LMFDB - Embedded newform 315.2.bl.j.146.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [315,2,Mod(41,315)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(315, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([5, 0, 3]))

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

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

chi := DirichletCharacter("315.41");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 315 = 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	315.bl (of order $6$, degree $2$, 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:	$2.51528766367$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			146.6
Character	$\chi$	$=$	315.146
Dual form			315.2.bl.j.41.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.552767 + 0.319140i) q^{2} +(-0.662870 + 1.60019i) q^{3} +(-0.796299 - 1.37923i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(-0.877097 + 0.672983i) q^{6} +(-1.77287 - 1.96391i) q^{7} -2.29308i q^{8} +(-2.12121 - 2.12143i) q^{9} +O(q^{10})$	\(q+(0.552767 + 0.319140i) q^{2} +(-0.662870 + 1.60019i) q^{3} +(-0.796299 - 1.37923i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(-0.877097 + 0.672983i) q^{6} +(-1.77287 - 1.96391i) q^{7} -2.29308i q^{8} +(-2.12121 - 2.12143i) q^{9} -0.638280i q^{10} +(-2.22872 - 1.28675i) q^{11} +(2.73487 - 0.359978i) q^{12} +(-2.91218 + 1.68135i) q^{13} +(-0.353221 - 1.65138i) q^{14} +(1.71724 - 0.226032i) q^{15} +(-0.860783 + 1.49092i) q^{16} +2.60840 q^{17} +(-0.495498 - 1.84962i) q^{18} -3.95039i q^{19} +(-0.796299 + 1.37923i) q^{20} +(4.31781 - 1.53511i) q^{21} +(-0.821308 - 1.42255i) q^{22} +(4.63797 - 2.67773i) q^{23} +(3.66937 + 1.52002i) q^{24} +(-0.500000 + 0.866025i) q^{25} -2.14634 q^{26} +(4.80078 - 1.98810i) q^{27} +(-1.29695 + 4.00905i) q^{28} +(-2.59976 - 1.50097i) q^{29} +(1.02137 + 0.423097i) q^{30} +(-5.64874 + 3.26130i) q^{31} +(-4.92336 + 2.84251i) q^{32} +(3.53639 - 2.71342i) q^{33} +(1.44184 + 0.832444i) q^{34} +(-0.814360 + 2.51730i) q^{35} +(-1.23683 + 4.61493i) q^{36} +7.47777 q^{37} +(1.26073 - 2.18365i) q^{38} +(-0.760076 - 5.77455i) q^{39} +(-1.98587 + 1.14654i) q^{40} +(-2.74102 - 4.74759i) q^{41} +(2.87666 + 0.529428i) q^{42} +(-4.78957 + 8.29578i) q^{43} +4.09855i q^{44} +(-0.776612 + 2.89774i) q^{45} +3.41829 q^{46} +(5.53943 - 9.59457i) q^{47} +(-1.81516 - 2.36570i) q^{48} +(-0.713871 + 6.96350i) q^{49} +(-0.552767 + 0.319140i) q^{50} +(-1.72903 + 4.17393i) q^{51} +(4.63793 + 2.67771i) q^{52} +8.57614i q^{53} +(3.28819 + 0.433167i) q^{54} +2.57350i q^{55} +(-4.50341 + 4.06534i) q^{56} +(6.32137 + 2.61860i) q^{57} +(-0.958039 - 1.65937i) q^{58} +(-4.28361 - 7.41944i) q^{59} +(-1.67919 - 2.18848i) q^{60} +(-3.81680 - 2.20363i) q^{61} -4.16325 q^{62} +(-0.405679 + 7.92688i) q^{63} -0.185501 q^{64} +(2.91218 + 1.68135i) q^{65} +(2.82076 - 0.371284i) q^{66} +(-4.92473 - 8.52989i) q^{67} +(-2.07706 - 3.59758i) q^{68} +(1.21051 + 9.19661i) q^{69} +(-1.25352 + 1.13159i) q^{70} -6.71360i q^{71} +(-4.86463 + 4.86411i) q^{72} +6.51892i q^{73} +(4.13346 + 2.38646i) q^{74} +(-1.05437 - 1.37416i) q^{75} +(-5.44850 + 3.14569i) q^{76} +(1.42416 + 6.65824i) q^{77} +(1.42274 - 3.43455i) q^{78} +(-1.07209 + 1.85691i) q^{79} +1.72157 q^{80} +(-0.000962727 + 9.00000i) q^{81} -3.49908i q^{82} +(3.62867 - 6.28503i) q^{83} +(-5.55553 - 4.73284i) q^{84} +(-1.30420 - 2.25894i) q^{85} +(-5.29503 + 3.05709i) q^{86} +(4.12513 - 3.16515i) q^{87} +(-2.95063 + 5.11064i) q^{88} +11.8056 q^{89} +(-1.35407 + 1.35392i) q^{90} +(8.46492 + 2.73844i) q^{91} +(-7.38642 - 4.26455i) q^{92} +(-1.47432 - 11.2009i) q^{93} +(6.12403 - 3.53571i) q^{94} +(-3.42114 + 1.97520i) q^{95} +(-1.28499 - 9.76252i) q^{96} +(-0.235631 - 0.136041i) q^{97} +(-2.61694 + 3.62137i) q^{98} +(1.99781 + 7.45754i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 6 q^{2} + 5 q^{3} + 18 q^{4} - 12 q^{5} + q^{6} + 9 q^{7} + q^{9}+O(q^{10}) $ 24 * q + 6 * q^2 + 5 * q^3 + 18 * q^4 - 12 * q^5 + q^6 + 9 * q^7 + q^9	$ 24 q + 6 q^{2} + 5 q^{3} + 18 q^{4} - 12 q^{5} + q^{6} + 9 q^{7} + q^{9} + 9 q^{11} - 18 q^{12} + 3 q^{13} + 18 q^{14} + 2 q^{15} - 18 q^{16} + 18 q^{17} + 2 q^{18} + 18 q^{20} + 8 q^{21} - 9 q^{22} + 9 q^{23} - 7 q^{24} - 12 q^{25} - 18 q^{26} - 4 q^{27} - 9 q^{28} + 9 q^{29} - 5 q^{30} - 42 q^{31} + 18 q^{32} + 13 q^{33} - 39 q^{34} - 9 q^{35} - 21 q^{36} - 12 q^{38} - 21 q^{39} - 6 q^{40} - 33 q^{41} - 65 q^{42} + 18 q^{43} + q^{45} - 30 q^{46} - 17 q^{48} + 9 q^{49} - 6 q^{50} - 12 q^{51} + 129 q^{52} + 52 q^{54} - 9 q^{56} + 6 q^{57} - 15 q^{58} + 12 q^{59} + 15 q^{60} - 15 q^{61} + 12 q^{62} + 46 q^{63} - 60 q^{64} - 3 q^{65} + 29 q^{66} - 15 q^{67} + 9 q^{68} + 61 q^{69} - 9 q^{70} + 61 q^{72} - 18 q^{74} - 7 q^{75} + 54 q^{76} - 45 q^{77} - 66 q^{78} + 21 q^{79} + 36 q^{80} + q^{81} - 30 q^{83} + 15 q^{84} - 9 q^{85} - 102 q^{86} + 10 q^{87} - 9 q^{88} + 102 q^{89} - 37 q^{90} + 42 q^{91} - 3 q^{92} - 6 q^{93} - 156 q^{94} - 18 q^{95} - 42 q^{96} - 45 q^{97} + 3 q^{98} + 23 q^{99}+O(q^{100}) $ 24 * q + 6 * q^2 + 5 * q^3 + 18 * q^4 - 12 * q^5 + q^6 + 9 * q^7 + q^9 + 9 * q^11 - 18 * q^12 + 3 * q^13 + 18 * q^14 + 2 * q^15 - 18 * q^16 + 18 * q^17 + 2 * q^18 + 18 * q^20 + 8 * q^21 - 9 * q^22 + 9 * q^23 - 7 * q^24 - 12 * q^25 - 18 * q^26 - 4 * q^27 - 9 * q^28 + 9 * q^29 - 5 * q^30 - 42 * q^31 + 18 * q^32 + 13 * q^33 - 39 * q^34 - 9 * q^35 - 21 * q^36 - 12 * q^38 - 21 * q^39 - 6 * q^40 - 33 * q^41 - 65 * q^42 + 18 * q^43 + q^45 - 30 * q^46 - 17 * q^48 + 9 * q^49 - 6 * q^50 - 12 * q^51 + 129 * q^52 + 52 * q^54 - 9 * q^56 + 6 * q^57 - 15 * q^58 + 12 * q^59 + 15 * q^60 - 15 * q^61 + 12 * q^62 + 46 * q^63 - 60 * q^64 - 3 * q^65 + 29 * q^66 - 15 * q^67 + 9 * q^68 + 61 * q^69 - 9 * q^70 + 61 * q^72 - 18 * q^74 - 7 * q^75 + 54 * q^76 - 45 * q^77 - 66 * q^78 + 21 * q^79 + 36 * q^80 + q^81 - 30 * q^83 + 15 * q^84 - 9 * q^85 - 102 * q^86 + 10 * q^87 - 9 * q^88 + 102 * q^89 - 37 * q^90 + 42 * q^91 - 3 * q^92 - 6 * q^93 - 156 * q^94 - 18 * q^95 - 42 * q^96 - 45 * q^97 + 3 * q^98 + 23 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/315\mathbb{Z}\right)^\times$.

$n$	$127$	$136$	$281$
$\chi(n)$	$1$	$-1$	$e\left(\frac{1}{6}\right)$

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 $

$2$	0.552767	+	0.319140i	0.390865	+	0.225666i	0.682535	−	0.730853i	$-0.260877\pi$
$2$	0.552767	+	0.319140i	0.390865	+	0.225666i	−0.291670	+	0.956519i	$0.594211\pi$
$3$	−0.662870	+	1.60019i	−0.382708	+	0.923869i
$3$	−0.662870	+	1.60019i	−0.382708	+	0.923869i
$4$	−0.796299	−	1.37923i	−0.398150	−	0.689615i
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i
$6$	−0.877097	+	0.672983i	−0.358073	+	0.274744i
$7$	−1.77287	−	1.96391i	−0.670081	−	0.742288i
$7$	−1.77287	−	1.96391i	−0.670081	−	0.742288i
$8$		−	2.29308i		−	0.810728i
$9$	−2.12121	−	2.12143i	−0.707069	−	0.707145i
$10$		−	0.638280i		−	0.201842i
$11$	−2.22872	−	1.28675i	−0.671984	−	0.387970i	0.124844	−	0.992176i	$-0.460157\pi$
$11$	−2.22872	−	1.28675i	−0.671984	−	0.387970i	−0.796828	+	0.604206i	$0.793490\pi$
$12$	2.73487	−	0.359978i	0.789489	−	0.103917i
$13$	−2.91218	+	1.68135i	−0.807692	+	0.466321i	−0.846154	−	0.532939i	$-0.821088\pi$
$13$	−2.91218	+	1.68135i	−0.807692	+	0.466321i	0.0384614	+	0.999260i	$0.487754\pi$
$14$	−0.353221	−	1.65138i	−0.0944024	−	0.441349i
$15$	1.71724	−	0.226032i	0.443389	−	0.0583612i
$16$	−0.860783	+	1.49092i	−0.215196	+	0.372730i
$17$	2.60840			0.632629			0.316315	−	0.948654i	$-0.397554\pi$
$17$	2.60840			0.632629			0.316315	+	0.948654i	$0.397554\pi$
$18$	−0.495498	−	1.84962i	−0.116790	−	0.435960i
$19$		−	3.95039i		−	0.906282i	−0.891439	−	0.453141i	$-0.850303\pi$
$19$		−	3.95039i		−	0.906282i	0.891439	−	0.453141i	$-0.149697\pi$
$20$	−0.796299	+	1.37923i	−0.178058	+	0.308405i
$21$	4.31781	−	1.53511i	0.942222	−	0.334988i
$22$	−0.821308	−	1.42255i	−0.175103	−	0.303288i
$23$	4.63797	−	2.67773i	0.967084	−	0.558346i	0.0687376	−	0.997635i	$-0.478103\pi$
$23$	4.63797	−	2.67773i	0.967084	−	0.558346i	0.898346	+	0.439289i	$0.144770\pi$
$24$	3.66937	+	1.52002i	0.749007	+	0.310272i
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$	−2.14634			−0.420932
$27$	4.80078	−	1.98810i	0.923910	−	0.382609i
$28$	−1.29695	+	4.00905i	−0.245100	+	0.757640i
$29$	−2.59976	−	1.50097i	−0.482762	−	0.278723i	0.238805	−	0.971068i	$-0.423244\pi$
$29$	−2.59976	−	1.50097i	−0.482762	−	0.278723i	−0.721567	+	0.692345i	$0.756578\pi$
$30$	1.02137	+	0.423097i	0.186476	+	0.0772466i
$31$	−5.64874	+	3.26130i	−1.01454	+	0.585747i	−0.912519	−	0.409035i	$-0.865866\pi$
$31$	−5.64874	+	3.26130i	−1.01454	+	0.585747i	−0.102025	+	0.994782i	$0.532532\pi$
$32$	−4.92336	+	2.84251i	−0.870336	+	0.502489i
$33$	3.53639	−	2.71342i	0.615607	−	0.472346i
$34$	1.44184	+	0.832444i	0.247273	+	0.142763i
$35$	−0.814360	+	2.51730i	−0.137652	+	0.425502i
$36$	−1.23683	+	4.61493i	−0.206139	+	0.769155i
$37$	7.47777			1.22934			0.614669	−	0.788785i	$-0.289290\pi$
$37$	7.47777			1.22934			0.614669	+	0.788785i	$0.289290\pi$
$38$	1.26073	−	2.18365i	0.204517	−	0.354234i
$39$	−0.760076	−	5.77455i	−0.121710	−	0.924667i
$40$	−1.98587	+	1.14654i	−0.313994	+	0.181284i
$41$	−2.74102	−	4.74759i	−0.428076	−	0.741449i	0.568626	−	0.822596i	$-0.307475\pi$
$41$	−2.74102	−	4.74759i	−0.428076	−	0.741449i	−0.996702	+	0.0811468i	$0.974142\pi$
$42$	2.87666	+	0.529428i	0.443878	+	0.0816924i
$43$	−4.78957	+	8.29578i	−0.730403	+	1.26509i	0.226308	+	0.974056i	$0.427334\pi$
$43$	−4.78957	+	8.29578i	−0.730403	+	1.26509i	−0.956711	+	0.291039i	$0.905999\pi$
