LMFDB - Embedded newform 392.3.k.o.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			$-0.575587 - 1.91538i$ of defining polynomial
Character	$\chi$	$=$	392.275
Dual form			392.3.k.o.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	$0.169606\pi$
$3$	2.61182	+	4.52380i	0.870605	+	1.50793i	0.00923321	+	0.999957i	$0.497061\pi$
$4$	−3.33740	+	2.20494i	−0.834350	+	0.551236i
$5$	5.42814	+	3.13394i	1.08563	+	0.626788i	0.932409	−	0.361404i	$-0.117703\pi$
$5$	5.42814	+	3.13394i	1.08563	+	0.626788i	0.153219	+	0.988192i	$0.451036\pi$
$6$	−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	$-0.970372\pi$
$13$		−	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	$-0.231664\pi$
$17$	−3.44726	−	5.97083i	−0.202780	−	0.351225i	−0.949423	+	0.313999i	$0.898331\pi$
$18$	−35.5955	−	8.39743i	−1.97753	−	0.466524i
$19$	−1.38818	+	2.40441i	−0.0730624	+	0.126548i	−0.900242	−	0.435390i	$-0.856611\pi$
$19$	−1.38818	+	2.40441i	−0.0730624	+	0.126548i	0.827180	+	0.561938i	$0.189944\pi$
$20$	−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	−0.396518	−	0.918027i	$-0.629782\pi$
$31$	6.20797	−	3.58417i	0.200257	−	0.115619i	0.596775	+	0.802408i	$0.296448\pi$
$32$	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	$-0.217753\pi$
$41$	63.5494			1.54999			0.774993	+	0.631970i	$0.217753\pi$
$42$		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	$-0.465480\pi$
$47$	−32.8335	−	18.9564i	−0.698586	−	0.403329i	−0.806820	+	0.590797i	$0.798814\pi$
$48$	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	$-0.818697\pi$
$59$	−52.3975	−	90.7551i	−0.888093	−	1.53822i	−0.0459650	−	0.998943i	$-0.514636\pi$
$60$	−72.1922	−	109.270i	−1.20320	−	1.82117i
$61$	37.9032	+	21.8834i	0.621364	+	0.358745i	0.777400	−	0.629007i	$-0.216538\pi$
$61$	37.9032	+	21.8834i	0.621364	+	0.358745i	−0.156036	+	0.987751i	$0.549872\pi$
$62$	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	0.999562	−	0.0295834i	$-0.00941808\pi$
$73$	34.6138	+	59.9528i	0.474161	+	0.821271i	−0.525401	+	0.850855i	$0.676085\pi$
$74$	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	$-0.509812\pi$
$83$	−5.11617			−0.0616406			−0.0308203	+	0.999525i	$0.509812\pi$
$84$		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	$-0.801110\pi$
$89$	8.99444	−	15.5788i	0.101061	−	0.175043i	0.912122	+	0.409919i	$0.134443\pi$
$90$	−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	$-0.479498\pi$
$97$	12.4864			0.128726			0.0643629	+	0.997927i	$0.479498\pi$
$98$		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	$-0.557252\pi$
$101$	58.9549	−	34.0376i	0.583712	−	0.337006i	0.762607	+	0.646862i	$0.223919\pi$
$102$	70.1045	+	16.5385i	0.687299	+	0.162142i
$103$	−50.4833	−	29.1465i	−0.490129	−	0.282976i	0.234499	−	0.972116i	$-0.424655\pi$
$103$	−50.4833	−	29.1465i	−0.490129	−	0.282976i	−0.724628	+	0.689140i	$0.757988\pi$
$104$	−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	−0.746117	−	0.665815i	$-0.768084\pi$
$131$	26.6655	−	46.1861i	0.203554	−	0.352565i	0.949671	+	0.313249i	$0.101417\pi$
$132$	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	$-0.712958\pi$
$139$	−172.422			−1.24045			−0.620224	+	0.784425i	$0.712958\pi$
$140$		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	0.118753	−	0.992924i	$-0.462110\pi$
$157$	162.970	−	94.0909i	1.03803	−	0.599305i	0.919274	+	0.393619i	$0.128777\pi$
$158$	−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	$-0.706045\pi$
$167$		−	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	$-0.225646\pi$
$173$	99.4501	+	57.4175i	0.574856	+	0.331893i	−0.184231	+	0.982883i	$0.558979\pi$
$174$	−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	$-0.946152\pi$
$181$		−	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	0.0375017	−	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	0.313580	−	0.949562i	$-0.398472\pi$
