LMFDB - Embedded newform 315.2.bl.i.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.i.41.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.552767 + 0.319140i) q^{2} +(0.662870 - 1.60019i) q^{3} +(-0.796299 - 1.37923i) q^{4} +(0.500000 + 0.866025i) q^{5} +(0.877097 - 0.672983i) q^{6} +(2.58723 + 0.553395i) q^{7} -2.29308i q^{8} +(-2.12121 - 2.12143i) q^{9} +O(q^{10})$	\(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} +(2.58723 + 0.553395i) 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} +(1.25352 + 1.13159i) 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} +(2.60053 - 3.77322i) 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} +(2.64168 - 1.25578i) 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} +(6.38751 + 2.86352i) 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} +(1.26898 - 5.93274i) 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} +(-4.31406 - 6.66250i) 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} +(-0.353221 + 1.65138i) 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} +(-5.05412 - 4.56248i) 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} +(-7.27495 - 0.582119i) 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} + q^{9}+O(q^{10}) $ 24 * q + 6 * q^2 - 5 * q^3 + 18 * q^4 + 12 * q^5 - q^6 + q^9	$ 24 q + 6 q^{2} - 5 q^{3} + 18 q^{4} + 12 q^{5} - q^{6} + q^{9} + 9 q^{11} + 18 q^{12} - 3 q^{13} + 9 q^{14} + 2 q^{15} - 18 q^{16} - 18 q^{17} + 2 q^{18} - 18 q^{20} + 4 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} + 26 q^{42} + 18 q^{43} - q^{45} - 30 q^{46} + 17 q^{48} - 6 q^{50} - 12 q^{51} - 129 q^{52} - 52 q^{54} + 6 q^{56} + 6 q^{57} - 15 q^{58} - 12 q^{59} + 15 q^{60} + 15 q^{61} - 12 q^{62} - 83 q^{63} - 60 q^{64} - 3 q^{65} - 29 q^{66} - 15 q^{67} - 9 q^{68} - 61 q^{69} + 18 q^{70} + 61 q^{72} - 18 q^{74} + 7 q^{75} - 54 q^{76} - 57 q^{77} - 66 q^{78} + 21 q^{79} - 36 q^{80} + q^{81} + 30 q^{83} - 42 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 + q^9 + 9 * q^11 + 18 * q^12 - 3 * q^13 + 9 * q^14 + 2 * q^15 - 18 * q^16 - 18 * q^17 + 2 * q^18 - 18 * q^20 + 4 * 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 + 26 * q^42 + 18 * q^43 - q^45 - 30 * q^46 + 17 * q^48 - 6 * q^50 - 12 * q^51 - 129 * q^52 - 52 * q^54 + 6 * q^56 + 6 * q^57 - 15 * q^58 - 12 * q^59 + 15 * q^60 + 15 * q^61 - 12 * q^62 - 83 * q^63 - 60 * q^64 - 3 * q^65 - 29 * q^66 - 15 * q^67 - 9 * q^68 - 61 * q^69 + 18 * q^70 + 61 * q^72 - 18 * q^74 + 7 * q^75 - 54 * q^76 - 57 * q^77 - 66 * q^78 + 21 * q^79 - 36 * q^80 + q^81 + 30 * q^83 - 42 * 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
$7$	2.58723	+	0.553395i	0.977881	+	0.209164i
$7$	2.58723	+	0.553395i	0.977881	+	0.209164i
$8$		−	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	−0.0384614	−	0.999260i	$-0.512246\pi$
$13$	2.91218	−	1.68135i	0.807692	−	0.466321i	0.846154	+	0.532939i	$0.178912\pi$
$14$	1.25352	+	1.13159i	0.335018	+	0.302429i
$15$	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	$-0.602446\pi$
$17$	−2.60840			−0.632629			−0.316315	+	0.948654i	$0.602446\pi$
$18$	−0.495498	−	1.84962i	−0.116790	−	0.435960i
$19$			3.95039i			0.906282i	0.891439	+	0.453141i	$0.149697\pi$
$19$			3.95039i			0.906282i	−0.891439	+	0.453141i	$0.850303\pi$
$20$	0.796299	−	1.37923i	0.178058	−	0.308405i
$21$	2.60053	−	3.77322i	0.567483	−	0.823385i
$22$	−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	0.102025	−	0.994782i	$-0.467468\pi$
$31$	5.64874	−	3.26130i	1.01454	−	0.585747i	0.912519	+	0.409035i	$0.134134\pi$
$32$	−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	0.996702	−	0.0811468i	$-0.0258583\pi$
$41$	2.74102	+	4.74759i	0.428076	+	0.741449i	−0.568626	+	0.822596i	$0.692525\pi$
$42$	2.64168	−	1.25578i	0.407620	−	0.193771i
$43$	−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	$0.466121\pi$
$47$	−5.53943	+	9.59457i	−0.808009	+	1.39951i	−0.914241	+	0.405171i	$0.867212\pi$
