LMFDB - Embedded newform 348.3.v.a.11.11

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			11.11
Character	$\chi$	$=$	348.11
Dual form			348.3.v.a.95.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.92037 - 0.558718i) q^{2} +(0.209671 - 2.99266i) q^{3} +(3.37567 + 2.14590i) q^{4} +(-7.42336 - 3.57490i) q^{5} +(-2.07470 + 5.62989i) q^{6} +(-9.85035 - 7.85539i) q^{7} +(-5.28359 - 6.00697i) q^{8} +(-8.91208 - 1.25495i) q^{9} +O(q^{10})$	\(q+(-1.92037 - 0.558718i) q^{2} +(0.209671 - 2.99266i) q^{3} +(3.37567 + 2.14590i) q^{4} +(-7.42336 - 3.57490i) q^{5} +(-2.07470 + 5.62989i) q^{6} +(-9.85035 - 7.85539i) q^{7} +(-5.28359 - 6.00697i) q^{8} +(-8.91208 - 1.25495i) q^{9} +(12.2583 + 11.0127i) q^{10} +(-4.76526 - 7.58386i) q^{11} +(7.12972 - 9.65231i) q^{12} +(10.8341 + 2.47281i) q^{13} +(14.5274 + 20.5888i) q^{14} +(-12.2549 + 21.4661i) q^{15} +(6.79027 + 14.4877i) q^{16} +(12.3870 + 12.3870i) q^{17} +(16.4134 + 7.38931i) q^{18} +(2.46170 - 21.8482i) q^{19} +(-17.3874 - 27.9974i) q^{20} +(-25.5739 + 27.8317i) q^{21} +(4.91383 + 17.2263i) q^{22} +(-2.97127 + 1.43089i) q^{23} +(-19.0847 + 14.5525i) q^{24} +(26.7391 + 33.5297i) q^{25} +(-19.4239 - 10.8019i) q^{26} +(-5.62425 + 26.4077i) q^{27} +(-16.3947 - 47.6550i) q^{28} +(14.6279 - 25.0405i) q^{29} +(35.5275 - 34.3758i) q^{30} +(-10.1421 - 28.9846i) q^{31} +(-4.94533 - 31.6156i) q^{32} +(-23.6951 + 12.6707i) q^{33} +(-16.8668 - 30.7084i) q^{34} +(45.0404 + 93.5274i) q^{35} +(-27.3912 - 23.3607i) q^{36} +(8.72637 - 13.8879i) q^{37} +(-16.9344 + 40.5813i) q^{38} +(9.67189 - 31.9043i) q^{39} +(17.7477 + 63.4802i) q^{40} +(-51.7371 + 51.7371i) q^{41} +(64.6615 - 39.1587i) q^{42} +(-2.01863 - 0.706350i) q^{43} +(0.188250 - 35.8263i) q^{44} +(61.6712 + 41.1757i) q^{45} +(6.50540 - 1.08774i) q^{46} +(49.9269 - 31.3712i) q^{47} +(44.7804 - 17.2833i) q^{48} +(24.4187 + 106.985i) q^{49} +(-32.6153 - 79.3292i) q^{50} +(39.6672 - 34.4728i) q^{51} +(31.2659 + 31.5962i) q^{52} +(0.423138 - 0.878656i) q^{53} +(25.5551 - 47.5703i) q^{54} +(8.26265 + 73.3330i) q^{55} +(4.85815 + 100.675i) q^{56} +(-64.8682 - 11.9480i) q^{57} +(-42.0816 + 39.9141i) q^{58} -67.8092 q^{59} +(-87.4325 + 46.1645i) q^{60} +(-6.75999 - 59.9966i) q^{61} +(3.28249 + 61.3278i) q^{62} +(77.9289 + 82.3695i) q^{63} +(-8.16731 + 63.4767i) q^{64} +(-71.5853 - 57.0874i) q^{65} +(52.5828 - 11.0936i) q^{66} +(11.6499 + 51.0414i) q^{67} +(15.2332 + 68.3954i) q^{68} +(3.65917 + 9.19201i) q^{69} +(-34.2390 - 204.772i) q^{70} +(-11.1173 - 2.53745i) q^{71} +(39.5493 + 60.1652i) q^{72} +(-3.22334 - 1.12789i) q^{73} +(-24.5173 + 21.7945i) q^{74} +(105.950 - 72.9908i) q^{75} +(55.1938 - 68.4697i) q^{76} +(-12.6348 + 112.137i) q^{77} +(-36.3992 + 55.8644i) q^{78} +(11.9669 - 19.0453i) q^{79} +(1.38535 - 131.822i) q^{80} +(77.8502 + 22.3684i) q^{81} +(128.261 - 70.4481i) q^{82} +(81.0372 + 101.617i) q^{83} +(-146.053 + 39.0718i) q^{84} +(-47.6707 - 136.235i) q^{85} +(3.48188 + 2.48430i) q^{86} +(-71.8706 - 49.0267i) q^{87} +(-20.3783 + 68.6948i) q^{88} +(-28.9409 - 82.7083i) q^{89} +(-95.4261 - 113.530i) q^{90} +(-87.2947 - 109.464i) q^{91} +(-13.1005 - 1.54583i) q^{92} +(-88.8675 + 24.2748i) q^{93} +(-113.406 + 32.3493i) q^{94} +(-96.3792 + 153.387i) q^{95} +(-95.6516 + 8.17085i) q^{96} +(-0.723496 + 6.42120i) q^{97} +(12.8816 - 219.095i) q^{98} +(32.9510 + 73.5681i) 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 $

$2$	−1.92037	−	0.558718i	−0.960187	−	0.279359i
$2$	−1.92037	−	0.558718i	−0.960187	−	0.279359i
$3$	0.209671	−	2.99266i	0.0698904	−	0.997555i
$3$	0.209671	−	2.99266i	0.0698904	−	0.997555i
$4$	3.37567	+	2.14590i	0.843917	+	0.536474i
$5$	−7.42336	−	3.57490i	−1.48467	−	0.714980i	−0.496458	−	0.868061i	$-0.665366\pi$
$5$	−7.42336	−	3.57490i	−1.48467	−	0.714980i	−0.988214	+	0.153081i	$0.951081\pi$
$6$	−2.07470	+	5.62989i	−0.345784	+	0.938314i
$7$	−9.85035	−	7.85539i	−1.40719	−	1.12220i	−0.975455	−	0.220199i	$-0.929329\pi$
$7$	−9.85035	−	7.85539i	−1.40719	−	1.12220i	−0.431737	−	0.901999i	$-0.642099\pi$
$8$	−5.28359	−	6.00697i	−0.660449	−	0.750871i
$9$	−8.91208	−	1.25495i	−0.990231	−	0.139439i
$10$	12.2583	+	11.0127i	1.22583	+	1.10127i
$11$	−4.76526	−	7.58386i	−0.433205	−	0.689442i	0.556773	−	0.830665i	$-0.312039\pi$
$11$	−4.76526	−	7.58386i	−0.433205	−	0.689442i	−0.989978	+	0.141223i	$0.954897\pi$
$12$	7.12972	−	9.65231i	0.594144	−	0.804359i
$13$	10.8341	+	2.47281i	0.833392	+	0.190216i	0.617868	−	0.786282i	$-0.287997\pi$
$13$	10.8341	+	2.47281i	0.833392	+	0.190216i	0.215524	+	0.976498i	$0.430854\pi$
$14$	14.5274	+	20.5888i	1.03767	+	1.47063i
$15$	−12.2549	+	21.4661i	−0.816996	+	1.43107i
$16$	6.79027	+	14.4877i	0.424392	+	0.905479i
$17$	12.3870	+	12.3870i	0.728645	+	0.728645i	0.970350	−	0.241705i	$-0.0777066\pi$
$17$	12.3870	+	12.3870i	0.728645	+	0.728645i	−0.241705	+	0.970350i	$0.577707\pi$
$18$	16.4134	+	7.38931i	0.911853	+	0.410517i
$19$	2.46170	−	21.8482i	0.129563	−	1.14991i	−0.745708	−	0.666273i	$-0.767889\pi$
$19$	2.46170	−	21.8482i	0.129563	−	1.14991i	0.875271	−	0.483632i	$-0.160683\pi$
$20$	−17.3874	−	27.9974i	−0.869371	−	1.39987i
$21$	−25.5739	+	27.8317i	−1.21780	+	1.32532i
$22$	4.91383	+	17.2263i	0.223356	+	0.783013i
$23$	−2.97127	+	1.43089i	−0.129185	+	0.0622124i	−0.497360	−	0.867544i	$-0.665697\pi$
$23$	−2.97127	+	1.43089i	−0.129185	+	0.0622124i	0.368175	+	0.929757i	$0.379983\pi$
$24$	−19.0847	+	14.5525i	−0.795194	+	0.606355i
$25$	26.7391	+	33.5297i	1.06956	+	1.34119i
$26$	−19.4239	−	10.8019i	−0.747073	−	0.415459i
$27$	−5.62425	+	26.4077i	−0.208306	+	0.978064i
$28$	−16.3947	−	47.6550i	−0.585523	−	1.70196i
$29$	14.6279	−	25.0405i	0.504411	−	0.863464i
$29$	14.6279	−	25.0405i	0.504411	−	0.863464i
$30$	35.5275	−	34.3758i	1.18425	−	1.14586i
$31$	−10.1421	−	28.9846i	−0.327166	−	0.934986i	−0.983562	−	0.180570i	$-0.942206\pi$
$31$	−10.1421	−	28.9846i	−0.327166	−	0.934986i	0.656397	−	0.754416i	$-0.272080\pi$
$32$	−4.94533	−	31.6156i	−0.154542	−	0.987986i
$33$	−23.6951	+	12.6707i	−0.718033	+	0.383960i
$34$	−16.8668	−	30.7084i	−0.496082	−	0.903189i
$35$	45.0404	+	93.5274i	1.28687	+	2.67221i
$36$	−27.3912	−	23.3607i	−0.760867	−	0.648908i
$37$	8.72637	−	13.8879i	0.235848	−	0.375350i	−0.707739	−	0.706474i	$-0.750285\pi$
$37$	8.72637	−	13.8879i	0.235848	−	0.375350i	0.943587	+	0.331124i	$0.107428\pi$
$38$	−16.9344	+	40.5813i	−0.445641	+	1.06793i
$39$	9.67189	−	31.9043i	0.247997	−	0.818060i
$40$	17.7477	+	63.4802i	0.443692	+	1.58700i
$41$	−51.7371	+	51.7371i	−1.26188	+	1.26188i	−0.311699	+	0.950181i	$0.600898\pi$
$41$	−51.7371	+	51.7371i	−1.26188	+	1.26188i	−0.950181	+	0.311699i	$0.899102\pi$
$42$	64.6615	−	39.1587i	1.53956	−	0.932351i
$43$	−2.01863	−	0.706350i	−0.0469450	−	0.0164268i	0.306704	−	0.951805i	$-0.400774\pi$
$43$	−2.01863	−	0.706350i	−0.0469450	−	0.0164268i	−0.353649	+	0.935378i	$0.615059\pi$
$44$	0.188250	−	35.8263i	0.00427840	−	0.814235i
$45$	61.6712	+	41.1757i	1.37047	+	0.915016i
$46$	6.50540	−	1.08774i	0.141422	−	0.0236464i
$47$	49.9269	−	31.3712i	1.06228	−	0.667472i	0.116796	−	0.993156i	$-0.462737\pi$
$47$	49.9269	−	31.3712i	1.06228	−	0.667472i	0.945479	+	0.325684i	$0.105595\pi$
$48$	44.7804	−	17.2833i	0.932925	−	0.360070i
$49$	24.4187	+	106.985i	0.498340	+	2.18337i
$50$	−32.6153	−	79.3292i	−0.652307	−	1.58658i
$51$	39.6672	−	34.4728i	0.777788	−	0.675938i
$52$	31.2659	+	31.5962i	0.601268	+	0.607620i
$53$	0.423138	−	0.878656i	0.00798374	−	0.0165784i	−0.896939	−	0.442155i	$-0.854214\pi$
$53$	0.423138	−	0.878656i	0.00798374	−	0.0165784i	0.904923	+	0.425576i	$0.139929\pi$
$54$	25.5551	−	47.5703i	0.473243	−	0.880932i
$55$	8.26265	+	73.3330i	0.150230	+	1.33333i
$56$	4.85815	+	100.675i	0.0867527	+	1.79777i
$57$	−64.8682	−	11.9480i	−1.13804	−	0.209614i
$58$	−42.0816	+	39.9141i	−0.725545	+	0.688175i
$59$	−67.8092			−1.14931			−0.574654	−	0.818396i	$-0.694863\pi$
$59$	−67.8092			−1.14931			−0.574654	+	0.818396i	$0.694863\pi$
$60$	−87.4325	+	46.1645i	−1.45721	+	0.769408i
$61$	−6.75999	−	59.9966i	−0.110820	−	0.983551i	−0.918903	−	0.394483i	$-0.870924\pi$
$61$	−6.75999	−	59.9966i	−0.110820	−	0.983551i	0.808084	−	0.589068i	$-0.200505\pi$
$62$	3.28249	+	61.3278i	0.0529433	+	0.989157i
$63$	77.9289	+	82.3695i	1.23697	+	1.30745i
$64$	−8.16731	+	63.4767i	−0.127614	+	0.991824i
$65$	−71.5853	−	57.0874i	−1.10131	−	0.878267i
$66$	52.5828	−	11.0936i	0.796709	−	0.168085i
$67$	11.6499	+	51.0414i	0.173879	+	0.761813i	0.984377	+	0.176072i	$0.0563391\pi$
$67$	11.6499	+	51.0414i	0.173879	+	0.761813i	−0.810499	+	0.585741i	$0.800804\pi$
$68$	15.2332	+	68.3954i	0.224017	+	1.00581i
$69$	3.65917	+	9.19201i	0.0530315	+	0.133218i
$70$	−34.2390	−	204.772i	−0.489128	−	2.92532i
$71$	−11.1173	−	2.53745i	−0.156582	−	0.0357388i	0.143511	−	0.989649i	$-0.454161\pi$
$71$	−11.1173	−	2.53745i	−0.156582	−	0.0357388i	−0.300093	+	0.953910i	$0.597018\pi$
$72$	39.5493	+	60.1652i	0.549296	+	0.835628i
$73$	−3.22334	−	1.12789i	−0.0441553	−	0.0154506i	0.308111	−	0.951350i	$-0.400303\pi$
$73$	−3.22334	−	1.12789i	−0.0441553	−	0.0154506i	−0.352266	+	0.935900i	$0.614589\pi$
$74$	−24.5173	+	21.7945i	−0.331315	+	0.294520i
$75$	105.950	−	72.9908i	1.41266	−	0.973211i
$76$	55.1938	−	68.4697i	0.726234	−	0.900917i
$77$	−12.6348	+	112.137i	−0.164088	+	1.45632i
$78$	−36.3992	+	55.8644i	−0.466656	+	0.716210i
$79$	11.9669	−	19.0453i	0.151480	−	0.241079i	−0.762360	−	0.647153i	$-0.775960\pi$
