LMFDB - Embedded newform 38.3.d.a.31.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [38,3,Mod(27,38)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(38, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([1]))

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

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

chi := DirichletCharacter("38.27");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 38 = 2 \cdot 19 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	38.d (of order $6$, degree $2$, 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:	$1.03542500457$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\sqrt{-2}, \sqrt{-3})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 2x^{2} + 4 $ x^4 - 2*x^2 + 4
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			31.2
Root			$1.22474 - 0.707107i$ of defining polynomial
Character	$\chi$	$=$	38.31
Dual form			38.3.d.a.27.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.22474 - 0.707107i) q^{2} +(0.275255 - 0.158919i) q^{3} +(1.00000 - 1.73205i) q^{4} +(0.500000 + 0.866025i) q^{5} +(0.224745 - 0.389270i) q^{6} -2.89898 q^{7} -2.82843i q^{8} +(-4.44949 + 7.70674i) q^{9} +O(q^{10})$	\(q+(1.22474 - 0.707107i) q^{2} +(0.275255 - 0.158919i) q^{3} +(1.00000 - 1.73205i) q^{4} +(0.500000 + 0.866025i) q^{5} +(0.224745 - 0.389270i) q^{6} -2.89898 q^{7} -2.82843i q^{8} +(-4.44949 + 7.70674i) q^{9} +(1.22474 + 0.707107i) q^{10} -5.10102 q^{11} -0.635674i q^{12} +(-0.151531 - 0.0874863i) q^{13} +(-3.55051 + 2.04989i) q^{14} +(0.275255 + 0.158919i) q^{15} +(-2.00000 - 3.46410i) q^{16} +(5.94949 + 10.3048i) q^{17} +12.5851i q^{18} +(-3.34847 - 18.7026i) q^{19} +2.00000 q^{20} +(-0.797959 + 0.460702i) q^{21} +(-6.24745 + 3.60697i) q^{22} +(8.52270 - 14.7618i) q^{23} +(-0.449490 - 0.778539i) q^{24} +(12.0000 - 20.7846i) q^{25} -0.247449 q^{26} +5.68896i q^{27} +(-2.89898 + 5.02118i) q^{28} +(38.5454 + 22.2542i) q^{29} +0.449490 q^{30} -31.1769i q^{31} +(-4.89898 - 2.82843i) q^{32} +(-1.40408 + 0.810647i) q^{33} +(14.5732 + 8.41385i) q^{34} +(-1.44949 - 2.51059i) q^{35} +(8.89898 + 15.4135i) q^{36} +21.9917i q^{37} +(-17.3258 - 20.5382i) q^{38} -0.0556128 q^{39} +(2.44949 - 1.41421i) q^{40} +(-46.9393 + 27.1004i) q^{41} +(-0.651531 + 1.12848i) q^{42} +(-18.6691 - 32.3359i) q^{43} +(-5.10102 + 8.83523i) q^{44} -8.89898 q^{45} -24.1058i q^{46} +(-40.7702 + 70.6160i) q^{47} +(-1.10102 - 0.635674i) q^{48} -40.5959 q^{49} -33.9411i q^{50} +(3.27526 + 1.89097i) q^{51} +(-0.303062 + 0.174973i) q^{52} +(48.2878 + 27.8789i) q^{53} +(4.02270 + 6.96753i) q^{54} +(-2.55051 - 4.41761i) q^{55} +8.19955i q^{56} +(-3.89388 - 4.61586i) q^{57} +62.9444 q^{58} +(-29.9166 + 17.2723i) q^{59} +(0.550510 - 0.317837i) q^{60} +(38.0959 - 65.9841i) q^{61} +(-22.0454 - 38.1838i) q^{62} +(12.8990 - 22.3417i) q^{63} -8.00000 q^{64} -0.174973i q^{65} +(-1.14643 + 1.98567i) q^{66} +(102.659 + 59.2702i) q^{67} +23.7980 q^{68} -5.41767i q^{69} +(-3.55051 - 2.04989i) q^{70} +(65.4773 - 37.8033i) q^{71} +(21.7980 + 12.5851i) q^{72} +(-14.6918 - 25.4470i) q^{73} +(15.5505 + 26.9343i) q^{74} -7.62809i q^{75} +(-35.7423 - 12.9029i) q^{76} +14.7878 q^{77} +(-0.0681115 + 0.0393242i) q^{78} +(-57.2196 + 33.0358i) q^{79} +(2.00000 - 3.46410i) q^{80} +(-39.1413 - 67.7948i) q^{81} +(-38.3258 + 66.3822i) q^{82} -30.6969 q^{83} +1.84281i q^{84} +(-5.94949 + 10.3048i) q^{85} +(-45.7298 - 26.4021i) q^{86} +14.1464 q^{87} +14.4279i q^{88} +(-8.84847 - 5.10867i) q^{89} +(-10.8990 + 6.29253i) q^{90} +(0.439285 + 0.253621i) q^{91} +(-17.0454 - 29.5235i) q^{92} +(-4.95459 - 8.58161i) q^{93} +115.315i q^{94} +(14.5227 - 12.2512i) q^{95} -1.79796 q^{96} +(-128.848 + 74.3907i) q^{97} +(-49.7196 + 28.7056i) q^{98} +(22.6969 - 39.3123i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 6 q^{3} + 4 q^{4} + 2 q^{5} - 4 q^{6} + 8 q^{7} - 8 q^{9}+O(q^{10}) $ 4 * q + 6 * q^3 + 4 * q^4 + 2 * q^5 - 4 * q^6 + 8 * q^7 - 8 * q^9	$ 4 q + 6 q^{3} + 4 q^{4} + 2 q^{5} - 4 q^{6} + 8 q^{7} - 8 q^{9} - 40 q^{11} - 30 q^{13} - 24 q^{14} + 6 q^{15} - 8 q^{16} + 14 q^{17} + 16 q^{19} + 8 q^{20} + 36 q^{21} + 24 q^{22} - 10 q^{23} + 8 q^{24} + 48 q^{25} + 48 q^{26} + 8 q^{28} + 66 q^{29} - 8 q^{30} - 84 q^{33} + 24 q^{34} + 4 q^{35} + 16 q^{36} - 84 q^{38} - 108 q^{39} + 18 q^{41} - 32 q^{42} + 38 q^{43} - 40 q^{44} - 16 q^{45} - 70 q^{47} - 24 q^{48} - 84 q^{49} + 18 q^{51} - 60 q^{52} - 42 q^{53} - 28 q^{54} - 20 q^{55} + 102 q^{57} + 144 q^{58} + 42 q^{59} + 12 q^{60} + 74 q^{61} + 32 q^{63} - 32 q^{64} + 64 q^{66} + 102 q^{67} + 56 q^{68} - 24 q^{70} + 306 q^{71} + 48 q^{72} + 98 q^{73} + 72 q^{74} + 4 q^{76} - 176 q^{77} + 132 q^{78} - 126 q^{79} + 8 q^{80} + 10 q^{81} - 168 q^{82} - 64 q^{83} - 14 q^{85} - 276 q^{86} - 12 q^{87} - 6 q^{89} - 24 q^{90} - 204 q^{91} + 20 q^{92} - 108 q^{93} + 14 q^{95} + 32 q^{96} - 486 q^{97} - 96 q^{98} + 32 q^{99}+O(q^{100}) $ 4 * q + 6 * q^3 + 4 * q^4 + 2 * q^5 - 4 * q^6 + 8 * q^7 - 8 * q^9 - 40 * q^11 - 30 * q^13 - 24 * q^14 + 6 * q^15 - 8 * q^16 + 14 * q^17 + 16 * q^19 + 8 * q^20 + 36 * q^21 + 24 * q^22 - 10 * q^23 + 8 * q^24 + 48 * q^25 + 48 * q^26 + 8 * q^28 + 66 * q^29 - 8 * q^30 - 84 * q^33 + 24 * q^34 + 4 * q^35 + 16 * q^36 - 84 * q^38 - 108 * q^39 + 18 * q^41 - 32 * q^42 + 38 * q^43 - 40 * q^44 - 16 * q^45 - 70 * q^47 - 24 * q^48 - 84 * q^49 + 18 * q^51 - 60 * q^52 - 42 * q^53 - 28 * q^54 - 20 * q^55 + 102 * q^57 + 144 * q^58 + 42 * q^59 + 12 * q^60 + 74 * q^61 + 32 * q^63 - 32 * q^64 + 64 * q^66 + 102 * q^67 + 56 * q^68 - 24 * q^70 + 306 * q^71 + 48 * q^72 + 98 * q^73 + 72 * q^74 + 4 * q^76 - 176 * q^77 + 132 * q^78 - 126 * q^79 + 8 * q^80 + 10 * q^81 - 168 * q^82 - 64 * q^83 - 14 * q^85 - 276 * q^86 - 12 * q^87 - 6 * q^89 - 24 * q^90 - 204 * q^91 + 20 * q^92 - 108 * q^93 + 14 * q^95 + 32 * q^96 - 486 * q^97 - 96 * q^98 + 32 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/38\mathbb{Z}\right)^\times$.

$n$	$21$
$\chi(n)$	$e\left(\frac{5}{6}\right)$

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 $

$2$	1.22474	−	0.707107i	0.612372	−	0.353553i
$2$	1.22474	−	0.707107i	0.612372	−	0.353553i
$3$	0.275255	−	0.158919i	0.0917517	−	0.0529729i	−0.453422	−	0.891296i	$-0.649797\pi$
$3$	0.275255	−	0.158919i	0.0917517	−	0.0529729i	0.545174	+	0.838323i	$0.316464\pi$
$4$	1.00000	−	1.73205i	0.250000	−	0.433013i
$5$	0.500000	+	0.866025i	0.100000	+	0.173205i	0.911684	−	0.410891i	$-0.134782\pi$
$5$	0.500000	+	0.866025i	0.100000	+	0.173205i	−0.811684	+	0.584096i	$0.801449\pi$
$6$	0.224745	−	0.389270i	0.0374575	−	0.0648783i
$7$	−2.89898			−0.414140			−0.207070	−	0.978326i	$-0.566393\pi$
$7$	−2.89898			−0.414140			−0.207070	+	0.978326i	$0.566393\pi$
$8$		−	2.82843i		−	0.353553i
$9$	−4.44949	+	7.70674i	−0.494388	+	0.856305i
$10$	1.22474	+	0.707107i	0.122474	+	0.0707107i
$11$	−5.10102			−0.463729			−0.231865	−	0.972748i	$-0.574483\pi$
$11$	−5.10102			−0.463729			−0.231865	+	0.972748i	$0.574483\pi$
$12$		−	0.635674i		−	0.0529729i
$13$	−0.151531	−	0.0874863i	−0.0116562	−	0.00672972i	0.494161	−	0.869371i	$-0.335475\pi$
$13$	−0.151531	−	0.0874863i	−0.0116562	−	0.00672972i	−0.505817	+	0.862641i	$0.668809\pi$
$14$	−3.55051	+	2.04989i	−0.253608	+	0.146421i
$15$	0.275255	+	0.158919i	0.0183503	+	0.0105946i
$16$	−2.00000	−	3.46410i	−0.125000	−	0.216506i
$17$	5.94949	+	10.3048i	0.349970	+	0.606166i	0.986244	−	0.165298i	$-0.0528584\pi$
$17$	5.94949	+	10.3048i	0.349970	+	0.606166i	−0.636274	+	0.771463i	$0.719525\pi$
$18$			12.5851i			0.699170i
$19$	−3.34847	−	18.7026i	−0.176235	−	0.984348i
$19$	−3.34847	−	18.7026i	−0.176235	−	0.984348i
$20$	2.00000			0.100000
$21$	−0.797959	+	0.460702i	−0.0379980	+	0.0219382i
$22$	−6.24745	+	3.60697i	−0.283975	+	0.163953i
$23$	8.52270	−	14.7618i	0.370552	−	0.641815i	−0.619098	−	0.785314i	$-0.712502\pi$
$23$	8.52270	−	14.7618i	0.370552	−	0.641815i	0.989651	+	0.143498i	$0.0458351\pi$
$24$	−0.449490	−	0.778539i	−0.0187287	−	0.0324391i
$25$	12.0000	−	20.7846i	0.480000	−	0.831384i
$26$	−0.247449			−0.00951726
$27$			5.68896i			0.210702i
$28$	−2.89898	+	5.02118i	−0.103535	+	0.179328i
$29$	38.5454	+	22.2542i	1.32915	+	0.767386i	0.985169	−	0.171589i	$-0.0548903\pi$
$29$	38.5454	+	22.2542i	1.32915	+	0.767386i	0.343983	+	0.938976i	$0.388224\pi$
$30$	0.449490			0.0149830
$31$		−	31.1769i		−	1.00571i	−0.864372	−	0.502853i	$-0.832284\pi$
$31$		−	31.1769i		−	1.00571i	0.864372	−	0.502853i	$-0.167716\pi$
$32$	−4.89898	−	2.82843i	−0.153093	−	0.0883883i
$33$	−1.40408	+	0.810647i	−0.0425479	+	0.0245651i
$34$	14.5732	+	8.41385i	0.428624	+	0.247466i
$35$	−1.44949	−	2.51059i	−0.0414140	−	0.0717311i
$36$	8.89898	+	15.4135i	0.247194	+	0.428152i
$37$			21.9917i			0.594371i	0.954820	+	0.297186i	$0.0960480\pi$
$37$			21.9917i			0.594371i	−0.954820	+	0.297186i	$0.903952\pi$
$38$	−17.3258	−	20.5382i	−0.455941	−	0.540479i
$39$	−0.0556128			−0.00142597
$40$	2.44949	−	1.41421i	0.0612372	−	0.0353553i
$41$	−46.9393	+	27.1004i	−1.14486	+	0.660986i	−0.947630	−	0.319371i	$-0.896528\pi$
$41$	−46.9393	+	27.1004i	−1.14486	+	0.660986i	−0.197231	+	0.980357i	$0.563195\pi$
$42$	−0.651531	+	1.12848i	−0.0155126	+	0.0268687i
$43$	−18.6691	−	32.3359i	−0.434166	−	0.751997i	0.563061	−	0.826415i	$-0.309623\pi$