$48$	1.81516	+	2.36570i	0.261996	+	0.341459i
$49$	6.38751	+	2.86352i	0.912501	+	0.409074i
$50$	−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
$56$	1.26898	−	5.93274i	0.169575	−	0.792795i
$57$	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	$0.0216413\pi$
$59$	4.28361	+	7.41944i	0.557679	+	0.965928i	−0.440011	+	0.897993i	$0.645025\pi$
$60$	−1.67919	−	2.18848i	−0.216782	−	0.282531i
$61$	3.81680	+	2.20363i	0.488691	+	0.282146i	0.724031	−	0.689767i	$-0.242287\pi$
$61$	3.81680	+	2.20363i	0.488691	+	0.282146i	−0.235340	+	0.971913i	$0.575620\pi$
$62$	4.16325			0.528733
$63$	−4.31406	−	6.66250i	−0.543520	−	0.839396i
$64$	−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
$70$	−0.353221	+	1.65138i	−0.0422180	+	0.197377i
$71$		−	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	$-0.875411\pi$
$73$		−	6.51892i		−	0.762982i	0.924373	−	0.381491i	$-0.124589\pi$
$74$	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
$77$	−5.05412	−	4.56248i	−0.575971	−	0.519943i
$78$	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	−0.993516	−	0.113692i	$-0.963732\pi$
$83$	−3.62867	+	6.28503i	−0.398298	+	0.689872i	0.595218	+	0.803564i	$0.297066\pi$
$84$	−7.27495	−	0.582119i	−0.793762	−	0.0635144i
$85$	−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	$-0.715185\pi$
$89$	−11.8056			−1.25139			−0.625696	+	0.780067i	$0.715185\pi$
$90$	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	0.511915	−	0.859036i	$-0.328936\pi$
$97$	0.235631	+	0.136041i	0.0239247	+	0.0138129i	−0.487990	+	0.872849i	$0.662270\pi$
$98$	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	−0.786752	−	0.617269i	$-0.788239\pi$
$101$	1.41899	−	2.45776i	0.141195	−	0.244556i	0.927947	+	0.372713i	$0.121572\pi$
$102$	−2.28782	+	1.75541i	−0.226528	+	0.173811i
$103$	−10.5034	+	6.06412i	−1.03493	+	0.597516i	−0.918392	−	0.395671i	$-0.870512\pi$
$103$	−10.5034	+	6.06412i	−1.03493	+	0.597516i	−0.116535	+	0.993187i	$0.537179\pi$
$104$	−3.85547	−	6.67787i	−0.378060	−	0.654819i
$105$	4.56798	+	0.365515i	0.445789	+	0.0356707i
$106$	−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
$112$	−3.05211	+	3.38100i	−0.288397	+	0.319474i
$113$	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
$119$	−6.74852	−	1.44348i	−0.618636	−	0.132323i
$120$	−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
$126$	−0.258396	−	5.05960i	−0.0230197	−	0.450745i
$127$	−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	0.699996	−	0.714147i	$-0.253185\pi$
$131$	−3.07279	−	5.32223i	−0.268471	−	0.465005i	−0.968467	+	0.249141i	$0.919852\pi$
$132$	6.55846	+	2.71681i	0.570841	+	0.236468i
$133$	−2.18613	+	10.2206i	−0.189561	+	0.886236i
$134$		−	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	−0.107778	−	0.994175i	$-0.534374\pi$
$139$	8.24478	−	4.76013i	0.699313	−	0.403749i	0.807092	+	0.590426i	$0.201040\pi$
$140$	2.82347	−	3.12772i	0.238627	−	0.264340i
$141$	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
$147$	8.81626	−	8.32307i	0.727153	−	0.686476i
$148$	−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	−0.609756	−	0.792589i	$-0.708733\pi$
$157$	−2.85973	+	1.65107i	−0.228232	+	0.131770i	0.381524	+	0.924359i	$0.375399\pi$
$158$	−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	$-0.895833\pi$
$167$	−9.71593	−	16.8285i	−0.751841	−	1.30223i	0.195088	−	0.980786i	$-0.437501\pi$
$168$	−8.65233	−	5.96324i	−0.667541	−	0.460074i
$169$	−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	−0.898410	−	0.439159i	$-0.855277\pi$
$173$	−0.906004	+	1.56925i	−0.0688822	+	0.119307i	0.829527	+	0.558466i	$0.188610\pi$
$174$	−3.29036	+	0.433095i	−0.249442	+	0.0328329i
$175$	−1.77287	+	1.96391i	−0.134016	+	0.148458i
$176$	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	$0.144889\pi$
$181$			11.8291i			0.879249i	−0.898182	+	0.439625i	$0.855111\pi$
$182$	5.55307	+	1.18777i	0.411621	+	0.0880437i