$79$	11.9669	−	19.0453i	0.151480	−	0.241079i	0.913840	+	0.406074i	$0.133102\pi$
$80$	1.38535	−	131.822i	0.0173169	−	1.64777i
$81$	77.8502	+	22.3684i	0.961114	+	0.276153i
$82$	128.261	−	70.4481i	1.56416	−	0.859123i
$83$	81.0372	+	101.617i	0.976351	+	1.22431i	0.974518	+	0.224308i	$0.0720121\pi$
$83$	81.0372	+	101.617i	0.976351	+	1.22431i	0.00183311	+	0.999998i	$0.499417\pi$
$84$	−146.053	+	39.0718i	−1.73872	+	0.465141i
$85$	−47.6707	−	136.235i	−0.560832	−	1.60276i
$86$	3.48188	+	2.48430i	0.0404870	+	0.0288873i
$87$	−71.8706	−	49.0267i	−0.826099	−	0.563525i
$88$	−20.3783	+	68.6948i	−0.231572	+	0.780622i
$89$	−28.9409	−	82.7083i	−0.325178	−	0.929307i	−0.984181	−	0.177166i	$-0.943307\pi$
$89$	−28.9409	−	82.7083i	−0.325178	−	0.929307i	0.659003	−	0.752141i	$-0.270979\pi$
$90$	−95.4261	−	113.530i	−1.06029	−	1.26144i
$91$	−87.2947	−	109.464i	−0.959283	−	1.20290i
$92$	−13.1005	−	1.54583i	−0.142397	−	0.0168025i
$93$	−88.8675	+	24.2748i	−0.955565	+	0.261019i
$94$	−113.406	+	32.3493i	−1.20645	+	0.344141i
$95$	−96.3792	+	153.387i	−1.01452	+	1.61460i
$96$	−95.6516	+	8.17085i	−0.996371	+	0.0851130i
$97$	−0.723496	+	6.42120i	−0.00745872	+	0.0661980i	−0.996890	−	0.0788034i	$-0.974890\pi$
$97$	−0.723496	+	6.42120i	−0.00745872	+	0.0661980i	0.989431	+	0.145001i	$0.0463186\pi$
$98$	12.8816	−	219.095i	0.131445	−	2.23566i
$99$	32.9510	+	73.5681i	0.332838	+	0.743112i
$100$	18.3109	+	170.564i	0.183109	+	1.70564i
$101$	−22.9053	−	8.01491i	−0.226785	−	0.0793556i	0.214494	−	0.976725i	$-0.431190\pi$
$101$	−22.9053	−	8.01491i	−0.226785	−	0.0793556i	−0.441280	+	0.897370i	$0.645475\pi$
$102$	−95.4365	+	44.0379i	−0.935652	+	0.431744i
$103$	−46.0913	−	10.5200i	−0.447488	−	0.102136i	−0.00716250	−	0.999974i	$-0.502280\pi$
$103$	−46.0913	−	10.5200i	−0.447488	−	0.102136i	−0.440326	+	0.897838i	$0.645137\pi$
$104$	−42.3889	−	78.1454i	−0.407585	−	0.751398i
$105$	289.340	−	115.181i	2.75562	−	1.09696i
$106$	−1.30350	+	1.45093i	−0.0122972	+	0.0136880i
$107$	−11.3705	−	49.8175i	−0.106267	−	0.465584i	−0.999860	−	0.0167077i	$-0.994682\pi$
$107$	−11.3705	−	49.8175i	−0.106267	−	0.465584i	0.893594	−	0.448876i	$-0.148176\pi$
$108$	−75.6538	+	77.0747i	−0.700498	+	0.713654i
$109$	−88.0007	−	70.1782i	−0.807346	−	0.643837i	0.130282	−	0.991477i	$-0.458412\pi$
$109$	−88.0007	−	70.1782i	−0.807346	−	0.643837i	−0.937628	+	0.347640i	$0.886983\pi$
$110$	25.1051	−	145.443i	0.228228	−	1.32221i
$111$	−39.7323	−	29.0270i	−0.357948	−	0.261505i
$112$	46.9197	−	196.049i	0.418926	−	1.75043i
$113$	11.5081	+	102.137i	0.101841	+	0.903867i	0.935918	+	0.352218i	$0.114572\pi$
$113$	11.5081	+	102.137i	0.101841	+	0.903867i	−0.834077	+	0.551649i	$0.813999\pi$
$114$	117.896	+	59.1876i	1.03417	+	0.519189i
$115$	27.1720			0.236279
$116$	103.113	−	53.1383i	0.888907	−	0.458089i
$117$	−93.4510	−	35.6341i	−0.798727	−	0.304565i
$118$	130.219	+	37.8862i	1.10355	+	0.321070i
$119$	−24.7115	−	219.320i	−0.207659	−	1.84303i
$120$	193.696	−	39.8029i	1.61413	−	0.331691i
$121$	17.6926	−	36.7391i	0.146220	−	0.303629i
$122$	−20.5395	+	118.993i	−0.168356	+	0.975351i
$123$	143.984	+	165.679i	1.17060	+	1.34699i
$124$	27.9613	−	119.606i	0.225495	−	0.964566i
$125$	−32.7928	−	143.674i	−0.262342	−	1.14940i
$126$	−103.631	−	201.721i	−0.822470	−	1.60096i
$127$	33.8975	−	21.2992i	0.266909	−	0.167710i	−0.391927	−	0.919996i	$-0.628192\pi$
$127$	33.8975	−	21.2992i	0.266909	−	0.167710i	0.658837	+	0.752286i	$0.271049\pi$
$128$	51.1499	−	117.336i	0.399608	−	0.916686i
$129$	−2.53712	+	5.89299i	−0.0196676	+	0.0456821i
$130$	105.575	+	149.625i	0.812114	+	1.15096i
$131$	−126.950	−	44.4218i	−0.969085	−	0.339098i	−0.201104	−	0.979570i	$-0.564453\pi$
$131$	−126.950	−	44.4218i	−0.969085	−	0.339098i	−0.767981	+	0.640472i	$0.778739\pi$
$132$	−107.177	−	8.07512i	−0.811945	−	0.0611751i
$133$	−195.875	+	195.875i	−1.47274	+	1.47274i
$134$	6.14567	−	104.528i	0.0458632	−	0.780057i
$135$	136.156	−	175.928i	1.00856	−	1.30317i
$136$	8.96042	−	139.856i	0.0658854	−	1.02835i
$137$	27.6837	−	44.0584i	0.202071	−	0.321594i	−0.730280	−	0.683148i	$-0.760611\pi$
$137$	27.6837	−	44.0584i	0.202071	−	0.321594i	0.932351	+	0.361553i	$0.117753\pi$
$138$	−1.89123	−	19.6965i	−0.0137046	−	0.142729i
$139$	−51.1707	−	106.257i	−0.368135	−	0.764440i	0.631808	−	0.775125i	$-0.282313\pi$
$139$	−51.1707	−	106.257i	−0.368135	−	0.764440i	−0.999943	+	0.0106851i	$0.996599\pi$
$140$	−48.6585	+	412.369i	−0.347560	+	2.94549i
$141$	−83.4151	−	155.992i	−0.591597	−	1.10633i
$142$	19.9317	+	11.0843i	0.140364	+	0.0780585i
$143$	−32.8738	−	93.9479i	−0.229887	−	0.656978i
$144$	−42.3341	−	137.637i	−0.293987	−	0.955809i
$145$	−198.105	+	133.591i	−1.36624	+	0.921316i
$146$	5.55984	+	3.96692i	0.0380811	+	0.0271707i
$147$	325.290	−	50.6451i	2.21286	−	0.344525i
$148$	59.2594	−	28.1552i	0.400401	−	0.190238i
$149$	143.830	+	180.357i	0.965303	+	1.21045i	0.977588	+	0.210527i	$0.0675179\pi$
$149$	143.830	+	180.357i	0.965303	+	1.21045i	−0.0122854	+	0.999925i	$0.503911\pi$
$150$	−244.244	+	80.9737i	−1.62829	+	0.539824i
$151$	−181.270	+	87.2952i	−1.20047	+	0.578114i	−0.923809	−	0.382855i	$-0.874941\pi$
$151$	−181.270	+	87.2952i	−1.20047	+	0.578114i	−0.276658	+	0.960969i	$0.589227\pi$
$152$	−144.248	+	100.650i	−0.949000	+	0.662168i
$153$	−94.8485	−	125.939i	−0.619925	−	0.823128i
$154$	86.9162	−	208.285i	0.564391	−	1.35250i
$155$	−28.3282	+	251.420i	−0.182763	+	1.62206i
$156$	101.112	−	86.9436i	0.648157	−	0.557331i
$157$	168.898	+	168.898i	1.07578	+	1.07578i	0.996883	+	0.0788995i	$0.0251406\pi$
$157$	168.898	+	168.898i	1.07578	+	1.07578i	0.0788995	+	0.996883i	$0.474859\pi$
$158$	−33.6219	+	29.8879i	−0.212797	+	0.189164i
$159$	−2.54080	−	1.45054i	−0.0159799	−	0.00912289i
$160$	−76.3115	+	252.373i	−0.476947	+	1.57733i
$161$	40.5082	+	9.24572i	0.251603	+	0.0574269i
$162$	−137.004	−	86.4521i	−0.845702	−	0.533655i
$163$	123.311	+	196.248i	0.756508	+	1.20398i	0.973697	+	0.227846i	$0.0731683\pi$
$163$	123.311	+	196.248i	0.756508	+	1.20398i	−0.217189	+	0.976130i	$0.569689\pi$
$164$	−285.670	+	63.6248i	−1.74189	+	0.387956i
$165$	221.194	−	9.35151i	1.34057	−	0.0566758i
$166$	−98.8461	−	240.420i	−0.595459	−	1.44832i
$167$	−156.400	−	124.725i	−0.936525	−	0.746854i	0.0310287	−	0.999518i	$-0.490122\pi$
$167$	−156.400	−	124.725i	−0.936525	−	0.746854i	−0.967554	+	0.252664i	$0.918693\pi$
$168$	302.306	+	6.56991i	1.79944	+	0.0391066i
$169$	−41.0009	−	19.7450i	−0.242609	−	0.116834i
$170$	15.4285	+	288.257i	0.0907562	+	1.69563i
$171$	−49.3573	+	191.623i	−0.288639	+	1.12061i
$172$	−5.29848	−	6.71618i	−0.0308051	−	0.0390476i
$173$	54.3576			0.314206			0.157103	−	0.987582i	$-0.449785\pi$
$173$	54.3576			0.314206			0.157103	+	0.987582i	$0.449785\pi$
$174$	110.626	+	134.305i	0.635783	+	0.771868i
$175$		−	540.325i		−	3.08757i
$176$	77.5150	−	120.534i	0.440426	−	0.684851i
$177$	−14.2176	+	202.930i	−0.0803256	+	1.14650i
$178$	9.36667	+	175.001i	0.0526218	+	0.983149i
$179$	41.2458	−	85.6477i	0.230423	−	0.478479i	−0.753413	−	0.657547i	$-0.771594\pi$
$179$	41.2458	−	85.6477i	0.230423	−	0.478479i	0.983837	+	0.179068i	$0.0573083\pi$
$180$	119.823	+	271.336i	0.665682	+	1.50742i
$181$	7.03803	−	8.82541i	0.0388841	−	0.0487592i	−0.762009	−	0.647566i	$-0.775787\pi$
$181$	7.03803	−	8.82541i	0.0388841	−	0.0487592i	0.800893	+	0.598807i	$0.204358\pi$
$182$	106.479	+	258.985i	0.585049	+	1.42300i
$183$	−180.967	+	7.65083i	−0.988891	+	0.0418078i
$184$	24.2942	+	10.2881i	0.132034	+	0.0559135i
$185$	−114.427	+	71.8992i	−0.618524	+	0.388645i
$186$	184.222	+	3.03528i	0.990439	+	0.0163187i
$187$	34.9140	−	152.968i	0.186706	−	0.818011i
$188$	235.856	+	1.23931i	1.25455	+	0.00659205i
$189$	262.844	−	215.945i	1.39071	−	1.14256i
$190$	270.784	−	240.711i	1.42518	−	1.26690i
$191$	27.7867	−	27.7867i	0.145480	−	0.145480i	−0.630615	−	0.776096i	$-0.717197\pi$
$191$	27.7867	−	27.7867i	0.145480	−	0.145480i	0.776096	+	0.630615i	$0.217197\pi$
$192$	188.252	+	37.7512i	0.980480	+	0.196621i
$193$	−347.108	−	39.1097i	−1.79849	−	0.202641i	−0.851596	−	0.524199i	$-0.824365\pi$
$193$	−347.108	−	39.1097i	−1.79849	−	0.202641i	−0.946890	+	0.321558i	$0.895794\pi$
$194$	4.97703	−	11.9269i	0.0256548	−	0.0614788i
$195$	−185.853	+	202.261i	−0.953091	+	1.03724i
$196$	−147.150	+	413.546i	−0.750763	+	2.10993i
$197$	24.2005	+	50.2528i	0.122845	+	0.255090i	0.953318	−	0.301969i	$-0.0976439\pi$
$197$	24.2005	+	50.2528i	0.122845	+	0.255090i	−0.830473	+	0.557059i	$0.811930\pi$
$198$	−22.1743	−	159.689i	−0.111991	−	0.806508i
$199$	−113.887	+	90.8221i	−0.572298	+	0.456393i	−0.866378	−	0.499388i	$-0.833558\pi$
$199$	−113.887	+	90.8221i	−0.572298	+	0.456393i	0.294080	+	0.955781i	$0.404987\pi$
$200$	60.1337	−	337.778i	0.300668	−	1.68889i
$201$	155.193	−	24.1622i	0.772102	−	0.120210i
$202$	39.5087	+	28.1892i	0.195587	+	0.139551i
$203$	−340.792	+	131.749i	−1.67878	+	0.649011i
$204$	207.878	−	31.2472i	1.01901	−	0.153172i
$205$	569.018	−	199.108i	2.77570	−	0.971258i
$206$	82.6348	+	45.9544i	0.401140	+	0.223080i
$207$	28.2758	−	9.02337i	0.136598	−	0.0435912i
$208$	37.7412	+	173.752i	0.181448	+	0.835345i
$209$	−177.424	+	85.4431i	−0.848920	+	0.408818i
$210$	−619.994	+	59.5308i	−2.95235	+	0.283480i
$211$	300.761	+	188.981i	1.42541	+	0.895644i	0.999956	−	0.00933739i	$-0.00297223\pi$
$211$	300.761	+	188.981i	1.42541	+	0.895644i	0.425452	+	0.904981i	$0.360115\pi$
