LMFDB - Embedded newform 348.3.v.a.95.83

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("348.11");

S:= CuspForms(chi, 3);

N := Newforms(S);

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

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$9.48231319974$
Analytic rank:	$0$
Dimension:	$1392$
Relative dimension:	$116$ over $\Q(\zeta_{28})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{28}]$

Embedding invariants

Embedding label			95.83
Character	$\chi$	$=$	348.95
Dual form			348.3.v.a.11.83

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.15305 + 1.63416i) q^{2} +(-0.209671 - 2.99266i) q^{3} +(-1.34094 + 3.76854i) q^{4} +(-7.42336 + 3.57490i) q^{5} +(4.64872 - 3.79334i) q^{6} +(9.85035 - 7.85539i) q^{7} +(-7.70456 + 2.15403i) q^{8} +(-8.91208 + 1.25495i) q^{9} +O(q^{10})$	\(q+(1.15305 + 1.63416i) q^{2} +(-0.209671 - 2.99266i) q^{3} +(-1.34094 + 3.76854i) q^{4} +(-7.42336 + 3.57490i) q^{5} +(4.64872 - 3.79334i) q^{6} +(9.85035 - 7.85539i) q^{7} +(-7.70456 + 2.15403i) q^{8} +(-8.91208 + 1.25495i) q^{9} +(-14.4015 - 8.00888i) q^{10} +(4.76526 - 7.58386i) q^{11} +(11.5591 + 3.22282i) q^{12} +(10.8341 - 2.47281i) q^{13} +(24.1949 + 7.03933i) q^{14} +(12.2549 + 21.4661i) q^{15} +(-12.4038 - 10.1067i) q^{16} +(12.3870 - 12.3870i) q^{17} +(-12.3269 - 13.1167i) q^{18} +(-2.46170 - 21.8482i) q^{19} +(-3.51790 - 32.7689i) q^{20} +(-25.5739 - 27.8317i) q^{21} +(17.8878 - 0.957421i) q^{22} +(2.97127 + 1.43089i) q^{23} +(8.06170 + 22.6055i) q^{24} +(26.7391 - 33.5297i) q^{25} +(16.5333 + 14.8533i) q^{26} +(5.62425 + 26.4077i) q^{27} +(16.3947 + 47.6550i) q^{28} +(14.6279 + 25.0405i) q^{29} +(-20.9483 + 44.7780i) q^{30} +(10.1421 - 28.9846i) q^{31} +(2.21378 - 31.9233i) q^{32} +(-23.6951 - 12.6707i) q^{33} +(34.5251 + 5.95941i) q^{34} +(-45.0404 + 93.5274i) q^{35} +(7.22120 - 35.2683i) q^{36} +(8.72637 + 13.8879i) q^{37} +(32.8649 - 29.2149i) q^{38} +(-9.67189 - 31.9043i) q^{39} +(49.4932 - 43.5331i) q^{40} +(-51.7371 - 51.7371i) q^{41} +(15.9934 - 73.8832i) q^{42} +(2.01863 - 0.706350i) q^{43} +(22.1902 + 28.1275i) q^{44} +(61.6712 - 41.1757i) q^{45} +(1.08774 + 6.50540i) q^{46} +(-49.9269 - 31.3712i) q^{47} +(-27.6454 + 39.2394i) q^{48} +(24.4187 - 106.985i) q^{49} +(85.6244 + 5.03426i) q^{50} +(-39.6672 - 34.4728i) q^{51} +(-5.20894 + 44.1446i) q^{52} +(0.423138 + 0.878656i) q^{53} +(-36.6693 + 39.6404i) q^{54} +(-8.26265 + 73.3330i) q^{55} +(-58.9718 + 81.7402i) q^{56} +(-64.8682 + 11.9480i) q^{57} +(-24.0533 + 52.7773i) q^{58} +67.8092 q^{59} +(-97.3288 + 17.3986i) q^{60} +(-6.75999 + 59.9966i) q^{61} +(59.0597 - 16.8469i) q^{62} +(-77.9289 + 82.3695i) q^{63} +(54.7203 - 33.1916i) q^{64} +(-71.5853 + 57.0874i) q^{65} +(-6.61580 - 53.3315i) q^{66} +(-11.6499 + 51.0414i) q^{67} +(30.0706 + 63.2909i) q^{68} +(3.65917 - 9.19201i) q^{69} +(-204.772 + 34.2390i) q^{70} +(11.1173 - 2.53745i) q^{71} +(65.9604 - 28.8657i) q^{72} +(-3.22334 + 1.12789i) q^{73} +(-12.6331 + 30.2738i) q^{74} +(-105.950 - 72.9908i) q^{75} +(85.6368 + 20.0200i) q^{76} +(-12.6348 - 112.137i) q^{77} +(40.9845 - 52.5928i) q^{78} +(-11.9669 - 19.0453i) q^{79} +(128.208 + 30.6837i) q^{80} +(77.8502 - 22.3684i) q^{81} +(24.8909 - 144.202i) q^{82} +(-81.0372 + 101.617i) q^{83} +(139.178 - 59.0556i) 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} +(138.398 + 53.3026i) q^{90} +(87.2947 - 109.464i) q^{91} +(-9.37663 + 9.27860i) q^{92} +(-88.8675 - 24.2748i) q^{93} +(-6.30300 - 117.761i) q^{94} +(96.3792 + 153.387i) q^{95} +(-96.0000 + 0.0682937i) q^{96} +(-0.723496 - 6.42120i) q^{97} +(202.986 - 83.4556i) 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 $\left(\mathbb{Z}/348\mathbb{Z}\right)^\times$.

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

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	1.15305	+	1.63416i	0.576527	+	0.817078i
$2$	1.15305	+	1.63416i	0.576527	+	0.817078i
$3$	−0.209671	−	2.99266i	−0.0698904	−	0.997555i
$3$	−0.209671	−	2.99266i	−0.0698904	−	0.997555i
$4$	−1.34094	+	3.76854i	−0.335234	+	0.942135i
$5$	−7.42336	+	3.57490i	−1.48467	+	0.714980i	−0.988214	−	0.153081i	$-0.951081\pi$
$5$	−7.42336	+	3.57490i	−1.48467	+	0.714980i	−0.496458	+	0.868061i	$0.665366\pi$
$6$	4.64872	−	3.79334i	0.774787	−	0.632223i
$7$	9.85035	−	7.85539i	1.40719	−	1.12220i	0.431737	−	0.901999i	$-0.357901\pi$
$7$	9.85035	−	7.85539i	1.40719	−	1.12220i	0.975455	−	0.220199i	$-0.0706707\pi$
$8$	−7.70456	+	2.15403i	−0.963069	+	0.269253i
$9$	−8.91208	+	1.25495i	−0.990231	+	0.139439i
$10$	−14.4015	−	8.00888i	−1.44015	−	0.800888i
$11$	4.76526	−	7.58386i	0.433205	−	0.689442i	−0.556773	−	0.830665i	$-0.687961\pi$
$11$	4.76526	−	7.58386i	0.433205	−	0.689442i	0.989978	+	0.141223i	$0.0451034\pi$
$12$	11.5591	+	3.22282i	0.963261	+	0.268568i
$13$	10.8341	−	2.47281i	0.833392	−	0.190216i	0.215524	−	0.976498i	$-0.430854\pi$
$13$	10.8341	−	2.47281i	0.833392	−	0.190216i	0.617868	+	0.786282i	$0.287997\pi$
$14$	24.1949	+	7.03933i	1.72821	+	0.502809i
$15$	12.2549	+	21.4661i	0.816996	+	1.43107i
$16$	−12.4038	−	10.1067i	−0.775236	−	0.631671i
$17$	12.3870	−	12.3870i	0.728645	−	0.728645i	−0.241705	−	0.970350i	$-0.577707\pi$
$17$	12.3870	−	12.3870i	0.728645	−	0.728645i	0.970350	+	0.241705i	$0.0777066\pi$
$18$	−12.3269	−	13.1167i	−0.684827	−	0.728706i
$19$	−2.46170	−	21.8482i	−0.129563	−	1.14991i	−0.875271	−	0.483632i	$-0.839317\pi$
$19$	−2.46170	−	21.8482i	−0.129563	−	1.14991i	0.745708	−	0.666273i	$-0.232111\pi$
$20$	−3.51790	−	32.7689i	−0.175895	−	1.63845i
$21$	−25.5739	−	27.8317i	−1.21780	−	1.32532i
$22$	17.8878	−	0.957421i	0.813082	−	0.0435192i
$23$	2.97127	+	1.43089i	0.129185	+	0.0622124i	0.497360	−	0.867544i	$-0.334303\pi$
$23$	2.97127	+	1.43089i	0.129185	+	0.0622124i	−0.368175	+	0.929757i	$0.620017\pi$
$24$	8.06170	+	22.6055i	0.335904	+	0.941896i
$25$	26.7391	−	33.5297i	1.06956	−	1.34119i
$26$	16.5333	+	14.8533i	0.635894	+	0.571282i
$27$	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
$30$	−20.9483	+	44.7780i	−0.698277	+	1.49260i
$31$	10.1421	−	28.9846i	0.327166	−	0.934986i	−0.656397	−	0.754416i	$-0.727920\pi$
$31$	10.1421	−	28.9846i	0.327166	−	0.934986i	0.983562	−	0.180570i	$-0.0577941\pi$
$32$	2.21378	−	31.9233i	0.0691807	−	0.997604i
$33$	−23.6951	−	12.6707i	−0.718033	−	0.383960i
$34$	34.5251	+	5.95941i	1.01544	+	0.175277i
$35$	−45.0404	+	93.5274i	−1.28687	+	2.67221i
$36$	7.22120	−	35.2683i	0.200589	−	0.979676i
$37$	8.72637	+	13.8879i	0.235848	+	0.375350i	0.943587	−	0.331124i	$-0.107428\pi$
$37$	8.72637	+	13.8879i	0.235848	+	0.375350i	−0.707739	+	0.706474i	$0.750285\pi$
$38$	32.8649	−	29.2149i	0.864866	−	0.768814i
$39$	−9.67189	−	31.9043i	−0.247997	−	0.818060i
$40$	49.4932	−	43.5331i	1.23733	−	1.08833i
$41$	−51.7371	−	51.7371i	−1.26188	−	1.26188i	−0.950181	−	0.311699i	$-0.899102\pi$
$41$	−51.7371	−	51.7371i	−1.26188	−	1.26188i	−0.311699	−	0.950181i	$-0.600898\pi$
$42$	15.9934	−	73.8832i	0.380794	−	1.75912i
$43$	2.01863	−	0.706350i	0.0469450	−	0.0164268i	−0.306704	−	0.951805i	$-0.599226\pi$
$43$	2.01863	−	0.706350i	0.0469450	−	0.0164268i	0.353649	+	0.935378i	$0.384941\pi$
$44$	22.1902	+	28.1275i	0.504322	+	0.639262i
$45$	61.6712	−	41.1757i	1.37047	−	0.915016i
$46$	1.08774	+	6.50540i	0.0236464	+	0.141422i
$47$	−49.9269	−	31.3712i	−1.06228	−	0.667472i	−0.116796	−	0.993156i	$-0.537263\pi$
$47$	−49.9269	−	31.3712i	−1.06228	−	0.667472i	−0.945479	+	0.325684i	$0.894405\pi$
$48$	−27.6454	+	39.2394i	−0.575945	+	0.817488i
$49$	24.4187	−	106.985i	0.498340	−	2.18337i
$50$	85.6244	+	5.03426i	1.71249	+	0.100685i
$51$	−39.6672	−	34.4728i	−0.777788	−	0.675938i
$52$	−5.20894	+	44.1446i	−0.100172	+	0.848935i
$53$	0.423138	+	0.878656i	0.00798374	+	0.0165784i	0.904923	−	0.425576i	$-0.139929\pi$
$53$	0.423138	+	0.878656i	0.00798374	+	0.0165784i	−0.896939	+	0.442155i	$0.854214\pi$
$54$	−36.6693	+	39.6404i	−0.679061	+	0.734082i
$55$	−8.26265	+	73.3330i	−0.150230	+	1.33333i
$56$	−58.9718	+	81.7402i	−1.05307	+	1.45965i
$57$	−64.8682	+	11.9480i	−1.13804	+	0.209614i
$58$	−24.0533	+	52.7773i	−0.414711	+	0.909953i
$59$	67.8092			1.14931			0.574654	−	0.818396i	$-0.305137\pi$
$59$	67.8092			1.14931			0.574654	+	0.818396i	$0.305137\pi$
$60$	−97.3288	+	17.3986i	−1.62215	+	0.289977i
$61$	−6.75999	+	59.9966i	−0.110820	+	0.983551i	0.808084	+	0.589068i	$0.200505\pi$
$61$	−6.75999	+	59.9966i	−0.110820	+	0.983551i	−0.918903	+	0.394483i	$0.870924\pi$
$62$	59.0597	−	16.8469i	0.952576	−	0.271724i
$63$	−77.9289	+	82.3695i	−1.23697	+	1.30745i
$64$	54.7203	−	33.1916i	0.855005	−	0.518619i
$65$	−71.5853	+	57.0874i	−1.10131	+	0.878267i
$66$	−6.61580	−	53.3315i	−0.100239	−	0.808053i
$67$	−11.6499	+	51.0414i	−0.173879	+	0.761813i	0.810499	+	0.585741i	$0.199196\pi$
$67$	−11.6499	+	51.0414i	−0.173879	+	0.761813i	−0.984377	+	0.176072i	$0.943661\pi$
$68$	30.0706	+	63.2909i	0.442215	+	0.930748i
$69$	3.65917	−	9.19201i	0.0530315	−	0.133218i
$70$	−204.772	+	34.2390i	−2.92532	+	0.489128i
$71$	11.1173	−	2.53745i	0.156582	−	0.0357388i	−0.143511	−	0.989649i	$-0.545839\pi$
$71$	11.1173	−	2.53745i	0.156582	−	0.0357388i	0.300093	+	0.953910i	$0.402982\pi$
$72$	65.9604	−	28.8657i	0.916116	−	0.400912i
