LMFDB - Embedded newform 348.3.v.a.95.34

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			95.34
Character	$\chi$	$=$	348.95
Dual form			348.3.v.a.11.34

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.15305 - 1.63416i) q^{2} +(-0.870345 + 2.87098i) q^{3} +(-1.34094 + 3.76854i) q^{4} +(7.42336 - 3.57490i) q^{5} +(5.69518 - 1.88811i) q^{6} +(9.85035 - 7.85539i) q^{7} +(7.70456 - 2.15403i) q^{8} +(-7.48500 - 4.99748i) q^{9} +O(q^{10})$	\(q+(-1.15305 - 1.63416i) q^{2} +(-0.870345 + 2.87098i) q^{3} +(-1.34094 + 3.76854i) q^{4} +(7.42336 - 3.57490i) q^{5} +(5.69518 - 1.88811i) q^{6} +(9.85035 - 7.85539i) q^{7} +(7.70456 - 2.15403i) q^{8} +(-7.48500 - 4.99748i) q^{9} +(-14.4015 - 8.00888i) q^{10} +(-4.76526 + 7.58386i) q^{11} +(-9.65231 - 7.12972i) q^{12} +(10.8341 - 2.47281i) q^{13} +(-24.1949 - 7.03933i) q^{14} +(3.80257 + 24.4237i) q^{15} +(-12.4038 - 10.1067i) q^{16} +(-12.3870 + 12.3870i) q^{17} +(0.463945 + 17.9940i) q^{18} +(-2.46170 - 21.8482i) q^{19} +(3.51790 + 32.7689i) q^{20} +(13.9794 + 35.1170i) q^{21} +(17.8878 - 0.957421i) q^{22} +(-2.97127 - 1.43089i) q^{23} +(-0.521460 + 23.9943i) q^{24} +(26.7391 - 33.5297i) q^{25} +(-16.5333 - 14.8533i) q^{26} +(20.8622 - 17.1397i) 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} +(-2.21378 + 31.9233i) q^{32} +(-17.6257 - 20.2815i) q^{33} +(34.5251 + 5.95941i) q^{34} +(45.0404 - 93.5274i) q^{35} +(28.8701 - 21.5062i) q^{36} +(8.72637 + 13.8879i) q^{37} +(-32.8649 + 29.2149i) q^{38} +(-2.33002 + 33.2566i) q^{39} +(49.4932 - 43.5331i) q^{40} +(51.7371 + 51.7371i) q^{41} +(41.2676 - 63.3364i) q^{42} +(2.01863 - 0.706350i) q^{43} +(-22.1902 - 28.1275i) q^{44} +(-73.4293 - 10.3399i) q^{45} +(1.08774 + 6.50540i) q^{46} +(49.9269 + 31.3712i) q^{47} +(39.8118 - 26.8146i) q^{48} +(24.4187 - 106.985i) q^{49} +(-85.6244 - 5.03426i) q^{50} +(-24.7817 - 46.3436i) q^{51} +(-5.20894 + 44.1446i) q^{52} +(-0.423138 - 0.878656i) q^{53} +(-52.0642 - 14.3290i) 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} +(-97.1406 - 18.4204i) q^{60} +(-6.75999 + 59.9966i) q^{61} +(-59.0597 + 16.8469i) q^{62} +(-112.987 + 9.57072i) q^{63} +(54.7203 - 33.1916i) q^{64} +(71.5853 - 57.0874i) q^{65} +(-12.8198 + 52.1888i) q^{66} +(-11.6499 + 51.0414i) q^{67} +(-30.0706 - 63.2909i) q^{68} +(6.69406 - 7.28507i) q^{69} +(-204.772 + 34.2390i) q^{70} +(-11.1173 + 2.53745i) q^{71} +(-68.4333 - 22.3804i) q^{72} +(-3.22334 + 1.12789i) q^{73} +(12.6331 - 30.2738i) q^{74} +(72.9908 + 105.950i) q^{75} +(85.6368 + 20.0200i) q^{76} +(12.6348 + 112.137i) q^{77} +(57.0332 - 34.5391i) q^{78} +(-11.9669 - 19.0453i) q^{79} +(-128.208 - 30.6837i) q^{80} +(31.0505 + 74.8122i) q^{81} +(24.8909 - 144.202i) q^{82} +(81.0372 - 101.617i) q^{83} +(-151.085 + 5.59239i) q^{84} +(-47.6707 + 136.235i) q^{85} +(-3.48188 - 2.48430i) q^{86} +(84.6218 - 20.2026i) q^{87} +(-20.3783 + 68.6948i) q^{88} +(28.9409 - 82.7083i) q^{89} +(67.7709 + 131.917i) q^{90} +(87.2947 - 109.464i) q^{91} +(9.37663 - 9.27860i) q^{92} +(74.3868 + 54.3444i) q^{93} +(-6.30300 - 117.761i) q^{94} +(-96.3792 - 153.387i) q^{95} +(-89.7244 - 34.1400i) q^{96} +(-0.723496 - 6.42120i) q^{97} +(-202.986 + 83.4556i) q^{98} +(73.5681 - 32.9510i) 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
$3$	−0.870345	+	2.87098i	−0.290115	+	0.956992i
$3$	−0.870345	+	2.87098i	−0.290115	+	0.956992i
$4$	−1.34094	+	3.76854i	−0.335234	+	0.942135i
$5$	7.42336	−	3.57490i	1.48467	−	0.714980i	0.496458	−	0.868061i	$-0.334634\pi$
$5$	7.42336	−	3.57490i	1.48467	−	0.714980i	0.988214	+	0.153081i	$0.0489195\pi$
$6$	5.69518	−	1.88811i	0.949196	−	0.314685i
$7$	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
$9$	−7.48500	−	4.99748i	−0.831667	−	0.555275i
$10$	−14.4015	−	8.00888i	−1.44015	−	0.800888i
$11$	−4.76526	+	7.58386i	−0.433205	+	0.689442i	−0.989978	−	0.141223i	$-0.954897\pi$
$11$	−4.76526	+	7.58386i	−0.433205	+	0.689442i	0.556773	+	0.830665i	$0.312039\pi$
$12$	−9.65231	−	7.12972i	−0.804359	−	0.594144i
$13$	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
$15$	3.80257	+	24.4237i	0.253505	+	1.62824i
$16$	−12.4038	−	10.1067i	−0.775236	−	0.631671i
$17$	−12.3870	+	12.3870i	−0.728645	+	0.728645i	−0.970350	−	0.241705i	$-0.922293\pi$
$17$	−12.3870	+	12.3870i	−0.728645	+	0.728645i	0.241705	+	0.970350i	$0.422293\pi$
$18$	0.463945	+	17.9940i	0.0257747	+	0.999668i
$19$	−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
$21$	13.9794	+	35.1170i	0.665687	+	1.67224i
$22$	17.8878	−	0.957421i	0.813082	−	0.0435192i
$23$	−2.97127	−	1.43089i	−0.129185	−	0.0622124i	0.368175	−	0.929757i	$-0.379983\pi$
$23$	−2.97127	−	1.43089i	−0.129185	−	0.0622124i	−0.497360	+	0.867544i	$0.665697\pi$
$24$	−0.521460	+	23.9943i	−0.0217275	+	0.999764i
$25$	26.7391	−	33.5297i	1.06956	−	1.34119i
$26$	−16.5333	−	14.8533i	−0.635894	−	0.571282i
$27$	20.8622	−	17.1397i	0.772673	−	0.634805i
$28$	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	−0.656397	−	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
$33$	−17.6257	−	20.2815i	−0.534111	−	0.614591i
$34$	34.5251	+	5.95941i	1.01544	+	0.175277i
$35$	45.0404	−	93.5274i	1.28687	−	2.67221i
$36$	28.8701	−	21.5062i	0.801947	−	0.597395i
$37$	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
$39$	−2.33002	+	33.2566i	−0.0597440	+	0.852734i
$40$	49.4932	−	43.5331i	1.23733	−	1.08833i
$41$	51.7371	+	51.7371i	1.26188	+	1.26188i	0.950181	+	0.311699i	$0.100898\pi$
$41$	51.7371	+	51.7371i	1.26188	+	1.26188i	0.311699	+	0.950181i	$0.399102\pi$
$42$	41.2676	−	63.3364i	0.982563	−	1.50801i
$43$	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
$45$	−73.4293	−	10.3399i	−1.63176	−	0.229776i
$46$	1.08774	+	6.50540i	0.0236464	+	0.141422i
$47$	49.9269	+	31.3712i	1.06228	+	0.667472i	0.945479	−	0.325684i	$-0.105595\pi$
$47$	49.9269	+	31.3712i	1.06228	+	0.667472i	0.116796	+	0.993156i	$0.462737\pi$
$48$	39.8118	−	26.8146i	0.829412	−	0.558637i
$49$	24.4187	−	106.985i	0.498340	−	2.18337i
$50$	−85.6244	−	5.03426i	−1.71249	−	0.100685i
$51$	−24.7817	−	46.3436i	−0.485917	−	0.908698i
$52$	−5.20894	+	44.1446i	−0.100172	+	0.848935i
$53$	−0.423138	−	0.878656i	−0.00798374	−	0.0165784i	0.896939	−	0.442155i	$-0.145786\pi$
$53$	−0.423138	−	0.878656i	−0.00798374	−	0.0165784i	−0.904923	+	0.425576i	$0.860071\pi$
$54$	−52.0642	−	14.3290i	−0.964152	−	0.265352i
$55$	−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	$-0.694863\pi$
$59$	−67.8092			−1.14931			−0.574654	+	0.818396i	$0.694863\pi$
$60$	−97.1406	−	18.4204i	−1.61901	−	0.307007i
$61$	−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
$63$	−112.987	+	9.57072i	−1.79344	+	0.151916i
$64$	54.7203	−	33.1916i	0.855005	−	0.518619i
$65$	71.5853	−	57.0874i	1.10131	−	0.878267i
$66$	−12.8198	+	52.1888i	−0.194240	+	0.790739i
$67$	−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
$69$	6.69406	−	7.28507i	0.0970154	−	0.105581i
$70$	−204.772	+	34.2390i	−2.92532	+	0.489128i
$71$	−11.1173	+	2.53745i	−0.156582	+	0.0357388i	−0.300093	−	0.953910i	$-0.597018\pi$
$71$	−11.1173	+	2.53745i	−0.156582	+	0.0357388i	0.143511	+	0.989649i	$0.454161\pi$
$72$	−68.4333	−	22.3804i	−0.950462	−	0.310839i
$73$	−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
$75$	72.9908	+	105.950i	0.973211	+	1.41266i
$76$	85.6368	+	20.0200i	1.12680	+	0.263421i