$212$	3.31388	−	2.05804i	0.0156315	−	0.00970773i
$213$	−9.92473	+	32.7384i	−0.0465950	+	0.153701i
$214$	−5.99830	+	102.021i	−0.0280294	+	0.476734i
$215$	12.4599	+	12.4599i	0.0579530	+	0.0579530i
$216$	188.347	−	105.743i	0.871975	−	0.489551i
$217$	−127.781	+	365.178i	−0.588854	+	1.68285i
$218$	129.784	+	183.936i	0.595341	+	0.843743i
$219$	−4.05125	+	9.40988i	−0.0184989	+	0.0429675i
$220$	−129.473	+	265.279i	−0.588514	+	1.20581i
$221$	103.571	+	164.832i	0.468647	+	0.745847i
$222$	60.0829	+	77.9418i	0.270644	+	0.351089i
$223$	−340.960	+	77.8220i	−1.52897	+	0.348978i	−0.902577	−	0.430529i	$-0.858327\pi$
$223$	−340.960	+	77.8220i	−1.52897	+	0.348978i	−0.626394	+	0.779507i	$0.715470\pi$
$224$	−199.639	+	350.272i	−0.891247	+	1.56371i
$225$	−196.222	−	332.376i	−0.872100	−	1.47723i
$226$	34.9660	−	202.571i	0.154717	−	0.896331i
$227$	229.770	+	110.651i	1.01220	+	0.487451i	0.865062	−	0.501665i	$-0.167279\pi$
$227$	229.770	+	110.651i	1.01220	+	0.487451i	0.147140	+	0.989116i	$0.452993\pi$
$228$	−193.334	−	179.533i	−0.847957	−	0.787424i
$229$	−25.2875	+	2.84922i	−0.110426	+	0.0124420i	−0.167004	−	0.985956i	$-0.553409\pi$
$229$	−25.2875	+	2.84922i	−0.110426	+	0.0124420i	0.0565786	+	0.998398i	$0.481981\pi$
$230$	−52.1805	−	15.1815i	−0.226872	−	0.0660066i
$231$	332.938	+	61.3234i	1.44129	+	0.265469i
$232$	−227.705	+	44.4342i	−0.981487	+	0.191527i
$233$		−	216.468i		−	0.929045i	−0.885561	−	0.464523i	$-0.846226\pi$
$233$		−	216.468i		−	0.929045i	0.885561	−	0.464523i	$-0.153774\pi$
$234$	159.551	+	120.644i	0.681844	+	0.515571i
$235$	−482.774	+	54.3956i	−2.05436	+	0.231471i
$236$	−228.901	−	145.511i	−0.969921	−	0.616574i
$237$	−54.4869	−	39.8062i	−0.229903	−	0.167959i
$238$	−75.0830	+	434.984i	−0.315475	+	1.82766i
$239$	17.6884	−	22.1805i	0.0740099	−	0.0928054i	−0.743448	−	0.668793i	$-0.766811\pi$
$239$	17.6884	−	22.1805i	0.0740099	−	0.0928054i	0.817458	+	0.575988i	$0.195382\pi$
$240$	−394.207	−	31.7851i	−1.64253	−	0.132438i
$241$	85.0984	−	19.4231i	0.353105	−	0.0805940i	−0.0422892	−	0.999105i	$-0.513465\pi$
$241$	85.0984	−	19.4231i	0.353105	−	0.0805940i	0.395394	+	0.918511i	$0.370608\pi$
$242$	−54.5033	+	60.6677i	−0.225220	+	0.250693i
$243$	83.2641	−	228.289i	0.342651	−	0.939463i
$244$	105.927	−	217.035i	0.434127	−	0.889487i
$245$	201.193	−	881.483i	0.821195	−	3.59789i
$246$	−183.935	−	398.613i	−0.747702	−	1.62038i
$247$	80.6968	−	230.618i	0.326708	−	0.933677i
$248$	−120.522	+	214.066i	−0.485977	+	0.863169i
$249$	321.098	−	221.211i	1.28955	−	0.888397i
$250$	−17.2992	+	294.231i	−0.0691968	+	1.17692i
$251$	110.753	+	12.4789i	0.441248	+	0.0497167i	0.329794	−	0.944053i	$-0.393021\pi$
$251$	110.753	+	12.4789i	0.441248	+	0.0497167i	0.111454	+	0.993770i	$0.464449\pi$
$252$	86.3058	+	445.279i	0.342483	+	1.76698i
$253$	25.0105	+	15.7151i	0.0988557	+	0.0621151i
$254$	−76.9961	+	21.9633i	−0.303134	+	0.0864696i
$255$	−417.701	+	114.098i	−1.63804	+	0.447442i
$256$	−163.785	+	196.750i	−0.639783	+	0.768555i
$257$	349.010	−	278.326i	1.35801	−	1.08298i	0.369932	−	0.929059i	$-0.379381\pi$
$257$	349.010	−	278.326i	1.35801	−	1.08298i	0.988083	−	0.153922i	$-0.0491903\pi$
$258$	8.16474	−	9.89921i	0.0316463	−	0.0383690i
$259$	−195.053	+	68.2520i	−0.753100	+	0.263521i
$260$	−119.145	−	346.323i	−0.458249	−	1.33201i
$261$	−161.790	+	204.805i	−0.619883	+	0.784694i
$262$	218.972	+	156.236i	0.835773	+	0.596320i
$263$	−152.957	+	53.5221i	−0.581587	+	0.203506i	−0.605008	−	0.796220i	$-0.706830\pi$
$263$	−152.957	+	53.5221i	−0.581587	+	0.203506i	0.0234209	+	0.999726i	$0.492544\pi$
$264$	201.308	+	75.3888i	0.762529	+	0.285564i
$265$	−6.28221	+	5.00990i	−0.0237065	+	0.0189053i
$266$	485.591	−	266.714i	1.82553	−	1.00268i
$267$	−253.586	+	69.2688i	−0.949761	+	0.259434i
$268$	−70.2035	+	197.298i	−0.261953	+	0.736188i
$269$	30.3333	+	19.0597i	0.112763	+	0.0708538i	0.587233	−	0.809418i	$-0.300217\pi$
$269$	30.3333	+	19.0597i	0.112763	+	0.0708538i	−0.474470	+	0.880272i	$0.657360\pi$
$270$	−359.764	+	261.774i	−1.33246	+	0.969535i
$271$	−105.443	−	11.8806i	−0.389088	−	0.0438397i	−0.0847462	−	0.996403i	$-0.527008\pi$
$271$	−105.443	−	11.8806i	−0.389088	−	0.0438397i	−0.304342	+	0.952563i	$0.598437\pi$
$272$	−95.3473	+	263.569i	−0.350542	+	0.969003i
$273$	−345.892	+	238.292i	−1.26701	+	0.872866i
$274$	−77.7794	+	69.1412i	−0.283866	+	0.252340i
$275$	126.866	−	362.563i	0.461332	−	1.31841i
$276$	−7.37295	+	38.8814i	−0.0267136	+	0.140875i
$277$	43.8368	−	192.062i	0.158256	−	0.693364i	−0.832078	−	0.554659i	$-0.812849\pi$
$277$	43.8368	−	192.062i	0.158256	−	0.693364i	0.990334	−	0.138705i	$-0.0442940\pi$
$278$	38.8991	+	232.643i	0.139925	+	0.836847i
$279$	54.0133	+	271.040i	0.193596	+	0.971471i
$280$	323.841	−	764.717i	1.15657	−	2.73113i
$281$	393.484	−	89.8101i	1.40030	−	0.319609i	0.545300	−	0.838241i	$-0.316416\pi$
$281$	393.484	−	89.8101i	1.40030	−	0.319609i	0.854997	+	0.518632i	$0.173559\pi$
$282$	73.0325	+	346.169i	0.258981	+	1.22755i
$283$	−115.562	+	144.911i	−0.408347	+	0.512051i	−0.942896	−	0.333086i	$-0.891910\pi$
$283$	−115.562	+	144.911i	−0.408347	+	0.512051i	0.534549	+	0.845137i	$0.320481\pi$
$284$	−32.0832	−	32.4222i	−0.112969	−	0.114163i
$285$	438.827	+	320.591i	1.53974	+	1.12488i
$286$	10.6396	+	198.782i	0.0372012	+	0.695043i
$287$	916.043	−	103.213i	3.19179	−	0.359628i
$288$	4.39721	+	287.966i	0.0152681	+	0.999883i
$289$			17.8738i			0.0618470i
$290$	455.076	−	145.859i	1.56923	−	0.502963i
$291$	19.0648	+	3.51152i	0.0655148	+	0.0120671i
$292$	−8.46057	−	10.7243i	−0.0289746	−	0.0367272i
$293$	242.837	−	27.3612i	0.828795	−	0.0933828i	0.312633	−	0.949874i	$-0.398789\pi$
$293$	242.837	−	27.3612i	0.828795	−	0.0933828i	0.516162	+	0.856491i	$0.327360\pi$
$294$	−652.975	−	84.4881i	−2.22101	−	0.287374i
$295$	503.372	+	242.411i	1.70634	+	0.821732i
$296$	−129.531	+	20.9592i	−0.437605	+	0.0708081i
$297$	227.074	−	83.1860i	0.764557	−	0.280088i
$298$	−175.439	−	426.714i	−0.588720	−	1.43193i
$299$	−35.7293	+	8.15498i	−0.119496	+	0.0272742i
$300$	514.281	−	19.0360i	1.71427	−	0.0634534i
$301$	14.3356	+	22.8149i	0.0476265	+	0.0757972i
$302$	396.880	−	66.3603i	1.31417	−	0.219736i
$303$	−28.7885	+	66.8674i	−0.0950116	+	0.220684i
$304$	333.245	−	112.691i	1.09620	−	0.370694i
$305$	−164.300	+	469.542i	−0.538688	+	1.53948i
$306$	111.780	+	294.843i	0.365296	+	0.963538i
$307$	113.195	+	113.195i	0.368715	+	0.368715i	0.867008	−	0.498294i	$-0.166040\pi$
$307$	113.195	+	113.195i	0.368715	+	0.368715i	−0.498294	+	0.867008i	$0.666040\pi$
$308$	−283.284	+	351.423i	−0.919754	+	1.14098i
$309$	−41.1469	+	135.730i	−0.133162	+	0.439256i
$310$	194.874	−	466.992i	0.628624	−	1.50643i
$311$	−232.388	−	146.019i	−0.747228	−	0.469514i	0.103824	−	0.994596i	$-0.466892\pi$
$311$	−232.388	−	146.019i	−0.747228	−	0.469514i	−0.851052	+	0.525081i	$0.824035\pi$
$312$	−242.751	+	110.471i	−0.778047	+	0.354073i
$313$	−4.36835	+	2.10369i	−0.0139564	+	0.00672105i	−0.440849	−	0.897581i	$-0.645323\pi$
$313$	−4.36835	+	2.10369i	−0.0139564	+	0.00672105i	0.426893	+	0.904302i	$0.359608\pi$
$314$	−229.981	−	418.713i	−0.732422	−	1.33348i
$315$	−284.031	−	890.046i	−0.901687	−	2.82554i
$316$	81.2655	−	38.6107i	0.257169	−	0.122186i
$317$	1.80121	−	0.630271i	0.00568205	−	0.00198824i	−0.327437	−	0.944873i	$-0.606185\pi$
$317$	1.80121	−	0.630271i	0.00568205	−	0.00198824i	0.333119	+	0.942885i	$0.391899\pi$
$318$	4.06884	+	4.20517i	0.0127951	+	0.0132238i
$319$	−259.609	+	8.38811i	−0.813822	+	0.0262950i
$320$	287.552	−	442.013i	0.898599	−	1.38129i
$321$	−151.471	+	23.5828i	−0.471873	+	0.0734668i
$322$	−72.6250	−	40.3879i	−0.225544	−	0.125428i
$323$	301.126	−	240.140i	0.932278	−	0.743467i
$324$	214.796	+	242.567i	0.662951	+	0.748663i
$325$	206.781	+	429.385i	0.636249	+	1.32118i
$326$	−127.155	−	445.765i	−0.390047	−	1.36738i
$327$	−228.471	+	248.642i	−0.698688	+	0.760373i
$328$	584.140	+	37.4253i	1.78092	+	0.114102i
$329$	−738.230	−	83.1786i	−2.24386	−	0.252822i
$330$	−429.999	−	105.626i	−1.30303	−	0.320080i
$331$	−32.8915	+	32.8915i	−0.0993700	+	0.0993700i	−0.755044	−	0.655674i	$-0.772385\pi$
$331$	−32.8915	+	32.8915i	−0.0993700	+	0.0993700i	0.655674	+	0.755044i	$0.272385\pi$
$332$	55.4943	+	516.924i	0.167152	+	1.55700i
$333$	−95.1988	+	112.819i	−0.285882	+	0.338797i
$334$	230.660	+	326.901i	0.690599	+	0.978746i
$335$	95.9869	−	420.546i	0.286528	−	1.25536i
$336$	−576.870	−	181.521i	−1.71688	−	0.540240i
$337$	−386.252	+	242.698i	−1.14615	+	0.720172i	−0.964732	−	0.263235i	$-0.915211\pi$
$337$	−386.252	+	242.698i	−1.14615	+	0.720172i	−0.181415	+	0.983407i	$0.558068\pi$
$338$	67.7051	+	60.8257i	0.200311	+	0.179958i
$339$	308.074	−	13.0246i	0.908774	−	0.0384207i
$340$	131.426	−	562.180i	0.386546	−	1.65347i
$341$	−171.485	+	215.035i	−0.502888	+	0.630602i
$342$	201.848	−	340.412i	0.590199	−	0.995356i
$343$	332.018	−	689.442i	0.967981	−	2.01003i
$344$	6.42261	+	15.8579i	0.0186704	+	0.0460986i
$345$	5.69719	−	81.3168i	0.0165136	−	0.235701i
$346$	−104.387	−	30.3706i	−0.301696	−	0.0877762i
$347$		−	107.269i		−	0.309133i	−0.987982	−	0.154567i	$-0.950602\pi$
$347$		−	107.269i		−	0.309133i	0.987982	−	0.154567i	$-0.0493981\pi$
$348$	−137.405	−	319.725i	−0.394842	−	0.918749i
$349$	−242.414			−0.694595			−0.347298	−	0.937755i	$-0.612901\pi$
$349$	−242.414			−0.694595			−0.347298	+	0.937755i	$0.612901\pi$
$350$	−301.890	+	1037.63i	−0.862542	+	2.96465i
