LMFDB - Embedded newform 348.3.v.a.11.9

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			11.9
Character	$\chi$	$=$	348.11
Dual form			348.3.v.a.95.9

$q$-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 $\left(\mathbb{Z}/348\mathbb{Z}\right)^\times$.

$n$	$175$	$205$	$233$
$\chi(n)$	$-1$	$e\left(\frac{25}{28}\right)$	$-1$

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	0.995064	−	0.0992385i	$-0.0316407\pi$
$5$	7.68944	+	3.70304i	1.53789	+	0.740608i	0.542824	+	0.839846i	$0.317355\pi$
$6$	1.47030	+	5.81706i	0.245050	+	0.969511i
$7$	−7.69057	−	6.13302i	−1.09865	−	0.876146i	−0.105669	−	0.994401i	$-0.533699\pi$
$7$	−7.69057	−	6.13302i	−1.09865	−	0.876146i	−0.992983	+	0.118255i	$0.962270\pi$
$8$	−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	0.860346	−	0.509711i	$-0.170248\pi$
$11$	0.306041	+	0.487062i	0.0278219	+	0.0442783i	−0.832524	+	0.553989i	$0.813105\pi$
$12$	−5.91086	−	10.4433i	−0.492572	−	0.870272i
$13$	−21.9986	−	5.02105i	−1.69220	−	0.386234i	−0.735551	−	0.677469i	$-0.763077\pi$
$13$	−21.9986	−	5.02105i	−1.69220	−	0.386234i	−0.956652	+	0.291234i	$0.905934\pi$
$14$	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	0.413317	−	0.910587i	$-0.364370\pi$
$17$	−8.45359	−	8.45359i	−0.497270	−	0.497270i	−0.910587	+	0.413317i	$0.864370\pi$
$18$	17.5355	−	4.06276i	0.974195	−	0.225709i
$19$	−0.492487	+	4.37094i	−0.0259204	+	0.230050i	0.974072	+	0.226237i	$0.0726423\pi$
$19$	−0.492487	+	4.37094i	−0.0259204	+	0.230050i	−0.999993	+	0.00381295i	$0.998786\pi$
$20$	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	−0.435394	−	0.900240i	$-0.643391\pi$
$23$	−0.0694880	+	0.0334637i	−0.00302122	+	0.00145494i	0.432373	+	0.901695i	$0.357677\pi$
$24$	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	−0.993764	−	0.111505i	$-0.964433\pi$
$31$	−8.87623	−	25.3668i	−0.286330	−	0.818285i	0.707434	−	0.706780i	$-0.249853\pi$
$32$	−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	−0.196054	−	0.980593i	$-0.562813\pi$
$37$	28.5823	−	45.4885i	0.772495	−	1.22942i	0.968548	−	0.248825i	$-0.0800445\pi$
$38$	−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	−0.894029	−	0.448010i	$-0.852133\pi$
$41$	−18.2868	+	18.2868i	−0.446019	+	0.446019i	0.448010	+	0.894029i	$0.352133\pi$
$42$	24.3688	−	53.7539i	0.580208	−	1.27985i
$43$	−34.1685	−	11.9561i	−0.794617	−	0.278049i	−0.0977147	−	0.995214i	$-0.531153\pi$
$43$	−34.1685	−	11.9561i	−0.794617	−	0.278049i	−0.696903	+	0.717166i	$0.745439\pi$
$44$	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	−0.857917	−	0.513788i	$-0.828242\pi$
$47$	−36.0606	+	22.6584i	−0.767246	+	0.482093i	0.0906709	+	0.995881i	$0.471099\pi$
$48$	−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	−0.799509	−	0.600654i	$-0.794907\pi$
$53$	8.93509	−	18.5539i	0.168587	−	0.350074i	0.968096	+	0.250580i	$0.0806213\pi$
$54$	−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	0.909987	+	0.414637i	$0.136092\pi$
$61$	7.01993	+	62.3036i	0.115081	+	1.02137i	−0.794906	+	0.606733i	$0.792480\pi$
$62$	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	−0.738970	−	0.673738i	$-0.764688\pi$
$67$	−24.4888	−	107.293i	−0.365505	−	1.60138i	0.373465	−	0.927644i	$-0.378170\pi$
$68$	−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	0.596501	−	0.802612i	$-0.296557\pi$
$71$	55.7840	+	12.7323i	0.785690	+	0.179329i	0.189189	+	0.981941i	$0.439414\pi$
$72$	52.0584	−	49.7386i	0.723033	−	0.690813i
$73$	−94.3500	−	33.0145i	−1.29247	−	0.452253i	−0.405502	−	0.914094i	$-0.632903\pi$
$73$	−94.3500	−	33.0145i	−1.29247	−	0.452253i	−0.886963	+	0.461841i	$0.847189\pi$
$74$	−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	0.433504	+	0.901152i	$0.357277\pi$
$79$	−44.7532	+	71.2243i	−0.566496	+	0.901573i	−1.00000		0.000421462i	$0.999866\pi$
$80$	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	0.807570	−	0.589771i	$-0.200782\pi$