$43$	−18.6691	−	32.3359i	−0.434166	−	0.751997i	−0.997227	+	0.0744178i	$0.976290\pi$
$44$	−5.10102	+	8.83523i	−0.115932	+	0.200801i
$45$	−8.89898			−0.197755
$46$		−	24.1058i		−	0.524040i
$47$	−40.7702	+	70.6160i	−0.867450	+	1.50247i	−0.00285637	+	0.999996i	$0.500909\pi$
$47$	−40.7702	+	70.6160i	−0.867450	+	1.50247i	−0.864594	+	0.502472i	$0.832424\pi$
$48$	−1.10102	−	0.635674i	−0.0229379	−	0.0132432i
$49$	−40.5959			−0.828488
$50$		−	33.9411i		−	0.678823i
$51$	3.27526	+	1.89097i	0.0642207	+	0.0370778i
$52$	−0.303062	+	0.174973i	−0.00582811	+	0.00336486i
$53$	48.2878	+	27.8789i	0.911090	+	0.526018i	0.880782	−	0.473523i	$-0.157018\pi$
$53$	48.2878	+	27.8789i	0.911090	+	0.526018i	0.0303081	+	0.999541i	$0.490351\pi$
$54$	4.02270	+	6.96753i	0.0744945	+	0.129028i
$55$	−2.55051	−	4.41761i	−0.0463729	−	0.0803202i
$56$			8.19955i			0.146421i
$57$	−3.89388	−	4.61586i	−0.0683136	−	0.0809799i
$58$	62.9444			1.08525
$59$	−29.9166	+	17.2723i	−0.507061	+	0.292752i	−0.731625	−	0.681708i	$-0.761238\pi$
$59$	−29.9166	+	17.2723i	−0.507061	+	0.292752i	0.224564	+	0.974459i	$0.427904\pi$
$60$	0.550510	−	0.317837i	0.00917517	−	0.00529729i
$61$	38.0959	−	65.9841i	0.624523	−	1.08171i	−0.364110	−	0.931356i	$-0.618627\pi$
$61$	38.0959	−	65.9841i	0.624523	−	1.08171i	0.988633	−	0.150350i	$-0.0480400\pi$
$62$	−22.0454	−	38.1838i	−0.355571	−	0.615867i
$63$	12.8990	−	22.3417i	0.204746	−	0.354630i
$64$	−8.00000			−0.125000
$65$		−	0.174973i		−	0.00269189i
$66$	−1.14643	+	1.98567i	−0.0173701	+	0.0300859i
$67$	102.659	+	59.2702i	1.53222	+	0.884629i	0.999259	+	0.0384912i	$0.0122552\pi$
$67$	102.659	+	59.2702i	1.53222	+	0.884629i	0.532964	+	0.846138i	$0.321078\pi$
$68$	23.7980			0.349970
$69$		−	5.41767i		−	0.0785169i
$70$	−3.55051	−	2.04989i	−0.0507216	−	0.0292841i
$71$	65.4773	−	37.8033i	0.922215	−	0.532441i	0.0378743	−	0.999283i	$-0.487941\pi$
$71$	65.4773	−	37.8033i	0.922215	−	0.532441i	0.884341	+	0.466841i	$0.154608\pi$
$72$	21.7980	+	12.5851i	0.302749	+	0.174792i
$73$	−14.6918	−	25.4470i	−0.201258	−	0.348589i	0.747676	−	0.664064i	$-0.231170\pi$
$73$	−14.6918	−	25.4470i	−0.201258	−	0.348589i	−0.948934	+	0.315475i	$0.897836\pi$
$74$	15.5505	+	26.9343i	0.210142	+	0.363977i
$75$		−	7.62809i		−	0.101708i
$76$	−35.7423	−	12.9029i	−0.470294	−	0.169775i
$77$	14.7878			0.192049
$78$	−0.0681115	+	0.0393242i	−0.000873225	+	0.000504157i
$79$	−57.2196	+	33.0358i	−0.724299	+	0.418174i	−0.816333	−	0.577582i	$-0.803997\pi$
$79$	−57.2196	+	33.0358i	−0.724299	+	0.418174i	0.0920338	+	0.995756i	$0.470663\pi$
$80$	2.00000	−	3.46410i	0.0250000	−	0.0433013i
$81$	−39.1413	−	67.7948i	−0.483226	−	0.836972i
$82$	−38.3258	+	66.3822i	−0.467387	+	0.809539i
$83$	−30.6969			−0.369843			−0.184921	−	0.982753i	$-0.559203\pi$
$83$	−30.6969			−0.369843			−0.184921	+	0.982753i	$0.559203\pi$
$84$			1.84281i			0.0219382i
$85$	−5.94949	+	10.3048i	−0.0699940	+	0.121233i
$86$	−45.7298	−	26.4021i	−0.531742	−	0.307002i
$87$	14.1464			0.162603
$88$			14.4279i			0.163953i
$89$	−8.84847	−	5.10867i	−0.0994210	−	0.0574007i	0.449465	−	0.893298i	$-0.351615\pi$
$89$	−8.84847	−	5.10867i	−0.0994210	−	0.0574007i	−0.548886	+	0.835897i	$0.684948\pi$
$90$	−10.8990	+	6.29253i	−0.121100	+	0.0699170i
$91$	0.439285	+	0.253621i	0.00482730	+	0.00278704i
$92$	−17.0454	−	29.5235i	−0.185276	−	0.320908i
$93$	−4.95459	−	8.58161i	−0.0532752	−	0.0922753i
$94$			115.315i			1.22676i
$95$	14.5227	−	12.2512i	0.152871	−	0.128960i
$96$	−1.79796			−0.0187287
$97$	−128.848	+	74.3907i	−1.32833	+	0.766914i	−0.985042	−	0.172314i	$-0.944876\pi$
$97$	−128.848	+	74.3907i	−1.32833	+	0.766914i	−0.343293	+	0.939228i	$0.611542\pi$
$98$	−49.7196	+	28.7056i	−0.507343	+	0.292915i
$99$	22.6969	−	39.3123i	0.229262	−	0.397093i
$100$	−24.0000	−	41.5692i	−0.240000	−	0.415692i
$101$	70.2423	−	121.663i	0.695469	−	1.20459i	−0.274554	−	0.961572i	$-0.588530\pi$
$101$	70.2423	−	121.663i	0.695469	−	1.20459i	0.970022	−	0.243015i	$-0.0781366\pi$
$102$	5.34847			0.0524360
$103$			113.965i			1.10646i	0.833028	+	0.553230i	$0.186605\pi$
$103$			113.965i			1.10646i	−0.833028	+	0.553230i	$0.813395\pi$
$104$	−0.247449	+	0.428594i	−0.00237931	+	0.00412109i
$105$	−0.797959	−	0.460702i	−0.00759961	−	0.00438764i
$106$	78.8536			0.743902
$107$			113.965i			1.06510i	0.846399	+	0.532549i	$0.178766\pi$
$107$			113.965i			1.06510i	−0.846399	+	0.532549i	$0.821234\pi$
$108$	9.85357	+	5.68896i	0.0912368	+	0.0526756i
$109$	59.2423	−	34.2036i	0.543508	−	0.313794i	−0.202992	−	0.979180i	$-0.565066\pi$
$109$	59.2423	−	34.2036i	0.543508	−	0.313794i	0.746499	+	0.665386i	$0.231733\pi$
$110$	−6.24745	−	3.60697i	−0.0567950	−	0.0327906i
$111$	3.49490	+	6.05334i	0.0314856	+	0.0545346i
$112$	5.79796	+	10.0424i	0.0517675	+	0.0896639i
$113$		−	81.9313i		−	0.725056i	−0.931973	−	0.362528i	$-0.881914\pi$
$113$		−	81.9313i		−	0.725056i	0.931973	−	0.362528i	$-0.118086\pi$
$114$	−8.03291	−	2.89986i	−0.0704641	−	0.0254374i
$115$	17.0454			0.148221
$116$	77.0908	−	44.5084i	0.664576	−	0.383693i
$117$	1.34847	−	0.778539i	0.0115254	−	0.00665418i
$118$	−24.4268	+	42.3084i	−0.207007	+	0.358546i
$119$	−17.2474	−	29.8735i	−0.144937	−	0.251037i
$120$	0.449490	−	0.778539i	0.00374575	−	0.00648783i
$121$	−94.9796			−0.784955
$122$		−	107.752i		−	0.883209i
$123$	−8.61352	+	14.9191i	−0.0700286	+	0.121293i
$124$	−54.0000	−	31.1769i	−0.435484	−	0.251427i
$125$	49.0000			0.392000
$126$		−	36.4838i		−	0.289554i
$127$	116.174	+	67.0732i	0.914758	+	0.528136i	0.881959	−	0.471326i	$-0.156225\pi$
$127$	116.174	+	67.0732i	0.914758	+	0.528136i	0.0327989	+	0.999462i	$0.489558\pi$
$128$	−9.79796	+	5.65685i	−0.0765466	+	0.0441942i
$129$	−10.2775	−	5.93375i	−0.0796709	−	0.0459980i
$130$	−0.123724	−	0.214297i	−0.000951726	−	0.00164844i
$131$	−41.3763	−	71.6658i	−0.315849	−	0.547067i	0.663768	−	0.747938i	$-0.268956\pi$
$131$	−41.3763	−	71.6658i	−0.315849	−	0.547067i	−0.979618	+	0.200871i	$0.935623\pi$
$132$			3.24259i			0.0245651i
$133$	9.70714	+	54.2185i	0.0729860	+	0.407658i
$134$	167.641			1.25105
$135$	−4.92679	+	2.84448i	−0.0364947	+	0.0210702i
$136$	29.1464	−	16.8277i	0.214312	−	0.123733i
$137$	5.94949	−	10.3048i	0.0434269	−	0.0752177i	−0.843495	−	0.537137i	$-0.819506\pi$
$137$	5.94949	−	10.3048i	0.0434269	−	0.0752177i	0.886922	+	0.461919i	$0.152839\pi$
$138$	−3.83087	−	6.63526i	−0.0277599	−	0.0480816i
$139$	−20.8712	+	36.1499i	−0.150152	+	0.260071i	−0.931283	−	0.364296i	$-0.881310\pi$
$139$	−20.8712	+	36.1499i	−0.150152	+	0.260071i	0.781131	+	0.624367i	$0.214643\pi$
$140$	−5.79796			−0.0414140
$141$			25.9165i			0.183805i
$142$	53.4620	−	92.5989i	0.376493	−	0.652105i
$143$	0.772962	+	0.446270i	0.00540533	+	0.00312077i
$144$	35.5959			0.247194
$145$			44.5084i			0.306955i
$146$	−35.9875	−	20.7774i	−0.246490	−	0.142311i
$147$	−11.1742	+	6.45145i	−0.0760152	+	0.0438874i
$148$	38.0908	+	21.9917i	0.257370	+	0.148593i
$149$	17.8383	+	30.8968i	0.119720	+	0.207361i	0.919657	−	0.392723i	$-0.128467\pi$
$149$	17.8383	+	30.8968i	0.119720	+	0.207361i	−0.799937	+	0.600084i	$0.795134\pi$
$150$	−5.39388	−	9.34247i	−0.0359592	−	0.0622831i
$151$		−	85.5527i		−	0.566574i	−0.959035	−	0.283287i	$-0.908575\pi$
$151$		−	85.5527i		−	0.566574i	0.959035	−	0.283287i	$-0.0914249\pi$
$152$	−52.8990	+	9.47090i	−0.348020	+	0.0623086i
$153$	−105.889			−0.692083
$154$	18.1112	−	10.4565i	0.117605	−	0.0678995i
$155$	27.0000	−	15.5885i	0.174194	−	0.100571i
$156$	−0.0556128	+	0.0963242i	−0.000356492	+	0.000617463i
$157$	100.076	+	173.336i	0.637424	+	1.10405i	0.985996	+	0.166768i	$0.0533332\pi$
$157$	100.076	+	173.336i	0.637424	+	1.10405i	−0.348573	+	0.937282i	$0.613333\pi$
$158$	−46.7196	+	80.9208i	−0.295694	+	0.512157i
$159$	17.7219			0.111459
$160$		−	5.65685i		−	0.0353553i
$161$	−24.7071	+	42.7940i	−0.153461	+	0.265801i
$162$	−95.8763	−	55.3542i	−0.591829	−	0.341693i
$163$	−127.303			−0.781000			−0.390500	−	0.920603i	$-0.627698\pi$
$163$	−127.303			−0.781000			−0.390500	+	0.920603i	$0.627698\pi$
$164$			108.402i			0.660986i
$165$	−1.40408	−	0.810647i	−0.00850959	−	0.00491301i
$166$	−37.5959	+	21.7060i	−0.226481	+	0.130759i
$167$	−158.917	−	91.7505i	−0.951596	−	0.549404i	−0.0580198	−	0.998315i	$-0.518479\pi$
$167$	−158.917	−	91.7505i	−0.951596	−	0.549404i	−0.893576	+	0.448911i	$0.851812\pi$
$168$	1.30306	+	2.25697i	0.00775632	+	0.0134343i
$169$	−84.4847	−	146.332i	−0.499909	−	0.865869i
$170$			16.8277i			0.0989865i
$171$	159.035	+	57.4113i	0.930030	+	0.335739i
$172$	−74.6765			−0.434166
$173$	−57.6214	+	33.2677i	−0.333072	+	0.192299i	−0.657204	−	0.753713i	$-0.728261\pi$
$173$	−57.6214	+	33.2677i	−0.333072	+	0.192299i	0.324132	+	0.946012i	$0.394928\pi$
$174$	17.3258	−	10.0030i	0.0995734	−	0.0574887i
$175$	−34.7878	+	60.2542i	−0.198787	+	0.344309i
$176$	10.2020	+	17.6705i	0.0579661	+	0.100400i
$177$	−5.48979	+	9.50860i	−0.0310158	+	0.0537209i
$178$	−14.4495			−0.0811769
$179$		−	24.2134i		−	0.135270i	−0.997710	−	0.0676351i	$-0.978455\pi$
$179$		−	24.2134i		−	0.135270i	0.997710	−	0.0676351i	$-0.0215454\pi$
$180$	−8.89898	+	15.4135i	−0.0494388	+	0.0856305i
$181$	30.8939	+	17.8366i	0.170684	+	0.0985447i	0.582909	−	0.812538i	$-0.301915\pi$
$181$	30.8939	+	17.8366i	0.170684	+	0.0985447i	−0.412224	+	0.911082i	$0.635248\pi$