$351$	−126.235	+	272.196i	−0.359644	+	0.775488i
$352$	−216.202	+	188.161i	−0.614211	+	0.534548i
$353$	−217.639	−	104.809i	−0.616541	−	0.296911i	0.0994255	−	0.995045i	$-0.468300\pi$
$353$	−217.639	−	104.809i	−0.616541	−	0.296911i	−0.715967	+	0.698134i	$0.754014\pi$
$354$	140.684	−	381.758i	0.397412	−	1.07841i
$355$	73.4566	+	58.5797i	0.206920	+	0.165013i
$356$	79.7885	−	341.300i	0.224125	−	0.958707i
$357$	−661.533	+	27.9680i	−1.85303	+	0.0783417i
$358$	−127.060	+	141.431i	−0.354917	+	0.395058i
$359$	158.797	+	252.724i	0.442332	+	0.703967i	0.991263	−	0.131900i	$-0.0421079\pi$
$359$	158.797	+	252.724i	0.442332	+	0.703967i	−0.548931	+	0.835868i	$0.684965\pi$
$360$	−78.5042	−	588.013i	−0.218067	−	1.63337i
$361$	−119.335	−	27.2374i	−0.330567	−	0.0754498i
$362$	−18.4466	+	13.0158i	−0.0509574	+	0.0359553i
$363$	−106.238	−	60.6513i	−0.292667	−	0.167083i
$364$	−59.7795	−	556.840i	−0.164229	−	1.52978i
$365$	19.8959	+	19.8959i	0.0545092	+	0.0545092i
$366$	351.799	+	86.4171i	0.961199	+	0.236112i
$367$	24.1405	−	214.253i	0.0657778	−	0.583795i	−0.916985	−	0.398922i	$-0.869384\pi$
$367$	24.1405	−	214.253i	0.0657778	−	0.583795i	0.982763	−	0.184872i	$-0.0591871\pi$
$368$	−40.9059	−	33.3306i	−0.111157	−	0.0905722i
$369$	526.012	−	396.157i	1.42551	−	1.07360i
$370$	259.914	−	74.1410i	0.702470	−	0.200381i
$371$	−11.0702	+	5.33115i	−0.0298389	+	0.0143697i
$372$	−352.078	−	108.757i	−0.946447	−	0.292357i
$373$	−36.1453	−	45.3248i	−0.0969043	−	0.121514i	0.731015	−	0.682361i	$-0.239047\pi$
$373$	−36.1453	−	45.3248i	−0.0969043	−	0.121514i	−0.827919	+	0.560847i	$0.810475\pi$
$374$	−152.514	+	274.249i	−0.407791	+	0.733286i
$375$	−436.845	+	68.0133i	−1.16492	+	0.181369i
$376$	−452.239	−	134.157i	−1.20276	−	0.356800i
$377$	220.401	−	235.119i	0.584617	−	0.623657i
$378$	−625.410	+	267.839i	−1.65452	+	0.708568i
$379$	236.972	+	677.226i	0.625255	+	1.78688i	0.617068	+	0.786909i	$0.288320\pi$
$379$	236.972	+	677.226i	0.625255	+	1.78688i	0.00818644	+	0.999966i	$0.497394\pi$
$380$	−654.496	+	310.963i	−1.72236	+	0.818323i
$381$	−56.6341	−	105.910i	−0.148646	−	0.277978i
$382$	−68.8858	+	37.8359i	−0.180329	+	0.0990469i
$383$	205.929	+	427.615i	0.537673	+	1.11649i	0.976020	+	0.217683i	$0.0698498\pi$
$383$	205.929	+	427.615i	0.537673	+	1.11649i	−0.438347	+	0.898806i	$0.644436\pi$
$384$	−340.422	−	177.676i	−0.886516	−	0.462699i
$385$	494.670	−	787.262i	1.28486	−	2.04484i
$386$	644.725	+	269.041i	1.67027	+	0.696996i
$387$	17.1038	+	8.82833i	0.0441958	+	0.0228122i
$388$	−16.2215	+	20.1233i	−0.0418080	+	0.0518642i
$389$	−116.655	+	116.655i	−0.299883	+	0.299883i	−0.840968	−	0.541085i	$-0.818014\pi$
$389$	−116.655	+	116.655i	−0.299883	+	0.299883i	0.541085	+	0.840968i	$0.318014\pi$
$390$	469.914	−	284.578i	1.20491	−	0.729687i
$391$	−54.5293	−	19.0806i	−0.139461	−	0.0487996i
$392$	513.638	−	711.948i	1.31030	−	1.81619i
$393$	−159.557	+	370.605i	−0.405998	+	0.943016i
$394$	−18.3968	−	110.025i	−0.0466924	−	0.279252i
$395$	−156.920	+	98.5992i	−0.397265	+	0.249618i
$396$	−46.6380	+	319.051i	−0.117773	+	0.805684i
$397$	−132.680	−	581.309i	−0.334207	−	1.46425i	−0.810900	−	0.585185i	$-0.801022\pi$
$397$	−132.680	−	581.309i	−0.334207	−	1.46425i	0.476693	−	0.879070i	$-0.341835\pi$
$398$	269.450	−	110.781i	0.677011	−	0.278345i
$399$	545.118	+	627.256i	1.36621	+	1.57207i
$400$	−304.202	+	615.062i	−0.760505	+	1.53766i
$401$	−164.525	+	341.640i	−0.410287	+	0.851970i	0.588759	+	0.808309i	$0.299617\pi$
$401$	−164.525	+	341.640i	−0.410287	+	0.851970i	−0.999046	+	0.0436618i	$0.986098\pi$
$402$	−311.527	−	40.3084i	−0.774944	−	0.100270i
$403$	−38.2075	−	339.101i	−0.0948077	−	0.841442i
$404$	−60.1215	−	76.2081i	−0.148816	−	0.188634i
$405$	−497.945	−	444.356i	−1.22949	−	1.09717i
$406$	728.059	−	62.6007i	1.79325	−	0.154189i
$407$	−146.908			−0.360952
$408$	−416.663	−	56.1392i	−1.02123	−	0.137596i
$409$	52.7403	+	468.083i	0.128949	+	1.14446i	0.876890	+	0.480692i	$0.159614\pi$
$409$	52.7403	+	468.083i	0.128949	+	1.14446i	−0.747940	+	0.663766i	$0.768957\pi$
$410$	−1203.97	+	64.4410i	−2.93652	+	0.157173i
$411$	−126.048	−	92.0859i	−0.306685	−	0.224053i
$412$	−133.014	−	134.419i	−0.322850	−	0.326260i
$413$	667.944	+	532.667i	1.61730	+	1.28975i
$414$	−59.3417	+	1.53002i	−0.143337	+	0.00369571i
$415$	−238.296	−	1044.04i	−0.574207	−	2.51576i
$416$	24.6011	−	354.755i	0.0591373	−	0.852776i
$417$	−328.721	+	130.858i	−0.788300	+	0.313808i
$418$	388.460	−	64.9524i	0.929329	−	0.155388i
$419$	−651.248	−	148.643i	−1.55429	−	0.354757i	−0.642786	−	0.766046i	$-0.722222\pi$
$419$	−651.248	−	148.643i	−1.55429	−	0.354757i	−0.911505	+	0.411289i	$0.865079\pi$
$420$	1223.88	+	232.080i	2.91400	+	0.552572i
$421$	−305.053	−	106.743i	−0.724592	−	0.253546i	−0.0573160	−	0.998356i	$-0.518254\pi$
$421$	−305.053	−	106.743i	−0.724592	−	0.253546i	−0.667276	+	0.744810i	$0.732540\pi$
$422$	−471.987	−	530.954i	−1.11845	−	1.25819i
$423$	−484.322	+	216.926i	−1.14497	+	0.512828i
$424$	−7.51374	+	2.10068i	−0.0177211	+	0.00495443i
$425$	−84.1157	+	746.548i	−0.197919	+	1.75658i
$426$	37.3507	−	57.3247i	0.0876777	−	0.134565i
$427$	−404.708	+	644.089i	−0.947795	+	1.50841i
$428$	68.5200	−	192.567i	0.160094	−	0.449923i
$429$	−288.047	+	78.6820i	−0.671439	+	0.183408i
$430$	−16.9661	−	30.8892i	−0.0394560	−	0.0718355i
$431$	−138.901	−	174.176i	−0.322275	−	0.404120i	0.594132	−	0.804367i	$-0.297496\pi$
$431$	−138.901	−	174.176i	−0.322275	−	0.404120i	−0.916407	+	0.400247i	$0.868924\pi$
$432$	−420.776	+	97.8333i	−0.974019	+	0.226466i
$433$	−215.756	−	616.596i	−0.498282	−	1.42401i	−0.868791	−	0.495179i	$-0.835102\pi$
$433$	−215.756	−	616.596i	−0.498282	−	1.42401i	0.370509	−	0.928829i	$-0.379183\pi$
$434$	449.420	−	629.885i	1.03553	−	1.45135i
$435$	358.256	+	620.873i	0.823576	+	1.42729i
$436$	−146.466	−	425.738i	−0.335931	−	0.976464i
$437$	23.9479	+	68.4392i	0.0548007	+	0.156611i
$438$	13.0374	−	15.8070i	0.0297657	−	0.0360890i
$439$	87.7701	+	110.060i	0.199932	+	0.250707i	0.871683	−	0.490070i	$-0.163029\pi$
$439$	87.7701	+	110.060i	0.199932	+	0.250707i	−0.671751	+	0.740777i	$0.734458\pi$
$440$	396.853	−	437.095i	0.901938	−	0.993398i
$441$	−83.3599	−	984.104i	−0.189025	−	2.23153i
$442$	−106.800	−	374.406i	−0.241629	−	0.847073i
$443$	−289.644	+	460.966i	−0.653825	+	1.04056i	0.341109	+	0.940024i	$0.389197\pi$
$443$	−289.644	+	460.966i	−0.653825	+	1.04056i	−0.994934	+	0.100532i	$0.967945\pi$
$444$	−71.8341	−	183.247i	−0.161788	−	0.412718i
$445$	−80.8354	+	717.434i	−0.181653	+	1.61221i
$446$	698.252	+	41.0535i	1.56559	+	0.0920482i
$447$	569.906	−	392.619i	1.27496	−	0.878343i
$448$	579.085	−	561.110i	1.29260	−	1.25248i
$449$	−345.703	−	120.967i	−0.769941	−	0.269414i	−0.0834105	−	0.996515i	$-0.526581\pi$
$449$	−345.703	−	120.967i	−0.769941	−	0.269414i	−0.686530	+	0.727101i	$0.740867\pi$
$450$	191.116	+	747.919i	0.424702	+	1.66204i
$451$	638.907	+	145.826i	1.41665	+	0.323340i
$452$	−180.328	+	369.476i	−0.398955	+	0.817424i
$453$	223.238	+	560.785i	0.492799	+	1.23794i
$454$	−379.421	−	340.869i	−0.835730	−	0.750812i
$455$	256.697	+	1124.66i	0.564168	+	2.47178i
$456$	270.966	+	452.789i	0.594223	+	0.992959i
$457$	435.404	+	347.223i	0.952744	+	0.759788i	0.970761	−	0.240050i	$-0.0771638\pi$
$457$	435.404	+	347.223i	0.952744	+	0.759788i	−0.0180167	+	0.999838i	$0.505735\pi$
$458$	50.1533	+	8.65703i	0.109505	+	0.0189018i
$459$	−396.779	+	257.444i	−0.864442	+	0.560880i
$460$	91.7238	+	58.3083i	0.199400	+	0.126757i
$461$	3.07648	+	27.3045i	0.00667349	+	0.0592288i	0.996608	−	0.0823003i	$-0.0262267\pi$
$461$	3.07648	+	27.3045i	0.00667349	+	0.0592288i	−0.989934	+	0.141529i	$0.954798\pi$
$462$	−605.103	−	303.782i	−1.30975	−	0.657538i
$463$	−86.2101			−0.186199			−0.0930995	−	0.995657i	$-0.529677\pi$
$463$	−86.2101			−0.186199			−0.0930995	+	0.995657i	$0.529677\pi$
$464$	462.105	+	41.8928i	0.995916	+	0.0902862i
$465$	746.475	+	137.492i	1.60532	+	0.295682i
$466$	−120.944	+	415.699i	−0.259537	+	0.892057i
$467$	−18.1798	−	161.350i	−0.0389288	−	0.345503i	−0.998045	−	0.0624918i	$-0.980095\pi$
$467$	−18.1798	−	161.350i	−0.0389288	−	0.345503i	0.959117	−	0.283011i	$-0.0913333\pi$
$468$	−238.993	−	320.825i	−0.510668	−	0.685524i
$469$	286.195	−	594.290i	0.610224	−	1.26714i
$470$	957.499	+	165.275i	2.03723	+	0.351649i
$471$	540.867	−	470.041i	1.14834	−	0.997965i
$472$	358.276	+	407.327i	0.759059	+	0.862982i
$473$	4.26244	+	18.6750i	0.00901150	+	0.0394820i
$474$	82.3948	+	106.886i	0.173829	+	0.225497i
$475$	798.388	−	501.660i	1.68082	−	1.05613i
$476$	387.221	−	793.381i	0.813489	−	1.66677i
$477$	−4.87371	+	7.29963i	−0.0102174	+	0.0153032i
$478$	−46.3609	+	32.7120i	−0.0969893	+	0.0684352i
$479$	289.622	+	101.343i	0.604639	+	0.211572i	0.615199	−	0.788372i	$-0.289076\pi$
$479$	289.622	+	101.343i	0.604639	+	0.211572i	−0.0105600	+	0.999944i	$0.503361\pi$
$480$	739.266	+	281.290i	1.54014	+	0.586021i
$481$	128.885	−	128.885i	0.267951	−	0.267951i
$482$	−174.273	−	10.2463i	−0.361562	−	0.0212579i
$483$	36.1627	−	119.289i	0.0748711	−	0.246975i
$484$	138.563	−	86.0526i	0.286287	−	0.177795i
$485$	28.3259	−	45.0805i	0.0584040	−	0.0929494i
$486$	−287.448	+	391.880i	−0.591456	+	0.806337i
$487$	22.8819	+	47.5147i	0.0469854	+	0.0975662i	0.923140	−	0.384464i	$-0.125614\pi$
$487$	22.8819	+	47.5147i	0.0469854	+	0.0975662i	−0.876155	+	0.482030i	$0.839899\pi$
$488$	−324.680	+	357.605i	−0.665329	+	0.732796i
