LMFDB - Embedded newform 392.3.k.n.275.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [392,3,Mod(67,392)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(392, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 3, 4]))

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

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

chi := DirichletCharacter("392.67");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 392 = 2^{3} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	392.k (of order $6$, degree $2$, not 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:	$10.6812263629$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - x^{15} + 3 x^{14} + 6 x^{13} - 22 x^{12} + 44 x^{11} - 20 x^{10} - 112 x^{9} + 368 x^{8} + \cdots + 65536 $ x^16 - x^15 + 3x^14 + 6x^13 - 22x^12 + 44x^11 - 20x^10 - 112x^9 + 368x^8 - 448x^7 - 320x^6 + 2816x^5 - 5632x^4 + 6144x^3 + 12288x^2 - 16384x + 65536
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 2^{14} $
Twist minimal:	no (minimal twist has level 56)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			275.6
Root			$1.94657 - 0.459219i$ of defining polynomial
Character	$\chi$	$=$	392.275
Dual form			392.3.k.n.67.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.575587 + 1.91538i) q^{2} +(-2.61182 - 4.52380i) q^{3} +(-3.33740 + 2.20494i) q^{4} +(-5.42814 - 3.13394i) q^{5} +(7.16148 - 7.60647i) q^{6} +(-6.14428 - 5.12327i) q^{8} +(-9.14316 + 15.8364i) q^{9} +O(q^{10})$	\(q+(0.575587 + 1.91538i) q^{2} +(-2.61182 - 4.52380i) q^{3} +(-3.33740 + 2.20494i) q^{4} +(-5.42814 - 3.13394i) q^{5} +(7.16148 - 7.60647i) q^{6} +(-6.14428 - 5.12327i) q^{8} +(-9.14316 + 15.8364i) q^{9} +(2.87833 - 12.2008i) q^{10} +(-4.90344 - 8.49301i) q^{11} +(18.6914 + 9.33881i) q^{12} +2.41653i q^{13} +32.7411i q^{15} +(6.27646 - 14.7175i) q^{16} +(3.44726 + 5.97083i) q^{17} +(-35.5955 - 8.39743i) q^{18} +(1.38818 - 2.40441i) q^{19} +(25.0260 - 1.50954i) q^{20} +(13.4450 - 14.2804i) q^{22} +(37.0947 + 21.4166i) q^{23} +(-7.12889 + 41.1765i) q^{24} +(7.14316 + 12.3723i) q^{25} +(-4.62858 + 1.39092i) q^{26} +48.5083 q^{27} +37.3505i q^{29} +(-62.7118 + 18.8454i) q^{30} +(-6.20797 + 3.58417i) q^{31} +(31.8024 + 3.55060i) q^{32} +(-25.6138 + 44.3643i) q^{33} +(-9.45224 + 10.0396i) q^{34} +(-4.40402 - 73.0126i) q^{36} +(-0.175502 - 0.101326i) q^{37} +(5.40439 + 1.27496i) q^{38} +(10.9319 - 6.31153i) q^{39} +(17.2960 + 47.0656i) q^{40} -63.5494 q^{41} -35.3384 q^{43} +(35.0913 + 17.5327i) q^{44} +(99.2607 - 57.3082i) q^{45} +(-19.6698 + 83.3777i) q^{46} +(32.8335 + 18.9564i) q^{47} +(-82.9721 + 10.0461i) q^{48} +(-19.5862 + 20.8032i) q^{50} +(18.0072 - 31.1894i) q^{51} +(-5.32831 - 8.06492i) q^{52} +(47.3414 - 27.3326i) q^{53} +(27.9208 + 92.9120i) q^{54} +61.4684i q^{55} -14.5027 q^{57} +(-71.5405 + 21.4985i) q^{58} +(52.3975 + 90.7551i) q^{59} +(-72.1922 - 109.270i) q^{60} +(-37.9032 - 21.8834i) q^{61} +(-10.4383 - 9.82765i) q^{62} +(11.5043 + 62.9575i) q^{64} +(7.57325 - 13.1173i) q^{65} +(-99.7177 - 23.5247i) q^{66} +(-15.5510 - 26.9352i) q^{67} +(-24.6702 - 12.3260i) q^{68} -223.745i q^{69} -23.1294i q^{71} +(137.312 - 50.4605i) q^{72} +(-34.6138 - 59.9528i) q^{73} +(0.0930619 - 0.394476i) q^{74} +(37.3132 - 64.6284i) q^{75} +(0.668652 + 11.0853i) q^{76} +(18.3813 + 17.3059i) q^{78} +(17.2624 + 9.96642i) q^{79} +(-80.1934 + 60.2189i) q^{80} +(-44.4063 - 76.9139i) q^{81} +(-36.5782 - 121.722i) q^{82} +5.11617 q^{83} -43.2140i q^{85} +(-20.3403 - 67.6866i) q^{86} +(168.966 - 97.5525i) q^{87} +(-13.3838 + 77.3050i) q^{88} +(-8.99444 + 15.5788i) q^{89} +(166.901 + 157.137i) q^{90} +(-171.022 + 10.3158i) q^{92} +(32.4282 + 18.7224i) q^{93} +(-17.4103 + 73.7999i) q^{94} +(-15.0705 + 8.70097i) q^{95} +(-66.9998 - 153.141i) q^{96} -12.4864 q^{97} +179.332 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - q^{2} - 8 q^{3} - 5 q^{4} + 44 q^{6} + 26 q^{8} - 48 q^{9}+O(q^{10}) $ 16 * q - q^2 - 8 * q^3 - 5 * q^4 + 44 * q^6 + 26 * q^8 - 48 * q^9	$ 16 q - q^{2} - 8 q^{3} - 5 q^{4} + 44 q^{6} + 26 q^{8} - 48 q^{9} + 16 q^{10} + 32 q^{11} + 30 q^{12} + 71 q^{16} - 80 q^{17} + 29 q^{18} + 56 q^{19} + 216 q^{20} + 132 q^{22} + 22 q^{24} + 16 q^{25} + 24 q^{26} + 64 q^{27} - 96 q^{30} + 19 q^{32} + 32 q^{33} - 148 q^{34} - 66 q^{36} - 14 q^{38} + 84 q^{40} - 256 q^{41} - 50 q^{44} + 152 q^{46} - 268 q^{48} + 66 q^{50} + 368 q^{51} + 132 q^{52} - 228 q^{54} + 112 q^{57} - 24 q^{58} + 104 q^{59} - 192 q^{60} - 240 q^{62} - 110 q^{64} + 72 q^{65} - 276 q^{66} - 304 q^{67} - 190 q^{68} + 209 q^{72} - 112 q^{73} - 8 q^{74} + 72 q^{75} - 140 q^{76} - 608 q^{78} + 124 q^{80} - 48 q^{81} + 450 q^{82} - 144 q^{83} - 210 q^{86} + 486 q^{88} - 512 q^{89} + 368 q^{90} - 944 q^{92} + 472 q^{94} + 558 q^{96} - 128 q^{97} + 512 q^{99}+O(q^{100}) $ 16 * q - q^2 - 8 * q^3 - 5 * q^4 + 44 * q^6 + 26 * q^8 - 48 * q^9 + 16 * q^10 + 32 * q^11 + 30 * q^12 + 71 * q^16 - 80 * q^17 + 29 * q^18 + 56 * q^19 + 216 * q^20 + 132 * q^22 + 22 * q^24 + 16 * q^25 + 24 * q^26 + 64 * q^27 - 96 * q^30 + 19 * q^32 + 32 * q^33 - 148 * q^34 - 66 * q^36 - 14 * q^38 + 84 * q^40 - 256 * q^41 - 50 * q^44 + 152 * q^46 - 268 * q^48 + 66 * q^50 + 368 * q^51 + 132 * q^52 - 228 * q^54 + 112 * q^57 - 24 * q^58 + 104 * q^59 - 192 * q^60 - 240 * q^62 - 110 * q^64 + 72 * q^65 - 276 * q^66 - 304 * q^67 - 190 * q^68 + 209 * q^72 - 112 * q^73 - 8 * q^74 + 72 * q^75 - 140 * q^76 - 608 * q^78 + 124 * q^80 - 48 * q^81 + 450 * q^82 - 144 * q^83 - 210 * q^86 + 486 * q^88 - 512 * q^89 + 368 * q^90 - 944 * q^92 + 472 * q^94 + 558 * q^96 - 128 * q^97 + 512 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/392\mathbb{Z}\right)^\times$.

$n$	$197$	$295$	$297$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{1}{3}\right)$

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 $

$2$	0.575587	+	1.91538i	0.287794	+	0.957692i
$2$	0.575587	+	1.91538i	0.287794	+	0.957692i
$3$	−2.61182	−	4.52380i	−0.870605	−	1.50793i	−0.861372	−	0.507975i	$-0.830394\pi$
$3$	−2.61182	−	4.52380i	−0.870605	−	1.50793i	−0.00923321	−	0.999957i	$-0.502939\pi$
$4$	−3.33740	+	2.20494i	−0.834350	+	0.551236i
$5$	−5.42814	−	3.13394i	−1.08563	−	0.626788i	−0.153219	−	0.988192i	$-0.548964\pi$
$5$	−5.42814	−	3.13394i	−1.08563	−	0.626788i	−0.932409	+	0.361404i	$0.882297\pi$
$6$	7.16148	−	7.60647i	1.19358	−	1.26775i
$7$		0			0
$7$		0			0
$8$	−6.14428	−	5.12327i	−0.768035	−	0.640408i
$9$	−9.14316	+	15.8364i	−1.01591	+	1.75960i
$10$	2.87833	−	12.2008i	0.287833	−	1.22008i
$11$	−4.90344	−	8.49301i	−0.445767	−	0.772092i	0.552338	−	0.833620i	$-0.313736\pi$
$11$	−4.90344	−	8.49301i	−0.445767	−	0.772092i	−0.998105	+	0.0615286i	$0.980402\pi$
$12$	18.6914	+	9.33881i	1.55762	+	0.778234i
$13$			2.41653i			0.185887i	0.995671	+	0.0929434i	$0.0296276\pi$
$13$			2.41653i			0.185887i	−0.995671	+	0.0929434i	$0.970372\pi$
$14$		0			0
$15$			32.7411i			2.18274i
$16$	6.27646	−	14.7175i	0.392279	−	0.919846i
$17$	3.44726	+	5.97083i	0.202780	+	0.351225i	0.949423	−	0.313999i	$-0.101669\pi$
$17$	3.44726	+	5.97083i	0.202780	+	0.351225i	−0.746643	+	0.665225i	$0.768336\pi$
$18$	−35.5955	−	8.39743i	−1.97753	−	0.466524i
$19$	1.38818	−	2.40441i	0.0730624	−	0.126548i	−0.827180	−	0.561938i	$-0.810056\pi$
$19$	1.38818	−	2.40441i	0.0730624	−	0.126548i	0.900242	+	0.435390i	$0.143389\pi$
$20$	25.0260	−	1.50954i	1.25130	−	0.0754769i
$21$		0			0
$22$	13.4450	−	14.2804i	0.611137	−	0.649111i
$23$	37.0947	+	21.4166i	1.61281	+	0.931157i	0.988715	+	0.149811i	$0.0478664\pi$
$23$	37.0947	+	21.4166i	1.61281	+	0.931157i	0.624097	+	0.781347i	$0.285467\pi$
$24$	−7.12889	+	41.1765i	−0.297037	+	1.71569i
$25$	7.14316	+	12.3723i	0.285726	+	0.494893i
$26$	−4.62858	+	1.39092i	−0.178022	+	0.0534970i
$27$	48.5083			1.79660
$28$		0			0
$29$			37.3505i			1.28795i	0.765048	+	0.643974i	$0.222715\pi$
$29$			37.3505i			1.28795i	−0.765048	+	0.643974i	$0.777285\pi$
$30$	−62.7118	+	18.8454i	−2.09039	+	0.628179i
$31$	−6.20797	+	3.58417i	−0.200257	+	0.115619i	−0.596775	−	0.802408i	$-0.703552\pi$
$31$	−6.20797	+	3.58417i	−0.200257	+	0.115619i	0.396518	+	0.918027i	$0.370218\pi$
$32$	31.8024	+	3.55060i	0.993825	+	0.110956i
$33$	−25.6138	+	44.3643i	−0.776175	+	1.34437i
$34$	−9.45224	+	10.0396i	−0.278007	+	0.295281i
$35$		0			0
$36$	−4.40402	−	73.0126i	−0.122334	−	2.02813i
$37$	−0.175502	−	0.101326i	−0.00474330	−	0.00273855i	0.497626	−	0.867391i	$-0.334205\pi$
$37$	−0.175502	−	0.101326i	−0.00474330	−	0.00273855i	−0.502370	+	0.864653i	$0.667538\pi$
$38$	5.40439	+	1.27496i	0.142221	+	0.0335516i
$39$	10.9319	−	6.31153i	0.280305	−	0.161834i
$40$	17.2960	+	47.0656i	0.432400	+	1.17664i
$41$	−63.5494			−1.54999			−0.774993	−	0.631970i	$-0.782247\pi$
$41$	−63.5494			−1.54999			−0.774993	+	0.631970i	$0.782247\pi$
$42$		0			0
$43$	−35.3384			−0.821823			−0.410911	−	0.911675i	$-0.634789\pi$
$43$	−35.3384			−0.821823			−0.410911	+	0.911675i	$0.634789\pi$