$182$	0.717349			0.00394148
$183$		−	24.2166i		−	0.132331i
$184$	−41.7526	−	24.1058i	−0.226916	−	0.131010i
$185$	−19.0454	+	10.9959i	−0.102948	+	0.0594371i
$186$	−12.1362	−	7.00685i	−0.0652485	−	0.0376712i
$187$	−30.3485	−	52.5651i	−0.162291	−	0.281097i
$188$	81.5403	+	141.232i	0.433725	+	0.751234i
$189$		−	16.4922i		−	0.0872602i
$190$	9.12372	−	25.2737i	0.0480196	−	0.133019i
$191$	−180.252			−0.943728			−0.471864	−	0.881671i	$-0.656419\pi$
$191$	−180.252			−0.943728			−0.471864	+	0.881671i	$0.656419\pi$
$192$	−2.20204	+	1.27135i	−0.0114690	+	0.00662161i
$193$	188.985	−	109.110i	0.979195	−	0.565339i	0.0771682	−	0.997018i	$-0.475412\pi$
$193$	188.985	−	109.110i	0.979195	−	0.565339i	0.902027	+	0.431679i	$0.142079\pi$
$194$	−105.204	+	182.219i	−0.542290	+	0.939274i
$195$	−0.0278064	−	0.0481621i	−0.000142597	−	0.000246985i
$196$	−40.5959	+	70.3142i	−0.207122	+	0.358746i
$197$	340.091			1.72635			0.863175	−	0.504905i	$-0.168473\pi$
$197$	340.091			1.72635			0.863175	+	0.504905i	$0.168473\pi$
$198$		−	64.1966i		−	0.324225i
$199$	166.694	−	288.723i	0.837659	−	1.45087i	−0.0541881	−	0.998531i	$-0.517257\pi$
$199$	166.694	−	288.723i	0.837659	−	1.45087i	0.891847	−	0.452337i	$-0.149410\pi$
$200$	−58.7878	−	33.9411i	−0.293939	−	0.169706i
$201$	37.6765			0.187445
$202$		−	198.675i		−	0.983541i
$203$	−111.742	−	64.5145i	−0.550455	−	0.317805i
$204$	6.55051	−	3.78194i	0.0321103	−	0.0185389i
$205$	−46.9393	−	27.1004i	−0.228972	−	0.132197i
$206$	80.5857	+	139.579i	0.391193	+	0.677566i
$207$	75.8434	+	131.365i	0.366393	+	0.634611i
$208$			0.699891i			0.00336486i
$209$	17.0806	+	95.4024i	0.0817254	+	0.456471i
$210$	−1.30306			−0.00620505
$211$	302.750	−	174.793i	1.43483	−	0.828401i	0.437349	−	0.899292i	$-0.355918\pi$
$211$	302.750	−	174.793i	1.43483	−	0.828401i	0.997484	+	0.0708908i	$0.0225842\pi$
$212$	96.5755	−	55.7579i	0.455545	−	0.263009i
$213$	12.0153	−	20.8111i	0.0564099	−	0.0977048i
$214$	80.5857	+	139.579i	0.376569	+	0.652236i
$215$	18.6691	−	32.3359i	0.0868332	−	0.150399i
$216$	16.0908			0.0744945
$217$			90.3812i			0.416503i
$218$	48.3712	−	83.7813i	0.221886	−	0.384318i
$219$	−8.08801	−	4.66961i	−0.0369315	−	0.0213224i
$220$	−10.2020			−0.0463729
$221$		−	2.08200i		−	0.00942080i
$222$	8.56072	+	4.94253i	0.0385618	+	0.0222637i
$223$	−27.5227	+	15.8902i	−0.123420	+	0.0712567i	−0.560439	−	0.828196i	$-0.689368\pi$
$223$	−27.5227	+	15.8902i	−0.123420	+	0.0712567i	0.437019	+	0.899452i	$0.356034\pi$
$224$	14.2020	+	8.19955i	0.0634020	+	0.0366051i
$225$	106.788	+	184.962i	0.474612	+	0.822053i
$226$	−57.9342	−	100.345i	−0.256346	−	0.444004i
$227$		−	249.730i		−	1.10013i	−0.835121	−	0.550066i	$-0.814603\pi$
$227$		−	249.730i		−	1.10013i	0.835121	−	0.550066i	$-0.185397\pi$
$228$	−11.8888	+	2.12854i	−0.0521437	+	0.00933569i
$229$	−259.687			−1.13400			−0.567002	−	0.823717i	$-0.691897\pi$
$229$	−259.687			−1.13400			−0.567002	+	0.823717i	$0.691897\pi$
$230$	20.8763	−	12.0529i	0.0907664	−	0.0524040i
$231$	4.07041	−	2.35005i	0.0176208	−	0.0101734i
$232$	62.9444	−	109.023i	0.271312	−	0.469926i
$233$	195.141	+	337.995i	0.837516	+	1.45062i	0.891965	+	0.452104i	$0.149327\pi$
$233$	195.141	+	337.995i	0.837516	+	1.45062i	−0.0544486	+	0.998517i	$0.517340\pi$
$234$	1.10102	−	1.90702i	0.00470522	−	0.00814967i
$235$	−81.5403			−0.346980
$236$			69.0894i			0.292752i
$237$	−10.5000	+	18.1865i	−0.0443038	+	0.0767364i
$238$	−42.2474	−	24.3916i	−0.177510	−	0.102486i
$239$	−296.677			−1.24132			−0.620662	−	0.784078i	$-0.713136\pi$
$239$	−296.677			−1.24132			−0.620662	+	0.784078i	$0.713136\pi$
$240$		−	1.27135i		−	0.00529729i
$241$	−99.7270	−	57.5774i	−0.413805	−	0.238911i	0.278618	−	0.960402i	$-0.410124\pi$
$241$	−99.7270	−	57.5774i	−0.413805	−	0.238911i	−0.692423	+	0.721491i	$0.743457\pi$
$242$	−116.326	+	67.1607i	−0.480685	+	0.277524i
$243$	−65.8888	−	38.0409i	−0.271147	−	0.156547i
$244$	−76.1918	−	131.968i	−0.312262	−	0.540853i
$245$	−20.2980	−	35.1571i	−0.0828488	−	0.143498i
$246$			24.3627i			0.0990354i
$247$	−1.12883	+	3.12697i	−0.00457015	+	0.0126598i
$248$	−88.1816			−0.355571
$249$	−8.44949	+	4.87832i	−0.0339337	+	0.0195916i
$250$	60.0125	−	34.6482i	0.240050	−	0.138593i
$251$	−244.962	+	424.287i	−0.975944	+	1.69038i	−0.299161	+	0.954203i	$0.596707\pi$
$251$	−244.962	+	424.287i	−0.975944	+	1.69038i	−0.676783	+	0.736182i	$0.736627\pi$
$252$	−25.7980	−	44.6834i	−0.102373	−	0.177315i
$253$	−43.4745	+	75.3000i	−0.171836	+	0.297629i
$254$	189.712			0.746897
$255$			3.78194i			0.0148311i
$256$	−8.00000	+	13.8564i	−0.0312500	+	0.0541266i
$257$	−197.379	−	113.957i	−0.768010	−	0.443411i	0.0641543	−	0.997940i	$-0.479565\pi$
$257$	−197.379	−	113.957i	−0.768010	−	0.443411i	−0.832164	+	0.554529i	$0.812898\pi$
$258$	−16.7832			−0.0650510
$259$		−	63.7536i		−	0.246153i
$260$	−0.303062	−	0.174973i	−0.00116562	−	0.000672972i
$261$	−343.015	+	198.040i	−1.31423	+	0.758773i
$262$	−101.351	−	58.5149i	−0.386835	−	0.223339i
$263$	−67.9620	−	117.714i	−0.258411	−	0.447580i	0.707406	−	0.706808i	$-0.249865\pi$
$263$	−67.9620	−	117.714i	−0.258411	−	0.447580i	−0.965816	+	0.259227i	$0.916532\pi$
$264$	2.29286	+	3.97134i	0.00868506	+	0.0150430i
$265$			55.7579i			0.210407i
$266$	50.2270	+	59.5398i	0.188823	+	0.223834i
$267$	−3.24745			−0.0121627
$268$	205.318	−	118.540i	0.766111	−	0.442315i
$269$	225.090	−	129.956i	0.836767	−	0.483108i	−0.0193970	−	0.999812i	$-0.506175\pi$
$269$	225.090	−	129.956i	0.836767	−	0.483108i	0.856164	+	0.516704i	$0.172841\pi$
$270$	−4.02270	+	6.96753i	−0.0148989	+	0.0258057i
$271$	116.492	+	201.770i	0.429860	+	0.744540i	0.996860	−	0.0791780i	$-0.0252295\pi$
$271$	116.492	+	201.770i	0.429860	+	0.744540i	−0.567000	+	0.823718i	$0.691896\pi$
$272$	23.7980	−	41.2193i	0.0874925	−	0.151541i
$273$	0.161220			0.000590551
$274$		−	16.8277i		−	0.0614150i
$275$	−61.2122	+	106.023i	−0.222590	+	0.385537i
$276$	−9.38367	−	5.41767i	−0.0339988	−	0.0196292i
$277$	−9.44387			−0.0340934			−0.0170467	−	0.999855i	$-0.505426\pi$
$277$	−9.44387			−0.0340934			−0.0170467	+	0.999855i	$0.505426\pi$
$278$			59.0326i			0.212347i
$279$	240.272	+	138.721i	0.861192	+	0.497209i
$280$	−7.10102	+	4.09978i	−0.0253608	+	0.0146421i
$281$	135.591	+	78.2834i	0.482530	+	0.278589i	0.721470	−	0.692446i	$-0.243467\pi$
$281$	135.591	+	78.2834i	0.482530	+	0.278589i	−0.238940	+	0.971034i	$0.576800\pi$
$282$	18.3258	+	31.7412i	0.0649850	+	0.112557i
$283$	−1.46709	−	2.54108i	−0.00518407	−	0.00897907i	0.863422	−	0.504483i	$-0.168317\pi$
$283$	−1.46709	−	2.54108i	−0.00518407	−	0.00897907i	−0.868606	+	0.495504i	$0.834983\pi$
$284$		−	151.213i		−	0.532441i
$285$	2.05051	−	5.68012i	0.00719477	−	0.0199303i
$286$	1.26224			0.00441343
$287$	136.076	−	78.5635i	0.474132	−	0.273741i
$288$	43.5959	−	25.1701i	0.151375	−	0.0873962i
$289$	73.7071	−	127.665i	0.255042	−	0.441746i
$290$	31.4722	+	54.5114i	0.108525	+	0.187970i
$291$	−23.6441	+	40.9528i	−0.0812513	+	0.140731i
$292$	−58.7673			−0.201258
$293$		−	332.361i		−	1.13434i	−0.823601	−	0.567169i	$-0.808039\pi$
$293$		−	332.361i		−	1.13434i	0.823601	−	0.567169i	$-0.191961\pi$
$294$	−9.12372	+	15.8028i	−0.0310331	+	0.0537509i
$295$	−29.9166	−	17.2723i	−0.101412	−	0.0585503i
$296$	62.2020			0.210142
$297$		−	29.0195i		−	0.0977088i
$298$	43.6946	+	25.2271i	0.146626	+	0.0846547i
$299$	−2.58290	+	1.49124i	−0.00863847	+	0.00498743i
$300$	−13.2122	−	7.62809i	−0.0440408	−	0.0254270i
$301$	54.1214	+	93.7411i	0.179805	+	0.311432i
$302$	−60.4949	−	104.780i	−0.200314	−	0.346954i
$303$		−	44.6513i		−	0.147364i
$304$	−58.0908	+	49.0047i	−0.191088	+	0.161200i
$305$	76.1918			0.249809
$306$	−129.687	+	74.8747i	−0.423813	+	0.244688i
$307$	222.962	−	128.727i	0.726261	−	0.419307i	−0.0907920	−	0.995870i	$-0.528940\pi$
$307$	222.962	−	128.727i	0.726261	−	0.419307i	0.817053	+	0.576563i	$0.195607\pi$
$308$	14.7878	−	25.6131i	0.0480122	−	0.0831595i
$309$	18.1112	+	31.3696i	0.0586124	+	0.101520i
$310$	22.0454	−	38.1838i	0.0711142	−	0.123173i
$311$	217.666			0.699892			0.349946	−	0.936770i	$-0.386200\pi$
$311$	217.666			0.699892			0.349946	+	0.936770i	$0.386200\pi$
$312$			0.157297i			0.000504157i
$313$	155.121	−	268.677i	0.495594	−	0.858394i	−0.504393	−	0.863474i	$-0.668284\pi$
$313$	155.121	−	268.677i	0.495594	−	0.858394i	0.999987	+	0.00508018i	$0.00161708\pi$
$314$	245.134	+	141.528i	0.780681	+	0.450727i
$315$	25.7980			0.0818983
$316$			132.143i			0.418174i
$317$	−298.939	−	172.593i	−0.943026	−	0.544456i	−0.0521185	−	0.998641i	$-0.516597\pi$
$317$	−298.939	−	172.593i	−0.943026	−	0.544456i	−0.890908	+	0.454185i	$0.849931\pi$
$318$	21.7049	−	12.5313i	0.0682542	−	0.0394066i
$319$	−196.621	−	113.519i	−0.616367	−	0.355859i
$320$	−4.00000	−	6.92820i	−0.0125000	−	0.0216506i
$321$	18.1112	+	31.3696i	0.0564213	+	0.0977245i
$322$			69.8824i			0.217026i
$323$	172.805	−	145.776i	0.535001	−	0.451320i
$324$	−156.565			−0.483226
$325$	−3.63674	+	2.09967i	−0.0111900	+	0.00646053i
$326$	−155.914	+	90.0169i	−0.478263	+	0.276125i
$327$	10.8712	−	18.8294i	0.0332452	−	0.0575823i
$328$	76.6515	+	132.764i	0.233694	+	0.404769i
$329$	118.192	−	204.714i	0.359246	−	0.622232i
$330$	−2.29286			−0.00694805
$331$			487.318i			1.47226i	0.676841	+	0.736130i	$0.263349\pi$