$73$	−3.22334	+	1.12789i	−0.0441553	+	0.0154506i	−0.352266	−	0.935900i	$-0.614589\pi$
$73$	−3.22334	+	1.12789i	−0.0441553	+	0.0154506i	0.308111	+	0.951350i	$0.400303\pi$
$74$	−12.6331	+	30.2738i	−0.170718	+	0.409105i
$75$	−105.950	−	72.9908i	−1.41266	−	0.973211i
$76$	85.6368	+	20.0200i	1.12680	+	0.263421i
$77$	−12.6348	−	112.137i	−0.164088	−	1.45632i
$78$	40.9845	−	52.5928i	0.525442	−	0.674267i
$79$	−11.9669	−	19.0453i	−0.151480	−	0.241079i	0.762360	−	0.647153i	$-0.224040\pi$
$79$	−11.9669	−	19.0453i	−0.151480	−	0.241079i	−0.913840	+	0.406074i	$0.866898\pi$
$80$	128.208	+	30.6837i	1.60260	+	0.383546i
$81$	77.8502	−	22.3684i	0.961114	−	0.276153i
$82$	24.8909	−	144.202i	0.303547	−	1.75856i
$83$	−81.0372	+	101.617i	−0.976351	+	1.22431i	−0.00183311	+	0.999998i	$0.500583\pi$
$83$	−81.0372	+	101.617i	−0.976351	+	1.22431i	−0.974518	+	0.224308i	$0.927988\pi$
$84$	139.178	−	59.0556i	1.65688	−	0.703043i
$85$	−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	0.659003	+	0.752141i	$0.270979\pi$
$89$	−28.9409	+	82.7083i	−0.325178	+	0.929307i	−0.984181	+	0.177166i	$0.943307\pi$
$90$	138.398	+	53.3026i	1.53775	+	0.592251i
$91$	87.2947	−	109.464i	0.959283	−	1.20290i
$92$	−9.37663	+	9.27860i	−0.101920	+	0.100854i
$93$	−88.8675	−	24.2748i	−0.955565	−	0.261019i
$94$	−6.30300	−	117.761i	−0.0670532	−	1.25278i
$95$	96.3792	+	153.387i	1.01452	+	1.61460i
$96$	−96.0000	+	0.0682937i	−1.00000	+	0.000711392i
$97$	−0.723496	−	6.42120i	−0.00745872	−	0.0661980i	0.989431	−	0.145001i	$-0.0463186\pi$
$97$	−0.723496	−	6.42120i	−0.00745872	−	0.0661980i	−0.996890	+	0.0788034i	$0.974890\pi$
$98$	202.986	−	83.4556i	2.07129	−	0.851588i
$99$	−32.9510	+	73.5681i	−0.332838	+	0.743112i
$100$	90.5027	+	145.728i	0.905027	+	1.45728i
$101$	−22.9053	+	8.01491i	−0.226785	+	0.0793556i	−0.441280	−	0.897370i	$-0.645475\pi$
$101$	−22.9053	+	8.01491i	−0.226785	+	0.0793556i	0.214494	+	0.976725i	$0.431190\pi$
$102$	10.5956	−	104.571i	0.103878	−	1.02521i
$103$	46.0913	−	10.5200i	0.447488	−	0.102136i	0.00716250	−	0.999974i	$-0.497720\pi$
$103$	46.0913	−	10.5200i	0.447488	−	0.102136i	0.440326	+	0.897838i	$0.354863\pi$
$104$	−78.1454	+	42.3889i	−0.751398	+	0.407585i
$105$	289.340	+	115.181i	2.75562	+	1.09696i
$106$	−0.947960	+	1.70461i	−0.00894302	+	0.0160812i
$107$	11.3705	−	49.8175i	0.106267	−	0.465584i	−0.893594	−	0.448876i	$-0.851824\pi$
$107$	11.3705	−	49.8175i	0.106267	−	0.465584i	0.999860	−	0.0167077i	$-0.00531848\pi$
$108$	−107.060	−	14.2159i	−0.991299	−	0.131628i
$109$	−88.0007	+	70.1782i	−0.807346	+	0.643837i	−0.937628	−	0.347640i	$-0.886983\pi$
$109$	−88.0007	+	70.1782i	−0.807346	+	0.643837i	0.130282	+	0.991477i	$0.458412\pi$
$110$	−129.365	+	71.0544i	−1.17604	+	0.645949i
$111$	39.7323	−	29.0270i	0.357948	−	0.261505i
$112$	−201.574	−	2.11840i	−1.79977	−	0.0189143i
$113$	11.5081	−	102.137i	0.101841	−	0.903867i	−0.834077	−	0.551649i	$-0.813999\pi$
$113$	11.5081	−	102.137i	0.101841	−	0.903867i	0.935918	−	0.352218i	$-0.114572\pi$
$114$	−94.3213	−	92.2281i	−0.827380	−	0.809018i
$115$	−27.1720			−0.236279
$116$	−113.981	+	21.5482i	−0.982595	+	0.185760i
$117$	−93.4510	+	35.6341i	−0.798727	+	0.304565i
$118$	78.1876	+	110.811i	0.662607	+	0.939075i
$119$	24.7115	−	219.320i	0.207659	−	1.84303i
$120$	−140.657	−	138.989i	−1.17214	−	1.15824i
$121$	17.6926	+	36.7391i	0.146220	+	0.303629i
$122$	−105.838	+	58.1324i	−0.867528	+	0.476495i
$123$	−143.984	+	165.679i	−1.17060	+	1.34699i
$124$	95.6295	+	77.0875i	0.771205	+	0.621673i
$125$	−32.7928	+	143.674i	−0.262342	+	1.14940i
$126$	−224.461	−	32.3716i	−1.78144	−	0.256918i
$127$	−33.8975	−	21.2992i	−0.266909	−	0.167710i	0.391927	−	0.919996i	$-0.371808\pi$
$127$	−33.8975	−	21.2992i	−0.266909	−	0.167710i	−0.658837	+	0.752286i	$0.728951\pi$
$128$	117.336	+	51.1499i	0.916686	+	0.399608i
$129$	−2.53712	−	5.89299i	−0.0196676	−	0.0456821i
$130$	−175.831	−	51.1568i	−1.35255	−	0.393514i
$131$	126.950	−	44.4218i	0.969085	−	0.339098i	0.201104	−	0.979570i	$-0.435547\pi$
$131$	126.950	−	44.4218i	0.969085	−	0.339098i	0.767981	+	0.640472i	$0.221261\pi$
$132$	79.5236	−	72.3053i	0.602452	−	0.547767i
$133$	−195.875	−	195.875i	−1.47274	−	1.47274i
$134$	−96.8426	+	39.8158i	−0.722706	+	0.297133i
$135$	−136.156	−	175.928i	−1.00856	−	1.30317i
$136$	−68.7542	+	122.118i	−0.505546	+	0.897926i
$137$	27.6837	+	44.0584i	0.202071	+	0.321594i	0.932351	−	0.361553i	$-0.117753\pi$
$137$	27.6837	+	44.0584i	0.202071	+	0.321594i	−0.730280	+	0.683148i	$0.760611\pi$
$138$	19.2404	−	4.61922i	0.139423	−	0.0334726i
$139$	51.1707	−	106.257i	0.368135	−	0.764440i	−0.631808	−	0.775125i	$-0.717687\pi$
$139$	51.1707	−	106.257i	0.368135	−	0.764440i	0.999943	+	0.0106851i	$0.00340122\pi$
$140$	−292.065	−	295.151i	−2.08618	−	2.10822i
$141$	−83.4151	+	155.992i	−0.591597	+	1.10633i
$142$	16.9655	+	15.2416i	0.119475	+	0.107335i
$143$	32.8738	−	93.9479i	0.229887	−	0.656978i
$144$	123.227	+	74.5059i	0.855742	+	0.517402i
$145$	−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
$148$	−64.0388	+	14.2628i	−0.432694	+	0.0963705i
$149$	143.830	−	180.357i	0.965303	−	1.21045i	−0.0122854	−	0.999925i	$-0.503911\pi$
$149$	143.830	−	180.357i	0.965303	−	1.21045i	0.977588	−	0.210527i	$-0.0675179\pi$
$150$	−2.88711	−	257.301i	−0.0192474	−	1.71534i
$151$	181.270	+	87.2952i	1.20047	+	0.578114i	0.923809	−	0.382855i	$-0.125059\pi$
$151$	181.270	+	87.2952i	1.20047	+	0.578114i	0.276658	+	0.960969i	$0.410773\pi$
$152$	66.0279	+	163.028i	0.434394	+	1.07255i
$153$	−94.8485	+	125.939i	−0.619925	+	0.823128i
$154$	168.680	−	149.947i	1.09533	−	0.973680i
$155$	28.3282	+	251.420i	0.182763	+	1.62206i
$156$	133.202	+	6.33277i	0.853860	+	0.0405947i
$157$	168.898	−	168.898i	1.07578	−	1.07578i	0.0788995	−	0.996883i	$-0.474859\pi$
$157$	168.898	−	168.898i	1.07578	−	1.07578i	0.996883	−	0.0788995i	$-0.0251406\pi$
$158$	17.3244	−	41.5160i	0.109648	−	0.262760i
$159$	2.54080	−	1.45054i	0.0159799	−	0.00912289i
$160$	97.6890	+	244.892i	0.610556	+	1.53058i
$161$	40.5082	−	9.24572i	0.251603	−	0.0574269i
$162$	126.319	+	101.427i	0.779747	+	0.626095i
$163$	−123.311	+	196.248i	−0.756508	+	1.20398i	0.217189	+	0.976130i	$0.430311\pi$
$163$	−123.311	+	196.248i	−0.756508	+	1.20398i	−0.973697	+	0.227846i	$0.926832\pi$
$164$	264.349	−	125.597i	1.61189	−	0.765836i
$165$	221.194	+	9.35151i	1.34057	+	0.0566758i
$166$	−259.499	−	15.2572i	−1.56325	−	0.0919106i
$167$	156.400	−	124.725i	0.936525	−	0.746854i	−0.0310287	−	0.999518i	$-0.509878\pi$
$167$	156.400	−	124.725i	0.936525	−	0.746854i	0.967554	+	0.252664i	$0.0813069\pi$
$168$	256.986	+	159.344i	1.52968	+	0.948478i
$169$	−41.0009	+	19.7450i	−0.242609	+	0.116834i
$170$	−277.596	+	79.1848i	−1.63292	+	0.465793i
$171$	49.3573	+	191.623i	0.288639	+	1.12061i
$172$	−0.0449495	+	8.55447i	−0.000261334	+	0.0497353i
$173$	54.3576			0.314206			0.157103	−	0.987582i	$-0.449785\pi$
$173$	54.3576			0.314206			0.157103	+	0.987582i	$0.449785\pi$
$174$	162.988	+	60.9175i	0.936712	+	0.350100i
$175$		−	540.325i		−	3.08757i
$176$	−135.755	+	45.9073i	−0.771337	+	0.260837i
$177$	−14.2176	−	202.930i	−0.0803256	−	1.14650i
$178$	−168.529	+	48.0731i	−0.946790	+	0.270074i
$179$	−41.2458	−	85.6477i	−0.230423	−	0.478479i	0.753413	−	0.657547i	$-0.228406\pi$
$179$	−41.2458	−	85.6477i	−0.230423	−	0.478479i	−0.983837	+	0.179068i	$0.942692\pi$
$180$	72.4752	+	287.624i	0.402640	+	1.59791i
$181$	7.03803	+	8.82541i	0.0388841	+	0.0487592i	0.800893	−	0.598807i	$-0.204358\pi$
$181$	7.03803	+	8.82541i	0.0388841	+	0.0487592i	−0.762009	+	0.647566i	$0.775787\pi$
$182$	279.537	+	16.4353i	1.53592	+	0.0903038i
$183$	180.967	+	7.65083i	0.988891	+	0.0418078i
$184$	−25.9744	−	4.62415i	−0.141165	−	0.0251313i
$185$	−114.427	−	71.8992i	−0.618524	−	0.388645i
$186$	−62.8002	−	173.214i	−0.337636	−	0.931256i
$187$	−34.9140	−	152.968i	−0.186706	−	0.818011i
$188$	185.172	−	146.085i	0.984959	−	0.777047i
$189$	262.844	+	215.945i	1.39071	+	1.14256i
$190$	−139.527	+	334.362i	−0.734355	+	1.75980i
$191$	−27.7867	−	27.7867i	−0.145480	−	0.145480i	0.630615	−	0.776096i	$-0.282803\pi$
$191$	−27.7867	−	27.7867i	−0.145480	−	0.145480i	−0.776096	+	0.630615i	$0.782803\pi$
$192$	−110.805	−	156.800i	−0.577108	−	0.816668i
$193$	−347.108	+	39.1097i	−1.79849	+	0.202641i	−0.946890	−	0.321558i	$-0.895794\pi$
$193$	−347.108	+	39.1097i	−1.79849	+	0.202641i	−0.851596	+	0.524199i	$0.824365\pi$
$194$	9.65903	−	8.58630i	0.0497888	−	0.0442593i
$195$	185.853	+	202.261i	0.953091	+	1.03724i
$196$	370.434	+	235.483i	1.88997	+	1.20144i
$197$	24.2005	−	50.2528i	0.122845	−	0.255090i	−0.830473	−	0.557059i	$-0.811930\pi$
$197$	24.2005	−	50.2528i	0.122845	−	0.255090i	0.953318	+	0.301969i	$0.0976439\pi$
$198$	−158.216	+	30.9809i	−0.799071	+	0.156469i
$199$	113.887	+	90.8221i	0.572298	+	0.456393i	0.866378	−	0.499388i	$-0.166442\pi$
$199$	113.887	+	90.8221i	0.572298	+	0.456393i	−0.294080	+	0.955781i	$0.595013\pi$
$200$	−133.789	+	315.928i	−0.668943	+	1.57964i
$201$	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
$204$	183.103	−	103.262i	0.897566	−	0.506184i
$205$	569.018	+	199.108i	2.77570	+	0.971258i
$206$	70.3371	+	63.1902i	0.341442	+	0.306749i
