LMFDB - Embedded newform 195.2.ba.a.94.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [195,2,Mod(94,195)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(195, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 2]))

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

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

chi := DirichletCharacter("195.94");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 195 = 3 \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	195.ba (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$1.55708283941$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			94.6
Character	$\chi$	$=$	195.94
Dual form			195.2.ba.a.139.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.521384 + 0.301021i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(-0.818772 + 1.41816i) q^{4} +(0.446511 + 2.19103i) q^{5} +(0.301021 - 0.521384i) q^{6} +(-3.08191 - 1.77934i) q^{7} -2.18996i q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(-0.521384 + 0.301021i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(-0.818772 + 1.41816i) q^{4} +(0.446511 + 2.19103i) q^{5} +(0.301021 - 0.521384i) q^{6} +(-3.08191 - 1.77934i) q^{7} -2.18996i q^{8} +(0.500000 - 0.866025i) q^{9} +(-0.892352 - 1.00796i) q^{10} +(-1.30769 - 2.26499i) q^{11} -1.63754i q^{12} +(-2.88598 + 2.16128i) q^{13} +2.14248 q^{14} +(-1.48221 - 1.67424i) q^{15} +(-0.978320 - 1.69450i) q^{16} +(1.94566 + 1.12333i) q^{17} +0.602043i q^{18} +(-4.00873 + 6.94332i) q^{19} +(-3.47282 - 1.16074i) q^{20} +3.55868 q^{21} +(1.36362 + 0.787287i) q^{22} +(1.43095 - 0.826160i) q^{23} +(1.09498 + 1.89656i) q^{24} +(-4.60126 + 1.95664i) q^{25} +(0.854110 - 1.99560i) q^{26} +1.00000i q^{27} +(5.04676 - 2.91375i) q^{28} +(2.26120 + 3.91651i) q^{29} +(1.27678 + 0.426744i) q^{30} -4.05655 q^{31} +(4.81328 + 2.77895i) q^{32} +(2.26499 + 1.30769i) q^{33} -1.35258 q^{34} +(2.52249 - 7.54706i) q^{35} +(0.818772 + 1.41816i) q^{36} +(3.64724 - 2.10574i) q^{37} -4.82685i q^{38} +(1.41869 - 3.31471i) q^{39} +(4.79827 - 0.977840i) q^{40} +(0.388612 + 0.673096i) q^{41} +(-1.85544 + 1.07124i) q^{42} +(0.197117 + 0.113806i) q^{43} +4.28281 q^{44} +(2.12075 + 0.708827i) q^{45} +(-0.497384 + 0.861494i) q^{46} +3.14738i q^{47} +(1.69450 + 0.978320i) q^{48} +(2.83211 + 4.90536i) q^{49} +(1.81003 - 2.40524i) q^{50} -2.24666 q^{51} +(-0.702078 - 5.86236i) q^{52} +6.42424i q^{53} +(-0.301021 - 0.521384i) q^{54} +(4.37877 - 3.87654i) q^{55} +(-3.89668 + 6.74925i) q^{56} -8.01746i q^{57} +(-2.35791 - 1.36134i) q^{58} +(-6.26747 + 10.8556i) q^{59} +(3.58791 - 0.731181i) q^{60} +(-1.46568 + 2.53863i) q^{61} +(2.11502 - 1.22111i) q^{62} +(-3.08191 + 1.77934i) q^{63} +0.567189 q^{64} +(-6.02406 - 5.35823i) q^{65} -1.57457 q^{66} +(-0.969664 + 0.559836i) q^{67} +(-3.18611 + 1.83950i) q^{68} +(-0.826160 + 1.43095i) q^{69} +(0.956640 + 4.69425i) q^{70} +(5.66772 - 9.81678i) q^{71} +(-1.89656 - 1.09498i) q^{72} +12.4350i q^{73} +(-1.26774 + 2.19579i) q^{74} +(3.00648 - 3.99513i) q^{75} +(-6.56447 - 11.3700i) q^{76} +9.30732i q^{77} +(0.258119 + 2.15530i) q^{78} +14.8640 q^{79} +(3.27588 - 2.90015i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-0.405233 - 0.233961i) q^{82} -11.7337i q^{83} +(-2.91375 + 5.04676i) q^{84} +(-1.59249 + 4.76459i) q^{85} -0.137032 q^{86} +(-3.91651 - 2.26120i) q^{87} +(-4.96023 + 2.86379i) q^{88} +(-8.60439 - 14.9032i) q^{89} +(-1.31910 + 0.268819i) q^{90} +(12.7400 - 1.52574i) q^{91} +2.70575i q^{92} +(3.51307 - 2.02827i) q^{93} +(-0.947430 - 1.64100i) q^{94} +(-17.0030 - 5.68299i) q^{95} -5.55790 q^{96} +(-10.6088 - 6.12499i) q^{97} +(-2.95324 - 1.70505i) q^{98} -2.61538 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 8 q^{4} + 4 q^{5} + 12 q^{9}+O(q^{10}) $ 24 * q + 8 * q^4 + 4 * q^5 + 12 * q^9	$ 24 q + 8 q^{4} + 4 q^{5} + 12 q^{9} - 4 q^{10} + 4 q^{11} + 24 q^{14} - 2 q^{15} + 16 q^{16} - 16 q^{19} - 16 q^{20} - 8 q^{21} - 16 q^{25} - 48 q^{26} - 12 q^{29} - 4 q^{30} + 8 q^{31} - 32 q^{34} + 10 q^{35} - 8 q^{36} + 8 q^{39} - 48 q^{40} - 40 q^{41} + 40 q^{44} + 2 q^{45} - 24 q^{46} - 16 q^{49} + 20 q^{50} - 24 q^{51} + 20 q^{55} - 24 q^{56} + 12 q^{59} + 48 q^{60} + 20 q^{61} + 48 q^{64} + 14 q^{65} - 56 q^{66} - 8 q^{69} - 56 q^{70} + 4 q^{71} - 12 q^{74} + 16 q^{75} + 8 q^{76} + 136 q^{79} - 4 q^{80} - 12 q^{81} - 16 q^{84} - 4 q^{85} + 48 q^{86} - 64 q^{89} - 8 q^{90} + 60 q^{91} - 48 q^{94} - 28 q^{95} + 40 q^{96} + 8 q^{99}+O(q^{100}) $ 24 * q + 8 * q^4 + 4 * q^5 + 12 * q^9 - 4 * q^10 + 4 * q^11 + 24 * q^14 - 2 * q^15 + 16 * q^16 - 16 * q^19 - 16 * q^20 - 8 * q^21 - 16 * q^25 - 48 * q^26 - 12 * q^29 - 4 * q^30 + 8 * q^31 - 32 * q^34 + 10 * q^35 - 8 * q^36 + 8 * q^39 - 48 * q^40 - 40 * q^41 + 40 * q^44 + 2 * q^45 - 24 * q^46 - 16 * q^49 + 20 * q^50 - 24 * q^51 + 20 * q^55 - 24 * q^56 + 12 * q^59 + 48 * q^60 + 20 * q^61 + 48 * q^64 + 14 * q^65 - 56 * q^66 - 8 * q^69 - 56 * q^70 + 4 * q^71 - 12 * q^74 + 16 * q^75 + 8 * q^76 + 136 * q^79 - 4 * q^80 - 12 * q^81 - 16 * q^84 - 4 * q^85 + 48 * q^86 - 64 * q^89 - 8 * q^90 + 60 * q^91 - 48 * q^94 - 28 * q^95 + 40 * q^96 + 8 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	−0.521384	+	0.301021i	−0.368674	+	0.212854i	−0.672879	−	0.739752i	$-0.734943\pi$
$2$	−0.521384	+	0.301021i	−0.368674	+	0.212854i	0.304205	+	0.952607i	$0.401609\pi$
$3$	−0.866025	+	0.500000i	−0.500000	+	0.288675i
$3$	−0.866025	+	0.500000i	−0.500000	+	0.288675i
$4$	−0.818772	+	1.41816i	−0.409386	+	0.709078i
$5$	0.446511	+	2.19103i	0.199686	+	0.979860i
$5$	0.446511	+	2.19103i	0.199686	+	0.979860i
$6$	0.301021	−	0.521384i	0.122891	−	0.212854i
$7$	−3.08191	−	1.77934i	−1.16485	−	0.672528i	−0.212390	−	0.977185i	$-0.568125\pi$
$7$	−3.08191	−	1.77934i	−1.16485	−	0.672528i	−0.952462	+	0.304657i	$0.901458\pi$
$8$		−	2.18996i		−	0.774267i
$9$	0.500000	−	0.866025i	0.166667	−	0.288675i
$10$	−0.892352	−	1.00796i	−0.282186	−	0.318745i
$11$	−1.30769	−	2.26499i	−0.394284	−	0.682920i	0.598726	−	0.800954i	$-0.295674\pi$
$11$	−1.30769	−	2.26499i	−0.394284	−	0.682920i	−0.993010	+	0.118034i	$0.962341\pi$
$12$		−	1.63754i		−	0.472718i
$13$	−2.88598	+	2.16128i	−0.800426	+	0.599432i
$13$	−2.88598	+	2.16128i	−0.800426	+	0.599432i
$14$	2.14248			0.572602
$15$	−1.48221	−	1.67424i	−0.382704	−	0.432286i
$16$	−0.978320	−	1.69450i	−0.244580	−	0.423625i
$17$	1.94566	+	1.12333i	0.471893	+	0.272447i	0.717032	−	0.697041i	$-0.245500\pi$
$17$	1.94566	+	1.12333i	0.471893	+	0.272447i	−0.245139	+	0.969488i	$0.578834\pi$
$18$			0.602043i			0.141903i
$19$	−4.00873	+	6.94332i	−0.919666	+	1.59291i	−0.119743	+	0.992805i	$0.538207\pi$
$19$	−4.00873	+	6.94332i	−0.919666	+	1.59291i	−0.799923	+	0.600103i	$0.795126\pi$
$20$	−3.47282	−	1.16074i	−0.776545	−	0.259548i
$21$	3.55868			0.776568
$22$	1.36362	+	0.787287i	0.290725	+	0.167850i
$23$	1.43095	−	0.826160i	0.298374	−	0.172266i	−0.343338	−	0.939212i	$-0.611558\pi$
$23$	1.43095	−	0.826160i	0.298374	−	0.172266i	0.641712	+	0.766946i	$0.278224\pi$
$24$	1.09498	+	1.89656i	0.223512	+	0.387133i
$25$	−4.60126	+	1.95664i	−0.920251	+	0.391328i
$26$	0.854110	−	1.99560i	0.167505	−	0.391369i
$27$			1.00000i			0.192450i
$28$	5.04676	−	2.91375i	0.953749	−	0.550647i
$29$	2.26120	+	3.91651i	0.419894	+	0.727277i	0.995928	−	0.0901479i	$-0.0287340\pi$
$29$	2.26120	+	3.91651i	0.419894	+	0.727277i	−0.576035	+	0.817425i	$0.695401\pi$
$30$	1.27678	+	0.426744i	0.233107	+	0.0779125i
$31$	−4.05655			−0.728577			−0.364289	−	0.931286i	$-0.618688\pi$
$31$	−4.05655			−0.728577			−0.364289	+	0.931286i	$0.618688\pi$
$32$	4.81328	+	2.77895i	0.850876	+	0.491253i
$33$	2.26499	+	1.30769i	0.394284	+	0.227640i
$34$	−1.35258			−0.231966
$35$	2.52249	−	7.54706i	0.426379	−	1.27569i
$36$	0.818772	+	1.41816i	0.136462	+	0.236359i
$37$	3.64724	−	2.10574i	0.599603	−	0.346181i	−0.169283	−	0.985568i	$-0.554145\pi$
$37$	3.64724	−	2.10574i	0.599603	−	0.346181i	0.768885	+	0.639387i	$0.220812\pi$
$38$		−	4.82685i		−	0.783019i
$39$	1.41869	−	3.31471i	0.227172	−	0.530779i
$40$	4.79827	−	0.977840i	0.758673	−	0.154610i
$41$	0.388612	+	0.673096i	0.0606910	+	0.105120i	0.894774	−	0.446518i	$-0.147336\pi$
$41$	0.388612	+	0.673096i	0.0606910	+	0.105120i	−0.834083	+	0.551638i	$0.814003\pi$
$42$	−1.85544	+	1.07124i	−0.286301	+	0.165296i
$43$	0.197117	+	0.113806i	0.0300601	+	0.0173552i	0.514955	−	0.857217i	$-0.327809\pi$
$43$	0.197117	+	0.113806i	0.0300601	+	0.0173552i	−0.484895	+	0.874573i	$0.661142\pi$
$44$	4.28281			0.645658
$45$	2.12075	+	0.708827i	0.316142	+	0.105666i
$46$	−0.497384	+	0.861494i	−0.0733352	+	0.127020i
$47$			3.14738i			0.459093i	0.973298	+	0.229547i	$0.0737243\pi$
$47$			3.14738i			0.459093i	−0.973298	+	0.229547i	$0.926276\pi$
$48$	1.69450	+	0.978320i	0.244580	+	0.141208i
$49$	2.83211	+	4.90536i	0.404588	+	0.700766i
$50$	1.81003	−	2.40524i	0.255977	−	0.340152i
$51$	−2.24666			−0.314595
$52$	−0.702078	−	5.86236i	−0.0973607	−	0.812963i
$53$			6.42424i			0.882437i	0.897400	+	0.441218i	$0.145454\pi$
$53$			6.42424i			0.882437i	−0.897400	+	0.441218i	$0.854546\pi$
$54$	−0.301021	−	0.521384i	−0.0409638	−	0.0709514i
$55$	4.37877	−	3.87654i	0.590433	−	0.522712i
