LMFDB - Embedded newform 348.3.v.a.95.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [348,3,Mod(11,348)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(348, base_ring=CyclotomicField(28))

chi = DirichletCharacter(H, H._module([14, 14, 25]))

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

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

chi := DirichletCharacter("348.11");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 348 = 2^{2} \cdot 3 \cdot 29 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	348.v (of order $28$, degree $12$, 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:	$9.48231319974$
Analytic rank:	$0$
Dimension:	$1392$
Relative dimension:	$116$ over $\Q(\zeta_{28})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{28}]$

Embedding invariants

Embedding label			95.9
Character	$\chi$	$=$	348.95
Dual form			348.3.v.a.11.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.92888 - 0.528587i) q^{2} +(0.0596975 + 2.99941i) q^{3} +(3.44119 + 2.03917i) q^{4} +(7.68944 - 3.70304i) q^{5} +(1.47030 - 5.81706i) q^{6} +(-7.69057 + 6.13302i) q^{7} +(-5.55978 - 5.75229i) q^{8} +(-8.99287 + 0.358114i) q^{9} +O(q^{10})$	\(q+(-1.92888 - 0.528587i) q^{2} +(0.0596975 + 2.99941i) q^{3} +(3.44119 + 2.03917i) q^{4} +(7.68944 - 3.70304i) q^{5} +(1.47030 - 5.81706i) q^{6} +(-7.69057 + 6.13302i) q^{7} +(-5.55978 - 5.75229i) q^{8} +(-8.99287 + 0.358114i) q^{9} +(-16.7894 + 3.07819i) q^{10} +(0.306041 - 0.487062i) q^{11} +(-5.91086 + 10.4433i) q^{12} +(-21.9986 + 5.02105i) q^{13} +(18.0761 - 7.76476i) q^{14} +(11.5660 + 22.8427i) q^{15} +(7.68359 + 14.0343i) q^{16} +(-8.45359 + 8.45359i) q^{17} +(17.5355 + 4.06276i) q^{18} +(-0.492487 - 4.37094i) q^{19} +(34.0119 + 2.93720i) q^{20} +(-18.8545 - 22.7010i) q^{21} +(-0.847773 + 0.777716i) q^{22} +(-0.0694880 - 0.0334637i) q^{23} +(16.9215 - 17.0194i) q^{24} +(29.8277 - 37.4028i) q^{25} +(45.0869 + 1.94319i) q^{26} +(-1.61098 - 26.9519i) q^{27} +(-38.9710 + 5.42254i) q^{28} +(-14.7947 + 24.9423i) q^{29} +(-10.2350 - 50.1745i) q^{30} +(-8.87623 + 25.3668i) q^{31} +(-7.40238 - 31.1321i) q^{32} +(1.47917 + 0.888866i) q^{33} +(20.7745 - 11.8375i) q^{34} +(-36.4253 + 75.6380i) q^{35} +(-31.6764 - 17.1056i) q^{36} +(28.5823 + 45.4885i) q^{37} +(-1.36047 + 8.69137i) q^{38} +(-16.3734 - 65.6831i) q^{39} +(-64.0526 - 23.6438i) q^{40} +(-18.2868 - 18.2868i) q^{41} +(24.3688 + 53.7539i) q^{42} +(-34.1685 + 11.9561i) q^{43} +(2.04635 - 1.05200i) q^{44} +(-67.8240 + 36.0547i) q^{45} +(0.116346 + 0.101278i) q^{46} +(-36.0606 - 22.6584i) q^{47} +(-41.6360 + 23.8840i) q^{48} +(10.6273 - 46.5614i) q^{49} +(-77.3049 + 56.3791i) q^{50} +(-25.8604 - 24.8511i) q^{51} +(-85.9403 - 27.5805i) q^{52} +(8.93509 + 18.5539i) q^{53} +(-11.1390 + 52.8386i) q^{54} +(0.549677 - 4.87852i) q^{55} +(78.0368 + 10.1401i) q^{56} +(13.0808 - 1.73810i) q^{57} +(41.7214 - 40.2905i) q^{58} +40.6648 q^{59} +(-6.77942 + 102.191i) q^{60} +(7.01993 - 62.3036i) q^{61} +(30.5298 - 44.2378i) q^{62} +(66.9640 - 57.9076i) q^{63} +(-2.17768 + 63.9629i) q^{64} +(-150.564 + 120.071i) q^{65} +(-2.38330 - 2.49639i) q^{66} +(-24.4888 + 107.293i) q^{67} +(-46.3287 + 11.8521i) q^{68} +(0.0962229 - 0.210421i) q^{69} +(110.242 - 126.643i) q^{70} +(55.7840 - 12.7323i) q^{71} +(52.0584 + 49.7386i) q^{72} +(-94.3500 + 33.0145i) q^{73} +(-31.0873 - 102.850i) q^{74} +(113.967 + 87.2327i) q^{75} +(7.21835 - 16.0455i) q^{76} +(0.633531 + 5.62274i) q^{77} +(-3.13683 + 135.350i) q^{78} +(-44.7532 - 71.2243i) q^{79} +(111.052 + 79.4635i) q^{80} +(80.7435 - 6.44095i) q^{81} +(25.6069 + 44.9392i) q^{82} +(4.38944 - 5.50419i) q^{83} +(-18.5909 - 116.566i) q^{84} +(-33.6994 + 96.3073i) q^{85} +(72.2270 - 5.00086i) q^{86} +(-75.6953 - 42.8862i) q^{87} +(-4.50324 + 0.947519i) q^{88} +(-16.2611 + 46.4714i) q^{89} +(149.883 - 33.6943i) q^{90} +(138.388 - 173.533i) q^{91} +(-0.170884 - 0.256853i) q^{92} +(-76.6153 - 25.1091i) q^{93} +(57.5798 + 62.7665i) q^{94} +(-19.9727 - 31.7864i) q^{95} +(92.9358 - 24.0612i) q^{96} +(-16.1070 - 142.953i) q^{97} +(-45.1107 + 84.1941i) q^{98} +(-2.57777 + 4.48968i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 1392 q - 28 q^{4} - 14 q^{6} - 28 q^{9}+O(q^{10}) $ 1392 * q - 28 * q^4 - 14 * q^6 - 28 * q^9	$ 1392 q - 28 q^{4} - 14 q^{6} - 28 q^{9} - 8 q^{10} + 36 q^{12} - 56 q^{13} - 52 q^{16} - 32 q^{18} - 76 q^{21} - 28 q^{22} - 10 q^{24} - 1040 q^{25} + 272 q^{30} - 28 q^{33} - 28 q^{34} + 58 q^{36} - 80 q^{37} - 36 q^{40} - 14 q^{42} + 180 q^{45} + 1032 q^{46} - 216 q^{48} + 1088 q^{49} + 120 q^{52} - 10 q^{54} - 308 q^{58} + 240 q^{60} + 112 q^{61} - 1792 q^{64} + 92 q^{66} + 124 q^{69} - 1096 q^{70} + 148 q^{72} - 160 q^{73} + 68 q^{76} - 154 q^{78} - 180 q^{81} - 20 q^{82} + 72 q^{84} - 72 q^{85} + 760 q^{88} + 256 q^{90} - 28 q^{93} - 632 q^{94} - 812 q^{96} + 32 q^{97}+O(q^{100}) $ 1392 * q - 28 * q^4 - 14 * q^6 - 28 * q^9 - 8 * q^10 + 36 * q^12 - 56 * q^13 - 52 * q^16 - 32 * q^18 - 76 * q^21 - 28 * q^22 - 10 * q^24 - 1040 * q^25 + 272 * q^30 - 28 * q^33 - 28 * q^34 + 58 * q^36 - 80 * q^37 - 36 * q^40 - 14 * q^42 + 180 * q^45 + 1032 * q^46 - 216 * q^48 + 1088 * q^49 + 120 * q^52 - 10 * q^54 - 308 * q^58 + 240 * q^60 + 112 * q^61 - 1792 * q^64 + 92 * q^66 + 124 * q^69 - 1096 * q^70 + 148 * q^72 - 160 * q^73 + 68 * q^76 - 154 * q^78 - 180 * q^81 - 20 * q^82 + 72 * q^84 - 72 * q^85 + 760 * q^88 + 256 * q^90 - 28 * q^93 - 632 * q^94 - 812 * q^96 + 32 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/348\mathbb{Z}\right)^\times$.

$n$	$175$	$205$	$233$
$\chi(n)$	$-1$	$e\left(\frac{3}{28}\right)$	$-1$

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 $

$2$	−1.92888	−	0.528587i	−0.964442	−	0.264294i
$2$	−1.92888	−	0.528587i	−0.964442	−	0.264294i
$3$	0.0596975	+	2.99941i	0.0198992	+	0.999802i
$3$	0.0596975	+	2.99941i	0.0198992	+	0.999802i
$4$	3.44119	+	2.03917i	0.860298	+	0.509792i
$5$	7.68944	−	3.70304i	1.53789	−	0.740608i	0.542824	−	0.839846i	$-0.317355\pi$
$5$	7.68944	−	3.70304i	1.53789	−	0.740608i	0.995064	+	0.0992385i	$0.0316407\pi$
$6$	1.47030	−	5.81706i	0.245050	−	0.969511i
$7$	−7.69057	+	6.13302i	−1.09865	+	0.876146i	−0.992983	−	0.118255i	$-0.962270\pi$
$7$	−7.69057	+	6.13302i	−1.09865	+	0.876146i	−0.105669	+	0.994401i	$0.533699\pi$
$8$	−5.55978	−	5.75229i	−0.694973	−	0.719036i
$9$	−8.99287	+	0.358114i	−0.999208	+	0.0397905i
$10$	−16.7894	+	3.07819i	−1.67894	+	0.307819i
$11$	0.306041	−	0.487062i	0.0278219	−	0.0442783i	−0.832524	−	0.553989i	$-0.813105\pi$
$11$	0.306041	−	0.487062i	0.0278219	−	0.0442783i	0.860346	+	0.509711i	$0.170248\pi$
$12$	−5.91086	+	10.4433i	−0.492572	+	0.870272i
$13$	−21.9986	+	5.02105i	−1.69220	+	0.386234i	−0.956652	−	0.291234i	$-0.905934\pi$
$13$	−21.9986	+	5.02105i	−1.69220	+	0.386234i	−0.735551	+	0.677469i	$0.763077\pi$
$14$	18.0761	−	7.76476i	1.29115	−	0.554626i
$15$	11.5660	+	22.8427i	0.771064	+	1.52285i
$16$	7.68359	+	14.0343i	0.480224	+	0.877146i
$17$	−8.45359	+	8.45359i	−0.497270	+	0.497270i	−0.910587	−	0.413317i	$-0.864370\pi$
$17$	−8.45359	+	8.45359i	−0.497270	+	0.497270i	0.413317	+	0.910587i	$0.364370\pi$
$18$	17.5355	+	4.06276i	0.974195	+	0.225709i
$19$	−0.492487	−	4.37094i	−0.0259204	−	0.230050i	−0.999993	−	0.00381295i	$-0.998786\pi$
$19$	−0.492487	−	4.37094i	−0.0259204	−	0.230050i	0.974072	−	0.226237i	$-0.0726423\pi$
$20$	34.0119	+	2.93720i	1.70060	+	0.146860i
$21$	−18.8545	−	22.7010i	−0.897835	−	1.08100i
$22$	−0.847773	+	0.777716i	−0.0385351	+	0.0353507i
$23$	−0.0694880	−	0.0334637i	−0.00302122	−	0.00145494i	0.432373	−	0.901695i	$-0.357677\pi$
$23$	−0.0694880	−	0.0334637i	−0.00302122	−	0.00145494i	−0.435394	+	0.900240i	$0.643391\pi$
$24$	16.9215	−	17.0194i	0.705064	−	0.709143i
$25$	29.8277	−	37.4028i	1.19311	−	1.49611i
$26$	45.0869	+	1.94319i	1.73411	+	0.0747379i
$27$	−1.61098	−	26.9519i	−0.0596660	−	0.998218i
$28$	−38.9710	+	5.42254i	−1.39182	+	0.193662i
$29$	−14.7947	+	24.9423i	−0.510161	+	0.860079i
$29$	−14.7947	+	24.9423i	−0.510161	+	0.860079i
$30$	−10.2350	−	50.1745i	−0.341168	−	1.67248i
$31$	−8.87623	+	25.3668i	−0.286330	+	0.818285i	0.707434	+	0.706780i	$0.249853\pi$
$31$	−8.87623	+	25.3668i	−0.286330	+	0.818285i	−0.993764	+	0.111505i	$0.964433\pi$
$32$	−7.40238	−	31.1321i	−0.231324	−	0.972877i
$33$	1.47917	+	0.888866i	0.0448232	+	0.0269353i
$34$	20.7745	−	11.8375i	0.611013	−	0.348163i
$35$	−36.4253	+	75.6380i	−1.04072	+	2.16109i
$36$	−31.6764	−	17.1056i	−0.879901	−	0.475157i
$37$	28.5823	+	45.4885i	0.772495	+	1.22942i	0.968548	+	0.248825i	$0.0800445\pi$
$37$	28.5823	+	45.4885i	0.772495	+	1.22942i	−0.196054	+	0.980593i	$0.562813\pi$
$38$	−1.36047	+	8.69137i	−0.0358020	+	0.228720i
$39$	−16.3734	−	65.6831i	−0.419831	−	1.68418i
$40$	−64.0526	−	23.6438i	−1.60131	−	0.591095i
$41$	−18.2868	−	18.2868i	−0.446019	−	0.446019i	0.448010	−	0.894029i	$-0.352133\pi$
$41$	−18.2868	−	18.2868i	−0.446019	−	0.446019i	−0.894029	+	0.448010i	$0.852133\pi$
$42$	24.3688	+	53.7539i	0.580208	+	1.27985i
$43$	−34.1685	+	11.9561i	−0.794617	+	0.278049i	−0.696903	−	0.717166i	$-0.745439\pi$
$43$	−34.1685	+	11.9561i	−0.794617	+	0.278049i	−0.0977147	+	0.995214i	$0.531153\pi$
$44$	2.04635	−	1.05200i	0.0465079	−	0.0239092i
$45$	−67.8240	+	36.0547i	−1.50720	+	0.801215i
$46$	0.116346	+	0.101278i	0.00252926	+	0.00220170i
$47$	−36.0606	−	22.6584i	−0.767246	−	0.482093i	0.0906709	−	0.995881i	$-0.471099\pi$
$47$	−36.0606	−	22.6584i	−0.767246	−	0.482093i	−0.857917	+	0.513788i	$0.828242\pi$
$48$	−41.6360	+	23.8840i	−0.867416	+	0.497584i
$49$	10.6273	−	46.5614i	0.216885	−	0.950233i
$50$	−77.3049	+	56.3791i	−1.54610	+	1.12758i
$51$	−25.8604	−	24.8511i	−0.507067	−	0.487276i
$52$	−85.9403	−	27.5805i	−1.65270	−	0.530395i
$53$	8.93509	+	18.5539i	0.168587	+	0.350074i	0.968096	−	0.250580i	$-0.0806213\pi$
$53$	8.93509	+	18.5539i	0.168587	+	0.350074i	−0.799509	+	0.600654i	$0.794907\pi$