$207$	−28.2758	−	9.02337i	−0.136598	−	0.0435912i
$208$	−159.376	−	78.8252i	−0.766230	−	0.378967i
$209$	−177.424	−	85.4431i	−0.848920	−	0.408818i
$210$	145.401	+	605.636i	0.692383	+	2.88398i
$211$	−300.761	+	188.981i	−1.42541	+	0.895644i	−0.999956	−	0.00933739i	$-0.997028\pi$
$211$	−300.761	+	188.981i	−1.42541	+	0.895644i	−0.425452	+	0.904981i	$0.639885\pi$
$212$	−3.87865	+	0.416392i	−0.0182955	+	0.00196411i
$213$	−9.92473	−	32.7384i	−0.0465950	−	0.153701i
$214$	94.5204	−	38.8610i	0.441684	−	0.181594i
$215$	−12.4599	+	12.4599i	−0.0579530	+	0.0579530i
$216$	−100.215	−	191.345i	−0.463960	−	0.885856i
$217$	−127.781	−	365.178i	−0.588854	−	1.68285i
$218$	−216.152	−	62.8877i	−0.991521	−	0.288476i
$219$	4.05125	+	9.40988i	0.0184989	+	0.0429675i
$220$	−265.279	−	129.473i	−1.20581	−	0.588514i
$221$	103.571	−	164.832i	0.468647	−	0.745847i
$222$	93.2481	+	31.4591i	0.420037	+	0.141708i
$223$	340.960	+	77.8220i	1.52897	+	0.348978i	0.902577	−	0.430529i	$-0.141673\pi$
$223$	340.960	+	77.8220i	1.52897	+	0.348978i	0.626394	+	0.779507i	$0.284530\pi$
$224$	−228.964	−	331.846i	−1.02216	−	1.48146i
$225$	−196.222	+	332.376i	−0.872100	+	1.47723i
$226$	180.177	−	98.9634i	0.797244	−	0.437891i
$227$	−229.770	+	110.651i	−1.01220	+	0.487451i	−0.865062	−	0.501665i	$-0.832721\pi$
$227$	−229.770	+	110.651i	−1.01220	+	0.487451i	−0.147140	+	0.989116i	$0.547007\pi$
$228$	41.9576	−	260.480i	0.184025	−	1.14245i
$229$	−25.2875	−	2.84922i	−0.110426	−	0.0124420i	0.0565786	−	0.998398i	$-0.481981\pi$
$229$	−25.2875	−	2.84922i	−0.110426	−	0.0124420i	−0.167004	+	0.985956i	$0.553409\pi$
$230$	−31.3308	−	44.4034i	−0.136221	−	0.193058i
$231$	−332.938	+	61.3234i	−1.44129	+	0.265469i
$232$	−166.639	−	161.417i	−0.718273	−	0.695761i
$233$			216.468i			0.929045i	0.885561	+	0.464523i	$0.153774\pi$
$233$			216.468i			0.929045i	−0.885561	+	0.464523i	$0.846226\pi$
$234$	−165.986	−	111.626i	−0.709341	−	0.477032i
$235$	482.774	+	54.3956i	2.05436	+	0.231471i
$236$	−90.9278	+	255.542i	−0.385287	+	1.08280i
$237$	−54.4869	+	39.8062i	−0.229903	+	0.167959i
$238$	386.897	−	212.506i	1.62562	−	0.892881i
$239$	−17.6884	−	22.1805i	−0.0740099	−	0.0928054i	0.743448	−	0.668793i	$-0.233189\pi$
$239$	−17.6884	−	22.1805i	−0.0740099	−	0.0928054i	−0.817458	+	0.575988i	$0.804618\pi$
$240$	64.9444	−	390.118i	0.270602	−	1.62549i
$241$	85.0984	+	19.4231i	0.353105	+	0.0805940i	0.395394	−	0.918511i	$-0.370608\pi$
$241$	85.0984	+	19.4231i	0.353105	+	0.0805940i	−0.0422892	+	0.999105i	$0.513465\pi$
$242$	−39.6370	+	71.2747i	−0.163789	+	0.294524i
$243$	−83.2641	−	228.289i	−0.342651	−	0.939463i
$244$	−217.035	−	105.927i	−0.889487	−	0.434127i
$245$	201.193	+	881.483i	0.821195	+	3.59789i
$246$	−436.767	−	44.2550i	−1.77548	−	0.179899i
$247$	−80.6968	−	230.618i	−0.326708	−	0.933677i
$248$	−15.7071	+	245.160i	−0.0633352	+	0.988546i
$249$	321.098	+	221.211i	1.28955	+	0.888397i
$250$	−272.598	+	112.076i	−1.09039	+	0.448303i
$251$	−110.753	+	12.4789i	−0.441248	+	0.0497167i	−0.329794	−	0.944053i	$-0.606979\pi$
$251$	−110.753	+	12.4789i	−0.441248	+	0.0497167i	−0.111454	+	0.993770i	$0.535551\pi$
$252$	−205.915	−	404.130i	−0.817123	−	1.60369i
$253$	25.0105	−	15.7151i	0.0988557	−	0.0621151i
$254$	−4.27937	−	79.9530i	−0.0168479	−	0.314775i
$255$	417.701	+	114.098i	1.63804	+	0.447442i
$256$	51.7075	+	250.724i	0.201982	+	0.979389i
$257$	349.010	+	278.326i	1.35801	+	1.08298i	0.988083	+	0.153922i	$0.0491903\pi$
$257$	349.010	+	278.326i	1.35801	+	1.08298i	0.369932	+	0.929059i	$0.379381\pi$
$258$	6.70464	−	10.9410i	0.0259870	−	0.0424069i
$259$	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	$-0.293170\pi$
$263$	152.957	+	53.5221i	0.581587	+	0.203506i	−0.0234209	+	0.999726i	$0.507456\pi$
$264$	209.853	+	46.5822i	0.794898	+	0.176448i
$265$	−6.28221	−	5.00990i	−0.0237065	−	0.0189053i
$266$	94.2360	−	545.944i	0.354271	−	2.05242i
$267$	253.586	+	69.2688i	0.949761	+	0.259434i
$268$	−176.730	−	112.346i	−0.659440	−	0.419203i
$269$	30.3333	−	19.0597i	0.112763	−	0.0708538i	−0.474470	−	0.880272i	$-0.657360\pi$
$269$	30.3333	−	19.0597i	0.112763	−	0.0708538i	0.587233	+	0.809418i	$0.300217\pi$
$270$	130.499	−	425.354i	0.483329	−	1.57539i
$271$	105.443	−	11.8806i	0.389088	−	0.0438397i	0.0847462	−	0.996403i	$-0.472992\pi$
$271$	105.443	−	11.8806i	0.389088	−	0.0438397i	0.304342	+	0.952563i	$0.401563\pi$
$272$	−278.837	+	28.4533i	−1.02514	+	0.104608i
$273$	−345.892	−	238.292i	−1.26701	−	0.872866i
$274$	−40.0775	+	96.0413i	−0.146268	+	0.350516i
$275$	−126.866	−	362.563i	−0.461332	−	1.31841i
$276$	29.7338	+	26.1156i	0.107731	+	0.0946219i
$277$	43.8368	+	192.062i	0.158256	+	0.693364i	0.990334	+	0.138705i	$0.0442940\pi$
$277$	43.8368	+	192.062i	0.158256	+	0.693364i	−0.832078	+	0.554659i	$0.812849\pi$
$278$	232.643	−	38.8991i	0.836847	−	0.139925i
$279$	−54.0133	+	271.040i	−0.193596	+	0.971471i
$280$	145.556	−	817.605i	0.519842	−	2.92002i
$281$	393.484	+	89.8101i	1.40030	+	0.319609i	0.854997	−	0.518632i	$-0.173559\pi$
$281$	393.484	+	89.8101i	1.40030	+	0.319609i	0.545300	+	0.838241i	$0.316416\pi$
$282$	−351.098	+	43.5539i	−1.24503	+	0.154446i
$283$	115.562	+	144.911i	0.408347	+	0.512051i	0.942896	−	0.333086i	$-0.108090\pi$
$283$	115.562	+	144.911i	0.408347	+	0.512051i	−0.534549	+	0.845137i	$0.679519\pi$
$284$	−5.34511	+	45.2986i	−0.0188208	+	0.159502i
$285$	438.827	−	320.591i	1.53974	−	1.12488i
$286$	191.431	−	54.6060i	0.669338	−	0.190930i
$287$	−916.043	−	103.213i	−3.19179	−	0.359628i
$288$	20.3328	+	287.281i	0.0706000	+	0.997505i
$289$		−	17.8738i		−	0.0618470i
$290$	−10.1175	−	477.773i	−0.0348881	−	1.64749i
$291$	−19.0648	+	3.51152i	−0.0655148	+	0.0120671i
$292$	0.0717750	−	13.6597i	0.000245805	−	0.0467798i
$293$	242.837	+	27.3612i	0.828795	+	0.0933828i	0.516162	−	0.856491i	$-0.327360\pi$
$293$	242.837	+	27.3612i	0.828795	+	0.0933828i	0.312633	+	0.949874i	$0.398789\pi$
$294$	−292.315	−	589.972i	−0.994269	−	2.00671i
$295$	−503.372	+	242.411i	−1.70634	+	0.821732i
$296$	−97.1478	−	88.2036i	−0.328202	−	0.297985i
$297$	227.074	+	83.1860i	0.764557	+	0.280088i
$298$	460.576	+	27.0794i	1.54556	+	0.0908705i
$299$	35.7293	+	8.15498i	0.119496	+	0.0272742i
$300$	417.141	−	301.399i	1.39047	−	1.00466i
$301$	14.3356	−	22.8149i	0.0476265	−	0.0757972i
$302$	66.3603	+	396.880i	0.219736	+	1.31417i
$303$	28.7885	+	66.8674i	0.0950116	+	0.220684i
$304$	−190.280	+	295.880i	−0.625920	+	0.973289i
$305$	−164.300	−	469.542i	−0.538688	−	1.53948i
$306$	−315.169	−	9.78347i	−1.02996	−	0.0319721i
$307$	−113.195	+	113.195i	−0.368715	+	0.368715i	−0.867008	−	0.498294i	$-0.833960\pi$
$307$	−113.195	+	113.195i	−0.368715	+	0.368715i	0.498294	+	0.867008i	$0.333960\pi$
$308$	439.534	+	102.753i	1.42706	+	0.333615i
$309$	−41.1469	−	135.730i	−0.133162	−	0.439256i
$310$	−378.195	+	336.193i	−1.21999	+	1.08449i
$311$	232.388	−	146.019i	0.747228	−	0.469514i	−0.103824	−	0.994596i	$-0.533108\pi$
$311$	232.388	−	146.019i	0.747228	−	0.469514i	0.851052	+	0.525081i	$0.175965\pi$
$312$	143.240	+	224.975i	0.459104	+	0.721074i
$313$	−4.36835	−	2.10369i	−0.0139564	−	0.00672105i	0.426893	−	0.904302i	$-0.359608\pi$
$313$	−4.36835	−	2.10369i	−0.0139564	−	0.00672105i	−0.440849	+	0.897581i	$0.645323\pi$
$314$	470.754	+	81.2573i	1.49922	+	0.258781i
$315$	284.031	−	890.046i	0.901687	−	2.82554i
$316$	87.8197	−	19.5594i	0.277910	−	0.0618967i
$317$	1.80121	+	0.630271i	0.00568205	+	0.00198824i	0.333119	−	0.942885i	$-0.391899\pi$
$317$	1.80121	+	0.630271i	0.00568205	+	0.00198824i	−0.327437	+	0.944873i	$0.606185\pi$
$318$	5.30009	+	2.47952i	0.0166669	+	0.00779723i
$319$	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
$322$	61.8170	+	55.5359i	0.191978	+	0.172472i
$323$	−301.126	−	240.140i	−0.932278	−	0.743467i
$324$	−20.0959	+	323.376i	−0.0620242	+	0.998075i
$325$	206.781	−	429.385i	0.636249	−	1.32118i
$326$	−462.884	+	24.7752i	−1.41989	+	0.0759977i
$327$	228.471	+	248.642i	0.698688	+	0.760373i
$328$	510.054	+	287.168i	1.55504	+	0.875512i
$329$	−738.230	+	83.1786i	−2.24386	+	0.252822i
$330$	239.766	+	372.248i	0.726564	+	1.12802i
$331$	32.8915	+	32.8915i	0.0993700	+	0.0993700i	0.755044	−	0.655674i	$-0.227615\pi$
$331$	32.8915	+	32.8915i	0.0993700	+	0.0993700i	−0.655674	+	0.755044i	$0.727615\pi$
$332$	−274.284	−	441.654i	−0.826155	−	1.33028i
$333$	−95.1988	−	112.819i	−0.285882	−	0.338797i
$334$	384.157	+	111.768i	1.15017	+	0.334633i
$335$	−95.9869	−	420.546i	−0.286528	−	1.25536i
$336$	35.9246	+	603.687i	0.106918	+	1.79669i
$337$	−386.252	−	242.698i	−1.14615	−	0.720172i	−0.181415	−	0.983407i	$-0.558068\pi$
$337$	−386.252	−	242.698i	−1.14615	−	0.720172i	−0.964732	+	0.263235i	$0.915211\pi$
$338$	−79.5426	−	44.2348i	−0.235333	−	0.130872i
$339$	−308.074	−	13.0246i	−0.908774	−	0.0384207i
$340$	−449.484	−	362.331i	−1.32201	−	1.06568i
$341$	−171.485	−	215.035i	−0.502888	−	0.630602i
$342$	−256.231	+	301.610i	−0.749214	+	0.881899i
$343$	−332.018	−	689.442i	−0.967981	−	2.01003i
$344$	−14.0312	+	9.79031i	−0.0407883	+	0.0284602i
$345$	5.69719	+	81.3168i	0.0165136	+	0.235701i
$346$	62.6772	+	88.8288i	0.181148	+	0.256731i
$347$		−	107.269i		−	0.309133i	−0.987982	−	0.154567i	$-0.950602\pi$
