$323$	2.13651	−	27.5000i	0.118879	−	1.53014i
$324$	−2.33242	−	7.17844i	−0.129579	−	0.398802i
$325$	−0.995779	−	3.06469i	−0.0552359	−	0.169998i
$326$	−18.0987	−	13.1495i	−1.00239	−	0.728282i
$327$	−4.83402	−	6.65346i	−0.267322	−	0.367937i
$328$	2.83095	−	8.71275i	0.156313	−	0.481081i
$329$		−	25.3701i		−	1.39870i
$330$	−13.0347	+	0.402157i	−0.717539	+	0.0221380i
$331$			25.1424i			1.38195i	0.722878	+	0.690975i	$0.242819\pi$
$331$			25.1424i			1.38195i	−0.722878	+	0.690975i	$0.757181\pi$
$332$	−3.80677	−	1.23690i	−0.208924	−	0.0678835i
$333$	1.19095	+	1.63920i	0.0652634	+	0.0898274i
$334$	0.188608	+	0.137032i	0.0103202	+	0.00749806i
$335$	34.4993	−	11.2095i	1.88490	−	0.612441i
$336$	−2.32414	−	7.15296i	−0.126792	−	0.390226i
$337$	10.8636	+	7.89286i	0.591777	+	0.429951i	0.842951	−	0.537991i	$-0.180816\pi$
$337$	10.8636	+	7.89286i	0.591777	+	0.429951i	−0.251173	+	0.967942i	$0.580816\pi$
$338$	−2.14995	+	1.56203i	−0.116942	+	0.0849633i
$339$	−7.41887	+	22.8329i	−0.402938	+	1.24011i
$340$		−	15.5028i		−	0.840759i
$341$	−20.5213	+	15.8991i	−1.11129	+	0.860986i
$342$	−1.57521	+	0.967468i	−0.0851777	+	0.0523147i
$343$	35.4753	+	11.5266i	1.91549	+	0.622379i
$344$	−3.89600	−	5.36238i	−0.210058	−	0.289120i
$345$	−0.327428	+	0.450666i	−0.0176281	+	0.0242630i
$346$	−3.32712	−	10.2398i	−0.178867	−	0.550496i
$347$	32.7783	−	10.6503i	1.75963	−	0.571738i	0.762468	−	0.647026i	$-0.223987\pi$
$347$	32.7783	−	10.6503i	1.75963	−	0.571738i	0.997162	+	0.0752875i	$0.0239874\pi$
$348$	−2.21897	+	3.05415i	−0.118949	+	0.163719i
$349$	12.4973	+	17.2010i	0.668963	+	0.920748i	0.999736	−	0.0229622i	$-0.00730972\pi$
$349$	12.4973	+	17.2010i	0.668963	+	0.920748i	−0.330774	+	0.943710i	$0.607310\pi$
$350$	4.46569	+	1.45099i	0.238701	+	0.0775587i
$351$			17.6736i			0.943344i
$352$	1.86579	−	2.74205i	0.0994470	−	0.146152i
$353$	−10.6179			−0.565136			−0.282568	−	0.959247i	$-0.591186\pi$
$353$	−10.6179			−0.565136			−0.282568	+	0.959247i	$0.591186\pi$
$354$	−5.75147	+	17.7012i	−0.305687	+	0.940809i
$355$	20.1887	+	27.7874i	1.07151	+	1.47480i
$356$	2.24084	−	3.08426i	0.118765	−	0.163465i
$357$	45.2636	−	14.7070i	2.39560	−	0.778379i
$358$	2.79398	−	0.907819i	0.147666	−	0.0479797i
$359$	9.49178	−	13.0643i	0.500957	−	0.689508i	−0.481405	−	0.876498i	$-0.659873\pi$
$359$	9.49178	−	13.0643i	0.500957	−	0.689508i	0.982362	+	0.186990i	$0.0598733\pi$
$360$	−0.840561	+	0.610704i	−0.0443015	+	0.0321869i
$361$	−13.4620	−	13.4080i	−0.708526	−	0.705685i
$362$		−	13.9105i		−	0.731119i
$363$	9.47688	−	14.8954i	0.497407	−	0.781806i
$364$			15.0705i			0.789909i
$365$	−3.23253	−	1.05031i	−0.169199	−	0.0549760i
$366$	7.24485	−	5.26369i	0.378694	−	0.275137i
$367$	−27.8056	−	20.2020i	−1.45144	−	1.05453i	−0.985492	−	0.169724i	$-0.945712\pi$
$367$	−27.8056	−	20.2020i	−1.45144	−	1.05453i	−0.465951	−	0.884811i	$-0.654288\pi$
$368$	−0.0437791	−	0.134738i	−0.00228214	−	0.00702371i
$369$	−1.20059	−	3.69504i	−0.0625003	−	0.192356i
$370$	−6.87980	+	9.46924i	−0.357664	+	0.492282i
$371$	−39.5260	+	28.7173i	−2.05209	+	1.49093i
$372$	3.88195	−	11.9474i	0.201270	−	0.619445i
$373$	11.2741			0.583753			0.291876	−	0.956456i	$-0.405720\pi$
$373$	11.2741			0.583753			0.291876	+	0.956456i	$0.405720\pi$
$374$	17.3515	+	11.8066i	0.897227	+	0.610507i
$375$		−	15.7201i		−	0.811783i
$376$	−1.67297	+	5.14889i	−0.0862771	+	0.265534i
$377$	6.11981	−	4.44630i	0.315186	−	0.228996i
$378$	−20.8345	−	15.1372i	−1.07161	−	0.778571i
$379$	8.44534	−	2.74406i	0.433808	−	0.140953i	−0.0839690	−	0.996468i	$-0.526760\pi$
$379$	8.44534	−	2.74406i	0.433808	−	0.140953i	0.517777	+	0.855516i	$0.326760\pi$
$380$	−8.12723	−	6.92720i	−0.416918	−	0.355358i
$381$	−5.45718	+	7.51116i	−0.279580	+	0.384808i
$382$	−3.69265	+	2.68287i	−0.188932	+	0.137267i
$383$	−30.6310	−	9.95262i	−1.56517	−	0.508555i	−0.606988	−	0.794711i	$-0.707623\pi$
$383$	−30.6310	−	9.95262i	−1.56517	−	0.508555i	−0.958183	+	0.286156i	$0.907623\pi$
$384$			1.60496i			0.0819029i
$385$	−30.0998	+	23.3202i	−1.53403	+	1.18851i
$386$	11.4016			0.580325
$387$	−2.67344	−	0.868652i	−0.135898	−	0.0441561i
$388$	−0.0438811	−	0.0603972i	−0.00222773	−	0.00306620i
$389$	1.19655	+	0.869345i	0.0606675	+	0.0440776i	0.617706	−	0.786409i	$-0.288062\pi$
$389$	1.19655	+	0.869345i	0.0606675	+	0.0440776i	−0.557038	+	0.830487i	$0.688062\pi$
$390$	−12.0263	+	3.90758i	−0.608976	+	0.197868i
$391$	0.852617	−	0.277032i	0.0431187	−	0.0140101i
$392$	−12.1028	−	8.79318i	−0.611283	−	0.444123i
$393$	8.01265	−	5.82153i	0.404184	−	0.293657i
$394$	−0.430117	−	0.139754i	−0.0216690	−	0.00704069i
$395$	21.3638			1.07493
$396$	−0.0433758	−	1.40590i	−0.00217971	−	0.0706490i
$397$	31.8914			1.60058			0.800292	−	0.599611i	$-0.204678\pi$
$397$	31.8914			1.60058			0.800292	+	0.599611i	$0.204678\pi$
$398$	−3.00261	+	9.24108i	−0.150507	+	0.463213i
$399$	12.5153	−	30.3007i	0.626549	−	1.51693i
$400$	−0.810634	−	0.588960i	−0.0405317	−	0.0294480i
$401$	−3.36285	+	1.09266i	−0.167933	+	0.0545646i	−0.391777	−	0.920060i	$-0.628139\pi$
$401$	−3.36285	+	1.09266i	−0.167933	+	0.0545646i	0.223844	+	0.974625i	$0.428139\pi$
$402$	−7.34351	−	22.6010i	−0.366261	−	1.12724i
$403$	−14.7957	+	20.3645i	−0.737025	+	1.01443i
$404$	−4.71197	−	6.48547i	−0.234429	−	0.322664i
$405$	5.71418	−	17.5864i	0.283940	−	0.873877i
$406$			11.0226i			0.547040i
$407$	−5.35893	−	14.9118i	−0.265632	−	0.739150i
$408$	−10.1561			−0.502803
$409$	−8.41353	+	25.8942i	−0.416022	+	1.28038i	0.495311	+	0.868716i	$0.335054\pi$
$409$	−8.41353	+	25.8942i	−0.416022	+	1.28038i	−0.911333	+	0.411669i	$0.864946\pi$
$410$	18.1574	−	13.1922i	0.896732	−	0.651514i
$411$	−10.4922	+	14.4413i	−0.517544	+	0.712338i
$412$	−0.809257	+	0.262944i	−0.0398692	+	0.0129543i
$413$	16.7930	+	51.6836i	0.826331	+	2.54318i
$414$	−0.0486078	−	0.0353156i	−0.00238894	−	0.00173567i
$415$	−5.76391	−	7.93334i	−0.282939	−	0.389433i
$416$	0.993792	−	3.05858i	0.0487247	−	0.149959i
$417$	−15.6362			−0.765707
$418$	13.9428	−	3.82078i	0.681965	−	0.186881i
$419$	−11.2242			−0.548336			−0.274168	−	0.961682i	$-0.588403\pi$