$489$	613.159	−	327.880i	1.25390	−	0.670512i
$490$	−878.866	+	1580.37i	−1.79360	+	3.22524i
$491$	125.103	+	357.523i	0.254792	+	0.728152i	0.998237	+	0.0593557i	$0.0189046\pi$
$491$	125.103	+	357.523i	0.254792	+	0.728152i	−0.743445	+	0.668797i	$0.766810\pi$
$492$	130.511	+	868.253i	0.265267	+	1.76474i
$493$	491.371	−	128.980i	0.996695	−	0.261622i
$494$	−283.819	+	397.786i	−0.574531	+	0.805235i
$495$	18.3920	−	663.919i	0.0371555	−	1.34125i
$496$	351.050	−	343.749i	0.707763	−	0.693042i
$497$	89.5767	+	112.326i	0.180235	+	0.226007i
$498$	−740.222	+	245.404i	−1.48639	+	0.492779i
$499$	−764.700	+	368.260i	−1.53246	+	0.737996i	−0.994477	−	0.104957i	$-0.966530\pi$
$499$	−764.700	+	368.260i	−1.53246	+	0.737996i	−0.537988	+	0.842953i	$0.680815\pi$
$500$	197.613	−	555.367i	0.395226	−	1.11073i
$501$	−406.051	+	441.901i	−0.810482	+	0.882037i
$502$	−205.716	−	85.8440i	−0.409792	−	0.171004i
$503$	19.2101	−	170.494i	0.0381910	−	0.338954i	−0.960058	−	0.279801i	$-0.909731\pi$
$503$	19.2101	−	170.494i	0.0381910	−	0.338954i	0.998249	−	0.0591531i	$-0.0188400\pi$
$504$	83.0464	−	903.323i	0.164775	−	1.79231i
$505$	141.382	+	141.382i	0.279964	+	0.279964i
$506$	−39.2491	−	44.1527i	−0.0775675	−	0.0872584i
$507$	−67.6868	+	118.562i	−0.133504	+	0.233850i
$508$	160.133	+	0.841417i	0.315222	+	0.00165633i
$509$	−653.008	−	149.045i	−1.28292	−	0.292819i	−0.473891	−	0.880584i	$-0.657151\pi$
$509$	−653.008	−	149.045i	−1.28292	−	0.292819i	−0.809032	+	0.587765i	$0.800008\pi$
$510$	865.890	+	14.2666i	1.69782	+	0.0279738i
$511$	22.8909	+	36.4307i	0.0447964	+	0.0712930i
$512$	424.455	−	286.324i	0.829014	−	0.559227i
$513$	563.116	+	187.888i	1.09769	+	0.366253i
$514$	−825.735	+	339.492i	−1.60649	+	0.660490i
$515$	304.544	+	242.866i	0.591348	+	0.471584i
$516$	−21.2102	+	14.4484i	−0.0411051	+	0.0280008i
$517$	−475.829	−	229.147i	−0.920366	−	0.443225i
$518$	412.708	−	22.0897i	0.796734	−	0.0426441i
$519$	11.3972	−	162.674i	0.0219600	−	0.313437i
$520$	35.3056	+	731.637i	0.0678953	+	1.40699i
$521$	−355.660			−0.682649			−0.341325	−	0.939945i	$-0.610876\pi$
$521$	−355.660			−0.682649			−0.341325	+	0.939945i	$0.610876\pi$
$522$	425.125	−	302.907i	0.814415	−	0.580283i
$523$		−	354.535i		−	0.677886i	−0.940807	−	0.338943i	$-0.889931\pi$
$523$		−	354.535i		−	0.677886i	0.940807	−	0.338943i	$-0.110069\pi$
$524$	−333.217	−	422.375i	−0.635910	−	0.806059i
$525$	−1617.01	−	113.291i	−3.08002	−	0.215792i
$526$	323.639	−	17.3223i	0.615283	−	0.0329322i
$527$	233.400	−	484.661i	0.442885	−	0.919660i
$528$	−344.465	−	257.249i	−0.652395	−	0.487214i
$529$	−323.045	+	405.086i	−0.610671	+	0.765758i
$530$	14.8633	−	6.11089i	0.0280440	−	0.0115300i
$531$	604.321	+	85.0972i	1.13808	+	0.160258i
$532$	−1081.53	+	240.881i	−2.03296	+	0.452784i
$533$	−688.461	+	432.588i	−1.29167	+	0.811611i
$534$	525.682	+	8.66126i	0.984423	+	0.0162196i
$535$	−93.6852	+	410.461i	−0.175112	+	0.767218i
$536$	245.051	−	339.663i	0.457185	−	0.633699i
$537$	−247.667	−	141.393i	−0.461204	−	0.263301i
$538$	−47.6023	−	53.5494i	−0.0884800	−	0.0995343i
$539$	694.999	−	694.999i	1.28942	−	1.28942i
$540$	837.139	−	301.698i	1.55026	−	0.558700i
$541$	650.212	+	73.2613i	1.20187	+	0.135418i	0.690106	−	0.723708i	$-0.257564\pi$
$541$	650.212	+	73.2613i	1.20187	+	0.135418i	0.511764	+	0.859126i	$0.328992\pi$
$542$	195.852	+	81.7280i	0.361350	+	0.150790i
$543$	−24.9358	−	22.9129i	−0.0459223	−	0.0421969i
$544$	330.363	−	452.878i	0.607285	−	0.832497i
$545$	402.380	+	835.551i	0.738313	+	1.53312i
$546$	797.381	−	264.354i	1.46040	−	0.484164i
$547$	−90.1814	+	71.9173i	−0.164866	+	0.131476i	−0.702447	−	0.711736i	$-0.747909\pi$
$547$	−90.1814	+	71.9173i	−0.164866	+	0.131476i	0.537582	+	0.843212i	$0.319338\pi$
$548$	187.996	−	89.3202i	0.343058	−	0.162993i
$549$	−15.0472	+	543.178i	−0.0274083	+	0.989395i
$550$	−446.201	+	625.374i	−0.811275	+	1.13704i
$551$	−511.079	−	381.236i	−0.927548	−	0.691898i
$552$	35.8826	−	70.5474i	0.0650046	−	0.127803i
$553$	−267.486	+	93.5975i	−0.483700	+	0.169254i
$554$	−191.491	+	344.338i	−0.345652	+	0.621548i
$555$	191.178	+	357.517i	0.344465	+	0.644174i
$556$	55.2812	−	468.496i	0.0994267	−	0.842618i
$557$	−430.201	+	207.174i	−0.772353	+	0.371946i	−0.778183	−	0.628037i	$-0.783859\pi$
$557$	−430.201	+	207.174i	−0.772353	+	0.371946i	0.00582995	+	0.999983i	$0.498144\pi$
$558$	47.7095	−	550.677i	0.0855009	−	0.986876i
$559$	−20.1234	−	12.6444i	−0.0359989	−	0.0226196i
$560$	−1049.16	+	1287.61i	−1.87349	+	2.29930i
$561$	−450.462	−	136.559i	−0.802962	−	0.243420i
$562$	−805.814	−	47.3776i	−1.43383	−	0.0843018i
$563$	−418.869	−	418.869i	−0.743994	−	0.743994i	0.229350	−	0.973344i	$-0.426340\pi$
$563$	−418.869	−	418.869i	−0.743994	−	0.743994i	−0.973344	+	0.229350i	$0.926340\pi$
$564$	53.1610	−	705.578i	0.0942571	−	1.25102i
$565$	279.701	−	799.339i	0.495046	−	1.41476i
$566$	302.887	−	213.716i	0.535136	−	0.377589i
$567$	−591.139	−	831.880i	−1.04257	−	1.46716i
$568$	43.4969	+	80.1882i	0.0765791	+	0.141176i
$569$	101.406	+	161.387i	0.178218	+	0.283632i	0.923872	−	0.382701i	$-0.125006\pi$
$569$	101.406	+	161.387i	0.178218	+	0.283632i	−0.745655	+	0.666333i	$0.767863\pi$
$570$	−663.591	−	860.835i	−1.16419	−	1.51024i
$571$	557.747	−	127.302i	0.976789	−	0.222946i	0.295809	−	0.955247i	$-0.404411\pi$
$571$	557.747	−	127.302i	0.976789	−	0.222946i	0.680981	+	0.732301i	$0.261554\pi$
$572$	90.6313	−	387.681i	0.158446	−	0.677763i
$573$	−77.3302	−	88.9824i	−0.134957	−	0.155292i
$574$	−1816.81	−	313.602i	−3.16518	−	0.546345i
$575$	−127.426	−	61.3652i	−0.221611	−	0.106722i
$576$	152.448	−	555.460i	0.264666	−	0.964340i
$577$	256.248	−	28.8722i	0.444104	−	0.0500385i	0.112919	−	0.993604i	$-0.463980\pi$
$577$	256.248	−	28.8722i	0.444104	−	0.0500385i	0.331185	+	0.943566i	$0.392552\pi$
$578$	9.98640	−	34.3243i	0.0172775	−	0.0593846i
$579$	−189.821	+	1030.58i	−0.327842	+	1.77993i
$580$	−955.410	+	25.8452i	−1.64726	+	0.0445607i
$581$		−	1637.55i		−	2.81849i
$582$	−34.6496	−	17.3953i	−0.0595354	−	0.0298888i
$583$	−8.67996	+	0.977997i	−0.0148884	+	0.00167752i
$584$	10.2556	+	25.3218i	0.0175609	+	0.0433593i
$585$	566.332	+	598.603i	0.968089	+	1.02325i
$586$	−481.625	−	83.1338i	−0.821886	−	0.141867i
$587$	67.7706	−	84.9816i	0.115452	−	0.144773i	−0.720747	−	0.693198i	$-0.756201\pi$
$587$	67.7706	−	84.9816i	0.115452	−	0.144773i	0.836200	+	0.548425i	$0.184773\pi$
$588$	1206.75	+	527.078i	2.05230	+	0.896391i
$589$	−658.227	+	150.236i	−1.11753	+	0.255070i
$590$	−831.222	−	746.763i	−1.40885	−	1.26570i
$591$	155.464	−	61.8873i	0.263052	−	0.104716i
$592$	260.458	+	32.1219i	0.439963	+	0.0542599i
$593$	106.769	−	467.784i	0.180048	−	0.788843i	−0.801557	−	0.597919i	$-0.795994\pi$
$593$	106.769	−	467.784i	0.180048	−	0.788843i	0.981605	−	0.190924i	$-0.0611484\pi$
$594$	−482.543	+	32.8781i	−0.812363	+	0.0553504i
$595$	−600.606	+	1716.43i	−1.00942	+	2.88476i
$596$	98.4949	+	917.470i	0.165260	+	1.53938i
$597$	247.921	+	359.869i	0.415278	+	0.602796i
$598$	73.1699	+	4.30200i	0.122358	+	0.00719399i
$599$	−310.835	−	35.0227i	−0.518923	−	0.0584686i	−0.151381	−	0.988476i	$-0.548372\pi$
$599$	−310.835	−	35.0227i	−0.518923	−	0.0584686i	−0.367542	+	0.930007i	$0.619801\pi$
$600$	−998.248	−	250.782i	−1.66375	−	0.417970i
$601$	895.781	+	562.857i	1.49048	+	0.936534i	0.997798	+	0.0663270i	$0.0211281\pi$
$601$	895.781	+	562.857i	1.49048	+	0.936534i	0.492687	+	0.870207i	$0.336015\pi$
$602$	−14.7825	−	51.8228i	−0.0245557	−	0.0860843i
$603$	−39.7701	−	469.505i	−0.0659537	−	0.778616i
$604$	−799.235	−	94.3076i	−1.32324	−	0.156138i
$605$	−262.678	+	209.478i	−0.434178	+	0.346245i
$606$	92.6447	−	112.326i	0.152879	−	0.185356i
$607$	163.798	−	57.3153i	0.269848	−	0.0944239i	−0.191963	−	0.981402i	$-0.561485\pi$
$607$	163.798	−	57.3153i	0.269848	−	0.0944239i	0.461811	+	0.886978i	$0.347200\pi$
$608$	−702.917	+	30.2185i	−1.15611	+	0.0497015i
$609$	322.827	+	1047.50i	0.530093	+	1.72004i
$610$	577.859	−	809.899i	0.947310	−	1.32770i
$611$	618.488	−	216.418i	1.01226	−	0.354204i
$612$	−49.9262	−	628.662i	−0.0815787	−	1.02723i
$613$	−58.3739	+	46.5516i	−0.0952266	+	0.0759407i	−0.669946	−	0.742410i	$-0.733683\pi$
$613$	−58.3739	+	46.5516i	−0.0952266	+	0.0759407i	0.574719	+	0.818351i	$0.305111\pi$
$614$	−154.133	−	280.622i	−0.251031	−	0.457039i
$615$	−476.556	−	1744.63i	−0.774889	−	2.83679i
$616$	740.358	−	516.588i	1.20188	−	0.838616i
$617$	192.136	+	120.727i	0.311404	+	0.195668i	0.678661	−	0.734451i	$-0.262560\pi$
$617$	192.136	+	120.727i	0.311404	+	0.195668i	−0.367258	+	0.930119i	$0.619703\pi$
$618$	154.852	−	237.663i	0.250570	−	0.384568i
$619$	698.399	+	78.6907i	1.12827	+	0.127126i	0.656308	−	0.754493i	$-0.272117\pi$
$619$	698.399	+	78.6907i	1.12827	+	0.127126i	0.471962	+	0.881619i	$0.343546\pi$
$620$	−635.147	+	787.920i	−1.02443	+	1.27084i
$621$	−21.0753	−	86.5120i	−0.0339377	−	0.139311i
$622$	364.688	+	410.250i	0.586315	+	0.659566i
$623$	−364.628	+	1042.05i	−0.585278	+	1.67263i
$624$	527.894	−	76.5159i	0.845984	−	0.122622i
$625$	−31.6130	+	138.505i	−0.0505808	+	0.221609i
$626$	9.56424	−	1.59919i	0.0152783	−	0.00255461i
$627$	218.502	+	548.886i	0.348487	+	0.875417i
$628$	207.706	+	932.580i	0.330742	+	1.48500i
$629$	280.123	−	63.9362i	0.445346	−	0.101647i
$630$	48.1610	+	1867.91i	0.0764460	+	2.96494i
$631$	−87.6828	+	109.951i	−0.138958	+	0.174248i	−0.846441	−	0.532482i	$-0.821259\pi$
