LMFDB - Embedded newform 392.3.k.i.275.2

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:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	8.0.796594176.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 4x^{7} + 18x^{6} - 40x^{5} + 83x^{4} - 104x^{3} + 22x^{2} + 24x + 4 $ x^8 - 4x^7 + 18x^6 - 40x^5 + 83x^4 - 104x^3 + 22x^2 + 24*x + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 56)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			275.2
Root			$1.20711 + 0.0981308i$ of defining polynomial
Character	$\chi$	$=$	392.275
Dual form			392.3.k.i.67.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.26663 - 1.54779i) q^{2} +(-0.292893 - 0.507306i) q^{3} +(-0.791288 + 3.92095i) q^{4} +(-7.82295 - 4.51658i) q^{5} +(-0.414214 + 1.09591i) q^{6} +(7.07107 - 3.74166i) q^{8} +(4.32843 - 7.49706i) q^{9} +O(q^{10})$	\(q+(-1.26663 - 1.54779i) q^{2} +(-0.292893 - 0.507306i) q^{3} +(-0.791288 + 3.92095i) q^{4} +(-7.82295 - 4.51658i) q^{5} +(-0.414214 + 1.09591i) q^{6} +(7.07107 - 3.74166i) q^{8} +(4.32843 - 7.49706i) q^{9} +(2.91809 + 17.8291i) q^{10} +(-6.24264 - 10.8126i) q^{11} +(2.22089 - 0.746995i) q^{12} -9.03316i q^{13} +5.29150i q^{15} +(-14.7477 - 6.20520i) q^{16} +(-6.17157 - 10.6895i) q^{17} +(-17.0864 + 2.79653i) q^{18} +(-14.4350 + 25.0022i) q^{19} +(23.8995 - 27.0995i) q^{20} +(-8.82843 + 23.3578i) q^{22} +(21.3404 + 12.3209i) q^{23} +(-3.96923 - 2.49129i) q^{24} +(28.2990 + 49.0153i) q^{25} +(-13.9814 + 11.4417i) q^{26} -10.3431 q^{27} +22.4499i q^{29} +(8.19012 - 6.70239i) q^{30} +(-14.5340 + 8.39119i) q^{31} +(9.07561 + 30.6860i) q^{32} +(-3.65685 + 6.33386i) q^{33} +(-8.72792 + 23.0919i) q^{34} +(25.9706 + 22.9039i) q^{36} +(-14.0734 - 8.12528i) q^{37} +(56.9819 - 9.32624i) q^{38} +(-4.58258 + 2.64575i) q^{39} +(-72.2161 - 2.66626i) q^{40} +6.97056 q^{41} -22.8284 q^{43} +(47.3353 - 15.9212i) q^{44} +(-67.7221 + 39.0994i) q^{45} +(-7.96032 - 48.6364i) q^{46} +(5.36882 + 3.09969i) q^{47} +(1.17157 + 9.29907i) q^{48} +(40.0208 - 105.885i) q^{50} +(-3.61522 + 6.26175i) q^{51} +(35.4186 + 7.14783i) q^{52} +(6.94131 - 4.00757i) q^{53} +(13.1010 + 16.0090i) q^{54} +112.782i q^{55} +16.9117 q^{57} +(34.7477 - 28.4358i) q^{58} +(-15.2218 - 26.3650i) q^{59} +(-20.7477 - 4.18710i) q^{60} +(13.1918 + 7.61627i) q^{61} +(31.3970 + 11.8669i) q^{62} +(36.0000 - 52.9150i) q^{64} +(-40.7990 + 70.6659i) q^{65} +(14.4353 - 2.36263i) q^{66} +(39.3137 + 68.0933i) q^{67} +(46.7964 - 15.7400i) q^{68} -14.4348i q^{69} -17.5345i q^{71} +(2.55519 - 69.2077i) q^{72} +(-23.3431 - 40.4315i) q^{73} +(5.24961 + 32.0744i) q^{74} +(16.5772 - 28.7125i) q^{75} +(-86.6102 - 76.3830i) q^{76} +(9.89949 + 3.74166i) q^{78} +(70.1762 + 40.5163i) q^{79} +(87.3444 + 115.152i) q^{80} +(-35.9264 - 62.2264i) q^{81} +(-8.82914 - 10.7889i) q^{82} +40.3848 q^{83} +111.498i q^{85} +(28.9152 + 35.3335i) q^{86} +(11.3890 - 6.57544i) q^{87} +(-84.5991 - 53.0986i) q^{88} +(-55.9706 + 96.9439i) q^{89} +(146.296 + 55.2949i) q^{90} +(-65.1960 + 73.9253i) q^{92} +(8.51380 + 4.91545i) q^{93} +(-2.00266 - 12.2360i) q^{94} +(225.849 - 130.394i) q^{95} +(12.9090 - 13.5918i) q^{96} -164.108 q^{97} -108.083 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 8 q^{3} + 12 q^{4} + 8 q^{6} + 12 q^{9}+O(q^{10}) $ 8 * q - 8 * q^3 + 12 * q^4 + 8 * q^6 + 12 * q^9	$ 8 q - 8 q^{3} + 12 q^{4} + 8 q^{6} + 12 q^{9} + 28 q^{10} - 16 q^{11} + 24 q^{12} - 8 q^{16} - 72 q^{17} - 16 q^{18} - 8 q^{19} + 112 q^{20} - 48 q^{22} + 40 q^{24} + 68 q^{25} - 28 q^{26} - 128 q^{27} + 16 q^{33} + 32 q^{34} + 72 q^{36} + 76 q^{38} - 56 q^{40} - 80 q^{41} - 160 q^{43} + 48 q^{44} - 224 q^{46} + 32 q^{48} + 224 q^{50} - 176 q^{51} + 56 q^{52} + 16 q^{54} - 272 q^{57} + 168 q^{58} - 184 q^{59} - 56 q^{60} - 224 q^{62} + 288 q^{64} - 168 q^{65} + 32 q^{66} + 224 q^{67} + 216 q^{68} + 160 q^{72} - 232 q^{73} + 280 q^{74} - 88 q^{75} - 48 q^{76} + 336 q^{80} + 52 q^{81} + 48 q^{82} + 176 q^{83} - 8 q^{86} - 240 q^{88} - 312 q^{89} + 616 q^{90} + 112 q^{92} + 112 q^{94} - 176 q^{96} - 272 q^{97} - 480 q^{99}+O(q^{100}) $ 8 * q - 8 * q^3 + 12 * q^4 + 8 * q^6 + 12 * q^9 + 28 * q^10 - 16 * q^11 + 24 * q^12 - 8 * q^16 - 72 * q^17 - 16 * q^18 - 8 * q^19 + 112 * q^20 - 48 * q^22 + 40 * q^24 + 68 * q^25 - 28 * q^26 - 128 * q^27 + 16 * q^33 + 32 * q^34 + 72 * q^36 + 76 * q^38 - 56 * q^40 - 80 * q^41 - 160 * q^43 + 48 * q^44 - 224 * q^46 + 32 * q^48 + 224 * q^50 - 176 * q^51 + 56 * q^52 + 16 * q^54 - 272 * q^57 + 168 * q^58 - 184 * q^59 - 56 * q^60 - 224 * q^62 + 288 * q^64 - 168 * q^65 + 32 * q^66 + 224 * q^67 + 216 * q^68 + 160 * q^72 - 232 * q^73 + 280 * q^74 - 88 * q^75 - 48 * q^76 + 336 * q^80 + 52 * q^81 + 48 * q^82 + 176 * q^83 - 8 * q^86 - 240 * q^88 - 312 * q^89 + 616 * q^90 + 112 * q^92 + 112 * q^94 - 176 * q^96 - 272 * q^97 - 480 * 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 $

$2$	−1.26663	−	1.54779i	−0.633316	−	0.773893i
$2$	−1.26663	−	1.54779i	−0.633316	−	0.773893i
$3$	−0.292893	−	0.507306i	−0.0976311	−	0.169102i	0.813073	−	0.582162i	$-0.197793\pi$
$3$	−0.292893	−	0.507306i	−0.0976311	−	0.169102i	−0.910704	+	0.413060i	$0.864460\pi$
$4$	−0.791288	+	3.92095i	−0.197822	+	0.980238i
$5$	−7.82295	−	4.51658i	−1.56459	−	0.903316i	−0.996782	−	0.0801541i	$-0.974459\pi$
$5$	−7.82295	−	4.51658i	−1.56459	−	0.903316i	−0.567807	−	0.823162i	$-0.692208\pi$
$6$	−0.414214	+	1.09591i	−0.0690356	+	0.182651i
$7$		0			0
$7$		0			0
$8$	7.07107	−	3.74166i	0.883883	−	0.467707i
$9$	4.32843	−	7.49706i	0.480936	−	0.833006i
$10$	2.91809	+	17.8291i	0.291809	+	1.78291i
$11$	−6.24264	−	10.8126i	−0.567513	−	0.982961i	−0.996811	−	0.0797982i	$-0.974572\pi$
$11$	−6.24264	−	10.8126i	−0.567513	−	0.982961i	0.429298	−	0.903163i	$-0.358761\pi$
$12$	2.22089	−	0.746995i	0.185074	−	0.0622496i
$13$		−	9.03316i		−	0.694858i	−0.937706	−	0.347429i	$-0.887055\pi$
$13$		−	9.03316i		−	0.694858i	0.937706	−	0.347429i	$-0.112945\pi$
$14$		0			0
$15$			5.29150i			0.352767i
$16$	−14.7477	−	6.20520i	−0.921733	−	0.387825i
$17$	−6.17157	−	10.6895i	−0.363034	−	0.628793i	0.625425	−	0.780284i	$-0.284926\pi$
$17$	−6.17157	−	10.6895i	−0.363034	−	0.628793i	−0.988459	+	0.151492i	$0.951592\pi$
$18$	−17.0864	+	2.79653i	−0.949243	+	0.155363i
$19$	−14.4350	+	25.0022i	−0.759738	+	1.31591i	0.183246	+	0.983067i	$0.441340\pi$
$19$	−14.4350	+	25.0022i	−0.759738	+	1.31591i	−0.942984	+	0.332838i	$0.891994\pi$
$20$	23.8995	−	27.0995i	1.19497	−	1.35497i
$21$		0			0
$22$	−8.82843	+	23.3578i	−0.401292	+	1.06172i
$23$	21.3404	+	12.3209i	0.927843	+	0.535690i	0.886129	−	0.463439i	$-0.153385\pi$
$23$	21.3404	+	12.3209i	0.927843	+	0.535690i	0.0417142	+	0.999130i	$0.486718\pi$
$24$	−3.96923	−	2.49129i	−0.165385	−	0.103804i
$25$	28.2990	+	49.0153i	1.13196	+	1.96061i
$26$	−13.9814	+	11.4417i	−0.537746	+	0.440065i
$27$	−10.3431			−0.383079
$28$		0			0
$29$			22.4499i			0.774136i	0.922051	+	0.387068i	$0.126512\pi$
$29$			22.4499i			0.774136i	−0.922051	+	0.387068i	$0.873488\pi$
$30$	8.19012	−	6.70239i	0.273004	−	0.223413i
$31$	−14.5340	+	8.39119i	−0.468838	+	0.270684i	−0.715753	−	0.698353i	$-0.753916\pi$
$31$	−14.5340	+	8.39119i	−0.468838	+	0.270684i	0.246915	+	0.969037i	$0.420583\pi$
$32$	9.07561	+	30.6860i	0.283613	+	0.958939i
$33$	−3.65685	+	6.33386i	−0.110814	+	0.191935i
$34$	−8.72792	+	23.0919i	−0.256704	+	0.679174i
$35$		0			0
$36$	25.9706	+	22.9039i	0.721405	+	0.636219i
$37$	−14.0734	−	8.12528i	−0.380362	−	0.219602i	0.297614	−	0.954686i	$-0.403809\pi$
$37$	−14.0734	−	8.12528i	−0.380362	−	0.219602i	−0.677976	+	0.735084i	$0.737143\pi$
$38$	56.9819	−	9.32624i	1.49952	−	0.245427i
$39$	−4.58258	+	2.64575i	−0.117502	+	0.0678398i
$40$	−72.2161	−	2.66626i	−1.80540	−	0.0666565i
$41$	6.97056			0.170014			0.0850069	−	0.996380i	$-0.472909\pi$
$41$	6.97056			0.170014			0.0850069	+	0.996380i	$0.472909\pi$
$42$		0			0
$43$	−22.8284			−0.530894			−0.265447	−	0.964126i	$-0.585519\pi$
$43$	−22.8284			−0.530894			−0.265447	+	0.964126i	$0.585519\pi$
$44$	47.3353	−	15.9212i	1.07580	−	0.361846i
$45$	−67.7221	+	39.0994i	−1.50494	+	0.868875i
$46$	−7.96032	−	48.6364i	−0.173050	−	1.05731i
$47$	5.36882	+	3.09969i	0.114230	+	0.0659509i	0.556027	−	0.831165i	$-0.312325\pi$
$47$	5.36882	+	3.09969i	0.114230	+	0.0659509i	−0.441796	+	0.897115i	$0.645659\pi$
$48$	1.17157	+	9.29907i	0.0244078	+	0.193731i
$49$		0			0
$50$	40.0208	−	105.885i	0.800416	−	2.11770i
$51$	−3.61522	+	6.26175i	−0.0708867	+	0.122779i
$52$	35.4186	+	7.14783i	0.681127	+	0.137458i
$53$	6.94131	−	4.00757i	0.130968	−	0.0756145i	−0.433084	−	0.901353i	$-0.642575\pi$
$53$	6.94131	−	4.00757i	0.130968	−	0.0756145i	0.564053	+	0.825739i	$0.309241\pi$
$54$	13.1010	+	16.0090i	0.242610	+	0.296463i
$55$			112.782i			2.05057i
$56$		0			0
$57$	16.9117			0.296696