$54$	−11.1390	+	52.8386i	−0.206278	+	0.978493i
$55$	0.549677	−	4.87852i	0.00999412	−	0.0887003i
$56$	78.0368	+	10.1401i	1.39351	+	0.181073i
$57$	13.0808	−	1.73810i	0.229488	−	0.0304930i
$58$	41.7214	−	40.2905i	0.719334	−	0.694664i
$59$	40.6648			0.689234			0.344617	−	0.938743i	$-0.388009\pi$
$59$	40.6648			0.689234			0.344617	+	0.938743i	$0.388009\pi$
$60$	−6.77942	+	102.191i	−0.112990	+	1.70318i
$61$	7.01993	−	62.3036i	0.115081	−	1.02137i	−0.794906	−	0.606733i	$-0.792480\pi$
$61$	7.01993	−	62.3036i	0.115081	−	1.02137i	0.909987	−	0.414637i	$-0.136092\pi$
$62$	30.5298	−	44.2378i	0.492416	−	0.713513i
$63$	66.9640	−	57.9076i	1.06292	−	0.919168i
$64$	−2.17768	+	63.9629i	−0.0340262	+	0.999421i
$65$	−150.564	+	120.071i	−2.31637	+	1.84724i
$66$	−2.38330	−	2.49639i	−0.0361106	−	0.0378241i
$67$	−24.4888	+	107.293i	−0.365505	+	1.60138i	0.373465	+	0.927644i	$0.378170\pi$
$67$	−24.4888	+	107.293i	−0.365505	+	1.60138i	−0.738970	+	0.673738i	$0.764688\pi$
$68$	−46.3287	+	11.8521i	−0.681304	+	0.174296i
$69$	0.0962229	−	0.210421i	0.00139453	−	0.00304957i
$70$	110.242	−	126.643i	1.57488	−	1.80919i
$71$	55.7840	−	12.7323i	0.785690	−	0.179329i	0.189189	−	0.981941i	$-0.439414\pi$
$71$	55.7840	−	12.7323i	0.785690	−	0.179329i	0.596501	+	0.802612i	$0.296557\pi$
$72$	52.0584	+	49.7386i	0.723033	+	0.690813i
$73$	−94.3500	+	33.0145i	−1.29247	+	0.452253i	−0.886963	−	0.461841i	$-0.847189\pi$
$73$	−94.3500	+	33.0145i	−1.29247	+	0.452253i	−0.405502	+	0.914094i	$0.632903\pi$
$74$	−31.0873	−	102.850i	−0.420099	−	1.38987i
$75$	113.967	+	87.2327i	1.51956	+	1.16310i
$76$	7.21835	−	16.0455i	0.0949782	−	0.211125i
$77$	0.633531	+	5.62274i	0.00822767	+	0.0730226i
$78$	−3.13683	+	135.350i	−0.0402157	+	1.73526i
$79$	−44.7532	−	71.2243i	−0.566496	−	0.901573i	−1.00000		0.000421462i	$-0.999866\pi$
$79$	−44.7532	−	71.2243i	−0.566496	−	0.901573i	0.433504	−	0.901152i	$-0.357277\pi$
$80$	111.052	+	79.4635i	1.38815	+	0.993294i
$81$	80.7435	−	6.44095i	0.996833	−	0.0795179i
$82$	25.6069	+	44.9392i	0.312279	+	0.548039i
$83$	4.38944	−	5.50419i	0.0528848	−	0.0663155i	−0.754686	−	0.656087i	$-0.772211\pi$
$83$	4.38944	−	5.50419i	0.0528848	−	0.0663155i	0.807570	+	0.589771i	$0.200782\pi$
$84$	−18.5909	−	116.566i	−0.221320	−	1.38769i
$85$	−33.6994	+	96.3073i	−0.396463	+	1.13303i
$86$	72.2270	−	5.00086i	0.839849	−	0.0581495i
$87$	−75.6953	−	42.8862i	−0.870061	−	0.492945i
$88$	−4.50324	+	0.947519i	−0.0511732	+	0.0107673i
$89$	−16.2611	+	46.4714i	−0.182709	+	0.522151i	−0.998413	−	0.0563181i	$-0.982064\pi$
$89$	−16.2611	+	46.4714i	−0.182709	+	0.522151i	0.815704	+	0.578469i	$0.196350\pi$
$90$	149.883	−	33.6943i	1.66536	−	0.374381i
$91$	138.388	−	173.533i	1.52075	−	1.90695i
$92$	−0.170884	−	0.256853i	−0.00185743	−	0.00279188i
$93$	−76.6153	−	25.1091i	−0.823820	−	0.269990i
$94$	57.5798	+	62.7665i	0.612551	+	0.667729i
$95$	−19.9727	−	31.7864i	−0.210239	−	0.334594i
$96$	92.9358	−	24.0612i	0.968081	−	0.250638i
$97$	−16.1070	−	142.953i	−0.166051	−	1.47375i	−0.749720	−	0.661755i	$-0.769812\pi$
$97$	−16.1070	−	142.953i	−0.166051	−	1.47375i	0.583669	−	0.811992i	$-0.301617\pi$
$98$	−45.1107	+	84.1941i	−0.460313	+	0.859124i
$99$	−2.57777	+	4.48968i	−0.0260380	+	0.0453503i
$100$	178.914	−	67.8864i	1.78914	−	0.678864i
$101$	150.259	−	52.5778i	1.48771	−	0.520572i	0.540543	−	0.841316i	$-0.318219\pi$
$101$	150.259	−	52.5778i	1.48771	−	0.520572i	0.947166	+	0.320744i	$0.103933\pi$
$102$	36.7458	+	61.6043i	0.360252	+	0.603964i
$103$	12.9865	−	2.96408i	0.126082	−	0.0287774i	−0.159014	−	0.987276i	$-0.550832\pi$
$103$	12.9865	−	2.96408i	0.126082	−	0.0287774i	0.285096	+	0.958499i	$0.407974\pi$
$104$	151.190	+	98.6266i	1.45375	+	0.948333i
$105$	−229.044	−	104.739i	−2.18137	−	0.997514i
$106$	−7.42740	−	40.5113i	−0.0700698	−	0.382182i
$107$	18.2129	−	79.7961i	0.170214	−	0.745758i	−0.815696	−	0.578481i	$-0.803646\pi$
$107$	18.2129	−	79.7961i	0.170214	−	0.745758i	0.985910	−	0.167277i	$-0.0534973\pi$
$108$	49.4157	−	96.0317i	0.457553	−	0.889182i
$109$	−44.7439	+	35.6821i	−0.410495	+	0.327359i	−0.806869	−	0.590730i	$-0.798840\pi$
$109$	−44.7439	+	35.6821i	−0.410495	+	0.327359i	0.396374	+	0.918089i	$0.370268\pi$
$110$	−3.63898	+	9.11954i	−0.0330817	+	0.0829049i
$111$	−134.732	+	88.4455i	−1.21380	+	0.796806i
$112$	−145.164	−	60.8084i	−1.29611	−	0.542932i
$113$	−14.1347	+	125.449i	−0.125086	+	1.11017i	0.761681	+	0.647952i	$0.224374\pi$
$113$	−14.1347	+	125.449i	−0.125086	+	1.11017i	−0.886767	+	0.462216i	$0.847054\pi$
$114$	−26.1502	−	3.56176i	−0.229387	−	0.0312435i
$115$	−0.658241			−0.00572384
$116$	−101.773	+	55.6624i	−0.877352	+	0.479848i
$117$	196.033	−	53.0317i	1.67549	−	0.453262i
$118$	−78.4377	−	21.4949i	−0.664727	−	0.182160i
$119$	13.1668	−	116.859i	0.110646	−	0.982008i
$120$	67.0936	−	193.531i	0.559113	−	1.61276i
$121$	52.3564	+	108.719i	0.432697	+	0.898505i
$122$	−46.4735	+	116.466i	−0.380930	+	0.954637i
$123$	53.7578	−	55.9411i	0.437055	−	0.454806i
$124$	−82.2720	+	69.1919i	−0.663484	+	0.557999i
$125$	43.3762	−	190.044i	0.347010	−	1.52035i
$126$	−159.775	+	76.3008i	−1.26806	+	0.605562i
$127$	161.716	+	101.613i	1.27336	+	0.800102i	0.987416	−	0.158145i	$-0.0505515\pi$
$127$	161.716	+	101.613i	1.27336	+	0.800102i	0.285940	+	0.958248i	$0.407694\pi$
$128$	38.0105	−	122.226i	0.296957	−	0.954891i
$129$	−37.9009	−	101.772i	−0.293806	−	0.788927i
$130$	353.889	−	152.017i	2.72222	−	1.16936i
$131$	−125.675	+	43.9757i	−0.959353	+	0.335692i	−0.764127	−	0.645066i	$-0.776830\pi$
$131$	−125.675	+	43.9757i	−0.959353	+	0.335692i	−0.195226	+	0.980758i	$0.562544\pi$
$132$	3.27755	+	6.07502i	0.0248299	+	0.0460229i
$133$	30.5946	+	30.5946i	0.230035	+	0.230035i
$134$	103.950	−	194.011i	0.775744	−	1.44784i
$135$	−112.191	−	201.279i	−0.831048	−	1.49096i
$136$	95.6276	+	1.62739i	0.703144	+	0.0119661i
$137$	−59.9893	−	95.4725i	−0.437878	−	0.696879i	0.552768	−	0.833335i	$-0.313572\pi$
$137$	−59.9893	−	95.4725i	−0.437878	−	0.696879i	−0.990646	+	0.136456i	$0.956429\pi$
$138$	−0.296828	+	0.355015i	−0.00215093	+	0.00257257i
$139$	−64.0480	+	132.997i	−0.460777	+	0.956813i	0.533072	+	0.846070i	$0.321037\pi$
$139$	−64.0480	+	132.997i	−0.460777	+	0.956813i	−0.993849	+	0.110743i	$0.964677\pi$
$140$	−279.585	+	186.007i	−1.99704	+	1.32862i
$141$	65.8089	−	109.513i	0.466730	−	0.776688i
$142$	−114.331	−	4.92752i	−0.805148	−	0.0347008i
$143$	−4.28693	+	12.2513i	−0.0299785	+	0.0856737i
$144$	−74.1234	−	123.457i	−0.514746	−	0.857343i
$145$	−21.4004	+	246.577i	−0.147589	+	1.70053i
$146$	199.441	−	13.8089i	1.36604	−	0.0945816i
$147$	140.291	+	29.0961i	0.954361	+	0.197933i
$148$	5.59851	+	214.819i	0.0378278	+	1.45148i
$149$	−65.4765	+	82.1049i	−0.439439	+	0.551040i	−0.951395	−	0.307972i	$-0.900350\pi$
$149$	−65.4765	+	82.1049i	−0.439439	+	0.551040i	0.511956	+	0.859012i	$0.328921\pi$
$150$	−173.719	−	228.503i	−1.15813	−	1.52335i
$151$	241.195	+	116.153i	1.59732	+	0.769226i	0.999475	−	0.0323891i	$-0.0103116\pi$
$151$	241.195	+	116.153i	1.59732	+	0.769226i	0.597840	+	0.801616i	$0.296026\pi$
$152$	−22.4048	+	27.1344i	−0.147400	+	0.178516i
$153$	72.9947	−	79.0494i	0.477089	−	0.516663i
$154$	1.75010	−	11.1805i	0.0113643	−	0.0726006i
$155$	25.6811	+	227.926i	0.165684	+	1.47049i
$156$	77.5948	−	259.416i	0.497403	−	1.66292i
$157$	−6.17340	+	6.17340i	−0.0393210	+	0.0393210i	−0.726494	−	0.687173i	$-0.758851\pi$
$157$	−6.17340	+	6.17340i	−0.0393210	+	0.0393210i	0.687173	+	0.726494i	$0.258851\pi$
$158$	48.6755	+	161.039i	0.308073	+	1.01924i
$159$	−55.1173	+	27.9076i	−0.346650	+	0.175519i
$160$	−172.203	−	211.977i	−1.07627	−	1.32485i
$161$	0.739636	−	0.168817i	0.00459401	−	0.00104855i
$162$	−159.150	−	30.2561i	−0.982404	−	0.186766i
$163$	−122.407	+	194.810i	−0.750966	+	1.19516i	0.224386	+	0.974500i	$0.427962\pi$
$163$	−122.407	+	194.810i	−0.750966	+	1.19516i	−0.975352	+	0.220655i	$0.929180\pi$
$164$	−25.6385	−	100.218i	−0.156332	−	0.611086i
$165$	14.6655	+	1.35747i	0.0888816	+	0.00822708i
$166$	−11.3762	+	8.29673i	−0.0685311	+	0.0499803i
$167$	200.177	−	159.635i	1.19866	−	0.955901i	0.198953	−	0.980009i	$-0.436246\pi$
$167$	200.177	−	159.635i	1.19866	−	0.955901i	0.999709	+	0.0241081i	$0.00767460\pi$
$168$	−25.7557	+	234.669i	−0.153308	+	1.39684i
$169$	306.466	−	147.586i	1.81341	−	0.873290i
$170$	115.909	−	167.953i	0.681818	−	0.987957i
$171$	5.99417	+	39.1310i	0.0350536	+	0.228836i
$172$	−141.961	−	28.5322i	−0.825354	−	0.165885i
$173$	222.375			1.28540			0.642702	−	0.766116i	$-0.277813\pi$
$173$	222.375			1.28540			0.642702	+	0.766116i	$0.277813\pi$
$174$	123.338	+	122.734i	0.708841	+	0.705368i
$175$			470.583i			2.68905i
$176$	9.18708	+	0.552703i	0.0521993	+	0.00314036i
$177$	2.42759	+	121.970i	0.0137152	+	0.689098i
$178$	55.9299	−	81.0426i	0.314213	−	0.455296i
$179$	39.4401	+	81.8982i	0.220336	+	0.457532i	0.981610	−	0.190899i	$-0.0611401\pi$
$179$	39.4401	+	81.8982i	0.220336	+	0.457532i	−0.761274	+	0.648430i	$0.775426\pi$
$180$	−306.917	−	14.2337i	−1.70509	−	0.0790760i
$181$	−38.8145	−	48.6718i	−0.214445	−	0.268905i	0.662961	−	0.748654i	$-0.269299\pi$
$181$	−38.8145	−	48.6718i	−0.214445	−	0.268905i	−0.877406	+	0.479749i	$0.840728\pi$
$182$	−358.662	+	261.575i	−1.97067	+	1.43722i
$183$	187.293	+	17.3362i	1.02346	+	0.0947335i
$184$	0.193845	+	0.585766i	0.00105351	+	0.00318351i
$185$	388.228	+	243.940i	2.09853	+	1.31859i
$186$	134.510	+	88.9304i	0.723170	+	0.478121i
$187$	1.53027	+	6.70457i	0.00818328	+	0.0358533i
$188$	−77.8871	−	151.505i	−0.414293	−	0.805879i
$189$	177.686	+	197.395i	0.940138	+	1.04442i
$190$	21.7232	+	71.8696i	0.114333	+	0.378261i
$191$	−67.5908	−	67.5908i	−0.353878	−	0.353878i	0.507672	−	0.861550i	$-0.330506\pi$
$191$	−67.5908	−	67.5908i	−0.353878	−	0.353878i	−0.861550	+	0.507672i	$0.830506\pi$
$192$	−191.981	−	2.71330i	−0.999900	−	0.0141318i
