LMFDB - Embedded newform 950.2.h.e.191.7

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			191.7
Character	$\chi$	$=$	950.191
Dual form			950.2.h.e.761.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.809017 + 0.587785i) q^{2} +(0.401228 + 1.23485i) q^{3} +(0.309017 + 0.951057i) q^{4} +(1.49048 + 1.66687i) q^{5} +(-0.401228 + 1.23485i) q^{6} -2.35656 q^{7} +(-0.309017 + 0.951057i) q^{8} +(1.06317 - 0.772440i) q^{9} +O(q^{10})$	\(q+(0.809017 + 0.587785i) q^{2} +(0.401228 + 1.23485i) q^{3} +(0.309017 + 0.951057i) q^{4} +(1.49048 + 1.66687i) q^{5} +(-0.401228 + 1.23485i) q^{6} -2.35656 q^{7} +(-0.309017 + 0.951057i) q^{8} +(1.06317 - 0.772440i) q^{9} +(0.226063 + 2.22461i) q^{10} +(-1.33001 - 0.966306i) q^{11} +(-1.05043 + 0.763181i) q^{12} +(-4.20336 + 3.05392i) q^{13} +(-1.90650 - 1.38515i) q^{14} +(-1.46032 + 2.50932i) q^{15} +(-0.809017 + 0.587785i) q^{16} +(-1.59694 + 4.91486i) q^{17} +1.31415 q^{18} +(0.309017 - 0.951057i) q^{19} +(-1.12470 + 1.93263i) q^{20} +(-0.945517 - 2.91000i) q^{21} +(-0.508017 - 1.56352i) q^{22} +(3.21222 + 2.33381i) q^{23} -1.29840 q^{24} +(-0.556922 + 4.96889i) q^{25} -5.19563 q^{26} +(4.53171 + 3.29248i) q^{27} +(-0.728216 - 2.24122i) q^{28} +(-0.627470 - 1.93116i) q^{29} +(-2.65637 + 1.17173i) q^{30} +(-0.781822 + 2.40620i) q^{31} -1.00000 q^{32} +(0.659610 - 2.03007i) q^{33} +(-4.18083 + 3.03755i) q^{34} +(-3.51241 - 3.92808i) q^{35} +(1.06317 + 0.772440i) q^{36} +(0.0385152 - 0.0279829i) q^{37} +(0.809017 - 0.587785i) q^{38} +(-5.45765 - 3.96521i) q^{39} +(-2.04587 + 0.902442i) q^{40} +(8.70066 - 6.32140i) q^{41} +(0.945517 - 2.91000i) q^{42} +5.73258 q^{43} +(0.508017 - 1.56352i) q^{44} +(2.87220 + 0.620863i) q^{45} +(1.22696 + 3.77619i) q^{46} +(-2.25611 - 6.94360i) q^{47} +(-1.05043 - 0.763181i) q^{48} -1.44664 q^{49} +(-3.37120 + 3.69256i) q^{50} -6.70987 q^{51} +(-4.20336 - 3.05392i) q^{52} +(2.75450 + 8.47748i) q^{53} +(1.73096 + 5.32735i) q^{54} +(-0.371643 - 3.65721i) q^{55} +(0.728216 - 2.24122i) q^{56} +1.29840 q^{57} +(0.627470 - 1.93116i) q^{58} +(-0.677743 + 0.492409i) q^{59} +(-2.83777 - 0.613422i) q^{60} +(0.747403 + 0.543020i) q^{61} +(-2.04684 + 1.48711i) q^{62} +(-2.50543 + 1.82030i) q^{63} +(-0.809017 - 0.587785i) q^{64} +(-11.3555 - 2.45464i) q^{65} +(1.72688 - 1.25465i) q^{66} +(2.91801 - 8.98072i) q^{67} -5.16779 q^{68} +(-1.59308 + 4.90301i) q^{69} +(-0.532731 - 5.24242i) q^{70} +(-3.43146 - 10.5609i) q^{71} +(0.406096 + 1.24983i) q^{72} +(2.38782 + 1.73486i) q^{73} +0.0476074 q^{74} +(-6.35930 + 1.30594i) q^{75} +1.00000 q^{76} +(3.13423 + 2.27715i) q^{77} +(-2.08464 - 6.41585i) q^{78} +(3.60413 + 11.0924i) q^{79} +(-2.18559 - 0.472444i) q^{80} +(-1.02919 + 3.16753i) q^{81} +10.7546 q^{82} +(2.00142 - 6.15974i) q^{83} +(2.47540 - 1.79848i) q^{84} +(-10.5727 + 4.66363i) q^{85} +(4.63776 + 3.36953i) q^{86} +(2.13293 - 1.54967i) q^{87} +(1.33001 - 0.966306i) q^{88} +(12.5447 + 9.11425i) q^{89} +(1.95872 + 2.19052i) q^{90} +(9.90545 - 7.19673i) q^{91} +(-1.22696 + 3.77619i) q^{92} -3.28499 q^{93} +(2.25611 - 6.94360i) q^{94} +(2.04587 - 0.902442i) q^{95} +(-0.401228 - 1.23485i) q^{96} +(2.84684 + 8.76167i) q^{97} +(-1.17035 - 0.850312i) q^{98} -2.16044 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 $\left(\mathbb{Z}/950\mathbb{Z}\right)^\times$.

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

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 $

$2$	0.809017	+	0.587785i	0.572061	+	0.415627i
$2$	0.809017	+	0.587785i	0.572061	+	0.415627i
$3$	0.401228	+	1.23485i	0.231649	+	0.712943i	0.997548	+	0.0699821i	$0.0222942\pi$
$3$	0.401228	+	1.23485i	0.231649	+	0.712943i	−0.765899	+	0.642961i	$0.777706\pi$
$4$	0.309017	+	0.951057i	0.154508	+	0.475528i
$5$	1.49048	+	1.66687i	0.666564	+	0.745448i
$5$	1.49048	+	1.66687i	0.666564	+	0.745448i
$6$	−0.401228	+	1.23485i	−0.163801	+	0.504127i
$7$	−2.35656			−0.890695			−0.445347	−	0.895358i	$-0.646920\pi$
$7$	−2.35656			−0.890695			−0.445347	+	0.895358i	$0.646920\pi$
$8$	−0.309017	+	0.951057i	−0.109254	+	0.336249i
$9$	1.06317	−	0.772440i	0.354391	−	0.257480i
$10$	0.226063	+	2.22461i	0.0714875	+	0.703484i
$11$	−1.33001	−	0.966306i	−0.401012	−	0.291352i	0.368941	−	0.929453i	$-0.379720\pi$
$11$	−1.33001	−	0.966306i	−0.401012	−	0.291352i	−0.769953	+	0.638101i	$0.779720\pi$
$12$	−1.05043	+	0.763181i	−0.303233	+	0.220311i
$13$	−4.20336	+	3.05392i	−1.16580	+	0.847004i	−0.990500	−	0.137511i	$-0.956090\pi$
$13$	−4.20336	+	3.05392i	−1.16580	+	0.847004i	−0.175301	+	0.984515i	$0.556090\pi$
$14$	−1.90650	−	1.38515i	−0.509532	−	0.370197i
$15$	−1.46032	+	2.50932i	−0.377053	+	0.647905i
$16$	−0.809017	+	0.587785i	−0.202254	+	0.146946i
$17$	−1.59694	+	4.91486i	−0.387314	+	1.19203i	0.547474	+	0.836823i	$0.315590\pi$
$17$	−1.59694	+	4.91486i	−0.387314	+	1.19203i	−0.934788	+	0.355207i	$0.884410\pi$
$18$	1.31415			0.309749
$19$	0.309017	−	0.951057i	0.0708934	−	0.218187i
$19$	0.309017	−	0.951057i	0.0708934	−	0.218187i
$20$	−1.12470	+	1.93263i	−0.251492	+	0.432148i
$21$	−0.945517	−	2.91000i	−0.206329	−	0.635015i
$22$	−0.508017	−	1.56352i	−0.108310	−	0.333343i
$23$	3.21222	+	2.33381i	0.669793	+	0.486633i	0.869956	−	0.493129i	$-0.164147\pi$
$23$	3.21222	+	2.33381i	0.669793	+	0.486633i	−0.200163	+	0.979763i	$0.564147\pi$
$24$	−1.29840			−0.265035
$25$	−0.556922	+	4.96889i	−0.111384	+	0.993777i
$26$	−5.19563			−1.01895
$27$	4.53171	+	3.29248i	0.872128	+	0.633638i
$28$	−0.728216	−	2.24122i	−0.137620	−	0.423551i
$29$	−0.627470	−	1.93116i	−0.116518	−	0.358607i	0.875742	−	0.482779i	$-0.160372\pi$
$29$	−0.627470	−	1.93116i	−0.116518	−	0.358607i	−0.992261	+	0.124172i	$0.960372\pi$
$30$	−2.65637	+	1.17173i	−0.484984	+	0.213928i
$31$	−0.781822	+	2.40620i	−0.140419	+	0.432166i	−0.996394	−	0.0848523i	$-0.972958\pi$
$31$	−0.781822	+	2.40620i	−0.140419	+	0.432166i	0.855974	+	0.517019i	$0.172958\pi$
$32$	−1.00000			−0.176777
$33$	0.659610	−	2.03007i	0.114823	−	0.353390i
$34$	−4.18083	+	3.03755i	−0.717007	+	0.520936i
$35$	−3.51241	−	3.92808i	−0.593705	−	0.663966i
$36$	1.06317	+	0.772440i	0.177195	+	0.128740i
$37$	0.0385152	−	0.0279829i	0.00633186	−	0.00460036i	−0.584615	−	0.811311i	$-0.698754\pi$
$37$	0.0385152	−	0.0279829i	0.00633186	−	0.00460036i	0.590947	+	0.806711i	$0.298754\pi$
$38$	0.809017	−	0.587785i	0.131240	−	0.0953514i
$39$	−5.45765	−	3.96521i	−0.873923	−	0.634942i
$40$	−2.04587	+	0.902442i	−0.323481	+	0.142689i
$41$	8.70066	−	6.32140i	1.35881	−	0.987237i	0.360295	−	0.932838i	$-0.382676\pi$
$41$	8.70066	−	6.32140i	1.35881	−	0.987237i	0.998519	−	0.0543984i	$-0.0173241\pi$
$42$	0.945517	−	2.91000i	0.145896	−	0.449023i
$43$	5.73258			0.874211			0.437105	−	0.899410i	$-0.356004\pi$
$43$	5.73258			0.874211			0.437105	+	0.899410i	$0.356004\pi$
$44$	0.508017	−	1.56352i	0.0765864	−	0.235709i
$45$	2.87220	+	0.620863i	0.428162	+	0.0925528i
$46$	1.22696	+	3.77619i	0.180905	+	0.556768i
$47$	−2.25611	−	6.94360i	−0.329088	−	1.01283i	−0.969562	−	0.244848i	$-0.921262\pi$
$47$	−2.25611	−	6.94360i	−0.329088	−	1.01283i	0.640474	−	0.767980i	$-0.278738\pi$
$48$	−1.05043	−	0.763181i	−0.151616	−	0.110156i
$49$	−1.44664			−0.206662
$50$	−3.37120	+	3.69256i	−0.476759	+	0.522207i
$51$	−6.70987			−0.939570
$52$	−4.20336	−	3.05392i	−0.582901	−	0.423502i
$53$	2.75450	+	8.47748i	0.378360	+	1.16447i	0.941184	+	0.337894i	$0.109715\pi$
$53$	2.75450	+	8.47748i	0.378360	+	1.16447i	−0.562824	+	0.826576i	$0.690285\pi$
$54$	1.73096	+	5.32735i	0.235554	+	0.724960i
$55$	−0.371643	−	3.65721i	−0.0501123	−	0.493138i
$56$	0.728216	−	2.24122i	0.0973120	−	0.299496i
$57$	1.29840			0.171978
$58$	0.627470	−	1.93116i	0.0823909	−	0.253573i
$59$	−0.677743	+	0.492409i	−0.0882346	+	0.0641062i	−0.631028	−	0.775760i	$-0.717367\pi$
$59$	−0.677743	+	0.492409i	−0.0882346	+	0.0641062i	0.542793	+	0.839866i	$0.317367\pi$
$60$	−2.83777	−	0.613422i	−0.366355	−	0.0791924i
$61$	0.747403	+	0.543020i	0.0956951	+	0.0695266i	0.634604	−	0.772838i	$-0.281163\pi$
$61$	0.747403	+	0.543020i	0.0956951	+	0.0695266i	−0.538909	+	0.842364i	$0.681163\pi$
$62$	−2.04684	+	1.48711i	−0.259948	+	0.188864i
$63$	−2.50543	+	1.82030i	−0.315654	+	0.229336i
$64$	−0.809017	−	0.587785i	−0.101127	−	0.0734732i
$65$	−11.3555	−	2.45464i	−1.40848	−	0.304461i
$66$	1.72688	−	1.25465i	0.212564	−	0.154437i
$67$	2.91801	−	8.98072i	0.356492	−	1.09717i	−0.598647	−	0.801013i	$-0.704295\pi$
$67$	2.91801	−	8.98072i	0.356492	−	1.09717i	0.955139	−	0.296157i	$-0.0957051\pi$
$68$	−5.16779			−0.626687
$69$	−1.59308	+	4.90301i	−0.191785	+	0.590253i
$70$	−0.532731	−	5.24242i	−0.0636736	−	0.626590i
$71$	−3.43146	−	10.5609i	−0.407239	−	1.25335i	−0.919011	−	0.394232i	$-0.871011\pi$
$71$	−3.43146	−	10.5609i	−0.407239	−	1.25335i	0.511772	−	0.859122i	$-0.328989\pi$
$72$	0.406096	+	1.24983i	0.0478588	+	0.147294i
$73$	2.38782	+	1.73486i	0.279474	+	0.203049i	0.718688	−	0.695333i	$-0.244743\pi$
$73$	2.38782	+	1.73486i	0.279474	+	0.203049i	−0.439214	+	0.898382i	$0.644743\pi$
