LMFDB - Embedded newform 197.3.f.a.20.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [197,3,Mod(20,197)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(197, base_ring=CyclotomicField(28))

chi = DirichletCharacter(H, H._module([13]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("197.20");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 197 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	197.f (of order $28$, degree $12$, 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:	$5.36786120790$
Analytic rank:	$0$
Dimension:	$384$
Relative dimension:	$32$ over $\Q(\zeta_{28})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{28}]$

Embedding invariants

Embedding label			20.8
Character	$\chi$	$=$	197.20
Dual form			197.3.f.a.69.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.262848 - 2.33284i) q^{2} +(-0.767376 - 0.0864625i) q^{3} +(-1.47335 + 0.336283i) q^{4} +(2.37800 + 3.78457i) q^{5} +1.81289i q^{6} +(-0.926942 + 0.739212i) q^{7} +(-1.92969 - 5.51475i) q^{8} +(-8.19296 - 1.86999i) q^{9} +(8.20375 - 6.54227i) q^{10} +(-2.35759 - 20.9242i) q^{11} +(1.15969 - 0.130666i) q^{12} +(4.64080 - 13.2626i) q^{13} +(1.96811 + 1.96811i) q^{14} +(-1.49760 - 3.10980i) q^{15} +(-17.8042 + 8.57403i) q^{16} +(14.0190 - 8.80872i) q^{17} +(-2.20889 + 19.6044i) q^{18} -6.64265i q^{19} +(-4.77632 - 4.77632i) q^{20} +(0.775228 - 0.487108i) q^{21} +(-48.1932 + 10.9998i) q^{22} +(-20.5055 + 25.7131i) q^{23} +(1.00398 + 4.39873i) q^{24} +(2.17902 - 4.52478i) q^{25} +(-32.1595 - 7.34019i) q^{26} +(12.6855 + 4.43884i) q^{27} +(1.11713 - 1.40083i) q^{28} +(15.6592 - 19.6361i) q^{29} +(-6.86103 + 4.31107i) q^{30} +(2.98826 + 26.5216i) q^{31} +(12.2478 + 19.4923i) q^{32} +16.2606i q^{33} +(-24.2342 - 30.3888i) q^{34} +(-5.00187 - 1.75023i) q^{35} +12.7000 q^{36} +(-29.3959 - 14.1563i) q^{37} +(-15.4963 + 1.74601i) q^{38} +(-4.70796 + 9.77619i) q^{39} +(16.2821 - 20.4172i) q^{40} +(57.5778 + 13.1418i) q^{41} +(-1.34011 - 1.68045i) q^{42} +(39.9684 + 31.8738i) q^{43} +(10.5100 + 30.0359i) q^{44} +(-12.4058 - 35.4537i) q^{45} +(65.3746 + 41.0776i) q^{46} +(-5.19541 + 10.7884i) q^{47} +(14.4038 - 5.04011i) q^{48} +(-10.5907 + 46.4011i) q^{49} +(-11.1283 - 3.89397i) q^{50} +(-11.5195 + 5.54749i) q^{51} +(-2.37753 + 21.1012i) q^{52} +(-15.3884 - 67.4209i) q^{53} +(7.02076 - 30.7599i) q^{54} +(73.5827 - 58.6803i) q^{55} +(5.86528 + 3.68540i) q^{56} +(-0.574341 + 5.09741i) q^{57} +(-49.9238 - 31.3692i) q^{58} +(7.71045 - 9.66859i) q^{59} +(3.25226 + 4.07821i) q^{60} +(-16.3183 + 20.4625i) q^{61} +(61.0851 - 13.9423i) q^{62} +(8.97672 - 4.32296i) q^{63} +(-19.5464 + 15.5877i) q^{64} +(61.2293 - 13.9752i) q^{65} +(37.9334 - 4.27406i) q^{66} +(-102.037 + 35.7044i) q^{67} +(-17.6927 + 17.6927i) q^{68} +(17.9587 - 17.9587i) q^{69} +(-2.76828 + 12.1286i) q^{70} +(35.7587 - 22.4687i) q^{71} +(5.49738 + 48.7906i) q^{72} +(111.199 - 38.9101i) q^{73} +(-25.2978 + 72.2968i) q^{74} +(-2.06335 + 3.28380i) q^{75} +(2.23381 + 9.78697i) q^{76} +(17.6528 + 17.6528i) q^{77} +(24.0438 + 8.41328i) q^{78} +(-0.849447 + 1.35189i) q^{79} +(-74.7873 - 46.9920i) q^{80} +(58.7922 + 28.3128i) q^{81} +(15.5234 - 137.774i) q^{82} -68.4529i q^{83} +(-0.978377 + 0.978377i) q^{84} +(66.6745 + 32.1087i) q^{85} +(63.8508 - 101.618i) q^{86} +(-13.7143 + 13.7143i) q^{87} +(-110.842 + 53.3788i) q^{88} +(-15.4483 + 137.108i) q^{89} +(-79.4470 + 38.2597i) q^{90} +(5.50215 + 15.7242i) q^{91} +(21.5650 - 44.7802i) q^{92} -20.6104i q^{93} +(26.5332 + 9.28436i) q^{94} +(25.1396 - 15.7962i) q^{95} +(-7.71332 - 16.0169i) q^{96} +(-85.5233 - 19.5201i) q^{97} +(111.030 + 12.5101i) q^{98} +(-19.8124 + 175.840i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 384 q - 12 q^{2} - 12 q^{3} - 14 q^{4} - 4 q^{5} - 14 q^{7} + 48 q^{8} - 14 q^{9} - 14 q^{10} + 32 q^{11} - 26 q^{12} - 16 q^{13} - 68 q^{14} - 14 q^{15} + 70 q^{16} + 16 q^{17} + 180 q^{18} - 128 q^{20}+ \cdots - 662 q^{99}+O(q^{100}) $ 384 * q - 12 * q^2 - 12 * q^3 - 14 * q^4 - 4 * q^5 - 14 * q^7 + 48 * q^8 - 14 * q^9 - 14 * q^10 + 32 * q^11 - 26 * q^12 - 16 * q^13 - 68 * q^14 - 14 * q^15 + 70 * q^16 + 16 * q^17 + 180 * q^18 - 128 * q^20 + 6 * q^21 - 14 * q^22 - 62 * q^23 + 150 * q^24 - 14 * q^25 - 168 * q^26 + 6 * q^27 + 420 * q^28 + 140 * q^29 - 98 * q^30 + 50 * q^31 + 142 * q^32 + 38 * q^34 + 78 * q^35 - 2260 * q^36 - 64 * q^37 + 2 * q^38 - 14 * q^39 - 626 * q^40 - 126 * q^41 + 410 * q^42 - 14 * q^43 - 154 * q^44 + 544 * q^45 + 136 * q^46 - 364 * q^47 + 1114 * q^48 - 18 * q^49 - 140 * q^50 - 138 * q^51 - 214 * q^52 + 2 * q^53 + 90 * q^54 - 14 * q^55 + 26 * q^56 + 506 * q^57 - 364 * q^58 - 350 * q^59 + 348 * q^60 + 434 * q^61 + 756 * q^62 - 1122 * q^63 + 1330 * q^64 - 126 * q^65 - 742 * q^66 + 98 * q^67 + 1016 * q^68 + 454 * q^69 - 62 * q^70 - 682 * q^71 + 908 * q^72 - 32 * q^73 - 880 * q^74 - 78 * q^75 + 470 * q^76 - 410 * q^77 - 1626 * q^78 + 1100 * q^79 - 810 * q^80 + 1118 * q^81 - 86 * q^82 + 784 * q^84 - 1068 * q^85 - 632 * q^86 - 478 * q^87 - 274 * q^88 - 430 * q^89 + 308 * q^90 - 1570 * q^91 - 1022 * q^92 + 190 * q^94 + 1366 * q^95 - 462 * q^96 - 602 * q^97 + 1412 * q^98 - 662 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/197\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{13}{28}\right)$

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 $

$2$	−0.262848	−	2.33284i	−0.131424	−	1.16642i	−0.870280	−	0.492558i	$-0.836062\pi$
$2$	−0.262848	−	2.33284i	−0.131424	−	1.16642i	0.738856	−	0.673864i	$-0.235366\pi$
$3$	−0.767376	−	0.0864625i	−0.255792	−	0.0288208i	−0.0168628	−	0.999858i	$-0.505368\pi$
$3$	−0.767376	−	0.0864625i	−0.255792	−	0.0288208i	−0.238929	+	0.971037i	$0.576796\pi$
$4$	−1.47335	+	0.336283i	−0.368338	+	0.0840708i
$5$	2.37800	+	3.78457i	0.475601	+	0.756914i	0.995238	−	0.0974727i	$-0.0310759\pi$
$5$	2.37800	+	3.78457i	0.475601	+	0.756914i	−0.519638	+	0.854387i	$0.673933\pi$
$6$			1.81289i			0.302149i
$7$	−0.926942	+	0.739212i	−0.132420	+	0.105602i	−0.687460	−	0.726222i	$-0.741274\pi$
$7$	−0.926942	+	0.739212i	−0.132420	+	0.105602i	0.555040	+	0.831824i	$0.312703\pi$
$8$	−1.92969	−	5.51475i	−0.241212	−	0.689344i
$9$	−8.19296	−	1.86999i	−0.910329	−	0.207777i
$10$	8.20375	−	6.54227i	0.820375	−	0.654227i
$11$	−2.35759	−	20.9242i	−0.214326	−	1.90220i	−0.395040	−	0.918664i	$-0.629269\pi$
$11$	−2.35759	−	20.9242i	−0.214326	−	1.90220i	0.180714	−	0.983536i	$-0.442159\pi$
$12$	1.15969	−	0.130666i	0.0966410	−	0.0108888i
$13$	4.64080	−	13.2626i	0.356985	−	1.02020i	−0.615681	−	0.787995i	$-0.711119\pi$
$13$	4.64080	−	13.2626i	0.356985	−	1.02020i	0.972666	−	0.232208i	$-0.0745952\pi$
$14$	1.96811	+	1.96811i	0.140579	+	0.140579i
$15$	−1.49760	−	3.10980i	−0.0998400	−	0.207320i
$16$	−17.8042	+	8.57403i	−1.11276	+	0.535877i
$17$	14.0190	−	8.80872i	0.824647	−	0.518160i	−0.0523653	−	0.998628i	$-0.516676\pi$
$17$	14.0190	−	8.80872i	0.824647	−	0.518160i	0.877012	+	0.480468i	$0.159533\pi$
$18$	−2.20889	+	19.6044i	−0.122716	+	1.08913i
$19$		−	6.64265i		−	0.349613i	−0.984603	−	0.174807i	$-0.944070\pi$
$19$		−	6.64265i		−	0.349613i	0.984603	−	0.174807i	$-0.0559300\pi$
$20$	−4.77632	−	4.77632i	−0.238816	−	0.238816i
$21$	0.775228	−	0.487108i	0.0369156	−	0.0231956i
$22$	−48.1932	+	10.9998i	−2.19060	+	0.499990i
$23$	−20.5055	+	25.7131i	−0.891546	+	1.11796i	0.100853	+	0.994901i	$0.467843\pi$
$23$	−20.5055	+	25.7131i	−0.891546	+	1.11796i	−0.992399	+	0.123061i	$0.960729\pi$
$24$	1.00398	+	4.39873i	0.0418326	+	0.183281i
$25$	2.17902	−	4.52478i	0.0871607	−	0.180991i
$26$	−32.1595	−	7.34019i	−1.23690	−	0.282315i
$27$	12.6855	+	4.43884i	0.469832	+	0.164401i
$28$	1.11713	−	1.40083i	0.0398974	−	0.0500298i
$29$	15.6592	−	19.6361i	0.539974	−	0.677105i	−0.434742	−	0.900555i	$-0.643160\pi$
$29$	15.6592	−	19.6361i	0.539974	−	0.677105i	0.974715	+	0.223450i	$0.0717318\pi$
$30$	−6.86103	+	4.31107i	−0.228701	+	0.143702i
$31$	2.98826	+	26.5216i	0.0963955	+	0.855534i	0.945126	+	0.326707i	$0.105939\pi$
$31$	2.98826	+	26.5216i	0.0963955	+	0.855534i	−0.848730	+	0.528826i	$0.822632\pi$
$32$	12.2478	+	19.4923i	0.382744	+	0.609133i
$33$			16.2606i			0.492745i
$34$	−24.2342	−	30.3888i	−0.712771	−	0.893787i
$35$	−5.00187	−	1.75023i	−0.142911	−	0.0500066i
$36$	12.7000			0.352777
$37$	−29.3959	−	14.1563i	−0.794483	−	0.382603i	−0.00780716	−	0.999970i	$-0.502485\pi$
$37$	−29.3959	−	14.1563i	−0.794483	−	0.382603i	−0.786675	+	0.617367i	$0.788199\pi$
$38$	−15.4963	+	1.74601i	−0.407796	+	0.0459476i
$39$	−4.70796	+	9.77619i	−0.120717	+	0.250671i
$40$	16.2821	−	20.4172i	0.407053	−	0.510429i
$41$	57.5778	+	13.1418i	1.40434	+	0.320531i	0.856540	−	0.516080i	$-0.172609\pi$
$41$	57.5778	+	13.1418i	1.40434	+	0.320531i	0.547797	+	0.836611i	$0.315467\pi$
$42$	−1.34011	−	1.68045i	−0.0319074	−	0.0400107i
$43$	39.9684	+	31.8738i	0.929498	+	0.741250i	0.966124	−	0.258079i	$-0.0830894\pi$
$43$	39.9684	+	31.8738i	0.929498	+	0.741250i	−0.0366255	+	0.999329i	$0.511661\pi$
$44$	10.5100	+	30.0359i	0.238864	+	0.682634i
$45$	−12.4058	−	35.4537i	−0.275684	−	0.787860i
$46$	65.3746	+	41.0776i	1.42119	+	0.892990i
$47$	−5.19541	+	10.7884i	−0.110541	+	0.229540i	−0.948899	−	0.315579i	$-0.897801\pi$
$47$	−5.19541	+	10.7884i	−0.110541	+	0.229540i	0.838359	+	0.545119i	$0.183516\pi$
$48$	14.4038	−	5.04011i	0.300079	−	0.105002i
$49$	−10.5907	+	46.4011i	−0.216138	+	0.946960i
$50$	−11.1283	−	3.89397i	−0.222567	−	0.0778795i
$51$	−11.5195	+	5.54749i	−0.225872	+	0.108774i
$52$	−2.37753	+	21.1012i	−0.0457218	+	0.405792i
$53$	−15.3884	−	67.4209i	−0.290347	−	1.27209i	−0.884044	−	0.467404i	$-0.845189\pi$
