LMFDB - Embedded newform 348.3.v.a.11.15

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			11.15
Character	$\chi$	$=$	348.11
Dual form			348.3.v.a.95.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.83763 + 0.789374i) q^{2} +(-0.725631 - 2.91092i) q^{3} +(2.75378 - 2.90116i) q^{4} +(-7.68944 - 3.70304i) q^{5} +(3.63125 + 4.77641i) q^{6} +(7.69057 + 6.13302i) q^{7} +(-2.77034 + 7.50501i) q^{8} +(-7.94692 + 4.22451i) q^{9} +O(q^{10})$	\(q+(-1.83763 + 0.789374i) q^{2} +(-0.725631 - 2.91092i) q^{3} +(2.75378 - 2.90116i) q^{4} +(-7.68944 - 3.70304i) q^{5} +(3.63125 + 4.77641i) q^{6} +(7.69057 + 6.13302i) q^{7} +(-2.77034 + 7.50501i) q^{8} +(-7.94692 + 4.22451i) q^{9} +(17.0534 + 0.734981i) q^{10} +(0.306041 + 0.487062i) q^{11} +(-10.4433 - 5.91086i) q^{12} +(-21.9986 - 5.02105i) q^{13} +(-18.9737 - 5.19951i) q^{14} +(-5.19955 + 25.0704i) q^{15} +(-0.833404 - 15.9783i) q^{16} +(8.45359 + 8.45359i) q^{17} +(11.2688 - 14.0362i) q^{18} +(0.492487 - 4.37094i) q^{19} +(-31.9181 + 12.1109i) q^{20} +(12.2722 - 26.8370i) q^{21} +(-0.946865 - 0.653459i) q^{22} +(-0.0694880 + 0.0334637i) q^{23} +(23.8567 + 2.61835i) q^{24} +(29.8277 + 37.4028i) q^{25} +(44.3889 - 8.13831i) q^{26} +(18.0637 + 20.0674i) 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} +(14.1443 + 28.7043i) q^{32} +(1.19573 - 1.24429i) q^{33} +(-22.2076 - 8.86154i) q^{34} +(-36.4253 - 75.6380i) q^{35} +(-9.62809 + 34.6886i) q^{36} +(28.5823 - 45.4885i) q^{37} +(2.54530 + 8.42094i) q^{38} +(1.34704 + 67.6797i) q^{39} +(49.0937 - 47.4507i) q^{40} +(18.2868 - 18.2868i) q^{41} +(-1.36745 + 59.0038i) q^{42} +(34.1685 + 11.9561i) q^{43} +(2.25581 + 0.453387i) q^{44} +(76.7509 - 3.05637i) q^{45} +(0.101278 - 0.116346i) q^{46} +(-36.0606 + 22.6584i) q^{47} +(-45.9068 + 14.0203i) q^{48} +(10.6273 + 46.5614i) q^{49} +(-84.3372 - 45.1873i) q^{50} +(18.4735 - 30.7419i) q^{51} +(-75.1462 + 49.9946i) q^{52} +(-8.93509 + 18.5539i) q^{53} +(-49.0352 - 22.6175i) q^{54} +(-0.549677 - 4.87852i) q^{55} +(-67.3339 + 40.7273i) q^{56} +(-13.0808 + 1.73810i) q^{57} +(-46.8759 - 34.1562i) q^{58} +40.6648 q^{59} +(58.4147 + 84.1230i) q^{60} +(7.01993 + 62.3036i) q^{61} +(-36.3351 - 39.6082i) q^{62} +(-87.0254 - 16.2497i) q^{63} +(-48.6505 - 41.5828i) q^{64} +(150.564 + 120.071i) q^{65} +(-1.21509 + 3.23042i) q^{66} +(24.4888 + 107.293i) q^{67} +(47.8045 - 1.24586i) q^{68} +(0.147833 + 0.177992i) q^{69} +(126.643 + 110.242i) q^{70} +(55.7840 + 12.7323i) q^{71} +(-9.68939 - 71.3450i) q^{72} +(-94.3500 - 33.0145i) q^{73} +(-16.6163 + 106.153i) q^{74} +(87.2327 - 113.967i) q^{75} +(-11.3246 - 13.4654i) q^{76} +(-0.633531 + 5.62274i) q^{77} +(-55.8999 - 123.307i) q^{78} +(44.7532 - 71.2243i) q^{79} +(-52.7598 + 125.950i) q^{80} +(45.3070 - 67.1437i) q^{81} +(-19.1693 + 48.0394i) q^{82} +(4.38944 + 5.50419i) q^{83} +(-44.0632 - 109.507i) q^{84} +(-33.6994 - 96.3073i) q^{85} +(-72.2270 + 5.00086i) q^{86} +(61.8696 - 61.1650i) q^{87} +(-4.50324 + 0.947519i) q^{88} +(16.2611 + 46.4714i) q^{89} +(-138.627 + 66.2016i) q^{90} +(-138.388 - 173.533i) q^{91} +(-0.0942714 + 0.293747i) q^{92} +(67.3999 - 44.2450i) q^{93} +(48.3801 - 70.1030i) q^{94} +(-19.9727 + 31.7864i) q^{95} +(73.2924 - 62.0018i) q^{96} +(-16.1070 + 142.953i) q^{97} +(-56.2835 - 77.1738i) q^{98} +(-4.48968 - 2.57777i) 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 $

$2$	−1.83763	+	0.789374i	−0.918816	+	0.394687i
$2$	−1.83763	+	0.789374i	−0.918816	+	0.394687i
$3$	−0.725631	−	2.91092i	−0.241877	−	0.970307i
$3$	−0.725631	−	2.91092i	−0.241877	−	0.970307i
$4$	2.75378	−	2.90116i	0.688445	−	0.725289i
$5$	−7.68944	−	3.70304i	−1.53789	−	0.740608i	−0.542824	−	0.839846i	$-0.682645\pi$
$5$	−7.68944	−	3.70304i	−1.53789	−	0.740608i	−0.995064	+	0.0992385i	$0.968359\pi$
$6$	3.63125	+	4.77641i	0.605208	+	0.796068i
$7$	7.69057	+	6.13302i	1.09865	+	0.876146i	0.992983	−	0.118255i	$-0.0377300\pi$
$7$	7.69057	+	6.13302i	1.09865	+	0.876146i	0.105669	+	0.994401i	$0.466301\pi$
$8$	−2.77034	+	7.50501i	−0.346292	+	0.938127i
$9$	−7.94692	+	4.22451i	−0.882991	+	0.469390i
$10$	17.0534	+	0.734981i	1.70534	+	0.0734981i
$11$	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	$0.813105\pi$
$12$	−10.4433	−	5.91086i	−0.870272	−	0.492572i
$13$	−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	$0.905934\pi$
$14$	−18.9737	−	5.19951i	−1.35526	−	0.371393i
$15$	−5.19955	+	25.0704i	−0.346637	+	1.67136i
$16$	−0.833404	−	15.9783i	−0.0520877	−	0.998643i
$17$	8.45359	+	8.45359i	0.497270	+	0.497270i	0.910587	−	0.413317i	$-0.135630\pi$
$17$	8.45359	+	8.45359i	0.497270	+	0.497270i	−0.413317	+	0.910587i	$0.635630\pi$
$18$	11.2688	−	14.0362i	0.626044	−	0.779788i
$19$	0.492487	−	4.37094i	0.0259204	−	0.230050i	−0.974072	−	0.226237i	$-0.927358\pi$
$19$	0.492487	−	4.37094i	0.0259204	−	0.230050i	0.999993	−	0.00381295i	$-0.00121370\pi$
$20$	−31.9181	+	12.1109i	−1.59591	+	0.605545i
$21$	12.2722	−	26.8370i	0.584392	−	1.27795i
$22$	−0.946865	−	0.653459i	−0.0430393	−	0.0297027i
$23$	−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	$0.357677\pi$
$24$	23.8567	+	2.61835i	0.994031	+	0.109098i
$25$	29.8277	+	37.4028i	1.19311	+	1.49611i
$26$	44.3889	−	8.13831i	1.70726	−	0.313012i
$27$	18.0637	+	20.0674i	0.669028	+	0.743237i
$28$	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	$0.0355671\pi$
$31$	8.87623	+	25.3668i	0.286330	+	0.818285i	−0.707434	+	0.706780i	$0.750147\pi$
$32$	14.1443	+	28.7043i	0.442010	+	0.897010i
$33$	1.19573	−	1.24429i	0.0362341	−	0.0377057i
$34$	−22.2076	−	8.86154i	−0.653165	−	0.260634i
$35$	−36.4253	−	75.6380i	−1.04072	−	2.16109i
$36$	−9.62809	+	34.6886i	−0.267447	+	0.963573i
$37$	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	$-0.0800445\pi$
$38$	2.54530	+	8.42094i	0.0669815	+	0.221604i
$39$	1.34704	+	67.6797i	0.0345394	+	1.73538i
$40$	49.0937	−	47.4507i	1.22734	−	1.18627i
$41$	18.2868	−	18.2868i	0.446019	−	0.446019i	−0.448010	−	0.894029i	$-0.647867\pi$
$41$	18.2868	−	18.2868i	0.446019	−	0.446019i	0.894029	+	0.448010i	$0.147867\pi$
$42$	−1.36745	+	59.0038i	−0.0325584	+	1.40485i
$43$	34.1685	+	11.9561i	0.794617	+	0.278049i	0.696903	−	0.717166i	$-0.254561\pi$
$43$	34.1685	+	11.9561i	0.794617	+	0.278049i	0.0977147	+	0.995214i	$0.468847\pi$
$44$	2.25581	+	0.453387i	0.0512685	+	0.0103043i
$45$	76.7509	−	3.05637i	1.70558	−	0.0679194i
$46$	0.101278	−	0.116346i	0.00220170	−	0.00252926i
$47$	−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	$0.471099\pi$
$48$	−45.9068	+	14.0203i	−0.956391	+	0.292090i
$49$	10.6273	+	46.5614i	0.216885	+	0.950233i
$50$	−84.3372	−	45.1873i	−1.68674	−	0.903747i
$51$	18.4735	−	30.7419i	0.362226	−	0.602783i
$52$	−75.1462	+	49.9946i	−1.44512	+	0.961435i
$53$	−8.93509	+	18.5539i	−0.168587	+	0.350074i	−0.968096	−	0.250580i	$-0.919379\pi$
$53$	−8.93509	+	18.5539i	−0.168587	+	0.350074i	0.799509	+	0.600654i	$0.205093\pi$
$54$	−49.0352	−	22.6175i	−0.908059	−	0.418842i
$55$	−0.549677	−	4.87852i	−0.00999412	−	0.0887003i
$56$	−67.3339	+	40.7273i	−1.20239	+	0.727273i
$57$	−13.0808	+	1.73810i	−0.229488	+	0.0304930i
$58$	−46.8759	−	34.1562i	−0.808206	−	0.588900i
$59$	40.6648			0.689234			0.344617	−	0.938743i	$-0.388009\pi$
$59$	40.6648			0.689234			0.344617	+	0.938743i	$0.388009\pi$
$60$	58.4147	+	84.1230i	0.973578	+	1.40205i
$61$	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	$0.792480\pi$
$62$	−36.3351	−	39.6082i	−0.586051	−	0.638842i
$63$	−87.0254	−	16.2497i	−1.38135	−	0.257932i
$64$	−48.6505	−	41.5828i	−0.760164	−	0.649732i
$65$	150.564	+	120.071i	2.31637	+	1.84724i
$66$	−1.21509	+	3.23042i	−0.0184105	+	0.0489457i
$67$	24.4888	+	107.293i	0.365505	+	1.60138i	0.738970	+	0.673738i	$0.235312\pi$
$67$	24.4888	+	107.293i	0.365505	+	1.60138i	−0.373465	+	0.927644i	$0.621830\pi$
$68$	47.8045	−	1.24586i	0.703007	−	0.0183215i
$69$	0.147833	+	0.177992i	0.00214250	+	0.00257959i
$70$	126.643	+	110.242i	1.80919	+	1.57488i
$71$	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	$0.439414\pi$
$72$	−9.68939	−	71.3450i	−0.134575	−	0.990903i
$73$	−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	$0.847189\pi$
$74$	−16.6163	+	106.153i	−0.224545	+	1.43450i
$75$	87.2327	−	113.967i	1.16310	−	1.51956i
