LMFDB - Embedded newform 392.3.k.i.67.4

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			67.4
Root			$1.20711 + 2.54762i$ of defining polynomial
Character	$\chi$	$=$	392.67
Dual form			392.3.k.i.275.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.97374 - 0.323042i) q^{2} +(-0.292893 + 0.507306i) q^{3} +(3.79129 - 1.27520i) q^{4} +(7.82295 - 4.51658i) q^{5} +(-0.414214 + 1.09591i) q^{6} +(7.07107 - 3.74166i) q^{8} +(4.32843 + 7.49706i) q^{9} +O(q^{10})$	\(q+(1.97374 - 0.323042i) q^{2} +(-0.292893 + 0.507306i) q^{3} +(3.79129 - 1.27520i) 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} +(13.9814 - 11.4417i) q^{10} +(-6.24264 + 10.8126i) q^{11} +(-0.463526 + 2.29684i) q^{12} -9.03316i q^{13} +5.29150i q^{15} +(12.7477 - 9.66930i) q^{16} +(-6.17157 + 10.6895i) q^{17} +(10.9650 + 13.3990i) 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} +(-0.172903 + 4.68310i) q^{24} +(28.2990 - 49.0153i) q^{25} +(-2.91809 - 17.8291i) q^{26} -10.3431 q^{27} +22.4499i q^{29} +(1.70938 + 10.4440i) q^{30} +(14.5340 + 8.39119i) q^{31} +(22.0371 - 23.2027i) 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} +(-36.5677 - 44.6847i) q^{38} +(4.58258 + 2.64575i) q^{39} +(38.4171 - 61.2078i) q^{40} +6.97056 q^{41} -22.8284 q^{43} +(-9.87945 + 48.9542i) q^{44} +(67.7221 + 39.0994i) q^{45} +(-38.1402 + 31.2120i) 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} +(-11.5191 - 34.2473i) q^{52} +(-6.94131 - 4.00757i) q^{53} +(-20.4147 + 3.34127i) q^{54} +112.782i q^{55} +16.9117 q^{57} +(7.25227 + 44.3103i) q^{58} +(-15.2218 + 26.3650i) q^{59} +(6.74773 + 20.0616i) 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} +(-9.26378 - 11.3201i) q^{66} +(39.3137 - 68.0933i) q^{67} +(-9.76698 + 48.3969i) q^{68} -14.4348i q^{69} -17.5345i q^{71} +(58.6580 + 36.8167i) q^{72} +(-23.3431 + 40.4315i) q^{73} +(25.1524 - 20.5835i) 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} +(56.0526 - 133.219i) q^{80} +(-35.9264 + 62.2264i) q^{81} +(13.7581 - 2.25178i) q^{82} +40.3848 q^{83} +111.498i q^{85} +(-45.0573 + 7.37454i) q^{86} +(-11.3890 - 6.57544i) q^{87} +(-3.68520 + 99.8142i) 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} +(-9.59532 + 7.85233i) q^{94} +(-225.849 - 130.394i) q^{95} +(5.31637 + 17.9755i) 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 $\left(\mathbb{Z}/392\mathbb{Z}\right)^\times$.

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

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	1.97374	−	0.323042i	0.986869	−	0.161521i
$2$	1.97374	−	0.323042i	0.986869	−	0.161521i
$3$	−0.292893	+	0.507306i	−0.0976311	+	0.169102i	−0.910704	−	0.413060i	$-0.864460\pi$
$3$	−0.292893	+	0.507306i	−0.0976311	+	0.169102i	0.813073	+	0.582162i	$0.197793\pi$
$4$	3.79129	−	1.27520i	0.947822	−	0.318800i
$5$	7.82295	−	4.51658i	1.56459	−	0.903316i	0.567807	−	0.823162i	$-0.307792\pi$
$5$	7.82295	−	4.51658i	1.56459	−	0.903316i	0.996782	−	0.0801541i	$-0.0255412\pi$
$6$	−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
$10$	13.9814	−	11.4417i	1.39814	−	1.14417i
$11$	−6.24264	+	10.8126i	−0.567513	+	0.982961i	0.429298	+	0.903163i	$0.358761\pi$
$11$	−6.24264	+	10.8126i	−0.567513	+	0.982961i	−0.996811	+	0.0797982i	$0.974572\pi$
$12$	−0.463526	+	2.29684i	−0.0386271	+	0.191403i
$13$		−	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
$16$	12.7477	−	9.66930i	0.796733	−	0.604332i
$17$	−6.17157	+	10.6895i	−0.363034	+	0.628793i	−0.988459	−	0.151492i	$-0.951592\pi$
$17$	−6.17157	+	10.6895i	−0.363034	+	0.628793i	0.625425	+	0.780284i	$0.284926\pi$
$18$	10.9650	+	13.3990i	0.609169	+	0.744387i
$19$	−14.4350	−	25.0022i	−0.759738	−	1.31591i	−0.942984	−	0.332838i	$-0.891994\pi$
$19$	−14.4350	−	25.0022i	−0.759738	−	1.31591i	0.183246	−	0.983067i	$-0.441340\pi$
$20$	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	$-0.846615\pi$
$23$	−21.3404	+	12.3209i	−0.927843	+	0.535690i	−0.0417142	+	0.999130i	$0.513282\pi$
$24$	−0.172903	+	4.68310i	−0.00720428	+	0.195129i
$25$	28.2990	−	49.0153i	1.13196	−	1.96061i
$26$	−2.91809	−	17.8291i	−0.112234	−	0.685734i
$27$	−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	$0.873488\pi$
$30$	1.70938	+	10.4440i	0.0569792	+	0.348135i
$31$	14.5340	+	8.39119i	0.468838	+	0.270684i	0.715753	−	0.698353i	$-0.246084\pi$
$31$	14.5340	+	8.39119i	0.468838	+	0.270684i	−0.246915	+	0.969037i	$0.579417\pi$
$32$	22.0371	−	23.2027i	0.688659	−	0.725085i
$33$	−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	$-0.596191\pi$
$37$	14.0734	−	8.12528i	0.380362	−	0.219602i	0.677976	+	0.735084i	$0.262857\pi$
$38$	−36.5677	−	44.6847i	−0.962309	−	1.17591i
$39$	4.58258	+	2.64575i	0.117502	+	0.0678398i
$40$	38.4171	−	61.2078i	0.960427	−	1.53020i
$41$	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	$0.585519\pi$
$44$	−9.87945	+	48.9542i	−0.224533	+	1.11260i
$45$	67.7221	+	39.0994i	1.50494	+	0.868875i
$46$	−38.1402	+	31.2120i	−0.829134	+	0.678522i
$47$	−5.36882	+	3.09969i	−0.114230	+	0.0659509i	−0.556027	−	0.831165i	$-0.687675\pi$
$47$	−5.36882	+	3.09969i	−0.114230	+	0.0659509i	0.441796	+	0.897115i	$0.354341\pi$
$48$	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
$52$	−11.5191	−	34.2473i	−0.221521	−	0.658602i
$53$	−6.94131	−	4.00757i	−0.130968	−	0.0756145i	0.433084	−	0.901353i	$-0.357425\pi$
$53$	−6.94131	−	4.00757i	−0.130968	−	0.0756145i	−0.564053	+	0.825739i	$0.690759\pi$
$54$	−20.4147	+	3.34127i	−0.378049	+	0.0618754i
$55$			112.782i			2.05057i
$56$		0			0
$57$	16.9117			0.296696
$58$	7.25227	+	44.3103i	0.125039	+	0.763971i
$59$	−15.2218	+	26.3650i	−0.257997	+	0.446864i	−0.965705	−	0.259641i	$-0.916396\pi$
$59$	−15.2218	+	26.3650i	−0.257997	+	0.446864i	0.707708	+	0.706505i	$0.249729\pi$
$60$	6.74773	+	20.0616i	0.112462	+	0.334360i
$61$	−13.1918	+	7.61627i	−0.216258	+	0.124857i	−0.604217	−	0.796820i	$-0.706514\pi$
$61$	−13.1918	+	7.61627i	−0.216258	+	0.124857i	0.387958	+	0.921677i	$0.373181\pi$
$62$	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
$66$	−9.26378	−	11.3201i	−0.140360	−	0.171516i
$67$	39.3137	−	68.0933i	0.586772	−	1.01632i	−0.407880	−	0.913035i	$-0.633732\pi$
$67$	39.3137	−	68.0933i	0.586772	−	1.01632i	0.994652	−	0.103283i	$-0.0329348\pi$
$68$	−9.76698	+	48.3969i	−0.143632	+	0.711719i
$69$		−	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	$-0.0394062\pi$
$72$	58.6580	+	36.8167i	0.814695	+	0.511343i