$44$			4.09855i			0.617880i
$45$	−0.776612	+	2.89774i	−0.115770	+	0.431969i
$46$	3.41829			0.503999
$47$	5.53943	−	9.59457i	0.808009	−	1.39951i	−0.106232	−	0.994341i	$-0.533879\pi$
$47$	5.53943	−	9.59457i	0.808009	−	1.39951i	0.914241	−	0.405171i	$-0.132788\pi$
$48$	−1.81516	−	2.36570i	−0.261996	−	0.341459i
$49$	−0.713871	+	6.96350i	−0.101982	+	0.994786i
$50$	−0.552767	+	0.319140i	−0.0781731	+	0.0451332i
$51$	−1.72903	+	4.17393i	−0.242112	+	0.584467i
$52$	4.63793	+	2.67771i	0.643165	+	0.371331i
$53$			8.57614i			1.17802i	0.808124	+	0.589012i	$0.200483\pi$
$53$			8.57614i			1.17802i	−0.808124	+	0.589012i	$0.799517\pi$
$54$	3.28819	+	0.433167i	0.447466	+	0.0589466i
$55$			2.57350i			0.347011i
$56$	−4.50341	+	4.06534i	−0.601793	+	0.543254i
$57$	6.32137	+	2.61860i	0.837286	+	0.346842i
$58$	−0.958039	−	1.65937i	−0.125797	−	0.217886i
$59$	−4.28361	−	7.41944i	−0.557679	−	0.965928i	−0.997690	−	0.0679359i	$-0.978359\pi$
$59$	−4.28361	−	7.41944i	−0.557679	−	0.965928i	0.440011	−	0.897993i	$-0.354975\pi$
$60$	−1.67919	−	2.18848i	−0.216782	−	0.282531i
$61$	−3.81680	−	2.20363i	−0.488691	−	0.282146i	0.235340	−	0.971913i	$-0.424380\pi$
$61$	−3.81680	−	2.20363i	−0.488691	−	0.282146i	−0.724031	+	0.689767i	$0.757713\pi$
$62$	−4.16325			−0.528733
$63$	−0.405679	+	7.92688i	−0.0511108	+	0.998693i
$64$	−0.185501			−0.0231876
$65$	2.91218	+	1.68135i	0.361211	+	0.208545i
$66$	2.82076	−	0.371284i	0.347212	−	0.0457019i
$67$	−4.92473	−	8.52989i	−0.601652	−	1.04209i	−0.992571	−	0.121666i	$-0.961176\pi$
$67$	−4.92473	−	8.52989i	−0.601652	−	1.04209i	0.390919	−	0.920425i	$-0.372157\pi$
$68$	−2.07706	−	3.59758i	−0.251881	−	0.436271i
$69$	1.21051	+	9.19661i	0.145728	+	1.10714i
$70$	−1.25352	+	1.13159i	−0.149825	+	0.135251i
$71$		−	6.71360i		−	0.796758i	−0.917221	−	0.398379i	$-0.869573\pi$
$71$		−	6.71360i		−	0.796758i	0.917221	−	0.398379i	$-0.130427\pi$
$72$	−4.86463	+	4.86411i	−0.573302	+	0.573241i
$73$			6.51892i			0.762982i	0.924373	+	0.381491i	$0.124589\pi$
$73$			6.51892i			0.762982i	−0.924373	+	0.381491i	$0.875411\pi$
$74$	4.13346	+	2.38646i	0.480505	+	0.277420i
$75$	−1.05437	−	1.37416i	−0.121748	−	0.158674i
$76$	−5.44850	+	3.14569i	−0.624986	+	0.360836i
$77$	1.42416	+	6.65824i	0.162299	+	0.758777i
$78$	1.42274	−	3.43455i	0.161094	−	0.388886i
$79$	−1.07209	+	1.85691i	−0.120619	+	0.208918i	−0.920012	−	0.391890i	$-0.871821\pi$
$79$	−1.07209	+	1.85691i	−0.120619	+	0.208918i	0.799393	+	0.600809i	$0.205155\pi$
$80$	1.72157			0.192477
$81$	−0.000962727		9.00000i	−0.000106970		1.00000i
$82$		−	3.49908i		−	0.386409i
$83$	3.62867	−	6.28503i	0.398298	−	0.689872i	−0.595218	−	0.803564i	$-0.702934\pi$
$83$	3.62867	−	6.28503i	0.398298	−	0.689872i	0.993516	+	0.113692i	$0.0362677\pi$
$84$	−5.55553	−	4.73284i	−0.606158	−	0.516395i
$85$	−1.30420	−	2.25894i	−0.141460	−	0.245016i
$86$	−5.29503	+	3.05709i	−0.570978	+	0.329654i
$87$	4.12513	−	3.16515i	0.442261	−	0.339340i
$88$	−2.95063	+	5.11064i	−0.314538	+	0.544796i
$89$	11.8056			1.25139			0.625696	−	0.780067i	$-0.284815\pi$
$89$	11.8056			1.25139			0.625696	+	0.780067i	$0.284815\pi$
$90$	−1.35407	+	1.35392i	−0.142731	+	0.142716i
$91$	8.46492	+	2.73844i	0.887364	+	0.287067i
$92$	−7.38642	−	4.26455i	−0.770088	−	0.444610i
$93$	−1.47432	−	11.2009i	−0.152880	−	1.16148i
$94$	6.12403	−	3.53571i	0.631645	−	0.364681i
$95$	−3.42114	+	1.97520i	−0.351002	+	0.202651i
$96$	−1.28499	−	9.76252i	−0.131149	−	0.996383i
$97$	−0.235631	−	0.136041i	−0.0239247	−	0.0138129i	0.487990	−	0.872849i	$-0.337730\pi$
$97$	−0.235631	−	0.136041i	−0.0239247	−	0.0138129i	−0.511915	+	0.859036i	$0.671064\pi$
$98$	−2.61694	+	3.62137i	−0.264351	+	0.365814i
$99$	1.99781	+	7.45754i	0.200788	+	0.749511i
$100$	1.59260			0.159260
$101$	−1.41899	+	2.45776i	−0.141195	+	0.244556i	−0.927947	−	0.372713i	$-0.878428\pi$
$101$	−1.41899	+	2.45776i	−0.141195	+	0.244556i	0.786752	+	0.617269i	$0.211761\pi$
$102$	−2.28782	+	1.75541i	−0.226528	+	0.173811i
$103$	10.5034	−	6.06412i	1.03493	−	0.597516i	0.116535	−	0.993187i	$-0.462821\pi$
$103$	10.5034	−	6.06412i	1.03493	−	0.597516i	0.918392	+	0.395671i	$0.129488\pi$
$104$	3.85547	+	6.67787i	0.378060	+	0.654819i
$105$	−3.48835	−	2.97177i	−0.340428	−	0.290015i
$106$	−2.73699	+	4.74061i	−0.265840	+	0.460449i
$107$		−	10.2861i		−	0.994392i	−0.867638	−	0.497196i	$-0.834363\pi$
$107$		−	10.2861i		−	0.994392i	0.867638	−	0.497196i	$-0.165637\pi$
$108$	−6.56490	−	5.03826i	−0.631708	−	0.484807i
$109$	17.9601			1.72026			0.860132	−	0.510071i	$-0.170381\pi$
$109$	17.9601			1.72026			0.860132	+	0.510071i	$0.170381\pi$
$110$	−0.821308	+	1.42255i	−0.0783086	+	0.135635i
$111$	−4.95679	+	11.9658i	−0.470478	+	1.13575i
$112$	4.45408	−	0.952706i	0.420871	−	0.0900223i
$113$	15.6229	−	9.01990i	1.46968	−	0.848521i	0.470260	−	0.882528i	$-0.344160\pi$
$113$	15.6229	−	9.01990i	1.46968	−	0.848521i	0.999422	+	0.0340066i	$0.0108267\pi$
$114$	2.65855	+	3.46488i	0.248996	+	0.324516i
$115$	−4.63797	−	2.67773i	−0.432493	−	0.249700i
$116$			4.78088i			0.443894i
$117$	9.74419	+	2.61151i	0.900851	+	0.241434i
$118$		−	5.46829i		−	0.503397i
$119$	−4.62435	−	5.12265i	−0.423913	−	0.469593i
$120$	−0.518311	−	3.93777i	−0.0473151	−	0.359468i
$121$	−2.18854	−	3.79067i	−0.198959	−	0.344606i
$122$	−1.40653	−	2.43619i	−0.127342	−	0.220562i
$123$	9.41398	−	1.23912i	0.848830	−	0.111728i
$124$	8.99618	+	5.19394i	0.807880	+	0.466430i
$125$	1.00000			0.0894427
$126$	−2.75403	+	4.25225i	−0.245349	+	0.378820i
$127$	−15.6765			−1.39107			−0.695534	−	0.718494i	$-0.744832\pi$
$127$	−15.6765			−1.39107			−0.695534	+	0.718494i	$0.744832\pi$
$128$	9.74419	+	5.62581i	0.861273	+	0.497256i
$129$	−10.1000	−	13.1632i	−0.889251	−	1.15896i
$130$	1.07317	+	1.85879i	0.0941233	+	0.163026i
$131$	3.07279	+	5.32223i	0.268471	+	0.465005i	0.968467	−	0.249141i	$-0.0801483\pi$
$131$	3.07279	+	5.32223i	0.268471	+	0.465005i	−0.699996	+	0.714147i	$0.746815\pi$
$132$	−6.55846	−	2.71681i	−0.570841	−	0.236468i
$133$	−7.75821	+	7.00353i	−0.672722	+	0.607283i
$134$		−	6.28672i		−	0.543090i
$135$	−4.12213	−	3.16355i	−0.354777	−	0.272275i
$136$		−	5.98128i		−	0.512890i
$137$	−7.67620	−	4.43186i	−0.655822	−	0.378639i	0.134861	−	0.990865i	$-0.456941\pi$
$137$	−7.67620	−	4.43186i	−0.655822	−	0.378639i	−0.790683	+	0.612225i	$0.790274\pi$
$138$	−2.26588	+	5.46991i	−0.192885	+	0.465629i
$139$	−8.24478	+	4.76013i	−0.699313	+	0.403749i	−0.807092	−	0.590426i	$-0.798960\pi$
$139$	−8.24478	+	4.76013i	−0.699313	+	0.403749i	0.107778	+	0.994175i	$0.465626\pi$
$140$	4.12042	−	0.881337i	0.348239	−	0.0744865i
$141$	11.6812	+	15.2241i	0.983735	+	1.28210i
$142$	2.14258	−	3.71106i	0.179801	−	0.311425i
$143$	8.65389			0.723675
$144$	4.98878	−	1.33645i	0.415732	−	0.111371i
$145$			3.00194i			0.249297i
$146$	−2.08045	+	3.60344i	−0.172179	+	0.298223i
$147$	−10.6697	−	5.75823i	−0.880023	−	0.474930i
$148$	−5.95454	−	10.3136i	−0.489460	−	0.847770i
$149$	−1.86456	+	1.07650i	−0.152750	+	0.0881904i	−0.574427	−	0.818556i	$-0.694775\pi$
$149$	−1.86456	+	1.07650i	−0.152750	+	0.0881904i	0.421677	+	0.906746i	$0.361442\pi$
$150$	−0.144272	−	1.09608i	−0.0117797	−	0.0894946i
$151$	10.8088	−	18.7214i	0.879608	−	1.52353i	0.0278368	−	0.999612i	$-0.491138\pi$
$151$	10.8088	−	18.7214i	0.879608	−	1.52353i	0.851771	−	0.523914i	$-0.175529\pi$
$152$	−9.05859			−0.734748
$153$	−5.53295	−	5.53354i	−0.447313	−	0.447360i
$154$	−1.33768	+	4.13496i	−0.107793	+	0.333205i
$155$	5.64874	+	3.26130i	0.453718	+	0.261954i
$156$	−7.35918	+	5.64659i	−0.589206	+	0.452089i
$157$	2.85973	−	1.65107i	0.228232	−	0.131770i	−0.381524	−	0.924359i	$-0.624601\pi$
$157$	2.85973	−	1.65107i	0.228232	−	0.131770i	0.609756	+	0.792589i	$0.291267\pi$
$158$	−1.18523	+	0.684291i	−0.0942916	+	0.0544393i
$159$	−13.7234	−	5.68487i	−1.08834	−	0.450839i
$160$	4.92336	+	2.84251i	0.389226	+	0.224720i
$161$	−13.4813	−	4.36128i	−1.06248	−	0.343717i
$162$	−2.87279	+	4.97460i	−0.225708	+	0.390841i
$163$	−22.1660			−1.73618			−0.868089	−	0.496408i	$-0.834652\pi$
$163$	−22.1660			−1.73618			−0.868089	+	0.496408i	$0.834652\pi$
$164$	−4.36535	+	7.56100i	−0.340876	+	0.590415i
$165$	−4.11809	−	1.70590i	−0.320593	−	0.132804i
$166$	4.01161	−	2.31611i	0.311362	−	0.179765i
$167$	9.71593	+	16.8285i	0.751841	+	1.30223i	0.946929	+	0.321442i	$0.104167\pi$
$167$	9.71593	+	16.8285i	0.751841	+	1.30223i	−0.195088	+	0.980786i	$0.562499\pi$
$168$	−3.52014	−	9.90109i	−0.271584	−	0.763886i
$169$	−0.846151	+	1.46558i	−0.0650886	+	0.112737i
$170$		−	1.66489i		−	0.127691i
$171$	−8.38050	+	8.37960i	−0.640873	+	0.640804i
$172$	15.2557			1.16324
$173$	0.906004	−	1.56925i	0.0688822	−	0.119307i	−0.829527	−	0.558466i	$-0.811390\pi$
$173$	0.906004	−	1.56925i	0.0688822	−	0.119307i	0.898410	+	0.439159i	$0.144723\pi$
$174$	3.29036	−	0.433095i	0.249442	−	0.0328329i
$175$	2.58723	−	0.553395i	0.195576	−	0.0418328i
$176$	3.83688	−	2.21523i	0.289216	−	0.166979i
$177$	14.7120	−	1.93647i	1.10582	−	0.145554i
$178$	6.52575	+	3.76765i	0.489126	+	0.282397i
$179$			6.19083i			0.462725i	0.972868	+	0.231362i	$0.0743183\pi$
$179$			6.19083i			0.462725i	−0.972868	+	0.231362i	$0.925682\pi$
$180$	4.61506	−	1.23634i	0.343986	−	0.0921511i
$181$		−	11.8291i		−	0.879249i	−0.898182	−	0.439625i	$-0.855111\pi$
$181$		−	11.8291i		−	0.879249i	0.898182	−	0.439625i	$-0.144889\pi$
$182$	3.80518	+	4.21522i	0.282059	+	0.312453i
$183$	6.05626	−	4.64688i	0.447692	−	0.343507i
$184$	−6.14027	−	10.6353i	−0.452667	−	0.784042i
$185$	−3.73888	−	6.47594i	−0.274888	−	0.476120i