$77$	12.6348	+	112.137i	0.164088	+	1.45632i
$78$	57.0332	−	34.5391i	0.731195	−	0.442808i
$79$	−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
$81$	31.0505	+	74.8122i	0.383339	+	0.923608i
$82$	24.8909	−	144.202i	0.303547	−	1.75856i
$83$	81.0372	−	101.617i	0.976351	−	1.22431i	0.00183311	−	0.999998i	$-0.499417\pi$
$83$	81.0372	−	101.617i	0.976351	−	1.22431i	0.974518	−	0.224308i	$-0.0720121\pi$
$84$	−151.085	+	5.59239i	−1.79863	+	0.0665761i
$85$	−47.6707	+	136.235i	−0.560832	+	1.60276i
$86$	−3.48188	−	2.48430i	−0.0404870	−	0.0288873i
$87$	84.6218	−	20.2026i	0.972665	−	0.232213i
$88$	−20.3783	+	68.6948i	−0.231572	+	0.780622i
$89$	28.9409	−	82.7083i	0.325178	−	0.929307i	−0.659003	−	0.752141i	$-0.729021\pi$
$89$	28.9409	−	82.7083i	0.325178	−	0.929307i	0.984181	−	0.177166i	$-0.0566929\pi$
$90$	67.7709	+	131.917i	0.753010	+	1.46575i
$91$	87.2947	−	109.464i	0.959283	−	1.20290i
$92$	9.37663	−	9.27860i	0.101920	−	0.100854i
$93$	74.3868	+	54.3444i	0.799858	+	0.584348i
$94$	−6.30300	−	117.761i	−0.0670532	−	1.25278i
$95$	−96.3792	−	153.387i	−1.01452	−	1.61460i
$96$	−89.7244	−	34.1400i	−0.934629	−	0.355625i
$97$	−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
$99$	73.5681	−	32.9510i	0.743112	−	0.332838i
$100$	90.5027	+	145.728i	0.905027	+	1.45728i
$101$	22.9053	−	8.01491i	0.226785	−	0.0793556i	−0.214494	−	0.976725i	$-0.568810\pi$
$101$	22.9053	−	8.01491i	0.226785	−	0.0793556i	0.441280	+	0.897370i	$0.354525\pi$
$102$	−47.1580	+	93.9339i	−0.462334	+	0.920921i
$103$	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
$105$	229.314	+	210.711i	2.18394	+	2.00677i
$106$	−0.947960	+	1.70461i	−0.00894302	+	0.0160812i
$107$	−11.3705	+	49.8175i	−0.106267	+	0.465584i	0.893594	+	0.448876i	$0.148176\pi$
$107$	−11.3705	+	49.8175i	−0.106267	+	0.465584i	−0.999860	+	0.0167077i	$0.994682\pi$
$108$	36.6169	+	101.603i	0.339045	+	0.940770i
$109$	−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
$111$	−47.4669	+	12.9659i	−0.427630	+	0.116810i
$112$	−201.574	−	2.11840i	−1.79977	−	0.0189143i
$113$	−11.5081	+	102.137i	−0.101841	+	0.903867i	0.834077	+	0.551649i	$0.186001\pi$
$113$	−11.5081	+	102.137i	−0.101841	+	0.903867i	−0.935918	+	0.352218i	$0.885428\pi$
$114$	−55.2716	−	119.781i	−0.484838	−	1.05071i
$115$	−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
$120$	81.9064	+	179.983i	0.682553	+	1.49986i
$121$	17.6926	+	36.7391i	0.146220	+	0.303629i
$122$	105.838	−	58.1324i	0.867528	−	0.476495i
$123$	−193.565	+	103.507i	−1.57370	+	0.841519i
$124$	95.6295	+	77.0875i	0.771205	+	0.621673i
$125$	32.7928	−	143.674i	0.262342	−	1.14940i
$126$	145.920	+	173.603i	1.15810	+	1.37780i
$127$	−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
$129$	0.271008	+	6.41022i	0.00210084	+	0.0496916i
$130$	−175.831	−	51.1568i	−1.35255	−	0.393514i
$131$	−126.950	+	44.4218i	−0.969085	+	0.339098i	−0.767981	−	0.640472i	$-0.778739\pi$
$131$	−126.950	+	44.4218i	−0.969085	+	0.339098i	−0.201104	+	0.979570i	$0.564453\pi$
$132$	100.067	−	39.2268i	0.758080	−	0.297173i
$133$	−195.875	−	195.875i	−1.47274	−	1.47274i
$134$	96.8426	−	39.8158i	0.722706	−	0.297133i
$135$	93.5945	−	201.814i	0.693292	−	1.49492i
$136$	−68.7542	+	122.118i	−0.505546	+	0.897926i
$137$	−27.6837	−	44.0584i	−0.202071	−	0.321594i	0.730280	−	0.683148i	$-0.239389\pi$
$137$	−27.6837	−	44.0584i	−0.202071	−	0.321594i	−0.932351	+	0.361553i	$0.882247\pi$
$138$	−19.6236	−	2.53908i	−0.142200	−	0.0183991i
$139$	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
$141$	−133.519	+	116.035i	−0.946947	+	0.822945i
$142$	16.9655	+	15.2416i	0.119475	+	0.107335i
$143$	−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
$147$	285.899	+	163.219i	1.94489	+	1.11034i
$148$	−64.0388	+	14.2628i	−0.432694	+	0.0963705i
$149$	−143.830	+	180.357i	−0.965303	+	1.21045i	0.0122854	+	0.999925i	$0.496089\pi$
$149$	−143.830	+	180.357i	−0.965303	+	1.21045i	−0.977588	+	0.210527i	$0.932482\pi$
$150$	88.9760	−	241.444i	0.593173	−	1.60963i
$151$	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
$153$	154.620	−	30.8129i	1.01059	−	0.201391i
$154$	168.680	−	149.947i	1.09533	−	0.973680i
$155$	−28.3282	−	251.420i	−0.182763	−	1.62206i
$156$	−122.205	−	53.3758i	−0.783362	−	0.342152i
$157$	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
$159$	2.89087	−	0.450086i	0.0181816	−	0.00283073i
$160$	97.6890	+	244.892i	0.610556	+	1.53058i
$161$	−40.5082	+	9.24572i	−0.251603	+	0.0574269i
$162$	86.4521	−	137.004i	0.533655	−	0.845702i
$163$	−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
$165$	−203.346	−	87.5469i	−1.23240	−	0.530587i
$166$	−259.499	−	15.2572i	−1.56325	−	0.0919106i
$167$	−156.400	+	124.725i	−0.936525	+	0.746854i	−0.967554	−	0.252664i	$-0.918693\pi$
$167$	−156.400	+	124.725i	−0.936525	+	0.746854i	0.0310287	+	0.999518i	$0.490122\pi$
$168$	183.348	+	240.449i	1.09136	+	1.43124i
$169$	−41.0009	+	19.7450i	−0.242609	+	0.116834i
$170$	277.596	−	79.1848i	1.63292	−	0.465793i
$171$	−90.7600	+	175.836i	−0.530760	+	1.02828i
$172$	−0.0449495	+	8.55447i	−0.000261334	+	0.0497353i
$173$	−54.3576			−0.314206			−0.157103	−	0.987582i	$-0.550215\pi$
$173$	−54.3576			−0.314206			−0.157103	+	0.987582i	$0.550215\pi$
$174$	−130.588	−	114.991i	−0.750504	−	0.660866i
$175$		−	540.325i		−	3.08757i
$176$	135.755	−	45.9073i	0.771337	−	0.260837i
$177$	59.0174	−	194.678i	0.333431	−	1.09988i
$178$	−168.529	+	48.0731i	−0.946790	+	0.270074i
$179$	41.2458	+	85.6477i	0.230423	+	0.478479i	0.983837	−	0.179068i	$-0.0573083\pi$
$179$	41.2458	+	85.6477i	0.230423	+	0.478479i	−0.753413	+	0.657547i	$0.771594\pi$
$180$	137.430	−	262.856i	0.763502	−	1.46031i
$181$	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
$183$	−166.365	−	71.6255i	−0.909099	−	0.391396i
$184$	−25.9744	−	4.62415i	−0.141165	−	0.0251313i
$185$	114.427	+	71.8992i	0.618524	+	0.388645i
$186$	3.03528	−	184.222i	0.0163187	−	0.990439i
$187$	−34.9140	−	152.968i	−0.186706	−	0.818011i
$188$	−185.172	+	146.085i	−0.984959	+	0.777047i
$189$	70.8603	−	332.713i	0.374922	−	1.76038i
$190$	−139.527	+	334.362i	−0.734355	+	1.75980i
$191$	27.7867	+	27.7867i	0.145480	+	0.145480i	0.776096	−	0.630615i	$-0.217197\pi$
$191$	27.7867	+	27.7867i	0.145480	+	0.145480i	−0.630615	+	0.776096i	$0.717197\pi$
$192$	47.6668	+	185.989i	0.248265	+	0.968692i
$193$	−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
$195$	101.593	+	255.205i	0.520988	+	1.30875i
$196$	370.434	+	235.483i	1.88997	+	1.20144i
$197$	−24.2005	+	50.2528i	−0.122845	+	0.255090i	−0.953318	−	0.301969i	$-0.902356\pi$
$197$	−24.2005	+	50.2528i	−0.122845	+	0.255090i	0.830473	+	0.557059i	$0.188070\pi$
$198$	−138.675	−	82.2276i	−0.700379	−	0.415291i
$199$	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
$201$	−136.399	−	77.8702i	−0.678604	−	0.387414i
$202$	−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
$206$	−70.3371	−	63.1902i	−0.341442	−	0.306749i
$207$	15.0891	+	25.5590i	0.0728942	+	0.123473i
$208$	−159.376	−	78.8252i	−0.766230	−	0.378967i
$209$	177.424	+	85.4431i	0.848920	+	0.408818i
$210$	79.9233	−	617.696i	0.380587	−	2.94141i
$211$	−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
$213$	2.39092	−	34.1260i	0.0112250	−	0.160216i
$214$	94.5204	−	38.8610i	0.441684	−	0.181594i
$215$	12.4599	−	12.4599i	0.0579530	−	0.0579530i
$216$	123.814	−	176.992i	0.573214	−	0.819406i