$56$	−3.89668	+	6.74925i	−0.520716	+	0.901907i
$57$		−	8.01746i		−	1.06194i
$58$	−2.35791	−	1.36134i	−0.309608	−	0.178752i
$59$	−6.26747	+	10.8556i	−0.815955	+	1.41328i	0.0926855	+	0.995695i	$0.470455\pi$
$59$	−6.26747	+	10.8556i	−0.815955	+	1.41328i	−0.908640	+	0.417580i	$0.862878\pi$
$60$	3.58791	−	0.731181i	0.463198	−	0.0943951i
$61$	−1.46568	+	2.53863i	−0.187661	+	0.325038i	−0.944470	−	0.328598i	$-0.893424\pi$
$61$	−1.46568	+	2.53863i	−0.187661	+	0.325038i	0.756809	+	0.653636i	$0.226757\pi$
$62$	2.11502	−	1.22111i	0.268608	−	0.155081i
$63$	−3.08191	+	1.77934i	−0.388284	+	0.224176i
$64$	0.567189			0.0708986
$65$	−6.02406	−	5.35823i	−0.747193	−	0.664607i
$66$	−1.57457			−0.193817
$67$	−0.969664	+	0.559836i	−0.118463	+	0.0683948i	−0.558061	−	0.829800i	$-0.688454\pi$
$67$	−0.969664	+	0.559836i	−0.118463	+	0.0683948i	0.439597	+	0.898195i	$0.355121\pi$
$68$	−3.18611	+	1.83950i	−0.386373	+	0.223072i
$69$	−0.826160	+	1.43095i	−0.0994580	+	0.172266i
$70$	0.956640	+	4.69425i	0.114340	+	0.561070i
$71$	5.66772	−	9.81678i	0.672635	−	1.16504i	−0.304520	−	0.952506i	$-0.598496\pi$
$71$	5.66772	−	9.81678i	0.672635	−	1.16504i	0.977154	−	0.212531i	$-0.0681708\pi$
$72$	−1.89656	−	1.09498i	−0.223512	−	0.129044i
$73$			12.4350i			1.45541i	0.685890	+	0.727705i	$0.259413\pi$
$73$			12.4350i			1.45541i	−0.685890	+	0.727705i	$0.740587\pi$
$74$	−1.26774	+	2.19579i	−0.147372	+	0.255256i
$75$	3.00648	−	3.99513i	0.347159	−	0.461318i
$76$	−6.56447	−	11.3700i	−0.752997	−	1.30423i
$77$			9.30732i			1.06067i
$78$	0.258119	+	2.15530i	0.0292262	+	0.244039i
$79$	14.8640			1.67234			0.836168	−	0.548474i	$-0.184791\pi$
$79$	14.8640			1.67234			0.836168	+	0.548474i	$0.184791\pi$
$80$	3.27588	−	2.90015i	0.366254	−	0.324246i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	−0.405233	−	0.233961i	−0.0447505	−	0.0258367i
$83$		−	11.7337i		−	1.28794i	−0.765050	−	0.643971i	$-0.777286\pi$
$83$		−	11.7337i		−	1.28794i	0.765050	−	0.643971i	$-0.222714\pi$
$84$	−2.91375	+	5.04676i	−0.317916	+	0.550647i
$85$	−1.59249	+	4.76459i	−0.172730	+	0.516793i
$86$	−0.137032			−0.0147765
$87$	−3.91651	−	2.26120i	−0.419894	−	0.242426i
$88$	−4.96023	+	2.86379i	−0.528762	+	0.305281i
$89$	−8.60439	−	14.9032i	−0.912064	−	1.57974i	−0.811144	−	0.584846i	$-0.801155\pi$
$89$	−8.60439	−	14.9032i	−0.912064	−	1.57974i	−0.100919	−	0.994895i	$-0.532178\pi$
$90$	−1.31910	+	0.268819i	−0.139045	+	0.0283360i
$91$	12.7400	−	1.52574i	1.33551	−	0.159941i
$92$			2.70575i			0.282094i
$93$	3.51307	−	2.02827i	0.364289	−	0.210322i
$94$	−0.947430	−	1.64100i	−0.0977200	−	0.169256i
$95$	−17.0030	−	5.68299i	−1.74447	−	0.583063i
$96$	−5.55790			−0.567250
$97$	−10.6088	−	6.12499i	−1.07716	−	0.621899i	−0.147032	−	0.989132i	$-0.546972\pi$
$97$	−10.6088	−	6.12499i	−1.07716	−	0.621899i	−0.930129	+	0.367233i	$0.880305\pi$
$98$	−2.95324	−	1.70505i	−0.298322	−	0.172236i
$99$	−2.61538			−0.262856
$100$	0.992561	−	8.12734i	0.0992561	−	0.812734i
$101$	8.61893	+	14.9284i	0.857616	+	1.48543i	0.874197	+	0.485571i	$0.161388\pi$
$101$	8.61893	+	14.9284i	0.857616	+	1.48543i	−0.0165815	+	0.999863i	$0.505278\pi$
$102$	1.17137	−	0.676292i	0.115983	−	0.0669629i
$103$			2.80894i			0.276773i	0.990378	+	0.138387i	$0.0441917\pi$
$103$			2.80894i			0.276773i	−0.990378	+	0.138387i	$0.955808\pi$
$104$	4.73312	+	6.32016i	0.464120	+	0.619743i
$105$	1.58899	+	7.79719i	0.155070	+	0.760928i
$106$	−1.93383	−	3.34950i	−0.187830	−	0.325332i
$107$	−8.58556	+	4.95687i	−0.829997	+	0.479199i	−0.853852	−	0.520516i	$-0.825739\pi$
$107$	−8.58556	+	4.95687i	−0.829997	+	0.479199i	0.0238546	+	0.999715i	$0.492406\pi$
$108$	−1.41816	−	0.818772i	−0.136462	−	0.0787864i
$109$	−7.17060			−0.686819			−0.343409	−	0.939186i	$-0.611582\pi$
$109$	−7.17060			−0.686819			−0.343409	+	0.939186i	$0.611582\pi$
$110$	−1.11610	+	3.33927i	−0.106416	+	0.318387i
$111$	−2.10574	+	3.64724i	−0.199868	+	0.346181i
$112$			6.96306i			0.657948i
$113$	−6.01823	−	3.47463i	−0.566148	−	0.326866i	0.189462	−	0.981888i	$-0.439326\pi$
$113$	−6.01823	−	3.47463i	−0.566148	−	0.326866i	−0.755609	+	0.655023i	$0.772659\pi$
$114$	2.41343	+	4.18018i	0.226038	+	0.391510i
$115$	2.44908	+	2.76637i	0.228378	+	0.257966i
$116$	−7.40562			−0.687595
$117$	0.428738	+	3.57997i	0.0396369	+	0.330968i
$118$		−	7.54657i		−	0.694718i
$119$	−3.99757	−	6.92400i	−0.366457	−	0.634722i
$120$	−3.66650	+	3.24597i	−0.334705	+	0.296315i
$121$	2.07988	−	3.60246i	0.189080	−	0.327497i
$122$		−	1.76480i		−	0.159778i
$123$	−0.673096	−	0.388612i	−0.0606910	−	0.0350400i
$124$	3.32139	−	5.75281i	0.298269	−	0.516618i
$125$	−6.34158	−	9.20785i	−0.567208	−	0.823575i
$126$	1.07124	−	1.85544i	0.0954336	−	0.165296i
$127$	−5.07705	+	2.93124i	−0.450515	+	0.260105i	−0.708048	−	0.706165i	$-0.750424\pi$
$127$	−5.07705	+	2.93124i	−0.450515	+	0.260105i	0.257533	+	0.966270i	$0.417091\pi$
$128$	−9.92228	+	5.72863i	−0.877014	+	0.506344i
$129$	−0.227611			−0.0200400
$130$	4.75380	+	0.980327i	0.416935	+	0.0859803i
$131$	10.0136			0.874892			0.437446	−	0.899245i	$-0.355883\pi$
$131$	10.0136			0.874892			0.437446	+	0.899245i	$0.355883\pi$
$132$	−3.70902	+	2.14140i	−0.322829	+	0.186385i
$133$	24.7091	−	14.2658i	2.14255	−	1.23700i
$134$	0.337045	−	0.583779i	0.0291163	−	0.0504309i
$135$	−2.19103	+	0.446511i	−0.188574	+	0.0384295i
$136$	2.46004	−	4.26092i	0.210947	−	0.365371i
$137$	15.9194	+	9.19109i	1.36009	+	0.785248i	0.989635	−	0.143603i	$-0.0458689\pi$
$137$	15.9194	+	9.19109i	1.36009	+	0.785248i	0.370454	+	0.928851i	$0.379202\pi$
$138$		−	0.994768i		−	0.0846802i
$139$	2.15531	−	3.73311i	0.182811	−	0.316638i	−0.760026	−	0.649893i	$-0.774814\pi$
$139$	2.15531	−	3.73311i	0.182811	−	0.316638i	0.942837	+	0.333255i	$0.108147\pi$
$140$	8.63756	+	9.75661i	0.730007	+	0.824584i
$141$	−1.57369	−	2.72572i	−0.132529	−	0.229547i
$142$			6.82442i			0.572693i
$143$	8.66925	+	3.71041i	0.724959	+	0.310280i
$144$	−1.95664			−0.163053
$145$	−7.57155	+	6.70312i	−0.628783	+	0.556664i
$146$	−3.74321	−	6.48343i	−0.309790	−	0.536572i
$147$	−4.90536	−	2.83211i	−0.404588	−	0.233589i
$148$			6.89647i			0.566886i
$149$	−1.13079	+	1.95858i	−0.0926377	+	0.160453i	−0.908620	−	0.417623i	$-0.862863\pi$
$149$	−1.13079	+	1.95858i	−0.0926377	+	0.160453i	0.815983	+	0.578077i	$0.196196\pi$
$150$	−0.364915	+	2.98801i	−0.0297952	+	0.243970i
$151$	8.52523			0.693773			0.346886	−	0.937907i	$-0.387239\pi$
$151$	8.52523			0.693773			0.346886	+	0.937907i	$0.387239\pi$
$152$	15.2056	+	8.77895i	1.23334	+	0.712067i
$153$	1.94566	−	1.12333i	0.157298	−	0.0908158i
$154$	−2.80170	−	4.85269i	−0.225768	−	0.391041i
$155$	−1.81129	−	8.88803i	−0.145487	−	0.713904i
$156$	3.53920	+	4.72591i	0.283363	+	0.378376i
$157$		−	6.53771i		−	0.521766i	−0.965370	−	0.260883i	$-0.915986\pi$
$157$		−	6.53771i		−	0.521766i	0.965370	−	0.260883i	$-0.0840137\pi$
$158$	−7.74988	+	4.47439i	−0.616547	+	0.355964i
$159$	−3.21212	−	5.56355i	−0.254738	−	0.441218i
$160$	−3.93959	+	11.7869i	−0.311452	+	0.931835i
$161$	−5.88008			−0.463416
$162$	0.521384	+	0.301021i	0.0409638	+	0.0236505i
$163$	−17.8665	−	10.3152i	−1.39941	−	0.807950i	−0.405080	−	0.914281i	$-0.632756\pi$
$163$	−17.8665	−	10.3152i	−1.39941	−	0.807950i	−0.994331	+	0.106331i	$0.966090\pi$
$164$	−1.27274			−0.0993843
$165$	−1.85386	+	5.54657i	−0.144322	+	0.431800i
$166$	3.53210	+	6.11777i	0.274144	+	0.474831i
$167$	16.6176	−	9.59418i	1.28591	−	0.742420i	0.307988	−	0.951390i	$-0.400344\pi$
$167$	16.6176	−	9.59418i	1.28591	−	0.742420i	0.977922	+	0.208970i	$0.0670111\pi$
$168$		−	7.79337i		−	0.601271i
$169$	3.65771	−	12.4748i	0.281362	−	0.959602i
$170$	−0.603944	−	2.96356i	−0.0463204	−	0.227295i
$171$	4.00873	+	6.94332i	0.306555	+	0.530969i
$172$	−0.322788	+	0.186362i	−0.0246123	+	0.0142099i
$173$	16.7006	+	9.64212i	1.26973	+	0.733077i	0.974936	−	0.222485i	$-0.0714168\pi$
$173$	16.7006	+	9.64212i	1.26973	+	0.733077i	0.294791	+	0.955562i	$0.404750\pi$
$174$	2.72268			0.206406
$175$	17.6622	+	2.15702i	1.33514	+	0.163055i
$176$	−2.55868	+	4.43177i	−0.192868	+	0.334057i
$177$		−	12.5349i		−	0.942183i
$178$	8.97239	+	5.18021i	0.672509	+	0.388273i
$179$	−2.85922	−	4.95232i	−0.213708	−	0.370153i	0.739164	−	0.673525i	$-0.235221\pi$
$179$	−2.85922	−	4.95232i	−0.213708	−	0.370153i	−0.952872	+	0.303372i	$0.901888\pi$
$180$	−2.74163	+	2.42718i	−0.204349	+	0.180911i
$181$	−5.05252			−0.375551			−0.187775	−	0.982212i	$-0.560128\pi$
$181$	−5.05252			−0.375551			−0.187775	+	0.982212i	$0.560128\pi$
$182$	−6.18314	+	4.63051i	−0.458325	+	0.343236i
$183$		−	2.93135i		−	0.216692i
$184$	−1.80926	−	3.13372i	−0.133380	−	0.231021i
$185$	6.24227	+	7.05099i	0.458941	+	0.518399i
$186$	−1.22111	+	2.11502i	−0.0895360	+	0.155081i
$187$		−	5.87588i		−	0.429687i
$188$	−4.46348	−	2.57699i	−0.325533	−	0.187946i
$189$	1.77934	−	3.08191i	0.129428	−	0.224176i
$190$	10.5758	−	2.15524i	0.767249	−	0.156358i
$191$	−8.82751	+	15.2897i	−0.638736	+	1.10632i	0.346974	+	0.937875i	$0.387209\pi$
$191$	−8.82751	+	15.2897i	−0.638736	+	1.10632i	−0.985710	+	0.168449i	$0.946124\pi$
$192$	−0.491200	+	0.283595i	−0.0354493	+	0.0204667i
$193$	−3.17329	+	1.83210i	−0.228418	+	0.131877i	−0.609842	−	0.792523i	$-0.708767\pi$