$83$	4.38944	+	5.50419i	0.0528848	+	0.0663155i	−0.754686	+	0.656087i	$0.772211\pi$
$84$	−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	0.815704	−	0.578469i	$-0.196350\pi$
$89$	−16.2611	−	46.4714i	−0.182709	−	0.522151i	−0.998413	+	0.0563181i	$0.982064\pi$
$90$	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	0.583669	+	0.811992i	$0.301617\pi$
$97$	−16.1070	+	142.953i	−0.166051	+	1.47375i	−0.749720	+	0.661755i	$0.769812\pi$
$98$	−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	0.947166	−	0.320744i	$-0.103933\pi$
$101$	150.259	+	52.5778i	1.48771	+	0.520572i	0.540543	+	0.841316i	$0.318219\pi$
$102$	36.7458	−	61.6043i	0.360252	−	0.603964i
$103$	12.9865	+	2.96408i	0.126082	+	0.0287774i	0.285096	−	0.958499i	$-0.407974\pi$
$103$	12.9865	+	2.96408i	0.126082	+	0.0287774i	−0.159014	+	0.987276i	$0.550832\pi$
$104$	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	0.985910	+	0.167277i	$0.0534973\pi$
$107$	18.2129	+	79.7961i	0.170214	+	0.745758i	−0.815696	+	0.578481i	$0.803646\pi$
$108$	49.4157	+	96.0317i	0.457553	+	0.889182i
$109$	−44.7439	−	35.6821i	−0.410495	−	0.327359i	0.396374	−	0.918089i	$-0.370268\pi$
$109$	−44.7439	−	35.6821i	−0.410495	−	0.327359i	−0.806869	+	0.590730i	$0.798840\pi$
$110$	−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	−0.886767	−	0.462216i	$-0.847054\pi$
$113$	−14.1347	−	125.449i	−0.125086	−	1.11017i	0.761681	−	0.647952i	$-0.224374\pi$
$114$	−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	0.285940	−	0.958248i	$-0.407694\pi$
$127$	161.716	−	101.613i	1.27336	−	0.800102i	0.987416	+	0.158145i	$0.0505515\pi$
$128$	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	−0.195226	−	0.980758i	$-0.562544\pi$
$131$	−125.675	−	43.9757i	−0.959353	−	0.335692i	−0.764127	+	0.645066i	$0.776830\pi$
$132$	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	−0.990646	−	0.136456i	$-0.956429\pi$
$137$	−59.9893	+	95.4725i	−0.437878	+	0.696879i	0.552768	+	0.833335i	$0.313572\pi$
$138$	−0.296828	−	0.355015i	−0.00215093	−	0.00257257i
$139$	−64.0480	−	132.997i	−0.460777	−	0.956813i	−0.993849	−	0.110743i	$-0.964677\pi$
$139$	−64.0480	−	132.997i	−0.460777	−	0.956813i	0.533072	−	0.846070i	$-0.321037\pi$
$140$	−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	0.511956	−	0.859012i	$-0.328921\pi$
$149$	−65.4765	−	82.1049i	−0.439439	−	0.551040i	−0.951395	+	0.307972i	$0.900350\pi$
$150$	−173.719	+	228.503i	−1.15813	+	1.52335i
$151$	241.195	−	116.153i	1.59732	−	0.769226i	0.597840	−	0.801616i	$-0.296026\pi$
$151$	241.195	−	116.153i	1.59732	−	0.769226i	0.999475	+	0.0323891i	$0.0103116\pi$
$152$	−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	0.687173	−	0.726494i	$-0.258851\pi$
$157$	−6.17340	−	6.17340i	−0.0393210	−	0.0393210i	−0.726494	+	0.687173i	$0.758851\pi$
$158$	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	−0.975352	−	0.220655i	$-0.929180\pi$
$163$	−122.407	−	194.810i	−0.750966	−	1.19516i	0.224386	−	0.974500i	$-0.427962\pi$
$164$	−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	0.999709	−	0.0241081i	$-0.00767460\pi$
$167$	200.177	+	159.635i	1.19866	+	0.955901i	0.198953	+	0.980009i	$0.436246\pi$
$168$	−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	−0.761274	−	0.648430i	$-0.775426\pi$
$179$	39.4401	−	81.8982i	0.220336	−	0.457532i	0.981610	+	0.190899i	$0.0611401\pi$
$180$	−306.917	+	14.2337i	−1.70509	+	0.0790760i
$181$	−38.8145	+	48.6718i	−0.214445	+	0.268905i	−0.877406	−	0.479749i	$-0.840728\pi$
$181$	−38.8145	+	48.6718i	−0.214445	+	0.268905i	0.662961	+	0.748654i	$0.269299\pi$
$182$	−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	−0.861550	−	0.507672i	$-0.830506\pi$
$191$	−67.5908	+	67.5908i	−0.353878	+	0.353878i	0.507672	+	0.861550i	$0.330506\pi$
$192$	−191.981	+	2.71330i	−0.999900	+	0.0141318i
$193$	86.9918	+	9.80163i	0.450735	+	0.0507856i	0.334414	−	0.942426i	$-0.391461\pi$
$193$	86.9918	+	9.80163i	0.450735	+	0.0507856i	0.116320	+	0.993212i	$0.462890\pi$
