LMFDB - Embedded newform 392.3.k.n.67.6

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			67.6
Root			$1.94657 + 0.459219i$ of defining polynomial
Character	$\chi$	$=$	392.67
Dual form			392.3.k.n.275.6

$q$-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 $\left(\mathbb{Z}/392\mathbb{Z}\right)^\times$.

$n$	$197$	$295$	$297$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{2}{3}\right)$

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	−0.00923321	+	0.999957i	$0.502939\pi$
$3$	−2.61182	+	4.52380i	−0.870605	+	1.50793i	−0.861372	+	0.507975i	$0.830394\pi$
$4$	−3.33740	−	2.20494i	−0.834350	−	0.551236i
$5$	−5.42814	+	3.13394i	−1.08563	+	0.626788i	−0.932409	−	0.361404i	$-0.882297\pi$
$5$	−5.42814	+	3.13394i	−1.08563	+	0.626788i	−0.153219	+	0.988192i	$0.548964\pi$
$6$	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	−0.998105	−	0.0615286i	$-0.980402\pi$
$11$	−4.90344	+	8.49301i	−0.445767	+	0.772092i	0.552338	+	0.833620i	$0.313736\pi$
$12$	18.6914	−	9.33881i	1.55762	−	0.778234i
$13$		−	2.41653i		−	0.185887i	−0.995671	−	0.0929434i	$-0.970372\pi$
$13$		−	2.41653i		−	0.185887i	0.995671	−	0.0929434i	$-0.0296276\pi$
$14$		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	−0.746643	−	0.665225i	$-0.768336\pi$
$17$	3.44726	−	5.97083i	0.202780	−	0.351225i	0.949423	+	0.313999i	$0.101669\pi$
$18$	−35.5955	+	8.39743i	−1.97753	+	0.466524i
$19$	1.38818	+	2.40441i	0.0730624	+	0.126548i	0.900242	−	0.435390i	$-0.143389\pi$
$19$	1.38818	+	2.40441i	0.0730624	+	0.126548i	−0.827180	+	0.561938i	$0.810056\pi$
$20$	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	0.624097	−	0.781347i	$-0.285467\pi$
$23$	37.0947	−	21.4166i	1.61281	−	0.931157i	0.988715	−	0.149811i	$-0.0478664\pi$
$24$	−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	$-0.777285\pi$
$29$		−	37.3505i		−	1.28795i	0.765048	−	0.643974i	$-0.222715\pi$
$30$	−62.7118	−	18.8454i	−2.09039	−	0.628179i
$31$	−6.20797	−	3.58417i	−0.200257	−	0.115619i	0.396518	−	0.918027i	$-0.370218\pi$
$31$	−6.20797	−	3.58417i	−0.200257	−	0.115619i	−0.596775	+	0.802408i	$0.703552\pi$
$32$	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	−0.502370	−	0.864653i	$-0.667538\pi$
$37$	−0.175502	+	0.101326i	−0.00474330	+	0.00273855i	0.497626	+	0.867391i	$0.334205\pi$
$38$	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	−0.108235	−	0.994125i	$-0.534520\pi$
$47$	32.8335	−	18.9564i	0.698586	−	0.403329i	0.806820	+	0.590797i	$0.201186\pi$
$48$	−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	0.874999	−	0.484125i	$-0.160862\pi$
$53$	47.3414	+	27.3326i	0.893234	+	0.515709i	0.0182349	+	0.999834i	$0.494195\pi$
$54$	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	0.0459650	−	0.998943i	$-0.485364\pi$
$59$	52.3975	−	90.7551i	0.888093	−	1.53822i	0.842128	−	0.539278i	$-0.181303\pi$
$60$	−72.1922	+	109.270i	−1.20320	+	1.82117i
$61$	−37.9032	+	21.8834i	−0.621364	+	0.358745i	−0.777400	−	0.629007i	$-0.783462\pi$
$61$	−37.9032	+	21.8834i	−0.621364	+	0.358745i	0.156036	+	0.987751i	$0.450128\pi$
$62$	−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	−0.958427	−	0.285336i	$-0.907895\pi$
$67$	−15.5510	+	26.9352i	−0.232105	+	0.402018i	0.726322	+	0.687354i	$0.241228\pi$
$68$	−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	$0.0520794\pi$
$71$			23.1294i			0.325766i	−0.986645	+	0.162883i	$0.947921\pi$