$58$	34.7477	−	28.4358i	0.599099	−	0.490273i
$59$	−15.2218	−	26.3650i	−0.257997	−	0.446864i	0.707708	−	0.706505i	$-0.249729\pi$
$59$	−15.2218	−	26.3650i	−0.257997	−	0.446864i	−0.965705	+	0.259641i	$0.916396\pi$
$60$	−20.7477	−	4.18710i	−0.345795	−	0.0697850i
$61$	13.1918	+	7.61627i	0.216258	+	0.124857i	0.604217	−	0.796820i	$-0.293486\pi$
$61$	13.1918	+	7.61627i	0.216258	+	0.124857i	−0.387958	+	0.921677i	$0.626819\pi$
$62$	31.3970	+	11.8669i	0.506403	+	0.191402i
$63$		0			0
$64$	36.0000	−	52.9150i	0.562500	−	0.826797i
$65$	−40.7990	+	70.6659i	−0.627677	+	1.08717i
$66$	14.4353	−	2.36263i	0.218717	−	0.0357975i
$67$	39.3137	+	68.0933i	0.586772	+	1.01632i	0.994652	+	0.103283i	$0.0329348\pi$
$67$	39.3137	+	68.0933i	0.586772	+	1.01632i	−0.407880	+	0.913035i	$0.633732\pi$
$68$	46.7964	−	15.7400i	0.688183	−	0.231470i
$69$		−	14.4348i		−	0.209200i
$70$		0			0
$71$		−	17.5345i		−	0.246965i	−0.992347	−	0.123482i	$-0.960594\pi$
$71$		−	17.5345i		−	0.246965i	0.992347	−	0.123482i	$-0.0394062\pi$
$72$	2.55519	−	69.2077i	0.0354887	−	0.961218i
$73$	−23.3431	−	40.4315i	−0.319769	−	0.553856i	0.660671	−	0.750676i	$-0.270272\pi$
$73$	−23.3431	−	40.4315i	−0.319769	−	0.553856i	−0.980440	+	0.196820i	$0.936939\pi$
$74$	5.24961	+	32.0744i	0.0709407	+	0.433437i
$75$	16.5772	−	28.7125i	0.221029	−	0.382833i
$76$	−86.6102	−	76.3830i	−1.13961	−	1.00504i
$77$		0			0
$78$	9.89949	+	3.74166i	0.126917	+	0.0479700i
$79$	70.1762	+	40.5163i	0.888307	+	0.512864i	0.873388	−	0.487025i	$-0.161918\pi$
$79$	70.1762	+	40.5163i	0.888307	+	0.512864i	0.0149184	+	0.999889i	$0.495251\pi$
$80$	87.3444	+	115.152i	1.09180	+	1.43940i
$81$	−35.9264	−	62.2264i	−0.443536	−	0.768227i
$82$	−8.82914	−	10.7889i	−0.107672	−	0.131572i
$83$	40.3848			0.486564			0.243282	−	0.969956i	$-0.421776\pi$
$83$	40.3848			0.486564			0.243282	+	0.969956i	$0.421776\pi$
$84$		0			0
$85$			111.498i			1.31174i
$86$	28.9152	+	35.3335i	0.336223	+	0.410855i
$87$	11.3890	−	6.57544i	0.130908	−	0.0755797i
$88$	−84.5991	−	53.0986i	−0.961353	−	0.603393i
$89$	−55.9706	+	96.9439i	−0.628883	+	1.08926i	0.358894	+	0.933379i	$0.383154\pi$
$89$	−55.9706	+	96.9439i	−0.628883	+	1.08926i	−0.987776	+	0.155878i	$0.950179\pi$
$90$	146.296	+	55.2949i	1.62552	+	0.614387i
$91$		0			0
$92$	−65.1960	+	73.9253i	−0.708652	+	0.803536i
$93$	8.51380	+	4.91545i	0.0915463	+	0.0528543i
$94$	−2.00266	−	12.2360i	−0.0213049	−	0.130170i
$95$	225.849	−	130.394i	2.37736	−	1.37257i
$96$	12.9090	−	13.5918i	0.134469	−	0.141582i
$97$	−164.108			−1.69183			−0.845916	−	0.533317i	$-0.820945\pi$
$97$	−164.108			−1.69183			−0.845916	+	0.533317i	$0.820945\pi$
$98$		0			0
$99$	−108.083			−1.09175
$100$	−214.579	+	72.1738i	−2.14579	+	0.721738i
$101$	10.5074	−	6.06643i	0.104033	−	0.0600636i	−0.447081	−	0.894494i	$-0.647536\pi$
$101$	10.5074	−	6.06643i	0.104033	−	0.0600636i	0.551114	+	0.834430i	$0.314203\pi$
$102$	14.2710	−	2.33574i	0.139912	−	0.0228994i
$103$	92.3029	+	53.2911i	0.896144	+	0.517389i	0.875947	−	0.482407i	$-0.160237\pi$
$103$	92.3029	+	53.2911i	0.896144	+	0.517389i	0.0201970	+	0.999796i	$0.493571\pi$
$104$	−33.7990	−	63.8741i	−0.324990	−	0.614174i
$105$		0			0
$106$	−14.9949	−	5.66756i	−0.141462	−	0.0534675i
$107$	31.7990	−	55.0775i	0.297187	−	0.514743i	−0.678304	−	0.734781i	$-0.737285\pi$
$107$	31.7990	−	55.0775i	0.297187	−	0.514743i	0.975491	+	0.220038i	$0.0706182\pi$
$108$	8.18441	−	40.5550i	0.0757815	−	0.375509i
$109$	−113.318	+	65.4239i	−1.03961	+	0.600220i	−0.919723	−	0.392568i	$-0.871587\pi$
$109$	−113.318	+	65.4239i	−1.03961	+	0.600220i	−0.119888	+	0.992787i	$0.538253\pi$
$110$	174.562	−	142.853i	1.58693	−	1.29866i
$111$			9.51936i			0.0857600i
$112$		0			0
$113$	−138.225			−1.22323			−0.611617	−	0.791154i	$-0.709481\pi$
$113$	−138.225			−1.22323			−0.611617	+	0.791154i	$0.709481\pi$
$114$	−21.4209	−	26.1757i	−0.187902	−	0.229611i
$115$	−111.296	−	192.771i	−0.967795	−	1.67627i
$116$	−88.0252	−	17.7644i	−0.758838	−	0.153141i
$117$	−67.7221	−	39.0994i	−0.578821	−	0.334183i
$118$	−21.5269	+	56.9549i	−0.182431	+	0.482668i
$119$		0			0
$120$	19.7990	+	37.4166i	0.164992	+	0.311805i
$121$	−17.4411	+	30.2089i	−0.144142	+	0.249660i
$122$	−4.92075	−	30.0651i	−0.0403340	−	0.246435i
$123$	−2.04163	−	3.53621i	−0.0165986	−	0.0287497i
$124$	−21.4009	−	63.6269i	−0.172588	−	0.513120i
$125$		−	285.430i		−	2.28344i
$126$		0			0
$127$		−	114.442i		−	0.901114i	−0.892748	−	0.450557i	$-0.851225\pi$
$127$		−	114.442i		−	0.901114i	0.892748	−	0.450557i	$-0.148775\pi$
$128$	−127.500	+	11.3035i	−0.996093	+	0.0883088i
$129$	6.68629	+	11.5810i	0.0518317	+	0.0897752i
$130$	161.053	−	26.3596i	1.23887	−	0.202766i
$131$	84.1751	−	145.796i	0.642558	−	1.11294i	−0.342301	−	0.939590i	$-0.611206\pi$
$131$	84.1751	−	145.796i	0.642558	−	1.11294i	0.984860	−	0.173353i	$-0.0554603\pi$
$132$	−21.9411	−	19.3503i	−0.166221	−	0.146593i
$133$		0			0
$134$	55.5980	−	147.098i	0.414910	−	1.09775i
$135$	80.9139	+	46.7156i	0.599362	+	0.346042i
$136$	−83.6360	−	52.4941i	−0.614970	−	0.385986i
$137$	−17.3431	−	30.0392i	−0.126592	−	0.219264i	0.795762	−	0.605610i	$-0.207071\pi$
$137$	−17.3431	−	30.0392i	−0.126592	−	0.219264i	−0.922354	+	0.386345i	$0.873737\pi$
$138$	−22.3420	+	18.2836i	−0.161899	+	0.132490i
$139$	107.664			0.774561			0.387281	−	0.921962i	$-0.373414\pi$
$139$	107.664			0.774561			0.387281	+	0.921962i	$0.373414\pi$
$140$		0			0
$141$		−	3.63151i		−	0.0257554i
$142$	−27.1397	+	22.2098i	−0.191124	+	0.156407i
$143$	−97.6717	+	56.3908i	−0.683019	+	0.394341i
$144$	−110.355	+	83.7058i	−0.766356	+	0.581290i
$145$	101.397	−	175.625i	0.699289	−	1.21120i
$146$	−33.0122	+	87.3421i	−0.226111	+	0.598233i
$147$		0			0
$148$	42.9949	−	48.7517i	0.290506	−	0.329403i
$149$	−218.391	−	126.088i	−1.46571	−	0.846229i	−0.466447	−	0.884549i	$-0.654466\pi$
$149$	−218.391	−	126.088i	−1.46571	−	0.846229i	−0.999266	+	0.0383198i	$0.987799\pi$
$150$	−65.4380	+	10.7102i	−0.436253	+	0.0714016i
$151$	−203.071	+	117.243i	−1.34484	+	0.776444i	−0.987513	−	0.157535i	$-0.949645\pi$
$151$	−203.071	+	117.243i	−1.34484	+	0.776444i	−0.357327	+	0.933979i	$0.616312\pi$
$152$	−8.52139	+	230.803i	−0.0560618	+	1.51844i
$153$	−106.853			−0.698384
$154$		0			0
$155$	151.598			0.978051
$156$	−6.74773	−	20.0616i	−0.0432547	−	0.128600i
$157$	−8.74409	+	5.04840i	−0.0556948	+	0.0321554i	−0.527589	−	0.849500i	$-0.676904\pi$
$157$	−8.74409	+	5.04840i	−0.0556948	+	0.0321554i	0.471894	+	0.881655i	$0.343570\pi$
$158$	−26.1769	−	159.937i	−0.165677	−	1.01226i
$159$	−4.06613	−	2.34758i	−0.0255731	−	0.0147647i
$160$	67.5980	−	281.046i	0.422487	−	1.75654i
$161$		0			0
$162$	−50.8076	+	134.424i	−0.313627	+	0.829780i
$163$	−52.2670	+	90.5291i	−0.320657	+	0.555394i	−0.980624	−	0.195901i	$-0.937237\pi$
$163$	−52.2670	+	90.5291i	−0.320657	+	0.555394i	0.659967	+	0.751295i	$0.270570\pi$
$164$	−5.51572	+	27.3312i	−0.0336324	+	0.166654i
$165$	57.2147	−	33.0329i	0.346756	−	0.200200i
$166$	−51.1526	−	62.5070i	−0.308148	−	0.376548i
$167$			296.765i			1.77703i	0.458843	+	0.888517i	$0.348264\pi$
$167$			296.765i			1.77703i	−0.458843	+	0.888517i	$0.651736\pi$
$168$		0			0
$169$	87.4020			0.517172
$170$	172.575	−	141.226i	1.01514	−	0.830744i
$171$	124.962	+	216.440i	0.730772	+	1.26573i
$172$	18.0639	−	89.5092i	0.105022	−	0.520402i
$173$	34.6671	+	20.0150i	0.200388	+	0.115694i	0.596836	−	0.802363i	$-0.296424\pi$
$173$	34.6671	+	20.0150i	0.200388	+	0.115694i	−0.396449	+	0.918057i	$0.629758\pi$
$174$	−24.6030	−	9.29907i	−0.141397	−	0.0534429i
$175$		0			0
$176$	24.9706	+	198.198i	0.141878	+	1.12612i
$177$	−8.91674	+	15.4442i	−0.0503771	+	0.0872556i
$178$	220.943	−	36.1617i	1.24125	−	0.203155i
$179$	−147.397	−	255.299i	−0.823447	−	1.42625i	−0.903101	−	0.429429i	$-0.858715\pi$
$179$	−147.397	−	255.299i	−0.823447	−	1.42625i	0.0796538	−	0.996823i	$-0.474619\pi$
$180$	−99.7191	−	296.474i	−0.553995	−	1.64708i
$181$		−	40.4706i		−	0.223595i	−0.993731	−	0.111797i	$-0.964339\pi$
$181$		−	40.4706i		−	0.223595i	0.993731	−	0.111797i	$-0.0356608\pi$
$182$		0			0
$183$		−	8.92302i		−	0.0487596i
$184$	197.000	+	7.27335i	1.07065	+	0.0395291i
$185$	73.3970	+	127.127i	0.396740	+	0.687174i
$186$	−3.17579	−	19.4036i	−0.0170741	−	0.104321i
$187$	−77.0538	+	133.461i	−0.412053	+	0.713696i
$188$	−16.4020	+	18.5981i	−0.0872448	+	0.0989263i
$189$		0			0
$190$	−487.889	−	184.405i	−2.56784	−	0.970552i
$191$	−135.905	−	78.4647i	−0.711543	−	0.410810i	0.100089	−	0.994979i	$-0.468087\pi$
$191$	−135.905	−	78.4647i	−0.711543	−	0.410810i	−0.811632	+	0.584169i	$0.801421\pi$
$192$	−37.3883	−	2.76456i	−0.194731	−	0.0143988i
$193$	130.652	+	226.296i	0.676952	+	1.17252i	0.975894	+	0.218245i	$0.0700330\pi$
$193$	130.652	+	226.296i	0.676952	+	1.17252i	−0.298942	+	0.954271i	$0.596634\pi$
$194$	207.864	+	254.004i	1.07146	+	1.30930i
$195$	47.7990			0.245123
