LMFDB - Embedded newform 950.2.h.e.381.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [950,2,Mod(191,950)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(950, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([2, 0]))

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

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

chi := DirichletCharacter("950.191");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 950 = 2 \cdot 5^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	950.h (of order $5$, degree $4$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$7.58578819202$
Analytic rank:	$0$
Dimension:	$44$
Relative dimension:	$11$ over $\Q(\zeta_{5})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			381.2
Character	$\chi$	$=$	950.381
Dual form			950.2.h.e.571.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.309017 - 0.951057i) q^{2} +(-2.47282 + 1.79661i) q^{3} +(-0.809017 + 0.587785i) q^{4} +(2.01410 - 0.971294i) q^{5} +(2.47282 + 1.79661i) q^{6} +3.79510 q^{7} +(0.809017 + 0.587785i) q^{8} +(1.95997 - 6.03218i) q^{9} +O(q^{10})$	\(q+(-0.309017 - 0.951057i) q^{2} +(-2.47282 + 1.79661i) q^{3} +(-0.809017 + 0.587785i) q^{4} +(2.01410 - 0.971294i) q^{5} +(2.47282 + 1.79661i) q^{6} +3.79510 q^{7} +(0.809017 + 0.587785i) q^{8} +(1.95997 - 6.03218i) q^{9} +(-1.54615 - 1.61537i) q^{10} +(1.05107 + 3.23487i) q^{11} +(0.944531 - 2.90697i) q^{12} +(1.39694 - 4.29934i) q^{13} +(-1.17275 - 3.60935i) q^{14} +(-3.23546 + 6.02037i) q^{15} +(0.309017 - 0.951057i) q^{16} +(-2.76200 - 2.00671i) q^{17} -6.34261 q^{18} +(-0.809017 - 0.587785i) q^{19} +(-1.05853 + 1.96965i) q^{20} +(-9.38457 + 6.81829i) q^{21} +(2.75174 - 1.99926i) q^{22} +(0.597352 + 1.83846i) q^{23} -3.05657 q^{24} +(3.11317 - 3.91256i) q^{25} -4.52059 q^{26} +(3.15720 + 9.71685i) q^{27} +(-3.07030 + 2.23070i) q^{28} +(2.48556 - 1.80586i) q^{29} +(6.72552 + 1.21671i) q^{30} +(-6.08193 - 4.41878i) q^{31} -1.00000 q^{32} +(-8.41089 - 6.11087i) q^{33} +(-1.05499 + 3.24693i) q^{34} +(7.64369 - 3.68616i) q^{35} +(1.95997 + 6.03218i) q^{36} +(1.37546 - 4.23322i) q^{37} +(-0.309017 + 0.951057i) q^{38} +(4.26984 + 13.1412i) q^{39} +(2.20035 + 0.398063i) q^{40} +(-3.36960 + 10.3706i) q^{41} +(9.38457 + 6.81829i) q^{42} +2.17247 q^{43} +(-2.75174 - 1.99926i) q^{44} +(-1.91144 - 14.0531i) q^{45} +(1.56389 - 1.13623i) q^{46} +(9.39999 - 6.82949i) q^{47} +(0.944531 + 2.90697i) q^{48} +7.40276 q^{49} +(-4.68309 - 1.75176i) q^{50} +10.4352 q^{51} +(1.39694 + 4.29934i) q^{52} +(7.00211 - 5.08733i) q^{53} +(8.26564 - 6.00534i) q^{54} +(5.25897 + 5.49444i) q^{55} +(3.07030 + 2.23070i) q^{56} +3.05657 q^{57} +(-2.48556 - 1.80586i) q^{58} +(0.339818 - 1.04585i) q^{59} +(-0.921145 - 6.77233i) q^{60} +(2.77235 + 8.53243i) q^{61} +(-2.32309 + 7.14974i) q^{62} +(7.43829 - 22.8927i) q^{63} +(0.309017 + 0.951057i) q^{64} +(-1.36235 - 10.0161i) q^{65} +(-3.21268 + 9.88760i) q^{66} +(-1.65592 - 1.20310i) q^{67} +3.41402 q^{68} +(-4.78013 - 3.47297i) q^{69} +(-5.86778 - 6.13050i) q^{70} +(11.2130 - 8.14671i) q^{71} +(5.13128 - 3.72809i) q^{72} +(-4.97210 - 15.3025i) q^{73} -4.45107 q^{74} +(-0.668973 + 15.2682i) q^{75} +1.00000 q^{76} +(3.98892 + 12.2766i) q^{77} +(11.1786 - 8.12172i) q^{78} +(-6.58774 + 4.78627i) q^{79} +(-0.301366 - 2.21567i) q^{80} +(-9.87067 - 7.17146i) q^{81} +10.9043 q^{82} +(4.33393 + 3.14878i) q^{83} +(3.58459 - 11.0322i) q^{84} +(-7.51205 - 1.35900i) q^{85} +(-0.671330 - 2.06614i) q^{86} +(-2.90190 + 8.93114i) q^{87} +(-1.05107 + 3.23487i) q^{88} +(1.12870 + 3.47379i) q^{89} +(-12.7746 + 6.16054i) q^{90} +(5.30152 - 16.3164i) q^{91} +(-1.56389 - 1.13623i) q^{92} +22.9783 q^{93} +(-9.39999 - 6.82949i) q^{94} +(-2.20035 - 0.398063i) q^{95} +(2.47282 - 1.79661i) q^{96} +(1.11365 - 0.809111i) q^{97} +(-2.28758 - 7.04045i) q^{98} +21.5734 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 44 q + 11 q^{2} - q^{3} - 11 q^{4} - 5 q^{5} + q^{6} + 28 q^{7} + 11 q^{8} - 8 q^{9}+O(q^{10}) $ 44 * q + 11 * q^2 - q^3 - 11 * q^4 - 5 * q^5 + q^6 + 28 * q^7 + 11 * q^8 - 8 * q^9	$ 44 q + 11 q^{2} - q^{3} - 11 q^{4} - 5 q^{5} + q^{6} + 28 q^{7} + 11 q^{8} - 8 q^{9} + 5 q^{10} - 6 q^{12} - 10 q^{13} + 12 q^{14} - 11 q^{16} - 20 q^{17} - 42 q^{18} - 11 q^{19} + 5 q^{20} - 3 q^{21} - 10 q^{22} - 6 q^{23} - 14 q^{24} - 15 q^{25} - 40 q^{26} + 5 q^{27} - 2 q^{28} + 6 q^{29} - 5 q^{31} - 44 q^{32} - 36 q^{33} - 10 q^{34} - 8 q^{36} - 10 q^{37} + 11 q^{38} + 39 q^{39} - 22 q^{41} + 3 q^{42} + 68 q^{43} + 10 q^{44} + 20 q^{45} + 6 q^{46} + 19 q^{47} - 6 q^{48} + 40 q^{49} - 30 q^{50} + 86 q^{51} - 10 q^{52} + 30 q^{54} + 2 q^{56} + 14 q^{57} - 6 q^{58} - 4 q^{59} + 15 q^{60} + 26 q^{61} - 15 q^{62} - 41 q^{63} - 11 q^{64} + 30 q^{65} - 4 q^{66} - 59 q^{67} + 20 q^{68} - 59 q^{69} - 25 q^{70} + 30 q^{71} + 13 q^{72} - 38 q^{73} - 50 q^{74} - 15 q^{75} + 44 q^{76} + 29 q^{77} + 16 q^{78} + 3 q^{79} + 5 q^{80} - 54 q^{81} - 8 q^{82} + 9 q^{83} + 7 q^{84} + 12 q^{86} - 43 q^{87} + 33 q^{89} - 6 q^{91} - 6 q^{92} + 84 q^{93} - 19 q^{94} + q^{96} + 30 q^{97} - 15 q^{98} - 54 q^{99}+O(q^{100}) $ 44 * q + 11 * q^2 - q^3 - 11 * q^4 - 5 * q^5 + q^6 + 28 * q^7 + 11 * q^8 - 8 * q^9 + 5 * q^10 - 6 * q^12 - 10 * q^13 + 12 * q^14 - 11 * q^16 - 20 * q^17 - 42 * q^18 - 11 * q^19 + 5 * q^20 - 3 * q^21 - 10 * q^22 - 6 * q^23 - 14 * q^24 - 15 * q^25 - 40 * q^26 + 5 * q^27 - 2 * q^28 + 6 * q^29 - 5 * q^31 - 44 * q^32 - 36 * q^33 - 10 * q^34 - 8 * q^36 - 10 * q^37 + 11 * q^38 + 39 * q^39 - 22 * q^41 + 3 * q^42 + 68 * q^43 + 10 * q^44 + 20 * q^45 + 6 * q^46 + 19 * q^47 - 6 * q^48 + 40 * q^49 - 30 * q^50 + 86 * q^51 - 10 * q^52 + 30 * q^54 + 2 * q^56 + 14 * q^57 - 6 * q^58 - 4 * q^59 + 15 * q^60 + 26 * q^61 - 15 * q^62 - 41 * q^63 - 11 * q^64 + 30 * q^65 - 4 * q^66 - 59 * q^67 + 20 * q^68 - 59 * q^69 - 25 * q^70 + 30 * q^71 + 13 * q^72 - 38 * q^73 - 50 * q^74 - 15 * q^75 + 44 * q^76 + 29 * q^77 + 16 * q^78 + 3 * q^79 + 5 * q^80 - 54 * q^81 - 8 * q^82 + 9 * q^83 + 7 * q^84 + 12 * q^86 - 43 * q^87 + 33 * q^89 - 6 * q^91 - 6 * q^92 + 84 * q^93 - 19 * q^94 + q^96 + 30 * q^97 - 15 * q^98 - 54 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/950\mathbb{Z}\right)^\times$.

$n$	$77$	$401$
$\chi(n)$	$e\left(\frac{2}{5}\right)$	$1$

Coefficient data

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

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

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

$2$	−0.309017	−	0.951057i	−0.218508	−	0.672499i
$2$	−0.309017	−	0.951057i	−0.218508	−	0.672499i
$3$	−2.47282	+	1.79661i	−1.42768	+	1.03727i	−0.437238	+	0.899346i	$0.644043\pi$
$3$	−2.47282	+	1.79661i	−1.42768	+	1.03727i	−0.990443	+	0.137925i	$0.955957\pi$
$4$	−0.809017	+	0.587785i	−0.404508	+	0.293893i
$5$	2.01410	−	0.971294i	0.900732	−	0.434376i
$5$	2.01410	−	0.971294i	0.900732	−	0.434376i
$6$	2.47282	+	1.79661i	1.00952	+	0.733461i
$7$	3.79510			1.43441			0.717206	−	0.696861i	$-0.245421\pi$
$7$	3.79510			1.43441			0.717206	+	0.696861i	$0.245421\pi$
$8$	0.809017	+	0.587785i	0.286031	+	0.207813i
$9$	1.95997	−	6.03218i	0.653324	−	2.01073i
$10$	−1.54615	−	1.61537i	−0.488934	−	0.510826i
$11$	1.05107	+	3.23487i	0.316910	+	0.975350i	0.974961	+	0.222376i	$0.0713813\pi$
$11$	1.05107	+	3.23487i	0.316910	+	0.975350i	−0.658050	+	0.752974i	$0.728619\pi$
$12$	0.944531	−	2.90697i	0.272663	−	0.839170i
$13$	1.39694	−	4.29934i	0.387441	−	1.19242i	−0.547252	−	0.836968i	$-0.684326\pi$
$13$	1.39694	−	4.29934i	0.387441	−	1.19242i	0.934694	−	0.355454i	$-0.115674\pi$
$14$	−1.17275	−	3.60935i	−0.313431	−	0.964640i
$15$	−3.23546	+	6.02037i	−0.835391	+	1.55445i
$16$	0.309017	−	0.951057i	0.0772542	−	0.237764i
$17$	−2.76200	−	2.00671i	−0.669884	−	0.486699i	0.200102	−	0.979775i	$-0.435873\pi$
$17$	−2.76200	−	2.00671i	−0.669884	−	0.486699i	−0.869986	+	0.493076i	$0.835873\pi$
$18$	−6.34261			−1.49497
$19$	−0.809017	−	0.587785i	−0.185601	−	0.134847i
$19$	−0.809017	−	0.587785i	−0.185601	−	0.134847i
$20$	−1.05853	+	1.96965i	−0.236694	+	0.440427i
$21$	−9.38457	+	6.81829i	−2.04788	+	1.48787i
$22$	2.75174	−	1.99926i	0.586674	−	0.426244i
$23$	0.597352	+	1.83846i	0.124556	+	0.383345i	0.993820	−	0.111004i	$-0.0354065\pi$
$23$	0.597352	+	1.83846i	0.124556	+	0.383345i	−0.869264	+	0.494349i	$0.835406\pi$
$24$	−3.05657			−0.623919
$25$	3.11317	−	3.91256i	0.622635	−	0.782513i
$26$	−4.52059			−0.886561
$27$	3.15720	+	9.71685i	0.607602	+	1.87001i
$28$	−3.07030	+	2.23070i	−0.580232	+	0.421563i
$29$	2.48556	−	1.80586i	0.461557	−	0.335341i	−0.332585	−	0.943073i	$-0.607921\pi$
$29$	2.48556	−	1.80586i	0.461557	−	0.335341i	0.794142	+	0.607733i	$0.207921\pi$
$30$	6.72552	+	1.21671i	1.22791	+	0.222139i
$31$	−6.08193	−	4.41878i	−1.09235	−	0.793637i	−0.112553	−	0.993646i	$-0.535903\pi$
$31$	−6.08193	−	4.41878i	−1.09235	−	0.793637i	−0.979794	+	0.200009i	$0.935903\pi$
$32$	−1.00000			−0.176777
$33$	−8.41089	−	6.11087i	−1.46415	−	1.06377i
$34$	−1.05499	+	3.24693i	−0.180929	+	0.556844i
$35$	7.64369	−	3.68616i	1.29202	−	0.623074i
$36$	1.95997	+	6.03218i	0.326662	+	1.00536i
$37$	1.37546	−	4.23322i	0.226124	−	0.695937i	−0.772052	−	0.635559i	$-0.780770\pi$
$37$	1.37546	−	4.23322i	0.226124	−	0.695937i	0.998176	−	0.0603775i	$-0.0192304\pi$
$38$	−0.309017	+	0.951057i	−0.0501292	+	0.154282i
$39$	4.26984	+	13.1412i	0.683722	+	2.10428i
$40$	2.20035	+	0.398063i	0.347906	+	0.0629393i
$41$	−3.36960	+	10.3706i	−0.526243	+	1.61961i	0.235601	+	0.971850i	$0.424294\pi$
$41$	−3.36960	+	10.3706i	−0.526243	+	1.61961i	−0.761844	+	0.647760i	$0.775706\pi$