$183$	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
$189$	−13.5209	+	2.48693i	−0.983502	+	0.180898i
$190$	−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
$196$	−1.13691	−	11.0901i	−0.0812079	−	0.792147i
$197$			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	$0.349049\pi$
$199$			25.1000i			1.77929i	−0.456649	+	0.889647i	$0.650951\pi$
$200$	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
$203$	−5.89553	−	5.32204i	−0.413785	−	0.373534i
$204$	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
$210$	2.40838	+	1.65987i	0.166194	+	0.114542i
$211$	−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	−0.171248	−	0.985228i	$-0.554780\pi$
$223$	−16.5774	−	9.57096i	−1.11010	−	0.640919i	−0.938856	+	0.344309i	$0.888113\pi$
$224$	−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	−0.629406	−	0.777076i	$-0.716702\pi$
$227$	5.39780	−	9.34927i	0.358265	−	0.620533i	0.987671	+	0.156544i	$0.0500352\pi$
$228$	−1.42206	−	10.8038i	−0.0941779	−	0.715500i
$229$	−1.09578	+	0.632652i	−0.0724115	+	0.0418068i	−0.535769	−	0.844365i	$-0.679978\pi$
$229$	−1.09578	+	0.632652i	−0.0724115	+	0.0418068i	0.463357	+	0.886172i	$0.346645\pi$
$230$	1.70914	+	2.96033i	0.112698	+	0.195198i
$231$	−10.6511	+	5.06322i	−0.700788	+	0.333135i
$232$	−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
$238$	−3.26969	−	2.95163i	−0.211942	−	0.191326i
$239$	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	0.463560	−	0.886066i	$-0.346572\pi$
$241$	−1.11798	−	0.645468i	−0.0720157	−	0.0415783i	−0.535575	+	0.844487i	$0.679905\pi$
$242$		−	2.79381i		−	0.179593i
$243$	14.4011	+	5.96737i	0.923828	+	0.382807i
$244$		−	7.01899i		−	0.449345i
$245$	0.713871	+	6.96350i	0.0456076	+	0.444882i
$246$	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	$-0.603402\pi$
$251$	−10.1130			−0.638328			−0.319164	+	0.947700i	$0.603402\pi$
$252$	−5.75385	+	11.2554i	−0.362458	+	0.709025i
$253$	−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	0.994366	−	0.106002i	$-0.0338051\pi$
$257$	6.49877	+	11.2562i	0.405382	+	0.702143i	−0.588984	+	0.808145i	$0.700472\pi$
$258$	1.38200	+	10.4995i	0.0860396	+	0.653671i
$259$	19.3467	+	4.13816i	1.20215	+	0.257133i
$260$		−	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
$266$	−4.47022	+	4.95191i	−0.274087	+	0.303621i
$267$	−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	$-0.346934\pi$
$269$	15.1728			0.925103			0.462552	+	0.886592i	$0.346934\pi$
$270$	−1.26896	−	3.06424i	−0.0772266	−	0.186484i
$271$			0.872890i			0.0530243i	0.999648	+	0.0265121i	$0.00844006\pi$
$271$			0.872890i			0.0530243i	−0.999648	+	0.0265121i	$0.991560\pi$
$272$	2.24526	−	3.88891i	0.136139	−	0.235800i
$273$	1.22912	−	15.3607i	0.0743895	−	0.929671i
$274$	−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	0.146742	−	0.989175i	$-0.453121\pi$
$283$	18.1140	−	10.4581i	1.07676	−	0.621669i	0.930021	+	0.367505i	$0.119788\pi$
$284$	−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	0.737470	−	0.675380i	$-0.236020\pi$
$293$	−3.70009	−	6.40874i	−0.216161	−	0.374403i	−0.953631	+	0.300978i	$0.902687\pi$
$294$	7.52957	−	1.78710i	0.439133	−	0.104226i
$295$	−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
$301$	−16.9826	+	18.8126i	−0.978859	+	1.08434i
$302$	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	$0.139941\pi$
$307$			14.9146i			0.851222i	−0.904906	+	0.425611i	$0.860059\pi$
$308$	−2.26812	+	10.6039i	−0.129238	+	0.604213i
$309$	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	$-0.906015\pi$
$311$	−12.8802	−	22.3091i	−0.730369	−	1.26504i	0.226357	−	0.974044i	$-0.427318\pi$
$312$	−13.2415	+	1.74292i	−0.749654	+	0.0986734i
$313$	−3.95612	−	2.28407i	−0.223613	−	0.129103i	0.384009	−	0.923329i	$-0.374543\pi$
$313$	−3.95612	−	2.28407i	−0.223613	−	0.129103i	−0.607622	+	0.794226i	$0.707877\pi$
$314$	−2.10769			−0.118944
$315$	3.61287	−	7.06733i	0.203562	−	0.398199i