$73$	−23.3431	+	40.4315i	−0.319769	+	0.553856i	−0.980440	−	0.196820i	$-0.936939\pi$
$73$	−23.3431	+	40.4315i	−0.319769	+	0.553856i	0.660671	+	0.750676i	$0.270272\pi$
$74$	25.1524	−	20.5835i	0.339897	−	0.278155i
$75$	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	$-0.838082\pi$
$79$	−70.1762	+	40.5163i	−0.888307	+	0.512864i	−0.0149184	+	0.999889i	$0.504749\pi$
$80$	56.0526	−	133.219i	0.700657	−	1.66523i
$81$	−35.9264	+	62.2264i	−0.443536	+	0.768227i
$82$	13.7581	−	2.25178i	0.167781	−	0.0274608i
$83$	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
$86$	−45.0573	+	7.37454i	−0.523923	+	0.0857505i
$87$	−11.3890	−	6.57544i	−0.130908	−	0.0755797i
$88$	−3.68520	+	99.8142i	−0.0418773	+	1.13425i
$89$	−55.9706	−	96.9439i	−0.628883	−	1.08926i	−0.987776	−	0.155878i	$-0.950179\pi$
$89$	−55.9706	−	96.9439i	−0.628883	−	1.08926i	0.358894	−	0.933379i	$-0.383154\pi$
$90$	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
$94$	−9.59532	+	7.85233i	−0.102078	+	0.0835355i
$95$	−225.849	−	130.394i	−2.37736	−	1.37257i
$96$	5.31637	+	17.9755i	0.0553788	+	0.187244i
$97$	−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
$100$	44.7853	−	221.918i	0.447853	−	2.21918i
$101$	−10.5074	−	6.06643i	−0.104033	−	0.0600636i	0.447081	−	0.894494i	$-0.352464\pi$
$101$	−10.5074	−	6.06643i	−0.104033	−	0.0600636i	−0.551114	+	0.834430i	$0.685797\pi$
$102$	−9.15831	−	11.1912i	−0.0897874	−	0.109718i
$103$	−92.3029	+	53.2911i	−0.896144	+	0.517389i	−0.875947	−	0.482407i	$-0.839763\pi$
$103$	−92.3029	+	53.2911i	−0.896144	+	0.517389i	−0.0201970	+	0.999796i	$0.506429\pi$
$104$	−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	0.975491	−	0.220038i	$-0.0706182\pi$
$107$	31.7990	+	55.0775i	0.297187	+	0.514743i	−0.678304	+	0.734781i	$0.737285\pi$
$108$	−39.2138	+	13.1896i	−0.363091	+	0.122126i
$109$	113.318	+	65.4239i	1.03961	+	0.600220i	0.919723	−	0.392568i	$-0.128413\pi$
$109$	113.318	+	65.4239i	1.03961	+	0.600220i	0.119888	+	0.992787i	$0.461747\pi$
$110$	36.4332	+	222.601i	0.331211	+	2.02365i
$111$			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	$0.709481\pi$
$114$	33.3793	−	5.46318i	0.292800	−	0.0479227i
$115$	−111.296	+	192.771i	−0.967795	+	1.67627i
$116$	28.6282	+	85.1142i	0.246795	+	0.733743i
$117$	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
$122$	−23.5767	+	19.2940i	−0.193252	+	0.158148i
$123$	−2.04163	+	3.53621i	−0.0165986	+	0.0287497i
$124$	65.8029	+	13.2797i	0.530669	+	0.107094i
$125$		−	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	$-0.148775\pi$
$128$	53.9608	−	116.070i	0.421569	−	0.906796i
$129$	6.68629	−	11.5810i	0.0518317	−	0.0897752i
$130$	−103.355	−	126.296i	−0.795035	−	0.971510i
$131$	84.1751	+	145.796i	0.642558	+	1.11294i	0.984860	+	0.173353i	$0.0554603\pi$
$131$	84.1751	+	145.796i	0.642558	+	1.11294i	−0.342301	+	0.939590i	$0.611206\pi$
$132$	−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
$136$	−3.64325	+	98.6779i	−0.0267886	+	0.725573i
$137$	−17.3431	+	30.0392i	−0.126592	+	0.219264i	−0.922354	−	0.386345i	$-0.873737\pi$
$137$	−17.3431	+	30.0392i	−0.126592	+	0.219264i	0.795762	+	0.605610i	$0.207071\pi$
$138$	−4.66305	−	28.4905i	−0.0337902	−	0.206453i
$139$	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
$142$	−5.66438	−	34.6085i	−0.0398900	−	0.243722i
$143$	97.6717	+	56.3908i	0.683019	+	0.394341i
$144$	127.669	+	53.7175i	0.886590	+	0.373038i
$145$	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	$-0.345534\pi$
$149$	218.391	−	126.088i	1.46571	−	0.846229i	0.999266	+	0.0383198i	$0.0122006\pi$
$150$	41.9943	+	51.3158i	0.279962	+	0.342106i
$151$	203.071	+	117.243i	1.34484	+	0.776444i	0.987513	−	0.157535i	$-0.0503548\pi$
$151$	203.071	+	117.243i	1.34484	+	0.776444i	0.357327	+	0.933979i	$0.383688\pi$
$152$	−195.621	−	122.781i	−1.28698	−	0.807772i
$153$	−106.853			−0.698384
$154$		0			0
$155$	151.598			0.978051
$156$	20.7477	+	4.18710i	0.132998	+	0.0268404i
$157$	8.74409	+	5.04840i	0.0556948	+	0.0321554i	0.527589	−	0.849500i	$-0.323096\pi$
$157$	8.74409	+	5.04840i	0.0556948	+	0.0321554i	−0.471894	+	0.881655i	$0.656430\pi$
$158$	−125.421	+	102.638i	−0.793804	+	0.649610i
$159$	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	0.659967	−	0.751295i	$-0.270570\pi$
$163$	−52.2670	−	90.5291i	−0.320657	−	0.555394i	−0.980624	+	0.195901i	$0.937237\pi$
$164$	26.4274	−	8.88887i	0.161143	−	0.0542004i
$165$	−57.2147	−	33.0329i	−0.346756	−	0.200200i
$166$	79.7090	−	13.0460i	0.480175	−	0.0785902i
$167$			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
$170$	36.0184	+	220.067i	0.211873	+	1.29451i
$171$	124.962	−	216.440i	0.730772	−	1.26573i
$172$	−86.5491	+	29.1108i	−0.503193	+	0.169249i
$173$	−34.6671	+	20.0150i	−0.200388	+	0.115694i	−0.596836	−	0.802363i	$-0.703576\pi$
$173$	−34.6671	+	20.0150i	−0.200388	+	0.115694i	0.396449	+	0.918057i	$0.370242\pi$
$174$	−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
$178$	−141.788	−	173.261i	−0.796563	−	0.973376i
$179$	−147.397	+	255.299i	−0.823447	+	1.42625i	0.0796538	+	0.996823i	$0.474619\pi$
$179$	−147.397	+	255.299i	−0.823447	+	1.42625i	−0.903101	+	0.429429i	$0.858715\pi$
$180$	306.614	+	61.8777i	1.70341	+	0.343765i
$181$		−	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
$184$	−104.799	+	166.970i	−0.569559	+	0.907447i
$185$	73.3970	−	127.127i	0.396740	−	0.687174i
$186$	−15.2161	+	12.4521i	−0.0818071	+	0.0669469i
$187$	−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	$-0.531913\pi$
$191$	135.905	−	78.4647i	0.711543	−	0.410810i	0.811632	+	0.584169i	$0.198579\pi$
$192$	16.3000	+	33.7615i	0.0848956	+	0.175841i
$193$	130.652	−	226.296i	0.676952	−	1.17252i	−0.298942	−	0.954271i	$-0.596634\pi$
$193$	130.652	−	226.296i	0.676952	−	1.17252i	0.975894	−	0.218245i	$-0.0700330\pi$
$194$	−323.906	+	53.0136i	−1.66962	+	0.273266i
$195$	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	$0.879790\pi$
$198$	−213.328	+	34.9154i	−1.07741	+	0.176341i
$199$	−338.189	−	195.254i	−1.69944	−	0.981175i	−0.946283	−	0.323339i	$-0.895195\pi$
$199$	−338.189	−	195.254i	−1.69944	−	0.981175i	−0.753161	−	0.657836i	$-0.771472\pi$
$200$	16.7057	−	452.476i	0.0835283	−	2.26238i
$201$	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
$206$	−164.966	+	135.000i	−0.800808	+	0.655342i
$207$	−184.741	−	106.660i	−0.892467	−	0.515266i
$208$	−87.3444	−	115.152i	−0.419925	−	0.553617i