$74$	0.0476074			0.00553425
$75$	−6.35930	+	1.30594i	−0.734309	+	0.150797i
$76$	1.00000			0.114708
$77$	3.13423	+	2.27715i	0.357179	+	0.259506i
$78$	−2.08464	−	6.41585i	−0.236038	−	0.726452i
$79$	3.60413	+	11.0924i	0.405496	+	1.24799i	0.920481	+	0.390788i	$0.127798\pi$
$79$	3.60413	+	11.0924i	0.405496	+	1.24799i	−0.514985	+	0.857199i	$0.672202\pi$
$80$	−2.18559	−	0.472444i	−0.244356	−	0.0528208i
$81$	−1.02919	+	3.16753i	−0.114355	+	0.351948i
$82$	10.7546			1.18765
$83$	2.00142	−	6.15974i	0.219685	−	0.676120i	−0.779103	−	0.626896i	$-0.784325\pi$
$83$	2.00142	−	6.15974i	0.219685	−	0.676120i	0.998788	−	0.0492239i	$-0.0156748\pi$
$84$	2.47540	−	1.79848i	0.270088	−	0.196230i
$85$	−10.5727	+	4.66363i	−1.14677	+	0.505842i
$86$	4.63776	+	3.36953i	0.500102	+	0.363346i
$87$	2.13293	−	1.54967i	0.228675	−	0.166142i
$88$	1.33001	−	0.966306i	0.141779	−	0.103009i
$89$	12.5447	+	9.11425i	1.32973	+	0.966108i	0.999755	+	0.0221196i	$0.00704145\pi$
$89$	12.5447	+	9.11425i	1.32973	+	0.966108i	0.329978	+	0.943989i	$0.392959\pi$
$90$	1.95872	+	2.19052i	0.206467	+	0.230902i
$91$	9.90545	−	7.19673i	1.03837	−	0.754422i
$92$	−1.22696	+	3.77619i	−0.127919	+	0.393695i
$93$	−3.28499			−0.340638
$94$	2.25611	−	6.94360i	0.232700	−	0.716177i
$95$	2.04587	−	0.902442i	0.209902	−	0.0925886i
$96$	−0.401228	−	1.23485i	−0.0409502	−	0.126032i
$97$	2.84684	+	8.76167i	0.289053	+	0.889613i	0.985155	+	0.171670i	$0.0549162\pi$
$97$	2.84684	+	8.76167i	0.289053	+	0.889613i	−0.696102	+	0.717943i	$0.745084\pi$
$98$	−1.17035	−	0.850312i	−0.118224	−	0.0858945i
$99$	−2.16044			−0.217132
$100$	−4.89779	+	1.00581i	−0.489779	+	0.100581i
$101$	18.2284			1.81380			0.906898	−	0.421350i	$-0.138444\pi$
$101$	18.2284			1.81380			0.906898	+	0.421350i	$0.138444\pi$
$102$	−5.42840	−	3.94396i	−0.537492	−	0.390511i
$103$	−2.12872	−	6.55152i	−0.209749	−	0.645541i	−0.999485	−	0.0320937i	$-0.989782\pi$
$103$	−2.12872	−	6.55152i	−0.209749	−	0.645541i	0.789736	−	0.613447i	$-0.210218\pi$
$104$	−1.60554	−	4.94134i	−0.157436	−	0.484538i
$105$	3.44132	−	5.91337i	0.335839	−	0.577085i
$106$	−2.75450	+	8.47748i	−0.267541	+	0.823405i
$107$	0.158490			0.0153218			0.00766089	−	0.999971i	$-0.497561\pi$
$107$	0.158490			0.0153218			0.00766089	+	0.999971i	$0.497561\pi$
$108$	−1.73096	+	5.32735i	−0.166562	+	0.512624i
$109$	−6.71968	+	4.88213i	−0.643629	+	0.467624i	−0.861095	−	0.508444i	$-0.830221\pi$
$109$	−6.71968	+	4.88213i	−0.643629	+	0.467624i	0.217466	+	0.976068i	$0.430221\pi$
$110$	1.84899	−	3.17719i	0.176294	−	0.302933i
$111$	0.0500082	+	0.0363331i	0.00474657	+	0.00344858i
$112$	1.90650	−	1.38515i	0.180147	−	0.130884i
$113$	−2.99198	+	2.17380i	−0.281462	+	0.204494i	−0.719555	−	0.694436i	$-0.755654\pi$
$113$	−2.99198	+	2.17380i	−0.281462	+	0.204494i	0.438093	+	0.898930i	$0.355654\pi$
$114$	1.05043	+	0.763181i	0.0983817	+	0.0714785i
$115$	0.897589	+	8.83286i	0.0837006	+	0.823668i
$116$	1.64274	−	1.19352i	0.152524	−	0.110816i
$117$	−2.10992	+	6.49368i	−0.195063	+	0.600341i
$118$	−0.837736			−0.0771199
$119$	3.76327	−	11.5822i	0.344979	−	1.06173i
$120$	−1.93525	−	2.16427i	−0.176663	−	0.197570i
$121$	−2.56402	−	7.89124i	−0.233093	−	0.717385i
$122$	0.285483	+	0.878625i	0.0258464	+	0.0795470i
$123$	11.2970	+	8.20772i	1.01861	+	0.740065i
$124$	−2.53003			−0.227203
$125$	−9.11258	+	6.47772i	−0.815054	+	0.579385i
$126$	−3.09688			−0.275892
$127$	0.557028	+	0.404705i	0.0494283	+	0.0359117i	0.612225	−	0.790684i	$-0.290275\pi$
$127$	0.557028	+	0.404705i	0.0494283	+	0.0359117i	−0.562797	+	0.826595i	$0.690275\pi$
$128$	−0.309017	−	0.951057i	−0.0273135	−	0.0840623i
$129$	2.30007	+	7.07890i	0.202510	+	0.623263i
$130$	−7.74400	−	8.66046i	−0.679194	−	0.759572i
$131$	4.90654	−	15.1008i	0.428686	−	1.31936i	−0.470734	−	0.882275i	$-0.656011\pi$
$131$	4.90654	−	15.1008i	0.428686	−	1.31936i	0.899420	−	0.437085i	$-0.143989\pi$
$132$	2.13454			0.185788
$133$	−0.728216	+	2.24122i	−0.0631444	+	0.194338i
$134$	7.63946	−	5.55039i	0.659948	−	0.479481i
$135$	1.26629	+	12.4612i	0.108985	+	1.07249i
$136$	−4.18083	−	3.03755i	−0.358503	−	0.260468i
$137$	−2.29932	+	1.67056i	−0.196444	+	0.142725i	−0.681659	−	0.731670i	$-0.738741\pi$
$137$	−2.29932	+	1.67056i	−0.196444	+	0.142725i	0.485215	+	0.874395i	$0.338741\pi$
$138$	−4.17075	+	3.03023i	−0.355038	+	0.257950i
$139$	6.42512	+	4.66812i	0.544971	+	0.395945i	0.825928	−	0.563776i	$-0.190652\pi$
$139$	6.42512	+	4.66812i	0.544971	+	0.395945i	−0.280957	+	0.959720i	$0.590652\pi$
$140$	2.65043	−	4.55434i	0.224002	−	0.384912i
$141$	7.66911	−	5.57193i	0.645856	−	0.469242i
$142$	3.43146	−	10.5609i	0.287962	−	0.886255i
$143$	8.54151			0.714277
$144$	−0.406096	+	1.24983i	−0.0338413	+	0.104153i
$145$	2.28375	−	3.92427i	0.189655	−	0.325893i
$146$	0.912067	+	2.80705i	0.0754832	+	0.232314i
$147$	−0.580432	−	1.78638i	−0.0478732	−	0.147339i
$148$	0.0385152	+	0.0279829i	0.00316593	+	0.00230018i
$149$	−23.1543			−1.89687			−0.948437	−	0.316966i	$-0.897336\pi$
$149$	−23.1543			−1.89687			−0.948437	+	0.316966i	$0.897336\pi$
$150$	−5.91239	−	2.68137i	−0.482745	−	0.218933i
$151$	−4.27440			−0.347846			−0.173923	−	0.984759i	$-0.555644\pi$
$151$	−4.27440			−0.347846			−0.173923	+	0.984759i	$0.555644\pi$
$152$	0.809017	+	0.587785i	0.0656199	+	0.0476757i
$153$	2.09862	+	6.45888i	0.169663	+	0.522170i
$154$	1.19717	+	3.68451i	0.0964708	+	0.296907i
$155$	−5.17612	+	2.28320i	−0.415756	+	0.183391i
$156$	2.08464	−	6.41585i	0.166904	−	0.513679i
$157$	17.1984			1.37258			0.686290	−	0.727328i	$-0.259238\pi$
$157$	17.1984			1.37258			0.686290	+	0.727328i	$0.259238\pi$
$158$	−3.60413	+	11.0924i	−0.286729	+	0.882461i
$159$	−9.36326	+	6.80280i	−0.742555	+	0.539498i
$160$	−1.49048	−	1.66687i	−0.117833	−	0.131778i
$161$	−7.56977	−	5.49976i	−0.596582	−	0.433442i
$162$	−2.69447	+	1.95764i	−0.211697	+	0.153807i
$163$	6.88077	−	4.99917i	0.538943	−	0.391565i	−0.284749	−	0.958602i	$-0.591910\pi$
$163$	6.88077	−	4.99917i	0.538943	−	0.391565i	0.823692	+	0.567037i	$0.191910\pi$
$164$	8.70066	+	6.32140i	0.679407	+	0.493618i
$165$	4.36701	−	1.92630i	0.339971	−	0.149962i
$166$	5.23979	−	3.80693i	0.406687	−	0.295475i
$167$	−4.17894	+	12.8615i	−0.323376	+	0.995250i	0.648792	+	0.760966i	$0.275275\pi$
$167$	−4.17894	+	12.8615i	−0.323376	+	0.995250i	−0.972168	+	0.234284i	$0.924725\pi$
$168$	3.05976			0.236065
$169$	4.32457	−	13.3097i	0.332660	−	1.02382i
$170$	−11.2947	−	2.44149i	−0.866262	−	0.187254i
$171$	−0.406096	−	1.24983i	−0.0310549	−	0.0955772i
$172$	1.77147	+	5.45201i	0.135073	+	0.415712i
$173$	−12.5005	−	9.08213i	−0.950394	−	0.690502i	0.000506058	−	1.00000i	$-0.499839\pi$
$173$	−12.5005	−	9.08213i	−0.950394	−	0.690502i	−0.950900	+	0.309498i	$0.899839\pi$
$174$	2.63645			0.199869
$175$	1.31242	−	11.7095i	0.0992095	−	0.885153i
$176$	1.64398			0.123919
$177$	−0.879983	−	0.639345i	−0.0661436	−	0.0480561i
$178$	4.79164	+	14.7472i	0.359149	+	1.10535i
$179$	7.83385	+	24.1101i	0.585530	+	1.80207i	0.597133	+	0.802142i	$0.296306\pi$
$179$	7.83385	+	24.1101i	0.585530	+	1.80207i	−0.0116037	+	0.999933i	$0.503694\pi$
$180$	0.297082	+	2.92348i	0.0221432	+	0.217903i
$181$	1.90904	−	5.87542i	0.141898	−	0.436716i	−0.854701	−	0.519120i	$-0.826260\pi$
$181$	1.90904	−	5.87542i	0.141898	−	0.436716i	0.996599	+	0.0824039i	$0.0262597\pi$
$182$	12.2438			0.907572
$183$	−0.370671	+	1.14081i	−0.0274008	+	0.0843310i
$184$	−3.21222	+	2.33381i	−0.236808	+	0.172051i
$185$	0.104050	+	0.0224918i	0.00764992	+	0.00165363i
$186$	−2.65762	−	1.93087i	−0.194866	−	0.141578i
$187$	6.87319	−	4.99367i	0.502618	−	0.365173i
$188$	5.90658	−	4.29138i	0.430781	−	0.312981i
$189$	−10.6792	−	7.75892i	−0.776800	−	0.564378i
$190$	2.18559	+	0.472444i	0.158559	+	0.0342747i
$191$	20.0245	−	14.5487i	1.44892	−	1.05270i	0.462841	−	0.886442i	$-0.346830\pi$
$191$	20.0245	−	14.5487i	1.44892	−	1.05270i	0.986082	−	0.166262i	$-0.0531698\pi$
$192$	0.401228	−	1.23485i	0.0289562	−	0.0891179i
$193$	11.2831			0.812173			0.406087	−	0.913835i	$-0.366893\pi$
$193$	11.2831			0.812173			0.406087	+	0.913835i	$0.366893\pi$
$194$	−2.84684	+	8.76167i	−0.204391	+	0.629051i
$195$	−1.52503	−	15.0073i	−0.109210	−	1.07469i
$196$	−0.447035	−	1.37583i	−0.0319311	−	0.0982738i
$197$	−1.85398	−	5.70595i	−0.132090	−	0.406532i	0.863036	−	0.505143i	$-0.168560\pi$
$197$	−1.85398	−	5.70595i	−0.132090	−	0.406532i	−0.995126	+	0.0986105i	$0.968560\pi$
$198$	−1.74783	−	1.26987i	−0.124213	−	0.0902460i
$199$	16.2866			1.15453			0.577263	−	0.816558i	$-0.304121\pi$
$199$	16.2866			1.15453			0.577263	+	0.816558i	$0.304121\pi$
$200$	−4.55359	−	2.06513i	−0.321988	−	0.146027i
$201$	12.2607			0.864800
$202$	14.7471	+	10.7144i	1.03760	+	0.753862i
$203$	1.47867	+	4.55088i	0.103782	+	0.319409i
$204$	−2.07346	−	6.38147i	−0.145172	−	0.446792i
$205$	23.5051	+	5.08095i	1.64167	+	0.354869i
$206$	2.12872	−	6.55152i	0.148315	−	0.456466i
$207$	5.21787			0.362667
$208$	1.60554	−	4.94134i	0.111324	−	0.342620i