$72$	137.312	+	50.4605i	1.90711	+	0.700840i
$73$	−34.6138	+	59.9528i	−0.474161	+	0.821271i	−0.999562	−	0.0295834i	$-0.990582\pi$
$73$	−34.6138	+	59.9528i	−0.474161	+	0.821271i	0.525401	+	0.850855i	$0.323915\pi$
$74$	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	−0.386750	−	0.922185i	$-0.626402\pi$
$79$	17.2624	−	9.96642i	0.218511	−	0.126157i	0.605261	+	0.796027i	$0.293069\pi$
$80$	−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	0.811061	−	0.584962i	$-0.198890\pi$
$89$	−8.99444	−	15.5788i	−0.101061	−	0.175043i	−0.912122	+	0.409919i	$0.865557\pi$
$90$	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	0.178895	−	0.983868i	$-0.442748\pi$
$101$	−58.9549	−	34.0376i	−0.583712	−	0.337006i	−0.762607	+	0.646862i	$0.776081\pi$
$102$	70.1045	−	16.5385i	0.687299	−	0.162142i
$103$	50.4833	−	29.1465i	0.490129	−	0.282976i	−0.234499	−	0.972116i	$-0.575345\pi$
$103$	50.4833	−	29.1465i	0.490129	−	0.282976i	0.724628	+	0.689140i	$0.242012\pi$
$104$	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	−0.986537	−	0.163538i	$-0.947709\pi$
$107$	−67.9340	−	117.665i	−0.634897	−	1.09967i	0.351640	−	0.936135i	$-0.385624\pi$
$108$	−161.891	−	106.958i	−1.49900	−	0.990352i
$109$	−38.5365	−	22.2490i	−0.353546	−	0.204120i	0.312700	−	0.949852i	$-0.398766\pi$
$109$	−38.5365	−	22.2490i	−0.353546	−	0.204120i	−0.666246	+	0.745732i	$0.732100\pi$
$110$	−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	$-0.827548\pi$
$127$		−	130.977i		−	1.03131i	0.856795	−	0.515657i	$-0.172452\pi$
$128$	−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	0.746117	−	0.665815i	$-0.231916\pi$
$131$	−26.6655	−	46.1861i	−0.203554	−	0.352565i	−0.949671	+	0.313249i	$0.898583\pi$
$132$	−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	−0.741269	−	0.671208i	$-0.765776\pi$
$137$	28.8589	−	49.9852i	0.210649	−	0.364855i	0.951918	+	0.306353i	$0.0991089\pi$
$138$	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	0.299853	−	0.953985i	$-0.403062\pi$
$149$	190.117	−	109.764i	1.27596	−	0.736673i	0.976102	+	0.217312i	$0.0697290\pi$
$150$	145.265	−	34.2699i	0.968435	−	0.228466i
$151$	160.793	+	92.8340i	1.06486	+	0.614795i	0.926771	−	0.375626i	$-0.122572\pi$
$151$	160.793	+	92.8340i	1.06486	+	0.614795i	0.138084	+	0.990421i	$0.455906\pi$
$152$	−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	−0.118753	−	0.992924i	$-0.537890\pi$
$157$	−162.970	−	94.0909i	−1.03803	−	0.599305i	−0.919274	+	0.393619i	$0.871223\pi$
$158$	−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	0.770218	−	0.637781i	$-0.220147\pi$
$163$	−27.2577	−	47.2117i	−0.167225	−	0.289642i	−0.937443	+	0.348138i	$0.886814\pi$
$164$	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	$-0.706045\pi$
$167$		−	266.435i		−	1.59542i	0.603042	−	0.797709i	$-0.293955\pi$
$168$		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	−0.759086	−	0.650990i	$-0.774354\pi$
$173$	−99.4501	+	57.4175i	−0.574856	+	0.331893i	0.184231	+	0.982883i	$0.441021\pi$
$174$	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	−0.979484	−	0.201521i	$-0.935412\pi$
$179$	−56.4243	+	97.7298i	−0.315220	+	0.545977i	0.664264	+	0.747498i	$0.268745\pi$
$180$	−204.911	−	410.125i	−1.13840	−	2.27847i
$181$		−	60.9470i		−	0.336724i	−0.985725	−	0.168362i	$-0.946152\pi$
$181$		−	60.9470i		−	0.336724i	0.985725	−	0.168362i	$-0.0538477\pi$