$44$	35.0913	+	17.5327i	0.797530	+	0.398472i
$45$	99.2607	−	57.3082i	2.20579	−	1.27352i
$46$	−19.6698	+	83.3777i	−0.427605	+	1.81256i
$47$	32.8335	+	18.9564i	0.698586	+	0.403329i	0.806820	−	0.590797i	$-0.201186\pi$
$47$	32.8335	+	18.9564i	0.698586	+	0.403329i	−0.108235	+	0.994125i	$0.534520\pi$
$48$	−82.9721	+	10.0461i	−1.72859	+	0.209294i
$49$		0			0
$50$	−19.5862	+	20.8032i	−0.391725	+	0.416065i
$51$	18.0072	−	31.1894i	0.353083	−	0.611557i
$52$	−5.32831	−	8.06492i	−0.102467	−	0.155095i
$53$	47.3414	−	27.3326i	0.893234	−	0.515709i	0.0182349	−	0.999834i	$-0.494195\pi$
$53$	47.3414	−	27.3326i	0.893234	−	0.515709i	0.874999	+	0.484125i	$0.160862\pi$
$54$	27.9208	+	92.9120i	0.517051	+	1.72059i
$55$			61.4684i			1.11761i
$56$		0			0
$57$	−14.5027			−0.254434
$58$	−71.5405	+	21.4985i	−1.23346	+	0.370663i
$59$	52.3975	+	90.7551i	0.888093	+	1.53822i	0.842128	+	0.539278i	$0.181303\pi$
$59$	52.3975	+	90.7551i	0.888093	+	1.53822i	0.0459650	+	0.998943i	$0.485364\pi$
$60$	−72.1922	−	109.270i	−1.20320	−	1.82117i
$61$	−37.9032	−	21.8834i	−0.621364	−	0.358745i	0.156036	−	0.987751i	$-0.450128\pi$
$61$	−37.9032	−	21.8834i	−0.621364	−	0.358745i	−0.777400	+	0.629007i	$0.783462\pi$
$62$	−10.4383	−	9.82765i	−0.168360	−	0.158511i
$63$		0			0
$64$	11.5043	+	62.9575i	0.179755	+	0.983711i
$65$	7.57325	−	13.1173i	0.116512	−	0.201804i
$66$	−99.7177	−	23.5247i	−1.51087	−	0.356434i
$67$	−15.5510	−	26.9352i	−0.232105	−	0.402018i	0.726322	−	0.687354i	$-0.241228\pi$
$67$	−15.5510	−	26.9352i	−0.232105	−	0.402018i	−0.958427	+	0.285336i	$0.907895\pi$
$68$	−24.6702	−	12.3260i	−0.362797	−	0.181265i
$69$		−	223.745i		−	3.24268i
$70$		0			0
$71$		−	23.1294i		−	0.325766i	−0.986645	−	0.162883i	$-0.947921\pi$
$71$		−	23.1294i		−	0.325766i	0.986645	−	0.162883i	$-0.0520794\pi$
$72$	137.312	−	50.4605i	1.90711	−	0.700840i
$73$	−34.6138	−	59.9528i	−0.474161	−	0.821271i	0.525401	−	0.850855i	$-0.323915\pi$
$73$	−34.6138	−	59.9528i	−0.474161	−	0.821271i	−0.999562	+	0.0295834i	$0.990582\pi$
$74$	0.0930619	−	0.394476i	0.00125759	−	0.00533076i
$75$	37.3132	−	64.6284i	0.497510	−	0.861712i
$76$	0.668652	+	11.0853i	0.00879806	+	0.145860i
$77$		0			0
$78$	18.3813	+	17.3059i	0.235657	+	0.221871i
$79$	17.2624	+	9.96642i	0.218511	+	0.126157i	0.605261	−	0.796027i	$-0.293069\pi$
$79$	17.2624	+	9.96642i	0.218511	+	0.126157i	−0.386750	+	0.922185i	$0.626402\pi$
$80$	−80.1934	+	60.2189i	−1.00242	+	0.752736i
$81$	−44.4063	−	76.9139i	−0.548225	−	0.949554i
$82$	−36.5782	−	121.722i	−0.446076	−	1.48441i
$83$	5.11617			0.0616406			0.0308203	−	0.999525i	$-0.490188\pi$
$83$	5.11617			0.0616406			0.0308203	+	0.999525i	$0.490188\pi$
$84$		0			0
$85$		−	43.2140i		−	0.508400i
$86$	−20.3403	−	67.6866i	−0.236515	−	0.787054i
$87$	168.966	−	97.5525i	1.94214	−	1.12129i
$88$	−13.3838	+	77.3050i	−0.152089	+	0.878466i
$89$	−8.99444	+	15.5788i	−0.101061	+	0.175043i	−0.912122	−	0.409919i	$-0.865557\pi$
$89$	−8.99444	+	15.5788i	−0.101061	+	0.175043i	0.811061	+	0.584962i	$0.198890\pi$
$90$	166.901	+	157.137i	1.85445	+	1.74596i
$91$		0			0
$92$	−171.022	+	10.3158i	−1.85894	+	0.112129i
$93$	32.4282	+	18.7224i	0.348690	+	0.201316i
$94$	−17.4103	+	73.7999i	−0.185216	+	0.785106i
$95$	−15.0705	+	8.70097i	−0.158637	+	0.0915892i
$96$	−66.9998	−	153.141i	−0.697915	−	1.59522i
$97$	−12.4864			−0.128726			−0.0643629	−	0.997927i	$-0.520502\pi$
$97$	−12.4864			−0.128726			−0.0643629	+	0.997927i	$0.520502\pi$
$98$		0			0
$99$	179.332			1.81143
$100$	−51.1198	−	25.5411i	−0.511198	−	0.255411i
$101$	−58.9549	+	34.0376i	−0.583712	+	0.337006i	−0.762607	−	0.646862i	$-0.776081\pi$
$101$	−58.9549	+	34.0376i	−0.583712	+	0.337006i	0.178895	+	0.983868i	$0.442748\pi$
$102$	70.1045	+	16.5385i	0.687299	+	0.162142i
$103$	50.4833	+	29.1465i	0.490129	+	0.282976i	0.724628	−	0.689140i	$-0.242012\pi$
$103$	50.4833	+	29.1465i	0.490129	+	0.282976i	−0.234499	+	0.972116i	$0.575345\pi$
$104$	12.3805	−	14.8478i	0.119043	−	0.142768i
$105$		0			0
$106$	79.6015	+	74.9447i	0.750957	+	0.707026i
$107$	−67.9340	+	117.665i	−0.634897	+	1.09967i	0.351640	+	0.936135i	$0.385624\pi$
$107$	−67.9340	+	117.665i	−0.634897	+	1.09967i	−0.986537	+	0.163538i	$0.947709\pi$
$108$	−161.891	+	106.958i	−1.49900	+	0.990352i
$109$	−38.5365	+	22.2490i	−0.353546	+	0.204120i	−0.666246	−	0.745732i	$-0.732100\pi$
$109$	−38.5365	+	22.2490i	−0.353546	+	0.204120i	0.312700	+	0.949852i	$0.398766\pi$
$110$	−117.736	+	35.3804i	−1.07032	+	0.321640i
$111$			1.05858i			0.00953677i
$112$		0			0
$113$	−133.391			−1.18045			−0.590224	−	0.807240i	$-0.700961\pi$
$113$	−133.391			−1.18045			−0.590224	+	0.807240i	$0.700961\pi$
$114$	−8.34759	−	27.7783i	−0.0732244	−	0.243669i
$115$	−134.237	−	232.505i	−1.16728	−	2.02178i
$116$	−82.3556	−	124.653i	−0.709962	−	1.07460i
$117$	−38.2691	−	22.0947i	−0.327087	−	0.188844i
$118$	−143.672	+	152.599i	−1.21756	+	1.29321i
$119$		0			0
$120$	167.741	−	201.170i	1.39784	−	1.67642i
$121$	12.4125	−	21.4991i	0.102583	−	0.177679i
$122$	20.0986	−	85.1950i	0.164742	−	0.698320i
$123$	165.979	+	287.485i	1.34943	+	2.33727i
$124$	12.8156	−	25.6500i	0.103351	−	0.206855i
$125$			67.1521i			0.537217i
$126$		0			0
$127$			130.977i			1.03131i	0.856795	+	0.515657i	$0.172452\pi$
$127$			130.977i			1.03131i	−0.856795	+	0.515657i	$0.827548\pi$
$128$	−113.966	+	58.2727i	−0.890361	+	0.455256i
$129$	92.2973	+	159.864i	0.715483	+	1.23925i
$130$	29.4837	+	6.95557i	0.226797	+	0.0535044i
$131$	−26.6655	+	46.1861i	−0.203554	+	0.352565i	−0.949671	−	0.313249i	$-0.898583\pi$
$131$	−26.6655	+	46.1861i	−0.203554	+	0.352565i	0.746117	+	0.665815i	$0.231916\pi$
$132$	−12.3375	−	204.538i	−0.0934658	−	1.54953i
$133$		0			0
$134$	42.6403	−	45.2898i	0.318211	−	0.337983i
$135$	−263.310	−	152.022i	−1.95044	−	1.12609i
$136$	9.40923	−	54.3477i	0.0691855	−	0.399615i
$137$	28.8589	+	49.9852i	0.210649	+	0.364855i	0.951918	−	0.306353i	$-0.0991089\pi$
$137$	28.8589	+	49.9852i	0.210649	+	0.364855i	−0.741269	+	0.671208i	$0.765776\pi$
$138$	428.558	−	128.785i	3.10549	−	0.933223i
$139$	172.422			1.24045			0.620224	−	0.784425i	$-0.287042\pi$
$139$	172.422			1.24045			0.620224	+	0.784425i	$0.287042\pi$
$140$		0			0
$141$		−	198.043i		−	1.40456i
$142$	44.3017	−	13.3130i	0.311984	−	0.0937535i
$143$	20.5236	−	11.8493i	0.143522	−	0.0828623i
$144$	175.686	+	233.961i	1.22004	+	1.62473i
$145$	117.054	−	202.744i	0.807270	−	1.39823i
$146$	94.9094	−	100.807i	0.650065	−	0.690457i
$147$		0			0
$148$	0.809139	−	0.0488062i	0.00546716	−	0.000329772i
$149$	190.117	+	109.764i	1.27596	+	0.736673i	0.976102	−	0.217312i	$-0.0697290\pi$
$149$	190.117	+	109.764i	1.27596	+	0.736673i	0.299853	+	0.953985i	$0.403062\pi$
$150$	145.265	+	34.2699i	0.968435	+	0.228466i
$151$	160.793	−	92.8340i	1.06486	−	0.614795i	0.138084	−	0.990421i	$-0.455906\pi$
$151$	160.793	−	92.8340i	1.06486	−	0.614795i	0.926771	+	0.375626i	$0.122572\pi$
$152$	−20.8478	+	7.66130i	−0.137157	+	0.0504033i
$153$	−126.075			−0.824022
$154$		0			0
$155$	44.9304			0.289873
$156$	−22.5675	+	45.1682i	−0.144663	+	0.289540i
$157$	−162.970	+	94.0909i	−1.03803	+	0.599305i	−0.919274	−	0.393619i	$-0.871223\pi$
$157$	−162.970	+	94.0909i	−1.03803	+	0.599305i	−0.118753	+	0.992924i	$0.537890\pi$
$158$	−9.15355	+	38.8006i	−0.0579338	+	0.245573i
$159$	−247.294	−	142.775i	−1.55531	−	0.897957i
$160$	−161.501	−	118.940i	−1.00938	−	0.743375i
$161$		0			0
$162$	121.760	−	129.326i	0.751605	−	0.798307i
$163$	−27.2577	+	47.2117i	−0.167225	+	0.289642i	−0.937443	−	0.348138i	$-0.886814\pi$
$163$	−27.2577	+	47.2117i	−0.167225	+	0.289642i	0.770218	+	0.637781i	$0.220147\pi$
$164$	212.090	−	140.123i	1.29323	−	0.854407i
$165$	278.070	−	160.544i	1.68527	−	0.972994i
$166$	2.94480	+	9.79944i	0.0177398	+	0.0590328i
$167$			266.435i			1.59542i	0.603042	+	0.797709i	$0.293955\pi$
$167$			266.435i			1.59542i	−0.603042	+	0.797709i	$0.706045\pi$
$168$		0			0
$169$	163.160			0.965446
$170$	82.7715	−	24.8735i	0.486891	−	0.146314i
$171$	25.3848	+	43.9677i	0.148449	+	0.257121i
$172$	117.938	−	77.9191i	0.685688	−	0.453018i
$173$	−99.4501	−	57.4175i	−0.574856	−	0.331893i	0.184231	−	0.982883i	$-0.441021\pi$
$173$	−99.4501	−	57.4175i	−0.574856	−	0.331893i	−0.759086	+	0.650990i	$0.774354\pi$
$174$	284.105	+	267.485i	1.63279	+	1.53727i
$175$		0			0
$176$	−155.772	+	18.8606i	−0.885071	+	0.107162i
$177$	273.705	−	474.071i	1.54636	−	2.67837i
$178$	−35.0165	−	8.26084i	−0.196722	−	0.0464092i
$179$	−56.4243	−	97.7298i	−0.315220	−	0.545977i	0.664264	−	0.747498i	$-0.268745\pi$
$179$	−56.4243	−	97.7298i	−0.315220	−	0.545977i	−0.979484	+	0.201521i	$0.935412\pi$
$180$	−204.911	+	410.125i	−1.13840	+	2.27847i
$181$			60.9470i			0.336724i	0.985725	+	0.168362i	$0.0538477\pi$
$181$			60.9470i			0.336724i	−0.985725	+	0.168362i	$0.946152\pi$
$182$		0			0
$183$			228.622i			1.24930i
$184$	−118.197	−	321.636i	−0.642375	−	1.74802i
$185$	0.635101	+	1.10003i	0.00343298	+	0.00594609i
$186$	−17.1954	+	72.8888i	−0.0924483	+	0.391875i
