LMFDB - Embedded newform 195.2.o.a.86.13

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			86.13
Character	$\chi$	$=$	195.86
Dual form			195.2.o.a.161.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.483812 - 0.483812i) q^{2} +(1.53965 - 0.793397i) q^{3} +1.53185i q^{4} +(0.707107 - 0.707107i) q^{5} +(0.361045 - 1.12876i) q^{6} +(-1.24531 + 1.24531i) q^{7} +(1.70875 + 1.70875i) q^{8} +(1.74104 - 2.44311i) q^{9} +O(q^{10})$	\(q+(0.483812 - 0.483812i) q^{2} +(1.53965 - 0.793397i) q^{3} +1.53185i q^{4} +(0.707107 - 0.707107i) q^{5} +(0.361045 - 1.12876i) 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} +(0.527680 - 1.64971i) q^{15} -1.41028 q^{16} -6.75010 q^{17} +(-0.339668 - 2.02434i) q^{18} +(1.33304 + 1.33304i) q^{19} +(1.08318 + 1.08318i) q^{20} +(-0.929314 + 2.90536i) q^{21} +0.374570 q^{22} -1.69635 q^{23} +(3.98660 + 1.27516i) 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} +(0.903130 + 0.288877i) 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} +(-4.12215 - 4.69126i) 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} +(-0.496436 - 2.95864i) 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} +(-2.12908 - 2.84728i) q^{54} +0.547447 q^{55} -4.25585 q^{56} +(3.11005 + 0.994786i) q^{57} +(-1.86446 - 1.86446i) q^{58} +(-1.30531 - 1.30531i) q^{59} +(2.52712 + 0.808328i) q^{60} -1.16343 q^{61} +3.92960 q^{62} +(0.874290 + 5.21056i) 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} +(7.14967 - 1.19966i) 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} +(-4.26403 - 0.275341i) 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} +(-4.45059 - 1.42357i) 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} +(9.47471 + 3.03059i) q^{93} +5.79622 q^{94} +1.88521 q^{95} +(-3.05949 + 9.56505i) q^{96} +(1.03487 + 1.03487i) q^{97} +(1.88610 + 1.88610i) q^{98} +(1.61970 - 0.271772i) 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 $\left(\mathbb{Z}/195\mathbb{Z}\right)^\times$.

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

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	$-0.672227\pi$
$2$	0.483812	−	0.483812i	0.342107	−	0.342107i	0.857159	+	0.515052i	$0.172227\pi$
$3$	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
$6$	0.361045	−	1.12876i	0.147396	−	0.460813i
$7$	−1.24531	+	1.24531i	−0.470683	+	0.470683i	−0.902135	−	0.431453i	$-0.858001\pi$
$7$	−1.24531	+	1.24531i	−0.470683	+	0.470683i	0.431453	+	0.902135i	$0.358001\pi$
$8$	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	$-0.223700\pi$
$11$	0.387103	+	0.387103i	0.116716	+	0.116716i	−0.646337	+	0.763053i	$0.723700\pi$
$12$	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
$15$	0.527680	−	1.64971i	0.136246	−	0.425954i
$16$	−1.41028			−0.352569
$17$	−6.75010			−1.63714			−0.818570	−	0.574407i	$-0.805233\pi$
$17$	−6.75010			−1.63714			−0.818570	+	0.574407i	$0.805233\pi$
$18$	−0.339668	−	2.02434i	−0.0800606	−	0.477142i
$19$	1.33304	+	1.33304i	0.305821	+	0.305821i	0.843286	−	0.537465i	$-0.180618\pi$
$19$	1.33304	+	1.33304i	0.305821	+	0.305821i	−0.537465	+	0.843286i	$0.680618\pi$
$20$	1.08318	+	1.08318i	0.242207	+	0.242207i
$21$	−0.929314	+	2.90536i	−0.202793	+	0.634003i
$22$	0.374570			0.0798586
$23$	−1.69635			−0.353713			−0.176856	−	0.984237i	$-0.556593\pi$
$23$	−1.69635			−0.353713			−0.176856	+	0.984237i	$0.556593\pi$
$24$	3.98660	+	1.27516i	0.813761	+	0.260291i
$25$		−	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	0.970499	−	0.241106i	$-0.0775102\pi$
$31$	4.06109	+	4.06109i	0.729393	+	0.729393i	−0.241106	+	0.970499i	$0.577510\pi$
$32$	−4.09981	+	4.09981i	−0.724751	+	0.724751i
$33$	0.903130	+	0.288877i	0.157215	+	0.0502869i
$34$	−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	−0.874389	−	0.485226i	$-0.838737\pi$
$37$	−2.36718	+	2.36718i	−0.389163	+	0.389163i	0.485226	+	0.874389i	$0.338737\pi$
$38$	1.28988			0.209247
$39$	−4.12215	−	4.69126i	−0.660072	−	0.751202i
$40$	2.41654			0.382088
$41$	−5.72121	+	5.72121i	−0.893502	+	0.893502i	−0.994851	−	0.101349i	$-0.967684\pi$
$41$	−5.72121	+	5.72121i	−0.893502	+	0.893502i	0.101349	+	0.994851i	$0.467684\pi$
$42$	0.956036	+	1.85526i	0.147520	+	0.286273i
$43$		−	11.7392i		−	1.79021i	−0.445853	−	0.895106i	$-0.647100\pi$
$43$		−	11.7392i		−	1.79021i	0.445853	−	0.895106i	$-0.352900\pi$
$44$	−0.592985	+	0.592985i	−0.0893958	+	0.0893958i
$45$	−0.496436	−	2.95864i	−0.0740044	−	0.441048i
$46$	−0.820713	+	0.820713i	−0.121008	+	0.121008i
$47$	5.99016	+	5.99016i	0.873755	+	0.873755i	0.992879	−	0.119124i	$-0.0380087\pi$
$47$	5.99016	+	5.99016i	0.873755	+	0.873755i	−0.119124	+	0.992879i	$0.538009\pi$
$48$	−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	$0.793042\pi$
$54$	−2.12908	−	2.84728i	−0.289731	−	0.387466i
$55$	0.547447			0.0738177
$56$	−4.25585			−0.568712
$57$	3.11005	+	0.994786i	0.411936	+	0.131763i
$58$	−1.86446	−	1.86446i	−0.244816	−	0.244816i
$59$	−1.30531	−	1.30531i	−0.169937	−	0.169937i	0.617015	−	0.786952i	$-0.288342\pi$
$59$	−1.30531	−	1.30531i	−0.169937	−	0.169937i	−0.786952	+	0.617015i	$0.788342\pi$
$60$	2.52712	+	0.808328i	0.326249	+	0.104355i
$61$	−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
$63$	0.874290	+	5.21056i	0.110150	+	0.656469i
$64$			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	0.361882	−	0.932224i	$-0.382134\pi$
$67$	−4.66845	−	4.66845i	−0.570341	−	0.570341i	−0.932224	+	0.361882i	$0.882134\pi$
$68$		−	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	$-0.725510\pi$
$71$	0.915921	−	0.915921i	0.108700	−	0.108700i	0.759365	+	0.650665i	$0.225510\pi$