$182$		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	−0.846665	−	0.532126i	$-0.821393\pi$
$191$	−154.550	+	89.2296i	−0.809164	+	0.467171i	0.0375017	+	0.999297i	$0.488060\pi$
$192$	254.760	+	216.477i	1.32687	+	1.12748i
$193$	−110.794	+	191.901i	−0.574062	+	0.994304i	0.422081	+	0.906558i	$0.361300\pi$
$193$	−110.794	+	191.901i	−0.574062	+	0.994304i	−0.996143	+	0.0877458i	$0.972034\pi$
$194$	−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	$-0.789168\pi$
$197$		−	242.298i		−	1.22994i	0.788550	−	0.614970i	$-0.210832\pi$
$198$	103.221	−	343.489i	0.521319	−	1.73479i
$199$	−257.250	−	148.523i	−1.29271	−	0.746349i	−0.313580	−	0.949562i	$-0.601528\pi$
$199$	−257.250	−	148.523i	−1.29271	−	0.746349i	−0.979135	+	0.203213i	$0.934862\pi$
$200$	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	$0.0291788\pi$
$223$			40.8267i			0.183079i	−0.995801	+	0.0915396i	$0.970821\pi$
$224$		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	−0.856869	−	0.515534i	$-0.827594\pi$
$227$	4.09299	−	7.08926i	0.0180308	−	0.0312302i	0.874900	+	0.484304i	$0.160927\pi$
$228$	48.4014	+	31.9777i	0.212287	+	0.140253i
$229$	287.738	−	166.126i	1.25650	−	0.725440i	0.284107	−	0.958792i	$-0.408303\pi$
$229$	287.738	−	166.126i	1.25650	−	0.725440i	0.972392	+	0.233352i	$0.0749695\pi$
$230$	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	−0.966123	−	0.258083i	$-0.916909\pi$
$233$	−164.630	−	285.148i	−0.706568	−	1.22381i	0.259555	−	0.965728i	$-0.416424\pi$
$234$	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	$0.0930286\pi$
$239$			137.719i			0.576230i	−0.957596	+	0.288115i	$0.906971\pi$
$240$	481.868	−	205.498i	2.00778	−	0.856242i
$241$	100.927	−	174.810i	0.418783	−	0.725354i	−0.577034	−	0.816720i	$-0.695790\pi$
$241$	100.927	−	174.810i	0.418783	−	0.725354i	0.995817	+	0.0913661i	$0.0291234\pi$
$242$	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	0.527953	−	0.849274i	$-0.322960\pi$
$257$	−121.180	−	209.889i	−0.471516	−	0.816690i	−0.999469	+	0.0325840i	$0.989626\pi$
$258$	−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	0.554691	−	0.832057i	$-0.312837\pi$
$263$	29.3124	+	16.9235i	0.111454	+	0.0643479i	−0.443237	+	0.896405i	$0.646170\pi$
$264$	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	0.209160	−	0.977881i	$-0.432927\pi$
$269$	−143.412	−	82.7990i	−0.533130	−	0.307803i	−0.742290	+	0.670078i	$0.766260\pi$
$270$	139.623	+	591.842i	0.517122	+	2.19201i
$271$	128.439	−	74.1542i	0.473944	−	0.273632i	−0.243945	−	0.969789i	$-0.578442\pi$
$271$	128.439	−	74.1542i	0.473944	−	0.273632i	0.717889	+	0.696157i	$0.245108\pi$
$272$	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	−0.495574	−	0.868566i	$-0.665042\pi$
$277$	−414.270	−	239.179i	−1.49556	−	0.863463i	−0.999987	+	0.00510300i	$0.998376\pi$
$278$	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	−0.998377	−	0.0569453i	$-0.981864\pi$
$283$	−127.314	+	220.514i	−0.449873	+	0.779202i	0.548505	+	0.836147i	$0.315197\pi$
$284$	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	$-0.917853\pi$
$293$		−	149.558i		−	0.510437i	0.966883	−	0.255218i	$-0.0821474\pi$
$294$		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	0.999898	−	0.0142534i	$-0.00453714\pi$
$311$	462.614	+	267.090i	1.48750	+	0.858811i	0.487605	+	0.873064i	$0.337870\pi$
$312$	−99.5041	+	17.2272i	−0.318924	+	0.0552153i