$419$	−11.2242			−0.548336			−0.274168	+	0.961682i	$0.588403\pi$
$420$	5.69390	−	17.5240i	0.277834	−	0.855085i
$421$	10.8823	+	14.9782i	0.530369	+	0.729990i	0.987187	−	0.159570i	$-0.0510108\pi$
$421$	10.8823	+	14.9782i	0.530369	+	0.729990i	−0.456818	+	0.889560i	$0.651011\pi$
$422$	18.7714	+	13.6382i	0.913777	+	0.663898i
$423$	0.709501	+	2.18362i	0.0344971	+	0.106171i
$424$	9.91555	−	3.22176i	0.481542	−	0.156462i
$425$	3.72691	−	5.12966i	0.180782	−	0.248825i
$426$	18.2039	−	13.2259i	0.881983	−	0.640798i
$427$	8.07986	−	24.8672i	0.391012	−	1.20341i
$428$	−8.75480			−0.423179
$429$	4.78542	−	16.4364i	0.231042	−	0.793556i
$430$		−	16.2386i		−	0.783093i
$431$	−8.71884	+	26.8338i	−0.419972	+	1.29254i	0.487756	+	0.872980i	$0.337815\pi$
$431$	−8.71884	+	26.8338i	−0.419972	+	1.29254i	−0.907728	+	0.419560i	$0.862185\pi$
$432$	3.23020	+	4.44599i	0.155413	+	0.213908i
$433$	4.28125	−	5.89263i	0.205744	−	0.283182i	−0.693658	−	0.720304i	$-0.744002\pi$
$433$	4.28125	−	5.89263i	0.205744	−	0.283182i	0.899402	+	0.437122i	$0.144002\pi$
$434$	−11.3344	−	34.8838i	−0.544071	−	1.67448i
$435$	−8.79603	+	2.85800i	−0.421737	+	0.137031i
$436$	4.14556	+	3.01192i	0.198536	+	0.144245i
$437$	0.235747	−	0.570764i	0.0112773	−	0.0273034i
$438$	−0.688076	+	2.11768i	−0.0328775	+	0.101187i
$439$	25.9882			1.24035			0.620174	−	0.784464i	$-0.287062\pi$
$439$	25.9882			1.24035			0.620174	+	0.784464i	$0.287062\pi$
$440$	7.64660	−	2.74800i	0.364537	−	0.131006i
$441$	−6.34441			−0.302115
$442$	19.3545	+	6.28867i	0.920601	+	0.299121i
$443$	−7.82326	+	5.68393i	−0.371694	+	0.270052i	−0.757913	−	0.652356i	$-0.773781\pi$
$443$	−7.82326	+	5.68393i	−0.371694	+	0.270052i	0.386219	+	0.922407i	$0.373781\pi$
$444$	6.20343	+	4.50706i	0.294402	+	0.213895i
$445$	8.88275	−	2.88618i	0.421083	−	0.136818i
$446$	−0.259529	+	0.0843262i	−0.0122891	+	0.00399296i
$447$	23.0471	+	16.7447i	1.09009	+	0.791996i
$448$	2.75444	+	3.79116i	0.130135	+	0.179116i
$449$	1.35499	+	0.440264i	0.0639460	+	0.0207773i	0.340815	−	0.940130i	$-0.389297\pi$
$449$	1.35499	+	0.440264i	0.0639460	+	0.0207773i	−0.276869	+	0.960908i	$0.589297\pi$
$450$	−0.424943			−0.0200320
$451$	0.936984	+	30.3696i	0.0441209	+	1.43005i
$452$		−	14.9586i		−	0.703593i
$453$	−6.40279	−	2.08039i	−0.300829	−	0.0977454i
$454$	−9.00572	+	6.54304i	−0.422659	+	0.307080i
$455$	−21.7017	+	29.8699i	−1.01739	+	1.40032i
$456$	−4.53811	+	5.32426i	−0.212516	+	0.249331i
$457$	−12.9694	+	4.21402i	−0.606684	+	0.197124i	−0.596219	−	0.802822i	$-0.703331\pi$
$457$	−12.9694	+	4.21402i	−0.606684	+	0.197124i	−0.0104646	+	0.999945i	$0.503331\pi$
$458$	11.2557	+	8.17774i	0.525944	+	0.382120i
$459$	−28.1340	+	20.4406i	−1.31318	+	0.954083i
$460$	0.107254	−	0.330095i	0.00500076	−	0.0153907i
$461$			8.86563i			0.412913i	0.978456	+	0.206457i	$0.0661933\pi$
$461$			8.86563i			0.412913i	−0.978456	+	0.206457i	$0.933807\pi$
$462$	15.2774	+	19.7188i	0.710769	+	0.917403i
$463$	0.588951			0.0273709			0.0136854	−	0.999906i	$-0.495644\pi$
$463$	0.588951			0.0273709			0.0136854	+	0.999906i	$0.495644\pi$
$464$	0.726858	−	2.23704i	0.0337436	−	0.103852i
$465$	24.8985	−	18.0898i	1.15464	−	0.838896i
$466$	6.05839	−	8.33866i	0.280649	−	0.386281i
$467$	3.97952	+	12.2477i	0.184150	+	0.566756i	0.999933	−	0.0116026i	$-0.00369331\pi$
$467$	3.97952	+	12.2477i	0.184150	+	0.566756i	−0.815782	+	0.578359i	$0.803693\pi$
$468$	−0.421463	−	1.29713i	−0.0194821	−	0.0599598i
$469$	−56.1344	−	40.7840i	−2.59204	−	1.88323i
$470$	−10.7303	+	7.79603i	−0.494953	+	0.359604i
$471$	−11.4603	−	3.72369i	−0.528065	−	0.171579i
$472$		−	11.5966i		−	0.533778i
$473$	18.1750	+	12.3670i	0.835688	+	0.568633i
$474$		−	13.9957i		−	0.642844i
$475$	−1.02386	−	4.24591i	−0.0469781	−	0.194816i
$476$	−23.9903	+	17.4300i	−1.09959	+	0.798901i
$477$	2.59892	−	3.57711i	0.118996	−	0.163785i
$478$	22.2673	−	7.23510i	1.01848	−	0.330926i
$479$	7.01634	−	2.27975i	0.320585	−	0.104164i	−0.144304	−	0.989533i	$-0.546094\pi$
$479$	7.01634	−	2.27975i	0.320585	−	0.104164i	0.464889	+	0.885369i	$0.346094\pi$
$480$	−2.31117	+	3.18105i	−0.105490	+	0.145194i
$481$	−9.03111	−	12.4303i	−0.411783	−	0.566771i
$482$	−0.118380	+	0.364335i	−0.00539204	+	0.0165950i
$483$	1.06553			0.0484831
$484$	−2.74780	+	10.6513i	−0.124900	+	0.484149i
$485$		−	0.182897i		−	0.00830493i
$486$	4.15860	+	1.35121i	0.188638	+	0.0612922i
$487$	4.77311	+	6.56962i	0.216290	+	0.297698i	0.903351	−	0.428902i	$-0.141099\pi$
$487$	4.77311	+	6.56962i	0.216290	+	0.297698i	−0.687061	+	0.726600i	$0.741099\pi$
$488$	−3.27963	+	4.51403i	−0.148462	+	0.204340i
$489$	−34.1477	+	11.0952i	−1.54421	+	0.501745i
$490$	−11.3255	−	34.8563i	−0.511634	−	1.57465i
$491$	5.79875	−	7.98129i	0.261694	−	0.360191i	−0.657870	−	0.753132i	$-0.728542\pi$
$491$	5.79875	−	7.98129i	0.261694	−	0.360191i	0.919564	+	0.392941i	$0.128542\pi$
$492$	−8.64237	−	11.8952i	−0.389628	−	0.536277i
$493$	14.1559	+	4.59953i	0.637549	+	0.207152i
$494$	11.9451	−	7.33645i	0.537433	−	0.330082i
$495$	1.93854	−	2.84896i	0.0871309	−	0.128051i
$496$			7.82714i			0.351449i
$497$	20.3020	−	62.4832i	0.910671	−	2.80276i
$498$	−5.19725	+	3.77602i	−0.232894	+	0.169207i
$499$	31.6729	+	23.0117i	1.41787	+	1.03015i	0.992118	+	0.125309i	$0.0399921\pi$
$499$	31.6729	+	23.0117i	1.41787	+	1.03015i	0.425757	+	0.904838i	$0.360008\pi$
$500$	3.02673	+	9.31531i	0.135359	+	0.416593i
$501$	0.355856	−	0.115625i	0.0158985	−	0.00516573i
$502$	4.18824	+	3.04294i	0.186930	+	0.135813i
$503$	−18.8809	−	25.9873i	−0.841857	−	1.15872i	−0.985599	−	0.169101i	$-0.945913\pi$
$503$	−18.8809	−	25.9873i	−0.841857	−	1.15872i	0.143742	−	0.989615i	$-0.454087\pi$
$504$	1.89010	+	0.614131i	0.0841918	+	0.0273556i
$505$		−	19.6395i		−	0.873948i
$506$	0.287776	+	0.371438i	0.0127932	+	0.0165124i
$507$			4.26517i			0.189423i
$508$	1.78759	−	5.50162i	0.0793113	−	0.244095i
$509$	13.2176	+	18.1924i	0.585859	+	0.806366i	0.994322	−	0.106409i	$-0.0339353\pi$
$509$	13.2176	+	18.1924i	0.585859	+	0.806366i	−0.408463	+	0.912775i	$0.633935\pi$
$510$	−20.1295	−	14.6250i	−0.891351	−	0.647604i