$42$	9.38457	+	6.81829i	1.44807	+	1.05209i
$43$	2.17247			0.331299			0.165649	−	0.986185i	$-0.447028\pi$
$43$	2.17247			0.331299			0.165649	+	0.986185i	$0.447028\pi$
$44$	−2.75174	−	1.99926i	−0.414841	−	0.301400i
$45$	−1.91144	−	14.0531i	−0.284941	−	2.09491i
$46$	1.56389	−	1.13623i	0.230583	−	0.167528i
$47$	9.39999	−	6.82949i	1.37113	−	0.996184i	0.373482	−	0.927638i	$-0.378164\pi$
$47$	9.39999	−	6.82949i	1.37113	−	0.996184i	0.997648	−	0.0685463i	$-0.0218361\pi$
$48$	0.944531	+	2.90697i	0.136331	+	0.419585i
$49$	7.40276			1.05754
$50$	−4.68309	−	1.75176i	−0.662289	−	0.247736i
$51$	10.4352			1.46122
$52$	1.39694	+	4.29934i	0.193721	+	0.596211i
$53$	7.00211	−	5.08733i	0.961813	−	0.698798i	0.00824201	−	0.999966i	$-0.497376\pi$
$53$	7.00211	−	5.08733i	0.961813	−	0.698798i	0.953571	+	0.301168i	$0.0973765\pi$
$54$	8.26564	−	6.00534i	1.12481	−	0.817224i
$55$	5.25897	+	5.49444i	0.709120	+	0.740870i
$56$	3.07030	+	2.23070i	0.410286	+	0.298090i
$57$	3.05657			0.404852
$58$	−2.48556	−	1.80586i	−0.326370	−	0.237122i
$59$	0.339818	−	1.04585i	0.0442405	−	0.136158i	−0.926497	−	0.376303i	$-0.877195\pi$
$59$	0.339818	−	1.04585i	0.0442405	−	0.136158i	0.970737	+	0.240145i	$0.0771951\pi$
$60$	−0.921145	−	6.77233i	−0.118919	−	0.874305i
$61$	2.77235	+	8.53243i	0.354964	+	1.09247i	0.956031	+	0.293267i	$0.0947425\pi$
$61$	2.77235	+	8.53243i	0.354964	+	1.09247i	−0.601067	+	0.799199i	$0.705258\pi$
$62$	−2.32309	+	7.14974i	−0.295033	+	0.908018i
$63$	7.43829	−	22.8927i	0.937136	−	2.88421i
$64$	0.309017	+	0.951057i	0.0386271	+	0.118882i
$65$	−1.36235	−	10.0161i	−0.168979	−	1.24235i
$66$	−3.21268	+	9.88760i	−0.395453	+	1.21708i
$67$	−1.65592	−	1.20310i	−0.202303	−	0.146982i	0.482021	−	0.876160i	$-0.339903\pi$
$67$	−1.65592	−	1.20310i	−0.202303	−	0.146982i	−0.684324	+	0.729178i	$0.739903\pi$
$68$	3.41402			0.414011
$69$	−4.78013	−	3.47297i	−0.575460	−	0.418096i
$70$	−5.86778	−	6.13050i	−0.701333	−	0.732735i
$71$	11.2130	−	8.14671i	1.33074	−	0.966837i	0.331006	−	0.943629i	$-0.392612\pi$
$71$	11.2130	−	8.14671i	1.33074	−	0.966837i	0.999731	−	0.0232079i	$-0.00738795\pi$
$72$	5.13128	−	3.72809i	0.604727	−	0.439360i
$73$	−4.97210	−	15.3025i	−0.581940	−	1.79103i	−0.611227	−	0.791455i	$-0.709324\pi$
$73$	−4.97210	−	15.3025i	−0.581940	−	1.79103i	0.0292872	−	0.999571i	$-0.490676\pi$
$74$	−4.45107			−0.517426
$75$	−0.668973	+	15.2682i	−0.0772464	+	1.76302i
$76$	1.00000			0.114708
$77$	3.98892	+	12.2766i	0.454580	+	1.39905i
$78$	11.1786	−	8.12172i	1.26573	−	0.919604i
$79$	−6.58774	+	4.78627i	−0.741179	+	0.538498i	−0.893080	−	0.449898i	$-0.851460\pi$
$79$	−6.58774	+	4.78627i	−0.741179	+	0.538498i	0.151901	+	0.988396i	$0.451460\pi$
$80$	−0.301366	−	2.21567i	−0.0336937	−	0.247719i
$81$	−9.87067	−	7.17146i	−1.09674	−	0.796829i
$82$	10.9043			1.20417
$83$	4.33393	+	3.14878i	0.475711	+	0.345624i	0.799663	−	0.600450i	$-0.205012\pi$
$83$	4.33393	+	3.14878i	0.475711	+	0.345624i	−0.323952	+	0.946073i	$0.605012\pi$
$84$	3.58459	−	11.0322i	0.391111	−	1.20371i
$85$	−7.51205	−	1.35900i	−0.814796	−	0.147404i
$86$	−0.671330	−	2.06614i	−0.0723914	−	0.222798i
$87$	−2.90190	+	8.93114i	−0.311117	+	0.957518i
$88$	−1.05107	+	3.23487i	−0.112045	+	0.344838i
$89$	1.12870	+	3.47379i	0.119642	+	0.368221i	0.992887	−	0.119061i	$-0.0379883\pi$
$89$	1.12870	+	3.47379i	0.119642	+	0.368221i	−0.873245	+	0.487282i	$0.837988\pi$
$90$	−12.7746	+	6.16054i	−1.34656	+	0.649378i
$91$	5.30152	−	16.3164i	0.555751	−	1.71042i
$92$	−1.56389	−	1.13623i	−0.163047	−	0.118460i
$93$	22.9783			2.38274
$94$	−9.39999	−	6.82949i	−0.969535	−	0.704408i
$95$	−2.20035	−	0.398063i	−0.225751	−	0.0408404i
$96$	2.47282	−	1.79661i	0.252381	−	0.183365i
$97$	1.11365	−	0.809111i	0.113074	−	0.0821528i	−0.529811	−	0.848115i	$-0.677737\pi$
$97$	1.11365	−	0.809111i	0.113074	−	0.0821528i	0.642885	+	0.765963i	$0.277737\pi$
$98$	−2.28758	−	7.04045i	−0.231080	−	0.711193i
$99$	21.5734			2.16821
$100$	−0.218864	+	4.99521i	−0.0218864	+	0.499521i
$101$	12.8094			1.27459			0.637293	−	0.770621i	$-0.280054\pi$
$101$	12.8094			1.27459			0.637293	+	0.770621i	$0.280054\pi$
$102$	−3.22465	−	9.92446i	−0.319288	−	0.982668i
$103$	−9.93172	+	7.21582i	−0.978601	+	0.710996i	−0.957396	−	0.288780i	$-0.906751\pi$
$103$	−9.93172	+	7.21582i	−0.978601	+	0.710996i	−0.0212058	+	0.999775i	$0.506751\pi$
$104$	3.65724	−	2.65714i	0.358621	−	0.260554i
$105$	−12.2789	+	22.8479i	−1.19830	+	2.22973i
$106$	−7.00211	−	5.08733i	−0.680105	−	0.494125i
$107$	8.49722			0.821458			0.410729	−	0.911758i	$-0.365274\pi$
$107$	8.49722			0.821458			0.410729	+	0.911758i	$0.365274\pi$
$108$	−8.26564	−	6.00534i	−0.795362	−	0.577864i
$109$	−5.49289	+	16.9054i	−0.526124	+	1.61924i	0.235959	+	0.971763i	$0.424177\pi$
$109$	−5.49289	+	16.9054i	−0.526124	+	1.61924i	−0.762083	+	0.647480i	$0.775823\pi$
$110$	3.60041	−	6.69946i	0.343286	−	0.638768i
$111$	4.20417	+	12.9391i	0.399043	+	1.22813i
$112$	1.17275	−	3.60935i	0.110814	−	0.341052i
$113$	0.500618	−	1.54074i	0.0470942	−	0.144941i	−0.924744	−	0.380589i	$-0.875721\pi$
$113$	0.500618	−	1.54074i	0.0470942	−	0.144941i	0.971838	+	0.235648i	$0.0757213\pi$
$114$	−0.944531	−	2.90697i	−0.0884635	−	0.272263i
$115$	2.98881	+	3.12263i	0.278708	+	0.291187i
$116$	−0.949399	+	2.92195i	−0.0881495	+	0.271296i
$117$	−23.1964	−	16.8532i	−2.14451	−	1.55808i
$118$	−1.09967			−0.101233
$119$	−10.4821	−	7.61567i	−0.960890	−	0.698127i
$120$	−6.15622	+	2.96883i	−0.561984	+	0.271016i
$121$	−0.460444	+	0.334532i	−0.0418585	+	0.0304120i
$122$	7.25812	−	5.27333i	0.657119	−	0.477425i
$123$	−10.2994	−	31.6983i	−0.928667	−	2.85814i
$124$	7.51768			0.675108
$125$	2.46998	−	10.9041i	0.220922	−	0.975291i
$126$	−24.0708			−2.14440
$127$	3.64354	+	11.2137i	0.323312	+	0.995053i	0.972197	+	0.234166i	$0.0752359\pi$
$127$	3.64354	+	11.2137i	0.323312	+	0.995053i	−0.648884	+	0.760887i	$0.724764\pi$
$128$	0.809017	−	0.587785i	0.0715077	−	0.0519534i
$129$	−5.37212	+	3.90307i	−0.472989	+	0.343646i
$130$	−9.10491	+	4.39083i	−0.798554	+	0.385101i
$131$	0.459260	+	0.333672i	0.0401257	+	0.0291530i	0.607667	−	0.794192i	$-0.292105\pi$
$131$	0.459260	+	0.333672i	0.0401257	+	0.0291530i	−0.567542	+	0.823345i	$0.692105\pi$
$132$	10.3964			0.904894
$133$	−3.07030	−	2.23070i	−0.266229	−	0.193426i
$134$	−0.632506	+	1.94665i	−0.0546402	+	0.168165i
$135$	15.7968	+	16.5041i	1.35957	+	1.42045i
$136$	−1.05499	−	3.24693i	−0.0904647	−	0.278422i
$137$	−4.41443	+	13.5862i	−0.377150	+	1.16075i	0.564867	+	0.825182i	$0.308928\pi$
$137$	−4.41443	+	13.5862i	−0.377150	+	1.16075i	−0.942017	+	0.335566i	$0.891072\pi$
$138$	−1.82585	+	5.61938i	−0.155426	+	0.478353i
$139$	5.34618	+	16.4538i	0.453457	+	1.39560i	0.872937	+	0.487832i	$0.162212\pi$
$139$	5.34618	+	16.4538i	0.453457	+	1.39560i	−0.419481	+	0.907764i	$0.637788\pi$
$140$	−4.01721	+	7.47501i	−0.339516	+	0.631754i
$141$	−10.9745	+	33.7761i	−0.924223	+	2.84446i
$142$	−11.2130	−	8.14671i	−0.940973	−	0.683657i
$143$	15.3761			1.28581
$144$	−5.13128	−	3.72809i	−0.427606	−	0.310674i
$145$	3.25213	−	6.05140i	0.270075	−	0.502541i
$146$	−13.0171	+	9.45749i	−1.07730	+	0.782707i
$147$	−18.3057	+	13.2998i	−1.50983	+	1.09695i
$148$	1.37546	+	4.23322i	0.113062	+	0.347968i
$149$	−6.66518			−0.546033			−0.273017	−	0.962009i	$-0.588021\pi$
$149$	−6.66518			−0.546033			−0.273017	+	0.962009i	$0.588021\pi$
$150$	14.7276	−	4.08190i	1.20251	−	0.333286i
$151$	−10.6389			−0.865778			−0.432889	−	0.901447i	$-0.642506\pi$
$151$	−10.6389			−0.865778			−0.432889	+	0.901447i	$0.642506\pi$
$152$	−0.309017	−	0.951057i	−0.0250646	−	0.0771409i
$153$	−17.5183	+	12.7278i	−1.41627	+	1.02898i
$154$	10.4431	−	7.58739i	0.841532	−	0.611409i
$155$	−16.5415	−	2.99251i	−1.32865	−	0.240364i
$156$	−11.1786	−	8.12172i	−0.895003	−	0.650258i
$157$	2.02927			0.161954			0.0809769	−	0.996716i	$-0.474196\pi$
$157$	2.02927			0.161954			0.0809769	+	0.996716i	$0.474196\pi$
$158$	6.58774	+	4.78627i	0.524093	+	0.380776i
$159$	−8.17499	+	25.1600i	−0.648319	+	1.99532i
$160$	−2.01410	+	0.971294i	−0.159228	+	0.0767876i
$161$	2.26701	+	6.97714i	0.178665	+	0.549875i
$162$	−3.77026	+	11.6037i	−0.296220	+	0.911671i
$163$	4.20937	−	12.9551i	0.329703	−	1.01472i	−0.639569	−	0.768733i	$-0.720887\pi$
$163$	4.20937	−	12.9551i	0.329703	−	1.01472i	0.969273	−	0.245989i	$-0.0791127\pi$
$164$	−3.36960	−	10.3706i	−0.263122	−	0.809805i
$165$	−22.8758	−	4.13844i	−1.78088	−	0.322177i
$166$	1.65541	−	5.09484i	0.128485	−	0.395436i
$167$	−3.52046	−	2.55776i	−0.272421	−	0.197926i	0.443184	−	0.896431i	$-0.353849\pi$
$167$	−3.52046	−	2.55776i	−0.272421	−	0.197926i	−0.715605	+	0.698505i	$0.753849\pi$
$168$	−11.6000			−0.894957
$169$	−6.01565	−	4.37063i	−0.462742	−	0.336202i
$170$	1.02887	+	7.56434i	0.0789107	+	0.580158i
$171$	−5.13128	+	3.72809i	−0.392398	+	0.285094i
$172$	−1.75757	+	1.27695i	−0.134013	+	0.0973662i
$173$	−1.19982	−	3.69268i	−0.0912210	−	0.280749i	0.895029	−	0.446007i	$-0.147154\pi$
$173$	−1.19982	−	3.69268i	−0.0912210	−	0.280749i	−0.986250	+	0.165258i	$0.947154\pi$
$174$	9.39075			0.711911
$175$	11.8148	−	14.8486i	0.893115	−	1.12245i
$176$	3.40134			0.256386
$177$	1.03868	+	3.19671i	0.0780716	+	0.240280i
$178$	2.95499	−	2.14692i	0.221485	−	0.160919i
$179$	10.9180	−	7.93241i	0.816051	−	0.592896i	−0.0995274	−	0.995035i	$-0.531733\pi$
$179$	10.9180	−	7.93241i	0.816051	−	0.592896i	0.915579	+	0.402139i	$0.131733\pi$
$180$	9.80659	+	10.2457i	0.730940	+	0.763668i
$181$	1.97899	+	1.43782i	0.147097	+	0.106873i	0.658900	−	0.752231i	$-0.271022\pi$