$199$	257.250	−	148.523i	1.29271	−	0.746349i	0.979135	+	0.203213i	$0.0651384\pi$
$200$	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	$-0.172406\pi$
$227$	−4.09299	−	7.08926i	−0.0180308	−	0.0312302i	−0.874900	+	0.484304i	$0.839073\pi$
$228$	48.4014	−	31.9777i	0.212287	−	0.140253i
$229$	−287.738	−	166.126i	−1.25650	−	0.725440i	−0.284107	−	0.958792i	$-0.591697\pi$
$229$	−287.738	−	166.126i	−1.25650	−	0.725440i	−0.972392	+	0.233352i	$0.925031\pi$
$230$	−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	0.577034	−	0.816720i	$-0.304210\pi$
$241$	−100.927	−	174.810i	−0.418783	−	0.725354i	−0.995817	+	0.0913661i	$0.970877\pi$
$242$	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	$-0.680164\pi$
$251$	−269.203			−1.07252			−0.536261	+	0.844052i	$0.680164\pi$
$252$		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	$-0.677040\pi$
$257$	121.180	−	209.889i	0.471516	−	0.816690i	0.999469	+	0.0325840i	$0.0103736\pi$
$258$	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	−0.209160	−	0.977881i	$-0.567073\pi$
$269$	143.412	−	82.7990i	0.533130	−	0.307803i	0.742290	+	0.670078i	$0.233740\pi$
$270$	139.623	−	591.842i	0.517122	−	2.19201i
$271$	−128.439	−	74.1542i	−0.473944	−	0.273632i	0.243945	−	0.969789i	$-0.421558\pi$
$271$	−128.439	−	74.1542i	−0.473944	−	0.273632i	−0.717889	+	0.696157i	$0.754892\pi$
$272$	−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	0.998377	−	0.0569453i	$-0.0181361\pi$
$283$	127.314	+	220.514i	0.449873	+	0.779202i	−0.548505	+	0.836147i	$0.684803\pi$
$284$	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	$-0.354043\pi$
$307$	271.779			0.885272			0.442636	+	0.896701i	$0.354043\pi$
$308$		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	$-0.995463\pi$
$311$	−462.614	+	267.090i	−1.48750	+	0.858811i	−0.487605	+	0.873064i	$0.662130\pi$
$312$	−99.5041	−	17.2272i	−0.318924	−	0.0552153i
$313$	278.116	−	481.711i	0.888550	−	1.53901i	0.0469600	−	0.998897i	$-0.485047\pi$
$313$	278.116	−	481.711i	0.888550	−	1.53901i	0.841590	−	0.540117i	$-0.181620\pi$
$314$	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	$0.317498\pi$
$349$			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	$-0.308285\pi$
$353$	−151.922	−	263.136i	−0.430373	−	0.745428i	−0.996905	+	0.0786114i	$0.974951\pi$
$354$	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	0.181520	−	0.983387i	$-0.441898\pi$
$367$	412.478	−	238.144i	1.12392	−	0.648894i	0.942398	+	0.334493i	$0.108565\pi$
$368$	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	−0.209034	−	0.977908i	$-0.567032\pi$
$383$	−444.450	−	256.604i	−1.16044	−	0.669983i	−0.951411	+	0.307925i	$0.900365\pi$
$384$	−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	0.797946	−	0.602729i	$-0.205920\pi$
$397$	267.952	+	154.702i	0.674941	+	0.389677i	−0.123005	+	0.992406i	$0.539253\pi$
$398$	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	$0.102886\pi$
$409$	306.415	+	530.726i	0.749181	+	1.29762i	−0.199035	+	0.979992i	$0.563781\pi$
$410$	−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	$-0.591523\pi$
$419$	−237.642			−0.567165			−0.283583	+	0.958948i	$0.591523\pi$
$420$		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	$-0.455849\pi$
$433$	119.733			0.276520			0.138260	+	0.990396i	$0.455849\pi$
$434$		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	$0.127841\pi$
$439$	754.721	+	435.738i	1.71918	+	0.992570i	0.798755	+	0.601657i	$0.205492\pi$
$440$	−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	$-0.653861\pi$
$461$		−	816.370i		−	1.77087i	0.464766	−	0.885434i	$-0.346139\pi$
$462$		0			0
$463$		−	115.161i		−	0.248727i	−0.992237	−	0.124363i	$-0.960311\pi$
$463$		−	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	$0.390253\pi$
$467$	−301.712	+	522.580i	−0.646064	+	1.11902i	−0.984055	+	0.177866i	$0.943081\pi$