$72$	7.14967	−	1.19966i	0.842597	−	0.141381i
$73$	8.11348	−	8.11348i	0.949611	−	0.949611i	−0.0491790	−	0.998790i	$-0.515660\pi$
$73$	8.11348	−	8.11348i	0.949611	−	0.949611i	0.998790	+	0.0491790i	$0.0156605\pi$
$74$			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
$78$	−4.26403	−	0.275341i	−0.482806	−	0.0311762i
$79$	−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	0.388586	−	0.921412i	$-0.372964\pi$
$83$	11.9347	−	11.9347i	1.31000	−	1.31000i	0.921412	−	0.388586i	$-0.127036\pi$
$84$	−4.45059	−	1.42357i	−0.485599	−	0.155325i
$85$	−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	$-0.101606\pi$
$89$	5.99694	+	5.99694i	0.635674	+	0.635674i	−0.313811	+	0.949485i	$0.601606\pi$
$90$	−1.67161	−	1.19124i	−0.176203	−	0.125568i
$91$	5.44533	+	3.26635i	0.570826	+	0.342406i
$92$		−	2.59855i		−	0.270918i
$93$	9.47471	+	3.03059i	0.982481	+	0.314258i
$94$	5.79622			0.597835
$95$	1.88521			0.193418
$96$	−3.05949	+	9.56505i	−0.312258	+	0.976229i
$97$	1.03487	+	1.03487i	0.105075	+	0.105075i	0.757690	−	0.652615i	$-0.226328\pi$
$97$	1.03487	+	1.03487i	0.105075	+	0.105075i	−0.652615	+	0.757690i	$0.726328\pi$
$98$	1.88610	+	1.88610i	0.190525	+	0.190525i
$99$	1.61970	−	0.271772i	0.162786	−	0.0273141i
$100$	1.53185			0.153185
$101$	18.2471			1.81565			0.907826	−	0.419347i	$-0.137741\pi$
$101$	18.2471			1.81565			0.907826	+	0.419347i	$0.137741\pi$
$102$	−2.43709	+	7.61921i	−0.241308	+	0.754415i
$103$			3.65487i			0.360125i	0.983655	+	0.180063i	$0.0576300\pi$
$103$			3.65487i			0.360125i	−0.983655	+	0.180063i	$0.942370\pi$
$104$	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	0.917150	−	0.398542i	$-0.130484\pi$
$109$	5.41443	+	5.41443i	0.518609	+	0.518609i	−0.398542	+	0.917150i	$0.630484\pi$
$110$	0.264861	−	0.264861i	0.0252535	−	0.0252535i
$111$	−1.76652	+	5.52275i	−0.167670	+	0.524196i
$112$	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
$117$	−10.0687	−	3.95239i	−0.930851	−	0.365398i
$118$	−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
$123$	−4.26946	+	13.3478i	−0.384964	+	1.20353i
$124$	−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	$-0.999506\pi$
$127$		−	0.0349646i		−	0.00310261i	0.999999	−	0.00155130i	$-0.000493796\pi$
$128$	−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	$0.984427\pi$
$132$	−0.442516	+	1.38346i	−0.0385161	+	0.120415i
$133$	−3.32010			−0.287889
$134$	−4.51730			−0.390235
$135$	−3.11172	−	4.16140i	−0.267814	−	0.358156i
$136$	−11.5342	−	11.5342i	−0.989054	−	0.989054i
$137$	−2.58611	−	2.58611i	−0.220946	−	0.220946i	0.587950	−	0.808897i	$-0.299935\pi$
$137$	−2.58611	−	2.58611i	−0.220946	−	0.220946i	−0.808897	+	0.587950i	$0.799935\pi$
$138$	−0.612459	+	1.91476i	−0.0521359	+	0.162995i
$139$	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
$141$	13.9753	+	4.47017i	1.17694	+	0.376456i
$142$		−	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	−0.557719	+	0.830030i	$0.688323\pi$
$149$	−16.9396	+	16.9396i	−1.38775	+	1.38775i	−0.830030	+	0.557719i	$0.811677\pi$
$150$	−1.12876	−	0.361045i	−0.0921625	−	0.0294792i
$151$	−5.21274	+	5.21274i	−0.424207	+	0.424207i	−0.886649	−	0.462442i	$-0.846973\pi$
$151$	−5.21274	+	5.21274i	−0.424207	+	0.424207i	0.462442	+	0.886649i	$0.346973\pi$
$152$			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
$156$	7.18631	−	6.31452i	0.575366	−	0.505566i
$157$	−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
$162$	−5.53706	−	2.69461i	−0.435032	−	0.211709i
$163$	3.83399	−	3.83399i	0.300301	−	0.300301i	−0.540830	−	0.841132i	$-0.681890\pi$
$163$	3.83399	−	3.83399i	0.300301	−	0.300301i	0.841132	+	0.540830i	$0.181890\pi$
$164$	−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	$-0.0847584\pi$
$167$	9.06688	+	9.06688i	0.701616	+	0.701616i	−0.263141	+	0.964757i	$0.584758\pi$
$168$	−6.55251	+	3.37658i	−0.505537	+	0.260509i
$169$	−11.4692	+	6.12029i	−0.882244	+	0.470792i
$170$			4.61851i			0.354223i
$171$	5.57765	−	0.935885i	0.426534	−	0.0715689i
$172$	17.9827			1.37117
$173$	−4.63904			−0.352700			−0.176350	−	0.984328i	$-0.556429\pi$
$173$	−4.63904			−0.352700			−0.176350	+	0.984328i	$0.556429\pi$
$174$	−4.34988	−	1.39136i	−0.329764	−	0.105479i
$175$	1.24531	+	1.24531i	0.0941365	+	0.0941365i
$176$	−0.545923	−	0.545923i	−0.0411505	−	0.0411505i
$177$	−3.04535	−	0.974090i	−0.228902	−	0.0732171i
$178$	5.80278			0.434936
$179$	13.2894			0.993298			0.496649	−	0.867951i	$-0.334564\pi$
$179$	13.2894			0.993298			0.496649	+	0.867951i	$0.334564\pi$
$180$	4.53220	−	0.760467i	0.337810	−	0.0566819i
$181$		−	23.3132i		−	1.73286i	−0.499299	−	0.866429i	$-0.666409\pi$
$181$		−	23.3132i		−	1.73286i	0.499299	−	0.866429i	$-0.333591\pi$
$182$	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
$189$	5.48014	+	7.32877i	0.398622	+	0.533090i
$190$	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	−0.175332	+	0.984509i	$0.556100\pi$
$193$	−16.1130	+	16.1130i	−1.15984	+	1.15984i	−0.984509	+	0.175332i	$0.943900\pi$
$194$	1.00136			0.0718936
$195$	−6.23202	−	0.402420i	−0.446284	−	0.0288179i
$196$	−5.97179			−0.426556
$197$	−11.3286	+	11.3286i	−0.807127	+	0.807127i	−0.984198	−	0.177071i	$-0.943338\pi$
$197$	−11.3286	+	11.3286i	−0.807127	+	0.807127i	0.177071	+	0.984198i	$0.443338\pi$
$198$	0.652142	−	0.915115i	0.0463457	−	0.0650344i
$199$			23.0814i			1.63620i	0.575079	+	0.818098i	$0.304971\pi$
$199$			23.0814i			1.63620i	−0.575079	+	0.818098i	$0.695029\pi$
$200$	1.70875	−	1.70875i	0.120827	−	0.120827i
$201$	−10.8917	−	3.48384i	−0.768242	−	0.245731i
$202$	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
$210$	1.98789	+	0.635849i	0.137177	+	0.0438778i