$193$	86.9918	−	9.80163i	0.450735	−	0.0507856i	0.116320	−	0.993212i	$-0.462890\pi$
$193$	86.9918	−	9.80163i	0.450735	−	0.0507856i	0.334414	+	0.942426i	$0.391461\pi$
$194$	−44.4949	+	284.255i	−0.229355	+	1.46523i
$195$	−369.130	−	444.435i	−1.89297	−	2.27915i
$196$	131.517	−	138.556i	0.671007	−	0.706917i
$197$	−61.8397	+	128.411i	−0.313907	+	0.651835i	−0.996908	−	0.0785831i	$-0.974960\pi$
$197$	−61.8397	+	128.411i	−0.313907	+	0.651835i	0.683000	+	0.730418i	$0.260675\pi$
$198$	7.34540	−	7.29750i	0.0370980	−	0.0368561i
$199$	−56.3787	−	44.9605i	−0.283310	−	0.225932i	0.471516	−	0.881858i	$-0.343707\pi$
$199$	−56.3787	−	44.9605i	−0.283310	−	0.225932i	−0.754826	+	0.655926i	$0.772279\pi$
$200$	−380.987	+	36.3736i	−1.90494	+	0.181868i
$201$	−323.276	−	67.0469i	−1.60834	−	0.333566i
$202$	−317.624	+	21.9916i	−1.57239	+	0.108869i
$203$	−39.1923	−	282.556i	−0.193065	−	1.39190i
$204$	−38.3150	−	138.251i	−0.187819	−	0.677701i
$205$	−208.332	−	72.8984i	−1.01625	−	0.355602i
$206$	−26.6162	−	1.14712i	−0.129205	−	0.00556855i
$207$	0.636881	+	0.276050i	0.00307672	+	0.00133357i
$208$	−239.496	−	270.157i	−1.15142	−	1.29883i
$209$	−2.27964	−	1.09782i	−0.0109074	−	0.00525271i
$210$	386.435	+	323.099i	1.84017	+	1.53857i
$211$	123.468	−	77.5804i	0.585159	−	0.367680i	−0.206681	−	0.978408i	$-0.566266\pi$
$211$	123.468	−	77.5804i	0.585159	−	0.367680i	0.791840	+	0.610729i	$0.209123\pi$
$212$	−7.08718	+	82.0677i	−0.0334301	+	0.387112i
$213$	41.5196	+	166.559i	0.194928	+	0.781966i
$214$	−77.3099	+	144.290i	−0.361261	+	0.674254i
$215$	−218.463	+	218.463i	−1.01611	+	1.01611i
$216$	−146.078	+	159.113i	−0.676289	+	0.736636i
$217$	−87.3120	−	249.523i	−0.402360	−	1.14988i
$218$	105.167	−	45.1756i	0.482417	−	0.207227i
$219$	−104.656	−	281.023i	−0.477883	−	1.28321i
$220$	11.8397	−	15.6670i	0.0538166	−	0.0712137i
$221$	143.522	−	228.413i	0.649419	−	1.03354i
$222$	306.634	−	99.3834i	1.38123	−	0.447673i
$223$	243.225	+	55.5144i	1.09069	+	0.248944i	0.729798	−	0.683663i	$-0.239614\pi$
$223$	243.225	+	55.5144i	1.09069	+	0.248944i	0.360895	+	0.932606i	$0.382471\pi$
$224$	247.862	+	194.024i	1.10653	+	0.866180i
$225$	−254.843	+	347.040i	−1.13263	+	1.54240i
$226$	93.5750	−	234.505i	0.414049	−	1.03763i
$227$	10.1838	−	4.90426i	0.0448626	−	0.0216047i	−0.411318	−	0.911492i	$-0.634931\pi$
$227$	10.1838	−	4.90426i	0.0448626	−	0.0216047i	0.456181	+	0.889887i	$0.349217\pi$
$228$	48.5579	+	20.6929i	0.212973	+	0.0907582i
$229$	−246.421	−	27.7650i	−1.07608	−	0.121245i	−0.443905	−	0.896074i	$-0.646407\pi$
$229$	−246.421	−	27.7650i	−1.07608	−	0.121245i	−0.632170	+	0.774829i	$0.717836\pi$
$230$	1.26967	+	0.347938i	0.00552031	+	0.00151277i
$231$	−16.8271	+	2.23588i	−0.0728444	+	0.00967913i
$232$	225.730	−	53.5705i	0.972976	−	0.230907i
$233$			242.677i			1.04153i	0.853699	+	0.520767i	$0.174354\pi$
$233$			242.677i			1.04153i	−0.853699	+	0.520767i	$0.825646\pi$
$234$	−406.157	−	1.32856i	−1.73571	−	0.00567762i
$235$	−361.190	−	40.6964i	−1.53698	−	0.173176i
$236$	139.935	+	82.9224i	0.592947	+	0.351366i
$237$	210.959	−	138.485i	0.890122	−	0.584324i
$238$	−87.1675	+	218.448i	−0.366250	+	0.917847i
$239$	184.662	+	231.559i	0.772644	+	0.968865i	0.999988	−	0.00494942i	$-0.00157545\pi$
$239$	184.662	+	231.559i	0.772644	+	0.968865i	−0.227344	+	0.973815i	$0.573004\pi$
$240$	−231.714	+	337.834i	−0.965474	+	1.40764i
$241$	23.3011	+	5.31833i	0.0966851	+	0.0220677i	0.270590	−	0.962695i	$-0.412781\pi$
$241$	23.3011	+	5.31833i	0.0966851	+	0.0220677i	−0.173905	+	0.984762i	$0.555638\pi$
$242$	−43.5218	−	237.382i	−0.179842	−	0.980915i
$243$	24.1392	+	241.798i	0.0993384	+	0.995054i
$244$	151.204	−	200.084i	0.619690	−	0.820015i
$245$	−90.7005	−	397.385i	−0.370206	−	1.62198i
$246$	−133.262	+	79.4883i	−0.541717	+	0.323123i
$247$	32.7807	+	93.6820i	0.132716	+	0.379279i
$248$	195.267	−	89.9753i	0.787368	−	0.362804i
$249$	16.7713	+	12.8371i	0.0673547	+	0.0515547i
$250$	−184.122	+	343.644i	−0.736489	+	1.37458i
$251$	−182.375	+	20.5488i	−0.726595	+	0.0818676i	−0.467511	−	0.883987i	$-0.654849\pi$
$251$	−182.375	+	20.5488i	−0.726595	+	0.0818676i	−0.259084	+	0.965855i	$0.583421\pi$
$252$	348.519	−	62.7203i	1.38301	−	0.248890i
$253$	−0.0375651	+	0.0236037i	−0.000148479	+	9.32953e-5i
$254$	−258.220	−	281.481i	−1.01662	−	1.10819i
$255$	−290.877	−	95.3288i	−1.14069	−	0.373839i
$256$	−137.925	+	215.668i	−0.538769	+	0.842453i
$257$	−237.099	−	189.080i	−0.922564	−	0.735720i	0.0421252	−	0.999112i	$-0.486587\pi$
$257$	−237.099	−	189.080i	−0.922564	−	0.735720i	−0.964689	+	0.263392i	$0.915159\pi$
$258$	19.3114	+	216.340i	0.0748503	+	0.838526i
$259$	−498.796	−	174.536i	−1.92585	−	0.673885i
$260$	−762.964	+	106.161i	−2.93448	+	0.408312i
$261$	124.114	−	229.601i	0.475534	−	0.879697i
$262$	265.658	−	18.3936i	1.01396	−	0.0702047i
$263$	−134.808	−	47.1715i	−0.512580	−	0.179359i	0.0615810	−	0.998102i	$-0.480386\pi$
$263$	−134.808	−	47.1715i	−0.512580	−	0.179359i	−0.574161	+	0.818743i	$0.694671\pi$
$264$	−3.11083	−	13.4505i	−0.0117834	−	0.0509488i
$265$	137.412	+	109.582i	0.518535	+	0.413518i
$266$	−42.8415	−	75.1854i	−0.161058	−	0.282652i
$267$	−140.357	−	45.9993i	−0.525683	−	0.172282i
$268$	−303.058	+	319.277i	−1.13082	+	1.19133i
$269$	322.850	−	202.860i	1.20019	−	0.754127i	0.224751	−	0.974416i	$-0.427843\pi$
$269$	322.850	−	202.860i	1.20019	−	0.754127i	0.975435	+	0.220290i	$0.0707002\pi$
$270$	110.011	+	447.548i	0.407447	+	1.65758i
$271$	−380.486	+	42.8705i	−1.40401	+	0.158194i	−0.781249	−	0.624219i	$-0.785417\pi$
$271$	−380.486	+	42.8705i	−1.40401	+	0.158194i	−0.622760	+	0.782413i	$0.713989\pi$
$272$	−183.594	−	53.6866i	−0.674979	−	0.197377i
$273$	528.757	+	404.722i	1.93684	+	1.48250i
$274$	65.2469	+	215.865i	0.238127	+	0.787828i
$275$	−9.08896	−	25.9748i	−0.0330508	−	0.0944537i
$276$	0.760204	−	0.527883i	0.00275436	−	0.00191262i
$277$	−55.4239	−	242.828i	−0.200086	−	0.876635i	−0.970883	−	0.239554i	$-0.922999\pi$
$277$	−55.4239	−	242.828i	−0.200086	−	0.876635i	0.770797	−	0.637081i	$-0.219858\pi$
$278$	193.842	−	222.681i	0.697272	−	0.801010i
$279$	70.7386	−	231.299i	0.253543	−	0.829030i
$280$	637.609	−	211.002i	2.27717	−	0.753577i
$281$	−26.5346	−	6.05635i	−0.0944292	−	0.0215528i	0.175045	−	0.984560i	$-0.443993\pi$
$281$	−26.5346	−	6.05635i	−0.0944292	−	0.0215528i	−0.269474	+	0.963008i	$0.586850\pi$
$282$	−184.825	+	176.452i	−0.655407	+	0.625717i
$283$	237.196	+	297.434i	0.838148	+	1.05100i	0.997959	+	0.0638570i	$0.0203402\pi$
$283$	237.196	+	297.434i	0.838148	+	1.05100i	−0.159811	+	0.987148i	$0.551088\pi$
$284$	217.927	+	69.9385i	0.767347	+	0.246262i
$285$	94.1480	−	61.8039i	0.330344	−	0.216856i
$286$	14.7449	−	21.3654i	0.0515556	−	0.0747042i
$287$	252.789	+	28.4825i	0.880798	+	0.0992421i
$288$	77.7175	+	277.316i	0.269852	+	0.962902i
$289$			146.074i			0.505445i
$290$	171.617	−	464.307i	0.591782	−	1.60106i
$291$	427.814	−	56.8454i	1.47015	−	0.195345i
$292$	−391.998	−	78.7863i	−1.34246	−	0.269816i
$293$	247.636	+	27.9019i	0.845174	+	0.0952282i	0.523923	−	0.851766i	$-0.324468\pi$
$293$	247.636	+	27.9019i	0.845174	+	0.0952282i	0.321251	+	0.946994i	$0.395897\pi$
$294$	−255.225	−	130.279i	−0.868114	−	0.443126i
$295$	312.690	−	150.583i	1.05996	−	0.510452i
$296$	102.752	−	417.320i	0.347134	−	1.40986i
$297$	−13.6203	−	7.46374i	−0.0458595	−	0.0251305i
$298$	169.696	−	123.761i	0.569450	−	0.415305i
$299$	1.69666	+	0.387253i	0.00567446	+	0.00129516i
$300$	214.300	+	532.582i	0.714332	+	1.77527i
$301$	189.449	−	301.506i	0.629397	−	1.00168i
$302$	−403.839	−	351.539i	−1.33722	−	1.16403i
$303$	166.672	+	447.548i	0.550073	+	1.47706i
$304$	57.5592	−	40.4962i	0.189339	−	0.133211i
$305$	−176.733	−	505.075i	−0.579453	−	1.65598i
$306$	−182.583	+	113.893i	−0.596676	+	0.372200i
$307$	70.3339	−	70.3339i	0.229101	−	0.229101i	−0.583216	−	0.812317i	$-0.698206\pi$
$307$	70.3339	−	70.3339i	0.229101	−	0.229101i	0.812317	+	0.583216i	$0.198206\pi$
$308$	−9.28561	+	20.6408i	−0.0301481	+	0.0670156i
$309$	9.66573	+	38.7747i	0.0312807	+	0.125485i
$310$	70.9429	−	453.217i	0.228848	−	1.46199i
$311$	142.750	−	89.6955i	0.459002	−	0.288410i	−0.282615	−	0.959233i	$-0.591202\pi$
$311$	142.750	−	89.6955i	0.459002	−	0.288410i	0.741617	+	0.670823i	$0.234059\pi$
$312$	−286.796	+	459.368i	−0.919217	+	1.47233i
$313$	79.8998	+	38.4777i	0.255271	+	0.122932i	0.557143	−	0.830416i	$-0.311897\pi$
$313$	79.8998	+	38.4777i	0.255271	+	0.122932i	−0.301872	+	0.953348i	$0.597612\pi$
$314$	15.1710	−	8.64460i	0.0483152	−	0.0275306i
$315$	300.481	−	693.247i	0.953909	−	2.20079i
$316$	−8.76595	−	336.356i	−0.0277403	−	1.06442i
$317$	−404.391	−	141.503i	−1.27568	−	0.446381i	−0.394386	−	0.918945i	$-0.629043\pi$
$317$	−404.391	−	141.503i	−1.27568	−	0.446381i	−0.881296	+	0.472564i	$0.843328\pi$
$318$	121.066	−	24.6962i	0.380712	−	0.0776610i
$319$	7.62066	+	14.8393i	0.0238892	+	0.0465181i
$320$	220.112	+	499.903i	0.687850	+	1.56220i
$321$	240.428	+	49.8644i	0.748997	+	0.155341i
$322$	−1.51591	−	0.0653336i	−0.00470779	−	0.000202899i
$323$	41.1134	+	32.7869i	0.127286	+	0.101507i
$324$	290.988	+	142.485i	0.898111	+	0.439769i
$325$	−468.369	+	972.577i	−1.44113	+	2.99255i
$326$	339.084	−	311.064i	1.04014	−	0.954183i
$327$	−109.696	−	132.075i	−0.335462	−	0.403899i
$328$	−3.52037	+	206.861i	−0.0107328	+	0.630675i
$329$	416.291	−	46.9047i	1.26532	−	0.142567i
$330$	−27.5704	−	10.3704i	−0.0835468	−	0.0314254i
$331$	−360.365	−	360.365i	−1.08872	−	1.08872i	−0.995661	−	0.0930555i	$-0.970337\pi$
$331$	−360.365	−	360.365i	−1.08872	−	1.08872i	−0.0930555	−	0.995661i	$-0.529663\pi$
$332$	26.3289	−	9.99014i	0.0793038	−	0.0300908i
$333$	−273.327	−	398.836i	−0.820802	−	1.19771i
$334$	−470.499	+	202.108i	−1.40868	+	0.605112i
$335$	209.003	+	915.703i	0.623890	+	2.73344i
$336$	173.723	−	439.036i	0.517033	−	1.30665i
$337$	−140.940	−	88.5583i	−0.418219	−	0.262784i	0.306443	−	0.951889i	$-0.400861\pi$