$193$	−3.17329	+	1.83210i	−0.228418	+	0.131877i	0.381424	+	0.924400i	$0.375434\pi$
$194$	7.37502			0.529495
$195$	7.89611	+	1.62833i	0.565452	+	0.116607i
$196$	−9.27542			−0.662530
$197$	6.03467	−	3.48412i	0.429952	−	0.248233i	−0.269374	−	0.963036i	$-0.586817\pi$
$197$	6.03467	−	3.48412i	0.429952	−	0.248233i	0.699326	+	0.714803i	$0.253483\pi$
$198$	1.36362	−	0.787287i	0.0969083	−	0.0559500i
$199$	−3.68996	+	6.39119i	−0.261574	+	0.453060i	−0.966660	−	0.256062i	$-0.917575\pi$
$199$	−3.68996	+	6.39119i	−0.261574	+	0.453060i	0.705086	+	0.709122i	$0.250908\pi$
$200$	4.28496	+	10.0766i	0.302992	+	0.712520i
$201$	0.559836	−	0.969664i	0.0394878	−	0.0683948i
$202$	−8.98755	−	5.18897i	−0.632362	−	0.365094i
$203$		−	16.0938i		−	1.12956i
$204$	1.83950	−	3.18611i	0.128791	−	0.223072i
$205$	−1.30126	+	1.15201i	−0.0908837	+	0.0804597i
$206$	−0.845552	−	1.46454i	−0.0589124	−	0.102039i
$207$		−	1.65232i		−	0.114844i
$208$	6.48570	+	2.77586i	0.449703	+	0.192471i
$209$	20.9687			1.45044
$210$	−3.17560	−	3.58702i	−0.219137	−	0.247528i
$211$	12.3017	+	21.3072i	0.846887	+	1.46685i	0.883973	+	0.467539i	$0.154859\pi$
$211$	12.3017	+	21.3072i	0.846887	+	1.46685i	−0.0370857	+	0.999312i	$0.511807\pi$
$212$	−9.11056	−	5.25999i	−0.625716	−	0.361257i
$213$			11.3354i			0.776692i
$214$	2.98425	−	5.16887i	0.203999	−	0.353337i
$215$	−0.161337	+	0.482705i	−0.0110031	+	0.0329202i
$216$	2.18996			0.149008
$217$	12.5019	+	7.21798i	0.848685	+	0.489989i
$218$	3.73864	−	2.15850i	0.253212	−	0.146192i
$219$	−6.21751	−	10.7691i	−0.420141	−	0.727705i
$220$	1.91232	+	9.38378i	0.128929	+	0.632654i
$221$	−8.04297	+	0.963229i	−0.541029	+	0.0647938i
$222$		−	2.53549i		−	0.170171i
$223$	−0.480551	+	0.277446i	−0.0321801	+	0.0185792i	−0.516004	−	0.856586i	$-0.672581\pi$
$223$	−0.480551	+	0.277446i	−0.0321801	+	0.0185792i	0.483824	+	0.875166i	$0.339248\pi$
$224$	−9.88940	−	17.1289i	−0.660763	−	1.14448i
$225$	−0.606128	+	4.96312i	−0.0404085	+	0.330875i
$226$	4.18375			0.278299
$227$	1.30934	+	0.755945i	0.0869037	+	0.0501739i	0.542822	−	0.839848i	$-0.317356\pi$
$227$	1.30934	+	0.755945i	0.0869037	+	0.0501739i	−0.455918	+	0.890022i	$0.650689\pi$
$228$	11.3700	+	6.56447i	0.752997	+	0.434743i
$229$	−5.42263			−0.358337			−0.179169	−	0.983818i	$-0.557341\pi$
$229$	−5.42263			−0.358337			−0.179169	+	0.983818i	$0.557341\pi$
$230$	−2.10965	−	0.705118i	−0.139106	−	0.0464941i
$231$	−4.65366	−	8.06038i	−0.306188	−	0.530334i
$232$	8.57699	−	4.95193i	0.563107	−	0.325110i
$233$		−	11.2530i		−	0.737206i	−0.929587	−	0.368603i	$-0.879836\pi$
$233$		−	11.2530i		−	0.737206i	0.929587	−	0.368603i	$-0.120164\pi$
$234$	−1.30119	−	1.73748i	−0.0850611	−	0.113583i
$235$	−6.89603	+	1.40534i	−0.449847	+	0.0916744i
$236$	−10.2633	−	17.7765i	−0.668081	−	1.15715i
$237$	−12.8726	+	7.43202i	−0.836168	+	0.482762i
$238$	4.16854	+	2.40671i	0.270207	+	0.156004i
$239$	−17.9281			−1.15967			−0.579837	−	0.814733i	$-0.696884\pi$
$239$	−17.9281			−1.15967			−0.579837	+	0.814733i	$0.696884\pi$
$240$	−1.38692	+	4.14954i	−0.0895253	+	0.267852i
$241$	−10.1675	+	17.6107i	−0.654949	+	1.13440i	0.326958	+	0.945039i	$0.393977\pi$
$241$	−10.1675	+	17.6107i	−0.654949	+	1.13440i	−0.981907	+	0.189366i	$0.939357\pi$
$242$			2.50436i			0.160986i
$243$	0.866025	+	0.500000i	0.0555556	+	0.0320750i
$244$	−2.40011	−	4.15711i	−0.153651	−	0.266132i
$245$	−9.48325	+	8.39555i	−0.605863	+	0.536372i
$246$	0.467923			0.0298336
$247$	−3.43739	−	28.7023i	−0.218716	−	1.82628i
$248$			8.88367i			0.564113i
$249$	5.86686	+	10.1617i	0.371797	+	0.643971i
$250$	6.07816	+	2.89188i	0.384416	+	0.182898i
$251$	9.42506	−	16.3247i	0.594904	−	1.03040i	−0.398656	−	0.917101i	$-0.630523\pi$
$251$	9.42506	−	16.3247i	0.594904	−	1.03040i	0.993560	−	0.113304i	$-0.0361434\pi$
$252$		−	5.82750i		−	0.367098i
$253$	−3.74249	−	2.16073i	−0.235288	−	0.135844i
$254$	1.76473	−	3.05660i	0.110729	−	0.191788i
$255$	−1.00316	−	4.92250i	−0.0628202	−	0.308259i
$256$	2.88169	−	4.99124i	0.180106	−	0.311952i
$257$	−24.5820	+	14.1924i	−1.53338	+	0.885298i	−0.534179	+	0.845372i	$0.679379\pi$
$257$	−24.5820	+	14.1924i	−1.53338	+	0.885298i	−0.999203	+	0.0399265i	$0.987288\pi$
$258$	0.118673	−	0.0685158i	0.00738825	−	0.00426561i
$259$	−14.9873			−0.931265
$260$	12.5311	−	4.15588i	0.777148	−	0.257737i
$261$	4.52240			0.279929
$262$	−5.22093	+	3.01431i	−0.322550	+	0.186224i
$263$	−12.3560	+	7.13372i	−0.761901	+	0.439884i	−0.829978	−	0.557796i	$-0.811647\pi$
$263$	−12.3560	+	7.13372i	−0.761901	+	0.439884i	0.0680767	+	0.997680i	$0.478314\pi$
$264$	2.86379	−	4.96023i	0.176254	−	0.305281i
$265$	−14.0757	+	2.86849i	−0.864664	+	0.176210i
$266$	−8.58862	+	14.8759i	−0.526602	+	0.912102i
$267$	14.9032	+	8.60439i	0.912064	+	0.526580i
$268$		−	1.83351i		−	0.112000i
$269$	12.7612	−	22.1031i	0.778067	−	1.34765i	−0.154988	−	0.987916i	$-0.549534\pi$
$269$	12.7612	−	22.1031i	0.778067	−	1.34765i	0.933055	−	0.359735i	$-0.117133\pi$
$270$	1.00796	−	0.892352i	0.0613426	−	0.0543068i
$271$	3.91226	+	6.77623i	0.237653	+	0.411627i	0.960040	−	0.279862i	$-0.0902886\pi$
$271$	3.91226	+	6.77623i	0.237653	+	0.411627i	−0.722387	+	0.691488i	$0.756955\pi$
$272$		−	4.39590i		−	0.266541i
$273$	−10.2703	+	7.69132i	−0.621585	+	0.465500i
$274$	−11.0669			−0.668573
$275$	10.4488	+	7.86311i	0.630086	+	0.474163i
$276$	−1.35287	−	2.34325i	−0.0814334	−	0.141047i
$277$	16.8514	+	9.72915i	1.01250	+	0.584568i	0.911923	−	0.410361i	$-0.134597\pi$
$277$	16.8514	+	9.72915i	1.01250	+	0.584568i	0.100578	+	0.994929i	$0.467931\pi$
$278$			2.59518i			0.155648i
$279$	−2.02827	+	3.51307i	−0.121430	+	0.210322i
$280$	−16.5278	−	5.52415i	−0.987722	−	0.330131i
$281$	23.1248			1.37951			0.689754	−	0.724043i	$-0.257718\pi$
$281$	23.1248			1.37951			0.689754	+	0.724043i	$0.257718\pi$
$282$	1.64100	+	0.947430i	0.0977200	+	0.0564187i
$283$	−22.4177	+	12.9429i	−1.33260	+	0.769374i	−0.985697	−	0.168528i	$-0.946099\pi$
$283$	−22.4177	+	12.9429i	−1.33260	+	0.769374i	−0.346899	+	0.937903i	$0.612765\pi$
$284$	9.28114	+	16.0754i	0.550735	+	0.953900i
$285$	17.5665	−	3.57988i	1.04055	−	0.212054i
$286$	−5.63693	+	0.675080i	−0.333318	+	0.0399183i
$287$		−	2.76590i		−	0.163266i
$288$	4.81328	−	2.77895i	0.283625	−	0.163751i
$289$	−5.97626	−	10.3512i	−0.351545	−	0.608894i
$290$	1.92991	−	5.77410i	0.113328	−	0.339067i
$291$	12.2500			0.718107
$292$	−17.6348	−	10.1815i	−1.03200	−	0.595825i
$293$	3.47269	+	2.00496i	0.202877	+	0.117131i	0.597997	−	0.801499i	$-0.295964\pi$
$293$	3.47269	+	2.00496i	0.202877	+	0.117131i	−0.395120	+	0.918630i	$0.629297\pi$
$294$	3.41011			0.198882
$295$	−26.5834	−	8.88510i	−1.54775	−	0.517311i
$296$	−4.61147	−	7.98730i	−0.268036	−	0.464252i
$297$	2.26499	−	1.30769i	0.131428	−	0.0758800i
$298$		−	1.36156i		−	0.0788733i
$299$	−2.34412	+	5.47697i	−0.135564	+	0.316741i
$300$	3.20409	+	7.53476i	0.184988	+	0.435020i
$301$	−0.404998	−	0.701477i	−0.0233437	−	0.0404325i
$302$	−4.44492	+	2.56628i	−0.255776	+	0.147673i
$303$	−14.9284	−	8.61893i	−0.857616	−	0.495145i
$304$	15.6873			0.899728
$305$	−6.21666	−	2.07782i	−0.355965	−	0.118976i
$306$	−0.676292	+	1.17137i	−0.0386611	+	0.0669629i
$307$			24.6936i			1.40934i	0.709537	+	0.704668i	$0.248904\pi$
$307$			24.6936i			1.40934i	−0.709537	+	0.704668i	$0.751096\pi$
$308$	−13.1992	−	7.62058i	−0.752096	−	0.434223i
$309$	−1.40447	−	2.43262i	−0.0798976	−	0.138387i
$310$	3.61987	+	4.08884i	0.205595	+	0.232231i
$311$	−11.7458			−0.666041			−0.333021	−	0.942920i	$-0.608068\pi$
$311$	−11.7458			−0.666041			−0.333021	+	0.942920i	$0.608068\pi$
$312$	−7.25908	−	3.10686i	−0.410965	−	0.175891i
$313$			6.16331i			0.348371i	0.984713	+	0.174185i	$0.0557292\pi$
$313$			6.16331i			0.348371i	−0.984713	+	0.174185i	$0.944271\pi$
$314$	1.96799	+	3.40866i	0.111060	+	0.192362i
$315$	−5.27470	−	5.95807i	−0.297196	−	0.335699i
$316$	−12.1703	+	21.0795i	−0.684631	+	1.18582i
$317$		−	12.9683i		−	0.728371i	−0.931326	−	0.364186i	$-0.881347\pi$
$317$		−	12.9683i		−	0.728371i	0.931326	−	0.364186i	$-0.118653\pi$
$318$	3.34950	+	1.93383i	0.187830	+	0.108444i
$319$	5.91390	−	10.2432i	0.331115	−	0.573508i
$320$	0.253256	+	1.24273i	0.0141574	+	0.0694707i
$321$	4.95687	−	8.58556i	0.276666	−	0.479199i
$322$	3.06578	−	1.77003i	0.170849	−	0.0986400i
$323$	−15.5993	+	9.00625i	−0.867967	+	0.501121i
$324$	1.63754			0.0909747
$325$	9.05026	−	15.5914i	0.502018	−	0.864857i
$326$	12.4204			0.687903
$327$	6.20992	−	3.58530i	0.343409	−	0.198267i
$328$	1.47405	−	0.851044i	0.0813909	−	0.0469911i
$329$	5.60027	−	9.69996i	0.308753	−	0.534776i
$330$	−0.703064	−	3.44994i	−0.0387024	−	0.189913i
$331$	−5.40749	+	9.36605i	−0.297223	+	0.514805i	−0.975499	−	0.220002i	$-0.929394\pi$
$331$	−5.40749	+	9.36605i	−0.297223	+	0.514805i	0.678277	+	0.734806i	$0.262727\pi$
$332$	16.6402	+	9.60724i	0.913251	+	0.527266i
$333$		−	4.21147i		−	0.230787i
$334$	−5.77611	+	10.0045i	−0.316055	+	0.547423i
$335$	−1.65959	−	1.87459i	−0.0906728	−	0.102420i
$336$	−3.48153	−	6.03019i	−0.189933	−	0.328974i
$337$			3.84210i			0.209292i	0.994510	+	0.104646i	$0.0333710\pi$
$337$			3.84210i			0.209292i	−0.994510	+	0.104646i	$0.966629\pi$
$338$	1.84812	+	7.60523i	0.100524	+	0.413670i
$339$	6.94926			0.377432