$187$	33.8069	−	58.5552i	0.180785	−	0.313130i
$188$	−151.376	+	9.13083i	−0.805194	+	0.0485682i
$189$		0			0
$190$	−25.3401	−	23.8577i	−0.133369	−	0.125567i
$191$	−154.550	−	89.2296i	−0.809164	−	0.467171i	0.0375017	−	0.999297i	$-0.488060\pi$
$191$	−154.550	−	89.2296i	−0.809164	−	0.467171i	−0.846665	+	0.532126i	$0.821393\pi$
$192$	254.760	−	216.477i	1.32687	−	1.12748i
$193$	−110.794	−	191.901i	−0.574062	−	0.994304i	−0.996143	−	0.0877458i	$-0.972034\pi$
$193$	−110.794	−	191.901i	−0.574062	−	0.994304i	0.422081	−	0.906558i	$-0.361300\pi$
$194$	−7.18702	−	23.9163i	−0.0370465	−	0.123280i
$195$	−79.1198			−0.405742
$196$		0			0
$197$			242.298i			1.22994i	0.788550	+	0.614970i	$0.210832\pi$
$197$			242.298i			1.22994i	−0.788550	+	0.614970i	$0.789168\pi$
$198$	103.221	+	343.489i	0.521319	+	1.73479i
$199$	−257.250	+	148.523i	−1.29271	+	0.746349i	−0.979135	−	0.203213i	$-0.934862\pi$
$199$	−257.250	+	148.523i	−1.29271	+	0.746349i	−0.313580	+	0.949562i	$0.601528\pi$
$200$	19.4971	−	112.615i	0.0974855	−	0.563076i
$201$	−81.2329	+	140.699i	−0.404144	+	0.699997i
$202$	−99.1289	−	93.3297i	−0.490737	−	0.462028i
$203$		0			0
$204$	8.67361	+	143.796i	0.0425177	+	0.704884i
$205$	344.955	+	199.160i	1.68271	+	0.971512i
$206$	−26.7693	+	113.471i	−0.129948	+	0.550832i
$207$	−678.325	+	391.631i	−3.27693	+	1.89194i
$208$	35.5654	+	15.1672i	0.170987	+	0.0729194i
$209$	−27.2275			−0.130275
$210$		0			0
$211$	−141.020			−0.668341			−0.334171	−	0.942513i	$-0.608456\pi$
$211$	−141.020			−0.668341			−0.334171	+	0.942513i	$0.608456\pi$
$212$	−97.7303	+	195.605i	−0.460992	+	0.922664i
$213$	−104.633	+	60.4098i	−0.491234	+	0.283614i
$214$	−264.476	−	62.3932i	−1.23587	−	0.291557i
$215$	191.822	+	110.748i	0.892194	+	0.515109i
$216$	−298.048	−	248.521i	−1.37985	−	1.15056i
$217$		0			0
$218$	−64.7966	−	61.0059i	−0.297232	−	0.279844i
$219$	−180.810	+	313.171i	−0.825614	+	1.43001i
$220$	−135.534	−	205.144i	−0.616064	−	0.932475i
$221$	−14.4287	+	8.33040i	−0.0652882	+	0.0376941i
$222$	−2.02759	+	0.609306i	−0.00913330	+	0.00274462i
$223$		−	40.8267i		−	0.183079i	−0.995801	−	0.0915396i	$-0.970821\pi$
$223$		−	40.8267i		−	0.183079i	0.995801	−	0.0915396i	$-0.0291788\pi$
$224$		0			0
$225$	−261.244			−1.16108
$226$	−76.7779	−	255.494i	−0.339725	−	1.13051i
$227$	4.09299	+	7.08926i	0.0180308	+	0.0312302i	0.874900	−	0.484304i	$-0.160927\pi$
$227$	4.09299	+	7.08926i	0.0180308	+	0.0312302i	−0.856869	+	0.515534i	$0.827594\pi$
$228$	48.4014	−	31.9777i	0.212287	−	0.140253i
$229$	287.738	+	166.126i	1.25650	+	0.725440i	0.972392	−	0.233352i	$-0.0749695\pi$
$229$	287.738	+	166.126i	1.25650	+	0.725440i	0.284107	+	0.958792i	$0.408303\pi$
$230$	368.071	−	390.942i	1.60031	−	1.69975i
$231$		0			0
$232$	191.356	−	229.492i	0.824812	−	0.989188i
$233$	−164.630	+	285.148i	−0.706568	+	1.22381i	0.259555	+	0.965728i	$0.416424\pi$
$233$	−164.630	+	285.148i	−0.706568	+	1.22381i	−0.966123	+	0.258083i	$0.916909\pi$
$234$	20.2926	−	86.0176i	0.0867206	−	0.367596i
$235$	−118.817	−	205.797i	−0.505603	−	0.875730i
$236$	−374.981	−	187.352i	−1.58890	−	0.793866i
$237$		−	104.122i		−	0.439333i
$238$		0			0
$239$		−	137.719i		−	0.576230i	−0.957596	−	0.288115i	$-0.906971\pi$
$239$		−	137.719i		−	0.576230i	0.957596	−	0.288115i	$-0.0930286\pi$
$240$	481.868	+	205.498i	2.00778	+	0.856242i
$241$	100.927	+	174.810i	0.418783	+	0.725354i	0.995817	−	0.0913661i	$-0.0291234\pi$
$241$	100.927	+	174.810i	0.418783	+	0.725354i	−0.577034	+	0.816720i	$0.695790\pi$
$242$	48.3236	+	11.4002i	0.199684	+	0.0471081i
$243$	−13.6746	+	23.6851i	−0.0562741	+	0.0974696i
$244$	174.750	−	10.5407i	0.716188	−	0.0431995i
$245$		0			0
$246$	−455.108	+	483.387i	−1.85003	+	1.96499i
$247$	5.81032	+	3.35459i	0.0235235	+	0.0135813i
$248$	56.5062	+	9.78293i	0.227848	+	0.0394473i
$249$	−13.3625	−	23.1445i	−0.0536647	−	0.0929499i
$250$	−128.622	+	38.6519i	−0.514488	+	0.154608i
$251$	269.203			1.07252			0.536261	−	0.844052i	$-0.319836\pi$
$251$	269.203			1.07252			0.536261	+	0.844052i	$0.319836\pi$
$252$		0			0
$253$		−	420.061i		−	1.66032i
$254$	−250.871	+	75.3886i	−0.987681	+	0.296805i
$255$	−195.492	+	112.867i	−0.766633	+	0.442616i
$256$	−177.212	−	184.748i	−0.692235	−	0.721672i
$257$	−121.180	+	209.889i	−0.471516	+	0.816690i	−0.999469	−	0.0325840i	$-0.989626\pi$
$257$	−121.180	+	209.889i	−0.471516	+	0.816690i	0.527953	+	0.849274i	$0.322960\pi$
$258$	−253.075	+	268.800i	−0.980912	+	1.04186i
$259$		0			0
$260$	3.64784	+	60.4761i	0.0140302	+	0.232600i
$261$	−591.498	−	341.501i	−2.26627	−	1.30843i
$262$	−103.812	−	24.4907i	−0.396231	−	0.0934758i
$263$	29.3124	−	16.9235i	0.111454	−	0.0643479i	−0.443237	−	0.896405i	$-0.646170\pi$
$263$	29.3124	−	16.9235i	0.111454	−	0.0643479i	0.554691	+	0.832057i	$0.312837\pi$
$264$	384.668	−	141.361i	1.45708	−	0.535457i
$265$	−342.634			−1.29296
$266$		0			0
$267$	93.9673			0.351937
$268$	111.291	+	55.6043i	0.415263	+	0.207479i
$269$	−143.412	+	82.7990i	−0.533130	+	0.307803i	−0.742290	−	0.670078i	$-0.766260\pi$
$269$	−143.412	+	82.7990i	−0.533130	+	0.307803i	0.209160	+	0.977881i	$0.432927\pi$
$270$	139.623	−	591.842i	0.517122	−	2.19201i
$271$	128.439	+	74.1542i	0.473944	+	0.273632i	0.717889	−	0.696157i	$-0.245108\pi$
$271$	128.439	+	74.1542i	0.473944	+	0.273632i	−0.243945	+	0.969789i	$0.578442\pi$
$272$	109.513	−	13.2595i	0.402620	−	0.0487483i
$273$		0			0
$274$	−79.1300	+	84.0468i	−0.288796	+	0.306740i
$275$	70.0521	−	121.334i	0.254735	−	0.441214i
$276$	493.345	+	746.726i	1.78748	+	2.70553i
$277$	−414.270	+	239.179i	−1.49556	+	0.863463i	−0.999987	−	0.00510300i	$-0.998376\pi$
$277$	−414.270	+	239.179i	−1.49556	+	0.863463i	−0.495574	+	0.868566i	$0.665042\pi$
$278$	99.2441	+	330.255i	0.356993	+	1.18797i
$279$		−	131.083i		−	0.469830i
$280$		0			0
$281$	−226.066			−0.804506			−0.402253	−	0.915528i	$-0.631773\pi$
$281$	−226.066			−0.804506			−0.402253	+	0.915528i	$0.631773\pi$
$282$	379.328	−	113.991i	1.34514	−	0.404223i
$283$	−127.314	−	220.514i	−0.449873	−	0.779202i	0.548505	−	0.836147i	$-0.315197\pi$
$283$	−127.314	−	220.514i	−0.449873	−	0.779202i	−0.998377	+	0.0569453i	$0.981864\pi$
$284$	50.9990	+	77.1921i	0.179574	+	0.271803i
$285$	78.7229	+	45.4507i	0.276221	+	0.159476i
$286$	34.5091	+	32.4903i	0.120661	+	0.113602i
$287$		0			0
$288$	−347.003	+	471.172i	−1.20487	+	1.63602i
$289$	120.733	−	209.115i	0.417760	−	0.723582i
$290$	455.707	+	107.507i	1.57140	+	0.370714i
$291$	32.6122	+	56.4860i	0.112069	+	0.194110i
$292$	247.712	+	123.765i	0.848330	+	0.423853i
$293$			149.558i			0.510437i	0.966883	+	0.255218i	$0.0821474\pi$
$293$			149.558i			0.510437i	−0.966883	+	0.255218i	$0.917853\pi$
$294$		0			0
$295$		−	656.842i		−	2.22658i
$296$	0.559213	+	1.52172i	0.00188923	+	0.00514095i
$297$	−237.858	−	411.981i	−0.800867	−	1.38714i
$298$	−100.812	+	427.327i	−0.338294	+	1.43398i
$299$	−51.7539	+	89.6403i	−0.173090	+	0.299800i
$300$	17.9728	+	297.964i	0.0599094	+	0.993214i
$301$		0			0
$302$	270.363	+	254.547i	0.895243	+	0.842870i
$303$	307.959	+	177.800i	1.01637	+	0.586799i
$304$	−26.6741	−	35.5218i	−0.0877437	−	0.116848i
$305$	137.163	+	237.573i	0.449714	+	0.778927i
$306$	−72.5674	−	241.483i	−0.237148	−	0.789160i
$307$	−271.779			−0.885272			−0.442636	−	0.896701i	$-0.645957\pi$
$307$	−271.779			−0.885272			−0.442636	+	0.896701i	$0.645957\pi$
$308$		0			0
$309$		−	304.502i		−	0.985442i
$310$	25.8613	+	86.0589i	0.0834237	+	0.277609i
$311$	462.614	−	267.090i	1.48750	−	0.858811i	0.487605	−	0.873064i	$-0.337870\pi$
$311$	462.614	−	267.090i	1.48750	−	0.858811i	0.999898	+	0.0142534i	$0.00453714\pi$
$312$	−99.5041	−	17.2272i	−0.318924	−	0.0552153i
$313$	−278.116	+	481.711i	−0.888550	+	1.53901i	−0.0469600	+	0.998897i	$0.514953\pi$
$313$	−278.116	+	481.711i	−0.888550	+	1.53901i	−0.841590	+	0.540117i	$0.818380\pi$
$314$	−274.024	−	257.993i	−0.872688	−	0.821634i
$315$		0			0
$316$	−79.5867	+	4.80057i	−0.251857	+	0.0151917i
$317$	−335.549	−	193.730i	−1.05852	−	0.611134i	−0.133494	−	0.991050i	$-0.542620\pi$
$317$	−335.549	−	193.730i	−1.05852	−	0.611134i	−0.925021	+	0.379916i	$0.875953\pi$
$318$	131.130	−	555.843i	0.412359	−	1.74793i
$319$	317.218	−	183.146i	0.994413	−	0.574125i
$320$	134.858	−	377.796i	0.421432	−	1.18061i
$321$	709.724			2.21098
$322$		0			0
$323$	19.1417			0.0592624
$324$	317.792	+	158.779i	0.980840	+	0.490059i
$325$	−29.8980	+	17.2616i	−0.0919940	+	0.0531127i
$326$	−106.118	−	25.0345i	−0.325515	−	0.0767929i
$327$	201.300	+	116.221i	0.615597	+	0.355415i
$328$	390.465	+	325.581i	1.19044	+	0.992624i
$329$		0			0
$330$	467.557	+	440.205i	1.41684	+	1.33395i
$331$	191.603	−	331.865i	0.578860	−	1.00261i	−0.416751	−	0.909021i	$-0.636831\pi$
$331$	191.603	−	331.865i	0.578860	−	1.00261i	0.995610	−	0.0935935i	$-0.0298354\pi$
$332$	−17.0747	+	11.2809i	−0.0514298	+	0.0339785i
$333$	3.20929	−	1.85288i	0.00963750	−	0.00556422i
$334$	−510.325	+	153.357i	−1.52792	+	0.459151i
$335$			194.944i			0.581923i
$336$		0			0