$347$		−	107.269i		−	0.309133i	0.987982	−	0.154567i	$-0.0493981\pi$
$348$	88.3851	+	336.589i	0.253980	+	0.967209i
$349$	−242.414			−0.694595			−0.347298	−	0.937755i	$-0.612901\pi$
$349$	−242.414			−0.694595			−0.347298	+	0.937755i	$0.612901\pi$
$350$	882.976	−	623.024i	2.52279	−	1.78007i
$351$	126.235	+	272.196i	0.359644	+	0.775488i
$352$	−231.553	−	168.912i	−0.657821	−	0.479863i
$353$	−217.639	+	104.809i	−0.616541	+	0.296911i	−0.715967	−	0.698134i	$-0.754014\pi$
$353$	−217.639	+	104.809i	−0.616541	+	0.296911i	0.0994255	+	0.995045i	$0.468300\pi$
$354$	315.226	−	257.223i	0.890469	−	0.726619i
$355$	−73.4566	+	58.5797i	−0.206920	+	0.165013i
$356$	−272.882	−	219.971i	−0.766521	−	0.617897i
$357$	−661.533	−	27.9680i	−1.85303	−	0.0783417i
$358$	92.4032	−	166.158i	0.258110	−	0.464130i
$359$	−158.797	+	252.724i	−0.442332	+	0.703967i	−0.991263	−	0.131900i	$-0.957892\pi$
$359$	−158.797	+	252.724i	−0.442332	+	0.703967i	0.548931	+	0.835868i	$0.315035\pi$
$360$	−386.456	+	450.082i	−1.07349	+	1.25023i
$361$	−119.335	+	27.2374i	−0.330567	+	0.0754498i
$362$	−6.30688	+	21.6774i	−0.0174223	+	0.0598824i
$363$	106.238	−	60.6513i	0.292667	−	0.167083i
$364$	295.463	+	475.758i	0.811712	+	1.30703i
$365$	19.8959	−	19.8959i	0.0545092	−	0.0545092i
$366$	196.162	+	304.550i	0.535962	+	0.832105i
$367$	−24.1405	−	214.253i	−0.0657778	−	0.583795i	−0.982763	−	0.184872i	$-0.940813\pi$
$367$	−24.1405	−	214.253i	−0.0657778	−	0.583795i	0.916985	−	0.398922i	$-0.130616\pi$
$368$	−22.3933	−	47.7782i	−0.0608514	−	0.129832i
$369$	526.012	+	396.157i	1.42551	+	1.07360i
$370$	−14.4458	−	269.895i	−0.0390427	−	0.729447i
$371$	11.0702	+	5.33115i	0.0298389	+	0.0143697i
$372$	210.646	−	302.350i	0.566253	−	0.812769i
$373$	−36.1453	+	45.3248i	−0.0969043	+	0.121514i	−0.827919	−	0.560847i	$-0.810475\pi$
$373$	−36.1453	+	45.3248i	−0.0969043	+	0.121514i	0.731015	+	0.682361i	$0.239047\pi$
$374$	209.716	−	233.435i	0.560738	−	0.624158i
$375$	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
$378$	−49.8144	+	678.523i	−0.131784	+	1.79504i
$379$	−236.972	+	677.226i	−0.625255	+	1.78688i	−0.00818644	+	0.999966i	$0.502606\pi$
$379$	−236.972	+	677.226i	−0.625255	+	1.78688i	−0.617068	+	0.786909i	$0.711680\pi$
$380$	−707.282	+	157.527i	−1.86127	+	0.414545i
$381$	−56.6341	+	105.910i	−0.148646	+	0.277978i
$382$	13.3683	−	77.4474i	0.0349955	−	0.202742i
$383$	−205.929	+	427.615i	−0.537673	+	1.11649i	0.438347	+	0.898806i	$0.355564\pi$
$383$	−205.929	+	427.615i	−0.537673	+	1.11649i	−0.976020	+	0.217683i	$0.930150\pi$
$384$	128.472	−	361.871i	0.334564	−	0.942373i
$385$	494.670	+	787.262i	1.28486	+	2.04484i
$386$	−464.145	−	522.133i	−1.20245	−	1.35268i
$387$	−17.1038	+	8.82833i	−0.0441958	+	0.0228122i
$388$	25.1687	+	5.88390i	0.0648679	+	0.0151647i
$389$	−116.655	−	116.655i	−0.299883	−	0.299883i	0.541085	−	0.840968i	$-0.318014\pi$
$389$	−116.655	−	116.655i	−0.299883	−	0.299883i	−0.840968	+	0.541085i	$0.818014\pi$
$390$	−116.228	+	536.930i	−0.298022	+	1.37674i
$391$	54.5293	−	19.0806i	0.139461	−	0.0487996i
$392$	42.3139	+	876.871i	0.107944	+	2.23692i
$393$	−159.557	−	370.605i	−0.405998	−	0.943016i
$394$	110.025	−	18.3968i	0.279252	−	0.0466924i
$395$	156.920	+	98.5992i	0.397265	+	0.249618i
$396$	−233.059	−	222.827i	−0.588533	−	0.562695i
$397$	−132.680	+	581.309i	−0.334207	+	1.46425i	0.476693	+	0.879070i	$0.341835\pi$
$397$	−132.680	+	581.309i	−0.334207	+	1.46425i	−0.810900	+	0.585185i	$0.801022\pi$
$398$	−17.0994	+	290.833i	−0.0429633	+	0.730735i
$399$	−545.118	+	627.256i	−1.36621	+	1.57207i
$400$	−670.542	+	145.651i	−1.67635	+	0.364126i
$401$	−164.525	−	341.640i	−0.410287	−	0.851970i	−0.999046	−	0.0436618i	$-0.986098\pi$
$401$	−164.525	−	341.640i	−0.410287	−	0.851970i	0.588759	−	0.808309i	$-0.299617\pi$
$402$	139.460	+	281.469i	0.346916	+	0.700172i
$403$	38.2075	−	339.101i	0.0948077	−	0.841442i
$404$	0.510039	−	97.0670i	0.00126247	−	0.240265i
$405$	−497.945	+	444.356i	−1.22949	+	1.09717i
$406$	177.653	+	708.822i	0.437569	+	1.74587i
$407$	146.908			0.360952
$408$	379.874	+	180.154i	0.931063	+	0.441553i
$409$	52.7403	−	468.083i	0.128949	−	1.14446i	−0.747940	−	0.663766i	$-0.768957\pi$
$409$	52.7403	−	468.083i	0.128949	−	1.14446i	0.876890	−	0.480692i	$-0.159614\pi$
$410$	330.734	+	1159.45i	0.806669	+	2.82792i
$411$	126.048	−	92.0859i	0.306685	−	0.224053i
$412$	−22.1603	+	187.804i	−0.0537872	+	0.455834i
$413$	667.944	−	532.667i	1.61730	−	1.28975i
$414$	−17.8579	−	56.6116i	−0.0431351	−	0.136743i
$415$	238.296	−	1044.04i	0.574207	−	2.51576i
$416$	−54.9561	−	351.335i	−0.132106	−	0.844555i
$417$	−328.721	−	130.858i	−0.788300	−	0.313808i
$418$	−64.9524	−	388.460i	−0.155388	−	0.929329i
$419$	651.248	−	148.643i	1.55429	−	0.354757i	0.642786	−	0.766046i	$-0.277778\pi$
$419$	651.248	−	148.643i	1.55429	−	0.354757i	0.911505	+	0.411289i	$0.134921\pi$
$420$	−822.049	+	935.938i	−1.95726	+	2.22842i
$421$	−305.053	+	106.743i	−0.724592	+	0.253546i	−0.667276	−	0.744810i	$-0.732540\pi$
$421$	−305.053	+	106.743i	−0.724592	+	0.253546i	−0.0573160	+	0.998356i	$0.518254\pi$
$422$	−655.618	−	273.586i	−1.55360	−	0.648308i
$423$	484.322	+	216.926i	1.14497	+	0.512828i
$424$	−5.15274	−	5.85820i	−0.0121527	−	0.0138165i
$425$	−84.1157	−	746.548i	−0.197919	−	1.75658i
$426$	42.0559	−	53.9676i	0.0987227	−	0.126685i
$427$	404.708	+	644.089i	0.947795	+	1.50841i
$428$	172.492	+	109.652i	0.403019	+	0.256197i
$429$	−288.047	−	78.6820i	−0.671439	−	0.183408i
$430$	−34.7284	−	5.99450i	−0.0807636	−	0.0139407i
$431$	138.901	−	174.176i	0.322275	−	0.404120i	−0.594132	−	0.804367i	$-0.702504\pi$
$431$	138.901	−	174.176i	0.322275	−	0.404120i	0.916407	+	0.400247i	$0.131076\pi$
$432$	197.134	−	384.398i	0.456329	−	0.889811i
$433$	−215.756	+	616.596i	−0.498282	+	1.42401i	0.370509	+	0.928829i	$0.379183\pi$
$433$	−215.756	+	616.596i	−0.498282	+	1.42401i	−0.868791	+	0.495179i	$0.835102\pi$
$434$	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
$438$	−10.7059	+	17.4705i	−0.0244427	+	0.0398869i
$439$	−87.7701	+	110.060i	−0.199932	+	0.250707i	−0.871683	−	0.490070i	$-0.836971\pi$
$439$	−87.7701	+	110.060i	−0.199932	+	0.250707i	0.671751	+	0.740777i	$0.265542\pi$
$440$	−94.3013	−	582.796i	−0.214321	−	1.32454i
$441$	−83.3599	+	984.104i	−0.189025	+	2.23153i
$442$	388.784	−	20.8092i	0.879603	−	0.0470796i
$443$	289.644	+	460.966i	0.653825	+	1.04056i	0.994934	+	0.100532i	$0.0320545\pi$
$443$	289.644	+	460.966i	0.653825	+	1.04056i	−0.341109	+	0.940024i	$0.610803\pi$
$444$	56.1110	+	188.656i	0.126376	+	0.424901i
$445$	−80.8354	−	717.434i	−0.181653	−	1.61221i
$446$	265.972	+	646.916i	0.596350	+	1.45048i
$447$	−569.906	−	392.619i	−1.27496	−	0.878343i
$448$	278.281	−	756.799i	0.621163	−	1.68928i
$449$	−345.703	+	120.967i	−0.769941	+	0.269414i	−0.686530	−	0.727101i	$-0.740867\pi$
$449$	−345.703	+	120.967i	−0.769941	+	0.269414i	−0.0834105	+	0.996515i	$0.526581\pi$
$450$	−769.409	+	62.5887i	−1.70980	+	0.139086i
$451$	−638.907	+	145.826i	−1.41665	+	0.323340i
$452$	369.476	+	180.328i	0.817424	+	0.398955i
$453$	223.238	−	560.785i	0.492799	−	1.23794i
$454$	−445.759	−	247.893i	−0.981848	−	0.546020i
$455$	−256.697	+	1124.66i	−0.564168	+	2.47178i
$456$	474.044	−	231.782i	1.03957	−	0.508293i
$457$	435.404	−	347.223i	0.952744	−	0.759788i	−0.0180167	−	0.999838i	$-0.505735\pi$
$457$	435.404	−	347.223i	0.952744	−	0.759788i	0.970761	+	0.240050i	$0.0771638\pi$
$458$	−24.5018	−	44.6090i	−0.0534973	−	0.0973996i
$459$	396.779	+	257.444i	0.864442	+	0.560880i
$460$	36.4360	−	102.399i	0.0792086	−	0.222606i
$461$	3.07648	−	27.3045i	0.00667349	−	0.0592288i	−0.989934	−	0.141529i	$-0.954798\pi$
$461$	3.07648	−	27.3045i	0.00667349	−	0.0592288i	0.996608	+	0.0823003i	$0.0262267\pi$
$462$	−484.107	−	473.364i	−1.04785	−	1.02460i
$463$	86.2101			0.186199			0.0930995	−	0.995657i	$-0.470323\pi$
$463$	86.2101			0.186199			0.0930995	+	0.995657i	$0.470323\pi$
$464$	71.6360	−	458.437i	0.154388	−	0.988010i
$465$	746.475	−	137.492i	1.60532	−	0.295682i
$466$	−353.742	+	249.599i	−0.759103	+	0.535619i
$467$	18.1798	−	161.350i	0.0389288	−	0.345503i	−0.959117	−	0.283011i	$-0.908667\pi$
$467$	18.1798	−	161.350i	0.0389288	−	0.345503i	0.998045	−	0.0624918i	$-0.0199047\pi$
$468$	−8.97678	−	399.957i	−0.0191812	−	0.854609i
$469$	286.195	+	594.290i	0.610224	+	1.26714i
$470$	467.773	+	851.650i	0.995263	+	1.81202i
$471$	−540.867	−	470.041i	−1.14834	−	0.997965i
$472$	−522.440	+	146.063i	−1.10686	+	0.309455i
$473$	4.26244	−	18.6750i	0.00901150	−	0.0394820i
$474$	−127.876	−	43.1415i	−0.269781	−	0.0910158i
$475$	−798.388	−	501.660i	−1.68082	−	1.05613i
$476$	793.381	+	387.221i	1.66677	+	0.813489i
$477$	−4.87371	−	7.29963i	−0.0102174	−	0.0153032i
$478$	15.8508	−	54.4809i	0.0331607	−	0.113977i
$479$	−289.622	+	101.343i	−0.604639	+	0.211572i	−0.615199	−	0.788372i	$-0.710924\pi$
$479$	−289.622	+	101.343i	−0.604639	+	0.211572i	0.0105600	+	0.999944i	$0.496639\pi$
$480$	712.398	−	343.697i	1.48416	−	0.716036i
$481$	128.885	+	128.885i	0.267951	+	0.267951i
$482$	66.3825	+	161.460i	0.137723	+	0.334979i
$483$	−36.1627	−	119.289i	−0.0748711	−	0.246975i
$484$	−162.178	+	17.4106i	−0.335078	+	0.0359722i