$53$	−15.3884	−	67.4209i	−0.290347	−	1.27209i	0.593697	−	0.804689i	$-0.297668\pi$
$54$	7.02076	−	30.7599i	0.130014	−	0.569629i
$55$	73.5827	−	58.6803i	1.33787	−	1.06691i
$56$	5.86528	+	3.68540i	0.104737	+	0.0658107i
$57$	−0.574341	+	5.09741i	−0.0100762	+	0.0894283i
$58$	−49.9238	−	31.3692i	−0.860756	−	0.540849i
$59$	7.71045	−	9.66859i	0.130686	−	0.163874i	−0.712183	−	0.701994i	$-0.752294\pi$
$59$	7.71045	−	9.66859i	0.130686	−	0.163874i	0.842869	+	0.538119i	$0.180865\pi$
$60$	3.25226	+	4.07821i	0.0542044	+	0.0679702i
$61$	−16.3183	+	20.4625i	−0.267513	+	0.335451i	−0.897385	−	0.441248i	$-0.854536\pi$
$61$	−16.3183	+	20.4625i	−0.267513	+	0.335451i	0.629872	+	0.776699i	$0.283107\pi$
$62$	61.0851	−	13.9423i	0.985244	−	0.224876i
$63$	8.97672	−	4.32296i	0.142488	−	0.0686184i
$64$	−19.5464	+	15.5877i	−0.305412	+	0.243558i
$65$	61.2293	−	13.9752i	0.941989	−	0.215003i
$66$	37.9334	−	4.27406i	0.574748	−	0.0647585i
$67$	−102.037	+	35.7044i	−1.52295	+	0.532902i	−0.956635	−	0.291289i	$-0.905916\pi$
$67$	−102.037	+	35.7044i	−1.52295	+	0.532902i	−0.566311	+	0.824191i	$0.691630\pi$
$68$	−17.6927	+	17.6927i	−0.260187	+	0.260187i
$69$	17.9587	−	17.9587i	0.260271	−	0.260271i
$70$	−2.76828	+	12.1286i	−0.0395468	+	0.173266i
$71$	35.7587	−	22.4687i	0.503643	−	0.316460i	−0.256136	−	0.966641i	$-0.582450\pi$
$71$	35.7587	−	22.4687i	0.503643	−	0.316460i	0.759780	+	0.650181i	$0.225307\pi$
$72$	5.49738	+	48.7906i	0.0763525	+	0.677648i
$73$	111.199	−	38.9101i	1.52327	−	0.533015i	0.566550	−	0.824027i	$-0.308278\pi$
$73$	111.199	−	38.9101i	1.52327	−	0.533015i	0.956719	+	0.291012i	$0.0939921\pi$
$74$	−25.2978	+	72.2968i	−0.341862	+	0.976984i
$75$	−2.06335	+	3.28380i	−0.0275113	+	0.0437840i
$76$	2.23381	+	9.78697i	0.0293923	+	0.128776i
$77$	17.6528	+	17.6528i	0.229257	+	0.229257i
$78$	24.0438	+	8.41328i	0.308254	+	0.107863i
$79$	−0.849447	+	1.35189i	−0.0107525	+	0.0171125i	−0.852057	−	0.523449i	$-0.824645\pi$
$79$	−0.849447	+	1.35189i	−0.0107525	+	0.0171125i	0.841305	+	0.540561i	$0.181788\pi$
$80$	−74.7873	−	46.9920i	−0.934842	−	0.587400i
$81$	58.7922	+	28.3128i	0.725829	+	0.349541i
$82$	15.5234	−	137.774i	0.189310	−	1.68017i
$83$		−	68.4529i		−	0.824733i	−0.911018	−	0.412367i	$-0.864702\pi$
$83$		−	68.4529i		−	0.824733i	0.911018	−	0.412367i	$-0.135298\pi$
$84$	−0.978377	+	0.978377i	−0.0116473	+	0.0116473i
$85$	66.6745	+	32.1087i	0.784405	+	0.377750i
$86$	63.8508	−	101.618i	0.742451	−	1.18160i
$87$	−13.7143	+	13.7143i	−0.157636	+	0.157636i
$88$	−110.842	+	53.3788i	−1.25957	+	0.606577i
$89$	−15.4483	+	137.108i	−0.173577	+	1.54054i	0.541026	+	0.841006i	$0.318036\pi$
$89$	−15.4483	+	137.108i	−0.173577	+	1.54054i	−0.714603	+	0.699530i	$0.753393\pi$
$90$	−79.4470	+	38.2597i	−0.882745	+	0.425107i
$91$	5.50215	+	15.7242i	0.0604632	+	0.172794i
$92$	21.5650	−	44.7802i	0.234402	−	0.486741i
$93$		−	20.6104i		−	0.221617i
$94$	26.5332	+	9.28436i	0.282268	+	0.0987698i
$95$	25.1396	−	15.7962i	0.264627	−	0.166276i
$96$	−7.71332	−	16.0169i	−0.0803471	−	0.166843i
$97$	−85.5233	−	19.5201i	−0.881684	−	0.201239i	−0.242369	−	0.970184i	$-0.577925\pi$
$97$	−85.5233	−	19.5201i	−0.881684	−	0.201239i	−0.639314	+	0.768945i	$0.720782\pi$
$98$	111.030	+	12.5101i	1.13296	+	0.127654i
$99$	−19.8124	+	175.840i	−0.200125	+	1.77616i
$100$	−1.68885	+	7.39936i	−0.0168885	+	0.0739936i
$101$	146.755	−	70.6733i	1.45302	−	0.699735i	0.469899	−	0.882720i	$-0.344290\pi$
$101$	146.755	−	70.6733i	1.45302	−	0.699735i	0.983116	+	0.182985i	$0.0585759\pi$
$102$	15.9693	+	25.4150i	0.156562	+	0.249166i
$103$	34.4671	−	98.5014i	0.334632	−	0.956324i	−0.646488	−	0.762925i	$-0.723763\pi$
$103$	34.4671	−	98.5014i	0.334632	−	0.956324i	0.981120	−	0.193400i	$-0.0619515\pi$
$104$	−82.0955			−0.789380
$105$	3.68699	+	1.77556i	0.0351142	+	0.0169101i
$106$	−153.238	+	53.6202i	−1.44564	+	0.505851i
$107$	9.81135	+	20.3735i	0.0916948	+	0.190406i	0.941772	−	0.336251i	$-0.109159\pi$
$107$	9.81135	+	20.3735i	0.0916948	+	0.190406i	−0.850077	+	0.526658i	$0.823445\pi$
$108$	−20.1829	−	2.27406i	−0.186878	−	0.0210561i
$109$	−19.5135	−	40.5202i	−0.179023	−	0.371745i	0.792076	−	0.610422i	$-0.209000\pi$
$109$	−19.5135	−	40.5202i	−0.179023	−	0.371745i	−0.971099	+	0.238678i	$0.923286\pi$
$110$	−156.233	−	156.233i	−1.42030	−	1.42030i
$111$	21.3337	+	13.4048i	0.192195	+	0.120764i
$112$	10.1654	−	21.1087i	0.0907625	−	0.188470i
$113$	153.681	+	153.681i	1.36001	+	1.36001i	0.873893	+	0.486118i	$0.161588\pi$
$113$	153.681	+	153.681i	1.36001	+	1.36001i	0.486118	+	0.873893i	$0.338412\pi$
$114$	12.0424			0.105635
$115$	−146.075	−	16.4588i	−1.27022	−	0.143120i
$116$	−16.4683	+	34.1968i	−0.141968	+	0.294800i
$117$	−62.8229	+	99.9821i	−0.536948	+	0.854548i
$118$	−24.5820	−	15.4459i	−0.208322	−	0.130897i
$119$	−6.48329	+	18.5282i	−0.0544814	+	0.155699i
$120$	−14.2598	+	14.2598i	−0.118832	+	0.118832i
$121$	−314.297	+	71.7363i	−2.59750	+	0.592862i
$122$	52.0251	+	32.6895i	0.426435	+	0.267947i
$123$	−43.0476	−	15.0630i	−0.349980	−	0.122463i
$124$	−13.3215	−	38.0707i	−0.107432	−	0.307022i
$125$	133.345	−	15.0244i	1.06676	−	0.120195i
$126$	−12.4443	−	19.8050i	−0.0987643	−	0.157182i
$127$	−173.551	−	39.6119i	−1.36654	−	0.311904i	−0.524544	−	0.851384i	$-0.675764\pi$
$127$	−173.551	−	39.6119i	−1.36654	−	0.311904i	−0.841999	+	0.539479i	$0.818621\pi$
$128$	106.614	+	106.614i	0.832922	+	0.832922i
$129$	−27.9149	−	27.9149i	−0.216395	−	0.216395i
$130$	−48.6959	−	139.165i	−0.374584	−	1.07050i
$131$	6.08041	+	53.9651i	0.0464153	+	0.411947i	0.995339	+	0.0964408i	$0.0307459\pi$
$131$	6.08041	+	53.9651i	0.0464153	+	0.411947i	−0.948923	+	0.315507i	$0.897826\pi$
$132$	−5.46816	−	23.9576i	−0.0414254	−	0.181497i
$133$	4.91033	+	6.15735i	0.0369197	+	0.0462959i
$134$	110.113	+	228.652i	0.821740	+	1.70636i
$135$	13.3670	+	58.5646i	0.0990148	+	0.433812i
$136$	−75.6303	−	60.3131i	−0.556105	−	0.443479i
$137$	163.625	−	130.487i	1.19434	−	0.952458i	0.194748	−	0.980853i	$-0.437611\pi$
$137$	163.625	−	130.487i	1.19434	−	0.952458i	0.999597	+	0.0283956i	$0.00903983\pi$
$138$	−46.6152	−	37.1744i	−0.337791	−	0.269380i
$139$	−64.4849	+	102.627i	−0.463920	+	0.738324i	−0.993971	−	0.109641i	$-0.965030\pi$
$139$	−64.4849	+	102.627i	−0.463920	+	0.738324i	0.530051	+	0.847966i	$0.322173\pi$
$140$	7.95809	+	0.896661i	0.0568435	+	0.00640472i
$141$	4.91962	−	7.82954i	0.0348909	−	0.0555286i
$142$	−61.8150	−	77.5135i	−0.435317	−	0.545870i
$143$	−288.451	−	65.8371i	−2.01714	−	0.460400i
$144$	161.902	−	36.9531i	1.12432	−	0.256619i
$145$	111.552	+	12.5689i	0.769322	+	0.0866818i
$146$	−119.999	−	249.181i	−0.821914	−	1.70672i
$147$	12.1390	−	34.6914i	0.0825785	−	0.235996i
$148$	48.0710	+	10.9719i	0.324804	+	0.0741344i
$149$	−19.1689	−	54.7817i	−0.128651	−	0.367662i	0.861483	−	0.507786i	$-0.169536\pi$
$149$	−19.1689	−	54.7817i	−0.128651	−	0.367662i	−0.990134	+	0.140123i	$0.955250\pi$
$150$	8.20294	+	3.95033i	0.0546863	+	0.0263355i
$151$	41.1853	−	65.5460i	0.272750	−	0.434079i	−0.682060	−	0.731296i	$-0.738916\pi$
$151$	41.1853	−	65.5460i	0.272750	−	0.434079i	0.954810	+	0.297217i	$0.0960585\pi$
$152$	−36.6326	+	12.8183i	−0.241004	+	0.0843308i
$153$	−131.329	+	45.9541i	−0.858362	+	0.300354i
$154$	36.5411	−	45.8211i	0.237280	−	0.297540i
$155$	−93.2666	+	74.3776i	−0.601720	+	0.479856i
$156$	3.64892	−	15.9870i	0.0233905	−	0.102481i
$157$	66.2249	+	52.8126i	0.421815	+	0.336386i	0.811283	−	0.584654i	$-0.198770\pi$
$157$	66.2249	+	52.8126i	0.421815	+	0.336386i	−0.389468	+	0.921040i	$0.627341\pi$
$158$	3.37701	+	1.62628i	0.0213735	+	0.0102929i
$159$	5.97930	+	53.0677i	0.0376057	+	0.333759i
$160$	−44.6445	+	92.7054i	−0.279028	+	0.579409i
$161$		−	38.9925i		−	0.242190i
$162$	50.5959	−	144.595i	0.312320	−	0.892561i
$163$	195.230	−	155.691i	1.19773	−	0.955157i	0.198043	−	0.980193i	$-0.436542\pi$
$163$	195.230	−	155.691i	1.19773	−	0.955157i	0.999687	+	0.0250362i	$0.00797009\pi$
$164$	−89.2518			−0.544218
$165$	−61.5393	+	38.6677i	−0.372965	+	0.234350i
$166$	−159.690	+	17.9927i	−0.961986	+	0.108390i
$167$	−42.0184	−	66.8718i	−0.251607	−	0.400430i	0.696909	−	0.717160i	$-0.254558\pi$
$167$	−42.0184	−	66.8718i	−0.251607	−	0.400430i	−0.948516	+	0.316729i	$0.897415\pi$
$168$	−4.18223	−	3.33522i	−0.0248942	−	0.0198525i
$169$	−22.2313	−	17.7289i	−0.131546	−	0.104904i
$170$	57.3793	−	163.981i	0.337525	−	0.964592i
$171$	−12.4217	+	54.4230i	−0.0726415	+	0.318263i
$172$	−69.6062	−	33.5206i	−0.404687	−	0.194887i
$173$	140.562	−	32.0824i	0.812499	−	0.185448i	0.203968	−	0.978978i	$-0.434616\pi$
$173$	140.562	−	32.0824i	0.812499	−	0.185448i	0.608531	+	0.793530i	$0.291759\pi$
$174$	35.5981	+	28.3885i	0.204587	+	0.163152i
$175$	1.32494	+	5.80496i	0.00757111	+	0.0331712i
$176$	221.380	+	352.323i	1.25784	+	2.00184i
$177$	−6.75278	+	6.75278i	−0.0381513	+	0.0381513i
$178$	323.911			1.81973
$179$	−40.3716	−	4.54878i	−0.225540	−	0.0254122i	−0.00152860	−	0.999999i	$-0.500487\pi$
$179$	−40.3716	−	4.54878i	−0.225540	−	0.0254122i	−0.224011	+	0.974587i	$0.571915\pi$
$180$	30.2006	+	48.0639i	0.167781	+	0.267022i
$181$	11.1197	+	23.0904i	0.0614350	+	0.127571i	0.929426	−	0.369010i	$-0.120303\pi$
$181$	11.1197	+	23.0904i	0.0614350	+	0.127571i	−0.867991	+	0.496581i	$0.834589\pi$
$182$	35.2359	−	16.9687i	0.193604	−	0.0932348i
$183$	14.2915	−	14.2915i	0.0780958	−	0.0780958i
$184$	181.371	+	63.4644i	0.985712	+	0.344915i
$185$	−16.3279	−	144.914i	−0.0882591	−	0.783321i
$186$	−48.0808	+	5.41740i	−0.258499	+	0.0291258i
$187$	−217.366	−	272.569i	−1.16239	−	1.45759i
$188$	4.02672	−	17.6422i	0.0214187	−	0.0938415i
$189$	−15.0399	+	5.26270i	−0.0795764	+	0.0278450i
$190$	−43.4581	−	54.4947i	−0.228727	−	0.286814i
$191$	248.554			1.30133			0.650664	−	0.759366i	$-0.274491\pi$