$181$	1.97899	+	1.43782i	0.147097	+	0.106873i	−0.511803	+	0.859103i	$0.671022\pi$
$182$	−17.1561			−1.27169
$183$	−22.1849	−	16.1183i	−1.63996	−	1.19150i
$184$	−0.597352	+	1.83846i	−0.0440374	+	0.135533i
$185$	−1.34140	−	9.86209i	−0.0986217	−	0.725075i
$186$	−7.10069	−	21.8537i	−0.520647	−	1.60239i
$187$	3.58839	−	11.0439i	0.262409	−	0.807611i
$188$	−3.59048	+	11.0504i	−0.261862	+	0.805930i
$189$	11.9819	+	36.8764i	0.871552	+	2.68236i
$190$	0.301366	+	2.21567i	0.0218634	+	0.160741i
$191$	3.99913	−	12.3081i	0.289367	−	0.890579i	−0.695689	−	0.718343i	$-0.744901\pi$
$191$	3.99913	−	12.3081i	0.289367	−	0.890579i	0.985056	−	0.172236i	$-0.0550992\pi$
$192$	−2.47282	−	1.79661i	−0.178460	−	0.129659i
$193$	−16.6558			−1.19891			−0.599455	−	0.800408i	$-0.704616\pi$
$193$	−16.6558			−1.19891			−0.599455	+	0.800408i	$0.704616\pi$
$194$	−1.11365	−	0.809111i	−0.0799551	−	0.0580908i
$195$	21.3639	+	22.3204i	1.52990	+	1.59840i
$196$	−5.98896	+	4.35124i	−0.427783	+	0.310803i
$197$	13.6774	−	9.93721i	0.974474	−	0.707997i	0.0180071	−	0.999838i	$-0.494268\pi$
$197$	13.6774	−	9.93721i	0.974474	−	0.707997i	0.956467	+	0.291841i	$0.0942678\pi$
$198$	−6.66654	−	20.5175i	−0.473770	−	1.45812i
$199$	−26.4500			−1.87499			−0.937496	−	0.347996i	$-0.886862\pi$
$199$	−26.4500			−1.87499			−0.937496	+	0.347996i	$0.886862\pi$
$200$	4.81836	−	1.33545i	0.340709	−	0.0944307i
$201$	6.25629			0.441284
$202$	−3.95833	−	12.1825i	−0.278507	−	0.857158i
$203$	9.43294	−	6.85343i	0.662062	−	0.481017i
$204$	−8.44225	+	6.13365i	−0.591075	+	0.429441i
$205$	3.28617	+	24.1602i	0.229516	+	1.68742i
$206$	9.93172	+	7.21582i	0.691976	+	0.502750i
$207$	12.2607			0.852178
$208$	−3.65724	−	2.65714i	−0.253584	−	0.184239i
$209$	1.05107	−	3.23487i	0.0727042	−	0.223761i
$210$	25.5240	+	4.61752i	1.76132	+	0.318639i
$211$	5.11284	+	15.7357i	0.351982	+	1.08329i	0.957739	+	0.287640i	$0.0928707\pi$
$211$	5.11284	+	15.7357i	0.351982	+	1.08329i	−0.605756	+	0.795650i	$0.707129\pi$
$212$	−2.67457	+	8.23147i	−0.183690	+	0.565340i
$213$	−13.0912	+	40.2906i	−0.896995	+	2.76067i
$214$	−2.62579	−	8.08134i	−0.179495	−	0.552429i
$215$	4.37557	−	2.11011i	0.298411	−	0.143908i
$216$	−3.15720	+	9.71685i	−0.214820	+	0.661148i
$217$	−23.0815	−	16.7697i	−1.56688	−	1.13840i
$218$	17.7754			1.20390
$219$	39.7877	+	28.9074i	2.68860	+	1.95338i
$220$	−7.48415	−	1.35395i	−0.504581	−	0.0912832i
$221$	−12.4859	+	9.07153i	−0.839892	+	0.610217i
$222$	11.0067	−	7.99681i	0.738719	−	0.536711i
$223$	−5.69804	−	17.5368i	−0.381569	−	1.17435i	−0.938939	−	0.344084i	$-0.888190\pi$
$223$	−5.69804	−	17.5368i	−0.381569	−	1.17435i	0.557370	−	0.830264i	$-0.311810\pi$
$224$	−3.79510			−0.253571
$225$	−17.4995	−	26.4477i	−1.16664	−	1.76318i
$226$	−1.62003			−0.107763
$227$	0.566678	+	1.74406i	0.0376118	+	0.115757i	0.968100	−	0.250566i	$-0.0806166\pi$
$227$	0.566678	+	1.74406i	0.0376118	+	0.115757i	−0.930488	+	0.366323i	$0.880617\pi$
$228$	−2.47282	+	1.79661i	−0.163766	+	0.118983i
$229$	3.55922	−	2.58593i	0.235200	−	0.170883i	−0.463942	−	0.885866i	$-0.653565\pi$
$229$	3.55922	−	2.58593i	0.235200	−	0.170883i	0.699142	+	0.714983i	$0.253565\pi$
$230$	2.04621	−	3.80748i	0.134923	−	0.251057i
$231$	−31.9202	−	23.1914i	−2.10019	−	1.52588i
$232$	3.07232			0.201708
$233$	14.5303	+	10.5569i	0.951913	+	0.691605i	0.951259	−	0.308394i	$-0.0997917\pi$
$233$	14.5303	+	10.5569i	0.951913	+	0.691605i	0.000654506		1.00000i	$0.499792\pi$
$234$	−8.86024	+	27.2690i	−0.579212	+	1.78263i
$235$	12.2990	−	22.8854i	0.802301	−	1.49288i
$236$	0.339818	+	1.04585i	0.0221202	+	0.0680791i
$237$	7.69122	−	23.6711i	0.499599	−	1.53761i
$238$	−4.00379	+	12.3224i	−0.259527	+	0.798743i
$239$	−1.85303	−	5.70305i	−0.119863	−	0.368900i	0.873067	−	0.487600i	$-0.162127\pi$
$239$	−1.85303	−	5.70305i	−0.119863	−	0.368900i	−0.992930	+	0.118700i	$0.962127\pi$
$240$	4.72590	+	4.93750i	0.305056	+	0.318714i
$241$	6.96571	−	21.4382i	0.448701	−	1.38096i	−0.429673	−	0.902985i	$-0.641371\pi$
$241$	6.96571	−	21.4382i	0.448701	−	1.38096i	0.878374	−	0.477974i	$-0.158629\pi$
$242$	0.460444	+	0.334532i	0.0295984	+	0.0215045i
$243$	6.64195			0.426081
$244$	−7.25812	−	5.27333i	−0.464653	−	0.337590i
$245$	14.9099	−	7.19026i	0.952558	−	0.459369i
$246$	−26.9642	+	19.5906i	−1.71918	+	1.24905i
$247$	−3.65724	+	2.65714i	−0.232704	+	0.169070i
$248$	−2.32309	−	7.14974i	−0.147516	−	0.454009i
$249$	−16.3741			−1.03767
$250$	−11.1337	+	1.02045i	−0.704155	+	0.0645392i
$251$	6.25195			0.394619			0.197310	−	0.980341i	$-0.436780\pi$
$251$	6.25195			0.394619			0.197310	+	0.980341i	$0.436780\pi$
$252$	7.43829	+	22.8927i	0.468568	+	1.44210i
$253$	−5.31932	+	3.86471i	−0.334423	+	0.242972i
$254$	9.53892	−	6.93043i	0.598525	−	0.434854i
$255$	21.0175	−	10.1356i	1.31617	−	0.634719i
$256$	−0.809017	−	0.587785i	−0.0505636	−	0.0367366i
$257$	12.1385			0.757176			0.378588	−	0.925565i	$-0.376410\pi$
$257$	12.1385			0.757176			0.378588	+	0.925565i	$0.376410\pi$
$258$	5.37212	+	3.90307i	0.334453	+	0.242995i
$259$	5.21999	−	16.0655i	0.324354	−	0.998260i
$260$	6.98950	+	7.30245i	0.433470	+	0.452878i
$261$	−6.02166	−	18.5328i	−0.372732	−	1.14715i
$262$	0.175422	−	0.539892i	0.0108376	−	0.0333546i
$263$	−8.94972	+	27.5444i	−0.551864	+	1.69846i	0.152222	+	0.988346i	$0.451357\pi$
$263$	−8.94972	+	27.5444i	−0.551864	+	1.69846i	−0.704086	+	0.710115i	$0.748643\pi$
$264$	−3.21268	−	9.88760i	−0.197727	−	0.608540i
$265$	9.16163	−	17.0475i	0.562794	−	1.04722i
$266$	−1.17275	+	3.60935i	−0.0719059	+	0.221304i
$267$	−9.03211	−	6.56221i	−0.552756	−	0.401601i
$268$	2.04683			0.125030
$269$	−17.7315	−	12.8827i	−1.08111	−	0.785470i	−0.103231	−	0.994657i	$-0.532918\pi$
$269$	−17.7315	−	12.8827i	−1.08111	−	0.785470i	−0.977875	+	0.209188i	$0.932918\pi$
$270$	10.8149	−	20.1237i	0.658171	−	1.22469i
$271$	−3.90334	+	2.83594i	−0.237111	+	0.172271i	−0.699995	−	0.714147i	$-0.746815\pi$
$271$	−3.90334	+	2.83594i	−0.237111	+	0.172271i	0.462884	+	0.886419i	$0.346815\pi$
$272$	−2.76200	+	2.00671i	−0.167471	+	0.121675i
$273$	16.2045	+	49.8722i	0.980739	+	3.01840i
$274$	14.2854			0.863012
$275$	15.9288	+	5.95833i	0.960543	+	0.359301i
$276$	5.90856			0.355654
$277$	−5.29561	−	16.2982i	−0.318182	−	0.979264i	−0.974425	−	0.224714i	$-0.927855\pi$
$277$	−5.29561	−	16.2982i	−0.318182	−	0.979264i	0.656243	−	0.754550i	$-0.272145\pi$
$278$	13.9965	−	10.1690i	0.839453	−	0.609898i
$279$	−38.5753	+	28.0266i	−2.30944	+	1.67791i
$280$	8.35055	+	1.51069i	0.499041	+	0.0902808i
$281$	1.00544	+	0.730497i	0.0599797	+	0.0435778i	0.617371	−	0.786672i	$-0.288198\pi$
$281$	1.00544	+	0.730497i	0.0599797	+	0.0435778i	−0.557391	+	0.830250i	$0.688198\pi$
$282$	35.5143			2.11485
$283$	25.4663	+	18.5023i	1.51381	+	1.09985i	0.964450	+	0.264267i	$0.0851300\pi$
$283$	25.4663	+	18.5023i	1.51381	+	1.09985i	0.549364	+	0.835583i	$0.314870\pi$
$284$	−4.28298	+	13.1817i	−0.254148	+	0.782187i
$285$	6.15622	−	2.96883i	0.364663	−	0.175858i
$286$	−4.75147	−	14.6235i	−0.280960	−	0.864707i
$287$	−12.7880	+	39.3573i	−0.754850	+	2.32319i
$288$	−1.95997	+	6.03218i	−0.115493	+	0.355449i
$289$	−1.65153	−	5.08287i	−0.0971486	−	0.298993i
$290$	−6.76018	−	1.22298i	−0.396972	−	0.0718156i
$291$	−1.30019	+	4.00156i	−0.0762183	+	0.234576i
$292$	13.0171	+	9.45749i	0.761769	+	0.553458i
$293$	−30.1271			−1.76004			−0.880022	−	0.474933i	$-0.842472\pi$
$293$	−30.1271			−1.76004			−0.880022	+	0.474933i	$0.842472\pi$
$294$	18.3057	+	13.2998i	1.06761	+	0.775663i
$295$	−0.331404	−	2.43651i	−0.0192951	−	0.141859i
$296$	3.60099	−	2.61627i	0.209303	−	0.152068i
$297$	−28.1143	+	20.4262i	−1.63136	+	1.18525i
$298$	2.05965	+	6.33897i	0.119313	+	0.367206i
$299$	8.73863			0.505368
$300$	−8.43321	−	12.7454i	−0.486891	−	0.735858i
$301$	8.24474			0.475219
$302$	3.28759	+	10.1182i	0.189179	+	0.582234i
$303$	−31.6754	+	23.0135i	−1.81970	+	1.32209i
$304$	−0.809017	+	0.587785i	−0.0464003	+	0.0337118i
$305$	13.8713	+	14.4924i	0.794268	+	0.829831i
$306$	17.5183	+	12.7278i	1.00145	+	0.727599i
$307$	17.1888			0.981015			0.490507	−	0.871437i	$-0.336811\pi$
$307$	17.1888			0.981015			0.490507	+	0.871437i	$0.336811\pi$
$308$	−10.4431	−	7.58739i	−0.595053	−	0.432331i
$309$	11.5953	−	35.6868i	0.659635	−	2.03015i
$310$	2.26557	+	16.6567i	0.128676	+	0.946036i
$311$	5.84249	+	17.9813i	0.331297	+	1.01963i	0.968517	+	0.248946i	$0.0800840\pi$
$311$	5.84249	+	17.9813i	0.331297	+	1.01963i	−0.637221	+	0.770682i	$0.719916\pi$
$312$	−4.26984	+	13.1412i	−0.241732	+	0.743975i
$313$	−2.63088	+	8.09701i	−0.148706	+	0.457670i	−0.997469	−	0.0711036i	$-0.977348\pi$
$313$	−2.63088	+	8.09701i	−0.148706	+	0.457670i	0.848763	+	0.528773i	$0.177348\pi$
$314$	−0.627080	−	1.92995i	−0.0353882	−	0.108914i
$315$	−7.25411	−	53.3329i	−0.408723	−	3.00497i
$316$	2.51629	−	7.74436i	0.141553	−	0.435654i
$317$	23.7886	+	17.2835i	1.33610	+	0.970736i	0.999578	+	0.0290620i	$0.00925201\pi$
$317$	23.7886	+	17.2835i	1.33610	+	0.970736i	0.336526	+	0.941674i	$0.390748\pi$
$318$	26.4548			1.48351
$319$	8.45424	+	6.14236i	0.473347	+	0.343906i
$320$	1.54615	+	1.61537i	0.0864322	+	0.0903021i
$321$	−21.0121	+	15.2662i	−1.17278	+	0.852074i
$322$	5.93511	−	4.31211i	0.330751	−	0.240304i
$323$	1.05499	+	3.24693i	0.0587013	+	0.180664i
$324$	12.2008			0.677824
$325$	−12.4725	−	18.8502i	−0.691851	−	1.04562i
$326$	−13.6218			−0.754442
$327$	−16.7894	−	51.6725i	−0.928456	−	2.85749i
$328$	−8.82173	+	6.40936i	−0.487099	+	0.353898i
$329$	35.6739	−	25.9186i	1.96676	−	1.42894i
$330$	3.13313	+	23.0350i	0.172473	+	1.26804i