$485$	28.3259	+	45.0805i	0.0584040	+	0.0929494i
$486$	277.053	−	399.297i	0.570068	−	0.821598i
$487$	−22.8819	+	47.5147i	−0.0469854	+	0.0975662i	−0.923140	−	0.384464i	$-0.874386\pi$
$487$	−22.8819	+	47.5147i	−0.0469854	+	0.0975662i	0.876155	+	0.482030i	$0.160101\pi$
$488$	−77.1515	−	476.808i	−0.158097	−	0.977066i
$489$	613.159	+	327.880i	1.25390	+	0.670512i
$490$	−1208.50	+	1345.18i	−2.46632	+	2.74526i
$491$	−125.103	+	357.523i	−0.254792	+	0.728152i	0.743445	+	0.668797i	$0.233190\pi$
$491$	−125.103	+	357.523i	−0.254792	+	0.728152i	−0.998237	+	0.0593557i	$0.981095\pi$
$492$	−431.296	−	764.775i	−0.876618	−	1.55442i
$493$	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
$496$	−418.740	+	257.014i	−0.844234	+	0.518174i
$497$	89.5767	−	112.326i	0.180235	−	0.226007i
$498$	8.74987	+	779.792i	0.0175700	+	1.56585i
$499$	764.700	+	368.260i	1.53246	+	0.737996i	0.994477	−	0.104957i	$-0.0334704\pi$
$499$	764.700	+	368.260i	1.53246	+	0.737996i	0.537988	+	0.842953i	$0.319185\pi$
$500$	−497.470	−	316.239i	−0.994940	−	0.632478i
$501$	−406.051	−	441.901i	−0.810482	−	0.882037i
$502$	−148.097	−	166.599i	−0.295014	−	0.331871i
$503$	−19.2101	−	170.494i	−0.0381910	−	0.338954i	−0.998249	−	0.0591531i	$-0.981160\pi$
$503$	−19.2101	−	170.494i	−0.0381910	−	0.338954i	0.960058	−	0.279801i	$-0.0902686\pi$
$504$	422.981	−	802.481i	0.839249	−	1.59223i
$505$	141.382	−	141.382i	0.279964	−	0.279964i
$506$	54.5194	+	22.7507i	0.107746	+	0.0449618i
$507$	67.6868	+	118.562i	0.133504	+	0.233850i
$508$	125.721	−	99.1832i	0.247483	−	0.195242i
$509$	−653.008	+	149.045i	−1.28292	+	0.292819i	−0.809032	−	0.587765i	$-0.800008\pi$
$509$	−653.008	+	149.045i	−1.28292	+	0.292819i	−0.473891	+	0.880584i	$0.657151\pi$
$510$	295.178	+	814.149i	0.578780	+	1.59637i
$511$	−22.8909	+	36.4307i	−0.0447964	+	0.0712930i
$512$	−350.100	+	373.596i	−0.683789	+	0.729679i
$513$	563.116	−	187.888i	1.09769	−	0.366253i
$514$	−52.4015	+	891.261i	−0.101948	+	1.73397i
$515$	−304.544	+	242.866i	−0.591348	+	0.471584i
$516$	25.6101	−	1.65911i	0.0496319	−	0.00321532i
$517$	−475.829	+	229.147i	−0.920366	+	0.443225i
$518$	113.372	+	397.445i	0.218865	+	0.767269i
$519$	−11.3972	−	162.674i	−0.0219600	−	0.313437i
$520$	428.565	−	594.030i	0.824164	−	1.14236i
$521$	−355.660			−0.682649			−0.341325	−	0.939945i	$-0.610876\pi$
$521$	−355.660			−0.682649			−0.341325	+	0.939945i	$0.610876\pi$
$522$	148.132	−	500.541i	0.283777	−	0.958890i
$523$		−	354.535i		−	0.677886i	−0.940807	−	0.338943i	$-0.889931\pi$
$523$		−	354.535i		−	0.677886i	0.940807	−	0.338943i	$-0.110069\pi$
$524$	−2.82684	+	537.983i	−0.00539472	+	1.02669i
$525$	−1617.01	+	113.291i	−3.08002	+	0.215792i
$526$	88.9045	+	311.670i	0.169020	+	0.592529i
$527$	−233.400	−	484.661i	−0.442885	−	0.919660i
$528$	165.849	+	396.645i	0.314108	+	0.751221i
$529$	−323.045	−	405.086i	−0.610671	−	0.765758i
$530$	0.943231	−	16.0428i	0.00177968	−	0.0302694i
$531$	−604.321	+	85.0972i	−1.13808	+	0.160258i
$532$	1000.82	−	475.506i	1.88123	−	0.893808i
$533$	−688.461	−	432.588i	−1.29167	−	0.811611i
$534$	179.202	+	494.270i	0.335585	+	0.925600i
$535$	93.6852	+	410.461i	0.175112	+	0.767218i
$536$	−20.1875	−	418.346i	−0.0376633	−	0.780496i
$537$	−247.667	+	141.393i	−0.461204	+	0.263301i
$538$	66.1224	+	27.5925i	0.122904	+	0.0512872i
$539$	−694.999	−	694.999i	−1.28942	−	1.28942i
$540$	845.567	−	277.200i	1.56587	−	0.513334i
$541$	650.212	−	73.2613i	1.20187	−	0.135418i	0.511764	−	0.859126i	$-0.328992\pi$
$541$	650.212	−	73.2613i	1.20187	−	0.135418i	0.690106	+	0.723708i	$0.257564\pi$
$542$	140.996	+	158.611i	0.260140	+	0.292641i
$543$	24.9358	−	22.9129i	0.0459223	−	0.0421969i
$544$	−368.011	−	422.855i	−0.676491	−	0.777307i
$545$	402.380	−	835.551i	0.738313	−	1.53312i
$546$	−9.42552	−	840.006i	−0.0172629	−	1.53847i
$547$	90.1814	+	71.9173i	0.164866	+	0.131476i	0.702447	−	0.711736i	$-0.252091\pi$
$547$	90.1814	+	71.9173i	0.164866	+	0.131476i	−0.537582	+	0.843212i	$0.680662\pi$
$548$	−203.158	+	45.2477i	−0.370726	+	0.0825689i
$549$	−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
$552$	−8.39245	+	78.7023i	−0.0152037	+	0.142577i
$553$	−267.486	−	93.5975i	−0.483700	−	0.169254i
$554$	−263.313	+	293.094i	−0.475294	+	0.529050i
$555$	−191.178	+	357.517i	−0.344465	+	0.644174i
$556$	331.817	+	335.323i	0.596794	+	0.603099i
$557$	−430.201	−	207.174i	−0.772353	−	0.371946i	0.00582995	−	0.999983i	$-0.498144\pi$
$557$	−430.201	−	207.174i	−0.772353	−	0.371946i	−0.778183	+	0.628037i	$0.783859\pi$
$558$	−505.203	+	224.258i	−0.905381	+	0.401896i
$559$	20.1234	−	12.6444i	0.0359989	−	0.0226196i
$560$	1503.93	−	704.881i	2.68559	−	1.25872i
$561$	−450.462	+	136.559i	−0.802962	+	0.243420i
$562$	306.944	+	746.570i	0.546163	+	1.32842i
$563$	418.869	−	418.869i	0.743994	−	0.743994i	−0.229350	−	0.973344i	$-0.573660\pi$
$563$	418.869	−	418.869i	0.743994	−	0.743994i	0.973344	+	0.229350i	$0.0736601\pi$
$564$	−476.008	−	523.529i	−0.843986	−	0.928242i
$565$	279.701	+	799.339i	0.495046	+	1.41476i
$566$	−103.557	+	355.937i	−0.182963	+	0.628863i
$567$	591.139	−	831.880i	1.04257	−	1.46716i
$568$	−80.1882	+	43.4969i	−0.141176	+	0.0765791i
$569$	101.406	−	161.387i	0.178218	−	0.283632i	−0.745655	−	0.666333i	$-0.767863\pi$
$569$	101.406	−	161.387i	0.178218	−	0.283632i	0.923872	+	0.382701i	$0.125006\pi$
$570$	1029.89	+	347.453i	1.80682	+	0.609566i
$571$	−557.747	−	127.302i	−0.976789	−	0.222946i	−0.295809	−	0.955247i	$-0.595589\pi$
$571$	−557.747	−	127.302i	−0.976789	−	0.222946i	−0.680981	+	0.732301i	$0.738446\pi$
$572$	309.965	+	249.864i	0.541896	+	0.436826i
$573$	−77.3302	+	88.9824i	−0.134957	+	0.155292i
$574$	−887.580	−	1615.97i	−1.54631	−	2.81528i
$575$	127.426	−	61.3652i	0.221611	−	0.106722i
$576$	−446.018	+	364.478i	−0.774337	+	0.632774i
$577$	256.248	+	28.8722i	0.444104	+	0.0500385i	0.331185	−	0.943566i	$-0.392552\pi$
$577$	256.248	+	28.8722i	0.444104	+	0.0500385i	0.112919	+	0.993604i	$0.463980\pi$
$578$	29.2086	−	20.6094i	0.0505338	−	0.0356564i
$579$	189.821	+	1030.58i	0.327842	+	1.77993i
$580$	769.089	−	567.431i	1.32602	−	0.978329i
$581$			1637.55i			2.81849i
$582$	−27.7211	−	27.1059i	−0.0476308	−	0.0465737i
$583$	8.67996	+	0.977997i	0.0148884	+	0.00167752i
$584$	22.4049	−	15.6331i	0.0383645	−	0.0267690i
$585$	566.332	−	598.603i	0.968089	−	1.02325i
$586$	235.292	+	428.383i	0.401522	+	0.731028i
$587$	−67.7706	−	84.9816i	−0.115452	−	0.144773i	0.720747	−	0.693198i	$-0.243799\pi$
$587$	−67.7706	−	84.9816i	−0.115452	−	0.144773i	−0.836200	+	0.548425i	$0.815227\pi$
$588$	627.052	−	1157.96i	1.06641	−	1.96932i
$589$	−658.227	−	150.236i	−1.11753	−	0.255070i
$590$	−976.552	−	543.075i	−1.65517	−	0.920467i
$591$	−155.464	−	61.8873i	−0.263052	−	0.104716i
$592$	32.1219	−	260.458i	0.0542599	−	0.439963i
$593$	106.769	+	467.784i	0.180048	+	0.788843i	0.981605	+	0.190924i	$0.0611484\pi$
$593$	106.769	+	467.784i	0.180048	+	0.788843i	−0.801557	+	0.597919i	$0.795994\pi$
$594$	125.889	+	466.992i	0.211934	+	0.786181i
$595$	600.606	+	1716.43i	1.00942	+	2.88476i
$596$	486.816	+	783.877i	0.816806	+	1.31523i
$597$	247.921	−	359.869i	0.415278	−	0.602796i
$598$	27.8713	+	67.7904i	0.0466075	+	0.113362i
$599$	310.835	−	35.0227i	0.518923	−	0.0584686i	0.151381	−	0.988476i	$-0.451628\pi$
$599$	310.835	−	35.0227i	0.518923	−	0.0584686i	0.367542	+	0.930007i	$0.380199\pi$
$600$	973.519	+	334.144i	1.62253	+	0.556906i
$601$	895.781	−	562.857i	1.49048	−	0.936534i	0.492687	−	0.870207i	$-0.336015\pi$
$601$	895.781	−	562.857i	1.49048	−	0.936534i	0.997798	−	0.0663270i	$-0.0211281\pi$
$602$	53.8129	−	2.88026i	0.0893902	−	0.00478449i
$603$	39.7701	−	469.505i	0.0659537	−	0.778616i
$604$	−572.048	+	566.067i	−0.947099	+	0.937197i
$605$	−262.678	−	209.478i	−0.434178	−	0.346245i
$606$	−76.0771	+	124.147i	−0.125540	+	0.204862i
$607$	−163.798	−	57.3153i	−0.269848	−	0.0944239i	0.191963	−	0.981402i	$-0.438515\pi$
$607$	−163.798	−	57.3153i	−0.269848	−	0.0944239i	−0.461811	+	0.886978i	$0.652800\pi$
$608$	−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
$612$	−347.419	−	526.316i	−0.567678	−	0.859994i
$613$	−58.3739	−	46.5516i	−0.0952266	−	0.0759407i	0.574719	−	0.818351i	$-0.305111\pi$
$613$	−58.3739	−	46.5516i	−0.0952266	−	0.0759407i	−0.669946	+	0.742410i	$0.733683\pi$
$614$	−315.499	−	54.4587i	−0.513842	−	0.0886949i
$615$	476.556	−	1744.63i	0.774889	−	2.83679i
$616$	338.890	+	836.747i	0.550147	+	1.35836i
$617$	192.136	−	120.727i	0.311404	−	0.195668i	−0.367258	−	0.930119i	$-0.619703\pi$
$617$	192.136	−	120.727i	0.311404	−	0.195668i	0.678661	+	0.734451i	$0.262560\pi$
$618$	174.359	−	223.744i	0.282135	−	0.362046i
$619$	−698.399	+	78.6907i	−1.12827	+	0.127126i	−0.656308	−	0.754493i	$-0.727883\pi$
$619$	−698.399	+	78.6907i	−1.12827	+	0.127126i	−0.471962	+	0.881619i	$0.656454\pi$
$620$	−985.472	−	230.382i	−1.58947	−	0.371584i
$621$	−21.0753	+	86.5120i	−0.0339377	+	0.139311i
$622$	506.573	+	211.391i	0.814427	+	0.339856i
$623$	364.628	+	1042.05i	0.585278	+	1.67263i
$624$	−202.481	+	493.486i	−0.324489	+	0.790842i
$625$	−31.6130	−	138.505i	−0.0505808	−	0.221609i
$626$	−1.59919	−	9.56424i	−0.00255461	−	0.0152783i
$627$	−218.502	+	548.886i	−0.348487	+	0.875417i