$191$	248.554			1.30133			0.650664	+	0.759366i	$0.274491\pi$
$192$	16.3472	−	10.2716i	0.0851416	−	0.0534980i
$193$	−16.7694	−	73.4716i	−0.0868882	−	0.380682i	0.912723	−	0.408580i	$-0.133976\pi$
$193$	−16.7694	−	73.4716i	−0.0868882	−	0.380682i	−0.999611	+	0.0278978i	$0.991119\pi$
$194$	−23.0578	+	204.643i	−0.118854	+	1.05486i
$195$	−48.1942	+	5.43018i	−0.247150	+	0.0278471i
$196$		−	71.9266i		−	0.366972i
$197$	−118.924	−	157.055i	−0.603674	−	0.797231i
$197$	−118.924	−	157.055i	−0.603674	−	0.797231i
$198$	415.414			2.09805
$199$	26.9084	+	238.819i	0.135218	+	1.20009i	0.859699	+	0.510800i	$0.170651\pi$
$199$	26.9084	+	238.819i	0.135218	+	1.20009i	−0.724481	+	0.689295i	$0.757921\pi$
$200$	−29.1578	−	3.28530i	−0.145789	−	0.0164265i
$201$	81.3882	−	18.5763i	0.404916	−	0.0924195i
$202$	−203.444	−	323.779i	−1.00715	−	1.60287i
$203$			29.7770i			0.146685i
$204$	15.1067	−	12.0472i	0.0740525	−	0.0590549i
$205$	87.1843	+	249.159i	0.425289	+	1.21541i
$206$	−238.848	−	54.5155i	−1.15946	−	0.264638i
$207$	216.084	−	172.322i	1.04389	−	0.832472i
$208$	31.0888	+	275.921i	0.149465	+	1.32654i
$209$	−138.992	+	15.6607i	−0.665034	+	0.0749314i
$210$	3.17298	−	9.06786i	0.0151094	−	0.0431803i
$211$	153.968	+	153.968i	0.729708	+	0.729708i	0.970561	−	0.240854i	$-0.0774275\pi$
$211$	153.968	+	153.968i	0.729708	+	0.729708i	−0.240854	+	0.970561i	$0.577427\pi$
$212$	45.3450	+	94.1599i	0.213892	+	0.444151i
$213$	−29.3831	+	14.1501i	−0.137949	+	0.0664326i
$214$	44.9492	−	28.2435i	0.210043	−	0.131979i
$215$	−25.5834	+	227.059i	−0.118993	+	1.05609i
$216$		−	78.5228i		−	0.363531i
$217$	−22.3750	−	22.3750i	−0.103111	−	0.103111i
$218$	−89.3981	+	56.1725i	−0.410083	+	0.257672i
$219$	−88.6955	+	20.2442i	−0.405002	+	0.0924391i
$220$	−88.6801	+	111.201i	−0.403091	+	0.505461i
$221$	−51.7676	−	226.809i	−0.234242	−	1.02628i
$222$	25.6639	−	53.2916i	0.115603	−	0.240052i
$223$	−331.838	−	75.7399i	−1.48806	−	0.339641i	−0.600238	−	0.799822i	$-0.704927\pi$
$223$	−331.838	−	75.7399i	−1.48806	−	0.339641i	−0.887825	+	0.460181i	$0.847785\pi$
$224$	−25.7619	−	9.01449i	−0.115009	−	0.0402432i
$225$	−26.3139	+	32.9966i	−0.116951	+	0.146651i
$226$	318.119	−	398.909i	1.40761	−	1.76508i
$227$	30.9307	−	19.4350i	0.136258	−	0.0856169i	−0.462178	−	0.886787i	$-0.652932\pi$
$227$	30.9307	−	19.4350i	0.136258	−	0.0856169i	0.598436	+	0.801170i	$0.295789\pi$
$228$	−0.867968	−	7.70343i	−0.00380688	−	0.0337870i
$229$	70.8218	+	112.712i	0.309265	+	0.492193i	0.964805	−	0.262968i	$-0.0847014\pi$
$229$	70.8218	+	112.712i	0.309265	+	0.492193i	−0.655539	+	0.755161i	$0.727559\pi$
$230$			345.097i			1.50042i
$231$	−12.0200	−	15.0726i	−0.0520347	−	0.0652494i
$232$	−138.505	−	48.4651i	−0.597006	−	0.208901i
$233$	−12.0598			−0.0517588			−0.0258794	−	0.999665i	$-0.508239\pi$
$233$	−12.0598			−0.0517588			−0.0258794	+	0.999665i	$0.508239\pi$
$234$	249.755	+	120.276i	1.06733	+	0.513999i
$235$	−53.1841	+	5.99241i	−0.226315	+	0.0254996i
$236$	−8.10882	+	16.8381i	−0.0343594	+	0.0713480i
$237$	0.768733	−	0.963960i	0.00324360	−	0.00406734i
$238$	44.9275	+	10.2544i	0.188771	+	0.0430857i
$239$	24.6737	+	30.9399i	0.103237	+	0.129455i	0.830766	−	0.556622i	$-0.187903\pi$
$239$	24.6737	+	30.9399i	0.103237	+	0.129455i	−0.727529	+	0.686077i	$0.759331\pi$
$240$	53.3270	+	42.5269i	0.222196	+	0.177195i
$241$	127.292	+	363.779i	0.528181	+	1.50946i	0.830925	+	0.556384i	$0.187812\pi$
$241$	127.292	+	363.779i	0.528181	+	1.50946i	−0.302744	+	0.953072i	$0.597903\pi$
$242$	249.962	+	714.351i	1.03290	+	2.95186i
$243$	−145.085	−	91.1629i	−0.597057	−	0.375156i
$244$	17.1614	−	35.6361i	0.0703337	−	0.146050i
$245$	−200.793	+	70.2605i	−0.819563	+	0.286777i
$246$	−23.8246	+	104.383i	−0.0968481	+	0.424319i
$247$	−88.0992	−	30.8272i	−0.356677	−	0.124807i
$248$	140.493	−	67.6580i	0.566505	−	0.272814i
$249$	−5.91861	+	52.5291i	−0.0237695	+	0.210960i
$250$	−70.0990	−	307.124i	−0.280396	−	1.22849i
$251$	−15.5647	+	68.1934i	−0.0620108	+	0.271687i	−0.996423	−	0.0845067i	$-0.973069\pi$
$251$	−15.5647	+	68.1934i	−0.0620108	+	0.271687i	0.934412	+	0.356194i	$0.115926\pi$
$252$	−11.7721	+	9.38796i	−0.0467148	+	0.0372538i
$253$	586.371	+	368.441i	2.31767	+	1.45629i
$254$	−46.7907	+	415.279i	−0.184215	+	1.63496i
$255$	−48.3882	−	30.4043i	−0.189758	−	0.119233i
$256$	158.340	−	198.552i	0.618514	−	0.775592i
$257$	10.8840	+	13.6481i	0.0423501	+	0.0531054i	0.802556	−	0.596577i	$-0.203473\pi$
$257$	10.8840	+	13.6481i	0.0423501	+	0.0531054i	−0.760205	+	0.649683i	$0.774902\pi$
$258$	−57.7838	+	72.4585i	−0.223968	+	0.280847i
$259$	37.7128	−	8.60769i	0.145609	−	0.0332343i
$260$	−85.5127	+	41.1807i	−0.328895	+	0.158387i
$261$	−165.015	+	131.595i	−0.632240	+	0.504195i
$262$	124.294	−	28.3693i	0.474404	−	0.108280i
$263$	−91.0827	+	10.2626i	−0.346322	+	0.0390211i	−0.283413	−	0.958998i	$-0.591467\pi$
$263$	−91.0827	+	10.2626i	−0.346322	+	0.0390211i	−0.0629096	+	0.998019i	$0.520038\pi$
$264$	89.6730	−	31.3779i	0.339670	−	0.118856i
$265$	218.566	−	218.566i	0.824776	−	0.824776i
$266$	13.0735	−	13.0735i	0.0491484	−	0.0491484i
$267$	23.7094	−	103.877i	0.0887991	−	0.389054i
$268$	138.330	−	86.9187i	0.516158	−	0.324323i
$269$	−33.4820	−	297.161i	−0.124469	−	1.10469i	−0.888297	−	0.459270i	$-0.848111\pi$
$269$	−33.4820	−	297.161i	−0.124469	−	1.10469i	0.763828	−	0.645420i	$-0.223317\pi$
$270$	133.109	−	46.5767i	0.492995	−	0.172506i
$271$	116.461	−	332.828i	0.429747	−	1.22815i	−0.501945	−	0.864899i	$-0.667382\pi$
$271$	116.461	−	332.828i	0.429747	−	1.22815i	0.931693	−	0.363248i	$-0.118332\pi$
$272$	−174.070	+	277.031i	−0.639964	+	1.01850i
$273$	−2.86266	−	12.5421i	−0.0104859	−	0.0459419i
$274$	−347.414	−	347.414i	−1.26793	−	1.26793i
$275$	−99.8145	−	34.9266i	−0.362962	−	0.127006i
$276$	−20.4203	+	32.4987i	−0.0739865	+	0.117749i
$277$	−260.022	−	163.383i	−0.938708	−	0.589829i	−0.0265406	−	0.999648i	$-0.508449\pi$
$277$	−260.022	−	163.383i	−0.938708	−	0.589829i	−0.912167	+	0.409819i	$0.865592\pi$
$278$	256.363	+	123.458i	0.922167	+	0.444092i
$279$	25.1123	−	222.878i	0.0900083	−	0.798846i
$280$			30.9615i			0.110577i
$281$	93.6817	−	93.6817i	0.333387	−	0.333387i	−0.520484	−	0.853871i	$-0.674249\pi$
$281$	93.6817	−	93.6817i	0.333387	−	0.333387i	0.853871	+	0.520484i	$0.174249\pi$
$282$	−19.5582	−	9.41873i	−0.0693553	−	0.0333997i
$283$	−2.64063	+	4.20254i	−0.00933085	+	0.0148500i	−0.851357	−	0.524587i	$-0.824220\pi$
$283$	−2.64063	+	4.20254i	−0.00933085	+	0.0148500i	0.842026	+	0.539437i	$0.181363\pi$
$284$	−45.1293	+	45.1293i	−0.158906	+	0.158906i
$285$	−20.6573	+	9.94803i	−0.0724818	+	0.0349054i
$286$	−77.7687	+	690.217i	−0.271919	+	2.41335i
$287$	−63.0859	+	30.3806i	−0.219811	+	0.105856i
$288$	−63.8954	−	182.603i	−0.221859	−	0.634037i
$289$	−6.45363	+	13.4011i	−0.0223309	+	0.0463706i
$290$		−	263.536i		−	0.908746i
$291$	63.9408	+	22.3739i	0.219728	+	0.0768861i
$292$	−150.750	+	94.7225i	−0.516267	+	0.324392i
$293$	−201.607	−	418.642i	−0.688080	−	1.42881i	−0.893011	−	0.450036i	$-0.851411\pi$
$293$	−201.607	−	418.642i	−0.688080	−	1.42881i	0.204931	−	0.978776i	$-0.434303\pi$
$294$	−84.1202	−	19.1999i	−0.286123	−	0.0653057i
$295$	54.9269	+	6.18878i	0.186193	+	0.0209789i
$296$	−21.3434	+	189.428i	−0.0721061	+	0.639960i
$297$	62.9720	−	275.898i	0.212027	−	0.928950i
$298$	−122.758	+	59.1174i	−0.411941	+	0.198380i
$299$	245.862	+	391.287i	0.822282	+	1.30865i
$300$	1.93575	−	5.53207i	0.00645251	−	0.0184402i
$301$	−60.6099			−0.201362
$302$	−163.734	−	78.8501i	−0.542165	−	0.261093i
$303$	−118.727	+	41.5442i	−0.391837	+	0.137110i
$304$	56.9543	+	118.267i	0.187350	+	0.389035i
$305$	−116.247	−	13.0979i	−0.381137	−	0.0429439i
$306$	141.723	+	294.292i	0.463148	+	0.961737i
$307$	73.5438	+	73.5438i	0.239556	+	0.239556i	0.816666	−	0.577110i	$-0.195820\pi$
$307$	73.5438	+	73.5438i	0.239556	+	0.239556i	−0.577110	+	0.816666i	$0.695820\pi$
$308$	−31.9451	−	20.0724i	−0.103718	−	0.0651702i
$309$	−34.9659	+	72.6075i	−0.113158	+	0.234976i
$310$	198.026	+	198.026i	0.638794	+	0.638794i
$311$	−82.1043			−0.264001			−0.132000	−	0.991250i	$-0.542140\pi$
$311$	−82.1043			−0.264001			−0.132000	+	0.991250i	$0.542140\pi$
$312$	62.9981	+	7.09819i	0.201917	+	0.0227506i
$313$	101.803	−	211.396i	0.325249	−	0.675387i	−0.672664	−	0.739948i	$-0.734850\pi$
$313$	101.803	−	211.396i	0.325249	−	0.675387i	0.997914	+	0.0645604i	$0.0205645\pi$
$314$	105.796	−	168.374i	0.336931	−	0.536223i
$315$	37.7072	+	23.6930i	0.119705	+	0.0752159i
$316$	0.796918	−	2.27746i	0.00252189	−	0.00720715i
$317$	53.9442	−	53.9442i	0.170171	−	0.170171i	−0.616883	−	0.787055i	$-0.711605\pi$
$317$	53.9442	−	53.9442i	0.170171	−	0.170171i	0.787055	+	0.616883i	$0.211605\pi$
$318$	122.227	−	27.8975i	0.384362	−	0.0877281i
$319$	−447.787	−	281.363i	−1.40372	−	0.882016i
$320$	−105.474	−	36.9070i	−0.329607	−	0.115334i
$321$	−5.76745	−	16.4824i	−0.0179671	−	0.0513472i
$322$	−90.9634	+	10.2491i	−0.282495	+	0.0318296i
$323$	−58.5133	−	93.1233i	−0.181156	−	0.288308i
$324$	−96.1427	−	21.9439i	−0.296737	−	0.0677282i
$325$	−49.8981	−	49.8981i	−0.153533	−	0.153533i
$326$	−414.517	−	414.517i	−1.27153	−	1.27153i
$327$	11.4707	+	32.7814i	0.0350786	+	0.100249i
$328$	−38.6341	−	342.887i	−0.117787	−	1.04539i
$329$	−3.15905	−	13.8407i	−0.00960198	−	0.0420690i
$330$	106.381	+	133.398i	0.322367	+	0.404236i
$331$	−12.0175	−	24.9546i	−0.0363067	−	0.0753916i	0.882027	−	0.471200i	$-0.156179\pi$
$331$	−12.0175	−	24.9546i	−0.0363067	−	0.0753916i	−0.918333	+	0.395808i	$0.870465\pi$
$332$	23.0195	+	100.855i	0.0693360	+	0.303781i
$333$	214.367	+	170.952i	0.643745	+	0.513369i
$334$	−144.957	+	115.599i	−0.434003	+	0.346106i