$331$			487.318i			1.47226i	−0.676841	+	0.736130i	$0.736651\pi$
$332$	−30.6969	+	53.1687i	−0.0924607	+	0.160147i
$333$	−169.485	−	97.8520i	−0.508963	−	0.293850i
$334$	−259.510			−0.776975
$335$			118.540i			0.353852i
$336$	3.19184	+	1.84281i	0.00949951	+	0.00548455i
$337$	144.393	−	83.3655i	0.428467	−	0.247376i	−0.270226	−	0.962797i	$-0.587099\pi$
$337$	144.393	−	83.3655i	0.428467	−	0.247376i	0.698693	+	0.715421i	$0.253765\pi$
$338$	−206.944	−	119.479i	−0.612262	−	0.353489i
$339$	−13.0204	−	22.5520i	−0.0384083	−	0.0665251i
$340$	11.8990	+	20.6096i	0.0349970	+	0.0606166i
$341$			159.034i			0.466376i
$342$	235.373	−	42.1407i	0.688227	−	0.123218i
$343$	259.737			0.757250
$344$	−91.4597	+	52.8043i	−0.265871	+	0.153501i
$345$	4.69184	−	2.70883i	0.0135995	−	0.00785169i
$346$	−47.0477	+	81.4890i	−0.135976	+	0.235517i
$347$	−188.871	−	327.134i	−0.544297	−	0.942751i	−0.998651	−	0.0519291i	$-0.983463\pi$
$347$	−188.871	−	327.134i	−0.544297	−	0.942751i	0.454353	−	0.890822i	$-0.349870\pi$
$348$	14.1464	−	24.5023i	0.0406507	−	0.0704090i
$349$	−586.434			−1.68033			−0.840163	−	0.542334i	$-0.817541\pi$
$349$	−586.434			−1.68033			−0.840163	+	0.542334i	$0.817541\pi$
$350$			98.3946i			0.281128i
$351$	0.497706	−	0.862053i	0.00141797	−	0.00245599i
$352$	24.9898	+	14.4279i	0.0709937	+	0.0409883i
$353$	476.817			1.35076			0.675379	−	0.737471i	$-0.263980\pi$
$353$	476.817			1.35076			0.675379	+	0.737471i	$0.263980\pi$
$354$			15.5275i			0.0438630i
$355$	65.4773	+	37.8033i	0.184443	+	0.106488i
$356$	−17.6969	+	10.2173i	−0.0497105	+	0.0287004i
$357$	−9.49490	−	5.48188i	−0.0265964	−	0.0153554i
$358$	−17.1214	−	29.6552i	−0.0478252	−	0.0828357i
$359$	123.704	+	214.262i	0.344580	+	0.596831i	0.985277	−	0.170963i	$-0.0546879\pi$
$359$	123.704	+	214.262i	0.344580	+	0.596831i	−0.640697	+	0.767794i	$0.721355\pi$
$360$			25.1701i			0.0699170i
$361$	−338.576	+	125.250i	−0.937882	+	0.346954i
$362$	50.4495			0.139363
$363$	−26.1436	+	15.0940i	−0.0720210	+	0.0415813i
$364$	0.878569	−	0.507242i	0.00241365	−	0.00139352i
$365$	14.6918	−	25.4470i	0.0402516	−	0.0697178i
$366$	−17.1237	−	29.6592i	−0.0467861	−	0.0810360i
$367$	−241.962	+	419.090i	−0.659297	+	1.14194i	0.321501	+	0.946909i	$0.395813\pi$
$367$	−241.962	+	419.090i	−0.659297	+	1.14194i	−0.980798	+	0.195027i	$0.937521\pi$
$368$	−68.1816			−0.185276
$369$		−	482.332i		−	1.30713i
$370$	−15.5505	+	26.9343i	−0.0420284	+	0.0727953i
$371$	−139.985	−	80.8205i	−0.377319	−	0.217845i
$372$	−19.8184			−0.0532752
$373$		−	140.908i		−	0.377768i	−0.981999	−	0.188884i	$-0.939513\pi$
$373$		−	140.908i		−	0.377768i	0.981999	−	0.188884i	$-0.0604871\pi$
$374$	−74.3383	−	42.9192i	−0.198765	−	0.114757i
$375$	13.4875	−	7.78701i	0.0359667	−	0.0207654i
$376$	199.732	+	115.315i	0.531203	+	0.306690i
$377$	−3.89388	−	6.74439i	−0.0103286	−	0.0178896i
$378$	−11.6617	−	20.1987i	−0.0308512	−	0.0534358i
$379$			468.633i			1.23650i	0.785982	+	0.618249i	$0.212158\pi$
$379$			468.633i			1.23650i	−0.785982	+	0.618249i	$0.787842\pi$
$380$	−6.69694	−	37.4052i	−0.0176235	−	0.0984348i
$381$	42.6367			0.111907
$382$	−220.763	+	127.457i	−0.577913	+	0.333658i
$383$	−482.552	+	278.602i	−1.25993	+	0.727420i	−0.973060	−	0.230551i	$-0.925947\pi$
$383$	−482.552	+	278.602i	−1.25993	+	0.727420i	−0.286867	+	0.957970i	$0.592614\pi$
$384$	−1.79796	+	3.11416i	−0.00468218	+	0.00810978i
$385$	7.39388	+	12.8066i	0.0192049	+	0.0332638i
$386$	154.305	−	267.265i	0.399755	−	0.692396i
$387$	332.272			0.858585
$388$			297.563i			0.766914i
$389$	−46.5602	+	80.6446i	−0.119692	+	0.207313i	−0.919646	−	0.392749i	$-0.871524\pi$
$389$	−46.5602	+	80.6446i	−0.119692	+	0.207313i	0.799954	+	0.600062i	$0.204857\pi$
$390$	−0.0681115	−	0.0393242i	−0.000174645	−	0.000100831i
$391$	202.823			0.518729
$392$			114.823i			0.292915i
$393$	−22.7781	−	13.1509i	−0.0579595	−	0.0334629i
$394$	416.524	−	240.481i	1.05717	−	0.610357i
$395$	−57.2196	−	33.0358i	−0.144860	−	0.0836349i
$396$	−45.3939	−	78.6245i	−0.114631	−	0.198547i
$397$	−129.682	−	224.615i	−0.326654	−	0.565781i	0.655192	−	0.755463i	$-0.272588\pi$
$397$	−129.682	−	224.615i	−0.326654	−	0.565781i	−0.981846	+	0.189681i	$0.939255\pi$
$398$		−	471.482i		−	1.18463i
$399$	11.2883	+	13.3813i	0.0282914	+	0.0335370i
$400$	−96.0000			−0.240000
$401$	−389.484	+	224.869i	−0.971282	+	0.560770i	−0.899627	−	0.436659i	$-0.856161\pi$
$401$	−389.484	+	224.869i	−0.971282	+	0.560770i	−0.0716553	+	0.997429i	$0.522828\pi$
$402$	46.1441	−	26.6413i	0.114786	−	0.0662720i
$403$	−2.72755	+	4.72426i	−0.00676812	+	0.0117227i
$404$	−140.485	−	243.327i	−0.347734	−	0.602294i
$405$	39.1413	−	67.7948i	0.0966452	−	0.167394i
$406$	−182.474			−0.449445
$407$		−	112.180i		−	0.275627i
$408$	5.34847	−	9.26382i	0.0131090	−	0.0227054i
$409$	90.8326	+	52.4423i	0.222085	+	0.128221i	0.606915	−	0.794767i	$-0.292407\pi$
$409$	90.8326	+	52.4423i	0.222085	+	0.128221i	−0.384830	+	0.922987i	$0.625740\pi$
$410$	−76.6515			−0.186955
$411$		−	3.78194i		−	0.00920180i
$412$	197.394	+	113.965i	0.479111	+	0.276615i
$413$	86.7276	−	50.0722i	0.209994	−	0.121240i
$414$	185.778	+	107.259i	0.448738	+	0.259079i
$415$	−15.3485	−	26.5843i	−0.0369843	−	0.0640586i
$416$	0.494897	+	0.857187i	0.00118966	+	0.00206055i
$417$			13.2673i			0.0318160i
$418$	88.3791	+	104.766i	0.211433	+	0.250636i
$419$	463.121			1.10530			0.552651	−	0.833413i	$-0.313616\pi$
$419$	463.121			1.10530			0.552651	+	0.833413i	$0.313616\pi$
$420$	−1.59592	+	0.921404i	−0.00379980	+	0.00219382i
$421$	−418.711	+	241.743i	−0.994563	+	0.574211i	−0.906635	−	0.421915i	$-0.861358\pi$
$421$	−418.711	+	241.743i	−0.994563	+	0.574211i	−0.0879282	+	0.996127i	$0.528025\pi$
$422$	247.194	−	428.153i	0.585768	−	1.01458i
$423$	−362.813	−	628.410i	−0.857713	−	1.48560i
$424$	78.8536	−	136.578i	0.185975	−	0.322119i
$425$	285.576			0.671942
$426$		−	33.9844i		−	0.0797756i
$427$	−110.439	+	191.286i	−0.258640	+	0.447978i
$428$	197.394	+	113.965i	0.461201	+	0.266274i
$429$	0.283682			0.000661264
$430$		−	52.8043i		−	0.122801i
$431$	392.447	+	226.579i	0.910549	+	0.525706i	0.880608	−	0.473846i	$-0.157135\pi$
$431$	392.447	+	226.579i	0.910549	+	0.525706i	0.0299413	+	0.999552i	$0.490468\pi$
$432$	19.7071	−	11.3779i	0.0456184	−	0.0263378i
$433$	650.651	+	375.654i	1.50266	+	0.867560i	0.999995	+	0.00307767i	$0.000979653\pi$
$433$	650.651	+	375.654i	1.50266	+	0.867560i	0.502663	+	0.864482i	$0.332354\pi$
$434$	63.9092	+	110.694i	0.147256	+	0.255055i
$435$	7.07321	+	12.2512i	0.0162603	+	0.0281636i
$436$		−	136.814i		−	0.313794i
$437$	−304.621	−	109.968i	−0.697074	−	0.251642i
$438$	−13.2077			−0.0301545
$439$	543.325	−	313.689i	1.23764	−	0.714553i	0.269031	−	0.963132i	$-0.413297\pi$
$439$	543.325	−	313.689i	1.23764	−	0.714553i	0.968612	+	0.248578i	$0.0799632\pi$
$440$	−12.4949	+	7.21393i	−0.0283975	+	0.0163953i
$441$	180.631	−	312.862i	0.409594	−	0.709438i
$442$	−1.47219	−	2.54991i	−0.00333075	−	0.00576904i
$443$	−220.628	+	382.139i	−0.498032	+	0.862617i	−0.999997	−	0.00227061i	$-0.999277\pi$
$443$	−220.628	+	382.139i	−0.498032	+	0.862617i	0.501965	+	0.864888i	$0.332611\pi$
$444$	13.9796			0.0314856
$445$		−	10.2173i		−	0.0229603i
$446$	−22.4722	+	38.9230i	−0.0503861	+	0.0872713i
$447$	9.82015	+	5.66966i	0.0219690	+	0.0126838i
$448$	23.1918			0.0517675
$449$			347.932i			0.774904i	0.921890	+	0.387452i	$0.126645\pi$
$449$			347.932i			0.774904i	−0.921890	+	0.387452i	$0.873355\pi$
$450$	261.576	+	151.021i	0.581279	+	0.335602i
$451$	239.438	−	138.240i	0.530905	−	0.306518i
$452$	−141.909	−	81.9313i	−0.313958	−	0.181264i
$453$	−13.5959	−	23.5488i	−0.0300131	−	0.0519842i
$454$	−176.586	−	305.855i	−0.388955	−	0.673690i
$455$			0.507242i			0.00111482i
$456$	−13.0556	+	11.0135i	−0.0286307	+	0.0241525i
$457$	443.576			0.970625			0.485312	−	0.874341i	$-0.338706\pi$
$457$	443.576			0.970625			0.485312	+	0.874341i	$0.338706\pi$
$458$	−318.050	+	183.626i	−0.694432	+	0.400931i
$459$	−58.6237	+	33.8464i	−0.127721	+	0.0737395i
$460$	17.0454	−	29.5235i	0.0370552	−	0.0641815i
$461$	−97.8076	−	169.408i	−0.212164	−	0.367479i	0.740227	−	0.672357i	$-0.234718\pi$
$461$	−97.8076	−	169.408i	−0.212164	−	0.367479i	−0.952392	+	0.304878i	$0.901384\pi$
$462$	3.32347	−	5.75642i	0.00719366	−	0.0124598i
$463$	−720.958			−1.55715			−0.778573	−	0.627555i	$-0.784056\pi$
$463$	−720.958			−1.55715			−0.778573	+	0.627555i	$0.784056\pi$
$464$		−	178.034i		−	0.383693i
$465$	4.95459	−	8.58161i	0.0106550	−	0.0184551i
$466$	477.997	+	275.972i	1.02574	+	0.592214i
$467$	271.889			0.582203			0.291101	−	0.956692i	$-0.405978\pi$
$467$	271.889			0.582203			0.291101	+	0.956692i	$0.405978\pi$
$468$		−	3.11416i		−	0.00665418i
$469$	−297.606	−	171.823i	−0.634555	−	0.366360i
$470$	−99.8661	+	57.6577i	−0.212481	+	0.122676i
$471$	55.0926	+	31.8077i	0.116969	+	0.0675323i
$472$	48.8536	+	84.6169i	0.103503	+	0.179273i
$473$	95.2316	+	164.946i	0.201335	+	0.348723i
$474$			29.6985i			0.0626550i
$475$	−428.908	−	154.835i	−0.902965	−	0.325968i
$476$	−68.9898			−0.144937
$477$	−429.712	+	248.094i	−0.900863	+	0.520114i
$478$	−363.353	+	209.782i	−0.760153	+	0.438874i
$479$	−173.599	+	300.682i	−0.362419	+	0.627728i	−0.988358	−	0.152144i	$-0.951382\pi$