$76$	−11.3246	−	13.4654i	−0.149008	−	0.177176i
$77$	−0.633531	+	5.62274i	−0.00822767	+	0.0730226i
$78$	−55.8999	−	123.307i	−0.716666	−	1.58086i
$79$	44.7532	−	71.2243i	0.566496	−	0.901573i	−0.433504	−	0.901152i	$-0.642723\pi$
$79$	44.7532	−	71.2243i	0.566496	−	0.901573i	1.00000		0.000421462i	$-0.000134155\pi$
$80$	−52.7598	+	125.950i	−0.659497	+	1.57438i
$81$	45.3070	−	67.1437i	0.559346	−	0.828934i
$82$	−19.1693	+	48.0394i	−0.233771	+	0.585847i
$83$	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	$0.772211\pi$
$84$	−44.0632	−	109.507i	−0.524561	−	1.30365i
$85$	−33.6994	−	96.3073i	−0.396463	−	1.13303i
$86$	−72.2270	+	5.00086i	−0.839849	+	0.0581495i
$87$	61.8696	−	61.1650i	0.711144	−	0.703046i
$88$	−4.50324	+	0.947519i	−0.0511732	+	0.0107673i
$89$	16.2611	+	46.4714i	0.182709	+	0.522151i	0.998413	−	0.0563181i	$-0.0179361\pi$
$89$	16.2611	+	46.4714i	0.182709	+	0.522151i	−0.815704	+	0.578469i	$0.803650\pi$
$90$	−138.627	+	66.2016i	−1.54030	+	0.735573i
$91$	−138.388	−	173.533i	−1.52075	−	1.90695i
$92$	−0.0942714	+	0.293747i	−0.00102469	+	0.00319290i
$93$	67.3999	−	44.2450i	0.724730	−	0.475752i
$94$	48.3801	−	70.1030i	0.514682	−	0.745776i
$95$	−19.9727	+	31.7864i	−0.210239	+	0.334594i
$96$	73.2924	−	62.0018i	0.763463	−	0.645852i
$97$	−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	$0.769812\pi$
$98$	−56.2835	−	77.1738i	−0.574321	−	0.787488i
$99$	−4.48968	−	2.57777i	−0.0453503	−	0.0260380i
$100$	190.650	+	16.4641i	1.90650	+	0.164641i
$101$	−150.259	−	52.5778i	−1.48771	−	0.520572i	−0.540543	−	0.841316i	$-0.681781\pi$
$101$	−150.259	−	52.5778i	−1.48771	−	0.520572i	−0.947166	+	0.320744i	$0.896067\pi$
$102$	−9.68070	+	71.0748i	−0.0949088	+	0.696812i
$103$	−12.9865	−	2.96408i	−0.126082	−	0.0287774i	0.159014	−	0.987276i	$-0.449168\pi$
$103$	−12.9865	−	2.96408i	−0.126082	−	0.0287774i	−0.285096	+	0.958499i	$0.592026\pi$
$104$	98.6266	−	151.190i	0.948333	−	1.45375i
$105$	−193.745	+	160.917i	−1.84519	+	1.53254i
$106$	1.77344	−	41.1484i	0.0167306	−	0.388192i
$107$	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	$0.803646\pi$
$108$	107.962	+	2.85547i	0.999650	+	0.0264395i
$109$	−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	$0.798840\pi$
$110$	4.86107	+	8.53101i	0.0441916	+	0.0775547i
$111$	−153.154	−	50.1930i	−1.37976	−	0.452189i
$112$	91.5858	−	127.993i	0.817731	−	1.14280i
$113$	14.1347	+	125.449i	0.125086	+	1.11017i	0.886767	+	0.462216i	$0.152946\pi$
$113$	14.1347	+	125.449i	0.125086	+	1.11017i	−0.761681	+	0.647952i	$0.775626\pi$
$114$	22.6657	−	13.5197i	0.198822	−	0.118593i
$115$	0.658241			0.00572384
$116$	113.103	+	25.7639i	0.975023	+	0.222103i
$117$	196.033	−	53.0317i	1.67549	−	0.453262i
$118$	−74.7269	+	32.0997i	−0.633279	+	0.272032i
$119$	13.1668	+	116.859i	0.110646	+	0.982008i
$120$	−173.749	−	108.476i	−1.44791	−	0.903968i
$121$	52.3564	−	108.719i	0.432697	−	0.898505i
$122$	−62.0808	−	108.950i	−0.508859	−	0.893030i
$123$	−66.5008	−	39.9619i	−0.540657	−	0.324893i
$124$	98.0363	+	44.1033i	0.790615	+	0.355672i
$125$	−43.3762	−	190.044i	−0.347010	−	1.52035i
$126$	172.748	−	38.8345i	1.37101	−	0.308210i
$127$	−161.716	+	101.613i	−1.27336	+	0.800102i	−0.987416	−	0.158145i	$-0.949449\pi$
$127$	−161.716	+	101.613i	−1.27336	+	0.800102i	−0.285940	+	0.958248i	$0.592306\pi$
$128$	122.226	+	38.0105i	0.954891	+	0.296957i
$129$	10.0095	−	108.138i	0.0775927	−	0.838276i
$130$	−371.462	−	101.795i	−2.85740	−	0.783036i
$131$	−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	$0.776830\pi$
$132$	−0.317113	−	6.89548i	−0.00240237	−	0.0522385i
$133$	30.5946	−	30.5946i	0.230035	−	0.230035i
$134$	−129.695	−	177.833i	−0.967876	−	1.32712i
$135$	−64.5897	−	221.198i	−0.478442	−	1.63850i
$136$	−86.8636	+	40.0250i	−0.638703	+	0.294302i
$137$	59.9893	−	95.4725i	0.437878	−	0.696879i	−0.552768	−	0.833335i	$-0.686428\pi$
$137$	59.9893	−	95.4725i	0.437878	−	0.696879i	0.990646	+	0.136456i	$0.0435712\pi$
$138$	−0.412164	−	0.210388i	−0.00298670	−	0.00152455i
$139$	64.0480	+	132.997i	0.460777	+	0.956813i	0.993849	+	0.110743i	$0.0353231\pi$
$139$	64.0480	+	132.997i	0.460777	+	0.956813i	−0.533072	+	0.846070i	$0.678963\pi$
$140$	−319.745	−	102.615i	−2.28389	−	0.732963i
$141$	92.1234	+	88.5278i	0.653357	+	0.627857i
$142$	−112.561	+	20.6371i	−0.792683	+	0.145331i
$143$	−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
$147$	127.825	−	64.7218i	0.869558	−	0.440284i
$148$	−53.2598	−	208.187i	−0.359864	−	1.40667i
$149$	65.4765	+	82.1049i	0.439439	+	0.551040i	0.951395	−	0.307972i	$-0.0996503\pi$
$149$	65.4765	+	82.1049i	0.439439	+	0.551040i	−0.511956	+	0.859012i	$0.671079\pi$
$150$	−70.3391	+	278.288i	−0.468927	+	1.85525i
$151$	−241.195	+	116.153i	−1.59732	+	0.769226i	−0.999475	−	0.0323891i	$-0.989688\pi$
$151$	−241.195	+	116.153i	−1.59732	+	0.769226i	−0.597840	+	0.801616i	$0.703974\pi$
$152$	31.4396	+	15.8051i	0.206840	+	0.103981i
$153$	−102.892	−	31.4677i	−0.672498	−	0.205671i
$154$	−3.27425	−	10.8326i	−0.0212613	−	0.0703417i
$155$	25.6811	−	227.926i	0.165684	−	1.47049i
$156$	200.059	+	182.467i	1.28243	+	1.16966i
$157$	−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	$0.758851\pi$
$158$	−26.0173	+	166.211i	−0.164666	+	1.05197i
$159$	60.4925	+	12.5460i	0.380456	+	0.0789059i
$160$	−2.46867	−	273.097i	−0.0154292	−	1.70686i
$161$	−0.739636	−	0.168817i	−0.00459401	−	0.00104855i
$162$	−30.2561	+	159.150i	−0.186766	+	0.982404i
$163$	122.407	+	194.810i	0.750966	+	1.19516i	0.975352	+	0.220655i	$0.0708196\pi$
$163$	122.407	+	194.810i	0.750966	+	1.19516i	−0.224386	+	0.974500i	$0.572038\pi$
$164$	−2.69504	−	103.411i	−0.0164332	−	0.630552i
$165$	−13.8021	+	5.14007i	−0.0836491	+	0.0311519i
$166$	−12.4110	−	6.64976i	−0.0747653	−	0.0400588i
$167$	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	$0.436246\pi$
$168$	167.414	+	166.451i	0.996509	+	0.990777i
$169$	306.466	+	147.586i	1.81341	+	0.873290i
$170$	137.949	+	150.376i	0.811468	+	0.884564i
$171$	14.5513	+	36.8160i	0.0850956	+	0.215298i
$172$	128.779	−	66.2038i	0.748716	−	0.384906i
$173$	−222.375			−1.28540			−0.642702	−	0.766116i	$-0.722187\pi$
$173$	−222.375			−1.28540			−0.642702	+	0.766116i	$0.722187\pi$
$174$	−65.4114	+	161.237i	−0.375928	+	0.926649i
$175$			470.583i			2.68905i
$176$	7.52735	−	5.29593i	0.0427691	−	0.0300905i
$177$	−29.5077	−	118.372i	−0.166710	−	0.668769i
$178$	−66.5651	−	72.5613i	−0.373962	−	0.407648i
$179$	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	$0.0611401\pi$
$180$	202.488	−	231.083i	1.12493	−	1.28379i
$181$	−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	$0.269299\pi$
$182$	391.288	+	209.650i	2.14994	+	1.15192i
$183$	176.267	−	65.6439i	0.963207	−	0.358710i
$184$	−0.0586402	−	0.614214i	−0.000318697	−	0.00333812i
$185$	−388.228	+	243.940i	−2.09853	+	1.31859i
$186$	−88.9304	+	134.510i	−0.478121	+	0.723170i
$187$	−1.53027	+	6.70457i	−0.00818328	+	0.0358533i
$188$	−33.5674	+	167.013i	−0.178550	+	0.888369i
$189$	15.8466	+	265.115i	0.0838445	+	1.40273i
$190$	11.6112	−	74.1776i	0.0611113	−	0.390409i
$191$	−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	$0.330506\pi$
$192$	−85.7420	+	171.791i	−0.446573	+	0.894747i
$193$	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	$0.462890\pi$
$194$	−83.2450	−	275.410i	−0.429098	−	1.41964i
$195$	240.263	−	525.407i	1.23212	−	2.69440i
$196$	164.347	+	97.3883i	0.838506	+	0.496879i
$197$	61.8397	+	128.411i	0.313907	+	0.651835i	0.996908	−	0.0785831i	$-0.0250396\pi$
$197$	61.8397	+	128.411i	0.313907	+	0.651835i	−0.683000	+	0.730418i	$0.739325\pi$
$198$	10.2852	+	1.19295i	0.0519455	+	0.00602499i
$199$	56.3787	−	44.9605i	0.283310	−	0.225932i	−0.471516	−	0.881858i	$-0.656293\pi$
$199$	56.3787	−	44.9605i	0.283310	−	0.225932i	0.754826	+	0.655926i	$0.227721\pi$
$200$	−363.341	+	120.239i	−1.81671	+	0.601197i
$201$	294.550	−	149.140i	1.46542	−	0.741990i
$202$	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
$206$	26.2041	−	4.80429i	0.127204	−	0.0233218i
$207$	0.410848	−	0.559486i	0.00198477	−	0.00270283i
$208$	−61.8939	+	355.685i	−0.297567	+	1.71002i
$209$	2.27964	−	1.09782i	0.0109074	−	0.00525271i
$210$	229.008	−	448.642i	1.09052	−	2.13639i
$211$	−123.468	−	77.5804i	−0.585159	−	0.367680i	0.206681	−	0.978408i	$-0.433734\pi$