$335$	−377.771	−	301.263i	−1.12768	−	0.899291i
$336$	−9.62579	+	15.3194i	−0.0286482	+	0.0455933i
$337$	−68.5608	−	7.72494i	−0.203444	−	0.0229227i	0.00965412	−	0.999953i	$-0.496927\pi$
$337$	−68.5608	−	7.72494i	−0.203444	−	0.0229227i	−0.213098	+	0.977031i	$0.568356\pi$
$338$	−35.5152	+	56.5221i	−0.105074	+	0.167225i
$339$	−104.644	−	131.219i	−0.308683	−	0.387077i
$340$	−109.033	−	24.8860i	−0.320684	−	0.0731940i
$341$	547.897	−	125.054i	1.60674	−	0.366727i
$342$	130.225	+	14.6729i	0.380776	+	0.0429031i
$343$	−49.6895	−	103.181i	−0.144867	−	0.300820i
$344$	98.6489	−	281.922i	0.286770	−	0.819542i
$345$	110.672	+	25.2601i	0.320788	+	0.0732177i
$346$	−111.790	−	319.477i	−0.323092	−	0.923344i
$347$	−50.1026	−	24.1281i	−0.144388	−	0.0695336i	0.360295	−	0.932839i	$-0.382676\pi$
$347$	−50.1026	−	24.1281i	−0.144388	−	0.0695336i	−0.504683	+	0.863305i	$0.668390\pi$
$348$	15.5941	−	24.8179i	0.0448107	−	0.0713158i
$349$	−178.311	+	62.3939i	−0.510921	+	0.178779i	−0.573413	−	0.819267i	$-0.694381\pi$
$349$	−178.311	+	62.3939i	−0.510921	+	0.178779i	0.0624920	+	0.998045i	$0.480095\pi$
$350$	13.1938	−	4.61671i	0.0376966	−	0.0131906i
$351$	117.742	−	147.643i	0.335446	−	0.420636i
$352$	378.985	−	302.230i	1.07666	−	0.858609i
$353$	−152.030	+	666.085i	−0.430679	+	1.88693i	0.0303445	+	0.999539i	$0.490340\pi$
$353$	−152.030	+	666.085i	−0.430679	+	1.88693i	−0.461023	+	0.887388i	$0.652518\pi$
$354$	17.5281	+	13.9782i	0.0495145	+	0.0394865i
$355$	170.069	+	81.9007i	0.479066	+	0.230706i
$356$	−23.3462	−	207.203i	−0.0655791	−	0.582031i
$357$	6.57712	−	13.6575i	0.0184233	−	0.0382564i
$358$			95.3762i			0.266414i
$359$	139.047	−	397.375i	0.387319	−	1.10689i	−0.570940	−	0.820992i	$-0.693421\pi$
$359$	139.047	−	397.375i	0.387319	−	1.10689i	0.958259	−	0.285902i	$-0.0922932\pi$
$360$	−171.579	+	136.830i	−0.476608	+	0.380082i
$361$	316.875			0.877771
$362$	50.9434	−	32.0098i	0.140727	−	0.0884249i
$363$	247.387	−	27.8738i	0.681507	−	0.0767874i
$364$	−13.3944	−	21.3171i	−0.0367978	−	0.0585634i
$365$	411.689	+	328.311i	1.12791	+	0.899482i
$366$	−37.0964	−	29.5834i	−0.101356	−	0.0808289i
$367$	16.2522	−	46.4460i	0.0442838	−	0.126556i	−0.919618	−	0.392814i	$-0.871502\pi$
$367$	16.2522	−	46.4460i	0.0442838	−	0.126556i	0.963902	+	0.266258i	$0.0857873\pi$
$368$	144.619	−	633.616i	0.392986	−	1.72178i
$369$	−447.158	−	215.340i	−1.21181	−	0.583577i
$370$	−333.771	+	76.1810i	−0.902083	+	0.205895i
$371$	64.1025	+	51.1200i	0.172783	+	0.137790i
$372$	6.93092	+	30.3664i	0.0186315	+	0.0816300i
$373$	−42.2210	−	67.1943i	−0.113193	−	0.180146i	0.785323	−	0.619086i	$-0.212497\pi$
$373$	−42.2210	−	67.1943i	−0.113193	−	0.180146i	−0.898516	+	0.438940i	$0.855354\pi$
$374$	−578.726	+	578.726i	−1.54740	+	1.54740i
$375$	−103.625			−0.276333
$376$	69.5207	+	7.83310i	0.184896	+	0.0208327i
$377$	−187.755	−	298.810i	−0.498023	−	0.792599i
$378$	16.2303	+	33.7025i	0.0429372	+	0.0891601i
$379$	−477.201	+	229.808i	−1.25911	+	0.606353i	−0.939938	−	0.341345i	$-0.889118\pi$
$379$	−477.201	+	229.808i	−1.25911	+	0.606353i	−0.319168	+	0.947698i	$0.603403\pi$
$380$	−31.7275	+	31.7275i	−0.0834933	+	0.0834933i
$381$	129.754	+	45.4029i	0.340561	+	0.119168i
$382$	−65.3319	−	579.837i	−0.171026	−	1.51790i
$383$	−503.649	+	56.7476i	−1.31501	+	0.148166i	−0.741456	−	0.671002i	$-0.765864\pi$
$383$	−503.649	+	56.7476i	−1.31501	+	0.148166i	−0.573554	+	0.819168i	$0.694436\pi$
$384$	−72.5950	−	91.0312i	−0.189049	−	0.237060i
$385$	−24.8298	+	108.786i	−0.0644930	+	0.282562i
$386$	−166.990	+	58.4323i	−0.432616	+	0.151379i
$387$	−267.856	−	335.881i	−0.692135	−	0.867910i
$388$	132.570			0.341676
$389$	−245.138	+	154.030i	−0.630174	+	0.395965i	−0.808910	−	0.587932i	$-0.799942\pi$
$389$	−245.138	+	154.030i	−0.630174	+	0.395965i	0.178736	+	0.983897i	$0.442799\pi$
$390$	25.3355	+	111.002i	0.0649629	+	0.284621i
$391$	−60.9673	+	541.100i	−0.155927	+	1.38389i
$392$	276.327	−	31.1346i	0.704916	−	0.0794249i
$393$		−	41.9373i		−	0.106711i
$394$	−335.124	+	318.712i	−0.850570	+	0.808914i
$395$	−7.13630			−0.0180666
$396$	−29.9413	−	265.737i	−0.0756094	−	0.671052i
$397$	597.561	+	67.3289i	1.50519	+	0.169594i	0.825708	−	0.564098i	$-0.190776\pi$
$397$	597.561	+	67.3289i	1.50519	+	0.169594i	0.679482	+	0.733692i	$0.262204\pi$
$398$	550.054	−	125.546i	1.38204	−	0.315443i
$399$	−3.23569	−	5.14957i	−0.00810949	−	0.0129062i
$400$			99.2428i			0.248107i
$401$	0.144253	−	0.115038i	0.000359734	−	0.000286878i	−0.623310	−	0.781975i	$-0.714212\pi$
$401$	0.144253	−	0.115038i	0.000359734	−	0.000286878i	0.623670	+	0.781688i	$0.285641\pi$
$402$	−64.7284	−	184.983i	−0.161016	−	0.460157i
$403$	365.614	+	83.4490i	0.907231	+	0.207069i
$404$	−192.455	+	153.478i	−0.476374	+	0.379895i
$405$	32.6561	+	289.831i	0.0806324	+	0.715632i
$406$	69.4650	−	7.82683i	0.171096	−	0.0192779i
$407$	−226.906	+	648.459i	−0.557508	+	1.59327i
$408$	52.8220	+	52.8220i	0.129466	+	0.129466i
$409$	212.969	+	442.235i	0.520707	+	1.08126i	0.981092	+	0.193540i	$0.0619968\pi$
$409$	212.969	+	442.235i	0.520707	+	1.08126i	−0.460386	+	0.887719i	$0.652289\pi$
$410$	558.331	−	268.878i	1.36178	−	0.655800i
$411$	−136.844	+	85.9850i	−0.332954	+	0.209209i
$412$	−17.6579	+	156.718i	−0.0428589	+	0.380384i
$413$			14.6619i			0.0355009i
$414$	−458.797	−	458.797i	−1.10820	−	1.10820i
$415$	259.065	−	162.781i	0.624252	−	0.392244i
$416$	315.359	−	71.9786i	0.758074	−	0.173025i
$417$	58.3576	−	73.1781i	0.139946	−	0.175487i
$418$	73.0677	+	320.130i	0.174803	+	0.765862i
$419$	−283.924	+	589.575i	−0.677624	+	1.40710i	0.224004	+	0.974588i	$0.428087\pi$
$419$	−283.924	+	589.575i	−0.677624	+	1.40710i	−0.901628	+	0.432512i	$0.857627\pi$
$420$	−6.02932	−	1.37615i	−0.0143555	−	0.00327656i
$421$	32.4695	+	11.3616i	0.0771248	+	0.0269871i	0.368566	−	0.929602i	$-0.379849\pi$
$421$	32.4695	+	11.3616i	0.0771248	+	0.0269871i	−0.291441	+	0.956589i	$0.594135\pi$
$422$	318.713	−	399.654i	0.755245	−	0.947047i
$423$	62.7399	−	78.6734i	0.148321	−	0.185989i
$424$	−342.115	+	214.965i	−0.806874	+	0.506993i
$425$	−9.30985	−	82.6272i	−0.0219055	−	0.194417i
$426$	40.7333	+	64.8267i	0.0956181	+	0.152175i
$427$		−	31.0303i		−	0.0726704i
$428$	−21.3068	−	26.7179i	−0.0497823	−	0.0624250i
$429$	215.658	+	75.4621i	0.502700	+	0.175902i
$430$	536.418			1.24748
$431$	−761.224	−	366.586i	−1.76618	−	0.850548i	−0.969096	−	0.246682i	$-0.920660\pi$
$431$	−761.224	−	366.586i	−1.76618	−	0.850548i	−0.797086	−	0.603866i	$-0.793626\pi$
$432$	−263.913	+	29.7358i	−0.610909	+	0.0688329i
$433$	123.809	−	257.091i	0.285932	−	0.593744i	−0.707688	−	0.706525i	$-0.750262\pi$
$433$	123.809	−	257.091i	0.285932	−	0.593744i	0.993620	+	0.112781i	$0.0359759\pi$
$434$	−46.3161	+	58.0785i	−0.106719	+	0.133822i
$435$	−84.5154	−	19.2901i	−0.194288	−	0.0443451i
$436$	42.3765	+	53.1384i	0.0971937	+	0.121877i
$437$	170.803	+	136.211i	0.390855	+	0.311696i
$438$	70.5399	+	201.591i	0.161050	+	0.460254i
$439$	235.730	+	673.676i	0.536969	+	1.53457i	0.818202	+	0.574931i	$0.194971\pi$
$439$	235.730	+	673.676i	0.536969	+	1.53457i	−0.281233	+	0.959640i	$0.590743\pi$
$440$	−465.599	−	292.555i	−1.05818	−	0.664898i
$441$	173.539	−	360.357i	0.393512	−	0.817137i
$442$	−515.502	+	180.382i	−1.16629	+	0.408104i
$443$	−132.937	+	582.433i	−0.300083	+	1.31475i	0.569920	+	0.821700i	$0.306974\pi$
$443$	−132.937	+	582.433i	−0.300083	+	1.31475i	−0.870002	+	0.493047i	$0.835883\pi$
$444$	−35.9399	−	12.5759i	−0.0809456	−	0.0283241i
$445$	−555.630	+	267.577i	−1.24861	+	0.601297i
$446$	−89.4661	+	794.034i	−0.200597	+	1.78035i
$447$	9.97322	+	43.6955i	0.0223115	+	0.0977529i
$448$	6.59574	−	28.8978i	0.0147226	−	0.0645041i
$449$	46.6240	−	37.1814i	0.103840	−	0.0828093i	−0.570194	−	0.821510i	$-0.693132\pi$
$449$	46.6240	−	37.1814i	0.103840	−	0.0828093i	0.674033	+	0.738701i	$0.264560\pi$
$450$	83.8924	+	52.7131i	0.186427	+	0.117140i
$451$	139.236	−	1235.75i	0.308727	−	2.74003i
$452$	−278.107	−	174.746i	−0.615281	−	0.386607i
$453$	−37.2719	+	46.7375i	−0.0822779	+	0.103173i
$454$	−53.4689	−	67.0479i	−0.117773	−	0.147683i
$455$	−46.4254	+	58.2156i	−0.102034	+	0.127946i
$456$	29.2193	−	6.66910i	0.0640773	−	0.0146252i
$457$	−120.106	+	57.8399i	−0.262814	+	0.126564i	−0.560651	−	0.828052i	$-0.689449\pi$
$457$	−120.106	+	57.8399i	−0.262814	+	0.126564i	0.297837	+	0.954617i	$0.403735\pi$
$458$	244.324	−	194.842i	0.533459	−	0.425420i
$459$	216.938	−	49.5147i	0.472632	−	0.107875i
$460$	220.755	−	24.8732i	0.479903	−	0.0540721i
$461$	−702.848	+	245.937i	−1.52462	+	0.533487i	−0.957071	−	0.289855i	$-0.906393\pi$
$461$	−702.848	+	245.937i	−1.52462	+	0.533487i	−0.567546	+	0.823341i	$0.692107\pi$
$462$	−32.0026	+	32.0026i	−0.0692697	+	0.0692697i
$463$	−230.223	+	230.223i	−0.497241	+	0.497241i	−0.910578	−	0.413337i	$-0.864363\pi$
$463$	−230.223	+	230.223i	−0.497241	+	0.497241i	0.413337	+	0.910578i	$0.364363\pi$
$464$	−110.439	+	483.866i	−0.238016	+	1.04281i
$465$	78.0015	−	49.0116i	0.167745	−	0.105401i
$466$	3.16990	+	28.1336i	0.00680235	+	0.0603725i
$467$	−7.78983	+	2.72578i	−0.0166806	+	0.00583679i	−0.338606	−	0.940928i	$-0.609956\pi$
$467$	−7.78983	+	2.72578i	−0.0166806	+	0.00583679i	0.321926	+	0.946765i	$0.395670\pi$
$468$	58.9380	−	168.435i	0.125936	−	0.359904i
$469$	68.1896	−	108.523i	0.145394	−	0.231393i
$470$	27.9587	+	122.495i	0.0594865	+	0.260628i
$471$	−46.2531	−	46.2531i	−0.0982020	−	0.0982020i
$472$	−68.1987	−	23.8637i	−0.144489	−	0.0505588i
$473$	572.704	−	911.453i	1.21079	−	1.92696i
$474$	−2.45083	−	1.53996i	−0.00517052	−	0.00324885i
$475$	−30.0565	−	14.4745i	−0.0632769	−	0.0304725i
$476$	3.32146	−	29.4788i	0.00697785	−	0.0619302i
$477$			581.153i			1.21835i