$217$	−127.781	−	365.178i	−0.588854	−	1.68285i
$218$	216.152	+	62.8877i	0.991521	+	0.288476i
$219$	−0.432743	−	10.2358i	−0.00197600	−	0.0467387i
$220$	−265.279	−	129.473i	−1.20581	−	0.588514i
$221$	−103.571	+	164.832i	−0.468647	+	0.745847i
$222$	75.9202	+	62.6180i	0.341983	+	0.282063i
$223$	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
$225$	−367.706	+	117.342i	−1.63425	+	0.521521i
$226$	180.177	−	98.9634i	0.797244	−	0.437891i
$227$	229.770	−	110.651i	1.01220	−	0.487451i	0.147140	−	0.989116i	$-0.452993\pi$
$227$	229.770	−	110.651i	1.01220	−	0.487451i	0.865062	+	0.501665i	$0.167279\pi$
$228$	−132.010	+	228.437i	−0.578993	+	1.00192i
$229$	−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	$-0.846226\pi$
$233$		−	216.468i		−	0.929045i	0.885561	−	0.464523i	$-0.153774\pi$
$234$	49.5223	+	193.802i	0.211634	+	0.828212i
$235$	482.774	+	54.3956i	2.05436	+	0.231471i
$236$	90.9278	−	255.542i	0.385287	−	1.08280i
$237$	65.0938	−	17.7808i	0.274657	−	0.0750246i
$238$	386.897	−	212.506i	1.62562	−	0.892881i
$239$	17.6884	+	22.1805i	0.0740099	+	0.0928054i	0.817458	−	0.575988i	$-0.195382\pi$
$239$	17.6884	+	22.1805i	0.0740099	+	0.0928054i	−0.743448	+	0.668793i	$0.766811\pi$
$240$	199.677	−	341.377i	0.831990	−	1.42241i
$241$	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
$243$	−241.809	+	24.0327i	−0.995097	+	0.0989000i
$244$	−217.035	−	105.927i	−0.889487	−	0.434127i
$245$	−201.193	−	881.483i	−0.821195	−	3.59789i
$246$	392.337	+	196.967i	1.59487	+	0.800677i
$247$	−80.6968	−	230.618i	−0.326708	−	0.933677i
$248$	15.7071	−	245.160i	0.0633352	−	0.988546i
$249$	221.211	+	321.098i	0.888397	+	1.28955i
$250$	−272.598	+	112.076i	−1.09039	+	0.448303i
$251$	110.753	−	12.4789i	0.441248	−	0.0497167i	0.111454	−	0.993770i	$-0.464449\pi$
$251$	110.753	−	12.4789i	0.441248	−	0.0497167i	0.329794	+	0.944053i	$0.393021\pi$
$252$	115.441	−	438.630i	0.458098	−	1.74059i
$253$	25.0105	−	15.7151i	0.0988557	−	0.0621151i
$254$	4.27937	+	79.9530i	0.0168479	+	0.314775i
$255$	−349.637	−	255.433i	−1.37113	−	1.00170i
$256$	51.7075	+	250.724i	0.201982	+	0.979389i
$257$	−349.010	−	278.326i	−1.35801	−	1.08298i	−0.988083	−	0.153922i	$-0.950810\pi$
$257$	−349.010	−	278.326i	−1.35801	−	1.08298i	−0.369932	−	0.929059i	$-0.620619\pi$
$258$	10.1628	−	7.83419i	0.0393907	−	0.0303651i
$259$	195.053	+	68.2520i	0.753100	+	0.263521i
$260$	119.145	+	346.323i	0.458249	+	1.33201i
$261$	−15.6491	+	260.530i	−0.0599584	+	0.998201i
$262$	218.972	+	156.236i	0.835773	+	0.596320i
$263$	−152.957	−	53.5221i	−0.581587	−	0.203506i	0.0234209	−	0.999726i	$-0.492544\pi$
$263$	−152.957	−	53.5221i	−0.581587	−	0.203506i	−0.605008	+	0.796220i	$0.706830\pi$
$264$	−179.485	−	118.294i	−0.679867	−	0.448083i
$265$	−6.28221	−	5.00990i	−0.0237065	−	0.0189053i
$266$	−94.2360	+	545.944i	−0.354271	+	2.05242i
$267$	212.265	+	155.073i	0.795000	+	0.580799i
$268$	−176.730	−	112.346i	−0.659440	−	0.419203i
$269$	−30.3333	+	19.0597i	−0.112763	+	0.0708538i	−0.587233	−	0.809418i	$-0.699783\pi$
$269$	−30.3333	+	19.0597i	−0.112763	+	0.0708538i	0.474470	+	0.880272i	$0.342640\pi$
$270$	−437.716	+	79.7548i	−1.62117	+	0.295388i
$271$	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
$273$	238.292	+	345.892i	0.872866	+	1.26701i
$274$	−40.0775	+	96.0413i	−0.146268	+	0.350516i
$275$	126.866	+	362.563i	0.461332	+	1.31841i
$276$	18.4777	+	34.9957i	0.0669484	+	0.126796i
$277$	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
$279$	−220.763	+	166.264i	−0.791267	+	0.595929i
$280$	145.556	−	817.605i	0.519842	−	2.92002i
$281$	−393.484	−	89.8101i	−1.40030	−	0.319609i	−0.545300	−	0.838241i	$-0.683584\pi$
$281$	−393.484	−	89.8101i	−1.40030	−	0.319609i	−0.854997	+	0.518632i	$0.826441\pi$
$282$	343.575	+	84.3969i	1.21835	+	0.299280i
$283$	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
$285$	524.252	−	143.203i	1.83948	−	0.502467i
$286$	191.431	−	54.6060i	0.669338	−	0.190930i
$287$	916.043	+	103.213i	3.19179	+	0.359628i
$288$	176.106	−	227.883i	0.611480	−	0.791260i
$289$		−	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	−0.312633	−	0.949874i	$-0.601211\pi$
$293$	−242.837	−	27.3612i	−0.828795	−	0.0933828i	−0.516162	+	0.856491i	$0.672640\pi$
$294$	−62.9309	−	655.404i	−0.214051	−	2.22927i
$295$	−503.372	+	242.411i	−1.70634	+	0.821732i
$296$	97.1478	+	88.2036i	0.328202	+	0.297985i
$297$	30.5718	+	239.891i	0.102935	+	0.807714i
$298$	460.576	+	27.0794i	1.54556	+	0.0908705i
$299$	−35.7293	−	8.15498i	−0.119496	−	0.0272742i
$300$	−497.151	+	132.997i	−1.65717	+	0.443324i
$301$	14.3356	−	22.8149i	0.0476265	−	0.0757972i
$302$	−66.3603	−	396.880i	−0.219736	−	1.31417i
$303$	3.07511	+	72.7363i	0.0101489	+	0.240054i
$304$	−190.280	+	295.880i	−0.625920	+	0.973289i
$305$	164.300	+	469.542i	0.538688	+	1.53948i
$306$	−228.638	−	217.144i	−0.747184	−	0.709622i
$307$	−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
$309$	−9.91254	+	141.483i	−0.0320794	+	0.457874i
$310$	−378.195	+	336.193i	−1.21999	+	1.08449i
$311$	−232.388	+	146.019i	−0.747228	+	0.469514i	−0.851052	−	0.525081i	$-0.824035\pi$
$311$	−232.388	+	146.019i	−0.747228	+	0.469514i	0.103824	+	0.994596i	$0.466892\pi$
$312$	53.6839	+	261.246i	0.172064	+	0.837328i
$313$	−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
$315$	−804.528	+	474.964i	−2.55406	+	1.50782i
$316$	87.8197	−	19.5594i	0.277910	−	0.0618967i
$317$	−1.80121	−	0.630271i	−0.00568205	−	0.00198824i	0.327437	−	0.944873i	$-0.393815\pi$
$317$	−1.80121	−	0.630271i	−0.00568205	−	0.00198824i	−0.333119	+	0.942885i	$0.608101\pi$
$318$	−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
$321$	−133.129	−	76.0029i	−0.414731	−	0.236769i
$322$	61.8170	+	55.5359i	0.191978	+	0.172472i
$323$	301.126	+	240.140i	0.932278	+	0.743467i
$324$	−323.570	+	16.6965i	−0.998671	+	0.0515323i
$325$	206.781	−	429.385i	0.636249	−	1.32118i
$326$	462.884	−	24.7752i	1.41989	−	0.0759977i
$327$	−124.889	−	313.727i	−0.381923	−	0.959410i
$328$	510.054	+	287.168i	1.55504	+	0.875512i
$329$	738.230	−	83.1786i	2.24386	−	0.252822i
$330$	91.4034	+	433.245i	0.276980	+	1.31286i
$331$	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
$333$	4.08776	−	147.561i	0.0122755	−	0.443126i
$334$	384.157	+	111.768i	1.15017	+	0.334633i
$335$	95.9869	+	420.546i	0.286528	+	1.25536i
$336$	181.521	−	576.870i	0.540240	−	1.71688i
$337$	−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
$339$	−283.217	−	121.934i	−0.835447	−	0.359687i
$340$	−449.484	−	362.331i	−1.32201	−	1.06568i
$341$	171.485	+	215.035i	0.502888	+	0.630602i
$342$	391.995	−	54.4323i	1.14618	−	0.159159i
$343$	−332.018	−	689.442i	−0.967981	−	2.01003i
$344$	14.0312	−	9.79031i	0.0407883	−	0.0284602i
$345$	23.6490	−	78.0103i	0.0685479	−	0.226117i
$346$	62.6772	+	88.8288i	0.181148	+	0.256731i
$347$			107.269i			0.309133i	0.987982	+	0.154567i	$0.0493981\pi$
$347$			107.269i			0.309133i	−0.987982	+	0.154567i	$0.950602\pi$
$348$	−37.3384	+	345.991i	−0.107294	+	0.994227i
$349$	−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
$351$	183.639	−	237.282i	0.523189	−	0.676016i
$352$	−231.553	−	168.912i	−0.657821	−	0.479863i
$353$	217.639	−	104.809i	0.616541	−	0.296911i	−0.0994255	−	0.995045i	$-0.531700\pi$
$353$	217.639	−	104.809i	0.616541	−	0.296911i	0.715967	+	0.698134i	$0.245986\pi$