$511$	2.00903	+	6.18315i	0.0888742	+	0.273527i
$512$	−0.309017	−	0.951057i	−0.0136568	−	0.0420312i
$513$	−1.85547	+	23.8826i	−0.0819208	+	1.05444i
$514$	−1.36990	−	1.88550i	−0.0604236	−	0.0831660i
$515$	−1.98260	−	0.644185i	−0.0873637	−	0.0283862i
$516$	−10.6381			−0.468317
$517$	−0.553720	−	17.9472i	−0.0243526	−	0.789317i
$518$	22.3885			0.983692
$519$	−16.4345	−	5.33990i	−0.721396	−	0.234396i
$520$	6.37410	−	4.63105i	0.279523	−	0.203085i
$521$	17.0895	−	23.5216i	0.748702	−	1.03050i	−0.249368	−	0.968409i	$-0.580223\pi$
$521$	17.0895	−	23.5216i	0.748702	−	1.03050i	0.998070	−	0.0620918i	$-0.0197771\pi$
$522$	−0.308258	−	0.948719i	−0.0134921	−	0.0415243i
$523$	−2.59466	−	7.98554i	−0.113456	−	0.349183i	0.878165	−	0.478357i	$-0.158767\pi$
$523$	−2.59466	−	7.98554i	−0.113456	−	0.349183i	−0.991622	+	0.129174i	$0.958767\pi$
$524$	−3.62720	+	4.99242i	−0.158455	+	0.218095i
$525$	6.09684	−	4.42961i	0.266088	−	0.193324i
$526$	−15.3914	−	5.00098i	−0.671098	−	0.218053i
$527$	−49.5298			−2.15755
$528$	−1.80025	−	5.00940i	−0.0783459	−	0.218006i
$529$	−22.9799			−0.999127
$530$	24.2921	+	7.89298i	1.05518	+	0.342849i
$531$	−2.89078	−	3.97881i	−0.125449	−	0.172666i
$532$	−1.58218	+	20.3650i	−0.0685964	+	0.882935i
$533$	9.10426	+	28.0200i	0.394349	+	1.21368i
$534$	−1.89078	−	5.81921i	−0.0818219	−	0.251822i
$535$	−17.3521	−	12.6070i	−0.750196	−	0.545049i
$536$	8.70312	+	11.9788i	0.375918	+	0.517406i
$537$	1.45702	−	4.48423i	0.0628749	−	0.193509i
$538$		−	8.74799i		−	0.377153i
$539$	47.6382	+	13.8698i	2.05192	+	0.597414i
$540$			13.4635i			0.579378i
$541$	−25.3349	−	8.23180i	−1.08923	−	0.353913i	−0.291282	−	0.956637i	$-0.594082\pi$
$541$	−25.3349	−	8.23180i	−1.08923	−	0.353913i	−0.797949	+	0.602724i	$0.794082\pi$
$542$	−3.65072	−	5.02479i	−0.156812	−	0.215833i
$543$	−18.0619	−	13.1228i	−0.775112	−	0.563152i
$544$	6.01824	−	1.95544i	0.258030	−	0.0838390i
$545$	3.87932	+	11.9393i	0.166172	+	0.511424i
$546$	19.5682	+	14.2171i	0.837440	+	0.608436i
$547$	15.7658	−	11.4546i	0.674099	−	0.489761i	−0.197296	−	0.980344i	$-0.563216\pi$
$547$	15.7658	−	11.4546i	0.674099	−	0.489761i	0.871395	+	0.490583i	$0.163216\pi$
$548$	3.43690	−	10.5777i	0.146817	−	0.451857i
$549$			2.36630i			0.100991i
$550$	3.19077	+	0.928987i	0.136055	+	0.0396121i
$551$	8.73660	−	5.36587i	0.372192	−	0.228594i
$552$	−0.216250	−	0.0702638i	−0.00920420	−	0.00299063i
$553$	−24.0195	−	33.0600i	−1.02141	−	1.40585i
$554$	−8.25274	+	11.3589i	−0.350625	+	0.482594i
$555$	5.80503	+	17.8660i	0.246410	+	0.758372i
$556$	9.26557	−	3.01057i	0.392948	−	0.127676i
$557$	−2.22062	+	3.05642i	−0.0940907	+	0.129505i	−0.853467	−	0.521147i	$-0.825504\pi$
$557$	−2.22062	+	3.05642i	−0.0940907	+	0.129505i	0.759376	+	0.650652i	$0.225504\pi$
$558$	1.95113	+	2.68550i	0.0825978	+	0.113686i
$559$	20.2731	+	6.58711i	0.857459	+	0.278605i
$560$			11.4805i			0.485142i
$561$	31.6992	−	11.3919i	1.33834	−	0.480967i
$562$	6.66271			0.281049
$563$	0.486219	−	1.49643i	0.0204917	−	0.0630669i	−0.940288	−	0.340381i	$-0.889444\pi$
$563$	0.486219	−	1.49643i	0.0204917	−	0.0630669i	0.960779	+	0.277314i	$0.0894441\pi$
$564$	5.10729	+	7.02958i	0.215056	+	0.295999i
$565$	21.5406	−	29.6480i	0.906218	−	1.24730i
$566$	16.0196	−	5.20507i	0.673352	−	0.218785i
$567$	−33.6391	+	10.9300i	−1.41271	+	0.459017i
$568$	−8.24064	+	11.3423i	−0.345770	+	0.475911i
$569$	25.7312	−	18.6948i	1.07871	−	0.783728i	0.101251	−	0.994861i	$-0.467715\pi$
$569$	25.7312	−	18.6948i	1.07871	−	0.783728i	0.977457	+	0.211133i	$0.0677153\pi$
$570$	−16.6616	+	4.01779i	−0.697877	+	0.168287i
$571$			39.2606i			1.64300i	0.570205	+	0.821502i	$0.306864\pi$
$571$			39.2606i			1.64300i	−0.570205	+	0.821502i	$0.693136\pi$
$572$	0.328925	+	10.6611i	0.0137530	+	0.445764i
$573$			7.32563i			0.306033i
$574$	−40.8291	−	13.2662i	−1.70417	−	0.553720i
$575$	0.114844	−	0.0834392i	0.00478934	−	0.00347966i
$576$	−0.343101	−	0.249277i	−0.0142959	−	0.0103865i
$577$	−3.70608	−	11.4062i	−0.154286	−	0.474844i	0.843802	−	0.536655i	$-0.180312\pi$
$577$	−3.70608	−	11.4062i	−0.154286	−	0.474844i	−0.998088	+	0.0618109i	$0.980312\pi$
$578$	7.12067	+	21.9152i	0.296181	+	0.911551i
$579$	10.7559	−	14.8043i	0.447002	−	0.615245i
$580$	4.66201	−	3.38715i	0.193579	−	0.140644i
$581$	−5.79626	+	17.8391i	−0.240469	+	0.740089i
$582$	−0.119818			−0.00496663
$583$	−27.3346	+	21.1778i	−1.13208	+	0.877094i
$584$		−	1.38736i		−	0.0574093i
$585$	1.03254	−	3.17783i	0.0426903	−	0.131387i
$586$	7.26667	−	5.27955i	0.300184	−	0.218096i
$587$	7.00285	+	5.08787i	0.289038	+	0.209999i	0.722850	−	0.691005i	$-0.242832\pi$
$587$	7.00285	+	5.08787i	0.289038	+	0.209999i	−0.433812	+	0.901004i	$0.642832\pi$
$588$	−22.8349	+	7.41950i	−0.941694	+	0.305975i
$589$	−22.1316	+	25.9656i	−0.911917	+	1.06989i
$590$	16.6993	−	22.9846i	0.687500	−	0.946262i
$591$	−0.587223	+	0.426643i	−0.0241551	+	0.0175497i
$592$	−4.54376	−	1.47636i	−0.186748	−	0.0606779i
$593$		−	1.92236i		−	0.0789420i	−0.999221	−	0.0394710i	$-0.987433\pi$
$593$		−	1.92236i		−	0.0789420i	0.999221	−	0.0394710i	$-0.0125673\pi$
$594$	−15.0690	−	10.2535i	−0.618290	−	0.420708i
$595$	−72.6484			−2.97829
$596$	−16.8811	−	5.48499i	−0.691475	−	0.224674i
$597$	9.16642	+	12.6165i	0.375157	+	0.516359i
$598$	0.368600	+	0.267803i	0.0150732	+	0.0109513i
$599$	−2.98999	+	0.971506i	−0.122168	+	0.0396947i	−0.369463	−	0.929246i	$-0.620458\pi$
$599$	−2.98999	+	0.971506i	−0.122168	+	0.0396947i	0.247295	+	0.968940i	$0.420458\pi$
$600$	−1.52946	+	0.496952i	−0.0624400	+	0.0202880i
$601$	−13.2051	−	9.59406i	−0.538647	−	0.391350i	0.284935	−	0.958547i	$-0.408028\pi$
$601$	−13.2051	−	9.59406i	−0.538647	−	0.391350i	−0.823582	+	0.567197i	$0.808028\pi$
$602$	−25.1288	+	18.2572i	−1.02417	+	0.744106i
$603$	5.97209	+	1.94045i	0.243202	+	0.0790212i
$604$	4.19467			0.170679
$605$	−20.7841	+	17.1541i	−0.844995	+	0.697411i
$606$	−12.8661			−0.522651
$607$	−4.91143	+	15.1158i	−0.199349	+	0.613533i	0.800549	+	0.599267i	$0.204541\pi$
$607$	−4.91143	+	15.1158i	−0.199349	+	0.613533i	−0.999898	+	0.0142661i	$0.995459\pi$