$340$	−5.45304	−	6.15952i	−0.295733	−	0.334047i
$341$	5.30472	+	9.18804i	0.287266	+	0.497560i
$342$	−4.18018	−	2.41343i	−0.226038	−	0.130503i
$343$			4.75359i			0.256670i
$344$	0.249229	−	0.431678i	0.0134375	−	0.0232745i
$345$	−3.50415	−	1.17121i	−0.188657	−	0.0630558i
$346$	−11.6099			−0.624154
$347$	10.1199	+	5.84271i	0.543263	+	0.313653i	0.746400	−	0.665497i	$-0.231781\pi$
$347$	10.1199	+	5.84271i	0.543263	+	0.313653i	−0.203137	+	0.979150i	$0.565114\pi$
$348$	6.41346	−	3.70281i	0.343797	−	0.198492i
$349$	0.812876	+	1.40794i	0.0435122	+	0.0753654i	0.886961	−	0.461844i	$-0.152812\pi$
$349$	0.812876	+	1.40794i	0.0435122	+	0.0753654i	−0.843449	+	0.537209i	$0.819479\pi$
$350$	−9.85810	+	4.19206i	−0.526938	+	0.224075i
$351$	−2.16128	−	2.88598i	−0.115361	−	0.154042i
$352$		−	14.5360i		−	0.774773i
$353$	7.90443	−	4.56363i	0.420710	−	0.242897i	−0.274671	−	0.961538i	$-0.588569\pi$
$353$	7.90443	−	4.56363i	0.420710	−	0.242897i	0.695381	+	0.718641i	$0.255236\pi$
$354$	3.77328	+	6.53552i	0.200548	+	0.347359i
$355$	24.0396	+	8.03487i	1.27589	+	0.426446i
$356$	28.1801			1.49354
$357$	6.92400	+	3.99757i	0.366457	+	0.211574i
$358$	2.98151	+	1.72137i	0.157577	+	0.0909774i
$359$	−23.8361			−1.25802			−0.629011	−	0.777396i	$-0.716540\pi$
$359$	−23.8361			−1.25802			−0.629011	+	0.777396i	$0.716540\pi$
$360$	1.55230	−	4.64434i	0.0818135	−	0.244778i
$361$	−22.6398	−	39.2133i	−1.19157	−	2.06386i
$362$	2.63431	−	1.52092i	0.138456	−	0.0799376i
$363$			4.15977i			0.218331i
$364$	−8.26740	+	19.3165i	−0.433329	+	1.01246i
$365$	−27.2456	+	5.55237i	−1.42610	+	0.290625i
$366$	0.882400	+	1.52836i	0.0461238	+	0.0798888i
$367$	−14.6989	+	8.48640i	−0.767275	+	0.442986i	−0.831902	−	0.554923i	$-0.812748\pi$
$367$	−14.6989	+	8.48640i	−0.767275	+	0.442986i	0.0646267	+	0.997910i	$0.479414\pi$
$368$	−2.79986	−	1.61650i	−0.145953	−	0.0842658i
$369$	0.777225			0.0404607
$370$	−5.37712	−	1.79722i	−0.279543	−	0.0934331i
$371$	11.4309	−	19.7989i	0.593463	−	1.02791i
$372$			6.64278i			0.344412i
$373$	−13.7766	−	7.95393i	−0.713326	−	0.411839i	0.0989655	−	0.995091i	$-0.468447\pi$
$373$	−13.7766	−	7.95393i	−0.713326	−	0.411839i	−0.812291	+	0.583252i	$0.801780\pi$
$374$	1.76876	+	3.06359i	0.0914606	+	0.158414i
$375$	10.0959	+	4.80344i	0.521349	+	0.248049i
$376$	6.89264			0.355461
$377$	−14.9904	−	6.41586i	−0.772047	−	0.330434i
$378$			2.14248i			0.110197i
$379$	10.4083	+	18.0277i	0.534638	+	0.926020i	0.999181	+	0.0404693i	$0.0128853\pi$
$379$	10.4083	+	18.0277i	0.534638	+	0.926020i	−0.464543	+	0.885551i	$0.653781\pi$
$380$	21.9809	−	19.4598i	1.12760	−	0.998267i
$381$	2.93124	−	5.07705i	0.150172	−	0.260105i
$382$		−	10.6291i		−	0.543831i
$383$	20.8749	+	12.0521i	1.06666	+	0.615834i	0.927266	−	0.374403i	$-0.122152\pi$
$383$	20.8749	+	12.0521i	1.06666	+	0.615834i	0.139391	+	0.990237i	$0.455486\pi$
$384$	5.72863	−	9.92228i	0.292338	−	0.506344i
$385$	−20.3927	+	4.15582i	−1.03931	+	0.211800i
$386$	1.10300	−	1.91046i	0.0561413	−	0.0972396i
$387$	0.197117	−	0.113806i	0.0100200	−	0.00578506i
$388$	17.3724	−	10.0300i	0.881949	−	0.509194i
$389$	17.6045			0.892583			0.446292	−	0.894888i	$-0.352744\pi$
$389$	17.6045			0.892583			0.446292	+	0.894888i	$0.352744\pi$
$390$	−4.60707	+	1.52791i	−0.233288	+	0.0773687i
$391$	3.71220			0.187734
$392$	10.7425	−	6.20221i	0.542580	−	0.313259i
$393$	−8.67203	+	5.00680i	−0.437446	+	0.252559i
$394$	−2.09759	+	3.63313i	−0.105675	+	0.183034i
$395$	6.63696	+	32.5676i	0.333941	+	1.63865i
$396$	2.14140	−	3.70902i	0.107610	−	0.186385i
$397$	11.1601	+	6.44331i	0.560111	+	0.323380i	0.753190	−	0.657803i	$-0.228514\pi$
$397$	11.1601	+	6.44331i	0.560111	+	0.323380i	−0.193079	+	0.981183i	$0.561847\pi$
$398$		−	4.44303i		−	0.222709i
$399$	−14.2658	+	24.7091i	−0.714183	+	1.23700i
$400$	7.81703	+	5.88261i	0.390852	+	0.294130i
$401$	7.96163	+	13.7899i	0.397585	+	0.688637i	0.993427	−	0.114464i	$-0.0365151\pi$
$401$	7.96163	+	13.7899i	0.397585	+	0.688637i	−0.595843	+	0.803101i	$0.703182\pi$
$402$			0.674090i			0.0336206i
$403$	11.7071	−	8.76735i	0.583172	−	0.436733i
$404$	−28.2278			−1.40438
$405$	1.67424	−	1.48221i	0.0831934	−	0.0736514i
$406$	4.84457	+	8.39104i	0.240432	+	0.416440i
$407$	−9.53893	−	5.50731i	−0.472827	−	0.272987i
$408$			4.92009i			0.243581i
$409$	2.18586	−	3.78602i	0.108084	−	0.187206i	−0.806910	−	0.590674i	$-0.798862\pi$
$409$	2.18586	−	3.78602i	0.108084	−	0.187206i	0.914994	+	0.403468i	$0.132195\pi$
$410$	0.331676	−	0.992345i	0.0163803	−	0.0490084i
$411$	−18.3822			−0.906726
$412$	−3.98352	−	2.29988i	−0.196254	−	0.113307i
$413$	38.6315	−	22.3039i	1.90093	−	1.09750i
$414$	0.497384	+	0.861494i	0.0244451	+	0.0423401i
$415$	25.7090	−	5.23923i	1.26200	−	0.257184i
$416$	−19.8971	+	2.38288i	−0.975536	+	0.116831i
$417$			4.31062i			0.211092i
$418$	−10.9328	+	6.31204i	−0.534739	+	0.308732i
$419$	4.51510	+	7.82039i	0.220577	+	0.382051i	0.954983	−	0.296659i	$-0.0958726\pi$
$419$	4.51510	+	7.82039i	0.220577	+	0.382051i	−0.734406	+	0.678710i	$0.762539\pi$
$420$	−12.3587	−	4.13069i	−0.603040	−	0.201557i
$421$	15.7927			0.769689			0.384845	−	0.922981i	$-0.374255\pi$
$421$	15.7927			0.769689			0.384845	+	0.922981i	$0.374255\pi$
$422$	−12.8279	−	7.40618i	−0.624451	−	0.360527i
$423$	2.72572	+	1.57369i	0.132529	+	0.0765155i
$424$	14.0688			0.683241
$425$	−11.1504	−	1.36176i	−0.540876	−	0.0660552i
$426$	−3.41221	−	5.91012i	−0.165322	−	0.286346i
$427$	9.03417	−	5.21588i	0.437194	−	0.252414i
$428$		−	16.2342i		−	0.784710i
$429$	−9.36300	+	1.12132i	−0.452050	+	0.0541376i
$430$	−0.0611861	−	0.300241i	−0.00295066	−	0.0144789i
$431$	−2.43056	−	4.20985i	−0.117076	−	0.202782i	0.801532	−	0.597952i	$-0.204019\pi$
$431$	−2.43056	−	4.20985i	−0.117076	−	0.202782i	−0.918608	+	0.395171i	$0.870685\pi$
$432$	1.69450	−	0.978320i	0.0815267	−	0.0470695i
$433$	2.66886	+	1.54087i	0.128257	+	0.0740494i	0.562756	−	0.826623i	$-0.309741\pi$
$433$	2.66886	+	1.54087i	0.128257	+	0.0740494i	−0.434499	+	0.900673i	$0.643074\pi$
$434$	−8.69107			−0.417185
$435$	3.20560	−	9.59085i	0.153697	−	0.459846i
$436$	5.87109	−	10.1690i	0.281174	−	0.487008i
$437$			13.2474i			0.633710i
$438$	6.48343	+	3.74321i	0.309790	+	0.178857i
$439$	1.92116	+	3.32754i	0.0916918	+	0.158815i	0.908223	−	0.418486i	$-0.137439\pi$
$439$	1.92116	+	3.32754i	0.0916918	+	0.158815i	−0.816531	+	0.577301i	$0.804106\pi$
$440$	−8.48946	−	9.58932i	−0.404719	−	0.457153i
$441$	5.66423			0.269725
$442$	3.90353	−	2.92332i	0.185672	−	0.139048i
$443$		−	7.40427i		−	0.351788i	−0.984409	−	0.175894i	$-0.943718\pi$
$443$		−	7.40427i		−	0.351788i	0.984409	−	0.175894i	$-0.0562815\pi$
$444$	−3.44823	−	5.97252i	−0.163646	−	0.283443i
$445$	28.8116	−	25.5070i	1.36580	−	1.20915i
$446$	0.167035	−	0.289312i	0.00790931	−	0.0136993i
$447$		−	2.26157i		−	0.106969i
$448$	−1.74803	−	1.00922i	−0.0825865	−	0.0476813i
$449$	−12.3270	+	21.3509i	−0.581745	+	1.00761i	0.413527	+	0.910492i	$0.364297\pi$
$449$	−12.3270	+	21.3509i	−0.581745	+	1.00761i	−0.995273	+	0.0971206i	$0.969037\pi$
$450$	−1.17798	−	2.77015i	−0.0555306	−	0.130586i
$451$	1.01637	−	1.76041i	0.0478590	−	0.0828942i
$452$	9.85512	−	5.68986i	0.463546	−	0.267628i
$453$	−7.38306	+	4.26261i	−0.346886	+	0.200275i
$454$	−0.910223			−0.0427189
$455$	9.03150	+	27.2325i	0.423403	+	1.27668i
$456$	−17.5579			−0.822224
$457$	−24.8930	+	14.3720i	−1.16444	+	0.672292i	−0.952365	−	0.304960i	$-0.901357\pi$
$457$	−24.8930	+	14.3720i	−1.16444	+	0.672292i	−0.212079	+	0.977252i	$0.568023\pi$
$458$	2.82727	−	1.63233i	0.132110	−	0.0762736i
$459$	−1.12333	+	1.94566i	−0.0524325	+	0.0908158i
$460$	−5.92838	+	1.20815i	−0.276412	+	0.0563301i
$461$	−1.99008	+	3.44692i	−0.0926874	+	0.160539i	−0.908641	−	0.417578i	$-0.862879\pi$
$461$	−1.99008	+	3.44692i	−0.0926874	+	0.160539i	0.815954	+	0.578117i	$0.196212\pi$
$462$	4.85269	+	2.80170i	0.225768	+	0.130347i
$463$			13.1195i			0.609717i	0.952398	+	0.304859i	$0.0986092\pi$
$463$			13.1195i			0.609717i	−0.952398	+	0.304859i	$0.901391\pi$
$464$	4.42435	−	7.66320i	0.205395	−	0.355755i
$465$	6.01264	+	6.79162i	0.278830	+	0.314954i
$466$	3.38738	+	5.86712i	0.156917	+	0.271789i
$467$		−	11.9144i		−	0.551332i	−0.961253	−	0.275666i	$-0.911102\pi$
$467$		−	11.9144i		−	0.551332i	0.961253	−	0.275666i	$-0.0888984\pi$
$468$	−5.42799	−	2.32316i	−0.250909	−	0.107388i
$469$	3.98456			0.183990
$470$	3.17244	−	2.80857i	0.146334	−	0.129550i
$471$	3.26886	+	5.66183i	0.150621	+	0.260883i
$472$	23.7732	+	13.7255i	1.09425	+	0.631767i
$473$		−	0.595290i		−	0.0273715i
$474$	4.47439	−	7.74988i	0.205516	−	0.355964i
$475$	4.85960	−	39.7917i	0.222974	−	1.82577i
$476$	13.0924			0.600089
$477$	5.56355	+	3.21212i	0.254738	+	0.147073i
$478$	9.34744	−	5.39675i	0.427542	−	0.246842i
$479$	20.6210	+	35.7167i	0.942199	+	1.63194i	0.761265	+	0.648441i	$0.224579\pi$
$479$	20.6210	+	35.7167i	0.942199	+	1.63194i	0.180934	+	0.983495i	$0.442088\pi$
$480$	−2.48166	−	12.1775i	−0.113272	−	0.555826i
$481$	−5.97476	+	13.9598i	−0.272425	+	0.636513i
$482$		−	12.2426i		−	0.557635i
$483$	5.09230	−	2.94004i	0.231708	−	0.133777i
$484$	3.40590	+	5.89919i	0.154814	+	0.268145i
$485$	8.68312	−	25.9791i	0.394280	−	1.17965i
$486$	−0.602043			−0.0273092