$194$	−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	0.683000	−	0.730418i	$-0.260675\pi$
$197$	−61.8397	−	128.411i	−0.313907	−	0.651835i	−0.996908	+	0.0785831i	$0.974960\pi$
$198$	7.34540	+	7.29750i	0.0370980	+	0.0368561i
$199$	−56.3787	+	44.9605i	−0.283310	+	0.225932i	−0.754826	−	0.655926i	$-0.772279\pi$
$199$	−56.3787	+	44.9605i	−0.283310	+	0.225932i	0.471516	+	0.881858i	$0.343707\pi$
$200$	−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	0.791840	−	0.610729i	$-0.209123\pi$
$211$	123.468	+	77.5804i	0.585159	+	0.367680i	−0.206681	+	0.978408i	$0.566266\pi$
$212$	−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	0.360895	−	0.932606i	$-0.382471\pi$
$223$	243.225	−	55.5144i	1.09069	−	0.248944i	0.729798	+	0.683663i	$0.239614\pi$
$224$	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	0.456181	−	0.889887i	$-0.349217\pi$
$227$	10.1838	+	4.90426i	0.0448626	+	0.0216047i	−0.411318	+	0.911492i	$0.634931\pi$
$228$	48.5579	−	20.6929i	0.212973	−	0.0907582i
$229$	−246.421	+	27.7650i	−1.07608	+	0.121245i	−0.632170	−	0.774829i	$-0.717836\pi$
$229$	−246.421	+	27.7650i	−1.07608	+	0.121245i	−0.443905	+	0.896074i	$0.646407\pi$
$230$	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	$-0.825646\pi$
$233$		−	242.677i		−	1.04153i	0.853699	−	0.520767i	$-0.174354\pi$
$234$	−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	−0.227344	−	0.973815i	$-0.573004\pi$
$239$	184.662	−	231.559i	0.772644	−	0.968865i	0.999988	+	0.00494942i	$0.00157545\pi$
$240$	−231.714	−	337.834i	−0.965474	−	1.40764i
$241$	23.3011	−	5.31833i	0.0966851	−	0.0220677i	−0.173905	−	0.984762i	$-0.555638\pi$
$241$	23.3011	−	5.31833i	0.0966851	−	0.0220677i	0.270590	+	0.962695i	$0.412781\pi$
$242$	−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	−0.259084	−	0.965855i	$-0.583421\pi$
$251$	−182.375	−	20.5488i	−0.726595	−	0.0818676i	−0.467511	+	0.883987i	$0.654849\pi$
$252$	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	−0.964689	−	0.263392i	$-0.915159\pi$
$257$	−237.099	+	189.080i	−0.922564	+	0.735720i	0.0421252	+	0.999112i	$0.486587\pi$
$258$	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	−0.574161	−	0.818743i	$-0.694671\pi$
$263$	−134.808	+	47.1715i	−0.512580	+	0.179359i	0.0615810	+	0.998102i	$0.480386\pi$
$264$	−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	0.975435	−	0.220290i	$-0.0707002\pi$
$269$	322.850	+	202.860i	1.20019	+	0.754127i	0.224751	+	0.974416i	$0.427843\pi$
$270$	110.011	−	447.548i	0.407447	−	1.65758i
$271$	−380.486	−	42.8705i	−1.40401	−	0.158194i	−0.622760	−	0.782413i	$-0.713989\pi$
$271$	−380.486	−	42.8705i	−1.40401	−	0.158194i	−0.781249	+	0.624219i	$0.785417\pi$
$272$	−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	0.770797	+	0.637081i	$0.219858\pi$
$277$	−55.4239	+	242.828i	−0.200086	+	0.876635i	−0.970883	+	0.239554i	$0.922999\pi$
$278$	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	−0.269474	−	0.963008i	$-0.586850\pi$
$281$	−26.5346	+	6.05635i	−0.0944292	+	0.0215528i	0.175045	+	0.984560i	$0.443993\pi$
$282$	−184.825	−	176.452i	−0.655407	−	0.625717i
$283$	237.196	−	297.434i	0.838148	−	1.05100i	−0.159811	−	0.987148i	$-0.551088\pi$
$283$	237.196	−	297.434i	0.838148	−	1.05100i	0.997959	−	0.0638570i	$-0.0203402\pi$
$284$	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	0.321251	−	0.946994i	$-0.395897\pi$
$293$	247.636	−	27.9019i	0.845174	−	0.0952282i	0.523923	+	0.851766i	$0.324468\pi$
$294$	−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	0.812317	−	0.583216i	$-0.198206\pi$
$307$	70.3339	+	70.3339i	0.229101	+	0.229101i	−0.583216	+	0.812317i	$0.698206\pi$
$308$	−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	0.741617	−	0.670823i	$-0.234059\pi$
$311$	142.750	+	89.6955i	0.459002	+	0.288410i	−0.282615	+	0.959233i	$0.591202\pi$
$312$	−286.796	−	459.368i	−0.919217	−	1.47233i