$478$	65.6924	−	65.6924i	0.137432	−	0.137432i
$479$	310.616	+	149.585i	0.648469	+	0.312286i	0.729048	−	0.684462i	$-0.239963\pi$
$479$	310.616	+	149.585i	0.648469	+	0.312286i	−0.0805798	+	0.996748i	$0.525677\pi$
$480$	42.2747	−	67.2798i	0.0880723	−	0.140166i
$481$	−324.170	+	324.170i	−0.673951	+	0.673951i
$482$	815.180	−	392.570i	1.69125	−	0.814461i
$483$	−3.37139	+	29.9220i	−0.00698011	+	0.0619502i
$484$	438.947	−	211.386i	0.906916	−	0.436748i
$485$	−129.499	−	370.088i	−0.267009	−	0.763068i
$486$	−174.533	+	362.422i	−0.359122	+	0.745725i
$487$			666.070i			1.36770i	0.729623	+	0.683850i	$0.239696\pi$
$487$			666.070i			1.36770i	−0.729623	+	0.683850i	$0.760304\pi$
$488$	144.335	+	50.5050i	0.295768	+	0.103494i
$489$	−163.276	+	102.593i	−0.333898	+	0.209802i
$490$	216.685	+	449.950i	0.442214	+	0.918266i
$491$	344.910	+	78.7235i	0.702465	+	0.160333i	0.558811	−	0.829295i	$-0.311258\pi$
$491$	344.910	+	78.7235i	0.702465	+	0.160333i	0.143654	+	0.989628i	$0.454115\pi$
$492$	68.4897	+	7.71694i	0.139207	+	0.0156848i
$493$	46.5582	−	413.216i	0.0944386	−	0.838166i
$494$	−48.7584	+	213.624i	−0.0987011	+	0.432438i
$495$	−712.592	+	343.166i	−1.43958	+	0.693265i
$496$	−280.600	−	446.572i	−0.565726	−	0.900347i
$497$	−16.5371	+	47.2604i	−0.0332739	+	0.0950913i
$498$	124.098			0.249192
$499$	823.366	+	396.512i	1.65003	+	0.794613i	0.999379	+	0.0352382i	$0.0112190\pi$
$499$	823.366	+	396.512i	1.65003	+	0.794613i	0.650653	+	0.759375i	$0.274495\pi$
$500$	−191.412	+	66.9778i	−0.382823	+	0.133956i
$501$	26.4620	+	54.9489i	0.0528183	+	0.109678i
$502$	163.176	+	18.3855i	0.325051	+	0.0366245i
$503$	−238.783	−	495.838i	−0.474718	−	0.985762i	−0.991556	−	0.129679i	$-0.958605\pi$
$503$	−238.783	−	495.838i	−0.474718	−	0.985762i	0.516838	−	0.856083i	$-0.327109\pi$
$504$	−41.1624	−	41.1624i	−0.0816713	−	0.0816713i
$505$	616.451	+	387.342i	1.22069	+	0.767013i
$506$	705.388	−	1464.75i	1.39405	−	2.89477i
$507$	15.5269	+	15.5269i	0.0306250	+	0.0306250i
$508$	269.022			0.529572
$509$	661.692	+	74.5548i	1.29998	+	0.146473i	0.734682	−	0.678411i	$-0.237331\pi$
$509$	661.692	+	74.5548i	1.29998	+	0.146473i	0.565302	+	0.824884i	$0.308760\pi$
$510$	−58.2097	+	120.874i	−0.114137	+	0.237007i
$511$	−74.3119	+	118.267i	−0.145425	+	0.231442i
$512$	5.85069	+	3.67624i	0.0114271	+	0.00718015i
$513$	29.4857	−	84.2652i	0.0574769	−	0.164260i
$514$	28.9780	−	28.9780i	0.0563774	−	0.0563774i
$515$	454.749	−	103.793i	0.883007	−	0.201541i
$516$	50.5159	+	31.7412i	0.0978990	+	0.0615140i
$517$	237.987	+	83.2752i	0.460322	+	0.161074i
$518$	−29.9931	−	85.7154i	−0.0579018	−	0.165474i
$519$	−110.638	+	12.4659i	−0.213176	+	0.0240191i
$520$	−195.223	−	310.696i	−0.375430	−	0.597493i
$521$	595.956	+	136.023i	1.14387	+	0.261081i	0.752142	−	0.659001i	$-0.229021\pi$
$521$	595.956	+	136.023i	1.14387	+	0.261081i	0.391727	+	0.920081i	$0.371878\pi$
$522$	350.364	+	350.364i	0.671195	+	0.671195i
$523$	295.836	+	295.836i	0.565651	+	0.565651i	0.930907	−	0.365256i	$-0.119019\pi$
$523$	295.836	+	295.836i	0.565651	+	0.565651i	−0.365256	+	0.930907i	$0.619019\pi$
$524$	−27.1061	−	77.4649i	−0.0517293	−	0.147834i
$525$	−0.514819	−	4.56915i	−0.000980608	−	0.00870314i
$526$	47.8819	+	209.784i	0.0910302	+	0.398829i
$527$	275.513	+	345.483i	0.522796	+	0.655565i
$528$	−139.419	−	289.506i	−0.264050	−	0.548306i
$529$	−122.975	−	538.787i	−0.232466	−	1.01850i
$530$	−567.329	−	452.430i	−1.07043	−	0.853641i
$531$	−81.2515	+	64.7959i	−0.153016	+	0.122026i
$532$	−9.30525	−	7.42069i	−0.0174911	−	0.0139487i
$533$	441.502	−	702.646i	0.828334	−	1.31829i
$534$	−248.562	−	28.0062i	−0.465471	−	0.0524460i
$535$	−53.7734	+	85.5799i	−0.100511	+	0.159963i
$536$	393.802	+	493.812i	0.734705	+	0.921291i
$537$	30.5869	+	6.98126i	0.0569588	+	0.0130005i
$538$	−684.430	+	156.217i	−1.27217	+	0.290366i
$539$	995.873	+	112.208i	1.84763	+	0.208178i
$540$	−39.3886	−	81.7912i	−0.0729418	−	0.151465i
$541$	243.623	−	696.235i	0.450320	−	1.28694i	−0.465391	−	0.885105i	$-0.654086\pi$
$541$	243.623	−	696.235i	0.450320	−	1.28694i	0.915712	−	0.401836i	$-0.131628\pi$
$542$	−807.046	−	184.203i	−1.48902	−	0.339858i
$543$	−6.53657	−	18.6804i	−0.0120379	−	0.0344023i
$544$	343.404	+	165.375i	0.631257	+	0.303997i
$545$	106.948	−	170.207i	0.196235	−	0.312307i
$546$	−28.5064	+	9.97482i	−0.0522095	+	0.0182689i
$547$	144.893	−	50.7004i	0.264887	−	0.0926881i	−0.194568	−	0.980889i	$-0.562330\pi$
$547$	144.893	−	50.7004i	0.264887	−	0.0926881i	0.459455	+	0.888201i	$0.348045\pi$
$548$	−197.197	+	247.277i	−0.359849	+	0.451236i
$549$	171.960	−	137.134i	0.313224	−	0.249788i
$550$	−55.2422	+	242.032i	−0.100440	+	0.440058i
$551$	−130.435	−	104.019i	−0.236725	−	0.188782i
$552$	−133.692	−	64.3829i	−0.242196	−	0.116636i
$553$	−0.211942	−	1.88104i	−0.000383259	−	0.00340152i
$554$	−312.800	+	649.535i	−0.564620	+	1.17245i
$555$			112.616i			0.202911i
$556$	60.4972	−	172.891i	0.108808	−	0.310955i
$557$	237.178	−	189.143i	0.425813	−	0.339575i	−0.387020	−	0.922071i	$-0.626496\pi$
$557$	237.178	−	189.143i	0.425813	−	0.339575i	0.812833	+	0.582497i	$0.197924\pi$
$558$	−526.540			−0.943620
$559$	608.216	−	382.167i	1.08804	−	0.683663i
$560$	104.061	−	11.7248i	0.185822	−	0.0209372i
$561$	143.235	+	227.957i	0.255321	+	0.406340i
$562$	−243.169	−	193.921i	−0.432685	−	0.345054i
$563$	−474.361	−	378.290i	−0.842559	−	0.671919i	0.103955	−	0.994582i	$-0.466850\pi$
$563$	−474.361	−	378.290i	−0.842559	−	0.671919i	−0.946514	+	0.322663i	$0.895422\pi$
$564$	−4.61540	+	13.1900i	−0.00818333	+	0.0233866i
$565$	−216.163	+	947.072i	−0.382590	+	1.67623i
$566$	10.4979	+	5.05554i	0.0185476	+	0.00893206i
$567$	−75.4261	+	17.2155i	−0.133027	+	0.0303625i
$568$	−192.912	−	153.842i	−0.339634	−	0.270849i
$569$	−15.6109	−	68.3959i	−0.0274357	−	0.120204i	0.959356	−	0.282200i	$-0.0910640\pi$
$569$	−15.6109	−	68.3959i	−0.0274357	−	0.120204i	−0.986791	+	0.161996i	$0.948207\pi$
$570$	28.6369	+	45.5754i	0.0502402	+	0.0799569i
$571$	641.359	−	641.359i	1.12322	−	1.12322i	0.131966	−	0.991254i	$-0.457871\pi$
$571$	641.359	−	641.359i	1.12322	−	1.12322i	0.991254	−	0.131966i	$-0.0421291\pi$
$572$	447.130			0.781696
$573$	−190.734	−	21.4906i	−0.332870	−	0.0375054i
$574$	87.4550	+	139.184i	0.152361	+	0.242481i
$575$	71.6643	+	148.812i	0.124634	+	0.258804i
$576$	189.292	−	91.1580i	0.328631	−	0.158260i
$577$	−130.100	+	130.100i	−0.225477	+	0.225477i	−0.810800	−	0.585323i	$-0.800968\pi$
$577$	−130.100	+	130.100i	−0.225477	+	0.225477i	0.585323	+	0.810800i	$0.300968\pi$
$578$	32.9590	+	11.5329i	0.0570225	+	0.0199530i
$579$	6.51591	+	57.8303i	0.0112537	+	0.0998796i
$580$	−168.582	+	18.9946i	−0.290658	+	0.0327493i
$581$	50.6012	+	63.4518i	0.0870932	+	0.109211i
$582$	35.3880	−	155.045i	0.0608041	−	0.266400i
$583$	−1374.45	+	480.941i	−2.35755	+	0.824941i
$584$	−429.159	−	538.148i	−0.734861	−	0.921486i
$585$	−527.782			−0.902192
$586$	−923.634	+	580.357i	−1.57617	+	0.990371i
$587$	68.4172	+	299.755i	0.116554	+	0.510656i	0.999177	+	0.0405740i	$0.0129187\pi$
$587$	68.4172	+	299.755i	0.116554	+	0.510656i	−0.882623	+	0.470082i	$0.844224\pi$
$588$	−6.21896	+	55.1948i	−0.0105765	+	0.0938686i
$589$	176.173	−	19.8500i	0.299106	−	0.0337012i
$590$		−	129.763i		−	0.219937i
$591$	77.6800	+	130.802i	0.131438	+	0.221324i
$592$	644.745			1.08910
$593$	27.6376	+	245.291i	0.0466065	+	0.413644i	0.995254	+	0.0973095i	$0.0310237\pi$
$593$	27.6376	+	245.291i	0.0466065	+	0.413644i	−0.948648	+	0.316335i	$0.897548\pi$
$594$	−660.179	−	74.3843i	−1.11141	−	0.125226i
$595$	−85.5385	+	19.5236i	−0.143762	+	0.0328128i
$596$	46.6647	+	74.2665i	0.0782965	+	0.124608i
$597$		−	185.591i		−	0.310872i
$598$	848.188	−	676.407i	1.41837	−	1.13112i
$599$	67.0541	+	191.630i	0.111943	+	0.319916i	0.986202	−	0.165544i	$-0.0529380\pi$
$599$	67.0541	+	191.630i	0.111943	+	0.319916i	−0.874259	+	0.485460i	$0.838652\pi$
$600$	22.0910	+	5.04212i	0.0368183	+	0.00840354i
$601$	−128.058	+	102.123i	−0.213075	+	0.169922i	−0.724212	−	0.689578i	$-0.757796\pi$
$601$	−128.058	+	102.123i	−0.213075	+	0.169922i	0.511136	+	0.859500i	$0.329225\pi$
$602$	15.9312	+	141.393i	0.0264638	+	0.234873i
$603$	902.755	−	101.716i	1.49711	−	0.168683i
$604$	−38.6384	+	110.422i	−0.0639709	+	0.182818i
$605$	−1018.89	−	1018.89i	−1.68412	−	1.68412i
$606$	128.123	+	266.050i	0.211424	+	0.439027i
$607$	165.858	−	79.8728i	0.273241	−	0.131586i	−0.292246	−	0.956343i	$-0.594402\pi$
$607$	165.858	−	79.8728i	0.273241	−	0.131586i	0.565487	+	0.824757i	$0.308688\pi$
$608$	129.480	−	81.3579i	0.212961	−	0.133812i
$609$	2.57459	−	22.8501i	0.00422758	−	0.0375208i
$610$			274.628i			0.450211i
$611$	118.972	+	118.972i	0.194716	+	0.194716i
$612$	178.041	−	111.870i	0.290916	−	0.182795i
$613$	97.6277	−	22.2829i	0.159262	−	0.0363506i	−0.142146	−	0.989846i	$-0.545400\pi$
$613$	97.6277	−	22.2829i	0.159262	−	0.0363506i	0.301409	+	0.953495i	$0.402543\pi$
$614$	152.235	−	190.897i	0.247940	−	0.310907i
$615$	−45.3603	−	198.737i	−0.0737566	−	0.323149i
$616$	63.2861	−	131.415i	0.102737	−	0.213336i
$617$	−655.527	−	149.620i	−1.06244	−	0.242496i	−0.344635	−	0.938737i	$-0.611997\pi$
$617$	−655.527	−	149.620i	−1.06244	−	0.242496i	−0.717808	+	0.696241i	$0.754854\pi$
$618$	178.573	+	62.4853i	0.288953	+	0.101109i
$619$	194.908	−	244.407i	0.314875	−	0.394841i	−0.599058	−	0.800706i	$-0.704458\pi$
$619$	194.908	−	244.407i	0.314875	−	0.394841i	0.913933	+	0.405865i	$0.133030\pi$
$620$	112.403	−	140.948i	0.181295	−	0.227336i
$621$	−374.259	+	235.163i	−0.602672	+	0.378684i
$622$	21.5810	+	191.536i	0.0346961	+	0.307936i
$623$	−87.0319	−	138.510i	−0.139698	−	0.222328i
$624$		−	214.423i		−	0.343626i
$625$	295.675	+	370.764i	0.473079	+	0.593223i