$337$	563.726			1.67278			0.836388	−	0.548138i	$-0.184663\pi$
$337$	563.726			1.67278			0.836388	+	0.548138i	$0.184663\pi$
$338$	93.9131	+	312.515i	0.277849	+	0.924600i
$339$	348.392	+	603.432i	1.02770	+	1.78004i
$340$	95.2845	+	144.222i	0.280248	+	0.424184i
$341$	60.8809	+	35.1496i	0.178536	+	0.103078i
$342$	−69.6040	+	73.9289i	−0.203520	+	0.216166i
$343$		0			0
$344$	217.129	+	181.048i	0.631188	+	0.526302i
$345$	−701.203	+	1214.52i	−2.03247	+	3.52035i
$346$	52.7345	−	223.534i	0.152412	−	0.646052i
$347$	−25.7945	−	44.6774i	−0.0743357	−	0.128753i	0.826462	−	0.562993i	$-0.190350\pi$
$347$	−25.7945	−	44.6774i	−0.0743357	−	0.128753i	−0.900797	+	0.434240i	$0.857017\pi$
$348$	−348.809	+	698.132i	−1.00232	+	2.00613i
$349$		−	586.383i		−	1.68018i	−0.542447	−	0.840090i	$-0.682502\pi$
$349$		−	586.383i		−	1.68018i	0.542447	−	0.840090i	$-0.317498\pi$
$350$		0			0
$351$			117.222i			0.333965i
$352$	−125.786	−	287.508i	−0.357346	−	0.816785i
$353$	151.922	+	263.136i	0.430373	+	0.745428i	0.996905	−	0.0786114i	$-0.0250486\pi$
$353$	151.922	+	263.136i	0.430373	+	0.745428i	−0.566532	+	0.824040i	$0.691715\pi$
$354$	1065.57	+	251.381i	3.01008	+	0.710116i
$355$	−72.4862	+	125.550i	−0.204187	+	0.353661i
$356$	−4.33239	−	71.8250i	−0.0121696	−	0.201756i
$357$		0			0
$358$	154.713	−	164.326i	0.432159	−	0.459012i
$359$	100.571	+	58.0649i	0.280143	+	0.161741i	0.633488	−	0.773752i	$-0.281623\pi$
$359$	100.571	+	58.0649i	0.280143	+	0.161741i	−0.353345	+	0.935493i	$0.614956\pi$
$360$	−903.491	−	156.422i	−2.50970	−	0.434504i
$361$	176.646	+	305.960i	0.489324	+	0.847534i
$362$	−116.737	+	35.0803i	−0.322478	+	0.0969069i
$363$	−129.677			−0.357237
$364$		0			0
$365$			433.910i			1.18879i
$366$	−437.899	+	131.592i	−1.19644	+	0.359541i
$367$	−412.478	+	238.144i	−1.12392	+	0.648894i	−0.942398	−	0.334493i	$-0.891435\pi$
$367$	−412.478	+	238.144i	−1.12392	+	0.648894i	−0.181520	+	0.983387i	$0.558102\pi$
$368$	548.023	−	411.522i	1.48919	−	1.11827i
$369$	581.042	−	1006.39i	1.57464	−	2.72736i
$370$	−1.74142	+	1.84962i	−0.00470654	+	0.00499898i
$371$		0			0
$372$	−149.507	+	9.01809i	−0.401902	+	0.0242422i
$373$	42.6827	+	24.6428i	0.114431	+	0.0660666i	0.556123	−	0.831100i	$-0.312288\pi$
$373$	42.6827	+	24.6428i	0.114431	+	0.0660666i	−0.441692	+	0.897167i	$0.645622\pi$
$374$	131.615	+	31.0495i	0.351911	+	0.0830202i
$375$	303.782	−	175.389i	0.810086	−	0.467704i
$376$	−104.619	−	284.689i	−0.278243	−	0.757150i
$377$	−90.2585			−0.239412
$378$		0			0
$379$	167.511			0.441983			0.220991	−	0.975276i	$-0.429071\pi$
$379$	167.511			0.441983			0.220991	+	0.975276i	$0.429071\pi$
$380$	31.1112	−	62.2683i	0.0818716	−	0.163864i
$381$	592.512	−	342.087i	1.55515	−	0.897866i
$382$	81.9519	−	347.383i	0.214534	−	0.909379i
$383$	444.450	+	256.604i	1.16044	+	0.669983i	0.951411	−	0.307925i	$-0.0996347\pi$
$383$	444.450	+	256.604i	1.16044	+	0.669983i	0.209034	+	0.977908i	$0.432968\pi$
$384$	561.273	+	363.362i	1.46165	+	0.946256i
$385$		0			0
$386$	303.792	−	322.668i	0.787026	−	0.835929i
$387$	323.104	−	559.633i	0.834895	−	1.44608i
$388$	41.6721	−	27.5318i	0.107402	−	0.0709583i
$389$	−614.357	+	354.699i	−1.57932	+	0.911823i	−0.584370	+	0.811487i	$0.698658\pi$
$389$	−614.357	+	354.699i	−1.57932	+	0.911823i	−0.994954	+	0.100336i	$0.968008\pi$
$390$	−45.5403	−	151.545i	−0.116770	−	0.388576i
$391$			295.315i			0.755281i
$392$		0			0
$393$	278.582			0.708860
$394$	−464.094	+	139.464i	−1.17790	+	0.353969i
$395$	−62.4683	−	108.198i	−0.158148	−	0.273920i
$396$	−598.501	+	395.416i	−1.51137	+	0.998526i
$397$	−267.952	−	154.702i	−0.674941	−	0.389677i	0.123005	−	0.992406i	$-0.460747\pi$
$397$	−267.952	−	154.702i	−0.674941	−	0.389677i	−0.797946	+	0.602729i	$0.794080\pi$
$398$	−432.549	−	407.245i	−1.08681	−	1.02323i
$399$		0			0
$400$	226.924	−	27.4754i	0.567309	−	0.0686886i
$401$	264.036	−	457.324i	0.658445	−	1.14046i	−0.322574	−	0.946544i	$-0.604548\pi$
$401$	264.036	−	457.324i	0.658445	−	1.14046i	0.981018	−	0.193915i	$-0.0621186\pi$
$402$	−316.250	−	74.6074i	−0.786692	−	0.185591i
$403$	−8.66126	−	15.0017i	−0.0214920	−	0.0372252i
$404$	121.705	−	243.589i	0.301250	−	0.602944i
$405$			556.666i			1.37448i
$406$		0			0
$407$			1.98739i			0.00488302i
$408$	−270.433	+	99.3807i	−0.662826	+	0.243580i
$409$	−306.415	−	530.726i	−0.749181	−	1.29762i	−0.948216	−	0.317627i	$-0.897114\pi$
$409$	−306.415	−	530.726i	−0.749181	−	1.29762i	0.199035	−	0.979992i	$-0.436219\pi$
$410$	−182.916	+	775.356i	−0.446137	+	1.89111i
$411$	150.748	−	261.104i	0.366785	−	0.635290i
$412$	−232.749	+	14.0391i	−0.564926	+	0.0340756i
$413$		0			0
$414$	−1140.56	−	1073.84i	−2.75497	−	2.59381i
$415$	−27.7713	−	16.0338i	−0.0669188	−	0.0386356i
$416$	−8.58012	+	76.8514i	−0.0206253	+	0.184739i
$417$	−450.335	−	780.003i	−1.07994	−	1.87051i
$418$	−15.6718	−	52.1512i	−0.0374924	−	0.124764i
$419$	237.642			0.567165			0.283583	−	0.958948i	$-0.408477\pi$
$419$	237.642			0.567165			0.283583	+	0.958948i	$0.408477\pi$
$420$		0			0
$421$			394.516i			0.937092i	0.883439	+	0.468546i	$0.155222\pi$
$421$			394.516i			0.937092i	−0.883439	+	0.468546i	$0.844778\pi$
$422$	−81.1693	−	270.108i	−0.192344	−	0.640065i
$423$	−600.404	+	346.644i	−1.41940	+	0.819488i
$424$	−430.911	−	74.6036i	−1.01630	−	0.175952i
$425$	−49.2487	+	85.3012i	−0.115879	+	0.200709i
$426$	−175.933	−	165.641i	−0.412989	−	0.388829i
$427$		0			0
$428$	−32.7220	−	542.486i	−0.0764533	−	1.26749i
$429$	−107.208	−	61.8964i	−0.249901	−	0.144281i
$430$	−101.716	+	431.158i	−0.236548	+	1.00269i
$431$	314.678	−	181.679i	0.730111	−	0.421530i	−0.0883519	−	0.996089i	$-0.528160\pi$
$431$	314.678	−	181.679i	0.730111	−	0.421530i	0.818463	+	0.574560i	$0.194827\pi$
$432$	304.460	−	713.923i	0.704769	−	1.65260i
$433$	−119.733			−0.276520			−0.138260	−	0.990396i	$-0.544151\pi$
$433$	−119.733			−0.276520			−0.138260	+	0.990396i	$0.544151\pi$
$434$		0			0
$435$	−1222.89			−2.81125
$436$	79.5537	−	159.225i	0.182463	−	0.365194i
$437$	102.989	−	59.4605i	0.235672	−	0.136065i
$438$	−703.915	−	166.062i	−1.60711	−	0.379138i
$439$	−754.721	−	435.738i	−1.71918	−	0.992570i	−0.920427	−	0.390914i	$-0.872159\pi$
$439$	−754.721	−	435.738i	−1.71918	−	0.992570i	−0.798755	−	0.601657i	$-0.794508\pi$
$440$	314.919	−	377.679i	0.715724	−	0.858361i
$441$		0			0
$442$	−24.2609	−	22.8416i	−0.0548889	−	0.0516778i
$443$	171.978	−	297.875i	0.388212	−	0.672403i	−0.603997	−	0.796987i	$-0.706426\pi$
$443$	171.978	−	297.875i	0.388212	−	0.672403i	0.992209	+	0.124584i	$0.0397595\pi$
$444$	−2.33411	−	3.53291i	−0.00525701	−	0.00795700i
$445$	97.6462	−	56.3761i	0.219430	−	0.126688i
$446$	78.1988	−	23.4993i	0.175334	−	0.0526890i
$447$		−	1146.74i		−	2.56541i
$448$		0			0
$449$	−242.849			−0.540866			−0.270433	−	0.962739i	$-0.587167\pi$
$449$	−242.849			−0.540866			−0.270433	+	0.962739i	$0.587167\pi$
$450$	−150.369	−	500.383i	−0.334153	−	1.11196i
$451$	311.611	+	539.726i	0.690933	+	1.19673i
$452$	445.178	−	294.119i	0.984906	−	0.650705i
$453$	−839.924	−	484.930i	−1.85414	−	1.07049i
$454$	−11.2228	+	11.9201i	−0.0247198	+	0.0262558i
$455$		0			0
$456$	89.1088	+	74.3013i	0.195414	+	0.162942i
$457$	21.1285	−	36.5957i	0.0462331	−	0.0800781i	−0.841983	−	0.539504i	$-0.818612\pi$
$457$	21.1285	−	36.5957i	0.0462331	−	0.0800781i	0.888216	+	0.459426i	$0.151945\pi$
$458$	−152.576	+	646.750i	−0.333136	+	1.41212i
$459$	167.221	+	289.635i	0.364315	+	0.631013i
$460$	960.662	+	479.977i	2.08840	+	1.04343i
$461$			816.370i			1.77087i	0.464766	+	0.885434i	$0.346139\pi$
$461$			816.370i			1.77087i	−0.464766	+	0.885434i	$0.653861\pi$
$462$		0			0
$463$		−	115.161i		−	0.248727i	−0.992237	−	0.124363i	$-0.960311\pi$
$463$		−	115.161i		−	0.248727i	0.992237	−	0.124363i	$-0.0396889\pi$
$464$	549.707	+	234.429i	1.18471	+	0.505234i
$465$	−117.350	−	203.256i	−0.252365	−	0.437109i
$466$	−640.927	−	151.203i	−1.37538	−	0.324469i
$467$	301.712	−	522.580i	0.646064	−	1.11902i	−0.337991	−	0.941149i	$-0.609747\pi$
$467$	301.712	−	522.580i	0.646064	−	1.11902i	0.984055	−	0.177866i	$-0.0569194\pi$
$468$	176.437	−	10.6424i	0.377002	−	0.0227403i
$469$		0			0
$470$	325.790	−	346.034i	0.693171	−	0.736242i
$471$	851.296	+	491.496i	1.80742	+	1.04352i
$472$	143.018	−	826.070i	0.303004	−	1.75015i
$473$	173.280	+	300.129i	0.366342	+	0.634523i
$474$	199.433	−	59.9312i	0.420746	−	0.126437i
$475$	39.6641			0.0835034
$476$		0			0
$477$			999.624i			2.09565i
$478$	263.785	−	79.2693i	0.551851	−	0.165835i
$479$	137.348	−	79.2977i	0.286738	−	0.165548i	−0.349732	−	0.936850i	$-0.613727\pi$
$479$	137.348	−	79.2977i	0.286738	−	0.165548i	0.636470	+	0.771302i	$0.280394\pi$
$480$	−116.251	+	1041.25i	−0.242189	+	2.16926i
$481$	0.244858	−	0.424106i	0.000509060	−	0.000881717i
$482$	−276.737	+	293.932i	−0.574143	+	0.609818i
$483$		0			0
$484$	5.97880	+	99.1201i	0.0123529	+	0.204794i
$485$	67.7780	+	39.1317i	0.139749	+	0.0806838i
$486$	−53.2370	−	12.5593i	−0.109541	−	0.0258421i