$313$	79.8998	−	38.4777i	0.255271	−	0.122932i	−0.301872	−	0.953348i	$-0.597612\pi$
$313$	79.8998	−	38.4777i	0.255271	−	0.122932i	0.557143	+	0.830416i	$0.311897\pi$
$314$	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	−0.881296	−	0.472564i	$-0.843328\pi$
$317$	−404.391	+	141.503i	−1.27568	+	0.446381i	−0.394386	+	0.918945i	$0.629043\pi$
$318$	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	−0.0930555	+	0.995661i	$0.529663\pi$
$331$	−360.365	+	360.365i	−1.08872	+	1.08872i	−0.995661	+	0.0930555i	$0.970337\pi$
$332$	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	−0.724662	−	0.689105i	$-0.758004\pi$
$337$	−140.940	+	88.5583i	−0.418219	+	0.262784i	0.306443	+	0.951889i	$0.400861\pi$
$338$	−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	$0.210597\pi$
$347$			426.386i			1.22878i	−0.789004	+	0.614389i	$0.789403\pi$
$348$	−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	−0.382162	−	0.924095i	$-0.624820\pi$
$353$	−474.052	−	228.291i	−1.34292	−	0.646717i	−0.960761	+	0.277378i	$0.910535\pi$
$354$	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	0.939894	−	0.341466i	$-0.110923\pi$
$359$	80.5738	+	128.232i	0.224440	+	0.357194i	−0.715455	+	0.698659i	$0.753780\pi$
$360$	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	−0.491541	−	0.870854i	$-0.663566\pi$
$367$	66.5956	−	591.052i	0.181459	−	1.61050i	0.673001	−	0.739642i	$-0.265005\pi$
$368$	−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	0.880316	−	0.474388i	$-0.157331\pi$
$373$	82.7810	+	103.804i	0.221933	+	0.278295i	−0.658383	+	0.752683i	$0.728759\pi$
$374$	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	0.970985	−	0.239138i	$-0.0768650\pi$
$379$	23.7777	+	67.9529i	0.0627381	+	0.179295i	−0.908247	+	0.418434i	$0.862579\pi$
$380$	−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	−0.929269	−	0.369403i	$-0.879562\pi$
$383$	−244.618	−	507.956i	−0.638691	−	1.32625i	0.290579	−	0.956851i	$-0.406152\pi$
$384$	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	−0.350949	−	0.936395i	$-0.614141\pi$
$389$	227.739	−	227.739i	0.585446	−	0.585446i	0.936395	+	0.350949i	$0.114141\pi$
$390$	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	0.983723	−	0.179690i	$-0.0575096\pi$
$397$	7.72345	+	33.8386i	0.0194545	+	0.0852358i	−0.964269	+	0.264926i	$0.914652\pi$
$398$	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	0.602172	+	0.798366i	$0.294302\pi$
$401$	−159.383	+	330.962i	−0.397464	+	0.825342i	−0.999636	+	0.0269760i	$0.991412\pi$
$402$	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	−0.859124	−	0.511767i	$-0.828991\pi$
$409$	−55.3864	−	491.568i	−0.135419	−	1.20188i	0.723705	−	0.690109i	$-0.242438\pi$
$410$	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	0.794539	−	0.607212i	$-0.207712\pi$
$419$	522.466	+	119.249i	1.24694	+	0.284605i	0.452396	+	0.891817i	$0.350569\pi$
$420$	−574.602	+	827.485i	−1.36810	+	1.97020i
$421$	−169.373	−	59.2661i	−0.402311	−	0.140775i	0.121536	−	0.992587i	$-0.461218\pi$
$421$	−169.373	−	59.2661i	−0.402311	−	0.140775i	−0.523847	+	0.851812i	$0.675504\pi$
$422$	−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	−0.999902	−	0.0140064i	$-0.995541\pi$
$431$	−340.946	−	427.533i	−0.791058	−	0.991955i	0.208844	−	0.977949i	$-0.433030\pi$
$432$	365.874	+	229.696i	0.846930	+	0.531704i
$433$	−108.814	−	310.971i	−0.251301	−	0.718178i	−0.998560	−	0.0536449i	$-0.982916\pi$
$433$	−108.814	−	310.971i	−0.251301	−	0.718178i	0.747259	−	0.664533i	$-0.231370\pi$
$434$	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	0.710453	−	0.703745i	$-0.248490\pi$
$439$	−58.7109	−	73.6211i	−0.133738	−	0.167702i	−0.844191	+	0.536043i	$0.819919\pi$
$440$	−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	−0.934225	−	0.356685i	$-0.883907\pi$
$443$	−91.9306	+	146.307i	−0.207518	+	0.330263i	0.726707	+	0.686948i	$0.241050\pi$