$468$	−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	$-0.719606\pi$
$479$	−137.348	+	79.2977i	−0.286738	+	0.165548i	0.349732	+	0.936850i	$0.386273\pi$
$480$	−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	$-0.952950\pi$
$503$		−	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	$-0.390831\pi$
$509$	−158.386	−	91.4444i	−0.311172	−	0.179655i	−0.647451	+	0.762107i	$0.724165\pi$
$510$	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	$-0.196723\pi$
$521$	−49.1230	−	85.0836i	−0.0942861	−	0.163308i	−0.909310	+	0.416118i	$0.863390\pi$
$522$	313.648	−	1329.51i	0.600858	−	2.54695i
$523$	287.382	−	497.760i	0.549488	−	0.951740i	−0.448822	−	0.893621i	$-0.648156\pi$
$523$	287.382	−	497.760i	0.549488	−	0.951740i	0.998310	−	0.0581192i	$-0.0185103\pi$
$524$	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	0.971990	−	0.235024i	$-0.0755168\pi$
$563$	159.024	+	275.438i	0.282458	+	0.489232i	−0.689531	+	0.724256i	$0.742183\pi$
$564$	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	$-0.933591\pi$
$577$	−385.742	−	668.124i	−0.668530	−	1.15793i	0.309786	−	0.950806i	$-0.399743\pi$
$578$	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	$-0.460756\pi$
$587$	144.376			0.245956			0.122978	+	0.992409i	$0.460756\pi$
$588$		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	$0.416780\pi$
$593$	−419.463	+	726.531i	−0.707357	+	1.22518i	−0.965834	+	0.259162i	$0.916554\pi$
$594$	−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	$-0.595820\pi$
$601$	−356.394			−0.593002			−0.296501	+	0.955033i	$0.595820\pi$
$602$		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	$-0.317497\pi$
$607$	52.2836	+	30.1860i	0.0861345	+	0.0497298i	−0.456314	+	0.889819i	$0.650831\pi$
$608$	−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	0.901168	−	0.433471i	$-0.142711\pi$
$619$	46.5409	+	80.6112i	0.0751872	+	0.130228i	−0.825980	+	0.563699i	$0.809378\pi$
$620$	−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	$-0.564289\pi$
$643$	−257.971			−0.401199			−0.200600	+	0.979673i	$0.564289\pi$
$644$		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	$-0.761532\pi$
$647$	−329.059	+	189.982i	−0.508591	+	0.293635i	0.223663	+	0.974667i	$0.428198\pi$
$648$	−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	−0.546222	−	0.837640i	$-0.683935\pi$
$661$	−62.0782	+	35.8409i	−0.0939156	+	0.0542222i	0.452307	+	0.891862i	$0.350601\pi$
$662$	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	$-0.141492\pi$
$677$	664.698	+	383.763i	0.981828	+	0.566859i	0.0790065	+	0.996874i	$0.474825\pi$
$678$	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	−0.579572	−	0.814921i	$-0.696780\pi$
$691$	287.425	−	497.835i	0.415956	−	0.720457i	0.995528	+	0.0944642i	$0.0301138\pi$
$692$	−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	0.228349	−	0.973579i	$-0.426667\pi$
$719$	−359.947	−	207.815i	−0.500621	−	0.289034i	−0.728970	+	0.684546i	$0.760001\pi$
$720$	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	$-0.220451\pi$
$733$	440.858	+	254.530i	0.601444	+	0.347244i	−0.168166	+	0.985759i	$0.553784\pi$
$734$	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	−0.826883	−	0.562374i	$-0.809888\pi$
$761$	56.0005	−	96.9958i	0.0735881	−	0.127458i	0.900471	+	0.434915i	$0.143222\pi$
$762$	−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	$-0.470829\pi$
$769$	140.749			0.183028			0.0915142	+	0.995804i	$0.470829\pi$
$770$		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	$-0.994426\pi$
$773$	−1147.60	+	662.568i	−1.48461	+	0.857138i	−0.484760	+	0.874647i	$0.661093\pi$
$774$	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	$-0.0998868\pi$
$787$	163.900	+	283.884i	0.208260	+	0.360716i	−0.742907	+	0.669395i	$0.766553\pi$