$608$	1.66403	−	4.02877i	0.0674855	−	0.163388i
$609$	14.3121	+	10.3984i	0.579957	+	0.421364i
$610$	−13.0005	+	4.22413i	−0.526376	+	0.171030i
$611$	−5.38025	−	16.5587i	−0.217662	−	0.669894i
$612$	1.57741	−	2.17112i	0.0637632	−	0.0877625i
$613$	3.48924	+	4.80252i	0.140929	+	0.193972i	0.873647	−	0.486560i	$-0.161749\pi$
$613$	3.48924	+	4.80252i	0.140929	+	0.193972i	−0.732718	+	0.680532i	$0.761749\pi$
$614$	−7.68296	+	23.6457i	−0.310059	+	0.954263i
$615$		−	36.0215i		−	1.45253i
$616$	−12.8496	−	8.74335i	−0.517725	−	0.352280i
$617$	−10.9260			−0.439865			−0.219932	−	0.975515i	$-0.570584\pi$
$617$	−10.9260			−0.439865			−0.219932	+	0.975515i	$0.570584\pi$
$618$	−0.422015	+	1.29883i	−0.0169759	+	0.0522465i
$619$	−13.9973	+	10.1697i	−0.562601	+	0.408753i	−0.832410	−	0.554161i	$-0.813039\pi$
$619$	−13.9973	+	10.1697i	−0.562601	+	0.408753i	0.269809	+	0.962914i	$0.413039\pi$
$620$	−11.2712	+	15.5135i	−0.452662	+	0.623036i
$621$	−0.740460	+	0.240590i	−0.0297136	+	0.00965454i
$622$	−9.62693	−	29.6286i	−0.386005	−	1.18800i
$623$	−14.4532	−	10.5009i	−0.579057	−	0.420710i
$624$	−3.03387	−	4.17576i	−0.121452	−	0.167164i
$625$	−8.96334	+	27.5863i	−0.358534	+	1.10345i
$626$	12.6302			0.504806
$627$	8.19220	−	21.7083i	0.327165	−	0.866947i
$628$	7.50804			0.299603
$629$	9.34232	−	28.7527i	0.372503	−	1.14645i
$630$	2.86184	+	3.93898i	0.114018	+	0.156933i
$631$	34.7105	+	25.2186i	1.38180	+	1.00394i	0.996709	+	0.0810593i	$0.0258303\pi$
$631$	34.7105	+	25.2186i	1.38180	+	1.00394i	0.385092	+	0.922878i	$0.374170\pi$
$632$	2.69471	+	8.29347i	0.107190	+	0.329897i
$633$	35.4169	−	11.5076i	1.40769	−	0.457387i
$634$	−12.5255	+	17.2399i	−0.497451	+	0.684682i
$635$	11.4654	−	8.33012i	0.454991	−	0.330571i
$636$	5.17080	−	15.9141i	0.205036	−	0.631035i
$637$	48.1106			1.90621
$638$	0.240575	+	7.79753i	0.00952446	+	0.308707i
$639$			5.94575i			0.235210i
$640$	0.757060	−	2.32999i	0.0299254	−	0.0921010i
$641$	−8.51876	−	11.7251i	−0.336471	−	0.463112i	0.606936	−	0.794751i	$-0.292399\pi$
$641$	−8.51876	−	11.7251i	−0.336471	−	0.463112i	−0.943407	+	0.331639i	$0.892399\pi$
$642$	−8.25904	+	11.3676i	−0.325958	+	0.448643i
$643$	−3.61380	−	11.1221i	−0.142515	−	0.438615i	0.854168	−	0.519996i	$-0.174067\pi$
$643$	−3.61380	−	11.1221i	−0.142515	−	0.438615i	−0.996683	+	0.0813817i	$0.974067\pi$
$644$	−0.631401	+	0.205155i	−0.0248807	+	0.00808423i
$645$	−21.0848	−	15.3190i	−0.830215	−	0.603186i
$646$	25.4939	+	10.5299i	1.00304	+	0.414294i
$647$	−7.50447	+	23.0964i	−0.295031	+	0.908012i	0.688180	+	0.725540i	$0.258410\pi$
$647$	−7.50447	+	23.0964i	−0.295031	+	0.908012i	−0.983211	+	0.182472i	$0.941590\pi$
$648$	7.54786			0.296508
$649$	13.0077	+	36.1953i	0.510596	+	1.42079i
$650$	3.22241			0.126393
$651$	−55.9872	−	18.1914i	−2.19431	−	0.712975i
$652$	18.0987	−	13.1495i	0.708800	−	0.514973i
$653$	0.831087	+	0.603820i	0.0325229	+	0.0236293i	0.603928	−	0.797039i	$-0.293601\pi$
$653$	0.831087	+	0.603820i	0.0325229	+	0.0236293i	−0.571405	+	0.820668i	$0.693601\pi$
$654$	7.82162	−	2.54140i	0.305849	−	0.0993765i
$655$	−14.3783	+	4.67179i	−0.561807	+	0.182542i
$656$	7.41151	+	5.38478i	0.289371	+	0.210240i
$657$	−0.345837	−	0.476004i	−0.0134924	−	0.0185707i
$658$	24.1284	+	7.83978i	0.940622	+	0.305627i
$659$	41.9456			1.63397			0.816985	−	0.576659i	$-0.195644\pi$
$659$	41.9456			1.63397			0.816985	+	0.576659i	$0.195644\pi$
$660$	3.64548	−	12.5211i	0.141900	−	0.487381i
$661$		−	21.5334i		−	0.837553i	−0.908089	−	0.418777i	$-0.862459\pi$
$661$		−	21.5334i		−	0.837553i	0.908089	−	0.418777i	$-0.137541\pi$
$662$	−23.9118	−	7.76942i	−0.929360	−	0.301967i
$663$	26.4240	−	19.1982i	1.02622	−	0.745595i
$664$	2.35272	−	3.23823i	0.0913031	−	0.125668i
$665$	−32.4618	+	38.0853i	−1.25881	+	1.47688i
$666$	−1.92699	+	0.626117i	−0.0746694	+	0.0242615i
$667$	0.269593	+	0.195871i	0.0104387	+	0.00758416i
$668$	−0.188608	+	0.137032i	−0.00729748	+	0.00530193i
$669$	−0.135340	+	0.416535i	−0.00523256	+	0.0161042i
$670$			36.2747i			1.40142i
$671$	5.17308	−	17.7678i	0.199704	−	0.685920i
$672$	7.52107			0.290132
$673$	4.57203	−	14.0712i	0.176239	−	0.542407i	−0.823449	−	0.567390i	$-0.807953\pi$
$673$	4.57203	−	14.0712i	0.176239	−	0.542407i	0.999688	+	0.0249832i	$0.00795323\pi$
$674$	−10.8636	+	7.89286i	−0.418450	+	0.304022i
$675$	−3.23666	+	4.45488i	−0.124579	+	0.171468i
$676$	−0.821209	−	2.52742i	−0.0315849	−	0.0972085i
$677$	2.42411	+	7.46065i	0.0931662	+	0.286736i	0.986771	−	0.162118i	$-0.0518324\pi$
$677$	2.42411	+	7.46065i	0.0931662	+	0.286736i	−0.893605	+	0.448854i	$0.851832\pi$
$678$	−19.4229	−	14.1115i	−0.745930	−	0.541950i
$679$	−0.283029	+	0.205633i	−0.0108617	+	0.00789146i
$680$	14.7441	+	4.79064i	0.565409	+	0.183713i
$681$			17.8659i			0.684624i
$682$	−8.77953	−	24.4300i	−0.336186	−	0.935473i
$683$			20.1559i			0.771246i	0.922656	+	0.385623i	$0.126013\pi$
$683$			20.1559i			0.771246i	−0.922656	+	0.385623i	$0.873987\pi$
$684$	−0.433350	−	1.79708i	−0.0165695	−	0.0687130i
$685$	22.0440	−	16.0159i	0.842258	−	0.611936i
$686$	−21.9249	+	30.1771i	−0.837098	+	1.15217i
$687$	21.2366	−	6.90020i	0.810228	−	0.263259i
$688$	6.30385	−	2.04825i	0.240332	−	0.0780886i
$689$	−19.7080	+	27.1257i	−0.750815	+	1.03341i
$690$	−0.327428	−	0.450666i	−0.0124650	−	0.0171566i
$691$	−7.19370	+	22.1399i	−0.273661	+	0.842243i	0.715909	+	0.698194i	$0.246013\pi$
$691$	−7.19370	+	22.1399i	−0.273661	+	0.842243i	−0.989570	+	0.144050i	$0.953987\pi$
$692$	10.7668			0.409292
$693$	−6.58822	+	0.203265i	−0.250266	+	0.00772138i
$694$			34.4651i			1.30828i
$695$	22.6997	+	7.37558i	0.861049	+	0.279772i
$696$	−2.21897	−	3.05415i	−0.0841098	−	0.115767i
$697$	−34.0746	+	46.8997i	−1.29067	+	1.77645i
$698$	−20.2210	+	6.57019i	−0.765375	+	0.248685i
$699$	−5.11194	−	15.7329i	−0.193351	−	0.595074i
$700$	−2.75995	+	3.79874i	−0.104316	+	0.143579i
$701$	−22.5389	−	31.0222i	−0.851283	−	1.17169i	−0.983579	−	0.180480i	$-0.942235\pi$
$701$	−22.5389	−	31.0222i	−0.851283	−	1.17169i	0.132295	−	0.991210i	$-0.457765\pi$
$702$	−16.8085	−	5.46143i	−0.634398	−	0.206128i