$628$	410.017	+	862.979i	0.652893	+	1.37417i
$629$	280.123	+	63.9362i	0.445346	+	0.101647i
$630$	1781.98	−	562.119i	2.82854	−	0.892253i
$631$	87.6828	+	109.951i	0.138958	+	0.174248i	0.846441	−	0.532482i	$-0.178741\pi$
$631$	87.6828	+	109.951i	0.138958	+	0.174248i	−0.707483	+	0.706731i	$0.750169\pi$
$632$	133.224	+	120.958i	0.210797	+	0.191389i
$633$	628.617	+	860.453i	0.993076	+	1.35933i
$634$	1.04693	+	3.67020i	0.00165131	+	0.00578895i
$635$	327.776	+	36.9315i	0.516182	+	0.0581598i
$636$	2.05936	+	11.5202i	0.00323799	+	0.0181135i
$637$		−	1219.47i		−	1.91440i
$638$	285.636	+	433.914i	0.447705	+	0.680116i
$639$	−95.8940	+	36.5657i	−0.150069	+	0.0572233i
$640$	−1053.88	+	39.7599i	−1.64669	+	0.0621249i
$641$	−1155.25	−	130.165i	−1.80226	−	0.203066i	−0.853937	−	0.520376i	$-0.825792\pi$
$641$	−1155.25	−	130.165i	−1.80226	−	0.203066i	−0.948322	+	0.317310i	$0.897220\pi$
$642$	−136.116	−	274.720i	−0.212019	−	0.427912i
$643$	−323.797	+	155.932i	−0.503572	+	0.242507i	−0.668382	−	0.743818i	$-0.733013\pi$
$643$	−323.797	+	155.932i	−0.503572	+	0.242507i	0.164811	+	0.986325i	$0.447299\pi$
$644$	−19.4760	+	165.055i	−0.0302422	+	0.256296i
$645$	39.9008	+	34.6758i	0.0618617	+	0.0537610i
$646$	45.2120	−	768.981i	0.0699876	−	1.19037i
$647$	798.040	+	182.147i	1.23345	+	0.281526i	0.789064	−	0.614311i	$-0.210566\pi$
$647$	798.040	+	182.147i	1.23345	+	0.281526i	0.444382	+	0.895837i	$0.353423\pi$
$648$	−551.619	+	340.030i	−0.851264	+	0.524738i
$649$	323.128	−	514.255i	0.497886	−	0.792381i
$650$	940.112	−	157.191i	1.44633	−	0.241833i
$651$	−1066.06	+	458.974i	−1.63758	+	0.705029i
$652$	−574.216	−	727.858i	−0.880700	−	1.11635i
$653$	−23.0323	−	65.8224i	−0.0352715	−	0.100800i	0.924901	−	0.380208i	$-0.124148\pi$
$653$	−23.0323	−	65.8224i	−0.0352715	−	0.100800i	−0.960173	+	0.279408i	$0.909862\pi$
$654$	−142.881	+	660.055i	−0.218472	+	1.00926i
$655$	−783.593	+	783.593i	−1.19632	+	1.19632i
$656$	118.842	+	1164.63i	0.181162	+	1.77535i
$657$	27.3112	−	14.0970i	0.0415695	−	0.0214566i
$658$	−987.146	−	1110.47i	−1.50022	−	1.68765i
$659$	−133.562	+	83.9224i	−0.202673	+	0.127348i	−0.629545	−	0.776964i	$-0.716759\pi$
$659$	−133.562	+	83.9224i	−0.202673	+	0.127348i	0.426871	+	0.904312i	$0.359616\pi$
$660$	−331.848	+	821.037i	−0.502800	+	1.24400i
$661$	1039.94	+	500.809i	1.57328	+	0.757654i	0.998173	−	0.0604213i	$-0.0192444\pi$
$661$	1039.94	+	500.809i	1.57328	+	0.757654i	0.575111	+	0.818075i	$0.304959\pi$
$662$	−15.8242	+	91.6754i	−0.0239036	+	0.138482i
$663$	−515.003	−	275.392i	−0.776777	−	0.415373i
$664$	405.469	−	957.473i	0.610646	−	1.44198i
$665$	2154.28	+	753.815i	3.23952	+	1.13356i
$666$	74.5951	−	285.656i	0.112005	−	0.428913i
$667$	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
$670$	576.560	−	641.769i	0.860537	−	0.957865i
$671$	422.793	+	337.166i	0.630093	+	0.502483i
$672$	−945.097	+	754.790i	−1.40639	+	1.12320i
$673$	−308.677	+	640.974i	−0.458658	+	0.952413i	0.535506	+	0.844531i	$0.320121\pi$
$673$	−308.677	+	640.974i	−0.458658	+	0.952413i	−0.994164	+	0.107881i	$0.965593\pi$
$674$	−48.7622	−	911.039i	−0.0723474	−	1.35169i
$675$	1035.83	+	517.538i	1.53456	+	0.766723i
$676$	−19.4302	−	180.990i	−0.0287429	−	0.267737i
$677$	1051.44	−	118.469i	1.55309	−	0.174991i	0.706685	−	0.707529i	$-0.250190\pi$
$677$	1051.44	−	118.469i	1.55309	−	0.174991i	0.846407	+	0.532537i	$0.178761\pi$
$678$	−333.942	−	518.460i	−0.492540	−	0.764690i
$679$	−57.5677	−	57.5677i	−0.0847831	−	0.0847831i
$680$	73.8276	−	1152.31i	0.108570	−	1.69458i
$681$	379.319	+	664.424i	0.557002	+	0.975659i
$682$	153.670	−	528.181i	0.225323	−	0.774458i
$683$	−168.547	−	738.453i	−0.246775	−	1.08119i	−0.934708	−	0.355416i	$-0.884339\pi$
$683$	−168.547	−	738.453i	−0.246775	−	1.08119i	0.687933	−	0.725774i	$-0.258518\pi$
$684$	−788.326	−	70.9501i	−1.15252	−	0.103728i
$685$	−363.011	−	228.095i	−0.529943	−	0.332985i
$686$	743.822	−	1337.53i	1.08429	−	1.94975i
$687$	−3.22469	+	76.2744i	−0.00469387	+	0.111025i
$688$	−32.1776	−	11.6404i	−0.0467697	−	0.0169192i
$689$	6.75707	+	8.47310i	0.00980707	+	0.0122977i
$690$	−126.315	+	103.073i	−0.183066	+	0.149381i
$691$	−418.512	−	869.049i	−0.605661	−	1.25767i	−0.948053	−	0.318111i	$-0.896951\pi$
$691$	−418.512	−	869.049i	−0.605661	−	1.25767i	0.342392	−	0.939557i	$-0.388763\pi$
$692$	−72.8901	+	204.849i	−0.105332	+	0.296024i
$693$	253.328	+	983.514i	0.365552	+	1.41921i
$694$	175.295	−	123.687i	0.252586	−	0.178223i
$695$			971.715i			1.39815i
$696$	−448.126	+	532.540i	−0.643860	+	0.765144i
$697$	−1281.73			−1.83892
$698$	−279.516	−	396.142i	−0.400453	−	0.567539i
$699$	647.815	−	45.3870i	0.926774	−	0.0649313i
$700$	2036.24	+	724.542i	2.90891	+	1.03506i
$701$	−706.242	+	340.108i	−1.00748	+	0.485176i	−0.863470	−	0.504401i	$-0.831713\pi$
$701$	−706.242	+	340.108i	−1.00748	+	0.485176i	−0.144008	+	0.989576i	$0.545999\pi$
$702$	−299.255	+	520.144i	−0.426290	+	0.740946i
$703$	281.945	−	224.843i	0.401059	−	0.319834i
$704$	9.03565	−	573.158i	0.0128347	−	0.814145i
$705$	61.5639	−	1456.19i	0.0873247	−	2.06551i
$706$	−422.225	−	234.805i	−0.598052	−	0.332586i
$707$	−162.665	+	258.880i	−0.230078	+	0.366167i
$708$	783.815	+	218.537i	1.10708	+	0.308668i
$709$	−842.252	+	192.239i	−1.18794	+	0.271140i	−0.770427	−	0.637528i	$-0.779957\pi$
$709$	−842.252	+	192.239i	−1.18794	+	0.271140i	−0.417517	+	0.908669i	$0.637100\pi$
$710$	−180.428	−	52.4941i	−0.254124	−	0.0739354i
$711$	130.551	+	154.715i	0.183616	+	0.217602i
$712$	44.8207	−	699.570i	0.0629505	−	0.982542i
$713$	71.6086	−	71.6086i	0.100433	−	0.100433i
$714$	−717.079	−	1113.30i	−1.00431	−	1.55924i
$715$	91.8205	+	814.929i	0.128420	+	1.13976i
$716$	378.075	−	40.5882i	0.528037	−	0.0566874i
$717$	−62.6701	+	57.5859i	−0.0874059	+	0.0803151i
$718$	−596.093	+	31.9051i	−0.830213	+	0.0444360i
$719$	551.083	+	265.388i	0.766458	+	0.369107i	0.775906	−	0.630849i	$-0.217293\pi$
$719$	551.083	+	265.388i	0.766458	+	0.369107i	−0.00944809	+	0.999955i	$0.503007\pi$
$720$	−1181.11	−	112.560i	−1.64043	−	0.156334i
$721$	371.376	−	465.691i	0.515085	−	0.645896i
$722$	−182.109	−	163.605i	−0.252229	−	0.226600i
$723$	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
$726$	221.612	+	103.676i	0.305251	+	0.142804i
$727$	329.675	−	942.157i	0.453473	−	1.29595i	−0.459589	−	0.888132i	$-0.652003\pi$
$727$	329.675	−	942.157i	0.453473	−	1.29595i	0.913062	−	0.407820i	$-0.133711\pi$
$728$	−436.778	+	1031.41i	−0.599970	+	1.41677i
$729$	−665.736	+	297.047i	−0.913218	+	0.407472i
$730$	55.4540	+	9.57197i	0.0759644	+	0.0131123i
$731$	16.2552	−	33.7543i	0.0222369	−	0.0461755i
$732$	−271.498	+	671.722i	−0.370898	+	0.917653i
$733$	−94.6858	−	150.692i	−0.129176	−	0.205582i	0.775874	−	0.630888i	$-0.217309\pi$
$733$	−94.6858	−	150.692i	−0.129176	−	0.205582i	−0.905050	+	0.425306i	$0.860166\pi$
$734$	322.287	−	286.494i	0.439083	−	0.390319i
$735$	2595.80	−	786.924i	3.53170	−	1.07064i
$736$	52.2564	−	91.6850i	0.0710005	−	0.124572i
$737$	331.577	+	331.577i	0.449900	+	0.449900i
$738$	−40.8630	+	1316.38i	−0.0553699	+	1.78371i
$739$	−496.501	+	173.733i	−0.671855	+	0.235092i	−0.644581	−	0.764536i	$-0.722968\pi$
$739$	−496.501	+	173.733i	−0.671855	+	0.235092i	−0.0272738	+	0.999628i	$0.508683\pi$
$740$	424.394	−	334.810i	0.573506	−	0.452446i
$741$	−673.243	+	289.852i	−0.908560	+	0.391164i
$742$	4.05265	+	24.2376i	0.00546179	+	0.0326652i
$743$	514.788	+	323.463i	0.692850	+	0.435347i	0.831890	−	0.554940i	$-0.187259\pi$
$743$	514.788	+	323.463i	0.692850	+	0.435347i	−0.139040	+	0.990287i	$0.544402\pi$
$744$	736.973	−	4.39672i	0.990556	−	0.00590957i
$745$	−422.943	+	1853.03i	−0.567709	+	2.48729i
$746$	−115.745	−	6.80520i	−0.155154	−	0.00912226i
$747$	594.685	−	1007.32i	0.796097	−	1.34849i
$748$	623.284	+	73.5458i	0.833267	+	0.0983233i
$749$	−279.332	−	580.039i	−0.372940	−	0.774418i
$750$	392.561	+	792.296i	0.523415	+	1.05640i
$751$	146.504	−	1300.26i	0.195079	−	1.73137i	−0.390365	−	0.920660i	$-0.627651\pi$
$751$	146.504	−	1300.26i	0.195079	−	1.73137i	0.585444	−	0.810713i	$-0.300920\pi$
$752$	302.222	+	893.720i	0.401891	+	1.18846i
$753$	60.5669	+	328.831i	0.0804342	+	0.436695i
$754$	−130.087	+	631.273i	−0.172529	+	0.837233i
$755$	−1657.71			−2.19564
$756$	−1166.25	+	700.969i	−1.54266	+	0.927208i
$757$	−55.8937	+	496.071i	−0.0738359	+	0.655311i	0.901222	+	0.433359i	$0.142672\pi$
$757$	−55.8937	+	496.071i	−0.0738359	+	0.655311i	−0.975057	+	0.221953i	$0.928757\pi$
$758$	−1379.93	+	393.629i	−1.82049	+	0.519299i
$759$	−52.2741	−	71.5530i	−0.0688723	−	0.0942727i
$760$	−1072.96	−	974.172i	−1.41179	−	1.28181i
$761$	−729.784	+	581.984i	−0.958981	+	0.764762i	−0.971958	−	0.235154i	$-0.924441\pi$
$761$	−729.784	+	581.984i	−0.958981	+	0.764762i	0.0129772	+	0.999916i	$0.495869\pi$
$762$	−238.375	+	29.5706i	−0.312828	+	0.0388065i
$763$	−315.560	+	1382.56i	−0.413578	+	1.81200i
$764$	141.976	−	67.4551i	0.185832	−	0.0882920i
$765$	253.877	−	1273.96i	0.331865	−	1.66531i
$766$	−936.237	+	156.543i	−1.22224	+	0.204365i
$767$	734.651	−	167.679i	0.957824	−	0.218617i
$768$	739.490	−	207.313i	0.962878	−	0.269938i
$769$	935.004	−	327.172i	1.21587	−	0.425451i	0.355285	−	0.934758i	$-0.384384\pi$