$196$		0			0
$197$			145.283i			0.737475i	0.929533	+	0.368738i	$0.120210\pi$
$197$			145.283i			0.737475i	−0.929533	+	0.368738i	$0.879790\pi$
$198$	136.902	+	167.290i	0.691423	+	0.844898i
$199$	338.189	−	195.254i	1.69944	−	0.981175i	0.753161	−	0.657836i	$-0.228528\pi$
$199$	338.189	−	195.254i	1.69944	−	0.981175i	0.946283	−	0.323339i	$-0.104805\pi$
$200$	383.502	+	240.705i	1.91751	+	1.20353i
$201$	23.0294	−	39.8882i	0.114574	−	0.198449i
$202$	−22.6985	−	8.57922i	−0.112369	−	0.0424714i
$203$		0			0
$204$	−21.6913	−	19.1300i	−0.106330	−	0.0937743i
$205$	−54.5303	−	31.4831i	−0.266002	−	0.153576i
$206$	−34.4305	−	210.365i	−0.167138	−	1.02119i
$207$	184.741	−	106.660i	0.892467	−	0.515266i
$208$	−56.0526	+	133.219i	−0.269484	+	0.640474i
$209$	360.451			1.72464
$210$		0			0
$211$	−164.049			−0.777482			−0.388741	−	0.921347i	$-0.627090\pi$
$211$	−164.049			−0.777482			−0.388741	+	0.921347i	$0.627090\pi$
$212$	10.2209	+	30.3877i	0.0482118	+	0.143338i
$213$	−8.89535	+	5.13574i	−0.0417622	+	0.0241114i
$214$	−125.526	+	20.5448i	−0.586569	+	0.0960038i
$215$	178.586	+	103.106i	0.830630	+	0.479565i
$216$	−73.1371	+	38.7005i	−0.338598	+	0.179169i
$217$		0			0
$218$	244.794	+	92.5234i	1.12291	+	0.424419i
$219$	−13.6741	+	23.6842i	−0.0624388	+	0.108147i
$220$	−442.211	−	89.2427i	−2.01005	−	0.405648i
$221$	−96.5598	+	55.7488i	−0.436922	+	0.252257i
$222$	14.7339	−	12.0575i	0.0663691	−	0.0543132i
$223$			10.5830i			0.0474574i	0.999718	+	0.0237287i	$0.00755379\pi$
$223$			10.5830i			0.0474574i	−0.999718	+	0.0237287i	$0.992446\pi$
$224$		0			0
$225$	489.960			2.17760
$226$	175.081	+	213.943i	0.774693	+	0.946652i
$227$	106.903	+	185.162i	0.470939	+	0.815690i	0.999447	−	0.0332382i	$-0.0105820\pi$
$227$	106.903	+	185.162i	0.470939	+	0.815690i	−0.528509	+	0.848928i	$0.677249\pi$
$228$	−13.3820	+	66.3099i	−0.0586930	+	0.290833i
$229$	−200.942	−	116.014i	−0.877478	−	0.506612i	−0.00765200	−	0.999971i	$-0.502436\pi$
$229$	−200.942	−	116.014i	−0.877478	−	0.506612i	−0.869826	+	0.493359i	$0.835769\pi$
$230$	−157.397	+	416.433i	−0.684335	+	1.81058i
$231$		0			0
$232$	84.0000	+	158.745i	0.362069	+	0.684246i
$233$	96.4315	−	167.024i	0.413869	−	0.716842i	−0.581440	−	0.813589i	$-0.697511\pi$
$233$	96.4315	−	167.024i	0.413869	−	0.716842i	0.995309	+	0.0967472i	$0.0308439\pi$
$234$	25.2615	+	154.344i	0.107955	+	0.659589i
$235$	−28.0000	−	48.4974i	−0.119149	−	0.206372i
$236$	115.421	−	38.8218i	0.489071	−	0.164499i
$237$		−	47.4678i		−	0.200286i
$238$		0			0
$239$		−	327.917i		−	1.37204i	−0.727583	−	0.686020i	$-0.759356\pi$
$239$		−	327.917i		−	1.37204i	0.727583	−	0.686020i	$-0.240644\pi$
$240$	32.8348	−	78.0376i	0.136812	−	0.325157i
$241$	−35.9361	−	62.2431i	−0.149112	−	0.258270i	0.781787	−	0.623545i	$-0.214308\pi$
$241$	−35.9361	−	62.2431i	−0.149112	−	0.258270i	−0.930900	+	0.365275i	$0.880975\pi$
$242$	68.8484	−	11.2684i	0.284498	−	0.0465638i
$243$	−67.5894	+	117.068i	−0.278146	+	0.481762i
$244$	−40.3015	+	45.6976i	−0.165170	+	0.187285i
$245$		0			0
$246$	−2.88730	+	7.63908i	−0.0117370	+	0.0310532i
$247$	225.849	+	130.394i	0.914368	+	0.527911i
$248$	−71.3737	+	113.716i	−0.287797	+	0.458532i
$249$	−11.8284	−	20.4874i	−0.0475037	−	0.0822789i
$250$	−441.784	+	361.534i	−1.76714	+	1.44614i
$251$	−256.919			−1.02358			−0.511790	−	0.859110i	$-0.671018\pi$
$251$	−256.919			−1.02358			−0.511790	+	0.859110i	$0.671018\pi$
$252$		0			0
$253$		−	307.659i		−	1.21604i
$254$	−177.131	+	144.955i	−0.697367	+	0.570690i
$255$	56.5634	−	32.6569i	0.221817	−	0.128066i
$256$	178.991	+	183.025i	0.699183	+	0.714943i
$257$	−159.676	+	276.567i	−0.621308	+	1.07614i	0.367934	+	0.929852i	$0.380065\pi$
$257$	−159.676	+	276.567i	−0.621308	+	1.07614i	−0.989242	+	0.146285i	$0.953268\pi$
$258$	9.45584	−	25.0178i	0.0366506	−	0.0969683i
$259$		0			0
$260$	−244.794	−	215.888i	−0.941515	−	0.830338i
$261$	168.308	+	97.1729i	0.644860	+	0.372310i
$262$	−332.279	+	54.3842i	−1.26824	+	0.207573i
$263$	−326.800	+	188.678i	−1.24259	+	0.717408i	−0.969620	−	0.244615i	$-0.921338\pi$
$263$	−326.800	+	188.678i	−1.24259	+	0.717408i	−0.272967	+	0.962023i	$0.588005\pi$
$264$	−2.15874	+	58.4698i	−0.00817705	+	0.221477i
$265$	−72.4020			−0.273215
$266$		0			0
$267$	65.5736			0.245594
$268$	−298.099	+	100.266i	−1.11231	+	0.374126i
$269$	24.3900	−	14.0816i	0.0906691	−	0.0523478i	−0.453980	−	0.891012i	$-0.649996\pi$
$269$	24.3900	−	14.0816i	0.0906691	−	0.0523478i	0.544649	+	0.838664i	$0.316663\pi$
$270$	−30.1822	−	184.409i	−0.111786	−	0.682996i
$271$	−346.164	−	199.858i	−1.27736	−	0.737482i	−0.300995	−	0.953626i	$-0.597319\pi$
$271$	−346.164	−	199.858i	−1.27736	−	0.737482i	−0.976362	+	0.216143i	$0.930652\pi$
$272$	24.6863	+	195.941i	0.0907584	+	0.720373i
$273$		0			0
$274$	−24.5269	+	64.8921i	−0.0895143	+	0.236833i
$275$	353.321	−	611.970i	1.28480	−	2.22534i
$276$	56.5982	+	11.4221i	0.205066	+	0.0413844i
$277$	−89.1579	+	51.4753i	−0.321870	+	0.185831i	−0.652226	−	0.758025i	$-0.726165\pi$
$277$	−89.1579	+	51.4753i	−0.321870	+	0.185831i	0.330356	+	0.943856i	$0.392831\pi$
$278$	−136.371	−	166.641i	−0.490542	−	0.599428i
$279$			145.283i			0.520726i
$280$		0			0
$281$	−150.235			−0.534646			−0.267323	−	0.963607i	$-0.586139\pi$
$281$	−150.235			−0.534646			−0.267323	+	0.963607i	$0.586139\pi$
$282$	−5.62081	+	4.59979i	−0.0199319	+	0.0163113i
$283$	89.2807	+	154.639i	0.315480	+	0.546427i	0.979539	−	0.201253i	$-0.0645013\pi$
$283$	89.2807	+	154.639i	0.315480	+	0.546427i	−0.664060	+	0.747679i	$0.731168\pi$
$284$	68.7519	+	13.8748i	0.242084	+	0.0488551i
$285$	−132.299	−	76.3830i	−0.464208	−	0.268011i
$286$	210.995	+	79.7486i	0.737745	+	0.278841i
$287$		0			0
$288$	269.338	+	64.7820i	0.935202	+	0.224937i
$289$	68.3234	−	118.340i	0.236413	−	0.409479i
$290$	−400.262	+	65.5109i	−1.38021	+	0.225900i
$291$	48.0660	+	83.2528i	0.165175	+	0.286092i
$292$	177.001	−	59.5344i	0.606168	−	0.203885i
$293$		−	219.189i		−	0.748085i	−0.927411	−	0.374043i	$-0.877971\pi$
$293$		−	219.189i		−	0.748085i	0.927411	−	0.374043i	$-0.122029\pi$
$294$		0			0
$295$			275.002i			0.932211i
$296$	−129.916	−	4.79657i	−0.438905	−	0.0162046i
$297$	64.5685	+	111.836i	0.217402	+	0.376552i
$298$	81.4635	+	497.730i	0.273368	+	1.67024i
$299$	111.296	−	192.771i	0.372229	−	0.644720i
$300$	99.4630	+	87.7181i	0.331543	+	0.292394i
$301$		0			0
$302$	438.683	+	165.807i	1.45259	+	0.549029i
$303$	−6.15507	−	3.55363i	−0.0203138	−	0.0117282i
$304$	368.028	−	279.153i	1.21062	−	0.918268i
$305$	−68.7990	−	119.163i	−0.225570	−	0.390699i
$306$	135.343	+	165.385i	0.442298	+	0.540475i
$307$	316.669			1.03150			0.515748	−	0.856741i	$-0.327514\pi$
$307$	316.669			1.03150			0.515748	+	0.856741i	$0.327514\pi$
$308$		0			0
$309$		−	62.4344i		−	0.202053i
$310$	−192.019	−	234.641i	−0.619416	−	0.756908i
$311$	62.5836	−	36.1326i	0.201233	−	0.116182i	−0.395997	−	0.918252i	$-0.629601\pi$
$311$	62.5836	−	36.1326i	0.201233	−	0.116182i	0.597231	+	0.802070i	$0.296268\pi$
$312$	−22.5042	+	35.8547i	−0.0721289	+	0.114919i
$313$	−40.9756	+	70.9718i	−0.130913	+	0.226747i	−0.924029	−	0.382323i	$-0.875124\pi$
$313$	−40.9756	+	70.9718i	−0.130913	+	0.226747i	0.793116	+	0.609071i	$0.208457\pi$
$314$	18.8894	+	7.13952i	0.0601573	+	0.0227373i
$315$		0			0
$316$	−214.392	+	243.098i	−0.678455	+	0.769296i
$317$	94.5267	+	54.5750i	0.298191	+	0.172161i	0.641630	−	0.767014i	$-0.278258\pi$
$317$	94.5267	+	54.5750i	0.298191	+	0.172161i	−0.343439	+	0.939175i	$0.611592\pi$
$318$	1.51673	+	9.26702i	0.00476960	+	0.0291416i
$319$	242.742	−	140.147i	0.760945	−	0.439332i
$320$	−520.621	+	251.355i	−1.62694	+	0.785483i
$321$	−37.2548			−0.116059
$322$		0			0
$323$	356.347			1.10324
$324$	272.415	−	91.6267i	0.840786	−	0.282799i
$325$	442.763	−	255.629i	1.36235	−	0.786552i
$326$	206.323	−	33.7689i	0.632892	−	0.103586i
$327$	66.3799	+	38.3245i	0.202997	+	0.117200i
$328$	49.2893	−	26.0815i	0.150272	−	0.0795166i
$329$		0			0
$330$	−123.598	−	46.7156i	−0.374539	−	0.141563i
$331$	−160.870	+	278.635i	−0.486012	+	0.841798i	−0.999871	−	0.0160770i	$-0.994882\pi$
$331$	−160.870	+	278.635i	−0.486012	+	0.841798i	0.513858	+	0.857875i	$0.328216\pi$
$332$	−31.9560	+	158.347i	−0.0962530	+	0.476948i
$333$	−121.831	+	70.3394i	−0.365860	+	0.211229i
$334$	459.329	−	375.892i	1.37524	−	1.12542i
$335$		−	710.254i		−	2.12016i
$336$		0			0
$337$	−164.049			−0.486792			−0.243396	−	0.969927i	$-0.578261\pi$
$337$	−164.049			−0.486792			−0.243396	+	0.969927i	$0.578261\pi$
$338$	−110.706	−	135.280i	−0.327533	−	0.400236i
$339$	40.4853	+	70.1226i	0.119426	+	0.206851i
$340$	−437.177	−	88.2267i	−1.28581	−	0.259490i
$341$	181.461	+	104.766i	0.532143	+	0.307233i
$342$	176.723	−	467.565i	0.516734	−	1.36715i
$343$		0			0
$344$	−161.421	+	85.4162i	−0.469248	+	0.248303i
$345$	−65.1960	+	112.923i	−0.188974	+	0.327312i