$703$	−10.8989	−	17.7453i	−0.411059	−	0.669278i
$704$	2.03128	+	2.62181i	0.0765568	+	0.0988133i
$705$			21.2873i			0.801725i
$706$	3.28112	−	10.0983i	0.123487	−	0.380053i
$707$	−30.3918	+	22.0809i	−1.14300	+	0.830438i
$708$	−15.0576	−	10.9400i	−0.565897	−	0.411149i
$709$	3.42694	+	10.5470i	0.128701	+	0.396102i	0.994557	−	0.104191i	$-0.0332254\pi$
$709$	3.42694	+	10.5470i	0.128701	+	0.396102i	−0.865856	+	0.500293i	$0.833225\pi$
$710$	−32.6661	+	10.6138i	−1.22594	+	0.398331i
$711$	2.99193	+	2.17376i	0.112206	+	0.0815225i
$712$	2.24084	+	3.08426i	0.0839792	+	0.115587i
$713$	−1.05461	−	0.342665i	−0.0394956	−	0.0128329i
$714$			47.5930i			1.78112i
$715$	−14.7002	+	21.6041i	−0.549757	+	0.807947i
$716$			2.93777i			0.109789i
$717$	11.6121	−	35.7382i	0.433660	−	1.33467i
$718$	9.49178	+	13.0643i	0.354230	+	0.487556i
$719$	−19.3957	−	14.0918i	−0.723339	−	0.525536i	0.164110	−	0.986442i	$-0.447525\pi$
$719$	−19.3957	−	14.0918i	−0.723339	−	0.525536i	−0.887449	+	0.460906i	$0.847525\pi$
$720$	−0.321066	−	0.988139i	−0.0119654	−	0.0368258i
$721$	1.23219	+	3.79229i	0.0458891	+	0.141232i
$722$	16.9118	−	8.65981i	0.629391	−	0.322285i
$723$	0.361392	+	0.497413i	0.0134403	+	0.0184990i
$724$	13.2297	+	4.29857i	0.491676	+	0.159755i
$725$	2.35687			0.0875318
$726$	11.2379	+	13.6160i	0.417076	+	0.505336i
$727$	−33.8653			−1.25599			−0.627997	−	0.778216i	$-0.716125\pi$
$727$	−33.8653			−1.25599			−0.627997	+	0.778216i	$0.716125\pi$
$728$	−14.3329	−	4.65704i	−0.531213	−	0.172601i
$729$	23.9966	−	17.4346i	0.888763	−	0.645724i
$730$	1.99782	−	2.74976i	0.0739425	−	0.101773i
$731$	12.9612	+	39.8905i	0.479387	+	1.47540i
$732$	2.76729	+	8.51683i	0.102282	+	0.314791i
$733$	24.1046	−	33.1771i	0.890324	−	1.22543i	−0.0831291	−	0.996539i	$-0.526491\pi$
$733$	24.1046	−	33.1771i	0.890324	−	1.22543i	0.973453	−	0.228887i	$-0.0735086\pi$
$734$	27.8056	−	20.2020i	1.02632	−	0.745669i
$735$	−55.9431	−	18.1770i	−2.06349	−	0.670469i
$736$	0.141672			0.00522210
$737$	−40.6005	−	27.6261i	−1.49554	−	1.01762i
$738$	3.88520			0.143016
$739$	−4.11412	−	1.33676i	−0.151340	−	0.0491734i	0.232367	−	0.972628i	$-0.425353\pi$
$739$	−4.11412	−	1.33676i	−0.151340	−	0.0491734i	−0.383707	+	0.923455i	$0.625353\pi$
$740$	−6.87980	−	9.46924i	−0.252907	−	0.348096i
$741$	1.74269	−	22.4310i	0.0640193	−	0.824022i
$742$	−15.0976	−	46.4656i	−0.554250	−	1.70581i
$743$	3.75699	+	11.5628i	0.137830	+	0.424199i	0.996020	−	0.0891352i	$-0.0284103\pi$
$743$	3.75699	+	11.5628i	0.137830	+	0.424199i	−0.858189	+	0.513334i	$0.828410\pi$
$744$	10.1631	+	7.38391i	0.372597	+	0.270707i
$745$	−25.5599	−	35.1802i	−0.936444	−	1.28890i
$746$	−3.48390	+	10.7223i	−0.127555	+	0.392573i
$747$		−	1.69752i		−	0.0621090i
$748$	−16.5907	+	12.8538i	−0.606616	+	0.469983i
$749$			41.0262i			1.49906i
$750$	14.9507	+	4.85778i	0.545923	+	0.177381i
$751$	−2.52141	−	3.47042i	−0.0920074	−	0.126637i	0.760532	−	0.649301i	$-0.224938\pi$
$751$	−2.52141	−	3.47042i	−0.0920074	−	0.126637i	−0.852539	+	0.522664i	$0.824938\pi$
$752$	−4.37990	−	3.18219i	−0.159719	−	0.116042i
$753$	7.90215	−	2.56756i	0.287970	−	0.0935673i
$754$	2.33756	+	7.19427i	0.0851289	+	0.262000i
$755$	8.31388	+	6.04039i	0.302573	+	0.219832i
$756$	20.8345	−	15.1372i	0.757744	−	0.550533i
$757$	11.0633	−	34.0493i	0.402103	−	1.23754i	−0.521188	−	0.853442i	$-0.674511\pi$
$757$	11.0633	−	34.0493i	0.402103	−	1.23754i	0.923290	−	0.384102i	$-0.125489\pi$
$758$			8.87996i			0.322535i
$759$	0.753770	−	0.0232559i	0.0273601	−	0.000844134i
$760$	9.09961	−	5.58883i	0.330078	−	0.202728i
$761$	14.8885	+	4.83756i	0.539707	+	0.175362i	0.566170	−	0.824288i	$-0.308424\pi$
$761$	14.8885	+	4.83756i	0.539707	+	0.175362i	−0.0264630	+	0.999650i	$0.508424\pi$
$762$	−5.45718	−	7.51116i	−0.197693	−	0.272101i
$763$	14.1143	−	19.4266i	0.510971	−	0.703292i
$764$	−1.41047	−	4.34097i	−0.0510289	−	0.157051i
$765$	6.25290	−	2.03169i	0.226074	−	0.0734559i
$766$	18.9310	−	26.0563i	0.684005	−	0.941452i
$767$	21.9212	+	30.1719i	0.791527	+	1.08944i
$768$	−1.52641	−	0.495961i	−0.0550796	−	0.0178964i
$769$			18.6239i			0.671595i	0.941934	+	0.335797i	$0.109006\pi$
$769$			18.6239i			0.671595i	−0.941934	+	0.335797i	$0.890994\pi$
$770$	−12.8775	−	35.8330i	−0.464072	−	1.29133i
$771$	−3.74054			−0.134712
$772$	−3.52328	+	10.8435i	−0.126806	+	0.390268i
$773$	1.31751	+	1.81339i	0.0473874	+	0.0652232i	0.832053	−	0.554696i	$-0.187165\pi$
$773$	1.31751	+	1.81339i	0.0473874	+	0.0652232i	−0.784666	+	0.619919i	$0.787165\pi$
$774$	1.65227	−	2.27416i	0.0593898	−	0.0817430i
$775$	−7.45893	+	2.42355i	−0.267933	+	0.0870567i
$776$	0.0710011	−	0.0230697i	0.00254879	−	0.000828153i
$777$	21.1207	−	29.0701i	0.757700	−	1.04288i
$778$	−1.19655	+	0.869345i	−0.0428984	+	0.0311675i
$779$	9.36103	+	38.8197i	0.335394	+	1.39086i
$780$		−	12.6452i		−	0.452771i
$781$	12.9982	−	44.6448i	0.465114	−	1.59752i
$782$			0.896494i			0.0320586i
$783$	−12.2938	−	3.99448i	−0.439343	−	0.142751i
$784$	12.1028	−	8.79318i	0.432242	−	0.314042i
$785$	14.8810	+	10.8117i	0.531126	+	0.385885i
$786$	3.06056	+	9.41943i	0.109166	+	0.335980i
$787$	−0.800017	−	2.46220i	−0.0285175	−	0.0877680i	0.935785	−	0.352572i	$-0.114693\pi$
$787$	−0.800017	−	2.46220i	−0.0285175	−	0.0877680i	−0.964302	+	0.264804i	$0.914693\pi$
$788$	0.265827	−	0.365880i	0.00946970	−	0.0130339i
$789$	−21.0133	+	15.2671i	−0.748095	+	0.543523i
$790$	−6.60177	+	20.3182i	−0.234880	+	0.722888i
$791$	−70.0979			−2.49240
$792$	1.35049	+	0.393193i	0.0479876	+	0.0139715i
$793$		−	17.9440i		−	0.637211i
$794$	−9.85498	+	30.3305i	−0.349740	+	1.07639i
$795$	33.1651	−	24.0958i	1.17624	−	0.854591i
$796$	−7.86093	−	5.71130i	−0.278623	−	0.202432i
$797$	−28.8080	+	9.36030i	−1.02043	+	0.331559i	−0.771001	−	0.636834i	$-0.780244\pi$
$797$	−28.8080	+	9.36030i	−1.02043	+	0.331559i	−0.249432	+	0.968392i	$0.580244\pi$
$798$	24.9502	+	21.2662i	0.883228	+	0.752815i
$799$	20.1367	−	27.7158i	0.712386	−	0.980516i
$800$	0.810634	−	0.588960i	0.0286603	−	0.0208229i
$801$	1.53767	+	0.499619i	0.0543309	+	0.0176532i