$487$	92.6539	−	53.4937i	0.190254	−	0.109843i	−0.401847	−	0.915707i	$-0.631632\pi$
$487$	92.6539	−	53.4937i	0.190254	−	0.109843i	0.592102	+	0.805863i	$0.298298\pi$
$488$	120.773	+	328.646i	0.247486	+	0.673455i
$489$	284.768			0.582348
$490$		0			0
$491$	616.591			1.25579			0.627893	−	0.778299i	$-0.283917\pi$
$491$	616.591			1.25579			0.627893	+	0.778299i	$0.283917\pi$
$492$	−1187.83	−	593.476i	−2.41428	−	1.20625i
$493$	−223.013	+	128.757i	−0.452360	+	0.261170i
$494$	−3.08098	+	13.0598i	−0.00623681	+	0.0264369i
$495$	−973.438	−	562.015i	−1.96654	−	1.13538i
$496$	13.7862	+	113.862i	0.0277947	+	0.229561i
$497$		0			0
$498$	36.6394	−	38.9160i	0.0735731	−	0.0781446i
$499$	−277.045	+	479.856i	−0.555200	+	0.961635i	0.442688	+	0.896676i	$0.354025\pi$
$499$	−277.045	+	479.856i	−0.555200	+	0.961635i	−0.997888	+	0.0649593i	$0.979308\pi$
$500$	−148.066	−	224.113i	−0.296133	−	0.448227i
$501$	1205.30	−	695.879i	2.40578	−	1.38898i
$502$	154.950	+	515.628i	0.308665	+	1.02715i
$503$			148.158i			0.294548i	0.989096	+	0.147274i	$0.0470499\pi$
$503$			148.158i			0.294548i	−0.989096	+	0.147274i	$0.952950\pi$
$504$		0			0
$505$	426.688			0.844926
$506$	804.578	−	241.782i	1.59007	−	0.477829i
$507$	−426.145	−	738.104i	−0.840522	−	1.45583i
$508$	−288.796	−	437.122i	−0.568496	−	0.860476i
$509$	158.386	+	91.4444i	0.311172	+	0.179655i	0.647451	−	0.762107i	$-0.275835\pi$
$509$	158.386	+	91.4444i	0.311172	+	0.179655i	−0.336279	+	0.941762i	$0.609169\pi$
$510$	−328.706	−	309.477i	−0.644522	−	0.606817i
$511$		0			0
$512$	251.863	−	445.768i	0.491919	−	0.870641i
$513$	67.3385	−	116.634i	0.131264	−	0.227356i
$514$	−471.768	−	111.296i	−0.917837	−	0.216529i
$515$	−182.687	−	316.423i	−0.354732	−	0.614414i
$516$	−660.523	−	330.018i	−1.28008	−	0.639571i
$517$		−	371.807i		−	0.719163i
$518$		0			0
$519$			599.856i			1.15579i
$520$	−113.735	+	41.7963i	−0.218722	+	0.0803775i
$521$	49.1230	+	85.0836i	0.0942861	+	0.163308i	0.909310	−	0.416118i	$-0.136610\pi$
$521$	49.1230	+	85.0836i	0.0942861	+	0.163308i	−0.815024	+	0.579427i	$0.803277\pi$
$522$	313.648	−	1329.51i	0.600858	−	2.54695i
$523$	−287.382	+	497.760i	−0.549488	+	0.951740i	0.448822	+	0.893621i	$0.351844\pi$
$523$	−287.382	+	497.760i	−0.549488	+	0.951740i	−0.998310	+	0.0581192i	$0.981490\pi$
$524$	−12.8441	−	212.937i	−0.0245116	−	0.406369i
$525$		0			0
$526$	49.2868	+	46.4035i	0.0937012	+	0.0882196i
$527$	−42.8010	−	24.7112i	−0.0812163	−	0.0468903i
$528$	492.170	+	655.423i	0.932141	+	1.24133i
$529$	652.843	+	1130.76i	1.23411	+	2.13754i
$530$	−197.216	−	656.277i	−0.372106	−	1.23826i
$531$	−1916.31			−3.60888
$532$		0			0
$533$		−	153.569i		−	0.288122i
$534$	54.0864	+	179.984i	0.101285	+	0.337048i
$535$	737.510	−	425.802i	1.37852	−	0.795891i
$536$	−42.4462	+	245.169i	−0.0791907	+	0.457406i
$537$	−294.740	+	510.504i	−0.548864	+	0.950660i
$538$	−241.138	−	227.031i	−0.448212	−	0.421991i
$539$		0			0
$540$	1213.97	−	73.2251i	2.24809	−	0.135602i
$541$	−320.996	−	185.327i	−0.593338	−	0.342564i	0.173078	−	0.984908i	$-0.444629\pi$
$541$	−320.996	−	185.327i	−0.593338	−	0.342564i	−0.766416	+	0.642344i	$0.777962\pi$
$542$	−68.1061	+	288.692i	−0.125657	+	0.532642i
$543$	275.712	−	159.182i	0.507756	−	0.293153i
$544$	88.4312	+	202.127i	0.162557	+	0.371556i
$545$	278.909			0.511759
$546$		0			0
$547$	−56.5966			−0.103467			−0.0517336	−	0.998661i	$-0.516475\pi$
$547$	−56.5966			−0.103467			−0.0517336	+	0.998661i	$0.516475\pi$
$548$	−206.528	−	103.188i	−0.376876	−	0.188299i
$549$	693.110	−	400.167i	1.26250	−	0.728902i
$550$	272.722	+	64.3385i	0.495858	+	0.116979i
$551$	89.8057	+	51.8494i	0.162987	+	0.0941005i
$552$	−1146.31	+	1374.75i	−2.07664	+	2.49049i
$553$		0			0
$554$	−696.569	−	655.819i	−1.25734	−	1.18379i
$555$	3.31753	−	5.74613i	0.00597753	−	0.0103534i
$556$	−575.442	+	380.181i	−1.03497	+	0.683779i
$557$	131.224	−	75.7624i	0.235591	−	0.136019i	−0.377558	−	0.925986i	$-0.623236\pi$
$557$	131.224	−	75.7624i	0.235591	−	0.136019i	0.613149	+	0.789968i	$0.289903\pi$
$558$	251.074	−	75.4495i	0.449953	−	0.135214i
$559$		−	85.3962i		−	0.152766i
$560$		0			0
$561$	−353.189			−0.629571
$562$	−130.121	−	433.004i	−0.231532	−	0.770470i
$563$	−159.024	−	275.438i	−0.282458	−	0.489232i	0.689531	−	0.724256i	$-0.257817\pi$
$563$	−159.024	−	275.438i	−0.282458	−	0.489232i	−0.971990	+	0.235024i	$0.924483\pi$
$564$	436.673	+	660.948i	0.774243	+	1.17189i
$565$	724.063	+	418.038i	1.28153	+	0.739891i
$566$	349.089	−	370.780i	0.616766	−	0.655089i
$567$		0			0
$568$	−118.498	+	142.114i	−0.208624	+	0.250200i
$569$	−178.327	+	308.871i	−0.313404	+	0.542831i	−0.979097	−	0.203394i	$-0.934803\pi$
$569$	−178.327	+	308.871i	−0.313404	+	0.542831i	0.665693	+	0.746226i	$0.268136\pi$
$570$	−41.7436	+	176.945i	−0.0732345	+	0.310431i
$571$	−415.507	−	719.679i	−0.727683	−	1.26038i	−0.957860	−	0.287235i	$-0.907264\pi$
$571$	−415.507	−	719.679i	−0.727683	−	1.26038i	0.230177	−	0.973149i	$-0.426069\pi$
$572$	−42.3684	+	84.7992i	−0.0740706	+	0.148250i
$573$			932.205i			1.62689i
$574$		0			0
$575$			611.929i			1.06422i
$576$	−1102.21	−	393.444i	−1.91355	−	0.683062i
$577$	385.742	+	668.124i	0.668530	+	1.15793i	0.978315	+	0.207121i	$0.0664094\pi$
$577$	385.742	+	668.124i	0.668530	+	1.15793i	−0.309786	+	0.950806i	$0.600257\pi$
$578$	470.029	+	110.886i	0.813198	+	0.191844i
$579$	−578.746	+	1002.42i	−0.999562	+	1.73129i
$580$	56.3819	+	934.734i	0.0972102	+	1.61161i
$581$		0			0
$582$	−89.4212	+	94.9775i	−0.153645	+	0.163192i
$583$	−464.271	−	268.047i	−0.796349	−	0.459772i
$584$	−94.4775	+	545.702i	−0.161777	+	0.934421i
$585$	138.487	+	239.866i	0.236730	+	0.410028i
$586$	−286.461	+	86.0837i	−0.488842	+	0.146900i
$587$	−144.376			−0.245956			−0.122978	−	0.992409i	$-0.539244\pi$
$587$	−144.376			−0.245956			−0.122978	+	0.992409i	$0.539244\pi$
$588$		0			0
$589$			19.9020i			0.0337894i
$590$	1258.11	−	378.070i	2.13238	−	0.640796i
$591$	1096.11	−	632.838i	1.85467	−	1.07079i
$592$	−2.59281	+	1.94699i	−0.00437974	+	0.00328884i
$593$	419.463	−	726.531i	0.707357	−	1.22518i	−0.258477	−	0.966018i	$-0.583220\pi$
$593$	419.463	−	726.531i	0.707357	−	1.22518i	0.965834	−	0.259162i	$-0.0834462\pi$
$594$	652.195	−	692.720i	1.09797	−	1.16620i
$595$		0			0
$596$	−876.521	+	52.8706i	−1.47067	+	0.0887090i
$597$	1343.78	+	775.831i	2.25089	+	1.29955i
$598$	−201.485	−	47.5327i	−0.336931	−	0.0794862i
$599$	−616.039	+	355.670i	−1.02845	+	0.593774i	−0.916539	−	0.399945i	$-0.869029\pi$
$599$	−616.039	+	355.670i	−1.02845	+	0.593774i	−0.111907	+	0.993719i	$0.535696\pi$
$600$	−560.371	+	205.929i	−0.933952	+	0.343215i
$601$	356.394			0.593002			0.296501	−	0.955033i	$-0.404180\pi$
$601$	356.394			0.593002			0.296501	+	0.955033i	$0.404180\pi$
$602$		0			0
$603$	568.742			0.943188
$604$	−331.937	+	664.364i	−0.549565	+	1.09994i
$605$	−134.754	+	77.8003i	−0.222734	+	0.128596i
$606$	−163.298	+	692.199i	−0.269469	+	1.14224i
$607$	−52.2836	−	30.1860i	−0.0861345	−	0.0497298i	0.456314	−	0.889819i	$-0.349169\pi$
$607$	−52.2836	−	30.1860i	−0.0861345	−	0.0497298i	−0.542449	+	0.840089i	$0.682503\pi$
$608$	52.6847	−	71.5370i	0.0866525	−	0.117660i
$609$		0			0
$610$	−376.094	+	399.463i	−0.616548	+	0.654858i
$611$	−45.8088	+	79.3431i	−0.0749735	+	0.129858i
$612$	420.764	−	277.989i	0.687523	−	0.454230i
$613$	−418.281	+	241.495i	−0.682351	+	0.393955i	−0.800740	−	0.599012i	$-0.795560\pi$
$613$	−418.281	+	241.495i	−0.682351	+	0.393955i	0.118389	+	0.992967i	$0.462227\pi$
$614$	−156.432	−	520.561i	−0.254776	−	0.847819i
$615$		−	2080.68i		−	3.38321i
$616$		0			0
$617$	712.490			1.15476			0.577382	−	0.816474i	$-0.304074\pi$
$617$	712.490			1.15476			0.577382	+	0.816474i	$0.304074\pi$
$618$	583.238	−	175.267i	0.943750	−	0.283604i
$619$	−46.5409	−	80.6112i	−0.0751872	−	0.130228i	0.825980	−	0.563699i	$-0.190622\pi$
$619$	−46.5409	−	80.6112i	−0.0751872	−	0.130228i	−0.901168	+	0.433471i	$0.857289\pi$
$620$	−149.950	+	99.0688i	−0.241856	+	0.159788i
$621$	1799.40	+	1038.88i	2.89758	+	1.67292i
$622$	777.855	+	732.350i	1.25057	+	1.17741i
$623$		0			0
$624$	−24.2767	−	200.504i	−0.0389049	−	0.321321i
$625$	389.030	−	673.819i	0.622447	−	1.07811i
$626$	−1082.74	−	255.433i	−1.72962	−	0.408039i
$627$	71.1133	+	123.172i	0.113418	+	0.196446i
$628$	336.432	−	673.359i	0.535719	−	1.07223i
$629$		−	1.39719i		−	0.00222129i
$630$		0			0
$631$		−	610.573i		−	0.967628i	−0.875171	−	0.483814i	$-0.839251\pi$
$631$		−	610.573i		−	0.967628i	0.875171	−	0.483814i	$-0.160749\pi$
$632$	−55.0040	−	149.676i	−0.0870317	−	0.236829i
$633$	368.318	+	637.946i	0.581861	+	1.00781i
$634$	177.929	−	754.214i	0.280645	−	1.18961i
$635$	410.473	−	710.961i	0.646415	−	1.11962i
$636$	1140.13	−	68.7711i	1.79266	−	0.108131i
$637$		0			0
$638$	533.381	+	502.178i	0.836021	+	0.787113i
$639$	366.287	+	211.476i	0.573219	+	0.330948i
$640$	801.248	+	40.8505i	1.25195	+	0.0638289i
$641$	−295.077	−	511.088i	−0.460338	−	0.797328i	0.538640	−	0.842536i	$-0.318938\pi$