$626$	−519.913	−	181.925i	−0.830532	−	0.290616i
$627$	108.013			0.172270
$628$	−115.333	−	55.5413i	−0.183651	−	0.0884415i
$629$	−536.799	+	60.4828i	−0.853417	+	0.0961570i
$630$	45.3608	−	94.1927i	0.0720013	−	0.149512i
$631$	−5.77969	+	7.24750i	−0.00915957	+	0.0114857i	−0.786390	−	0.617730i	$-0.788052\pi$
$631$	−5.77969	+	7.24750i	−0.00915957	+	0.0114857i	0.777231	+	0.629216i	$0.216624\pi$
$632$	9.09449	+	2.07576i	0.0143900	+	0.00328443i
$633$	−104.839	−	131.464i	−0.165623	−	0.207684i
$634$	−140.022	−	111.664i	−0.220856	−	0.176127i
$635$	−262.791	−	751.013i	−0.413844	−	1.18270i
$636$	−26.6554	−	76.1768i	−0.0419110	−	0.119775i
$637$	566.251	+	355.799i	0.888935	+	0.558555i
$638$	−538.676	+	1118.57i	−0.844319	+	1.75325i
$639$	−334.986	+	117.217i	−0.524234	+	0.183437i
$640$	−149.960	+	657.017i	−0.234312	+	1.02659i
$641$	−192.744	−	67.4440i	−0.300693	−	0.105217i	0.175716	−	0.984441i	$-0.443776\pi$
$641$	−192.744	−	67.4440i	−0.300693	−	0.105217i	−0.476409	+	0.879224i	$0.658062\pi$
$642$	−36.9350	+	17.7869i	−0.0575311	+	0.0277055i
$643$	59.8541	−	531.220i	0.0930857	−	0.826158i	−0.857243	−	0.514911i	$-0.827825\pi$
$643$	59.8541	−	531.220i	0.0930857	−	0.826158i	0.950329	−	0.311247i	$-0.100747\pi$
$644$	13.1125	+	57.4497i	0.0203611	+	0.0892077i
$645$	39.2642	−	172.028i	0.0608748	−	0.266710i
$646$	−201.862	+	160.980i	−0.312480	+	0.249194i
$647$	−450.889	−	283.312i	−0.696891	−	0.437886i	0.136448	−	0.990647i	$-0.456431\pi$
$647$	−450.889	−	283.312i	−0.696891	−	0.437886i	−0.833340	+	0.552761i	$0.813574\pi$
$648$	42.6872	−	378.859i	0.0658753	−	0.584659i
$649$	−220.486	−	138.540i	−0.339731	−	0.213467i
$650$	−103.289	+	129.520i	−0.158906	+	0.199262i
$651$	15.2354	+	19.1046i	0.0234031	+	0.0293466i
$652$	−235.286	+	295.040i	−0.360868	+	0.452515i
$653$	654.276	−	149.334i	1.00195	−	0.228690i	0.310082	−	0.950710i	$-0.399643\pi$
$653$	654.276	−	149.334i	1.00195	−	0.228690i	0.691872	+	0.722020i	$0.256786\pi$
$654$	73.4588	−	35.3759i	0.112322	−	0.0540916i
$655$	−189.776	+	151.341i	−0.289734	+	0.231055i
$656$	−1137.80	+	259.696i	−1.73445	+	0.395878i
$657$	−983.808	+	110.849i	−1.49742	+	0.168719i
$658$	−31.4578	+	11.0076i	−0.0478083	+	0.0167288i
$659$	14.1912	−	14.1912i	0.0215344	−	0.0215344i	−0.696258	−	0.717792i	$-0.745153\pi$
$659$	14.1912	−	14.1912i	0.0215344	−	0.0215344i	0.717792	+	0.696258i	$0.245153\pi$
$660$	77.6658	−	77.6658i	0.117675	−	0.117675i
$661$	−218.950	+	959.283i	−0.331241	+	1.45126i	0.485491	+	0.874242i	$0.338641\pi$
$661$	−218.950	+	959.283i	−0.331241	+	1.45126i	−0.816731	+	0.577018i	$0.804216\pi$
$662$	−55.0564	+	34.5942i	−0.0831667	+	0.0522571i
$663$	20.1148	+	178.523i	0.0303390	+	0.269266i
$664$	−377.500	+	132.093i	−0.568525	+	0.198935i
$665$	−11.6262	+	33.2257i	−0.0174830	+	0.0499634i
$666$	342.458	−	545.019i	0.514201	−	0.818346i
$667$	183.804	+	805.296i	0.275568	+	1.20734i
$668$	84.3957	+	84.3957i	0.126341	+	0.126341i
$669$	248.096	+	86.8125i	0.370846	+	0.129765i
$670$	−603.501	+	960.467i	−0.900749	+	1.43353i
$671$	466.634	+	293.205i	0.695430	+	0.436968i
$672$	18.9897	+	9.14494i	0.0282584	+	0.0136085i
$673$	−34.4729	+	305.956i	−0.0512228	+	0.454615i	0.941754	+	0.336303i	$0.109177\pi$
$673$	−34.4729	+	305.956i	−0.0512228	+	0.454615i	−0.992977	+	0.118311i	$0.962252\pi$
$674$			161.972i			0.240314i
$675$	47.7266	−	47.7266i	0.0707061	−	0.0707061i
$676$	38.7164	+	18.6448i	0.0572728	+	0.0275811i
$677$	−92.9593	+	147.944i	−0.137311	+	0.218529i	−0.908300	−	0.418319i	$-0.862619\pi$
$677$	−92.9593	+	147.944i	−0.137311	+	0.218529i	0.770989	+	0.636848i	$0.219762\pi$
$678$	−278.608	+	278.608i	−0.410926	+	0.410926i
$679$	93.7047	−	45.1258i	0.138004	−	0.0664592i
$680$	48.4102	−	429.653i	0.0711915	−	0.631842i
$681$	−25.4159	+	12.2396i	−0.0373214	+	0.0179730i
$682$	−435.745	−	1245.29i	−0.638922	−	1.82593i
$683$	408.112	−	847.453i	0.597528	−	1.24078i	−0.354582	−	0.935025i	$-0.615377\pi$
$683$	408.112	−	847.453i	0.597528	−	1.24078i	0.952110	−	0.305755i	$-0.0989088\pi$
$684$		−	84.3614i		−	0.123335i
$685$	882.937	+	308.953i	1.28896	+	0.451027i
$686$	−227.645	+	143.039i	−0.331844	+	0.208511i
$687$	−44.6016	−	92.6161i	−0.0649222	−	0.134812i
$688$	−984.890	−	224.795i	−1.43153	−	0.326737i
$689$	−965.595	−	108.796i	−1.40144	−	0.157905i
$690$	29.8380	−	264.819i	0.0432435	−	0.383796i
$691$	80.6978	−	353.560i	0.116784	−	0.511665i	−0.882371	−	0.470555i	$-0.844054\pi$
$691$	80.6978	−	353.560i	0.116784	−	0.511665i	0.999155	−	0.0411094i	$-0.0130892\pi$
$692$	−196.309	+	94.5375i	−0.283684	+	0.136615i
$693$	−111.618	−	177.639i	−0.161065	−	0.256333i
$694$	−43.1178	+	123.224i	−0.0621294	+	0.177556i
$695$	−541.745			−0.779489
$696$	102.095	+	49.1665i	0.146689	+	0.0706416i
$697$	922.946	−	322.953i	1.32417	−	0.463347i
$698$	192.424	+	399.572i	0.275679	+	0.572453i
$699$	9.25440	+	1.04272i	0.0132395	+	0.00149173i
$700$	−3.90422	−	8.10720i	−0.00557746	−	0.0115817i
$701$	149.921	+	149.921i	0.213868	+	0.213868i	0.805908	−	0.592041i	$-0.201678\pi$
$701$	149.921	+	149.921i	0.213868	+	0.213868i	−0.592041	+	0.805908i	$0.701678\pi$
$702$	−375.376	−	235.865i	−0.534724	−	0.335989i
$703$	−94.0353	+	195.266i	−0.133763	+	0.277762i
$704$	372.243	+	372.243i	0.528754	+	0.528754i
$705$	41.3303			0.0586246
$706$	1593.83	+	179.582i	2.25755	+	0.254365i
$707$	−83.7905	+	173.993i	−0.118516	+	0.246100i
$708$	7.67838	−	12.2201i	0.0108452	−	0.0172600i
$709$	−784.282	−	492.797i	−1.10618	−	0.695059i	−0.150249	−	0.988648i	$-0.548008\pi$
$709$	−784.282	−	492.797i	−1.10618	−	0.695059i	−0.955932	+	0.293589i	$0.905150\pi$
$710$	146.359	−	418.270i	0.206140	−	0.589113i
$711$	9.48750	−	9.48750i	0.0133439	−	0.0133439i
$712$	785.925	−	179.382i	1.10383	−	0.251941i
$713$	−743.228	−	467.001i	−1.04240	−	0.654981i
$714$	−33.5896	−	11.7535i	−0.0470443	−	0.0164615i
$715$	−436.773	−	1248.23i	−0.610871	−	1.74577i
$716$	61.0112	−	6.87432i	0.0852112	−	0.00960100i
$717$	−16.2589	−	25.8759i	−0.0226763	−	0.0360891i
$718$	−963.561	−	219.927i	−1.34201	−	0.306304i
$719$	−536.048	−	536.048i	−0.745546	−	0.745546i	0.228093	−	0.973639i	$-0.426751\pi$
$719$	−536.048	−	536.048i	−0.745546	−	0.745546i	−0.973639	+	0.228093i	$0.926751\pi$
$720$	524.855	+	524.855i	0.728966	+	0.728966i
$721$	40.8644	+	116.784i	0.0566773	+	0.161975i
$722$	−83.2901	−	739.220i	−0.115360	−	1.02385i
$723$	−66.2274	−	290.161i	−0.0916008	−	0.401330i
$724$	−24.1482	−	30.2808i	−0.0333538	−	0.0418244i
$725$	−54.7270	−	113.642i	−0.0754856	−	0.156747i
$726$	−130.050	−	569.788i	−0.179133	−	0.784832i
$727$	1023.52	+	816.228i	1.40786	+	1.12273i	0.975237	+	0.221162i	$0.0709849\pi$
$727$	1023.52	+	816.228i	1.40786	+	1.12273i	0.432628	+	0.901573i	$0.357586\pi$
$728$	76.0978	−	60.6860i	0.104530	−	0.0833598i
$729$	−355.709	−	283.668i	−0.487941	−	0.389120i
$730$	657.686	−	1046.70i	0.900939	−	1.43384i
$731$	841.084	+	94.7675i	1.15059	+	0.129641i
$732$	−16.2505	+	25.8625i	−0.0222001	+	0.0353312i
$733$	340.638	+	427.146i	0.464717	+	0.582737i	0.957869	−	0.287206i	$-0.0927266\pi$
$733$	340.638	+	427.146i	0.464717	+	0.582737i	−0.493151	+	0.869943i	$0.664155\pi$
$734$	−112.623	−	25.7055i	−0.153438	−	0.0350211i
$735$	160.159	−	36.5552i	0.217903	−	0.0497349i
$736$	−752.355	−	84.7701i	−1.02222	−	0.115177i
$737$	987.649	+	2050.87i	1.34009	+	2.78273i
$738$	−384.819	+	1099.75i	−0.521435	+	1.49018i
$739$	−1208.01	−	275.721i	−1.63466	−	0.373100i	−0.696026	−	0.718016i	$-0.745050\pi$
$739$	−1208.01	−	275.721i	−1.63466	−	0.373100i	−0.938634	+	0.344916i	$0.887907\pi$
$740$	72.7891	+	208.019i	0.0983636	+	0.281107i
$741$	64.9398	+	31.2734i	0.0876381	+	0.0422043i
$742$	102.406	−	162.978i	0.138013	−	0.219647i
$743$	1205.06	−	421.668i	1.62188	−	0.567521i	0.641932	−	0.766762i	$-0.278133\pi$
$743$	1205.06	−	421.668i	1.62188	−	0.567521i	0.979951	+	0.199240i	$0.0638474\pi$
$744$	−113.661	+	39.7717i	−0.152770	+	0.0534566i
$745$	161.741	−	202.817i	0.217102	−	0.272238i
$746$	−145.656	+	116.157i	−0.195249	+	0.155706i
$747$	−128.006	+	560.832i	−0.171360	+	0.750779i
$748$	411.918	+	328.493i	0.550692	+	0.439162i
$749$	−24.1549	−	11.6324i	−0.0322495	−	0.0155305i
$750$	27.2376	+	241.740i	0.0363168	+	0.322321i
$751$	194.334	−	403.540i	0.258768	−	0.537336i	−0.730594	−	0.682812i	$-0.760757\pi$
$751$	194.334	−	403.540i	0.258768	−	0.537336i	0.989362	+	0.145475i	$0.0464712\pi$
$752$		−	236.623i		−	0.314659i
$753$	17.8402	−	50.9843i	0.0236921	−	0.0677082i
$754$	−647.725	+	516.544i	−0.859052	+	0.685071i
$755$	346.002			0.458281
$756$	20.3894	−	12.8115i	0.0269701	−	0.0169464i
$757$	549.248	−	61.8854i	0.725558	−	0.0817508i	0.258543	−	0.966000i	$-0.416758\pi$
$757$	549.248	−	61.8854i	0.725558	−	0.0817508i	0.467016	+	0.884249i	$0.345329\pi$
$758$	661.537	+	1052.83i	0.872740	+	1.38896i
$759$	−418.111	−	333.432i	−0.550870	−	0.439304i
$760$	−135.624	−	108.157i	−0.178453	−	0.142311i
$761$	−415.857	+	1188.45i	−0.546462	+	1.56170i	0.257044	+	0.966400i	$0.417252\pi$
$761$	−415.857	+	1188.45i	−0.546462	+	1.56170i	−0.803505	+	0.595298i	$0.797034\pi$
$762$	71.8121	−	314.629i	0.0942416	−	0.412900i
$763$	48.0408	+	23.1353i	0.0629631	+	0.0303214i
$764$	−366.207	+	83.5844i	−0.479329	+	0.109404i
$765$	−486.218	−	387.746i	−0.635579	−	0.506858i
$766$	264.766	+	1160.02i	0.345648	+	1.51438i
$767$	−92.4485	−	147.131i	−0.120533	−	0.191827i
$768$	−138.673	+	138.673i	−0.180564	+	0.180564i
$769$	−508.217			−0.660880			−0.330440	−	0.943827i	$-0.607197\pi$
$769$	−508.217			−0.660880			−0.330440	+	0.943827i	$0.607197\pi$
$770$	260.308	+	29.3297i	0.338062	+	0.0380905i
$771$	−7.17206	−	11.4143i	−0.00930228	−	0.0148045i
$772$	49.4145	+	102.610i	0.0640084	+	0.132915i