$354$	−386.185	+	128.031i	−1.09092	+	0.361670i
$355$	−73.4566	+	58.5797i	−0.206920	+	0.165013i
$356$	272.882	+	219.971i	0.766521	+	0.617897i
$357$	−608.156	−	261.830i	−1.70352	−	0.733418i
$358$	92.4032	−	166.158i	0.258110	−	0.464130i
$359$	158.797	−	252.724i	0.442332	−	0.703967i	−0.548931	−	0.835868i	$-0.684965\pi$
$359$	158.797	−	252.724i	0.442332	−	0.703967i	0.991263	+	0.131900i	$0.0421079\pi$
$360$	−588.013	+	78.5042i	−1.63337	+	0.218067i
$361$	−119.335	+	27.2374i	−0.330567	+	0.0754498i
$362$	6.30688	−	21.6774i	0.0174223	−	0.0598824i
$363$	−120.876	+	18.8194i	−0.332991	+	0.0518441i
$364$	295.463	+	475.758i	0.811712	+	1.30703i
$365$	−19.8959	+	19.8959i	−0.0545092	+	0.0545092i
$366$	74.7807	+	354.455i	0.204319	+	0.968456i
$367$	−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
$369$	−128.697	−	645.807i	−0.348773	−	1.75015i
$370$	−14.4458	−	269.895i	−0.0390427	−	0.729447i
$371$	−11.0702	−	5.33115i	−0.0298389	−	0.0143697i
$372$	−304.547	+	207.457i	−0.818674	+	0.557681i
$373$	−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
$375$	383.945	+	219.194i	1.02385	+	0.584516i
$376$	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	−0.00818644	+	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
$381$	90.6520	−	78.7812i	0.237932	−	0.206775i
$382$	13.3683	−	77.4474i	0.0349955	−	0.202742i
$383$	205.929	−	427.615i	0.537673	−	1.11649i	−0.438347	−	0.898806i	$-0.644436\pi$
$383$	205.929	−	427.615i	0.537673	−	1.11649i	0.976020	−	0.217683i	$-0.0698498\pi$
$384$	248.973	−	292.350i	0.648366	−	0.761329i
$385$	494.670	+	787.262i	1.28486	+	2.04484i
$386$	464.145	+	522.133i	1.20245	+	1.35268i
$387$	−18.6394	−	4.80104i	−0.0481639	−	0.0124058i
$388$	25.1687	+	5.88390i	0.0648679	+	0.0151647i
$389$	116.655	+	116.655i	0.299883	+	0.299883i	0.840968	−	0.541085i	$-0.181986\pi$
$389$	116.655	+	116.655i	0.299883	+	0.299883i	−0.541085	+	0.840968i	$0.681986\pi$
$390$	299.904	−	460.284i	0.768984	−	1.18021i
$391$	54.5293	−	19.0806i	0.139461	−	0.0487996i
$392$	−42.3139	−	876.871i	−0.107944	−	2.23692i
$393$	−17.0435	−	403.133i	−0.0433676	−	1.02578i
$394$	110.025	−	18.3968i	0.279252	−	0.0466924i
$395$	−156.920	−	98.5992i	−0.397265	−	0.249618i
$396$	25.5268	+	321.429i	0.0644617	+	0.811691i
$397$	−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
$399$	732.830	−	391.873i	1.83667	−	0.982138i
$400$	−670.542	+	145.651i	−1.67635	+	0.364126i
$401$	164.525	+	341.640i	0.410287	+	0.851970i	0.999046	+	0.0436618i	$0.0139024\pi$
$401$	164.525	+	341.640i	0.410287	+	0.851970i	−0.588759	+	0.808309i	$0.700383\pi$
$402$	30.0237	+	312.686i	0.0746857	+	0.777827i
$403$	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
$408$	−290.758	−	303.676i	−0.712641	−	0.744305i
$409$	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
$411$	150.585	−	41.1333i	0.366387	−	0.100081i
$412$	−22.1603	+	187.804i	−0.0537872	+	0.455834i
$413$	−667.944	+	532.667i	−1.61730	+	1.28975i
$414$	24.3689	−	54.1289i	0.0588620	−	0.130746i
$415$	238.296	−	1044.04i	0.574207	−	2.51576i
$416$	54.9561	+	351.335i	0.132106	+	0.844555i
$417$	260.525	+	239.390i	0.624761	+	0.574077i
$418$	−64.9524	−	388.460i	−0.155388	−	0.929329i
$419$	−651.248	+	148.643i	−1.55429	+	0.354757i	−0.911505	−	0.411289i	$-0.865079\pi$
$419$	−651.248	+	148.643i	−1.55429	+	0.354757i	−0.642786	+	0.766046i	$0.722222\pi$
$420$	−1101.57	+	581.629i	−2.62278	+	1.38483i
$421$	−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
$423$	−216.926	−	484.322i	−0.512828	−	1.14497i
$424$	−5.15274	−	5.85820i	−0.0121527	−	0.0138165i
$425$	84.1157	+	746.548i	0.197919	+	1.75658i
$426$	−58.5241	+	35.4419i	−0.137380	+	0.0831970i
$427$	404.708	+	644.089i	0.947795	+	1.50841i
$428$	−172.492	−	109.652i	−0.403019	−	0.256197i
$429$	−241.111	−	176.147i	−0.562029	−	0.410599i
$430$	−34.7284	−	5.99450i	−0.0807636	−	0.0139407i
$431$	−138.901	+	174.176i	−0.322275	+	0.404120i	−0.916407	−	0.400247i	$-0.868924\pi$
$431$	−138.901	+	174.176i	−0.322275	+	0.404120i	0.594132	+	0.804367i	$0.297496\pi$
$432$	−431.996	+	1.74889i	−0.999992	+	0.00404837i
$433$	−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
$435$	555.956	−	452.485i	1.27806	−	1.04020i
$436$	−146.466	−	425.738i	−0.335931	−	0.976464i
$437$	−23.9479	+	68.4392i	−0.0548007	+	0.156611i
$438$	−16.2279	+	12.5096i	−0.0370500	+	0.0285607i
$439$	−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
$441$	−717.429	+	678.752i	−1.62682	+	1.53912i
$442$	388.784	−	20.8092i	0.879603	−	0.0470796i
$443$	−289.644	−	460.966i	−0.653825	−	1.04056i	−0.994934	−	0.100532i	$-0.967945\pi$
$443$	−289.644	−	460.966i	−0.653825	−	1.04056i	0.341109	−	0.940024i	$-0.389197\pi$
$444$	14.7876	−	196.267i	0.0333053	−	0.442044i
$445$	−80.8354	−	717.434i	−0.181653	−	1.61221i
$446$	−265.972	−	646.916i	−0.596350	−	1.45048i
$447$	−392.619	−	569.906i	−0.878343	−	1.27496i
$448$	278.281	−	756.799i	0.621163	−	1.68928i
$449$	345.703	−	120.967i	0.769941	−	0.269414i	0.0834105	−	0.996515i	$-0.473419\pi$
$449$	345.703	−	120.967i	0.769941	−	0.269414i	0.686530	+	0.727101i	$0.259133\pi$
$450$	615.740	+	465.587i	1.36831	+	1.03464i
$451$	−638.907	+	145.826i	−1.41665	+	0.323340i
$452$	−369.476	−	180.328i	−0.817424	−	0.398955i
$453$	−408.390	+	444.446i	−0.901523	+	0.981117i
$454$	−445.759	−	247.893i	−0.981848	−	0.546020i
$455$	256.697	−	1124.66i	0.564168	−	2.47178i
$456$	525.517	−	47.6739i	1.15245	−	0.104548i
$457$	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
$459$	−46.1097	+	470.728i	−0.100457	+	1.02555i
$460$	36.4360	−	102.399i	0.0792086	−	0.222606i
$461$	−3.07648	+	27.3045i	−0.00667349	+	0.0592288i	−0.996608	−	0.0823003i	$-0.973773\pi$
$461$	−3.07648	+	27.3045i	−0.00667349	+	0.0592288i	0.989934	+	0.141529i	$0.0452019\pi$
$462$	283.683	+	614.782i	0.614033	+	1.33070i
$463$	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	$0.0913333\pi$
$467$	−18.1798	+	161.350i	−0.0389288	+	0.345503i	−0.998045	+	0.0624918i	$0.980095\pi$
$468$	259.601	−	304.391i	0.554702	−	0.650408i
$469$	286.195	+	594.290i	0.610224	+	1.26714i
$470$	−467.773	−	851.650i	−0.995263	−	1.81202i
$471$	337.902	+	631.901i	0.717414	+	1.34162i
$472$	−522.440	+	146.063i	−1.10686	+	0.309455i
$473$	−4.26244	+	18.6750i	−0.00901150	+	0.0394820i
$474$	−104.113	−	85.8713i	−0.219648	−	0.181163i
$475$	−798.388	−	501.660i	−1.68082	−	1.05613i
$476$	−793.381	−	387.221i	−1.66677	−	0.813489i
$477$	−1.22387	+	8.69136i	−0.00256577	+	0.0182209i
$478$	15.8508	−	54.4809i	0.0331607	−	0.113977i
$479$	289.622	−	101.343i	0.604639	−	0.211572i	−0.0105600	−	0.999944i	$-0.503361\pi$
$479$	289.622	−	101.343i	0.604639	−	0.211572i	0.615199	+	0.788372i	$0.289076\pi$
$480$	−788.103	+	67.3221i	−1.64188	+	0.140254i
$481$	128.885	+	128.885i	0.267951	+	0.267951i
$482$	−66.3825	−	161.460i	−0.137723	−	0.334979i
$483$	8.71181	−	124.345i	0.0180369	−	0.257443i
$484$	−162.178	+	17.4106i	−0.335078	+	0.0359722i
$485$	−28.3259	−	45.0805i	−0.0584040	−	0.0929494i
$486$	318.091	+	367.442i	0.654509	+	0.756054i
$487$	−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
$489$	−456.100	−	524.826i	−0.932720	−	1.07326i
$490$	−1208.50	+	1345.18i	−2.46632	+	2.74526i
$491$	125.103	−	357.523i	0.254792	−	0.728152i	−0.743445	−	0.668797i	$-0.766810\pi$
$491$	125.103	−	357.523i	0.254792	−	0.728152i	0.998237	−	0.0593557i	$-0.0189046\pi$