$479$	−173.599	+	300.682i	−0.362419	+	0.627728i	0.625939	+	0.779872i	$0.284716\pi$
$480$	−0.898979	−	1.55708i	−0.00187287	−	0.00324391i
$481$	1.92398	−	3.33243i	0.00399995	−	0.00692812i
$482$	−162.854			−0.337870
$483$			15.7057i			0.0325170i
$484$	−94.9796	+	164.509i	−0.196239	+	0.339896i
$485$	−128.848	−	74.3907i	−0.265667	−	0.153383i
$486$	−107.596			−0.221391
$487$		−	495.960i		−	1.01840i	−0.860648	−	0.509200i	$-0.829942\pi$
$487$		−	495.960i		−	1.01840i	0.860648	−	0.509200i	$-0.170058\pi$
$488$	−186.631	−	107.752i	−0.382441	−	0.220802i
$489$	−35.0408	+	20.2308i	−0.0716581	+	0.0413718i
$490$	−49.7196	−	28.7056i	−0.101469	−	0.0585830i
$491$	−267.174	−	462.759i	−0.544143	−	0.942483i	−0.998660	−	0.0517455i	$-0.983522\pi$
$491$	−267.174	−	462.759i	−0.544143	−	0.942483i	0.454517	−	0.890738i	$-0.349812\pi$
$492$	17.2270	+	29.8381i	0.0350143	+	0.0606466i
$493$			529.605i			1.07425i
$494$	0.828574	+	4.62794i	0.00167728	+	0.00936829i
$495$	45.3939			0.0917048
$496$	−108.000	+	62.3538i	−0.217742	+	0.125713i
$497$	−189.817	+	109.591i	−0.381926	+	0.220505i
$498$	−6.89898	+	11.9494i	−0.0138534	+	0.0239947i
$499$	−395.457	−	684.951i	−0.792499	−	1.37265i	−0.924415	−	0.381387i	$-0.875446\pi$
$499$	−395.457	−	684.951i	−0.792499	−	1.37265i	0.131917	−	0.991261i	$-0.457887\pi$
$500$	49.0000	−	84.8705i	0.0980000	−	0.169741i
$501$	−58.3235			−0.116414
$502$			692.857i			1.38019i
$503$	−209.841	+	363.455i	−0.417178	+	0.722574i	−0.995654	−	0.0931256i	$-0.970314\pi$
$503$	−209.841	+	363.455i	−0.417178	+	0.722574i	0.578476	+	0.815699i	$0.303648\pi$
$504$	−63.1918	−	36.4838i	−0.125381	−	0.0723885i
$505$	140.485			0.278188
$506$			122.964i			0.243013i
$507$	−46.5097	−	26.8524i	−0.0917351	−	0.0529633i
$508$	232.348	−	134.146i	0.457379	−	0.264068i
$509$	695.515	+	401.556i	1.36643	+	0.788911i	0.990471	−	0.137724i	$-0.0439786\pi$
$509$	695.515	+	401.556i	1.36643	+	0.788911i	0.375963	+	0.926635i	$0.377312\pi$
$510$	2.67423	+	4.63191i	0.00524360	+	0.00908218i
$511$	42.5913	+	73.7703i	0.0833490	+	0.144365i
$512$			22.6274i			0.0441942i
$513$	106.398	−	19.0493i	0.207404	−	0.0371332i
$514$	−322.318			−0.627078
$515$	−98.6969	+	56.9827i	−0.191645	+	0.110646i
$516$	−20.5551	+	11.8675i	−0.0398355	+	0.0229990i
$517$	207.969	−	360.214i	0.402262	−	0.696738i
$518$	−45.0806	−	78.0819i	−0.0870282	−	0.150737i
$519$	−10.5737	+	18.3142i	−0.0203733	+	0.0352875i
$520$	−0.494897			−0.000951726
$521$		−	413.663i		−	0.793979i	−0.917823	−	0.396990i	$-0.870055\pi$
$521$		−	413.663i		−	0.793979i	0.917823	−	0.396990i	$-0.129945\pi$
$522$	−280.070	+	485.096i	−0.536533	+	0.929303i
$523$	434.144	+	250.653i	0.830103	+	0.479260i	0.853888	−	0.520457i	$-0.174238\pi$
$523$	434.144	+	250.653i	0.830103	+	0.479260i	−0.0237853	+	0.999717i	$0.507572\pi$
$524$	−165.505			−0.315849
$525$			22.1137i			0.0421213i
$526$	−166.472	−	96.1128i	−0.316487	−	0.182724i
$527$	321.272	−	185.487i	0.609625	−	0.351967i
$528$	5.61633	+	3.24259i	0.0106370	+	0.00614127i
$529$	119.227	+	206.507i	0.225382	+	0.390373i
$530$	39.4268	+	68.2892i	0.0743902	+	0.128848i
$531$		−	307.413i		−	0.578931i
$532$	103.616	+	37.4052i	0.194768	+	0.0703106i
$533$	9.48366			0.0177930
$534$	−3.97730	+	2.29629i	−0.00744812	+	0.00430017i
$535$	−98.6969	+	56.9827i	−0.184480	+	0.106510i
$536$	167.641	−	290.363i	0.312764	−	0.541723i
$537$	−3.84795	−	6.66485i	−0.00716565	−	0.0124113i
$538$	183.785	−	318.326i	0.341609	−	0.591684i
$539$	207.081			0.384194
$540$			11.3779i			0.0210702i
$541$	196.576	−	340.480i	0.363357	−	0.629352i	−0.625154	−	0.780501i	$-0.714964\pi$
$541$	196.576	−	340.480i	0.363357	−	0.629352i	0.988511	+	0.151149i	$0.0482973\pi$
$542$	285.346	+	164.745i	0.526469	+	0.303957i
$543$	11.3383			0.0208808
$544$		−	67.3108i		−	0.123733i
$545$	59.2423	+	34.2036i	0.108702	+	0.0627589i
$546$	0.197454	−	0.114000i	0.000361637	−	0.000208791i
$547$	−418.159	−	241.424i	−0.764460	−	0.441361i	0.0664350	−	0.997791i	$-0.478838\pi$
$547$	−418.159	−	241.424i	−0.764460	−	0.441361i	−0.830895	+	0.556430i	$0.812171\pi$
$548$	−11.8990	−	20.6096i	−0.0217135	−	0.0376088i
$549$	339.015	+	587.191i	0.617513	+	1.06956i
$550$			173.134i			0.314790i
$551$	287.144	−	795.417i	0.521132	−	1.44359i
$552$	−15.3235			−0.0277599
$553$	165.879	−	95.7700i	0.299961	−	0.173183i
$554$	−11.5663	+	6.67783i	−0.0208779	+	0.0120538i
$555$	−3.49490	+	6.05334i	−0.00629711	+	0.0109069i
$556$	41.7423	+	72.2999i	0.0750762	+	0.130036i
$557$	75.8531	−	131.381i	0.136181	−	0.235873i	−0.789867	−	0.613279i	$-0.789850\pi$
$557$	75.8531	−	131.381i	0.136181	−	0.235873i	0.926048	+	0.377405i	$0.123184\pi$
$558$	392.363			0.703160
$559$			6.53318i			0.0116873i
$560$	−5.79796	+	10.0424i	−0.0103535	+	0.0179328i
$561$	−16.7071	−	9.64587i	−0.0297810	−	0.0171941i
$562$	221.419			0.393984
$563$		−	176.634i		−	0.313737i	−0.987620	−	0.156868i	$-0.949860\pi$
$563$		−	176.634i		−	0.313737i	0.987620	−	0.156868i	$-0.0501399\pi$
$564$	44.8888	+	25.9165i	0.0795900	+	0.0459513i
$565$	70.9546	−	40.9657i	0.125583	−	0.0725056i
$566$	−3.59362	−	2.07478i	−0.00634916	−	0.00366569i
$567$	113.470	+	196.536i	0.200123	+	0.346624i
$568$	−106.924	−	185.198i	−0.188246	−	0.326052i
$569$			957.928i			1.68353i	0.539844	+	0.841765i	$0.318483\pi$
$569$			957.928i			1.68353i	−0.539844	+	0.841765i	$0.681517\pi$
$570$	−1.50510	−	8.40663i	−0.00264053	−	0.0147485i
$571$	833.242			1.45927			0.729634	−	0.683838i	$-0.239691\pi$
$571$	833.242			1.45927			0.729634	+	0.683838i	$0.239691\pi$
$572$	1.54592	−	0.892539i	0.00270266	−	0.00156038i
$573$	−49.6153	+	28.6454i	−0.0865887	+	0.0499920i
$574$	111.106	−	192.441i	0.193564	−	0.335262i
$575$	−204.545	−	354.282i	−0.355730	−	0.616143i
$576$	35.5959	−	61.6539i	0.0617985	−	0.107038i
$577$	−484.595			−0.839852			−0.419926	−	0.907558i	$-0.637944\pi$
$577$	−484.595			−0.839852			−0.419926	+	0.907558i	$0.637944\pi$
$578$		−	208.475i		−	0.360684i
$579$	34.6793	−	60.0664i	0.0598952	−	0.103742i
$580$	77.0908	+	44.5084i	0.132915	+	0.0767386i
$581$	88.9898			0.153167
$582$			66.8757i			0.114907i
$583$	−246.317	−	142.211i	−0.422499	−	0.243930i
$584$	−71.9750	+	41.5548i	−0.123245	+	0.0711555i
$585$	1.34847	+	0.778539i	0.00230508	+	0.00133084i
$586$	−235.015	−	407.058i	−0.401049	−	0.694637i
$587$	309.432	+	535.952i	0.527141	+	0.913035i	0.999500	+	0.0316288i	$0.0100694\pi$
$587$	309.432	+	535.952i	0.527141	+	0.913035i	−0.472358	+	0.881407i	$0.656597\pi$
$588$			25.8058i			0.0438874i
$589$	−583.090	+	104.395i	−0.989966	+	0.177241i
$590$	−48.8536			−0.0828027
$591$	93.6117	−	54.0468i	0.158396	−	0.0914497i
$592$	76.1816	−	43.9835i	0.128685	−	0.0742964i
$593$	93.9699	−	162.761i	0.158465	−	0.274470i	−0.775850	−	0.630917i	$-0.782679\pi$
$593$	93.9699	−	162.761i	0.158465	−	0.274470i	0.934315	+	0.356447i	$0.116012\pi$
$594$	−20.5199	−	35.5415i	−0.0345453	−	0.0598342i
$595$	17.2474	−	29.8735i	0.0289873	−	0.0502075i
$596$	71.3531			0.119720
$597$		−	105.963i		−	0.177493i
$598$	−2.10893	+	3.65278i	−0.00352664	+	0.00610832i
$599$	−69.5533	−	40.1566i	−0.116116	−	0.0670394i	0.440817	−	0.897597i	$-0.354689\pi$
$599$	−69.5533	−	40.1566i	−0.116116	−	0.0670394i	−0.556933	+	0.830557i	$0.688022\pi$
$600$	−21.5755			−0.0359592
$601$		−	665.929i		−	1.10804i	−0.832505	−	0.554018i	$-0.813094\pi$
$601$		−	665.929i		−	1.10804i	0.832505	−	0.554018i	$-0.186906\pi$
$602$	132.570	+	76.5393i	0.220216	+	0.127142i
$603$	−913.560	+	527.444i	−1.51502	+	0.874700i
$604$	−148.182	−	85.5527i	−0.245334	−	0.141644i
$605$	−47.4898	−	82.2547i	−0.0784955	−	0.135958i
$606$	−31.5732	−	54.6864i	−0.0521010	−	0.0902416i
$607$			105.952i			0.174550i	0.996184	+	0.0872751i	$0.0278159\pi$
$607$			105.952i			0.174550i	−0.996184	+	0.0872751i	$0.972184\pi$
$608$	−36.4949	+	101.095i	−0.0600245	+	0.166274i
$609$	−41.0102			−0.0673402
$610$	93.3156	−	53.8758i	0.152976	−	0.0883209i
$611$	12.3559	−	7.13366i	0.0202224	−	0.0116754i
$612$	−105.889	+	183.405i	−0.173021	+	0.299681i
$613$	569.171	+	985.833i	0.928501	+	1.60821i	0.785832	+	0.618440i	$0.212235\pi$
$613$	569.171	+	985.833i	0.928501	+	1.60821i	0.142668	+	0.989771i	$0.454432\pi$
$614$	182.048	−	315.316i	0.296495	−	0.513544i
$615$	−17.2270			−0.0280114
$616$		−	41.8261i		−	0.0678995i
$617$	−459.131	+	795.238i	−0.744135	+	1.28888i	0.206463	+	0.978454i	$0.433805\pi$
$617$	−459.131	+	795.238i	−0.744135	+	1.28888i	−0.950598	+	0.310425i	$0.899529\pi$
$618$	44.3633	+	25.6131i	0.0717852	+	0.0414452i
$619$	−1123.85			−1.81559			−0.907793	−	0.419418i	$-0.862234\pi$
$619$	−1123.85			−1.81559			−0.907793	+	0.419418i	$0.862234\pi$
$620$		−	62.3538i		−	0.100571i
$621$	83.9791	+	48.4853i	0.135232	+	0.0780762i
$622$	266.586	−	153.913i	0.428594	−	0.247449i
$623$	25.6515	+	14.8099i	0.0411742	+	0.0237719i
$624$	0.111226	+	0.192648i	0.000178246	+	0.000308732i
$625$	−275.500	−	477.180i	−0.440800	−	0.763488i
$626$		−	438.748i		−	0.700876i
$627$	19.8627	+	23.5456i	0.0316790	+	0.0375528i
$628$	400.302			0.637424
$629$	−226.621	+	130.840i	−0.360288	+	0.208012i
$630$	31.5959	−	18.2419i	0.0501523	−	0.0289554i
$631$	−40.2753	+	69.7588i	−0.0638277	+	0.110553i	−0.896173	−	0.443704i	$-0.853664\pi$
$631$	−40.2753	+	69.7588i	−0.0638277	+	0.110553i	0.832346	+	0.554257i	$0.186997\pi$