$211$	−123.468	−	77.5804i	−0.585159	−	0.367680i	−0.791840	+	0.610729i	$0.790877\pi$
$212$	29.2225	+	77.0154i	0.137842	+	0.363280i
$213$	−3.41581	−	171.622i	−0.0160367	−	0.805736i
$214$	−96.4576	−	132.259i	−0.450736	−	0.618033i
$215$	−218.463	−	218.463i	−1.01611	−	1.01611i
$216$	−200.649	+	79.9752i	−0.928930	+	0.370256i
$217$	−87.3120	+	249.523i	−0.402360	+	1.14988i
$218$	110.389	+	30.2509i	0.506373	+	0.138765i
$219$	−27.6392	+	298.602i	−0.126207	+	1.36348i
$220$	−15.6670	−	11.8397i	−0.0712137	−	0.0538166i
$221$	−143.522	−	228.413i	−0.649419	−	1.03354i
$222$	321.061	−	28.6592i	1.44622	−	0.129096i
$223$	−243.225	+	55.5144i	−1.09069	+	0.248944i	−0.729798	−	0.683663i	$-0.760386\pi$
$223$	−243.225	+	55.5144i	−1.09069	+	0.248944i	−0.360895	+	0.932606i	$0.617529\pi$
$224$	−67.2664	+	307.500i	−0.300297	+	1.37277i
$225$	−395.047	−	171.229i	−1.75577	−	0.761020i
$226$	−125.001	−	219.372i	−0.553100	−	0.970670i
$227$	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	$0.634931\pi$
$228$	−30.9792	+	42.7359i	−0.135874	+	0.187438i
$229$	−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	$0.646407\pi$
$230$	−1.20960	+	0.519598i	−0.00525915	+	0.00225912i
$231$	16.8271	−	2.23588i	0.0728444	−	0.00967913i
$232$	−228.178	+	41.9356i	−0.983528	+	0.180757i
$233$			242.677i			1.04153i	0.853699	+	0.520767i	$0.174354\pi$
$233$			242.677i			1.04153i	−0.853699	+	0.520767i	$0.825646\pi$
$234$	−318.374	+	252.196i	−1.36057	+	1.07776i
$235$	361.190	−	40.6964i	1.53698	−	0.173176i
$236$	111.982	−	117.975i	0.474500	−	0.499894i
$237$	−239.803	−	78.5904i	−1.01183	−	0.331605i
$238$	−116.441	−	204.350i	−0.489249	−	0.858614i
$239$	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	$0.00157545\pi$
$240$	404.915	+	62.1862i	1.68715	+	0.259109i
$241$	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	$0.412781\pi$
$242$	−10.3917	+	241.114i	−0.0429410	+	0.996340i
$243$	−228.326	−	83.1636i	−0.939614	−	0.342237i
$244$	200.084	+	151.204i	0.820015	+	0.619690i
$245$	90.7005	−	397.385i	0.370206	−	1.62198i
$246$	153.749	+	20.9413i	0.624995	+	0.0851270i
$247$	−32.7807	+	93.6820i	−0.132716	+	0.379279i
$248$	−214.968	−	3.65834i	−0.866808	−	0.0147514i
$249$	12.8371	−	16.7713i	0.0515547	−	0.0673547i
$250$	229.725	+	314.990i	0.918899	+	1.25996i
$251$	−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	$0.654849\pi$
$252$	−286.792	+	207.726i	−1.13806	+	0.824309i
$253$	−0.0375651	−	0.0236037i	−0.000148479	−	9.32953e-5i
$254$	216.964	−	314.382i	0.854189	−	1.23772i
$255$	−255.890	+	167.980i	−1.00349	+	0.658745i
$256$	−254.611	+	26.6327i	−0.994574	+	0.104034i
$257$	237.099	−	189.080i	0.922564	−	0.735720i	−0.0421252	−	0.999112i	$-0.513413\pi$
$257$	237.099	−	189.080i	0.922564	−	0.735720i	0.964689	+	0.263392i	$0.0848414\pi$
$258$	66.9673	+	206.618i	0.259563	+	0.800846i
$259$	498.796	−	174.536i	1.92585	−	0.673885i
$260$	762.964	−	106.161i	2.93448	−	0.408312i
$261$	−222.941	−	135.714i	−0.854180	−	0.519978i
$262$	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	$0.480386\pi$
$264$	6.02585	+	12.4210i	0.0228252	+	0.0470494i
$265$	137.412	−	109.582i	0.518535	−	0.413518i
$266$	−32.0710	+	80.3722i	−0.120568	+	0.302151i
$267$	123.475	−	81.0558i	0.462454	−	0.303580i
$268$	378.709	+	224.414i	1.41309	+	0.837366i
$269$	−322.850	−	202.860i	−1.20019	−	0.754127i	−0.224751	−	0.974416i	$-0.572157\pi$
$269$	−322.850	−	202.860i	−1.20019	−	0.754127i	−0.975435	+	0.220290i	$0.929300\pi$
$270$	293.300	+	355.495i	1.08630	+	1.31665i
$271$	380.486	+	42.8705i	1.40401	+	0.158194i	0.781249	−	0.624219i	$-0.214583\pi$
$271$	380.486	+	42.8705i	1.40401	+	0.158194i	0.622760	+	0.782413i	$0.286011\pi$
$272$	128.029	−	142.119i	0.470693	−	0.522496i
$273$	−404.722	+	528.757i	−1.48250	+	1.93684i
$274$	−34.8748	+	222.797i	−0.127280	+	0.813128i
$275$	−9.08896	+	25.9748i	−0.0330508	+	0.0944537i
$276$	0.923481	+	0.0612643i	0.00334595	+	0.000221972i
$277$	−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	$0.922999\pi$
$278$	−222.681	−	193.842i	−0.801010	−	0.697272i
$279$	−177.701	−	164.090i	−0.636922	−	0.588137i
$280$	668.575	−	63.8301i	2.38777	−	0.227965i
$281$	26.5346	−	6.05635i	0.0944292	−	0.0215528i	−0.175045	−	0.984560i	$-0.556007\pi$
$281$	26.5346	−	6.05635i	0.0944292	−	0.0215528i	0.269474	+	0.963008i	$0.413150\pi$
$282$	−239.170	−	89.9618i	−0.848122	−	0.319013i
$283$	−237.196	+	297.434i	−0.838148	+	1.05100i	0.159811	+	0.987148i	$0.448912\pi$
$283$	−237.196	+	297.434i	−0.838148	+	1.05100i	−0.997959	+	0.0638570i	$0.979660\pi$
$284$	190.555	−	126.776i	0.670969	−	0.446394i
$285$	107.021	+	35.0738i	0.375511	+	0.123066i
$286$	17.5487	+	19.1295i	0.0613591	+	0.0668863i
$287$	252.789	−	28.4825i	0.880798	−	0.0992421i
$288$	−233.665	−	168.358i	−0.811338	−	0.584577i
$289$		−	146.074i		−	0.505445i
$290$	233.968	+	436.226i	0.806785	+	1.50423i
$291$	427.814	−	56.8454i	1.47015	−	0.195345i
$292$	−355.599	+	182.809i	−1.21780	+	0.626059i
$293$	−247.636	+	27.9019i	−0.845174	+	0.0952282i	−0.523923	−	0.851766i	$-0.675532\pi$
$293$	−247.636	+	27.9019i	−0.845174	+	0.0952282i	−0.321251	+	0.946994i	$0.604103\pi$
$294$	−183.806	+	219.837i	−0.625190	+	0.747743i
$295$	−312.690	−	150.583i	−1.05996	−	0.510452i
$296$	262.209	+	340.529i	0.885842	+	1.15044i
$297$	−4.24582	+	14.9396i	−0.0142957	+	0.0503017i
$298$	−185.133	−	99.1932i	−0.621252	−	0.332863i
$299$	1.69666	−	0.387253i	0.00567446	−	0.00129516i
$300$	−90.4161	−	566.915i	−0.301387	−	1.88972i
$301$	189.449	+	301.506i	0.629397	+	1.00168i
$302$	351.539	−	403.839i	1.16403	−	1.33722i
$303$	−44.0173	+	475.543i	−0.145272	+	1.56945i
$304$	−70.2506	−	4.22633i	−0.231087	−	0.0139024i
$305$	176.733	−	505.075i	0.579453	−	1.65598i
$306$	213.918	−	23.3944i	0.699078	−	0.0764522i
$307$	−70.3339	−	70.3339i	−0.229101	−	0.229101i	0.583216	−	0.812317i	$-0.301794\pi$
$307$	−70.3339	−	70.3339i	−0.229101	−	0.229101i	−0.812317	+	0.583216i	$0.801794\pi$
$308$	14.5678	+	17.3218i	0.0472982	+	0.0562395i
$309$	0.795197	+	39.9534i	0.00257345	+	0.129299i
$310$	132.726	+	439.115i	0.428149	+	1.41650i
$311$	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	$0.591202\pi$
$312$	−511.669	−	177.386i	−1.63997	−	0.568545i
$313$	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	$0.311897\pi$
$314$	16.2176	+	6.47132i	0.0516483	+	0.0206093i
$315$	609.003	+	447.210i	1.93334	+	1.41971i
$316$	−83.3923	−	325.972i	−0.263900	−	1.03156i
$317$	404.391	−	141.503i	1.27568	−	0.446381i	0.394386	−	0.918945i	$-0.370957\pi$
$317$	404.391	−	141.503i	1.27568	−	0.446381i	0.881296	+	0.472564i	$0.156672\pi$
$318$	−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
$321$	219.064	−	110.919i	0.682443	−	0.345542i
$322$	1.49244	−	0.273625i	0.00463490	−	0.000849769i
$323$	41.1134	−	32.7869i	0.127286	−	0.101507i
$324$	−70.0288	−	316.342i	−0.216138	−	0.976363i
$325$	−468.369	−	972.577i	−1.44113	−	2.99255i
$326$	−378.718	−	261.365i	−1.16171	−	0.801732i
$327$	−71.4001	+	156.138i	−0.218349	+	0.477486i
$328$	86.5820	+	187.903i	0.263970	+	0.572875i
$329$	−416.291	−	46.9047i	−1.26532	−	0.142567i
$330$	21.3058	−	20.3406i	0.0645629	−	0.0616381i
$331$	360.365	−	360.365i	1.08872	−	1.08872i	0.0930555	−	0.995661i	$-0.470337\pi$
$331$	360.365	−	360.365i	1.08872	−	1.08872i	0.995661	−	0.0930555i	$-0.0296634\pi$
$332$	28.0560	+	2.42286i	0.0845062	+	0.00729777i
$333$	−34.9747	+	482.240i	−0.105029	+	1.44817i
$334$	−493.863	−	135.337i	−1.47863	−	0.405201i
$335$	209.003	−	915.703i	0.623890	−	2.73344i
$336$	−439.036	−	173.723i	−1.30665	−	0.517033i
$337$	−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	$0.400861\pi$
$338$	−679.671	−	29.2929i	−2.01086	−	0.0866655i
$339$	354.916	−	132.175i	1.04695	−	0.389896i
$340$	−372.203	−	167.442i	−1.09472	−	0.492476i
$341$	−9.63872	+	12.0866i	−0.0282660	+	0.0354445i
$342$	−55.8016	−	56.1679i	−0.163163	−	0.164234i
$343$	5.29721	−	10.9998i	0.0154438	−	0.0320693i
$344$	−184.389	+	223.313i	−0.536014	+	0.649166i
$345$	−0.477641	−	1.91609i	−0.00138447	−	0.00555388i
$346$	408.643	−	175.537i	1.18105	−	0.507332i
$347$			426.386i			1.22878i	0.789004	+	0.614389i	$0.210597\pi$
$347$			426.386i			1.22878i	−0.789004	+	0.614389i	$0.789403\pi$
$348$	−7.07409	−	347.928i	−0.0203278	−	0.999793i