$209$	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	$0.627090\pi$
$212$	−31.4270	−	6.34228i	−0.148240	−	0.0299164i
$213$	8.89535	+	5.13574i	0.0417622	+	0.0241114i
$214$	80.5552	+	98.4361i	0.376426	+	0.459982i
$215$	−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
$220$	143.819	+	427.587i	0.653723	+	1.94358i
$221$	96.5598	+	55.7488i	0.436922	+	0.252257i
$222$	3.07515	+	18.7887i	0.0138520	+	0.0846339i
$223$			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
$226$	−272.821	+	44.6526i	−1.20717	+	0.197578i
$227$	106.903	−	185.162i	0.470939	−	0.815690i	−0.528509	−	0.848928i	$-0.677249\pi$
$227$	106.903	−	185.162i	0.470939	−	0.815690i	0.999447	+	0.0332382i	$0.0105820\pi$
$228$	64.1171	−	21.5658i	0.281215	−	0.0945868i
$229$	200.942	−	116.014i	0.877478	−	0.506612i	0.00765200	−	0.999971i	$-0.497564\pi$
$229$	200.942	−	116.014i	0.877478	−	0.506612i	0.869826	+	0.493359i	$0.164231\pi$
$230$	−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	0.995309	−	0.0967472i	$-0.0308439\pi$
$233$	96.4315	+	167.024i	0.413869	+	0.716842i	−0.581440	+	0.813589i	$0.697511\pi$
$234$	121.035	−	99.0490i	0.517244	−	0.423286i
$235$	−28.0000	+	48.4974i	−0.119149	+	0.206372i
$236$	−24.0897	+	119.368i	−0.102075	+	0.505797i
$237$		−	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	$-0.240644\pi$
$240$	51.1652	+	67.4546i	0.213188	+	0.281061i
$241$	−35.9361	+	62.2431i	−0.149112	+	0.258270i	−0.930900	−	0.365275i	$-0.880975\pi$
$241$	−35.9361	+	62.2431i	−0.149112	+	0.258270i	0.781787	+	0.623545i	$0.214308\pi$
$242$	−44.1830	−	53.9903i	−0.182574	−	0.223100i
$243$	−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
$248$	134.168	+	4.95355i	0.540999	+	0.0199740i
$249$	−11.8284	+	20.4874i	−0.0475037	+	0.0822789i
$250$	−92.2057	−	563.363i	−0.368823	−	2.25345i
$251$	−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
$254$	−36.9694	−	225.878i	−0.145549	−	0.889282i
$255$	−56.5634	−	32.6569i	−0.221817	−	0.128066i
$256$	69.0091	−	246.523i	0.269567	−	0.962982i
$257$	−159.676	−	276.567i	−0.621308	−	1.07614i	−0.989242	−	0.146285i	$-0.953268\pi$
$257$	−159.676	−	276.567i	−0.621308	−	1.07614i	0.367934	−	0.929852i	$-0.380065\pi$
$258$	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
$262$	213.238	+	260.570i	0.813885	+	0.994543i
$263$	326.800	+	188.678i	1.24259	+	0.717408i	0.969620	−	0.244615i	$-0.0786616\pi$
$263$	326.800	+	188.678i	1.24259	+	0.717408i	0.272967	+	0.962023i	$0.411995\pi$
$264$	−49.5570	−	31.1044i	−0.187716	−	0.117820i
$265$	−72.4020			−0.273215
$266$		0			0
$267$	65.5736			0.245594
$268$	62.2169	−	308.294i	0.232153	−	1.15035i
$269$	−24.3900	−	14.0816i	−0.0906691	−	0.0523478i	0.453980	−	0.891012i	$-0.350004\pi$
$269$	−24.3900	−	14.0816i	−0.0906691	−	0.0523478i	−0.544649	+	0.838664i	$0.683337\pi$
$270$	−144.612	+	118.343i	−0.535599	+	0.438308i
$271$	346.164	−	199.858i	1.27736	−	0.737482i	0.300995	−	0.953626i	$-0.402681\pi$
$271$	346.164	−	199.858i	1.27736	−	0.737482i	0.976362	+	0.216143i	$0.0693479\pi$
$272$	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
$276$	−18.4073	−	54.7265i	−0.0666930	−	0.198284i
$277$	89.1579	+	51.4753i	0.321870	+	0.185831i	0.652226	−	0.758025i	$-0.273835\pi$
$277$	89.1579	+	51.4753i	0.321870	+	0.185831i	−0.330356	+	0.943856i	$0.607169\pi$
$278$	212.501	−	34.7800i	0.764391	−	0.125108i
$279$			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	$0.586139\pi$
$282$	−1.17313	−	7.16766i	−0.00416004	−	0.0254172i
$283$	89.2807	−	154.639i	0.315480	−	0.546427i	−0.664060	−	0.747679i	$-0.731168\pi$
$283$	89.2807	−	154.639i	0.315480	−	0.546427i	0.979539	+	0.201253i	$0.0645013\pi$
$284$	−22.3600	−	66.4783i	−0.0787324	−	0.234079i
$285$	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
$290$	256.865	+	313.882i	0.885742	+	1.08235i
$291$	48.0660	−	83.2528i	0.165175	−	0.286092i
$292$	−36.9423	+	183.055i	−0.126515	+	0.626900i
$293$		−	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
$296$	69.1120	−	110.112i	0.233486	−	0.372001i
$297$	64.5685	−	111.836i	0.217402	−	0.376552i
$298$	390.315	−	319.415i	1.30978	−	1.07186i
$299$	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
$304$	−425.768	−	179.145i	−1.40055	−	0.589291i
$305$	−68.7990	+	119.163i	−0.225570	+	0.390699i
$306$	−210.900	+	34.5179i	−0.689214	+	0.112804i
$307$	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
$310$	299.215	−	48.9725i	0.965209	−	0.157976i
$311$	−62.5836	−	36.1326i	−0.201233	−	0.116182i	0.395997	−	0.918252i	$-0.370399\pi$
$311$	−62.5836	−	36.1326i	−0.201233	−	0.116182i	−0.597231	+	0.802070i	$0.703732\pi$
$312$	42.3032	+	1.56186i	0.135587	+	0.00500596i
$313$	−40.9756	−	70.9718i	−0.130913	−	0.226747i	0.793116	−	0.609071i	$-0.208457\pi$
$313$	−40.9756	−	70.9718i	−0.130913	−	0.226747i	−0.924029	+	0.382323i	$0.875124\pi$
$314$	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	$-0.721742\pi$
$317$	−94.5267	+	54.5750i	−0.298191	+	0.172161i	0.343439	+	0.939175i	$0.388408\pi$
$318$	7.26710	−	5.94704i	0.0228525	−	0.0187014i
$319$	−242.742	−	140.147i	−0.760945	−	0.439332i
$320$	42.6311	−	576.548i	0.133222	−	1.80171i
$321$	−37.2548			−0.116059
$322$		0			0
$323$	356.347			1.10324
$324$	−56.8563	+	281.731i	−0.175482	+	0.869541i
$325$	−442.763	−	255.629i	−1.36235	−	0.786552i
$326$	−132.406	−	161.796i	−0.406154	−	0.496308i
$327$	−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	0.513858	−	0.857875i	$-0.328216\pi$
$331$	−160.870	−	278.635i	−0.486012	−	0.841798i	−0.999871	+	0.0160770i	$0.994882\pi$
$332$	153.110	−	51.4987i	0.461176	−	0.155117i
$333$	121.831	+	70.3394i	0.365860	+	0.211229i
$334$	95.8674	+	585.736i	0.287028	+	1.75370i
$335$		−	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	$0.578261\pi$
$338$	172.509	−	28.2345i	0.510381	−	0.0835341i
$339$	40.4853	−	70.1226i	0.119426	−	0.206851i
$340$	142.182	+	422.720i	0.418182	+	1.24329i
$341$	−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
$346$	−61.9580	+	50.7034i	−0.179069	+	0.146541i
$347$	165.154	−	286.056i	0.475949	−	0.824368i	−0.523671	−	0.851920i	$-0.675438\pi$
$347$	165.154	−	286.056i	0.475949	−	0.824368i	0.999620	+	0.0275524i	$0.00877132\pi$
$348$	−51.5639	−	10.4061i	−0.148172	−	0.0299027i
$349$			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
$352$	113.312	+	383.124i	0.321908	+	1.08842i
$353$	289.049	−	500.647i	0.818835	−	1.41826i	−0.0877061	−	0.996146i	$-0.527954\pi$