$632$	93.4393	+	161.842i	0.147847	+	0.256078i
$633$	55.5556	−	96.2251i	0.0877656	−	0.152014i
$634$	−488.166			−0.769978
$635$			134.146i			0.211254i
$636$	17.7219	−	30.6953i	0.0278647	−	0.0482630i
$637$	6.15153	+	3.55159i	0.00965703	+	0.00557549i
$638$	−321.081			−0.503261
$639$			672.822i			1.05293i
$640$	−9.79796	−	5.65685i	−0.0153093	−	0.00883883i
$641$	−428.893	+	247.621i	−0.669100	+	0.386305i	−0.795735	−	0.605644i	$-0.792915\pi$
$641$	−428.893	+	247.621i	−0.669100	+	0.386305i	0.126636	+	0.991949i	$0.459582\pi$
$642$	44.3633	+	25.6131i	0.0691017	+	0.0398959i
$643$	−245.123	−	424.566i	−0.381218	−	0.660289i	0.610019	−	0.792387i	$-0.291162\pi$
$643$	−245.123	−	424.566i	−0.381218	−	0.660289i	−0.991237	+	0.132098i	$0.957829\pi$
$644$	49.4143	+	85.5881i	0.0767303	+	0.132901i
$645$		−	11.8675i		−	0.0183992i
$646$	108.563	−	300.731i	0.168054	−	0.465527i
$647$	−494.132			−0.763727			−0.381864	−	0.924219i	$-0.624718\pi$
$647$	−494.132			−0.763727			−0.381864	+	0.924219i	$0.624718\pi$
$648$	−191.753	+	110.708i	−0.295914	+	0.170846i
$649$	152.605	−	88.1066i	0.235139	−	0.135757i
$650$	−2.96938	+	5.14312i	−0.00456828	+	0.00791250i
$651$	14.3633	+	24.8779i	0.0220634	+	0.0382149i
$652$	−127.303	+	220.495i	−0.195250	+	0.338183i
$653$	475.383			0.727998			0.363999	−	0.931399i	$-0.381411\pi$
$653$	475.383			0.727998			0.363999	+	0.931399i	$0.381411\pi$
$654$		−	30.7483i		−	0.0470158i
$655$	41.3763	−	71.6658i	0.0631699	−	0.109413i
$656$	187.757	+	108.402i	0.286215	+	0.165246i
$657$	261.485			0.397998
$658$		−	334.297i		−	0.508050i
$659$	494.082	+	285.259i	0.749746	+	0.432866i	0.825602	−	0.564253i	$-0.190836\pi$
$659$	494.082	+	285.259i	0.749746	+	0.432866i	−0.0758563	+	0.997119i	$0.524169\pi$
$660$	−2.80816	+	1.62129i	−0.00425479	+	0.00245651i
$661$	−18.6964	−	10.7944i	−0.0282851	−	0.0163304i	0.485791	−	0.874075i	$-0.338532\pi$
$661$	−18.6964	−	10.7944i	−0.0282851	−	0.0163304i	−0.514076	+	0.857745i	$0.671865\pi$
$662$	344.586	+	596.840i	0.520522	+	0.901571i
$663$	−0.330868	−	0.573080i	−0.000499047	−	0.000864374i
$664$			86.8241i			0.130759i
$665$	−42.1010	+	35.5159i	−0.0633098	+	0.0534073i
$666$	−276.767			−0.415567
$667$	657.022	−	379.332i	0.985041	−	0.568714i
$668$	−317.833	+	183.501i	−0.475798	+	0.274702i
$669$	−5.05051	+	8.74774i	−0.00754934	+	0.0130758i
$670$	83.8207	+	145.182i	0.125105	+	0.216689i
$671$	−194.328	+	336.586i	−0.289610	+	0.501619i
$672$	5.21225			0.00775632
$673$			256.395i			0.380973i	0.981690	+	0.190486i	$0.0610065\pi$
$673$			256.395i			0.380973i	−0.981690	+	0.190486i	$0.938993\pi$
$674$	117.897	−	204.203i	0.174921	−	0.302972i
$675$	118.243	+	68.2675i	0.175175	+	0.101137i
$676$	−337.939			−0.499909
$677$		−	662.815i		−	0.979048i	−0.871990	−	0.489524i	$-0.837171\pi$
$677$		−	662.815i		−	0.979048i	0.871990	−	0.489524i	$-0.162829\pi$
$678$	−31.8934	−	18.4136i	−0.0470404	−	0.0271588i
$679$	373.529	−	215.657i	0.550116	−	0.317610i
$680$	29.1464	+	16.8277i	0.0428624	+	0.0247466i
$681$	−39.6867	−	68.7394i	−0.0582771	−	0.100939i
$682$	112.454	+	194.776i	0.164889	+	0.285596i
$683$		−	310.334i		−	0.454369i	−0.973852	−	0.227184i	$-0.927048\pi$
$683$		−	310.334i		−	0.454369i	0.973852	−	0.227184i	$-0.0729520\pi$
$684$	258.474	−	218.046i	0.377887	−	0.318780i
$685$	11.8990			0.0173708
$686$	318.111	−	183.662i	0.463719	−	0.267728i
$687$	−71.4801	+	41.2691i	−0.104047	+	0.0600714i
$688$	−74.6765	+	129.344i	−0.108541	+	0.187999i
$689$	−4.87805	−	8.44904i	−0.00707990	−	0.0122628i
$690$	3.83087	−	6.63526i	0.00555198	−	0.00961632i
$691$	187.789			0.271764			0.135882	−	0.990725i	$-0.456613\pi$
$691$	187.789			0.271764			0.135882	+	0.990725i	$0.456613\pi$
$692$			133.071i			0.192299i
$693$	−65.7980	+	113.965i	−0.0949465	+	0.164452i
$694$	−462.638	−	267.104i	−0.666625	−	0.384876i
$695$	−41.7423			−0.0600609
$696$		−	40.0121i		−	0.0574887i
$697$	−558.530	−	322.467i	−0.801334	−	0.462650i
$698$	−718.232	+	414.671i	−1.02899	+	0.594085i
$699$	107.427	+	62.0232i	0.153687	+	0.0887313i
$700$	69.5755	+	120.508i	0.0993936	+	0.172155i
$701$	−270.818	−	469.070i	−0.386331	−	0.669144i	0.605622	−	0.795752i	$-0.292924\pi$
$701$	−270.818	−	469.070i	−0.386331	−	0.669144i	−0.991953	+	0.126608i	$0.959591\pi$
$702$		−	1.40773i		−	0.00200531i
$703$	411.303	−	73.6387i	0.585068	−	0.104749i
$704$	40.8082			0.0579661
$705$	−22.4444	+	12.9583i	−0.0318360	+	0.0183805i
$706$	583.980	−	337.161i	0.827167	−	0.477565i
$707$	−203.631	+	352.699i	−0.288021	+	0.498868i
$708$	10.9796	+	19.0172i	0.0155079	+	0.0268605i
$709$	245.621	−	425.429i	0.346434	−	0.600041i	−0.639180	−	0.769058i	$-0.720726\pi$
$709$	245.621	−	425.429i	0.346434	−	0.600041i	0.985613	+	0.169017i	$0.0540593\pi$
$710$	106.924			0.150597
$711$		−	587.969i		−	0.826961i
$712$	−14.4495	+	25.0273i	−0.0202942	+	0.0351506i
$713$	−460.226	−	265.712i	−0.645478	−	0.372667i
$714$	−15.5051			−0.0217158
$715$			0.892539i			0.00124831i
$716$	−41.9388	−	24.2134i	−0.0585737	−	0.0338175i
$717$	−81.6617	+	47.1474i	−0.113894	+	0.0657565i
$718$	303.012	+	174.944i	0.422023	+	0.243655i
$719$	287.734	+	498.370i	0.400186	+	0.693143i	0.993748	−	0.111645i	$-0.0356121\pi$
$719$	287.734	+	498.370i	0.400186	+	0.693143i	−0.593562	+	0.804788i	$0.702279\pi$
$720$	17.7980	+	30.8270i	0.0247194	+	0.0428152i
$721$		−	330.383i		−	0.458229i
$722$	−326.103	+	392.809i	−0.451667	+	0.544056i
$723$	−36.6005			−0.0506231
$724$	61.7878	−	35.6732i	0.0853422	−	0.0492723i
$725$	925.090	−	534.101i	1.27599	−	0.736691i
$726$	−21.3462	+	36.9727i	−0.0294024	+	0.0509265i
$727$	409.552	+	709.365i	0.563346	+	0.975743i	0.997201	+	0.0747610i	$0.0238194\pi$
$727$	409.552	+	709.365i	0.563346	+	0.975743i	−0.433856	+	0.900982i	$0.642847\pi$
$728$	0.717349	−	1.24248i	0.000985369	−	0.00170671i
$729$	680.362			0.933282
$730$		−	41.5548i		−	0.0569244i
$731$	222.144	−	384.764i	0.303890	−	0.526353i
$732$	−41.9444	−	24.2166i	−0.0573011	−	0.0330828i
$733$	804.332			1.09731			0.548657	−	0.836047i	$-0.315139\pi$
$733$	804.332			1.09731			0.548657	+	0.836047i	$0.315139\pi$
$734$			684.372i			0.932387i
$735$	−11.1742	−	6.45145i	−0.0152030	−	0.00877748i
$736$	−83.5051	+	48.2117i	−0.113458	+	0.0655050i
$737$	−523.665	−	302.338i	−0.710536	−	0.410228i
$738$	−341.060	−	590.734i	−0.462141	−	0.800452i
$739$	−37.9314	−	65.6991i	−0.0513280	−	0.0889027i	0.839220	−	0.543792i	$-0.183012\pi$
$739$	−37.9314	−	65.6991i	−0.0513280	−	0.0889027i	−0.890548	+	0.454890i	$0.849679\pi$
$740$			43.9835i			0.0594371i
$741$	0.186218	+	1.04011i	0.000251306	+	0.00140365i
$742$	−228.595			−0.308079
$743$	505.810	−	292.030i	0.680767	−	0.393041i	−0.119377	−	0.992849i	$-0.538090\pi$
$743$	505.810	−	292.030i	0.680767	−	0.393041i	0.800144	+	0.599808i	$0.204756\pi$
$744$	−24.2724	+	14.0137i	−0.0326243	+	0.0188356i
$745$	−17.8383	+	30.8968i	−0.0239440	+	0.0414722i
$746$	−99.6367	−	172.576i	−0.133561	−	0.231335i
$747$	136.586	−	236.573i	0.182846	−	0.316698i
$748$	−121.394			−0.162291
$749$		−	330.383i		−	0.441099i
$750$	11.0125	−	19.0742i	0.0146833	−	0.0254323i
$751$	513.931	+	296.718i	0.684329	+	0.395098i	0.801484	−	0.598016i	$-0.204044\pi$
$751$	513.931	+	296.718i	0.684329	+	0.395098i	−0.117155	+	0.993114i	$0.537377\pi$
$752$	326.161			0.433725
$753$			155.716i			0.206794i
$754$	−9.53801	−	5.50677i	−0.0126499	−	0.00730341i
$755$	74.0908	−	42.7764i	0.0981335	−	0.0566574i
$756$	−28.5653	−	16.4922i	−0.0377848	−	0.0218151i
$757$	278.257	+	481.956i	0.367579	+	0.636665i	0.989186	−	0.146664i	$-0.0468535\pi$
$757$	278.257	+	481.956i	0.367579	+	0.636665i	−0.621608	+	0.783329i	$0.713520\pi$
$758$	331.373	+	573.956i	0.437168	+	0.757197i
$759$			27.6356i			0.0364106i
$760$	−34.6515	−	41.0764i	−0.0455941	−	0.0540479i
$761$	−1211.85			−1.59244			−0.796219	−	0.605008i	$-0.793170\pi$
$761$	−1211.85			−1.59244			−0.796219	+	0.605008i	$0.793170\pi$
$762$	52.2191	−	30.1487i	0.0685290	−	0.0395653i
$763$	−171.742	+	99.1555i	−0.225088	+	0.129955i
$764$	−180.252	+	312.206i	−0.235932	+	0.408646i
$765$	−52.9444	−	91.7024i	−0.0692083	−	0.119872i
$766$	−394.002	+	682.432i	−0.514363	+	0.890903i
$767$	6.04438			0.00788054
$768$			5.08540i			0.00662161i
$769$	479.115	−	829.852i	0.623037	−	1.07913i	−0.365880	−	0.930662i	$-0.619232\pi$
$769$	479.115	−	829.852i	0.623037	−	1.07913i	0.988917	−	0.148469i	$-0.0474347\pi$
$770$	18.1112	+	10.4565i	0.0235211	+	0.0135799i
$771$	−72.4393			−0.0939550
$772$		−	436.441i		−	0.565339i
$773$	−404.409	−	233.486i	−0.523168	−	0.302051i	0.215062	−	0.976600i	$-0.431005\pi$
$773$	−404.409	−	233.486i	−0.523168	−	0.302051i	−0.738230	+	0.674549i	$0.764338\pi$
$774$	406.949	−	234.952i	0.525774	−	0.303556i
$775$	−648.000	−	374.123i	−0.836129	−	0.482739i
$776$	210.409	+	364.439i	0.271145	+	0.469637i
$777$	−10.1316	−	17.5485i	−0.0130394	−	0.0225850i
$778$			131.692i			0.169270i
$779$	664.023	+	787.142i	0.852405	+	1.01045i
$780$	−0.111226			−0.000142597
$781$	−334.001	+	192.836i	−0.427658	+	0.246909i
$782$	248.406	−	143.417i	0.317655	−	0.183398i
$783$	−126.603	+	219.283i	−0.161690	+	0.280055i
$784$	81.1918	+	140.628i	0.103561	+	0.179373i
$785$	−100.076	+	173.336i	−0.127485	+	0.220810i
$786$	−37.1964			−0.0473237
$787$			1410.48i			1.79223i	0.443824	+	0.896114i	$0.353621\pi$