$349$	481.329			1.37916			0.689582	−	0.724207i	$-0.257794\pi$
$349$	481.329			1.37916			0.689582	+	0.724207i	$0.257794\pi$
$350$	−371.466	−	864.758i	−1.06133	−	2.47074i
$351$	−296.619	−	532.155i	−0.845067	−	1.51611i
$352$	−9.65204	+	15.6739i	−0.0274206	+	0.0445280i
$353$	474.052	+	228.291i	1.34292	+	0.646717i	0.960761	−	0.277378i	$-0.0894654\pi$
$353$	474.052	+	228.291i	1.34292	+	0.646717i	0.382162	+	0.924095i	$0.375180\pi$
$354$	147.664	+	194.232i	0.417130	+	0.548677i
$355$	−381.799	−	304.475i	−1.07549	−	0.857675i
$356$	179.600	+	80.7962i	0.504495	+	0.226956i
$357$	330.613	−	123.124i	0.926086	−	0.344886i
$358$	−7.82808	+	181.632i	−0.0218662	+	0.507351i
$359$	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	$0.753780\pi$
$360$	−189.688	+	584.484i	−0.526910	+	1.62357i
$361$	333.086	+	76.0248i	0.922677	+	0.210595i
$362$	32.9065	−	120.080i	0.0909018	−	0.331713i
$363$	−354.464	−	73.5152i	−0.976485	−	0.202521i
$364$	−884.535	−	76.3865i	−2.43004	−	0.209853i
$365$	603.244	+	603.244i	1.65272	+	1.65272i
$366$	−272.096	+	259.770i	−0.743432	+	0.709753i
$367$	−66.5956	+	591.052i	−0.181459	+	1.61050i	0.491541	+	0.870854i	$0.336434\pi$
$367$	−66.5956	+	591.052i	−0.181459	+	1.61050i	−0.673001	+	0.739642i	$0.734995\pi$
$368$	0.592604	+	1.08241i	0.00161034	+	0.00294133i
$369$	−68.0708	+	222.576i	−0.184474	+	0.603187i
$370$	520.860	−	754.728i	1.40773	−	2.03980i
$371$	−182.507	+	87.8910i	−0.491934	+	0.236903i
$372$	57.2429	−	317.379i	0.153879	−	0.853168i
$373$	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	$0.728759\pi$
$374$	−2.48033	−	13.5285i	−0.00663189	−	0.0361724i
$375$	−521.727	+	264.166i	−1.39127	+	0.704443i
$376$	−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	$-0.137421\pi$
$379$	−23.7777	−	67.9529i	−0.0627381	−	0.179295i	−0.970985	+	0.239138i	$0.923135\pi$
$380$	37.2168	+	145.477i	0.0979390	+	0.382833i
$381$	413.134	+	397.009i	1.08434	+	1.04202i
$382$	70.8526	−	177.561i	0.185478	−	0.464820i
$383$	−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	$-0.406152\pi$
$384$	21.9545	−	383.372i	0.0571731	−	0.998364i
$385$	25.6927	−	40.8897i	0.0667344	−	0.106207i
$386$	−167.596	+	50.6573i	−0.434187	+	0.131236i
$387$	−322.043	+	49.3313i	−0.832153	+	0.127471i
$388$	370.375	+	440.391i	0.954575	+	1.13503i
$389$	−227.739	+	227.739i	−0.585446	+	0.585446i	−0.936395	−	0.350949i	$-0.885859\pi$
$389$	−227.739	+	227.739i	−0.585446	+	0.585446i	0.350949	+	0.936395i	$0.385859\pi$
$390$	−26.7717	+	1155.16i	−0.0686453	+	2.96195i
$391$	−0.870311	−	0.304535i	−0.00222586	−	0.000778862i
$392$	−378.885	−	49.2324i	−0.966545	−	0.125593i
$393$	−36.8158	+	397.741i	−0.0936788	+	1.01206i
$394$	−215.003	−	187.158i	−0.545693	−	0.475021i
$395$	−607.873	+	381.952i	−1.53892	+	0.966967i
$396$	−19.8421	+	5.92667i	−0.0501063	+	0.0149663i
$397$	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	$0.914652\pi$
$398$	−68.1126	+	127.125i	−0.171137	+	0.319409i
$399$	−111.259	−	66.8581i	−0.278844	−	0.167564i
$400$	572.774	−	507.768i	1.43193	−	1.26942i
$401$	159.383	−	330.962i	0.397464	−	0.825342i	−0.602172	−	0.798366i	$-0.705698\pi$
$401$	159.383	−	330.962i	0.397464	−	0.825342i	0.999636	−	0.0269760i	$-0.00858778\pi$
$402$	−423.548	+	506.575i	−1.05360	+	1.26014i
$403$	−67.8971	−	602.604i	−0.168479	−	1.49529i
$404$	−566.315	+	291.136i	−1.40177	+	0.720634i
$405$	−597.021	+	348.524i	−1.47413	+	0.860552i
$406$	−151.022	−	550.172i	−0.371974	−	1.35510i
$407$	30.9031			0.0759289
$408$	179.541	+	223.810i	0.440050	+	0.548553i
$409$	−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	$-0.242438\pi$
$410$	325.293	−	298.412i	0.793397	−	0.727834i
$411$	−321.443	−	105.346i	−0.782099	−	0.256317i
$412$	−44.3611	+	29.5133i	−0.107673	+	0.0716343i
$413$	312.736	+	249.398i	0.757229	+	0.603870i
$414$	−0.313344	+	1.35244i	−0.000756869	+	0.00326677i
$415$	−13.3701	−	58.5784i	−0.0322172	−	0.141153i
$416$	−167.030	−	702.475i	−0.401515	−	1.68864i
$417$	340.668	−	282.945i	0.816951	−	0.678526i
$418$	−3.32255	+	3.81687i	−0.00794869	+	0.00913127i
$419$	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	$0.350569\pi$
$420$	−66.6865	+	1005.21i	−0.158777	+	2.39336i
$421$	−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	$0.675504\pi$
$422$	288.129	+	45.1014i	0.682771	+	0.106875i
$423$	190.850	−	332.402i	0.451182	−	0.785821i
$424$	−114.494	−	118.459i	−0.270033	−	0.279383i
$425$	−64.0365	+	568.339i	−0.150674	+	1.33727i
$426$	141.751	+	312.681i	0.332748	+	0.733993i
$427$	−328.122	+	522.203i	−0.768436	+	1.22296i
$428$	281.655	+	166.902i	0.658073	+	0.389959i
$429$	−32.5520	+	21.3689i	−0.0758787	+	0.0498109i
$430$	573.904	+	229.006i	1.33466	+	0.532571i
$431$	−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	$-0.433030\pi$
$432$	305.588	−	305.352i	0.707380	−	0.706833i
$433$	−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
$435$	−702.239	+	241.219i	−1.61434	+	0.554527i
$436$	−226.734	+	31.5485i	−0.520032	+	0.0723589i
$437$	0.112046	+	0.320209i	0.000256398	+	0.000732743i
$438$	−184.917	−	570.537i	−0.422186	−	1.30260i
$439$	58.7109	+	73.6211i	0.133738	+	0.167702i	0.844191	−	0.536043i	$-0.180081\pi$
$439$	58.7109	+	73.6211i	0.133738	+	0.167702i	−0.710453	+	0.703745i	$0.751510\pi$
$440$	38.1361	+	9.38979i	0.0866730	+	0.0213404i
$441$	−281.154	−	325.125i	−0.637537	−	0.737244i
$442$	444.043	+	306.447i	1.00462	+	0.693320i
$443$	−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	$0.241050\pi$
$444$	−567.369	+	306.102i	−1.27786	+	0.689419i
$445$	47.0471	−	417.555i	0.105724	−	0.938325i
$446$	403.136	−	294.010i	0.903891	−	0.659216i
$447$	191.489	−	250.175i	0.428387	−	0.559675i
$448$	−119.121	−	618.170i	−0.265896	−	1.37984i
$449$	47.6750	+	16.6822i	0.106180	+	0.0371541i	0.382846	−	0.923812i	$-0.374944\pi$
$449$	47.6750	+	16.6822i	0.106180	+	0.0371541i	−0.276666	+	0.960966i	$0.589230\pi$
$450$	861.115	+	2.81676i	1.91359	+	0.00625947i
$451$	14.5033	+	3.31028i	0.0321581	+	0.00733987i
$452$	402.871	+	304.452i	0.891307	+	0.673566i
$453$	513.131	+	617.814i	1.13274	+	1.36383i
$454$	−22.5854	−	0.973400i	−0.0497475	−	0.00214405i
$455$	421.526	+	1846.83i	0.926431	+	4.05896i
$456$	23.1938	−	102.987i	0.0508636	−	0.225849i
$457$	−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	$0.783847\pi$
$458$	430.914	−	245.540i	0.940861	−	0.536114i
$459$	−16.9381	+	322.345i	−0.0369022	+	0.702277i
$460$	1.81265	−	1.90966i	0.00394055	−	0.00415144i
$461$	12.3838	+	109.909i	0.0268629	+	0.238415i	0.999968	+	0.00805139i	$0.00256287\pi$
$461$	12.3838	+	109.909i	0.0268629	+	0.238415i	−0.973105	+	0.230363i	$0.926009\pi$
$462$	−29.1570	+	17.3916i	−0.0631104	+	0.0376441i
$463$	−231.869			−0.500797			−0.250398	−	0.968143i	$-0.580562\pi$
$463$	−231.869			−0.500797			−0.250398	+	0.968143i	$0.580562\pi$
$464$	386.205	−	257.180i	0.832338	−	0.554268i
$465$	−682.109	+	90.6345i	−1.46690	+	0.194913i
$466$	−191.563	−	445.951i	−0.411079	−	0.956977i
$467$	−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	$-0.357310\pi$
$468$	385.978	−	714.759i	0.824740	−	1.52726i
$469$	−469.695	+	975.332i	−1.00148	+	2.07960i
$470$	−631.610	+	359.899i	−1.34385	+	0.765743i
$471$	−13.4907	+	22.4499i	−0.0286426	+	0.0476643i
$472$	−112.655	+	305.190i	−0.238676	+	0.646589i
$473$	4.63363	+	20.3012i	0.00979625	+	0.0429202i
$474$	502.706	−	44.8736i	1.06056	−	0.0946701i
$475$	178.175	−	111.955i	0.375106	−	0.235695i
$476$	375.285	+	283.605i	0.788413	+	0.595808i
$477$	−7.37475	−	185.193i	−0.0154607	−	0.388245i
$478$	−156.554	+	571.287i	−0.327519	+	1.19516i
$479$	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	$0.473143\pi$
$480$	−793.173	+	205.354i	−1.65244	+	0.427821i
$481$	−857.172	+	857.172i	−1.78206	+	1.78206i
$482$	−38.6207	+	28.1664i	−0.0801259	+	0.0584365i
$483$	0.0452900	+	2.27552i	9.37680e−5	+	0.00471122i
$484$	−171.233	−	451.282i	−0.353788	−	0.932402i
$485$	653.216	−	1039.59i	1.34684	−	2.14348i
$486$	485.226	−	27.4106i	0.998408	−	0.0564005i
$487$	311.846	+	647.556i	0.640342	+	1.32968i	0.928225	+	0.372018i	$0.121334\pi$
$487$	311.846	+	647.556i	0.640342	+	1.32968i	−0.287884	+	0.957665i	$0.592952\pi$
$488$	−487.037	−	119.917i	−0.998026	−	0.245732i
$489$	478.255	−	497.679i	0.978026	−	1.01775i