$631$	−87.6828	+	109.951i	−0.138958	+	0.174248i	0.707483	+	0.706731i	$0.249831\pi$
$632$	−177.633	+	28.7424i	−0.281064	+	0.0454785i
$633$	628.617	−	860.453i	0.993076	−	1.35933i
$634$	−3.81114	+	0.203986i	−0.00601126	+	0.000321745i
$635$	−327.776	+	36.9315i	−0.516182	+	0.0581598i
$636$	−5.46420	−	10.3488i	−0.00859150	−	0.0162717i
$637$			1219.47i			1.91440i
$638$	503.233	+	128.940i	0.788766	+	0.202100i
$639$	95.8940	+	36.5657i	0.150069	+	0.0572233i
$640$	−799.168	+	688.170i	−1.24870	+	1.07527i
$641$	−1155.25	+	130.165i	−1.80226	+	0.203066i	−0.948322	−	0.317310i	$-0.897220\pi$
$641$	−1155.25	+	130.165i	−1.80226	+	0.203066i	−0.853937	+	0.520376i	$0.825792\pi$
$642$	304.057	+	39.3418i	0.473609	+	0.0612800i
$643$	323.797	+	155.932i	0.503572	+	0.242507i	0.668382	−	0.743818i	$-0.266987\pi$
$643$	323.797	+	155.932i	0.503572	+	0.242507i	−0.164811	+	0.986325i	$0.552701\pi$
$644$	116.902	+	118.137i	0.181524	+	0.183442i
$645$	39.9008	−	34.6758i	0.0618617	−	0.0537610i
$646$	−712.444	+	292.914i	−1.10286	+	0.453427i
$647$	−798.040	+	182.147i	−1.23345	+	0.281526i	−0.789064	−	0.614311i	$-0.789434\pi$
$647$	−798.040	+	182.147i	−1.23345	+	0.281526i	−0.444382	+	0.895837i	$0.646577\pi$
$648$	−276.962	−	585.829i	−0.427411	−	0.904057i
$649$	323.128	+	514.255i	0.497886	+	0.792381i
$650$	−157.191	−	940.112i	−0.241833	−	1.44633i
$651$	1066.06	+	458.974i	1.63758	+	0.705029i
$652$	−4.87134	+	927.080i	−0.00747139	+	1.42190i
$653$	−23.0323	+	65.8224i	−0.0352715	+	0.100800i	−0.960173	−	0.279408i	$-0.909862\pi$
$653$	−23.0323	+	65.8224i	−0.0352715	+	0.100800i	0.924901	+	0.380208i	$0.124148\pi$
$654$	577.670	−	349.835i	0.883288	−	0.534916i
$655$	783.593	+	783.593i	1.19632	+	1.19632i
$656$	−1100.86	−	398.240i	−1.67814	−	0.607074i
$657$	27.3112	+	14.0970i	0.0415695	+	0.0214566i
$658$	1371.20	+	572.197i	2.08390	+	0.869600i
$659$	133.562	+	83.9224i	0.202673	+	0.127348i	0.629545	−	0.776964i	$-0.283241\pi$
$659$	133.562	+	83.9224i	0.202673	+	0.127348i	−0.426871	+	0.904312i	$0.640384\pi$
$660$	766.743	+	443.091i	1.16173	+	0.671349i
$661$	1039.94	−	500.809i	1.57328	−	0.757654i	0.575111	−	0.818075i	$-0.304959\pi$
$661$	1039.94	−	500.809i	1.57328	−	0.757654i	0.998173	+	0.0604213i	$0.0192444\pi$
$662$	81.5409	−	44.7868i	0.123174	−	0.0676538i
$663$	515.003	−	275.392i	0.776777	−	0.415373i
$664$	182.245	−	1023.69i	0.274465	−	1.54171i
$665$	2154.28	−	753.815i	3.23952	−	1.13356i
$666$	245.851	−	163.466i	0.369146	−	0.245444i
$667$	−7.63338	+	95.3327i	−0.0114443	+	0.142928i
$668$	−260.308	−	756.646i	−0.389682	−	1.13270i
$669$	161.406	+	1036.70i	0.241264	+	1.54962i
$670$	−419.297	+	753.976i	−0.625817	+	1.12534i
$671$	−422.793	+	337.166i	−0.630093	+	0.502483i
$672$	1006.39	+	670.895i	1.49760	+	0.998356i
$673$	−308.677	−	640.974i	−0.458658	−	0.952413i	−0.994164	−	0.107881i	$-0.965593\pi$
$673$	−308.677	−	640.974i	−0.458658	−	0.952413i	0.535506	−	0.844531i	$-0.320121\pi$
$674$	877.347	−	250.265i	1.30170	−	0.371313i
$675$	−1035.83	+	517.538i	−1.53456	+	0.766723i
$676$	−96.0347	−	154.636i	−0.142063	−	0.228752i
$677$	1051.44	+	118.469i	1.55309	+	0.174991i	0.846407	−	0.532537i	$-0.178761\pi$
$677$	1051.44	+	118.469i	1.55309	+	0.174991i	0.706685	+	0.707529i	$0.250190\pi$
$678$	−598.895	−	147.115i	−0.883326	−	0.216983i
$679$	57.5677	−	57.5677i	0.0847831	−	0.0847831i
$680$	−566.487	+	1006.17i	−0.833069	+	1.47966i
$681$	379.319	−	664.424i	0.557002	−	0.975659i
$682$	449.459	−	317.136i	0.659031	−	0.465009i
$683$	168.547	−	738.453i	0.246775	−	1.08119i	−0.687933	−	0.725774i	$-0.741482\pi$
$683$	168.547	−	738.453i	0.246775	−	1.08119i	0.934708	−	0.355416i	$-0.115661\pi$
$684$	−577.818	+	540.942i	−0.844763	+	0.790850i
$685$	−363.011	+	228.095i	−0.529943	+	0.332985i
$686$	−1022.80	+	1138.48i	−1.49096	+	1.65959i
$687$	3.22469	+	76.2744i	0.00469387	+	0.111025i
$688$	−3.47370	−	34.0416i	−0.00504898	−	0.0494790i
$689$	6.75707	−	8.47310i	0.00980707	−	0.0122977i
$690$	−56.3739	+	152.975i	−0.0817013	+	0.221704i
$691$	418.512	−	869.049i	0.605661	−	1.25767i	−0.342392	−	0.939557i	$-0.611237\pi$
$691$	418.512	−	869.049i	0.605661	−	1.25767i	0.948053	−	0.318111i	$-0.103049\pi$
$692$	183.493	+	116.646i	0.265164	+	0.168563i
$693$	253.328	−	983.514i	0.365552	−	1.41921i
$694$	−59.9332	+	205.997i	−0.0863591	+	0.296825i
$695$			971.715i			1.39815i
$696$	85.2333	+	690.761i	0.122462	+	0.992473i
$697$	−1281.73			−1.83892
$698$	465.525	+	135.441i	0.666941	+	0.194041i
$699$	−647.815	−	45.3870i	−0.926774	−	0.0649313i
$700$	1159.48	−	1823.96i	1.65640	−	2.60566i
$701$	−706.242	−	340.108i	−1.00748	−	0.485176i	−0.144008	−	0.989576i	$-0.545999\pi$
$701$	−706.242	−	340.108i	−1.00748	−	0.485176i	−0.863470	+	0.504401i	$0.831713\pi$
$702$	394.499	−	452.188i	0.561965	−	0.644143i
$703$	−281.945	−	224.843i	−0.401059	−	0.319834i
$704$	520.318	−	240.543i	0.739088	−	0.341681i
$705$	61.5639	+	1456.19i	0.0873247	+	2.06551i
$706$	359.389	+	322.872i	0.509050	+	0.457326i
$707$	162.665	+	258.880i	0.230078	+	0.366167i
$708$	−483.461	+	654.515i	−0.682854	+	0.924456i
$709$	−842.252	−	192.239i	−1.18794	−	0.271140i	−0.417517	−	0.908669i	$-0.637100\pi$
$709$	−842.252	−	192.239i	−1.18794	−	0.271140i	−0.770427	+	0.637528i	$0.779957\pi$
$710$	−108.335	−	153.536i	−0.152584	−	0.216249i
$711$	−130.551	+	154.715i	−0.183616	+	0.217602i
$712$	−343.914	+	610.844i	−0.483025	+	0.857927i
$713$	71.6086	+	71.6086i	0.100433	+	0.100433i
$714$	1286.02	+	315.902i	1.80114	+	0.442439i
$715$	−91.8205	+	814.929i	−0.128420	+	1.13976i
$716$	323.023	−	200.609i	0.451149	−	0.280180i
$717$	−62.6701	−	57.5859i	−0.0874059	−	0.0803151i
$718$	−163.748	−	574.048i	−0.228062	−	0.799510i
$719$	−551.083	+	265.388i	−0.766458	+	0.369107i	−0.775906	−	0.630849i	$-0.782707\pi$
$719$	−551.083	+	265.388i	−0.766458	+	0.369107i	0.00944809	+	0.999955i	$0.496993\pi$
$720$	−177.776	+	1173.07i	−0.246911	+	1.62926i
$721$	371.376	+	465.691i	0.515085	+	0.645896i
$722$	213.949	+	118.980i	0.296328	+	0.164793i
$723$	−40.2843	−	258.743i	−0.0557182	−	0.357874i
$724$	42.6965	−	14.6888i	0.0589730	−	0.0202884i
$725$	1230.74	−	179.088i	1.69757	−	0.247019i
$726$	170.130	+	175.830i	0.234339	+	0.242191i
$727$	−329.675	−	942.157i	−0.453473	−	1.29595i	−0.913062	−	0.407820i	$-0.866289\pi$
$727$	−329.675	−	942.157i	−0.453473	−	1.29595i	0.459589	−	0.888132i	$-0.347997\pi$
$728$	−196.318	+	1102.74i	−0.269667	+	1.51475i
$729$	−665.736	−	297.047i	−0.913218	−	0.407472i
$730$	−27.0913	−	49.3237i	−0.0371114	−	0.0675667i
$731$	−16.2552	−	33.7543i	−0.0222369	−	0.0461755i
$732$	−627.302	−	362.510i	−0.856970	−	0.495232i
$733$	−94.6858	+	150.692i	−0.129176	+	0.205582i	−0.905050	−	0.425306i	$-0.860166\pi$
$733$	−94.6858	+	150.692i	−0.129176	+	0.205582i	0.775874	+	0.630888i	$0.217309\pi$
$734$	−166.066	+	397.957i	−0.226247	+	0.542176i
$735$	−2595.80	−	786.924i	−3.53170	−	1.07064i
$736$	59.9322	+	86.8620i	0.0814296	+	0.118019i
$737$	331.577	−	331.577i	0.449900	−	0.449900i
$738$	−1231.48	+	466.877i	−1.66867	+	0.632625i
$739$	496.501	+	173.733i	0.671855	+	0.235092i	0.644581	−	0.764536i	$-0.277032\pi$
$739$	496.501	+	173.733i	0.671855	+	0.235092i	0.0272738	+	0.999628i	$0.491317\pi$
$740$	−540.556	−	2.84035i	−0.730481	−	0.00383831i
$741$	−673.243	−	289.852i	−0.908560	−	0.391164i
$742$	24.2376	−	4.05265i	0.0326652	−	0.00546179i
$743$	−514.788	+	323.463i	−0.692850	+	0.435347i	−0.831890	−	0.554940i	$-0.812741\pi$
$743$	−514.788	+	323.463i	−0.692850	+	0.435347i	0.139040	+	0.990287i	$0.455598\pi$
$744$	615.358	+	405.566i	0.827094	+	0.545116i
$745$	−422.943	−	1853.03i	−0.567709	−	2.48729i
$746$	44.0887	+	107.235i	0.0591001	+	0.143747i
$747$	−594.685	−	1007.32i	−0.796097	−	1.34849i
$748$	446.111	−	441.448i	0.596406	−	0.590171i
$749$	−279.332	+	580.039i	−0.372940	+	0.774418i
$750$	876.906	+	113.462i	1.16921	+	0.151283i
$751$	−146.504	−	1300.26i	−0.195079	−	1.73137i	−0.585444	−	0.810713i	$-0.699080\pi$
$751$	−146.504	−	1300.26i	−0.195079	−	1.73137i	0.390365	−	0.920660i	$-0.372349\pi$
$752$	793.512	+	510.306i	1.05520	+	0.678598i
$753$	60.5669	−	328.831i	0.0804342	−	0.436695i
$754$	−554.616	+	328.374i	−0.735566	+	0.435509i
$755$	1657.71			2.19564
$756$	1350.67	−	164.922i	1.78660	−	0.218151i
$757$	−55.8937	−	496.071i	−0.0738359	−	0.655311i	−0.975057	−	0.221953i	$-0.928757\pi$
$757$	−55.8937	−	496.071i	−0.0738359	−	0.655311i	0.901222	−	0.433359i	$-0.142672\pi$
$758$	−76.6955	−	1432.93i	−0.101181	−	1.89041i
$759$	52.2741	−	71.5530i	0.0688723	−	0.0942727i
$760$	1430.62	−	231.486i	1.88239	−	0.304586i
$761$	−729.784	−	581.984i	−0.958981	−	0.764762i	0.0129772	−	0.999916i	$-0.495869\pi$
$761$	−729.784	−	581.984i	−0.958981	−	0.764762i	−0.971958	+	0.235154i	$0.924441\pi$
$762$	49.5849	+	235.029i	0.0650720	+	0.308436i
$763$	315.560	+	1382.56i	0.413578	+	1.81200i
$764$	153.426	−	34.1713i	0.200819	−	0.0447269i
$765$	253.877	+	1273.96i	0.331865	+	1.66531i
$766$	−156.543	−	936.237i	−0.204365	−	1.22224i
$767$	−734.651	−	167.679i	−0.957824	−	0.218617i
$768$	554.466	+	531.405i	0.721961	+	0.691933i
$769$	935.004	+	327.172i	1.21587	+	0.425451i	0.860585	−	0.509307i	$-0.170098\pi$
$769$	935.004	+	327.172i	1.21587	+	0.425451i	0.355285	+	0.934758i	$0.384384\pi$
$770$	−1389.81	+	1235.46i	−1.80495	+	1.60449i
$771$	−759.759	−	1102.83i	−0.985420	−	1.43038i
$772$	−1087.80	−	876.878i	−1.40906	−	1.13585i
$773$	25.2027	−	223.681i	0.0326038	−	0.289367i	−0.966821	−	0.255455i	$-0.917775\pi$