$487$	12.5440	+	7.24227i	0.568422	+	0.328179i	0.756519	−	0.653972i	$-0.226898\pi$
$487$	12.5440	+	7.24227i	0.568422	+	0.328179i	−0.188097	+	0.982151i	$0.560232\pi$
$488$	5.55948	+	3.20977i	0.251666	+	0.145299i
$489$	20.6304			0.932940
$490$	2.41718	−	7.23197i	0.109197	−	0.326707i
$491$	−8.84200	−	15.3148i	−0.399034	−	0.691147i	0.594573	−	0.804042i	$-0.297321\pi$
$491$	−8.84200	−	15.3148i	−0.399034	−	0.691147i	−0.993607	+	0.112894i	$0.963988\pi$
$492$	1.10222	−	0.636370i	0.0496921	−	0.0286898i
$493$			10.1603i			0.457596i
$494$	10.4322	+	13.9302i	0.469367	+	0.626749i
$495$	−1.16780	−	5.73039i	−0.0524886	−	0.257562i
$496$	3.96860	+	6.87382i	0.178196	+	0.308644i
$497$	−34.9348	+	20.1696i	−1.56704	+	0.904731i
$498$	−6.11777	−	3.53210i	−0.274144	−	0.158277i
$499$	0.690775			0.0309233			0.0154617	−	0.999880i	$-0.495078\pi$
$499$	0.690775			0.0309233			0.0154617	+	0.999880i	$0.495078\pi$
$500$	18.2505	−	1.45421i	0.816185	−	0.0650342i
$501$	−9.59418	+	16.6176i	−0.428637	+	0.742420i
$502$			11.3486i			0.506512i
$503$	9.08724	+	5.24652i	0.405180	+	0.233931i	0.688717	−	0.725031i	$-0.258174\pi$
$503$	9.08724	+	5.24652i	0.405180	+	0.233931i	−0.283537	+	0.958961i	$0.591508\pi$
$504$	3.89668	+	6.74925i	0.173572	+	0.300636i
$505$	−28.8602	+	25.5501i	−1.28426	+	1.13696i
$506$	2.60170			0.115660
$507$	3.06974	+	12.6324i	0.136332	+	0.561023i
$508$		−	9.60006i		−	0.425934i
$509$	11.1971	+	19.3939i	0.496302	+	0.859621i	0.999991	−	0.00426454i	$-0.00135745\pi$
$509$	11.1971	+	19.3939i	0.496302	+	0.859621i	−0.503689	+	0.863885i	$0.668024\pi$
$510$	2.00481	+	2.26455i	0.0887745	+	0.100276i
$511$	22.1262	−	38.3236i	0.978804	−	1.69534i
$512$		−	19.4447i		−	0.859344i
$513$	−6.94332	−	4.00873i	−0.306555	−	0.176990i
$514$	8.54444	−	14.7994i	0.376879	−	0.652774i
$515$	−6.15449	+	1.25422i	−0.271199	+	0.0552677i
$516$	0.186362	−	0.322788i	0.00820411	−	0.0142099i
$517$	7.12879	−	4.11581i	0.313524	−	0.181013i
$518$	7.81414	−	4.51149i	0.343334	−	0.198224i
$519$	−19.2842			−0.846484
$520$	−11.7343	+	13.1924i	−0.514583	+	0.578527i
$521$	−24.8874			−1.09034			−0.545168	−	0.838327i	$-0.683534\pi$
$521$	−24.8874			−1.09034			−0.545168	+	0.838327i	$0.683534\pi$
$522$	−2.35791	+	1.36134i	−0.103203	+	0.0595841i
$523$	19.1352	−	11.0477i	0.836725	−	0.483083i	−0.0194246	−	0.999811i	$-0.506183\pi$
$523$	19.1352	−	11.0477i	0.836725	−	0.483083i	0.856150	+	0.516728i	$0.172850\pi$
$524$	−8.19885	+	14.2008i	−0.358168	+	0.620366i
$525$	−16.3744	+	6.96306i	−0.714638	+	0.303893i
$526$	4.29480	−	7.43882i	0.187262	−	0.324348i
$527$	−7.89268	−	4.55684i	−0.343810	−	0.198499i
$528$		−	5.11737i		−	0.222705i
$529$	−10.1349	+	17.5542i	−0.440649	+	0.763226i
$530$	6.47538	−	5.73268i	0.281273	−	0.249012i
$531$	6.26747	+	10.8556i	0.271985	+	0.471092i
$532$			46.7218i			2.02565i
$533$	−2.57628	−	1.10264i	−0.111591	−	0.0477606i
$534$	−10.3604			−0.448339
$535$	−14.6942	−	16.5979i	−0.635287	−	0.717592i
$536$	1.22602	+	2.12352i	0.0529559	+	0.0917223i
$537$	4.95232	+	2.85922i	0.213708	+	0.123384i
$538$			15.3656i			0.662459i
$539$	7.40707	−	12.8294i	0.319045	−	0.552602i
$540$	1.16074	−	3.47282i	0.0499501	−	0.149446i
$541$	−11.0259			−0.474039			−0.237020	−	0.971505i	$-0.576171\pi$
$541$	−11.0259			−0.474039			−0.237020	+	0.971505i	$0.576171\pi$
$542$	−4.07958	−	2.35535i	−0.175233	−	0.101171i
$543$	4.37561	−	2.52626i	0.187775	−	0.108412i
$544$	6.24335	+	10.8138i	0.267681	+	0.463638i
$545$	−3.20175	−	15.7110i	−0.137148	−	0.672986i
$546$	3.03951	−	7.10171i	0.130079	−	0.303925i
$547$			6.51100i			0.278390i	0.990265	+	0.139195i	$0.0444515\pi$
$547$			6.51100i			0.278390i	−0.990265	+	0.139195i	$0.955548\pi$
$548$	−26.0688	+	15.0508i	−1.11360	+	0.642939i
$549$	1.46568	+	2.53863i	0.0625536	+	0.108346i
$550$	−7.81480	−	0.954393i	−0.333224	−	0.0406954i
$551$	−36.2581			−1.54465
$552$	3.13372	+	1.80926i	0.133380	+	0.0770070i
$553$	−45.8096	−	26.4482i	−1.94802	−	1.12469i
$554$	−11.7147			−0.497711
$555$	−8.93146	−	2.98520i	−0.379119	−	0.126715i
$556$	3.52942	+	6.11313i	0.149681	+	0.259254i
$557$	3.09063	−	1.78437i	0.130954	−	0.0756064i	−0.433092	−	0.901350i	$-0.642577\pi$
$557$	3.09063	−	1.78437i	0.130954	−	0.0756064i	0.564046	+	0.825743i	$0.309244\pi$
$558$		−	2.44222i		−	0.103387i
$559$	−0.814841	+	0.0975856i	−0.0344641	+	0.00412743i
$560$	−15.2563	+	3.10908i	−0.644697	+	0.131383i
$561$	2.93794	+	5.08866i	0.124040	+	0.214843i
$562$	−12.0569	+	6.96105i	−0.508590	+	0.293634i
$563$	−13.5374	−	7.81582i	−0.570533	−	0.329397i	0.186829	−	0.982392i	$-0.440179\pi$
$563$	−13.5374	−	7.81582i	−0.570533	−	0.329397i	−0.757362	+	0.652995i	$0.773512\pi$
$564$	5.15398			0.217022
$565$	4.92582	−	14.7376i	0.207231	−	0.620016i
$566$	7.79217	−	13.4964i	0.327529	−	0.567297i
$567$			3.55868i			0.149451i
$568$	−21.4983	−	12.4121i	−0.902050	−	0.520799i
$569$	−3.64767	−	6.31796i	−0.152918	−	0.264863i	0.779381	−	0.626551i	$-0.215534\pi$
$569$	−3.64767	−	6.31796i	−0.152918	−	0.264863i	−0.932299	+	0.361688i	$0.882201\pi$
$570$	−8.08129	+	7.15439i	−0.338488	+	0.299665i
$571$	−4.57292			−0.191371			−0.0956853	−	0.995412i	$-0.530504\pi$
$571$	−4.57292			−0.191371			−0.0956853	+	0.995412i	$0.530504\pi$
$572$	−12.3601	+	9.25636i	−0.516801	+	0.387028i
$573$		−	17.6550i		−	0.737549i
$574$	0.832594	+	1.44210i	0.0347518	+	0.0601919i
$575$	−4.96768	+	6.60123i	−0.207166	+	0.275290i
$576$	0.283595	−	0.491200i	0.0118164	−	0.0204667i
$577$		−	39.0134i		−	1.62415i	−0.583555	−	0.812074i	$-0.698339\pi$
$577$		−	39.0134i		−	1.62415i	0.583555	−	0.812074i	$-0.301661\pi$
$578$	6.23186	+	3.59797i	0.259211	+	0.149656i
$579$	1.83210	−	3.17329i	0.0761394	−	0.131877i
$580$	−3.30669	−	16.2260i	−0.137303	−	0.673747i
$581$	−20.8783	+	36.1622i	−0.866177	+	1.50026i
$582$	−6.38695	+	3.68751i	−0.264748	+	0.152852i
$583$	14.5508	−	8.40092i	0.602634	−	0.347931i
$584$	27.2322			1.12688
$585$	−7.65240	+	2.53788i	−0.316388	+	0.104928i
$586$	−2.41414			−0.0997274
$587$	−11.0611	+	6.38611i	−0.456539	+	0.263583i	−0.710588	−	0.703609i	$-0.751571\pi$
$587$	−11.0611	+	6.38611i	−0.456539	+	0.263583i	0.254049	+	0.967191i	$0.418238\pi$
$588$	8.03275	−	4.63771i	0.331265	−	0.191256i
$589$	16.2616	−	28.1659i	0.670048	−	1.16056i
$590$	16.5348	−	3.36962i	0.680726	−	0.138725i
$591$	−3.48412	+	6.03467i	−0.143317	+	0.248233i
$592$	−7.13634	−	4.12017i	−0.293302	−	0.169338i
$593$		−	2.51648i		−	0.103339i	−0.998664	−	0.0516697i	$-0.983546\pi$
$593$		−	2.51648i		−	0.103339i	0.998664	−	0.0516697i	$-0.0164543\pi$
$594$	−0.787287	+	1.36362i	−0.0323028	+	0.0559500i
$595$	13.3858	−	11.8505i	0.548762	−	0.485821i
$596$	−1.85171	−	3.20726i	−0.0758491	−	0.131375i
$597$		−	7.37992i		−	0.302040i
$598$	−0.426495	−	3.56124i	−0.0174407	−	0.145630i
$599$	−20.2305			−0.826594			−0.413297	−	0.910596i	$-0.635623\pi$
$599$	−20.2305			−0.826594			−0.413297	+	0.910596i	$0.635623\pi$
$600$	−8.74916	−	6.58407i	−0.357183	−	0.268794i
$601$	−22.2480	−	38.5346i	−0.907514	−	1.57186i	−0.817506	−	0.575920i	$-0.804644\pi$
$601$	−22.2480	−	38.5346i	−0.907514	−	1.57186i	−0.0900081	−	0.995941i	$-0.528689\pi$
$602$	0.422319	+	0.243826i	0.0172124	+	0.00993761i
$603$			1.11967i			0.0455966i
$604$	−6.98022	+	12.0901i	−0.284021	+	0.491939i
$605$	8.82181	+	2.94855i	0.358657	+	0.119876i
$606$	10.3779			0.421575
$607$	34.4077	+	19.8653i	1.39657	+	0.806307i	0.994031	−	0.109097i	$-0.0347961\pi$
$607$	34.4077	+	19.8653i	1.39657	+	0.806307i	0.402534	+	0.915405i	$0.368129\pi$
$608$	−38.5903	+	22.2801i	−1.56504	+	0.903578i
$609$	8.04689	+	13.9376i	0.326076	+	0.564781i
$610$	3.86674	−	0.788002i	0.156560	−	0.0319053i
$611$	−6.80239	−	9.08328i	−0.275195	−	0.367470i
$612$			3.67900i			0.148715i
$613$	−8.58710	+	4.95776i	−0.346830	+	0.200242i	−0.663288	−	0.748364i	$-0.730840\pi$
$613$	−8.58710	+	4.95776i	−0.346830	+	0.200242i	0.316458	+	0.948606i	$0.397506\pi$
$614$	−7.43329	−	12.8748i	−0.299983	−	0.519586i
$615$	0.550918	−	1.64830i	0.0222151	−	0.0664657i
$616$	20.3826			0.821240
$617$	−31.1563	−	17.9881i	−1.25431	−	0.724174i	−0.282344	−	0.959313i	$-0.591112\pi$
$617$	−31.1563	−	17.9881i	−1.25431	−	0.724174i	−0.971962	+	0.235140i	$0.924445\pi$
$618$	1.46454	+	0.845552i	0.0589124	+	0.0340131i
$619$	−30.5783			−1.22905			−0.614523	−	0.788899i	$-0.710651\pi$
$619$	−30.5783			−1.22905			−0.614523	+	0.788899i	$0.710651\pi$
$620$	14.0876	+	4.70858i	0.565773	+	0.189101i
$621$	0.826160	+	1.43095i	0.0331527	+	0.0574221i
$622$	6.12406	−	3.53573i	0.245552	−	0.141770i
$623$			61.2406i			2.45355i
$624$	−7.00471	+	0.838887i	−0.280413	+	0.0335824i
$625$	17.3431	−	18.0060i	0.693725	−	0.720240i
$626$	−1.85529	−	3.21345i	−0.0741522	−	0.128435i
$627$	−18.1595	+	10.4844i	−0.725219	+	0.418705i
$628$	9.27149	+	5.35290i	0.369973	+	0.213604i
$629$	9.46173			0.377264
$630$	4.54366	+	1.51865i	0.181024	+	0.0605044i
$631$	13.8644	−	24.0138i	0.551933	−	0.955976i	−0.446202	−	0.894932i	$-0.647224\pi$
$631$	13.8644	−	24.0138i	0.551933	−	0.955976i	0.998135	−	0.0610440i	$-0.0194430\pi$
$632$		−	32.5516i		−	1.29483i
$633$	−21.3072	−	12.3017i	−0.846887	−	0.488950i
$634$	3.90373	+	6.76146i	0.155037	+	0.268532i
$635$	−8.68939	−	9.81516i	−0.344828	−	0.389503i
$636$	10.5200			0.417144