$490$	147.011	+	801.843i	0.300022	+	1.63641i
$491$	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
$495$	24.9776	+	36.4470i	0.0504598	+	0.0736304i
$496$	397.921	−	162.968i	0.802259	−	0.328564i
$497$	350.923	+	440.043i	0.706082	+	0.885399i
$498$	−10.3511	+	40.9528i	−0.0207853	+	0.0822346i
$499$	594.736	−	286.410i	1.19186	−	0.573968i	0.270512	−	0.962717i	$-0.412807\pi$
$499$	594.736	−	286.410i	1.19186	−	0.573968i	0.921344	+	0.388749i	$0.127093\pi$
$500$	−670.794	−	397.497i	−1.34159	−	0.794994i
$501$	319.432	−	698.535i	0.637588	−	1.39428i
$502$	351.359	−	106.201i	0.699919	−	0.211556i
$503$	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	$-0.190994\pi$
$504$	363.044	−	608.109i	0.720325	−	1.20657i
$505$	960.707	+	960.707i	1.90239	+	1.90239i
$506$	0.0876629	+	0.0137220i	0.000173247	+	2.71186e-5i
$507$	207.230	−	999.190i	0.408738	−	1.97079i
$508$	−150.535	+	748.983i	−0.296330	+	1.47438i
$509$	249.059	+	56.8460i	0.489309	+	0.111682i	0.460055	−	0.887890i	$-0.347830\pi$
$509$	249.059	+	56.8460i	0.489309	+	0.111682i	0.0292543	+	0.999572i	$0.490687\pi$
$510$	337.632	−	510.678i	0.662023	−	1.00133i
$511$	−523.126	−	832.551i	−1.02373	−	1.62926i
$512$	446.858	−	249.924i	0.872769	−	0.488133i
$513$	96.6097	−	69.0727i	0.188323	−	0.134645i
$514$	−286.446	+	534.619i	−0.557287	+	1.04011i
$515$	88.8826	+	70.8815i	0.172588	+	0.137634i
$516$	−286.160	−	326.826i	−0.554574	−	0.633384i
$517$	−22.0720	−	10.6293i	−0.0426925	−	0.0205596i
$518$	−778.829	+	714.470i	−1.50353	+	1.37929i
$519$	161.362	+	647.316i	0.310910	+	1.24724i
$520$	−1318.25	+	797.349i	−2.53509	+	1.53336i
$521$	396.229			0.760517			0.380258	−	0.924880i	$-0.375835\pi$
$521$	396.229			0.760517			0.380258	+	0.924880i	$0.375835\pi$
$522$	516.812	+	73.4089i	0.990062	+	0.140630i
$523$		−	3.46615i		−	0.00662743i	−0.999995	−	0.00331372i	$-0.998945\pi$
$523$		−	3.46615i		−	0.00662743i	0.999995	−	0.00331372i	$-0.00105479\pi$
$524$	−473.662	+	243.504i	−0.903935	+	0.464703i
$525$	1369.83	−	341.470i	2.60920	−	0.650419i
$526$	210.492	−	193.098i	0.400175	−	0.367107i
$527$	−139.405	+	289.477i	−0.264525	+	0.549292i
$528$	−20.8781	−	18.0686i	−0.0395419	−	0.0342209i
$529$	−329.822	+	413.584i	−0.623483	+	0.781823i
$530$	−166.011	+	309.841i	−0.313228	+	0.584605i
$531$	−323.160	+	171.789i	−0.608587	+	0.323520i
$532$	−4.50892	−	173.010i	−0.00847542	−	0.325208i
$533$	−494.103	+	310.465i	−0.927022	+	0.582487i
$534$	−162.918	+	246.419i	−0.305091	+	0.461458i
$535$	155.441	−	681.030i	0.290543	−	1.27295i
$536$	−873.075	−	113.447i	−1.62887	−	0.211656i
$537$	−267.018	−	55.3790i	−0.497240	−	0.103127i
$538$	753.412	+	117.933i	1.40039	+	0.219206i
$539$	−19.4259	+	19.4259i	−0.0360406	+	0.0360406i
$540$	−819.595	−	421.745i	−1.51777	−	0.781010i
$541$	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	$0.510776\pi$
$542$	−733.035	+	221.566i	−1.35246	+	0.408793i
$543$	169.845	+	77.6681i	0.312790	+	0.143035i
$544$	−123.084	+	362.225i	−0.226258	+	0.665854i
$545$	211.924	+	440.064i	0.388851	+	0.807456i
$546$	326.343	−	1291.14i	0.597698	−	2.36472i
$547$	−32.4522	+	25.8797i	−0.0593275	+	0.0473121i	−0.652705	−	0.757612i	$-0.726366\pi$
$547$	−32.4522	+	25.8797i	−0.0593275	+	0.0473121i	0.593377	+	0.804925i	$0.297794\pi$
$548$	−111.783	−	436.948i	−0.203984	−	0.797351i
$549$	−318.989	−	465.466i	−0.581036	−	0.847843i
$550$	−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
$554$	−89.8332	−	489.978i	−0.162154	−	0.884437i
$555$	991.799	+	953.090i	1.78702	+	1.71728i
$556$	562.219	+	180.431i	1.01118	+	0.324516i
$557$	−199.104	+	95.8834i	−0.357458	+	0.172143i	−0.603990	−	0.796992i	$-0.706423\pi$
$557$	−199.104	+	95.8834i	−0.357458	+	0.172143i	0.246532	+	0.969135i	$0.420709\pi$
$558$	456.078	+	161.265i	0.817344	+	0.289005i
$559$	−691.629	−	434.580i	−1.23726	−	0.777423i
$560$	−1178.21	+	645.051i	−2.10394	+	1.15188i
$561$	20.6269	−	0.410539i	0.0367680	−	0.000731799i
$562$	−43.9801	+	32.0751i	−0.0782564	+	0.0570730i
$563$	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	$0.700829\pi$
$564$	510.520	−	23.4781i	0.905178	−	0.0416278i
$565$	355.855	−	1016.97i	0.629831	−	1.79995i
$566$	201.092	−	733.811i	0.355286	−	1.29649i
$567$	760.231	−	238.504i	1.34079	−	0.420642i
$568$	−250.097	+	383.387i	−0.440311	+	0.674977i
$569$	−136.970	−	217.986i	−0.240720	−	0.383104i	0.704413	−	0.709791i	$-0.251211\pi$
$569$	−136.970	−	217.986i	−0.240720	−	0.383104i	−0.945133	+	0.326687i	$0.894068\pi$
$570$	−224.351	+	20.0265i	−0.393598	+	0.0351342i
$571$	−98.6107	+	22.5072i	−0.172698	+	0.0394172i	−0.307996	−	0.951388i	$-0.599658\pi$
$571$	−98.6107	+	22.5072i	−0.172698	+	0.0394172i	0.135297	+	0.990805i	$0.456801\pi$
$572$	−47.3483	−	21.3004i	−0.0827768	−	0.0372385i
$573$	245.797	+	147.705i	0.428966	+	0.257776i
$574$	−442.050	+	251.885i	−0.770121	+	0.438824i
$575$	−3.32431	−	1.60090i	−0.00578140	−	0.00278418i
$576$	562.288	+	124.931i	0.976195	+	0.216894i
$577$	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	$0.307923\pi$
$578$	115.307	+	268.430i	0.199493	+	0.464411i
$579$	−34.5923	−	260.339i	−0.0597448	−	0.449635i
$580$	−774.292	−	616.934i	−1.33499	−	1.06368i
$581$			69.2509i			0.119193i
$582$	−741.292	+	442.166i	−1.27370	+	0.759735i
$583$	−11.7714	+	1.32632i	−0.0201911	+	0.00227499i
$584$	509.155	−	616.637i	0.871841	−	1.05588i
$585$	−1703.76	−	318.134i	−2.91241	−	0.543818i
$586$	433.038	−	246.751i	0.738973	−	0.421076i
$587$	−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	$0.941467\pi$
$588$	164.234	−	549.070i	0.279310	−	0.933792i
$589$	115.248	−	26.3047i	0.195668	−	0.0446599i
$590$	693.475	+	29.8879i	1.17538	+	0.0506574i
$591$	328.923	−	273.190i	0.556553	−	0.462250i
$592$	−750.648	−	418.786i	−1.26799	−	0.707409i
$593$	39.5566	−	173.309i	0.0667060	−	0.292258i	−0.930561	−	0.366136i	$-0.880680\pi$
$593$	39.5566	−	173.309i	0.0667060	−	0.292258i	0.997267	+	0.0738782i	$0.0235376\pi$
$594$	−3.99069	−	30.8050i	−0.00671834	−	0.0518604i
$595$	331.488	−	947.337i	0.557122	−	1.59216i
$596$	418.507	+	36.1413i	0.702193	+	0.0606398i
$597$	−171.787	−	131.489i	−0.287750	−	0.220250i
$598$	−2.81216	+	2.05093i	−0.00470261	+	0.00342965i
$599$	−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	$0.833113\pi$
$600$	613.659	+	970.409i	1.02277	+	1.61735i
$601$	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	$0.666807\pi$
$602$	−586.137	−	404.511i	−0.973650	−	0.671944i
$603$	−647.870	−	749.192i	−1.07441	−	1.24244i
$604$	−327.218	+	1019.60i	−0.541752	+	1.68808i
$605$	−805.182	+	642.111i	−1.33088	+	1.06134i
$606$	−294.493	−	908.619i	−0.485963	−	1.49937i
$607$	−446.043	+	156.077i	−0.734832	+	0.257129i	−0.671645	−	0.740873i	$-0.734412\pi$
$607$	−446.043	+	156.077i	−0.734832	+	0.257129i	−0.0631865	+	0.998002i	$0.520126\pi$
$608$	132.431	−	47.6875i	0.217814	−	0.0784334i
$609$	850.939	−	90.9462i	1.39727	−	0.149337i
$610$	73.9219	+	1067.65i	0.121183	+	1.75024i
$611$	907.052	−	317.391i	1.48454	−	0.519462i
$612$	−374.635	+	211.851i	−0.612149	+	0.346162i
$613$	−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	$0.342121\pi$
$614$	184.768	+	73.7281i	0.300924	+	0.120078i
$615$	363.374	+	553.540i	0.590851	+	0.900064i
$616$	−40.4437	−	20.3315i	−0.0656553	−	0.0330057i
$617$	−460.865	−	289.581i	−0.746945	−	0.469336i	0.104010	−	0.994576i	$-0.466833\pi$
$617$	−460.865	−	289.581i	−0.746945	−	0.469336i	−0.850954	+	0.525240i	$0.823976\pi$
$618$	−32.9994	−	72.7919i	−0.0533971	−	0.117786i
$619$	572.788	+	64.5377i	0.925344	+	0.104261i	0.561760	−	0.827300i	$-0.310124\pi$
$619$	572.788	+	64.5377i	0.925344	+	0.104261i	0.363584	+	0.931561i	$0.381553\pi$
$620$	−590.528	−	702.162i	−0.952464	−	1.13252i
$621$	−1.92674	−	0.789965i	−0.00310265	−	0.00127209i
$622$	−333.124	−	52.1446i	−0.535570	−	0.0838337i
$623$	−159.954	+	457.121i	−0.256747	+	0.733742i
$624$	1080.28	−	77.9279i	1.73122	−	0.124884i
$625$	−104.065	+	455.939i	−0.166504	+	0.729503i
$626$	−116.453	+	133.779i	−0.186027	+	0.213704i
$627$	−4.84984	−	5.83924i	−0.00773499	−	0.00931299i
$628$	−34.9102	+	0.909814i	−0.0555895	+	0.00144875i
$629$	626.164	−	142.918i	0.995491	−	0.227214i
$630$	−1472.14	−	341.076i	−2.33673	−	0.541391i
$631$	115.584	−	144.937i	0.183175	−	0.229694i	−0.681763	−	0.731573i	$-0.738786\pi$
