LMFDB - Embedded newform 195.2.o.a.161.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [195,2,Mod(86,195)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(195, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 0, 1]))

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

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

chi := DirichletCharacter("195.86");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 195 = 3 \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	195.o (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$1.55708283941$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$20$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			161.8
Character	$\chi$	$=$	195.161
Dual form			195.2.o.a.86.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.483812 - 0.483812i) q^{2} +(1.53965 - 0.793397i) q^{3} -1.53185i q^{4} +(-0.707107 - 0.707107i) q^{5} +(-1.12876 - 0.361045i) q^{6} +(-1.24531 - 1.24531i) q^{7} +(-1.70875 + 1.70875i) q^{8} +(1.74104 - 2.44311i) q^{9} +O(q^{10})$	\(q+(-0.483812 - 0.483812i) q^{2} +(1.53965 - 0.793397i) q^{3} -1.53185i q^{4} +(-0.707107 - 0.707107i) q^{5} +(-1.12876 - 0.361045i) q^{6} +(-1.24531 - 1.24531i) q^{7} +(-1.70875 + 1.70875i) q^{8} +(1.74104 - 2.44311i) q^{9} +0.684213i q^{10} +(-0.387103 + 0.387103i) q^{11} +(-1.21537 - 2.35852i) q^{12} +(-0.874878 + 3.49780i) q^{13} +1.20499i q^{14} +(-1.64971 - 0.527680i) q^{15} -1.41028 q^{16} +6.75010 q^{17} +(-2.02434 + 0.339668i) q^{18} +(1.33304 - 1.33304i) q^{19} +(-1.08318 + 1.08318i) q^{20} +(-2.90536 - 0.929314i) q^{21} +0.374570 q^{22} +1.69635 q^{23} +(-1.27516 + 3.98660i) q^{24} +1.00000i q^{25} +(2.11555 - 1.26900i) q^{26} +(0.742237 - 5.14287i) q^{27} +(-1.90763 + 1.90763i) q^{28} -3.85370i q^{29} +(0.542853 + 1.05345i) q^{30} +(4.06109 - 4.06109i) q^{31} +(4.09981 + 4.09981i) q^{32} +(-0.288877 + 0.903130i) q^{33} +(-3.26578 - 3.26578i) q^{34} +1.76113i q^{35} +(-3.74248 - 2.66702i) q^{36} +(-2.36718 - 2.36718i) q^{37} -1.28988 q^{38} +(1.42814 + 6.07951i) q^{39} +2.41654 q^{40} +(5.72121 + 5.72121i) q^{41} +(0.956036 + 1.85526i) q^{42} +11.7392i q^{43} +(0.592985 + 0.592985i) q^{44} +(-2.95864 + 0.496436i) q^{45} +(-0.820713 - 0.820713i) q^{46} +(-5.99016 + 5.99016i) q^{47} +(-2.17133 + 1.11891i) q^{48} -3.89841i q^{49} +(0.483812 - 0.483812i) q^{50} +(10.3928 - 5.35551i) q^{51} +(5.35811 + 1.34018i) q^{52} +8.81372i q^{53} +(-2.84728 + 2.12908i) q^{54} +0.547447 q^{55} +4.25585 q^{56} +(0.994786 - 3.11005i) q^{57} +(-1.86446 + 1.86446i) q^{58} +(1.30531 - 1.30531i) q^{59} +(-0.808328 + 2.52712i) q^{60} -1.16343 q^{61} -3.92960 q^{62} +(-5.21056 + 0.874290i) q^{63} -1.14652i q^{64} +(3.09195 - 1.85468i) q^{65} +(0.576707 - 0.297183i) q^{66} +(-4.66845 + 4.66845i) q^{67} -10.3402i q^{68} +(2.61178 - 1.34588i) q^{69} +(0.852057 - 0.852057i) q^{70} +(-0.915921 - 0.915921i) q^{71} +(1.19966 + 7.14967i) q^{72} +(8.11348 + 8.11348i) q^{73} +2.29054i q^{74} +(0.793397 + 1.53965i) q^{75} +(-2.04202 - 2.04202i) q^{76} +0.964126 q^{77} +(2.25039 - 3.63229i) q^{78} -3.85408 q^{79} +(0.997216 + 0.997216i) q^{80} +(-2.93755 - 8.50710i) q^{81} -5.53597i q^{82} +(-11.9347 - 11.9347i) q^{83} +(-1.42357 + 4.45059i) q^{84} +(-4.77304 - 4.77304i) q^{85} +(5.67957 - 5.67957i) q^{86} +(-3.05751 - 5.93334i) q^{87} -1.32293i q^{88} +(-5.99694 + 5.99694i) q^{89} +(1.67161 + 1.19124i) q^{90} +(5.44533 - 3.26635i) q^{91} -2.59855i q^{92} +(3.03059 - 9.47471i) q^{93} +5.79622 q^{94} -1.88521 q^{95} +(9.56505 + 3.05949i) q^{96} +(1.03487 - 1.03487i) q^{97} +(-1.88610 + 1.88610i) q^{98} +(0.271772 + 1.61970i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q + 12 q^{6} - 16 q^{7}+O(q^{10}) $ 40 * q + 12 * q^6 - 16 * q^7	$ 40 q + 12 q^{6} - 16 q^{7} + 4 q^{15} - 64 q^{16} + 4 q^{18} - 16 q^{19} - 12 q^{21} + 8 q^{24} - 24 q^{27} + 32 q^{28} + 32 q^{31} - 4 q^{33} - 16 q^{34} + 32 q^{37} - 8 q^{39} + 8 q^{42} - 8 q^{45} - 40 q^{46} + 8 q^{48} - 32 q^{54} + 8 q^{55} - 36 q^{57} + 24 q^{58} + 16 q^{60} + 8 q^{61} + 8 q^{63} - 48 q^{66} - 32 q^{67} + 132 q^{72} - 64 q^{73} + 16 q^{76} - 12 q^{78} + 40 q^{79} + 72 q^{81} + 124 q^{84} - 24 q^{85} + 16 q^{87} + 8 q^{91} - 108 q^{93} - 32 q^{94} - 76 q^{96} + 24 q^{97} - 20 q^{99}+O(q^{100}) $ 40 * q + 12 * q^6 - 16 * q^7 + 4 * q^15 - 64 * q^16 + 4 * q^18 - 16 * q^19 - 12 * q^21 + 8 * q^24 - 24 * q^27 + 32 * q^28 + 32 * q^31 - 4 * q^33 - 16 * q^34 + 32 * q^37 - 8 * q^39 + 8 * q^42 - 8 * q^45 - 40 * q^46 + 8 * q^48 - 32 * q^54 + 8 * q^55 - 36 * q^57 + 24 * q^58 + 16 * q^60 + 8 * q^61 + 8 * q^63 - 48 * q^66 - 32 * q^67 + 132 * q^72 - 64 * q^73 + 16 * q^76 - 12 * q^78 + 40 * q^79 + 72 * q^81 + 124 * q^84 - 24 * q^85 + 16 * q^87 + 8 * q^91 - 108 * q^93 - 32 * q^94 - 76 * q^96 + 24 * q^97 - 20 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/195\mathbb{Z}\right)^\times$.

$n$	$106$	$131$	$157$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$-1$	$1$

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 $

$2$	−0.483812	−	0.483812i	−0.342107	−	0.342107i	0.515052	−	0.857159i	$-0.327773\pi$
$2$	−0.483812	−	0.483812i	−0.342107	−	0.342107i	−0.857159	+	0.515052i	$0.827773\pi$
$3$	1.53965	−	0.793397i	0.888917	−	0.458068i
$3$	1.53965	−	0.793397i	0.888917	−	0.458068i
$4$		−	1.53185i		−	0.765926i
$5$	−0.707107	−	0.707107i	−0.316228	−	0.316228i
$5$	−0.707107	−	0.707107i	−0.316228	−	0.316228i
$6$	−1.12876	−	0.361045i	−0.460813	−	0.147396i
$7$	−1.24531	−	1.24531i	−0.470683	−	0.470683i	0.431453	−	0.902135i	$-0.358001\pi$
$7$	−1.24531	−	1.24531i	−0.470683	−	0.470683i	−0.902135	+	0.431453i	$0.858001\pi$
$8$	−1.70875	+	1.70875i	−0.604135	+	0.604135i
$9$	1.74104	−	2.44311i	0.580347	−	0.814369i
$10$			0.684213i			0.216367i
$11$	−0.387103	+	0.387103i	−0.116716	+	0.116716i	−0.763053	−	0.646337i	$-0.776300\pi$
$11$	−0.387103	+	0.387103i	−0.116716	+	0.116716i	0.646337	+	0.763053i	$0.276300\pi$
$12$	−1.21537	−	2.35852i	−0.350846	−	0.680845i
$13$	−0.874878	+	3.49780i	−0.242647	+	0.970115i
$13$	−0.874878	+	3.49780i	−0.242647	+	0.970115i
$14$			1.20499i			0.322047i
$15$	−1.64971	−	0.527680i	−0.425954	−	0.136246i
$16$	−1.41028			−0.352569
$17$	6.75010			1.63714			0.818570	−	0.574407i	$-0.194767\pi$
$17$	6.75010			1.63714			0.818570	+	0.574407i	$0.194767\pi$
$18$	−2.02434	+	0.339668i	−0.477142	+	0.0800606i
$19$	1.33304	−	1.33304i	0.305821	−	0.305821i	−0.537465	−	0.843286i	$-0.680618\pi$
$19$	1.33304	−	1.33304i	0.305821	−	0.305821i	0.843286	+	0.537465i	$0.180618\pi$
$20$	−1.08318	+	1.08318i	−0.242207	+	0.242207i
$21$	−2.90536	−	0.929314i	−0.634003	−	0.202793i
$22$	0.374570			0.0798586
$23$	1.69635			0.353713			0.176856	−	0.984237i	$-0.443407\pi$
$23$	1.69635			0.353713			0.176856	+	0.984237i	$0.443407\pi$
$24$	−1.27516	+	3.98660i	−0.260291	+	0.813761i
$25$			1.00000i			0.200000i
$26$	2.11555	−	1.26900i	0.414894	−	0.248871i
$27$	0.742237	−	5.14287i	0.142844	−	0.989745i
$28$	−1.90763	+	1.90763i	−0.360508	+	0.360508i
$29$		−	3.85370i		−	0.715614i	−0.933796	−	0.357807i	$-0.883525\pi$
$29$		−	3.85370i		−	0.715614i	0.933796	−	0.357807i	$-0.116475\pi$
$30$	0.542853	+	1.05345i	0.0991109	+	0.192332i
$31$	4.06109	−	4.06109i	0.729393	−	0.729393i	−0.241106	−	0.970499i	$-0.577510\pi$
$31$	4.06109	−	4.06109i	0.729393	−	0.729393i	0.970499	+	0.241106i	$0.0775102\pi$
$32$	4.09981	+	4.09981i	0.724751	+	0.724751i
$33$	−0.288877	+	0.903130i	−0.0502869	+	0.157215i
$34$	−3.26578	−	3.26578i	−0.560076	−	0.560076i
$35$			1.76113i			0.297686i
$36$	−3.74248	−	2.66702i	−0.623747	−	0.444503i
$37$	−2.36718	−	2.36718i	−0.389163	−	0.389163i	0.485226	−	0.874389i	$-0.338737\pi$
$37$	−2.36718	−	2.36718i	−0.389163	−	0.389163i	−0.874389	+	0.485226i	$0.838737\pi$
$38$	−1.28988			−0.209247
$39$	1.42814	+	6.07951i	0.228685	+	0.973500i
$40$	2.41654			0.382088
$41$	5.72121	+	5.72121i	0.893502	+	0.893502i	0.994851	−	0.101349i	$-0.0323158\pi$
$41$	5.72121	+	5.72121i	0.893502	+	0.893502i	−0.101349	+	0.994851i	$0.532316\pi$
$42$	0.956036	+	1.85526i	0.147520	+	0.286273i
$43$			11.7392i			1.79021i	0.445853	+	0.895106i	$0.352900\pi$
$43$			11.7392i			1.79021i	−0.445853	+	0.895106i	$0.647100\pi$
$44$	0.592985	+	0.592985i	0.0893958	+	0.0893958i
$45$	−2.95864	+	0.496436i	−0.441048	+	0.0740044i
$46$	−0.820713	−	0.820713i	−0.121008	−	0.121008i
$47$	−5.99016	+	5.99016i	−0.873755	+	0.873755i	−0.992879	−	0.119124i	$-0.961991\pi$
$47$	−5.99016	+	5.99016i	−0.873755	+	0.873755i	0.119124	+	0.992879i	$0.461991\pi$
$48$	−2.17133	+	1.11891i	−0.313405	+	0.161501i
$49$		−	3.89841i		−	0.556916i
$50$	0.483812	−	0.483812i	0.0684213	−	0.0684213i
$51$	10.3928	−	5.35551i	1.45528	−	0.749922i
$52$	5.35811	+	1.34018i	0.743036	+	0.185850i
$53$			8.81372i			1.21066i	0.795976	+	0.605328i	$0.206958\pi$
$53$			8.81372i			1.21066i	−0.795976	+	0.605328i	$0.793042\pi$
$54$	−2.84728	+	2.12908i	−0.387466	+	0.289731i
$55$	0.547447			0.0738177
$56$	4.25585			0.568712