$353$	289.049	−	500.647i	0.818835	−	1.41826i	0.906541	−	0.422118i	$-0.138713\pi$
$354$	−22.5884	−	27.6024i	−0.0638092	−	0.0779729i
$355$	−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	$-0.496861\pi$
$359$	316.198	−	182.557i	0.880774	−	0.508515i	0.870913	+	0.491437i	$0.163528\pi$
$360$	625.164	+	23.0814i	1.73657	+	0.0641151i
$361$	−236.240	+	409.180i	−0.654405	+	1.13346i
$362$	−13.0737	−	79.8785i	−0.0361152	−	0.220659i
$363$	20.4335			0.0562908
$364$		0			0
$365$			421.725i			1.15541i
$366$	−2.88251	−	17.6117i	−0.00787571	−	0.0481194i
$367$	450.395	+	260.036i	1.22723	+	0.708544i	0.966451	−	0.256853i	$-0.0826856\pi$
$367$	450.395	+	260.036i	1.22723	+	0.708544i	0.260784	+	0.965397i	$0.416019\pi$
$368$	−152.907	+	363.410i	−0.415508	+	0.987527i
$369$	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	$-0.417143\pi$
$373$	456.145	−	263.356i	1.22291	−	0.706048i	0.965537	+	0.260265i	$0.0838098\pi$
$374$	−195.198	−	238.526i	−0.521919	−	0.637769i
$375$	144.800	+	83.6004i	0.386134	+	0.222934i
$376$	−26.3653	+	42.0064i	−0.0701205	+	0.111719i
$377$	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	$0.448555\pi$
$380$	−1022.54	−	206.358i	−2.69089	−	0.543048i
$381$	58.0569	+	33.5191i	0.152380	+	0.0879768i
$382$	242.893	−	198.772i	0.635846	−	0.520345i
$383$	274.033	−	158.213i	0.715492	−	0.413089i	−0.0975993	−	0.995226i	$-0.531116\pi$
$383$	274.033	−	158.213i	0.715492	−	0.413089i	0.813091	+	0.582136i	$0.197783\pi$
$384$	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
$388$	−622.179	+	209.270i	−1.60355	+	0.539356i
$389$	79.8020	+	46.0737i	0.205146	+	0.118441i	0.599054	−	0.800709i	$-0.295544\pi$
$389$	79.8020	+	46.0737i	0.205146	+	0.118441i	−0.393907	+	0.919150i	$0.628877\pi$
$390$	94.3427	−	15.4411i	0.241904	−	0.0395925i
$391$		−	304.157i		−	0.777895i
$392$		0			0
$393$	−98.6173			−0.250935
$394$	46.9324	+	286.750i	0.119118	+	0.727792i
$395$	−365.990	+	633.913i	−0.926557	+	1.60484i
$396$	−409.775	+	137.828i	−1.03478	+	0.348050i
$397$	−486.937	+	281.133i	−1.22654	+	0.708144i	−0.966305	−	0.257400i	$-0.917134\pi$
$397$	−486.937	+	281.133i	−1.22654	+	0.708144i	−0.260237	+	0.965545i	$0.583801\pi$
$398$	−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	0.810947	−	0.585119i	$-0.198952\pi$
$401$	−40.6030	−	70.3265i	−0.101254	−	0.175378i	−0.912202	+	0.409741i	$0.865619\pi$
$402$	58.3396	+	71.2893i	0.145123	+	0.177337i
$403$	75.7990	−	131.288i	0.188087	−	0.325776i
$404$	−47.5723	−	9.60058i	−0.117753	−	0.0237638i
$405$			649.058i			1.60261i
$406$		0			0
$407$			202.893i			0.498508i
$408$	−48.9928	−	30.7503i	−0.120080	−	0.0753685i
$409$	−225.368	+	390.348i	−0.551021	+	0.954396i	0.447180	+	0.894444i	$0.352428\pi$
$409$	−225.368	+	390.348i	−0.551021	+	0.954396i	−0.998201	+	0.0599523i	$0.980905\pi$
$410$	97.4583	−	79.7550i	0.237703	−	0.194524i
$411$	−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
$416$	−209.594	−	199.065i	−0.503832	−	0.478521i
$417$	−31.5341	+	54.6186i	−0.0756212	+	0.130980i
$418$	711.436	−	116.441i	1.70200	−	0.278566i
$419$	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	$-0.234897\pi$
$422$	−323.789	+	52.9946i	−0.767273	+	0.125580i
$423$	−46.4771	−	26.8336i	−0.109875	−	0.0634363i
$424$	−64.0774	−	2.36578i	−0.151126	−	0.00557966i
$425$	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
$430$	−319.174	+	261.196i	−0.742264	+	0.607432i
$431$	250.739	+	144.764i	0.581761	+	0.335880i	0.761833	−	0.647774i	$-0.224300\pi$
$431$	250.739	+	144.764i	0.581761	+	0.335880i	−0.180072	+	0.983653i	$0.557633\pi$
$432$	−131.852	+	100.011i	−0.305212	+	0.231507i
$433$	−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
$436$	513.048	+	103.538i	1.17672	+	0.237473i
$437$	616.098	+	355.704i	1.40984	+	0.813969i
$438$	−34.6401	−	42.3292i	−0.0790870	−	0.0966420i
$439$	33.2458	−	19.1945i	0.0757308	−	0.0437232i	−0.461656	−	0.887059i	$-0.652745\pi$
$439$	33.2458	−	19.1945i	0.0757308	−	0.0437232i	0.537387	+	0.843336i	$0.319411\pi$
$440$	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	−0.976135	−	0.217165i	$-0.930319\pi$
$443$	−299.529	−	518.799i	−0.676138	−	1.17110i	0.299997	−	0.953940i	$-0.403014\pi$
$444$	12.1391	+	36.0906i	0.0273403	+	0.0812852i
$445$	−875.709	−	505.591i	−1.96789	−	1.13616i
$446$	3.41875	+	20.8881i	0.00766537	+	0.0468343i
$447$			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	$0.671204\pi$
$450$	967.054	−	158.278i	2.14901	−	0.351728i
$451$	−43.5147	+	75.3697i	−0.0964850	+	0.167117i
$452$	−524.052	+	176.265i	−1.15941	+	0.389967i
$453$	−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	0.682755	−	0.730647i	$-0.260782\pi$
$457$	−133.161	−	230.642i	−0.291382	−	0.504688i	−0.974137	+	0.225959i	$0.927448\pi$
$458$	359.130	−	293.895i	0.784128	−	0.641691i
$459$	63.8335	−	110.563i	0.139071	−	0.240878i
$460$	−176.135	+	872.776i	−0.382902	+	1.89734i
$461$			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	$-0.0427488\pi$
$464$	217.075	+	286.186i	0.467835	+	0.616780i
$465$	−44.4020	+	76.9066i	−0.0954882	+	0.165390i
$466$	244.286	+	298.511i	0.524220	+	0.640581i
$467$	384.359	+	665.729i	0.823038	+	1.42554i	0.903409	+	0.428779i	$0.141056\pi$
$467$	384.359	+	665.729i	0.823038	+	1.42554i	−0.0803710	+	0.996765i	$0.525610\pi$
$468$	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
$472$	−8.98586	+	243.383i	−0.0190378	+	0.515643i
$473$	142.510	−	246.834i	0.301289	−	0.521848i
$474$	−15.3341	−	93.6889i	−0.0323504	−	0.197656i
$475$	−1633.99			−3.43997
$476$		0			0
$477$		−	69.3859i		−	0.145463i
$478$	−105.931	−	647.223i	−0.221613	−	1.35402i
$479$	−103.041	−	59.4905i	−0.215116	−	0.124197i	0.388571	−	0.921419i	$-0.372969\pi$
$479$	−103.041	−	59.4905i	−0.215116	−	0.124197i	−0.603687	+	0.797222i	$0.706302\pi$
$480$	122.777	+	116.609i	0.255786	+	0.242936i
$481$	−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
$486$	−171.222	−	209.228i	−0.352308	−	0.430510i
$487$	−244.719	−	141.288i	−0.502503	−	0.290120i	0.227244	−	0.973838i	$-0.427029\pi$
$487$	−244.719	−	141.288i	−0.502503	−	0.290120i	−0.729746	+	0.683718i	$0.760362\pi$
$488$	−64.7824	+	103.214i	−0.132751	+	0.211505i
$489$	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	$0.629311\pi$
$492$	−3.23103	+	16.0103i	−0.00656714	+	0.0325412i
$493$	−239.978	−	138.551i	−0.486771	−	0.281037i
$494$	−403.644	+	330.322i	−0.817093	+	0.668668i