$209$	−1.33001	+	0.966306i	−0.0919984	+	0.0668408i
$210$	6.25988	−	2.76125i	0.431973	−	0.190545i
$211$	−19.0516	−	13.8418i	−1.31157	−	0.952909i	−0.999996	−	0.00268567i	$-0.999145\pi$
$211$	−19.0516	−	13.8418i	−1.31157	−	0.952909i	−0.311570	−	0.950223i	$-0.600855\pi$
$212$	−7.21137	+	5.23937i	−0.495279	+	0.359841i
$213$	11.6644	−	8.47470i	0.799233	−	0.580677i
$214$	0.128221	+	0.0931579i	0.00876500	+	0.00636814i
$215$	8.54432	+	9.55548i	0.582718	+	0.651679i
$216$	−4.53171	+	3.29248i	−0.308344	+	0.224025i
$217$	1.84241	−	5.67035i	0.125071	−	0.384928i
$218$	−8.30598			−0.562552
$219$	−1.18423	+	3.64468i	−0.0800228	+	0.246285i
$220$	3.36337	−	1.48359i	0.226758	−	0.100024i
$221$	−8.29710	−	25.5358i	−0.558123	−	1.71773i
$222$	0.0191014	+	0.0587881i	0.00128200	+	0.00394560i
$223$	−9.15136	−	6.64885i	−0.612821	−	0.445240i	0.237586	−	0.971367i	$-0.423644\pi$
$223$	−9.15136	−	6.64885i	−0.612821	−	0.445240i	−0.850406	+	0.526126i	$0.823644\pi$
$224$	2.35656			0.157454
$225$	3.24606	+	5.71297i	0.216404	+	0.380865i
$226$	−3.69829			−0.246007
$227$	−5.81360	−	4.22383i	−0.385862	−	0.280345i	0.377896	−	0.925848i	$-0.376648\pi$
$227$	−5.81360	−	4.22383i	−0.385862	−	0.280345i	−0.763758	+	0.645503i	$0.776648\pi$
$228$	0.401228	+	1.23485i	0.0265720	+	0.0817802i
$229$	4.24599	+	13.0678i	0.280583	+	0.863545i	0.987688	+	0.156437i	$0.0500008\pi$
$229$	4.24599	+	13.0678i	0.280583	+	0.863545i	−0.707105	+	0.707109i	$0.749999\pi$
$230$	−4.46566	+	7.67352i	−0.294457	+	0.505977i
$231$	−1.55441	+	4.78398i	−0.102273	+	0.314763i
$232$	2.03054			0.133311
$233$	−4.41594	+	13.5909i	−0.289298	+	0.890367i	0.695780	+	0.718255i	$0.255059\pi$
$233$	−4.41594	+	13.5909i	−0.289298	+	0.890367i	−0.985077	+	0.172112i	$0.944941\pi$
$234$	−5.52385	+	4.01331i	−0.361106	+	0.262359i
$235$	8.21139	−	14.1100i	0.535652	−	0.920432i
$236$	−0.677743	−	0.492409i	−0.0441173	−	0.0320531i
$237$	−12.2514	+	8.90113i	−0.795811	+	0.578191i
$238$	9.85237	−	7.15817i	0.638634	−	0.463995i
$239$	−13.8110	−	10.0343i	−0.893361	−	0.649065i	0.0433913	−	0.999058i	$-0.486184\pi$
$239$	−13.8110	−	10.0343i	−0.893361	−	0.649065i	−0.936752	+	0.349994i	$0.886184\pi$
$240$	−0.293521	−	2.88844i	−0.0189467	−	0.186448i
$241$	1.61161	−	1.17090i	0.103813	−	0.0754246i	−0.534668	−	0.845062i	$-0.679563\pi$
$241$	1.61161	−	1.17090i	0.103813	−	0.0754246i	0.638481	+	0.769638i	$0.279563\pi$
$242$	2.56402	−	7.89124i	0.164821	−	0.507268i
$243$	12.4801			0.800601
$244$	−0.285483	+	0.878625i	−0.0182761	+	0.0562482i
$245$	−2.15619	−	2.41136i	−0.137754	−	0.154056i
$246$	4.31505	+	13.2804i	0.275118	+	0.846725i
$247$	1.60554	+	4.94134i	0.102158	+	0.314410i
$248$	−2.04684	−	1.48711i	−0.129974	−	0.0944318i
$249$	8.40941			0.532925
$250$	−11.1797	−	0.115651i	−0.707069	−	0.00731444i
$251$	−1.26233			−0.0796777			−0.0398389	−	0.999206i	$-0.512684\pi$
$251$	−1.26233			−0.0796777			−0.0398389	+	0.999206i	$0.512684\pi$
$252$	−2.50543	−	1.82030i	−0.157827	−	0.114668i
$253$	−2.01709	−	6.20797i	−0.126813	−	0.390291i
$254$	0.212766	+	0.654826i	0.0133501	+	0.0410874i
$255$	−10.0009	−	11.1845i	−0.626284	−	0.700400i
$256$	0.309017	−	0.951057i	0.0193136	−	0.0594410i
$257$	17.5409			1.09417			0.547085	−	0.837077i	$-0.315738\pi$
$257$	17.5409			1.09417			0.547085	+	0.837077i	$0.315738\pi$
$258$	−2.30007	+	7.07890i	−0.143196	+	0.440713i
$259$	−0.0907632	+	0.0659433i	−0.00563975	+	0.00409752i
$260$	−1.17454	−	11.5583i	−0.0728420	−	0.716813i
$261$	−2.15881	−	1.56847i	−0.133627	−	0.0970857i
$262$	12.8455	−	9.33279i	0.793597	−	0.576582i
$263$	−0.0312897	+	0.0227333i	−0.00192941	+	0.00140180i	−0.588750	−	0.808316i	$-0.700380\pi$
$263$	−0.0312897	+	0.0227333i	−0.00192941	+	0.00140180i	0.586820	+	0.809717i	$0.300380\pi$
$264$	1.72688	+	1.25465i	0.106282	+	0.0772185i
$265$	−10.0253	+	17.2269i	−0.615851	+	1.05824i
$266$	−1.90650	+	1.38515i	−0.116895	+	0.0849290i
$267$	−6.22148	+	19.1477i	−0.380748	+	1.17182i
$268$	9.44289			0.576816
$269$	−0.366984	+	1.12946i	−0.0223754	+	0.0688645i	−0.961621	−	0.274382i	$-0.911527\pi$
$269$	−0.366984	+	1.12946i	−0.0223754	+	0.0688645i	0.939245	+	0.343247i	$0.111527\pi$
$270$	−6.30004	+	10.8256i	−0.383408	+	0.658825i
$271$	2.88060	+	8.86558i	0.174984	+	0.538545i	0.999633	−	0.0270998i	$-0.00862718\pi$
$271$	2.88060	+	8.86558i	0.174984	+	0.538545i	−0.824649	+	0.565645i	$0.808627\pi$
$272$	−1.59694	−	4.91486i	−0.0968285	−	0.298007i
$273$	12.8613	+	9.34425i	0.778399	+	0.565540i
$274$	−2.84212			−0.171699
$275$	5.54217	−	6.07049i	0.334206	−	0.366064i
$276$	−5.15533			−0.310314
$277$	4.09112	+	2.97237i	0.245812	+	0.178593i	0.703869	−	0.710330i	$-0.251454\pi$
$277$	4.09112	+	2.97237i	0.245812	+	0.178593i	−0.458057	+	0.888923i	$0.651454\pi$
$278$	2.45418	+	7.55318i	0.147192	+	0.453009i
$279$	1.02743	+	3.16211i	0.0615108	+	0.189311i
$280$	4.82122	−	2.12666i	0.288123	−	0.127092i
$281$	−9.05199	+	27.8592i	−0.539996	+	1.66194i	0.192602	+	0.981277i	$0.438307\pi$
$281$	−9.05199	+	27.8592i	−0.539996	+	1.66194i	−0.732599	+	0.680661i	$0.761693\pi$
$282$	9.47954			0.564498
$283$	4.16870	−	12.8299i	0.247803	−	0.762660i	−0.747359	−	0.664420i	$-0.768679\pi$
$283$	4.16870	−	12.8299i	0.247803	−	0.762660i	0.995163	−	0.0982403i	$-0.0313214\pi$
$284$	8.98368	−	6.52702i	0.533083	−	0.387308i
$285$	1.93525	+	2.16427i	0.114634	+	0.128200i
$286$	6.91022	+	5.02057i	0.408610	+	0.296873i
$287$	−20.5036	+	14.8967i	−1.21029	+	0.879327i
$288$	−1.06317	+	0.772440i	−0.0626480	+	0.0455164i
$289$	−7.85239	−	5.70510i	−0.461905	−	0.335594i
$290$	4.15422	−	1.83244i	0.243944	−	0.107605i
$291$	−9.67715	+	7.03086i	−0.567285	+	0.412156i
$292$	−0.912067	+	2.80705i	−0.0533747	+	0.164270i
$293$	−6.76161			−0.395017			−0.197509	−	0.980301i	$-0.563285\pi$
$293$	−6.76161			−0.395017			−0.197509	+	0.980301i	$0.563285\pi$
$294$	0.580432	−	1.78638i	0.0338515	−	0.104184i
$295$	−1.83095	−	0.395783i	−0.106602	−	0.0230434i
$296$	0.0147115	+	0.0452773i	0.000855088	+	0.00263169i
$297$	−2.84566	−	8.75804i	−0.165122	−	0.508193i
$298$	−18.7322	−	13.6098i	−1.08513	−	0.788392i
$299$	−20.6294			−1.19303
$300$	−3.20716	−	5.64450i	−0.185165	−	0.325885i
$301$	−13.5092			−0.778655
$302$	−3.45806	−	2.51243i	−0.198989	−	0.144574i
$303$	7.31376	+	22.5094i	0.420164	+	1.29313i
$304$	0.309017	+	0.951057i	0.0177233	+	0.0545468i
$305$	0.208847	+	2.05519i	0.0119585	+	0.117680i
$306$	−2.09862	+	6.45888i	−0.119970	+	0.369230i
$307$	−6.28209			−0.358538			−0.179269	−	0.983800i	$-0.557373\pi$
$307$	−6.28209			−0.358538			−0.179269	+	0.983800i	$0.557373\pi$
$308$	−1.19717	+	3.68451i	−0.0682152	+	0.209945i
$309$	7.23607	−	5.25731i	0.411645	−	0.299078i
$310$	−5.52960	−	1.19530i	−0.314060	−	0.0678882i
$311$	10.3438	+	7.51521i	0.586543	+	0.426148i	0.841077	−	0.540916i	$-0.181922\pi$
$311$	10.3438	+	7.51521i	0.586543	+	0.426148i	−0.254534	+	0.967064i	$0.581922\pi$
$312$	5.45765	−	3.96521i	0.308978	−	0.224486i
$313$	−13.1004	+	9.51801i	−0.740479	+	0.537990i	−0.892861	−	0.450332i	$-0.851306\pi$
$313$	−13.1004	+	9.51801i	−0.740479	+	0.537990i	0.152382	+	0.988322i	$0.451306\pi$
$314$	13.9138	+	10.1090i	0.785200	+	0.570482i
$315$	−6.76850	−	1.46310i	−0.381362	−	0.0824363i
$316$	−9.43572	+	6.85545i	−0.530801	+	0.385649i
$317$	2.72208	−	8.37771i	0.152887	−	0.470539i	−0.845053	−	0.534682i	$-0.820431\pi$
$317$	2.72208	−	8.37771i	0.152887	−	0.470539i	0.997941	+	0.0641429i	$0.0204313\pi$
$318$	−11.5736			−0.649017
$319$	−1.03155	+	3.17478i	−0.0577555	+	0.177753i
$320$	−0.226063	−	2.22461i	−0.0126373	−	0.124360i
$321$	0.0635905	+	0.195712i	0.00354928	+	0.0109236i
$322$	−2.89140	−	8.89880i	−0.161131	−	0.495911i
$323$	4.18083	+	3.03755i	0.232628	+	0.169014i
$324$	−3.33054			−0.185030
$325$	−12.8336	−	22.5868i	−0.711882	−	1.25289i
$326$	8.50510			0.471054
$327$	−8.72484	−	6.33897i	−0.482485	−	0.350546i
$328$	3.32336	+	10.2282i	0.183502	+	0.564760i
$329$	5.31666	+	16.3630i	0.293117	+	0.902121i
$330$	4.66523	+	1.00845i	0.256813	+	0.0555134i
$331$	10.3444	−	31.8367i	0.568578	−	1.74990i	−0.0884945	−	0.996077i	$-0.528206\pi$
$331$	10.3444	−	31.8367i	0.568578	−	1.74990i	0.657073	−	0.753827i	$-0.271794\pi$
$332$	6.47674			0.355457
$333$	0.0193331	−	0.0595013i	0.00105945	−	0.00326065i
$334$	−10.9406	+	7.94882i	−0.598644	+	0.434940i
$335$	19.3190	−	8.52165i	1.05551	−	0.465588i
$336$	2.47540	+	1.79848i	0.135044	+	0.0981152i
$337$	12.2522	−	8.90177i	0.667422	−	0.484910i	−0.201739	−	0.979439i	$-0.564659\pi$
$337$	12.2522	−	8.90177i	0.667422	−	0.484910i	0.869161	+	0.494529i	$0.164659\pi$
$338$	11.3219	−	8.22583i	0.615829	−	0.447426i
$339$	−3.88480	−	2.82247i	−0.210993	−	0.153296i
$340$	−7.70251	−	8.61405i	−0.417727	−	0.467162i
$341$	3.36495	−	2.44478i	0.182222	−	0.132392i
$342$	0.406096	−	1.24983i	0.0219591	−	0.0675833i
$343$	19.9050			1.07477
$344$	−1.77147	+	5.45201i	−0.0955111	+	0.293953i
$345$	−10.5471	+	4.65238i	−0.567839	+	0.250476i
$346$	−4.77476	−	14.6952i	−0.256693	−	0.790019i