$773$	−92.6639	+	44.6246i	−0.119876	+	0.0577291i	−0.492860	−	0.870108i	$-0.664049\pi$
$773$	−92.6639	+	44.6246i	−0.119876	+	0.0577291i	0.372985	+	0.927837i	$0.378334\pi$
$774$	−713.152	+	713.152i	−0.921385	+	0.921385i
$775$	126.516	+	44.2697i	0.163246	+	0.0571222i
$776$	57.3852	+	509.308i	0.0739500	+	0.656324i
$777$	−29.6841	+	3.34460i	−0.0382035	+	0.00430450i
$778$	423.762	+	531.381i	0.544682	+	0.683009i
$779$	87.2962	−	382.469i	0.112062	−	0.490975i
$780$	69.1810	−	24.2075i	0.0886936	−	0.0310352i
$781$	−554.443	−	695.250i	−0.709914	−	0.890204i
$782$	1278.33			1.63469
$783$	285.806	−	179.584i	0.365014	−	0.229354i
$784$	−209.285	−	916.937i	−0.266945	−	1.16956i
$785$	−42.3900	+	376.222i	−0.0540000	+	0.479263i
$786$	−97.8330	+	11.0231i	−0.124470	+	0.0140243i
$787$			608.359i			0.773010i	0.922287	+	0.386505i	$0.126318\pi$
$787$			608.359i			0.773010i	−0.922287	+	0.386505i	$0.873682\pi$
$788$	228.031	+	191.405i	0.289380	+	0.242899i
$789$	70.7821			0.0897111
$790$	1.87576	+	16.6479i	0.00237438	+	0.0210732i
$791$	−256.057	−	28.8507i	−0.323713	−	0.0364737i
$792$	1007.94	−	230.057i	1.27266	−	0.290476i
$793$	195.657	+	311.387i	0.246730	+	0.392669i
$794$		−	1411.71i		−	1.77797i
$795$	−186.620	+	148.824i	−0.234742	+	0.187200i
$796$	−119.956	−	342.815i	−0.150699	−	0.430673i
$797$	−971.849	−	221.818i	−1.21938	−	0.278317i	−0.436053	−	0.899921i	$-0.643624\pi$
$797$	−971.849	−	221.818i	−1.21938	−	0.278317i	−0.783331	+	0.621604i	$0.786481\pi$
$798$	−11.1626	+	8.90190i	−0.0139883	+	0.0111553i
$799$	22.1974	+	197.007i	0.0277814	+	0.246567i
$800$	114.886	−	12.9446i	0.143608	−	0.0161807i
$801$	382.958	−	1094.43i	0.478099	−	1.36633i
$802$	−0.306282	−	0.306282i	−0.000381898	−	0.000381898i
$803$	−1076.32	−	2235.01i	−1.34038	−	2.78332i
$804$	−113.667	+	54.7389i	−0.141376	+	0.0680833i
$805$	147.570	−	92.7244i	0.183317	−	0.115186i
$806$	98.5724	−	874.854i	0.122298	−	1.08543i
$807$			230.930i			0.286158i
$808$	−672.937	−	672.937i	−0.832842	−	0.832842i
$809$	−540.505	+	339.622i	−0.668115	+	0.419804i	−0.822933	−	0.568139i	$-0.807664\pi$
$809$	−540.505	+	339.622i	−0.668115	+	0.419804i	0.154818	+	0.987943i	$0.450521\pi$
$810$	667.547	−	152.363i	0.824132	−	0.188103i
$811$	550.586	−	690.413i	0.678898	−	0.851311i	−0.316354	−	0.948641i	$-0.602459\pi$
$811$	550.586	−	690.413i	0.678898	−	0.851311i	0.995252	+	0.0973299i	$0.0310302\pi$
$812$	−10.0135	−	43.8720i	−0.0123319	−	0.0540295i
$813$	−118.147	+	245.335i	−0.145322	+	0.301765i
$814$	1572.40	+	358.889i	1.93169	+	0.440895i
$815$	1053.48	+	368.628i	1.29261	+	0.452305i
$816$	157.530	−	197.537i	0.193052	−	0.242079i
$817$	211.726	−	265.496i	0.259151	−	0.324965i
$818$	975.686	−	613.064i	1.19277	−	0.749467i
$819$	−15.6747	−	139.117i	−0.0191389	−	0.169862i
$820$	−212.241	−	337.780i	−0.258831	−	0.411926i
$821$		−	622.098i		−	0.757732i	−0.925452	−	0.378866i	$-0.876314\pi$
$821$		−	622.098i		−	0.757732i	0.925452	−	0.378866i	$-0.123686\pi$
$822$	236.559	+	296.635i	0.287784	+	0.360870i
$823$	−25.2304	−	8.82851i	−0.0306567	−	0.0107272i	0.314907	−	0.949122i	$-0.398027\pi$
$823$	−25.2304	−	8.82851i	−0.0306567	−	0.0107272i	−0.345564	+	0.938395i	$0.612312\pi$
$824$	−609.722			−0.739953
$825$	73.5755	+	35.4321i	0.0891824	+	0.0429480i
$826$	34.2038	−	3.85385i	0.0414090	−	0.00466568i
$827$	−123.182	+	255.790i	−0.148950	+	0.309298i	−0.962072	−	0.272795i	$-0.912052\pi$
$827$	−123.182	+	255.790i	−0.148950	+	0.309298i	0.813122	+	0.582093i	$0.197766\pi$
$828$	−260.420	+	326.556i	−0.314517	+	0.394391i
$829$	−632.309	−	144.321i	−0.762738	−	0.174090i	−0.176579	−	0.984286i	$-0.556503\pi$
$829$	−632.309	−	144.321i	−0.762738	−	0.174090i	−0.586158	+	0.810197i	$0.699360\pi$
$830$	−447.837	−	561.570i	−0.539563	−	0.676591i
$831$	185.408	+	147.858i	0.223115	+	0.177928i
$832$	116.024	+	331.576i	0.139451	+	0.398529i
$833$	260.262	+	743.787i	0.312440	+	0.892902i
$834$	−186.052	−	116.904i	−0.223084	−	0.140173i
$835$	153.161	−	318.043i	0.183427	−	0.380890i
$836$	199.518	−	69.8144i	0.238658	−	0.0835100i
$837$	−79.8174	+	349.703i	−0.0953613	+	0.417805i
$838$	1450.01	+	507.382i	1.73033	+	0.605468i
$839$	821.170	−	395.455i	0.978748	−	0.471340i	0.125074	−	0.992147i	$-0.460083\pi$
$839$	821.170	−	395.455i	0.978748	−	0.471340i	0.853674	+	0.520807i	$0.174369\pi$
$840$	2.67701	−	23.7591i	0.00318691	−	0.0282846i
$841$	46.7770	+	204.943i	0.0556206	+	0.243690i
$842$	17.9702	−	78.7327i	0.0213423	−	0.0935067i
$843$	−79.9891	+	63.7892i	−0.0948862	+	0.0756693i
$844$	−278.626	−	175.073i	−0.330126	−	0.207432i
$845$	14.2300	−	126.295i	0.0168403	−	0.149462i
$846$	−200.024	−	125.683i	−0.236435	−	0.148562i
$847$	238.307	−	298.828i	0.281354	−	0.352807i
$848$	852.046	+	1068.43i	1.00477	+	1.25994i
$849$	2.38972	−	2.99661i	0.00281475	−	0.00352958i
$850$	−190.309	+	43.4368i	−0.223893	+	0.0511021i
$851$	966.781	−	465.577i	1.13605	−	0.547094i
$852$	38.5331	−	30.7292i	0.0452267	−	0.0360671i
$853$	800.178	−	182.635i	0.938075	−	0.214110i	0.273961	−	0.961741i	$-0.411666\pi$
$853$	800.178	−	182.635i	0.938075	−	0.214110i	0.664114	+	0.747631i	$0.268809\pi$
$854$	−72.3887	+	8.15625i	−0.0847643	+	0.00955064i
$855$	−235.506	+	82.4073i	−0.275446	+	0.0963828i
$856$	93.4217	−	93.4217i	0.109137	−	0.109137i
$857$	940.602	−	940.602i	1.09755	−	1.09755i	0.102855	−	0.994696i	$-0.467202\pi$
$857$	940.602	−	940.602i	1.09755	−	1.09755i	0.994696	−	0.102855i	$-0.0327979\pi$
$858$	119.356	−	522.932i	0.139109	−	0.609478i
$859$	−455.828	+	286.416i	−0.530650	+	0.333429i	−0.770562	−	0.637365i	$-0.780024\pi$
$859$	−455.828	+	286.416i	−0.530650	+	0.333429i	0.239912	+	0.970795i	$0.422881\pi$
$860$	−38.6628	−	343.142i	−0.0449567	−	0.399002i
$861$	51.0374	−	17.8588i	0.0592769	−	0.0207419i
$862$	−655.102	+	1872.17i	−0.759979	+	2.17189i
$863$	−425.494	+	677.170i	−0.493040	+	0.784669i	−0.996864	−	0.0791374i	$-0.974783\pi$
$863$	−425.494	+	677.170i	−0.493040	+	0.784669i	0.503823	+	0.863807i	$0.331926\pi$
$864$	68.8461	+	301.635i	0.0796830	+	0.349114i
$865$	455.676	+	455.676i	0.526793	+	0.526793i
$866$	−632.296	−	221.250i	−0.730134	−	0.255485i
$867$	6.11106	−	9.72570i	0.00704851	−	0.0112176i
$868$	40.4906	+	25.4419i	0.0466481	+	0.0293110i
$869$	30.2898	+	14.5868i	0.0348559	+	0.0167857i
$870$	−22.7860	+	202.232i	−0.0261908	+	0.232450i
$871$			1518.98i			1.74395i
$872$	−185.803	+	185.803i	−0.213077	+	0.213077i
$873$	664.187	+	319.856i	0.760810	+	0.366387i
$874$	272.864	−	434.260i	0.312201	−	0.496865i
$875$	−112.497	+	112.497i	−0.128568	+	0.128568i
$876$	123.872	−	59.6536i	0.141406	−	0.0680977i
$877$	11.7823	−	104.571i	0.0134348	−	0.119237i	−0.985205	−	0.171381i	$-0.945177\pi$
$877$	11.7823	−	104.571i	0.0134348	−	0.119237i	0.998640	+	0.0521443i	$0.0166056\pi$
$878$	1509.62	−	726.995i	1.71938	−	0.828012i
$879$	118.512	+	338.687i	0.134826	+	0.385310i
$880$	−806.952	+	1675.65i	−0.916991	+	1.90415i
$881$			906.966i			1.02947i	0.857348	+	0.514737i	$0.172110\pi$
$881$			906.966i			1.02947i	−0.857348	+	0.514737i	$0.827890\pi$
$882$	−886.271	−	310.120i	−1.00484	−	0.351610i
$883$	−653.268	+	410.475i	−0.739828	+	0.464865i	−0.848488	−	0.529214i	$-0.822487\pi$
$883$	−653.268	+	410.475i	−0.739828	+	0.464865i	0.108660	+	0.994079i	$0.465344\pi$
$884$	152.544	+	316.760i	0.172561	+	0.358326i
$885$	−41.6145	−	9.49825i	−0.0470221	−	0.0107325i
$886$	1393.67	+	157.029i	1.57299	+	0.177233i
$887$	52.1975	−	463.265i	0.0588472	−	0.522284i	−0.929362	−	0.369171i	$-0.879642\pi$
$887$	52.1975	−	463.265i	0.0588472	−	0.522284i	0.988209	−	0.153113i	$-0.0489297\pi$
$888$	32.7569	−	143.517i	0.0368884	−	0.161618i
$889$	190.153	−	91.5730i	0.213896	−	0.103007i
$890$	770.262	+	1225.86i	0.865463	+	1.37738i
$891$	453.815	−	1296.93i	0.509332	−	1.45559i
$892$	514.384			0.576664
$893$	71.6634	+	34.5113i	0.0802502	+	0.0386465i
$894$	99.3134	−	34.7513i	0.111089	−	0.0388717i
$895$	−78.7886	−	163.606i	−0.0880319	−	0.182800i
$896$	−177.635	−	20.0147i	−0.198254	−	0.0223378i
$897$	−154.837	−	321.523i	−0.172617	−	0.358442i
$898$	−98.9933	−	98.9933i	−0.110238	−	0.110238i
$899$	567.573	+	356.629i	0.631338	+	0.396696i
$900$	27.6734	−	57.4645i	0.0307483	−	0.0638494i
$901$	−809.622	−	809.622i	−0.898582	−	0.898582i
$902$	−2919.41			−3.23660
$903$	46.5106	+	5.24048i	0.0515067	+	0.00580342i
$904$	550.956	−	1144.07i	0.609464	−	1.26557i
$905$	−60.9443	+	96.9923i	−0.0673418	+	0.107174i
$906$	118.828	+	74.6646i	0.131157	+	0.0824112i
$907$	−490.219	+	1400.96i	−0.540484	+	1.54461i	0.272398	+	0.962185i	$0.412183\pi$
$907$	−490.219	+	1400.96i	−0.540484	+	1.54461i	−0.812882	+	0.582429i	$0.802102\pi$
$908$	−39.0361	+	39.0361i	−0.0429913	+	0.0429913i
$909$	−1334.51	+	304.594i	−1.46811	+	0.335087i
$910$	148.011	+	93.0012i	0.162649	+	0.102199i
$911$	−1254.70	−	439.038i	−1.37728	−	0.481930i	−0.462762	−	0.886483i	$-0.653141\pi$
$911$	−1254.70	−	439.038i	−1.37728	−	0.481930i	−0.914515	+	0.404553i	$0.867427\pi$
$912$	−33.4797	−	95.6795i	−0.0367102	−	0.104912i
$913$	−1432.32	+	161.384i	−1.56881	+	0.176762i
$914$	166.501	+	264.985i	0.182168	+	0.289918i
$915$	88.0726	+	20.1020i	0.0962542	+	0.0219694i
$916$	−142.249	−	142.249i	−0.155293	−	0.155293i
$917$	−45.5278	−	45.5278i	−0.0496487	−	0.0496487i
$918$	−172.532	−	493.068i	−0.187943	−	0.537111i
$919$	53.8713	+	478.121i	0.0586195	+	0.520262i	0.988370	+	0.152071i	$0.0485942\pi$
$919$	53.8713	+	478.121i	0.0586195	+	0.520262i	−0.929750	+	0.368191i	$0.879977\pi$
$920$	191.115	+	837.330i	0.207734	+	0.910141i
$921$	−50.0770	−	62.7945i	−0.0543724	−	0.0681808i
$922$	758.475	+	1574.99i	0.822641	+	1.70823i
$923$	−132.045	−	578.527i	−0.143061	−	0.626790i
$924$	22.7784	+	18.1651i	0.0246519	+	0.0196592i
$925$	−128.108	+	102.163i	−0.138495	+	0.110446i