$57$	0.994786	−	3.11005i	0.131763	−	0.411936i
$58$	−1.86446	+	1.86446i	−0.244816	+	0.244816i
$59$	1.30531	−	1.30531i	0.169937	−	0.169937i	−0.617015	−	0.786952i	$-0.711658\pi$
$59$	1.30531	−	1.30531i	0.169937	−	0.169937i	0.786952	+	0.617015i	$0.211658\pi$
$60$	−0.808328	+	2.52712i	−0.104355	+	0.326249i
$61$	−1.16343			−0.148961			−0.0744807	−	0.997222i	$-0.523730\pi$
$61$	−1.16343			−0.148961			−0.0744807	+	0.997222i	$0.523730\pi$
$62$	−3.92960			−0.499060
$63$	−5.21056	+	0.874290i	−0.656469	+	0.110150i
$64$		−	1.14652i		−	0.143315i
$65$	3.09195	−	1.85468i	0.383509	−	0.230045i
$66$	0.576707	−	0.297183i	0.0709877	−	0.0365807i
$67$	−4.66845	+	4.66845i	−0.570341	+	0.570341i	−0.932224	−	0.361882i	$-0.882134\pi$
$67$	−4.66845	+	4.66845i	−0.570341	+	0.570341i	0.361882	+	0.932224i	$0.382134\pi$
$68$		−	10.3402i		−	1.25393i
$69$	2.61178	−	1.34588i	0.314421	−	0.162025i
$70$	0.852057	−	0.852057i	0.101840	−	0.101840i
$71$	−0.915921	−	0.915921i	−0.108700	−	0.108700i	0.650665	−	0.759365i	$-0.274490\pi$
$71$	−0.915921	−	0.915921i	−0.108700	−	0.108700i	−0.759365	+	0.650665i	$0.774490\pi$
$72$	1.19966	+	7.14967i	0.141381	+	0.842597i
$73$	8.11348	+	8.11348i	0.949611	+	0.949611i	0.998790	−	0.0491790i	$-0.0156605\pi$
$73$	8.11348	+	8.11348i	0.949611	+	0.949611i	−0.0491790	+	0.998790i	$0.515660\pi$
$74$			2.29054i			0.266270i
$75$	0.793397	+	1.53965i	0.0916136	+	0.177783i
$76$	−2.04202	−	2.04202i	−0.234236	−	0.234236i
$77$	0.964126			0.109872
$78$	2.25039	−	3.63229i	0.254806	−	0.411276i
$79$	−3.85408			−0.433617			−0.216809	−	0.976214i	$-0.569565\pi$
$79$	−3.85408			−0.433617			−0.216809	+	0.976214i	$0.569565\pi$
$80$	0.997216	+	0.997216i	0.111492	+	0.111492i
$81$	−2.93755	−	8.50710i	−0.326395	−	0.945234i
$82$		−	5.53597i		−	0.611346i
$83$	−11.9347	−	11.9347i	−1.31000	−	1.31000i	−0.921412	−	0.388586i	$-0.872964\pi$
$83$	−11.9347	−	11.9347i	−1.31000	−	1.31000i	−0.388586	−	0.921412i	$-0.627036\pi$
$84$	−1.42357	+	4.45059i	−0.155325	+	0.485599i
$85$	−4.77304	−	4.77304i	−0.517709	−	0.517709i
$86$	5.67957	−	5.67957i	0.612443	−	0.612443i
$87$	−3.05751	−	5.93334i	−0.327800	−	0.636121i
$88$		−	1.32293i		−	0.141024i
$89$	−5.99694	+	5.99694i	−0.635674	+	0.635674i	−0.949485	−	0.313811i	$-0.898394\pi$
$89$	−5.99694	+	5.99694i	−0.635674	+	0.635674i	0.313811	+	0.949485i	$0.398394\pi$
$90$	1.67161	+	1.19124i	0.176203	+	0.125568i
$91$	5.44533	−	3.26635i	0.570826	−	0.342406i
$92$		−	2.59855i		−	0.270918i
$93$	3.03059	−	9.47471i	0.314258	−	0.982481i
$94$	5.79622			0.597835
$95$	−1.88521			−0.193418
$96$	9.56505	+	3.05949i	0.976229	+	0.312258i
$97$	1.03487	−	1.03487i	0.105075	−	0.105075i	−0.652615	−	0.757690i	$-0.726328\pi$
$97$	1.03487	−	1.03487i	0.105075	−	0.105075i	0.757690	+	0.652615i	$0.226328\pi$
$98$	−1.88610	+	1.88610i	−0.190525	+	0.190525i
$99$	0.271772	+	1.61970i	0.0273141	+	0.162786i
$100$	1.53185			0.153185
$101$	−18.2471			−1.81565			−0.907826	−	0.419347i	$-0.862259\pi$
$101$	−18.2471			−1.81565			−0.907826	+	0.419347i	$0.862259\pi$
$102$	−7.61921	−	2.43709i	−0.754415	−	0.241308i
$103$		−	3.65487i		−	0.360125i	−0.983655	−	0.180063i	$-0.942370\pi$
$103$		−	3.65487i		−	0.360125i	0.983655	−	0.180063i	$-0.0576300\pi$
$104$	−4.48192	−	7.47182i	−0.439488	−	0.732672i
$105$	1.39728	+	2.71153i	0.136360	+	0.264618i
$106$	4.26418	−	4.26418i	0.414174	−	0.414174i
$107$		−	14.9588i		−	1.44612i	−0.690786	−	0.723060i	$-0.742735\pi$
$107$		−	14.9588i		−	1.44612i	0.690786	−	0.723060i	$-0.257265\pi$
$108$	−7.87811	−	1.13700i	−0.758072	−	0.109408i
$109$	5.41443	−	5.41443i	0.518609	−	0.518609i	−0.398542	−	0.917150i	$-0.630484\pi$
$109$	5.41443	−	5.41443i	0.518609	−	0.518609i	0.917150	+	0.398542i	$0.130484\pi$
$110$	−0.264861	−	0.264861i	−0.0252535	−	0.0252535i
$111$	−5.52275	−	1.76652i	−0.524196	−	0.167670i
$112$	1.75623	+	1.75623i	0.165948	+	0.165948i
$113$			5.56044i			0.523083i	0.965192	+	0.261541i	$0.0842308\pi$
$113$			5.56044i			0.523083i	−0.965192	+	0.261541i	$0.915769\pi$
$114$	−1.98597	+	1.02339i	−0.186003	+	0.0958493i
$115$	−1.19950	−	1.19950i	−0.111854	−	0.111854i
$116$	−5.90330			−0.548107
$117$	7.02230	+	8.22723i	0.649212	+	0.760608i
$118$	−1.26305			−0.116273
$119$	−8.40596	−	8.40596i	−0.770573	−	0.770573i
$120$	3.72062	−	1.91728i	0.339645	−	0.175023i
$121$			10.7003i			0.972755i
$122$	0.562879	+	0.562879i	0.0509607	+	0.0509607i
$123$	13.3478	+	4.26946i	1.20353	+	0.384964i
$124$	−6.22098	−	6.22098i	−0.558661	−	0.558661i
$125$	0.707107	−	0.707107i	0.0632456	−	0.0632456i
$126$	2.94392	+	2.09794i	0.262265	+	0.186899i
$127$			0.0349646i			0.00310261i	0.999999	+	0.00155130i	$0.000493796\pi$
$127$			0.0349646i			0.00310261i	−0.999999	+	0.00155130i	$0.999506\pi$
$128$	7.64492	−	7.64492i	0.675722	−	0.675722i
$129$	9.31386	+	18.0743i	0.820039	+	1.59135i
$130$	−2.39324	−	0.598603i	−0.209901	−	0.0525009i
$131$			1.11950i			0.0978111i	0.998803	+	0.0489056i	$0.0155733\pi$
$131$			1.11950i			0.0978111i	−0.998803	+	0.0489056i	$0.984427\pi$
$132$	1.38346	+	0.442516i	0.120415	+	0.0385161i
$133$	−3.32010			−0.287889
$134$	4.51730			0.390235
$135$	−4.16140	+	3.11172i	−0.358156	+	0.267814i
$136$	−11.5342	+	11.5342i	−0.989054	+	0.989054i
$137$	2.58611	−	2.58611i	0.220946	−	0.220946i	−0.587950	−	0.808897i	$-0.700065\pi$
$137$	2.58611	−	2.58611i	0.220946	−	0.220946i	0.808897	+	0.587950i	$0.200065\pi$
$138$	−1.91476	−	0.612459i	−0.162995	−	0.0521359i
$139$	16.6867			1.41535			0.707673	−	0.706540i	$-0.249745\pi$
$139$	16.6867			1.41535			0.707673	+	0.706540i	$0.249745\pi$
$140$	2.69780			0.228005
$141$	−4.47017	+	13.9753i	−0.376456	+	1.17694i
$142$			0.886267i			0.0743739i
$143$	−1.01534	−	1.69268i	−0.0849071	−	0.141549i
$144$	−2.45535	+	3.44546i	−0.204612	+	0.287121i
$145$	−2.72498	+	2.72498i	−0.226297	+	0.226297i
$146$		−	7.85079i		−	0.649736i
$147$	−3.09299	−	6.00219i	−0.255105	−	0.495052i
$148$	−3.62618	+	3.62618i	−0.298070	+	0.298070i
$149$	16.9396	+	16.9396i	1.38775	+	1.38775i	0.830030	+	0.557719i	$0.188323\pi$
$149$	16.9396	+	16.9396i	1.38775	+	1.38775i	0.557719	+	0.830030i	$0.311677\pi$
$150$	0.361045	−	1.12876i	0.0294792	−	0.0921625i
$151$	−5.21274	−	5.21274i	−0.424207	−	0.424207i	0.462442	−	0.886649i	$-0.346973\pi$
$151$	−5.21274	−	5.21274i	−0.424207	−	0.424207i	−0.886649	+	0.462442i	$0.846973\pi$
$152$			4.55568i			0.369514i
$153$	11.7522	−	16.4912i	0.950109	−	1.33324i
$154$	−0.466456	−	0.466456i	−0.0375881	−	0.0375881i
$155$	−5.74324			−0.461308
$156$	9.31291	−	2.18770i	0.745629	−	0.175156i
$157$	−13.0314			−1.04002			−0.520008	−	0.854161i	$-0.674071\pi$
$157$	−13.0314			−1.04002			−0.520008	+	0.854161i	$0.674071\pi$
$158$	1.86465	+	1.86465i	0.148343	+	0.148343i
$159$	6.99278	+	13.5700i	0.554563	+	1.07617i
$160$		−	5.79801i		−	0.458373i
$161$	−2.11248	−	2.11248i	−0.166487	−	0.166487i
$162$	−2.69461	+	5.53706i	−0.211709	+	0.435032i
$163$	3.83399	+	3.83399i	0.300301	+	0.300301i	0.841132	−	0.540830i	$-0.181890\pi$
$163$	3.83399	+	3.83399i	0.300301	+	0.300301i	−0.540830	+	0.841132i	$0.681890\pi$
$164$	8.76404	−	8.76404i	0.684357	−	0.684357i
$165$	0.842876	−	0.434343i	0.0656178	−	0.0338135i
$166$			11.5483i			0.896318i
$167$	−9.06688	+	9.06688i	−0.701616	+	0.701616i	−0.964757	−	0.263141i	$-0.915242\pi$
$167$	−9.06688	+	9.06688i	−0.701616	+	0.701616i	0.263141	+	0.964757i	$0.415242\pi$
$168$	6.55251	−	3.37658i	0.505537	−	0.260509i
$169$	−11.4692	−	6.12029i	−0.882244	−	0.470792i
$170$			4.61851i			0.354223i
$171$	−0.935885	−	5.57765i	−0.0715689	−	0.426534i
$172$	17.9827			1.37117
$173$	4.63904			0.352700			0.176350	−	0.984328i	$-0.443571\pi$
$173$	4.63904			0.352700			0.176350	+	0.984328i	$0.443571\pi$
$174$	−1.39136	+	4.34988i	−0.105479	+	0.329764i
$175$	1.24531	−	1.24531i	0.0941365	−	0.0941365i
$176$	0.545923	−	0.545923i	0.0411505	−	0.0411505i
$177$	0.974090	−	3.04535i	0.0732171	−	0.228902i
$178$	5.80278			0.434936
$179$	−13.2894			−0.993298			−0.496649	−	0.867951i	$-0.665436\pi$
$179$	−13.2894			−0.993298			−0.496649	+	0.867951i	$0.665436\pi$
$180$	0.760467	+	4.53220i	0.0566819	+	0.337810i
$181$			23.3132i			1.73286i	0.499299	+	0.866429i	$0.333591\pi$
$181$			23.3132i			1.73286i	−0.499299	+	0.866429i	$0.666409\pi$
$182$	−4.21481	−	1.05422i	−0.312423	−	0.0781439i
$183$	−1.79127	+	0.923059i	−0.132414	+	0.0682345i
$184$	−2.89864	+	2.89864i	−0.213690	+	0.213690i
$185$			3.34770i			0.246128i
$186$	−6.05021	+	3.11774i	−0.443623	+	0.228604i
$187$	−2.61299	+	2.61299i	−0.191080	+	0.191080i
$188$	9.17605	+	9.17605i	0.669232	+	0.669232i
$189$	−7.32877	+	5.48014i	−0.533090	+	0.398622i
$190$	0.912085	+	0.912085i	0.0661696	+	0.0661696i
$191$		−	6.40782i		−	0.463654i	−0.972757	−	0.231827i	$-0.925530\pi$
$191$		−	6.40782i		−	0.463654i	0.972757	−	0.231827i	$-0.0744703\pi$
$192$	−0.909647	−	1.76524i	−0.0656481	−	0.127395i
$193$	−16.1130	−	16.1130i	−1.15984	−	1.15984i	−0.984509	−	0.175332i	$-0.943900\pi$
$193$	−16.1130	−	16.1130i	−1.15984	−	1.15984i	−0.175332	−	0.984509i	$-0.556100\pi$