$492$	−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
$495$	428.326	−	507.605i	0.865305	−	1.02547i
$496$	−418.740	+	257.014i	−0.844234	+	0.518174i
$497$	−89.5767	+	112.326i	−0.180235	+	0.226007i
$498$	269.656	−	731.736i	0.541479	−	1.46935i
$499$	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
$501$	−221.960	−	557.573i	−0.443033	−	1.11292i
$502$	−148.097	−	166.599i	−0.295014	−	0.331871i
$503$	19.2101	+	170.494i	0.0381910	+	0.338954i	0.998249	+	0.0591531i	$0.0188400\pi$
$503$	19.2101	+	170.494i	0.0381910	+	0.338954i	−0.960058	+	0.279801i	$0.909731\pi$
$504$	−849.899	+	317.115i	−1.68631	+	0.629197i
$505$	141.382	−	141.382i	0.279964	−	0.279964i
$506$	−54.5194	−	22.7507i	−0.107746	−	0.0449618i
$507$	−21.0025	−	134.897i	−0.0414250	−	0.266070i
$508$	125.721	−	99.1832i	0.247483	−	0.195242i
$509$	653.008	−	149.045i	1.28292	−	0.292819i	0.473891	−	0.880584i	$-0.342849\pi$
$509$	653.008	−	149.045i	1.28292	−	0.292819i	0.809032	+	0.587765i	$0.199992\pi$
$510$	−14.2666	+	865.890i	−0.0279738	+	1.69782i
$511$	−22.8909	+	36.4307i	−0.0447964	+	0.0712930i
$512$	350.100	−	373.596i	0.683789	−	0.729679i
$513$	−425.828	−	413.608i	−0.830075	−	0.806253i
$514$	−52.4015	+	891.261i	−0.101948	+	1.73397i
$515$	304.544	−	242.866i	0.591348	−	0.471584i
$516$	−24.5206	−	7.57439i	−0.0475205	−	0.0146790i
$517$	−475.829	+	229.147i	−0.920366	+	0.443225i
$518$	−113.372	−	397.445i	−0.218865	−	0.767269i
$519$	47.3098	−	156.059i	0.0911558	−	0.300692i
$520$	428.565	−	594.030i	0.824164	−	1.14236i
$521$	355.660			0.682649			0.341325	−	0.939945i	$-0.389124\pi$
$521$	355.660			0.682649			0.341325	+	0.939945i	$0.389124\pi$
$522$	443.792	−	274.832i	0.850176	−	0.526499i
$523$		−	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
$525$	1551.26	+	470.269i	2.95478	+	0.895751i
$526$	88.9045	+	311.670i	0.169020	+	0.592529i
$527$	233.400	+	484.661i	0.442885	+	0.919660i
$528$	13.6449	+	429.705i	0.0258426	+	0.813836i
$529$	−323.045	−	405.086i	−0.610671	−	0.765758i
$530$	−0.943231	+	16.0428i	−0.00177968	+	0.0302694i
$531$	507.552	+	338.875i	0.955841	+	0.638182i
$532$	1000.82	−	475.506i	1.88123	−	0.893808i
$533$	688.461	+	432.588i	1.29167	+	0.811611i
$534$	8.66126	−	525.682i	0.0162196	−	0.984423i
$535$	93.6852	+	410.461i	0.175112	+	0.767218i
$536$	20.1875	+	418.346i	0.0376633	+	0.780496i
$537$	−281.791	+	43.8726i	−0.524750	+	0.0816994i
$538$	66.1224	+	27.5925i	0.122904	+	0.0512872i
$539$	694.999	+	694.999i	1.28942	+	1.28942i
$540$	635.042	+	623.335i	1.17600	+	1.15432i
$541$	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
$543$	−31.4631	+	12.5249i	−0.0579430	+	0.0230660i
$544$	−368.011	−	422.855i	−0.676491	−	0.777307i
$545$	−402.380	+	835.551i	−0.738313	+	1.53312i
$546$	290.479	−	788.239i	0.532012	−	1.44366i
$547$	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
$549$	350.430	−	415.292i	0.638306	−	0.756451i
$550$	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
$554$	263.313	−	293.094i	0.475294	−	0.529050i
$555$	−306.012	+	265.940i	−0.551373	+	0.479171i
$556$	331.817	+	335.323i	0.596794	+	0.603099i
$557$	430.201	+	207.174i	0.772353	+	0.371946i	0.778183	−	0.628037i	$-0.216141\pi$
$557$	430.201	+	207.174i	0.772353	+	0.371946i	−0.00582995	+	0.999983i	$0.501856\pi$
$558$	526.254	+	169.051i	0.943108	+	0.302958i
$559$	20.1234	−	12.6444i	0.0359989	−	0.0226196i
$560$	−1503.93	+	704.881i	−2.68559	+	1.25872i
$561$	469.555	+	32.8978i	0.836996	+	0.0586414i
$562$	306.944	+	746.570i	0.546163	+	1.32842i
$563$	−418.869	+	418.869i	−0.743994	+	0.743994i	−0.973344	−	0.229350i	$-0.926340\pi$
$563$	−418.869	+	418.869i	−0.743994	+	0.743994i	0.229350	+	0.973344i	$0.426340\pi$
$564$	−258.242	−	658.769i	−0.457876	−	1.16803i
$565$	279.701	+	799.339i	0.495046	+	1.41476i
$566$	103.557	−	355.937i	0.182963	−	0.628863i
$567$	893.537	+	493.013i	1.57590	+	0.869511i
$568$	−80.1882	+	43.4969i	−0.141176	+	0.0765791i
$569$	−101.406	+	161.387i	−0.178218	+	0.283632i	−0.923872	−	0.382701i	$-0.874994\pi$
$569$	−101.406	+	161.387i	−0.178218	+	0.283632i	0.745655	+	0.666333i	$0.232137\pi$
$570$	−838.507	−	691.590i	−1.47107	−	1.21332i
$571$	−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
$573$	−103.959	+	55.5910i	−0.181429	+	0.0970174i
$574$	−887.580	−	1615.97i	−1.54631	−	2.81528i
$575$	−127.426	+	61.3652i	−0.221611	+	0.106722i
$576$	−575.456	−	25.0242i	−0.999056	−	0.0434447i
$577$	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
$582$	−16.2444	−	35.2039i	−0.0279113	−	0.0604877i
$583$	8.67996	+	0.977997i	0.0148884	+	0.00167752i
$584$	−22.4049	+	15.6331i	−0.0383645	+	0.0267690i
$585$	−821.109	+	69.5532i	−1.40361	+	0.118894i
$586$	235.292	+	428.383i	0.401522	+	0.731028i
$587$	67.7706	+	84.9816i	0.115452	+	0.144773i	0.836200	−	0.548425i	$-0.184773\pi$
$587$	67.7706	+	84.9816i	0.115452	+	0.144773i	−0.720747	+	0.693198i	$0.756201\pi$
$588$	−998.471	+	858.555i	−1.69808	+	1.46013i
$589$	−658.227	−	150.236i	−1.11753	−	0.255070i
$590$	976.552	+	543.075i	1.65517	+	0.920467i
$591$	−123.212	−	113.216i	−0.208480	−	0.191567i
$592$	32.1219	−	260.458i	0.0542599	−	0.439963i
$593$	−106.769	−	467.784i	−0.180048	−	0.788843i	−0.981605	−	0.190924i	$-0.938852\pi$
$593$	−106.769	−	467.784i	−0.180048	−	0.788843i	0.801557	−	0.597919i	$-0.204006\pi$
$594$	356.769	−	326.566i	0.600620	−	0.549775i
$595$	600.606	+	1716.43i	1.00942	+	2.88476i
$596$	−486.816	−	783.877i	−0.816806	−	1.31523i
$597$	−359.869	+	247.921i	−0.602796	+	0.415278i
$598$	27.8713	+	67.7904i	0.0466075	+	0.113362i
$599$	−310.835	+	35.0227i	−0.518923	+	0.0584686i	−0.367542	−	0.930007i	$-0.619801\pi$
$599$	−310.835	+	35.0227i	−0.518923	+	0.0584686i	−0.151381	+	0.988476i	$0.548372\pi$
$600$	790.580	+	659.071i	1.31763	+	1.09845i
$601$	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
$603$	342.278	−	323.825i	0.567625	−	0.537024i
$604$	−572.048	+	566.067i	−0.947099	+	0.937197i
$605$	262.678	+	209.478i	0.434178	+	0.346245i
$606$	115.317	−	88.8941i	0.190292	−	0.146690i
$607$	−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
$609$	674.856	−	863.740i	1.10814	−	1.41829i
$610$	577.859	−	809.899i	0.947310	−	1.32770i
$611$	618.488	+	216.418i	1.01226	+	0.354204i
$612$	−91.2160	+	624.010i	−0.149046	+	1.01962i
$613$	−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
$615$	−1066.88	+	1460.34i	−1.73476	+	2.37454i
$616$	338.890	+	836.747i	0.550147	+	1.35836i
$617$	−192.136	+	120.727i	−0.311404	+	0.195668i	−0.678661	−	0.734451i	$-0.737440\pi$
$617$	−192.136	+	120.727i	−0.311404	+	0.195668i	0.367258	+	0.930119i	$0.380297\pi$
$618$	242.635	−	146.939i	0.392613	−	0.237765i
$619$	−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
$621$	−86.5120	+	21.0753i	−0.139311	+	0.0339377i
$622$	506.573	+	211.391i	0.814427	+	0.339856i
$623$	−364.628	−	1042.05i	−0.585278	−	1.67263i
$624$	365.017	−	388.959i	0.584963	−	0.623332i
$625$	−31.6130	−	138.505i	−0.0505808	−	0.221609i
$626$	1.59919	+	9.56424i	0.00255461	+	0.0152783i
$627$	−399.725	+	435.016i	−0.637520	+	0.693805i
$628$	410.017	+	862.979i	0.652893	+	1.37417i
$629$	−280.123	−	63.9362i	−0.445346	−	0.101647i
$630$	1703.83	+	767.066i	2.70449	+	1.21757i
$631$	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
$633$	−280.793	−	1027.96i	−0.443591	−	1.62394i
$634$	1.04693	+	3.67020i	0.00165131	+	0.00578895i
$635$	−327.776	−	36.9315i	−0.516182	−	0.0581598i