$331$	11.0483	+	8.02704i	0.607268	+	0.441206i	0.848451	−	0.529273i	$-0.177535\pi$
$331$	11.0483	+	8.02704i	0.607268	+	0.441206i	−0.241183	+	0.970480i	$0.577535\pi$
$332$	−5.35703			−0.294005
$333$	−22.8397	−	16.5940i	−1.25161	−	0.909345i
$334$	−1.34470	+	4.13855i	−0.0735785	+	0.226451i
$335$	−4.50375	−	0.814769i	−0.246066	−	0.0445156i
$336$	3.58459	+	11.0322i	0.195555	+	0.601857i
$337$	−0.101953	+	0.313780i	−0.00555374	+	0.0170927i	−0.953795	−	0.300458i	$-0.902860\pi$
$337$	−0.101953	+	0.313780i	−0.00555374	+	0.0170927i	0.948241	+	0.317551i	$0.102860\pi$
$338$	−2.29777	+	7.07182i	−0.124982	+	0.384656i
$339$	1.53017	+	4.70939i	0.0831075	+	0.255779i
$340$	6.87617	−	3.31602i	0.372913	−	0.179837i
$341$	7.90163	−	24.3187i	0.427897	−	1.31693i
$342$	5.13128	+	3.72809i	0.277468	+	0.201592i
$343$	1.52853			0.0825328
$344$	1.75757	+	1.27695i	0.0947616	+	0.0688483i
$345$	−13.0009	−	2.35198i	−0.699946	−	0.126626i
$346$	−3.14118	+	2.28220i	−0.168871	+	0.122692i
$347$	−24.6429	+	17.9041i	−1.32290	+	0.961142i	−0.323008	+	0.946396i	$0.604694\pi$
$347$	−24.6429	+	17.9041i	−1.32290	+	0.961142i	−0.999891	+	0.0147460i	$0.995306\pi$
$348$	−2.90190	−	8.93114i	−0.155558	−	0.478759i
$349$	−34.0127			−1.82066			−0.910329	−	0.413886i	$-0.864171\pi$
$349$	−34.0127			−1.82066			−0.910329	+	0.413886i	$0.864171\pi$
$350$	−17.7728	−	6.64809i	−0.949996	−	0.355355i
$351$	46.1864			2.46525
$352$	−1.05107	−	3.23487i	−0.0560224	−	0.172419i
$353$	−5.75206	+	4.17912i	−0.306151	+	0.222432i	−0.730243	−	0.683187i	$-0.760593\pi$
$353$	−5.75206	+	4.17912i	−0.306151	+	0.222432i	0.424092	+	0.905619i	$0.360593\pi$
$354$	2.71929	−	1.97568i	0.144528	−	0.105006i
$355$	14.6712	−	27.2994i	0.778666	−	1.44890i
$356$	−2.95499	−	2.14692i	−0.156614	−	0.113787i
$357$	39.6026			2.09599
$358$	−10.9180	−	7.93241i	−0.577035	−	0.419241i
$359$	−9.27780	+	28.5541i	−0.489664	+	1.50703i	0.335448	+	0.942059i	$0.391112\pi$
$359$	−9.27780	+	28.5541i	−0.489664	+	1.50703i	−0.825111	+	0.564971i	$0.808888\pi$
$360$	6.71381	−	12.4927i	0.353849	−	0.658424i
$361$	0.309017	+	0.951057i	0.0162641	+	0.0500556i
$362$	0.755908	−	2.32645i	0.0397297	−	0.122275i
$363$	0.537570	−	1.65447i	0.0282151	−	0.0868372i
$364$	5.30152	+	16.3164i	0.277875	+	0.855212i
$365$	−24.8776	−	25.9914i	−1.30215	−	1.36045i
$366$	−8.47389	+	26.0799i	−0.442937	+	1.36322i
$367$	−12.2072	−	8.86904i	−0.637210	−	0.462960i	0.221681	−	0.975119i	$-0.428846\pi$
$367$	−12.2072	−	8.86904i	−0.637210	−	0.462960i	−0.858891	+	0.512159i	$0.828846\pi$
$368$	1.93307			0.100768
$369$	55.9527	+	40.6520i	2.91278	+	2.11626i
$370$	−8.96489	+	4.32330i	−0.466062	+	0.224758i
$371$	26.5737	−	19.3069i	1.37964	−	1.00236i
$372$	−18.5898	+	13.5063i	−0.963838	+	0.700269i
$373$	5.33855	+	16.4304i	0.276420	+	0.850732i	0.988840	+	0.148979i	$0.0475988\pi$
$373$	5.33855	+	16.4304i	0.276420	+	0.850732i	−0.712421	+	0.701753i	$0.752401\pi$
$374$	−11.6123			−0.600456
$375$	13.4825	+	31.4014i	0.696235	+	1.62156i
$376$	11.6190			0.599206
$377$	−4.29185	−	13.2089i	−0.221041	−	0.680295i
$378$	31.3689	−	22.7909i	1.61344	−	1.17224i
$379$	10.9563	−	7.96023i	0.562788	−	0.408890i	−0.269690	−	0.962947i	$-0.586921\pi$
$379$	10.9563	−	7.96023i	0.562788	−	0.408890i	0.832478	+	0.554058i	$0.186921\pi$
$380$	2.01410	−	0.971294i	0.103321	−	0.0498264i
$381$	−29.1564	−	21.1833i	−1.49373	−	1.08526i
$382$	−12.9415			−0.662142
$383$	−23.7743	−	17.2730i	−1.21481	−	0.882611i	−0.219151	−	0.975691i	$-0.570329\pi$
$383$	−23.7743	−	17.2730i	−1.21481	−	0.882611i	−0.995659	+	0.0930802i	$0.970329\pi$
$384$	−0.944531	+	2.90697i	−0.0482004	+	0.148346i
$385$	19.9583	+	20.8519i	1.01717	+	1.06271i
$386$	5.14693	+	15.8406i	0.261972	+	0.806266i
$387$	4.25798	−	13.1047i	0.216445	−	0.666151i
$388$	−0.425375	+	1.30917i	−0.0215951	+	0.0664630i
$389$	−4.33380	−	13.3381i	−0.219732	−	0.676267i	−0.998784	−	0.0493066i	$-0.984299\pi$
$389$	−4.33380	−	13.3381i	−0.219732	−	0.676267i	0.779051	−	0.626960i	$-0.215701\pi$
$390$	14.6262	−	27.2156i	0.740625	−	1.37812i
$391$	2.03937	−	6.27655i	0.103136	−	0.317419i
$392$	5.98896	+	4.35124i	0.302488	+	0.219771i
$393$	−1.73514			−0.0875263
$394$	−13.6774	−	9.93721i	−0.689057	−	0.500629i
$395$	−8.61947	+	16.0387i	−0.433693	+	0.806993i
$396$	−17.4532	+	12.6805i	−0.877058	+	0.637220i
$397$	10.5112	−	7.63685i	0.527543	−	0.383282i	−0.291895	−	0.956450i	$-0.594286\pi$
$397$	10.5112	−	7.63685i	0.527543	−	0.383282i	0.819438	+	0.573168i	$0.194286\pi$
$398$	8.17351	+	25.1555i	0.409701	+	1.26093i
$399$	11.6000			0.580725
$400$	−2.75904	−	4.16985i	−0.137952	−	0.208493i
$401$	−11.4900			−0.573781			−0.286891	−	0.957963i	$-0.592622\pi$
$401$	−11.4900			−0.573781			−0.286891	+	0.957963i	$0.592622\pi$
$402$	−1.93330	−	5.95008i	−0.0964242	−	0.296763i
$403$	−27.4939	+	19.9755i	−1.36957	+	0.995051i
$404$	−10.3631	+	7.52920i	−0.515581	+	0.374592i
$405$	−26.8461	−	4.85669i	−1.33399	−	0.241331i
$406$	−9.43294	−	6.85343i	−0.468149	−	0.340130i
$407$	15.1396			0.750443
$408$	8.44225	+	6.13365i	0.417953	+	0.303661i
$409$	−0.0855561	+	0.263314i	−0.00423048	+	0.0130201i	−0.953149	−	0.302500i	$-0.902179\pi$
$409$	−0.0855561	+	0.263314i	−0.00423048	+	0.0130201i	0.948919	+	0.315520i	$0.102179\pi$
$410$	21.9622	−	10.5912i	1.08464	−	0.523064i
$411$	−13.4930	−	41.5272i	−0.665560	−	2.04838i
$412$	3.79358	−	11.6754i	0.186896	−	0.575207i
$413$	1.28964	−	3.96911i	0.0634591	−	0.195307i
$414$	−3.78877	−	11.6606i	−0.186208	−	0.573089i
$415$	11.7874	+	2.13244i	0.578618	+	0.104677i
$416$	−1.39694	+	4.29934i	−0.0684906	+	0.210792i
$417$	−42.7812	−	31.0823i	−2.09500	−	1.52211i
$418$	−3.40134			−0.166365
$419$	−5.86897	−	4.26406i	−0.286718	−	0.208313i	0.435124	−	0.900370i	$-0.356704\pi$
$419$	−5.86897	−	4.26406i	−0.286718	−	0.208313i	−0.721842	+	0.692058i	$0.756704\pi$
$420$	−3.49583	−	25.7017i	−0.170579	−	1.25411i
$421$	1.43301	−	1.04115i	0.0698408	−	0.0507423i	−0.552317	−	0.833634i	$-0.686256\pi$
$421$	1.43301	−	1.04115i	0.0698408	−	0.0507423i	0.622158	+	0.782892i	$0.286256\pi$
$422$	13.3856	−	9.72520i	0.651600	−	0.473415i
$423$	−22.7730	−	70.0880i	−1.10726	−	3.40780i
$424$	8.65508			0.420328
$425$	−16.4500	+	4.55926i	−0.797941	+	0.221157i
$426$	42.3641			2.05255
$427$	10.5214	+	32.3814i	0.509164	+	1.56705i
$428$	−6.87440	+	4.99454i	−0.332287	+	0.241420i
$429$	−38.0222	+	27.6248i	−1.83573	+	1.33374i
$430$	−3.35896	−	3.50935i	−0.161983	−	0.169236i
$431$	−3.97766	−	2.88994i	−0.191597	−	0.139203i	0.487851	−	0.872927i	$-0.337781\pi$
$431$	−3.97766	−	2.88994i	−0.191597	−	0.139203i	−0.679448	+	0.733723i	$0.737781\pi$
$432$	10.2169			0.491561
$433$	−7.68514	−	5.58358i	−0.369324	−	0.268330i	0.387606	−	0.921825i	$-0.373302\pi$
$433$	−7.68514	−	5.58358i	−0.369324	−	0.268330i	−0.756931	+	0.653495i	$0.773302\pi$
$434$	−8.81636	+	27.1340i	−0.423199	+	1.30247i
$435$	2.83005	+	20.8068i	0.135691	+	0.997609i
$436$	−5.49289	−	16.9054i	−0.263062	−	0.809621i
$437$	0.597352	−	1.83846i	0.0285752	−	0.0879455i
$438$	15.1975	−	46.7732i	0.726167	−	2.23491i
$439$	1.61784	+	4.97920i	0.0772153	+	0.237644i	0.982212	−	0.187774i	$-0.0601271\pi$
$439$	1.61784	+	4.97920i	0.0772153	+	0.237644i	−0.904997	+	0.425418i	$0.860127\pi$
$440$	1.02505	+	7.53624i	0.0488673	+	0.359276i
$441$	14.5092	−	44.6548i	0.690915	−	2.12642i
$442$	12.4859	+	9.07153i	0.593893	+	0.431489i
$443$	−19.3073			−0.917317			−0.458659	−	0.888613i	$-0.651670\pi$
$443$	−19.3073			−0.917317			−0.458659	+	0.888613i	$0.651670\pi$
$444$	−11.0067	−	7.99681i	−0.522353	−	0.379512i
$445$	5.64740	+	5.90025i	0.267712	+	0.279699i
$446$	−14.9177	+	10.8383i	−0.706371	+	0.513209i
$447$	16.4818	−	11.9747i	0.779561	−	0.566384i
$448$	1.17275	+	3.60935i	0.0554072	+	0.170526i
$449$	9.40487			0.443843			0.221922	−	0.975065i	$-0.428767\pi$
$449$	9.40487			0.443843			0.221922	+	0.975065i	$0.428767\pi$
$450$	−19.7456	+	24.8158i	−0.930818	+	1.16983i
$451$	−37.0891			−1.74646
$452$	0.500618	+	1.54074i	0.0235471	+	0.0724705i
$453$	26.3079	−	19.1138i	1.23605	−	0.898046i
$454$	1.48358	−	1.07789i	0.0696280	−	0.0505877i
$455$	−5.17026	−	38.0122i	−0.242385	−	1.78204i
$456$	2.47282	+	1.79661i	0.115800	+	0.0841338i
$457$	−16.3853			−0.766472			−0.383236	−	0.923651i	$-0.625190\pi$
$457$	−16.3853			−0.766472			−0.383236	+	0.923651i	$0.625190\pi$
$458$	−3.55922	−	2.58593i	−0.166312	−	0.120832i
$459$	10.7787	−	33.1735i	0.503108	−	1.54841i
$460$	−4.25344	−	0.769484i	−0.198318	−	0.0358774i
$461$	−1.29692	−	3.99151i	−0.0604036	−	0.185903i	0.916302	−	0.400489i	$-0.131160\pi$
$461$	−1.29692	−	3.99151i	−0.0604036	−	0.185903i	−0.976705	+	0.214586i	$0.931160\pi$
$462$	−12.1924	+	37.5244i	−0.567243	+	1.74579i
$463$	4.50425	−	13.8626i	0.209330	−	0.644252i	−0.790178	−	0.612878i	$-0.790012\pi$
$463$	4.50425	−	13.8626i	0.209330	−	0.644252i	0.999508	−	0.0313739i	$-0.00998827\pi$
$464$	−0.949399	−	2.92195i	−0.0440747	−	0.135648i
$465$	46.2805	−	22.3187i	2.14621	−	1.03500i
$466$	5.55009	−	17.0814i	0.257103	−	0.791281i
$467$	−2.81375	−	2.04431i	−0.130205	−	0.0945992i	0.520777	−	0.853693i	$-0.325642\pi$
$467$	−2.81375	−	2.04431i	−0.130205	−	0.0945992i	−0.650981	+	0.759094i	$0.725642\pi$
$468$	28.6723			1.32538
$469$	−6.28439	−	4.56588i	−0.290186	−	0.210833i
$470$	−25.5659	−	4.62510i	−1.17927	−	0.213340i
$471$	−5.01802	+	3.64581i	−0.231218	+	0.167990i
$472$	0.889654	−	0.646371i	0.0409496	−	0.0297517i
$473$	2.28343	+	7.02766i	0.104992	+	0.323132i
$474$	−24.8893			−1.14320
$475$	−4.81836	+	1.33545i	−0.221081	+	0.0612747i
$476$	12.9565			0.593862
$477$	−16.9637	−	52.2090i	−0.776715	−	2.39048i
$478$	−4.85131	+	3.52468i	−0.221894	+	0.161215i