$211$	−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
$213$	0.683508	−	2.13689i	0.0468332	−	0.146417i
$214$	−7.23723	−	7.23723i	−0.494727	−	0.494727i
$215$	−8.30087	−	8.30087i	−0.566115	−	0.566115i
$216$	10.0562	−	7.51958i	0.684237	−	0.511643i
$217$	−10.1146			−0.686625
$218$	5.23913			0.354839
$219$	6.05470	−	18.9291i	0.409139	−	1.27911i
$220$			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	0.986142	−	0.165901i	$-0.0530532\pi$
$223$	12.2488	+	12.2488i	0.820241	+	0.820241i	−0.165901	+	0.986142i	$0.553053\pi$
$224$		−	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	$-0.585852\pi$
$227$	10.5073	−	10.5073i	0.697394	−	0.697394i	0.963848	+	0.266454i	$0.0858519\pi$
$228$	−1.52387	+	4.76414i	−0.100920	+	0.315513i
$229$	−4.44578	+	4.44578i	−0.293785	+	0.293785i	−0.838574	−	0.544788i	$-0.816610\pi$
$229$	−4.44578	+	4.44578i	−0.293785	+	0.293785i	0.544788	+	0.838574i	$0.316610\pi$
$230$			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	$-0.696729\pi$
$233$	−17.6896			−1.15888			−0.579441	+	0.815014i	$0.696729\pi$
$234$	−6.78357	+	2.95914i	−0.443456	+	0.193445i
$235$	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	$-0.680914\pi$
$239$	4.70800	−	4.70800i	0.304535	−	0.304535i	0.842785	+	0.538250i	$0.180914\pi$
$240$	−0.744175	+	2.32655i	−0.0480363	+	0.150178i
$241$	13.7965	−	13.7965i	0.888710	−	0.888710i	−0.105689	−	0.994399i	$-0.533705\pi$
$241$	13.7965	−	13.7965i	0.888710	−	0.888710i	0.994399	+	0.105689i	$0.0337048\pi$
$242$	−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
$249$	8.90626	−	27.8441i	0.564411	−	1.76455i
$250$	−0.684213			−0.0432734
$251$	−5.80617			−0.366482			−0.183241	−	0.983068i	$-0.558659\pi$
$251$	−5.80617			−0.366482			−0.183241	+	0.983068i	$0.558659\pi$
$252$	−7.98181	+	1.33928i	−0.502807	+	0.0843670i
$253$	−0.656662	−	0.656662i	−0.0412840	−	0.0412840i
$254$	−0.0169163	−	0.0169163i	−0.00106142	−	0.00106142i
$255$	−3.56189	+	11.1357i	−0.223054	+	0.697347i
$256$	−9.69045			−0.605653
$257$	8.29597			0.517488			0.258744	−	0.965946i	$-0.416691\pi$
$257$	8.29597			0.517488			0.258744	+	0.965946i	$0.416691\pi$
$258$	−13.2507	−	4.23839i	−0.824952	−	0.263870i
$259$		−	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
$267$	13.9911	+	4.47522i	0.856243	+	0.273879i
$268$	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	−0.807323	−	0.590110i	$-0.799084\pi$
$271$	−3.57577	+	3.57577i	−0.217213	+	0.217213i	0.590110	+	0.807323i	$0.299084\pi$
$272$	9.51951			0.577205
$273$	10.9754	+	0.708715i	0.664262	+	0.0428934i
$274$	−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	$-0.823924\pi$
$277$		−	17.4880i		−	1.05075i	0.850870	−	0.525377i	$-0.176076\pi$
$278$	8.07321	−	8.07321i	0.484199	−	0.484199i
$279$	16.9922	−	2.85115i	1.01730	−	0.170694i
$280$	−3.00934	+	3.00934i	−0.179842	+	0.179842i
$281$	−3.48513	−	3.48513i	−0.207906	−	0.207906i	0.595471	−	0.803377i	$-0.296965\pi$
$281$	−3.48513	−	3.48513i	−0.207906	−	0.207906i	−0.803377	+	0.595471i	$0.796965\pi$
$282$	8.92415	−	4.59871i	0.531426	−	0.273849i
$283$			9.47252i			0.563083i	0.959549	+	0.281541i	$0.0908457\pi$
$283$			9.47252i			0.563083i	−0.959549	+	0.281541i	$0.909154\pi$
$284$	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
$288$	2.87834	+	17.1542i	0.169608	+	1.01082i
$289$	28.5639			1.68023
$290$	−2.63675			−0.154835
$291$	2.41439	+	0.772272i	0.141534	+	0.0452714i
$292$	12.4287	+	12.4287i	0.727332	+	0.727332i
$293$	−15.2096	−	15.2096i	−0.888556	−	0.888556i	0.105828	−	0.994384i	$-0.466251\pi$
$293$	−15.2096	−	15.2096i	−0.888556	−	0.888556i	−0.994384	+	0.105828i	$0.966251\pi$
$294$	4.40035	+	1.40750i	0.256634	+	0.0820873i
$295$	−1.84599			−0.107477
$296$	−8.08986			−0.470214
$297$	2.27814	−	1.70350i	0.132191	−	0.0988470i
$298$			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
$306$	2.29280	+	13.6645i	0.131070	+	0.781148i
$307$	−8.64829	+	8.64829i	−0.493584	+	0.493584i	−0.909433	−	0.415850i	$-0.863484\pi$
$307$	−8.64829	+	8.64829i	−0.493584	+	0.493584i	0.415850	+	0.909433i	$0.363484\pi$
$308$		−	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	$-0.486312\pi$
$311$	1.51624			0.0859779			0.0429890	+	0.999076i	$0.486312\pi$
$312$	0.972464	−	15.0599i	0.0550550	−	0.852600i
$313$	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	$-0.542114\pi$
$317$	15.3001	−	15.3001i	0.859342	−	0.859342i	0.991261	+	0.131919i	$0.0421138\pi$
$318$	9.94853	+	3.18215i	0.557886	+	0.178446i
$319$	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
$327$	12.6321	+	4.04053i	0.698558	+	0.223442i
$328$	−19.5522			−1.07959
$329$	−14.9192			−0.822523
$330$	0.197653	−	0.617933i	0.0108804	−	0.0340161i
$331$	22.1751	+	22.1751i	1.21885	+	1.21885i	0.968034	+	0.250818i	$0.0806997\pi$
$331$	22.1751	+	22.1751i	1.21885	+	1.21885i	0.250818	+	0.968034i	$0.419300\pi$
$332$	18.2821	+	18.2821i	1.00336	+	1.00336i
$333$	1.66192	+	9.90465i	0.0910727	+	0.542771i
$334$	8.77333			0.480055
$335$	−6.60218			−0.360716
$336$	1.31059	−	4.09737i	0.0714986	−	0.223530i
$337$			1.11379i			0.0606718i	0.999540	+	0.0303359i	$0.00965769\pi$
$337$			1.11379i			0.0606718i	−0.999540	+	0.0303359i	$0.990342\pi$
$338$	−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
$345$	−0.895128	+	2.79849i	−0.0481921	+	0.150665i
$346$	−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	−0.455192	−	0.890393i	$-0.650430\pi$
$349$	8.13022	−	8.13022i	0.435201	−	0.435201i	0.890393	+	0.455192i	$0.150430\pi$
$350$	1.20499			0.0644094
$351$	−18.6381	+	1.90318i	−0.994827	+	0.101584i
$352$	−3.17410			−0.169180