$444$	−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	0.276666	−	0.960966i	$-0.410770\pi$
$449$	−47.6750	−	16.6822i	−0.106180	−	0.0371541i	−0.382846	+	0.923812i	$0.625056\pi$
$450$	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	0.439162	−	0.898408i	$-0.355275\pi$
$457$	−154.922	−	123.546i	−0.338998	−	0.270342i	−0.778160	+	0.628066i	$0.783847\pi$
$458$	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	−0.999968	−	0.00805139i	$-0.997437\pi$
$461$	−12.3838	−	109.909i	−0.0268629	−	0.238415i	0.973105	−	0.230363i	$-0.0739914\pi$
$462$	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	−0.623078	−	0.782159i	$-0.714118\pi$
$467$	−88.5753	−	786.127i	−0.189669	−	1.68336i	0.433410	−	0.901197i	$-0.357310\pi$
$468$	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	0.687159	−	0.726507i	$-0.258858\pi$
$479$	369.516	+	129.299i	0.771432	+	0.269936i	0.0842728	+	0.996443i	$0.473143\pi$
$480$	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	−0.928225	−	0.372018i	$-0.878666\pi$
$487$	−311.846	−	647.556i	−0.640342	−	1.32968i	0.287884	−	0.957665i	$-0.407048\pi$
$488$	−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	0.999307	+	0.0372267i	$0.0118524\pi$
$491$	118.443	+	338.490i	0.241228	+	0.689389i	−0.758079	+	0.652163i	$0.773862\pi$
$492$	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	−0.921344	−	0.388749i	$-0.872907\pi$
$499$	−594.736	+	286.410i	−1.19186	+	0.573968i	−0.270512	+	0.962717i	$0.587193\pi$
$500$	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	−0.678980	−	0.734157i	$-0.737578\pi$
$503$	73.6099	−	653.306i	0.146342	−	1.29882i	0.825322	−	0.564663i	$-0.190994\pi$
$504$	−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	−0.0292543	−	0.999572i	$-0.509313\pi$
$509$	−249.059	−	56.8460i	−0.489309	−	0.111682i	−0.460055	+	0.887890i	$0.652170\pi$
$510$	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	$0.00105479\pi$
$523$			3.46615i			0.00662743i	−0.999995	+	0.00331372i	$0.998945\pi$
$524$	−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	0.189393	−	0.981901i	$-0.439348\pi$
$541$	84.1497	+	9.48140i	0.155545	+	0.0175257i	−0.0338487	+	0.999427i	$0.510776\pi$
$542$	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	−0.593377	−	0.804925i	$-0.702206\pi$
$547$	32.4522	−	25.8797i	0.0593275	−	0.0473121i	0.652705	+	0.757612i	$0.273634\pi$
$548$	−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	−0.246532	−	0.969135i	$-0.579291\pi$
$557$	199.104	−	95.8834i	0.357458	−	0.172143i	0.603990	+	0.796992i	$0.293577\pi$
$558$	−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	0.807483	−	0.589890i	$-0.200829\pi$
$563$	122.505	+	122.505i	0.217593	+	0.217593i	−0.589890	+	0.807483i	$0.700829\pi$
$564$	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	0.945133	−	0.326687i	$-0.105932\pi$
$569$	136.970	+	217.986i	0.240720	+	0.383104i	−0.704413	+	0.709791i	$0.748789\pi$
$570$	−214.269	−	69.4471i	−0.375911	−	0.121837i
$571$	98.6107	−	22.5072i	0.172698	−	0.0394172i	−0.135297	−	0.990805i	$-0.543199\pi$
$571$	98.6107	−	22.5072i	0.172698	−	0.0394172i	0.307996	+	0.951388i	$0.400342\pi$
$572$	−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	0.370018	−	0.929024i	$-0.379351\pi$
$577$	540.930	−	60.9482i	0.937487	−	0.105629i	0.567469	+	0.823395i	$0.307923\pi$
$578$	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	0.0405011	+	0.999179i	$0.487105\pi$
$587$	−553.329	+	693.853i	−0.942639	+	1.18203i	−0.983140	+	0.182853i	$0.941467\pi$
$588$	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	−0.997267	−	0.0738782i	$-0.976462\pi$
$593$	−39.5566	+	173.309i	−0.0667060	+	0.292258i	0.930561	+	0.366136i	$0.119320\pi$
$594$	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	−0.732581	−	0.680680i	$-0.761684\pi$
$599$	−957.357	−	107.868i	−1.59826	−	0.180081i	−0.865679	+	0.500600i	$0.833113\pi$
$600$	−131.843	+	1140.56i	−0.219739	+	1.90094i
$601$	37.6075	+	23.6304i	0.0625749	+	0.0393184i	0.562956	−	0.826487i	$-0.309664\pi$