$787$			1410.48i			1.79223i	−0.443824	+	0.896114i	$0.646379\pi$
$788$	340.091	−	589.055i	0.431587	−	0.747531i
$789$	−37.4138	−	21.6009i	−0.0474192	−	0.0273775i
$790$	−93.4393			−0.118278
$791$			237.517i			0.300275i
$792$	−111.192	−	64.1966i	−0.140394	−	0.0810564i
$793$	−11.5454	+	6.66574i	−0.0145592	+	0.00840573i
$794$	−317.654	−	183.398i	−0.400068	−	0.230979i
$795$	8.86097	+	15.3476i	0.0111459	+	0.0193052i
$796$	−333.388	−	577.445i	−0.418829	−	0.725434i
$797$		−	774.540i		−	0.971819i	−0.874009	−	0.485909i	$-0.838489\pi$
$797$		−	774.540i		−	0.971819i	0.874009	−	0.485909i	$-0.161511\pi$
$798$	23.2872	+	8.40663i	0.0291820	+	0.0105346i
$799$	−970.246			−1.21433
$800$	−117.576	+	67.8823i	−0.146969	+	0.0848528i
$801$	78.7423	−	45.4619i	0.0983051	−	0.0567564i
$802$	−318.012	+	550.814i	−0.396524	+	0.686800i
$803$	74.9434	+	129.806i	0.0933292	+	0.161651i
$804$	37.6765	−	65.2577i	0.0468614	−	0.0811662i
$805$	−49.4143			−0.0613842
$806$			7.71469i			0.00957157i
$807$	41.3048	−	71.5421i	0.0511832	−	0.0886519i
$808$	−344.116	−	198.675i	−0.425886	−	0.245885i
$809$	−1114.09			−1.37712			−0.688559	−	0.725180i	$-0.741756\pi$
$809$	−1114.09			−1.37712			−0.688559	+	0.725180i	$0.741756\pi$
$810$		−	110.708i		−	0.136677i
$811$	−13.7656	−	7.94755i	−0.0169736	−	0.00979970i	0.491489	−	0.870884i	$-0.336453\pi$
$811$	−13.7656	−	7.94755i	−0.0169736	−	0.00979970i	−0.508463	+	0.861084i	$0.669786\pi$
$812$	−223.485	+	129.029i	−0.275227	+	0.158903i
$813$	64.1301	+	37.0255i	0.0788808	+	0.0455419i
$814$	−79.3235	−	137.392i	−0.0974490	−	0.168787i
$815$	−63.6515	−	110.248i	−0.0781000	−	0.135273i
$816$		−	15.1278i		−	0.0185389i
$817$	−542.253	+	457.437i	−0.663712	+	0.559899i
$818$	148.329			0.181331
$819$	−3.90918	+	2.25697i	−0.00477312	+	0.00275576i
$820$	−93.8786	+	54.2008i	−0.114486	+	0.0660986i
$821$	102.444	−	177.439i	0.124780	−	0.216125i	−0.796867	−	0.604155i	$-0.793511\pi$
$821$	102.444	−	177.439i	0.124780	−	0.216125i	0.921647	+	0.388030i	$0.126844\pi$
$822$	−2.67423	−	4.63191i	−0.00325333	−	0.00563493i
$823$	−621.052	+	1075.69i	−0.754619	+	1.30704i	0.190944	+	0.981601i	$0.438845\pi$
$823$	−621.052	+	1075.69i	−0.754619	+	1.30704i	−0.945563	+	0.325438i	$0.894488\pi$
$824$	322.343			0.391193
$825$			38.9111i			0.0471649i
$826$	70.8128	−	122.651i	0.0857297	−	0.148488i
$827$	−990.128	−	571.651i	−1.19725	−	0.691234i	−0.237311	−	0.971434i	$-0.576266\pi$
$827$	−990.128	−	571.651i	−1.19725	−	0.691234i	−0.959942	+	0.280200i	$0.909599\pi$
$828$	303.373			0.366393
$829$			1080.66i			1.30357i	0.758404	+	0.651784i	$0.225979\pi$
$829$			1080.66i			1.30357i	−0.758404	+	0.651784i	$0.774021\pi$
$830$	−37.5959	−	21.7060i	−0.0452963	−	0.0261518i
$831$	−2.59947	+	1.50081i	−0.00312813	+	0.00180603i
$832$	1.21225	+	0.699891i	0.00145703	+	0.000841215i
$833$	−241.525	−	418.334i	−0.289946	−	0.502201i
$834$	9.38138	+	16.2490i	0.0112487	+	0.0194832i
$835$		−	183.501i		−	0.219762i
$836$	182.322	+	65.8179i	0.218089	+	0.0787296i
$837$	177.364			0.211905
$838$	567.206	−	327.476i	0.676856	−	0.390783i
$839$	582.598	−	336.363i	0.694395	−	0.400909i	−0.110861	−	0.993836i	$-0.535361\pi$
$839$	582.598	−	336.363i	0.694395	−	0.400909i	0.805257	+	0.592927i	$0.202028\pi$
$840$	−1.30306	+	2.25697i	−0.00155126	+	0.00268687i
$841$	569.999	+	987.267i	0.677763	+	1.17392i
$842$	−341.876	+	592.147i	−0.406029	+	0.703263i
$843$	49.7628			0.0590306
$844$		−	699.171i		−	0.828401i
$845$	84.4847	−	146.332i	0.0999819	−	0.173174i
$846$	−888.706	−	513.095i	−1.05048	−	0.606495i
$847$	275.344			0.325081
$848$		−	223.032i		−	0.263009i
$849$	−0.807649	−	0.466296i	−0.000951294	−	0.000549230i
$850$	349.757	−	201.932i	0.411479	−	0.237568i
$851$	324.637	+	187.429i	0.381477	+	0.220246i
$852$	−24.0306	−	41.6222i	−0.0282049	−	0.0488524i
$853$	−123.620	−	214.117i	−0.144924	−	0.251016i	0.784420	−	0.620229i	$-0.212961\pi$
$853$	−123.620	−	214.117i	−0.144924	−	0.251016i	−0.929345	+	0.369213i	$0.879627\pi$
$854$			312.369i			0.365772i
$855$	29.7980	+	166.434i	0.0348514	+	0.194660i
$856$	322.343			0.376569
$857$	−615.227	+	355.201i	−0.717884	+	0.414470i	−0.813973	−	0.580902i	$-0.802700\pi$
$857$	−615.227	+	355.201i	−0.717884	+	0.414470i	0.0960894	+	0.995373i	$0.469367\pi$
$858$	0.347438	−	0.200594i	0.000404940	−	0.000233792i
$859$	−505.183	+	875.003i	−0.588106	+	1.01863i	0.406374	+	0.913707i	$0.366793\pi$
$859$	−505.183	+	875.003i	−0.588106	+	1.01863i	−0.994480	+	0.104923i	$0.966540\pi$
$860$	−37.3383	−	64.6718i	−0.0434166	−	0.0751997i
$861$	24.9704	−	43.2500i	0.0290016	−	0.0502323i
$862$	640.863			0.743460
$863$		−	455.826i		−	0.528188i	−0.964497	−	0.264094i	$-0.914927\pi$
$863$		−	455.826i		−	0.528188i	0.964497	−	0.264094i	$-0.0850729\pi$
$864$	16.0908	−	27.8701i	0.0186236	−	0.0322571i
$865$	−57.6214	−	33.2677i	−0.0666144	−	0.0384598i
$866$	1062.51			1.22692
$867$		−	46.8538i		−	0.0540412i
$868$	156.545	+	90.3812i	0.180351	+	0.104126i
$869$	291.879	−	168.516i	0.335879	−	0.193920i
$870$	17.3258	+	10.0030i	0.0199147	+	0.0114977i
$871$	−10.3707	−	17.9625i	−0.0119066	−	0.0206229i
$872$	−96.7423	−	167.563i	−0.110943	−	0.192159i
$873$		−	1324.00i		−	1.51661i
$874$	−450.842	+	80.7177i	−0.515838	+	0.0923543i
$875$	−142.050			−0.162343
$876$	−16.1760	+	9.33923i	−0.0184658	+	0.0106612i
$877$	564.060	−	325.660i	0.643170	−	0.371334i	−0.142665	−	0.989771i	$-0.545567\pi$
$877$	564.060	−	325.660i	0.643170	−	0.371334i	0.785834	+	0.618437i	$0.212234\pi$
$878$	443.623	−	768.378i	0.505266	−	0.875146i
$879$	−52.8184	−	91.4841i	−0.0600892	−	0.104077i
$880$	−10.2020	+	17.6705i	−0.0115932	+	0.0200801i
$881$	−518.293			−0.588301			−0.294150	−	0.955759i	$-0.595037\pi$
$881$	−518.293			−0.588301			−0.294150	+	0.955759i	$0.595037\pi$
$882$		−	510.902i		−	0.579254i
$883$	336.532	−	582.890i	0.381123	−	0.660125i	−0.610100	−	0.792325i	$-0.708871\pi$
$883$	336.532	−	582.890i	0.381123	−	0.660125i	0.991223	+	0.132200i	$0.0422040\pi$
$884$	−3.60612	−	2.08200i	−0.00407932	−	0.00235520i
$885$	−10.9796			−0.0124063
$886$			624.031i			0.704324i
$887$	1296.33	+	748.434i	1.46147	+	0.843781i	0.999080	−	0.0428947i	$-0.0136580\pi$
$887$	1296.33	+	748.434i	1.46147	+	0.843781i	0.462392	+	0.886676i	$0.346991\pi$
$888$	17.1214	−	9.88506i	0.0192809	−	0.0111318i
$889$	−336.787	−	194.444i	−0.378838	−	0.218722i
$890$	−7.22474	−	12.5136i	−0.00811769	−	0.0140603i
$891$	199.661	+	345.822i	0.224086	+	0.388128i
$892$			63.5610i			0.0712567i
$893$	1457.22	+	526.053i	1.63183	+	0.589085i
$894$	16.0362			0.0179376
$895$	20.9694	−	12.1067i	0.0234295	−	0.0135270i
$896$	28.4041	−	16.3991i	0.0317010	−	0.0183026i
$897$	−0.473972	+	0.820943i	−0.000528397	+	0.000915210i
$898$	246.025	+	426.128i	0.273970	+	0.474530i
$899$	693.817	−	1201.73i	0.771766	−	1.33674i
$900$	427.151			0.474612
$901$			663.462i			0.736362i
$902$	195.501	−	338.617i	0.216741	−	0.375407i
$903$	29.7944	+	17.2018i	0.0329949	+	0.0190496i
$904$	−231.737			−0.256346
$905$			35.6732i			0.0394179i
$906$	−33.3031	−	19.2275i	−0.0367583	−	0.0212224i
$907$	243.114	−	140.362i	0.268042	−	0.154754i	−0.359956	−	0.932969i	$-0.617208\pi$
$907$	243.114	−	140.362i	0.268042	−	0.154754i	0.627997	+	0.778215i	$0.283875\pi$
$908$	−432.545	−	249.730i	−0.476371	−	0.275033i
$909$	625.085	+	1082.68i	0.687662	+	1.19107i
$910$	0.358674	+	0.621242i	0.000394148	+	0.000682684i
$911$		−	783.689i		−	0.860252i	−0.902769	−	0.430126i	$-0.858469\pi$
$911$		−	783.689i		−	0.860252i	0.902769	−	0.430126i	$-0.141531\pi$
$912$	−8.20204	+	22.7205i	−0.00899347	+	0.0249128i
$913$	156.586			0.171507
$914$	543.267	−	313.655i	0.594384	−	0.343168i
$915$	20.9722	−	12.1083i	0.0229204	−	0.0132331i
$916$	−259.687	+	449.791i	−0.283501	+	0.491038i
$917$	119.949	+	207.758i	0.130806	+	0.226562i
$918$	−47.8661	+	82.9065i	−0.0521417	+	0.0903121i
$919$	−220.334			−0.239754			−0.119877	−	0.992789i	$-0.538250\pi$
$919$	−220.334			−0.239754			−0.119877	+	0.992789i	$0.538250\pi$
$920$		−	48.2117i		−	0.0524040i
$921$	40.9143	−	70.8656i	0.0444238	−	0.0769442i
$922$	−239.579	−	138.321i	−0.259847	−	0.150023i
$923$	−13.2291			−0.0143327
$924$		−	9.40020i		−	0.0101734i
$925$	457.090	+	263.901i	0.494151	+	0.285298i
$926$	−882.990	+	509.794i	−0.953553	+	0.550534i
$927$	−878.302	−	507.088i	−0.947467	−	0.547020i
$928$	−125.889	−	218.046i	−0.135656	−	0.234963i
$929$	−614.742	−	1064.76i	−0.661724	−	1.14614i	−0.980162	−	0.198196i	$-0.936492\pi$
$929$	−614.742	−	1064.76i	−0.661724	−	1.14614i	0.318438	−	0.947944i	$-0.396842\pi$
$930$		−	14.0137i		−	0.0150685i
$931$	135.934	+	759.250i	0.146009	+	0.815521i
$932$	780.565			0.837516
$933$	59.9138	−	34.5912i	0.0642163	−	0.0370753i
$934$	332.994	−	192.254i	0.356525	−	0.205840i
$935$	30.3485	−	52.5651i	0.0324583	−	0.0562193i
$936$	−2.20204	−	3.81405i	−0.00235261	−	0.00407484i
$937$	67.1061	−	116.231i	0.0716181	−	0.124046i	−0.827993	−	0.560739i	$-0.810517\pi$
$937$	67.1061	−	116.231i	0.0716181	−	0.124046i	0.899611	+	0.436693i	$0.143850\pi$
$938$	−485.989			−0.518112
$939$		−	98.6064i		−	0.105012i
$940$	−81.5403	+	141.232i	−0.0867450	+	0.150247i
$941$	−518.348	−	299.268i	−0.550848	−	0.318032i	0.198616	−	0.980077i	$-0.436355\pi$
$941$	−518.348	−	299.268i	−0.550848	−	0.318032i	−0.749464	+	0.662045i	$0.769689\pi$
$942$	89.9658			0.0955051