$636$	−2.18031	+	11.4979i	−0.00342816	+	0.0180785i
$637$		−	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	0.948322	−	0.317310i	$-0.102780\pi$
$641$	1155.25	+	130.165i	1.80226	+	0.203066i	0.853937	+	0.520376i	$0.174208\pi$
$642$	29.3037	+	305.188i	0.0456444	+	0.475371i
$643$	−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
$645$	24.9277	+	46.6165i	0.0386475	+	0.0722736i
$646$	45.2120	−	768.981i	0.0699876	−	1.19037i
$647$	−798.040	−	182.147i	−1.23345	−	0.281526i	−0.444382	−	0.895837i	$-0.646577\pi$
$647$	−798.040	−	182.147i	−1.23345	−	0.281526i	−0.789064	+	0.614311i	$0.789434\pi$
$648$	400.378	+	509.511i	0.617867	+	0.786283i
$649$	323.128	−	514.255i	0.497886	−	0.792381i
$650$	−940.112	+	157.191i	−1.44633	+	0.241833i
$651$	1159.63	−	49.0263i	1.78131	−	0.0753093i
$652$	−574.216	−	727.858i	−0.880700	−	1.11635i
$653$	23.0323	+	65.8224i	0.0352715	+	0.100800i	0.960173	−	0.279408i	$-0.0901382\pi$
$653$	23.0323	+	65.8224i	0.0352715	+	0.100800i	−0.924901	+	0.380208i	$0.875852\pi$
$654$	−368.675	+	565.832i	−0.563724	+	0.865187i
$655$	−783.593	+	783.593i	−1.19632	+	1.19632i
$656$	−118.842	−	1164.63i	−0.181162	−	1.77535i
$657$	29.7633	+	7.66626i	0.0453018	+	0.0116686i
$658$	−987.146	−	1110.47i	−1.50022	−	1.68765i
$659$	133.562	−	83.9224i	0.202673	−	0.127348i	−0.426871	−	0.904312i	$-0.640384\pi$
$659$	133.562	−	83.9224i	0.202673	−	0.127348i	0.629545	+	0.776964i	$0.283241\pi$
$660$	602.598	−	648.923i	0.913027	−	0.983216i
$661$	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
$663$	−383.087	−	440.810i	−0.577808	−	0.664873i
$664$	405.469	−	957.473i	0.610646	−	1.44198i
$665$	−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
$669$	−520.178	+	911.157i	−0.777546	+	1.36197i
$670$	576.560	−	641.769i	0.860537	−	0.957865i
$671$	−422.793	−	337.166i	−0.630093	−	0.502483i
$672$	−1152.00	+	368.529i	−1.71428	+	0.548406i
$673$	−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
$675$	−16.8557	−	1157.80i	−0.0249713	−	1.71526i
$676$	−19.4302	−	180.990i	−0.0287429	−	0.267737i
$677$	−1051.44	+	118.469i	−1.55309	+	0.174991i	−0.846407	−	0.532537i	$-0.821239\pi$
$677$	−1051.44	+	118.469i	−1.55309	+	0.174991i	−0.706685	+	0.707529i	$0.749810\pi$
$678$	127.305	+	603.417i	0.187766	+	0.889995i
$679$	−57.5677	−	57.5677i	−0.0847831	−	0.0847831i
$680$	−73.8276	+	1152.31i	−0.108570	+	1.69458i
$681$	117.698	+	755.969i	0.172832	+	1.11009i
$682$	153.670	−	528.181i	0.225323	−	0.774458i
$683$	168.547	+	738.453i	0.246775	+	1.08119i	0.934708	+	0.355416i	$0.115661\pi$
$683$	168.547	+	738.453i	0.246775	+	1.08119i	−0.687933	+	0.725774i	$0.741482\pi$
$684$	−540.942	−	577.818i	−0.790850	−	0.844763i
$685$	−363.011	−	228.095i	−0.529943	−	0.332985i
$686$	−743.822	+	1337.53i	−1.08429	+	1.94975i
$687$	30.1889	−	70.1200i	0.0439430	−	0.102067i
$688$	−32.1776	−	11.6404i	−0.0467697	−	0.0169192i
$689$	−6.75707	−	8.47310i	−0.00980707	−	0.0122977i
$690$	−154.750	+	51.3037i	−0.224275	+	0.0743533i
$691$	−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
$693$	465.829	−	902.484i	0.672192	−	1.30229i
$694$	175.295	−	123.687i	0.252586	−	0.178223i
$695$		−	971.715i		−	1.39815i
$696$	608.457	−	337.929i	0.874220	−	0.485531i
$697$	−1281.73			−1.83892
$698$	279.516	+	396.142i	0.400453	+	0.567539i
$699$	621.473	+	188.401i	0.889089	+	0.269530i
$700$	2036.24	+	724.542i	2.90891	+	1.03506i
$701$	706.242	−	340.108i	1.00748	−	0.485176i	0.144008	−	0.989576i	$-0.454001\pi$
$701$	706.242	−	340.108i	1.00748	−	0.485176i	0.863470	+	0.504401i	$0.168287\pi$
$702$	−599.501	−	26.4971i	−0.853991	−	0.0377452i
$703$	281.945	−	224.843i	0.401059	−	0.319834i
$704$	−9.03565	+	573.158i	−0.0128347	+	0.814145i
$705$	−576.348	+	1338.69i	−0.817515	+	1.89885i
$706$	−422.225	−	234.805i	−0.598052	−	0.332586i
$707$	162.665	−	258.880i	0.230078	−	0.366167i
$708$	654.515	+	483.461i	0.924456	+	0.682854i
$709$	−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
$711$	−5.60576	+	202.358i	−0.00788433	+	0.284611i
$712$	44.8207	−	699.570i	0.0629505	−	0.982542i
$713$	−71.6086	+	71.6086i	−0.100433	+	0.100433i
$714$	273.364	+	1295.73i	0.382863	+	1.81474i
$715$	91.8205	+	814.929i	0.128420	+	1.13976i
$716$	−378.075	+	40.5882i	−0.528037	+	0.0566874i
$717$	−79.0746	+	31.4782i	−0.110285	+	0.0439026i
$718$	−596.093	+	31.9051i	−0.830213	+	0.0444360i
$719$	−551.083	−	265.388i	−0.766458	−	0.369107i	0.00944809	−	0.999955i	$-0.496993\pi$
$719$	−551.083	−	265.388i	−0.766458	−	0.369107i	−0.775906	+	0.630849i	$0.782707\pi$
$720$	806.298	+	870.385i	1.11986	+	1.20887i
$721$	371.376	−	465.691i	0.515085	−	0.645896i
$722$	182.109	+	163.605i	0.252229	+	0.226600i
$723$	−129.828	+	227.410i	−0.179569	+	0.314537i
$724$	−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	−0.459589	−	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
$729$	141.460	−	715.143i	0.194046	−	0.980992i
$730$	55.4540	+	9.57197i	0.0759644	+	0.0131123i
$731$	−16.2552	+	33.7543i	−0.0222369	+	0.0461755i
$732$	493.009	−	530.909i	0.673509	−	0.725285i
$733$	−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
$735$	2705.82	+	189.575i	3.68139	+	0.257925i
$736$	52.2564	−	91.6850i	0.0710005	−	0.124572i
$737$	−331.577	−	331.577i	−0.449900	−	0.449900i
$738$	−906.955	+	954.961i	−1.22894	+	1.29399i
$739$	−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
$741$	732.333	−	30.9612i	0.988304	−	0.0417830i
$742$	4.05265	+	24.2376i	0.00546179	+	0.0326652i
$743$	−514.788	−	323.463i	−0.692850	−	0.435347i	0.139040	−	0.990287i	$-0.455598\pi$
$743$	−514.788	−	323.463i	−0.692850	−	0.435347i	−0.831890	+	0.554940i	$0.812741\pi$
$744$	690.176	+	258.468i	0.927656	+	0.347403i
$745$	−422.943	+	1853.03i	−0.567709	+	2.48729i
$746$	115.745	+	6.80520i	0.155154	+	0.00912226i
$747$	−1114.39	+	355.625i	−1.49183	+	0.476071i
$748$	623.284	+	73.5458i	0.833267	+	0.0983233i
$749$	279.332	+	580.039i	0.372940	+	0.774418i
$750$	−84.5124	−	880.168i	−0.112683	−	1.17356i
$751$	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
$756$	1158.82	+	713.186i	1.53283	+	0.943368i
$757$	−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
$759$	23.3500	+	85.4821i	0.0307642	+	0.112625i
$760$	−1072.96	−	974.172i	−1.41179	−	1.28181i
$761$	729.784	−	581.984i	0.958981	−	0.764762i	−0.0129772	−	0.999916i	$-0.504131\pi$
$761$	729.784	−	581.984i	0.958981	−	0.764762i	0.971958	+	0.235154i	$0.0755595\pi$
$762$	−233.267	−	57.3006i	−0.306125	−	0.0751977i
$763$	−315.560	+	1382.56i	−0.413578	+	1.81200i
$764$	−141.976	+	67.4551i	−0.185832	+	0.0882920i
$765$	1037.65	−	781.486i	1.35640	−	1.02155i
$766$	−936.237	+	156.543i	−1.22224	+	0.204365i
$767$	−734.651	+	167.679i	−0.957824	+	0.218617i
$768$	−764.825	−	69.7650i	−0.995866	−	0.0908398i
$769$	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
$771$	1102.83	−	759.759i	1.43038	−	0.985420i
$772$	318.063	−	1360.53i	0.411999	−	1.76235i
$773$	−25.2027	−	223.681i	−0.0326038	−	0.289367i	−0.999425	−	0.0339120i	$-0.989203\pi$
$773$	−25.2027	−	223.681i	−0.0326038	−	0.289367i	0.966821	−	0.255455i	$-0.0822252\pi$
$774$	13.6466	+	35.9956i	0.0176313	+	0.0465060i
$775$	−700.653	−	1115.08i	−0.904068	−	1.43882i
$776$	−19.4057	−	47.9141i	−0.0250073	−	0.0617450i
$777$	−365.713	+	500.590i	−0.470673	+	0.644259i
$778$	56.1229	−	325.141i	0.0721374	−	0.417919i
$779$	1003.00	−	1257.72i	1.28755	−	1.61454i