$186$	2.75969	−	6.66199i	0.202351	−	0.488481i
$187$	−5.81338	−	3.35636i	−0.425117	−	0.245441i
$188$	−17.6442			−1.28683
$189$	−12.4156	−	5.90365i	−0.903101	−	0.429428i
$190$	−2.52146			−0.182926
$191$	−8.65572	−	4.99738i	−0.626306	−	0.361598i	0.153014	−	0.988224i	$-0.451102\pi$
$191$	−8.65572	−	4.99738i	−0.626306	−	0.361598i	−0.779320	+	0.626626i	$0.784435\pi$
$192$	0.122963	−	0.296836i	0.00887409	−	0.0214223i
$193$	2.05829	+	3.56507i	0.148159	+	0.256619i	0.930547	−	0.366172i	$-0.119332\pi$
$193$	2.05829	+	3.56507i	0.148159	+	0.256619i	−0.782388	+	0.622791i	$0.785999\pi$
$194$	−0.0868325	−	0.150398i	−0.00623421	−	0.0107980i
$195$	−4.62087	+	3.54552i	−0.330907	+	0.253900i
$196$	10.1727	−	4.56044i	0.726624	−	0.325746i
$197$			3.98010i			0.283570i	0.989897	+	0.141785i	$0.0452842\pi$
$197$			3.98010i			0.283570i	−0.989897	+	0.141785i	$0.954716\pi$
$198$	−1.27568	+	4.75987i	−0.0906583	+	0.338269i
$199$		−	25.1000i		−	1.77929i	−0.456649	−	0.889647i	$-0.650951\pi$
$199$		−	25.1000i		−	1.77929i	0.456649	−	0.889647i	$-0.349049\pi$
$200$	1.98587	+	1.14654i	0.140422	+	0.0810728i
$201$	16.9139	−	2.22629i	1.19301	−	0.157031i
$202$	−1.56874	+	0.905713i	−0.110376	+	0.0637257i
$203$	1.66126	+	7.76670i	0.116598	+	0.545116i
$204$	7.13363	−	0.938966i	0.499454	−	0.0657408i
$205$	−2.74102	+	4.74759i	−0.191441	+	0.331586i
$206$	7.74122			0.539356
$207$	−15.5187	−	4.15912i	−1.07863	−	0.289079i
$208$		−	5.78909i		−	0.401401i
$209$	−5.08317	+	8.80431i	−0.351610	+	0.609007i
$210$	−0.979830	−	2.75597i	−0.0676147	−	0.190180i
$211$	−6.14184	−	10.6380i	−0.422822	−	0.732349i	0.573392	−	0.819281i	$-0.305627\pi$
$211$	−6.14184	−	10.6380i	−0.422822	−	0.732349i	−0.996214	+	0.0869318i	$0.972294\pi$
$212$	11.8285	−	6.82917i	0.812383	−	0.469029i
$213$	10.7430	+	4.45025i	0.736100	+	0.304926i
$214$	3.28270	−	5.68580i	0.224401	−	0.388673i
$215$	9.57914			0.653292
$216$	−4.55887	−	11.0086i	−0.310192	−	0.749040i
$217$	16.4194	+	5.31175i	1.11462	+	0.360585i
$218$	9.92775	+	5.73179i	0.672392	+	0.388206i
$219$	−10.4315	−	4.32120i	−0.704896	−	0.291999i
$220$	3.54945	−	2.04928i	0.239304	−	0.138162i
$221$	−7.59611	+	4.38562i	−0.510970	+	0.295009i
$222$	−6.55873	+	5.03241i	−0.440193	+	0.337753i
$223$	16.5774	+	9.57096i	1.11010	+	0.640919i	0.938856	−	0.344309i	$-0.111887\pi$
$223$	16.5774	+	9.57096i	1.11010	+	0.640919i	0.171248	+	0.985228i	$0.445220\pi$
$224$	14.3109	+	4.62965i	0.956187	+	0.309331i
$225$	2.89782	−	0.776302i	0.193188	−	0.0517535i
$226$	11.5145			0.765930
$227$	−5.39780	+	9.34927i	−0.358265	+	0.620533i	−0.987671	−	0.156544i	$-0.949965\pi$
$227$	−5.39780	+	9.34927i	−0.358265	+	0.620533i	0.629406	+	0.777076i	$0.283298\pi$
$228$	−1.42206	−	10.8038i	−0.0941779	−	0.715500i
$229$	1.09578	−	0.632652i	0.0724115	−	0.0418068i	−0.463357	−	0.886172i	$-0.653355\pi$
$229$	1.09578	−	0.632652i	0.0724115	−	0.0418068i	0.535769	+	0.844365i	$0.320022\pi$
$230$	−1.70914	−	2.96033i	−0.112698	−	0.195198i
$231$	−11.5985	−	2.13461i	−0.763123	−	0.140447i
$232$	−3.44185	+	5.96146i	−0.225969	+	0.391389i
$233$			2.66444i			0.174553i	0.996184	+	0.0872766i	$0.0278164\pi$
$233$			2.66444i			0.174553i	−0.996184	+	0.0872766i	$0.972184\pi$
$234$	4.55283	+	4.55332i	0.297628	+	0.297660i
$235$	−11.0789			−0.722705
$236$	−6.82208	+	11.8162i	−0.444079	+	0.769168i
$237$	−2.26075	−	2.94643i	−0.146851	−	0.191391i
$238$	−0.921342	−	4.30745i	−0.0597217	−	0.279210i
$239$	4.50900	−	2.60327i	0.291663	−	0.168392i	−0.347028	−	0.937855i	$-0.612809\pi$
$239$	4.50900	−	2.60327i	0.291663	−	0.168392i	0.638692	+	0.769463i	$0.279476\pi$
$240$	−1.14117	+	2.75483i	−0.0736625	+	0.177823i
$241$	1.11798	+	0.645468i	0.0720157	+	0.0415783i	0.535575	−	0.844487i	$-0.320095\pi$
$241$	1.11798	+	0.645468i	0.0720157	+	0.0415783i	−0.463560	+	0.886066i	$0.653428\pi$
$242$		−	2.79381i		−	0.179593i
$243$	−14.4011	−	5.96737i	−0.923828	−	0.382807i
$244$			7.01899i			0.449345i
$245$	6.38751	−	2.86352i	0.408083	−	0.182944i
$246$	5.59919	+	2.31944i	0.356991	+	0.147882i
$247$	6.64198	+	11.5042i	0.422619	+	0.731997i
$248$	7.47844	+	12.9530i	0.474882	+	0.822519i
$249$	7.65191	+	9.97271i	0.484920	+	0.631995i
$250$	0.552767	+	0.319140i	0.0349601	+	0.0201842i
$251$	10.1130			0.638328			0.319164	−	0.947700i	$-0.396598\pi$
$251$	10.1130			0.638328			0.319164	+	0.947700i	$0.396598\pi$
$252$	11.2560	−	5.75264i	0.709064	−	0.362382i
$253$	−13.7823			−0.866486
$254$	−8.66547	−	5.00301i	−0.543720	−	0.313917i
$255$	4.47924	−	0.589581i	0.280501	−	0.0369210i
$256$	3.77635	+	6.54082i	0.236022	+	0.408801i
$257$	−6.49877	−	11.2562i	−0.405382	−	0.702143i	0.588984	−	0.808145i	$-0.299528\pi$
$257$	−6.49877	−	11.2562i	−0.405382	−	0.702143i	−0.994366	+	0.106002i	$0.966195\pi$
$258$	−1.38200	−	10.4995i	−0.0860396	−	0.653671i
$259$	−13.2571	−	14.6857i	−0.823756	−	0.912522i
$260$		−	5.35542i		−	0.332129i
$261$	2.33041	+	8.69907i	0.144249	+	0.538459i
$262$			3.92260i			0.242339i
$263$	16.4072	+	9.47268i	1.01171	+	0.584110i	0.911692	−	0.410875i	$-0.134777\pi$
$263$	16.4072	+	9.47268i	1.01171	+	0.584110i	0.100017	+	0.994986i	$0.468110\pi$
$264$	−6.22210	−	8.10925i	−0.382944	−	0.499090i
$265$	7.42716	−	4.28807i	0.456247	−	0.263414i
$266$	−6.52359	+	1.39536i	−0.399987	+	0.0855552i
$267$	−7.82559	+	18.8912i	−0.478918	+	1.15612i
$268$	−7.84312	+	13.5847i	−0.479095	+	0.829816i
$269$	−15.1728			−0.925103			−0.462552	−	0.886592i	$-0.653066\pi$
$269$	−15.1728			−0.925103			−0.462552	+	0.886592i	$0.653066\pi$
$270$	−1.26896	−	3.06424i	−0.0772266	−	0.186484i
$271$		−	0.872890i		−	0.0530243i	−0.999648	−	0.0265121i	$-0.991560\pi$
$271$		−	0.872890i		−	0.0530243i	0.999648	−	0.0265121i	$-0.00844006\pi$
$272$	−2.24526	+	3.88891i	−0.136139	+	0.235800i
$273$	−9.99316	+	11.7302i	−0.604814	+	0.709946i
$274$	−2.82877	−	4.89957i	−0.170892	−	0.295994i
$275$	2.22872	−	1.28675i	0.134397	−	0.0775940i
$276$	11.7203	−	8.99282i	0.705481	−	0.541304i
$277$	−4.56721	+	7.91063i	−0.274417	+	0.475304i	−0.969988	−	0.243153i	$-0.921818\pi$
$277$	−4.56721	+	7.91063i	−0.274417	+	0.475304i	0.695571	+	0.718457i	$0.255151\pi$
$278$	−6.07659			−0.364450
$279$	18.9008	+	5.06553i	1.13156	+	0.303266i
$280$	5.77239	+	1.86740i	0.344966	+	0.111598i
$281$	−16.8697	−	9.73975i	−1.00636	−	0.581025i	−0.0962390	−	0.995358i	$-0.530681\pi$
$281$	−16.8697	−	9.73975i	−1.00636	−	0.581025i	−0.910125	+	0.414334i	$0.864015\pi$
$282$	1.59837	+	12.1433i	0.0951814	+	0.723124i
$283$	−18.1140	+	10.4581i	−1.07676	+	0.621669i	−0.930021	−	0.367505i	$-0.880212\pi$
$283$	−18.1140	+	10.4581i	−1.07676	+	0.621669i	−0.146742	+	0.989175i	$0.546879\pi$
$284$	−9.25961	+	5.34604i	−0.549457	+	0.317229i
$285$	−0.892916	−	6.78377i	−0.0528918	−	0.401836i
$286$	4.78359	+	2.76181i	0.282859	+	0.163309i
$287$	−4.46436	+	13.8000i	−0.263523	+	0.814587i
$288$	16.4737	+	4.41505i	0.970720	+	0.260159i
$289$	−10.1963			−0.599780
$290$	−0.958039	+	1.65937i	−0.0562580	+	0.0974417i
$291$	0.373884	−	0.286876i	0.0219175	−	0.0168169i
$292$	8.99109	−	5.19101i	0.526164	−	0.303781i
$293$	3.70009	+	6.40874i	0.216161	+	0.374403i	0.953631	−	0.300978i	$-0.0973129\pi$
$293$	3.70009	+	6.40874i	0.216161	+	0.374403i	−0.737470	+	0.675380i	$0.763980\pi$
$294$	−4.06019	−	6.58809i	−0.236795	−	0.384225i
$295$	−4.28361	+	7.41944i	−0.249402	+	0.431976i
$296$		−	17.1472i		−	0.996658i
$297$	−13.2578	−	1.74650i	−0.769294	−	0.101342i
$298$	−1.37422			−0.0796064
$299$	−9.00439	+	15.5961i	−0.520737	+	0.901944i
$300$	−1.05569	+	2.54846i	−0.0609500	+	0.147135i
$301$	24.7834	−	5.30105i	1.42849	−	0.305548i
$302$	11.9495	−	6.89905i	0.687617	−	0.396996i
$303$	−2.99228	−	3.89983i	−0.171902	−	0.224039i
$304$	5.88972	+	3.40043i	0.337798	+	0.195028i
$305$			4.40726i			0.252359i
$306$	−1.29246	−	4.82455i	−0.0738848	−	0.275801i
$307$		−	14.9146i		−	0.851222i	−0.904906	−	0.425611i	$-0.860059\pi$
$307$		−	14.9146i		−	0.851222i	0.904906	−	0.425611i	$-0.139941\pi$
$308$	8.04918	−	7.26620i	0.458645	−	0.414030i
$309$	2.74137	+	20.8271i	0.155951	+	1.18481i
$310$	2.08163	+	3.60548i	0.118228	+	0.204778i
$311$	12.8802	+	22.3091i	0.730369	+	1.26504i	0.956726	+	0.290991i	$0.0939851\pi$
$311$	12.8802	+	22.3091i	0.730369	+	1.26504i	−0.226357	+	0.974044i	$0.572682\pi$
$312$	−13.2415	+	1.74292i	−0.749654	+	0.0986734i
$313$	3.95612	+	2.28407i	0.223613	+	0.129103i	0.607622	−	0.794226i	$-0.292123\pi$
$313$	3.95612	+	2.28407i	0.223613	+	0.129103i	−0.384009	+	0.923329i	$0.625457\pi$
$314$	2.10769			0.118944
$315$	7.06772	−	3.61211i	0.398221	−	0.203519i
$316$	3.41480			0.192098
$317$	21.7653	+	12.5662i	1.22246	+	0.705790i	0.965443	−	0.260616i	$-0.0839257\pi$
$317$	21.7653	+	12.5662i	1.22246	+	0.705790i	0.257021	+	0.966406i	$0.417259\pi$
$318$	−5.77160	−	7.52211i	−0.323655	−	0.421819i
$319$	3.86275	+	6.69047i	0.216272	+	0.374595i
$320$	0.0927504	+	0.160648i	0.00518491	+	0.00898052i
$321$	16.4596	+	6.81832i	0.918688	+	0.380562i
$322$	−6.06018	−	6.71321i	−0.337721	−	0.374112i
$323$		−	10.3042i		−	0.573341i
$324$	12.4138	−	7.16536i	0.689658	−	0.398076i
$325$		−	3.36269i		−	0.186529i
$326$	−12.2527	−	7.07407i	−0.678612	−	0.391797i
$327$	−11.9052	+	28.7395i	−0.658359	+	1.58930i
$328$	−10.8866	+	6.28540i	−0.601114	+	0.347053i
$329$	−28.6635	+	6.13099i	−1.58027	+	0.338012i
$330$	−1.73192	−	2.25721i	−0.0953392	−	0.124255i
$331$	−9.30506	+	16.1168i	−0.511453	+	0.885862i	0.488459	+	0.872587i	$0.337559\pi$
$331$	−9.30506	+	16.1168i	−0.511453	+	0.885862i	−0.999912	+	0.0132751i	$0.995774\pi$
$332$	−11.5580			−0.634328
$333$	−15.8619	−	15.8636i	−0.869226	−	0.869319i