$495$	−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	0.879577	−	0.475757i	$-0.157826\pi$
$499$	13.8579	+	24.0025i	0.0277713	+	0.0481013i	−0.851806	+	0.523858i	$0.824492\pi$
$500$	−363.980	−	1082.15i	−0.727960	−	2.16429i
$501$	−150.551	−	86.9204i	−0.300500	−	0.173494i
$502$	−507.091	+	82.9956i	−1.01014	+	0.165330i
$503$		−	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
$506$	−99.3868	−	607.239i	−0.196417	−	1.20008i
$507$	−25.5995	+	44.3396i	−0.0504920	+	0.0874548i
$508$	−145.936	−	433.881i	−0.287275	−	0.854096i
$509$	549.218	−	317.091i	1.07901	−	0.622969i	0.148384	−	0.988930i	$-0.452593\pi$
$509$	549.218	−	317.091i	1.07901	−	0.622969i	0.930630	+	0.365961i	$0.119260\pi$
$510$	−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
$514$	−404.502	−	494.289i	−0.786969	−	0.961653i
$515$	−481.387	+	833.787i	−0.934732	+	1.61900i
$516$	10.5816	−	52.4333i	0.0205069	−	0.101615i
$517$		−	77.4010i		−	0.149712i
$518$		0			0
$519$		−	23.4491i		−	0.0451813i
$520$	−552.900	−	347.028i	−1.06327	−	0.667361i
$521$	−416.563	+	721.509i	−0.799546	+	1.38485i	0.120366	+	0.992730i	$0.461593\pi$
$521$	−416.563	+	721.509i	−0.799546	+	1.38485i	−0.919912	+	0.392125i	$0.871740\pi$
$522$	−300.806	+	246.165i	−0.576257	+	0.471580i
$523$	−438.217	−	759.014i	−0.837891	−	1.45127i	−0.891655	−	0.452715i	$-0.850455\pi$
$523$	−438.217	−	759.014i	−0.837891	−	1.45127i	0.0537645	−	0.998554i	$-0.482878\pi$
$524$	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
$528$	−107.861	−	45.3830i	−0.204281	−	0.0859527i
$529$	39.1081	−	67.7372i	0.0739283	−	0.128048i
$530$	−142.903	+	23.3889i	−0.269628	+	0.0441300i
$531$	−263.546			−0.496321
$532$		0			0
$533$		−	62.9662i		−	0.118135i
$534$	129.425	−	21.1830i	0.242369	−	0.0396686i
$535$	497.524	+	287.245i	0.929951	+	0.536907i
$536$	23.2079	−	628.591i	0.0432984	−	1.17274i
$537$	−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	$-0.789076\pi$
$541$	−351.532	+	202.957i	−0.649783	+	0.375152i	0.138590	+	0.990350i	$0.455743\pi$
$542$	618.674	−	506.292i	1.14147	−	0.934118i
$543$	20.5310	+	11.8536i	0.0378103	+	0.0218298i
$544$	112.022	+	378.762i	0.205922	+	0.696254i
$545$	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	$0.686881\pi$
$548$	−27.4468	+	136.003i	−0.0500855	+	0.248181i
$549$	−114.199	−	65.9329i	−0.208013	−	0.120096i
$550$	895.055	+	1093.73i	1.62737	+	1.98860i
$551$	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
$556$	408.185	−	137.293i	0.734146	−	0.246930i
$557$	−31.5616	−	18.2221i	−0.0566635	−	0.0327147i	0.471401	−	0.881919i	$-0.343749\pi$
$557$	−31.5616	−	18.2221i	−0.0566635	−	0.0327147i	−0.528064	+	0.849204i	$0.677082\pi$
$558$	46.9324	+	286.750i	0.0841082	+	0.513889i
$559$			206.213i			0.368896i
$560$		0			0
$561$	90.2742			0.160917
$562$	−296.526	+	48.5324i	−0.527626	+	0.0863565i
$563$	93.1945	−	161.418i	0.165532	−	0.286710i	−0.771312	−	0.636457i	$-0.780399\pi$
$563$	93.1945	−	161.418i	0.165532	−	0.286710i	0.936844	+	0.349747i	$0.113733\pi$
$564$	−4.63091	−	13.7681i	−0.00821083	−	0.0244115i
$565$	−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	0.994293	+	0.106682i	$0.0340225\pi$
$569$	335.446	+	581.009i	0.589536	+	1.02111i	−0.404758	+	0.914424i	$0.632644\pi$
$570$	236.449	−	193.498i	0.414823	−	0.339471i
$571$	338.541	−	586.371i	0.592892	−	1.02692i	−0.400949	−	0.916100i	$-0.631320\pi$
$571$	338.541	−	586.371i	0.592892	−	1.02692i	0.993841	−	0.110818i	$-0.0353471\pi$
$572$	442.211	+	89.2427i	0.773096	+	0.156019i
$573$			91.9271i			0.160431i
$574$		0			0
$575$			1394.67i			2.42552i
$576$	552.530	+	40.8552i	0.959254	+	0.0709291i
$577$	−463.950	+	803.586i	−0.804073	+	1.39270i	0.112841	+	0.993613i	$0.464005\pi$
$577$	−463.950	+	803.586i	−0.804073	+	1.39270i	−0.916915	+	0.399083i	$0.869329\pi$
$578$	173.081	+	211.500i	0.299448	+	0.365917i
$579$	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
$584$	−13.7801	+	373.236i	−0.0235960	+	0.639103i
$585$	353.191	−	611.745i	0.603745	−	1.04572i
$586$	−70.8072	−	432.622i	−0.120831	−	0.738263i
$587$	−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
$590$	88.8373	+	542.783i	0.150572	+	0.919971i
$591$	−73.7028	−	42.5523i	−0.124709	−	0.0720005i
$592$	100.838	−	239.659i	0.170335	−	0.404829i
$593$	109.627	+	189.880i	0.184869	+	0.320203i	0.943532	−	0.331280i	$-0.107481\pi$
$593$	109.627	+	189.880i	0.184869	+	0.320203i	−0.758663	+	0.651483i	$0.774147\pi$
$594$	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
$598$	281.943	+	344.526i	0.471477	+	0.576131i
$599$	−134.062	−	77.4010i	−0.223811	−	0.129217i	0.383903	−	0.923373i	$-0.374580\pi$
$599$	−134.062	−	77.4010i	−0.223811	−	0.129217i	−0.607713	+	0.794156i	$0.707913\pi$
$600$	224.651	+	141.002i	0.374418	+	0.235003i
$601$	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
$604$	919.409	+	185.546i	1.52220	+	0.307195i
$605$	−272.882	−	157.548i	−0.451045	−	0.260411i
$606$	11.0005	−	9.00228i	0.0181527	−	0.0148552i
$607$	684.735	−	395.332i	1.12806	−	0.651288i	0.184616	−	0.982811i	$-0.440896\pi$
$607$	684.735	−	395.332i	1.12806	−	0.651288i	0.943447	+	0.331523i	$0.107562\pi$
$608$	−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
$612$	−405.110	+	136.259i	−0.661944	+	0.222645i
$613$	−642.133	−	370.736i	−1.04753	−	0.604789i	−0.125570	−	0.992085i	$-0.540076\pi$
$613$	−642.133	−	370.736i	−1.04753	−	0.604789i	−0.921955	+	0.387296i	$0.873409\pi$
$614$	625.022	−	102.297i	1.01795	−	0.166608i
$615$			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	$0.455598\pi$
$618$	−20.1689	−	123.229i	−0.0326358	−	0.199400i
$619$	270.099	−	467.825i	0.436347	−	0.755776i	−0.561057	−	0.827777i	$-0.689605\pi$
$619$	270.099	−	467.825i	0.436347	−	0.755776i	0.997405	+	0.0720012i	$0.0229386\pi$
$620$	574.752	−	193.318i	0.927019	−	0.311803i
$621$	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
$626$	−103.802	−	126.843i	−0.165818	−	0.202625i
$627$	−105.574	+	182.859i	−0.168379	+	0.291641i
$628$	39.5891	+	7.98948i	0.0630400	+	0.0127221i
$629$			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	$0.931523\pi$
$632$	−344.623	+	549.069i	−0.545289	+	0.868780i
$633$	48.0488	−	83.2229i	0.0759064	−	0.131474i
$634$	−168.941	+	138.253i	−0.266468	+	0.218065i
$635$	−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
$640$	−102.107	−	1151.73i	−0.159542	−	1.79957i
$641$	−18.0934	+	31.3386i	−0.0282268	+	0.0488902i	−0.879794	−	0.475356i	$-0.842319\pi$