$780$	−1097.98	+	40.6415i	−1.40767	+	0.0521045i
$781$	33.7331	−	96.4038i	0.0431922	−	0.123436i
$782$	−94.0559	−	67.1084i	−0.120276	−	0.0858164i
$783$	−734.356	−	271.680i	−0.937875	−	0.346973i
$784$	−1384.15	+	1080.23i	−1.76550	+	1.37784i
$785$	649.996	−	1857.58i	0.828020	−	2.36635i
$786$	−639.130	+	492.686i	−0.813143	+	0.626826i
$787$	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
$789$	286.786	−	392.554i	0.363481	−	0.497534i
$790$	19.8103	+	370.121i	0.0250763	+	0.468508i
$791$	688.967	+	1096.48i	0.871008	+	1.38620i
$792$	495.832	−	412.340i	0.626051	−	0.520631i
$793$	75.1219	+	666.725i	0.0947312	+	0.840763i
$794$	1102.94	−	453.460i	1.38909	−	0.571109i
$795$	19.8510	−	13.6757i	0.0249698	−	0.0172022i
$796$	−494.982	+	307.402i	−0.621837	+	0.386184i
$797$	−13.2134	+	4.62356i	−0.0165789	+	0.00580120i	−0.338556	−	0.940946i	$-0.609938\pi$
$797$	−13.2134	+	4.62356i	−0.0165789	+	0.00580120i	0.321977	+	0.946748i	$0.395653\pi$
$798$	−1485.37	−	745.708i	−1.86137	−	0.934472i
$799$	−1007.04	+	229.850i	−1.26037	+	0.287672i
$800$	1011.19	+	927.828i	1.26398	+	1.15978i
$801$	−629.955	+	474.440i	−0.786461	+	0.592310i
$802$	368.587	−	662.789i	0.459585	−	0.826421i
$803$	6.80623	−	29.8201i	0.00847601	−	0.0371358i
$804$	476.360	−	409.607i	0.592487	−	0.509462i
$805$	−267.654	+	213.447i	−0.332489	+	0.265151i
$806$	−598.200	+	328.565i	−0.742183	+	0.407648i
$807$	−28.3194	−	103.675i	−0.0350922	−	0.128469i
$808$	159.211	−	111.090i	0.197043	−	0.137488i
$809$	53.3424	−	473.427i	0.0659363	−	0.585201i	−0.916689	−	0.399601i	$-0.869149\pi$
$809$	53.3424	−	473.427i	0.0659363	−	0.585201i	0.982625	−	0.185600i	$-0.0594227\pi$
$810$	151.990	−	1326.09i	0.187641	−	1.63714i
$811$	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
$816$	−160.996	+	825.299i	−0.197298	+	1.01140i
$817$	−20.4018	−	42.3647i	−0.0249715	−	0.0518539i
$818$	−825.734	+	453.539i	−1.00945	+	0.554449i
$819$	−1200.45	+	383.086i	−1.46575	+	0.467748i
$820$	−1513.36	+	1877.37i	−1.84556	+	2.28948i
$821$	228.992	−	1003.28i	0.278919	−	1.22202i	−0.620245	−	0.784409i	$-0.712967\pi$
$821$	228.992	−	1003.28i	0.278919	−	1.22202i	0.899163	−	0.437614i	$-0.144176\pi$
$822$	−240.851	−	198.651i	−0.293006	−	0.241668i
$823$	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
$825$	−1151.33	+	48.6753i	−1.39555	+	0.0590003i
$826$	1640.64	+	477.331i	1.98624	+	0.577883i
$827$	−1386.08	+	485.010i	−1.67603	+	0.586470i	−0.989996	−	0.141096i	$-0.954937\pi$
$827$	−1386.08	+	485.010i	−1.67603	+	0.586470i	−0.686038	+	0.727565i	$0.740652\pi$
$828$	−116.554	+	22.5909i	−0.140765	+	0.0272837i
$829$	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
$831$	−589.558	−	41.3054i	−0.709456	−	0.0497057i
$832$	510.769	−	494.915i	0.613905	−	0.594849i
$833$	1022.75	+	1627.69i	1.22779	+	1.95401i
$834$	90.8015	−	701.769i	0.108875	−	0.841450i
$835$	−715.133	+	1484.99i	−0.856447	+	1.77843i
$836$	−559.910	+	554.057i	−0.669749	+	0.662747i
$837$	−285.200	−	778.514i	−0.340741	−	0.930124i
$838$	993.830	+	892.848i	1.18595	+	1.06545i
$839$	−76.3761	+	218.270i	−0.0910323	+	0.260155i	−0.980393	−	0.197050i	$-0.936864\pi$
$839$	−76.3761	+	218.270i	−0.0910323	+	0.260155i	0.889361	+	0.457205i	$0.151150\pi$
$840$	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
$843$	600.309	−	1051.52i	0.712110	−	1.24735i
$844$	−308.880	−	1386.84i	−0.365972	−	1.64318i
$845$	−233.778	+	293.148i	−0.276660	+	0.346921i
$846$	−541.330	+	912.941i	−0.639870	+	1.07913i
$847$	462.879	+	222.911i	0.546492	+	0.263177i
$848$	−3.63183	+	15.1752i	−0.00428282	+	0.0178953i
$849$	−516.614	+	205.654i	−0.608497	+	0.242231i
$850$	1122.99	−	998.267i	1.32116	−	1.17443i
$851$	−6.05631	−	53.7512i	−0.00711669	−	0.0631624i
$852$	125.399	+	54.7711i	0.147182	+	0.0642853i
$853$	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
$855$	−45.1476	+	1629.75i	−0.0528042	+	1.90614i
$856$	19.7034	+	408.314i	0.0230180	+	0.477002i
$857$	−1052.39	+	240.202i	−1.22800	+	0.280283i	−0.786846	−	0.617150i	$-0.788287\pi$
$857$	−1052.39	+	240.202i	−1.22800	+	0.280283i	−0.441152	+	0.897432i	$0.645430\pi$
$858$	−9.83828	+	597.119i	−0.0114665	+	0.695943i
$859$	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
$861$	−1093.60	+	2540.11i	−1.27015	+	2.95018i
$862$	444.790	+	26.1513i	0.515998	+	0.0303379i
$863$	705.619	−	562.713i	0.817635	−	0.652042i	−0.122642	−	0.992451i	$-0.539137\pi$
$863$	705.619	−	562.713i	0.817635	−	0.652042i	0.940278	+	0.340409i	$0.110565\pi$
$864$	500.973	+	703.933i	0.579830	+	0.814738i
$865$	−403.516	+	194.323i	−0.466492	+	0.224651i
$866$	1256.39	−	358.388i	1.45080	−	0.413843i
$867$	51.3152	+	15.5563i	0.0591871	+	0.0179427i
$868$	1547.54	+	8.13153i	1.78287	+	0.00936812i
$869$	201.462			0.231832
$870$	−1380.48	−	386.780i	−1.58676	−	0.444574i
$871$			581.796i			0.667963i
$872$	−526.840	+	730.248i	−0.604175	+	0.837440i
$873$	−26.6744	+	51.6784i	−0.0305549	+	0.0591963i
$874$	139.454	−	39.7794i	0.159558	−	0.0455142i
$875$	−805.599	−	1672.84i	−0.920684	−	1.91182i
$876$	39.1542	+	12.0947i	0.0446966	+	0.0138068i
$877$	−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
$879$	289.905	−	673.366i	0.329812	−	0.766059i
$880$	843.646	−	826.098i	0.958689	−	0.938748i
$881$	−1239.93	−	779.100i	−1.40741	−	0.884336i	−0.407826	−	0.913060i	$-0.633713\pi$
$881$	−1239.93	−	779.100i	−1.40741	−	0.884336i	−0.999587	+	0.0287237i	$0.990856\pi$
$882$	1936.42	+	389.755i	2.19549	+	0.441899i
$883$	−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
$885$	−257.849	−	1656.15i	−0.291355	−	1.87135i
$886$	−419.316	+	1004.84i	−0.473268	+	1.13413i
$887$	451.385	+	451.385i	0.508890	+	0.508890i	0.914186	−	0.405296i	$-0.132831\pi$
$887$	451.385	+	451.385i	0.508890	+	0.508890i	−0.405296	+	0.914186i	$0.632831\pi$
$888$	−337.782	+	202.142i	−0.380386	+	0.227637i
$889$	−501.216	+	56.4734i	−0.563797	+	0.0635247i
$890$	−1079.19	+	959.337i	−1.21258	+	1.07791i
$891$	−715.329	−	121.017i	−0.802838	−	0.135822i
$892$	−750.481	+	1180.57i	−0.841347	+	1.32351i
$893$	562.498	−	1168.04i	0.629897	−	1.30800i
$894$	−478.604	+	1298.73i	−0.535351	+	1.45272i
$895$	612.364	+	488.344i	0.684206	+	0.545636i
$896$	−1557.60	+	417.874i	−1.73839	+	0.466378i
$897$	54.5095	−	95.4803i	0.0607687	−	0.106444i
$898$	−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
$902$	974.997	+	875.929i	1.08093	+	0.971096i
$903$	53.0243	+	61.0140i	0.0587201	+	0.0675681i
$904$	131.341	+	811.708i	0.145289	+	0.897908i
$905$	83.7958	+	40.3539i	0.0925920	+	0.0445900i
$906$	1197.19	+	154.904i	1.32140	+	0.170975i
$907$	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
$909$	−211.501	−	54.4771i	−0.232674	−	0.0599308i
$910$	−2133.86	+	877.312i	−2.34490	+	0.964079i
$911$	−788.911	+	788.911i	−0.865983	+	0.865983i	−0.992025	−	0.126042i	$-0.959773\pi$
$911$	−788.911	+	788.911i	−0.865983	+	0.865983i	0.126042	+	0.992025i	$0.459773\pi$
$912$	−683.855	−	803.806i	−0.749841	−	0.881366i
$913$	384.489	+	1098.81i	0.421128	+	1.20351i
$914$	−1069.46	−	311.152i	−1.17009	−	0.340428i
$915$	−1491.04	+	63.0375i	−1.62955	+	0.0688935i
$916$	44.6463	−	91.4763i	0.0487405	−	0.0998650i
$917$	−901.553	+	1434.81i	−0.983154	+	1.56468i
$918$	822.410	−	467.424i	0.895872	−	0.509177i
$919$	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
$921$	−226.462	−	423.500i	−0.245887	−	0.459826i