$334$			12.4030i			0.678661i
$335$	−4.92473	+	8.52989i	−0.269067	+	0.466037i
$336$	−1.42797	+	7.75889i	−0.0779020	+	0.423282i
$337$	−3.96789	−	6.87259i	−0.216145	−	0.374374i	0.737481	−	0.675367i	$-0.236015\pi$
$337$	−3.96789	−	6.87259i	−0.216145	−	0.374374i	−0.953626	+	0.300994i	$0.902682\pi$
$338$	−0.935449	+	0.540082i	−0.0508817	+	0.0293766i
$339$	4.07758	+	30.9787i	0.221463	+	1.68253i
$340$	−2.07706	+	3.59758i	−0.112645	+	0.195106i
$341$	16.7859			0.909009
$342$	−7.30673	+	1.95741i	−0.395103	+	0.105845i
$343$	14.9413	−	10.9434i	0.806753	−	0.590888i
$344$	19.0229	+	10.9829i	1.02565	+	0.592158i
$345$	7.35925	−	5.64664i	0.396209	−	0.304005i
$346$	1.00162	−	0.578285i	0.0538473	−	0.0310888i
$347$	−24.5808	+	14.1917i	−1.31957	+	0.761853i	−0.983659	−	0.180041i	$-0.942377\pi$
$347$	−24.5808	+	14.1917i	−1.31957	+	0.761853i	−0.335909	+	0.941894i	$0.609043\pi$
$348$	−7.65031	−	3.16910i	−0.410100	−	0.169882i
$349$	4.22045	+	2.43668i	0.225916	+	0.130433i	0.608686	−	0.793411i	$-0.291697\pi$
$349$	4.22045	+	2.43668i	0.225916	+	0.130433i	−0.382771	+	0.923843i	$0.625030\pi$
$350$	1.60675	+	0.519790i	0.0858842	+	0.0277839i
$351$	−10.6380	+	13.8615i	−0.567816	+	0.739870i
$352$	14.6304			0.779802
$353$	11.3820	−	19.7142i	0.605802	−	1.04928i	−0.386122	−	0.922448i	$-0.626186\pi$
$353$	11.3820	−	19.7142i	0.605802	−	1.04928i	0.991924	−	0.126833i	$-0.0404811\pi$
$354$	8.75030	+	3.62477i	0.465073	+	0.192654i
$355$	−5.81415	+	3.35680i	−0.308583	+	0.178161i
$356$	−9.40080	−	16.2827i	−0.498241	−	0.862979i
$357$	11.2626	−	4.00417i	0.596077	−	0.211923i
$358$	−1.97574	+	3.42209i	−0.104421	+	0.180863i
$359$		−	17.2003i		−	0.907799i	−0.891053	−	0.453900i	$-0.850032\pi$
$359$		−	17.2003i		−	0.907799i	0.891053	−	0.453900i	$-0.149968\pi$
$360$	6.64475	+	1.78084i	0.350209	+	0.0938584i
$361$	3.39439			0.178652
$362$	3.77514	−	6.53873i	0.198417	−	0.343668i
$363$	7.51651	−	0.989363i	0.394514	−	0.0519281i
$364$	−2.96366	−	13.8557i	−0.155338	−	0.726235i
$365$	5.64555	−	3.25946i	0.295502	−	0.170608i
$366$	4.83071	−	0.635843i	0.252505	−	0.0332361i
$367$	−2.88343	−	1.66475i	−0.150514	−	0.0868992i	0.422852	−	0.906199i	$-0.361029\pi$
$367$	−2.88343	−	1.66475i	−0.150514	−	0.0868992i	−0.573365	+	0.819300i	$0.694362\pi$
$368$			9.21978i			0.480614i
$369$	−4.25742	+	15.8855i	−0.221633	+	0.826967i
$370$		−	4.77291i		−	0.248132i
$371$	16.8428	−	15.2044i	0.874432	−	0.789372i
$372$	−14.2746	+	10.9527i	−0.740103	+	0.567869i
$373$	8.03809	+	13.9224i	0.416197	+	0.720874i	0.995553	−	0.0942003i	$-0.0300294\pi$
$373$	8.03809	+	13.9224i	0.416197	+	0.720874i	−0.579357	+	0.815074i	$0.696696\pi$
$374$	−2.14230	−	3.71057i	−0.110776	−	0.191869i
$375$	−0.662870	+	1.60019i	−0.0342305	+	0.0826334i
$376$	−22.0012	−	12.7024i	−1.13462	−	0.655075i
$377$	10.0946			0.519898
$378$	−4.97884	−	7.22566i	−0.256084	−	0.371648i
$379$	−16.9619			−0.871275			−0.435638	−	0.900122i	$-0.643477\pi$
$379$	−16.9619			−0.871275			−0.435638	+	0.900122i	$0.643477\pi$
$380$	5.44850	+	3.14569i	0.279502	+	0.161371i
$381$	10.3915	−	25.0854i	0.532373	−	1.28516i
$382$	−3.18973	−	5.52478i	−0.163201	−	0.282672i
$383$	1.61770	+	2.80195i	0.0826608	+	0.143173i	0.904392	−	0.426703i	$-0.140325\pi$
$383$	1.61770	+	2.80195i	0.0826608	+	0.143173i	−0.821731	+	0.569875i	$0.806992\pi$
$384$	−15.4615	+	11.8634i	−0.789016	+	0.605400i
$385$	5.05412	−	4.56248i	0.257582	−	0.232526i
$386$			2.62754i			0.133738i
$387$	27.7586	−	7.43631i	1.41105	−	0.378009i
$388$			0.433318i			0.0219984i
$389$	14.1105	+	8.14671i	0.715431	+	0.413054i	0.813069	−	0.582168i	$-0.197795\pi$
$389$	14.1105	+	8.14671i	0.715431	+	0.413054i	−0.0976375	+	0.995222i	$0.531129\pi$
$390$	−3.68578	+	0.485142i	−0.186637	+	0.0245661i
$391$	12.0977	−	6.98459i	0.611805	−	0.353226i
$392$	15.9679	+	1.63697i	0.806501	+	0.0826793i
$393$	−10.5534	+	1.38910i	−0.532350	+	0.0700708i
$394$	−1.27021	+	2.20007i	−0.0639922	+	0.110838i
$395$	2.14417			0.107885
$396$	8.69481	−	8.69388i	0.436931	−	0.436884i
$397$			35.9834i			1.80596i	0.429686	+	0.902978i	$0.358624\pi$
$397$			35.9834i			1.80596i	−0.429686	+	0.902978i	$0.641376\pi$
$398$	8.01043	−	13.8745i	0.401526	−	0.695464i
$399$	−6.06428	−	17.0570i	−0.303594	−	0.853920i
$400$	−0.860783	−	1.49092i	−0.0430391	−	0.0745460i
$401$	−1.55394	+	0.897167i	−0.0776000	+	0.0448024i	−0.538298	−	0.842755i	$-0.680932\pi$
$401$	−1.55394	+	0.897167i	−0.0776000	+	0.0448024i	0.460698	+	0.887557i	$0.347599\pi$
$402$	10.0599	+	4.16728i	0.501744	+	0.207845i
$403$	10.9668	−	18.9950i	0.546293	−	0.946207i
$404$	4.51976			0.224866
$405$	7.79471	−	4.49917i	0.387322	−	0.223565i
$406$	−1.56038	+	4.82335i	−0.0774402	+	0.239379i
$407$	−16.6658	−	9.62203i	−0.826095	−	0.476946i
$408$	9.57117	+	3.96481i	0.473844	+	0.196287i
$409$	−5.48011	+	3.16395i	−0.270974	+	0.156447i	−0.629330	−	0.777138i	$-0.716671\pi$
$409$	−5.48011	+	3.16395i	−0.270974	+	0.156447i	0.358356	+	0.933585i	$0.383337\pi$
$410$	−3.03029	+	1.74954i	−0.149656	+	0.0864037i
$411$	12.1801	−	9.34562i	0.600801	−	0.460986i
$412$	−16.7276	−	9.65771i	−0.824112	−	0.475801i
$413$	−6.97681	+	21.5663i	−0.343306	+	1.06121i
$414$	−7.25090	−	7.25167i	−0.356362	−	0.356400i
$415$	−7.25733			−0.356248
$416$	9.55847	−	16.5558i	0.468643	−	0.811713i
$417$	−2.15188	−	16.3486i	−0.105378	−	0.800592i
$418$	−5.61962	+	3.24449i	−0.274865	+	0.158693i
$419$	−9.78420	−	16.9467i	−0.477990	−	0.827902i	0.521692	−	0.853134i	$-0.325301\pi$
$419$	−9.78420	−	16.9467i	−0.477990	−	0.827902i	−0.999682	+	0.0252316i	$0.991968\pi$
$420$	−1.32100	+	7.17765i	−0.0644580	+	0.350234i
$421$	11.6203	−	20.1269i	0.566338	−	0.980926i	−0.430586	−	0.902550i	$-0.641693\pi$
$421$	11.6203	−	20.1269i	0.566338	−	0.980926i	0.996924	−	0.0783764i	$-0.0249736\pi$
$422$		−	7.84044i		−	0.381667i
$423$	−32.1045	+	8.60054i	−1.56098	+	0.418173i
$424$	19.6658			0.955057
$425$	−1.30420	+	2.25894i	−0.0632629	+	0.109575i
$426$	4.51814	+	5.88848i	0.218905	+	0.285298i
$427$	2.43896	+	11.4026i	0.118029	+	0.551810i
$428$	−14.1869	+	8.19079i	−0.685748	+	0.395917i
$429$	−5.73641	+	13.8479i	−0.276956	+	0.668581i
$430$	5.29503	+	3.05709i	0.255349	+	0.147426i
$431$		−	8.50547i		−	0.409694i	−0.978794	−	0.204847i	$-0.934330\pi$
$431$		−	8.50547i		−	0.409694i	0.978794	−	0.204847i	$-0.0656697\pi$
$432$	−1.16834	+	8.86889i	−0.0562116	+	0.426705i
$433$			7.10048i			0.341228i	0.985338	+	0.170614i	$0.0545750\pi$
$433$			7.10048i			0.341228i	−0.985338	+	0.170614i	$0.945425\pi$
$434$	7.38090	+	8.17624i	0.354294	+	0.392472i
$435$	−4.80367	−	1.98989i	−0.230318	−	0.0954082i
$436$	−14.3016	−	24.7711i	−0.684923	−	1.18632i
$437$	−10.5781	−	18.3218i	−0.506019	−	0.876451i
$438$	−4.38712	−	5.71773i	−0.209625	−	0.273204i
$439$	−6.36593	−	3.67537i	−0.303829	−	0.175416i	0.340332	−	0.940305i	$-0.389460\pi$
$439$	−6.36593	−	3.67537i	−0.303829	−	0.175416i	−0.644162	+	0.764889i	$0.722794\pi$
$440$	5.90126			0.281331
$441$	16.2869	−	13.2566i	0.775566	−	0.631267i
$442$	−5.59851			−0.266294
$443$	−26.6244	−	15.3716i	−1.26496	−	0.730328i	−0.290934	−	0.956743i	$-0.593966\pi$
$443$	−26.6244	−	15.3716i	−1.26496	−	0.730328i	−0.974031	+	0.226416i	$0.927299\pi$
$444$	20.4507	−	2.69183i	0.970549	−	0.127749i
$445$	−5.90281	−	10.2240i	−0.279820	−	0.484662i
$446$	6.10896	+	10.5810i	0.289267	+	0.501026i
$447$	−0.486648	−	3.69722i	−0.0230177	−	0.174873i
$448$	0.328869	+	0.364307i	0.0155376	+	0.0172119i
$449$		−	31.4977i		−	1.48647i	−0.669031	−	0.743234i	$-0.733291\pi$
$449$		−	31.4977i		−	1.48647i	0.669031	−	0.743234i	$-0.266709\pi$
$450$	1.84957	+	0.495696i	0.0871895	+	0.0233673i
$451$			14.1081i			0.664322i
$452$	−24.8811	−	14.3651i	−1.17031	−	0.675677i
$453$	22.7929	+	29.7060i	1.07091	+	1.39571i
$454$	−5.96745	+	3.44531i	−0.280066	+	0.161696i
$455$	−1.86090	−	8.70005i	−0.0872403	−	0.407865i
$456$	6.00467	−	14.4954i	0.281194	−	0.678812i
$457$	5.54440	−	9.60319i	0.259356	−	0.449218i	−0.706713	−	0.707500i	$-0.749823\pi$
$457$	5.54440	−	9.60319i	0.259356	−	0.449218i	0.966070	+	0.258282i	$0.0831563\pi$
$458$	0.807618			0.0377375
$459$	12.5223	−	5.18575i	0.584493	−	0.242050i
$460$			8.52911i			0.397672i
$461$	19.3153	−	33.4552i	0.899605	−	1.55816i	0.0716059	−	0.997433i	$-0.477188\pi$
$461$	19.3153	−	33.4552i	0.899605	−	1.55816i	0.827999	−	0.560729i	$-0.189479\pi$
$462$	−5.73001	−	4.88148i	−0.266584	−	0.227107i
$463$	3.99332	+	6.91664i	0.185585	+	0.321444i	0.943774	−	0.330592i	$-0.107249\pi$
$463$	3.99332	+	6.91664i	0.185585	+	0.321444i	−0.758188	+	0.652036i	$0.773915\pi$
$464$	4.47565	−	2.58402i	0.207777	−	0.119960i
$465$	−8.96308	+	6.87723i	−0.415653	+	0.318924i
$466$	−0.850330	+	1.47281i	−0.0393908	+	0.0682268i
$467$	−11.2412			−0.520179			−0.260089	−	0.965585i	$-0.583752\pi$
$467$	−11.2412			−0.520179			−0.260089	+	0.965585i	$0.583752\pi$
$468$	−4.15742	−	15.5190i	−0.192177	−	0.717367i
$469$	−8.02101	+	24.7941i	−0.370376	+	1.14488i
$470$	−6.12403	−	3.53571i	−0.282480	−	0.163090i
$471$	0.746389	+	5.67056i	0.0343918	+	0.261285i
$472$	−17.0134	+	9.82269i	−0.783105	+	0.452126i
$473$	21.3492	−	12.3260i	0.981637	−	0.566749i
$474$	−0.309343	−	2.35018i	−0.0142086	−	0.107947i
$475$	3.42114	+	1.97520i	0.156973	+	0.0906282i
$476$	−3.38296	+	10.4572i	−0.155058	+	0.479305i
$477$	18.1937	−	18.1918i	0.833033	−	0.832944i
$478$	3.32324			0.152001
$479$	−7.35486	+	12.7390i	−0.336052	+	0.582059i	−0.983686	−	0.179892i	$-0.942425\pi$
$479$	−7.35486	+	12.7390i	−0.336052	+	0.582059i	0.647634	+	0.761951i	$0.275758\pi$
$480$	−7.81209	+	5.99410i	−0.356572	+	0.273592i