$641$	−18.0934	+	31.3386i	−0.0282268	+	0.0488902i	0.851567	+	0.524246i	$0.175653\pi$
$642$	−73.5313	+	12.0349i	−0.114535	+	0.0187459i
$643$	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
$646$	703.336	−	115.115i	1.08876	−	0.178197i
$647$	940.708	+	543.118i	1.45395	+	0.839440i	0.998703	−	0.0509233i	$-0.0162164\pi$
$647$	940.708	+	543.118i	1.45395	+	0.839440i	0.455250	+	0.890363i	$0.349550\pi$
$648$	−21.2083	+	574.431i	−0.0327289	+	0.886468i
$649$	−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	0.591234	−	0.806500i	$-0.298641\pi$
$653$	1035.20	−	597.674i	1.58530	−	0.915274i	0.994066	−	0.108774i	$-0.0346926\pi$
$654$	−118.636	+	97.0859i	−0.181401	+	0.148449i
$655$	1317.00	+	760.368i	2.01068	+	1.16087i
$656$	88.8588	−	67.4005i	0.135456	−	0.102745i
$657$	−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	$0.674029\pi$
$660$	−259.041	−	52.2771i	−0.392487	−	0.0792078i
$661$	860.294	+	496.691i	1.30150	+	0.751423i	0.980662	−	0.195710i	$-0.0627010\pi$
$661$	860.294	+	496.691i	1.30150	+	0.751423i	0.320842	+	0.947133i	$0.396034\pi$
$662$	−407.526	−	497.985i	−0.615599	−	0.752243i
$663$	−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
$668$	378.435	+	1125.12i	0.566519	+	1.68431i
$669$	−5.36882	−	3.09969i	−0.00802514	−	0.00463332i
$670$	−229.442	−	1401.86i	−0.342450	−	2.09232i
$671$		−	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	$0.474772\pi$
$674$	−323.789	+	52.9946i	−0.480400	+	0.0786270i
$675$	−292.701	+	506.972i	−0.433630	+	0.751070i
$676$	331.366	−	111.455i	0.490187	−	0.164874i
$677$	869.650	−	502.092i	1.28456	−	0.741643i	0.306885	−	0.951747i	$-0.400713\pi$
$677$	869.650	−	502.092i	1.28456	−	0.741643i	0.977679	+	0.210103i	$0.0673801\pi$
$678$	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
$682$	−324.312	+	265.401i	−0.475531	+	0.389151i
$683$	339.113	−	587.360i	0.496505	−	0.859971i	−0.503487	−	0.864003i	$-0.667950\pi$
$683$	339.113	−	587.360i	0.496505	−	0.859971i	0.999992	+	0.00403135i	$0.00128322\pi$
$684$	197.762	−	979.940i	0.289125	−	1.43266i
$685$			313.327i			0.457411i
$686$		0			0
$687$			135.919i			0.197844i
$688$	−291.011	+	220.735i	−0.422980	+	0.320836i
$689$	−36.2010	+	62.7020i	−0.0525414	+	0.0910043i
$690$	−165.159	−	201.819i	−0.239360	−	0.292491i
$691$	182.587	+	316.250i	0.264236	+	0.457671i	0.967363	−	0.253394i	$-0.0815468\pi$
$691$	182.587	+	316.250i	0.264236	+	0.457671i	−0.703127	+	0.711064i	$0.748213\pi$
$692$	−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
$696$	−105.135	−	3.88166i	−0.151057	−	0.00557710i
$697$	−43.0193	+	74.5117i	−0.0617207	+	0.106903i
$698$	84.7669	+	517.913i	0.121443	+	0.741996i
$699$	−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	$0.766003\pi$
$702$	30.1822	+	184.409i	0.0429946	+	0.262691i
$703$	−406.300	−	234.577i	−0.577951	−	0.333680i
$704$	347.412	+	719.582i	0.493484	+	1.02213i
$705$	−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	$-0.934570\pi$
$709$	−915.785	+	528.729i	−1.29166	+	0.745738i	−0.312709	+	0.949849i	$0.601236\pi$
$710$	−200.624	−	245.157i	−0.282569	−	0.345291i
$711$	−607.505	−	350.743i	−0.854438	−	0.493310i
$712$	−758.502	−	476.074i	−1.06531	−	0.668643i
$713$	−413.547			−0.580010
$714$		0			0
$715$	1018.77			1.42486
$716$	−233.267	+	1155.87i	−0.325792	+	1.61435i
$717$	166.354	+	96.0448i	0.232015	+	0.133954i
$718$	565.118	−	462.465i	0.787073	−	0.644101i
$719$	−896.185	+	517.412i	−1.24643	+	0.719628i	−0.970396	−	0.241520i	$-0.922354\pi$
$719$	−896.185	+	517.412i	−1.24643	+	0.719628i	−0.276036	+	0.961147i	$0.589021\pi$
$720$	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
$724$	−51.6082	−	153.436i	−0.0712820	−	0.211928i
$725$	1100.39	+	635.311i	1.51778	+	0.876291i
$726$	40.3305	−	6.60089i	0.0555516	−	0.00909214i
$727$		−	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
$730$	136.235	+	832.374i	0.186623	+	1.14024i
$731$	140.887	−	244.024i	0.192732	−	0.333822i
$732$	−11.3786	−	33.8297i	−0.0155446	−	0.0462155i
$733$	−491.464	+	283.747i	−0.670483	+	0.387103i	−0.796260	−	0.604955i	$-0.793191\pi$
$733$	−491.464	+	283.747i	−0.670483	+	0.387103i	0.125777	+	0.992059i	$0.459858\pi$
$734$	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
$738$	76.4325	+	93.3983i	0.103567	+	0.126556i
$739$	272.350	−	471.725i	0.368539	−	0.638328i	−0.620798	−	0.783970i	$-0.713191\pi$
$739$	272.350	−	471.725i	0.368539	−	0.638328i	0.989337	+	0.145642i	$0.0465248\pi$
$740$	116.156	−	575.572i	0.156968	−	0.777800i
$741$		−	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	$-0.163771\pi$
$744$	−41.8098	+	66.6132i	−0.0561959	+	0.0895339i
$745$	1138.97	−	1972.76i	1.52883	−	2.64800i
$746$	815.237	−	667.149i	1.09281	−	0.894302i
$747$	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	$-0.812960\pi$
$751$	−577.000	+	333.131i	−0.768309	+	0.443583i	0.0639622	+	0.997952i	$0.479626\pi$
$752$	−38.4684	+	91.4268i	−0.0511548	+	0.121578i
$753$	75.2498	−	130.336i	0.0999333	−	0.173090i
$754$	400.262	−	65.5109i	0.530852	−	0.0868845i
$755$	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	$0.949621\pi$
$758$	240.748	−	39.4032i	0.317609	−	0.0519832i
$759$	156.077	+	90.1113i	0.205636	+	0.118724i
$760$	−2084.88	−	76.9751i	−2.74327	−	0.101283i
$761$	−307.465	−	532.545i	−0.404028	−	0.699797i	0.590180	−	0.807272i	$-0.299057\pi$
$761$	−307.465	−	532.545i	−0.404028	−	0.699797i	−0.994208	+	0.107475i	$0.965723\pi$
$762$	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
$766$	489.761	−	400.796i	0.639374	−	0.523232i
$767$	238.159	+	137.501i	0.310507	+	0.179271i
$768$	104.850	+	107.214i	0.136524	+	0.139601i
$769$	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
$772$	206.766	−	1024.56i	0.267832	−	1.32715i
$773$	−546.994	−	315.807i	−0.707625	−	0.408548i	0.102556	−	0.994727i	$-0.467298\pi$
$773$	−546.994	−	315.807i	−0.707625	−	0.408548i	−0.810181	+	0.586180i	$0.800631\pi$
$774$	−250.315	−	305.877i	−0.323404	−	0.395190i
$775$	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
$780$	181.220	−	60.9533i	0.232333	−	0.0781453i
$781$	189.593	+	109.462i	0.242757	+	0.140156i
$782$	−98.2554	−	600.326i	−0.125646	−	0.767680i
$783$		−	232.203i		−	0.296556i
$784$		0			0
$785$	91.2061			0.116186
$786$	−194.645	+	31.8575i	−0.247640	+	0.0405312i
$787$	−228.327	+	395.475i	−0.290124	+	0.502509i	−0.973839	−	0.227240i	$-0.927030\pi$
$787$	−228.327	+	395.475i	−0.290124	+	0.502509i	0.683715	+	0.729749i	$0.260363\pi$