$313$	−278.116	−	481.711i	−0.888550	−	1.53901i	−0.841590	−	0.540117i	$-0.818380\pi$
$313$	−278.116	−	481.711i	−0.888550	−	1.53901i	−0.0469600	−	0.998897i	$-0.514953\pi$
$314$	−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	−0.925021	−	0.379916i	$-0.875953\pi$
$317$	−335.549	+	193.730i	−1.05852	+	0.611134i	−0.133494	+	0.991050i	$0.542620\pi$
$318$	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	0.995610	+	0.0935935i	$0.0298354\pi$
$331$	191.603	+	331.865i	0.578860	+	1.00261i	−0.416751	+	0.909021i	$0.636831\pi$
$332$	−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	−0.900797	−	0.434240i	$-0.857017\pi$
$347$	−25.7945	+	44.6774i	−0.0743357	+	0.128753i	0.826462	+	0.562993i	$0.190350\pi$
$348$	−348.809	−	698.132i	−1.00232	−	2.00613i
$349$			586.383i			1.68018i	0.542447	+	0.840090i	$0.317498\pi$
$349$			586.383i			1.68018i	−0.542447	+	0.840090i	$0.682502\pi$
$350$		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	−0.566532	−	0.824040i	$-0.691715\pi$
$353$	151.922	−	263.136i	0.430373	−	0.745428i	0.996905	+	0.0786114i	$0.0250486\pi$
$354$	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	−0.353345	−	0.935493i	$-0.614956\pi$
$359$	100.571	−	58.0649i	0.280143	−	0.161741i	0.633488	+	0.773752i	$0.281623\pi$
$360$	−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	−0.181520	−	0.983387i	$-0.558102\pi$
$367$	−412.478	−	238.144i	−1.12392	−	0.648894i	−0.942398	+	0.334493i	$0.891435\pi$
$368$	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	−0.441692	−	0.897167i	$-0.645622\pi$
$373$	42.6827	−	24.6428i	0.114431	−	0.0660666i	0.556123	+	0.831100i	$0.312288\pi$
$374$	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	0.209034	−	0.977908i	$-0.432968\pi$
$383$	444.450	−	256.604i	1.16044	−	0.669983i	0.951411	+	0.307925i	$0.0996347\pi$
$384$	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	−0.994954	−	0.100336i	$-0.968008\pi$
$389$	−614.357	−	354.699i	−1.57932	−	0.911823i	−0.584370	−	0.811487i	$-0.698658\pi$
$390$	−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	−0.797946	−	0.602729i	$-0.794080\pi$
$397$	−267.952	+	154.702i	−0.674941	+	0.389677i	0.123005	+	0.992406i	$0.460747\pi$
$398$	−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	0.981018	+	0.193915i	$0.0621186\pi$
$401$	264.036	+	457.324i	0.658445	+	1.14046i	−0.322574	+	0.946544i	$0.604548\pi$
$402$	−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	0.199035	+	0.979992i	$0.436219\pi$
$409$	−306.415	+	530.726i	−0.749181	+	1.29762i	−0.948216	+	0.317627i	$0.897114\pi$
$410$	−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	$-0.844778\pi$
$421$		−	394.516i		−	0.937092i	0.883439	−	0.468546i	$-0.155222\pi$
$422$	−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	0.818463	−	0.574560i	$-0.194827\pi$
$431$	314.678	+	181.679i	0.730111	+	0.421530i	−0.0883519	+	0.996089i	$0.528160\pi$
$432$	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	−0.798755	+	0.601657i	$0.794508\pi$
$439$	−754.721	+	435.738i	−1.71918	+	0.992570i	−0.920427	+	0.390914i	$0.872159\pi$
$440$	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	0.992209	−	0.124584i	$-0.0397595\pi$
$443$	171.978	+	297.875i	0.388212	+	0.672403i	−0.603997	+	0.796987i	$0.706426\pi$
$444$	−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	0.888216	−	0.459426i	$-0.151945\pi$