$316$	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
$322$	8.84390	+	1.89167i	0.492851	+	0.105418i
$323$		−	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
$329$	−19.6414	+	21.7579i	−1.08286	+	1.19955i
$330$	−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
$336$	3.38708	+	7.12511i	0.184780	+	0.388707i
$337$	−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	0.382771	−	0.923843i	$-0.374970\pi$
$349$	−4.22045	−	2.43668i	−0.225916	−	0.130433i	−0.608686	+	0.793411i	$0.708303\pi$
$350$	−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	$0.373814\pi$
$353$	−11.3820	+	19.7142i	−0.605802	+	1.04928i	−0.991924	+	0.126833i	$0.959519\pi$
$354$	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
$357$	−6.78322	+	9.84207i	−0.359006	+	0.520898i
$358$	−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
$364$	−10.5175	−	9.49445i	−0.551269	−	0.497645i
$365$	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	0.573365	−	0.819300i	$-0.305638\pi$
$367$	2.88343	+	1.66475i	0.150514	+	0.0868992i	−0.422852	+	0.906199i	$0.638971\pi$
$368$			9.21978i			0.480614i
$369$	4.25742	−	15.8855i	0.221633	−	0.826967i
$370$			4.77291i			0.248132i
$371$	−4.74600	+	22.1884i	−0.246400	+	1.15197i
$372$	−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
$378$	−8.26760	−	2.94037i	−0.425239	−	0.151237i
$379$	−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	0.821731	−	0.569875i	$-0.193008\pi$
$383$	−1.61770	−	2.80195i	−0.0826608	−	0.143173i	−0.904392	+	0.426703i	$0.859675\pi$
$384$	15.4615	−	11.8634i	0.789016	−	0.605400i
$385$	1.42416	−	6.65824i	0.0725821	−	0.339335i
$386$			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
$392$	6.56630	−	14.6471i	0.331648	−	0.739790i
$393$	−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	$-0.641376\pi$
$397$		−	35.9834i		−	1.80596i	0.429686	−	0.902978i	$-0.358624\pi$
$398$	−8.01043	+	13.8745i	−0.401526	+	0.695464i
$399$	14.9057	+	10.2731i	0.746220	+	0.514300i
$400$	−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	−0.358356	−	0.933585i	$-0.616663\pi$
$409$	5.48011	−	3.16395i	0.270974	−	0.156447i	0.629330	+	0.777138i	$0.283329\pi$
$410$	−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	0.999682	−	0.0252316i	$-0.00803233\pi$
$419$	9.78420	+	16.9467i	0.477990	+	0.827902i	−0.521692	+	0.853134i	$0.674699\pi$
$420$	−3.13334	−	6.59135i	−0.152892	−	0.321625i
$421$	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
$427$	8.65545	+	7.81349i	0.418867	+	0.378121i
$428$	−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	$-0.945425\pi$
$433$		−	7.10048i		−	0.341228i	0.985338	−	0.170614i	$-0.0545750\pi$
$434$	10.7713	+	2.30392i	0.517038	+	0.110592i
$435$	−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	0.644162	−	0.764889i	$-0.277206\pi$
$439$	6.36593	+	3.67537i	0.303829	+	0.175416i	−0.340332	+	0.940305i	$0.610540\pi$
$440$	−5.90126			−0.281331
$441$	−7.47445	−	19.6248i	−0.355926	−	0.934514i
$442$	−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
$448$	−0.479933	−	0.102655i	−0.0226747	−	0.00485001i
$449$		−	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
$455$	6.60402	+	5.96161i	0.309601	+	0.279485i
$456$	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	$0.522812\pi$
$461$	−19.3153	+	33.4552i	−0.899605	+	1.55816i	−0.827999	+	0.560729i	$0.810521\pi$
$462$	−7.50343	−	0.600401i	−0.349091	−	0.0279332i
$463$	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	$-0.416248\pi$
$467$	11.2412			0.520179			0.260089	+	0.965585i	$0.416248\pi$
$468$	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	−0.647634	−	0.761951i	$-0.724242\pi$
$479$	7.35486	−	12.7390i	0.336052	−	0.582059i	0.983686	+	0.179892i	$0.0575749\pi$
$480$	−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
$483$	1.95751	−	24.4636i	0.0890696	−	1.11313i
$484$	−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
$490$	−1.82773	+	4.07702i	−0.0825684	+	0.184181i