$346$	−12.9314	−	79.0089i	−0.0373740	−	0.228349i
$347$	165.154	+	286.056i	0.475949	+	0.824368i	0.999620	−	0.0275524i	$-0.00877132\pi$
$347$	165.154	+	286.056i	0.475949	+	0.824368i	−0.523671	+	0.851920i	$0.675438\pi$
$348$	16.7700	+	49.8587i	0.0481897	+	0.143272i
$349$			262.402i			0.751869i	0.926646	+	0.375934i	$0.122678\pi$
$349$			262.402i			0.751869i	−0.926646	+	0.375934i	$0.877322\pi$
$350$		0			0
$351$			93.4313i			0.266186i
$352$	275.139	−	289.693i	0.781646	−	0.822990i
$353$	289.049	+	500.647i	0.818835	+	1.41826i	0.906541	+	0.422118i	$0.138713\pi$
$353$	289.049	+	500.647i	0.818835	+	1.41826i	−0.0877061	+	0.996146i	$0.527954\pi$
$354$	35.1986	−	5.76096i	0.0994311	−	0.0162739i
$355$	−79.1960	+	137.171i	−0.223087	+	0.386398i
$356$	−335.823	−	296.168i	−0.943324	−	0.831934i
$357$		0			0
$358$	−208.451	+	551.509i	−0.582265	+	1.54053i
$359$	−316.198	−	182.557i	−0.880774	−	0.508515i	−0.00986020	−	0.999951i	$-0.503139\pi$
$359$	−316.198	−	182.557i	−0.880774	−	0.508515i	−0.870913	+	0.491437i	$0.836472\pi$
$360$	−332.571	+	529.867i	−0.923809	+	1.47185i
$361$	−236.240	−	409.180i	−0.654405	−	1.13346i
$362$	−62.6399	+	51.2614i	−0.173038	+	0.141606i
$363$	20.4335			0.0562908
$364$		0			0
$365$			421.725i			1.15541i
$366$	−13.8109	+	11.3022i	−0.0377348	+	0.0308803i
$367$	−450.395	+	260.036i	−1.22723	+	0.708544i	−0.966451	−	0.256853i	$-0.917314\pi$
$367$	−450.395	+	260.036i	−1.22723	+	0.708544i	−0.260784	+	0.965397i	$0.583981\pi$
$368$	−238.269	−	314.126i	−0.647469	−	0.853604i
$369$	30.1716	−	52.2587i	0.0817658	−	0.141622i
$370$	103.799	−	274.626i	0.280538	−	0.742233i
$371$		0			0
$372$	−26.0101	+	29.4927i	−0.0699196	+	0.0792814i
$373$	−456.145	−	263.356i	−1.22291	−	0.706048i	−0.257373	−	0.966312i	$-0.582857\pi$
$373$	−456.145	−	263.356i	−1.22291	−	0.706048i	−0.965537	+	0.260265i	$0.916190\pi$
$374$	304.168	−	49.7832i	0.813284	−	0.133110i
$375$	−144.800	+	83.6004i	−0.386134	+	0.222934i
$376$	49.5613	+	1.82983i	0.131812	+	0.00486657i
$377$	202.794			0.537915
$378$		0			0
$379$	121.976			0.321835			0.160918	−	0.986968i	$-0.448555\pi$
$379$	121.976			0.321835			0.160918	+	0.986968i	$0.448555\pi$
$380$	332.557	+	988.722i	0.875150	+	2.60190i
$381$	−58.0569	+	33.5191i	−0.152380	+	0.0879768i
$382$	50.6947	+	309.737i	0.132709	+	0.810831i
$383$	−274.033	−	158.213i	−0.715492	−	0.413089i	0.0975993	−	0.995226i	$-0.468884\pi$
$383$	−274.033	−	158.213i	−0.715492	−	0.413089i	−0.813091	+	0.582136i	$0.802217\pi$
$384$	43.0782	+	61.3707i	0.112183	+	0.159820i
$385$		0			0
$386$	184.770	−	488.854i	0.478678	−	1.26646i
$387$	−98.8112	+	171.146i	−0.255326	+	0.442238i
$388$	129.856	−	643.458i	0.334681	−	1.65840i
$389$	−79.8020	+	46.0737i	−0.205146	+	0.118441i	−0.599054	−	0.800709i	$-0.704456\pi$
$389$	−79.8020	+	46.0737i	−0.205146	+	0.118441i	0.393907	+	0.919150i	$0.371123\pi$
$390$	−60.5437	−	73.9826i	−0.155240	−	0.189699i
$391$		−	304.157i		−	0.777895i
$392$		0			0
$393$	−98.6173			−0.250935
$394$	224.867	−	184.020i	0.570727	−	0.467055i
$395$	−365.990	−	633.913i	−0.926557	−	1.60484i
$396$	85.5250	−	423.789i	0.215972	−	1.07017i
$397$	486.937	+	281.133i	1.22654	+	0.708144i	0.966305	−	0.257400i	$-0.0828659\pi$
$397$	486.937	+	281.133i	1.22654	+	0.708144i	0.260237	+	0.965545i	$0.416199\pi$
$398$	−730.573	−	276.131i	−1.83561	−	0.693795i
$399$		0			0
$400$	−113.196	−	898.465i	−0.282990	−	2.24616i
$401$	−40.6030	+	70.3265i	−0.101254	+	0.175378i	−0.912202	−	0.409741i	$-0.865619\pi$
$401$	−40.6030	+	70.3265i	−0.101254	+	0.175378i	0.810947	+	0.585119i	$0.198952\pi$
$402$	−90.9082	+	14.8789i	−0.226140	+	0.0370123i
$403$	75.7990	+	131.288i	0.188087	+	0.325776i
$404$	15.4718	+	45.9991i	0.0382966	+	0.113859i
$405$			649.058i			1.60261i
$406$		0			0
$407$			202.893i			0.498508i
$408$	−2.13416	+	57.8042i	−0.00523080	+	0.141677i
$409$	−225.368	−	390.348i	−0.551021	−	0.954396i	−0.998201	−	0.0599523i	$-0.980905\pi$
$409$	−225.368	−	390.348i	−0.551021	−	0.954396i	0.447180	−	0.894444i	$-0.352428\pi$
$410$	20.3407	+	124.279i	0.0496115	+	0.303119i
$411$	−10.1594	+	17.5966i	−0.0247187	+	0.0428140i
$412$	−281.990	+	319.746i	−0.684442	+	0.776084i
$413$		0			0
$414$	−399.085	−	150.840i	−0.963974	−	0.364348i
$415$	−315.928	−	182.401i	−0.761272	−	0.439521i
$416$	277.192	−	81.9814i	0.666327	−	0.197071i
$417$	−31.5341	−	54.6186i	−0.0756212	−	0.130980i
$418$	−456.558	−	557.901i	−1.09225	−	1.33469i
$419$	624.988			1.49162			0.745809	−	0.666160i	$-0.232063\pi$
$419$	624.988			1.49162			0.745809	+	0.666160i	$0.232063\pi$
$420$		0			0
$421$		−	566.476i		−	1.34555i	−0.739848	−	0.672774i	$-0.765103\pi$
$421$		−	566.476i		−	1.34555i	0.739848	−	0.672774i	$-0.234897\pi$
$422$	207.789	+	253.913i	0.492392	+	0.601688i
$423$	46.4771	−	26.8336i	0.109875	−	0.0634363i
$424$	34.0875	−	54.3098i	0.0803952	−	0.128089i
$425$	349.299	−	605.003i	0.821879	−	1.42354i
$426$	19.2162	+	7.26303i	0.0451084	+	0.0170494i
$427$		0			0
$428$	190.794	+	168.264i	0.445780	+	0.393141i
$429$	57.2147	+	33.0329i	0.133368	+	0.0769999i
$430$	−66.6154	−	407.010i	−0.154920	−	0.946535i
$431$	−250.739	+	144.764i	−0.581761	+	0.335880i	−0.761833	−	0.647774i	$-0.775700\pi$
$431$	−250.739	+	144.764i	−0.581761	+	0.335880i	0.180072	+	0.983653i	$0.442367\pi$
$432$	152.538	+	64.1813i	0.353097	+	0.148568i
$433$	−597.696			−1.38036			−0.690180	−	0.723638i	$-0.742468\pi$
$433$	−597.696			−1.38036			−0.690180	+	0.723638i	$0.742468\pi$
$434$		0			0
$435$	−118.794			−0.273090
$436$	−166.857	−	496.082i	−0.382700	−	1.13780i
$437$	−616.098	+	355.704i	−1.40984	+	0.813969i
$438$	53.9782	−	8.83461i	0.123238	−	0.0201704i
$439$	−33.2458	−	19.1945i	−0.0757308	−	0.0437232i	0.461656	−	0.887059i	$-0.347255\pi$
$439$	−33.2458	−	19.1945i	−0.0757308	−	0.0437232i	−0.537387	+	0.843336i	$0.680589\pi$
$440$	421.990	+	797.486i	0.959068	+	1.81247i
$441$		0			0
$442$	208.593	+	78.8407i	0.471930	+	0.178373i
$443$	−299.529	+	518.799i	−0.676138	+	1.17110i	0.299997	+	0.953940i	$0.403014\pi$
$443$	−299.529	+	518.799i	−0.676138	+	1.17110i	−0.976135	+	0.217165i	$0.930319\pi$
$444$	−37.3250	−	7.53255i	−0.0840652	−	0.0169652i
$445$	875.709	−	505.591i	1.96789	−	1.13616i
$446$	16.3802	−	13.4048i	0.0367270	−	0.0300555i
$447$			147.721i			0.330473i
$448$		0			0
$449$	−460.039			−1.02459			−0.512293	−	0.858811i	$-0.671204\pi$
$449$	−460.039			−1.02459			−0.512293	+	0.858811i	$0.671204\pi$
$450$	−620.599	−	758.354i	−1.37911	−	1.68523i
$451$	−43.5147	−	75.3697i	−0.0964850	−	0.167117i
$452$	109.376	−	541.975i	0.241982	−	1.19906i
$453$	118.956	+	68.6794i	0.262596	+	0.151610i
$454$	151.184	−	399.995i	0.333004	−	0.881045i
$455$		0			0
$456$	119.584	−	63.2777i	0.262245	−	0.138767i
$457$	−133.161	+	230.642i	−0.291382	+	0.504688i	−0.974137	−	0.225959i	$-0.927448\pi$
$457$	−133.161	+	230.642i	−0.291382	+	0.504688i	0.682755	+	0.730647i	$0.260782\pi$
$458$	74.9549	+	457.963i	0.163657	+	0.999920i
$459$	63.8335	+	110.563i	0.139071	+	0.240878i
$460$	843.914	−	283.851i	1.83460	−	0.617067i
$461$			763.123i			1.65537i	0.561196	+	0.827683i	$0.310341\pi$
$461$			763.123i			1.65537i	−0.561196	+	0.827683i	$0.689659\pi$
$462$		0			0
$463$		−	123.988i		−	0.267792i	−0.990995	−	0.133896i	$-0.957251\pi$
$463$		−	123.988i		−	0.267792i	0.990995	−	0.133896i	$-0.0427488\pi$
$464$	139.306	−	331.086i	0.300229	−	0.713547i
$465$	−44.4020	−	76.9066i	−0.0954882	−	0.165390i
$466$	−380.661	+	62.3028i	−0.816869	+	0.133697i
$467$	384.359	−	665.729i	0.823038	−	1.42554i	−0.0803710	−	0.996765i	$-0.525610\pi$
$467$	384.359	−	665.729i	0.823038	−	1.42554i	0.903409	−	0.428779i	$-0.141056\pi$
$468$	206.894	−	234.596i	0.442082	−	0.501274i
$469$		0			0
$470$	−39.5980	+	104.766i	−0.0842510	+	0.222907i
$471$	5.12217	+	2.95729i	0.0108751	+	0.00627874i
$472$	−206.283	−	129.474i	−0.437041	−	0.274309i
$473$	142.510	+	246.834i	0.301289	+	0.521848i
$474$	−73.4700	+	60.1242i	−0.155000	+	0.126844i
$475$	−1633.99			−3.43997
$476$		0			0
$477$		−	69.3859i		−	0.145463i
$478$	−507.546	+	415.351i	−1.06181	+	0.868934i
$479$	103.041	−	59.4905i	0.215116	−	0.124197i	−0.388571	−	0.921419i	$-0.627031\pi$
$479$	103.041	−	59.4905i	0.215116	−	0.124197i	0.603687	+	0.797222i	$0.293698\pi$
$480$	−162.375	+	48.0236i	−0.338282	+	0.100049i
$481$	−73.3970	+	127.127i	−0.152592	+	0.264298i
$482$	−50.8213	+	134.460i	−0.105438	+	0.278964i
$483$		0			0
$484$	−104.647	−	92.2898i	−0.216212	−	0.190681i
$485$	1283.81	+	741.205i	2.64702	+	1.52826i
$486$	266.807	−	43.6684i	0.548987	−	0.0898527i
$487$	244.719	−	141.288i	0.502503	−	0.290120i	−0.227244	−	0.973838i	$-0.572971\pi$
$487$	244.719	−	141.288i	0.502503	−	0.290120i	0.729746	+	0.683718i	$0.239638\pi$
$488$	121.777	+	4.49609i	0.249544	+	0.00921330i
$489$	61.2346			0.125224
$490$		0			0
$491$	−388.049			−0.790323			−0.395162	−	0.918612i	$-0.629311\pi$