$347$	−5.52516	−	17.0047i	−0.296606	−	0.912860i	−0.982677	−	0.185325i	$-0.940666\pi$
$347$	−5.52516	−	17.0047i	−0.296606	−	0.912860i	0.686071	−	0.727534i	$-0.259334\pi$
$348$	2.13293	+	1.54967i	0.114337	+	0.0830709i
$349$	−33.6455			−1.80100			−0.900500	−	0.434856i	$-0.856799\pi$
$349$	−33.6455			−1.80100			−0.900500	+	0.434856i	$0.856799\pi$
$350$	7.94442	−	8.70174i	0.424647	−	0.465127i
$351$	−29.1034			−1.55342
$352$	1.33001	+	0.966306i	0.0708895	+	0.0515043i
$353$	8.56747	+	26.3680i	0.456000	+	1.40342i	0.869957	+	0.493128i	$0.164147\pi$
$353$	8.56747	+	26.3680i	0.456000	+	1.40342i	−0.413957	+	0.910297i	$0.635853\pi$
$354$	−0.336124	−	1.03448i	−0.0178648	−	0.0549821i
$355$	12.4892	−	21.4607i	0.662858	−	1.13902i
$356$	−4.79164	+	14.7472i	−0.253957	+	0.781598i
$357$	15.8122			0.836870
$358$	−7.83385	+	24.1101i	−0.414032	+	1.27426i
$359$	−3.05514	+	2.21969i	−0.161244	+	0.117151i	−0.665481	−	0.746415i	$-0.731774\pi$
$359$	−3.05514	+	2.21969i	−0.161244	+	0.117151i	0.504237	+	0.863565i	$0.331774\pi$
$360$	−1.47803	+	2.53976i	−0.0778992	+	0.133857i
$361$	−0.809017	−	0.587785i	−0.0425798	−	0.0309361i
$362$	4.99793	−	3.63121i	0.262685	−	0.190852i
$363$	8.71577	−	6.33237i	0.457459	−	0.332363i
$364$	9.90545	+	7.19673i	0.519187	+	0.377211i
$365$	0.667229	+	6.56597i	0.0349244	+	0.343678i
$366$	−0.970429	+	0.705058i	−0.0507251	+	0.0368540i
$367$	5.18597	−	15.9608i	0.270705	−	0.833145i	−0.719619	−	0.694369i	$-0.755683\pi$
$367$	5.18597	−	15.9608i	0.270705	−	0.833145i	0.990324	−	0.138775i	$-0.0443166\pi$
$368$	−3.97052			−0.206978
$369$	4.36740	−	13.4415i	0.227358	−	0.699735i
$370$	0.0709580	+	0.0793554i	0.00368893	+	0.00412549i
$371$	−6.49114	−	19.9777i	−0.337003	−	1.03719i
$372$	−1.01512	−	3.12421i	−0.0526315	−	0.161983i
$373$	−22.2835	−	16.1899i	−1.15379	−	0.838281i	−0.164814	−	0.986325i	$-0.552702\pi$
$373$	−22.2835	−	16.1899i	−1.15379	−	0.838281i	−0.988981	+	0.148044i	$0.952702\pi$
$374$	8.49574			0.439304
$375$	−11.6553	−	8.65365i	−0.601875	−	0.446873i
$376$	7.30093			0.376517
$377$	8.53507	+	6.20109i	0.439578	+	0.319372i
$378$	−4.07911	−	12.5542i	−0.209807	−	0.645718i
$379$	−1.82285	−	5.61016i	−0.0936336	−	0.288175i	0.893262	−	0.449537i	$-0.148411\pi$
$379$	−1.82285	−	5.61016i	−0.0936336	−	0.288175i	−0.986895	+	0.161363i	$0.948411\pi$
$380$	1.49048	+	1.66687i	0.0764602	+	0.0855087i
$381$	−0.276256	+	0.850227i	−0.0141530	+	0.0435585i
$382$	24.7516			1.26640
$383$	−10.5231	+	32.3868i	−0.537706	+	1.65489i	0.200022	+	0.979791i	$0.435899\pi$
$383$	−10.5231	+	32.3868i	−0.537706	+	1.65489i	−0.737728	+	0.675098i	$0.764101\pi$
$384$	1.05043	−	0.763181i	0.0536045	−	0.0389459i
$385$	0.875798	+	8.61843i	0.0446348	+	0.439236i
$386$	9.12820	+	6.63202i	0.464613	+	0.337561i
$387$	6.09472	−	4.42808i	0.309812	−	0.225092i
$388$	−7.45312	+	5.41501i	−0.378375	+	0.274906i
$389$	−9.84442	−	7.15239i	−0.499132	−	0.362640i	0.309553	−	0.950882i	$-0.399820\pi$
$389$	−9.84442	−	7.15239i	−0.499132	−	0.362640i	−0.808685	+	0.588242i	$0.799820\pi$
$390$	7.58728	−	13.0375i	0.384197	−	0.660181i
$391$	−16.6001	+	12.0607i	−0.839502	+	0.609934i
$392$	0.447035	−	1.37583i	0.0225787	−	0.0694901i
$393$	20.6159			1.03993
$394$	1.85398	−	5.70595i	0.0934020	−	0.287462i
$395$	−13.1176	+	22.5406i	−0.660021	+	1.13414i
$396$	−0.667612	−	2.05470i	−0.0335488	−	0.103252i
$397$	4.69700	+	14.4559i	0.235736	+	0.725520i	0.997023	+	0.0771050i	$0.0245677\pi$
$397$	4.69700	+	14.4559i	0.235736	+	0.725520i	−0.761287	+	0.648415i	$0.775432\pi$
$398$	13.1761	+	9.57302i	0.660460	+	0.479852i
$399$	−3.05976			−0.153180
$400$	−2.47008	−	4.34726i	−0.123504	−	0.217363i
$401$	−16.4370			−0.820825			−0.410412	−	0.911900i	$-0.634615\pi$
$401$	−16.4370			−0.820825			−0.410412	+	0.911900i	$0.634615\pi$
$402$	9.91908	+	7.20663i	0.494719	+	0.359434i
$403$	−4.06206	−	12.5017i	−0.202346	−	0.622756i
$404$	5.63289	+	17.3363i	0.280247	+	0.862511i
$405$	−6.81387	+	3.00562i	−0.338584	+	0.149351i
$406$	−1.47867	+	4.55088i	−0.0733852	+	0.225856i
$407$	−0.0782654			−0.00387947
$408$	2.07346	−	6.38147i	0.102652	−	0.315930i
$409$	9.00908	−	6.54548i	0.445470	−	0.323653i	−0.342334	−	0.939578i	$-0.611218\pi$
$409$	9.00908	−	6.54548i	0.445470	−	0.323653i	0.787805	+	0.615925i	$0.211218\pi$
$410$	16.0296	+	17.9265i	0.791643	+	0.885329i
$411$	−2.98544	−	2.16905i	−0.147261	−	0.106991i
$412$	5.57306	−	4.04906i	0.274565	−	0.199483i
$413$	1.59714	−	1.16039i	0.0785901	−	0.0570991i
$414$	4.22134	+	3.06699i	0.207468	+	0.150734i
$415$	13.2506	−	5.84488i	0.650446	−	0.286914i
$416$	4.20336	−	3.05392i	0.206087	−	0.149731i
$417$	−3.18651	+	9.80706i	−0.156044	+	0.480254i
$418$	−1.64398			−0.0804096
$419$	2.45909	−	7.56831i	0.120135	−	0.369736i	−0.872849	−	0.487991i	$-0.837730\pi$
$419$	2.45909	−	7.56831i	0.120135	−	0.369736i	0.992983	+	0.118255i	$0.0377299\pi$
$420$	6.68737	+	1.44556i	0.326310	+	0.0705363i
$421$	−3.34179	−	10.2850i	−0.162869	−	0.501259i	0.836004	−	0.548723i	$-0.184886\pi$
$421$	−3.34179	−	10.2850i	−0.162869	−	0.501259i	−0.998873	+	0.0474646i	$0.984886\pi$
$422$	−7.27707	−	22.3965i	−0.354242	−	1.09024i
$423$	−7.76215	−	5.63953i	−0.377408	−	0.274203i
$424$	−8.91375			−0.432890
$425$	−23.5320	−	10.6722i	−1.14147	−	0.517677i
$426$	14.4180			0.698555
$427$	−1.76130	−	1.27966i	−0.0852352	−	0.0619270i
$428$	0.0489760	+	0.150733i	0.00236734	+	0.00728594i
$429$	3.42709	+	10.5475i	0.165462	+	0.509238i
$430$	1.29593	+	12.7528i	0.0624952	+	0.614993i
$431$	−8.64153	+	26.5959i	−0.416248	+	1.28108i	0.494882	+	0.868960i	$0.335211\pi$
$431$	−8.64153	+	26.5959i	−0.416248	+	1.28108i	−0.911130	+	0.412119i	$0.864789\pi$
$432$	−5.60150			−0.269502
$433$	10.1649	−	31.2842i	0.488492	−	1.50342i	−0.338368	−	0.941014i	$-0.609875\pi$
$433$	10.1649	−	31.2842i	0.488492	−	1.50342i	0.826859	−	0.562409i	$-0.190125\pi$
$434$	4.82349	−	3.50447i	0.231535	−	0.168220i
$435$	5.76220	+	1.24558i	0.276276	+	0.0597208i
$436$	−6.71968	−	4.88213i	−0.321814	−	0.233812i
$437$	3.21222	−	2.33381i	0.153661	−	0.111641i
$438$	−3.10035	+	2.25254i	−0.148141	+	0.107630i
$439$	21.6694	+	15.7438i	1.03423	+	0.751408i	0.969150	−	0.246472i	$-0.0792713\pi$
$439$	21.6694	+	15.7438i	1.03423	+	0.751408i	0.0650751	+	0.997880i	$0.479271\pi$
$440$	3.59306	+	0.776687i	0.171292	+	0.0370271i
$441$	−1.53802	+	1.11744i	−0.0732392	+	0.0532114i
$442$	8.29710	−	25.5358i	0.394653	−	1.21462i
$443$	−17.1885			−0.816648			−0.408324	−	0.912837i	$-0.633887\pi$
$443$	−17.1885			−0.816648			−0.408324	+	0.912837i	$0.633887\pi$
$444$	−0.0191014	+	0.0587881i	−0.000906513	+	0.00278996i
$445$	3.50536	+	34.4950i	0.166170	+	1.63522i
$446$	−3.49551	−	10.7581i	−0.165517	−	0.509410i
$447$	−9.29016	−	28.5922i	−0.439409	−	1.35236i
$448$	1.90650	+	1.38515i	0.0900734	+	0.0654422i
$449$	−4.96434			−0.234282			−0.117141	−	0.993115i	$-0.537373\pi$
$449$	−4.96434			−0.234282			−0.117141	+	0.993115i	$0.537373\pi$
$450$	−0.731881	+	6.52988i	−0.0345012	+	0.307821i
$451$	−17.6803			−0.832534
$452$	−2.99198	−	2.17380i	−0.140731	−	0.102247i
$453$	−1.71501	−	5.27826i	−0.0805782	−	0.247994i
$454$	−2.22060	−	6.83430i	−0.104218	−	0.320749i
$455$	26.7599	+	5.78451i	1.25453	+	0.271182i
$456$	−0.401228	+	1.23485i	−0.0187892	+	0.0578273i
$457$	−17.6129			−0.823897			−0.411949	−	0.911207i	$-0.635152\pi$
$457$	−17.6129			−0.823897			−0.411949	+	0.911207i	$0.635152\pi$
$458$	−4.24599	+	13.0678i	−0.198402	+	0.610619i
$459$	−23.4190	+	17.0149i	−1.09310	+	0.794186i
$460$	−8.12318	+	3.58316i	−0.378745	+	0.167066i
$461$	−16.0275	−	11.6447i	−0.746476	−	0.542346i	0.148257	−	0.988949i	$-0.452634\pi$
$461$	−16.0275	−	11.6447i	−0.746476	−	0.542346i	−0.894732	+	0.446603i	$0.852634\pi$
$462$	−4.06950	+	2.95666i	−0.189330	+	0.137556i
$463$	12.6169	−	9.16674i	0.586358	−	0.426014i	−0.254652	−	0.967033i	$-0.581961\pi$
$463$	12.6169	−	9.16674i	0.586358	−	0.426014i	0.841011	+	0.541018i	$0.181961\pi$
$464$	1.64274	+	1.19352i	0.0762622	+	0.0554078i
$465$	−4.89623	−	5.47566i	−0.227057	−	0.253928i
$466$	−11.5611	+	8.39962i	−0.535557	+	0.389105i
$467$	4.06416	−	12.5082i	0.188067	−	0.578811i	−0.811921	−	0.583768i	$-0.801578\pi$
$467$	4.06416	−	12.5082i	0.188067	−	0.578811i	0.999988	+	0.00495710i	$0.00157790\pi$
$468$	−6.82786			−0.315618
$469$	−6.87646	+	21.1636i	−0.317526	+	0.977243i
$470$	14.9368	−	6.58867i	0.688982	−	0.303912i
$471$	6.90048	+	21.2375i	0.317957	+	0.978572i
$472$	−0.258875	−	0.796735i	−0.0119157	−	0.0366727i
$473$	−7.62437	−	5.53943i	−0.350569	−	0.254703i
$474$	−15.1435			−0.695565
$475$	4.55359	+	2.06513i	0.208933	+	0.0947549i
$476$	12.1782			0.558187
$477$	9.47685	+	6.88533i	0.433915	+	0.315258i
$478$	−5.27534	−	16.2358i	−0.241289	−	0.742610i
$479$	−12.5671	−	38.6774i	−0.574204	−	1.76722i	−0.638875	−	0.769311i	$-0.720600\pi$
$479$	−12.5671	−	38.6774i	−0.574204	−	1.76722i	0.0646710	−	0.997907i	$-0.479400\pi$
$480$	1.46032	−	2.50932i	0.0666541	−	0.114534i
$481$	−0.0764355	+	0.235244i	−0.00348516	+	0.0107262i
$482$	1.99206			0.0907359