$637$	−18.7753	−	8.03576i	−0.743904	−	0.318388i
$638$			7.12084i			0.281917i
$639$	−5.66772	−	9.81678i	−0.224212	−	0.388346i
$640$	−16.9820	−	19.1822i	−0.671274	−	0.758241i
$641$	−1.61226	+	2.79251i	−0.0636803	+	0.110297i	−0.896108	−	0.443836i	$-0.853617\pi$
$641$	−1.61226	+	2.79251i	−0.0636803	+	0.110297i	0.832428	+	0.554134i	$0.186950\pi$
$642$			5.96850i			0.235558i
$643$	5.46209	+	3.15354i	0.215404	+	0.124363i	0.603820	−	0.797121i	$-0.293644\pi$
$643$	5.46209	+	3.15354i	0.215404	+	0.124363i	−0.388417	+	0.921484i	$0.626978\pi$
$644$	4.81445	−	8.33887i	0.189716	−	0.328598i
$645$	−0.101631	−	0.498704i	−0.00400171	−	0.0196364i
$646$	5.42215	−	9.39143i	0.213332	−	0.369501i
$647$	10.6571	−	6.15288i	0.418974	−	0.241895i	−0.275664	−	0.961254i	$-0.588898\pi$
$647$	10.6571	−	6.15288i	0.418974	−	0.241895i	0.694638	+	0.719359i	$0.255564\pi$
$648$	−1.89656	+	1.09498i	−0.0745039	+	0.0430148i
$649$	32.7837			1.28687
$650$	−0.0253076	+	10.8535i	−0.000992645	+	0.425707i
$651$	−14.4360			−0.565790
$652$	29.2572	−	16.8916i	1.14580	−	0.661527i
$653$	12.8047	−	7.39280i	0.501087	−	0.289302i	−0.228076	−	0.973643i	$-0.573243\pi$
$653$	12.8047	−	7.39280i	0.501087	−	0.289302i	0.729162	+	0.684341i	$0.239910\pi$
$654$	−2.15850	+	3.73864i	−0.0844042	+	0.146192i
$655$	4.47118	+	21.9401i	0.174703	+	0.857271i
$656$	0.760375	−	1.31701i	0.0296876	−	0.0514205i
$657$	10.7691	+	6.21751i	0.420141	+	0.242568i
$658$			6.74321i			0.262878i
$659$	−5.20958	+	9.02326i	−0.202937	+	0.351496i	−0.949473	−	0.313848i	$-0.898382\pi$
$659$	−5.20958	+	9.02326i	−0.202937	+	0.351496i	0.746537	+	0.665344i	$0.231715\pi$
$660$	−6.34801	−	7.17043i	−0.247096	−	0.279109i
$661$	−1.78786	−	3.09666i	−0.0695396	−	0.120446i	0.829159	−	0.559013i	$-0.188820\pi$
$661$	−1.78786	−	3.09666i	−0.0695396	−	0.120446i	−0.898699	+	0.438567i	$0.855486\pi$
$662$		−	6.51108i		−	0.253060i
$663$	6.48380	−	4.85567i	0.251810	−	0.188578i
$664$	−25.6963			−0.997211
$665$	42.2897	+	47.7686i	1.63993	+	1.85239i
$666$	1.26774	+	2.19579i	0.0491240	+	0.0850853i
$667$	6.47133	+	3.73622i	0.250571	+	0.144667i
$668$			31.4218i			1.21575i
$669$	0.277446	−	0.480551i	0.0107267	−	0.0185792i
$670$	1.42957	+	0.477814i	0.0552293	+	0.0184595i
$671$	7.66661			0.295966
$672$	17.1289	+	9.88940i	0.660763	+	0.381492i
$673$	4.62917	−	2.67265i	0.178441	−	0.103023i	−0.408119	−	0.912929i	$-0.633815\pi$
$673$	4.62917	−	2.67265i	0.178441	−	0.103023i	0.586560	+	0.809906i	$0.300482\pi$
$674$	−1.15655	−	2.00321i	−0.0445488	−	0.0771607i
$675$	−1.95664	−	4.60126i	−0.0753111	−	0.177102i
$676$	14.6964	+	15.4012i	0.565246	+	0.592355i
$677$		−	30.1981i		−	1.16061i	−0.814400	−	0.580304i	$-0.802934\pi$
$677$		−	30.1981i		−	1.16061i	0.814400	−	0.580304i	$-0.197066\pi$
$678$	−3.62323	+	2.09188i	−0.139149	+	0.0803380i
$679$	21.7969	+	37.7534i	0.836489	+	1.44884i
$680$	10.4343	+	3.48749i	0.400135	+	0.133739i
$681$	−1.51189			−0.0579358
$682$	−5.53159	−	3.19367i	−0.211816	−	0.122292i
$683$	3.35693	+	1.93812i	0.128449	+	0.0741602i	0.562848	−	0.826561i	$-0.309706\pi$
$683$	3.35693	+	1.93812i	0.128449	+	0.0741602i	−0.434399	+	0.900721i	$0.643039\pi$
$684$	−13.1289			−0.501998
$685$	−13.0298	+	38.9839i	−0.497843	+	1.48950i
$686$	−1.43093	−	2.47845i	−0.0546333	−	0.0946276i
$687$	4.69613	−	2.71131i	0.179169	−	0.103443i
$688$		−	0.445353i		−	0.0169789i
$689$	−13.8846	−	18.5402i	−0.528961	−	0.706325i
$690$	2.17957	−	0.444175i	0.0829748	−	0.0169094i
$691$	19.4333	+	33.6594i	0.739277	+	1.28046i	0.952821	+	0.303532i	$0.0981658\pi$
$691$	19.4333	+	33.6594i	0.739277	+	1.28046i	−0.213545	+	0.976933i	$0.568501\pi$
$692$	−27.3481	+	15.7894i	−1.03962	+	0.600223i
$693$	8.06038	+	4.65366i	0.306188	+	0.176778i
$694$	−7.03512			−0.267049
$695$	9.14173	+	3.05548i	0.346766	+	0.115901i
$696$	−4.95193	+	8.57699i	−0.187702	+	0.325110i
$697$			1.74616i			0.0661405i
$698$	−0.847642	−	0.489386i	−0.0320837	−	0.0185235i
$699$	5.62648	+	9.74535i	0.212813	+	0.368603i
$700$	−17.5203	+	23.2816i	−0.662205	+	0.879962i
$701$	18.2792			0.690396			0.345198	−	0.938530i	$-0.387812\pi$
$701$	18.2792			0.690396			0.345198	+	0.938530i	$0.387812\pi$
$702$	1.99560	+	0.854110i	0.0753191	+	0.0322363i
$703$			33.7653i			1.27348i
$704$	−0.741709	−	1.28468i	−0.0279542	−	0.0484181i
$705$	5.26946	−	4.66507i	0.198459	−	0.175697i
$706$	−2.74750	+	4.75881i	−0.103403	+	0.179100i
$707$		−	61.3441i		−	2.30708i
$708$	17.7765	+	10.2633i	0.668081	+	0.385717i
$709$	3.19243	−	5.52946i	0.119894	−	0.207663i	−0.799831	−	0.600225i	$-0.795078\pi$
$709$	3.19243	−	5.52946i	0.119894	−	0.207663i	0.919726	+	0.392562i	$0.128411\pi$
$710$	−14.9525	+	3.04718i	−0.561159	+	0.114359i
$711$	7.43202	−	12.8726i	0.278723	−	0.482762i
$712$	−32.6375	+	18.8433i	−1.22314	+	0.706181i
$713$	−5.80472	+	3.35136i	−0.217389	+	0.125509i
$714$	−4.81342			−0.180138
$715$	−4.25872	+	20.6514i	−0.159267	+	0.772317i
$716$	9.36420			0.349957
$717$	15.5262	−	8.96406i	0.579837	−	0.334769i
$718$	12.4278	−	7.17519i	0.463801	−	0.267776i
$719$	−7.18151	+	12.4387i	−0.267825	+	0.463887i	−0.968300	−	0.249790i	$-0.919638\pi$
$719$	−7.18151	+	12.4387i	−0.267825	+	0.463887i	0.700475	+	0.713677i	$0.252972\pi$
$720$	−0.873661	−	4.28706i	−0.0325594	−	0.159769i
$721$	4.99807	−	8.65691i	0.186138	−	0.322400i
$722$	23.6081	+	13.6301i	0.878603	+	0.507262i
$723$		−	20.3351i		−	0.756270i
$724$	4.13686	−	7.16526i	0.153745	−	0.266295i
$725$	−18.0675	−	13.5965i	−0.671012	−	0.504962i
$726$	−1.25218	−	2.16884i	−0.0464727	−	0.0804931i
$727$		−	12.8444i		−	0.476372i	−0.971220	−	0.238186i	$-0.923447\pi$
$727$		−	12.8444i		−	0.476372i	0.971220	−	0.238186i	$-0.0765528\pi$
$728$	−3.34132	−	27.9000i	−0.123837	−	1.03404i
$729$	−1.00000			−0.0370370
$730$	12.5340	−	11.0964i	0.463905	−	0.410697i
$731$	0.255682	+	0.442855i	0.00945675	+	0.0163796i
$732$	4.15711	+	2.40011i	0.153651	+	0.0887106i
$733$		−	3.30801i		−	0.122184i	−0.998132	−	0.0610922i	$-0.980542\pi$
$733$		−	3.30801i		−	0.122184i	0.998132	−	0.0610922i	$-0.0194584\pi$
$734$	5.10918	−	8.84935i	0.188583	−	0.326636i
$735$	4.01496	−	12.0124i	0.148094	−	0.443084i
$736$	9.18343			0.338506
$737$	2.53604	+	1.46419i	0.0934164	+	0.0539340i
$738$	−0.405233	+	0.233961i	−0.0149168	+	0.00861223i
$739$	−1.95497	−	3.38611i	−0.0719147	−	0.124560i	0.827826	−	0.560985i	$-0.189578\pi$
$739$	−1.95497	−	3.38611i	−0.0719147	−	0.124560i	−0.899740	+	0.436425i	$0.856244\pi$
$740$	−15.1104	+	3.07935i	−0.555469	+	0.113199i
$741$	17.3280	+	23.1382i	0.636560	+	0.850003i
$742$			13.7638i			0.505285i
$743$	30.5991	−	17.6664i	1.12257	−	0.648116i	0.180515	−	0.983572i	$-0.442224\pi$
$743$	30.5991	−	17.6664i	1.12257	−	0.648116i	0.942056	+	0.335456i	$0.108890\pi$
$744$	−4.44183	−	7.69348i	−0.162846	−	0.282057i
$745$	−4.79622	−	1.60306i	−0.175720	−	0.0587317i
$746$	9.57721			0.350647
$747$	−10.1617	−	5.86686i	−0.371797	−	0.214657i
$748$	8.33290	+	4.81100i	0.304681	+	0.175908i
$749$	35.2799			1.28910
$750$	−6.70978	+	0.534640i	−0.245006	+	0.0195223i
$751$	1.57264	+	2.72389i	0.0573864	+	0.0993962i	0.893291	−	0.449478i	$-0.148390\pi$
$751$	1.57264	+	2.72389i	0.0573864	+	0.0993962i	−0.835905	+	0.548874i	$0.815057\pi$
$752$	5.33324	−	3.07915i	0.194483	−	0.112285i
$753$			18.8501i			0.686936i
$754$	9.74710	−	1.16732i	0.354968	−	0.0425111i
$755$	3.80661	+	18.6791i	0.138537	+	0.679800i
$756$	2.91375	+	5.04676i	0.105972	+	0.183549i
$757$	18.0555	−	10.4244i	0.656240	−	0.378880i	−0.134603	−	0.990900i	$-0.542976\pi$
$757$	18.0555	−	10.4244i	0.656240	−	0.378880i	0.790843	+	0.612019i	$0.209643\pi$
$758$	−10.8534	−	6.26623i	−0.394215	−	0.227600i
$759$	4.32145			0.156859
$760$	−12.4455	+	37.2358i	−0.451446	+	1.35069i
$761$	22.2187	−	38.4839i	0.805427	−	1.39504i	−0.110576	−	0.993868i	$-0.535269\pi$
$761$	22.2187	−	38.4839i	0.805427	−	1.39504i	0.916002	−	0.401173i	$-0.131397\pi$
$762$			3.52946i			0.127859i
$763$	22.0991	+	12.7589i	0.800042	+	0.461905i
$764$	−14.4554	−	25.0376i	−0.522979	−	0.905827i
$765$	3.33001	+	3.76143i	0.120397	+	0.135995i
$766$	−14.5118			−0.524332
$767$	−5.37421	−	44.8747i	−0.194051	−	1.62033i
$768$			5.76339i			0.207968i
$769$	−11.8333	−	20.4959i	−0.426719	−	0.739100i	0.569860	−	0.821742i	$-0.306997\pi$
$769$	−11.8333	−	20.4959i	−0.426719	−	0.739100i	−0.996579	+	0.0826421i	$0.973664\pi$
$770$	9.38142	−	8.30541i	0.338083	−	0.299306i
$771$	14.1924	−	24.5820i	0.511127	−	0.885298i
$772$		−	6.00029i		−	0.215955i
$773$	16.4540	+	9.49970i	0.591808	+	0.341680i	0.765812	−	0.643064i	$-0.222337\pi$
$773$	16.4540	+	9.49970i	0.591808	+	0.341680i	−0.174004	+	0.984745i	$0.555671\pi$
$774$	−0.0685158	+	0.118673i	−0.00246275	+	0.00426561i
$775$	18.6652	−	7.93721i	0.670474	−	0.285113i
$776$	−13.4135	+	23.2328i	−0.481516	+	0.834010i
$777$	12.9794	−	7.49364i	0.465632	−	0.268833i
$778$	−9.17871	+	5.29933i	−0.329073	+	0.189990i
$779$	−6.23137			−0.223262
$780$	−8.77434	+	9.86467i	−0.314172	+	0.353212i
$781$	−29.6465			−1.06084
$782$	−1.93548	+	1.11745i	−0.0692127	+	0.0399600i
$783$	−3.91651	+	2.26120i	−0.139965	+	0.0808086i
$784$	5.54143	−	9.59804i	0.197908	−	0.342787i
$785$	14.3244	−	2.91916i	0.511258	−	0.104189i
$786$	3.01431	−	5.22093i	0.107517	−	0.186224i
$787$	38.0294	+	21.9563i	1.35560	+	0.782657i	0.989027	−	0.147732i	$-0.0471972\pi$