$194$	−1.00136			−0.0718936
$195$	3.28901	−	5.30871i	0.235531	−	0.380164i
$196$	−5.97179			−0.426556
$197$	11.3286	+	11.3286i	0.807127	+	0.807127i	0.984198	−	0.177071i	$-0.0566622\pi$
$197$	11.3286	+	11.3286i	0.807127	+	0.807127i	−0.177071	+	0.984198i	$0.556662\pi$
$198$	0.652142	−	0.915115i	0.0463457	−	0.0650344i
$199$		−	23.0814i		−	1.63620i	−0.575079	−	0.818098i	$-0.695029\pi$
$199$		−	23.0814i		−	1.63620i	0.575079	−	0.818098i	$-0.304971\pi$
$200$	−1.70875	−	1.70875i	−0.120827	−	0.120827i
$201$	−3.48384	+	10.8917i	−0.245731	+	0.768242i
$202$	8.82815	+	8.82815i	0.621147	+	0.621147i
$203$	−4.79904	+	4.79904i	−0.336827	+	0.336827i
$204$	−8.20386	−	15.9202i	−0.574385	−	1.11464i
$205$		−	8.09101i		−	0.565100i
$206$	−1.76827	+	1.76827i	−0.123201	+	0.123201i
$207$	2.95341	−	4.14436i	0.205276	−	0.288053i
$208$	1.23382	−	4.93286i	0.0855500	−	0.342032i
$209$			1.03205i			0.0713884i
$210$	0.635849	−	1.98789i	0.0438778	−	0.137177i
$211$	−9.04618			−0.622765			−0.311382	−	0.950285i	$-0.600792\pi$
$211$	−9.04618			−0.622765			−0.311382	+	0.950285i	$0.600792\pi$
$212$	13.5013			0.927274
$213$	−2.13689	−	0.683508i	−0.146417	−	0.0468332i
$214$	−7.23723	+	7.23723i	−0.494727	+	0.494727i
$215$	8.30087	−	8.30087i	0.566115	−	0.566115i
$216$	7.51958	+	10.0562i	0.511643	+	0.684237i
$217$	−10.1146			−0.686625
$218$	−5.23913			−0.354839
$219$	18.9291	+	6.05470i	1.27911	+	0.409139i
$220$		−	0.838607i		−	0.0565389i
$221$	−5.90551	+	23.6105i	−0.397248	+	1.58821i
$222$	1.81731	+	3.52663i	0.121970	+	0.236692i
$223$	12.2488	−	12.2488i	0.820241	−	0.820241i	−0.165901	−	0.986142i	$-0.553053\pi$
$223$	12.2488	−	12.2488i	0.820241	−	0.820241i	0.986142	+	0.165901i	$0.0530532\pi$
$224$		−	10.2111i		−	0.682256i
$225$	2.44311	+	1.74104i	0.162874	+	0.116069i
$226$	2.69021	−	2.69021i	0.178950	−	0.178950i
$227$	−10.5073	−	10.5073i	−0.697394	−	0.697394i	0.266454	−	0.963848i	$-0.414148\pi$
$227$	−10.5073	−	10.5073i	−0.697394	−	0.697394i	−0.963848	+	0.266454i	$0.914148\pi$
$228$	−4.76414	−	1.52387i	−0.315513	−	0.100920i
$229$	−4.44578	−	4.44578i	−0.293785	−	0.293785i	0.544788	−	0.838574i	$-0.316610\pi$
$229$	−4.44578	−	4.44578i	−0.293785	−	0.293785i	−0.838574	+	0.544788i	$0.816610\pi$
$230$			1.16066i			0.0765319i
$231$	1.48442	−	0.764935i	0.0976674	−	0.0503290i
$232$	6.58501	+	6.58501i	0.432327	+	0.432327i
$233$	17.6896			1.15888			0.579441	−	0.815014i	$-0.303271\pi$
$233$	17.6896			1.15888			0.579441	+	0.815014i	$0.303271\pi$
$234$	0.582959	−	7.37790i	0.0381092	−	0.482309i
$235$	8.47137			0.552611
$236$	−1.99954	−	1.99954i	−0.130159	−	0.130159i
$237$	−5.93393	+	3.05781i	−0.385450	+	0.198626i
$238$			8.13381i			0.527236i
$239$	−4.70800	−	4.70800i	−0.304535	−	0.304535i	0.538250	−	0.842785i	$-0.319086\pi$
$239$	−4.70800	−	4.70800i	−0.304535	−	0.304535i	−0.842785	+	0.538250i	$0.819086\pi$
$240$	2.32655	+	0.744175i	0.150178	+	0.0480363i
$241$	13.7965	+	13.7965i	0.888710	+	0.888710i	0.994399	−	0.105689i	$-0.0337048\pi$
$241$	13.7965	+	13.7965i	0.888710	+	0.888710i	−0.105689	+	0.994399i	$0.533705\pi$
$242$	5.17693	−	5.17693i	0.332786	−	0.332786i
$243$	−11.2723	−	10.7673i	−0.723119	−	0.690723i
$244$			1.78220i			0.114093i
$245$	−2.75659	+	2.75659i	−0.176112	+	0.176112i
$246$	−4.39223	−	8.52346i	−0.280038	−	0.543436i
$247$	3.49647	+	5.82896i	0.222475	+	0.370888i
$248$			13.8788i			0.881303i
$249$	−27.8441	−	8.90626i	−1.76455	−	0.564411i
$250$	−0.684213			−0.0432734
$251$	5.80617			0.366482			0.183241	−	0.983068i	$-0.441341\pi$
$251$	5.80617			0.366482			0.183241	+	0.983068i	$0.441341\pi$
$252$	1.33928	+	7.98181i	0.0843670	+	0.502807i
$253$	−0.656662	+	0.656662i	−0.0412840	+	0.0412840i
$254$	0.0169163	−	0.0169163i	0.00106142	−	0.00106142i
$255$	−11.1357	−	3.56189i	−0.697347	−	0.223054i
$256$	−9.69045			−0.605653
$257$	−8.29597			−0.517488			−0.258744	−	0.965946i	$-0.583309\pi$
$257$	−8.29597			−0.517488			−0.258744	+	0.965946i	$0.583309\pi$
$258$	4.23839	−	13.2507i	0.263870	−	0.824952i
$259$			5.89575i			0.366344i
$260$	−2.84110	−	4.73641i	−0.176198	−	0.293740i
$261$	−9.41500	−	6.70944i	−0.582774	−	0.415304i
$262$	0.541627	−	0.541627i	0.0334618	−	0.0334618i
$263$			10.8718i			0.670383i	0.942150	+	0.335191i	$0.108801\pi$
$263$			10.8718i			0.670383i	−0.942150	+	0.335191i	$0.891199\pi$
$264$	−1.04961	−	2.03684i	−0.0645988	−	0.125359i
$265$	6.23224	−	6.23224i	0.382843	−	0.382843i
$266$	1.60630	+	1.60630i	0.0984888	+	0.0984888i
$267$	−4.47522	+	13.9911i	−0.273879	+	0.856243i
$268$	7.15137	+	7.15137i	0.436839	+	0.436839i
$269$			21.6607i			1.32068i	0.750968	+	0.660339i	$0.229587\pi$
$269$			21.6607i			1.32068i	−0.750968	+	0.660339i	$0.770413\pi$
$270$	3.51882	+	0.507848i	0.214148	+	0.0309067i
$271$	−3.57577	−	3.57577i	−0.217213	−	0.217213i	0.590110	−	0.807323i	$-0.299084\pi$
$271$	−3.57577	−	3.57577i	−0.217213	−	0.217213i	−0.807323	+	0.590110i	$0.799084\pi$
$272$	−9.51951			−0.577205
$273$	5.79239	−	9.34934i	0.350572	−	0.565848i
$274$	−2.50238			−0.151174
$275$	−0.387103	−	0.387103i	−0.0233432	−	0.0233432i
$276$	−2.06169	−	4.00086i	−0.124099	−	0.240824i
$277$			17.4880i			1.05075i	0.850870	+	0.525377i	$0.176076\pi$
$277$			17.4880i			1.05075i	−0.850870	+	0.525377i	$0.823924\pi$
$278$	−8.07321	−	8.07321i	−0.484199	−	0.484199i
$279$	−2.85115	−	16.9922i	−0.170694	−	1.01730i
$280$	−3.00934	−	3.00934i	−0.179842	−	0.179842i
$281$	3.48513	−	3.48513i	0.207906	−	0.207906i	−0.595471	−	0.803377i	$-0.703035\pi$
$281$	3.48513	−	3.48513i	0.207906	−	0.207906i	0.803377	+	0.595471i	$0.203035\pi$
$282$	8.92415	−	4.59871i	0.531426	−	0.273849i
$283$		−	9.47252i		−	0.563083i	−0.959549	−	0.281541i	$-0.909154\pi$
$283$		−	9.47252i		−	0.563083i	0.959549	−	0.281541i	$-0.0908457\pi$
$284$	−1.40306	+	1.40306i	−0.0832561	+	0.0832561i
$285$	−2.90256	+	1.49572i	−0.171933	+	0.0885987i
$286$	−0.327703	+	1.31017i	−0.0193775	+	0.0774720i
$287$		−	14.2493i		−	0.841112i
$288$	17.1542	−	2.87834i	1.01082	−	0.169608i
$289$	28.5639			1.68023
$290$	2.63675			0.154835
$291$	0.772272	−	2.41439i	0.0452714	−	0.141534i
$292$	12.4287	−	12.4287i	0.727332	−	0.727332i
$293$	15.2096	−	15.2096i	0.888556	−	0.888556i	−0.105828	−	0.994384i	$-0.533749\pi$
$293$	15.2096	−	15.2096i	0.888556	−	0.888556i	0.994384	+	0.105828i	$0.0337494\pi$
$294$	−1.40750	+	4.40035i	−0.0820873	+	0.256634i
$295$	−1.84599			−0.107477
$296$	8.08986			0.470214
$297$	1.70350	+	2.27814i	0.0988470	+	0.132191i
$298$		−	16.3912i		−	0.949516i
$299$	−1.48410	+	5.93348i	−0.0858275	+	0.343142i
$300$	2.35852	−	1.21537i	0.136169	−	0.0701693i
$301$	14.6189	−	14.6189i	0.842622	−	0.842622i
$302$			5.04397i			0.290248i
$303$	−28.0941	+	14.4772i	−1.61396	+	0.831693i
$304$	−1.87996	+	1.87996i	−0.107823	+	0.107823i
$305$	0.822666	+	0.822666i	0.0471057	+	0.0471057i
$306$	−13.6645	+	2.29280i	−0.781148	+	0.131070i
$307$	−8.64829	−	8.64829i	−0.493584	−	0.493584i	0.415850	−	0.909433i	$-0.363484\pi$
$307$	−8.64829	−	8.64829i	−0.493584	−	0.493584i	−0.909433	+	0.415850i	$0.863484\pi$
$308$		−	1.47690i		−	0.0841541i
$309$	−2.89976	−	5.62722i	−0.164962	−	0.320121i
$310$	2.77865	+	2.77865i	0.157817	+	0.157817i
$311$	−1.51624			−0.0859779			−0.0429890	−	0.999076i	$-0.513688\pi$
$311$	−1.51624			−0.0859779			−0.0429890	+	0.999076i	$0.513688\pi$
$312$	−12.8287	−	7.94804i	−0.726282	−	0.449969i
$313$	0.929202			0.0525216			0.0262608	−	0.999655i	$-0.491640\pi$
$313$	0.929202			0.0525216			0.0262608	+	0.999655i	$0.491640\pi$
$314$	6.30473	+	6.30473i	0.355796	+	0.355796i
$315$	4.30264	+	3.06620i	0.242426	+	0.172761i
$316$			5.90388i			0.332119i
$317$	−15.3001	−	15.3001i	−0.859342	−	0.859342i	0.131919	−	0.991261i	$-0.457886\pi$
$317$	−15.3001	−	15.3001i	−0.859342	−	0.859342i	−0.991261	+	0.131919i	$0.957886\pi$
$318$	3.18215	−	9.94853i	0.178446	−	0.557886i
$319$	1.49178	+	1.49178i	0.0835236	+	0.0835236i
$320$	−0.810713	+	0.810713i	−0.0453202	+	0.0453202i
$321$	−11.8683	−	23.0313i	−0.662421	−	1.28548i
$322$			2.04408i			0.113912i
$323$	8.99818	−	8.99818i	0.500672	−	0.500672i
$324$	−13.0316	+	4.49990i	−0.723979	+	0.249994i
$325$	−3.49780	−	0.874878i	−0.194023	−	0.0485295i
$326$		−	3.70986i		−	0.205470i
$327$	4.04053	−	12.6321i	0.223442	−	0.698558i
$328$	−19.5522			−1.07959
$329$	14.9192			0.822523
$330$	−0.617933	−	0.197653i	−0.0340161	−	0.0108804i
$331$	22.1751	−	22.1751i	1.21885	−	1.21885i	0.250818	−	0.968034i	$-0.419300\pi$
$331$	22.1751	−	22.1751i	1.21885	−	1.21885i	0.968034	−	0.250818i	$-0.0806997\pi$
$332$	−18.2821	+	18.2821i	−1.00336	+	1.00336i
$333$	−9.90465	+	1.66192i	−0.542771	+	0.0910727i
$334$	8.77333			0.480055
$335$	6.60218			0.360716
$336$	4.09737	+	1.31059i	0.223530	+	0.0714986i
$337$		−	1.11379i		−	0.0606718i	−0.999540	−	0.0303359i	$-0.990342\pi$
$337$		−	1.11379i		−	0.0606718i	0.999540	−	0.0303359i	$-0.00965769\pi$
$338$	2.58785	+	8.50999i	0.140761	+	0.462883i
$339$	4.41164	+	8.56113i	0.239607	+	0.464977i
$340$	−7.31160	+	7.31160i	−0.396527	+	0.396527i
$341$			3.14412i			0.170264i