$773$	25.2027	−	223.681i	0.0326038	−	0.289367i	0.999425	−	0.0339120i	$-0.0107966\pi$
$774$	−27.9131	−	26.5099i	−0.0360634	−	0.0342505i
$775$	700.653	−	1115.08i	0.904068	−	1.43882i
$776$	42.3946	−	29.5810i	0.0546322	−	0.0381199i
$777$	163.358	+	598.039i	0.210242	+	0.769676i
$778$	289.197	−	158.843i	0.371719	−	0.204169i
$779$	1003.00	+	1257.72i	1.28755	+	1.61454i
$780$	−1061.41	+	283.946i	−1.36078	+	0.364034i
$781$	33.7331	+	96.4038i	0.0431922	+	0.123436i
$782$	94.0559	+	67.1084i	0.120276	+	0.0858164i
$783$	578.990	+	527.124i	0.739451	+	0.673210i
$784$	−1384.15	+	1080.23i	−1.76550	+	1.37784i
$785$	−649.996	−	1857.58i	−0.828020	−	2.36635i
$786$	513.473	−	622.553i	0.653274	−	0.792052i
$787$	−503.140	−	630.918i	−0.639314	−	0.801674i	0.351603	−	0.936149i	$-0.385637\pi$
$787$	−503.140	−	630.918i	−0.639314	−	0.801674i	−0.990917	+	0.134475i	$0.957065\pi$
$788$	−26.1445	+	221.568i	−0.0331783	+	0.281178i
$789$	128.103	+	468.972i	0.162361	+	0.594388i
$790$	356.434	−	101.673i	0.451182	−	0.128700i
$791$	688.967	−	1096.48i	0.871008	−	1.38620i
$792$	267.822	−	586.639i	0.338159	−	0.740706i
$793$	75.1219	−	666.725i	0.0947312	−	0.840763i
$794$	−69.9928	+	1190.46i	−0.0881522	+	1.49932i
$795$	13.6757	+	19.8510i	0.0172022	+	0.0249698i
$796$	−579.341	+	62.1950i	−0.727815	+	0.0781345i
$797$	13.2134	+	4.62356i	0.0165789	+	0.00580120i	0.338556	−	0.940946i	$-0.390062\pi$
$797$	13.2134	+	4.62356i	0.0165789	+	0.00580120i	−0.321977	+	0.946748i	$0.604347\pi$
$798$	−696.370	−	1509.13i	−0.872644	−	1.89114i
$799$	1007.04	+	229.850i	1.26037	+	0.287672i
$800$	927.828	−	1011.19i	1.15978	−	1.26398i
$801$	154.129	+	773.422i	0.192420	+	0.965570i
$802$	506.830	−	564.153i	0.631958	−	0.703433i
$803$	6.80623	+	29.8201i	0.00847601	+	0.0371358i
$804$	575.728	+	251.463i	0.716080	+	0.312765i
$805$	−267.654	−	213.447i	−0.332489	−	0.265151i
$806$	−116.089	+	672.548i	−0.144031	+	0.834427i
$807$	63.3992	−	86.7811i	0.0785616	−	0.107535i
$808$	72.8770	+	179.939i	0.0901943	+	0.222697i
$809$	−53.3424	−	473.427i	−0.0659363	−	0.585201i	−0.982625	−	0.185600i	$-0.940577\pi$
$809$	−53.3424	−	473.427i	−0.0659363	−	0.585201i	0.916689	−	0.399601i	$-0.130851\pi$
$810$	707.971	+	1131.54i	0.874038	+	1.39696i
$811$	−1355.13			−1.67094			−0.835471	−	0.549535i	$-0.814805\pi$
$811$	−1355.13			−1.67094			−0.835471	+	0.549535i	$0.814805\pi$
$812$	−1433.12	−	286.563i	−1.76493	−	0.352911i
$813$	−57.6628	+	313.064i	−0.0709260	+	0.385073i
$814$	282.118	+	82.0800i	0.346582	+	0.100835i
$815$	−213.813	−	1897.64i	−0.262347	−	2.32840i
$816$	768.782	+	340.605i	0.942134	+	0.417408i
$817$	−20.4018	+	42.3647i	−0.0249715	+	0.0518539i
$818$	160.246	−	928.362i	0.195899	−	1.13492i
$819$	640.605	+	1085.10i	0.782180	+	1.32491i
$820$	2348.08	+	548.930i	2.86351	+	0.669427i
$821$	−228.992	−	1003.28i	−0.278919	−	1.22202i	−0.899163	−	0.437614i	$-0.855824\pi$
$821$	−228.992	−	1003.28i	−0.278919	−	1.22202i	0.620245	−	0.784409i	$-0.287033\pi$
$822$	190.608	+	247.264i	0.231884	+	0.300808i
$823$	−1301.21	+	817.602i	−1.58105	+	0.993441i	−0.599930	+	0.800053i	$0.704805\pi$
$823$	−1301.21	+	817.602i	−1.58105	+	0.993441i	−0.981122	+	0.193388i	$0.938052\pi$
$824$	180.334	+	332.452i	0.218852	+	0.403462i
$825$	−1058.43	−	455.687i	−1.28294	−	0.552348i
$826$	−985.091	−	1396.11i	−1.19260	−	1.69021i
$827$	−1386.08	−	485.010i	−1.67603	−	0.586470i	−0.686038	−	0.727565i	$-0.740652\pi$
$827$	−1386.08	−	485.010i	−1.67603	−	0.586470i	−0.989996	+	0.141096i	$0.954937\pi$
$828$	114.813	+	30.2171i	0.138663	+	0.0364940i
$829$	713.493	−	713.493i	0.860667	−	0.860667i	−0.130749	−	0.991416i	$-0.541738\pi$
$829$	713.493	−	713.493i	0.860667	−	0.860667i	0.991416	+	0.130749i	$0.0417381\pi$
$830$	−125.708	+	2138.09i	−0.151456	+	2.57601i
$831$	−565.585	−	171.459i	−0.680608	−	0.206328i
$832$	−245.451	+	667.517i	−0.295014	+	0.802304i
$833$	−1022.75	+	1627.69i	−1.22779	+	1.95401i
$834$	704.380	−	67.6334i	0.844580	−	0.0810952i
$835$	715.133	+	1484.99i	0.856447	+	1.77843i
$836$	−782.277	−	92.3066i	−0.935739	−	0.110415i
$837$	822.458	−	104.814i	0.982626	−	0.125226i
$838$	1167.59	+	649.314i	1.39331	+	0.774838i
$839$	−76.3761	−	218.270i	−0.0910323	−	0.260155i	0.889361	−	0.457205i	$-0.151150\pi$
$839$	−76.3761	−	218.270i	−0.0910323	−	0.260155i	−0.980393	+	0.197050i	$0.936864\pi$
$840$	−2220.64	−	1129.49i	−2.64362	−	1.34463i
$841$	−413.048	−	732.579i	−0.491140	−	0.871081i
$842$	526.177	+	375.425i	0.624914	+	0.445873i
$843$	−186.269	−	1196.39i	−0.220960	−	1.41921i
$844$	609.737	+	1283.34i	0.722437	+	1.52054i
$845$	233.778	+	293.148i	0.276660	+	0.346921i
$846$	1051.28	−	145.980i	1.24265	−	0.172554i
$847$	−462.879	+	222.911i	−0.546492	+	0.263177i
$848$	15.6029	+	0.163975i	0.0183996	+	0.000193367i
$849$	409.439	+	376.223i	0.482260	+	0.443136i
$850$	578.643	−	1386.65i	0.680757	−	1.63136i
$851$	−6.05631	+	53.7512i	−0.00711669	+	0.0631624i
$852$	−103.756	+	89.2164i	−0.121779	+	0.104714i
$853$	15.4221	+	15.4221i	0.0180798	+	0.0180798i	0.716089	−	0.698009i	$-0.245930\pi$
$853$	15.4221	+	15.4221i	0.0180798	+	0.0180798i	−0.698009	+	0.716089i	$0.745930\pi$
$854$	1137.06	−	1010.77i	1.33145	−	1.18358i
$855$	1051.43	−	1246.04i	1.22974	−	1.45736i
$856$	−239.175	+	331.518i	−0.279410	+	0.387287i
$857$	1052.39	+	240.202i	1.22800	+	0.280283i	0.786846	−	0.617150i	$-0.211713\pi$
$857$	1052.39	+	240.202i	1.22800	+	0.280283i	0.441152	+	0.897432i	$0.354570\pi$
$858$	597.119	+	9.83828i	0.695943	+	0.0114665i
$859$	−45.2492	−	72.0136i	−0.0526766	−	0.0838343i	0.819348	−	0.573297i	$-0.194336\pi$
$859$	−45.2492	−	72.0136i	−0.0526766	−	0.0838343i	−0.872024	+	0.489463i	$0.837193\pi$
$860$	15.3229	+	68.7981i	0.0178173	+	0.0799978i
$861$	−116.815	−	2763.05i	−0.135673	−	3.20912i
$862$	169.426	+	412.089i	0.196550	+	0.478061i
$863$	705.619	+	562.713i	0.817635	+	0.652042i	0.940278	−	0.340409i	$-0.110565\pi$
$863$	705.619	+	562.713i	0.817635	+	0.652042i	−0.122642	+	0.992451i	$0.539137\pi$
$864$	862.709	+	47.2189i	0.998505	+	0.0546515i
$865$	−403.516	−	194.323i	−0.466492	−	0.224651i
$866$	69.8292	+	1304.64i	0.0806341	+	1.50651i
$867$	53.4902	+	3.74761i	0.0616957	+	0.00432251i
$868$	−1214.98	+	958.515i	−1.39975	+	1.10428i
$869$	−201.462			−0.231832
$870$	−341.092	−	1392.47i	−0.392059	−	1.60054i
$871$			581.796i			0.667963i
$872$	43.4016	+	899.410i	0.0497724	+	1.03143i
$873$	14.5061	−	56.3183i	0.0166164	−	0.0645112i
$874$	−7.75071	−	144.809i	−0.00886808	−	0.165685i
$875$	−805.599	+	1672.84i	−0.920684	+	1.91182i
$876$	−33.8683	+	23.0711i	−0.0386624	+	0.0263368i
$877$	−1069.26	+	1340.81i	−1.21923	+	1.52886i	−0.445591	+	0.895237i	$0.647006\pi$
$877$	−1069.26	+	1340.81i	−1.21923	+	1.52886i	−0.773638	+	0.633628i	$0.781565\pi$
$878$	−107.059	−	260.395i	−0.121935	−	0.296578i
$879$	−30.9669	−	732.466i	−0.0352296	−	0.833295i
$880$	−1006.32	+	617.657i	−1.14354	+	0.701883i
$881$	1239.93	−	779.100i	1.40741	−	0.884336i	0.407826	−	0.913060i	$-0.366287\pi$
$881$	1239.93	−	779.100i	1.40741	−	0.884336i	0.999587	+	0.0287237i	$0.00914431\pi$
$882$	−389.755	+	1936.42i	−0.441899	+	2.19549i
$883$	205.202	−	899.047i	0.232392	−	1.01817i	−0.715258	−	0.698861i	$-0.753691\pi$
$883$	205.202	−	899.047i	0.232392	−	1.01817i	0.947649	−	0.319313i	$-0.103452\pi$
$884$	−4.09153	+	778.671i	−0.00462843	+	0.880850i
$885$	830.997	−	1455.60i	0.938980	−	1.64474i
$886$	813.775	−	723.398i	0.918482	−	0.816476i
$887$	451.385	−	451.385i	0.508890	−	0.508890i	−0.405296	−	0.914186i	$-0.632831\pi$
$887$	451.385	−	451.385i	0.508890	−	0.508890i	0.914186	+	0.405296i	$0.132831\pi$
$888$	35.5649	+	392.037i	0.0400506	+	0.441483i
$889$	−501.216	−	56.4734i	−0.563797	−	0.0635247i
$890$	556.077	−	1332.58i	0.624806	−	1.49728i
$891$	−201.337	−	696.996i	−0.225968	−	0.782263i
$892$	−1317.97	−	468.964i	−1.47754	−	0.525745i
$893$	−562.498	−	1168.04i	−0.629897	−	1.30800i
$894$	−1313.80	+	435.559i	−1.46957	+	0.487203i
$895$	−612.364	+	488.344i	−0.684206	+	0.545636i
$896$	−1425.56	+	753.996i	−1.59103	+	0.841513i
$897$	16.9137	+	108.636i	0.0188559	+	0.121110i
$898$	596.293	+	425.452i	0.664023	+	0.473777i
$899$	−874.144	−	170.020i	−0.972352	−	0.189121i
$900$	50.8616	−	1543.06i	0.0565129	−	1.71451i
$901$	16.1253	−	5.64248i	0.0178971	−	0.00626246i
$902$	−1145.46	−	637.010i	−1.26992	−	0.706220i
$903$	71.2832	−	38.1179i	0.0789405	−	0.0422126i
$904$	552.729	−	608.779i	0.611426	−	0.673428i
$905$	−83.7958	+	40.3539i	−0.0925920	+	0.0445900i
$906$	−115.380	−	1201.64i	−0.127351	−	1.32632i
$907$	−558.644	−	351.019i	−0.615925	−	0.387011i	0.187632	−	0.982239i	$-0.439919\pi$
$907$	−558.644	−	351.019i	−0.615925	−	0.387011i	−0.803557	+	0.595228i	$0.797062\pi$
$908$	538.181	+	866.585i	0.592710	+	0.954388i
$909$	194.076	+	100.175i	0.213504	+	0.110203i
$910$	135.415	−	2303.19i	0.148808	−	2.53098i
$911$	−788.911	−	788.911i	−0.865983	−	0.865983i	0.126042	−	0.992025i	$-0.459773\pi$
$911$	−788.911	−	788.911i	−0.865983	−	0.865983i	−0.992025	+	0.126042i	$0.959773\pi$
$912$	−267.374	−	1020.92i	−0.293173	−	1.11943i
$913$	384.489	−	1098.81i	0.421128	−	1.20351i
$914$	−642.138	−	910.066i	−0.702558	−	0.995696i
$915$	1370.73	+	590.144i	1.49807	+	0.644966i
$916$	−91.4763	−	44.6463i	−0.0998650	−	0.0487405i
$917$	901.553	+	1434.81i	0.983154	+	1.56468i
$918$	905.802	−	272.701i	0.986713	−	0.297060i
$919$	−404.957	+	92.4288i	−0.440650	+	0.100575i	−0.437089	−	0.899418i	$-0.643991\pi$