$787$	38.0294	+	21.9563i	1.35560	+	0.782657i	0.366574	+	0.930389i	$0.380531\pi$
$788$			11.4108i			0.406493i
$789$	7.13372	−	12.3560i	0.253967	−	0.439884i
$790$	−13.2640	−	14.9824i	−0.471910	−	0.533049i
$791$	12.3651	+	21.4170i	0.439652	+	0.761500i
$792$			5.72758i			0.203521i
$793$	−1.25678	−	10.4942i	−0.0446297	−	0.372658i
$794$	−7.75829			−0.275332
$795$	10.7557	−	9.52204i	0.381465	−	0.337712i
$796$	−6.04247	−	10.4659i	−0.214170	−	0.370953i
$797$	16.1870	+	9.34557i	0.573373	+	0.331037i	0.758495	−	0.651678i	$-0.225935\pi$
$797$	16.1870	+	9.34557i	0.573373	+	0.331037i	−0.185122	+	0.982715i	$0.559268\pi$
$798$		−	17.1772i		−	0.608068i
$799$	−3.53555	+	6.12375i	−0.125079	+	0.216643i
$800$	−27.5845	−	3.36880i	−0.975261	−	0.119105i
$801$	−17.2088			−0.608042
$802$	−8.30214	−	4.79324i	−0.293159	−	0.169255i
$803$	28.1652	−	16.2612i	0.993928	−	0.573845i
$804$	0.916756	+	1.58787i	0.0323315	+	0.0559998i
$805$	−2.62552	−	12.8835i	−0.0925375	−	0.454082i
$806$	−3.46474	+	8.09525i	−0.122040	+	0.285143i
$807$			25.5225i			0.898434i
$808$	32.6926	−	18.8751i	1.15012	−	0.664023i
$809$	8.01688	+	13.8856i	0.281859	+	0.488193i	0.971843	−	0.235631i	$-0.0757158\pi$
$809$	8.01688	+	13.8856i	0.281859	+	0.488193i	−0.689984	+	0.723825i	$0.742382\pi$
$810$	−0.426744	+	1.27678i	−0.0149943	+	0.0448615i
$811$	−46.1871			−1.62185			−0.810923	−	0.585152i	$-0.801035\pi$
$811$	−46.1871			−1.62185			−0.810923	+	0.585152i	$0.801035\pi$
$812$	22.8235	+	13.1771i	0.800947	+	0.462427i
$813$	−6.77623	−	3.91226i	−0.237653	−	0.137209i
$814$	6.63127			0.232426
$815$	14.6234	−	43.7519i	0.512236	−	1.53256i
$816$	2.19795	+	3.80696i	0.0769437	+	0.133270i
$817$	−1.58038	+	0.912431i	−0.0552904	+	0.0319219i
$818$			2.63196i			0.0920243i
$819$	5.04866	−	11.7960i	0.176414	−	0.412186i
$820$	−0.568292	−	2.78862i	−0.0198456	−	0.0973827i
$821$	−14.8976	−	25.8033i	−0.519929	−	0.900543i	−0.999732	−	0.0231666i	$-0.992625\pi$
$821$	−14.8976	−	25.8033i	−0.519929	−	0.900543i	0.479803	−	0.877376i	$-0.340708\pi$
$822$	9.58418	−	5.53343i	0.334287	−	0.193001i
$823$	−45.0733	−	26.0231i	−1.57116	−	0.907108i	−0.996028	−	0.0890459i	$-0.971618\pi$
$823$	−45.0733	−	26.0231i	−1.57116	−	0.907108i	−0.575130	−	0.818062i	$-0.695048\pi$
$824$	6.15147			0.214296
$825$	−12.9805	−	1.58526i	−0.451922	−	0.0551916i
$826$	−13.4279	+	23.2578i	−0.467217	+	0.809244i
$827$			12.1419i			0.422215i	0.977463	+	0.211108i	$0.0677071\pi$
$827$			12.1419i			0.422215i	−0.977463	+	0.211108i	$0.932293\pi$
$828$	2.34325	+	1.35287i	0.0814334	+	0.0470156i
$829$	−10.2500	−	17.7535i	−0.355997	−	0.616604i	0.631291	−	0.775546i	$-0.282525\pi$
$829$	−10.2500	−	17.7535i	−0.355997	−	0.616604i	−0.987288	+	0.158941i	$0.949192\pi$
$830$	−11.8271	+	10.4706i	−0.410526	+	0.363440i
$831$	−19.4583			−0.675001
$832$	−1.63689	+	1.22586i	−0.0567491	+	0.0424989i
$833$			12.7256i			0.440915i
$834$	−1.29759	−	2.24749i	−0.0449318	−	0.0778242i
$835$	28.4411	+	32.1258i	0.984246	+	1.11176i
$836$	−17.1686	+	29.7369i	−0.593789	+	1.02847i
$837$		−	4.05655i		−	0.140215i
$838$	−4.70821	−	2.71829i	−0.162642	−	0.0939016i
$839$	−9.41471	+	16.3068i	−0.325032	+	0.562972i	−0.981519	−	0.191366i	$-0.938708\pi$
$839$	−9.41471	+	16.3068i	−0.325032	+	0.562972i	0.656487	+	0.754337i	$0.272042\pi$
$840$	17.0755	−	3.47982i	0.589162	−	0.120065i
$841$	4.27397	−	7.40274i	0.147378	−	0.255267i
$842$	−8.23407	+	4.75394i	−0.283765	+	0.163832i
$843$	−20.0266	+	11.5624i	−0.689754	+	0.398230i
$844$	−40.2893			−1.38681
$845$	28.9660	+	2.44402i	0.996459	+	0.0840769i
$846$	−1.89486			−0.0651466
$847$	−12.8200	+	7.40164i	−0.440501	+	0.254323i
$848$	10.8859	−	6.28496i	0.373822	−	0.215826i
$849$	12.9429	−	22.4177i	0.444199	−	0.769374i
$850$	6.22359	−	2.64652i	0.213467	−	0.0907750i
$851$	3.47935	−	6.02641i	0.119271	−	0.206583i
$852$	−16.0754	−	9.28114i	−0.550735	−	0.317967i
$853$		−	27.6509i		−	0.946748i	−0.880861	−	0.473374i	$-0.843036\pi$
$853$		−	27.6509i		−	0.946748i	0.880861	−	0.473374i	$-0.156964\pi$
$854$	−3.14018	+	5.43896i	−0.107455	+	0.186117i
$855$	−13.4231	+	11.8835i	−0.459061	+	0.406408i
$856$	10.8553	+	18.8020i	0.371028	+	0.642639i
$857$			35.5356i			1.21387i	0.794751	+	0.606936i	$0.207601\pi$
$857$			35.5356i			1.21387i	−0.794751	+	0.606936i	$0.792399\pi$
$858$	4.54418	−	3.40310i	0.155136	−	0.116180i
$859$	−14.8039			−0.505101			−0.252550	−	0.967584i	$-0.581269\pi$
$859$	−14.8039			−0.505101			−0.252550	+	0.967584i	$0.581269\pi$
$860$	−0.552453	−	0.624026i	−0.0188385	−	0.0212791i
$861$	1.38295	+	2.39534i	0.0471307	+	0.0816328i
$862$	2.53451	+	1.46330i	0.0863258	+	0.0498402i
$863$			37.6157i			1.28045i	0.768187	+	0.640226i	$0.221159\pi$
$863$			37.6157i			1.28045i	−0.768187	+	0.640226i	$0.778841\pi$
$864$	−2.77895	+	4.81328i	−0.0945417	+	0.163751i
$865$	−13.6692	+	40.8970i	−0.464767	+	1.39054i
$866$	−1.85534			−0.0630469
$867$	10.3512	+	5.97626i	0.351545	+	0.202965i
$868$	−20.4724	+	11.8198i	−0.694880	+	0.401189i
$869$	−19.4376	−	33.6669i	−0.659375	−	1.14207i
$870$	1.21570	+	5.96547i	0.0412162	+	0.202248i
$871$	1.58846	−	3.71139i	0.0538230	−	0.125756i
$872$			15.7033i			0.531781i
$873$	−10.6088	+	6.12499i	−0.359054	+	0.207300i
$874$	−3.98775	−	6.90699i	−0.134888	−	0.233633i
$875$	3.16026	+	39.6616i	0.106836	+	1.34081i
$876$	20.3629			0.687999
$877$	−1.18072	−	0.681691i	−0.0398702	−	0.0230191i	0.479932	−	0.877305i	$-0.340661\pi$
$877$	−1.18072	−	0.681691i	−0.0398702	−	0.0230191i	−0.519803	+	0.854286i	$0.673995\pi$
$878$	−2.00332	−	1.15662i	−0.0676088	−	0.0390340i
$879$	−4.00992			−0.135251
$880$	−10.8526	−	3.62733i	−0.365842	−	0.122277i
$881$	24.0121	+	41.5901i	0.808987	+	1.40121i	0.913566	+	0.406690i	$0.133317\pi$
$881$	24.0121	+	41.5901i	0.808987	+	1.40121i	−0.104580	+	0.994517i	$0.533350\pi$
$882$	−2.95324	+	1.70505i	−0.0994408	+	0.0574121i
$883$		−	26.6427i		−	0.896597i	−0.893884	−	0.448299i	$-0.852030\pi$
$883$		−	26.6427i		−	0.896597i	0.893884	−	0.448299i	$-0.147970\pi$
$884$	5.21935	−	12.1948i	0.175546	−	0.410157i
$885$	27.4645	−	5.59698i	0.923208	−	0.188141i
$886$	2.22884	+	3.86047i	0.0748795	+	0.129695i
$887$	15.7414	−	9.08828i	0.528543	−	0.305155i	−0.211880	−	0.977296i	$-0.567958\pi$
$887$	15.7414	−	9.08828i	0.528543	−	0.305155i	0.740423	+	0.672141i	$0.234625\pi$
$888$	7.98730	+	4.61147i	0.268036	+	0.154751i
$889$	20.8627			0.699712
$890$	−7.34375	+	21.9718i	−0.246163	+	0.736497i
$891$	−1.30769	+	2.26499i	−0.0438093	+	0.0758800i
$892$		−	0.908661i		−	0.0304242i
$893$	−21.8533	−	12.6170i	−0.731293	−	0.422212i
$894$	0.680782	+	1.17915i	0.0227688	+	0.0394366i
$895$	9.57402	−	8.47591i	0.320024	−	0.283318i
$896$	40.7728			1.36212
$897$	−0.708413	−	5.91526i	−0.0236532	−	0.197505i
$898$		−	14.8427i		−	0.495308i
$899$	−9.17266	−	15.8875i	−0.305925	−	0.529878i
$900$	−6.54220	−	4.92325i	−0.218073	−	0.164108i
$901$	−7.21653	+	12.4994i	−0.240418	+	0.416415i
$902$			1.22380i			0.0407480i
$903$	0.701477	+	0.404998i	0.0233437	+	0.0134775i
$904$	−7.60929	+	13.1797i	−0.253081	+	0.438349i
$905$	−2.25601	−	11.0702i	−0.0749922	−	0.367987i
$906$	2.56628	−	4.44492i	0.0852588	−	0.147673i
$907$	−23.7753	+	13.7267i	−0.789447	+	0.455787i	−0.839768	−	0.542946i	$-0.817309\pi$
$907$	−23.7753	+	13.7267i	−0.789447	+	0.455787i	0.0503208	+	0.998733i	$0.483976\pi$
$908$	−2.14410	+	1.23789i	−0.0711543	+	0.0410810i
$909$	17.2379			0.571744
$910$	−12.9064	−	11.4799i	−0.427844	−	0.380555i
$911$	52.6351			1.74388			0.871939	−	0.489615i	$-0.162863\pi$
$911$	52.6351			1.74388			0.871939	+	0.489615i	$0.162863\pi$
$912$	−13.5856	+	7.84364i	−0.449864	+	0.259729i
$913$	−26.5767	+	15.3441i	−0.879561	+	0.507815i
$914$	8.65254	−	14.9866i	0.286201	−	0.495714i
$915$	6.42269	−	1.30888i	0.212328	−	0.0432703i
$916$	4.43990	−	7.69013i	0.146698	−	0.254089i
$917$	−30.8610	−	17.8176i	−1.01912	−	0.588389i
$918$		−	1.35258i		−	0.0446419i
$919$	13.0246	−	22.5593i	0.429642	−	0.744161i	−0.567200	−	0.823580i	$-0.691973\pi$
$919$	13.0246	−	22.5593i	0.429642	−	0.744161i	0.996841	+	0.0794191i	$0.0253065\pi$
$920$	6.05824	−	5.36338i	0.199734	−	0.176825i
$921$	−12.3468	−	21.3852i	−0.406840	−	0.704668i
$922$		−	2.39623i		−	0.0789156i
$923$	4.85994	+	40.5805i	0.159967	+	1.33572i
$924$	15.2412			0.501397
$925$	−12.6617	+	16.8254i	−0.416315	+	0.553215i
$926$	−3.94926	−	6.84033i	−0.129781	−	0.224787i
$927$	2.43262	+	1.40447i	0.0798976	+	0.0461289i
$928$			25.1350i			0.825097i
$929$	7.32957	−	12.6952i	0.240475	−	0.416516i	−0.720374	−	0.693585i	$-0.756030\pi$
$929$	7.32957	−	12.6952i	0.240475	−	0.416516i	0.960850	+	0.277070i	$0.0893633\pi$
$930$	−5.17932	−	1.73111i	−0.169837	−	0.0567653i
$931$	−45.4127			−1.48834
$932$	15.9584	+	9.21361i	0.522736	+	0.301802i
$933$	10.1721	−	5.87288i	0.333021	−	0.192270i
$934$	3.58649	+	6.21198i	0.117353	+	0.203262i
$935$	12.8742	−	2.62364i	0.421033	−	0.0858023i
$936$	7.83998	−	0.938919i	0.256258	−	0.0306895i
$937$		−	58.6364i		−	1.91557i	−0.287489	−	0.957784i	$-0.592821\pi$
$937$		−	58.6364i		−	1.91557i	0.287489	−	0.957784i	$-0.407179\pi$
$938$	−2.07749	+	1.19944i	−0.0678323	+	0.0391630i
$939$	−3.08165	−	5.33758i	−0.100566	−	0.174185i
$940$	3.65328	−	10.9303i	0.119157	−	0.356507i