$641$	−295.077	−	511.088i	−0.460338	−	0.797328i	−0.998978	+	0.0452077i	$0.985605\pi$
$642$	408.508	+	1359.39i	0.636305	+	2.11744i
$643$	257.971			0.401199			0.200600	−	0.979673i	$-0.435711\pi$
$643$	257.971			0.401199			0.200600	+	0.979673i	$0.435711\pi$
$644$		0			0
$645$		−	1157.02i		−	1.79383i
$646$	11.0177	+	36.6638i	0.0170553	+	0.0567551i
$647$	329.059	−	189.982i	0.508591	−	0.293635i	−0.223663	−	0.974667i	$-0.571802\pi$
$647$	329.059	−	189.982i	0.508591	−	0.293635i	0.732254	+	0.681031i	$0.238468\pi$
$648$	−121.206	+	700.085i	−0.187046	+	1.08038i
$649$	513.856	−	890.024i	0.791765	−	1.37138i
$650$	−50.2716	−	47.3307i	−0.0773410	−	0.0728164i
$651$		0			0
$652$	−13.1293	−	217.666i	−0.0201370	−	0.333843i
$653$	−825.126	−	476.386i	−1.26359	−	0.729535i	−0.289824	−	0.957080i	$-0.593597\pi$
$653$	−825.126	−	476.386i	−1.26359	−	0.729535i	−0.973768	+	0.227545i	$0.926930\pi$
$654$	−106.742	+	452.463i	−0.163213	+	0.691839i
$655$	289.489	−	167.136i	0.441968	−	0.255170i
$656$	−398.865	+	935.291i	−0.608026	+	1.42575i
$657$	1265.92			1.92681
$658$		0			0
$659$	−963.119			−1.46149			−0.730743	−	0.682653i	$-0.760826\pi$
$659$	−963.119			−1.46149			−0.730743	+	0.682653i	$0.760826\pi$
$660$	−574.041	+	1148.93i	−0.869760	+	1.74080i
$661$	62.0782	−	35.8409i	0.0939156	−	0.0542222i	−0.452307	−	0.891862i	$-0.649399\pi$
$661$	62.0782	−	35.8409i	0.0939156	−	0.0542222i	0.546222	+	0.837640i	$0.316065\pi$
$662$	745.934	+	175.975i	1.12679	+	0.265823i
$663$	75.3701	+	43.5150i	0.113680	+	0.0656334i
$664$	−31.4352	−	26.2115i	−0.0473422	−	0.0394752i
$665$		0			0
$666$	5.39621	+	5.08053i	0.00810242	+	0.00762842i
$667$	−799.921	+	1385.50i	−1.19928	+	2.07722i
$668$	−587.473	−	889.199i	−0.879451	−	1.33114i
$669$	−184.692	+	106.632i	−0.276071	+	0.159390i
$670$	−373.393	+	112.207i	−0.557303	+	0.167474i
$671$			429.216i			0.639667i
$672$		0			0
$673$	−712.783			−1.05911			−0.529556	−	0.848275i	$-0.677642\pi$
$673$	−712.783			−1.05911			−0.529556	+	0.848275i	$0.677642\pi$
$674$	324.473	+	1079.75i	0.481414	+	1.60201i
$675$	346.502	+	600.160i	0.513337	+	0.889125i
$676$	−544.531	+	359.759i	−0.805520	+	0.532188i
$677$	−664.698	−	383.763i	−0.981828	−	0.566859i	−0.0790065	−	0.996874i	$-0.525175\pi$
$677$	−664.698	−	383.763i	−0.981828	−	0.566859i	−0.902822	+	0.430015i	$0.858508\pi$
$678$	−955.275	+	1014.63i	−1.40896	+	1.49651i
$679$		0			0
$680$	−221.397	+	265.519i	−0.325584	+	0.390469i
$681$	21.3803	−	37.0317i	0.0313954	−	0.0543784i
$682$	−32.2827	+	136.842i	−0.0473354	+	0.200648i
$683$	242.177	+	419.462i	0.354578	+	0.614147i	0.987046	−	0.160440i	$-0.0512912\pi$
$683$	242.177	+	419.462i	0.354578	+	0.614147i	−0.632468	+	0.774587i	$0.717958\pi$
$684$	−181.665	−	90.7659i	−0.265593	−	0.132699i
$685$		−	361.769i		−	0.528130i
$686$		0			0
$687$		−	1735.56i		−	2.52629i
$688$	−221.800	+	520.094i	−0.322384	+	0.755951i
$689$	66.0499	+	114.402i	0.0958634	+	0.166040i
$690$	−2729.88	−	644.012i	−3.95634	−	0.933351i
$691$	−287.425	+	497.835i	−0.415956	+	0.720457i	−0.995528	−	0.0944642i	$-0.969886\pi$
$691$	−287.425	+	497.835i	−0.415956	+	0.720457i	0.579572	+	0.814921i	$0.303220\pi$
$692$	458.507	−	27.6565i	0.662582	−	0.0399661i
$693$		0			0
$694$	70.7274	−	75.1221i	0.101913	−	0.108245i
$695$	−935.933	−	540.361i	−1.34667	−	0.777498i
$696$	−1537.96	−	266.268i	−2.20971	−	0.382568i
$697$	−219.071	−	379.443i	−0.314306	−	0.544394i
$698$	1123.15	−	337.515i	1.60910	−	0.483545i
$699$	1719.94			2.46057
$700$		0			0
$701$			143.138i			0.204191i	0.994775	+	0.102096i	$0.0325548\pi$
$701$			143.138i			0.204191i	−0.994775	+	0.102096i	$0.967445\pi$
$702$	−224.525	+	67.4713i	−0.319836	+	0.0961129i
$703$	−0.487259	+	0.281319i	−0.000693114	+	0.000400169i
$704$	478.288	−	406.415i	0.679387	−	0.577294i
$705$	−620.655	+	1075.01i	−0.880361	+	1.52483i
$706$	−416.563	+	442.446i	−0.590032	+	0.626695i
$707$		0			0
$708$	131.837	+	2185.67i	0.186210	+	3.08710i
$709$	221.106	+	127.656i	0.311856	+	0.180050i	0.647757	−	0.761847i	$-0.275707\pi$
$709$	221.106	+	127.656i	0.311856	+	0.180050i	−0.335901	+	0.941897i	$0.609041\pi$
$710$	−282.198	−	66.5741i	−0.397462	−	0.0937664i
$711$	−315.665	+	182.249i	−0.443973	+	0.256328i
$712$	135.079	−	49.6398i	0.189717	−	0.0697188i
$713$	−307.044			−0.430636
$714$		0			0
$715$	−148.540			−0.207748
$716$	403.799	+	201.751i	0.563965	+	0.281775i
$717$	−623.013	+	359.697i	−0.868916	+	0.501669i
$718$	−53.3290	+	226.054i	−0.0742744	+	0.314839i
$719$	359.947	+	207.815i	0.500621	+	0.289034i	0.728970	−	0.684546i	$-0.239999\pi$
$719$	359.947	+	207.815i	0.500621	+	0.289034i	−0.228349	+	0.973579i	$0.573333\pi$
$720$	−220.430	−	1820.57i	−0.306153	−	2.52857i
$721$		0			0
$722$	−484.355	+	514.451i	−0.670852	+	0.712537i
$723$	527.204	−	913.144i	0.729190	−	1.26299i
$724$	−134.385	−	203.404i	−0.185614	−	0.280945i
$725$	−462.112	+	266.800i	−0.637395	+	0.368000i
$726$	−74.6404	−	248.381i	−0.102811	−	0.342123i
$727$		−	896.838i		−	1.23361i	−0.787114	−	0.616807i	$-0.788426\pi$
$727$		−	896.838i		−	1.23361i	0.787114	−	0.616807i	$-0.211574\pi$
$728$		0			0
$729$	−656.451			−0.900481
$730$	−831.104	+	249.753i	−1.13850	+	0.342127i
$731$	−121.821	−	211.000i	−0.166649	−	0.288645i
$732$	−504.098	−	763.002i	−0.688658	−	1.04235i
$733$	−440.858	−	254.530i	−0.601444	−	0.347244i	0.168166	−	0.985759i	$-0.446216\pi$
$733$	−440.858	−	254.530i	−0.601444	−	0.347244i	−0.769609	+	0.638515i	$0.779549\pi$
$734$	−693.555	−	652.981i	−0.944898	−	0.889620i
$735$		0			0
$736$	1103.66	+	812.808i	1.49954	+	1.10436i
$737$	−152.507	+	264.150i	−0.206930	+	0.358413i
$738$	2262.07	+	533.652i	3.06514	+	0.723105i
$739$	−370.714	−	642.095i	−0.501642	−	0.868870i	−0.999998	−	0.00189750i	$-0.999396\pi$
$739$	−370.714	−	642.095i	−0.501642	−	0.868870i	0.498356	−	0.866973i	$-0.333937\pi$
$740$	−4.54508	−	2.27087i	−0.00614200	−	0.00306874i
$741$		−	35.0463i		−	0.0472959i
$742$		0			0
$743$			1344.98i			1.81021i	0.425191	+	0.905104i	$0.360207\pi$
$743$			1344.98i			1.81021i	−0.425191	+	0.905104i	$0.639793\pi$
$744$	−103.328	−	281.174i	−0.138881	−	0.377922i
$745$	−687.989	−	1191.63i	−0.923476	−	1.59951i
$746$	−22.6329	+	95.9378i	−0.0303391	+	0.128603i
$747$	−46.7780	+	81.0218i	−0.0626211	+	0.108463i
$748$	16.2839	+	269.964i	0.0217699	+	0.360915i
$749$		0			0
$750$	510.790	+	480.909i	0.681054	+	0.641211i
$751$	−23.9829	−	13.8465i	−0.0319346	−	0.0184375i	0.483948	−	0.875097i	$-0.339202\pi$
$751$	−23.9829	−	13.8465i	−0.0319346	−	0.0184375i	−0.515882	+	0.856659i	$0.672536\pi$
$752$	485.071	−	364.250i	0.645041	−	0.484374i
$753$	−703.109	−	1217.82i	−0.933743	−	1.61729i
$754$	−51.9516	−	172.880i	−0.0689014	−	0.229283i
$755$	−1163.74			−1.54138
$756$		0			0
$757$			1341.69i			1.77238i	0.463318	+	0.886192i	$0.346659\pi$
$757$			1341.69i			1.77238i	−0.463318	+	0.886192i	$0.653341\pi$
$758$	96.4174	+	320.849i	0.127200	+	0.423283i
$759$	−1900.27	+	1097.12i	−2.50365	+	1.44548i
$760$	137.175	+	23.7491i	0.180493	+	0.0312488i
$761$	−56.0005	+	96.9958i	−0.0735881	+	0.127458i	−0.900471	−	0.434915i	$-0.856778\pi$
$761$	−56.0005	+	96.9958i	−0.0735881	+	0.127458i	0.826883	+	0.562374i	$0.190112\pi$
$762$	996.271	+	937.988i	1.30744	+	1.23096i
$763$		0			0
$764$	712.542	−	42.9796i	0.932647	−	0.0562560i
$765$	684.355	+	395.113i	0.894582	+	0.516487i
$766$	−235.675	+	998.991i	−0.307669	+	1.30417i
$767$	−219.312	+	126.620i	−0.285935	+	0.165085i
$768$	−372.917	+	1284.20i	−0.485569	+	1.67213i
$769$	−140.749			−0.183028			−0.0915142	−	0.995804i	$-0.529171\pi$
$769$	−140.749			−0.183028			−0.0915142	+	0.995804i	$0.529171\pi$
$770$		0			0
$771$	1265.99			1.64202
$772$	792.893	+	396.155i	1.02706	+	0.513154i
$773$	1147.60	−	662.568i	1.48461	−	0.857138i	0.484760	−	0.874647i	$-0.338907\pi$
$773$	1147.60	−	662.568i	1.48461	−	0.857138i	0.999847	+	0.0175096i	$0.00557375\pi$
$774$	1257.89	+	296.752i	1.62518	+	0.383400i
$775$	−88.6891	−	51.2047i	−0.114437	−	0.0660705i
$776$	76.7200	+	63.9712i	0.0988660	+	0.0824371i
$777$		0			0
$778$	−1033.00	−	972.570i	−1.32777	−	1.25009i
$779$	−88.2183	+	152.799i	−0.113246	+	0.196147i
$780$	264.054	−	174.455i	0.338531	−	0.223660i
$781$	−196.438	+	113.414i	−0.251522	+	0.145216i
$782$	−565.641	+	169.979i	−0.723327	+	0.217365i
$783$			1811.81i			2.31393i
$784$		0			0
$785$	1179.50			1.50255
$786$	160.348	+	533.592i	0.204005	+	0.678870i
$787$	−163.900	−	283.884i	−0.208260	−	0.360716i	0.742907	−	0.669395i	$-0.233447\pi$
$787$	−163.900	−	283.884i	−0.208260	−	0.360716i	−0.951166	+	0.308679i	$0.900113\pi$
$788$	−534.254	−	808.646i	−0.677987	−	1.02620i
$789$	−153.117	−	88.4021i	−0.194065	−	0.112043i
$790$	171.285	−	181.929i	0.216817	−	0.230289i
$791$		0			0
$792$	−1101.86	−	918.764i	−1.39124	−	1.16006i
$793$	52.8819	−	91.5941i	0.0666859	−	0.115503i
$794$	142.084	−	602.275i	0.178947	−	0.758532i
$795$	894.898	+	1550.01i	1.12566	+	1.94970i
$796$	531.061	−	1062.90i	0.667161	−	1.33531i
$797$		−	393.650i		−	0.493915i	−0.969026	−	0.246958i	$-0.920569\pi$