$337$	−140.940	−	88.5583i	−0.418219	−	0.262784i	−0.724662	+	0.689105i	$0.758004\pi$
$338$	−669.149	+	122.683i	−1.97973	+	0.362966i
$339$	−377.116	−	34.9067i	−1.11244	−	0.102970i
$340$	−312.353	+	262.693i	−0.918685	+	0.772627i
$341$	9.63872	+	12.0866i	0.0282660	+	0.0354445i
$342$	9.12207	−	78.6475i	0.0266727	−	0.229964i
$343$	−5.29721	−	10.9998i	−0.0154438	−	0.0320693i
$344$	258.744	+	130.074i	0.752164	+	0.378122i
$345$	−0.0392954	−	1.97433i	−0.000113900	−	0.00572270i
$346$	−428.936	−	117.545i	−1.23970	−	0.339724i
$347$		−	426.386i		−	1.22878i	−0.789004	−	0.614389i	$-0.789403\pi$
$347$		−	426.386i		−	1.22878i	0.789004	−	0.614389i	$-0.210597\pi$
$348$	−173.030	−	301.935i	−0.497212	−	0.867629i
$349$	481.329			1.37916			0.689582	−	0.724207i	$-0.257794\pi$
$349$	481.329			1.37916			0.689582	+	0.724207i	$0.257794\pi$
$350$	248.744	−	907.700i	0.710698	−	2.59343i
$351$	170.766	+	584.816i	0.486513	+	1.66614i
$352$	−17.4287	−	5.92228i	−0.0495133	−	0.0168246i
$353$	−474.052	+	228.291i	−1.34292	+	0.646717i	−0.960761	−	0.277378i	$-0.910535\pi$
$353$	−474.052	+	228.291i	−1.34292	+	0.646717i	−0.382162	+	0.924095i	$0.624820\pi$
$354$	59.7894	−	236.550i	0.168897	−	0.668220i
$355$	381.799	−	304.475i	1.07549	−	0.857675i
$356$	−150.720	+	126.758i	−0.423372	+	0.356062i
$357$	351.293	+	32.5165i	0.984015	+	0.0910827i
$358$	−32.7850	−	178.820i	−0.0915782	−	0.499496i
$359$	80.5738	−	128.232i	0.224440	−	0.357194i	−0.715455	−	0.698659i	$-0.753780\pi$
$359$	80.5738	−	128.232i	0.224440	−	0.357194i	0.939894	+	0.341466i	$0.110923\pi$
$360$	584.484	+	189.688i	1.62357	+	0.526910i
$361$	333.086	−	76.0248i	0.922677	−	0.210595i
$362$	49.1413	+	114.399i	0.135750	+	0.316020i
$363$	−322.967	+	163.528i	−0.889717	+	0.450491i
$364$	830.082	−	314.964i	2.28044	−	0.865285i
$365$	−603.244	+	603.244i	−1.65272	+	1.65272i
$366$	−352.102	−	132.440i	−0.962028	−	0.361858i
$367$	66.5956	+	591.052i	0.181459	+	1.61050i	0.673001	+	0.739642i	$0.265005\pi$
$367$	66.5956	+	591.052i	0.181459	+	1.61050i	−0.491541	+	0.870854i	$0.663566\pi$
$368$	−0.0642770	−	1.23234i	−0.000174666	−	0.00334875i
$369$	170.999	+	157.902i	0.463413	+	0.427918i
$370$	−619.903	−	675.743i	−1.67541	−	1.82633i
$371$	−182.507	−	87.8910i	−0.491934	−	0.236903i
$372$	−212.446	−	242.637i	−0.571092	−	0.652249i
$373$	82.7810	−	103.804i	0.221933	−	0.278295i	−0.658383	−	0.752683i	$-0.728759\pi$
$373$	82.7810	−	103.804i	0.221933	−	0.278295i	0.880316	+	0.474388i	$0.157331\pi$
$374$	0.592228	−	13.7412i	0.00158350	−	0.0367412i
$375$	572.607	+	118.758i	1.52695	+	0.316687i
$376$	70.1514	+	333.406i	0.186573	+	0.886719i
$377$	200.226	−	622.981i	0.531104	−	1.65247i
$378$	−238.395	−	474.675i	−0.630675	−	1.25575i
$379$	23.7777	−	67.9529i	0.0627381	−	0.179295i	−0.908247	−	0.418434i	$-0.862579\pi$
$379$	23.7777	−	67.9529i	0.0627381	−	0.179295i	0.970985	+	0.239138i	$0.0768650\pi$
$380$	−3.91212	−	150.111i	−0.0102951	−	0.395028i
$381$	−295.125	+	491.118i	−0.774605	+	1.28902i
$382$	94.6472	+	166.102i	0.247768	+	0.434823i
$383$	−244.618	+	507.956i	−0.638691	+	1.32625i	0.290579	+	0.956851i	$0.406152\pi$
$383$	−244.618	+	507.956i	−0.638691	+	1.32625i	−0.929269	+	0.369403i	$0.879562\pi$
$384$	368.875	+	106.712i	0.960611	+	0.277897i
$385$	25.6927	+	40.8897i	0.0667344	+	0.106207i
$386$	−172.978	−	27.0766i	−0.448130	−	0.0701466i
$387$	302.992	−	119.756i	0.782924	−	0.309447i
$388$	236.079	−	524.775i	0.608451	−	1.35251i
$389$	227.739	+	227.739i	0.585446	+	0.585446i	0.936395	−	0.350949i	$-0.114141\pi$
$389$	227.739	+	227.739i	0.585446	+	0.585446i	−0.350949	+	0.936395i	$0.614141\pi$
$390$	477.086	+	1052.38i	1.22330	+	2.69841i
$391$	0.870311	−	0.304535i	0.00222586	−	0.000778862i
$392$	−326.920	+	197.740i	−0.833981	+	0.504438i
$393$	−139.403	−	374.326i	−0.354716	−	0.952483i
$394$	187.158	−	215.003i	0.475021	−	0.545693i
$395$	−607.873	−	381.952i	−1.53892	−	0.966967i
$396$	−18.0258	+	10.1934i	−0.0455197	+	0.0257408i
$397$	7.72345	−	33.8386i	0.0194545	−	0.0852358i	−0.964269	−	0.264926i	$-0.914652\pi$
$397$	7.72345	−	33.8386i	0.0194545	−	0.0852358i	0.983723	+	0.179690i	$0.0575096\pi$
$398$	84.9824	+	116.525i	0.213524	+	0.292776i
$399$	−89.9392	+	93.5921i	−0.225412	+	0.234567i
$400$	754.107	+	131.225i	1.88527	+	0.328062i
$401$	−159.383	−	330.962i	−0.397464	−	0.825342i	−0.999636	−	0.0269760i	$-0.991412\pi$
$401$	−159.383	−	330.962i	−0.397464	−	0.825342i	0.602172	−	0.798366i	$-0.294302\pi$
$402$	588.122	+	300.205i	1.46299	+	0.746779i
$403$	67.8971	−	602.604i	0.168479	−	1.49529i
$404$	624.284	+	125.472i	1.54526	+	0.310575i
$405$	597.021	−	348.524i	1.47413	−	0.860552i
$406$	−73.7584	+	565.735i	−0.181671	+	1.39344i
$407$	30.9031			0.0759289
$408$	0.827522	+	286.923i	0.00202824	+	0.703243i
$409$	−55.3864	+	491.568i	−0.135419	+	1.20188i	0.723705	+	0.690109i	$0.242438\pi$
$409$	−55.3864	+	491.568i	−0.135419	+	1.20188i	−0.859124	+	0.511767i	$0.828991\pi$
$410$	363.315	+	250.734i	0.886133	+	0.611547i
$411$	282.779	−	185.632i	0.688028	−	0.451659i
$412$	50.7332	+	16.2816i	0.123139	+	0.0395185i
$413$	−312.736	+	249.398i	−0.757229	+	0.603870i
$414$	−1.08255	−	0.869116i	−0.00261486	−	0.00209931i
$415$	13.3701	−	58.5784i	0.0322172	−	0.141153i
$416$	319.158	+	647.695i	0.767206	+	1.55696i
$417$	−402.735	−	184.166i	−0.965792	−	0.441646i
$418$	3.81687	+	3.32255i	0.00913127	+	0.00794869i
$419$	522.466	−	119.249i	1.24694	−	0.284605i	0.452396	−	0.891817i	$-0.350569\pi$
$419$	522.466	−	119.249i	1.24694	−	0.284605i	0.794539	+	0.607212i	$0.207712\pi$
$420$	−574.602	−	827.485i	−1.36810	−	1.97020i
$421$	−169.373	+	59.2661i	−0.402311	+	0.140775i	−0.523847	−	0.851812i	$-0.675504\pi$
$421$	−169.373	+	59.2661i	−0.402311	+	0.140775i	0.121536	+	0.992587i	$0.461218\pi$
$422$	−279.164	+	84.3797i	−0.661527	+	0.199952i
$423$	332.402	+	190.850i	0.785821	+	0.451182i
$424$	57.0503	−	154.553i	0.134553	−	0.364512i
$425$	64.0365	+	568.339i	0.150674	+	1.33727i
$426$	7.95434	−	343.219i	0.0186722	−	0.805679i
$427$	328.122	+	522.203i	0.768436	+	1.22296i
$428$	225.392	−	237.454i	0.526616	−	0.554800i
$429$	−37.0027	−	12.1269i	−0.0862533	−	0.0282678i
$430$	536.867	−	305.913i	1.24853	−	0.711426i
$431$	−340.946	+	427.533i	−0.791058	+	0.991955i	0.208844	+	0.977949i	$0.433030\pi$
$431$	−340.946	+	427.533i	−0.791058	+	0.991955i	−0.999902	+	0.0140064i	$0.995541\pi$
$432$	365.874	−	229.696i	0.846930	−	0.531704i
$433$	−108.814	+	310.971i	−0.251301	+	0.718178i	0.747259	+	0.664533i	$0.231370\pi$
$433$	−108.814	+	310.971i	−0.251301	+	0.718178i	−0.998560	+	0.0536449i	$0.982916\pi$
$434$	36.5199	+	527.454i	0.0841472	+	1.21533i
$435$	−740.863	−	49.4684i	−1.70313	−	0.113720i
$436$	−226.734	+	31.5485i	−0.520032	+	0.0723589i
$437$	−0.112046	+	0.320209i	−0.000256398	+	0.000732743i
$438$	53.3247	+	597.381i	0.121746	+	1.36388i
$439$	−58.7109	+	73.6211i	−0.133738	+	0.167702i	−0.844191	−	0.536043i	$-0.819919\pi$
$439$	−58.7109	+	73.6211i	−0.133738	+	0.167702i	0.710453	+	0.703745i	$0.248490\pi$
$440$	−31.1187	+	23.9616i	−0.0707244	+	0.0544581i
$441$	−78.8960	+	422.527i	−0.178903	+	0.958111i
$442$	−397.573	+	364.719i	−0.899486	+	0.825156i
$443$	−91.9306	−	146.307i	−0.207518	−	0.330263i	0.726707	−	0.686948i	$-0.241050\pi$
$443$	−91.9306	−	146.307i	−0.207518	−	0.330263i	−0.934225	+	0.356685i	$0.883907\pi$
$444$	−643.994	+	29.6164i	−1.45044	+	0.0667035i
$445$	47.0471	+	417.555i	0.105724	+	0.938325i
$446$	−439.808	−	235.646i	−0.986116	−	0.528355i
$447$	−250.175	−	191.489i	−0.559675	−	0.428387i
$448$	−375.539	−	505.267i	−0.838256	−	1.12783i
$449$	−47.6750	+	16.6822i	−0.106180	+	0.0371541i	−0.382846	−	0.923812i	$-0.625056\pi$
$449$	−47.6750	+	16.6822i	−0.106180	+	0.0371541i	0.276666	+	0.960966i	$0.410770\pi$
$450$	675.003	−	534.694i	1.50001	−	1.18821i
$451$	−14.5033	+	3.31028i	−0.0321581	+	0.00733987i
$452$	−304.452	+	402.871i	−0.673566	+	0.891307i
$453$	−333.992	+	730.375i	−0.737289	+	1.61231i
$454$	−22.2357	+	4.07672i	−0.0489774	+	0.00897957i
$455$	421.526	−	1846.83i	0.926431	−	4.05896i
$456$	−82.7246	−	65.5813i	−0.181414	−	0.143819i
$457$	−154.922	+	123.546i	−0.338998	+	0.270342i	−0.778160	−	0.628066i	$-0.783847\pi$
$457$	−154.922	+	123.546i	−0.338998	+	0.270342i	0.439162	+	0.898408i	$0.355275\pi$
$458$	460.642	+	183.811i	1.00577	+	0.401333i
$459$	241.459	+	214.222i	0.526054	+	0.466714i
$460$	−2.26513	−	1.34226i	−0.00492420	−	0.00291797i
$461$	−12.3838	+	109.909i	−0.0268629	+	0.238415i	0.973105	+	0.230363i	$0.0739914\pi$
$461$	−12.3838	+	109.909i	−0.0268629	+	0.238415i	−0.999968	+	0.00805139i	$0.997437\pi$
$462$	33.6393	+	4.58182i	0.0728124	+	0.00991736i
$463$	231.869			0.500797			0.250398	−	0.968143i	$-0.419438\pi$
$463$	231.869			0.500797			0.250398	+	0.968143i	$0.419438\pi$
$464$	−463.725	−	15.9870i	−0.999406	−	0.0344547i
$465$	−682.109	+	90.6345i	−1.46690	+	0.194913i
$466$	128.276	−	468.096i	0.275271	−	1.00450i
$467$	−88.5753	+	786.127i	−0.189669	+	1.68336i	0.433410	+	0.901197i	$0.357310\pi$
$467$	−88.5753	+	786.127i	−0.189669	+	1.68336i	−0.623078	+	0.782159i	$0.714118\pi$
$468$	782.727	+	217.252i	1.67249	+	0.464214i
$469$	−469.695	−	975.332i	−1.00148	−	2.07960i
$470$	675.183	+	269.419i	1.43656	+	0.573233i
$471$	−18.8851	−	18.1480i	−0.0400957	−	0.0385308i
$472$	−226.087	−	233.916i	−0.478999	−	0.495584i
$473$	−4.63363	+	20.3012i	−0.00979625	+	0.0429202i
$474$	−480.117	+	155.611i	−1.01290	+	0.328293i
$475$	−178.175	−	111.955i	−0.375106	−	0.235695i
$476$	283.605	−	375.285i	0.595808	−	0.788413i
$477$	−86.9966	−	163.653i	−0.182383	−	0.343088i
$478$	−233.793	−	544.260i	−0.489106	−	1.13862i
$479$	369.516	−	129.299i	0.771432	−	0.269936i	0.0842728	−	0.996443i	$-0.473143\pi$
$479$	369.516	−	129.299i	0.771432	−	0.269936i	0.687159	+	0.726507i	$0.258858\pi$
$480$	625.524	−	529.162i	1.30318	−	1.10242i
$481$	−857.172	−	857.172i	−1.78206	−	1.78206i
$482$	−42.1339	−	22.5751i	−0.0874148	−	0.0468363i
$483$	0.550505	+	2.20839i	0.00113976	+	0.00457224i