$457$	21.1285	+	36.5957i	0.0462331	+	0.0800781i	−0.841983	+	0.539504i	$0.818612\pi$
$458$	−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	$-0.653861\pi$
$461$		−	816.370i		−	1.77087i	0.464766	−	0.885434i	$-0.346139\pi$
$462$		0			0
$463$			115.161i			0.248727i	0.992237	+	0.124363i	$0.0396889\pi$
$463$			115.161i			0.248727i	−0.992237	+	0.124363i	$0.960311\pi$
$464$	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	0.984055	+	0.177866i	$0.0569194\pi$
$467$	301.712	+	522.580i	0.646064	+	1.11902i	−0.337991	+	0.941149i	$0.609747\pi$
$468$	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	0.636470	−	0.771302i	$-0.280394\pi$
$479$	137.348	+	79.2977i	0.286738	+	0.165548i	−0.349732	+	0.936850i	$0.613727\pi$
$480$	−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	0.592102	−	0.805863i	$-0.298298\pi$
$487$	92.6539	+	53.4937i	0.190254	+	0.109843i	−0.401847	+	0.915707i	$0.631632\pi$
$488$	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	−0.997888	−	0.0649593i	$-0.979308\pi$
$499$	−277.045	−	479.856i	−0.555200	−	0.961635i	0.442688	−	0.896676i	$-0.354025\pi$
$500$	−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	$-0.952950\pi$
$503$		−	148.158i		−	0.294548i	0.989096	−	0.147274i	$-0.0470499\pi$
$504$		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	−0.336279	−	0.941762i	$-0.609169\pi$
$509$	158.386	−	91.4444i	0.311172	−	0.179655i	0.647451	+	0.762107i	$0.275835\pi$
$510$	−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	−0.815024	−	0.579427i	$-0.803277\pi$
$521$	49.1230	−	85.0836i	0.0942861	−	0.163308i	0.909310	+	0.416118i	$0.136610\pi$
$522$	313.648	+	1329.51i	0.600858	+	2.54695i
$523$	−287.382	−	497.760i	−0.549488	−	0.951740i	−0.998310	−	0.0581192i	$-0.981490\pi$
$523$	−287.382	−	497.760i	−0.549488	−	0.951740i	0.448822	−	0.893621i	$-0.351844\pi$
$524$	−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	−0.766416	−	0.642344i	$-0.777962\pi$
$541$	−320.996	+	185.327i	−0.593338	+	0.342564i	0.173078	+	0.984908i	$0.444629\pi$
$542$	−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	0.613149	−	0.789968i	$-0.289903\pi$
$557$	131.224	+	75.7624i	0.235591	+	0.136019i	−0.377558	+	0.925986i	$0.623236\pi$
$558$	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	−0.971990	−	0.235024i	$-0.924483\pi$
$563$	−159.024	+	275.438i	−0.282458	+	0.489232i	0.689531	+	0.724256i	$0.257817\pi$
$564$	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	0.665693	−	0.746226i	$-0.268136\pi$
$569$	−178.327	−	308.871i	−0.313404	−	0.542831i	−0.979097	+	0.203394i	$0.934803\pi$
$570$	−41.7436	−	176.945i	−0.0732345	−	0.310431i
$571$	−415.507	+	719.679i	−0.727683	+	1.26038i	0.230177	+	0.973149i	$0.426069\pi$
$571$	−415.507	+	719.679i	−0.727683	+	1.26038i	−0.957860	+	0.287235i	$0.907264\pi$
$572$	−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	−0.309786	−	0.950806i	$-0.600257\pi$
$577$	385.742	−	668.124i	0.668530	−	1.15793i	0.978315	−	0.207121i	$-0.0664094\pi$
$578$	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	0.965834	+	0.259162i	$0.0834462\pi$
$593$	419.463	+	726.531i	0.707357	+	1.22518i	−0.258477	+	0.966018i	$0.583220\pi$
$594$	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	−0.111907	−	0.993719i	$-0.535696\pi$
$599$	−616.039	−	355.670i	−1.02845	−	0.593774i	−0.916539	+	0.399945i	$0.869029\pi$
$600$	−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	−0.542449	−	0.840089i	$-0.682503\pi$