$481$	−21.7766	+	12.5727i	−0.992927	+	0.573267i
$482$	0.411990	+	0.713587i	0.0187656	+	0.0325030i
$483$	15.9152	−	18.6817i	0.724168	−	0.850048i
$484$	−3.48547	+	6.03701i	−0.158431	+	0.274410i
$485$			0.272083i			0.0123546i
$486$	−6.05600	−	7.89452i	−0.274706	−	0.358103i
$487$	−36.6576			−1.66112			−0.830558	−	0.556932i	$-0.811978\pi$
$487$	−36.6576			−1.66112			−0.830558	+	0.556932i	$0.811978\pi$
$488$	−5.05311	+	8.75224i	−0.228744	+	0.396195i
$489$	14.6932	−	35.4698i	0.664450	−	1.60400i
$490$	4.44467	+	0.455650i	0.200790	+	0.0205842i
$491$	27.7690	−	16.0325i	1.25320	−	0.723535i	0.281456	−	0.959574i	$-0.409183\pi$
$491$	27.7690	−	16.0325i	1.25320	−	0.723535i	0.971743	+	0.236039i	$0.0758495\pi$
$492$	−9.20537	−	11.9973i	−0.415010	−	0.540882i
$493$	−6.78119	−	3.91512i	−0.305410	−	0.176328i
$494$			8.47889i			0.381483i
$495$	5.45951	−	5.45893i	0.245387	−	0.245361i
$496$		−	11.2291i		−	0.504201i
$497$	−13.1849	+	11.9023i	−0.591424	+	0.533893i
$498$	1.04703	+	7.95462i	0.0469185	+	0.356455i
$499$	13.9529	+	24.1672i	0.624620	+	1.08187i	0.988614	+	0.150472i	$0.0480794\pi$
$499$	13.9529	+	24.1672i	0.624620	+	1.08187i	−0.363994	+	0.931401i	$0.618587\pi$
$500$	−0.796299	−	1.37923i	−0.0356116	−	0.0616811i
$501$	−33.3691	+	4.39222i	−1.49082	+	0.196230i
$502$	5.59014	+	3.22747i	0.249500	+	0.144049i
$503$	−1.50267			−0.0670006			−0.0335003	−	0.999439i	$-0.510665\pi$
$503$	−1.50267			−0.0670006			−0.0335003	+	0.999439i	$0.510665\pi$
$504$	18.1770	+	0.930258i	0.809668	+	0.0414370i
$505$	2.83798			0.126288
$506$	−7.61840	−	4.39849i	−0.338679	−	0.195537i
$507$	−1.78431	−	2.32549i	−0.0792441	−	0.103279i
$508$	12.4832	+	21.6215i	0.553853	+	0.959301i
$509$	−18.0390	−	31.2444i	−0.799563	−	1.38488i	−0.919901	−	0.392151i	$-0.871731\pi$
$509$	−18.0390	−	31.2444i	−0.799563	−	1.38488i	0.120338	−	0.992733i	$-0.461602\pi$
$510$	2.66414	+	1.10360i	0.117970	+	0.0488684i
$511$	12.8026	−	11.5572i	0.566352	−	0.511260i
$512$		−	17.6825i		−	0.781464i
$513$	−7.85376	−	18.9650i	−0.346752	−	0.837324i
$514$		−	8.29608i		−	0.365924i
$515$	−10.5034	−	6.06412i	−0.462834	−	0.267217i
$516$	−10.1126	+	24.4120i	−0.445181	+	1.07468i
$517$	−24.6916	+	14.2557i	−1.08594	+	0.626966i
$518$	−2.64131	−	12.3486i	−0.116052	−	0.542567i
$519$	1.91053	+	2.48998i	0.0838627	+	0.109298i
$520$	3.85547	−	6.67787i	0.169074	−	0.292844i
$521$	−40.0264			−1.75359			−0.876794	−	0.480866i	$-0.840322\pi$
$521$	−40.0264			−1.75359			−0.876794	+	0.480866i	$0.840322\pi$
$522$	−1.48805	+	5.55229i	−0.0651302	+	0.243017i
$523$			22.6116i			0.988737i	0.869252	+	0.494369i	$0.164601\pi$
$523$			22.6116i			0.988737i	−0.869252	+	0.494369i	$0.835399\pi$
$524$	4.89372	−	8.47617i	0.213783	−	0.370283i
$525$	−0.829459	+	4.50688i	−0.0362006	+	0.196697i
$526$	6.04622	+	10.4724i	0.263628	+	0.456617i
$527$	−14.7342	+	8.50677i	−0.641830	+	0.370561i
$528$	1.00142	+	7.60814i	0.0435814	+	0.331102i
$529$	2.84051	−	4.91990i	0.123500	−	0.213909i
$530$	5.47398			0.237775
$531$	−6.65341	+	24.8256i	−0.288734	+	1.07734i
$532$	15.8373	+	5.12346i	0.686636	+	0.222130i
$533$	15.9647	+	9.21722i	0.691507	+	0.399242i
$534$	−10.3547	+	7.94498i	−0.448090	+	0.343813i
$535$	−8.90800	+	5.14303i	−0.385126	+	0.222353i
$536$	−19.5598	+	11.2928i	−0.844853	+	0.487776i
$537$	−9.90650	−	4.10372i	−0.427497	−	0.177088i
$538$	−8.38703	−	4.84226i	−0.361591	−	0.208764i
$539$	10.5513	−	14.6011i	0.454477	−	0.628914i
$540$	−1.08081	+	8.20450i	−0.0465108	+	0.353065i
$541$	−0.766443			−0.0329520			−0.0164760	−	0.999864i	$-0.505245\pi$
$541$	−0.766443			−0.0329520			−0.0164760	+	0.999864i	$0.505245\pi$
$542$	0.278574	−	0.482505i	0.0119658	−	0.0207254i
$543$	18.9288	+	7.84115i	0.812312	+	0.336496i
$544$	−12.8421	+	7.41438i	−0.550600	+	0.317889i
$545$	−8.98004	−	15.5539i	−0.384663	−	0.666256i
$546$	−9.26748	+	3.29487i	−0.396611	+	0.141007i
$547$	9.59685	−	16.6222i	0.410332	−	0.710715i	−0.584594	−	0.811326i	$-0.698746\pi$
$547$	9.59685	−	16.6222i	0.410332	−	0.710715i	0.994926	+	0.100610i	$0.0320796\pi$
$548$			14.1163i			0.603020i
$549$	3.42136	+	12.7714i	0.146020	+	0.545072i
$550$	1.64262			0.0700414
$551$	−5.92942	+	10.2701i	−0.252602	+	0.437519i
$552$	21.0886	−	2.77580i	0.897591	−	0.118146i
$553$	5.54746	−	1.18657i	0.235902	−	0.0504583i
$554$	−5.04920	+	2.91516i	−0.214520	+	0.123853i
$555$	12.8411	−	1.69022i	0.545075	−	0.0717457i
$556$	13.1306	+	7.58097i	0.556863	+	0.321505i
$557$			24.8020i			1.05090i	0.850826	+	0.525448i	$0.176102\pi$
$557$			24.8020i			1.05090i	−0.850826	+	0.525448i	$0.823898\pi$
$558$	8.83112	+	8.83206i	0.373851	+	0.373891i
$559$		−	32.2117i		−	1.36241i
$560$	−3.05211	−	3.38100i	−0.128975	−	0.142873i
$561$	9.22432	−	7.07768i	0.389451	−	0.298820i
$562$	−6.21669	−	10.7676i	−0.262235	−	0.454205i
$563$	5.29797	+	9.17636i	0.223283	+	0.386737i	0.955803	−	0.294008i	$-0.0949893\pi$
$563$	5.29797	+	9.17636i	0.223283	+	0.386737i	−0.732520	+	0.680746i	$0.761656\pi$
$564$	11.6958	−	28.2340i	0.492482	−	1.18887i
$565$	−15.6229	−	9.01990i	−0.657262	−	0.379470i
$566$	−13.3504			−0.561159
$567$	17.6769	−	15.9539i	0.742359	−	0.670002i
$568$	−15.3949			−0.645954
$569$	−15.7502	−	9.09337i	−0.660282	−	0.381214i	0.132103	−	0.991236i	$-0.457827\pi$
$569$	−15.7502	−	9.09337i	−0.660282	−	0.381214i	−0.792384	+	0.610022i	$0.791161\pi$
$570$	1.67140	−	4.03481i	0.0700072	−	0.169000i
$571$	17.0719	+	29.5693i	0.714435	+	1.23744i	0.963177	+	0.268868i	$0.0866495\pi$
$571$	17.0719	+	29.5693i	0.714435	+	1.23744i	−0.248742	+	0.968570i	$0.580017\pi$
$572$	−6.89109	−	11.9357i	−0.288131	−	0.499057i
$573$	13.7344	−	10.5382i	0.573762	−	0.440239i
$574$	−6.87188	+	6.20341i	−0.286827	+	0.258926i
$575$			5.35547i			0.223338i
$576$	0.393486	+	0.393528i	0.0163952	+	0.0163970i
$577$		−	8.14778i		−	0.339196i	−0.985513	−	0.169598i	$-0.945753\pi$
$577$		−	8.14778i		−	0.339196i	0.985513	−	0.169598i	$-0.0542470\pi$
$578$	−5.63616	−	3.25404i	−0.234433	−	0.135350i
$579$	−7.06916	+	0.930480i	−0.293784	+	0.0386694i
$580$	4.14037	−	2.39044i	0.171919	−	0.0992577i
$581$	−18.7764	+	4.01617i	−0.778976	+	0.166619i
$582$	0.298224	−	0.0392539i	0.0123618	−	0.00162713i
$583$	11.0354	−	19.1138i	0.457038	−	0.791613i
$584$	14.9484			0.618571
$585$	−2.61047	−	9.74447i	−0.107929	−	0.402884i
$586$			4.72339i			0.195121i
$587$	16.3555	−	28.3286i	0.675066	−	1.16925i	−0.301384	−	0.953503i	$-0.597449\pi$
$587$	16.3555	−	28.3286i	0.675066	−	1.16925i	0.976450	−	0.215745i	$-0.0692181\pi$
$588$	0.554364	+	19.3013i	0.0228616	+	0.795971i
$589$	12.8834	+	22.3148i	0.530852	+	0.919463i
$590$	−4.73568	+	2.73415i	−0.194965	+	0.112563i
$591$	−6.36891	−	2.63829i	−0.261982	−	0.108525i
$592$	−6.43673	+	11.1487i	−0.264548	+	0.458211i
$593$	−40.6769			−1.67040			−0.835201	−	0.549945i	$-0.814649\pi$
$593$	−40.6769			−1.67040			−0.835201	+	0.549945i	$0.814649\pi$
$594$	−6.77108	−	5.19649i	−0.277821	−	0.213215i
$595$	−2.12417	+	6.56613i	−0.0870827	+	0.269185i
$596$	2.96949	+	1.71443i	0.121635	+	0.0702260i
$597$	40.1648	+	16.6381i	1.64383	+	0.680950i
$598$	−9.95466	+	5.74733i	−0.407076	+	0.235026i
$599$	41.6861	−	24.0675i	1.70325	−	0.983370i	0.760816	−	0.648968i	$-0.224799\pi$
$599$	41.6861	−	24.0675i	1.70325	−	0.983370i	0.942430	−	0.334402i	$-0.108534\pi$
$600$	−3.15106	+	2.41776i	−0.128641	+	0.0987045i
$601$	11.4167	+	6.59141i	0.465695	+	0.268869i	0.714436	−	0.699701i	$-0.246683\pi$
$601$	11.4167	+	6.59141i	0.465695	+	0.268869i	−0.248741	+	0.968570i	$0.580017\pi$
$602$	15.3912	+	4.97914i	0.627300	+	0.202935i
$603$	−7.64921	+	28.5411i	−0.311500	+	1.16229i
$604$	−34.4282			−1.40086
$605$	−2.18854	+	3.79067i	−0.0889770	+	0.154113i
$606$	−0.409440	−	3.11065i	−0.0166324	−	0.126362i
$607$	41.2641	−	23.8238i	1.67486	−	0.966979i	0.710001	−	0.704200i	$-0.248694\pi$
$607$	41.2641	−	23.8238i	1.67486	−	0.966979i	0.964856	−	0.262779i	$-0.0846391\pi$
$608$	11.2290	+	19.4492i	0.455397	+	0.788770i
$609$	−13.5294	−	2.48999i	−0.548238	−	0.100899i
$610$	−1.40653	+	2.43619i	−0.0569489	+	0.0986384i
$611$			37.2548i			1.50717i
$612$	−3.22615	+	12.0376i	−0.130409	+	0.486590i
$613$	17.6569			0.713155			0.356578	−	0.934266i	$-0.383943\pi$
$613$	17.6569			0.713155			0.356578	+	0.934266i	$0.383943\pi$
$614$	4.75985	−	8.24431i	0.192092	−	0.332713i
$615$	−5.78010	−	7.53319i	−0.233076	−	0.303767i
$616$	15.2679	−	3.26573i	0.615161	−	0.131580i
$617$	5.32696	−	3.07552i	0.214455	−	0.123816i	−0.388925	−	0.921269i	$-0.627153\pi$
$617$	5.32696	−	3.07552i	0.214455	−	0.123816i	0.603380	+	0.797454i	$0.293820\pi$
$618$	−5.13142	+	12.3874i	−0.206416	+	0.498295i
$619$	29.8898	+	17.2569i	1.20137	+	0.693612i	0.960860	−	0.277035i	$-0.0893518\pi$
$619$	29.8898	+	17.2569i	1.20137	+	0.693612i	0.240511	+	0.970646i	$0.422685\pi$
$620$		−	10.3879i		−	0.417188i
$621$	16.9423	−	22.0759i	0.679870	−	0.885877i
$622$			16.4423i			0.659278i
$623$	−20.9298	−	23.1851i	−0.838535	−	0.928893i
$624$	9.26364	+	3.83742i	0.370842	+	0.153620i
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	1.45788	+	2.52512i	0.0582684	+	0.100924i
$627$	−10.7191	−	13.9701i	−0.428079	−	0.557914i
$628$	−4.55441	−	2.62949i	−0.181741	−	0.104928i
$629$	19.5050			0.777715
$630$	5.05957	+	0.258937i	0.201578	+	0.0103163i
$631$	−14.8371			−0.590657			−0.295329	−	0.955396i	$-0.595429\pi$
$631$	−14.8371			−0.590657			−0.295329	+	0.955396i	$0.595429\pi$
$632$	4.25804	+	2.45838i	0.169376	+	0.0977892i
$633$	21.0940	−	2.77651i	0.838412	−	0.110356i
$634$	8.02078	+	13.8924i	0.318546	+	0.551737i
$635$	7.83826	+	13.5763i	0.311052	+	0.538758i