$342$	−2.24574	+	3.15132i	−0.121436	+	0.170404i
$343$	−13.5719	+	13.5719i	−0.732813	+	0.732813i
$344$	−20.0594	−	20.0594i	−1.08153	−	1.08153i
$345$	−2.79849	−	0.895128i	−0.150665	−	0.0481921i
$346$	−2.24442	−	2.24442i	−0.120661	−	0.120661i
$347$			14.9572i			0.802946i	0.915871	+	0.401473i	$0.131502\pi$
$347$			14.9572i			0.802946i	−0.915871	+	0.401473i	$0.868498\pi$
$348$	−9.08901	+	4.68366i	−0.487222	+	0.251071i
$349$	8.13022	+	8.13022i	0.435201	+	0.435201i	0.890393	−	0.455192i	$-0.150430\pi$
$349$	8.13022	+	8.13022i	0.435201	+	0.435201i	−0.455192	+	0.890393i	$0.650430\pi$
$350$	−1.20499			−0.0644094
$351$	17.3393	+	7.09558i	0.925506	+	0.378734i
$352$	−3.17410			−0.169180
$353$	14.0281	+	14.0281i	0.746638	+	0.746638i	0.973846	−	0.227208i	$-0.0729598\pi$
$353$	14.0281	+	14.0281i	0.746638	+	0.746638i	−0.227208	+	0.973846i	$0.572960\pi$
$354$	−1.94465	+	1.00210i	−0.103357	+	0.0532610i
$355$			1.29531i			0.0687478i
$356$	9.18642	+	9.18642i	0.486879	+	0.486879i
$357$	−19.6115	−	6.27297i	−1.03795	−	0.332001i
$358$	6.42958	+	6.42958i	0.339814	+	0.339814i
$359$	14.0085	−	14.0085i	0.739341	−	0.739341i	−0.233109	−	0.972451i	$-0.574890\pi$
$359$	14.0085	−	14.0085i	0.739341	−	0.739341i	0.972451	+	0.233109i	$0.0748900\pi$
$360$	4.20729	−	5.90387i	0.221744	−	0.311161i
$361$			15.4460i			0.812947i
$362$	11.2792	−	11.2792i	0.592822	−	0.592822i
$363$	8.48959	+	16.4747i	0.445588	+	0.864698i
$364$	−5.00356	−	8.34145i	−0.262258	−	0.437211i
$365$		−	11.4742i		−	0.600587i
$366$	1.31322	+	0.420050i	0.0686433	+	0.0219564i
$367$	−26.2282			−1.36910			−0.684549	−	0.728966i	$-0.740001\pi$
$367$	−26.2282			−1.36910			−0.684549	+	0.728966i	$0.740001\pi$
$368$	−2.39232			−0.124708
$369$	23.9384	−	4.01667i	1.24618	−	0.209099i
$370$	1.61966	−	1.61966i	0.0842020	−	0.0842020i
$371$	10.9758	−	10.9758i	0.569835	−	0.569835i
$372$	−14.5138	−	4.64242i	−0.752508	−	0.240698i
$373$	6.83702			0.354007			0.177004	−	0.984210i	$-0.443360\pi$
$373$	6.83702			0.354007			0.177004	+	0.984210i	$0.443360\pi$
$374$	2.52839			0.130740
$375$	0.527680	−	1.64971i	0.0272493	−	0.0851908i
$376$		−	20.4714i		−	1.05573i
$377$	13.4795	+	3.37151i	0.694227	+	0.173642i
$378$	6.19711	+	0.894389i	0.318745	+	0.0460024i
$379$	−24.8881	+	24.8881i	−1.27842	+	1.27842i	−0.336864	+	0.941553i	$0.609366\pi$
$379$	−24.8881	+	24.8881i	−1.27842	+	1.27842i	−0.941553	+	0.336864i	$0.890634\pi$
$380$			2.88786i			0.148144i
$381$	0.0277408	+	0.0538332i	0.00142121	+	0.00275796i
$382$	−3.10018	+	3.10018i	−0.158619	+	0.158619i
$383$	−7.76391	−	7.76391i	−0.396717	−	0.396717i	0.480356	−	0.877073i	$-0.340507\pi$
$383$	−7.76391	−	7.76391i	−0.396717	−	0.396717i	−0.877073	+	0.480356i	$0.840507\pi$
$384$	5.70504	−	17.8360i	0.291134	−	0.910188i
$385$	−0.681740	−	0.681740i	−0.0347447	−	0.0347447i
$386$			15.5914i			0.793579i
$387$	28.6801	+	20.4384i	1.45789	+	1.03894i
$388$	−1.58526	−	1.58526i	−0.0804796	−	0.0804796i
$389$	−6.30333			−0.319591			−0.159796	−	0.987150i	$-0.551084\pi$
$389$	−6.30333			−0.319591			−0.159796	+	0.987150i	$0.551084\pi$
$390$	−4.15968	+	0.977151i	−0.210634	+	0.0494800i
$391$	11.4505			0.579078
$392$	6.66141	+	6.66141i	0.336452	+	0.336452i
$393$	0.888208	+	1.72364i	0.0448042	+	0.0869460i
$394$		−	10.9618i		−	0.552247i
$395$	2.72524	+	2.72524i	0.137122	+	0.137122i
$396$	2.48114	−	0.416315i	0.124682	−	0.0209206i
$397$	−24.3714	−	24.3714i	−1.22317	−	1.22317i	−0.966500	−	0.256665i	$-0.917376\pi$
$397$	−24.3714	−	24.3714i	−1.22317	−	1.22317i	−0.256665	−	0.966500i	$-0.582624\pi$
$398$	−11.1670	+	11.1670i	−0.559753	+	0.559753i
$399$	−5.11179	+	2.63416i	−0.255910	+	0.131873i
$400$		−	1.41028i		−	0.0705138i
$401$	8.82040	−	8.82040i	0.440470	−	0.440470i	−0.451700	−	0.892170i	$-0.649182\pi$
$401$	8.82040	−	8.82040i	0.440470	−	0.440470i	0.892170	+	0.451700i	$0.149182\pi$
$402$	6.95506	−	3.58401i	0.346887	−	0.178754i
$403$	10.6519	+	17.7578i	0.530609	+	0.884580i
$404$			27.9518i			1.39066i
$405$	−3.93827	+	8.09259i	−0.195694	+	0.402124i
$406$	4.64367			0.230461
$407$	1.83269			0.0908430
$408$	−8.60746	+	26.9099i	−0.426133	+	1.33224i
$409$	−10.2362	+	10.2362i	−0.506149	+	0.506149i	−0.913342	−	0.407193i	$-0.866508\pi$
$409$	−10.2362	+	10.2362i	−0.506149	+	0.506149i	0.407193	+	0.913342i	$0.366508\pi$
$410$	−3.91452	+	3.91452i	−0.193325	+	0.193325i
$411$	1.92989	−	6.03352i	0.0951945	−	0.297612i
$412$	−5.59872			−0.275829
$413$	−3.25103			−0.159973
$414$	−3.43398	+	0.576195i	−0.168771	+	0.0283185i
$415$			16.8782i			0.828516i
$416$	−17.9271	+	10.7535i	−0.878951	+	0.527233i
$417$	25.6916	−	13.2392i	1.25812	−	0.648325i
$418$	0.499318	−	0.499318i	0.0244224	−	0.0244224i
$419$			39.8238i			1.94552i	0.231818	+	0.972759i	$0.425533\pi$
$419$			39.8238i			1.94552i	−0.231818	+	0.972759i	$0.574467\pi$
$420$	4.15366	−	2.14042i	0.202678	−	0.104442i
$421$	−11.1187	+	11.1187i	−0.541893	+	0.541893i	−0.924084	−	0.382190i	$-0.875170\pi$
$421$	−11.1187	+	11.1187i	−0.541893	+	0.541893i	0.382190	+	0.924084i	$0.375170\pi$
$422$	4.37665	+	4.37665i	0.213052	+	0.213052i
$423$	4.20550	+	25.0637i	0.204478	+	1.21864i
$424$	−15.0605	−	15.0605i	−0.731400	−	0.731400i
$425$			6.75010i			0.327428i
$426$	0.703162	+	1.36454i	0.0340683	+	0.0661122i
$427$	1.44883	+	1.44883i	0.0701136	+	0.0701136i
$428$	−22.9146			−1.10762
$429$	−2.90623	−	1.80056i	−0.140314	−	0.0869318i
$430$	−8.03212			−0.387343
$431$	5.22718	+	5.22718i	0.251784	+	0.251784i	0.821702	−	0.569917i	$-0.193025\pi$
$431$	5.22718	+	5.22718i	0.251784	+	0.251784i	−0.569917	+	0.821702i	$0.693025\pi$
$432$	−1.04676	+	7.25286i	−0.0503623	+	0.348954i
$433$		−	2.96201i		−	0.142345i	−0.997464	−	0.0711727i	$-0.977326\pi$
$433$		−	2.96201i		−	0.142345i	0.997464	−	0.0711727i	$-0.0226741\pi$
$434$	4.89357	+	4.89357i	0.234899	+	0.234899i
$435$	−2.03352	+	6.35750i	−0.0974997	+	0.304819i
$436$	−8.29411	−	8.29411i	−0.397216	−	0.397216i
$437$	2.26130	−	2.26130i	0.108173	−	0.108173i
$438$	−6.22880	−	12.0875i	−0.297624	−	0.577562i
$439$			21.3756i			1.02020i	0.860114	+	0.510101i	$0.170392\pi$
$439$			21.3756i			1.02020i	−0.860114	+	0.510101i	$0.829608\pi$
$440$	−0.935450	+	0.935450i	−0.0445958	+	0.0445958i
$441$	−9.52424	−	6.78729i	−0.453535	−	0.323204i
$442$	14.2802	−	8.56588i	0.679239	−	0.407437i
$443$		−	20.6824i		−	0.982650i	−0.870976	−	0.491325i	$-0.836513\pi$
$443$		−	20.6824i		−	0.982650i	0.870976	−	0.491325i	$-0.163487\pi$
$444$	−2.70604	+	8.46004i	−0.128423	+	0.401496i
$445$	8.48095			0.402035
$446$	−11.8522			−0.561220
$447$	39.5210	+	12.6412i	1.86928	+	0.597910i
$448$	−1.42777	+	1.42777i	−0.0674559	+	0.0674559i
$449$	29.1294	−	29.1294i	1.37470	−	1.37470i	0.521375	−	0.853328i	$-0.325419\pi$
$449$	29.1294	−	29.1294i	1.37470	−	1.37470i	0.853328	−	0.521375i	$-0.174581\pi$
$450$	−0.339668	−	2.02434i	−0.0160121	−	0.0954283i
$451$	−4.42939			−0.208572
$452$	8.51778			0.400643
$453$	−12.1616	−	3.89002i	−0.571401	−	0.182769i
$454$			10.1671i			0.477166i
$455$	−6.16009	−	1.54078i	−0.288789	−	0.0722327i
$456$	3.61446	+	7.01415i	0.169263	+	0.328468i
$457$	−2.59392	+	2.59392i	−0.121338	+	0.121338i	−0.765168	−	0.643830i	$-0.777344\pi$
$457$	−2.59392	+	2.59392i	−0.121338	+	0.121338i	0.643830	+	0.765168i	$0.277344\pi$
$458$			4.30184i			0.201012i
$459$	5.01018	−	34.7149i	0.233855	−	1.62035i
$460$	−1.83746	+	1.83746i	−0.0856718	+	0.0856718i
$461$	−18.1031	−	18.1031i	−0.843144	−	0.843144i	0.146123	−	0.989266i	$-0.453321\pi$
$461$	−18.1031	−	18.1031i	−0.843144	−	0.843144i	−0.989266	+	0.146123i	$0.953321\pi$
$462$	−1.08826	−	0.348093i	−0.0506306	−	0.0161948i
$463$	19.7500	+	19.7500i	0.917862	+	0.917862i	0.996874	−	0.0790114i	$-0.0251764\pi$
$463$	19.7500	+	19.7500i	0.917862	+	0.917862i	−0.0790114	+	0.996874i	$0.525176\pi$
$464$			5.43478i			0.252303i
$465$	−8.84258	+	4.55667i	−0.410065	+	0.211311i
$466$	−8.55842	−	8.55842i	−0.396461	−	0.396461i
$467$	−2.98569			−0.138161			−0.0690807	−	0.997611i	$-0.522007\pi$
$467$	−2.98569			−0.138161			−0.0690807	+	0.997611i	$0.522007\pi$
$468$	12.6029	−	10.7571i	0.582569	−	0.497248i
$469$	11.6273			0.536900
$470$	−4.09855	−	4.09855i	−0.189052	−	0.189052i
$471$	−20.0637	+	10.3391i	−0.924488	+	0.476398i
$472$			4.46090i			0.205330i
$473$	−4.54428	−	4.54428i	−0.208946	−	0.208946i
$474$	4.35031	+	1.39150i	0.199816	+	0.0639136i
$475$	1.33304	+	1.33304i	0.0611642	+	0.0611642i
$476$	−12.8767	+	12.8767i	−0.590202	+	0.590202i
$477$	21.5329	+	15.3450i	0.985922	+	0.702601i
$478$			4.55557i			0.208367i
$479$	−4.61160	+	4.61160i	−0.210710	+	0.210710i	−0.804569	−	0.593859i	$-0.797604\pi$
$479$	−4.61160	+	4.61160i	−0.210710	+	0.210710i	0.593859	+	0.804569i	$0.297604\pi$
$480$	−4.60013	−	8.92690i	−0.209966	−	0.407455i
$481$	10.3509	−	6.20893i	0.471962	−	0.283103i
$482$		−	13.3498i		−	0.608067i
$483$	−4.92851	−	1.57644i	−0.224255	−	0.0717305i
$484$	16.3913			0.745058
$485$	−1.46352			−0.0664552
$486$	0.244328	+	10.6630i	0.0110829	+	0.483685i
$487$	22.7100	−	22.7100i	1.02909	−	1.02909i	0.0295239	−	0.999564i	$-0.490601\pi$