$926$	597.586	+	476.559i	0.645342	+	0.514643i
$927$	−466.585	+	742.565i	−0.503327	+	0.801041i
$928$	574.542	+	64.7354i	0.619119	+	0.0697580i
$929$	−113.018	+	179.867i	−0.121656	+	0.193614i	−0.902000	−	0.431736i	$-0.857901\pi$
$929$	−113.018	+	179.867i	−0.121656	+	0.193614i	0.780344	+	0.625350i	$0.215044\pi$
$930$	−134.839	−	169.082i	−0.144988	−	0.181809i
$931$	308.226	+	70.3506i	0.331070	+	0.0755645i
$932$	17.7683	−	4.05550i	0.0190647	−	0.00435140i
$933$	63.0049	+	7.09894i	0.0675293	+	0.00760873i
$934$	8.40636	+	17.4560i	0.00900039	+	0.0186895i
$935$	514.658	−	1470.81i	0.550437	−	1.57306i
$936$	672.605	+	153.518i	0.718595	+	0.164015i
$937$	−79.2910	−	226.601i	−0.0846222	−	0.241836i	0.893795	−	0.448476i	$-0.148033\pi$
$937$	−79.2910	−	226.601i	−0.0846222	−	0.241836i	−0.978417	+	0.206640i	$0.933747\pi$
$938$	−271.091	−	130.551i	−0.289010	−	0.139180i
$939$	−96.3991	+	153.418i	−0.102661	+	0.163385i
$940$	76.3437	−	26.7138i	0.0812167	−	0.0284190i
$941$	69.8096	−	24.4274i	0.0741866	−	0.0259590i	−0.292931	−	0.956134i	$-0.594630\pi$
$941$	69.8096	−	24.4274i	0.0741866	−	0.0259590i	0.367117	+	0.930175i	$0.380345\pi$
$942$	−95.7437	+	120.059i	−0.101639	+	0.127451i
$943$	−1518.58	+	1211.03i	−1.61037	+	1.28423i
$944$	−54.3792	+	238.251i	−0.0576050	+	0.252384i
$945$	−55.6821	−	44.4050i	−0.0589229	−	0.0469894i
$946$	−2276.81	−	1096.45i	−2.40678	−	1.15904i
$947$	147.524	+	1309.31i	0.155780	+	1.38259i	0.791737	+	0.610862i	$0.209177\pi$
$947$	147.524	+	1309.31i	0.155780	+	1.38259i	−0.635957	+	0.771725i	$0.719394\pi$
$948$	−0.808451	+	1.67876i	−0.000852796	+	0.00177085i
$949$		−	1655.36i		−	1.74432i
$950$	−25.8663	+	73.9217i	−0.0272277	+	0.0778123i
$951$	−46.0597	+	36.7314i	−0.0484329	+	0.0386239i
$952$	114.689			0.120472
$953$	−1131.72	+	711.109i	−1.18754	+	0.746180i	−0.973061	−	0.230549i	$-0.925948\pi$
$953$	−1131.72	+	711.109i	−1.18754	+	0.746180i	−0.214478	+	0.976729i	$0.568805\pi$
$954$	1355.74	−	152.755i	1.42111	−	0.160121i
$955$	591.062	+	940.669i	0.618913	+	0.984994i
$956$	−46.7576	−	37.2880i	−0.0489096	−	0.0390041i
$957$	319.294	+	254.628i	0.333640	+	0.266069i
$958$	267.313	−	763.937i	0.279033	−	0.797429i
$959$	−55.2138	+	241.907i	−0.0575743	+	0.252250i
$960$	77.7473	+	37.4411i	0.0809868	+	0.0390012i
$961$	242.443	−	55.3360i	0.252282	−	0.0575817i
$962$	841.446	+	671.031i	0.874684	+	0.697537i
$963$	−42.2858	−	185.266i	−0.0439105	−	0.192384i
$964$	−309.878	−	493.168i	−0.321450	−	0.511585i
$965$	238.181	−	238.181i	0.246820	−	0.246820i
$966$	70.6894			0.0731774
$967$	−428.309	−	48.2588i	−0.442926	−	0.0499057i	−0.112314	−	0.993673i	$-0.535826\pi$
$967$	−428.309	−	48.2588i	−0.442926	−	0.0499057i	−0.330611	+	0.943767i	$0.607255\pi$
$968$	1002.11	+	1594.84i	1.03523	+	1.64756i
$969$	36.8500	+	76.5198i	0.0380289	+	0.0789678i
$970$	−829.318	+	399.379i	−0.854968	+	0.411731i
$971$	28.6346	−	28.6346i	0.0294898	−	0.0294898i	−0.692208	−	0.721698i	$-0.743362\pi$
$971$	28.6346	−	28.6346i	0.0294898	−	0.0294898i	0.721698	+	0.692208i	$0.243362\pi$
$972$	244.418	+	85.5254i	0.251459	+	0.0879891i
$973$	−16.0894	−	142.797i	−0.0165359	−	0.146760i
$974$	1553.84	−	175.075i	1.59531	−	0.179749i
$975$	33.9763	+	42.6050i	0.0348475	+	0.0436974i
$976$	115.088	−	504.232i	0.117918	−	0.516631i
$977$	−93.0645	+	32.5647i	−0.0952554	+	0.0333313i	−0.377486	−	0.926015i	$-0.623211\pi$
$977$	−93.0645	+	32.5647i	−0.0952554	+	0.0333313i	0.282231	+	0.959347i	$0.408926\pi$
$978$	282.251	+	353.931i	0.288600	+	0.361893i
$979$	2905.29			2.96761
$980$	272.211	−	171.042i	0.277767	−	0.174532i
$981$	84.1009	+	368.470i	0.0857298	+	0.375607i
$982$	92.9905	−	825.313i	0.0946950	−	0.840441i
$983$	−1350.98	+	152.219i	−1.37434	+	0.154851i	−0.768049	−	0.640391i	$-0.778772\pi$
$983$	−1350.98	+	152.219i	−1.37434	+	0.154851i	−0.606292	+	0.795242i	$0.707344\pi$
$984$			266.464i			0.270796i
$985$	311.583	−	823.552i	0.316327	−	0.836093i
$986$	−976.205			−0.990066
$987$	1.22748	+	10.8942i	0.00124365	+	0.0110377i
$988$	140.168	+	15.7931i	0.141870	+	0.0159849i
$989$	−1639.15	+	374.125i	−1.65738	+	0.378286i
$990$	987.856	+	1572.16i	0.997835	+	1.58804i
$991$			1008.06i			1.01721i	0.860999	+	0.508607i	$0.169839\pi$
$991$			1008.06i			1.01721i	−0.860999	+	0.508607i	$0.830161\pi$
$992$	−480.366	+	383.079i	−0.484239	+	0.386168i
$993$	7.06431	+	20.1886i	0.00711411	+	0.0203310i
$994$	114.598	+	26.1562i	0.115290	+	0.0263141i
$995$	−839.839	+	669.749i	−0.844059	+	0.673114i
$996$	−8.94445	−	79.3842i	−0.00898037	−	0.0797030i
$997$	−1372.14	+	154.603i	−1.37627	+	0.155068i	−0.768909	−	0.639358i	$-0.779200\pi$
$997$	−1372.14	+	154.603i	−1.37627	+	0.155068i	−0.607361	+	0.794426i	$0.707772\pi$
$998$	708.580	−	2025.01i	0.710000	−	2.02906i
$999$	−310.063	−	310.063i	−0.310373	−	0.310373i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	197.3.f.a.20.8	✓	384
197.69	odd	28	inner	197.3.f.a.69.8	yes	384

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
197.3.f.a.20.8	✓	384	1.1	even	1	trivial
197.3.f.a.69.8	yes	384	197.69	odd	28	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 197 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	197.f (of order \(28\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.262848 - 2.33284i) q^{2} +(-0.767376 - 0.0864625i) q^{3} +(-1.47335 + 0.336283i) q^{4} +(2.37800 + 3.78457i) q^{5} +1.81289i q^{6} +(-0.926942 + 0.739212i) q^{7} +(-1.92969 - 5.51475i) q^{8} +(-8.19296 - 1.86999i) q^{9} +(8.20375 - 6.54227i) q^{10} +(-2.35759 - 20.9242i) q^{11} +(1.15969 - 0.130666i) q^{12} +(4.64080 - 13.2626i) q^{13} +(1.96811 + 1.96811i) q^{14} +(-1.49760 - 3.10980i) q^{15} +(-17.8042 + 8.57403i) q^{16} +(14.0190 - 8.80872i) q^{17} +(-2.20889 + 19.6044i) q^{18} -6.64265i q^{19} +(-4.77632 - 4.77632i) q^{20} +(0.775228 - 0.487108i) q^{21} +(-48.1932 + 10.9998i) q^{22} +(-20.5055 + 25.7131i) q^{23} +(1.00398 + 4.39873i) q^{24} +(2.17902 - 4.52478i) q^{25} +(-32.1595 - 7.34019i) q^{26} +(12.6855 + 4.43884i) q^{27} +(1.11713 - 1.40083i) q^{28} +(15.6592 - 19.6361i) q^{29} +(-6.86103 + 4.31107i) q^{30} +(2.98826 + 26.5216i) q^{31} +(12.2478 + 19.4923i) q^{32} +16.2606i q^{33} +(-24.2342 - 30.3888i) q^{34} +(-5.00187 - 1.75023i) q^{35} +12.7000 q^{36} +(-29.3959 - 14.1563i) q^{37} +(-15.4963 + 1.74601i) q^{38} +(-4.70796 + 9.77619i) q^{39} +(16.2821 - 20.4172i) q^{40} +(57.5778 + 13.1418i) q^{41} +(-1.34011 - 1.68045i) q^{42} +(39.9684 + 31.8738i) q^{43} +(10.5100 + 30.0359i) q^{44} +(-12.4058 - 35.4537i) q^{45} +(65.3746 + 41.0776i) q^{46} +(-5.19541 + 10.7884i) q^{47} +(14.4038 - 5.04011i) q^{48} +(-10.5907 + 46.4011i) q^{49} +(-11.1283 - 3.89397i) q^{50} +(-11.5195 + 5.54749i) q^{51} +(-2.37753 + 21.1012i) q^{52} +(-15.3884 - 67.4209i) q^{53} +(7.02076 - 30.7599i) q^{54} +(73.5827 - 58.6803i) q^{55} +(5.86528 + 3.68540i) q^{56} +(-0.574341 + 5.09741i) q^{57} +(-49.9238 - 31.3692i) q^{58} +(7.71045 - 9.66859i) q^{59} +(3.25226 + 4.07821i) q^{60} +(-16.3183 + 20.4625i) q^{61} +(61.0851 - 13.9423i) q^{62} +(8.97672 - 4.32296i) q^{63} +(-19.5464 + 15.5877i) q^{64} +(61.2293 - 13.9752i) q^{65} +(37.9334 - 4.27406i) q^{66} +(-102.037 + 35.7044i) q^{67} +(-17.6927 + 17.6927i) q^{68} +(17.9587 - 17.9587i) q^{69} +(-2.76828 + 12.1286i) q^{70} +(35.7587 - 22.4687i) q^{71} +(5.49738 + 48.7906i) q^{72} +(111.199 - 38.9101i) q^{73} +(-25.2978 + 72.2968i) q^{74} +(-2.06335 + 3.28380i) q^{75} +(2.23381 + 9.78697i) q^{76} +(17.6528 + 17.6528i) q^{77} +(24.0438 + 8.41328i) q^{78} +(-0.849447 + 1.35189i) q^{79} +(-74.7873 - 46.9920i) q^{80} +(58.7922 + 28.3128i) q^{81} +(15.5234 - 137.774i) q^{82} -68.4529i q^{83} +(-0.978377 + 0.978377i) q^{84} +(66.6745 + 32.1087i) q^{85} +(63.8508 - 101.618i) q^{86} +(-13.7143 + 13.7143i) q^{87} +(-110.842 + 53.3788i) q^{88} +(-15.4483 + 137.108i) q^{89} +(-79.4470 + 38.2597i) q^{90} +(5.50215 + 15.7242i) q^{91} +(21.5650 - 44.7802i) q^{92} -20.6104i q^{93} +(26.5332 + 9.28436i) q^{94} +(25.1396 - 15.7962i) q^{95} +(-7.71332 - 16.0169i) q^{96} +(-85.5233 - 19.5201i) q^{97} +(111.030 + 12.5101i) q^{98} +(-19.8124 + 175.840i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 384 q - 12 q^{2} - 12 q^{3} - 14 q^{4} - 4 q^{5} - 14 q^{7} + 48 q^{8} - 14 q^{9} - 14 q^{10} + 32 q^{11} - 26 q^{12} - 16 q^{13} - 68 q^{14} - 14 q^{15} + 70 q^{16} + 16 q^{17} + 180 q^{18} - 128 q^{20}+ \cdots - 662 q^{99}+O(q^{100}) \) 384 * q - 12 * q^2 - 12 * q^3 - 14 * q^4 - 4 * q^5 - 14 * q^7 + 48 * q^8 - 14 * q^9 - 14 * q^10 + 32 * q^11 - 26 * q^12 - 16 * q^13 - 68 * q^14 - 14 * q^15 + 70 * q^16 + 16 * q^17 + 180 * q^18 - 128 * q^20 + 6 * q^21 - 14 * q^22 - 62 * q^23 + 150 * q^24 - 14 * q^25 - 168 * q^26 + 6 * q^27 + 420 * q^28 + 140 * q^29 - 98 * q^30 + 50 * q^31 + 142 * q^32 + 38 * q^34 + 78 * q^35 - 2260 * q^36 - 64 * q^37 + 2 * q^38 - 14 * q^39 - 626 * q^40 - 126 * q^41 + 410 * q^42 - 14 * q^43 - 154 * q^44 + 544 * q^45 + 136 * q^46 - 364 * q^47 + 1114 * q^48 - 18 * q^49 - 140 * q^50 - 138 * q^51 - 214 * q^52 + 2 * q^53 + 90 * q^54 - 14 * q^55 + 26 * q^56 + 506 * q^57 - 364 * q^58 - 350 * q^59 + 348 * q^60 + 434 * q^61 + 756 * q^62 - 1122 * q^63 + 1330 * q^64 - 126 * q^65 - 742 * q^66 + 98 * q^67 + 1016 * q^68 + 454 * q^69 - 62 * q^70 - 682 * q^71 + 908 * q^72 - 32 * q^73 - 880 * q^74 - 78 * q^75 + 470 * q^76 - 410 * q^77 - 1626 * q^78 + 1100 * q^79 - 810 * q^80 + 1118 * q^81 - 86 * q^82 + 784 * q^84 - 1068 * q^85 - 632 * q^86 - 478 * q^87 - 274 * q^88 - 430 * q^89 + 308 * q^90 - 1570 * q^91 - 1022 * q^92 + 190 * q^94 + 1366 * q^95 - 462 * q^96 - 602 * q^97 + 1412 * q^98 - 662 * q^99

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