$636$	3.08722	+	23.4546i	0.122416	+	0.930037i
$637$	−9.62914	−	21.4792i	−0.381520	−	0.851038i
$638$			4.93103i			0.195221i
$639$	−14.2425	+	14.2409i	−0.563423	+	0.563363i
$640$		−	11.2516i		−	0.444759i
$641$	38.8970	+	22.4572i	1.53634	+	0.887007i	0.999049	+	0.0436106i	$0.0138861\pi$
$641$	38.8970	+	22.4572i	1.53634	+	0.887007i	0.537292	+	0.843396i	$0.319447\pi$
$642$	6.92235	+	9.02188i	0.273203	+	0.356065i
$643$	29.7285	−	17.1637i	1.17238	−	0.676872i	0.218138	−	0.975918i	$-0.430002\pi$
$643$	29.7285	−	17.1637i	1.17238	−	0.676872i	0.954239	+	0.299046i	$0.0966685\pi$
$644$	4.71997	+	22.0667i	0.185993	+	0.869552i
$645$	−6.34973	+	15.3284i	−0.250020	+	0.603556i
$646$	3.28848	−	5.69582i	0.129384	−	0.224099i
$647$	31.2211			1.22743			0.613714	−	0.789528i	$-0.289675\pi$
$647$	31.2211			1.22743			0.613714	+	0.789528i	$0.289675\pi$
$648$	20.6378	+	0.00220761i	0.810728	+	8.67233e-5i
$649$			22.0478i			0.865451i
$650$	1.07317	−	1.85879i	0.0420932	−	0.0729076i
$651$	−19.3837	+	22.7531i	−0.759708	+	0.891764i
$652$	17.6508	+	30.5721i	0.691259	+	1.19729i
$653$	9.41757	−	5.43723i	0.368538	−	0.212775i	−0.304282	−	0.952582i	$-0.598416\pi$
$653$	9.41757	−	5.43723i	0.368538	−	0.212775i	0.672819	+	0.739807i	$0.265083\pi$
$654$	−15.7527	+	12.0868i	−0.615981	+	0.472633i
$655$	3.07279	−	5.32223i	0.120064	−	0.207957i
$656$	9.43770			0.368480
$657$	13.8295	−	13.8280i	0.539539	−	0.539481i
$658$	−17.8009	−	5.75868i	−0.693952	−	0.224497i
$659$	10.0790	+	5.81909i	0.392620	+	0.226679i	0.683295	−	0.730143i	$-0.260546\pi$
$659$	10.0790	+	5.81909i	0.392620	+	0.226679i	−0.290675	+	0.956822i	$0.593880\pi$
$660$	0.926405	+	7.03820i	0.0360603	+	0.273961i
$661$	−25.1880	+	14.5423i	−0.979700	+	0.565630i	−0.902180	−	0.431360i	$-0.858034\pi$
$661$	−25.1880	+	14.5423i	−0.979700	+	0.565630i	−0.0775208	+	0.996991i	$0.524700\pi$
$662$	−10.2871	+	5.93924i	−0.399818	+	0.230835i
$663$	−1.98258	−	15.0623i	−0.0769971	−	0.584972i
$664$	−14.4121	−	8.32084i	−0.559299	−	0.322911i
$665$	9.94434	+	3.21704i	0.385625	+	0.124752i
$666$	−3.70522	−	13.8310i	−0.143574	−	0.535942i
$667$	−16.0768			−0.622495
$668$	15.4736	−	26.8010i	0.598691	−	1.03696i
$669$	−26.3040	+	20.1826i	−1.01697	+	0.780306i
$670$	−5.44446	+	3.14336i	−0.210338	+	0.121439i
$671$	5.67104	+	9.82254i	0.218928	+	0.379195i
$672$	−16.8946	+	19.8313i	−0.651722	+	0.765008i
$673$	−0.591588	+	1.02466i	−0.0228040	+	0.0394977i	−0.877202	−	0.480121i	$-0.840593\pi$
$673$	−0.591588	+	1.02466i	−0.0228040	+	0.0394977i	0.854398	+	0.519619i	$0.173926\pi$
$674$		−	5.06525i		−	0.195106i
$675$	−0.678647	+	5.15164i	−0.0261211	+	0.198287i
$676$	2.69516			0.103660
$677$	−20.4807	+	35.4736i	−0.787137	+	1.36336i	0.140577	+	0.990070i	$0.455104\pi$
$677$	−20.4807	+	35.4736i	−0.787137	+	1.36336i	−0.927714	+	0.373291i	$0.878229\pi$
$678$	−7.63259	+	18.4253i	−0.293128	+	0.707619i
$679$	0.150569	+	0.703940i	0.00577832	+	0.0270147i
$680$	−5.17994	+	2.99064i	−0.198642	+	0.114686i
$681$	−11.3825	−	14.8348i	−0.436180	−	0.568473i
$682$	9.27871	+	5.35707i	0.355300	+	0.205133i
$683$		−	2.27228i		−	0.0869463i	−0.999055	−	0.0434731i	$-0.986158\pi$
$683$		−	2.27228i		−	0.0869463i	0.999055	−	0.0434731i	$-0.0138423\pi$
$684$	18.2308	+	4.88597i	0.697071	+	0.186820i
$685$			8.86371i			0.338665i
$686$	11.7515	−	1.28079i	0.448675	−	0.0489007i
$687$	0.285999	+	2.17283i	0.0109115	+	0.0828985i
$688$	−8.24556	−	14.2817i	−0.314359	−	0.544486i
$689$	−14.4195	−	24.9752i	−0.549338	−	0.951481i
$690$	5.87002	−	0.772643i	0.223468	−	0.0294140i
$691$	−42.1997	−	24.3640i	−1.60535	−	0.926851i	−0.990391	−	0.138293i	$-0.955838\pi$
$691$	−42.1997	−	24.3640i	−1.60535	−	0.926851i	−0.614961	−	0.788557i	$-0.710828\pi$
$692$	−2.88580			−0.109702
$693$	11.1041	−	17.1448i	0.421809	−	0.651276i
$694$	−18.1166			−0.687698
$695$	8.24478	+	4.76013i	0.312742	+	0.180562i
$696$	−7.25796	−	9.45928i	−0.275112	−	0.358553i
$697$	−7.14968	−	12.3836i	−0.270813	−	0.469062i
$698$	1.55529	+	2.69383i	0.0588684	+	0.101963i
$699$	−4.26361	−	1.76618i	−0.161264	−	0.0668029i
$700$	−2.82347	−	3.12772i	−0.106717	−	0.118217i
$701$			4.12119i			0.155655i	0.996967	+	0.0778276i	$0.0247984\pi$
$701$			4.12119i			0.155655i	−0.996967	+	0.0778276i	$0.975202\pi$
$702$	−10.3041	+	4.26713i	−0.388903	+	0.161052i
$703$		−	29.5401i		−	1.11413i
$704$	0.413429	+	0.238693i	0.0155817	+	0.00899610i
$705$	7.34384	−	17.7283i	0.276585	−	0.667685i
$706$	12.5832	−	7.26490i	0.473574	−	0.273418i
$707$	7.34250	−	1.57052i	0.276143	−	0.0590656i
$708$	−14.3860	−	18.7492i	−0.540658	−	0.704638i
$709$	6.53830	−	11.3247i	0.245551	−	0.425307i	−0.716735	−	0.697345i	$-0.754364\pi$
$709$	6.53830	−	11.3247i	0.245551	−	0.425307i	0.962286	+	0.272038i	$0.0876978\pi$
$710$	−4.28516			−0.160819
$711$	6.21342	−	1.66452i	0.233021	−	0.0624245i
$712$		−	27.0713i		−	1.01454i
$713$	−17.4658	+	30.2516i	−0.654099	+	1.13293i
$714$	7.50346	+	1.38096i	0.280810	+	0.0516810i
$715$	−4.32695	−	7.49449i	−0.161819	−	0.280278i
$716$	8.53859	−	4.92976i	0.319102	−	0.184234i
$717$	1.17685	+	8.94089i	0.0439502	+	0.333904i
$718$	5.48932	−	9.50778i	0.204860	−	0.354827i
$719$	30.0774			1.12170			0.560849	−	0.827918i	$-0.310475\pi$
$719$	30.0774			1.12170			0.560849	+	0.827918i	$0.310475\pi$
$720$	−3.65180	−	3.65219i	−0.136094	−	0.136109i
$721$	−30.5305	−	9.87676i	−1.13701	−	0.367830i
$722$	1.87631	+	1.08329i	0.0698289	+	0.0403158i
$723$	−1.77395	+	1.36112i	−0.0659739	+	0.0506207i
$724$	−16.3150	+	9.41949i	−0.606344	+	0.350073i
$725$	2.59976	−	1.50097i	0.0965525	−	0.0557446i
$726$	4.47062	+	1.85193i	0.165920	+	0.0687317i
$727$	−4.91269	−	2.83634i	−0.182202	−	0.105194i	0.406125	−	0.913818i	$-0.366880\pi$
$727$	−4.91269	−	2.83634i	−0.182202	−	0.105194i	−0.588327	+	0.808623i	$0.700213\pi$
$728$	6.27948	−	19.4108i	0.232733	−	0.719411i
$729$	19.0949	−	19.0888i	0.707220	−	0.706993i
$730$	4.16090			0.154002
$731$	−12.4931	+	21.6387i	−0.462074	+	0.800336i
$732$	−11.2317	−	4.65268i	−0.415136	−	0.171968i
$733$	33.7147	−	19.4652i	1.24528	−	0.718963i	0.275117	−	0.961411i	$-0.411284\pi$
$733$	33.7147	−	19.4652i	1.24528	−	0.718963i	0.970165	+	0.242447i	$0.0779502\pi$
$734$	−1.06258	−	1.84044i	−0.0392204	−	0.0679317i
$735$	0.348088	+	12.1194i	0.0128394	+	0.447029i
$736$	−15.2229	+	26.3669i	−0.561125	+	0.971897i
$737$			25.3476i			0.933691i
$738$	−7.42307	+	7.42228i	−0.273247	+	0.273218i
$739$	11.1939			0.411773			0.205886	−	0.978576i	$-0.433992\pi$
$739$	11.1939			0.411773			0.205886	+	0.978576i	$0.433992\pi$
$740$	−5.95454	+	10.3136i	−0.218893	+	0.379134i
$741$	−22.8117	+	3.00260i	−0.838010	+	0.110303i
$742$	14.1624	−	3.02928i	0.519920	−	0.111208i
$743$	−32.7743	+	18.9223i	−1.20237	+	0.694191i	−0.961082	−	0.276262i	$-0.910904\pi$
$743$	−32.7743	+	18.9223i	−1.20237	+	0.694191i	−0.241291	+	0.970453i	$0.577571\pi$
$744$	−25.6846	+	3.38074i	−0.941641	+	0.123944i
$745$	1.86456	+	1.07650i	0.0683120	+	0.0394400i
$746$			10.2611i			0.375686i
$747$	−21.0304	+	5.63388i	−0.769463	+	0.206133i
$748$			10.6907i			0.390889i
$749$	−20.2009	+	18.2358i	−0.738125	+	0.666323i
$750$	−0.877097	+	0.672983i	−0.0320271	+	0.0245739i
$751$	13.4719	+	23.3340i	0.491596	+	0.851468i	0.999953	−	0.00967764i	$-0.00308054\pi$
$751$	13.4719	+	23.3340i	0.491596	+	0.851468i	−0.508358	+	0.861146i	$0.669747\pi$
$752$	9.53649	+	16.5177i	0.347760	+	0.602338i
$753$	−6.70361	+	16.1827i	−0.244293	+	0.589732i
$754$	5.57996	+	3.22159i	0.203210	+	0.117323i
$755$	−21.6176			−0.786745
$756$	1.74402	+	21.8250i	0.0634295	+	0.793769i
$757$	−24.7154			−0.898295			−0.449147	−	0.893458i	$-0.648272\pi$
$757$	−24.7154			−0.898295			−0.449147	+	0.893458i	$0.648272\pi$
$758$	−9.37599	−	5.41323i	−0.340551	−	0.196617i
$759$	9.13587	−	22.0543i	0.331611	−	0.800520i
$760$	4.52929	+	7.84497i	0.164295	+	0.284567i
$761$	24.6236	+	42.6493i	0.892604	+	1.54604i	0.836743	+	0.547596i	$0.184457\pi$
$761$	24.6236	+	42.6493i	0.892604	+	1.54604i	0.0558612	+	0.998439i	$0.482210\pi$
$762$	13.7498	−	10.5500i	0.498104	−	0.382188i
$763$	−31.8409	−	35.2720i	−1.15272	−	1.27693i
$764$			15.9177i			0.575880i
$765$	−2.02571	+	7.55845i	−0.0732398	+	0.273276i
$766$			2.06510i			0.0746150i
$767$	24.9493	+	14.4045i	0.900866	+	0.520115i
$768$	−12.9698	+	1.70715i	−0.468006	+	0.0616015i
$769$	14.9460	−	8.62908i	0.538967	−	0.311173i	−0.205693	−	0.978617i	$-0.565945\pi$
$769$	14.9460	−	8.62908i	0.538967	−	0.311173i	0.744660	+	0.667444i	$0.232612\pi$
$770$	4.24982	−	0.909016i	0.153153	−	0.0327587i
$771$	22.3199	−	2.93786i	0.803831	−	0.105805i
$772$	3.27803	−	5.67772i	0.117979	−	0.204346i
$773$	−8.12844			−0.292360			−0.146180	−	0.989258i	$-0.546698\pi$
$773$	−8.12844			−0.292360			−0.146180	+	0.989258i	$0.546698\pi$
$774$	17.7173	+	4.74835i	0.636834	+	0.170676i
$775$		−	6.52261i		−	0.234299i
$776$	−0.311954	+	0.540321i	−0.0111985	+	0.0193964i
$777$	32.2875	−	11.4792i	1.15831	−	0.411814i
$778$	5.19988	+	9.00646i	0.186425	+	0.322897i
$779$	−18.7549	+	10.8281i	−0.671962	+	0.387958i
$780$	8.56968	+	3.54994i	0.306844	+	0.127108i
$781$	−8.63874	+	14.9627i	−0.309118	+	0.535409i
$782$	8.91626			0.318845
$783$	−15.4649	−	2.03726i	−0.552671	−	0.0728056i
$784$	−9.76753	−	7.05839i	−0.348840	−	0.252085i
$785$	−2.85973	−	1.65107i	−0.102068	−	0.0589291i
$786$	−6.27691	−	2.60018i	−0.223890	−	0.0927452i
$787$	23.3372	−	13.4737i	0.831880	−	0.480286i	−0.0226158	−	0.999744i	$-0.507199\pi$
$787$	23.3372	−	13.4737i	0.831880	−	0.480286i	0.854496	+	0.519458i	$0.173866\pi$
$788$	5.48947	−	3.16935i	0.195554	−	0.112903i