$802$		−	3.53591i		−	0.124857i
$803$	1.55617	+	4.33021i	0.0549161	+	0.152810i
$804$	23.7641			0.838095
$805$	−1.54687	−	0.502608i	−0.0545199	−	0.0177146i
$806$	−14.7957	−	20.3645i	−0.521155	−	0.717309i
$807$	−11.3588	−	8.25262i	−0.399847	−	0.290506i
$808$	7.62412	−	2.47723i	0.268216	−	0.0871486i
$809$	−14.0387	+	4.56145i	−0.493575	+	0.160372i	−0.545219	−	0.838293i	$-0.683554\pi$
$809$	−14.0387	+	4.56145i	−0.493575	+	0.160372i	0.0516447	+	0.998666i	$0.483554\pi$
$810$	14.9599	+	10.8690i	0.525638	+	0.381898i
$811$	14.3357	−	10.4155i	0.503395	−	0.365738i	−0.306917	−	0.951736i	$-0.599297\pi$
$811$	14.3357	−	10.4155i	0.503395	−	0.365738i	0.810312	+	0.585998i	$0.199297\pi$
$812$	−10.4831	−	3.40616i	−0.367884	−	0.119533i
$813$	−9.96840			−0.349607
$814$	15.8380	−	0.488644i	0.555120	−	0.0171270i
$815$	54.8072			1.91981
$816$	3.13842	−	9.65905i	0.109867	−	0.338134i
$817$	26.7038	+	11.0296i	0.934246	+	0.385879i
$818$	−22.0269	−	16.0035i	−0.770153	−	0.559549i
$819$	−6.07852	+	1.97503i	−0.212401	+	0.0690132i
$820$	6.93553	+	21.3454i	0.242199	+	0.745412i
$821$	23.6026	−	32.4861i	0.823735	−	1.13377i	−0.165322	−	0.986240i	$-0.552866\pi$
$821$	23.6026	−	32.4861i	0.823735	−	1.13377i	0.989057	−	0.147534i	$-0.0471337\pi$
$822$	−10.4922	−	14.4413i	−0.365959	−	0.503699i
$823$	5.17898	−	15.9392i	0.180528	−	0.555607i	−0.819315	−	0.573344i	$-0.805646\pi$
$823$	5.17898	−	15.9392i	0.180528	−	0.555607i	0.999843	+	0.0177364i	$0.00564598\pi$
$824$		−	0.850903i		−	0.0296426i
$825$	4.21632	−	3.26665i	0.146793	−	0.113730i
$826$	−54.3434			−1.89085
$827$	13.2077	−	40.6492i	0.459277	−	1.41351i	−0.406762	−	0.913534i	$-0.633342\pi$
$827$	13.2077	−	40.6492i	0.459277	−	1.41351i	0.866039	−	0.499976i	$-0.166658\pi$
$828$	0.0486078	−	0.0353156i	0.00168924	−	0.00122730i
$829$	14.6431	−	20.1545i	0.508577	−	0.699996i	−0.475102	−	0.879931i	$-0.657589\pi$
$829$	14.6431	−	20.1545i	0.508577	−	0.699996i	0.983678	+	0.179935i	$0.0575888\pi$
$830$	9.32621	−	3.03027i	0.323717	−	0.105182i
$831$	6.96348	+	21.4314i	0.241561	+	0.743447i
$832$	2.60178	+	1.89030i	0.0902005	+	0.0655345i
$833$	55.6428	+	76.5858i	1.92791	+	2.65354i
$834$	4.83185	−	14.8709i	0.167313	−	0.514937i
$835$	−0.571151			−0.0197655
$836$	−0.674782	+	14.4411i	−0.0233378	+	0.499455i
$837$	43.0144			1.48680
$838$	3.46846	−	10.6748i	0.119816	−	0.368755i
$839$	−1.02942	−	1.41688i	−0.0355396	−	0.0489161i	0.790877	−	0.611975i	$-0.209625\pi$
$839$	−1.02942	−	1.41688i	−0.0355396	−	0.0489161i	−0.826417	+	0.563059i	$0.809625\pi$
$840$	14.9068	+	10.8304i	0.514334	+	0.373686i
$841$	−7.25180	−	22.3188i	−0.250062	−	0.769612i
$842$	−17.6079	+	5.72114i	−0.606807	+	0.197164i
$843$	6.28542	−	8.65114i	0.216481	−	0.297961i
$844$	−18.7714	+	13.6382i	−0.646138	+	0.469447i
$845$	2.01188	−	6.19192i	0.0692107	−	0.213009i
$846$	−2.29599			−0.0789379
$847$	49.9133	+	12.8765i	1.71504	+	0.442443i
$848$			10.4258i			0.358024i
$849$	8.35394	−	25.7108i	0.286707	−	0.882392i
$850$	3.72691	+	5.12966i	0.127832	+	0.175946i
$851$	0.397844	−	0.547585i	0.0136379	−	0.0187710i
$852$	6.95328	+	21.4000i	0.238215	+	0.733152i
$853$	34.2415	−	11.1258i	1.17241	−	0.380938i	0.342867	−	0.939384i	$-0.388602\pi$
$853$	34.2415	−	11.1258i	1.17241	−	0.380938i	0.829541	+	0.558446i	$0.188602\pi$
$854$	21.1533	+	15.3688i	0.723853	+	0.525910i
$855$	1.72892	−	4.18586i	0.0591277	−	0.143153i
$856$	2.70538	−	8.32631i	0.0924680	−	0.284587i
$857$	−28.8843			−0.986671			−0.493335	−	0.869839i	$-0.664222\pi$
$857$	−28.8843			−0.986671			−0.493335	+	0.869839i	$0.664222\pi$
$858$	14.1531	+	9.63032i	0.483180	+	0.328774i
$859$	34.0921			1.16321			0.581603	−	0.813472i	$-0.302426\pi$
$859$	34.0921			1.16321			0.581603	+	0.813472i	$0.302426\pi$
$860$	15.4438	+	5.01799i	0.526629	+	0.171112i
$861$	−55.7425	+	40.4993i	−1.89970	+	1.38021i
$862$	−22.8262	−	16.5842i	−0.777464	−	0.564860i
$863$	53.6546	−	17.4334i	1.82642	−	0.593441i	0.826907	−	0.562338i	$-0.190098\pi$
$863$	53.6546	−	17.4334i	1.82642	−	0.593441i	0.999516	−	0.0311031i	$-0.00990201\pi$
$864$	−5.22657	+	1.69822i	−0.177812	+	0.0577745i
$865$	21.3399	+	15.5043i	0.725577	+	0.527163i
$866$	4.28125	+	5.89263i	0.145483	+	0.200240i
$867$	35.1730	+	11.4284i	1.19454	+	0.388129i
$868$	36.6790			1.24497
$869$	−17.7133	−	22.8629i	−0.600883	−	0.775571i
$870$		−	9.24869i		−	0.313560i
$871$	−45.2872	−	14.7147i	−1.53450	−	0.498589i
$872$	−4.14556	+	3.01192i	−0.140386	+	0.101997i
$873$	0.0186098	−	0.0256142i	0.000629846	−	0.000866908i
$874$	0.469979	+	0.400585i	0.0158973	+	0.0135500i
$875$	43.6528	−	14.1836i	1.47573	−	0.479495i
$876$	−1.80141	−	1.30880i	−0.0608638	−	0.0442202i
$877$	38.6971	−	28.1151i	1.30671	−	0.949378i	0.306710	−	0.951803i	$-0.400772\pi$
$877$	38.6971	−	28.1151i	1.30671	−	0.949378i	0.999997	+	0.00242469i	$0.000771805\pi$
$878$	−8.03079	+	24.7162i	−0.271026	+	0.834133i
$879$		−	14.4159i		−	0.486237i
$880$	0.250571	+	8.12153i	0.00844675	+	0.273777i
$881$	−14.6542			−0.493712			−0.246856	−	0.969052i	$-0.579397\pi$
$881$	−14.6542			−0.493712			−0.246856	+	0.969052i	$0.579397\pi$
$882$	1.96053	−	6.03389i	0.0660145	−	0.203172i
$883$	30.9639	−	22.4966i	1.04202	−	0.757072i	0.0713410	−	0.997452i	$-0.477272\pi$
$883$	30.9639	−	22.4966i	1.04202	−	0.757072i	0.970679	+	0.240380i	$0.0772721\pi$
$884$	−11.9618	+	16.4639i	−0.402317	+	0.553742i
$885$	−14.0905	−	43.3662i	−0.473648	−	1.45774i
$886$	−2.98822	−	9.19679i	−0.100391	−	0.308972i
$887$	−31.9203	−	23.1915i	−1.07178	−	0.778694i	−0.0955488	−	0.995425i	$-0.530461\pi$
$887$	−31.9203	−	23.1915i	−1.07178	−	0.778694i	−0.976231	+	0.216731i	$0.930461\pi$
$888$	−6.20343	+	4.50706i	−0.208173	+	0.151247i
$889$	−25.7813	−	8.37687i	−0.864678	−	0.280951i
$890$			9.33988i			0.313073i
$891$	−23.5583	+	8.46627i	−0.789233	+	0.283631i
$892$		−	0.272885i		−	0.00913687i
$893$	−5.53199	−	22.9409i	−0.185121	−	0.767688i
$894$	−23.0471	+	16.7447i	−0.770809	+	0.560026i
$895$	−4.23042	+	5.82268i	−0.141407	+	0.194631i
$896$	−4.45678	+	1.44810i	−0.148891	+	0.0483775i
$897$	0.695454	−	0.225967i	0.0232205	−	0.00754481i