$769$	935.004	−	327.172i	1.21587	−	0.425451i	0.860585	+	0.509307i	$0.170098\pi$
$770$	−716.129	+	1716.12i	−0.930038	+	2.22873i
$771$	759.759	−	1102.83i	0.985420	−	1.43038i
$772$	318.063	−	1360.53i	0.411999	−	1.76235i
$773$	25.2027	+	223.681i	0.0326038	+	0.289367i	0.999425	+	0.0339120i	$0.0107966\pi$
$773$	25.2027	+	223.681i	0.0326038	+	0.289367i	−0.966821	+	0.255455i	$0.917775\pi$
$774$	−34.1484	−	17.7707i	−0.0441194	−	0.0229596i
$775$	−700.653	−	1115.08i	−0.904068	−	1.43882i
$776$	19.4057	+	47.9141i	0.0250073	+	0.0617450i
$777$	163.358	−	598.039i	0.210242	−	0.769676i
$778$	56.1229	−	325.141i	0.0721374	−	0.417919i
$779$	−1003.00	+	1257.72i	−1.28755	+	1.61454i
$780$	−1011.45	+	429.174i	−1.29673	+	0.550223i
$781$	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
$786$	421.649	−	688.069i	0.536449	−	0.875406i
$787$	503.140	−	630.918i	0.639314	−	0.801674i	−0.351603	−	0.936149i	$-0.614363\pi$
$787$	503.140	−	630.918i	0.639314	−	0.801674i	0.990917	+	0.134475i	$0.0429347\pi$
$788$	156.928	+	158.586i	0.199148	+	0.201252i
$789$	128.103	−	468.972i	0.162361	−	0.594388i
$790$	19.8103	+	370.121i	0.0250763	+	0.468508i
$791$	−688.967	−	1096.48i	−0.871008	−	1.38620i
$792$	95.4048	−	637.787i	0.120461	−	0.805286i
$793$	75.1219	+	666.725i	0.0947312	+	0.840763i
$794$	−1102.94	+	453.460i	−1.38909	+	0.571109i
$795$	−13.6757	+	19.8510i	−0.0172022	+	0.0249698i
$796$	−494.982	+	307.402i	−0.621837	+	0.386184i
$797$	13.2134	−	4.62356i	0.0165789	−	0.00580120i	−0.321977	−	0.946748i	$-0.604347\pi$
$797$	13.2134	−	4.62356i	0.0165789	−	0.00580120i	0.338556	+	0.940946i	$0.390062\pi$
$798$	−1653.59	−	167.548i	−2.07216	−	0.209960i
$799$	−1007.04	+	229.850i	−1.26037	+	0.287672i
$800$	−1011.19	−	927.828i	−1.26398	−	1.15978i
$801$	154.129	−	773.422i	0.192420	−	0.965570i
$802$	368.587	−	662.789i	0.459585	−	0.826421i
$803$	−6.80623	+	29.8201i	−0.00847601	+	0.0371358i
$804$	−299.160	+	552.449i	−0.372089	+	0.687126i
$805$	−267.654	+	213.447i	−0.332489	+	0.265151i
$806$	598.200	−	328.565i	0.742183	−	0.407648i
$807$	−63.3992	−	86.7811i	−0.0785616	−	0.107535i
$808$	159.211	−	111.090i	0.197043	−	0.137488i
$809$	−53.3424	+	473.427i	−0.0659363	+	0.585201i	0.916689	+	0.399601i	$0.130851\pi$
$809$	−53.3424	+	473.427i	−0.0659363	+	0.585201i	−0.982625	+	0.185600i	$0.940577\pi$
$810$	−1300.30	−	301.354i	−1.60531	−	0.372043i
$811$	1355.13			1.67094			0.835471	−	0.549535i	$-0.185195\pi$
$811$	1355.13			1.67094			0.835471	+	0.549535i	$0.185195\pi$
$812$	−953.483	+	1107.62i	−1.17424	+	1.36407i
$813$	−57.6628	−	313.064i	−0.0709260	−	0.385073i
$814$	169.392	+	240.070i	0.208099	+	0.294926i
$815$	213.813	−	1897.64i	0.262347	−	2.32840i
$816$	143.615	+	828.500i	0.175999	+	1.01532i
$817$	−20.4018	−	42.3647i	−0.0249715	−	0.0518539i
$818$	825.734	−	453.539i	1.00945	−	0.554449i
$819$	−640.605	+	1085.10i	−0.782180	+	1.32491i
$820$	−1513.36	+	1877.37i	−1.84556	+	2.28948i
$821$	−228.992	+	1003.28i	−0.278919	+	1.22202i	0.620245	+	0.784409i	$0.287033\pi$
$821$	−228.992	+	1003.28i	−0.278919	+	1.22202i	−0.899163	+	0.437614i	$0.855824\pi$
$822$	295.822	+	99.8015i	0.359881	+	0.121413i
$823$	1301.21	+	817.602i	1.58105	+	0.993441i	0.981122	+	0.193388i	$0.0619477\pi$
$823$	1301.21	+	817.602i	1.58105	+	0.993441i	0.599930	+	0.800053i	$0.295195\pi$
$824$	−332.452	+	180.334i	−0.403462	+	0.218852i
$825$	−1058.43	+	455.687i	−1.28294	+	0.552348i
$826$	1640.64	+	477.331i	1.98624	+	0.577883i
$827$	1386.08	−	485.010i	1.67603	−	0.586470i	0.686038	−	0.727565i	$-0.259348\pi$
$827$	1386.08	−	485.010i	1.67603	−	0.586470i	0.989996	+	0.141096i	$0.0450625\pi$
$828$	71.9210	−	94.4588i	0.0868612	−	0.114081i
$829$	713.493	+	713.493i	0.860667	+	0.860667i	0.991416	−	0.130749i	$-0.0417381\pi$
$829$	713.493	+	713.493i	0.860667	+	0.860667i	−0.130749	+	0.991416i	$0.541738\pi$
$830$	1980.90	−	814.423i	2.38662	−	0.981233i
$831$	565.585	−	171.459i	0.680608	−	0.206328i
$832$	510.769	−	494.915i	0.613905	−	0.594849i
$833$	−1022.75	−	1627.69i	−1.22779	−	1.95401i
$834$	−165.191	−	688.067i	−0.198070	−	0.825021i
$835$	−715.133	+	1484.99i	−0.856447	+	1.77843i
$836$	559.910	−	554.057i	0.669749	−	0.662747i
$837$	822.458	+	104.814i	0.982626	+	0.125226i
$838$	993.830	+	892.848i	1.18595	+	1.06545i
$839$	76.3761	−	218.270i	0.0910323	−	0.260155i	−0.889361	−	0.457205i	$-0.848850\pi$
$839$	76.3761	−	218.270i	0.0910323	−	0.260155i	0.980393	+	0.197050i	$0.0631361\pi$
$840$	−2477.34	−	264.172i	−2.94921	−	0.314490i
$841$	−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
$844$	−308.880	−	1386.84i	−0.365972	−	1.64318i
$845$	233.778	−	293.148i	0.276660	−	0.346921i
$846$	203.957	+	1041.59i	0.241084	+	1.23119i
$847$	462.879	+	222.911i	0.546492	+	0.263177i
$848$	3.63183	−	15.1752i	0.00428282	−	0.0178953i
$849$	409.439	−	376.223i	0.482260	−	0.443136i
$850$	1122.99	−	998.267i	1.32116	−	1.17443i
$851$	6.05631	+	53.7512i	0.00711669	+	0.0631624i
$852$	136.684	+	6.49832i	0.160427	+	0.00762713i
$853$	15.4221	−	15.4221i	0.0180798	−	0.0180798i	−0.698009	−	0.716089i	$-0.745930\pi$
$853$	15.4221	−	15.4221i	0.0180798	−	0.0180798i	0.716089	+	0.698009i	$0.245930\pi$
$854$	−585.893	+	1404.03i	−0.686057	+	1.64406i
$855$	−1051.43	−	1246.04i	−1.22974	−	1.45736i
$856$	19.7034	+	408.314i	0.0230180	+	0.477002i
$857$	1052.39	−	240.202i	1.22800	−	0.280283i	0.441152	−	0.897432i	$-0.354570\pi$
$857$	1052.39	−	240.202i	1.22800	−	0.280283i	0.786846	+	0.617150i	$0.211713\pi$
$858$	−203.555	−	561.439i	−0.237243	−	0.654358i
$859$	45.2492	−	72.0136i	0.0526766	−	0.0838343i	−0.819348	−	0.573297i	$-0.805664\pi$
$859$	45.2492	−	72.0136i	0.0526766	−	0.0838343i	0.872024	+	0.489463i	$0.162807\pi$
$860$	−30.2477	−	63.6636i	−0.0351717	−	0.0740274i
$861$	−116.815	+	2763.05i	−0.135673	+	3.20912i
$862$	444.790	+	26.1513i	0.515998	+	0.0303379i
$863$	−705.619	+	562.713i	−0.817635	+	0.652042i	−0.940278	−	0.340409i	$-0.889435\pi$
$863$	−705.619	+	562.713i	−0.817635	+	0.652042i	0.122642	+	0.992451i	$0.460863\pi$
$864$	855.473	−	121.084i	0.990131	−	0.140143i
$865$	−403.516	+	194.323i	−0.466492	+	0.224651i
$866$	−1256.39	+	358.388i	−1.45080	+	0.413843i
$867$	−53.4902	+	3.74761i	−0.0616957	+	0.00432251i
$868$	1547.54	+	8.13153i	1.78287	+	0.00936812i
$869$	−201.462			−0.231832
$870$	−1427.69	+	130.454i	−1.64102	+	0.149947i
$871$			581.796i			0.667963i
$872$	526.840	−	730.248i	0.604175	−	0.837440i
$873$	14.5061	+	56.3183i	0.0166164	+	0.0645112i
$874$	139.454	−	39.7794i	0.159558	−	0.0455142i
$875$	805.599	+	1672.84i	0.920684	+	1.91182i
$876$	−40.8940	+	2.64925i	−0.0466826	+	0.00302426i
$877$	−1069.26	−	1340.81i	−1.21923	−	1.52886i	−0.773638	−	0.633628i	$-0.781565\pi$
$877$	−1069.26	−	1340.81i	−1.21923	−	1.52886i	−0.445591	−	0.895237i	$-0.647006\pi$
$878$	−281.059	−	16.5248i	−0.320113	−	0.0188209i
$879$	30.9669	−	732.466i	0.0352296	−	0.833295i
$880$	843.646	−	826.098i	0.958689	−	0.938748i
$881$	1239.93	+	779.100i	1.40741	+	0.884336i	0.999587	−	0.0287237i	$-0.00914431\pi$
$881$	1239.93	+	779.100i	1.40741	+	0.884336i	0.407826	+	0.913060i	$0.366287\pi$
$882$	−1704.30	+	998.501i	−1.93231	+	1.13209i
$883$	−205.202	−	899.047i	−0.232392	−	1.01817i	−0.947649	−	0.319313i	$-0.896548\pi$
$883$	−205.202	−	899.047i	−0.232392	−	1.01817i	0.715258	−	0.698861i	$-0.246309\pi$
$884$	482.295	+	611.341i	0.545582	+	0.691562i
$885$	830.997	+	1455.60i	0.938980	+	1.64474i
$886$	−419.316	+	1004.84i	−0.473268	+	1.13413i
$887$	−451.385	−	451.385i	−0.508890	−	0.508890i	0.405296	−	0.914186i	$-0.367169\pi$
$887$	−451.385	−	451.385i	−0.508890	−	0.508890i	−0.914186	+	0.405296i	$0.867169\pi$
$888$	−243.595	+	309.225i	−0.274318	+	0.348226i
$889$	−501.216	+	56.4734i	−0.563797	+	0.0635247i
$890$	1079.19	−	959.337i	1.21258	−	1.07791i
$891$	201.337	−	696.996i	0.225968	−	0.782263i
$892$	−750.481	+	1180.57i	−0.841347	+	1.32351i
$893$	−562.498	+	1168.04i	−0.629897	+	1.30800i
$894$	−15.5298	−	1384.03i	−0.0173712	−	1.54813i
$895$	612.364	+	488.344i	0.684206	+	0.545636i
$896$	1557.60	−	417.874i	1.73839	−	0.466378i
$897$	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
$900$	−989.449	−	1185.17i	−1.09939	−	1.31685i
$901$	16.1253	+	5.64248i	0.0178971	+	0.00626246i
$902$	−974.997	−	875.929i	−1.08093	−	0.971096i
$903$	−71.2832	−	38.1179i	−0.0789405	−	0.0422126i
$904$	131.341	+	811.708i	0.145289	+	0.897908i
$905$	−83.7958	−	40.3539i	−0.0925920	−	0.0445900i
$906$	1173.82	−	281.809i	1.29560	−	0.311047i
$907$	558.644	−	351.019i	0.615925	−	0.387011i	−0.187632	−	0.982239i	$-0.560081\pi$
$907$	558.644	−	351.019i	0.615925	−	0.387011i	0.803557	+	0.595228i	$0.202938\pi$
$908$	−108.887	−	1014.27i	−0.119920	−	1.11704i
$909$	194.076	−	100.175i	0.213504	−	0.110203i
$910$	−2133.86	+	877.312i	−2.34490	+	0.964079i
$911$	788.911	−	788.911i	0.865983	−	0.865983i	−0.126042	−	0.992025i	$-0.540227\pi$
$911$	788.911	−	788.911i	0.865983	−	0.865983i	0.992025	+	0.126042i	$0.0402273\pi$
$912$	925.366	+	507.406i	1.01466	+	0.556366i
$913$	384.489	+	1098.81i	0.421128	+	1.20351i
$914$	1069.46	+	311.152i	1.17009	+	0.340428i
$915$	−1370.73	+	590.144i	−1.49807	+	0.644966i
$916$	44.6463	−	91.4763i	0.0487405	−	0.0998650i