$631$	115.584	−	144.937i	0.183175	−	0.229694i	0.864938	+	0.501879i	$0.167358\pi$
$632$	410.558	+	533.188i	0.649617	+	0.843653i
$633$	−136.238	+	415.702i	−0.215225	+	0.656717i
$634$	−631.424	+	579.246i	−0.995937	+	0.913636i
$635$	1619.78	−	182.506i	2.55084	−	0.287411i
$636$	202.981	−	140.949i	0.319153	−	0.221618i
$637$		−	1077.65i		−	1.69176i
$638$	2.29023	−	33.2847i	0.00358970	−	0.0521704i
$639$	−497.099	+	134.477i	−0.777932	+	0.210450i
$640$	−799.095	−	744.887i	−1.24859	−	1.16389i
$641$	−476.540	+	53.6931i	−0.743432	+	0.0837646i	−0.475552	−	0.879688i	$-0.657752\pi$
$641$	−476.540	+	53.6931i	−0.743432	+	0.0837646i	−0.267880	+	0.963452i	$0.586323\pi$
$642$	−315.003	+	376.752i	−0.490659	+	0.586841i
$643$	1109.04	+	534.084i	1.72479	+	0.830613i	0.987994	+	0.154494i	$0.0493747\pi$
$643$	1109.04	+	534.084i	1.72479	+	0.830613i	0.736792	+	0.676119i	$0.236340\pi$
$644$	−2.52656	+	1.68091i	−0.00392323	+	0.00261011i
$645$	−477.405	+	794.452i	−0.740163	+	1.23171i
$646$	−49.6702	+	92.7040i	−0.0768889	+	0.143505i
$647$	−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	$0.468457\pi$
$648$	378.399	+	526.040i	0.583949	+	0.811791i
$649$	12.4451	+	19.8063i	0.0191758	+	0.0305181i
$650$	1628.42	+	1417.52i	2.50525	+	2.18080i
$651$	789.699	+	73.0963i	1.21306	+	0.112283i
$652$	902.258	+	181.342i	1.38383	+	0.278131i
$653$	161.526	−	461.615i	0.247360	−	0.706914i	−0.751525	−	0.659704i	$-0.770681\pi$
$653$	161.526	−	461.615i	0.247360	−	0.706914i	0.998885	−	0.0472094i	$-0.0150328\pi$
$654$	7.95588	−	343.286i	0.0121650	−	0.524902i
$655$	803.529	+	803.529i	1.22676	+	1.22676i
$656$	−307.431	−	276.951i	−0.468646	−	0.422181i
$657$	889.261	−	136.219i	1.35352	−	0.207335i
$658$	802.014	−	242.415i	1.21887	−	0.368412i
$659$	−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	$-0.654012\pi$
$660$	−23.0958	+	54.1967i	−0.0349937	+	0.0821162i
$661$	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	$0.300736\pi$
$662$	−377.756	+	946.681i	−0.570628	+	1.43003i
$663$	−560.749	+	583.524i	−0.845776	+	0.880126i
$664$	−53.4692	+	17.6944i	−0.0805259	+	0.0266482i
$665$	−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
$669$	338.090	+	667.725i	0.505365	+	0.998093i
$670$	338.761	+	1847.71i	0.505613	+	2.75777i
$671$	−28.1973	+	22.4866i	−0.0420228	+	0.0335121i
$672$	943.919	−	27.3244i	1.40464	−	0.0406614i
$673$	−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	$0.978491\pi$
$674$	189.090	−	273.992i	0.280548	−	0.406516i
$675$	−211.777	+	1274.20i	−0.313743	+	1.88770i
$676$	1272.11	−	482.685i	1.88182	−	0.714031i
$677$	−338.577	−	38.1485i	−0.500114	−	0.0563493i	−0.141695	−	0.989910i	$-0.545255\pi$
$677$	−338.577	−	38.1485i	−0.500114	−	0.0563493i	−0.358419	+	0.933561i	$0.616684\pi$
$678$	−547.869	+	523.049i	−0.808066	+	0.771459i
$679$	−1000.61	+	1000.61i	−1.47365	+	1.47365i
$680$	816.146	+	13.8892i	1.20022	+	0.0204253i
$681$	6.88623	−	33.2029i	0.0101119	−	0.0487562i
$682$	8.17159	−	29.8192i	0.0119818	−	0.0437232i
$683$	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	$0.0631350\pi$
$684$	146.880	+	59.1675i	0.214737	+	0.0865022i
$685$	−814.822	+	511.987i	−1.18952	+	0.747426i
$686$	−1.05139	+	24.3950i	−0.00153264	+	0.0355612i
$687$	259.633	+	697.165i	0.377922	+	1.01480i
$688$	162.562	−	555.919i	0.236281	−	0.808021i
$689$	289.720	−	363.297i	0.420493	−	0.527282i
$690$	2.39024	+	3.14403i	0.00346411	+	0.00455656i
$691$	511.948	−	1063.07i	0.740880	−	1.53845i	−0.0986390	−	0.995123i	$-0.531449\pi$
$691$	511.948	−	1063.07i	0.740880	−	1.53845i	0.839519	−	0.543330i	$-0.182837\pi$
$692$	−612.372	+	645.144i	−0.884930	+	0.932290i
$693$	−18.7187	−	47.3598i	−0.0270111	−	0.0683403i
$694$	−336.578	−	783.540i	−0.484982	−	1.12902i
$695$		−	1259.84i		−	1.81273i
$696$	287.645	+	633.780i	0.413283	+	0.910603i
$697$	309.178			0.443583
$698$	−884.504	+	379.948i	−1.26720	+	0.544338i
$699$	706.414	−	176.094i	1.01061	−	0.251923i
$700$	1365.23	+	1295.88i	1.95034	+	1.85126i
$701$	603.262	+	290.516i	0.860573	+	0.414430i	0.811491	−	0.584364i	$-0.198656\pi$
$701$	603.262	+	290.516i	0.860573	+	0.414430i	0.0490820	+	0.998795i	$0.484370\pi$
$702$	965.144	+	743.761i	1.37485	+	1.05949i
$703$	−184.751	−	147.334i	−0.262804	−	0.209579i
$704$	5.36435	−	36.4219i	0.00761981	−	0.0517356i
$705$	−380.555	−	1021.87i	−0.539794	−	1.44946i
$706$	−1051.34	−	45.3114i	−1.48915	−	0.0641804i
$707$	−833.114	−	1325.89i	−1.17838	−	1.87538i
$708$	−424.673	−	240.364i	−0.599821	−	0.339497i
$709$	−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	$0.665774\pi$
$710$	941.951	+	258.130i	1.32669	+	0.363564i
$711$	−54.7621	+	755.074i	−0.0770213	+	1.06199i
$712$	−393.817	−	6.70199i	−0.553114	−	0.00941291i
$713$	−1.46566	−	1.46566i	−0.00205562	−	0.00205562i
$714$	−510.354	+	487.234i	−0.714781	+	0.682400i
$715$	−12.4031	+	110.081i	−0.0173470	+	0.153959i
$716$	−128.990	−	339.951i	−0.180154	−	0.474792i
$717$	−808.046	−	369.510i	−1.12698	−	0.515356i
$718$	−249.288	−	172.041i	−0.347198	−	0.239612i
$719$	−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	$0.563868\pi$
$720$	−112.800	−	1223.80i	−0.156667	−	1.69972i
$721$	−81.6946	−	102.442i	−0.113307	−	0.142083i
$722$	−672.102	+	123.224i	−0.930889	+	0.170670i
$723$	−32.3892	−	63.9685i	−0.0447984	−	0.0884765i
$724$	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	$-0.162487\pi$
$727$	−83.0756	−	237.417i	−0.114272	−	0.326570i	−0.986788	+	0.162014i	$0.948201\pi$
$728$	1685.75	−	557.859i	2.31559	−	0.766289i
$729$	−76.4019	+	724.985i	−0.104804	+	0.994493i
$730$	−1584.73	−	632.356i	−2.17086	−	0.866241i
$731$	187.775	+	389.919i	0.256874	+	0.533404i
$732$	294.957	−	692.146i	0.402947	−	0.945555i
$733$	−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	$0.241708\pi$
$734$	−344.183	−	1138.70i	−0.468914	−	1.55137i
$735$	−1222.57	+	24.3330i	−1.66336	+	0.0331061i
$736$	−1.94341	−	1.52129i	−0.00264051	−	0.00206696i
$737$	−44.7635	+	44.7635i	−0.0607375	+	0.0607375i
$738$	−50.6067	−	462.746i	−0.0685727	−	0.627027i
$739$	558.345	+	195.373i	0.755541	+	0.264375i	0.680443	−	0.732801i	$-0.261787\pi$
$739$	558.345	+	195.373i	0.755541	+	0.264375i	0.0750979	+	0.997176i	$0.476073\pi$
$740$	−361.386	+	1798.06i	−0.488360	+	2.42982i
$741$	296.488	+	27.4436i	0.400118	+	0.0370358i
$742$	266.003	−	305.578i	0.358494	−	0.411830i
$743$	−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	$0.448446\pi$
$744$	145.339	+	628.411i	0.195348	+	0.844638i
$745$	−199.440	−	873.803i	−0.267704	−	1.17289i
$746$	−234.061	−	125.409i	−0.313755	−	0.168108i
$747$	−58.1350	−	25.1981i	−0.0778247	−	0.0337324i
$748$	15.2370	+	22.9025i	0.0203703	+	0.0306183i
$749$	−349.324	+	725.378i	−0.466387	+	0.968462i
$750$	750.215	−	897.278i	1.00029	−	1.19637i
$751$	70.1828	+	622.890i	0.0934525	+	0.829414i	0.949767	+	0.312959i	$0.101320\pi$
$751$	70.1828	+	622.890i	0.0934525	+	0.829414i	−0.856314	+	0.516455i	$0.827251\pi$
$752$	392.095	+	557.302i	0.521402	+	0.741094i
$753$	72.5215	+	545.791i	0.0963101	+	0.724822i
$754$	859.707	+	986.757i	1.14019	+	1.30870i
$755$	2284.77			3.02619
$756$	812.778	+	684.095i	1.07510	+	0.904888i
$757$	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	$0.798184\pi$
$758$	97.3350	+	106.103i	0.128410	+	0.139977i
$759$	−0.0414501	+	0.126477i	−5.46115e−5	+	0.000166636i
$760$	−183.226	−	237.955i	−0.241087	−	0.313098i
$761$	3.82796	+	3.05270i	0.00503017	+	0.00401143i	0.626002	−	0.779822i	$-0.284690\pi$
$761$	3.82796	+	3.05270i	0.00503017	+	0.00401143i	−0.620971	+	0.783833i	$0.713262\pi$
$762$	−1072.58	−	403.440i	−1.40758	−	0.529449i
$763$	−125.267	−	548.831i	−0.164177	−	0.719307i
$764$	9.96129	+	382.221i	0.0130383	+	0.500290i
$765$	674.658	+	622.983i	0.881905	+	0.814357i
$766$	850.485	+	740.340i	1.11029	+	0.966501i
$767$	−894.571	−	204.180i	−1.16632	−	0.266206i
$768$	262.279	+	721.827i	0.341510	+	0.939878i
$769$	−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	$0.812016\pi$
$770$	−14.9365	+	95.4214i	−0.0193980	+	0.123924i
$771$	−722.443	−	552.974i	−0.937021	−	0.717216i
$772$	267.992	−	225.385i	0.347140	−	0.291950i
$773$	82.5542	−	732.689i	0.106797	−	0.947852i	−0.820019	−	0.572336i	$-0.806037\pi$
$773$	82.5542	−	732.689i	0.106797	−	0.947852i	0.926816	−	0.375515i	$-0.122534\pi$