$607$	−52.2836	+	30.1860i	−0.0861345	+	0.0497298i	0.456314	+	0.889819i	$0.349169\pi$
$608$	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	0.118389	−	0.992967i	$-0.462227\pi$
$613$	−418.281	−	241.495i	−0.682351	−	0.393955i	−0.800740	+	0.599012i	$0.795560\pi$
$614$	−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	−0.901168	−	0.433471i	$-0.857289\pi$
$619$	−46.5409	+	80.6112i	−0.0751872	+	0.130228i	0.825980	+	0.563699i	$0.190622\pi$
$620$	−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	$0.160749\pi$
$631$			610.573i			0.967628i	−0.875171	+	0.483814i	$0.839251\pi$
$632$	−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	−0.998978	−	0.0452077i	$-0.985605\pi$
$641$	−295.077	+	511.088i	−0.460338	+	0.797328i	0.538640	+	0.842536i	$0.318938\pi$
$642$	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	0.732254	−	0.681031i	$-0.238468\pi$
$647$	329.059	+	189.982i	0.508591	+	0.293635i	−0.223663	+	0.974667i	$0.571802\pi$
$648$	−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	−0.973768	−	0.227545i	$-0.926930\pi$
$653$	−825.126	+	476.386i	−1.26359	+	0.729535i	−0.289824	+	0.957080i	$0.593597\pi$
$654$	−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	0.546222	−	0.837640i	$-0.316065\pi$
$661$	62.0782	+	35.8409i	0.0939156	+	0.0542222i	−0.452307	+	0.891862i	$0.649399\pi$
$662$	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	−0.902822	−	0.430015i	$-0.858508\pi$
$677$	−664.698	+	383.763i	−0.981828	+	0.566859i	−0.0790065	+	0.996874i	$0.525175\pi$
$678$	−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	−0.632468	−	0.774587i	$-0.717958\pi$
$683$	242.177	−	419.462i	0.354578	−	0.614147i	0.987046	+	0.160440i	$0.0512912\pi$
$684$	−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	0.579572	−	0.814921i	$-0.303220\pi$
$691$	−287.425	−	497.835i	−0.415956	−	0.720457i	−0.995528	+	0.0944642i	$0.969886\pi$
$692$	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	$-0.967445\pi$
$701$		−	143.138i		−	0.204191i	0.994775	−	0.102096i	$-0.0325548\pi$
$702$	−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	−0.335901	−	0.941897i	$-0.609041\pi$
$709$	221.106	−	127.656i	0.311856	−	0.180050i	0.647757	+	0.761847i	$0.275707\pi$
$710$	−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	−0.228349	−	0.973579i	$-0.573333\pi$
$719$	359.947	−	207.815i	0.500621	−	0.289034i	0.728970	+	0.684546i	$0.239999\pi$
$720$	−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	$0.211574\pi$
$727$			896.838i			1.23361i	−0.787114	+	0.616807i	$0.788426\pi$
$728$		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	−0.769609	−	0.638515i	$-0.779549\pi$
$733$	−440.858	+	254.530i	−0.601444	+	0.347244i	0.168166	+	0.985759i	$0.446216\pi$
$734$	−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	0.498356	+	0.866973i	$0.333937\pi$
$739$	−370.714	+	642.095i	−0.501642	+	0.868870i	−0.999998	+	0.00189750i	$0.999396\pi$
$740$	−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	$-0.639793\pi$
$743$		−	1344.98i		−	1.81021i	0.425191	−	0.905104i	$-0.360207\pi$
$744$	−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	−0.515882	−	0.856659i	$-0.672536\pi$
$751$	−23.9829	+	13.8465i	−0.0319346	+	0.0184375i	0.483948	+	0.875097i	$0.339202\pi$
$752$	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	$-0.653341\pi$