$919$	−404.957	+	92.4288i	−0.440650	+	0.100575i	−0.00356075	+	0.999994i	$0.501133\pi$
$920$	−143.566	−	163.222i	−0.156050	−	0.177415i
$921$	362.490	−	315.022i	0.393583	−	0.342043i
$922$	9.34753	−	54.1537i	0.0101383	−	0.0587350i
$923$	−114.171	−	54.9820i	−0.123696	−	0.0595689i
$924$	992.295	+	921.458i	1.07391	+	0.997248i
$925$	698.994	−	78.7577i	0.755669	−	0.0851435i
$926$	165.556	+	48.1672i	0.178786	+	0.0520164i
$927$	397.567	+	151.598i	0.428875	+	0.163536i
$928$	−864.008	−	338.636i	−0.931043	−	0.364910i
$929$		−	424.259i		−	0.456684i	−0.973581	−	0.228342i	$-0.926670\pi$
$929$		−	424.259i		−	0.456684i	0.973581	−	0.228342i	$-0.0733304\pi$
$930$	−1356.69	−	681.106i	−1.45881	−	0.732372i
$931$	2397.54	−	270.138i	2.57523	−	0.290159i
$932$	464.517	−	730.723i	0.498409	−	0.784037i
$933$	−485.711	+	664.843i	−0.520590	+	0.712586i
$934$	−55.2372	+	320.009i	−0.0591404	+	0.342622i
$935$	−806.025	+	1010.72i	−0.862058	+	1.08099i
$936$	279.704	+	749.634i	0.298829	+	0.800891i
$937$	1499.58	−	342.270i	1.60041	−	0.365283i	0.673091	−	0.739560i	$-0.264966\pi$
$937$	1499.58	−	342.270i	1.60041	−	0.365283i	0.927317	+	0.374277i	$0.122109\pi$
$938$	−881.642	+	981.357i	−0.939917	+	1.04622i
$939$	5.37971	+	13.5141i	0.00572919	+	0.0143920i
$940$	−1746.41	−	852.361i	−1.85789	−	0.906767i
$941$	−35.1036	+	153.799i	−0.0373046	+	0.163442i	−0.990149	−	0.140017i	$-0.955284\pi$
$941$	−35.1036	+	153.799i	−0.0373046	+	0.163442i	0.952845	+	0.303459i	$0.0981415\pi$
$942$	−1301.29	+	600.462i	−1.38141	+	0.637434i
$943$	79.6947	−	227.754i	0.0845119	−	0.241521i
$944$	−460.442	−	982.396i	−0.487757	−	1.04067i
$945$	−2723.16	+	663.393i	−2.88165	+	0.702003i
$946$	2.24857	−	38.2444i	0.00237692	−	0.0404275i
$947$	−1303.17	−	146.832i	−1.37610	−	0.155050i	−0.607269	−	0.794496i	$-0.707735\pi$
$947$	−1303.17	−	146.832i	−1.37610	−	0.155050i	−0.768836	+	0.639446i	$0.779164\pi$
$948$	−98.5098	−	251.296i	−0.103913	−	0.265080i
$949$	−32.1329	−	20.1904i	−0.0338597	−	0.0212755i
$950$	−1813.49	+	517.301i	−1.90894	+	0.544528i
$951$	−1.50853	−	5.52257i	−0.00158625	−	0.00580712i
$952$	−1186.88	+	1307.24i	−1.24673	+	1.37315i
$953$	−1270.31	+	1013.04i	−1.33296	+	1.06300i	−0.340521	+	0.940237i	$0.610603\pi$
$953$	−1270.31	+	1013.04i	−1.33296	+	1.06300i	−0.992436	+	0.122761i	$0.960825\pi$
$954$	13.4378	−	11.2950i	0.0140857	−	0.0118396i
$955$	−305.605	+	106.936i	−0.320006	+	0.111975i
$956$	107.307	−	36.9166i	0.112246	−	0.0386157i
$957$	−29.3297	+	778.681i	−0.0306476	+	0.813669i
$958$	−499.560	−	356.434i	−0.521462	−	0.372060i
$959$	−618.791	+	216.524i	−0.645246	+	0.225781i
$960$	−1262.51	−	953.223i	−1.31511	−	0.992941i
$961$	14.0987	−	11.2433i	0.0146709	−	0.0116996i
$962$	−319.517	+	175.496i	−0.332138	+	0.182429i
$963$	38.8164	+	458.247i	0.0403078	+	0.475853i
$964$	328.944	+	117.046i	0.341228	+	0.121417i
$965$	2436.89	+	1531.20i	2.52528	+	1.58674i
$966$	−136.095	+	208.874i	−0.140885	+	0.216226i
$967$	831.807	+	93.7221i	0.860193	+	0.0969205i	0.531030	−	0.847353i	$-0.321805\pi$
$967$	831.807	+	93.7221i	0.860193	+	0.0969205i	0.329163	+	0.944273i	$0.393234\pi$
$968$	−314.171	+	87.8355i	−0.324557	+	0.0907392i
$969$	−655.520	−	951.519i	−0.676492	−	0.981960i
$970$	−79.5837	+	70.7451i	−0.0820450	+	0.0729331i
$971$	168.407	−	481.279i	0.173436	−	0.495653i	−0.824050	−	0.566518i	$-0.808290\pi$
$971$	168.407	−	481.279i	0.173436	−	0.495653i	0.997486	+	0.0708652i	$0.0225760\pi$
$972$	770.957	−	591.953i	0.793166	−	0.609006i
$973$	−330.642	+	1448.64i	−0.339817	+	1.48883i
$974$	−17.3944	−	104.031i	−0.0178588	−	0.106808i
$975$	1328.36	−	528.796i	1.36242	−	0.542355i
$976$	823.308	−	505.329i	0.843553	−	0.517755i
$977$	1171.08	−	267.292i	1.19865	−	0.273585i	0.423817	−	0.905748i	$-0.360690\pi$
$977$	1171.08	−	267.292i	1.19865	−	0.273585i	0.774835	+	0.632163i	$0.217833\pi$
$978$	−1360.69	+	287.069i	−1.39130	+	0.293527i
$979$	−489.337	+	613.610i	−0.499834	+	0.626772i
$980$	2570.73	−	2543.86i	2.62319	−	2.59577i
$981$	696.198	+	735.870i	0.709682	+	0.750122i
$982$	−40.4893	−	756.474i	−0.0412315	−	0.770341i
$983$	679.979	−	76.6152i	0.691738	−	0.0779402i	0.240906	−	0.970549i	$-0.422556\pi$
$983$	679.979	−	76.6152i	0.691738	−	0.0779402i	0.450833	+	0.892608i	$0.351127\pi$
$984$	234.479	−	1740.29i	0.238291	−	1.76859i
$985$		−	459.559i		−	0.466557i
$986$	−1015.68	−	26.8484i	−1.03010	−	0.0272296i
$987$	−403.711	+	2191.84i	−0.409028	+	2.22070i
$988$	767.288	−	605.323i	0.776607	−	0.612676i
$989$	7.00860	−	0.789680i	0.00708655	−	0.000798463i
$990$	−406.263	+	1264.70i	−0.410367	+	1.27747i
$991$	−324.113	−	156.085i	−0.327056	−	0.157502i	0.263149	−	0.964755i	$-0.415239\pi$
$991$	−324.113	−	156.085i	−0.327056	−	0.157502i	−0.590205	+	0.807253i	$0.700953\pi$
$992$	−866.207	+	463.987i	−0.873192	+	0.467729i
$993$	91.5367	+	105.329i	0.0921820	+	0.106072i
$994$	−109.262	−	265.755i	−0.109922	−	0.267359i
$995$	1170.11	−	267.069i	1.17599	−	0.268411i
$996$	1558.62	−	57.6918i	1.56487	−	0.0579235i
$997$	889.614	+	1415.81i	0.892291	+	1.42007i	0.907437	+	0.420188i	$0.138036\pi$
$997$	889.614	+	1415.81i	0.892291	+	1.42007i	−0.0151460	+	0.999885i	$0.504821\pi$
$998$	1674.26	−	279.945i	1.67762	−	0.280506i
$999$	317.670	+	308.553i	0.317988	+	0.308862i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	348.3.v.a.11.11	✓	1392
3.2	odd	2	inner	348.3.v.a.11.106	yes	1392
4.3	odd	2	inner	348.3.v.a.11.83	yes	1392
12.11	even	2	inner	348.3.v.a.11.34	yes	1392
29.8	odd	28	inner	348.3.v.a.95.34	yes	1392
87.8	even	28	inner	348.3.v.a.95.83	yes	1392
116.95	even	28	inner	348.3.v.a.95.106	yes	1392
348.95	odd	28	inner	348.3.v.a.95.11	yes	1392

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
348.3.v.a.11.11	✓	1392	1.1	even	1	trivial
348.3.v.a.11.34	yes	1392	12.11	even	2	inner
348.3.v.a.11.83	yes	1392	4.3	odd	2	inner
348.3.v.a.11.106	yes	1392	3.2	odd	2	inner
348.3.v.a.95.11	yes	1392	348.95	odd	28	inner
348.3.v.a.95.34	yes	1392	29.8	odd	28	inner
348.3.v.a.95.83	yes	1392	87.8	even	28	inner
348.3.v.a.95.106	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)

\(f(q)\)	\(=\)	\(q+(-1.92037 - 0.558718i) q^{2} +(0.209671 - 2.99266i) q^{3} +(3.37567 + 2.14590i) q^{4} +(-7.42336 - 3.57490i) q^{5} +(-2.07470 + 5.62989i) q^{6} +(-9.85035 - 7.85539i) q^{7} +(-5.28359 - 6.00697i) q^{8} +(-8.91208 - 1.25495i) q^{9} +O(q^{10})\)	\(q+(-1.92037 - 0.558718i) q^{2} +(0.209671 - 2.99266i) q^{3} +(3.37567 + 2.14590i) q^{4} +(-7.42336 - 3.57490i) q^{5} +(-2.07470 + 5.62989i) q^{6} +(-9.85035 - 7.85539i) q^{7} +(-5.28359 - 6.00697i) q^{8} +(-8.91208 - 1.25495i) q^{9} +(12.2583 + 11.0127i) q^{10} +(-4.76526 - 7.58386i) q^{11} +(7.12972 - 9.65231i) q^{12} +(10.8341 + 2.47281i) q^{13} +(14.5274 + 20.5888i) q^{14} +(-12.2549 + 21.4661i) q^{15} +(6.79027 + 14.4877i) q^{16} +(12.3870 + 12.3870i) q^{17} +(16.4134 + 7.38931i) q^{18} +(2.46170 - 21.8482i) q^{19} +(-17.3874 - 27.9974i) q^{20} +(-25.5739 + 27.8317i) q^{21} +(4.91383 + 17.2263i) q^{22} +(-2.97127 + 1.43089i) q^{23} +(-19.0847 + 14.5525i) q^{24} +(26.7391 + 33.5297i) q^{25} +(-19.4239 - 10.8019i) q^{26} +(-5.62425 + 26.4077i) q^{27} +(-16.3947 - 47.6550i) q^{28} +(14.6279 - 25.0405i) q^{29} +(35.5275 - 34.3758i) q^{30} +(-10.1421 - 28.9846i) q^{31} +(-4.94533 - 31.6156i) q^{32} +(-23.6951 + 12.6707i) q^{33} +(-16.8668 - 30.7084i) q^{34} +(45.0404 + 93.5274i) q^{35} +(-27.3912 - 23.3607i) q^{36} +(8.72637 - 13.8879i) q^{37} +(-16.9344 + 40.5813i) q^{38} +(9.67189 - 31.9043i) q^{39} +(17.7477 + 63.4802i) q^{40} +(-51.7371 + 51.7371i) q^{41} +(64.6615 - 39.1587i) q^{42} +(-2.01863 - 0.706350i) q^{43} +(0.188250 - 35.8263i) q^{44} +(61.6712 + 41.1757i) q^{45} +(6.50540 - 1.08774i) q^{46} +(49.9269 - 31.3712i) q^{47} +(44.7804 - 17.2833i) q^{48} +(24.4187 + 106.985i) q^{49} +(-32.6153 - 79.3292i) q^{50} +(39.6672 - 34.4728i) q^{51} +(31.2659 + 31.5962i) q^{52} +(0.423138 - 0.878656i) q^{53} +(25.5551 - 47.5703i) q^{54} +(8.26265 + 73.3330i) q^{55} +(4.85815 + 100.675i) q^{56} +(-64.8682 - 11.9480i) q^{57} +(-42.0816 + 39.9141i) q^{58} -67.8092 q^{59} +(-87.4325 + 46.1645i) q^{60} +(-6.75999 - 59.9966i) q^{61} +(3.28249 + 61.3278i) q^{62} +(77.9289 + 82.3695i) q^{63} +(-8.16731 + 63.4767i) q^{64} +(-71.5853 - 57.0874i) q^{65} +(52.5828 - 11.0936i) q^{66} +(11.6499 + 51.0414i) q^{67} +(15.2332 + 68.3954i) q^{68} +(3.65917 + 9.19201i) q^{69} +(-34.2390 - 204.772i) q^{70} +(-11.1173 - 2.53745i) q^{71} +(39.5493 + 60.1652i) q^{72} +(-3.22334 - 1.12789i) q^{73} +(-24.5173 + 21.7945i) q^{74} +(105.950 - 72.9908i) q^{75} +(55.1938 - 68.4697i) q^{76} +(-12.6348 + 112.137i) q^{77} +(-36.3992 + 55.8644i) q^{78} +(11.9669 - 19.0453i) q^{79} +(1.38535 - 131.822i) q^{80} +(77.8502 + 22.3684i) q^{81} +(128.261 - 70.4481i) q^{82} +(81.0372 + 101.617i) q^{83} +(-146.053 + 39.0718i) q^{84} +(-47.6707 - 136.235i) q^{85} +(3.48188 + 2.48430i) q^{86} +(-71.8706 - 49.0267i) q^{87} +(-20.3783 + 68.6948i) q^{88} +(-28.9409 - 82.7083i) q^{89} +(-95.4261 - 113.530i) q^{90} +(-87.2947 - 109.464i) q^{91} +(-13.1005 - 1.54583i) q^{92} +(-88.8675 + 24.2748i) q^{93} +(-113.406 + 32.3493i) q^{94} +(-96.3792 + 153.387i) q^{95} +(-95.6516 + 8.17085i) q^{96} +(-0.723496 + 6.42120i) q^{97} +(12.8816 - 219.095i) q^{98} +(32.9510 + 73.5681i) 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

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