$943$			923.875i			0.979719i
$944$	119.666	+	69.0894i	0.126765	+	0.0731879i
$945$	14.2827	−	8.24609i	0.0151139	−	0.00872602i
$946$	233.269	+	134.678i	0.246584	+	0.142366i
$947$	−410.265	−	710.600i	−0.433226	−	0.750369i	0.563923	−	0.825827i	$-0.309291\pi$
$947$	−410.265	−	710.600i	−0.433226	−	0.750369i	−0.997149	+	0.0754579i	$0.975958\pi$
$948$	21.0000	+	36.3731i	0.0221519	+	0.0383682i
$949$			5.14134i			0.00541764i
$950$	−634.788	+	113.651i	−0.668198	+	0.119632i
$951$	−109.713			−0.115366
$952$	−84.4949	+	48.7832i	−0.0887551	+	0.0512428i
$953$	−68.1367	+	39.3388i	−0.0714971	+	0.0412789i	−0.535322	−	0.844648i	$-0.679810\pi$
$953$	−68.1367	+	39.3388i	−0.0714971	+	0.0412789i	0.463825	+	0.885927i	$0.346477\pi$
$954$	−350.858	+	607.704i	−0.367776	+	0.637006i
$955$	−90.1260	−	156.103i	−0.0943728	−	0.163458i
$956$	−296.677	+	513.859i	−0.310331	+	0.537509i
$957$	−72.1612			−0.0754036
$958$			491.011i			0.512538i
$959$	−17.2474	+	29.8735i	−0.0179848	+	0.0311506i
$960$	−2.20204	−	1.27135i	−0.00229379	−	0.00132432i
$961$	−11.0000			−0.0114464
$962$		−	5.44183i		−	0.00565679i
$963$	−878.302	−	507.088i	−0.912048	−	0.526571i
$964$	−199.454	+	115.155i	−0.206903	+	0.119455i
$965$	188.985	+	109.110i	0.195839	+	0.113068i
$966$	11.1056	+	19.2355i	0.0114965	+	0.0199125i
$967$	−664.628	−	1151.17i	−0.687310	−	1.19046i	−0.972705	−	0.232045i	$-0.925458\pi$
$967$	−664.628	−	1151.17i	−0.687310	−	1.19046i	0.285395	−	0.958410i	$-0.407875\pi$
$968$			268.643i			0.277524i
$969$	24.3990	−	67.5877i	0.0251795	−	0.0697499i
$970$	−210.409			−0.216916
$971$	−492.584	+	284.393i	−0.507296	+	0.292887i	−0.731721	−	0.681604i	$-0.761283\pi$
$971$	−492.584	+	284.393i	−0.507296	+	0.292887i	0.224426	+	0.974491i	$0.427949\pi$
$972$	−131.778	+	76.0818i	−0.135574	+	0.0782735i
$973$	60.5051	−	104.798i	0.0621841	−	0.107706i
$974$	−350.697	−	607.425i	−0.360058	−	0.623640i
$975$	−0.667354	+	1.15589i	−0.000684466	+	0.00118553i
$976$	−304.767			−0.312262
$977$			884.903i			0.905735i	0.891578	+	0.452867i	$0.149599\pi$
$977$			884.903i			0.905735i	−0.891578	+	0.452867i	$0.850401\pi$
$978$	−28.6107	+	49.5552i	−0.0292543	+	0.0506699i
$979$	45.1362	+	26.0594i	0.0461044	+	0.0266184i
$980$	−81.1918			−0.0828488
$981$			608.754i			0.620544i
$982$	−654.441	−	377.841i	−0.666436	−	0.384767i
$983$	290.842	−	167.917i	0.295871	−	0.170821i	−0.344715	−	0.938707i	$-0.612025\pi$
$983$	290.842	−	167.917i	0.295871	−	0.170821i	0.640587	+	0.767886i	$0.278691\pi$
$984$	42.1975	+	24.3627i	0.0428836	+	0.0247589i
$985$	170.045	+	294.527i	0.172635	+	0.299012i
$986$	374.487	+	648.630i	0.379804	+	0.657840i
$987$		−	75.1315i		−	0.0761211i
$988$	4.28724	+	5.08215i	0.00433931	+	0.00514388i
$989$	−636.446			−0.643525
$990$	55.5959	−	32.0983i	0.0561575	−	0.0324225i
$991$	−491.433	+	283.729i	−0.495896	+	0.286306i	−0.727017	−	0.686619i	$-0.759094\pi$
$991$	−491.433	+	283.729i	−0.495896	+	0.286306i	0.231121	+	0.972925i	$0.425761\pi$
$992$	−88.1816	+	152.735i	−0.0888928	+	0.153967i
$993$	77.4439	+	134.137i	0.0779898	+	0.135082i
$994$	−154.985	+	268.442i	−0.155921	+	0.270063i
$995$	333.388			0.335064
$996$			19.5133i			0.0195916i
$997$	217.379	−	376.511i	0.218033	−	0.377644i	−0.736174	−	0.676793i	$-0.763369\pi$
$997$	217.379	−	376.511i	0.218033	−	0.377644i	0.954206	+	0.299149i	$0.0967027\pi$
$998$	−968.668	−	559.260i	−0.970609	−	0.560381i
$999$	−125.110			−0.125235

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	38.3.d.a.31.2	yes	4
3.2	odd	2		342.3.m.a.145.1		4
4.3	odd	2		304.3.r.a.145.2		4
19.7	even	3		722.3.b.b.721.4		4
19.8	odd	6	inner	38.3.d.a.27.2	✓	4
19.12	odd	6		722.3.b.b.721.1		4
57.8	even	6		342.3.m.a.217.1		4
76.27	even	6		304.3.r.a.65.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
38.3.d.a.27.2	✓	4	19.8	odd	6	inner
38.3.d.a.31.2	yes	4	1.1	even	1	trivial
304.3.r.a.65.2		4	76.27	even	6
304.3.r.a.145.2		4	4.3	odd	2
342.3.m.a.145.1		4	3.2	odd	2
342.3.m.a.217.1		4	57.8	even	6
722.3.b.b.721.1		4	19.12	odd	6
722.3.b.b.721.4		4	19.7	even	3

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:	\( N \)	\(=\)	\( 38 = 2 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	38.d (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.22474 - 0.707107i) q^{2} +(0.275255 - 0.158919i) q^{3} +(1.00000 - 1.73205i) q^{4} +(0.500000 + 0.866025i) q^{5} +(0.224745 - 0.389270i) q^{6} -2.89898 q^{7} -2.82843i q^{8} +(-4.44949 + 7.70674i) q^{9} +O(q^{10})\)	\(q+(1.22474 - 0.707107i) q^{2} +(0.275255 - 0.158919i) q^{3} +(1.00000 - 1.73205i) q^{4} +(0.500000 + 0.866025i) q^{5} +(0.224745 - 0.389270i) q^{6} -2.89898 q^{7} -2.82843i q^{8} +(-4.44949 + 7.70674i) q^{9} +(1.22474 + 0.707107i) q^{10} -5.10102 q^{11} -0.635674i q^{12} +(-0.151531 - 0.0874863i) q^{13} +(-3.55051 + 2.04989i) q^{14} +(0.275255 + 0.158919i) q^{15} +(-2.00000 - 3.46410i) q^{16} +(5.94949 + 10.3048i) q^{17} +12.5851i q^{18} +(-3.34847 - 18.7026i) q^{19} +2.00000 q^{20} +(-0.797959 + 0.460702i) q^{21} +(-6.24745 + 3.60697i) q^{22} +(8.52270 - 14.7618i) q^{23} +(-0.449490 - 0.778539i) q^{24} +(12.0000 - 20.7846i) q^{25} -0.247449 q^{26} +5.68896i q^{27} +(-2.89898 + 5.02118i) q^{28} +(38.5454 + 22.2542i) q^{29} +0.449490 q^{30} -31.1769i q^{31} +(-4.89898 - 2.82843i) q^{32} +(-1.40408 + 0.810647i) q^{33} +(14.5732 + 8.41385i) q^{34} +(-1.44949 - 2.51059i) q^{35} +(8.89898 + 15.4135i) q^{36} +21.9917i q^{37} +(-17.3258 - 20.5382i) q^{38} -0.0556128 q^{39} +(2.44949 - 1.41421i) q^{40} +(-46.9393 + 27.1004i) q^{41} +(-0.651531 + 1.12848i) q^{42} +(-18.6691 - 32.3359i) q^{43} +(-5.10102 + 8.83523i) q^{44} -8.89898 q^{45} -24.1058i q^{46} +(-40.7702 + 70.6160i) q^{47} +(-1.10102 - 0.635674i) q^{48} -40.5959 q^{49} -33.9411i q^{50} +(3.27526 + 1.89097i) q^{51} +(-0.303062 + 0.174973i) q^{52} +(48.2878 + 27.8789i) q^{53} +(4.02270 + 6.96753i) q^{54} +(-2.55051 - 4.41761i) q^{55} +8.19955i q^{56} +(-3.89388 - 4.61586i) q^{57} +62.9444 q^{58} +(-29.9166 + 17.2723i) q^{59} +(0.550510 - 0.317837i) q^{60} +(38.0959 - 65.9841i) q^{61} +(-22.0454 - 38.1838i) q^{62} +(12.8990 - 22.3417i) q^{63} -8.00000 q^{64} -0.174973i q^{65} +(-1.14643 + 1.98567i) q^{66} +(102.659 + 59.2702i) q^{67} +23.7980 q^{68} -5.41767i q^{69} +(-3.55051 - 2.04989i) q^{70} +(65.4773 - 37.8033i) q^{71} +(21.7980 + 12.5851i) q^{72} +(-14.6918 - 25.4470i) q^{73} +(15.5505 + 26.9343i) q^{74} -7.62809i q^{75} +(-35.7423 - 12.9029i) q^{76} +14.7878 q^{77} +(-0.0681115 + 0.0393242i) q^{78} +(-57.2196 + 33.0358i) q^{79} +(2.00000 - 3.46410i) q^{80} +(-39.1413 - 67.7948i) q^{81} +(-38.3258 + 66.3822i) q^{82} -30.6969 q^{83} +1.84281i q^{84} +(-5.94949 + 10.3048i) q^{85} +(-45.7298 - 26.4021i) q^{86} +14.1464 q^{87} +14.4279i q^{88} +(-8.84847 - 5.10867i) q^{89} +(-10.8990 + 6.29253i) q^{90} +(0.439285 + 0.253621i) q^{91} +(-17.0454 - 29.5235i) q^{92} +(-4.95459 - 8.58161i) q^{93} +115.315i q^{94} +(14.5227 - 12.2512i) q^{95} -1.79796 q^{96} +(-128.848 + 74.3907i) q^{97} +(-49.7196 + 28.7056i) q^{98} +(22.6969 - 39.3123i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 6 q^{3} + 4 q^{4} + 2 q^{5} - 4 q^{6} + 8 q^{7} - 8 q^{9}+O(q^{10}) \) 4 * q + 6 * q^3 + 4 * q^4 + 2 * q^5 - 4 * q^6 + 8 * q^7 - 8 * q^9	\( 4 q + 6 q^{3} + 4 q^{4} + 2 q^{5} - 4 q^{6} + 8 q^{7} - 8 q^{9} - 40 q^{11} - 30 q^{13} - 24 q^{14} + 6 q^{15} - 8 q^{16} + 14 q^{17} + 16 q^{19} + 8 q^{20} + 36 q^{21} + 24 q^{22} - 10 q^{23} + 8 q^{24} + 48 q^{25} + 48 q^{26} + 8 q^{28} + 66 q^{29} - 8 q^{30} - 84 q^{33} + 24 q^{34} + 4 q^{35} + 16 q^{36} - 84 q^{38} - 108 q^{39} + 18 q^{41} - 32 q^{42} + 38 q^{43} - 40 q^{44} - 16 q^{45} - 70 q^{47} - 24 q^{48} - 84 q^{49} + 18 q^{51} - 60 q^{52} - 42 q^{53} - 28 q^{54} - 20 q^{55} + 102 q^{57} + 144 q^{58} + 42 q^{59} + 12 q^{60} + 74 q^{61} + 32 q^{63} - 32 q^{64} + 64 q^{66} + 102 q^{67} + 56 q^{68} - 24 q^{70} + 306 q^{71} + 48 q^{72} + 98 q^{73} + 72 q^{74} + 4 q^{76} - 176 q^{77} + 132 q^{78} - 126 q^{79} + 8 q^{80} + 10 q^{81} - 168 q^{82} - 64 q^{83} - 14 q^{85} - 276 q^{86} - 12 q^{87} - 6 q^{89} - 24 q^{90} - 204 q^{91} + 20 q^{92} - 108 q^{93} + 14 q^{95} + 32 q^{96} - 486 q^{97} - 96 q^{98} + 32 q^{99}+O(q^{100}) \) 4 * q + 6 * q^3 + 4 * q^4 + 2 * q^5 - 4 * q^6 + 8 * q^7 - 8 * q^9 - 40 * q^11 - 30 * q^13 - 24 * q^14 + 6 * q^15 - 8 * q^16 + 14 * q^17 + 16 * q^19 + 8 * q^20 + 36 * q^21 + 24 * q^22 - 10 * q^23 + 8 * q^24 + 48 * q^25 + 48 * q^26 + 8 * q^28 + 66 * q^29 - 8 * q^30 - 84 * q^33 + 24 * q^34 + 4 * q^35 + 16 * q^36 - 84 * q^38 - 108 * q^39 + 18 * q^41 - 32 * q^42 + 38 * q^43 - 40 * q^44 - 16 * q^45 - 70 * q^47 - 24 * q^48 - 84 * q^49 + 18 * q^51 - 60 * q^52 - 42 * q^53 - 28 * q^54 - 20 * q^55 + 102 * q^57 + 144 * q^58 + 42 * q^59 + 12 * q^60 + 74 * q^61 + 32 * q^63 - 32 * q^64 + 64 * q^66 + 102 * q^67 + 56 * q^68 - 24 * q^70 + 306 * q^71 + 48 * q^72 + 98 * q^73 + 72 * q^74 + 4 * q^76 - 176 * q^77 + 132 * q^78 - 126 * q^79 + 8 * q^80 + 10 * q^81 - 168 * q^82 - 64 * q^83 - 14 * q^85 - 276 * q^86 - 12 * q^87 - 6 * q^89 - 24 * q^90 - 204 * q^91 + 20 * q^92 - 108 * q^93 + 14 * q^95 + 32 * q^96 - 486 * q^97 - 96 * q^98 + 32 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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