$484$	−41.5283	+	480.887i	−0.0858023	+	0.993567i
$485$	−653.216	−	1039.59i	−1.34684	−	2.14348i
$486$	81.2496	−	479.160i	0.167180	−	0.985926i
$487$	−311.846	+	647.556i	−0.640342	+	1.32968i	0.287884	+	0.957665i	$0.407048\pi$
$487$	−311.846	+	647.556i	−0.640342	+	1.32968i	−0.928225	+	0.372018i	$0.878666\pi$
$488$	−397.417	+	306.013i	−0.814380	+	0.627077i
$489$	−591.623	−	355.520i	−1.20986	−	0.727035i
$490$	−35.1018	+	814.452i	−0.0716364	+	1.66215i
$491$	118.443	−	338.490i	0.241228	−	0.689389i	−0.758079	−	0.652163i	$-0.773862\pi$
$491$	118.443	−	338.490i	0.241228	−	0.689389i	0.999307	−	0.0372267i	$-0.0118524\pi$
$492$	299.064	−	82.8830i	0.607854	−	0.168461i
$493$	−85.7839	−	335.920i	−0.174004	−	0.681379i
$494$	−13.7112	−	198.029i	−0.0277554	−	0.400869i
$495$	−3.19611	+	44.0687i	−0.00645678	+	0.0890277i
$496$	−424.208	+	70.3361i	−0.855257	+	0.141807i
$497$	−350.923	+	440.043i	−0.706082	+	0.885399i
$498$	−25.5644	−	33.6265i	−0.0513341	−	0.0675230i
$499$	−594.736	−	286.410i	−1.19186	−	0.573968i	−0.270512	−	0.962717i	$-0.587193\pi$
$499$	−594.736	−	286.410i	−1.19186	−	0.573968i	−0.921344	+	0.388749i	$0.872907\pi$
$500$	536.797	−	565.525i	1.07359	−	1.13105i
$501$	490.762	+	590.881i	0.979564	+	1.17940i
$502$	362.643	+	56.7651i	0.722396	+	0.113078i
$503$	73.6099	+	653.306i	0.146342	+	1.29882i	0.825322	+	0.564663i	$0.190994\pi$
$503$	73.6099	+	653.306i	0.146342	+	1.29882i	−0.678980	+	0.734157i	$0.737578\pi$
$504$	−705.406	−	63.2426i	−1.39962	−	0.125481i
$505$	960.707	−	960.707i	1.90239	−	1.90239i
$506$	0.0849353	−	0.0256724i	0.000167856	−	5.07360e-5i
$507$	460.966	+	910.404i	0.909203	+	1.79567i
$508$	349.290	+	679.436i	0.687579	+	1.33747i
$509$	−249.059	+	56.8460i	−0.489309	+	0.111682i	−0.460055	−	0.887890i	$-0.652170\pi$
$509$	−249.059	+	56.8460i	−0.489309	+	0.111682i	−0.0292543	+	0.999572i	$0.509313\pi$
$510$	510.678	+	337.632i	1.00133	+	0.662023i
$511$	523.126	−	832.551i	1.02373	−	1.62926i
$512$	380.041	−	343.093i	0.742267	−	0.670104i
$513$	−117.012	+	20.3150i	−0.228093	+	0.0396003i
$514$	357.391	+	490.041i	0.695313	+	0.953387i
$515$	88.8826	−	70.8815i	0.172588	−	0.137634i
$516$	77.1050	−	427.502i	0.149428	−	0.828492i
$517$	−22.0720	+	10.6293i	−0.0426925	+	0.0205596i
$518$	869.863	+	600.318i	1.67927	+	1.15891i
$519$	13.2752	+	666.993i	0.0255785	+	1.28515i
$520$	1527.79	+	198.521i	2.93805	+	0.381771i
$521$	−396.229			−0.760517			−0.380258	−	0.924880i	$-0.624165\pi$
$521$	−396.229			−0.760517			−0.380258	+	0.924880i	$0.624165\pi$
$522$	−360.766	+	377.269i	−0.691123	+	0.722737i
$523$		−	3.46615i		−	0.00662743i	−0.999995	−	0.00331372i	$-0.998945\pi$
$523$		−	3.46615i		−	0.00662743i	0.999995	−	0.00331372i	$-0.00105479\pi$
$524$	−522.146	−	104.944i	−0.996462	−	0.200275i
$525$	−1411.47	+	28.0927i	−2.68851	+	0.0535098i
$526$	235.096	+	162.246i	0.446950	+	0.308453i
$527$	−139.405	−	289.477i	−0.264525	−	0.549292i
$528$	−1.10933	+	27.5888i	−0.00210101	+	0.0522515i
$529$	−329.822	−	413.584i	−0.623483	−	0.781823i
$530$	−207.128	−	284.005i	−0.390807	−	0.535859i
$531$	−365.693	+	14.5627i	−0.688688	+	0.0274250i
$532$	42.8943	+	167.669i	0.0806284	+	0.315168i
$533$	494.103	+	310.465i	0.927022	+	0.582487i
$534$	246.419	+	162.918i	0.461458	+	0.305091i
$535$	−155.441	−	681.030i	−0.290543	−	1.27295i
$536$	753.331	−	455.657i	1.40547	−	0.850105i
$537$	−243.291	+	123.186i	−0.453056	+	0.229396i
$538$	−729.970	+	220.639i	−1.35682	+	0.410110i
$539$	−19.4259	−	19.4259i	−0.0360406	−	0.0360406i
$540$	24.3704	−	921.418i	0.0451303	−	1.70633i
$541$	84.1497	−	9.48140i	0.155545	−	0.0175257i	−0.0338487	−	0.999427i	$-0.510776\pi$
$541$	84.1497	−	9.48140i	0.155545	−	0.0175257i	0.189393	+	0.981901i	$0.439348\pi$
$542$	756.575	+	118.428i	1.39590	+	0.218502i
$543$	143.669	−	119.326i	0.264585	−	0.219753i
$544$	325.754	+	200.601i	0.598813	+	0.368752i
$545$	−211.924	+	440.064i	−0.388851	+	0.807456i
$546$	−805.980	−	1060.16i	−1.47615	−	1.94168i
$547$	32.4522	+	25.8797i	0.0593275	+	0.0473121i	0.652705	−	0.757612i	$-0.273634\pi$
$547$	32.4522	+	25.8797i	0.0593275	+	0.0473121i	−0.593377	+	0.804925i	$0.702206\pi$
$548$	−11.7503	−	450.867i	−0.0214422	−	0.822750i
$549$	−40.8175	+	562.802i	−0.0743488	+	1.02514i
$550$	3.80163	+	54.9066i	0.00691205	+	0.0998302i
$551$	116.308	+	52.3829i	0.211084	+	0.0950687i
$552$	−1.74538	+	0.616390i	−0.00316192	+	0.00111665i
$553$	780.998	+	273.283i	1.41229	+	0.494182i
$554$	−21.4495	+	497.683i	−0.0387175	+	0.898345i
$555$	−708.498	+	1179.01i	−1.27657	+	2.12435i
$556$	−491.604	+	327.063i	−0.884181	+	0.588243i
$557$	199.104	+	95.8834i	0.357458	+	0.172143i	0.603990	−	0.796992i	$-0.293577\pi$
$557$	199.104	+	95.8834i	0.357458	+	0.172143i	−0.246532	+	0.969135i	$0.579291\pi$
$558$	−258.709	+	408.758i	−0.463635	+	0.732541i
$559$	691.629	−	434.580i	1.23726	−	0.777423i
$560$	−1341.41	+	69.9658i	−2.39537	+	0.124939i
$561$	−20.0184	+	4.99016i	−0.0356834	+	0.00889511i
$562$	47.9809	+	25.7079i	0.0853752	+	0.0457435i
$563$	122.505	−	122.505i	0.217593	−	0.217593i	−0.589890	−	0.807483i	$-0.700829\pi$
$563$	122.505	−	122.505i	0.217593	−	0.217593i	0.807483	+	0.589890i	$0.200829\pi$
$564$	449.776	−	242.660i	0.797476	−	0.430247i
$565$	355.855	+	1016.97i	0.629831	+	1.79995i
$566$	−300.304	−	699.095i	−0.530572	−	1.23515i
$567$	−581.461	+	544.736i	−1.02550	+	0.960735i
$568$	−383.387	−	250.097i	−0.674977	−	0.440311i
$569$	136.970	−	217.986i	0.240720	−	0.383104i	−0.704413	−	0.709791i	$-0.748789\pi$
$569$	136.970	−	217.986i	0.240720	−	0.383104i	0.945133	+	0.326687i	$0.105932\pi$
$570$	−214.269	+	69.4471i	−0.375911	+	0.121837i
$571$	98.6107	+	22.5072i	0.172698	+	0.0394172i	0.307996	−	0.951388i	$-0.400342\pi$
$571$	98.6107	+	22.5072i	0.172698	+	0.0394172i	−0.135297	+	0.990805i	$0.543199\pi$
$572$	−39.7347	+	33.4174i	−0.0694663	+	0.0584221i
$573$	198.697	−	206.767i	0.346767	−	0.360850i
$574$	−472.545	−	188.560i	−0.823249	−	0.328503i
$575$	−3.32431	+	1.60090i	−0.00578140	+	0.00278418i
$576$	−3.32248	−	575.990i	−0.00576820	−	0.999983i
$577$	540.930	+	60.9482i	0.937487	+	0.105629i	0.567469	−	0.823395i	$-0.307923\pi$
$577$	540.930	+	60.9482i	0.937487	+	0.105629i	0.370018	+	0.929024i	$0.379351\pi$
$578$	77.2127	−	281.759i	0.133586	−	0.487473i
$579$	34.5923	+	260.339i	0.0597448	+	0.449635i
$580$	−576.456	+	804.881i	−0.993889	+	1.38773i
$581$			69.2509i			0.119193i
$582$	−855.251	−	116.489i	−1.46950	−	0.200153i
$583$	11.7714	+	1.32632i	0.0201911	+	0.00227499i
$584$	714.474	+	359.175i	1.22341	+	0.615026i
$585$	1311.00	−	1133.70i	2.24103	−	1.93795i
$586$	−462.912	−	184.717i	−0.789953	−	0.315216i
$587$	−553.329	−	693.853i	−0.942639	−	1.18203i	−0.983140	−	0.182853i	$-0.941467\pi$
$587$	−553.329	−	693.853i	−0.942639	−	1.18203i	0.0405011	−	0.999179i	$-0.487105\pi$
$588$	423.436	+	386.202i	0.720130	+	0.656807i
$589$	115.248	+	26.3047i	0.195668	+	0.0446599i
$590$	−682.739	+	125.174i	−1.15718	+	0.212160i
$591$	−388.850	−	177.817i	−0.657952	−	0.300874i
$592$	−418.786	+	750.648i	−0.707409	+	1.26799i
$593$	−39.5566	−	173.309i	−0.0667060	−	0.292258i	0.930561	−	0.366136i	$-0.119320\pi$
$593$	−39.5566	−	173.309i	−0.0667060	−	0.292258i	−0.997267	+	0.0738782i	$0.976462\pi$
$594$	22.3267	+	21.5962i	0.0375870	+	0.0363572i
$595$	−331.488	−	947.337i	−0.557122	−	1.59216i
$596$	−392.743	+	149.021i	−0.658964	+	0.250035i
$597$	131.489	−	171.787i	0.220250	−	0.287750i
$598$	−3.06797	−	1.64380i	−0.00513039	−	0.00274883i
$599$	−957.357	+	107.868i	−1.59826	+	0.180081i	−0.865679	−	0.500600i	$-0.833113\pi$
$599$	−957.357	+	107.868i	−1.59826	+	0.180081i	−0.732581	+	0.680680i	$0.761684\pi$
$600$	−131.843	−	1140.56i	−0.219739	−	1.90094i
$601$	37.6075	−	23.6304i	0.0625749	−	0.0393184i	−0.500381	−	0.865805i	$-0.666807\pi$
$601$	37.6075	−	23.6304i	0.0625749	−	0.0393184i	0.562956	+	0.826487i	$0.309664\pi$
$602$	−524.796	+	481.429i	−0.871755	+	0.799717i
$603$	181.802	−	973.639i	0.301496	−	1.61466i
$604$	593.141	+	891.542i	0.982021	+	1.47606i
$605$	805.182	+	642.111i	1.33088	+	1.06134i
$606$	−84.9232	−	951.369i	−0.140137	−	1.56992i
$607$	446.043	+	156.077i	0.734832	+	0.257129i	0.671645	−	0.740873i	$-0.265588\pi$
$607$	446.043	+	156.077i	0.734832	+	0.257129i	0.0631865	+	0.998002i	$0.479874\pi$
$608$	−132.431	+	47.6875i	−0.217814	+	0.0784334i
$609$	845.162	−	134.422i	1.38779	−	0.220725i
$610$	73.9219	+	1067.65i	0.121183	+	1.75024i
$611$	907.052	+	317.391i	1.48454	+	0.519462i
$612$	412.384	−	123.176i	0.673829	−	0.201267i
$613$	−168.970	−	134.749i	−0.275644	−	0.219819i	0.475904	−	0.879497i	$-0.342121\pi$
$613$	−168.970	−	134.749i	−0.275644	−	0.219819i	−0.751548	+	0.659679i	$0.770692\pi$
$614$	−172.844	+	98.4884i	−0.281504	+	0.160405i
$615$	206.215	−	629.223i	0.335309	−	1.02313i
$616$	28.8213	−	34.9055i	0.0467879	−	0.0566647i
$617$	460.865	−	289.581i	0.746945	−	0.469336i	−0.104010	−	0.994576i	$-0.533167\pi$
$617$	460.865	−	289.581i	0.746945	−	0.469336i	0.850954	+	0.525240i	$0.176024\pi$
$618$	1.85177	−	79.9012i	0.00299638	−	0.129290i
$619$	−572.788	+	64.5377i	−0.925344	+	0.104261i	−0.561760	−	0.827300i	$-0.689876\pi$
$619$	−572.788	+	64.5377i	−0.925344	+	0.104261i	−0.363584	+	0.931561i	$0.618447\pi$
$620$	−376.405	+	836.704i	−0.607105	+	1.34952i
$621$	−0.789965	+	1.92674i	−0.00127209	+	0.00310265i
$622$	−322.759	+	97.5567i	−0.518906	+	0.156844i
$623$	−159.954	−	457.121i	−0.256747	−	0.733742i
$624$	796.012	−	734.472i	1.27566	−	1.17704i
$625$	−104.065	−	455.939i	−0.166504	−	0.729503i
$626$	−133.779	−	116.453i	−0.213704	−	0.186027i
$627$	3.15671	−	6.90310i	0.00503463	−	0.0110097i
$628$	−33.8325	+	8.65525i	−0.0538733	+	0.0137822i
$629$	−626.164	−	142.918i	−0.995491	−	0.227214i
$630$	−946.036	+	1178.36i	−1.50164	+	1.87042i
$631$	−115.584	−	144.937i	−0.183175	−	0.229694i	0.681763	−	0.731573i	$-0.261214\pi$
$631$	−115.584	−	144.937i	−0.183175	−	0.229694i	−0.864938	+	0.501879i	$0.832642\pi$