$898$	−0.837431	+	1.15263i	−0.0279454	+	0.0384636i
$899$	−10.8215	−	14.8946i	−0.360919	−	0.496762i
$900$	0.131315	−	0.404145i	0.00437716	−	0.0134715i
$901$	−65.9741			−2.19792
$902$	−29.1727	−	8.49359i	−0.971346	−	0.282806i
$903$			49.8516i			1.65896i
$904$	14.2265	+	4.62246i	0.473165	+	0.153741i
$905$	20.0313	+	27.5707i	0.665862	+	0.916481i
$906$	3.95714	−	5.44654i	0.131467	−	0.180949i
$907$	−28.2216	+	9.16974i	−0.937082	+	0.304476i	−0.737455	−	0.675396i	$-0.763973\pi$
$907$	−28.2216	+	9.16974i	−0.937082	+	0.304476i	−0.199626	+	0.979872i	$0.563973\pi$
$908$	−3.43988	−	10.5869i	−0.114156	−	0.351337i
$909$	1.99832	−	2.75046i	0.0662802	−	0.0912269i
$910$	−21.7017	−	29.8699i	−0.719405	−	0.990177i
$911$	30.6433	+	9.95660i	1.01526	+	0.329877i	0.768946	−	0.639314i	$-0.220782\pi$
$911$	30.6433	+	9.95660i	1.01526	+	0.329877i	0.246311	+	0.969191i	$0.420782\pi$
$912$	−3.66132	−	5.96128i	−0.121238	−	0.197398i
$913$	−3.71102	+	12.7461i	−0.122817	+	0.421836i
$914$		−	13.6369i		−	0.451067i
$915$	−6.77957	+	20.8654i	−0.224126	+	0.689787i
$916$	−11.2557	+	8.17774i	−0.371898	+	0.270200i
$917$	23.3951	+	16.9976i	0.772576	+	0.561309i
$918$	−10.7462	−	33.0735i	−0.354679	−	1.09159i
$919$	−12.9617	+	4.21151i	−0.427567	+	0.138925i	−0.514892	−	0.857255i	$-0.672168\pi$
$919$	−12.9617	+	4.21151i	−0.427567	+	0.138925i	0.0873251	+	0.996180i	$0.472168\pi$
$920$	0.280795	+	0.204010i	0.00925755	+	0.00672600i
$921$	23.4547	+	32.2826i	0.772858	+	1.06375i
$922$	−8.43171	−	2.73963i	−0.277684	−	0.0902249i
$923$		−	45.0874i		−	1.48407i
$924$	−23.4747	+	8.43622i	−0.772261	+	0.277531i
$925$		−	4.78715i		−	0.157400i
$926$	−0.181996	+	0.560125i	−0.00598075	+	0.0184069i
$927$	−0.212111	−	0.291945i	−0.00696663	−	0.00958875i
$928$	1.90294	+	1.38257i	0.0624671	+	0.0453850i
$929$	−13.1974	−	40.6174i	−0.432993	−	1.33261i	−0.895130	−	0.445806i	$-0.852917\pi$
$929$	−13.1974	−	40.6174i	−0.432993	−	1.33261i	0.462137	−	0.886809i	$-0.347083\pi$
$930$	9.51039	+	29.2700i	0.311858	+	0.959800i
$931$	65.0126	+	5.05091i	2.13070	+	0.165537i
$932$	6.05839	+	8.33866i	0.198449	+	0.273142i
$933$	−47.5529	−	15.4509i	−1.55681	−	0.505838i
$934$	−12.8780			−0.421381
$935$	−51.3926	+	1.58560i	−1.68072	+	0.0518547i
$936$	1.36388			0.0445799
$937$	4.07715	+	1.32475i	0.133195	+	0.0432775i	0.374856	−	0.927083i	$-0.377692\pi$
$937$	4.07715	+	1.32475i	0.133195	+	0.0432775i	−0.241661	+	0.970361i	$0.577692\pi$
$938$	56.1344	−	40.7840i	1.83285	−	1.33164i
$939$	11.9150	−	16.3996i	0.388833	−	0.535182i
$940$	−4.09862	−	12.6142i	−0.133682	−	0.411431i
$941$	−12.0186	−	36.9896i	−0.391796	−	1.20583i	−0.931428	−	0.363924i	$-0.881437\pi$
$941$	−12.0186	−	36.9896i	−0.391796	−	1.20583i	0.539632	−	0.841901i	$-0.318563\pi$
$942$	7.08288	−	9.74875i	0.230773	−	0.317631i
$943$	−1.05000	+	0.762873i	−0.0341928	+	0.0248426i
$944$	11.0291	+	3.58356i	0.358965	+	0.116635i
$945$	63.0919			2.05238
$946$	−17.3781	+	13.4639i	−0.565009	+	0.437748i
$947$	10.6100			0.344780			0.172390	−	0.985029i	$-0.444851\pi$
$947$	10.6100			0.344780			0.172390	+	0.985029i	$0.444851\pi$
$948$	13.3107	+	4.32491i	0.432312	+	0.140467i
$949$	2.62253	+	3.60960i	0.0851310	+	0.117173i
$950$	4.35449	+	0.338306i	0.141278	+	0.0109761i
$951$	10.5687	+	32.5272i	0.342715	+	1.05477i
$952$	−9.16348	−	28.2023i	−0.296990	−	0.914041i
$953$	4.82346	+	3.50445i	0.156247	+	0.113520i	0.663162	−	0.748476i	$-0.269214\pi$
$953$	4.82346	+	3.50445i	0.156247	+	0.113520i	−0.506915	+	0.861996i	$0.669214\pi$
$954$	2.59892	+	3.57711i	0.0841432	+	0.115813i
$955$	3.45550	−	10.6349i	0.111817	−	0.344138i
$956$			23.4133i			0.757239i
$957$	10.3516	+	7.04361i	0.334620	+	0.227688i
$958$			7.37742i			0.238354i
$959$	−49.5685	−	16.1058i	−1.60065	−	0.520083i
$960$	−2.31117	−	3.18105i	−0.0745926	−	0.102668i
$961$	24.4842	+	17.7888i	0.789813	+	0.573832i
$962$	14.6126	−	4.74793i	0.471130	−	0.153080i
$963$	−1.14734	−	3.53115i	−0.0369725	−	0.113790i
$964$	−0.309922	−	0.225171i	−0.00998191	−	0.00725228i
$965$	−22.5980	+	16.4184i	−0.727457	+	0.528528i
$966$	−0.329266	+	1.01338i	−0.0105939	+	0.0326048i
$967$			23.0610i			0.741591i	0.928715	+	0.370795i	$0.120915\pi$
$967$			23.0610i			0.741591i	−0.928715	+	0.370795i	$0.879085\pi$
$968$	−9.28085	−	5.90473i	−0.298298	−	0.189785i
$969$	37.7227	−	23.1687i	1.21183	−	0.744285i
$970$	0.173945	+	0.0565183i	0.00558505	+	0.00181469i
$971$	18.6578	+	25.6803i	0.598758	+	0.824120i	0.995594	−	0.0937698i	$-0.0298918\pi$
$971$	18.6578	+	25.6803i	0.598758	+	0.824120i	−0.396836	+	0.917890i	$0.629892\pi$
$972$	−2.57016	+	3.53752i	−0.0824378	+	0.113466i
$973$	−14.1079	−	43.4197i	−0.452279	−	1.39197i
$974$	−7.72305	+	2.50937i	−0.247463	+	0.0804055i
$975$	3.03993	−	4.18411i	0.0973558	−	0.133999i
$976$	−3.27963	−	4.51403i	−0.104979	−	0.144491i
$977$	−6.33331	−	2.05782i	−0.202620	−	0.0658354i	0.205949	−	0.978563i	$-0.433972\pi$
$977$	−6.33331	−	2.05782i	−0.202620	−	0.0658354i	−0.408569	+	0.912727i	$0.633972\pi$
$978$		−	35.9050i		−	1.14811i
$979$	−10.4537	−	7.11305i	−0.334100	−	0.227334i
$980$	36.6501			1.17074
$981$	−0.671539	+	2.06679i	−0.0214406	+	0.0659874i
$982$	5.79875	+	7.98129i	0.185045	+	0.254693i
$983$	−11.2295	+	15.4561i	−0.358165	+	0.492972i	−0.949636	−	0.313354i	$-0.898547\pi$
$983$	−11.2295	+	15.4561i	−0.358165	+	0.492972i	0.591471	+	0.806326i	$0.298547\pi$
$984$	13.9836	−	4.54356i	0.445782	−	0.144843i
$985$	1.05374	−	0.342382i	0.0335751	−	0.0109092i
$986$	−8.74882	+	12.0417i	−0.278619	+	0.383486i
$987$	32.9416	−	23.9334i	1.04854	−	0.761810i
$988$	3.28615	+	13.6275i	0.104546	+	0.433549i
$989$			0.939040i			0.0298597i
$990$	2.11048	+	2.72404i	0.0670755	+	0.0865756i
$991$			33.8415i			1.07501i	0.843261	+	0.537505i	$0.180633\pi$
$991$			33.8415i			1.07501i	−0.843261	+	0.537505i	$0.819367\pi$
$992$	−7.44405	−	2.41872i	−0.236349	−	0.0767944i
$993$	−32.6459	+	23.7187i	−1.03599	+	0.752689i
$994$	53.1514	+	38.6168i	1.68586	+	1.22485i
$995$	−7.35608	−	22.6397i	−0.233204	−	0.717727i
$996$	−1.98517	−	6.10973i	−0.0629026	−	0.193594i
$997$	−25.4622	+	35.0457i	−0.806397	+	1.10991i	0.185473	+	0.982649i	$0.440618\pi$