$353$	−14.0281	+	14.0281i	−0.746638	+	0.746638i	−0.973846	−	0.227208i	$-0.927040\pi$
$353$	−14.0281	+	14.0281i	−0.746638	+	0.746638i	0.227208	+	0.973846i	$0.427040\pi$
$354$	−1.94465	+	1.00210i	−0.103357	+	0.0532610i
$355$		−	1.29531i		−	0.0687478i
$356$	−9.18642	+	9.18642i	−0.486879	+	0.486879i
$357$	6.27297	−	19.6115i	0.332001	−	1.03795i
$358$	6.42958	−	6.42958i	0.339814	−	0.339814i
$359$	−14.0085	−	14.0085i	−0.739341	−	0.739341i	0.233109	−	0.972451i	$-0.425110\pi$
$359$	−14.0085	−	14.0085i	−0.739341	−	0.739341i	−0.972451	+	0.233109i	$0.925110\pi$
$360$	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
$366$	−0.420050	+	1.31322i	−0.0219564	+	0.0686433i
$367$	−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
$369$	4.01667	+	23.9384i	0.209099	+	1.24618i
$370$	1.61966	+	1.61966i	0.0842020	+	0.0842020i
$371$	−10.9758	−	10.9758i	−0.569835	−	0.569835i
$372$	−4.64242	+	14.5138i	−0.240698	+	0.752508i
$373$	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
$375$	−1.64971	−	0.527680i	−0.0851908	−	0.0272493i
$376$			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	−0.941553	−	0.336864i	$-0.890634\pi$
$379$	−24.8881	−	24.8881i	−1.27842	−	1.27842i	−0.336864	−	0.941553i	$-0.609366\pi$
$380$			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	$-0.659493\pi$
$383$	7.76391	−	7.76391i	0.396717	−	0.396717i	0.877073	+	0.480356i	$0.159493\pi$
$384$	−17.8360	−	5.70504i	−0.910188	−	0.291134i
$385$	−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	$-0.448916\pi$
$389$	6.30333			0.319591			0.159796	+	0.987150i	$0.448916\pi$
$390$	−3.20982	+	2.82043i	−0.162536	+	0.142818i
$391$	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
$396$	0.416315	+	2.48114i	0.0209206	+	0.124682i
$397$	−24.3714	+	24.3714i	−1.22317	+	1.22317i	−0.256665	+	0.966500i	$0.582624\pi$
$397$	−24.3714	+	24.3714i	−1.22317	+	1.22317i	−0.966500	+	0.256665i	$0.917376\pi$
$398$	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	$-0.350818\pi$
$401$	−8.82040	−	8.82040i	−0.440470	−	0.440470i	−0.892170	+	0.451700i	$0.850818\pi$
$402$	−6.95506	+	3.58401i	−0.346887	+	0.178754i
$403$	10.6519	−	17.7578i	0.530609	−	0.884580i
$404$			27.9518i			1.39066i
$405$	−8.09259	−	3.93827i	−0.402124	−	0.195694i
$406$	4.64367			0.230461
$407$	−1.83269			−0.0908430
$408$	−26.9099	−	8.60746i	−1.33224	−	0.426133i
$409$	−10.2362	−	10.2362i	−0.506149	−	0.506149i	0.407193	−	0.913342i	$-0.366508\pi$
$409$	−10.2362	−	10.2362i	−0.506149	−	0.506149i	−0.913342	+	0.407193i	$0.866508\pi$
$410$	3.91452	+	3.91452i	0.193325	+	0.193325i
$411$	−6.03352	−	1.92989i	−0.297612	−	0.0951945i
$412$	−5.59872			−0.275829
$413$	3.25103			0.159973
$414$	0.576195	+	3.43398i	0.0283185	+	0.168771i
$415$		−	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	0.382190	−	0.924084i	$-0.375170\pi$
$421$	−11.1187	−	11.1187i	−0.541893	−	0.541893i	−0.924084	+	0.382190i	$0.875170\pi$
$422$	−4.37665	+	4.37665i	−0.213052	+	0.213052i
$423$	25.0637	−	4.20550i	1.21864	−	0.204478i
$424$	−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
$429$	0.220304	−	3.41170i	0.0106364	−	0.164718i
$430$	−8.03212			−0.387343
$431$	−5.22718	+	5.22718i	−0.251784	+	0.251784i	−0.821702	−	0.569917i	$-0.806975\pi$
$431$	−5.22718	+	5.22718i	−0.251784	+	0.251784i	0.569917	+	0.821702i	$0.306975\pi$
$432$	−1.04676	+	7.25286i	−0.0503623	+	0.348954i
$433$			2.96201i			0.142345i	0.997464	+	0.0711727i	$0.0226741\pi$
$433$			2.96201i			0.142345i	−0.997464	+	0.0711727i	$0.977326\pi$
$434$	−4.89357	+	4.89357i	−0.234899	+	0.234899i
$435$	−6.35750	−	2.03352i	−0.304819	−	0.0974997i
$436$	−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	$-0.829608\pi$
$439$		−	21.3756i		−	1.02020i	0.860114	−	0.510101i	$-0.170392\pi$
$440$	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	$-0.163487\pi$
$444$	−8.46004	−	2.70604i	−0.401496	−	0.128423i
$445$	8.48095			0.402035
$446$	11.8522			0.561220
$447$	−12.6412	+	39.5210i	−0.597910	+	1.86928i
$448$	−1.42777	−	1.42777i	−0.0674559	−	0.0674559i
$449$	−29.1294	−	29.1294i	−1.37470	−	1.37470i	−0.853328	−	0.521375i	$-0.825419\pi$
$449$	−29.1294	−	29.1294i	−1.37470	−	1.37470i	−0.521375	−	0.853328i	$-0.674581\pi$
$450$	−2.02434	+	0.339668i	−0.0954283	+	0.0160121i
$451$	−4.42939			−0.208572
$452$	−8.51778			−0.400643
$453$	−3.89002	+	12.1616i	−0.182769	+	0.571401i
$454$		−	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	0.643830	−	0.765168i	$-0.277344\pi$
$457$	−2.59392	−	2.59392i	−0.121338	−	0.121338i	−0.765168	+	0.643830i	$0.777344\pi$
$458$			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	$-0.546679\pi$
$461$	18.1031	−	18.1031i	0.843144	−	0.843144i	0.989266	+	0.146123i	$0.0466794\pi$
$462$	−0.348093	+	1.08826i	−0.0161948	+	0.0506306i
$463$	19.7500	−	19.7500i	0.917862	−	0.917862i	−0.0790114	−	0.996874i	$-0.525176\pi$
$463$	19.7500	−	19.7500i	0.917862	−	0.917862i	0.996874	+	0.0790114i	$0.0251764\pi$
$464$			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	$-0.477993\pi$
$467$	2.98569			0.138161			0.0690807	+	0.997611i	$0.477993\pi$
$468$	6.05448	−	15.4238i	0.279868	−	0.712963i
$469$	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
$474$	−1.39150	+	4.35031i	−0.0639136	+	0.199816i
$475$	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	$-0.202396\pi$
$479$	4.61160	+	4.61160i	0.210710	+	0.210710i	−0.593859	+	0.804569i	$0.702396\pi$
$480$	4.60013	+	8.92690i	0.209966	+	0.407455i
$481$	10.3509	+	6.20893i	0.471962	+	0.283103i
$482$		−	13.3498i		−	0.608067i
$483$	1.57644	−	4.92851i	0.0717305	−	0.224255i
$484$	16.3913			0.745058
$485$	1.46352			0.0664552