$491$	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
$497$	3.71528	−	17.3696i	0.166653	−	0.779134i
$498$	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	$-0.489335\pi$
$503$	1.50267			0.0670006			0.0335003	+	0.999439i	$0.489335\pi$
$504$	−15.2777	+	9.89250i	−0.680522	+	0.440647i
$505$	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	$0.128269\pi$
$509$	18.0390	+	31.2444i	0.799563	+	1.38488i	−0.120338	+	0.992733i	$0.538398\pi$
$510$	−2.66414	−	1.10360i	−0.117970	−	0.0488684i
$511$	3.60754	−	16.8659i	0.159588	−	0.746105i
$512$		−	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
$518$	9.37356	+	8.46175i	0.411851	+	0.371788i
$519$	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	$-0.159678\pi$
$521$	40.0264			1.75359			0.876794	+	0.480866i	$0.159678\pi$
$522$	−1.48805	+	5.55229i	−0.0651302	+	0.243017i
$523$		−	22.6116i		−	0.988737i	−0.869252	−	0.494369i	$-0.835399\pi$
$523$		−	22.6116i		−	0.988737i	0.869252	−	0.494369i	$-0.164601\pi$
$524$	−4.89372	+	8.47617i	−0.213783	+	0.370283i
$525$	1.96744	+	4.13874i	0.0858662	+	0.180629i
$526$	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
$546$	5.58163	−	8.09862i	0.238872	−	0.346589i
$547$	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
$553$	−3.80133	+	4.21095i	−0.161649	+	0.179068i
$554$	−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
$560$	−4.45408	−	0.952706i	−0.188219	−	0.0402592i
$561$	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	0.732520	−	0.680746i	$-0.238344\pi$
$563$	−5.29797	−	9.17636i	−0.223283	−	0.386737i	−0.955803	+	0.294008i	$0.905011\pi$
$564$	11.6958	−	28.2340i	0.492482	−	1.18887i
$565$	15.6229	+	9.01990i	0.657262	+	0.379470i
$566$	13.3504			0.561159
$567$	−4.98305	+	23.2845i	−0.209268	+	0.977858i
$568$	−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
$574$	−1.93638	+	9.05293i	−0.0808228	+	0.377862i
$575$			5.35547i			0.223338i
$576$	0.393486	+	0.393528i	0.0163952	+	0.0163970i
$577$			8.14778i			0.339196i	0.985513	+	0.169598i	$0.0542470\pi$
$577$			8.14778i			0.339196i	−0.985513	+	0.169598i	$0.945753\pi$
$578$	−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
$581$	−12.8663	+	14.2527i	−0.533784	+	0.591303i
$582$	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	$0.402551\pi$
$587$	−16.3555	+	28.3286i	−0.675066	+	1.16925i	−0.976450	+	0.215745i	$0.930782\pi$
$588$	−18.4998	−	5.53200i	−0.762920	−	0.228136i
$589$	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	$-0.185351\pi$
$593$	40.6769			1.67040			0.835201	+	0.549945i	$0.185351\pi$
$594$	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	0.248741	−	0.968570i	$-0.419983\pi$
$601$	−11.4167	−	6.59141i	−0.465695	−	0.268869i	−0.714436	+	0.699701i	$0.753317\pi$
$602$	−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	$0.751306\pi$
$607$	−41.2641	+	23.8238i	−1.67486	+	0.966979i	−0.964856	+	0.262779i	$0.915361\pi$
$608$	−11.2290	−	19.4492i	−0.455397	−	0.788770i
$609$	−12.4242	+	5.90614i	−0.503456	+	0.239329i
$610$	−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
$616$	−10.4622	+	11.5895i	−0.421532	+	0.466955i
$617$	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	−0.240511	−	0.970646i	$-0.577315\pi$
$619$	−29.8898	−	17.2569i	−1.20137	−	0.693612i	−0.960860	+	0.277035i	$0.910648\pi$
$620$		−	10.3879i		−	0.417188i
$621$	−16.9423	+	22.0759i	−0.679870	+	0.885877i
$622$		−	16.4423i		−	0.659278i
$623$	−30.5438	−	6.53317i	−1.22371	−	0.261746i
$624$	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
$630$	4.25254	−	2.75358i	0.169425	−	0.109705i
$631$	−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
$637$	23.4161	−	2.40053i	0.927780	−	0.0951124i
$638$			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	−0.954239	−	0.299046i	$-0.903331\pi$
$643$	−29.7285	+	17.1637i	−1.17238	+	0.676872i	−0.218138	+	0.975918i	$0.569998\pi$
$644$	−16.7504	−	15.1210i	−0.660057	−	0.595850i