$479$	−24.4158	+	17.7391i	−1.11558	+	0.810520i	−0.983534	−	0.180723i	$-0.942156\pi$
$479$	−24.4158	+	17.7391i	−1.11558	+	0.810520i	−0.132051	+	0.991243i	$0.542156\pi$
$480$	3.23546	−	6.02037i	0.147678	−	0.274791i
$481$	−16.2786	−	11.8271i	−0.742241	−	0.539269i
$482$	−22.5415			−1.02674
$483$	−18.1411	−	13.1802i	−0.825447	−	0.599722i
$484$	0.175874	−	0.541284i	0.00799427	−	0.0246038i
$485$	1.45711	−	2.71131i	0.0661638	−	0.123114i
$486$	−2.05247	−	6.31687i	−0.0931021	−	0.286539i
$487$	−10.9452	+	33.6857i	−0.495972	+	1.52645i	0.319464	+	0.947598i	$0.396497\pi$
$487$	−10.9452	+	33.6857i	−0.495972	+	1.52645i	−0.815436	+	0.578847i	$0.803503\pi$
$488$	−2.77235	+	8.53243i	−0.125499	+	0.386245i
$489$	12.8662	+	39.5982i	0.581831	+	1.79069i
$490$	−11.4458	−	11.9582i	−0.517066	−	0.540218i
$491$	−8.58236	+	26.4138i	−0.387316	+	1.19204i	0.547470	+	0.836826i	$0.315591\pi$
$491$	−8.58236	+	26.4138i	−0.387316	+	1.19204i	−0.934786	+	0.355212i	$0.884409\pi$
$492$	26.9642	+	19.5906i	1.21564	+	0.883215i
$493$	−10.4890			−0.472399
$494$	3.65724	+	2.65714i	0.164547	+	0.119550i
$495$	43.4509	−	20.9541i	1.95297	−	0.941817i
$496$	−6.08193	+	4.41878i	−0.273087	+	0.198409i
$497$	42.5544	−	30.9176i	1.90882	−	1.38684i
$498$	5.05988	+	15.5727i	0.226739	+	0.697830i
$499$	−33.0663			−1.48025			−0.740126	−	0.672468i	$-0.765234\pi$
$499$	−33.0663			−1.48025			−0.740126	+	0.672468i	$0.765234\pi$
$500$	4.41100	+	10.2734i	0.197266	+	0.459441i
$501$	13.3007			0.594233
$502$	−1.93196	−	5.94596i	−0.0862275	−	0.265381i
$503$	−19.5186	+	14.1811i	−0.870291	+	0.632303i	−0.930665	−	0.365872i	$-0.880771\pi$
$503$	−19.5186	+	14.1811i	−0.870291	+	0.632303i	0.0603740	+	0.998176i	$0.480771\pi$
$504$	19.4737	−	14.1485i	0.867427	−	0.630223i
$505$	25.7995	−	12.4417i	1.14806	−	0.553650i
$506$	5.31932	+	3.86471i	0.236473	+	0.171807i
$507$	22.7279			1.00938
$508$	−9.53892	−	6.93043i	−0.423221	−	0.307488i
$509$	−9.61709	+	29.5984i	−0.426270	+	1.31192i	0.475503	+	0.879714i	$0.342266\pi$
$509$	−9.61709	+	29.5984i	−0.426270	+	1.31192i	−0.901773	+	0.432210i	$0.857734\pi$
$510$	−16.1343	−	16.8567i	−0.714440	−	0.746429i
$511$	−18.8696	−	58.0746i	−0.834741	−	2.56907i
$512$	−0.309017	+	0.951057i	−0.0136568	+	0.0420312i
$513$	3.15720	−	9.71685i	0.139394	−	0.429009i
$514$	−3.75099	−	11.5444i	−0.165449	−	0.509200i
$515$	−12.9948	+	24.1800i	−0.572618	+	1.06550i
$516$	2.05197	−	6.31530i	0.0903328	−	0.278016i
$517$	31.9726	+	23.2295i	1.40615	+	1.02163i
$518$	−16.8922			−0.742202
$519$	9.60124	+	6.97571i	0.421448	+	0.306200i
$520$	4.78517	−	8.90399i	0.209843	−	0.390466i
$521$	−1.10179	+	0.800495i	−0.0482701	+	0.0350703i	−0.611659	−	0.791122i	$-0.709497\pi$
$521$	−1.10179	+	0.800495i	−0.0482701	+	0.0350703i	0.563389	+	0.826192i	$0.309497\pi$
$522$	−15.7649	+	11.4539i	−0.690012	+	0.501323i
$523$	0.844675	+	2.59964i	0.0369351	+	0.113674i	0.967824	−	0.251627i	$-0.0809658\pi$
$523$	0.844675	+	2.59964i	0.0369351	+	0.113674i	−0.930889	+	0.365302i	$0.880966\pi$
$524$	−0.567676			−0.0247990
$525$	−2.53882	+	57.9443i	−0.110803	+	2.52890i
$526$	28.9619			1.26280
$527$	7.93109	+	24.4094i	0.345484	+	1.06329i
$528$	−8.41089	+	6.11087i	−0.366037	+	0.265942i
$529$	15.5843	−	11.3226i	0.677578	−	0.492289i
$530$	−19.0442	−	3.44527i	−0.827228	−	0.149653i
$531$	−5.64272	−	4.09968i	−0.244873	−	0.177911i
$532$	3.79510			0.164538
$533$	39.8794	+	28.9741i	1.72737	+	1.25501i
$534$	−3.44996	+	10.6179i	−0.149294	+	0.459481i
$535$	17.1142	−	8.25331i	0.739913	−	0.356822i
$536$	−0.632506	−	1.94665i	−0.0273201	−	0.0840827i
$537$	−12.7468	+	39.2308i	−0.550067	+	1.69293i
$538$	−6.77281	+	20.8446i	−0.291997	+	0.898674i
$539$	7.78085	+	23.9470i	0.335145	+	1.03147i
$540$	−22.4808	−	4.06697i	−0.967418	−	0.175014i
$541$	0.541617	−	1.66693i	0.0232859	−	0.0716668i	−0.938738	−	0.344631i	$-0.888004\pi$
$541$	0.541617	−	1.66693i	0.0232859	−	0.0716668i	0.962024	+	0.272964i	$0.0880041\pi$
$542$	3.90334	+	2.83594i	0.167663	+	0.121814i
$543$	−7.47688			−0.320864
$544$	2.76200	+	2.00671i	0.118420	+	0.0860371i
$545$	5.35689	+	39.3843i	0.229464	+	1.68704i
$546$	42.4238	−	30.8227i	1.81557	−	1.31909i
$547$	3.40219	−	2.47184i	0.145467	−	0.105688i	−0.512671	−	0.858585i	$-0.671344\pi$
$547$	3.40219	−	2.47184i	0.145467	−	0.105688i	0.658139	+	0.752897i	$0.271344\pi$
$548$	−4.41443	−	13.5862i	−0.188575	−	0.580374i
$549$	56.9028			2.42855
$550$	0.744432	−	16.9904i	0.0317427	−	0.724474i
$551$	−3.07232			−0.130885
$552$	−1.82585	−	5.61938i	−0.0777132	−	0.239177i
$553$	−25.0011	+	18.1644i	−1.06316	+	0.772428i
$554$	−13.8641	+	10.0728i	−0.589028	+	0.427954i
$555$	21.0353	+	21.9771i	0.892899	+	0.932878i
$556$	−13.9965	−	10.1690i	−0.593583	−	0.431263i
$557$	−11.0691			−0.469013			−0.234506	−	0.972115i	$-0.575347\pi$
$557$	−11.0691			−0.469013			−0.234506	+	0.972115i	$0.575347\pi$
$558$	38.5753	+	28.0266i	1.63302	+	1.18646i
$559$	3.03481	−	9.34019i	0.128359	−	0.395048i
$560$	−1.14371	−	8.40867i	−0.0483307	−	0.355331i
$561$	10.9681	+	33.7565i	0.463076	+	1.42520i
$562$	0.384045	−	1.18197i	0.0162000	−	0.0498583i
$563$	12.0805	−	37.1799i	0.509132	−	1.56695i	−0.284580	−	0.958652i	$-0.591854\pi$
$563$	12.0805	−	37.1799i	0.509132	−	1.56695i	0.793711	−	0.608294i	$-0.208146\pi$
$564$	−10.9745	−	33.7761i	−0.462111	−	1.42223i
$565$	−0.488222	−	3.58945i	−0.0205397	−	0.151009i
$566$	9.72726	−	29.9374i	0.408867	−	1.25836i
$567$	−37.4602	−	27.2164i	−1.57318	−	1.14298i
$568$	13.8600			0.581553
$569$	26.5764	+	19.3089i	1.11414	+	0.809470i	0.983310	−	0.181935i	$-0.0582362\pi$
$569$	26.5764	+	19.3089i	1.11414	+	0.809470i	0.130829	+	0.991405i	$0.458236\pi$
$570$	−4.72590	−	4.93750i	−0.197946	−	0.206809i
$571$	27.4819	−	19.9668i	1.15008	−	0.835585i	0.161592	−	0.986858i	$-0.448337\pi$
$571$	27.4819	−	19.9668i	1.15008	−	0.835585i	0.988492	+	0.151273i	$0.0483373\pi$
$572$	−12.4395	+	9.03784i	−0.520122	+	0.377891i
$573$	12.2236	+	37.6204i	0.510648	+	1.57161i
$574$	41.3827			1.72728
$575$	9.05275	+	3.38627i	0.377526	+	0.141217i
$576$	6.34261			0.264275
$577$	3.94022	+	12.1267i	0.164033	+	0.504843i	0.998964	−	0.0455127i	$-0.0144921\pi$
$577$	3.94022	+	12.1267i	0.164033	+	0.504843i	−0.834930	+	0.550356i	$0.814492\pi$
$578$	−4.32375	+	3.14139i	−0.179844	+	0.130665i
$579$	41.1867	−	29.9239i	1.71166	−	1.24360i
$580$	0.925892	+	6.80724i	0.0384456	+	0.282655i
$581$	16.4477	+	11.9499i	0.682365	+	0.495767i
$582$	4.20749			0.174406
$583$	23.8166	+	17.3037i	0.986381	+	0.716648i
$584$	4.97210	−	15.3025i	0.205747	−	0.633223i
$585$	−63.0892	−	11.4134i	−2.60842	−	0.471886i
$586$	9.30978	+	28.6526i	0.384584	+	1.18363i
$587$	−3.15551	+	9.71165i	−0.130242	+	0.400843i	−0.994820	−	0.101656i	$-0.967586\pi$
$587$	−3.15551	+	9.71165i	−0.130242	+	0.400843i	0.864578	+	0.502499i	$0.167586\pi$
$588$	6.99214	−	21.5196i	0.288351	−	0.887453i
$589$	2.32309	+	7.14974i	0.0957213	+	0.294600i
$590$	−2.21485	+	1.06811i	−0.0911838	+	0.0439732i
$591$	−15.9684	+	49.1458i	−0.656853	+	2.02159i
$592$	−3.60099	−	2.61627i	−0.148000	−	0.107528i
$593$	34.5966			1.42071			0.710356	−	0.703843i	$-0.248534\pi$
$593$	34.5966			1.42071			0.710356	+	0.703843i	$0.248534\pi$
$594$	28.1143	+	20.4262i	1.15354	+	0.838098i
$595$	−28.5090	−	5.15752i	−1.16875	−	0.211438i
$596$	5.39225	−	3.91770i	0.220875	−	0.160475i
$597$	65.4060	−	47.5203i	2.67689	−	1.94487i
$598$	−2.70038	−	8.31093i	−0.110427	−	0.339859i
$599$	−13.4961			−0.551435			−0.275717	−	0.961239i	$-0.588915\pi$
$599$	−13.4961			−0.551435			−0.275717	+	0.961239i	$0.588915\pi$
$600$	−9.51563	+	11.9590i	−0.388474	+	0.488225i
$601$	30.2522			1.23401			0.617007	−	0.786958i	$-0.288345\pi$
$601$	30.2522			1.23401			0.617007	+	0.786958i	$0.288345\pi$
$602$	−2.54776	−	7.84121i	−0.103839	−	0.319584i
$603$	−10.5029	+	7.63078i	−0.427710	+	0.310749i
$604$	8.60701	−	6.25336i	0.350214	−	0.254446i
$605$	−0.602449	+	1.12101i	−0.0244930	+	0.0455754i
$606$	31.6754	+	23.0135i	1.28672	+	0.934860i
$607$	−12.8304			−0.520768			−0.260384	−	0.965505i	$-0.583849\pi$
$607$	−12.8304			−0.520768			−0.260384	+	0.965505i	$0.583849\pi$
$608$	0.809017	+	0.587785i	0.0328100	+	0.0238378i
$609$	−11.0130	+	33.8945i	−0.446269	+	1.37348i
$610$	9.49660	−	17.6708i	0.384506	−	0.715469i
$611$	−16.2311	−	49.9541i	−0.656639	−	2.02093i
$612$	6.69139	−	20.5940i	0.270483	−	0.832462i
$613$	−9.30281	+	28.6311i	−0.375737	+	1.15640i	0.567243	+	0.823550i	$0.308010\pi$
$613$	−9.30281	+	28.6311i	−0.375737	+	1.15640i	−0.942980	+	0.332849i	$0.891990\pi$
$614$	−5.31162	−	16.3475i	−0.214360	−	0.659731i
$615$	−51.5324	−	53.8398i	−2.07799	−	2.17103i
$616$	−3.98892	+	12.2766i	−0.160718	+	0.494640i
$617$	−22.9401	−	16.6669i	−0.923532	−	0.670985i	0.0208687	−	0.999782i	$-0.493357\pi$
$617$	−22.9401	−	16.6669i	−0.923532	−	0.670985i	−0.944401	+	0.328797i	$0.893357\pi$
$618$	−37.5233			−1.50941
$619$	−21.8331	−	15.8627i	−0.877547	−	0.637575i	0.0550546	−	0.998483i	$-0.482467\pi$
$619$	−21.8331	−	15.8627i	−0.877547	−	0.637575i	−0.932601	+	0.360908i	$0.882467\pi$
$620$	15.1413	−	7.30188i	0.608091	−	0.293251i
$621$	−15.9781	+	11.6088i	−0.641178	+	0.465843i
$622$	15.2958	−	11.1131i	0.613307	−	0.445593i
$623$	4.28354	+	13.1834i	0.171616	+	0.528181i
$624$	13.8175			0.553142
$625$	−5.61629	−	24.3610i	−0.224652	−	0.974439i
$626$	8.51370			0.340276
$627$	3.21268	+	9.88760i	0.128302	+	0.394873i
$628$	−1.64172	+	1.19278i	−0.0655117	+	0.0475970i
$629$	−12.2939	+	8.93201i	−0.490188	+	0.356143i
$630$	−48.4809	+	23.3798i	−1.93153	+	0.931475i
$631$	−31.7047	−	23.0348i	−1.26214	−	0.917002i	−0.263283	−	0.964719i	$-0.584805\pi$