$757$		−	1341.69i		−	1.77238i	0.463318	−	0.886192i	$-0.346659\pi$
$758$	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	0.826883	−	0.562374i	$-0.190112\pi$
$761$	−56.0005	−	96.9958i	−0.0735881	−	0.127458i	−0.900471	+	0.434915i	$0.856778\pi$
$762$	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	0.999847	−	0.0175096i	$-0.00557375\pi$
$773$	1147.60	+	662.568i	1.48461	+	0.857138i	0.484760	+	0.874647i	$0.338907\pi$
$774$	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	−0.951166	−	0.308679i	$-0.900113\pi$
$787$	−163.900	+	283.884i	−0.208260	+	0.360716i	0.742907	+	0.669395i	$0.233447\pi$
$788$	−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	$0.0794308\pi$
$797$			393.650i			0.493915i	−0.969026	+	0.246958i	$0.920569\pi$
$798$		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	−0.965573	−	0.260134i	$-0.916233\pi$
$809$	−208.321	+	360.822i	−0.257504	+	0.446010i	0.708069	+	0.706144i	$0.249567\pi$
$810$	−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	−0.762944	−	0.646465i	$-0.776247\pi$
$821$	−479.925	+	277.085i	−0.584561	+	0.337496i	0.178383	+	0.983961i	$0.442913\pi$
$822$	586.884	−	138.453i	0.713970	−	0.168435i
$823$	105.180	+	60.7260i	0.127801	+	0.0737861i	0.562538	−	0.826772i	$-0.309825\pi$
$823$	105.180	+	60.7260i	0.127801	+	0.0737861i	−0.434736	+	0.900558i	$0.643158\pi$
$824$	−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	0.660077	−	0.751198i	$-0.270524\pi$
$829$	281.494	+	162.521i	0.339559	+	0.196044i	−0.320518	+	0.947242i	$0.603857\pi$
$830$	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	$-0.755539\pi$
$839$		−	1165.70i		−	1.38939i	0.719303	−	0.694696i	$-0.244461\pi$
$840$		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	$-0.971611\pi$
$853$		−	151.949i		−	0.178134i	0.996026	−	0.0890672i	$-0.0283886\pi$
$854$		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	−0.720440	−	0.693517i	$-0.756060\pi$
$857$	206.009	−	356.818i	0.240384	−	0.416357i	0.960824	+	0.277160i	$0.0893934\pi$
$858$	56.8480	+	240.971i	0.0662564	+	0.280852i
$859$	79.9965	+	138.558i	0.0931274	+	0.161301i	0.908826	−	0.417176i	$-0.136980\pi$
$859$	79.9965	+	138.558i	0.0931274	+	0.161301i	−0.815698	+	0.578478i	$0.803647\pi$
$860$	−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	−0.907178	−	0.420746i	$-0.861768\pi$
$863$	−859.885	+	496.455i	−0.996391	+	0.575266i	−0.0892122	+	0.996013i	$0.528435\pi$
$864$	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	−0.0338388	−	0.999427i	$-0.510773\pi$
$877$	714.554	−	412.548i	0.814771	−	0.470408i	0.848610	+	0.529019i	$0.177440\pi$
$878$	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	−0.609756	−	0.792589i	$-0.708733\pi$
$887$	−202.442	+	116.880i	−0.228233	+	0.131770i	0.381524	+	0.924359i	$0.375399\pi$
$888$	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	−0.804438	−	0.594037i	$-0.797533\pi$
$907$	101.795	−	176.314i	0.112233	−	0.194393i	0.916670	+	0.399645i	$0.130866\pi$
$908$	−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	$-0.872201\pi$
$911$		−	712.022i		−	0.781583i	0.920479	−	0.390792i	$-0.127799\pi$
$912$	−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	−0.0811591	−	0.996701i	$-0.525862\pi$
$919$	681.374	−	393.391i	0.741430	−	0.428065i	0.822589	+	0.568636i	$0.192529\pi$
$920$	−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	−0.837047	−	0.547131i	$-0.815720\pi$