$645$	−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	$-0.710325\pi$
$647$	−31.2211			−1.22743			−0.613714	+	0.789528i	$0.710325\pi$
$648$	20.6378	+	0.00220761i	0.810728	+	8.67233e-5i
$649$		−	22.0478i		−	0.865451i
$650$	−1.07317	+	1.85879i	−0.0420932	+	0.0729076i
$651$	2.38411	−	29.7951i	0.0934408	−	1.16776i
$652$	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	0.0775208	−	0.996991i	$-0.475300\pi$
$661$	25.1880	−	14.5423i	0.979700	−	0.565630i	0.902180	+	0.431360i	$0.141966\pi$
$662$	−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
$672$	−2.07796	+	25.9690i	−0.0801590	+	1.00178i
$673$	−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	$-0.544896\pi$
$677$	20.4807	−	35.4736i	0.787137	−	1.36336i	0.927714	−	0.373291i	$-0.121771\pi$
$678$	7.63259	−	18.4253i	0.293128	−	0.707619i
$679$	0.534346	+	0.482367i	0.0205063	+	0.0185115i
$680$	−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
$686$	4.76657	+	10.8175i	0.181988	+	0.413015i
$687$	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	$0.0441617\pi$
$691$	42.1997	+	24.3640i	1.60535	+	0.926851i	0.614961	+	0.788557i	$0.289172\pi$
$692$	2.88580			0.109702
$693$	1.04183	+	20.4000i	0.0395760	+	0.774930i
$694$	−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
$700$	4.12042	+	0.881337i	0.155737	+	0.0333114i
$701$			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
$707$	5.03136	−	5.57353i	0.189224	−	0.209614i
$708$	−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
$714$	−6.89054	+	3.27557i	−0.257872	+	0.122585i
$715$	−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	$-0.689525\pi$
$719$	−30.0774			−1.12170			−0.560849	+	0.827918i	$0.689525\pi$
$720$	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	0.588327	−	0.808623i	$-0.299787\pi$
$727$	4.91269	+	2.83634i	0.182202	+	0.105194i	−0.406125	+	0.913818i	$0.633120\pi$
$728$	−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	−0.970165	−	0.242447i	$-0.922050\pi$
$733$	−33.7147	+	19.4652i	−1.24528	+	0.718963i	−0.275117	+	0.961411i	$0.588716\pi$
$734$	1.06258	+	1.84044i	0.0392204	+	0.0679317i
$735$	11.6161	+	3.47357i	0.428467	+	0.128125i
$736$	−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
$742$	−9.70465	+	10.7504i	−0.356269	+	0.394660i
$743$	−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
$749$	5.69226	−	26.6124i	0.207991	−	0.972396i
$750$	−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
$756$	14.1967	+	16.6681i	0.516331	+	0.606214i
$757$	−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	$-0.815543\pi$
$761$	−24.6236	−	42.6493i	−0.892604	−	1.54604i	−0.0558612	−	0.998439i	$-0.517790\pi$
$762$	−13.7498	+	10.5500i	−0.498104	+	0.382188i
$763$	46.4669	+	9.93903i	1.68221	+	0.359817i
$764$			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	−0.744660	−	0.667444i	$-0.767388\pi$
$769$	−14.9460	+	8.62908i	−0.538967	+	0.311173i	0.205693	+	0.978617i	$0.434055\pi$
$770$	2.91214	−	3.22595i	0.104946	−	0.116255i
$771$	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	$-0.453302\pi$
$773$	8.12844			0.292360			0.146180	+	0.989258i	$0.453302\pi$
$774$	17.7173	+	4.74835i	0.636834	+	0.170676i
$775$			6.52261i			0.234299i
$776$	0.311954	−	0.540321i	0.0111985	−	0.0193964i
$777$	19.4462	−	28.2153i	0.697628	−	1.01222i
$778$	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	−0.854496	−	0.519458i	$-0.826134\pi$
$787$	−23.3372	+	13.4737i	−0.831880	+	0.480286i	0.0226158	+	0.999744i	$0.492801\pi$
$788$	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	0.519152	−	0.854682i	$-0.326248\pi$
$797$	−13.5679	−	23.5003i	−0.480601	−	0.832425i	−0.999752	+	0.0222575i	$0.992915\pi$
$798$	4.96082	+	10.4357i	0.175611	+	0.369418i
$799$	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
$805$	10.5176	+	9.49454i	0.370698	+	0.334639i
$806$	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	$-0.861528\pi$