$774$	552.856	−	344.865i	0.714284	−	0.445562i
$775$	−684.032	+	1088.63i	−0.882622	+	1.40469i
$776$	−1028.25	−	516.912i	−1.32506	−	0.666124i
$777$	−870.004	−	1325.31i	−1.11970	−	1.70567i
$778$	238.729	−	598.270i	0.306849	−	0.768985i
$779$	−70.9244	−	88.9364i	−0.0910455	−	0.114167i
$780$	−862.658	−	2143.90i	−1.10597	−	2.74858i
$781$	10.8708	+	31.0669i	0.0139190	+	0.0397783i
$782$	1.83970	−	0.127377i	0.00235256	−	0.000162887i
$783$	−233.280	+	747.442i	−0.297931	+	0.954587i
$784$	735.115	−	208.611i	0.937646	−	0.266086i
$785$	24.6097	+	70.3304i	0.0313499	+	0.0895928i
$786$	−246.312	−	759.962i	−0.313374	−	0.966873i
$787$	−611.914	−	767.316i	−0.777527	−	0.974988i	−1.00000		4.94981e-5i	$-0.999984\pi$
$787$	−611.914	−	767.316i	−0.777527	−	0.974988i	0.222473	−	0.974939i	$-0.428587\pi$
$788$	542.835	+	174.210i	0.688876	+	0.221079i
$789$	235.134	+	358.187i	0.298015	+	0.453977i
$790$	815.544	−	1181.73i	1.03233	−	1.49586i
$791$	−660.678	+	1051.46i	−0.835244	+	1.32928i
$792$	31.7841	−	26.5539i	0.0401314	−	0.0335276i
$793$	158.400	−	1405.84i	0.199748	−	1.77281i
$794$	−40.9042	−	56.0862i	−0.0515166	−	0.0706376i
$795$	−418.695	−	320.478i	−0.526661	−	0.403117i
$796$	24.8170	−	287.375i	0.0311772	−	0.361023i
$797$	−714.650	−	250.067i	−0.896675	−	0.313760i	−0.157695	−	0.987488i	$-0.550406\pi$
$797$	−714.650	−	250.067i	−0.896675	−	0.313760i	−0.738980	+	0.673728i	$0.764692\pi$
$798$	257.229	+	35.0357i	0.322342	+	0.0439043i
$799$	−496.386	−	113.297i	−0.621259	−	0.141798i
$800$	−651.729	+	1385.22i	−0.814661	+	1.73153i
$801$	−325.544	−	300.610i	−0.406422	−	0.375293i
$802$	−31.6344	+	733.999i	−0.0394444	+	0.915211i
$803$	−12.7949	−	56.0581i	−0.0159339	−	0.0698108i
$804$	378.449	−	1265.23i	0.470707	−	1.57368i
$805$	5.06225	+	4.03701i	0.00628851	+	0.00501492i
$806$	600.449	+	1053.77i	0.744974	+	1.30740i
$807$	−356.240	+	1086.99i	−0.441437	+	1.34695i
$808$	810.864	−	982.035i	1.00354	−	1.21539i
$809$	148.484	+	1317.84i	0.183541	+	1.62897i	0.661050	+	0.750342i	$0.270111\pi$
$809$	148.484	+	1317.84i	0.183541	+	1.62897i	−0.477509	+	0.878627i	$0.658460\pi$
$810$	821.990	−	1111.73i	1.01480	−	1.37251i
$811$	−287.423			−0.354406			−0.177203	−	0.984174i	$-0.556705\pi$
$811$	−287.423			−0.354406			−0.177203	+	0.984174i	$0.556705\pi$
$812$	711.813	+	891.801i	0.876617	+	1.09828i
$813$	−151.300	−	1138.67i	−0.186101	−	1.40058i
$814$	−56.7885	+	24.3941i	−0.0697647	+	0.0299681i
$815$	−219.855	−	1951.26i	−0.269760	−	2.39419i
$816$	−506.599	−	269.555i	−0.620832	−	0.330337i
$817$	69.0869	−	143.461i	0.0845617	−	0.175594i
$818$	489.810	+	859.599i	0.598790	+	1.05086i
$819$	1832.85	+	794.431i	2.23791	+	0.970001i
$820$	−362.210	+	805.149i	−0.441719	+	0.981889i
$821$	−36.0936	−	158.136i	−0.0439630	−	0.192614i	0.948178	−	0.317740i	$-0.102924\pi$
$821$	−36.0936	−	158.136i	−0.0439630	−	0.192614i	−0.992141	+	0.125125i	$0.960067\pi$
$822$	673.851	−	60.1508i	0.819770	−	0.0731761i
$823$	427.280	−	268.478i	0.519173	−	0.326218i	−0.246826	−	0.969060i	$-0.579388\pi$
$823$	427.280	−	268.478i	0.519173	−	0.326218i	0.765999	+	0.642842i	$0.222245\pi$
$824$	58.2223	−	89.2521i	0.0706581	−	0.108316i
$825$	82.2057	+	7.60914i	0.0996433	+	0.00922320i
$826$	−771.561	−	211.437i	−0.934093	−	0.255977i
$827$	−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	$0.621628\pi$
$828$	−0.491771	−	2.73263i	−0.000593926	−	0.00330028i
$829$	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	$0.112302\pi$
$830$	70.8096	+	97.0914i	0.0853128	+	0.116978i
$831$	747.070	−	14.8690i	0.899001	−	0.0178929i
$832$	861.455	+	1159.04i	1.03540	+	1.39308i
$833$	−303.772	+	483.450i	−0.364672	+	0.580372i
$834$	−402.673	+	788.864i	−0.482822	+	0.945880i
$835$	−948.109	−	1968.77i	−1.13546	−	2.35781i
$836$	3.09269	−	9.63674i	0.00369939	−	0.0115272i
$837$	−348.708	+	636.343i	−0.416617	+	0.760266i
$838$	−1054.23	+	193.284i	−1.25803	+	0.230649i
$839$	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
$843$	−36.8839	−	72.8454i	−0.0437531	−	0.0864122i
$844$	−565.078	+	144.562i	−0.669523	+	0.171282i
$845$	−1810.03	−	2269.71i	−2.14205	−	2.68604i
$846$	−88.3222	+	761.485i	−0.104400	+	0.900100i
$847$	1069.43	−	515.009i	1.26261	−	0.608039i
$848$	303.906	+	127.304i	0.358380	+	0.150123i
$849$	1037.92	+	474.631i	1.22253	+	0.559047i
$850$	−330.957	−	1094.95i	−0.389361	−	1.28817i
$851$	−0.463917	+	4.11737i	−0.000545143	+	0.00483828i
$852$	−507.308	−	462.698i	−0.595431	−	0.543073i
$853$	−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	$0.801203\pi$
$854$	190.754	−	1218.63i	0.223365	−	1.42696i
$855$	24.4396	−	336.979i	0.0285843	−	0.394127i
$856$	−649.327	−	84.3736i	−0.758559	−	0.0985673i
$857$	−903.739	−	206.272i	−1.05454	−	0.240691i	−0.340099	−	0.940390i	$-0.610461\pi$
$857$	−903.739	−	206.272i	−1.05454	−	0.240691i	−0.714438	+	0.699698i	$0.753318\pi$
$858$	42.9505	−	64.9638i	0.0500588	−	0.0757154i
$859$	92.9570	+	147.940i	0.108215	+	0.172224i	0.896442	−	0.443162i	$-0.146143\pi$
$859$	92.9570	+	147.940i	0.108215	+	0.172224i	−0.788226	+	0.615385i	$0.789000\pi$
$860$	−1235.39	+	32.1963i	−1.43651	+	0.0374376i
$861$	−266.342	−	715.181i	−0.309340	−	0.830640i
$862$	964.016	+	516.514i	1.11835	+	0.599204i
$863$	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	$0.545241\pi$
$864$	−320.522	+	802.348i	−0.370975	+	0.928643i
$865$	1709.94	+	823.463i	1.97681	+	0.951981i
$866$	445.432	+	485.556i	0.514355	+	0.560688i
$867$	−425.209	+	105.996i	−0.490437	+	0.122256i
$868$	483.468	+	940.438i	0.556991	+	1.08345i
$869$	48.3869			0.0556812
$870$	1100.04	−	997.601i	1.26442	−	1.14667i
$871$		−	2483.25i		−	2.85103i
$872$	391.750	−	236.952i	0.449255	−	0.271734i
$873$	−475.908	−	1204.08i	−0.545140	−	1.37925i
$874$	−0.458663	−	0.499979i	−0.000524786	−	0.000572059i
$875$	831.954	−	1727.57i	0.950805	−	1.97437i
$876$	790.177	+	902.468i	0.902029	+	1.03022i
$877$	−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	$0.340335\pi$
$878$	−166.004	−	88.9437i	−0.189070	−	0.101303i
$879$	260.912	+	700.602i	0.296829	+	0.797044i
$880$	−77.4922	+	12.8487i	−0.0880593	+	0.0146008i
$881$	−465.381	+	292.418i	−0.528242	+	0.331917i	−0.769607	−	0.638518i	$-0.779548\pi$
$881$	−465.381	+	292.418i	−0.528242	+	0.331917i	0.241365	+	0.970434i	$0.422405\pi$
$882$	773.302	+	375.524i	0.876759	+	0.425764i
$883$	−69.6525	+	305.168i	−0.0788817	+	0.345603i	−0.998932	−	0.0461961i	$-0.985290\pi$
$883$	−69.6525	+	305.168i	−0.0788817	+	0.345603i	0.920051	+	0.391799i	$0.128147\pi$
$884$	−1057.89	−	212.621i	−1.19671	−	0.240522i
$885$	−211.439	+	1019.48i	−0.238914	+	1.15196i
$886$	53.4439	−	341.425i	0.0603204	−	0.385356i
$887$	−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	$0.396348\pi$
$888$	800.986	−	1010.37i	0.902011	−	1.13780i
$889$	−1866.88	−	210.347i	−2.09998	−	0.236611i
$890$	243.151	+	804.449i	0.273204	+	0.903876i
$891$	46.5689	+	1.51858i	0.0522659	+	0.00170436i
$892$	−508.731	+	858.507i	−0.570326	+	0.962452i
$893$	81.2790	+	168.778i	0.0910179	+	0.189001i
$894$	−154.405	+	610.885i	−0.172713	+	0.683317i
$895$	−606.544	+	483.703i	−0.677703	+	0.540450i
$896$	706.868	+	1041.94i	0.788916	+	1.16288i
$897$	−2.35842	−	4.65785i	−0.00262923	−	0.00519270i
$898$	−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
$902$	−29.2648	+	5.36544i	−0.0324443	+	0.00594838i
$903$	740.189	−	770.252i	0.819700	−	0.852992i
$904$	−980.655	−	241.455i	−1.08479	−	0.267096i
$905$	478.695	−	230.527i	0.528945	−	0.254726i
$906$	−1430.63	−	730.262i	−1.57906	−	0.806029i
$907$	187.357	+	117.724i	0.206567	+	0.129795i	0.631343	−	0.775504i	$-0.282504\pi$
$907$	187.357	+	117.724i	0.206567	+	0.129795i	−0.424775	+	0.905299i	$0.639647\pi$
$908$	42.2720	−	16.0396i	0.0465550	−	0.0176647i
$909$	1416.21	−	216.938i	1.55799	−	0.238656i
$910$	−2232.45	−	3061.05i	−2.45324	−	3.36379i
$911$	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	$0.515667\pi$
$912$	38.6735	+	207.561i	0.0424052	+	0.227588i
$913$	−1.33753	+	3.82244i	−0.00146498	+	0.00418668i
$914$	382.214	+	104.741i	0.418177	+	0.114596i
$915$	−1598.48	−	147.958i	−1.74697	−	0.161703i
$916$	−598.039	+	791.365i	−0.652881	+	0.863935i
$917$	−696.810	−	1108.97i	−0.759880	−	1.20934i
$918$	−223.325	−	605.722i	−0.243273	−	0.659828i