$483$	3.75419	−	11.5542i	0.170822	−	0.525735i
$484$	6.71269	−	4.87705i	0.305122	−	0.221684i
$485$	−10.3614	+	17.8044i	−0.470488	+	0.808458i
$486$	10.0966	+	7.33564i	0.457993	+	0.332751i
$487$	−31.3490	+	22.7764i	−1.42056	+	1.03210i	−0.428879	+	0.903362i	$0.641092\pi$
$487$	−31.3490	+	22.7764i	−1.42056	+	1.03210i	−0.991679	+	0.128735i	$0.958908\pi$
$488$	−0.747403	+	0.543020i	−0.0338333	+	0.0245814i
$489$	8.93400	+	6.49093i	0.404010	+	0.293530i
$490$	−0.327032	−	3.21820i	−0.0147738	−	0.145384i
$491$	−21.2578	+	15.4447i	−0.959351	+	0.697009i	−0.953000	−	0.302971i	$-0.902022\pi$
$491$	−21.2578	+	15.4447i	−0.959351	+	0.697009i	−0.00635111	+	0.999980i	$0.502022\pi$
$492$	−4.31505	+	13.2804i	−0.194538	+	0.598725i
$493$	10.4934			0.472599
$494$	−1.60554	+	4.94134i	−0.0722366	+	0.222321i
$495$	−3.22010	−	3.60117i	−0.144733	−	0.161861i
$496$	−0.781822	−	2.40620i	−0.0351048	−	0.108042i
$497$	8.08643	+	24.8875i	0.362726	+	1.11636i
$498$	6.80335	+	4.94293i	0.304866	+	0.221498i
$499$	−16.0961			−0.720563			−0.360281	−	0.932844i	$-0.617319\pi$
$499$	−16.0961			−0.720563			−0.360281	+	0.932844i	$0.617319\pi$
$500$	−8.97662	−	6.66485i	−0.401447	−	0.298061i
$501$	−17.5587			−0.784466
$502$	−1.02125	−	0.741981i	−0.0455806	−	0.0331162i
$503$	0.983580	+	3.02715i	0.0438557	+	0.134974i	0.970587	−	0.240751i	$-0.0773937\pi$
$503$	0.983580	+	3.02715i	0.0438557	+	0.134974i	−0.926731	+	0.375725i	$0.877394\pi$
$504$	−0.956988	−	2.94530i	−0.0426276	−	0.131194i
$505$	27.1692	+	30.3844i	1.20901	+	1.35209i
$506$	2.01709	−	6.20797i	0.0896706	−	0.275978i
$507$	18.1706			0.806986
$508$	−0.212766	+	0.654826i	−0.00943996	+	0.0290532i
$509$	−17.6494	+	12.8231i	−0.782298	+	0.568373i	−0.905668	−	0.423988i	$-0.860630\pi$
$509$	−17.6494	+	12.8231i	−0.782298	+	0.568373i	0.123370	+	0.992361i	$0.460630\pi$
$510$	−1.51686	−	14.9269i	−0.0671675	−	0.660972i
$511$	−5.62704	−	4.08829i	−0.248926	−	0.180855i
$512$	0.809017	−	0.587785i	0.0357538	−	0.0259767i
$513$	4.53171	−	3.29248i	0.200080	−	0.145367i
$514$	14.1909	+	10.3103i	0.625932	+	0.454766i
$515$	7.74773	−	13.3132i	0.341406	−	0.586651i
$516$	−6.02167	+	4.37500i	−0.265089	+	0.192599i
$517$	−3.70900	+	11.4151i	−0.163121	+	0.502036i
$518$	−0.112190			−0.00492932
$519$	6.19956	−	19.0803i	0.272130	−	0.837531i
$520$	5.84355	−	10.0412i	0.256257	−	0.440336i
$521$	−4.87342	−	14.9988i	−0.213508	−	0.657111i	−0.999256	−	0.0385639i	$-0.987722\pi$
$521$	−4.87342	−	14.9988i	−0.213508	−	0.657111i	0.785748	−	0.618547i	$-0.212278\pi$
$522$	−0.824592	−	2.53783i	−0.0360914	−	0.111078i
$523$	−4.86442	−	3.53421i	−0.212706	−	0.154540i	0.476331	−	0.879266i	$-0.341966\pi$
$523$	−4.86442	−	3.53421i	−0.212706	−	0.154540i	−0.689037	+	0.724726i	$0.741966\pi$
$524$	15.8779			0.693629
$525$	14.9861	−	3.07752i	0.654045	−	0.134314i
$526$	−0.0386762			−0.00168636
$527$	−10.5776	−	7.68509i	−0.460769	−	0.334768i
$528$	0.659610	+	2.03007i	0.0287058	+	0.0883475i
$529$	−2.23573	−	6.88088i	−0.0972058	−	0.299169i
$530$	−18.2364	+	8.04414i	−0.792138	+	0.349415i
$531$	−0.340201	+	1.04703i	−0.0147635	+	0.0454373i
$532$	−2.35656			−0.102170
$533$	−17.2669	+	53.1422i	−0.747914	+	2.30184i
$534$	−16.2880	+	11.8340i	−0.704852	+	0.512105i
$535$	0.236226	+	0.264182i	0.0102129	+	0.0114216i
$536$	7.63946	+	5.55039i	0.329974	+	0.239740i
$537$	−26.6293	+	19.3473i	−1.14914	+	0.834898i
$538$	−0.960778	+	0.698046i	−0.0414221	+	0.0300949i
$539$	1.92404	+	1.39789i	0.0828741	+	0.0602115i
$540$	−11.4600	+	5.05503i	−0.493159	+	0.217534i
$541$	31.4282	−	22.8339i	1.35120	−	0.981707i	0.352253	−	0.935905i	$-0.385416\pi$
$541$	31.4282	−	22.8339i	1.35120	−	0.981707i	0.998951	−	0.0458016i	$-0.0145842\pi$
$542$	−2.88060	+	8.86558i	−0.123732	+	0.380809i
$543$	8.02124			0.344224
$544$	1.59694	−	4.91486i	0.0684681	−	0.210723i
$545$	−18.1535	−	3.92411i	−0.777609	−	0.168090i
$546$	4.91256	+	15.1193i	0.210238	+	0.647047i
$547$	−9.68214	−	29.7986i	−0.413978	−	1.27409i	−0.913162	−	0.407598i	$-0.866367\pi$
$547$	−9.68214	−	29.7986i	−0.413978	−	1.27409i	0.499183	−	0.866496i	$-0.333633\pi$
$548$	−2.29932	−	1.67056i	−0.0982222	−	0.0713626i
$549$	1.21407			0.0518152
$550$	8.05186	−	1.65352i	0.343332	−	0.0705064i
$551$	−2.03054			−0.0865038
$552$	−4.17075	−	3.03023i	−0.177519	−	0.128975i
$553$	−8.49333	−	26.1398i	−0.361173	−	1.11158i
$554$	1.56267	+	4.80940i	0.0663914	+	0.204332i
$555$	0.0139738	+	0.137511i	0.000593153	+	0.00583702i
$556$	−2.45418	+	7.55318i	−0.104080	+	0.320326i
$557$	13.5607			0.574585			0.287292	−	0.957843i	$-0.407245\pi$
$557$	13.5607			0.574585			0.287292	+	0.957843i	$0.407245\pi$
$558$	−1.02743	+	3.16211i	−0.0434947	+	0.133863i
$559$	−24.0961	+	17.5068i	−1.01916	+	0.740460i
$560$	5.15046	+	1.11334i	0.217647	+	0.0470472i
$561$	8.92417	+	6.48379i	0.376779	+	0.273746i
$562$	−23.6984	+	17.2179i	−0.999657	+	0.726293i
$563$	−14.8456	+	10.7859i	−0.625667	+	0.454573i	−0.854896	−	0.518799i	$-0.826379\pi$
$563$	−14.8456	+	10.7859i	−0.625667	+	0.454573i	0.229230	+	0.973372i	$0.426379\pi$
$564$	7.66911	+	5.57193i	0.322928	+	0.234621i
$565$	−8.08295	−	1.74724i	−0.340052	−	0.0735068i
$566$	10.9138	−	7.92933i	0.458741	−	0.333295i
$567$	2.42536	−	7.46448i	0.101855	−	0.313479i
$568$	11.1044			0.465932
$569$	−1.15541	+	3.55598i	−0.0484372	+	0.149074i	−0.972350	−	0.233529i	$-0.924973\pi$
$569$	−1.15541	+	3.55598i	−0.0484372	+	0.149074i	0.923913	+	0.382604i	$0.124973\pi$
$570$	0.293521	+	2.88844i	0.0122942	+	0.120983i
$571$	5.08975	+	15.6646i	0.212999	+	0.655545i	0.999290	+	0.0376874i	$0.0119991\pi$
$571$	5.08975	+	15.6646i	0.212999	+	0.655545i	−0.786290	+	0.617857i	$0.788001\pi$
$572$	2.63947	+	8.12345i	0.110362	+	0.339659i
$573$	25.9998	+	18.8900i	1.08616	+	0.789141i
$574$	−25.3438			−1.05783
$575$	−13.3854	+	14.6614i	−0.558210	+	0.611422i
$576$	−1.31415			−0.0547564
$577$	12.4331	+	9.03320i	0.517598	+	0.376057i	0.815698	−	0.578478i	$-0.196353\pi$
$577$	12.4331	+	9.03320i	0.517598	+	0.376057i	−0.298100	+	0.954535i	$0.596353\pi$
$578$	−2.99935	−	9.23104i	−0.124756	−	0.383961i
$579$	4.52709	+	13.9329i	0.188139	+	0.579033i
$580$	4.43792	+	0.959314i	0.184275	+	0.0398334i
$581$	−4.71647	+	14.5158i	−0.195672	+	0.602216i
$582$	−11.9616			−0.495825
$583$	4.52833	−	13.9368i	0.187544	−	0.577202i
$584$	−2.38782	+	1.73486i	−0.0988088	+	0.0717888i
$585$	−13.9689	+	6.16174i	−0.577544	+	0.254757i
$586$	−5.47025	−	3.97437i	−0.225974	−	0.164180i
$587$	−3.80343	+	2.76335i	−0.156984	+	0.114056i	−0.663504	−	0.748172i	$-0.730932\pi$
$587$	−3.80343	+	2.76335i	−0.156984	+	0.114056i	0.506520	+	0.862228i	$0.330932\pi$
$588$	1.51959	−	1.10405i	0.0626668	−	0.0455301i
$589$	2.04684	+	1.48711i	0.0843384	+	0.0612754i
$590$	−1.24863	−	1.39640i	−0.0514054	−	0.0574888i
$591$	6.30215	−	4.57878i	0.259236	−	0.188346i
$592$	−0.0147115	+	0.0452773i	−0.000604638	+	0.00186089i
$593$	23.6621			0.971685			0.485842	−	0.874046i	$-0.338513\pi$
$593$	23.6621			0.971685			0.485842	+	0.874046i	$0.338513\pi$
$594$	2.84566	−	8.75804i	0.116759	−	0.359347i
$595$	24.9151	−	10.9901i	1.02142	−	0.450551i
$596$	−7.15507	−	22.0210i	−0.293083	−	0.902017i
$597$	6.53464	+	20.1116i	0.267445	+	0.823111i
$598$	−16.6895	−	12.1256i	−0.682485	−	0.495854i
$599$	−21.9549			−0.897054			−0.448527	−	0.893769i	$-0.648051\pi$
$599$	−21.9549			−0.897054			−0.448527	+	0.893769i	$0.648051\pi$
$600$	0.723108	−	6.45161i	0.0295208	−	0.263386i
$601$	11.8301			0.482558			0.241279	−	0.970456i	$-0.422433\pi$
$601$	11.8301			0.482558			0.241279	+	0.970456i	$0.422433\pi$
$602$	−10.9291	−	7.94049i	−0.445439	−	0.323630i
$603$	−3.83471	−	11.8020i	−0.156162	−	0.480616i
$604$	−1.32086	−	4.06520i	−0.0537451	−	0.165410i
$605$	9.33205	−	16.0356i	0.379402	−	0.651942i
$606$	−7.31376	+	22.5094i	−0.297101	+	0.914383i
$607$	−29.3786			−1.19244			−0.596220	−	0.802821i	$-0.703331\pi$
$607$	−29.3786			−1.19244			−0.596220	+	0.802821i	$0.703331\pi$
$608$	−0.309017	+	0.951057i	−0.0125323	+	0.0385704i
$609$	−5.02638	+	3.65188i	−0.203679	+	0.147982i
$610$	−1.03905	+	1.78544i	−0.0420698	+	0.0722903i
$611$	30.6884	+	22.2964i	1.24152	+	0.902017i
$612$	−5.49425	+	3.99181i	−0.222092	+	0.161359i
$613$	−21.5767	+	15.6764i	−0.871473	+	0.633163i	−0.930982	−	0.365065i	$-0.881047\pi$
$613$	−21.5767	+	15.6764i	−0.871473	+	0.633163i	0.0595085	+	0.998228i	$0.481047\pi$
$614$	−5.08232	−	3.69252i	−0.205106	−	0.149018i
$615$	3.15670	+	31.0640i	0.127291	+	1.25262i
$616$	−3.13423	+	2.27715i	−0.126282	+	0.0917492i
$617$	13.2552	−	40.7954i	0.533635	−	1.64236i	−0.212944	−	0.977064i	$-0.568305\pi$
$617$	13.2552	−	40.7954i	0.533635	−	1.64236i	0.746579	−	0.665296i	$-0.231695\pi$
$618$	8.94427			0.359791
$619$	9.09314	−	27.9858i	0.365484	−	1.12484i	−0.584193	−	0.811615i	$-0.698589\pi$
$619$	9.09314	−	27.9858i	0.365484	−	1.12484i	0.949677	−	0.313230i	$-0.101411\pi$
$620$	−3.77096	−	4.21723i	−0.151446	−	0.169368i
$621$	6.87281	+	21.1523i	0.275796	+	0.848814i
$622$	3.95098	+	12.1599i	0.158420	+	0.487566i