$487$	22.7100	−	22.7100i	1.02909	−	1.02909i	0.999564	−	0.0295239i	$-0.00939911\pi$
$488$	1.98801	−	1.98801i	0.0899928	−	0.0899928i
$489$	8.94488	+	2.86112i	0.404501	+	0.129384i
$490$	2.66734			0.120498
$491$	32.8134			1.48085			0.740423	−	0.672141i	$-0.234625\pi$
$491$	32.8134			1.48085			0.740423	+	0.672141i	$0.234625\pi$
$492$	6.54019	−	20.4469i	0.294854	−	0.921819i
$493$		−	26.0128i		−	1.17156i
$494$	1.12849	−	4.51175i	0.0507732	−	0.202993i
$495$	0.953127	−	1.33747i	0.0428399	−	0.0601149i
$496$	−5.72725	+	5.72725i	−0.257161	+	0.257161i
$497$			2.28121i			0.102326i
$498$	9.16235	+	17.7803i	0.410575	+	0.796753i
$499$	0.358414	−	0.358414i	0.0160448	−	0.0160448i	−0.699039	−	0.715084i	$-0.746389\pi$
$499$	0.358414	−	0.358414i	0.0160448	−	0.0160448i	0.715084	+	0.699039i	$0.246389\pi$
$500$	−1.08318	−	1.08318i	−0.0484414	−	0.0484414i
$501$	−6.76618	+	21.1535i	−0.302291	+	0.945067i
$502$	−2.80909	−	2.80909i	−0.125376	−	0.125376i
$503$		−	1.20071i		−	0.0535371i	−0.999642	−	0.0267685i	$-0.991478\pi$
$503$		−	1.20071i		−	0.0535371i	0.999642	−	0.0267685i	$-0.00852171\pi$
$504$	7.40961	−	10.3975i	0.330050	−	0.463141i
$505$	12.9026	+	12.9026i	0.574160	+	0.574160i
$506$	0.635401			0.0282470
$507$	−22.5143	−	0.323485i	−0.999897	−	0.0143665i
$508$	0.0535606			0.00237637
$509$	−16.5736	−	16.5736i	−0.734613	−	0.734613i	0.236917	−	0.971530i	$-0.423863\pi$
$509$	−16.5736	−	16.5736i	−0.734613	−	0.734613i	−0.971530	+	0.236917i	$0.923863\pi$
$510$	3.66431	+	7.11088i	0.162258	+	0.314875i
$511$		−	20.2076i		−	0.893931i
$512$	−10.6015	−	10.6015i	−0.468524	−	0.468524i
$513$	−5.86623	−	7.84510i	−0.259000	−	0.346369i
$514$	4.01369	+	4.01369i	0.177036	+	0.177036i
$515$	−2.58438	+	2.58438i	−0.113882	+	0.113882i
$516$	27.6871	−	14.2675i	1.21886	−	0.628090i
$517$		−	4.63762i		−	0.203962i
$518$	2.85243	−	2.85243i	0.125329	−	0.125329i
$519$	7.14250	−	3.68061i	0.313521	−	0.161561i
$520$	−2.11418	+	8.45257i	−0.0927128	+	0.370670i
$521$		−	24.5938i		−	1.07747i	−0.842474	−	0.538736i	$-0.818902\pi$
$521$		−	24.5938i		−	1.07747i	0.842474	−	0.538736i	$-0.181098\pi$
$522$	1.30898	+	7.80120i	0.0572924	+	0.341449i
$523$	−38.6626			−1.69060			−0.845299	−	0.534294i	$-0.820578\pi$
$523$	−38.6626			−1.69060			−0.845299	+	0.534294i	$0.820578\pi$
$524$	1.71491			0.0749161
$525$	0.929314	−	2.90536i	0.0405586	−	0.126801i
$526$	5.25989	−	5.25989i	0.229342	−	0.229342i
$527$	27.4127	−	27.4127i	1.19412	−	1.19412i
$528$	0.407396	−	1.27366i	0.0177296	−	0.0554291i
$529$	−20.1224			−0.874887
$530$	−6.03046			−0.261946
$531$	−0.916415	−	5.46161i	−0.0397690	−	0.237014i
$532$			5.08590i			0.220502i
$533$	−25.0170	+	15.0063i	−1.08361	+	0.649994i
$534$	8.93424	−	4.60391i	0.386622	−	0.199231i
$535$	−10.5775	+	10.5775i	−0.457303	+	0.457303i
$536$		−	15.9544i		−	0.689126i
$537$	−20.4611	+	10.5438i	−0.882960	+	0.454998i
$538$	10.4797	−	10.4797i	0.451812	−	0.451812i
$539$	1.50909	+	1.50909i	0.0650010	+	0.0650010i
$540$	4.76669	+	6.37465i	0.205126	+	0.274321i
$541$	−1.35568	−	1.35568i	−0.0582854	−	0.0582854i	0.677363	−	0.735649i	$-0.263123\pi$
$541$	−1.35568	−	1.35568i	−0.0582854	−	0.0582854i	−0.735649	+	0.677363i	$0.763123\pi$
$542$			3.46000i			0.148620i
$543$	18.4967	+	35.8942i	0.793768	+	1.54037i
$544$	27.6741	+	27.6741i	1.18652	+	1.18652i
$545$	−7.65717			−0.327997
$546$	−7.32575	+	1.72089i	−0.313513	+	0.0736475i
$547$	19.9892			0.854675			0.427338	−	0.904092i	$-0.359452\pi$
$547$	19.9892			0.854675			0.427338	+	0.904092i	$0.359452\pi$
$548$	−3.96154	−	3.96154i	−0.169229	−	0.169229i
$549$	−2.02557	+	2.84238i	−0.0864493	+	0.121310i
$550$			0.374570i			0.0159717i
$551$	−5.13714	−	5.13714i	−0.218850	−	0.218850i
$552$	−2.16311	+	6.76266i	−0.0920682	+	0.287838i
$553$	4.79952	+	4.79952i	0.204096	+	0.204096i
$554$	8.46092	−	8.46092i	0.359470	−	0.359470i
$555$	2.65606	+	5.15429i	0.112743	+	0.218787i
$556$		−	25.5615i		−	1.08405i
$557$	−9.29058	+	9.29058i	−0.393655	+	0.393655i	−0.875988	−	0.482333i	$-0.839789\pi$
$557$	−9.29058	+	9.29058i	−0.393655	+	0.393655i	0.482333	+	0.875988i	$0.339789\pi$
$558$	−6.84160	+	9.60044i	−0.289628	+	0.406419i
$559$	−41.0614	−	10.2704i	−1.73671	−	0.434390i
$560$		−	2.48368i		−	0.104955i
$561$	−1.94995	+	6.09622i	−0.0823268	+	0.257383i
$562$	−3.37230			−0.142252
$563$	−43.3391			−1.82653			−0.913263	−	0.407370i	$-0.866446\pi$
$563$	−43.3391			−1.82653			−0.913263	+	0.407370i	$0.866446\pi$
$564$	21.4081	+	6.84764i	0.901446	+	0.288338i
$565$	3.93183	−	3.93183i	0.165413	−	0.165413i
$566$	−4.58292	+	4.58292i	−0.192634	+	0.192634i
$567$	−6.93581	+	14.2521i	−0.291277	+	0.598533i
$568$	3.13016			0.131339
$569$	7.47436			0.313342			0.156671	−	0.987651i	$-0.449924\pi$
$569$	7.47436			0.313342			0.156671	+	0.987651i	$0.449924\pi$
$570$	2.12794	+	0.680646i	0.0891295	+	0.0285091i
$571$		−	20.1324i		−	0.842516i	−0.906941	−	0.421258i	$-0.861589\pi$
$571$		−	20.1324i		−	0.842516i	0.906941	−	0.421258i	$-0.138411\pi$
$572$	−2.59293	+	1.55535i	−0.108416	+	0.0650325i
$573$	−5.08395	−	9.86580i	−0.212385	−	0.412150i
$574$	−6.89400	+	6.89400i	−0.287750	+	0.287750i
$575$			1.69635i			0.0707426i
$576$	−2.80107	−	1.99614i	−0.116711	−	0.0831725i
$577$	12.5798	−	12.5798i	0.523705	−	0.523705i	−0.394983	−	0.918688i	$-0.629250\pi$
$577$	12.5798	−	12.5798i	0.523705	−	0.523705i	0.918688	+	0.394983i	$0.129250\pi$
$578$	−13.8195	−	13.8195i	−0.574817	−	0.574817i
$579$	−37.5925	−	12.0244i	−1.56229	−	0.499716i
$580$	4.17426	+	4.17426i	0.173327	+	0.173327i
$581$			29.7247i			1.23319i
$582$	−1.54175	+	0.794478i	−0.0639075	+	0.0329322i
$583$	−3.41182	−	3.41182i	−0.141303	−	0.141303i
$584$	−27.7278			−1.14739
$585$	0.852014	−	10.7830i	0.0352265	−	0.445824i
$586$	−14.7172			−0.607962
$587$	−0.511868	−	0.511868i	−0.0211270	−	0.0211270i	0.696464	−	0.717591i	$-0.254755\pi$
$587$	−0.511868	−	0.511868i	−0.0211270	−	0.0211270i	−0.717591	+	0.696464i	$0.754755\pi$
$588$	−9.19446	+	4.73800i	−0.379173	+	0.195392i
$589$		−	10.8272i		−	0.446127i
$590$	0.893110	+	0.893110i	0.0367688	+	0.0367688i
$591$	26.4301	+	8.45397i	1.08719	+	0.347750i
$592$	3.33838	+	3.33838i	0.137207	+	0.137207i
$593$	13.2208	−	13.2208i	0.542911	−	0.542911i	−0.381470	−	0.924381i	$-0.624582\pi$
$593$	13.2208	−	13.2208i	0.542911	−	0.542911i	0.924381	+	0.381470i	$0.124582\pi$
$594$	0.278020	−	1.92636i	0.0114073	−	0.0790397i
$595$			11.8878i			0.487353i
$596$	25.9490	−	25.9490i	1.06291	−	1.06291i
$597$	−18.3127	−	35.5372i	−0.749489	−	1.45444i
$598$	3.58871	−	2.15266i	0.146753	−	0.0880290i
$599$		−	32.7474i		−	1.33802i	−0.743253	−	0.669011i	$-0.766718\pi$
$599$		−	32.7474i		−	1.33802i	0.743253	−	0.669011i	$-0.233282\pi$
$600$	−3.98660	−	1.27516i	−0.162752	−	0.0520582i
$601$	11.3682			0.463718			0.231859	−	0.972749i	$-0.425519\pi$
$601$	11.3682			0.463718			0.231859	+	0.972749i	$0.425519\pi$
$602$	−14.1456			−0.576533
$603$	3.27756	+	19.5335i	0.133473	+	0.795465i
$604$	−7.98515	+	7.98515i	−0.324911	+	0.324911i
$605$	7.56626	−	7.56626i	0.307612	−	0.307612i
$606$	20.5965	+	6.58803i	0.836675	+	0.267620i
$607$	−17.5226			−0.711221			−0.355610	−	0.934634i	$-0.615727\pi$
$607$	−17.5226			−0.711221			−0.355610	+	0.934634i	$0.615727\pi$
$608$	10.9304			0.443288
$609$	−3.58130	+	11.1964i	−0.145121	+	0.453701i
$610$		−	0.796031i		−	0.0322304i
$611$	−15.7117	−	26.1930i	−0.635628	−	1.05966i
$612$	−25.2621	−	18.0026i	−1.02116	−	0.727714i
$613$	22.5157	−	22.5157i	0.909399	−	0.909399i	−0.0868247	−	0.996224i	$-0.527672\pi$
$613$	22.5157	−	22.5157i	0.909399	−	0.909399i	0.996224	+	0.0868247i	$0.0276720\pi$
$614$			8.36829i			0.337717i
$615$	−6.41938	−	12.4573i	−0.258855	−	0.502327i
$616$	−1.64745	+	1.64745i	−0.0663777	+	0.0663777i
$617$	3.20157	+	3.20157i	0.128891	+	0.128891i	0.768609	−	0.639719i	$-0.220949\pi$
$617$	3.20157	+	3.20157i	0.128891	+	0.128891i	−0.639719	+	0.768609i	$0.720949\pi$
$618$	−1.31957	+	4.12545i	−0.0530811	+	0.165950i
$619$	6.99088	+	6.99088i	0.280987	+	0.280987i	0.833503	−	0.552515i	$-0.186332\pi$
$619$	6.99088	+	6.99088i	0.280987	+	0.280987i	−0.552515	+	0.833503i	$0.686332\pi$
$620$			8.79780i			0.353328i
$621$	1.25909	−	8.72409i	0.0505256	−	0.350086i
$622$	0.733573	+	0.733573i	0.0294136	+	0.0294136i
$623$	14.9361			0.598401
$624$	−2.01407	−	8.57379i	−0.0806274	−	0.343226i
$625$	−1.00000			−0.0400000
$626$	−0.449559	−	0.449559i	−0.0179680	−	0.0179680i
$627$	0.818826	+	1.58900i	0.0327008	+	0.0634584i
$628$			19.9621i			0.796576i
$629$	−15.9787	−	15.9787i	−0.637114	−	0.637114i
$630$	−0.598201	−	3.56513i	−0.0238329	−	0.142038i
$631$	19.6866	+	19.6866i	0.783711	+	0.783711i	0.980455	−	0.196744i	$-0.0630369\pi$
$631$	19.6866	+	19.6866i	0.783711	+	0.783711i	−0.196744	+	0.980455i	$0.563037\pi$
$632$	6.58566	−	6.58566i	0.261963	−	0.261963i
$633$	−13.9279	+	7.17722i	−0.553586	+	0.285269i
$634$			14.8048i			0.587973i
$635$	0.0247237	−	0.0247237i	0.000981131	−	0.000981131i
$636$	20.7873	−	10.7119i	0.824270	−	0.424755i