$797$		−	393.650i		−	0.493915i	0.969026	−	0.246958i	$-0.0794308\pi$
$798$		0			0
$799$			261.391i			0.327148i
$800$	183.241	+	418.832i	0.229051	+	0.523540i
$801$	−164.475	−	284.879i	−0.205337	−	0.355655i
$802$	1027.93	+	242.501i	1.28171	+	0.302370i
$803$	−339.453	+	587.950i	−0.422731	+	0.732192i
$804$	−39.1278	−	648.684i	−0.0486664	−	0.806821i
$805$		0			0
$806$	23.7488	−	25.2245i	0.0294650	−	0.0312959i
$807$	749.132	+	432.511i	0.928292	+	0.535950i
$808$	536.619	+	92.9050i	0.664133	+	0.114981i
$809$	−208.321	−	360.822i	−0.257504	−	0.446010i	0.708069	−	0.706144i	$-0.249567\pi$
$809$	−208.321	−	360.822i	−0.257504	−	0.446010i	−0.965573	+	0.260134i	$0.916233\pi$
$810$	−1066.23	+	320.410i	−1.31633	+	0.395568i
$811$	748.707			0.923190			0.461595	−	0.887091i	$-0.347277\pi$
$811$	748.707			0.923190			0.461595	+	0.887091i	$0.347277\pi$
$812$		0			0
$813$		−	774.708i		−	0.952901i
$814$	−3.80662	+	1.14392i	−0.00467643	+	0.00140530i
$815$	295.917	−	170.848i	0.363089	−	0.209629i
$816$	−346.010	−	460.781i	−0.424032	−	0.564683i
$817$	−49.0562	+	84.9678i	−0.0600443	+	0.104000i
$818$	840.176	−	892.382i	1.02711	−	1.09093i
$819$		0			0
$820$	−1590.39	+	95.9302i	−1.93950	+	0.116988i
$821$	−479.925	−	277.085i	−0.584561	−	0.337496i	0.178383	−	0.983961i	$-0.442913\pi$
$821$	−479.925	−	277.085i	−0.584561	−	0.337496i	−0.762944	+	0.646465i	$0.776247\pi$
$822$	586.884	+	138.453i	0.713970	+	0.168435i
$823$	105.180	−	60.7260i	0.127801	−	0.0737861i	−0.434736	−	0.900558i	$-0.643158\pi$
$823$	105.180	−	60.7260i	0.127801	−	0.0737861i	0.562538	+	0.826772i	$0.309825\pi$
$824$	−160.858	−	437.724i	−0.195216	−	0.531218i
$825$	−731.853			−0.887094
$826$		0			0
$827$	−1516.61			−1.83386			−0.916932	−	0.399043i	$-0.869343\pi$
$827$	−1516.61			−1.83386			−0.916932	+	0.399043i	$0.869343\pi$
$828$	1400.32	−	2802.70i	1.69120	−	3.38490i
$829$	281.494	−	162.521i	0.339559	−	0.196044i	−0.320518	−	0.947242i	$-0.603857\pi$
$829$	281.494	−	162.521i	0.339559	−	0.196044i	0.660077	+	0.751198i	$0.270524\pi$
$830$	14.7260	−	62.4216i	0.0177422	−	0.0752068i
$831$	2164.00	+	1249.38i	2.60409	+	1.50347i
$832$	−152.139	+	27.8005i	−0.182859	+	0.0334140i
$833$		0			0
$834$	1234.80	−	1311.53i	1.48057	−	1.57257i
$835$	834.991	−	1446.25i	0.999989	−	1.73203i
$836$	90.8691	−	60.0351i	0.108695	−	0.0718124i
$837$	−301.138	+	173.862i	−0.359783	+	0.207721i
$838$	136.784	+	455.176i	0.163227	+	0.543170i
$839$			1165.70i			1.38939i	0.719303	+	0.694696i	$0.244461\pi$
$839$			1165.70i			1.38939i	−0.719303	+	0.694696i	$0.755539\pi$
$840$		0			0
$841$	−554.058			−0.658808
$842$	−755.649	+	227.078i	−0.897446	+	0.269689i
$843$	590.443	+	1022.68i	0.700407	+	1.21314i
$844$	470.640	−	310.941i	0.557630	−	0.368413i
$845$	−885.658	−	511.335i	−1.04812	−	0.605130i
$846$	−1009.54	−	950.482i	−1.19331	−	1.12350i
$847$		0			0
$848$	−105.132	−	868.301i	−0.123976	−	1.02394i
$849$	−665.041	+	1151.88i	−0.783323	+	1.35675i
$850$	−191.732	−	45.2319i	−0.225566	−	0.0532140i
$851$	−4.34013	−	7.51733i	−0.00510004	−	0.00883352i
$852$	216.001	−	432.321i	0.253523	−	0.507419i
$853$			151.949i			0.178134i	0.996026	+	0.0890672i	$0.0283886\pi$
$853$			151.949i			0.178134i	−0.996026	+	0.0890672i	$0.971611\pi$
$854$		0			0
$855$		−	318.218i		−	0.372184i
$856$	1020.23	−	374.923i	1.19186	−	0.437994i
$857$	206.009	+	356.818i	0.240384	+	0.416357i	0.960824	−	0.277160i	$-0.0893934\pi$
$857$	206.009	+	356.818i	0.240384	+	0.416357i	−0.720440	+	0.693517i	$0.756060\pi$
$858$	56.8480	−	240.971i	0.0662564	−	0.280852i
$859$	79.9965	−	138.558i	0.0931274	−	0.161301i	−0.815698	−	0.578478i	$-0.803647\pi$
$859$	79.9965	−	138.558i	0.0931274	−	0.161301i	0.908826	+	0.417176i	$0.136980\pi$
$860$	−884.380	+	53.3446i	−1.02835	+	0.0620286i
$861$		0			0
$862$	529.110	+	498.157i	0.613817	+	0.577908i
$863$	−859.885	−	496.455i	−0.996391	−	0.575266i	−0.0892122	−	0.996013i	$-0.528435\pi$
$863$	−859.885	−	496.455i	−0.996391	−	0.575266i	−0.907178	+	0.420746i	$0.861768\pi$
$864$	1542.68	+	172.234i	1.78551	+	0.199344i
$865$	359.886	+	623.341i	0.416053	+	0.720625i
$866$	−68.9170	−	229.335i	−0.0795808	−	0.264822i
$867$	−1261.33			−1.45482
$868$		0			0
$869$		−	195.479i		−	0.224947i
$870$	−703.883	−	2342.31i	−0.809061	−	2.69232i
$871$	65.0896	−	37.5795i	0.0747298	−	0.0431453i
$872$	350.767	+	60.7283i	0.402255	+	0.0696425i
$873$	114.165	−	197.740i	0.130773	−	0.226506i
$874$	173.169	+	163.038i	0.198133	+	0.186542i
$875$		0			0
$876$	−87.0912	−	1443.85i	−0.0994192	−	1.64823i
$877$	714.554	+	412.548i	0.814771	+	0.470408i	0.848610	−	0.529019i	$-0.177440\pi$
$877$	714.554	+	412.548i	0.814771	+	0.470408i	−0.0338388	+	0.999427i	$0.510773\pi$
$878$	400.199	−	1696.39i	0.455807	−	1.93210i
$879$	676.570	−	390.618i	0.769704	−	0.444389i
$880$	904.663	+	385.803i	1.02803	+	0.438413i
$881$	−1352.83			−1.53556			−0.767780	−	0.640714i	$-0.778639\pi$
$881$	−1352.83			−1.53556			−0.767780	+	0.640714i	$0.778639\pi$
$882$		0			0
$883$	−1013.40			−1.14768			−0.573838	−	0.818969i	$-0.694546\pi$
$883$	−1013.40			−1.14768			−0.573838	+	0.818969i	$0.694546\pi$
$884$	29.7862	−	59.6163i	0.0336948	−	0.0674392i
$885$	−2971.42	+	1715.55i	−3.35754	+	1.93847i
$886$	669.533	+	157.951i	0.755680	+	0.178274i
$887$	−202.442	−	116.880i	−0.228233	−	0.131770i	0.381524	−	0.924359i	$-0.375399\pi$
$887$	−202.442	−	116.880i	−0.228233	−	0.131770i	−0.609756	+	0.792589i	$0.708733\pi$
$888$	5.42340	−	6.50422i	0.00610743	−	0.00732457i
$889$		0			0
$890$	164.186	+	154.581i	0.184478	+	0.173686i
$891$	−435.487	+	754.285i	−0.488762	+	0.846561i
$892$	90.0204	+	136.255i	0.100920	+	0.152752i
$893$	91.1580	−	52.6301i	0.102081	−	0.0589363i
$894$	2196.44	−	660.047i	2.45687	−	0.738307i
$895$			707.322i			0.790304i
$896$		0			0
$897$	540.686			0.602772
$898$	−139.781	−	465.149i	−0.155658	−	0.517983i
$899$	−133.871	−	231.871i	−0.148911	−	0.257921i
$900$	871.876	−	576.028i	0.968751	−	0.640031i
$901$	326.396	+	188.445i	0.362260	+	0.209151i
$902$	−854.423	+	907.514i	−0.947254	+	1.00611i
$903$		0			0
$904$	819.589	+	683.396i	0.906625	+	0.755968i
$905$	191.004	−	330.829i	0.211054	−	0.365557i
$906$	445.379	−	1887.90i	0.491588	−	2.08377i
$907$	101.795	+	176.314i	0.112233	+	0.194393i	0.916670	−	0.399645i	$-0.130866\pi$
$907$	101.795	+	176.314i	0.112233	+	0.194393i	−0.804438	+	0.594037i	$0.797533\pi$
$908$	−29.2914	−	14.6349i	−0.0322592	−	0.0161177i
$909$		−	1244.85i		−	1.36947i
$910$		0			0
$911$			712.022i			0.781583i	0.920479	+	0.390792i	$0.127799\pi$
$911$			712.022i			0.781583i	−0.920479	+	0.390792i	$0.872201\pi$
$912$	−91.0258	+	213.445i	−0.0998089	+	0.234040i
$913$	−25.0869	−	43.4517i	−0.0274774	−	0.0475922i
$914$	82.2561	+	19.4053i	0.0899958	+	0.0212311i
$915$	716.487	−	1240.99i	0.783046	−	1.35628i
$916$	−1326.60	+	80.0185i	−1.44825	+	0.0873564i
$917$		0			0
$918$	−458.512	+	487.002i	−0.499468	+	0.530503i
$919$	681.374	+	393.391i	0.741430	+	0.428065i	0.822589	−	0.568636i	$-0.192529\pi$
$919$	681.374	+	393.391i	0.741430	+	0.428065i	−0.0811591	+	0.996701i	$0.525862\pi$
$920$	−366.396	+	2116.31i	−0.398257	+	2.30033i
$921$	709.836	+	1229.47i	0.770723	+	1.33493i
$922$	−1563.66	+	469.892i	−1.69595	+	0.509644i
$923$	55.8929			0.0605557
$924$		0			0
$925$		−	2.89516i		−	0.00312990i
$926$	220.577	−	66.2849i	0.238204	−	0.0715820i
$927$	−923.154	+	532.983i	−0.995851	+	0.574955i
$928$	−132.617	+	1187.83i	−0.142906	+	1.27999i
$929$	−828.996	+	1435.86i	−0.892353	+	1.54560i	−0.0553061	+	0.998469i	$0.517613\pi$
$929$	−828.996	+	1435.86i	−0.892353	+	1.54560i	−0.837047	+	0.547131i	$0.815720\pi$
$930$	321.768	−	341.761i	0.345987	−	0.367485i
$931$		0			0
$932$	−79.2981	−	1314.65i	−0.0850838	−	1.41057i
$933$	−2416.52	−	1395.18i	−2.59006	−	1.49537i
$934$	1174.60	+	277.104i	1.25761	+	0.296685i
$935$	−367.017	+	211.897i	−0.392532	+	0.226628i
$936$	121.939	+	331.819i	0.130277	+	0.354507i
$937$	−333.736			−0.356175			−0.178088	−	0.984015i	$-0.556991\pi$
$937$	−333.736			−0.356175			−0.178088	+	0.984015i	$0.556991\pi$
$938$		0			0
$939$	2905.55			3.09430
$940$	850.308	+	424.841i	0.904583	+	0.451959i
$941$	−470.533	+	271.662i	−0.500035	+	0.288695i	−0.728728	−	0.684803i	$-0.759888\pi$
$941$	−470.533	+	271.662i	−0.500035	+	0.288695i	0.228693	+	0.973499i	$0.426555\pi$
$942$	−451.409	+	1913.46i	−0.479203	+	2.03127i
$943$	−2357.34	−	1361.01i	−2.49984	−	1.44328i
$944$	1664.56	−	201.542i	1.76331	−	0.213497i
$945$		0			0
$946$	−475.125	+	504.648i	−0.502247	+	0.533454i
$947$	179.864	−	311.534i	0.189930	−	0.328969i	−0.755296	−	0.655383i	$-0.772507\pi$
$947$	179.864	−	311.534i	0.189930	−	0.328969i	0.945227	+	0.326414i	$0.105840\pi$
$948$	229.583	+	347.496i	0.242176	+	0.366557i
$949$	144.878	−	83.6451i	0.152663	−	0.0881403i
$950$	22.8301	+	75.9720i	0.0240317	+	0.0799705i
$951$			2023.94i			2.12823i
$952$		0			0
$953$	−904.225			−0.948820			−0.474410	−	0.880304i	$-0.657339\pi$
$953$	−904.225			−0.948820			−0.474410	+	0.880304i	$0.657339\pi$
$954$	−1914.66	+	575.371i	−2.00699	+	0.603114i