$486$	−10.6630	+	0.244328i	−0.483685	+	0.0110829i
$487$	22.7100	+	22.7100i	1.02909	+	1.02909i	0.999564	+	0.0295239i	$0.00939911\pi$
$487$	22.7100	+	22.7100i	1.02909	+	1.02909i	0.0295239	+	0.999564i	$0.490601\pi$
$488$	−1.98801	−	1.98801i	−0.0899928	−	0.0899928i
$489$	2.86112	−	8.94488i	0.129384	−	0.404501i
$490$	2.66734			0.120498
$491$	−32.8134			−1.48085			−0.740423	−	0.672141i	$-0.765375\pi$
$491$	−32.8134			−1.48085			−0.740423	+	0.672141i	$0.765375\pi$
$492$	−20.4469	−	6.54019i	−0.921819	−	0.294854i
$493$			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	0.715084	−	0.699039i	$-0.246389\pi$
$499$	0.358414	+	0.358414i	0.0160448	+	0.0160448i	−0.699039	+	0.715084i	$0.746389\pi$
$500$	1.08318	−	1.08318i	0.0484414	−	0.0484414i
$501$	21.1535	+	6.76618i	0.945067	+	0.302291i
$502$	−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
$507$	−12.8027	+	18.5227i	−0.568587	+	0.822623i
$508$	0.0535606			0.00237637
$509$	16.5736	−	16.5736i	0.734613	−	0.734613i	−0.236917	−	0.971530i	$-0.576137\pi$
$509$	16.5736	−	16.5736i	0.734613	−	0.734613i	0.971530	+	0.236917i	$0.0761368\pi$
$510$	3.66431	+	7.11088i	0.162258	+	0.314875i
$511$			20.2076i			0.893931i
$512$	10.6015	−	10.6015i	0.468524	−	0.468524i
$513$	7.84510	−	5.86623i	0.346369	−	0.259000i
$514$	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	$-0.181098\pi$
$522$	−7.80120	+	1.30898i	−0.341449	+	0.0572924i
$523$	−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
$525$	2.90536	+	0.929314i	0.126801	+	0.0405586i
$526$	5.25989	+	5.25989i	0.229342	+	0.229342i
$527$	−27.4127	−	27.4127i	−1.19412	−	1.19412i
$528$	−1.27366	−	0.407396i	−0.0554291	−	0.0177296i
$529$	−20.1224			−0.874887
$530$	6.03046			0.261946
$531$	−5.46161	+	0.916415i	−0.237014	+	0.0397690i
$532$		−	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
$540$	6.37465	−	4.76669i	0.274321	−	0.205126i
$541$	−1.35568	+	1.35568i	−0.0582854	+	0.0582854i	−0.735649	−	0.677363i	$-0.763123\pi$
$541$	−1.35568	+	1.35568i	−0.0582854	+	0.0582854i	0.677363	+	0.735649i	$0.263123\pi$
$542$			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
$546$	5.65292	−	4.96715i	0.241923	−	0.212574i
$547$	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
$552$	−6.76266	−	2.16311i	−0.287838	−	0.0920682i
$553$	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	$-0.160211\pi$
$557$	9.29058	+	9.29058i	0.393655	+	0.393655i	−0.482333	+	0.875988i	$0.660211\pi$
$558$	6.84160	−	9.60044i	0.289628	−	0.406419i
$559$	−41.0614	+	10.2704i	−1.73671	+	0.434390i
$560$		−	2.48368i		−	0.104955i
$561$	−6.09622	−	1.94995i	−0.257383	−	0.0823268i
$562$	−3.37230			−0.142252
$563$	43.3391			1.82653			0.913263	−	0.407370i	$-0.133554\pi$
$563$	43.3391			1.82653			0.913263	+	0.407370i	$0.133554\pi$
$564$	−6.84764	+	21.4081i	−0.288338	+	0.901446i
$565$	3.93183	+	3.93183i	0.165413	+	0.165413i
$566$	4.58292	+	4.58292i	0.192634	+	0.192634i
$567$	14.2521	+	6.93581i	0.598533	+	0.291277i
$568$	3.13016			0.131339
$569$	−7.47436			−0.313342			−0.156671	−	0.987651i	$-0.550076\pi$
$569$	−7.47436			−0.313342			−0.156671	+	0.987651i	$0.550076\pi$
$570$	0.680646	−	2.12794i	0.0285091	−	0.0891295i
$571$			20.1324i			0.842516i	0.906941	+	0.421258i	$0.138411\pi$
$571$			20.1324i			0.842516i	−0.906941	+	0.421258i	$0.861589\pi$
$572$	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	0.918688	−	0.394983i	$-0.129250\pi$
$577$	12.5798	+	12.5798i	0.523705	+	0.523705i	−0.394983	+	0.918688i	$0.629250\pi$
$578$	13.8195	−	13.8195i	0.574817	−	0.574817i
$579$	−12.0244	+	37.5925i	−0.499716	+	1.56229i
$580$	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
$585$	−9.91440	+	4.32488i	−0.409910	+	0.178812i
$586$	−14.7172			−0.607962
$587$	0.511868	−	0.511868i	0.0211270	−	0.0211270i	−0.696464	−	0.717591i	$-0.745245\pi$
$587$	0.511868	−	0.511868i	0.0211270	−	0.0211270i	0.717591	+	0.696464i	$0.245245\pi$
$588$	−9.19446	+	4.73800i	−0.379173	+	0.195392i
$589$			10.8272i			0.446127i
$590$	−0.893110	+	0.893110i	−0.0367688	+	0.0367688i
$591$	−8.45397	+	26.4301i	−0.347750	+	1.08719i
$592$	3.33838	−	3.33838i	0.137207	−	0.137207i
$593$	−13.2208	−	13.2208i	−0.542911	−	0.542911i	0.381470	−	0.924381i	$-0.375418\pi$
$593$	−13.2208	−	13.2208i	−0.542911	−	0.542911i	−0.924381	+	0.381470i	$0.875418\pi$
$594$	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	$-0.233282\pi$
$600$	1.27516	−	3.98660i	0.0520582	−	0.162752i
$601$	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
$603$	−19.5335	+	3.27756i	−0.795465	+	0.133473i
$604$	−7.98515	−	7.98515i	−0.324911	−	0.324911i
$605$	−7.56626	−	7.56626i	−0.307612	−	0.307612i
$606$	6.58803	−	20.5965i	0.267620	−	0.836675i
$607$	−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
$609$	11.1964	+	3.58130i	0.453701	+	0.145121i
$610$			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	0.996224	−	0.0868247i	$-0.0276720\pi$
$613$	22.5157	+	22.5157i	0.909399	+	0.909399i	−0.0868247	+	0.996224i	$0.527672\pi$
$614$			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	$-0.779051\pi$
$617$	−3.20157	+	3.20157i	−0.128891	+	0.128891i	0.639719	+	0.768609i	$0.279051\pi$
$618$	4.12545	+	1.31957i	0.165950	+	0.0530811i
$619$	6.99088	−	6.99088i	0.280987	−	0.280987i	−0.552515	−	0.833503i	$-0.686332\pi$
$619$	6.99088	−	6.99088i	0.280987	−	0.280987i	0.833503	+	0.552515i	$0.186332\pi$
$620$			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
$624$	5.81337	+	6.61597i	0.232721	+	0.264851i
$625$	−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
$630$	3.56513	−	0.598201i	0.142038	−	0.0238329i
$631$	19.6866	−	19.6866i	0.783711	−	0.783711i	−0.196744	−	0.980455i	$-0.563037\pi$