$491$	−388.049			−0.790323			−0.395162	+	0.918612i	$0.629311\pi$
$492$	15.4808	−	5.20698i	0.0314651	−	0.0105833i
$493$	239.978	−	138.551i	0.486771	−	0.281037i
$494$	−84.2454	−	514.727i	−0.170537	−	1.04196i
$495$	845.530	+	488.167i	1.70814	+	0.986195i
$496$	266.412	−	33.5648i	0.537121	−	0.0676709i
$497$		0			0
$498$	−16.7279	+	44.2579i	−0.0335902	+	0.0888713i
$499$	13.8579	−	24.0025i	0.0277713	−	0.0481013i	−0.851806	−	0.523858i	$-0.824492\pi$
$499$	13.8579	−	24.0025i	0.0277713	−	0.0481013i	0.879577	+	0.475757i	$0.157826\pi$
$500$	1119.16	+	225.857i	2.23831	+	0.451714i
$501$	150.551	−	86.9204i	0.300500	−	0.173494i
$502$	325.422	+	397.656i	0.648250	+	0.792143i
$503$		−	727.477i		−	1.44628i	−0.690703	−	0.723138i	$-0.742699\pi$
$503$		−	727.477i		−	1.44628i	0.690703	−	0.723138i	$-0.257301\pi$
$504$		0			0
$505$	−109.598			−0.217026
$506$	−476.191	+	389.691i	−0.941089	+	0.770140i
$507$	−25.5995	−	44.3396i	−0.0504920	−	0.0874548i
$508$	448.720	+	90.5562i	0.883307	+	0.178260i
$509$	−549.218	−	317.091i	−1.07901	−	0.622969i	−0.148384	−	0.988930i	$-0.547407\pi$
$509$	−549.218	−	317.091i	−1.07901	−	0.622969i	−0.930630	+	0.365961i	$0.880740\pi$
$510$	−122.191	−	46.1838i	−0.239590	−	0.0905565i
$511$		0			0
$512$	56.5685	−	508.865i	0.110485	−	0.993878i
$513$	149.304	−	258.601i	0.291040	−	0.504096i
$514$	630.318	−	103.164i	1.22630	−	0.200709i
$515$	−481.387	−	833.787i	−0.934732	−	1.61900i
$516$	−50.6993	+	17.0527i	−0.0982545	+	0.0330479i
$517$		−	77.4010i		−	0.149712i
$518$		0			0
$519$		−	23.4491i		−	0.0451813i
$520$	−24.0847	+	652.339i	−0.0463168	+	1.25450i
$521$	−416.563	−	721.509i	−0.799546	−	1.38485i	−0.919912	−	0.392125i	$-0.871740\pi$
$521$	−416.563	−	721.509i	−0.799546	−	1.38485i	0.120366	−	0.992730i	$-0.461593\pi$
$522$	−62.7819	−	383.588i	−0.120272	−	0.734843i
$523$	−438.217	+	759.014i	−0.837891	+	1.45127i	0.0537645	+	0.998554i	$0.482878\pi$
$523$	−438.217	+	759.014i	−0.837891	+	1.45127i	−0.891655	+	0.452715i	$0.850455\pi$
$524$	505.051	+	445.413i	0.963838	+	0.850025i
$525$		0			0
$526$	705.970	+	266.831i	1.34215	+	0.507284i
$527$	179.395	+	103.574i	0.340408	+	0.196535i
$528$	93.2332	−	70.7185i	0.176578	−	0.133937i
$529$	39.1081	+	67.7372i	0.0739283	+	0.128048i
$530$	91.7067	+	112.063i	0.173032	+	0.211439i
$531$	−263.546			−0.496321
$532$		0			0
$533$		−	62.9662i		−	0.118135i
$534$	−83.0576	−	101.494i	−0.155539	−	0.190064i
$535$	−497.524	+	287.245i	−0.929951	+	0.536907i
$536$	532.772	+	334.394i	0.993977	+	0.623870i
$537$	−86.3431	+	149.551i	−0.160788	+	0.278493i
$538$	−52.6884	−	19.9143i	−0.0979338	−	0.0370155i
$539$		0			0
$540$	−247.196	+	280.294i	−0.457770	+	0.519063i
$541$	351.532	+	202.957i	0.649783	+	0.375152i	0.788373	−	0.615198i	$-0.210924\pi$
$541$	351.532	+	202.957i	0.649783	+	0.375152i	−0.138590	+	0.990350i	$0.544257\pi$
$542$	129.125	+	788.934i	0.238238	+	1.45560i
$543$	−20.5310	+	11.8536i	−0.0378103	+	0.0218298i
$544$	272.007	−	286.395i	0.500013	−	0.526461i
$545$	1181.97			2.16875
$546$		0			0
$547$	−606.024			−1.10791			−0.553953	−	0.832548i	$-0.686881\pi$
$547$	−606.024			−1.10791			−0.553953	+	0.832548i	$0.686881\pi$
$548$	131.506	−	44.2320i	0.239974	−	0.0807153i
$549$	114.199	−	65.9329i	0.208013	−	0.120096i
$550$	−1394.73	+	228.275i	−2.53587	+	0.415045i
$551$	−561.298	−	324.066i	−1.01869	−	0.588141i
$552$	−54.0101	−	102.069i	−0.0978444	−	0.184909i
$553$		0			0
$554$	192.603	+	72.7971i	0.347659	+	0.131403i
$555$	42.9949	−	74.4694i	0.0774684	−	0.134179i
$556$	−85.1932	+	422.145i	−0.153225	+	0.759254i
$557$	31.5616	−	18.2221i	0.0566635	−	0.0327147i	−0.471401	−	0.881919i	$-0.656251\pi$
$557$	31.5616	−	18.2221i	0.0566635	−	0.0327147i	0.528064	+	0.849204i	$0.322918\pi$
$558$	224.867	−	184.020i	0.402987	−	0.329784i
$559$			206.213i			0.368896i
$560$		0			0
$561$	90.2742			0.160917
$562$	190.293	+	232.533i	0.338600	+	0.413759i
$563$	93.1945	+	161.418i	0.165532	+	0.286710i	0.936844	−	0.349747i	$-0.113733\pi$
$563$	93.1945	+	161.418i	0.165532	+	0.286710i	−0.771312	+	0.636457i	$0.780399\pi$
$564$	14.2390	+	2.87357i	0.0252464	+	0.00509499i
$565$	1081.33	+	624.306i	1.91386	+	1.10497i
$566$	126.262	−	334.058i	0.223078	−	0.590208i
$567$		0			0
$568$	−65.6081	−	123.988i	−0.115507	−	0.218288i
$569$	335.446	−	581.009i	0.589536	−	1.02111i	−0.404758	−	0.914424i	$-0.632644\pi$
$569$	335.446	−	581.009i	0.589536	−	1.02111i	0.994293	−	0.106682i	$-0.0340225\pi$
$570$	49.3498	+	301.520i	0.0865786	+	0.528983i
$571$	338.541	+	586.371i	0.592892	+	1.02692i	0.993841	+	0.110818i	$0.0353471\pi$
$571$	338.541	+	586.371i	0.592892	+	1.02692i	−0.400949	+	0.916100i	$0.631320\pi$
$572$	−143.819	−	427.587i	−0.251432	−	0.747530i
$573$			91.9271i			0.160431i
$574$		0			0
$575$			1394.67i			2.42552i
$576$	−240.884	−	498.933i	−0.418201	−	0.866203i
$577$	−463.950	−	803.586i	−0.804073	−	1.39270i	−0.916915	−	0.399083i	$-0.869329\pi$
$577$	−463.950	−	803.586i	−0.804073	−	1.39270i	0.112841	−	0.993613i	$-0.464005\pi$
$578$	−269.705	+	44.1426i	−0.466618	+	0.0763713i
$579$	76.5341	−	132.561i	0.132183	−	0.228948i
$580$	608.382	+	536.542i	1.04893	+	0.925073i
$581$		0			0
$582$	67.9756	−	179.847i	0.116797	−	0.309015i
$583$	−86.6642	−	50.0356i	−0.148652	−	0.0858244i
$584$	−316.342	−	198.552i	−0.541681	−	0.339986i
$585$	353.191	+	611.745i	0.603745	+	1.04572i
$586$	−339.258	+	277.632i	−0.578938	+	0.473774i
$587$	−321.120			−0.547053			−0.273526	−	0.961865i	$-0.588190\pi$
$587$	−321.120			−0.547053			−0.273526	+	0.961865i	$0.588190\pi$
$588$		0			0
$589$		−	484.508i		−	0.822595i
$590$	425.645	−	348.327i	0.721432	−	0.590384i
$591$	73.7028	−	42.5523i	0.124709	−	0.0720005i
$592$	157.132	+	207.158i	0.265425	+	0.349929i
$593$	109.627	−	189.880i	0.184869	−	0.320203i	−0.758663	−	0.651483i	$-0.774147\pi$
$593$	109.627	−	189.880i	0.184869	−	0.320203i	0.943532	+	0.331280i	$0.107481\pi$
$594$	91.3137	−	241.593i	0.153727	−	0.406723i
$595$		0			0
$596$	667.196	−	756.529i	1.11946	−	1.26934i
$597$	−198.107	−	114.377i	−0.331837	−	0.191586i
$598$	−439.340	+	71.9068i	−0.734683	+	0.120246i
$599$	134.062	−	77.4010i	0.223811	−	0.129217i	−0.383903	−	0.923373i	$-0.625420\pi$
$599$	134.062	−	77.4010i	0.223811	−	0.129217i	0.607713	+	0.794156i	$0.292087\pi$
$600$	9.78595	−	265.054i	0.0163099	−	0.441757i
$601$	205.862			0.342533			0.171266	−	0.985225i	$-0.445214\pi$
$601$	205.862			0.342533			0.171266	+	0.985225i	$0.445214\pi$
$602$		0			0
$603$	680.666			1.12880
$604$	−299.017	−	889.004i	−0.495061	−	1.47186i
$605$	272.882	−	157.548i	0.451045	−	0.260411i
$606$	2.29594	+	14.0279i	0.00378868	+	0.0231483i
$607$	−684.735	−	395.332i	−1.12806	−	0.651288i	−0.184616	−	0.982811i	$-0.559104\pi$
$607$	−684.735	−	395.332i	−1.12806	−	0.651288i	−0.943447	+	0.331523i	$0.892438\pi$
$608$	−898.225	−	216.044i	−1.47734	−	0.355335i
$609$		0			0
$610$	−97.2965	+	257.422i	−0.159502	+	0.422004i
$611$	28.0000	−	48.4974i	0.0458265	−	0.0793739i
$612$	84.5513	−	418.965i	0.138156	−	0.684583i
$613$	642.133	−	370.736i	1.04753	−	0.604789i	0.125570	−	0.992085i	$-0.459924\pi$
$613$	642.133	−	370.736i	1.04753	−	0.604789i	0.921955	+	0.387296i	$0.126591\pi$
$614$	−401.103	−	490.136i	−0.653262	−	0.798267i
$615$			36.8848i			0.0599752i
$616$		0			0
$617$	171.578			0.278084			0.139042	−	0.990286i	$-0.455598\pi$
$617$	171.578			0.278084			0.139042	+	0.990286i	$0.455598\pi$
$618$	−96.6351	+	79.0814i	−0.156368	+	0.127963i
$619$	270.099	+	467.825i	0.436347	+	0.755776i	0.997405	−	0.0720012i	$-0.0229386\pi$
$619$	270.099	+	467.825i	0.436347	+	0.755776i	−0.561057	+	0.827777i	$0.689605\pi$
$620$	−119.958	+	594.408i	−0.193480	+	0.958723i
$621$	−220.727	−	127.437i	−0.355438	−	0.205212i
$622$	−135.196	−	51.0993i	−0.217357	−	0.0821532i
$623$		0			0
$624$	84.0000	−	10.5830i	0.134615	−	0.0169599i
$625$	−581.691	+	1007.52i	−0.930705	+	1.61203i
$626$	161.750	−	26.4737i	0.258387	−	0.0422902i
$627$	−105.574	−	182.859i	−0.168379	−	0.291641i
$628$	−12.8755	−	38.2799i	−0.0205023	−	0.0609552i
$629$			200.583i			0.318892i
$630$		0			0
$631$			269.399i			0.426940i	0.976950	+	0.213470i	$0.0684766\pi$
$631$			269.399i			0.426940i	−0.976950	+	0.213470i	$0.931523\pi$
$632$	647.819	+	23.9178i	1.02503	+	0.0378447i
$633$	48.0488	+	83.2229i	0.0759064	+	0.131474i
$634$	−35.2600	−	215.434i	−0.0556152	−	0.339801i
$635$	−516.884	+	895.270i	−0.813991	+	1.40987i
$636$	12.4222	−	14.0855i	0.0195318	−	0.0221470i
$637$		0			0
$638$	−524.382	−	198.198i	−0.821915	−	0.310655i
$639$	−131.457	−	75.8968i	−0.205723	−	0.118774i
$640$	1048.48	+	487.437i	1.63825	+	0.761620i
$641$	−18.0934	−	31.3386i	−0.0282268	−	0.0488902i	0.851567	−	0.524246i	$-0.175653\pi$
$641$	−18.0934	−	31.3386i	−0.0282268	−	0.0488902i	−0.879794	+	0.475356i	$0.842319\pi$
$642$	47.1882	+	57.6625i	0.0735018	+	0.0898170i
$643$	266.297			0.414148			0.207074	−	0.978325i	$-0.433606\pi$