$919$	−1386.03	+	316.352i	−1.50819	+	0.344235i	−0.895132	−	0.445802i	$-0.852919\pi$
$919$	−1386.03	+	316.352i	−1.50819	+	0.344235i	−0.613060	+	0.790037i	$0.710061\pi$
$920$	−1.82355	+	4.94011i	−0.00198212	+	0.00536969i
$921$	−153.700	+	255.773i	−0.166884	+	0.277712i
$922$	−109.516	−	192.197i	−0.118781	−	0.208457i
$923$	−1163.24	−	560.188i	−1.26028	−	0.606921i
$924$	39.8514	−	54.9750i	0.0431292	−	0.0594968i
$925$	2553.94	−	287.760i	2.76102	−	0.311092i
$926$	426.090	−	183.031i	0.460140	−	0.197658i
$927$	115.724	−	31.3062i	0.124837	−	0.0337715i
$928$	−506.691	+	777.463i	−0.546003	+	0.837783i
$929$			925.055i			0.995754i	0.867248	+	0.497877i	$0.165887\pi$
$929$			925.055i			0.995754i	−0.867248	+	0.497877i	$0.834113\pi$
$930$	1181.92	−	704.991i	1.27088	−	0.758055i
$931$	208.751	−	23.5206i	0.224222	−	0.0252638i
$932$	704.045	+	668.280i	0.755413	+	0.717038i
$933$	157.513	−	480.619i	0.168824	−	0.515133i
$934$	783.317	+	1374.69i	0.838669	+	1.47183i
$935$	36.5942	−	45.8877i	0.0391382	−	0.0490777i
$936$	−145.073	+	1618.14i	−0.154993	+	1.72879i
$937$	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	$0.392508\pi$
$938$	93.2253	−	2163.07i	0.0993873	−	2.30604i
$939$	−169.983	−	204.661i	−0.181026	−	0.217957i
$940$	876.572	−	1159.94i	0.932523	−	1.23398i
$941$	−278.978	+	1222.28i	−0.296470	+	1.29892i	0.578874	+	0.815417i	$0.303492\pi$
$941$	−278.978	+	1222.28i	−0.296470	+	1.29892i	−0.875343	+	0.483502i	$0.839365\pi$
$942$	7.06952	−	51.9038i	0.00750480	−	0.0550996i
$943$	−0.658769	+	1.88265i	−0.000698589	+	0.00199645i
$944$	−33.8902	−	649.754i	−0.0359006	−	0.688299i
$945$	859.881	−	2097.27i	0.909926	−	2.21933i
$946$	−24.5402	−	33.6486i	−0.0259410	−	0.0355693i
$947$	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	$0.393322\pi$
$948$	−888.366	+	479.284i	−0.937095	+	0.505574i
$949$	1909.80	+	1200.01i	2.01244	+	1.26450i
$950$	−239.046	+	346.379i	−0.251628	+	0.364609i
$951$	−705.342	−	1074.47i	−0.741685	−	1.12983i
$952$	−913.505	−	224.921i	−0.959564	−	0.236262i
$953$	793.016	−	632.409i	0.832126	−	0.663598i	−0.111809	−	0.993730i	$-0.535664\pi$
$953$	793.016	−	632.409i	0.832126	−	0.663598i	0.943935	+	0.330131i	$0.107093\pi$
$954$	159.738	+	334.495i	0.167441	+	0.350623i
$955$	770.027	−	269.444i	0.806311	−	0.282140i
$956$	−163.270	−	1173.39i	−0.170784	−	1.22740i
$957$	48.7258	+	11.4153i	0.0509151	+	0.0119282i
$958$	−781.099	+	54.0818i	−0.815344	+	0.0564528i
$959$	1046.89	−	366.322i	1.09164	−	0.381983i
$960$	1295.46	−	1003.47i	1.34944	−	1.04529i
$961$	186.652	−	148.850i	0.194227	−	0.154891i
$962$	898.537	−	2251.79i	0.934030	−	2.34074i
$963$	−481.836	−	557.192i	−0.500349	−	0.578600i
$964$	48.7368	−	82.2456i	0.0505569	−	0.0853170i
$965$	−632.623	−	397.503i	−0.655568	−	0.411920i
$966$	−1.87946	−	4.14582i	−0.00194561	−	0.00429174i
$967$	567.723	+	63.9670i	0.587097	+	0.0661499i	0.400516	−	0.916290i	$-0.368831\pi$
$967$	567.723	+	63.9670i	0.587097	+	0.0661499i	0.186581	+	0.982440i	$0.440259\pi$
$968$	670.894	+	694.124i	0.693072	+	0.717070i
$969$	−125.273	−	95.8867i	−0.129281	−	0.0989543i
$970$	−379.748	+	2426.01i	−0.391492	+	2.50104i
$971$	−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	$0.177862\pi$
$972$	−870.030	+	433.396i	−0.895093	+	0.445880i
$973$	−323.108	+	1415.63i	−0.332074	+	1.45491i
$974$	−1084.22	−	943.806i	−1.11316	−	0.969000i
$975$	−2491.23	+	2069.12i	−2.55511	+	2.12217i
$976$	989.653	−	164.090i	1.01399	−	0.168125i
$977$	−890.386	+	203.225i	−0.911347	+	0.208009i	−0.652393	−	0.757881i	$-0.726235\pi$
$977$	−890.386	+	203.225i	−0.911347	+	0.208009i	−0.258954	+	0.965890i	$0.583378\pi$
$978$	−486.002	+	1292.07i	−0.496934	+	1.32114i
$979$	−17.6579	+	22.1423i	−0.0180367	+	0.0226173i
$980$	−903.106	−	1357.45i	−0.921537	−	1.38515i
$981$	506.316	+	94.5414i	0.516122	+	0.0963725i
$982$	−484.849	−	528.524i	−0.493737	−	0.538212i
$983$	−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	$0.662576\pi$
$984$	484.144	−	388.382i	0.492016	−	0.394697i
$985$		−	1216.41i		−	1.23493i
$986$	−107.527	−	685.012i	−0.109054	−	0.694739i
$987$	165.538	+	1245.82i	0.167718	+	1.26223i
$988$	181.515	+	353.082i	0.183720	+	0.357370i
$989$	−2.77440	+	0.312600i	−0.00280526	+	0.000316077i
$990$	−74.6699	−	47.2596i	−0.0754242	−	0.0477370i
$991$	852.219	+	410.407i	0.859958	+	0.414134i	0.811264	−	0.584680i	$-0.198780\pi$
$991$	852.219	+	410.407i	0.859958	+	0.414134i	0.0486940	+	0.998814i	$0.484494\pi$
$992$	−602.589	+	613.583i	−0.607449	+	0.618531i
$993$	−1310.49	−	787.502i	−1.31972	−	0.793053i
$994$	−992.225	−	531.628i	−0.998215	−	0.534837i
$995$	−600.011	+	136.949i	−0.603026	+	0.137637i
$996$	−13.3056	−	83.4270i	−0.0133590	−	0.0837621i
$997$	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	$0.698820\pi$
$998$	−866.821	+	995.785i	−0.868559	+	0.997780i
$999$	1429.14	−	248.120i	1.43057	−	0.248368i

Twists

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

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

\(f(q)\)	\(=\)	\(q+(-1.83763 + 0.789374i) q^{2} +(-0.725631 - 2.91092i) q^{3} +(2.75378 - 2.90116i) q^{4} +(-7.68944 - 3.70304i) q^{5} +(3.63125 + 4.77641i) q^{6} +(7.69057 + 6.13302i) q^{7} +(-2.77034 + 7.50501i) q^{8} +(-7.94692 + 4.22451i) q^{9} +O(q^{10})\)	\(q+(-1.83763 + 0.789374i) q^{2} +(-0.725631 - 2.91092i) q^{3} +(2.75378 - 2.90116i) q^{4} +(-7.68944 - 3.70304i) q^{5} +(3.63125 + 4.77641i) q^{6} +(7.69057 + 6.13302i) q^{7} +(-2.77034 + 7.50501i) q^{8} +(-7.94692 + 4.22451i) q^{9} +(17.0534 + 0.734981i) q^{10} +(0.306041 + 0.487062i) q^{11} +(-10.4433 - 5.91086i) q^{12} +(-21.9986 - 5.02105i) q^{13} +(-18.9737 - 5.19951i) q^{14} +(-5.19955 + 25.0704i) q^{15} +(-0.833404 - 15.9783i) q^{16} +(8.45359 + 8.45359i) q^{17} +(11.2688 - 14.0362i) q^{18} +(0.492487 - 4.37094i) q^{19} +(-31.9181 + 12.1109i) q^{20} +(12.2722 - 26.8370i) q^{21} +(-0.946865 - 0.653459i) q^{22} +(-0.0694880 + 0.0334637i) q^{23} +(23.8567 + 2.61835i) q^{24} +(29.8277 + 37.4028i) q^{25} +(44.3889 - 8.13831i) q^{26} +(18.0637 + 20.0674i) 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} +(14.1443 + 28.7043i) q^{32} +(1.19573 - 1.24429i) q^{33} +(-22.2076 - 8.86154i) q^{34} +(-36.4253 - 75.6380i) q^{35} +(-9.62809 + 34.6886i) q^{36} +(28.5823 - 45.4885i) q^{37} +(2.54530 + 8.42094i) q^{38} +(1.34704 + 67.6797i) q^{39} +(49.0937 - 47.4507i) q^{40} +(18.2868 - 18.2868i) q^{41} +(-1.36745 + 59.0038i) q^{42} +(34.1685 + 11.9561i) q^{43} +(2.25581 + 0.453387i) q^{44} +(76.7509 - 3.05637i) q^{45} +(0.101278 - 0.116346i) q^{46} +(-36.0606 + 22.6584i) q^{47} +(-45.9068 + 14.0203i) q^{48} +(10.6273 + 46.5614i) q^{49} +(-84.3372 - 45.1873i) q^{50} +(18.4735 - 30.7419i) q^{51} +(-75.1462 + 49.9946i) q^{52} +(-8.93509 + 18.5539i) q^{53} +(-49.0352 - 22.6175i) q^{54} +(-0.549677 - 4.87852i) q^{55} +(-67.3339 + 40.7273i) q^{56} +(-13.0808 + 1.73810i) q^{57} +(-46.8759 - 34.1562i) q^{58} +40.6648 q^{59} +(58.4147 + 84.1230i) q^{60} +(7.01993 + 62.3036i) q^{61} +(-36.3351 - 39.6082i) q^{62} +(-87.0254 - 16.2497i) q^{63} +(-48.6505 - 41.5828i) q^{64} +(150.564 + 120.071i) q^{65} +(-1.21509 + 3.23042i) q^{66} +(24.4888 + 107.293i) q^{67} +(47.8045 - 1.24586i) q^{68} +(0.147833 + 0.177992i) q^{69} +(126.643 + 110.242i) q^{70} +(55.7840 + 12.7323i) q^{71} +(-9.68939 - 71.3450i) q^{72} +(-94.3500 - 33.0145i) q^{73} +(-16.6163 + 106.153i) q^{74} +(87.2327 - 113.967i) q^{75} +(-11.3246 - 13.4654i) q^{76} +(-0.633531 + 5.62274i) q^{77} +(-55.8999 - 123.307i) q^{78} +(44.7532 - 71.2243i) q^{79} +(-52.7598 + 125.950i) q^{80} +(45.3070 - 67.1437i) q^{81} +(-19.1693 + 48.0394i) q^{82} +(4.38944 + 5.50419i) q^{83} +(-44.0632 - 109.507i) q^{84} +(-33.6994 - 96.3073i) q^{85} +(-72.2270 + 5.00086i) q^{86} +(61.8696 - 61.1650i) q^{87} +(-4.50324 + 0.947519i) q^{88} +(16.2611 + 46.4714i) q^{89} +(-138.627 + 66.2016i) q^{90} +(-138.388 - 173.533i) q^{91} +(-0.0942714 + 0.293747i) q^{92} +(67.3999 - 44.2450i) q^{93} +(48.3801 - 70.1030i) q^{94} +(-19.9727 + 31.7864i) q^{95} +(73.2924 - 62.0018i) q^{96} +(-16.1070 + 142.953i) q^{97} +(-56.2835 - 77.1738i) q^{98} +(-4.48968 - 2.57777i) 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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