$997$	−25.4622	+	35.0457i	−0.806397	+	1.10991i	−0.991869	+	0.127260i	$0.959382\pi$
$998$	−31.6729	+	23.0117i	−1.00259	+	0.728423i
$999$	−8.11339	+	24.9705i	−0.256696	+	0.790030i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	418.2.m.b.189.8	yes	40
11.6	odd	10		418.2.m.a.303.3	yes	40
19.18	odd	2		418.2.m.a.189.3	✓	40
209.94	even	10	inner	418.2.m.b.303.8	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
418.2.m.a.189.3	✓	40	19.18	odd	2
418.2.m.a.303.3	yes	40	11.6	odd	10
418.2.m.b.189.8	yes	40	1.1	even	1	trivial
418.2.m.b.303.8	yes	40	209.94	even	10	inner

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:	\( N \)	\(=\)	\( 418 = 2 \cdot 11 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	418.m (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.309017 + 0.951057i) q^{2} +(0.943373 + 1.29844i) q^{3} +(-0.809017 - 0.587785i) q^{4} +(-0.757060 - 2.32999i) q^{5} +(-1.52641 + 0.495961i) q^{6} +(-2.75444 + 3.79116i) q^{7} +(0.809017 - 0.587785i) q^{8} +(0.131053 - 0.403339i) q^{9} +O(q^{10})\)	\(q+(-0.309017 + 0.951057i) q^{2} +(0.943373 + 1.29844i) q^{3} +(-0.809017 - 0.587785i) q^{4} +(-0.757060 - 2.32999i) q^{5} +(-1.52641 + 0.495961i) q^{6} +(-2.75444 + 3.79116i) q^{7} +(0.809017 - 0.587785i) q^{8} +(0.131053 - 0.403339i) q^{9} +2.44990 q^{10} +(-1.86579 + 2.74205i) q^{11} -1.60496i q^{12} +(-0.993792 + 3.05858i) q^{13} +(-2.75444 - 3.79116i) q^{14} +(2.31117 - 3.18105i) q^{15} +(0.309017 + 0.951057i) q^{16} +(-6.01824 + 1.95544i) q^{17} +(0.343101 + 0.249277i) q^{18} +(-1.66403 + 4.02877i) q^{19} +(-0.757060 + 2.32999i) q^{20} -7.52107 q^{21} +(-2.03128 - 2.62181i) q^{22} -0.141672 q^{23} +(1.52641 + 0.495961i) q^{24} +(-0.810634 + 0.588960i) q^{25} +(-2.60178 - 1.89030i) q^{26} +(5.22657 - 1.69822i) q^{27} +(4.45678 - 1.44810i) q^{28} +(-1.90294 - 1.38257i) q^{29} +(2.31117 + 3.18105i) q^{30} +(7.44405 + 2.41872i) q^{31} -1.00000 q^{32} +(-5.32053 + 0.164153i) q^{33} -6.32795i q^{34} +(10.9187 + 3.54769i) q^{35} +(-0.343101 + 0.249277i) q^{36} +(-2.80820 + 3.86516i) q^{37} +(-3.31737 - 2.82755i) q^{38} +(-4.90890 + 1.59500i) q^{39} +(-1.98201 - 1.44001i) q^{40} +(7.41151 - 5.38478i) q^{41} +(2.32414 - 7.15296i) q^{42} -6.62826i q^{43} +(3.12119 - 1.12168i) q^{44} -1.03899 q^{45} +(0.0437791 - 0.134738i) q^{46} +(-4.37990 + 3.18219i) q^{47} +(-0.943373 + 1.29844i) q^{48} +(-4.62285 - 14.2277i) q^{49} +(-0.309635 - 0.952958i) q^{50} +(-8.21648 - 5.96962i) q^{51} +(2.60178 - 1.89030i) q^{52} +(9.91555 + 3.22176i) q^{53} +5.49554i q^{54} +(7.80146 + 2.27138i) q^{55} +4.68613i q^{56} +(-6.80093 + 1.63998i) q^{57} +(1.90294 - 1.38257i) q^{58} +(6.81633 - 9.38187i) q^{59} +(-3.73955 + 1.21505i) q^{60} +(-5.30656 + 1.72421i) q^{61} +(-4.60068 + 6.33229i) q^{62} +(1.16815 + 1.60782i) q^{63} +(0.309017 - 0.951057i) q^{64} +7.87882 q^{65} +(1.48801 - 5.11085i) q^{66} +14.8066i q^{67} +(6.01824 + 1.95544i) q^{68} +(-0.133650 - 0.183953i) q^{69} +(-6.74810 + 9.28796i) q^{70} +(-13.3336 + 4.33236i) q^{71} +(-0.131053 - 0.403339i) q^{72} +(0.815469 - 1.12240i) q^{73} +(-2.80820 - 3.86516i) q^{74} +(-1.52946 - 0.496952i) q^{75} +(3.71428 - 2.28125i) q^{76} +(-5.25634 - 14.6263i) q^{77} -5.16152i q^{78} +(-2.69471 + 8.29347i) q^{79} +(1.98201 - 1.44001i) q^{80} +(6.10634 + 4.43652i) q^{81} +(2.83095 + 8.71275i) q^{82} +(3.80677 - 1.23690i) q^{83} +(6.08467 + 4.42077i) q^{84} +(9.11234 + 12.5421i) q^{85} +(6.30385 + 2.04825i) q^{86} -3.77513i q^{87} +(0.102278 + 3.31505i) q^{88} +3.81235i q^{89} +(0.321066 - 0.988139i) q^{90} +(-8.85822 - 12.1923i) q^{91} +(0.114615 + 0.0832728i) q^{92} +(3.88195 + 11.9474i) q^{93} +(-1.67297 - 5.14889i) q^{94} +(10.6468 + 0.827162i) q^{95} +(-0.943373 - 1.29844i) q^{96} +(0.0710011 + 0.0230697i) q^{97} +14.9599 q^{98} +(0.861457 + 1.11190i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 10 q^{2} - 10 q^{4} + 2 q^{5} + 5 q^{6} - 5 q^{7} + 10 q^{8} + 8 q^{9}+O(q^{10}) \) 40 * q + 10 * q^2 - 10 * q^4 + 2 * q^5 + 5 * q^6 - 5 * q^7 + 10 * q^8 + 8 * q^9	\( 40 q + 10 q^{2} - 10 q^{4} + 2 q^{5} + 5 q^{6} - 5 q^{7} + 10 q^{8} + 8 q^{9} - 2 q^{10} + 4 q^{11} - 8 q^{13} - 5 q^{14} - 30 q^{15} - 10 q^{16} - 15 q^{17} - 13 q^{18} + 11 q^{19} + 2 q^{20} - 4 q^{22} + 6 q^{23} - 5 q^{24} - 36 q^{25} - 2 q^{26} + 45 q^{27} + 2 q^{29} - 30 q^{30} - 40 q^{32} - 27 q^{33} - 5 q^{35} + 13 q^{36} + 14 q^{38} + 30 q^{39} + 3 q^{40} + 8 q^{41} + 20 q^{42} - 6 q^{44} + 18 q^{45} - q^{46} - 8 q^{47} + 31 q^{49} - 9 q^{50} - 41 q^{51} + 2 q^{52} + 40 q^{53} - 31 q^{55} - 10 q^{57} - 2 q^{58} - 35 q^{59} - 20 q^{60} + 5 q^{61} + 30 q^{62} - 25 q^{63} - 10 q^{64} - 8 q^{65} - 48 q^{66} + 15 q^{68} + 60 q^{69} + 10 q^{70} - 50 q^{71} - 8 q^{72} + 10 q^{73} + 35 q^{75} + 11 q^{76} - 64 q^{77} + 42 q^{79} - 3 q^{80} + 11 q^{81} + 7 q^{82} + 25 q^{83} + 20 q^{84} - 45 q^{85} + 40 q^{86} + 6 q^{88} + 22 q^{90} + 70 q^{91} - 4 q^{92} - 18 q^{93} - 7 q^{94} - 5 q^{95} + 15 q^{97} + 74 q^{98} + 50 q^{99}+O(q^{100}) \) 40 * q + 10 * q^2 - 10 * q^4 + 2 * q^5 + 5 * q^6 - 5 * q^7 + 10 * q^8 + 8 * q^9 - 2 * q^10 + 4 * q^11 - 8 * q^13 - 5 * q^14 - 30 * q^15 - 10 * q^16 - 15 * q^17 - 13 * q^18 + 11 * q^19 + 2 * q^20 - 4 * q^22 + 6 * q^23 - 5 * q^24 - 36 * q^25 - 2 * q^26 + 45 * q^27 + 2 * q^29 - 30 * q^30 - 40 * q^32 - 27 * q^33 - 5 * q^35 + 13 * q^36 + 14 * q^38 + 30 * q^39 + 3 * q^40 + 8 * q^41 + 20 * q^42 - 6 * q^44 + 18 * q^45 - q^46 - 8 * q^47 + 31 * q^49 - 9 * q^50 - 41 * q^51 + 2 * q^52 + 40 * q^53 - 31 * q^55 - 10 * q^57 - 2 * q^58 - 35 * q^59 - 20 * q^60 + 5 * q^61 + 30 * q^62 - 25 * q^63 - 10 * q^64 - 8 * q^65 - 48 * q^66 + 15 * q^68 + 60 * q^69 + 10 * q^70 - 50 * q^71 - 8 * q^72 + 10 * q^73 + 35 * q^75 + 11 * q^76 - 64 * q^77 + 42 * q^79 - 3 * q^80 + 11 * q^81 + 7 * q^82 + 25 * q^83 + 20 * q^84 - 45 * q^85 + 40 * q^86 + 6 * q^88 + 22 * q^90 + 70 * q^91 - 4 * q^92 - 18 * q^93 - 7 * q^94 - 5 * q^95 + 15 * q^97 + 74 * q^98 + 50 * q^99

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