$632$	−160.885	+	653.425i	−0.254565	+	1.03390i
$633$	240.066	+	365.701i	0.379251	+	0.577726i
$634$	705.228	+	486.698i	1.11235	+	0.767663i
$635$	1619.78	+	182.506i	2.55084	+	0.287411i
$636$	−246.577	−	16.3581i	−0.387700	−	0.0257203i
$637$			1077.65i			1.69176i
$638$	−6.85552	−	32.6515i	−0.0107453	−	0.0511778i
$639$	−497.099	+	134.477i	−0.777932	+	0.210450i
$640$	−160.328	−	1080.60i	−0.250513	−	1.68844i
$641$	476.540	+	53.6931i	0.743432	+	0.0837646i	0.475552	−	0.879688i	$-0.342248\pi$
$641$	476.540	+	53.6931i	0.743432	+	0.0837646i	0.267880	+	0.963452i	$0.413677\pi$
$642$	−437.400	−	223.270i	−0.681309	−	0.347772i
$643$	−1109.04	+	534.084i	−1.72479	+	0.830613i	−0.736792	+	0.676119i	$0.763660\pi$
$643$	−1109.04	+	534.084i	−1.72479	+	0.830613i	−0.987994	+	0.154494i	$0.950625\pi$
$644$	2.88948	+	0.927310i	0.00448676	+	0.00143992i
$645$	−668.301	−	642.218i	−1.03613	−	0.995686i
$646$	−61.9723	−	84.9741i	−0.0959324	−	0.131539i
$647$	−157.666	−	35.9863i	−0.243689	−	0.0556203i	0.0989320	−	0.995094i	$-0.468457\pi$
$647$	−157.666	−	35.9863i	−0.243689	−	0.0556203i	−0.342621	+	0.939474i	$0.611315\pi$
$648$	−485.966	−	428.650i	−0.749948	−	0.661497i
$649$	12.4451	−	19.8063i	0.0191758	−	0.0305181i
$650$	1417.52	−	1628.42i	2.18080	−	2.50525i
$651$	743.210	−	276.780i	1.14164	−	0.425162i
$652$	−818.479	+	420.770i	−1.25534	+	0.645353i
$653$	−161.526	−	461.615i	−0.247360	−	0.706914i	−0.998885	−	0.0472094i	$-0.984967\pi$
$653$	−161.526	−	461.615i	−0.247360	−	0.706914i	0.751525	−	0.659704i	$-0.229319\pi$
$654$	141.778	+	312.742i	0.216786	+	0.478198i
$655$	−803.529	+	803.529i	−1.22676	+	1.22676i
$656$	116.135	−	397.151i	0.177035	−	0.605413i
$657$	836.654	−	330.683i	1.27345	−	0.503323i
$658$	−827.770	−	129.572i	−1.25801	−	0.196918i
$659$	−965.152	+	606.445i	−1.46457	+	0.920251i	−0.465184	+	0.885214i	$0.654012\pi$
$659$	−965.152	+	606.445i	−1.46457	+	0.920251i	−0.999386	+	0.0350367i	$0.988845\pi$
$660$	47.6985	+	34.5767i	0.0722705	+	0.0523889i
$661$	209.966	+	101.114i	0.317648	+	0.152971i	0.585913	−	0.810374i	$-0.300736\pi$
$661$	209.966	+	101.114i	0.317648	+	0.152971i	−0.268265	+	0.963345i	$0.586450\pi$
$662$	504.618	+	885.587i	0.762263	+	1.33775i
$663$	693.672	+	416.844i	1.04626	+	0.628724i
$664$	−56.0660	+	5.35273i	−0.0844367	+	0.00806133i
$665$	348.548	+	121.962i	0.524133	+	0.183402i
$666$	316.397	+	913.787i	0.475070	+	1.37205i
$667$	1.86271	−	1.23811i	0.00279267	−	0.00185623i
$668$	1014.37	−	141.142i	1.51852	−	0.211291i
$669$	−151.990	+	732.843i	−0.227190	+	1.09543i
$670$	80.8860	−	1876.76i	0.120725	−	2.80114i
$671$	−28.1973	−	22.4866i	−0.0420228	−	0.0335121i
$672$	−567.161	+	755.022i	−0.843989	+	1.12354i
$673$	−217.285	+	451.197i	−0.322860	+	0.670427i	−0.997718	−	0.0675216i	$-0.978491\pi$
$673$	−217.285	+	451.197i	−0.322860	+	0.670427i	0.674857	+	0.737948i	$0.264205\pi$
$674$	225.046	+	245.318i	0.333896	+	0.363973i
$675$	−1056.13	−	743.659i	−1.56463	−	1.10172i
$676$	1355.56	+	117.063i	2.00527	+	0.173170i
$677$	338.577	−	38.1485i	0.500114	−	0.0563493i	0.141695	−	0.989910i	$-0.454745\pi$
$677$	338.577	−	38.1485i	0.500114	−	0.0563493i	0.358419	+	0.933561i	$0.383316\pi$
$678$	708.963	+	266.670i	1.04567	+	0.393319i
$679$	1000.61	+	1000.61i	1.47365	+	1.47365i
$680$	741.349	−	341.599i	1.09022	−	0.502351i
$681$	15.3178	+	30.2526i	0.0224931	+	0.0444238i
$682$	−12.2032	−	28.4085i	−0.0178932	−	0.0416547i
$683$	7.91892	+	34.6951i	0.0115943	+	0.0507981i	0.980394	−	0.197046i	$-0.0631350\pi$
$683$	7.91892	+	34.6951i	0.0115943	+	0.0507981i	−0.968800	+	0.247844i	$0.920278\pi$
$684$	−59.1675	+	146.880i	−0.0865022	+	0.214737i
$685$	−814.822	−	511.987i	−1.18952	−	0.747426i
$686$	4.40336	+	24.0173i	0.00641890	+	0.0350107i
$687$	68.5678	−	740.775i	0.0998075	−	1.07827i
$688$	−430.333	−	387.667i	−0.625484	−	0.563470i
$689$	−289.720	−	363.297i	−0.420493	−	0.527282i
$690$	−0.967811	+	3.82903i	−0.00140263	+	0.00554932i
$691$	−511.948	−	1063.07i	−0.740880	−	1.53845i	−0.839519	−	0.543330i	$-0.817163\pi$
$691$	−511.948	−	1063.07i	−0.740880	−	1.53845i	0.0986390	−	0.995123i	$-0.468551\pi$
$692$	765.235	+	453.460i	1.10583	+	0.655289i
$693$	−7.71085	−	50.3377i	−0.0111268	−	0.0726374i
$694$	−225.382	+	822.449i	−0.324758	+	1.18508i
$695$			1259.84i			1.81273i
$696$	174.155	+	673.859i	0.250223	+	0.968188i
$697$	309.178			0.443583
$698$	−928.427	−	254.424i	−1.33012	−	0.364505i
$699$	−727.888	+	14.4872i	−1.04133	+	0.0207257i
$700$	−959.598	+	1619.37i	−1.37085	+	2.31338i
$701$	−603.262	+	290.516i	−0.860573	+	0.414430i	−0.811491	−	0.584364i	$-0.801344\pi$
$701$	−603.262	+	290.516i	−0.860573	+	0.414430i	−0.0490820	+	0.998795i	$0.515630\pi$
$702$	−20.2617	−	1218.31i	−0.0288628	−	1.73548i
$703$	184.751	−	147.334i	0.262804	−	0.209579i
$704$	30.4874	+	20.6360i	0.0433060	+	0.0293124i
$705$	100.503	−	1085.79i	0.142557	−	1.54012i
$706$	1035.06	−	189.770i	1.46609	−	0.268796i
$707$	−833.114	+	1325.89i	−1.17838	+	1.87538i
$708$	−240.364	+	424.673i	−0.339497	+	0.599821i
$709$	−403.778	+	92.1598i	−0.569504	+	0.129986i	−0.497570	−	0.867424i	$-0.665774\pi$
$709$	−403.778	+	92.1598i	−0.569504	+	0.129986i	−0.0719341	+	0.997409i	$0.522917\pi$
$710$	−897.388	+	385.482i	−1.26393	+	0.542933i
$711$	427.966	+	624.484i	0.601921	+	0.878318i
$712$	357.725	−	164.833i	0.502423	−	0.231507i
$713$	1.46566	−	1.46566i	0.00205562	−	0.00205562i
$714$	−660.417	−	248.410i	−0.924953	−	0.347913i
$715$	12.4031	+	110.081i	0.0173470	+	0.153959i
$716$	−31.2833	+	362.252i	−0.0436918	+	0.505939i
$717$	−683.515	+	567.700i	−0.953298	+	0.791771i
$718$	−223.200	+	204.755i	−0.310863	+	0.285175i
$719$	−783.503	−	377.315i	−1.08971	−	0.524778i	−0.199302	−	0.979938i	$-0.563868\pi$
$719$	−783.503	−	377.315i	−1.08971	−	0.524778i	−0.890409	+	0.455160i	$0.849582\pi$
$720$	−1027.13	−	674.836i	−1.42658	−	0.937272i
$721$	−81.6946	+	102.442i	−0.113307	+	0.142083i
$722$	−682.671	−	29.4222i	−0.945528	−	0.0407510i
$723$	−14.5608	+	70.2070i	−0.0201394	+	0.0971051i
$724$	−34.3180	−	246.638i	−0.0474006	−	0.340661i
$725$	491.620	+	1297.33i	0.678097	+	1.78943i
$726$	709.405	−	144.711i	0.977142	−	0.199326i
$727$	83.0756	−	237.417i	0.114272	−	0.326570i	−0.872517	−	0.488585i	$-0.837513\pi$
$727$	83.0756	−	237.417i	0.114272	−	0.326570i	0.986788	+	0.162014i	$0.0517991\pi$
$728$	−1767.62	+	168.758i	−2.42805	+	0.231810i
$729$	−723.809	+	86.8381i	−0.992880	+	0.119119i
$730$	1482.46	−	844.721i	2.03076	−	1.15715i
$731$	187.775	−	389.919i	0.256874	−	0.533404i
$732$	609.159	+	441.579i	0.832184	+	0.603250i
$733$	−153.691	−	244.598i	−0.209674	−	0.333694i	0.725286	−	0.688448i	$-0.241708\pi$
$733$	−153.691	−	244.598i	−0.209674	−	0.333694i	−0.934960	+	0.354754i	$0.884565\pi$
$734$	183.968	−	1175.27i	0.250637	−	1.60119i
$735$	1186.50	−	295.770i	1.61429	−	0.402409i
$736$	−0.527416	+	2.41102i	−0.000716598	+	0.00327584i
$737$	44.7635	+	44.7635i	0.0607375	+	0.0607375i
$738$	−246.373	−	394.963i	−0.333839	−	0.535180i
$739$	−558.345	+	195.373i	−0.755541	+	0.264375i	−0.680443	−	0.732801i	$-0.738213\pi$
$739$	−558.345	+	195.373i	−0.755541	+	0.264375i	−0.0750979	+	0.997176i	$0.523927\pi$
$740$	838.531	+	1631.10i	1.13315	+	2.20419i
$741$	−279.033	+	103.915i	−0.376563	+	0.140237i
$742$	305.578	+	266.003i	0.411830	+	0.358494i
$743$	−488.864	−	307.174i	−0.657960	−	0.413423i	0.161253	−	0.986913i	$-0.448446\pi$
$743$	−488.864	−	307.174i	−0.657960	−	0.413423i	−0.819213	+	0.573490i	$0.805589\pi$
$744$	281.529	+	580.314i	0.378400	+	0.779992i
$745$	−199.440	+	873.803i	−0.267704	+	1.17289i
$746$	−214.544	+	156.469i	−0.287593	+	0.209744i
$747$	−37.5026	+	51.0704i	−0.0502042	+	0.0683673i
$748$	−8.40577	+	26.1922i	−0.0112377	+	0.0350163i
$749$	349.324	+	725.378i	0.466387	+	0.968462i
$750$	−1041.72	−	531.743i	−1.38896	−	0.708991i
$751$	−70.1828	+	622.890i	−0.0934525	+	0.829414i	0.856314	+	0.516455i	$0.172749\pi$
$751$	−70.1828	+	622.890i	−0.0934525	+	0.829414i	−0.949767	+	0.312959i	$0.898680\pi$
$752$	40.9204	−	680.184i	0.0544154	−	0.904499i
$753$	−72.5215	−	545.791i	−0.0963101	−	0.724822i
$754$	−715.513	+	1095.82i	−0.948956	+	1.45334i
$755$	2284.77			3.02619
$756$	208.929	+	1041.61i	0.276362	+	1.37779i
$757$	84.4965	−	749.927i	0.111620	−	0.990656i	−0.805650	−	0.592391i	$-0.798184\pi$
$757$	84.4965	−	749.927i	0.111620	−	0.990656i	0.917270	−	0.398265i	$-0.130388\pi$
$758$	−81.7836	+	118.505i	−0.107894	+	0.156339i
$759$	−0.0730396	−	0.111264i	−9.62314e−5	−	0.000146593i
$760$	−71.8007	+	291.614i	−0.0944745	+	0.383703i
$761$	−3.82796	+	3.05270i	−0.00503017	+	0.00401143i	−0.626002	−	0.779822i	$-0.715310\pi$
$761$	−3.82796	+	3.05270i	−0.00503017	+	0.00401143i	0.620971	+	0.783833i	$0.286738\pi$
$762$	828.860	−	791.312i	1.08774	−	1.03847i
$763$	125.267	−	548.831i	0.164177	−	0.719307i
$764$	−94.7638	−	370.422i	−0.124036	−	0.484845i
$765$	268.565	−	878.148i	0.351066	−	1.14791i
$766$	740.340	−	850.485i	0.966501	−	1.11029i
$767$	−894.571	+	204.180i	−1.16632	+	0.266206i
$768$	−655.110	−	400.818i	−0.853007	−	0.521899i
$769$	−871.164	+	304.834i	−1.13285	+	0.396403i	−0.830625	−	0.556833i	$-0.812016\pi$
$769$	−871.164	+	304.834i	−1.13285	+	0.396403i	−0.302229	+	0.953235i	$0.597731\pi$
$770$	−27.9445	−	92.4524i	−0.0362916	−	0.120068i
$771$	552.974	−	722.443i	0.717216	−	0.937021i
$772$	319.343	+	143.662i	0.413656	+	0.186090i
$773$	−82.5542	−	732.689i	−0.106797	−	0.947852i	−0.926816	−	0.375515i	$-0.877466\pi$
$773$	−82.5542	−	732.689i	−0.106797	−	0.947852i	0.820019	−	0.572336i	$-0.193963\pi$
$774$	−647.737	+	70.8376i	−0.836870	+	0.0915214i
$775$	684.032	+	1088.63i	0.882622	+	1.40469i
$776$	−732.759	+	887.442i	−0.944276	+	1.14361i
$777$	493.728	−	1506.51i	0.635429	−	1.93888i
$778$	−318.902	−	559.661i	−0.409899	−	0.719359i
$779$	−70.9244	+	88.9364i	−0.0910455	+	0.114167i
$780$	−363.968	−	2282.10i	−0.466625	−	2.92577i
$781$	10.8708	−	31.0669i	0.0139190	−	0.0397783i