$631$	−31.7047	−	23.0348i	−1.26214	−	0.917002i	−0.998861	+	0.0477170i	$0.984805\pi$
$632$	−8.14290			−0.323907
$633$	−40.9140	−	29.7257i	−1.62618	−	1.18149i
$634$	9.08646	−	27.9652i	0.360869	−	1.11064i
$635$	18.2302	+	19.0465i	0.723445	+	0.755836i
$636$	−8.17499	−	25.1600i	−0.324160	−	0.997660i
$637$	10.3412	−	31.8270i	0.409734	−	1.26103i
$638$	3.22923	−	9.93856i	0.127847	−	0.393471i
$639$	−27.1652	−	83.6060i	−1.07464	−	3.30740i
$640$	1.05853	−	1.96965i	0.0418419	−	0.0778573i
$641$	0.0827323	−	0.254624i	0.00326773	−	0.0100570i	−0.949409	−	0.314041i	$-0.898317\pi$
$641$	0.0827323	−	0.254624i	0.00326773	−	0.0100570i	0.952677	+	0.303984i	$0.0983170\pi$
$642$	21.0121	+	15.2662i	0.829280	+	0.602507i
$643$	1.21626			0.0479647			0.0239824	−	0.999712i	$-0.492365\pi$
$643$	1.21626			0.0479647			0.0239824	+	0.999712i	$0.492365\pi$
$644$	−5.93511	−	4.31211i	−0.233876	−	0.169921i
$645$	−7.02894	+	13.0791i	−0.276764	+	0.514988i
$646$	2.76200	−	2.00671i	0.108670	−	0.0789530i
$647$	−31.7416	+	23.0617i	−1.24789	+	0.906647i	−0.998098	−	0.0616517i	$-0.980363\pi$
$647$	−31.7416	+	23.0617i	−1.24789	+	0.906647i	−0.249795	+	0.968299i	$0.580363\pi$
$648$	−3.77026	−	11.6037i	−0.148110	−	0.455835i
$649$	3.74036			0.146822
$650$	−14.0734	+	17.6871i	−0.552004	+	0.693745i
$651$	87.2049			3.41783
$652$	4.20937	+	12.9551i	0.164852	+	0.507361i
$653$	12.2194	−	8.87794i	0.478183	−	0.347420i	−0.322439	−	0.946590i	$-0.604503\pi$
$653$	12.2194	−	8.87794i	0.478183	−	0.347420i	0.800622	+	0.599170i	$0.204503\pi$
$654$	−43.9552	+	31.9353i	−1.71879	+	1.24877i
$655$	1.24909	+	0.225971i	0.0488059	+	0.00882941i
$656$	8.82173	+	6.40936i	0.344431	+	0.250244i
$657$	−102.053			−3.98146
$658$	−35.6739	−	25.9186i	−1.39071	−	1.01041i
$659$	−2.31626	+	7.12872i	−0.0902287	+	0.277695i	−0.985981	−	0.166858i	$-0.946638\pi$
$659$	−2.31626	+	7.12872i	−0.0902287	+	0.277695i	0.895752	+	0.444554i	$0.146638\pi$
$660$	20.9394	−	10.0980i	0.815066	−	0.393064i
$661$	0.575419	+	1.77096i	0.0223812	+	0.0688823i	0.961623	−	0.274373i	$-0.0884703\pi$
$661$	0.575419	+	1.77096i	0.0223812	+	0.0688823i	−0.939242	+	0.343255i	$0.888470\pi$
$662$	4.22007	−	12.9880i	0.164018	−	0.504794i
$663$	14.5773	−	44.8644i	0.566137	−	1.74239i
$664$	1.65541	+	5.09484i	0.0642425	+	0.197718i
$665$	−8.35055	−	1.51069i	−0.323820	−	0.0585819i
$666$	−8.72397	+	26.8496i	−0.338047	+	1.04040i
$667$	4.80476	+	3.49086i	0.186041	+	0.135167i
$668$	4.35153			0.168366
$669$	45.5968	+	33.1280i	1.76287	+	1.28080i
$670$	0.616846	+	4.53510i	0.0238308	+	0.175206i
$671$	−24.6874	+	17.9364i	−0.953045	+	0.692427i
$672$	9.38457	−	6.81829i	0.362018	−	0.263021i
$673$	−2.00537	−	6.17190i	−0.0773014	−	0.237909i	0.904937	−	0.425545i	$-0.139918\pi$
$673$	−2.00537	−	6.17190i	−0.0773014	−	0.237909i	−0.982239	+	0.187636i	$0.939918\pi$
$674$	0.329927			0.0127083
$675$	47.8467	+	17.8975i	1.84162	+	0.688876i
$676$	7.43575			0.285990
$677$	14.0429	+	43.2195i	0.539711	+	1.66106i	0.733244	+	0.679966i	$0.238005\pi$
$677$	14.0429	+	43.2195i	0.539711	+	1.66106i	−0.193533	+	0.981094i	$0.561995\pi$
$678$	4.00604	−	2.91056i	0.153851	−	0.111779i
$679$	4.22640	−	3.07066i	0.162194	−	0.117841i
$680$	−5.27858	−	5.51492i	−0.202424	−	0.211488i
$681$	−4.53467	−	3.29463i	−0.173769	−	0.126251i
$682$	−25.5702			−0.979134
$683$	19.8607	+	14.4297i	0.759950	+	0.552136i	0.898895	−	0.438164i	$-0.144371\pi$
$683$	19.8607	+	14.4297i	0.759950	+	0.552136i	−0.138945	+	0.990300i	$0.544371\pi$
$684$	1.95997	−	6.03218i	0.0749414	−	0.230646i
$685$	4.30513	+	31.6517i	0.164490	+	1.20935i
$686$	−0.472341	−	1.45372i	−0.0180341	−	0.0555032i
$687$	−4.15541	+	12.7890i	−0.158539	+	0.487932i
$688$	0.671330	−	2.06614i	0.0255942	−	0.0787709i
$689$	−12.0906	−	37.2111i	−0.460616	−	1.41763i
$690$	1.78064	+	13.0914i	0.0677877	+	0.498381i
$691$	−8.65546	+	26.6388i	−0.329269	+	1.01339i	0.640208	+	0.768202i	$0.278848\pi$
$691$	−8.65546	+	26.6388i	−0.329269	+	1.01339i	−0.969477	+	0.245184i	$0.921152\pi$
$692$	3.14118	+	2.28220i	0.119410	+	0.0867563i
$693$	81.8731			3.11010
$694$	24.6429	+	17.9041i	0.935431	+	0.679630i
$695$	26.7492	+	27.9469i	1.01466	+	1.06009i
$696$	−7.59728	+	5.51975i	−0.287974	+	0.209225i
$697$	30.1176	−	21.8817i	1.14078	−	0.828829i
$698$	10.5105	+	32.3480i	0.397828	+	1.22439i
$699$	−54.8974			−2.07641
$700$	−0.830611	+	18.9573i	−0.0313941	+	0.716519i
$701$	−15.9675			−0.603083			−0.301542	−	0.953453i	$-0.597501\pi$
$701$	−15.9675			−0.603083			−0.301542	+	0.953453i	$0.597501\pi$
$702$	−14.2724	−	43.9259i	−0.538677	−	1.65788i
$703$	−3.60099	+	2.61627i	−0.135814	+	0.0986746i
$704$	−2.75174	+	1.99926i	−0.103710	+	0.0753499i
$705$	10.7028	+	78.6879i	0.403091	+	2.96356i
$706$	5.75206	+	4.17912i	0.216482	+	0.157283i
$707$	48.6131			1.82828
$708$	−2.71929	−	1.97568i	−0.102197	−	0.0742505i
$709$	4.24464	−	13.0637i	0.159411	−	0.490616i	−0.839170	−	0.543869i	$-0.816959\pi$
$709$	4.24464	−	13.0637i	0.159411	−	0.490616i	0.998581	+	0.0532526i	$0.0169589\pi$
$710$	−30.4969	−	5.51716i	−1.14453	−	0.207055i
$711$	15.9599	+	49.1194i	0.598541	+	1.84212i
$712$	−1.12870	+	3.47379i	−0.0423000	+	0.130186i
$713$	4.49070	−	13.8210i	0.168178	−	0.517599i
$714$	−12.2379	−	37.6643i	−0.457991	−	1.40955i
$715$	30.9689	−	14.9347i	1.15817	−	0.558526i
$716$	−4.17031	+	12.8349i	−0.155852	+	0.479663i
$717$	14.8283	+	10.7734i	0.553775	+	0.402341i
$718$	30.0236			1.12047
$719$	−10.4100	−	7.56334i	−0.388229	−	0.282065i	0.376500	−	0.926416i	$-0.377127\pi$
$719$	−10.4100	−	7.56334i	−0.388229	−	0.282065i	−0.764729	+	0.644351i	$0.777127\pi$
$720$	−13.9560	−	2.52476i	−0.520108	−	0.0940921i
$721$	−37.6918	+	27.3847i	−1.40372	+	1.01986i
$722$	0.809017	−	0.587785i	0.0301085	−	0.0218751i
$723$	21.2912	+	65.5275i	0.791827	+	2.43699i
$724$	−2.44617			−0.0909112
$725$	0.672421	−	15.3469i	0.0249731	−	0.569969i
$726$	−1.73961			−0.0645631
$727$	−9.29265	−	28.5998i	−0.344645	−	1.06071i	−0.961773	−	0.273846i	$-0.911704\pi$
$727$	−9.29265	−	28.5998i	−0.344645	−	1.06071i	0.617128	−	0.786863i	$-0.288296\pi$
$728$	13.8796	−	10.0841i	0.514411	−	0.373741i
$729$	13.1877	−	9.58143i	0.488434	−	0.354868i
$730$	−17.0317	+	31.6917i	−0.630373	+	1.17296i
$731$	−6.00037	−	4.35952i	−0.221932	−	0.161243i
$732$	27.4221			1.01355
$733$	−42.3987	−	30.8045i	−1.56603	−	1.13779i	−0.930835	−	0.365440i	$-0.880918\pi$
$733$	−42.3987	−	30.8045i	−1.56603	−	1.13779i	−0.635198	−	0.772349i	$-0.719082\pi$
$734$	−4.66273	+	14.3504i	−0.172105	+	0.529683i
$735$	−23.9513	+	44.5674i	−0.883458	+	1.64389i
$736$	−0.597352	−	1.83846i	−0.0220187	−	0.0677665i
$737$	2.15137	−	6.62124i	0.0792468	−	0.243897i
$738$	21.3720	−	65.7764i	0.786716	−	2.42126i
$739$	−5.93413	−	18.2634i	−0.218291	−	0.671830i	−0.998904	−	0.0468148i	$-0.985093\pi$
$739$	−5.93413	−	18.2634i	−0.218291	−	0.671830i	0.780613	−	0.625015i	$-0.214907\pi$
$740$	6.88200	+	7.19014i	0.252987	+	0.264315i
$741$	4.26984	−	13.1412i	0.156857	−	0.482755i
$742$	−26.5737	−	19.3069i	−0.975550	−	0.708779i
$743$	49.2402			1.80645			0.903224	−	0.429170i	$-0.141194\pi$
$743$	49.2402			1.80645			0.903224	+	0.429170i	$0.141194\pi$
$744$	18.5898	+	13.5063i	0.681536	+	0.495165i
$745$	−13.4243	+	6.47386i	−0.491829	+	0.237184i
$746$	13.9765	−	10.1545i	0.511716	−	0.371783i
$747$	27.4884	−	19.9715i	1.00575	−	0.730719i
$748$	3.58839	+	11.0439i	0.131204	+	0.403806i
$749$	32.2478			1.17831
$750$	25.6982	−	22.5262i	0.938364	−	0.822541i
$751$	22.7167			0.828943			0.414472	−	0.910062i	$-0.363966\pi$
$751$	22.7167			0.828943			0.414472	+	0.910062i	$0.363966\pi$
$752$	−3.59048	−	11.0504i	−0.130931	−	0.402965i
$753$	−15.4599	+	11.2323i	−0.563390	+	0.409327i
$754$	−11.2362	+	8.16358i	−0.409198	+	0.297300i
$755$	−21.4277	+	10.3335i	−0.779833	+	0.376073i
$756$	−31.3689	−	22.7909i	−1.14088	−	0.828895i
$757$	−10.4683			−0.380478			−0.190239	−	0.981738i	$-0.560926\pi$
$757$	−10.4683			−0.380478			−0.190239	+	0.981738i	$0.560926\pi$
$758$	−10.9563	−	7.96023i	−0.397951	−	0.289129i
$759$	6.21033	−	19.1134i	0.225421	−	0.693774i
$760$	−1.54615	−	1.61537i	−0.0560846	−	0.0585958i
$761$	−3.17983	−	9.78653i	−0.115269	−	0.354761i	0.876734	−	0.480975i	$-0.159717\pi$
$761$	−3.17983	−	9.78653i	−0.115269	−	0.354761i	−0.992003	+	0.126214i	$0.959717\pi$
$762$	−11.1367	+	34.2754i	−0.403442	+	1.24167i
$763$	−20.8461	+	64.1576i	−0.754678	+	2.32266i
$764$	3.99913	+	12.3081i	0.144683	+	0.445290i
$765$	−22.9211	+	42.6504i	−0.828715	+	1.54203i
$766$	−9.08097	+	27.9484i	−0.328109	+	1.00982i
$767$	−4.02176	−	2.92198i	−0.145217	−	0.105507i
$768$	3.05657			0.110294
$769$	−20.0065	−	14.5356i	−0.721453	−	0.524166i	0.165395	−	0.986227i	$-0.447110\pi$
$769$	−20.0065	−	14.5356i	−0.721453	−	0.524166i	−0.886848	+	0.462061i	$0.847110\pi$
$770$	13.6639	−	25.4251i	0.492413	−	0.916257i
$771$	−30.0162	+	21.8080i	−1.08101	+	0.785397i
$772$	13.4748	−	9.79004i	0.484970	−	0.352351i
$773$	3.42606	+	10.5443i	0.123227	+	0.379253i	0.993574	−	0.113186i	$-0.0361055\pi$
$773$	3.42606	+	10.5443i	0.123227	+	0.379253i	−0.870347	+	0.492439i	$0.836105\pi$
$774$	−13.7791			−0.495280
$775$	−36.2229	+	10.0395i	−1.30116	+	0.360630i
$776$	1.37654			0.0494150
$777$	15.9553	+	49.1052i	0.572391	+	1.76164i
$778$	−11.3460	+	8.24338i	−0.406775	+	0.295539i
$779$	8.82173	−	6.40936i	0.316071	−	0.229639i
$780$	−30.4033	−	5.50023i	−1.08861	−	0.196940i
$781$	38.1392	+	27.7098i	1.36473	+	0.991533i
$782$	−6.59955			−0.235999
$783$	25.3947	+	18.4503i	0.907533	+	0.659361i
$784$	2.28758	−	7.04045i	0.0816993	−	0.251445i
$785$	4.08716	−	1.97102i	0.145877	−	0.0703488i