$623$	−29.5623	−	21.4782i	−1.18439	−	0.860508i
$624$	6.74602			0.270057
$625$	−24.3797	−	5.53456i	−0.975187	−	0.221383i
$626$	−16.1930			−0.647203
$627$	−1.72688	−	1.25465i	−0.0689650	−	0.0501060i
$628$	5.31459	+	16.3566i	0.212075	+	0.652701i
$629$	0.0760259	+	0.233984i	0.00303135	+	0.00932954i
$630$	−4.61584	−	5.16210i	−0.183900	−	0.205663i
$631$	11.2947	−	34.7616i	0.449635	−	1.38384i	−0.427684	−	0.903928i	$-0.640670\pi$
$631$	11.2947	−	34.7616i	0.449635	−	1.38384i	0.877319	−	0.479907i	$-0.159330\pi$
$632$	−11.6632			−0.463937
$633$	9.44855	−	29.0797i	0.375546	−	1.15581i
$634$	7.12651	−	5.17771i	0.283030	−	0.205633i
$635$	0.155650	+	1.53170i	0.00617679	+	0.0607837i
$636$	−9.36326	−	6.80280i	−0.371277	−	0.269749i
$637$	6.08073	−	4.41791i	0.240927	−	0.175044i
$638$	−2.70063	+	1.96212i	−0.106919	+	0.0776810i
$639$	−11.8059	−	8.57751i	−0.467035	−	0.339321i
$640$	1.12470	−	1.93263i	0.0444579	−	0.0763937i
$641$	0.991302	−	0.720223i	0.0391541	−	0.0284471i	−0.568036	−	0.823004i	$-0.692297\pi$
$641$	0.991302	−	0.720223i	0.0391541	−	0.0284471i	0.607190	+	0.794557i	$0.292297\pi$
$642$	−0.0635905	+	0.195712i	−0.00250972	+	0.00772412i
$643$	−22.6721			−0.894100			−0.447050	−	0.894509i	$-0.647525\pi$
$643$	−22.6721			−0.894100			−0.447050	+	0.894509i	$0.647525\pi$
$644$	2.89140	−	8.89880i	0.113937	−	0.350662i
$645$	−8.37140	+	14.3849i	−0.329624	+	0.566405i
$646$	1.59694	+	4.91486i	0.0628306	+	0.193373i
$647$	5.41201	+	16.6565i	0.212768	+	0.654833i	0.999305	+	0.0372891i	$0.0118722\pi$
$647$	5.41201	+	16.6565i	0.212768	+	0.654833i	−0.786536	+	0.617544i	$0.788128\pi$
$648$	−2.69447	−	1.95764i	−0.105849	−	0.0769035i
$649$	1.37722			0.0540606
$650$	2.89356	−	25.8165i	0.113495	−	1.01261i
$651$	7.74127			0.303404
$652$	6.88077	+	4.99917i	0.269472	+	0.195783i
$653$	9.91892	+	30.5273i	0.388157	+	1.19463i	0.934164	+	0.356845i	$0.116147\pi$
$653$	9.91892	+	30.5273i	0.388157	+	1.19463i	−0.546006	+	0.837781i	$0.683853\pi$
$654$	−3.33259	−	10.2567i	−0.130315	−	0.401068i
$655$	32.4842	−	14.3289i	1.26926	−	0.559875i
$656$	−3.32336	+	10.2282i	−0.129755	+	0.399346i
$657$	3.87874			0.151324
$658$	−5.31666	+	16.3630i	−0.207265	+	0.637896i
$659$	−15.9588	+	11.5948i	−0.621668	+	0.451668i	−0.853504	−	0.521087i	$-0.825527\pi$
$659$	−15.9588	+	11.5948i	−0.621668	+	0.451668i	0.231836	+	0.972755i	$0.425527\pi$
$660$	3.18150	+	3.55801i	0.123840	+	0.138495i
$661$	25.5784	+	18.5838i	0.994883	+	0.722825i	0.960985	−	0.276600i	$-0.0892078\pi$
$661$	25.5784	+	18.5838i	0.994883	+	0.722825i	0.0338981	+	0.999425i	$0.489208\pi$
$662$	27.0819	−	19.6762i	1.05257	−	0.764736i
$663$	28.2040	−	20.4914i	1.09535	−	0.795820i
$664$	5.23979	+	3.80693i	0.203343	+	0.147738i
$665$	−4.82122	+	2.12666i	−0.186959	+	0.0824682i
$666$	0.0506148	−	0.0367738i	0.00196128	−	0.00142496i
$667$	2.49138	−	7.66769i	0.0964667	−	0.296894i
$668$	−13.5233			−0.523234
$669$	4.53858	−	13.9683i	0.175471	−	0.540046i
$670$	20.6383	+	4.46123i	0.797326	+	0.172352i
$671$	−0.469327	−	1.44444i	−0.0181182	−	0.0557620i
$672$	0.945517	+	2.91000i	0.0364741	+	0.112256i
$673$	21.9496	+	15.9473i	0.846094	+	0.614723i	0.924066	−	0.382232i	$-0.124845\pi$
$673$	21.9496	+	15.9473i	0.846094	+	0.614723i	−0.0779722	+	0.996956i	$0.524845\pi$
$674$	15.1446			0.583348
$675$	−18.8838	+	20.6839i	−0.726837	+	0.796124i
$676$	13.9946			0.538255
$677$	−31.9998	−	23.2492i	−1.22985	−	0.893541i	−0.232974	−	0.972483i	$-0.574846\pi$
$677$	−31.9998	−	23.2492i	−1.22985	−	0.893541i	−0.996879	+	0.0789421i	$0.974846\pi$
$678$	−1.48386	−	4.56685i	−0.0569873	−	0.175389i
$679$	−6.70874	−	20.6474i	−0.257458	−	0.792374i
$680$	−1.16825	−	11.4963i	−0.0448003	−	0.440864i
$681$	2.88323	−	8.87366i	0.110486	−	0.340039i
$682$	4.15931			0.159268
$683$	0.173176	−	0.532981i	0.00662639	−	0.0203939i	−0.947689	−	0.319196i	$-0.896587\pi$
$683$	0.173176	−	0.532981i	0.00662639	−	0.0203939i	0.954315	+	0.298802i	$0.0965871\pi$
$684$	1.06317	−	0.772440i	0.0406514	−	0.0295350i
$685$	−6.21170	−	1.34274i	−0.237337	−	0.0513035i
$686$	16.1035	+	11.6999i	0.614833	+	0.446703i
$687$	−14.4332	+	10.4864i	−0.550662	+	0.400079i
$688$	−4.63776	+	3.36953i	−0.176813	+	0.128462i
$689$	−37.4677	−	27.2218i	−1.42740	−	1.03707i
$690$	−11.2674	−	2.43560i	−0.428944	−	0.0927218i
$691$	10.1870	−	7.40127i	0.387531	−	0.281558i	−0.376912	−	0.926249i	$-0.623014\pi$
$691$	10.1870	−	7.40127i	0.387531	−	0.281558i	0.764443	+	0.644691i	$0.223014\pi$
$692$	4.77476	−	14.6952i	0.181509	−	0.558628i
$693$	5.09120			0.193399
$694$	5.52516	−	17.0047i	0.209732	−	0.645489i
$695$	1.79537	+	17.6676i	0.0681022	+	0.670170i
$696$	0.814709	+	2.50742i	0.0308814	+	0.0950433i
$697$	17.1744	+	52.8574i	0.650527	+	2.00212i
$698$	−27.2197	−	19.7763i	−1.03028	−	0.748544i
$699$	−18.5545			−0.701797
$700$	11.5419	−	2.37024i	0.436244	−	0.0895867i
$701$	39.2794			1.48356			0.741781	−	0.670642i	$-0.233981\pi$
$701$	39.2794			1.48356			0.741781	+	0.670642i	$0.233981\pi$
$702$	−23.5451	−	17.1065i	−0.888653	−	0.645644i
$703$	−0.0147115	−	0.0452773i	−0.000554854	−	0.00170767i
$704$	0.508017	+	1.56352i	0.0191466	+	0.0589272i
$705$	20.7184	+	4.47855i	0.780299	+	0.168672i
$706$	−8.56747	+	26.3680i	−0.322441	+	0.992371i
$707$	−42.9563			−1.61554
$708$	0.336124	−	1.03448i	0.0126323	−	0.0388782i
$709$	9.74834	−	7.08258i	0.366107	−	0.265992i	−0.389488	−	0.921032i	$-0.627348\pi$
$709$	9.74834	−	7.08258i	0.366107	−	0.265992i	0.755595	+	0.655039i	$0.227348\pi$
$710$	22.7183	−	10.0211i	0.852602	−	0.376085i
$711$	12.4000	+	9.00912i	0.465036	+	0.337868i
$712$	−12.5447	+	9.11425i	−0.470132	+	0.341571i
$713$	−8.12700	+	5.90461i	−0.304358	+	0.221129i
$714$	12.7923	+	9.29418i	0.478741	+	0.347826i
$715$	12.7310	+	14.2376i	0.476111	+	0.532456i
$716$	−20.5093	+	14.9009i	−0.766468	+	0.556872i
$717$	6.84951	−	21.0806i	0.255800	−	0.787271i
$718$	−3.77636			−0.140932
$719$	4.62395	−	14.2310i	0.172444	−	0.530728i	−0.827063	−	0.562109i	$-0.809990\pi$
$719$	4.62395	−	14.2310i	0.172444	−	0.530728i	0.999508	+	0.0313803i	$0.00999030\pi$
$720$	−2.68859	+	1.18595i	−0.100198	+	0.0441976i
$721$	5.01645	+	15.4390i	0.186822	+	0.574980i
$722$	−0.309017	−	0.951057i	−0.0115004	−	0.0353947i
$723$	2.09252	+	1.52030i	0.0778216	+	0.0565407i
$724$	6.17778			0.229595
$725$	9.94514	−	2.04233i	0.369353	−	0.0758501i
$726$	10.7733			0.399834
$727$	24.2397	+	17.6112i	0.899001	+	0.653163i	0.938209	−	0.346069i	$-0.112484\pi$
$727$	24.2397	+	17.6112i	0.899001	+	0.653163i	−0.0392082	+	0.999231i	$0.512484\pi$
$728$	3.78355	+	11.6446i	0.140228	+	0.431576i
$729$	8.09496	+	24.9137i	0.299813	+	0.922731i
$730$	−3.31958	+	5.70417i	−0.122863	+	0.211121i
$731$	−9.15457	+	28.1749i	−0.338594	+	1.04209i
$732$	−1.19952			−0.0443354
$733$	5.54274	−	17.0588i	0.204726	−	0.630081i	−0.794999	−	0.606611i	$-0.792529\pi$
$733$	5.54274	−	17.0588i	0.204726	−	0.630081i	0.999725	−	0.0234701i	$-0.00747144\pi$
$734$	13.5770	−	9.86429i	0.501137	−	0.364098i
$735$	2.11255	−	3.63008i	0.0779226	−	0.133898i
$736$	−3.21222	−	2.33381i	−0.118404	−	0.0860255i
$737$	−12.5591	+	9.12471i	−0.462620	+	0.336113i
$738$	11.4340	−	8.30728i	0.420891	−	0.305795i
$739$	−32.4027	−	23.5419i	−1.19195	−	0.866004i	−0.198483	−	0.980104i	$-0.563602\pi$
$739$	−32.4027	−	23.5419i	−1.19195	−	0.866004i	−0.993469	+	0.114100i	$0.963602\pi$
$740$	0.0107623	+	0.105908i	0.000395629	+	0.00389325i
$741$	−5.45765	+	3.96521i	−0.200492	+	0.145666i
$742$	6.49114	−	19.9777i	0.238297	−	0.733403i
$743$	3.05996			0.112259			0.0561294	−	0.998423i	$-0.482124\pi$
$743$	3.05996			0.112259			0.0561294	+	0.998423i	$0.482124\pi$
$744$	1.01512	−	3.12421i	0.0372161	−	0.114539i
$745$	−34.5111	−	38.5952i	−1.26439	−	1.41402i
$746$	−8.51153	−	26.1958i	−0.311629	−	0.959096i
$747$	−2.63017	−	8.09484i	−0.0962331	−	0.296175i
$748$	6.87319	+	4.99367i	0.251309	+	0.182587i
$749$	−0.373490			−0.0136470
$750$	−4.34282	−	13.8517i	−0.158577	−	0.505794i
$751$	−17.1547			−0.625983			−0.312992	−	0.949756i	$-0.601331\pi$
$751$	−17.1547			−0.625983			−0.312992	+	0.949756i	$0.601331\pi$
$752$	5.90658	+	4.29138i	0.215391	+	0.156491i
$753$	−0.506484	−	1.55880i	−0.0184573	−	0.0568057i
$754$	3.26011	+	10.0336i	0.118726	+	0.365401i
$755$	−6.37092	−	7.12488i	−0.231861	−	0.259301i
$756$	4.07911	−	12.5542i	0.148356	−	0.456592i
$757$	37.1257			1.34936			0.674678	−	0.738112i	$-0.264282\pi$
$757$	37.1257			1.34936			0.674678	+	0.738112i	$0.264282\pi$
$758$	1.82285	−	5.61016i	0.0662090	−	0.203770i
$759$	6.85661	−	4.98162i	0.248879	−	0.180821i
$760$	0.226063	+	2.22461i	0.00820018	+	0.0806951i
$761$	−40.5010	−	29.4257i	−1.46816	−	1.06668i	−0.981142	−	0.193290i	$-0.938084\pi$
$761$	−40.5010	−	29.4257i	−1.46816	−	1.06668i	−0.487019	−	0.873391i	$-0.661916\pi$
$762$	−0.723246	+	0.525469i	−0.0262005	+	0.0190357i
$763$	15.8353	−	11.5050i	0.573277	−	0.416510i
$764$	20.0245	+	14.5487i	0.724461	+	0.526352i
$765$	−7.63817	+	13.1250i	−0.276159	+	0.474535i
$766$	−27.5499	+	20.0162i	−0.995417	+	0.723213i