$782$	−1.83970	+	0.127377i	−0.00235256	+	0.000162887i
$783$	696.076	+	358.563i	0.888986	+	0.457934i
$784$	735.115	−	208.611i	0.937646	−	0.266086i
$785$	−24.6097	+	70.3304i	−0.0313499	+	0.0895928i
$786$	71.0291	+	795.718i	0.0903678	+	1.01236i
$787$	611.914	−	767.316i	0.777527	−	0.974988i	−0.222473	−	0.974939i	$-0.571413\pi$
$787$	611.914	−	767.316i	0.777527	−	0.974988i	1.00000		4.94981e-5i	$-1.57557e-5\pi$
$788$	−474.655	+	315.787i	−0.602354	+	0.400745i
$789$	133.439	−	407.161i	0.169124	−	0.516047i
$790$	970.622	+	1058.06i	1.22864	+	1.33931i
$791$	−660.678	−	1051.46i	−0.835244	−	1.32928i
$792$	40.1578	−	10.1336i	0.0507043	−	0.0127949i
$793$	158.400	+	1405.84i	0.199748	+	1.77281i
$794$	−32.7843	+	61.1883i	−0.0412901	+	0.0770633i
$795$	−320.478	+	418.695i	−0.403117	+	0.526661i
$796$	−102.328	−	269.683i	−0.128553	−	0.338798i
$797$	714.650	−	250.067i	0.896675	−	0.313760i	0.157695	−	0.987488i	$-0.449594\pi$
$797$	714.650	−	250.067i	0.896675	−	0.313760i	0.738980	+	0.673728i	$0.235308\pi$
$798$	222.954	−	132.988i	0.279391	−	0.166651i
$799$	496.386	−	113.297i	0.621259	−	0.141798i
$800$	−1385.22	−	651.729i	−1.73153	−	0.814661i
$801$	129.592	−	423.735i	0.161787	−	0.529007i
$802$	132.489	+	722.636i	0.165198	+	0.901042i
$803$	−12.7949	+	56.0581i	−0.0159339	+	0.0698108i
$804$	−975.735	−	889.935i	−1.21360	−	1.10688i
$805$	5.06225	−	4.03701i	0.00628851	−	0.00501492i
$806$	−449.494	+	1126.46i	−0.557685	+	1.39760i
$807$	627.733	+	956.248i	0.777860	+	1.18494i
$808$	−1137.85	−	572.010i	−1.40823	−	0.707934i
$809$	−148.484	+	1317.84i	−0.183541	+	1.62897i	0.477509	+	0.878627i	$0.341540\pi$
$809$	−148.484	+	1317.84i	−0.183541	+	1.62897i	−0.661050	+	0.750342i	$0.729889\pi$
$810$	−1335.81	+	356.684i	−1.64915	+	0.440351i
$811$	287.423			0.354406			0.177203	−	0.984174i	$-0.443295\pi$
$811$	287.423			0.354406			0.177203	+	0.984174i	$0.443295\pi$
$812$	441.312	−	1052.25i	0.543488	−	1.29587i
$813$	−151.300	−	1138.67i	−0.186101	−	1.40058i
$814$	−59.6085	−	16.3350i	−0.0732291	−	0.0200675i
$815$	−219.855	+	1951.26i	−0.269760	+	2.39419i
$816$	150.068	−	553.879i	0.183907	−	0.678773i
$817$	69.0869	+	143.461i	0.0845617	+	0.175594i
$818$	366.670	−	918.900i	0.448252	−	1.12335i
$819$	−1182.36	+	1610.12i	−1.44366	+	1.96596i
$820$	−568.257	−	675.681i	−0.692996	−	0.824001i
$821$	36.0936	−	158.136i	0.0439630	−	0.192614i	−0.948178	−	0.317740i	$-0.897076\pi$
$821$	36.0936	−	158.136i	0.0439630	−	0.192614i	0.992141	+	0.125125i	$0.0399333\pi$
$822$	−643.571	+	208.589i	−0.782934	+	0.253757i
$823$	−427.280	−	268.478i	−0.519173	−	0.326218i	0.246826	−	0.969060i	$-0.420612\pi$
$823$	−427.280	−	268.478i	−0.519173	−	0.326218i	−0.765999	+	0.642842i	$0.777755\pi$
$824$	−89.2521	−	58.2223i	−0.108316	−	0.0706581i
$825$	77.3663	−	28.8121i	0.0937773	−	0.0349238i
$826$	735.060	−	315.752i	0.889903	−	0.382267i
$827$	−71.0209	+	24.8513i	−0.0858778	+	0.0300499i	−0.372876	−	0.927881i	$-0.621628\pi$
$827$	−71.0209	+	24.8513i	−0.0858778	+	0.0300499i	0.286998	+	0.957931i	$0.407343\pi$
$828$	1.62872	+	2.24865i	0.00196705	+	0.00271576i
$829$	491.492	+	491.492i	0.592873	+	0.592873i	0.938406	−	0.345533i	$-0.112302\pi$
$829$	491.492	+	491.492i	0.592873	+	0.592873i	−0.345533	+	0.938406i	$0.612302\pi$
$830$	−56.7532	+	105.924i	−0.0683774	+	0.127619i
$831$	725.030	−	180.735i	0.872479	−	0.217491i
$832$	−273.255	−	1418.03i	−0.328431	−	1.70437i
$833$	303.772	+	483.450i	0.364672	+	0.580372i
$834$	679.482	+	568.116i	0.814727	+	0.681195i
$835$	948.109	−	1968.77i	1.13546	−	2.35781i
$836$	−5.60604	−	8.42637i	−0.00670580	−	0.0100794i
$837$	697.983	+	198.366i	0.833911	+	0.236996i
$838$	−1070.81	−	46.1505i	−1.27782	−	0.0550722i
$839$	303.103	−	866.220i	0.361267	−	1.03244i	−0.609576	−	0.792728i	$-0.708660\pi$
$839$	303.103	−	866.220i	0.361267	−	1.03244i	0.970843	−	0.239715i	$-0.0770541\pi$
$840$	670.943	+	1899.85i	0.798742	+	2.26173i
$841$	−403.236	−	738.026i	−0.479472	−	0.877557i
$842$	358.028	−	24.7892i	0.425212	−	0.0294408i
$843$	16.5814	−	79.9496i	0.0196695	−	0.0948394i
$844$	583.078	−	15.1959i	0.690851	−	0.0180046i
$845$	1810.03	−	2269.71i	2.14205	−	2.68604i
$846$	−540.285	−	543.831i	−0.638635	−	0.642826i
$847$	−1069.43	−	515.009i	−1.26261	−	0.608039i
$848$	−191.738	+	267.959i	−0.226106	+	0.315989i
$849$	−877.966	+	729.203i	−1.03412	+	0.858896i
$850$	176.898	−	1130.11i	0.208115	−	1.32954i
$851$	−0.463917	−	4.11737i	−0.000545143	−	0.00483828i
$852$	−196.764	+	657.826i	−0.230944	+	0.772096i
$853$	−193.212	+	193.212i	−0.226509	+	0.226509i	−0.811233	−	0.584724i	$-0.801203\pi$
$853$	−193.212	+	193.212i	−0.226509	+	0.226509i	0.584724	+	0.811233i	$0.301203\pi$
$854$	−356.879	−	1180.71i	−0.417892	−	1.38257i
$855$	190.995	+	278.699i	0.223386	+	0.325963i
$856$	−560.270	+	338.883i	−0.654521	+	0.395891i
$857$	903.739	−	206.272i	1.05454	−	0.240691i	0.340099	−	0.940390i	$-0.389539\pi$
$857$	903.739	−	206.272i	1.05454	−	0.240691i	0.714438	+	0.699698i	$0.246682\pi$
$858$	64.9638	+	42.9505i	0.0757154	+	0.0500588i
$859$	−92.9570	+	147.940i	−0.108215	+	0.172224i	−0.896442	−	0.443162i	$-0.853857\pi$
$859$	−92.9570	+	147.940i	−0.108215	+	0.172224i	0.788226	+	0.615385i	$0.211000\pi$
$860$	−1197.26	+	306.290i	−1.39216	+	0.356151i
$861$	−70.3396	+	759.917i	−0.0816953	+	0.882598i
$862$	883.634	−	644.442i	1.02510	−	0.747612i
$863$	683.432	−	545.019i	0.791926	−	0.631540i	−0.141651	−	0.989917i	$-0.545241\pi$
$863$	683.432	−	545.019i	0.791926	−	0.631540i	0.933577	+	0.358377i	$0.116670\pi$
$864$	−827.143	+	249.661i	−0.957341	+	0.288960i
$865$	1709.94	−	823.463i	1.97681	−	0.951981i
$866$	374.264	−	542.310i	0.432176	−	0.626224i
$867$	−438.134	+	8.72024i	−0.505345	+	0.0100580i
$868$	208.363	−	1036.70i	0.240049	−	1.19436i
$869$	−48.3869			−0.0556812
$870$	1402.89	+	487.030i	1.61252	+	0.559805i
$871$		−	2483.25i		−	2.85103i
$872$	454.020	+	58.9954i	0.520665	+	0.0676553i
$873$	196.042	+	1279.79i	0.224561	+	1.46597i
$874$	0.385382	−	0.558419i	0.000440940	−	0.000638924i
$875$	831.954	+	1727.57i	0.950805	+	1.97437i
$876$	212.911	−	1180.47i	0.243049	−	1.34756i
$877$	−421.833	−	528.962i	−0.480995	−	0.603149i	0.480830	−	0.876814i	$-0.340335\pi$
$877$	−421.833	−	528.962i	−0.480995	−	0.603149i	−0.961825	+	0.273665i	$0.911764\pi$
$878$	152.162	−	110.973i	0.173305	−	0.126393i
$879$	−68.9058	+	744.426i	−0.0783911	+	0.846901i
$880$	72.6902	−	29.7702i	0.0826025	−	0.0338297i
$881$	465.381	+	292.418i	0.528242	+	0.331917i	0.769607	−	0.638518i	$-0.220452\pi$
$881$	465.381	+	292.418i	0.528242	+	0.331917i	−0.241365	+	0.970434i	$0.577595\pi$
$882$	375.524	−	773.302i	0.425764	−	0.876759i
$883$	69.6525	+	305.168i	0.0788817	+	0.345603i	0.998932	−	0.0461961i	$-0.0147099\pi$
$883$	69.6525	+	305.168i	0.0788817	+	0.345603i	−0.920051	+	0.391799i	$0.871853\pi$
$884$	959.658	−	493.349i	1.08559	−	0.558087i
$885$	470.328	+	928.894i	0.531444	+	1.04960i
$886$	99.9876	+	330.802i	0.112853	+	0.373366i
$887$	−556.628	−	556.628i	−0.627540	−	0.627540i	0.319909	−	0.947448i	$-0.396348\pi$
$887$	−556.628	−	556.628i	−0.627540	−	0.627540i	−0.947448	+	0.319909i	$0.896348\pi$
$888$	1257.85	+	283.281i	1.41649	+	0.319010i
$889$	−1866.88	+	210.347i	−2.09998	+	0.236611i
$890$	129.966	−	830.283i	0.146029	−	0.932902i
$891$	21.5737	−	41.2983i	0.0242129	−	0.0463505i
$892$	723.779	+	687.012i	0.811411	+	0.770192i
$893$	−81.2790	+	168.778i	−0.0910179	+	0.189001i
$894$	381.339	+	501.600i	0.426554	+	0.561073i
$895$	606.544	+	483.703i	0.677703	+	0.540450i
$896$	457.293	+	1173.11i	0.510372	+	1.30927i
$897$	−1.06024	+	5.11210i	−0.00118199	+	0.00569911i
$898$	100.777	−	6.97763i	0.112224	−	0.00777019i
$899$	−501.386	−	596.687i	−0.557715	−	0.663723i
$900$	−1584.64	+	674.565i	−1.76071	+	0.749517i
$901$	−232.381	−	81.3135i	−0.257914	−	0.0902481i
$902$	29.7250	+	1.28111i	0.0329545	+	0.00142030i
$903$	915.647	+	550.234i	1.01401	+	0.609340i
$904$	800.205	−	616.162i	0.885183	−	0.681595i
$905$	−478.695	−	230.527i	−0.528945	−	0.254726i
$906$	1030.30	−	1232.26i	1.13719	−	1.36012i
$907$	−187.357	+	117.724i	−0.206567	+	0.129795i	−0.631343	−	0.775504i	$-0.717496\pi$
$907$	−187.357	+	117.724i	−0.206567	+	0.129795i	0.424775	+	0.905299i	$0.360353\pi$
$908$	45.0450	+	3.88999i	0.0496091	+	0.00428413i
$909$	−1332.43	+	526.635i	−1.46582	+	0.579356i
$910$	−1789.28	+	3339.50i	−1.96625	+	3.66978i
$911$	865.075	−	865.075i	0.949588	−	0.949588i	−0.0492007	−	0.998789i	$-0.515667\pi$
$911$	865.075	−	865.075i	0.949588	−	0.949588i	0.998789	+	0.0492007i	$0.0156674\pi$
$912$	124.901	+	170.226i	0.136953	+	0.186651i
$913$	−1.33753	−	3.82244i	−0.00146498	−	0.00418668i
$914$	364.132	−	156.416i	0.398393	−	0.171134i
$915$	1504.37	−	560.246i	1.64412	−	0.612291i
$916$	−791.365	−	598.039i	−0.863935	−	0.652881i
$917$	696.810	−	1108.97i	0.759880	−	1.20934i
$918$	−352.511	−	540.841i	−0.383999	−	0.589151i
$919$	1386.03	+	316.352i	1.50819	+	0.344235i	0.895132	−	0.445802i	$-0.147081\pi$
$919$	1386.03	+	316.352i	1.50819	+	0.344235i	0.613060	+	0.790037i	$0.289939\pi$
$920$	3.65968	+	3.78639i	0.00397791	+	0.00411565i
$921$	215.159	+	206.761i	0.233614	+	0.224496i
$922$	81.9835	−	205.456i	0.0889192	−	0.222837i
$923$	−1163.24	+	560.188i	−1.26028	+	0.606921i
$924$	−62.4645	−	26.6191i	−0.0676022	−	0.0288086i
$925$	2553.94	+	287.760i	2.76102	+	0.311092i
$926$	−447.249	−	122.563i	−0.482990	−	0.132357i
$927$	−115.724	+	31.3062i	−0.124837	+	0.0337715i
$928$	886.020	+	275.956i	0.954763	+	0.297366i
$929$			925.055i			0.995754i	0.867248	+	0.497877i	$0.165887\pi$
$929$			925.055i			0.995754i	−0.867248	+	0.497877i	$0.834113\pi$
$930$	1363.62	+	185.730i	1.46625	+	0.199710i
$931$	−208.751	−	23.5206i	−0.224222	−	0.0252638i
$932$	−494.860	+	835.099i	−0.530965	+	0.896029i
$933$	277.555	+	422.809i	0.297487	+	0.453172i
$934$	586.389	−	1469.53i	0.627825	−	1.57337i
$935$	36.5942	+	45.8877i	0.0391382	+	0.0490777i
$936$	−1394.95	−	832.793i	−1.49033	−	0.889737i