$786$	0.536188	+	1.65022i	0.0191252	+	0.0588613i
$787$	−9.29296	+	28.6008i	−0.331258	+	1.01951i	0.637278	+	0.770634i	$0.280061\pi$
$787$	−9.29296	+	28.6008i	−0.331258	+	1.01951i	−0.968536	+	0.248874i	$0.919939\pi$
$788$	−5.22430	+	16.0787i	−0.186108	+	0.572781i
$789$	−27.3554	−	84.1914i	−0.973879	−	2.99729i
$790$	17.9172	+	3.24138i	0.637467	+	0.115323i
$791$	1.89989	−	5.84727i	0.0675524	−	0.207905i
$792$	17.4532	+	12.6805i	0.620174	+	0.450582i
$793$	40.5566			1.44021
$794$	−10.5112	−	7.63685i	−0.373029	−	0.271021i
$795$	7.97258	+	58.6151i	0.282758	+	2.07886i
$796$	21.3985	−	15.5469i	0.758450	−	0.551046i
$797$	−23.0933	+	16.7783i	−0.818008	+	0.594317i	−0.916141	−	0.400856i	$-0.868713\pi$
$797$	−23.0933	+	16.7783i	−0.818008	+	0.594317i	0.0981334	+	0.995173i	$0.468713\pi$
$798$	−3.58459	−	11.0322i	−0.126893	−	0.390537i
$799$	−39.6676			−1.40334
$800$	−3.11317	+	3.91256i	−0.110067	+	0.138330i
$801$	23.1668			0.818557
$802$	3.55059	+	10.9276i	0.125376	+	0.385867i
$803$	44.2757	−	32.1682i	1.56245	−	1.13519i
$804$	−5.06144	+	3.67735i	−0.178503	+	0.129690i
$805$	11.3428	+	11.8507i	0.399782	+	0.417682i
$806$	27.4939	+	19.9755i	0.968432	+	0.703607i
$807$	66.9917			2.35822
$808$	10.3631	+	7.52920i	0.364571	+	0.264876i
$809$	−8.99300	+	27.6776i	−0.316177	+	0.973093i	0.659090	+	0.752064i	$0.270941\pi$
$809$	−8.99300	+	27.6776i	−0.316177	+	0.973093i	−0.975267	+	0.221029i	$0.929059\pi$
$810$	3.67691	+	27.0330i	0.129193	+	0.949841i
$811$	−11.0804	−	34.1020i	−0.389086	−	1.19748i	−0.933472	−	0.358649i	$-0.883237\pi$
$811$	−11.0804	−	34.1020i	−0.389086	−	1.19748i	0.544386	−	0.838835i	$-0.316763\pi$
$812$	−3.60306	+	11.0891i	−0.126443	+	0.389151i
$813$	4.55717	−	14.0255i	0.159827	−	0.491897i
$814$	−4.67840	−	14.3986i	−0.163978	−	0.504672i
$815$	−4.10515	−	30.1814i	−0.143797	−	1.05721i
$816$	3.22465	−	9.92446i	0.112885	−	0.347425i
$817$	−1.75757	−	1.27695i	−0.0614894	−	0.0446747i
$818$	0.276865			0.00968037
$819$	−88.0326	−	63.9594i	−3.07611	−	2.23492i
$820$	−16.8596	−	17.6145i	−0.588762	−	0.615123i
$821$	18.6681	−	13.5631i	0.651520	−	0.473357i	−0.212269	−	0.977211i	$-0.568085\pi$
$821$	18.6681	−	13.5631i	0.651520	−	0.473357i	0.863789	+	0.503854i	$0.168085\pi$
$822$	−35.3251	+	25.6652i	−1.23210	+	0.895177i
$823$	13.7964	+	42.4609i	0.480912	+	1.48009i	0.837816	+	0.545953i	$0.183832\pi$
$823$	13.7964	+	42.4609i	0.480912	+	1.48009i	−0.356904	+	0.934141i	$0.616168\pi$
$824$	−12.2763			−0.427665
$825$	−50.0937	+	13.8839i	−1.74404	+	0.483377i
$826$	−4.17336			−0.145210
$827$	1.95898	+	6.02912i	0.0681204	+	0.209653i	0.979322	−	0.202308i	$-0.0648441\pi$
$827$	1.95898	+	6.02912i	0.0681204	+	0.209653i	−0.911202	+	0.411961i	$0.864844\pi$
$828$	−9.91912	+	7.20666i	−0.344713	+	0.250449i
$829$	−41.4495	+	30.1148i	−1.43960	+	1.04593i	−0.451476	+	0.892283i	$0.649102\pi$
$829$	−41.4495	+	30.1148i	−1.43960	+	1.04593i	−0.988126	+	0.153649i	$0.950898\pi$
$830$	−1.61443	−	11.8694i	−0.0560375	−	0.411993i
$831$	42.3765	+	30.7883i	1.47002	+	1.06803i
$832$	4.52059			0.156723
$833$	−20.4465	−	14.8552i	−0.708428	−	0.514703i
$834$	−16.3409	+	50.2923i	−0.565841	+	1.74148i
$835$	−9.57489	−	1.73218i	−0.331353	−	0.0599446i
$836$	1.05107	+	3.23487i	0.0363521	+	0.111880i
$837$	23.7348	−	73.0482i	0.820394	−	2.52491i
$838$	−2.24175	+	6.89939i	−0.0774398	+	0.238335i
$839$	3.86809	+	11.9048i	0.133541	+	0.410998i	0.995360	−	0.0962182i	$-0.0306746\pi$
$839$	3.86809	+	11.9048i	0.133541	+	0.410998i	−0.861819	+	0.507216i	$0.830675\pi$
$840$	−23.3635	+	11.2670i	−0.806116	+	0.388748i
$841$	−6.04464	+	18.6035i	−0.208436	+	0.641499i
$842$	−1.43301	−	1.04115i	−0.0493849	−	0.0358802i
$843$	−3.79869			−0.130834
$844$	−13.3856	−	9.72520i	−0.460751	−	0.334755i
$845$	−16.3613	−	2.95990i	−0.562845	−	0.101824i
$846$	−59.6204	+	43.3168i	−2.04979	+	1.48926i
$847$	−1.74743	+	1.26958i	−0.0600424	+	0.0436233i
$848$	−2.67457	−	8.23147i	−0.0918450	−	0.282670i
$849$	−96.2148			−3.30208
$850$	9.41944	+	14.2360i	0.323084	+	0.488290i
$851$	8.60424			0.294949
$852$	−13.0912	−	40.2906i	−0.448498	−	1.38033i
$853$	32.3041	−	23.4703i	1.10607	−	0.803607i	0.124030	−	0.992278i	$-0.460418\pi$
$853$	32.3041	−	23.4703i	1.10607	−	0.803607i	0.982040	+	0.188671i	$0.0604181\pi$
$854$	27.5453	−	20.0128i	0.942579	−	0.684824i
$855$	−6.71381	+	12.4927i	−0.229608	+	0.427242i
$856$	6.87440	+	4.99454i	0.234962	+	0.170710i
$857$	−4.46055			−0.152369			−0.0761847	−	0.997094i	$-0.524274\pi$
$857$	−4.46055			−0.152369			−0.0761847	+	0.997094i	$0.524274\pi$
$858$	38.0222	+	27.6248i	1.29806	+	0.943094i
$859$	−1.99847	+	6.15065i	−0.0681868	+	0.209857i	−0.979344	−	0.202202i	$-0.935190\pi$
$859$	−1.99847	+	6.15065i	−0.0681868	+	0.209857i	0.911157	+	0.412059i	$0.135190\pi$
$860$	−2.29962	+	4.27901i	−0.0784163	+	0.145913i
$861$	−39.0873	−	120.298i	−1.33209	−	4.09975i
$862$	−1.51933	+	4.67602i	−0.0517486	+	0.159266i
$863$	−4.70238	+	14.4724i	−0.160071	+	0.492648i	−0.998639	−	0.0521486i	$-0.983393\pi$
$863$	−4.70238	+	14.4724i	−0.160071	+	0.492648i	0.838568	+	0.544796i	$0.183393\pi$
$864$	−3.15720	−	9.71685i	−0.107410	−	0.330574i
$865$	−6.00325	−	6.27204i	−0.204116	−	0.213256i
$866$	−2.93546	+	9.03442i	−0.0997511	+	0.307002i
$867$	13.2158	+	9.60187i	0.448833	+	0.326096i
$868$	28.5303			0.968383
$869$	−22.4072	−	16.2798i	−0.760111	−	0.552253i
$870$	18.9139	−	9.12119i	0.641241	−	0.309237i
$871$	−7.48575	+	5.43872i	−0.253645	+	0.184284i
$872$	−14.3806	+	10.4481i	−0.486988	+	0.353818i
$873$	−2.69799	−	8.30354i	−0.0913130	−	0.281032i
$874$	−1.93307			−0.0653871
$875$	9.37383	−	41.3821i	0.316893	−	1.39897i
$876$	−49.1803			−1.66165
$877$	−2.08888	−	6.42890i	−0.0705363	−	0.217089i	0.909574	−	0.415542i	$-0.136408\pi$
$877$	−2.08888	−	6.42890i	−0.0705363	−	0.217089i	−0.980110	+	0.198454i	$0.936408\pi$
$878$	4.23556	−	3.07731i	0.142943	−	0.103854i
$879$	74.4987	−	54.1265i	2.51278	−	1.82564i
$880$	6.85064	−	3.30371i	0.230935	−	0.111368i
$881$	26.3418	+	19.1384i	0.887476	+	0.644789i	0.935219	−	0.354070i	$-0.115203\pi$
$881$	26.3418	+	19.1384i	0.887476	+	0.644789i	−0.0477424	+	0.998860i	$0.515203\pi$
$882$	−46.9528			−1.58098
$883$	5.17992	+	3.76343i	0.174318	+	0.126650i	0.671523	−	0.740983i	$-0.265640\pi$
$883$	5.17992	+	3.76343i	0.174318	+	0.126650i	−0.497205	+	0.867633i	$0.665640\pi$
$884$	4.76918	−	14.6780i	0.160405	−	0.493676i
$885$	5.19694	+	5.42963i	0.174693	+	0.182515i
$886$	5.96628	+	18.3623i	0.200441	+	0.616895i
$887$	16.8896	−	51.9808i	0.567096	−	1.74534i	−0.0945427	−	0.995521i	$-0.530139\pi$
$887$	16.8896	−	51.9808i	0.567096	−	1.74534i	0.661639	−	0.749822i	$-0.269861\pi$
$888$	−4.20417	+	12.9391i	−0.141083	+	0.434208i
$889$	13.8276	+	42.5570i	0.463763	+	1.42732i
$890$	3.86633	−	7.19427i	0.129600	−	0.241152i
$891$	12.8240	−	39.4681i	0.429619	−	1.32223i
$892$	14.9177	+	10.8383i	0.499480	+	0.362894i
$893$	−11.6190			−0.388816
$894$	−16.4818	−	11.9747i	−0.551233	−	0.400494i
$895$	14.2853	−	26.5813i	0.477503	−	0.888513i
$896$	3.07030	−	2.23070i	0.102571	−	0.0745225i
$897$	−21.6090	+	15.6999i	−0.721504	+	0.524203i
$898$	−2.90626	−	8.94456i	−0.0969833	−	0.298484i
$899$	−23.0967			−0.770319
$900$	29.7030	+	11.1107i	0.990100	+	0.370357i
$901$	−29.5486			−0.984408
$902$	11.4612	+	35.2739i	0.381615	+	1.17449i
$903$	−20.3877	+	14.8125i	−0.678461	+	0.492930i
$904$	1.31063	−	0.952232i	0.0435911	−	0.0316708i
$905$	5.38243	+	0.973730i	0.178918	+	0.0323679i
$906$	−26.3079	−	19.1138i	−0.874022	−	0.635014i
$907$	28.6925			0.952717			0.476359	−	0.879251i	$-0.341956\pi$
$907$	28.6925			0.952717			0.476359	+	0.879251i	$0.341956\pi$
$908$	−1.48358	−	1.07789i	−0.0492344	−	0.0357709i
$909$	25.1062	−	77.2688i	0.832718	−	2.56284i
$910$	−34.5540	+	16.6636i	−1.14545	+	0.552393i
$911$	5.37460	+	16.5413i	0.178068	+	0.548038i	0.999760	−	0.0218939i	$-0.00696960\pi$
$911$	5.37460	+	16.5413i	0.178068	+	0.548038i	−0.821692	+	0.569932i	$0.806970\pi$
$912$	0.944531	−	2.90697i	0.0312766	−	0.0962593i
$913$	−5.63063	+	17.3293i	−0.186347	+	0.573516i
$914$	5.06333	+	15.5833i	0.167480	+	0.515451i
$915$	−60.3382	−	10.9157i	−1.99472	−	0.360862i
$916$	−1.35950	+	4.18412i	−0.0449192	+	0.138247i
$917$	1.74294	+	1.26632i	0.0575568	+	0.0418175i
$918$	−34.8807			−1.15124
$919$	28.2354	+	20.5142i	0.931399	+	0.676701i	0.946335	−	0.323187i	$-0.104754\pi$
$919$	28.2354	+	20.5142i	0.931399	+	0.676701i	−0.0149357	+	0.999888i	$0.504754\pi$
$920$	0.582561	+	4.28304i	0.0192065	+	0.141208i
$921$	−42.5046	+	30.8814i	−1.40058	+	1.01758i
$922$	−3.39538	+	2.46689i	−0.111821	+	0.0812426i
$923$	−19.3616	−	59.5889i	−0.637295	−	1.96139i
$924$	39.4555			1.29799
$925$	−12.2807	−	18.5603i	−0.403787	−	0.610259i
$926$	−14.5760			−0.478999
$927$	24.0612	+	74.0527i	0.790273	+	2.43221i
$928$	−2.48556	+	1.80586i	−0.0815925	+	0.0592804i
$929$	−6.54324	+	4.75394i	−0.214677	+	0.155972i	−0.689927	−	0.723879i	$-0.742357\pi$
$929$	−6.54324	+	4.75394i	−0.214677	+	0.155972i	0.475250	+	0.879851i	$0.342357\pi$
$930$	−35.5278	−	37.1185i	−1.16500	−	1.21716i
$931$	−5.98896	−	4.35124i	−0.196280	−	0.142606i
$932$	−17.9605			−0.588315
$933$	−46.7527	−	33.9678i	−1.53062	−	1.11206i
$934$	−1.07476	+	3.30776i	−0.0351671	+	0.108233i
$935$	−3.49954	−	25.7289i	−0.114447	−	0.841425i
$936$	−8.86024	−	27.2690i	−0.289606	−	0.891315i
$937$	12.0575	−	37.1093i	0.393903	−	1.21231i	−0.535910	−	0.844275i	$-0.680031\pi$
$937$	12.0575	−	37.1093i	0.393903	−	1.21231i	0.929813	−	0.368033i	$-0.119969\pi$
$938$	−2.40042	+	7.38774i	−0.0783766	+	0.241218i
$939$	−8.04145	−	24.7490i	−0.262423	−	0.807655i