$788$	185.265	+	550.808i	0.235107	+	0.698995i
$789$	−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
$794$	−870.269	+	712.185i	−1.09606	+	0.896958i
$795$	21.2061	−	36.7300i	0.0266743	−	0.0462012i
$796$	−1531.16	−	309.004i	−1.92357	−	0.388196i
$797$		−	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
$800$	−513.661	−	1736.77i	−0.642076	−	2.17096i
$801$	484.529	−	839.229i	0.604905	−	1.04773i
$802$	−102.858	−	125.690i	−0.128252	−	0.156720i
$803$	−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
$808$	−96.9967	−	3.58118i	−0.120045	−	0.00443215i
$809$	−673.730	+	1166.93i	−0.832794	+	1.44244i	0.0630207	+	0.998012i	$0.479927\pi$
$809$	−673.730	+	1166.93i	−0.832794	+	1.44244i	−0.895814	+	0.444429i	$0.853407\pi$
$810$	209.673	+	1281.07i	0.258855	+	1.58157i
$811$	−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
$814$	65.5429	+	400.457i	0.0805195	+	0.491962i
$815$	−817.764	−	472.136i	−1.00339	−	0.579308i
$816$	−106.633	−	44.8664i	−0.130677	−	0.0549833i
$817$	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	$-0.416254\pi$
$821$	1006.82	−	581.286i	1.22633	−	0.708022i	0.966260	+	0.257567i	$0.0829209\pi$
$822$	−25.7364	−	31.4491i	−0.0313095	−	0.0382593i
$823$	−902.093	−	520.824i	−1.09610	−	0.632835i	−0.160908	−	0.986969i	$-0.551442\pi$
$823$	−902.093	−	520.824i	−1.09610	−	0.632835i	−0.935195	+	0.354134i	$0.884776\pi$
$824$	−453.283	+	722.191i	−0.550101	+	0.876445i
$825$	−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	$0.446160\pi$
$828$	−836.418	−	168.798i	−1.01017	−	0.203862i
$829$	−922.956	−	532.869i	−1.11334	−	0.642785i	−0.173645	−	0.984808i	$-0.555555\pi$
$829$	−922.956	−	532.869i	−1.11334	−	0.642785i	−0.939692	+	0.342023i	$0.888888\pi$
$830$	564.636	−	462.070i	0.680284	−	0.556711i
$831$	−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
$836$	1366.57	−	459.647i	1.63466	−	0.549817i
$837$	−150.327	−	86.7913i	−0.179602	−	0.103693i
$838$	1233.56	−	201.897i	1.47203	−	0.240928i
$839$		−	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
$842$	−182.995	−	1118.07i	−0.217334	−	1.32788i
$843$	44.0030	−	76.2154i	0.0521981	−	0.0904097i
$844$	−621.956	+	209.195i	−0.736915	+	0.247861i
$845$	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
$850$	884.865	+	1081.28i	1.04102	+	1.27209i
$851$	−200.221	+	346.793i	−0.235278	+	0.407513i
$852$	40.2739	+	8.12769i	0.0472699	+	0.00953954i
$853$			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
$856$	430.934	+	270.476i	0.503427	+	0.315976i
$857$	−425.534	+	737.047i	−0.496539	+	0.860031i	−0.999992	−	0.00399164i	$-0.998729\pi$
$857$	−425.534	+	737.047i	−0.496539	+	0.860031i	0.503453	+	0.864023i	$0.332063\pi$
$858$	−102.256	+	83.6812i	−0.119179	+	0.0975305i
$859$	589.846	+	1021.64i	0.686666	+	1.18934i	0.972910	+	0.231184i	$0.0742599\pi$
$859$	589.846	+	1021.64i	0.686666	+	1.18934i	−0.286244	+	0.958157i	$0.592407\pi$
$860$	−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	$-0.718356\pi$
$863$	−241.662	+	139.524i	−0.280026	+	0.161673i	0.353409	+	0.935469i	$0.385022\pi$
$864$	−227.933	+	239.989i	−0.263811	+	0.277765i
$865$	−180.799	+	313.153i	−0.209016	+	0.362027i
$866$	−1179.69	+	193.081i	−1.36223	+	0.222957i
$867$	−80.0458			−0.0923250
$868$		0			0
$869$		−	1011.71i		−	1.16423i
$870$	−234.468	+	38.3754i	−0.269504	+	0.0441097i
$871$	−615.098	−	355.127i	−0.706198	−	0.407723i
$872$	1046.07	+	38.6215i	1.19962	+	0.0442907i
$873$	−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	$-0.541090\pi$
$877$	583.839	−	337.080i	0.665723	−	0.384355i	0.794454	+	0.607324i	$0.207757\pi$
$878$	59.4179	−	48.6247i	0.0676742	−	0.0553812i
$879$	111.196	+	64.1990i	0.126503	+	0.0730364i
$880$	1090.52	+	1437.71i	1.23923	+	1.63376i
$881$	−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	$0.333539\pi$
$884$	437.177	+	88.2267i	0.494544	+	0.0998040i
$885$	−139.510	−	80.5463i	−0.157639	−	0.0910128i
$886$	−758.786	−	927.214i	−0.856418	−	1.04652i
$887$	−6.13192	+	3.54027i	−0.00691310	+	0.00399128i	−0.503453	−	0.864023i	$-0.667937\pi$
$887$	−6.13192	+	3.54027i	−0.00691310	+	0.00399128i	0.496539	+	0.868014i	$0.334604\pi$
$888$	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
$892$	13.4955	+	40.1232i	0.0151294	+	0.0449812i
$893$	154.998	+	89.4882i	0.173570	+	0.100211i
$894$	47.7202	+	291.564i	0.0533783	+	0.326134i
$895$			2662.92i			2.97533i
$896$		0			0
$897$	−130.392			−0.145364
$898$	−907.996	+	148.612i	−1.01113	+	0.165492i
$899$	−188.382	+	326.287i	−0.209546	+	0.362944i
$900$	1857.58	−	624.798i	2.06398	−	0.694220i
$901$	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
$906$	−212.602	+	173.983i	−0.234660	+	0.192034i
$907$	−225.186	+	390.033i	−0.248275	+	0.430026i	−0.963047	−	0.269332i	$-0.913197\pi$
$907$	−225.186	+	390.033i	−0.248275	+	0.430026i	0.714772	+	0.699358i	$0.246530\pi$
$908$	169.182	−	838.324i	0.186324	−	0.923264i
$909$		−	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	$-0.0354376\pi$
$912$	215.586	−	163.524i	0.236388	−	0.179303i
$913$	−252.108	+	436.663i	−0.276131	+	0.478273i
$914$	−337.333	−	412.211i	−0.369073	−	0.450997i
$915$	−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	−0.501860	+	0.864949i	$0.667351\pi$
$919$	−1380.21	+	796.863i	−1.50186	+	0.867098i	−0.999998	+	0.00214879i	$0.999316\pi$
$920$	−65.7013	+	1779.53i	−0.0714145	+	1.93427i
$921$	−92.7502	+	160.648i	−0.100706	+	0.174428i
$922$	246.521	+	1506.21i	0.267376	+	1.63363i
$923$	−158.392			−0.171606
$924$		0			0
$925$		−	919.749i		−	0.994323i
$926$	−40.0532	−	244.719i	−0.0432540	−	0.264276i
$927$	−799.052	−	461.333i	−0.861977	−	0.497662i
$928$	520.900	+	494.731i	0.561315	+	0.533116i
$929$	519.701	+	900.148i	0.559419	+	0.968943i	0.997545	+	0.0700290i	$0.0223092\pi$
$929$	519.701	+	900.148i	0.559419	+	0.968943i	−0.438126	+	0.898914i	$0.644357\pi$
$930$	−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
$934$	973.682	+	1189.81i	1.04249	+	1.27389i
$935$	−1205.58	−	696.040i	−1.28939	−	0.744427i
$936$	332.571	−	529.867i	0.355311	−	0.566097i
$937$	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
$940$	−44.3121	+	219.573i	−0.0471406	+	0.233589i
$941$	825.620	+	476.672i	0.877386	+	0.506559i	0.869796	−	0.493412i	$-0.164251\pi$
$941$	825.620	+	476.672i	0.877386	+	0.506559i	0.00759016	+	0.999971i	$0.497584\pi$
$942$	−9.15450	+	7.49158i	−0.00971815	+	0.00795285i