$631$	19.6866	−	19.6866i	0.783711	−	0.783711i	0.980455	+	0.196744i	$0.0630369\pi$
$632$	−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
$639$	−0.643038	−	3.83235i	−0.0254382	−	0.151605i
$640$	−10.8116			−0.427364
$641$	7.99599			0.315822			0.157911	−	0.987453i	$-0.449524\pi$
$641$	7.99599			0.315822			0.157911	+	0.987453i	$0.449524\pi$
$642$	−16.8848	−	5.40080i	−0.666390	−	0.213153i
$643$	−15.0350	−	15.0350i	−0.592922	−	0.592922i	0.345498	−	0.938420i	$-0.387710\pi$
$643$	−15.0350	−	15.0350i	−0.592922	−	0.592922i	−0.938420	+	0.345498i	$0.887710\pi$
$644$	3.23600	+	3.23600i	0.127516	+	0.127516i
$645$	−19.3663	−	6.19454i	−0.762548	−	0.243910i
$646$	−8.70685			−0.342566
$647$	5.28617			0.207821			0.103910	−	0.994587i	$-0.466864\pi$
$647$	5.28617			0.207821			0.103910	+	0.994587i	$0.466864\pi$
$648$	9.51698	−	19.5561i	0.373862	−	0.768235i
$649$		−	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
$657$	−5.69621	−	33.9480i	−0.222230	−	1.32444i
$658$	−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	−0.979475	−	0.201567i	$-0.935397\pi$
$661$	−19.9999	+	19.9999i	−0.777907	+	0.777907i	0.201567	+	0.979475i	$0.435397\pi$
$662$	21.4571			0.833955
$663$	27.8249	+	31.6665i	1.08063	+	1.22982i
$664$	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
$669$	28.5771	+	9.14070i	1.10485	+	0.353400i
$670$	−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	$-0.998584\pi$
$673$		−	0.230805i		−	0.00889689i	0.999990	−	0.00444844i	$-0.00141599\pi$
$674$	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	$0.706289\pi$
$678$	6.27638	+	2.00757i	0.241043	+	0.0771004i
$679$	−2.57746			−0.0989138
$680$	−16.3119			−0.625532
$681$	7.84109	−	24.5140i	0.300471	−	0.939379i
$682$	1.52116	+	1.52116i	0.0582483	+	0.0582483i
$683$	31.7789	+	31.7789i	1.21599	+	1.21599i	0.969026	+	0.246960i	$0.0794317\pi$
$683$	31.7789	+	31.7789i	1.21599	+	1.21599i	0.246960	+	0.969026i	$0.420568\pi$
$684$	1.43364	+	8.54414i	0.0548165	+	0.326693i
$685$	−3.65731			−0.139739
$686$	−13.1325			−0.501400
$687$	−3.31767	+	10.3722i	−0.126577	+	0.395724i
$688$			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	0.998913	−	0.0466196i	$-0.0148449\pi$
$691$	25.0328	+	25.0328i	0.952293	+	0.952293i	−0.0466196	+	0.998913i	$0.514845\pi$
$692$		−	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
$696$	4.91408	−	15.3631i	0.186268	−	0.582338i
$697$	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	$-0.673280\pi$
$701$	−27.4234			−1.03577			−0.517883	+	0.855451i	$0.673280\pi$
$702$	−8.09654	+	9.93810i	−0.305584	+	0.375090i
$703$	−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
$708$	1.49216	−	4.66502i	0.0560789	−	0.175322i
$709$	−0.997734	+	0.997734i	−0.0374707	+	0.0374707i	−0.725594	−	0.688123i	$-0.758435\pi$
$709$	−0.997734	+	0.997734i	−0.0374707	+	0.0374707i	0.688123	+	0.725594i	$0.258435\pi$
$710$	−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
$717$	3.51336	−	10.9840i	0.131209	−	0.410205i
$718$	−13.5550			−0.505867
$719$	−13.8518			−0.516585			−0.258292	−	0.966067i	$-0.583160\pi$
$719$	−13.8518			−0.516585			−0.258292	+	0.966067i	$0.583160\pi$
$720$	0.700112	+	4.17250i	0.0260916	+	0.155500i
$721$	−4.55144	−	4.55144i	−0.169505	−	0.169505i
$722$	−7.47295	−	7.47295i	−0.278115	−	0.278115i
$723$	10.2957	−	32.1879i	0.382900	−	1.19708i
$724$	35.7124			1.32724
$725$	−3.85370			−0.143123
$726$	−12.0780	−	3.86330i	−0.448258	−	0.143380i
$727$		−	36.0915i		−	1.33856i	−0.743010	−	0.669280i	$-0.766603\pi$
$727$		−	36.0915i		−	1.33856i	0.743010	−	0.669280i	$-0.233397\pi$
$728$	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	0.905849	−	0.423601i	$-0.139234\pi$
$733$	13.0564	+	13.0564i	0.482248	+	0.482248i	−0.423601	+	0.905849i	$0.639234\pi$
$734$	−12.6895	+	12.6895i	−0.468378	+	0.468378i
$735$	6.43126	+	2.05711i	0.237221	+	0.0758777i
$736$	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	−0.429483	−	0.903075i	$-0.641304\pi$
$739$	12.8744	−	12.8744i	0.473592	−	0.473592i	0.903075	+	0.429483i	$0.141304\pi$
$740$	−5.12819			−0.188516
$741$	0.758645	−	11.7486i	0.0278695	−	0.431597i
$742$	−10.6204			−0.389889
$743$	−20.7742	+	20.7742i	−0.762133	+	0.762133i	−0.976708	−	0.214575i	$-0.931163\pi$
$743$	−20.7742	+	20.7742i	−0.762133	+	0.762133i	0.214575	+	0.976708i	$0.431163\pi$
$744$	11.0114	+	21.3685i	0.403697	+	0.783405i
$745$			23.9563i			0.877689i
$746$	3.30783	−	3.30783i	0.121108	−	0.121108i
$747$	−8.37893	−	49.9364i	−0.306569	−	1.82708i
$748$	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	$0.0832413\pi$
$751$			14.1702i			0.517080i	−0.966001	+	0.258540i	$0.916759\pi$
$752$	−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
$756$	−11.2266	+	8.39477i	−0.408308	+	0.305315i
$757$	−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
$759$	−1.53202	−	0.490035i	−0.0556089	−	0.0177871i
$760$	3.22135	+	3.22135i	0.116851	+	0.116851i
$761$	−3.88054	−	3.88054i	−0.140669	−	0.140669i	0.633265	−	0.773935i	$-0.281714\pi$
$761$	−3.88054	−	3.88054i	−0.140669	−	0.140669i	−0.773935	+	0.633265i	$0.781714\pi$
$762$	−0.0394665	−	0.0126238i	−0.00142972	−	0.000457313i
$763$	−13.4853			−0.488200
$764$	9.81584			0.355125
$765$	3.35100	+	19.9711i	0.121156	+	0.722057i
$766$		−	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	0.170813	−	0.985304i	$-0.445361\pi$
$769$	−22.5865	−	22.5865i	−0.814491	−	0.814491i	−0.985304	+	0.170813i	$0.945361\pi$
$770$			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	$-0.977274\pi$
$773$	−25.7487	+	25.7487i	−0.926116	+	0.926116i	0.0713367	+	0.997452i	$0.477274\pi$