$917$	901.553	−	1434.81i	0.983154	−	1.56468i
$918$	36.8032	+	945.246i	0.0400906	+	1.02968i
$919$	404.957	+	92.4288i	0.440650	+	0.100575i	0.437089	−	0.899418i	$-0.356009\pi$
$919$	404.957	+	92.4288i	0.440650	+	0.100575i	0.00356075	+	0.999994i	$0.498867\pi$
$920$	209.348	−	58.5293i	0.227553	−	0.0636188i
$921$	362.490	+	315.022i	0.393583	+	0.342043i
$922$	48.1672	−	26.4561i	0.0522420	−	0.0286942i
$923$	114.171	−	54.9820i	0.123696	−	0.0595689i
$924$	215.349	−	1336.92i	0.233062	−	1.44688i
$925$	698.994	+	78.7577i	0.755669	+	0.0851435i
$926$	99.4049	+	140.881i	0.107349	+	0.152139i
$927$	−397.567	+	151.598i	−0.428875	+	0.163536i
$928$	831.758	−	411.538i	0.896291	−	0.443467i
$929$			424.259i			0.456684i	0.973581	+	0.228342i	$0.0733304\pi$
$929$			424.259i			0.456684i	−0.973581	+	0.228342i	$0.926670\pi$
$930$	1085.41	+	1061.32i	1.16711	+	1.14121i
$931$	−2397.54	−	270.138i	−2.57523	−	0.290159i
$932$	−815.767	−	290.269i	−0.875286	−	0.311448i
$933$	−485.711	−	664.843i	−0.520590	−	0.712586i
$934$	284.633	−	156.336i	0.304746	−	0.167384i
$935$	806.025	+	1010.72i	0.862058	+	1.08099i
$936$	643.242	−	475.841i	0.687224	−	0.508377i
$937$	1499.58	+	342.270i	1.60041	+	0.365283i	0.927317	−	0.374277i	$-0.122109\pi$
$937$	1499.58	+	342.270i	1.60041	+	0.365283i	0.673091	+	0.739560i	$0.264966\pi$
$938$	−641.165	+	1152.94i	−0.683545	+	1.22914i
$939$	−5.37971	+	13.5141i	−0.00572919	+	0.0143920i
$940$	−852.361	+	1746.41i	−0.906767	+	1.85789i
$941$	−35.1036	−	153.799i	−0.0373046	−	0.163442i	0.952845	−	0.303459i	$-0.0981415\pi$
$941$	−35.1036	−	153.799i	−0.0373046	−	0.163442i	−0.990149	+	0.140017i	$0.955284\pi$
$942$	144.472	−	1425.84i	0.153368	−	1.51364i
$943$	−79.6947	−	227.754i	−0.0845119	−	0.241521i
$944$	−841.090	−	685.330i	−0.890985	−	0.725985i
$945$	−2723.16	−	663.393i	−2.88165	−	0.702003i
$946$	35.4327	−	14.5677i	0.0374552	−	0.0153993i
$947$	1303.17	−	146.832i	1.37610	−	0.155050i	0.607269	−	0.794496i	$-0.292265\pi$
$947$	1303.17	−	146.832i	1.37610	−	0.155050i	0.768836	+	0.639446i	$0.220836\pi$
$948$	−76.9479	−	258.714i	−0.0811686	−	0.272905i
$949$	−32.1329	+	20.1904i	−0.0338597	+	0.0212755i
$950$	−100.792	−	1883.13i	−0.106097	−	1.98224i
$951$	1.50853	−	5.52257i	0.00158625	−	0.00580712i
$952$	282.031	+	1742.99i	0.296251	+	1.83088i
$953$	−1270.31	−	1013.04i	−1.33296	−	1.06300i	−0.992436	−	0.122761i	$-0.960825\pi$
$953$	−1270.31	−	1013.04i	−1.33296	−	1.06300i	−0.340521	−	0.940237i	$-0.610603\pi$
$954$	6.30909	−	16.3813i	0.00661330	−	0.0171711i
$955$	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
$960$	1383.09	+	767.869i	1.44072	+	0.799863i
$961$	14.0987	+	11.2433i	0.0146709	+	0.0116996i
$962$	−62.0068	+	359.229i	−0.0644562	+	0.373418i
$963$	−38.8164	+	458.247i	−0.0403078	+	0.475853i
$964$	−187.308	+	294.651i	−0.194303	+	0.305655i
$965$	2436.89	−	1531.20i	2.52528	−	1.58674i
$966$	153.239	−	196.642i	0.158632	−	0.203563i
$967$	−831.807	+	93.7221i	−0.860193	+	0.0969205i	−0.531030	−	0.847353i	$-0.678195\pi$
$967$	−831.807	+	93.7221i	−0.860193	+	0.0969205i	−0.329163	+	0.944273i	$0.606766\pi$
$968$	−215.451	−	244.948i	−0.222573	−	0.253046i
$969$	−655.520	+	951.519i	−0.676492	+	0.981960i
$970$	−41.0072	+	98.2692i	−0.0422755	+	0.101308i
$971$	−168.407	−	481.279i	−0.173436	−	0.495653i	0.824050	−	0.566518i	$-0.191710\pi$
$971$	−168.407	−	481.279i	−0.173436	−	0.495653i	−0.997486	+	0.0708652i	$0.977424\pi$
$972$	971.970	−	7.66250i	0.999969	−	0.00788323i
$973$	−330.642	−	1448.64i	−0.339817	−	1.48883i
$974$	−104.031	+	17.3944i	−0.106808	+	0.0178588i
$975$	−1328.36	−	528.796i	−1.36242	−	0.542355i
$976$	690.219	−	675.863i	0.707192	−	0.692483i
$977$	1171.08	+	267.292i	1.19865	+	0.273585i	0.774835	−	0.632163i	$-0.217833\pi$
$977$	1171.08	+	267.292i	1.19865	+	0.273585i	0.423817	+	0.905748i	$0.360690\pi$
$978$	171.197	+	1380.06i	0.175048	+	1.41111i
$979$	489.337	+	613.610i	0.499834	+	0.626772i
$980$	−3591.69	−	423.810i	−3.66499	−	0.432459i
$981$	696.198	−	735.870i	0.709682	−	0.750122i
$982$	−728.498	+	207.806i	−0.741852	+	0.211615i
$983$	−679.979	−	76.6152i	−0.691738	−	0.0779402i	−0.240906	−	0.970549i	$-0.577444\pi$
$983$	−679.979	−	76.6152i	−0.691738	−	0.0779402i	−0.450833	+	0.892608i	$0.648873\pi$
$984$	752.454	−	1586.63i	0.764689	−	1.61243i
$985$			459.559i			0.466557i
$986$	355.803	+	951.697i	0.360855	+	0.965210i
$987$	403.711	+	2191.84i	0.409028	+	2.22070i
$988$	977.303	+	5.13524i	0.989173	+	0.00519761i
$989$	7.00860	+	0.789680i	0.00708655	+	0.000798463i
$990$	1063.74	−	795.589i	1.07449	−	0.803625i
$991$	324.113	−	156.085i	0.327056	−	0.157502i	−0.263149	−	0.964755i	$-0.584761\pi$
$991$	324.113	−	156.085i	0.327056	−	0.157502i	0.590205	+	0.807253i	$0.299047\pi$
$992$	−902.831	−	387.936i	−0.910112	−	0.391065i
$993$	91.5367	−	105.329i	0.0921820	−	0.106072i
$994$	286.844	+	16.8649i	0.288576	+	0.0169667i
$995$	−1170.11	−	267.069i	−1.17599	−	0.268411i
$996$	−1264.21	+	913.441i	−1.26929	+	0.917109i
$997$	889.614	−	1415.81i	0.892291	−	1.42007i	−0.0151460	−	0.999885i	$-0.504821\pi$
$997$	889.614	−	1415.81i	0.892291	−	1.42007i	0.907437	−	0.420188i	$-0.138036\pi$
$998$	279.945	+	1674.26i	0.280506	+	1.67762i
$999$	−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.95.83	yes	1392
3.2	odd	2	inner	348.3.v.a.95.34	yes	1392
4.3	odd	2	inner	348.3.v.a.95.11	yes	1392
12.11	even	2	inner	348.3.v.a.95.106	yes	1392
29.11	odd	28	inner	348.3.v.a.11.106	yes	1392
87.11	even	28	inner	348.3.v.a.11.11	✓	1392
116.11	even	28	inner	348.3.v.a.11.34	yes	1392
348.11	odd	28	inner	348.3.v.a.11.83	yes	1392

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
348.3.v.a.11.11	✓	1392	87.11	even	28	inner
348.3.v.a.11.34	yes	1392	116.11	even	28	inner
348.3.v.a.11.83	yes	1392	348.11	odd	28	inner
348.3.v.a.11.106	yes	1392	29.11	odd	28	inner
348.3.v.a.95.11	yes	1392	4.3	odd	2	inner
348.3.v.a.95.34	yes	1392	3.2	odd	2	inner
348.3.v.a.95.83	yes	1392	1.1	even	1	trivial
348.3.v.a.95.106	yes	1392	12.11	even	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(1.15305 + 1.63416i) q^{2} +(-0.209671 - 2.99266i) q^{3} +(-1.34094 + 3.76854i) q^{4} +(-7.42336 + 3.57490i) q^{5} +(4.64872 - 3.79334i) q^{6} +(9.85035 - 7.85539i) q^{7} +(-7.70456 + 2.15403i) q^{8} +(-8.91208 + 1.25495i) q^{9} +O(q^{10})\)	\(q+(1.15305 + 1.63416i) q^{2} +(-0.209671 - 2.99266i) q^{3} +(-1.34094 + 3.76854i) q^{4} +(-7.42336 + 3.57490i) q^{5} +(4.64872 - 3.79334i) q^{6} +(9.85035 - 7.85539i) q^{7} +(-7.70456 + 2.15403i) q^{8} +(-8.91208 + 1.25495i) q^{9} +(-14.4015 - 8.00888i) q^{10} +(4.76526 - 7.58386i) q^{11} +(11.5591 + 3.22282i) q^{12} +(10.8341 - 2.47281i) q^{13} +(24.1949 + 7.03933i) q^{14} +(12.2549 + 21.4661i) q^{15} +(-12.4038 - 10.1067i) q^{16} +(12.3870 - 12.3870i) q^{17} +(-12.3269 - 13.1167i) q^{18} +(-2.46170 - 21.8482i) q^{19} +(-3.51790 - 32.7689i) q^{20} +(-25.5739 - 27.8317i) q^{21} +(17.8878 - 0.957421i) q^{22} +(2.97127 + 1.43089i) q^{23} +(8.06170 + 22.6055i) q^{24} +(26.7391 - 33.5297i) q^{25} +(16.5333 + 14.8533i) q^{26} +(5.62425 + 26.4077i) q^{27} +(16.3947 + 47.6550i) q^{28} +(14.6279 + 25.0405i) q^{29} +(-20.9483 + 44.7780i) q^{30} +(10.1421 - 28.9846i) q^{31} +(2.21378 - 31.9233i) q^{32} +(-23.6951 - 12.6707i) q^{33} +(34.5251 + 5.95941i) q^{34} +(-45.0404 + 93.5274i) q^{35} +(7.22120 - 35.2683i) q^{36} +(8.72637 + 13.8879i) q^{37} +(32.8649 - 29.2149i) q^{38} +(-9.67189 - 31.9043i) q^{39} +(49.4932 - 43.5331i) q^{40} +(-51.7371 - 51.7371i) q^{41} +(15.9934 - 73.8832i) q^{42} +(2.01863 - 0.706350i) q^{43} +(22.1902 + 28.1275i) q^{44} +(61.6712 - 41.1757i) q^{45} +(1.08774 + 6.50540i) q^{46} +(-49.9269 - 31.3712i) q^{47} +(-27.6454 + 39.2394i) q^{48} +(24.4187 - 106.985i) q^{49} +(85.6244 + 5.03426i) q^{50} +(-39.6672 - 34.4728i) q^{51} +(-5.20894 + 44.1446i) q^{52} +(0.423138 + 0.878656i) q^{53} +(-36.6693 + 39.6404i) q^{54} +(-8.26265 + 73.3330i) q^{55} +(-58.9718 + 81.7402i) q^{56} +(-64.8682 + 11.9480i) q^{57} +(-24.0533 + 52.7773i) q^{58} +67.8092 q^{59} +(-97.3288 + 17.3986i) q^{60} +(-6.75999 + 59.9966i) q^{61} +(59.0597 - 16.8469i) q^{62} +(-77.9289 + 82.3695i) q^{63} +(54.7203 - 33.1916i) q^{64} +(-71.5853 + 57.0874i) q^{65} +(-6.61580 - 53.3315i) q^{66} +(-11.6499 + 51.0414i) q^{67} +(30.0706 + 63.2909i) q^{68} +(3.65917 - 9.19201i) q^{69} +(-204.772 + 34.2390i) q^{70} +(11.1173 - 2.53745i) q^{71} +(65.9604 - 28.8657i) q^{72} +(-3.22334 + 1.12789i) q^{73} +(-12.6331 + 30.2738i) q^{74} +(-105.950 - 72.9908i) q^{75} +(85.6368 + 20.0200i) q^{76} +(-12.6348 - 112.137i) q^{77} +(40.9845 - 52.5928i) q^{78} +(-11.9669 - 19.0453i) q^{79} +(128.208 + 30.6837i) q^{80} +(77.8502 - 22.3684i) q^{81} +(24.8909 - 144.202i) q^{82} +(-81.0372 + 101.617i) q^{83} +(139.178 - 59.0556i) 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} +(138.398 + 53.3026i) q^{90} +(87.2947 - 109.464i) q^{91} +(-9.37663 + 9.27860i) q^{92} +(-88.8675 - 24.2748i) q^{93} +(-6.30300 - 117.761i) q^{94} +(96.3792 + 153.387i) q^{95} +(-96.0000 + 0.0682937i) q^{96} +(-0.723496 - 6.42120i) q^{97} +(202.986 - 83.4556i) 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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