$955$	559.281	+	968.702i	0.585634	+	1.01435i
$956$	303.663	+	459.623i	0.317639	+	0.480778i
$957$	−1657.03	−	956.686i	−1.73148	−	0.999672i
$958$	230.941	+	217.431i	0.241066	+	0.226963i
$959$		0			0
$960$	−2061.30	+	376.663i	−2.14719	+	0.392358i
$961$	−454.807	+	787.749i	−0.473265	+	0.819719i
$962$	0.953263	+	0.224887i	0.000990918	+	0.000233770i
$963$	−1242.26	−	2151.66i	−1.28999	−	2.23433i
$964$	−722.280	−	360.874i	−0.749253	−	0.374351i
$965$			1388.89i			1.43926i
$966$		0			0
$967$		−	920.961i		−	0.952390i	−0.879340	−	0.476195i	$-0.842016\pi$
$967$		−	920.961i		−	0.952390i	0.879340	−	0.476195i	$-0.157984\pi$
$968$	−186.412	+	68.5040i	−0.192574	+	0.0707686i
$969$	−49.9947	−	86.5933i	−0.0515941	−	0.0893636i
$970$	−35.9400	+	152.345i	−0.0370516	+	0.157056i
$971$	663.655	−	1149.48i	0.683476	−	1.18381i	−0.290438	−	0.956894i	$-0.593801\pi$
$971$	663.655	−	1149.48i	0.683476	−	1.18381i	0.973913	−	0.226921i	$-0.0728658\pi$
$972$	−6.58670	−	109.198i	−0.00677644	−	0.112344i
$973$		0			0
$974$	155.791	+	146.677i	0.159950	+	0.150593i
$975$	156.176	+	90.1684i	0.160181	+	0.0924805i
$976$	−559.968	+	420.492i	−0.573738	+	0.430832i
$977$	344.245	+	596.250i	0.352349	+	0.610286i	0.986661	−	0.162791i	$-0.0520497\pi$
$977$	344.245	+	596.250i	0.352349	+	0.610286i	−0.634312	+	0.773077i	$0.718716\pi$
$978$	163.909	+	545.441i	0.167596	+	0.557710i
$979$	176.415			0.180199
$980$		0			0
$981$		−	813.706i		−	0.829466i
$982$	354.902	+	1181.01i	0.361407	+	1.20266i
$983$	−1461.05	+	843.539i	−1.48632	+	0.858127i	−0.999879	−	0.0155866i	$-0.995038\pi$
$983$	−1461.05	+	843.539i	−1.48632	+	0.858127i	−0.486441	+	0.873714i	$0.661705\pi$
$984$	453.037	−	2616.74i	0.460404	−	2.65929i
$985$	759.348	−	1315.23i	0.770912	−	1.33526i
$986$	−374.983	−	353.046i	−0.380307	−	0.358058i
$987$		0			0
$988$	−26.7880	+	1.61582i	−0.0271134	+	0.00163544i
$989$	−1310.87	−	756.829i	−1.32545	−	0.765246i
$990$	516.176	−	2188.00i	0.521390	−	2.21010i
$991$	986.597	−	569.612i	0.995557	−	0.574785i	0.0886266	−	0.996065i	$-0.471752\pi$
$991$	986.597	−	569.612i	0.995557	−	0.574785i	0.906931	+	0.421280i	$0.138419\pi$
$992$	−210.154	+	91.9434i	−0.211849	+	0.0926848i
$993$	−2001.72			−2.01583
$994$		0			0
$995$	1861.85			1.87121
$996$	95.6283	+	47.7790i	0.0960124	+	0.0479709i
$997$	178.475	−	103.043i	0.179012	−	0.103353i	−0.407816	−	0.913064i	$-0.633710\pi$
$997$	178.475	−	103.043i	0.179012	−	0.103353i	0.586828	+	0.809711i	$0.300376\pi$
$998$	−1078.57	−	254.449i	−1.08073	−	0.254959i
$999$	−8.51331	−	4.91516i	−0.00852183	−	0.00492008i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	392.3.k.n.275.6		16
7.2	even	3		392.3.g.m.99.5		8
7.3	odd	6		392.3.k.o.67.1		16
7.4	even	3	inner	392.3.k.n.67.1		16
7.5	odd	6		56.3.g.b.43.5	✓	8
7.6	odd	2		392.3.k.o.275.6		16
8.3	odd	2	inner	392.3.k.n.275.1		16
21.5	even	6		504.3.g.b.379.4		8
28.19	even	6		224.3.g.b.15.7		8
28.23	odd	6		1568.3.g.m.687.2		8
56.3	even	6		392.3.k.o.67.6		16
56.5	odd	6		224.3.g.b.15.8		8
56.11	odd	6	inner	392.3.k.n.67.6		16
56.19	even	6		56.3.g.b.43.6	yes	8
56.27	even	2		392.3.k.o.275.1		16
56.37	even	6		1568.3.g.m.687.1		8
56.51	odd	6		392.3.g.m.99.6		8
84.47	odd	6		2016.3.g.b.1135.8		8
112.5	odd	12		1792.3.d.j.1023.16		16
112.19	even	12		1792.3.d.j.1023.15		16
112.61	odd	12		1792.3.d.j.1023.1		16
112.75	even	12		1792.3.d.j.1023.2		16
168.5	even	6		2016.3.g.b.1135.1		8
168.131	odd	6		504.3.g.b.379.3		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
56.3.g.b.43.5	✓	8	7.5	odd	6
56.3.g.b.43.6	yes	8	56.19	even	6
224.3.g.b.15.7		8	28.19	even	6
224.3.g.b.15.8		8	56.5	odd	6
392.3.g.m.99.5		8	7.2	even	3
392.3.g.m.99.6		8	56.51	odd	6
392.3.k.n.67.1		16	7.4	even	3	inner
392.3.k.n.67.6		16	56.11	odd	6	inner
392.3.k.n.275.1		16	8.3	odd	2	inner
392.3.k.n.275.6		16	1.1	even	1	trivial
392.3.k.o.67.1		16	7.3	odd	6
392.3.k.o.67.6		16	56.3	even	6
392.3.k.o.275.1		16	56.27	even	2
392.3.k.o.275.6		16	7.6	odd	2
504.3.g.b.379.3		8	168.131	odd	6
504.3.g.b.379.4		8	21.5	even	6
1568.3.g.m.687.1		8	56.37	even	6
1568.3.g.m.687.2		8	28.23	odd	6
1792.3.d.j.1023.1		16	112.61	odd	12
1792.3.d.j.1023.2		16	112.75	even	12
1792.3.d.j.1023.15		16	112.19	even	12
1792.3.d.j.1023.16		16	112.5	odd	12
2016.3.g.b.1135.1		8	168.5	even	6
2016.3.g.b.1135.8		8	84.47	odd	6

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:	\( N \)	\(=\)	\( 392 = 2^{3} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	392.k (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.575587 + 1.91538i) q^{2} +(-2.61182 - 4.52380i) q^{3} +(-3.33740 + 2.20494i) q^{4} +(-5.42814 - 3.13394i) q^{5} +(7.16148 - 7.60647i) q^{6} +(-6.14428 - 5.12327i) q^{8} +(-9.14316 + 15.8364i) q^{9} +O(q^{10})\)	\(q+(0.575587 + 1.91538i) q^{2} +(-2.61182 - 4.52380i) q^{3} +(-3.33740 + 2.20494i) q^{4} +(-5.42814 - 3.13394i) q^{5} +(7.16148 - 7.60647i) q^{6} +(-6.14428 - 5.12327i) q^{8} +(-9.14316 + 15.8364i) q^{9} +(2.87833 - 12.2008i) q^{10} +(-4.90344 - 8.49301i) q^{11} +(18.6914 + 9.33881i) q^{12} +2.41653i q^{13} +32.7411i q^{15} +(6.27646 - 14.7175i) q^{16} +(3.44726 + 5.97083i) q^{17} +(-35.5955 - 8.39743i) q^{18} +(1.38818 - 2.40441i) q^{19} +(25.0260 - 1.50954i) q^{20} +(13.4450 - 14.2804i) q^{22} +(37.0947 + 21.4166i) q^{23} +(-7.12889 + 41.1765i) q^{24} +(7.14316 + 12.3723i) q^{25} +(-4.62858 + 1.39092i) q^{26} +48.5083 q^{27} +37.3505i q^{29} +(-62.7118 + 18.8454i) q^{30} +(-6.20797 + 3.58417i) q^{31} +(31.8024 + 3.55060i) q^{32} +(-25.6138 + 44.3643i) q^{33} +(-9.45224 + 10.0396i) q^{34} +(-4.40402 - 73.0126i) q^{36} +(-0.175502 - 0.101326i) q^{37} +(5.40439 + 1.27496i) q^{38} +(10.9319 - 6.31153i) q^{39} +(17.2960 + 47.0656i) q^{40} -63.5494 q^{41} -35.3384 q^{43} +(35.0913 + 17.5327i) q^{44} +(99.2607 - 57.3082i) q^{45} +(-19.6698 + 83.3777i) q^{46} +(32.8335 + 18.9564i) q^{47} +(-82.9721 + 10.0461i) q^{48} +(-19.5862 + 20.8032i) q^{50} +(18.0072 - 31.1894i) q^{51} +(-5.32831 - 8.06492i) q^{52} +(47.3414 - 27.3326i) q^{53} +(27.9208 + 92.9120i) q^{54} +61.4684i q^{55} -14.5027 q^{57} +(-71.5405 + 21.4985i) q^{58} +(52.3975 + 90.7551i) q^{59} +(-72.1922 - 109.270i) q^{60} +(-37.9032 - 21.8834i) q^{61} +(-10.4383 - 9.82765i) q^{62} +(11.5043 + 62.9575i) q^{64} +(7.57325 - 13.1173i) q^{65} +(-99.7177 - 23.5247i) q^{66} +(-15.5510 - 26.9352i) q^{67} +(-24.6702 - 12.3260i) q^{68} -223.745i q^{69} -23.1294i q^{71} +(137.312 - 50.4605i) q^{72} +(-34.6138 - 59.9528i) q^{73} +(0.0930619 - 0.394476i) q^{74} +(37.3132 - 64.6284i) q^{75} +(0.668652 + 11.0853i) q^{76} +(18.3813 + 17.3059i) q^{78} +(17.2624 + 9.96642i) q^{79} +(-80.1934 + 60.2189i) q^{80} +(-44.4063 - 76.9139i) q^{81} +(-36.5782 - 121.722i) q^{82} +5.11617 q^{83} -43.2140i q^{85} +(-20.3403 - 67.6866i) q^{86} +(168.966 - 97.5525i) q^{87} +(-13.3838 + 77.3050i) q^{88} +(-8.99444 + 15.5788i) q^{89} +(166.901 + 157.137i) q^{90} +(-171.022 + 10.3158i) q^{92} +(32.4282 + 18.7224i) q^{93} +(-17.4103 + 73.7999i) q^{94} +(-15.0705 + 8.70097i) q^{95} +(-66.9998 - 153.141i) q^{96} -12.4864 q^{97} +179.332 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - q^{2} - 8 q^{3} - 5 q^{4} + 44 q^{6} + 26 q^{8} - 48 q^{9}+O(q^{10}) \) 16 * q - q^2 - 8 * q^3 - 5 * q^4 + 44 * q^6 + 26 * q^8 - 48 * q^9	\( 16 q - q^{2} - 8 q^{3} - 5 q^{4} + 44 q^{6} + 26 q^{8} - 48 q^{9} + 16 q^{10} + 32 q^{11} + 30 q^{12} + 71 q^{16} - 80 q^{17} + 29 q^{18} + 56 q^{19} + 216 q^{20} + 132 q^{22} + 22 q^{24} + 16 q^{25} + 24 q^{26} + 64 q^{27} - 96 q^{30} + 19 q^{32} + 32 q^{33} - 148 q^{34} - 66 q^{36} - 14 q^{38} + 84 q^{40} - 256 q^{41} - 50 q^{44} + 152 q^{46} - 268 q^{48} + 66 q^{50} + 368 q^{51} + 132 q^{52} - 228 q^{54} + 112 q^{57} - 24 q^{58} + 104 q^{59} - 192 q^{60} - 240 q^{62} - 110 q^{64} + 72 q^{65} - 276 q^{66} - 304 q^{67} - 190 q^{68} + 209 q^{72} - 112 q^{73} - 8 q^{74} + 72 q^{75} - 140 q^{76} - 608 q^{78} + 124 q^{80} - 48 q^{81} + 450 q^{82} - 144 q^{83} - 210 q^{86} + 486 q^{88} - 512 q^{89} + 368 q^{90} - 944 q^{92} + 472 q^{94} + 558 q^{96} - 128 q^{97} + 512 q^{99}+O(q^{100}) \) 16 * q - q^2 - 8 * q^3 - 5 * q^4 + 44 * q^6 + 26 * q^8 - 48 * q^9 + 16 * q^10 + 32 * q^11 + 30 * q^12 + 71 * q^16 - 80 * q^17 + 29 * q^18 + 56 * q^19 + 216 * q^20 + 132 * q^22 + 22 * q^24 + 16 * q^25 + 24 * q^26 + 64 * q^27 - 96 * q^30 + 19 * q^32 + 32 * q^33 - 148 * q^34 - 66 * q^36 - 14 * q^38 + 84 * q^40 - 256 * q^41 - 50 * q^44 + 152 * q^46 - 268 * q^48 + 66 * q^50 + 368 * q^51 + 132 * q^52 - 228 * q^54 + 112 * q^57 - 24 * q^58 + 104 * q^59 - 192 * q^60 - 240 * q^62 - 110 * q^64 + 72 * q^65 - 276 * q^66 - 304 * q^67 - 190 * q^68 + 209 * q^72 - 112 * q^73 - 8 * q^74 + 72 * q^75 - 140 * q^76 - 608 * q^78 + 124 * q^80 - 48 * q^81 + 450 * q^82 - 144 * q^83 - 210 * q^86 + 486 * q^88 - 512 * q^89 + 368 * q^90 - 944 * q^92 + 472 * q^94 + 558 * q^96 - 128 * q^97 + 512 * q^99

Introduction

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