$811$		−	24.0030i		−	0.842859i	0.906861	−	0.421430i	$-0.138472\pi$
$812$	−2.64572	+	12.3692i	−0.0928465	+	0.434075i
$813$	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
$819$	−23.7653	−	12.1490i	−0.830425	−	0.424519i
$820$	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
$826$	−3.02613	+	14.1477i	−0.105292	+	0.492262i
$827$			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	$-0.959251\pi$
$829$		−	7.35170i		−	0.255335i	0.991817	−	0.127668i	$-0.0407491\pi$
$830$	−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
$833$	−16.6612	−	7.46920i	−0.577275	−	0.258792i
$834$	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	$-0.645357\pi$
$839$	16.1284	−	27.9352i	0.556815	−	0.964431i	0.997760	−	0.0668972i	$-0.0213099\pi$
$840$	0.838158	−	10.4748i	0.0289192	−	0.361413i
$841$	−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	−0.160339	−	0.987062i	$-0.551259\pi$
$853$	−31.9904	−	18.4696i	−1.09533	−	0.632389i	−0.934990	+	0.354674i	$0.884592\pi$
$854$	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	−0.983393	−	0.181487i	$-0.941909\pi$
$857$	−9.79305	+	16.9621i	−0.334524	+	0.579413i	0.648869	+	0.760900i	$0.275242\pi$
$858$	−7.59031	+	5.82392i	−0.259129	+	0.198825i
$859$	−49.4732	+	28.5634i	−1.68800	+	0.974570i	−0.731960	+	0.681348i	$0.761394\pi$
$859$	−49.4732	+	28.5634i	−1.68800	+	0.974570i	−0.956044	+	0.293222i	$0.905272\pi$
$860$	7.62786	+	13.2118i	0.260108	+	0.450520i
$861$	25.0418	+	2.00377i	0.853424	+	0.0682884i
$862$	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
$868$	−20.4009	−	18.4164i	−0.692450	−	0.625092i
$869$	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
$875$	−2.58723	−	0.553395i	−0.0874643	−	0.0187082i
$876$	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	$-0.230023\pi$
$881$	44.5262			1.50013			0.750063	+	0.661367i	$0.230023\pi$
$882$	2.13143	−	13.2333i	0.0717690	−	0.445590i
$883$	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	$0.159421\pi$
$887$	25.4468	+	44.0752i	0.854421	+	1.47990i	−0.0227610	+	0.999741i	$0.507246\pi$
$888$	−27.4387	−	11.3663i	−0.920782	−	0.381429i
$889$	−40.5588	−	8.67532i	−1.36030	−	0.290961i
$890$		−	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
$896$	22.0972	+	19.9476i	0.738214	+	0.666404i
$897$	−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
$903$	18.8464	+	39.6456i	0.627169	+	1.31932i
$904$	−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
$924$	15.4648	+	10.6584i	0.508753	+	0.350636i
$925$	−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	−0.736487	−	0.676452i	$-0.763517\pi$
$929$	6.63177	−	11.4866i	0.217581	−	0.376862i	0.954068	+	0.299590i	$0.0968499\pi$
$930$	7.14930	−	0.941028i	0.234435	−	0.0308575i
$931$	−11.3120	+	25.2332i	−0.370737	+	0.826984i
$932$	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	$-0.943304\pi$
$937$		−	10.8468i		−	0.354349i	0.984179	−	0.177174i	$-0.0566957\pi$
$938$	3.47904	−	16.2652i	0.113595	−	0.531077i
$939$	−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	0.828779	−	0.559576i	$-0.189036\pi$
$941$	−2.15398	−	3.73079i	−0.0702176	−	0.121620i	−0.898997	+	0.437956i	$0.855703\pi$
$942$	−1.39712	+	3.37270i	−0.0455207	+	0.109888i
$943$	25.4256	+	14.6795i	0.827970	+	0.478029i
$944$	−14.7490			−0.480040
$945$	−8.91420	−	10.4660i	−0.289979	−	0.340459i
$946$	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
$952$	−3.31001	+	15.4749i	−0.107278	+	0.501545i
$953$		−	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
$959$	−17.4075	−	15.7142i	−0.562118	−	0.507438i
$960$	−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
$966$	8.88937	−	12.8980i	0.286011	−	0.414985i
$967$	−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	$-0.592059\pi$
$971$	−17.7740			−0.570394			−0.285197	+	0.958469i	$0.592059\pi$
$972$	−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	−0.767355	−	0.641222i	$-0.778428\pi$
$983$	5.38132	−	9.32072i	0.171637	−	0.297285i	0.938992	+	0.343938i	$0.111761\pi$