$601$	37.6075	+	23.6304i	0.0625749	+	0.0393184i	−0.500381	+	0.865805i	$0.666807\pi$
$602$	−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	0.0631865	−	0.998002i	$-0.479874\pi$
$607$	446.043	−	156.077i	0.734832	−	0.257129i	0.671645	+	0.740873i	$0.265588\pi$
$608$	−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	−0.751548	−	0.659679i	$-0.770692\pi$
$613$	−168.970	+	134.749i	−0.275644	+	0.219819i	0.475904	+	0.879497i	$0.342121\pi$
$614$	−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	0.850954	−	0.525240i	$-0.176024\pi$
$617$	460.865	+	289.581i	0.746945	+	0.469336i	−0.104010	+	0.994576i	$0.533167\pi$
$618$	1.85177	+	79.9012i	0.00299638	+	0.129290i
$619$	−572.788	−	64.5377i	−0.925344	−	0.104261i	−0.363584	−	0.931561i	$-0.618447\pi$
$619$	−572.788	−	64.5377i	−0.925344	−	0.104261i	−0.561760	+	0.827300i	$0.689876\pi$
$620$	−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	−0.864938	−	0.501879i	$-0.832642\pi$
$631$	−115.584	+	144.937i	−0.183175	+	0.229694i	0.681763	+	0.731573i	$0.261214\pi$
$632$	−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	0.267880	−	0.963452i	$-0.413677\pi$
$641$	476.540	−	53.6931i	0.743432	−	0.0837646i	0.475552	+	0.879688i	$0.342248\pi$
$642$	−437.400	+	223.270i	−0.681309	+	0.347772i
$643$	−1109.04	−	534.084i	−1.72479	−	0.830613i	−0.987994	−	0.154494i	$-0.950625\pi$
$643$	−1109.04	−	534.084i	−1.72479	−	0.830613i	−0.736792	−	0.676119i	$-0.763660\pi$
$644$	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	−0.342621	−	0.939474i	$-0.611315\pi$
$647$	−157.666	+	35.9863i	−0.243689	+	0.0556203i	0.0989320	+	0.995094i	$0.468457\pi$
$648$	−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	0.751525	+	0.659704i	$0.229319\pi$
$653$	−161.526	+	461.615i	−0.247360	+	0.706914i	−0.998885	+	0.0472094i	$0.984967\pi$
$654$	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	−0.999386	−	0.0350367i	$-0.988845\pi$
$659$	−965.152	−	606.445i	−1.46457	−	0.920251i	−0.465184	−	0.885214i	$-0.654012\pi$
$660$	47.6985	−	34.5767i	0.0722705	−	0.0523889i
$661$	209.966	−	101.114i	0.317648	−	0.152971i	−0.268265	−	0.963345i	$-0.586450\pi$
$661$	209.966	−	101.114i	0.317648	−	0.152971i	0.585913	+	0.810374i	$0.300736\pi$
$662$	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	0.674857	−	0.737948i	$-0.264205\pi$
$673$	−217.285	−	451.197i	−0.322860	−	0.670427i	−0.997718	+	0.0675216i	$0.978491\pi$
$674$	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	0.358419	−	0.933561i	$-0.383316\pi$
$677$	338.577	+	38.1485i	0.500114	+	0.0563493i	0.141695	+	0.989910i	$0.454745\pi$
$678$	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	−0.968800	−	0.247844i	$-0.920278\pi$
$683$	7.91892	−	34.6951i	0.0115943	−	0.0507981i	0.980394	+	0.197046i	$0.0631350\pi$
$684$	−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	0.0986390	+	0.995123i	$0.468551\pi$
$691$	−511.948	+	1063.07i	−0.740880	+	1.53845i	−0.839519	+	0.543330i	$0.817163\pi$
$692$	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	−0.0490820	−	0.998795i	$-0.515630\pi$
$701$	−603.262	−	290.516i	−0.860573	−	0.414430i	−0.811491	+	0.584364i	$0.801344\pi$
$702$	−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	−0.0719341	−	0.997409i	$-0.522917\pi$
$709$	−403.778	−	92.1598i	−0.569504	−	0.129986i	−0.497570	+	0.867424i	$0.665774\pi$
$710$	−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	−0.890409	−	0.455160i	$-0.849582\pi$
$719$	−783.503	+	377.315i	−1.08971	+	0.524778i	−0.199302	+	0.979938i	$0.563868\pi$
$720$	−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	0.986788	−	0.162014i	$-0.0517991\pi$
$727$	83.0756	+	237.417i	0.114272	+	0.326570i	−0.872517	+	0.488585i	$0.837513\pi$
$728$	−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	−0.934960	−	0.354754i	$-0.884565\pi$
$733$	−153.691	+	244.598i	−0.209674	+	0.333694i	0.725286	+	0.688448i	$0.241708\pi$