$789$	−26.0339	+	19.9754i	−0.926831	+	0.711143i
$790$	1.18523	+	0.684291i	0.0421685	+	0.0243460i
$791$	−45.4117	−	14.6909i	−1.61465	−	0.522348i
$792$	17.1008	−	4.58116i	0.607650	−	0.162784i
$793$	14.8203			0.526283
$794$	−11.4838	+	19.8905i	−0.407543	+	0.705886i
$795$	1.93848	+	14.7273i	0.0687509	+	0.522323i
$796$	−34.6187	+	19.9871i	−1.22703	+	0.708425i
$797$	13.5679	+	23.5003i	0.480601	+	0.832425i	0.999752	−	0.0222575i	$-0.00708535\pi$
$797$	13.5679	+	23.5003i	0.480601	+	0.832425i	−0.519152	+	0.854682i	$0.673752\pi$
$798$	2.09145	−	11.3639i	0.0740364	−	0.402278i
$799$	14.4490	−	25.0265i	0.511170	−	0.885372i
$800$		−	5.68501i		−	0.200995i
$801$	−25.0422	−	25.0448i	−0.884821	−	0.884916i
$802$	−1.14529			−0.0404415
$803$	8.38823	−	14.5288i	0.296014	−	0.512711i
$804$	−16.5391	−	21.5553i	−0.583288	−	0.760198i
$805$	2.96369	+	13.8558i	0.104456	+	0.488353i
$806$	12.1241	−	6.99987i	0.427054	−	0.246560i
$807$	10.0576	−	24.2794i	0.354044	−	0.854674i
$808$	5.63585	+	3.25386i	0.198269	+	0.114470i
$809$		−	34.5525i		−	1.21480i	−0.794395	−	0.607401i	$-0.792212\pi$
$809$		−	34.5525i		−	1.21480i	0.794395	−	0.607401i	$-0.207788\pi$
$810$	5.74452		0.000614489i	0.201842		2.15910e-5i
$811$			24.0030i			0.842859i	0.906861	+	0.421430i	$0.138472\pi$
$811$			24.0030i			0.842859i	−0.906861	+	0.421430i	$0.861528\pi$
$812$	9.38921	−	8.47588i	0.329497	−	0.297445i
$813$	1.39679	+	0.578612i	0.0489875	+	0.0202928i
$814$	−6.14155	−	10.6375i	−0.215261	−	0.372843i
$815$	11.0830	+	19.1964i	0.388221	+	0.672419i
$816$	−4.73467	−	6.17069i	−0.165747	−	0.216017i
$817$	32.7716	+	18.9207i	1.14653	+	0.661951i
$818$	−4.03897			−0.141219
$819$	−12.1464	−	23.7666i	−0.424430	−	0.830471i
$820$	8.73070			0.304889
$821$	7.98520	+	4.61026i	0.278685	+	0.160899i	0.632828	−	0.774292i	$-0.281894\pi$
$821$	7.98520	+	4.61026i	0.278685	+	0.160899i	−0.354143	+	0.935191i	$0.615227\pi$
$822$	9.71534	−	1.27878i	0.338861	−	0.0446027i
$823$	−0.276082	−	0.478188i	−0.00962362	−	0.0166686i	0.861173	−	0.508311i	$-0.169730\pi$
$823$	−0.276082	−	0.478188i	−0.00962362	−	0.0166686i	−0.870797	+	0.491643i	$0.836397\pi$
$824$	−13.9055	−	24.0851i	−0.484423	−	0.839045i
$825$	0.581694	+	4.41932i	0.0202520	+	0.153861i
$826$	−10.7392	+	9.69457i	−0.373665	+	0.337317i
$827$			27.9487i			0.971871i	0.873995	+	0.485935i	$0.161521\pi$
$827$			27.9487i			0.971871i	−0.873995	+	0.485935i	$0.838479\pi$
$828$	6.62116	+	24.7158i	0.230101	+	0.858934i
$829$			7.35170i			0.255335i	0.991817	+	0.127668i	$0.0407491\pi$
$829$			7.35170i			0.255335i	−0.991817	+	0.127668i	$0.959251\pi$
$830$	−4.01161	−	2.31611i	−0.139245	−	0.0803932i
$831$	−9.63104	−	12.5521i	−0.334097	−	0.435428i
$832$	0.540211	−	0.311891i	0.0187285	−	0.0108129i
$833$	−1.86206	+	18.1636i	−0.0645165	+	0.629331i
$834$	4.02799	−	9.72369i	0.139478	−	0.336704i
$835$	9.71593	−	16.8285i	0.336234	−	0.582374i
$836$	16.1909			0.559974
$837$	−20.6346	+	26.8870i	−0.713235	+	0.929352i
$838$		−	12.4901i		−	0.431464i
$839$	−16.1284	+	27.9352i	−0.556815	+	0.964431i	0.440945	+	0.897534i	$0.354643\pi$
$839$	−16.1284	+	27.9352i	−0.556815	+	0.964431i	−0.997760	+	0.0668972i	$0.978690\pi$
$840$	−6.81453	+	7.99907i	−0.235124	+	0.275994i
$841$	−9.99418	−	17.3104i	−0.344627	−	0.596911i
$842$	12.8466	−	7.41700i	0.442724	−	0.255607i
$843$	26.7679	−	20.5386i	0.921934	−	0.707386i
$844$	−9.78149	+	16.9420i	−0.336693	+	0.583169i
$845$	1.69230			0.0582170
$846$	−20.4911	−	5.49175i	−0.704499	−	0.188810i
$847$	−3.56453	+	11.0185i	−0.122479	+	0.378599i
$848$	−12.7863	−	7.38219i	−0.439084	−	0.253506i
$849$	−4.72773	−	35.9181i	−0.162255	−	1.23271i
$850$	−1.44184	+	0.832444i	−0.0494546	+	0.0285526i
$851$	34.6817	−	20.0235i	1.18887	−	0.686396i
$852$	−2.41675	−	18.3608i	−0.0827965	−	0.629032i
$853$	31.9904	+	18.4696i	1.09533	+	0.632389i	0.934990	−	0.354674i	$-0.115408\pi$
$853$	31.9904	+	18.4696i	1.09533	+	0.632389i	0.160339	+	0.987062i	$0.448741\pi$
$854$	−2.29085	+	7.08134i	−0.0783912	+	0.242319i
$855$	11.4472	+	3.06792i	0.391486	+	0.104921i
$856$	−23.5868			−0.806181
$857$	9.79305	−	16.9621i	0.334524	−	0.579413i	−0.648869	−	0.760900i	$-0.724758\pi$
$857$	9.79305	−	16.9621i	0.334524	−	0.579413i	0.983393	+	0.181487i	$0.0580910\pi$
$858$	−7.59031	+	5.82392i	−0.259129	+	0.198825i
$859$	49.4732	−	28.5634i	1.68800	−	0.974570i	0.731960	−	0.681348i	$-0.238606\pi$
$859$	49.4732	−	28.5634i	1.68800	−	0.974570i	0.956044	−	0.293222i	$-0.0947276\pi$
$860$	−7.62786	−	13.2118i	−0.260108	−	0.450520i
$861$	−19.1233	−	16.2914i	−0.651719	−	0.555210i
$862$	2.71444	−	4.70154i	0.0924541	−	0.160135i
$863$		−	11.2281i		−	0.382208i	−0.981570	−	0.191104i	$-0.938793\pi$
$863$		−	11.2281i		−	0.382208i	0.981570	−	0.191104i	$-0.0612067\pi$
$864$	−17.9848	+	23.4344i	−0.611855	+	0.797253i
$865$	−1.81201			−0.0616101
$866$	−2.26605	+	3.92491i	−0.0770035	+	0.133374i
$867$	6.75880	−	16.3159i	0.229541	−	0.554119i
$868$	−5.74861	−	26.8758i	−0.195121	−	0.912226i
$869$	4.77875	−	2.75901i	0.162108	−	0.0935931i
$870$	−2.02025	−	2.63299i	−0.0684930	−	0.0892668i
$871$	28.6834	+	16.5604i	0.971899	+	0.561126i
$872$		−	41.1840i		−	1.39467i
$873$	0.211218	+	0.788447i	0.00714866	+	0.0266849i
$874$		−	13.5036i		−	0.456766i
$875$	−1.77287	−	1.96391i	−0.0599339	−	0.0663922i
$876$	2.34667	+	17.8284i	0.0792866	+	0.602366i
$877$	−1.20428	−	2.08587i	−0.0406656	−	0.0704348i	0.844976	−	0.534804i	$-0.179614\pi$
$877$	−1.20428	−	2.08587i	−0.0406656	−	0.0704348i	−0.885642	+	0.464369i	$0.846281\pi$
$878$	−2.34592	−	4.06325i	−0.0791709	−	0.137128i
$879$	−12.7079	+	1.67268i	−0.428626	+	0.0564180i
$880$	−3.83688	−	2.21523i	−0.129341	−	0.0746752i
$881$	−44.5262			−1.50013			−0.750063	−	0.661367i	$-0.769977\pi$
$881$	−44.5262			−1.50013			−0.750063	+	0.661367i	$0.769977\pi$
$882$	13.2336	−	2.13001i	0.445597	−	0.0717213i
$883$	36.5403			1.22968			0.614840	−	0.788652i	$-0.289221\pi$
$883$	36.5403			1.22968			0.614840	+	0.788652i	$0.289221\pi$
$884$	12.0976	+	6.98453i	0.406885	+	0.234915i
$885$	−9.03302	−	11.7727i	−0.303642	−	0.395735i
$886$	−9.81140	−	16.9938i	−0.329621	−	0.570920i
$887$	−25.4468	−	44.0752i	−0.854421	−	1.47990i	−0.877182	−	0.480159i	$-0.840579\pi$
$887$	−25.4468	−	44.0752i	−0.854421	−	1.47990i	0.0227610	−	0.999741i	$-0.492754\pi$
$888$	27.4387	+	11.3663i	0.920782	+	0.381429i
$889$	27.7924	+	30.7873i	0.932128	+	1.03257i
$890$		−	7.53529i		−	0.252584i
$891$	11.5829	−	20.0572i	0.388042	−	0.671942i
$892$		−	30.4854i		−	1.02073i
$893$	−37.9023	−	21.8829i	−1.26835	−	0.732284i
$894$	0.910929	−	2.19901i	0.0304660	−	0.0735459i
$895$	5.36142	−	3.09542i	0.179212	−	0.103468i
$896$	−6.22660	−	29.1105i	−0.208016	−	0.972514i
$897$	−18.9879	−	24.7469i	−0.633988	−	0.826274i
$898$	10.0522	−	17.4109i	0.335446	−	0.581009i
$899$	19.5805			0.653045
$900$	−3.37823	−	3.37859i	−0.112608	−	0.112620i
$901$			22.3700i			0.745252i
$902$	−4.50245	+	7.79847i	−0.149915	+	0.259661i
$903$	−7.94551	+	43.1721i	−0.264410	+	1.43668i
$904$	−20.6834	−	35.8247i	−0.687920	−	1.19151i
$905$	−10.2443	+	5.91455i	−0.340532	+	0.196606i
$906$	3.11881	+	23.6946i	0.103616	+	0.787201i
$907$	3.82592	−	6.62669i	0.127038	−	0.220036i	−0.795490	−	0.605967i	$-0.792786\pi$
$907$	3.82592	−	6.62669i	0.127038	−	0.220036i	0.922528	+	0.385931i	$0.126120\pi$
$908$	17.1931			0.570572
$909$	8.22395	−	2.20313i	0.272771	−	0.0730732i
$910$	1.74789	−	5.40299i	0.0579421	−	0.179107i
$911$	7.28269	+	4.20466i	0.241286	+	0.139307i	0.615768	−	0.787928i	$-0.288846\pi$
$911$	7.28269	+	4.20466i	0.241286	+	0.139307i	−0.374482	+	0.927234i	$0.622179\pi$
$912$	−9.34545	+	7.17062i	−0.309459	+	0.237443i
$913$	−16.1745	+	9.33838i	−0.535299	+	0.309055i
$914$	6.12953	−	3.53888i	0.202747	−	0.117056i
$915$	−7.05245	−	2.92144i	−0.233147	−	0.0965798i
$916$	−1.74514	−	1.00756i	−0.0576612	−	0.0332907i
$917$	5.00472	−	15.4703i	0.165270	−	0.510874i
$918$	8.57692	+	1.12987i	0.283080	+	0.0372913i
$919$	5.71809			0.188622			0.0943112	−	0.995543i	$-0.469935\pi$
$919$	5.71809			0.188622			0.0943112	+	0.995543i	$0.469935\pi$
$920$	−6.14027	+	10.6353i	−0.202439	+	0.350634i
$921$	23.8662	+	9.88645i	0.786418	+	0.325770i
$922$	21.3538	−	12.3286i	0.703249	−	0.406021i
$923$	11.2879	+	19.5512i	0.371545	+	0.643536i
$924$	6.29173	+	17.6968i	0.206983	+	0.582181i
$925$	−3.73888	+	6.47594i	−0.122934	+	0.212928i
$926$			5.09772i			0.167521i
$927$	−35.1444	−	9.41894i	−1.15430	−	0.309359i
$928$	17.0661			0.560221
$929$	−6.63177	+	11.4866i	−0.217581	+	0.376862i	−0.954068	−	0.299590i	$-0.903150\pi$
$929$	−6.63177	+	11.4866i	−0.217581	+	0.376862i	0.736487	+	0.676452i	$0.236483\pi$
$930$	−7.14930	+	0.941028i	−0.234435	+	0.0308575i
$931$	27.5086	+	2.82007i	0.901557	+	0.0924241i
$932$	3.67488	−	2.12169i	0.120375	−	0.0694983i
$933$	−44.2367	+	5.82267i	−1.44825	+	0.190626i
$934$	−6.21374	−	3.58751i	−0.203320	−	0.117387i
$935$			6.71271i			0.219529i
$936$	5.98841	−	22.3443i	0.195737	−	0.730345i
$937$			10.8468i			0.354349i	0.984179	+	0.177174i	$0.0566957\pi$
$937$			10.8468i			0.354349i	−0.984179	+	0.177174i	$0.943304\pi$
$938$	−12.3465	+	11.1455i	−0.403129	+	0.363914i
$939$	−6.27733	+	4.81650i	−0.204853	+	0.157181i
$940$	8.82208	+	15.2803i	0.287745	+	0.498388i
$941$	2.15398	+	3.73079i	0.0702176	+	0.121620i	0.898997	−	0.437956i	$-0.144297\pi$
$941$	2.15398	+	3.73079i	0.0702176	+	0.121620i	−0.828779	+	0.559576i	$0.810964\pi$
$942$	−1.39712	+	3.37270i	−0.0455207	+	0.109888i
$943$	−25.4256	−	14.6795i	−0.827970	−	0.478029i
$944$	14.7490			0.480040
$945$	1.09508	+	13.7040i	0.0356230	+	0.445793i
$946$	15.7348			0.511584