$788$	−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	0.708069	−	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	$-0.652723\pi$
$811$	−748.707			−0.923190			−0.461595	+	0.887091i	$0.652723\pi$
$812$		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	−0.660077	−	0.751198i	$-0.729476\pi$
$829$	−281.494	+	162.521i	−0.339559	+	0.196044i	0.320518	+	0.947242i	$0.396143\pi$
$830$	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	$-0.243940\pi$
$857$	−206.009	−	356.818i	−0.240384	−	0.416357i	−0.960824	+	0.277160i	$0.910607\pi$
$858$	56.8480	−	240.971i	0.0662564	−	0.280852i
$859$	−79.9965	+	138.558i	−0.0931274	+	0.161301i	−0.908826	−	0.417176i	$-0.863020\pi$
$859$	−79.9965	+	138.558i	−0.0931274	+	0.161301i	0.815698	+	0.578478i	$0.196353\pi$
$860$	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	$-0.221361\pi$
$881$	1352.83			1.53556			0.767780	+	0.640714i	$0.221361\pi$
$882$		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	$-0.291267\pi$
$887$	202.442	+	116.880i	0.228233	+	0.131770i	−0.381524	+	0.924359i	$0.624601\pi$
$888$	−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	$-0.482387\pi$
$929$	828.996	−	1435.86i	0.892353	−	1.54560i	0.837047	−	0.547131i	$-0.184280\pi$
$930$	−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	$-0.443009\pi$
$937$	333.736			0.356175			0.178088	+	0.984015i	$0.443009\pi$
$938$		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	$-0.573445\pi$
$941$	470.533	−	271.662i	0.500035	−	0.288695i	0.728728	+	0.684803i	$0.240112\pi$
$942$	−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	$0.406199\pi$
$971$	−663.655	+	1149.48i	−0.683476	+	1.18381i	−0.973913	+	0.226921i	$0.927134\pi$
$972$	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	0.486441	−	0.873714i	$-0.338295\pi$
$983$	1461.05	−	843.539i	1.48632	−	0.858127i	0.999879	+	0.0155866i	$0.00496158\pi$
$984$	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	−0.586828	−	0.809711i	$-0.699624\pi$
$997$	−178.475	+	103.043i	−0.179012	+	0.103353i	0.407816	+	0.913064i	$0.366290\pi$
$998$	−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.o.275.6		16
7.2	even	3		56.3.g.b.43.5	✓	8
7.3	odd	6		392.3.k.n.67.1		16
7.4	even	3	inner	392.3.k.o.67.1		16
7.5	odd	6		392.3.g.m.99.5		8
7.6	odd	2		392.3.k.n.275.6		16
8.3	odd	2	inner	392.3.k.o.275.1		16
21.2	odd	6		504.3.g.b.379.4		8
28.19	even	6		1568.3.g.m.687.2		8
28.23	odd	6		224.3.g.b.15.7		8
56.3	even	6		392.3.k.n.67.6		16
56.5	odd	6		1568.3.g.m.687.1		8
56.11	odd	6	inner	392.3.k.o.67.6		16
56.19	even	6		392.3.g.m.99.6		8
56.27	even	2		392.3.k.n.275.1		16
56.37	even	6		224.3.g.b.15.8		8
56.51	odd	6		56.3.g.b.43.6	yes	8
84.23	even	6		2016.3.g.b.1135.8		8
112.37	even	12		1792.3.d.j.1023.16		16
112.51	odd	12		1792.3.d.j.1023.15		16
112.93	even	12		1792.3.d.j.1023.1		16
112.107	odd	12		1792.3.d.j.1023.2		16
168.107	even	6		504.3.g.b.379.3		8
168.149	odd	6		2016.3.g.b.1135.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
56.3.g.b.43.5	✓	8	7.2	even	3
56.3.g.b.43.6	yes	8	56.51	odd	6
224.3.g.b.15.7		8	28.23	odd	6
224.3.g.b.15.8		8	56.37	even	6
392.3.g.m.99.5		8	7.5	odd	6
392.3.g.m.99.6		8	56.19	even	6
392.3.k.n.67.1		16	7.3	odd	6
392.3.k.n.67.6		16	56.3	even	6
392.3.k.n.275.1		16	56.27	even	2
392.3.k.n.275.6		16	7.6	odd	2
392.3.k.o.67.1		16	7.4	even	3	inner
392.3.k.o.67.6		16	56.11	odd	6	inner
392.3.k.o.275.1		16	8.3	odd	2	inner
392.3.k.o.275.6		16	1.1	even	1	trivial
504.3.g.b.379.3		8	168.107	even	6
504.3.g.b.379.4		8	21.2	odd	6
1568.3.g.m.687.1		8	56.5	odd	6
1568.3.g.m.687.2		8	28.19	even	6
1792.3.d.j.1023.1		16	112.93	even	12
1792.3.d.j.1023.2		16	112.107	odd	12
1792.3.d.j.1023.15		16	112.51	odd	12
1792.3.d.j.1023.16		16	112.37	even	12
2016.3.g.b.1135.1		8	168.149	odd	6
2016.3.g.b.1135.8		8	84.23	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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