$637$	13.6359	+	3.41063i	0.540272	+	0.135134i
$638$		−	1.44348i		−	0.0571479i
$639$	−3.83235	+	0.643038i	−0.151605	+	0.0254382i
$640$	−10.8116			−0.427364
$641$	−7.99599			−0.315822			−0.157911	−	0.987453i	$-0.550476\pi$
$641$	−7.99599			−0.315822			−0.157911	+	0.987453i	$0.550476\pi$
$642$	−5.40080	+	16.8848i	−0.213153	+	0.666390i
$643$	−15.0350	+	15.0350i	−0.592922	+	0.592922i	−0.938420	−	0.345498i	$-0.887710\pi$
$643$	−15.0350	+	15.0350i	−0.592922	+	0.592922i	0.345498	+	0.938420i	$0.387710\pi$
$644$	−3.23600	+	3.23600i	−0.127516	+	0.127516i
$645$	6.19454	−	19.3663i	0.243910	−	0.762548i
$646$	−8.70685			−0.342566
$647$	−5.28617			−0.207821			−0.103910	−	0.994587i	$-0.533136\pi$
$647$	−5.28617			−0.207821			−0.103910	+	0.994587i	$0.533136\pi$
$648$	19.5561	+	9.51698i	0.768235	+	0.373862i
$649$			1.01058i			0.0396687i
$650$	1.26900	+	2.11555i	0.0497743	+	0.0829788i
$651$	−15.5730	+	8.02491i	−0.610353	+	0.314521i
$652$	5.87311	−	5.87311i	0.230009	−	0.230009i
$653$		−	26.0947i		−	1.02116i	−0.859829	−	0.510581i	$-0.829430\pi$
$653$		−	26.0947i		−	1.02116i	0.859829	−	0.510581i	$-0.170570\pi$
$654$	−8.06643	+	4.15671i	−0.315422	+	0.162540i
$655$	0.791606	−	0.791606i	0.0309306	−	0.0309306i
$656$	−8.06848	−	8.06848i	−0.315021	−	0.315021i
$657$	33.9480	−	5.69621i	1.32444	−	0.222230i
$658$	−7.21809	−	7.21809i	−0.281390	−	0.281390i
$659$		−	10.5160i		−	0.409646i	−0.978799	−	0.204823i	$-0.934338\pi$
$659$		−	10.5160i		−	0.409646i	0.978799	−	0.204823i	$-0.0656618\pi$
$660$	−0.665349	−	1.29116i	−0.0258987	−	0.0502584i
$661$	−19.9999	−	19.9999i	−0.777907	−	0.777907i	0.201567	−	0.979475i	$-0.435397\pi$
$661$	−19.9999	−	19.9999i	−0.777907	−	0.777907i	−0.979475	+	0.201567i	$0.935397\pi$
$662$	−21.4571			−0.833955
$663$	9.64008	+	41.0373i	0.374390	+	1.59376i
$664$	40.7867			1.58283
$665$	2.34767	+	2.34767i	0.0910386	+	0.0910386i
$666$	5.59604	+	3.98793i	0.216842	+	0.154529i
$667$		−	6.53721i		−	0.253122i
$668$	13.8891	+	13.8891i	0.537386	+	0.537386i
$669$	9.14070	−	28.5771i	0.353400	−	1.10485i
$670$	−3.19421	−	3.19421i	−0.123403	−	0.123403i
$671$	0.450366	−	0.450366i	0.0173862	−	0.0173862i
$672$	−8.10143	−	15.7215i	−0.312520	−	0.606469i
$673$			0.230805i			0.00889689i	0.999990	+	0.00444844i	$0.00141599\pi$
$673$			0.230805i			0.00889689i	−0.999990	+	0.00444844i	$0.998584\pi$
$674$	−0.538863	+	0.538863i	−0.0207562	+	0.0207562i
$675$	5.14287	+	0.742237i	0.197949	+	0.0285687i
$676$	−9.37538	+	17.5691i	−0.360592	+	0.675734i
$677$			41.4875i			1.59449i	0.603654	+	0.797247i	$0.293711\pi$
$677$			41.4875i			1.59449i	−0.603654	+	0.797247i	$0.706289\pi$
$678$	2.00757	−	6.27638i	0.0771004	−	0.241043i
$679$	−2.57746			−0.0989138
$680$	16.3119			0.625532
$681$	−24.5140	−	7.84109i	−0.939379	−	0.300471i
$682$	1.52116	−	1.52116i	0.0582483	−	0.0582483i
$683$	−31.7789	+	31.7789i	−1.21599	+	1.21599i	−0.246960	+	0.969026i	$0.579432\pi$
$683$	−31.7789	+	31.7789i	−1.21599	+	1.21599i	−0.969026	+	0.246960i	$0.920568\pi$
$684$	−8.54414	+	1.43364i	−0.326693	+	0.0548165i
$685$	−3.65731			−0.139739
$686$	13.1325			0.501400
$687$	−10.3722	−	3.31767i	−0.395724	−	0.126577i
$688$		−	16.5555i		−	0.631174i
$689$	−30.8286	−	7.71092i	−1.17448	−	0.293763i
$690$	0.920867	+	1.78701i	0.0350568	+	0.0680305i
$691$	25.0328	−	25.0328i	0.952293	−	0.952293i	−0.0466196	−	0.998913i	$-0.514845\pi$
$691$	25.0328	−	25.0328i	0.952293	−	0.952293i	0.998913	+	0.0466196i	$0.0148449\pi$
$692$		−	7.10633i		−	0.270142i
$693$	1.67858	−	2.35546i	0.0637641	−	0.0894767i
$694$	7.23648	−	7.23648i	0.274693	−	0.274693i
$695$	−11.7993	−	11.7993i	−0.447572	−	0.447572i
$696$	15.3631	+	4.91408i	0.582338	+	0.186268i
$697$	38.6187	+	38.6187i	1.46279	+	1.46279i
$698$		−	7.86699i		−	0.297770i
$699$	27.2357	−	14.0349i	1.03015	−	0.530847i
$700$	−1.90763	−	1.90763i	−0.0721016	−	0.0721016i
$701$	27.4234			1.03577			0.517883	−	0.855451i	$-0.326720\pi$
$701$	27.4234			1.03577			0.517883	+	0.855451i	$0.326720\pi$
$702$	−4.95606	−	11.8219i	−0.187054	−	0.446189i
$703$	−6.31112			−0.238028
$704$	0.443822	+	0.443822i	0.0167272	+	0.0167272i
$705$	13.0429	−	6.72116i	0.491226	−	0.253134i
$706$		−	13.5739i		−	0.510859i
$707$	22.7233	+	22.7233i	0.854596	+	0.854596i
$708$	−4.66502	−	1.49216i	−0.175322	−	0.0560789i
$709$	−0.997734	−	0.997734i	−0.0374707	−	0.0374707i	0.688123	−	0.725594i	$-0.258435\pi$
$709$	−0.997734	−	0.997734i	−0.0374707	−	0.0374707i	−0.725594	+	0.688123i	$0.758435\pi$
$710$	0.626685	−	0.626685i	0.0235191	−	0.0235191i
$711$	−6.71010	+	9.41592i	−0.251649	+	0.353125i
$712$		−	20.4945i		−	0.768066i
$713$	6.88901	−	6.88901i	0.257996	−	0.257996i
$714$	6.45334	+	12.5232i	0.241510	+	0.468669i
$715$	−0.478949	+	1.91486i	−0.0179117	+	0.0716116i
$716$			20.3574i			0.760793i
$717$	−10.9840	−	3.51336i	−0.410205	−	0.131209i
$718$	−13.5550			−0.505867
$719$	13.8518			0.516585			0.258292	−	0.966067i	$-0.416840\pi$
$719$	13.8518			0.516585			0.258292	+	0.966067i	$0.416840\pi$
$720$	4.17250	−	0.700112i	0.155500	−	0.0260916i
$721$	−4.55144	+	4.55144i	−0.169505	+	0.169505i
$722$	7.47295	−	7.47295i	0.278115	−	0.278115i
$723$	32.1879	+	10.2957i	1.19708	+	0.382900i
$724$	35.7124			1.32724
$725$	3.85370			0.143123
$726$	3.86330	−	12.0780i	0.143380	−	0.448258i
$727$			36.0915i			1.33856i	0.743010	+	0.669280i	$0.233397\pi$
$727$			36.0915i			1.33856i	−0.743010	+	0.669280i	$0.766603\pi$
$728$	−3.72335	+	14.8861i	−0.137996	+	0.551715i
$729$	−25.8982	−	7.63446i	−0.959191	−	0.282758i
$730$	−5.55135	+	5.55135i	−0.205465	+	0.205465i
$731$			79.2408i			2.93083i
$732$	1.41399	+	2.74396i	0.0522626	+	0.101420i
$733$	13.0564	−	13.0564i	0.482248	−	0.482248i	−0.423601	−	0.905849i	$-0.639234\pi$
$733$	13.0564	−	13.0564i	0.482248	−	0.482248i	0.905849	+	0.423601i	$0.139234\pi$
$734$	12.6895	+	12.6895i	0.468378	+	0.468378i
$735$	−2.05711	+	6.43126i	−0.0758777	+	0.237221i
$736$	6.95471	+	6.95471i	0.256354	+	0.256354i
$737$		−	3.61434i		−	0.133136i
$738$	−13.5250	−	9.63836i	−0.497861	−	0.354793i
$739$	12.8744	+	12.8744i	0.473592	+	0.473592i	0.903075	−	0.429483i	$-0.141304\pi$
$739$	12.8744	+	12.8744i	0.473592	+	0.473592i	−0.429483	+	0.903075i	$0.641304\pi$
$740$	5.12819			0.188516
$741$	10.0080	+	6.20047i	0.367654	+	0.227780i
$742$	−10.6204			−0.389889
$743$	20.7742	+	20.7742i	0.762133	+	0.762133i	0.976708	−	0.214575i	$-0.0688366\pi$
$743$	20.7742	+	20.7742i	0.762133	+	0.762133i	−0.214575	+	0.976708i	$0.568837\pi$
$744$	11.0114	+	21.3685i	0.403697	+	0.783405i
$745$		−	23.9563i		−	0.877689i
$746$	−3.30783	−	3.30783i	−0.121108	−	0.121108i
$747$	−49.9364	+	8.37893i	−1.82708	+	0.306569i
$748$	4.00271	+	4.00271i	0.146354	+	0.146354i
$749$	−18.6283	+	18.6283i	−0.680663	+	0.680663i
$750$	−1.05345	+	0.542853i	−0.0384665	+	0.0198222i
$751$		−	14.1702i		−	0.517080i	−0.966001	−	0.258540i	$-0.916759\pi$
$751$		−	14.1702i		−	0.517080i	0.966001	−	0.258540i	$-0.0832413\pi$
$752$	8.44779	−	8.44779i	0.308059	−	0.308059i
$753$	8.93946	−	4.60660i	0.325772	−	0.167874i
$754$	−4.89034	−	8.15270i	−0.178096	−	0.296904i
$755$			7.37193i			0.268292i
$756$	8.39477	+	11.2266i	0.305315	+	0.408308i
$757$	−27.8108			−1.01080			−0.505400	−	0.862885i	$-0.668655\pi$
$757$	−27.8108			−1.01080			−0.505400	+	0.862885i	$0.668655\pi$
$758$	24.0823			0.874710
$759$	−0.490035	+	1.53202i	−0.0177871	+	0.0556089i
$760$	3.22135	−	3.22135i	0.116851	−	0.116851i
$761$	3.88054	−	3.88054i	0.140669	−	0.140669i	−0.633265	−	0.773935i	$-0.718286\pi$
$761$	3.88054	−	3.88054i	0.140669	−	0.140669i	0.773935	+	0.633265i	$0.218286\pi$
$762$	0.0126238	−	0.0394665i	0.000457313	−	0.00142972i
$763$	−13.4853			−0.488200
$764$	−9.81584			−0.355125
$765$	−19.9711	+	3.35100i	−0.722057	+	0.121156i
$766$			7.51254i			0.271439i
$767$	3.42372	+	5.70769i	0.123623	+	0.206093i
$768$	−14.9199	+	7.68838i	−0.538375	+	0.277430i
$769$	−22.5865	+	22.5865i	−0.814491	+	0.814491i	−0.985304	−	0.170813i	$-0.945361\pi$
$769$	−22.5865	+	22.5865i	−0.814491	+	0.814491i	0.170813	+	0.985304i	$0.445361\pi$
$770$			0.659668i			0.0237728i
$771$	−12.7729	+	6.58200i	−0.460004	+	0.237045i
$772$	−24.6828	+	24.6828i	−0.888353	+	0.888353i
$773$	25.7487	+	25.7487i	0.926116	+	0.926116i	0.997452	−	0.0713367i	$-0.0227265\pi$
$773$	25.7487	+	25.7487i	0.926116	+	0.926116i	−0.0713367	+	0.997452i	$0.522726\pi$
$774$	−3.98744	−	23.7642i	−0.143325	−	0.854185i
$775$	4.06109	+	4.06109i	0.145879	+	0.145879i
$776$			3.53666i			0.126959i
$777$	4.67767	+	9.07739i	0.167811	+	0.325650i
$778$	3.04962	+	3.04962i	0.109334	+	0.109334i
$779$	15.2532			0.546504
$780$	−8.13216	−	5.03829i	−0.291178	−	0.180400i
$781$	0.709112			0.0253740
$782$	−5.53990	−	5.53990i	−0.198106	−	0.198106i
$783$	−19.8191	−	2.86036i	−0.708275	−	0.102221i
$784$			5.49784i			0.196351i
$785$	9.21457	+	9.21457i	0.328882	+	0.328882i
$786$	0.404190	−	1.26364i	0.0144170	−	0.0450726i
$787$	−19.7231	−	19.7231i	−0.703054	−	0.703054i	0.262011	−	0.965065i	$-0.415614\pi$