$643$	266.297			0.414148			0.207074	+	0.978325i	$0.433606\pi$
$644$		0			0
$645$		−	120.797i		−	0.187282i
$646$	−451.361	−	551.550i	−0.698701	−	0.853792i
$647$	−940.708	+	543.118i	−1.45395	+	0.839440i	−0.998703	−	0.0509233i	$-0.983784\pi$
$647$	−940.708	+	543.118i	−1.45395	+	0.839440i	−0.455250	+	0.890363i	$0.650450\pi$
$648$	−486.868	−	305.583i	−0.751339	−	0.471578i
$649$	−190.049	+	329.174i	−0.292833	+	0.507202i
$650$	−956.477	−	361.514i	−1.47150	−	0.556176i
$651$		0			0
$652$	−313.602	−	276.571i	−0.480985	−	0.424189i
$653$	−1035.20	−	597.674i	−1.58530	−	0.915274i	−0.994066	−	0.108774i	$-0.965307\pi$
$653$	−1035.20	−	597.674i	−1.58530	−	0.915274i	−0.591234	−	0.806500i	$-0.701359\pi$
$654$	−24.7608	−	151.285i	−0.0378606	−	0.231322i
$655$	−1317.00	+	760.368i	−2.01068	+	1.16087i
$656$	−102.800	−	43.2538i	−0.156707	−	0.0659356i
$657$	−404.156			−0.615154
$658$		0			0
$659$	−685.220			−1.03979			−0.519894	−	0.854231i	$-0.674029\pi$
$659$	−685.220			−1.03979			−0.519894	+	0.854231i	$0.674029\pi$
$660$	84.2473	+	250.475i	0.127647	+	0.379507i
$661$	−860.294	+	496.691i	−1.30150	+	0.751423i	−0.980662	−	0.195710i	$-0.937299\pi$
$661$	−860.294	+	496.691i	−1.30150	+	0.751423i	−0.320842	+	0.947133i	$0.603966\pi$
$662$	635.031	−	103.936i	0.959261	−	0.157002i
$663$	56.5634	+	32.6569i	0.0853143	+	0.0492563i
$664$	285.563	−	151.106i	0.430065	−	0.227569i
$665$		0			0
$666$	263.186	+	99.4749i	0.395174	+	0.149362i
$667$	−276.603	+	479.091i	−0.414697	+	0.718277i
$668$	−1163.60	−	234.826i	−1.74192	−	0.351536i
$669$	5.36882	−	3.09969i	0.00802514	−	0.00463332i
$670$	−1099.32	+	899.630i	−1.64078	+	1.34273i
$671$		−	190.183i		−	0.283432i
$672$		0			0
$673$	106.569			0.158349			0.0791743	−	0.996861i	$-0.474772\pi$
$673$	106.569			0.158349			0.0791743	+	0.996861i	$0.474772\pi$
$674$	207.789	+	253.913i	0.308293	+	0.376725i
$675$	−292.701	−	506.972i	−0.433630	−	0.751070i
$676$	−69.1602	+	342.699i	−0.102308	+	0.506951i
$677$	−869.650	−	502.092i	−1.28456	−	0.741643i	−0.306885	−	0.951747i	$-0.599287\pi$
$677$	−869.650	−	502.092i	−1.28456	−	0.741643i	−0.977679	+	0.210103i	$0.932620\pi$
$678$	57.2548	−	151.482i	0.0844467	−	0.223425i
$679$		0			0
$680$	417.186	+	788.407i	0.613509	+	1.15942i
$681$	62.6224	−	108.465i	0.0919565	−	0.159273i
$682$	−67.6879	−	413.563i	−0.0992491	−	0.606397i
$683$	339.113	+	587.360i	0.496505	+	0.859971i	0.999992	−	0.00403135i	$-0.00128322\pi$
$683$	339.113	+	587.360i	0.496505	+	0.859971i	−0.503487	+	0.864003i	$0.667950\pi$
$684$	−947.533	+	318.703i	−1.38528	+	0.465940i
$685$			313.327i			0.457411i
$686$		0			0
$687$			135.919i			0.197844i
$688$	336.667	+	141.655i	0.489342	+	0.205894i
$689$	−36.2010	−	62.7020i	−0.0525414	−	0.0910043i
$690$	257.360	−	42.1221i	0.372985	−	0.0610465i
$691$	182.587	−	316.250i	0.264236	−	0.457671i	−0.703127	−	0.711064i	$-0.748213\pi$
$691$	182.587	−	316.250i	0.264236	−	0.457671i	0.967363	+	0.253394i	$0.0815468\pi$
$692$	−105.910	+	120.090i	−0.153049	+	0.173541i
$693$		0			0
$694$	233.563	−	617.951i	0.336547	−	0.890419i
$695$	−842.250	−	486.273i	−1.21187	−	0.699673i
$696$	55.9293	−	89.1091i	0.0803582	−	0.128030i
$697$	−43.0193	−	74.5117i	−0.0617207	−	0.106903i
$698$	406.143	−	332.367i	0.581866	−	0.476170i
$699$	−112.976			−0.161626
$700$		0			0
$701$			940.292i			1.34136i	0.741748	+	0.670679i	$0.233997\pi$
$701$			940.292i			1.34136i	−0.741748	+	0.670679i	$0.766003\pi$
$702$	144.612	−	118.343i	0.206000	−	0.168580i
$703$	406.300	−	234.577i	0.577951	−	0.333680i
$704$	−796.883	−	58.9231i	−1.13194	−	0.0836975i
$705$	−16.4020	+	28.4091i	−0.0232653	+	0.0402966i
$706$	408.777	−	1081.52i	0.579004	−	1.53190i
$707$		0			0
$708$	−53.5004	−	47.1829i	−0.0755656	−	0.0666426i
$709$	915.785	+	528.729i	1.29166	+	0.745738i	0.978948	−	0.204110i	$-0.0654302\pi$
$709$	915.785	+	528.729i	1.29166	+	0.745738i	0.312709	+	0.949849i	$0.398764\pi$
$710$	312.624	−	51.1672i	0.440316	−	0.0720665i
$711$	607.505	−	350.743i	0.854438	−	0.493310i
$712$	−33.0409	+	894.919i	−0.0464058	+	1.25691i
$713$	−413.547			−0.580010
$714$		0			0
$715$	1018.77			1.42486
$716$	1117.65	−	375.921i	1.56096	−	0.525030i
$717$	−166.354	+	96.0448i	−0.232015	+	0.133954i
$718$	117.947	+	720.639i	0.164272	+	1.00368i
$719$	896.185	+	517.412i	1.24643	+	0.719628i	0.970396	−	0.241520i	$-0.0776458\pi$
$719$	896.185	+	517.412i	1.24643	+	0.719628i	0.276036	+	0.961147i	$0.410979\pi$
$720$	1241.37	−	156.397i	1.72412	−	0.217219i
$721$		0			0
$722$	−334.094	+	883.930i	−0.462734	+	1.22428i
$723$	−21.0509	+	36.4612i	−0.0291160	+	0.0504304i
$724$	158.683	+	32.0239i	0.219176	+	0.0442319i
$725$	−1100.39	+	635.311i	−1.51778	+	0.876291i
$726$	−25.8818	−	31.6268i	−0.0356498	−	0.0435631i
$727$		−	495.145i		−	0.681080i	−0.940230	−	0.340540i	$-0.889390\pi$
$727$		−	495.145i		−	0.681080i	0.940230	−	0.340540i	$-0.110610\pi$
$728$		0			0
$729$	−567.489			−0.778449
$730$	652.740	−	534.170i	0.894164	−	0.731740i
$731$	140.887	+	244.024i	0.192732	+	0.333822i
$732$	34.9867	+	7.06067i	0.0477961	+	0.00964573i
$733$	491.464	+	283.747i	0.670483	+	0.387103i	0.796260	−	0.604955i	$-0.206809\pi$
$733$	491.464	+	283.747i	0.670483	+	0.387103i	−0.125777	+	0.992059i	$0.540142\pi$
$734$	972.965	+	367.746i	1.32556	+	0.501016i
$735$		0			0
$736$	−184.402	+	766.672i	−0.250546	+	1.04167i
$737$	490.843	−	850.165i	0.666001	−	1.15355i
$738$	−119.102	+	19.4934i	−0.161384	+	0.0264138i
$739$	272.350	+	471.725i	0.368539	+	0.638328i	0.989337	−	0.145642i	$-0.0465248\pi$
$739$	272.350	+	471.725i	0.368539	+	0.638328i	−0.620798	+	0.783970i	$0.713191\pi$
$740$	−556.538	+	187.192i	−0.752078	+	0.252962i
$741$		−	152.766i		−	0.206162i
$742$		0			0
$743$		−	731.264i		−	0.984205i	−0.870537	−	0.492102i	$-0.836229\pi$
$743$		−	731.264i		−	0.984205i	0.870537	−	0.492102i	$-0.163771\pi$
$744$	78.5936	+	2.90172i	0.105637	+	0.00390016i
$745$	1138.97	+	1972.76i	1.52883	+	2.64800i
$746$	170.150	+	1039.59i	0.228083	+	1.39355i
$747$	174.803	−	302.767i	0.234006	−	0.405310i
$748$	−462.323	−	407.731i	−0.618079	−	0.545094i
$749$		0			0
$750$	312.804	+	118.229i	0.417072	+	0.157638i
$751$	577.000	+	333.131i	0.768309	+	0.443583i	0.832271	−	0.554369i	$-0.187040\pi$
$751$	577.000	+	333.131i	0.768309	+	0.443583i	−0.0639622	+	0.997952i	$0.520374\pi$
$752$	−59.9437	−	79.0280i	−0.0797124	−	0.105090i
$753$	75.2498	+	130.336i	0.0999333	+	0.173090i
$754$	−256.865	−	313.882i	−0.340670	−	0.416289i
$755$	2118.15			2.80550
$756$		0			0
$757$			238.623i			0.315222i	0.987501	+	0.157611i	$0.0503791\pi$
$757$			238.623i			0.315222i	−0.987501	+	0.157611i	$0.949621\pi$
$758$	−154.498	−	188.792i	−0.203823	−	0.249066i
$759$	−156.077	+	90.1113i	−0.205636	+	0.118724i
$760$	1109.10	−	1767.07i	1.45935	−	2.32510i
$761$	−307.465	+	532.545i	−0.404028	+	0.699797i	−0.994208	−	0.107475i	$-0.965723\pi$
$761$	−307.465	+	532.545i	−0.404028	+	0.699797i	0.590180	+	0.807272i	$0.299057\pi$
$762$	125.417	+	47.4032i	0.164589	+	0.0622090i
$763$		0			0
$764$	415.196	−	470.788i	0.543450	−	0.616215i
$765$	835.904	+	482.609i	1.09268	+	0.630862i
$766$	102.219	+	624.543i	0.133445	+	0.815331i
$767$	−238.159	+	137.501i	−0.310507	+	0.179271i
$768$	40.4246	−	144.410i	0.0526362	−	0.188034i
$769$	178.950			0.232705			0.116353	−	0.993208i	$-0.462880\pi$
$769$	178.950			0.232705			0.116353	+	0.993208i	$0.462880\pi$
$770$		0			0
$771$	187.072			0.242636
$772$	−990.677	+	333.215i	−1.28326	+	0.431625i
$773$	546.994	−	315.807i	0.707625	−	0.408548i	−0.102556	−	0.994727i	$-0.532702\pi$
$773$	546.994	−	315.807i	0.707625	−	0.408548i	0.810181	+	0.586180i	$0.199369\pi$
$774$	390.055	−	63.8403i	0.503947	−	0.0824810i
$775$	−822.593	−	474.925i	−1.06141	−	0.612806i
$776$	−1160.42	+	614.035i	−1.49538	+	0.791282i
$777$		0			0
$778$	172.392	+	65.1580i	0.221583	+	0.0837507i
$779$	−100.620	+	174.279i	−0.129166	+	0.223722i
$780$	−37.8228	+	187.418i	−0.0484907	+	0.240279i
$781$	−189.593	+	109.462i	−0.242757	+	0.140156i
$782$	−470.770	+	385.255i	−0.602007	+	0.492653i
$783$		−	232.203i		−	0.296556i
$784$		0			0
$785$	91.2061			0.116186
$786$	124.912	+	152.639i	0.158921	+	0.194197i
$787$	−228.327	−	395.475i	−0.290124	−	0.502509i	0.683715	−	0.729749i	$-0.260363\pi$
$787$	−228.327	−	395.475i	−0.290124	−	0.502509i	−0.973839	+	0.227240i	$0.927030\pi$
$788$	−569.646	−	114.960i	−0.722901	−	0.145889i
$789$	191.435	+	110.525i	0.242630	+	0.140083i
$790$	−517.588	+	1369.41i	−0.655175	+	1.73343i
$791$		0			0
$792$	−764.264	+	404.411i	−0.964980	+	0.510619i
$793$	68.7990	−	119.163i	0.0867579	−	0.150269i
$794$	−181.636	−	1109.77i	−0.228760	−	1.39769i
$795$	21.2061	+	36.7300i	0.0266743	+	0.0462012i
$796$	497.975	+	1480.53i	0.625597	+	1.85996i
$797$		−	218.566i		−	0.274236i	−0.990555	−	0.137118i	$-0.956216\pi$
$797$		−	218.566i		−	0.274236i	0.990555	−	0.137118i	$-0.0437839\pi$