$767$	1.34502	−	4.13954i	0.0485658	−	0.149470i
$768$	1.29840			0.0468520
$769$	11.3656	−	34.9797i	0.409854	−	1.26140i	−0.506920	−	0.861993i	$-0.669216\pi$
$769$	11.3656	−	34.9797i	0.409854	−	1.26140i	0.916774	−	0.399407i	$-0.130784\pi$
$770$	−4.35725	+	7.48723i	−0.157024	+	0.269821i
$771$	7.03789	+	21.6604i	0.253463	+	0.780080i
$772$	3.48666	+	10.7308i	0.125488	+	0.386211i
$773$	6.60586	+	4.79943i	0.237596	+	0.172624i	0.700212	−	0.713935i	$-0.253089\pi$
$773$	6.60586	+	4.79943i	0.237596	+	0.172624i	−0.462616	+	0.886559i	$0.653089\pi$
$774$	7.53349			0.270786
$775$	−11.5207	−	5.22485i	−0.413837	−	0.187682i
$776$	−9.21257			−0.330712
$777$	−0.117847	−	0.0856210i	−0.00422774	−	0.00307163i
$778$	−3.76023	−	11.5728i	−0.134811	−	0.414905i
$779$	−3.32336	−	10.2282i	−0.119072	−	0.366465i
$780$	13.8015	−	6.08789i	0.494173	−	0.217981i
$781$	−5.64124	+	17.3620i	−0.201859	+	0.621260i
$782$	−20.5188			−0.733751
$783$	3.51478	−	10.8174i	0.125608	−	0.386581i
$784$	1.17035	−	0.850312i	0.0417984	−	0.0303683i
$785$	25.6339	+	28.6675i	0.914913	+	1.02319i
$786$	16.6786	+	12.1177i	0.594906	+	0.432224i
$787$	13.6035	−	9.88355i	0.484914	−	0.352311i	−0.318311	−	0.947986i	$-0.603116\pi$
$787$	13.6035	−	9.88355i	0.484914	−	0.352311i	0.803225	+	0.595676i	$0.203116\pi$
$788$	4.85377	−	3.52647i	0.172909	−	0.125625i
$789$	−0.0406266	−	0.0295170i	−0.00144635	−	0.00105083i
$790$	−23.8614	+	10.5254i	−0.848951	+	0.374475i
$791$	7.05078	−	5.12269i	0.250697	−	0.182142i
$792$	0.667612	−	2.05470i	0.0237226	−	0.0730105i
$793$	−4.79994			−0.170451
$794$	−4.69700	+	14.4559i	−0.166690	+	0.513020i
$795$	−25.2952	−	5.46788i	−0.897127	−	0.193926i
$796$	5.03283	+	15.4895i	0.178384	+	0.549010i
$797$	9.48075	+	29.1788i	0.335825	+	1.03356i	0.966314	+	0.257366i	$0.0828546\pi$
$797$	9.48075	+	29.1788i	0.335825	+	1.03356i	−0.630489	+	0.776199i	$0.717145\pi$
$798$	−2.47540	−	1.79848i	−0.0876281	−	0.0636655i
$799$	37.7297			1.33478
$800$	0.556922	−	4.96889i	0.0196902	−	0.175677i
$801$	20.3774			0.719999
$802$	−13.2978	−	9.66143i	−0.469562	−	0.341157i
$803$	−1.49942	−	4.61473i	−0.0529133	−	0.162850i
$804$	3.78875	+	11.6606i	0.133619	+	0.411237i
$805$	−2.11522	−	20.8151i	−0.0745517	−	0.733637i
$806$	4.06206	−	12.5017i	0.143080	−	0.440355i
$807$	−1.54196			−0.0542797
$808$	−5.63289	+	17.3363i	−0.198164	+	0.609888i
$809$	13.5598	−	9.85176i	0.476737	−	0.346369i	−0.323324	−	0.946288i	$-0.604800\pi$
$809$	13.5598	−	9.85176i	0.476737	−	0.346369i	0.800061	+	0.599919i	$0.204800\pi$
$810$	−7.27920	−	1.57349i	−0.255765	−	0.0552869i
$811$	12.5967	+	9.15206i	0.442331	+	0.321372i	0.786560	−	0.617513i	$-0.211860\pi$
$811$	12.5967	+	9.15206i	0.442331	+	0.321372i	−0.344230	+	0.938886i	$0.611860\pi$
$812$	−3.87121	+	2.81260i	−0.135853	+	0.0987028i
$813$	−9.79191	+	7.11424i	−0.343417	+	0.249507i
$814$	−0.0633181	−	0.0460033i	−0.00221930	−	0.00161241i
$815$	18.5886	+	4.01818i	0.651132	+	0.140751i
$816$	5.42840	−	3.94396i	0.190032	−	0.138066i
$817$	1.77147	−	5.45201i	0.0619758	−	0.190742i
$818$	11.1358			0.389355
$819$	4.97216	−	15.3027i	0.173741	−	0.534721i
$820$	2.43122	+	23.9248i	0.0849020	+	0.835491i
$821$	−4.07961	−	12.5557i	−0.142379	−	0.438199i	0.854285	−	0.519804i	$-0.173995\pi$
$821$	−4.07961	−	12.5557i	−0.142379	−	0.438199i	−0.996665	+	0.0816058i	$0.973995\pi$
$822$	−1.14034	−	3.50960i	−0.0397739	−	0.122411i
$823$	7.11468	+	5.16912i	0.248002	+	0.180184i	0.704841	−	0.709365i	$-0.251018\pi$
$823$	7.11468	+	5.16912i	0.248002	+	0.180184i	−0.456839	+	0.889550i	$0.651018\pi$
$824$	6.88868			0.239978
$825$	9.71984	+	4.40812i	0.338401	+	0.153471i
$826$	1.97417			0.0686903
$827$	10.5760	+	7.68395i	0.367765	+	0.267197i	0.756284	−	0.654244i	$-0.227013\pi$
$827$	10.5760	+	7.68395i	0.367765	+	0.267197i	−0.388518	+	0.921441i	$0.627013\pi$
$828$	1.61241	+	4.96249i	0.0560351	+	0.172458i
$829$	9.94630	+	30.6116i	0.345449	+	1.06318i	0.961343	+	0.275354i	$0.0887952\pi$
$829$	9.94630	+	30.6116i	0.345449	+	1.06318i	−0.615893	+	0.787829i	$0.711205\pi$
$830$	14.1555	+	3.05989i	0.491344	+	0.106210i
$831$	−2.02897	+	6.24453i	−0.0703843	+	0.216620i
$832$	5.19563			0.180126
$833$	2.31019	−	7.11002i	0.0800432	−	0.246348i
$834$	−8.34238	+	6.06109i	−0.288873	+	0.209879i
$835$	−27.6671	+	12.2040i	−0.957458	+	0.422338i
$836$	−1.33001	−	0.966306i	−0.0459992	−	0.0334204i
$837$	−11.4654	+	8.33007i	−0.396301	+	0.287929i
$838$	6.43799	−	4.67748i	0.222397	−	0.161581i
$839$	26.4068	+	19.1857i	0.911665	+	0.662363i	0.941435	−	0.337193i	$-0.109478\pi$
$839$	26.4068	+	19.1857i	0.911665	+	0.662363i	−0.0297704	+	0.999557i	$0.509478\pi$
$840$	4.56052	+	5.10022i	0.157353	+	0.175974i
$841$	20.1259	−	14.6223i	0.693995	−	0.504217i
$842$	3.34179	−	10.2850i	0.115166	−	0.354443i
$843$	−38.0339			−1.30996
$844$	7.27707	−	22.3965i	0.250487	−	0.770919i
$845$	28.6312	−	12.6293i	0.984944	−	0.434462i
$846$	−2.96488	−	9.12495i	−0.101935	−	0.313722i
$847$	6.04226	+	18.5962i	0.207614	+	0.638971i
$848$	−7.21137	−	5.23937i	−0.247640	−	0.179921i
$849$	17.5157			0.601137
$850$	−12.7649	−	22.4658i	−0.437831	−	0.770569i
$851$	0.189026			0.00647973
$852$	11.6644	+	8.47470i	0.399617	+	0.290338i
$853$	−13.5637	−	41.7448i	−0.464412	−	1.42931i	−0.859720	−	0.510765i	$-0.829362\pi$
$853$	−13.5637	−	41.7448i	−0.464412	−	1.42931i	0.395308	−	0.918549i	$-0.370638\pi$
$854$	−0.672756	−	2.07053i	−0.0230212	−	0.0708521i
$855$	1.47803	−	2.53976i	0.0505477	−	0.0868581i
$856$	−0.0489760	+	0.150733i	−0.00167397	+	0.00515194i
$857$	18.2382			0.623006			0.311503	−	0.950245i	$-0.399168\pi$
$857$	18.2382			0.623006			0.311503	+	0.950245i	$0.399168\pi$
$858$	−3.42709	+	10.5475i	−0.116999	+	0.360086i
$859$	5.96678	−	4.33512i	0.203584	−	0.147912i	−0.481322	−	0.876544i	$-0.659843\pi$
$859$	5.96678	−	4.33512i	0.203584	−	0.147912i	0.684906	+	0.728631i	$0.259843\pi$
$860$	−6.44746	+	11.0789i	−0.219857	+	0.377789i
$861$	−26.6219	−	19.3420i	−0.907272	−	0.659172i
$862$	−22.6238	+	16.4372i	−0.770570	+	0.559852i
$863$	−46.1483	+	33.5287i	−1.57091	+	1.14133i	−0.644625	+	0.764499i	$0.722987\pi$
$863$	−46.1483	+	33.5287i	−1.57091	+	1.14133i	−0.926282	+	0.376832i	$0.877013\pi$
$864$	−4.53171	−	3.29248i	−0.154172	−	0.112012i
$865$	−3.49301	−	34.3735i	−0.118766	−	1.16873i
$866$	26.6119	−	19.3347i	0.904310	−	0.657020i
$867$	3.89436	−	11.9856i	0.132259	−	0.407052i
$868$	5.96216			0.202369
$869$	5.92510	−	18.2356i	0.200995	−	0.618600i
$870$	3.92959	+	4.39463i	0.133225	+	0.148992i
$871$	15.1609	+	46.6605i	0.513708	+	1.58103i
$872$	−2.56669	−	7.89946i	−0.0869191	−	0.267509i
$873$	9.79454	+	7.11615i	0.331495	+	0.240845i
$874$	3.97052			0.134305
$875$	21.4743	−	15.2651i	0.725964	−	0.516055i
$876$	−3.83225			−0.129480
$877$	10.3344	+	7.50841i	0.348969	+	0.253541i	0.748437	−	0.663206i	$-0.230805\pi$
$877$	10.3344	+	7.50841i	0.348969	+	0.253541i	−0.399467	+	0.916747i	$0.630805\pi$
$878$	8.27698	+	25.4739i	0.279335	+	0.859704i
$879$	−2.71295	−	8.34959i	−0.0915054	−	0.281625i
$880$	2.45032	+	2.74030i	0.0826003	+	0.0923755i
$881$	12.0518	−	37.0916i	0.406035	−	1.24965i	−0.513992	−	0.857795i	$-0.671834\pi$
$881$	12.0518	−	37.0916i	0.406035	−	1.24965i	0.920028	−	0.391854i	$-0.128166\pi$
$882$	−1.90110			−0.0640134
$883$	6.09561	−	18.7604i	0.205134	−	0.631336i	−0.794574	−	0.607167i	$-0.792306\pi$
$883$	6.09561	−	18.7604i	0.205134	−	0.631336i	0.999708	−	0.0241693i	$-0.00769407\pi$
$884$	21.7221	−	15.7820i	0.730593	−	0.530807i
$885$	−0.245893	−	2.41975i	−0.00826561	−	0.0813390i
$886$	−13.9058	−	10.1031i	−0.467173	−	0.339421i
$887$	−42.1122	+	30.5963i	−1.41399	+	1.02732i	−0.421261	+	0.906939i	$0.638412\pi$
$887$	−42.1122	+	30.5963i	−1.41399	+	1.02732i	−0.992727	+	0.120384i	$0.961588\pi$
$888$	−0.0500082	+	0.0363331i	−0.00167816	+	0.00121926i
$889$	−1.31267	−	0.953710i	−0.0440255	−	0.0319864i
$890$	−17.4398	+	29.9674i	−0.584582	+	1.00451i
$891$	4.42964	−	3.21832i	0.148399	−	0.107818i
$892$	3.49551	−	10.7581i	0.117038	−	0.360207i
$893$	−7.30093			−0.244316
$894$	9.29016	−	28.5922i	0.310709	−	0.956265i
$895$	−28.5122	+	48.9937i	−0.953059	+	1.63768i
$896$	0.728216	+	2.24122i	0.0243280	+	0.0748739i
$897$	−8.27708	−	25.4742i	−0.276364	−	0.850560i
$898$	−4.01623	−	2.91797i	−0.134023	−	0.0973738i
$899$	5.13732			0.171339
$900$	−4.43027	+	4.85259i	−0.147676	+	0.161753i
$901$	−46.0644			−1.53463
$902$	−14.3037	−	10.3922i	−0.476261	−	0.346024i
$903$	−5.42026	−	16.6818i	−0.180375	−	0.555137i
$904$	−1.14284	−	3.51729i	−0.0380102	−	0.116983i
$905$	12.6390	−	5.57508i	0.420133	−	0.185322i
$906$	1.71501	−	5.27826i	0.0569774	−	0.175358i
$907$	6.52574			0.216684			0.108342	−	0.994114i	$-0.465446\pi$
$907$	6.52574			0.216684			0.108342	+	0.994114i	$0.465446\pi$
$908$	2.22060	−	6.83430i	0.0736931	−	0.226804i
$909$	19.3800	−	14.0804i	0.642792	−	0.467016i
$910$	18.2492	+	20.4089i	0.604955	+	0.676547i
$911$	26.1416	+	18.9930i	0.866111	+	0.629266i	0.929541	−	0.368720i	$-0.120204\pi$