$787$	−19.7231	−	19.7231i	−0.703054	−	0.703054i	−0.965065	+	0.262011i	$0.915614\pi$
$788$	17.3537	−	17.3537i	0.618200	−	0.618200i
$789$	8.62564	+	16.7387i	0.307081	+	0.595915i
$790$		−	2.63701i		−	0.0938206i
$791$	6.92447	−	6.92447i	0.246206	−	0.246206i
$792$	−3.23205	−	2.30327i	−0.114846	−	0.0818431i
$793$	1.01786	−	4.06943i	0.0361451	−	0.144510i
$794$			23.5823i			0.836906i
$795$	4.65082	−	14.5401i	0.164948	−	0.515684i
$796$	−35.3573			−1.25321
$797$	−27.0871			−0.959474			−0.479737	−	0.877412i	$-0.659268\pi$
$797$	−27.0871			−0.959474			−0.479737	+	0.877412i	$0.659268\pi$
$798$	3.74758	+	1.19871i	0.132663	+	0.0424338i
$799$	−40.4342	+	40.4342i	−1.43046	+	1.43046i
$800$	−4.09981	+	4.09981i	−0.144950	+	0.144950i
$801$	4.21025	+	25.0921i	0.148762	+	0.886585i
$802$	−8.53483			−0.301375
$803$	−6.28151			−0.221670
$804$	16.6845	+	5.33672i	0.588416	+	0.188212i
$805$			2.98749i			0.105295i
$806$	3.43792	−	13.7450i	0.121096	−	0.484145i
$807$	17.1856	+	33.3499i	0.604960	+	1.17397i
$808$	31.1797	−	31.1797i	1.09690	−	1.09690i
$809$		−	12.8814i		−	0.452886i	−0.974024	−	0.226443i	$-0.927290\pi$
$809$		−	12.8814i		−	0.452886i	0.974024	−	0.226443i	$-0.0727097\pi$
$810$	5.82067	−	2.00991i	0.204518	−	0.0706211i
$811$	−37.1318	+	37.1318i	−1.30387	+	1.30387i	−0.378116	+	0.925758i	$0.623428\pi$
$811$	−37.1318	+	37.1318i	−1.30387	+	1.30387i	−0.925758	+	0.378116i	$0.876572\pi$
$812$	7.35143	+	7.35143i	0.257985	+	0.257985i
$813$	−8.34244	−	2.66843i	−0.292582	−	0.0935858i
$814$	−0.886676	−	0.886676i	−0.0310780	−	0.0310780i
$815$		−	5.42208i		−	0.189927i
$816$	−14.6567	+	7.55275i	−0.513087	+	0.264399i
$817$	15.6489	+	15.6489i	0.547485	+	0.547485i
$818$	9.90483			0.346314
$819$	1.50051	−	18.9904i	0.0524321	−	0.663578i
$820$	−12.3942			−0.432825
$821$	10.6744	+	10.6744i	0.372540	+	0.372540i	0.868402	−	0.495861i	$-0.165148\pi$
$821$	10.6744	+	10.6744i	0.372540	+	0.372540i	−0.495861	+	0.868402i	$0.665148\pi$
$822$	−3.85279	+	1.98538i	−0.134382	+	0.0692482i
$823$		−	22.6990i		−	0.791236i	−0.918415	−	0.395618i	$-0.870530\pi$
$823$		−	22.6990i		−	0.791236i	0.918415	−	0.395618i	$-0.129470\pi$
$824$	6.24527	+	6.24527i	0.217564	+	0.217564i
$825$	−0.903130	−	0.288877i	−0.0314429	−	0.0100574i
$826$	1.57289	+	1.57289i	0.0547277	+	0.0547277i
$827$	−13.2802	+	13.2802i	−0.461799	+	0.461799i	−0.899245	−	0.437446i	$-0.855883\pi$
$827$	−13.2802	+	13.2802i	−0.461799	+	0.461799i	0.437446	+	0.899245i	$0.355883\pi$
$828$	−6.34855	−	4.52419i	−0.220627	−	0.157226i
$829$		−	11.0522i		−	0.383858i	−0.981409	−	0.191929i	$-0.938526\pi$
$829$		−	11.0522i		−	0.383858i	0.981409	−	0.191929i	$-0.0614743\pi$
$830$	8.16585	−	8.16585i	0.283441	−	0.283441i
$831$	13.8750	+	26.9254i	0.481317	+	0.934033i
$832$	4.01030	+	1.00307i	0.139032	+	0.0347750i
$833$		−	26.3147i		−	0.911749i
$834$	−18.8352	−	6.02465i	−0.652209	−	0.208617i
$835$	12.8225			0.443741
$836$	1.58095			0.0546783
$837$	−17.8713	−	23.8999i	−0.617724	−	0.826102i
$838$	19.2672	−	19.2672i	0.665575	−	0.665575i
$839$	2.03658	−	2.03658i	0.0703107	−	0.0703107i	−0.671077	−	0.741388i	$-0.734168\pi$
$839$	2.03658	−	2.03658i	0.0703107	−	0.0703107i	0.741388	+	0.671077i	$0.234168\pi$
$840$	−7.02093	−	2.24573i	−0.242245	−	0.0774849i
$841$	14.1490			0.487897
$842$	10.7587			0.370771
$843$	2.60079	−	8.13098i	0.0895759	−	0.280046i
$844$			13.8574i			0.476992i
$845$	3.78224	+	12.4376i	0.130113	+	0.427868i
$846$	10.0915	−	14.1608i	0.346952	−	0.486858i
$847$	13.3252	−	13.3252i	0.457859	−	0.457859i
$848$		−	12.4298i		−	0.426840i
$849$	−7.51547	−	14.5844i	−0.257930	−	0.500534i
$850$	3.26578	−	3.26578i	0.112015	−	0.112015i
$851$	−4.01557	−	4.01557i	−0.137652	−	0.137652i
$852$	−1.04703	+	3.27340i	−0.0358708	+	0.112145i
$853$	−26.1501	−	26.1501i	−0.895364	−	0.895364i	0.0996578	−	0.995022i	$-0.468225\pi$
$853$	−26.1501	−	26.1501i	−0.895364	−	0.895364i	−0.995022	+	0.0996578i	$0.968225\pi$
$854$		−	1.40192i		−	0.0479726i
$855$	−3.28222	+	4.60577i	−0.112250	+	0.157514i
$856$	25.5608	+	25.5608i	0.873651	+	0.873651i
$857$	21.8580			0.746653			0.373327	−	0.927700i	$-0.378217\pi$
$857$	21.8580			0.746653			0.373327	+	0.927700i	$0.378217\pi$
$858$	0.534938	+	2.27720i	0.0182625	+	0.0777424i
$859$	3.08718			0.105333			0.0526666	−	0.998612i	$-0.483228\pi$
$859$	3.08718			0.105333			0.0526666	+	0.998612i	$0.483228\pi$
$860$	−12.7157	−	12.7157i	−0.433602	−	0.433602i
$861$	−11.3054	−	21.9390i	−0.385287	−	0.747679i
$862$		−	5.05794i		−	0.172274i
$863$	16.2854	+	16.2854i	0.554363	+	0.554363i	0.927697	−	0.373334i	$-0.121786\pi$
$863$	16.2854	+	16.2854i	0.554363	+	0.554363i	−0.373334	+	0.927697i	$0.621786\pi$
$864$	24.1278	−	18.0418i	0.820845	−	0.613793i
$865$	−3.28030	−	3.28030i	−0.111534	−	0.111534i
$866$	−1.43306	+	1.43306i	−0.0486973	+	0.0486973i
$867$	43.9784	−	22.6625i	1.49358	−	0.769659i
$868$			15.4941i			0.525904i
$869$	1.49193	−	1.49193i	0.0506101	−	0.0506101i
$870$	4.05967	−	2.09199i	0.137636	−	0.0709251i
$871$	−12.2450	−	20.4136i	−0.414905	−	0.691688i
$872$			18.5038i			0.626619i
$873$	−0.726546	−	4.33004i	−0.0245899	−	0.146550i
$874$	−2.18809			−0.0740133
$875$	−1.76113			−0.0595372
$876$	9.27491	−	28.9966i	0.313370	−	0.979705i
$877$	−9.53726	+	9.53726i	−0.322050	+	0.322050i	−0.849553	−	0.527503i	$-0.823128\pi$
$877$	−9.53726	+	9.53726i	−0.322050	+	0.322050i	0.527503	+	0.849553i	$0.323128\pi$
$878$	10.3418	−	10.3418i	0.349018	−	0.349018i
$879$	11.3502	−	35.4848i	0.382833	−	1.19687i
$880$	−0.772051			−0.0260258
$881$	−45.3231			−1.52697			−0.763487	−	0.645823i	$-0.776514\pi$
$881$	−45.3231			−1.52697			−0.763487	+	0.645823i	$0.776514\pi$
$882$	1.32417	+	7.89171i	0.0445870	+	0.265728i
$883$		−	39.8456i		−	1.34091i	−0.741949	−	0.670456i	$-0.766098\pi$
$883$		−	39.8456i		−	1.34091i	0.741949	−	0.670456i	$-0.233902\pi$
$884$	36.1678	+	9.04637i	1.21645	+	0.304263i
$885$	−2.84217	+	1.46460i	−0.0955386	+	0.0492320i
$886$	−10.0064	+	10.0064i	−0.336171	+	0.336171i
$887$		−	3.65752i		−	0.122807i	−0.998113	−	0.0614037i	$-0.980442\pi$
$887$		−	3.65752i		−	0.122807i	0.998113	−	0.0614037i	$-0.0195577\pi$
$888$	12.4555	−	6.41847i	0.417981	−	0.215390i
$889$	0.0435418	−	0.0435418i	0.00146034	−	0.00146034i
$890$	−4.10318	−	4.10318i	−0.137539	−	0.137539i
$891$	4.43026	+	2.15599i	0.148419	+	0.0722284i
$892$	−18.7634	−	18.7634i	−0.628244	−	0.628244i
$893$			15.9703i			0.534425i
$894$	−13.0047	−	25.2367i	−0.434943	−	0.844041i
$895$	9.39704	+	9.39704i	0.314108	+	0.314108i
$896$	−19.0406			−0.636101
$897$	2.42262	+	10.3130i	0.0808889	+	0.344340i
$898$	−28.1863			−0.940590
$899$	−15.6502	−	15.6502i	−0.521963	−	0.521963i
$900$	2.66702	−	3.74248i	0.0889006	−	0.124749i
$901$			59.4935i			1.98202i
$902$	2.14299	+	2.14299i	0.0713539	+	0.0713539i
$903$	10.9094	−	34.1067i	0.363043	−	1.13500i
$904$	−9.50142	−	9.50142i	−0.316012	−	0.316012i
$905$	16.4849	−	16.4849i	0.547978	−	0.547978i
$906$	4.00188	+	7.76595i	0.132953	+	0.258006i
$907$		−	22.0580i		−	0.732422i	−0.930532	−	0.366211i	$-0.880655\pi$
$907$		−	22.0580i		−	0.732422i	0.930532	−	0.366211i	$-0.119345\pi$
$908$	−16.0956	+	16.0956i	−0.534152	+	0.534152i
$909$	−31.7689	+	44.5796i	−1.05371	+	1.47861i
$910$	2.23488	+	3.72577i	0.0740855	+	0.123508i
$911$			9.96697i			0.330220i	0.986275	+	0.165110i	$0.0527980\pi$
$911$			9.96697i			0.330220i	−0.986275	+	0.165110i	$0.947202\pi$
$912$	−1.40292	+	4.38603i	−0.0464554	+	0.145236i
$913$	9.23989			0.305796
$914$	2.50993			0.0830212
$915$	1.91932	+	0.613917i	0.0634507	+	0.0202955i
$916$	−6.81027	+	6.81027i	−0.225018	+	0.225018i
$917$	1.39412	−	1.39412i	0.0460380	−	0.0460380i
$918$	−19.2194	+	14.3715i	−0.634336	+	0.474330i
$919$	44.1088			1.45502			0.727508	−	0.686100i	$-0.240679\pi$
$919$	44.1088			1.45502			0.727508	+	0.686100i	$0.240679\pi$
$920$	4.09929			0.135150
$921$	−20.1769	−	6.45380i	−0.664850	−	0.212660i
$922$			17.5169i			0.576890i
$923$	4.00503	−	2.40239i	0.131827	−	0.0790756i
$924$	−1.17177	−	2.27391i	−0.0385483	−	0.0748060i
$925$	2.36718	−	2.36718i	0.0778325	−	0.0778325i
$926$		−	19.1106i		−	0.628013i
$927$	−8.92924	−	6.36328i	−0.293275	−	0.208997i
$928$	15.7994	−	15.7994i	0.518642	−	0.518642i
$929$	−13.0994	−	13.0994i	−0.429776	−	0.429776i	0.458776	−	0.888552i	$-0.348288\pi$
$929$	−13.0994	−	13.0994i	−0.429776	−	0.429776i	−0.888552	+	0.458776i	$0.848288\pi$
$930$	6.48272	+	2.07357i	0.212577	+	0.0679951i
$931$	−5.19675	−	5.19675i	−0.170317	−	0.170317i
$932$		−	27.0978i		−	0.887618i
$933$	−2.33447	+	1.20298i	−0.0764272	+	0.0393838i
$934$	1.44451	+	1.44451i	0.0472659	+	0.0472659i
$935$	3.69532			0.120850
$936$	−26.0577	−	2.05893i	−0.851721	−	0.0672981i
$937$	23.1567			0.756496			0.378248	−	0.925704i	$-0.376527\pi$
$937$	23.1567			0.756496			0.378248	+	0.925704i	$0.376527\pi$
$938$	−5.62543	−	5.62543i	−0.183677	−	0.183677i
$939$	1.43065	−	0.737227i	0.0466874	−	0.0240585i
$940$		−	12.9769i		−	0.423259i
$941$	−14.3573	−	14.3573i	−0.468035	−	0.468035i	0.433242	−	0.901277i	$-0.357369\pi$