$922$	48.1672	−	26.4561i	0.0522420	−	0.0286942i
$923$	−114.171	+	54.9820i	−0.123696	+	0.0595689i
$924$	677.548	−	1172.46i	0.733277	−	1.26890i
$925$	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	$-0.926670\pi$
$929$		−	424.259i		−	0.456684i	0.973581	−	0.228342i	$-0.0733304\pi$
$930$	−636.042	−	1378.39i	−0.683916	−	1.48214i
$931$	−2397.54	−	270.138i	−2.57523	−	0.290159i
$932$	815.767	+	290.269i	0.875286	+	0.311448i
$933$	−216.959	−	794.267i	−0.232540	−	0.851304i
$934$	284.633	−	156.336i	0.304746	−	0.167384i
$935$	−806.025	−	1010.72i	−0.862058	−	1.08099i
$936$	−796.756	−	73.2492i	−0.851235	−	0.0782577i
$937$	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
$939$	9.84161	−	10.7105i	0.0104809	−	0.0114063i
$940$	−852.361	+	1746.41i	−0.906767	+	1.85789i
$941$	35.1036	+	153.799i	0.0373046	+	0.163442i	0.990149	−	0.140017i	$-0.0447157\pi$
$941$	35.1036	+	153.799i	0.0373046	+	0.163442i	−0.952845	+	0.303459i	$0.901859\pi$
$942$	643.006	−	1280.80i	0.682596	−	1.35966i
$943$	−79.6947	−	227.754i	−0.0845119	−	0.241521i
$944$	841.090	+	685.330i	0.890985	+	0.725985i
$945$	−663.393	−	2723.16i	−0.702003	−	2.88165i
$946$	35.4327	−	14.5677i	0.0374552	−	0.0153993i
$947$	−1303.17	+	146.832i	−1.37610	+	0.155050i	−0.768836	−	0.639446i	$-0.779164\pi$
$947$	−1303.17	+	146.832i	−1.37610	+	0.155050i	−0.607269	+	0.794496i	$0.707735\pi$
$948$	−20.2789	+	269.152i	−0.0213913	+	0.283915i
$949$	−32.1329	+	20.1904i	−0.0338597	+	0.0212755i
$950$	100.792	+	1883.13i	0.106097	+	1.98224i
$951$	3.37717	−	4.62268i	0.00355117	−	0.00486086i
$952$	282.031	+	1742.99i	0.296251	+	1.83088i
$953$	1270.31	+	1013.04i	1.33296	+	1.06300i	0.992436	+	0.122761i	$0.0391748\pi$
$953$	1270.31	+	1013.04i	1.33296	+	1.06300i	0.340521	+	0.940237i	$0.389397\pi$
$954$	15.6142	−	8.02161i	0.0163671	−	0.00840839i
$955$	305.605	+	106.936i	0.320006	+	0.111975i
$956$	−107.307	+	36.9166i	−0.112246	+	0.0386157i
$957$	−250.031	+	738.031i	−0.261266	+	0.771192i
$958$	−499.560	−	356.434i	−0.521462	−	0.372060i
$959$	−618.791	−	216.524i	−0.645246	−	0.225781i
$960$	1018.74	+	1210.26i	1.06119	+	1.26069i
$961$	14.0987	+	11.2433i	0.0146709	+	0.0116996i
$962$	62.0068	−	359.229i	0.0644562	−	0.373418i
$963$	334.070	−	316.060i	0.346906	−	0.328204i
$964$	−187.308	+	294.651i	−0.194303	+	0.305655i
$965$	−2436.89	+	1531.20i	−2.52528	+	1.58674i
$966$	−213.244	+	129.140i	−0.220750	+	0.133685i
$967$	−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
$969$	−951.519	+	655.520i	−0.981960	+	0.676492i
$970$	−41.0072	+	98.2692i	−0.0422755	+	0.101308i
$971$	168.407	+	481.279i	0.173436	+	0.495653i	0.997486	−	0.0708652i	$-0.0225760\pi$
$971$	168.407	+	481.279i	0.173436	+	0.495653i	−0.824050	+	0.566518i	$0.808290\pi$
$972$	233.682	−	943.492i	0.240413	−	0.970671i
$973$	−330.642	−	1448.64i	−0.339817	−	1.48883i
$974$	104.031	−	17.3944i	0.106808	−	0.0178588i
$975$	1052.78	+	967.376i	1.07978	+	0.992181i
$976$	690.219	−	675.863i	0.707192	−	0.692483i
$977$	−1171.08	−	267.292i	−1.19865	−	0.273585i	−0.423817	−	0.905748i	$-0.639310\pi$
$977$	−1171.08	−	267.292i	−1.19865	−	0.273585i	−0.774835	+	0.632163i	$0.782167\pi$
$978$	−331.739	+	1350.49i	−0.339202	+	1.38087i
$979$	489.337	+	613.610i	0.499834	+	0.626772i
$980$	3591.69	+	423.810i	3.66499	+	0.432459i
$981$	1009.40	−	85.5026i	1.02895	−	0.0871586i
$982$	−728.498	+	207.806i	−0.741852	+	0.211615i
$983$	679.979	+	76.6152i	0.691738	+	0.0779402i	0.450833	−	0.892608i	$-0.351127\pi$
$983$	679.979	+	76.6152i	0.691738	+	0.0779402i	0.240906	+	0.970549i	$0.422556\pi$
$984$	−1268.38	+	1214.42i	−1.28900	+	1.23416i
$985$			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
$990$	−1323.39	−	114.656i	−1.33676	−	0.115814i
$991$	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
$993$	−123.057	+	65.8037i	−0.123925	+	0.0662675i
$994$	286.844	+	16.8649i	0.288576	+	0.0169667i
$995$	1170.11	+	267.069i	1.17599	+	0.268411i
$996$	−1506.70	+	403.070i	−1.51275	+	0.404689i
$997$	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
$999$	420.087	+	140.165i	0.420507	+	0.140305i

Twists

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

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-1.15305 - 1.63416i) q^{2} +(-0.870345 + 2.87098i) q^{3} +(-1.34094 + 3.76854i) q^{4} +(7.42336 - 3.57490i) q^{5} +(5.69518 - 1.88811i) q^{6} +(9.85035 - 7.85539i) q^{7} +(7.70456 - 2.15403i) q^{8} +(-7.48500 - 4.99748i) q^{9} +O(q^{10})\)	\(q+(-1.15305 - 1.63416i) q^{2} +(-0.870345 + 2.87098i) q^{3} +(-1.34094 + 3.76854i) q^{4} +(7.42336 - 3.57490i) q^{5} +(5.69518 - 1.88811i) q^{6} +(9.85035 - 7.85539i) q^{7} +(7.70456 - 2.15403i) q^{8} +(-7.48500 - 4.99748i) q^{9} +(-14.4015 - 8.00888i) q^{10} +(-4.76526 + 7.58386i) q^{11} +(-9.65231 - 7.12972i) q^{12} +(10.8341 - 2.47281i) q^{13} +(-24.1949 - 7.03933i) q^{14} +(3.80257 + 24.4237i) q^{15} +(-12.4038 - 10.1067i) q^{16} +(-12.3870 + 12.3870i) q^{17} +(0.463945 + 17.9940i) q^{18} +(-2.46170 - 21.8482i) q^{19} +(3.51790 + 32.7689i) q^{20} +(13.9794 + 35.1170i) q^{21} +(17.8878 - 0.957421i) q^{22} +(-2.97127 - 1.43089i) q^{23} +(-0.521460 + 23.9943i) q^{24} +(26.7391 - 33.5297i) q^{25} +(-16.5333 - 14.8533i) q^{26} +(20.8622 - 17.1397i) 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} +(-2.21378 + 31.9233i) q^{32} +(-17.6257 - 20.2815i) q^{33} +(34.5251 + 5.95941i) q^{34} +(45.0404 - 93.5274i) q^{35} +(28.8701 - 21.5062i) q^{36} +(8.72637 + 13.8879i) q^{37} +(-32.8649 + 29.2149i) q^{38} +(-2.33002 + 33.2566i) q^{39} +(49.4932 - 43.5331i) q^{40} +(51.7371 + 51.7371i) q^{41} +(41.2676 - 63.3364i) q^{42} +(2.01863 - 0.706350i) q^{43} +(-22.1902 - 28.1275i) q^{44} +(-73.4293 - 10.3399i) q^{45} +(1.08774 + 6.50540i) q^{46} +(49.9269 + 31.3712i) q^{47} +(39.8118 - 26.8146i) q^{48} +(24.4187 - 106.985i) q^{49} +(-85.6244 - 5.03426i) q^{50} +(-24.7817 - 46.3436i) q^{51} +(-5.20894 + 44.1446i) q^{52} +(-0.423138 - 0.878656i) q^{53} +(-52.0642 - 14.3290i) 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} +(-97.1406 - 18.4204i) q^{60} +(-6.75999 + 59.9966i) q^{61} +(-59.0597 + 16.8469i) q^{62} +(-112.987 + 9.57072i) q^{63} +(54.7203 - 33.1916i) q^{64} +(71.5853 - 57.0874i) q^{65} +(-12.8198 + 52.1888i) q^{66} +(-11.6499 + 51.0414i) q^{67} +(-30.0706 - 63.2909i) q^{68} +(6.69406 - 7.28507i) q^{69} +(-204.772 + 34.2390i) q^{70} +(-11.1173 + 2.53745i) q^{71} +(-68.4333 - 22.3804i) q^{72} +(-3.22334 + 1.12789i) q^{73} +(12.6331 - 30.2738i) q^{74} +(72.9908 + 105.950i) q^{75} +(85.6368 + 20.0200i) q^{76} +(12.6348 + 112.137i) q^{77} +(57.0332 - 34.5391i) q^{78} +(-11.9669 - 19.0453i) q^{79} +(-128.208 - 30.6837i) q^{80} +(31.0505 + 74.8122i) q^{81} +(24.8909 - 144.202i) q^{82} +(81.0372 - 101.617i) q^{83} +(-151.085 + 5.59239i) q^{84} +(-47.6707 + 136.235i) q^{85} +(-3.48188 - 2.48430i) q^{86} +(84.6218 - 20.2026i) q^{87} +(-20.3783 + 68.6948i) q^{88} +(28.9409 - 82.7083i) q^{89} +(67.7709 + 131.917i) q^{90} +(87.2947 - 109.464i) q^{91} +(9.37663 - 9.27860i) q^{92} +(74.3868 + 54.3444i) q^{93} +(-6.30300 - 117.761i) q^{94} +(-96.3792 - 153.387i) q^{95} +(-89.7244 - 34.1400i) q^{96} +(-0.723496 - 6.42120i) q^{97} +(-202.986 + 83.4556i) q^{98} +(73.5681 - 32.9510i) 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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