$911$	26.1416	+	18.9930i	0.866111	+	0.629266i	−0.0634296	+	0.997986i	$0.520204\pi$
$912$	−1.05043	+	0.763181i	−0.0347832	+	0.0252715i
$913$	−8.61410	+	6.25851i	−0.285085	+	0.207126i
$914$	−14.2491	−	10.3526i	−0.471320	−	0.342434i
$915$	−2.45406	+	1.08249i	−0.0811287	+	0.0357861i
$916$	−11.1161	+	8.07635i	−0.367288	+	0.266850i
$917$	−11.5625	+	35.5858i	−0.381829	+	1.17515i
$918$	−28.9474			−0.955407
$919$	10.7005	−	32.9326i	0.352975	−	1.08635i	−0.604199	−	0.796834i	$-0.706507\pi$
$919$	10.7005	−	32.9326i	0.352975	−	1.08635i	0.957174	−	0.289513i	$-0.0934933\pi$
$920$	−8.67792	−	1.87585i	−0.286103	−	0.0618448i
$921$	−2.52055	−	7.75746i	−0.0830550	−	0.255617i
$922$	−6.12196	−	18.8415i	−0.201616	−	0.620511i
$923$	46.6759	+	33.9120i	1.53636	+	1.11623i
$924$	−5.03017			−0.165481
$925$	0.117594	+	0.206962i	0.00386647	+	0.00680486i
$926$	15.5954			0.512496
$927$	−7.32385	−	5.32109i	−0.240547	−	0.174767i
$928$	0.627470	+	1.93116i	0.0205977	+	0.0633933i
$929$	0.0199525	+	0.0614076i	0.000654622	+	0.00201472i	0.951383	−	0.308009i	$-0.0996628\pi$
$929$	0.0199525	+	0.0614076i	0.000654622	+	0.00201472i	−0.950729	+	0.310024i	$0.899663\pi$
$930$	−0.742617	−	7.30783i	−0.0243514	−	0.239633i
$931$	−0.447035	+	1.37583i	−0.0146510	+	0.0450911i
$932$	−14.2903			−0.468094
$933$	−5.12996	+	15.7884i	−0.167947	+	0.516888i
$934$	10.6401	−	7.73049i	0.348155	−	0.252949i
$935$	18.5682	+	4.01376i	0.607244	+	0.131264i
$936$	−5.52385	−	4.01331i	−0.180553	−	0.131179i
$937$	5.95659	−	4.32771i	0.194593	−	0.141380i	−0.486222	−	0.873835i	$-0.661625\pi$
$937$	5.95659	−	4.32771i	0.194593	−	0.141380i	0.680816	+	0.732455i	$0.261625\pi$
$938$	−18.0028	+	13.0798i	−0.587813	+	0.427071i
$939$	−17.0096	−	12.3582i	−0.555087	−	0.403295i
$940$	15.9568	+	3.44928i	0.520454	+	0.112503i
$941$	25.8903	−	18.8104i	0.844001	−	0.613202i	−0.0794847	−	0.996836i	$-0.525327\pi$
$941$	25.8903	−	18.8104i	0.844001	−	0.613202i	0.923485	+	0.383634i	$0.125327\pi$
$942$	−6.90048	+	21.2375i	−0.224830	+	0.691955i
$943$	42.7014			1.39055
$944$	0.258875	−	0.796735i	0.00842566	−	0.0259315i
$945$	−2.98410	−	29.3655i	−0.0970727	−	0.955258i
$946$	−2.91225	−	8.96298i	−0.0946854	−	0.291412i
$947$	13.3603	+	41.1188i	0.434152	+	1.33618i	0.893954	+	0.448160i	$0.147920\pi$
$947$	13.3603	+	41.1188i	0.434152	+	1.33618i	−0.459802	+	0.888021i	$0.652080\pi$
$948$	−12.2514	−	8.90113i	−0.397906	−	0.289095i
$949$	−15.3350			−0.497794
$950$	2.47008	+	4.34726i	0.0801400	+	0.141044i
$951$	11.4374			0.370884
$952$	9.85237	+	7.15817i	0.319317	+	0.231998i
$953$	−2.23635	−	6.88276i	−0.0724423	−	0.222955i	0.908279	−	0.418364i	$-0.137396\pi$
$953$	−2.23635	−	6.88276i	−0.0724423	−	0.222955i	−0.980722	+	0.195410i	$0.937396\pi$
$954$	3.61983	+	11.1407i	0.117196	+	0.360693i
$955$	54.0969	+	11.6938i	1.75054	+	0.378401i
$956$	5.27534	−	16.2358i	0.170617	−	0.525104i
$957$	−4.33427			−0.140107
$958$	12.5671	−	38.6774i	0.406023	−	1.24961i
$959$	5.41849	−	3.93676i	0.174972	−	0.127125i
$960$	2.65637	−	1.17173i	0.0857338	−	0.0378175i
$961$	19.9010	+	14.4589i	0.641967	+	0.466416i
$962$	−0.200111	+	0.145389i	−0.00645183	+	0.00468753i
$963$	0.168502	−	0.122424i	0.00542990	−	0.00394505i
$964$	1.61161	+	1.17090i	0.0519065	+	0.0377123i
$965$	16.8172	+	18.8074i	0.541366	+	0.605433i
$966$	9.82861	−	7.14090i	0.316230	−	0.229755i
$967$	13.5831	−	41.8044i	0.436802	−	1.34434i	−0.454426	−	0.890785i	$-0.650156\pi$
$967$	13.5831	−	41.8044i	0.436802	−	1.34434i	0.891228	−	0.453555i	$-0.149844\pi$
$968$	8.29734			0.266687
$969$	−2.07346	+	6.38147i	−0.0666093	+	0.205002i
$970$	−18.8477	+	8.31381i	−0.605165	+	0.266940i
$971$	10.5367	+	32.4286i	0.338139	+	1.04068i	0.965155	+	0.261678i	$0.0842758\pi$
$971$	10.5367	+	32.4286i	0.338139	+	1.04068i	−0.627017	+	0.779006i	$0.715724\pi$
$972$	3.85657	+	11.8693i	0.123700	+	0.380708i
$973$	−15.1412	−	11.0007i	−0.485403	−	0.352666i
$974$	−38.7495			−1.24161
$975$	22.7422	−	24.9101i	0.728332	−	0.797762i
$976$	−0.923841			−0.0295714
$977$	−34.3251	−	24.9387i	−1.09816	−	0.797858i	−0.117400	−	0.993085i	$-0.537456\pi$
$977$	−34.3251	−	24.9387i	−1.09816	−	0.797858i	−0.980758	+	0.195226i	$0.937456\pi$
$978$	3.41249	+	10.5026i	0.109119	+	0.335835i
$979$	−7.87735	−	24.2440i	−0.251761	−	0.774841i
$980$	1.62704	−	2.79581i	0.0519739	−	0.0893088i
$981$	−3.37302	+	10.3811i	−0.107692	+	0.331443i
$982$	−26.2761			−0.838504
$983$	16.6321	−	51.1884i	0.530482	−	1.63266i	−0.222732	−	0.974880i	$-0.571497\pi$
$983$	16.6321	−	51.1884i	0.530482	−	1.63266i	0.753214	−	0.657776i	$-0.228503\pi$
$984$	−11.2970	+	8.20772i	−0.360134	+	0.261652i
$985$	6.74777	−	11.5950i	0.215002	−	0.369446i
$986$	8.48933	+	6.16786i	0.270355	+	0.196425i
$987$	−18.0727	+	13.1306i	−0.575260	+	0.417951i
$988$	−4.20336	+	3.05392i	−0.133727	+	0.0971581i
$989$	18.4143	+	13.3788i	0.585541	+	0.425420i
$990$	−0.488396	−	4.80613i	−0.0155222	−	0.152749i
$991$	−4.76324	+	3.46070i	−0.151309	+	0.109933i	−0.660864	−	0.750505i	$-0.729810\pi$
$991$	−4.76324	+	3.46070i	−0.151309	+	0.109933i	0.509555	+	0.860438i	$0.329810\pi$
$992$	0.781822	−	2.40620i	0.0248229	−	0.0763969i
$993$	43.4641			1.37929
$994$	−8.08643	+	24.8875i	−0.256486	+	0.789383i
$995$	24.2749	+	27.1477i	0.769566	+	0.860639i
$996$	2.59865	+	7.99782i	0.0823414	+	0.253421i
$997$	−3.40552	−	10.4811i	−0.107854	−	0.331940i	0.882536	−	0.470245i	$-0.155835\pi$
$997$	−3.40552	−	10.4811i	−0.107854	−	0.331940i	−0.990390	+	0.138305i	$0.955835\pi$
$998$	−13.0221	−	9.46108i	−0.412206	−	0.299485i
$999$	0.266673			0.00843716

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	950.2.h.e.191.7	✓	44
25.11	even	5	inner	950.2.h.e.761.7	yes	44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
950.2.h.e.191.7	✓	44	1.1	even	1	trivial
950.2.h.e.761.7	yes	44	25.11	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)

\(f(q)\)	\(=\)	\(q+(0.809017 + 0.587785i) q^{2} +(0.401228 + 1.23485i) q^{3} +(0.309017 + 0.951057i) q^{4} +(1.49048 + 1.66687i) q^{5} +(-0.401228 + 1.23485i) q^{6} -2.35656 q^{7} +(-0.309017 + 0.951057i) q^{8} +(1.06317 - 0.772440i) q^{9} +O(q^{10})\)	\(q+(0.809017 + 0.587785i) q^{2} +(0.401228 + 1.23485i) q^{3} +(0.309017 + 0.951057i) q^{4} +(1.49048 + 1.66687i) q^{5} +(-0.401228 + 1.23485i) q^{6} -2.35656 q^{7} +(-0.309017 + 0.951057i) q^{8} +(1.06317 - 0.772440i) q^{9} +(0.226063 + 2.22461i) q^{10} +(-1.33001 - 0.966306i) q^{11} +(-1.05043 + 0.763181i) q^{12} +(-4.20336 + 3.05392i) q^{13} +(-1.90650 - 1.38515i) q^{14} +(-1.46032 + 2.50932i) q^{15} +(-0.809017 + 0.587785i) q^{16} +(-1.59694 + 4.91486i) q^{17} +1.31415 q^{18} +(0.309017 - 0.951057i) q^{19} +(-1.12470 + 1.93263i) q^{20} +(-0.945517 - 2.91000i) q^{21} +(-0.508017 - 1.56352i) q^{22} +(3.21222 + 2.33381i) q^{23} -1.29840 q^{24} +(-0.556922 + 4.96889i) q^{25} -5.19563 q^{26} +(4.53171 + 3.29248i) q^{27} +(-0.728216 - 2.24122i) q^{28} +(-0.627470 - 1.93116i) q^{29} +(-2.65637 + 1.17173i) q^{30} +(-0.781822 + 2.40620i) q^{31} -1.00000 q^{32} +(0.659610 - 2.03007i) q^{33} +(-4.18083 + 3.03755i) q^{34} +(-3.51241 - 3.92808i) q^{35} +(1.06317 + 0.772440i) q^{36} +(0.0385152 - 0.0279829i) q^{37} +(0.809017 - 0.587785i) q^{38} +(-5.45765 - 3.96521i) q^{39} +(-2.04587 + 0.902442i) q^{40} +(8.70066 - 6.32140i) q^{41} +(0.945517 - 2.91000i) q^{42} +5.73258 q^{43} +(0.508017 - 1.56352i) q^{44} +(2.87220 + 0.620863i) q^{45} +(1.22696 + 3.77619i) q^{46} +(-2.25611 - 6.94360i) q^{47} +(-1.05043 - 0.763181i) q^{48} -1.44664 q^{49} +(-3.37120 + 3.69256i) q^{50} -6.70987 q^{51} +(-4.20336 - 3.05392i) q^{52} +(2.75450 + 8.47748i) q^{53} +(1.73096 + 5.32735i) q^{54} +(-0.371643 - 3.65721i) q^{55} +(0.728216 - 2.24122i) q^{56} +1.29840 q^{57} +(0.627470 - 1.93116i) q^{58} +(-0.677743 + 0.492409i) q^{59} +(-2.83777 - 0.613422i) q^{60} +(0.747403 + 0.543020i) q^{61} +(-2.04684 + 1.48711i) q^{62} +(-2.50543 + 1.82030i) q^{63} +(-0.809017 - 0.587785i) q^{64} +(-11.3555 - 2.45464i) q^{65} +(1.72688 - 1.25465i) q^{66} +(2.91801 - 8.98072i) q^{67} -5.16779 q^{68} +(-1.59308 + 4.90301i) q^{69} +(-0.532731 - 5.24242i) q^{70} +(-3.43146 - 10.5609i) q^{71} +(0.406096 + 1.24983i) q^{72} +(2.38782 + 1.73486i) q^{73} +0.0476074 q^{74} +(-6.35930 + 1.30594i) q^{75} +1.00000 q^{76} +(3.13423 + 2.27715i) q^{77} +(-2.08464 - 6.41585i) q^{78} +(3.60413 + 11.0924i) q^{79} +(-2.18559 - 0.472444i) q^{80} +(-1.02919 + 3.16753i) q^{81} +10.7546 q^{82} +(2.00142 - 6.15974i) q^{83} +(2.47540 - 1.79848i) q^{84} +(-10.5727 + 4.66363i) q^{85} +(4.63776 + 3.36953i) q^{86} +(2.13293 - 1.54967i) q^{87} +(1.33001 - 0.966306i) q^{88} +(12.5447 + 9.11425i) q^{89} +(1.95872 + 2.19052i) q^{90} +(9.90545 - 7.19673i) q^{91} +(-1.22696 + 3.77619i) q^{92} -3.28499 q^{93} +(2.25611 - 6.94360i) q^{94} +(2.04587 - 0.902442i) q^{95} +(-0.401228 - 1.23485i) q^{96} +(2.84684 + 8.76167i) q^{97} +(-1.17035 - 0.850312i) q^{98} -2.16044 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

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