$929$	−828.996	−	1435.86i	−0.892353	−	1.54560i	−0.0553061	−	0.998469i	$-0.517613\pi$
$930$	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	0.228693	−	0.973499i	$-0.426555\pi$
$941$	−470.533	−	271.662i	−0.500035	−	0.288695i	−0.728728	+	0.684803i	$0.759888\pi$
$942$	−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	0.945227	−	0.326414i	$-0.105840\pi$
$947$	179.864	+	311.534i	0.189930	+	0.328969i	−0.755296	+	0.655383i	$0.772507\pi$
$948$	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	$0.157984\pi$
$967$			920.961i			0.952390i	−0.879340	+	0.476195i	$0.842016\pi$
$968$	−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	0.973913	+	0.226921i	$0.0728658\pi$
$971$	663.655	+	1149.48i	0.683476	+	1.18381i	−0.290438	+	0.956894i	$0.593801\pi$
$972$	−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	−0.634312	−	0.773077i	$-0.718716\pi$
$977$	344.245	−	596.250i	0.352349	−	0.610286i	0.986661	+	0.162791i	$0.0520497\pi$
$978$	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	−0.486441	−	0.873714i	$-0.661705\pi$
$983$	−1461.05	−	843.539i	−1.48632	−	0.858127i	−0.999879	+	0.0155866i	$0.995038\pi$
$984$	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	0.906931	−	0.421280i	$-0.138419\pi$
$991$	986.597	+	569.612i	0.995557	+	0.574785i	0.0886266	+	0.996065i	$0.471752\pi$
$992$	−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	0.586828	−	0.809711i	$-0.300376\pi$
$997$	178.475	+	103.043i	0.179012	+	0.103353i	−0.407816	+	0.913064i	$0.633710\pi$
$998$	−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.67.6		16
7.2	even	3	inner	392.3.k.n.275.1		16
7.3	odd	6		56.3.g.b.43.6	yes	8
7.4	even	3		392.3.g.m.99.6		8
7.5	odd	6		392.3.k.o.275.1		16
7.6	odd	2		392.3.k.o.67.6		16
8.3	odd	2	inner	392.3.k.n.67.1		16
21.17	even	6		504.3.g.b.379.3		8
28.3	even	6		224.3.g.b.15.8		8
28.11	odd	6		1568.3.g.m.687.1		8
56.3	even	6		56.3.g.b.43.5	✓	8
56.11	odd	6		392.3.g.m.99.5		8
56.19	even	6		392.3.k.o.275.6		16
56.27	even	2		392.3.k.o.67.1		16
56.45	odd	6		224.3.g.b.15.7		8
56.51	odd	6	inner	392.3.k.n.275.6		16
56.53	even	6		1568.3.g.m.687.2		8
84.59	odd	6		2016.3.g.b.1135.1		8
112.3	even	12		1792.3.d.j.1023.16		16
112.45	odd	12		1792.3.d.j.1023.2		16
112.59	even	12		1792.3.d.j.1023.1		16
112.101	odd	12		1792.3.d.j.1023.15		16
168.59	odd	6		504.3.g.b.379.4		8
168.101	even	6		2016.3.g.b.1135.8		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
56.3.g.b.43.5	✓	8	56.3	even	6
56.3.g.b.43.6	yes	8	7.3	odd	6
224.3.g.b.15.7		8	56.45	odd	6
224.3.g.b.15.8		8	28.3	even	6
392.3.g.m.99.5		8	56.11	odd	6
392.3.g.m.99.6		8	7.4	even	3
392.3.k.n.67.1		16	8.3	odd	2	inner
392.3.k.n.67.6		16	1.1	even	1	trivial
392.3.k.n.275.1		16	7.2	even	3	inner
392.3.k.n.275.6		16	56.51	odd	6	inner
392.3.k.o.67.1		16	56.27	even	2
392.3.k.o.67.6		16	7.6	odd	2
392.3.k.o.275.1		16	7.5	odd	6
392.3.k.o.275.6		16	56.19	even	6
504.3.g.b.379.3		8	21.17	even	6
504.3.g.b.379.4		8	168.59	odd	6
1568.3.g.m.687.1		8	28.11	odd	6
1568.3.g.m.687.2		8	56.53	even	6
1792.3.d.j.1023.1		16	112.59	even	12
1792.3.d.j.1023.2		16	112.45	odd	12
1792.3.d.j.1023.15		16	112.101	odd	12
1792.3.d.j.1023.16		16	112.3	even	12
2016.3.g.b.1135.1		8	84.59	odd	6
2016.3.g.b.1135.8		8	168.101	even	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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