$798$		0			0
$799$		−	76.5199i		−	0.0957695i
$800$	−1247.25	+	1313.23i	−1.55907	+	1.64153i
$801$	484.529	+	839.229i	0.604905	+	1.04773i
$802$	160.280	−	26.2330i	0.199850	−	0.0327094i
$803$	−291.446	+	504.799i	−0.362946	+	0.628641i
$804$	138.177	+	121.860i	0.171861	+	0.151568i
$805$		0			0
$806$	107.196	−	283.614i	0.132997	−	0.351878i
$807$	−14.2873	−	8.24879i	−0.0177042	−	0.0102215i
$808$	51.5997	−	82.2110i	0.0638611	−	0.101746i
$809$	−673.730	−	1166.93i	−0.832794	−	1.44244i	−0.895814	−	0.444429i	$-0.853407\pi$
$809$	−673.730	−	1166.93i	−0.832794	−	1.44244i	0.0630207	−	0.998012i	$-0.479927\pi$
$810$	1004.60	−	822.117i	1.24025	−	1.01496i
$811$	−672.620			−0.829371			−0.414686	−	0.909965i	$-0.636108\pi$
$811$	−672.620			−0.829371			−0.414686	+	0.909965i	$0.636108\pi$
$812$		0			0
$813$			234.148i			0.288005i
$814$	314.035	−	256.991i	0.385792	−	0.315713i
$815$	817.764	−	472.136i	1.00339	−	0.579308i
$816$	92.1718	−	69.9134i	0.112956	−	0.0856782i
$817$	329.529	−	570.761i	0.403340	−	0.698606i
$818$	−318.718	+	843.248i	−0.389631	+	1.03087i
$819$		0			0
$820$	166.593	−	188.899i	0.203162	−	0.230364i
$821$	−1006.82	−	581.286i	−1.22633	−	0.708022i	−0.260070	−	0.965590i	$-0.583746\pi$
$821$	−1006.82	−	581.286i	−1.22633	−	0.708022i	−0.966260	+	0.257567i	$0.917079\pi$
$822$	40.1039	−	6.56381i	0.0487882	−	0.00798517i
$823$	902.093	−	520.824i	1.09610	−	0.632835i	0.160908	−	0.986969i	$-0.448558\pi$
$823$	902.093	−	520.824i	1.09610	−	0.632835i	0.935195	+	0.354134i	$0.115224\pi$
$824$	852.077	+	31.4592i	1.03407	+	0.0381786i
$825$	−413.941			−0.501747
$826$		0			0
$827$	278.432			0.336678			0.168339	−	0.985729i	$-0.446160\pi$
$827$	278.432			0.336678			0.168339	+	0.985729i	$0.446160\pi$
$828$	272.026	+	808.758i	0.328534	+	0.976761i
$829$	922.956	−	532.869i	1.11334	−	0.642785i	0.173645	−	0.984808i	$-0.444445\pi$
$829$	922.956	−	532.869i	1.11334	−	0.642785i	0.939692	+	0.342023i	$0.111112\pi$
$830$	117.846	+	720.024i	0.141984	+	0.867499i
$831$	52.2275	+	30.1535i	0.0628489	+	0.0362859i
$832$	−477.990	−	325.194i	−0.574507	−	0.390858i
$833$		0			0
$834$	−44.5959	+	117.990i	−0.0534723	+	0.141474i
$835$	1340.36	−	2321.57i	1.60522	−	2.78033i
$836$	−285.220	+	1413.31i	−0.341173	+	1.69056i
$837$	150.327	−	86.7913i	0.179602	−	0.103693i
$838$	−791.629	−	967.348i	−0.944665	−	1.15435i
$839$		−	305.844i		−	0.364533i	−0.983249	−	0.182267i	$-0.941657\pi$
$839$		−	305.844i		−	0.364533i	0.983249	−	0.182267i	$-0.0583434\pi$
$840$		0			0
$841$	337.000			0.400713
$842$	−876.783	+	717.516i	−1.04131	+	0.852157i
$843$	44.0030	+	76.2154i	0.0521981	+	0.0904097i
$844$	129.810	−	643.227i	0.153803	−	0.762118i
$845$	−683.741	−	394.758i	−0.809161	−	0.467169i
$846$	−100.402	−	37.9484i	−0.118679	−	0.0448563i
$847$		0			0
$848$	−127.236	+	16.0303i	−0.150043	+	0.0189036i
$849$	52.2994	−	90.5853i	0.0616012	−	0.106696i
$850$	−1378.85	+	225.676i	−1.62217	+	0.265501i
$851$	−200.221	−	346.793i	−0.235278	−	0.407513i
$852$	−13.0982	−	38.9421i	−0.0153735	−	0.0457067i
$853$			164.018i			0.192283i	0.995368	+	0.0961417i	$0.0306502\pi$
$853$			164.018i			0.192283i	−0.995368	+	0.0961417i	$0.969350\pi$
$854$		0			0
$855$		−	2257.60i		−	2.64047i
$856$	18.7718	−	508.437i	0.0219297	−	0.593969i
$857$	−425.534	−	737.047i	−0.496539	−	0.860031i	0.503453	−	0.864023i	$-0.332063\pi$
$857$	−425.534	−	737.047i	−0.496539	−	0.860031i	−0.999992	+	0.00399164i	$0.998729\pi$
$858$	−21.3421	−	130.397i	−0.0248742	−	0.151978i
$859$	589.846	−	1021.64i	0.686666	−	1.18934i	−0.286244	−	0.958157i	$-0.592407\pi$
$859$	589.846	−	1021.64i	0.686666	−	1.18934i	0.972910	−	0.231184i	$-0.0742599\pi$
$860$	−545.588	+	618.639i	−0.634405	+	0.719347i
$861$		0			0
$862$	541.658	+	204.728i	0.628374	+	0.237503i
$863$	241.662	+	139.524i	0.280026	+	0.161673i	0.633435	−	0.773796i	$-0.281644\pi$
$863$	241.662	+	139.524i	0.280026	+	0.161673i	−0.353409	+	0.935469i	$0.614978\pi$
$864$	−93.8703	−	317.390i	−0.108646	−	0.367350i
$865$	−180.799	−	313.153i	−0.209016	−	0.362027i
$866$	757.060	+	925.105i	0.874203	+	1.06825i
$867$	−80.0458			−0.0923250
$868$		0			0
$869$		−	1011.71i		−	1.16423i
$870$	150.468	+	183.868i	0.172952	+	0.211342i
$871$	615.098	−	355.127i	0.706198	−	0.407723i
$872$	−556.482	+	886.613i	−0.638168	+	1.01676i
$873$	−710.328	+	1230.32i	−0.813663	+	1.40931i
$874$	1330.92	+	503.042i	1.52280	+	0.575563i
$875$		0			0
$876$	−82.0446	−	72.3565i	−0.0936582	−	0.0825988i
$877$	−583.839	−	337.080i	−0.665723	−	0.384355i	0.128731	−	0.991680i	$-0.458910\pi$
$877$	−583.839	−	337.080i	−0.665723	−	0.384355i	−0.794454	+	0.607324i	$0.792243\pi$
$878$	12.4012	+	75.7698i	0.0141244	+	0.0862982i
$879$	−111.196	+	64.1990i	−0.126503	+	0.0730364i
$880$	699.832	−	1663.27i	0.795264	−	1.89008i
$881$	−1001.29			−1.13654			−0.568271	−	0.822841i	$-0.692387\pi$
$881$	−1001.29			−1.13654			−0.568271	+	0.822841i	$0.692387\pi$
$882$		0			0
$883$	882.010			0.998879			0.499439	−	0.866349i	$-0.333539\pi$
$883$	882.010			0.998879			0.499439	+	0.866349i	$0.333539\pi$
$884$	−142.182	−	422.720i	−0.160839	−	0.478190i
$885$	139.510	−	80.5463i	0.157639	−	0.0910128i
$886$	1182.38	−	193.521i	1.33452	−	0.218421i
$887$	6.13192	+	3.54027i	0.00691310	+	0.00399128i	0.503453	−	0.864023i	$-0.332063\pi$
$887$	6.13192	+	3.54027i	0.00691310	+	0.00399128i	−0.496539	+	0.868014i	$0.665396\pi$
$888$	35.6182	+	67.3120i	0.0401106	+	0.0758018i
$889$		0			0
$890$	−1891.75	−	715.014i	−2.12556	−	0.803386i
$891$	−448.551	+	776.914i	−0.503425	+	0.871957i
$892$	−41.4955	−	8.37420i	−0.0465196	−	0.00938812i
$893$	−154.998	+	89.4882i	−0.173570	+	0.100211i
$894$	228.641	−	187.109i	0.255751	−	0.209294i
$895$			2662.92i			2.97533i
$896$		0			0
$897$	−130.392			−0.145364
$898$	582.700	+	712.042i	0.648886	+	0.792920i
$899$	−188.382	−	326.287i	−0.209546	−	0.362944i
$900$	−387.700	+	1921.11i	−0.430778	+	2.13457i
$901$	−85.6776	−	49.4660i	−0.0950917	−	0.0549012i
$902$	−61.5391	+	162.817i	−0.0682252	+	0.180507i
$903$		0			0
$904$	−977.401	+	517.192i	−1.08120	+	0.572115i
$905$	−182.789	+	316.600i	−0.201977	+	0.349834i
$906$	−44.3726	−	271.110i	−0.0489764	−	0.299239i
$907$	−225.186	−	390.033i	−0.248275	−	0.430026i	0.714772	−	0.699358i	$-0.246530\pi$
$907$	−225.186	−	390.033i	−0.248275	−	0.430026i	−0.963047	+	0.269332i	$0.913197\pi$
$908$	−810.601	+	272.646i	−0.892732	+	0.300271i
$909$		−	105.032i		−	0.115547i
$910$		0			0
$911$		−	202.426i		−	0.222201i	−0.993809	−	0.111101i	$-0.964562\pi$
$911$		−	202.426i		−	0.222201i	0.993809	−	0.111101i	$-0.0354376\pi$
$912$	−249.409	−	104.940i	−0.273475	−	0.115066i
$913$	−252.108	−	436.663i	−0.276131	−	0.478273i
$914$	525.652	−	86.0335i	0.575111	−	0.0941285i
$915$	−40.3015	+	69.8043i	−0.0440454	+	0.0762888i
$916$	613.889	−	696.085i	0.670185	−	0.759918i
$917$		0			0
$918$	90.2742	−	238.843i	0.0983379	−	0.260178i
$919$	1380.21	+	796.863i	1.50186	+	0.867098i	0.999998	+	0.00214879i	$0.000683983\pi$
$919$	1380.21	+	796.863i	1.50186	+	0.867098i	0.501860	+	0.864949i	$0.332649\pi$
$920$	−1508.27	−	946.665i	−1.63942	−	1.02898i
$921$	−92.7502	−	160.648i	−0.100706	−	0.174428i
$922$	1181.15	−	966.596i	1.28108	−	1.04837i
$923$	−158.392			−0.171606
$924$		0			0
$925$		−	919.749i		−	0.994323i
$926$	−191.906	+	157.047i	−0.207242	+	0.169597i
$927$	799.052	−	461.333i	0.861977	−	0.497662i
$928$	−688.900	+	203.747i	−0.742349	+	0.219555i
$929$	519.701	−	900.148i	0.559419	−	0.968943i	−0.438126	−	0.898914i	$-0.644357\pi$
$929$	519.701	−	900.148i	0.559419	−	0.968943i	0.997545	−	0.0700290i	$-0.0223092\pi$
$930$	−62.7939	+	166.137i	−0.0675204	+	0.178642i
$931$		0			0
$932$	578.589	+	510.267i	0.620803	+	0.547497i
$933$	−36.6606	−	21.1660i	−0.0392933	−	0.0226860i
$934$	−1517.25	+	248.328i	−1.62446	+	0.265876i
$935$	1205.58	−	696.040i	1.28939	−	0.744427i
$936$	−625.164	−	23.0814i	−0.667910	−	0.0246596i
$937$	881.765			0.941051			0.470525	−	0.882386i	$-0.344064\pi$
$937$	881.765			0.941051			0.470525	+	0.882386i	$0.344064\pi$
$938$		0			0
$939$	48.0059			0.0511245
$940$	212.312	−	71.4112i	0.225864	−	0.0759694i
$941$	−825.620	+	476.672i	−0.877386	+	0.506559i	−0.869796	−	0.493412i	$-0.835749\pi$
$941$	−825.620	+	476.672i	−0.877386	+	0.506559i	−0.00759016	+	0.999971i	$0.502416\pi$
$942$	−1.91065	−	11.6738i	−0.00202830	−	0.0123926i
$943$	148.755	+	85.8835i	0.157746	+	0.0910747i
$944$	60.8873	+	483.278i	0.0644993	+	0.511947i
$945$		0			0
$946$	201.539	−	533.222i	0.213043	−	0.563660i
$947$	−8.44783	+	14.6321i	−0.00892063	+	0.0154510i	−0.870451	−	0.492255i	$-0.836173\pi$
$947$	−8.44783	+	14.6321i	−0.00892063	+	0.0154510i	0.861531	+	0.507706i	$0.169506\pi$
$948$	186.119	+	37.5607i	0.196328	+	0.0396209i
$949$	−365.224	+	210.862i	−0.384852	+	0.222194i
$950$	2069.66	+	2529.06i	2.17859	+	2.66217i
$951$		−	63.9386i		−	0.0672330i
$952$		0			0