$774$	−23.7642	+	3.98744i	−0.854185	+	0.143325i
$775$	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
$780$	0.616448	−	9.54653i	0.0220724	−	0.341821i
$781$	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
$786$	1.26364	+	0.404190i	0.0450726	+	0.0144170i
$787$	−19.7231	+	19.7231i	−0.703054	+	0.703054i	−0.965065	−	0.262011i	$-0.915614\pi$
$787$	−19.7231	+	19.7231i	−0.703054	+	0.703054i	0.262011	+	0.965065i	$0.415614\pi$
$788$	−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
$795$	14.5401	+	4.65082i	0.515684	+	0.164948i
$796$	−35.3573			−1.25321
$797$	27.0871			0.959474			0.479737	−	0.877412i	$-0.340732\pi$
$797$	27.0871			0.959474			0.479737	+	0.877412i	$0.340732\pi$
$798$	−1.19871	+	3.74758i	−0.0424338	+	0.132663i
$799$	−40.4342	−	40.4342i	−1.43046	−	1.43046i
$800$	4.09981	+	4.09981i	0.144950	+	0.144950i
$801$	25.0921	−	4.21025i	0.886585	−	0.148762i
$802$	−8.53483			−0.301375
$803$	6.28151			0.221670
$804$	5.33672	−	16.6845i	0.188212	−	0.588416i
$805$		−	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	−0.925758	−	0.378116i	$-0.876572\pi$
$811$	−37.1318	−	37.1318i	−1.30387	−	1.30387i	−0.378116	−	0.925758i	$-0.623428\pi$
$812$	−7.35143	+	7.35143i	−0.257985	+	0.257985i
$813$	−2.66843	+	8.34244i	−0.0935858	+	0.292582i
$814$	−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
$819$	17.4606	−	7.61669i	0.610122	−	0.266149i
$820$	−12.3942			−0.432825
$821$	−10.6744	+	10.6744i	−0.372540	+	0.372540i	−0.868402	−	0.495861i	$-0.834852\pi$
$821$	−10.6744	+	10.6744i	−0.372540	+	0.372540i	0.495861	+	0.868402i	$0.334852\pi$
$822$	−3.85279	+	1.98538i	−0.134382	+	0.0692482i
$823$			22.6990i			0.791236i	0.918415	+	0.395618i	$0.129470\pi$
$823$			22.6990i			0.791236i	−0.918415	+	0.395618i	$0.870530\pi$
$824$	−6.24527	+	6.24527i	−0.217564	+	0.217564i
$825$	0.288877	−	0.903130i	0.0100574	−	0.0314429i
$826$	1.57289	−	1.57289i	0.0547277	−	0.0547277i
$827$	13.2802	+	13.2802i	0.461799	+	0.461799i	0.899245	−	0.437446i	$-0.144117\pi$
$827$	13.2802	+	13.2802i	0.461799	+	0.461799i	−0.437446	+	0.899245i	$0.644117\pi$
$828$	−6.34855	−	4.52419i	−0.220627	−	0.157226i
$829$			11.0522i			0.383858i	0.981409	+	0.191929i	$0.0614743\pi$
$829$			11.0522i			0.383858i	−0.981409	+	0.191929i	$0.938526\pi$
$830$	−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
$834$	6.02465	−	18.8352i	0.208617	−	0.652209i
$835$	12.8225			0.443741
$836$	−1.58095			−0.0546783
$837$	23.8999	−	17.8713i	0.826102	−	0.617724i
$838$	19.2672	+	19.2672i	0.665575	+	0.665575i
$839$	−2.03658	−	2.03658i	−0.0703107	−	0.0703107i	0.671077	−	0.741388i	$-0.265832\pi$
$839$	−2.03658	−	2.03658i	−0.0703107	−	0.0703107i	−0.741388	+	0.671077i	$0.765832\pi$
$840$	−2.24573	+	7.02093i	−0.0774849	+	0.242245i
$841$	14.1490			0.487897
$842$	−10.7587			−0.370771
$843$	−8.13098	−	2.60079i	−0.280046	−	0.0895759i
$844$		−	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
$852$	3.27340	+	1.04703i	0.112145	+	0.0358708i
$853$	−26.1501	+	26.1501i	−0.895364	+	0.895364i	−0.995022	−	0.0996578i	$-0.968225\pi$
$853$	−26.1501	+	26.1501i	−0.895364	+	0.895364i	0.0996578	+	0.995022i	$0.468225\pi$
$854$		−	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	$-0.621783\pi$
$857$	−21.8580			−0.746653			−0.373327	+	0.927700i	$0.621783\pi$
$858$	−1.54403	−	1.75720i	−0.0527124	−	0.0599900i
$859$	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	$-0.878214\pi$
$863$	−16.2854	+	16.2854i	−0.554363	+	0.554363i	0.373334	+	0.927697i	$0.378214\pi$
$864$	18.0418	+	24.1278i	0.613793	+	0.820845i
$865$	−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
$873$	4.33004	−	0.726546i	0.146550	−	0.0245899i
$874$	−2.18809			−0.0740133
$875$	1.76113			0.0595372
$876$	28.9966	+	9.27491i	0.979705	+	0.313370i
$877$	−9.53726	−	9.53726i	−0.322050	−	0.322050i	0.527503	−	0.849553i	$-0.323128\pi$
$877$	−9.53726	−	9.53726i	−0.322050	−	0.322050i	−0.849553	+	0.527503i	$0.823128\pi$
$878$	−10.3418	−	10.3418i	−0.349018	−	0.349018i
$879$	−35.4848	−	11.3502i	−1.19687	−	0.382833i
$880$	−0.772051			−0.0260258
$881$	45.3231			1.52697			0.763487	−	0.645823i	$-0.223486\pi$
$881$	45.3231			1.52697			0.763487	+	0.645823i	$0.223486\pi$
$882$	7.89171	−	1.32417i	0.265728	−	0.0445870i
$883$			39.8456i			1.34091i	0.741949	+	0.670456i	$0.233902\pi$
$883$			39.8456i			1.34091i	−0.741949	+	0.670456i	$0.766098\pi$
$884$	−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
$891$	2.15599	−	4.43026i	0.0722284	−	0.148419i
$892$	−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
$897$	6.99260	+	7.95800i	0.233476	+	0.265710i
$898$	−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
$903$	34.1067	+	10.9094i	1.13500	+	0.363043i
$904$	−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	$0.119345\pi$
$907$			22.0580i			0.732422i	−0.930532	+	0.366211i	$0.880655\pi$
$908$	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	$0.947202\pi$
$912$	−4.38603	−	1.40292i	−0.145236	−	0.0464554i
$913$	9.23989			0.305796
$914$	−2.50993			−0.0830212
$915$	−0.613917	+	1.91932i	−0.0202955	+	0.0634507i
$916$	−6.81027	−	6.81027i	−0.225018	−	0.225018i
$917$	−1.39412	−	1.39412i	−0.0460380	−	0.0460380i
$918$	14.3715	+	19.2194i	0.474330	+	0.634336i
$919$	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
$921$	−6.45380	+	20.1769i	−0.212660	+	0.664850i
$922$		−	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	$-0.651712\pi$
$929$	13.0994	−	13.0994i	0.429776	−	0.429776i	0.888552	+	0.458776i	$0.151712\pi$
$930$	2.07357	−	6.48272i	0.0679951	−	0.212577i
$931$	−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