$984$	−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
$987$	21.7970	+	45.8525i	0.693806	+	1.45950i
$988$	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
$994$	7.59703	−	8.41566i	0.240963	−	0.266929i
$995$	−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	$-0.993172\pi$
$997$	−47.9386	−	27.6774i	−1.51823	−	0.876551i	−0.518462	−	0.855101i	$-0.673495\pi$
$998$			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.i.146.6	yes	24
3.2	odd	2		945.2.bl.i.251.7		24
7.6	odd	2		315.2.bl.j.146.6	yes	24
9.4	even	3		945.2.bl.j.881.7		24
9.5	odd	6		315.2.bl.j.41.6	yes	24
21.20	even	2		945.2.bl.j.251.7		24
63.13	odd	6		945.2.bl.i.881.7		24
63.41	even	6	inner	315.2.bl.i.41.6	✓	24

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

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)

\(f(q)\)	\(=\)	\(q+(0.552767 + 0.319140i) q^{2} +(0.662870 - 1.60019i) q^{3} +(-0.796299 - 1.37923i) q^{4} +(0.500000 + 0.866025i) q^{5} +(0.877097 - 0.672983i) q^{6} +(2.58723 + 0.553395i) q^{7} -2.29308i q^{8} +(-2.12121 - 2.12143i) q^{9} +O(q^{10})\)	\(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} +(2.58723 + 0.553395i) 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} +(1.25352 + 1.13159i) 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} +(2.60053 - 3.77322i) 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} +(2.64168 - 1.25578i) 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} +(6.38751 + 2.86352i) 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} +(1.26898 - 5.93274i) 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} +(-4.31406 - 6.66250i) 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} +(-0.353221 + 1.65138i) 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} +(-5.05412 - 4.56248i) 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} +(-7.27495 - 0.582119i) 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})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 6 q^{2} - 5 q^{3} + 18 q^{4} + 12 q^{5} - q^{6} + q^{9}+O(q^{10}) \) 24 * q + 6 * q^2 - 5 * q^3 + 18 * q^4 + 12 * q^5 - q^6 + q^9	\( 24 q + 6 q^{2} - 5 q^{3} + 18 q^{4} + 12 q^{5} - q^{6} + q^{9} + 9 q^{11} + 18 q^{12} - 3 q^{13} + 9 q^{14} + 2 q^{15} - 18 q^{16} - 18 q^{17} + 2 q^{18} - 18 q^{20} + 4 q^{21} - 9 q^{22} + 9 q^{23} + 7 q^{24} - 12 q^{25} + 18 q^{26} + 4 q^{27} - 9 q^{28} + 9 q^{29} - 5 q^{30} + 42 q^{31} + 18 q^{32} - 13 q^{33} + 39 q^{34} + 9 q^{35} - 21 q^{36} + 12 q^{38} - 21 q^{39} + 6 q^{40} + 33 q^{41} + 26 q^{42} + 18 q^{43} - q^{45} - 30 q^{46} + 17 q^{48} - 6 q^{50} - 12 q^{51} - 129 q^{52} - 52 q^{54} + 6 q^{56} + 6 q^{57} - 15 q^{58} - 12 q^{59} + 15 q^{60} + 15 q^{61} - 12 q^{62} - 83 q^{63} - 60 q^{64} - 3 q^{65} - 29 q^{66} - 15 q^{67} - 9 q^{68} - 61 q^{69} + 18 q^{70} + 61 q^{72} - 18 q^{74} + 7 q^{75} - 54 q^{76} - 57 q^{77} - 66 q^{78} + 21 q^{79} - 36 q^{80} + q^{81} + 30 q^{83} - 42 q^{84} - 9 q^{85} - 102 q^{86} - 10 q^{87} - 9 q^{88} - 102 q^{89} + 37 q^{90} + 42 q^{91} - 3 q^{92} - 6 q^{93} + 156 q^{94} - 18 q^{95} + 42 q^{96} + 45 q^{97} - 3 q^{98} + 23 q^{99}+O(q^{100}) \) 24 * q + 6 * q^2 - 5 * q^3 + 18 * q^4 + 12 * q^5 - q^6 + q^9 + 9 * q^11 + 18 * q^12 - 3 * q^13 + 9 * q^14 + 2 * q^15 - 18 * q^16 - 18 * q^17 + 2 * q^18 - 18 * q^20 + 4 * 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 + 26 * q^42 + 18 * q^43 - q^45 - 30 * q^46 + 17 * q^48 - 6 * q^50 - 12 * q^51 - 129 * q^52 - 52 * q^54 + 6 * q^56 + 6 * q^57 - 15 * q^58 - 12 * q^59 + 15 * q^60 + 15 * q^61 - 12 * q^62 - 83 * q^63 - 60 * q^64 - 3 * q^65 - 29 * q^66 - 15 * q^67 - 9 * q^68 - 61 * q^69 + 18 * q^70 + 61 * q^72 - 18 * q^74 + 7 * q^75 - 54 * q^76 - 57 * q^77 - 66 * q^78 + 21 * q^79 - 36 * q^80 + q^81 + 30 * q^83 - 42 * 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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more