$953$	1526.31			1.60159			0.800794	−	0.598940i	$-0.204411\pi$
$953$	1526.31			1.60159			0.800794	+	0.598940i	$0.204411\pi$
$954$	−107.395	+	87.8864i	−0.112573	+	0.0921241i
$955$	708.784	+	1227.65i	0.742182	+	1.28550i
$956$	1285.75	+	259.477i	1.34493	+	0.271420i
$957$	−142.195	−	82.0962i	−0.148584	−	0.0857849i
$958$	−222.593	−	84.1322i	−0.232352	−	0.0878207i
$959$		0			0
$960$	280.000	+	190.494i	0.291667	+	0.198431i
$961$	−339.676	+	588.336i	−0.353461	+	0.612212i
$962$	289.733	−	47.4206i	0.301178	−	0.0492938i
$963$	−275.279	−	476.798i	−0.285856	−	0.495117i
$964$	272.488	−	91.6514i	0.282664	−	0.0950741i
$965$		−	2360.40i		−	2.44601i
$966$		0			0
$967$			1410.39i			1.45852i	0.684235	+	0.729262i	$0.260136\pi$
$967$			1410.39i			1.45852i	−0.684235	+	0.729262i	$0.739864\pi$
$968$	−10.2960	+	278.868i	−0.0106363	+	0.288087i
$969$	−104.372	−	180.777i	−0.107711	−	0.186560i
$970$	−478.881	−	2925.89i	−0.493692	−	3.01638i
$971$	298.248	−	516.581i	0.307156	−	0.532009i	−0.670583	−	0.741834i	$-0.733956\pi$
$971$	298.248	−	516.581i	0.307156	−	0.532009i	0.977739	+	0.209825i	$0.0672894\pi$
$972$	−405.536	−	357.649i	−0.417218	−	0.367952i
$973$		0			0
$974$	−528.653	−	199.812i	−0.542765	−	0.205146i
$975$	−259.365	−	149.744i	−0.266015	−	0.153584i
$976$	−147.288	−	194.180i	−0.150910	−	0.198955i
$977$	−73.3431	−	127.034i	−0.0750698	−	0.130025i	0.826047	−	0.563601i	$-0.190585\pi$
$977$	−73.3431	−	127.034i	−0.0750698	−	0.130025i	−0.901117	+	0.433577i	$0.857251\pi$
$978$	−77.5617	−	94.7782i	−0.0793065	−	0.0969102i
$979$	1397.62			1.42760
$980$		0			0
$981$			1132.73i			1.15467i
$982$	491.515	+	600.617i	0.500524	+	0.611626i
$983$	146.754	−	84.7286i	0.149292	−	0.0861939i	−0.423493	−	0.905899i	$-0.639196\pi$
$983$	146.754	−	84.7286i	0.149292	−	0.0861939i	0.572785	+	0.819705i	$0.305863\pi$
$984$	−27.6678	−	17.3657i	−0.0281177	−	0.0176481i
$985$	656.181	−	1136.54i	0.666173	−	1.15385i
$986$	−518.412	−	195.941i	−0.525773	−	0.198723i
$987$		0			0
$988$	−689.980	+	782.364i	−0.698360	+	0.791866i
$989$	−487.167	−	281.266i	−0.492586	−	0.284395i
$990$	−315.397	−	1927.03i	−0.318582	−	1.94649i
$991$	−1460.90	+	843.449i	−1.47416	+	0.851109i	−0.999577	−	0.0290984i	$-0.990736\pi$
$991$	−1460.90	+	843.449i	−1.47416	+	0.851109i	−0.474588	+	0.880208i	$0.657403\pi$
$992$	−389.397	−	369.835i	−0.392537	−	0.372817i
$993$	188.471			0.189800
$994$		0			0
$995$	−3527.52			−3.54524
$996$	89.6899	−	30.1672i	0.0900501	−	0.0302884i
$997$	1503.54	−	868.068i	1.50806	−	0.870680i	0.508107	−	0.861294i	$-0.330345\pi$
$997$	1503.54	−	868.068i	1.50806	−	0.870680i	0.999956	−	0.00938643i	$-0.00298784\pi$
$998$	−54.7036	+	8.95334i	−0.0548132	+	0.00897128i
$999$	145.563	+	84.0410i	0.145709	+	0.0841251i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	392.3.k.i.275.2		8
7.2	even	3		56.3.g.a.43.2	yes	4
7.3	odd	6		392.3.k.j.67.4		8
7.4	even	3	inner	392.3.k.i.67.4		8
7.5	odd	6		392.3.g.h.99.2		4
7.6	odd	2		392.3.k.j.275.2		8
8.3	odd	2	inner	392.3.k.i.275.4		8
21.2	odd	6		504.3.g.a.379.3		4
28.19	even	6		1568.3.g.h.687.1		4
28.23	odd	6		224.3.g.a.15.4		4
56.3	even	6		392.3.k.j.67.2		8
56.5	odd	6		1568.3.g.h.687.2		4
56.11	odd	6	inner	392.3.k.i.67.2		8
56.19	even	6		392.3.g.h.99.1		4
56.27	even	2		392.3.k.j.275.4		8
56.37	even	6		224.3.g.a.15.3		4
56.51	odd	6		56.3.g.a.43.1	✓	4
84.23	even	6		2016.3.g.a.1135.1		4
112.37	even	12		1792.3.d.g.1023.3		8
112.51	odd	12		1792.3.d.g.1023.4		8
112.93	even	12		1792.3.d.g.1023.6		8
112.107	odd	12		1792.3.d.g.1023.5		8
168.107	even	6		504.3.g.a.379.4		4
168.149	odd	6		2016.3.g.a.1135.4		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
56.3.g.a.43.1	✓	4	56.51	odd	6
56.3.g.a.43.2	yes	4	7.2	even	3
224.3.g.a.15.3		4	56.37	even	6
224.3.g.a.15.4		4	28.23	odd	6
392.3.g.h.99.1		4	56.19	even	6
392.3.g.h.99.2		4	7.5	odd	6
392.3.k.i.67.2		8	56.11	odd	6	inner
392.3.k.i.67.4		8	7.4	even	3	inner
392.3.k.i.275.2		8	1.1	even	1	trivial
392.3.k.i.275.4		8	8.3	odd	2	inner
392.3.k.j.67.2		8	56.3	even	6
392.3.k.j.67.4		8	7.3	odd	6
392.3.k.j.275.2		8	7.6	odd	2
392.3.k.j.275.4		8	56.27	even	2
504.3.g.a.379.3		4	21.2	odd	6
504.3.g.a.379.4		4	168.107	even	6
1568.3.g.h.687.1		4	28.19	even	6
1568.3.g.h.687.2		4	56.5	odd	6
1792.3.d.g.1023.3		8	112.37	even	12
1792.3.d.g.1023.4		8	112.51	odd	12
1792.3.d.g.1023.5		8	112.107	odd	12
1792.3.d.g.1023.6		8	112.93	even	12
2016.3.g.a.1135.1		4	84.23	even	6
2016.3.g.a.1135.4		4	168.149	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-1.26663 - 1.54779i) q^{2} +(-0.292893 - 0.507306i) q^{3} +(-0.791288 + 3.92095i) q^{4} +(-7.82295 - 4.51658i) q^{5} +(-0.414214 + 1.09591i) q^{6} +(7.07107 - 3.74166i) q^{8} +(4.32843 - 7.49706i) q^{9} +O(q^{10})\)	\(q+(-1.26663 - 1.54779i) q^{2} +(-0.292893 - 0.507306i) q^{3} +(-0.791288 + 3.92095i) q^{4} +(-7.82295 - 4.51658i) q^{5} +(-0.414214 + 1.09591i) q^{6} +(7.07107 - 3.74166i) q^{8} +(4.32843 - 7.49706i) q^{9} +(2.91809 + 17.8291i) q^{10} +(-6.24264 - 10.8126i) q^{11} +(2.22089 - 0.746995i) q^{12} -9.03316i q^{13} +5.29150i q^{15} +(-14.7477 - 6.20520i) q^{16} +(-6.17157 - 10.6895i) q^{17} +(-17.0864 + 2.79653i) q^{18} +(-14.4350 + 25.0022i) q^{19} +(23.8995 - 27.0995i) q^{20} +(-8.82843 + 23.3578i) q^{22} +(21.3404 + 12.3209i) q^{23} +(-3.96923 - 2.49129i) q^{24} +(28.2990 + 49.0153i) q^{25} +(-13.9814 + 11.4417i) q^{26} -10.3431 q^{27} +22.4499i q^{29} +(8.19012 - 6.70239i) q^{30} +(-14.5340 + 8.39119i) q^{31} +(9.07561 + 30.6860i) q^{32} +(-3.65685 + 6.33386i) q^{33} +(-8.72792 + 23.0919i) q^{34} +(25.9706 + 22.9039i) q^{36} +(-14.0734 - 8.12528i) q^{37} +(56.9819 - 9.32624i) q^{38} +(-4.58258 + 2.64575i) q^{39} +(-72.2161 - 2.66626i) q^{40} +6.97056 q^{41} -22.8284 q^{43} +(47.3353 - 15.9212i) q^{44} +(-67.7221 + 39.0994i) q^{45} +(-7.96032 - 48.6364i) q^{46} +(5.36882 + 3.09969i) q^{47} +(1.17157 + 9.29907i) q^{48} +(40.0208 - 105.885i) q^{50} +(-3.61522 + 6.26175i) q^{51} +(35.4186 + 7.14783i) q^{52} +(6.94131 - 4.00757i) q^{53} +(13.1010 + 16.0090i) q^{54} +112.782i q^{55} +16.9117 q^{57} +(34.7477 - 28.4358i) q^{58} +(-15.2218 - 26.3650i) q^{59} +(-20.7477 - 4.18710i) q^{60} +(13.1918 + 7.61627i) q^{61} +(31.3970 + 11.8669i) q^{62} +(36.0000 - 52.9150i) q^{64} +(-40.7990 + 70.6659i) q^{65} +(14.4353 - 2.36263i) q^{66} +(39.3137 + 68.0933i) q^{67} +(46.7964 - 15.7400i) q^{68} -14.4348i q^{69} -17.5345i q^{71} +(2.55519 - 69.2077i) q^{72} +(-23.3431 - 40.4315i) q^{73} +(5.24961 + 32.0744i) q^{74} +(16.5772 - 28.7125i) q^{75} +(-86.6102 - 76.3830i) q^{76} +(9.89949 + 3.74166i) q^{78} +(70.1762 + 40.5163i) q^{79} +(87.3444 + 115.152i) q^{80} +(-35.9264 - 62.2264i) q^{81} +(-8.82914 - 10.7889i) q^{82} +40.3848 q^{83} +111.498i q^{85} +(28.9152 + 35.3335i) q^{86} +(11.3890 - 6.57544i) q^{87} +(-84.5991 - 53.0986i) q^{88} +(-55.9706 + 96.9439i) q^{89} +(146.296 + 55.2949i) q^{90} +(-65.1960 + 73.9253i) q^{92} +(8.51380 + 4.91545i) q^{93} +(-2.00266 - 12.2360i) q^{94} +(225.849 - 130.394i) q^{95} +(12.9090 - 13.5918i) q^{96} -164.108 q^{97} -108.083 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 8 q^{3} + 12 q^{4} + 8 q^{6} + 12 q^{9}+O(q^{10}) \) 8 * q - 8 * q^3 + 12 * q^4 + 8 * q^6 + 12 * q^9	\( 8 q - 8 q^{3} + 12 q^{4} + 8 q^{6} + 12 q^{9} + 28 q^{10} - 16 q^{11} + 24 q^{12} - 8 q^{16} - 72 q^{17} - 16 q^{18} - 8 q^{19} + 112 q^{20} - 48 q^{22} + 40 q^{24} + 68 q^{25} - 28 q^{26} - 128 q^{27} + 16 q^{33} + 32 q^{34} + 72 q^{36} + 76 q^{38} - 56 q^{40} - 80 q^{41} - 160 q^{43} + 48 q^{44} - 224 q^{46} + 32 q^{48} + 224 q^{50} - 176 q^{51} + 56 q^{52} + 16 q^{54} - 272 q^{57} + 168 q^{58} - 184 q^{59} - 56 q^{60} - 224 q^{62} + 288 q^{64} - 168 q^{65} + 32 q^{66} + 224 q^{67} + 216 q^{68} + 160 q^{72} - 232 q^{73} + 280 q^{74} - 88 q^{75} - 48 q^{76} + 336 q^{80} + 52 q^{81} + 48 q^{82} + 176 q^{83} - 8 q^{86} - 240 q^{88} - 312 q^{89} + 616 q^{90} + 112 q^{92} + 112 q^{94} - 176 q^{96} - 272 q^{97} - 480 q^{99}+O(q^{100}) \) 8 * q - 8 * q^3 + 12 * q^4 + 8 * q^6 + 12 * q^9 + 28 * q^10 - 16 * q^11 + 24 * q^12 - 8 * q^16 - 72 * q^17 - 16 * q^18 - 8 * q^19 + 112 * q^20 - 48 * q^22 + 40 * q^24 + 68 * q^25 - 28 * q^26 - 128 * q^27 + 16 * q^33 + 32 * q^34 + 72 * q^36 + 76 * q^38 - 56 * q^40 - 80 * q^41 - 160 * q^43 + 48 * q^44 - 224 * q^46 + 32 * q^48 + 224 * q^50 - 176 * q^51 + 56 * q^52 + 16 * q^54 - 272 * q^57 + 168 * q^58 - 184 * q^59 - 56 * q^60 - 224 * q^62 + 288 * q^64 - 168 * q^65 + 32 * q^66 + 224 * q^67 + 216 * q^68 + 160 * q^72 - 232 * q^73 + 280 * q^74 - 88 * q^75 - 48 * q^76 + 336 * q^80 + 52 * q^81 + 48 * q^82 + 176 * q^83 - 8 * q^86 - 240 * q^88 - 312 * q^89 + 616 * q^90 + 112 * q^92 + 112 * q^94 - 176 * q^96 - 272 * q^97 - 480 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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