$937$	206.553	+	47.1444i	0.220441	+	0.0503142i	0.331315	−	0.943520i	$-0.392508\pi$
$937$	206.553	+	47.1444i	0.220441	+	0.0503142i	−0.110874	+	0.993834i	$0.535365\pi$
$938$	390.439	+	2129.58i	0.416247	+	2.27034i
$939$	−110.641	+	241.949i	−0.117828	+	0.257667i
$940$	−1159.94	−	876.572i	−1.23398	−	0.932523i
$941$	278.978	+	1222.28i	0.296470	+	1.29892i	0.875343	+	0.483502i	$0.160635\pi$
$941$	278.978	+	1222.28i	0.296470	+	1.29892i	−0.578874	+	0.815417i	$0.696508\pi$
$942$	26.8343	+	44.9878i	0.0284865	+	0.0477578i
$943$	0.658769	+	1.88265i	0.000698589	+	0.00199645i
$944$	312.452	+	570.704i	0.330987	+	0.604559i
$945$	2097.27	+	859.881i	2.21933	+	0.909926i
$946$	19.6687	−	36.7095i	0.0207915	−	0.0388050i
$947$	814.131	−	91.7306i	0.859695	−	0.0968644i	0.328900	−	0.944365i	$-0.393322\pi$
$947$	814.131	−	91.7306i	0.859695	−	0.0968644i	0.530795	+	0.847500i	$0.321893\pi$
$948$	1008.34	−	46.3722i	1.06365	−	0.0489159i
$949$	1909.80	−	1200.01i	2.01244	−	1.26450i
$950$	284.502	+	310.129i	0.299475	+	0.326452i
$951$	400.283	−	1221.38i	0.420907	−	1.28431i
$952$	−745.411	+	573.971i	−0.782995	+	0.602910i
$953$	−793.016	−	632.409i	−0.832126	−	0.663598i	0.111809	−	0.993730i	$-0.464336\pi$
$953$	−793.016	−	632.409i	−0.832126	−	0.663598i	−0.943935	+	0.330131i	$0.892907\pi$
$954$	81.3013	+	361.653i	0.0852215	+	0.379091i
$955$	−770.027	−	269.444i	−0.806311	−	0.282140i
$956$	163.270	+	1173.39i	0.170784	+	1.22740i
$957$	−44.0541	+	23.7433i	−0.0460336	+	0.0248102i
$958$	−781.099	+	54.0818i	−0.815344	+	0.0564528i
$959$	1046.89	+	366.322i	1.09164	+	0.381983i
$960$	−1486.27	+	690.049i	−1.54820	+	0.718801i
$961$	186.652	+	148.850i	0.194227	+	0.154891i
$962$	1200.30	+	2106.48i	1.24771	+	2.18968i
$963$	−135.211	+	724.118i	−0.140406	+	0.751940i
$964$	69.3386	+	65.8162i	0.0719280	+	0.0682741i
$965$	632.623	−	397.503i	0.655568	−	0.411920i
$966$	0.105466	−	4.55072i	0.000109178	−	0.00471089i
$967$	−567.723	+	63.9670i	−0.587097	+	0.0661499i	−0.400516	−	0.916290i	$-0.631169\pi$
$967$	−567.723	+	63.9670i	−0.587097	+	0.0661499i	−0.186581	+	0.982440i	$0.559741\pi$
$968$	334.294	−	905.623i	0.345345	−	0.935561i
$969$	−95.8867	+	125.273i	−0.0989543	+	0.129281i
$970$	710.466	+	2350.53i	0.732439	+	2.42322i
$971$	−141.332	−	403.904i	−0.145553	−	0.415967i	0.847907	−	0.530145i	$-0.177862\pi$
$971$	−141.332	−	403.904i	−0.145553	−	0.415967i	−0.993460	+	0.114178i	$0.963577\pi$
$972$	−409.999	+	881.297i	−0.421810	+	0.906684i
$973$	−323.108	−	1415.63i	−0.332074	−	1.45491i
$974$	943.806	−	1084.22i	0.969000	−	1.11316i
$975$	−2945.11	−	1346.77i	−3.02063	−	1.38130i
$976$	928.327	−	380.195i	0.951155	−	0.389544i
$977$	890.386	+	203.225i	0.911347	+	0.208009i	0.652393	−	0.757881i	$-0.273765\pi$
$977$	890.386	+	203.225i	0.911347	+	0.208009i	0.258954	+	0.965890i	$0.416622\pi$
$978$	953.249	+	998.482i	0.974692	+	1.02094i
$979$	17.6579	+	22.1423i	0.0180367	+	0.0226173i
$980$	498.217	−	1552.43i	0.508384	−	1.58411i
$981$	389.598	−	336.908i	0.397144	−	0.343433i
$982$	−407.384	+	590.301i	−0.414851	+	0.601121i
$983$	−1139.81	−	128.426i	−1.15953	−	0.130647i	−0.488830	−	0.872379i	$-0.662576\pi$
$983$	−1139.81	−	128.426i	−1.15953	−	0.130647i	−0.670697	+	0.741732i	$0.734005\pi$
$984$	−620.671	+	1.79009i	−0.630763	+	0.00181920i
$985$			1216.41i			1.23493i
$986$	−12.0958	+	693.295i	−0.0122676	+	0.703139i
$987$	165.538	+	1245.82i	0.167718	+	1.26223i
$988$	−78.2285	+	389.223i	−0.0791787	+	0.393950i
$989$	2.77440	+	0.312600i	0.00280526	+	0.000316077i
$990$	29.4591	−	83.3140i	0.0297567	−	0.0841556i
$991$	−852.219	+	410.407i	−0.859958	+	0.414134i	−0.811264	−	0.584680i	$-0.801220\pi$
$991$	−852.219	+	410.407i	−0.859958	+	0.414134i	−0.0486940	+	0.998814i	$0.515506\pi$
$992$	855.426	+	88.5606i	0.862325	+	0.0892748i
$993$	1059.37	−	1102.39i	1.06684	−	1.11017i
$994$	909.491	−	663.299i	0.914981	−	0.667303i
$995$	−600.011	−	136.949i	−0.603026	−	0.137637i
$996$	31.5363	+	78.3746i	0.0316629	+	0.0786893i
$997$	398.602	−	634.371i	0.399801	−	0.636280i	−0.584783	−	0.811190i	$-0.698820\pi$
$997$	398.602	−	634.371i	0.399801	−	0.636280i	0.984584	+	0.174910i	$0.0559633\pi$
$998$	995.785	+	866.821i	0.997780	+	0.868559i
$999$	1179.96	−	843.629i	1.18114	−	0.844473i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	348.3.v.a.95.9	yes	1392
3.2	odd	2	inner	348.3.v.a.95.108	yes	1392
4.3	odd	2	inner	348.3.v.a.95.102	yes	1392
12.11	even	2	inner	348.3.v.a.95.15	yes	1392
29.11	odd	28	inner	348.3.v.a.11.15	yes	1392
87.11	even	28	inner	348.3.v.a.11.102	yes	1392
116.11	even	28	inner	348.3.v.a.11.108	yes	1392
348.11	odd	28	inner	348.3.v.a.11.9	✓	1392

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
348.3.v.a.11.9	✓	1392	348.11	odd	28	inner
348.3.v.a.11.15	yes	1392	29.11	odd	28	inner
348.3.v.a.11.102	yes	1392	87.11	even	28	inner
348.3.v.a.11.108	yes	1392	116.11	even	28	inner
348.3.v.a.95.9	yes	1392	1.1	even	1	trivial
348.3.v.a.95.15	yes	1392	12.11	even	2	inner
348.3.v.a.95.102	yes	1392	4.3	odd	2	inner
348.3.v.a.95.108	yes	1392	3.2	odd	2	inner

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:	\( N \)	\(=\)	\( 348 = 2^{2} \cdot 3 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	348.v (of order \(28\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.92888 - 0.528587i) q^{2} +(0.0596975 + 2.99941i) q^{3} +(3.44119 + 2.03917i) q^{4} +(7.68944 - 3.70304i) q^{5} +(1.47030 - 5.81706i) q^{6} +(-7.69057 + 6.13302i) q^{7} +(-5.55978 - 5.75229i) q^{8} +(-8.99287 + 0.358114i) q^{9} +O(q^{10})\)	\(q+(-1.92888 - 0.528587i) q^{2} +(0.0596975 + 2.99941i) q^{3} +(3.44119 + 2.03917i) q^{4} +(7.68944 - 3.70304i) q^{5} +(1.47030 - 5.81706i) q^{6} +(-7.69057 + 6.13302i) q^{7} +(-5.55978 - 5.75229i) q^{8} +(-8.99287 + 0.358114i) q^{9} +(-16.7894 + 3.07819i) q^{10} +(0.306041 - 0.487062i) q^{11} +(-5.91086 + 10.4433i) q^{12} +(-21.9986 + 5.02105i) q^{13} +(18.0761 - 7.76476i) q^{14} +(11.5660 + 22.8427i) q^{15} +(7.68359 + 14.0343i) q^{16} +(-8.45359 + 8.45359i) q^{17} +(17.5355 + 4.06276i) q^{18} +(-0.492487 - 4.37094i) q^{19} +(34.0119 + 2.93720i) q^{20} +(-18.8545 - 22.7010i) q^{21} +(-0.847773 + 0.777716i) q^{22} +(-0.0694880 - 0.0334637i) q^{23} +(16.9215 - 17.0194i) q^{24} +(29.8277 - 37.4028i) q^{25} +(45.0869 + 1.94319i) q^{26} +(-1.61098 - 26.9519i) q^{27} +(-38.9710 + 5.42254i) q^{28} +(-14.7947 + 24.9423i) q^{29} +(-10.2350 - 50.1745i) q^{30} +(-8.87623 + 25.3668i) q^{31} +(-7.40238 - 31.1321i) q^{32} +(1.47917 + 0.888866i) q^{33} +(20.7745 - 11.8375i) q^{34} +(-36.4253 + 75.6380i) q^{35} +(-31.6764 - 17.1056i) q^{36} +(28.5823 + 45.4885i) q^{37} +(-1.36047 + 8.69137i) q^{38} +(-16.3734 - 65.6831i) q^{39} +(-64.0526 - 23.6438i) q^{40} +(-18.2868 - 18.2868i) q^{41} +(24.3688 + 53.7539i) q^{42} +(-34.1685 + 11.9561i) q^{43} +(2.04635 - 1.05200i) q^{44} +(-67.8240 + 36.0547i) q^{45} +(0.116346 + 0.101278i) q^{46} +(-36.0606 - 22.6584i) q^{47} +(-41.6360 + 23.8840i) q^{48} +(10.6273 - 46.5614i) q^{49} +(-77.3049 + 56.3791i) q^{50} +(-25.8604 - 24.8511i) q^{51} +(-85.9403 - 27.5805i) q^{52} +(8.93509 + 18.5539i) q^{53} +(-11.1390 + 52.8386i) q^{54} +(0.549677 - 4.87852i) q^{55} +(78.0368 + 10.1401i) q^{56} +(13.0808 - 1.73810i) q^{57} +(41.7214 - 40.2905i) q^{58} +40.6648 q^{59} +(-6.77942 + 102.191i) q^{60} +(7.01993 - 62.3036i) q^{61} +(30.5298 - 44.2378i) q^{62} +(66.9640 - 57.9076i) q^{63} +(-2.17768 + 63.9629i) q^{64} +(-150.564 + 120.071i) q^{65} +(-2.38330 - 2.49639i) q^{66} +(-24.4888 + 107.293i) q^{67} +(-46.3287 + 11.8521i) q^{68} +(0.0962229 - 0.210421i) q^{69} +(110.242 - 126.643i) q^{70} +(55.7840 - 12.7323i) q^{71} +(52.0584 + 49.7386i) q^{72} +(-94.3500 + 33.0145i) q^{73} +(-31.0873 - 102.850i) q^{74} +(113.967 + 87.2327i) q^{75} +(7.21835 - 16.0455i) q^{76} +(0.633531 + 5.62274i) q^{77} +(-3.13683 + 135.350i) q^{78} +(-44.7532 - 71.2243i) q^{79} +(111.052 + 79.4635i) q^{80} +(80.7435 - 6.44095i) q^{81} +(25.6069 + 44.9392i) q^{82} +(4.38944 - 5.50419i) q^{83} +(-18.5909 - 116.566i) q^{84} +(-33.6994 + 96.3073i) q^{85} +(72.2270 - 5.00086i) q^{86} +(-75.6953 - 42.8862i) q^{87} +(-4.50324 + 0.947519i) q^{88} +(-16.2611 + 46.4714i) q^{89} +(149.883 - 33.6943i) q^{90} +(138.388 - 173.533i) q^{91} +(-0.170884 - 0.256853i) q^{92} +(-76.6153 - 25.1091i) q^{93} +(57.5798 + 62.7665i) q^{94} +(-19.9727 - 31.7864i) q^{95} +(92.9358 - 24.0612i) q^{96} +(-16.1070 - 142.953i) q^{97} +(-45.1107 + 84.1941i) q^{98} +(-2.57777 + 4.48968i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 1392 q - 28 q^{4} - 14 q^{6} - 28 q^{9}+O(q^{10}) \) 1392 * q - 28 * q^4 - 14 * q^6 - 28 * q^9	\( 1392 q - 28 q^{4} - 14 q^{6} - 28 q^{9} - 8 q^{10} + 36 q^{12} - 56 q^{13} - 52 q^{16} - 32 q^{18} - 76 q^{21} - 28 q^{22} - 10 q^{24} - 1040 q^{25} + 272 q^{30} - 28 q^{33} - 28 q^{34} + 58 q^{36} - 80 q^{37} - 36 q^{40} - 14 q^{42} + 180 q^{45} + 1032 q^{46} - 216 q^{48} + 1088 q^{49} + 120 q^{52} - 10 q^{54} - 308 q^{58} + 240 q^{60} + 112 q^{61} - 1792 q^{64} + 92 q^{66} + 124 q^{69} - 1096 q^{70} + 148 q^{72} - 160 q^{73} + 68 q^{76} - 154 q^{78} - 180 q^{81} - 20 q^{82} + 72 q^{84} - 72 q^{85} + 760 q^{88} + 256 q^{90} - 28 q^{93} - 632 q^{94} - 812 q^{96} + 32 q^{97}+O(q^{100}) \) 1392 * q - 28 * q^4 - 14 * q^6 - 28 * q^9 - 8 * q^10 + 36 * q^12 - 56 * q^13 - 52 * q^16 - 32 * q^18 - 76 * q^21 - 28 * q^22 - 10 * q^24 - 1040 * q^25 + 272 * q^30 - 28 * q^33 - 28 * q^34 + 58 * q^36 - 80 * q^37 - 36 * q^40 - 14 * q^42 + 180 * q^45 + 1032 * q^46 - 216 * q^48 + 1088 * q^49 + 120 * q^52 - 10 * q^54 - 308 * q^58 + 240 * q^60 + 112 * q^61 - 1792 * q^64 + 92 * q^66 + 124 * q^69 - 1096 * q^70 + 148 * q^72 - 160 * q^73 + 68 * q^76 - 154 * q^78 - 180 * q^81 - 20 * q^82 + 72 * q^84 - 72 * q^85 + 760 * q^88 + 256 * q^90 - 28 * q^93 - 632 * q^94 - 812 * q^96 + 32 * q^97

Introduction

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