$734$	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	−0.0750979	−	0.997176i	$-0.523927\pi$
$739$	−558.345	−	195.373i	−0.755541	−	0.264375i	−0.680443	+	0.732801i	$0.738213\pi$
$740$	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	−0.819213	−	0.573490i	$-0.805589\pi$
$743$	−488.864	+	307.174i	−0.657960	+	0.413423i	0.161253	+	0.986913i	$0.448446\pi$
$744$	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	−0.949767	−	0.312959i	$-0.898680\pi$
$751$	−70.1828	−	622.890i	−0.0934525	−	0.829414i	0.856314	−	0.516455i	$-0.172749\pi$
$752$	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	0.917270	+	0.398265i	$0.130388\pi$
$757$	84.4965	+	749.927i	0.111620	+	0.990656i	−0.805650	+	0.592391i	$0.798184\pi$
$758$	−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	0.620971	−	0.783833i	$-0.286738\pi$
$761$	−3.82796	−	3.05270i	−0.00503017	−	0.00401143i	−0.626002	+	0.779822i	$0.715310\pi$
$762$	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	−0.302229	−	0.953235i	$-0.597731\pi$
$769$	−871.164	−	304.834i	−1.13285	−	0.396403i	−0.830625	+	0.556833i	$0.812016\pi$
$770$	−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	0.820019	+	0.572336i	$0.193963\pi$
$773$	−82.5542	+	732.689i	−0.106797	+	0.947852i	−0.926816	+	0.375515i	$0.877466\pi$
$774$	−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	1.00000		4.94981e-5i	$1.57557e-5\pi$
$787$	611.914	+	767.316i	0.777527	+	0.974988i	−0.222473	+	0.974939i	$0.571413\pi$
$788$	−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	0.738980	−	0.673728i	$-0.235308\pi$
$797$	714.650	+	250.067i	0.896675	+	0.313760i	0.157695	+	0.987488i	$0.449594\pi$
$798$	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	−0.661050	−	0.750342i	$-0.729889\pi$
$809$	−148.484	−	1317.84i	−0.183541	−	1.62897i	0.477509	−	0.878627i	$-0.341540\pi$
$810$	−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	0.992141	−	0.125125i	$-0.0399333\pi$
$821$	36.0936	+	158.136i	0.0439630	+	0.192614i	−0.948178	+	0.317740i	$0.897076\pi$
$822$	−643.571	−	208.589i	−0.782934	−	0.253757i
$823$	−427.280	+	268.478i	−0.519173	+	0.326218i	−0.765999	−	0.642842i	$-0.777755\pi$
$823$	−427.280	+	268.478i	−0.519173	+	0.326218i	0.246826	+	0.969060i	$0.420612\pi$
$824$	−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	0.286998	−	0.957931i	$-0.407343\pi$
$827$	−71.0209	−	24.8513i	−0.0858778	−	0.0300499i	−0.372876	+	0.927881i	$0.621628\pi$
$828$	1.62872	−	2.24865i	0.00196705	−	0.00271576i
$829$	491.492	−	491.492i	0.592873	−	0.592873i	−0.345533	−	0.938406i	$-0.612302\pi$
$829$	491.492	−	491.492i	0.592873	−	0.592873i	0.938406	+	0.345533i	$0.112302\pi$
$830$	−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	0.970843	+	0.239715i	$0.0770541\pi$
$839$	303.103	+	866.220i	0.361267	+	1.03244i	−0.609576	+	0.792728i	$0.708660\pi$
$840$	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	0.584724	−	0.811233i	$-0.301203\pi$
$853$	−193.212	−	193.212i	−0.226509	−	0.226509i	−0.811233	+	0.584724i	$0.801203\pi$
$854$	−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	0.714438	−	0.699698i	$-0.246682\pi$
$857$	903.739	+	206.272i	1.05454	+	0.240691i	0.340099	+	0.940390i	$0.389539\pi$
$858$	64.9638	−	42.9505i	0.0757154	−	0.0500588i
$859$	−92.9570	−	147.940i	−0.108215	−	0.172224i	0.788226	−	0.615385i	$-0.211000\pi$
$859$	−92.9570	−	147.940i	−0.108215	−	0.172224i	−0.896442	+	0.443162i	$0.853857\pi$
$860$	−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	0.933577	−	0.358377i	$-0.116670\pi$
$863$	683.432	+	545.019i	0.791926	+	0.631540i	−0.141651	+	0.989917i	$0.545241\pi$
$864$	−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	−0.961825	−	0.273665i	$-0.911764\pi$
$877$	−421.833	+	528.962i	−0.480995	+	0.603149i	0.480830	+	0.876814i	$0.340335\pi$
$878$	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	−0.241365	−	0.970434i	$-0.577595\pi$