$941$	−23.6082			−0.769604			−0.384802	−	0.922999i	$-0.625730\pi$
$941$	−23.6082			−0.769604			−0.384802	+	0.922999i	$0.625730\pi$
$942$	−3.40866	−	1.96799i	−0.111060	−	0.0641206i
$943$	1.11217	+	0.642112i	0.0362173	+	0.0209100i
$944$	24.5264			0.798265
$945$	7.54706	+	2.52249i	0.245506	+	0.0820566i
$946$	0.179195	+	0.310375i	0.00582614	+	0.0100912i
$947$	0.455045	−	0.262720i	0.0147870	−	0.00853726i	−0.492588	−	0.870262i	$-0.663949\pi$
$947$	0.455045	−	0.262720i	0.0147870	−	0.00853726i	0.507375	+	0.861725i	$0.330616\pi$
$948$		−	24.3405i		−	0.790544i
$949$	−26.8756	−	35.8872i	−0.872419	−	1.16495i
$950$	9.44442	+	22.2096i	0.306417	+	0.720574i
$951$	6.48414	+	11.2309i	0.210263	+	0.364186i
$952$	−15.1633	+	8.75452i	−0.491444	+	0.283735i
$953$	−23.0586	−	13.3129i	−0.746942	−	0.431247i	0.0776460	−	0.996981i	$-0.475260\pi$
$953$	−23.0586	−	13.3129i	−0.746942	−	0.431247i	−0.824588	+	0.565734i	$0.808593\pi$
$954$	−3.86767			−0.125220
$955$	−37.4418	−	12.5144i	−1.21159	−	0.404955i
$956$	14.6790	−	25.4249i	0.474754	−	0.822299i
$957$			11.8278i			0.382338i
$958$	−21.5030	−	12.4147i	−0.694729	−	0.401102i
$959$	−32.7082	−	56.6522i	−1.05620	−	1.82940i
$960$	−0.840691	−	0.949608i	−0.0271332	−	0.0306485i
$961$	−14.5444			−0.469175
$962$	−1.08706	−	9.07696i	−0.0350482	−	0.292653i
$963$			9.91375i			0.319466i
$964$	−16.6498	−	28.8383i	−0.536254	−	0.928819i
$965$	−5.43110	−	6.13473i	−0.174833	−	0.197484i
$966$	−1.77003	+	3.06578i	−0.0569498	+	0.0986400i
$967$			21.7977i			0.700967i	0.936569	+	0.350484i	$0.113983\pi$
$967$			21.7977i			0.700967i	−0.936569	+	0.350484i	$0.886017\pi$
$968$	−7.88924	−	4.55485i	−0.253570	−	0.146399i
$969$	9.00625	−	15.5993i	0.289322	−	0.501121i
$970$	3.29303	+	16.1589i	0.105733	+	0.518831i
$971$	−17.6354	+	30.5454i	−0.565946	+	0.980248i	0.431015	+	0.902345i	$0.358156\pi$
$971$	−17.6354	+	30.5454i	−0.565946	+	0.980248i	−0.996961	+	0.0779030i	$0.975178\pi$
$972$	−1.41816	+	0.818772i	−0.0454873	+	0.0262621i
$973$	−13.2849	+	7.67007i	−0.425896	+	0.245891i
$974$	−8.72032			−0.279417
$975$	−0.0420362	+	18.0277i	−0.00134624	+	0.577349i
$976$	5.73560			0.183592
$977$	−21.2906	+	12.2921i	−0.681147	+	0.393261i	−0.800287	−	0.599617i	$-0.795320\pi$
$977$	−21.2906	+	12.2921i	−0.681147	+	0.393261i	0.119140	+	0.992877i	$0.461986\pi$
$978$	−10.7564	+	6.21020i	−0.343951	+	0.198580i
$979$	−22.5038	+	38.9777i	−0.719224	+	1.24573i
$980$	−4.14158	−	20.3228i	−0.132298	−	0.649187i
$981$	−3.58530	+	6.20992i	−0.114470	+	0.198267i
$982$	9.22016	+	5.32326i	0.294227	+	0.169872i
$983$		−	35.5716i		−	1.13456i	−0.823526	−	0.567279i	$-0.807996\pi$
$983$		−	35.5716i		−	1.13456i	0.823526	−	0.567279i	$-0.192004\pi$
$984$	−0.851044	+	1.47405i	−0.0271303	+	0.0469911i
$985$	10.3284	+	11.6665i	0.329089	+	0.371724i
$986$	−3.05846	−	5.29741i	−0.0974012	−	0.168704i
$987$			11.2005i			0.356517i
$988$	43.5187	+	18.6259i	1.38451	+	0.592567i
$989$	0.376086			0.0119589
$990$	2.33384	+	2.63621i	0.0741744	+	0.0837841i
$991$	20.2390	+	35.0550i	0.642914	+	1.11356i	0.984779	+	0.173811i	$0.0556082\pi$
$991$	20.2390	+	35.0550i	0.642914	+	1.11356i	−0.341865	+	0.939749i	$0.611058\pi$
$992$	−19.5253	−	11.2729i	−0.619929	−	0.357916i
$993$		−	10.8150i		−	0.343203i
$994$	12.1430	−	21.0323i	0.385152	−	0.667103i
$995$	−15.6509	−	5.23108i	−0.496168	−	0.165836i
$996$	−19.2145			−0.608834
$997$	23.3429	+	13.4770i	0.739277	+	0.426822i	0.821806	−	0.569767i	$-0.192967\pi$
$997$	23.3429	+	13.4770i	0.739277	+	0.426822i	−0.0825297	+	0.996589i	$0.526300\pi$
$998$	−0.360159	+	0.207938i	−0.0114006	+	0.00658216i
$999$	2.10574	+	3.64724i	0.0666225	+	0.115394i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	195.2.ba.a.94.6	✓	24
3.2	odd	2		585.2.bs.b.289.7		24
5.2	odd	4		975.2.i.q.601.3		12
5.3	odd	4		975.2.i.o.601.4		12
5.4	even	2	inner	195.2.ba.a.94.7	yes	24
13.9	even	3	inner	195.2.ba.a.139.7	yes	24
15.14	odd	2		585.2.bs.b.289.6		24
39.35	odd	6		585.2.bs.b.334.6		24
65.9	even	6	inner	195.2.ba.a.139.6	yes	24
65.22	odd	12		975.2.i.q.451.3		12
65.48	odd	12		975.2.i.o.451.4		12
195.74	odd	6		585.2.bs.b.334.7		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
195.2.ba.a.94.6	✓	24	1.1	even	1	trivial
195.2.ba.a.94.7	yes	24	5.4	even	2	inner
195.2.ba.a.139.6	yes	24	65.9	even	6	inner
195.2.ba.a.139.7	yes	24	13.9	even	3	inner
585.2.bs.b.289.6		24	15.14	odd	2
585.2.bs.b.289.7		24	3.2	odd	2
585.2.bs.b.334.6		24	39.35	odd	6
585.2.bs.b.334.7		24	195.74	odd	6
975.2.i.o.451.4		12	65.48	odd	12
975.2.i.o.601.4		12	5.3	odd	4
975.2.i.q.451.3		12	65.22	odd	12
975.2.i.q.601.3		12	5.2	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.ba (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.521384 + 0.301021i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(-0.818772 + 1.41816i) q^{4} +(0.446511 + 2.19103i) q^{5} +(0.301021 - 0.521384i) q^{6} +(-3.08191 - 1.77934i) q^{7} -2.18996i q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(-0.521384 + 0.301021i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(-0.818772 + 1.41816i) q^{4} +(0.446511 + 2.19103i) q^{5} +(0.301021 - 0.521384i) q^{6} +(-3.08191 - 1.77934i) q^{7} -2.18996i q^{8} +(0.500000 - 0.866025i) q^{9} +(-0.892352 - 1.00796i) q^{10} +(-1.30769 - 2.26499i) q^{11} -1.63754i q^{12} +(-2.88598 + 2.16128i) q^{13} +2.14248 q^{14} +(-1.48221 - 1.67424i) q^{15} +(-0.978320 - 1.69450i) q^{16} +(1.94566 + 1.12333i) q^{17} +0.602043i q^{18} +(-4.00873 + 6.94332i) q^{19} +(-3.47282 - 1.16074i) q^{20} +3.55868 q^{21} +(1.36362 + 0.787287i) q^{22} +(1.43095 - 0.826160i) q^{23} +(1.09498 + 1.89656i) q^{24} +(-4.60126 + 1.95664i) q^{25} +(0.854110 - 1.99560i) q^{26} +1.00000i q^{27} +(5.04676 - 2.91375i) q^{28} +(2.26120 + 3.91651i) q^{29} +(1.27678 + 0.426744i) q^{30} -4.05655 q^{31} +(4.81328 + 2.77895i) q^{32} +(2.26499 + 1.30769i) q^{33} -1.35258 q^{34} +(2.52249 - 7.54706i) q^{35} +(0.818772 + 1.41816i) q^{36} +(3.64724 - 2.10574i) q^{37} -4.82685i q^{38} +(1.41869 - 3.31471i) q^{39} +(4.79827 - 0.977840i) q^{40} +(0.388612 + 0.673096i) q^{41} +(-1.85544 + 1.07124i) q^{42} +(0.197117 + 0.113806i) q^{43} +4.28281 q^{44} +(2.12075 + 0.708827i) q^{45} +(-0.497384 + 0.861494i) q^{46} +3.14738i q^{47} +(1.69450 + 0.978320i) q^{48} +(2.83211 + 4.90536i) q^{49} +(1.81003 - 2.40524i) q^{50} -2.24666 q^{51} +(-0.702078 - 5.86236i) q^{52} +6.42424i q^{53} +(-0.301021 - 0.521384i) q^{54} +(4.37877 - 3.87654i) q^{55} +(-3.89668 + 6.74925i) q^{56} -8.01746i q^{57} +(-2.35791 - 1.36134i) q^{58} +(-6.26747 + 10.8556i) q^{59} +(3.58791 - 0.731181i) q^{60} +(-1.46568 + 2.53863i) q^{61} +(2.11502 - 1.22111i) q^{62} +(-3.08191 + 1.77934i) q^{63} +0.567189 q^{64} +(-6.02406 - 5.35823i) q^{65} -1.57457 q^{66} +(-0.969664 + 0.559836i) q^{67} +(-3.18611 + 1.83950i) q^{68} +(-0.826160 + 1.43095i) q^{69} +(0.956640 + 4.69425i) q^{70} +(5.66772 - 9.81678i) q^{71} +(-1.89656 - 1.09498i) q^{72} +12.4350i q^{73} +(-1.26774 + 2.19579i) q^{74} +(3.00648 - 3.99513i) q^{75} +(-6.56447 - 11.3700i) q^{76} +9.30732i q^{77} +(0.258119 + 2.15530i) q^{78} +14.8640 q^{79} +(3.27588 - 2.90015i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-0.405233 - 0.233961i) q^{82} -11.7337i q^{83} +(-2.91375 + 5.04676i) q^{84} +(-1.59249 + 4.76459i) q^{85} -0.137032 q^{86} +(-3.91651 - 2.26120i) q^{87} +(-4.96023 + 2.86379i) q^{88} +(-8.60439 - 14.9032i) q^{89} +(-1.31910 + 0.268819i) q^{90} +(12.7400 - 1.52574i) q^{91} +2.70575i q^{92} +(3.51307 - 2.02827i) q^{93} +(-0.947430 - 1.64100i) q^{94} +(-17.0030 - 5.68299i) q^{95} -5.55790 q^{96} +(-10.6088 - 6.12499i) q^{97} +(-2.95324 - 1.70505i) q^{98} -2.61538 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 8 q^{4} + 4 q^{5} + 12 q^{9}+O(q^{10}) \) 24 * q + 8 * q^4 + 4 * q^5 + 12 * q^9	\( 24 q + 8 q^{4} + 4 q^{5} + 12 q^{9} - 4 q^{10} + 4 q^{11} + 24 q^{14} - 2 q^{15} + 16 q^{16} - 16 q^{19} - 16 q^{20} - 8 q^{21} - 16 q^{25} - 48 q^{26} - 12 q^{29} - 4 q^{30} + 8 q^{31} - 32 q^{34} + 10 q^{35} - 8 q^{36} + 8 q^{39} - 48 q^{40} - 40 q^{41} + 40 q^{44} + 2 q^{45} - 24 q^{46} - 16 q^{49} + 20 q^{50} - 24 q^{51} + 20 q^{55} - 24 q^{56} + 12 q^{59} + 48 q^{60} + 20 q^{61} + 48 q^{64} + 14 q^{65} - 56 q^{66} - 8 q^{69} - 56 q^{70} + 4 q^{71} - 12 q^{74} + 16 q^{75} + 8 q^{76} + 136 q^{79} - 4 q^{80} - 12 q^{81} - 16 q^{84} - 4 q^{85} + 48 q^{86} - 64 q^{89} - 8 q^{90} + 60 q^{91} - 48 q^{94} - 28 q^{95} + 40 q^{96} + 8 q^{99}+O(q^{100}) \) 24 * q + 8 * q^4 + 4 * q^5 + 12 * q^9 - 4 * q^10 + 4 * q^11 + 24 * q^14 - 2 * q^15 + 16 * q^16 - 16 * q^19 - 16 * q^20 - 8 * q^21 - 16 * q^25 - 48 * q^26 - 12 * q^29 - 4 * q^30 + 8 * q^31 - 32 * q^34 + 10 * q^35 - 8 * q^36 + 8 * q^39 - 48 * q^40 - 40 * q^41 + 40 * q^44 + 2 * q^45 - 24 * q^46 - 16 * q^49 + 20 * q^50 - 24 * q^51 + 20 * q^55 - 24 * q^56 + 12 * q^59 + 48 * q^60 + 20 * q^61 + 48 * q^64 + 14 * q^65 - 56 * q^66 - 8 * q^69 - 56 * q^70 + 4 * q^71 - 12 * q^74 + 16 * q^75 + 8 * q^76 + 136 * q^79 - 4 * q^80 - 12 * q^81 - 16 * q^84 - 4 * q^85 + 48 * q^86 - 64 * q^89 - 8 * q^90 + 60 * q^91 - 48 * q^94 - 28 * q^95 + 40 * q^96 + 8 * q^99

Introduction

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