$941$	−14.3573	−	14.3573i	−0.468035	−	0.468035i	−0.901277	+	0.433242i	$0.857369\pi$
$942$	14.7092	+	4.70492i	0.479253	+	0.153294i
$943$	9.70515	+	9.70515i	0.316043	+	0.316043i
$944$	−1.84085	+	1.84085i	−0.0599145	+	0.0599145i
$945$	9.05727	+	1.30718i	0.294633	+	0.0425225i
$946$			4.39716i			0.142964i
$947$	−0.485543	+	0.485543i	−0.0157780	+	0.0157780i	−0.714952	−	0.699174i	$-0.753551\pi$
$947$	−0.485543	+	0.485543i	−0.0157780	+	0.0157780i	0.699174	+	0.714952i	$0.253551\pi$
$948$	4.68412	+	9.08990i	0.152133	+	0.295226i
$949$	−35.4776	+	21.2810i	−1.15165	+	0.690811i
$950$		−	1.28988i		−	0.0418494i
$951$	−35.6960	−	11.4178i	−1.15752	−	0.370246i
$952$	28.7274			0.931061
$953$	29.1833			0.945339			0.472670	−	0.881240i	$-0.343290\pi$
$953$	29.1833			0.945339			0.472670	+	0.881240i	$0.343290\pi$
$954$	−2.99374	−	17.8420i	−0.0969259	−	0.577655i
$955$	−4.53102	+	4.53102i	−0.146620	+	0.146620i
$956$	−7.21196	+	7.21196i	−0.233252	+	0.233252i
$957$	3.48039	+	1.11324i	0.112505	+	0.0359860i
$958$	4.46230			0.144170
$959$	−6.44102			−0.207991
$960$	−0.604996	+	1.89143i	−0.0195262	+	0.0610457i
$961$		−	1.98485i		−	0.0640273i
$962$	−8.01186	−	2.00394i	−0.258313	−	0.0646098i
$963$	−36.5459	−	26.0438i	−1.17768	−	0.839251i
$964$	21.1342	−	21.1342i	0.680687	−	0.680687i
$965$			22.7873i			0.733548i
$966$	1.62177	+	3.14717i	0.0521796	+	0.101259i
$967$	14.9051	−	14.9051i	0.479316	−	0.479316i	−0.425597	−	0.904913i	$-0.639936\pi$
$967$	14.9051	−	14.9051i	0.479316	−	0.479316i	0.904913	+	0.425597i	$0.139936\pi$
$968$	−18.2842	−	18.2842i	−0.587675	−	0.587675i
$969$	6.71491	−	20.9932i	0.215714	−	0.674398i
$970$	0.708070	+	0.708070i	0.0227348	+	0.0227348i
$971$		−	46.0892i		−	1.47907i	−0.673116	−	0.739537i	$-0.735045\pi$
$971$		−	46.0892i		−	1.47907i	0.673116	−	0.739537i	$-0.264955\pi$
$972$	−16.4939	+	17.2675i	−0.529043	+	0.553856i
$973$	−20.7801	−	20.7801i	−0.666179	−	0.666179i
$974$	−21.9747			−0.704116
$975$	−6.07951	+	1.42814i	−0.194700	+	0.0457370i
$976$	1.64075			0.0525192
$977$	11.8734	+	11.8734i	0.379864	+	0.379864i	0.871053	−	0.491189i	$-0.163438\pi$
$977$	11.8734	+	11.8734i	0.379864	+	0.379864i	−0.491189	+	0.871053i	$0.663438\pi$
$978$	−2.94339	−	5.71188i	−0.0941193	−	0.182646i
$979$		−	4.64287i		−	0.148387i
$980$	4.22269	+	4.22269i	0.134889	+	0.134889i
$981$	−3.80129	−	22.6548i	−0.121366	−	0.723312i
$982$	−15.8755	−	15.8755i	−0.506607	−	0.506607i
$983$	8.05185	−	8.05185i	0.256814	−	0.256814i	−0.566943	−	0.823757i	$-0.691874\pi$
$983$	8.05185	−	8.05185i	0.256814	−	0.256814i	0.823757	+	0.566943i	$0.191874\pi$
$984$	−30.1036	+	15.5127i	−0.959668	+	0.494527i
$985$		−	16.0210i		−	0.510472i
$986$	−12.5853	+	12.5853i	−0.400798	+	0.400798i
$987$	22.9704	−	11.8369i	0.731155	−	0.376772i
$988$	8.92911	−	5.35607i	0.284073	−	0.170399i
$989$			19.9138i			0.633221i
$990$	−1.10822	+	0.185950i	−0.0352215	+	0.00590989i
$991$	52.2270			1.65905			0.829523	−	0.558473i	$-0.188612\pi$
$991$	52.2270			1.65905			0.829523	+	0.558473i	$0.188612\pi$
$992$	33.2994			1.05726
$993$	16.5482	−	51.7355i	0.525141	−	1.64178i
$994$	1.10368	−	1.10368i	0.0350065	−	0.0350065i
$995$	−16.3210	+	16.3210i	−0.517411	+	0.517411i
$996$	−13.6431	+	42.6531i	−0.432297	+	1.35151i
$997$	−28.9060			−0.915462			−0.457731	−	0.889091i	$-0.651338\pi$
$997$	−28.9060			−0.915462			−0.457731	+	0.889091i	$0.651338\pi$
$998$	−0.346810			−0.0109781
$999$	−13.9311	+	10.4171i	−0.440761	+	0.329582i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	195.2.o.a.161.8	yes	40
3.2	odd	2	inner	195.2.o.a.161.13	yes	40
5.2	odd	4		975.2.n.r.824.13		40
5.3	odd	4		975.2.n.q.824.8		40
5.4	even	2		975.2.o.p.551.13		40
13.8	odd	4	inner	195.2.o.a.86.13	yes	40
15.2	even	4		975.2.n.r.824.8		40
15.8	even	4		975.2.n.q.824.13		40
15.14	odd	2		975.2.o.p.551.8		40
39.8	even	4	inner	195.2.o.a.86.8	✓	40
65.8	even	4		975.2.n.r.749.8		40
65.34	odd	4		975.2.o.p.476.8		40
65.47	even	4		975.2.n.q.749.13		40
195.8	odd	4		975.2.n.r.749.13		40
195.47	odd	4		975.2.n.q.749.8		40
195.164	even	4		975.2.o.p.476.13		40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
195.2.o.a.86.8	✓	40	39.8	even	4	inner
195.2.o.a.86.13	yes	40	13.8	odd	4	inner
195.2.o.a.161.8	yes	40	1.1	even	1	trivial
195.2.o.a.161.13	yes	40	3.2	odd	2	inner
975.2.n.q.749.8		40	195.47	odd	4
975.2.n.q.749.13		40	65.47	even	4
975.2.n.q.824.8		40	5.3	odd	4
975.2.n.q.824.13		40	15.8	even	4
975.2.n.r.749.8		40	65.8	even	4
975.2.n.r.749.13		40	195.8	odd	4
975.2.n.r.824.8		40	15.2	even	4
975.2.n.r.824.13		40	5.2	odd	4
975.2.o.p.476.8		40	65.34	odd	4
975.2.o.p.476.13		40	195.164	even	4
975.2.o.p.551.8		40	15.14	odd	2
975.2.o.p.551.13		40	5.4	even	2

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:	\( N \)	\(=\)	\( 195 = 3 \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	195.o (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.483812 - 0.483812i) q^{2} +(1.53965 - 0.793397i) q^{3} -1.53185i q^{4} +(-0.707107 - 0.707107i) q^{5} +(-1.12876 - 0.361045i) q^{6} +(-1.24531 - 1.24531i) q^{7} +(-1.70875 + 1.70875i) q^{8} +(1.74104 - 2.44311i) q^{9} +O(q^{10})\)	\(q+(-0.483812 - 0.483812i) q^{2} +(1.53965 - 0.793397i) q^{3} -1.53185i q^{4} +(-0.707107 - 0.707107i) q^{5} +(-1.12876 - 0.361045i) q^{6} +(-1.24531 - 1.24531i) q^{7} +(-1.70875 + 1.70875i) q^{8} +(1.74104 - 2.44311i) q^{9} +0.684213i q^{10} +(-0.387103 + 0.387103i) q^{11} +(-1.21537 - 2.35852i) q^{12} +(-0.874878 + 3.49780i) q^{13} +1.20499i q^{14} +(-1.64971 - 0.527680i) q^{15} -1.41028 q^{16} +6.75010 q^{17} +(-2.02434 + 0.339668i) q^{18} +(1.33304 - 1.33304i) q^{19} +(-1.08318 + 1.08318i) q^{20} +(-2.90536 - 0.929314i) q^{21} +0.374570 q^{22} +1.69635 q^{23} +(-1.27516 + 3.98660i) q^{24} +1.00000i q^{25} +(2.11555 - 1.26900i) q^{26} +(0.742237 - 5.14287i) q^{27} +(-1.90763 + 1.90763i) q^{28} -3.85370i q^{29} +(0.542853 + 1.05345i) q^{30} +(4.06109 - 4.06109i) q^{31} +(4.09981 + 4.09981i) q^{32} +(-0.288877 + 0.903130i) q^{33} +(-3.26578 - 3.26578i) q^{34} +1.76113i q^{35} +(-3.74248 - 2.66702i) q^{36} +(-2.36718 - 2.36718i) q^{37} -1.28988 q^{38} +(1.42814 + 6.07951i) q^{39} +2.41654 q^{40} +(5.72121 + 5.72121i) q^{41} +(0.956036 + 1.85526i) q^{42} +11.7392i q^{43} +(0.592985 + 0.592985i) q^{44} +(-2.95864 + 0.496436i) q^{45} +(-0.820713 - 0.820713i) q^{46} +(-5.99016 + 5.99016i) q^{47} +(-2.17133 + 1.11891i) q^{48} -3.89841i q^{49} +(0.483812 - 0.483812i) q^{50} +(10.3928 - 5.35551i) q^{51} +(5.35811 + 1.34018i) q^{52} +8.81372i q^{53} +(-2.84728 + 2.12908i) q^{54} +0.547447 q^{55} +4.25585 q^{56} +(0.994786 - 3.11005i) q^{57} +(-1.86446 + 1.86446i) q^{58} +(1.30531 - 1.30531i) q^{59} +(-0.808328 + 2.52712i) q^{60} -1.16343 q^{61} -3.92960 q^{62} +(-5.21056 + 0.874290i) q^{63} -1.14652i q^{64} +(3.09195 - 1.85468i) q^{65} +(0.576707 - 0.297183i) q^{66} +(-4.66845 + 4.66845i) q^{67} -10.3402i q^{68} +(2.61178 - 1.34588i) q^{69} +(0.852057 - 0.852057i) q^{70} +(-0.915921 - 0.915921i) q^{71} +(1.19966 + 7.14967i) q^{72} +(8.11348 + 8.11348i) q^{73} +2.29054i q^{74} +(0.793397 + 1.53965i) q^{75} +(-2.04202 - 2.04202i) q^{76} +0.964126 q^{77} +(2.25039 - 3.63229i) q^{78} -3.85408 q^{79} +(0.997216 + 0.997216i) q^{80} +(-2.93755 - 8.50710i) q^{81} -5.53597i q^{82} +(-11.9347 - 11.9347i) q^{83} +(-1.42357 + 4.45059i) q^{84} +(-4.77304 - 4.77304i) q^{85} +(5.67957 - 5.67957i) q^{86} +(-3.05751 - 5.93334i) q^{87} -1.32293i q^{88} +(-5.99694 + 5.99694i) q^{89} +(1.67161 + 1.19124i) q^{90} +(5.44533 - 3.26635i) q^{91} -2.59855i q^{92} +(3.03059 - 9.47471i) q^{93} +5.79622 q^{94} -1.88521 q^{95} +(9.56505 + 3.05949i) q^{96} +(1.03487 - 1.03487i) q^{97} +(-1.88610 + 1.88610i) q^{98} +(0.271772 + 1.61970i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 12 q^{6} - 16 q^{7}+O(q^{10}) \) 40 * q + 12 * q^6 - 16 * q^7	\( 40 q + 12 q^{6} - 16 q^{7} + 4 q^{15} - 64 q^{16} + 4 q^{18} - 16 q^{19} - 12 q^{21} + 8 q^{24} - 24 q^{27} + 32 q^{28} + 32 q^{31} - 4 q^{33} - 16 q^{34} + 32 q^{37} - 8 q^{39} + 8 q^{42} - 8 q^{45} - 40 q^{46} + 8 q^{48} - 32 q^{54} + 8 q^{55} - 36 q^{57} + 24 q^{58} + 16 q^{60} + 8 q^{61} + 8 q^{63} - 48 q^{66} - 32 q^{67} + 132 q^{72} - 64 q^{73} + 16 q^{76} - 12 q^{78} + 40 q^{79} + 72 q^{81} + 124 q^{84} - 24 q^{85} + 16 q^{87} + 8 q^{91} - 108 q^{93} - 32 q^{94} - 76 q^{96} + 24 q^{97} - 20 q^{99}+O(q^{100}) \) 40 * q + 12 * q^6 - 16 * q^7 + 4 * q^15 - 64 * q^16 + 4 * q^18 - 16 * q^19 - 12 * q^21 + 8 * q^24 - 24 * q^27 + 32 * q^28 + 32 * q^31 - 4 * q^33 - 16 * q^34 + 32 * q^37 - 8 * q^39 + 8 * q^42 - 8 * q^45 - 40 * q^46 + 8 * q^48 - 32 * q^54 + 8 * q^55 - 36 * q^57 + 24 * q^58 + 16 * q^60 + 8 * q^61 + 8 * q^63 - 48 * q^66 - 32 * q^67 + 132 * q^72 - 64 * q^73 + 16 * q^76 - 12 * q^78 + 40 * q^79 + 72 * q^81 + 124 * q^84 - 24 * q^85 + 16 * q^87 + 8 * q^91 - 108 * q^93 - 32 * q^94 - 76 * q^96 + 24 * q^97 - 20 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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