$936$	−10.4512	−	23.9586i	−0.341610	−	0.783110i
$937$	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	$-0.642631\pi$
$941$	14.3573	−	14.3573i	0.468035	−	0.468035i	0.901277	+	0.433242i	$0.142631\pi$
$942$	−4.70492	+	14.7092i	−0.153294	+	0.479253i
$943$	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	$-0.246449\pi$
$947$	0.485543	+	0.485543i	0.0157780	+	0.0157780i	−0.699174	+	0.714952i	$0.746449\pi$
$948$	−4.68412	−	9.08990i	−0.152133	−	0.295226i
$949$	−35.4776	−	21.2810i	−1.15165	−	0.690811i
$950$		−	1.28988i		−	0.0418494i
$951$	11.4178	−	35.6960i	0.370246	−	1.15752i
$952$	28.7274			0.931061
$953$	−29.1833			−0.945339			−0.472670	−	0.881240i	$-0.656710\pi$
$953$	−29.1833			−0.945339			−0.472670	+	0.881240i	$0.656710\pi$
$954$	17.8420	−	2.99374i	0.577655	−	0.0969259i
$955$	−4.53102	−	4.53102i	−0.146620	−	0.146620i
$956$	7.21196	+	7.21196i	0.233252	+	0.233252i
$957$	1.11324	−	3.48039i	0.0359860	−	0.112505i
$958$	4.46230			0.144170
$959$	6.44102			0.207991
$960$	1.89143	+	0.604996i	0.0610457	+	0.0195262i
$961$			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	0.904913	−	0.425597i	$-0.139936\pi$
$967$	14.9051	+	14.9051i	0.479316	+	0.479316i	−0.425597	+	0.904913i	$0.639936\pi$
$968$	18.2842	−	18.2842i	0.587675	−	0.587675i
$969$	−20.9932	−	6.71491i	−0.674398	−	0.215714i
$970$	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
$975$	−4.69126	+	4.12215i	−0.150240	+	0.132014i
$976$	1.64075			0.0525192
$977$	−11.8734	+	11.8734i	−0.379864	+	0.379864i	−0.871053	−	0.491189i	$-0.836562\pi$
$977$	−11.8734	+	11.8734i	−0.379864	+	0.379864i	0.491189	+	0.871053i	$0.336562\pi$
$978$	−2.94339	−	5.71188i	−0.0941193	−	0.182646i
$979$			4.64287i			0.148387i
$980$	−4.22269	+	4.22269i	−0.134889	+	0.134889i
$981$	22.6548	−	3.80129i	0.723312	−	0.121366i
$982$	−15.8755	+	15.8755i	−0.506607	+	0.506607i
$983$	−8.05185	−	8.05185i	−0.256814	−	0.256814i	0.566943	−	0.823757i	$-0.308126\pi$
$983$	−8.05185	−	8.05185i	−0.256814	−	0.256814i	−0.823757	+	0.566943i	$0.808126\pi$
$984$	−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
$990$	−0.185950	−	1.10822i	−0.00590989	−	0.0352215i
$991$	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
$993$	51.7355	+	16.5482i	1.64178	+	0.525141i
$994$	1.10368	+	1.10368i	0.0350065	+	0.0350065i
$995$	16.3210	+	16.3210i	0.517411	+	0.517411i
$996$	42.6531	+	13.6431i	1.35151	+	0.432297i
$997$	−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
$999$	10.4171	+	13.9311i	0.329582	+	0.440761i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	195.2.o.a.86.13	yes	40
3.2	odd	2	inner	195.2.o.a.86.8	✓	40
5.2	odd	4		975.2.n.q.749.13		40
5.3	odd	4		975.2.n.r.749.8		40
5.4	even	2		975.2.o.p.476.8		40
13.5	odd	4	inner	195.2.o.a.161.8	yes	40
15.2	even	4		975.2.n.q.749.8		40
15.8	even	4		975.2.n.r.749.13		40
15.14	odd	2		975.2.o.p.476.13		40
39.5	even	4	inner	195.2.o.a.161.13	yes	40
65.18	even	4		975.2.n.q.824.8		40
65.44	odd	4		975.2.o.p.551.13		40
65.57	even	4		975.2.n.r.824.13		40
195.44	even	4		975.2.o.p.551.8		40
195.83	odd	4		975.2.n.q.824.13		40
195.122	odd	4		975.2.n.r.824.8		40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
195.2.o.a.86.8	✓	40	3.2	odd	2	inner
195.2.o.a.86.13	yes	40	1.1	even	1	trivial
195.2.o.a.161.8	yes	40	13.5	odd	4	inner
195.2.o.a.161.13	yes	40	39.5	even	4	inner
975.2.n.q.749.8		40	15.2	even	4
975.2.n.q.749.13		40	5.2	odd	4
975.2.n.q.824.8		40	65.18	even	4
975.2.n.q.824.13		40	195.83	odd	4
975.2.n.r.749.8		40	5.3	odd	4
975.2.n.r.749.13		40	15.8	even	4
975.2.n.r.824.8		40	195.122	odd	4
975.2.n.r.824.13		40	65.57	even	4
975.2.o.p.476.8		40	5.4	even	2
975.2.o.p.476.13		40	15.14	odd	2
975.2.o.p.551.8		40	195.44	even	4
975.2.o.p.551.13		40	65.44	odd	4

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)

\(f(q)\)	\(=\)	\(q+(0.483812 - 0.483812i) q^{2} +(1.53965 - 0.793397i) q^{3} +1.53185i q^{4} +(0.707107 - 0.707107i) q^{5} +(0.361045 - 1.12876i) q^{6} +(-1.24531 + 1.24531i) q^{7} +(1.70875 + 1.70875i) q^{8} +(1.74104 - 2.44311i) q^{9} +O(q^{10})\)	\(q+(0.483812 - 0.483812i) q^{2} +(1.53965 - 0.793397i) q^{3} +1.53185i q^{4} +(0.707107 - 0.707107i) q^{5} +(0.361045 - 1.12876i) 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} +(0.527680 - 1.64971i) q^{15} -1.41028 q^{16} -6.75010 q^{17} +(-0.339668 - 2.02434i) q^{18} +(1.33304 + 1.33304i) q^{19} +(1.08318 + 1.08318i) q^{20} +(-0.929314 + 2.90536i) q^{21} +0.374570 q^{22} -1.69635 q^{23} +(3.98660 + 1.27516i) 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} +(0.903130 + 0.288877i) 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} +(-4.12215 - 4.69126i) 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} +(-0.496436 - 2.95864i) 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} +(-2.12908 - 2.84728i) q^{54} +0.547447 q^{55} -4.25585 q^{56} +(3.11005 + 0.994786i) q^{57} +(-1.86446 - 1.86446i) q^{58} +(-1.30531 - 1.30531i) q^{59} +(2.52712 + 0.808328i) q^{60} -1.16343 q^{61} +3.92960 q^{62} +(0.874290 + 5.21056i) 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} +(7.14967 - 1.19966i) 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} +(-4.26403 - 0.275341i) 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} +(-4.45059 - 1.42357i) 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} +(9.47471 + 3.03059i) q^{93} +5.79622 q^{94} +1.88521 q^{95} +(-3.05949 + 9.56505i) q^{96} +(1.03487 + 1.03487i) q^{97} +(1.88610 + 1.88610i) q^{98} +(1.61970 - 0.271772i) 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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