$943$	−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	0.861531	−	0.507706i	$-0.169506\pi$
$947$	−8.44783	−	14.6321i	−0.00892063	−	0.0154510i	−0.870451	+	0.492255i	$0.836173\pi$
$948$	−60.5309	−	179.964i	−0.0638512	−	0.189835i
$949$	365.224	+	210.862i	0.384852	+	0.222194i
$950$	−3225.06	+	527.846i	−3.39480	+	0.555628i
$951$		−	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	$0.204411\pi$
$954$	−22.4145	−	136.950i	−0.0234953	−	0.143553i
$955$	708.784	−	1227.65i	0.742182	−	1.28550i
$956$	−418.160	−	1243.23i	−0.437406	−	1.30045i
$957$	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
$962$	−185.934	−	227.206i	−0.193278	−	0.236181i
$963$	−275.279	+	476.798i	−0.285856	+	0.495117i
$964$	−56.8716	+	281.807i	−0.0589954	+	0.292331i
$965$		−	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	$0.739864\pi$
$968$	−236.359	−	148.351i	−0.244172	−	0.153255i
$969$	−104.372	+	180.777i	−0.107711	+	0.186560i
$970$	−2294.46	+	1877.67i	−2.36542	+	1.93574i
$971$	298.248	+	516.581i	0.307156	+	0.532009i	0.977739	−	0.209825i	$-0.0672894\pi$
$971$	298.248	+	516.581i	0.307156	+	0.532009i	−0.670583	+	0.741834i	$0.733956\pi$
$972$	−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
$976$	−94.5210	+	224.645i	−0.0968453	+	0.230169i
$977$	−73.3431	+	127.034i	−0.0750698	+	0.130025i	−0.901117	−	0.433577i	$-0.857251\pi$
$977$	−73.3431	+	127.034i	−0.0750698	+	0.130025i	0.826047	+	0.563601i	$0.190585\pi$
$978$	120.861	−	19.7814i	0.123580	−	0.0202263i
$979$	1397.62			1.42760
$980$		0			0
$981$			1132.73i			1.15467i
$982$	−765.907	+	125.356i	−0.779946	+	0.127654i
$983$	−146.754	−	84.7286i	−0.149292	−	0.0861939i	0.423493	−	0.905899i	$-0.360804\pi$
$983$	−146.754	−	84.7286i	−0.149292	−	0.0861939i	−0.572785	+	0.819705i	$0.694137\pi$
$984$	−1.20523	+	32.6438i	−0.00122483	+	0.0331746i
$985$	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
$990$	−1511.16	+	1236.65i	−1.52642	+	1.24915i
$991$	1460.90	+	843.449i	1.47416	+	0.851109i	0.999577	−	0.0290984i	$-0.00926363\pi$
$991$	1460.90	+	843.449i	1.47416	+	0.851109i	0.474588	+	0.880208i	$0.342597\pi$
$992$	514.985	−	152.310i	0.519138	−	0.153539i
$993$	188.471			0.189800
$994$		0			0
$995$	−3527.52			−3.54524
$996$	−18.7194	+	92.7574i	−0.0187946	+	0.0931299i
$997$	−1503.54	−	868.068i	−1.50806	−	0.870680i	−0.999956	−	0.00938643i	$-0.997012\pi$
$997$	−1503.54	−	868.068i	−1.50806	−	0.870680i	−0.508107	−	0.861294i	$-0.669655\pi$
$998$	35.1056	+	42.8980i	0.0351760	+	0.0429840i
$999$	−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.67.4		8
7.2	even	3	inner	392.3.k.i.275.2		8
7.3	odd	6		392.3.g.h.99.2		4
7.4	even	3		56.3.g.a.43.2	yes	4
7.5	odd	6		392.3.k.j.275.2		8
7.6	odd	2		392.3.k.j.67.4		8
8.3	odd	2	inner	392.3.k.i.67.2		8
21.11	odd	6		504.3.g.a.379.3		4
28.3	even	6		1568.3.g.h.687.1		4
28.11	odd	6		224.3.g.a.15.4		4
56.3	even	6		392.3.g.h.99.1		4
56.11	odd	6		56.3.g.a.43.1	✓	4
56.19	even	6		392.3.k.j.275.4		8
56.27	even	2		392.3.k.j.67.2		8
56.45	odd	6		1568.3.g.h.687.2		4
56.51	odd	6	inner	392.3.k.i.275.4		8
56.53	even	6		224.3.g.a.15.3		4
84.11	even	6		2016.3.g.a.1135.1		4
112.11	odd	12		1792.3.d.g.1023.5		8
112.53	even	12		1792.3.d.g.1023.3		8
112.67	odd	12		1792.3.d.g.1023.4		8
112.109	even	12		1792.3.d.g.1023.6		8
168.11	even	6		504.3.g.a.379.4		4
168.53	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	56.11	odd	6
56.3.g.a.43.2	yes	4	7.4	even	3
224.3.g.a.15.3		4	56.53	even	6
224.3.g.a.15.4		4	28.11	odd	6
392.3.g.h.99.1		4	56.3	even	6
392.3.g.h.99.2		4	7.3	odd	6
392.3.k.i.67.2		8	8.3	odd	2	inner
392.3.k.i.67.4		8	1.1	even	1	trivial
392.3.k.i.275.2		8	7.2	even	3	inner
392.3.k.i.275.4		8	56.51	odd	6	inner
392.3.k.j.67.2		8	56.27	even	2
392.3.k.j.67.4		8	7.6	odd	2
392.3.k.j.275.2		8	7.5	odd	6
392.3.k.j.275.4		8	56.19	even	6
504.3.g.a.379.3		4	21.11	odd	6
504.3.g.a.379.4		4	168.11	even	6
1568.3.g.h.687.1		4	28.3	even	6
1568.3.g.h.687.2		4	56.45	odd	6
1792.3.d.g.1023.3		8	112.53	even	12
1792.3.d.g.1023.4		8	112.67	odd	12
1792.3.d.g.1023.5		8	112.11	odd	12
1792.3.d.g.1023.6		8	112.109	even	12
2016.3.g.a.1135.1		4	84.11	even	6
2016.3.g.a.1135.4		4	168.53	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)

\(f(q)\)	\(=\)	\(q+(1.97374 - 0.323042i) q^{2} +(-0.292893 + 0.507306i) q^{3} +(3.79129 - 1.27520i) q^{4} +(7.82295 - 4.51658i) q^{5} +(-0.414214 + 1.09591i) q^{6} +(7.07107 - 3.74166i) q^{8} +(4.32843 + 7.49706i) q^{9} +O(q^{10})\)	\(q+(1.97374 - 0.323042i) q^{2} +(-0.292893 + 0.507306i) q^{3} +(3.79129 - 1.27520i) 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} +(13.9814 - 11.4417i) q^{10} +(-6.24264 + 10.8126i) q^{11} +(-0.463526 + 2.29684i) q^{12} -9.03316i q^{13} +5.29150i q^{15} +(12.7477 - 9.66930i) q^{16} +(-6.17157 + 10.6895i) q^{17} +(10.9650 + 13.3990i) 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} +(-0.172903 + 4.68310i) q^{24} +(28.2990 - 49.0153i) q^{25} +(-2.91809 - 17.8291i) q^{26} -10.3431 q^{27} +22.4499i q^{29} +(1.70938 + 10.4440i) q^{30} +(14.5340 + 8.39119i) q^{31} +(22.0371 - 23.2027i) 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} +(-36.5677 - 44.6847i) q^{38} +(4.58258 + 2.64575i) q^{39} +(38.4171 - 61.2078i) q^{40} +6.97056 q^{41} -22.8284 q^{43} +(-9.87945 + 48.9542i) q^{44} +(67.7221 + 39.0994i) q^{45} +(-38.1402 + 31.2120i) 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} +(-11.5191 - 34.2473i) q^{52} +(-6.94131 - 4.00757i) q^{53} +(-20.4147 + 3.34127i) q^{54} +112.782i q^{55} +16.9117 q^{57} +(7.25227 + 44.3103i) q^{58} +(-15.2218 + 26.3650i) q^{59} +(6.74773 + 20.0616i) 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} +(-9.26378 - 11.3201i) q^{66} +(39.3137 - 68.0933i) q^{67} +(-9.76698 + 48.3969i) q^{68} -14.4348i q^{69} -17.5345i q^{71} +(58.6580 + 36.8167i) q^{72} +(-23.3431 + 40.4315i) q^{73} +(25.1524 - 20.5835i) 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} +(56.0526 - 133.219i) q^{80} +(-35.9264 + 62.2264i) q^{81} +(13.7581 - 2.25178i) q^{82} +40.3848 q^{83} +111.498i q^{85} +(-45.0573 + 7.37454i) q^{86} +(-11.3890 - 6.57544i) q^{87} +(-3.68520 + 99.8142i) 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} +(-9.59532 + 7.85233i) q^{94} +(-225.849 - 130.394i) q^{95} +(5.31637 + 17.9755i) 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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Groups

Database

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