$881$	465.381	−	292.418i	0.528242	−	0.331917i	0.769607	+	0.638518i	$0.220452\pi$
$882$	375.524	+	773.302i	0.425764	+	0.876759i
$883$	69.6525	−	305.168i	0.0788817	−	0.345603i	−0.920051	−	0.391799i	$-0.871853\pi$
$883$	69.6525	−	305.168i	0.0788817	−	0.345603i	0.998932	+	0.0461961i	$0.0147099\pi$
$884$	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	−0.947448	−	0.319909i	$-0.896348\pi$
$887$	−556.628	+	556.628i	−0.627540	+	0.627540i	0.319909	+	0.947448i	$0.396348\pi$
$888$	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	0.424775	−	0.905299i	$-0.360353\pi$
$907$	−187.357	−	117.724i	−0.206567	−	0.129795i	−0.631343	+	0.775504i	$0.717496\pi$
$908$	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	0.998789	−	0.0492007i	$-0.0156674\pi$
$911$	865.075	+	865.075i	0.949588	+	0.949588i	−0.0492007	+	0.998789i	$0.515667\pi$
$912$	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	0.613060	−	0.790037i	$-0.289939\pi$
$919$	1386.03	−	316.352i	1.50819	−	0.344235i	0.895132	+	0.445802i	$0.147081\pi$
$920$	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	$-0.834113\pi$
$929$		−	925.055i		−	0.995754i	0.867248	−	0.497877i	$-0.165887\pi$
$930$	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	−0.110874	−	0.993834i	$-0.535365\pi$
$937$	206.553	−	47.1444i	0.220441	−	0.0503142i	0.331315	+	0.943520i	$0.392508\pi$
$938$	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	−0.578874	−	0.815417i	$-0.696508\pi$
$941$	278.978	−	1222.28i	0.296470	−	1.29892i	0.875343	−	0.483502i	$-0.160635\pi$
$942$	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	0.530795	−	0.847500i	$-0.321893\pi$
$947$	814.131	+	91.7306i	0.859695	+	0.0968644i	0.328900	+	0.944365i	$0.393322\pi$
$948$	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	−0.943935	−	0.330131i	$-0.892907\pi$
$953$	−793.016	+	632.409i	−0.832126	+	0.663598i	0.111809	+	0.993730i	$0.464336\pi$
$954$	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	−0.186581	−	0.982440i	$-0.559741\pi$
$967$	−567.723	−	63.9670i	−0.587097	−	0.0661499i	−0.400516	+	0.916290i	$0.631169\pi$
$968$	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	−0.993460	−	0.114178i	$-0.963577\pi$
$971$	−141.332	+	403.904i	−0.145553	+	0.415967i	0.847907	+	0.530145i	$0.177862\pi$
$972$	−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	0.258954	−	0.965890i	$-0.416622\pi$
$977$	890.386	−	203.225i	0.911347	−	0.208009i	0.652393	+	0.757881i	$0.273765\pi$
$978$	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	−0.670697	−	0.741732i	$-0.734005\pi$
$983$	−1139.81	+	128.426i	−1.15953	+	0.130647i	−0.488830	+	0.872379i	$0.662576\pi$
$984$	−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	−0.0486940	−	0.998814i	$-0.515506\pi$
$991$	−852.219	−	410.407i	−0.859958	−	0.414134i	−0.811264	+	0.584680i	$0.801220\pi$
$992$	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	0.984584	−	0.174910i	$-0.0559633\pi$
$997$	398.602	+	634.371i	0.399801	+	0.636280i	−0.584783	+	0.811190i	$0.698820\pi$
$998$	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.11.9	✓	1392
3.2	odd	2	inner	348.3.v.a.11.108	yes	1392
4.3	odd	2	inner	348.3.v.a.11.102	yes	1392
12.11	even	2	inner	348.3.v.a.11.15	yes	1392
29.8	odd	28	inner	348.3.v.a.95.15	yes	1392
87.8	even	28	inner	348.3.v.a.95.102	yes	1392
116.95	even	28	inner	348.3.v.a.95.108	yes	1392
348.95	odd	28	inner	348.3.v.a.95.9	yes	1392

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
348.3.v.a.11.9	✓	1392	1.1	even	1	trivial
348.3.v.a.11.15	yes	1392	12.11	even	2	inner
348.3.v.a.11.102	yes	1392	4.3	odd	2	inner
348.3.v.a.11.108	yes	1392	3.2	odd	2	inner
348.3.v.a.95.9	yes	1392	348.95	odd	28	inner
348.3.v.a.95.15	yes	1392	29.8	odd	28	inner
348.3.v.a.95.102	yes	1392	87.8	even	28	inner
348.3.v.a.95.108	yes	1392	116.95	even	28	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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