$947$	33.1900	+	19.1623i	1.07853	+	0.622690i	0.930500	−	0.366293i	$-0.119373\pi$
$947$	33.1900	+	19.1623i	1.07853	+	0.622690i	0.148031	+	0.988983i	$0.452706\pi$
$948$	−2.26357	+	5.46433i	−0.0735173	+	0.177473i
$949$	−10.9606	−	18.9842i	−0.355795	−	0.616255i
$950$	1.26073	+	2.18365i	0.0409035	+	0.0708469i
$951$	−34.5359	+	26.4989i	−1.11990	+	0.859285i
$952$	−11.7467	+	10.6040i	−0.380712	+	0.343678i
$953$		−	44.4892i		−	1.44115i	−0.693379	−	0.720573i	$-0.743879\pi$
$953$		−	44.4892i		−	1.44115i	0.693379	−	0.720573i	$-0.256121\pi$
$954$	15.8626	−	4.24946i	0.513571	−	0.137581i
$955$			9.99477i			0.323423i
$956$	−7.18103	−	4.14597i	−0.232251	−	0.134090i
$957$	−13.2665	+	1.74621i	−0.428846	+	0.0564469i
$958$	−8.13104	+	4.69446i	−0.262702	+	0.151671i
$959$	4.90514	+	22.9325i	0.158395	+	0.740528i
$960$	−0.318549	+	0.0419291i	−0.0102811	+	0.00135326i
$961$	5.77219	−	9.99773i	0.186200	−	0.322507i
$962$	−16.0498			−0.517468
$963$	−21.8212	+	21.8189i	−0.703179	+	0.703103i
$964$		−	2.05594i		−	0.0662175i
$965$	2.05829	−	3.56507i	0.0662588	−	0.114764i
$966$	14.7595	−	5.24745i	0.474879	−	0.168834i
$967$	−11.5983	−	20.0889i	−0.372977	−	0.646016i	0.617045	−	0.786928i	$-0.288330\pi$
$967$	−11.5983	−	20.0889i	−0.372977	−	0.646016i	−0.990022	+	0.140912i	$0.954996\pi$
$968$	−8.69233	+	5.01852i	−0.279382	+	0.161301i
$969$	16.4887	+	6.83034i	0.529692	+	0.219422i
$970$	−0.0868325	+	0.150398i	−0.00278802	+	0.00482900i
$971$	17.7740			0.570394			0.285197	−	0.958469i	$-0.407941\pi$
$971$	17.7740			0.570394			0.285197	+	0.958469i	$0.407941\pi$
$972$	3.23717	+	24.6142i	0.103832	+	0.789501i
$973$	23.9654	+	7.75292i	0.768295	+	0.248547i
$974$	−20.2631	−	11.6989i	−0.649273	−	0.374858i
$975$	5.38094	+	2.22903i	0.172328	+	0.0713860i
$976$	6.57087	−	3.79369i	0.210328	−	0.121433i
$977$	15.8434	−	9.14717i	0.506874	−	0.292644i	−0.224674	−	0.974434i	$-0.572132\pi$
$977$	15.8434	−	9.14717i	0.506874	−	0.292644i	0.731548	+	0.681790i	$0.238798\pi$
$978$	19.4418	−	14.9174i	0.621679	−	0.477005i
$979$	−26.3114	−	15.1909i	−0.840915	−	0.485503i
$980$	−9.03582	−	6.52962i	−0.288639	−	0.208581i
$981$	−38.0971	−	38.1011i	−1.21635	−	1.21648i
$982$	20.4664			0.653109
$983$	−5.38132	+	9.32072i	−0.171637	+	0.297285i	−0.938992	−	0.343938i	$-0.888239\pi$
$983$	−5.38132	+	9.32072i	−0.171637	+	0.297285i	0.767355	+	0.641222i	$0.221572\pi$
$984$	−2.84140	−	21.5871i	−0.0905806	−	0.688170i
$985$	3.44687	−	1.99005i	0.109826	−	0.0634082i
$986$	−2.49895	−	4.32830i	−0.0795827	−	0.137841i
$987$	9.18946	−	49.9311i	0.292504	−	1.58933i
$988$	10.5780	−	18.3216i	0.336531	−	0.582889i
$989$			51.3008i			1.63127i
$990$	4.76000	−	1.27517i	0.151283	−	0.0405274i
$991$	−50.4106			−1.60135			−0.800673	−	0.599101i	$-0.795525\pi$
$991$	−50.4106			−1.60135			−0.800673	+	0.599101i	$0.795525\pi$
$992$	18.5405	−	32.1132i	0.588663	−	1.01959i
$993$	−19.6219	−	25.5732i	−0.622683	−	0.811542i
$994$	−11.0867	+	2.37139i	−0.351649	+	0.0752159i
$995$	−21.7373	+	12.5500i	−0.689117	+	0.397862i
$996$	7.66146	−	18.4950i	0.242763	−	0.586037i
$997$	47.9386	+	27.6774i	1.51823	+	0.876551i	0.999770	+	0.0214505i	$0.00682844\pi$
$997$	47.9386	+	27.6774i	1.51823	+	0.876551i	0.518462	+	0.855101i	$0.326505\pi$
$998$			17.8118i			0.563822i
$999$	35.8991	−	14.8665i	1.13580	−	0.470356i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	315.2.bl.j.146.6	yes	24
3.2	odd	2		945.2.bl.j.251.7		24
7.6	odd	2		315.2.bl.i.146.6	yes	24
9.4	even	3		945.2.bl.i.881.7		24
9.5	odd	6		315.2.bl.i.41.6	✓	24
21.20	even	2		945.2.bl.i.251.7		24
63.13	odd	6		945.2.bl.j.881.7		24
63.41	even	6	inner	315.2.bl.j.41.6	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
315.2.bl.i.41.6	✓	24	9.5	odd	6
315.2.bl.i.146.6	yes	24	7.6	odd	2
315.2.bl.j.41.6	yes	24	63.41	even	6	inner
315.2.bl.j.146.6	yes	24	1.1	even	1	trivial
945.2.bl.i.251.7		24	21.20	even	2
945.2.bl.i.881.7		24	9.4	even	3
945.2.bl.j.251.7		24	3.2	odd	2
945.2.bl.j.881.7		24	63.13	odd	6

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:	\( N \)	\(=\)	\( 315 = 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	315.bl (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.552767 + 0.319140i) q^{2} +(-0.662870 + 1.60019i) q^{3} +(-0.796299 - 1.37923i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(-0.877097 + 0.672983i) q^{6} +(-1.77287 - 1.96391i) q^{7} -2.29308i q^{8} +(-2.12121 - 2.12143i) q^{9} +O(q^{10})\)	\(q+(0.552767 + 0.319140i) q^{2} +(-0.662870 + 1.60019i) q^{3} +(-0.796299 - 1.37923i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(-0.877097 + 0.672983i) q^{6} +(-1.77287 - 1.96391i) q^{7} -2.29308i q^{8} +(-2.12121 - 2.12143i) q^{9} -0.638280i q^{10} +(-2.22872 - 1.28675i) q^{11} +(2.73487 - 0.359978i) q^{12} +(-2.91218 + 1.68135i) q^{13} +(-0.353221 - 1.65138i) q^{14} +(1.71724 - 0.226032i) q^{15} +(-0.860783 + 1.49092i) q^{16} +2.60840 q^{17} +(-0.495498 - 1.84962i) q^{18} -3.95039i q^{19} +(-0.796299 + 1.37923i) q^{20} +(4.31781 - 1.53511i) q^{21} +(-0.821308 - 1.42255i) q^{22} +(4.63797 - 2.67773i) q^{23} +(3.66937 + 1.52002i) q^{24} +(-0.500000 + 0.866025i) q^{25} -2.14634 q^{26} +(4.80078 - 1.98810i) q^{27} +(-1.29695 + 4.00905i) q^{28} +(-2.59976 - 1.50097i) q^{29} +(1.02137 + 0.423097i) q^{30} +(-5.64874 + 3.26130i) q^{31} +(-4.92336 + 2.84251i) q^{32} +(3.53639 - 2.71342i) q^{33} +(1.44184 + 0.832444i) q^{34} +(-0.814360 + 2.51730i) q^{35} +(-1.23683 + 4.61493i) q^{36} +7.47777 q^{37} +(1.26073 - 2.18365i) q^{38} +(-0.760076 - 5.77455i) q^{39} +(-1.98587 + 1.14654i) q^{40} +(-2.74102 - 4.74759i) q^{41} +(2.87666 + 0.529428i) q^{42} +(-4.78957 + 8.29578i) q^{43} +4.09855i q^{44} +(-0.776612 + 2.89774i) q^{45} +3.41829 q^{46} +(5.53943 - 9.59457i) q^{47} +(-1.81516 - 2.36570i) q^{48} +(-0.713871 + 6.96350i) q^{49} +(-0.552767 + 0.319140i) q^{50} +(-1.72903 + 4.17393i) q^{51} +(4.63793 + 2.67771i) q^{52} +8.57614i q^{53} +(3.28819 + 0.433167i) q^{54} +2.57350i q^{55} +(-4.50341 + 4.06534i) q^{56} +(6.32137 + 2.61860i) q^{57} +(-0.958039 - 1.65937i) q^{58} +(-4.28361 - 7.41944i) q^{59} +(-1.67919 - 2.18848i) q^{60} +(-3.81680 - 2.20363i) q^{61} -4.16325 q^{62} +(-0.405679 + 7.92688i) q^{63} -0.185501 q^{64} +(2.91218 + 1.68135i) q^{65} +(2.82076 - 0.371284i) q^{66} +(-4.92473 - 8.52989i) q^{67} +(-2.07706 - 3.59758i) q^{68} +(1.21051 + 9.19661i) q^{69} +(-1.25352 + 1.13159i) q^{70} -6.71360i q^{71} +(-4.86463 + 4.86411i) q^{72} +6.51892i q^{73} +(4.13346 + 2.38646i) q^{74} +(-1.05437 - 1.37416i) q^{75} +(-5.44850 + 3.14569i) q^{76} +(1.42416 + 6.65824i) q^{77} +(1.42274 - 3.43455i) q^{78} +(-1.07209 + 1.85691i) q^{79} +1.72157 q^{80} +(-0.000962727 + 9.00000i) q^{81} -3.49908i q^{82} +(3.62867 - 6.28503i) q^{83} +(-5.55553 - 4.73284i) q^{84} +(-1.30420 - 2.25894i) q^{85} +(-5.29503 + 3.05709i) q^{86} +(4.12513 - 3.16515i) q^{87} +(-2.95063 + 5.11064i) q^{88} +11.8056 q^{89} +(-1.35407 + 1.35392i) q^{90} +(8.46492 + 2.73844i) q^{91} +(-7.38642 - 4.26455i) q^{92} +(-1.47432 - 11.2009i) q^{93} +(6.12403 - 3.53571i) q^{94} +(-3.42114 + 1.97520i) q^{95} +(-1.28499 - 9.76252i) q^{96} +(-0.235631 - 0.136041i) q^{97} +(-2.61694 + 3.62137i) q^{98} +(1.99781 + 7.45754i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 6 q^{2} + 5 q^{3} + 18 q^{4} - 12 q^{5} + q^{6} + 9 q^{7} + q^{9}+O(q^{10}) \) 24 * q + 6 * q^2 + 5 * q^3 + 18 * q^4 - 12 * q^5 + q^6 + 9 * q^7 + q^9	\( 24 q + 6 q^{2} + 5 q^{3} + 18 q^{4} - 12 q^{5} + q^{6} + 9 q^{7} + q^{9} + 9 q^{11} - 18 q^{12} + 3 q^{13} + 18 q^{14} + 2 q^{15} - 18 q^{16} + 18 q^{17} + 2 q^{18} + 18 q^{20} + 8 q^{21} - 9 q^{22} + 9 q^{23} - 7 q^{24} - 12 q^{25} - 18 q^{26} - 4 q^{27} - 9 q^{28} + 9 q^{29} - 5 q^{30} - 42 q^{31} + 18 q^{32} + 13 q^{33} - 39 q^{34} - 9 q^{35} - 21 q^{36} - 12 q^{38} - 21 q^{39} - 6 q^{40} - 33 q^{41} - 65 q^{42} + 18 q^{43} + q^{45} - 30 q^{46} - 17 q^{48} + 9 q^{49} - 6 q^{50} - 12 q^{51} + 129 q^{52} + 52 q^{54} - 9 q^{56} + 6 q^{57} - 15 q^{58} + 12 q^{59} + 15 q^{60} - 15 q^{61} + 12 q^{62} + 46 q^{63} - 60 q^{64} - 3 q^{65} + 29 q^{66} - 15 q^{67} + 9 q^{68} + 61 q^{69} - 9 q^{70} + 61 q^{72} - 18 q^{74} - 7 q^{75} + 54 q^{76} - 45 q^{77} - 66 q^{78} + 21 q^{79} + 36 q^{80} + q^{81} - 30 q^{83} + 15 q^{84} - 9 q^{85} - 102 q^{86} + 10 q^{87} - 9 q^{88} + 102 q^{89} - 37 q^{90} + 42 q^{91} - 3 q^{92} - 6 q^{93} - 156 q^{94} - 18 q^{95} - 42 q^{96} - 45 q^{97} + 3 q^{98} + 23 q^{99}+O(q^{100}) \) 24 * q + 6 * q^2 + 5 * q^3 + 18 * q^4 - 12 * q^5 + q^6 + 9 * q^7 + q^9 + 9 * q^11 - 18 * q^12 + 3 * q^13 + 18 * q^14 + 2 * q^15 - 18 * q^16 + 18 * q^17 + 2 * q^18 + 18 * q^20 + 8 * q^21 - 9 * q^22 + 9 * q^23 - 7 * q^24 - 12 * q^25 - 18 * q^26 - 4 * q^27 - 9 * q^28 + 9 * q^29 - 5 * q^30 - 42 * q^31 + 18 * q^32 + 13 * q^33 - 39 * q^34 - 9 * q^35 - 21 * q^36 - 12 * q^38 - 21 * q^39 - 6 * q^40 - 33 * q^41 - 65 * q^42 + 18 * q^43 + q^45 - 30 * q^46 - 17 * q^48 + 9 * q^49 - 6 * q^50 - 12 * q^51 + 129 * q^52 + 52 * q^54 - 9 * q^56 + 6 * q^57 - 15 * q^58 + 12 * q^59 + 15 * q^60 - 15 * q^61 + 12 * q^62 + 46 * q^63 - 60 * q^64 - 3 * q^65 + 29 * q^66 - 15 * q^67 + 9 * q^68 + 61 * q^69 - 9 * q^70 + 61 * q^72 - 18 * q^74 - 7 * q^75 + 54 * q^76 - 45 * q^77 - 66 * q^78 + 21 * q^79 + 36 * q^80 + q^81 - 30 * q^83 + 15 * q^84 - 9 * q^85 - 102 * q^86 + 10 * q^87 - 9 * q^88 + 102 * q^89 - 37 * q^90 + 42 * q^91 - 3 * q^92 - 6 * q^93 - 156 * q^94 - 18 * q^95 - 42 * q^96 - 45 * q^97 + 3 * q^98 + 23 * q^99

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