$940$	3.50158	+	25.7439i	0.114209	+	0.839673i
$941$	11.7483	−	36.1577i	0.382985	−	1.17871i	−0.554946	−	0.831886i	$-0.687261\pi$
$941$	11.7483	−	36.1577i	0.382985	−	1.17871i	0.937931	−	0.346821i	$-0.112739\pi$
$942$	5.01802	+	3.64581i	0.163496	+	0.118787i
$943$	−21.0787			−0.686417
$944$	−0.889654	−	0.646371i	−0.0289558	−	0.0210376i
$945$	59.9505	+	62.6347i	1.95019	+	2.03751i
$946$	5.97809	−	4.34333i	0.194364	−	0.141214i
$947$	−37.6795	+	27.3758i	−1.22442	+	0.889593i	−0.996459	−	0.0840772i	$-0.973206\pi$
$947$	−37.6795	+	27.3758i	−1.22442	+	0.889593i	−0.227961	+	0.973670i	$0.573206\pi$
$948$	7.69122	+	23.6711i	0.249799	+	0.768803i
$949$	−72.7365			−2.36113
$950$	2.75904	+	4.16985i	0.0895152	+	0.135288i
$951$	−89.8765			−2.91445
$952$	−4.00379	−	12.3224i	−0.129764	−	0.399372i
$953$	29.7130	−	21.5877i	0.962498	−	0.699295i	0.00876817	−	0.999962i	$-0.497209\pi$
$953$	29.7130	−	21.5877i	0.962498	−	0.699295i	0.953729	+	0.300666i	$0.0972090\pi$
$954$	−44.4116	+	32.2669i	−1.43788	+	1.04468i
$955$	−3.90011	−	28.6739i	−0.126205	−	0.927867i
$956$	4.85131	+	3.52468i	0.156902	+	0.113996i
$957$	−31.9412			−1.03251
$958$	24.4158	+	17.7391i	0.788838	+	0.573124i
$959$	−16.7532	+	51.5610i	−0.540988	+	1.66499i
$960$	−6.72552	−	1.21671i	−0.217065	−	0.0392690i
$961$	7.88473	+	24.2667i	0.254346	+	0.782797i
$962$	−6.21788	+	19.1367i	−0.200472	+	0.616990i
$963$	16.6543	−	51.2568i	0.536678	−	1.65173i
$964$	6.96571	+	21.4382i	0.224350	+	0.690479i
$965$	−33.5464	+	16.1777i	−1.07990	+	0.520778i
$966$	−6.92927	+	21.3261i	−0.222945	+	0.686156i
$967$	−49.6511	−	36.0736i	−1.59667	−	1.16005i	−0.893535	−	0.448993i	$-0.851783\pi$
$967$	−49.6511	−	36.0736i	−1.59667	−	1.16005i	−0.703136	−	0.711056i	$-0.748217\pi$
$968$	−0.569140			−0.0182928
$969$	−8.44225	−	6.13365i	−0.271204	−	0.197041i
$970$	−3.02888	−	0.547950i	−0.0972514	−	0.0175936i
$971$	−2.53489	+	1.84170i	−0.0813484	+	0.0591031i	−0.627716	−	0.778442i	$-0.716010\pi$
$971$	−2.53489	+	1.84170i	−0.0813484	+	0.0591031i	0.546368	+	0.837545i	$0.316010\pi$
$972$	−5.37345	+	3.90404i	−0.172353	+	0.125222i
$973$	20.2893	+	62.4439i	0.650444	+	2.00186i
$974$	35.4193			1.13491
$975$	64.7086	+	24.2049i	2.07233	+	0.775177i
$976$	8.97153			0.287172
$977$	−4.25982	−	13.1104i	−0.136284	−	0.419438i	0.859504	−	0.511129i	$-0.170773\pi$
$977$	−4.25982	−	13.1104i	−0.136284	−	0.419438i	−0.995787	+	0.0916915i	$0.970773\pi$
$978$	33.6842	−	24.4730i	1.07710	−	0.782561i
$979$	−10.0509	+	7.30242i	−0.321229	+	0.233386i
$980$	−7.83602	+	14.5809i	−0.250312	+	0.465768i
$981$	91.2104	+	66.2682i	2.91212	+	2.11578i
$982$	27.7731			0.886275
$983$	−22.2476	−	16.1638i	−0.709588	−	0.515546i	0.173453	−	0.984842i	$-0.444508\pi$
$983$	−22.2476	−	16.1638i	−0.709588	−	0.515546i	−0.883041	+	0.469296i	$0.844508\pi$
$984$	10.2994	−	31.6983i	0.328333	−	1.01051i
$985$	17.8956	−	33.2993i	0.570203	−	1.06100i
$986$	3.24127	+	9.97560i	0.103223	+	0.317688i
$987$	−41.6494	+	128.184i	−1.32572	+	4.08013i
$988$	1.39694	−	4.29934i	0.0444426	−	0.136780i
$989$	1.29773	+	3.99400i	0.0412654	+	0.127002i
$990$	−33.3556	−	34.8491i	−1.06011	−	1.10758i
$991$	−4.39806	+	13.5358i	−0.139709	+	0.429980i	−0.996293	−	0.0860282i	$-0.972582\pi$
$991$	−4.39806	+	13.5358i	−0.139709	+	0.429980i	0.856584	+	0.516008i	$0.172582\pi$
$992$	6.08193	+	4.41878i	0.193102	+	0.140296i
$993$	−41.7418			−1.32463
$994$	−42.5544	−	30.9176i	−1.34974	−	0.980645i
$995$	−53.2729	+	25.6908i	−1.68886	+	0.814452i
$996$	13.2469	−	9.62447i	0.419746	−	0.304963i
$997$	5.96720	−	4.33542i	0.188983	−	0.137304i	−0.489271	−	0.872132i	$-0.662737\pi$
$997$	5.96720	−	4.33542i	0.188983	−	0.137304i	0.678254	+	0.734828i	$0.262737\pi$
$998$	10.2181	+	31.4480i	0.323447	+	0.995468i
$999$	45.4761			1.43880

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	950.2.h.e.381.2	✓	44
25.21	even	5	inner	950.2.h.e.571.2	yes	44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
950.2.h.e.381.2	✓	44	1.1	even	1	trivial
950.2.h.e.571.2	yes	44	25.21	even	5	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 950 = 2 \cdot 5^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	950.h (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.309017 - 0.951057i) q^{2} +(-2.47282 + 1.79661i) q^{3} +(-0.809017 + 0.587785i) q^{4} +(2.01410 - 0.971294i) q^{5} +(2.47282 + 1.79661i) q^{6} +3.79510 q^{7} +(0.809017 + 0.587785i) q^{8} +(1.95997 - 6.03218i) q^{9} +O(q^{10})\)	\(q+(-0.309017 - 0.951057i) q^{2} +(-2.47282 + 1.79661i) q^{3} +(-0.809017 + 0.587785i) q^{4} +(2.01410 - 0.971294i) q^{5} +(2.47282 + 1.79661i) q^{6} +3.79510 q^{7} +(0.809017 + 0.587785i) q^{8} +(1.95997 - 6.03218i) q^{9} +(-1.54615 - 1.61537i) q^{10} +(1.05107 + 3.23487i) q^{11} +(0.944531 - 2.90697i) q^{12} +(1.39694 - 4.29934i) q^{13} +(-1.17275 - 3.60935i) q^{14} +(-3.23546 + 6.02037i) q^{15} +(0.309017 - 0.951057i) q^{16} +(-2.76200 - 2.00671i) q^{17} -6.34261 q^{18} +(-0.809017 - 0.587785i) q^{19} +(-1.05853 + 1.96965i) q^{20} +(-9.38457 + 6.81829i) q^{21} +(2.75174 - 1.99926i) q^{22} +(0.597352 + 1.83846i) q^{23} -3.05657 q^{24} +(3.11317 - 3.91256i) q^{25} -4.52059 q^{26} +(3.15720 + 9.71685i) q^{27} +(-3.07030 + 2.23070i) q^{28} +(2.48556 - 1.80586i) q^{29} +(6.72552 + 1.21671i) q^{30} +(-6.08193 - 4.41878i) q^{31} -1.00000 q^{32} +(-8.41089 - 6.11087i) q^{33} +(-1.05499 + 3.24693i) q^{34} +(7.64369 - 3.68616i) q^{35} +(1.95997 + 6.03218i) q^{36} +(1.37546 - 4.23322i) q^{37} +(-0.309017 + 0.951057i) q^{38} +(4.26984 + 13.1412i) q^{39} +(2.20035 + 0.398063i) q^{40} +(-3.36960 + 10.3706i) q^{41} +(9.38457 + 6.81829i) q^{42} +2.17247 q^{43} +(-2.75174 - 1.99926i) q^{44} +(-1.91144 - 14.0531i) q^{45} +(1.56389 - 1.13623i) q^{46} +(9.39999 - 6.82949i) q^{47} +(0.944531 + 2.90697i) q^{48} +7.40276 q^{49} +(-4.68309 - 1.75176i) q^{50} +10.4352 q^{51} +(1.39694 + 4.29934i) q^{52} +(7.00211 - 5.08733i) q^{53} +(8.26564 - 6.00534i) q^{54} +(5.25897 + 5.49444i) q^{55} +(3.07030 + 2.23070i) q^{56} +3.05657 q^{57} +(-2.48556 - 1.80586i) q^{58} +(0.339818 - 1.04585i) q^{59} +(-0.921145 - 6.77233i) q^{60} +(2.77235 + 8.53243i) q^{61} +(-2.32309 + 7.14974i) q^{62} +(7.43829 - 22.8927i) q^{63} +(0.309017 + 0.951057i) q^{64} +(-1.36235 - 10.0161i) q^{65} +(-3.21268 + 9.88760i) q^{66} +(-1.65592 - 1.20310i) q^{67} +3.41402 q^{68} +(-4.78013 - 3.47297i) q^{69} +(-5.86778 - 6.13050i) q^{70} +(11.2130 - 8.14671i) q^{71} +(5.13128 - 3.72809i) q^{72} +(-4.97210 - 15.3025i) q^{73} -4.45107 q^{74} +(-0.668973 + 15.2682i) q^{75} +1.00000 q^{76} +(3.98892 + 12.2766i) q^{77} +(11.1786 - 8.12172i) q^{78} +(-6.58774 + 4.78627i) q^{79} +(-0.301366 - 2.21567i) q^{80} +(-9.87067 - 7.17146i) q^{81} +10.9043 q^{82} +(4.33393 + 3.14878i) q^{83} +(3.58459 - 11.0322i) q^{84} +(-7.51205 - 1.35900i) q^{85} +(-0.671330 - 2.06614i) q^{86} +(-2.90190 + 8.93114i) q^{87} +(-1.05107 + 3.23487i) q^{88} +(1.12870 + 3.47379i) q^{89} +(-12.7746 + 6.16054i) q^{90} +(5.30152 - 16.3164i) q^{91} +(-1.56389 - 1.13623i) q^{92} +22.9783 q^{93} +(-9.39999 - 6.82949i) q^{94} +(-2.20035 - 0.398063i) q^{95} +(2.47282 - 1.79661i) q^{96} +(1.11365 - 0.809111i) q^{97} +(-2.28758 - 7.04045i) q^{98} +21.5734 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q + 11 q^{2} - q^{3} - 11 q^{4} - 5 q^{5} + q^{6} + 28 q^{7} + 11 q^{8} - 8 q^{9}+O(q^{10}) \) 44 * q + 11 * q^2 - q^3 - 11 * q^4 - 5 * q^5 + q^6 + 28 * q^7 + 11 * q^8 - 8 * q^9	\( 44 q + 11 q^{2} - q^{3} - 11 q^{4} - 5 q^{5} + q^{6} + 28 q^{7} + 11 q^{8} - 8 q^{9} + 5 q^{10} - 6 q^{12} - 10 q^{13} + 12 q^{14} - 11 q^{16} - 20 q^{17} - 42 q^{18} - 11 q^{19} + 5 q^{20} - 3 q^{21} - 10 q^{22} - 6 q^{23} - 14 q^{24} - 15 q^{25} - 40 q^{26} + 5 q^{27} - 2 q^{28} + 6 q^{29} - 5 q^{31} - 44 q^{32} - 36 q^{33} - 10 q^{34} - 8 q^{36} - 10 q^{37} + 11 q^{38} + 39 q^{39} - 22 q^{41} + 3 q^{42} + 68 q^{43} + 10 q^{44} + 20 q^{45} + 6 q^{46} + 19 q^{47} - 6 q^{48} + 40 q^{49} - 30 q^{50} + 86 q^{51} - 10 q^{52} + 30 q^{54} + 2 q^{56} + 14 q^{57} - 6 q^{58} - 4 q^{59} + 15 q^{60} + 26 q^{61} - 15 q^{62} - 41 q^{63} - 11 q^{64} + 30 q^{65} - 4 q^{66} - 59 q^{67} + 20 q^{68} - 59 q^{69} - 25 q^{70} + 30 q^{71} + 13 q^{72} - 38 q^{73} - 50 q^{74} - 15 q^{75} + 44 q^{76} + 29 q^{77} + 16 q^{78} + 3 q^{79} + 5 q^{80} - 54 q^{81} - 8 q^{82} + 9 q^{83} + 7 q^{84} + 12 q^{86} - 43 q^{87} + 33 q^{89} - 6 q^{91} - 6 q^{92} + 84 q^{93} - 19 q^{94} + q^{96} + 30 q^{97} - 15 q^{98} - 54 q^{99}+O(q^{100}) \) 44 * q + 11 * q^2 - q^3 - 11 * q^4 - 5 * q^5 + q^6 + 28 * q^7 + 11 * q^8 - 8 * q^9 + 5 * q^10 - 6 * q^12 - 10 * q^13 + 12 * q^14 - 11 * q^16 - 20 * q^17 - 42 * q^18 - 11 * q^19 + 5 * q^20 - 3 * q^21 - 10 * q^22 - 6 * q^23 - 14 * q^24 - 15 * q^25 - 40 * q^26 + 5 * q^27 - 2 * q^28 + 6 * q^29 - 5 * q^31 - 44 * q^32 - 36 * q^33 - 10 * q^34 - 8 * q^36 - 10 * q^37 + 11 * q^38 + 39 * q^39 - 22 * q^41 + 3 * q^42 + 68 * q^43 + 10 * q^44 + 20 * q^45 + 6 * q^46 + 19 * q^47 - 6 * q^48 + 40 * q^49 - 30 * q^50 + 86 * q^51 - 10 * q^52 + 30 * q^54 + 2 * q^56 + 14 * q^57 - 6 * q^58 - 4 * q^59 + 15 * q^60 + 26 * q^61 - 15 * q^62 - 41 * q^63 - 11 * q^64 + 30 * q^65 - 4 * q^66 - 59 * q^67 + 20 * q^68 - 59 * q^69 - 25 * q^70 + 30 * q^71 + 13 * q^72 - 38 * q^73 - 50 * q^74 - 15 * q^75 + 44 * q^76 + 29 * q^77 + 16 * q^78 + 3 * q^79 + 5 * q^80 - 54 * q^81 - 8 * q^82 + 9 * q^83 + 7 * q^84 + 12 * q^86 - 43 * q^87 + 33 * q^89 - 6 * q^91 - 6 * q^92 + 84 * q^93 - 19 * q^94 + q^96 + 30 * q^97 - 15 * q^98 - 54 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more